Finite Group Databasebeta

← #14800482

Subgroups — #14800482

Order 2816.

1172 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622662C211yesmaximal, characteristic, complemented
2C2×#10622670C211yesmaximal, characteristic, complemented
3C2×#10622851C211yesmaximal, characteristic
4C2×#10622845C211yesmaximal, characteristic, complemented
5#13071630C211yesmaximal, characteristic, complemented
6#13070011C211yesmaximal, characteristic, complemented
7#13069926C211yesmaximal, characteristic, complemented
8#13069852C211yesmaximal, characteristic, complemented
9#13069699C211yesmaximal, characteristic, complemented
10#13069540C211yesmaximal, characteristic, complemented
11#13069233C211yesmaximal, characteristic, complemented
12#13068953C211yesmaximal, characteristic, complemented
13#13068924C211yesmaximal, characteristic, complemented
14#13068801C211yesmaximal, characteristic, complemented
15C11×#2432C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C2×C11×C4⋊Q8C2211yescharacteristic
18C2×C11×#124C2211yescharacteristic
19C2×C11×C22⋊Q8C2211yescharacteristic
20C22×#4325C2211yescharacteristic
21C22×#4325C2211yescharacteristic
22C22×#4323C2211yescharacteristic
23C2×#66983C2211yescharacteristic
24C22×C4⋊Dic11C2211yescharacteristic
25C22×#4318C2211yescharacteristic
26C2×(C22⋊D11)⋊C4—21no—
27C2×C4×D44C2211yescharacteristic
28C11×#394—21no—
29C11×#394—21no—
30C11×#391C2211yescharacteristic
31C11×#390C2211yescharacteristic
32C11×#385—21no—
33C11×#385—21no—
34C4×C11×C22⋊C4C2211yescharacteristic
35#10622851—24no—
36#10622845—24no—
37C2×#66899C2211yescharacteristic
38C2×#66899C2211yescharacteristic
39C2×#66899C2211yescharacteristic
40C2×#66899C2211yescharacteristic
41C2×#66899C2211yescharacteristic
42C2×#66899C2211yescharacteristic
43C2×#66896C2211yescharacteristic
44C2×#66896C2211yescharacteristic
45C2×#66896C2211yescharacteristic
46C2×C22⋊(C11⋊C8)C2211yescharacteristic
47#10622670—24no—
48#10622662—24no—
49C2×#66873C2211yescharacteristic
50C2×#66871C2211yescharacteristic
51#10622571—21no—
52#10622552C2211yescharacteristic
53C4×C4⋊Dic11C2211yescharacteristic
54#10622541C2211yescharacteristic
55C2×C4⋊(C11⋊C8)C2211yescharacteristic
56C2×C4⋊(C11⋊C8)C2211yescharacteristic
57#10622283—21no—
58#10622281—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×Q8×C11C2311yescharacteristic
71C22×D4×C11—21no—
72C22×D4×C11C2311yescharacteristic
73C23×C4×C11—21no—
74C23×C4×C11C2311yescharacteristic
75C22×C22⋊D11—21no—
76C23×Dic11—21no—
77C22×D44C2311yescharacteristic
78C22×C4×D11—21no—
79C11×C4⋊Q8—22no—
80C11×C4⋊Q8—41no—
81C11×#124—22no—
82C11×#124—41no—
83C11×C22⋊Q8—22no—
84C11×C22⋊Q8—22no—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4—21no—
93C2×C11×C22⋊C4—21no—
