Finite Group Databasebeta

← #14769935

Subgroups — #14769935

Order 2816.

1068 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623072C211yesmaximal, characteristic
2D4×#4318C211yesmaximal, characteristic
3#13069609C211yesmaximal, characteristic, complemented
4#13069608C211yesmaximal, characteristic, complemented
5#13069084C211yesmaximal, characteristic, complemented
6#13069084C211yesmaximal, characteristic, complemented
7#13069082C211yesmaximal, characteristic, complemented
8#13069082C211yesmaximal, characteristic, complemented
9#13068697C211yesmaximal, characteristic, complemented
10#13068694C211yesmaximal, characteristic, complemented
11#13068609C211yesmaximal, characteristic, complemented
12C4×#66888C211yesmaximal, characteristic, complemented
13#13068354C211yesmaximal, characteristic, complemented
14C2×#10622192C211yesmaximal, characteristic, complemented
15D4×C11×M16C211yesmaximal, characteristic
16C22×C11×M16C2211yescharacteristic
17C22×C11×M16C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×#66988C412yes—
20C2×#66979C2211yescharacteristic
21C22×C4⋊Dic11C2211yescharacteristic
22C2×#66977C2211yescharacteristic
23C2×#66977C2211yescharacteristic
24C22×#4318C2211yescharacteristic
25C22×#4318C2211yescharacteristic
26#10623072—21no—
27#10623072—21no—
28#10623072—21no—
29#10623072—21no—
30#10623072—21no—
31#10623072—21no—
32#10623072—21no—
33#10623072—21no—
34C2×#66942C412yes—
35C2×#66932C412yes—
36C2×#66930C412yes—
37C2×#66923C2211yescharacteristic
38C2×C4×Dic22C2211yescharacteristic
39C11×#436—21no—
40C11×#435—21no—
41C11×#435—21no—
42C8×D4×C11—21no—
43C11×#423C2211yescharacteristic
44C11×#407C2211yescharacteristic
45C11×#407C2211yescharacteristic
46C4×C11×M16C2211yescharacteristic
47#10622820C2211yescharacteristic
48#10622820C2211yescharacteristic
49C2×#66888C2211yescharacteristic
50C2×#66888C2211yescharacteristic
51C2×#66888C2211yescharacteristic
52C2×#66888C2211yescharacteristic
53#10622625—21no—
54#10622624—21no—
55#10622624—21no—
56D4×C11⋊C8—21no—
57#10622537C2211yescharacteristic
58C4×#4318C2211yescharacteristic
59#10622192C2211yescharacteristic
60#10622192C2211yescharacteristic
61#10622192C2211yescharacteristic
62#10622192C2211yescharacteristic
63#10622192C2211yescharacteristic
64#10622192C2211yescharacteristic
65#10622192C2211yescharacteristic
66#10622192C2211yescharacteristic
67#10622192C2211yescharacteristic
68#10622192C2211yescharacteristic
69#10622192C2211yescharacteristic
70#10622192C2211yescharacteristic
71C22×D4×C11C2×C411yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×Dic11C2×C412yes—
75C22×Dic22C2311yescharacteristic
76C2×C11×M16—21no—
77C2×C11×M16—21no—
78C2×C11×M16—22no—
79C2×C11×M16—22no—
80C2×C11×M16—41no—
81C2×C11×M16—41no—
82C2×C11×M16C2311yescharacteristic
83C2×C11×M16C2311yescharacteristic
