Finite Group Databasebeta

← #14914334

Subgroups — #14914334

Order 2816.

2698 conjugacy classes of subgroups.

The subgroup lattice has 1140 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623137C211yesmaximal, characteristic
2#13071750C212yesmaximal, complemented
3#13071744C212yesmaximal, complemented
4#13071658C211yesmaximal, characteristic, complemented
5#13071643C211yesmaximal, characteristic, complemented
6#13071641C211yesmaximal, characteristic, complemented
7#13071588C212yesmaximal, complemented
8#13071554C212yesmaximal, complemented
9#13071505C211yesmaximal, characteristic, complemented
10#13071500C211yesmaximal, characteristic, complemented
11#13071455C211yesmaximal, characteristic, complemented
12#13071441C211yesmaximal, characteristic, complemented
13#13071275C212yesmaximal, complemented
14#13071272C212yesmaximal, complemented
15#13071246C212yesmaximal, complemented
16C4×#66950C211yesmaximal, characteristic, complemented
17#13071146C211yesmaximal, characteristic, complemented
18#13071132C211yesmaximal, characteristic, complemented
19C4×#66991C211yesmaximal, characteristic, complemented
20#13070995C211yesmaximal, characteristic, complemented
21#13070975C212yesmaximal, complemented
22C4×C22⋊C4×D11C211yesmaximal, characteristic, complemented
23C11×#2363C211yesmaximal, characteristic, complemented
24C22×#4341C2211yescharacteristic
25C23×C4×D11C2211yescharacteristic
26C2×C11×#121C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic, complemented
28C2×C11×#117C2211yescharacteristic
29C2×#66991C2211yescharacteristic
30C2×#66990C2212yes—
31C2×D4×Dic11C2212yes—
32C2×D4×Dic11C2211yescharacteristic, complemented
33C2×C4×C22⋊D11C2212yes—
34C2×#66979C2211yescharacteristic
35C2×#66977C2211yescharacteristic
36#10623137C4116yescomplemented
37C2×#66950C2211yescharacteristic
38C2×#66945C2211yescharacteristic
39C2×#66940C2211yescharacteristic, complemented
40C2×#66936C2212yes—
41C2×(C22⋊D11)⋊C4C2212yes—
42C2×(C22⋊D11)⋊C4C2212yes—
43C2×C22⋊C4×D11C2211yescharacteristic
44C2×C22⋊C4×D11C2211yescharacteristic
45C2×C42×D11C2211yescharacteristic
46C2×C42×D11C2211yescharacteristic
47C2×C4×Dic22C2211yescharacteristic, complemented
48C11×#390C2212yes—
49C11×#390C2211yescharacteristic, complemented
50C11×#389C2211yescharacteristic, complemented
51C11×#388C2212yescomplemented
52C11×#386C2212yes—
53C4×C11×C4⋊C4C2211yescharacteristic, complemented
54C4×C11×C22⋊C4C2211yescharacteristic
55C4×C11×C22⋊C4C2212yescomplemented
56#10622834C2212yes—
57#10622834C2211yescharacteristic, complemented
58#10622833C2212yes—
59#10622826C2212yes—
60C4×C22⋊Dic11C2211yescharacteristic
61C4×C22⋊Dic11C2212yescomplemented
62C2×C11⋊#95C2212yescomplemented
63#10622603C2212yes—
64#10622602C2212yes—
65#10622600C2211yescharacteristic
66#10622600C2211yescharacteristic
67#10622600C2211yescharacteristic
68#10622600C2211yescharacteristic
69#10622598C2211yescharacteristic, complemented
70#10622590C2212yescomplemented
71C4⋊C4×Dic11C2211yescharacteristic, complemented
72C4⋊C4×Dic11C2211yescharacteristic, complemented
73C4⋊C4×Dic11C2212yescomplemented
74#10622587C2211yescharacteristic, complemented
75#10622586C2211yescharacteristic, complemented
76#10622571C2212yes—
77#10622570C2212yes—
78#10622570C2212yes—
79#10622569C2212yes—
80#10622569C2212yes—
81#10622568C2212yes—
82#10622564C2212yescomplemented
83#10622558C2212yes—
84#10622558C2212yes—
85#10622558C2212yescomplemented
86#10622557C2212yes—
87#10622557C2212yes—
