Finite Group Databasebeta

← #14913218

Subgroups — #14913218

Order 2816.

3142 conjugacy classes of subgroups.

The subgroup lattice has 1108 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×D11C211yesmaximal, characteristic
2#13071590C211yesmaximal, characteristic, complemented
3#13071584C211yesmaximal, characteristic, complemented
4#13071557C211yesmaximal, characteristic, complemented
5#13071556C211yesmaximal, characteristic, complemented
6#13071549C211yesmaximal, characteristic, complemented
7#13071523C211yesmaximal, characteristic, complemented
8#13071520C211yesmaximal, characteristic, complemented
9#13071490C212yesmaximal, complemented
10#13071460C212yesmaximal, complemented
11#13071459C212yesmaximal, complemented
12#13071434C212yesmaximal
13#13071076C212yesmaximal, complemented
14#13071056C212yesmaximal, complemented
15#13071054C212yesmaximal, complemented
16#13071013C211yesmaximal, characteristic, complemented
17#13070998C211yesmaximal, characteristic, complemented
18#13070996C211yesmaximal, characteristic, complemented
19C4×(C22⋊D11)⋊C4C212yesmaximal, complemented
20#13070955C211yesmaximal, characteristic, complemented
21C2×#10622279C211yesmaximal, characteristic, complemented
22C4×C22⋊C4×D11C211yesmaximal, characteristic, complemented
23C11×#2353C211yesmaximal, characteristic, complemented
24C22×D4×D11C2211yescharacteristic
25C23×C4×D11C2211yescharacteristic
26C23×C4×D11C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic
28C2×D4×Dic11C2211yescharacteristic
29C2×C4×C22⋊D11C2212yes—
30C2×C4×C22⋊D11C2211yescharacteristic
31C2×C4×C22⋊D11C2211yescharacteristic
32C22×(C2×D11)⋊C4C2212yes—
33C22×C4×Dic11C2212yescomplemented
34C4×D4×D11C4116yescomplemented
35C2×#66946C2211yescharacteristic
36C2×#66945C2212yescomplemented
37C2×C4⋊C4×D11C2211yescharacteristic
38C2×(C22⋊D11)⋊C4C2212yes—
39C2×(C22⋊D11)⋊C4C2211yescharacteristic
40C2×(C22⋊D11)⋊C4C2211yescharacteristic
41C2×C22⋊C4×D11C2212yes—
42C2×C22⋊C4×D11C2211yescharacteristic
43C2×C22⋊C4×D11C2211yescharacteristic
44C2×#66930C2212yescomplemented
45C2×C4×D44C2211yescharacteristic
46C2×#66925C2212yes—
47C2×C42×D11C2211yescharacteristic
48C2×C42×D11C2212yescomplemented
49C11×#388C2212yescomplemented
50C11×#387C2212yescomplemented
51C11×#386C2212yes—
52C11×#383C2211yescharacteristic, complemented
53C11×#381C2211yescharacteristic, complemented
54C11×#380C2211yescharacteristic, complemented
55C4×C11×C22⋊C4C2211yescharacteristic, complemented
56C4×C11×C22⋊C4C2212yescomplemented
57C11×#376C2211yescharacteristic, complemented
58C2×C11×#95C2211yescharacteristic, complemented
59#10622833C2212yes—
60#10622825C2211yescharacteristic, complemented
61#10622824C2211yescharacteristic, complemented
62#10622823C2212yescomplemented
63C4×C22⋊Dic11C2211yescharacteristic, complemented
64C2×C11⋊#95C2211yescharacteristic, complemented
65#10622602C2212yescomplemented
66#10622600C2212yes—
67#10622594C2212yescomplemented
68#10622585C2212yescomplemented
69#10622570C2212yes—
70#10622570C2212yes—
71#10622568C2212yes—
72#10622568C2212yes—
73#10622564C2212yescomplemented
74#10622559C2212yescomplemented
75#10622558C2212yescomplemented
76#10622557C2212yescomplemented
77C22⋊C4×Dic11C2212yescomplemented
78C22⋊C4×Dic11C2212yescomplemented
79C22⋊C4×Dic11C2212yescomplemented
80#10622553C2212yescomplemented
81#10622553C2212yescomplemented
82C4×(C2×D11)⋊C4C2212yes—
83C4×(C2×D11)⋊C4C2212yescomplemented
84#10622550C2211yescharacteristic, complemented
85#10622545C2211yescharacteristic, complemented
86C4×Dic11⋊C4C2212yescomplemented
