Finite Group Databasebeta

← #14801263

Subgroups — #14801263

Order 2816.

1268 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622696C211yesmaximal, characteristic, complemented
2C2×#10622659C211yesmaximal, characteristic
3C2×#10622659C211yesmaximal, characteristic
4C2×C4×#4325C211yesmaximal, characteristic, complemented
5C22⋊C4×D44C211yesmaximal, characteristic
6#13069987C211yesmaximal, characteristic, complemented
7#13069809C211yesmaximal, characteristic, complemented
8#13069809C211yesmaximal, characteristic, complemented
9#13069699C211yesmaximal, characteristic, complemented
10#13069473C211yesmaximal, characteristic, complemented
11#13069224C211yesmaximal, characteristic, complemented
12#13068971C211yesmaximal, characteristic, complemented
13#13068953C211yesmaximal, characteristic, complemented
14#13068876C211yesmaximal, characteristic, complemented
15C11×#2429C211yesmaximal, characteristic, complemented
16C23×D44C2211yescharacteristic
17C2×C11×C4⋊Q8C2211yescharacteristic, complemented
18C2×C11×C22⋊Q8C2211yescharacteristic
19C2×C11×C22⋊Q8C2211yescharacteristic
20C2×C4×Q8×C11C2211yescharacteristic, complemented
21C22×#4325C2211yescharacteristic
22C22×#4325C2211yescharacteristic
23C22×#4325C2211yescharacteristic
24C22×#4325C2211yescharacteristic
25C2×C22⋊C4×D11—21no—
26C2×C4×D44C2211yescharacteristic
27C2×C4×D44C2211yescharacteristic
28C11×#398—21no—
29C11×#396—21no—
30C11×#391C2211yescharacteristic, complemented
31C11×#389—21no—
32C11×#389C2211yescharacteristic, complemented
33C11×#388—21no—
34C4×C11×C22⋊C4C2211yescharacteristic
35C2×#66899C2211yescharacteristic, complemented
36C2×#66899C2211yescharacteristic, complemented
37C2×#66899C2211yescharacteristic, complemented
38C2×#66899C2211yescharacteristic, complemented
39#10622825C2211yescharacteristic
40C2×C22⋊(C11⋊C8)C2211yescharacteristic
41C2×C22⋊(C11⋊C8)C2211yescharacteristic
42#10622696—24no—
43#10622659—24no—
44#10622659—24no—
45C4×#4325—24no—
46C2×#66873C2211yescharacteristic
47C2×#66873C2211yescharacteristic
48C2×#66873C2211yescharacteristic
49C2×#66873C2211yescharacteristic
50C2×#66872C2211yescharacteristic, complemented
51C2×#66872C2211yescharacteristic, complemented
52#10622568—21no—
53#10622552C2211yescharacteristic
54#10622552C2211yescharacteristic
55C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
56C2×C4×C11⋊C8C2211yescharacteristic, complemented
57#10622278—21no—
58#10622278—21no—
59#10622167C2211yescharacteristic, complemented
60#10622167C2211yescharacteristic, complemented
61#10622162C2211yescharacteristic, complemented
62#10622162C2211yescharacteristic, complemented
63C24×D11—21no—
64C22×Q8×C11C2311yescharacteristic
65C22×Q8×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C22×D44—21no—
68C22×D44—22no—
69C22×D44—22no—
70C22×D44—22no—
71C22×D44—22no—
72C22×D44—41no—
73C22×D44—41no—
74C22×D44C2311yescharacteristic
75C22×D44C2311yescharacteristic
76C22×C4×D11—21no—
77C22×C4×D11—21no—
78C11×C4⋊Q8—22no—
