Finite Group Databasebeta

← #14914131

Subgroups — #14914131

Order 2816.

3170 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623363C211yesmaximal, characteristic
2C2×#10623035C211yesmaximal, characteristic, complemented
3#13071689C212yesmaximal, complemented
4#13071683C212yesmaximal, complemented
5#13071678C212yesmaximal, complemented
6#13071670C212yesmaximal, complemented
7#13071566C212yesmaximal, complemented
8#13071546C212yesmaximal, complemented
9#13071541C212yesmaximal, complemented
10C4⋊C4×C22⋊D11C212yesmaximal, complemented
11#13071314C214yesmaximal, complemented
12#13071208C211yesmaximal, characteristic, complemented
13#13071204C211yesmaximal, characteristic, complemented
14C4×#66992C214yesmaximal, complemented
15#13071019C211yesmaximal, characteristic, complemented
16C2×C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
17C2×C11×#520C211yesmaximal, characteristic, complemented
18C22×C11×#41C2211yescharacteristic
19C22×#4339C2211yescharacteristic
20C11×#520—28no—
21C2×C4×Q8×C11C2212yes—
22C2×C4×D4×C11C2214yes—
23C2×C4×D4×C11C2212yes—
24C2×C11×#117C2211yescharacteristic
25C2×C11×#117C2212yes—
26C22×C11×C4⋊C4C2212yes—
27C22×C11×C4⋊C4C2211yescharacteristic
28#10623363C4116yescomplemented
29C2×#67000C2211yescharacteristic
30C2×#66997C2211yescharacteristic
31C2×#66993C2211yescharacteristic
32C2×#66992C2212yes—
33C2×#66992C2212yes—
34C2×#66989C2211yescharacteristic
35C2×C4×C22⋊D11C2214yes—
36C2×C4×C22⋊D11C2214yes—
37C2×C4×C22⋊D11C2212yes—
38C2×C4×C22⋊D11C2212yes—
39C2×#66979C2211yescharacteristic
40C22×C4⋊Dic11C2211yescharacteristic
41C22×C4×Dic11C2212yes—
42C22×C4×Dic11C2211yescharacteristic
43#10623035—28no—
44C2×#66946C2212yes—
45C2×#66945C2212yes—
46C2×C4⋊C4×D11C2212yes—
47C2×#66940C2212yes—
48#10622843C2212yes—
49#10622834C2212yes—
50#10622833C2214yes—
51#10622826C2214yes—
52#10622825C2212yes—
53#10622825C2212yes—
54#10622823C2214yes—
55C4×C22⋊Dic11C2214yes—
56C2×C11⋊#95C2212yes—
57#10622603C2214yes—
58#10622602C2214yes—
59#10622600C2212yes—
60#10622600C2212yes—
61#10622591C2214yes—
62#10622590C2211yescharacteristic
63#10622590C2211yescharacteristic
64#10622589C2211yescharacteristic
65#10622589C2211yescharacteristic
66C4⋊C4×Dic11C2212yes—
67C4⋊C4×Dic11C2212yes—
68C4⋊C4×Dic11C2212yes—
69C4⋊C4×Dic11C2212yes—
70#10622585C2214yes—
71#10622571C2214yes—
72#10622570C2214yes—
73#10622569C2214yes—
74#10622558C2214yes—
75#10622557C2214yes—
76#10622555C2212yes—
