Finite Group Databasebeta

← #14770061

Subgroups — #14770061

Order 2816.

1194 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622624C211yesmaximal, characteristic
2D4×C4⋊Dic11C211yesmaximal, characteristic
3#13069586C211yesmaximal, characteristic, complemented
4#13069574C211yesmaximal, characteristic, complemented
5#13069050C211yesmaximal, characteristic, complemented
6#13069040C211yesmaximal, characteristic, complemented
7#13068924C211yesmaximal, characteristic, complemented
8#13068924C211yesmaximal, characteristic, complemented
9#13068711C211yesmaximal, characteristic, complemented
10#13068702C211yesmaximal, characteristic, complemented
11#13068621C211yesmaximal, characteristic, complemented
12#13068446C211yesmaximal, characteristic, complemented
13#13068337C211yesmaximal, characteristic, complemented
14C2×#10622167C211yesmaximal, characteristic, complemented
15C2×C11×#552C211yesmaximal, characteristic
16C11×#552—24no—
17C11×#552C418yescomplemented
18C2×C11×#126—21no—
19C2×C11×#125—21no—
20C2×C11×#125C2211yescharacteristic
21C2×C11×#123—21no—
22C2×C11×C22⋊Q8C2211yescharacteristic
23C2×C11×C22⋊Q8C2211yescharacteristic
24C2×C4×Q8×C11C2211yescharacteristic
25C2×C4×D4×C11C2211yescharacteristic
26C2×C11×#117—21no—
27C2×C11×#117C2211yescharacteristic
28C22×C11×C4⋊C4C2211yescharacteristic
29C2×D4×Dic11—21no—
30C22×C4⋊Dic11C2211yescharacteristic
31C22×C4⋊Dic11C2211yescharacteristic
32C22×#4318C2211yescharacteristic
33C23×C11⋊C8C2211yescharacteristic
34C2×#66899C2211yescharacteristic
35C2×#66899C2211yescharacteristic
36C2×#66899C2211yescharacteristic
37C2×#66899C2211yescharacteristic
38#10622825C2211yescharacteristic
39#10622825C2211yescharacteristic
40C2×C22⋊(C11⋊C8)C2211yescharacteristic
41C2×C22⋊(C11⋊C8)C2211yescharacteristic
42#10622624—24no—
43#10622598—21no—
44#10622563—21no—
45#10622563—21no—
46#10622548C2211yescharacteristic
47C4×C4⋊Dic11C2211yescharacteristic
48C2×C4⋊(C11⋊C8)C2211yescharacteristic
49C2×#66867C2211yescharacteristic
50#10622167C2211yescharacteristic
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C22×D4×C11D411yescharacteristic
64C23×C4×C11—21no—
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×Dic11—21no—
68C23×Dic11—21no—
69C11×#126—28no—
70C11×#125—28no—
71C11×#125—22no—
72C11×#125C2×C414yescomplemented
73C11×#123—28no—
74C11×C22⋊Q8—22no—
75C11×C22⋊Q8—22no—
76C11×C22⋊Q8C2×C414yescomplemented
77C11×C22⋊Q8C2×C414yescomplemented
78C4×Q8×C11—22no—
79C4×Q8×C11C2×C414yescomplemented
80C4×D4×C11C2×C414yes—
81C4×D4×C11D414yes—
82C11×#117—22no—
83C11×#117—28no—
84C11×#117C2×C414yescomplemented
