Finite Group Databasebeta

← #26376017

Subgroups — #26376017

Order 12032.

2954 conjugacy classes of subgroups.

The subgroup lattice has 1134 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689632C211yesmaximal, characteristic
2#20246520C212yesmaximal, complemented
3#20246516C212yesmaximal, complemented
4#20246469C212yesmaximal, complemented
5#20246465C212yesmaximal, complemented
6#20246436C212yesmaximal, complemented
7#20246432C212yesmaximal, complemented
8#20246368C212yesmaximal, complemented
9#20246364C212yesmaximal, complemented
10#20245883C211yesmaximal, characteristic, complemented
11#20245881C211yesmaximal, characteristic, complemented
12#20245876C211yesmaximal, characteristic, complemented
13#20245874C211yesmaximal, characteristic, complemented
14#20245832C211yesmaximal, characteristic, complemented
15#20245827C211yesmaximal, characteristic, complemented
16#20245825C211yesmaximal, characteristic, complemented
17C4×D4×Dic47C211yesmaximal, characteristic, complemented
18C42×C22⋊D47C211yesmaximal, characteristic, complemented
19C4×#13093986C211yesmaximal, characteristic, complemented
20C4×(C22⋊D47)⋊C4C211yesmaximal, characteristic, complemented
21C2×C4×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
22C4×C22⋊C4×D47C211yesmaximal, characteristic, complemented
23C47×#2290C211yesmaximal, characteristic, complemented
24C22×#10625350C2211yescharacteristic
25C23×C4×D47C2211yescharacteristic
26#15689632C4116yescomplemented
27C2×#13094009C2211yescharacteristic
28C2×#13094006C2211yescharacteristic
29C2×#13094002C2211yescharacteristic
30C2×#13094001C2211yescharacteristic
31C2×#13093997C2211yescharacteristic
32C2×#13093996C2211yescharacteristic
33C2×#13093994C2211yescharacteristic
34C2×#13093992C2211yescharacteristic
35C2×C4×D188C2211yescharacteristic
36C2×D4×Dic47C2212yes—
37C2×#13093986C2212yes—
38C2×C4×C22⋊D47C2212yes—
39C2×C4×C22⋊D47C2211yescharacteristic
40C2×C4×C22⋊D47C2211yescharacteristic
41C2×(C22⋊D47)⋊C4C2212yes—
42C2×#13093981C2211yescharacteristic
43C2×#13093981C2211yescharacteristic, complemented
44C22×(C2×D47)⋊C4C2212yes—
45C2×C22⋊C4×D47C2212yes—
46C22×C4×Dic47C2211yescharacteristic
47C22×C4×Dic47C2211yescharacteristic, complemented
48C2×C42×D47C2211yescharacteristic
49C2×C42×D47C2211yescharacteristic
50C2×C42×D47C2211yescharacteristic, complemented
51#15689028C2212yescomplemented
52#15689027C2212yescomplemented
53#15689024C2212yes—
54#15689023C2212yes—
55#15689015C2212yes—
56#15689015C2212yescomplemented
57#15689013C2212yes—
58#15689012C2212yes—
59#15689012C2212yes—
60#15689012C2212yescomplemented
61#15689011C2212yescomplemented
62#15689010C2212yescomplemented
63#15689008C2212yescomplemented
64#15689005C2212yescomplemented
65#15689005C2212yescomplemented
66#15689005C2212yescomplemented
67#15689004C2212yescomplemented
68#15689004C2212yescomplemented
69#15689001C2212yes—
70#15689001C2212yes—
71#15689000C2212yes—
72#15689000C2212yes—
73#15689000C2212yescomplemented
74#15688999C2212yes—
75#15688999C2212yescomplemented
76#15688997C2212yes—
77#15688995C2212yes—
78#15688994C2212yes—
79C4⋊C4×Dic47C2212yescomplemented
80C4⋊C4×Dic47C2212yescomplemented
81C4×Dic47⋊C4C2211yescharacteristic, complemented
82C4×Dic47⋊C4C2211yescharacteristic, complemented
83C4×Dic47⋊C4C2212yescomplemented
84C4×C4⋊Dic47C2211yescharacteristic, complemented
85#15688974C2212yescomplemented
86C22⋊C4×Dic47C2212yes—
87C22⋊C4×Dic47C2212yes—
88C22⋊C4×Dic47C2212yescomplemented
89C22⋊C4×Dic47C2212yescomplemented
90C4×(C2×D47)⋊C4C2211yescharacteristic
91C4×(C2×D47)⋊C4C2211yescharacteristic