77#10622555C2212yes—
78#10622553C2214yes—
79#10622552C2212yes—
80C4×(C2×D11)⋊C4C2214yes—
81#10622546C2214yes—
82C4×Dic11⋊C4C2214yes—
83C4×Dic11⋊C4C2212yes—
84C4×Dic11⋊C4C2212yes—
85#10622542C2212yes—
86C2×C11×#41—24no—
87C2×C11×#41—24no—
88C2×C11×#41C2×C418yescomplemented
89C22×Q8×C11C2311yescharacteristic
90C22×D4×C11C2311yescharacteristic
91C22×D4×C11C2312yes—
92C23×C4×C11C2312yes—
93C23×C4×C11C2314yes—
94C23×C4×C11C2312yes—
95C23×C4×C11C2311yescharacteristic
96C22×C22⋊D11C2312yes—
97C22×C22⋊D11C2312yes—
98C22×C22⋊D11C2312yes—
99C23×Dic11C2311yescharacteristic
100C23×Dic11C2312yes—
101C23×Dic11C2311yescharacteristic
102C2×#4339—24no—
103C2×#4339—24no—
104C2×#4339C2×C418yescomplemented
105C22×D44C2311yescharacteristic
106C22×C4×D11C2312yes—
107C22×C4×D11C2314yes—
108C22×Dic22C2311yescharacteristic
109C4×Q8×C11—28no—
110C4×D4×C11—216no—
111C4×D4×C11—28no—
112C11×#117—24no—
113C11×#117—28no—
114C2×C11×C4⋊C4—28no—
115C2×C11×C4⋊C4D418yescomplemented
116C2×C11×C4⋊C4C2314yes—
117C2×C11×C4⋊C4C2311yescharacteristic
118C2×C11×C4⋊C4C2311yescharacteristic
119C2×C11×C4⋊C4C2312yes—
120C2×C11×C4⋊C4C2312yes—
121C2×C11×C22⋊C4C2312yes—
122C2×C11×C22⋊C4C2314yes—
123C2×C42×C11C2312yes—
124C2×C42×C11C2314yes—
125C2×C22⋊Dic11C2312yes—
126C2×C22⋊Dic11C2314yes—
127C2×C22⋊Dic11C2314yes—
128C2×C22⋊Dic11C2312yes—
129C2×C22⋊Dic11C2312yes—
130#67000C2×C418yescomplemented
131#66997C2×C418yescomplemented
132#66993C2×C418yescomplemented
133#66992C2×C4116yescomplemented
134#66992C2×C4116yescomplemented
135#66989C2×C418yescomplemented
136C4×C22⋊D11—216no—
137C4×C22⋊D11—48no—
138C4×C22⋊D11C2×C4116yescomplemented
139C4×C22⋊D11C2×C4116yescomplemented
140C2×(C2×D11)⋊C4C2314yes—
141C2×(C2×D11)⋊C4C2314yes—
142C2×(C2×D11)⋊C4C2314yes—
143C2×(C2×D11)⋊C4C2312yes—
144C2×(C2×D11)⋊C4C2312yes—
145#66979—24no—
146C2×C4⋊Dic11—24no—
147C2×C4⋊Dic11C2311yescharacteristic
148C2×C4⋊Dic11C2311yescharacteristic
149C2×C4⋊Dic11C2312yes—
150C2×C4⋊Dic11C2312yes—
151C2×Dic11⋊C4C2314yes—
152C2×Dic11⋊C4C2312yes—
153C2×Dic11⋊C4C2312yes—
154C2×Dic11⋊C4C2312yes—
155C2×Dic11⋊C4C2312yes—
156C2×Dic11⋊C4C2312yes—
157C2×Dic11⋊C4C2312yes—
158C2×C4×Dic11—44no—
159C2×C4×Dic11C2×C418yescomplemented
160C2×C4×Dic11C2314yes—
161C2×C4×Dic11C2312yes—
162C2×C4×Dic11C2314yes—
163C2×C4×Dic11C2314yes—
164C2×C4×Dic11C2311yescharacteristic
165C2×C4×Dic11C2311yescharacteristic
166C2×C4×Dic11C2311yescharacteristic
167C2×C4×Dic11C2311yescharacteristic
