Finite Group Databasebeta

← #14914975

Subgroups — #14914975

Order 2816.

3426 conjugacy classes of subgroups.

The subgroup lattice has 1206 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623205C211yesmaximal, characteristic
2C2×#10623076C211yesmaximal, characteristic, complemented
3C2×C4×#4343C211yesmaximal, characteristic, complemented
4#13071692C211yesmaximal, characteristic, complemented
5#13071691C211yesmaximal, characteristic, complemented
6#13071683C211yesmaximal, characteristic, complemented
7#13071680C211yesmaximal, characteristic, complemented
8#13071680C211yesmaximal, characteristic, complemented
9#13071678C211yesmaximal, characteristic, complemented
10#13071677C211yesmaximal, characteristic, complemented
11#13071598C212yesmaximal, complemented
12#13071594C212yesmaximal, complemented
13#13071594C212yesmaximal, complemented
14#13071592C212yesmaximal, complemented
15#13071308C212yesmaximal, complemented
16#13071304C212yesmaximal, complemented
17#13071207C211yesmaximal, characteristic, complemented
18#13071128C212yesmaximal, complemented
19C4×#66937C212yesmaximal, complemented
20#13071096C211yesmaximal, characteristic, complemented
21D11×#390C211yesmaximal, characteristic, complemented
22#13070970C211yesmaximal, characteristic, complemented
23C11×#2367C211yesmaximal, characteristic, complemented
24C22×#4343C2211yescharacteristic
25C22×D4×D11C2211yescharacteristic
26C2×C11×#124C2211yescharacteristic
27C2×C4×Q8×C11C2211yescharacteristic, complemented
28C2×C4×D4×C11C2211yescharacteristic
29C2×#67000C2211yescharacteristic
30C2×Q8×Dic11C2211yescharacteristic, complemented
31C2×#66993C2211yescharacteristic
32C2×D4×Dic11C2211yescharacteristic
33C2×C4×C22⋊D11C2212yes—
34C2×C4×C22⋊D11C2212yescomplemented
35C22×(C2×D11)⋊C4C2212yes—
36#10623205C4116yescomplemented
37C4×#4343—28no—
38#10623076—28no—
39C2×#66946C2211yescharacteristic
40C2×#66946C2212yes—
41C2×#66946C2211yescharacteristic, complemented
42C2×#66946C2212yescomplemented
43C2×#66945C2211yescharacteristic
44C2×#66945C2212yescomplemented
45C2×C4⋊C4×D11C2211yescharacteristic
46C2×#66937C2212yes—
47C2×#66937C2212yes—
48C2×#66935C2212yes—
49C2×#66935C2212yes—
50C2×(C22⋊D11)⋊C4C2212yes—
51C2×(C22⋊D11)⋊C4C2212yescomplemented
52C2×C22⋊C4×D11C2212yes—
53C2×C22⋊C4×D11C2212yes—
54C2×C22⋊C4×D11C2212yes—
55C2×#66927C2211yescharacteristic
56C2×C4×D44C2211yescharacteristic
57C2×C4×D44C2212yes—
58C2×C4×D44C2211yescharacteristic, complemented
59C2×C4×D44C2212yescomplemented
60C2×#66925C2211yescharacteristic
61C2×#66925C2211yescharacteristic
62C2×C42×D11C2211yescharacteristic
63C2×C42×D11C2212yescomplemented
64C11×#391C2211yescharacteristic, complemented
65C11×#390C2211yescharacteristic
66C11×#388C2212yescomplemented
67C11×#388C2212yescomplemented
68C11×#385C2212yescomplemented
69C4×C11×C4⋊C4C2211yescharacteristic, complemented
70C4×C11×C4⋊C4C2211yescharacteristic, complemented
71C4×C11×C22⋊C4C2212yescomplemented
72#10622843C2211yescharacteristic, complemented
73#10622834C2211yescharacteristic
74#10622826C2212yescomplemented
75#10622603C2212yescomplemented
76#10622602C2211yescharacteristic
77#10622602C2211yescharacteristic
78#10622602C2212yescomplemented
79#10622601C2211yescharacteristic
80#10622601C2211yescharacteristic, complemented
81#10622601C2212yescomplemented
82C4⋊C4×Dic11C2211yescharacteristic, complemented
83C4⋊C4×Dic11C2211yescharacteristic, complemented
84#10622585C2211yescharacteristic, complemented
85#10622585C2211yescharacteristic, complemented
86#10622571C2212yescomplemented
87#10622570C2212yes—
88#10622570C2212yes—
89#10622570C2212yescomplemented
90#10622570C2212yescomplemented
91#10622569C2212yescomplemented
92#10622569C2212yescomplemented