92C4×(C2×D47)⋊C4C2211yescharacteristic
93C4×(C2×D47)⋊C4C2211yescharacteristic
94C4×(C2×D47)⋊C4C2211yescharacteristic
95C4×(C2×D47)⋊C4C2212yes—
96C4×(C2×D47)⋊C4C2211yescharacteristic
97C4×(C2×D47)⋊C4C2212yes—
98C4×(C2×D47)⋊C4C2211yescharacteristic, complemented
99C4×(C2×D47)⋊C4C2211yescharacteristic, complemented
100C4×(C2×D47)⋊C4C2212yescomplemented
101C4×C22⋊Dic47C2212yes—
102C4×C22⋊Dic47C2211yescharacteristic
103C4×C22⋊Dic47C2211yescharacteristic, complemented
104#15688970C2212yes—
105#15688970C2212yes—
106#15688970C2212yes—
107#15688970C2212yescomplemented
108#15688969C2211yescharacteristic, complemented
109C2×C47⋊#95C2212yes—
110#95×D47C2212yes—
111C42×Dic47C2211yescharacteristic, complemented
112C42×Dic47C2211yescharacteristic, complemented
113C2×C4×D4×C47C2211yescharacteristic
114C2×#117×C47C2211yescharacteristic, complemented
115C22×C42×C47C2211yescharacteristic
116C47×#388C2212yescomplemented
117C47×#387C2212yescomplemented
118C47×#386C2212yes—
119C47×#385C2212yes—
120C4×C4⋊C4×C47C2211yescharacteristic, complemented
121C4×C22⋊C4×C47C2211yescharacteristic
122C4×C22⋊C4×C47C2211yescharacteristic, complemented
123C47×#376C2211yescharacteristic, complemented
124C24×D47C2311yescharacteristic
125C2×#10625350—42no—
126C2×#10625350—42no—
127C2×#10625350C2×C418yescomplemented
128C22×Dic94C2311yescharacteristic
129C22×D188C2311yescharacteristic
130C22×D188C2311yescharacteristic
131C22×C22⋊D47C2311yescharacteristic
132C22×C22⋊D47C2311yescharacteristic
133C22×C22⋊D47C2311yescharacteristic
134C22×C22⋊D47C2311yescharacteristic
135C23×Dic47C2312yes—
136C23×Dic47C2312yes—
137C23×Dic47C2311yescharacteristic
138C22×C4×D47—42no—
139C22×C4×D47—42no—
140C22×C4×D47C2×C418yescomplemented
141C22×C4×D47C2312yes—
142C22×C4×D47C2312yes—
143C22×C4×D47C2312yes—
144C22×C4×D47C2311yescharacteristic
145C22×C4×D47C2311yescharacteristic
146C22×C4×D47C2311yescharacteristic
147C22×C4×D47C2311yescharacteristic
148C22×C4×D47C2311yescharacteristic
149#13094009C2×C418yescomplemented
150#13094006C2×C418yescomplemented
151#13094002C2×C418yescomplemented
152#13094001C2×C418yescomplemented
153#13093997C2×C418yescomplemented
154#13093996C2×C418yescomplemented
155#13093994C2×C418yescomplemented
156#13093992C2×C418yescomplemented
157C4×D188C2×C418yescomplemented
158D4×Dic47—28no—
159#13093986—28no—
160C4×C22⋊D47—28no—
161C4×C22⋊D47C2×C418yescomplemented
162C4×C22⋊D47C2×C418yescomplemented
163(C22⋊D47)⋊C4—28no—
164#13093981—42no—
165#13093981C2×C418yescomplemented
166C2×C4⋊Dic47C2312yes—
167C2×C4⋊Dic47C2311yescharacteristic
168C2×Dic47⋊C4C2312yes—
169C2×Dic47⋊C4C2312yes—
170C2×Dic47⋊C4C2312yes—
171C2×Dic47⋊C4C2311yescharacteristic
172C2×Dic47⋊C4C2311yescharacteristic
173C2×Dic47⋊C4C2311yescharacteristic
174C2×Dic47⋊C4C2311yescharacteristic
175C2×C22⋊Dic47C2312yes—
176C2×C22⋊Dic47C2311yescharacteristic
177C2×C22⋊Dic47C2311yescharacteristic
178C2×C22⋊Dic47C2312yes—
179C2×(C2×D47)⋊C4—28no—
180C2×(C2×D47)⋊C4C2312yes—
181C2×(C2×D47)⋊C4C2312yes—
182C2×(C2×D47)⋊C4C2312yes—
183C2×(C2×D47)⋊C4C2312yes—
184C2×(C2×D47)⋊C4C2312yes—
185C2×(C2×D47)⋊C4C2312yes—
186C2×(C2×D47)⋊C4C2312yes—
187C2×(C2×D47)⋊C4C2312yes—
188C2×(C2×D47)⋊C4C2311yescharacteristic
189C2×(C2×D47)⋊C4C2311yescharacteristic
190C2×(C2×D47)⋊C4C2311yescharacteristic
191C2×(C2×D47)⋊C4C2311yescharacteristic
192C2×(C2×D47)⋊C4C2311yescharacteristic
193C2×(C2×D47)⋊C4C2311yescharacteristic
194C2×(C2×D47)⋊C4C2312yes—
195C22⋊C4×D47—28no—
196C2×C4×Dic47—42no—
197C2×C4×Dic47—42no—
198C2×C4×Dic47C2312yes—
199C2×C4×Dic47C2312yes—
200C2×C4×Dic47C2311yescharacteristic
201C2×C4×Dic47C2311yescharacteristic
