Finite Group Databasebeta

← #14796147

Subgroups — #14796147

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×#10622608C211yesmaximal, characteristic, complemented
5#13072056C211yesmaximal, characteristic, complemented
6#13070004C211yesmaximal, characteristic, complemented
7#13069987C211yesmaximal, characteristic, complemented
8#13069802C211yesmaximal, characteristic, complemented
9#13069798C211yesmaximal, characteristic, complemented
10#13069481C211yesmaximal, characteristic, complemented
11#13069341C211yesmaximal, characteristic, complemented
12#13068938C211yesmaximal, characteristic, complemented
13#13068934C211yesmaximal, characteristic, complemented
14#13068647C211yesmaximal, characteristic, complemented
15C11×#2414C211yesmaximal, characteristic, complemented
16C2×C11×#121C2211yescharacteristic
17C2×C11×#121C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×C11×#117C2211yescharacteristic
20C2×#66992—21no—
21C22×#4323C2211yescharacteristic
22C2×#66983C2211yescharacteristic
23C2×#66983C2211yescharacteristic
24C22×C4⋊Dic11C2211yescharacteristic
25C22×#4318C2211yescharacteristic
26C22×#4318C2211yescharacteristic
27C11×#394—21no—
28C11×#392—21no—
29C11×#390—21no—
30C11×#390C2211yescharacteristic
31C11×#389C2211yescharacteristic
32C11×#388—21no—
33C11×#380C2211yescharacteristic
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#10622608—24no—
44#10622607—21no—
45C2×#66873C2211yescharacteristic
46C2×#66873C2211yescharacteristic
47C2×#66873C2211yescharacteristic
48C2×#66872C2211yescharacteristic
49C2×#66872C2211yescharacteristic
50C2×#66872C2211yescharacteristic
51C2×#66871C2211yescharacteristic
52C2×#66871C2211yescharacteristic
53#10622574—21no—
54#10622571—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×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C22×C22⋊D11—21no—
70C22×C22⋊D11—21no—
71C23×Dic11—21no—
72C22×D44C2311yescharacteristic
73C11×#121—22no—
74C11×#121—22no—
75C11×#121—22no—
76C11×#121—41no—
77C4×D4×C11—22no—
78C4×D4×C11—22no—
79C11×#117—22no—
80C11×#117—41no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4D411yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
92C2×C11×C22⋊C4D411yescharacteristic
93C2×C11×C22⋊C4D411yescharacteristic
94C2×C42×C11—21no—
95C2×C42×C11C2311yescharacteristic
96C2×C22⋊Dic11—21no—
97#66992—44no—
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—
109C2×C4⋊Dic11—22no—
110C2×C4⋊Dic11—21no—
111C2×C4⋊Dic11—41no—
112C2×C4⋊Dic11C2311yescharacteristic
113C2×C4⋊Dic11C2311yescharacteristic
114C2×C4⋊Dic11C2311yescharacteristic
115C2×Dic11⋊C4—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—81no—
163C2×D4×C11—81no—
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×C11C2×D411yescharacteristic
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2×D412yes—
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11#4112yes—
184C22×C4×C11C2411yescharacteristic
185C2×C22⋊D11—42no—
186C2×C22⋊D11—42no—
187C2×C22⋊D11—42no—
188C2×C22⋊D11—42no—
189C2×C22⋊D11—42no—
190C2×C22⋊D11—81no—
191C22×Dic11—21no—
192C22×Dic11—21no—
193C22×Dic11—21no—
194C22×Dic11—42no—
195C22×Dic11—42no—
196C22×Dic11—81no—
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—81no—
210C11×C4⋊C4C2×D412yes—
211C11×C22⋊C4—22no—
212C11×C22⋊C4—22no—
213C11×C22⋊C4—42no—
214C11×C22⋊C4—42no—
215C11×C22⋊C4—42no—
216C11×C22⋊C4—42no—
217C11×C22⋊C4—81no—
218C11×C22⋊C4—81no—
219C42×C11—21no—
220C42×C11—21no—
221C42×C11—42no—
222C22⋊Dic11—42no—
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⋊Dic11—42no—
234C4⋊Dic11C2×D412yes—
235Dic11⋊C4—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#2416—111no—
255#2414D1111yescharacteristic, complemented
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#12112yes—
329C2×C4×C11AGL(1,ℤ/8)12yes—
330C2×C4×C11C22×D411yescharacteristic