88#10622557C2212yescomplemented
89#10622556C2212yes—
90#10622556C2212yescomplemented
91#10622555C2212yescomplemented
92C22⋊C4×Dic11C2211yescharacteristic
93C22⋊C4×Dic11C2211yescharacteristic
94C22⋊C4×Dic11C2212yescomplemented
95C22⋊C4×Dic11C2212yescomplemented
96C22⋊C4×Dic11C2212yescomplemented
97#10622553C2212yes—
98C4×(C2×D11)⋊C4C2212yes—
99C4×(C2×D11)⋊C4C2211yescharacteristic
100C4×(C2×D11)⋊C4C2211yescharacteristic
101C4×(C2×D11)⋊C4C2212yes—
102C4×(C2×D11)⋊C4C2212yes—
103C4×C4⋊Dic11C2211yescharacteristic, complemented
104C4×C4⋊Dic11C2212yescomplemented
105#10622546C2212yescomplemented
106C4×Dic11⋊C4C2212yescomplemented
107C4×Dic11⋊C4C2212yescomplemented
108#10622542C2211yescharacteristic, complemented
109#10622541C2211yescharacteristic, complemented
110#10622283C2212yes—
111#10622282C2212yes—
112#10622281C2212yes—
113#10622279C2212yes—
114#10622279C2211yescharacteristic
115#10622279C2211yescharacteristic
116D11×#95C2211yescharacteristic
117D11×#95C2211yescharacteristic
118#10622267C2212yescomplemented
119#10622266C2212yescomplemented
120#10622265C2212yescomplemented
121#10622264C2212yescomplemented
122#10622262C2212yescomplemented
123#10622261C2212yescomplemented
124C24×D11C2311yescharacteristic
125C22×D4×C11C2311yescharacteristic
126C22×D4×C11C2312yes—
127C23×C4×C11C2311yescharacteristic
128C23×C4×C11C2312yes—
129C22×C22⋊D11C2312yes—
130C22×C22⋊D11C2312yes—
131C23×Dic11C2312yes—
132C23×Dic11C2312yes—
133C23×Dic11C2311yescharacteristic
134C2×#4341—42no—
135C2×#4341—42no—
136C2×#4341C2×C418yescomplemented
137C22×C4×D11—42no—
138C22×C4×D11—42no—
139C22×C4×D11C2×C418yescomplemented
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×Dic22C2311yescharacteristic
149C11×#121C2×C418yescomplemented
150C4×D4×C11—42no—
151C11×#117—42no—
152C2×C11×C4⋊C4C2311yescharacteristic
153C2×C11×C4⋊C4C2311yescharacteristic
154C2×C11×C4⋊C4C2312yes—
155C2×C11×C4⋊C4C2311yescharacteristic
156C2×C11×C22⋊C4C2311yescharacteristic
157C2×C11×C22⋊C4C2311yescharacteristic
158C2×C11×C22⋊C4C2312yes—
159C2×C11×C22⋊C4C2312yes—
160C2×C11×C22⋊C4C2312yes—
161C2×C11×C22⋊C4C2312yes—
162C2×C11×C22⋊C4C2312yes—
163C2×C42×C11C2311yescharacteristic
164C2×C42×C11C2311yescharacteristic
165C2×C42×C11C2312yes—
166C2×C42×C11C2312yes—
167C2×C22⋊Dic11C2311yescharacteristic
168C2×C22⋊Dic11C2311yescharacteristic
169C2×C22⋊Dic11C2312yes—
170C2×C22⋊Dic11C2312yes—
171C2×C22⋊Dic11C2312yes—
172C2×C22⋊Dic11C2312yes—
173C2×C22⋊Dic11C2312yes—
174C2×C22⋊Dic11C2312yes—
175#66991C2×C418yes—
176#66990C2×C4116yescomplemented
177D4×Dic11—42no—
178D4×Dic11C2×C4116yescomplemented
179C4×C22⋊D11—28no—
180C2×(C2×D11)⋊C4C2311yescharacteristic
181C2×(C2×D11)⋊C4C2311yescharacteristic
182C2×(C2×D11)⋊C4C2311yescharacteristic
183C2×(C2×D11)⋊C4C2311yescharacteristic
184C2×(C2×D11)⋊C4C2312yes—
185C2×(C2×D11)⋊C4C2312yes—
186C2×(C2×D11)⋊C4C2312yes—
187C2×(C2×D11)⋊C4C2312yes—
188C2×(C2×D11)⋊C4C2312yes—
189C2×(C2×D11)⋊C4C2312yes—
190#66979—42no—
191C2×C4⋊Dic11C2311yescharacteristic
192C2×C4⋊Dic11C2311yescharacteristic
193C2×C4⋊Dic11C2312yes—
194C2×C4⋊Dic11C2312yes—
195C2×C4⋊Dic11C2311yescharacteristic
196#66977C2×C418yescomplemented
197C2×Dic11⋊C4C2312yes—
198C2×Dic11⋊C4C2312yes—
199C2×Dic11⋊C4C2312yes—
200C2×Dic11⋊C4C2312yes—
201C2×Dic11⋊C4C2312yes—
202C2×C4×Dic11C2311yescharacteristic
203C2×C4×Dic11C2311yescharacteristic
204C2×C4×Dic11C2312yes—
205C2×C4×Dic11C2312yes—
206C2×C4×Dic11C2312yes—
207C2×C4×Dic11C2311yescharacteristic
208C2×C4×Dic11C2311yescharacteristic