202C2×C4×Dic47C2312yes—
203C2×C4×Dic47C2311yescharacteristic
204C2×C4×Dic47C2312yes—
205C2×C4×Dic47C2311yescharacteristic
206C2×C4×Dic47C2312yes—
207C2×C4×Dic47C2312yes—
208C2×C4×Dic47C2312yes—
209C2×C4×Dic47C2312yes—
210C2×C4×Dic47C2312yes—
211C2×C4×Dic47C2311yescharacteristic
212C42×D47—42no—
213C42×D47—42no—
214C42×D47—42no—
215C47⋊#95C2312yes—
216C47⋊#95C2312yes—
217C47⋊#95C2312yes—
218C47⋊#95C2312yes—
219C47⋊#95C2312yes—
220C47⋊#95C2312yes—
221C47⋊#95C2312yes—
222C47⋊#95C2312yes—
223C47⋊#95C2312yes—
224C47⋊#95C2312yes—
225C47⋊#95C2312yes—
226C47⋊#95C2312yes—
227C47⋊#95C2312yes—
228C47⋊#95C2312yes—
229C47⋊#95C2312yes—
230C22×D4×C47C2311yescharacteristic
231C23×C4×C47C2312yes—
232C23×C4×C47C2311yescharacteristic
233C23×C4×C47C2311yescharacteristic
234C4×D4×C47C2×C418yescomplemented
235#117×C47—42no—
236C2×C4⋊C4×C47C2312yes—
237C2×C4⋊C4×C47C2312yes—
238C2×C4⋊C4×C47C2311yescharacteristic
239C2×C22⋊C4×C47C2312yes—
240C2×C22⋊C4×C47C2312yes—
241C2×C22⋊C4×C47C2312yes—
242C2×C22⋊C4×C47C2311yescharacteristic
243C2×C22⋊C4×C47C2311yescharacteristic
244C2×C42×C47—42no—
245C2×C42×C47C2311yescharacteristic
246C2×C42×C47C2311yescharacteristic
247C2×C42×C47C2311yescharacteristic
248C2×C42×C47C2311yescharacteristic
249C2×C42×C47C2312yes—
250C2×C42×C47C2311yescharacteristic
251#95×C47C2312yes—
252#95×C47C2312yes—
253#95×C47C2312yes—
254#95×C47C2312yes—
255#95×C47C2312yes—
256C24×C47C2411yescharacteristic
257C24×C47C2411yescharacteristic
258C23×D47—24no—
259C23×D47—24no—
260C23×D47—41no—
261C23×D47—41no—
262C23×D47C22×C414yes—
263C23×D47C2411yescharacteristic
264C23×D47C2411yescharacteristic
265C23×D47C2411yescharacteristic
266C2×D4×C47—24no—
267C2×D4×C47C22×C414yes—
268C22×C4×C47—22no—
269C22×C4×C47—22no—
270C22×C4×C47—22no—
271C22×C4×C47—22no—
272C22×C4×C47—24no—
273C22×C4×C47—24no—
274C22×C4×C47—42no—
275C22×C4×C47C22×C414yes—
276C22×C4×C47C22×C414yes—
277C22×C4×C47C2412yes—
278C22×C4×C47C2412yes—
279C22×C4×C47C2412yes—
280C22×C4×C47C2411yescharacteristic
281C22×C4×C47C2411yescharacteristic
282C22×C4×C47C2411yescharacteristic
283C22×C4×C47C2411yescharacteristic
284C22×C4×C47C2412yes—
285C22×C4×C47C2411yescharacteristic
286C2×C22⋊D47—24no—
287C2×C22⋊D47—24no—
288C2×C22⋊D47—41no—
289C2×C22⋊D47—41no—
290C2×C22⋊D47—41no—
291C2×C22⋊D47—41no—
292C2×C22⋊D47C22×C414yes—
293C2×C22⋊D47C22×C414yes—
294C2×C22⋊D47C22×C414yes—
295C2×C22⋊D47C22×C414yes—
296C22×Dic47—24no—
297C22×Dic47—24no—
298C22×Dic47—24no—
299C22×Dic47—24no—
300C22×Dic47—42no—
301C22×Dic47—42no—
302C22×Dic47—41no—
303C22×Dic47—41no—
304C22×Dic47C22×C414yes—
305C22×Dic47C2412yes—
306C22×Dic47C2411yescharacteristic
307C22×Dic47C2411yescharacteristic
308C22×Dic47C2411yescharacteristic
309C22×Dic47C2411yescharacteristic
310C22×Dic47C2411yescharacteristic
311C22×Dic47C2412yes—
312C22×Dic47C2412yes—
313C22×Dic47C2412yes—
314#10625350—416no—
315C2×D188—24no—
316C2×D188—41no—
317C2×D188—41no—
318C2×D188C22×C414yes—
319C2×D188C22×C414yes—
320C2×C4×D47—22no—
321C2×C4×D47—22no—
322C2×C4×D47—22no—
323C2×C4×D47—22no—
324C2×C4×D47—22no—
325C2×C4×D47—22no—
326C2×C4×D47—24no—
327C2×C4×D47—24no—
328C2×C4×D47—24no—
329C2×C4×D47—24no—
330C2×C4×D47—24no—
331C2×C4×D47—24no—
332C2×C4×D47—416no—
333C2×C4×D47—42no—
334C2×C4×D47—42no—
335C2×C4×D47—42no—
336C2×C4×D47—41no—
337C2×C4×D47—41no—
338C2×C4×D47—41no—
339C2×C4×D47—41no—
340C2×C4×D47C22×C414yes—
341C2×C4×D47C22×C414yes—
342C2×C4×D47C22×C414yes—
343C2×C4×D47C22×C414yes—
344C2×C4×D47C22×C414yes—
345C2×Dic94—41no—
346C2×Dic94—41no—
347C2×Dic94C22×C414yes—
348C4⋊C4×C47—24no—
349C4⋊C4×C47—42no—
