Finite Group Databasebeta

← #14926693

Subgroups — #14926693

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×#10623091C212yesmaximal, complemented
2#13076966C211yesmaximal, characteristic, complemented
3#13076959C211yesmaximal, characteristic, complemented
4#13076899C211yesmaximal, characteristic, complemented
5#13076895C211yesmaximal, characteristic, complemented
6#13074546C212yesmaximal, complemented
7#13074356C212yesmaximal, complemented
8#13073747C212yesmaximal, complemented
9#13073745C212yesmaximal, complemented
10#13073717C212yesmaximal, complemented
11#13073715C212yesmaximal, complemented
12#13073039C211yesmaximal, characteristic, complemented
13#13073032C211yesmaximal, characteristic, complemented
14#13072980C211yesmaximal, characteristic, complemented
15#13072973C211yesmaximal, characteristic, complemented
16#13072205C211yesmaximal, characteristic, complemented
17#13072198C211yesmaximal, characteristic, complemented
18#13072131C211yesmaximal, characteristic, complemented
19#13072124C211yesmaximal, characteristic, complemented
20#13071314C212yesmaximal, complemented
21C4×#66983C211yesmaximal, characteristic, complemented
22C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
23C4×C11×#121C211yesmaximal, characteristic, complemented
24C23×C4×D11C2211yescharacteristic
25C2×C11×#121C2211yescharacteristic
26C2×C4×D4×C11C2212yes—
27C2×C4×D4×C11C2211yescharacteristic, complemented
28C22×C42×C11C2211yescharacteristic
29C2×#66993C2211yescharacteristic, complemented
30C2×#66992C2212yes—
31C2×#66992C2212yes—
32C2×#66991C2211yescharacteristic
33C2×#66991C2211yescharacteristic
34C2×#66990C2212yes—
35C2×#66983C2211yescharacteristic
36C2×#66983C2212yes—
37C2×#66982C2212yes—
38C2×C4×C22⋊D11C2212yes—
39C22×(C2×D11)⋊C4C2211yescharacteristic
40C22×(C2×D11)⋊C4C2211yescharacteristic
41C22×C4×Dic11C2211yescharacteristic
42#10623091—216no—
43C2×#66951C2212yes—
44C2×#66948C2211yescharacteristic
45C2×#66948C2211yescharacteristic
46C2×#66947C2212yes—
47C2×#66941C2211yescharacteristic, complemented
48C2×#66938C2212yes—
49C2×#66937C2212yes—
50C2×#66935C2212yes—
51C2×#66931C2212yes—
52C2×#66929C2212yes—
53C2×#66928C2212yes—
54C2×C4×D44C2211yescharacteristic, complemented
55C11×#390C2211yescharacteristic, complemented
56C11×#389C2211yescharacteristic, complemented
57C11×#388C2212yescomplemented
58C11×#386C2212yes—
59C11×#380C2211yescharacteristic
60C4×C11×C4⋊C4C2211yescharacteristic, complemented
61C4×C11×C22⋊C4C2212yescomplemented
62#10622834C2211yescharacteristic, complemented
63#10622833C2212yes—
64#10622826C2212yes—
65#10622826C2212yescomplemented
66#10622825C2211yescharacteristic
67#10622823C2212yescomplemented
68C2×C11⋊#95C2211yescharacteristic
69C2×C11⋊#95C2211yescharacteristic
70#10622602C2212yescomplemented
71#10622601C2211yescharacteristic, complemented
72#10622600C2211yescharacteristic
73#10622600C2211yescharacteristic
74#10622600C2211yescharacteristic
75#10622600C2211yescharacteristic
76#10622598C2211yescharacteristic, complemented
77#10622591C2212yescomplemented
78#10622589C2211yescharacteristic, complemented
79#10622589C2211yescharacteristic, complemented
80#10622586C2211yescharacteristic, complemented
81#10622574C2212yescomplemented
82#10622573C2212yes—
83#10622573C2212yes—
84#10622572C2212yes—
85#10622572C2212yes—
86#10622572C2212yescomplemented
