Finite Group Databasebeta

← #14926699

Subgroups — #14926699

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×#10623235C212yesmaximal, complemented
2#13076967C211yesmaximal, characteristic, complemented
3#13076962C211yesmaximal, characteristic, complemented
4#13076899C211yesmaximal, characteristic, complemented
5#13076899C211yesmaximal, characteristic, complemented
6#13074548C212yesmaximal, complemented
7#13074351C212yesmaximal, complemented
8#13073748C212yesmaximal, complemented
9#13073743C212yesmaximal, complemented
10#13073721C212yesmaximal, complemented
11#13073710C212yesmaximal, complemented
12#13073041C211yesmaximal, characteristic, complemented
13#13072975C211yesmaximal, characteristic, complemented
14#13072973C211yesmaximal, characteristic, complemented
15#13072204C211yesmaximal, characteristic, complemented
16#13072202C211yesmaximal, characteristic, complemented
17#13072132C211yesmaximal, characteristic, complemented
18#13072131C211yesmaximal, characteristic, complemented
19#13071315C212yesmaximal, complemented
20C4×#66948C211yesmaximal, characteristic, complemented
21#13071124C211yesmaximal, characteristic, complemented
22C4×C22⋊C4×D11C211yesmaximal, characteristic, complemented
23C11×#2496C211yesmaximal, characteristic, complemented
24C23×C4×D11C2211yescharacteristic
25C2×C11×#126C2212yes—
26C2×#66983C2211yescharacteristic
27C2×#66983C2211yescharacteristic
28#10623235—216no—
29C2×#66951C2212yes—
30C2×#66949C2212yes—
31C2×#66948C2211yescharacteristic
32C2×#66948C2211yescharacteristic
33C2×#66948C2212yes—
34C2×#66948C2212yes—
35C2×#66948C2212yes—
36C2×#66948C2211yescharacteristic
37C2×#66948C2211yescharacteristic
38C2×#66947C2212yes—
39C2×#66946C2212yes—
40C2×#66946C2211yescharacteristic, complemented
41C2×#66941C2211yescharacteristic, complemented
42C2×#66938C2212yes—
43C2×#66937C2212yes—
44C2×#66936C2212yes—
45C2×#66935C2212yes—
46C2×#66935C2212yes—
47C2×C22⋊C4×D11C2211yescharacteristic
48C2×C22⋊C4×D11C2211yescharacteristic
49C2×#66928C2212yes—
50C2×#66927C2211yescharacteristic, complemented
51C2×C4×D44C2212yes—
52C2×C4×D44C2211yescharacteristic, complemented
53C2×C42×D11C2211yescharacteristic
54C2×C42×D11C2211yescharacteristic
55C11×#400C2212yescomplemented
56C11×#397C2212yes—
57C11×#389C2211yescharacteristic, complemented
58C11×#389C2211yescharacteristic, complemented
59C11×#387C2212yescomplemented
60C11×#384C2211yescharacteristic, complemented
61C11×#380C2211yescharacteristic
62C11×#380C2211yescharacteristic
63C4×C11×C4⋊C4C2211yescharacteristic, complemented
64C4×C11×C22⋊C4C2211yescharacteristic
65C4×C22⋊Dic11C2211yescharacteristic
66#10622606C2212yes—
67#10622604C2212yescomplemented
68#10622603C2212yescomplemented
69#10622602C2212yescomplemented
70#10622601C2211yescharacteristic, complemented
71#10622601C2211yescharacteristic, complemented
72#10622601C2211yescharacteristic, complemented
73#10622601C2212yescomplemented
74#10622601C2212yescomplemented
75#10622600C2211yescharacteristic
76#10622600C2211yescharacteristic
77#10622600C2211yescharacteristic
78#10622600C2211yescharacteristic
