Finite Group Databasebeta

← #14914060

Subgroups — #14914060

Order 2816.

3118 conjugacy classes of subgroups.

The subgroup lattice has 1156 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623158C211yesmaximal, characteristic
2C2×#10623105C211yesmaximal, characteristic, complemented
3C2×D11×#117C211yesmaximal, characteristic, complemented
4#13071656C211yesmaximal, characteristic, complemented
5#13071654C211yesmaximal, characteristic, complemented
6#13071653C211yesmaximal, characteristic, complemented
7#13071652C211yesmaximal, characteristic, complemented
8#13071648C211yesmaximal, characteristic, complemented
9#13071647C211yesmaximal, characteristic, complemented
10#13071639C211yesmaximal, characteristic, complemented
11#13071562C212yesmaximal, complemented
12#13071561C212yesmaximal, complemented
13#13071544C212yesmaximal, complemented
14#13071540C212yesmaximal, complemented
15#13071278C212yesmaximal, complemented
16#13071269C212yesmaximal, complemented
17#13071238C211yesmaximal, characteristic, complemented
18#13071207C211yesmaximal, characteristic, complemented
19C4×#66947C212yesmaximal, complemented
20#13071137C212yesmaximal, complemented
21#13070997C211yesmaximal, characteristic, complemented
22#13070970C211yesmaximal, characteristic, complemented
23C11×#2362C211yesmaximal, characteristic, complemented
24C22×#4343C2211yescharacteristic
25C23×C4×D11C2211yescharacteristic
26C2×C11×C22⋊Q8C2211yescharacteristic
27C2×C4×Q8×C11C2211yescharacteristic, complemented
28C2×C11×#117C2211yescharacteristic
29C2×#66999C2211yescharacteristic
30C2×Q8×Dic11C2211yescharacteristic, complemented
31C2×#66983C2211yescharacteristic
32C2×#66979C2211yescharacteristic
33#10623158C4116yescomplemented
34#10623105—28no—
35D11×#117—28no—
36C2×#66948C2211yescharacteristic
37C2×#66947C2212yes—
38C2×#66946C2212yes—
39C2×#66946C2212yes—
40C2×#66946C2211yescharacteristic, complemented
41C2×#66945C2211yescharacteristic
42C2×#66945C2211yescharacteristic
43C2×#66945C2211yescharacteristic
44C2×C4⋊C4×D11C2211yescharacteristic
45C2×C4⋊C4×D11C2211yescharacteristic
46C2×C4⋊C4×D11C2212yescomplemented
47C2×#66935C2212yes—
48C2×(C22⋊D11)⋊C4C2212yes—
49C2×C22⋊C4×D11C2212yes—
50C2×#66930C2212yes—
51C2×C4×D44C2212yes—
52C2×C4×D44C2211yescharacteristic, complemented
53C2×#66925C2211yescharacteristic
54C2×#66925C2211yescharacteristic
55C2×#66925C2212yes—
56C2×#66925C2212yescomplemented
57C2×C42×D11C2212yes—
58C11×#391C2211yescharacteristic, complemented
59C11×#389C2211yescharacteristic, complemented
60C11×#388C2212yes—
61C11×#388C2212yes—
62C11×#387C2212yescomplemented
63C4×C11×C4⋊C4C2212yescomplemented
64C4×C11×C4⋊C4C2211yescharacteristic, complemented
65C4×C11×C22⋊C4C2211yescharacteristic
66#10622843C2211yescharacteristic, complemented
67C4×C22⋊Dic11C2211yescharacteristic
68#10622603C2212yes—
69#10622603C2212yescomplemented
70#10622602C2212yes—
71#10622601C2212yes—
72#10622601C2211yescharacteristic, complemented
73#10622598C2211yescharacteristic, complemented
74#10622594C2212yescomplemented
75#10622591C2212yescomplemented
76#10622589C2212yescomplemented
77C4⋊C4×Dic11C2211yescharacteristic, complemented
78C4⋊C4×Dic11C2212yescomplemented
79C4⋊C4×Dic11C2211yescharacteristic, complemented
80#10622586C2211yescharacteristic, complemented
81#10622570C2212yes—
82#10622570C2212yes—
83#10622569C2212yes—
84#10622569C2212yes—
85#10622568C2211yescharacteristic
86#10622568C2211yescharacteristic
87#10622564C2212yes—
88#10622564C2212yes—
89#10622555C2211yescharacteristic
90#10622555C2211yescharacteristic
91#10622553C2212yes—
