Finite Group Databasebeta

← #14797558

Subgroups — #14797558

Order 2816.

1042 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622851C211yesmaximal, characteristic
2C2×C4×#4325C211yesmaximal, characteristic, complemented
3#13072130C211yesmaximal, characteristic, complemented
4#13070149C211yesmaximal, characteristic, complemented
5#13070052C211yesmaximal, characteristic, complemented
6#13069926C211yesmaximal, characteristic, complemented
7#13069805C211yesmaximal, characteristic, complemented
8#13069302C211yesmaximal, characteristic, complemented
9#13069224C211yesmaximal, characteristic, complemented
10#13068971C211yesmaximal, characteristic, complemented
11#13068967C211yesmaximal, characteristic, complemented
12#13068884C211yesmaximal, characteristic, complemented
13#13068621C211yesmaximal, characteristic, complemented
14#13068556C211yesmaximal, characteristic, complemented
15C11×#2341C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C22×#4325C2211yescharacteristic
20C22×#4323C2211yescharacteristic
21C2×#66983C2211yescharacteristic
22C2×#66936—21no—
23C2×C4×D44C2211yescharacteristic
24C11×#390—21no—
25C11×#390—21no—
26C11×#390C2211yescharacteristic
27C11×#390C2211yescharacteristic
28C11×#380—21no—
29C11×#380C2211yescharacteristic
30C4×C11×C22⋊C4—21no—
31C4×C11×C22⋊C4C2211yescharacteristic
32#10622851—24no—
33C2×#66899C2211yescharacteristic
34C2×#66899C2211yescharacteristic
35C2×#66899C2211yescharacteristic
36C2×#66896C2211yescharacteristic
37C2×#66896C2211yescharacteristic
38C2×#66896C2211yescharacteristic
39#10622825C2211yescharacteristic
40C2×C22⋊(C11⋊C8)C2211yescharacteristic
41C2×C22⋊(C11⋊C8)C2211yescharacteristic
42C4×#4325—24no—
43C2×#66873C2211yescharacteristic
44C2×#66873C2211yescharacteristic
45C2×#66872C2211yescharacteristic
46C2×#66872C2211yescharacteristic
47#10622574—21no—
48#10622552C2211yescharacteristic
49#10622548C2211yescharacteristic
50#10622541C2211yescharacteristic
51C2×C4⋊(C11⋊C8)C2211yescharacteristic
52C2×C4×C11⋊C8C2211yescharacteristic
53#10622287—21no—
54#10622281—21no—
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C2×C11×#41—22no—
62C2×C11×#41—22no—
63C2×C11×#41—22no—
64C2×C11×#41—22no—
65C2×C11×#41—41no—
66C2×C11×#41—41no—
67C22×Q8×C11C2311yescharacteristic
68C22×D4×C11—21no—
69C22×D4×C11C2311yescharacteristic
70C23×C4×C11—21no—
71C23×C4×C11C2311yescharacteristic
72C22×C22⋊D11—21no—
73C22×D44C2311yescharacteristic
74C22×C4×D11—21no—
75C4×Q8×C11—22no—
76C4×Q8×C11—22no—
77C4×Q8×C11—41no—
78C4×Q8×C11—41no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4D411yescharacteristic
89C2×C11×C22⋊C4D411yescharacteristic
90C2×C42×C11—21no—
91C2×C42×C11—21no—
92C2×C42×C11C2311yescharacteristic
93C2×C42×C11C2311yescharacteristic
94C2×C22⋊Dic11—21no—
95C2×#4325—22no—
96C2×#4325—22no—
97C2×#4325D414yes—
98C2×#4323—22no—
99C2×#4323—22no—
100C2×#4323—41no—
101#66983—22no—
102#66983—41no—
103C2×(C2×D11)⋊C4—21no—
104C2×(C2×D11)⋊C4—21no—
105C2×(C2×D11)⋊C4—21no—
106C2×(C2×D11)⋊C4—21no—
107C2×C4⋊Dic11—21no—
108C2×C4⋊Dic11—21no—
109C2×C4⋊Dic11C2311yescharacteristic
110C2×C4⋊Dic11C2311yescharacteristic