209C2×C4×Dic11C2311yescharacteristic
210C2×C4×Dic11C2311yescharacteristic
211C2×C4×Dic11C2312yes—
212C2×C4×Dic11C2312yes—
213C2×C4×Dic11C2312yes—
214C2×C4×Dic11C2312yes—
215#66950C2×C418yescomplemented
216#66945C2×C418yescomplemented
217#66940—42no—
218#66936C2×C4116yescomplemented
219(C22⋊D11)⋊C4—28no—
220(C22⋊D11)⋊C4C2×C4116yescomplemented
221C22⋊C4×D11—24no—
222C22⋊C4×D11—24no—
223C42×D11—42no—
224C42×D11—42no—
225C4×Dic22—42no—
226C11×#95C2312yes—
227C11×#95C2311yescharacteristic
228C11×#95C2312yes—
229C11×#95C2311yescharacteristic
230C11⋊#95C2311yescharacteristic
231C11⋊#95C2312yes—
232C11⋊#95C2312yes—
233C11⋊#95C2312yes—
234C11⋊#95C2311yescharacteristic
235C11⋊#95C2312yes—
236C11⋊#95C2312yes—
237C11⋊#95C2312yes—
238C11⋊#95C2312yes—
239C11⋊#95C2312yes—
240C11⋊#95C2312yes—
241C11⋊#95C2312yes—
242C11⋊#95C2312yes—
243C11⋊#95C2312yes—
244C11⋊#95C2311yescharacteristic
245C11⋊#95C2311yescharacteristic
246C11⋊#95C2311yescharacteristic
247C11⋊#95C2311yescharacteristic
248C11⋊#95C2312yes—
249C11⋊#95C2312yes—
250#34223—111nomaximal, Sylow
251C24×C11C2411yescharacteristic
252C24×C11C2412yes—
253C23×D11—22no—
254C23×D11—22no—
255C23×D11—41no—
256C23×D11—41no—
257C23×D11—41no—
258C23×D11—41no—
259C23×D11C22×C414yes—
260C23×D11C2411yescharacteristic
261C23×D11C2411yescharacteristic
262C2×D4×C11—22no—
263C2×D4×C11—22no—
264C2×D4×C11—42no—
265C2×D4×C11—42no—
266C2×D4×C11C22×C414yes—
267C2×D4×C11C22×C418yes—
268C22×C4×C11—22no—
269C22×C4×C11—22no—
270C22×C4×C11—24no—
271C22×C4×C11—42no—
272C22×C4×C11—42no—
273C22×C4×C11C22×C414yes—
274C22×C4×C11C2411yescharacteristic
275C22×C4×C11C2412yes—
276C22×C4×C11C2411yescharacteristic
277C22×C4×C11C2412yes—
278C22×C4×C11C2411yescharacteristic
279C22×C4×C11C2412yes—
280C22×C4×C11C2411yescharacteristic
281C22×C4×C11C2411yescharacteristic
282C22×C4×C11C2411yescharacteristic
283C2×C22⋊D11—24no—
284C2×C22⋊D11—24no—
285C2×C22⋊D11—42no—
286C2×C22⋊D11—42no—
287C2×C22⋊D11C22×C418yes—
288C2×C22⋊D11C22×C418yes—
289C22×Dic11—24no—
290C22×Dic11—41no—
291C22×Dic11—41no—
292C22×Dic11—42no—
293C22×Dic11—42no—
294C22×Dic11—42no—
295C22×Dic11—42no—
296C22×Dic11C22×C418yes—
297C22×Dic11C22×C414yes—
298C22×Dic11C2411yescharacteristic
299C22×Dic11C2412yes—
300C22×Dic11C2411yescharacteristic
301C22×Dic11C2412yes—
302C22×Dic11C2411yescharacteristic
303C22×Dic11C2411yescharacteristic
304C22×Dic11C2412yes—
305C22×Dic11C2412yes—
306C22×Dic11C2411yescharacteristic
307C22×Dic11C2411yescharacteristic
308#4341—416no—
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—41no—
316C2×C4×D11—41no—
317C2×C4×D11—41no—
318C2×C4×D11—41no—
319C2×C4×D11—41no—
320C2×C4×D11—41no—
321C2×C4×D11—41no—
322C2×C4×D11—41no—
323C2×C4×D11—41no—
324C2×C4×D11—41no—
325C2×C4×D11—41no—
326C2×C4×D11—41no—
327C2×C4×D11—416no—
328C2×C4×D11C22×C414yes—
329C2×C4×D11C22×C414yes—
330C2×C4×D11C22×C414yes—
331C2×C4×D11C22×C414yes—
332C2×C4×D11#4114yescomplemented
333C2×C4×D11#4114yescomplemented
334C2×Dic22—22no—
335C2×Dic22—22no—
336C2×Dic22C22×C414yes—
337C11×C4⋊C4—22no—
338C11×C4⋊C4—22no—
339C11×C4⋊C4—42no—
340C11×C4⋊C4C22×C414yes—
341C11×C22⋊C4—22no—
342C11×C22⋊C4—22no—
343C11×C22⋊C4—24no—
344C11×C22⋊C4—42no—
345C11×C22⋊C4—42no—
346C11×C22⋊C4—42no—
347C11×C22⋊C4C22×C418yes—
348C42×C11—22no—
349C42×C11—22no—
350C42×C11—42no—
351C42×C11—42no—
352C22⋊Dic11—22no—
353C22⋊Dic11—22no—
354C22⋊Dic11—24no—
355C22⋊Dic11—42no—
356C22⋊Dic11—42no—
357C22⋊Dic11—42no—
358C22⋊Dic11C22×C418yes—
359C22⋊Dic11C22×C418yes—
360(C2×D11)⋊C4—22no—
