Finite Group Databasebeta

← #14926691

Subgroups — #14926691

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×#10623124C212yesmaximal, complemented
2#13076966C211yesmaximal, characteristic, complemented
3#13076959C211yesmaximal, characteristic, complemented
4#13076898C211yesmaximal, characteristic, complemented
5#13074546C212yesmaximal, complemented
6#13074354C212yesmaximal, complemented
7#13073744C212yesmaximal, complemented
8#13073742C212yesmaximal, complemented
9#13073714C212yesmaximal, complemented
10#13073712C212yesmaximal, complemented
11#13073040C211yesmaximal, characteristic, complemented
12#13073034C211yesmaximal, characteristic, complemented
13#13072981C211yesmaximal, characteristic, complemented
14#13072975C211yesmaximal, characteristic, complemented
15#13072206C211yesmaximal, characteristic, complemented
16#13072200C211yesmaximal, characteristic, complemented
17#13072132C211yesmaximal, characteristic, complemented
18#13072126C211yesmaximal, characteristic, complemented
19#13071317C212yesmaximal, complemented
20#121×Dic11C211yesmaximal, characteristic, complemented
21#13071122C211yesmaximal, characteristic, complemented
22C2×C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
23C11×#2847C211yesmaximal, characteristic, complemented
24C24×C4×C11C2211yescharacteristic
25C2×C11×#121C2211yescharacteristic
26C2×C11×#121C2211yescharacteristic
27C2×C11×#121C2211yescharacteristic
28C2×C11×#120C2212yes—
29C2×#67006C2212yes—
30C22×C22⋊Dic11C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C2×#66993C2211yescharacteristic, complemented
33C2×#66992C2212yes—
34C2×#66992C2212yes—
35C2×#66992C2212yes—
36C2×#66991C2212yes—
37C2×#66989C2212yes—
38C2×#66988C2212yes—
39C2×D4×Dic11C2212yes—
40C2×D4×Dic11C2211yescharacteristic, complemented
41C2×#66983C2211yescharacteristic
42C2×#66983C2211yescharacteristic
43C2×#66983C2211yescharacteristic
44C22×C4×Dic11C2211yescharacteristic
45C22×C4×Dic11C2211yescharacteristic
46#10623124—216no—
47C2×#66946C2211yescharacteristic, complemented
48C2×#66941C2211yescharacteristic, complemented
49C2×#66938C2212yes—
50C2×#66936C2212yes—
51C2×(C22⋊D11)⋊C4C2212yes—
52C2×#66932C2212yes—
53C2×#66932C2212yes—
54C2×#66931C2212yes—
55C11×#386C2212yes—
56C11×#386C2212yes—
57C11×#386C2212yes—
58C11×#380C2211yescharacteristic
59C11×#380C2211yescharacteristic
60C11×#380C2211yescharacteristic
61#10622836C2212yes—
62#10622836C2212yes—
63#10622835C2212yes—
64#10622835C2212yes—
65#10622834C2211yescharacteristic, complemented
66#10622834C2211yescharacteristic, complemented
67#10622833C2212yes—
68#10622826C2212yes—
69#10622826C2212yes—
70#10622826C2212yes—
71#10622825C2211yescharacteristic
72#10622825C2211yescharacteristic
73#10622825C2211yescharacteristic
74C4×C22⋊Dic11C2211yescharacteristic
75C4×C22⋊Dic11C2211yescharacteristic
76C4×C22⋊Dic11C2211yescharacteristic
77C4×C22⋊Dic11C2211yescharacteristic
78C4×C22⋊Dic11C2211yescharacteristic
79C4×C22⋊Dic11C2211yescharacteristic
80C4×C22⋊Dic11C2211yescharacteristic
81C4×C22⋊Dic11C2211yescharacteristic
82C2×C11⋊#95C2211yescharacteristic
83C2×C11⋊#95C2211yescharacteristic
