Finite Group Databasebeta

← #14801176

Subgroups — #14801176

Order 2816.

1154 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622629C211yesmaximal, characteristic, complemented
2C2×#10622852C211yesmaximal, characteristic, complemented
3C2×#10622851C211yesmaximal, characteristic
4C2×C4×#4323C211yesmaximal, characteristic, complemented
5#13072193C211yesmaximal, characteristic, complemented
6#13070011C211yesmaximal, characteristic, complemented
7#13069819C211yesmaximal, characteristic, complemented
8#13069798C211yesmaximal, characteristic, complemented
9#13069709C211yesmaximal, characteristic, complemented
10#13069476C211yesmaximal, characteristic, complemented
11#13069224C211yesmaximal, characteristic, complemented
12#13068953C211yesmaximal, characteristic, complemented
13#13068950C211yesmaximal, characteristic, complemented
14#13068863C211yesmaximal, characteristic, complemented
15C11×#2339C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C22×#4326C2211yescharacteristic
20C22×#4325C2211yescharacteristic
21C22×#4324C2211yescharacteristic
22C22×#4323C2211yescharacteristic
23C2×#66983C2211yescharacteristic
24C2×#66977C2211yescharacteristic
25C2×#66928C2211yescharacteristic
26C2×C4×D44C2211yescharacteristic
27C11×#391C2211yescharacteristic
28C11×#391C2211yescharacteristic
29C11×#386—21no—
30C11×#386—21no—
31C11×#381—21no—
32C11×#380C2211yescharacteristic
33C4×C11×C22⋊C4C2211yescharacteristic
34C2×C11×#95—21no—
35#10622852—24no—
36#10622851—24no—
37C2×#66899C2211yescharacteristic
38C2×#66899C2211yescharacteristic
39C2×#66896C2211yescharacteristic
40C2×#66896C2211yescharacteristic
41C2×C22⋊(C11⋊C8)C2211yescharacteristic
42C2×C22⋊(C11⋊C8)C2211yescharacteristic
43#10622629—24no—
44C4×#4323—24no—
45C2×#66874C2211yescharacteristic
46C2×#66874C2211yescharacteristic
47C2×#66873C2211yescharacteristic
48C2×#66873C2211yescharacteristic
49C2×#66871C2211yescharacteristic
50C2×#66871C2211yescharacteristic
51#10622572—21no—
52#10622569—21no—
53#10622542C2211yescharacteristic
54#10622541C2211yescharacteristic
55C2×C4⋊(C11⋊C8)C2211yescharacteristic
56C2×C4×C11⋊C8C2211yescharacteristic
57#10622288—21no—
58#10622280—21no—
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622162C2211yescharacteristic
62#10622162C2211yescharacteristic
63C2×C11×#41—22no—
64C2×C11×#41—22no—
65C2×C11×#41—22no—
66C2×C11×#41—22no—
67C2×C11×#41—41no—
68C2×C11×#41—41no—
69C22×Q8×C11C2311yescharacteristic
70C22×D4×C11—21no—
71C22×D4×C11C2311yescharacteristic
72C23×C4×C11—21no—
73C23×C4×C11—21no—
74C23×C4×C11—21no—
75C23×C4×C11C2311yescharacteristic
76C22×C22⋊D11—21no—
77C22×D44C2311yescharacteristic
78C22×C4×D11—21no—
79C22×Dic22C2311yescharacteristic
80C4×D4×C11—22no—
81C4×D4×C11—22no—
82C4×D4×C11—41no—