79#10622598C2211yescharacteristic, complemented
80#10622595C2212yescomplemented
81#10622594C2212yescomplemented
82#10622589C2211yescharacteristic, complemented
83C4⋊C4×Dic11C2211yescharacteristic, complemented
84#10622585C2212yescomplemented
85#10622573C2212yes—
86#10622572C2212yes—
87#10622572C2212yes—
88#10622571C2212yes—
89#10622571C2212yes—
90C22⋊C4×Dic11C2211yescharacteristic
91C22⋊C4×Dic11C2211yescharacteristic
92#10622553C2212yescomplemented
93#10622552C2211yescharacteristic, complemented
94C4×(C2×D11)⋊C4C2211yescharacteristic
95C4×(C2×D11)⋊C4C2211yescharacteristic
96C4×(C2×D11)⋊C4C2212yescomplemented
97#10622541C2211yescharacteristic, complemented
98#10622288C2212yescomplemented
99#10622288C2212yescomplemented
100#10622286C2212yescomplemented
101#10622286C2212yescomplemented
102#10622285C2212yes—
103#10622285C2212yes—
104#10622285C2212yescomplemented
105#10622284C2212yes—
106#10622283C2212yescomplemented
107#10622282C2212yescomplemented
108#10622281C2212yescomplemented
109#10622280C2212yes—
110#10622279C2211yescharacteristic
111#10622279C2211yescharacteristic
112#10622279C2212yescomplemented
113#10622278C2212yes—
114#10622278C2212yes—
115#10622278C2212yes—
116#10622278C2212yes—
117#10622278C2212yes—
118#10622278C2212yes—
119#10622278C2212yescomplemented
120#10622278C2212yescomplemented
121D11×#95C2211yescharacteristic
122D11×#95C2211yescharacteristic
123#10622259C2212yescomplemented
124C24×D11C2311yescharacteristic
125C23×C4×C11C2311yescharacteristic
126C22×C22⋊D11C2312yes—
127C22×C22⋊D11C2312yes—
128C23×Dic11C2311yescharacteristic
129C22×D44C2312yes—
130C22×D44C2311yescharacteristic
131C22×D44C2311yescharacteristic
132C22×D44C2312yes—
133C22×D44C2312yes—
134C22×D44C2312yes—
135C22×D44C2312yes—
136C22×D44C2312yes—
137C22×C4×D11—24no—
138C22×C4×D11—42no—
139C22×C4×D11—42no—
140C22×C4×D11C2311yescharacteristic
141C22×C4×D11C2311yescharacteristic
142C22×C4×D11C2311yescharacteristic
143C22×C4×D11C2312yes—
144C22×C4×D11C2312yes—
145C22×C4×D11C2311yescharacteristic
146C22×C4×D11C2311yescharacteristic
147C22×C4×D11C2311yescharacteristic
148C22×C4×D11C2311yescharacteristic
149C22×C4×D11C2311yescharacteristic
150C22×Dic22C2312yes—
151C11×#126—28no—
152C2×C11×C4⋊C4C2311yescharacteristic
153C2×C11×C4⋊C4C2312yes—
154C2×C11×C4⋊C4C2311yescharacteristic
155C2×C11×C4⋊C4C2312yes—
156C2×C11×C4⋊C4C2312yes—
157C2×C11×C4⋊C4C2311yescharacteristic
158C2×C11×C4⋊C4C2312yes—
159C2×C11×C4⋊C4C2311yescharacteristic
160C2×C11×C22⋊C4C2311yescharacteristic
161C2×C11×C22⋊C4C2312yes—
162C2×C11×C22⋊C4C2312yes—
163C2×C11×C22⋊C4C2311yescharacteristic
164C2×C42×C11C2311yescharacteristic
165C2×C42×C11C2311yescharacteristic
166C2×C42×C11C2312yes—
167C2×C22⋊Dic11C2311yescharacteristic
168C2×C22⋊Dic11C2311yescharacteristic
169#66983—42no—
170#66983—42no—
171C2×(C2×D11)⋊C4C2312yes—
172C2×(C2×D11)⋊C4C2312yes—
173C2×(C2×D11)⋊C4C2312yes—
174C2×(C2×D11)⋊C4C2312yes—
175C2×(C2×D11)⋊C4C2312yes—
176C2×(C2×D11)⋊C4C2311yescharacteristic
177C2×(C2×D11)⋊C4C2311yescharacteristic
178C2×(C2×D11)⋊C4C2312yes—
179C2×(C2×D11)⋊C4C2312yes—
180C2×(C2×D11)⋊C4C2312yes—
