Finite Group Databasebeta

← #14916573

Subgroups — #14916573

Order 2816.

2954 conjugacy classes of subgroups.

The subgroup lattice has 1204 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#121C211yesmaximal, characteristic
2#13071774C212yesmaximal, complemented
3#13071767C212yesmaximal, complemented
4#13071658C211yesmaximal, characteristic, complemented
5#13071654C211yesmaximal, characteristic, complemented
6#13071652C211yesmaximal, characteristic, complemented
7#13071484C211yesmaximal, characteristic, complemented
8#13071481C211yesmaximal, characteristic, complemented
9#13071464C212yesmaximal, complemented
10#13071459C212yesmaximal, complemented
11#13071437C211yesmaximal, characteristic, complemented
12D4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
13#13071379C212yesmaximal, complemented
14#13071376C212yesmaximal, complemented
15#13071312C211yesmaximal, characteristic, complemented
16#13071310C211yesmaximal, characteristic, complemented
17#13071307C211yesmaximal, characteristic, complemented
18#13071303C211yesmaximal, characteristic, complemented
19#13071195C212yesmaximal, complemented
20#13071190C212yesmaximal, complemented
21#13070997C211yesmaximal, characteristic, complemented
22#13070995C211yesmaximal, characteristic, complemented
23C11×#2363C211yesmaximal, characteristic, complemented
24C22×D4×D11C2211yescharacteristic
25C22×D4×D11C2212yes—
26C23×C4×D11C2211yescharacteristic
27C2×C11×#121C2211yescharacteristic
28C2×C4×D4×C11C2211yescharacteristic, complemented
29C2×C11×#117C2211yescharacteristic, complemented
30C2×#66992C2212yes—
31C2×#66991C2211yescharacteristic
32C2×D4×Dic11C2211yescharacteristic, complemented
33C2×#66983C2211yescharacteristic
34C22×(C2×D11)⋊C4C2212yes—
35C2×#66979C2211yescharacteristic, complemented
36D11×#121C4116yescomplemented
37C2×#66948C2211yescharacteristic
38C2×#66946C2211yescharacteristic, complemented
39C2×#66945C2212yes—
40C2×C4⋊C4×D11C2211yescharacteristic
41C2×#66937C2212yes—
42C2×C22⋊C4×D11C2212yes—
43C2×C22⋊C4×D11C2212yes—
44C2×C4×D44C2211yescharacteristic, complemented
45C2×#66925C2212yes—
46C2×#66925C2211yescharacteristic, complemented
47C2×#66925C2211yescharacteristic, complemented
48C11×#390C2211yescharacteristic, complemented
49C11×#390C2212yescomplemented
50C11×#389C2211yescharacteristic, complemented
51C11×#388C2212yescomplemented
52C11×#386C2212yescomplemented
53C4×C11×C4⋊C4C2211yescharacteristic, complemented
54C4×C11×C22⋊C4C2212yescomplemented
55C4×C11×C22⋊C4C2211yescharacteristic, complemented
56#10622834C2211yescharacteristic, complemented
57#10622834C2212yescomplemented
58#10622833C2212yescomplemented
59#10622826C2212yescomplemented
60#10622826C2212yescomplemented
61#10622823C2212yescomplemented
62C4×C22⋊Dic11C2211yescharacteristic, complemented
63#10622602C2212yescomplemented
64#10622601C2212yescomplemented
65#10622601C2211yescharacteristic, complemented
66#10622600C2211yescharacteristic
67#10622600C2211yescharacteristic
68#10622600C2211yescharacteristic, complemented
69#10622600C2211yescharacteristic, complemented
70#10622598C2211yescharacteristic, complemented
71#10622591C2212yescomplemented
72C4⋊C4×Dic11C2211yescharacteristic, complemented
73C4⋊C4×Dic11C2211yescharacteristic, complemented
74#10622586C2211yescharacteristic, complemented
75#10622571C2212yescomplemented
76#10622571C2212yescomplemented
77#10622570C2212yescomplemented
78#10622570C2212yescomplemented
79#10622570C2212yescomplemented
80#10622570C2212yescomplemented
81#10622569C2212yescomplemented
82#10622569C2212yescomplemented
83#10622569C2212yescomplemented
84#10622569C2212yescomplemented
85#10622568C2212yes—
86#10622568C2212yes—
87#10622568C2211yescharacteristic
88#10622568C2212yes—
89#10622568C2211yescharacteristic
90#10622564C2212yescomplemented