111C2×C4⋊Dic11C2311yescharacteristic
112C2×Dic11⋊C4—21no—
113C22×C11⋊C8C2311yescharacteristic
114C22×C11⋊C8C2311yescharacteristic
115C22×C11⋊C8C2311yescharacteristic
116C22×C11⋊C8C2311yescharacteristic
117#66936—44no—
118C4×D44—22no—
119C4×D44—41no—
120C11×#95—21no—
121C11×#95D411yescharacteristic
122C11×#95D411yescharacteristic
123#66899—22no—
124#66899—22no—
125#66899—22no—
126#66896—22no—
127#66896—22no—
128#66896—41no—
129C11⋊#95—21no—
130C11⋊#95—21no—
131C22⋊(C11⋊C8)—22no—
132C22⋊(C11⋊C8)—41no—
133#66873—22no—
134#66873—41no—
135#66872—22no—
136#66872—41no—
137C4⋊(C11⋊C8)—41no—
138C4×C11⋊C8—22no—
139#24896—111nomaximal, Sylow
140C24×C11—21no—
141C24×C11C2×D411yescharacteristic
142C23×D11—21no—
143C11×#41—44no—
144C11×#41—44no—
145C11×#41—44no—
146C11×#41—44no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11C2×D412yes—
151C2×Q8×C11#4112yes—
152C2×Q8×C11#4112yes—
153C2×D4×C11—24no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—42no—
160C2×D4×C11—42no—
161C2×D4×C11#4112yes—
162C22×C4×C11—21no—
163C22×C4×C11—24no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—42no—
173C22×C4×C11—42no—
174C22×C4×C11C2×D411yescharacteristic
175C22×C4×C11C2×D411yescharacteristic
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11C2411yescharacteristic
180C2×C22⋊D11—42no—
181C2×C22⋊D11—42no—
182C2×C22⋊D11—81no—
183C22×Dic11—21no—
184C22×Dic11—21no—
185C22×Dic11—21no—
186C2×D44—21no—
187C2×D44—21no—
188C2×D44—21no—
189C2×D44—21no—
190C2×D44—21no—
191C2×D44C2×D412yes—
192C2×C4×D11—42no—
193C2×C4×D11—42no—
194C2×C4×D11—81no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4—42no—
200C11×C4⋊C4—42no—
201C11×C22⋊C4—22no—
202C11×C22⋊C4—22no—
203C11×C22⋊C4—42no—
204C11×C22⋊C4—42no—
205C11×C22⋊C4—81no—
206C11×C22⋊C4—81no—
207C11×C22⋊C4—81no—
208C42×C11—21no—
209C42×C11—21no—
210C42×C11—21no—
211C42×C11—21no—
212C42×C11—42no—
213C42×C11—42no—
214C22⋊Dic11—42no—
215#4325—28no—
216#4323—44no—
217(C2×D11)⋊C4—42no—
218(C2×D11)⋊C4—42no—
219(C2×D11)⋊C4—42no—
220(C2×D11)⋊C4—42no—
221C4⋊Dic11—21no—
222C4⋊Dic11—21no—
223C4⋊Dic11—21no—
224C4⋊Dic11—21no—
225C4⋊Dic11—21no—
226C4⋊Dic11—21no—
227C4⋊Dic11—42no—
228C4⋊Dic11—81no—
229Dic11⋊C4—42no—
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—
240C2×C11⋊C8—21no—
241C2×C11⋊C8C2×D412yes—
242C2×#449—111no—
243C2×C4×SD16—111no—
244#2422—111no—
245#2341D1111yescharacteristic, complemented
246#2094—111no—
247#2077—111no—
248#2054—111no—
249#2034—111no—
250#1934—111no—
251#1923—111no—
252#1880—111no—
253#1879—111no—
254#1865—111no—
255#1803—111no—
256#1788—111no—
257C23×C11—21no—
258C23×C11—22no—
259C23×C11—21no—
260C23×C11—21no—
261C23×C11—21no—
262C23×C11—21no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11—41no—
266C23×C11—41no—
267C23×C11—41no—
268C23×C11—41no—
269C23×C11—41no—
270C23×C11—41no—
271C23×C11C22×D411yescharacteristic
272C22×D11—22no—
273C22×D11—41no—
274C22×D11—41no—
275C22×D11—41no—
276C22×D11—41no—
277C22×D11—41no—
278C22×D11—41no—
279Q8×C11—22no—
280Q8×C11—22no—
281Q8×C11—22no—
282Q8×C11#12314yescomplemented
283D4×C11—22no—
284D4×C11—22no—
285D4×C11—48no—
286D4×C11—41no—
287D4×C11—41no—
