Finite Group Databasebeta

← C2×#20257331 #27124256

Subgroups — C2×#20257331 #27124256

Order 12032.

8082 conjugacy classes of subgroups.

The subgroup lattice has 1356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257331C2132yesmaximal, direct product factor
2C2×#15689858C211yesmaximal, characteristic, complemented
3C2×#15689826C211yesmaximal, characteristic, complemented
4C2×#15689821C212yesmaximal, complemented
5C2×#15689811C211yesmaximal, characteristic, complemented
6C2×#15689800C212yesmaximal, complemented
7C2×#15689800C212yesmaximal, complemented
8C2×#15689776C211yesmaximal, characteristic, complemented
9C2×#15689768C211yesmaximal, characteristic, complemented
10C2×#15689768C211yesmaximal, characteristic, complemented
11C2×#15689764C212yesmaximal, complemented
12C2×D4×D188C211yesmaximal, characteristic, complemented
13C2×#15689747C211yesmaximal, characteristic, complemented
14C2×#15689729C211yesmaximal, characteristic, complemented
15C2×#15689722C212yesmaximal, complemented
16C2×#15689713C212yesmaximal, complemented
17C2×#15689660C211yesmaximal, characteristic, complemented
18C2×#15689658C211yesmaximal, characteristic, complemented
19C2×#15689636C212yesmaximal, complemented
20C22×#13094009C212yesmaximal, complemented
21C2×#15689602C211yesmaximal, characteristic, complemented
22C2×#15689595C211yesmaximal, characteristic, complemented
23C2×C4×D4×D47C211yesmaximal, characteristic, complemented
24C2×C47×#554C211yesmaximal, characteristic, complemented
25C22×#10625354C2212yescomplemented
26C22×#10625352C2211yescharacteristic
27C23×D188C2212yes—
28C22×D4×D47C2211yescharacteristic
29C22×D4×D47C2211yescharacteristic
30C23×C4×D47C2212yescomplemented
31#15689858C22116yescomplemented
32#15689826C22116yescomplemented
33#15689821C22132yescomplemented
34#15689811C22116yescomplemented
35#15689800C22132yescomplemented
36#15689800C22132yescomplemented
37#15689776C22116yescomplemented
38#15689768C22116yescomplemented
39#15689768C22116yescomplemented
40#15689764C22132yescomplemented
41D4×D188C22116yescomplemented
42#15689747C22116yescomplemented
43#15689729C22116yescomplemented
44#15689722C22132yescomplemented
45#15689713C22132yescomplemented
46C2×#13094021C2211yescharacteristic
47#15689660C22116yescomplemented
48#15689658C22116yescomplemented
49C2×#13094019C2212yescomplemented
50C2×#13094019C2211yescharacteristic, complemented
51C2×#13094019C2212yescomplemented
52C2×#13094019C2212yescomplemented
53C2×#13094019C2211yescharacteristic, complemented
54C2×#13094019C2212yescomplemented
55C2×#13094015C2212yescomplemented
56C2×#13094015C2211yescharacteristic, complemented
57C2×#13094013C2212yescomplemented
58C2×#13094013C2212yescomplemented
59C2×#13094013C2211yescharacteristic, complemented
60C2×#13094012C2211yescharacteristic, complemented
61C2×#13094012C2211yescharacteristic, complemented
62#15689636C22132yescomplemented
63C2×#13094009C2212yes—
64C2×#13094009C2211yescharacteristic
65C2×#13094009C2212yescomplemented
66C2×#13094009C2212yescomplemented
67C2×#13094009C2212yescomplemented
68C2×#13094009C2212yescomplemented
69C2×#13094009C2212yescomplemented
70C2×#13094009C2212yescomplemented
71C2×#13094009C2212yescomplemented
72C2×#13094009C2212yescomplemented
73C2×#13094009C2212yescomplemented
74C2×#13094009C2211yescharacteristic, complemented
75C2×#13094009C22132yescomplemented
76C2×#13094008C2212yescomplemented
77C2×#13094008C2212yescomplemented
78C2×#13094004C2211yescharacteristic, complemented
79C2×#13094004C2211yescharacteristic, complemented
80C2×#13094000C2212yescomplemented
81C2×#13094000C2212yescomplemented
82C2×#13094000C2211yescharacteristic, complemented
83C2×#13093999C2211yescharacteristic
84C2×#13093999C2211yescharacteristic
85C2×#13093999C2211yescharacteristic
86C2×#13093999C2212yescomplemented
87C2×#13093999C2212yescomplemented
88C2×#13093999C2211yescharacteristic, complemented
89C2×#13093999C2211yescharacteristic, complemented
90C2×#13093999C2212yescomplemented
91C2×#13093998C2212yes—
92C2×#13093998C2212yescomplemented
93C2×#13093998C2212yescomplemented
94C2×#13093994C2212yes—
95C2×#13093994C2212yes—
96C2×#13093994C2212yescomplemented
97C2×#13093994C2212yescomplemented
98#15689602C22116yescomplemented
99#15689595C22116yescomplemented
100C2×C4×Dic94C2211yescharacteristic, complemented
101C2×#13093989C2211yescharacteristic, complemented
102C2×C4×D188C2211yescharacteristic
103C2×C4×D188C2211yescharacteristic, complemented
104C2×C4×D188C2211yescharacteristic, complemented
105C2×C4×D188C2211yescharacteristic, complemented
106C2×C4×D188C2211yescharacteristic, complemented
107C2×D4×Dic47C2211yescharacteristic
108C2×#13093986C2211yescharacteristic, complemented
109C2×#13093986C2211yescharacteristic, complemented
110C2×#13093986C2212yescomplemented
111C2×#13093986C2212yescomplemented
112C2×#13093986C2212yescomplemented
113C2×C4×C22⋊D47C2212yescomplemented
114C2×C4×C22⋊D47C2212yescomplemented
115C2×C4×C22⋊D47C2212yescomplemented
116C2×(C22⋊D47)⋊C4C2212yescomplemented