92#10622553C2212yescomplemented
93#10622552C2212yes—
94#10622552C2211yescharacteristic, complemented
95C4×(C2×D11)⋊C4C2211yescharacteristic
96C4×(C2×D11)⋊C4C2211yescharacteristic
97C4×(C2×D11)⋊C4C2212yes—
98C4×(C2×D11)⋊C4C2212yescomplemented
99C4×(C2×D11)⋊C4C2212yescomplemented
100C4×C4⋊Dic11C2211yescharacteristic, complemented
101C4×Dic11⋊C4C2212yescomplemented
102C4×Dic11⋊C4C2212yescomplemented
103#10622541C2211yescharacteristic, complemented
104#10622283C2212yes—
105#10622283C2212yescomplemented
106#10622282C2212yes—
107#10622282C2212yescomplemented
108#10622281C2212yes—
109#10622280C2211yescharacteristic
110#10622280C2211yescharacteristic
111#10622280C2212yescomplemented
112#10622280C2212yescomplemented
113#10622279C2212yes—
114#10622279C2212yescomplemented
115#10622279C2212yescomplemented
116#10622278C2212yes—
117#10622278C2212yes—
118#10622278C2212yes—
119#10622278C2212yes—
120#10622277C2211yescharacteristic
121#10622277C2211yescharacteristic
122#10622268C2212yescomplemented
123#10622263C2212yescomplemented
124#10622262C2212yescomplemented
125#10622262C2212yescomplemented
126C24×D11C2311yescharacteristic
127C22×Q8×C11C2311yescharacteristic
128C23×C4×C11C2311yescharacteristic
129C22×C22⋊D11C2312yes—
130C23×Dic11C2311yescharacteristic
131C2×#4343—24no—
132C2×#4343—24no—
133C2×#4343C2×C418yes—
134C22×D44C2312yes—
135C22×D44C2311yescharacteristic
136C22×D44C2312yes—
137C22×C4×D11—24no—
138C22×C4×D11—24no—
139C22×C4×D11C2×C418yescomplemented
140C22×C4×D11C2311yescharacteristic
141C22×C4×D11C2311yescharacteristic
142C22×C4×D11C2312yes—
143C22×C4×D11C2311yescharacteristic
144C22×C4×D11C2312yes—
145C22×C4×D11C2312yes—
146C22×C4×D11C2312yes—
147C22×C4×D11C2312yes—
148C22×C4×D11C2311yescharacteristic
149C11×C22⋊Q8C2×C418yescomplemented
150C4×Q8×C11—24no—
151C11×#117—24no—
152C2×C11×C4⋊C4C2311yescharacteristic
153C2×C11×C4⋊C4C2312yes—
154C2×C11×C4⋊C4C2312yes—
155C2×C11×C4⋊C4C2311yescharacteristic
156C2×C11×C4⋊C4C2312yes—
157C2×C11×C4⋊C4C2311yescharacteristic
158C2×C11×C22⋊C4C2312yes—
159C2×C11×C22⋊C4C2311yescharacteristic
160C2×C11×C22⋊C4C2311yescharacteristic
161C2×C11×C22⋊C4C2312yes—
162C2×C42×C11C2312yes—
163C2×C42×C11C2311yescharacteristic
164C2×C42×C11C2311yescharacteristic
165C2×C42×C11C2312yes—
166C2×C42×C11C2312yes—
167C2×C22⋊Dic11C2312yes—
168C2×C22⋊Dic11C2311yescharacteristic
169C2×C22⋊Dic11C2311yescharacteristic
170#66999C2×C418yescomplemented
171Q8×Dic11—24no—
172#66983C2×C418yescomplemented
173C2×(C2×D11)⋊C4C2311yescharacteristic
174C2×(C2×D11)⋊C4C2312yes—
175C2×(C2×D11)⋊C4C2312yes—
176C2×(C2×D11)⋊C4C2311yescharacteristic
177C2×(C2×D11)⋊C4C2311yescharacteristic
178C2×(C2×D11)⋊C4C2311yescharacteristic
179C2×(C2×D11)⋊C4C2312yes—
180C2×(C2×D11)⋊C4C2312yes—
181C2×(C2×D11)⋊C4C2312yes—
182C2×(C2×D11)⋊C4C2311yescharacteristic
183C2×(C2×D11)⋊C4C2311yescharacteristic
184C2×(C2×D11)⋊C4C2312yes—
185C2×(C2×D11)⋊C4C2312yes—
186C2×(C2×D11)⋊C4C2312yes—
187C2×(C2×D11)⋊C4C2311yescharacteristic
188C2×(C2×D11)⋊C4C2311yescharacteristic
189C2×(C2×D11)⋊C4C2312yes—
190C2×(C2×D11)⋊C4C2312yes—
191C2×(C2×D11)⋊C4C2312yes—
192C2×(C2×D11)⋊C4C2312yes—
193#66979—24no—
194C2×C4⋊Dic11C2312yes—
195C2×C4⋊Dic11C2311yescharacteristic
196C2×C4⋊Dic11C2312yes—
197C2×C4⋊Dic11C2311yescharacteristic
198C2×C4⋊Dic11C2311yescharacteristic
199C2×Dic11⋊C4C2311yescharacteristic
200C2×Dic11⋊C4C2312yes—
201C2×Dic11⋊C4C2311yescharacteristic
202C2×Dic11⋊C4C2311yescharacteristic
203C2×Dic11⋊C4C2311yescharacteristic
204C2×Dic11⋊C4C2312yes—
205C2×Dic11⋊C4C2312yes—
206C2×Dic11⋊C4C2312yes—
207C2×Dic11⋊C4C2312yes—