94C2×C11×C22⋊C4D411yescharacteristic
95C2×C11×C22⋊C4D411yescharacteristic
96C2×C42×C11C2311yescharacteristic
97C2×C42×C11C2311yescharacteristic
98C2×#4325—22no—
99C2×#4325—22no—
100C2×#4325—22no—
101C2×#4325—22no—
102C2×#4325—41no—
103C2×#4325—41no—
104C2×#4323—22no—
105C2×#4323—22no—
106C2×#4323—41no—
107#66983—22no—
108#66983D414yes—
109C2×(C2×D11)⋊C4—21no—
110C2×(C2×D11)⋊C4—21no—
111C2×(C2×D11)⋊C4—21no—
112C2×(C2×D11)⋊C4—21no—
113C2×C4⋊Dic11—22no—
114C2×C4⋊Dic11—21no—
115C2×C4⋊Dic11—41no—
116C2×C4⋊Dic11C2311yescharacteristic
117C2×C4⋊Dic11C2311yescharacteristic
118C2×C4⋊Dic11C2311yescharacteristic
119C2×Dic11⋊C4—21no—
120C2×C4×Dic11—21no—
121C2×#4318—22no—
122C2×#4318—22no—
123C2×#4318—41no—
124C22×C11⋊C8C2311yescharacteristic
125C22×C11⋊C8C2311yescharacteristic
126C22×C11⋊C8C2311yescharacteristic
127C22×C11⋊C8C2311yescharacteristic
128(C22⋊D11)⋊C4—44no—
129C4×D44—22no—
130C4×D44—41no—
131C11×#95—21no—
132C11×#95—21no—
133C11×#95D411yescharacteristic
134C11×#95D411yescharacteristic
135#66899—22no—
136#66899—22no—
137#66899—22no—
138#66899—22no—
139#66899—22no—
140#66899—41no—
141#66896—22no—
142#66896—22no—
143#66896D414yescomplemented
144C11⋊#95—21no—
145C11⋊#95—21no—
146C22⋊(C11⋊C8)—22no—
147#66873—22no—
148#66871—22no—
149C4⋊(C11⋊C8)—22no—
150C4⋊(C11⋊C8)—41no—
151#25104—111nomaximal, Sylow
152C24×C11—21no—
153C24×C11C2×D411yescharacteristic
154C23×D11—21no—
155C11×#41—28no—
156C11×#41—44no—
157C11×#41—44no—
158C11×#41—44no—
159C2×Q8×C11—21no—
160C2×Q8×C11—21no—
161C2×Q8×C11—21no—
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#4112yes—
171C2×D4×C11—21no—
172C2×D4×C11—21no—
173C2×D4×C11—21no—
174C2×D4×C11—21no—
175C2×D4×C11—21no—
176C2×D4×C11—42no—
177C2×D4×C11—42no—
178C2×D4×C11—42no—
179C2×D4×C11C2×D412yes—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—42no—
188C22×C4×C11—42no—
189C22×C4×C11—42no—
190C22×C4×C11C2×D411yescharacteristic
191C22×C4×C11C2×D411yescharacteristic
192C22×C4×C11C2×D411yescharacteristic
193C22×C4×C11C2×D411yescharacteristic
194C22×C4×C11C2×D412yes—
195C22×C4×C11C2×D411yescharacteristic
196C22×C4×C11#4112yes—
197C22×C4×C11C2411yescharacteristic
198C2×C22⋊D11—24no—
199C2×C22⋊D11—42no—
200C2×C22⋊D11—42no—
201C22×Dic11—21no—
202C22×Dic11—21no—
203C22×Dic11—21no—
204C22×Dic11—42no—
205C22×Dic11—42no—
206C22×Dic11—81no—
207C2×D44—21no—
208C2×D44—21no—
209C2×D44—21no—
210C2×D44—21no—
211C2×D44—21no—
212C2×D44C2×D412yes—
213C2×C4×D11—42no—
214C2×C4×D11—42no—
215C2×C4×D11—81no—
216C11×C4⋊C4—21no—
217C11×C4⋊C4—21no—
218C11×C4⋊C4—42no—
219C11×C4⋊C4—42no—
220C11×C4⋊C4—42no—
221C11×C22⋊C4—22no—
222C11×C22⋊C4—41no—
223C11×C22⋊C4—42no—
224C11×C22⋊C4—42no—
225C11×C22⋊C4—42no—
226C11×C22⋊C4—42no—
227C11×C22⋊C4—42no—
228C42×C11—21no—