117C2×(C22⋊D47)⋊C4C2212yescomplemented
118C2×(C22⋊D47)⋊C4C2212yescomplemented
119C4×D4×D47C22116yescomplemented
120C2×#13093982C2211yescharacteristic, complemented
121C2×#13093982C2212yescomplemented
122C2×#13093982C2212yescomplemented
123C2×#13093981C2211yescharacteristic, complemented
124C2×#13093981C2211yescharacteristic, complemented
125C2×#13093980C2212yescomplemented
126C22×Dic47⋊C4C2212yescomplemented
127C2×C4⋊C4×D47C2211yescharacteristic, complemented
128C2×C4⋊C4×D47C2211yescharacteristic, complemented
129C22×(C2×D47)⋊C4C2212yescomplemented
130C22×(C2×D47)⋊C4C2212yescomplemented
131C22×(C2×D47)⋊C4C2212yescomplemented
132C2×C22⋊C4×D47C2212yescomplemented
133C2×C22⋊C4×D47C2212yescomplemented
134C2×C42×D47C2211yescharacteristic, complemented
135C47×#554C22116yescomplemented
136C2×C4⋊Q8×C47C2211yescharacteristic, complemented
137C2×#125×C47C2211yescharacteristic, complemented
138C2×#125×C47C2211yescharacteristic, complemented
139C2×C22⋊Q8×C47C2212yescomplemented
140C2×C22⋊Q8×C47C2212yescomplemented
141C2×C22⋊Q8×C47C2212yescomplemented
142C2×C4×Q8×C47C2211yescharacteristic, complemented
143C2×C4×D4×C47C2211yescharacteristic
144C2×C4×D4×C47C2211yescharacteristic
145C2×C4×D4×C47C2211yescharacteristic
146C22×C4⋊C4×C47C2212yescomplemented
147C24×D47C2312yes—
148C24×D47C2312yes—
149C2×#10625354—48no—
150C2×#10625354C23116yescomplemented
151C2×#10625352—28no—
152C2×#10625352C2318yes—
153C22×Dic94C2311yescharacteristic
154C22×D188—48no—
155C22×D188C2311yescharacteristic
156C22×D188C2311yescharacteristic
157C22×D188C2312yes—
158C22×D188C2311yescharacteristic
159C22×D188C2311yescharacteristic
160C22×D188C23116yes—
161C22×D188C2312yes—
162C22×D188C2312yes—
163C22×D188C2311yescharacteristic
164C22×D188C2312yes—
165C22×D188C2312yes—
166C22×D188C2312yes—
167C22×C22⋊D47C2312yes—
168C22×C22⋊D47C2312yes—
169C22×C22⋊D47C2312yes—
170C2×D4×D47—28no—
171C2×D4×D47—28no—
172C2×D4×D47C2318yes—
173C2×D4×D47C2318yes—
174C23×Dic47C2312yes—
175C23×Dic47C2312yes—
176C22×C4×D47—48no—
177C22×C4×D47C2311yescharacteristic
178C22×C4×D47C2311yescharacteristic
179C22×C4×D47C2312yes—
180C22×C4×D47C2311yescharacteristic
181C22×C4×D47C2311yescharacteristic
182C22×C4×D47C2311yescharacteristic
183C22×C4×D47C2312yes—
184C22×C4×D47C2312yes—
185C22×C4×D47C2312yes—
186C22×C4×D47C2312yes—
187C22×C4×D47C2312yes—
188C22×C4×D47C23116yescomplemented
189#13094021C2318yes—
190#13094019C23116yescomplemented
191#13094019C2318yescomplemented
192#13094019C23116yescomplemented
193#13094019C23116yescomplemented
194#13094019C2318yescomplemented
195#13094019C23116yescomplemented
196#13094015C23116yescomplemented
197#13094015C2318yescomplemented
198#13094013C23116yescomplemented
199#13094013C23116yescomplemented
200#13094013C2318yescomplemented
201#13094012C2318yescomplemented
202#13094012C2318yescomplemented
203#13094009C23116yes—
204#13094009C2318yes—
205#13094009C23116yescomplemented
206#13094009C23116yescomplemented
207#13094009C23116yescomplemented
208#13094009C23116yescomplemented
209#13094009C23116yescomplemented
210#13094009C23116yescomplemented
211#13094009C23116yescomplemented
212#13094009C23116yescomplemented
213#13094009C23116yescomplemented
214#13094009C2318yescomplemented
215#13094008C23116yescomplemented
216#13094008C23116yescomplemented
217#13094004C2318yescomplemented
218#13094004C2318yescomplemented
219#13094000C23116yescomplemented
220#13094000C23116yescomplemented
221#13094000C2318yescomplemented
222#13093999C2318yes—
223#13093999C2318yes—
224#13093999C2318yes—
225#13093999C23116yescomplemented
226#13093999C2318yescomplemented
227#13093999C2318yescomplemented
228#13093999C23116yescomplemented
229#13093999C23116yescomplemented
230#13093998C23116yes—
231#13093998C23116yescomplemented
232#13093998C23116yescomplemented
233#13093994C23116yes—
234#13093994C23116yes—
235#13093994C23116yescomplemented
236#13093994C23116yescomplemented
237C4×Dic94C2318yescomplemented
238#13093989C2318yescomplemented
239C4×D188C2318yes—
240C4×D188C2318yescomplemented
241C4×D188C2318yescomplemented
242C4×D188C2318yescomplemented
243C4×D188C2318yescomplemented
244D4×Dic47C2318yes—
245#13093986C2318yescomplemented
246#13093986C2318yescomplemented
247#13093986C23116yescomplemented
248#13093986C23116yescomplemented
249#13093986C23116yescomplemented
250C4×C22⋊D47C23116yescomplemented
251C4×C22⋊D47C23116yescomplemented
252C4×C22⋊D47C23116yescomplemented
253(C22⋊D47)⋊C4C23116yescomplemented
254(C22⋊D47)⋊C4C23116yescomplemented
255(C22⋊D47)⋊C4C23116yescomplemented
256#13093982C23116yescomplemented
257#13093982C23116yescomplemented
258#13093982C2318yescomplemented
259#13093981C2318yescomplemented
260#13093981C2318yescomplemented
261#13093980C23116yescomplemented
262C2×C4⋊Dic47C2311yescharacteristic
263C2×C4⋊Dic47C2312yes—
264C2×C4⋊Dic47C2312yes—
265C2×C4⋊Dic47C2311yescharacteristic
266C2×C4⋊Dic47C2311yescharacteristic
267C2×C4⋊Dic47C2311yescharacteristic
268C2×Dic47⋊C4C2312yes—
269C2×Dic47⋊C4C2312yes—
