Finite Group Databasebeta

← C2×#20257074 #27124189

Subgroups — C2×#20257074 #27124189

Order 12032.

9502 conjugacy classes of subgroups.

The subgroup lattice has 1316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257074C2132yesmaximal, direct product factor
2C2×#15689803C212yesmaximal, complemented
3C2×#15689801C212yesmaximal, complemented
4C2×#15689798C212yesmaximal, complemented
5C2×#15689798C212yesmaximal, complemented
6C2×#15689770C212yesmaximal, complemented
7C2×#15689766C212yesmaximal, complemented
8C2×#15689765C212yesmaximal, complemented
9C2×#15689762C212yesmaximal, complemented
10C2×#15689748C211yesmaximal, characteristic, complemented
11C2×#15689711C211yesmaximal, characteristic, complemented
12C2×#15689708C212yesmaximal, complemented
13C2×#15689681C211yesmaximal, characteristic, complemented
14C2×#15689636C211yesmaximal, characteristic, complemented
15C2×#15689633C211yesmaximal, characteristic, complemented
16C2×#15689632C212yesmaximal, complemented
17C2×#120×D47C212yesmaximal, complemented
18C2×#15689595C212yesmaximal, complemented
19C22×C22⋊C4×D47C211yesmaximal, characteristic, complemented
20C2×C47×#538C211yesmaximal, characteristic, complemented
21C25×D47C2211yescharacteristic
22C22×#10625354C2211yescharacteristic, complemented
23C22×#10625350C2212yescomplemented
24C22×#10625352C2211yescharacteristic, complemented
25C22×D4×D47C2212yes—
26C22×D4×D47C2212yescomplemented
27C22×D4×D47C2212yescomplemented
28C23×C4×D47C2211yescharacteristic, complemented
29C23×C4×D47C2211yescharacteristic, complemented
30#15689803C22132yescomplemented
31#15689801C22132yescomplemented
32#15689798C22132yescomplemented
33#15689798C22132yescomplemented
34#15689770C22132yescomplemented
35#15689766C22132yescomplemented
36#15689765C22132yescomplemented
37#15689762C22132yescomplemented
38#15689748C22116yescomplemented
39#15689711C22116yescomplemented
40#15689708C22132yescomplemented
41#15689681C22116yescomplemented
42C2×#13094017C2212yescomplemented
43C2×#13094017C2212yescomplemented
44C2×#13094017C2212yescomplemented
45C2×#13094011C2212yescomplemented
46C2×#13094010C2212yescomplemented
47C2×#13094010C2212yescomplemented
48#15689636C22116yescomplemented
49#15689633C22116yescomplemented
50#15689632C22132yescomplemented
51C2×#13094009C2212yescomplemented
52C2×#13094009C2212yescomplemented
53C2×#13094009C2212yescomplemented
54C2×#13094006C2212yescomplemented
55C2×#13094006C2212yescomplemented
56C2×#13094006C2212yescomplemented
57C2×#13094006C2212yescomplemented
58C2×#13094006C2212yescomplemented
59C2×#13094005C2212yescomplemented
60C2×#13094004C2212yescomplemented
61C2×#13094004C2211yescharacteristic, complemented
62C2×#13094003C2211yescharacteristic, complemented
63C2×#13094002C2212yescomplemented
64C2×#13094002C2212yescomplemented
65C2×#13094002C2212yescomplemented
66C2×#13094001C2212yescomplemented
67C2×#13094000C2212yescomplemented
68C2×#13094000C2211yescharacteristic, complemented
69C2×#13093999C2211yescharacteristic, complemented
70C2×#13093998C2211yescharacteristic, complemented
71C2×#13093997C2212yescomplemented
72C2×#13093997C2212yescomplemented
73C2×#13093996C2212yescomplemented
74C2×#13093996C2212yescomplemented
75C2×#13093995C2212yescomplemented
76C2×#13093995C2211yescharacteristic, complemented
77C2×#13093994C2212yes—
78C2×#13093994C2212yes—
79C2×#13093994C2212yescomplemented
80C2×#13093994C2212yescomplemented
81C2×#13093993C2212yescomplemented
82C2×#13093992C2212yes—
83C2×#13093992C2212yes—
84C2×#13093992C2212yescomplemented
85C2×#13093992C2212yescomplemented
86#120×D47C22132yescomplemented
87#15689595C22132yescomplemented
88C2×C4×D188C2212yescomplemented
89C2×C4×D188C2212yescomplemented
90C2×D4×Dic47C2212yescomplemented
91C2×#13093986C2212yescomplemented
92C2×#13093986C2212yescomplemented
93C2×C4×C22⋊D47C2212yescomplemented
94C2×C4×C22⋊D47C2212yescomplemented
95C2×C4×C22⋊D47C2212yescomplemented
96C2×(C22⋊D47)⋊C4C2212yescomplemented
97C2×(C22⋊D47)⋊C4C2212yescomplemented
98C2×(C22⋊D47)⋊C4C2212yescomplemented
99C2×#13093982C2212yescomplemented
100C2×#13093982C2211yescharacteristic, complemented
101C2×#13093982C2211yescharacteristic, complemented
102C2×#13093981C2212yescomplemented
103C2×#13093981C2212yescomplemented
104C22×C22⋊Dic47C2211yescharacteristic, complemented
105C22×(C2×D47)⋊C4C2211yescharacteristic
106C22×(C2×D47)⋊C4C2211yescharacteristic
107C22×(C2×D47)⋊C4C2212yescomplemented
108C2×C22⋊C4×D47C2212yes—
109C2×C22⋊C4×D47C2212yescomplemented
110C2×C22⋊C4×D47C2212yescomplemented
111C2×C22⋊C4×D47C2212yescomplemented
112C2×C22⋊C4×D47C2212yescomplemented
113C2×C22⋊C4×D47C2212yescomplemented
114C2×C22⋊C4×D47C2212yescomplemented
115C2×C22⋊C4×D47C22116yescomplemented
116C2×C22⋊C4×D47C2212yescomplemented
117C47×#538C22116yescomplemented
118C2×#126×C47C2212yescomplemented
119C2×#124×C47C2212yescomplemented
120C2×#123×C47C2212yescomplemented
121C2×C22⋊Q8×C47C2211yescharacteristic, complemented
122C2×#121×C47C2212yescomplemented
123C2×#121×C47C2211yescharacteristic, complemented
124C2×#120×C47C2212yescomplemented
125C2×C4×D4×C47C2212yescomplemented
