Finite Group Databasebeta

← #14775899

Subgroups — #14775899

Order 2816.

1098 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622319C211yesmaximal, characteristic, complemented
2C2×#10622449C211yesmaximal, characteristic, complemented
3C2×#10622447C211yesmaximal, characteristic, complemented
4C2×D11×C4⋊C8C211yesmaximal, characteristic, complemented
5C4×#66948C211yesmaximal, characteristic
6#13069413C211yesmaximal, characteristic, complemented
7#13069227C211yesmaximal, characteristic, complemented
8#13069220C211yesmaximal, characteristic, complemented
9#13068907C211yesmaximal, characteristic, complemented
10#13068907C211yesmaximal, characteristic, complemented
11#13068797C211yesmaximal, characteristic, complemented
12#13068792C211yesmaximal, characteristic, complemented
13#13068491C211yesmaximal, characteristic, complemented
14#13068379C211yesmaximal, characteristic, complemented
15C11×#1940C211yesmaximal, characteristic, complemented
16C22×#4313C2211yescharacteristic
17C22×C8×D11C2211yescharacteristic
18C22×C8×D11C2211yescharacteristic
19C22×C8×D11C2211yescharacteristic
20C2×#66948C411yescharacteristic
21C2×C4×D44C2211yescharacteristic
22C2×C4×D44C2211yescharacteristic
23C2×C4×D44C2211yescharacteristic
24C2×C42×D11C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C11×C4⋊C8C2211yescharacteristic
28C2×C11×#97C2211yescharacteristic
29C4×C11×C4⋊C4C2211yescharacteristic
30C2×(C2×D11)⋊C8C2211yescharacteristic
31C2×(C2×D11)⋊C8C2211yescharacteristic
32C2×(C2×D11)⋊C8C2211yescharacteristic
33C2×(C2×D11)⋊C8C2211yescharacteristic
34C2×(C2×D11)⋊C8C2211yescharacteristic
35C2×(C2×D11)⋊C8C2211yescharacteristic
36C2×(C2×D11)⋊C8C2211yescharacteristic
37C2×(C2×D11)⋊C8C2211yescharacteristic
38C2×Dic11⋊C8C2211yescharacteristic
39C2×Dic11⋊C8C2211yescharacteristic
40#10622601C411yescharacteristic
41#10622600C411yescharacteristic
42#10622598C411yescharacteristic
43C4×(C2×D11)⋊C4C2211yescharacteristic
44C4×(C2×D11)⋊C4C2211yescharacteristic
45C2×C4⋊(C11⋊C8)C2211yescharacteristic
46C2×#66867C2211yescharacteristic
47C2×#66867C2211yescharacteristic
48C2×C4×C11⋊C8C2211yescharacteristic
49#10622449—24no—
50#10622447—24no—
51D11×C4⋊C8—24no—
52#10622319—24no—
53#10622283C411yescharacteristic
54#10622283C411yescharacteristic
55#10622278C411yescharacteristic
56#10622278C411yescharacteristic
57C11×#336C2211yescharacteristic
58C11×#336C2211yescharacteristic
59#10622188C2211yescharacteristic
60#10622188C2211yescharacteristic
61#10622162C2211yescharacteristic
62#10622162C2211yescharacteristic
63C22×D44C2×C411yescharacteristic
64C22×D44C2×C411yescharacteristic
65C22×D44C2×C411yescharacteristic
66C22×C4×D11C2×C411yescharacteristic
67C22×C4×D11C2×C411yescharacteristic
68C22×C4×D11C2311yescharacteristic
69C22×C4×D11C2311yescharacteristic
70C22×C4×D11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C2×C11×C4⋊C4C2×C411yescharacteristic
76C2×C11×C4⋊C4C2×C411yescharacteristic
77C2×C42×C11C2311yescharacteristic