84#10622601C2211yescharacteristic, complemented
85#10622601C2211yescharacteristic, complemented
86#10622598C2211yescharacteristic, complemented
87#10622598C2211yescharacteristic, complemented
88#10622589C2211yescharacteristic, complemented
89#10622589C2211yescharacteristic, complemented
90C4⋊C4×Dic11C2211yescharacteristic, complemented
91C4⋊C4×Dic11C2211yescharacteristic, complemented
92#10622586C2211yescharacteristic, complemented
93#10622586C2211yescharacteristic, complemented
94#10622574C2212yescomplemented
95#10622572C2212yes—
96#10622572C2212yes—
97#10622572C2212yescomplemented
98#10622571C2212yes—
99#10622571C2212yescomplemented
100#10622570C2212yescomplemented
101#10622570C2212yescomplemented
102#10622569C2212yescomplemented
103#10622565C2212yes—
104#10622565C2212yes—
105#10622565C2212yescomplemented
106#10622564C2212yescomplemented
107#10622560C2212yescomplemented
108#10622559C2212yescomplemented
109#10622558C2212yescomplemented
110#10622555C2212yes—
111C22⋊C4×Dic11C2212yescomplemented
112#10622288C2212yescomplemented
113#10622286C2212yescomplemented
114#10622282C2212yescomplemented
115#10622282C2212yescomplemented
116#10622281C2212yescomplemented
117#10622279C2212yescomplemented
118#10622273C2212yescomplemented
119#10622271C2212yescomplemented
120#10622268C2212yescomplemented
121#10622265C2212yescomplemented
122#10622260C2212yescomplemented
123#10622259C2212yescomplemented
124C25×C11C2311yescharacteristic
125C22×D4×C11C2312yes—
126C22×D4×C11C2311yescharacteristic
127C22×D4×C11C2312yes—
128C22×D4×C11C2312yes—
129C23×C4×C11—24no—
130C23×C4×C11—42no—
131C23×C4×C11—42no—
132C23×C4×C11C2311yescharacteristic
133C23×C4×C11C2311yescharacteristic
134C23×C4×C11C2311yescharacteristic
135C23×C4×C11C2311yescharacteristic
136C23×C4×C11C2311yescharacteristic
137C23×C4×C11C2311yescharacteristic
138C22×C22⋊D11C2312yes—
139C22×C22⋊D11C2312yes—
140C22×C22⋊D11C2312yes—
141C22×C22⋊D11C2312yes—
142C22×C22⋊D11C2312yes—
143C23×Dic11C2311yescharacteristic
144C23×Dic11C2312yes—
145C23×Dic11C2311yescharacteristic
146C23×Dic11C2311yescharacteristic
147C23×Dic11C2311yescharacteristic
148C22×D44C2311yescharacteristic
149C22×C4×D11C2312yes—
150C22×Dic22C2312yes—
151C11×#121—24no—
152C11×#121—42no—
153C11×#121—42no—
154C11×#120—28no—
155C2×C11×C4⋊C4C2311yescharacteristic
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×C11×C22⋊C4C2312yes—
164#67006—28no—
165C2×C22⋊Dic11—24no—
166C2×C22⋊Dic11D418yescomplemented
167C2×C22⋊Dic11C2312yes—
168C2×C22⋊Dic11C2312yes—
169C2×C22⋊Dic11C2312yes—
170C2×C22⋊Dic11C2312yes—
171C2×C22⋊Dic11C2312yes—
172C2×C22⋊Dic11C2312yes—
173C2×C22⋊Dic11C2311yescharacteristic
174C2×C22⋊Dic11C2311yescharacteristic
175C2×C22⋊Dic11C2311yescharacteristic
176C2×C22⋊Dic11C2311yescharacteristic
177C2×C22⋊Dic11C2312yes—
178C2×C22⋊Dic11C2312yes—
179C2×C22⋊Dic11C2311yescharacteristic
180C2×C22⋊Dic11C2311yescharacteristic
181C2×C22⋊Dic11C2311yescharacteristic
182C2×C22⋊Dic11C2311yescharacteristic
183#66993—42no—
184#66992—28no—
185#66992—28no—
186#66992—28no—
187#66991—28no—
188#66989—28no—
189#66988—28no—
190D4×Dic11—28no—