87#10622571C2212yes—
88#10622570C2212yescomplemented
89#10622570C2212yescomplemented
90#10622569C2212yes—
91#10622569C2212yes—
92#10622569C2212yescomplemented
93#10622565C2212yescomplemented
94#10622560C2212yescomplemented
95#10622557C2212yescomplemented
96#10622555C2212yes—
97#10622553C2212yescomplemented
98#10622553C2212yescomplemented
99#10622552C2211yescharacteristic, complemented
100C4×(C2×D11)⋊C4C2211yescharacteristic
101C4×(C2×D11)⋊C4C2211yescharacteristic
102C4×(C2×D11)⋊C4C2211yescharacteristic
103C4×(C2×D11)⋊C4C2211yescharacteristic
104C4×(C2×D11)⋊C4C2211yescharacteristic
105C4×(C2×D11)⋊C4C2211yescharacteristic
106C4×(C2×D11)⋊C4C2211yescharacteristic
107C4×(C2×D11)⋊C4C2211yescharacteristic
108C4×(C2×D11)⋊C4C2212yescomplemented
109C4×C4⋊Dic11C2211yescharacteristic, complemented
110#10622546C2212yescomplemented
111#10622541C2211yescharacteristic, complemented
112#10622288C2212yes—
113#10622288C2212yes—
114#10622288C2212yescomplemented
115#10622286C2212yescomplemented
116#10622285C2212yes—
117#10622285C2212yes—
118#10622278C2212yes—
119#10622278C2212yes—
120#10622273C2212yescomplemented
121#10622271C2212yescomplemented
122#10622260C2212yescomplemented
123#10622259C2212yescomplemented
124C24×D11C2311yescharacteristic
125C22×D4×C11C2312yes—
126C22×D4×C11C2311yescharacteristic
127C23×C4×C11C2311yescharacteristic
128C23×C4×C11C2311yescharacteristic
129C23×C4×C11C2312yes—
130C23×C4×C11C2311yescharacteristic
131C22×C22⋊D11C2312yes—
132C22×C22⋊D11C2312yes—
133C22×C22⋊D11C2312yes—
134C22×C22⋊D11C2312yes—
135C22×C22⋊D11C2312yes—
136C23×Dic11C2311yescharacteristic
137C23×Dic11C2311yescharacteristic
138C23×Dic11C2311yescharacteristic
139C22×D44C2311yescharacteristic
140C22×D44C2312yes—
141C22×D44C2312yes—
142C22×C4×D11—24no—
143C22×C4×D11—42no—
144C22×C4×D11—42no—
145C22×C4×D11C2311yescharacteristic
146C22×C4×D11C2311yescharacteristic
147C22×C4×D11C2312yes—
148C22×C4×D11C2311yescharacteristic
149C22×C4×D11C2311yescharacteristic
150C22×Dic22C2312yes—
151C11×#121—24no—
152C4×D4×C11—28no—
153C4×D4×C11—42no—
154C2×C11×C4⋊C4C2311yescharacteristic
155C2×C11×C4⋊C4C2312yes—
156C2×C11×C4⋊C4C2311yescharacteristic
157C2×C11×C4⋊C4C2311yescharacteristic
158C2×C11×C22⋊C4C2312yes—
159C2×C11×C22⋊C4C2312yes—
160C2×C11×C22⋊C4C2312yes—
161C2×C11×C22⋊C4C2312yes—
162C2×C11×C22⋊C4C2312yes—
163C2×C42×C11—42no—
164C2×C42×C11C2311yescharacteristic
165C2×C42×C11C2312yes—
166C2×C42×C11C2311yescharacteristic
167C2×C42×C11C2311yescharacteristic
168C2×C42×C11C2311yescharacteristic
169C2×C22⋊Dic11C2312yes—
170C2×C22⋊Dic11C2312yes—
171C2×C22⋊Dic11C2312yes—
172C2×C22⋊Dic11C2312yes—
173C2×C22⋊Dic11C2312yes—
174#66993—42no—
175#66992—28no—
176#66992—28no—
177#66991—42no—
178#66991—42no—
179#66990—28no—
180#66983—24no—
181#66983—28no—
182#66982—28no—
183C4×C22⋊D11—28no—
184C2×(C2×D11)⋊C4—24no—
185C2×(C2×D11)⋊C4D418yescomplemented
186C2×(C2×D11)⋊C4C2312yes—
187C2×(C2×D11)⋊C4C2312yes—
188C2×(C2×D11)⋊C4C2312yes—
189C2×(C2×D11)⋊C4C2312yes—
190C2×(C2×D11)⋊C4C2312yes—
191C2×(C2×D11)⋊C4C2312yes—
192C2×(C2×D11)⋊C4C2312yes—
193C2×(C2×D11)⋊C4C2311yescharacteristic
194C2×(C2×D11)⋊C4C2311yescharacteristic
195C2×(C2×D11)⋊C4C2312yes—
196C2×(C2×D11)⋊C4C2311yescharacteristic
197C2×(C2×D11)⋊C4C2311yescharacteristic
198C2×(C2×D11)⋊C4C2312yes—
199C2×(C2×D11)⋊C4C2312yes—
200C2×(C2×D11)⋊C4C2312yes—
201C2×(C2×D11)⋊C4C2312yes—
