Finite Group Databasebeta

← #14923719

Subgroups — #14923719

Order 2816.

2646 conjugacy classes of subgroups.

The subgroup lattice has 1150 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623219C211yesmaximal, characteristic, complemented
2C2×#10623158C211yesmaximal, characteristic
3#13072992C211yesmaximal, characteristic, complemented
4#13072991C211yesmaximal, characteristic, complemented
5#13072975C211yesmaximal, characteristic, complemented
6#13072973C211yesmaximal, characteristic, complemented
7#13072971C211yesmaximal, characteristic, complemented
8#13072968C211yesmaximal, characteristic, complemented
9#13072955C211yesmaximal, characteristic, complemented
10#13072939C212yesmaximal, complemented
11#13072937C212yesmaximal, complemented
12#13072746C212yesmaximal, complemented
13#13072735C212yesmaximal, complemented
14#13071905C212yesmaximal, complemented
15#13071901C212yesmaximal, complemented
16#13071157C212yesmaximal, complemented
17#13071155C212yesmaximal, complemented
18#13071105C211yesmaximal, characteristic, complemented
19#13071105C211yesmaximal, characteristic, complemented
20#13070998C211yesmaximal, characteristic, complemented
21C4×#66945C211yesmaximal, characteristic, complemented
22C4×C22⋊C4×D11C211yesmaximal, characteristic, complemented
23C11×#2489C211yesmaximal, characteristic, complemented
24C22×#4343C2211yescharacteristic
25C23×C4×D11C2211yescharacteristic
26C2×C11×#125C2211yescharacteristic, complemented
27C2×C11×C22⋊Q8C2211yescharacteristic
28C2×#66999C2211yescharacteristic
29C2×#66983C2211yescharacteristic
30#10623219—28no—
31#10623158—28no—
32C2×#66949C2212yes—
33C2×#66949C2212yes—
34C2×#66948C2211yescharacteristic
35C2×#66947C2212yes—
36C2×#66946C2212yes—
37C2×#66945C2211yescharacteristic
38C2×#66945C2211yescharacteristic
39C2×#66945C2211yescharacteristic
40C2×#66941C2211yescharacteristic, complemented
41C2×#66941C2211yescharacteristic, complemented
42C2×#66940C2212yescomplemented
43C2×#66940C2212yescomplemented
44C2×#66938C2212yes—
45C2×#66935C2212yes—
46C2×(C22⋊D11)⋊C4C2212yes—
47C2×C22⋊C4×D11C2211yescharacteristic
48C2×C22⋊C4×D11C2211yescharacteristic
49C2×#66928C2212yes—
50C2×C42×D11C2211yescharacteristic
51C2×C42×D11C2211yescharacteristic
52C2×#66923C2211yescharacteristic, complemented
53C11×#400C2212yescomplemented
54C11×#397C2212yes—
55C11×#391C2211yescharacteristic, complemented
56C11×#391C2211yescharacteristic, complemented
57C11×#388C2212yes—
58C11×#382C2212yescomplemented
59C11×#380C2211yescharacteristic
60C4×C11×C4⋊C4C2211yescharacteristic, complemented
61C4×C11×C22⋊C4C2211yescharacteristic
62#10622843C2211yescharacteristic, complemented
63#10622843C2211yescharacteristic, complemented
64#10622825C2211yescharacteristic
65C4×C22⋊Dic11C2211yescharacteristic
66#10622606C2212yescomplemented
67#10622604C2212yes—
68#10622603C2212yescomplemented
69#10622601C2212yes—
70#10622601C2211yescharacteristic, complemented
71#10622601C2211yescharacteristic, complemented
72#10622600C2211yescharacteristic
73#10622600C2211yescharacteristic
74#10622595C2212yescomplemented
75C4⋊C4×Dic11C2211yescharacteristic, complemented
76C4⋊C4×Dic11C2211yescharacteristic, complemented
77#10622587C2212yescomplemented
78#10622572C2212yes—
79#10622572C2212yes—
80#10622570C2212yes—
81#10622568C2212yes—
82#10622560C2212yes—
83#10622558C2212yes—
84C22⋊C4×Dic11C2211yescharacteristic
85C22⋊C4×Dic11C2212yes—