208C2×C4×Dic11C2312yes—
209C2×C4×Dic11C2312yes—
210C2×C4×Dic11C2312yes—
211C2×C4×Dic11C2311yescharacteristic
212C2×C4×Dic11C2311yescharacteristic
213C2×C4×Dic11C2312yes—
214C2×C4×Dic11C2312yes—
215C2×C4×Dic11C2312yes—
216C2×C4×Dic11C2312yes—
217C2×C4×Dic11C2312yes—
218#66948C2×C418yescomplemented
219#66947C2×C4116yescomplemented
220#66946—28no—
221#66946—24no—
222#66946C2×C4116yescomplemented
223#66945—24no—
224#66945—24no—
225#66945C2×C418yescomplemented
226C4⋊C4×D11—24no—
227C4⋊C4×D11—28no—
228C4⋊C4×D11D418yescomplemented
229#66935C2×C4116yescomplemented
230(C22⋊D11)⋊C4C2×C4116yescomplemented
231C22⋊C4×D11—28no—
232#66930—28no—
233C4×D44—28no—
234C4×D44—24no—
235#66925—24no—
236#66925—24no—
237#66925—28no—
238#66925—28no—
239C42×D11—28no—
240C11×#95C2312yes—
241C11×#95C2312yes—
242C11×#95C2312yes—
243C11×#95C2312yes—
244C11×#95C2311yescharacteristic
245C11×#95C2311yescharacteristic
246C11⋊#95C2311yescharacteristic
247C11⋊#95C2312yes—
248C11⋊#95C2312yes—
249C11⋊#95C2312yes—
250C11⋊#95C2312yes—
251C11⋊#95C2311yescharacteristic
252C11⋊#95C2312yes—
253C11⋊#95C2311yescharacteristic
254C11⋊#95C2311yescharacteristic
255C11⋊#95C2311yescharacteristic
256C11⋊#95C2311yescharacteristic
257C11⋊#95C2312yes—
258C11⋊#95C2312yes—
259C11⋊#95C2312yes—
260#34201—111nomaximal, Sylow
261C24×C11C2411yescharacteristic
262C23×D11—22no—
263C23×D11—22no—
264C23×D11—41no—
265C23×D11—41no—
266C23×D11—41no—
267C23×D11—41no—
268C23×D11C22×C414yes—
269C23×D11C2411yescharacteristic
270C23×D11C2412yes—
271C23×D11C2411yescharacteristic
272C2×Q8×C11—22no—
273C2×Q8×C11—22no—
274C2×Q8×C11C22×C414yes—
275C22×C4×C11—22no—
276C22×C4×C11—22no—
277C22×C4×C11C22×C414yes—
278C22×C4×C11C2411yescharacteristic
279C22×C4×C11C2411yescharacteristic
280C22×C4×C11C2411yescharacteristic
281C22×C4×C11C2412yes—
282C22×C4×C11C2411yescharacteristic
283C22×C4×C11C2412yes—
284C22×C4×C11C2411yescharacteristic
285C22×C4×C11C2412yes—
286C22×C4×C11C2412yes—
287C22×C4×C11C2411yescharacteristic
288C2×C22⋊D11—42no—
289C2×C22⋊D11—42no—
290C2×C22⋊D11C22×C418yes—
291C22×Dic11—22no—
292C22×Dic11—22no—
293C22×Dic11C22×C414yes—
294C22×Dic11C2411yescharacteristic
295C22×Dic11C2411yescharacteristic
296C22×Dic11C2411yescharacteristic
297C22×Dic11C2412yes—
298C22×Dic11C2411yescharacteristic
299C22×Dic11C2411yescharacteristic
300C22×Dic11C2412yes—
301C22×Dic11C2412yes—
302C22×Dic11C2411yescharacteristic
303#4343—232no—
304C2×D44—24no—
305C2×D44—24no—
306C2×D44—22no—
307C2×D44—22no—
308C2×D44—42no—
309C2×D44—42no—
310C2×D44C22×C418yes—
311C2×D44C22×C414yes—
312C2×D44C22×C418yes—
313C2×C4×D11—22no—
314C2×C4×D11—24no—
315C2×C4×D11—22no—
316C2×C4×D11—24no—
317C2×C4×D11—232no—
318C2×C4×D11—24no—
319C2×C4×D11—22no—
320C2×C4×D11—24no—
321C2×C4×D11—22no—
322C2×C4×D11—22no—
323C2×C4×D11—24no—
324C2×C4×D11—22no—
325C2×C4×D11—42no—
326C2×C4×D11—42no—
327C2×C4×D11—42no—
328C2×C4×D11—42no—
329C2×C4×D11—42no—
330C2×C4×D11—42no—
331C2×C4×D11—42no—
332C2×C4×D11—42no—
333C2×C4×D11C22×C418yes—
334C2×C4×D11C22×C414yes—
335C2×C4×D11C22×C414yes—
336C2×C4×D11C22×C414yes—
337C2×C4×D11C22×C414yes—
338C2×C4×D11C2×D418yes—
339C2×C4×D11C2×D414yes—
340C2×C4×D11#4114yes—
341C11×C4⋊C4—22no—
342C11×C4⋊C4—24no—
343C11×C4⋊C4—42no—
344C11×C4⋊C4C22×C414yes—
345C11×C4⋊C4C22×C418yes—
346C11×C4⋊C4C2×D414yes—
347C11×C22⋊C4—24no—
348C11×C22⋊C4—41no—
349C11×C22⋊C4—41no—
350C11×C22⋊C4C22×C418yes—
351C42×C11—24no—
352C42×C11—24no—
353C42×C11—22no—
354C42×C11—22no—
355C42×C11—42no—
356C22⋊Dic11—24no—
357C22⋊Dic11—41no—
358C22⋊Dic11—41no—
359(C2×D11)⋊C4—24no—
360(C2×D11)⋊C4—24no—