91#10622559C2212yescomplemented
92#10622558C2212yescomplemented
93#10622557C2212yescomplemented
94#10622556C2212yescomplemented
95#10622555C2211yescharacteristic, complemented
96#10622555C2211yescharacteristic, complemented
97C22⋊C4×Dic11C2212yescomplemented
98#10622553C2212yescomplemented
99#10622553C2212yescomplemented
100#10622552C2212yescomplemented
101#10622552C2211yescharacteristic, complemented
102C4×(C2×D11)⋊C4C2211yescharacteristic
103C4×(C2×D11)⋊C4C2211yescharacteristic
104C4×(C2×D11)⋊C4C2212yes—
105C4×(C2×D11)⋊C4C2212yescomplemented
106C4×(C2×D11)⋊C4C2212yescomplemented
107C4×C4⋊Dic11C2211yescharacteristic, complemented
108#10622546C2212yescomplemented
109#10622541C2211yescharacteristic, complemented
110#10622282C2212yescomplemented
111#10622282C2212yescomplemented
112#10622281C2212yescomplemented
113#10622280C2211yescharacteristic
114#10622280C2211yescharacteristic
115#10622279C2212yescomplemented
116#10622278C2212yescomplemented
117#10622278C2212yescomplemented
118#10622277C2212yes—
119#10622277C2212yes—
120#10622277C2211yescharacteristic, complemented
121#10622277C2211yescharacteristic, complemented
122#10622268C2212yescomplemented
123#10622265C2212yescomplemented
124C24×D11C2312yes—
125C24×D11C2311yescharacteristic
126C22×D4×C11C2311yescharacteristic
127C22×D4×C11C2312yes—
128C23×C4×C11C2311yescharacteristic
129C23×C4×C11C2312yes—
130C22×C22⋊D11C2312yes—
131C22×C22⋊D11C2312yes—
132C22×C22⋊D11C2312yes—
133C23×Dic11C2312yes—
134C23×Dic11C2311yescharacteristic
135C2×D4×D11—42no—
136C2×D4×D11—42no—
137C2×D4×D11—44no—
138C2×D4×D11—44no—
139C2×D4×D11C2×C418yes—
140C2×D4×D11C2×C4116yescomplemented
141C22×D44C2311yescharacteristic
142C22×D44C2312yes—
143C22×C4×D11—42no—
144C22×C4×D11—42no—
145C22×C4×D11C2×C418yescomplemented
146C22×C4×D11C2312yes—
147C22×C4×D11C2311yescharacteristic
148C22×C4×D11C2311yescharacteristic
149C22×C4×D11C2312yes—
150C22×C4×D11C2312yes—
151C22×C4×D11C2311yescharacteristic
152C22×C4×D11C2311yescharacteristic
153C11×#121C2×C418yescomplemented
154C4×D4×C11—42no—
155C11×#117—42no—
156C2×C11×C4⋊C4C2311yescharacteristic
157C2×C11×C4⋊C4C2311yescharacteristic
158C2×C11×C4⋊C4C2312yes—
159C2×C11×C4⋊C4C2311yescharacteristic
160C2×C11×C22⋊C4C2312yes—
161C2×C11×C22⋊C4C2311yescharacteristic
162C2×C11×C22⋊C4C2311yescharacteristic
163C2×C11×C22⋊C4C2312yes—
164C2×C11×C22⋊C4C2312yes—
165C2×C11×C22⋊C4C2312yes—
166C2×C11×C22⋊C4C2312yes—
167C2×C42×C11C2311yescharacteristic
168C2×C42×C11C2311yescharacteristic
169C2×C42×C11C2312yes—
170C2×C42×C11C2312yes—
171C2×C22⋊Dic11C2312yes—
172C2×C22⋊Dic11C2312yes—
173C2×C22⋊Dic11C2312yes—
174C2×C22⋊Dic11C2311yescharacteristic
175C2×C22⋊Dic11C2311yescharacteristic
176C2×C22⋊Dic11C2312yes—
177C2×C22⋊Dic11C2312yes—
178#66992C2×C4116yescomplemented
179#66991C2×C418yescomplemented
180D4×Dic11—42no—
181#66983C2×C418yescomplemented
182C2×(C2×D11)⋊C4—44no—
183C2×(C2×D11)⋊C4C2311yescharacteristic
184C2×(C2×D11)⋊C4C2312yes—
185C2×(C2×D11)⋊C4C2311yescharacteristic
186C2×(C2×D11)⋊C4C2312yes—
187C2×(C2×D11)⋊C4C2311yescharacteristic
188C2×(C2×D11)⋊C4C2311yescharacteristic
189C2×(C2×D11)⋊C4C2311yescharacteristic
190C2×(C2×D11)⋊C4C2311yescharacteristic
191C2×(C2×D11)⋊C4C2311yescharacteristic
192C2×(C2×D11)⋊C4C2311yescharacteristic
193C2×(C2×D11)⋊C4C2312yes—
194C2×(C2×D11)⋊C4C2312yes—
195C2×(C2×D11)⋊C4C2312yes—
196C2×(C2×D11)⋊C4C2312yes—
197C2×(C2×D11)⋊C4C2312yes—
198C2×(C2×D11)⋊C4C2312yes—
199C2×(C2×D11)⋊C4C2312yes—
200C2×(C2×D11)⋊C4C2312yes—
201C2×(C2×D11)⋊C4C2312yes—
202C2×(C2×D11)⋊C4C2312yes—
203#66979—42no—
204C2×C4⋊Dic11C2311yescharacteristic
205C2×C4⋊Dic11C2311yescharacteristic
206C2×C4⋊Dic11C2312yes—
207C2×C4⋊Dic11C2311yescharacteristic
208C2×Dic11⋊C4C2312yes—
209C2×Dic11⋊C4C2312yes—
210C2×Dic11⋊C4C2311yescharacteristic
211C2×Dic11⋊C4C2311yescharacteristic