350C4⋊C4×C47C22×C414yes—
351C22⋊C4×C47—24no—
352C22⋊C4×C47—24no—
353C22⋊C4×C47—42no—
354C22⋊C4×C47C22×C414yes—
355C22⋊C4×C47C22×C414yes—
356C42×C47—22no—
357C42×C47—22no—
358C42×C47—22no—
359C42×C47—22no—
360C42×C47—42no—
361C42×C47C22×C414yes—
362C22⋊Dic47—24no—
363C22⋊Dic47C22×C414yes—
364C22⋊Dic47C22×C414yes—
365C22⋊Dic47#4118yescomplemented
366(C2×D47)⋊C4—24no—
367(C2×D47)⋊C4—24no—
368(C2×D47)⋊C4—24no—
369(C2×D47)⋊C4—24no—
370(C2×D47)⋊C4—24no—
371(C2×D47)⋊C4—24no—
372(C2×D47)⋊C4—24no—
373(C2×D47)⋊C4—42no—
374(C2×D47)⋊C4C22×C414yes—
375(C2×D47)⋊C4C22×C414yes—
376(C2×D47)⋊C4C22×C414yes—
377(C2×D47)⋊C4C22×C414yes—
378(C2×D47)⋊C4C22×C414yes—
379(C2×D47)⋊C4C22×C414yes—
380(C2×D47)⋊C4#4118yescomplemented
381C4⋊Dic47—24no—
382C4⋊Dic47C22×C414yes—
383Dic47⋊C4—24no—
384Dic47⋊C4—24no—
385Dic47⋊C4—42no—
386Dic47⋊C4C22×C414yes—
387Dic47⋊C4C22×C414yes—
388Dic47⋊C4C22×C414yes—
389Dic47⋊C4C22×C414yes—
390C4×Dic47—24no—
391C4×Dic47—22no—
392C4×Dic47—22no—
393C4×Dic47—22no—
394C4×Dic47—22no—
395C4×Dic47—24no—
396C4×Dic47—24no—
397C4×Dic47—24no—
398C4×Dic47—42no—
399C4×Dic47—42no—
400C4×Dic47—42no—
401C4×Dic47—42no—
402C4×Dic47—42no—
403C4×Dic47C22×C414yes—
404C23×C47—22no—
405C23×C47—21no—
406C23×C47—21no—
407C23×C47—22no—
408C23×C47—22no—
409C23×C47—21no—
410C23×C47—21no—
411C23×C47C23×C412yes—
412C23×C47C23×C412yes—
413C23×C47C2×#4114yes—
414C23×C47C2511yescharacteristic
415C22×D47—22no—
416C22×D47—21no—
417C22×D47—21no—
418C22×D47—28no—
419C22×D47—22no—
420C22×D47—22no—
421C22×D47—22no—
422C22×D47—22no—
423C22×D47—21no—
424C22×D47—21no—
425C22×D47—21no—
426C22×D47—21no—
427C22×D47—28no—
428C22×D47—44no—
429C22×D47—48no—
430C22×D47—48no—
431C22×D47C23×C412yes—
432C22×D47C23×C412yes—
433C22×D47C23×C412yes—
434C22×D47C2×#4114yes—
435D4×C47—28no—
436C2×C4×C47—22no—
437C2×C4×C47—22no—
438C2×C4×C47—22no—
439C2×C4×C47—21no—
440C2×C4×C47—21no—
441C2×C4×C47—22no—
442C2×C4×C47—21no—
443C2×C4×C47—21no—
444C2×C4×C47—28no—
445C2×C4×C47—28no—
446C2×C4×C47—22no—
447C2×C4×C47—22no—
448C2×C4×C47—22no—
449C2×C4×C47—22no—
450C2×C4×C47—22no—
451C2×C4×C47—22no—
452C2×C4×C47—22no—
453C2×C4×C47—22no—
454C2×C4×C47—22no—
455C2×C4×C47—48no—
456C2×C4×C47C23×C412yes—
457C2×C4×C47C23×C412yes—
458C2×C4×C47C23×C412yes—
459C2×C4×C47C23×C412yes—
460C2×C4×C47C23×C412yes—
461C2×C4×C47C2×#4114yes—
462C2×C4×C47H(5,𝔽2)12yes—
463C2×C4×C47H(5,𝔽2)12yes—
464C22⋊D47—28no—
465C22⋊D47—28no—
466C22⋊D47—44no—
467C22⋊D47—44no—
468C2×Dic47—22no—
469C2×Dic47—22no—
470C2×Dic47—22no—
471C2×Dic47—22no—
472C2×Dic47—22no—
473C2×Dic47—22no—
474C2×Dic47—22no—
475C2×Dic47—22no—
476C2×Dic47—21no—
477C2×Dic47—21no—
478C2×Dic47—21no—
479C2×Dic47—21no—
480C2×Dic47—21no—
481C2×Dic47—21no—
482C2×Dic47—22no—
483C2×Dic47—22no—
484C2×Dic47—22no—
485C2×Dic47—44no—
486C2×Dic47—48no—
487C2×Dic47—48no—
488C2×Dic47C23×C412yes—
489C2×Dic47C23×C412yes—
490C2×Dic47C23×C412yes—
491C2×Dic47C23×C412yes—
492C2×Dic47C23×C412yes—
493C2×Dic47C2×#4114yes—
494C2×Dic47C2×#4114yes—
495C2×Dic47C2×#4114yes—
496D188—28no—
497D188—44no—
498C4×D47—28no—
499C4×D47—28no—
500C4×D47—28no—
501C4×D47—44no—
502C4×D47—44no—
503C4×D47—48no—
504C4×D47—48no—
505C4×D47—48no—
506Dic94—44no—
507#34152—471nomaximal, Sylow
508C22×C47—22no—
509C22×C47—22no—
510C22×C47—24no—
511C22×C47—24no—
512C22×C47—22no—
513C22×C47—22no—
514C22×C47—22no—
515C22×C47—42no—
516C22×C47—42no—
517C22×C47C4×#4114yes—
518C22×C47C24×C411yescharacteristic
519C22×C47C22×#4112yes—
520C22×C47C22×#4112yes—
521C22×C47C2×H(5,𝔽2)11yescharacteristic
522C22×C47C2×H(5,𝔽2)11yescharacteristic
523C2×D47—22no—
524C2×D47—22no—
525C2×D47—24no—