83C4×D4×C11—41no—
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⋊C4D411yescharacteristic
90C2×C11×C22⋊C4D411yescharacteristic
91C2×C42×C11C2311yescharacteristic
92C2×C42×C11C2311yescharacteristic
93C2×C22⋊Dic11—21no—
94C2×#4326—22no—
95C2×#4326—22no—
96C2×#4326—41no—
97C2×#4325—22no—
98C2×#4325—22no—
99C2×#4325—41no—
100C2×#4324—22no—
101C2×#4324—22no—
102C2×#4324—22no—
103C2×#4323—22no—
104C2×#4323—22no—
105C2×#4323D414yes—
106#66983—22no—
107#66983—41no—
108C2×(C2×D11)⋊C4—21no—
109C2×(C2×D11)⋊C4—21no—
110C2×(C2×D11)⋊C4—21no—
111C2×(C2×D11)⋊C4—21no—
112C2×C4⋊Dic11C2311yescharacteristic
113C2×C4⋊Dic11C2311yescharacteristic
114#66977—22no—
115#66977—41no—
116C2×Dic11⋊C4—21no—
117C2×Dic11⋊C4—21no—
118C22×C11⋊C8C2311yescharacteristic
119C22×C11⋊C8C2311yescharacteristic
120C22×C11⋊C8C2311yescharacteristic
121C22×C11⋊C8C2311yescharacteristic
122#66928—22no—
123#66928—41no—
124C4×D44—22no—
125C4×D44—41no—
126C11×#95—21no—
127C11×#95—21no—
128C11×#95—21no—
129C11×#95—21no—
130C11×#95—21no—
131C11×#95D411yescharacteristic
132C11×#95D411yescharacteristic
133#66899—22no—
134#66899—22no—
135#66896—22no—
136#66896D414yescomplemented
137C11⋊#95—21no—
138C11⋊#95—21no—
139C11⋊#95—21no—
140C22⋊(C11⋊C8)—22no—
141C22⋊(C11⋊C8)—22no—
142#66874—22no—
143#66874—41no—
144#66873—22no—
145#66873—22no—
146#66871—22no—
147#66871—41no—
148C4⋊(C11⋊C8)—22no—
149C4×C11⋊C8—22no—
150#25150—111nomaximal, Sylow
151C24×C11—21no—
152C24×C11C2×D411yescharacteristic
153C23×D11—21no—
154C11×#41—44no—
155C11×#41—44no—
156C11×#41—44no—
157C11×#41—44no—
158C2×Q8×C11—21no—
159C2×Q8×C11—21no—
160C2×Q8×C11—21no—
161C2×Q8×C11—21no—
162C2×Q8×C11—21no—
163C2×Q8×C11#4112yes—
164C2×D4×C11—24no—
165C2×D4×C11—21no—
166C2×D4×C11—21no—
167C2×D4×C11—21no—
168C2×D4×C11—42no—
169C2×D4×C11—42no—
170C2×D4×C11C2×D412yes—
171C2×D4×C11C2×D412yes—
172C2×D4×C11#4112yes—
173C22×C4×C11—24no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—42no—
184C22×C4×C11—42no—
185C22×C4×C11—42no—
186C22×C4×C11—42no—
187C22×C4×C11—42no—
188C22×C4×C11—42no—
189C22×C4×C11—81no—
190C22×C4×C11—81no—
191C22×C4×C11C2×D411yescharacteristic
192C22×C4×C11C2×D411yescharacteristic
193C22×C4×C11C2×D411yescharacteristic
194C22×C4×C11C2×D411yescharacteristic
195C22×C4×C11C2×D411yescharacteristic
196C22×C4×C11C2411yescharacteristic
197C2×C22⋊D11—42no—
198C2×C22⋊D11—42no—
199C2×C22⋊D11—81no—
200C22×Dic11—21no—
201C22×Dic11—21no—
202C22×Dic11—21no—
203C2×D44—21no—
204C2×D44—21no—
205C2×D44—21no—
206C2×D44—21no—
207C2×D44—21no—
208C2×D44C2×D412yes—
209C2×C4×D11—42no—
210C2×C4×D11—42no—
211C2×C4×D11—81no—
212C2×Dic22—21no—
213C2×Dic22—21no—
214C2×Dic22—21no—
215C2×Dic22—21no—
216C2×Dic22—21no—
217C2×Dic22—21no—
218C11×C4⋊C4—21no—
219C11×C4⋊C4—21no—