84C2×C11×M16C2311yescharacteristic
85C2×C11×M16C2311yescharacteristic
86C22×C8×C11—21no—
87C22×C8×C11—21no—
88C4×D4×C11D411yescharacteristic
89C4×D4×C11D411yescharacteristic
90C4×D4×C11D411yescharacteristic
91C4×D4×C11D411yescharacteristic
92C4×D4×C11D411yescharacteristic
93C4×D4×C11D411yescharacteristic
94C4×D4×C11D411yescharacteristic
95C4×D4×C11D411yescharacteristic
96C2×C11×C4⋊C4C2×C411yescharacteristic
97C2×C11×C22⋊C4C2×C411yescharacteristic
98C2×C11×C22⋊C4C2×C411yescharacteristic
99C2×C42×C11C2311yescharacteristic
100C2×C22⋊Dic11C2×C412yes—
101C2×C22⋊Dic11C2×C412yes—
102C2×C22⋊Dic11C2×C412yes—
103#66988—22no—
104#66988—22no—
105#66988—22no—
106#66988—22no—
107#66979—21no—
108#66979—21no—
109#66979—21no—
110#66979—21no—
111C2×C4⋊Dic11—21no—
112C2×C4⋊Dic11—21no—
113C2×C4⋊Dic11—21no—
114C2×C4⋊Dic11—21no—
115C2×C4⋊Dic11C2×C412yes—
116C2×C4⋊Dic11C2311yescharacteristic
117C2×C4⋊Dic11C2311yescharacteristic
118C2×C4⋊Dic11C2311yescharacteristic
119#66977—21no—
120#66977—21no—
121#66977—21no—
122#66977—21no—
123#66977—21no—
124#66977—21no—
125#66977—21no—
126#66977—21no—
127C2×Dic11⋊C4C2×C412yes—
128C2×Dic11⋊C4C2×C412yes—
129C2×Dic11⋊C4C2×C412yes—
130C2×Dic11⋊C4C2×C412yes—
131C2×Dic11⋊C4C2×C412yes—
132C2×C4×Dic11C2×C412yes—
133C2×C4×Dic11C2×C412yes—
134C2×#4318—21no—
135C2×#4318—21no—
136C2×#4318—22no—
137C2×#4318—22no—
138C2×#4318—41no—
139C2×#4318—41no—
140C2×#4318C2311yescharacteristic
141C2×#4318C2311yescharacteristic
142C2×#4318C2311yescharacteristic
143C2×#4318C2311yescharacteristic
144C22×C11⋊C8—21no—
145C22×C11⋊C8—21no—
146#66942—22no—
147#66942—22no—
148#66942—22no—
149#66942—22no—
150#66932—22no—
151#66932—22no—
152#66932—22no—
153#66932—22no—
154#66930—22no—
155#66930—22no—
156#66930—22no—
157#66930—22no—
158#66923—21no—
159#66923—21no—
160#66923—21no—
161#66923—21no—
162C4×Dic22—21no—
163C4×Dic22—21no—
164C4×Dic22—21no—
165C4×Dic22—21no—
166C11×C4⋊C8—21no—
167C11×C4⋊C8—21no—
168C11×C22⋊C8—21no—
169C11×C22⋊C8—21no—
170C11×C22⋊C8—21no—
171C11×C22⋊C8—21no—
172C11×#97—21no—
173C4×C8×C11—21no—
174C22⋊(C11⋊C8)—21no—
175C22⋊(C11⋊C8)—21no—
176C22⋊(C11⋊C8)—21no—
177C22⋊(C11⋊C8)—21no—
178#66888—22no—
179#66888—22no—
180#66888—41no—
181#66888—41no—
182C4⋊(C11⋊C8)—21no—
183C4⋊(C11⋊C8)—21no—
184#66867—21no—
185C4×C11⋊C8—21no—
186#22480—111nomaximal, Sylow
187C24×C11C22×C411yescharacteristic
188C24×C11C22×C411yescharacteristic
189C2×D4×C11—42no—
190C2×D4×C11C22⋊C411yescharacteristic
191C2×D4×C11C22⋊C411yescharacteristic
192C2×D4×C11C22⋊C411yescharacteristic
193C2×D4×C11C22⋊C411yescharacteristic
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11C22×C411yescharacteristic
203C22×C4×C11C22×C411yescharacteristic
204C22×C4×C11C22×C411yescharacteristic
205C22×C4×C11C22×C411yescharacteristic
206C22×C4×C11C2×D411yescharacteristic
207C22×C4×C11C2×D411yescharacteristic