270C2×Dic47⋊C4C2311yescharacteristic
271C2×Dic47⋊C4C2312yes—
272C2×Dic47⋊C4C2312yes—
273C2×Dic47⋊C4C2311yescharacteristic
274C2×Dic47⋊C4C2311yescharacteristic
275C2×Dic47⋊C4C2311yescharacteristic
276C2×Dic47⋊C4C23116yescomplemented
277C4⋊C4×D47C2318yescomplemented
278C4⋊C4×D47C2318yescomplemented
279C2×C22⋊Dic47C2312yes—
280C2×(C2×D47)⋊C4C2311yescharacteristic
281C2×(C2×D47)⋊C4C2312yes—
282C2×(C2×D47)⋊C4C2312yes—
283C2×(C2×D47)⋊C4C2312yes—
284C2×(C2×D47)⋊C4C2311yescharacteristic
285C2×(C2×D47)⋊C4C2311yescharacteristic
286C2×(C2×D47)⋊C4C2311yescharacteristic
287C2×(C2×D47)⋊C4C2312yes—
288C2×(C2×D47)⋊C4C2312yes—
289C2×(C2×D47)⋊C4C2312yes—
290C2×(C2×D47)⋊C4C2312yes—
291C2×(C2×D47)⋊C4C2312yes—
292C2×(C2×D47)⋊C4C2312yes—
293C2×(C2×D47)⋊C4C2312yes—
294C2×(C2×D47)⋊C4C2312yes—
295C2×(C2×D47)⋊C4C2311yescharacteristic
296C2×(C2×D47)⋊C4C2311yescharacteristic
297C2×(C2×D47)⋊C4C2311yescharacteristic
298C2×(C2×D47)⋊C4C2312yes—
299C2×(C2×D47)⋊C4C2311yescharacteristic
300C2×(C2×D47)⋊C4C2312yes—
301C2×(C2×D47)⋊C4C2312yes—
302C2×(C2×D47)⋊C4C2312yes—
303C2×(C2×D47)⋊C4C2311yescharacteristic
304C2×(C2×D47)⋊C4C2311yescharacteristic
305C2×(C2×D47)⋊C4C23116yescomplemented
306C2×(C2×D47)⋊C4C23116yescomplemented
307C2×(C2×D47)⋊C4C23116yescomplemented
308C22⋊C4×D47C23116yescomplemented
309C22⋊C4×D47C23116yescomplemented
310C2×C4×Dic47C2311yescharacteristic
311C2×C4×Dic47C2311yescharacteristic
312C2×C4×Dic47C2311yescharacteristic
313C2×C4×Dic47C2312yes—
314C2×C4×Dic47C2312yes—
315C2×C4×Dic47C2312yes—
316C42×D47C2318yescomplemented
317C22×Q8×C47C2311yescharacteristic
318C22×Q8×C47C2312yes—
319C22×D4×C47C2311yescharacteristic
320C23×C4×C47C2312yes—
321C23×C4×C47C2312yes—
322C23×C4×C47C2312yes—
323C4⋊Q8×C47C2318yescomplemented
324#125×C47C2318yescomplemented
325#125×C47C2318yescomplemented
326C22⋊Q8×C47C23116yescomplemented
327C22⋊Q8×C47C23116yescomplemented
328C22⋊Q8×C47C23116yescomplemented
329C4×Q8×C47C2318yescomplemented
330C4×D4×C47C2318yes—
331C4×D4×C47C2318yes—
332C4×D4×C47C2318yes—
333C2×C4⋊C4×C47C2311yescharacteristic
334C2×C4⋊C4×C47C2312yes—
335C2×C4⋊C4×C47C2312yes—
336C2×C4⋊C4×C47C2312yes—
337C2×C4⋊C4×C47C2311yescharacteristic
338C2×C4⋊C4×C47C2311yescharacteristic
339C2×C4⋊C4×C47C2311yescharacteristic
340C2×C4⋊C4×C47C2311yescharacteristic
341C2×C4⋊C4×C47C2311yescharacteristic
342C2×C4⋊C4×C47C2312yes—
343C2×C4⋊C4×C47C2312yes—
344C2×C4⋊C4×C47C23116yescomplemented
345C2×C22⋊C4×C47C2312yes—
346C2×C22⋊C4×C47C2312yes—
347C2×C22⋊C4×C47C2312yes—
348C2×C42×C47C2311yescharacteristic
349C2×C42×C47C2311yescharacteristic
350C2×C42×C47C2311yescharacteristic
351C24×C47C2412yes—
352C23×D47—28no—
353C23×D47—28no—
354C23×D47—28no—
355C23×D47—44no—
356C23×D47—44no—
357C23×D47—44no—
358C23×D47C2411yescharacteristic
359C23×D47C2412yes—
360C23×D47C2412yes—
361C23×D47C2411yescharacteristic
362C23×D47C2418yes—
363C23×D47C2411yescharacteristic
364C23×D47C2418yes—
365C2×Q8×C47—42no—
366C2×Q8×C47—44no—
367C2×Q8×C47C2414yes—
368C2×Q8×C47C2418yes—
369C2×D4×C47#4118yescomplemented
370C2×D4×C47C2414yes—
371C22×C4×C47—44no—
372C22×C4×C47—44no—
373C22×C4×C47—44no—
374C22×C4×C47C2411yescharacteristic
375C22×C4×C47C2411yescharacteristic
376C22×C4×C47C2411yescharacteristic
377C22×C4×C47C2411yescharacteristic
378C22×C4×C47C2411yescharacteristic
379C22×C4×C47C2411yescharacteristic
380C22×C4×C47C2412yes—
381C22×C4×C47C2412yes—
382C22×C4×C47C2412yes—
383C22×C4×C47C2418yes—
384C22×C4×C47C2418yes—
385C22×C4×C47C2418yes—
386C22×C4×C47C2411yescharacteristic
387C2×C22⋊D47—28no—
388C2×C22⋊D47—28no—
389C2×C22⋊D47—28no—
390C2×C22⋊D47C2418yes—
391C2×C22⋊D47C2418yes—
392C2×C22⋊D47C2418yes—
393C22×Dic47—28no—
394C22×Dic47—44no—
395C22×Dic47C2411yescharacteristic
396C22×Dic47C2412yes—
397C22×Dic47C2411yescharacteristic
398C22×Dic47C2411yescharacteristic
399C22×Dic47C2411yescharacteristic
400C22×Dic47C2412yes—
401C22×Dic47C2411yescharacteristic
402C22×Dic47C2418yes—
403C22×Dic47C2418yes—
404#10625354—432no—
405#10625352—232no—
406D4×D47—232no—
407D4×D47—232no—
408C2×D188—24no—
409C2×D188—28no—
410C2×D188—24no—
411C2×D188—24no—
412C2×D188—24no—
413C2×D188—432no—
414C2×D188—44no—
415C2×D188—44no—
416C2×D188—44no—
417C2×D188—42no—
418C2×D188—44no—
419C2×D188—44no—
420C2×D188C2414yes—
421C2×D188C2414yes—
422C2×D188C2418yes—
423C2×D188C2414yes—
424C2×D188C2414yes—
425C2×D188C2418yes—
426C2×D188C2418yes—
427C2×D188C2414yes—
428C2×D188C2418yes—
429C2×D188C2418yes—
430C2×D188C2418yes—
431C2×C4×D47—24no—
432C2×C4×D47—28no—
433C2×C4×D47—24no—
434C2×C4×D47—24no—
435C2×C4×D47—24no—
436C2×C4×D47—432no—
437C2×C4×D47—44no—
438C2×C4×D47—44no—
439C2×C4×D47—44no—
440C2×C4×D47—42no—
441C2×C4×D47—44no—
442C2×C4×D47—44no—
443C2×C4×D47C2414yes—
444C2×C4×D47C2414yes—
445C2×C4×D47C2418yes—
446C2×C4×D47C2414yes—
447C2×C4×D47C2414yes—
448C2×C4×D47C2414yes—
449C2×C4×D47C2418yes—
450C2×C4×D47C2418yes—
451C2×C4×D47C2418yes—
452C2×C4×D47C2418yes—
453C2×C4×D47C2418yes—
454C2×Dic94—24no—
455C2×Dic94C2414yes—
456C4⋊C4×C47C2414yes—
457C4⋊C4×C47C2418yes—
458C4⋊C4×C47C2418yes—
