Finite Group Databasebeta

← #14926692

Subgroups — #14926692

Order 2816.

2642 conjugacy classes of subgroups.

The subgroup lattice has 1208 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623144C212yesmaximal, complemented
2#13076967C211yesmaximal, characteristic, complemented
3#13076958C211yesmaximal, characteristic, complemented
4#13076895C211yesmaximal, characteristic, complemented
5#13076895C211yesmaximal, characteristic, complemented
6#13074547C212yesmaximal, complemented
7#13074349C212yesmaximal, complemented
8#13073746C212yesmaximal, complemented
9#13073741C212yesmaximal, complemented
10#13073719C212yesmaximal, complemented
11#13073708C212yesmaximal, complemented
12#13073038C211yesmaximal, characteristic, complemented
13#13073036C211yesmaximal, characteristic, complemented
14#13072981C211yesmaximal, characteristic, complemented
15#13072980C211yesmaximal, characteristic, complemented
16#13072207C211yesmaximal, characteristic, complemented
17#13072126C211yesmaximal, characteristic, complemented
18#13072124C211yesmaximal, characteristic, complemented
19#13071318C212yesmaximal, complemented
20#13071132C211yesmaximal, characteristic, complemented
21C4×#66991C211yesmaximal, characteristic, complemented
22C4×C22⋊C4×D11C211yesmaximal, characteristic, complemented
23C11×#2428C211yesmaximal, characteristic, complemented
24C23×C4×D11C2211yescharacteristic
25C2×C11×#127C2211yescharacteristic, complemented
26C2×C11×#121C2212yes—
27C2×C11×#121C2211yescharacteristic
28C2×C11×#121C2211yescharacteristic
29C2×C4×D4×C11C2211yescharacteristic, complemented
30C2×#66992C2212yes—
31C2×#66991C2211yescharacteristic
32C2×#66991C2211yescharacteristic
33C2×#66991C2212yes—
34C2×#66991C2212yes—
35C2×#66991C2211yescharacteristic
36C2×#66991C2211yescharacteristic
37C2×#66990C2212yes—
38C2×#66990C2212yes—
39C2×#66989C2212yes—
40C2×#66988C2212yes—
41C2×D4×Dic11C2211yescharacteristic, complemented
42C2×#66982C2212yes—
43C2×C4×C22⋊D11C2212yes—
44#10623144—216no—
45C2×#66951C2212yes—
46C2×#66949C2212yes—
47C2×#66941C2211yescharacteristic, complemented
48C2×#66938C2212yes—
49C2×(C22⋊D11)⋊C4C2212yes—
50C2×C22⋊C4×D11C2211yescharacteristic
51C2×C22⋊C4×D11C2211yescharacteristic
52C2×#66932C2212yes—
53C2×C42×D11C2211yescharacteristic
54C2×C42×D11C2211yescharacteristic
55C11×#394C2212yescomplemented
56C11×#392C2212yes—
57C11×#390C2211yescharacteristic, complemented
58C11×#389C2211yescharacteristic, complemented
59C11×#386C2212yescomplemented
60C4×C11×C22⋊C4C2211yescharacteristic
61#10622836C2212yes—
62#10622835C2212yes—
63#10622835C2212yes—
64#10622835C2212yescomplemented
65#10622834C2211yescharacteristic, complemented
66#10622834C2212yescomplemented
67#10622834C2212yescomplemented
68#10622834C2211yescharacteristic, complemented
69#10622834C2211yescharacteristic, complemented
70#10622833C2212yes—
71#10622833C2212yes—
72#10622833C2212yescomplemented
73#10622825C2211yescharacteristic
74#10622825C2211yescharacteristic
75#10622823C2212yescomplemented
76C4×C22⋊Dic11C2211yescharacteristic
77C4×C22⋊Dic11C2212yescomplemented
78#10622600C2211yescharacteristic
79#10622600C2211yescharacteristic
80#10622600C2211yescharacteristic
81#10622600C2211yescharacteristic
82#10622599C2212yescomplemented
83#10622589C2211yescharacteristic, complemented
84C4⋊C4×Dic11C2211yescharacteristic, complemented
85#10622586C2211yescharacteristic, complemented
86#10622585C2212yescomplemented
87#10622572C2212yes—
88#10622572C2212yes—
89#10622569C2212yes—
90#10622569C2212yes—
91#10622569C2212yes—
92#10622569C2212yes—
