Finite Group Databasebeta

← #14770786

Subgroups — #14770786

Order 2816.

1060 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622333C211yesmaximal, characteristic, complemented
2C2×#10622339C211yesmaximal, characteristic
3#13070995C211yesmaximal, characteristic
4#13069230C211yesmaximal, characteristic, complemented
5#13069229C211yesmaximal, characteristic, complemented
6#13069223C211yesmaximal, characteristic, complemented
7#13069222C211yesmaximal, characteristic, complemented
8#13068800C211yesmaximal, characteristic, complemented
9#13068800C211yesmaximal, characteristic, complemented
10#13068685C211yesmaximal, characteristic, complemented
11#13068600C211yesmaximal, characteristic, complemented
12#13068525C211yesmaximal, characteristic
13#13068401C211yesmaximal, characteristic, complemented
14#13068399C211yesmaximal, characteristic, complemented
15C11×#1750C211yesmaximal, characteristic, complemented
16C23×C4×D11C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C2×#66979C2211yescharacteristic
19C22×#4313C2211yescharacteristic
20C22×#4313C2211yescharacteristic
21C2×C11×C22⋊C8C2211yescharacteristic
22C2×C11×C22⋊C8C2211yescharacteristic
23C2×C11×#97C2211yescharacteristic, complemented
24C2×C4×C8×C11C2211yescharacteristic, complemented
25C2×C22⋊(C11⋊C8)C2211yescharacteristic
26C2×C22⋊(C11⋊C8)C2211yescharacteristic
27C2×(C2×D11)⋊C8C2211yescharacteristic
28C2×(C2×D11)⋊C8C2211yescharacteristic
29C2×(C2×D11)⋊C8C2211yescharacteristic
30C2×(C2×D11)⋊C8C2211yescharacteristic
31C2×(C2×D11)⋊C8C2211yescharacteristic
32C2×(C2×D11)⋊C8C2211yescharacteristic
33C2×#66879C2211yescharacteristic, complemented
34C2×Dic11⋊C8C2211yescharacteristic, complemented
35C2×Dic11⋊C8C2211yescharacteristic, complemented
36C2×C8×Dic11C2211yescharacteristic, complemented
37#10622600C411yescharacteristic
38#10622600C411yescharacteristic
39#10622600C411yescharacteristic
40#10622600C411yescharacteristic
41#10622568C411yescharacteristic
42#10622568C411yescharacteristic
43#10622556C411yescharacteristic
44#10622556C411yescharacteristic
45C4×(C2×D11)⋊C4C2211yescharacteristic
46C4×(C2×D11)⋊C4C2211yescharacteristic
47C4×(C2×D11)⋊C4C2211yescharacteristic
48C4×(C2×D11)⋊C4C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
50C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
51#10622339—24no—
52#10622333—24no—
53C11×#336C2211yescharacteristic, complemented
54C11×#336C2211yescharacteristic, complemented
55#10622188C2211yescharacteristic, complemented
56#10622188C2211yescharacteristic, complemented
57#10622188C2211yescharacteristic, complemented
58#10622188C2211yescharacteristic, complemented
59#10622162C2211yescharacteristic, complemented
60#10622162C2211yescharacteristic, complemented
61C24×D11C2×C411yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×Dic11C2×C411yescharacteristic
64C22×C4×D11—22no—
65C22×C4×D11—22no—