331C2×C4×C11C22×D411yescharacteristic
332C2×C4×C11C2×#4111yescharacteristic
333C2×C4×C11C2×#4111yescharacteristic
334C2×C4×C11H(5,𝔽2)11yescharacteristic
335C2×C4×C112−1+411yescharacteristic
336C22⋊D11—84no—
337C22⋊D11—84no—
338C2×Dic11—22no—
339C2×Dic11—41no—
340C2×Dic11—41no—
341C2×Dic11—41no—
342C2×Dic11—41no—
343C2×Dic11—41no—
344C2×Dic11—41no—
345C2×Dic11—41no—
346C2×Dic11—41no—
347C2×Dic11—84no—
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—111no—
360C2×#121—111no—
361C2×#121—221no—
362C2×#121C2×D1111yescharacteristic
363C2×#121C2×D1111yescharacteristic
364C2×C4×D4C2×D1111yescharacteristic
365C2×#117C2×D1111yescharacteristic
366C22×C4⋊C4—111no—
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—221no—
387#394—21no—
388#394—221no—
389#392—21no—
390#390—21no—
391#390—111no—
392#390C2×D1111yescharacteristic
393#389—111no—
394#389C2×D1111yescharacteristic
395#388—21no—
396#386—221no—
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—221no—
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—222no—
480#121—222no—
481#121—222no—
482#121—441no—
483#121—444no—
484C4×D4—22no—
485C4×D4—22no—
486#117—22no—
487#117—41no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—111no—
490C2×C4⋊C4—111no—
491C2×C4⋊C4—111no—
492C2×C4⋊C4—222no—
493C2×C4⋊C4—221no—
494C2×C4⋊C4—221no—
495C2×C4⋊C4—441no—
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—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×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—81no—
562C2×D4—81no—
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—442no—
574C2×D4—442no—
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—221no—
590C22×C4—221no—
591C22×C4—221no—
592C22×C4—442no—
593C22×C4—442no—
594C22×C4—881no—
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—81no—
624C4⋊C4—112no—
625C4⋊C4—221no—
626C4⋊C4—221no—
627C4⋊C4—221no—
628C4⋊C4—221no—
629C4⋊C4—221no—
630C4⋊C4—442no—
631C4⋊C4—442no—
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—81no—
641C22⋊C4—442no—
642C22⋊C4—442no—
643C22⋊C4—442no—
644C22⋊C4—442no—
645C22⋊C4—881no—
646C42—21no—
647C42—21no—
648C42—42no—
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—22no—
701C2×C4—21no—
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—222no—
720C2×C4—441no—
721C2×C4—441no—
722C2×C4—441no—
723C2×C4—441no—
724C2×C4—441no—
725C2×C4—441no—
726C2×C4—441no—
727C2×C4—441no—
728C2×C4—884no—
729C2×C4#6699212yes—
730C2×C4#6700212yes—
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—
769C22D4×C22⋊D1111yescharacteristic
770C22C2×#6699211yescharacteristic
771C22C2×#6700211yescharacteristic
772C22#1062335311yescharacteristic
773C22#1062335511yescharacteristic
774C22#1062336611yescharacteristic
775C22#1062336711yescharacteristic
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#1307823711yescharacteristic
796C2#1307829211yescharacteristic
797C2#1308023611yescharacteristic
798C2#1308024311yescharacteristic
799C2#1308120511yescharacteristic
800C2#1308121611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2414C2
socleC23×C11C22×D4
hypercenter#2414D11
hypocenterC11#24792
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2414

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×#10622608C2semidirect
5. #13072056C2semidirect
6. #13070004C2semidirect
7. #13069987C2semidirect
8. #13069802C2semidirect
9. #13069798C2semidirect
10. #13069481C2semidirect
11. #13069341C2semidirect
12. #13068938C2semidirect
13. #13068934C2semidirect
14. #13068647C2semidirect
15. C11×#2414C2semidirect
121. C2×#4318D4semidirect
140. #66872D4semidirect
255. #2414D11semidirect
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×#106226082
#130720562
#130700042
#130699872
#130698022
#130697982
#130694812
#130693412
#130689382
#130689342
#130686472
C11×#24142
#2479211