361(C2×D11)⋊C4—22no—
362(C2×D11)⋊C4—24no—
363(C2×D11)⋊C4—24no—
364(C2×D11)⋊C4—22no—
365(C2×D11)⋊C4—22no—
366(C2×D11)⋊C4—42no—
367(C2×D11)⋊C4—42no—
368(C2×D11)⋊C4C22×C418yes—
369(C2×D11)⋊C4C22×C418yes—
370C4⋊Dic11—22no—
371C4⋊Dic11—22no—
372C4⋊Dic11—42no—
373C4⋊Dic11C22×C418yes—
374C4⋊Dic11C22×C414yes—
375Dic11⋊C4—24no—
376Dic11⋊C4—24no—
377Dic11⋊C4—42no—
378Dic11⋊C4—42no—
379Dic11⋊C4C22×C418yes—
380C4×Dic11—24no—
381C4×Dic11—24no—
382C4×Dic11—22no—
383C4×Dic11—22no—
384C4×Dic11—42no—
385C4×Dic11—41no—
386C4×Dic11—41no—
387C4×Dic11—41no—
388C4×Dic11—41no—
389C4×Dic11—42no—
390C4×Dic11—42no—
391C4×Dic11—42no—
392C4×Dic11C22×C418yes—
393C2×#525—111no—
394#2374—112no—
395#2374—112no—
396#2363—111no—
397#2363D1111yescharacteristic, complemented
398#2362—111no—
399#2362—111no—
400#2357—112no—
401#2353—112no—
402#2347—111no—
403#2346—111no—
404#2341—111no—
405#2339—111no—
406#2321—112no—
407#2321—112no—
408#2318—112no—
409C4×C22⋊Q8—111no—
410C4×C22⋊Q8—111no—
411C4×#121—111no—
412C4×#121—111no—
413#2280—111no—
414#2275—112no—
415C2×C4×C22⋊C4—111no—
416C23×C11—21no—
417C23×C11—21no—
418C23×C11—22no—
419C23×C11—22no—
420C23×C11—21no—
421C23×C11—22no—
422C23×C11—21no—
423C23×C11—22no—
424C23×C11—22no—
425C23×C11—22no—
426C23×C11—21no—
427C23×C11—21no—
428C23×C11C23×C412yes—
429C23×C11C23×C414yes—
430C23×C11C2511yescharacteristic
431C22×D11—21no—
432C22×D11—21no—
433C22×D11—21no—
434C22×D11—21no—
435C22×D11—21no—
436C22×D11—21no—
437C22×D11—21no—
438C22×D11—21no—
439C22×D11—21no—
440C22×D11—21no—
441C22×D11—28no—
442C22×D11—44no—
443C22×D11—44no—
444C22×D11—44no—
445C22×D11—44no—
446C22×D11—44no—
447C22×D11—44no—
448C22×D11C23×C412yes—
449C22×D11C23×C412yes—
450C22×D11C2×#4112yes—
451C22×D11C2×#4112yes—
452D4×C11—28no—
453D4×C11—48no—
454C2×C4×C11—21no—
455C2×C4×C11—21no—
456C2×C4×C11—21no—
457C2×C4×C11—21no—
458C2×C4×C11—22no—
459C2×C4×C11—22no—
460C2×C4×C11—21no—
461C2×C4×C11—21no—
462C2×C4×C11—28no—
463C2×C4×C11—22no—
464C2×C4×C11—22no—
465C2×C4×C11—21no—
466C2×C4×C11—21no—
467C2×C4×C11—21no—
468C2×C4×C11—22no—
469C2×C4×C11—21no—
470C2×C4×C11—22no—
471C2×C4×C11—22no—
472C2×C4×C11—22no—
473C2×C4×C11—21no—
474C2×C4×C11—21no—
475C2×C4×C11—84no—
476C2×C4×C11C23×C414yes—
477C2×C4×C11C23×C412yes—
478C2×C4×C11C23×C412yes—
479C2×C4×C11C2×#4112yes—
480C2×C4×C11C2×#4112yes—
481C2×C4×C11H(5,𝔽2)12yes—
482C2×C4×C11H(5,𝔽2)12yes—
483C22⋊D11—216no—
484C22⋊D11—48no—
485C2×Dic11—22no—
486C2×Dic11—22no—
487C2×Dic11—21no—
488C2×Dic11—21no—
489C2×Dic11—21no—
490C2×Dic11—21no—
491C2×Dic11—22no—
492C2×Dic11—22no—
493C2×Dic11—21no—
494C2×Dic11—21no—
495C2×Dic11—21no—
496C2×Dic11—21no—
497C2×Dic11—22no—
498C2×Dic11—22no—
499C2×Dic11—21no—
500C2×Dic11—21no—
501C2×Dic11—21no—
502C2×Dic11—21no—
503C2×Dic11—22no—
504C2×Dic11—22no—
505C2×Dic11—22no—
506C2×Dic11—21no—
507C2×Dic11—22no—
508C2×Dic11—21no—
509C2×Dic11—44no—
510C2×Dic11—48no—
511C2×Dic11—84no—
512C2×Dic11C23×C412yes—
513C2×Dic11C23×C414yes—
514C2×Dic11C23×C414yes—
515C2×Dic11C23×C412yes—
516C2×Dic11C2×#4112yes—
517C2×Dic11C2×#4112yes—
518C4×D11—28no—
519C4×D11—28no—
520C4×D11—44no—
521C4×D11—44no—
522C4×D11—44no—
523C4×D11—44no—
524C4×D11—44no—
525C4×D11—44no—
526Dic22—28no—
527C22×#41—111no—
528C24×C4—111no—
529#525—1116no—
530C2×#123—112no—
531C2×C22⋊Q8—111no—
532C2×C22⋊Q8—111no—
533C2×#121—111no—
534C2×#121C2×D1111yescharacteristic
535C2×#120—112no—
536C2×C4×Q8—111no—
537C2×C4×Q8—111no—
538C2×C4×D4—112no—
539C2×C4×D4—112no—
540C2×C4×D4—111no—
541C2×C4×D4—112no—