181C2×(C2×D11)⋊C4C2312yes—
182C2×(C2×D11)⋊C4C2312yes—
183C2×(C2×D11)⋊C4C2312yes—
184C2×(C2×D11)⋊C4C2312yes—
185C2×(C2×D11)⋊C4C2312yes—
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×C4⋊Dic11C2312yes—
196C2×C4⋊Dic11C2311yescharacteristic
197C2×C4⋊Dic11C2311yescharacteristic
198C2×Dic11⋊C4C2312yes—
199C2×Dic11⋊C4C2312yes—
200C2×Dic11⋊C4C2312yes—
201C2×Dic11⋊C4C2312yes—
202C2×C4×Dic11C2311yescharacteristic
203C2×C4×Dic11C2311yescharacteristic
204C2×C4×Dic11C2312yes—
205C2×C4×Dic11C2311yescharacteristic
206C2×C4×Dic11C2311yescharacteristic
207C2×C4×Dic11C2311yescharacteristic
208C2×C4×Dic11C2311yescharacteristic
209#66951—28no—
210#66949—28no—
211#66948—28no—
212#66948—24no—
213#66948—24no—
214#66948—28no—
215#66948—28no—
216#66948—42no—
217#66948—42no—
218#66947—28no—
219#66946—28no—
220#66946—42no—
221#66941—42no—
222#66938—28no—
223#66937—28no—
224#66936—28no—
225#66935—28no—
226#66935—28no—
227C22⋊C4×D11—24no—
228C22⋊C4×D11D418yescomplemented
229#66928—28no—
230#66927—42no—
231C4×D44—28no—
232C4×D44—42no—
233C42×D11—42no—
234C42×D11—42no—
235C11×#95C2312yes—
236C11×#95C2311yescharacteristic
237C11×#95C2311yescharacteristic
238C11×#95C2312yes—
239C11×#95C2312yes—
240C11×#95C2312yes—
241C11×#95C2312yes—
242C11⋊#95C2312yes—
243C11⋊#95C2312yes—
244C11⋊#95C2312yes—
245C11⋊#95C2311yescharacteristic
246C11⋊#95C2311yescharacteristic
247C11⋊#95C2311yescharacteristic
248C11⋊#95C2311yescharacteristic
249C11⋊#95C2311yescharacteristic
250C11⋊#95C2311yescharacteristic
251C11⋊#95C2312yes—
252C11⋊#95C2312yes—
253C11⋊#95C2312yes—
254C11⋊#95C2312yes—
255#35005—111nomaximal, Sylow
256C24×C11C2411yescharacteristic
257C23×D11—22no—
258C23×D11—22no—
259C23×D11—41no—
260C23×D11—41no—
261C23×D11—41no—
262C23×D11—41no—
263C23×D11C2×D414yes—
264C23×D11C2412yes—
265C23×D11C2412yes—
266C23×D11C2411yescharacteristic
267C23×D11C2411yescharacteristic
268C22×C4×C11—22no—
269C22×C4×C11—22no—
270C22×C4×C11—22no—
271C22×C4×C11C2411yescharacteristic
272C22×C4×C11C2412yes—
273C22×C4×C11C2412yes—
274C22×C4×C11C2411yescharacteristic
275C22×C4×C11C2412yes—
276C22×C4×C11C2412yes—
277C22×C4×C11C2411yescharacteristic
278C22×C4×C11C2411yescharacteristic
279C22×C4×C11C2411yescharacteristic
280C22×C4×C11C2411yescharacteristic
281C2×C22⋊D11—24no—
282C2×C22⋊D11—24no—
283C2×C22⋊D11—42no—
284C2×C22⋊D11—42no—
285C2×C22⋊D11—42no—
286C2×C22⋊D11—42no—
287C22×Dic11—22no—
288C22×Dic11—41no—
289C22×Dic11—41no—
290C22×Dic11C2411yescharacteristic
291C22×Dic11C2411yescharacteristic
292C22×Dic11C2412yes—
293C22×Dic11C2412yes—
294C22×Dic11C2411yescharacteristic
295C22×Dic11C2411yescharacteristic
296C22×Dic11C2411yescharacteristic
297C22×Dic11C2411yescharacteristic
298C2×D44—24no—
299C2×D44—24no—
300C2×D44—24no—
301C2×D44—24no—
302C2×D44—24no—
303C2×D44—24no—
304C2×D44—24no—
305C2×D44—24no—
306C2×D44—24no—
307C2×D44—22no—
308C2×D44—22no—
309C2×D44—24no—
310C2×D44—22no—
311C2×D44—22no—
312C2×D44—22no—
313C2×D44—22no—
314C2×D44—42no—
315C2×D44—42no—
316C2×D44—42no—
317C2×D44—42no—
318C2×D44—42no—
319C2×D44—42no—
320C2×D44—42no—
321C2×D44—42no—
322C2×C4×D11—22no—
323C2×C4×D11—24no—