208C22×C4×C11C2×D411yescharacteristic
209C22×C4×C11C2×D411yescharacteristic
210C22×C4×C11C2×D411yescharacteristic
211C22×C4×C11C2×D411yescharacteristic
212C22×C4×C11C2×D411yescharacteristic
213C22×C4×C11C2×D411yescharacteristic
214C22×C4×C11C2411yescharacteristic
215C22×Dic11—22no—
216C22×Dic11—22no—
217C22×Dic11—44no—
218C22×Dic11C22×C412yes—
219C22×Dic11C22×C412yes—
220C22×Dic11C22×C412yes—
221C22×Dic11C22×C412yes—
222C2×Dic22—21no—
223C2×Dic22—21no—
224C2×Dic22—21no—
225C2×Dic22—21no—
226C2×Dic22—21no—
227C2×Dic22—21no—
228C11×M16—21no—
229C11×M16—21no—
230C11×M16—21no—
231C11×M16—21no—
232C11×M16—21no—
233C11×M16—21no—
234C11×M16—21no—
235C11×M16—42no—
236C11×M16—42no—
237C11×M16#4112yes—
238C2×C8×C11—21no—
239C2×C8×C11—21no—
240C2×C8×C11—21no—
241C2×C8×C11—21no—
242C2×C8×C11—42no—
243C2×C8×C11—42no—
244C11×C4⋊C4C22⋊C411yescharacteristic
245C11×C4⋊C4C22⋊C411yescharacteristic
246C11×C4⋊C4C22⋊C411yescharacteristic
247C11×C4⋊C4C22⋊C411yescharacteristic
248C11×C22⋊C4C22⋊C411yescharacteristic
249C11×C22⋊C4C22⋊C411yescharacteristic
250C11×C22⋊C4C22⋊C411yescharacteristic
251C11×C22⋊C4C22⋊C411yescharacteristic
252C11×C22⋊C4C22⋊C411yescharacteristic
253C11×C22⋊C4C22⋊C411yescharacteristic
254C11×C22⋊C4C22⋊C411yescharacteristic
255C11×C22⋊C4C22⋊C411yescharacteristic
256C42×C11C2×D411yescharacteristic
257C42×C11C2×D411yescharacteristic
258C42×C11C2×D411yescharacteristic
259C42×C11C2×D411yescharacteristic
260C22⋊Dic11—22no—
261C22⋊Dic11—22no—
262C22⋊Dic11—22no—
263C22⋊Dic11—22no—
264C22⋊Dic11—22no—
265C22⋊Dic11—22no—
266C4⋊Dic11—22no—
267C4⋊Dic11—22no—
268C4⋊Dic11—21no—
269C4⋊Dic11—21no—
270C4⋊Dic11—21no—
271C4⋊Dic11—21no—
272C4⋊Dic11—21no—
273C4⋊Dic11—21no—
274Dic11⋊C4—22no—
275Dic11⋊C4—22no—
276Dic11⋊C4—22no—
277Dic11⋊C4—22no—
278Dic11⋊C4—22no—
279Dic11⋊C4—22no—
280Dic11⋊C4—22no—
281Dic11⋊C4—22no—
282Dic11⋊C4—22no—
283Dic11⋊C4—22no—
284C4×Dic11—22no—
285C4×Dic11—22no—
286C4×Dic11—22no—
287C4×Dic11—22no—
288#4318—21no—
289#4318—21no—
290#4318—21no—
291#4318—21no—
292#4318—21no—
293#4318—21no—
294#4318—21no—
295#4318—42no—
296#4318—42no—
297#4318#4112yes—
298C2×C11⋊C8—21no—
299C2×C11⋊C8—21no—
300C2×C11⋊C8—21no—
301C2×C11⋊C8—21no—
302C2×C11⋊C8—42no—
303C2×C11⋊C8—42no—
304C2×#552—111no—
305D4×M16—111no—
306D4×M16D1111yescharacteristic
307#1998—111no—
308#1998—111no—
309#1901—111no—
310#1901—111no—
311#1901—111no—
312#1901—111no—
313#1822—111no—
314#1821—111no—
315#1801—111no—
316C4×#101—111no—
317#1742—111no—
318C2×#343—111no—
319C23×C11—21no—
320C23×C11—21no—
321C23×C11—22no—
322C23×C11—21no—
323C23×C11—21no—
324C23×C11—41no—
325C23×C11—41no—
326C23×C11—41no—
327C23×C11C2×C22⋊C411yescharacteristic
328C23×C11C2×C22⋊C411yescharacteristic
329C23×C11C2×C22⋊C411yescharacteristic
330C23×C11C2×C22⋊C411yescharacteristic
331C23×C11C23×C411yescharacteristic
