Finite Group Databasebeta

← #14796155

Subgroups — #14796155

Order 2816.

1076 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622652C211yesmaximal, characteristic, complemented
2C2×#10622652C211yesmaximal, characteristic, complemented
3C2×#10622625C211yesmaximal, characteristic, complemented
4C2×#10622577C211yesmaximal, characteristic, complemented
5#13072034C211yesmaximal, characteristic, complemented
6#13070001C211yesmaximal, characteristic, complemented
7#13069990C211yesmaximal, characteristic, complemented
8#13069805C211yesmaximal, characteristic, complemented
9#13069795C211yesmaximal, characteristic, complemented
10#13069481C211yesmaximal, characteristic, complemented
11#13069341C211yesmaximal, characteristic, complemented
12#13068939C211yesmaximal, characteristic, complemented
13#13068933C211yesmaximal, characteristic, complemented
14#13068647C211yesmaximal, characteristic, complemented
15C11×#2416C211yesmaximal, characteristic, complemented
16C2×C11×#121—21no—
17C2×C11×#121C2211yescharacteristic
18C2×C11×#121C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×#4323C2211yescharacteristic
22C2×#66983C2211yescharacteristic
23C2×#66983C2211yescharacteristic
24C2×#66979C2211yescharacteristic
25C22×#4318C2211yescharacteristic
26C22×#4318C2211yescharacteristic
27C11×#396—21no—
28C11×#394—21no—
29C11×#390C2211yescharacteristic
30C11×#389C2211yescharacteristic
31C11×#386—21no—
32C11×#380C2211yescharacteristic
33#10622836—21no—
34C2×#66896C2211yescharacteristic
35C2×#66896C2211yescharacteristic
36C2×#66896C2211yescharacteristic
37#10622825C2211yescharacteristic
38C2×C22⋊(C11⋊C8)C2211yescharacteristic
39C2×C22⋊(C11⋊C8)C2211yescharacteristic
40#10622652—24no—
41#10622652—24no—
42#10622625—24no—
43#10622603—21no—
44C2×#66873C2211yescharacteristic
45C2×#66873C2211yescharacteristic
46C2×#66873C2211yescharacteristic
47#10622577—24no—
48C2×#66872C2211yescharacteristic
49C2×#66872C2211yescharacteristic
50C2×#66872C2211yescharacteristic
51C2×#66871C2211yescharacteristic
52C2×#66871C2211yescharacteristic
53#10622572—21no—
54#10622570—21no—
55#10622552C2211yescharacteristic
56#10622541C2211yescharacteristic
57C2×C4⋊(C11⋊C8)C2211yescharacteristic
58C2×C4×C11⋊C8C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62#10622167C2211yescharacteristic
63C22×D4×C11—21no—
64C22×D4×C11—21no—
65C22×D4×C11D411yescharacteristic
66C22×D4×C11C2311yescharacteristic
67C23×C4×C11—21no—
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C22×C22⋊D11—21no—
71C22×C22⋊D11—21no—
72C22×D44C2311yescharacteristic
73C11×#121—22no—
74C11×#121—22no—
75C11×#121—22no—
76C11×#121—41no—
77C11×#121—44no—
78C4×D4×C11—22no—
79C4×D4×C11—22no—
80C2×C11×C4⋊C4—22no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4—41no—
84C2×C11×C4⋊C4D411yescharacteristic
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4—21no—
93C2×C11×C22⋊C4D411yescharacteristic
94C2×C11×C22⋊C4D411yescharacteristic
95C2×C42×C11C2311yescharacteristic
96C2×C22⋊Dic11—21no—
97C2×C22⋊Dic11—21no—
98C2×#4323—22no—
99C2×#4323—22no—
100C2×#4323—22no—
101#66983—22no—
102#66983—22no—
103#66983—22no—
104#66983—41no—
