Finite Group Databasebeta

← #14920627

Subgroups — #14920627

Order 2816.

2362 conjugacy classes of subgroups.

The subgroup lattice has 1060 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623237C211yesmaximal, characteristic, complemented
2C2×#10623211C211yesmaximal, characteristic, complemented
3#13074781C212yesmaximal, complemented
4#13074778C211yesmaximal, characteristic, complemented
5#13074775C211yesmaximal, characteristic, complemented
6#13074757C212yesmaximal, complemented
7#13074755C211yesmaximal, characteristic, complemented
8#13074729C211yesmaximal, characteristic, complemented
9#13074717C211yesmaximal, characteristic
10#13074547C211yesmaximal, characteristic, complemented
11#13074545C211yesmaximal, characteristic, complemented
12#13074363C212yesmaximal, complemented
13#13074357C212yesmaximal, complemented
14#13071891C212yesmaximal, complemented
15#13071887C211yesmaximal, characteristic, complemented
16#13071883C211yesmaximal, characteristic, complemented
17#13071859C212yesmaximal, complemented
18#13071855C211yesmaximal, characteristic, complemented
19#13071851C211yesmaximal, characteristic, complemented
20#13071132C212yesmaximal, complemented
21#13071128C212yesmaximal, complemented
22C4×C4⋊C4×D11C211yesmaximal, characteristic, complemented
23C11×#2662C211yesmaximal, characteristic, complemented
24C2×C11×#126C2211yescharacteristic
25C2×C11×#124C2211yescharacteristic
26C2×#66999C2211yescharacteristic
27C2×Q8×Dic11C2211yescharacteristic
28C2×#66991C2211yescharacteristic
29C2×#66991C2212yes—
30C2×D4×Dic11C2211yescharacteristic
31C2×D4×Dic11C2212yes—
32#10623237—28no—
33#10623211—28no—
34C2×#66949C2211yescharacteristic
35C2×#66947C2211yescharacteristic
36C2×#66946C2211yescharacteristic
37C2×#66945C2211yescharacteristic
38C2×C4⋊C4×D11C2212yes—
39C2×#66942C2211yescharacteristic
40C2×#66940C2211yescharacteristic
41C2×#66938C2211yescharacteristic
42C2×#66937C2212yes—
43C2×#66937C2211yescharacteristic
44C2×#66936C2212yes—
45C2×#66936C2211yescharacteristic
46C2×(C22⋊D11)⋊C4C2212yes—
47C2×(C22⋊D11)⋊C4C2211yescharacteristic
48C2×(C22⋊D11)⋊C4C2211yescharacteristic
49C2×(C22⋊D11)⋊C4C2212yes—
50C2×#66932C2212yes—
51C2×#66930C2211yescharacteristic
52C2×#66930C2212yes—
53C2×#66929C2211yescharacteristic
54C2×C42×D11C2212yes—
55C2×C42×D11C2211yescharacteristic
56C2×#66923C2211yescharacteristic
57C11×#396C2212yes—
58C11×#395C2211yescharacteristic
59C11×#394C2211yescharacteristic
60C11×#394C2212yes—
61C11×#393C2211yescharacteristic
62C11×#392C2211yescharacteristic
63C11×#390C2212yes—
64C11×#388C2212yes—
65C4×C11×C4⋊C4C2211yescharacteristic
66#10622844C2211yescharacteristic
67#10622842C2211yescharacteristic
68#10622836C2211yescharacteristic
69#10622836C2212yes—
70#10622835C2211yescharacteristic
71#10622835C2212yes—
72#10622607C2212yes—
73#10622607C2212yes—
74#10622600C2212yes—
75#10622599C2211yescharacteristic
76#10622597C2212yes—
77#10622596C2212yes—
78#10622596C2211yescharacteristic
