Finite Group Databasebeta

← #14826534

Subgroups — #14826534

Order 2816.

700 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073012C211yesmaximal, characteristic
2#13071621C211yesmaximal, characteristic
3#13070038C211yesmaximal, characteristic, complemented
4#13069998C211yesmaximal, characteristic, complemented
5#13069820C211yesmaximal, characteristic
6#13069812C211yesmaximal, characteristic
7#13069387C211yesmaximal, characteristic, complemented
8#13069343C211yesmaximal, characteristic, complemented
9#13069219C211yesmaximal, characteristic
10#13069207C211yesmaximal, characteristic, complemented
11#13069199C211yesmaximal, characteristic, complemented
12#13068885C211yesmaximal, characteristic, complemented
13#13068809C211yesmaximal, characteristic
14#13068435C211yesmaximal, characteristic, complemented
15C11×#1823C211yesmaximal, characteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C2×#66977C2211yescharacteristic
18C2×#66940C2211yescharacteristic
19C2×C11×C22⋊C8C2211yescharacteristic
20C11×#380C2211yescharacteristic
21#10622825C2211yescharacteristic
22#10622823—21no—
23C4×C22⋊Dic11—21no—
24C4×C22⋊Dic11C2211yescharacteristic
25C2×C22⋊(C11⋊C8)C2211yescharacteristic
26C2×#66882C2211yescharacteristic
27C2×#66880C2211yescharacteristic
28C2×#66880C2211yescharacteristic
29C2×Dic11⋊C8C2211yescharacteristic
30C2×C8×Dic11C2211yescharacteristic
31#10622598C2211yescharacteristic
32#10622591—21no—
33#10622590C2211yescharacteristic
34C4⋊C4×Dic11C2211yescharacteristic
35C4⋊C4×Dic11C2211yescharacteristic
36#10622587C2211yescharacteristic
37#10622586C2211yescharacteristic
38#10622586C2211yescharacteristic
39#10622585—21no—
40C2×#66874C2211yescharacteristic
41C2×#66874C2211yescharacteristic
42C2×#66872C2211yescharacteristic
43C2×#66872C2211yescharacteristic
44C2×#66872C2211yescharacteristic
45#10622565—21no—
46#10622564—21no—
47C11⋊#401—21no—
48#10622266—21no—
49C11×#340C2211yescharacteristic
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59C23×C4×C11—21no—
60C23×C4×C11C2311yescharacteristic
61C22×Dic22C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—41no—
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C22⋊C4—21no—
72C2×C22⋊Dic11—21no—
73C2×C22⋊Dic11—21no—
74C2×C22⋊Dic11D411yescharacteristic
75C2×C22⋊Dic11D411yescharacteristic
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11C2311yescharacteristic
78C2×C4⋊Dic11C2311yescharacteristic
79C2×C4⋊Dic11C2311yescharacteristic
80#66977—22no—
81#66977—22no—
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×C4×Dic11—21no—
87C2×C4×Dic11—21no—
88C2×C4×Dic11—21no—
89C2×C4×Dic11C2311yescharacteristic
90C2×C4×Dic11C2311yescharacteristic
91C22×C11⋊C8C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93#66940—22no—
94#66940—41no—
95C11×C22⋊C8—41no—
96C11×#95—21no—
97C11⋊#95—21no—
98C11⋊#95—21no—
99C11⋊#95—21no—
100C11⋊#95—21no—
101C11⋊#95—21no—
102C11⋊#95—21no—
103C11⋊#95—21no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95D411yescharacteristic
108C11⋊#95D411yescharacteristic
109C22⋊(C11⋊C8)—22no—
110#66882—22no—
111#66880—22no—
112#66880—41no—
113Dic11⋊C8—22no—
114C8×Dic11—41no—
115#66874—22no—
116#66874—22no—