229C42×C11—21no—
230C42×C11—21no—
231C42×C11—21no—
232#4325—44no—
233#4325—44no—
234#4323—44no—
235(C2×D11)⋊C4—24no—
236(C2×D11)⋊C4—42no—
237(C2×D11)⋊C4—42no—
238(C2×D11)⋊C4—81no—
239C4⋊Dic11—21no—
240C4⋊Dic11—21no—
241C4⋊Dic11—21no—
242C4⋊Dic11—21no—
243C4⋊Dic11—42no—
244C4⋊Dic11C2×D412yes—
245C4⋊Dic11C2×D412yes—
246Dic11⋊C4—42no—
247C4×Dic11—42no—
248#4318—44no—
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⋊C8—21no—
257C2×C11⋊C8—21no—
258C2×C11⋊C8—21no—
259C2×C11⋊C8—21no—
260C2×C11⋊C8C2×D412yes—
261C2×#468—111no—
262C2×#463—111no—
263C2×#449—111no—
264C2×#417—111no—
265#2432D1111yescharacteristic, complemented
266#2361—111no—
267#2068—111no—
268#2054—111no—
269#2042—111no—
270#2013—111no—
271#1981—111no—
272#1925—111no—
273#1877—111no—
274#1872—111no—
275#1851—111no—
276C23×C11—21no—
277C23×C11—21no—
278C23×C11—21no—
279C23×C11—21no—
280C23×C11—21no—
281C23×C11—21no—
282C23×C11—22no—
283C23×C11—41no—
284C23×C11—41no—
285C23×C11—41no—
286C23×C11—41no—
287C23×C11—41no—
288C23×C11—41no—
289C23×C11#12112yes—
290C23×C11C22×D411yescharacteristic
291C22×D11—22no—
292C22×D11—41no—
293C22×D11—41no—
294C22×D11—41no—
295C22×D11—41no—
296C22×D11—41no—
297C22×D11—41no—
298Q8×C11—22no—
299Q8×C11—22no—
300Q8×C11—41no—
301Q8×C11—41no—
302Q8×C11—41no—
303Q8×C11—41no—
304Q8×C11—41no—
305Q8×C11—41no—
306D4×C11—22no—
307D4×C11—22no—
308D4×C11—48no—
309D4×C11—41no—
310D4×C11—41no—
311C2×C4×C11—21no—
312C2×C4×C11—21no—
313C2×C4×C11—21no—
314C2×C4×C11—21no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—21no—
320C2×C4×C11—21no—
321C2×C4×C11—21no—
322C2×C4×C11—22no—
323C2×C4×C11—21no—
324C2×C4×C11—21no—
325C2×C4×C11—21no—
326C2×C4×C11—21no—
327C2×C4×C11—21no—
328C2×C4×C11—21no—
329C2×C4×C11—48no—
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#12112yes—
339C2×C4×C11AGL(1,ℤ/8)12yes—
340C2×C4×C11C22×D411yescharacteristic
341C2×C4×C11C22×D411yescharacteristic
342C2×C4×C11C2×#4111yescharacteristic
343C2×C4×C11C2×#4111yescharacteristic
344C2×C4×C11H(5,𝔽2)11yescharacteristic
345C2×C4×C11H(5,𝔽2)11yescharacteristic
346C22⋊D11—48no—
347C2×Dic11—22no—
348C2×Dic11—22no—
349C2×Dic11—41no—
350C2×Dic11—41no—
351C2×Dic11—41no—
352C2×Dic11—41no—
353C2×Dic11—41no—
354C2×Dic11—41no—
355C2×Dic11—41no—
356C2×Dic11—84no—
357D44—22no—
358D44—22no—
359D44—41no—
360D44—41no—
361C4×D11—84no—
362C11⋊C8—22no—
363C11⋊C8—41no—
364C11⋊C8—41no—
365C11⋊C8—41no—
366C22×#41C2×D1111yescharacteristic
367C22×SD16—111no—
368C22×SD16—111no—
369C22×D8—111no—
370C22×M16—111no—
371C2×C4⋊Q8C2×D1111yescharacteristic
372C2×#124C2×D1111yescharacteristic
373C2×C22⋊Q8C2×D1111yescharacteristic
374C2×#121—111no—
375C2×C4×D4—111no—
376C2×C4×D4—221no—
377C22×C4⋊C4—111no—
378#468—224no—
379#463—224no—