202C2×(C2×D11)⋊C4C2311yescharacteristic
203C2×(C2×D11)⋊C4C2311yescharacteristic
204C2×(C2×D11)⋊C4C2311yescharacteristic
205C2×(C2×D11)⋊C4C2311yescharacteristic
206C2×C4⋊Dic11C2311yescharacteristic
207C2×C4⋊Dic11C2312yes—
208C2×C4⋊Dic11C2311yescharacteristic
209C2×C4⋊Dic11C2311yescharacteristic
210C2×Dic11⋊C4C2312yes—
211C2×Dic11⋊C4C2312yes—
212C2×Dic11⋊C4C2312yes—
213C2×Dic11⋊C4C2312yes—
214C2×Dic11⋊C4C2312yes—
215C2×Dic11⋊C4C2312yes—
216C2×Dic11⋊C4C2312yes—
217C2×C4×Dic11—42no—
218C2×C4×Dic11C2312yes—
219C2×C4×Dic11C2311yescharacteristic
220C2×C4×Dic11C2311yescharacteristic
221C2×C4×Dic11C2311yescharacteristic
222C2×C4×Dic11C2311yescharacteristic
223#66951—28no—
224#66948—42no—
225#66948—42no—
226#66947—28no—
227#66941—42no—
228#66938—28no—
229#66937—28no—
230#66935—28no—
231#66931—28no—
232#66929—28no—
233#66928—28no—
234C4×D44—42no—
235C11×#95C2312yes—
236C11×#95C2312yes—
237C11×#95C2312yes—
238C11⋊#95C2312yes—
239C11⋊#95C2312yes—
240C11⋊#95C2312yes—
241C11⋊#95C2311yescharacteristic
242C11⋊#95C2312yes—
243C11⋊#95C2312yes—
244C11⋊#95C2312yes—
245C11⋊#95C2311yescharacteristic
246C11⋊#95C2312yes—
247C11⋊#95C2312yes—
248C11⋊#95C2312yes—
249C11⋊#95C2311yescharacteristic
250C11⋊#95C2311yescharacteristic
251C11⋊#95C2311yescharacteristic
252C11⋊#95C2311yescharacteristic
253C11⋊#95C2311yescharacteristic
254C11⋊#95C2311yescharacteristic
255#35005—111nomaximal, Sylow
256C24×C11C2412yes—
257C24×C11C2411yescharacteristic
258C23×D11—22no—
259C23×D11—22no—
260C23×D11—41no—
261C23×D11—41no—
262C23×D11—41no—
263C23×D11—41no—
264C23×D11C2×D414yes—
265C23×D11C2412yes—
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—22no—
274C22×C4×C11—22no—
275C22×C4×C11—22no—
276C22×C4×C11—22no—
277C22×C4×C11—24no—
278C22×C4×C11—41no—
279C22×C4×C11—41no—
280C22×C4×C11—41no—
281C22×C4×C11—41no—
282C22×C4×C11—42no—
283C22×C4×C11—42no—
284C22×C4×C11C2×D414yes—
285C22×C4×C11#4114yes—
286C22×C4×C11C2411yescharacteristic
287C22×C4×C11C2411yescharacteristic
288C22×C4×C11C2412yes—
289C22×C4×C11C2412yes—
290C22×C4×C11C2412yes—
291C22×C4×C11C2411yescharacteristic
292C22×C4×C11C2411yescharacteristic
293C22×C4×C11C2411yescharacteristic
294C22×C4×C11C2411yescharacteristic
295C2×C22⋊D11—24no—
296C2×C22⋊D11—24no—
297C2×C22⋊D11—24no—
298C2×C22⋊D11—24no—
299C2×C22⋊D11—24no—
300C2×C22⋊D11—24no—
301C2×C22⋊D11—24no—
302C2×C22⋊D11—42no—
303C2×C22⋊D11—42no—
304C2×C22⋊D11—42no—
305C2×C22⋊D11—42no—
306C2×C22⋊D11—42no—
307C2×C22⋊D11—42no—
308C2×C22⋊D11—42no—
309C2×C22⋊D11—42no—
310C22×Dic11—22no—
311C22×Dic11—41no—
312C22×Dic11—41no—
313C22×Dic11—41no—
314C22×Dic11—41no—
315C22×Dic11—41no—
316C22×Dic11—41no—
317C22×Dic11C2×D414yes—
318C22×Dic11#4114yes—
319C22×Dic11C2411yescharacteristic
320C22×Dic11C2411yescharacteristic
321C22×Dic11C2412yes—
322C22×Dic11C2412yes—
323C22×Dic11C2412yes—
324C22×Dic11C2411yescharacteristic
325C22×Dic11C2411yescharacteristic
326C22×Dic11C2411yescharacteristic
327C22×Dic11C2411yescharacteristic
328C2×D44—24no—
329C2×D44—24no—
330C2×D44—22no—
331C2×D44—22no—
332C2×D44—22no—
333C2×D44—42no—
334C2×D44—42no—
335C2×D44—42no—
336C2×D44—42no—
337C2×C4×D11—24no—
338C2×C4×D11—22no—
339C2×C4×D11—22no—
340C2×C4×D11—22no—
341C2×C4×D11—22no—
342C2×C4×D11—22no—
343C2×C4×D11—22no—
344C2×C4×D11—22no—
345C2×C4×D11—22no—
346C2×C4×D11—41no—
347C2×C4×D11—41no—
348C2×C4×D11—41no—
