Finite Group Databasebeta

← #14806864

Subgroups — #14806864

Order 2816.

1178 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622616C211yesmaximal, characteristic, complemented
2C2×#10622662C211yesmaximal, characteristic, complemented
3#13072056C211yesmaximal, characteristic
4#13069951C211yesmaximal, characteristic, complemented
5#13069809C211yesmaximal, characteristic, complemented
6#13069759C211yesmaximal, characteristic, complemented
7#13069617C211yesmaximal, characteristic, complemented
8#13068971C211yesmaximal, characteristic, complemented
9#13068933C211yesmaximal, characteristic, complemented
10#13068924C211yesmaximal, characteristic, complemented
11#13068914C211yesmaximal, characteristic, complemented
12#13068870C211yesmaximal, characteristic, complemented
13#13068804C211yesmaximal, characteristic, complemented
14#13068337C211yesmaximal, characteristic, complemented
15C2×C11×#552C211yesmaximal, characteristic, complemented
16C11×#552—24no—
17C11×#552—24no—
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
29C22×#4325C2211yescharacteristic
30C2×#66992—21no—
31C2×#66983C2211yescharacteristic
32C2×#66983C2211yescharacteristic
33C22×C4⋊Dic11C2211yescharacteristic
34C22×#4318C2211yescharacteristic
35C2×#66899C2211yescharacteristic
36C2×#66899C2211yescharacteristic
37C2×#66899C2211yescharacteristic
38#10622825C2211yescharacteristic
39C2×C22⋊(C11⋊C8)C2211yescharacteristic
40C2×C22⋊(C11⋊C8)C2211yescharacteristic
41C2×C22⋊(C11⋊C8)C2211yescharacteristic
42#10622662—24no—
43#10622616—24no—
44#10622607—21no—
45C2×#66873C2211yescharacteristic
46C2×#66873C2211yescharacteristic
47C2×#66873C2211yescharacteristic
48C2×#66872C2211yescharacteristic
49C2×#66871C2211yescharacteristic
50C2×#66871C2211yescharacteristic
51#10622574—21no—
52#10622571—21no—
53#10622552C2211yescharacteristic
54#10622541C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622162C2211yescharacteristic
62#10622162C2211yescharacteristic
63C22×Q8×C11C2311yescharacteristic
64C22×D4×C11D411yescharacteristic
65C23×C4×C11—21no—
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C22×C22⋊D11—21no—
69C22×C22⋊D11—21no—
70C23×Dic11—21no—
71C22×D44C2311yescharacteristic
72C11×#126—28no—
73C11×#125—28no—
74C11×#125—22no—
75C11×#125—22no—
76C11×#123—28no—
77C11×C22⋊Q8—22no—
78C11×C22⋊Q8—22no—
79C11×C22⋊Q8—22no—
80C11×C22⋊Q8D414yescomplemented
81C4×Q8×C11—22no—
82C4×Q8×C11—22no—
83C4×D4×C11—22no—
84C4×D4×C11—22no—
85C11×#117—28no—
86C11×#117—22no—
87C11×#117D414yescomplemented
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4—22no—
95C2×C11×C4⋊C4—22no—
96C2×C11×C4⋊C4D411yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C22⋊C4—21no—
101C2×C11×C22⋊C4—21no—
102C2×C11×C22⋊C4—21no—
103C2×C11×C22⋊C4D411yescharacteristic
104C2×C11×C22⋊C4D411yescharacteristic
105C2×C42×C11—21no—
106C2×C42×C11—21no—
107C2×C42×C11C2311yescharacteristic
108C2×C22⋊Dic11—21no—
109C2×#4325—22no—
110C2×#4325—22no—
111C2×#4325—41no—
112#66992—44no—
113#66983—22no—
114#66983—22no—
115#66983—22no—
116#66983—41no—
117C2×(C2×D11)⋊C4—21no—
118C2×(C2×D11)⋊C4—21no—
119C2×(C2×D11)⋊C4—21no—
120C2×(C2×D11)⋊C4—21no—
121C2×C4⋊Dic11—22no—
122C2×C4⋊Dic11—21no—
123C2×C4⋊Dic11—41no—