191D4×Dic11—42no—
192#66983—24no—
193#66983—42no—
194#66983—42no—
195C2×(C2×D11)⋊C4C2312yes—
196C2×(C2×D11)⋊C4C2312yes—
197C2×(C2×D11)⋊C4C2312yes—
198C2×(C2×D11)⋊C4C2312yes—
199C2×(C2×D11)⋊C4C2312yes—
200C2×(C2×D11)⋊C4C2312yes—
201C2×(C2×D11)⋊C4C2312yes—
202C2×(C2×D11)⋊C4C2312yes—
203C2×C4⋊Dic11C2312yes—
204C2×C4⋊Dic11C2312yes—
205C2×C4⋊Dic11C2311yescharacteristic
206C2×C4⋊Dic11C2311yescharacteristic
207C2×C4⋊Dic11C2311yescharacteristic
208C2×Dic11⋊C4C2312yes—
209C2×Dic11⋊C4C2312yes—
210C2×Dic11⋊C4C2312yes—
211C2×Dic11⋊C4C2312yes—
212C2×Dic11⋊C4C2312yes—
213C2×Dic11⋊C4C2312yes—
214C2×Dic11⋊C4C2312yes—
215C2×C4×Dic11—42no—
216C2×C4×Dic11—42no—
217C2×C4×Dic11C2312yes—
218C2×C4×Dic11C2312yes—
219C2×C4×Dic11C2311yescharacteristic
220C2×C4×Dic11C2311yescharacteristic
221C2×C4×Dic11C2311yescharacteristic
222C2×C4×Dic11C2311yescharacteristic
223C2×C4×Dic11C2311yescharacteristic
224C2×C4×Dic11C2311yescharacteristic
225C2×C4×Dic11C2311yescharacteristic
226C2×C4×Dic11C2311yescharacteristic
227#66946—42no—
228#66941—42no—
229#66938—28no—
230#66936—28no—
231(C22⋊D11)⋊C4—28no—
232#66932—28no—
233#66932—28no—
234#66931—28no—
235C11×#95C2312yes—
236C11×#95C2312yes—
237C11×#95C2312yes—
238C11⋊#95C2312yes—
239C11⋊#95C2312yes—
240C11⋊#95C2312yes—
241C11⋊#95C2311yescharacteristic
242C11⋊#95C2312yes—
243C11⋊#95C2311yescharacteristic
244C11⋊#95C2312yes—
245C11⋊#95C2311yescharacteristic
246C11⋊#95C2312yes—
247C11⋊#95C2312yes—
248C11⋊#95C2311yescharacteristic
249C11⋊#95C2312yes—
250C11⋊#95C2312yes—
251C11⋊#95C2311yescharacteristic
252C11⋊#95C2311yescharacteristic
253C11⋊#95C2311yescharacteristic
254C11⋊#95C2311yescharacteristic
255#35005—111nomaximal, Sylow
256C24×C11—22no—
257C24×C11—22no—
258C24×C11—41no—
259C24×C11—41no—
260C24×C11—41no—
261C24×C11—41no—
262C24×C11C2×D414yes—
263C24×C11C2412yes—
264C24×C11C2411yescharacteristic
265C24×C11C2411yescharacteristic
266C24×C11C2411yescharacteristic
267C23×D11C2412yes—
268C2×D4×C11—24no—
269C2×D4×C11—24no—
270C2×D4×C11—24no—
271C2×D4×C11—24no—
272C2×D4×C11—24no—
273C2×D4×C11—22no—
274C2×D4×C11—22no—
275C2×D4×C11—22no—
276C2×D4×C11—42no—
277C2×D4×C11—42no—
278C2×D4×C11—42no—
279C2×D4×C11—42no—
280C22×C4×C11—22no—
281C22×C4×C11—22no—
282C22×C4×C11—22no—
283C22×C4×C11—22no—
284C22×C4×C11—22no—
285C22×C4×C11—22no—
286C22×C4×C11—22no—
287C22×C4×C11—22no—
288C22×C4×C11—22no—
289C22×C4×C11—22no—
290C22×C4×C11—22no—
291C22×C4×C11—41no—
292C22×C4×C11—41no—
293C22×C4×C11—41no—
294C22×C4×C11—41no—
295C22×C4×C11—41no—
296C22×C4×C11—41no—
297C22×C4×C11—416no—
298C22×C4×C11#4114yes—
299C22×C4×C11C2411yescharacteristic
300C22×C4×C11C2411yescharacteristic
301C22×C4×C11C2412yes—
302C22×C4×C11C2412yes—
303C22×C4×C11C2412yes—
304C22×C4×C11C2411yescharacteristic
305C22×C4×C11C2411yescharacteristic
306C2×C22⋊D11—24no—
307C2×C22⋊D11—24no—
308C2×C22⋊D11—24no—
309C2×C22⋊D11—24no—
310C2×C22⋊D11—24no—
311C2×C22⋊D11—24no—
312C2×C22⋊D11—24no—
313C2×C22⋊D11—42no—
314C2×C22⋊D11—42no—
315C2×C22⋊D11—42no—
316C2×C22⋊D11—42no—
317C2×C22⋊D11—42no—
318C2×C22⋊D11—42no—
319C2×C22⋊D11—42no—
320C2×C22⋊D11—42no—
321C22×Dic11—24no—