87C42×Dic11C2212yescomplemented
88#10622282C2212yescomplemented
89#10622282C2212yescomplemented
90#10622281C2212yescomplemented
91#10622280C2212yes—
92#10622280C2212yes—
93#10622280C2211yescharacteristic, complemented
94#10622280C2211yescharacteristic, complemented
95#10622279C2212yes—
96#10622279C2211yescharacteristic
97#10622279C2211yescharacteristic
98#10622279C2212yes—
99#10622279C2211yescharacteristic
100#10622279C2211yescharacteristic
101#10622279C2211yescharacteristic, complemented
102#10622279C2211yescharacteristic, complemented
103#10622279C2212yescomplemented
104#10622279C2212yescomplemented
105#10622279C2212yescomplemented
106#10622278C2212yes—
107#10622278C2212yes—
108#10622277C2212yes—
109#10622277C2211yescharacteristic, complemented
110#10622277C2211yescharacteristic, complemented
111D11×#95C2211yescharacteristic, complemented
112D11×#95C2211yescharacteristic, complemented
113#10622267C2212yescomplemented
114#10622266C2212yescomplemented
115#10622263C2211yescharacteristic, complemented
116#10622263C2211yescharacteristic, complemented
117#10622262C2211yescharacteristic, complemented
118#10622262C2211yescharacteristic, complemented
119#10622262C2212yescomplemented
120#10622262C2212yescomplemented
121#10622262C2212yescomplemented
122#10622261C2212yescomplemented
123#10622260C2212yescomplemented
124C24×D11C2311yescharacteristic
125C24×D11C2311yescharacteristic
126C22×D4×C11C2311yescharacteristic
127C23×C4×C11C2312yes—
128C23×C4×C11C2311yescharacteristic
129C23×C4×C11C2311yescharacteristic
130C22×C22⋊D11C2311yescharacteristic
131C22×C22⋊D11C2311yescharacteristic
132C23×Dic11C2312yes—
133C23×Dic11C2311yescharacteristic
134C23×Dic11C2311yescharacteristic
135C2×D4×D11—24no—
136C2×D4×D11—24no—
137C2×D4×D11C2×C418yes—
138C22×D44C2311yescharacteristic
139C22×C4×D11—44no—
140C22×C4×D11—44no—
141C22×C4×D11C2×C418yescomplemented
142C22×C4×D11C2×C418yescomplemented
143C22×C4×D11C2312yes—
144C22×C4×D11C2312yes—
145C22×C4×D11C2311yescharacteristic
146C22×C4×D11C2311yescharacteristic
147C22×C4×D11C2311yescharacteristic
148C22×C4×D11C2311yescharacteristic
149C22×C4×D11C2311yescharacteristic
150C22×C4×D11C2311yescharacteristic
151C22×C4×D11C2311yescharacteristic
152C22×C4×D11C2311yescharacteristic
153C22×C4×D11C2311yescharacteristic
154C4×D4×C11C2×C418yescomplemented
155C2×C11×C4⋊C4C2312yes—
156C2×C11×C4⋊C4C2311yescharacteristic
157C2×C11×C22⋊C4C2312yes—
158C2×C11×C22⋊C4C2312yes—
159C2×C11×C22⋊C4C2312yes—
160C2×C11×C22⋊C4C2311yescharacteristic
161C2×C11×C22⋊C4C2311yescharacteristic
162C2×C42×C11C2312yes—
163C2×C42×C11C2312yes—
164C2×C42×C11C2311yescharacteristic
165C2×C22⋊Dic11C2312yes—
166C2×C22⋊Dic11C2312yes—
167C2×C22⋊Dic11C2312yes—
168C2×C22⋊Dic11C2311yescharacteristic
169C2×C22⋊Dic11C2311yescharacteristic
170D4×Dic11C2×C418yescomplemented
171C4×C22⋊D11—28no—
172C4×C22⋊D11C2×C418yes—
173C4×C22⋊D11C2×C418yescomplemented
174C2×(C2×D11)⋊C4—28no—
175C2×(C2×D11)⋊C4C2312yes—
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)⋊C4C2311yescharacteristic
185C2×(C2×D11)⋊C4C2311yescharacteristic
186C2×(C2×D11)⋊C4C2311yescharacteristic
187C2×(C2×D11)⋊C4C2311yescharacteristic
188C2×(C2×D11)⋊C4C2312yes—
189C2×C4⋊Dic11C2312yes—
190C2×C4⋊Dic11C2311yescharacteristic
191C2×Dic11⋊C4C2312yes—
192C2×Dic11⋊C4C2312yes—
193C2×Dic11⋊C4C2312yes—
194C2×Dic11⋊C4C2312yes—
195C2×Dic11⋊C4C2312yes—
196C2×Dic11⋊C4C2312yes—
197C2×Dic11⋊C4C2311yescharacteristic
198C2×Dic11⋊C4C2311yescharacteristic
199C2×C4×Dic11—44no—
200C2×C4×Dic11C2312yes—
201C2×C4×Dic11C2312yes—