66C22×C4×D11—22no—
67C22×C4×D11—22no—
68C22×C4×D11—41no—
69C22×C4×D11—41no—
70C22×C4×D11C2×C411yescharacteristic
71C22×C4×D11C2×C411yescharacteristic
72C22×C4×D11C2311yescharacteristic
73C22×C4×D11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C11×#117—41no—
79C11×#117—41no—
80C2×C11×C4⋊C4C2×C411yescharacteristic
81C2×C11×C4⋊C4C2×C411yescharacteristic
82C2×C11×C22⋊C4C2×C411yescharacteristic
83C2×C11×C22⋊C4C2×C411yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C2×C22⋊Dic11C2×C411yescharacteristic
87C2×C22⋊Dic11C2×C411yescharacteristic
88C2×(C2×D11)⋊C4C2×C411yescharacteristic
89C2×(C2×D11)⋊C4C2×C411yescharacteristic
90C2×(C2×D11)⋊C4C2×C411yescharacteristic
91C2×(C2×D11)⋊C4C2×C411yescharacteristic
92C2×(C2×D11)⋊C4C2×C411yescharacteristic
93C2×(C2×D11)⋊C4C2×C411yescharacteristic
94C2×(C2×D11)⋊C4C2×C411yescharacteristic
95C2×(C2×D11)⋊C4C2×C411yescharacteristic
96#66979—22no—
97#66979—22no—
98C2×C4⋊Dic11C2×C411yescharacteristic
99C2×C4⋊Dic11C2×C411yescharacteristic
100C2×C4×Dic11C2311yescharacteristic
101C2×C4×Dic11C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C2×#4313—22no—
107C2×#4313—22no—
108C2×#4313—22no—
109C2×#4313—22no—
110C2×#4313—41no—
111C2×#4313—41no—
112C11×C22⋊C8—22no—
113C11×C22⋊C8D414yes—
114C11×#97—41no—
115C4×C8×C11—41no—
116C11⋊#95C2×C411yescharacteristic
117C11⋊#95C2×C411yescharacteristic
118C11⋊#95C2×C411yescharacteristic
119C11⋊#95C2×C411yescharacteristic
120C11⋊#95C2×C411yescharacteristic
121C11⋊#95C2×C411yescharacteristic
122C11⋊#95C2×C411yescharacteristic
123C11⋊#95C2×C411yescharacteristic
124C22⋊(C11⋊C8)—22no—
125C22⋊(C11⋊C8)—22no—
126(C2×D11)⋊C8—22no—
127(C2×D11)⋊C8—22no—
128(C2×D11)⋊C8—22no—
129(C2×D11)⋊C8—22no—
130(C2×D11)⋊C8—41no—
131(C2×D11)⋊C8—41no—
132#66879—22no—
133Dic11⋊C8—22no—
134Dic11⋊C8—22no—
135C8×Dic11—22no—
136C4⋊(C11⋊C8)—41no—
137C4⋊(C11⋊C8)—41no—
138#22559—111nomaximal, Sylow
139C24×C11C22×C411yescharacteristic
140C23×D11—22no—
141C23×D11—22no—
142C23×D11—22no—
143C23×D11—41no—
144C23×D11—41no—
145C23×D11—41no—
146C23×D11—41no—
147C23×D11C22×C411yescharacteristic
148C23×D11C22×C411yescharacteristic
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11C22×C411yescharacteristic
154C22×C4×C11C22×C411yescharacteristic
155C22×C4×C11C22×C411yescharacteristic
156C22×C4×C11C22×C411yescharacteristic
157C22×C4×C11C22×C411yescharacteristic
158C22×C4×C11C2×D412yes—
159C22×C4×C11#4112yes—
160C22×C4×C11C2411yescharacteristic
161C22×Dic11—22no—
162C22×Dic11—22no—
163C22×Dic11—41no—
164C22×Dic11C22×C411yescharacteristic
165C22×Dic11C22×C411yescharacteristic
166C22×Dic11C22×C411yescharacteristic
167C22×Dic11C22×C411yescharacteristic
168C22×Dic11C22×C411yescharacteristic
169C22×Dic11C22×C411yescharacteristic
170C2×C4×D11—22no—
171C2×C4×D11—22no—
172C2×C4×D11—22no—
173C2×C4×D11—22no—
174C2×C4×D11—21no—
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—41no—