324C2×C4×D11—22no—
325C2×C4×D11—22no—
326C2×C4×D11—24no—
327C2×C4×D11—22no—
328C2×C4×D11—22no—
329C2×C4×D11—22no—
330C2×C4×D11—22no—
331C2×C4×D11—22no—
332C2×C4×D11—41no—
333C2×C4×D11—41no—
334C2×C4×D11—41no—
335C2×C4×D11—41no—
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—42no—
345C2×C4×D11—42no—
346C2×C4×D11—42no—
347C2×C4×D11—42no—
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—24no—
358C11×C4⋊C4—24no—
359C11×C4⋊C4—24no—
360C11×C4⋊C4—22no—
361C11×C4⋊C4—22no—
362C11×C4⋊C4—22no—
363C11×C4⋊C4—22no—
364C11×C22⋊C4—24no—
365C11×C22⋊C4—24no—
366C11×C22⋊C4—22no—
367C11×C22⋊C4C2×D414yes—
368C42×C11—24no—
369C42×C11—22no—
370C42×C11—22no—
371C22⋊Dic11—22no—
372C22⋊Dic11C2×D414yes—
373(C2×D11)⋊C4—24no—
374(C2×D11)⋊C4—24no—
375(C2×D11)⋊C4—24no—
376(C2×D11)⋊C4—22no—
377(C2×D11)⋊C4—24no—
378(C2×D11)⋊C4—24no—
379(C2×D11)⋊C4—24no—
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—22no—
387(C2×D11)⋊C4—42no—
388(C2×D11)⋊C4—42no—
389(C2×D11)⋊C4—42no—
390(C2×D11)⋊C4—42no—
391(C2×D11)⋊C4—42no—
392(C2×D11)⋊C4—42no—
393(C2×D11)⋊C4—42no—
394(C2×D11)⋊C4—42no—
395(C2×D11)⋊C4C2×D414yes—
396(C2×D11)⋊C4C2×D414yes—
397C4⋊Dic11—24no—
398C4⋊Dic11—22no—
399C4⋊Dic11—22no—
400Dic11⋊C4—24no—
401Dic11⋊C4—24no—
402Dic11⋊C4—42no—
403Dic11⋊C4—42no—
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#2496D1111yescharacteristic, complemented
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—21no—
439C23×C11—21no—
440C23×C11C22×D412yes—
441C23×C11C2511yescharacteristic
442C22×D11—21no—
443C22×D11—21no—
444C22×D11—21no—
445C22×D11—21no—
446C22×D11—21no—
447C22×D11—21no—
448C22×D11—21no—
449C22×D11—21no—
450C22×D11—21no—
451C22×D11—21no—
452C22×D11—28no—
453C22×D11—22no—
454C22×D11—22no—
455C22×D11—22no—
456C22×D11—22no—
457C22×D11—22no—
458C22×D11—22no—
459C22×D11—22no—
460C22×D11—22no—
461C22×D11—22no—
462C22×D11—22no—
463C22×D11—22no—
464C22×D11—22no—
465C22×D11—22no—
466C22×D11—22no—
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—
477C2×C4×C11—21no—
478C2×C4×C11—21no—
479C2×C4×C11—21no—
480C2×C4×C11—21no—
481C2×C4×C11—21no—
482C2×C4×C11—21no—
483C2×C4×C11—22no—
484C2×C4×C11—22no—
485C2×C4×C11—22no—
486C2×C4×C11—22no—
487C2×C4×C11—21no—
488C2×C4×C11—22no—
489C2×C4×C11—22no—
490C2×C4×C11—22no—
491C2×C4×C11—22no—
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×C11C22×D412yes—
503C2×C4×C11C22×D412yes—
504C2×C4×C11C2×#4112yes—
505C2×C4×C11C2×#4112yes—
506C2×C4×C11H(5,𝔽2)12yes—
507C2×C4×C11H(5,𝔽2)12yes—
508C22⋊D11—84no—
509C22⋊D11—84no—
510C2×Dic11—21no—
511C2×Dic11—21no—
512C2×Dic11—21no—
513C2×Dic11—21no—
514C2×Dic11—21no—
515C2×Dic11—21no—
516C2×Dic11—21no—
517C2×Dic11—21no—
518C2×Dic11—22no—
519C2×Dic11—22no—
520C2×Dic11—21no—
521C2×Dic11—21no—
522C2×Dic11—21no—
523C2×Dic11—22no—
524C2×Dic11—22no—
525C2×Dic11—21no—
526C2×Dic11—21no—
527C2×Dic11—22no—
528C2×Dic11—21no—
529C2×Dic11—22no—
530C2×Dic11—44no—
531C2×Dic11C22×D412yes—
532C2×Dic11C22×D412yes—
533C2×Dic11C2×#4112yes—
534C2×Dic11C2×#4112yes—
535D44—48no—
536D44—48no—
537D44—44no—
538D44—44no—
539D44—84no—
540D44—84no—
541D44—84no—
542D44—84no—
543C4×D11—28no—