349C2×C4×D11—41no—
350C2×C4×D11—42no—
351C2×C4×D11—42no—
352C2×C4×D11—416no—
353C2×Dic22—24no—
354C2×Dic22—42no—
355C2×Dic22—42no—
356C11×C4⋊C4—24no—
357C11×C4⋊C4—22no—
358C11×C4⋊C4—22no—
359C11×C4⋊C4—22no—
360C11×C22⋊C4—24no—
361C11×C22⋊C4—24no—
362C11×C22⋊C4—24no—
363C11×C22⋊C4—42no—
364C11×C22⋊C4—42no—
365C42×C11—24no—
366C42×C11—22no—
367C42×C11—22no—
368C42×C11—41no—
369C42×C11—41no—
370C22⋊Dic11—24no—
371C22⋊Dic11—24no—
372C22⋊Dic11—24no—
373C22⋊Dic11—42no—
374C22⋊Dic11—42no—
375(C2×D11)⋊C4—24no—
376(C2×D11)⋊C4—22no—
377(C2×D11)⋊C4—22no—
378(C2×D11)⋊C4—22no—
379(C2×D11)⋊C4—22no—
380(C2×D11)⋊C4—24no—
381(C2×D11)⋊C4—24no—
382(C2×D11)⋊C4—24no—
383(C2×D11)⋊C4—24no—
384(C2×D11)⋊C4—24no—
385(C2×D11)⋊C4—24no—
386(C2×D11)⋊C4—24no—
387(C2×D11)⋊C4—42no—
388(C2×D11)⋊C4—42no—
389(C2×D11)⋊C4—42no—
390(C2×D11)⋊C4—42no—
391(C2×D11)⋊C4C2×D414yes—
392(C2×D11)⋊C4C2×D414yes—
393(C2×D11)⋊C4C2×D414yes—
394(C2×D11)⋊C4C2×D414yes—
395C4⋊Dic11—24no—
396C4⋊Dic11—22no—
397C4⋊Dic11—22no—
398C4⋊Dic11—22no—
399Dic11⋊C4—24no—
400Dic11⋊C4—24no—
401Dic11⋊C4—24no—
402Dic11⋊C4—24no—
403Dic11⋊C4—24no—
404Dic11⋊C4—42no—
405Dic11⋊C4—42no—
406C4×Dic11—24no—
407C4×Dic11—22no—
408C4×Dic11—22no—
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#2428—111no—
428#2422—111no—
429#2422—111no—
430#2325—112no—
431C4×#121—111no—
432C4×#121D1111yescharacteristic, complemented
433C2×C4×C22⋊C4—111no—
434C23×C11—21no—
435C23×C11—21no—
436C23×C11—21no—
437C23×C11—21no—
438C23×C11—22no—
439C23×C11—22no—
440C23×C11—22no—
441C23×C11—22no—
442C23×C11—22no—
443C23×C11—22no—
444C23×C11—22no—
445C23×C11C22×D412yes—
446C23×C11C2×#4112yes—
447C23×C11C2×#4112yes—
448C23×C11C2511yescharacteristic
449C22×D11—28no—
450C22×D11—21no—
451C22×D11—21no—
452C22×D11—21no—
453C22×D11—21no—
454C22×D11—21no—
455C22×D11—21no—
456C22×D11—21no—
457C22×D11—21no—
458C22×D11—21no—
459C22×D11—21no—
460C22×D11—21no—
461C22×D11—21no—
462C22×D11—22no—
463C22×D11—22no—
464C22×D11—22no—
465C22×D11—22no—
466C22×D11—22no—
467C22×D11—22no—
468C22×D11—22no—
469C22×D11—44no—
470C22×D11—44no—
471C22×D11—44no—
472C22×D11—44no—
473C22×D11—44no—
474C22×D11—44no—
475C22×D11C22×D412yes—
476C22×D11C22×D412yes—
477D4×C11—48no—
478D4×C11—44no—
479C2×C4×C11—21no—
480C2×C4×C11—21no—
481C2×C4×C11—21no—
482C2×C4×C11—21no—
483C2×C4×C11—21no—
484C2×C4×C11—21no—
485C2×C4×C11—28no—
486C2×C4×C11—22no—
487C2×C4×C11—22no—
488C2×C4×C11—22no—
489C2×C4×C11—22no—
490C2×C4×C11—21no—
491C2×C4×C11—21no—
492C2×C4×C11—22no—
493C2×C4×C11—22no—
494C2×C4×C11—21no—
495C2×C4×C11—22no—
496C2×C4×C11—21no—
497C2×C4×C11—22no—
498C2×C4×C11—21no—
499C2×C4×C11—21no—
500C2×C4×C11—22no—
501C2×C4×C11—44no—
502C2×C4×C11—44no—
503C2×C4×C11—84no—
504C2×C4×C11C22×D412yes—
505C2×C4×C11C22×D412yes—
506C2×C4×C11C2×#4112yes—
507C2×C4×C11C2×#4112yes—
508C2×C4×C11H(5,𝔽2)12yes—
509C2×C4×C11H(5,𝔽2)12yes—
510C22⋊D11—48no—
511C22⋊D11—84no—
512C22⋊D11—84no—
513C22⋊D11—84no—
514C22⋊D11—84no—
515C2×Dic11—21no—
516C2×Dic11—21no—
517C2×Dic11—21no—
518C2×Dic11—21no—
519C2×Dic11—21no—
520C2×Dic11—21no—
521C2×Dic11—21no—
522C2×Dic11—21no—
523C2×Dic11—22no—
524C2×Dic11—22no—
525C2×Dic11—22no—
526C2×Dic11—22no—
527C2×Dic11—22no—
528C2×Dic11—21no—
529C2×Dic11—21no—
530C2×Dic11—22no—
531C2×Dic11—22no—
532C2×Dic11—21no—
533C2×Dic11—21no—
534C2×Dic11—21no—
535C2×Dic11—21no—
536C2×Dic11—22no—
537C2×Dic11—22no—