185C2×C4×D11—41no—
186C2×C4×D11—44no—
187C2×C4×D11—44no—
188C2×C4×D11—44no—
189C2×C4×D11—44no—
190C2×C4×D11#4112yes—
191C2×C4×D11#4112yes—
192C2×C8×C11—21no—
193C2×C8×C11—21no—
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×C11C2×D412yes—
203C2×C8×C11C2×D412yes—
204C11×C4⋊C4—41no—
205C11×C4⋊C4—41no—
206C11×C22⋊C4—41no—
207C11×C22⋊C4—41no—
208C42×C11—21no—
209C42×C11—21no—
210C42×C11—21no—
211C42×C11—21no—
212C22⋊Dic11—22no—
213C22⋊Dic11—22no—
214(C2×D11)⋊C4—22no—
215(C2×D11)⋊C4—22no—
216(C2×D11)⋊C4—41no—
217(C2×D11)⋊C4—41no—
218(C2×D11)⋊C4—41no—
219(C2×D11)⋊C4—41no—
220(C2×D11)⋊C4—41no—
221(C2×D11)⋊C4—41no—
222C4⋊Dic11—22no—
223C4⋊Dic11—22no—
224C4×Dic11—21no—
225C4×Dic11—21no—
226C4×Dic11—21no—
227C4×Dic11—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—21no—
238C2×C11⋊C8—21no—
239C2×C11⋊C8—21no—
240#4313—44no—
241#4313—44no—
242C2×#433—111no—
243C2×#407—111no—
244#2280—111no—
245#1924—111no—
246#1924—111no—
247#1923—111no—
248#1923—111no—
249#1851—111no—
250#1851—111no—
251#1818—111no—
252#1798—111no—
253#1779—111no—
254#1753—111no—
255#1753—111no—
256#1750D1111yescharacteristic, complemented
257C23×C11—21no—
258C23×C11—21no—
259C23×C11—21no—
260C23×C11—21no—
261C23×C11—21no—
262C23×C11—21no—
263C23×C11C4×D412yes—
264C23×C11C23×C411yescharacteristic
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—44no—
278C22×D11—44no—
279C22×D11—44no—
280C22×D11—44no—
281C22×D11—44no—
282C22×D11—44no—
283C22×D11—44no—
284C22×D11#11712yes—
285C22×D11#13112yes—
286C2×C4×C11—21no—
287C2×C4×C11—21no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
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×C11—21no—
300C2×C4×C11—21no—
301C2×C4×C11—21no—
302C2×C4×C11—21no—
303C2×C4×C11—21no—
304C2×C4×C11C4×D412yes—
305C2×C4×C11C22×D411yescharacteristic
306C2×C4×C11C2×#4111yescharacteristic
307C2×C4×C11C2×#4111yescharacteristic
308C2×C4×C11C2×#4111yescharacteristic
309C2×C4×C11H(5,𝔽2)11yescharacteristic
310C2×C4×C11H(5,𝔽2)11yescharacteristic
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×Dic11—21no—
322C2×Dic11—21no—
323C2×Dic11—21no—
324C2×Dic11—21no—
325C2×Dic11—21no—
326C2×Dic11—21no—
327C2×Dic11—21no—
328C2×Dic11—44no—
329C2×Dic11#11712yes—
330C4×D11—22no—
331C4×D11—22no—
332C4×D11—22no—
333C4×D11—22no—
334C4×D11—44no—
335C4×D11—44no—
336C4×D11—41no—
337C4×D11—41no—
338C4×D11—41no—
339C4×D11—41no—
340C8×C11—22no—
341C8×C11—22no—
342C8×C11—41no—
343C8×C11—41no—
344C11⋊C8—41no—
345C11⋊C8—41no—
346C11⋊C8—41no—
347C11⋊C8—41no—
348C24×C4—111no—
349C22×M16—111no—
350C22×M16—111no—
351C2×#117—111no—
352C2×#117C2×D1111yescharacteristic
353#433—224no—
354C2×C4⋊C8—111no—
355C2×C4⋊C8—111no—
356C2×C4⋊C8—111no—
357C2×C4⋊C8—111no—
358#407—224no—
359C2×C22⋊C8—111no—
360C2×C22⋊C8—111no—
361C2×C22⋊C8—111no—
362C2×C22⋊C8—111no—
363C2×C22⋊C8—111no—
364C2×C22⋊C8—111no—
365C2×C22⋊C8—111no—
366C2×C22⋊C8—111no—