212C2×Dic11⋊C4C2311yescharacteristic
213C2×Dic11⋊C4C2311yescharacteristic
214C2×Dic11⋊C4C2312yes—
215C2×C4×Dic11C2311yescharacteristic
216C2×C4×Dic11C2311yescharacteristic
217C2×C4×Dic11C2312yes—
218C2×C4×Dic11C2312yes—
219C2×C4×Dic11C2312yes—
220C2×C4×Dic11C2312yes—
221#66948C2×C418yescomplemented
222#66946—42no—
223#66945—44no—
224C4⋊C4×D11C2×C418yescomplemented
225#66937C2×C4116yescomplemented
226C22⋊C4×D11—44no—
227C22⋊C4×D11C2×C4116yescomplemented
228C4×D44—42no—
229#66925—42no—
230#66925—42no—
231#66925—44no—
232C11×#95C2312yes—
233C11×#95C2312yes—
234C11×#95C2311yescharacteristic
235C11×#95C2311yescharacteristic
236C11⋊#95C2311yescharacteristic
237C11⋊#95C2312yes—
238C11⋊#95C2312yes—
239C11⋊#95C2311yescharacteristic
240C11⋊#95C2312yes—
241C11⋊#95C2312yes—
242C11⋊#95C2312yes—
243C11⋊#95C2312yes—
244C11⋊#95C2312yes—
245C11⋊#95C2312yes—
246C11⋊#95C2311yescharacteristic
247C11⋊#95C2311yescharacteristic
248C11⋊#95C2311yescharacteristic
249C11⋊#95C2311yescharacteristic
250C11⋊#95C2312yes—
251C11⋊#95C2312yes—
252#34363—111nomaximal, Sylow
253C24×C11C2411yescharacteristic
254C24×C11C2412yes—
255C23×D11—22no—
256C23×D11—22no—
257C23×D11—24no—
258C23×D11—24no—
259C23×D11—41no—
260C23×D11—41no—
261C23×D11—41no—
262C23×D11—41no—
263C23×D11—42no—
264C23×D11—42no—
265C23×D11—42no—
266C23×D11—42no—
267C23×D11C22×C418yes—
268C23×D11C22×C414yes—
269C23×D11C2411yescharacteristic
270C23×D11C2412yes—
271C23×D11C2411yescharacteristic
272C2×D4×C11—22no—
273C2×D4×C11—22no—
274C2×D4×C11—42no—
275C2×D4×C11—42no—
276C2×D4×C11C22×C414yes—
277C2×D4×C11C22×C418yes—
278C22×C4×C11—22no—
279C22×C4×C11—22no—
280C22×C4×C11—42no—
281C22×C4×C11—42no—
282C22×C4×C11—42no—
283C22×C4×C11C22×C414yes—
284C22×C4×C11C2411yescharacteristic
285C22×C4×C11C2411yescharacteristic
286C22×C4×C11C2412yes—
287C22×C4×C11C2412yes—
288C22×C4×C11C2411yescharacteristic
289C22×C4×C11C2411yescharacteristic
290C22×C4×C11C2411yescharacteristic
291C22×C4×C11C2412yes—
292C22×C4×C11C2411yescharacteristic
293C2×C22⋊D11—42no—
294C2×C22⋊D11—42no—
295C2×C22⋊D11—42no—
296C2×C22⋊D11—42no—
297C2×C22⋊D11—42no—
298C2×C22⋊D11—42no—
299C2×C22⋊D11C22×C418yes—
300C2×C22⋊D11C22×C418yes—
301C2×C22⋊D11C22×C418yes—
302C22×Dic11—41no—
303C22×Dic11—41no—
304C22×Dic11—42no—
305C22×Dic11—42no—
306C22×Dic11—42no—
307C22×Dic11C22×C414yes—
308C22×Dic11C2411yescharacteristic
309C22×Dic11C2411yescharacteristic
310C22×Dic11C2412yes—
311C22×Dic11C2412yes—
312C22×Dic11C2411yescharacteristic
313C22×Dic11C2411yescharacteristic
314C22×Dic11C2411yescharacteristic
315C22×Dic11C2412yes—
316C22×Dic11C2411yescharacteristic
317D4×D11—416no—
318D4×D11—432no—
319C2×D44—22no—
320C2×D44—22no—
321C2×D44—42no—
322C2×D44—42no—
323C2×D44C22×C414yes—
324C2×D44C22×C418yes—
325C2×C4×D11—24no—
326C2×C4×D11—24no—
327C2×C4×D11—22no—
328C2×C4×D11—22no—
329C2×C4×D11—22no—
330C2×C4×D11—22no—
331C2×C4×D11—41no—
332C2×C4×D11—41no—
333C2×C4×D11—41no—
334C2×C4×D11—41no—
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—416no—
342C2×C4×D11C22×C418yes—
343C2×C4×D11C22×C414yes—
344C2×C4×D11C22×C414yes—
345C2×C4×D11C22×C414yes—
346C2×C4×D11C22×C414yes—
347C11×C4⋊C4—22no—
348C11×C4⋊C4—22no—
349C11×C4⋊C4—42no—
350C11×C4⋊C4C22×C414yes—
351C11×C22⋊C4—42no—
352C11×C22⋊C4—41no—
353C11×C22⋊C4—42no—
354C11×C22⋊C4—41no—
355C11×C22⋊C4—42no—
356C11×C22⋊C4—42no—
357C11×C22⋊C4C22×C418yes—
358C42×C11—22no—
359C42×C11—22no—
360C42×C11—42no—
361C42×C11—42no—
362C22⋊Dic11—42no—
363C22⋊Dic11—42no—
364C22⋊Dic11—42no—
365C22⋊Dic11—41no—
366C22⋊Dic11—41no—
367C22⋊Dic11—42no—
368C22⋊Dic11C22×C418yes—
369(C2×D11)⋊C4—22no—
370(C2×D11)⋊C4—24no—
371(C2×D11)⋊C4—22no—
372(C2×D11)⋊C4—24no—
373(C2×D11)⋊C4—22no—
374(C2×D11)⋊C4—22no—
375(C2×D11)⋊C4—41no—
376(C2×D11)⋊C4—41no—
377(C2×D11)⋊C4—41no—
378(C2×D11)⋊C4—41no—
379(C2×D11)⋊C4—42no—
380(C2×D11)⋊C4—42no—