168#66946—28no—
169#66945—28no—
170C4⋊C4×D11—28no—
171#66940—28no—
172C11⋊#95C2314yes—
173C11⋊#95C2314yes—
174C11⋊#95C2312yes—
175C11⋊#95C2312yes—
176C11⋊#95C2314yes—
177C11⋊#95C2312yes—
178C11⋊#95C2312yes—
179C11⋊#95C2314yes—
180C11⋊#95C2314yes—
181C11⋊#95C2314yes—
182#34206—111nomaximal, Sylow
183C24×C11C2412yes—
184C24×C11C2411yescharacteristic
185C23×D11C2412yes—
186C11×#41—232no—
187C2×Q8×C11—22no—
188C2×Q8×C11—22no—
189C2×Q8×C11C22×C414yes—
190C2×D4×C11—24no—
191C2×D4×C11—24no—
192C2×D4×C11—22no—
193C2×D4×C11—22no—
194C2×D4×C11C22×C414yes—
195C2×D4×C11C22×C418yes—
196C22×C4×C11—24no—
197C22×C4×C11—24no—
198C22×C4×C11—28no—
199C22×C4×C11—42no—
200C22×C4×C11—42no—
201C22×C4×C11—44no—
202C22×C4×C11—44no—
203C22×C4×C11C22×C418yes—
204C22×C4×C11C22×C414yes—
205C22×C4×C11C2×D418yes—
206C22×C4×C11C2×D414yes—
207C22×C4×C11#4114yes—
208C22×C4×C11C2412yes—
209C22×C4×C11C2412yes—
210C22×C4×C11C2412yes—
211C22×C4×C11C2414yes—
212C22×C4×C11C2411yescharacteristic
213C22×C4×C11C2411yescharacteristic
214C2×C22⋊D11—24no—
215C2×C22⋊D11—24no—
216C2×C22⋊D11—24no—
217C2×C22⋊D11—24no—
218C2×C22⋊D11—42no—
219C2×C22⋊D11—42no—
220C2×C22⋊D11C22×C418yes—
221C2×C22⋊D11C22×C418yes—
222C2×C22⋊D11C22×C418yes—
223C22×Dic11—22no—
224C22×Dic11—22no—
225C22×Dic11—24no—
226C22×Dic11—42no—
227C22×Dic11—41no—
228C22×Dic11—42no—
229C22×Dic11—41no—
230C22×Dic11C22×C414yes—
231C22×Dic11C22×C414yes—
232C22×Dic11C2414yes—
233C22×Dic11C2412yes—
234C22×Dic11C2412yes—
235C22×Dic11C2411yescharacteristic
236C22×Dic11C2411yescharacteristic
237C22×Dic11C2411yescharacteristic
238C22×Dic11C2412yes—
239C22×Dic11C2411yescharacteristic
240#4339—232no—
241C2×D44—22no—
242C2×D44—22no—
243C2×D44C22×C414yes—
244C2×C4×D11—24no—
245C2×C4×D11—28no—
246C2×C4×D11—24no—
247C2×C4×D11—44no—
248C2×C4×D11—44no—
249C2×C4×D11C22×C418yes—
250C2×Dic22—22no—
251C2×Dic22—22no—
252C2×Dic22C22×C414yes—
253C11×C4⋊C4—22no—
254C11×C4⋊C4—28no—
255C11×C4⋊C4—22no—
256C11×C4⋊C4C2×D418yes—
257C11×C4⋊C4C2×D418yes—
258C11×C22⋊C4—24no—
259C11×C22⋊C4—28no—
260C42×C11—28no—
261C42×C11—24no—
262C22⋊Dic11—24no—
263C22⋊Dic11—44no—
264C22⋊Dic11—44no—
265C22⋊Dic11C22×C418yes—
266C22⋊Dic11C22×C418yes—
267(C2×D11)⋊C4—28no—
268(C2×D11)⋊C4—44no—
269(C2×D11)⋊C4—44no—
270(C2×D11)⋊C4C22×C418yes—
271(C2×D11)⋊C4C22×C418yes—
272C4⋊Dic11—22no—
273C4⋊Dic11—22no—
274C4⋊Dic11—24no—
275C4⋊Dic11—24no—
276Dic11⋊C4—24no—
277Dic11⋊C4—24no—
278Dic11⋊C4—28no—