126C22×C22⋊C4×C47C2211yescharacteristic, complemented
127C24×D47—28no—
128C24×D47—44no—
129C24×D47—44no—
130C24×D47C2311yescharacteristic
131C24×D47C2312yes—
132C24×D47C2312yes—
133C24×D47C2318yes—
134C24×D47C2312yes—
135C24×D47C2311yescharacteristic
136C2×#10625354—44no—
137C2×#10625354C2318yescomplemented
138C2×#10625350—48no—
139C2×#10625350C23116yescomplemented
140C2×#10625352—44no—
141C2×#10625352C2318yescomplemented
142C22×Dic94C2312yescomplemented
143C22×Dic94C2311yescharacteristic, complemented
144C22×D188C2312yes—
145C22×D188C2312yes—
146C22×D188C2312yes—
147C22×D188C2311yescharacteristic, complemented
148C22×C22⋊D47C2312yes—
149C22×C22⋊D47C2312yes—
150C22×C22⋊D47C2312yes—
151C22×C22⋊D47C2312yes—
152C22×C22⋊D47C2312yes—
153C22×C22⋊D47C2312yes—
154C22×C22⋊D47C2312yescomplemented
155C2×D4×D47—216no—
156C2×D4×D47—48no—
157C2×D4×D47—48no—
158C2×D4×D47C23116yes—
159C2×D4×D47C23116yescomplemented
160C2×D4×D47C23116yescomplemented
161C23×Dic47C2311yescharacteristic
162C23×Dic47C2311yescharacteristic
163C23×Dic47C2312yescomplemented
164C22×C4×D47—44no—
165C22×C4×D47—44no—
166C22×C4×D47C2312yes—
167C22×C4×D47C2312yes—
168C22×C4×D47C2311yescharacteristic
169C22×C4×D47C2311yescharacteristic
170C22×C4×D47C2312yes—
171C22×C4×D47C2312yes—
172C22×C4×D47C2311yescharacteristic
173C22×C4×D47C2312yes—
174C22×C4×D47C2311yescharacteristic
175C22×C4×D47C2318yescomplemented
176C22×C4×D47C2318yescomplemented
177C22×C4×D47C2312yescomplemented
178C22×C4×D47C2312yescomplemented
179#13094017C23116yescomplemented
180#13094017C23116yescomplemented
181#13094017C23116yescomplemented
182#13094011C23116yescomplemented
183#13094010C23116yescomplemented
184#13094010C23116yescomplemented
185#13094009C23116yescomplemented
186#13094009C23116yescomplemented
187#13094009C23116yescomplemented
188#13094006C23116yescomplemented
189#13094006C23116yescomplemented
190#13094006C23116yescomplemented
191#13094006C23116yescomplemented
192#13094006C23116yescomplemented
193#13094005C23116yescomplemented
194#13094004C23116yescomplemented
195#13094004C2318yescomplemented
196#13094003C2318yescomplemented
197#13094002C23116yescomplemented
198#13094002C23116yescomplemented
199#13094002C23116yescomplemented
200#13094001C23116yescomplemented
201#13094000C23116yescomplemented
202#13094000C2318yescomplemented
203#13093999C2318yescomplemented
204#13093998C2318yescomplemented
205#13093997C23116yescomplemented
206#13093997C23116yescomplemented
207#13093996C23116yescomplemented
208#13093996C23116yescomplemented
209#13093995C23116yescomplemented
210#13093995C2318yescomplemented
211#13093994C23116yes—
212#13093994C23116yes—
213#13093994C23116yescomplemented
214#13093994C23116yescomplemented
215#13093993C23116yescomplemented
216#13093992C23116yes—
217#13093992C23116yes—
218#13093992C23116yescomplemented
219#13093992C23116yescomplemented
220C4×D188C23116yescomplemented
221C4×D188C23116yescomplemented
222D4×Dic47C23116yescomplemented
223#13093986C23116yescomplemented
224#13093986C23116yescomplemented
225C4×C22⋊D47C23116yescomplemented
226C4×C22⋊D47C23116yescomplemented
227C4×C22⋊D47C23116yescomplemented
228(C22⋊D47)⋊C4C23116yescomplemented
229(C22⋊D47)⋊C4C23116yescomplemented
230(C22⋊D47)⋊C4C23116yescomplemented
231#13093982C2318yescomplemented
232#13093982C23116yescomplemented
233#13093982C2318yescomplemented
234#13093981C23116yescomplemented
235#13093981C23116yescomplemented
236C2×C4⋊Dic47C2312yescomplemented
237C2×C4⋊Dic47C2311yescharacteristic, complemented
238C2×C4⋊Dic47C2311yescharacteristic, complemented
239C2×C4⋊Dic47C2312yescomplemented
240C2×Dic47⋊C4C2312yescomplemented
241C2×Dic47⋊C4C2312yescomplemented
242C2×Dic47⋊C4C2312yescomplemented
243C2×Dic47⋊C4C2312yescomplemented
244C2×Dic47⋊C4C2312yescomplemented
245C2×Dic47⋊C4C2312yescomplemented
246C2×C22⋊Dic47C2312yes—
247C2×C22⋊Dic47C2312yes—
248C2×C22⋊Dic47C2312yes—
249C2×C22⋊Dic47C2312yes—
250C2×C22⋊Dic47C2312yes—
251C2×C22⋊Dic47C2318yescomplemented
252C2×C22⋊Dic47C2312yescomplemented
253C2×C22⋊Dic47C2312yescomplemented
254C2×(C2×D47)⋊C4C2318yes—
255C2×(C2×D47)⋊C4C2312yes—
256C2×(C2×D47)⋊C4C2312yes—
257C2×(C2×D47)⋊C4C2312yes—
258C2×(C2×D47)⋊C4C2312yes—
259C2×(C2×D47)⋊C4C2318yes—
260C2×(C2×D47)⋊C4C2312yes—
261C2×(C2×D47)⋊C4C2312yes—
262C2×(C2×D47)⋊C4C2312yes—
263C2×(C2×D47)⋊C4C2312yes—
264C2×(C2×D47)⋊C4C2312yes—
265C2×(C2×D47)⋊C4C2312yes—
266C2×(C2×D47)⋊C4C23116yescomplemented
267C2×(C2×D47)⋊C4C2312yescomplemented
268C2×(C2×D47)⋊C4C2312yescomplemented
269C2×(C2×D47)⋊C4C2312yescomplemented
270C2×(C2×D47)⋊C4C2312yescomplemented
271C22⋊C4×D47C23116yes—
272C22⋊C4×D47C23116yescomplemented
273C22⋊C4×D47C23116yescomplemented
274C22⋊C4×D47C23116yescomplemented
275C22⋊C4×D47C23116yescomplemented
276C22⋊C4×D47C23116yescomplemented
277C22⋊C4×D47C23116yescomplemented
278C22⋊C4×D47C23116yescomplemented
279C2×C4×Dic47C2312yescomplemented
280C2×C4×Dic47C2312yescomplemented
281C2×C4×Dic47C2312yescomplemented
282C25×C47C2311yescharacteristic
283C22×Q8×C47C2311yescharacteristic, complemented
284C22×D4×C47C2312yes—
285C22×D4×C47C2312yes—
286C22×D4×C47C2312yes—