544C4×D11—44no—
545C4×D11—44no—
546C4×D11—44no—
547C4×D11—44no—
548C4×D11—44no—
549C4×D11—44no—
550C4×D11—44no—
551C4×D11—84no—
552C4×D11—84no—
553Dic22—84no—
554C24×C4—111no—
555#538—2216no—
556C2×C4⋊Q8—111no—
557C2×#127—111no—
558C2×#126—112no—
559C2×#126C2×D1112yes—
560C2×#124—112no—
561C2×#124—112no—
562C2×#123—112no—
563C2×#123—112no—
564C2×C22⋊Q8—112no—
565C2×#121—111no—
566C2×#121—111no—
567C2×#121—112no—
568C2×#121—111no—
569C2×#121—111no—
570C2×#121—112no—
571C2×#121—112no—
572C2×#121—111no—
573C2×#121—111no—
574C2×#121—112no—
575C2×#120—112no—
576C2×#120—112no—
577C2×C4×D4—112no—
578C2×C4×D4—111no—
579C2×C4×D4—112no—
580C2×C4×D4—111no—
581C22×C22⋊C4—111no—
582C22×C22⋊C4—111no—
583C22×C42—111no—
584C22×C42—111no—
585#400—112no—
586#400C2×D1112yescomplemented
587#397—112no—
588#397—112no—
589#397—112no—
590#397C2×D1112yes—
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#390—111no—
608#389—112no—
609#389—111no—
610#389—111no—
611#389C2×D1111yescharacteristic, complemented
612#389C2×D1111yescharacteristic, complemented
613#388—112no—
614#388—112no—
615#388—112no—
616#388—112no—
617#387—112no—
618#387C2×D1112yescomplemented
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#386—112no—
629#385—112no—
630#385—112no—
631#384—111no—
632#384C2×D1111yescharacteristic, complemented
633#380—111no—
634#380—111no—
635#380—111no—
636#380—111no—
637#380—112no—
638#380C2×D1111yescharacteristic
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—112no—
648C4×C22⋊C4—111no—
649C4×C22⋊C4—111no—
650C4×C22⋊C4—112no—
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×C11C23×D411yescharacteristic
662C22×C11C22×#4111yescharacteristic
663C22×C11C22×#4111yescharacteristic
664C22×C11C2×H(5,𝔽2)11yescharacteristic
665C22×C11C2×H(5,𝔽2)11yescharacteristic
666C22×C11#58511yescharacteristic
667C22×C11#58511yescharacteristic
668C2×D11—22no—
669C2×D11—22no—
670C2×D11—22no—
671C2×D11—22no—
672C2×D11—22no—
673C2×D11—22no—
674C2×D11—22no—
675C2×D11—22no—
676C2×D11—22no—
677C2×D11—416no—
678C2×D11—41no—
679C2×D11—41no—
680C2×D11—41no—
681C2×D11—41no—
682C2×D11—42no—
683C2×D11—42no—
684C2×D11—42no—
685C2×D11—42no—
686C2×D11—42no—
687C2×D11—42no—
688C2×D11—42no—
689C2×D11—42no—
690C2×D11—42no—
691C2×D11—42no—
692C2×D11—42no—
693C2×D11—42no—
694C2×D11—42no—
695C2×D11—42no—
696C2×D11#53214yes—
697C4×C11—22no—
698C4×C11—22no—
699C4×C11—22no—
700C4×C11—42no—
701C4×C11—42no—
702C4×C11—41no—
703C4×C11—42no—
704C4×C11—42no—
705C4×C11—41no—
706C4×C11#53814yescomplemented
707Dic11—22no—
708Dic11—22no—
709Dic11—22no—
710Dic11—22no—
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×D4—111no—
722C22×D4—111no—
723C22×D4—112no—
724C22×D4—112no—
725C22×D4—112no—
726C22×D4—112no—
727C23×C4—111no—
728C23×C4—111no—
729C23×C4—111no—
730C23×C4—111no—
731C23×C4—111no—
732C23×C4—111no—
733C23×C4—111no—
734C23×C4—112no—
735C23×C4—112no—
736C23×C4—111no—
737C23×C4—111no—
738C23×C4—224no—
739C23×C4—442no—
740C23×C4—442no—
741C23×C4C22×D1111yescharacteristic
742C4⋊Q8—442no—
743#127—442no—
744#126—28no—
745#126—228no—
746#124—228no—
747#124—228no—