86C22⋊C4×Dic11C2211yescharacteristic
87#10622553C2212yescomplemented
88#10622552C2211yescharacteristic, complemented
89#10622552C2211yescharacteristic, complemented
90C4×(C2×D11)⋊C4C2212yes—
91C4×(C2×D11)⋊C4C2211yescharacteristic
92C4×(C2×D11)⋊C4C2211yescharacteristic
93C4×C4⋊Dic11C2211yescharacteristic, complemented
94C42×Dic11C2212yescomplemented
95#10622288C2212yes—
96#10622288C2212yescomplemented
97#10622286C2212yes—
98#10622286C2212yescomplemented
99#10622286C2212yescomplemented
100#10622285C2212yes—
101#10622282C2212yes—
102#10622282C2212yes—
103#10622282C2212yescomplemented
104#10622282C2212yescomplemented
105#10622279C2211yescharacteristic
106#10622279C2212yes—
107#10622279C2212yes—
108#10622279C2211yescharacteristic
109#10622279C2212yescomplemented
110#10622279C2212yescomplemented
111#10622279C2212yescomplemented
112#10622279C2212yescomplemented
113#10622278C2212yes—
114#10622278C2212yes—
115#10622278C2212yes—
116#10622278C2212yes—
117#10622277C2212yes—
118D11×#95C2211yescharacteristic
119D11×#95C2211yescharacteristic
120#10622271C2212yescomplemented
121#10622271C2212yescomplemented
122#10622263C2212yescomplemented
123#10622261C2212yescomplemented
124#10622259C2212yescomplemented
125C24×D11C2311yescharacteristic
126C22×Q8×C11C2311yescharacteristic
127C23×C4×C11C2311yescharacteristic
128C22×C22⋊D11C2312yes—
129C23×Dic11C2311yescharacteristic
130C2×#4343—24no—
131C2×#4343—24no—
132C2×#4343—24no—
133C22×D44C2312yes—
134C22×D44C2311yescharacteristic
135C22×D44C2312yes—
136C22×C4×D11—24no—
137C22×C4×D11—24no—
138C22×C4×D11—24no—
139C22×C4×D11C2312yes—
140C22×C4×D11C2311yescharacteristic
141C22×C4×D11C2311yescharacteristic
142C22×C4×D11C2311yescharacteristic
143C22×C4×D11C2311yescharacteristic
144C22×C4×D11C2311yescharacteristic
145C22×C4×D11C2311yescharacteristic
146C22×C4×D11C2311yescharacteristic
147C22×C4×D11C2311yescharacteristic
148C22×Dic22C2312yes—
149C22×Dic22C2312yes—
150C11×#125—24no—
151C11×C22⋊Q8—24no—
152C2×C11×C4⋊C4C2312yes—
153C2×C11×C4⋊C4C2312yes—
154C2×C11×C4⋊C4C2311yescharacteristic
155C2×C11×C4⋊C4C2311yescharacteristic
156C2×C11×C4⋊C4C2312yes—
157C2×C11×C4⋊C4C2311yescharacteristic
158C2×C11×C22⋊C4C2311yescharacteristic
159C2×C11×C22⋊C4C2311yescharacteristic
160C2×C11×C22⋊C4C2312yes—
161C2×C11×C22⋊C4C2312yes—
162C2×C42×C11C2311yescharacteristic
163C2×C42×C11C2311yescharacteristic
164C2×C42×C11C2312yes—
165C2×C22⋊Dic11C2311yescharacteristic
166C2×C22⋊Dic11C2312yes—
167C2×C22⋊Dic11C2311yescharacteristic
168#66999—24no—
169#66983—24no—
170C2×(C2×D11)⋊C4C2312yes—
171C2×(C2×D11)⋊C4C2312yes—
172C2×(C2×D11)⋊C4C2312yes—
173C2×(C2×D11)⋊C4C2311yescharacteristic
174C2×(C2×D11)⋊C4C2311yescharacteristic
175C2×(C2×D11)⋊C4C2311yescharacteristic
176C2×(C2×D11)⋊C4C2312yes—
177C2×(C2×D11)⋊C4C2312yes—
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)⋊C4C2311yescharacteristic
190C2×C4⋊Dic11C2311yescharacteristic
191C2×C4⋊Dic11C2311yescharacteristic
192C2×C4⋊Dic11C2311yescharacteristic
193C2×Dic11⋊C4C2312yes—
194C2×Dic11⋊C4C2312yes—
195C2×Dic11⋊C4C2312yes—
196C2×Dic11⋊C4C2312yes—
197C2×Dic11⋊C4C2312yes—
198C2×C4×Dic11C2311yescharacteristic
199C2×C4×Dic11C2311yescharacteristic
200C2×C4×Dic11C2311yescharacteristic
201C2×C4×Dic11C2311yescharacteristic
202C2×C4×Dic11C2311yescharacteristic
203C2×C4×Dic11C2311yescharacteristic
204C2×C4×Dic11C2312yes—
205C2×C4×Dic11C2312yes—
206C2×C4×Dic11C2312yes—
