Finite Group Databasebeta

← #14812650

Subgroups — #14812650

Order 2816.

782 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622678C211yesmaximal, characteristic, complemented
2C2×#10622577C211yesmaximal, characteristic
3#13072307C211yesmaximal, characteristic
4#13070098C211yesmaximal, characteristic, complemented
5#13070097C211yesmaximal, characteristic, complemented
6#13069951C211yesmaximal, characteristic, complemented
7#13069944C211yesmaximal, characteristic, complemented
8#13069351C211yesmaximal, characteristic, complemented
9#13069346C211yesmaximal, characteristic, complemented
10#13068813C211yesmaximal, characteristic
11#13068804C211yesmaximal, characteristic
12#13068778C211yesmaximal, characteristic, complemented
13#13068647C211yesmaximal, characteristic
14#13068400C211yesmaximal, characteristic
15C11×#2442C211yesmaximal, characteristic
16C2×C11×#125C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C2×#66979C2211yescharacteristic
19C22×#4318C2211yescharacteristic
20C2×#66922C2211yescharacteristic
21C11×#400—21no—
22C11×#398—21no—
23C11×#389C2211yescharacteristic
24C11×#389C2211yescharacteristic
25C11×#385—21no—
26C11×#382C2211yescharacteristic
27C11×#380—21no—
28C11×#380C2211yescharacteristic
29C4×C11×C22⋊C4C2211yescharacteristic
30#10622825C2211yescharacteristic
31C2×C22⋊(C11⋊C8)C2211yescharacteristic
32#10622678—24no—
33#10622577—24no—
34C2×#66872C2211yescharacteristic
35C2×#66872C2211yescharacteristic
36C2×#66872C2211yescharacteristic
37C2×#66872C2211yescharacteristic
38C2×#66871C2211yescharacteristic
39C2×#66871C2211yescharacteristic
40C2×#66871C2211yescharacteristic
41C2×#66871C2211yescharacteristic
42C2×#66871C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44#10622561—21no—
45#10622560—21no—
46#10622549C2211yescharacteristic
47#10622541C2211yescharacteristic
48#10622541C2211yescharacteristic
49C2×#66867C2211yescharacteristic
50C2×C4×C11⋊C8C2211yescharacteristic
51#10622268—21no—
52#10622259—21no—
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C23×C4×C11—21no—
62C23×C4×C11C2311yescharacteristic
63C22×Dic22—21no—
64C11×#125—22no—
65C11×#125—41no—
66C2×C11×C4⋊C4—22no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—41no—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4D411yescharacteristic
79C2×C11×C22⋊C4D411yescharacteristic
80C2×C42×C11C2311yescharacteristic
81C2×C42×C11C2311yescharacteristic
82C2×C22⋊Dic11—21no—
83C2×C22⋊Dic11—21no—
84#66979—22no—
85#66979—41no—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×C4×Dic11—21no—
94C2×#4318—22no—
95C2×#4318—22no—
96C2×#4318Q814yescomplemented
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101#66922—22no—
102#66922—41no—
103C11×#95—21no—
104C11×#95—21no—
105C11×#95—21no—
106C11×#95—21no—
107C11×#95—21no—
108C11×#95D411yescharacteristic
109C11×#95D411yescharacteristic
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C22⋊(C11⋊C8)Q814yescomplemented
116#66872—22no—
117#66872—22no—
118#66872—22no—
