Finite Group Databasebeta

← #14914698

Subgroups — #14914698

Order 2816.

3578 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623017C211yesmaximal, characteristic
2C2×#10623017C211yesmaximal, characteristic
3C22×C4×C22⋊D11C211yesmaximal, characteristic
4#13071523C214yesmaximal, complemented
5#13071522C214yesmaximal, complemented
6C4⋊C4×C22⋊D11C214yesmaximal, complemented
7#13071514C214yesmaximal, complemented
8#13071235C212yesmaximal, complemented
9#13071230C211yesmaximal, characteristic, complemented
10#13071228C211yesmaximal, characteristic, complemented
11#13071227C212yesmaximal, complemented
12#13071095C212yesmaximal, complemented
13C2×#10622823C211yesmaximal, characteristic, complemented
14D11×#385C212yesmaximal, complemented
15C2×C11×#385C211yesmaximal, characteristic, complemented
16C24×C4×C11C2211yescharacteristic
17C23×C22⋊D11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C22×C11×C4⋊C4C2212yescomplemented
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C2×C4×C22⋊D11—28no—
26C2×C4×C22⋊D11C2214yes—
27C2×C4×C22⋊D11C2212yes—
28C2×C4×C22⋊D11C2214yes—
29C2×C4×C22⋊D11C2212yes—
30C2×C4×C22⋊D11C2214yes—
31C22×(C2×D11)⋊C4C2211yescharacteristic
32C22×Dic11⋊C4C2211yescharacteristic
33C22×Dic11⋊C4C2212yescomplemented
34C22×C4×Dic11C2211yescharacteristic
35C2×C4⋊C4×D11C2214yescomplemented
36#10623017—28no—
37#10623017C4116yescomplemented
38C2×(C22⋊D11)⋊C4C2212yes—
39C2×(C22⋊D11)⋊C4C2212yes—
40C2×(C22⋊D11)⋊C4C2214yes—
41C2×C22⋊C4×D11C2212yes—
42C2×C22⋊C4×D11C2212yes—
43C2×#66930C2212yes—
44C2×#66930C2212yes—
45C11×#385C2212yes—
46C11×#385C2212yes—
47C11×#385C2214yescomplemented
48C2×C11×#95C2212yescomplemented
49#10622825C2214yescomplemented
50#10622823C2212yes—
51#10622823C2212yes—
52#10622823C2212yescomplemented
53#10622823C2212yescomplemented
54#10622823C2214yescomplemented
55C2×C11⋊#95C2212yescomplemented
56#10622602C2214yescomplemented
57#10622602C2214yescomplemented
58#10622600C2214yescomplemented
59#10622589C2214yescomplemented
60C4⋊C4×Dic11C2214yescomplemented
61#10622585C2214yescomplemented
62#10622585C2214yescomplemented
63#10622563C2212yes—
64#10622563C2212yes—
65#10622563C2212yescomplemented
66#10622563C2212yescomplemented
67#10622559C2212yes—
68#10622559C2212yes—
69#10622555C2214yescomplemented
70#10622281C2214yescomplemented
71#10622281C2214yescomplemented
72#10622280C2214yescomplemented
73D11×#95C2214yescomplemented
74#10622263C2214yescomplemented
75#10622262C2214yescomplemented
76#10622260C2214yescomplemented
77#10622260C2214yescomplemented
78C25×C11C2311yescharacteristic
79C24×D11C2311yescharacteristic
80C23×C4×C11—24no—
81C23×C4×C11—44no—
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2312yes—
84C23×C4×C11C2312yes—