381(C2×D11)⋊C4—42no—
382(C2×D11)⋊C4—42no—
383(C2×D11)⋊C4—42no—
384(C2×D11)⋊C4—42no—
385(C2×D11)⋊C4—42no—
386(C2×D11)⋊C4—42no—
387(C2×D11)⋊C4C22×C418yes—
388(C2×D11)⋊C4C22×C418yes—
389C4⋊Dic11—22no—
390C4⋊Dic11—22no—
391C4⋊Dic11—42no—
392C4⋊Dic11C22×C414yes—
393Dic11⋊C4—42no—
394Dic11⋊C4—42no—
395Dic11⋊C4—41no—
396Dic11⋊C4—41no—
397Dic11⋊C4—41no—
398Dic11⋊C4—41no—
399Dic11⋊C4C22×C418yes—
400C4×Dic11—22no—
401C4×Dic11—22no—
402C4×Dic11—42no—
403C4×Dic11—42no—
404C4×Dic11—42no—
405C4×Dic11—42no—
406C22×#121—111no—
407#2377—112no—
408#2377—112no—
409#2363—111no—
410#2363—111no—
411#2363—111no—
412#2363D1111yescharacteristic, complemented
413#2344—111no—
414#2344—111no—
415#2342—112no—
416#2342—112no—
417D4×C22⋊C4—111no—
418D4×C22⋊C4—111no—
419#2333—112no—
420#2333—112no—
421#2324—111no—
422#2324—111no—
423#2324—111no—
424#2324—111no—
425#2309—112no—
426#2308—112no—
427#2280—111no—
428#2280—111no—
429C23×C11—21no—
430C23×C11—22no—
431C23×C11—22no—
432C23×C11—21no—
433C23×C11—22no—
434C23×C11—22no—
435C23×C11—21no—
436C23×C11—21no—
437C23×C11—21no—
438C23×C11—21no—
439C23×C11—22no—
440C23×C11—22no—
441C23×C11C23×C414yes—
442C23×C11C23×C412yes—
443C23×C11C2511yescharacteristic
444C22×D11—21no—
445C22×D11—21no—
446C22×D11—21no—
447C22×D11—21no—
448C22×D11—21no—
449C22×D11—21no—
450C22×D11—22no—
451C22×D11—22no—
452C22×D11—22no—
453C22×D11—22no—
454C22×D11—21no—
455C22×D11—21no—
456C22×D11—21no—
457C22×D11—21no—
458C22×D11—22no—
459C22×D11—22no—
460C22×D11—28no—
461C22×D11—216no—
462C22×D11—44no—
463C22×D11—44no—
464C22×D11—48no—
465C22×D11—48no—
466C22×D11—44no—
467C22×D11—44no—
468C22×D11—44no—
469C22×D11—44no—
470C22×D11—84no—
471C22×D11—84no—
472C22×D11—84no—
473C22×D11—84no—
474C22×D11C23×C414yes—
475C22×D11C23×C412yes—
476C22×D11C23×C412yes—
477C22×D11H(5,𝔽2)12yes—
478C22×D11H(5,𝔽2)12yes—
479D4×C11—28no—
480D4×C11—48no—
481C2×C4×C11—21no—
482C2×C4×C11—22no—
483C2×C4×C11—22no—
484C2×C4×C11—21no—
485C2×C4×C11—28no—
486C2×C4×C11—21no—
487C2×C4×C11—22no—
488C2×C4×C11—21no—
489C2×C4×C11—22no—
490C2×C4×C11—21no—
491C2×C4×C11—21no—
492C2×C4×C11—21no—
493C2×C4×C11—21no—
494C2×C4×C11—21no—
495C2×C4×C11—21no—
496C2×C4×C11—22no—
497C2×C4×C11—22no—
498C2×C4×C11—21no—
499C2×C4×C11—22no—
500C2×C4×C11—22no—
501C2×C4×C11—21no—
502C2×C4×C11—21no—
503C2×C4×C11—21no—
504C2×C4×C11—84no—
505C2×C4×C11C23×C414yes—
506C2×C4×C11C23×C412yes—
507C2×C4×C11C23×C412yes—
508C2×C4×C11H(5,𝔽2)12yes—
509C2×C4×C11H(5,𝔽2)12yes—
510C22⋊D11—48no—
511C22⋊D11—48no—
512C22⋊D11—48no—
513C2×Dic11—22no—
514C2×Dic11—21no—
515C2×Dic11—21no—
516C2×Dic11—22no—
517C2×Dic11—21no—
518C2×Dic11—21no—
519C2×Dic11—21no—
520C2×Dic11—21no—
521C2×Dic11—21no—
522C2×Dic11—21no—
523C2×Dic11—21no—
524C2×Dic11—21no—
525C2×Dic11—22no—
526C2×Dic11—22no—
527C2×Dic11—22no—
528C2×Dic11—22no—
529C2×Dic11—21no—
530C2×Dic11—21no—
531C2×Dic11—21no—
532C2×Dic11—22no—
533C2×Dic11—22no—
534C2×Dic11—21no—
535C2×Dic11—21no—
536C2×Dic11—21no—
537C2×Dic11—44no—
538C2×Dic11—84no—
539C2×Dic11C23×C412yes—
540C2×Dic11C23×C414yes—
541C2×Dic11C23×C412yes—
542D44—28no—
543D44—48no—
544C4×D11—216no—
545C4×D11—28no—
546C4×D11—28no—
547C4×D11—44no—
548C4×D11—44no—
549C4×D11—84no—
550C4×D11—84no—
551C23×D4—112no—
552C23×D4—111no—
553C24×C4—111no—
554C2×#121—111no—
555C2×#121—112no—
556C2×#121—111no—
557C2×#121—1116no—
558C2×#121—111no—
559C2×#121—112no—
560C2×#121C2×D1111yescharacteristic
561C2×C4×D4—111no—
562C2×C4×D4—111no—
563C2×C4×D4—111no—
564C2×C4×D4C2×D1111yescharacteristic, complemented
565C2×#117—111no—
566C2×#117—112no—
567C2×#117—112no—
568C2×#117—111no—
569C2×#117—111no—
570C2×#117C2×D1111yescharacteristic, complemented
571C22×C4⋊C4—111no—
572C22×C22⋊C4—112no—
573C22×C22⋊C4—112no—
574C22×C22⋊C4—112no—
575#390—112no—
576#390—111no—
577#390—112no—
578#390—111no—
