Finite Group Databasebeta

← #14926795

Subgroups — #14926795

Order 2816.

2930 conjugacy classes of subgroups.

The subgroup lattice has 1142 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×C4×D4×D11C211yesmaximal, characteristic
3#13076951C212yesmaximal, complemented
4#13076902C212yesmaximal, complemented
5#13074430C211yesmaximal, characteristic, complemented
6#13074428C211yesmaximal, characteristic, complemented
7#13074422C211yesmaximal, characteristic, complemented
8#13074420C211yesmaximal, characteristic, complemented
9#13073967C212yesmaximal, complemented
10#13073961C212yesmaximal, complemented
11#13073798C211yesmaximal, characteristic, complemented
12#13073796C211yesmaximal, characteristic, complemented
13#13073792C211yesmaximal, characteristic, complemented
14#13072928C211yesmaximal, characteristic, complemented
15#13072926C211yesmaximal, characteristic, complemented
16#13072066C212yesmaximal, complemented
17#13072064C212yesmaximal, complemented
18#13071976C211yesmaximal, characteristic, complemented
19#13071974C211yesmaximal, characteristic, complemented
20#13071229C212yesmaximal, complemented
21#13071190C212yesmaximal
22C2×#10622280C211yesmaximal, characteristic, complemented
23C11×#2564C211yesmaximal, characteristic, complemented
24C22×Q8×D11C2211yescharacteristic, complemented
25C22×D4×D11C2211yescharacteristic
26C23×C4×D11C2211yescharacteristic
27C23×C4×D11C2211yescharacteristic
28C2×C11×C22⋊Q8C2211yescharacteristic, complemented
29C2×C4×D4×C11C2211yescharacteristic
30C2×#66999C2211yescharacteristic
31C2×D4×Dic11C2211yescharacteristic
32C2×C4×C22⋊D11C2211yescharacteristic
33C2×C4×C22⋊D11C2211yescharacteristic
34C22×(C2×D11)⋊C4C2212yes—
35C2×#66977C2211yescharacteristic, complemented
36C22×Dic11⋊C4C2212yescomplemented
37D11×C22⋊Q8—28no—
38C4×D4×D11—28no—
39C2×#66950C2211yescharacteristic
40C2×#66949C2212yes—
41C2×#66949C2212yescomplemented
42C2×#66946C2211yescharacteristic
43C2×C4⋊C4×D11C2211yescharacteristic
44C2×C4⋊C4×D11C2211yescharacteristic, complemented
45C2×C4⋊C4×D11C2212yescomplemented
46C2×(C22⋊D11)⋊C4C2211yescharacteristic
47C2×(C22⋊D11)⋊C4C2211yescharacteristic
48C2×C22⋊C4×D11C2212yes—
49C2×C22⋊C4×D11C2211yescharacteristic
50C2×C22⋊C4×D11C2211yescharacteristic
51C2×#66931C2212yescomplemented
52C2×#66931C2212yescomplemented
53C2×C4×D44C2211yescharacteristic
54C2×C42×D11C2211yescharacteristic
55C11×#400C2211yescharacteristic, complemented
56C11×#399C2211yescharacteristic, complemented
57C11×#395C2211yescharacteristic, complemented
58C11×#393C2211yescharacteristic, complemented
59C11×#387C2212yescomplemented
60C11×#386C2212yes—
61C11×#385C2212yescomplemented
62C11×#380C2212yescomplemented
63C2×C11×#95C2211yescharacteristic, complemented
64#10622844C2211yescharacteristic, complemented
65#10622842C2211yescharacteristic, complemented
66#10622833C2212yes—
67#10622826C2212yes—
68#10622825C2212yescomplemented
69#10622823C2212yescomplemented
70C2×C11⋊#95C2211yescharacteristic, complemented
71#10622607C2212yescomplemented
72#10622605C2211yescharacteristic, complemented
73#10622602C2212yes—
74#10622602C2212yes—
75#10622602C2212yescomplemented
76#10622602C2212yescomplemented
77#10622602C2212yescomplemented
78#10622599C2211yescharacteristic, complemented
79#10622595C2211yescharacteristic, complemented
80#10622593C2212yescomplemented
81#10622592C2211yescharacteristic, complemented
82#10622591C2212yescomplemented
83#10622585C2212yescomplemented
84#10622571C2212yes—
85#10622569C2212yes—