288C2×C4×C11—22no—
289C2×C4×C11—21no—
290C2×C4×C11—22no—
291C2×C4×C11—21no—
292C2×C4×C11—22no—
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×C11—48no—
305C2×C4×C11—41no—
306C2×C4×C11—41no—
307C2×C4×C11—41no—
308C2×C4×C11—41no—
309C2×C4×C11—41no—
310C2×C4×C11—41no—
311C2×C4×C11—41no—
312C2×C4×C11—41no—
313C2×C4×C11—41no—
314C2×C4×C11—41no—
315C2×C4×C11#13512yes—
316C2×C4×C11AGL(1,ℤ/8)12yes—
317C2×C4×C11C22×D411yescharacteristic
318C2×C4×C11C2×#4111yescharacteristic
319C2×C4×C11C2×#4111yescharacteristic
320C2×C4×C11C2×#4111yescharacteristic
321C2×C4×C11H(5,𝔽2)11yescharacteristic
322C2×C4×C11H(5,𝔽2)11yescharacteristic
323C22⋊D11—84no—
324C2×Dic11—41no—
325C2×Dic11—41no—
326C2×Dic11—41no—
327C2×Dic11—41no—
328C2×Dic11—41no—
329C2×Dic11—41no—
330C2×Dic11—41no—
331C2×Dic11—41no—
332C2×Dic11—41no—
333D44—22no—
334D44—22no—
335D44—41no—
336D44—41no—
337C4×D11—84no—
338C11⋊C8—22no—
339C11⋊C8—41no—
340C11⋊C8—41no—
341C11⋊C8—41no—
342C22×#41C2×D1111yescharacteristic
343C22×SD16—111no—
344C22×D8—111no—
345C2×#123—221no—
346C2×#121—111no—
347C2×C4×Q8C2×D1111yescharacteristic
348C2×C4×Q8C2×D1111yescharacteristic
349C2×C4×D4—111no—
350#449—224no—
351C4×SD16—224no—
352C2×#106—111no—
353C2×#106—111no—
354C2×C4⋊C8—111no—
355C2×#103—111no—
356C2×#103—111no—
357C2×#103—111no—
358C2×#102—111no—
359C2×#102—111no—
360C2×#102—111no—
361C2×#102—111no—
362C2×#102—111no—
363C2×C22⋊C8—111no—
364C2×C22⋊C8—111no—
365C2×C4×C8—111no—
366#397—221no—
367#394—221no—
368#390—21no—
369#390—21no—
370#390—111no—
371#390C2×D1111yescharacteristic
372#390C2×D1111yescharacteristic
373#389—111no—
374#385—221no—
375#384—111no—
376#380—21no—
377#380—111no—
378#380C2×D1111yescharacteristic
379C4×C22⋊C4—21no—
380C4×C22⋊C4C2×D1111yescharacteristic
381#340—111no—
382#340—111no—
383#340—111no—
384#340—111no—
385#336—111no—
386#336—111no—
387C22×C11—41no—
388C22×C11—41no—
389C22×C11—42no—
390C22×C11—41no—
391C22×C11—42no—
392C22×C11—42no—
393C22×C11—41no—
394C22×C11—41no—
395C22×C11—41no—
396C22×C11—41no—
397C22×C11—81no—
398C22×C11—81no—
399C22×C11—81no—
400C22×C11—81no—
401C22×C11#52511yescharacteristic
402C22×C11D4211yescharacteristic
403C22×C11#54611yescharacteristic
404C22×C11C2×#13511yescharacteristic
405C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
406C22×C11#57711yescharacteristic
407C22×C11#57711yescharacteristic
408C2×D11—42no—
409C2×D11—42no—
410C2×D11—42no—
411C2×D11—81no—
412C2×D11—81no—
413C2×D11—81no—
414C2×D11—81no—
415C4×C11—24no—
416C4×C11—22no—
417C4×C11—22no—
418C4×C11—41no—
419C4×C11—41no—
420C4×C11—41no—
421C4×C11—81no—
422C4×C11—81no—
423C4×C11C2×#12311yescharacteristic
424C4×C11#53811yescharacteristic
425C4×C11#54611yescharacteristic
426C4×C11#55111yescharacteristic
427Dic11—81no—
428Dic11—81no—
429Dic11—81no—
430C2×#41—22no—
431C2×#41—22no—
432C2×#41—22no—
433C2×#41—22no—
434C2×#41—41no—
435C2×#41—41no—
436C22×Q8C22×D1111yescharacteristic
437C22×D4—21no—
438C22×D4—111no—
439C22×D4—221no—
440C22×D4C22×D1111yescharacteristic
441C23×C4—21no—
442C23×C4—221no—
443C23×C4C22×D1111yescharacteristic
444C2×SD16—114no—
445C2×SD16—222no—
446C2×SD16—222no—