220C11×C4⋊C4—21no—
221C11×C4⋊C4—21no—
222C11×C22⋊C4—22no—
223C11×C22⋊C4—41no—
224C11×C22⋊C4—42no—
225C11×C22⋊C4—42no—
226C11×C22⋊C4—81no—
227C42×C11—21no—
228C42×C11—21no—
229C42×C11—21no—
230C42×C11—21no—
231C22⋊Dic11—42no—
232#4326—44no—
233#4325—44no—
234#4324—44no—
235#4323—28no—
236(C2×D11)⋊C4—42no—
237(C2×D11)⋊C4—42no—
238(C2×D11)⋊C4—42no—
239(C2×D11)⋊C4—42no—
240C4⋊Dic11—21no—
241C4⋊Dic11—21no—
242C4⋊Dic11—21no—
243C4⋊Dic11C2×D412yes—
244Dic11⋊C4—42no—
245Dic11⋊C4—81no—
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—21no—
253C2×C11⋊C8—21no—
254C2×C11⋊C8—21no—
255C2×C11⋊C8—21no—
256C2×C11⋊C8C2×D412yes—
257C2×C11⋊C8C2×D412yes—
258C2×#463—111no—
259C2×#452—111no—
260C2×#449—111no—
261C2×C4×D8—111no—
262#2427—111no—
263#2339D1111yescharacteristic, complemented
264#2068—111no—
265#2036—111no—
266#2033—111no—
267#2015—111no—
268#1969—111no—
269#1923—111no—
270#1877—111no—
271#1877—111no—
272#1862—111no—
273C23×C11—22no—
274C23×C11—22no—
275C23×C11—22no—
276C23×C11—21no—
277C23×C11—21no—
278C23×C11—21no—
279C23×C11—21no—
280C23×C11—21no—
281C23×C11—21no—
282C23×C11—21no—
283C23×C11—41no—
284C23×C11—41no—
285C23×C11—41no—
286C23×C11—41no—
287C23×C11C22×D411yescharacteristic
288C22×D11—22no—
289C22×D11—41no—
290C22×D11—41no—
291C22×D11—41no—
292C22×D11—41no—
293C22×D11—41no—
294C22×D11—41no—
295Q8×C11—22no—
296Q8×C11—22no—
297Q8×C11—41no—
298Q8×C11—41no—
299D4×C11—22no—
300D4×C11—22no—
301D4×C11—22no—
302D4×C11—48no—
303D4×C11#12114yes—
304C2×C4×C11—21no—
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—21no—
315C2×C4×C11—21no—
316C2×C4×C11—21no—
317C2×C4×C11—21no—
318C2×C4×C11—21no—
319C2×C4×C11—48no—
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—41no—
329C2×C4×C11—41no—
330C2×C4×C11—41no—
331C2×C4×C11—41no—
332C2×C4×C11—84no—
333C2×C4×C11—84no—
334C2×C4×C11#13512yes—
335C2×C4×C11C22×D411yescharacteristic
336C2×C4×C11C22×D411yescharacteristic
337C2×C4×C11C2×#4111yescharacteristic
338C2×C4×C11C2×#4111yescharacteristic
339C2×C4×C11H(5,𝔽2)11yescharacteristic
340C2×C4×C11H(5,𝔽2)11yescharacteristic
341C22⋊D11—84no—
342C2×Dic11—22no—
343C2×Dic11—41no—
344C2×Dic11—41no—
345C2×Dic11—41no—
346C2×Dic11—41no—
347C2×Dic11—41no—
348C2×Dic11—41no—
349C2×Dic11—41no—
350C2×Dic11—41no—
351D44—22no—
352D44—22no—
353D44—41no—
354D44—41no—
355C4×D11—84no—
356Dic22—41no—
357Dic22—41no—
358Dic22—41no—
359Dic22—41no—
360C11⋊C8—22no—
361C11⋊C8—22no—
362C11⋊C8—41no—
363C11⋊C8—41no—
364C22×#41C2×D1111yescharacteristic
365C22×Q16—111no—
366C22×SD16—111no—
367C22×SD16—111no—
368C22×D8—111no—
369C2×#124—111no—
370C2×C22⋊Q8—111no—
371C2×#121—111no—
372C2×C4×D4—111no—
373C2×C4×D4C2×D1111yescharacteristic
374C2×C4×D4C2×D1111yescharacteristic
375#463—224no—
376#452—224no—