279Dic11⋊C4—42no—
280Dic11⋊C4—42no—
281Dic11⋊C4C22×C418yes—
282Dic11⋊C4C22×C418yes—
283C4×Dic11—28no—
284C4×Dic11—28no—
285C4×Dic11—24no—
286C4×Dic11—44no—
287C4×Dic11C22×C414yes—
288C4×Dic11C22×C414yes—
289C4×Dic11C22×C414yes—
290C4×Dic11C22×C414yes—
291C2×#532—111no—
292C2×#520—111no—
293C2×#520D1111yescharacteristic, complemented
294#2367—112no—
295#2367—112no—
296#2366—112no—
297#2365—112no—
298#2354—112no—
299#2352—112no—
300#2352—112no—
301D4×C4⋊C4—112no—
302#2325—114no—
303#2311—111no—
304#2311—111no—
305C4×#121—114no—
306#2285—111no—
307C2×C4×C4⋊C4—111no—
308C23×C11—21no—
309C23×C11—21no—
310C23×C11—21no—
311C23×C11—21no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11—22no—
315C23×C11—22no—
316C23×C11—22no—
317C23×C11—22no—
318C23×C11C23×C414yes—
319C23×C11C23×C412yes—
320C23×C11C22×D412yes—
321C23×C11C2×#4112yes—
322C23×C11C2511yescharacteristic
323C22×D11—22no—
324C22×D11—22no—
325C22×D11—22no—
326C22×D11—22no—
327C22×D11—22no—
328C22×D11—22no—
329C22×D11C23×C414yes—
330Q8×C11—28no—
331D4×C11—216no—
332D4×C11—28no—
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—24no—
336C2×C4×C11—24no—
337C2×C4×C11—216no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—48no—
345C2×C4×C11—88no—
346C2×C4×C11C4×D4116yescomplemented
347C2×C4×C11C23×C414yes—
348C2×C4×C11C23×C412yes—
349C2×C4×C11C23×C412yes—
350C2×C4×C11C22×D418yes—
351C2×C4×C11C22×D412yes—
352C2×C4×C11C22×D412yes—
353C2×C4×C11C2×#4112yes—
354C2×C4×C11C2×#4112yes—
355C22⋊D11—216no—
356C22⋊D11—216no—
357C22⋊D11—48no—
358C2×Dic11—22no—
359C2×Dic11—22no—
360C2×Dic11—21no—
361C2×Dic11—21no—
362C2×Dic11—21no—
363C2×Dic11—21no—
364C2×Dic11—21no—
365C2×Dic11—21no—
366C2×Dic11—28no—
367C2×Dic11—22no—
368C2×Dic11—22no—
369C2×Dic11—24no—
370C2×Dic11—24no—
371C2×Dic11—22no—
372C2×Dic11—22no—
373C2×Dic11—22no—
374C2×Dic11—22no—
375C2×Dic11—24no—
376C2×Dic11—44no—
377C2×Dic11—48no—
378C2×Dic11C23×C412yes—
379C2×Dic11C23×C412yes—
380C2×Dic11C23×C412yes—
381C2×Dic11C23×C414yes—
382C2×Dic11C23×C412yes—
383C2×Dic11H(5,𝔽2)12yes—
384C2×Dic112−1+412yes—
385D44—28no—
386C4×D11—216no—
387C4×D11—88no—
388Dic22—28no—
389C22×#41—111no—
390C22×#41C2×D1111yescharacteristic
391#532—1116no—
392C2×C4⋊Q8—111no—
393C2×#127—111no—
394C2×#124—111no—
395C2×#124—111no—
396C2×#121—112no—
397C2×#121—112no—
398#520—28no—
399#520—228no—
400C2×C4×Q8—112no—
401C2×C4×Q8C2×D1112yes—
402C2×C4×D4—112no—
403C2×C4×D4—112no—