105C2×(C2×D11)⋊C4—21no—
106C2×(C2×D11)⋊C4—21no—
107C2×(C2×D11)⋊C4—21no—
108C2×(C2×D11)⋊C4—21no—
109#66979—22no—
110#66979—41no—
111C2×C4⋊Dic11C2311yescharacteristic
112C2×C4⋊Dic11C2311yescharacteristic
113C2×C4⋊Dic11C2311yescharacteristic
114C2×Dic11⋊C4—21no—
115C2×C4×Dic11—21no—
116C2×#4318—22no—
117C2×#4318—22no—
118C2×#4318—22no—
119C2×#4318—22no—
120C2×#4318—22no—
121C2×#4318D414yescomplemented
122C22×C11⋊C8C2311yescharacteristic
123C22×C11⋊C8C2311yescharacteristic
124C22×C11⋊C8C2311yescharacteristic
125C22×C11⋊C8C2311yescharacteristic
126C11×#95—21no—
127C11×#95—21no—
128#66896—22no—
129#66896—22no—
130#66896—41no—
131C11⋊#95—21no—
132C11⋊#95—21no—
133C22⋊(C11⋊C8)—22no—
134C22⋊(C11⋊C8)—22no—
135#66873—22no—
136#66873—22no—
137#66873—41no—
138#66872—22no—
139#66872—22no—
140#66872D414yescomplemented
141#66871—22no—
142#66871—22no—
143C4⋊(C11⋊C8)—22no—
144C4×C11⋊C8—22no—
145#24792—111nomaximal, Sylow
146C24×C11—21no—
147C24×C11C2×D411yescharacteristic
148C24×C11C2×D411yescharacteristic
149C23×D11—21no—
150C2×D4×C11—22no—
151C2×D4×C11—22no—
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—41no—
159C2×D4×C11—42no—
160C2×D4×C11—42no—
161C2×D4×C11—42no—
162C2×D4×C11—42no—
163C2×D4×C11—42no—
164C2×D4×C11—81no—
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—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—42no—
179C22×C4×C11—42no—
180C22×C4×C11—81no—
181C22×C4×C11C2×D411yescharacteristic
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11C2×D412yes—
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11#4112yes—
187C22×C4×C11C2411yescharacteristic
188C2×C22⋊D11—42no—
189C2×C22⋊D11—42no—
190C2×C22⋊D11—42no—
191C2×C22⋊D11—81no—
192C2×C22⋊D11—81no—
193C2×C22⋊D11—81no—
194C22×Dic11—21no—
195C22×Dic11—21no—
196C22×Dic11—21no—
197C2×D44—21no—
198C2×D44—21no—
199C2×D44—21no—
200C2×D44—21no—
201C2×D44—21no—
202C2×D44—21no—
203C11×C4⋊C4—22no—
204C11×C4⋊C4—21no—
205C11×C4⋊C4—21no—
206C11×C4⋊C4—21no—
207C11×C4⋊C4—21no—
208C11×C4⋊C4—21no—
209C11×C4⋊C4—42no—
210C11×C4⋊C4—42no—
211C11×C4⋊C4C2×D412yes—
212C11×C22⋊C4—22no—
213C11×C22⋊C4—22no—
214C11×C22⋊C4—42no—
215C11×C22⋊C4—42no—
216C11×C22⋊C4—42no—
217C11×C22⋊C4—42no—
218C11×C22⋊C4—81no—
219C42×C11—21no—
220C42×C11—21no—
221C22⋊Dic11—42no—
222C22⋊Dic11—81no—
223#4323—44no—
224(C2×D11)⋊C4—42no—
225(C2×D11)⋊C4—42no—
226(C2×D11)⋊C4—42no—
227(C2×D11)⋊C4—81no—
228C4⋊Dic11—21no—
229C4⋊Dic11—21no—
230C4⋊Dic11—21no—
231C4⋊Dic11—21no—
232C4⋊Dic11—21no—
233C4⋊Dic11C2×D412yes—
234Dic11⋊C4—81no—
235C4×Dic11—42no—
236#4318—28no—
237#4318—44no—
238C2×C11⋊C8—21no—
239C2×C11⋊C8—21no—
240C2×C11⋊C8—21no—
241C2×C11⋊C8—21no—
242C2×C11⋊C8—21no—
243C2×C11⋊C8—21no—
244C2×C11⋊C8—21no—
245C2×C11⋊C8—21no—
246C2×C11⋊C8C2×D412yes—
247C2×C11⋊C8C2×D412yes—
248C2×C11⋊C8C2×D412yes—
249C2×C11⋊C8#4112yes—
250C2×#469—111no—
251C2×#469—111no—
252C2×#436—111no—
253C2×#428—111no—
254#2416D1111yescharacteristic, complemented
255#2414—111no—
256#2067—111no—
257#2065—111no—
258#2034—111no—
259#2033—111no—
260#1970—111no—
261#1941—111no—
262#1875—111no—
263#1874—111no—
264#1809—111no—
265C23×C11—21no—
266C23×C11—21no—
267C23×C11—21no—