93#10622569C2212yes—
94#10622569C2212yes—
95#10622566C2212yes—
96#10622565C2212yescomplemented
97#10622565C2212yescomplemented
98#10622560C2212yescomplemented
99#10622560C2212yescomplemented
100#10622559C2212yescomplemented
101#10622558C2212yescomplemented
102#10622558C2212yescomplemented
103#10622557C2212yescomplemented
104#10622557C2212yescomplemented
105C22⋊C4×Dic11C2211yescharacteristic
106C22⋊C4×Dic11C2211yescharacteristic
107C22⋊C4×Dic11C2212yescomplemented
108C4×(C2×D11)⋊C4C2211yescharacteristic
109C4×(C2×D11)⋊C4C2211yescharacteristic
110#10622548C2211yescharacteristic, complemented
111C4×C4⋊Dic11C2211yescharacteristic, complemented
112#10622541C2211yescharacteristic, complemented
113#10622541C2211yescharacteristic, complemented
114#10622287C2212yes—
115#10622280C2212yes—
116#10622279C2211yescharacteristic
117#10622279C2211yescharacteristic
118D11×#95C2211yescharacteristic
119D11×#95C2211yescharacteristic
120#10622272C2212yescomplemented
121#10622267C2212yescomplemented
122#10622266C2212yescomplemented
123#10622259C2212yescomplemented
124C24×D11C2311yescharacteristic
125C22×D4×C11C2311yescharacteristic
126C22×D4×C11C2311yescharacteristic
127C22×D4×C11C2312yes—
128C22×D4×C11C2312yes—
129C22×D4×C11C2312yes—
130C22×D4×C11C2312yes—
131C23×C4×C11C2311yescharacteristic
132C23×C4×C11C2312yes—
133C22×C22⋊D11C2312yes—
134C22×C22⋊D11C2312yes—
135C22×C22⋊D11C2312yes—
136C22×C22⋊D11C2312yes—
137C23×Dic11C2312yes—
138C23×Dic11C2311yescharacteristic
139C22×C4×D11—24no—
140C22×C4×D11—42no—
141C22×C4×D11—42no—
142C22×C4×D11C2311yescharacteristic
143C22×C4×D11C2311yescharacteristic
144C22×C4×D11C2311yescharacteristic
145C22×C4×D11C2311yescharacteristic
146C22×C4×D11C2311yescharacteristic
147C22×C4×D11C2311yescharacteristic
148C22×C4×D11C2311yescharacteristic
149C22×C4×D11C2311yescharacteristic
150C22×Dic22C2312yes—
151C11×#127—42no—
152C11×#121—28no—
153C11×#121—42no—
154C11×#121—42no—
155C4×D4×C11—42no—
156C2×C11×C4⋊C4C2311yescharacteristic
157C2×C11×C4⋊C4C2312yes—
158C2×C11×C4⋊C4C2311yescharacteristic
159C2×C11×C22⋊C4C2311yescharacteristic
160C2×C11×C22⋊C4C2312yes—
161C2×C11×C22⋊C4C2312yes—
162C2×C11×C22⋊C4C2312yes—
163C2×C11×C22⋊C4C2312yes—
164C2×C11×C22⋊C4C2312yes—
165C2×C11×C22⋊C4C2311yescharacteristic
166C2×C42×C11C2311yescharacteristic
167C2×C42×C11C2311yescharacteristic
168C2×C22⋊Dic11C2312yes—
169C2×C22⋊Dic11C2312yes—
170C2×C22⋊Dic11C2311yescharacteristic
171C2×C22⋊Dic11C2312yes—
172C2×C22⋊Dic11C2312yes—
173C2×C22⋊Dic11C2312yes—
174C2×C22⋊Dic11C2312yes—
175C2×C22⋊Dic11C2312yes—
176C2×C22⋊Dic11C2312yes—
177C2×C22⋊Dic11C2312yes—
178C2×C22⋊Dic11C2312yes—
179C2×C22⋊Dic11C2312yes—
180C2×C22⋊Dic11C2312yes—
181C2×C22⋊Dic11C2312yes—
182C2×C22⋊Dic11C2311yescharacteristic
183#66992—28no—
184#66991—28no—
185#66991—24no—
186#66991—24no—
187#66991—28no—
188#66991—42no—
189#66991—42no—
190#66990—28no—
191#66990—28no—
192#66989—28no—
193#66988—28no—
194D4×Dic11—42no—
195#66982—28no—
196C4×C22⋊D11—28no—
197C2×(C2×D11)⋊C4C2311yescharacteristic
198C2×(C2×D11)⋊C4C2311yescharacteristic
199C2×(C2×D11)⋊C4C2312yes—
200C2×(C2×D11)⋊C4C2312yes—
201C2×(C2×D11)⋊C4C2312yes—
202C2×(C2×D11)⋊C4C2312yes—
203C2×(C2×D11)⋊C4C2311yescharacteristic
204C2×(C2×D11)⋊C4C2311yescharacteristic
205C2×C4⋊Dic11C2312yes—
206C2×C4⋊Dic11C2311yescharacteristic
207C2×C4⋊Dic11C2312yes—
208C2×C4⋊Dic11C2311yescharacteristic
209C2×C4⋊Dic11C2311yescharacteristic
210C2×C4⋊Dic11C2311yescharacteristic
211C2×Dic11⋊C4C2312yes—
212C2×Dic11⋊C4C2312yes—
213C2×Dic11⋊C4C2312yes—
214C2×Dic11⋊C4C2312yes—
215C2×Dic11⋊C4C2312yes—