332D4×C11—22no—
333D4×C11—22no—
334D4×C11—41no—
335D4×C11—41no—
336C2×C4×C11—21no—
337C2×C4×C11—21no—
338C2×C4×C11—21no—
339C2×C4×C11—21no—
340C2×C4×C11—21no—
341C2×C4×C11—21no—
342C2×C4×C11—21no—
343C2×C4×C11—21no—
344C2×C4×C11—21no—
345C2×C4×C11—21no—
346C2×C4×C11—21no—
347C2×C4×C11—21no—
348C2×C4×C11—21no—
349C2×C4×C11—21no—
350C2×C4×C11—21no—
351C2×C4×C11—21no—
352C2×C4×C11—21no—
353C2×C4×C11—21no—
354C2×C4×C11—21no—
355C2×C4×C11—21no—
356C2×C4×C11—41no—
357C2×C4×C11—41no—
358C2×C4×C11C2×C22⋊C411yescharacteristic
359C2×C4×C11C2×C22⋊C411yescharacteristic
360C2×C4×C11C2×C22⋊C411yescharacteristic
361C2×C4×C11C2×C22⋊C411yescharacteristic
362C2×C4×C11C2×C22⋊C411yescharacteristic
363C2×C4×C11C2×C22⋊C411yescharacteristic
364C2×C4×C11C2×C22⋊C411yescharacteristic
365C2×C4×C11C2×C22⋊C411yescharacteristic
366C2×C4×C11C22×D411yescharacteristic
367C2×C4×C11C22×D411yescharacteristic
368C2×C4×C11C2×#4111yescharacteristic
369C2×C4×C11C2×#4111yescharacteristic
370C2×C4×C11H(5,𝔽2)11yescharacteristic
371C2×C4×C112−1+411yescharacteristic
372C2×Dic11—22no—
373C2×Dic11—22no—
374C2×Dic11—22no—
375C2×Dic11—22no—
376C2×Dic11—22no—
377C2×Dic11—22no—
378C2×Dic11—44no—
379C2×Dic11—44no—
380C2×Dic11—42no—
381C2×Dic11—42no—
382C2×Dic11—42no—
383Dic22—41no—
384Dic22—41no—
385Dic22—41no—
386Dic22—41no—
387C8×C11—22no—
388C8×C11—41no—
389C8×C11—41no—
390C8×C11—41no—
391C11⋊C8—22no—
392C11⋊C8—41no—
393C11⋊C8—41no—
394C11⋊C8—41no—
395C22×M16—111no—
396C22×M16—111no—
397C22×M16C2×D1111yescharacteristic
398C22×M16C2×D1111yescharacteristic
399#552—221no—
400#552—221no—
401#552—221no—
402#552—221no—
403#552—221no—
404#552—221no—
405#552—221no—
406#552—221no—
407C2×#126—112no—
408C2×#125—112no—
409C2×#125—111no—
410C2×#123—112no—
411C2×C22⋊Q8—111no—
412C2×C22⋊Q8—111no—
413C2×C4×Q8—111no—
414C2×C4×D4C2×D1111yescharacteristic
415C2×#117—111no—
416C2×#117—112no—
417C22×C4⋊C4—111no—
418#436—21no—
419#436—221no—
420#435—21no—
421#435—21no—
422#435—221no—
423#435—221no—
424C8×D4—21no—
425C8×D4—221no—
426#423—111no—
427#423C2×D1111yescharacteristic
428C2×#101—111no—
429C2×#101—111no—
430C2×#101—111no—
431C2×#101—111no—
432#407—111no—
433#407—111no—
434#407C2×D1111yescharacteristic
435#407C2×D1111yescharacteristic
436C4×M16—111no—
437C4×M16C2×D1111yescharacteristic
438#343—111no—
439#343—111no—
440#343—111no—
441#343—111no—
442#343—111no—
443#343—111no—
444#343—111no—
445#343—111no—
446#343—111no—
447#343—111no—
448#343—111no—
449#343—111no—
450C22×C11—21no—
451C22×C11—21no—
452C22×C11—21no—
453C22×C11—21no—
454C22×C11—21no—
455C22×C11—21no—
456C22×C11—21no—
457C22×C11—21no—
458C22×C11—21no—
459C22×C11—21no—
460C22×C11—21no—
461C22×C11—21no—
462C22×C11—21no—
463C22×C11—42no—
464C22×C11—42no—
465C22×C11—81no—
466C22×C11—81no—
467C22×C11#41312yes—
468C22×C11C22×C22⋊C411yescharacteristic