459C4⋊C4×C47C2418yes—
460C4⋊C4×C47C2414yes—
461C4⋊C4×C47C2414yes—
462C4⋊C4×C47C2414yes—
463C4⋊C4×C47C2414yes—
464C4⋊C4×C47C2414yes—
465C4⋊C4×C47C2418yes—
466C4⋊C4×C47C2418yes—
467C22⋊C4×C47C2418yes—
468C22⋊C4×C47C2418yes—
469C22⋊C4×C47C2418yes—
470C42×C47C2414yes—
471C42×C47C2414yes—
472C42×C47C2414yes—
473C22⋊Dic47C2418yes—
474(C2×D47)⋊C4C2414yes—
475(C2×D47)⋊C4C2418yes—
476(C2×D47)⋊C4C2418yes—
477(C2×D47)⋊C4C2418yes—
478(C2×D47)⋊C4C2414yes—
479(C2×D47)⋊C4C2414yes—
480(C2×D47)⋊C4C2414yes—
481(C2×D47)⋊C4C2418yes—
482(C2×D47)⋊C4C2418yes—
483(C2×D47)⋊C4C2418yes—
484(C2×D47)⋊C4C2418yes—
485(C2×D47)⋊C4C2418yes—
486(C2×D47)⋊C4C2418yes—
487(C2×D47)⋊C4C2418yes—
488(C2×D47)⋊C4C2418yes—
489(C2×D47)⋊C4C2414yes—
490(C2×D47)⋊C4C2414yes—
491(C2×D47)⋊C4C2414yes—
492(C2×D47)⋊C4C2418yes—
493(C2×D47)⋊C4C2414yes—
494(C2×D47)⋊C4C2418yes—
495(C2×D47)⋊C4C2418yes—
496(C2×D47)⋊C4C2418yes—
497(C2×D47)⋊C4C2414yes—
498(C2×D47)⋊C4C2414yes—
499C4⋊Dic47C2414yes—
500C4⋊Dic47C2418yes—
501C4⋊Dic47C2418yes—
502C4⋊Dic47C2414yes—
503C4⋊Dic47C2414yes—
504C4⋊Dic47C2414yes—
505Dic47⋊C4C2418yes—
506Dic47⋊C4C2418yes—
507Dic47⋊C4C2414yes—
508Dic47⋊C4C2418yes—
509Dic47⋊C4C2418yes—
510Dic47⋊C4C2414yes—
511Dic47⋊C4C2414yes—
512Dic47⋊C4C2414yes—
513C4×Dic47C2414yes—
514C4×Dic47C2414yes—
515C4×Dic47C2414yes—
516C4×Dic47C2418yes—
517C4×Dic47C2418yes—
518C4×Dic47C2418yes—
519C23×C47—24no—
520C23×C47—24no—
521C23×C47C2×#4118yes—
522C23×C47C2514yes—
523C23×C47C2511yescharacteristic
524C22×D47—22no—
525C22×D47—22no—
526C22×D47—22no—
527C22×D47—22no—
528C22×D47—24no—
529C22×D47—24no—
530C22×D47—216no—
531C22×D47—22no—
532C22×D47—24no—
533C22×D47—24no—
534C22×D47—22no—
535C22×D47—24no—
536C22×D47—22no—
537C22×D47—24no—
538C22×D47—22no—
539C22×D47—216no—
540C22×D47—216no—
541C22×D47—48no—
542C22×D47—48no—
543C22×D47—48no—
544C22×D47—432no—
545C22×D47—816no—
546C22×D47H(5,𝔽2)14yes—
547C22×D47C2512yes—
548C22×D47C2514yes—
549C22×D47C2514yes—
550C22×D47C2512yes—
551C22×D47C2512yes—
552Q8×C47—48no—
553Q8×C47—44no—
554D4×C47C2×#41116yescomplemented
555C2×C4×C47—22no—
556C2×C4×C47—24no—
557C2×C4×C47—22no—
558C2×C4×C47—24no—
559C2×C4×C47—22no—
560C2×C4×C47—24no—
561C2×C4×C47—22no—
562C2×C4×C47—22no—
563C2×C4×C47—22no—
564C2×C4×C47—48no—
565C2×C4×C47—48no—
566C2×C4×C47—48no—
567C2×C4×C47C2×#4114yes—
568C2×C4×C47C2512yes—
569C2×C4×C47C2514yes—
570C2×C4×C47C2512yes—
571C2×C4×C47C2514yes—
572C2×C4×C47C2512yes—
573C2×C4×C47C2512yes—
574C2×C4×C47C2512yes—
575C2×C4×C47C2514yes—
576C2×C4×C47C2512yes—
577C2×C4×C47C2512yes—
578C22⋊D47—216no—
579C22⋊D47—216no—
580C22⋊D47—216no—
581C2×Dic47—24no—
582C2×Dic47—22no—
583C2×Dic47—22no—
584C2×Dic47—22no—
585C2×Dic47—216no—
586C2×Dic47—24no—
587C2×Dic47—22no—
588C2×Dic47—22no—
589C2×Dic47—48no—
590C2×Dic47C2512yes—
591C2×Dic47C2512yes—
592C2×Dic47C2514yes—
593C2×Dic47C2512yes—
594C2×Dic47C2512yes—
595C2×Dic47C2514yes—
596C2×Dic47C2512yes—
597D188—28no—
598D188—216no—
599D188—28no—
600D188—28no—
601D188—28no—
602D188—48no—
603D188—48no—
604D188—48no—
605D188—44no—
606D188—48no—
607D188—48no—
608C4×D47—28no—
609C4×D47—216no—
610C4×D47—28no—
611C4×D47—28no—
612C4×D47—28no—
613C4×D47—48no—
614C4×D47—48no—
615C4×D47—48no—
616C4×D47—44no—
617C4×D47—48no—
618C4×D47—48no—
619Dic94—28no—
620C2×#3513—471nomaximal, Sylow
621C22×C47—24no—
622C22×C47—24no—
623C22×C47—216no—
624C22×C47C22×#4118yes—
625C22×C47C22×#4112yes—
626C22×C47C2×H(5,𝔽2)12yes—
627C22×C47#58512yes—
628C22×C47C2611yescharacteristic
629C2×D47—22no—
630C2×D47—22no—
631C2×D47—28no—
632C2×D47—22no—
633C2×D47—22no—
634C2×D47—24no—
635C2×D47—24no—
636C2×D47—22no—
637C2×D47—24no—
638C2×D47—24no—
639C2×D47—22no—
640C2×D47—24no—
641C2×D47—22no—
642C2×D47—24no—
643C2×D47—22no—
644C2×D47—432no—
645C2×D47—44no—
646C2×D47—48no—
647C2×D47—48no—
648C2×D47—44no—
649C2×D47—816no—
650C2×D47C2×H(5,𝔽2)14yes—
651C4×C47—22no—
652C4×C47—24no—
653C4×C47—22no—
654C4×C47—24no—
655C4×C47—22no—
656C4×C47—24no—
657C4×C47—22no—
658C4×C47—22no—
659C4×C47—22no—
660C4×C47C22×#4114yes—
661Dic47—24no—
662Dic47—22no—
663Dic47—22no—
664Dic47—22no—
665Dic47—24no—
666Dic47—22no—
667Dic47—22no—
668#3513—4732no—
669C2×#559—471no—
670C2×#554D4711yescharacteristic, complemented
671C2×#553—471no—
672C2×#553—472no—
673C2×#552—471no—
674C2×#551—472no—
675C2×#551—472no—
676C2×#547—471no—
677C2×#546—472no—
678C2×#546—471no—
679C2×#546—471no—
680C2×D42—471no—
681C2×#542—471no—
682C2×#540—471no—
683C2×#539—472no—
684C2×#538—472no—
685C2×#529—471no—
686C2×#529—471no—
687C2×#525—472no—
688C22×#123—472no—
689C2×#520—471no—
690C2×#518—471no—
691C22×C4×D4—471no—
692C2×C47—28no—
693C2×C47#351314yescomplemented
694C2×C47C23×#4111yescharacteristic
695C2×C47C22×H(5,𝔽2)11yescharacteristic
696C2×C47C2×#58511yescharacteristic
697D47—24no—
698D47—42no—
699D47—44no—
700D47—44no—
701D47—42no—
702C22×#41—472no—
703C22×#41—471no—
704C23×D4—471no—
705C23×D4—471no—
706C23×D4—472no—
707C24×C4—472no—
708#559—4716no—
709#554C2×D47116yescomplemented
710#553—4716no—
711#553—4732no—
712#552—4716no—
