Finite Group Databasebeta

← #14913860

Subgroups — #14913860

Order 2816.

3578 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623076C212yesmaximal
2C2×C4×D4×D11C211yesmaximal, characteristic
3#13071527C211yesmaximal, characteristic, complemented
4#13071526C211yesmaximal, characteristic, complemented
5#13071524C211yesmaximal, characteristic, complemented
6#13071523C212yesmaximal, complemented
7#13071520C212yesmaximal, complemented
8#13071517C212yesmaximal, complemented
9#13071514C214yesmaximal, complemented
10D4×Dic11⋊C4C212yesmaximal, complemented
11#13071231C212yesmaximal, complemented
12#13071227C214yesmaximal, complemented
13#13071022C211yesmaximal, characteristic, complemented
14#13071020C211yesmaximal, characteristic, complemented
15C2×#10622280C212yesmaximal, complemented
16D11×#380C212yesmaximal, complemented
17C11×#2349C211yesmaximal, characteristic, complemented
18C22×D4×D11C2211yescharacteristic
19C23×C4×D11C2212yes—
20C2×C4×D4×C11C2212yes—
21C2×C4×D4×C11C2211yescharacteristic
22C2×D4×Dic11C2212yes—
23C2×D4×Dic11C2211yescharacteristic
24C2×C4×C22⋊D11C2214yes—
25C2×C4×C22⋊D11C2212yes—
26C22×(C2×D11)⋊C4C2214yes—
27C22×Dic11⋊C4C2214yescomplemented
28#10623076—216no—
29C4×D4×D11C4116yescomplemented
30C2×#66946C2212yes—
31C2×#66946C2211yescharacteristic
32C2×#66945C2212yes—
33C2×C4⋊C4×D11C2211yescharacteristic
34C2×C4⋊C4×D11C2214yescomplemented
35C2×(C22⋊D11)⋊C4C2214yes—
36C2×(C22⋊D11)⋊C4C2212yes—
37C2×C22⋊C4×D11C2214yes—
38C2×C22⋊C4×D11C2212yes—
39C2×C4×D44C2212yes—
40C2×C4×D44C2211yescharacteristic
41C2×#66925C2212yes—
42C2×C42×D11C2211yescharacteristic
43C11×#389C2212yescomplemented
44C11×#385C2214yescomplemented
45C11×#382C2211yescharacteristic, complemented
46C11×#380C2212yescomplemented
47C4×C11×C4⋊C4C2211yescharacteristic, complemented
48C2×C11×#95C2212yescomplemented
49#10622825C2212yescomplemented
50#10622823C2214yescomplemented
51C2×C11⋊#95C2212yescomplemented
52#10622602C2214yescomplemented
53#10622602C2214yescomplemented
54#10622600C2212yes—
55#10622600C2214yes—
56#10622598C2212yescomplemented
57#10622589C2212yescomplemented
58#10622589C2212yescomplemented
59#10622586C2212yescomplemented
60#10622585C2214yescomplemented
61#10622563C2214yescomplemented
62#10622559C2214yescomplemented
63#10622555C2214yescomplemented
64#10622549C2211yescharacteristic, complemented
65C4×C4⋊Dic11C2211yescharacteristic, complemented
66C4×Dic11⋊C4C2212yescomplemented
67#10622541C2212yescomplemented
68#10622281C2214yescomplemented