124C2×C4⋊Dic11C2311yescharacteristic
125C2×C4⋊Dic11C2311yescharacteristic
126C2×C4⋊Dic11C2311yescharacteristic
127C2×Dic11⋊C4—21no—
128C2×#4318—22no—
129C2×#4318—22no—
130C2×#4318—41no—
131C22×C11⋊C8C2311yescharacteristic
132C22×C11⋊C8C2311yescharacteristic
133C22×C11⋊C8C2311yescharacteristic
134C22×C11⋊C8C2311yescharacteristic
135#66899—22no—
136#66899—22no—
137#66899—41no—
138C11⋊#95—21no—
139C11⋊#95—21no—
140C22⋊(C11⋊C8)—22no—
141C22⋊(C11⋊C8)—22no—
142C22⋊(C11⋊C8)—41no—
143#66873—22no—
144#66873—22no—
145#66873—22no—
146#66872—22no—
147#66871—22no—
148#66871—22no—
149#25560—111nomaximal, Sylow
150C24×C11C2×D411yescharacteristic
151C24×C11C2×D411yescharacteristic
152C23×D11—21no—
153C2×Q8×C11—21no—
154C2×Q8×C11—21no—
155C2×Q8×C11—21no—
156C2×Q8×C11—21no—
157C2×Q8×C11—21no—
158C2×Q8×C11C2×D412yes—
159C2×D4×C11—22no—
160C2×D4×C11—22no—
161C2×D4×C11—41no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—24no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—42no—
178C22×C4×C11—42no—
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2×D411yescharacteristic
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11C2×D412yes—
184C22×C4×C11C2×D412yes—
185C22×C4×C11C2411yescharacteristic
186C2×C22⋊D11—42no—
187C2×C22⋊D11—42no—
188C2×C22⋊D11—42no—
189C2×C22⋊D11—42no—
190C2×C22⋊D11—42no—
191C2×C22⋊D11—81no—
192C22×Dic11—21no—
193C22×Dic11—21no—
194C22×Dic11—21no—
195C22×Dic11—42no—
196C22×Dic11—42no—
197C22×Dic11—81no—
198C2×D44—21no—
199C2×D44—21no—
200C2×D44—21no—
201C2×D44—21no—
202C2×D44—21no—
203C2×D44—21no—
204C11×C4⋊C4—24no—
205C11×C4⋊C4—24no—
206C11×C4⋊C4—24no—
207C11×C4⋊C4—24no—
208C11×C4⋊C4—24no—
209C11×C4⋊C4—24no—
210C11×C4⋊C4—22no—
211C11×C4⋊C4—21no—
212C11×C4⋊C4—21no—
213C11×C4⋊C4—21no—
214C11×C4⋊C4C2×D412yes—
215C11×C4⋊C4C2×D412yes—
216C11×C4⋊C4C2×D412yes—
217C11×C22⋊C4—24no—
218C11×C22⋊C4—24no—
219C11×C22⋊C4—24no—
220C11×C22⋊C4—22no—
221C11×C22⋊C4—22no—
222C42×C11—24no—
223C42×C11—24no—
224C42×C11—21no—
225C42×C11—21no—
226C22⋊Dic11—42no—
227#4325—44no—
228(C2×D11)⋊C4—42no—
229(C2×D11)⋊C4—42no—
230(C2×D11)⋊C4—42no—
231(C2×D11)⋊C4—81no—
232C4⋊Dic11—21no—
233C4⋊Dic11—21no—
234C4⋊Dic11—21no—
235C4⋊Dic11—21no—
236C4⋊Dic11—21no—
237C4⋊Dic11—42no—
238C4⋊Dic11#4112yes—
239Dic11⋊C4—42no—
240#4318—44no—
241C2×C11⋊C8—21no—
242C2×C11⋊C8—21no—
243C2×C11⋊C8—21no—
244C2×C11⋊C8—21no—
245C2×C11⋊C8—21no—
246C2×C11⋊C8—21no—
247C2×C11⋊C8—21no—
248C2×C11⋊C8—21no—
249C2×C11⋊C8—21no—
250C2×C11⋊C8—21no—
251C2×C11⋊C8—21no—
252C2×C11⋊C8#4112yes—
253C2×#552D1111yescharacteristic, complemented
254C2×#482—111no—
255C2×#468—111no—
256#2416—111no—
257#2059—111no—
258#2035—111no—
259#2025—111no—
260#2000—111no—
261#1880—111no—
262#1874—111no—
263#1872—111no—
264#1870—111no—
265#1863—111no—
266#1852—111no—
267#1736—111no—
268C23×C11—21no—
269C23×C11—21no—
270C23×C11—21no—
271C23×C11—21no—
272C23×C11—21no—
273C23×C11—21no—
274C23×C11—21no—
275C23×C11—21no—
276C23×C11—21no—
277C23×C11—21no—
278C23×C11—21no—
279C23×C11—21no—
280C23×C11#12012yes—
281C23×C11AGL(1,ℤ/8)12yes—
282C23×C11C22×D411yescharacteristic
283C22×D11—41no—
284C22×D11—41no—
285C22×D11—41no—
286C22×D11—41no—
287C22×D11—41no—
288C22×D11—41no—
289C22×D11—41no—
290Q8×C11—22no—