404C2×C4×D4—114no—
405C2×C4×D4—114no—
406C2×C4×D4—112no—
407C2×C4×D4C2×D1114yes—
408C2×C4×D4C2×D1112yes—
409C2×#117—111no—
410C2×#117—112no—
411C2×#117C2×D1111yescharacteristic
412C2×#117C2×D1112yes—
413C22×C4⋊C4—111no—
414C22×C4⋊C4—112no—
415C22×C4⋊C4C2×D1112yes—
416C22×C4⋊C4C2×D1111yescharacteristic
417C22×C42—111no—
418C22×C42—112no—
419#391—112no—
420#391—112no—
421#390—112no—
422#390—114no—
423#390—112no—
424#389—114no—
425#388—114no—
426#388—114no—
427#388—114no—
428#388—114no—
429#387—114no—
430#387—114no—
431#386—114no—
432#386—114no—
433#386—114no—
434#386—114no—
435#385—114no—
436#385—114no—
437#384—111no—
438#384—111no—
439#382—111no—
440#382—111no—
441#380—112no—
442#380—112no—
443#380—112no—
444#380—112no—
445#380—112no—
446#380—112no—
447C4×C4⋊C4—112no—
448C4×C4⋊C4—112no—
449C4×C4⋊C4—112no—
450C4×C4⋊C4—112no—
451C4×C4⋊C4—114no—
452C4×C4⋊C4—112no—
453C4×C4⋊C4—112no—
454C4×C22⋊C4—114no—
455C4×C22⋊C4—114no—
456C2×#95—112no—
457C22×C11—22no—
458C22×C11—22no—
459C22×C11—22no—
460C22×C11—22no—
461C22×C11—22no—
462C22×C11—22no—
463C22×C11—24no—
464C22×C11—24no—
465C22×C11—24no—
466C22×C11—42no—
467C22×C11—42no—
468C22×C11—42no—
469C22×C11—42no—
470C22×C11C2×C4×D414yes—
471C22×C11C24×C411yescharacteristic
472C22×C11C23×D411yescharacteristic
473C22×C11C22×#4111yescharacteristic
474C22×C11C2×H(5,𝔽2)11yescharacteristic
475C22×C11C2×2−1+411yescharacteristic
476C22×C11#58511yescharacteristic
477C22×C11#58511yescharacteristic
478C2×D11—24no—
479C2×D11—24no—
480C2×D11—24no—
481C2×D11—42no—
482C2×D11—42no—
483C2×D11—42no—
484C2×D11—42no—
485C4×C11—24no—
486C4×C11—28no—
487C4×C11—42no—
488C4×C11—42no—
489C4×C11C2×C4×D414yes—
490C4×C11C2×C4×D414yes—
491Dic11—24no—
492Dic11—22no—
493Dic11—22no—
494Dic11—22no—
495Dic11—42no—
496Dic11—42no—
497Dic11—44no—
498Dic11#52014yescomplemented
499C2×#41—24no—
500C2×#41—24no—
501C2×#41—118no—
502C2×#41—224no—
503C2×#41—224no—
504C2×#41C4×D1118yescomplemented
505C22×Q8—111no—
506C22×Q8C22×D1111yescharacteristic
507C22×D4—112no—
508C22×D4—112no—
509C22×D4—112no—
510C22×D4—111no—
511C22×D4C22×D1112yes—
512C22×D4C22×D1111yescharacteristic
513C23×C4—111no—
514C23×C4—111no—
515C23×C4—112no—
516C23×C4—112no—
517C23×C4—114no—
518C23×C4C22×D1112yes—
519C23×C4C22×D1114yes—
520C23×C4C22×D1112yes—
521C23×C4C22×D1111yescharacteristic
522C4⋊Q8—118no—
523#127—118no—
524#124—118no—
525#124—118no—
526#121—1116no—
527#121—1116no—
528C4×Q8—28no—
