Finite Group Databasebeta

← #14792558

Subgroups — #14792558

Order 2816.

1098 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622830C211yesmaximal, characteristic
2C2×#10622613C211yesmaximal, characteristic, complemented
3#13074405C211yesmaximal, characteristic, complemented
4#13070004C211yesmaximal, characteristic, complemented
5#13069990C211yesmaximal, characteristic, complemented
6#13069926C211yesmaximal, characteristic, complemented
7#13069926C211yesmaximal, characteristic, complemented
8#13069491C211yesmaximal, characteristic, complemented
9#13069481C211yesmaximal, characteristic, complemented
10#13069316C211yesmaximal, characteristic, complemented
11#13069302C211yesmaximal, characteristic, complemented
12#13068938C211yesmaximal, characteristic, complemented
13#13068815C211yesmaximal, characteristic, complemented
14#13068547C211yesmaximal, characteristic, complemented
15C11×#2309C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19C22×#4323C2211yescharacteristic
20C22×#4323C2211yescharacteristic
21C2×#66983C2211yescharacteristic
22C11×#390—21no—
23C11×#390—21no—
24C11×#390C2211yescharacteristic
25C11×#390C2211yescharacteristic
26C11×#390C2211yescharacteristic
27C11×#390C2211yescharacteristic
28C11×#379—21no—
29C11×#379—21no—
30#10622830—24no—
31C2×#66896C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33C2×#66896C2211yescharacteristic
34C2×#66896C2211yescharacteristic
35C2×#66896C2211yescharacteristic
36C2×#66896C2211yescharacteristic
37#10622825C2211yescharacteristic
38C2×C22⋊(C11⋊C8)C2211yescharacteristic
39C2×C22⋊(C11⋊C8)C2211yescharacteristic
40#10622613—24no—
41#10622606—21no—
42#10622605—21no—
43C2×#66873C2211yescharacteristic, complemented
44C2×#66873C2211yescharacteristic, complemented
45C2×#66872C2211yescharacteristic, complemented
46C2×#66871C2211yescharacteristic, complemented
47#10622572—21no—
48#10622572—21no—
49#10622552C2211yescharacteristic, complemented
50#10622552C2211yescharacteristic, complemented
51#10622541C2211yescharacteristic, complemented
52#10622541C2211yescharacteristic, complemented
53C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
54C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
55C2×#66867C2211yescharacteristic, complemented
56C2×C4×C11⋊C8C2211yescharacteristic, complemented
57#10622167C2211yescharacteristic, complemented
58#10622167C2211yescharacteristic, complemented
59#10622167C2211yescharacteristic, complemented
60#10622167C2211yescharacteristic, complemented
61C25×C11—21no—
62C22×D4×C11—22no—
63C22×D4×C11—22no—
64C22×D4×C11—21no—
65C22×D4×C11—22no—
66C22×D4×C11—22no—
67C22×D4×C11—41no—
68C22×D4×C11—41no—
69C22×D4×C11C2311yescharacteristic
70C22×D4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C22×C22⋊D11—21no—
73C22×D44C2311yescharacteristic
74C11×#117—22no—
75C11×#117—22no—
76C11×#117—41no—
77C11×#117—41no—
78C2×C11×C4⋊C4D411yescharacteristic
79C2×C11×C4⋊C4D411yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C22⋊C4—21no—
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⋊C4—21no—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4D411yescharacteristic
92C2×C11×C22⋊C4D411yescharacteristic
93C2×C42×C11—21no—
94C2×C42×C11C2311yescharacteristic
95C2×C42×C11C2311yescharacteristic
96C2×C22⋊Dic11—21no—
97C2×#4323—22no—
98C2×#4323—22no—
99C2×#4323—22no—
100C2×#4323—22no—
101C2×#4323—41no—
102C2×#4323—41no—
103#66983—22no—
104#66983—22no—
105C2×(C2×D11)⋊C4—21no—
106C2×(C2×D11)⋊C4—21no—
107C2×(C2×D11)⋊C4—21no—
108C2×(C2×D11)⋊C4—21no—
109C2×(C2×D11)⋊C4—21no—
110C2×C4⋊Dic11C2311yescharacteristic
111C2×C4⋊Dic11C2311yescharacteristic
112C2×C4⋊Dic11C2311yescharacteristic
113C2×Dic11⋊C4—21no—
114C2×Dic11⋊C4—21no—
115C22×C11⋊C8C2311yescharacteristic
116C22×C11⋊C8C2311yescharacteristic
117C22×C11⋊C8C2311yescharacteristic
118C22×C11⋊C8C2311yescharacteristic