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4—22no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4C2×C414yescomplemented
93C2×C11×C4⋊C4D411yescharacteristic
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C22⋊C4—21no—
98C2×C11×C22⋊C4—21no—
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4D411yescharacteristic
101C2×C11×C22⋊C4D411yescharacteristic
102C2×C42×C11—21no—
103C2×C42×C11—21no—
104C2×C42×C11C2311yescharacteristic
105C2×C22⋊Dic11—21no—
106C2×C22⋊Dic11—21no—
107D4×Dic11—44no—
108C2×C4⋊Dic11—22no—
109C2×C4⋊Dic11—22no—
110C2×C4⋊Dic11—21no—
111C2×C4⋊Dic11—21no—
112C2×C4⋊Dic11—21no—
113C2×C4⋊Dic11—21no—
114C2×C4⋊Dic11—41no—
115C2×C4⋊Dic11—41no—
116C2×C4⋊Dic11C2311yescharacteristic
117C2×C4⋊Dic11C2311yescharacteristic
118C2×C4⋊Dic11C2311yescharacteristic
119C2×C4⋊Dic11C2311yescharacteristic
120C2×C4×Dic11—21no—
121C2×#4318—22no—
122C2×#4318—22no—
123C2×#4318—41no—
124C22×C11⋊C8—22no—
125C22×C11⋊C8—22no—
126C22×C11⋊C8—41no—
127C22×C11⋊C8C2311yescharacteristic
128C22×C11⋊C8C2311yescharacteristic
129C22×C11⋊C8C2311yescharacteristic
130C22×C11⋊C8C2311yescharacteristic
131#66899—22no—
132#66899—22no—
133#66899—41no—
134#66899—41no—
135C11⋊#95—21no—
136C11⋊#95—21no—
137C11⋊#95—21no—
138C22⋊(C11⋊C8)—22no—
139C22⋊(C11⋊C8)—22no—
140C4⋊(C11⋊C8)—22no—
141#66867—22no—
142#22491—111nomaximal, Sylow
143C24×C11C2×D411yescharacteristic
144C24×C11C2×D411yescharacteristic
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11C22×C412yes—
151C2×D4×C11—22no—
152C2×D4×C11—22no—
153C2×D4×C11C22⋊C414yes—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—24no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—42no—
168C22×C4×C11—42no—
169C22×C4×C11C22×C412yes—
170C22×C4×C11C22×C412yes—
171C22×C4×C11C2×D411yescharacteristic
172C22×C4×C11C2×D411yescharacteristic
173C22×C4×C11C2×D411yescharacteristic
174C22×C4×C11C2×D411yescharacteristic
175C22×C4×C11C2×D412yes—
176C22×C4×C11C2×D412yes—
177C22×C4×C11C2411yescharacteristic
178C22×Dic11—21no—
179C22×Dic11—21no—
180C22×Dic11—21no—
181C22×Dic11—21no—
182C22×Dic11—42no—
183C22×Dic11—42no—
184C22×Dic11—42no—
185C22×Dic11—42no—
186C22×Dic11—81no—
187C22×Dic11—81no—
188C11×C4⋊C4—24no—
189C11×C4⋊C4—24no—
190C11×C4⋊C4—24no—
191C11×C4⋊C4—24no—
192C11×C4⋊C4—24no—
193C11×C4⋊C4—24no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4C22⋊C414yes—
198C11×C4⋊C4C22×C412yes—
199C11×C4⋊C4C22×C412yes—
200C11×C4⋊C4C22×C412yes—
201C11×C22⋊C4—24no—
202C11×C22⋊C4—24no—
203C11×C22⋊C4—24no—
204C11×C22⋊C4C22⋊C414yes—
205C11×C22⋊C4C22⋊C414yes—
206C42×C11—24no—
207C42×C11—24no—
208C42×C11C22×C412yes—
209C42×C11C2×D412yes—
210C22⋊Dic11—42no—
211C22⋊Dic11—42no—
212C4⋊Dic11—21no—
213C4⋊Dic11—21no—
214C4⋊Dic11—21no—