93#10622564C2212yescomplemented
94#10622564C2212yescomplemented
95#10622563C2212yescomplemented
96C22⋊C4×Dic11C2212yescomplemented
97#10622553C2212yescomplemented
98#10622552C2211yescharacteristic
99#10622552C2211yescharacteristic, complemented
100#10622552C2212yescomplemented
101C4×(C2×D11)⋊C4C2212yes—
102C4×(C2×D11)⋊C4C2212yescomplemented
103C4×C4⋊Dic11C2211yescharacteristic, complemented
104C4×C4⋊Dic11C2211yescharacteristic, complemented
105C4×Dic11⋊C4C2212yescomplemented
106C4×Dic11⋊C4C2211yescharacteristic, complemented
107C4×Dic11⋊C4C2211yescharacteristic, complemented
108#10622283C2212yescomplemented
109#10622282C2212yescomplemented
110#10622281C2211yescharacteristic
111#10622281C2211yescharacteristic
112#10622281C2212yescomplemented
113#10622280C2212yescomplemented
114#10622280C2212yescomplemented
115#10622279C2212yes—
116#10622279C2212yescomplemented
117#10622278C2212yes—
118#10622278C2212yes—
119#10622278C2212yescomplemented
120#10622278C2212yescomplemented
121#10622278C2212yescomplemented
122#10622278C2212yescomplemented
123#10622262C2212yescomplemented
124#10622260C2211yescharacteristic, complemented
125#10622260C2211yescharacteristic, complemented
126C24×D11C2312yes—
127C22×Q8×C11C2311yescharacteristic
128C22×D4×C11C2311yescharacteristic
129C23×C4×C11C2312yes—
130C22×C22⋊D11C2312yes—
131C22×C22⋊D11C2312yes—
132C22×C22⋊D11C2312yes—
133C23×Dic11C2312yes—
134C2×#4343—24no—
135C2×#4343—24no—
136C2×#4343C2×C418yescomplemented
137C2×D4×D11—24no—
138C2×D4×D11—24no—
139C2×D4×D11C2×C418yescomplemented
140C22×D44C2311yescharacteristic
141C22×D44C2312yes—
142C22×D44C2311yescharacteristic
143C22×D44C2312yes—
144C22×D44C2312yes—
145C22×C4×D11C2311yescharacteristic
146C22×C4×D11C2311yescharacteristic
147C22×C4×D11C2312yes—
148C22×C4×D11C2312yes—
149C22×C4×D11C2312yes—
150C22×C4×D11C2312yes—
151C22×C4×D11C2312yes—
152C22×C4×D11C2312yes—
153C22×C4×D11C2311yescharacteristic
154C11×#124C2×C418yescomplemented
155C4×Q8×C11—24no—
156C4×D4×C11—24no—
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⋊C4C2312yes—
166C2×C11×C22⋊C4C2312yes—
167C2×C42×C11C2311yescharacteristic
168C2×C42×C11C2312yes—
169C2×C42×C11C2311yescharacteristic
170C2×C42×C11C2312yes—
171C2×C42×C11C2311yescharacteristic
172C2×C22⋊Dic11C2312yes—
173C2×C22⋊Dic11C2312yes—
174C2×C22⋊Dic11C2312yes—
175#67000C2×C418yescomplemented
176Q8×Dic11—24no—
177#66993C2×C418yescomplemented
178D4×Dic11—24no—
179C4×C22⋊D11—28no—
180C4×C22⋊D11—44no—
181C2×(C2×D11)⋊C4—28no—
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—
190C2×(C2×D11)⋊C4C2312yes—
191C2×(C2×D11)⋊C4C2312yes—
192C2×(C2×D11)⋊C4C2312yes—
193C2×(C2×D11)⋊C4C2312yes—
194C2×(C2×D11)⋊C4C2312yes—
195C2×(C2×D11)⋊C4C2312yes—
196C2×(C2×D11)⋊C4C2311yescharacteristic
197C2×(C2×D11)⋊C4C2311yescharacteristic
198C2×(C2×D11)⋊C4C2312yes—
199C2×(C2×D11)⋊C4C2312yes—
200C2×(C2×D11)⋊C4C2312yes—
201C2×C4⋊Dic11C2312yes—
202C2×C4⋊Dic11C2311yescharacteristic
203C2×C4⋊Dic11C2311yescharacteristic
204C2×C4⋊Dic11C2311yescharacteristic
205C2×C4⋊Dic11C2311yescharacteristic
206C2×Dic11⋊C4C2311yescharacteristic
207C2×Dic11⋊C4C2311yescharacteristic
208C2×Dic11⋊C4C2311yescharacteristic
209C2×Dic11⋊C4C2311yescharacteristic
210C2×Dic11⋊C4C2312yes—
211C2×Dic11⋊C4C2311yescharacteristic
212C2×Dic11⋊C4C2311yescharacteristic
213C2×Dic11⋊C4C2311yescharacteristic
214C2×Dic11⋊C4C2311yescharacteristic
215C2×C4×Dic11C2311yescharacteristic
216C2×C4×Dic11C2311yescharacteristic
217C2×C4×Dic11C2311yescharacteristic
218C2×C4×Dic11C2312yes—
219C2×C4×Dic11C2311yescharacteristic
220C2×C4×Dic11C2312yes—
221C2×C4×Dic11C2312yes—
222C2×C4×Dic11C2312yes—
223C2×C4×Dic11C2311yescharacteristic
224C2×C4×Dic11C2312yes—
225#66946—24no—
226#66946—24no—
227#66946—28no—
228#66946—44no—