538C2×Dic11—44no—
539C2×Dic11—44no—
540C2×Dic11—44no—
541C2×Dic11C22×D412yes—
542C2×Dic11C22×D412yes—
543C2×Dic11C2×#4112yes—
544C2×Dic11C2×#4112yes—
545D44—44no—
546D44—84no—
547D44—84no—
548C4×D11—44no—
549C4×D11—44no—
550C4×D11—44no—
551C4×D11—44no—
552C4×D11—84no—
553Dic22—84no—
554C24×C4—111no—
555#538—2216no—
556C2×C4⋊Q8—111no—
557C2×#127—111no—
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—112no—
567C2×#121—111no—
568C2×#121—112no—
569C2×#121—111no—
570C2×#121—111no—
571C2×#121—111no—
572C2×#121—111no—
573C2×#121—112no—
574C2×#121C2×D1111yescharacteristic
575C2×#120—112no—
576C2×#120—112no—
577C2×C4×D4—112no—
578C2×C4×D4—111no—
579C2×C4×D4C2×D1112yes—
580C2×C4×D4C2×D1111yescharacteristic, complemented
581C22×C22⋊C4—111no—
582C22×C22⋊C4—111no—
583C22×C42—111no—
584C22×C42C2×D1111yescharacteristic
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#394—112no—
597#393—112no—
598#393—112no—
599#392—112no—
600#392—112no—
601#391—112no—
602#390—111no—
603#390—111no—
604#390—112no—
605#390—112no—
606#390—111no—
607#390C2×D1111yescharacteristic, complemented
608#389—111no—
609#389—111no—
610#389—111no—
611#389—112no—
612#389C2×D1111yescharacteristic, complemented
613#388—112no—
614#388—112no—
615#388—112no—
616#388C2×D1112yescomplemented
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×D1112yes—
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—112no—
639#380C2×D1111yescharacteristic
640C4×C4⋊C4—111no—
641C4×C4⋊C4C2×D1111yescharacteristic, complemented
642C4×C22⋊C4—111no—
643C4×C22⋊C4—111no—
644C4×C22⋊C4—111no—
645C4×C22⋊C4—111no—
646C4×C22⋊C4—111no—
647C4×C22⋊C4—111no—
648C4×C22⋊C4—111no—
649C4×C22⋊C4—111no—
650C4×C22⋊C4—112no—
651C4×C22⋊C4C2×D1112yescomplemented
652C2×#95—111no—
653C2×#95—111no—
654C22×C11—22no—
655C22×C11—22no—
656C22×C11—22no—
657C22×C11—22no—
658C22×C11—22no—
659C22×C11—22no—
660C22×C11—42no—
661C22×C11—42no—
662C22×C11—42no—
663C22×C11—42no—
664C22×C11—42no—
665C22×C11—42no—
666C22×C11—42no—
667C22×C11#53214yes—
668C22×C11C23×D411yescharacteristic
669C22×C11C22×#4111yescharacteristic
670C22×C11C22×#4111yescharacteristic
671C22×C11C2×H(5,𝔽2)11yescharacteristic
672C22×C11C2×H(5,𝔽2)11yescharacteristic
673C22×C11#58511yescharacteristic
674C22×C11#58511yescharacteristic
675C2×D11—22no—
676C2×D11—22no—
677C2×D11—22no—
678C2×D11—22no—
679C2×D11—22no—
680C2×D11—22no—
681C2×D11—416no—
682C2×D11—41no—
683C2×D11—41no—
684C2×D11—41no—
685C2×D11—41no—
686C2×D11—41no—
687C2×D11—41no—
688C2×D11—41no—
689C2×D11—41no—
690C2×D11—42no—
691C2×D11—42no—
692C2×D11—42no—
693C2×D11—42no—
694C2×D11—42no—
695C2×D11—42no—
696C2×D11—42no—
697C4×C11—22no—
698C4×C11—22no—
699C4×C11—22no—
700C4×C11—42no—
701C4×C11—42no—
702C4×C11—42no—
703C4×C11—41no—
704C4×C11—41no—
705C4×C11#53814yescomplemented
706Dic11—22no—
707Dic11—22no—
708Dic11—22no—
709Dic11—22no—
710Dic11—42no—
711Dic11—41no—
712Dic11—41no—
713Dic11—42no—
714Dic11—42no—
715C25—111no—
716C22×Q8—112no—
717C22×D4—112no—
718C22×D4—112no—
719C22×D4—112no—
720C22×D4—112no—
721C22×D4—112no—
722C22×D4—111no—
723C22×D4—112no—
724C22×D4—112no—
725C22×D4C22×D1112yes—
726C22×D4C22×D1111yescharacteristic
727C23×C4—111no—
728C23×C4—111no—
729C23×C4—111no—
730C23×C4—111no—
731C23×C4—111no—
732C23×C4—112no—
733C23×C4—111no—
734C23×C4—111no—
735C23×C4—224no—
736C23×C4—442no—
737C23×C4—442no—