216C2×Dic11⋊C4C2312yes—
217C2×C4×Dic11C2311yescharacteristic
218C2×C4×Dic11C2311yescharacteristic
219C2×C4×Dic11C2312yes—
220C2×C4×Dic11C2312yes—
221C2×C4×Dic11C2311yescharacteristic
222C2×C4×Dic11C2311yescharacteristic
223C2×C4×Dic11C2311yescharacteristic
224C2×C4×Dic11C2311yescharacteristic
225#66951—28no—
226#66949—28no—
227#66941—42no—
228#66938—28no—
229(C22⋊D11)⋊C4—28no—
230C22⋊C4×D11—24no—
231C22⋊C4×D11D418yescomplemented
232#66932—28no—
233C42×D11—42no—
234C42×D11—42no—
235C11×#95C2312yes—
236C11×#95C2311yescharacteristic
237C11×#95C2311yescharacteristic
238C11⋊#95C2312yes—
239C11⋊#95C2312yes—
240C11⋊#95C2312yes—
241C11⋊#95C2312yes—
242C11⋊#95C2312yes—
243C11⋊#95C2311yescharacteristic
244C11⋊#95C2312yes—
245C11⋊#95C2312yes—
246C11⋊#95C2312yes—
247C11⋊#95C2312yes—
248C11⋊#95C2311yescharacteristic
249C11⋊#95C2311yescharacteristic
250C11⋊#95C2311yescharacteristic
251C11⋊#95C2311yescharacteristic
252C11⋊#95C2311yescharacteristic
253C11⋊#95C2312yes—
254C11⋊#95C2312yes—
255#35005—111nomaximal, Sylow
256C24×C11C2412yes—
257C24×C11C2412yes—
258C24×C11C2411yescharacteristic
259C23×D11—22no—
260C23×D11—22no—
261C23×D11—41no—
262C23×D11—41no—
263C23×D11—41no—
264C23×D11—41no—
265C23×D11C2×D414yes—
266C23×D11C2411yescharacteristic
267C23×D11C2411yescharacteristic
268C2×D4×C11—24no—
269C2×D4×C11—24no—
270C2×D4×C11—24no—
271C2×D4×C11—22no—
272C2×D4×C11—22no—
273C2×D4×C11—24no—
274C2×D4×C11—22no—
275C2×D4×C11—22no—
276C2×D4×C11—22no—
277C2×D4×C11—22no—
278C2×D4×C11—42no—
279C2×D4×C11—42no—
280C2×D4×C11—42no—
281C2×D4×C11—42no—
282C2×D4×C11—42no—
283C2×D4×C11—42no—
284C2×D4×C11—42no—
285C2×D4×C11—42no—
286C22×C4×C11—22no—
287C22×C4×C11—22no—
288C22×C4×C11—22no—
289C22×C4×C11—24no—
290C22×C4×C11—42no—
291C22×C4×C11—42no—
292C22×C4×C11C2411yescharacteristic
293C22×C4×C11C2411yescharacteristic
294C22×C4×C11C2412yes—
295C22×C4×C11C2412yes—
296C22×C4×C11C2411yescharacteristic
297C22×C4×C11C2411yescharacteristic
298C22×C4×C11C2411yescharacteristic
299C22×C4×C11C2411yescharacteristic
300C2×C22⋊D11—24no—
301C2×C22⋊D11—24no—
302C2×C22⋊D11—24no—
303C2×C22⋊D11—24no—
304C2×C22⋊D11—24no—
305C2×C22⋊D11—24no—
306C2×C22⋊D11—24no—
307C2×C22⋊D11—24no—
308C2×C22⋊D11—42no—
309C2×C22⋊D11—42no—
310C2×C22⋊D11—42no—
311C2×C22⋊D11—42no—
312C22×Dic11—22no—
313C22×Dic11—24no—
314C22×Dic11—41no—
315C22×Dic11—41no—
316C22×Dic11—42no—
317C22×Dic11—42no—
318C22×Dic11C2411yescharacteristic
319C22×Dic11C2411yescharacteristic
320C22×Dic11C2412yes—
321C22×Dic11C2412yes—
322C22×Dic11C2412yes—
323C22×Dic11C2412yes—
324C22×Dic11C2411yescharacteristic
325C22×Dic11C2411yescharacteristic
326C22×Dic11C2411yescharacteristic
327C22×Dic11C2411yescharacteristic
328C2×C4×D11—22no—
329C2×C4×D11—22no—
330C2×C4×D11—22no—
331C2×C4×D11—22no—
332C2×C4×D11—22no—
333C2×C4×D11—22no—
334C2×C4×D11—22no—
335C2×C4×D11—22no—
336C2×C4×D11—41no—
337C2×C4×D11—41no—
338C2×C4×D11—41no—
339C2×C4×D11—41no—
340C2×C4×D11—41no—
341C2×C4×D11—41no—
342C2×C4×D11—41no—
343C2×C4×D11—41no—
344C2×C4×D11—41no—
345C2×C4×D11—41no—
346C2×C4×D11—41no—
347C2×C4×D11—41no—
348C2×C4×D11—416no—
349C2×C4×D11C2×D414yes—
350C2×C4×D11C2×D414yes—
351C2×C4×D11#4114yes—
352C2×C4×D11#4114yes—
353C2×Dic22—24no—
354C2×Dic22—42no—
355C2×Dic22—42no—
356C11×C4⋊C4—24no—
357C11×C4⋊C4—22no—
358C11×C4⋊C4—22no—
359C11×C22⋊C4—24no—
360C11×C22⋊C4—22no—
361C11×C22⋊C4—42no—
362C11×C22⋊C4—42no—
363C11×C22⋊C4—42no—
364C11×C22⋊C4—42no—
365C11×C22⋊C4C2×D414yes—
366C42×C11—22no—
367C42×C11—22no—
368C22⋊Dic11—24no—
369C22⋊Dic11—24no—
370C22⋊Dic11—24no—
371C22⋊Dic11—22no—