526C2×D47—24no—
527C2×D47—22no—
528C2×D47—22no—
529C2×D47—22no—
530C2×D47—22no—
531C2×D47—22no—
532C2×D47—22no—
533C2×D47—416no—
534C2×D47—42no—
535C2×D47—42no—
536C2×D47—42no—
537C2×D47—42no—
538C2×D47C4×#4114yes—
539C4×C47—22no—
540C4×C47—22no—
541C4×C47—22no—
542C4×C47—22no—
543C4×C47—24no—
544C4×C47—42no—
545C4×C47—42no—
546C4×C47—42no—
547C4×C47#51814yes—
548Dic47—22no—
549Dic47—22no—
550Dic47—22no—
551Dic47—22no—
552Dic47—22no—
553Dic47—24no—
554Dic47—24no—
555Dic47—24no—
556Dic47—42no—
557C2×#525—471no—
558#2374—472no—
559#2374—472no—
560#2368—472no—
561#2368—472no—
562#2364—472no—
563#2364—472no—
564#2358—472no—
565#2358—472no—
566#2298—471no—
567#2298—471no—
568#2297—471no—
569#2297—471no—
570#2290—471no—
571#2290—471no—
572#2290—471no—
573#2290D4711yescharacteristic, complemented
574C42×D4—471no—
575C42×D4—471no—
576C42×D4—471no—
577C42×D4—471no—
578C2×C4×C22⋊C4—471no—
579C2×C4×C22⋊C4—471no—
580C2×C47—24no—
581C2×C47—42no—
582C2×C47C2×C4×#4111yescharacteristic
583C2×C47C2×C4×#4111yescharacteristic
584C2×C47C2×#51811yescharacteristic
585C2×C47#348112yes—
586C2×C47#348112yes—
587D47—24no—
588D47—42no—
589D47—42no—
590C22×#41—471no—
591C24×C4—471no—
592#525—4716no—
593C2×#123—471no—
594C2×#123—471no—
595C2×C22⋊Q8—471no—
596C2×C22⋊Q8—471no—
597C2×#121—471no—
598C2×#121—471no—
599C2×#120—471no—
600C2×#120—471no—
601C2×C4×D4—471no—
602C2×C4×D4—471no—
603C2×C4×D4—472no—
604C2×C4×D4—472no—
605C2×C4×D4—472no—
606C2×C4×D4—472no—
607C2×C4×D4—471no—
608C2×C4×D4C2×D4711yescharacteristic
609C2×#117—471no—
610C2×#117—471no—
611C2×#117C2×D4711yescharacteristic, complemented
612C22×C22⋊C4—472no—
613C22×C22⋊C4—472no—
614C22×C42—471no—
615C22×C42—471no—
616C22×C42—471no—
617C22×C42—471no—
618C22×C42—471no—
619C22×C42C2×D4711yescharacteristic
620#391—472no—
621#391—472no—
622#390—472no—
623#390—472no—
624#388—472no—
625#388—472no—
626#388—472no—
627#388—472no—
628#388—472no—
629#388—472no—
630#388—472no—
631#388C2×D4712yescomplemented
632#387—472no—
633#387—472no—
634#387—472no—
635#387—472no—
636#387—472no—
637#387—472no—
638#387—472no—
639#387C2×D4712yescomplemented
640#386—472no—
641#386—472no—
642#386—472no—
643#386—472no—
644#386—472no—
645#386—472no—
646#386—472no—
647#386C2×D4712yes—
648#385—472no—
649#385—472no—
650#385—472no—
651#385C2×D4712yes—
652C4×C4⋊C4—472no—
653C4×C4⋊C4—472no—
654C4×C4⋊C4—471no—
655C4×C4⋊C4—472no—
656C4×C4⋊C4—471no—
657C4×C4⋊C4—471no—
658C4×C4⋊C4—472no—
659C4×C4⋊C4C2×D4711yescharacteristic, complemented
660C4×C22⋊C4—472no—
661C4×C22⋊C4—471no—
662C4×C22⋊C4—471no—
663C4×C22⋊C4—472no—
664C4×C22⋊C4—472no—
665C4×C22⋊C4—472no—
666C4×C22⋊C4—472no—
667C4×C22⋊C4—472no—
668C4×C22⋊C4—472no—
669C4×C22⋊C4—471no—
670C4×C22⋊C4—471no—
671C4×C22⋊C4—471no—
672C4×C22⋊C4—471no—
673C4×C22⋊C4—471no—
674C4×C22⋊C4—471no—
675C4×C22⋊C4—472no—
676C4×C22⋊C4—471no—
677C4×C22⋊C4—471no—
678C4×C22⋊C4—472no—
679C4×C22⋊C4—472no—
680C4×C22⋊C4—472no—
681C4×C22⋊C4—472no—
682C4×C22⋊C4C2×D4711yescharacteristic
683C4×C22⋊C4C2×D4711yescharacteristic, complemented
684#376—471no—
685#376C2×D4711yescharacteristic, complemented
686C2×#95—472no—
687C2×#95—472no—
688C43—471no—
689C43—471no—
690C47#3415211yescharacteristic, complemented, Sylow
691C25—471no—
692C2×#41—478no—
693C2×#41—1882no—
694C2×#41—1882no—
695C22×Q8—471no—
696C22×D4—471no—
697C22×D4—471no—
698C22×D4—471no—
699C22×D4—471no—
700C22×D4—471no—
701C22×D4—471no—
702C22×D4C22×D4711yescharacteristic
703C23×C4—471no—
704C23×C4—471no—
705C23×C4—471no—
706C23×C4—471no—
707C23×C4—478no—
708C23×C4—471no—
709C23×C4—471no—
710C23×C4—472no—