229#66945—28no—
230#66945D418yescomplemented
231C4⋊C4×D11—24no—
232#66937C2×C4116yescomplemented
233#66937C2×C4116yescomplemented
234#66935C2×C4116yescomplemented
235#66935C2×C4116yescomplemented
236(C22⋊D11)⋊C4—28no—
237(C22⋊D11)⋊C4—44no—
238C22⋊C4×D11—28no—
239C22⋊C4×D11—44no—
240C22⋊C4×D11—44no—
241#66927C2×C418yescomplemented
242C4×D44—28no—
243C4×D44—24no—
244C4×D44—24no—
245C4×D44—44no—
246#66925—24no—
247#66925C2×C418yescomplemented
248C42×D11—24no—
249C42×D11—28no—
250C11×#95C2311yescharacteristic
251C11×#95C2311yescharacteristic
252C11×#95C2312yes—
253C11×#95C2312yes—
254C11×#95C2312yes—
255C11⋊#95C2311yescharacteristic
256C11⋊#95C2311yescharacteristic
257C11⋊#95C2312yes—
258C11⋊#95C2312yes—
259C11⋊#95C2312yes—
260C11⋊#95C2312yes—
261C11⋊#95C2311yescharacteristic
262C11⋊#95C2311yescharacteristic
263C11⋊#95C2312yes—
264C11⋊#95C2311yescharacteristic
265C11⋊#95C2311yescharacteristic
266#34269—111nomaximal, Sylow
267C24×C11C2412yes—
268C23×D11—24no—
269C23×D11—24no—
270C23×D11—42no—
271C23×D11—42no—
272C23×D11—42no—
273C23×D11—42no—
274C23×D11C22×C418yes—
275C23×D11C2412yes—
276C23×D11C2412yes—
277C23×D11C2411yescharacteristic
278C2×Q8×C11—22no—
279C2×Q8×C11—22no—
280C2×Q8×C11C22×C414yes—
281C2×D4×C11—22no—
282C2×D4×C11—22no—
283C2×D4×C11C22×C414yes—
284C22×C4×C11—24no—
285C22×C4×C11—42no—
286C22×C4×C11—42no—
287C22×C4×C11C2412yes—
288C22×C4×C11C2411yescharacteristic
289C22×C4×C11C2411yescharacteristic
290C22×C4×C11C2411yescharacteristic
291C22×C4×C11C2411yescharacteristic
292C22×C4×C11C2412yes—
293C22×C4×C11C2411yescharacteristic
294C22×C4×C11C2412yes—
295C22×C4×C11C2411yescharacteristic
296C22×C4×C11C2411yescharacteristic
297C2×C22⋊D11—24no—
298C2×C22⋊D11—24no—
299C2×C22⋊D11—42no—
300C2×C22⋊D11—42no—
301C2×C22⋊D11—42no—
302C2×C22⋊D11—42no—
303C2×C22⋊D11C22×C418yes—
304C2×C22⋊D11C22×C418yes—
305C2×C22⋊D11C22×C418yes—
306C22×Dic11—24no—
307C22×Dic11—42no—
308C22×Dic11—42no—
309C22×Dic11C2412yes—
310C22×Dic11C2411yescharacteristic
311C22×Dic11C2411yescharacteristic
312C22×Dic11C2411yescharacteristic
313C22×Dic11C2411yescharacteristic
314C22×Dic11C2411yescharacteristic
315C22×Dic11C2412yes—
316C22×Dic11C2411yescharacteristic
317C22×Dic11C2411yescharacteristic
318#4343—232no—
319D4×D11—232no—
320C2×D44—24no—
321C2×D44—24no—
322C2×D44—22no—
323C2×D44—22no—
324C2×D44—22no—
325C2×D44—22no—
326C2×D44—42no—
327C2×D44—42no—
328C2×D44—42no—
329C2×D44—42no—
330C2×D44C22×C414yes—
331C2×D44C22×C414yes—
332C2×D44C22×C418yes—
333C2×D44C22×C418yes—
334C2×D44C22×C418yes—
335C2×C4×D11—24no—
336C2×C4×D11—24no—
337C2×C4×D11—24no—
338C2×C4×D11—24no—
339C2×C4×D11—22no—
340C2×C4×D11—24no—
341C2×C4×D11—22no—
342C2×C4×D11—22no—
343C2×C4×D11—24no—
344C2×C4×D11—24no—
345C2×C4×D11—24no—
346C2×C4×D11—22no—
347C2×C4×D11—24no—
348C2×C4×D11—41no—
349C2×C4×D11—42no—
350C2×C4×D11—42no—
351C2×C4×D11—41no—
352C2×C4×D11—42no—
353C2×C4×D11—42no—
354C2×C4×D11—42no—
355C2×C4×D11—42no—
356C2×C4×D11—42no—
357C2×C4×D11—42no—
358C2×C4×D11C22×C418yes—
359C2×C4×D11C22×C414yes—
360C2×C4×D11C2×D414yes—
361C2×C4×D11#4114yes—
362C11×C4⋊C4—24no—
363C11×C4⋊C4—22no—
364C11×C4⋊C4—22no—
365C11×C4⋊C4—41no—
366C11×C4⋊C4C2×D414yes—
367C11×C22⋊C4—24no—
368C11×C22⋊C4—24no—
369C11×C22⋊C4—42no—
370C11×C22⋊C4C22×C418yes—
371C11×C22⋊C4C22×C418yes—
372C42×C11—24no—
373C42×C11—22no—
374C42×C11—22no—
375C42×C11—42no—
376C42×C11C22×C414yes—
377C22⋊Dic11—24no—
378C22⋊Dic11—24no—
379C22⋊Dic11—42no—
380(C2×D11)⋊C4—24no—
381(C2×D11)⋊C4—24no—
382(C2×D11)⋊C4—24no—
383(C2×D11)⋊C4—22no—
384(C2×D11)⋊C4—22no—
385(C2×D11)⋊C4—24no—
386(C2×D11)⋊C4—24no—
387(C2×D11)⋊C4—24no—
388(C2×D11)⋊C4—42no—
389(C2×D11)⋊C4—42no—
390(C2×D11)⋊C4—42no—
391(C2×D11)⋊C4—42no—
392(C2×D11)⋊C4—42no—