202C2×C4×Dic11C2312yes—
203C2×C4×Dic11C2312yes—
204C2×C4×Dic11C2312yes—
205C2×C4×Dic11C2312yes—
206C2×C4×Dic11C2312yes—
207C2×C4×Dic11C2312yes—
208C2×C4×Dic11C2312yes—
209C2×C4×Dic11C2312yes—
210C2×C4×Dic11C2311yescharacteristic
211C2×C4×Dic11C2311yescharacteristic
212C2×C4×Dic11C2311yescharacteristic
213#66946C2×C418yescomplemented
214#66945—44no—
215C4⋊C4×D11C2×C418yescomplemented
216(C22⋊D11)⋊C4—28no—
217(C22⋊D11)⋊C4C2×C418yes—
218(C22⋊D11)⋊C4C2×C418yescomplemented
219C22⋊C4×D11—28no—
220C22⋊C4×D11C2×C418yescomplemented
221C22⋊C4×D11C2×C418yescomplemented
222#66930—44no—
223C4×D44C2×C418yescomplemented
224#66925—28no—
225C42×D11—44no—
226C42×D11C2×C418yescomplemented
227C11×#95C2312yes—
228C11×#95C2312yes—
229C11×#95C2312yes—
230C11×#95C2311yescharacteristic
231C11×#95C2312yes—
232C11×#95C2311yescharacteristic
233C11×#95C2312yes—
234C11×#95C2311yescharacteristic
235C11×#95C2311yescharacteristic
236C11⋊#95C2312yes—
237C11⋊#95C2312yes—
238C11⋊#95C2312yes—
239C11⋊#95C2312yes—
240C11⋊#95C2312yes—
241C11⋊#95C2312yes—
242C11⋊#95C2311yescharacteristic
243C11⋊#95C2312yes—
244C11⋊#95C2311yescharacteristic
245C11⋊#95C2311yescharacteristic
246C11⋊#95C2311yescharacteristic
247C11⋊#95C2312yes—
248C11⋊#95C2312yes—
249C11⋊#95C2312yes—
250C11⋊#95C2312yes—
251#34126—111nomaximal, Sylow
252C24×C11C2411yescharacteristic
253C24×C11C2411yescharacteristic
254C23×D11—22no—
255C23×D11—22no—
256C23×D11—24no—
257C23×D11—24no—
258C23×D11—22no—
259C23×D11—22no—
260C23×D11—42no—
261C23×D11—42no—
262C23×D11C22×C414yes—
263C23×D11C22×C414yes—
264C23×D11C2411yescharacteristic
265C23×D11C2411yescharacteristic
266C23×D11C2411yescharacteristic
267C2×D4×C11—22no—
268C2×D4×C11—22no—
269C2×D4×C11C22×C414yes—
270C22×C4×C11—24no—
271C22×C4×C11—24no—
272C22×C4×C11—42no—
273C22×C4×C11—42no—
274C22×C4×C11—42no—
275C22×C4×C11C22×C414yes—
276C22×C4×C11C22×C414yes—
277C22×C4×C11C2412yes—
278C22×C4×C11C2412yes—
279C22×C4×C11C2412yes—
280C22×C4×C11C2411yescharacteristic
281C22×C4×C11C2411yescharacteristic
282C22×C4×C11C2411yescharacteristic
283C22×C4×C11C2411yescharacteristic
284C22×C4×C11C2411yescharacteristic
285C22×C4×C11C2412yes—
286C2×C22⋊D11—22no—
287C2×C22⋊D11—22no—
288C2×C22⋊D11C22×C414yes—
289C2×C22⋊D11C22×C414yes—
290C2×C22⋊D11#4114yes—
291C2×C22⋊D11#4114yes—
292C22×Dic11—24no—
293C22×Dic11—24no—
294C22×Dic11—24no—
295C22×Dic11—24no—
296C22×Dic11—42no—
297C22×Dic11C22×C414yes—
298C22×Dic11C22×C414yes—
299C22×Dic11C2412yes—
300C22×Dic11C2412yes—
301C22×Dic11C2412yes—
302C22×Dic11C2411yescharacteristic
303C22×Dic11C2411yescharacteristic
304C22×Dic11C2411yescharacteristic
305C22×Dic11C2412yes—
306C22×Dic11C2411yescharacteristic
307C22×Dic11C2411yescharacteristic
308D4×D11—232no—
309C2×D44—22no—
310C2×D44—22no—
311C2×D44C22×C414yes—
312C2×C4×D11—22no—
313C2×C4×D11—22no—
314C2×C4×D11—24no—
315C2×C4×D11—24no—
316C2×C4×D11—24no—
317C2×C4×D11—24no—
318C2×C4×D11—24no—
319C2×C4×D11—24no—
320C2×C4×D11—24no—
321C2×C4×D11—24no—
322C2×C4×D11—42no—
323C2×C4×D11—42no—
324C2×C4×D11—42no—
325C2×C4×D11—42no—
326C2×C4×D11—42no—
327C2×C4×D11—42no—
328C2×C4×D11—416no—
329C2×C4×D11—416no—
330C2×C4×D11C22×C414yes—
331C2×C4×D11C22×C414yes—
332C2×C4×D11C22×C414yes—
333C2×C4×D11C22×C414yes—
334C2×C4×D11C22×C414yes—
335C2×C4×D11C22×C414yes—
336C2×C4×D11C22×C414yes—
337C2×C4×D11C22×C414yes—
338C2×C4×D11C22×C414yes—
339C11×C4⋊C4—42no—
340C11×C4⋊C4C22×C414yes—
341C11×C22⋊C4—24no—
342C11×C22⋊C4—24no—
343C11×C22⋊C4—42no—
344C11×C22⋊C4C22×C414yes—
345C11×C22⋊C4C22×C414yes—
346C42×C11—24no—