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2311yescharacteristic
88C23×C4×C11C2312yes—
89C22×C22⋊D11C2×C418yes—
90C22×C22⋊D11D418yes—
91C22×C22⋊D11Q818yes—
92C22×C22⋊D11C2312yes—
93C22×C22⋊D11C2312yes—
94C23×Dic11C2311yescharacteristic
95C23×Dic11C2311yescharacteristic
96C23×Dic11C2311yescharacteristic
97C23×Dic11C2311yescharacteristic
98C23×Dic11C2312yes—
99C23×Dic11C2311yescharacteristic
100C22×C4×D11—24no—
101C22×C4×D11—44no—
102C22×C4×D11C2314yes—
103C22×C4×D11C2312yes—
104C22×C4×D11C2312yes—
105C22×C4×D11C2314yes—
106C2×C11×C4⋊C4—44no—
107C2×C11×C4⋊C4C2314yes—
108C2×C11×C4⋊C4C2314yes—
109C2×C11×C22⋊C4—24no—
110C2×C11×C22⋊C4C2×C418yescomplemented
111C2×C11×C22⋊C4C2312yes—
112C2×C11×C22⋊C4C2312yes—
113C2×C11×C22⋊C4C2312yes—
114C2×C11×C22⋊C4C2312yes—
115C2×C22⋊Dic11—24no—
116C2×C22⋊Dic11—24no—
117C2×C22⋊Dic11C2×C418yescomplemented
118C2×C22⋊Dic11C2312yes—
119C2×C22⋊Dic11C2312yes—
120C2×C22⋊Dic11C2312yes—
121C2×C22⋊Dic11C2312yes—
122C2×C22⋊Dic11C2312yes—
123C2×C22⋊Dic11C2312yes—
124C4×C22⋊D11—28no—
125C4×C22⋊D11—28no—
126C4×C22⋊D11—216no—
127C4×C22⋊D11—216no—
128C4×C22⋊D11C2×C4132yescomplemented
129C2×(C2×D11)⋊C4—24no—
130C2×(C2×D11)⋊C4C2312yes—
131C2×(C2×D11)⋊C4C2312yes—
132C2×(C2×D11)⋊C4C2314yes—
133C2×(C2×D11)⋊C4C2314yes—
134C2×C4⋊Dic11C2314yes—
135C2×C4⋊Dic11C2314yes—
136C2×Dic11⋊C4—24no—
137C2×Dic11⋊C4—44no—
138C2×Dic11⋊C4C2312yes—
139C2×Dic11⋊C4C2312yes—
140C2×Dic11⋊C4C2314yes—
141C2×Dic11⋊C4C2314yes—
142C2×Dic11⋊C4C2314yes—
143C2×Dic11⋊C4C2314yes—
144C2×Dic11⋊C4C2314yes—
145C2×Dic11⋊C4C2314yes—
146C2×C4×Dic11—24no—
147C2×C4×Dic11C2312yes—
148C2×C4×Dic11C2312yes—
149C2×C4×Dic11C2314yes—
150C2×C4×Dic11C2314yes—
151C4⋊C4×D11—48no—
152(C22⋊D11)⋊C4—28no—
153(C22⋊D11)⋊C4—28no—
154(C22⋊D11)⋊C4C2×C4132yescomplemented
155C22⋊C4×D11—28no—
156C22⋊C4×D11C2×C4116yescomplemented
157#66930—28no—
158#66930C2×C4116yescomplemented
159C11×#95C2314yes—
160C11×#95C2314yes—
161C11⋊#95C2314yes—
162C11⋊#95C2314yes—
163C11⋊#95C2314yes—
164C11⋊#95C2314yes—
165C11⋊#95C2314yes—
166C11⋊#95C2314yes—
167#34248—111nomaximal, Sylow
168C24×C11—42no—
169C24×C11—42no—
170C24×C11C22×C414yes—
171C24×C11C2×D414yes—
172C24×C11C2×Q814yes—
173C24×C11C2411yescharacteristic
174C24×C11C2411yescharacteristic
175C24×C11C2411yescharacteristic
176C23×D11—42no—
177C23×D11—42no—
178C23×D11C22×C414yes—
179C23×D11C2×D414yes—
180C23×D11C2×Q814yes—
181C23×D11C2412yes—
182C22×C4×C11—22no—
183C22×C4×C11—24no—
184C22×C4×C11—22no—
185C22×C4×C11—24no—
186C22×C4×C11—24no—
187C22×C4×C11—22no—
188C22×C4×C11—22no—
189C22×C4×C11—24no—
190C22×C4×C11—24no—
191C22×C4×C11—42no—
192C22×C4×C11—42no—
193C22×C4×C11—42no—
194C22×C4×C11—42no—
195C22×C4×C11—42no—
196C22×C4×C11—42no—
197C22×C4×C11—42no—
198C22×C4×C11—416no—
199C22×C4×C11C22×C418yescomplemented