287C22×D4×C47C2311yescharacteristic, complemented
288C23×C4×C47C2311yescharacteristic
289C23×C4×C47C2311yescharacteristic
290C23×C4×C47C2312yescomplemented
291#126×C47C23116yescomplemented
292#124×C47C23116yescomplemented
293#123×C47C23116yescomplemented
294C22⋊Q8×C47C2318yescomplemented
295#121×C47C23116yescomplemented
296#121×C47C2318yescomplemented
297#120×C47C23116yescomplemented
298C4×D4×C47C23116yescomplemented
299C2×C4⋊C4×C47C2312yescomplemented
300C2×C4⋊C4×C47C2312yescomplemented
301C2×C4⋊C4×C47C2311yescharacteristic, complemented
302C2×C4⋊C4×C47C2311yescharacteristic, complemented
303C2×C22⋊C4×C47C2312yes—
304C2×C22⋊C4×C47C2312yes—
305C2×C22⋊C4×C47C2312yes—
306C2×C22⋊C4×C47C2312yes—
307C2×C22⋊C4×C47C2312yes—
308C2×C22⋊C4×C47C2318yescomplemented
309C2×C22⋊C4×C47C2312yescomplemented
310C2×C22⋊C4×C47C2312yescomplemented
311C2×C42×C47C2312yescomplemented
312C24×C47—24no—
313C24×C47—42no—
314C24×C47—42no—
315C24×C47C2412yes—
316C24×C47C2412yes—
317C24×C47C2411yescharacteristic
318C24×C47C2414yes—
319C23×D47—24no—
320C23×D47—24no—
321C23×D47—24no—
322C23×D47—28no—
323C23×D47—28no—
324C23×D47—232no—
325C23×D47—28no—
326C23×D47—28no—
327C23×D47—28no—
328C23×D47—416no—
329C23×D47—416no—
330C23×D47—44no—
331C23×D47—44no—
332C23×D47—42no—
333C23×D47—42no—
334C23×D47—44no—
335C23×D47—44no—
336C23×D47—464no—
337C23×D47#4118yescomplemented
338C23×D47C2412yes—
339C23×D47C2414yes—
340C23×D47C2418yes—
341C23×D47C2418yes—
342C23×D47C2412yes—
343C23×D47C2411yescharacteristic
344C23×D47C2411yescharacteristic
345C23×D47C2418yes—
346C23×D47C2414yes—
347C2×Q8×C47—42no—
348C2×Q8×C47C2414yescomplemented
349C2×D4×C47—28no—
350C2×D4×C47—44no—
351C2×D4×C47—44no—
352C2×D4×C47—42no—
353C2×D4×C47C2418yes—
354C2×D4×C47C2418yes—
355C2×D4×C47C2418yes—
356C2×D4×C47C2414yescomplemented
357C22×C4×C47—42no—
358C22×C4×C47—42no—
359C22×C4×C47—44no—
360C22×C4×C47C2412yes—
361C22×C4×C47C2412yes—
362C22×C4×C47C2412yes—
363C22×C4×C47C2411yescharacteristic
364C22×C4×C47C2411yescharacteristic
365C22×C4×C47C2412yes—
366C22×C4×C47C2414yes—
367C22×C4×C47C2414yes—
368C22×C4×C47C2418yescomplemented
369C2×C22⋊D47—28no—
370C2×C22⋊D47—28no—
371C2×C22⋊D47—28no—
372C2×C22⋊D47—28no—
373C2×C22⋊D47—44no—
374C2×C22⋊D47—44no—
375C2×C22⋊D47—44no—
376C2×C22⋊D47C2418yes—
377C2×C22⋊D47C2418yes—
378C2×C22⋊D47C2418yes—
379C2×C22⋊D47C2418yes—
380C2×C22⋊D47C2418yes—
381C2×C22⋊D47C2418yes—
382C2×C22⋊D47C2418yescomplemented
383C22×Dic47—42no—
384C22×Dic47—42no—
385C22×Dic47—44no—
386C22×Dic47C2411yescharacteristic
387C22×Dic47C2412yes—
388C22×Dic47C2411yescharacteristic
389C22×Dic47C2412yes—
390C22×Dic47C2412yes—
391C22×Dic47C2412yes—
392C22×Dic47C2414yes—
393C22×Dic47C2414yes—
394C22×Dic47C2418yescomplemented
395#10625354—416no—
396#10625352—416no—
397D4×D47—264no—
398D4×D47—432no—
399D4×D47—432no—
400#10625350—432no—
401C2×D188—28no—
402C2×D188—28no—
403C2×D188—28no—
404C2×D188—42no—
405C2×D188C2418yes—
406C2×D188C2418yes—
407C2×D188C2418yes—
408C2×D188C2414yescomplemented
409C2×C4×D47—28no—
410C2×C4×D47—24no—
411C2×C4×D47—28no—
412C2×C4×D47—24no—
413C2×C4×D47—416no—
414C2×C4×D47—416no—
415C2×C4×D47—44no—
416C2×C4×D47—42no—
417C2×C4×D47—42no—
418C2×C4×D47—44no—
419C2×C4×D47—44no—
420C2×C4×D47—44no—
421C2×C4×D47—44no—
422C2×C4×D47C2418yes—
423C2×C4×D47C2418yes—
424C2×C4×D47C2414yes—
425C2×C4×D47C2414yes—
426C2×C4×D47C2418yes—
427C2×C4×D47C2418yes—
428C2×C4×D47C2414yes—
429C2×C4×D47C2418yes—
430C2×C4×D47C2414yes—
431C2×C4×D47C2418yescomplemented
432C2×C4×D47C2418yescomplemented
433C2×Dic94—42no—
434C2×Dic94—44no—
435C2×Dic94C2418yescomplemented
436C2×Dic94C2414yescomplemented
437C4⋊C4×C47C2418yescomplemented
438C4⋊C4×C47C2418yescomplemented
439C4⋊C4×C47C2414yescomplemented
440C4⋊C4×C47C2414yescomplemented
441C22⋊C4×C47C2418yes—
442C22⋊C4×C47C2418yes—
443C22⋊C4×C47C2418yes—
444C22⋊C4×C47C2418yes—
445C22⋊C4×C47C2418yes—
446C22⋊C4×C47C2418yescomplemented
447C22⋊C4×C47C2418yescomplemented
448C42×C47C2418yescomplemented
449C22⋊Dic47C2418yes—
450C22⋊Dic47C2418yes—
451C22⋊Dic47C2418yes—
452C22⋊Dic47C2418yes—
453C22⋊Dic47C2418yes—
454C22⋊Dic47C2418yescomplemented
455C22⋊Dic47C2418yescomplemented
456(C2×D47)⋊C4C2418yes—
457(C2×D47)⋊C4C2418yes—
458(C2×D47)⋊C4C2418yes—
459(C2×D47)⋊C4C2418yes—
460(C2×D47)⋊C4C2418yes—
461(C2×D47)⋊C4C2418yes—
462(C2×D47)⋊C4C2418yes—
463(C2×D47)⋊C4C2418yes—
464(C2×D47)⋊C4C2418yes—
465(C2×D47)⋊C4C2418yes—
466(C2×D47)⋊C4C2418yescomplemented
467(C2×D47)⋊C4C2418yescomplemented
468(C2×D47)⋊C4C2418yescomplemented
469(C2×D47)⋊C4C2418yescomplemented
470C4⋊Dic47C2418yescomplemented
471C4⋊Dic47C2414yescomplemented
472C4⋊Dic47C2414yescomplemented
473C4⋊Dic47C2418yescomplemented
474Dic47⋊C4C2418yescomplemented
475Dic47⋊C4C2418yescomplemented
476Dic47⋊C4C2418yescomplemented
477Dic47⋊C4C2418yescomplemented
478Dic47⋊C4C2418yescomplemented
479Dic47⋊C4C2418yescomplemented
480C4×Dic47C2418yescomplemented
481C4×Dic47C2418yescomplemented
482C4×Dic47C2418yescomplemented
483C23×C47—22no—
484C23×C47—22no—
485C23×C47—24no—
486C23×C47—28no—
487C23×C47—24no—
488C23×C47—24no—
489C23×C47—24no—
490C23×C47—24no—
491C23×C47—24no—