393(C2×D11)⋊C4—42no—
394(C2×D11)⋊C4C22×C414yes—
395(C2×D11)⋊C4C22×C414yes—
396(C2×D11)⋊C4C22×C418yes—
397(C2×D11)⋊C4C22×C418yes—
398(C2×D11)⋊C4C2×D418yes—
399C4⋊Dic11—24no—
400C4⋊Dic11—22no—
401C4⋊Dic11—22no—
402C4⋊Dic11—41no—
403C4⋊Dic11C2×D414yes—
404Dic11⋊C4—22no—
405Dic11⋊C4—22no—
406Dic11⋊C4—24no—
407Dic11⋊C4—22no—
408Dic11⋊C4—22no—
409Dic11⋊C4—41no—
410Dic11⋊C4—41no—
411Dic11⋊C4C22×C414yes—
412Dic11⋊C4C22×C414yes—
413C4×Dic11—22no—
414C4×Dic11—22no—
415C4×Dic11—24no—
416C4×Dic11—22no—
417C4×Dic11—22no—
418C4×Dic11—42no—
419C4×Dic11—42no—
420C4×Dic11—42no—
421C4×Dic11C22×C414yes—
422C4×Dic11C2×D418yes—
423C2×#535—111no—
424C2×#518—111no—
425C2×C4×#41—111no—
426#2367—111no—
427#2367—111no—
428#2367—111no—
429#2367D1111yescharacteristic, complemented
430#2366—111no—
431#2366—111no—
432#2366—111no—
433#2366—111no—
434#2358—112no—
435#2358—112no—
436#2358—112no—
437#2358—112no—
438#2324—112no—
439#2324—112no—
440#2311—111no—
441C4×#121—112no—
442C4×#121—112no—
443#2296—111no—
444C2×#390—111no—
445#2274—111no—
446C23×C11—22no—
447C23×C11—22no—
448C23×C11—22no—
449C23×C11—22no—
450C23×C11—22no—
451C23×C11—22no—
452C23×C11C23×C414yes—
453C23×C11C2511yescharacteristic
454C22×D11—21no—
455C22×D11—21no—
456C22×D11—21no—
457C22×D11—21no—
458C22×D11—22no—
459C22×D11—22no—
460C22×D11—22no—
461C22×D11—22no—
462C22×D11—22no—
463C22×D11—22no—
464C22×D11—22no—
465C22×D11—22no—
466C22×D11—22no—
467C22×D11—22no—
468C22×D11—22no—
469C22×D11—22no—
470C22×D11—216no—
471C22×D11—48no—
472C22×D11—48no—
473C22×D11—84no—
474C22×D11—84no—
475C22×D11—84no—
476C22×D11—84no—
477C22×D11C23×C414yes—
478C22×D11C23×C414yes—
479C22×D11C23×C412yes—
480C22×D11C22×D412yes—
481C22×D11C2×#4112yes—
482Q8×C11—28no—
483D4×C11—28no—
484C2×C4×C11—22no—
485C2×C4×C11—21no—
486C2×C4×C11—22no—
487C2×C4×C11—21no—
488C2×C4×C11—22no—
489C2×C4×C11—21no—
490C2×C4×C11—21no—
491C2×C4×C11—21no—
492C2×C4×C11—21no—
493C2×C4×C11—22no—
494C2×C4×C11—21no—
495C2×C4×C11—21no—
496C2×C4×C11—21no—
497C2×C4×C11—22no—
498C2×C4×C11—22no—
499C2×C4×C11—21no—
500C2×C4×C11—22no—
501C2×C4×C11—21no—
502C2×C4×C11—21no—
503C2×C4×C11—21no—
504C2×C4×C11—21no—
505C2×C4×C11—21no—
506C2×C4×C11—84no—
507C2×C4×C11C23×C412yes—
508C2×C4×C11C23×C412yes—
509C2×C4×C11C23×C414yes—
510C2×C4×C11C23×C412yes—
511C2×C4×C11C22×D414yes—
512C2×C4×C11C22×D412yes—
513C2×C4×C11C2×#4112yes—
514C2×C4×C11H(5,𝔽2)12yes—
515C22⋊D11—216no—
516C22⋊D11—48no—
517C22⋊D11—48no—
518C2×Dic11—21no—
519C2×Dic11—21no—
520C2×Dic11—21no—
521C2×Dic11—22no—
522C2×Dic11—21no—
523C2×Dic11—21no—
524C2×Dic11—21no—
525C2×Dic11—22no—
526C2×Dic11—21no—
527C2×Dic11—21no—
528C2×Dic11—21no—
529C2×Dic11—22no—
530C2×Dic11—22no—
531C2×Dic11—22no—
532C2×Dic11—21no—
533C2×Dic11—21no—
534C2×Dic11—21no—
535C2×Dic11—21no—
536C2×Dic11—21no—
537C2×Dic11—21no—
538C2×Dic11—84no—
539C2×Dic11C23×C412yes—
540C2×Dic11C23×C412yes—
541C2×Dic11C23×C412yes—
542C2×Dic11C22×D414yes—
543C2×Dic11C22×D412yes—
544C2×Dic11C2×#4112yes—
545C2×Dic11H(5,𝔽2)12yes—
546D44—216no—
547D44—28no—
548D44—28no—
549D44—48no—
550D44—48no—
551C4×D11—216no—
552C4×D11—48no—
553C4×D11—48no—
554C4×D11—44no—
555C4×D11—44no—
556C4×D11—84no—
557C4×D11—84no—
558C4×D11—84no—
559C4×D11C4×D4116yescomplemented
560C22×#41—111no—
561C23×D4—111no—
562#535—1116no—
563C2×#127—111no—
564C2×#127—111no—
565C2×#124—111no—
566C2×#124C2×D1111yescharacteristic
567C2×#121—112no—
568C2×#121—112no—
569C2×#120—112no—
570C2×#120—112no—
571#518—228no—
572C4×#41—228no—
573C2×C4×Q8—111no—
574C2×C4×Q8C2×D1111yescharacteristic, complemented
575C2×C4×D4—111no—
576C2×C4×D4—112no—
577C2×C4×D4—112no—
578C2×C4×D4—112no—
579C2×C4×D4—111no—
580C2×C4×D4—111no—
581C2×C4×D4—112no—
582C2×C4×D4—112no—
583C2×C4×D4—112no—
584C2×C4×D4—112no—