78C2×C42×C11C2311yescharacteristic
79C2×C42×C11C2311yescharacteristic
80C2×(C2×D11)⋊C4C2×C411yescharacteristic
81C2×(C2×D11)⋊C4C2×C411yescharacteristic
82C2×(C2×D11)⋊C4C2×C411yescharacteristic
83C2×(C2×D11)⋊C4C2×C411yescharacteristic
84C2×(C2×D11)⋊C4C2×C411yescharacteristic
85C2×(C2×D11)⋊C4C2×C411yescharacteristic
86C2×(C2×D11)⋊C4C2×C411yescharacteristic
87C2×(C2×D11)⋊C4C2×C411yescharacteristic
88C2×(C2×D11)⋊C4C2×C411yescharacteristic
89C2×(C2×D11)⋊C4C2×C411yescharacteristic
90C2×C4⋊Dic11C2×C411yescharacteristic
91C2×C4⋊Dic11C2×C411yescharacteristic
92C2×C4⋊Dic11C2×C411yescharacteristic
93C2×C4×Dic11C2×C411yescharacteristic
94C2×C4×Dic11C2×C411yescharacteristic
95C2×C4×Dic11C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C2×#4313—22no—
101C2×#4313—22no—
102C2×#4313—41no—
103C2×C8×D11—22no—
104C2×C8×D11—22no—
105C2×C8×D11—22no—
106C2×C8×D11—22no—
107C2×C8×D11—22no—
108C2×C8×D11—22no—
109C2×C8×D11—41no—
110C2×C8×D11—41no—
111C2×C8×D11—41no—
112#66948—24no—
113C4×D44—22no—
114C4×D44—22no—
115C4×D44—22no—
116C4×D44—22no—
117C4×D44—22no—
118C4×D44—22no—
119C42×D11—22no—
120C42×D11—22no—
121C11×C4⋊C8—22no—
122C11×C4⋊C8—22no—
123C11×C4⋊C8—22no—
124C11×#97—22no—
125C11×#95C2×C411yescharacteristic
126C11×#95C2×C411yescharacteristic
127C11⋊#95C2×C411yescharacteristic
128C11⋊#95C2×C411yescharacteristic
129C11⋊#95C2×C411yescharacteristic
130C11⋊#95C2×C411yescharacteristic
131(C2×D11)⋊C8—22no—
132(C2×D11)⋊C8—22no—
133(C2×D11)⋊C8—22no—
134(C2×D11)⋊C8—22no—
135(C2×D11)⋊C8—22no—
136(C2×D11)⋊C8—41no—
137(C2×D11)⋊C8—41no—
138(C2×D11)⋊C8D414yescomplemented
139Dic11⋊C8—22no—
140Dic11⋊C8—22no—
141C4⋊(C11⋊C8)D414yescomplemented
142#66867—22no—
143#66867—22no—
144C4×C11⋊C8—22no—
145#22987—111nomaximal, Sylow
146C23×D11C22×C411yescharacteristic
147C23×D11C22×C411yescharacteristic
148C23×D11C22×C411yescharacteristic
149C22×C4×C11C22×C411yescharacteristic
150C22×C4×C11C22×C411yescharacteristic
151C22×C4×C11C22×C411yescharacteristic
152C22×C4×C11C22×C411yescharacteristic
153C22×C4×C11C22×C411yescharacteristic
154C22×C4×C11C22×C411yescharacteristic
155C22×C4×C11C2411yescharacteristic
156C22×Dic11C22×C411yescharacteristic
157C22×Dic11C22×C411yescharacteristic
158C22×Dic11C22×C411yescharacteristic
159C22×Dic11C22×C411yescharacteristic
160C22×Dic11C22×C411yescharacteristic
161C2×D44—22no—
162C2×D44—22no—
163C2×D44—22no—
164C2×D44—22no—
165C2×D44—22no—
166C2×D44—22no—
167C2×D44—22no—
168C2×D44—41no—
169C2×D44M1614yescomplemented
170C2×C4×D11—22no—
171C2×C4×D11—22no—
172C2×C4×D11—22no—
173C2×C4×D11—22no—
174C2×C4×D11—22no—
175C2×C4×D11—21no—
176C2×C4×D11—21no—
177C2×C4×D11—21no—
178C2×C4×D11—21no—
179C2×C4×D11—21no—
180C2×C4×D11—21no—
181C2×C4×D11—21no—
182C2×C4×D11—21no—
183C2×C4×D11—21no—
184C2×C4×D11—21no—
185C2×C4×D11—21no—
186C2×C4×D11—21no—
187C2×C4×D11—21no—
188C2×C4×D11—21no—
189C2×C4×D11—21no—
190C2×C4×D11—21no—
191C2×C4×D11—41no—
192C2×C4×D11C2×D412yes—
193C2×C4×D11#4112yes—
194C2×C8×C11—21no—