69#10622281C2214yescomplemented
70#10622280C2212yes—
71#10622280C2214yes—
72#10622280C2211yescharacteristic
73#10622280C2212yes—
74#10622280C2211yescharacteristic
75#10622280C2214yescomplemented
76#10622280C2212yescomplemented
77#10622280C2212yescomplemented
78D11×#95C2212yescomplemented
79D11×#95C2212yescomplemented
80#10622263C2211yescharacteristic, complemented
81#10622263C2211yescharacteristic, complemented
82#10622262C2212yescomplemented
83#10622262C2212yescomplemented
84#10622260C2214yescomplemented
85C24×D11C2312yes—
86C22×D4×C11C2311yescharacteristic
87C23×C4×C11C2314yes—
88C23×C4×C11C2312yes—
89C22×C22⋊D11C2312yes—
90C23×Dic11C2312yes—
91C23×Dic11C2314yes—
92C2×D4×D11C2×C418yes—
93C2×D4×D11D418yes—
94C2×D4×D11Q818yes—
95C22×D44C2311yescharacteristic
96C22×C4×D11—48no—
97C22×C4×D11C2×C4116yescomplemented
98C22×C4×D11C2311yescharacteristic
99C22×C4×D11C2312yes—
100C22×C4×D11C2314yes—
101C22×C4×D11C2314yes—
102C22×C4×D11C2311yescharacteristic
103C22×C4×D11C2312yes—
104C22×C4×D11C2312yes—
105C22×C4×D11C2311yescharacteristic
106C4×D4×C11—28no—
107C4×D4×C11C2×C418yescomplemented
108C2×C11×C4⋊C4C2312yes—
109C2×C11×C4⋊C4C2314yes—
110C2×C11×C4⋊C4C2312yes—
111C2×C11×C4⋊C4C2311yescharacteristic
112C2×C11×C22⋊C4C2314yes—
113C2×C11×C22⋊C4C2312yes—
114C2×C42×C11C2312yes—
115C2×C42×C11C2311yescharacteristic
116C2×C22⋊Dic11C2314yes—
117C2×C22⋊Dic11C2312yes—
118D4×Dic11—28no—
119D4×Dic11C2×C418yescomplemented
120C4×C22⋊D11—216no—
121C4×C22⋊D11C2×C4116yescomplemented
122C2×(C2×D11)⋊C4—216no—
123C2×(C2×D11)⋊C4C2312yes—
124C2×(C2×D11)⋊C4C2312yes—
125C2×(C2×D11)⋊C4C2314yes—
126C2×(C2×D11)⋊C4C2314yes—
127C2×(C2×D11)⋊C4C2314yes—
128C2×(C2×D11)⋊C4C2312yes—
129C2×(C2×D11)⋊C4C2312yes—
130C2×C4⋊Dic11C2312yes—
131C2×C4⋊Dic11C2314yes—
132C2×C4⋊Dic11C2312yes—
133C2×C4⋊Dic11C2311yescharacteristic
134C2×Dic11⋊C4—48no—
135C2×Dic11⋊C4C2312yes—
136C2×Dic11⋊C4C2312yes—
137C2×Dic11⋊C4C2314yes—
138C2×Dic11⋊C4C2312yes—
139C2×Dic11⋊C4C2312yes—
140C2×Dic11⋊C4C2314yes—
141C2×Dic11⋊C4C2314yes—
142C2×Dic11⋊C4C2314yes—
143C2×Dic11⋊C4C2312yes—
144C2×C4×Dic11C2312yes—
145C2×C4×Dic11C2314yes—
146C2×C4×Dic11C2311yescharacteristic
147C2×C4×Dic11C2311yescharacteristic
148C2×C4×Dic11C2311yescharacteristic
149#66946—28no—
150#66946C2×C418yescomplemented
151#66945—28no—
152C4⋊C4×D11—48no—
153C4⋊C4×D11C2×C418yescomplemented
154(C22⋊D11)⋊C4—216no—
155(C22⋊D11)⋊C4C2×C4116yescomplemented
156C22⋊C4×D11—216no—
157C22⋊C4×D11C2×C4116yescomplemented
158C4×D44—28no—
159C4×D44C2×C418yescomplemented
