Finite Group Databasebeta

← #14916575

Subgroups — #14916575

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#13071772C212yesmaximal, complemented
3#13071769C212yesmaximal, complemented
4#13071659C211yesmaximal, characteristic, complemented
5#13071656C211yesmaximal, characteristic, complemented
6#13071653C211yesmaximal, characteristic, complemented
7#13071650C211yesmaximal, characteristic, complemented
8#13071484C211yesmaximal, characteristic, complemented
9#13071481C211yesmaximal, characteristic, complemented
10#13071463C212yesmaximal, complemented
11#13071460C212yesmaximal, complemented
12#13071437C211yesmaximal, characteristic, complemented
13D4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
14#13071382C212yesmaximal, complemented
15#13071375C212yesmaximal, complemented
16#13071311C211yesmaximal, characteristic, complemented
17#13071309C211yesmaximal, characteristic, complemented
18#13071305C211yesmaximal, characteristic, complemented
19#13071195C212yesmaximal, complemented
20#13071190C212yesmaximal, complemented
21#13070998C211yesmaximal, characteristic, complemented
22#13070995C211yesmaximal, characteristic, complemented
23C11×#2324C211yesmaximal, 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×#66945C2211yescharacteristic, complemented
41C2×#66945C2211yescharacteristic, complemented
42C2×C4⋊C4×D11C2211yescharacteristic
43C2×#66937C2212yes—
44C2×C22⋊C4×D11C2212yes—
45C2×C22⋊C4×D11C2212yes—
46C2×C4×D44C2211yescharacteristic, complemented
47C2×#66925C2212yes—
48C11×#390C2212yescomplemented
49C11×#390C2211yescharacteristic, complemented
50C11×#389C2211yescharacteristic, complemented
51C11×#388C2212yescomplemented
52C11×#386C2212yescomplemented
53C11×#385C2212yescomplemented
54C11×#380C2211yescharacteristic, complemented
55C4×C11×C4⋊C4C2211yescharacteristic, complemented
56#10622834C2212yescomplemented
57#10622834C2211yescharacteristic, complemented
58#10622833C2212yescomplemented
59#10622826C2212yescomplemented
60#10622826C2212yescomplemented
61#10622825C2211yescharacteristic, complemented
62C4×C22⋊Dic11C2212yescomplemented
63#10622603C2212yescomplemented
64#10622603C2212yescomplemented
65#10622602C2212yescomplemented
66#10622601C2211yescharacteristic, complemented
67#10622601C2212yescomplemented
68#10622600C2211yescharacteristic
69#10622600C2211yescharacteristic
70#10622600C2211yescharacteristic
71#10622600C2211yescharacteristic
72#10622600C2211yescharacteristic, complemented
73#10622600C2211yescharacteristic, complemented
74#10622598C2211yescharacteristic, complemented
75#10622591C2212yescomplemented
76C4⋊C4×Dic11C2211yescharacteristic, complemented
77C4⋊C4×Dic11C2211yescharacteristic, complemented
78#10622586C2211yescharacteristic, complemented
79#10622571C2212yescomplemented
80#10622571C2212yescomplemented
81#10622570C2212yescomplemented
82#10622570C2212yescomplemented
83#10622570C2212yescomplemented
84#10622570C2212yescomplemented
85#10622569C2212yescomplemented