200C22×C4×C11C2412yes—
201C22×C4×C11C2412yes—
202C22×C4×C11C2412yes—
203C22×C4×C11C2414yes—
204C22×C4×C11C2412yes—
205C2×C22⋊D11C4⋊C4164yescomplemented
206C2×C22⋊D11C22×C418yes—
207C2×C22⋊D11C22×C418yes—
208C2×C22⋊D11C2×D418yes—
209C2×C22⋊D11C2×D418yes—
210C2×C22⋊D11C2×Q818yes—
211C2×C22⋊D11C2×Q818yes—
212C22×Dic11—22no—
213C22×Dic11—22no—
214C22×Dic11—22no—
215C22×Dic11—22no—
216C22×Dic11—42no—
217C22×Dic11—42no—
218C22×Dic11—42no—
219C22×Dic11—42no—
220C22×Dic11—42no—
221C22×Dic11—42no—
222C22×Dic11C22×C414yes—
223C22×Dic11C22×C418yescomplemented
224C22×Dic11C2×D414yes—
225C22×Dic11C2×Q814yes—
226C22×Dic11C2412yes—
227C22×Dic11C2412yes—
228C22×Dic11C2412yes—
229C22×Dic11C2412yes—
230C22×Dic11C2414yes—
231C22×Dic11C2412yes—
232C2×C4×D11—28no—
233C2×C4×D11—24no—
234C2×C4×D11—24no—
235C2×C4×D11—28no—
236C2×C4×D11—44no—
237C2×C4×D11—44no—
238C2×C4×D11—44no—
239C2×C4×D11—44no—
240C2×C4×D11—44no—
241C2×C4×D11—416no—
242C2×C4×D11C22×C4116yescomplemented
243C11×C4⋊C4—28no—
244C11×C4⋊C4—44no—
245C11×C22⋊C4—24no—
246C11×C22⋊C4—24no—
247C11×C22⋊C4C22×C418yes—
248C11×C22⋊C4C22×C418yescomplemented
249C22⋊Dic11—24no—
250C22⋊Dic11—24no—
251C22⋊Dic11—24no—
252C22⋊Dic11—24no—
253C22⋊Dic11C22×C418yes—
254C22⋊Dic11C22×C418yescomplemented
255(C2×D11)⋊C4—24no—
256(C2×D11)⋊C4—24no—
257(C2×D11)⋊C4—28no—
258(C2×D11)⋊C4C22×C4116yescomplemented
259C4⋊Dic11—44no—
260C4⋊Dic11—44no—
261Dic11⋊C4—24no—
262Dic11⋊C4—24no—
263Dic11⋊C4—28no—
264Dic11⋊C4—28no—
265Dic11⋊C4—44no—
266Dic11⋊C4—44no—
267Dic11⋊C4—44no—
268Dic11⋊C4C22×C4116yescomplemented
269C4×Dic11—24no—
270C4×Dic11—24no—
271C4×Dic11—28no—
272C4×Dic11C22×C4116yescomplemented
273C2×#518—111no—
274C2×#518—111no—
275C22×C4×D4—111no—
276#2349—114no—
277#2349—114no—
278D4×C4⋊C4—114no—
279D4×C4⋊C4—114no—
280#2317—112no—
281#2315—112no—
282#2315—111no—
283#2315—111no—
284#2296—112no—
285C2×#385—112no—
286C2×#385—111no—
287C2×#385D1111yescharacteristic, complemented
288C23×C11—22no—
289C23×C11—22no—
290C23×C11—22no—
291C23×C11—22no—
292C23×C11—22no—
293C23×C11—22no—
294C23×C11—44no—
295C23×C11—48no—
296C23×C11—44no—
297C23×C11—48no—
298C23×C11C2×C4⋊C4116yescomplemented
299C23×C11C23×C412yes—
300C23×C11C23×C412yes—
301C23×C11C23×C412yes—
302C23×C11C22×D412yes—
303C23×C11C22×D412yes—
304C23×C11C22×D412yes—
305C23×C11C22×Q812yes—
306C23×C11C22×Q812yes—
307C23×C11C22×Q812yes—
308C23×C11C2511yescharacteristic
309C22×D11—24no—
310C22×D11—24no—
311C22×D11—44no—
312C22×D11—48no—
313C22×D11—44no—
314C22×D11—48no—
315C22×D11C2×C4⋊C4116yescomplemented
316C22×D11C23×C414yes—
317C22×D11C22×D414yes—
318C22×D11C22×Q814yes—
319C2×C4×C11—28no—
320C2×C4×C11—22no—
321C2×C4×C11—24no—
322C2×C4×C11—22no—
323C2×C4×C11—24no—
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—22no—