207C2×C4×Dic11C2312yes—
208C2×C4×Dic11C2312yes—
209C2×C4×Dic11C2312yes—
210#66949—28no—
211#66949—28no—
212#66948—24no—
213#66947—28no—
214#66946—28no—
215#66945—24no—
216#66945—24no—
217#66945D418yes—
218#66941—24no—
219#66941—24no—
220#66940—28no—
221#66940—28no—
222#66938—28no—
223#66935—28no—
224(C22⋊D11)⋊C4—28no—
225C22⋊C4×D11—24no—
226C22⋊C4×D11—24no—
227#66928—28no—
228C42×D11—24no—
229C42×D11—24no—
230#66923—24no—
231C11×#95C2312yes—
232C11×#95C2312yes—
233C11×#95C2312yes—
234C11×#95C2312yes—
235C11×#95C2312yes—
236C11×#95C2311yescharacteristic
237C11×#95C2311yescharacteristic
238C11×#95C2312yes—
239C11⋊#95C2311yescharacteristic
240C11⋊#95C2312yes—
241C11⋊#95C2312yes—
242C11⋊#95C2312yes—
243C11⋊#95C2312yes—
244C11⋊#95C2312yes—
245C11⋊#95C2311yescharacteristic
246C11⋊#95C2312yes—
247C11⋊#95C2312yes—
248C11⋊#95C2311yescharacteristic
249C11⋊#95C2311yescharacteristic
250C11⋊#95C2312yes—
251C11⋊#95C2312yes—
252C11⋊#95C2311yescharacteristic
253C11⋊#95C2311yescharacteristic
254C11⋊#95C2312yes—
255#34813—111nomaximal, Sylow
256C24×C11C2411yescharacteristic
257C23×D11—22no—
258C23×D11—22no—
259C23×D11—22no—
260C23×D11—22no—
261C23×D11—22no—
262C23×D11—41no—
263C23×D11—41no—
264C23×D11C2412yes—
265C23×D11C2411yescharacteristic
266C23×D11C2411yescharacteristic
267C2×Q8×C11—22no—
268C2×Q8×C11—22no—
269C2×Q8×C11—22no—
270C22×C4×C11—22no—
271C22×C4×C11—22no—
272C22×C4×C11—22no—
273C22×C4×C11C2412yes—
274C22×C4×C11C2411yescharacteristic
275C22×C4×C11C2411yescharacteristic
276C22×C4×C11C2412yes—
277C22×C4×C11C2411yescharacteristic
278C22×C4×C11C2411yescharacteristic
279C22×C4×C11C2412yes—
280C22×C4×C11C2412yes—
281C22×C4×C11C2411yescharacteristic
282C22×C4×C11C2411yescharacteristic
283C2×C22⋊D11—24no—
284C2×C22⋊D11—24no—
285C2×C22⋊D11—42no—
286C22×Dic11—22no—
287C22×Dic11—22no—
288C22×Dic11—22no—
289C22×Dic11C2411yescharacteristic
290C22×Dic11C2411yescharacteristic
291C22×Dic11C2412yes—
292C22×Dic11C2412yes—
293C22×Dic11C2412yes—
294C22×Dic11C2411yescharacteristic
295C22×Dic11C2411yescharacteristic
296C22×Dic11C2411yescharacteristic
297C22×Dic11C2411yescharacteristic
298#4343—416no—
299C2×D44—24no—
300C2×D44—24no—
301C2×D44—24no—
302C2×D44—24no—
303C2×D44—24no—
304C2×D44—22no—
305C2×D44—22no—
306C2×D44—22no—
307C2×D44—42no—
308C2×C4×D11—24no—
309C2×C4×D11—22no—
310C2×C4×D11—22no—
311C2×C4×D11—22no—
312C2×C4×D11—22no—
313C2×C4×D11—22no—
314C2×C4×D11—22no—
315C2×C4×D11—24no—
316C2×C4×D11—24no—
317C2×C4×D11—22no—
318C2×C4×D11—22no—
319C2×C4×D11—22no—
320C2×C4×D11—22no—
321C2×C4×D11—22no—
322C2×C4×D11—22no—
323C2×C4×D11—22no—
324C2×C4×D11—22no—
325C2×C4×D11—22no—
326C2×C4×D11—22no—
327C2×C4×D11—22no—
328C2×C4×D11—41no—
329C2×C4×D11—41no—
330C2×C4×D11—41no—
331C2×C4×D11—41no—
332C2×C4×D11—416no—
333C2×C4×D11C2×D414yes—
334C2×C4×D11#4114yes—
335C2×C4×D11#4114yes—
336C2×Dic22—24no—
337C2×Dic22—24no—
338C2×Dic22—24no—
339C2×Dic22—24no—
340C2×Dic22—42no—
341C2×Dic22—42no—
342C11×C4⋊C4—24no—
343C11×C4⋊C4—24no—
344C11×C4⋊C4—22no—
345C11×C4⋊C4—24no—
346C11×C4⋊C4—22no—
347C11×C4⋊C4C2×D414yes—
348C11×C22⋊C4—22no—
349C11×C22⋊C4—24no—
350C11×C22⋊C4—24no—
351C11×C22⋊C4—22no—
352C42×C11—22no—
353C42×C11—22no—
354C42×C11—24no—
355C22⋊Dic11—22no—
356C22⋊Dic11—42no—
357C22⋊Dic11#4114yescomplemented
358(C2×D11)⋊C4—24no—
359(C2×D11)⋊C4—24no—
360(C2×D11)⋊C4—24no—
361(C2×D11)⋊C4—22no—
362(C2×D11)⋊C4—22no—
363(C2×D11)⋊C4—24no—
364(C2×D11)⋊C4—24no—