86#10622569C2212yes—
87#10622568C2212yes—
88#10622568C2212yes—
89#10622562C2211yescharacteristic, complemented
90#10622561C2212yescomplemented
91#10622561C2212yescomplemented
92#10622560C2211yescharacteristic, complemented
93#10622555C2212yescomplemented
94#10622555C2212yescomplemented
95#10622555C2212yescomplemented
96#10622546C2212yescomplemented
97#10622290C2211yescharacteristic, complemented
98#10622289C2212yescomplemented
99#10622286C2211yescharacteristic, complemented
100#10622281C2212yes—
101#10622281C2212yes—
102#10622281C2212yescomplemented
103#10622281C2212yescomplemented
104#10622281C2212yescomplemented
105#10622280C2212yes—
106#10622280C2211yescharacteristic
107#10622280C2211yescharacteristic
108#10622280C2211yescharacteristic, complemented
109#10622280C2211yescharacteristic, complemented
110#10622280C2212yescomplemented
111#10622280C2212yescomplemented
112#10622278C2212yes—
113#10622278C2212yes—
114#10622277C2212yes—
115#10622277C2212yes—
116#10622274C2212yescomplemented
117#10622272C2211yescharacteristic, complemented
118#10622270C2212yescomplemented
119#10622270C2212yescomplemented
120#10622269C2211yescharacteristic, complemented
121#10622266C2212yescomplemented
122#10622260C2212yescomplemented
123#10622259C2212yescomplemented
124#10622259C2212yescomplemented
125C24×D11C2311yescharacteristic
126C24×D11C2311yescharacteristic
127C22×Q8×C11C2311yescharacteristic
128C22×D4×C11C2311yescharacteristic
129C23×C4×C11C2312yes—
130C23×C4×C11C2311yescharacteristic
131C23×C4×C11C2311yescharacteristic
132C22×C22⋊D11C2311yescharacteristic
133C22×C22⋊D11C2311yescharacteristic
134C23×Dic11C2311yescharacteristic
135C23×Dic11C2311yescharacteristic
136C23×Dic11C2312yes—
137C2×Q8×D11—24no—
138C2×Q8×D11—44no—
139C2×D4×D11—24no—
140C2×D4×D11—24no—
141C2×D4×D11Q818yescomplemented
142C22×D44C2311yescharacteristic
143C22×C4×D11—24no—
144C22×C4×D11—44no—
145C22×C4×D11—44no—
146C22×C4×D11D418yes—
147C22×C4×D11C2311yescharacteristic
148C22×C4×D11C2311yescharacteristic
149C22×C4×D11C2311yescharacteristic
150C22×C4×D11C2311yescharacteristic
151C22×C4×D11C2311yescharacteristic
152C22×C4×D11C2311yescharacteristic
153C22×C4×D11C2311yescharacteristic
154C22×C4×D11C2312yes—
155C22×C4×D11C2312yes—
156C22×C4×D11C2311yescharacteristic
157C22×C4×D11C2311yescharacteristic
158C22×Dic22C2312yes—
159C22×Dic22C2311yescharacteristic
160C11×C22⋊Q8—24no—
161C4×D4×C11—24no—
162C2×C11×C4⋊C4C2311yescharacteristic
163C2×C11×C4⋊C4C2312yes—
164C2×C11×C4⋊C4C2311yescharacteristic
165C2×C11×C4⋊C4C2312yes—
166C2×C11×C4⋊C4C2312yes—
167C2×C11×C22⋊C4C2312yes—
168C2×C11×C22⋊C4C2311yescharacteristic
169C2×C11×C22⋊C4C2311yescharacteristic
170C2×C11×C22⋊C4C2312yes—
171C2×C11×C22⋊C4C2312yes—
172C2×C42×C11C2311yescharacteristic
173C2×C22⋊Dic11C2312yes—
174C2×C22⋊Dic11C2311yescharacteristic
175C2×C22⋊Dic11C2311yescharacteristic
176C2×C22⋊Dic11C2312yes—
177C2×C22⋊Dic11C2312yes—
178#66999—24no—
179D4×Dic11—24no—
180C4×C22⋊D11—24no—
181C4×C22⋊D11—24no—
182C2×(C2×D11)⋊C4—28no—
183C2×(C2×D11)⋊C4C2311yescharacteristic
184C2×(C2×D11)⋊C4C2311yescharacteristic
185C2×(C2×D11)⋊C4C2311yescharacteristic
186C2×(C2×D11)⋊C4C2311yescharacteristic
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)⋊C4C2312yes—
194C2×(C2×D11)⋊C4C2312yes—
195C2×(C2×D11)⋊C4C2312yes—
196C2×(C2×D11)⋊C4C2312yes—
197C2×C4⋊Dic11C2311yescharacteristic
198C2×C4⋊Dic11C2312yes—
199C2×C4⋊Dic11C2311yescharacteristic
200C2×C4⋊Dic11C2312yes—
201C2×C4⋊Dic11C2312yes—
202#66977—24no—
203C2×Dic11⋊C4—44no—
204C2×Dic11⋊C4C2312yes—