322C22×Dic11—22no—
323C22×Dic11—41no—
324C22×Dic11—41no—
325C22×Dic11—41no—
326C22×Dic11—41no—
327C22×Dic11—41no—
328C22×Dic11—41no—
329C22×Dic11—41no—
330C22×Dic11—41no—
331C22×Dic11—42no—
332C22×Dic11—42no—
333C22×Dic11C2×D414yes—
334C22×Dic11C2×D414yes—
335C22×Dic11#4114yes—
336C22×Dic11C2411yescharacteristic
337C22×Dic11C2411yescharacteristic
338C22×Dic11C2412yes—
339C22×Dic11C2412yes—
340C22×Dic11C2412yes—
341C22×Dic11C2411yescharacteristic
342C22×Dic11C2411yescharacteristic
343C22×Dic11C2411yescharacteristic
344C22×Dic11C2411yescharacteristic
345C22×Dic11C2411yescharacteristic
346C22×Dic11C2411yescharacteristic
347C2×D44—22no—
348C2×D44—22no—
349C2×D44—22no—
350C2×C4×D11—24no—
351C2×C4×D11—42no—
352C2×C4×D11—42no—
353C2×Dic22—24no—
354C2×Dic22—42no—
355C2×Dic22—42no—
356C11×C4⋊C4—22no—
357C11×C4⋊C4—22no—
358C11×C4⋊C4—22no—
359C11×C22⋊C4—24no—
360C11×C22⋊C4—24no—
361C11×C22⋊C4—24no—
362C11×C22⋊C4—24no—
363C11×C22⋊C4—42no—
364C11×C22⋊C4—42no—
365C22⋊Dic11—24no—
366C22⋊Dic11—24no—
367C22⋊Dic11—24no—
368C22⋊Dic11—22no—
369C22⋊Dic11—22no—
370C22⋊Dic11—22no—
371C22⋊Dic11—22no—
372C22⋊Dic11—24no—
373C22⋊Dic11—24no—
374C22⋊Dic11—24no—
375C22⋊Dic11—42no—
376C22⋊Dic11—42no—
377C22⋊Dic11C2×D414yes—
378C22⋊Dic11C2×D414yes—
379C22⋊Dic11C2×D414yes—
380C22⋊Dic11C2×D414yes—
381(C2×D11)⋊C4—24no—
382(C2×D11)⋊C4—24no—
383(C2×D11)⋊C4—24no—
384(C2×D11)⋊C4—24no—
385(C2×D11)⋊C4—42no—
386(C2×D11)⋊C4—42no—
387(C2×D11)⋊C4—42no—
388(C2×D11)⋊C4—42no—
389C4⋊Dic11—24no—
390C4⋊Dic11—24no—
391C4⋊Dic11—22no—
392C4⋊Dic11—22no—
393C4⋊Dic11—22no—
394Dic11⋊C4—24no—
395Dic11⋊C4—24no—
396Dic11⋊C4—24no—
397Dic11⋊C4—24no—
398Dic11⋊C4—24no—
399Dic11⋊C4—42no—
400Dic11⋊C4—42no—
401C4×Dic11—24no—
402C4×Dic11—24no—
403C4×Dic11—22no—
404C4×Dic11—22no—
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#2847D1111yescharacteristic, complemented
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×#121—111no—
433C2×C4×C22⋊C4—111no—
434C23×C11—21no—
435C23×C11—21no—
436C23×C11—21no—
437C23×C11—21no—
438C23×C11—28no—
439C23×C11—21no—
440C23×C11—21no—
441C23×C11—21no—
442C23×C11—21no—
443C23×C11—21no—
444C23×C11—21no—
445C23×C11—21no—
446C23×C11—21no—
447C23×C11—21no—
448C23×C11—21no—
449C23×C11—21no—
450C23×C11—21no—
451C23×C11—22no—
452C23×C11—22no—
453C23×C11—22no—
454C23×C11—22no—
455C23×C11—22no—
456C23×C11—22no—
457C23×C11—22no—
458C23×C11—44no—
459C23×C11—44no—
460C23×C11—44no—
461C23×C11—44no—
462C23×C11—44no—
463C23×C11—44no—
464C23×C11C22×D412yes—
465C23×C11C22×D412yes—
466C23×C11C22×D412yes—
467C23×C11C2×#4112yes—
468C23×C11C2×#4112yes—
469C23×C11C2511yescharacteristic
470C22×D11—22no—
471C22×D11—22no—
472C22×D11—22no—
473C22×D11—22no—
474C22×D11—22no—
475C22×D11—22no—
476C22×D11—22no—
477D4×C11—48no—
478D4×C11—44no—
479D4×C11—84no—
480D4×C11—84no—
481C2×C4×C11—21no—
482C2×C4×C11—21no—
483C2×C4×C11—28no—
484C2×C4×C11—22no—
485C2×C4×C11—22no—
486C2×C4×C11—22no—
487C2×C4×C11—22no—
488C2×C4×C11—22no—
489C2×C4×C11—21no—
490C2×C4×C11—21no—
491C2×C4×C11—22no—
492C2×C4×C11—21no—
493C2×C4×C11—21no—
494C2×C4×C11—22no—
495C2×C4×C11—21no—
496C2×C4×C11—21no—
497C2×C4×C11—22no—