585C2×C4×D4—111no—
586C2×C4×D4—111no—
587C2×C4×D4—112no—
588C2×C4×D4C2×D1111yescharacteristic
589C2×#117—111no—
590C2×#117—112no—
591C2×#117—111no—
592C2×#117—111no—
593C22×C4⋊C4—111no—
594C22×C22⋊C4—112no—
595C22×C22⋊C4—112no—
596C22×C22⋊C4—112no—
597C22×C22⋊C4—112no—
598C22×C42—111no—
599C22×C42—112no—
600#391—111no—
601#391C2×D1111yescharacteristic, complemented
602#390—111no—
603#390—111no—
604#390—112no—
605#390—111no—
606#390—112no—
607#390—112no—
608#390—112no—
609#390—112no—
610#390—111no—
611#390—112no—
612#390—111no—
613#390C2×D1111yescharacteristic
614#389—111no—
615#389—111no—
616#389—111no—
617#389—111no—
618#388—112no—
619#388—112no—
620#388—112no—
621#388—112no—
622#388—112no—
623#388—112no—
624#388C2×D1112yescomplemented
625#388C2×D1112yescomplemented
626#386—112no—
627#386—112no—
628#386—112no—
629#386—112no—
630#386—112no—
631#386—112no—
632#386—112no—
633#386—112no—
634#386—112no—
635#386—112no—
636#385—112no—
637#385—111no—
638#385—111no—
639#385—112no—
640#385—112no—
641#385—111no—
642#385—111no—
643#385C2×D1112yescomplemented
644#380—112no—
645#380—112no—
646C4×C4⋊C4—111no—
647C4×C4⋊C4—111no—
648C4×C4⋊C4—112no—
649C4×C4⋊C4—111no—
650C4×C4⋊C4—111no—
651C4×C4⋊C4—111no—
652C4×C4⋊C4—111no—
653C4×C4⋊C4—112no—
654C4×C4⋊C4C2×D1111yescharacteristic, complemented
655C4×C4⋊C4C2×D1111yescharacteristic, complemented
656C4×C22⋊C4—112no—
657C4×C22⋊C4—112no—
658C4×C22⋊C4—112no—
659C4×C22⋊C4—112no—
660C4×C22⋊C4—112no—
661C4×C22⋊C4C2×D1112yescomplemented
662C22×C11—24no—
663C22×C11—24no—
664C22×C11—24no—
665C22×C11—42no—
666C22×C11—42no—
667C22×C11—42no—
668C22×C11—42no—
669C22×C11C24×C411yescharacteristic
670C22×C11C23×D411yescharacteristic
671C22×C11C22×#4111yescharacteristic
672C22×C11C2×H(5,𝔽2)11yescharacteristic
673C22×C11C2×H(5,𝔽2)11yescharacteristic
674C22×C11#58511yescharacteristic
675C22×C11#58511yescharacteristic
676C2×D11—22no—
677C2×D11—22no—
678C2×D11—22no—
679C2×D11—22no—
680C2×D11—22no—
681C2×D11—22no—
682C2×D11—24no—
683C2×D11—24no—
684C2×D11—24no—
685C2×D11—24no—
686C2×D11—24no—
687C2×D11—24no—
688C2×D11—42no—
689C2×D11—42no—
690C2×D11—42no—
691C2×D11—42no—
692C2×D11—42no—
693C2×D11—42no—
694C2×D11—42no—
695C2×D11—42no—
696C2×D11—816no—
697C2×D11C2×C4×D414yes—
698C4×C11—24no—
699C4×C11—22no—
700C4×C11—22no—
701C4×C11—24no—
702C4×C11—22no—
703C4×C11—41no—
704C4×C11—41no—
705C4×C11—41no—
706C4×C11—42no—
707C4×C11C2×C4×D414yes—
708Dic11—22no—
709Dic11—22no—
710Dic11—22no—
711Dic11—24no—
712Dic11—41no—
713Dic11—41no—
714Dic11—41no—
715Dic11—42no—
716Dic11C2×C4×D414yes—
717C25—112no—
718C2×#41—118no—
719C2×#41—224no—
720C2×#41—224no—
721C22×Q8C22×D1111yescharacteristic
722C22×D4—112no—
723C22×D4—112no—
724C22×D4—112no—
725C22×D4—118no—
726C22×D4—112no—
727C22×D4—111no—
728C22×D4—111no—
729C22×D4—112no—
730C22×D4—112no—
731C22×D4—224no—
732C22×D4—224no—
733C22×D4C22×D1111yescharacteristic
734C23×C4—111no—
735C23×C4—112no—
736C23×C4—112no—
737C23×C4—111no—
738C23×C4—111no—
739C23×C4—112no—
740C23×C4—112no—
741C23×C4—112no—
742C23×C4—112no—
743C23×C4—112no—
744C23×C4C22×D1112yes—
745#127—118no—
746#127—118no—
747#124—118no—
748#124C4×D1118yescomplemented
749#121—1116no—
750#121—1116no—
751#120—1116no—
752#120—1116no—
753C4×Q8—24no—
754C4×Q8—224no—
755C4×D4—24no—
756C4×D4—228no—
757C4×D4—224no—
758C4×D4—224no—
759C4×D4—228no—
760C4×D4—228no—
761C4×D4—228no—
762C4×D4—224no—
763C4×D4—224no—
764C4×D4—224no—
765C4×D4—444no—
766C4×D4—444no—
767C4×D4—444no—
768C4×D4—444no—
769#117—118no—
770#117—118no—
771#117—224no—
772#117—228no—
773C2×C4⋊C4—111no—
774C2×C4⋊C4—111no—
775C2×C4⋊C4—111no—
776C2×C4⋊C4—112no—
777C2×C4⋊C4—111no—
778C2×C4⋊C4—111no—
779C2×C4⋊C4—111no—
780C2×C4⋊C4—112no—
781C2×C4⋊C4—111no—