711C23×C4—472no—
712C23×C4—472no—
713C23×C4—472no—
714C23×C4—472no—
715C23×C4—1882no—
716C23×C4—1882no—
717C23×C4C22×D4712yes—
718C23×C4C22×D4711yescharacteristic
719C23×C4C22×D4711yescharacteristic
720#123—478no—
721#123—478no—
722C22⋊Q8—478no—
723C22⋊Q8—478no—
724#121—478no—
725#121—478no—
726#120—478no—
727#120—478no—
728C4×D4—478no—
729C4×D4—478no—
730C4×D4—478no—
731C4×D4—948no—
732C4×D4—948no—
733C4×D4—948no—
734C4×D4—948no—
735C4×D4C4×D4718yescomplemented
736#117—42no—
737#117—478no—
738#117—1882no—
739C2×C4⋊C4—471no—
740C2×C4⋊C4—471no—
741C2×C4⋊C4—471no—
742C2×C4⋊C4—471no—
743C2×C4⋊C4—471no—
744C2×C4⋊C4—472no—
745C2×C4⋊C4—472no—
746C2×C4⋊C4—472no—
747C2×C4⋊C4—472no—
748C2×C4⋊C4C22×D4712yes—
749C2×C4⋊C4C22×D4712yes—
750C2×C4⋊C4C22×D4711yescharacteristic
751C2×C22⋊C4—472no—
752C2×C22⋊C4—471no—
753C2×C22⋊C4—471no—
754C2×C22⋊C4—472no—
755C2×C22⋊C4—471no—
756C2×C22⋊C4—471no—
757C2×C22⋊C4—471no—
758C2×C22⋊C4—471no—
759C2×C22⋊C4—471no—
760C2×C22⋊C4—471no—
761C2×C22⋊C4—472no—
762C2×C22⋊C4—472no—
763C2×C22⋊C4—472no—
764C2×C22⋊C4—472no—
765C2×C22⋊C4—472no—
766C2×C22⋊C4—472no—
767C2×C22⋊C4—472no—
768C2×C22⋊C4—472no—
769C2×C22⋊C4—472no—
770C2×C22⋊C4—948no—
771C2×C22⋊C4—948no—
772C2×C22⋊C4C22×D4712yes—
773C2×C22⋊C4C22×D4712yes—
774C2×C22⋊C4C22×D4712yes—
775C2×C22⋊C4C22×D4711yescharacteristic
776C2×C22⋊C4C22×D4711yescharacteristic
777C2×C42—42no—
778C2×C42—471no—
779C2×C42—472no—
780C2×C42—472no—
781C2×C42—472no—
782C2×C42—472no—
783C2×C42—471no—
784C2×C42—471no—
785C2×C42—471no—
786C2×C42—471no—
787C2×C42—472no—
788C2×C42—472no—
789C2×C42—472no—
790C2×C42—472no—
791C2×C42—472no—
792C2×C42—1882no—
793C2×C42—1882no—
794C2×C42—1882no—
795C2×C42—1882no—
796C2×C42—1882no—
797C2×C42C22×D4711yescharacteristic
798C2×C42C22×D4711yescharacteristic
799C2×C42C22×D4711yescharacteristic
800C2×C42C22×D4711yescharacteristic
801C2×C42C22×D4712yes—
802C2×C42C22×D4711yescharacteristic
803#95—472no—
804#95—472no—
805#95—472no—
806#95—472no—
807#95—472no—
808#95—472no—
809#95—472no—
810#95—472no—
811#95—472no—
812#95—472no—
813#95—472no—
814#95—472no—
815#95—472no—
816#95—472no—
817#95—472no—
818#95C22×D4712yes—
819#95C22×D4712yes—
820#95C22×D4712yes—
821#95C22×D4712yes—
822#95C22×D4712yes—
823C24—471no—
824C24—471no—
825C24—471no—
826C24—474no—
827C24—944no—
828C24—944no—
829C24—1881no—
830C24—1881no—
831C24C23×D4711yescharacteristic
832C24C23×D4711yescharacteristic
833#41—18816no—
834C2×Q8—474no—
835C2×Q8—1881no—
836C2×Q8—1881no—
837C2×D4—24no—
838C2×D4—474no—
839C2×D4—474no—
840C2×D4—474no—
841C2×D4—474no—
842C2×D4—474no—
843C2×D4—474no—
844C2×D4—944no—
845C2×D4—944no—
846C2×D4—944no—
847C2×D4—1881no—
848C2×D4—1881no—
849C2×D4—1881no—
850C2×D4—1881no—
851C2×D4—1881no—
852C2×D4—1881no—
853C2×D4C2×C4×D4714yes—
854C22×C4—22no—
855C22×C4—22no—
856C22×C4—22no—
857C22×C4—22no—
858C22×C4—24no—
859C22×C4—24no—
860C22×C4—42no—
861C22×C4—471no—
862C22×C4—472no—
863C22×C4—472no—
864C22×C4—472no—
865C22×C4—471no—
866C22×C4—471no—
867C22×C4—471no—
868C22×C4—471no—
869C22×C4—474no—
870C22×C4—474no—
871C22×C4—474no—
872C22×C4—474no—
873C22×C4—474no—
874C22×C4—474no—
875C22×C4—472no—
876C22×C4—944no—
877C22×C4—944no—
878C22×C4—944no—
879C22×C4—944no—
880C22×C4—944no—
881C22×C4—944no—
882C22×C4—944no—
883C22×C4—944no—
884C22×C4—942no—
885C22×C4—942no—
886C22×C4—942no—
887C22×C4—942no—
888C22×C4—942no—
889C22×C4—942no—
890C22×C4—944no—
891C22×C4—944no—
892C22×C4—18816no—
893C22×C4—1882no—
894C22×C4—1882no—
895C22×C4—1882no—
896C22×C4—1881no—
897C22×C4—1881no—
898C22×C4—1881no—
899C22×C4—1881no—
900C22×C4—1882no—
901C22×C4—1882no—