86#10622569C2212yescomplemented
87#10622569C2212yescomplemented
88#10622569C2212yescomplemented
89#10622568C2212yes—
90#10622568C2212yes—
91#10622568C2211yescharacteristic
92#10622568C2212yes—
93#10622568C2211yescharacteristic
94#10622564C2212yescomplemented
95#10622563C2212yescomplemented
96#10622558C2212yescomplemented
97#10622557C2212yescomplemented
98#10622556C2211yescharacteristic, complemented
99#10622556C2211yescharacteristic, complemented
100C22⋊C4×Dic11C2212yescomplemented
101C22⋊C4×Dic11C2212yescomplemented
102#10622552C2211yescharacteristic, complemented
103#10622552C2212yescomplemented
104C4×(C2×D11)⋊C4C2211yescharacteristic
105C4×(C2×D11)⋊C4C2211yescharacteristic
106C4×(C2×D11)⋊C4C2212yescomplemented
107C4×(C2×D11)⋊C4C2211yescharacteristic, complemented
108C4×(C2×D11)⋊C4C2211yescharacteristic, complemented
109C4×C4⋊Dic11C2211yescharacteristic, complemented
110#10622546C2212yescomplemented
111#10622541C2211yescharacteristic, complemented
112#10622283C2212yescomplemented
113#10622283C2212yescomplemented
114#10622281C2212yescomplemented
115#10622279C2212yes—
116#10622279C2212yescomplemented
117#10622278C2212yescomplemented
118#10622278C2212yescomplemented
119#10622277C2212yes—
120#10622277C2212yes—
121#10622277C2212yescomplemented
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×C4⋊C4C2311yescharacteristic
161C2×C11×C4⋊C4C2311yescharacteristic
162C2×C11×C22⋊C4C2312yes—
163C2×C11×C22⋊C4C2312yes—
164C2×C11×C22⋊C4C2312yes—
165C2×C11×C22⋊C4C2311yescharacteristic
166C2×C11×C22⋊C4C2311yescharacteristic
167C2×C11×C22⋊C4C2312yes—
168C2×C11×C22⋊C4C2312yes—
169C2×C42×C11C2311yescharacteristic
170C2×C42×C11C2311yescharacteristic
171C2×C42×C11C2312yes—
172C2×C22⋊Dic11C2312yes—
173C2×C22⋊Dic11C2311yescharacteristic
174C2×C22⋊Dic11C2311yescharacteristic
175C2×C22⋊Dic11C2312yes—
176C2×C22⋊Dic11C2312yes—
177C2×C22⋊Dic11C2312yes—
178C2×C22⋊Dic11C2312yes—
179#66992C2×C4116yescomplemented
180#66991C2×C418yescomplemented
181D4×Dic11—42no—
182#66983C2×C418yescomplemented
183C2×(C2×D11)⋊C4—44no—
184C2×(C2×D11)⋊C4C2311yescharacteristic
185C2×(C2×D11)⋊C4C2312yes—
186C2×(C2×D11)⋊C4C2311yescharacteristic
187C2×(C2×D11)⋊C4C2311yescharacteristic
188C2×(C2×D11)⋊C4C2312yes—
189C2×(C2×D11)⋊C4C2311yescharacteristic
190C2×(C2×D11)⋊C4C2312yes—
191C2×(C2×D11)⋊C4C2312yes—
192C2×(C2×D11)⋊C4C2312yes—
193C2×(C2×D11)⋊C4C2312yes—
194C2×(C2×D11)⋊C4C2311yescharacteristic
195C2×(C2×D11)⋊C4C2311yescharacteristic
196C2×(C2×D11)⋊C4C2312yes—
197C2×(C2×D11)⋊C4C2312yes—
198C2×(C2×D11)⋊C4C2312yes—
199C2×(C2×D11)⋊C4C2311yescharacteristic
200C2×(C2×D11)⋊C4C2312yes—
201C2×(C2×D11)⋊C4C2311yescharacteristic
202C2×(C2×D11)⋊C4C2312yes—
203C2×(C2×D11)⋊C4C2312yes—
204#66979—42no—
205C2×C4⋊Dic11C2311yescharacteristic
206C2×C4⋊Dic11C2311yescharacteristic
207C2×C4⋊Dic11C2312yes—
208C2×C4⋊Dic11C2311yescharacteristic
209C2×C4⋊Dic11C2311yescharacteristic
210C2×C4⋊Dic11C2311yescharacteristic
211C2×Dic11⋊C4C2312yes—