327C2×C4×C11—22no—
328C2×C4×C11—24no—
329C2×C4×C11—22no—
330C2×C4×C11—24no—
331C2×C4×C11—48no—
332C2×C4×C11—48no—
333C2×C4×C11—48no—
334C2×C4×C11—44no—
335C2×C4×C11—82no—
336C2×C4×C11—82no—
337C2×C4×C11C23×C418yes—
338C2×C4×C11H(5,𝔽2)14yes—
339C22⋊D11C2×C4⋊C4132yescomplemented
340C22⋊D11C2×C4⋊C4132yescomplemented
341C2×Dic11—24no—
342C2×Dic11—24no—
343C2×Dic11—22no—
344C2×Dic11—22no—
345C2×Dic11—22no—
346C2×Dic11—22no—
347C2×Dic11—24no—
348C2×Dic11—24no—
349C2×Dic11—24no—
350C2×Dic11—24no—
351C2×Dic11—48no—
352C2×Dic11—44no—
353C2×Dic11—44no—
354C2×Dic11—82no—
355C2×Dic11—82no—
356C2×Dic11C2×C4⋊C4116yescomplemented
357C2×Dic11C23×C418yes—
358C2×Dic11C23×C414yes—
359C2×Dic11C22×D414yes—
360C2×Dic11C22×Q814yes—
361C4×D11—416no—
362C4×D11—416no—
363C4×D11—84no—
364C4×D11—84no—
365C23×D4—111no—
366C24×C4—111no—
367C24×C4C2×D1111yescharacteristic
368#518—1116no—
369#518—228no—
370C2×C4×D4—114no—
371C2×C4×D4—112no—
372C2×C4×D4—114no—
373C2×C4×D4—114no—
374C2×C4×D4—112no—
375C2×C4×D4—114no—
376C2×C4×D4—112no—
377C2×C4×D4—112no—
378C2×C4×D4—228no—
379C2×#117—112no—
380C2×#117—112no—
381C22×C4⋊C4—111no—
382C22×C4⋊C4—112no—
383C22×C4⋊C4—114no—
384C22×C4⋊C4C2×D1112yescomplemented
385C22×C22⋊C4—111no—
386C22×C22⋊C4—112no—
387C22×C22⋊C4—111no—
388C22×C22⋊C4—111no—
389C22×C22⋊C4—111no—
390C22×C22⋊C4—112no—
391C22×C22⋊C4C2×D1111yescharacteristic
392C22×C22⋊C4C2×D1111yescharacteristic
393C22×C42—111no—
394#389—114no—
395#389—114no—
396#389—114no—
397#389—114no—
398#385—112no—
399#385—112no—
400#385—112no—
401#385—114no—
402#385—112no—
403#385—114no—
404#385—114no—
405#385—112no—
406#385—112no—
407#385—112no—
408#385—112no—
409#385—112no—
410#385—112no—
411#385—114no—
412#385—114no—
413#385C2×D1112yes—
414#385C2×D1112yes—
415#385C2×D1114yescomplemented
416#384—114no—
417#382—114no—
418#380—114no—
419#380—114no—
420#380—114no—
421#380—114no—
422C4×C4⋊C4—114no—
423C4×C4⋊C4—114no—
424C2×#95—112no—
425C2×#95—114no—
426C2×#95C2×D1112yescomplemented
427C22×C11—24no—
428C22×C11—24no—
429C22×C11—24no—
430C22×C11—22no—
431C22×C11—22no—
432C22×C11—22no—
433C22×C11—22no—
434C22×C11—22no—
435C22×C11—22no—
436C22×C11—24no—
437C22×C11—24no—
438C22×C11—24no—
439C22×C11—416no—
440C22×C11C22×C4⋊C414yes—
441C22×C11C22×C4⋊C414yes—
442C22×C11C22×C4⋊C414yes—
443C22×C11C24×C411yescharacteristic
444C22×C11C23×D411yescharacteristic
445C22×C11C23×Q811yescharacteristic
446C22×C11C2×H(5,𝔽2)12yes—
447C22×C11#58512yes—
448C2×D11—28no—
449C2×D11—24no—
450C2×D11—24no—
451C2×D11—28no—
452C2×D11—416no—
453C2×D11C22×C4⋊C418yes—
454C4×C11—28no—
455C4×C11—24no—
456C4×C11—42no—
457C4×C11—42no—
458C4×C11—42no—
459Dic11—28no—
460Dic11—42no—
461Dic11—42no—
462Dic11—42no—
463Dic11—42no—
464Dic11C22×C4⋊C418yes—
465C25—111no—