469C22×C11C4×#4111yescharacteristic
470C22×C11#52011yescharacteristic
471C4×C11—21no—
472C4×C11—21no—
473C4×C11—21no—
474C4×C11—21no—
475C4×C11—21no—
476C4×C11—21no—
477C4×C11—21no—
478C4×C11—21no—
479C4×C11#54611yescharacteristic
480C4×C11#54611yescharacteristic
481C4×C11#54711yescharacteristic
482C4×C11#54711yescharacteristic
483Dic11—42no—
484Dic11—42no—
485Dic11—42no—
486Dic11—42no—
487C22×Q8—111no—
488C22×D4C4×D1111yescharacteristic
489C23×C4—112no—
490C23×C4C22×D1111yescharacteristic
491C23×C4C22×D1111yescharacteristic
492C2×M16—21no—
493C2×M16—21no—
494C2×M16—22no—
495C2×M16—22no—
496C2×M16—41no—
497C2×M16—41no—
498C2×M16—111no—
499C2×M16—111no—
500C2×M16—111no—
501C2×M16—111no—
502C2×M16—221no—
503C2×M16—221no—
504C2×M16—222no—
505C2×M16—222no—
506C2×M16—441no—
507C2×M16—441no—
508C2×M16C22×D1111yescharacteristic
509C2×M16C22×D1111yescharacteristic
510C2×M16C22×D1111yescharacteristic
511C2×M16C22×D1111yescharacteristic
512C22×C8—21no—
513C22×C8—21no—
514C22×C8—221no—
515C22×C8—221no—
516#126—222no—
517#126—222no—
518#126—222no—
519#126—222no—
520#125—222no—
521#125—222no—
522#125—222no—
523#125—222no—
524#125—221no—
525#125—221no—
526#125—221no—
527#125—221no—
528#123—222no—
529#123—222no—
530#123—222no—
531#123—222no—
532C22⋊Q8—221no—
533C22⋊Q8—221no—
534C22⋊Q8—221no—
535C22⋊Q8—221no—
536C22⋊Q8—221no—
537C22⋊Q8—221no—
538C22⋊Q8—221no—
539C22⋊Q8—221no—
540C4×Q8—221no—
541C4×Q8—221no—
542C4×Q8—221no—
543C4×Q8—221no—
544C4×D4D4411yescharacteristic
545C4×D4D4411yescharacteristic
546C4×D4D4411yescharacteristic
547C4×D4D4411yescharacteristic
548C4×D4C22⋊D1111yescharacteristic
549C4×D4C22⋊D1111yescharacteristic
550C4×D4C22⋊D1111yescharacteristic
551C4×D4C22⋊D1111yescharacteristic
552#117—221no—
553#117—221no—
554#117—221no—
555#117—221no—
556#117—222no—
557#117—222no—
558#117—222no—
559#117—222no—
560C2×C4⋊C4—112no—
561C2×C4⋊C4—112no—
562C2×C4⋊C4—112no—
563C2×C4⋊C4—112no—
564C2×C4⋊C4—112no—
565C2×C4⋊C4—112no—
566C2×C4⋊C4—111no—
567C2×C4⋊C4—111no—
568C2×C4⋊C4—111no—
569C2×C4⋊C4—221no—
570C2×C4⋊C4—221no—
571C2×C4⋊C4—221no—
572C2×C4⋊C4—221no—
573C2×C4⋊C4C4×D1111yescharacteristic
574C2×C22⋊C4—112no—
575C2×C22⋊C4—112no—
576C2×C22⋊C4—112no—
577C2×C22⋊C4C4×D1111yescharacteristic
578C2×C22⋊C4C4×D1111yescharacteristic
579C2×C42—112no—
580C2×C42—112no—
581C2×C42C22×D1111yescharacteristic
582C4⋊C8—21no—
583C4⋊C8—21no—
584C4⋊C8—221no—
585C4⋊C8—221no—
586#101—222no—
587#101—222no—
588#101—441no—
589#101—441no—
590C22⋊C8—21no—
591C22⋊C8—21no—
592C22⋊C8—21no—
593C22⋊C8—21no—
594C22⋊C8—221no—
595C22⋊C8—221no—
596C22⋊C8—221no—
597C22⋊C8—221no—
598#97—21no—
599#97—221no—
600C4×C8—21no—
601C4×C8—221no—
602C2×C11—21no—
603C2×C11—21no—
604C2×C11—22no—
605C2×C11—41no—
606C2×C11—41no—
607C2×C11—41no—
608C2×C11#233911yescharacteristic