212C2×Dic11⋊C4C2312yes—
213C2×Dic11⋊C4C2312yes—
214C2×C4×Dic11C2311yescharacteristic
215C2×C4×Dic11C2311yescharacteristic
216C2×C4×Dic11C2312yes—
217C2×C4×Dic11C2312yes—
218C2×C4×Dic11C2312yes—
219C2×C4×Dic11C2312yes—
220C2×C4×Dic11C2312yes—
221#66948C2×C418yescomplemented
222#66946—42no—
223#66945—42no—
224#66945—42no—
225#66945—44no—
226C4⋊C4×D11C2×C418yescomplemented
227#66937C2×C4116yescomplemented
228C22⋊C4×D11—44no—
229C22⋊C4×D11C2×C4116yescomplemented
230C4×D44—42no—
231#66925—44no—
232C11×#95C2312yes—
233C11×#95C2312yes—
234C11×#95C2312yes—
235C11⋊#95C2311yescharacteristic
236C11⋊#95C2312yes—
237C11⋊#95C2312yes—
238C11⋊#95C2311yescharacteristic
239C11⋊#95C2312yes—
240C11⋊#95C2312yes—
241C11⋊#95C2312yes—
242C11⋊#95C2312yes—
243C11⋊#95C2312yes—
244C11⋊#95C2312yes—
245C11⋊#95C2312yes—
246C11⋊#95C2311yescharacteristic
247C11⋊#95C2311yescharacteristic
248C11⋊#95C2311yescharacteristic
249C11⋊#95C2311yescharacteristic
250C11⋊#95C2311yescharacteristic
251C11⋊#95C2311yescharacteristic
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×C11C2412yes—
291C22×C4×C11C2411yescharacteristic
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×Dic11C2411yescharacteristic
316C22×Dic11C2412yes—
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⋊C4—41no—
351C11×C4⋊C4—41no—
352C11×C4⋊C4C22×C414yes—
353C11×C22⋊C4—42no—
354C11×C22⋊C4—42no—
355C11×C22⋊C4—42no—
356C11×C22⋊C4—41no—
357C11×C22⋊C4—41no—
358C11×C22⋊C4—42no—
359C11×C22⋊C4C22×C418yes—
360C42×C11—22no—
361C42×C11—22no—
362C42×C11—42no—
363C22⋊Dic11—42no—
364C22⋊Dic11—41no—
365C22⋊Dic11—41no—
366C22⋊Dic11—42no—
367C22⋊Dic11—42no—
368C22⋊Dic11—42no—
369C22⋊Dic11C22×C418yes—
370(C2×D11)⋊C4—22no—
371(C2×D11)⋊C4—24no—
372(C2×D11)⋊C4—22no—
373(C2×D11)⋊C4—22no—
374(C2×D11)⋊C4—24no—
375(C2×D11)⋊C4—22no—
376(C2×D11)⋊C4—42no—
377(C2×D11)⋊C4—42no—
378(C2×D11)⋊C4—42no—
379(C2×D11)⋊C4—42no—
380(C2×D11)⋊C4—42no—
381(C2×D11)⋊C4—42no—
382(C2×D11)⋊C4—41no—
383(C2×D11)⋊C4—42no—
384(C2×D11)⋊C4—41no—
385(C2×D11)⋊C4—42no—
386(C2×D11)⋊C4—41no—
387(C2×D11)⋊C4—41no—
388(C2×D11)⋊C4C22×C418yes—
389(C2×D11)⋊C4C22×C418yes—
390C4⋊Dic11—22no—
391C4⋊Dic11—22no—
392C4⋊Dic11—42no—
393C4⋊Dic11—41no—
394C4⋊Dic11—41no—
395C4⋊Dic11C22×C414yes—
396Dic11⋊C4—42no—
397Dic11⋊C4—42no—
398Dic11⋊C4C22×C418yes—
399C4×Dic11—22no—
400C4×Dic11—22no—
401C4×Dic11—42no—
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#2363—111no—
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#2324D1111yescharacteristic, complemented
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—22no—
439C23×C11—21no—
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—22no—
482C2×C4×C11—21no—
483C2×C4×C11—22no—
484C2×C4×C11—21no—
485C2×C4×C11—28no—
486C2×C4×C11—21no—
487C2×C4×C11—22no—
488C2×C4×C11—22no—
489C2×C4×C11—22no—
490C2×C4×C11—21no—
491C2×C4×C11—22no—
492C2×C4×C11—21no—
493C2×C4×C11—21no—
494C2×C4×C11—21no—
495C2×C4×C11—21no—
496C2×C4×C11—21no—
497C2×C4×C11—21no—