160#66925—28no—
161C42×D11C2×C418yescomplemented
162C11×#95C2314yes—
163C11×#95C2312yes—
164C11×#95C2312yes—
165C11×#95C2311yescharacteristic
166C11×#95C2311yescharacteristic
167C11⋊#95C2314yes—
168C11⋊#95C2312yes—
169C11⋊#95C2312yes—
170C11⋊#95C2311yescharacteristic
171C11⋊#95C2311yescharacteristic
172C11⋊#95C2312yes—
173C11⋊#95C2312yes—
174C11⋊#95C2314yes—
175C11⋊#95C2314yes—
176#34181—111nomaximal, Sylow
177C24×C11C2412yes—
178C23×D11—44no—
179C23×D11—44no—
180C23×D11C22×C418yes—
181C23×D11C2×D418yes—
182C23×D11C2×Q818yes—
183C23×D11C2411yescharacteristic
184C23×D11C2412yes—
185C2×D4×C11C22×C414yes—
186C2×D4×C11C2×D414yes—
187C2×D4×C11C2×Q814yes—
188C22×C4×C11—28no—
189C22×C4×C11—44no—
190C22×C4×C11—44no—
191C22×C4×C11—44no—
192C22×C4×C11C22×C418yes—
193C22×C4×C11C2412yes—
194C22×C4×C11C2414yes—
195C22×C4×C11C2412yes—
196C22×C4×C11C2411yescharacteristic
197C22×C4×C11C2411yescharacteristic
198C22×C4×C11C2412yes—
199C22×C4×C11C2411yescharacteristic
200C2×C22⋊D11C22×C418yes—
201C2×C22⋊D11C2×D418yes—
202C2×C22⋊D11C2×Q818yes—
203C22×Dic11—28no—
204C22×Dic11—28no—
205C22×Dic11—44no—
206C22×Dic11—44no—
207C22×Dic11C22×C418yes—
208C22×Dic11C2412yes—
209C22×Dic11C2414yes—
210C22×Dic11C2412yes—
211C22×Dic11C2411yescharacteristic
212C22×Dic11C2412yes—
213C22×Dic11C2411yescharacteristic
214C22×Dic11C2411yescharacteristic
215D4×D11C4⋊C4164yescomplemented
216C2×D44C22×C414yes—
217C2×D44C2×D414yes—
218C2×D44C2×Q814yes—
219C2×C4×D11—28no—
220C2×C4×D11—24no—
221C2×C4×D11—28no—
222C2×C4×D11—28no—
223C2×C4×D11—44no—
224C2×C4×D11—44no—
225C2×C4×D11—42no—
226C2×C4×D11—44no—
227C2×C4×D11—44no—
228C2×C4×D11—44no—
229C2×C4×D11—44no—
230C2×C4×D11—432no—
231C2×C4×D11C22×C414yes—
232C2×C4×D11C22×C418yes—
233C2×C4×D11C22×C414yes—
234C2×C4×D11C22×C418yes—
235C2×C4×D11C22×C418yes—
236C2×C4×D11C22×C414yes—
237C2×C4×D11C2×D414yes—
238C2×C4×D11C2×Q814yes—
239C11×C4⋊C4—24no—
240C11×C4⋊C4—44no—
241C11×C4⋊C4—42no—
242C11×C4⋊C4C22×C414yes—
243C11×C22⋊C4—28no—
244C11×C22⋊C4C22×C418yes—
245C42×C11—24no—
246C42×C11C22×C414yes—
247C22⋊Dic11—28no—
248C22⋊Dic11C22×C418yes—
249(C2×D11)⋊C4—24no—
250(C2×D11)⋊C4—24no—
251(C2×D11)⋊C4—28no—
252(C2×D11)⋊C4—28no—
253(C2×D11)⋊C4—28no—
254(C2×D11)⋊C4C22×C418yes—
255(C2×D11)⋊C4C22×C418yes—
256C4⋊Dic11—24no—
257C4⋊Dic11—44no—
258C4⋊Dic11—42no—
259C4⋊Dic11C22×C414yes—
260Dic11⋊C4—24no—
261Dic11⋊C4—24no—
262Dic11⋊C4—24no—
263Dic11⋊C4—28no—
264Dic11⋊C4—24no—
265Dic11⋊C4—44no—
266Dic11⋊C4—44no—
267Dic11⋊C4—44no—
268Dic11⋊C4C22×C418yes—