291Q8×C11—22no—
292Q8×C11—41no—
293Q8×C11—41no—
294D4×C11—44no—
295C2×C4×C11—21no—
296C2×C4×C11—21no—
297C2×C4×C11—22no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—21no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—21no—
306C2×C4×C11—21no—
307C2×C4×C11—22no—
308C2×C4×C11—21no—
309C2×C4×C11—21no—
310C2×C4×C11—21no—
311C2×C4×C11—21no—
312C2×C4×C11—21no—
313C2×C4×C11—21no—
314C2×C4×C11—48no—
315C2×C4×C11—41no—
316C2×C4×C11—41no—
317C2×C4×C11—41no—
318C2×C4×C11—41no—
319C2×C4×C11—41no—
320C2×C4×C11—41no—
321C2×C4×C11—41no—
322C2×C4×C11—41no—
323C2×C4×C11—41no—
324C2×C4×C11—41no—
325C2×C4×C11—41no—
326C2×C4×C11—41no—
327C2×C4×C11#12012yes—
328C2×C4×C11C22×D411yescharacteristic
329C2×C4×C11C22×D411yescharacteristic
330C2×C4×C11C2×#4111yescharacteristic
331C2×C4×C11C2×#4111yescharacteristic
332C2×C4×C11H(5,𝔽2)11yescharacteristic
333C2×C4×C112−1+411yescharacteristic
334C22⋊D11—84no—
335C22⋊D11—84no—
336C2×Dic11—22no—
337C2×Dic11—41no—
338C2×Dic11—41no—
339C2×Dic11—41no—
340C2×Dic11—41no—
341C2×Dic11—41no—
342C2×Dic11—41no—
343C2×Dic11—41no—
344C2×Dic11—41no—
345C2×Dic11—84no—
346D44—41no—
347D44—41no—
348D44—41no—
349D44—41no—
350C11⋊C8—22no—
351C11⋊C8—41no—
352C11⋊C8—41no—
353C11⋊C8—41no—
354C22×SD16—111no—
355C22×M16—111no—
356#552—24no—
357#552—24no—
358C2×#126—21no—
359C2×#125—21no—
360C2×#125C2×D1111yescharacteristic
361C2×#123—21no—
362C2×C22⋊Q8C2×D1111yescharacteristic
363C2×C22⋊Q8C2×D1111yescharacteristic
364C2×#121—111no—
365C2×#121—111no—
366C2×#121—221no—
367C2×C4×Q8C2×D1111yescharacteristic
368C2×C4×D4C2×D1111yescharacteristic
369C2×#117—21no—
370C2×#117C2×D1111yescharacteristic
371C22×C4⋊C4—111no—
372C22×C4⋊C4C2×D1111yescharacteristic
373#482—224no—
374#468—224no—
375C2×#107—111no—
376C2×#107—111no—
377C2×#106—111no—
378C2×#103—111no—
379C2×#103—111no—
380C2×#103—111no—
381C2×#102—111no—
382C2×#102—111no—
383C2×#102—111no—
384C2×C22⋊C8—111no—
385C2×C22⋊C8—111no—
386C2×C22⋊C8—111no—
387#396—221no—
388#394—221no—
389#390—111no—
390#389—111no—
391#386—221no—
392#380—111no—
393#340—111no—
394#340—111no—
395#340—111no—
396#340—111no—
397#340—111no—
398#340—111no—
399#336—111no—
400#336—111no—
401C22×C11—22no—
402C22×C11—22no—
403C22×C11—22no—
404C22×C11—22no—
405C22×C11—22no—
406C22×C11—22no—
407C22×C11—41no—
408C22×C11—41no—
409C22×C11—41no—
410C22×C11—41no—
411C22×C11—41no—
412C22×C11—41no—
413C22×C11—41no—
414C22×C11—41no—
415C22×C11C2×#12011yescharacteristic
416C22×C11#54611yescharacteristic
417C22×C11#54711yescharacteristic
418C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
419C22×C11#57511yescharacteristic
420C22×C11#57711yescharacteristic
421C22×C11#57811yescharacteristic
422C2×D11—81no—
423C2×D11—81no—
424C2×D11—81no—
425C2×D11—81no—
426C2×D11—81no—
427C2×D11—81no—
428C2×D11—81no—
429C4×C11—22no—
430C4×C11—41no—
431C4×C11—42no—
432C4×C11—41no—
433C4×C11—42no—
434C4×C11—42no—
435C4×C11—41no—
436C4×C11—42no—
437C4×C11#53211yescharacteristic
438C4×C11#53711yescharacteristic
439C4×C11#54611yescharacteristic
440C4×C11#54711yescharacteristic
441Dic11—42no—
442Dic11—81no—
443Dic11—81no—
444C22×Q8C22×D1111yescharacteristic
445C22×D4—111no—
446C22×D4—221no—
447C22×D4—221no—