738C23×C4C22×D1111yescharacteristic
739C23×C4C22×D1111yescharacteristic
740C23×C4C22×D1112yes—
741C23×C4C22×D1111yescharacteristic
742C4⋊Q8—442no—
743#127—442no—
744#126—228no—
745#126—228no—
746#124—228no—
747#124—228no—
748#123—228no—
749#123—228no—
750C22⋊Q8—228no—
751#121—24no—
752#121—228no—
753#121—228no—
754#121—228no—
755#121—228no—
756#121—224no—
757#121—442no—
758#121—442no—
759#121—442no—
760#121—442no—
761#120—228no—
762#120—228no—
763C4×D4—28no—
764C4×D4—42no—
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—112no—
775C2×C4⋊C4—112no—
776C2×C4⋊C4—112no—
777C2×C4⋊C4—112no—
778C2×C4⋊C4C22×D1112yes—
779C2×C4⋊C4C22×D1111yescharacteristic
780C2×C4⋊C4C22×D1111yescharacteristic
781C2×C4⋊C4C22×D1111yescharacteristic
782C2×C22⋊C4—118no—
783C2×C22⋊C4—111no—
784C2×C22⋊C4—111no—
785C2×C22⋊C4—111no—
786C2×C22⋊C4—111no—
787C2×C22⋊C4—112no—
788C2×C22⋊C4—112no—
789C2×C22⋊C4—112no—
790C2×C22⋊C4—111no—
791C2×C22⋊C4—111no—
792C2×C22⋊C4—111no—
793C2×C22⋊C4—111no—
794C2×C22⋊C4—112no—
795C2×C22⋊C4—112no—
796C2×C22⋊C4—112no—
797C2×C22⋊C4—112no—
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—112no—
807C2×C22⋊C4—112no—
808C2×C22⋊C4—224no—
809C2×C22⋊C4C22×D1112yes—
810C2×C22⋊C4C22×D1112yes—
811C2×C22⋊C4C22×D1112yes—
812C2×C22⋊C4C22×D1112yes—
813C2×C22⋊C4C22×D1112yes—
814C2×C42—42no—
815C2×C42—112no—
816C2×C42—111no—
817C2×C42—111no—
818C2×C42—111no—
819C2×C42—111no—
820C2×C42—442no—
821C2×C42C22×D1111yescharacteristic
822C2×C42C22×D1112yes—
823C2×C42C22×D1111yescharacteristic
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—111no—
833#95—111no—
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×D1112yes—
844#95C22×D1112yes—
845#95C22×D1112yes—
846C2×C11—24no—
847C2×C11—82no—
848C2×C11C2×#53211yescharacteristic
849C2×C11C2×#53811yescharacteristic
850C2×C11#345511yescharacteristic
851C2×C11#349611yescharacteristic
852C2×C11#349611yescharacteristic
853C2×C11#350511yescharacteristic
854C2×C11#350611yescharacteristic
855D11—42no—
856D11—42no—
857D11—82no—
858C24—111no—
859C24—111no—
860C24—114no—
861C24—112no—
862C24—222no—
863C24—222no—
864C24—441no—
865C24—441no—
866C24—441no—
867C24—441no—
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—224no—
880C2×D4—224no—
881C2×D4—224no—
882C2×D4—224no—
883C2×D4—224no—
884C2×D4—224no—
885C2×D4—224no—
886C2×D4—224no—
887C2×D4—224no—
888C2×D4—222no—
889C2×D4—222no—
890C2×D4—222no—
891C2×D4—442no—
892C2×D4—442no—
893C2×D4—442no—
894C2×D4—442no—
895C2×D4—442no—
896C2×D4—442no—
897C2×D4—442no—
898C2×D4—442no—
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—41no—
908C22×C4—41no—
909C22×C4—41no—
910C22×C4—41no—
911C22×C4—42no—
912C22×C4—42no—
913C22×C4—111no—
914C22×C4—111no—
915C22×C4—111no—
916C22×C4—111no—
917C22×C4—114no—
918C22×C4—114no—
919C22×C4—111no—
920C22×C4—111no—
921C22×C4—112no—
922C22×C4—112no—
923C22×C4—112no—
924C22×C4—222no—
925C22×C4—222no—
926C22×C4—222no—
927C22×C4—222no—
928C22×C4—222no—
929C22×C4—222no—
930C22×C4—222no—
931C22×C4—222no—
932C22×C4—222no—
933C22×C4—224no—
934C22×C4—441no—
935C22×C4—441no—
936C22×C4—441no—
937C22×C4—441no—
938C22×C4—442no—
939C22×C4—442no—
940C22×C4—4416no—
941C22×C4—441no—
942C22×C4—441no—
943C22×C4—441no—
944C22×C4—441no—
945C22×C4—441no—
946C22×C4—441no—
947C22×C4#433914yes—
948C22×C4D4×D1114yes—
949C22×C4C23×D1111yescharacteristic
950C22×C4C23×D1111yescharacteristic