579#390—112no—
580#390—112no—
581#390—112no—
582#390—112no—
583#390—112no—
584#390—111no—
585#390C2×D1112yescomplemented
586#390C2×D1111yescharacteristic, complemented
587#389—111no—
588#389—111no—
589#389—111no—
590#389C2×D1111yescharacteristic, complemented
591#388—112no—
592#388—112no—
593#388—112no—
594#388—112no—
595#388—112no—
596#388—112no—
597#388—112no—
598#388C2×D1112yescomplemented
599#387—112no—
600#387—112no—
601#387—112no—
602#387—112no—
603#386—112no—
604#386—112no—
605#386—112no—
606#386—112no—
607#386—112no—
608#386—112no—
609#386—112no—
610#386—112no—
611#386—112no—
612#386—112no—
613#386—112no—
614#386C2×D1112yescomplemented
615#385—112no—
616#385—112no—
617#385—112no—
618#385—112no—
619#381—112no—
620#381—112no—
621#381—112no—
622#381—111no—
623#381—111no—
624#380—111no—
625#380—111no—
626#380—111no—
627#380—111no—
628#380—111no—
629#380—111no—
630#380—111no—
631#380—111no—
632#379—111no—
633#379—112no—
634#379—111no—
635#379—112no—
636#379—112no—
637C4×C4⋊C4—111no—
638C4×C4⋊C4—111no—
639C4×C4⋊C4—111no—
640C4×C4⋊C4C2×D1111yescharacteristic, complemented
641C4×C22⋊C4—111no—
642C4×C22⋊C4—112no—
643C4×C22⋊C4—112no—
644C4×C22⋊C4—112no—
645C4×C22⋊C4—111no—
646C4×C22⋊C4—111no—
647C4×C22⋊C4—112no—
648C4×C22⋊C4—112no—
649C4×C22⋊C4C2×D1112yescomplemented
650C4×C22⋊C4C2×D1111yescharacteristic, complemented
651C22×C11—22no—
652C22×C11—24no—
653C22×C11—22no—
654C22×C11—24no—
655C22×C11—22no—
656C22×C11—24no—
657C22×C11—42no—
658C22×C11—41no—
659C22×C11—41no—
660C22×C11—41no—
661C22×C11—41no—
662C22×C11—42no—
663C22×C11—42no—
664C22×C11—42no—
665C22×C11C24×C411yescharacteristic
666C22×C11C2×H(5,𝔽2)11yescharacteristic
667C22×C11C2×H(5,𝔽2)11yescharacteristic
668C22×C11C2×H(5,𝔽2)11yescharacteristic
669C22×C11C2×H(5,𝔽2)11yescharacteristic
670C22×C11#58511yescharacteristic
671C22×C11#58511yescharacteristic
672C2×D11—22no—
673C2×D11—22no—
674C2×D11—22no—
675C2×D11—22no—
676C2×D11—22no—
677C2×D11—22no—
678C2×D11—22no—
679C2×D11—24no—
680C2×D11—22no—
681C2×D11—24no—
682C2×D11—22no—
683C2×D11—24no—
684C2×D11—416no—
685C2×D11—41no—
686C2×D11—41no—
687C2×D11—41no—
688C2×D11—41no—
689C2×D11—42no—
690C2×D11—42no—
691C2×D11—42no—
692C2×D11—42no—
693C2×D11—816no—
694C2×D11#51814yes—
695C4×C11—22no—
696C4×C11—24no—
697C4×C11—41no—
698C4×C11—41no—
699C4×C11—42no—
700C4×C11—41no—
701C4×C11—42no—
702C4×C11—41no—
703C4×C11#51814yes—
704Dic11—22no—
705Dic11—22no—
706Dic11—24no—
707Dic11—41no—
708Dic11—42no—
709Dic11—41no—
710Dic11—41no—
711Dic11—42no—
712Dic11—41no—
713C25—112no—
714C25—111no—
715C22×D4—112no—
716C22×D4—112no—
717C22×D4—112no—
718C22×D4—118no—
719C22×D4—1116no—
720C22×D4—111no—
721C22×D4—112no—
722C22×D4—442no—
723C22×D4—442no—
724C22×D4—444no—
725C22×D4—444no—
726C22×D4C22×D1111yescharacteristic
727C22×D4C22×D1112yes—
728C23×C4—111no—
729C23×C4—112no—
730C23×C4—111no—
731C23×C4—111no—
732C23×C4—118no—
733C23×C4—111no—
734C23×C4—111no—
735C23×C4—112no—
736C23×C4—112no—
737C23×C4—112no—
738C23×C4—442no—
739C23×C4—442no—
740C23×C4C22×D1111yescharacteristic
741C23×C4C22×D1112yes—
742#121—118no—
743#121—1116no—
744#121—118no—
745#121—118no—
746#121—1116no—
747#121C4×D1118yescomplemented
748C4×D4—42no—
749C4×D4—442no—
750C4×D4—442no—
751C4×D4—442no—
752#117—42no—
753#117—442no—
754#117—442no—
755#117—444no—
756#117—444no—
757#117—442no—
758C2×C4⋊C4—111no—
759C2×C4⋊C4—112no—
760C2×C4⋊C4—118no—
761C2×C4⋊C4—111no—
762C2×C4⋊C4—111no—
763C2×C4⋊C4—111no—
764C2×C4⋊C4—111no—
765C2×C4⋊C4—111no—
766C2×C4⋊C4—111no—
767C2×C4⋊C4—112no—
768C2×C4⋊C4—112no—
769C2×C4⋊C4—112no—
770C2×C4⋊C4C22×D1111yescharacteristic
771C2×C4⋊C4C22×D1111yescharacteristic
772C2×C4⋊C4C22×D1112yes—
773C2×C4⋊C4C22×D1111yescharacteristic
774C2×C22⋊C4—112no—
775C2×C22⋊C4—112no—
776C2×C22⋊C4—112no—
777C2×C22⋊C4—1116no—
778C2×C22⋊C4—111no—