448C22×D4C22⋊D1111yescharacteristic
449C23×C4—21no—
450C23×C4—221no—
451C23×C4C22×D1111yescharacteristic
452C23×C4C22×D1111yescharacteristic
453C2×SD16—222no—
454C2×SD16—222no—
455C2×SD16—441no—
456C2×M16—222no—
457C2×M16—222no—
458C2×M16—441no—
459C22×C8—111no—
460C22×C8—111no—
461C22×C8—111no—
462C22×C8—111no—
463#126—28no—
464#125—28no—
465#125—22no—
466#125—22no—
467#123—28no—
468C22⋊Q8—22no—
469C22⋊Q8—22no—
470C22⋊Q8—22no—
471C22⋊Q8C22⋊D1114yescomplemented
472#121—222no—
473#121—222no—
474#121—222no—
475#121—441no—
476#121—444no—
477C4×Q8—22no—
478C4×Q8—22no—
479C4×D4—22no—
480C4×D4—22no—
481#117—28no—
482#117—22no—
483#117C22⋊D1114yescomplemented
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—22no—
491C2×C4⋊C4—22no—
492C2×C4⋊C4—111no—
493C2×C4⋊C4—111no—
494C2×C4⋊C4—111no—
495C2×C4⋊C4—222no—
496C2×C4⋊C4—221no—
497C2×C4⋊C4—221no—
498C2×C4⋊C4—441no—
499C2×C4⋊C4C22⋊D1111yescharacteristic
500C2×C4⋊C4C22×D1111yescharacteristic
501C2×C4⋊C4C22×D1111yescharacteristic
502C2×C4⋊C4C22×D1111yescharacteristic
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—221no—
507C2×C22⋊C4—221no—
508C2×C22⋊C4—221no—
509C2×C22⋊C4—221no—
510C2×C22⋊C4—221no—
511C2×C22⋊C4C22⋊D1111yescharacteristic
512C2×C22⋊C4C22⋊D1111yescharacteristic
513C2×C42—21no—
514C2×C42—21no—
515C2×C42C22×D1111yescharacteristic
516#107—222no—
517#107—222no—
518#106—222no—
519#103—222no—
520#103—222no—
521#103—441no—
522#102—222no—
523#102—222no—
524#102—222no—
525C22⋊C8—222no—
526C22⋊C8—222no—
527C22⋊C8—441no—
528#95—221no—
529#95—221no—
530C2×C11—42no—
531C2×C11—42no—
532C2×C11#243011yescharacteristic
533C2×C11#300611yescharacteristic
534C2×C11#301311yescharacteristic
535C2×C11#331011yescharacteristic
536C2×C11#332711yescharacteristic
537C2×C11#334311yescharacteristic
538C2×C11#335111yescharacteristic
539D11—161no—
540C24—221no—
541C24C2×C22⋊D1111yescharacteristic
542C24C2×C22⋊D1111yescharacteristic
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8C2×C22⋊D1112yes—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—41no—
552C2×D4—221no—
553C2×D4—221no—
554C2×D4—221no—
555C2×D4—221no—
556C2×D4—221no—
557C2×D4—221no—
558C2×D4—442no—
559C2×D4—442no—
560C2×D4—442no—
561C2×D4—442no—
562C2×D4—442no—
563C2×D4—881no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—24no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—221no—
582C22×C4—221no—
583C22×C4—221no—
584C22×C4—442no—
585C22×C4—442no—
586C22×C4—881no—
587C22×C4C2×C22⋊D1111yescharacteristic
588C22×C4C2×C22⋊D1111yescharacteristic
589C22×C4C2×C22⋊D1111yescharacteristic
590C22×C4C2×C22⋊D1111yescharacteristic
591C22×C4C2×C22⋊D1112yes—
592C22×C4C2×C22⋊D1112yes—
593C22×C4C23×D1111yescharacteristic
594SD16—444no—
595M16—444no—
596C2×C8—112no—
597C2×C8—221no—
598C2×C8—221no—
599C2×C8—221no—
600C2×C8—221no—
601C2×C8—221no—
602C2×C8—221no—
603C2×C8—221no—
604C2×C8—221no—
605C2×C8—221no—
606C2×C8—221no—
607C2×C8—221no—
608C4⋊C4—24no—
609C4⋊C4—24no—
610C4⋊C4—24no—
611C4⋊C4—24no—
612C4⋊C4—24no—
613C4⋊C4—24no—
614C4⋊C4—22no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—112no—
619C4⋊C4—221no—
620C4⋊C4—221no—
621C4⋊C4—221no—
622C4⋊C4—221no—
623C4⋊C4—221no—
624C4⋊C4—442no—
625C4⋊C4—442no—
626C4⋊C4C2×C22⋊D1112yes—