347C42×C11—42no—
348C42×C11C22×C414yes—
349C22⋊Dic11—24no—
350C22⋊Dic11—24no—
351C22⋊Dic11—42no—
352C22⋊Dic11C22×C414yes—
353C22⋊Dic11C22×C414yes—
354(C2×D11)⋊C4—24no—
355(C2×D11)⋊C4—24no—
356(C2×D11)⋊C4—24no—
357(C2×D11)⋊C4—24no—
358(C2×D11)⋊C4—24no—
359(C2×D11)⋊C4—24no—
360(C2×D11)⋊C4—24no—
361(C2×D11)⋊C4—42no—
362(C2×D11)⋊C4—42no—
363(C2×D11)⋊C4C22×C414yes—
364(C2×D11)⋊C4C22×C414yes—
365(C2×D11)⋊C4C22×C414yes—
366(C2×D11)⋊C4C22×C414yes—
367(C2×D11)⋊C4#4118yes—
368C4⋊Dic11—42no—
369C4⋊Dic11C22×C414yes—
370Dic11⋊C4—24no—
371Dic11⋊C4—24no—
372Dic11⋊C4—24no—
373Dic11⋊C4—24no—
374Dic11⋊C4—42no—
375Dic11⋊C4—42no—
376Dic11⋊C4C22×C414yes—
377Dic11⋊C4C22×C414yes—
378C4×Dic11—24no—
379C4×Dic11—24no—
380C4×Dic11—24no—
381C4×Dic11—24no—
382C4×Dic11—24no—
383C4×Dic11—24no—
384C4×Dic11—24no—
385C4×Dic11—42no—
386C4×Dic11—42no—
387C4×Dic11—42no—
388C4×Dic11C22×C414yes—
389C4×Dic11C22×C414yes—
390C4×Dic11C22×C414yes—
391C22×C4×D4—111no—
392#2357—111no—
393#2357—111no—
394#2353—111no—
395#2353—111no—
396#2353—111no—
397#2353D1111yescharacteristic, complemented
398#2349—111no—
399#2349—111no—
400#2345—112no—
401#2342—112no—
402#2342—112no—
403D4×C22⋊C4—112no—
404#2293—112no—
405#2290—112no—
406#2290—112no—
407#2283—111no—
408#2280—111no—
409#2280—111no—
410C42×D4—112no—
411C4×#117—111no—
412C2×C4×C22⋊C4—111no—
413C2×C4×C22⋊C4—111no—
414C23×C11—22no—
415C23×C11—22no—
416C23×C11—22no—
417C23×C11—21no—
418C23×C11—21no—
419C23×C11—22no—
420C23×C11C23×C412yes—
421C23×C11C23×C412yes—
422C23×C11C2×#4112yes—
423C23×C11C2×#4112yes—
424C23×C11C2511yescharacteristic
425C22×D11—22no—
426C22×D11—21no—
427C22×D11—21no—
428C22×D11—22no—
429C22×D11—22no—
430C22×D11—28no—
431C22×D11—22no—
432C22×D11—21no—
433C22×D11—21no—
434C22×D11—22no—
435C22×D11—28no—
436C22×D11—28no—
437C22×D11—28no—
438C22×D11—44no—
439C22×D11—44no—
440C22×D11—48no—
441C22×D11—48no—
442C22×D11—48no—
443C22×D11—48no—
444C22×D11C23×C412yes—
445C22×D11C23×C412yes—
446C22×D11C23×C412yes—
447C22×D11C2×#4112yes—
448C22×D11C2×#4112yes—
449C22×D11C2×#4114yes—
450D4×C11—28no—
451C2×C4×C11—22no—
452C2×C4×C11—22no—
453C2×C4×C11—21no—
454C2×C4×C11—21no—
455C2×C4×C11—22no—
456C2×C4×C11—22no—
457C2×C4×C11—22no—
458C2×C4×C11—22no—
459C2×C4×C11—22no—
460C2×C4×C11—22no—
461C2×C4×C11—22no—
462C2×C4×C11—22no—
463C2×C4×C11—22no—
464C2×C4×C11—22no—
465C2×C4×C11—22no—
466C2×C4×C11—22no—
467C2×C4×C11—22no—
468C2×C4×C11—44no—
469C2×C4×C11—44no—
470C2×C4×C11—48no—
471C2×C4×C11C23×C412yes—
472C2×C4×C11C23×C412yes—
473C2×C4×C11C23×C412yes—
474C2×C4×C11C23×C412yes—
475C2×C4×C11C23×C412yes—
476C2×C4×C11C2×#4114yes—
477C22⋊D11—28no—
478C22⋊D11#117116yescomplemented
479C2×Dic11—22no—
480C2×Dic11—22no—
481C2×Dic11—22no—
482C2×Dic11—22no—
483C2×Dic11—22no—
484C2×Dic11—28no—
485C2×Dic11—28no—
486C2×Dic11—22no—
487C2×Dic11—22no—
488C2×Dic11—22no—
489C2×Dic11—22no—
490C2×Dic11—22no—
491C2×Dic11—22no—
492C2×Dic11—22no—
493C2×Dic11—22no—
494C2×Dic11—22no—
495C2×Dic11—48no—
496C2×Dic11C23×C412yes—
497C2×Dic11C23×C412yes—
498C2×Dic11C23×C412yes—
499C2×Dic11C23×C412yes—
500C2×Dic11C23×C412yes—
501C2×Dic11C2×#4114yes—
502C2×Dic11C2×#4112yes—
503C2×Dic11C2×#4112yes—
504C2×Dic11H(5,𝔽2)14yes—
505D44—28no—
506C4×D11—28no—
507C4×D11—28no—
508C4×D11—28no—
509C4×D11—28no—
510C4×D11—28no—
511C4×D11—44no—
512C4×D11—44no—
513C4×D11—44no—
514C4×D11—44no—
515C4×D11—48no—
516C4×D11—48no—
517C23×D4—111no—
518C24×C4—111no—
519C24×C4—111no—
520C2×C4×D4—111no—
521C2×C4×D4—111no—
522C2×C4×D4—111no—
523C2×C4×D4—1116no—
524C2×C4×D4—112no—
525C2×C4×D4—111no—