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—41no—
279C23×C11—41no—
280C23×C11—41no—
281C23×C11—41no—
282C23×C11—41no—
283C23×C11—41no—
284C23×C11—41no—
285C23×C11#12112yes—
286C23×C11C22×D411yescharacteristic
287C22×D11—41no—
288C22×D11—41no—
289C22×D11—41no—
290C22×D11—41no—
291C22×D11—41no—
292C22×D11—41no—
293C22×D11—41no—
294D4×C11—44no—
295D4×C11—41no—
296D4×C11—41no—
297D4×C11—41no—
298D4×C11—41no—
299D4×C11—84no—
300D4×C11—84no—
301C2×C4×C11—21no—
302C2×C4×C11—21no—
303C2×C4×C11—21no—
304C2×C4×C11—21no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11—21no—
310C2×C4×C11—21no—
311C2×C4×C11—21no—
312C2×C4×C11—22no—
313C2×C4×C11—21no—
314C2×C4×C11—21no—
315C2×C4×C11—21no—
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—41no—
328C2×C4×C11—84no—
329C2×C4×C11#12112yes—
330C2×C4×C11AGL(1,ℤ/8)12yes—
331C2×C4×C11C22×D411yescharacteristic
332C2×C4×C11C22×D411yescharacteristic
333C2×C4×C11C2×#4111yescharacteristic
334C2×C4×C11C2×#4111yescharacteristic
335C2×C4×C11H(5,𝔽2)11yescharacteristic
336C2×C4×C112−1+411yescharacteristic
337C22⋊D11—84no—
338C22⋊D11—84no—
339C2×Dic11—22no—
340C2×Dic11—41no—
341C2×Dic11—41no—
342C2×Dic11—41no—
343C2×Dic11—41no—
344C2×Dic11—41no—
345C2×Dic11—41no—
346C2×Dic11—41no—
347C2×Dic11—41no—
348D44—41no—
349D44—41no—
350D44—41no—
351D44—41no—
352C11⋊C8—22no—
353C11⋊C8—41no—
354C11⋊C8—41no—
355C11⋊C8#12114yescomplemented
356C22×D8—111no—
357C22×M16—111no—
358C22×M16—111no—
359C2×#121—21no—
360C2×#121—111no—
361C2×#121—111no—
362C2×#121C2×D1111yescharacteristic
363C2×#121C2×D1111yescharacteristic
364C2×C4×D4C2×D1111yescharacteristic
365C2×#117—111no—
366C22×C4⋊C4C2×D1111yescharacteristic
367#469—224no—
368#469—224no—
369#436—224no—
370#428—224no—
371C2×#107—111no—
372C2×#107—111no—
373C2×#106—111no—
374C2×#106—111no—
375C2×#106—111no—
376C2×C4⋊C8—111no—
377C2×#102—111no—
378C2×#102—111no—
379C2×#102—111no—
380C2×#102—111no—
381C2×#102—111no—
382C2×#102—111no—
383C2×C22⋊C8—111no—
384C2×C22⋊C8—111no—
385C2×C4×C8—111no—
386#396—21no—
387#394—21no—
388#394—221no—
389#392—221no—
390#390—111no—
391#390—221no—
392#390C2×D1111yescharacteristic
393#389—111no—
394#389C2×D1111yescharacteristic
395#388—221no—
396#386—21no—
397#380—111no—
398#380C2×D1111yescharacteristic
399#340—111no—
400#340—111no—
401#340—111no—
402#340—111no—
403C22×C11—22no—
404C22×C11—22no—
405C22×C11—22no—
406C22×C11—41no—
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×C11—41no—
416C22×C11—41no—
417C22×C11—81no—
418C22×C11—81no—
419C22×C11—81no—
420C22×C11—81no—
421C22×C11—81no—
422C22×C11—81no—
423C22×C11—81no—
424C22×C11C2×#12111yescharacteristic
425C22×C11D4211yescharacteristic
426C22×C11#54711yescharacteristic
427C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
428C22×C11#57511yescharacteristic
429C22×C11#57611yescharacteristic
430C22×C11#57711yescharacteristic
431C2×D11—81no—
432C2×D11—81no—
433C2×D11—81no—
434C2×D11—81no—
435C2×D11—81no—
436C2×D11—81no—
437C2×D11—81no—
438C4×C11—22no—
439C4×C11—22no—
440C4×C11—41no—
441C4×C11—42no—
442C4×C11—41no—
443C4×C11—81no—
444C4×C11—81no—
445C4×C11C2×#12111yescharacteristic
446C4×C11#53711yescharacteristic