79#10622592C2212yes—
80C4⋊C4×Dic11C2212yes—
81C4⋊C4×Dic11C2212yes—
82#10622585C2212yes—
83#10622574C2212yes—
84#10622572C2212yes—
85#10622572C2212yes—
86#10622570C2212yes—
87#10622569C2212yes—
88#10622569C2212yes—
89#10622569C2212yes—
90#10622566C2211yescharacteristic
91#10622565C2212yes—
92#10622562C2211yescharacteristic
93#10622562C2212yes—
94#10622561C2212yes—
95#10622561C2212yes—
96#10622561C2212yes—
97#10622561C2212yes—
98#10622561C2212yes—
99#10622560C2212yes—
100#10622558C2212yes—
101#10622558C2212yes—
102C22⋊C4×Dic11C2212yes—
103C22⋊C4×Dic11C2212yes—
104C22⋊C4×Dic11C2212yes—
105#10622553C2212yes—
106C4×C4⋊Dic11C2211yescharacteristic
107C4×Dic11⋊C4C2212yes—
108#10622541C2212yes—
109#10622290C2211yescharacteristic
110#10622287C2211yescharacteristic
111#10622280C2212yes—
112#10622279C2212yes—
113#10622278C2212yes—
114D11×#95C2211yescharacteristic
115D11×#95C2211yescharacteristic
116#10622274C2212yes—
117#10622274C2211yescharacteristic
118#10622272C2211yescharacteristic
119#10622271C2212yes—
120#10622270C2212yes—
121#10622270C2212yes—
122#10622262C2212yes—
123#10622262C2211yescharacteristic
124#10622262C2211yescharacteristic
125C22×Q8×C11C2311yescharacteristic
126C22×D4×C11C2311yescharacteristic
127C22×D4×C11C2312yes—
128C22×C22⋊D11C2311yescharacteristic
129C22×C22⋊D11C2312yes—
130C22×C22⋊D11C2311yescharacteristic
131C22×C22⋊D11C2312yes—
132C23×Dic11C2311yescharacteristic
133C23×Dic11C2312yes—
134C22×D44C2311yescharacteristic
135C22×C4×D11C2311yescharacteristic
136C22×C4×D11C2311yescharacteristic
137C22×C4×D11C2311yescharacteristic
138C22×C4×D11C2312yes—
139C22×C4×D11C2311yescharacteristic
140C22×C4×D11C2312yes—
141C22×Dic22C2311yescharacteristic
142C11×#126—24no—
143C11×#124—24no—
144C2×C11×C4⋊C4C2311yescharacteristic
145C2×C11×C4⋊C4C2311yescharacteristic
146C2×C11×C4⋊C4C2312yes—
147C2×C11×C4⋊C4C2311yescharacteristic
148C2×C11×C4⋊C4C2312yes—
149C2×C11×C22⋊C4C2312yes—
150C2×C11×C22⋊C4C2311yescharacteristic
151C2×C11×C22⋊C4C2312yes—
152C2×C11×C22⋊C4C2311yescharacteristic
153C2×C11×C22⋊C4C2311yescharacteristic
154C2×C11×C22⋊C4C2312yes—
155C2×C11×C22⋊C4C2312yes—
156C2×C11×C22⋊C4C2312yes—
157C2×C11×C22⋊C4C2312yes—
158C2×C42×C11C2312yes—
159C2×C42×C11C2311yescharacteristic
160C2×C22⋊Dic11C2312yes—
161C2×C22⋊Dic11C2311yescharacteristic
162C2×C22⋊Dic11C2312yes—
163C2×C22⋊Dic11C2312yes—
164C2×C22⋊Dic11C2312yes—
165C2×C22⋊Dic11C2312yes—
166C2×C22⋊Dic11C2312yes—
167C2×C22⋊Dic11C2312yes—
168#66999—24no—
169Q8×Dic11—24no—
170#66991—24no—
171#66991—28no—
172D4×Dic11—24no—
173D4×Dic11—44no—
174C2×(C2×D11)⋊C4C2311yescharacteristic
175C2×(C2×D11)⋊C4C2311yescharacteristic
176C2×(C2×D11)⋊C4C2311yescharacteristic
177C2×(C2×D11)⋊C4C2312yes—
178C2×(C2×D11)⋊C4C2311yescharacteristic
179C2×(C2×D11)⋊C4C2311yescharacteristic
180C2×(C2×D11)⋊C4C2312yes—
181C2×(C2×D11)⋊C4C2311yescharacteristic
182C2×(C2×D11)⋊C4C2312yes—
183C2×(C2×D11)⋊C4C2312yes—
184C2×C4⋊Dic11C2311yescharacteristic
185C2×C4⋊Dic11C2311yescharacteristic