195C2×C8×C11—21no—
196C2×C8×C11—21no—
197C2×C8×C11—21no—
198C2×C8×C11—21no—
199C2×C8×C11—21no—
200C2×C8×C11—21no—
201C2×C8×C11—21no—
202C2×C8×C11—21no—
203C2×C8×C11—21no—
204C2×C8×C11—21no—
205C2×C8×C11C2×D412yes—
206C11×C4⋊C4—22no—
207C11×C4⋊C4—41no—
208C42×C11—21no—
209C42×C11—21no—
210C42×C11—21no—
211C42×C11—21no—
212C42×C11C2×D412yes—
213C42×C11#4112yes—
214(C2×D11)⋊C4—22no—
215(C2×D11)⋊C4—22no—
216(C2×D11)⋊C4—22no—
217(C2×D11)⋊C4—22no—
218(C2×D11)⋊C4—22no—
219(C2×D11)⋊C4—22no—
220(C2×D11)⋊C4—22no—
221(C2×D11)⋊C4—22no—
222(C2×D11)⋊C4—22no—
223(C2×D11)⋊C4—22no—
224C4⋊Dic11—22no—
225C4⋊Dic11—22no—
226C4⋊Dic11—22no—
227C4×Dic11—22no—
228C4×Dic11—22no—
229C4×Dic11—21no—
230C4×Dic11—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—21no—
238C2×C11⋊C8—21no—
239C2×C11⋊C8—21no—
240C2×C11⋊C8C2×D412yes—
241C2×C11⋊C8C2×D412yes—
242C2×C11⋊C8C2×D412yes—
243#4313—44no—
244C8×D11—44no—
245C8×D11—44no—
246C8×D11—44no—
247C2×#435—111no—
248C2×#435—111no—
249C2×C8×D4—111no—
250C22×C4⋊C8—111no—
251C4×#121—111no—
252#1955—111no—
253#1940D1111yescharacteristic, complemented
254#1924—111no—
255#1923—111no—
256#1869—111no—
257#1869—111no—
258#1851—111no—
259#1850—111no—
260#1771—111no—
261#1749—111no—
262C23×C11C23×C411yescharacteristic
263C22×D11—21no—
264C22×D11—21no—
265C22×D11—21no—
266C22×D11—21no—
267C22×D11—21no—
268C22×D11—21no—
269C22×D11—21no—
270C22×D11—21no—
271C22×D11—21no—
272C22×D11—21no—
273C22×D11—21no—
274C22×D11—21no—
275C22×D11—21no—
276C22×D11—21no—
277C22×D11—21no—
278C22×D11—21no—
279C22×D11—21no—
280C22×D11C4×D412yes—
281C22×D11C2×M1612yes—
282C22×D11C2×M1612yes—
283C22×D11#13112yes—
284C2×C4×C11—21no—
285C2×C4×C11—21no—
286C2×C4×C11—21no—
287C2×C4×C11—21no—
288C2×C4×C11—21no—
289C2×C4×C11—21no—
290C2×C4×C11—21no—
291C2×C4×C11—21no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
294C2×C4×C11—21no—
295C2×C4×C11—21no—
296C2×C4×C11—21no—
297C2×C4×C11—21no—
298C2×C4×C11—21no—
299C2×C4×C11C4×D412yes—
300C2×C4×C11C4×D412yes—
301C2×C4×C11C2×M1612yes—
302C2×C4×C11C22×D411yescharacteristic
303C2×C4×C11C22×D411yescharacteristic
304C2×C4×C11C2×#4111yescharacteristic
305C2×C4×C11C2×#4111yescharacteristic
306C2×C4×C11H(5,𝔽2)11yescharacteristic
307C2×C4×C112−1+411yescharacteristic
308C2×Dic11—21no—
309C2×Dic11—21no—
310C2×Dic11—21no—
311C2×Dic11—21no—
312C2×Dic11—21no—
313C2×Dic11—21no—
314C2×Dic11—21no—
315C2×Dic11—21no—
316C2×Dic11—21no—
317C2×Dic11—21no—
318C2×Dic11—21no—
319C2×Dic11—21no—
320C2×Dic11—21no—
321C2×Dic11C4×D412yes—
322C2×Dic11#13112yes—
323D44—28no—
324D44—44no—
325D44—44no—
326C4×D11—28no—
327C4×D11—22no—
328C4×D11—22no—
329C4×D11—22no—
330C4×D11—22no—
331C4×D11—44no—
332C4×D11—41no—
333C4×D11—41no—
334C4×D11—41no—
335C4×D11—41no—
336C4×D11—41no—
337C4×D11—41no—
338C4×D11—41no—
339C4×D11—41no—
340C8×C11—22no—
341C8×C11—41no—
342C8×C11—41no—
343C8×C11—41no—
344C11⋊C8—22no—
345C11⋊C8—22no—
346C11⋊C8—22no—
347C11⋊C8—41no—
348C22×M16—111no—
349C23×C8—111no—