713#551—4732no—
714#551—4732no—
715#547—4716no—
716#546—4732no—
717#546—4716no—
718#546—4716no—
719D42—4716no—
720#542—4716no—
721#540—4716no—
722#539—4732no—
723#538—4732no—
724C2×C4⋊Q8C2×D4711yescharacteristic, complemented
725C2×#127—471no—
726#529—4716no—
727#529—4716no—
728C2×#126—472no—
729C2×#126—471no—
730C2×#126—471no—
731C2×#126—472no—
732C2×#126—472no—
733C2×#126—472no—
734C2×#125—471no—
735C2×#125—472no—
736C2×#125C2×D4711yescharacteristic, complemented
737C2×#125C2×D4711yescharacteristic, complemented
738C2×#124—471no—
739C2×#124—472no—
740C2×#124—472no—
741C2×#124—471no—
742C2×#124—471no—
743#525—4732no—
744C2×#123—471no—
745C2×#123—472no—
746C2×#123—472no—
747C2×#123—472no—
748C2×#123—472no—
749C2×#123—472no—
750C2×#123—472no—
751C2×#123—472no—
752C2×#123—471no—
753C2×#123—472no—
754C2×#123—472no—
755C2×#123—472no—
756C2×#123—4732no—
757C2×#123—472no—
758C2×#123—472no—
759C2×C22⋊Q8—472no—
760C2×C22⋊Q8—471no—
761C2×C22⋊Q8—472no—
762C2×C22⋊Q8—471no—
763C2×C22⋊Q8—471no—
764C2×C22⋊Q8C2×D4712yescomplemented
765C2×C22⋊Q8C2×D4712yescomplemented
766C2×C22⋊Q8C2×D4712yescomplemented
767C2×#121—472no—
768C2×#121—472no—
769C2×#121—472no—
770C2×#121—472no—
771C2×#121—471no—
772C2×#121—471no—
773C2×#121—472no—
774C2×#121—471no—
775C2×#121—472no—
776C2×#121—471no—
777C2×#121—471no—
778C2×#120—472no—
779C2×#120—472no—
780C2×#120—472no—
781C2×#120—472no—
782#520—4716no—
783#518—4716no—
784C2×C4×Q8—471no—
785C2×C4×Q8—471no—
786C2×C4×Q8C2×D4711yescharacteristic, complemented
787C2×C4×D4—471no—
788C2×C4×D4—472no—
789C2×C4×D4—472no—
790C2×C4×D4—472no—
791C2×C4×D4—4716no—
792C2×C4×D4—471no—
793C2×C4×D4—471no—
794C2×C4×D4—472no—
795C2×C4×D4—472no—
796C2×C4×D4—472no—
797C2×C4×D4—472no—
798C2×C4×D4—472no—
799C2×C4×D4—472no—
800C2×C4×D4—471no—
801C2×C4×D4—471no—
802C2×C4×D4—471no—
803C2×C4×D4—471no—
804C2×C4×D4—471no—
805C2×C4×D4C2×D4711yescharacteristic
806C2×C4×D4C2×D4711yescharacteristic
807C2×C4×D4C2×D4711yescharacteristic
808C2×#117—471no—
809C2×#117—472no—
810C2×#117—472no—
811C2×#117—472no—
812C2×#117—471no—
813C2×#117—471no—
814C22×C4⋊C4—472no—
815C22×C4⋊C4—471no—
816C22×C4⋊C4—471no—
817C22×C4⋊C4C2×D4712yescomplemented
818C22×C22⋊C4—472no—
819C22×C22⋊C4—472no—
820C22×C22⋊C4—472no—
821C22×C22⋊C4—472no—
822C22×C22⋊C4—472no—
823C22×C42—471no—
824C47C2×#351311yescharacteristic, complemented, Sylow
825C25—472no—
826C25—472no—
827C2×#41—4716no—
828C2×#41—478no—
829C2×#41—948no—
830C2×#41—1888no—
831C22×Q8—471no—
832C22×Q8C22×D4711yescharacteristic
833C22×Q8C22×D4712yes—
834C22×D4—472no—
835C22×D4—472no—
836C22×D4—472no—
837C22×D4—478no—
838C22×D4—478no—
839C22×D4—471no—
840C22×D4—471no—
841C22×D4—471no—
842C22×D4—472no—
843C22×D4—471no—
844C22×D4—471no—
845C22×D4—472no—
846C22×D4—472no—
847C22×D4—472no—
848C22×D4—472no—
849C22×D4—472no—
850C22×D4—4716no—
851C22×D4—948no—
852C22×D4—948no—
853C22×D4—1888no—
854C22×D4C22×D4711yescharacteristic
855C23×C4—472no—
856C23×C4—472no—
857C23×C4—472no—
858C23×C4—471no—
859C23×C4—471no—
860C23×C4—471no—
861C23×C4—471no—
862C23×C4—471no—
863C23×C4—472no—
864C23×C4—472no—
865C23×C4—472no—
866C23×C4—472no—
867C23×C4—472no—
868C23×C4—4716no—
869C23×C4—1888no—
870C23×C4C22×D4712yes—
871C23×C4C22×D4712yes—
872C23×C4C22×D4712yes—
873C4⋊Q8C22×D4718yescomplemented
874#127—478no—
875#126—4716no—
876#126—478no—
877#126—478no—
878#126—4716no—
879#126—4716no—
880#126—4716no—
881#125—478no—
882#125—4716no—
883#125C22×D4718yescomplemented
884#125C22×D4718yescomplemented
885#124—478no—
886#124—4716no—
887#124—4716no—
888#124—478no—
889#124—478no—
890#123—478no—
891#123—4716no—
892#123—4716no—
893#123—4716no—
894#123—4716no—
895#123—4716no—
896#123—4716no—
897#123—4716no—
898#123—478no—
899#123—4716no—
900#123—4716no—
901#123—4716no—
902#123—4716no—
903#123—4716no—
904C22⋊Q8—4716no—
905C22⋊Q8—478no—
906C22⋊Q8—4716no—
907C22⋊Q8—478no—
908C22⋊Q8—478no—
909C22⋊Q8C22×D47116yescomplemented
910C22⋊Q8C22×D47116yescomplemented
911C22⋊Q8C22×D47116yescomplemented
912#121—4716no—
913#121—4716no—
914#121—4716no—
915#121—4716no—
916#121—478no—
917#121—478no—
918#121—4716no—
919#121—478no—
920#121—4716no—
921#121—478no—
922#121—478no—
923#120—4716no—
924#120—4716no—
925#120—4716no—
926#120—4716no—
927C4×Q8—478no—
928C4×Q8—478no—
929C4×Q8C22×D4718yescomplemented
930C4×D4—478no—
931C4×D4—4716no—
932C4×D4—4716no—
933C4×D4—4716no—
934C4×D4—478no—
935C4×D4—478no—
936C4×D4—4716no—
937C4×D4—4716no—
938C4×D4—4716no—
939C4×D4—4716no—
940C4×D4—4716no—
941C4×D4—4716no—
942C4×D4—478no—
943C4×D4—478no—
944C4×D4—478no—
945C4×D4—478no—
946C4×D4—478no—
947C4×D4C22×D4718yes—
948C4×D4C22×D4718yes—
949C4×D4C22×D4718yes—
950#117—478no—
951#117—4716no—
952#117—4716no—
953#117—4716no—
954#117—478no—
955#117—478no—
956C2×C4⋊C4—471no—
957C2×C4⋊C4—472no—
958C2×C4⋊C4—471no—
959C2×C4⋊C4—472no—
960C2×C4⋊C4—472no—
961C2×C4⋊C4—472no—
962C2×C4⋊C4—4716no—
963C2×C4⋊C4—471no—
964C2×C4⋊C4—471no—
965C2×C4⋊C4—471no—
966C2×C4⋊C4—472no—
967C2×C4⋊C4—472no—
968C2×C4⋊C4—471no—
969C2×C4⋊C4—471no—