380#449—224no—
381C2×#107—111no—
382C2×C4⋊C8—111no—
383C2×C4⋊C8—111no—
384#417—224no—
385C2×#103—111no—
386C2×#103—111no—
387C2×#103—111no—
388C2×#103—111no—
389C2×#103—111no—
390C2×#103—111no—
391C2×#102—111no—
392C2×#102—111no—
393C2×#102—111no—
394C2×#102—111no—
395C2×C22⋊C8—111no—
396#394—21no—
397#394—21no—
398#391C2×D1111yescharacteristic
399#390—111no—
400#390C2×D1111yescharacteristic
401#389—111no—
402#388—221no—
403#386—221no—
404#385—21no—
405#385—21no—
406#385—221no—
407C4×C4⋊C4—111no—
408C4×C22⋊C4C2×D1111yescharacteristic
409#340—111no—
410#340—111no—
411#336—111no—
412#336—111no—
413C22×C11—22no—
414C22×C11—22no—
415C22×C11—22no—
416C22×C11—41no—
417C22×C11—41no—
418C22×C11—41no—
419C22×C11—41no—
420C22×C11—42no—
421C22×C11—42no—
422C22×C11—42no—
423C22×C11—81no—
424C22×C11—81no—
425C22×C11—81no—
426C22×C11—81no—
427C22×C11C2×#12111yescharacteristic
428C22×C11D4211yescharacteristic
429C22×C11#54611yescharacteristic
430C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
431C22×C11#57511yescharacteristic
432C22×C11#57711yescharacteristic
433C22×C11#57811yescharacteristic
434C2×D11—42no—
435C2×D11—42no—
436C2×D11—42no—
437C2×D11—81no—
438C2×D11—81no—
439C2×D11—81no—
440C2×D11—81no—
441C4×C11—22no—
442C4×C11—22no—
443C4×C11—42no—
444C4×C11—41no—
445C4×C11—41no—
446C4×C11—41no—
447C4×C11—81no—
448C4×C11—81no—
449C4×C11#52511yescharacteristic
450C4×C11#53811yescharacteristic
451C4×C11D4211yescharacteristic
452C4×C11#54611yescharacteristic
453Dic11—42no—
454Dic11—42no—
455Dic11—81no—
456C2×#41—22no—
457C2×#41—22no—
458C2×#41—22no—
459C2×#41—22no—
460C2×#41—41no—
461C2×#41—41no—
462C22×Q8C22×D1111yescharacteristic
463C22×Q8C22×D1111yescharacteristic
464C22×D4—21no—
465C22×D4—111no—
466C22×D4—221no—
467C22×D4C22×D1111yescharacteristic
468C23×C4—21no—
469C23×C4—221no—
470C23×C4—221no—
471C23×C4C22×D1111yescharacteristic
472C2×SD16—222no—
473C2×SD16—222no—
474C2×SD16—222no—
475C2×SD16—222no—
476C2×SD16—441no—
477C2×SD16—441no—
478C2×D8—222no—
479C2×D8—222no—
480C2×D8—441no—
481C2×M16—222no—
482C2×M16—222no—
483C2×M16—441no—
484C22×C8—111no—
485C22×C8—111no—
486C22×C8—111no—
487C22×C8—111no—
488C4⋊Q8—22no—
489C4⋊Q8—41no—
490#124—22no—
491#124—41no—
492C22⋊Q8—22no—
493C22⋊Q8—22no—
494#121—114no—
495#121—222no—
496C4×D4—222no—
497C4×D4—441no—
498C4×D4—444no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—111no—
503C2×C4⋊C4—111no—
504C2×C4⋊C4—111no—
505C2×C4⋊C4—222no—
506C2×C4⋊C4—221no—
507C2×C4⋊C4—221no—
508C2×C4⋊C4—441no—
509C2×C4⋊C4C22×D1111yescharacteristic
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—221no—
516C2×C22⋊C4—221no—
517C2×C22⋊C4—221no—
518C2×C22⋊C4—221no—
519C2×C22⋊C4C22⋊D1111yescharacteristic
520C2×C22⋊C4C22⋊D1111yescharacteristic