367C2×C22⋊C8C2×D1111yescharacteristic
368C2×C22⋊C8C2×D1111yescharacteristic
369C2×#97—111no—
370C2×#97C2×D1111yescharacteristic, complemented
371C2×C4×C8—111no—
372C2×C4×C8C2×D1111yescharacteristic, complemented
373#381—111no—
374#381—111no—
375#380—111no—
376#380—111no—
377#380—111no—
378#380—111no—
379#379—111no—
380#379—111no—
381C4×C22⋊C4—111no—
382C4×C22⋊C4—111no—
383C4×C22⋊C4—111no—
384C4×C22⋊C4—111no—
385#336—111no—
386#336—111no—
387#336—111no—
388#336—111no—
389#336—111no—
390#336—111no—
391#336C2×D1111yescharacteristic, complemented
392#336C2×D1111yescharacteristic, complemented
393C22×C11—22no—
394C22×C11—22no—
395C22×C11—22no—
396C22×C11—41no—
397C22×C11—41no—
398C22×C11—41no—
399C22×C11—41no—
400C22×C11C2×#11711yescharacteristic
401C22×C11C2×C4×D411yescharacteristic
402C22×C11#51811yescharacteristic
403C22×C11C2×#13111yescharacteristic
404C22×C11#56811yescharacteristic
405C22×C11#56811yescharacteristic
406C22×C11#56811yescharacteristic
407C2×D11—22no—
408C2×D11—22no—
409C2×D11—22no—
410C2×D11—22no—
411C2×D11—22no—
412C2×D11—22no—
413C2×D11—416no—
414C2×D11—41no—
415C2×D11—41no—
416C2×D11—41no—
417C2×D11—41no—
418C2×D11—41no—
419C2×D11—41no—
420C2×D11—41no—
421C2×D11—41no—
422C4×C11—22no—
423C4×C11—41no—
424C4×C11—41no—
425C4×C11—41no—
426C4×C11—41no—
427C4×C11#54611yescharacteristic
428C4×C11#54611yescharacteristic
429C4×C11#55111yescharacteristic
430C4×C11#55111yescharacteristic
431Dic11—22no—
432Dic11—41no—
433Dic11—41no—
434Dic11—41no—
435Dic11—41no—
436Dic11—41no—
437C25—111no—
438C23×C4—111no—
439C23×C4—111no—
440C23×C4—111no—
441C23×C4—111no—
442C23×C4—111no—
443C23×C4—222no—
444C23×C4—222no—
445C23×C4—222no—
446C23×C4—222no—
447C23×C4—441no—
448C23×C4—441no—
449C23×C4C22×D1111yescharacteristic
450C2×M16—222no—
451C2×M16—222no—
452C2×M16—222no—
453C2×M16—222no—
454C2×M16—441no—
455C2×M16—441no—
456C22×C8—111no—
457C22×C8—111no—
458C22×C8—111no—
459C22×C8—111no—
460C22×C8C22×D1111yescharacteristic
461C22×C8C22×D1111yescharacteristic
462C22×C8C22×D1111yescharacteristic
463C22×C8C22×D1111yescharacteristic
464#117—41no—
465#117—41no—
466#117—222no—
467#117—222no—
468C2×C4⋊C4—111no—
469C2×C4⋊C4—111no—
470C2×C4⋊C4C4×D1111yescharacteristic
471C2×C4⋊C4C4×D1111yescharacteristic
472C2×C22⋊C4—111no—
473C2×C22⋊C4—111no—
474C2×C22⋊C4—111no—
475C2×C22⋊C4—111no—
476C2×C22⋊C4—111no—
477C2×C22⋊C4—111no—
478C2×C22⋊C4—111no—
479C2×C22⋊C4—111no—
480C2×C22⋊C4—111no—
481C2×C22⋊C4—111no—
482C2×C22⋊C4C4×D1111yescharacteristic
483C2×C22⋊C4C4×D1111yescharacteristic
484C2×C42—111no—
485C2×C42—111no—
486C2×C42C22×D1111yescharacteristic
487C2×C42C22×D1111yescharacteristic
488C4⋊C8—222no—
489C4⋊C8—222no—
490C4⋊C8—441no—
491C4⋊C8—441no—
492C22⋊C8—22no—
493C22⋊C8—222no—
494C22⋊C8—222no—
495C22⋊C8—222no—
496C22⋊C8—222no—
497C22⋊C8—222no—
498C22⋊C8—222no—
499C22⋊C8—441no—
500C22⋊C8—441no—
501C22⋊C8D4414yes—