970C2×C4⋊C4—471no—
971C2×C4⋊C4—478no—
972C2×C4⋊C4—478no—
973C2×C4⋊C4C22×D4711yescharacteristic
974C2×C4⋊C4C22×D4711yescharacteristic
975C2×C4⋊C4C22×D4711yescharacteristic
976C2×C4⋊C4C22×D4712yes—
977C2×C4⋊C4C22×D4712yes—
978C2×C4⋊C4C22×D4712yes—
979C2×C4⋊C4C22×D4711yescharacteristic
980C2×C4⋊C4C22×D4712yes—
981C2×C4⋊C4C22×D4711yescharacteristic
982C2×C4⋊C4C22×D4712yes—
983C2×C4⋊C4C22×D4711yescharacteristic
984C2×C4⋊C4C22×D47116yescomplemented
985C2×C22⋊C4—472no—
986C2×C22⋊C4—472no—
987C2×C22⋊C4—471no—
988C2×C22⋊C4—471no—
989C2×C22⋊C4—471no—
990C2×C22⋊C4—471no—
991C2×C22⋊C4—472no—
992C2×C22⋊C4—472no—
993C2×C22⋊C4—472no—
994C2×C22⋊C4—472no—
995C2×C22⋊C4—472no—
996C2×C22⋊C4—472no—
997C2×C22⋊C4—4716no—
998C2×C22⋊C4—472no—
999C2×C22⋊C4—472no—
1000C2×C22⋊C4—472no—
1001C2×C22⋊C4—472no—
1002C2×C22⋊C4—4716no—
1003C2×C22⋊C4—4716no—
1004C2×C22⋊C4—471no—
1005C2×C22⋊C4—471no—
1006C2×C22⋊C4—471no—
1007C2×C22⋊C4—472no—
1008C2×C22⋊C4—471no—
1009C2×C22⋊C4—471no—
1010C2×C22⋊C4—472no—
1011C2×C22⋊C4—472no—
1012C2×C22⋊C4—472no—
1013C2×C22⋊C4—471no—
1014C2×C22⋊C4—4716no—
1015C2×C22⋊C4—4716no—
1016C2×C22⋊C4C22×D4712yes—
1017C2×C22⋊C4C22×D4712yes—
1018C2×C22⋊C4C22×D4712yes—
1019C2×C42—471no—
1020C2×C42—472no—
1021C2×C42—472no—
1022C2×C42—472no—
1023C2×C42—471no—
1024C2×C42—471no—
1025C2×C42—478no—
1026C2×C42C22×D4711yescharacteristic
1027C2×C42C22×D4711yescharacteristic
1028C2×C42C22×D4711yescharacteristic
1029C24—471no—
1030C24—471no—
1031C24—472no—
1032C24—472no—
1033C24—471no—
1034C24—478no—
1035C24—478no—
1036C24—948no—
1037C24—948no—
1038C24—948no—
1039C24—1884no—
1040C24—1884no—
1041C24—1884no—
1042C24C23×D4712yes—
1043#41—9432no—
1044#41—18832no—
1045C2×Q8—42no—
1046C2×Q8—44no—
1047C2×Q8—474no—
1048C2×Q8—944no—
1049C2×Q8C23×D4714yes—
1050C2×Q8C23×D4718yes—
1051C2×D4—478no—
1052C2×D4—478no—
1053C2×D4—478no—
1054C2×D4—474no—
1055C2×D4—474no—
1056C2×D4—474no—
1057C2×D4—478no—
1058C2×D4—474no—
1059C2×D4—474no—
1060C2×D4—478no—
1061C2×D4—478no—
1062C2×D4—478no—
1063C2×D4—478no—
1064C2×D4—478no—
1065C2×D4—944no—
1066C2×D4—948no—
1067C2×D4—944no—
1068C2×D4—948no—
1069C2×D4—948no—
1070C2×D4—948no—
1071C2×D4—9432no—
1072C2×D4—9432no—
1073C2×D4—944no—
1074C2×D4—944no—
1075C2×D4—1884no—
1076C2×D4—1882no—
1077C2×D4—1884no—
1078C2×D4—1884no—
1079C2×D4—1884no—
1080C2×D4—1884no—
1081C2×D4—18832no—
1082C2×D4#1062535418yescomplemented
1083C2×D4C23×D4714yes—
1084C22×C4—44no—
1085C22×C4—44no—
1086C22×C4—44no—
1087C22×C4—478no—
1088C22×C4—471no—
1089C22×C4—472no—
1090C22×C4—471no—
1091C22×C4—471no—
1092C22×C4—471no—
1093C22×C4—472no—
1094C22×C4—471no—
1095C22×C4—478no—
1096C22×C4—474no—
1097C22×C4—474no—
1098C22×C4—478no—
1099C22×C4—474no—
1100C22×C4—474no—
1101C22×C4—474no—
1102C22×C4—478no—
1103C22×C4—478no—
1104C22×C4—478no—
1105C22×C4—478no—
1106C22×C4—478no—
1107C22×C4—944no—
1108C22×C4—948no—
1109C22×C4—948no—
1110C22×C4—944no—
1111C22×C4—944no—
1112C22×C4—944no—
1113C22×C4—1884no—
1114C22×C4—1882no—
1115C22×C4—1884no—
1116C22×C4—1884no—
1117C22×C4—1884no—
1118C22×C4—1884no—
1119C22×C4—18832no—
1120C22×C4—1884no—
1121C22×C4C23×D4711yescharacteristic
1122C22×C4C23×D4711yescharacteristic
1123C22×C4C23×D4711yescharacteristic
1124C22×C4C23×D4712yes—
1125C22×C4C23×D4712yes—
1126C22×C4C23×D4711yescharacteristic
1127C22×C4C23×D4711yescharacteristic
1128C22×C4C23×D4711yescharacteristic
1129C22×C4C23×D4712yes—
1130C22×C4C23×D4718yes—
1131C22×C4C23×D4718yes—
1132C22×C4C23×D4718yes—
1133C22×C4C23×D4711yescharacteristic
1134C4⋊C4—478no—
1135C4⋊C4—474no—
1136C4⋊C4—478no—
1137C4⋊C4—478no—
1138C4⋊C4—478no—
1139C4⋊C4—474no—
1140C4⋊C4—474no—
1141C4⋊C4—474no—
1142C4⋊C4—474no—
1143C4⋊C4—478no—
1144C4⋊C4—478no—
1145C4⋊C4—474no—
1146C4⋊C4—474no—
1147C4⋊C4—474no—
1148C4⋊C4C23×D4714yes—
1149C4⋊C4C23×D4714yes—
1150C4⋊C4C23×D4714yes—
1151C4⋊C4C23×D4718yes—
1152C4⋊C4C23×D4718yes—
1153C4⋊C4C23×D4718yes—
1154C4⋊C4C23×D4714yes—
1155C4⋊C4C23×D4718yes—
1156C4⋊C4C23×D4714yes—
1157C4⋊C4C23×D4718yes—
1158C4⋊C4C23×D4714yes—
1159C22⋊C4—478no—
1160C22⋊C4—478no—
1161C22⋊C4—474no—
1162C22⋊C4—474no—
1163C22⋊C4—474no—
1164C22⋊C4—474no—
1165C22⋊C4—478no—
1166C22⋊C4—478no—
1167C22⋊C4—478no—
1168C22⋊C4—478no—
1169C22⋊C4—478no—
1170C22⋊C4—478no—
1171C22⋊C4—478no—
1172C22⋊C4—478no—
1173C22⋊C4—478no—
1174C22⋊C4—478no—
1175C22⋊C4—474no—
1176C22⋊C4—474no—
1177C22⋊C4—474no—
1178C22⋊C4—478no—
1179C22⋊C4—474no—
1180C22⋊C4—474no—
1181C22⋊C4—478no—
1182C22⋊C4—478no—
1183C22⋊C4—478no—
1184C22⋊C4—474no—
1185C22⋊C4C23×D4718yes—
1186C22⋊C4C23×D4718yes—
1187C22⋊C4C23×D4718yes—
1188C42—474no—
1189C42—474no—
1190C42—474no—
1191C42—478no—
1192C42—478no—
1193C42—478no—
1194C42C23×D4714yes—
1195C42C23×D4714yes—
1196C42C23×D4714yes—
1197C23—24no—
1198C23—24no—
1199C23—474no—
1200C23—472no—
1201C23—472no—
1202C23—474no—
1203C23—474no—
1204C23—472no—
1205C23—9416no—
1206C23—942no—
1207C23—942no—
1208C23—9416no—
1209C23—942no—
1210C23—942no—
1211C23—9416no—
1212C23—944no—
1213C23—944no—
1214C23—942no—
1215C23—944no—
1216C23—944no—
1217C23—942no—
