Finite Group Databasebeta

← #14914137

Subgroups — #14914137

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×#10623358C211yesmaximal, characteristic, complemented
3C2×#10623054C211yesmaximal, characteristic, complemented
4#13071692C212yesmaximal, complemented
5#13071686C212yesmaximal, complemented
6#13071677C212yesmaximal, complemented
7#13071673C212yesmaximal, complemented
8#13071560C212yesmaximal, complemented
9#13071547C212yesmaximal, complemented
10#13071538C212yesmaximal, complemented
11#13071512C212yesmaximal, complemented
12#13071317C214yesmaximal, complemented
13#13071209C211yesmaximal, characteristic, complemented
14#13071126C214yesmaximal, complemented
15#13071019C211yesmaximal, characteristic, complemented
16C2×C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
17C11×#2311C211yesmaximal, characteristic, complemented
18C22×C11×#41C2211yescharacteristic
19C22×#4339C2211yescharacteristic
20C2×C11×#117C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22#10623363C4116yescomplemented
23#10623358—28no—
24C2×#67000C2211yescharacteristic
25C2×Q8×Dic11C2212yes—
26C2×#66997C2211yescharacteristic
27C2×#66993C2211yescharacteristic
28C2×#66992C2212yes—
29C2×#66992C2212yes—
30C2×#66989C2211yescharacteristic
31C2×D4×Dic11C2214yes—
32C2×D4×Dic11C2212yes—
33C2×C4×C22⋊D11C2212yes—
34C2×C4×C22⋊D11C2212yes—
35C2×#66979C2211yescharacteristic
36C2×#66979C2212yes—
37C22×C4⋊Dic11C2212yes—
38C22×C4⋊Dic11C2211yescharacteristic
39C22×C4×Dic11C2212yes—
40C22×C4×Dic11C2211yescharacteristic
41#10623054—28no—
42C2×#66945C2212yes—
43C2×C4⋊C4×D11C2212yes—
44C2×(C22⋊D11)⋊C4C2214yes—
45C2×(C22⋊D11)⋊C4C2214yes—
46C2×C4×D44C2212yes—
47C2×C4×Dic22C2212yes—
48C11×#391C2212yes—
49C11×#390C2212yes—
50C11×#386C2214yes—
51C11×#380C2212yes—
52C11×#380C2212yes—
53#10622826C2214yes—
54C2×C11⋊#95C2212yes—
55#10622601C2212yes—
56#10622600C2212yes—
57#10622600C2212yes—
58#10622590C2211yescharacteristic
59#10622590C2211yescharacteristic
60#10622589C2211yescharacteristic
61#10622589C2211yescharacteristic
62C4⋊C4×Dic11C2212yes—
63C4⋊C4×Dic11C2212yes—
64C4⋊C4×Dic11C2212yes—
65C4⋊C4×Dic11C2212yes—
66#10622587C2212yes—
67#10622571C2214yes—
68#10622570C2214yes—
69#10622569C2214yes—
70#10622559C2214yes—
71#10622558C2214yes—
72#10622557C2214yes—
73#10622555C2212yes—
74#10622555C2212yes—
75C22⋊C4×Dic11C2214yes—
76C4×Dic11⋊C4C2212yes—
77C4×Dic11⋊C4C2212yes—
78#10622283C2214yes—
79#10622282C2214yes—
80#10622281C2214yes—
81#10622279C2214yes—
82#10622268C2214yes—
83#10622265C2214yes—
84#10622262C2214yes—
85#10622260C2214yes—
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×C11C2312yes—
94C23×C4×C11C2311yescharacteristic
95C22×C22⋊D11C2312yes—
96C22×C22⋊D11C2312yes—
97C22×C22⋊D11C2312yes—
98C23×Dic11C2311yescharacteristic
99C23×Dic11C2314yes—
100C23×Dic11C2311yescharacteristic
101C23×Dic11C2312yes—
102C2×#4339—24no—
103C2×#4339—24no—
104C2×#4339C2×C418yescomplemented
105C22×D44C2311yescharacteristic
106C22×C4×D11C2312yes—
107C22×C4×D11C2314yes—