466C25C22×D1111yescharacteristic
467C22×D4—118no—
468C22×D4—118no—
469C22×D4—118no—
470C22×D4—112no—
471C22×D4—112no—
472C23×C4—24no—
473C23×C4—44no—
474C23×C4—111no—
475C23×C4—112no—
476C23×C4—114no—
477C23×C4—111no—
478C23×C4—111no—
479C23×C4—111no—
480C23×C4—111no—
481C23×C4—114no—
482C23×C4—112no—
483C23×C4—112no—
484C23×C4—224no—
485C23×C4—444no—
486C23×C4C22×D1111yescharacteristic
487C23×C4C22×D1112yes—
488C23×C4C22×D1112yes—
489C23×C4C22×D1111yescharacteristic
490C23×C4C22×D1111yescharacteristic
491C23×C4C22×D1111yescharacteristic
492C23×C4C22×D1112yes—
493C4×D4—1132no—
494C4×D4—1132no—
495C4×D4—228no—
496C4×D4—228no—
497C4×D4—2216no—
498C4×D4—2216no—
499C4×D4—228no—
500C4×D4—228no—
501#117—1116no—
502#117—228no—
503C2×C4⋊C4—44no—
504C2×C4⋊C4—114no—
505C2×C4⋊C4—114no—
506C2×C4⋊C4—114no—
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—114no—
514C2×C4⋊C4—224no—
515C2×C4⋊C4—448no—
516C2×C4⋊C4—444no—
517C2×C4⋊C4C22×D1114yes—
518C2×C4⋊C4C22×D1114yes—
519C2×C22⋊C4—24no—
520C2×C22⋊C4—118no—
521C2×C22⋊C4—112no—
522C2×C22⋊C4—112no—
523C2×C22⋊C4—114no—
524C2×C22⋊C4—1116no—
525C2×C22⋊C4—112no—
526C2×C22⋊C4—112no—
527C2×C22⋊C4—112no—
528C2×C22⋊C4—112no—
529C2×C22⋊C4—112no—
530C2×C22⋊C4—114no—
531C2×C22⋊C4—112no—
532C2×C22⋊C4—228no—
533C2×C22⋊C4—224no—
534C2×C22⋊C4—224no—
535C2×C22⋊C4—224no—
536C2×C22⋊C4C4×D1118yescomplemented
537C2×C22⋊C4C22×D1112yes—
538C2×C22⋊C4C22×D1112yes—
539C2×C22⋊C4C22×D1112yes—
540C2×C22⋊C4C22×D1112yes—
541C2×C42—114no—
542C2×C42—112no—
543C2×C42—112no—
544C2×C42—114no—
545C2×C42—224no—
546#95—114no—
547#95—114no—
548#95—114no—
549#95—114no—
550#95—114no—
551#95—114no—
552#95C22×D1114yes—
553#95C22×D1114yes—
554C2×C11—24no—
555C2×C11—24no—
556C2×C11—24no—
557C2×C11C23×C4⋊C411yescharacteristic
558C2×C11C4×H(5,𝔽2)12yes—
559C2×C11#348411yescharacteristic
560C2×C11#348511yescharacteristic
561C2×C11#350112yes—
562D11—28no—
563C24—42no—
564C24—42no—
565C24—112no—
566C24—114no—
567C24—114no—
568C24—114no—
569C24—442no—
570C24—442no—
571C24C2×C4×D1114yes—
572C24D4×D1114yes—
573C24Q8×D1114yes—
574C24C23×D1111yescharacteristic
575C24C23×D1111yescharacteristic
576C24C23×D1111yescharacteristic
577C2×D4—1164no—
578C2×D4—118no—
579C2×D4—118no—
580C2×D4—118no—
581C2×D4—118no—
582C2×D4—118no—
583C2×D4—118no—
584C22×C4—22no—
585C22×C4—24no—
586C22×C4—22no—
587C22×C4—24no—
588C22×C4—24no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—24no—
592C22×C4—24no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—416no—
601C22×C4—114no—
602C22×C4—114no—
603C22×C4—114no—
604C22×C4—112no—
605C22×C4—114no—
606C22×C4—118no—
607C22×C4—1116no—
608C22×C4—112no—
609C22×C4—112no—
610C22×C4—112no—
611C22×C4—112no—
612C22×C4—228no—
613C22×C4—224no—
614C22×C4—224no—
615C22×C4—222no—