215C4⋊Dic11—21no—
216C4⋊Dic11—21no—
217C4⋊Dic11—21no—
218C4⋊Dic11—21no—
219C4⋊Dic11—42no—
220C4⋊Dic11—42no—
221C4⋊Dic11—42no—
222C4⋊Dic11—81no—
223C4⋊Dic11#4112yes—
224C4×Dic11—42no—
225#4318—44no—
226C2×C11⋊C8—21no—
227C2×C11⋊C8—21no—
228C2×C11⋊C8—21no—
229C2×C11⋊C8—21no—
230C2×C11⋊C8—21no—
231C2×C11⋊C8—21no—
232C2×C11⋊C8—21no—
233C2×C11⋊C8—21no—
234C2×C11⋊C8—21no—
235C2×C11⋊C8—21no—
236C2×C11⋊C8—21no—
237C2×C11⋊C8—44no—
238C2×C11⋊C8#4112yes—
239C2×#552D1111yescharacteristic
240C2×#435—111no—
241D4×C4⋊C4—111no—
242#1992—111no—
243#1989—111no—
244#1894—111no—
245#1892—111no—
246#1872—111no—
247#1872—111no—
248#1825—111no—
249#1823—111no—
250#1803—111no—
251#1763—111no—
252#1736—111no—
253C2×#340—111no—
254C23×C11—21no—
255C23×C11—21no—
256C23×C11—21no—
257C23×C11—21no—
258C23×C11—21no—
259C23×C11—21no—
260C23×C11—21no—
261C23×C11—21no—
262C23×C11—21no—
263C23×C11—21no—
264C23×C11C2×C22⋊C412yes—
265C23×C11C2×C22⋊C412yes—
266C23×C11AGL(1,ℤ/8)12yes—
267C23×C11#13712yes—
268C23×C11C22×D411yescharacteristic
269Q8×C11—22no—
270Q8×C11—22no—
271Q8×C11—41no—
272Q8×C11—41no—
273D4×C11—28no—
274C2×C4×C11—21no—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
277C2×C4×C11—21no—
278C2×C4×C11—21no—
279C2×C4×C11—21no—
280C2×C4×C11—21no—
281C2×C4×C11—21no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—41no—
295C2×C4×C11—41no—
296C2×C4×C11—41no—
297C2×C4×C11—41no—
298C2×C4×C11—41no—
299C2×C4×C11—41no—
300C2×C4×C11—41no—
301C2×C4×C11—41no—
302C2×C4×C11—48no—
303C2×C4×C11C2×C22⋊C412yes—
304C2×C4×C11C2×C22⋊C412yes—
305C2×C4×C11C2×C22⋊C412yes—
306C2×C4×C11C2×C22⋊C412yes—
307C2×C4×C11C23×C411yescharacteristic
308C2×C4×C11C22×D411yescharacteristic
309C2×C4×C11C2×#4111yescharacteristic
310C2×C4×C11C2×#4111yescharacteristic
311C2×C4×C11H(5,𝔽2)11yescharacteristic
312C2×C4×C112−1+411yescharacteristic
313C2×Dic11—22no—
314C2×Dic11—41no—
315C2×Dic11—41no—
316C2×Dic11—41no—
317C2×Dic11—41no—
318C2×Dic11—41no—
319C2×Dic11—41no—
320C2×Dic11—41no—
321C2×Dic11—41no—
322C2×Dic11—41no—
323C2×Dic11—41no—
324C2×Dic11—41no—
325C2×Dic11—84no—
326C2×Dic11—84no—
327C11⋊C8—22no—
328C11⋊C8—41no—
329C11⋊C8—41no—
330C11⋊C8—41no—
331C22×M16—111no—
332C23×C8—111no—
333#552—24no—
334#552Dic1118yescomplemented
335C2×#126—21no—
336C2×#125—21no—
337C2×#125C2×D1111yescharacteristic
338C2×#123—21no—
339C2×C22⋊Q8C2×D1111yescharacteristic
340C2×C22⋊Q8C2×D1111yescharacteristic
341C2×C4×Q8C2×D1111yescharacteristic
342C2×C4×D4—221no—
343C2×C4×D4C2×D1111yescharacteristic
344C2×#117—21no—
345C2×#117C2×D1111yescharacteristic
346C22×C4⋊C4—111no—
347C22×C4⋊C4—111no—
348C22×C4⋊C4C2×D1111yescharacteristic
349#435—224no—
350C2×C4⋊C8—111no—