79C11×C4⋊Q8—41no—
80C11×C22⋊Q8—22no—
81C11×C22⋊Q8—22no—
82C11×C22⋊Q8—41no—
83C11×C22⋊Q8—41no—
84C4×Q8×C11—22no—
85C4×Q8×C11—41no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4C2311yescharacteristic
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C22⋊C4—21no—
95C2×C11×C22⋊C4—21no—
96C2×C11×C22⋊C4D411yescharacteristic
97C2×C11×C22⋊C4D411yescharacteristic
98C2×C42×C11—21no—
99C2×C42×C11C2311yescharacteristic
100C2×C42×C11C2311yescharacteristic
101C2×C22⋊Dic11—21no—
102C2×#4325—22no—
103C2×#4325—22no—
104C2×#4325—22no—
105C2×#4325—22no—
106C2×#4325—22no—
107C2×#4325—22no—
108C2×#4325—22no—
109C2×#4325—22no—
110C2×#4325—22no—
111C2×#4325—41no—
112C2×#4325—41no—
113C2×#4325D414yes—
114C2×(C2×D11)⋊C4—21no—
115C2×(C2×D11)⋊C4—21no—
116C2×(C2×D11)⋊C4—21no—
117C2×(C2×D11)⋊C4—21no—
118C2×(C2×D11)⋊C4—21no—
119C2×(C2×D11)⋊C4—21no—
120C2×C4⋊Dic11C2311yescharacteristic
121C2×C4⋊Dic11C2311yescharacteristic
122C22×C11⋊C8C2311yescharacteristic
123C22×C11⋊C8C2311yescharacteristic
124C22×C11⋊C8C2311yescharacteristic
125C22×C11⋊C8C2311yescharacteristic
126C22⋊C4×D11—44no—
127C4×D44—22no—
128C4×D44—22no—
129C4×D44—41no—
130C4×D44—41no—
131C11×#95—21no—
132C11×#95—21no—
133C11×#95—21no—
134C11×#95D411yescharacteristic
135C11×#95D411yescharacteristic
136#66899—22no—
137#66899—22no—
138#66899—22no—
139#66899—41no—
140C11⋊#95—21no—
141C22⋊(C11⋊C8)—22no—
142C22⋊(C11⋊C8)—22no—
143#66873—22no—
144#66873—22no—
145#66873—22no—
146#66873D414yes—
147#66872—22no—
148#66872—41no—
149C4⋊(C11⋊C8)—22no—
150C4×C11⋊C8—22no—
151#25156—111nomaximal, Sylow
152C24×C11C2×D411yescharacteristic
153C23×D11—21no—
154C23×D11—21no—
155C23×D11—24no—
156C23×D11—42no—
157C23×D11—42no—
158C23×D11—42no—
159C23×D11—42no—
160C23×D11—81no—
161C23×D11—81no—
162C2×Q8×C11—21no—
163C2×Q8×C11—21no—
164C2×Q8×C11—21no—
165C2×Q8×C11—21no—
166C2×Q8×C11—21no—
167C2×Q8×C11—21no—
168C2×Q8×C11—21no—
169C2×Q8×C11—21no—
170C2×Q8×C11—21no—
171C2×Q8×C11—21no—
172C2×Q8×C11—21no—
173C2×Q8×C11C2×D412yes—
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—21no—
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11C2×D411yescharacteristic
189C22×C4×C11C2411yescharacteristic
190C22×Dic11—21no—
191C22×Dic11—21no—
192C2×D44—24no—
193C2×D44—21no—
194C2×D44—21no—
195C2×D44—21no—
196C2×D44—21no—
197C2×D44—21no—
198C2×D44—21no—
199C2×D44—21no—
200C2×D44—21no—
201C2×D44—42no—
202C2×D44—42no—
203C2×D44—44no—
204C2×D44—44no—
205C2×D44—44no—
206C2×D44—44no—
207C2×D44C2×D412yes—
208C2×D44C2×D412yes—
209C2×D44#4112yes—
210C2×D44#4112yes—
211C2×C4×D11—42no—
212C2×C4×D11—42no—
213C2×C4×D11—42no—
214C2×C4×D11—42no—
215C2×C4×D11—81no—
216C2×C4×D11—81no—
217C11×C4⋊C4—21no—
218C11×C4⋊C4—21no—
219C11×C4⋊C4—21no—
220C11×C4⋊C4—42no—
221C11×C4⋊C4—42no—
222C11×C4⋊C4—42no—
223C11×C4⋊C4—42no—
224C11×C4⋊C4—42no—
225C11×C4⋊C4—42no—
226C11×C4⋊C4C2×D412yes—
227C11×C22⋊C4—41no—
228C11×C22⋊C4—42no—
229C11×C22⋊C4—42no—
230C11×C22⋊C4SD1614yescomplemented
231C42×C11—21no—
232C42×C11—21no—