1218C23—944no—
1219C23—942no—
1220C23—944no—
1221C23—942no—
1222C23—37616no—
1223C23—1888no—
1224C23—1888no—
1225C23—1888no—
1226C23—18832no—
1227C23C2×#1062535418yes—
1228C23C24×D4714yes—
1229C23C24×D4711yescharacteristic
1230Q8—44no—
1231Q8—48no—
1232Q8—948no—
1233D4—948no—
1234D4—9416no—
1235D4—948no—
1236D4—9416no—
1237D4—9416no—
1238D4—9416no—
1239D4—948no—
1240D4—948no—
1241D4—1888no—
1242D4—1884no—
1243D4—1888no—
1244D4—1888no—
1245D4—1888no—
1246D4—1888no—
1247D4C2×#10625354116yescomplemented
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—24no—
1251C2×C4—24no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—24no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—48no—
1258C2×C4—48no—
1259C2×C4—48no—
1260C2×C4—472no—
1261C2×C4—474no—
1262C2×C4—472no—
1263C2×C4—472no—
1264C2×C4—472no—
1265C2×C4—474no—
1266C2×C4—472no—
1267C2×C4—948no—
1268C2×C4—9416no—
1269C2×C4—942no—
1270C2×C4—942no—
1271C2×C4—942no—
1272C2×C4—944no—
1273C2×C4—9416no—
1274C2×C4—944no—
1275C2×C4—942no—
1276C2×C4—942no—
1277C2×C4—948no—
1278C2×C4—948no—
1279C2×C4—948no—
1280C2×C4—1888no—
1281C2×C4—1884no—
1282C2×C4—1888no—
1283C2×C4—1888no—
1284C2×C4—1888no—
1285C2×C4—1888no—
1286C2×C4—1888no—
1287C2×C4C2×#1062535414yes—
1288C2×C4C24×D4712yes—
1289C2×C4C24×D4712yes—
1290C2×C4C24×D4712yes—
1291C2×C4C24×D4714yes—
1292C2×C4C24×D4714yes—
1293C2×C4C24×D4712yes—
1294C2×C4C24×D4712yes—
1295C2×C4C24×D4712yes—
1296C2×C4C24×D4714yes—
1297C2×C4C24×D4712yes—
1298C22—216no—
1299C22—24no—
1300C22—24no—
1301C22—474no—
1302C22—948no—
1303C22—942no—
1304C22—942no—
1305C22—942no—
1306C22—942no—
1307C22—944no—
1308C22—944no—
1309C22—942no—
1310C22—944no—
1311C22—944no—
1312C22—942no—
1313C22—944no—
1314C22—942no—
1315C22—944no—
1316C22—942no—
1317C22—37616no—
1318C22—18832no—
1319C22—1884no—
1320C22—1888no—
1321C22—1888no—
1322C22—1884no—
1323C22C22×#1062535418yes—
1324C22C22×#1062535412yes—
1325C22H(5,𝔽2)×D4712yes—
1326C22#1568995912yes—
1327C22C25×D4711yescharacteristic
1328C4—22no—
1329C4—22no—
1330C4—24no—
1331C4—24no—
1332C4—22no—
1333C4—22no—
1334C4—24no—
1335C4—22no—
1336C4—22no—
1337C4—942no—
1338C4—942no—
1339C4—942no—
1340C4—944no—
1341C4—942no—
1342C4—944no—
1343C4—942no—
1344C4C22×#1062535414yes—
1345C2—28no—
1346C2—944no—
1347C2—1882no—
1348C2—1884no—
1349C2—1884no—
1350C2—1882no—
1351C2#2025733114yesdirect product factor
1352C2C23×#1062535411yescharacteristic
1353C2C2×H(5,𝔽2)×D4711yescharacteristic
1354C2C2×#1568995911yescharacteristic
subgroupG/H
centerC23C24×D47
commutator, cosocleC22×C47C26
FrattiniC22C25×D47
FittingC2×C47×#554C2
socleC23×C47C25
hypercenterC2×#554D47
hypocenterC47C2×#3513
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. #20257331C2direct (N × H)
2. C2×#15689858C2semidirect
3. C2×#15689826C2semidirect
4. C2×#15689821C2semidirect
5. C2×#15689811C2semidirect
6. C2×#15689800C2semidirect
7. C2×#15689800C2semidirect
8. C2×#15689776C2semidirect
9. C2×#15689768C2semidirect
10. C2×#15689768C2semidirect
11. C2×#15689764C2semidirect
12. C2×D4×D188C2semidirect
13. C2×#15689747C2semidirect
14. C2×#15689729C2semidirect
15. C2×#15689722C2semidirect
16. C2×#15689713C2semidirect
17. C2×#15689660C2semidirect
18. C2×#15689658C2semidirect
19. C2×#15689636C2semidirect
20. C22×#13094009C2semidirect
21. C2×#15689602C2semidirect
22. C2×#15689595C2semidirect
23. C2×C4×D4×D47C2semidirect
24. C2×C47×#554C2semidirect
25. C22×#10625354C22semidirect
30. C23×C4×D47C22semidirect
31. #15689858C22semidirect
32. #15689826C22semidirect
33. #15689821C22semidirect
34. #15689811C22semidirect
35. #15689800C22semidirect
36. #15689800C22semidirect
37. #15689776C22semidirect
38. #15689768C22semidirect
39. #15689768C22semidirect
40. #15689764C22semidirect
41. D4×D188C22semidirect
42. #15689747C22semidirect
43. #15689729C22semidirect
44. #15689722C22semidirect
45. #15689713C22semidirect
47. #15689660C22semidirect
48. #15689658C22semidirect
49. C2×#13094019C22semidirect
50. C2×#13094019C22semidirect
51. C2×#13094019C22semidirect
52. C2×#13094019C22semidirect
53. C2×#13094019C22semidirect
54. C2×#13094019C22semidirect
55. C2×#13094015C22semidirect
56. C2×#13094015C22semidirect
57. C2×#13094013C22semidirect
58. C2×#13094013C22semidirect
59. C2×#13094013C22semidirect
60. C2×#13094012C22semidirect
61. C2×#13094012C22semidirect
62. #15689636C22semidirect
65. C2×#13094009C22semidirect
66. C2×#13094009C22semidirect
67. C2×#13094009C22semidirect
68. C2×#13094009C22semidirect
69. C2×#13094009C22semidirect
70. C2×#13094009C22semidirect
71. C2×#13094009C22semidirect
72. C2×#13094009C22semidirect
73. C2×#13094009C22semidirect
74. C2×#13094009C22semidirect
75. C2×#13094009C22semidirect
76. C2×#13094008C22semidirect
77. C2×#13094008C22semidirect
78. C2×#13094004C22semidirect
79. C2×#13094004C22semidirect
80. C2×#13094000C22semidirect
81. C2×#13094000C22semidirect
82. C2×#13094000C22semidirect
86. C2×#13093999C22semidirect
87. C2×#13093999C22semidirect
88. C2×#13093999C22semidirect
89. C2×#13093999C22semidirect