361(C2×D11)⋊C4—22no—
362(C2×D11)⋊C4—22no—
363(C2×D11)⋊C4—22no—
364(C2×D11)⋊C4—22no—
365(C2×D11)⋊C4—24no—
366(C2×D11)⋊C4—24no—
367(C2×D11)⋊C4—41no—
368(C2×D11)⋊C4—41no—
369(C2×D11)⋊C4—42no—
370(C2×D11)⋊C4—42no—
371(C2×D11)⋊C4—41no—
372(C2×D11)⋊C4—42no—
373(C2×D11)⋊C4—42no—
374(C2×D11)⋊C4—41no—
375(C2×D11)⋊C4C22×C418yes—
376(C2×D11)⋊C4C22×C418yes—
377(C2×D11)⋊C4C22×C418yes—
378(C2×D11)⋊C4C22×C418yes—
379C4⋊Dic11—24no—
380C4⋊Dic11—22no—
381C4⋊Dic11—42no—
382C4⋊Dic11C22×C414yes—
383C4⋊Dic11C2×D414yes—
384Dic11⋊C4—22no—
385Dic11⋊C4—24no—
386Dic11⋊C4—22no—
387Dic11⋊C4—22no—
388Dic11⋊C4—22no—
389Dic11⋊C4—42no—
390Dic11⋊C4—42no—
391Dic11⋊C4C22×C418yes—
392Dic11⋊C4C2×D418yes—
393C4×Dic11—24no—
394C4×Dic11—24no—
395C4×Dic11—24no—
396C4×Dic11—24no—
397C4×Dic11—22no—
398C4×Dic11—22no—
399C4×Dic11—42no—
400C4×Dic11—42no—
401C4×Dic11—42no—
402C4×Dic11C22×C418yes—
403C2×#525—111no—
404C2×#520—111no—
405C22×#117—111no—
406#2363—111no—
407#2363—111no—
408#2363—111no—
409#2363—111no—
410#2362—111no—
411#2362—111no—
412#2362—111no—
413#2362D1111yescharacteristic, complemented
414#2354—112no—
415#2354—112no—
416#2352—112no—
417#2352—112no—
418#2321—112no—
419#2321—112no—
420#2317—111no—
421#2311—111no—
422C4×#123—112no—
423C4×#123—112no—
424#2280—111no—
425#2274—111no—
426C23×C11—21no—
427C23×C11—21no—
428C23×C11—21no—
429C23×C11—21no—
430C23×C11—21no—
431C23×C11—21no—
432C23×C11C23×C412yes—
433C23×C11C2511yescharacteristic
434C22×D11—21no—
435C22×D11—21no—
436C22×D11—21no—
437C22×D11—21no—
438C22×D11—21no—
439C22×D11—22no—
440C22×D11—21no—
441C22×D11—22no—
442C22×D11—22no—
443C22×D11—22no—
444C22×D11—21no—
445C22×D11—21no—
446C22×D11—22no—
447C22×D11—22no—
448C22×D11—21no—
449C22×D11—21no—
450C22×D11—28no—
451C22×D11—44no—
452C22×D11—44no—
453C22×D11—44no—
454C22×D11—44no—
455C22×D11—44no—
456C22×D11—44no—
457C22×D11C23×C412yes—
458C22×D11C23×C414yes—
459C22×D11C23×C412yes—
460C22×D11C22×D412yes—
461C22×D11C2×#4112yes—
462Q8×C11—28no—
463C2×C4×C11—21no—
464C2×C4×C11—22no—
465C2×C4×C11—21no—
466C2×C4×C11—22no—
467C2×C4×C11—22no—
468C2×C4×C11—22no—
469C2×C4×C11—22no—
470C2×C4×C11—22no—
471C2×C4×C11—28no—
472C2×C4×C11—22no—
473C2×C4×C11—21no—
474C2×C4×C11—21no—
475C2×C4×C11—21no—
476C2×C4×C11—21no—
477C2×C4×C11—21no—
478C2×C4×C11—21no—
479C2×C4×C11—22no—
480C2×C4×C11—21no—
481C2×C4×C11—21no—
482C2×C4×C11—22no—
483C2×C4×C11—21no—
484C2×C4×C11—21no—
485C2×C4×C11—21no—
486C2×C4×C11—21no—
487C2×C4×C11C23×C414yes—
488C2×C4×C11C23×C414yes—
489C2×C4×C11C23×C412yes—
490C2×C4×C11C23×C412yes—
491C2×C4×C11C22×D414yes—
492C2×C4×C11C22×D412yes—
493C2×C4×C11C2×#4112yes—
494C22⋊D11—48no—
495C2×Dic11—21no—
496C2×Dic11—21no—
497C2×Dic11—22no—
498C2×Dic11—22no—
499C2×Dic11—22no—
500C2×Dic11—22no—
501C2×Dic11—28no—
502C2×Dic11—21no—
503C2×Dic11—22no—
504C2×Dic11—21no—
505C2×Dic11—21no—
506C2×Dic11—21no—
507C2×Dic11—21no—
508C2×Dic11—21no—
509C2×Dic11—21no—
510C2×Dic11—22no—
511C2×Dic11—21no—
512C2×Dic11—22no—
513C2×Dic11—21no—
514C2×Dic11—21no—
515C2×Dic11—21no—
516C2×Dic11—21no—
517C2×Dic11C23×C414yes—
518C2×Dic11C23×C412yes—
519C2×Dic11C23×C412yes—
520C2×Dic11C22×D414yes—
521C2×Dic11C22×D412yes—
522C2×Dic11C2×#4112yes—
523D44—216no—
524D44—28no—
525D44—48no—
526C4×D11—28no—
527C4×D11—28no—
528C4×D11—28no—
529C4×D11—216no—
530C4×D11—48no—
531C4×D11—48no—
532C4×D11—84no—
533C4×D11—84no—
534C4×D11C4×D4116yes—
535C22×#41—111no—
536C24×C4—111no—
537#525—1116no—
538C2×#123—112no—
539C2×C22⋊Q8—111no—
540C2×C22⋊Q8C2×D1111yescharacteristic
541C2×#121—111no—
542C2×#121—111no—
543C2×#120—112no—