233C42×C11—21no—
234C42×C11—21no—
235C42×C11—42no—
236C22⋊Dic11—42no—
237#4325—28no—
238#4325—44no—
239#4325—44no—
240#4325—44no—
241(C2×D11)⋊C4—42no—
242(C2×D11)⋊C4—42no—
243(C2×D11)⋊C4—42no—
244(C2×D11)⋊C4—42no—
245(C2×D11)⋊C4—81no—
246(C2×D11)⋊C4—81no—
247C4⋊Dic11—21no—
248C4⋊Dic11—21no—
249C4⋊Dic11—21no—
250C4⋊Dic11—21no—
251C2×C11⋊C8—21no—
252C2×C11⋊C8—21no—
253C2×C11⋊C8—21no—
254C2×C11⋊C8—21no—
255C2×C11⋊C8—21no—
256C2×C11⋊C8—21no—
257C2×C11⋊C8—21no—
258C2×C11⋊C8—21no—
259C2×C11⋊C8—21no—
260C2×C11⋊C8—21no—
261C2×C11⋊C8C2×D412yes—
262C2×C11⋊C8C2×D412yes—
263C2×#461—111no—
264C2×#450—111no—
265C2×#450—111no—
266C2×C4×SD16—111no—
267#2429D1111yescharacteristic, complemented
268D4×C22⋊C4—111no—
269#2065—111no—
270#2035—111no—
271#2035—111no—
272#2013—111no—
273#1968—111no—
274#1923—111no—
275#1880—111no—
276#1877—111no—
277#1864—111no—
278C23×C11—21no—
279C23×C11—21no—
280C23×C11—21no—
281C23×C11—21no—
282C23×C11—21no—
283C23×C11—21no—
284C23×C11C2×SD1612yes—
285C23×C11C22×D411yescharacteristic
286C22×D11—22no—
287C22×D11—22no—
288C22×D11—22no—
289C22×D11—22no—
290C22×D11—48no—
291C22×D11—41no—
292C22×D11—41no—
293C22×D11—41no—
294C22×D11—41no—
295C22×D11—48no—
296C22×D11—41no—
297C22×D11—41no—
298C22×D11—41no—
299C22×D11—41no—
300C22×D11—41no—
301C22×D11—41no—
302C22×D11—84no—
303C22×D11—84no—
304C22×D11—84no—
305C22×D11—84no—
306C22×D11—84no—
307Q8×C11—22no—
308Q8×C11—22no—
309Q8×C11—41no—
310Q8×C11—41no—
311Q8×C11—41no—
312Q8×C11—41no—
313Q8×C11—41no—
314Q8×C11—41no—
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—22no—
323C2×C4×C11—22no—
324C2×C4×C11—21no—
325C2×C4×C11—21no—
326C2×C4×C11—21no—
327C2×C4×C11—21no—
328C2×C4×C11—21no—
329C2×C4×C11—21no—
330C2×C4×C11—41no—
331C2×C4×C11—41no—
332C2×C4×C11—41no—
333C2×C4×C11—41no—
334C2×C4×C11—41no—
335C2×C4×C11—41no—
336C2×C4×C11—41no—
337C2×C4×C11—41no—
338C2×C4×C11—41no—
339C2×C4×C11—41no—
340C2×C4×C11—41no—
341C2×C4×C11—41no—
342C2×C4×C11—41no—
343C2×C4×C11—41no—
344C2×C4×C11C2×SD1612yes—
345C2×C4×C11C2×SD1612yes—
346C2×C4×C11C22×D411yescharacteristic
347C2×C4×C11C22×D411yescharacteristic
348C2×C4×C11C2×#4111yescharacteristic
349C2×C4×C11C2×#4111yescharacteristic
350C2×C4×C11H(5,𝔽2)11yescharacteristic
351C2×C4×C11H(5,𝔽2)11yescharacteristic
352C2×Dic11—41no—
353C2×Dic11—41no—
354C2×Dic11—41no—
355C2×Dic11—41no—
356C2×Dic11—41no—
357C2×Dic11—41no—
358D44—22no—
359D44—22no—
360D44—22no—
361D44—22no—
362D44—22no—
363D44—48no—
364D44—41no—
365D44—41no—
366D44#12114yes—
367C4×D11—84no—
368C4×D11—84no—
369C11⋊C8—22no—
370C11⋊C8—22no—
371C11⋊C8—41no—
372C11⋊C8—41no—
373C23×D4—111no—
374C22×SD16—111no—
375C22×SD16—111no—
376C22×SD16—111no—
377C22×SD16—111no—
378C2×C4⋊Q8C2×D1111yescharacteristic, complemented
379C2×C22⋊Q8C2×D1111yescharacteristic
380C2×C22⋊Q8C2×D1111yescharacteristic
381C2×C4×Q8C2×D1111yescharacteristic, complemented
382C2×C4×D4—111no—
383C2×C4×D4—111no—
384C22×C22⋊C4—221no—
385#461—224no—
386#450—224no—
387#450—224no—