447C4×C11#54811yescharacteristic
448C4×C11#55311yescharacteristic
449Dic11—42no—
450Dic11—81no—
451Dic11—81no—
452C22×D4—21no—
453C22×D4—21no—
454C22×D4—111no—
455C22×D4—221no—
456C22×D4—221no—
457C22×D4C22⋊D1111yescharacteristic
458C22×D4C22×D1111yescharacteristic
459C23×C4—21no—
460C23×C4C22×D1111yescharacteristic
461C23×C4C22×D1111yescharacteristic
462C2×D8—222no—
463C2×D8—222no—
464C2×D8—222no—
465C2×M16—114no—
466C2×M16—222no—
467C2×M16—222no—
468C2×M16—222no—
469C2×M16—222no—
470C2×M16—222no—
471C22×C8—111no—
472C22×C8—111no—
473C22×C8—111no—
474C22×C8—111no—
475#121—22no—
476#121—22no—
477#121—22no—
478#121—41no—
479#121—44no—
480#121—222no—
481#121—222no—
482#121—222no—
483#121—441no—
484C4×D4—22no—
485C4×D4—22no—
486#117—222no—
487#117—441no—
488C2×C4⋊C4—22no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—41no—
492C2×C4⋊C4—111no—
493C2×C4⋊C4—111no—
494C2×C4⋊C4—111no—
495C2×C4⋊C4—221no—
496C2×C4⋊C4C22⋊D1111yescharacteristic
497C2×C4⋊C4C22×D1111yescharacteristic
498C2×C4⋊C4C22×D1111yescharacteristic
499C2×C4⋊C4C22×D1111yescharacteristic
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—221no—
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—221no—
514C2×C42C22×D1111yescharacteristic
515#107—222no—
516#107—222no—
517#106—114no—
518#106—222no—
519#106—222no—
520C4⋊C8—222no—
521#102—222no—
522#102—222no—
523#102—222no—
524#102—222no—
525#102—441no—
526#102—441no—
527C22⋊C8—222no—
528C22⋊C8—222no—
529C4×C8—222no—
530#95—21no—
531#95—21no—
532#95—221no—
533#95—221no—
534C2×C11—42no—
535C2×C11—81no—
536C2×C11—161no—
537C2×C11#241611yescharacteristic
538C2×C11#305511yescharacteristic
539C2×C11#306211yescharacteristic
540C2×C11#327411yescharacteristic
541C2×C11#327511yescharacteristic
542C2×C11#335411yescharacteristic
543C2×C11#335511yescharacteristic
544D11—161no—
545C24—21no—
546C24—221no—
547C24C2×C22⋊D1111yescharacteristic
548C24C2×C22⋊D1111yescharacteristic
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—41no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4—81no—
564C2×D4—221no—
565C2×D4—221no—
566C2×D4—221no—
567C2×D4—221no—
568C2×D4—221no—
569C2×D4—221no—
570C2×D4—442no—
571C2×D4—442no—
572C2×D4—442no—
573C2×D4—881no—
574C2×D4—881no—
575C2×D4—881no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—81no—
592C22×C4—221no—
593C22×C4—221no—
594C22×C4—221no—
595C22×C4D4×D1112yes—
596C22×C4#434112yes—
597C22×C4C2×C22⋊D1111yescharacteristic
598C22×C4C2×C22⋊D1111yescharacteristic
599C22×C4C2×C22⋊D1111yescharacteristic
600C22×C4C2×C22⋊D1111yescharacteristic
601C22×C4C23×D1111yescharacteristic
602D8—444no—
603M16—228no—
604M16—444no—
605C2×C8—112no—
606C2×C8—112no—
607C2×C8—112no—
608C2×C8—112no—
609C2×C8—221no—
610C2×C8—221no—
611C2×C8—221no—
612C2×C8—221no—
613C2×C8—221no—
614C2×C8—221no—
615C2×C8—221no—
616C2×C8—221no—
617C4⋊C4—22no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—42no—
624C4⋊C4—42no—
625C4⋊C4—112no—
626C4⋊C4—221no—
627C4⋊C4—221no—
628C4⋊C4—221no—
629C4⋊C4—221no—
630C4⋊C4—221no—
631C4⋊C4—881no—
632C4⋊C4D4×D1112yes—
633C22⋊C4—22no—
634C22⋊C4—22no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—81no—