119#66896—22no—
120#66896—22no—
121#66896—22no—
122#66896—22no—
123#66896—41no—
124#66896—41no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127C11⋊#95—21no—
128C22⋊(C11⋊C8)—22no—
129C22⋊(C11⋊C8)D414yes—
130#66873—41no—
131#66873—41no—
132#66872—41no—
133#66871—41no—
134C4⋊(C11⋊C8)—22no—
135C4⋊(C11⋊C8)—22no—
136#66867—22no—
137C4×C11⋊C8—22no—
138#24512—111nomaximal, Sylow
139C24×C11—24no—
140C24×C11—21no—
141C24×C11—21no—
142C24×C11—42no—
143C24×C11—42no—
144C24×C11—81no—
145C24×C11—81no—
146C24×C11—81no—
147C24×C11—81no—
148C24×C11C2×D411yescharacteristic
149C23×D11—21no—
150C2×D4×C11—24no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11—21no—
161C2×D4×C11—44no—
162C2×D4×C11—44no—
163C2×D4×C11—44no—
164C2×D4×C11—44no—
165C2×D4×C11—42no—
166C2×D4×C11—42no—
167C2×D4×C11#4112yes—
168C2×D4×C11#4112yes—
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×C11C2×D411yescharacteristic
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2×D412yes—
181C22×C4×C11#4112yes—
182C22×C4×C11C2411yescharacteristic
183C2×C22⋊D11—42no—
184C2×C22⋊D11—81no—
185C2×C22⋊D11—81no—
186C22×Dic11—21no—
187C22×Dic11—21no—
188C22×Dic11—21no—
189C2×D44—21no—
190C2×D44—21no—
191C2×D44—21no—
192C2×D44—21no—
193C2×D44—21no—
194C2×D44—21no—
195C11×C4⋊C4—22no—
196C11×C4⋊C4—22no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4—21no—
200C11×C4⋊C4—21no—
201C11×C22⋊C4—22no—
202C11×C22⋊C4—22no—
203C11×C22⋊C4—42no—
204C11×C22⋊C4—81no—
205C11×C22⋊C4—81no—
206C11×C22⋊C4—81no—
207C11×C22⋊C4—81no—
208C11×C22⋊C4—81no—
209C11×C22⋊C4—81no—
210C11×C22⋊C4—81no—
211C11×C22⋊C4—81no—
212C42×C11—21no—
213C42×C11—21no—
214C42×C11—21no—
215C42×C11—21no—
216C42×C11—42no—
217C22⋊Dic11—81no—
218#4323—44no—
219#4323—44no—
220(C2×D11)⋊C4—42no—
221(C2×D11)⋊C4—81no—
222(C2×D11)⋊C4—81no—
223(C2×D11)⋊C4—81no—
224(C2×D11)⋊C4—81no—
225C4⋊Dic11—21no—
226C4⋊Dic11—21no—
227C4⋊Dic11—21no—
228C4⋊Dic11—21no—
229C4⋊Dic11—21no—
230C4⋊Dic11—21no—
231Dic11⋊C4—81no—
232Dic11⋊C4—81no—
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⋊C8—21no—
242C2×C11⋊C8—21no—
243C2×C11⋊C8C2×D412yes—
244C2×C11⋊C8C2×D412yes—
245C2×#447—111no—
246C2×#433—111no—
247#2624—111no—
248#2309D1111yescharacteristic, complemented
249#2067—111no—
250#2065—111no—
251#2054—111no—
252#2054—111no—
253#1972—111no—
254#1970—111no—
255#1936—111no—
256#1934—111no—
257#1875—111no—
258#1854—111no—
259#1786—111no—
260C23×C11—21no—
261C23×C11—21no—
262C23×C11—21no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11—21no—
266C23×C11—22no—
267C23×C11—22no—
268C23×C11—48no—
269C23×C11—41no—
270C23×C11—41no—
271C23×C11—41no—
272C23×C11—41no—
273C23×C11—41no—
274C23×C11—41no—
275C23×C11—41no—
276C23×C11—41no—
277C23×C11—41no—
278C23×C11—41no—
279C23×C11—41no—
280C23×C11—41no—
281C23×C11—84no—
282C23×C11—84no—
283C23×C11—84no—
284C23×C11—84no—
285C23×C11—84no—
286C23×C11—84no—
287C23×C11#12112yes—
288C23×C11C22×D411yescharacteristic
289C22×D11—41no—
290C22×D11—41no—
291C22×D11—41no—
292C22×D11—41no—
293C22×D11—41no—
294C22×D11—41no—
295C22×D11—41no—
296D4×C11—22no—
297D4×C11—22no—
298D4×C11—22no—
299D4×C11—22no—
300D4×C11—48no—
301D4×C11—41no—
302D4×C11—41no—
303D4×C11—41no—
304D4×C11—41no—
305C2×C4×C11—21no—
306C2×C4×C11—21no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11—22no—
310C2×C4×C11—22no—
311C2×C4×C11—21no—
312C2×C4×C11—21no—
313C2×C4×C11—21no—
314C2×C4×C11—21no—
315C2×C4×C11—21no—
316C2×C4×C11—21no—
317C2×C4×C11—21no—
318C2×C4×C11—21no—
319C2×C4×C11—21no—
320C2×C4×C11—21no—
321C2×C4×C11—21no—
322C2×C4×C11—21no—
323C2×C4×C11—41no—
324C2×C4×C11—41no—
325C2×C4×C11—41no—
326C2×C4×C11—41no—
327C2×C4×C11—41no—
328C2×C4×C11—41no—
329C2×C4×C11#12112yes—
330C2×C4×C11C22×D411yescharacteristic
331C2×C4×C11C2×#4111yescharacteristic
332C2×C4×C11C2×#4111yescharacteristic
333C2×C4×C11C2×#4111yescharacteristic
334C2×C4×C11H(5,𝔽2)11yescharacteristic