365(C2×D11)⋊C4—24no—
366(C2×D11)⋊C4—24no—
367(C2×D11)⋊C4—22no—
368(C2×D11)⋊C4—24no—
369(C2×D11)⋊C4—24no—
370(C2×D11)⋊C4—24no—
371(C2×D11)⋊C4—42no—
372(C2×D11)⋊C4—42no—
373(C2×D11)⋊C4—42no—
374(C2×D11)⋊C4—42no—
375(C2×D11)⋊C4—42no—
376(C2×D11)⋊C4C2×D418yes—
377(C2×D11)⋊C4#4114yescomplemented
378C4⋊Dic11—22no—
379C4⋊Dic11—22no—
380C4⋊Dic11C2×D414yes—
381Dic11⋊C4—24no—
382Dic11⋊C4—24no—
383Dic11⋊C4—24no—
384Dic11⋊C4—24no—
385Dic11⋊C4—24no—
386C4×Dic11—22no—
387C4×Dic11—22no—
388C4×Dic11—24no—
389C4×Dic11—22no—
390C4×Dic11—22no—
391C4×Dic11—24no—
392C4×Dic11—24no—
393C4×Dic11—22no—
394C4×Dic11—22no—
395C4×Dic11—42no—
396C4×Dic11—42no—
397C4×Dic11C2×D418yes—
398C2×#533—111no—
399C2×#525—111no—
400#2492—111no—
401#2492—111no—
402#2491—111no—
403#2491—111no—
404#2490—111no—
405#2490—111no—
406#2489—111no—
407#2489D1111yescharacteristic, complemented
408#2488—112no—
409#2488—112no—
410#2472—112no—
411#2472—112no—
412#2398—112no—
413#2398—112no—
414C4×#124—112no—
415C4×#124—112no—
416#2297—111no—
417#2297—111no—
418#2280—111no—
419C4×#117—111no—
420C2×C4×C22⋊C4—111no—
421C23×C11—21no—
422C23×C11—21no—
423C23×C11—21no—
424C23×C11—21no—
425C23×C11—21no—
426C23×C11—21no—
427C23×C11C2×#4112yes—
428C23×C11C2511yescharacteristic
429C22×D11—21no—
430C22×D11—21no—
431C22×D11—21no—
432C22×D11—21no—
433C22×D11—28no—
434C22×D11—21no—
435C22×D11—21no—
436C22×D11—21no—
437C22×D11—21no—
438C22×D11—21no—
439C22×D11—21no—
440C22×D11—22no—
441C22×D11—22no—
442C22×D11—22no—
443C22×D11—22no—
444C22×D11—22no—
445C22×D11—22no—
446C22×D11—22no—
447C22×D11—44no—
448C22×D11—44no—
449C22×D11—44no—
450C22×D11—44no—
451C22×D11—44no—
452C22×D11—44no—
453C22×D11C22×D412yes—
454C22×D11C2×#4112yes—
455C22×D11C2×#4112yes—
456C22×D11C2×#4112yes—
457Q8×C11—44no—
458C2×C4×C11—21no—
459C2×C4×C11—22no—
460C2×C4×C11—21no—
461C2×C4×C11—22no—
462C2×C4×C11—21no—
463C2×C4×C11—21no—
464C2×C4×C11—22no—
465C2×C4×C11—22no—
466C2×C4×C11—21no—
467C2×C4×C11—22no—
468C2×C4×C11—22no—
469C2×C4×C11—21no—
470C2×C4×C11—22no—
471C2×C4×C11—22no—
472C2×C4×C11—21no—
473C2×C4×C11—21no—
474C2×C4×C11—21no—
475C2×C4×C11—21no—
476C2×C4×C11—21no—
477C2×C4×C11—22no—
478C2×C4×C11—22no—
479C2×C4×C11—22no—
480C2×C4×C11—21no—
481C2×C4×C11—21no—
482C2×C4×C11—21no—
483C2×C4×C11—44no—
484C2×C4×C11C22×D414yes—
485C2×C4×C11C22×D412yes—
486C2×C4×C11C2×#4112yes—
487C2×C4×C11C2×#4112yes—
488C2×C4×C11C2×#4112yes—
489C22⋊D11—48no—
490C2×Dic11—21no—
491C2×Dic11—21no—
492C2×Dic11—21no—
493C2×Dic11—22no—
494C2×Dic11—21no—
495C2×Dic11—22no—
496C2×Dic11—21no—
497C2×Dic11—21no—
498C2×Dic11—22no—
499C2×Dic11—21no—
500C2×Dic11—21no—
501C2×Dic11—22no—
502C2×Dic11—22no—
503C2×Dic11—21no—
504C2×Dic11—21no—
505C2×Dic11—21no—
506C2×Dic11—22no—
507C2×Dic11—22no—
508C2×Dic11—21no—
509C2×Dic11—22no—
510C2×Dic11—44no—
511C2×Dic11C22×D414yes—
512C2×Dic11C22×D412yes—
513C2×Dic11C2×#4112yes—
514C2×Dic11C2×#4112yes—
515C2×Dic11C2×#4112yes—
516C2×Dic11C2×#4112yes—
517C2×Dic11C2×#4112yes—
518D44—48no—
519D44—48no—
520D44—44no—
521C4×D11—44no—
522C4×D11—44no—
523C4×D11—44no—
524C4×D11—44no—
525C4×D11—44no—
526C4×D11—44no—
527C4×D11—44no—
528C4×D11—48no—
529C4×D11#124116yescomplemented
530Dic22—48no—
531Dic22—48no—
532C22×#41—111no—
533C24×C4—111no—
534#533—228no—
535C2×C4⋊Q8—111no—
536C2×C4⋊Q8—111no—
537C2×#125—111no—
538C2×#125C2×D1111yescharacteristic, complemented
539C2×#124—112no—
540C2×#124—112no—