351C2×#103—111no—
352C2×#103—111no—
353C2×#103—111no—
354C2×#103—111no—
355C2×C22⋊C8—111no—
356C2×C22⋊C8—111no—
357C2×#97—111no—
358#389—221no—
359#385—221no—
360#385—221no—
361#384—111no—
362#380—111no—
363#380—111no—
364C4×C4⋊C4—111no—
365#340—111no—
366#340—111no—
367#340—111no—
368#340—111no—
369#340—111no—
370#340—111no—
371#340—111no—
372#340—111no—
373#340—111no—
374#340—111no—
375#340—111no—
376#340—111no—
377C22×C11—22no—
378C22×C11—22no—
379C22×C11—22no—
380C22×C11—22no—
381C22×C11—22no—
382C22×C11—22no—
383C22×C11—22no—
384C22×C11—22no—
385C22×C11—22no—
386C22×C11—41no—
387C22×C11—41no—
388C22×C11—41no—
389C22×C11—41no—
390C22×C11#41714yes—
391C22×C11C22×C22⋊C411yescharacteristic
392C22×C11#54611yescharacteristic
393C22×C11#54711yescharacteristic
394C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
395C22×C11C2×#13711yescharacteristic
396C22×C11#57711yescharacteristic
397C22×C11#57811yescharacteristic
398C4×C11—22no—
399C4×C11—22no—
400C4×C11—22no—
401C4×C11—22no—
402C4×C11—42no—
403C4×C11—42no—
404C4×C11—42no—
405C4×C11—42no—
406C4×C11C4×#4111yescharacteristic
407C4×C11#52011yescharacteristic
408C4×C11#54611yescharacteristic
409C4×C11#54711yescharacteristic
410Dic11—42no—
411Dic11—81no—
412Dic11—81no—
413Dic11—81no—
414C22×Q8C22×D1111yescharacteristic
415C22×D4C22⋊D1111yescharacteristic
416C23×C4—21no—
417C23×C4—221no—
418C23×C4—221no—
419C23×C4C22×D1111yescharacteristic
420C23×C4C22×D1111yescharacteristic
421C2×M16—222no—
422C2×M16—222no—
423C2×M16—441no—
424C22×C8—111no—
425C22×C8—111no—
426C22×C8—111no—
427C22×C8—111no—
428C22×C8—222no—
429C22×C8—222no—
430C22×C8—441no—
431#126—28no—
432#125—28no—
433#125—22no—
434#125C2×Dic1114yescomplemented
435#123—28no—
436C22⋊Q8—22no—
437C22⋊Q8—22no—
438C22⋊Q8C2×Dic1114yescomplemented
439C22⋊Q8C2×Dic1114yescomplemented
440C4×Q8—22no—
441C4×Q8C2×Dic1114yescomplemented
442C4×D4—444no—
443C4×D4C2×Dic1114yes—
444C4×D4C22⋊D1114yes—
445#117—22no—
446#117—28no—
447#117C2×Dic1114yescomplemented
448C2×C4⋊C4—21no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—111no—
456C2×C4⋊C4—111no—
457C2×C4⋊C4—111no—
458C2×C4⋊C4—111no—
459C2×C4⋊C4—222no—
460C2×C4⋊C4—222no—
461C2×C4⋊C4—221no—
462C2×C4⋊C4—221no—
463C2×C4⋊C4—221no—
464C2×C4⋊C4—221no—
465C2×C4⋊C4—441no—
466C2×C4⋊C4—441no—
467C2×C4⋊C4C2×Dic1114yescomplemented
468C2×C4⋊C4C22⋊D1111yescharacteristic
469C2×C4⋊C4C22×D1111yescharacteristic
470C2×C4⋊C4C22×D1111yescharacteristic
471C2×C4⋊C4C22×D1111yescharacteristic
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—221no—
476C2×C22⋊C4—221no—
477C2×C22⋊C4C22⋊D1111yescharacteristic
478C2×C22⋊C4C22⋊D1111yescharacteristic
479C2×C42—21no—