782C2×C4⋊C4—111no—
783C2×C4⋊C4—111no—
784C2×C4⋊C4—111no—
785C2×C4⋊C4—111no—
786C2×C4⋊C4—111no—
787C2×C4⋊C4—224no—
788C2×C4⋊C4C22×D1111yescharacteristic
789C2×C4⋊C4C22×D1112yes—
790C2×C4⋊C4C22×D1111yescharacteristic
791C2×C4⋊C4C22×D1111yescharacteristic
792C2×C4⋊C4C22×D1111yescharacteristic
793C2×C22⋊C4—112no—
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—111no—
801C2×C22⋊C4—111no—
802C2×C22⋊C4—112no—
803C2×C22⋊C4—112no—
804C2×C22⋊C4—112no—
805C2×C22⋊C4—112no—
806C2×C22⋊C4—112no—
807C2×C22⋊C4—112no—
808C2×C22⋊C4—112no—
809C2×C22⋊C4—112no—
810C2×C22⋊C4—112no—
811C2×C22⋊C4—112no—
812C2×C22⋊C4—112no—
813C2×C22⋊C4—112no—
814C2×C22⋊C4—112no—
815C2×C22⋊C4—228no—
816C2×C22⋊C4—228no—
817C2×C22⋊C4—444no—
818C2×C22⋊C4—444no—
819C2×C22⋊C4C22×D1112yes—
820C2×C22⋊C4C22×D1112yes—
821C2×C22⋊C4C22×D1112yes—
822C2×C22⋊C4C22×D1112yes—
823C2×C22⋊C4C22×D1112yes—
824C2×C42—112no—
825C2×C42—111no—
826C2×C42—111no—
827C2×C42—111no—
828C2×C42—112no—
829C2×C42—111no—
830C2×C42—111no—
831C2×C42—112no—
832C2×C42—112no—
833C2×C42—112no—
834C2×C42—228no—
835C2×C42—224no—
836C2×C42C22×D1111yescharacteristic
837C2×C42C22×D1112yes—
838C2×C42C22×D1111yescharacteristic
839C2×C42C22×D1112yes—
840C2×C42C22×D1111yescharacteristic
841#95—111no—
842#95—111no—
843#95—111no—
844#95—112no—
845#95—112no—
846#95—112no—
847#95—112no—
848#95—112no—
849#95—111no—
850#95—111no—
851#95—111no—
852#95C22×D1112yes—
853#95C22×D1112yes—
854#95C22×D1111yescharacteristic
855#95C22×D1112yes—
856#95C22×D1111yescharacteristic
857C2×C11—44no—
858C2×C11C22×C4×D411yescharacteristic
859C2×C11C4×H(5,𝔽2)11yescharacteristic
860C2×C11C4×H(5,𝔽2)11yescharacteristic
861C2×C11#348811yescharacteristic
862C2×C11#348811yescharacteristic
863C2×C11#350811yescharacteristic
864C2×C11#351011yescharacteristic
865D11—24no—
866D11—44no—
867D11—44no—
868C24—111no—
869C24—112no—
870C24—112no—
871C24—118no—
872C24—224no—
873C24—224no—
874C24—442no—
875C24—442no—
876C24—442no—
877C24—442no—
878C24C23×D1112yes—
879#41—2232no—
880C2×Q8—22no—
881C2×Q8—22no—
882C2×Q8C2×C4×D1114yes—
883C2×D4—22no—
884C2×D4—22no—
885C2×D4—118no—
886C2×D4—118no—
887C2×D4—118no—
888C2×D4—118no—
889C2×D4—114no—
890C2×D4—114no—
891C2×D4—118no—
892C2×D4—118no—
893C2×D4—224no—
894C2×D4—224no—
895C2×D4—2232no—
896C2×D4—224no—
897C2×D4—224no—
898C2×D4—222no—
899C2×D4—222no—
900C2×D4—222no—
901C2×D4—222no—
902C2×D4—442no—
903C2×D4—442no—
904C2×D4—442no—
905C2×D4—442no—
906C2×D4—442no—
907C2×D4—442no—
908C2×D4—442no—
909C2×D4—442no—
910C2×D4C2×C4×D1114yes—
911C22×C4—24no—
912C22×C4—42no—
913C22×C4—42no—
914C22×C4—111no—
915C22×C4—114no—
916C22×C4—114no—
917C22×C4—114no—
918C22×C4—111no—
919C22×C4—111no—
920C22×C4—112no—
921C22×C4—111no—
922C22×C4—118no—
923C22×C4—112no—
924C22×C4—111no—
925C22×C4—111no—
926C22×C4—111no—
927C22×C4—224no—
928C22×C4—224no—
929C22×C4—224no—
930C22×C4—222no—
931C22×C4—224no—
932C22×C4—224no—
933C22×C4—222no—
934C22×C4—222no—
935C22×C4—224no—
936C22×C4—224no—
937C22×C4—224no—
938C22×C4—222no—
939C22×C4—224no—
940C22×C4—224no—
941C22×C4—442no—
942C22×C4—442no—
943C22×C4—441no—
944C22×C4—441no—
945C22×C4—442no—
946C22×C4—442no—
947C22×C4—442no—
948C22×C4—442no—
949C22×C4—442no—
950C22×C4—442no—
951C22×C4—442no—
952C22×C4—442no—
953C22×C4C23×D1112yes—
954C22×C4C23×D1111yescharacteristic
955C22×C4C23×D1111yescharacteristic
956C22×C4C23×D1111yescharacteristic
957C22×C4C23×D1111yescharacteristic
958C22×C4C23×D1112yes—
959C22×C4C23×D1111yescharacteristic
960C22×C4C23×D1112yes—
961C22×C4C23×D1111yescharacteristic
962C22×C4C23×D1111yescharacteristic
963C4⋊C4—24no—
964C4⋊C4—22no—
965C4⋊C4—22no—
966C4⋊C4—41no—
967C4⋊C4—114no—
968C4⋊C4—114no—
969C4⋊C4—114no—
970C4⋊C4—224no—
971C4⋊C4—222no—
972C4⋊C4—222no—
973C4⋊C4—224no—