492C23×C47—44no—
493C23×C47—44no—
494C23×C47—416no—
495C23×C47C2×#4114yes—
496C23×C47C2514yes—
497C23×C47C2514yes—
498C23×C47C2512yes—
499C23×C47C2511yescharacteristic
500C22×D47—232no—
501C22×D47—28no—
502C22×D47—22no—
503C22×D47—22no—
504C22×D47—22no—
505C22×D47—22no—
506C22×D47—24no—
507C22×D47—24no—
508C22×D47—28no—
509C22×D47—28no—
510C22×D47—24no—
511C22×D47—24no—
512C22×D47—24no—
513C22×D47—216no—
514C22×D47—216no—
515C22×D47—216no—
516C22×D47—216no—
517C22×D47—216no—
518C22×D47—416no—
519C22×D47—48no—
520C22×D47—48no—
521C22×D47—44no—
522C22×D47—44no—
523C22×D47—432no—
524C22×D47—432no—
525C22×D47—48no—
526C22×D47—48no—
527C22×D47—4128no—
528C22×D47—816no—
529C22×D47C2×#4118yes—
530C22×D47C2×#41116yescomplemented
531C22×D47H(5,𝔽2)14yes—
532C22×D47H(5,𝔽2)14yes—
533C22×D47C2514yes—
534C22×D47C2514yes—
535C22×D47C2512yes—
536C22×D47C2512yes—
537Q8×C47—44no—
538D4×C47—216no—
539D4×C47—48no—
540D4×C47—48no—
541D4×C47—44no—
542C2×C4×C47—24no—
543C2×C4×C47—22no—
544C2×C4×C47—24no—
545C2×C4×C47—24no—
546C2×C4×C47—22no—
547C2×C4×C47—24no—
548C2×C4×C47—44no—
549C2×C4×C47—44no—
550C2×C4×C47—48no—
551C2×C4×C47C2514yes—
552C2×C4×C47C2514yes—
553C2×C4×C47C2514yes—
554C2×C4×C47C2514yes—
555C2×C4×C47C2512yes—
556C2×C4×C47C2512yes—
557C22⋊D47—216no—
558C22⋊D47—216no—
559C22⋊D47—216no—
560C22⋊D47—216no—
561C22⋊D47—48no—
562C22⋊D47—48no—
563C22⋊D47—48no—
564C2×Dic47—24no—
565C2×Dic47—24no—
566C2×Dic47—24no—
567C2×Dic47—24no—
568C2×Dic47—22no—
569C2×Dic47—22no—
570C2×Dic47—44no—
571C2×Dic47—44no—
572C2×Dic47—48no—
573C2×Dic47C2514yes—
574C2×Dic47C2512yes—
575C2×Dic47C2512yes—
576C2×Dic47C2514yes—
577C2×Dic47C2514yes—
578C2×Dic47C2514yes—
579D188—216no—
580D188—216no—
581D188—216no—
582D188—44no—
583C4×D47—216no—
584C4×D47—216no—
585C4×D47—28no—
586C4×D47—28no—
587C4×D47—48no—
588C4×D47—44no—
589C4×D47—44no—
590C4×D47—48no—
591C4×D47—48no—
592C4×D47—48no—
593C4×D47—48no—
594Dic94—48no—
595Dic94—44no—
596C2×#3490—471nomaximal, Sylow
597C22×C47—22no—
598C22×C47—22no—
599C22×C47—28no—
600C22×C47—24no—
601C22×C47—24no—
602C22×C47—24no—
603C22×C47—24no—
604C22×C47—24no—
605C22×C47—24no—
606C22×C47—416no—
607C22×C47—48no—
608C22×C47—48no—
609C22×C47C22×#4114yes—
610C22×C47C22×#4112yes—
611C22×C47C2×H(5,𝔽2)12yes—
612C22×C47C2×H(5,𝔽2)12yes—
613C22×C47C2611yescharacteristic
614C2×D47—232no—
615C2×D47—22no—
616C2×D47—22no—
617C2×D47—22no—
618C2×D47—22no—
619C2×D47—24no—
620C2×D47—24no—
621C2×D47—28no—
622C2×D47—28no—
623C2×D47—216no—
624C2×D47—24no—
625C2×D47—24no—
626C2×D47—24no—
627C2×D47—416no—
628C2×D47—432no—
629C2×D47—432no—
630C2×D47—48no—
631C2×D47—816no—
632C2×D47C22×#4118yes—
633C2×D47C2×H(5,𝔽2)14yes—
634C2×D47C2×H(5,𝔽2)14yes—
635C4×C47—24no—
636C4×C47—22no—
637C4×C47—24no—
638C4×C47—24no—
639C4×C47—22no—
640C4×C47—24no—
641Dic47—24no—
642Dic47—24no—
643Dic47—24no—
644Dic47—24no—
645Dic47—22no—
646Dic47—22no—
647#3490—4732no—
648C2×#551—472no—
649C2×#551—472no—
650C2×#551—472no—
651C2×#551—472no—
652C2×#546—472no—
653C2×#546—472no—
654C2×#546—472no—
655C2×#546—472no—
656C2×#543—471no—
657C2×#538—472no—
658C2×#538—471no—
659C2×#538D4711yescharacteristic, complemented
660C2×#534—471no—
661C2×#525—471no—
662C2×#525—471no—
663C2×#525—472no—
664C22×#120—472no—
665C2×#518—472no—
666C23×C22⋊C4—471no—
667C2×C47—24no—
668C2×C47—44no—
669C2×C47—44no—
670C2×C47#349014yescomplemented
671C2×C47C23×#4111yescharacteristic
672C2×C47C22×H(5,𝔽2)11yescharacteristic
673C2×C47C22×H(5,𝔽2)11yescharacteristic
674D47—24no—
675D47—24no—
676D47—28no—
677D47—44no—
678C26—471no—
679C22×#41—471no—
680C22×#41—471no—
681C22×#41—472no—
682C23×D4—472no—
683C23×D4—472no—
684C23×D4—472no—
685C24×C4—471no—
686C24×C4—471no—
687#551—4732no—
688#551—4732no—
689#551—4732no—
690#551—4732no—
691#546—4732no—
692#546—4732no—
693#546—4732no—
694#546—4732no—
695#543—4716no—
696#538—4732no—
697#538—4716no—
698#538C2×D47116yescomplemented
699#534—4716no—
700C2×#126—472no—
701C2×#126—472no—
702C2×#126—472no—
703C2×#126C2×D4712yescomplemented
704C2×#124—472no—
705C2×#124—472no—
706C2×#124—472no—
707C2×#124C2×D4712yescomplemented
708#525—4716no—
709#525—4716no—
710#525—4732no—
711C2×#123—472no—
712C2×#123—472no—
713C2×#123—472no—
714C2×#123—472no—
715C2×#123—472no—
716C2×#123—472no—
717C2×#123—472no—
718C2×#123—472no—
719C2×#123—472no—
720C2×#123C2×D4712yescomplemented
721C2×C22⋊Q8—471no—
722C2×C22⋊Q8—472no—
723C2×C22⋊Q8—471no—
724C2×C22⋊Q8—472no—
725C2×C22⋊Q8—471no—
726C2×C22⋊Q8—472no—
727C2×C22⋊Q8—472no—
728C2×C22⋊Q8—472no—
729C2×C22⋊Q8—472no—
730C2×C22⋊Q8C2×D4711yescharacteristic, complemented
731C2×#121—472no—
732C2×#121—472no—
733C2×#121—472no—
734C2×#121—471no—
735C2×#121—471no—
736C2×#121—471no—
737C2×#121—472no—
738C2×#121—472no—
739C2×#121C2×D4712yescomplemented
740C2×#121C2×D4711yescharacteristic, complemented
741C2×#120—472no—
742C2×#120—472no—
743C2×#120—472no—
744C2×#120—472no—
745C2×#120—472no—
746C2×#120—4732no—
747C2×#120—472no—
748C2×#120—472no—
749C2×#120—472no—
750C2×#120—472no—
751C2×#120C2×D4712yescomplemented
752#518—4732no—
753C2×C4×D4—472no—
754C2×C4×D4—472no—
755C2×C4×D4—472no—
756C2×C4×D4—472no—