779C2×C22⋊C4—111no—
780C2×C22⋊C4—112no—
781C2×C22⋊C4—112no—
782C2×C22⋊C4—111no—
783C2×C22⋊C4—111no—
784C2×C22⋊C4—112no—
785C2×C22⋊C4—112no—
786C2×C22⋊C4—112no—
787C2×C22⋊C4—111no—
788C2×C22⋊C4—111no—
789C2×C22⋊C4—112no—
790C2×C22⋊C4—112no—
791C2×C22⋊C4—112no—
792C2×C22⋊C4—111no—
793C2×C22⋊C4—111no—
794C2×C22⋊C4—111no—
795C2×C22⋊C4—111no—
796C2×C22⋊C4—112no—
797C2×C22⋊C4—112no—
798C2×C22⋊C4—112no—
799C2×C22⋊C4—112no—
800C2×C22⋊C4—112no—
801C2×C22⋊C4—112no—
802C2×C22⋊C4—444no—
803C2×C22⋊C4—444no—
804C2×C22⋊C4C22×D1112yes—
805C2×C22⋊C4C22×D1112yes—
806C2×C22⋊C4C22×D1112yes—
807C2×C22⋊C4C22×D1111yescharacteristic
808C2×C22⋊C4C22×D1111yescharacteristic
809C2×C22⋊C4C22×D1112yes—
810C2×C22⋊C4C22×D1112yes—
811C2×C42—111no—
812C2×C42—111no—
813C2×C42—112no—
814C2×C42—112no—
815C2×C42—112no—
816C2×C42—112no—
817C2×C42C22×D1111yescharacteristic
818C2×C42C22×D1111yescharacteristic
819C2×C42C22×D1112yes—
820C2×C42C22×D1112yes—
821#95—111no—
822#95—111no—
823#95—112no—
824#95—112no—
825#95—111no—
826#95—111no—
827#95—112no—
828#95—112no—
829#95—111no—
830#95—111no—
831#95—112no—
832#95—112no—
833#95—112no—
834#95—112no—
835#95—112no—
836#95—112no—
837#95C22×D1111yescharacteristic
838#95C22×D1111yescharacteristic
839#95C22×D1112yes—
840#95C22×D1112yes—
841C2×C11—42no—
842C2×C11—44no—
843C2×C11C2×#51811yescharacteristic
844C2×C11C2×#51811yescharacteristic
845C2×C11#342811yescharacteristic
846C2×C11#354211yescharacteristic
847C2×C11#354211yescharacteristic
848C2×C11#354211yescharacteristic
849C2×C11#354211yescharacteristic
850D11—24no—
851D11—42no—
852D11—44no—
853C24—111no—
854C24—112no—
855C24—111no—
856C24—118no—
857C24—114no—
858C24—222no—
859C24—222no—
860C24—224no—
861C24—224no—
862C24—441no—
863C24—441no—
864C24—441no—
865C24—441no—
866C24—442no—
867C24—442no—
868C24—442no—
869C24—442no—
870C24C23×D1111yescharacteristic
871C24C23×D1112yes—
872C2×D4—22no—
873C2×D4—22no—
874C2×D4—42no—
875C2×D4—42no—
876C2×D4—118no—
877C2×D4—118no—
878C2×D4—118no—
879C2×D4—114no—
880C2×D4—118no—
881C2×D4—222no—
882C2×D4—222no—
883C2×D4—442no—
884C2×D4—442no—
885C2×D4—4416no—
886C2×D4—4432no—
887C2×D4—442no—
888C2×D4—442no—
889C2×D4—442no—
890C2×D4—442no—
891C2×D4—442no—
892C2×D4—442no—
893C2×D4C2×C4×D1114yes—
894C2×D4C2×C4×D1118yes—
895C22×C4—22no—
896C22×C4—22no—
897C22×C4—42no—
898C22×C4—42no—
899C22×C4—42no—
900C22×C4—111no—
901C22×C4—112no—
902C22×C4—111no—
903C22×C4—114no—
904C22×C4—118no—
905C22×C4—114no—
906C22×C4—114no—
907C22×C4—114no—
908C22×C4—114no—
909C22×C4—111no—
910C22×C4—111no—
911C22×C4—112no—
912C22×C4—112no—
913C22×C4—111no—
914C22×C4—111no—
915C22×C4—224no—
916C22×C4—224no—
917C22×C4—222no—
918C22×C4—222no—
919C22×C4—222no—
920C22×C4—222no—
921C22×C4—4416no—
922C22×C4—441no—
923C22×C4—441no—
924C22×C4—441no—
925C22×C4—441no—
926C22×C4—442no—
927C22×C4—442no—
928C22×C4—442no—
929C22×C4—442no—
930C22×C4—442no—
931C22×C4—442no—
932C22×C4—441no—
933C22×C4—441no—
934C22×C4—442no—
935C22×C4—442no—
936C22×C4—442no—
937C22×C4C2×C4×D1114yes—
938C22×C4C23×D1111yescharacteristic
939C22×C4C23×D1111yescharacteristic
940C22×C4C23×D1112yes—
941C22×C4C23×D1112yes—
942C22×C4C23×D1111yescharacteristic
943C22×C4C23×D1111yescharacteristic
944C22×C4C23×D1111yescharacteristic
945C22×C4C23×D1112yes—
946C22×C4C23×D1111yescharacteristic
947C4⋊C4—22no—
948C4⋊C4—22no—
949C4⋊C4—42no—
950C4⋊C4—118no—
951C4⋊C4—114no—
952C4⋊C4—222no—
953C4⋊C4—222no—
954C4⋊C4—441no—
955C4⋊C4—441no—
956C4⋊C4—441no—
957C4⋊C4—441no—
958C4⋊C4—442no—
959C4⋊C4—442no—
960C4⋊C4—442no—
961C4⋊C4C2×C4×D1114yes—
962C22⋊C4—42no—
963C22⋊C4—42no—
964C22⋊C4—42no—
965C22⋊C4—41no—
966C22⋊C4—42no—
967C22⋊C4—41no—
968C22⋊C4—118no—
969C22⋊C4—118no—
970C22⋊C4—118no—
971C22⋊C4—222no—
972C22⋊C4—222no—
973C22⋊C4—224no—
974C22⋊C4—224no—
975C22⋊C4—222no—
976C22⋊C4—222no—
977C22⋊C4—442no—