447C2×D8—222no—
448C2×D8—222no—
449C2×D8—441no—
450C22×C8—111no—
451C22×C8—111no—
452C22×C8—111no—
453C22×C8—111no—
454#123—444no—
455#121—222no—
456#121—441no—
457C4×Q8—22no—
458C4×Q8—22no—
459C4×Q8—41no—
460C4×Q8—41no—
461C4×D4—222no—
462C4×D4—441no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—111no—
466C2×C4⋊C4—111no—
467C2×C4⋊C4—111no—
468C2×C4⋊C4—221no—
469C2×C4⋊C4—221no—
470C2×C4⋊C4—221no—
471C2×C4⋊C4C22×D1111yescharacteristic
472C2×C4⋊C4C22×D1111yescharacteristic
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—221no—
479C2×C22⋊C4—221no—
480C2×C22⋊C4—221no—
481C2×C22⋊C4—221no—
482C2×C22⋊C4—221no—
483C2×C22⋊C4C22⋊D1111yescharacteristic
484C2×C22⋊C4C22⋊D1111yescharacteristic
485C2×C42—21no—
486C2×C42—21no—
487C2×C42C22×D1111yescharacteristic
488C2×C42C22×D1111yescharacteristic
489#106—222no—
490#106—441no—
491C4⋊C8—441no—
492#103—222no—
493#103—222no—
494#103—222no—
495#102—222no—
496#102—222no—
497#102—222no—
498#102—441no—
499#102—441no—
500C22⋊C8—222no—
501C22⋊C8—441no—
502C4×C8—222no—
503#95—21no—
504#95—221no—
505#95—221no—
506#95C22⋊D1111yescharacteristic
507#95C22⋊D1111yescharacteristic
508C2×C11—81no—
509C2×C11—82no—
510C2×C11#241811yescharacteristic
511C2×C11#310611yescharacteristic
512C2×C11#312511yescharacteristic
513C2×C11#326511yescharacteristic
514C2×C11#328411yescharacteristic
515C2×C11#330111yescharacteristic
516C2×C11#333211yescharacteristic
517D11—82no—
518C24—21no—
519C24—221no—
520C24C2×C22⋊D1111yescharacteristic
521#41—44no—
522#41—44no—
523#41—44no—
524#41—44no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8#433912yes—
529C2×Q8D4×D1112yes—
530C2×Q8#434112yes—
531C2×D4—24no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—42no—
538C2×D4—42no—
539C2×D4—112no—
540C2×D4—221no—
541C2×D4—221no—
542C2×D4—221no—
543C2×D4—221no—
544C2×D4—221no—
545C2×D4—442no—
546C2×D4—442no—
547C2×D4—881no—
548C2×D4#433912yes—
549C22×C4—21no—
550C22×C4—24no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—221no—
562C22×C4—221no—
563C22×C4—221no—
564C22×C4—442no—
565C22×C4—442no—
566C22×C4—881no—
567C22×C4C2×C22⋊D1111yescharacteristic
568C22×C4C2×C22⋊D1111yescharacteristic
569C22×C4C2×C22⋊D1111yescharacteristic
570C22×C4C2×C22⋊D1111yescharacteristic
571C22×C4C2×C22⋊D1111yescharacteristic
572C22×C4C23×D1111yescharacteristic
573SD16—228no—
574D8—444no—
575C2×C8—112no—
576C2×C8—221no—
577C2×C8—221no—
578C2×C8—221no—
579C2×C8—221no—
580C2×C8—221no—
581C2×C8—221no—
582C2×C8—221no—
583C2×C8—221no—
584C2×C8—221no—
585C2×C8—221no—
586C2×C8—221no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—42no—
592C4⋊C4—42no—
593C4⋊C4—221no—
594C4⋊C4—221no—
595C4⋊C4—221no—
596C4⋊C4—221no—
597C4⋊C4—221no—
598C4⋊C4—221no—
599C4⋊C4—442no—
600C4⋊C4—442no—
601C4⋊C4—881no—
602C22⋊C4—22no—
603C22⋊C4—22no—
604C22⋊C4—42no—
605C22⋊C4—42no—
606C22⋊C4—81no—
607C22⋊C4—81no—
608C22⋊C4—81no—
609C22⋊C4—442no—
610C22⋊C4—442no—
611C22⋊C4—442no—
612C22⋊C4—442no—
613C22⋊C4—442no—
614C42—21no—
615C42—21no—
616C42—21no—
617C42—21no—
618C42—42no—
619C42—42no—
620C11#2489611yescharacteristic, complemented, Sylow
621C23—21no—