541#525—228no—
542C2×#123—112no—
543C2×C22⋊Q8—111no—
544C2×C22⋊Q8—112no—
545C2×C22⋊Q8—112no—
546C2×C22⋊Q8C2×D1111yescharacteristic
547C2×#121—111no—
548C2×#121—111no—
549C2×#120—112no—
550C2×C4×Q8—112no—
551C2×C4×Q8—112no—
552C2×C4×D4—112no—
553C2×C4×D4—112no—
554C2×#117—111no—
555C2×#117—111no—
556C2×#117—111no—
557C22×C22⋊C4—111no—
558C22×C22⋊C4—111no—
559C22×C42—111no—
560C22×C42—111no—
561#400—112no—
562#400—112no—
563#400—112no—
564#400C2×D1112yescomplemented
565#397—112no—
566#397—112no—
567#397—112no—
568#397C2×D1112yes—
569#394—112no—
570#394—112no—
571#394—112no—
572#394—112no—
573#393—112no—
574#393—112no—
575#393—112no—
576#393—112no—
577#391—111no—
578#391—111no—
579#391—112no—
580#391—112no—
581#391C2×D1111yescharacteristic, complemented
582#391C2×D1111yescharacteristic, complemented
583#390—112no—
584#390—111no—
585#390—111no—
586#390—112no—
587#390—111no—
588#390—111no—
589#388—112no—
590#388—112no—
591#388—112no—
592#388—112no—
593#388—112no—
594#388—112no—
595#388—112no—
596#388C2×D1112yes—
597#386—112no—
598#386—112no—
599#386—112no—
600#386—112no—
601#382—112no—
602#382C2×D1112yescomplemented
603#381—112no—
604#380—111no—
605#380—111no—
606#380—111no—
607#380C2×D1111yescharacteristic
608#379—112no—
609C4×C4⋊C4—111no—
610C4×C4⋊C4—111no—
611C4×C4⋊C4—111no—
612C4×C4⋊C4C2×D1111yescharacteristic, complemented
613C4×C22⋊C4—111no—
614C4×C22⋊C4—111no—
615C4×C22⋊C4—112no—
616C4×C22⋊C4—111no—
617C4×C22⋊C4—112no—
618C4×C22⋊C4—111no—
619C4×C22⋊C4—111no—
620C4×C22⋊C4—111no—
621C4×C22⋊C4—112no—
622C4×C22⋊C4—112no—
623C4×C22⋊C4—111no—
624C4×C22⋊C4—112no—
625C4×C22⋊C4—112no—
626C4×C22⋊C4—112no—
627C4×C22⋊C4—112no—
628C4×C22⋊C4C2×D1111yescharacteristic
629#376—112no—
630C2×#95—111no—
631C2×#95—111no—
632C43—112no—
633C22×C11—22no—
634C22×C11—22no—
635C22×C11—22no—
636C22×C11—41no—
637C22×C11—41no—
638C22×C11—41no—
639C22×C11—41no—
640C22×C11C23×D411yescharacteristic
641C22×C11C22×#4111yescharacteristic
642C22×C11C22×#4111yescharacteristic
643C22×C11C22×#4111yescharacteristic
644C22×C11C22×#4111yescharacteristic
645C22×C11#58511yescharacteristic
646C22×C11#58511yescharacteristic
647C2×D11—22no—
648C2×D11—22no—
649C2×D11—22no—
650C2×D11—22no—
651C2×D11—22no—
652C2×D11—22no—
653C2×D11—22no—
654C2×D11—22no—
655C2×D11—22no—
656C2×D11—416no—
657C2×D11—41no—
658C2×D11—41no—
659C2×D11—41no—
660C2×D11—41no—
661C2×D11—42no—
662C2×D11—42no—
663C2×D11—42no—
664C2×D11—42no—
665C2×D11—42no—
666C2×D11—42no—
667C2×D11—42no—
668C2×D11C2×#12414yes—
669C4×C11—24no—
670C4×C11—22no—
671C4×C11—41no—
672C4×C11—42no—
673C4×C11—42no—
674C4×C11—42no—
675C4×C11—41no—
676C4×C11—41no—
677C4×C11—41no—
678C4×C11C2×#12414yes—
679Dic11—22no—
680Dic11—22no—
681Dic11—24no—
682Dic11—22no—
683Dic11—41no—
684Dic11—42no—
685Dic11—42no—
686Dic11—41no—
687Dic11C2×#12414yes—
688C25—111no—
689C2×#41—224no—
690C2×#41—224no—
691C2×#41—224no—
692C22×Q8—112no—
693C22×Q8—112no—
694C22×Q8C22×D1111yescharacteristic
695C22×D4—112no—
696C22×D4—112no—
697C22×D4—111no—
698C22×D4—112no—
699C23×C4—111no—
700C23×C4—111no—
701C23×C4—111no—
702C23×C4—112no—
703C23×C4—111no—
704C23×C4—111no—
705C23×C4—111no—
706C23×C4—111no—
707C23×C4—111no—
708C23×C4—111no—
709C23×C4—224no—
710C23×C4—224no—
711C23×C4—224no—
712C23×C4C22×D1111yescharacteristic
713C4⋊Q8—224no—
714C4⋊Q8—224no—
715#125—24no—
716#125—224no—
717#124—228no—
718#124—228no—
719#123—228no—
720C22⋊Q8—24no—