542C2×C4×D4—112no—
543C2×C4×D4C2×D1111yescharacteristic, complemented
544C2×#117—111no—
545C2×#117—111no—
546C2×#117C2×D1111yescharacteristic
547C22×C22⋊C4—111no—
548C22×C22⋊C4—111no—
549C22×C42—111no—
550C22×C42—111no—
551#391—111no—
552#391—111no—
553#390—112no—
554#390—111no—
555#390—112no—
556#390—112no—
557#390C2×D1112yes—
558#390C2×D1111yescharacteristic, complemented
559#389—111no—
560#389—111no—
561#389—111no—
562#389C2×D1111yescharacteristic, complemented
563#388—112no—
564#388—112no—
565#388—112no—
566#388—112no—
567#388—112no—
568#388—112no—
569#388—112no—
570#388—112no—
571#388—112no—
572#388—112no—
573#388—112no—
574#388C2×D1112yescomplemented
575#387—112no—
576#387—112no—
577#387—112no—
578#387—112no—
579#386—112no—
580#386—112no—
581#386—112no—
582#386—112no—
583#386—112no—
584#386C2×D1112yes—
585#385—112no—
586#385—112no—
587#383—112no—
588#382—112no—
589#381—112no—
590#381—112no—
591#380—111no—
592#380—111no—
593#380—111no—
594#380—111no—
595#380—112no—
596#379—112no—
597C4×C4⋊C4—111no—
598C4×C4⋊C4—111no—
599C4×C4⋊C4—112no—
600C4×C4⋊C4—111no—
601C4×C4⋊C4—112no—
602C4×C4⋊C4—112no—
603C4×C4⋊C4—112no—
604C4×C4⋊C4—112no—
605C4×C4⋊C4C2×D1111yescharacteristic, complemented
606C4×C22⋊C4—112no—
607C4×C22⋊C4—111no—
608C4×C22⋊C4—112no—
609C4×C22⋊C4—111no—
610C4×C22⋊C4—112no—
611C4×C22⋊C4—111no—
612C4×C22⋊C4—112no—
613C4×C22⋊C4—112no—
614C4×C22⋊C4—112no—
615C4×C22⋊C4—111no—
616C4×C22⋊C4—111no—
617C4×C22⋊C4—112no—
618C4×C22⋊C4—112no—
619C4×C22⋊C4—111no—
620C4×C22⋊C4—111no—
621C4×C22⋊C4C2×D1111yescharacteristic
622C4×C22⋊C4C2×D1112yescomplemented
623#376—112no—
624C2×#95—112no—
625C2×#95—111no—
626C2×#95—111no—
627C22×C11—22no—
628C22×C11—24no—
629C22×C11—22no—
630C22×C11—24no—
631C22×C11—22no—
632C22×C11—24no—
633C22×C11—42no—
634C22×C11—41no—
635C22×C11—41no—
636C22×C11—42no—
637C22×C11—41no—
638C22×C11—41no—
639C22×C11—42no—
640C22×C11—42no—
641C22×C11C24×C411yescharacteristic
642C22×C11C22×#4111yescharacteristic
643C22×C11C22×#4111yescharacteristic
644C22×C11C2×H(5,𝔽2)11yescharacteristic
645C22×C11C2×H(5,𝔽2)11yescharacteristic
646C22×C11#58511yescharacteristic
647C22×C11#58511yescharacteristic
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—22no—
657C2×D11—416no—
658C2×D11—41no—
659C2×D11—41no—
660C2×D11—41no—
661C2×D11—41no—
662C2×D11C4×#4114yes—
663C4×C11—22no—
664C4×C11—24no—
665C4×C11—22no—
666C4×C11—22no—
667C4×C11—42no—
668C4×C11—42no—
669C4×C11—41no—
670C4×C11—41no—
671C4×C11#51814yes—
672Dic11—24no—
673Dic11—24no—
674Dic11—22no—
675Dic11—22no—
676Dic11—22no—
677Dic11—22no—
678Dic11—42no—
679Dic11—41no—
680Dic11—41no—
681Dic11—42no—
682C25—111no—
683C2×#41—118no—
684C2×#41—442no—
685C2×#41—442no—
686C22×Q8—111no—
687C22×D4—112no—
688C22×D4—112no—
689C22×D4C22×D1111yescharacteristic
690C22×D4C22×D1112yes—
691C23×C4—111no—
692C23×C4—112no—
693C23×C4—111no—
694C23×C4—111no—
695C23×C4—118no—
696C23×C4—111no—
697C23×C4—111no—
698C23×C4—111no—
699C23×C4—111no—
700C23×C4—112no—
701C23×C4—111no—
702C23×C4—111no—
703C23×C4—442no—
704C23×C4—442no—
705C23×C4C22×D1111yescharacteristic
706C23×C4C22×D1112yes—
707#123—1116no—
708C22⋊Q8—118no—
709C22⋊Q8—118no—
710#121—118no—
711#121C4×D1118yescomplemented
712#120—1116no—
713C4×Q8—442no—
714C4×Q8—442no—
715C4×D4—42no—
716C4×D4—1116no—
717C4×D4—1116no—
718C4×D4—228no—
719C4×D4—228no—
720C4×D4—442no—
721#117—42no—
722#117—118no—
723#117—442no—
724C2×C4⋊C4—111no—
725C2×C4⋊C4—112no—
726C2×C4⋊C4—112no—
727C2×C4⋊C4—111no—
728C2×C4⋊C4—111no—