108C22×Dic22C2311yescharacteristic
109C11×#117—24no—
110C2×C11×C4⋊C4—24no—
111C2×C11×C4⋊C4C2311yescharacteristic
112C2×C11×C4⋊C4C2311yescharacteristic
113C2×C11×C4⋊C4C2312yes—
114C2×C11×C4⋊C4C2312yes—
115C2×C11×C22⋊C4C2312yes—
116C2×C11×C22⋊C4C2314yes—
117C2×C11×C22⋊C4C2314yes—
118C2×C42×C11C2312yes—
119C2×C22⋊Dic11C2312yes—
120C2×C22⋊Dic11C2314yes—
121C2×C22⋊Dic11C2312yes—
122C2×C22⋊Dic11C2312yes—
123#67000C2×C418yescomplemented
124Q8×Dic11—28no—
125#66997C2×C418yescomplemented
126#66993C2×C418yescomplemented
127#66992C2×C4116yescomplemented
128#66992C2×C4116yescomplemented
129#66989C2×C418yescomplemented
130D4×Dic11—216no—
131D4×Dic11—28no—
132C4×C22⋊D11C2×C4116yescomplemented
133C4×C22⋊D11C2×C4116yescomplemented
134C2×(C2×D11)⋊C4C2314yes—
135C2×(C2×D11)⋊C4C2314yes—
136C2×(C2×D11)⋊C4C2314yes—
137C2×(C2×D11)⋊C4C2312yes—
138C2×(C2×D11)⋊C4C2312yes—
139#66979—24no—
140#66979—28no—
141C2×C4⋊Dic11—28no—
142C2×C4⋊Dic11D418yescomplemented
143C2×C4⋊Dic11C2314yes—
144C2×C4⋊Dic11C2311yescharacteristic
145C2×C4⋊Dic11C2311yescharacteristic
146C2×C4⋊Dic11C2312yes—
147C2×C4⋊Dic11C2312yes—
148C2×Dic11⋊C4C2314yes—
149C2×Dic11⋊C4C2312yes—
150C2×Dic11⋊C4C2312yes—
151C2×Dic11⋊C4C2312yes—
152C2×Dic11⋊C4C2312yes—
153C2×Dic11⋊C4C2312yes—
154C2×Dic11⋊C4C2312yes—
155C2×C4×Dic11—44no—
156C2×C4×Dic11C2×C418yescomplemented
157C2×C4×Dic11C2314yes—
158C2×C4×Dic11C2314yes—
159C2×C4×Dic11C2314yes—
160C2×C4×Dic11C2312yes—
161C2×C4×Dic11C2314yes—
162C2×C4×Dic11C2311yescharacteristic
163C2×C4×Dic11C2311yescharacteristic
164C2×C4×Dic11C2311yescharacteristic
165C2×C4×Dic11C2311yescharacteristic
166#66945—28no—
167C4⋊C4×D11—28no—
168(C22⋊D11)⋊C4—216no—
169(C22⋊D11)⋊C4—48no—
170C4×D44—28no—
171C4×Dic22—28no—
172C11×#95C2314yes—
173C11×#95C2314yes—
174C11⋊#95C2314yes—
175C11⋊#95C2314yes—
176C11⋊#95C2312yes—
177C11⋊#95C2314yes—
178C11⋊#95C2312yes—
179C11⋊#95C2312yes—
180C11⋊#95C2314yes—
181C11⋊#95C2312yes—
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—24no—
199C22×C4×C11—42no—
200C22×C4×C11—42no—
201C22×C4×C11C22×C418yes—
202C22×C4×C11C22×C414yes—
203C22×C4×C11C2×D414yes—
204C22×C4×C11#4114yes—
205C22×C4×C11C2414yes—
206C22×C4×C11C2412yes—
207C22×C4×C11C2412yes—
208C22×C4×C11C2412yes—
209C22×C4×C11C2411yescharacteristic
210C22×C4×C11C2411yescharacteristic
211C2×C22⋊D11—24no—
212C2×C22⋊D11—24no—
213C2×C22⋊D11—24no—
214C2×C22⋊D11—24no—
215C2×C22⋊D11—42no—
216C2×C22⋊D11—42no—
217C2×C22⋊D11C22×C418yes—
218C2×C22⋊D11C22×C418yes—
219C2×C22⋊D11C22×C418yes—
220C22×Dic11—22no—
221C22×Dic11—22no—
222C22×Dic11—28no—
223C22×Dic11—42no—
224C22×Dic11—41no—
225C22×Dic11—42no—
226C22×Dic11—41no—
227C22×Dic11—44no—
228C22×Dic11—44no—
229C22×Dic11C22×C414yes—
230C22×Dic11C22×C414yes—
231C22×Dic11C2×D418yes—
232C22×Dic11C2412yes—
233C22×Dic11C2412yes—
234C22×Dic11C2411yescharacteristic
235C22×Dic11C2411yescharacteristic
236C22×Dic11C2411yescharacteristic
237C22×Dic11C2412yes—
238C22×Dic11C2414yes—
239C22×Dic11C2411yescharacteristic
240#4339—232no—
241C2×D44—22no—
242C2×D44—22no—