335C2×C4×C11H(5,𝔽2)11yescharacteristic
336C22⋊D11—84no—
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—41no—
346D44—41no—
347D44—41no—
348D44—41no—
349D44—41no—
350C11⋊C8—22no—
351C11⋊C8—22no—
352C11⋊C8—41no—
353C11⋊C8—41no—
354C23×D4C2×D1111yescharacteristic
355C22×D8—111no—
356C22×D8—111no—
357C2×#121—111no—
358C2×#117C2×D1111yescharacteristic
359C2×#117C2×D1111yescharacteristic
360#447—224no—
361#433—224no—
362C2×#107—111no—
363C2×#106—111no—
364C2×C4⋊C8—111no—
365C2×C4⋊C8—111no—
366C2×#102—111no—
367C2×#102—111no—
368C2×#102—111no—
369C2×#102—111no—
370C2×#102—111no—
371C2×#102—111no—
372C2×#102—111no—
373C2×#102—111no—
374C2×C22⋊C8—111no—
375C2×C22⋊C8—111no—
376C2×#97—111no—
377C2×C4×C8—111no—
378#399—221no—
379#397—221no—
380#394—221no—
381#394—221no—
382#390—21no—
383#390—21no—
384#390—111no—
385#390—111no—
386#390C2×D1111yescharacteristic
387#390C2×D1111yescharacteristic
388#390C2×D1111yescharacteristic
389#390C2×D1111yescharacteristic
390#389—111no—
391#389—111no—
392#380—111no—
393#379—21no—
394#379—21no—
395#340—111no—
396#340—111no—
397#340—111no—
398#340—111no—
399C22×C11—22no—
400C22×C11—22no—
401C22×C11—22no—
402C22×C11—41no—
403C22×C11—41no—
404C22×C11—41no—
405C22×C11—41no—
406C22×C11—42no—
407C22×C11—42no—
408C22×C11—42no—
409C22×C11—42no—
410C22×C11—42no—
411C22×C11—42no—
412C22×C11—816no—
413C22×C11—81no—
414C22×C11—81no—
415C22×C11—81no—
416C22×C11—81no—
417C22×C11—81no—
418C22×C11—81no—
419C22×C11—81no—
420C22×C11—81no—
421C22×C11C2×#12111yescharacteristic
422C22×C11#52511yescharacteristic
423C22×C11#53511yescharacteristic
424C22×C11#57611yescharacteristic
425C22×C11#57611yescharacteristic
426C22×C11#57611yescharacteristic
427C22×C11#57711yescharacteristic
428C2×D11—81no—
429C2×D11—81no—
430C2×D11—81no—
431C2×D11—81no—
432C2×D11—81no—
433C2×D11—81no—
434C2×D11—81no—
435C4×C11—22no—
436C4×C11—41no—
437C4×C11—41no—
438C4×C11—41no—
439C4×C11—41no—
440C4×C11—81no—
441C4×C11—81no—
442C4×C11#54611yescharacteristic
443C4×C11#54611yescharacteristic
444C4×C11#55111yescharacteristic
445C4×C11#55111yescharacteristic
446Dic11—81no—
447Dic11—81no—
448Dic11—81no—
449C25—21no—
450C22×D4—22no—
451C22×D4—22no—
452C22×D4—22no—
453C22×D4—22no—
454C22×D4—21no—
455C22×D4—41no—
456C22×D4—41no—
457C22×D4—111no—
458C22×D4—221no—
459C22×D4C22×D1111yescharacteristic
460C22×D4C22×D1111yescharacteristic
461C23×C4C22×D1111yescharacteristic
462C2×D8—222no—
463C2×D8—222no—
464C2×D8—222no—
465C2×D8—222no—
466C2×D8—441no—
467C2×D8—441no—
468C22×C8—111no—
469C22×C8—111no—
470C22×C8—111no—
471C22×C8—111no—
472#121—222no—
473#121—222no—
474#117—22no—
475#117—22no—
476#117—41no—
477#117—41no—
478C2×C4⋊C4—111no—
479C2×C4⋊C4—111no—
480C2×C4⋊C4—111no—
481C2×C4⋊C4—221no—
482C2×C4⋊C4—221no—
483C2×C4⋊C4C22⋊D1111yescharacteristic
484C2×C4⋊C4C22⋊D1111yescharacteristic
485C2×C4⋊C4C22×D1111yescharacteristic
486C2×C4⋊C4C22×D1111yescharacteristic
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—221no—
497C2×C22⋊C4—221no—
498C2×C22⋊C4—221no—
499C2×C22⋊C4—221no—
500C2×C22⋊C4—221no—
501C2×C22⋊C4—221no—
502C2×C22⋊C4C22⋊D1111yescharacteristic
503C2×C22⋊C4C22⋊D1111yescharacteristic
504C2×C42—21no—
505C2×C42C22×D1111yescharacteristic
506C2×C42C22×D1111yescharacteristic
507#107—441no—
508#106—441no—
509C4⋊C8—222no—
510C4⋊C8—222no—
511#102—222no—
512#102—222no—
513#102—222no—
514#102—222no—
515#102—441no—
516#102—441no—
517#102—441no—
518#102—441no—
519C22⋊C8—114no—
520C22⋊C8—222no—
521#97—222no—
522C4×C8—222no—
523#95—221no—
524#95—221no—
525#95—221no—
526C2×C11—42no—
527C2×C11—82no—
528C2×C11—82no—
529C2×C11#241111yescharacteristic
530C2×C11#305811yescharacteristic
531C2×C11#306211yescharacteristic
532C2×C11#311811yescharacteristic
533C2×C11#312211yescharacteristic
534C2×C11#322011yescharacteristic
535C2×C11#322411yescharacteristic
536D11—161no—