269C4×Dic11—28no—
270C4×Dic11—24no—
271C4×Dic11C22×C414yes—
272C4×Dic11C22×C414yes—
273C4×Dic11C22×C414yes—
274C2×#518—112no—
275C22×C4×D4—111no—
276#2349—111no—
277#2349—112no—
278#2349—111no—
279#2349—112no—
280#2349—111no—
281#2349D1111yescharacteristic, complemented
282D4×C4⋊C4—112no—
283D4×C4⋊C4—114no—
284D4×C4⋊C4—112no—
285#2316—112no—
286#2315—114no—
287#2285—111no—
288#2285—111no—
289C2×#380—112no—
290C2×#380—112no—
291C23×C11—24no—
292C23×C11—24no—
293C23×C11C23×C414yes—
294C23×C11C22×D414yes—
295C23×C11C22×Q814yes—
296C23×C11C2511yescharacteristic
297C22×D11—24no—
298C22×D11—22no—
299C22×D11—24no—
300C22×D11—22no—
301C22×D11—48no—
302C22×D11—48no—
303C22×D11—416no—
304C22×D11—416no—
305C22×D11C2×C4⋊C4132yescomplemented
306C22×D11C23×C414yes—
307C22×D11C23×C412yes—
308C22×D11C22×D412yes—
309C22×D11C22×D414yes—
310C22×D11C22×Q812yes—
311C22×D11C22×Q814yes—
312D4×C11C2×C4⋊C4116yescomplemented
313C2×C4×C11—24no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—24no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—24no—
321C2×C4×C11—22no—
322C2×C4×C11—24no—
323C2×C4×C11—22no—
324C2×C4×C11—22no—
325C2×C4×C11—48no—
326C2×C4×C11—88no—
327C2×C4×C11C23×C412yes—
328C2×C4×C11C23×C412yes—
329C2×C4×C11C23×C414yes—
330C2×C4×C11C23×C412yes—
331C2×C4×C11C22×D412yes—
332C2×C4×C11C22×Q812yes—
333C22⋊D11C2×C4⋊C4132yescomplemented
334C2×Dic11—24no—
335C2×Dic11—22no—
336C2×Dic11—216no—
337C2×Dic11—22no—
338C2×Dic11—22no—
339C2×Dic11—24no—
340C2×Dic11—22no—
341C2×Dic11—24no—
342C2×Dic11—22no—
343C2×Dic11—24no—
344C2×Dic11—22no—
345C2×Dic11—22no—
346C2×Dic11—88no—
347C2×Dic11C23×C412yes—
348C2×Dic11C23×C414yes—
349C2×Dic11C23×C412yes—
350C2×Dic11C23×C412yes—
351C2×Dic11C22×D412yes—
352C2×Dic11C22×Q812yes—
353C2×Dic11H(5,𝔽2)14yes—
354D44C2×C4⋊C4116yescomplemented
355C4×D11—28no—
356C4×D11—216no—
357C4×D11—48no—
358C4×D11—48no—
359C4×D11—44no—
360C4×D11—88no—
361C4×D11—88no—
362C4×D11C2×C4⋊C4116yescomplemented
363C23×D4—111no—
364C24×C4—112no—
365#518—2216no—
366C2×C4×D4—111no—
367C2×C4×D4—112no—
368C2×C4×D4—1116no—
369C2×C4×D4—112no—
370C2×C4×D4—114no—
371C2×C4×D4—111no—
372C2×C4×D4—112no—
373C2×C4×D4—112no—
374C2×C4×D4—114no—
375C2×C4×D4—111no—
376C2×C4×D4—112no—
377C2×C4×D4C2×D1112yes—
378C2×C4×D4C2×D1111yescharacteristic
379C2×#117—112no—
380C2×#117—112no—
381C22×C4⋊C4—111no—
382C22×C4⋊C4—114no—
383C22×C4⋊C4—114no—
384C22×C22⋊C4—112no—
385C22×C22⋊C4—114no—
386C22×C22⋊C4—114no—
387C22×C42—111no—
388#389—114no—
389#389—112no—