186C2×C4⋊Dic11C2312yes—
187C2×C4⋊Dic11C2311yescharacteristic
188C2×C4⋊Dic11C2312yes—
189C2×C4⋊Dic11C2312yes—
190C2×C4⋊Dic11C2312yes—
191C2×Dic11⋊C4C2312yes—
192C2×Dic11⋊C4C2312yes—
193C2×Dic11⋊C4C2311yescharacteristic
194C2×Dic11⋊C4C2311yescharacteristic
195C2×Dic11⋊C4C2311yescharacteristic
196C2×Dic11⋊C4C2312yes—
197C2×Dic11⋊C4C2311yescharacteristic
198C2×Dic11⋊C4C2311yescharacteristic
199C2×Dic11⋊C4C2311yescharacteristic
200C2×Dic11⋊C4C2312yes—
201C2×Dic11⋊C4C2312yes—
202C2×Dic11⋊C4C2312yes—
203C2×Dic11⋊C4C2312yes—
204C2×Dic11⋊C4C2312yes—
205C2×C4×Dic11C2312yes—
206C2×C4×Dic11C2312yes—
207C2×C4×Dic11C2312yes—
208C2×C4×Dic11C2311yescharacteristic
209C2×C4×Dic11C2311yescharacteristic
210C2×C4×Dic11C2312yes—
211C2×C4×Dic11C2311yescharacteristic
212C2×C4×Dic11C2311yescharacteristic
213C2×C4×Dic11C2311yescharacteristic
214#66949—24no—
215#66947—24no—
216#66946—24no—
217#66945—24no—
218C4⋊C4×D11—28no—
219#66942—24no—
220#66940—24no—
221#66938—24no—
222#66937—24no—
223#66937—28no—
224#66936—24no—
225#66936—28no—
226(C22⋊D11)⋊C4—24no—
227(C22⋊D11)⋊C4—28no—
228(C22⋊D11)⋊C4—24no—
229(C22⋊D11)⋊C4—44no—
230#66932—28no—
231#66930—24no—
232#66930—28no—
233#66929—24no—
234C42×D11—44no—
235C42×D11D418yescomplemented
236#66923—24no—
237C11×#95C2312yes—
238C11×#95C2311yescharacteristic
239C11×#95C2311yescharacteristic
240C11×#95C2312yes—
241C11⋊#95C2312yes—
242C11⋊#95C2311yescharacteristic
243C11⋊#95C2311yescharacteristic
244C11⋊#95C2312yes—
245C11⋊#95C2312yes—
246C11⋊#95C2312yes—
247C11⋊#95C2312yes—
248C11⋊#95C2312yes—
249C11⋊#95C2312yes—
250C11⋊#95C2312yes—
251C11⋊#95C2312yes—
252C11⋊#95C2312yes—
253C11⋊#95C2312yes—
254C11⋊#95C2312yes—
255#34594—111nomaximal, Sylow
256C24×C11C2412yes—
257C24×C11C2411yescharacteristic
258C23×D11C2411yescharacteristic
259C23×D11C2411yescharacteristic
260C2×Q8×C11—22no—
261C2×Q8×C11—42no—
262C2×D4×C11—22no—
263C2×D4×C11—24no—
264C2×D4×C11—42no—
265C2×D4×C11—42no—
266C2×D4×C11—42no—
267C22×C4×C11C2412yes—
268C22×C4×C11C2411yescharacteristic
269C22×C4×C11C2411yescharacteristic
270C22×C4×C11C2412yes—
271C22×C4×C11C2411yescharacteristic
272C22×C4×C11C2411yescharacteristic
273C22×C4×C11C2411yescharacteristic
274C22×C4×C11C2411yescharacteristic
275C22×C4×C11C2412yes—
276C2×C22⋊D11—22no—
277C2×C22⋊D11—24no—
278C2×C22⋊D11—22no—
279C2×C22⋊D11—24no—
280C2×C22⋊D11—24no—
281C2×C22⋊D11—24no—
282C2×C22⋊D11—24no—
283C2×C22⋊D11—42no—
284C2×C22⋊D11—42no—
285C2×C22⋊D11—42no—
286C22×Dic11—22no—
287C22×Dic11—24no—
288C22×Dic11—24no—
289C22×Dic11—22no—
290C22×Dic11—22no—
291C22×Dic11—24no—
292C22×Dic11C2412yes—
293C22×Dic11C2411yescharacteristic
294C22×Dic11C2411yescharacteristic
295C22×Dic11C2412yes—
296C22×Dic11C2411yescharacteristic
297C22×Dic11C2412yes—
298C22×Dic11C2411yescharacteristic
299C22×Dic11C2411yescharacteristic
300C22×Dic11C2412yes—
301C22×Dic11C2411yescharacteristic
302C2×D44—22no—
303C2×D44—24no—
304C2×C4×D11—22no—
305C2×C4×D11—22no—
306C2×C4×D11—22no—
307C2×C4×D11—22no—
308C2×C4×D11—22no—