205C2×Dic11⋊C4C2312yes—
206C2×Dic11⋊C4C2312yes—
207C2×Dic11⋊C4C2311yescharacteristic
208C2×Dic11⋊C4C2311yescharacteristic
209C2×Dic11⋊C4C2312yes—
210C2×Dic11⋊C4C2312yes—
211C2×Dic11⋊C4C2312yes—
212C2×Dic11⋊C4C2312yes—
213C2×Dic11⋊C4C2312yes—
214C2×Dic11⋊C4C2312yes—
215C2×Dic11⋊C4C2312yes—
216C2×Dic11⋊C4C2312yes—
217C2×C4×Dic11C2311yescharacteristic
218C2×C4×Dic11C2311yescharacteristic
219C2×C4×Dic11C2311yescharacteristic
220#66950—24no—
221#66949—28no—
222#66949—44no—
223#66946—24no—
224C4⋊C4×D11—24no—
225C4⋊C4×D11—24no—
226C4⋊C4×D11—28no—
227(C22⋊D11)⋊C4—24no—
228(C22⋊D11)⋊C4—24no—
229C22⋊C4×D11—24no—
230C22⋊C4×D11—28no—
231C22⋊C4×D11—24no—
232#66931—28no—
233#66931—44no—
234C4×D44—24no—
235C42×D11—24no—
236C11×#95C2312yes—
237C11×#95C2312yes—
238C11×#95C2312yes—
239C11×#95C2312yes—
240C11×#95C2311yescharacteristic
241C11×#95C2312yes—
242C11×#95C2311yescharacteristic
243C11⋊#95C2312yes—
244C11⋊#95C2312yes—
245C11⋊#95C2312yes—
246C11⋊#95C2312yes—
247C11⋊#95C2312yes—
248C11⋊#95C2312yes—
249C11⋊#95C2312yes—
250C11⋊#95C2312yes—
251C11⋊#95C2312yes—
252C11⋊#95C2312yes—
253C11⋊#95C2312yes—
254C11⋊#95C2312yes—
255C11⋊#95C2311yescharacteristic
256C11⋊#95C2311yescharacteristic
257C11⋊#95C2312yes—
258#35010—111nomaximal, Sylow
259C24×C11C2411yescharacteristic
260C24×C11C2411yescharacteristic
261C23×D11—22no—
262C23×D11—22no—
263C23×D11—42no—
264C23×D11—42no—
265C23×D11—42no—
266C23×D11—42no—
267C23×D11C2×D414yes—
268C23×D11C2×Q814yes—
269C23×D11C2×Q814yescomplemented
270C23×D11#4114yes—
271C23×D11C2411yescharacteristic
272C23×D11C2411yescharacteristic
273C23×D11C2411yescharacteristic
274C2×Q8×C11—22no—
275C2×Q8×C11—42no—
276C2×D4×C11—22no—
277C2×D4×C11—22no—
278C2×D4×C11C2×Q814yescomplemented
279C22×C4×C11—24no—
280C22×C4×C11—22no—
281C22×C4×C11—42no—
282C22×C4×C11—42no—
283C22×C4×C11—42no—
284C22×C4×C11—42no—
285C22×C4×C11C2×D414yes—
286C22×C4×C11C2412yes—
287C22×C4×C11C2411yescharacteristic
288C22×C4×C11C2411yescharacteristic
289C22×C4×C11C2412yes—
290C22×C4×C11C2412yes—
291C22×C4×C11C2412yes—
292C22×C4×C11C2411yescharacteristic
293C22×C4×C11C2411yescharacteristic
294C22×C4×C11C2411yescharacteristic
295C2×C22⋊D11—22no—
296C2×C22⋊D11—22no—
297C2×C22⋊D11—22no—
298C2×C22⋊D11—22no—
299C2×C22⋊D11C2×Q814yes—
300C2×C22⋊D11C2×Q814yescomplemented
301C22×Dic11—24no—
302C22×Dic11—22no—
303C22×Dic11—24no—
304C22×Dic11—24no—
305C22×Dic11—42no—
306C22×Dic11—42no—
307C22×Dic11C2×D414yes—
308C22×Dic11C2412yes—
309C22×Dic11C2412yes—
310C22×Dic11C2411yescharacteristic
311C22×Dic11C2412yes—
312C22×Dic11C2411yescharacteristic
313C22×Dic11C2412yes—
314C22×Dic11C2411yescharacteristic
315C22×Dic11C2411yescharacteristic
316C22×Dic11C2411yescharacteristic
317Q8×D11—416no—
318D4×D11—232no—
319C2×D44—22no—
320C2×D44—22no—
321C2×D44C2×Q814yes—
322C2×C4×D11—24no—
323C2×C4×D11—24no—
324C2×C4×D11—22no—
325C2×C4×D11—24no—
326C2×C4×D11—22no—
327C2×C4×D11—22no—
328C2×C4×D11—24no—
329C2×C4×D11—22no—
330C2×C4×D11—24no—
331C2×C4×D11—22no—
332C2×C4×D11—22no—
333C2×C4×D11—42no—
334C2×C4×D11—42no—
335C2×C4×D11—42no—
336C2×C4×D11—42no—
337C2×C4×D11—42no—
338C2×C4×D11—42no—
339C2×C4×D11—42no—
340C2×C4×D11—42no—
341C2×C4×D11—42no—
342C2×C4×D11—416no—
343C2×C4×D11—416no—
344C2×C4×D11C2×D414yes—
345C2×C4×D11C2×D414yes—
346C2×C4×D11C2×D414yes—
347C2×C4×D11C2×D414yes—
348C2×C4×D11C2×Q814yescomplemented
349C2×Dic22—24no—
350C2×Dic22—24no—
351C2×Dic22—24no—
352C2×Dic22—22no—
353C2×Dic22—42no—
354C11×C4⋊C4—22no—
355C11×C4⋊C4—24no—
356C11×C4⋊C4—22no—