748#123—228no—
749#123—228no—
750C22⋊Q8—228no—
751#121—228no—
752#121—228no—
753#121—224no—
754#121—224no—
755#121—228no—
756#121—228no—
757#121—442no—
758#121—442no—
759#121—442no—
760#121—442no—
761#120—228no—
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—111no—
771C2×C4⋊C4—112no—
772C2×C4⋊C4—112no—
773C2×C4⋊C4—112no—
774C2×C4⋊C4C22×D1111yescharacteristic
775C2×C4⋊C4C22×D1112yes—
776C2×C4⋊C4C22×D1112yes—
777C2×C4⋊C4C22×D1112yes—
778C2×C4⋊C4C22×D1111yescharacteristic
779C2×C4⋊C4C22×D1111yescharacteristic
780C2×C4⋊C4C22×D1111yescharacteristic
781C2×C4⋊C4C22×D1112yes—
782C2×C22⋊C4—111no—
783C2×C22⋊C4—111no—
784C2×C22⋊C4—111no—
785C2×C22⋊C4—118no—
786C2×C22⋊C4—111no—
787C2×C22⋊C4—111no—
788C2×C22⋊C4—111no—
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—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—112no—
809C2×C22⋊C4—224no—
810C2×C22⋊C4C22×D1111yescharacteristic
811C2×C22⋊C4C22×D1112yes—
812C2×C22⋊C4C22×D1112yes—
813C2×C22⋊C4C22×D1111yescharacteristic
814C2×C42—112no—
815C2×C42—111no—
816C2×C42—111no—
817C2×C42—111no—
818C2×C42—111no—
819C2×C42—111no—
820C2×C42—111no—
821C2×C42—442no—
822C2×C42—442no—
823C2×C42C22×D1112yes—
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#95C22×D1111yescharacteristic
840#95C22×D1111yescharacteristic
841#95C22×D1112yes—
842#95C22×D1112yes—
843#95C22×D1112yes—
844#95C22×D1112yes—
845#95C22×D1112yes—
846C2×C11—42no—
847C2×C11C2×#53211yescharacteristic
848C2×C11C2×#53811yescharacteristic
849C2×C11#345511yescharacteristic
850C2×C11#349611yescharacteristic
851C2×C11#349611yescharacteristic
852C2×C11#350511yescharacteristic
853C2×C11#350611yescharacteristic
854D11—24no—
855D11—42no—
856D11—82no—
857D11—82no—
858C24—111no—
859C24—111no—
860C24—114no—
861C24—112no—
862C24—112no—
863C24—222no—
864C24—222no—
865C24—441no—
866C24—441no—
867C24—441no—
868C24—441no—
869C24C23×D1111yescharacteristic
870C2×Q8—224no—
871C2×Q8—442no—
872C2×Q8—442no—
873C2×D4—224no—
874C2×D4—224no—
875C2×D4—224no—
876C2×D4—224no—
877C2×D4—224no—
878C2×D4—224no—
879C2×D4—224no—
880C2×D4—224no—
881C2×D4—224no—
882C2×D4—224no—
883C2×D4—224no—
884C2×D4—222no—
885C2×D4—222no—
886C2×D4—224no—
887C2×D4—222no—
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—111no—
907C22×C4—111no—
908C22×C4—111no—
909C22×C4—111no—
910C22×C4—114no—
911C22×C4—114no—
912C22×C4—114no—
913C22×C4—114no—
914C22×C4—111no—
915C22×C4—111no—
916C22×C4—112no—
917C22×C4—112no—
918C22×C4—222no—
919C22×C4—224no—
920C22×C4—222no—
921C22×C4—222no—
922C22×C4—222no—
923C22×C4—222no—
924C22×C4—222no—
925C22×C4—222no—
926C22×C4—222no—
927C22×C4—222no—
928C22×C4—224no—
929C22×C4—441no—
930C22×C4—441no—
931C22×C4—441no—
932C22×C4—441no—
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—442no—
942C22×C4—442no—
943C22×C4—442no—
944C22×C4—442no—
945C22×C4—4416no—
946C22×C4—441no—
947C22×C4—441no—
948C22×C4C23×D1111yescharacteristic
949C22×C4C23×D1112yes—
950C22×C4C23×D1112yes—
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—24no—
960C4⋊C4—24no—
961C4⋊C4—24no—
962C4⋊C4—22no—
963C4⋊C4—22no—
964C4⋊C4—22no—
965C4⋊C4—22no—
966C4⋊C4—224no—