498C2×C4×C11—21no—
499C2×C4×C11—21no—
500C2×C4×C11—22no—
501C2×C4×C11—21no—
502C2×C4×C11—21no—
503C2×C4×C11—22no—
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—21no—
514C2×Dic11—21no—
515C2×Dic11—22no—
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—21no—
533C2×Dic11—22no—
534C2×Dic11—21no—
535C2×Dic11—21no—
536C2×Dic11—22no—
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—112no—
555C2×#121—111no—
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—111no—
568C2×#117—111no—
569C2×#117—112no—
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#385C2×D1112yescomplemented
619#381—111no—
620#381—111no—
621#381—112no—
622#381—112no—
623#381—112no—
624#380—111no—
625#380—111no—
626#380—111no—
627#380—111no—
628#380—111no—
629#380—111no—
630#380—111no—
631#380C2×D1111yescharacteristic, complemented
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—112no—
642C4×C22⋊C4—112no—
643C4×C22⋊C4—112no—
644C4×C22⋊C4—112no—
645C4×C22⋊C4—111no—
646C4×C22⋊C4—111no—
647C4×C22⋊C4—111no—
648C4×C22⋊C4—111no—
649C4×C22⋊C4—112no—
650C4×C22⋊C4—112no—
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—444no—
754#117—442no—
755#117—444no—
756#117—442no—
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—112no—
766C2×C4⋊C4—112no—
767C2×C4⋊C4—112no—
768C2×C4⋊C4C22×D1111yescharacteristic
769C2×C4⋊C4C22×D1111yescharacteristic
770C2×C4⋊C4C22×D1112yes—
771C2×C4⋊C4C22×D1111yescharacteristic
772C2×C4⋊C4C22×D1111yescharacteristic
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—111no—
786C2×C22⋊C4—111no—
787C2×C22⋊C4—112no—
788C2×C22⋊C4—112no—
789C2×C22⋊C4—112no—
790C2×C22⋊C4—112no—
791C2×C22⋊C4—112no—
792C2×C22⋊C4—112no—
793C2×C22⋊C4—112no—
794C2×C22⋊C4—112no—
795C2×C22⋊C4—112no—
796C2×C22⋊C4—111no—
797C2×C22⋊C4—111no—
798C2×C22⋊C4—111no—
799C2×C22⋊C4—111no—
800C2×C22⋊C4—112no—
801C2×C22⋊C4—112no—
802C2×C22⋊C4—444no—
803C2×C22⋊C4—444no—
804C2×C22⋊C4C22×D1112yes—
805C2×C22⋊C4C22×D1111yescharacteristic
806C2×C22⋊C4C22×D1111yescharacteristic
807C2×C22⋊C4C22×D1112yes—
808C2×C22⋊C4C22×D1112yes—
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×C42—112no—
818C2×C42C22×D1111yescharacteristic
819C2×C42C22×D1111yescharacteristic
820C2×C42C22×D1112yes—
821#95—111no—
822#95—111no—
823#95—111no—
824#95—111no—
825#95—112no—
826#95—111no—
827#95—111no—
828#95—112no—
829#95—112no—
830#95—111no—
831#95—111no—
832#95—112no—
833#95—112no—
834#95—112no—
835#95—112no—
836#95—112no—
837#95—112no—
838#95C22×D1112yes—
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—111no—
902C22×C4—112no—
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×D1112yes—
945C22×C4C23×D1111yescharacteristic
946C22×C4C23×D1111yescharacteristic
947C4⋊C4—22no—
948C4⋊C4—22no—
949C4⋊C4—41no—
950C4⋊C4—41no—
951C4⋊C4—42no—
952C4⋊C4—118no—
953C4⋊C4—114no—
954C4⋊C4—222no—
955C4⋊C4—222no—
956C4⋊C4—442no—
957C4⋊C4—442no—
958C4⋊C4—441no—
959C4⋊C4—441no—
960C4⋊C4—442no—
961C4⋊C4C2×C4×D1114yes—
962C22⋊C4—42no—
963C22⋊C4—41no—