309C2×C4×D11—24no—
310C2×C4×D11—24no—
311C2×C4×D11—42no—
312C2×C4×D11—42no—
313C2×C4×D11—42no—
314C2×C4×D11—42no—
315C2×C4×D11—42no—
316C2×C4×D11C2×D414yes—
317C2×C4×D11C2×D414yes—
318C2×C4×D11C2×D414yes—
319C2×C4×D11#4118yes—
320C2×Dic22—22no—
321C2×Dic22—42no—
322C11×C4⋊C4—22no—
323C11×C4⋊C4—22no—
324C11×C4⋊C4—22no—
325C11×C4⋊C4—24no—
326C11×C4⋊C4—42no—
327C11×C22⋊C4—24no—
328C11×C22⋊C4—22no—
329C11×C22⋊C4—24no—
330C11×C22⋊C4—22no—
331C11×C22⋊C4—22no—
332C11×C22⋊C4—24no—
333C11×C22⋊C4—42no—
334C11×C22⋊C4—42no—
335C11×C22⋊C4—42no—
336C42×C11—42no—
337C42×C11C2×D414yes—
338C22⋊Dic11—24no—
339C22⋊Dic11—22no—
340C22⋊Dic11—24no—
341C22⋊Dic11—24no—
342C22⋊Dic11—24no—
343C22⋊Dic11—42no—
344C22⋊Dic11—42no—
345C22⋊Dic11—42no—
346(C2×D11)⋊C4—22no—
347(C2×D11)⋊C4—24no—
348(C2×D11)⋊C4—22no—
349(C2×D11)⋊C4—22no—
350(C2×D11)⋊C4—22no—
351(C2×D11)⋊C4—22no—
352(C2×D11)⋊C4—22no—
353(C2×D11)⋊C4—24no—
354(C2×D11)⋊C4—42no—
355(C2×D11)⋊C4—42no—
356C4⋊Dic11—24no—
357C4⋊Dic11—22no—
358C4⋊Dic11—24no—
359C4⋊Dic11—22no—
360C4⋊Dic11—22no—
361C4⋊Dic11—24no—
362C4⋊Dic11—42no—
363Dic11⋊C4—24no—
364Dic11⋊C4—22no—
365Dic11⋊C4—22no—
366Dic11⋊C4—22no—
367Dic11⋊C4—24no—
368Dic11⋊C4—24no—
369Dic11⋊C4—24no—
370Dic11⋊C4—24no—
371Dic11⋊C4—22no—
372Dic11⋊C4—22no—
373Dic11⋊C4—22no—
374Dic11⋊C4—24no—
375Dic11⋊C4—42no—
376Dic11⋊C4—42no—
377C4×Dic11—24no—
378C4×Dic11—22no—
379C4×Dic11—22no—
380C4×Dic11—24no—
381C4×Dic11—24no—
382C4×Dic11—42no—
383C4×Dic11C2×D414yes—
384C4×Dic11C2×D414yes—
385C4×Dic11C2×D414yes—
386C2×#529—111no—
387C2×#529—111no—
388#2664—112no—
389#2664—111no—
390#2664—111no—
391#2662—112no—
392#2662—111no—
393#2662D1111yescharacteristic, complemented
394#2659—111no—
395#2656—111no—
396#2639—111no—
397#2639—111no—
398#2618—112no—
399#2618—112no—
400#2396—112no—
401#2396—111no—
402#2396—111no—
403#2392—111no—
404#2392—112no—
405#2392—111no—
406C4×#121—112no—
407C4×#121—112no—
408C2×C4×C4⋊C4—111no—
409C23×C11—22no—
410C23×C11—21no—
411C23×C11—22no—
412C23×C11—22no—
413C23×C11—22no—
414C23×C11—21no—
415C23×C11—22no—
416C23×C11—22no—
417C23×C11—21no—
418C23×C11—22no—
419C23×C11—22no—
420C23×C11—22no—
421C23×C11C2511yescharacteristic
422C22×D11—21no—
423C22×D11—21no—
424C22×D11—22no—
425C22×D11—21no—
426C22×D11—22no—
427C22×D11—21no—
428C22×D11—21no—
429C22×D11—22no—
430C22×D11C22×D412yes—
431C22×D11C2×#4114yes—
432Q8×C11—44no—
433D4×C11—44no—
434D4×C11—48no—
435C2×C4×C11—22no—
436C2×C4×C11—22no—
437C2×C4×C11—21no—
438C2×C4×C11—21no—
439C2×C4×C11—22no—
440C2×C4×C11—22no—
441C2×C4×C11—21no—
442C2×C4×C11—22no—
443C2×C4×C11—21no—
444C2×C4×C11—21no—
445C2×C4×C11—22no—
446C2×C4×C11—22no—
447C2×C4×C11—22no—
448C2×C4×C11—21no—
449C2×C4×C11—21no—
450C2×C4×C11—22no—
451C2×C4×C11—22no—
452C2×C4×C11—22no—
453C2×C4×C11—22no—
454C2×C4×C11C22×D412yes—
455C2×C4×C11C22×D412yes—
456C2×C4×C11C22×D412yes—
457C2×C4×C11C2×#4114yes—
458C22⋊D11—44no—
459C22⋊D11—48no—
460C22⋊D11—44no—
461C22⋊D11—48no—
462C2×Dic11—22no—
463C2×Dic11—22no—