544#520—228no—
545C2×C4×Q8—111no—
546C2×C4×Q8C2×D1111yescharacteristic, complemented
547C2×C4×D4—112no—
548C2×C4×D4—112no—
549C2×C4×D4—111no—
550C2×C4×D4—112no—
551C2×C4×D4—112no—
552C2×C4×D4—111no—
553C2×#117—111no—
554C2×#117—111no—
555C2×#117—111no—
556C2×#117—111no—
557C2×#117—112no—
558C2×#117—111no—
559C2×#117—111no—
560C2×#117—112no—
561C2×#117—112no—
562C2×#117—228no—
563C2×#117C2×D1111yescharacteristic
564C22×C4⋊C4—111no—
565C22×C4⋊C4—111no—
566C22×C4⋊C4—112no—
567C22×C22⋊C4—112no—
568C22×C42—112no—
569#391—111no—
570#391C2×D1111yescharacteristic, complemented
571#390—111no—
572#390—112no—
573#390—112no—
574#390—112no—
575#390—111no—
576#390—112no—
577#389—111no—
578#389—111no—
579#389—111no—
580#389C2×D1111yescharacteristic, complemented
581#388—112no—
582#388—112no—
583#388—112no—
584#388—112no—
585#388—112no—
586#388—112no—
587#388—112no—
588#388—112no—
589#388—112no—
590#388—112no—
591#388C2×D1112yes—
592#388C2×D1112yes—
593#387—112no—
594#387—112no—
595#387—112no—
596#387C2×D1112yescomplemented
597#386—112no—
598#386—112no—
599#386—112no—
600#386—112no—
601#386—112no—
602#386—112no—
603#385—112no—
604#385—112no—
605#384—112no—
606#382—112no—
607#381—111no—
608#381—111no—
609#380—111no—
610#380—111no—
611#380—112no—
612#380—112no—
613#380—111no—
614#380—111no—
615#379—111no—
616#379—111no—
617C4×C4⋊C4—112no—
618C4×C4⋊C4—111no—
619C4×C4⋊C4—111no—
620C4×C4⋊C4—112no—
621C4×C4⋊C4—112no—
622C4×C4⋊C4—111no—
623C4×C4⋊C4—112no—
624C4×C4⋊C4—112no—
625C4×C4⋊C4C2×D1112yescomplemented
626C4×C4⋊C4C2×D1111yescharacteristic, complemented
627C4×C22⋊C4—111no—
628C4×C22⋊C4—112no—
629C4×C22⋊C4—112no—
630C4×C22⋊C4—112no—
631C4×C22⋊C4—111no—
632C4×C22⋊C4—111no—
633C4×C22⋊C4—112no—
634C4×C22⋊C4—112no—
635C4×C22⋊C4—112no—
636C4×C22⋊C4C2×D1111yescharacteristic
637C22×C11—22no—
638C22×C11—22no—
639C22×C11—22no—
640C22×C11—41no—
641C22×C11—41no—
642C22×C11—41no—
643C22×C11—41no—
644C22×C11C24×C411yescharacteristic
645C22×C11C23×D411yescharacteristic
646C22×C11C22×#4111yescharacteristic
647C22×C11#58511yescharacteristic
648C22×C11#58511yescharacteristic
649C22×C11#58511yescharacteristic
650C22×C11#58511yescharacteristic
651C2×D11—22no—
652C2×D11—22no—
653C2×D11—22no—
654C2×D11—22no—
655C2×D11—22no—
656C2×D11—22no—
657C2×D11—22no—
658C2×D11—24no—
659C2×D11—22no—
660C2×D11—22no—
661C2×D11—24no—
662C2×D11—24no—
663C2×D11—416no—
664C2×D11—41no—
665C2×D11—42no—
666C2×D11—42no—
667C2×D11—41no—
668C2×D11—42no—
669C2×D11—42no—
670C2×D11—41no—
671C2×D11—41no—
672C2×D11C2×C4×D414yes—
673C4×C11—22no—
674C4×C11—24no—
675C4×C11—24no—
676C4×C11—24no—
677C4×C11—41no—
678C4×C11—41no—
679C4×C11—42no—
680C4×C11—41no—
681C4×C11—41no—
682C4×C11C2×C4×D414yes—
683Dic11—22no—
684Dic11—24no—
685Dic11—24no—
686Dic11—41no—
687Dic11—42no—
688Dic11—41no—
689Dic11—41no—
690Dic11—41no—
691Dic11C2×C4×D414yes—
692C25—111no—
693C2×#41—118no—
694C2×#41—224no—
695C2×#41—224no—
696C22×Q8C22×D1111yescharacteristic
697C22×D4—112no—
698C22×D4—112no—
699C22×D4—111no—
700C22×D4—112no—
701C23×C4—111no—
702C23×C4—111no—
703C23×C4—118no—
704C23×C4—112no—
705C23×C4—111no—
706C23×C4—111no—
707C23×C4—111no—
708C23×C4—112no—
709C23×C4—112no—
710C23×C4—112no—
711C23×C4—112no—
712C23×C4—224no—
713C23×C4—224no—
714C23×C4C22×D1111yescharacteristic
715#123—1116no—
716C22⋊Q8—118no—
717C22⋊Q8C4×D1118yescomplemented
718#121—118no—
719#121—118no—
720#120—1116no—
721C4×Q8—24no—
722C4×Q8—224no—
723C4×D4—1116no—
724C4×D4—1116no—
725C4×D4—224no—
726C4×D4—228no—
727C4×D4—228no—
728C4×D4—224no—
729#117—24no—
730#117—118no—
731#117—228no—