964C22⋊C4—41no—
965C22⋊C4—42no—
966C22⋊C4—42no—
967C22⋊C4—42no—
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—442no—
980C22⋊C4—442no—
981C22⋊C4—442no—
982C22⋊C4—442no—
983C22⋊C4—441no—
984C22⋊C4—442no—
985C22⋊C4—441no—
986C22⋊C4—441no—
987C22⋊C4—442no—
988C22⋊C4—441no—
989C22⋊C4—442no—
990C22⋊C4—441no—
991C22⋊C4—441no—
992C22⋊C4—442no—
993C22⋊C4—442no—
994C22⋊C4—442no—
995C22⋊C4C2×C4×D1118yes—
996C42—22no—
997C42—22no—
998C42—42no—
999C42—222no—
1000C42—222no—
1001C42—442no—
1002C42—442no—
1003C42—442no—
1004C42—442no—
1005C42—442no—
1006C11#3436311yescharacteristic, complemented, Sylow
1007C23—21no—
1008C23—22no—
1009C23—21no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—21no—
1014C23—21no—
1015C23—21no—
1016C23—22no—
1017C23—21no—
1018C23—22no—
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—222no—
1035C23—222no—
1036C23—221no—
1037C23—221no—
1038C23—221no—
1039C23—222no—
1040C23—221no—
1041C23—222no—
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—21no—
1072C2×C4—21no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—21no—
1076C2×C4—22no—
1077C2×C4—21no—
1078C2×C4—22no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—21no—
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—222no—
1101C2×C4—221no—
1102C2×C4—221no—
1103C2×C4—221no—
1104C2×C4—221no—
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—221no—
1115C2×C4—222no—
1116C2×C4—222no—
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
1169C22D11×H(5,𝔽2)11yescharacteristic
1170C22D11×H(5,𝔽2)11yescharacteristic
1171C22#1062345511yescharacteristic
1172C22#1062345711yescharacteristic
1173C4—24no—
1174C4—22no—
1175C4—41no—
1176C4—41no—
1177C4—41no—
1178C4—42no—
1179C4—41no—
1180C4—42no—
1181C4—224no—
1182C4—222no—
1183C4—222no—
1184C4—442no—
1185C4—441no—
1186C4—442no—
1187C4—441no—
1188C4—441no—
1189C4—441no—
1190C4#1062307614yes—
1191C2—42no—
1192C2—44no—
1193C2—224no—
1194C2—442no—
1195C2—444no—
1196C2D11×#51811yescharacteristic
1197C2C2×#1062307611yescharacteristic
1198C2#1308181611yescharacteristic
1199C2#1308292011yescharacteristic
1200C2#1308292811yescharacteristic
1201C2#1308293411yescharacteristic
1202C2#1308293811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2324C2
socle, cosocleC23×C11C25
prime radicalC2×D11×#121C2
hypercenter#2324D11
hypocenterC11#34363
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2324

Complements

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

NH ≅ G/Ntype
2. #13071772C2semidirect
3. #13071769C2semidirect
4. #13071659C2semidirect
5. #13071656C2semidirect
6. #13071653C2semidirect
7. #13071650C2semidirect
8. #13071484C2semidirect
9. #13071481C2semidirect
10. #13071463C2semidirect
11. #13071460C2semidirect
12. #13071437C2semidirect
13. D4×(C2×D11)⋊C4C2semidirect
14. #13071382C2semidirect
15. #13071375C2semidirect
16. #13071311C2semidirect
17. #13071309C2semidirect
18. #13071305C2semidirect
19. #13071195C2semidirect
20. #13071190C2semidirect