502#97—41no—
503#97—222no—
504C4×C8—41no—
505C4×C8—222no—
506#95—111no—
507#95—111no—
508#95—111no—
509#95—111no—
510#95—111no—
511#95—111no—
512#95—111no—
513#95—111no—
514C2×C11—42no—
515C2×C11#234211yescharacteristic
516C2×C11#292111yescharacteristic
517C2×C11#292411yescharacteristic
518C2×C11#293011yescharacteristic
519C2×C11#293311yescharacteristic
520C2×C11#297611yescharacteristic
521C2×C11#297811yescharacteristic
522D11—42no—
523D11—42no—
524C24—111no—
525C24—111no—
526C24—222no—
527C24—222no—
528C24—222no—
529C24—441no—
530C24—441no—
531C24—441no—
532C24—441no—
533C24C2×C4×D1111yescharacteristic
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—111no—
539C22×C4—112no—
540C22×C4—112no—
541C22×C4—111no—
542C22×C4—111no—
543C22×C4—111no—
544C22×C4—111no—
545C22×C4—111no—
546C22×C4—222no—
547C22×C4—222no—
548C22×C4—222no—
549C22×C4—221no—
550C22×C4—221no—
551C22×C4—221no—
552C22×C4—221no—
553C22×C4—222no—
554C22×C4—222no—
555C22×C4—222no—
556C22×C4—221no—
557C22×C4—221no—
558C22×C4—221no—
559C22×C4—221no—
560C22×C4—221no—
561C22×C4—221no—
562C22×C4—441no—
563C22×C4—441no—
564C22×C4—444no—
565C22×C4—444no—
566C22×C4—444no—
567C22×C4—444no—
568C22×C4—441no—
569C22×C4C2×C4×D1111yescharacteristic
570C22×C4C2×C4×D1111yescharacteristic
571C22×C4C2×C4×D1111yescharacteristic
572C22×C4C2×C4×D1111yescharacteristic
573C22×C4C2×C4×D1111yescharacteristic
574C22×C4C2×D4412yes—
575C22×C4#433912yes—
576C22×C4C23×D1111yescharacteristic
577M16—444no—
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—221no—
590C2×C8—221no—
591C2×C8—221no—
592C2×C8—221no—
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×C8C2×D4412yes—
602C2×C8C2×D4412yes—
603C4⋊C4—41no—
604C4⋊C4—41no—
605C4⋊C4—222no—
606C4⋊C4—222no—
607C22⋊C4—41no—
608C22⋊C4—41no—
609C22⋊C4—222no—
610C22⋊C4—222no—
611C22⋊C4—222no—
612C22⋊C4—222no—
613C22⋊C4—441no—
614C22⋊C4—441no—
615C22⋊C4—441no—
616C22⋊C4—441no—
617C22⋊C4—441no—
618C22⋊C4—441no—
619C42—21no—
620C42—21no—
621C42—21no—
622C42—21no—
623C42—221no—
624C42—221no—
625C42—221no—
626C42—221no—
627C11#2255911yescharacteristic, complemented, Sylow
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
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—444no—
649C23—444no—
650C23—444no—
651C23—444no—
652C23—444no—
653C23—444no—
654C23—444no—
655C23C4×D4412yes—
656C23C22×C4×D1111yescharacteristic
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
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—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—112no—
676C2×C4—221no—
677C2×C4—221no—
678C2×C4—222no—
679C2×C4—222no—
680C2×C4—222no—
681C2×C4—222no—
682C2×C4—221no—
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—221no—
693C2×C4—221no—
694C2×C4—221no—
695C2×C4—221no—
696C2×C4—221no—
697C2×C4—444no—
698C2×C4—444no—
699C2×C4—444no—
700C2×C4—441no—
701C2×C4—441no—
702C2×C4—441no—