372C22⋊Dic11—24no—
373C22⋊Dic11—24no—
374C22⋊Dic11—24no—
375C22⋊Dic11—24no—
376C22⋊Dic11—24no—
377C22⋊Dic11—24no—
378C22⋊Dic11—42no—
379C22⋊Dic11—42no—
380C22⋊Dic11—42no—
381C22⋊Dic11—42no—
382C22⋊Dic11C2×D414yes—
383(C2×D11)⋊C4—22no—
384(C2×D11)⋊C4—24no—
385(C2×D11)⋊C4—24no—
386(C2×D11)⋊C4—24no—
387(C2×D11)⋊C4—24no—
388(C2×D11)⋊C4—22no—
389(C2×D11)⋊C4C2×D414yes—
390(C2×D11)⋊C4C2×D414yes—
391C4⋊Dic11—24no—
392C4⋊Dic11—24no—
393C4⋊Dic11—22no—
394C4⋊Dic11—22no—
395C4⋊Dic11—22no—
396C4⋊Dic11—22no—
397Dic11⋊C4—24no—
398Dic11⋊C4—24no—
399Dic11⋊C4—24no—
400Dic11⋊C4—24no—
401Dic11⋊C4—42no—
402Dic11⋊C4—42no—
403C4×Dic11—24no—
404C4×Dic11—24no—
405C4×Dic11—22no—
406C4×Dic11—22no—
407C4×Dic11—41no—
408C4×Dic11—41no—
409C4×Dic11—41no—
410C4×Dic11—41no—
411C2×#538—112no—
412#2857—111no—
413#2856—111no—
414#2847—111no—
415#2847—111no—
416#2639—112no—
417#2617—112no—
418#2559—112no—
419#2559—112no—
420#2557—112no—
421#2557—112no—
422#2496—111no—
423#2496—111no—
424#2491—111no—
425#2491—111no—
426#2428—111no—
427#2428D1111yescharacteristic, complemented
428#2422—111no—
429#2422—111no—
430#2325—112no—
431C4×#121—111no—
432C4×#121—111no—
433C2×C4×C22⋊C4—111no—
434C23×C11—21no—
435C23×C11—21no—
436C23×C11—21no—
437C23×C11—21no—
438C23×C11—21no—
439C23×C11—21no—
440C23×C11—22no—
441C23×C11—22no—
442C23×C11—22no—
443C23×C11—22no—
444C23×C11—22no—
445C23×C11—22no—
446C23×C11—22no—
447C23×C11—22no—
448C23×C11—22no—
449C23×C11—22no—
450C23×C11—22no—
451C23×C11—22no—
452C23×C11—22no—
453C23×C11—22no—
454C23×C11C22×D412yes—
455C23×C11C2511yescharacteristic
456C22×D11—21no—
457C22×D11—21no—
458C22×D11—21no—
459C22×D11—21no—
460C22×D11—21no—
461C22×D11—21no—
462C22×D11—21no—
463C22×D11—21no—
464C22×D11—21no—
465C22×D11—21no—
466C22×D11—28no—
467C22×D11—44no—
468C22×D11—44no—
469C22×D11—44no—
470C22×D11—44no—
471C22×D11—44no—
472C22×D11—44no—
473C22×D11C22×D412yes—
474C22×D11C22×D412yes—
475C22×D11C2×#4112yes—
476C22×D11C2×#4112yes—
477D4×C11—44no—
478D4×C11—44no—
479D4×C11—84no—
480D4×C11—84no—
481D4×C11—84no—
482D4×C11—84no—
483C2×C4×C11—21no—
484C2×C4×C11—21no—
485C2×C4×C11—21no—
486C2×C4×C11—21no—
487C2×C4×C11—21no—
488C2×C4×C11—21no—
489C2×C4×C11—22no—
490C2×C4×C11—22no—
491C2×C4×C11—21no—
492C2×C4×C11—21no—
493C2×C4×C11—21no—
494C2×C4×C11—22no—
495C2×C4×C11—22no—
496C2×C4×C11—21no—
497C2×C4×C11—21no—
498C2×C4×C11—22no—
499C2×C4×C11—21no—
500C2×C4×C11—22no—
501C2×C4×C11—44no—
502C2×C4×C11—84no—
503C2×C4×C11C22×D412yes—
504C2×C4×C11C22×D412yes—
505C2×C4×C11C2×#4112yes—
506C2×C4×C11C2×#4112yes—
507C2×C4×C11H(5,𝔽2)12yes—
508C2×C4×C11H(5,𝔽2)12yes—
509C22⋊D11—48no—
510C22⋊D11—48no—
511C22⋊D11—84no—
512C22⋊D11—84no—
513C2×Dic11—21no—
514C2×Dic11—21no—
515C2×Dic11—21no—
516C2×Dic11—21no—
517C2×Dic11—21no—
518C2×Dic11—21no—
519C2×Dic11—21no—
520C2×Dic11—21no—
521C2×Dic11—22no—
522C2×Dic11—22no—
523C2×Dic11—22no—
524C2×Dic11—22no—
525C2×Dic11—22no—
526C2×Dic11—22no—
527C2×Dic11—22no—
528C2×Dic11—22no—
529C2×Dic11—21no—
530C2×Dic11—21no—
531C2×Dic11—21no—
532C2×Dic11—22no—
533C2×Dic11—22no—
534C2×Dic11—21no—
535C2×Dic11—21no—
536C2×Dic11—22no—
537C2×Dic11—21no—
538C2×Dic11—22no—
539C2×Dic11—44no—
540C2×Dic11—84no—
541C2×Dic11C22×D412yes—
542C2×Dic11C22×D412yes—
543C2×Dic11C2×#4112yes—
544C2×Dic11C2×#4112yes—
545C4×D11—28no—
546C4×D11—44no—
547C4×D11—44no—
548C4×D11—44no—
549C4×D11—44no—
550C4×D11—44no—
551C4×D11—44no—
552C4×D11—44no—
553Dic22—84no—
554C24×C4—111no—
555#538—2216no—
556C2×C4⋊Q8—111no—
557C2×#127C2×D1111yescharacteristic, complemented
558C2×#126—112no—