526C2×C4×D4—111no—
527C2×C4×D4—111no—
528C2×C4×D4—112no—
529C2×C4×D4—111no—
530C2×C4×D4C2×D1111yescharacteristic
531C2×#117—112no—
532C2×#117—112no—
533C2×#117—112no—
534C22×C4⋊C4—111no—
535C22×C22⋊C4—111no—
536C22×C22⋊C4—111no—
537C22×C22⋊C4—112no—
538C22×C22⋊C4—112no—
539C22×C42—111no—
540C22×C42—112no—
541C22×C42—112no—
542#390—112no—
543#390—112no—
544#389—112no—
545#389—112no—
546#388—112no—
547#388—112no—
548#388—112no—
549#388—112no—
550#388—112no—
551#388—112no—
552#388—112no—
553#388C2×D1112yescomplemented
554#387—112no—
555#387—112no—
556#387—112no—
557#387C2×D1112yescomplemented
558#386—112no—
559#386—112no—
560#386—112no—
561#386C2×D1112yes—
562#385—112no—
563#385—112no—
564#385—112no—
565#385—112no—
566#383—111no—
567#383C2×D1111yescharacteristic, complemented
568#382—111no—
569#382—111no—
570#381—111no—
571#381—112no—
572#381—111no—
573#381—111no—
574#381C2×D1111yescharacteristic, complemented
575#380—111no—
576#380—112no—
577#380—112no—
578#380—112no—
579#380—111no—
580#380—111no—
581#380C2×D1111yescharacteristic, complemented
582#379—112no—
583#379—112no—
584C4×C4⋊C4—112no—
585C4×C4⋊C4—112no—
586C4×C4⋊C4—111no—
587C4×C4⋊C4—111no—
588C4×C4⋊C4—112no—
589C4×C4⋊C4—112no—
590C4×C22⋊C4—111no—
591C4×C22⋊C4—112no—
592C4×C22⋊C4—112no—
593C4×C22⋊C4—112no—
594C4×C22⋊C4—112no—
595C4×C22⋊C4—112no—
596C4×C22⋊C4—112no—
597C4×C22⋊C4—112no—
598C4×C22⋊C4—112no—
599C4×C22⋊C4—111no—
600C4×C22⋊C4—111no—
601C4×C22⋊C4—111no—
602C4×C22⋊C4—111no—
603C4×C22⋊C4—111no—
604C4×C22⋊C4—111no—
605C4×C22⋊C4—112no—
606C4×C22⋊C4—112no—
607C4×C22⋊C4C2×D1112yescomplemented
608C4×C22⋊C4C2×D1111yescharacteristic, complemented
609#376—111no—
610#376—112no—
611#376C2×D1111yescharacteristic, complemented
612C2×#95—111no—
613C2×#95—111no—
614C2×#95—111no—
615C2×#95C2×D1111yescharacteristic, complemented
616C43—112no—
617C22×C11—22no—
618C22×C11—22no—
619C22×C11—24no—
620C22×C11—24no—
621C22×C11—22no—
622C22×C11—22no—
623C22×C11—22no—
624C22×C11—42no—
625C22×C11—42no—
626C22×C11C2×#11714yes—
627C22×C11C24×C411yescharacteristic
628C22×C11C22×#4111yescharacteristic
629C22×C11C22×#4111yescharacteristic
630C22×C11C22×#4112yes—
631C22×C11C2×H(5,𝔽2)12yes—
632C2×D11—22no—
633C2×D11—22no—
634C2×D11—22no—
635C2×D11—22no—
636C2×D11—24no—
637C2×D11—24no—
638C2×D11—24no—
639C2×D11—24no—
640C2×D11—22no—
641C2×D11—22no—
642C2×D11—22no—
643C2×D11—416no—
644C2×D11—416no—
645C2×D11—42no—
646C2×D11—42no—
647C2×D11C2×#11714yes—
648C2×D11C4×#4114yes—
649C4×C11—22no—
650C4×C11—22no—
651C4×C11—22no—
652C4×C11—22no—
653C4×C11—22no—
654C4×C11—24no—
655C4×C11—42no—
656C4×C11—42no—
657C4×C11—42no—
658Dic11—22no—
659Dic11—22no—
660Dic11—22no—
661Dic11—24no—
662Dic11—42no—
663Dic11—42no—
664Dic11—42no—
665Dic11C2×#11714yes—
666Dic11#51814yes—
667C25—111no—
668C25—111no—
669C22×D4—111no—
670C22×D4—111no—
671C22×D4—118no—
672C22×D4—111no—
673C22×D4—224no—
674C22×D4—224no—
675C22×D4C22×D1111yescharacteristic
676C23×C4—111no—
677C23×C4—111no—
678C23×C4—111no—
679C23×C4—111no—
680C23×C4—111no—
681C23×C4—111no—
682C23×C4—111no—
683C23×C4—118no—
684C23×C4—118no—
685C23×C4—111no—
686C23×C4—111no—
687C23×C4—111no—
688C23×C4—111no—
689C23×C4—112no—
690C23×C4—112no—
691C23×C4—112no—
692C23×C4—444no—
693C23×C4—444no—
694C23×C4C22×D1112yes—
695C23×C4C22×D1111yescharacteristic
696C23×C4C22×D1111yescharacteristic
697C4×D4—118no—
698C4×D4—118no—
699C4×D4—118no—
700C4×D4—118no—
701C4×D4—118no—
702C4×D4—118no—
703C4×D4—118no—
704C4×D4—228no—
705C4×D4—228no—
706C4×D4C4×D1118yescomplemented
707#117—228no—