480C2×C42—21no—
481C2×C42—221no—
482C2×C42C22×D1111yescharacteristic
483C4⋊C8—222no—
484#103—222no—
485#103—222no—
486#103—441no—
487#103—441no—
488C22⋊C8—222no—
489C22⋊C8—222no—
490#97—222no—
491#95—221no—
492#95—221no—
493#95—221no—
494C2×C11—24no—
495C2×C11—42no—
496C2×C11#233911yescharacteristic
497C2×C11C2×#41711yescharacteristic
498C2×C11#289811yescharacteristic
499C2×C11#331011yescharacteristic
500C2×C11#331211yescharacteristic
501C2×C11#334311yescharacteristic
502C2×C11#334411yescharacteristic
503C24C2×C22⋊D1111yescharacteristic
504C24C2×C22⋊D1111yescharacteristic
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8C22×Dic1112yes—
511C2×D4—22no—
512C2×D4—22no—
513C2×D4C22⋊Dic1114yes—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—24no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—221no—
530C22×C4—221no—
531C22×C4—221no—
532C22×C4—221no—
533C22×C4—442no—
534C22×C4—442no—
535C22×C4—442no—
536C22×C4—442no—
537C22×C4—881no—
538C22×C4—881no—
539C22×C4C22×Dic1112yes—
540C22×C4C22×Dic1112yes—
541C22×C4C2×C22⋊D1111yescharacteristic
542C22×C4C2×C22⋊D1111yescharacteristic
543C22×C4C2×C22⋊D1111yescharacteristic
544C22×C4C2×C22⋊D1111yescharacteristic
545C22×C4C2×C22⋊D1112yes—
546C22×C4C2×C22⋊D1112yes—
547C22×C4C23×D1111yescharacteristic
548M16—444no—
549C2×C8—112no—
550C2×C8—221no—
551C2×C8—221no—
552C2×C8—221no—
553C2×C8—221no—
554C2×C8—221no—
555C2×C8—221no—
556C2×C8—221no—
557C2×C8—221no—
558C2×C8—221no—
559C2×C8—221no—
560C2×C8—221no—
561C2×C8—444no—
562C4⋊C4—24no—
563C4⋊C4—24no—
564C4⋊C4—24no—
565C4⋊C4—24no—
566C4⋊C4—24no—
567C4⋊C4—24no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—112no—
572C4⋊C4—221no—
573C4⋊C4—221no—
574C4⋊C4—221no—
575C4⋊C4—221no—
576C4⋊C4—221no—
577C4⋊C4—221no—
578C4⋊C4—221no—
579C4⋊C4—442no—
580C4⋊C4—442no—
581C4⋊C4—442no—
582C4⋊C4—881no—
583C4⋊C4C22⋊Dic1114yes—
584C4⋊C4C22×Dic1112yes—
585C4⋊C4C22×Dic1112yes—
586C4⋊C4C22×Dic1112yes—
587C22⋊C4—24no—
588C22⋊C4—24no—
589C22⋊C4—24no—
590C22⋊C4—442no—
591C22⋊C4—442no—
592C22⋊C4C22⋊Dic1114yes—
593C22⋊C4C22⋊Dic1114yes—
594C42—24no—
595C42—24no—
596C42—442no—
597C42C22×Dic1112yes—
598C42C2×C22⋊D1112yes—
599C11#2249111yescharacteristic, complemented, Sylow
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23#6700212yes—
611C23#6700412yes—
612C23C2×C22⋊Dic1112yes—
613C23C2×C22⋊Dic1112yes—
614C23C22×C22⋊D1111yescharacteristic
615Q8—22no—
616Q8—22no—
617Q8—41no—
618Q8—41no—
619D4—28no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—48no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—222no—
650C2×C4—441no—
651C2×C4—441no—
652C2×C4—441no—
653C2×C4—441no—
654C2×C4—441no—
655C2×C4—441no—
656C2×C4—441no—