119#66872—22no—
120#66871—22no—
121#66871—22no—
122#66871—22no—
123#66871—41no—
124#66871—41no—
125#66871D414yes—
126#66867—22no—
127C4×C11⋊C8—22no—
128#26079—111nomaximal, Sylow
129C24×C11C2×D411yescharacteristic
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—42no—
139C22×C4×C11—42no—
140C22×C4×C11—81no—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×Q812yes—
147C22×C4×C11C2×Q812yes—
148C22×C4×C11C2411yescharacteristic
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C2×Dic22—42no—
154C2×Dic22—42no—
155C2×Dic22—81no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—42no—
164C11×C4⋊C4—42no—
165C11×C4⋊C4—42no—
166C11×C4⋊C4—81no—
167C11×C4⋊C4—81no—
168C11×C4⋊C4C2×D412yes—
169C11×C22⋊C4—41no—
170C11×C22⋊C4—41no—
171C11×C22⋊C4—42no—
172C42×C11—21no—
173C42×C11—21no—
174C42×C11—21no—
175C42×C11—21no—
176C22⋊Dic11—42no—
177C22⋊Dic11—81no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—42no—
186C4⋊Dic11C2×D412yes—
187Dic11⋊C4—42no—
188Dic11⋊C4—81no—
189C4×Dic11—42no—
190#4318—28no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8C2×D412yes—
198C2×C11⋊C8C2×Q812yes—
199C2×C11⋊C8C2×Q812yes—
200C2×C11⋊C8C2×Q812yes—
201C2×C11⋊C8C2×Q812yes—
202C2×C11⋊C8#4112yes—
203C2×#501—111no—
204C2×#428—111no—
205#2442D1111yescharacteristic
206#2439—111no—
207#2085—111no—
208#2085—111no—
209#2059—111no—
210#2057—111no—
211#1943—111no—
212#1942—111no—
213#1854—111no—
214#1852—111no—
215#1846—111no—
216#1809—111no—
217#1753—111no—
218C23×C11—21no—
219C23×C11—21no—
220C23×C11—21no—
221C23×C11—21no—
222C23×C11—21no—
223C23×C11—21no—
224C23×C11C4⋊Q812yes—
225C23×C11C22×D411yescharacteristic
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—22no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—84no—
257C2×C4×C11C4⋊Q812yes—
258C2×C4×C11C22×D411yescharacteristic
259C2×C4×C11C22×Q811yescharacteristic
260C2×C4×C11C22×Q811yescharacteristic
261C2×C4×C11C2×#4111yescharacteristic
262C2×C4×C11H(5,𝔽2)11yescharacteristic
263C2×C4×C112−1+411yescharacteristic
264C2×Dic11—22no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276Dic22—84no—
277C11⋊C8—22no—
278C11⋊C8—22no—
279C11⋊C8—22no—
280C11⋊C8C22⋊Q814yes—
281C22×M16—111no—
282C2×C4⋊Q8—111no—
283C2×#125C2×D1111yescharacteristic
284C2×#117—111no—
285C22×C4⋊C4C2×D1111yescharacteristic
286#501—224no—
287#428—224no—
288C2×#107—111no—
289C2×#107—111no—
290C2×#107—111no—
291C2×#107—111no—
292C2×#107—111no—
293C2×#107—111no—
294C2×#106—111no—
295C2×#106—111no—
296C2×#106—111no—
297C2×#106—111no—
298C2×C22⋊C8—111no—
299C2×#97—111no—
300C2×C4×C8—111no—
301#400—21no—
302#398—21no—
303#396—221no—
304#393—221no—
305#391—221no—
306#389—111no—
307#389—111no—
308#389C2×D1111yescharacteristic
309#389C2×D1111yescharacteristic
310#387—221no—
311#385—21no—
312#382—111no—
313#382C2×D1111yescharacteristic
314#380—21no—
315#380—111no—
316#380C2×D1111yescharacteristic
317C4×C22⋊C4C2×D1111yescharacteristic
318#340—111no—
319#340—111no—
320#340—111no—
321#340—111no—
322#340—111no—