357C11×C4⋊C4—42no—
358C11×C4⋊C4—42no—
359C11×C22⋊C4—24no—
360C11×C22⋊C4—22no—
361C11×C22⋊C4—22no—
362C11×C22⋊C4—42no—
363C11×C22⋊C4—42no—
364C42×C11—22no—
365C22⋊Dic11—22no—
366C22⋊Dic11—24no—
367C22⋊Dic11—22no—
368C22⋊Dic11—42no—
369C22⋊Dic11—42no—
370(C2×D11)⋊C4—22no—
371(C2×D11)⋊C4—22no—
372(C2×D11)⋊C4—22no—
373(C2×D11)⋊C4—24no—
374(C2×D11)⋊C4—24no—
375(C2×D11)⋊C4—24no—
376(C2×D11)⋊C4—24no—
377(C2×D11)⋊C4—24no—
378(C2×D11)⋊C4—24no—
379(C2×D11)⋊C4—22no—
380(C2×D11)⋊C4—42no—
381(C2×D11)⋊C4—42no—
382(C2×D11)⋊C4—42no—
383(C2×D11)⋊C4—42no—
384C4⋊Dic11—22no—
385C4⋊Dic11—24no—
386C4⋊Dic11—22no—
387C4⋊Dic11—42no—
388C4⋊Dic11—42no—
389Dic11⋊C4—24no—
390Dic11⋊C4—24no—
391Dic11⋊C4—22no—
392Dic11⋊C4—24no—
393Dic11⋊C4—24no—
394Dic11⋊C4—22no—
395Dic11⋊C4—24no—
396Dic11⋊C4—42no—
397Dic11⋊C4—42no—
398Dic11⋊C4—42no—
399Dic11⋊C4—42no—
400Dic11⋊C4—42no—
401Dic11⋊C4—42no—
402C4×Dic11—22no—
403C4×Dic11—22no—
404C4×Dic11—22no—
405C22×C22⋊Q8—111no—
406C22×C4×D4—111no—
407#2855—112no—
408#2848—112no—
409#2627—111no—
410#2627—111no—
411#2626—111no—
412#2626—111no—
413#2579—112no—
414#2579—112no—
415#2564—111no—
416#2564—111no—
417#2564—111no—
418#2564D1111yescharacteristic, complemented
419#2487—111no—
420#2487—111no—
421#2417—112no—
422#2417—112no—
423#2409—111no—
424#2409—111no—
425#2315—112no—
426#2308—112no—
427C2×#380—111no—
428C23×C11—22no—
429C23×C11—22no—
430C23×C11—21no—
431C23×C11—21no—
432C23×C11—22no—
433C23×C11—22no—
434C23×C11C22×D412yes—
435C23×C11C22×Q812yes—
436C23×C11C22×Q812yes—
437C23×C11C2×#4112yes—
438C23×C11C2511yescharacteristic
439C22×D11—22no—
440C22×D11—22no—
441C22×D11—22no—
442C22×D11—22no—
443C22×D11—21no—
444C22×D11—21no—
445C22×D11—22no—
446C22×D11—22no—
447C22×D11—28no—
448C22×D11—44no—
449C22×D11—44no—
450C22×D11—48no—
451C22×D11—48no—
452C22×D11—48no—
453C22×D11—44no—
454C22×D11—44no—
455C22×D11—48no—
456C22×D11C22⋊Q8116yescomplemented
457C22×D11C22×D412yes—
458C22×D11C22×D412yes—
459C22×D11C22×Q812yes—
460C22×D11C22×Q812yes—
461C22×D11C22×Q812yes—
462C22×D11C2×#4112yes—
463C22×D11C2×#4112yes—
464Q8×C11—44no—
465D4×C11—28no—
466C2×C4×C11—21no—
467C2×C4×C11—21no—
468C2×C4×C11—22no—
469C2×C4×C11—22no—
470C2×C4×C11—21no—
471C2×C4×C11—22no—
472C2×C4×C11—22no—
473C2×C4×C11—21no—
474C2×C4×C11—22no—
475C2×C4×C11—22no—
476C2×C4×C11—22no—
477C2×C4×C11—22no—
478C2×C4×C11—22no—
479C2×C4×C11—22no—
480C2×C4×C11—22no—
481C2×C4×C11—22no—
482C2×C4×C11—22no—
483C2×C4×C11—22no—
484C2×C4×C11—22no—
485C2×C4×C11—22no—
486C2×C4×C11—44no—
487C2×C4×C11—44no—
488C2×C4×C11—84no—
489C2×C4×C11C22×D412yes—
490C2×C4×C11C22×D412yes—
491C2×C4×C11C22×Q812yes—
492C22⋊D11—28no—
493C22⋊D11—28no—
494C2×Dic11—21no—
495C2×Dic11—21no—
496C2×Dic11—22no—
497C2×Dic11—28no—
498C2×Dic11—21no—
499C2×Dic11—22no—
500C2×Dic11—22no—
501C2×Dic11—21no—
502C2×Dic11—22no—
503C2×Dic11—22no—
504C2×Dic11—22no—
505C2×Dic11—22no—
506C2×Dic11—22no—
507C2×Dic11—22no—
508C2×Dic11—22no—
509C2×Dic11—22no—
510C2×Dic11—22no—
511C2×Dic11—22no—
512C2×Dic11—22no—
513C2×Dic11—22no—
514C2×Dic11—44no—
515C2×Dic11—84no—
516C2×Dic11C22×D412yes—
517C2×Dic11C22×D412yes—
518C2×Dic11C22×Q812yes—
519C2×Dic11H(5,𝔽2)14yes—
520D44—28no—
521C4×D11—28no—
522C4×D11—28no—
523C4×D11—28no—
524C4×D11—44no—
525C4×D11—44no—
526C4×D11—44no—
527C4×D11—44no—
528C4×D11—48no—
529C4×D11—44no—
530C4×D11—48no—
531C4×D11—44no—
532Dic22—44no—
533Dic22—48no—
534C23×Q8—111no—
535C23×D4—111no—
536C24×C4—111no—
537C24×C4—111no—
538C2×C22⋊Q8—111no—
539C2×C22⋊Q8—111no—
540C2×C22⋊Q8—112no—
541C2×C22⋊Q8—111no—