708#117—444no—
709#117—444no—
710C2×C4⋊C4—111no—
711C2×C4⋊C4—111no—
712C2×C4⋊C4—111no—
713C2×C4⋊C4—118no—
714C2×C4⋊C4—112no—
715C2×C4⋊C4—112no—
716C2×C4⋊C4—112no—
717C2×C4⋊C4—112no—
718C2×C4⋊C4—112no—
719C2×C4⋊C4—112no—
720C2×C4⋊C4—112no—
721C2×C4⋊C4C22×D1112yes—
722C2×C4⋊C4C22×D1111yescharacteristic
723C2×C22⋊C4—111no—
724C2×C22⋊C4—111no—
725C2×C22⋊C4—112no—
726C2×C22⋊C4—111no—
727C2×C22⋊C4—111no—
728C2×C22⋊C4—111no—
729C2×C22⋊C4—111no—
730C2×C22⋊C4—118no—
731C2×C22⋊C4—118no—
732C2×C22⋊C4—112no—
733C2×C22⋊C4—112no—
734C2×C22⋊C4—112no—
735C2×C22⋊C4—112no—
736C2×C22⋊C4—112no—
737C2×C22⋊C4—112no—
738C2×C22⋊C4—112no—
739C2×C22⋊C4—112no—
740C2×C22⋊C4—112no—
741C2×C22⋊C4—112no—
742C2×C22⋊C4—112no—
743C2×C22⋊C4—112no—
744C2×C22⋊C4—228no—
745C2×C22⋊C4—228no—
746C2×C22⋊C4C22×D1112yes—
747C2×C22⋊C4C22×D1112yes—
748C2×C22⋊C4C22×D1112yes—
749C2×C22⋊C4C22×D1111yescharacteristic
750C2×C22⋊C4C22×D1111yescharacteristic
751C2×C42—111no—
752C2×C42—111no—
753C2×C42—111no—
754C2×C42—118no—
755C2×C42—112no—
756C2×C42—112no—
757C2×C42—112no—
758C2×C42—112no—
759C2×C42—112no—
760C2×C42—112no—
761C2×C42—112no—
762C2×C42—112no—
763C2×C42—112no—
764C2×C42—112no—
765C2×C42—444no—
766C2×C42—444no—
767C2×C42C22×D1112yes—
768C2×C42C22×D1112yes—
769C2×C42C22×D1111yescharacteristic
770#95—111no—
771#95—111no—
772#95—111no—
773#95—112no—
774#95—112no—
775#95—112no—
776#95—111no—
777#95—112no—
778#95—112no—
779#95—112no—
780#95—112no—
781#95—112no—
782#95—112no—
783#95—112no—
784#95—112no—
785#95C22×D1111yescharacteristic
786#95C22×D1111yescharacteristic
787#95C22×D1111yescharacteristic
788#95C22×D1112yes—
789#95C22×D1112yes—
790#95C22×D1111yescharacteristic
791#95C22×D1112yes—
792#95C22×D1112yes—
793#95C22×D1112yes—
794C2×C11—24no—
795C2×C11—42no—
796C2×C11C22×#11711yescharacteristic
797C2×C11C2×C4×#4111yescharacteristic
798C2×C11C2×#51811yescharacteristic
799C2×C11#348112yes—
800C2×C11#348112yes—
801D11—24no—
802D11—24no—
803D11—42no—
804C24—111no—
805C24—111no—
806C24—111no—
807C24—114no—
808C24—114no—
809C24—224no—
810C24—224no—
811C24—222no—
812C24—222no—
813C24—222no—
814C24—222no—
815C24—442no—
816C24—442no—
817C24C23×D1111yescharacteristic
818C24C23×D1111yescharacteristic
819C2×D4—22no—
820C2×D4—22no—
821C2×D4—114no—
822C2×D4—114no—
823C2×D4—114no—
824C2×D4—114no—
825C2×D4—114no—
826C2×D4—222no—
827C2×D4—222no—
828C2×D4—222no—
829C2×D4—222no—
830C2×D4—2232no—
831C2×D4C2×C4×D1114yes—
832C22×C4—24no—
833C22×C4—24no—
834C22×C4—42no—
835C22×C4—42no—
836C22×C4—42no—
837C22×C4—111no—
838C22×C4—111no—
839C22×C4—114no—
840C22×C4—114no—
841C22×C4—112no—
842C22×C4—111no—
843C22×C4—111no—
844C22×C4—111no—
845C22×C4—114no—
846C22×C4—114no—
847C22×C4—114no—
848C22×C4—114no—
849C22×C4—114no—
850C22×C4—114no—
851C22×C4—114no—
852C22×C4—114no—
853C22×C4—114no—
854C22×C4—112no—
855C22×C4—112no—
856C22×C4—112no—
857C22×C4—224no—
858C22×C4—224no—
859C22×C4—224no—
860C22×C4—222no—
861C22×C4—222no—
862C22×C4—224no—
863C22×C4—224no—
864C22×C4—224no—
865C22×C4—224no—
866C22×C4—224no—
867C22×C4—224no—
868C22×C4—224no—
869C22×C4—224no—
870C22×C4—224no—
871C22×C4—442no—
872C22×C4—442no—
873C22×C4—442no—
874C22×C4—442no—
875C22×C4—442no—
876C22×C4—442no—
877C22×C4—4416no—
878C22×C4—4416no—
879C22×C4—442no—
880C22×C4C2×C4×D1114yes—
881C22×C4C2×C4×D1114yes—
882C22×C4C23×D1112yes—
883C22×C4C23×D1112yes—
884C22×C4C23×D1112yes—
885C22×C4C23×D1111yescharacteristic
886C22×C4C23×D1111yescharacteristic
887C22×C4C23×D1111yescharacteristic
888C22×C4C23×D1111yescharacteristic