967C4⋊C4—224no—
968C4⋊C4—224no—
969C4⋊C4—222no—
970C4⋊C4—222no—
971C4⋊C4—442no—
972C4⋊C4—442no—
973C22⋊C4—24no—
974C22⋊C4—24no—
975C22⋊C4—22no—
976C22⋊C4—114no—
977C22⋊C4—114no—
978C22⋊C4—114no—
979C22⋊C4—222no—
980C22⋊C4—224no—
981C22⋊C4—224no—
982C22⋊C4—224no—
983C22⋊C4—224no—
984C22⋊C4—224no—
985C22⋊C4—224no—
986C22⋊C4—224no—
987C22⋊C4—224no—
988C22⋊C4—224no—
989C22⋊C4—224no—
990C22⋊C4—224no—
991C22⋊C4—222no—
992C22⋊C4—224no—
993C22⋊C4—222no—
994C22⋊C4—442no—
995C22⋊C4—442no—
996C22⋊C4—442no—
997C22⋊C4—442no—
998C22⋊C4—442no—
999C22⋊C4—442no—
1000C22⋊C4—442no—
1001C22⋊C4—442no—
1002C22⋊C4D4×D1114yes—
1003C42—24no—
1004C42—22no—
1005C42—22no—
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—112no—
1021C23—112no—
1022C23—112no—
1023C23—112no—
1024C23—228no—
1025C23—221no—
1026C23—221no—
1027C23—221no—
1028C23—221no—
1029C23—221no—
1030C23—221no—
1031C23—221no—
1032C23—221no—
1033C23—221no—
1034C23—221no—
1035C23—222no—
1036C23—222no—
1037C23—222no—
1038C23—222no—
1039C23—222no—
1040C23—222no—
1041C23—222no—
1042C23—222no—
1043C23—222no—
1044C23—222no—
1045C23—222no—
1046C23—222no—
1047C23—222no—
1048C23—222no—
1049C23—444no—
1050C23—444no—
1051C23—444no—
1052C23—444no—
1053C23—444no—
1054C23—444no—
1055C23C2×D4×D1112yes—
1056C23C24×D1111yescharacteristic
1057Q8—884no—
1058D4—448no—
1059D4—448no—
1060D4—444no—
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—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—21no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—22no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—22no—
1089C2×C4—21no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—44no—
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—228no—
1106C2×C4—222no—
1107C2×C4—222no—
1108C2×C4—221no—
1109C2×C4—221no—
1110C2×C4—221no—
1111C2×C4—222no—
1112C2×C4—221no—
1113C2×C4—221no—
1114C2×C4—222no—
1115C2×C4—221no—
1116C2×C4—222no—
1117C2×C4—222no—
1118C2×C4—444no—
1119C2×C4—444no—
1120C2×C4—444no—
1121C2×C4—444no—
1122C2×C4—444no—
1123C2×C4—444no—
1124C2×C4—444no—
1125C2×C4—444no—
1126C2×C4—884no—
1127C2×C4—884no—
1128C2×C4C2×D4×D1112yes—
1129C2×C4C2×D4×D1112yes—
1130C2×C4#41×D1112yes—
1131C2×C4#41×D1112yes—
1132C2×C4#6704212yes—
1133C2×C4#6704212yes—
1134C22—22no—
1135C22—22no—
1136C22—22no—
1137C22—41no—
1138C22—41no—
1139C22—41no—
1140C22—41no—
1141C22—114no—
1142C22—222no—
1143C22—222no—
1144C22—222no—
1145C22—222no—
1146C22—222no—
1147C22—222no—
1148C22—222no—
1149C22—222no—
1150C22—222no—
1151C22—4416no—
1152C22—441no—
1153C22—441no—
1154C22—441no—
1155C22—441no—
1156C22—442no—
1157C22—442no—
1158C22—442no—
1159C22—442no—
1160C22—442no—
1161C22—442no—
1162C22—442no—
1163C22—442no—
1164C22—442no—
1165C22—442no—
1166C22—442no—
1167C22—442no—
1168C22—442no—
1169C22—442no—
1170C22C22×D4×D1111yescharacteristic
1171C22C2×#41×D1111yescharacteristic
1172C22C2×#41×D1111yescharacteristic
1173C22C2×#6704211yescharacteristic
1174C22C2×#6704211yescharacteristic
1175C22#1062345711yescharacteristic
1176C22#1062345711yescharacteristic
1177C4—22no—
1178C4—22no—
1179C4—22no—
1180C4—42no—
1181C4—42no—