951C22×C4C23×D1112yes—
952C22×C4C23×D1112yes—
953C22×C4C23×D1112yes—
954C22×C4C23×D1111yescharacteristic
955C22×C4C23×D1111yescharacteristic
956C22×C4C23×D1111yescharacteristic
957C22×C4C23×D1111yescharacteristic
958C4⋊C4—22no—
959C4⋊C4—24no—
960C4⋊C4—22no—
961C4⋊C4—22no—
962C4⋊C4—224no—
963C4⋊C4—224no—
964C4⋊C4—224no—
965C4⋊C4—224no—
966C4⋊C4—224no—
967C4⋊C4—222no—
968C4⋊C4—224no—
969C4⋊C4—222no—
970C4⋊C4—222no—
971C4⋊C4—442no—
972C4⋊C4—442no—
973C22⋊C4—24no—
974C22⋊C4—24no—
975C22⋊C4—24no—
976C22⋊C4—42no—
977C22⋊C4—42no—
978C22⋊C4—114no—
979C22⋊C4—114no—
980C22⋊C4—114no—
981C22⋊C4—114no—
982C22⋊C4—222no—
983C22⋊C4—222no—
984C22⋊C4—222no—
985C22⋊C4—222no—
986C22⋊C4—224no—
987C22⋊C4—224no—
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—442no—
998C22⋊C4—442no—
999C22⋊C4—442no—
1000C22⋊C4—442no—
1001C22⋊C4—442no—
1002C22⋊C4—442no—
1003C42—24no—
1004C42—22no—
1005C42—22no—
1006C42—41no—
1007C42—41no—
1008C42—224no—
1009C42—222no—
1010C42—222no—
1011C42—441no—
1012C42—441no—
1013C11#3500511yescharacteristic, complemented, Sylow
1014C23—21no—
1015C23—21no—
1016C23—21no—
1017C23—21no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—112no—
1026C23—112no—
1027C23—228no—
1028C23—221no—
1029C23—221no—
1030C23—221no—
1031C23—221no—
1032C23—221no—
1033C23—221no—
1034C23—221no—
1035C23—221no—
1036C23—221no—
1037C23—221no—
1038C23—221no—
1039C23—221no—
1040C23—222no—
1041C23—222no—
1042C23—222no—
1043C23—222no—
1044C23—222no—
1045C23—222no—
1046C23—222no—
1047C23—444no—
1048C23—444no—
1049C23—444no—
1050C23—444no—
1051C23—444no—
1052C23—444no—
1053C23C2×#433912yes—
1054C23C2×D4×D1112yes—
1055C23#41×D1112yes—
1056C23C24×D1111yescharacteristic
1057Q8—884no—
1058D4—48no—
1059D4—44no—
1060D4—448no—
1061D4—444no—
1062D4—884no—
1063D4—884no—
1064D4—884no—
1065D4—884no—
1066D4—884no—
1067D4—884no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—28no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—22no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—21no—
1087C2×C4—22no—
1088C2×C4—21no—
1089C2×C4—22no—
1090C2×C4—44no—
1091C2×C4—44no—
1092C2×C4—84no—
1093C2×C4—112no—
1094C2×C4—112no—
1095C2×C4—112no—
1096C2×C4—112no—
1097C2×C4—221no—
1098C2×C4—221no—
1099C2×C4—221no—
1100C2×C4—221no—
1101C2×C4—221no—
1102C2×C4—221no—
1103C2×C4—221no—
1104C2×C4—221no—
1105C2×C4—222no—
1106C2×C4—221no—
1107C2×C4—221no—
1108C2×C4—222no—
1109C2×C4—222no—
1110C2×C4—222no—
1111C2×C4—222no—
1112C2×C4—221no—
1113C2×C4—221no—
1114C2×C4—222no—
1115C2×C4—221no—
1116C2×C4—221no—
1117C2×C4—222no—
1118C2×C4—222no—
1119C2×C4—222no—
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×#433912yes—
1129C2×C4C2×#433912yes—
1130C2×C4C2×D4×D1112yes—
1131C2×C4C2×D4×D1112yes—
1132C2×C4#6703712yes—
1133C2×C4#6704212yes—
1134C22—22no—
1135C22—22no—
1136C22—22no—
1137C22—22no—
1138C22—22no—
1139C22—22no—
1140C22—42no—
1141C22—42no—
1142C22—42no—
1143C22—42no—
1144C22—42no—
1145C22—42no—
1146C22—42no—
1147C22—222no—
1148C22—222no—
1149C22—222no—
1150C22—222no—
1151C22—222no—
1152C22—222no—
1153C22—4416no—
1154C22—441no—
1155C22—441no—
1156C22—441no—
1157C22—441no—
1158C22—441no—
1159C22—441no—
1160C22—441no—
1161C22—441no—
1162C22—442no—
1163C22—442no—
1164C22—442no—
1165C22—442no—
1166C22—442no—
1167C22—442no—
1168C22—442no—
1169C22#1062307914yes—
1170C22C22×#433911yescharacteristic