757C2×C4×D4—472no—
758C2×C4×D4—472no—
759C2×C4×D4—472no—
760C2×C4×D4—472no—
761C2×C4×D4—472no—
762C2×C4×D4—472no—
763C2×C4×D4—472no—
764C2×C4×D4C2×D4712yescomplemented
765C2×#117—472no—
766C2×#117—471no—
767C2×#117—471no—
768C2×#117—472no—
769C2×#117—472no—
770C22×C22⋊C4—471no—
771C22×C22⋊C4—471no—
772C22×C22⋊C4—471no—
773C22×C22⋊C4—472no—
774C22×C22⋊C4—472no—
775C22×C22⋊C4—472no—
776C22×C22⋊C4—472no—
777C22×C22⋊C4—472no—
778C22×C22⋊C4—472no—
779C22×C22⋊C4—472no—
780C22×C22⋊C4—472no—
781C22×C22⋊C4—4716no—
782C22×C22⋊C4—472no—
783C22×C22⋊C4C2×D4711yescharacteristic, complemented
784C47C2×#349011yescharacteristic, complemented, Sylow
785C25—471no—
786C25—471no—
787C25—472no—
788C25—472no—
789C25—478no—
790C25—472no—
791C25—948no—
792C25—1884no—
793C25—1884no—
794C25C22×D4711yescharacteristic
795C2×#41—478no—
796C2×#41—478no—
797C2×#41—4716no—
798C2×#41—1888no—
799C2×#41—1884no—
800C2×#41—1884no—
801C22×Q8—471no—
802C22×Q8—472no—
803C22×Q8C22×D4711yescharacteristic, complemented
804C22×D4—472no—
805C22×D4—472no—
806C22×D4—472no—
807C22×D4—472no—
808C22×D4—472no—
809C22×D4—472no—
810C22×D4—472no—
811C22×D4—4716no—
812C22×D4—4716no—
813C22×D4—4716no—
814C22×D4—472no—
815C22×D4—472no—
816C22×D4—472no—
817C22×D4—471no—
818C22×D4—9416no—
819C22×D4—1888no—
820C22×D4—1888no—
821C22×D4C22×D4712yes—
822C22×D4C22×D4712yes—
823C22×D4C22×D4712yes—
824C22×D4C22×D4711yescharacteristic, complemented
825C23×C4—471no—
826C23×C4—471no—
827C23×C4—472no—
828C23×C4—472no—
829C23×C4—471no—
830C23×C4—471no—
831C23×C4—472no—
832C23×C4—471no—
833C23×C4—471no—
834C23×C4—472no—
835C23×C4—472no—
836C23×C4—472no—
837C23×C4—478no—
838C23×C4—478no—
839C23×C4—472no—
840C23×C4—472no—
841C23×C4—1884no—
842C23×C4—1884no—
843C23×C4C22×D4711yescharacteristic
844C23×C4C22×D4711yescharacteristic
845C23×C4C22×D4712yescomplemented
846#126—4716no—
847#126—4716no—
848#126—4716no—
849#126C22×D47116yescomplemented
850#124—4716no—
851#124—4716no—
852#124—4716no—
853#124C22×D47116yescomplemented
854#123—4716no—
855#123—4716no—
856#123—4716no—
857#123—4716no—
858#123—4716no—
859#123—4716no—
860#123—4716no—
861#123—4716no—
862#123—4716no—
863#123C22×D47116yescomplemented
864C22⋊Q8—478no—
865C22⋊Q8—4716no—
866C22⋊Q8—478no—
867C22⋊Q8—4716no—
868C22⋊Q8—478no—
869C22⋊Q8—4716no—
870C22⋊Q8—4716no—
871C22⋊Q8—4716no—
872C22⋊Q8—4716no—
873C22⋊Q8C22×D4718yescomplemented
874#121—4716no—
875#121—4716no—
876#121—4716no—
877#121—478no—
878#121—478no—
879#121—478no—
880#121—4716no—
881#121—4716no—
882#121C22×D47116yescomplemented
883#121C22×D4718yescomplemented
884#120—4716no—
885#120—4716no—
886#120—4716no—
887#120—4716no—
888#120—4716no—
889#120—4716no—
890#120—4716no—
891#120—4716no—
892#120—4716no—
893#120C22×D47116yescomplemented
894C4×D4—4716no—
895C4×D4—4716no—
896C4×D4—4716no—
897C4×D4—4716no—
898C4×D4—4716no—
899C4×D4—4716no—
900C4×D4—4716no—
901C4×D4—4716no—
902C4×D4—4716no—
903C4×D4—4716no—
904C4×D4—4716no—
905C4×D4C22×D47116yescomplemented
906#117—4716no—
907#117—478no—
908#117—478no—
909#117—4716no—
910#117—4716no—
911C2×C4⋊C4—472no—
912C2×C4⋊C4—472no—
913C2×C4⋊C4—472no—
914C2×C4⋊C4—472no—
915C2×C4⋊C4—471no—
916C2×C4⋊C4—472no—
917C2×C4⋊C4—471no—
918C2×C4⋊C4—472no—
919C2×C4⋊C4—472no—
920C2×C4⋊C4—472no—
921C2×C4⋊C4C22×D4712yescomplemented
922C2×C4⋊C4C22×D4711yescharacteristic, complemented
923C2×C4⋊C4C22×D4711yescharacteristic, complemented
924C2×C4⋊C4C22×D4712yescomplemented
925C2×C22⋊C4—472no—
926C2×C22⋊C4—472no—
927C2×C22⋊C4—478no—
928C2×C22⋊C4—472no—
929C2×C22⋊C4—472no—
930C2×C22⋊C4—472no—
931C2×C22⋊C4—472no—
932C2×C22⋊C4—472no—
933C2×C22⋊C4—472no—
934C2×C22⋊C4—472no—
935C2×C22⋊C4—478no—
936C2×C22⋊C4—472no—
937C2×C22⋊C4—472no—
938C2×C22⋊C4—478no—
939C2×C22⋊C4—472no—
940C2×C22⋊C4—472no—
941C2×C22⋊C4—472no—
942C2×C22⋊C4—472no—
943C2×C22⋊C4—472no—
944C2×C22⋊C4—472no—
945C2×C22⋊C4—472no—
946C2×C22⋊C4—472no—
947C2×C22⋊C4—472no—
948C2×C22⋊C4—472no—
949C2×C22⋊C4—4716no—
950C2×C22⋊C4—4716no—
951C2×C22⋊C4—4716no—
952C2×C22⋊C4—4716no—
953C2×C22⋊C4—4716no—
954C2×C22⋊C4—4716no—
955C2×C22⋊C4—4716no—
956C2×C22⋊C4—4716no—
957C2×C22⋊C4—4716no—
958C2×C22⋊C4C22×D4712yes—
959C2×C22⋊C4C22×D4712yes—
960C2×C22⋊C4C22×D4712yes—
961C2×C22⋊C4C22×D4712yes—
962C2×C22⋊C4C22×D4712yes—
963C2×C22⋊C4C22×D4718yescomplemented
964C2×C22⋊C4C22×D4712yescomplemented
965C2×C22⋊C4C22×D4712yescomplemented
966C2×C42—472no—
967C2×C42—472no—
968C2×C42—472no—
969C2×C42C22×D4712yescomplemented
970C24—24no—
971C24—42no—
972C24—42no—
973C24—472no—
974C24—471no—
975C24—471no—
976C24—478no—
977C24—474no—
978C24—474no—
979C24—472no—
980C24—478no—
981C24—478no—
982C24—478no—
983C24—944no—
984C24—944no—
985C24—948no—
986C24—948no—
987C24—948no—
988C24—948no—
989C24—948no—
990C24—9432no—
991C24—944no—
992C24—1884no—
993C24—1884no—
994C24—1882no—
995C24—1882no—
996C24—1884no—
997C24—1884no—
998C24—18816no—
999C24—18816no—
1000C24—18864no—
1001C24C23×D4712yes—
1002C24C23×D4712yes—
1003C24C23×D4711yescharacteristic
1004C24C23×D4714yes—
1005#41—18832no—
1006#41—18816no—
1007#41—18816no—
1008C2×Q8—42no—
1009C2×Q8—474no—
1010C2×Q8—478no—
1011C2×Q8—1882no—