902C22×C4—1881no—
903C22×C4—1881no—
904C22×C4C2×C4×D4714yes—
905C22×C4C2×C4×D4714yes—
906C22×C4C23×D4712yes—
907C22×C4C23×D4712yes—
908C22×C4C23×D4712yes—
909C22×C4C23×D4711yescharacteristic
910C22×C4C23×D4711yescharacteristic
911C22×C4C23×D4711yescharacteristic
912C22×C4C23×D4711yescharacteristic
913C22×C4C23×D4712yes—
914C22×C4C23×D4711yescharacteristic
915C4⋊C4—24no—
916C4⋊C4—42no—
917C4⋊C4—474no—
918C4⋊C4—474no—
919C4⋊C4—474no—
920C4⋊C4—474no—
921C4⋊C4—474no—
922C4⋊C4—944no—
923C4⋊C4—944no—
924C4⋊C4—944no—
925C4⋊C4—1882no—
926C4⋊C4C2×C4×D4714yes—
927C22⋊C4—24no—
928C22⋊C4—24no—
929C22⋊C4—42no—
930C22⋊C4—474no—
931C22⋊C4—474no—
932C22⋊C4—478no—
933C22⋊C4—474no—
934C22⋊C4—474no—
935C22⋊C4—474no—
936C22⋊C4—474no—
937C22⋊C4—474no—
938C22⋊C4—474no—
939C22⋊C4—478no—
940C22⋊C4—944no—
941C22⋊C4—944no—
942C22⋊C4—944no—
943C22⋊C4—944no—
944C22⋊C4—944no—
945C22⋊C4—944no—
946C22⋊C4—944no—
947C22⋊C4—944no—
948C22⋊C4—1882no—
949C22⋊C4C2×C4×D4714yes—
950C22⋊C4C2×C4×D4714yes—
951C42—22no—
952C42—22no—
953C42—22no—
954C42—22no—
955C42—42no—
956C42—474no—
957C42—944no—
958C42—944no—
959C42—944no—
960C42—944no—
961C42—942no—
962C42—942no—
963C42—942no—
964C42—942no—
965C42—1882no—
966C42—1882no—
967C42—1882no—
968C42—1882no—
969C42—1882no—
970C42C2×C4×D4714yes—
971C23—22no—
972C23—21no—
973C23—21no—
974C23—22no—
975C23—22no—
976C23—21no—
977C23—21no—
978C23—472no—
979C23—474no—
980C23—472no—
981C23—472no—
982C23—948no—
983C23—942no—
984C23—941no—
985C23—941no—
986C23—948no—
987C23—942no—
988C23—942no—
989C23—942no—
990C23—942no—
991C23—941no—
992C23—941no—
993C23—941no—
994C23—941no—
995C23—1884no—
996C23—1888no—
997C23—1888no—
998C23C22×C4×D4712yes—
999C23C22×C4×D4712yes—
1000C23#41×D4714yes—
1001C23C24×D4711yescharacteristic
1002Q8—1884no—
1003D4—28no—
1004D4—948no—
1005D4—948no—
1006D4—948no—
1007D4—1884no—
1008D4—1884no—
1009D4—1884no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—21no—
1015C2×C4—21no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—28no—
1019C2×C4—28no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—48no—
1030C2×C4—472no—
1031C2×C4—472no—
1032C2×C4—472no—
1033C2×C4—472no—
1034C2×C4—472no—
1035C2×C4—474no—
1036C2×C4—474no—
1037C2×C4—474no—
1038C2×C4—942no—
1039C2×C4—942no—
1040C2×C4—942no—
1041C2×C4—942no—
1042C2×C4—942no—
1043C2×C4—942no—
1044C2×C4—941no—
1045C2×C4—941no—
1046C2×C4—941no—
1047C2×C4—942no—
1048C2×C4—942no—
1049C2×C4—941no—
1050C2×C4—941no—
1051C2×C4—941no—
1052C2×C4—948no—
1053C2×C4—948no—
1054C2×C4—948no—
1055C2×C4—942no—
1056C2×C4—942no—
1057C2×C4—942no—
1058C2×C4—1884no—
1059C2×C4—1884no—
1060C2×C4—1888no—
1061C2×C4—1888no—
1062C2×C4—1888no—
1063C2×C4—1884no—
1064C2×C4—1888no—
1065C2×C4—1888no—
1066C2×C4C22×C4×D4712yes—
1067C2×C4C22×C4×D4712yes—
1068C2×C4C22×C4×D4712yes—
1069C2×C4C22×C4×D4712yes—
1070C2×C4C22×C4×D4712yes—
1071C2×C4#41×D4714yes—
1072C2×C4#1309406912yes—
1073C2×C4#1309407012yes—
1074C22—22no—
1075C22—22no—
1076C22—24no—
1077C22—24no—
1078C22—22no—
1079C22—22no—
1080C22—22no—
1081C22—42no—
1082C22—42no—
1083C22—474no—
1084C22—942no—
1085C22—942no—
1086C22—944no—
1087C22—944no—
1088C22—942no—
1089C22—942no—
1090C22—942no—
1091C22—942no—
1092C22—942no—
1093C22—942no—
1094C22—18816no—
1095C22—1882no—
1096C22—1882no—
1097C22—1882no—
1098C22—1882no—
1099C22#1568959114yes—
1100C22C23×C4×D4711yescharacteristic
1101C22C2×#41×D4712yes—
1102C22C2×#41×D4712yes—
1103C22C2×#1309406911yescharacteristic
1104C22C2×#1309407011yescharacteristic
1105C4—22no—
1106C4—22no—
1107C4—22no—
1108C4—22no—
1109C4—24no—
1110C4—42no—
1111C4—42no—