498C2×C4×C11—22no—
499C2×C4×C11—44no—
500C2×C4×C11—44no—
501C2×C4×C11—44no—
502C2×C4×C11—44no—
503C2×C4×C11—44no—
504C2×C4×C11C2×#4112yes—
505C2×C4×C11C2×#4112yes—
506C2×C4×C11H(5,𝔽2)12yes—
507C2×C4×C11H(5,𝔽2)12yes—
508C22⋊D11—48no—
509C22⋊D11—84no—
510C22⋊D11—84no—
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—21no—
522C2×Dic11—21no—
523C2×Dic11—21no—
524C2×Dic11—21no—
525C2×Dic11—22no—
526C2×Dic11—22no—
527C2×Dic11—22no—
528C2×Dic11—22no—
529C2×Dic11—22no—
530C2×Dic11—21no—
531C2×Dic11—21no—
532C2×Dic11—21no—
533C2×Dic11—21no—
534C2×Dic11—22no—
535C2×Dic11—22no—
536C2×Dic11—22no—
537C2×Dic11—21no—
538C2×Dic11—21no—
539C2×Dic11—22no—
540C2×Dic11—44no—
541C2×Dic11—44no—
542C2×Dic11—44no—
543C2×Dic11—44no—
544C2×Dic11—84no—
545C2×Dic11C22×D412yes—
546C2×Dic11C22×D412yes—
547C2×Dic11C22×D412yes—
548C2×Dic11C22×D412yes—
549C2×Dic11C2×#4112yes—
550C2×Dic11C2×#4112yes—
551D44—44no—
552C4×D11—84no—
553Dic22—84no—
554C24×C4C2×D1111yescharacteristic
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—112no—
568C2×#121—112no—
569C2×#121—111no—
570C2×#121—111no—
571C2×#121—111no—
572C2×#121C2×D1111yescharacteristic
573C2×#121C2×D1111yescharacteristic
574C2×#121C2×D1111yescharacteristic
575C2×#120—112no—
576C2×#120C2×D1112yes—
577C2×C4×D4—112no—
578C2×C4×D4—111no—
579C2×C4×D4—111no—
580C2×C4×D4—112no—
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#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—111no—
605#390—111no—
606#390—112no—
607#390—112no—
608#389—111no—
609#389—111no—
610#389—111no—
611#389—111no—
612#389—112no—
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#386C2×D1112yes—
627#386C2×D1112yes—
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—112no—
637#380C2×D1111yescharacteristic
638#380C2×D1111yescharacteristic
639#380C2×D1111yescharacteristic
640C4×C4⋊C4—111no—
641C4×C4⋊C4—111no—
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⋊C4—112no—
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—22no—
661C22×C11—22no—
662C22×C11—22no—
663C22×C11—22no—
664C22×C11—22no—
665C22×C11—22no—
666C22×C11—416no—
667C22×C11—41no—
668C22×C11—41no—
669C22×C11—41no—
670C22×C11—41no—
671C22×C11—41no—
672C22×C11—41no—
673C22×C11—41no—
674C22×C11—41no—
675C22×C11—42no—
676C22×C11—42no—
677C22×C11—42no—
678C22×C11—42no—
679C22×C11—42no—
680C22×C11—42no—
681C22×C11—42no—
682C22×C11#53214yes—
683C22×C11C23×D411yescharacteristic
684C22×C11C22×#4111yescharacteristic
685C22×C11C22×#4111yescharacteristic
686C22×C11C2×H(5,𝔽2)11yescharacteristic
687C22×C11C2×H(5,𝔽2)11yescharacteristic
688C22×C11#58511yescharacteristic
689C22×C11#58511yescharacteristic
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—42no—
699C4×C11—41no—
700C4×C11—41no—
701C4×C11—42no—
702C4×C11—42no—
703C4×C11#53814yescomplemented
704Dic11—22no—
705Dic11—22no—
706Dic11—22no—
707Dic11—22no—
708Dic11—22no—
709Dic11—22no—
710Dic11—42no—
711Dic11—42no—
712Dic11—42no—
713Dic11—41no—
714Dic11—41no—
715C25C22×D1111yescharacteristic
716C22×Q8—112no—
717C22×D4—112no—
718C22×D4—112no—
719C22×D4—112no—
720C22×D4—112no—
721C22×D4—112no—
722C22×D4—111no—