559C2×#126—112no—
560C2×#124—112no—
561C2×#124—112no—
562C2×#123—112no—
563C2×#123—112no—
564C2×C22⋊Q8—112no—
565C2×#121—112no—
566C2×#121—111no—
567C2×#121—111no—
568C2×#121—112no—
569C2×#121—112no—
570C2×#121—111no—
571C2×#121—111no—
572C2×#121C2×D1112yes—
573C2×#121C2×D1111yescharacteristic
574C2×#121C2×D1111yescharacteristic
575C2×#120—112no—
576C2×#120—112no—
577C2×C4×D4—112no—
578C2×C4×D4—111no—
579C2×C4×D4—112no—
580C2×C4×D4C2×D1111yescharacteristic, complemented
581C22×C22⋊C4—111no—
582C22×C22⋊C4—111no—
583C22×C42—111no—
584C22×C42—111no—
585#400—112no—
586#400—112no—
587#397—112no—
588#397—112no—
589#397—112no—
590#397—112no—
591#394—112no—
592#394—112no—
593#394—112no—
594#394—112no—
595#394—112no—
596#394C2×D1112yescomplemented
597#393—112no—
598#393—112no—
599#392—112no—
600#392C2×D1112yes—
601#391—112no—
602#390—111no—
603#390—111no—
604#390—112no—
605#390—112no—
606#390—111no—
607#390C2×D1111yescharacteristic, complemented
608#389—112no—
609#389—111no—
610#389—111no—
611#389—111no—
612#389C2×D1111yescharacteristic, complemented
613#388—112no—
614#388—112no—
615#388—112no—
616#388—112no—
617#387—112no—
618#387—112no—
619#386—112no—
620#386—112no—
621#386—112no—
622#386—112no—
623#386—112no—
624#386—112no—
625#386—112no—
626#386—112no—
627#386—112no—
628#386C2×D1112yescomplemented
629#385—112no—
630#385—112no—
631#384—111no—
632#384—111no—
633#380—111no—
634#380—111no—
635#380—111no—
636#380—111no—
637#380—111no—
638#380—111no—
639#380—112no—
640C4×C4⋊C4—111no—
641C4×C4⋊C4—111no—
642C4×C22⋊C4—111no—
643C4×C22⋊C4—112no—
644C4×C22⋊C4—111no—
645C4×C22⋊C4—111no—
646C4×C22⋊C4—112no—
647C4×C22⋊C4—111no—
648C4×C22⋊C4—111no—
649C4×C22⋊C4—111no—
650C4×C22⋊C4—111no—
651C4×C22⋊C4C2×D1111yescharacteristic
652C2×#95—111no—
653C2×#95—111no—
654C22×C11—22no—
655C22×C11—22no—
656C22×C11—22no—
657C22×C11—41no—
658C22×C11—41no—
659C22×C11—41no—
660C22×C11—41no—
661C22×C11—42no—
662C22×C11—42no—
663C22×C11—42no—
664C22×C11—42no—
665C22×C11—42no—
666C22×C11—42no—
667C22×C11—42no—
668C22×C11—42no—
669C22×C11—42no—
670C22×C11—42no—
671C22×C11—42no—
672C22×C11—42no—
673C22×C11—42no—
674C22×C11—42no—
675C22×C11C23×D411yescharacteristic
676C22×C11C22×#4111yescharacteristic
677C22×C11C22×#4111yescharacteristic
678C22×C11C2×H(5,𝔽2)11yescharacteristic
679C22×C11C2×H(5,𝔽2)11yescharacteristic
680C22×C11#58511yescharacteristic
681C22×C11#58511yescharacteristic
682C2×D11—22no—
683C2×D11—22no—
684C2×D11—22no—
685C2×D11—22no—
686C2×D11—22no—
687C2×D11—22no—
688C2×D11—22no—
689C2×D11—22no—
690C2×D11—22no—
691C2×D11—416no—
692C2×D11—41no—
693C2×D11—41no—
694C2×D11—41no—
695C2×D11—41no—
696C2×D11#53214yes—
697C4×C11—22no—
698C4×C11—22no—
699C4×C11—22no—
700C4×C11—41no—
701C4×C11—42no—
702C4×C11—42no—
703C4×C11—41no—
704C4×C11#53814yescomplemented
705Dic11—22no—
706Dic11—22no—
707Dic11—22no—
708Dic11—22no—
709Dic11—42no—
710Dic11—42no—
711Dic11—41no—
712Dic11—42no—
713Dic11—42no—
714Dic11—41no—
715C25—111no—
716C22×Q8—112no—
717C22×D4—112no—
718C22×D4—112no—
719C22×D4—112no—
720C22×D4—112no—
721C22×D4C22×D1111yescharacteristic
722C22×D4C22×D1111yescharacteristic
723C22×D4C22×D1112yes—
724C22×D4C22×D1112yes—
725C22×D4C22×D1112yes—
726C22×D4C22×D1112yes—
727C23×C4—111no—
728C23×C4—111no—
729C23×C4—111no—
730C23×C4—111no—
731C23×C4—112no—
732C23×C4—111no—
733C23×C4—111no—
734C23×C4—111no—
735C23×C4—111no—
736C23×C4—111no—
737C23×C4—224no—
738C23×C4—442no—
739C23×C4—442no—
740C23×C4C22×D1111yescharacteristic
741C23×C4C22×D1112yes—
742C4⋊Q8—442no—
743#127—42no—
744#126—228no—
745#126—228no—