729C2×C4⋊C4—112no—
730C2×C4⋊C4—112no—
731C2×C4⋊C4—112no—
732C2×C4⋊C4—112no—
733C2×C4⋊C4—112no—
734C2×C4⋊C4C22×D1111yescharacteristic
735C2×C4⋊C4C22×D1111yescharacteristic
736C2×C4⋊C4C22×D1112yes—
737C2×C4⋊C4C22×D1111yescharacteristic
738C2×C22⋊C4—112no—
739C2×C22⋊C4—112no—
740C2×C22⋊C4—112no—
741C2×C22⋊C4—112no—
742C2×C22⋊C4—111no—
743C2×C22⋊C4—111no—
744C2×C22⋊C4—112no—
745C2×C22⋊C4—111no—
746C2×C22⋊C4—111no—
747C2×C22⋊C4—111no—
748C2×C22⋊C4—111no—
749C2×C22⋊C4—112no—
750C2×C22⋊C4—112no—
751C2×C22⋊C4—112no—
752C2×C22⋊C4—112no—
753C2×C22⋊C4—112no—
754C2×C22⋊C4—112no—
755C2×C22⋊C4—112no—
756C2×C22⋊C4—224no—
757C2×C22⋊C4—224no—
758C2×C22⋊C4C22×D1111yescharacteristic
759C2×C22⋊C4C22×D1111yescharacteristic
760C2×C22⋊C4C22×D1112yes—
761C2×C22⋊C4C22×D1112yes—
762C2×C22⋊C4C22×D1112yes—
763C2×C22⋊C4C22×D1112yes—
764C2×C22⋊C4C22×D1112yes—
765C2×C42—112no—
766C2×C42—112no—
767C2×C42—112no—
768C2×C42—111no—
769C2×C42—111no—
770C2×C42—112no—
771C2×C42—112no—
772C2×C42—112no—
773C2×C42—111no—
774C2×C42—111no—
775C2×C42—112no—
776C2×C42—111no—
777C2×C42—111no—
778C2×C42—442no—
779C2×C42—442no—
780C2×C42C22×D1111yescharacteristic
781C2×C42C22×D1111yescharacteristic
782C2×C42C22×D1112yes—
783C2×C42C22×D1112yes—
784#95—111no—
785#95—111no—
786#95—111no—
787#95—111no—
788#95—111no—
789#95—111no—
790#95—112no—
791#95—112no—
792#95—112no—
793#95—112no—
794#95—112no—
795#95—112no—
796#95—112no—
797#95—112no—
798#95—112no—
799#95—112no—
800#95—112no—
801#95—112no—
802#95—112no—
803#95—112no—
804#95C22×D1111yescharacteristic
805#95C22×D1111yescharacteristic
806#95C22×D1112yes—
807#95C22×D1112yes—
808C2×C11—42no—
809C2×C11—44no—
810C2×C11C2×C4×#4111yescharacteristic
811C2×C11C2×#51811yescharacteristic
812C2×C11#342811yescharacteristic
813C2×C11#350511yescharacteristic
814C2×C11#350511yescharacteristic
815C2×C11#350611yescharacteristic
816C2×C11#350611yescharacteristic
817D11—24no—
818D11—42no—
819C24—111no—
820C24—111no—
821C24—114no—
822C24—222no—
823C24—222no—
824C24—441no—
825C24—441no—
826C24—441no—
827C24—441no—
828C24C23×D1111yescharacteristic
829C24C23×D1112yes—
830#41—4416no—
831C2×Q8—114no—
832C2×Q8—222no—
833C2×Q8—222no—
834C2×D4—22no—
835C2×D4—22no—
836C2×D4—42no—
837C2×D4—42no—
838C2×D4—118no—
839C2×D4—118no—
840C2×D4—224no—
841C2×D4—224no—
842C2×D4—442no—
843C2×D4—442no—
844C2×D4C2×C4×D1114yes—
845C2×D4C2×C4×D1118yes—
846C22×C4—22no—
847C22×C4—22no—
848C22×C4—24no—
849C22×C4—42no—
850C22×C4—42no—
851C22×C4—111no—
852C22×C4—111no—
853C22×C4—111no—
854C22×C4—112no—
855C22×C4—112no—
856C22×C4—111no—
857C22×C4—114no—
858C22×C4—118no—
859C22×C4—114no—
860C22×C4—114no—
861C22×C4—114no—
862C22×C4—114no—
863C22×C4—114no—
864C22×C4—114no—
865C22×C4—111no—
866C22×C4—111no—
867C22×C4—112no—
868C22×C4—112no—
869C22×C4—222no—
870C22×C4—222no—
871C22×C4—224no—
872C22×C4—222no—
873C22×C4—222no—
874C22×C4—222no—
875C22×C4—222no—
876C22×C4—4416no—
877C22×C4—441no—
878C22×C4—441no—
879C22×C4—441no—
880C22×C4—441no—
881C22×C4—441no—
882C22×C4—441no—
883C22×C4—441no—
884C22×C4—441no—
885C22×C4—441no—
886C22×C4—441no—
887C22×C4—441no—
888C22×C4—441no—
889C22×C4—441no—
890C22×C4—441no—
891C22×C4—442no—
892C22×C4—442no—
893C22×C4—442no—
894C22×C4—442no—
895C22×C4C2×C4×D1114yes—
896C22×C4C23×D1111yescharacteristic
897C22×C4C23×D1112yes—
898C22×C4C23×D1111yescharacteristic
899C22×C4C23×D1112yes—
900C22×C4C23×D1111yescharacteristic
901C22×C4C23×D1112yes—
902C22×C4C23×D1111yescharacteristic
903C22×C4C23×D1111yescharacteristic