609C2×C11C2×#41311yescharacteristic
610C2×C11#288911yescharacteristic
611C24C2×C4×D1111yescharacteristic
612C24C2×C4×D1111yescharacteristic
613C2×Q8—221no—
614C2×Q8—221no—
615C2×Q8—221no—
616C2×Q8—221no—
617C2×Q8—221no—
618C2×Q8—221no—
619C2×D4—42no—
620C2×D4(C2×D11)⋊C411yescharacteristic
621C2×D4(C2×D11)⋊C411yescharacteristic
622C2×D4(C2×D11)⋊C411yescharacteristic
623C2×D4(C2×D11)⋊C411yescharacteristic
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—112no—
633C22×C4—112no—
634C22×C4—112no—
635C22×C4—112no—
636C22×C4—222no—
637C22×C4—222no—
638C22×C4—444no—
639C22×C4C2×C4×D1111yescharacteristic
640C22×C4C2×C4×D1111yescharacteristic
641C22×C4C2×C4×D1111yescharacteristic
642C22×C4C2×C4×D1111yescharacteristic
643C22×C4C2×D4411yescharacteristic
644C22×C4C2×D4411yescharacteristic
645C22×C4C2×D4411yescharacteristic
646C22×C4C2×D4411yescharacteristic
647C22×C4C2×C22⋊D1111yescharacteristic
648C22×C4C2×C22⋊D1111yescharacteristic
649C22×C4C2×C22⋊D1111yescharacteristic
650C22×C4C2×C22⋊D1111yescharacteristic
651C22×C4C23×D1111yescharacteristic
652M16—21no—
653M16—21no—
654M16—21no—
655M16—21no—
656M16—21no—
657M16—21no—
658M16—21no—
659M16—42no—
660M16—42no—
661M16—112no—
662M16—221no—
663M16—221no—
664M16—221no—
665M16—221no—
666M16—221no—
667M16—221no—
668M16—221no—
669M16—442no—
670M16—442no—
671M16#434112yes—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—42no—
677C2×C8—42no—
678C2×C8—221no—
679C2×C8—221no—
680C2×C8—221no—
681C2×C8—221no—
682C2×C8—442no—
683C2×C8—442no—
684C4⋊C4—222no—
685C4⋊C4—222no—
686C4⋊C4—222no—
687C4⋊C4—222no—
688C4⋊C4—222no—
689C4⋊C4—222no—
690C4⋊C4—222no—
691C4⋊C4—222no—
692C4⋊C4—222no—
693C4⋊C4—222no—
694C4⋊C4—222no—
695C4⋊C4—222no—
696C4⋊C4—221no—
697C4⋊C4—221no—
698C4⋊C4—221no—
699C4⋊C4—221no—
700C4⋊C4—221no—
701C4⋊C4—221no—
702C4⋊C4(C2×D11)⋊C411yescharacteristic
703C4⋊C4(C2×D11)⋊C411yescharacteristic
704C4⋊C4(C2×D11)⋊C411yescharacteristic
705C4⋊C4(C2×D11)⋊C411yescharacteristic
706C22⋊C4—222no—
707C22⋊C4—222no—
708C22⋊C4—222no—
709C22⋊C4—222no—
710C22⋊C4—222no—
711C22⋊C4—222no—
712C22⋊C4(C2×D11)⋊C411yescharacteristic
713C22⋊C4(C2×D11)⋊C411yescharacteristic
714C22⋊C4(C2×D11)⋊C411yescharacteristic
715C22⋊C4(C2×D11)⋊C411yescharacteristic
716C22⋊C4(C2×D11)⋊C411yescharacteristic
717C22⋊C4(C2×D11)⋊C411yescharacteristic
718C22⋊C4(C2×D11)⋊C411yescharacteristic
719C22⋊C4(C2×D11)⋊C411yescharacteristic
720C42—222no—
721C42—222no—
722C42—222no—
723C42—222no—
724C42C2×D4411yescharacteristic
725C42C2×D4411yescharacteristic
726C42C2×C22⋊D1111yescharacteristic
727C42C2×C22⋊D1111yescharacteristic
728C11#2248011yescharacteristic, complemented, Sylow
729C23—22no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23C2×(C2×D11)⋊C411yescharacteristic
738C23C2×(C2×D11)⋊C411yescharacteristic
739C23C2×(C2×D11)⋊C411yescharacteristic