616C22×C4—222no—
617C22×C4—222no—
618C22×C4—222no—
619C22×C4—228no—
620C22×C4—444no—
621C22×C4—444no—
622C22×C4—444no—
623C22×C4—444no—
624C22×C4—444no—
625C22×C4—4416no—
626C22×C4—442no—
627C22×C4—442no—
628C22×C4—442no—
629C22×C4—442no—
630C22×C4—442no—
631C22×C4—442no—
632C22×C4C2×C4×D1118yescomplemented
633C22×C4C23×D1112yes—
634C22×C4C23×D1112yes—
635C22×C4C23×D1112yes—
636C22×C4C23×D1114yes—
637C22×C4C23×D1112yes—
638C4⋊C4—28no—
639C4⋊C4—44no—
640C4⋊C4—1116no—
641C4⋊C4—228no—
642C4⋊C4—224no—
643C4⋊C4—224no—
644C4⋊C4—228no—
645C4⋊C4—444no—
646C4⋊C4—444no—
647C4⋊C4—444no—
648C4⋊C4—444no—
649C4⋊C4—444no—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—118no—
653C22⋊C4—118no—
654C22⋊C4—1116no—
655C22⋊C4—224no—
656C22⋊C4—224no—
657C22⋊C4—228no—
658C22⋊C4—224no—
659C22⋊C4—224no—
660C22⋊C4—224no—
661C22⋊C4—224no—
662C22⋊C4C2×C4×D1118yes—
663C22⋊C4C2×C4×D1118yescomplemented
664C42—1116no—
665C42—228no—
666C42—224no—
667C42—224no—
668C11#3424811yescharacteristic, complemented, Sylow
669C23—22no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—44no—
676C23—48no—
677C23—44no—
678C23—48no—
679C23—114no—
680C23—114no—
681C23—114no—
682C23—1116no—
683C23—224no—
684C23—224no—
685C23—444no—
686C23—448no—
687C23—444no—
688C23—448no—
689C23C4⋊C4×D11116yescomplemented
690C23C22×C4×D1112yes—
691C23C22×C4×D1112yes—
692C23C22×C4×D1112yes—
693C23C2×D4×D1112yes—
694C23C2×D4×D1112yes—
695C23C2×D4×D1112yes—
696C23C2×Q8×D1112yes—
697C23C2×Q8×D1112yes—
698C23C2×Q8×D1112yes—
699C23C24×D1111yescharacteristic
700D4—1132no—
701D4—1132no—
702C2×C4—28no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—22no—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—48no—
715C2×C4—48no—
716C2×C4—48no—
717C2×C4—44no—
718C2×C4—82no—
719C2×C4—82no—
720C2×C4—1116no—
721C2×C4—114no—
722C2×C4—114no—
723C2×C4—114no—
724C2×C4—118no—
725C2×C4—224no—
726C2×C4—224no—
727C2×C4—222no—
728C2×C4—222no—
729C2×C4—222no—
730C2×C4—222no—
731C2×C4—224no—
732C2×C4—224no—
733C2×C4—224no—
734C2×C4—224no—
735C2×C4—4416no—
736C2×C4—4416no—
737C2×C4—448no—
738C2×C4—444no—
739C2×C4—444no—
740C2×C4—884no—
741C2×C4—884no—
742C2×C4—882no—
743C2×C4—882no—
744C2×C4C22×C4×D1118yes—
745C2×C4#6703714yes—
746C22—24no—
747C22—24no—
748C22—24no—
749C22—22no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—24no—
756C22—24no—
757C22—24no—
758C22—416no—
759C22—118no—
760C22—228no—
761C22—224no—
762C22—224no—
763C22—228no—
764C22—4416no—
765C22C2×C4⋊C4×D1114yes—
766C22C2×C4⋊C4×D1114yes—
767C22C2×C4⋊C4×D1114yes—
768C22C23×C4×D1111yescharacteristic
769C22C22×D4×D1111yescharacteristic
770C22C2×#6703712yes—
771C22C22×Q8×D1111yescharacteristic
772C22#1062345312yes—
773C4—24no—
774C4—28no—
775C4—42no—
776C4—42no—
777C4—42no—
778C4—118no—