377#449—224no—
378C4×D8—224no—
379C2×#107—111no—
380C2×#107—111no—
381C2×C4⋊C8—111no—
382C2×#103—111no—
383C2×#103—111no—
384C2×#103—111no—
385C2×#103—111no—
386C2×#102—111no—
387C2×#102—111no—
388C2×#102—111no—
389C2×#102—111no—
390C2×C22⋊C8—111no—
391C2×C22⋊C8—111no—
392C2×C4×C8—111no—
393#397—221no—
394#394—221no—
395#391—111no—
396#391C2×D1111yescharacteristic
397#391C2×D1111yescharacteristic
398#389—111no—
399#386—21no—
400#386—21no—
401#386—221no—
402#381—21no—
403#380—221no—
404#380C2×D1111yescharacteristic
405C4×C22⋊C4C2×D1111yescharacteristic
406C2×#95—21no—
407#340—111no—
408#340—111no—
409#336—111no—
410#336—111no—
411C22×C11—24no—
412C22×C11—42no—
413C22×C11—42no—
414C22×C11—42no—
415C22×C11—42no—
416C22×C11—42no—
417C22×C11—42no—
418C22×C11—41no—
419C22×C11—41no—
420C22×C11—41no—
421C22×C11—41no—
422C22×C11—41no—
423C22×C11—41no—
424C22×C11—41no—
425C22×C11#52511yescharacteristic
426C22×C11D4211yescharacteristic
427C22×C11D4211yescharacteristic
428C22×C11C2×#13511yescharacteristic
429C22×C11#57511yescharacteristic
430C22×C11#57611yescharacteristic
431C22×C11#57811yescharacteristic
432C2×D11—42no—
433C2×D11—42no—
434C2×D11—42no—
435C2×D11—81no—
436C2×D11—81no—
437C2×D11—81no—
438C2×D11—81no—
439C4×C11—22no—
440C4×C11—41no—
441C4×C11—42no—
442C4×C11—41no—
443C4×C11—41no—
444C4×C11—41no—
445C4×C11—81no—
446C4×C11—81no—
447C4×C11C2×#12111yescharacteristic
448C4×C11#53811yescharacteristic
449C4×C11#54611yescharacteristic
450C4×C11#54611yescharacteristic
451Dic11—42no—
452Dic11—81no—
453Dic11—81no—
454C2×#41—22no—
455C2×#41—22no—
456C2×#41—22no—
457C2×#41—22no—
458C2×#41—41no—
459C2×#41—41no—
460C22×Q8—111no—
461C22×Q8C22×D1111yescharacteristic
462C22×D4—21no—
463C22×D4—111no—
464C22×D4—221no—
465C22×D4C22×D1111yescharacteristic
466C23×C4—21no—
467C23×C4—21no—
468C23×C4—21no—
469C23×C4—221no—
470C23×C4C22×D1111yescharacteristic
471C2×Q16—222no—
472C2×Q16—222no—
473C2×Q16—441no—
474C2×SD16—222no—
475C2×SD16—222no—
476C2×SD16—222no—
477C2×SD16—222no—
478C2×SD16—222no—
479C2×SD16—441no—
480C2×D8—114no—
481C2×D8—222no—
482C2×D8—222no—
483C22×C8—111no—
484C22×C8—111no—
485C22×C8—111no—
486C22×C8—111no—
487#124—222no—
488#124—441no—
489C22⋊Q8—222no—
490C22⋊Q8—441no—
491#121—222no—
492#121—441no—
493C4×D4—22no—
494C4×D4—22no—
495C4×D4—41no—
496C4×D4—41no—
497C4×D4—222no—
498C4×D4—441no—
499C2×C4⋊C4—111no—
500C2×C4⋊C4—111no—
501C2×C4⋊C4—221no—
502C2×C4⋊C4—221no—
503C2×C4⋊C4C22×D1111yescharacteristic
504C2×C4⋊C4C22×D1111yescharacteristic
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—221no—
509C2×C22⋊C4—221no—
510C2×C22⋊C4—221no—
511C2×C22⋊C4—221no—
512C2×C22⋊C4—221no—
513C2×C22⋊C4C22⋊D1111yescharacteristic
514C2×C22⋊C4C22⋊D1111yescharacteristic