350C23×C8—111no—
351C23×C8—111no—
352C2×#121—111no—
353C2×C4×D4—111no—
354C2×C4×D4—111no—
355C2×C4×D4—111no—
356C22×C42—111no—
357#435—224no—
358#435—224no—
359C8×D4—224no—
360C2×C4⋊C8—111no—
361C2×C4⋊C8—111no—
362C2×C4⋊C8—111no—
363C2×C4⋊C8—224no—
364C2×C4⋊C8C2×D1111yescharacteristic
365C2×C4⋊C8C2×D1111yescharacteristic
366C2×C4⋊C8C2×D1111yescharacteristic
367C2×C22⋊C8—111no—
368C2×C22⋊C8—111no—
369C2×C22⋊C8—111no—
370C2×C22⋊C8—111no—
371C2×C22⋊C8—111no—
372C2×C22⋊C8—111no—
373C2×C22⋊C8—111no—
374C2×C22⋊C8—111no—
375C2×#97—111no—
376C2×#97—111no—
377C2×#97C2×D1111yescharacteristic
378C2×C4×C8—111no—
379#390—111no—
380#389—111no—
381#388—111no—
382#388—111no—
383#386—111no—
384#386—111no—
385#380—111no—
386C4×C4⋊C4C2×D1111yescharacteristic
387C4×C22⋊C4—111no—
388C4×C22⋊C4—111no—
389#336—111no—
390#336—111no—
391#336—111no—
392#336—111no—
393#336C2×D1111yescharacteristic
394#336C2×D1111yescharacteristic
395C22×C11C2×C4×D411yescharacteristic
396C22×C11C2×C4×D411yescharacteristic
397C22×C11#52011yescharacteristic
398C22×C11C22×M1611yescharacteristic
399C22×C11C2×#13111yescharacteristic
400C22×C11C2×#13111yescharacteristic
401C22×C11#56811yescharacteristic
402C2×D11—22no—
403C2×D11—22no—
404C2×D11—22no—
405C2×D11—22no—
406C2×D11—22no—
407C2×D11—22no—
408C2×D11—22no—
409C2×D11—22no—
410C2×D11—22no—
411C2×D11—41no—
412C2×D11—41no—
413C2×D11—41no—
414C2×D11—41no—
415C2×D11—41no—
416C2×D11—41no—
417C2×D11—41no—
418C2×D11—41no—
419C2×D11—41no—
420C2×D11—41no—
421C2×D11—41no—
422C2×D11#43514yescomplemented
423C4×C11—22no—
424C4×C11—22no—
425C4×C11—22no—
426C4×C11—41no—
427C4×C11—41no—
428C4×C11—41no—
429C4×C11D4211yescharacteristic
430C4×C11#54711yescharacteristic
431C4×C11#54811yescharacteristic
432C4×C11#55311yescharacteristic
433Dic11—22no—
434Dic11—22no—
435Dic11—41no—
436Dic11—41no—
437Dic11—41no—
438C22×D4—111no—
439C22×D4—111no—
440C22×D4—111no—
441C23×C4—111no—
442C23×C4—111no—
443C23×C4—111no—
444C23×C4—111no—
445C23×C4—111no—
446C2×M16—222no—
447C2×M16—222no—
448C2×M16—441no—
449C22×C8—111no—
450C22×C8—111no—
451C22×C8—111no—
452C22×C8—111no—
453C22×C8—222no—
454C22×C8—222no—
455C22×C8—222no—
456C22×C8—222no—
457C22×C8—222no—
458C22×C8—222no—
459C22×C8—441no—
460C22×C8—441no—
461C22×C8—441no—
462C22×C8C22×D1111yescharacteristic
463C22×C8C22×D1111yescharacteristic
464C22×C8C22×D1111yescharacteristic
465C22×C8C22×D1111yescharacteristic
466#121—224no—
467C4×D4—222no—
468C4×D4—222no—
469C4×D4—222no—
470C4×D4—222no—
471C4×D4—222no—
472C4×D4—222no—
473C2×C4⋊C4—111no—
474C2×C4⋊C4—111no—
475C2×C4⋊C4—111no—
476C2×C4⋊C4C4×D1111yescharacteristic
477C2×C4⋊C4C4×D1111yescharacteristic
478C2×C22⋊C4—111no—
479C2×C22⋊C4—111no—
480C2×C22⋊C4—111no—
481C2×C22⋊C4—111no—
482C2×C22⋊C4—111no—
483C2×C22⋊C4—111no—
484C2×C22⋊C4—111no—
485C2×C22⋊C4—111no—
486C2×C22⋊C4—111no—
487C2×C22⋊C4—111no—
488C2×C42—111no—
489C2×C42—111no—
490C2×C42—111no—
491C2×C42—222no—
492C2×C42—222no—
493C2×C42C22×D1111yescharacteristic