904C22×C4C23×D1111yescharacteristic
905C4⋊C4—22no—
906C4⋊C4—22no—
907C4⋊C4—42no—
908C4⋊C4—114no—
909C4⋊C4—118no—
910C4⋊C4—118no—
911C4⋊C4—224no—
912C4⋊C4—224no—
913C4⋊C4—222no—
914C4⋊C4—222no—
915C4⋊C4—442no—
916C4⋊C4—442no—
917C4⋊C4—442no—
918C4⋊C4C2×C4×D1114yes—
919C22⋊C4—22no—
920C22⋊C4—22no—
921C22⋊C4—24no—
922C22⋊C4—42no—
923C22⋊C4—42no—
924C22⋊C4—42no—
925C22⋊C4—118no—
926C22⋊C4—118no—
927C22⋊C4—118no—
928C22⋊C4—118no—
929C22⋊C4—222no—
930C22⋊C4—222no—
931C22⋊C4—224no—
932C22⋊C4—224no—
933C22⋊C4—222no—
934C22⋊C4—222no—
935C22⋊C4—224no—
936C22⋊C4—222no—
937C22⋊C4—222no—
938C22⋊C4—442no—
939C22⋊C4—442no—
940C22⋊C4—442no—
941C22⋊C4—442no—
942C22⋊C4—442no—
943C22⋊C4C2×C4×D1118yes—
944C42—22no—
945C42—22no—
946C42—42no—
947C42—42no—
948C42—118no—
949C42—224no—
950C42—222no—
951C42—224no—
952C42—222no—
953C42—441no—
954C42—441no—
955C42—441no—
956C42—441no—
957C42—442no—
958C42—442no—
959C42—442no—
960C42—442no—
961C11#3422311yescharacteristic, complemented, Sylow
962C23—21no—
963C23—22no—
964C23—21no—
965C23—21no—
966C23—22no—
967C23—22no—
968C23—21no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—21no—
973C23—21no—
974C23—112no—
975C23—112no—
976C23—112no—
977C23—112no—
978C23—228no—
979C23—221no—
980C23—221no—
981C23—221no—
982C23—221no—
983C23—221no—
984C23—221no—
985C23—221no—
986C23—221no—
987C23—221no—
988C23—221no—
989C23—444no—
990C23—444no—
991C23—444no—
992C23—444no—
993C23—444no—
994C23—444no—
995C23C22×C4×D1112yes—
996C23C22×C4×D1114yes—
997C23C24×D1111yescharacteristic
998Q8—228no—
999D4—28no—
1000D4—48no—
1001D4—2216no—
1002D4—448no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—21no—
1011C2×C4—28no—
1012C2×C4—21no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—22no—
1019C2×C4—21no—
1020C2×C4—22no—
1021C2×C4—21no—
1022C2×C4—22no—
1023C2×C4—21no—
1024C2×C4—84no—
1025C2×C4—112no—
1026C2×C4—114no—
1027C2×C4—112no—
1028C2×C4—114no—
1029C2×C4—112no—
1030C2×C4—112no—
1031C2×C4—221no—
1032C2×C4—221no—
1033C2×C4—222no—
1034C2×C4—221no—
1035C2×C4—222no—
1036C2×C4—222no—
1037C2×C4—221no—
1038C2×C4—221no—
1039C2×C4—222no—
1040C2×C4—221no—
1041C2×C4—221no—
1042C2×C4—221no—
1043C2×C4—228no—
1044C2×C4—228no—
1045C2×C4—221no—
1046C2×C4—222no—
1047C2×C4—221no—
1048C2×C4—221no—
1049C2×C4—222no—
1050C2×C4—221no—
1051C2×C4—222no—
1052C2×C4—222no—
1053C2×C4—222no—
1054C2×C4—222no—
1055C2×C4—221no—
1056C2×C4—221no—
1057C2×C4—444no—
1058C2×C4—444no—
1059C2×C4—444no—
1060C2×C4—444no—
1061C2×C4—444no—
1062C2×C4—444no—
1063C2×C4—444no—
1064C2×C4—448no—
1065C2×C4—884no—
1066C2×C4C22×C4×D1114yes—
1067C2×C4C22×C4×D1112yes—
1068C2×C4C22×C4×D1112yes—
1069C2×C4#6703712yes—
1070C2×C4#41×D1112yes—
1071C2×C4#41×D1112yes—
1072C2×C4#6704212yes—
1073C22—24no—
1074C22—22no—
1075C22—22no—
1076C22—24no—
1077C22—22no—
1078C22—24no—
1079C22—42no—
1080C22—41no—
1081C22—42no—
1082C22—41no—
1083C22—41no—
1084C22—42no—
1085C22—41no—
1086C22—42no—
1087C22—114no—
1088C22—222no—
1089C22—222no—
1090C22—222no—
1091C22—222no—
1092C22—222no—
1093C22—222no—
1094C22—222no—
1095C22—222no—
1096C22—222no—
1097C22—4416no—
1098C22—441no—
1099C22—441no—
1100C22—441no—
1101C22—441no—
1102C22C23×C4×D1111yescharacteristic
1103C22C2×#6703711yescharacteristic
1104C22C2×#41×D1111yescharacteristic
1105C22C2×#41×D1111yescharacteristic
1106C22C2×#6704211yescharacteristic
1107C22#1062345511yescharacteristic
1108C22#1062345511yescharacteristic
1109C4—22no—
1110C4—22no—
1111C4—22no—
1112C4—24no—
1113C4—42no—