779C4—228no—
780C4—442no—
781C4—442no—
782C4—442no—
783C4—442no—
784C2—24no—
785C2—24no—
786C2—24no—
787C2—228no—
788C2C22×C4⋊C4×D1111yescharacteristic
789C2C4×#6703712yes—
790C2#1308224511yescharacteristic
791C2#1308225411yescharacteristic
792C2#1308241212yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC2×C11×#385C2
socle, cosocleC23×C11C25
prime radicalC23×C22⋊D11C22
hypercenterC2×#385D11
hypocenterC11#34248
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
4. #13071523C2semidirect
5. #13071522C2semidirect
6. C4⋊C4×C22⋊D11C2semidirect
7. #13071514C2semidirect
8. #13071235C2semidirect
9. #13071230C2semidirect
10. #13071228C2semidirect
11. #13071227C2semidirect
12. #13071095C2semidirect
13. C2×#10622823C2semidirect
14. D11×#385C2semidirect
15. C2×C11×#385C2semidirect
19. C22×C11×C4⋊C4C22semidirect
33. C22×Dic11⋊C4C22semidirect
35. C2×C4⋊C4×D11C22semidirect
37. #10623017C4semidirect
47. C11×#385C22semidirect
48. C2×C11×#95C22semidirect
49. #10622825C22semidirect
52. #10622823C22semidirect
53. #10622823C22semidirect
54. #10622823C22semidirect
55. C2×C11⋊#95C22semidirect
56. #10622602C22semidirect
57. #10622602C22semidirect
58. #10622600C22semidirect
59. #10622589C22semidirect
60. C4⋊C4×Dic11C22semidirect
61. #10622585C22semidirect
62. #10622585C22semidirect
65. #10622563C22semidirect
66. #10622563C22semidirect
69. #10622555C22semidirect
70. #10622281C22semidirect
71. #10622281C22semidirect
72. #10622280C22semidirect
73. D11×#95C22semidirect
74. #10622263C22semidirect
75. #10622262C22semidirect
76. #10622260C22semidirect
77. #10622260C22semidirect
110. C2×C11×C22⋊C4C2×C4semidirect
117. C2×C22⋊Dic11C2×C4semidirect
128. C4×C22⋊D11C2×C4semidirect
154. (C22⋊D11)⋊C4C2×C4semidirect
156. C22⋊C4×D11C2×C4semidirect
158. #66930C2×C4semidirect
199. C22×C4×C11C22×C4semidirect
205. C2×C22⋊D11C4⋊C4semidirect
223. C22×Dic11C22×C4semidirect
242. C2×C4×D11C22×C4semidirect
248. C11×C22⋊C4C22×C4semidirect
254. C22⋊Dic11C22×C4semidirect
258. (C2×D11)⋊C4C22×C4semidirect
268. Dic11⋊C4C22×C4semidirect
272. C4×Dic11C22×C4semidirect
287. C2×#385D11semidirect
298. C23×C11C2×C4⋊C4semidirect
315. C22×D11C2×C4⋊C4semidirect
339. C22⋊D11C2×C4⋊C4semidirect
340. C22⋊D11C2×C4⋊C4semidirect
356. C2×Dic11C2×C4⋊C4semidirect
384. C22×C4⋊C4C2×D11semidirect
415. #385C2×D11semidirect
426. C2×#95C2×D11semidirect
536. C2×C22⋊C4C4×D11semidirect
632. C22×C4C2×C4×D11semidirect
663. C22⋊C4C2×C4×D11semidirect
668. C11#34248semidirect
689. C23C4⋊C4×D11semidirect

Maximal subgroups

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

subgroupindex
C2×#106230172
C22×C4×C22⋊D112
#130715232
#130715222
C4⋊C4×C22⋊D112
#130715142
#130712352
#130712302
#130712282
#130712272
#130710952
C2×#106228232
D11×#3852
C2×C11×#3852
#3424811