1112C4—42no—
1113C4—942no—
1114C4—942no—
1115C4—942no—
1116C4—942no—
1117C4—942no—
1118C4—944no—
1119C4—944no—
1120C4—944no—
1121C4—1882no—
1122C4#1568959514yes—
1123C2—24no—
1124C2—42no—
1125C2—944no—
1126C2—1882no—
1127C2—1882no—
1128C2C4×#41×D4711yescharacteristic
1129C2C2×#1568959111yescharacteristic
1130C2C2×#1568959511yescharacteristic
1131C2#2025699012yes—
1132C2#2025699412yes—
subgroupG/H
centerC22×C4C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC47×#2290C2
socle, cosocleC23×C47C25
prime radicalC2×#15689632C2
hypercenter#2290D47
hypocenterC47#34152
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ #2290

Complements

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

NH ≅ G/Ntype
2. #20246520C2semidirect
3. #20246516C2semidirect
4. #20246469C2semidirect
5. #20246465C2semidirect
6. #20246436C2semidirect
7. #20246432C2semidirect
8. #20246368C2semidirect
9. #20246364C2semidirect
10. #20245883C2semidirect
11. #20245881C2semidirect
12. #20245876C2semidirect
13. #20245874C2semidirect
14. #20245832C2semidirect
15. #20245827C2semidirect
16. #20245825C2semidirect
17. C4×D4×Dic47C2semidirect
18. C42×C22⋊D47C2semidirect
19. C4×#13093986C2semidirect
20. C4×(C22⋊D47)⋊C4C2semidirect
21. C2×C4×(C2×D47)⋊C4C2semidirect
22. C4×C22⋊C4×D47C2semidirect
23. C47×#2290C2semidirect
26. #15689632C4semidirect
43. C2×#13093981C22semidirect
47. C22×C4×Dic47C22semidirect
50. C2×C42×D47C22semidirect
51. #15689028C22semidirect
52. #15689027C22semidirect
56. #15689015C22semidirect
60. #15689012C22semidirect
61. #15689011C22semidirect
62. #15689010C22semidirect
63. #15689008C22semidirect
64. #15689005C22semidirect
65. #15689005C22semidirect
66. #15689005C22semidirect
67. #15689004C22semidirect
68. #15689004C22semidirect
73. #15689000C22semidirect
75. #15688999C22semidirect
79. C4⋊C4×Dic47C22semidirect
80. C4⋊C4×Dic47C22semidirect
81. C4×Dic47⋊C4C22semidirect
82. C4×Dic47⋊C4C22semidirect
83. C4×Dic47⋊C4C22semidirect
84. C4×C4⋊Dic47C22semidirect
85. #15688974C22semidirect
88. C22⋊C4×Dic47C22semidirect
89. C22⋊C4×Dic47C22semidirect
98. C4×(C2×D47)⋊C4C22semidirect
99. C4×(C2×D47)⋊C4C22semidirect
100. C4×(C2×D47)⋊C4C22semidirect
103. C4×C22⋊Dic47C22semidirect
107. #15688970C22semidirect
108. #15688969C22semidirect
111. C42×Dic47C22semidirect
112. C42×Dic47C22semidirect
114. C2×#117×C47C22semidirect
116. C47×#388C22semidirect
117. C47×#387C22semidirect
120. C4×C4⋊C4×C47C22semidirect
122. C4×C22⋊C4×C47C22semidirect
123. C47×#376C22semidirect
127. C2×#10625350C2×C4semidirect
140. C22×C4×D47C2×C4semidirect
149. #13094009C2×C4semidirect
150. #13094006C2×C4semidirect
151. #13094002C2×C4semidirect
152. #13094001C2×C4semidirect
153. #13093997C2×C4semidirect
154. #13093996C2×C4semidirect
155. #13093994C2×C4semidirect
156. #13093992C2×C4semidirect
157. C4×D188C2×C4semidirect
161. C4×C22⋊D47C2×C4semidirect
162. C4×C22⋊D47C2×C4semidirect
165. #13093981C2×C4semidirect
234. C4×D4×C47C2×C4semidirect
365. C22⋊Dic47#41semidirect
380. (C2×D47)⋊C4#41semidirect
573. #2290D47semidirect
611. C2×#117C2×D47semidirect
631. #388C2×D47semidirect
639. #387C2×D47semidirect
659. C4×C4⋊C4C2×D47semidirect
683. C4×C22⋊C4C2×D47semidirect
685. #376C2×D47semidirect
690. C47#34152semidirect
735. C4×D4C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156896322
#202465202
#202465162
#202464692
#202464652
#202464362
#202464322
#202463682
#202463642
#202458832
#202458812
#202458762
#202458742
#202458322
#202458272
#202458252
C4×D4×Dic472
C42×C22⋊D472
C4×#130939862
C4×(C22⋊D47)⋊C42
C2×C4×(C2×D47)⋊C42
C4×C22⋊C4×D472
C47×#22902
#3415247