388C4×SD16—224no—
389C2×#106—111no—
390C2×#106—111no—
391C2×C4⋊C8—111no—
392C2×#103—111no—
393C2×#103—111no—
394C2×#103—111no—
395C2×#103—111no—
396C2×#102—111no—
397C2×#102—111no—
398C2×#102—111no—
399C2×#102—111no—
400C2×C22⋊C8—111no—
401C2×C22⋊C8—111no—
402C2×C4×C8—111no—
403#398—21no—
404#396—21no—
405#391C2×D1111yescharacteristic, complemented
406#390—111no—
407#390—111no—
408#389—21no—
409#389C2×D1111yescharacteristic, complemented
410#388—21no—
411#386—221no—
412#386—221no—
413#380—111no—
414#379—221no—
415C4×C22⋊C4C2×D1111yescharacteristic
416#340—111no—
417#340—111no—
418#336—111no—
419#336—111no—
420C22×C11—22no—
421C22×C11—22no—
422C22×C11—22no—
423C22×C11—41no—
424C22×C11—41no—
425C22×C11—41no—
426C22×C11—41no—
427C22×C11#52511yescharacteristic
428C22×C11D4211yescharacteristic
429C22×C11D4211yescharacteristic
430C22×C11C22×SD1611yescharacteristic
431C22×C11#57511yescharacteristic
432C22×C11#57711yescharacteristic
433C22×C11#57711yescharacteristic
434C2×D11—24no—
435C2×D11—42no—
436C2×D11—42no—
437C2×D11—42no—
438C2×D11—42no—
439C2×D11—42no—
440C2×D11—42no—
441C2×D11—42no—
442C2×D11—42no—
443C2×D11—42no—
444C2×D11—816no—
445C2×D11—81no—
446C2×D11—81no—
447C2×D11—81no—
448C2×D11—81no—
449C4×C11—22no—
450C4×C11—22no—
451C4×C11—41no—
452C4×C11—42no—
453C4×C11—41no—
454C4×C11—42no—
455C4×C11—41no—
456C4×C11—81no—
457C4×C11—81no—
458C4×C11C2×#12111yescharacteristic
459C4×C11#53811yescharacteristic
460C4×C11#54611yescharacteristic
461C4×C11#54611yescharacteristic
462Dic11—81no—
463Dic11—81no—
464C25—221no—
465C22×Q8C22×D1111yescharacteristic
466C22×Q8C22×D1111yescharacteristic
467C22×D4—111no—
468C22×D4—111no—
469C22×D4—222no—
470C22×D4—222no—
471C22×D4—222no—
472C22×D4—222no—
473C22×D4—221no—
474C22×D4—441no—
475C22×D4—441no—
476C23×C4—221no—
477C23×C4—221no—
478C23×C4C22×D1111yescharacteristic
479C2×SD16—114no—
480C2×SD16—222no—
481C2×SD16—222no—
482C2×SD16—222no—
483C2×SD16—222no—
484C2×SD16—222no—
485C2×SD16—222no—
486C2×SD16—222no—
487C2×SD16—222no—
488C2×SD16—222no—
489C2×SD16—441no—
490C2×SD16—441no—
491C22×C8—111no—
492C22×C8—111no—
493C22×C8—111no—
494C22×C8—111no—
495C4⋊Q8—22no—
496C4⋊Q8—41no—
497C22⋊Q8—22no—
498C22⋊Q8—22no—
499C22⋊Q8—41no—
500C22⋊Q8—41no—
501C4×Q8—22no—
502C4×Q8—41no—
503C4×D4—222no—
504C4×D4—222no—
505C4×D4—441no—
506C4×D4—441no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—111no—
514C2×C4⋊C4—111no—
515C2×C4⋊C4C22×D1111yescharacteristic
516C2×C4⋊C4C22×D1111yescharacteristic
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—221no—
520C2×C22⋊C4—221no—
521C2×C22⋊C4—221no—
522C2×C22⋊C4—221no—
523C2×C22⋊C4—221no—
524C2×C22⋊C4—221no—
525C2×C22⋊C4—221no—
526C2×C22⋊C4—444no—
527C2×C22⋊C4C22⋊D1111yescharacteristic
528C2×C22⋊C4C22⋊D1111yescharacteristic
529C2×C42—21no—
530C2×C42C22×D1111yescharacteristic
531C2×C42C22×D1111yescharacteristic
532#106—222no—
533#106—441no—
534C4⋊C8—222no—
535#103—222no—
536#103—222no—
537#103—222no—
538#103—441no—
539#102—114no—