243C2×D44C22×C414yes—
244C2×C4×D11—28no—
245C2×C4×D11—24no—
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—22no—
255C11×C4⋊C4—24no—
256C11×C4⋊C4—24no—
257C11×C22⋊C4—24no—
258C11×C22⋊C4—44no—
259C11×C22⋊C4—44no—
260C42×C11—24no—
261C22⋊Dic11—28no—
262C22⋊Dic11—24no—
263C22⋊Dic11C22×C418yes—
264C22⋊Dic11C22×C418yes—
265(C2×D11)⋊C4—28no—
266(C2×D11)⋊C4—44no—
267(C2×D11)⋊C4—44no—
268(C2×D11)⋊C4C22×C418yes—
269(C2×D11)⋊C4C22×C418yes—
270C4⋊Dic11—28no—
271C4⋊Dic11—22no—
272C4⋊Dic11—22no—
273C4⋊Dic11C2×D418yes—
274C4⋊Dic11C2×D418yes—
275Dic11⋊C4—28no—
276Dic11⋊C4—24no—
277Dic11⋊C4—24no—
278Dic11⋊C4—42no—
279Dic11⋊C4—42no—
280Dic11⋊C4C22×C418yes—
281Dic11⋊C4C22×C418yes—
282C4×Dic11—28no—
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×#520—111no—
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#2311D1111yescharacteristic, complemented
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—216no—
336C2×C4×C11—22no—
337C2×C4×C11—22no—
338C2×C4×C11—24no—
339C2×C4×C11—24no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—24no—
345C2×C4×C11—48no—
346C2×C4×C11C4×D4116yescomplemented
347C2×C4×C11C23×C414yes—
348C2×C4×C11C23×C412yes—
349C2×C4×C11C23×C412yes—
350C2×C4×C11C22×D412yes—
351C2×C4×C11C22×D412yes—
352C2×C4×C11C2×#4112yes—
353C2×C4×C11C2×#4112yes—
354C22⋊D11—216no—
355C22⋊D11—216no—
356C22⋊D11—48no—
357C2×Dic11—22no—
358C2×Dic11—22no—
359C2×Dic11—24no—
360C2×Dic11—21no—
361C2×Dic11—21no—
362C2×Dic11—21no—
363C2×Dic11—21no—
364C2×Dic11—24no—
365C2×Dic11—21no—
366C2×Dic11—21no—
367C2×Dic11—28no—
368C2×Dic11—22no—
369C2×Dic11—22no—
370C2×Dic11—22no—
371C2×Dic11—22no—
372C2×Dic11—22no—
373C2×Dic11—22no—
374C2×Dic11—44no—
375C2×Dic11—48no—
376C2×Dic11—88no—
377C2×Dic11C23×C412yes—
378C2×Dic11C23×C412yes—
379C2×Dic11C23×C412yes—
380C2×Dic11C23×C414yes—
381C2×Dic11C23×C412yes—
382C2×Dic11C22×D418yes—
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—228no—
399#520—228no—
400C2×C4×Q8—112no—
401C2×C4×Q8—112no—
402C2×C4×D4—112no—
403C2×C4×D4—112no—
404C2×C4×D4—114no—
405C2×C4×D4—112no—
406C2×C4×D4—114no—
407C2×C4×D4—114no—
408C2×C4×D4—112no—
409C2×#117—111no—
410C2×#117—112no—
411C2×#117—112no—
412C2×#117C2×D1111yescharacteristic
413C22×C4⋊C4—111no—
414C22×C4⋊C4—112no—
415C22×C4⋊C4—112no—
416C22×C4⋊C4C2×D1111yescharacteristic
417C22×C42—111no—
418C22×C42—112no—
419#391—112no—
420#391C2×D1112yes—
421#390—112no—
422#390—114no—
423#390C2×D1112yes—
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#386C2×D1114yes—
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#380C2×D1112yes—
446#380C2×D1112yes—
447C4×C4⋊C4—112no—
448C4×C4⋊C4—112no—
449C4×C4⋊C4—112no—
450C4×C4⋊C4—112no—
451C4×C4⋊C4—112no—
452C4×C4⋊C4—112no—
453C4×C4⋊C4—114no—
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—42no—
487C4×C11—42no—
488C4×C11—44no—
489C4×C11C2×C4×D414yes—
490C4×C11C2×C4×D414yes—
491Dic11—24no—
492Dic11—22no—
493Dic11—22no—
494Dic11—22no—
495Dic11—28no—
496Dic11—42no—
497Dic11—42no—
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—112no—