889C22×C4C23×D1111yescharacteristic
890C22×C4C23×D1112yes—
891C4⋊C4—42no—
892C4⋊C4—114no—
893C4⋊C4—114no—
894C4⋊C4—114no—
895C4⋊C4—224no—
896C4⋊C4—224no—
897C4⋊C4—224no—
898C4⋊C4—224no—
899C4⋊C4—442no—
900C4⋊C4—442no—
901C4⋊C4—442no—
902C4⋊C4C2×C4×D1114yes—
903C22⋊C4—24no—
904C22⋊C4—24no—
905C22⋊C4—42no—
906C22⋊C4—114no—
907C22⋊C4—114no—
908C22⋊C4—114no—
909C22⋊C4—114no—
910C22⋊C4—114no—
911C22⋊C4—114no—
912C22⋊C4—118no—
913C22⋊C4—224no—
914C22⋊C4—224no—
915C22⋊C4—224no—
916C22⋊C4—224no—
917C22⋊C4—224no—
918C22⋊C4—224no—
919C22⋊C4—224no—
920C22⋊C4—224no—
921C22⋊C4—224no—
922C22⋊C4—442no—
923C22⋊C4—442no—
924C22⋊C4—442no—
925C22⋊C4C2×C4×D1114yes—
926C22⋊C4C2×C4×D1114yes—
927C42—24no—
928C42—42no—
929C42—114no—
930C42—114no—
931C42—114no—
932C42—224no—
933C42—224no—
934C42—224no—
935C42—224no—
936C42—224no—
937C42—224no—
938C42—224no—
939C42—442no—
940C42—442no—
941C42—442no—
942C42C2×C4×D1114yes—
943C11#3412611yescharacteristic, complemented, Sylow
944C23—22no—
945C23—22no—
946C23—22no—
947C23—21no—
948C23—21no—
949C23—22no—
950C23—112no—
951C23—112no—
952C23—114no—
953C23—112no—
954C23—112no—
955C23—112no—
956C23—228no—
957C23—228no—
958C23—228no—
959C23—222no—
960C23—221no—
961C23—221no—
962C23—222no—
963C23—222no—
964C23—228no—
965C23—222no—
966C23—221no—
967C23—221no—
968C23—222no—
969C23—444no—
970C23—444no—
971C23—448no—
972C23—448no—
973C23—448no—
974C23—448no—
975C23C22×C4×D1112yes—
976C23C22×C4×D1112yes—
977C23#41×D1112yes—
978C23#41×D1112yes—
979C23C24×D1111yescharacteristic
980D4—28no—
981D4—1116no—
982D4—228no—
983D4—228no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—44no—
1002C2×C4—44no—
1003C2×C4—48no—
1004C2×C4—112no—
1005C2×C4—112no—
1006C2×C4—112no—
1007C2×C4—112no—
1008C2×C4—114no—
1009C2×C4—112no—
1010C2×C4—112no—
1011C2×C4—112no—
1012C2×C4—114no—
1013C2×C4—228no—
1014C2×C4—228no—
1015C2×C4—228no—
1016C2×C4—228no—
1017C2×C4—228no—
1018C2×C4—228no—
1019C2×C4—228no—
1020C2×C4—222no—
1021C2×C4—222no—
1022C2×C4—222no—
1023C2×C4—222no—
1024C2×C4—222no—
1025C2×C4—222no—
1026C2×C4—222no—
1027C2×C4—222no—
1028C2×C4—222no—
1029C2×C4—222no—
1030C2×C4—222no—
1031C2×C4—222no—
1032C2×C4—222no—
1033C2×C4—222no—
1034C2×C4—444no—
1035C2×C4—444no—
1036C2×C4—444no—
1037C2×C4—444no—
1038C2×C4—448no—
1039C2×C4—448no—
1040C2×C4—448no—
1041C2×C4C22×C4×D1112yes—
1042C2×C4C22×C4×D1112yes—
1043C2×C4C22×C4×D1112yes—
1044C2×C4C22×C4×D1112yes—
1045C2×C4C22×C4×D1112yes—
1046C2×C4#41×D1114yes—
1047C22—24no—
1048C22—24no—
1049C22—22no—
1050C22—22no—
1051C22—22no—
1052C22—22no—
1053C22—22no—
1054C22—42no—
1055C22—42no—
1056C22—114no—
1057C22—114no—
1058C22—224no—
1059C22—224no—
1060C22—224no—
1061C22—224no—
1062C22—222no—
1063C22—222no—
1064C22—222no—
1065C22—222no—
1066C22—222no—
1067C22—222no—
1068C22—222no—
1069C22—4416no—
1070C22—4416no—
1071C22—442no—
1072C22—442no—
1073C22D11×#11714yes—
1074C22C23×C4×D1111yescharacteristic
1075C22C2×#41×D1111yescharacteristic
1076C22C2×#41×D1112yes—
1077C22C2×#41×D1111yescharacteristic
1078C22D11×H(5,𝔽2)12yes—
1079C4—24no—
1080C4—22no—
1081C4—22no—
1082C4—22no—
1083C4—22no—
1084C4—22no—
1085C4—42no—
1086C4—42no—
1087C4—42no—
1088C4—114no—
1089C4—114no—
1090C4—224no—
1091C4—222no—
1092C4—222no—
1093C4—222no—
1094C4—442no—
1095C4—442no—
1096C4—442no—
1097C2—24no—
1098C2—42no—
1099C2—224no—
1100C2—224no—
1101C2—442no—
1102C2C2×D11×#11711yescharacteristic
1103C2C4×#41×D1111yescharacteristic
1104C2D11×#51811yescharacteristic
1105C2#1308221912yes—
1106C2#1308222312yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2353C2