540#102—222no—
541#102—222no—
542#102—222no—
543C22⋊C8—222no—
544C22⋊C8—222no—
545C4×C8—222no—
546#95—21no—
547#95—21no—
548#95—21no—
549#95—221no—
550#95C22⋊D1111yescharacteristic
551#95C22⋊D1111yescharacteristic
552C2×C11—42no—
553C2×C11#242411yescharacteristic
554C2×C11#310111yescharacteristic
555C2×C11#312311yescharacteristic
556C2×C11#326711yescharacteristic
557C2×C11#327511yescharacteristic
558C2×C11D4×SD1611yescharacteristic
559C2×C11D4×SD1611yescharacteristic
560D11—44no—
561D11—82no—
562C24—224no—
563C24—221no—
564C24—221no—
565C24—442no—
566C24—442no—
567C24—442no—
568C24—442no—
569C24—881no—
570C24—881no—
571C24C2×C22⋊D1111yescharacteristic
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8D4×D1112yes—
584C2×D4—112no—
585C2×D4—112no—
586C2×D4—112no—
587C2×D4—112no—
588C2×D4—224no—
589C2×D4—221no—
590C2×D4—221no—
591C2×D4—221no—
592C2×D4—221no—
593C2×D4—221no—
594C2×D4—221no—
595C2×D4—221no—
596C2×D4—221no—
597C2×D4—442no—
598C2×D4—442no—
599C2×D4—444no—
600C2×D4—444no—
601C2×D4—444no—
602C2×D4—444no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—221no—
614C22×C4—221no—
615C22×C4—442no—
616C22×C4—442no—
617C22×C4—442no—
618C22×C4—442no—
619C22×C4—881no—
620C22×C4—881no—
621C22×C4C2×C22⋊D1111yescharacteristic
622C22×C4C2×C22⋊D1111yescharacteristic
623C22×C4C2×C22⋊D1111yescharacteristic
624C22×C4C2×C22⋊D1111yescharacteristic
625C22×C4C2×C22⋊D1111yescharacteristic
626C22×C4C23×D1111yescharacteristic
627SD16—228no—
628SD16—444no—
629SD16—444no—
630SD16—444no—
631C2×C8—112no—
632C2×C8—112no—
633C2×C8—221no—
634C2×C8—221no—
635C2×C8—221no—
636C2×C8—221no—
637C2×C8—221no—
638C2×C8—221no—
639C2×C8—221no—
640C2×C8—221no—
641C2×C8—221no—
642C2×C8—221no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—42no—
647C4⋊C4—42no—
648C4⋊C4—42no—
649C4⋊C4—42no—
650C4⋊C4—42no—
651C4⋊C4—42no—
652C4⋊C4—221no—
653C4⋊C4—221no—
654C4⋊C4—221no—
655C4⋊C4—221no—
656C4⋊C4D4×D1112yes—
657C22⋊C4—41no—
658C22⋊C4—42no—
659C22⋊C4—42no—
660C22⋊C4—442no—
661C22⋊C4—442no—
662C22⋊C4—442no—
663C22⋊C4—442no—
664C22⋊C4—442no—
665C22⋊C4—881no—
666C22⋊C4—881no—
667C22⋊C4#432514yescomplemented
668C42—21no—
669C42—21no—
670C42—21no—
671C42—21no—
672C42—42no—
673C11#2515611yescharacteristic, complemented, Sylow
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—222no—
681C23—222no—
682C23—222no—
683C23—222no—
684C23—448no—
685C23—448no—
686C23—441no—
687C23—441no—
688C23—441no—
689C23—441no—
690C23—441no—
691C23—441no—
692C23—441no—
693C23—441no—
694C23—441no—
695C23—441no—
696C23—884no—
697C23—884no—
698C23—884no—
699C23—884no—
700C23—884no—
701C23C2×#432512yes—
702C23C22×C22⋊D1111yescharacteristic
703Q8—22no—
704Q8—22no—
705Q8—41no—
706Q8—41no—
707Q8—41no—
708Q8—41no—
709Q8—41no—
710Q8—41no—
711D4—114no—
712D4—222no—
713D4—222no—
714D4—222no—
715D4—222no—
716D4—222no—
717D4—448no—
718D4—441no—
719D4—441no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—441no—
750C2×C4—441no—
751C2×C4—441no—
752C2×C4—441no—