494C2×C42C22×D1111yescharacteristic
495C2×C42C22×D1111yescharacteristic
496C4⋊C8—22no—
497C4⋊C8—22no—
498C4⋊C8—22no—
499C4⋊C8—114no—
500C4⋊C8—222no—
501C4⋊C8—222no—
502C22⋊C8—114no—
503C22⋊C8—222no—
504C22⋊C8—222no—
505C22⋊C8—222no—
506C22⋊C8—222no—
507C22⋊C8—222no—
508C22⋊C8—441no—
509C22⋊C8—441no—
510#97—22no—
511#97—222no—
512#97—222no—
513C4×C8—222no—
514#95—111no—
515#95—111no—
516#95—111no—
517#95—111no—
518#95C4×D1111yescharacteristic
519#95C4×D1111yescharacteristic
520C2×C11#236111yescharacteristic
521C2×C11C2×#43511yescharacteristic
522C2×C11#292911yescharacteristic
523C2×C11D4×M1611yescharacteristic
524C2×C11#293511yescharacteristic
525C2×C11#299011yescharacteristic
526C2×C11#299211yescharacteristic
527D11—24no—
528D11—42no—
529D11—81no—
530C24—111no—
531C24—111no—
532C24—111no—
533C2×D4—114no—
534C2×D4—222no—
535C2×D4—222no—
536C2×D4—222no—
537C2×D4—222no—
538C2×D4—222no—
539C2×D4—222no—
540C2×D4—222no—
541C2×D4—441no—
542C22×C4—111no—
543C22×C4—111no—
544C22×C4—112no—
545C22×C4—112no—
546C22×C4—111no—
547C22×C4—111no—
548C22×C4—111no—
549C22×C4—222no—
550C22×C4—222no—
551C22×C4—222no—
552C22×C4—222no—
553C22×C4—221no—
554C22×C4—221no—
555C22×C4—221no—
556C22×C4—221no—
557C22×C4—222no—
558C22×C4—221no—
559C22×C4—221no—
560C22×C4—221no—
561C22×C4—221no—
562C22×C4—221no—
563C22×C4—221no—
564C22×C4—221no—
565C22×C4—221no—
566C22×C4—221no—
567C22×C4—221no—
568C22×C4—221no—
569C22×C4—221no—
570C22×C4—441no—
571C22×C4C2×C4×D1111yescharacteristic
572C22×C4C2×C4×D1111yescharacteristic
573C22×C4C2×C4×D1111yescharacteristic
574C22×C4C2×C4×D1111yescharacteristic
575C22×C4C2×C4×D1111yescharacteristic
576C22×C4C2×C4×D1111yescharacteristic
577C22×C4C23×D1111yescharacteristic
578M16—444no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—112no—
591C2×C8—112no—
592C2×C8—112no—
593C2×C8—221no—
594C2×C8—221no—
595C2×C8—221no—
596C2×C8—221no—
597C2×C8—221no—
598C2×C8—221no—
599C2×C8—221no—
600C2×C8—221no—
601C2×C8—221no—
602C2×C8—444no—
603C2×C8—444no—
604C2×C8—444no—
605C2×C8D4×D1112yes—
606C4⋊C4—22no—
607C4⋊C4—41no—
608C4⋊C4—222no—
609C4⋊C4—222no—
610C4⋊C4—222no—
611C22⋊C4—222no—
612C22⋊C4—222no—
613C22⋊C4—222no—
614C22⋊C4—222no—
615C22⋊C4—222no—
616C22⋊C4—222no—
617C22⋊C4—222no—
618C22⋊C4—222no—
619C22⋊C4—222no—
620C22⋊C4—222no—
621C42—21no—
622C42—21no—
623C42—21no—
624C42—21no—
625C42—222no—
626C42—222no—
627C42—221no—
628C42—221no—
629C42D4×D1112yes—
630C42#434312yes—
631C11#2298711yescharacteristic, complemented, Sylow
632C23—112no—
633C23—112no—
634C23—112no—
635C23—112no—
636C23—221no—
637C23—221no—
638C23—221no—
639C23—221no—
640C23—221no—
641C23—221no—
642C23—221no—
643C23—221no—
644C23—221no—
645C23—221no—
646C23—221no—
647C23—221no—
648C23—221no—
649C23—221no—
650C23—221no—
651C23—221no—
652C23—221no—
653C23C22×C4×D1111yescharacteristic
654D4—228no—
655D4—444no—
656D4—444no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—112no—
673C2×C4—112no—
674C2×C4—228no—