529C4×Q8—228no—
530C4×D4—216no—
531C4×D4—28no—
532C4×D4—1116no—
533C4×D4—1116no—
534C4×D4—2216no—
535C4×D4—228no—
536C4×D4—448no—
537#117—24no—
538#117—28no—
539#117—224no—
540#117—228no—
541C2×C4⋊C4—28no—
542C2×C4⋊C4—112no—
543C2×C4⋊C4—112no—
544C2×C4⋊C4—111no—
545C2×C4⋊C4—114no—
546C2×C4⋊C4—112no—
547C2×C4⋊C4—112no—
548C2×C4⋊C4—111no—
549C2×C4⋊C4—112no—
550C2×C4⋊C4—112no—
551C2×C4⋊C4—112no—
552C2×C4⋊C4—112no—
553C2×C4⋊C4—224no—
554C2×C4⋊C4—228no—
555C2×C4⋊C4C22⋊D1118yescomplemented
556C2×C4⋊C4C22×D1111yescharacteristic
557C2×C4⋊C4C22×D1114yes—
558C2×C4⋊C4C22×D1111yescharacteristic
559C2×C4⋊C4C22×D1112yes—
560C2×C4⋊C4C22×D1112yes—
561C2×C22⋊C4—112no—
562C2×C22⋊C4—112no—
563C2×C22⋊C4—112no—
564C2×C22⋊C4—112no—
565C2×C22⋊C4—112no—
566C2×C22⋊C4—114no—
567C2×C22⋊C4—114no—
568C2×C22⋊C4—114no—
569C2×C22⋊C4—114no—
570C2×C22⋊C4—114no—
571C2×C22⋊C4C22×D1112yes—
572C2×C22⋊C4C22×D1114yes—
573C2×C42—118no—
574C2×C42—111no—
575C2×C42—111no—
576C2×C42—111no—
577C2×C42—111no—
578C2×C42—114no—
579C2×C42—112no—
580C2×C42—114no—
581C2×C42—114no—
582C2×C42—444no—
583C2×C42C22×D1114yes—
584C2×C42C22×D1112yes—
585#95—114no—
586#95—114no—
587#95—112no—
588#95—112no—
589#95—114no—
590#95—114no—
591#95—112no—
592#95—112no—
593#95—114no—
594#95—114no—
595C2×C11—24no—
596C2×C11—44no—
597C2×C11C22×C4×D411yescharacteristic
598C2×C11C2×#52011yescharacteristic
599C2×C11#342811yescharacteristic
600C2×C11#349611yescharacteristic
601C2×C11#349711yescharacteristic
602C2×C11#350611yescharacteristic
603C2×C11#350711yescharacteristic
604D11—44no—
605C24—112no—
606C24C23×D1112yes—
607C24C23×D1111yescharacteristic
608#41—232no—
609#41—2232no—
610C2×Q8—22no—
611C2×Q8—22no—
612C2×Q8—114no—
613C2×Q8—222no—
614C2×Q8—222no—
615C2×Q8C2×C4×D1114yes—
616C2×D4—24no—
617C2×D4—24no—
618C2×D4—22no—
619C2×D4—22no—
620C2×D4—118no—
621C2×D4—118no—
622C2×D4—118no—
623C2×D4—114no—
624C2×D4—224no—
625C2×D4—224no—
626C2×D4—224no—
627C2×D4—224no—
628C2×D4—222no—
629C2×D4—222no—
630C2×D4—442no—
631C2×D4—442no—
632C2×D4C2×C4×D1118yes—
633C2×D4C2×C4×D1114yes—
634C22×C4—24no—
635C22×C4—24no—
636C22×C4—28no—
637C22×C4—42no—
638C22×C4—42no—
639C22×C4—44no—
640C22×C4—44no—
641C22×C4—111no—
642C22×C4—114no—
643C22×C4—111no—
644C22×C4—111no—
645C22×C4—111no—
646C22×C4—112no—
647C22×C4—114no—
648C22×C4—118no—
649C22×C4—114no—
650C22×C4—112no—
651C22×C4—112no—
652C22×C4—222no—
653C22×C4—222no—
654C22×C4—224no—
655C22×C4—224no—