1012C2×Q8—1884no—
1013C2×Q8C23×D4714yescomplemented
1014C2×D4—28no—
1015C2×D4—44no—
1016C2×D4—44no—
1017C2×D4—42no—
1018C2×D4—478no—
1019C2×D4—478no—
1020C2×D4—478no—
1021C2×D4—478no—
1022C2×D4—478no—
1023C2×D4—478no—
1024C2×D4—478no—
1025C2×D4—478no—
1026C2×D4—478no—
1027C2×D4—478no—
1028C2×D4—474no—
1029C2×D4—948no—
1030C2×D4—948no—
1031C2×D4—948no—
1032C2×D4—9464no—
1033C2×D4—948no—
1034C2×D4—948no—
1035C2×D4—948no—
1036C2×D4—948no—
1037C2×D4—1882no—
1038C2×D4—1884no—
1039C2×D4—1884no—
1040C2×D4—1884no—
1041C2×D4—18832no—
1042C2×D4—18832no—
1043C2×D4C23×D4718yes—
1044C2×D4C23×D4718yes—
1045C2×D4C23×D4718yes—
1046C2×D4C23×D4714yescomplemented
1047C22×C4—42no—
1048C22×C4—42no—
1049C22×C4—44no—
1050C22×C4—472no—
1051C22×C4—471no—
1052C22×C4—471no—
1053C22×C4—472no—
1054C22×C4—472no—
1055C22×C4—472no—
1056C22×C4—474no—
1057C22×C4—474no—
1058C22×C4—478no—
1059C22×C4—478no—
1060C22×C4—474no—
1061C22×C4—474no—
1062C22×C4—478no—
1063C22×C4—474no—
1064C22×C4—474no—
1065C22×C4—478no—
1066C22×C4—478no—
1067C22×C4—478no—
1068C22×C4—478no—
1069C22×C4—478no—
1070C22×C4—948no—
1071C22×C4—944no—
1072C22×C4—944no—
1073C22×C4—948no—
1074C22×C4—1884no—
1075C22×C4—1882no—
1076C22×C4—1882no—
1077C22×C4—1884no—
1078C22×C4—1884no—
1079C22×C4—1884no—
1080C22×C4—1884no—
1081C22×C4—18816no—
1082C22×C4—18816no—
1083C22×C4—1882no—
1084C22×C4—1882no—
1085C22×C4—1884no—
1086C22×C4C23×D4712yes—
1087C22×C4C23×D4712yes—
1088C22×C4C23×D4712yes—
1089C22×C4C23×D4712yes—
1090C22×C4C23×D4711yescharacteristic
1091C22×C4C23×D4711yescharacteristic
1092C22×C4C23×D4714yes—
1093C22×C4C23×D4714yes—
1094C22×C4C23×D4718yescomplemented
1095C4⋊C4—478no—
1096C4⋊C4—478no—
1097C4⋊C4—478no—
1098C4⋊C4—478no—
1099C4⋊C4—478no—
1100C4⋊C4—478no—
1101C4⋊C4—478no—
1102C4⋊C4—474no—
1103C4⋊C4—474no—
1104C4⋊C4—478no—
1105C4⋊C4C23×D4718yescomplemented
1106C4⋊C4C23×D4714yescomplemented
1107C4⋊C4C23×D4714yescomplemented
1108C4⋊C4C23×D4718yescomplemented
1109C22⋊C4—478no—
1110C22⋊C4—478no—
1111C22⋊C4—478no—
1112C22⋊C4—478no—
1113C22⋊C4—478no—
1114C22⋊C4—478no—
1115C22⋊C4—478no—
1116C22⋊C4—478no—
1117C22⋊C4—478no—
1118C22⋊C4—478no—
1119C22⋊C4—478no—
1120C22⋊C4—478no—
1121C22⋊C4—478no—
1122C22⋊C4—478no—
1123C22⋊C4—478no—
1124C22⋊C4—478no—
1125C22⋊C4—478no—
1126C22⋊C4—478no—
1127C22⋊C4—478no—
1128C22⋊C4—478no—
1129C22⋊C4—478no—
1130C22⋊C4C23×D4718yes—
1131C22⋊C4C23×D4718yes—
1132C22⋊C4C23×D4718yes—
1133C22⋊C4C23×D4718yes—
1134C22⋊C4C23×D4718yes—
1135C22⋊C4C23×D4718yescomplemented
1136C22⋊C4C23×D4718yescomplemented
1137C42—478no—
1138C42—478no—
1139C42—478no—
1140C42C23×D4718yescomplemented
1141C23—22no—
1142C23—22no—
1143C23—24no—
1144C23—28no—
1145C23—24no—
1146C23—24no—
1147C23—24no—
1148C23—24no—
1149C23—24no—
1150C23—44no—
1151C23—44no—
1152C23—416no—
1153C23—478no—
1154C23—474no—
1155C23—474no—
1156C23—474no—
1157C23—472no—
1158C23—472no—
1159C23—4716no—
1160C23—474no—
1161C23—948no—
1162C23—948no—
1163C23—9416no—
1164C23—9416no—
1165C23—9416no—
1166C23—9416no—
1167C23—9416no—
1168C23—9432no—
1169C23—948no—
1170C23—942no—
1171C23—942no—
1172C23—942no—
1173C23—942no—
1174C23—944no—
1175C23—944no—
1176C23—944no—
1177C23—944no—
1178C23—944no—
1179C23—37616no—
1180C23—1888no—
1181C23—1888no—
1182C23—18816no—
1183C23—1884no—
1184C23—1884no—
1185C23—1888no—
1186C23—1888no—
1187C23—18832no—
1188C23—18832no—
1189C23—188128no—
1190C23#41×D4714yes—
1191C23C24×D4714yes—
1192C23C24×D4714yes—
1193C23C24×D4712yes—
1194C23C24×D4711yescharacteristic
1195Q8—44no—
1196Q8—1884no—
1197Q8—1888no—
1198D4—216no—
1199D4—48no—
1200D4—48no—
1201D4—44no—
1202D4—9416no—
1203D4—9416no—
1204D4—9416no—
1205D4—9416no—
1206D4—9416no—
1207D4—9416no—
1208D4—9416no—
1209D4—1884no—
1210D4—1888no—
1211D4—1888no—
1212D4—1888no—
1213C2×C4—24no—
1214C2×C4—24no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—24no—
1218C2×C4—24no—
1219C2×C4—44no—
1220C2×C4—44no—
1221C2×C4—48no—
1222C2×C4—474no—
1223C2×C4—472no—
1224C2×C4—472no—
1225C2×C4—474no—
1226C2×C4—474no—
1227C2×C4—474no—
1228C2×C4—9416no—
1229C2×C4—948no—
1230C2×C4—948no—
1231C2×C4—9416no—
1232C2×C4—944no—
1233C2×C4—942no—
1234C2×C4—942no—
1235C2×C4—944no—
1236C2×C4—944no—
1237C2×C4—944no—
1238C2×C4—1888no—
1239C2×C4—1884no—
1240C2×C4—1884no—
1241C2×C4—1888no—
1242C2×C4—1888no—
1243C2×C4—1888no—
1244C2×C4—1888no—
1245C2×C4—1884no—
1246C2×C4—1884no—
1247C2×C4—1888no—
1248C2×C4C24×D4714yes—
1249C2×C4C24×D4714yes—
1250C2×C4C24×D4714yes—
1251C2×C4C24×D4714yes—
1252C2×C4C24×D4712yes—
1253C2×C4C24×D4712yes—
1254C22—28no—
1255C22—22no—
1256C22—22no—
1257C22—24no—
1258C22—24no—
1259C22—24no—
1260C22—24no—
1261C22—24no—
1262C22—24no—
1263C22—416no—
1264C22—48no—
1265C22—48no—
1266C22—478no—
1267C22—474no—
1268C22—474no—
1269C22—9432no—
1270C22—948no—
1271C22—948no—
1272C22—9416no—
1273C22—942no—
1274C22—942no—
1275C22—942no—
1276C22—942no—
1277C22—944no—
1278C22—944no—
1279C22—944no—
1280C22—944no—
1281C22—944no—
1282C22—37616no—
1283C22—18816no—
1284C22—18832no—
1285C22—18832no—
1286C22—1888no—
1287C22C2×#41×D4714yes—
1288C22C2×#41×D4712yes—
1289C22H(5,𝔽2)×D4712yes—
1290C22H(5,𝔽2)×D4712yes—