732#117—228no—
733#117—224no—
734#117—224no—
735#117—228no—
736#117—224no—
737#117—224no—
738#117—224no—
739C2×C4⋊C4—112no—
740C2×C4⋊C4—111no—
741C2×C4⋊C4—111no—
742C2×C4⋊C4—112no—
743C2×C4⋊C4—118no—
744C2×C4⋊C4—111no—
745C2×C4⋊C4—112no—
746C2×C4⋊C4—111no—
747C2×C4⋊C4—112no—
748C2×C4⋊C4—111no—
749C2×C4⋊C4—111no—
750C2×C4⋊C4—111no—
751C2×C4⋊C4—112no—
752C2×C4⋊C4—112no—
753C2×C4⋊C4—112no—
754C2×C4⋊C4—228no—
755C2×C4⋊C4—224no—
756C2×C4⋊C4C22×D1111yescharacteristic
757C2×C4⋊C4C22×D1112yes—
758C2×C4⋊C4C22×D1112yes—
759C2×C4⋊C4C22×D1111yescharacteristic
760C2×C4⋊C4C22×D1112yes—
761C2×C4⋊C4C22×D1111yescharacteristic
762C2×C22⋊C4—112no—
763C2×C22⋊C4—112no—
764C2×C22⋊C4—112no—
765C2×C22⋊C4—112no—
766C2×C22⋊C4—112no—
767C2×C22⋊C4—112no—
768C2×C22⋊C4—112no—
769C2×C22⋊C4—111no—
770C2×C22⋊C4—111no—
771C2×C22⋊C4—112no—
772C2×C22⋊C4—112no—
773C2×C22⋊C4—111no—
774C2×C22⋊C4—111no—
775C2×C22⋊C4—111no—
776C2×C22⋊C4—111no—
777C2×C22⋊C4—111no—
778C2×C22⋊C4—111no—
779C2×C22⋊C4—111no—
780C2×C22⋊C4—111no—
781C2×C22⋊C4—112no—
782C2×C22⋊C4—112no—
783C2×C22⋊C4—112no—
784C2×C22⋊C4—112no—
785C2×C22⋊C4—228no—
786C2×C22⋊C4C22×D1112yes—
787C2×C22⋊C4C22×D1111yescharacteristic
788C2×C22⋊C4C22×D1111yescharacteristic
789C2×C22⋊C4C22×D1112yes—
790C2×C42—112no—
791C2×C42—112no—
792C2×C42—112no—
793C2×C42—112no—
794C2×C42—111no—
795C2×C42—112no—
796C2×C42—111no—
797C2×C42—112no—
798C2×C42—112no—
799C2×C42—112no—
800C2×C42—228no—
801C2×C42C22×D1112yes—
802C2×C42C22×D1111yescharacteristic
803C2×C42C22×D1112yes—
804C2×C42C22×D1111yescharacteristic
805C2×C42C22×D1112yes—
806#95—111no—
807#95—111no—
808#95—111no—
809#95—111no—
810#95—111no—
811#95—111no—
812#95—112no—
813#95—112no—
814#95—112no—
815#95—112no—
816#95—112no—
817#95—112no—
818#95—112no—
819#95—112no—
820#95C22×D1111yescharacteristic
821#95C22×D1112yes—
822#95C22×D1112yes—
823#95C22×D1111yescharacteristic
824#95C22×D1112yes—
825#95C22×D1112yes—
826C2×C11—42no—
827C2×C11C22×C4×D411yescharacteristic
828C2×C11#342811yescharacteristic
829C2×C11#342811yescharacteristic
830C2×C11#348511yescharacteristic
831C2×C11#348711yescharacteristic
832C2×C11#349311yescharacteristic
833C2×C11#349311yescharacteristic
834D11—24no—
835D11—44no—
836D11—42no—
837C24—111no—
838C24—111no—
839C24—112no—
840C24—114no—
841C24—222no—
842C24—222no—
843C24—441no—
844C24—441no—
845C24—441no—
846C24—441no—
847C24C23×D1111yescharacteristic
848#41—2232no—
849C2×Q8—22no—
850C2×Q8—22no—
851C2×Q8C2×C4×D1114yes—
852C2×D4—118no—
853C2×D4—118no—
854C2×D4—114no—
855C2×D4—118no—
856C2×D4—224no—
857C2×D4—224no—
858C2×D4—222no—
859C2×D4—222no—
860C2×D4—442no—
861C2×D4—442no—
862C2×D4—442no—
863C2×D4—442no—
864C22×C4—22no—
865C22×C4—22no—
866C22×C4—111no—
867C22×C4—114no—
868C22×C4—114no—
869C22×C4—114no—
870C22×C4—114no—
871C22×C4—111no—
872C22×C4—112no—
873C22×C4—112no—
874C22×C4—114no—
875C22×C4—118no—
876C22×C4—114no—
877C22×C4—114no—
878C22×C4—118no—
879C22×C4—111no—
880C22×C4—111no—
881C22×C4—111no—
882C22×C4—112no—
883C22×C4—111no—
884C22×C4—224no—
885C22×C4—222no—
886C22×C4—222no—
887C22×C4—2232no—
888C22×C4—224no—
889C22×C4—224no—
890C22×C4—222no—
891C22×C4—222no—
892C22×C4—224no—
893C22×C4—222no—
894C22×C4—222no—
895C22×C4—222no—
896C22×C4—222no—
897C22×C4—224no—
898C22×C4—442no—
899C22×C4—442no—
900C22×C4—442no—
901C22×C4—442no—
902C22×C4—442no—
903C22×C4—442no—
904C22×C4—442no—
905C22×C4—442no—
906C22×C4C2×C4×D1114yes—
907C22×C4C23×D1111yescharacteristic
908C22×C4C23×D1111yescharacteristic
909C22×C4C23×D1111yescharacteristic
910C22×C4C23×D1112yes—
911C22×C4C23×D1111yescharacteristic