515C2×C42C22×D1111yescharacteristic
516C2×C42C22×D1111yescharacteristic
517#107—222no—
518#107—441no—
519C4⋊C8—222no—
520#103—222no—
521#103—222no—
522#103—222no—
523#103—441no—
524#102—114no—
525#102—222no—
526#102—222no—
527#102—222no—
528C22⋊C8—222no—
529C22⋊C8—222no—
530C4×C8—222no—
531#95—21no—
532#95—21no—
533#95—21no—
534#95—21no—
535#95—21no—
536#95—221no—
537#95—221no—
538#95—221no—
539#95C22⋊D1111yescharacteristic
540#95C22⋊D1111yescharacteristic
541C2×C11—44no—
542C2×C11—81no—
543C2×C11#242411yescharacteristic
544C2×C11#310211yescharacteristic
545C2×C11#312411yescharacteristic
546C2×C11#326911yescharacteristic
547C2×C11#327311yescharacteristic
548C2×C11#328011yescharacteristic
549C2×C11#328311yescharacteristic
550D11—82no—
551C24—21no—
552C24—221no—
553C24C2×C22⋊D1111yescharacteristic
554#41—44no—
555#41—44no—
556#41—44no—
557#41—44no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—221no—
564C2×Q8—221no—
565C2×Q8—221no—
566C2×Q8—221no—
567C2×Q8—221no—
568C2×Q8—221no—
569C2×Q8#433912yes—
570C2×D4—24no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—42no—
575C2×D4—42no—
576C2×D4—112no—
577C2×D4—221no—
578C2×D4—221no—
579C2×D4—221no—
580C2×D4—221no—
581C2×D4—221no—
582C2×D4—442no—
583C2×D4—442no—
584C2×D4—881no—
585C2×D4#433912yes—
586C2×D4D4×D1112yes—
587C2×D4D4×D1112yes—
588C22×C4—24no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—81no—
605C22×C4—81no—
606C22×C4—221no—
607C22×C4—221no—
608C22×C4—221no—
609C22×C4—442no—
610C22×C4—442no—
611C22×C4—881no—
612C22×C4C2×C22⋊D1111yescharacteristic
613C22×C4C2×C22⋊D1111yescharacteristic
614C22×C4C2×C22⋊D1111yescharacteristic
615C22×C4C2×C22⋊D1111yescharacteristic
616C22×C4C2×C22⋊D1111yescharacteristic
617C22×C4C23×D1111yescharacteristic
618Q16—444no—
619SD16—444no—
620SD16—444no—
621D8—228no—
622C2×C8—112no—
623C2×C8—112no—
624C2×C8—221no—
625C2×C8—221no—
626C2×C8—221no—
627C2×C8—221no—
628C2×C8—221no—
629C2×C8—221no—
630C2×C8—221no—
631C2×C8—221no—
632C2×C8—221no—
633C2×C8—221no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—112no—
639C4⋊C4—221no—
640C4⋊C4—221no—
641C4⋊C4—221no—
642C4⋊C4—442no—
643C4⋊C4—881no—
644C22⋊C4—22no—
645C22⋊C4—41no—
646C22⋊C4—42no—
647C22⋊C4—42no—
648C22⋊C4—81no—
649C22⋊C4—442no—
650C22⋊C4—442no—
651C22⋊C4—442no—
652C22⋊C4—442no—
653C22⋊C4—442no—
654C42—21no—
655C42—21no—
656C42—21no—
657C42—21no—
658C11#2515011yescharacteristic, complemented, Sylow
659C23—22no—
660C23—22no—
661C23—22no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—222no—
674C23—441no—
675C23—441no—
676C23—441no—
677C23—441no—
678C23—441no—
679C23—441no—
680C23C22×C22⋊D1111yescharacteristic
681Q8—22no—
682Q8—22no—
683Q8—41no—
684Q8—41no—
685Q8—441no—
686Q8—441no—
687Q8—441no—
688Q8—441no—
689D4—22no—