627C4⋊C4C2×C22⋊D1112yes—
628C4⋊C4C2×C22⋊D1112yes—
629C22⋊C4—24no—
630C22⋊C4—24no—
631C22⋊C4—24no—
632C22⋊C4—22no—
633C22⋊C4—22no—
634C22⋊C4—442no—
635C22⋊C4—442no—
636C22⋊C4—442no—
637C22⋊C4—442no—
638C22⋊C4—881no—
639C42—24no—
640C42—24no—
641C42—21no—
642C42—21no—
643C11#2556011yescharacteristic, complemented, Sylow
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—441no—
657C23—441no—
658C23—441no—
659C23—441no—
660C23—441no—
661C23—441no—
662C23—441no—
663C23#6700212yes—
664C23#6700612yes—
665C23C22×C22⋊D1111yescharacteristic
666Q8—22no—
667Q8—22no—
668Q8—41no—
669Q8—41no—
670D4—44no—
671D4—441no—
672D4—441no—
673D4—441no—
674D4—441no—
675D4—884no—
676D4—884no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—22no—
696C2×C4—48no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—222no—
710C2×C4—441no—
711C2×C4—441no—
712C2×C4—441no—
713C2×C4—441no—
714C2×C4—441no—
715C2×C4—441no—
716C2×C4—441no—
717C2×C4—441no—
718C2×C4—884no—
719C2×C4#6700612yes—
720C2×C4#41×D1111yescharacteristic
721C2×C4#41×D1111yescharacteristic
722C2×C4#6704211yescharacteristic
723C2×C4#6704311yescharacteristic
724C2×C4C22×C22⋊D1111yescharacteristic
725C2×C4C22×C22⋊D1111yescharacteristic
726C8—222no—
727C8—441no—
728C8—441no—
729C8—441no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—881no—
745C22—881no—
746C22—881no—
747C22—881no—
748C22—881no—
749C22—881no—
750C22—881no—
751C22C2×#6700211yescharacteristic
752C22#1062335311yescharacteristic
753C22#1062335511yescharacteristic
754C22#1062336011yescharacteristic
755C22#1062336811yescharacteristic
756C22#1062336911yescharacteristic
757C22C2×#6700611yescharacteristic
758C4—22no—
759C4—41no—
760C4—42no—
761C4—41no—
762C4—42no—
763C4—42no—
764C4—41no—
765C4—42no—
766C4—442no—
767C4—881no—
768C4—881no—
769C4#1062335511yescharacteristic
770C4#1062336011yescharacteristic
771C4#1062336311yescharacteristic
772C4#1062336411yescharacteristic
773C2—42no—
774C2—42no—
775C2—1761no—
776C2#1307222011yescharacteristic
777C2#1307786811yescharacteristic
778C2#1307793111yescharacteristic
779C2#1308063111yescharacteristic
780C2#1308087811yescharacteristic
781C2#1308105611yescharacteristic
782C2#1308117611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#552C2
socleC23×C11C22×D4
prime radical#13072056C2
hypercenterC2×#552D11
hypocenterC11#25560
LCSG ▷ C22×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
1. C2×#10622616C2semidirect
2. C2×#10622662C2semidirect
4. #13069951C2semidirect
5. #13069809C2semidirect
6. #13069759C2semidirect
7. #13069617C2semidirect
8. #13068971C2semidirect
9. #13068933C2semidirect
10. #13068924C2semidirect
11. #13068914C2semidirect
12. #13068870C2semidirect
13. #13068804C2semidirect
14. #13068337C2semidirect
15. C2×C11×#552C2semidirect
80. C11×C22⋊Q8D4semidirect
87. C11×#117D4semidirect
253. C2×#552D11semidirect
471. C22⋊Q8C22⋊D11semidirect
483. #117C22⋊D11semidirect
643. C11#25560semidirect

Maximal subgroups

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

subgroupindex
C2×#106226162
C2×#106226622
#130720562
#130699512
#130698092
#130697592
#130696172
#130689712
#130689332
#130689242
#130689142
#130688702
#130688042
#130683372
C2×C11×#5522
#2556011