542C2×C22⋊Q8—112no—
543C2×C22⋊Q8—112no—
544C2×C22⋊Q8—112no—
545C2×C22⋊Q8—228no—
546C2×C22⋊Q8C2×D1111yescharacteristic, complemented
547C2×C4×D4—111no—
548C2×C4×D4—111no—
549C2×C4×D4—111no—
550C2×C4×D4—111no—
551C2×C4×D4—111no—
552C2×C4×D4—111no—
553C2×C4×D4—111no—
554C2×C4×D4—228no—
555C2×C4×D4C2×D1111yescharacteristic
556C22×C4⋊C4—112no—
557C22×C4⋊C4—112no—
558C22×C4⋊C4—111no—
559C22×C4⋊C4—111no—
560C22×C22⋊C4—112no—
561C22×C22⋊C4—112no—
562C22×C22⋊C4—111no—
563C22×C22⋊C4—111no—
564C22×C42—111no—
565#400—111no—
566#400—111no—
567#400—111no—
568#400C2×D1111yescharacteristic, complemented
569#399—111no—
570#399—111no—
571#399—111no—
572#399C2×D1111yescharacteristic, complemented
573#398—112no—
574#398—112no—
575#398—112no—
576#398—112no—
577#396—112no—
578#396—112no—
579#396—112no—
580#396—112no—
581#395—111no—
582#395—111no—
583#395—111no—
584#395C2×D1111yescharacteristic, complemented
585#393—111no—
586#393—111no—
587#393—111no—
588#393C2×D1111yescharacteristic, complemented
589#391—112no—
590#391—112no—
591#389—112no—
592#389—112no—
593#387—112no—
594#387—112no—
595#387—112no—
596#387C2×D1112yescomplemented
597#386—112no—
598#386—112no—
599#386—112no—
600#386—112no—
601#386—112no—
602#386—112no—
603#386—112no—
604#386C2×D1112yes—
605#385—112no—
606#385—112no—
607#385—112no—
608#385—112no—
609#385—112no—
610#385—112no—
611#385—112no—
612#385—112no—
613#385—112no—
614#385—112no—
615#385—112no—
616#385C2×D1112yescomplemented
617#381—112no—
618#381—112no—
619#380—112no—
620#380—112no—
621#380—112no—
622#380—112no—
623#380—112no—
624#380—112no—
625#380—112no—
626#380—111no—
627#380—111no—
628#380—111no—
629#380—111no—
630#380C2×D1112yescomplemented
631#379—112no—
632#379—112no—
633C2×#95—111no—
634C2×#95C2×D1111yescharacteristic, complemented
635C22×C11—22no—
636C22×C11—22no—
637C22×C11—24no—
638C22×C11—24no—
639C22×C11—22no—
640C22×C11—24no—
641C22×C11—41no—
642C22×C11—41no—
643C22×C11—42no—
644C22×C11C2×C22⋊Q814yes—
645C22×C11C23×D411yescharacteristic
646C22×C11C23×Q811yescharacteristic
647C22×C11C22×#4111yescharacteristic
648C22×C11C2×H(5,𝔽2)12yes—
649C22×C11#58512yes—
650C2×D11—22no—
651C2×D11—22no—
652C2×D11—22no—
653C2×D11—22no—
654C2×D11—24no—
655C2×D11—24no—
656C2×D11—24no—
657C2×D11—24no—
658C2×D11—22no—
659C2×D11—24no—
660C2×D11—416no—
661C2×D11—416no—
662C2×D11—41no—
663C2×D11—41no—
664C2×D11—42no—
665C2×D11C2×C22⋊Q814yes—
666C2×D11C2×C22⋊Q814yes—
667C4×C11—22no—
668C4×C11—22no—
669C4×C11—22no—
670C4×C11—41no—
671C4×C11—42no—
672C4×C11—41no—
673C4×C11—42no—
674C4×C11—42no—
675C4×C11—42no—
676Dic11—22no—
677Dic11—22no—
678Dic11—42no—
679Dic11—41no—
680Dic11—41no—
681Dic11—42no—
682Dic11—42no—
683Dic11—42no—
684Dic11#53414yes—
685C25—111no—
686C25—111no—
687C22×Q8—112no—
688C22×Q8—111no—
689C22×Q8—224no—
690C22×Q8—444no—
691C22×Q8C22×D1111yescharacteristic
692C22×D4—111no—
693C22×D4—111no—
694C22×D4—118no—
695C22×D4—111no—
696C22×D4—224no—
697C22×D4—224no—
698C22×D4C22×D1111yescharacteristic
699C23×C4—111no—
700C23×C4—111no—
701C23×C4—111no—
702C23×C4—111no—
703C23×C4—118no—
704C23×C4—111no—
705C23×C4—111no—
706C23×C4—111no—
707C23×C4—112no—
708C23×C4—111no—
709C23×C4—111no—
710C23×C4—112no—
711C23×C4—111no—
712C23×C4—112no—
713C23×C4—111no—
714C23×C4—224no—
715C23×C4—444no—
716C23×C4—444no—
717C23×C4C22×D1112yes—
718C23×C4C22×D1111yescharacteristic
719C23×C4C22×D1111yescharacteristic
720C22⋊Q8—24no—
721C22⋊Q8—228no—
722C22⋊Q8—228no—
723C22⋊Q8—224no—
724C22⋊Q8—224no—
725C22⋊Q8—224no—
726C22⋊Q8—444no—