323#340—111no—
324#336—111no—
325#336—111no—
326C22×C11—22no—
327C22×C11—22no—
328C22×C11—22no—
329C22×C11—41no—
330C22×C11—41no—
331C22×C11—41no—
332C22×C11—41no—
333C22×C11C2×C4⋊Q811yescharacteristic
334C22×C11D4211yescharacteristic
335C22×C11#54711yescharacteristic
336C22×C11#57511yescharacteristic
337C22×C11#57511yescharacteristic
338C22×C11#57611yescharacteristic
339C22×C11#57811yescharacteristic
340C4×C11—22no—
341C4×C11—41no—
342C4×C11—41no—
343C4×C11—41no—
344C4×C11—42no—
345C4×C11—41no—
346C4×C11—81no—
347C4×C11—81no—
348C4×C11—81no—
349C4×C11C2×C22⋊Q811yescharacteristic
350C4×C11#54411yescharacteristic
351C4×C11D4×Q811yescharacteristic
352C4×C11#55411yescharacteristic
353Dic11—42no—
354Dic11—81no—
355Dic11—81no—
356Dic11—81no—
357C22×Q8—221no—
358C23×C4—21no—
359C23×C4C22×D1111yescharacteristic
360C2×M16—114no—
361C2×M16—222no—
362C2×M16—222no—
363C22×C8—111no—
364C22×C8—111no—
365C22×C8—111no—
366C22×C8—111no—
367C4⋊Q8—222no—
368C4⋊Q8—441no—
369#125—22no—
370#125—41no—
371#117—222no—
372#117—441no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—41no—
380C2×C4⋊C4—111no—
381C2×C4⋊C4—111no—
382C2×C4⋊C4—111no—
383C2×C4⋊C4—111no—
384C2×C4⋊C4—221no—
385C2×C4⋊C4—221no—
386C2×C4⋊C4—221no—
387C2×C4⋊C4C22×D1111yescharacteristic
388C2×C4⋊C4C22×D1111yescharacteristic
389C2×C4⋊C4C22×D1111yescharacteristic
390C2×C4⋊C4C22×D1111yescharacteristic
391C2×C22⋊C4—21no—
392C2×C22⋊C4—221no—
393C2×C22⋊C4—221no—
394C2×C22⋊C4C22⋊D1111yescharacteristic
395C2×C22⋊C4C22⋊D1111yescharacteristic
396C2×C42—221no—
397C2×C42C22×D1111yescharacteristic
398C2×C42C22×D1111yescharacteristic
399#107—114no—
400#107—222no—
401#107—222no—
402#107—222no—
403#107—441no—
404#107—441no—
405#106—222no—
406#106—222no—
407#106—222no—
408#106—222no—
409C22⋊C8—114no—
410#97—222no—
411C4×C8—222no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—221no—
418#95—221no—
419#95—221no—
420#95—221no—
421#95—221no—
422#95C22⋊D1111yescharacteristic
423#95C22⋊D1111yescharacteristic
424C2×C11—42no—
425C2×C11#244011yescharacteristic
426C2×C11#316411yescharacteristic
427C2×C11#316611yescharacteristic
428C2×C11#327311yescharacteristic
429C2×C11#327711yescharacteristic
430C2×C11#334711yescharacteristic
431C2×C11#334911yescharacteristic
432C24C2×C22⋊D1111yescharacteristic
433C2×Q8—442no—
434C2×Q8—442no—
435C2×Q8—881no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—42no—
445C22×C4—42no—
446C22×C4—81no—
447C22×C4—221no—
448C22×C4—221no—
449C22×C4—221no—
450C22×C4—221no—
451C22×C4Q8×D1112yes—
452C22×C4Q8×D1112yes—
453C22×C4C2×C22⋊D1111yescharacteristic
454C22×C4C2×C22⋊D1111yescharacteristic
455C22×C4C2×C22⋊D1111yescharacteristic
456C22×C4C2×C22⋊D1111yescharacteristic
457C22×C4C2×C22⋊D1111yescharacteristic
458C22×C4C23×D1111yescharacteristic
459M16—228no—
460C2×C8—112no—
461C2×C8—112no—
462C2×C8—112no—
463C2×C8—112no—
464C2×C8—112no—
465C2×C8—112no—
466C2×C8—221no—
467C2×C8—221no—
468C2×C8—221no—
469C2×C8—221no—
470C2×C8—221no—