537C24—24no—
538C24—21no—
539C24—21no—
540C24—42no—
541C24—42no—
542C24—81no—
543C24—81no—
544C24—81no—
545C24—81no—
546C24—221no—
547C24C2×C22⋊D1111yescharacteristic
548C2×D4—24no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—44no—
560C2×D4—44no—
561C2×D4—44no—
562C2×D4—44no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—221no—
566C2×D4—221no—
567C2×D4—221no—
568C2×D4—221no—
569C2×D4—221no—
570C2×D4—221no—
571C2×D4—442no—
572C2×D4—881no—
573C2×D4—881no—
574C2×D4#433912yes—
575C2×D4#433912yes—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—221no—
583C22×C4—221no—
584C22×C4—221no—
585C22×C4D4×D1112yes—
586C22×C4#434112yes—
587C22×C4C2×C22⋊D1111yescharacteristic
588C22×C4C2×C22⋊D1111yescharacteristic
589C22×C4C2×C22⋊D1111yescharacteristic
590C22×C4C2×C22⋊D1111yescharacteristic
591C22×C4C2×C22⋊D1111yescharacteristic
592C22×C4C23×D1111yescharacteristic
593D8—444no—
594D8—444no—
595C2×C8—112no—
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—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—221no—
614C4⋊C4—221no—
615C4⋊C4—221no—
616C4⋊C4—221no—
617C4⋊C4—221no—
618C4⋊C4—221no—
619C4⋊C4—881no—
620C4⋊C4—881no—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—42no—
624C22⋊C4—81no—
625C22⋊C4—81no—
626C22⋊C4—81no—
627C22⋊C4—81no—
628C22⋊C4—81no—
629C22⋊C4—81no—
630C22⋊C4—81no—
631C22⋊C4—81no—
632C22⋊C4—442no—
633C22⋊C4—881no—
634C22⋊C4—881no—
635C22⋊C4—881no—
636C22⋊C4—881no—
637C22⋊C4—881no—
638C42—21no—
639C42—21no—
640C42—21no—
641C42—21no—
642C42—42no—
643C11#2451211yescharacteristic, complemented, Sylow
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—22no—
651C23—22no—
652C23—48no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—84no—
666C23—84no—
667C23—84no—
668C23—84no—
669C23—84no—
670C23—84no—
671C23—441no—
672C23—441no—
673C23—441no—
674C23—441no—
675C23—441no—
676C23—441no—
677C23—441no—
678C23#6699212yes—
679C23C22×C22⋊D1111yescharacteristic
680D4—22no—
681D4—22no—
682D4—22no—
683D4—22no—
684D4—48no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—41no—
689D4—441no—
690D4—441no—
691D4—441no—
692D4—441no—
693D4—884no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—441no—
719C2×C4—441no—
720C2×C4—441no—
721C2×C4—441no—
722C2×C4—441no—
723C2×C4—441no—
724C2×C4—441no—
725C2×C4—441no—
726C2×C4—441no—
727C2×C4#6699212yes—
728C2×C4C2×#433911yescharacteristic
729C2×C4C2×#433911yescharacteristic
730C2×C4C2×D4×D1111yescharacteristic
731C2×C4C2×#434111yescharacteristic
732C2×C4#6703711yescharacteristic
733C2×C4#6703711yescharacteristic
734C8—222no—
735C8—222no—
736C8—441no—
737C8—441no—
738C22—22no—
739C22—22no—
740C22—22no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—816no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—881no—
761C22—881no—
762C22—881no—
763C22—881no—
764C22—881no—
765C22—881no—
766C22—881no—
767C22#1062332211yescharacteristic
768C22C2×#6699211yescharacteristic
769C22#1062333611yescharacteristic
770C22#1062336611yescharacteristic
771C22#1062336611yescharacteristic
772C22#1062336611yescharacteristic
773C22#1062336711yescharacteristic
774C4—22no—
775C4—41no—
776C4—41no—
777C4—41no—
778C4—41no—
779C4—81no—
780C4—81no—
781C4—881no—
782C4—881no—
783C4—881no—
784C4#1062302111yescharacteristic
785C4#1062302111yescharacteristic
786C4#1062302611yescharacteristic
787C4#1062302611yescharacteristic
788C2—42no—
789C2—82no—
790C2—82no—
791C2—1761no—
792C2#1307200111yescharacteristic
793C2#1307826111yescharacteristic
794C2#1307829211yescharacteristic
795C2#1307880011yescharacteristic
796C2#1307885911yescharacteristic
797C2#1307966611yescharacteristic
798C2#1307971011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2309C2
socleC23×C11C22×D4
prime radicalC2×#10622830C2
hypercenter#2309D11
hypocenterC11#24512
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2309