727C22⋊Q8—444no—
728C4×D4—24no—
729C4×D4—224no—
730C4×D4—224no—
731C4×D4—224no—
732C4×D4—224no—
733C4×D4—224no—
734C4×D4—224no—
735C4×D4—224no—
736C2×C4⋊C4—111no—
737C2×C4⋊C4—111no—
738C2×C4⋊C4—111no—
739C2×C4⋊C4—112no—
740C2×C4⋊C4—112no—
741C2×C4⋊C4—112no—
742C2×C4⋊C4—112no—
743C2×C4⋊C4—111no—
744C2×C4⋊C4—112no—
745C2×C4⋊C4—112no—
746C2×C4⋊C4—112no—
747C2×C4⋊C4—112no—
748C2×C4⋊C4—112no—
749C2×C4⋊C4—112no—
750C2×C4⋊C4—112no—
751C2×C4⋊C4—112no—
752C2×C4⋊C4—112no—
753C2×C4⋊C4—112no—
754C2×C4⋊C4—224no—
755C2×C4⋊C4—224no—
756C2×C4⋊C4—228no—
757C2×C4⋊C4—444no—
758C2×C4⋊C4C22×D1111yescharacteristic
759C2×C4⋊C4C22×D1112yes—
760C2×C4⋊C4C22×D1111yescharacteristic
761C2×C4⋊C4C22×D1112yes—
762C2×C4⋊C4C22×D1112yes—
763C2×C22⋊C4—111no—
764C2×C22⋊C4—111no—
765C2×C22⋊C4—112no—
766C2×C22⋊C4—111no—
767C2×C22⋊C4—111no—
768C2×C22⋊C4—111no—
769C2×C22⋊C4—111no—
770C2×C22⋊C4—112no—
771C2×C22⋊C4—112no—
772C2×C22⋊C4—112no—
773C2×C22⋊C4—112no—
774C2×C22⋊C4—112no—
775C2×C22⋊C4—112no—
776C2×C22⋊C4—112no—
777C2×C22⋊C4—112no—
778C2×C22⋊C4—112no—
779C2×C22⋊C4—112no—
780C2×C22⋊C4—112no—
781C2×C22⋊C4—112no—
782C2×C22⋊C4—224no—
783C2×C22⋊C4—224no—
784C2×C22⋊C4—228no—
785C2×C22⋊C4—228no—
786C2×C22⋊C4C22×D1111yescharacteristic
787C2×C22⋊C4C22×D1111yescharacteristic
788C2×C22⋊C4C22×D1112yes—
789C2×C22⋊C4C22×D1112yes—
790C2×C22⋊C4C22×D1112yes—
791C2×C42—111no—
792C2×C42—111no—
793C2×C42—111no—
794C2×C42—224no—
795C2×C42C22×D1111yescharacteristic
796#95—112no—
797#95—111no—
798#95—111no—
799#95—112no—
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#95—112no—
811#95C22×D1112yes—
812#95C22×D1111yescharacteristic
813#95C22×D1111yescharacteristic
814#95C22×D1112yes—
815#95C22×D1112yes—
816#95C22×D1112yes—
817#95C22×D1112yes—
818C2×C11—24no—
819C2×C11—42no—
820C2×C11C22×C22⋊Q811yescharacteristic
821C2×C11C2×#53411yescharacteristic
822C2×C11#344911yescharacteristic
823C2×C11#350112yes—
824C2×C11#350512yes—
825D11—24no—
826D11—24no—
827D11—42no—
828C24—111no—
829C24—111no—
830C24—114no—
831C24—114no—
832C24—114no—
833C24—111no—
834C24—114no—
835C24—222no—
836C24—222no—
837C24—442no—
838C24—442no—
839C24—442no—
840C24—442no—
841C24C23×D1111yescharacteristic
842C24C23×D1111yescharacteristic
843C2×Q8—22no—
844C2×Q8—42no—
845C2×Q8—224no—
846C2×Q8—224no—
847C2×Q8—224no—
848C2×Q8—222no—
849C2×Q8—442no—
850C2×Q8—4416no—
851C2×D4—22no—
852C2×D4—22no—
853C2×D4—114no—
854C2×D4—114no—
855C2×D4—114no—
856C2×D4—222no—
857C2×D4—222no—
858C2×D4—2232no—
859C2×D4—222no—
860C2×D4—222no—
861C2×D4—222no—
862C2×D4—222no—
863C2×D4Q8×D1114yescomplemented
864C22×C4—24no—
865C22×C4—22no—
866C22×C4—42no—
867C22×C4—42no—
868C22×C4—42no—
869C22×C4—42no—
870C22×C4—111no—
871C22×C4—114no—
872C22×C4—111no—
873C22×C4—111no—
874C22×C4—114no—
875C22×C4—114no—
876C22×C4—114no—
877C22×C4—114no—
878C22×C4—114no—
879C22×C4—112no—
880C22×C4—112no—
881C22×C4—111no—
882C22×C4—112no—
883C22×C4—112no—
884C22×C4—111no—
885C22×C4—224no—
886C22×C4—224no—
887C22×C4—222no—
888C22×C4—224no—
889C22×C4—222no—
890C22×C4—222no—
891C22×C4—222no—
892C22×C4—224no—
893C22×C4—222no—
894C22×C4—224no—
895C22×C4—224no—
896C22×C4—222no—
897C22×C4—224no—
898C22×C4—224no—
899C22×C4—222no—
900C22×C4—442no—
901C22×C4—442no—
902C22×C4—442no—
903C22×C4—442no—
904C22×C4—442no—
905C22×C4—442no—
906C22×C4—442no—
907C22×C4—442no—
908C22×C4—442no—
909C22×C4—4416no—
910C22×C4—4416no—
911C22×C4—442no—
912C22×C4—442no—
913C22×C4D4×D1114yes—
914C22×C4C23×D1112yes—
915C22×C4C23×D1111yescharacteristic
916C22×C4C23×D1112yes—