464C2×Dic11—22no—
465C2×Dic11—22no—
466C2×Dic11—21no—
467C2×Dic11—22no—
468C2×Dic11—21no—
469C2×Dic11—21no—
470C2×Dic11—22no—
471C2×Dic11—22no—
472C2×Dic11—22no—
473C2×Dic11—22no—
474C2×Dic11—22no—
475C2×Dic11—22no—
476C2×Dic11—22no—
477C2×Dic11—21no—
478C2×Dic11—21no—
479C2×Dic11—22no—
480C2×Dic11—22no—
481C2×Dic11—22no—
482C2×Dic11—44no—
483C2×Dic11—48no—
484C2×Dic11C22×D412yes—
485C2×Dic11C22×D412yes—
486C2×Dic11C22×D412yes—
487C2×Dic11C2×#4114yes—
488C2×Dic11H(5,𝔽2)12yes—
489C2×Dic112−1+412yes—
490D44—44no—
491C4×D11—28no—
492C4×D11—28no—
493C4×D11—44no—
494C4×D11—48no—
495C4×D11—48no—
496C4×D11—44no—
497Dic22—44no—
498#529—228no—
499#529—228no—
500C2×#126—112no—
501C2×#126—111no—
502C2×#126C2×D1111yescharacteristic
503C2×#125—111no—
504C2×#125—111no—
505C2×#124—111no—
506C2×#124C2×D1111yescharacteristic
507C2×#123—111no—
508C2×#123—111no—
509C2×#123—112no—
510C2×C22⋊Q8—111no—
511C2×C22⋊Q8—111no—
512C2×#121—112no—
513C2×#121—111no—
514C2×#121—112no—
515C2×#121—111no—
516C2×C4×Q8—111no—
517C2×C4×Q8—111no—
518C2×C4×D4—111no—
519C2×C4×D4—112no—
520C2×C4×D4—111no—
521C2×C4×D4—111no—
522C2×C4×D4—111no—
523C2×C4×D4—112no—
524C2×C4×D4—112no—
525C2×#117—111no—
526C2×#117—112no—
527C2×#117—111no—
528C22×C4⋊C4—112no—
529C22×C42—111no—
530C22×C42—112no—
531#400—111no—
532#400—112no—
533#400—111no—
534#399—112no—
535#399—111no—
536#399—111no—
537#398—112no—
538#398—112no—
539#398—111no—
540#398—112no—
541#398—112no—
542#398—112no—
543#398—111no—
544#397—112no—
545#397—111no—
546#397—111no—
547#396—112no—
548#396—112no—
549#396—112no—
550#396—112no—
551#396—112no—
552#396—112no—
553#396—112no—
554#396C2×D1112yes—
555#395—111no—
556#395—112no—
557#395C2×D1111yescharacteristic
558#394—112no—
559#394—111no—
560#394—112no—
561#394—112no—
562#394—112no—
563#394C2×D1112yes—
564#394C2×D1111yescharacteristic
565#393—111no—
566#393—112no—
567#393C2×D1111yescharacteristic
568#392—112no—
569#392—111no—
570#392C2×D1111yescharacteristic
571#390—112no—
572#390C2×D1112yes—
573#389—112no—
574#389—112no—
575#388—112no—
576#388—112no—
577#388—112no—
578#388C2×D1112yes—
579#386—112no—
580#386—112no—
581#386—112no—
582#386—112no—
583#380—112no—
584#380—112no—
585C4×C4⋊C4—112no—
586C4×C4⋊C4—112no—
587C4×C4⋊C4—112no—
588C4×C4⋊C4—111no—
589C4×C4⋊C4—111no—
590C4×C4⋊C4—111no—
591C4×C4⋊C4—112no—
592C4×C4⋊C4C2×D1111yescharacteristic
593C4×C22⋊C4—112no—
594C4×C22⋊C4—112no—
595C4×C22⋊C4—112no—
596C4×C22⋊C4—112no—
597C2×#95—111no—
598C2×#95—111no—
599C22×C11—42no—
600C22×C11—41no—
601C22×C11—42no—
602C22×C11—41no—
603C22×C11—42no—
604C22×C11—41no—
605C22×C11—42no—
606C22×C11—42no—
607C22×C11—42no—
608C22×C11—42no—
609C22×C11—42no—
610C22×C11—42no—
611C22×C11C23×D411yescharacteristic
612C22×C11C22×#4112yes—
613C22×C11C2×H(5,𝔽2)11yescharacteristic
614C22×C11C2×2−1+411yescharacteristic
615C22×C11#58512yes—
616C2×D11—22no—
617C2×D11—22no—
618C2×D11—24no—
619C2×D11—24no—
620C2×D11—41no—
621C2×D11—41no—
622C2×D11—41no—
623C2×D11—42no—