746#124—228no—
747#124—228no—
748#123—228no—
749#123—228no—
750C22⋊Q8—228no—
751#121—28no—
752#121—42no—
753#121—42no—
754#121—228no—
755#121—228no—
756#121—224no—
757#121—224no—
758#121—228no—
759#121—442no—
760#121—442no—
761#120—228no—
762#120—228no—
763C4×D4—42no—
764C4×D4—228no—
765C4×D4—228no—
766C4×D4—442no—
767C2×C4⋊C4—111no—
768C2×C4⋊C4—112no—
769C2×C4⋊C4—112no—
770C2×C4⋊C4—112no—
771C2×C4⋊C4—112no—
772C2×C4⋊C4—111no—
773C2×C4⋊C4—111no—
774C2×C4⋊C4—111no—
775C2×C4⋊C4—112no—
776C2×C4⋊C4—112no—
777C2×C4⋊C4—112no—
778C2×C4⋊C4—112no—
779C2×C4⋊C4C22×D1111yescharacteristic
780C2×C4⋊C4C22×D1112yes—
781C2×C4⋊C4C22×D1111yescharacteristic
782C2×C22⋊C4—111no—
783C2×C22⋊C4—111no—
784C2×C22⋊C4—111no—
785C2×C22⋊C4—118no—
786C2×C22⋊C4—111no—
787C2×C22⋊C4—112no—
788C2×C22⋊C4—112no—
789C2×C22⋊C4—112no—
790C2×C22⋊C4—112no—
791C2×C22⋊C4—112no—
792C2×C22⋊C4—112no—
793C2×C22⋊C4—112no—
794C2×C22⋊C4—112no—
795C2×C22⋊C4—112no—
796C2×C22⋊C4—111no—
797C2×C22⋊C4—111no—
798C2×C22⋊C4—112no—
799C2×C22⋊C4—112no—
800C2×C22⋊C4—112no—
801C2×C22⋊C4—112no—
802C2×C22⋊C4—112no—
803C2×C22⋊C4—112no—
804C2×C22⋊C4—112no—
805C2×C22⋊C4—112no—
806C2×C22⋊C4—224no—
807C2×C22⋊C4C22×D1111yescharacteristic
808C2×C22⋊C4C22×D1112yes—
809C2×C22⋊C4C22×D1112yes—
810C2×C22⋊C4C22×D1112yes—
811C2×C22⋊C4C22×D1112yes—
812C2×C22⋊C4C22×D1112yes—
813C2×C22⋊C4C22×D1111yescharacteristic
814C2×C42—112no—
815C2×C42—112no—
816C2×C42—111no—
817C2×C42—111no—
818C2×C42—111no—
819C2×C42—111no—
820C2×C42—111no—
821C2×C42—111no—
822C2×C42—442no—
823C2×C42—442no—
824C2×C42C22×D1111yescharacteristic
825C2×C42C22×D1111yescharacteristic
826#95—111no—
827#95—111no—
828#95—111no—
829#95—111no—
830#95—111no—
831#95—111no—
832#95—112no—
833#95—112no—
834#95—112no—
835#95—112no—
836#95—112no—
837#95—112no—
838#95—112no—
839#95—112no—
840#95—112no—
841#95—112no—
842#95—112no—
843#95C22×D1111yescharacteristic
844#95C22×D1111yescharacteristic
845#95C22×D1112yes—
846C2×C11—42no—
847C2×C11—82no—
848C2×C11—82no—
849C2×C11C2×#53211yescharacteristic
850C2×C11C2×#53811yescharacteristic
851C2×C11#345511yescharacteristic
852C2×C11#349611yescharacteristic
853C2×C11#349611yescharacteristic
854C2×C11#350511yescharacteristic
855C2×C11#350611yescharacteristic
856D11—24no—
857D11—42no—
858C24—111no—
859C24—111no—
860C24—114no—
861C24—222no—
862C24—222no—
863C24—441no—
864C24—441no—
865C24—441no—
866C24—441no—
867C24C23×D1112yes—
868C24C23×D1112yes—
869C24C23×D1111yescharacteristic
870C2×Q8—224no—
871C2×Q8—442no—
872C2×Q8—442no—
873C2×D4—24no—
874C2×D4—24no—
875C2×D4—24no—
876C2×D4—22no—
877C2×D4—22no—
878C2×D4—22no—
879C2×D4—22no—
880C2×D4—22no—
881C2×D4—22no—
882C2×D4—24no—
883C2×D4—42no—
884C2×D4—42no—
885C2×D4—42no—
886C2×D4—42no—
887C2×D4—42no—
888C2×D4—42no—
889C2×D4—42no—
890C2×D4—42no—
891C2×D4—224no—
892C2×D4—224no—
893C2×D4—224no—
894C2×D4—224no—
895C2×D4—224no—
896C2×D4—224no—
897C2×D4—224no—
898C2×D4—224no—
899C2×D4—442no—
900C2×D4—442no—
901C2×D4—442no—
902C2×D4—442no—
903C22×C4—22no—
904C22×C4—22no—
905C22×C4—22no—
906C22×C4—24no—
907C22×C4—42no—
908C22×C4—42no—
909C22×C4—111no—
910C22×C4—111no—
911C22×C4—111no—
912C22×C4—111no—
913C22×C4—114no—
914C22×C4—114no—
915C22×C4—114no—
916C22×C4—114no—
917C22×C4—111no—
918C22×C4—111no—
919C22×C4—112no—
920C22×C4—112no—
921C22×C4—112no—
922C22×C4—112no—
923C22×C4—222no—
924C22×C4—222no—
925C22×C4—222no—
926C22×C4—222no—
927C22×C4—224no—
928C22×C4—222no—
929C22×C4—222no—
930C22×C4—222no—
931C22×C4—222no—
932C22×C4—222no—
933C22×C4—441no—
934C22×C4—441no—
935C22×C4—441no—
936C22×C4—441no—