917C22×C4C23×D1112yes—
918C22×C4C23×D1111yescharacteristic
919C22×C4C23×D1112yes—
920C22×C4C23×D1111yescharacteristic
921C22×C4C23×D1111yescharacteristic
922C22×C4C23×D1111yescharacteristic
923C4⋊C4—22no—
924C4⋊C4—22no—
925C4⋊C4—24no—
926C4⋊C4—42no—
927C4⋊C4—42no—
928C4⋊C4—222no—
929C4⋊C4—222no—
930C4⋊C4—224no—
931C4⋊C4—224no—
932C4⋊C4—224no—
933C4⋊C4—224no—
934C4⋊C4—224no—
935C4⋊C4—222no—
936C4⋊C4—224no—
937C4⋊C4—222no—
938C4⋊C4—442no—
939C4⋊C4—442no—
940C4⋊C4—442no—
941C4⋊C4—442no—
942C4⋊C4—442no—
943C4⋊C4—442no—
944C4⋊C4—442no—
945C4⋊C4—442no—
946C22⋊C4—22no—
947C22⋊C4—24no—
948C22⋊C4—22no—
949C22⋊C4—42no—
950C22⋊C4—42no—
951C22⋊C4—222no—
952C22⋊C4—222no—
953C22⋊C4—222no—
954C22⋊C4—224no—
955C22⋊C4—224no—
956C22⋊C4—224no—
957C22⋊C4—224no—
958C22⋊C4—224no—
959C22⋊C4—224no—
960C22⋊C4—222no—
961C22⋊C4—222no—
962C22⋊C4—224no—
963C22⋊C4—222no—
964C22⋊C4—442no—
965C22⋊C4—442no—
966C22⋊C4—442no—
967C22⋊C4—442no—
968C22⋊C4—442no—
969C22⋊C4—442no—
970C42—22no—
971C42—222no—
972C42—222no—
973C42—222no—
974C11#3501011yescharacteristic, complemented, Sylow
975C23—22no—
976C23—22no—
977C23—21no—
978C23—21no—
979C23—22no—
980C23—22no—
981C23—112no—
982C23—112no—
983C23—112no—
984C23—112no—
985C23—112no—
986C23—112no—
987C23—1116no—
988C23—112no—
989C23—228no—
990C23—222no—
991C23—222no—
992C23—222no—
993C23—222no—
994C23—221no—
995C23—221no—
996C23—222no—
997C23—222no—
998C23—444no—
999C23—448no—
1000C23—448no—
1001C23—444no—
1002C23—448no—
1003C23—444no—
1004C23—448no—
1005C23—444no—
1006C23C2×D4×D1112yes—
1007C23C2×Q8×D1112yes—
1008C23C2×Q8×D1112yes—
1009C23#41×D1112yes—
1010C23C24×D1111yescharacteristic
1011Q8—44no—
1012Q8—444no—
1013Q8—448no—
1014D4—28no—
1015D4—228no—
1016D4—228no—
1017D4—228no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—21no—
1023C2×C4—22no—
1024C2×C4—21no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—44no—
1039C2×C4—44no—
1040C2×C4—84no—
1041C2×C4—112no—
1042C2×C4—114no—
1043C2×C4—112no—
1044C2×C4—112no—
1045C2×C4—228no—
1046C2×C4—228no—
1047C2×C4—228no—
1048C2×C4—228no—
1049C2×C4—221no—
1050C2×C4—221no—
1051C2×C4—222no—
1052C2×C4—221no—
1053C2×C4—222no—
1054C2×C4—221no—
1055C2×C4—222no—
1056C2×C4—222no—
1057C2×C4—222no—
1058C2×C4—222no—
1059C2×C4—222no—
1060C2×C4—222no—
1061C2×C4—222no—
1062C2×C4—222no—
1063C2×C4—222no—
1064C2×C4—222no—
1065C2×C4—222no—
1066C2×C4—222no—
1067C2×C4—222no—
1068C2×C4—444no—
1069C2×C4—444no—
1070C2×C4—444no—
1071C2×C4—444no—
1072C2×C4—444no—
1073C2×C4—448no—
1074C2×C4—448no—
1075C2×C4—444no—
1076C2×C4—444no—
1077C2×C4—884no—
1078C2×C4C2×D4×D1112yes—
1079C2×C4C2×D4×D1112yes—
1080C2×C4C2×Q8×D1112yes—
1081C22—24no—
1082C22—22no—
1083C22—24no—
1084C22—22no—
1085C22—24no—
1086C22—22no—
1087C22—41no—
1088C22—42no—
1089C22—41no—
1090C22—114no—
1091C22—114no—
1092C22—224no—
1093C22—224no—
1094C22—222no—
1095C22—222no—
1096C22—224no—
1097C22—224no—
1098C22—222no—
1099C22—222no—
1100C22—224no—
1101C22—222no—
1102C22—4416no—
1103C22—4416no—
1104C22—441no—
1105C22—442no—
1106C22—441no—
1107C22D11×C22⋊Q814yes—
1108C22C22×D4×D1111yescharacteristic
1109C22C22×Q8×D1111yescharacteristic
1110C22C2×#41×D1111yescharacteristic
1111C22#1062345312yes—
1112C22D11×H(5,𝔽2)12yes—
1113C4—22no—
1114C4—22no—
1115C4—22no—
1116C4—41no—
1117C4—42no—
1118C4—42no—
1119C4—42no—
1120C4—41no—
1121C4—42no—
1122C4—114no—
1123C4—222no—
1124C4—222no—
1125C4—441no—
1126C4—442no—
1127C4—442no—
1128C4—442no—
1129C4—441no—
1130C4—442no—
1131C2—24no—
1132C2—42no—
1133C2—224no—
1134C2—224no—