974C4⋊C4—222no—
975C4⋊C4—222no—
976C4⋊C4—222no—
977C4⋊C4—222no—
978C4⋊C4—441no—
979C4⋊C4—441no—
980C4⋊C4—441no—
981C4⋊C4D4×D1114yes—
982C22⋊C4—24no—
983C22⋊C4—24no—
984C22⋊C4—42no—
985C22⋊C4—114no—
986C22⋊C4—114no—
987C22⋊C4—118no—
988C22⋊C4—118no—
989C22⋊C4—118no—
990C22⋊C4—224no—
991C22⋊C4—224no—
992C22⋊C4—224no—
993C22⋊C4—222no—
994C22⋊C4—222no—
995C22⋊C4—224no—
996C22⋊C4—224no—
997C22⋊C4—224no—
998C22⋊C4—224no—
999C22⋊C4—224no—
1000C22⋊C4—442no—
1001C22⋊C4—442no—
1002C22⋊C4—442no—
1003C22⋊C4—442no—
1004C22⋊C4—442no—
1005C22⋊C4—442no—
1006C22⋊C4—442no—
1007C22⋊C4C2×C4×D1118yes—
1008C22⋊C4C2×C4×D1118yes—
1009C42—24no—
1010C42—22no—
1011C42—22no—
1012C42—42no—
1013C42—114no—
1014C42—118no—
1015C42—222no—
1016C42—222no—
1017C42—224no—
1018C42—222no—
1019C42—222no—
1020C42—442no—
1021C42—442no—
1022C42—442no—
1023C42C2×C4×D1114yes—
1024C11#3426911yescharacteristic, complemented, Sylow
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—112no—
1032C23—112no—
1033C23—112no—
1034C23—114no—
1035C23—114no—
1036C23—2216no—
1037C23—221no—
1038C23—221no—
1039C23—221no—
1040C23—221no—
1041C23—222no—
1042C23—222no—
1043C23—222no—
1044C23—222no—
1045C23—222no—
1046C23—222no—
1047C23—222no—
1048C23—222no—
1049C23—222no—
1050C23—222no—
1051C23—222no—
1052C23—222no—
1053C23—448no—
1054C23—448no—
1055C23—884no—
1056C23—884no—
1057C23—884no—
1058C23—884no—
1059C23C22×C4×D1114yes—
1060C23C24×D1111yescharacteristic
1061Q8—28no—
1062D4—28no—
1063D4—2216no—
1064D4—2216no—
1065D4—228no—
1066D4—228no—
1067D4—448no—
1068D4—448no—
1069D4—448no—
1070D4—448no—
1071C2×C4—21no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—22no—
1077C2×C4—21no—
1078C2×C4—22no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—22no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—84no—
1094C2×C4—112no—
1095C2×C4—112no—
1096C2×C4—112no—
1097C2×C4—1116no—
1098C2×C4—112no—
1099C2×C4—112no—
1100C2×C4—114no—
1101C2×C4—112no—
1102C2×C4—2216no—
1103C2×C4—221no—
1104C2×C4—221no—
1105C2×C4—222no—
1106C2×C4—221no—
1107C2×C4—221no—
1108C2×C4—221no—
1109C2×C4—221no—
1110C2×C4—222no—
1111C2×C4—221no—
1112C2×C4—221no—
1113C2×C4—221no—
1114C2×C4—222no—
1115C2×C4—222no—
1116C2×C4—221no—
1117C2×C4—221no—
1118C2×C4—221no—
1119C2×C4—222no—
1120C2×C4—221no—
1121C2×C4—221no—
1122C2×C4—221no—
1123C2×C4—448no—
1124C2×C4—448no—
1125C2×C4—444no—
1126C2×C4—444no—
1127C2×C4—884no—
1128C2×C4—884no—
1129C2×C4—884no—
1130C2×C4—884no—
1131C2×C4C22×C4×D1112yes—
1132C2×C4C22×C4×D1112yes—
1133C2×C4C22×C4×D1114yes—
1134C2×C4C22×C4×D1112yes—
1135C2×C4C2×D4×D1114yes—
1136C2×C4C2×D4×D1112yes—
1137C2×C4#41×D1112yes—
1138C2×C4#6704212yes—
1139C22—24no—
1140C22—24no—
1141C22—24no—
1142C22—42no—
1143C22—42no—
1144C22—42no—
1145C22—42no—
1146C22—114no—
1147C22—222no—
1148C22—222no—
1149C22—222no—
1150C22—222no—
1151C22—222no—
1152C22—222no—
1153C22—224no—
1154C22—224no—
1155C22—224no—
1156C22—224no—
1157C22—224no—
1158C22—224no—
1159C22—442no—
1160C22—442no—
1161C22—442no—
1162C22—442no—
1163C22—442no—
1164C22—442no—
1165C22—442no—
1166C22—442no—
1167C22—8816no—
1168C22C23×C4×D1111yescharacteristic
1169C22C22×D4×D1111yescharacteristic
1170C22C2×#41×D1111yescharacteristic
1171C22C2×#6704211yescharacteristic
1172C22#1062345311yescharacteristic
1173C22D11×H(5,𝔽2)11yescharacteristic
1174C22#1062345711yescharacteristic
1175C4—24no—
1176C4—22no—
1177C4—24no—
1178C4—22no—
1179C4—22no—
1180C4—42no—
1181C4—41no—
1182C4—41no—
1183C4—41no—
1184C4—114no—
1185C4—222no—
1186C4—224no—
1187C4—222no—
1188C4—222no—
1189C4—442no—
1190C4—441no—
1191C4—441no—
1192C4—441no—
1193C4C4×D4×D1114yes—
1194C2—44no—
1195C2—224no—
1196C2—444no—
1197C2—444no—
1198C2C2×C4×D4×D1111yescharacteristic