90. C2×#13093999C22semidirect
92. C2×#13093998C22semidirect
93. C2×#13093998C22semidirect
96. C2×#13093994C22semidirect
97. C2×#13093994C22semidirect
98. #15689602C22semidirect
99. #15689595C22semidirect
100. C2×C4×Dic94C22semidirect
101. C2×#13093989C22semidirect
103. C2×C4×D188C22semidirect
104. C2×C4×D188C22semidirect
105. C2×C4×D188C22semidirect
106. C2×C4×D188C22semidirect
108. C2×#13093986C22semidirect
109. C2×#13093986C22semidirect
110. C2×#13093986C22semidirect
111. C2×#13093986C22semidirect
112. C2×#13093986C22semidirect
113. C2×C4×C22⋊D47C22semidirect
114. C2×C4×C22⋊D47C22semidirect
115. C2×C4×C22⋊D47C22semidirect
116. C2×(C22⋊D47)⋊C4C22semidirect
117. C2×(C22⋊D47)⋊C4C22semidirect
118. C2×(C22⋊D47)⋊C4C22semidirect
119. C4×D4×D47C22semidirect
120. C2×#13093982C22semidirect
121. C2×#13093982C22semidirect
122. C2×#13093982C22semidirect
123. C2×#13093981C22semidirect
124. C2×#13093981C22semidirect
125. C2×#13093980C22semidirect
126. C22×Dic47⋊C4C22semidirect
127. C2×C4⋊C4×D47C22semidirect
128. C2×C4⋊C4×D47C22semidirect
129. C22×(C2×D47)⋊C4C22semidirect
130. C22×(C2×D47)⋊C4C22semidirect
131. C22×(C2×D47)⋊C4C22semidirect
132. C2×C22⋊C4×D47C22semidirect
133. C2×C22⋊C4×D47C22semidirect
134. C2×C42×D47C22semidirect
135. C47×#554C22semidirect
136. C2×C4⋊Q8×C47C22semidirect
137. C2×#125×C47C22semidirect
138. C2×#125×C47C22semidirect
139. C2×C22⋊Q8×C47C22semidirect
140. C2×C22⋊Q8×C47C22semidirect
141. C2×C22⋊Q8×C47C22semidirect
142. C2×C4×Q8×C47C22semidirect
146. C22×C4⋊C4×C47C22semidirect
150. C2×#10625354C23semidirect
188. C22×C4×D47C23semidirect
190. #13094019C23semidirect
191. #13094019C23semidirect
192. #13094019C23semidirect
193. #13094019C23semidirect
194. #13094019C23semidirect
195. #13094019C23semidirect
196. #13094015C23semidirect
197. #13094015C23semidirect
198. #13094013C23semidirect
199. #13094013C23semidirect
200. #13094013C23semidirect
201. #13094012C23semidirect
202. #13094012C23semidirect
205. #13094009C23semidirect
206. #13094009C23semidirect
207. #13094009C23semidirect
208. #13094009C23semidirect
209. #13094009C23semidirect
210. #13094009C23semidirect
211. #13094009C23semidirect
212. #13094009C23semidirect
213. #13094009C23semidirect
214. #13094009C23semidirect
215. #13094008C23semidirect
216. #13094008C23semidirect
217. #13094004C23semidirect
218. #13094004C23semidirect
219. #13094000C23semidirect
220. #13094000C23semidirect
221. #13094000C23semidirect
225. #13093999C23semidirect
226. #13093999C23semidirect
227. #13093999C23semidirect
228. #13093999C23semidirect
229. #13093999C23semidirect
231. #13093998C23semidirect
232. #13093998C23semidirect
235. #13093994C23semidirect
236. #13093994C23semidirect
237. C4×Dic94C23semidirect
238. #13093989C23semidirect
240. C4×D188C23semidirect
241. C4×D188C23semidirect
242. C4×D188C23semidirect
243. C4×D188C23semidirect
245. #13093986C23semidirect
246. #13093986C23semidirect
247. #13093986C23semidirect
248. #13093986C23semidirect
249. #13093986C23semidirect
250. C4×C22⋊D47C23semidirect
251. C4×C22⋊D47C23semidirect
252. C4×C22⋊D47C23semidirect
253. (C22⋊D47)⋊C4C23semidirect
254. (C22⋊D47)⋊C4C23semidirect
255. (C22⋊D47)⋊C4C23semidirect
256. #13093982C23semidirect
257. #13093982C23semidirect
258. #13093982C23semidirect
259. #13093981C23semidirect
260. #13093981C23semidirect
261. #13093980C23semidirect
276. C2×Dic47⋊C4C23semidirect
277. C4⋊C4×D47C23semidirect
278. C4⋊C4×D47C23semidirect
305. C2×(C2×D47)⋊C4C23semidirect
306. C2×(C2×D47)⋊C4C23semidirect
307. C2×(C2×D47)⋊C4C23semidirect
308. C22⋊C4×D47C23semidirect
309. C22⋊C4×D47C23semidirect
316. C42×D47C23semidirect
323. C4⋊Q8×C47C23semidirect
324. #125×C47C23semidirect
325. #125×C47C23semidirect
326. C22⋊Q8×C47C23semidirect
327. C22⋊Q8×C47C23semidirect
328. C22⋊Q8×C47C23semidirect
329. C4×Q8×C47C23semidirect
344. C2×C4⋊C4×C47C23semidirect
369. C2×D4×C47#41semidirect
554. D4×C47C2×#41semidirect
670. C2×#554D47semidirect
693. C2×C47#3513semidirect
709. #554C2×D47semidirect
724. C2×C4⋊Q8C2×D47semidirect
736. C2×#125C2×D47semidirect
737. C2×#125C2×D47semidirect
764. C2×C22⋊Q8C2×D47semidirect
765. C2×C22⋊Q8C2×D47semidirect
766. C2×C22⋊Q8C2×D47semidirect
786. C2×C4×Q8C2×D47semidirect
817. C22×C4⋊C4C2×D47semidirect
824. C47C2×#3513semidirect
873. C4⋊Q8C22×D47semidirect
883. #125C22×D47semidirect
884. #125C22×D47semidirect
909. C22⋊Q8C22×D47semidirect
910. C22⋊Q8C22×D47semidirect
911. C22⋊Q8C22×D47semidirect
929. C4×Q8C22×D47semidirect
984. C2×C4⋊C4C22×D47semidirect
1082. C2×D4#10625354semidirect
1247. D4C2×#10625354semidirect
1351. C2#20257331direct (N × H)

Maximal subgroups

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

subgroupindex
#202573312
C2×#156898582
C2×#156898262
C2×#156898212
C2×#156898112
C2×#156898002
C2×#156897762
C2×#156897682
C2×#156897642
C2×D4×D1882
C2×#156897472
C2×#156897292
C2×#156897222
C2×#156897132
C2×#156896602
C2×#156896582
C2×#156896362
C22×#130940092
C2×#156896022
C2×#156895952
C2×C4×D4×D472
C2×C47×#5542
C2×#351347