socle, cosocleC23×C11C25
prime radicalC22×D4×D11C22
hypercenter#2353D11
hypocenterC11#34126
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2353

Complements

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

NH ≅ G/Ntype
2. #13071590C2semidirect
3. #13071584C2semidirect
4. #13071557C2semidirect
5. #13071556C2semidirect
6. #13071549C2semidirect
7. #13071523C2semidirect
8. #13071520C2semidirect
9. #13071490C2semidirect
10. #13071460C2semidirect
11. #13071459C2semidirect
13. #13071076C2semidirect
14. #13071056C2semidirect
15. #13071054C2semidirect
16. #13071013C2semidirect
17. #13070998C2semidirect
18. #13070996C2semidirect
19. C4×(C22⋊D11)⋊C4C2semidirect
20. #13070955C2semidirect
21. C2×#10622279C2semidirect
22. C4×C22⋊C4×D11C2semidirect
23. C11×#2353C2semidirect
33. C22×C4×Dic11C22semidirect
34. C4×D4×D11C4semidirect
36. C2×#66945C22semidirect
44. C2×#66930C22semidirect
48. C2×C42×D11C22semidirect
49. C11×#388C22semidirect
50. C11×#387C22semidirect
52. C11×#383C22semidirect
53. C11×#381C22semidirect
54. C11×#380C22semidirect
55. C4×C11×C22⋊C4C22semidirect
56. C4×C11×C22⋊C4C22semidirect
57. C11×#376C22semidirect
58. C2×C11×#95C22semidirect
60. #10622825C22semidirect
61. #10622824C22semidirect
62. #10622823C22semidirect
63. C4×C22⋊Dic11C22semidirect
64. C2×C11⋊#95C22semidirect
65. #10622602C22semidirect
67. #10622594C22semidirect
68. #10622585C22semidirect
73. #10622564C22semidirect
74. #10622559C22semidirect
75. #10622558C22semidirect
76. #10622557C22semidirect
77. C22⋊C4×Dic11C22semidirect
78. C22⋊C4×Dic11C22semidirect
79. C22⋊C4×Dic11C22semidirect
80. #10622553C22semidirect
81. #10622553C22semidirect
83. C4×(C2×D11)⋊C4C22semidirect
84. #10622550C22semidirect
85. #10622545C22semidirect
86. C4×Dic11⋊C4C22semidirect
87. C42×Dic11C22semidirect
88. #10622282C22semidirect
89. #10622282C22semidirect
90. #10622281C22semidirect
93. #10622280C22semidirect
94. #10622280C22semidirect
101. #10622279C22semidirect
102. #10622279C22semidirect
103. #10622279C22semidirect
104. #10622279C22semidirect
105. #10622279C22semidirect
109. #10622277C22semidirect
110. #10622277C22semidirect
111. D11×#95C22semidirect
112. D11×#95C22semidirect
113. #10622267C22semidirect
114. #10622266C22semidirect
115. #10622263C22semidirect
116. #10622263C22semidirect
117. #10622262C22semidirect
118. #10622262C22semidirect
119. #10622262C22semidirect
120. #10622262C22semidirect
121. #10622262C22semidirect
122. #10622261C22semidirect
123. #10622260C22semidirect
141. C22×C4×D11C2×C4semidirect
142. C22×C4×D11C2×C4semidirect
154. C4×D4×C11C2×C4semidirect
170. D4×Dic11C2×C4semidirect
173. C4×C22⋊D11C2×C4semidirect
213. #66946C2×C4semidirect
215. C4⋊C4×D11C2×C4semidirect
218. (C22⋊D11)⋊C4C2×C4semidirect
220. C22⋊C4×D11C2×C4semidirect
221. C22⋊C4×D11C2×C4semidirect
223. C4×D44C2×C4semidirect
226. C42×D11C2×C4semidirect
397. #2353D11semidirect
478. C22⋊D11#117semidirect
553. #388C2×D11semidirect
557. #387C2×D11semidirect
567. #383C2×D11semidirect
574. #381C2×D11semidirect
581. #380C2×D11semidirect
607. C4×C22⋊C4C2×D11semidirect
608. C4×C22⋊C4C2×D11semidirect
611. #376C2×D11semidirect
615. C2×#95C2×D11semidirect
706. C4×D4C4×D11semidirect
943. C11#34126semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×D112
#130715902
#130715842
#130715572
#130715562
#130715492
#130715232
#130715202
#130714902
#130714602
#130714592
#130714342
#130710762
#130710562
#130710542
#130710132
#130709982
#130709962
C4×(C22⋊D11)⋊C42
#130709552
C2×#106222792
C4×C22⋊C4×D112
C11×#23532
#3412611