656C22×C4—224no—
657C22×C4—228no—
658C22×C4—444no—
659C22×C4—444no—
660C22×C4—442no—
661C22×C4—441no—
662C22×C4—441no—
663C22×C4—442no—
664C22×C4C2×C4×D1118yes—
665C22×C4C2×C4×D1114yes—
666C22×C4#433914yes—
667C22×C4C2×C22⋊D1118yes—
668C22×C4C2×C22⋊D1114yes—
669C22×C4C23×D1112yes—
670C22×C4C23×D1112yes—
671C22×C4C23×D1112yes—
672C22×C4C23×D1114yes—
673C22×C4C23×D1111yescharacteristic
674C22×C4C23×D1111yescharacteristic
675C4⋊C4—22no—
676C4⋊C4—28no—
677C4⋊C4—22no—
678C4⋊C4—118no—
679C4⋊C4—118no—
680C4⋊C4—224no—
681C4⋊C4—224no—
682C4⋊C4—224no—
683C4⋊C4—224no—
684C4⋊C4—222no—
685C4⋊C4—228no—
686C4⋊C4—222no—
687C4⋊C4—442no—
688C4⋊C4—442no—
689C4⋊C4C2×C22⋊D1118yes—
690C4⋊C4C2×C22⋊D1118yes—
691C22⋊C4—24no—
692C22⋊C4—28no—
693C22⋊C4—118no—
694C22⋊C4—118no—
695C22⋊C4—118no—
696C22⋊C4—118no—
697C22⋊C4—224no—
698C22⋊C4—228no—
699C22⋊C4—444no—
700C22⋊C4—444no—
701C22⋊C4—444no—
702C22⋊C4—444no—
703C42—28no—
704C42—24no—
705C42—114no—
706C42—114no—
707C42—114no—
708C42—114no—
709C42—228no—
710C42—228no—
711C42—224no—
712C42—444no—
713C11#3420611yescharacteristic, complemented, Sylow
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—114no—
725C23—222no—
726C23—222no—
727C23—222no—
728C23—222no—
729C23—222no—
730C23—222no—
731C23C22×C4×D1114yes—
732C23C22×C4×D1112yes—
733C23C2×#433912yes—
734C23C22×C22⋊D1112yes—
735C23C24×D1111yescharacteristic
736Q8—28no—
737Q8—228no—
738D4—216no—
739D4—28no—
740D4—2216no—
741D4—2216no—
742D4—228no—
743D4—448no—
744C2×C4—22no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—22no—
748C2×C4—216no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—48no—
756C2×C4—88no—
757C2×C4—112no—
758C2×C4—112no—
759C2×C4—112no—
760C2×C4—112no—
761C2×C4—112no—
762C2×C4—112no—
763C2×C4—114no—
764C2×C4—228no—
765C2×C4—222no—
766C2×C4—221no—
767C2×C4—221no—
768C2×C4—221no—
769C2×C4—221no—
770C2×C4—221no—
771C2×C4—221no—
772C2×C4—222no—
773C2×C4—2216no—
774C2×C4—224no—
775C2×C4—224no—
776C2×C4—222no—
777C2×C4—222no—
778C2×C4—222no—
779C2×C4—222no—
780C2×C4—224no—
781C2×C4—222no—
782C2×C4—222no—
783C2×C4—444no—
784C2×C4—448no—
785C2×C4—888no—
786C2×C4C4×C22⋊D11116yescomplemented
787C2×C4C22×C4×D1114yes—
788C2×C4C22×C4×D1112yes—
789C2×C4C22×C4×D1112yes—
790C2×C4C2×#433912yes—
791C2×C4C2×#433912yes—
792C2×C4C22×C22⋊D1118yes—
793C2×C4C22×C22⋊D1112yes—
794C2×C4C22×C22⋊D1112yes—
795C22—22no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—24no—
802C22—24no—