624C2×D11—42no—
625C2×D11#53214yes—
626C4×C11—22no—
627C4×C11—22no—
628C4×C11—22no—
629C4×C11—24no—
630C4×C11—41no—
631C4×C11—41no—
632C4×C11—42no—
633C4×C11—41no—
634C4×C11—42no—
635Dic11—22no—
636Dic11—22no—
637Dic11—24no—
638Dic11—41no—
639Dic11—42no—
640Dic11—41no—
641Dic11—42no—
642Dic11—41no—
643Dic11—42no—
644Dic11#53714yes—
645C22×Q8—111no—
646C22×Q8C22×D1111yescharacteristic
647C22×D4—111no—
648C22×D4—112no—
649C22×D4—111no—
650C22×D4—112no—
651C22×D4—111no—
652C22×D4C22×D1111yescharacteristic
653C22×D4C22×D1112yes—
654C23×C4—111no—
655C23×C4—111no—
656C23×C4—112no—
657C23×C4—111no—
658C23×C4—112no—
659C23×C4—111no—
660C23×C4—111no—
661C23×C4—112no—
662#126—24no—
663#126—228no—
664#126—224no—
665#125—224no—
666#125—224no—
667#124—24no—
668#124—224no—
669#123—228no—
670#123—224no—
671#123—224no—
672C22⋊Q8—224no—
673C22⋊Q8—224no—
674#121—224no—
675#121—228no—
676#121—224no—
677#121—228no—
678C4×Q8—224no—
679C4×Q8—224no—
680C4×D4—224no—
681C4×D4—224no—
682C4×D4—228no—
683C4×D4—224no—
684C4×D4—224no—
685C4×D4—444no—
686C4×D4—444no—
687#117—224no—
688#117—228no—
689#117—224no—
690C2×C4⋊C4—112no—
691C2×C4⋊C4—112no—
692C2×C4⋊C4—112no—
693C2×C4⋊C4—112no—
694C2×C4⋊C4—111no—
695C2×C4⋊C4—111no—
696C2×C4⋊C4—112no—
697C2×C4⋊C4—111no—
698C2×C4⋊C4—111no—
699C2×C4⋊C4—111no—
700C2×C4⋊C4—111no—
701C2×C4⋊C4—112no—
702C2×C4⋊C4—111no—
703C2×C4⋊C4—111no—
704C2×C4⋊C4—111no—
705C2×C4⋊C4—112no—
706C2×C4⋊C4—112no—
707C2×C4⋊C4—112no—
708C2×C4⋊C4—112no—
709C2×C4⋊C4—112no—
710C2×C4⋊C4—112no—
711C2×C4⋊C4—228no—
712C2×C4⋊C4C22×D1112yes—
713C2×C4⋊C4C22×D1111yescharacteristic
714C2×C4⋊C4C22×D1111yescharacteristic
715C2×C4⋊C4C22×D1111yescharacteristic
716C2×C4⋊C4C22×D1112yes—
717C2×C22⋊C4—112no—
718C2×C22⋊C4—111no—
719C2×C22⋊C4—112no—
720C2×C22⋊C4—112no—
721C2×C22⋊C4—112no—
722C2×C22⋊C4—111no—
723C2×C22⋊C4—111no—
724C2×C22⋊C4—111no—
725C2×C22⋊C4—111no—
726C2×C22⋊C4—112no—
727C2×C22⋊C4—111no—
728C2×C22⋊C4—111no—
729C2×C22⋊C4—112no—
730C2×C22⋊C4—112no—
731C2×C22⋊C4—112no—
732C2×C22⋊C4—112no—
733C2×C22⋊C4—112no—
734C2×C22⋊C4—112no—
735C2×C22⋊C4C22×D1111yescharacteristic
736C2×C22⋊C4C22×D1112yes—
737C2×C22⋊C4C22×D1111yescharacteristic
738C2×C22⋊C4C22×D1111yescharacteristic
739C2×C22⋊C4C22×D1112yes—
740C2×C22⋊C4C22×D1112yes—
741C2×C22⋊C4C22×D1112yes—
742C2×C22⋊C4C22×D1112yes—
743C2×C22⋊C4C22×D1112yes—
744C2×C42—111no—
745C2×C42—111no—
746C2×C42—111no—
747C2×C42—118no—
748C2×C42—111no—
749C2×C42—111no—
750C2×C42—112no—
751C2×C42—112no—
752C2×C42—112no—
753C2×C42—112no—
754C2×C42—444no—
755C2×C42C22×D1112yes—
756C2×C42C22×D1111yescharacteristic
757#95—111no—
758#95—112no—
759#95—112no—
760#95—111no—
761#95—112no—
762#95—112no—
763#95—112no—
764#95—112no—
765#95—112no—
766#95—112no—
767#95—112no—
768#95—112no—
769#95—112no—
770#95—112no—
771#95C22×D1111yescharacteristic
772#95C22×D1111yescharacteristic
773#95C22×D1112yes—
774#95C22×D1112yes—
775C2×C11—82no—
776C2×C11—81no—
777C2×C11C2×#53211yescharacteristic