657C2×C4—441no—
658C2×C4—441no—
659C2×C4—441no—
660C2×C4—441no—
661C2×C4—884no—
662C2×C4—884no—
663C2×C4C2×C22⋊Dic1112yes—
664C2×C4C2×C22⋊Dic1112yes—
665C2×C4C2×C22⋊Dic1112yes—
666C2×C4C2×C22⋊Dic1112yes—
667C2×C4#41×D1111yescharacteristic
668C2×C4#41×D1111yescharacteristic
669C2×C4#6704211yescharacteristic
670C2×C4#6704311yescharacteristic
671C2×C4C23×Dic1111yescharacteristic
672C2×C4C22×C22⋊D1111yescharacteristic
673C8—222no—
674C8—441no—
675C8—441no—
676C8—441no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—22no—
684C22—22no—
685C22—22no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22#1062284514yes—
691C22C2×#6700211yescharacteristic
692C22C2×#6700411yescharacteristic
693C22#1062335511yescharacteristic
694C22#1062336011yescharacteristic
695C22#1062336811yescharacteristic
696C22#1062336911yescharacteristic
697C22C22×C22⋊Dic1111yescharacteristic
698C4—22no—
699C4—22no—
700C4—22no—
701C4—22no—
702C4—42no—
703C4—42no—
704C4—42no—
705C4—42no—
706C4—442no—
707C4—881no—
708C4—881no—
709C4—881no—
710C4#1062335511yescharacteristic
711C4#41×Dic1111yescharacteristic
712C4#1062335811yescharacteristic
713C4#1062336011yescharacteristic
714C2—24no—
715C2—42no—
716C2#1307144611yescharacteristic
717C2C2×#1062284511yescharacteristic
718C2#1307714911yescharacteristic
719C2#1308063111yescharacteristic
720C2#1308066111yescharacteristic
721C2#1308105611yescharacteristic
722C2#1308107111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#552C2
socleC23×C11C22×D4
prime radicalC22×D4×C11D4
cosocleC22×C4×C11C24
hypercenterC2×#552D11
hypocenterC11#22491
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
3. #13069586C2semidirect
4. #13069574C2semidirect
5. #13069050C2semidirect
6. #13069040C2semidirect
7. #13068924C2semidirect
8. #13068924C2semidirect
9. #13068711C2semidirect
10. #13068702C2semidirect
11. #13068621C2semidirect
12. #13068446C2semidirect
13. #13068337C2semidirect
14. C2×#10622167C2semidirect
17. C11×#552C4semidirect
72. C11×#125C2×C4semidirect
76. C11×C22⋊Q8C2×C4semidirect
77. C11×C22⋊Q8C2×C4semidirect
79. C4×Q8×C11C2×C4semidirect
84. C11×#117C2×C4semidirect
92. C2×C11×C4⋊C4C2×C4semidirect
334. #552Dic11semidirect
434. #125C2×Dic11semidirect
438. C22⋊Q8C2×Dic11semidirect
439. C22⋊Q8C2×Dic11semidirect
441. C4×Q8C2×Dic11semidirect
447. #117C2×Dic11semidirect
467. C2×C4⋊C4C2×Dic11semidirect
599. C11#22491semidirect

Maximal subgroups

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

subgroupindex
C2×#106226242
D4×C4⋊Dic112
#130695862
#130695742
#130690502
#130690402
#130689242
#130687112
#130687022
#130686212
#130684462
#130683372
C2×#106221672
C2×C11×#5522
#2249111