740C23C2×(C2×D11)⋊C411yescharacteristic
741C23C22×C4×D1111yescharacteristic
742Q8—441no—
743Q8—441no—
744Q8—441no—
745Q8—441no—
746D4—22no—
747D4—22no—
748D4—41no—
749D4—41no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—222no—
773C2×C4—222no—
774C2×C4—222no—
775C2×C4—222no—
776C2×C4—222no—
777C2×C4—222no—
778C2×C4—444no—
779C2×C4—444no—
780C2×C4—442no—
781C2×C4—442no—
782C2×C4—442no—
783C2×C4C2×(C2×D11)⋊C411yescharacteristic
784C2×C4C2×(C2×D11)⋊C411yescharacteristic
785C2×C4C2×(C2×D11)⋊C411yescharacteristic
786C2×C4C2×(C2×D11)⋊C411yescharacteristic
787C2×C4C2×(C2×D11)⋊C411yescharacteristic
788C2×C4C2×(C2×D11)⋊C411yescharacteristic
789C2×C4C2×(C2×D11)⋊C411yescharacteristic
790C2×C4C2×(C2×D11)⋊C411yescharacteristic
791C2×C4C22×D4411yescharacteristic
792C2×C4C2×#434111yescharacteristic
793C2×C4#6703711yescharacteristic
794C2×C4#41×D1111yescharacteristic
795C2×C4#6704311yescharacteristic
796C2×C4C22×C22⋊D1111yescharacteristic
797C8—22no—
798C8—41no—
799C8—41no—
800C8—41no—
801C8—222no—
802C8—441no—
803C8—441no—
804C8—441no—
805C22—21no—
806C22—21no—
807C22—21no—
808C22—21no—
809C22—21no—
810C22—21no—
811C22—21no—
812C22—21no—
813C22—21no—
814C22—21no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—42no—
819C22—42no—
820C22—81no—
821C22—81no—
822C22#1062274512yes—
823C22C4×#434111yescharacteristic
824C22#1062307711yescharacteristic
825C22C22×(C2×D11)⋊C411yescharacteristic
826C4—21no—
827C4—21no—
828C4—21no—
829C4—21no—
830C4—21no—
831C4—21no—
832C4—21no—
833C4—21no—
834C4—442no—
835C4—442no—
836C4—442no—
837C4—442no—
838C4#1062308511yescharacteristic
839C4#1062308611yescharacteristic
840C4#1062333711yescharacteristic
841C4#1062335511yescharacteristic
842C2—21no—
843C2—21no—
844C2—22no—
845C2—41no—
846C2—41no—
847C2—41no—
848C2#1307144111yescharacteristic
849C2C2×#1062274511yescharacteristic
850C2#1307709811yescharacteristic
subgroupG/H
centerC22C22×(C2×D11)⋊C4
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingD4×C11×M16C2
socleC22×C11C22×C22⋊C4
prime radicalC22×D4×C11C2×C4
cosocleC22×C4×C11C24
hypercenterD4×M16D11
hypocenterC11#22480
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ D4×M16

Complements

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

NH ≅ G/Ntype
3. #13069609C2semidirect
4. #13069608C2semidirect
5. #13069084C2semidirect
6. #13069084C2semidirect
7. #13069082C2semidirect
8. #13069082C2semidirect
9. #13068697C2semidirect
10. #13068694C2semidirect
11. #13068609C2semidirect
12. C4×#66888C2semidirect
13. #13068354C2semidirect
14. C2×#10622192C2semidirect
728. C11#22480semidirect

Maximal subgroups

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

subgroupindex
C2×#106230722
D4×#43182
#130696092
#130696082
#130690842
#130690822
#130686972
#130686942
#130686092
C4×#668882
#130683542
C2×#106221922
D4×C11×M162
#2248011