703C2×C4—441no—
704C2×C4C4×D4412yes—
705C2×C4C22×D4411yescharacteristic
706C2×C4C2×#433911yescharacteristic
707C2×C4#6703711yescharacteristic
708C2×C4#6703711yescharacteristic
709C2×C4#41×D1111yescharacteristic
710C2×C4#41×D1111yescharacteristic
711C8—22no—
712C8—22no—
713C8—41no—
714C8—41no—
715C8—441no—
716C8—441no—
717C8—441no—
718C8—441no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—222no—
727C22—222no—
728C22—222no—
729C22—222no—
730C22—222no—
731C22—222no—
732C22—4416no—
733C22—441no—
734C22—441no—
735C22—441no—
736C22—441no—
737C22—441no—
738C22—441no—
739C22—441no—
740C22—441no—
741C22C2×C4×D4411yescharacteristic
742C22#1062301711yescharacteristic
743C22D11×#11711yescharacteristic
744C22D11×#13111yescharacteristic
745C22#1062328111yescharacteristic
746C22#1062328111yescharacteristic
747C22#1062328111yescharacteristic
748C4—22no—
749C4—41no—
750C4—41no—
751C4—41no—
752C4—41no—
753C4—222no—
754C4—441no—
755C4—441no—
756C4—441no—
757C4—441no—
758C4—441no—
759C4#1062308511yescharacteristic
760C4#1062308511yescharacteristic
761C4#1062308711yescharacteristic
762C4#1062308711yescharacteristic
763C2—42no—
764C2—442no—
765C2—442no—
766C2#1307146811yescharacteristic
767C2#1307725011yescharacteristic
768C2#1307727211yescharacteristic
769C2#1307732111yescharacteristic
770C2#1307734411yescharacteristic
771C2#1307765911yescharacteristic
772C2#1307767411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1750C2
prime radicalC24×D11C2×C4
cosocleC22×C4×C11C24
hypercenter#1750D11
hypocenterC11#22559
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1750

Complements

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

NH ≅ G/Ntype
1. C2×#10622333C2semidirect
4. #13069230C2semidirect
5. #13069229C2semidirect
6. #13069223C2semidirect
7. #13069222C2semidirect
8. #13068800C2semidirect
9. #13068800C2semidirect
10. #13068685C2semidirect
11. #13068600C2semidirect
13. #13068401C2semidirect
14. #13068399C2semidirect
15. C11×#1750C2semidirect
23. C2×C11×#97C22semidirect
24. C2×C4×C8×C11C22semidirect
33. C2×#66879C22semidirect
34. C2×Dic11⋊C8C22semidirect
35. C2×Dic11⋊C8C22semidirect
36. C2×C8×Dic11C22semidirect
49. C2×C4⋊(C11⋊C8)C22semidirect
50. C2×C4⋊(C11⋊C8)C22semidirect
53. C11×#336C22semidirect
54. C11×#336C22semidirect
55. #10622188C22semidirect
56. #10622188C22semidirect
57. #10622188C22semidirect
58. #10622188C22semidirect
59. #10622162C22semidirect
60. #10622162C22semidirect
256. #1750D11semidirect
370. C2×#97C2×D11semidirect
372. C2×C4×C8C2×D11semidirect
391. #336C2×D11semidirect
392. #336C2×D11semidirect
627. C11#22559semidirect

Maximal subgroups

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

subgroupindex
C2×#106223332
C2×#106223392
#130709952
#130692302
#130692292
#130692232
#130692222
#130688002
#130686852
#130686002
#130685252
#130684012
#130683992
C11×#17502
#2255911