521C2×C42—221no—
522C2×C42C22×D1111yescharacteristic
523C2×C42C22×D1111yescharacteristic
524#107—222no—
525C4⋊C8—222no—
526C4⋊C8—441no—
527#103—222no—
528#103—222no—
529#103—222no—
530#103—222no—
531#103—222no—
532#103—441no—
533#102—114no—
534#102—222no—
535#102—222no—
536#102—222no—
537C22⋊C8—222no—
538#95—21no—
539#95—21no—
540#95—221no—
541#95—221no—
542#95C22⋊D1111yescharacteristic
543#95C22⋊D1111yescharacteristic
544C2×C11—42no—
545C2×C11—82no—
546C2×C11#242411yescharacteristic
547C2×C11#303611yescharacteristic
548C2×C11#304611yescharacteristic
549C2×C11#326911yescharacteristic
550C2×C11#327211yescharacteristic
551C2×C11#330811yescharacteristic
552C2×C11#332611yescharacteristic
553D11—82no—
554C24—21no—
555C24—221no—
556C24C2×C22⋊D1111yescharacteristic
557#41—28no—
558#41—44no—
559#41—44no—
560#41—44no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8#434112yes—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—42no—
579C2×D4—42no—
580C2×D4—42no—
581C2×D4—112no—
582C2×D4—224no—
583C2×D4—221no—
584C2×D4—221no—
585C2×D4—221no—
586C2×D4—221no—
587C2×D4—221no—
588C2×D4—442no—
589C2×D4—442no—
590C2×D4D4×D1112yes—
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—221no—
602C22×C4—221no—
603C22×C4—221no—
604C22×C4—442no—
605C22×C4—442no—
606C22×C4—442no—
607C22×C4—442no—
608C22×C4—881no—
609C22×C4—881no—
610C22×C4D4×D1112yes—
611C22×C4#434112yes—
612C22×C4C2×C22⋊D1111yescharacteristic
613C22×C4C2×C22⋊D1111yescharacteristic
614C22×C4C2×C22⋊D1111yescharacteristic
615C22×C4C2×C22⋊D1111yescharacteristic
616C22×C4C2×C22⋊D1111yescharacteristic
617C22×C4C23×D1111yescharacteristic
618SD16—444no—
619SD16—444no—
620D8—444no—
621M16—444no—
622C2×C8—112no—
623C2×C8—221no—
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—42no—
637C4⋊C4—42no—
638C4⋊C4—42no—
639C4⋊C4—112no—
640C4⋊C4—112no—
641C4⋊C4—221no—
642C4⋊C4—221no—
643C4⋊C4—221no—
644C4⋊C4—221no—
645C4⋊C4—442no—
646C4⋊C4—442no—
647C22⋊C4—22no—
648C22⋊C4—41no—
649C22⋊C4—42no—
650C22⋊C4—42no—
651C22⋊C4—42no—
652C22⋊C4—42no—
653C22⋊C4—42no—
654C22⋊C4—224no—
655C22⋊C4—442no—
656C22⋊C4—442no—
657C22⋊C4—881no—
658C42—21no—
659C42—21no—
660C42—21no—
661C42—21no—
662C42—442no—
663C11#2510411yescharacteristic, complemented, Sylow
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—22no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—222no—
678C23—441no—
679C23—441no—
680C23—441no—
681C23—441no—
682C23—441no—
683C23—441no—
684C23#6699112yes—
685C23C22×C22⋊D1111yescharacteristic
686Q8—22no—
687Q8—22no—
688Q8—41no—
689Q8—41no—
690Q8—41no—
691Q8—41no—
692Q8—41no—
693Q8—41no—
694D4—22no—
695D4—22no—
696D4—48no—
697D4—41no—
698D4—41no—
699D4—222no—
700D4—222no—
701D4—448no—
702D4—441no—