Complements

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

NH ≅ G/Ntype
2. C2×#10622613C2semidirect
3. #13074405C2semidirect
4. #13070004C2semidirect
5. #13069990C2semidirect
6. #13069926C2semidirect
7. #13069926C2semidirect
8. #13069491C2semidirect
9. #13069481C2semidirect
10. #13069316C2semidirect
11. #13069302C2semidirect
12. #13068938C2semidirect
13. #13068815C2semidirect
14. #13068547C2semidirect
15. C11×#2309C2semidirect
43. C2×#66873C22semidirect
44. C2×#66873C22semidirect
45. C2×#66872C22semidirect
46. C2×#66871C22semidirect
49. #10622552C22semidirect
50. #10622552C22semidirect
51. #10622541C22semidirect
52. #10622541C22semidirect
53. C2×C4⋊(C11⋊C8)C22semidirect
54. C2×C4⋊(C11⋊C8)C22semidirect
55. C2×#66867C22semidirect
56. C2×C4×C11⋊C8C22semidirect
57. #10622167C22semidirect
58. #10622167C22semidirect
59. #10622167C22semidirect
60. #10622167C22semidirect
248. #2309D11semidirect
643. C11#24512semidirect

Maximal subgroups

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

subgroupindex
C2×#106228302
C2×#106226132
#130744052
#130700042
#130699902
#130699262
#130694912
#130694812
#130693162
#130693022
#130689382
#130688152
#130685472
C11×#23092
#2451211