723C22×D4C22×D1112yes—
724C22×D4C22×D1111yescharacteristic
725C22×D4C22×D1112yes—
726C22×D4C22×D1112yes—
727C23×C4—24no—
728C23×C4—42no—
729C23×C4—42no—
730C23×C4—111no—
731C23×C4—111no—
732C23×C4—111no—
733C23×C4—111no—
734C23×C4—112no—
735C23×C4—112no—
736C23×C4C22×D1111yescharacteristic
737C23×C4C22×D1111yescharacteristic
738C23×C4C22×D1111yescharacteristic
739C23×C4C22×D1111yescharacteristic
740C23×C4C22×D1111yescharacteristic
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—42no—
753#121—42no—
754#121—228no—
755#121—228no—
756#121—228no—
757#121—228no—
758#121—224no—
759#121—442no—
760#121—442no—
761#120—28no—
762#120—228no—
763C4×D4—228no—
764C4×D4—228no—
765C4×D4—442no—
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—112no—
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×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—111no—
788C2×C22⋊C4—111no—
789C2×C22⋊C4—111no—
790C2×C22⋊C4—111no—
791C2×C22⋊C4—112no—
792C2×C22⋊C4—112no—
793C2×C22⋊C4—112no—
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—224no—
808C2×C22⋊C4C22×D1112yes—
809C2×C22⋊C4C22×D1112yes—
810C2×C22⋊C4C22×D1112yes—
811C2×C22⋊C4C22×D1112yes—
812C2×C22⋊C4C22×D1112yes—
813C2×C22⋊C4C22×D1112yes—
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—111no—
823C2×C42—111no—
824C2×C42—442no—
825C2×C42—442no—
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—42no—
848C2×C11—42no—
849C2×C11—82no—
850C2×C11C2×#53211yescharacteristic
851C2×C11C2×#53811yescharacteristic
852C2×C11#345511yescharacteristic
853C2×C11#349611yescharacteristic
854C2×C11#349611yescharacteristic
855C2×C11#350511yescharacteristic
856C2×C11#350611yescharacteristic
857D11—82no—
858C24—22no—
859C24—22no—
860C24—41no—
861C24—41no—
862C24—41no—
863C24—41no—
864C24—112no—
865C24D4×D1114yes—
866C24C23×D1112yes—
867C24C23×D1111yescharacteristic
868C24C23×D1111yescharacteristic
869C24C23×D1111yescharacteristic
870C2×Q8—224no—
871C2×Q8—442no—
872C2×Q8—442no—
873C2×D4—24no—
874C2×D4—24no—
875C2×D4—24no—
876C2×D4—24no—
877C2×D4—24no—
878C2×D4—22no—
879C2×D4—22no—
880C2×D4—22no—
881C2×D4—42no—
882C2×D4—42no—
883C2×D4—42no—
884C2×D4—42no—
885C2×D4—224no—
886C2×D4—224no—
887C2×D4—224no—
888C2×D4—224no—
889C2×D4—224no—
890C2×D4—224no—
891C2×D4—224no—
892C2×D4—222no—
893C2×D4—222no—
894C2×D4—222no—
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—22no—
907C22×C4—22no—
908C22×C4—22no—
909C22×C4—22no—
910C22×C4—22no—
911C22×C4—22no—
912C22×C4—22no—
913C22×C4—22no—
914C22×C4—41no—
915C22×C4—41no—
916C22×C4—41no—
917C22×C4—41no—
918C22×C4—41no—
919C22×C4—41no—
920C22×C4—416no—
921C22×C4—111no—
922C22×C4—111no—
923C22×C4—111no—
924C22×C4—111no—
925C22×C4—111no—
926C22×C4—111no—
927C22×C4—114no—
928C22×C4—114no—
929C22×C4—114no—
930C22×C4—111no—
931C22×C4—111no—
932C22×C4—112no—
933C22×C4—112no—
934C22×C4—112no—
935C22×C4—224no—
936C22×C4—224no—
937C22×C4—222no—
938C22×C4—442no—
939C22×C4—442no—
940C22×C4—441no—
941C22×C4—441no—
942C22×C4—441no—
943C22×C4—441no—
944C22×C4—441no—
945C22×C4—441no—
946C22×C4—441no—
947C22×C4—441no—
948C22×C4—442no—
949C22×C4—442no—
950C22×C4#434114yes—