690D4—22no—
691D4—22no—
692D4—48no—
693D4—222no—
694D4—222no—
695D4—441no—
696D4—441no—
697D4—884no—
698D4#6693714yes—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—22no—
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—21no—
713C2×C4—21no—
714C2×C4—48no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—84no—
728C2×C4—84no—
729C2×C4—222no—
730C2×C4—441no—
731C2×C4—441no—
732C2×C4—441no—
733C2×C4—441no—
734C2×C4—441no—
735C2×C4—441no—
736C2×C4—441no—
737C2×C4—441no—
738C2×C4—884no—
739C2×C4#6700312yes—
740C2×C4C2×#433911yescharacteristic
741C2×C4C2×#433911yescharacteristic
742C2×C4C2×D4×D1111yescharacteristic
743C2×C4C2×D4×D1111yescharacteristic
744C2×C4#6703711yescharacteristic
745C2×C4#6703711yescharacteristic
746C8—222no—
747C8—222no—
748C8—441no—
749C8—441no—
750C22—24no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—442no—
765C22—442no—
766C22—442no—
767C22—881no—
768C22—881no—
769C22—881no—
770C22—881no—
771C22#1062332211yescharacteristic
772C22D4×C22⋊D1111yescharacteristic
773C22D4×C22⋊D1111yescharacteristic
774C22C2×#6700311yescharacteristic
775C22#1062335311yescharacteristic
776C22#1062336611yescharacteristic
777C22#1062336911yescharacteristic
778C4—22no—
779C4—41no—
780C4—41no—
781C4—42no—
782C4—41no—
783C4—41no—
784C4—81no—
785C4—81no—
786C4—442no—
787C4—881no—
788C4—881no—
789C4C2×#6693711yescharacteristic
790C4#1062302111yescharacteristic
791C4#1062302111yescharacteristic
792C4#1062302511yescharacteristic
793C2—44no—
794C2—81no—
795C2—882no—
796C2#1307215211yescharacteristic
797C2#1307863411yescharacteristic
798C2#1307887811yescharacteristic
799C2#1308016711yescharacteristic
800C2#1308022311yescharacteristic
801C2#1308029711yescharacteristic
802C2#1308033411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2339C2
socleC23×C11C22×D4
prime radicalC2×#10622851C2
hypercenter#2339D11
hypocenterC11#25150
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2339

Complements

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

NH ≅ G/Ntype
1. C2×#10622629C2semidirect
2. C2×#10622852C2semidirect
4. C2×C4×#4323C2semidirect
5. #13072193C2semidirect
6. #13070011C2semidirect
7. #13069819C2semidirect
8. #13069798C2semidirect
9. #13069709C2semidirect
10. #13069476C2semidirect
11. #13069224C2semidirect
12. #13068953C2semidirect
13. #13068950C2semidirect
14. #13068863C2semidirect
15. C11×#2339C2semidirect
136. #66896D4semidirect
263. #2339D11semidirect
658. C11#25150semidirect

Maximal subgroups

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

subgroupindex
C2×#106226292
C2×#106228522
C2×#106228512
C2×C4×#43232
#130721932
#130700112
#130698192
#130697982
#130697092
#130694762
#130692242
#130689532
#130689502
#130688632
C11×#23392
#2515011