703D4—441no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—22no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—48no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—222no—
732C2×C4—222no—
733C2×C4—441no—
734C2×C4—441no—
735C2×C4—441no—
736C2×C4—441no—
737C2×C4—441no—
738C2×C4—441no—
739C2×C4—441no—
740C2×C4—884no—
741C2×C4—884no—
742C2×C4#6699112yes—
743C2×C4#6700212yes—
744C2×C4C2×D4×D1111yescharacteristic
745C2×C4C2×D4×D1111yescharacteristic
746C2×C4C2×#434111yescharacteristic
747C2×C4C2×#434111yescharacteristic
748C2×C4#6703711yescharacteristic
749C2×C4#6703711yescharacteristic
750C8—222no—
751C8—441no—
752C8—441no—
753C8—441no—
754C22—22no—
755C22—22no—
756C22—22no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—42no—
762C22—42no—
763C22—42no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22—81no—
768C22—442no—
769C22—442no—
770C22—442no—
771C22—881no—
772C22—881no—
773C22—881no—
774C22—881no—
775C22C2×#6699111yescharacteristic
776C22D4×C22⋊D1111yescharacteristic
777C22#1062333711yescharacteristic
778C22C2×#6700211yescharacteristic
779C22#1062335311yescharacteristic
780C22#1062336811yescharacteristic
781C22#1062336911yescharacteristic
782C4—22no—
783C4—22no—
784C4—42no—
785C4—41no—
786C4—41no—
787C4—41no—
788C4—81no—
789C4—81no—
790C4—442no—
791C4—442no—
792C4—881no—
793C4#1062311711yescharacteristic
794C4#1062312111yescharacteristic
795C4#1062312211yescharacteristic
796C4#1062312411yescharacteristic
797C2—42no—
798C2—82no—
799C2—882no—
800C2#1307214811yescharacteristic
801C2#1307807611yescharacteristic
802C2#1307816211yescharacteristic
803C2#1308016711yescharacteristic
804C2#1308021611yescharacteristic
805C2#1308060711yescharacteristic
806C2#1308086911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2432C2
socleC23×C11C22×D4
prime radicalC2×#10622851C2
hypercenter#2432D11
hypocenterC11#25104
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2432

Complements

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

NH ≅ G/Ntype
1. C2×#10622662C2semidirect
2. C2×#10622670C2semidirect
4. C2×#10622845C2semidirect
5. #13071630C2semidirect
6. #13070011C2semidirect
7. #13069926C2semidirect
8. #13069852C2semidirect
9. #13069699C2semidirect
10. #13069540C2semidirect
11. #13069233C2semidirect
12. #13068953C2semidirect
13. #13068924C2semidirect
14. #13068801C2semidirect
15. C11×#2432C2semidirect
143. #66896D4semidirect
265. #2432D11semidirect
663. C11#25104semidirect

Maximal subgroups

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

subgroupindex
C2×#106226622
C2×#106226702
C2×#106228512
C2×#106228452
#130716302
#130700112
#130699262
#130698522
#130696992
#130695402
#130692332
#130689532
#130689242
#130688012
C11×#24322
#2510411