978C22⋊C4—442no—
979C22⋊C4—441no—
980C22⋊C4—441no—
981C22⋊C4—441no—
982C22⋊C4—441no—
983C22⋊C4—442no—
984C22⋊C4—442no—
985C22⋊C4—442no—
986C22⋊C4—442no—
987C22⋊C4—442no—
988C22⋊C4—442no—
989C22⋊C4—442no—
990C22⋊C4—442no—
991C22⋊C4—442no—
992C22⋊C4—441no—
993C22⋊C4—442no—
994C22⋊C4—441no—
995C22⋊C4C2×C4×D1118yes—
996C42—22no—
997C42—22no—
998C42—42no—
999C42—42no—
1000C42—222no—
1001C42—222no—
1002C42—442no—
1003C42—442no—
1004C42—442no—
1005C42—442no—
1006C11#3436311yescharacteristic, complemented, Sylow
1007C23—21no—
1008C23—22no—
1009C23—21no—
1010C23—22no—
1011C23—21no—
1012C23—21no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—21no—
1018C23—21no—
1019C23—112no—
1020C23—112no—
1021C23—112no—
1022C23—114no—
1023C23—112no—
1024C23—228no—
1025C23—2216no—
1026C23—221no—
1027C23—221no—
1028C23—221no—
1029C23—221no—
1030C23—221no—
1031C23—222no—
1032C23—221no—
1033C23—222no—
1034C23—221no—
1035C23—221no—
1036C23—222no—
1037C23—222no—
1038C23—222no—
1039C23—222no—
1040C23—221no—
1041C23—221no—
1042C23—444no—
1043C23—444no—
1044C23—448no—
1045C23—448no—
1046C23—444no—
1047C23—444no—
1048C23—444no—
1049C23—444no—
1050C23—884no—
1051C23—884no—
1052C23—884no—
1053C23—884no—
1054C23C22×C4×D1114yes—
1055C23C22×C4×D1112yes—
1056C23C24×D1111yescharacteristic
1057D4—28no—
1058D4—48no—
1059D4—228no—
1060D4—448no—
1061D4—448no—
1062D4—448no—
1063D4—448no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—28no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—22no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—22no—
1081C2×C4—21no—
1082C2×C4—22no—
1083C2×C4—21no—
1084C2×C4—22no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—84no—
1088C2×C4—112no—
1089C2×C4—114no—
1090C2×C4—112no—
1091C2×C4—2216no—
1092C2×C4—221no—
1093C2×C4—221no—
1094C2×C4—221no—
1095C2×C4—221no—
1096C2×C4—222no—
1097C2×C4—222no—
1098C2×C4—228no—
1099C2×C4—228no—
1100C2×C4—221no—
1101C2×C4—221no—
1102C2×C4—221no—
1103C2×C4—221no—
1104C2×C4—222no—
1105C2×C4—222no—
1106C2×C4—221no—
1107C2×C4—221no—
1108C2×C4—222no—
1109C2×C4—222no—
1110C2×C4—221no—
1111C2×C4—221no—
1112C2×C4—221no—
1113C2×C4—221no—
1114C2×C4—222no—
1115C2×C4—222no—
1116C2×C4—221no—
1117C2×C4—221no—
1118C2×C4—444no—
1119C2×C4—444no—
1120C2×C4—444no—
1121C2×C4—884no—
1122C2×C4—884no—
1123C2×C4—884no—
1124C2×C4C22×C4×D1112yes—
1125C2×C4C22×C4×D1114yes—
1126C2×C4C22×C4×D1112yes—
1127C2×C4#6703712yes—
1128C2×C4#6704212yes—
1129C22—22no—
1130C22—24no—
1131C22—22no—
1132C22—24no—
1133C22—22no—
1134C22—24no—
1135C22—41no—
1136C22—42no—
1137C22—42no—
1138C22—41no—
1139C22—42no—
1140C22—41no—
1141C22—41no—
1142C22—42no—
1143C22—114no—
1144C22—222no—
1145C22—222no—
1146C22—222no—
1147C22—222no—
1148C22—222no—
1149C22—222no—
1150C22—222no—
1151C22—224no—
1152C22—222no—
1153C22—224no—
1154C22—222no—
1155C22—224no—
1156C22—4416no—
1157C22—442no—
1158C22—441no—
1159C22—441no—
1160C22—442no—
1161C22—441no—
1162C22—442no—
1163C22—442no—
1164C22—441no—
1165C22—8816no—
1166C22C23×C4×D1111yescharacteristic
1167C22C2×#6703711yescharacteristic
1168C22C2×#6704211yescharacteristic
1169C22#1062345311yescharacteristic
1170C22#1062345311yescharacteristic
1171C22D11×H(5,𝔽2)11yescharacteristic
1172C22D11×H(5,𝔽2)11yescharacteristic
1173C4—24no—
1174C4—22no—
1175C4—42no—
1176C4—41no—
1177C4—41no—
1178C4—42no—
1179C4—41no—
1180C4—41no—
1181C4—224no—
1182C4—222no—
1183C4—222no—
1184C4—441no—
1185C4—441no—
1186C4—441no—
1187C4—442no—
1188C4—442no—
1189C4—441no—
1190C4#1062307614yes—
1191C2—42no—
1192C2—44no—
1193C2—224no—
1194C2—442no—
1195C2—444no—
1196C2D11×#51811yescharacteristic
1197C2C2×#1062307611yescharacteristic
1198C2#1308181511yescharacteristic
1199C2#1308292211yescharacteristic
1200C2#1308293011yescharacteristic
1201C2#1308293511yescharacteristic