471C2×C8—221no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—42no—
480C4⋊C4—42no—
481C4⋊C4—42no—
482C4⋊C4—81no—
483C4⋊C4—81no—
484C4⋊C4—112no—
485C4⋊C4—221no—
486C4⋊C4—221no—
487C4⋊C4—221no—
488C4⋊C4—221no—
489C4⋊C4—221no—
490C4⋊C4—221no—
491C4⋊C4—221no—
492C4⋊C4—442no—
493C4⋊C4—442no—
494C4⋊C4—881no—
495C4⋊C4D4×D1112yes—
496C22⋊C4—41no—
497C22⋊C4—41no—
498C22⋊C4—42no—
499C22⋊C4—442no—
500C22⋊C4—881no—
501C42—21no—
502C42—21no—
503C42—21no—
504C42—21no—
505C42—442no—
506C11#2607911yescharacteristic, complemented, Sylow
507C23—21no—
508C23—21no—
509C23—21no—
510C23—21no—
511C23—21no—
512C23—21no—
513C23#6699712yes—
514C23C22×C22⋊D1111yescharacteristic
515Q8—884no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—22no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—84no—
547C2×C4—222no—
548C2×C4—441no—
549C2×C4—441no—
550C2×C4—441no—
551C2×C4—441no—
552C2×C4—441no—
553C2×C4—441no—
554C2×C4—441no—
555C2×C4—441no—
556C2×C4—441no—
557C2×C4—441no—
558C2×C4—441no—
559C2×C4#6699712yes—
560C2×C4C2×D4×D1111yescharacteristic
561C2×C4#6703711yescharacteristic
562C2×C4C2×Q8×D1111yescharacteristic
563C2×C4C2×Q8×D1111yescharacteristic
564C2×C4#41×D1111yescharacteristic
565C2×C4#6704311yescharacteristic
566C8—114no—
567C8—222no—
568C8—222no—
569C8—222no—
570C22—22no—
571C22—22no—
572C22—22no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22D4×C22⋊D1111yescharacteristic
578C22C2×#6699711yescharacteristic
579C22#1062335311yescharacteristic
580C22#1062335311yescharacteristic
581C22#1062335511yescharacteristic
582C22#1062336611yescharacteristic
583C22#1062336911yescharacteristic
584C4—22no—
585C4—41no—
586C4—41no—
587C4—41no—
588C4—42no—
589C4—41no—
590C4—81no—
591C4—81no—
592C4—81no—
593C4—442no—
594C4—881no—
595C4—881no—
596C4—881no—
597C4#1062315411yescharacteristic
598C4D11×C22⋊Q811yescharacteristic
599C4#1062316311yescharacteristic
600C4#1062316711yescharacteristic
601C2—42no—
602C2#1307231511yescharacteristic
603C2#1307915011yescharacteristic
604C2#1307916511yescharacteristic
605C2#1308022311yescharacteristic
606C2#1308026911yescharacteristic
607C2#1308111011yescharacteristic
608C2#1308114611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2442C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#2442D11
hypocenterC11#26079
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2442

Complements

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

NH ≅ G/Ntype
1. C2×#10622678C2semidirect
4. #13070098C2semidirect
5. #13070097C2semidirect
6. #13069951C2semidirect
7. #13069944C2semidirect
8. #13069351C2semidirect
9. #13069346C2semidirect
12. #13068778C2semidirect
96. C2×#4318Q8semidirect
115. C22⋊(C11⋊C8)Q8semidirect
506. C11#26079semidirect

Maximal subgroups

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

subgroupindex
C2×#106226782
C2×#106225772
#130723072
#130700982
#130700972
#130699512
#130699442
#130693512
#130693462
#130688132
#130688042
#130687782
#130686472
#130684002
C11×#24422
#2607911