640C22⋊C4—442no—
641C22⋊C4—442no—
642C22⋊C4—442no—
643C22⋊C4—442no—
644C22⋊C4—881no—
645C22⋊C4—881no—
646C42—21no—
647C42—21no—
648C42—442no—
649C11#2479211yescharacteristic, complemented, Sylow
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—441no—
671C23—441no—
672C23—441no—
673C23—441no—
674C23—441no—
675C23—441no—
676C23—441no—
677C23#6699212yes—
678C23C22×C22⋊D1111yescharacteristic
679D4—44no—
680D4—41no—
681D4—41no—
682D4—41no—
683D4—41no—
684D4—84no—
685D4—84no—
686D4—441no—
687D4—441no—
688D4—441no—
689D4—441no—
690D4—884no—
691D4—884no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—21no—
701C2×C4—22no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—84no—
720C2×C4—222no—
721C2×C4—441no—
722C2×C4—441no—
723C2×C4—441no—
724C2×C4—441no—
725C2×C4—441no—
726C2×C4—441no—
727C2×C4—441no—
728C2×C4—441no—
729C2×C4#6698512yes—
730C2×C4#6699212yes—
731C2×C4C2×D4×D1111yescharacteristic
732C2×C4C2×D4×D1111yescharacteristic
733C2×C4C2×#434111yescharacteristic
734C2×C4#6703711yescharacteristic
735C2×C4#41×D1111yescharacteristic
736C2×C4#6704311yescharacteristic
737C8—114no—
738C8—222no—
739C8—441no—
740C8—441no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—881no—
763C22—881no—
764C22—881no—
765C22—881no—
766C22—881no—
767C22—881no—
768C22—881no—
769C22C2×#6698511yescharacteristic
770C22D4×C22⋊D1111yescharacteristic
771C22C2×#6699211yescharacteristic
772C22#1062335311yescharacteristic
773C22#1062335511yescharacteristic
774C22#1062336611yescharacteristic
775C22#1062336811yescharacteristic
776C4—22no—
777C4—22no—
778C4—41no—
779C4—42no—
780C4—41no—
781C4—81no—
782C4—81no—
783C4—442no—
784C4—881no—
785C4—881no—
786C4#1062312811yescharacteristic
787C4#1062312911yescharacteristic
788C4#1062313211yescharacteristic
789C4D11×#12111yescharacteristic
790C2—42no—
791C2—81no—
792C2—161no—
793C2—1761no—
794C2#1307205311yescharacteristic
795C2#1307823111yescharacteristic
796C2#1307829811yescharacteristic
797C2#1308023211yescharacteristic
798C2#1308024811yescharacteristic
799C2#1308121111yescharacteristic
800C2#1308121611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2416C2
socleC23×C11C22×D4
hypercenter#2416D11
hypocenterC11#24792
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2416

Complements

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

NH ≅ G/Ntype
1. C2×#10622652C2semidirect
2. C2×#10622652C2semidirect
3. C2×#10622625C2semidirect
4. C2×#10622577C2semidirect
5. #13072034C2semidirect
6. #13070001C2semidirect
7. #13069990C2semidirect
8. #13069805C2semidirect
9. #13069795C2semidirect
10. #13069481C2semidirect
11. #13069341C2semidirect
12. #13068939C2semidirect
13. #13068933C2semidirect
14. #13068647C2semidirect
15. C11×#2416C2semidirect
121. C2×#4318D4semidirect
140. #66872D4semidirect
254. #2416D11semidirect
355. C11⋊C8#121semidirect
649. C11#24792semidirect

Maximal subgroups

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

subgroupindex
C2×#106226522
C2×#106226252
C2×#106225772
#130720342
#130700012
#130699902
#130698052
#130697952
#130694812
#130693412
#130689392
#130689332
#130686472
C11×#24162
#2479211