912C22×C4C23×D1111yescharacteristic
913C22×C4C23×D1112yes—
914C22×C4C23×D1112yes—
915C22×C4C23×D1112yes—
916C22×C4C23×D1111yescharacteristic
917C4⋊C4—22no—
918C4⋊C4—24no—
919C4⋊C4—42no—
920C4⋊C4—114no—
921C4⋊C4—118no—
922C4⋊C4—118no—
923C4⋊C4—114no—
924C4⋊C4—222no—
925C4⋊C4—224no—
926C4⋊C4—224no—
927C4⋊C4—222no—
928C4⋊C4—222no—
929C4⋊C4—222no—
930C4⋊C4—222no—
931C4⋊C4—442no—
932C4⋊C4—442no—
933C4⋊C4—442no—
934C4⋊C4C2×C4×D1114yes—
935C4⋊C4C2×C4×D1118yes—
936C4⋊C4D4×D1114yes—
937C22⋊C4—24no—
938C22⋊C4—41no—
939C22⋊C4—41no—
940C22⋊C4—118no—
941C22⋊C4—118no—
942C22⋊C4—118no—
943C22⋊C4—118no—
944C22⋊C4—224no—
945C22⋊C4—224no—
946C22⋊C4—222no—
947C22⋊C4—222no—
948C22⋊C4—222no—
949C22⋊C4—222no—
950C22⋊C4—224no—
951C22⋊C4—224no—
952C22⋊C4—224no—
953C22⋊C4—442no—
954C22⋊C4—442no—
955C22⋊C4—441no—
956C22⋊C4—441no—
957C22⋊C4—442no—
958C22⋊C4—441no—
959C22⋊C4—442no—
960C22⋊C4—441no—
961C22⋊C4—441no—
962C22⋊C4—441no—
963C22⋊C4C2×C4×D1118yes—
964C42—24no—
965C42—24no—
966C42—22no—
967C42—22no—
968C42—42no—
969C42—118no—
970C42—224no—
971C42—224no—
972C42—224no—
973C42—224no—
974C42—222no—
975C42—222no—
976C42—442no—
977C42—442no—
978C42—442no—
979C11#3420111yescharacteristic, complemented, Sylow
980C23—21no—
981C23—21no—
982C23—21no—
983C23—21no—
984C23—21no—
985C23—21no—
986C23—112no—
987C23—112no—
988C23—112no—
989C23—112no—
990C23—114no—
991C23—228no—
992C23—221no—
993C23—221no—
994C23—221no—
995C23—221no—
996C23—221no—
997C23—222no—
998C23—221no—
999C23—222no—
1000C23—222no—
1001C23—222no—
1002C23—221no—
1003C23—221no—
1004C23—222no—
1005C23—221no—
1006C23—221no—
1007C23—222no—
1008C23—444no—
1009C23—444no—
1010C23—444no—
1011C23—444no—
1012C23—444no—
1013C23—444no—
1014C23C22×C4×D1112yes—
1015C23C24×D1111yescharacteristic
1016Q8—28no—
1017D4—2216no—
1018D4—228no—
1019D4—448no—
1020D4—448no—
1021C2×C4—21no—
1022C2×C4—22no—
1023C2×C4—21no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—28no—
1030C2×C4—21no—
1031C2×C4—22no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—22no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—22no—
1044C2×C4—21no—
1045C2×C4—112no—
1046C2×C4—112no—
1047C2×C4—112no—
1048C2×C4—1116no—
1049C2×C4—114no—
1050C2×C4—112no—
1051C2×C4—114no—
1052C2×C4—228no—
1053C2×C4—2216no—
1054C2×C4—228no—
1055C2×C4—228no—
1056C2×C4—221no—
1057C2×C4—221no—
1058C2×C4—222no—
1059C2×C4—222no—
1060C2×C4—222no—
1061C2×C4—222no—
1062C2×C4—228no—
1063C2×C4—221no—
1064C2×C4—222no—
1065C2×C4—221no—
1066C2×C4—221no—
1067C2×C4—221no—
1068C2×C4—221no—
1069C2×C4—221no—
1070C2×C4—221no—
1071C2×C4—222no—
1072C2×C4—221no—
1073C2×C4—221no—
1074C2×C4—221no—
1075C2×C4—221no—
1076C2×C4—222no—
1077C2×C4—221no—
1078C2×C4—448no—
1079C2×C4—448no—
1080C2×C4—884no—
1081C2×C4—884no—
1082C2×C4C22×C4×D1114yes—
1083C2×C4C22×C4×D1112yes—
1084C2×C4C22×C4×D1114yes—
1085C2×C4C22×C4×D1112yes—
1086C2×C4C2×D4×D1114yes—
1087C2×C4C2×D4×D1112yes—
1088C2×C4#41×D1112yes—
1089C22—22no—
1090C22—22no—
1091C22—22no—
1092C22—41no—
1093C22—41no—
1094C22—41no—
1095C22—41no—
1096C22—114no—
1097C22—222no—
1098C22—222no—
1099C22—222no—
1100C22—222no—
1101C22—222no—
1102C22—222no—
1103C22—222no—
1104C22—224no—
1105C22—222no—
1106C22—224no—
1107C22—224no—
1108C22—222no—
1109C22—4416no—
1110C22—442no—
1111C22—441no—
1112C22—441no—
1113C22—442no—
1114C22—441no—
1115C22—442no—
1116C22—441no—
1117C22—442no—
1118C22C23×C4×D1111yescharacteristic
1119C22C22×D4×D1111yescharacteristic
1120C22C2×#41×D1111yescharacteristic
1121C22#1062345311yescharacteristic
1122C22#1062345311yescharacteristic
1123C22#1062345711yescharacteristic