803C22—24no—
804C22—42no—
805C22—42no—
806C22—42no—
807C22—42no—
808C22—224no—
809C22—224no—
810C22—224no—
811C22—442no—
812C22—442no—
813C22—442no—
814C22—442no—
815C22C2×C4×C22⋊D1114yes—
816C22C23×C4×D1111yescharacteristic
817C22C22×#433911yescharacteristic
818C22D11×H(5,𝔽2)11yescharacteristic
819C22#1062345511yescharacteristic
820C22D11×2−1+411yescharacteristic
821C22#1062345711yescharacteristic
822C22C23×C22⋊D1111yescharacteristic
823C4—28no—
824C4—24no—
825C4—42no—
826C4—42no—
827C4—114no—
828C4—224no—
829C4—222no—
830C4—222no—
831C4—222no—
832C4—442no—
833C4—442no—
834C4—444no—
835C4C2×C4×C22⋊D1114yes—
836C4C2×C4×C22⋊D1114yes—
837C2—24no—
838C2—44no—
839C2—444no—
840C2C22×C4×C22⋊D1111yescharacteristic
841C2D11×#52011yescharacteristic
842C2#1308181611yescharacteristic
843C2#1308237511yescharacteristic
844C2#1308238311yescharacteristic
845C2#1308246111yescharacteristic
846C2#1308247411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC2×C11×#520C2
socle, cosocleC23×C11C25
prime radicalC2×#10623363C2
hypercenterC2×#520D11
hypocenterC11#34206
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
2. C2×#10623035C2semidirect
3. #13071689C2semidirect
4. #13071683C2semidirect
5. #13071678C2semidirect
6. #13071670C2semidirect
7. #13071566C2semidirect
8. #13071546C2semidirect
9. #13071541C2semidirect
10. C4⋊C4×C22⋊D11C2semidirect
11. #13071314C2semidirect
12. #13071208C2semidirect
13. #13071204C2semidirect
14. C4×#66992C2semidirect
15. #13071019C2semidirect
16. C2×C4⋊C4×Dic11C2semidirect
17. C2×C11×#520C2semidirect
28. #10623363C4semidirect
88. C2×C11×#41C2×C4semidirect
104. C2×#4339C2×C4semidirect
115. C2×C11×C4⋊C4D4semidirect
130. #67000C2×C4semidirect
131. #66997C2×C4semidirect
132. #66993C2×C4semidirect
133. #66992C2×C4semidirect
134. #66992C2×C4semidirect
135. #66989C2×C4semidirect
138. C4×C22⋊D11C2×C4semidirect
139. C4×C22⋊D11C2×C4semidirect
159. C2×C4×Dic11C2×C4semidirect
293. C2×#520D11semidirect
346. C2×C4×C11C4×D4semidirect
498. Dic11#520semidirect
504. C2×#41C4×D11semidirect
555. C2×C4⋊C4C22⋊D11semidirect
713. C11#34206semidirect
786. C2×C4C4×C22⋊D11semidirect

Maximal subgroups

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

subgroupindex
C2×#106233632
C2×#106230352
#130716892
#130716832
#130716782
#130716702
#130715662
#130715462
#130715412
C4⋊C4×C22⋊D112
#130713142
#130712082
#130712042
C4×#669922
#130710192
C2×C4⋊C4×Dic112
C2×C11×#5202
#3420611