390#389—112no—
391#389—112no—
392#389—114no—
393#389C2×D1112yescomplemented
394#385—114no—
395#385—114no—
396#385—114no—
397#385—114no—
398#385—114no—
399#385—114no—
400#385—114no—
401#385C2×D1114yescomplemented
402#384—112no—
403#384—112no—
404#382—111no—
405#382—111no—
406#382—111no—
407#382C2×D1111yescharacteristic, complemented
408#380—112no—
409#380—112no—
410#380—114no—
411#380—114no—
412#380—112no—
413#380—114no—
414#380—114no—
415#380—112no—
416#380—112no—
417#380—111no—
418#380—112no—
419#380—111no—
420#380C2×D1112yescomplemented
421C4×C4⋊C4—112no—
422C4×C4⋊C4—111no—
423C4×C4⋊C4—112no—
424C4×C4⋊C4—112no—
425C4×C4⋊C4C2×D1111yescharacteristic, complemented
426C2×#95—112no—
427C2×#95—112no—
428C2×#95—112no—
429C2×#95C2×D1112yescomplemented
430C22×C11—24no—
431C22×C11—24no—
432C22×C11—28no—
433C22×C11—28no—
434C22×C11C22×C4⋊C418yes—
435C22×C11C24×C411yescharacteristic
436C22×C11C23×D411yescharacteristic
437C22×C11C23×Q811yescharacteristic
438C22×C11C2×H(5,𝔽2)12yes—
439C22×C11#58512yes—
440C2×D11—22no—
441C2×D11—24no—
442C2×D11—22no—
443C2×D11—24no—
444C2×D11—24no—
445C2×D11—28no—
446C2×D11—24no—
447C2×D11—28no—
448C2×D11—432no—
449C2×D11C22×C4⋊C414yes—
450C2×D11C22×C4⋊C418yes—
451C4×C11—22no—
452C4×C11—24no—
453C4×C11—22no—
454C4×C11—42no—
455C4×C11—44no—
456C4×C11—42no—
457C4×C11C22×C4⋊C414yes—
458Dic11—24no—
459Dic11—22no—
460Dic11—42no—
461Dic11—44no—
462Dic11—42no—
463Dic11C22×C4⋊C414yes—
464Dic11#51814yescomplemented
465C25—112no—
466C22×D4—112no—
467C22×D4—118no—
468C22×D4—118no—
469C22×D4—118no—
470C22×D4—111no—
471C22×D4C22×D1111yescharacteristic
472C23×C4—111no—
473C23×C4—112no—
474C23×C4—112no—
475C23×C4—111no—
476C23×C4—1116no—
477C23×C4—111no—
478C23×C4—112no—
479C23×C4—112no—
480C23×C4—114no—
481C23×C4—114no—
482C23×C4—114no—
483C23×C4—448no—
484C23×C4C22×D1114yes—
485C23×C4C22×D1112yes—
486C4×D4—28no—
487C4×D4—118no—
488C4×D4—1116no—
489C4×D4—118no—
490C4×D4—1116no—
491C4×D4—118no—
492C4×D4—228no—
493C4×D4—2216no—
494C4×D4—228no—
495C4×D4—2216no—
496C4×D4—228no—
497C4×D4C4×D1118yescomplemented
498#117—228no—
499#117—228no—
500C2×C4⋊C4—112no—
501C2×C4⋊C4—111no—
502C2×C4⋊C4—118no—
503C2×C4⋊C4—112no—
504C2×C4⋊C4—114no—
505C2×C4⋊C4—112no—
506C2×C4⋊C4—112no—
507C2×C4⋊C4—112no—
508C2×C4⋊C4—112no—
509C2×C4⋊C4—114no—
510C2×C4⋊C4—114no—
511C2×C4⋊C4—114no—
512C2×C4⋊C4—114no—
513C2×C4⋊C4—112no—
514C2×C4⋊C4—448no—
515C2×C4⋊C4—448no—
516C2×C4⋊C4C22×D1112yes—
517C2×C4⋊C4C22×D1114yes—
518C2×C4⋊C4C22×D1112yes—
519C2×C4⋊C4C22×D1111yescharacteristic