778C2×C11C2×#53711yescharacteristic
779C2×C11#344911yescharacteristic
780C2×C11#345912yes—
781C2×C11#346112yes—
782D11—24no—
783D11—81no—
784C24—111no—
785C24—111no—
786C24C23×D1111yescharacteristic
787C24C23×D1112yes—
788C2×Q8—22no—
789C2×Q8—42no—
790C2×Q8—222no—
791C2×Q8—442no—
792C2×D4—22no—
793C2×D4—24no—
794C2×D4—42no—
795C2×D4—42no—
796C2×D4—42no—
797C2×D4—222no—
798C2×D4—224no—
799C2×D4—222no—
800C2×D4—224no—
801C2×D4—222no—
802C2×D4—224no—
803C2×D4—224no—
804C2×D4—224no—
805C2×D4—224no—
806C2×D4—442no—
807C2×D4—442no—
808C2×D4—442no—
809C22×C4—111no—
810C22×C4—112no—
811C22×C4—111no—
812C22×C4—111no—
813C22×C4—114no—
814C22×C4—114no—
815C22×C4—114no—
816C22×C4—118no—
817C22×C4—112no—
818C22×C4—111no—
819C22×C4—112no—
820C22×C4—111no—
821C22×C4—112no—
822C22×C4—111no—
823C22×C4—222no—
824C22×C4—222no—
825C22×C4—222no—
826C22×C4—222no—
827C22×C4—222no—
828C22×C4—224no—
829C22×C4—224no—
830C22×C4—222no—
831C22×C4—224no—
832C22×C4—224no—
833C22×C4—222no—
834C22×C4—224no—
835C22×C4—222no—
836C22×C4—442no—
837C22×C4—442no—
838C22×C4—442no—
839C22×C4—442no—
840C22×C4—442no—
841C22×C4C23×D1112yes—
842C22×C4C23×D1111yescharacteristic
843C22×C4C23×D1112yes—
844C22×C4C23×D1111yescharacteristic
845C22×C4C23×D1111yescharacteristic
846C22×C4C23×D1111yescharacteristic
847C22×C4C23×D1111yescharacteristic
848C22×C4C23×D1111yescharacteristic
849C22×C4C23×D1112yes—
850C4⋊C4—22no—
851C4⋊C4—22no—
852C4⋊C4—22no—
853C4⋊C4—24no—
854C4⋊C4—42no—
855C4⋊C4—224no—
856C4⋊C4—224no—
857C4⋊C4—224no—
858C4⋊C4—222no—
859C4⋊C4—222no—
860C4⋊C4—222no—
861C4⋊C4—222no—
862C4⋊C4—224no—
863C4⋊C4—224no—
864C4⋊C4—222no—
865C4⋊C4—224no—
866C4⋊C4—222no—
867C4⋊C4—222no—
868C4⋊C4—224no—
869C4⋊C4—222no—
870C4⋊C4—222no—
871C4⋊C4—224no—
872C4⋊C4—224no—
873C4⋊C4—442no—
874C4⋊C4—442no—
875C4⋊C4—442no—
876C22⋊C4—22no—
877C22⋊C4—24no—
878C22⋊C4—22no—
879C22⋊C4—24no—
880C22⋊C4—22no—
881C22⋊C4—24no—
882C22⋊C4—42no—
883C22⋊C4—42no—
884C22⋊C4—42no—
885C22⋊C4—222no—
886C22⋊C4—224no—
887C22⋊C4—222no—
888C22⋊C4—222no—
889C22⋊C4—224no—
890C22⋊C4—222no—
891C22⋊C4—224no—
892C22⋊C4—224no—
893C22⋊C4—224no—
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—
903C42—42no—
904C42—114no—
905C42—114no—
906C42—114no—
907C42—224no—
908C42—224no—
909C42—224no—
910C42—222no—
911C42—222no—
912C42—442no—
913C42D4×D1114yes—
914C11#3459411yescharacteristic, complemented, Sylow
915C23—21no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—21no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—21no—
926C23—22no—
927C23—112no—
928C23—114no—
929C23—221no—
930C23—222no—
931C23—221no—
932C23—221no—
933C23—222no—
934C23—221no—
935C23—222no—
936C23—221no—
937C23C24×D1111yescharacteristic
938Q8—44no—
939Q8—444no—
940D4—44no—
941D4—48no—
942D4—444no—
943D4—444no—
944D4—448no—
945D4—444no—
946D4—448no—
947C2×C4—22no—
948C2×C4—21no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—21no—