1291C22C25×D4711yescharacteristic
1292C4—24no—
1293C4—24no—
1294C4—22no—
1295C4—22no—
1296C4—24no—
1297C4—24no—
1298C4—944no—
1299C4—942no—
1300C4—942no—
1301C4—944no—
1302C4—944no—
1303C4—944no—
1304C2—24no—
1305C2—44no—
1306C2—44no—
1307C2—944no—
1308C2—944no—
1309C2—948no—
1310C2—1884no—
1311C2#2025707414yesdirect product factor
1312C2C22×#41×D4711yescharacteristic
1313C2C2×H(5,𝔽2)×D4711yescharacteristic
1314C2C2×H(5,𝔽2)×D4711yescharacteristic
subgroupG/H
centerC23C24×D47
commutator, cosocleC22×C47C26
FrattiniC22C25×D47
FittingC2×C47×#538C2
socleC23×C47C25
hypercenterC2×#538D47
hypocenterC47C2×#3490
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#538

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #20257074C2direct (N × H)
2. C2×#15689803C2semidirect
3. C2×#15689801C2semidirect
4. C2×#15689798C2semidirect
5. C2×#15689798C2semidirect
6. C2×#15689770C2semidirect
7. C2×#15689766C2semidirect
8. C2×#15689765C2semidirect
9. C2×#15689762C2semidirect
10. C2×#15689748C2semidirect
11. C2×#15689711C2semidirect
12. C2×#15689708C2semidirect
13. C2×#15689681C2semidirect
14. C2×#15689636C2semidirect
15. C2×#15689633C2semidirect
16. C2×#15689632C2semidirect
17. C2×#120×D47C2semidirect
18. C2×#15689595C2semidirect
19. C22×C22⋊C4×D47C2semidirect
20. C2×C47×#538C2semidirect
22. C22×#10625354C22semidirect
23. C22×#10625350C22semidirect
24. C22×#10625352C22semidirect
26. C22×D4×D47C22semidirect
27. C22×D4×D47C22semidirect
28. C23×C4×D47C22semidirect
29. C23×C4×D47C22semidirect
30. #15689803C22semidirect
31. #15689801C22semidirect
32. #15689798C22semidirect
33. #15689798C22semidirect
34. #15689770C22semidirect
35. #15689766C22semidirect
36. #15689765C22semidirect
37. #15689762C22semidirect
38. #15689748C22semidirect
39. #15689711C22semidirect
40. #15689708C22semidirect
41. #15689681C22semidirect
42. C2×#13094017C22semidirect
43. C2×#13094017C22semidirect
44. C2×#13094017C22semidirect
45. C2×#13094011C22semidirect
46. C2×#13094010C22semidirect
47. C2×#13094010C22semidirect
48. #15689636C22semidirect
49. #15689633C22semidirect
50. #15689632C22semidirect
51. C2×#13094009C22semidirect
52. C2×#13094009C22semidirect
53. C2×#13094009C22semidirect
54. C2×#13094006C22semidirect
55. C2×#13094006C22semidirect
56. C2×#13094006C22semidirect
57. C2×#13094006C22semidirect
58. C2×#13094006C22semidirect
59. C2×#13094005C22semidirect
60. C2×#13094004C22semidirect
61. C2×#13094004C22semidirect
62. C2×#13094003C22semidirect
63. C2×#13094002C22semidirect
64. C2×#13094002C22semidirect
65. C2×#13094002C22semidirect
66. C2×#13094001C22semidirect
67. C2×#13094000C22semidirect
68. C2×#13094000C22semidirect
69. C2×#13093999C22semidirect
70. C2×#13093998C22semidirect
71. C2×#13093997C22semidirect
72. C2×#13093997C22semidirect
73. C2×#13093996C22semidirect
74. C2×#13093996C22semidirect
75. C2×#13093995C22semidirect
76. C2×#13093995C22semidirect
79. C2×#13093994C22semidirect
80. C2×#13093994C22semidirect
81. C2×#13093993C22semidirect
84. C2×#13093992C22semidirect
85. C2×#13093992C22semidirect
86. #120×D47C22semidirect
87. #15689595C22semidirect
88. C2×C4×D188C22semidirect
89. C2×C4×D188C22semidirect
90. C2×D4×Dic47C22semidirect
91. C2×#13093986C22semidirect
92. C2×#13093986C22semidirect
93. C2×C4×C22⋊D47C22semidirect
94. C2×C4×C22⋊D47C22semidirect
95. C2×C4×C22⋊D47C22semidirect
96. C2×(C22⋊D47)⋊C4C22semidirect
97. C2×(C22⋊D47)⋊C4C22semidirect
98. C2×(C22⋊D47)⋊C4C22semidirect
99. C2×#13093982C22semidirect
100. C2×#13093982C22semidirect
101. C2×#13093982C22semidirect
102. C2×#13093981C22semidirect
103. C2×#13093981C22semidirect
104. C22×C22⋊Dic47C22semidirect
107. C22×(C2×D47)⋊C4C22semidirect
109. C2×C22⋊C4×D47C22semidirect
110. C2×C22⋊C4×D47C22semidirect
111. C2×C22⋊C4×D47C22semidirect
112. C2×C22⋊C4×D47C22semidirect
113. C2×C22⋊C4×D47C22semidirect
114. C2×C22⋊C4×D47C22semidirect
115. C2×C22⋊C4×D47C22semidirect
116. C2×C22⋊C4×D47C22semidirect
117. C47×#538C22semidirect
118. C2×#126×C47C22semidirect
119. C2×#124×C47C22semidirect
120. C2×#123×C47C22semidirect
121. C2×C22⋊Q8×C47C22semidirect
122. C2×#121×C47C22semidirect
123. C2×#121×C47C22semidirect
124. C2×#120×C47C22semidirect
125. C2×C4×D4×C47C22semidirect
126. C22×C22⋊C4×C47C22semidirect
137. C2×#10625354C23semidirect
139. C2×#10625350C23semidirect
141. C2×#10625352C23semidirect
142. C22×Dic94C23semidirect
143. C22×Dic94C23semidirect
147. C22×D188C23semidirect
154. C22×C22⋊D47C23semidirect
159. C2×D4×D47C23semidirect
160. C2×D4×D47C23semidirect
163. C23×Dic47C23semidirect
175. C22×C4×D47C23semidirect
176. C22×C4×D47C23semidirect
177. C22×C4×D47C23semidirect
178. C22×C4×D47C23semidirect
179. #13094017C23semidirect
180. #13094017C23semidirect
181. #13094017C23semidirect
182. #13094011C23semidirect
183. #13094010C23semidirect
184. #13094010C23semidirect
185. #13094009C23semidirect
186. #13094009C23semidirect
187. #13094009C23semidirect
188. #13094006C23semidirect
189. #13094006C23semidirect
190. #13094006C23semidirect
191. #13094006C23semidirect
192. #13094006C23semidirect
193. #13094005C23semidirect
194. #13094004C23semidirect
195. #13094004C23semidirect