1202C2#1308293911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2363C2
socle, cosocleC23×C11C25
prime radicalC2×D11×#121C2
hypercenter#2363D11
hypocenterC11#34363
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2363

Complements

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

NH ≅ G/Ntype
2. #13071774C2semidirect
3. #13071767C2semidirect
4. #13071658C2semidirect
5. #13071654C2semidirect
6. #13071652C2semidirect
7. #13071484C2semidirect
8. #13071481C2semidirect
9. #13071464C2semidirect
10. #13071459C2semidirect
11. #13071437C2semidirect
12. D4×(C2×D11)⋊C4C2semidirect
13. #13071379C2semidirect
14. #13071376C2semidirect
15. #13071312C2semidirect
16. #13071310C2semidirect
17. #13071307C2semidirect
18. #13071303C2semidirect
19. #13071195C2semidirect
20. #13071190C2semidirect
21. #13070997C2semidirect
22. #13070995C2semidirect
23. C11×#2363C2semidirect
28. C2×C4×D4×C11C22semidirect
29. C2×C11×#117C22semidirect
32. C2×D4×Dic11C22semidirect
35. C2×#66979C22semidirect
36. D11×#121C4semidirect
38. C2×#66946C22semidirect
44. C2×C4×D44C22semidirect
46. C2×#66925C22semidirect
47. C2×#66925C22semidirect
48. C11×#390C22semidirect
49. C11×#390C22semidirect
50. C11×#389C22semidirect
51. C11×#388C22semidirect
52. C11×#386C22semidirect
53. C4×C11×C4⋊C4C22semidirect
54. C4×C11×C22⋊C4C22semidirect
55. C4×C11×C22⋊C4C22semidirect
56. #10622834C22semidirect
57. #10622834C22semidirect
58. #10622833C22semidirect
59. #10622826C22semidirect
60. #10622826C22semidirect
61. #10622823C22semidirect
62. C4×C22⋊Dic11C22semidirect
63. #10622602C22semidirect
64. #10622601C22semidirect
65. #10622601C22semidirect
68. #10622600C22semidirect
69. #10622600C22semidirect
70. #10622598C22semidirect
71. #10622591C22semidirect
72. C4⋊C4×Dic11C22semidirect
73. C4⋊C4×Dic11C22semidirect
74. #10622586C22semidirect
75. #10622571C22semidirect
76. #10622571C22semidirect
77. #10622570C22semidirect
78. #10622570C22semidirect
79. #10622570C22semidirect
80. #10622570C22semidirect
81. #10622569C22semidirect
82. #10622569C22semidirect
83. #10622569C22semidirect
84. #10622569C22semidirect
90. #10622564C22semidirect
91. #10622559C22semidirect
92. #10622558C22semidirect
93. #10622557C22semidirect
94. #10622556C22semidirect
95. #10622555C22semidirect
96. #10622555C22semidirect
97. C22⋊C4×Dic11C22semidirect
98. #10622553C22semidirect
99. #10622553C22semidirect
100. #10622552C22semidirect
101. #10622552C22semidirect
105. C4×(C2×D11)⋊C4C22semidirect
106. C4×(C2×D11)⋊C4C22semidirect
107. C4×C4⋊Dic11C22semidirect
108. #10622546C22semidirect
109. #10622541C22semidirect
110. #10622282C22semidirect
111. #10622282C22semidirect
112. #10622281C22semidirect
115. #10622279C22semidirect
116. #10622278C22semidirect
117. #10622278C22semidirect
120. #10622277C22semidirect
121. #10622277C22semidirect
122. #10622268C22semidirect
123. #10622265C22semidirect
140. C2×D4×D11C2×C4semidirect
145. C22×C4×D11C2×C4semidirect
153. C11×#121C2×C4semidirect
178. #66992C2×C4semidirect
179. #66991C2×C4semidirect
181. #66983C2×C4semidirect
221. #66948C2×C4semidirect
224. C4⋊C4×D11C2×C4semidirect
225. #66937C2×C4semidirect
227. C22⋊C4×D11C2×C4semidirect
412. #2363D11semidirect
564. C2×C4×D4C2×D11semidirect
570. C2×#117C2×D11semidirect
585. #390C2×D11semidirect
586. #390C2×D11semidirect
590. #389C2×D11semidirect
598. #388C2×D11semidirect
614. #386C2×D11semidirect
640. C4×C4⋊C4C2×D11semidirect
649. C4×C22⋊C4C2×D11semidirect
650. C4×C22⋊C4C2×D11semidirect
747. #121C4×D11semidirect
1006. C11#34363semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1212
#130717742
#130717672
#130716582
#130716542
#130716522
#130714842
#130714812
#130714642
#130714592
#130714372
D4×(C2×D11)⋊C42
#130713792
#130713762
#130713122
#130713102
#130713072
#130713032
#130711952
#130711902
#130709972
#130709952
C11×#23632
#3436311