622C23—22no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—222no—
636C23—441no—
637C23—441no—
638C23—441no—
639C23—441no—
640C23—441no—
641C23—441no—
642C23C22×C22⋊D1111yescharacteristic
643Q8—22no—
644Q8—22no—
645Q8—22no—
646Q8#6693614yescomplemented
647D4—22no—
648D4—22no—
649D4—48no—
650D4—41no—
651D4—41no—
652D4—222no—
653D4—222no—
654D4—441no—
655D4—441no—
656D4—884no—
657C2×C4—22no—
658C2×C4—21no—
659C2×C4—22no—
660C2×C4—21no—
661C2×C4—22no—
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—21no—
673C2×C4—48no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—441no—
685C2×C4—441no—
686C2×C4—441no—
687C2×C4—441no—
688C2×C4—441no—
689C2×C4—441no—
690C2×C4—441no—
691C2×C4—441no—
692C2×C4—441no—
693C2×C4—884no—
694C2×C4#6700212yes—
695C2×C4#6700312yes—
696C2×C4C2×#433911yescharacteristic
697C2×C4C2×#433911yescharacteristic
698C2×C4C2×D4×D1111yescharacteristic
699C2×C4C2×#434111yescharacteristic
700C2×C4#6703711yescharacteristic
701C2×C4#6703711yescharacteristic
702C8—222no—
703C8—441no—
704C8—441no—
705C8—441no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—42no—
710C22—41no—
711C22—41no—
712C22—42no—
713C22—41no—
714C22—42no—
715C22—41no—
716C22—81no—
717C22—81no—
718C22—81no—
719C22—81no—
720C22—442no—
721C22—442no—
722C22—442no—
723C22—881no—
724C22—881no—
725C22—881no—
726C22—881no—
727C22#1062332211yescharacteristic
728C22D4×C22⋊D1111yescharacteristic
729C22#1062333711yescharacteristic
730C22C2×#6700211yescharacteristic
731C22C2×#6700311yescharacteristic
732C22#1062336711yescharacteristic
733C22#1062336811yescharacteristic
734C4—22no—
735C4—22no—
736C4—24no—
737C4—41no—
738C4—41no—
739C4—41no—
740C4—81no—
741C4—81no—
742C4—881no—
743C4—881no—
744C4—881no—
745C4C2×#6693611yescharacteristic
746C4#1062302111yescharacteristic
747C4#1062302511yescharacteristic
748C4#1062302611yescharacteristic
749C2—81no—
750C2—82no—
751C2—882no—
752C2#1307207811yescharacteristic
753C2#1307867611yescharacteristic
754C2#1307889311yescharacteristic
755C2#1308011211yescharacteristic
756C2#1308034611yescharacteristic
757C2#1308051811yescharacteristic
758C2#1308094311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2341C2
socleC23×C11C22×D4
prime radicalC2×#10622851C2
hypercenter#2341D11
hypocenterC11#24896
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2341

Complements

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

NH ≅ G/Ntype
2. C2×C4×#4325C2semidirect
3. #13072130C2semidirect
4. #13070149C2semidirect
5. #13070052C2semidirect
6. #13069926C2semidirect
7. #13069805C2semidirect
8. #13069302C2semidirect
9. #13069224C2semidirect
10. #13068971C2semidirect
11. #13068967C2semidirect
12. #13068884C2semidirect
13. #13068621C2semidirect
14. #13068556C2semidirect
15. C11×#2341C2semidirect
245. #2341D11semidirect
282. Q8×C11#123semidirect
620. C11#24896semidirect
646. Q8#66936semidirect

Maximal subgroups

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

subgroupindex
C2×#106228512
C2×C4×#43252
#130721302
#130701492
#130700522
#130699262
#130698052
#130693022
#130692242
#130689712
#130689672
#130688842
#130686212
#130685562
C11×#23412
#2489611