1199C2#1308182211yescharacteristic
1200C2C4×#6704211yescharacteristic
1201C2#1308227911yescharacteristic
1202C2#1308228211yescharacteristic
1203C2#1308248911yescharacteristic
1204C2#1308250611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2367C2
socle, cosocleC23×C11C25
prime radicalC2×#10623205C2
hypercenter#2367D11
hypocenterC11#34269
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2367

Complements

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

NH ≅ G/Ntype
2. C2×#10623076C2semidirect
3. C2×C4×#4343C2semidirect
4. #13071692C2semidirect
5. #13071691C2semidirect
6. #13071683C2semidirect
7. #13071680C2semidirect
8. #13071680C2semidirect
9. #13071678C2semidirect
10. #13071677C2semidirect
11. #13071598C2semidirect
12. #13071594C2semidirect
13. #13071594C2semidirect
14. #13071592C2semidirect
15. #13071308C2semidirect
16. #13071304C2semidirect
17. #13071207C2semidirect
18. #13071128C2semidirect
19. C4×#66937C2semidirect
20. #13071096C2semidirect
21. D11×#390C2semidirect
22. #13070970C2semidirect
23. C11×#2367C2semidirect
27. C2×C4×Q8×C11C22semidirect
30. C2×Q8×Dic11C22semidirect
34. C2×C4×C22⋊D11C22semidirect
36. #10623205C4semidirect
41. C2×#66946C22semidirect
42. C2×#66946C22semidirect
44. C2×#66945C22semidirect
51. C2×(C22⋊D11)⋊C4C22semidirect
58. C2×C4×D44C22semidirect
59. C2×C4×D44C22semidirect
63. C2×C42×D11C22semidirect
64. C11×#391C22semidirect
66. C11×#388C22semidirect
67. C11×#388C22semidirect
68. C11×#385C22semidirect
69. C4×C11×C4⋊C4C22semidirect
70. C4×C11×C4⋊C4C22semidirect
71. C4×C11×C22⋊C4C22semidirect
72. #10622843C22semidirect
74. #10622826C22semidirect
75. #10622603C22semidirect
78. #10622602C22semidirect
80. #10622601C22semidirect
81. #10622601C22semidirect
82. C4⋊C4×Dic11C22semidirect
83. C4⋊C4×Dic11C22semidirect
84. #10622585C22semidirect
85. #10622585C22semidirect
86. #10622571C22semidirect
89. #10622570C22semidirect
90. #10622570C22semidirect
91. #10622569C22semidirect
92. #10622569C22semidirect
93. #10622564C22semidirect
94. #10622564C22semidirect
95. #10622563C22semidirect
96. C22⋊C4×Dic11C22semidirect
97. #10622553C22semidirect
99. #10622552C22semidirect
100. #10622552C22semidirect
102. C4×(C2×D11)⋊C4C22semidirect
103. C4×C4⋊Dic11C22semidirect
104. C4×C4⋊Dic11C22semidirect
105. C4×Dic11⋊C4C22semidirect
106. C4×Dic11⋊C4C22semidirect
107. C4×Dic11⋊C4C22semidirect
108. #10622283C22semidirect
109. #10622282C22semidirect
112. #10622281C22semidirect
113. #10622280C22semidirect
114. #10622280C22semidirect
116. #10622279C22semidirect
119. #10622278C22semidirect
120. #10622278C22semidirect
121. #10622278C22semidirect
122. #10622278C22semidirect
123. #10622262C22semidirect
124. #10622260C22semidirect
125. #10622260C22semidirect
136. C2×#4343C2×C4semidirect
139. C2×D4×D11C2×C4semidirect
154. C11×#124C2×C4semidirect
175. #67000C2×C4semidirect
177. #66993C2×C4semidirect
230. #66945D4semidirect
232. #66937C2×C4semidirect
233. #66937C2×C4semidirect
234. #66935C2×C4semidirect
235. #66935C2×C4semidirect
241. #66927C2×C4semidirect
247. #66925C2×C4semidirect
429. #2367D11semidirect
559. C4×D11C4×D4semidirect
574. C2×C4×Q8C2×D11semidirect
601. #391C2×D11semidirect
624. #388C2×D11semidirect
625. #388C2×D11semidirect
643. #385C2×D11semidirect
654. C4×C4⋊C4C2×D11semidirect
655. C4×C4⋊C4C2×D11semidirect
661. C4×C22⋊C4C2×D11semidirect
748. #124C4×D11semidirect
1024. C11#34269semidirect

Maximal subgroups

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

subgroupindex
C2×#106232052
C2×#106230762
C2×C4×#43432
#130716922
#130716912
#130716832
#130716802
#130716782
#130716772
#130715982
#130715942
#130715922
#130713082
#130713042
#130712072
#130711282
C4×#669372
#130710962
D11×#3902
#130709702
C11×#23672
#3426911