721C22⋊Q8—228no—
722C22⋊Q8—228no—
723C22⋊Q8—224no—
724#121—224no—
725#121—224no—
726#120—228no—
727C4×Q8—228no—
728C4×Q8—228no—
729C4×D4—228no—
730C4×D4—228no—
731#117—118no—
732#117—224no—
733#117—224no—
734C2×C4⋊C4—111no—
735C2×C4⋊C4—111no—
736C2×C4⋊C4—111no—
737C2×C4⋊C4—112no—
738C2×C4⋊C4—112no—
739C2×C4⋊C4—112no—
740C2×C4⋊C4—112no—
741C2×C4⋊C4—112no—
742C2×C4⋊C4C22×D1111yescharacteristic
743C2×C4⋊C4C22×D1111yescharacteristic
744C2×C4⋊C4C22×D1112yes—
745C2×C4⋊C4C22×D1112yes—
746C2×C4⋊C4C22×D1112yes—
747C2×C4⋊C4C22×D1111yescharacteristic
748C2×C22⋊C4—111no—
749C2×C22⋊C4—111no—
750C2×C22⋊C4—112no—
751C2×C22⋊C4—111no—
752C2×C22⋊C4—111no—
753C2×C22⋊C4—111no—
754C2×C22⋊C4—111no—
755C2×C22⋊C4—112no—
756C2×C22⋊C4—112no—
757C2×C22⋊C4—112no—
758C2×C22⋊C4—112no—
759C2×C22⋊C4—112no—
760C2×C22⋊C4—112no—
761C2×C22⋊C4—112no—
762C2×C22⋊C4—112no—
763C2×C22⋊C4—112no—
764C2×C22⋊C4—112no—
765C2×C22⋊C4—112no—
766C2×C22⋊C4—112no—
767C2×C22⋊C4—112no—
768C2×C22⋊C4—112no—
769C2×C22⋊C4—112no—
770C2×C22⋊C4—112no—
771C2×C22⋊C4—224no—
772C2×C22⋊C4—224no—
773C2×C22⋊C4C22×D1111yescharacteristic
774C2×C22⋊C4C22×D1111yescharacteristic
775C2×C22⋊C4C22×D1112yes—
776C2×C22⋊C4C22×D1112yes—
777C2×C42—112no—
778C2×C42—112no—
779C2×C42—112no—
780C2×C42—111no—
781C2×C42—111no—
782C2×C42—112no—
783C2×C42—111no—
784C2×C42—111no—
785C2×C42—111no—
786C2×C42—111no—
787C2×C42—112no—
788C2×C42—112no—
789C2×C42—224no—
790C2×C42—224no—
791C2×C42C22×D1112yes—
792C2×C42C22×D1111yescharacteristic
793C2×C42C22×D1111yescharacteristic
794#95—111no—
795#95—111no—
796#95—111no—
797#95—111no—
798#95—111no—
799#95—111no—
800#95—112no—
801#95—112no—
802#95—112no—
803#95—112no—
804#95—112no—
805#95—112no—
806#95—112no—
807#95—112no—
808#95—112no—
809#95—112no—
810#95C22×D1111yescharacteristic
811#95C22×D1111yescharacteristic
812#95C22×D1112yes—
813#95C22×D1112yes—
814#95C22×D1112yes—
815#95C22×D1112yes—
816#95C22×D1112yes—
817#95C22×D1112yes—
818C2×C11—42no—
819C2×C11C22×#12411yescharacteristic
820C2×C11#344411yescharacteristic
821C2×C11#345511yescharacteristic
822C2×C11D4×#4111yescharacteristic
823C2×C11D4×#4111yescharacteristic
824C2×C11#347511yescharacteristic
825C2×C11#347511yescharacteristic
826D11—24no—
827D11—42no—
828D11—82no—
829C24—111no—
830C24—111no—
831C24—112no—
832C24—222no—
833C24—222no—
834C24—222no—
835C24—222no—
836C24—222no—
837C24—441no—
838C24—441no—
839C24C23×D1111yescharacteristic
840#41—4416no—
841C2×Q8—22no—
842C2×Q8—22no—
843C2×Q8—22no—
844C2×Q8—224no—
845C2×Q8—224no—
846C2×Q8—224no—
847C2×Q8—224no—
848C2×Q8—442no—
849C2×Q8—442no—
850C2×D4—224no—
851C2×D4—224no—
852C2×D4—224no—
853C2×D4—224no—
854C2×D4—224no—
855C2×D4—224no—
856C2×D4—224no—
857C2×D4—222no—
858C2×D4—222no—
859C2×D4—222no—
860C2×D4—442no—
861C2×D4—442no—
862C22×C4—22no—
863C22×C4—22no—
864C22×C4—22no—
865C22×C4—111no—
866C22×C4—114no—
867C22×C4—114no—
868C22×C4—114no—
869C22×C4—111no—
870C22×C4—111no—
871C22×C4—111no—
872C22×C4—112no—
873C22×C4—111no—
874C22×C4—111no—
875C22×C4—112no—
876C22×C4—112no—
877C22×C4—222no—
878C22×C4—222no—
879C22×C4—222no—
880C22×C4—222no—
881C22×C4—224no—
882C22×C4—222no—
883C22×C4—222no—
884C22×C4—224no—
885C22×C4—224no—
886C22×C4—222no—
887C22×C4—222no—
888C22×C4—222no—
889C22×C4—222no—
890C22×C4—222no—
891C22×C4—222no—
892C22×C4—222no—
893C22×C4—222no—
894C22×C4—222no—
895C22×C4—222no—
896C22×C4—222no—
897C22×C4—222no—
898C22×C4—222no—