520C2×C22⋊C4—112no—
521C2×C22⋊C4—112no—
522C2×C22⋊C4—112no—
523C2×C22⋊C4—1116no—
524C2×C22⋊C4—114no—
525C2×C22⋊C4—112no—
526C2×C22⋊C4—114no—
527C2×C22⋊C4—112no—
528C2×C22⋊C4—114no—
529C2×C22⋊C4—114no—
530C2×C22⋊C4—2216no—
531C2×C22⋊C4—2216no—
532C2×C22⋊C4C22×D1114yes—
533C2×C22⋊C4C22×D1112yes—
534C2×C42—111no—
535C2×C42—111no—
536C2×C42—111no—
537C2×C42—118no—
538C2×C42—114no—
539C2×C42—112no—
540C2×C42C22×D1112yes—
541C2×C42C22×D1111yescharacteristic
542#95—112no—
543#95—111no—
544#95—111no—
545#95—114no—
546#95—114no—
547#95—114no—
548#95—112no—
549#95—112no—
550#95—112no—
551#95C22×D1111yescharacteristic
552#95C22×D1112yes—
553#95C22×D1111yescharacteristic
554#95C22×D1114yes—
555#95C22×D1112yes—
556C2×C11—28no—
557C2×C11C23×C4⋊C411yescharacteristic
558C2×C11C2×#51811yescharacteristic
559C2×C11#342811yescharacteristic
560C2×C11#349612yes—
561C2×C11#350112yes—
562D11—24no—
563D11—28no—
564C24—111no—
565C24—112no—
566C24—118no—
567C24—118no—
568C24—118no—
569C24—444no—
570C24—444no—
571C24C23×D1112yes—
572C2×D4—118no—
573C2×D4—118no—
574C2×D4—118no—
575C2×D4—1164no—
576C2×D4—114no—
577C2×D4—114no—
578C2×D4—114no—
579C2×D4C2×C4×D1114yes—
580C2×D4D4×D1114yes—
581C2×D4Q8×D1114yes—
582C22×C4—28no—
583C22×C4—44no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—111no—
587C22×C4—111no—
588C22×C4—114no—
589C22×C4—114no—
590C22×C4—114no—
591C22×C4—118no—
592C22×C4—111no—
593C22×C4—112no—
594C22×C4—114no—
595C22×C4—118no—
596C22×C4—114no—
597C22×C4—118no—
598C22×C4—118no—
599C22×C4—112no—
600C22×C4—114no—
601C22×C4—112no—
602C22×C4—228no—
603C22×C4—224no—
604C22×C4—228no—
605C22×C4—228no—
606C22×C4—228no—
607C22×C4—228no—
608C22×C4—444no—
609C22×C4—444no—
610C22×C4—442no—
611C22×C4—444no—
612C22×C4—444no—
613C22×C4—444no—
614C22×C4—444no—
615C22×C4—4432no—
616C22×C4—444no—
617C22×C4—444no—
618C22×C4C2×C4×D1118yes—
619C22×C4C23×D1112yes—
620C22×C4C23×D1114yes—
621C22×C4C23×D1112yes—
622C22×C4C23×D1111yescharacteristic
623C22×C4C23×D1111yescharacteristic
624C22×C4C23×D1112yes—
625C22×C4C23×D1111yescharacteristic
626C4⋊C4—24no—
627C4⋊C4—44no—
628C4⋊C4—42no—
629C4⋊C4—118no—
630C4⋊C4—114no—
631C4⋊C4—224no—
632C4⋊C4—228no—
633C4⋊C4—224no—
634C4⋊C4—224no—
635C4⋊C4—224no—
636C4⋊C4—224no—
637C4⋊C4—444no—
638C4⋊C4—444no—
639C4⋊C4—444no—
640C4⋊C4—444no—
641C4⋊C4—442no—
642C4⋊C4C2×C4×D1114yes—
643C22⋊C4—28no—
644C22⋊C4—118no—
645C22⋊C4—118no—
646C22⋊C4—118no—
647C22⋊C4—224no—
648C22⋊C4—224no—
649C22⋊C4—228no—
650C22⋊C4—228no—