953C2×C4—22no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—21no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—21no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—21no—
966C2×C4—112no—
967C2×C4—112no—
968C2×C4—112no—
969C2×C4—112no—
970C2×C4—112no—
971C2×C4—114no—
972C2×C4—228no—
973C2×C4—228no—
974C2×C4—222no—
975C2×C4—222no—
976C2×C4—222no—
977C2×C4—222no—
978C2×C4—221no—
979C2×C4—222no—
980C2×C4—221no—
981C2×C4—222no—
982C2×C4—221no—
983C2×C4—222no—
984C2×C4—222no—
985C2×C4—222no—
986C2×C4—222no—
987C2×C4—222no—
988C2×C4—222no—
989C2×C4—221no—
990C2×C4—222no—
991C2×C4—222no—
992C2×C4—222no—
993C2×C4—221no—
994C2×C4—444no—
995C2×C4—448no—
996C2×C4—444no—
997C2×C4—448no—
998C2×C4—444no—
999C2×C4—448no—
1000C2×C4C2×D4×D1112yes—
1001C2×C4C2×D4×D1112yes—
1002C2×C4C2×D4×D1112yes—
1003C2×C4#41×D1114yes—
1004C22—41no—
1005C22—42no—
1006C22—41no—
1007C22—42no—
1008C22—42no—
1009C22—41no—
1010C22—42no—
1011C22—42no—
1012C22—42no—
1013C22—42no—
1014C22—42no—
1015C22—42no—
1016C22—114no—
1017C22—222no—
1018C22—222no—
1019C22—224no—
1020C22—224no—
1021C22—441no—
1022C22—441no—
1023C22—441no—
1024C22—442no—
1025C22—442no—
1026C22C22×D4×D1111yescharacteristic
1027C22C2×#41×D1112yes—
1028C22D11×H(5,𝔽2)11yescharacteristic
1029C22#1062345512yes—
1030C22D11×2−1+411yescharacteristic
1031C4—22no—
1032C4—22no—
1033C4—22no—
1034C4—24no—
1035C4—41no—
1036C4—41no—
1037C4—42no—
1038C4—41no—
1039C4—42no—
1040C4—114no—
1041C4—222no—
1042C4—222no—
1043C4—224no—
1044C4—442no—
1045C4—441no—
1046C4—442no—
1047C4—441no—
1048C4—441no—
1049C4—442no—
1050C2—82no—
1051C2—81no—
1052C2—224no—
1053C2—881no—
1054C2D11×#53211yescharacteristic
1055C2D11×#53711yescharacteristic
1056C2#1308194711yescharacteristic
1057C2#1308202712yes—
1058C2#1308204212yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2662C2
prime radical#13074717C2
hypercenter#2662D11
hypocenterC11#34594
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2662

Complements

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

NH ≅ G/Ntype
1. C2×#10623237C2semidirect
2. C2×#10623211C2semidirect
3. #13074781C2semidirect
4. #13074778C2semidirect
5. #13074775C2semidirect
6. #13074757C2semidirect
7. #13074755C2semidirect
8. #13074729C2semidirect
10. #13074547C2semidirect
11. #13074545C2semidirect
12. #13074363C2semidirect
13. #13074357C2semidirect
14. #13071891C2semidirect
15. #13071887C2semidirect
16. #13071883C2semidirect
17. #13071859C2semidirect
18. #13071855C2semidirect
19. #13071851C2semidirect
20. #13071132C2semidirect
21. #13071128C2semidirect
22. C4×C4⋊C4×D11C2semidirect
23. C11×#2662C2semidirect
235. C42×D11D4semidirect
393. #2662D11semidirect
914. C11#34594semidirect

Maximal subgroups

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

subgroupindex
C2×#106232372
C2×#106232112
#130747812
#130747782
#130747752
#130747572
#130747552
#130747292
#130747172
#130745472
#130745452
#130743632
#130743572
#130718912
#130718872
#130718832
#130718592
#130718552
#130718512
#130711322
#130711282
C4×C4⋊C4×D112
C11×#26622
#3459411