1114C4—41no—
1115C4—41no—
1116C4—42no—
1117C4—222no—
1118C4—222no—
1119C4—224no—
1120C4—222no—
1121C4—222no—
1122C4—224no—
1123C4—442no—
1124C4—441no—
1125C4—442no—
1126C4—441no—
1127C4#1062307614yes—
1128C2—42no—
1129C2—44no—
1130C2—224no—
1131C2—442no—
1132C2C4×#41×D1111yescharacteristic
1133C2C2×#1062307611yescharacteristic
1134C2#1308181411yescharacteristic
1135C2#1308244311yescharacteristic
1136C2#1308244511yescharacteristic
1137C2#1308245811yescharacteristic
1138C2#1308246011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2363C2
socle, cosocleC23×C11C25
prime radicalC2×#10623137C2
hypercenter#2363D11
hypocenterC11#34223
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2363

Complements

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

NH ≅ G/Ntype
2. #13071750C2semidirect
3. #13071744C2semidirect
4. #13071658C2semidirect
5. #13071643C2semidirect
6. #13071641C2semidirect
7. #13071588C2semidirect
8. #13071554C2semidirect
9. #13071505C2semidirect
10. #13071500C2semidirect
11. #13071455C2semidirect
12. #13071441C2semidirect
13. #13071275C2semidirect
14. #13071272C2semidirect
15. #13071246C2semidirect
16. C4×#66950C2semidirect
17. #13071146C2semidirect
18. #13071132C2semidirect
19. C4×#66991C2semidirect
20. #13070995C2semidirect
21. #13070975C2semidirect
22. C4×C22⋊C4×D11C2semidirect
23. C11×#2363C2semidirect
27. C2×C4×D4×C11C22semidirect
32. C2×D4×Dic11C22semidirect
36. #10623137C4semidirect
39. C2×#66940C22semidirect
47. C2×C4×Dic22C22semidirect
49. C11×#390C22semidirect
50. C11×#389C22semidirect
51. C11×#388C22semidirect
53. C4×C11×C4⋊C4C22semidirect
55. C4×C11×C22⋊C4C22semidirect
57. #10622834C22semidirect
61. C4×C22⋊Dic11C22semidirect
62. C2×C11⋊#95C22semidirect
69. #10622598C22semidirect
70. #10622590C22semidirect
71. C4⋊C4×Dic11C22semidirect
72. C4⋊C4×Dic11C22semidirect
73. C4⋊C4×Dic11C22semidirect
74. #10622587C22semidirect
75. #10622586C22semidirect
82. #10622564C22semidirect
85. #10622558C22semidirect
88. #10622557C22semidirect
90. #10622556C22semidirect
91. #10622555C22semidirect
94. C22⋊C4×Dic11C22semidirect
95. C22⋊C4×Dic11C22semidirect
96. C22⋊C4×Dic11C22semidirect
103. C4×C4⋊Dic11C22semidirect
104. C4×C4⋊Dic11C22semidirect
105. #10622546C22semidirect
106. C4×Dic11⋊C4C22semidirect
107. C4×Dic11⋊C4C22semidirect
108. #10622542C22semidirect
109. #10622541C22semidirect
118. #10622267C22semidirect
119. #10622266C22semidirect
120. #10622265C22semidirect
121. #10622264C22semidirect
122. #10622262C22semidirect
123. #10622261C22semidirect
136. C2×#4341C2×C4semidirect
139. C22×C4×D11C2×C4semidirect
149. C11×#121C2×C4semidirect
176. #66990C2×C4semidirect
178. D4×Dic11C2×C4semidirect
196. #66977C2×C4semidirect
215. #66950C2×C4semidirect
216. #66945C2×C4semidirect
218. #66936C2×C4semidirect
220. (C22⋊D11)⋊C4C2×C4semidirect
332. C2×C4×D11#41semidirect
333. C2×C4×D11#41semidirect
397. #2363D11semidirect
543. C2×C4×D4C2×D11semidirect
558. #390C2×D11semidirect
562. #389C2×D11semidirect
574. #388C2×D11semidirect
605. C4×C4⋊C4C2×D11semidirect
622. C4×C22⋊C4C2×D11semidirect
711. #121C4×D11semidirect
961. C11#34223semidirect

Maximal subgroups

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

subgroupindex
C2×#106231372
#130717502
#130717442
#130716582
#130716432
#130716412
#130715882
#130715542
#130715052
#130715002
#130714552
#130714412
#130712752
#130712722
#130712462
C4×#669502
#130711462
#130711322
C4×#669912
#130709952
#130709752
C4×C22⋊C4×D112
C11×#23632
#3422311