651C22⋊C4—228no—
652C22⋊C4—228no—
653C22⋊C4C2×C4×D1118yes—
654C42—24no—
655C42—114no—
656C42—114no—
657C42—114no—
658C42—228no—
659C42—224no—
660C42C2×C4×D1114yes—
661C11#3418111yescharacteristic, complemented, Sylow
662C23—24no—
663C23—24no—
664C23—114no—
665C23—112no—
666C23—112no—
667C23—114no—
668C23—112no—
669C23—114no—
670C23—1132no—
671C23—224no—
672C23—222no—
673C23—224no—
674C23—222no—
675C23—448no—
676C23—4416no—
677C23—4416no—
678C23—448no—
679C23C22×C4×D1114yes—
680C23C2×D4×D1114yes—
681C23C2×Q8×D1114yes—
682C23C24×D1111yescharacteristic
683D4—1132no—
684D4—1116no—
685D4C4⋊C4×D11116yescomplemented
686C2×C4—22no—
687C2×C4—24no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—24no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—22no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—48no—
699C2×C4—88no—
700C2×C4—112no—
701C2×C4—112no—
702C2×C4—112no—
703C2×C4—112no—
704C2×C4—114no—
705C2×C4—1116no—
706C2×C4—112no—
707C2×C4—114no—
708C2×C4—228no—
709C2×C4—2216no—
710C2×C4—2216no—
711C2×C4—222no—
712C2×C4—224no—
713C2×C4—224no—
714C2×C4—222no—
715C2×C4—222no—
716C2×C4—224no—
717C2×C4—222no—
718C2×C4—222no—
719C2×C4—222no—
720C2×C4—224no—
721C2×C4—222no—
722C2×C4—448no—
723C2×C4—448no—
724C2×C4—444no—
725C2×C4—888no—
726C2×C4—888no—
727C2×C4—888no—
728C2×C4C22×C4×D1112yes—
729C2×C4C22×C4×D1112yes—
730C2×C4C22×C4×D1114yes—
731C2×C4C22×C4×D1112yes—
732C2×C4C2×D4×D1112yes—
733C2×C4C2×Q8×D1112yes—
734C22—28no—
735C22—28no—
736C22—24no—
737C22—24no—
738C22—114no—
739C22—118no—
740C22—228no—
741C22—224no—
742C22—224no—
743C22—228no—
744C22—222no—
745C22—224no—
746C22—222no—
747C22—224no—
748C22—4432no—
749C22C2×C4⋊C4×D1118yes—
750C22C23×C4×D1111yescharacteristic
751C22C22×D4×D1111yescharacteristic
752C22C22×Q8×D1111yescharacteristic
753C22#1062345312yes—
754C22D11×H(5,𝔽2)12yes—
755C4—22no—
756C4—24no—
757C4—22no—
758C4—42no—
759C4—44no—
760C4—42no—
761C4—114no—
762C4—114no—
763C4—224no—
764C4—222no—
765C4—442no—
766C4—444no—
767C4—442no—
768C4C2×C4⋊C4×D1114yes—
769C2—28no—
770C2—224no—
771C2—228no—
772C2C22×C4⋊C4×D1111yescharacteristic
773C2D11×#51811yescharacteristic
774C2#1308181511yescharacteristic
775C2#1308237612yes—
776C2#1308241512yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2349C2
socle, cosocleC23×C11C25
prime radicalC22×D4×D11C22
hypercenter#2349D11
hypocenterC11#34181
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2349

Complements

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

NH ≅ G/Ntype