937C22×C4—441no—
938C22×C4—441no—
939C22×C4—441no—
940C22×C4—441no—
941C22×C4—441no—
942C22×C4—441no—
943C22×C4—441no—
944C22×C4—441no—
945C22×C4—4416no—
946C22×C4—441no—
947C22×C4—441no—
948C22×C4—442no—
949C22×C4—442no—
950C22×C4C23×D1111yescharacteristic
951C22×C4C23×D1111yescharacteristic
952C22×C4C23×D1112yes—
953C22×C4C23×D1112yes—
954C22×C4C23×D1111yescharacteristic
955C22×C4C23×D1111yescharacteristic
956C22×C4C23×D1111yescharacteristic
957C22×C4C23×D1111yescharacteristic
958C4⋊C4—24no—
959C4⋊C4—22no—
960C4⋊C4—22no—
961C4⋊C4—224no—
962C4⋊C4—224no—
963C4⋊C4—224no—
964C4⋊C4—224no—
965C4⋊C4—224no—
966C4⋊C4—222no—
967C4⋊C4—222no—
968C4⋊C4—224no—
969C4⋊C4—222no—
970C4⋊C4—222no—
971C4⋊C4—442no—
972C4⋊C4—442no—
973C22⋊C4—24no—
974C22⋊C4—22no—
975C22⋊C4—42no—
976C22⋊C4—42no—
977C22⋊C4—42no—
978C22⋊C4—42no—
979C22⋊C4—114no—
980C22⋊C4—114no—
981C22⋊C4—114no—
982C22⋊C4—222no—
983C22⋊C4—224no—
984C22⋊C4—224no—
985C22⋊C4—224no—
986C22⋊C4—224no—
987C22⋊C4—222no—
988C22⋊C4—224no—
989C22⋊C4—224no—
990C22⋊C4—224no—
991C22⋊C4—224no—
992C22⋊C4—224no—
993C22⋊C4—224no—
994C22⋊C4—224no—
995C22⋊C4—224no—
996C22⋊C4—224no—
997C22⋊C4—222no—
998C22⋊C4—442no—
999C22⋊C4—442no—
1000C22⋊C4—442no—
1001C22⋊C4—442no—
1002C22⋊C4D4×D1114yes—
1003C42—22no—
1004C42—22no—
1005C42—224no—
1006C42—224no—
1007C42—222no—
1008C42—222no—
1009C42—441no—
1010C42—441no—
1011C42—441no—
1012C42—441no—
1013C11#3500511yescharacteristic, complemented, Sylow
1014C23—21no—
1015C23—21no—
1016C23—21no—
1017C23—21no—
1018C23—21no—
1019C23—21no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—112no—
1035C23—112no—
1036C23—112no—
1037C23—112no—
1038C23—228no—
1039C23—221no—
1040C23—221no—
1041C23—221no—
1042C23—221no—
1043C23—221no—
1044C23—221no—
1045C23—221no—
1046C23—221no—
1047C23—221no—
1048C23—221no—
1049C23—444no—
1050C23—444no—
1051C23—444no—
1052C23—444no—
1053C23—444no—
1054C23—444no—
1055C23C2×D4×D1112yes—
1056C23C24×D1111yescharacteristic
1057Q8—884no—
1058D4—44no—
1059D4—44no—
1060D4—84no—
1061D4—84no—
1062D4—84no—
1063D4—84no—
1064D4—448no—
1065D4—448no—
1066D4—884no—
1067D4—884no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—21no—
1077C2×C4—22no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—22no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—44no—
1087C2×C4—84no—
1088C2×C4—112no—
1089C2×C4—112no—
1090C2×C4—112no—
1091C2×C4—112no—
1092C2×C4—221no—
1093C2×C4—221no—
1094C2×C4—221no—
1095C2×C4—221no—
1096C2×C4—221no—
1097C2×C4—221no—
1098C2×C4—221no—
1099C2×C4—221no—
1100C2×C4—228no—
1101C2×C4—222no—
1102C2×C4—222no—
1103C2×C4—222no—
1104C2×C4—222no—
1105C2×C4—221no—
1106C2×C4—222no—
1107C2×C4—221no—
1108C2×C4—221no—
1109C2×C4—222no—
1110C2×C4—221no—
1111C2×C4—222no—
1112C2×C4—222no—
1113C2×C4—222no—
1114C2×C4—222no—
1115C2×C4—221no—
1116C2×C4—221no—
1117C2×C4—222no—
1118C2×C4—222no—
1119C2×C4—444no—
1120C2×C4—444no—
1121C2×C4—444no—
1122C2×C4—444no—
1123C2×C4—444no—
1124C2×C4—444no—
1125C2×C4—444no—
1126C2×C4—444no—
1127C2×C4—884no—
1128C2×C4C2×D4×D1112yes—
1129C2×C4C2×D4×D1112yes—
1130C2×C4#6703712yes—
1131C2×C4#6703712yes—
1132C2×C4#41×D1112yes—
1133C2×C4#41×D1112yes—
1134C22—22no—
1135C22—22no—
1136C22—22no—
1137C22—41no—
1138C22—41no—
1139C22—41no—
1140C22—41no—
1141C22—42no—
1142C22—42no—
1143C22—42no—
1144C22—42no—
1145C22—42no—
1146C22—42no—
1147C22—42no—
1148C22—42no—
1149C22—42no—
1150C22—42no—
1151C22—42no—
1152C22—42no—
1153C22—42no—
1154C22—42no—
1155C22—114no—
1156C22—222no—
1157C22—222no—
1158C22—222no—
1159C22—222no—
1160C22—222no—
1161C22—222no—