1182C4—42no—
1183C4—42no—
1184C4—41no—
1185C4—41no—
1186C4—222no—
1187C4—222no—
1188C4—222no—
1189C4—222no—
1190C4—442no—
1191C4—442no—
1192C4—441no—
1193C4—441no—
1194C4#1062323514yescomplemented
1195C2—42no—
1196C2—224no—
1197C2—442no—
1198C2—882no—
1199C2—882no—
1200C2D11×#53211yescharacteristic
1201C2C2×#1062323511yescharacteristic
1202C2#1308200711yescharacteristic
1203C2#1308237411yescharacteristic
1204C2#1308237411yescharacteristic
1205C2#1308245611yescharacteristic
1206C2#1308246911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2496C2
hypercenter#2496D11
hypocenterC11#35005
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2496

Complements

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

NH ≅ G/Ntype
1. C2×#10623235C2semidirect
2. #13076967C2semidirect
3. #13076962C2semidirect
4. #13076899C2semidirect
5. #13076899C2semidirect
6. #13074548C2semidirect
7. #13074351C2semidirect
8. #13073748C2semidirect
9. #13073743C2semidirect
10. #13073721C2semidirect
11. #13073710C2semidirect
12. #13073041C2semidirect
13. #13072975C2semidirect
14. #13072973C2semidirect
15. #13072204C2semidirect
16. #13072202C2semidirect
17. #13072132C2semidirect
18. #13072131C2semidirect
19. #13071315C2semidirect
20. C4×#66948C2semidirect
21. #13071124C2semidirect
22. C4×C22⋊C4×D11C2semidirect
23. C11×#2496C2semidirect
40. C2×#66946C22semidirect
41. C2×#66941C22semidirect
50. C2×#66927C22semidirect
52. C2×C4×D44C22semidirect
55. C11×#400C22semidirect
57. C11×#389C22semidirect
58. C11×#389C22semidirect
59. C11×#387C22semidirect
60. C11×#384C22semidirect
63. C4×C11×C4⋊C4C22semidirect
67. #10622604C22semidirect
68. #10622603C22semidirect
69. #10622602C22semidirect
70. #10622601C22semidirect
71. #10622601C22semidirect
72. #10622601C22semidirect
73. #10622601C22semidirect
74. #10622601C22semidirect
79. #10622598C22semidirect
80. #10622595C22semidirect
81. #10622594C22semidirect
82. #10622589C22semidirect
83. C4⋊C4×Dic11C22semidirect
84. #10622585C22semidirect
92. #10622553C22semidirect
93. #10622552C22semidirect
96. C4×(C2×D11)⋊C4C22semidirect
97. #10622541C22semidirect
98. #10622288C22semidirect
99. #10622288C22semidirect
100. #10622286C22semidirect
101. #10622286C22semidirect
104. #10622285C22semidirect
106. #10622283C22semidirect
107. #10622282C22semidirect
108. #10622281C22semidirect
112. #10622279C22semidirect
119. #10622278C22semidirect
120. #10622278C22semidirect
123. #10622259C22semidirect
228. C22⋊C4×D11D4semidirect
423. #2496D11semidirect
586. #400C2×D11semidirect
611. #389C2×D11semidirect
612. #389C2×D11semidirect
618. #387C2×D11semidirect
632. #384C2×D11semidirect
641. C4×C4⋊C4C2×D11semidirect
706. C4×C11#538semidirect
1013. C11#35005semidirect
1194. C4#10623235semidirect

Maximal subgroups

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

subgroupindex
C2×#106232352
#130769672
#130769622
#130768992
#130745482
#130743512
#130737482
#130737432
#130737212
#130737102
#130730412
#130729752
#130729732
#130722042
#130722022
#130721322
#130721312
#130713152
C4×#669482
#130711242
C4×C22⋊C4×D112
C11×#24962
#3500511