515C23×C4—111no—
516C23×C4—112no—
517C23×C4—114no—
518C23×C4—114no—
519C23×C4C22×D1112yes—
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—228no—
529C4×Q8—228no—
530C4×D4—1116no—
531C4×D4—1116no—
532C4×D4—228no—
533C4×D4—2216no—
534C4×D4—228no—
535C4×D4—2216no—
536C4×D4—448no—
537#117—24no—
538#117—228no—
539#117—228no—
540#117—224no—
541C2×C4⋊C4—24no—
542C2×C4⋊C4—118no—
543C2×C4⋊C4—112no—
544C2×C4⋊C4—112no—
545C2×C4⋊C4—112no—
546C2×C4⋊C4—112no—
547C2×C4⋊C4—111no—
548C2×C4⋊C4—114no—
549C2×C4⋊C4—114no—
550C2×C4⋊C4—111no—
551C2×C4⋊C4—112no—
552C2×C4⋊C4—112no—
553C2×C4⋊C4—112no—
554C2×C4⋊C4—112no—
555C2×C4⋊C4—228no—
556C2×C4⋊C4—228no—
557C2×C4⋊C4C22×D1111yescharacteristic
558C2×C4⋊C4C22×D1112yes—
559C2×C4⋊C4C22×D1112yes—
560C2×C4⋊C4C22×D1111yescharacteristic
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⋊C4C22×D1112yes—
571C2×C22⋊C4C22×D1114yes—
572C2×C22⋊C4C22×D1114yes—
573C2×C42—118no—
574C2×C42—111no—
575C2×C42—111no—
576C2×C42—111no—
577C2×C42—111no—
578C2×C42—114no—
579C2×C42—114no—
580C2×C42—112no—
581C2×C42—114no—
582C2×C42—114no—
583C2×C42—444no—
584C2×C42C22×D1112yes—
585#95—114no—
586#95—114no—
587#95—112no—
588#95—112no—
589#95—114no—
590#95—112no—
591#95—112no—
592#95—114no—
593#95C22×D1114yes—
594#95C22×D1114yes—
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—24no—
637C22×C4—42no—
638C22×C4—42no—
639C22×C4—111no—
640C22×C4—114no—
641C22×C4—111no—
642C22×C4—111no—
643C22×C4—111no—
644C22×C4—112no—
645C22×C4—114no—
646C22×C4—114no—
647C22×C4—118no—
648C22×C4—118no—
649C22×C4—112no—
650C22×C4—112no—
651C22×C4—228no—
652C22×C4—222no—
653C22×C4—222no—
654C22×C4—228no—
655C22×C4—224no—
656C22×C4—224no—
657C22×C4—444no—
658C22×C4—444no—
659C22×C4—442no—
660C22×C4—441no—
661C22×C4—441no—
662C22×C4—442no—
663C22×C4—444no—
664C22×C4—444no—
665C22×C4C2×C4×D1118yes—
666C22×C4C2×C4×D1114yes—
667C22×C4D4×D1114yes—
668C22×C4#434114yes—
669C22×C4C23×D1114yes—
670C22×C4C23×D1112yes—
671C22×C4C23×D1112yes—
672C22×C4C23×D1112yes—
673C22×C4C23×D1111yescharacteristic
674C22×C4C23×D1111yescharacteristic
675C4⋊C4—22no—
676C4⋊C4—22no—
677C4⋊C4—24no—
678C4⋊C4—24no—
679C4⋊C4—118no—
680C4⋊C4—118no—
681C4⋊C4—118no—
682C4⋊C4—118no—
683C4⋊C4—228no—
684C4⋊C4—228no—
685C4⋊C4—224no—
686C4⋊C4—224no—
687C4⋊C4—222no—
688C4⋊C4—222no—
689C4⋊C4—442no—
690C4⋊C4—442no—
691C22⋊C4—24no—
692C22⋊C4—44no—
693C22⋊C4—44no—
694C22⋊C4—118no—
695C22⋊C4—118no—
696C22⋊C4—118no—
697C22⋊C4—118no—
698C22⋊C4—228no—
699C22⋊C4—228no—
700C22⋊C4—224no—
701C22⋊C4—444no—
702C22⋊C4—444no—
703C42—24no—
704C42—114no—
705C42—114no—
706C42—114no—
707C42—114no—
708C42—228no—
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×D4×D1112yes—
734C23C2×#434112yes—
735C23C24×D1111yescharacteristic
736Q8—28no—
737Q8—228no—
738D4—216no—
739D4—28no—
740D4—2216no—
741D4—2216no—
742D4—228no—
743D4—448no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—216no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—24no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—48no—