899C22×C4—222no—
900C22×C4—441no—
901C22×C4—441no—
902C22×C4—441no—
903C22×C4—441no—
904C22×C4—4416no—
905C22×C4C23×D1111yescharacteristic
906C22×C4C23×D1112yes—
907C22×C4C23×D1111yescharacteristic
908C22×C4C23×D1112yes—
909C22×C4C23×D1111yescharacteristic
910C22×C4C23×D1111yescharacteristic
911C22×C4C23×D1112yes—
912C22×C4C23×D1112yes—
913C22×C4C23×D1111yescharacteristic
914C22×C4C23×D1111yescharacteristic
915C4⋊C4—22no—
916C4⋊C4—24no—
917C4⋊C4—24no—
918C4⋊C4—24no—
919C4⋊C4—22no—
920C4⋊C4—114no—
921C4⋊C4—224no—
922C4⋊C4—224no—
923C4⋊C4—224no—
924C4⋊C4—224no—
925C4⋊C4—222no—
926C4⋊C4—224no—
927C4⋊C4—222no—
928C4⋊C4D4×D1114yes—
929C22⋊C4—22no—
930C22⋊C4—24no—
931C22⋊C4—24no—
932C22⋊C4—22no—
933C22⋊C4—114no—
934C22⋊C4—118no—
935C22⋊C4—114no—
936C22⋊C4—222no—
937C22⋊C4—222no—
938C22⋊C4—224no—
939C22⋊C4—224no—
940C22⋊C4—224no—
941C22⋊C4—224no—
942C22⋊C4—224no—
943C22⋊C4—222no—
944C22⋊C4—224no—
945C22⋊C4—224no—
946C22⋊C4—224no—
947C22⋊C4—222no—
948C22⋊C4—224no—
949C22⋊C4—224no—
950C22⋊C4—442no—
951C22⋊C4—442no—
952C22⋊C4—442no—
953C22⋊C4—442no—
954C22⋊C4—442no—
955C22⋊C4—442no—
956C42—22no—
957C42—22no—
958C42—24no—
959C42—118no—
960C42—222no—
961C42—222no—
962C42—222no—
963C42—222no—
964C42—224no—
965C42—224no—
966C42—224no—
967C42—222no—
968C42—222no—
969C42—442no—
970C42—442no—
971C11#3481311yescharacteristic, complemented, Sylow
972C23—21no—
973C23—21no—
974C23—21no—
975C23—21no—
976C23—21no—
977C23—21no—
978C23—112no—
979C23—112no—
980C23—112no—
981C23—112no—
982C23—228no—
983C23—221no—
984C23—221no—
985C23—221no—
986C23—221no—
987C23—221no—
988C23—221no—
989C23—221no—
990C23—221no—
991C23—221no—
992C23—221no—
993C23—222no—
994C23—222no—
995C23—222no—
996C23—222no—
997C23—222no—
998C23—222no—
999C23—222no—
1000C23—444no—
1001C23—444no—
1002C23—444no—
1003C23—444no—
1004C23—444no—
1005C23—444no—
1006C23#41×D1112yes—
1007C23C24×D1111yescharacteristic
1008Q8—44no—
1009Q8—448no—
1010Q8—448no—
1011D4—448no—
1012D4—448no—
1013D4—448no—
1014D4—444no—
1015C2×C4—21no—
1016C2×C4—22no—
1017C2×C4—21no—
1018C2×C4—22no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—22no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—22no—
1040C2×C4—44no—
1041C2×C4—112no—
1042C2×C4—112no—
1043C2×C4—112no—
1044C2×C4—1116no—
1045C2×C4—114no—
1046C2×C4—112no—
1047C2×C4—112no—
1048C2×C4—112no—
1049C2×C4—221no—
1050C2×C4—221no—
1051C2×C4—221no—
1052C2×C4—222no—
1053C2×C4—221no—
1054C2×C4—222no—
1055C2×C4—221no—
1056C2×C4—221no—
1057C2×C4—222no—
1058C2×C4—221no—
1059C2×C4—221no—
1060C2×C4—222no—
1061C2×C4—221no—
1062C2×C4—222no—
1063C2×C4—221no—
1064C2×C4—221no—
1065C2×C4—222no—
1066C2×C4—222no—
1067C2×C4—221no—
1068C2×C4—222no—
1069C2×C4—444no—
1070C2×C4—444no—
1071C2×C4—448no—
1072C2×C4—444no—
1073C2×C4—444no—
1074C2×C4—444no—
1075C2×C4—444no—
1076C2×C4—444no—
1077C2×C4—444no—
1078C2×C4C2×D4×D1114yes—
1079C2×C4C2×D4×D1112yes—
1080C2×C4#41×D1112yes—
1081C2×C4#41×D1112yes—
1082C2×C4#41×D1112yes—
1083C22—22no—
1084C22—22no—
1085C22—22no—
1086C22—41no—
1087C22—41no—
1088C22—41no—
1089C22—41no—
1090C22—114no—
1091C22—222no—
1092C22—222no—
1093C22—222no—
1094C22—222no—
1095C22—222no—
1096C22—222no—
1097C22—222no—
1098C22—222no—
1099C22—222no—
1100C22—4416no—
1101C22—441no—
1102C22—441no—
1103C22—441no—
1104C22—441no—
1105C22—442no—
1106C22—442no—
1107C22—442no—
1108C22—442no—
1109C22—442no—
1110C22—442no—
1111C22—442no—
1112C22C22×D4×D1111yescharacteristic