951C22×C4C23×D1111yescharacteristic
952C22×C4C23×D1111yescharacteristic
953C22×C4C23×D1112yes—
954C22×C4C23×D1112yes—
955C22×C4C23×D1112yes—
956C22×C4C23×D1111yescharacteristic
957C22×C4C23×D1111yescharacteristic
958C4⋊C4—22no—
959C4⋊C4—22no—
960C4⋊C4—22no—
961C4⋊C4—224no—
962C4⋊C4—224no—
963C4⋊C4—224no—
964C4⋊C4—224no—
965C4⋊C4—224no—
966C4⋊C4—224no—
967C4⋊C4—224no—
968C4⋊C4—222no—
969C4⋊C4—222no—
970C4⋊C4—222no—
971C4⋊C4—442no—
972C4⋊C4—442no—
973C22⋊C4—24no—
974C22⋊C4—24no—
975C22⋊C4—24no—
976C22⋊C4—24no—
977C22⋊C4—42no—
978C22⋊C4—42no—
979C22⋊C4—114no—
980C22⋊C4—114no—
981C22⋊C4—114no—
982C22⋊C4—114no—
983C22⋊C4—224no—
984C22⋊C4—224no—
985C22⋊C4—224no—
986C22⋊C4—222no—
987C22⋊C4—222no—
988C22⋊C4—222no—
989C22⋊C4—222no—
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—224no—
1004C42—224no—
1005C42—222no—
1006C42—222no—
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—28no—
1019C23—21no—
1020C23—21no—
1021C23—21no—
1022C23—21no—
1023C23—21no—
1024C23—21no—
1025C23—21no—
1026C23—21no—
1027C23—21no—
1028C23—21no—
1029C23—21no—
1030C23—21no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—44no—
1039C23—44no—
1040C23—44no—
1041C23—44no—
1042C23—44no—
1043C23—44no—
1044C23—222no—
1045C23—222no—
1046C23—222no—
1047C23—222no—
1048C23—222no—
1049C23—222no—
1050C23—222no—
1051C23C2×D4×D1112yes—
1052C23C2×D4×D1112yes—
1053C23C2×D4×D1112yes—
1054C23C2×#434112yes—
1055C23#41×D1112yes—
1056C23C24×D1111yescharacteristic
1057Q8—884no—
1058D4—48no—
1059D4—44no—
1060D4—84no—
1061D4—84no—
1062D4—448no—
1063D4—444no—
1064D4—884no—
1065D4—884no—
1066D4—884no—
1067D4—884no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—28no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—44no—
1087C2×C4—44no—
1088C2×C4—44no—
1089C2×C4—44no—
1090C2×C4—44no—
1091C2×C4—112no—
1092C2×C4—112no—
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—221no—
1106C2×C4—221no—
1107C2×C4—221no—
1108C2×C4—221no—
1109C2×C4—222no—
1110C2×C4—222no—
1111C2×C4—222no—
1112C2×C4—222no—
1113C2×C4—221no—
1114C2×C4—221no—
1115C2×C4—222no—
1116C2×C4—222no—
1117C2×C4—221no—
1118C2×C4—221no—
1119C2×C4—222no—
1120C2×C4—221no—
1121C2×C4—221no—
1122C2×C4—222no—
1123C2×C4—222no—
1124C2×C4—444no—
1125C2×C4—444no—
1126C2×C4—444no—
1127C2×C4—444no—
1128C2×C4—884no—
1129C2×C4—884no—
1130C2×C4C2×#434112yes—
1131C2×C4C2×#434112yes—
1132C2×C4#6703712yes—
1133C2×C4#6703712yes—
1134C22—22no—
1135C22—22no—
1136C22—22no—
1137C22—22no—
1138C22—22no—
1139C22—22no—
1140C22—22no—
1141C22—22no—
1142C22—22no—
1143C22—22no—
1144C22—22no—
1145C22—22no—
1146C22—416no—
1147C22—41no—
1148C22—41no—
1149C22—41no—
1150C22—41no—
1151C22—41no—
1152C22—41no—
1153C22—41no—
1154C22—41no—
1155C22—42no—
1156C22—42no—
1157C22—42no—
1158C22—42no—
1159C22—42no—
1160C22—42no—
1161C22—42no—
1162C22—442no—
1163C22—442no—
1164C22—442no—
1165C22—442no—
1166C22—442no—
1167C22—442no—
1168C22—442no—
1169C22#1062312714yes—
1170C22C22×D4×D1111yescharacteristic
1171C22C22×#434111yescharacteristic
1172C22C2×#6703711yescharacteristic
1173C22C2×#6703711yescharacteristic
1174C22C2×#41×D1111yescharacteristic