196. #13094003C23semidirect
197. #13094002C23semidirect
198. #13094002C23semidirect
199. #13094002C23semidirect
200. #13094001C23semidirect
201. #13094000C23semidirect
202. #13094000C23semidirect
203. #13093999C23semidirect
204. #13093998C23semidirect
205. #13093997C23semidirect
206. #13093997C23semidirect
207. #13093996C23semidirect
208. #13093996C23semidirect
209. #13093995C23semidirect
210. #13093995C23semidirect
213. #13093994C23semidirect
214. #13093994C23semidirect
215. #13093993C23semidirect
218. #13093992C23semidirect
219. #13093992C23semidirect
220. C4×D188C23semidirect
221. C4×D188C23semidirect
222. D4×Dic47C23semidirect
223. #13093986C23semidirect
224. #13093986C23semidirect
225. C4×C22⋊D47C23semidirect
226. C4×C22⋊D47C23semidirect
227. C4×C22⋊D47C23semidirect
228. (C22⋊D47)⋊C4C23semidirect
229. (C22⋊D47)⋊C4C23semidirect
230. (C22⋊D47)⋊C4C23semidirect
231. #13093982C23semidirect
232. #13093982C23semidirect
233. #13093982C23semidirect
234. #13093981C23semidirect
235. #13093981C23semidirect
236. C2×C4⋊Dic47C23semidirect
237. C2×C4⋊Dic47C23semidirect
238. C2×C4⋊Dic47C23semidirect
239. C2×C4⋊Dic47C23semidirect
240. C2×Dic47⋊C4C23semidirect
241. C2×Dic47⋊C4C23semidirect
242. C2×Dic47⋊C4C23semidirect
243. C2×Dic47⋊C4C23semidirect
244. C2×Dic47⋊C4C23semidirect
245. C2×Dic47⋊C4C23semidirect
251. C2×C22⋊Dic47C23semidirect
252. C2×C22⋊Dic47C23semidirect
253. C2×C22⋊Dic47C23semidirect
266. C2×(C2×D47)⋊C4C23semidirect
267. C2×(C2×D47)⋊C4C23semidirect
268. C2×(C2×D47)⋊C4C23semidirect
269. C2×(C2×D47)⋊C4C23semidirect
270. C2×(C2×D47)⋊C4C23semidirect
272. C22⋊C4×D47C23semidirect
273. C22⋊C4×D47C23semidirect
274. C22⋊C4×D47C23semidirect
275. C22⋊C4×D47C23semidirect
276. C22⋊C4×D47C23semidirect
277. C22⋊C4×D47C23semidirect
278. C22⋊C4×D47C23semidirect
279. C2×C4×Dic47C23semidirect
280. C2×C4×Dic47C23semidirect
281. C2×C4×Dic47C23semidirect
283. C22×Q8×C47C23semidirect
287. C22×D4×C47C23semidirect
290. C23×C4×C47C23semidirect
291. #126×C47C23semidirect
292. #124×C47C23semidirect
293. #123×C47C23semidirect
294. C22⋊Q8×C47C23semidirect
295. #121×C47C23semidirect
296. #121×C47C23semidirect
297. #120×C47C23semidirect
298. C4×D4×C47C23semidirect
299. C2×C4⋊C4×C47C23semidirect
300. C2×C4⋊C4×C47C23semidirect
301. C2×C4⋊C4×C47C23semidirect
302. C2×C4⋊C4×C47C23semidirect
308. C2×C22⋊C4×C47C23semidirect
309. C2×C22⋊C4×C47C23semidirect
310. C2×C22⋊C4×C47C23semidirect
311. C2×C42×C47C23semidirect
337. C23×D47#41semidirect
348. C2×Q8×C47C24semidirect
356. C2×D4×C47C24semidirect
368. C22×C4×C47C24semidirect
382. C2×C22⋊D47C24semidirect
394. C22×Dic47C24semidirect
408. C2×D188C24semidirect
431. C2×C4×D47C24semidirect
432. C2×C4×D47C24semidirect
435. C2×Dic94C24semidirect
436. C2×Dic94C24semidirect
437. C4⋊C4×C47C24semidirect
438. C4⋊C4×C47C24semidirect
439. C4⋊C4×C47C24semidirect
440. C4⋊C4×C47C24semidirect
446. C22⋊C4×C47C24semidirect
447. C22⋊C4×C47C24semidirect
448. C42×C47C24semidirect
454. C22⋊Dic47C24semidirect
455. C22⋊Dic47C24semidirect
466. (C2×D47)⋊C4C24semidirect
467. (C2×D47)⋊C4C24semidirect
468. (C2×D47)⋊C4C24semidirect
469. (C2×D47)⋊C4C24semidirect
470. C4⋊Dic47C24semidirect
471. C4⋊Dic47C24semidirect
472. C4⋊Dic47C24semidirect
473. C4⋊Dic47C24semidirect
474. Dic47⋊C4C24semidirect
475. Dic47⋊C4C24semidirect
476. Dic47⋊C4C24semidirect
477. Dic47⋊C4C24semidirect
478. Dic47⋊C4C24semidirect
479. Dic47⋊C4C24semidirect
480. C4×Dic47C24semidirect
481. C4×Dic47C24semidirect
482. C4×Dic47C24semidirect
530. C22×D47C2×#41semidirect
659. C2×#538D47semidirect
670. C2×C47#3490semidirect
698. #538C2×D47semidirect
703. C2×#126C2×D47semidirect
707. C2×#124C2×D47semidirect
720. C2×#123C2×D47semidirect
730. C2×C22⋊Q8C2×D47semidirect
739. C2×#121C2×D47semidirect
740. C2×#121C2×D47semidirect
751. C2×#120C2×D47semidirect
764. C2×C4×D4C2×D47semidirect
783. C22×C22⋊C4C2×D47semidirect
784. C47C2×#3490semidirect
803. C22×Q8C22×D47semidirect
824. C22×D4C22×D47semidirect
845. C23×C4C22×D47semidirect
849. #126C22×D47semidirect
853. #124C22×D47semidirect
863. #123C22×D47semidirect
873. C22⋊Q8C22×D47semidirect
882. #121C22×D47semidirect
883. #121C22×D47semidirect
893. #120C22×D47semidirect
905. C4×D4C22×D47semidirect
921. C2×C4⋊C4C22×D47semidirect
922. C2×C4⋊C4C22×D47semidirect
923. C2×C4⋊C4C22×D47semidirect
924. C2×C4⋊C4C22×D47semidirect
963. C2×C22⋊C4C22×D47semidirect
964. C2×C22⋊C4C22×D47semidirect
965. C2×C22⋊C4C22×D47semidirect
969. C2×C42C22×D47semidirect
1013. C2×Q8C23×D47semidirect
1046. C2×D4C23×D47semidirect
1094. C22×C4C23×D47semidirect
1105. C4⋊C4C23×D47semidirect
1106. C4⋊C4C23×D47semidirect
1107. C4⋊C4C23×D47semidirect
1108. C4⋊C4C23×D47semidirect
1135. C22⋊C4C23×D47semidirect
1136. C22⋊C4C23×D47semidirect
1140. C42C23×D47semidirect
1311. C2#20257074direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#202570742
C2×#156898032
C2×#156898012
C2×#156897982
C2×#156897702
C2×#156897662
C2×#156897652
C2×#156897622
C2×#156897482
C2×#156897112
C2×#156897082
C2×#156896812
C2×#156896362
C2×#156896332
C2×#156896322
C2×#120×D472
C2×#156895952
C22×C22⋊C4×D472
C2×C47×#5382
C2×#349047