757C2×C4—112no—
758C2×C4—112no—
759C2×C4—112no—
760C2×C4—112no—
761C2×C4—112no—
762C2×C4—112no—
763C2×C4—114no—
764C2×C4—118no—
765C2×C4—228no—
766C2×C4—222no—
767C2×C4—222no—
768C2×C4—224no—
769C2×C4—221no—
770C2×C4—221no—
771C2×C4—221no—
772C2×C4—221no—
773C2×C4—221no—
774C2×C4—224no—
775C2×C4—221no—
776C2×C4—2216no—
777C2×C4—222no—
778C2×C4—222no—
779C2×C4—222no—
780C2×C4—222no—
781C2×C4—222no—
782C2×C4—222no—
783C2×C4—448no—
784C2×C4—444no—
785C2×C4—888no—
786C2×C4—888no—
787C2×C4(C22⋊D11)⋊C4116yescomplemented
788C2×C4C22×C4×D1114yes—
789C2×C4C22×C4×D1112yes—
790C2×C4C22×C4×D1112yes—
791C2×C4C2×D4×D1112yes—
792C2×C4C2×D4×D1112yes—
793C2×C4C2×#434112yes—
794C2×C4C2×#434112yes—
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×(C22⋊D11)⋊C414yes—
816C22C23×C4×D1111yescharacteristic
817C22C22×D4×D1111yescharacteristic
818C22C22×#434111yescharacteristic
819C22D11×H(5,𝔽2)11yescharacteristic
820C22#1062345511yescharacteristic
821C22D11×2−1+411yescharacteristic
822C22#1062345711yescharacteristic
823C4—24no—
824C4—42no—
825C4—42no—
826C4—44no—
827C4—114no—
828C4—228no—
829C4—224no—
830C4—222no—
831C4—222no—
832C4—222no—
833C4—442no—
834C4—442no—
835C4C2×(C22⋊D11)⋊C414yes—
836C4C2×(C22⋊D11)⋊C414yes—
837C2—24no—
838C2—44no—
839C2—444no—
840C2C22×(C22⋊D11)⋊C411yescharacteristic
841C2D11×#52011yescharacteristic
842C2#1308181611yescharacteristic
843C2#1308237911yescharacteristic
844C2#1308238511yescharacteristic
845C2#1308246711yescharacteristic
846C2#1308248011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2311C2
socle, cosocleC23×C11C25
prime radicalC2×#10623363C2
hypercenter#2311D11
hypocenterC11#34206
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2311

Complements

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

NH ≅ G/Ntype
2. C2×#10623358C2semidirect
3. C2×#10623054C2semidirect
4. #13071692C2semidirect
5. #13071686C2semidirect
6. #13071677C2semidirect
7. #13071673C2semidirect
8. #13071560C2semidirect
9. #13071547C2semidirect
10. #13071538C2semidirect
11. #13071512C2semidirect
12. #13071317C2semidirect
13. #13071209C2semidirect
14. #13071126C2semidirect
15. #13071019C2semidirect
16. C2×C4⋊C4×Dic11C2semidirect
17. C11×#2311C2semidirect
22. #10623363C4semidirect
88. C2×C11×#41C2×C4semidirect
104. C2×#4339C2×C4semidirect
123. #67000C2×C4semidirect
125. #66997C2×C4semidirect
126. #66993C2×C4semidirect
127. #66992C2×C4semidirect
128. #66992C2×C4semidirect
129. #66989C2×C4semidirect
132. C4×C22⋊D11C2×C4semidirect
133. C4×C22⋊D11C2×C4semidirect
142. C2×C4⋊Dic11D4semidirect
156. C2×C4×Dic11C2×C4semidirect
304. #2311D11semidirect
346. C2×C4×C11C4×D4semidirect
498. Dic11#520semidirect
504. C2×#41C4×D11semidirect
713. C11#34206semidirect
787. C2×C4(C22⋊D11)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#106233632
C2×#106233582
C2×#106230542
#130716922
#130716862
#130716772
#130716732
#130715602
#130715472
#130715382
#130715122
#130713172
#130712092
#130711262
#130710192
C2×C4⋊C4×Dic112
C11×#23112
#3420611