1171C22C22×D4×D1111yescharacteristic
1172C22C2×#6703711yescharacteristic
1173C22C2×#41×D1111yescharacteristic
1174C22C2×#6704211yescharacteristic
1175C22#1062345311yescharacteristic
1176C22#1062345311yescharacteristic
1177C4—22no—
1178C4—22no—
1179C4—22no—
1180C4—42no—
1181C4—42no—
1182C4—42no—
1183C4—41no—
1184C4—41no—
1185C4—222no—
1186C4—222no—
1187C4—222no—
1188C4—222no—
1189C4—442no—
1190C4—442no—
1191C4—442no—
1192C4—441no—
1193C4—441no—
1194C4#1062309114yescomplemented
1195C2—24no—
1196C2—82no—
1197C2—442no—
1198C2—442no—
1199C2—882no—
1200C2C2×#1062307911yescharacteristic
1201C2C2×#1062309111yescharacteristic
1202C2#1308200111yescharacteristic
1203C2#1308237311yescharacteristic
1204C2#1308237811yescharacteristic
1205C2#1308245111yescharacteristic
1206C2#1308245911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC4×C11×#121C2
hypercenterC4×#121D11
hypocenterC11#35005
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
1. C2×#10623091C2semidirect
2. #13076966C2semidirect
3. #13076959C2semidirect
4. #13076899C2semidirect
5. #13076895C2semidirect
6. #13074546C2semidirect
7. #13074356C2semidirect
8. #13073747C2semidirect
9. #13073745C2semidirect
10. #13073717C2semidirect
11. #13073715C2semidirect
12. #13073039C2semidirect
13. #13073032C2semidirect
14. #13072980C2semidirect
15. #13072973C2semidirect
16. #13072205C2semidirect
17. #13072198C2semidirect
18. #13072131C2semidirect
19. #13072124C2semidirect
20. #13071314C2semidirect
21. C4×#66983C2semidirect
22. C2×C4×(C2×D11)⋊C4C2semidirect
23. C4×C11×#121C2semidirect
27. C2×C4×D4×C11C22semidirect
29. C2×#66993C22semidirect
47. C2×#66941C22semidirect
54. C2×C4×D44C22semidirect
55. C11×#390C22semidirect
56. C11×#389C22semidirect
57. C11×#388C22semidirect
60. C4×C11×C4⋊C4C22semidirect
61. C4×C11×C22⋊C4C22semidirect
62. #10622834C22semidirect
65. #10622826C22semidirect
67. #10622823C22semidirect
70. #10622602C22semidirect
71. #10622601C22semidirect
76. #10622598C22semidirect
77. #10622591C22semidirect
78. #10622589C22semidirect
79. #10622589C22semidirect
80. #10622586C22semidirect
81. #10622574C22semidirect
86. #10622572C22semidirect
88. #10622570C22semidirect
89. #10622570C22semidirect
92. #10622569C22semidirect
93. #10622565C22semidirect
94. #10622560C22semidirect
95. #10622557C22semidirect
97. #10622553C22semidirect
98. #10622553C22semidirect
99. #10622552C22semidirect
108. C4×(C2×D11)⋊C4C22semidirect
109. C4×C4⋊Dic11C22semidirect
110. #10622546C22semidirect
111. #10622541C22semidirect
114. #10622288C22semidirect
115. #10622286C22semidirect
120. #10622273C22semidirect
121. #10622271C22semidirect
122. #10622260C22semidirect
123. #10622259C22semidirect
185. C2×(C2×D11)⋊C4D4semidirect
432. C4×#121D11semidirect
580. C2×C4×D4C2×D11semidirect
607. #390C2×D11semidirect
612. #389C2×D11semidirect
616. #388C2×D11semidirect
641. C4×C4⋊C4C2×D11semidirect
651. C4×C22⋊C4C2×D11semidirect
705. C4×C11#538semidirect
1013. C11#35005semidirect
1194. C4#10623091semidirect

Maximal subgroups

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

subgroupindex
C2×#106230912
#130769662
#130769592
#130768992
#130768952
#130745462
#130743562
#130737472
#130737452
#130737172
#130737152
#130730392
#130730322
#130729802
#130729732
#130722052
#130721982
#130721312
#130721242
#130713142
C4×#669832
C2×C4×(C2×D11)⋊C42
C4×C11×#1212
#3500511