675C2×C4—221no—
676C2×C4—221no—
677C2×C4—221no—
678C2×C4—221no—
679C2×C4—222no—
680C2×C4—222no—
681C2×C4—222no—
682C2×C4—222no—
683C2×C4—221no—
684C2×C4—221no—
685C2×C4—221no—
686C2×C4—221no—
687C2×C4—221no—
688C2×C4—221no—
689C2×C4—221no—
690C2×C4—221no—
691C2×C4—221no—
692C2×C4—444no—
693C2×C4—441no—
694C2×C4—441no—
695C2×C4—441no—
696C2×C4—441no—
697C2×C4—441no—
698C2×C4—441no—
699C2×C4—441no—
700C2×C4—441no—
701C2×C4#6694612yes—
702C2×C4#6694612yes—
703C2×C4M16×D1112yes—
704C2×C4C2×D4×D1111yescharacteristic
705C2×C4C2×D4×D1111yescharacteristic
706C2×C4C2×#434311yescharacteristic
707C2×C4#6704011yescharacteristic
708C2×C4#41×D1111yescharacteristic
709C2×C4#6704211yescharacteristic
710C8—22no—
711C8—41no—
712C8—41no—
713C8—41no—
714C8—222no—
715C8—222no—
716C8—222no—
717C8—441no—
718C22—114no—
719C22—222no—
720C22—222no—
721C22—222no—
722C22—222no—
723C22—222no—
724C22—222no—
725C22—222no—
726C22—222no—
727C22—222no—
728C22—441no—
729C22—441no—
730C22—441no—
731C22—441no—
732C22—441no—
733C22—441no—
734C22—441no—
735C22—441no—
736C22—441no—
737C22—441no—
738C22—441no—
739C22C2×#6694611yescharacteristic
740C22C4×D4×D1111yescharacteristic
741C22#1062310511yescharacteristic
742C22C2×M16×D1111yescharacteristic
743C22#1062327611yescharacteristic
744C22D11×#13111yescharacteristic
745C22D11×#13111yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—41no—
750C4—41no—
751C4—41no—
752C4—222no—
753C4—222no—
754C4—441no—
755C4—441no—
756C4—441no—
757C4#1062314011yescharacteristic
758C4#1062316411yescharacteristic
759C4#1062322611yescharacteristic
760C4#1062325711yescharacteristic
761C2—224no—
762C2—442no—
763C2—881no—
764C2#1307163111yescharacteristic
765C2D11×#43511yescharacteristic
766C2#1307730911yescharacteristic
767C2#1307735111yescharacteristic
768C2#1307735711yescharacteristic
769C2#1307774011yescharacteristic
770C2#1307775411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1940C2
prime radicalC2×#66948C4
cosocleC22×C4×C11C24
hypercenter#1940D11
hypocenterC11#22987
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1940

Complements

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

NH ≅ G/Ntype
1. C2×#10622319C2semidirect
2. C2×#10622449C2semidirect
3. C2×#10622447C2semidirect
4. C2×D11×C4⋊C8C2semidirect
6. #13069413C2semidirect
7. #13069227C2semidirect
8. #13069220C2semidirect
9. #13068907C2semidirect
10. #13068907C2semidirect
11. #13068797C2semidirect
12. #13068792C2semidirect
13. #13068491C2semidirect
14. #13068379C2semidirect
15. C11×#1940C2semidirect
138. (C2×D11)⋊C8D4semidirect
141. C4⋊(C11⋊C8)D4semidirect
169. C2×D44M16semidirect
253. #1940D11semidirect
422. C2×D11#435semidirect
631. C11#22987semidirect

Maximal subgroups

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

subgroupindex
C2×#106223192
C2×#106224492
C2×#106224472
C2×D11×C4⋊C82
C4×#669482
#130694132
#130692272
#130692202
#130689072
#130687972
#130687922
#130684912
#130683792
C11×#19402
#2298711