1175C22#1062345311yescharacteristic
1176C22#1062345311yescharacteristic
1177C4—22no—
1178C4—42no—
1179C4—42no—
1180C4—42no—
1181C4—41no—
1182C4—41no—
1183C4—222no—
1184C4—222no—
1185C4—222no—
1186C4—222no—
1187C4—222no—
1188C4—222no—
1189C4—442no—
1190C4—442no—
1191C4—442no—
1192C4—441no—
1193C4—441no—
1194C4#1062312414yescomplemented
1195C2—24no—
1196C2—42no—
1197C2—42no—
1198C2—82no—
1199C2—882no—
1200C2C2×#1062312711yescharacteristic
1201C2C2×#1062312411yescharacteristic
1202C2#1308200411yescharacteristic
1203C2#1308237311yescharacteristic
1204C2#1308237311yescharacteristic
1205C2#1308244411yescharacteristic
1206C2#1308245911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2847C2
hypercenter#2847D11
hypocenterC11#35005
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2847

Complements

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

NH ≅ G/Ntype
1. C2×#10623124C2semidirect
2. #13076966C2semidirect
3. #13076959C2semidirect
4. #13076898C2semidirect
5. #13074546C2semidirect
6. #13074354C2semidirect
7. #13073744C2semidirect
8. #13073742C2semidirect
9. #13073714C2semidirect
10. #13073712C2semidirect
11. #13073040C2semidirect
12. #13073034C2semidirect
13. #13072981C2semidirect
14. #13072975C2semidirect
15. #13072206C2semidirect
16. #13072200C2semidirect
17. #13072132C2semidirect
18. #13072126C2semidirect
19. #13071317C2semidirect
20. #121×Dic11C2semidirect
21. #13071122C2semidirect
22. C2×C4×C22⋊Dic11C2semidirect
23. C11×#2847C2semidirect
32. C2×#66993C22semidirect
40. C2×D4×Dic11C22semidirect
47. C2×#66946C22semidirect
48. C2×#66941C22semidirect
65. #10622834C22semidirect
66. #10622834C22semidirect
84. #10622601C22semidirect
85. #10622601C22semidirect
86. #10622598C22semidirect
87. #10622598C22semidirect
88. #10622589C22semidirect
89. #10622589C22semidirect
90. C4⋊C4×Dic11C22semidirect
91. C4⋊C4×Dic11C22semidirect
92. #10622586C22semidirect
93. #10622586C22semidirect
94. #10622574C22semidirect
97. #10622572C22semidirect
99. #10622571C22semidirect
100. #10622570C22semidirect
101. #10622570C22semidirect
102. #10622569C22semidirect
105. #10622565C22semidirect
106. #10622564C22semidirect
107. #10622560C22semidirect
108. #10622559C22semidirect
109. #10622558C22semidirect
111. C22⋊C4×Dic11C22semidirect
112. #10622288C22semidirect
113. #10622286C22semidirect
114. #10622282C22semidirect
115. #10622282C22semidirect
116. #10622281C22semidirect
117. #10622279C22semidirect
118. #10622273C22semidirect
119. #10622271C22semidirect
120. #10622268C22semidirect
121. #10622265C22semidirect
122. #10622260C22semidirect
123. #10622259C22semidirect
166. C2×C22⋊Dic11D4semidirect
415. #2847D11semidirect
703. C4×C11#538semidirect
1013. C11#35005semidirect
1194. C4#10623124semidirect

Maximal subgroups

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

subgroupindex
C2×#106231242
#130769662
#130769592
#130768982
#130745462
#130743542
#130737442
#130737422
#130737142
#130737122
#130730402
#130730342
#130729812
#130729752
#130722062
#130722002
#130721322
#130721262
#130713172
#121×Dic112
#130711222
C2×C4×C22⋊Dic112
C11×#28472
#3500511