21. #13070998C2semidirect
22. #13070995C2semidirect
23. C11×#2324C2semidirect
28. C2×C4×D4×C11C22semidirect
29. C2×C11×#117C22semidirect
32. C2×D4×Dic11C22semidirect
35. C2×#66979C22semidirect
36. D11×#121C4semidirect
38. C2×#66946C22semidirect
40. C2×#66945C22semidirect
41. C2×#66945C22semidirect
46. C2×C4×D44C22semidirect
48. C11×#390C22semidirect
49. C11×#390C22semidirect
50. C11×#389C22semidirect
51. C11×#388C22semidirect
52. C11×#386C22semidirect
53. C11×#385C22semidirect
54. C11×#380C22semidirect
55. C4×C11×C4⋊C4C22semidirect
56. #10622834C22semidirect
57. #10622834C22semidirect
58. #10622833C22semidirect
59. #10622826C22semidirect
60. #10622826C22semidirect
61. #10622825C22semidirect
62. C4×C22⋊Dic11C22semidirect
63. #10622603C22semidirect
64. #10622603C22semidirect
65. #10622602C22semidirect
66. #10622601C22semidirect
67. #10622601C22semidirect
72. #10622600C22semidirect
73. #10622600C22semidirect
74. #10622598C22semidirect
75. #10622591C22semidirect
76. C4⋊C4×Dic11C22semidirect
77. C4⋊C4×Dic11C22semidirect
78. #10622586C22semidirect
79. #10622571C22semidirect
80. #10622571C22semidirect
81. #10622570C22semidirect
82. #10622570C22semidirect
83. #10622570C22semidirect
84. #10622570C22semidirect
85. #10622569C22semidirect
86. #10622569C22semidirect
87. #10622569C22semidirect
88. #10622569C22semidirect
94. #10622564C22semidirect
95. #10622563C22semidirect
96. #10622558C22semidirect
97. #10622557C22semidirect
98. #10622556C22semidirect
99. #10622556C22semidirect
100. C22⋊C4×Dic11C22semidirect
101. C22⋊C4×Dic11C22semidirect
102. #10622552C22semidirect
103. #10622552C22semidirect
106. C4×(C2×D11)⋊C4C22semidirect
107. C4×(C2×D11)⋊C4C22semidirect
108. C4×(C2×D11)⋊C4C22semidirect
109. C4×C4⋊Dic11C22semidirect
110. #10622546C22semidirect
111. #10622541C22semidirect
112. #10622283C22semidirect
113. #10622283C22semidirect
114. #10622281C22semidirect
116. #10622279C22semidirect
117. #10622278C22semidirect
118. #10622278C22semidirect
121. #10622277C22semidirect
122. #10622268C22semidirect
123. #10622265C22semidirect
140. C2×D4×D11C2×C4semidirect
145. C22×C4×D11C2×C4semidirect
153. C11×#121C2×C4semidirect
179. #66992C2×C4semidirect
180. #66991C2×C4semidirect
182. #66983C2×C4semidirect
221. #66948C2×C4semidirect
226. C4⋊C4×D11C2×C4semidirect
227. #66937C2×C4semidirect
229. C22⋊C4×D11C2×C4semidirect
424. #2324D11semidirect
564. C2×C4×D4C2×D11semidirect
570. C2×#117C2×D11semidirect
585. #390C2×D11semidirect
586. #390C2×D11semidirect
590. #389C2×D11semidirect
598. #388C2×D11semidirect
614. #386C2×D11semidirect
618. #385C2×D11semidirect
631. #380C2×D11semidirect
640. C4×C4⋊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
#130717722
#130717692
#130716592
#130716562
#130716532
#130716502
#130714842
#130714812
#130714632
#130714602
#130714372
D4×(C2×D11)⋊C42
#130713822
#130713752
#130713112
#130713092
#130713052
#130711952
#130711902
#130709982
#130709952
C11×#23242
#3436311