1113C22C2×#41×D1111yescharacteristic
1114C22C2×#41×D1111yescharacteristic
1115C22C2×#41×D1111yescharacteristic
1116C22C2×#41×D1111yescharacteristic
1117C22#1062345711yescharacteristic
1118C22#1062345711yescharacteristic
1119C4—22no—
1120C4—24no—
1121C4—41no—
1122C4—42no—
1123C4—42no—
1124C4—41no—
1125C4—41no—
1126C4—41no—
1127C4—42no—
1128C4—114no—
1129C4—222no—
1130C4—222no—
1131C4—222no—
1132C4—224no—
1133C4—441no—
1134C4—441no—
1135C4—442no—
1136C4—442no—
1137C4D11×#12414yes—
1138C2—42no—
1139C2—224no—
1140C2—442no—
1141C2—882no—
1142C2C2×D11×#12411yescharacteristic
1143C2#1308191011yescharacteristic
1144C2#1308200711yescharacteristic
1145C2#1308210311yescharacteristic
1146C2#1308210511yescharacteristic
1147C2#1308216911yescharacteristic
1148C2#1308216911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2489C2
prime radicalC2×#10623158C2
hypercenter#2489D11
hypocenterC11#34813
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2489

Complements

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

NH ≅ G/Ntype
1. C2×#10623219C2semidirect
3. #13072992C2semidirect
4. #13072991C2semidirect
5. #13072975C2semidirect
6. #13072973C2semidirect
7. #13072971C2semidirect
8. #13072968C2semidirect
9. #13072955C2semidirect
10. #13072939C2semidirect
11. #13072937C2semidirect
12. #13072746C2semidirect
13. #13072735C2semidirect
14. #13071905C2semidirect
15. #13071901C2semidirect
16. #13071157C2semidirect
17. #13071155C2semidirect
18. #13071105C2semidirect
19. #13071105C2semidirect
20. #13070998C2semidirect
21. C4×#66945C2semidirect
22. C4×C22⋊C4×D11C2semidirect
23. C11×#2489C2semidirect
26. C2×C11×#125C22semidirect
40. C2×#66941C22semidirect
41. C2×#66941C22semidirect
42. C2×#66940C22semidirect
43. C2×#66940C22semidirect
52. C2×#66923C22semidirect
53. C11×#400C22semidirect
55. C11×#391C22semidirect
56. C11×#391C22semidirect
58. C11×#382C22semidirect
60. C4×C11×C4⋊C4C22semidirect
62. #10622843C22semidirect
63. #10622843C22semidirect
66. #10622606C22semidirect
68. #10622603C22semidirect
70. #10622601C22semidirect
71. #10622601C22semidirect
74. #10622595C22semidirect
75. C4⋊C4×Dic11C22semidirect
76. C4⋊C4×Dic11C22semidirect
77. #10622587C22semidirect
87. #10622553C22semidirect
88. #10622552C22semidirect
89. #10622552C22semidirect
93. C4×C4⋊Dic11C22semidirect
94. C42×Dic11C22semidirect
96. #10622288C22semidirect
98. #10622286C22semidirect
99. #10622286C22semidirect
103. #10622282C22semidirect
104. #10622282C22semidirect
109. #10622279C22semidirect
110. #10622279C22semidirect
111. #10622279C22semidirect
112. #10622279C22semidirect
120. #10622271C22semidirect
121. #10622271C22semidirect
122. #10622263C22semidirect
123. #10622261C22semidirect
124. #10622259C22semidirect
357. C22⋊Dic11#41semidirect
377. (C2×D11)⋊C4#41semidirect
407. #2489D11semidirect
529. C4×D11#124semidirect
538. C2×#125C2×D11semidirect
564. #400C2×D11semidirect
581. #391C2×D11semidirect
582. #391C2×D11semidirect
602. #382C2×D11semidirect
612. C4×C4⋊C4C2×D11semidirect
971. C11#34813semidirect

Maximal subgroups

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

subgroupindex
C2×#106232192
C2×#106231582
#130729922
#130729912
#130729752
#130729732
#130729712
#130729682
#130729552
#130729392
#130729372
#130727462
#130727352
#130719052
#130719012
#130711572
#130711552
#130711052
#130709982
C4×#669452
C4×C22⋊C4×D112
C11×#24892
#3481311