753C2×C4—441no—
754C2×C4—441no—
755C2×C4—884no—
756C2×C4—884no—
757C2×C4C2×#432512yes—
758C2×C4C2×#432512yes—
759C2×C4C2×D4×D1111yescharacteristic
760C2×C4C2×D4×D1111yescharacteristic
761C2×C4#6703711yescharacteristic
762C2×C4#6703711yescharacteristic
763C2×C4#41×D1111yescharacteristic
764C2×C4#41×D1111yescharacteristic
765C8—222no—
766C8—222no—
767C8—441no—
768C8—441no—
769C22—22no—
770C22—22no—
771C22—22no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—224no—
777C22—442no—
778C22—442no—
779C22—442no—
780C22—442no—
781C22—442no—
782C22—442no—
783C22—442no—
784C22—442no—
785C22—442no—
786C22—8816no—
787C22—881no—
788C22—881no—
789C22—881no—
790C22—881no—
791C22D4×C22⋊D1111yescharacteristic
792C22D4×C22⋊D1111yescharacteristic
793C22C22×#432511yescharacteristic
794C22#1062335311yescharacteristic
795C22#1062335911yescharacteristic
796C22#1062336811yescharacteristic
797C22#1062336811yescharacteristic
798C4—22no—
799C4—22no—
800C4—41no—
801C4—42no—
802C4—41no—
803C4—42no—
804C4—41no—
805C4—81no—
806C4—81no—
807C4—881no—
808C4—881no—
809C4D11×#12111yescharacteristic
810C4#1062314111yescharacteristic
811C4#1062314311yescharacteristic
812C4#1062314411yescharacteristic
813C2—42no—
814C2—444no—
815C2—882no—
816C2#1307214911yescharacteristic
817C2#1307862011yescharacteristic
818C2#1307886311yescharacteristic
819C2#1308014211yescharacteristic
820C2#1308024811yescharacteristic
821C2D4×#432511yescharacteristic
822C2D4×#432511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2429C2
socleC23×C11C22×D4
prime radicalC23×D44C22
hypercenter#2429D11
hypocenterC11#25156
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2429

Complements

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

NH ≅ G/Ntype
1. C2×#10622696C2semidirect
4. C2×C4×#4325C2semidirect
6. #13069987C2semidirect
7. #13069809C2semidirect
8. #13069809C2semidirect
9. #13069699C2semidirect
10. #13069473C2semidirect
11. #13069224C2semidirect
12. #13068971C2semidirect
13. #13068953C2semidirect
14. #13068876C2semidirect
15. C11×#2429C2semidirect
17. C2×C11×C4⋊Q8C22semidirect
20. C2×C4×Q8×C11C22semidirect
30. C11×#391C22semidirect
32. C11×#389C22semidirect
35. C2×#66899C22semidirect
36. C2×#66899C22semidirect
37. C2×#66899C22semidirect
38. C2×#66899C22semidirect
50. C2×#66872C22semidirect
51. C2×#66872C22semidirect
55. C2×C4⋊(C11⋊C8)C22semidirect
56. C2×C4×C11⋊C8C22semidirect
59. #10622167C22semidirect
60. #10622167C22semidirect
61. #10622162C22semidirect
62. #10622162C22semidirect
230. C11×C22⋊C4SD16semidirect
267. #2429D11semidirect
378. C2×C4⋊Q8C2×D11semidirect
381. C2×C4×Q8C2×D11semidirect
405. #391C2×D11semidirect
409. #389C2×D11semidirect
667. C22⋊C4#4325semidirect
673. C11#25156semidirect

Maximal subgroups

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

subgroupindex
C2×#106226962
C2×#106226592
C2×C4×#43252
C22⋊C4×D442
#130699872
#130698092
#130696992
#130694732
#130692242
#130689712
#130689532
#130688762
C11×#24292
#2515611