1124C22#1062345711yescharacteristic
1125C4—24no—
1126C4—22no—
1127C4—24no—
1128C4—24no—
1129C4—41no—
1130C4—42no—
1131C4—41no—
1132C4—41no—
1133C4—41no—
1134C4—114no—
1135C4—224no—
1136C4—222no—
1137C4—224no—
1138C4—441no—
1139C4—442no—
1140C4—441no—
1141C4—441no—
1142C4—441no—
1143C4C4×D4×D1114yes—
1144C2—42no—
1145C2—224no—
1146C2—442no—
1147C2—444no—
1148C2C2×C4×D4×D1111yescharacteristic
1149C2#1308181511yescharacteristic
1150C2#1308181811yescharacteristic
1151C2#1308225511yescharacteristic
1152C2#1308227311yescharacteristic
1153C2#1308233011yescharacteristic
1154C2#1308233411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2362C2
socle, cosocleC23×C11C25
prime radicalC2×#10623158C2
hypercenter#2362D11
hypocenterC11#34201
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2362

Complements

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

NH ≅ G/Ntype
2. C2×#10623105C2semidirect
3. C2×D11×#117C2semidirect
4. #13071656C2semidirect
5. #13071654C2semidirect
6. #13071653C2semidirect
7. #13071652C2semidirect
8. #13071648C2semidirect
9. #13071647C2semidirect
10. #13071639C2semidirect
11. #13071562C2semidirect
12. #13071561C2semidirect
13. #13071544C2semidirect
14. #13071540C2semidirect
15. #13071278C2semidirect
16. #13071269C2semidirect
17. #13071238C2semidirect
18. #13071207C2semidirect
19. C4×#66947C2semidirect
20. #13071137C2semidirect
21. #13070997C2semidirect
22. #13070970C2semidirect
23. C11×#2362C2semidirect
27. C2×C4×Q8×C11C22semidirect
30. C2×Q8×Dic11C22semidirect
33. #10623158C4semidirect
40. C2×#66946C22semidirect
46. C2×C4⋊C4×D11C22semidirect
52. C2×C4×D44C22semidirect
56. C2×#66925C22semidirect
58. C11×#391C22semidirect
59. C11×#389C22semidirect
62. C11×#387C22semidirect
63. C4×C11×C4⋊C4C22semidirect
64. C4×C11×C4⋊C4C22semidirect
66. #10622843C22semidirect
69. #10622603C22semidirect
72. #10622601C22semidirect
73. #10622598C22semidirect
74. #10622594C22semidirect
75. #10622591C22semidirect
76. #10622589C22semidirect
77. C4⋊C4×Dic11C22semidirect
78. C4⋊C4×Dic11C22semidirect
79. C4⋊C4×Dic11C22semidirect
80. #10622586C22semidirect
92. #10622553C22semidirect
94. #10622552C22semidirect
98. C4×(C2×D11)⋊C4C22semidirect
99. C4×(C2×D11)⋊C4C22semidirect
100. C4×C4⋊Dic11C22semidirect
101. C4×Dic11⋊C4C22semidirect
102. C4×Dic11⋊C4C22semidirect
103. #10622541C22semidirect
105. #10622283C22semidirect
107. #10622282C22semidirect
111. #10622280C22semidirect
112. #10622280C22semidirect
114. #10622279C22semidirect
115. #10622279C22semidirect
122. #10622268C22semidirect
123. #10622263C22semidirect
124. #10622262C22semidirect
125. #10622262C22semidirect
139. C22×C4×D11C2×C4semidirect
149. C11×C22⋊Q8C2×C4semidirect
170. #66999C2×C4semidirect
172. #66983C2×C4semidirect
218. #66948C2×C4semidirect
219. #66947C2×C4semidirect
222. #66946C2×C4semidirect
225. #66945C2×C4semidirect
228. C4⋊C4×D11D4semidirect
229. #66935C2×C4semidirect
230. (C22⋊D11)⋊C4C2×C4semidirect
413. #2362D11semidirect
546. C2×C4×Q8C2×D11semidirect
570. #391C2×D11semidirect
580. #389C2×D11semidirect
596. #387C2×D11semidirect
625. C4×C4⋊C4C2×D11semidirect
626. C4×C4⋊C4C2×D11semidirect
717. C22⋊Q8C4×D11semidirect
979. C11#34201semidirect

Maximal subgroups

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

subgroupindex
C2×#106231582
C2×#106231052
C2×D11×#1172
#130716562
#130716542
#130716532
#130716522
#130716482
#130716472
#130716392
#130715622
#130715612
#130715442
#130715402
#130712782
#130712692
#130712382
#130712072
C4×#669472
#130711372
#130709972
#130709702
C11×#23622
#3420111