1135C2—442no—
1136C2C2×D11×C22⋊Q811yescharacteristic
1137C2D11×#53411yescharacteristic
1138C2#1308194311yescharacteristic
1139C2#1308241512yes—
1140C2#1308244712yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2564C2
prime radicalC22×D4×D11C22
hypercenter#2564D11
hypocenterC11#35010
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2564

Complements

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

NH ≅ G/Ntype
1. C2×D11×C22⋊Q8C2semidirect
3. #13076951C2semidirect
4. #13076902C2semidirect
5. #13074430C2semidirect
6. #13074428C2semidirect
7. #13074422C2semidirect
8. #13074420C2semidirect
9. #13073967C2semidirect
10. #13073961C2semidirect
11. #13073798C2semidirect
12. #13073796C2semidirect
13. #13073792C2semidirect
14. #13072928C2semidirect
15. #13072926C2semidirect
16. #13072066C2semidirect
17. #13072064C2semidirect
18. #13071976C2semidirect
19. #13071974C2semidirect
20. #13071229C2semidirect
22. C2×#10622280C2semidirect
23. C11×#2564C2semidirect
24. C22×Q8×D11C22semidirect
28. C2×C11×C22⋊Q8C22semidirect
35. C2×#66977C22semidirect
36. C22×Dic11⋊C4C22semidirect
41. C2×#66949C22semidirect
44. C2×C4⋊C4×D11C22semidirect
45. C2×C4⋊C4×D11C22semidirect
51. C2×#66931C22semidirect
52. C2×#66931C22semidirect
55. C11×#400C22semidirect
56. C11×#399C22semidirect
57. C11×#395C22semidirect
58. C11×#393C22semidirect
59. C11×#387C22semidirect
61. C11×#385C22semidirect
62. C11×#380C22semidirect
63. C2×C11×#95C22semidirect
64. #10622844C22semidirect
65. #10622842C22semidirect
68. #10622825C22semidirect
69. #10622823C22semidirect
70. C2×C11⋊#95C22semidirect
71. #10622607C22semidirect
72. #10622605C22semidirect
75. #10622602C22semidirect
76. #10622602C22semidirect
77. #10622602C22semidirect
78. #10622599C22semidirect
79. #10622595C22semidirect
80. #10622593C22semidirect
81. #10622592C22semidirect
82. #10622591C22semidirect
83. #10622585C22semidirect
89. #10622562C22semidirect
90. #10622561C22semidirect
91. #10622561C22semidirect
92. #10622560C22semidirect
93. #10622555C22semidirect
94. #10622555C22semidirect
95. #10622555C22semidirect
96. #10622546C22semidirect
97. #10622290C22semidirect
98. #10622289C22semidirect
99. #10622286C22semidirect
102. #10622281C22semidirect
103. #10622281C22semidirect
104. #10622281C22semidirect
108. #10622280C22semidirect
109. #10622280C22semidirect
110. #10622280C22semidirect
111. #10622280C22semidirect
116. #10622274C22semidirect
117. #10622272C22semidirect
118. #10622270C22semidirect
119. #10622270C22semidirect
120. #10622269C22semidirect
121. #10622266C22semidirect
122. #10622260C22semidirect
123. #10622259C22semidirect
124. #10622259C22semidirect
141. C2×D4×D11Q8semidirect
269. C23×D11C2×Q8semidirect
278. C2×D4×C11C2×Q8semidirect
300. C2×C22⋊D11C2×Q8semidirect
348. C2×C4×D11C2×Q8semidirect
418. #2564D11semidirect
456. C22×D11C22⋊Q8semidirect
546. C2×C22⋊Q8C2×D11semidirect
568. #400C2×D11semidirect
572. #399C2×D11semidirect
584. #395C2×D11semidirect
588. #393C2×D11semidirect
596. #387C2×D11semidirect
616. #385C2×D11semidirect
630. #380C2×D11semidirect
634. C2×#95C2×D11semidirect
863. C2×D4Q8×D11semidirect
974. C11#35010semidirect

Maximal subgroups

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

subgroupindex
C2×D11×C22⋊Q82
C2×C4×D4×D112
#130769512
#130769022
#130744302
#130744282
#130744222
#130744202
#130739672
#130739612
#130737982
#130737962
#130737922
#130729282
#130729262
#130720662
#130720642
#130719762
#130719742
#130712292
#130711902
C2×#106222802
C11×#25642
#3501011