1162C22—222no—
1163C22—222no—
1164C22—222no—
1165C22—4416no—
1166C22—441no—
1167C22—441no—
1168C22—441no—
1169C22—441no—
1170C22C22×D4×D1111yescharacteristic
1171C22C2×#6703711yescharacteristic
1172C22C2×#6703711yescharacteristic
1173C22C2×#41×D1111yescharacteristic
1174C22C2×#41×D1111yescharacteristic
1175C22#1062345511yescharacteristic
1176C22#1062345511yescharacteristic
1177C4—22no—
1178C4—22no—
1179C4—22no—
1180C4—42no—
1181C4—42no—
1182C4—41no—
1183C4—41no—
1184C4—222no—
1185C4—222no—
1186C4—222no—
1187C4—222no—
1188C4—442no—
1189C4—442no—
1190C4—442no—
1191C4—442no—
1192C4—441no—
1193C4—441no—
1194C4#1062314414yescomplemented
1195C2—42no—
1196C2—82no—
1197C2—82no—
1198C2—224no—
1199C2—442no—
1200C2D11×#53211yescharacteristic
1201C2C2×#1062314411yescharacteristic
1202C2#1308200011yescharacteristic
1203C2#1308237211yescharacteristic
1204C2#1308237211yescharacteristic
1205C2#1308244311yescharacteristic
1206C2#1308246011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2428C2
hypercenter#2428D11
hypocenterC11#35005
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2428

Complements

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

NH ≅ G/Ntype
1. C2×#10623144C2semidirect
2. #13076967C2semidirect
3. #13076958C2semidirect
4. #13076895C2semidirect
5. #13076895C2semidirect
6. #13074547C2semidirect
7. #13074349C2semidirect
8. #13073746C2semidirect
9. #13073741C2semidirect
10. #13073719C2semidirect
11. #13073708C2semidirect
12. #13073038C2semidirect
13. #13073036C2semidirect
14. #13072981C2semidirect
15. #13072980C2semidirect
16. #13072207C2semidirect
17. #13072126C2semidirect
18. #13072124C2semidirect
19. #13071318C2semidirect
20. #13071132C2semidirect
21. C4×#66991C2semidirect
22. C4×C22⋊C4×D11C2semidirect
23. C11×#2428C2semidirect
25. C2×C11×#127C22semidirect
29. C2×C4×D4×C11C22semidirect
41. C2×D4×Dic11C22semidirect
47. C2×#66941C22semidirect
55. C11×#394C22semidirect
57. C11×#390C22semidirect
58. C11×#389C22semidirect
59. C11×#386C22semidirect
64. #10622835C22semidirect
65. #10622834C22semidirect
66. #10622834C22semidirect
67. #10622834C22semidirect
68. #10622834C22semidirect
69. #10622834C22semidirect
72. #10622833C22semidirect
75. #10622823C22semidirect
77. C4×C22⋊Dic11C22semidirect
82. #10622599C22semidirect
83. #10622589C22semidirect
84. C4⋊C4×Dic11C22semidirect
85. #10622586C22semidirect
86. #10622585C22semidirect
96. #10622565C22semidirect
97. #10622565C22semidirect
98. #10622560C22semidirect
99. #10622560C22semidirect
100. #10622559C22semidirect
101. #10622558C22semidirect
102. #10622558C22semidirect
103. #10622557C22semidirect
104. #10622557C22semidirect
107. C22⋊C4×Dic11C22semidirect
110. #10622548C22semidirect
111. C4×C4⋊Dic11C22semidirect
112. #10622541C22semidirect
113. #10622541C22semidirect
120. #10622272C22semidirect
121. #10622267C22semidirect
122. #10622266C22semidirect
123. #10622259C22semidirect
231. C22⋊C4×D11D4semidirect
427. #2428D11semidirect
557. C2×#127C2×D11semidirect
580. C2×C4×D4C2×D11semidirect
596. #394C2×D11semidirect
607. #390C2×D11semidirect
612. #389C2×D11semidirect
628. #386C2×D11semidirect
704. C4×C11#538semidirect
1013. C11#35005semidirect
1194. C4#10623144semidirect

Maximal subgroups

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

subgroupindex
C2×#106231442
#130769672
#130769582
#130768952
#130745472
#130743492
#130737462
#130737412
#130737192
#130737082
#130730382
#130730362
#130729812
#130729802
#130722072
#130721262
#130721242
#130713182
#130711322
C4×#669912
C4×C22⋊C4×D112
C11×#24282
#3500511