3. #13071527C2semidirect
4. #13071526C2semidirect
5. #13071524C2semidirect
6. #13071523C2semidirect
7. #13071520C2semidirect
8. #13071517C2semidirect
9. #13071514C2semidirect
10. D4×Dic11⋊C4C2semidirect
11. #13071231C2semidirect
12. #13071227C2semidirect
13. #13071022C2semidirect
14. #13071020C2semidirect
15. C2×#10622280C2semidirect
16. D11×#380C2semidirect
17. C11×#2349C2semidirect
27. C22×Dic11⋊C4C22semidirect
29. C4×D4×D11C4semidirect
34. C2×C4⋊C4×D11C22semidirect
43. C11×#389C22semidirect
44. C11×#385C22semidirect
45. C11×#382C22semidirect
46. C11×#380C22semidirect
47. C4×C11×C4⋊C4C22semidirect
48. C2×C11×#95C22semidirect
49. #10622825C22semidirect
50. #10622823C22semidirect
51. C2×C11⋊#95C22semidirect
52. #10622602C22semidirect
53. #10622602C22semidirect
56. #10622598C22semidirect
57. #10622589C22semidirect
58. #10622589C22semidirect
59. #10622586C22semidirect
60. #10622585C22semidirect
61. #10622563C22semidirect
62. #10622559C22semidirect
63. #10622555C22semidirect
64. #10622549C22semidirect
65. C4×C4⋊Dic11C22semidirect
66. C4×Dic11⋊C4C22semidirect
67. #10622541C22semidirect
68. #10622281C22semidirect
69. #10622281C22semidirect
75. #10622280C22semidirect
76. #10622280C22semidirect
77. #10622280C22semidirect
78. D11×#95C22semidirect
79. D11×#95C22semidirect
80. #10622263C22semidirect
81. #10622263C22semidirect
82. #10622262C22semidirect
83. #10622262C22semidirect
84. #10622260C22semidirect
97. C22×C4×D11C2×C4semidirect
107. C4×D4×C11C2×C4semidirect
119. D4×Dic11C2×C4semidirect
121. C4×C22⋊D11C2×C4semidirect
150. #66946C2×C4semidirect
153. C4⋊C4×D11C2×C4semidirect
155. (C22⋊D11)⋊C4C2×C4semidirect
157. C22⋊C4×D11C2×C4semidirect
159. C4×D44C2×C4semidirect
161. C42×D11C2×C4semidirect
215. D4×D11C4⋊C4semidirect
281. #2349D11semidirect
305. C22×D11C2×C4⋊C4semidirect
312. D4×C11C2×C4⋊C4semidirect
333. C22⋊D11C2×C4⋊C4semidirect
354. D44C2×C4⋊C4semidirect
362. C4×D11C2×C4⋊C4semidirect
393. #389C2×D11semidirect
401. #385C2×D11semidirect
407. #382C2×D11semidirect
420. #380C2×D11semidirect
425. C4×C4⋊C4C2×D11semidirect
429. C2×#95C2×D11semidirect
464. Dic11#518semidirect
497. C4×D4C4×D11semidirect
661. C11#34181semidirect
685. D4C4⋊C4×D11semidirect

Maximal subgroups

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

subgroupindex
C2×#106230762
C2×C4×D4×D112
#130715272
#130715262
#130715242
#130715232
#130715202
#130715172
#130715142
D4×Dic11⋊C42
#130712312
#130712272
#130710222
#130710202
C2×#106222802
D11×#3802
C11×#23492
#3418111