117#66872—22no—
118#66872—22no—
119#66872—41no—
120#27037—111nomaximal, Sylow
121C24×C11C2×D411yescharacteristic
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—42no—
133C22×C4×C11—42no—
134C22×C4×C11—81no—
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2411yescharacteristic
137C22×Dic11—21no—
138C22×Dic11—21no—
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11C2×D411yescharacteristic
142C22×Dic11C2×D411yescharacteristic
143C22×Dic11C2×D411yescharacteristic
144C22×Dic11C2×D411yescharacteristic
145C2×Dic22—21no—
146C2×Dic22—21no—
147C2×Dic22—21no—
148C2×Dic22—21no—
149C2×Dic22—21no—
150C2×Dic22#4112yes—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11—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—21no—
164C11×C4⋊C4—42no—
165C11×C4⋊C4#4112yes—
166C11×C22⋊C4—42no—
167C22⋊Dic11—24no—
168C22⋊Dic11—22no—
169C22⋊Dic11—22no—
170C22⋊Dic11—81no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—42no—
177C4⋊Dic11#4112yes—
178Dic11⋊C4—24no—
179Dic11⋊C4—42no—
180Dic11⋊C4—81no—
181Dic11⋊C4—81no—
182C4×Dic11—21no—
183C4×Dic11—21no—
184C4×Dic11—21no—
185C4×Dic11—21no—
186C4×Dic11—42no—
187C4×Dic11—81no—
188C4×Dic11—81no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8#4112yes—
195#2494—111no—
196#2360—111no—
197#2074—111no—
198#2066—111no—
199#2036—111no—
200#2035—111no—
201#1949—111no—
202#1941—111no—
203#1923—111no—
204#1921—111no—
205#1920—111no—
206#1865—111no—
207#1853—111no—
208#1823D1111yescharacteristic
209C4×#103—111no—
210C23×C11—21no—
211C23×C11—21no—
212C23×C11—21no—
213C23×C11—21no—
214C23×C11—21no—
215C23×C11—21no—
216C23×C11#13512yes—
217C23×C11C22×D411yescharacteristic
218C2×C4×C11—21no—
219C2×C4×C11—22no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—41no—
223C2×C4×C11—41no—
224C2×C4×C11—41no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—84no—
238C2×C4×C11C2×#4111yescharacteristic
239C2×C4×C11C2×#4111yescharacteristic
240C2×C4×C11C2×#4111yescharacteristic
241C2×C4×C11C2×#4111yescharacteristic
242C2×C4×C11H(5,𝔽2)11yescharacteristic
243C2×C4×C112−1+411yescharacteristic
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11—22no—
247C2×Dic11—22no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—21no—
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11#13712yes—
268Dic22—22no—
269Dic22—22no—
270Dic22—41no—
271Dic22—41no—
272C8×C11—41no—
273C8×C11—41no—
274C11⋊C8—22no—
275C11⋊C8—41no—
276C2×C22⋊Q8—111no—
277C2×C4×Q8—111no—
278C22×C4⋊C4C2×D1111yescharacteristic
279C2×#107—111no—
280C2×#106—111no—
281C2×#106—111no—
282C2×#106—111no—
283C2×C4⋊C8—111no—
284C2×#103—111no—
285C2×#103—111no—
286C2×#103—111no—
287C2×#103—111no—
288C2×C22⋊C8—111no—
289C2×C22⋊C8C2×D1111yescharacteristic
290C2×C4×C8—111no—
291#401—221no—
292#397—221no—
293#391—111no—
294#389—111no—
295#389—111no—
296#389—111no—
297#389—221no—
298#388—221no—
299#387—221no—
300#387—221no—
301#385—221no—
302#382—111no—
303#380—111no—
304#380C2×D1111yescharacteristic
305C4×C4⋊C4—111no—
306C4×C4⋊C4—111no—
307C4×C22⋊C4—111no—
308C4×C22⋊C4—221no—
309#340—111no—
310#340—111no—
311#340—111no—
312#340—111no—
313#340C2×D1111yescharacteristic
314#340C2×D1111yescharacteristic
315#340C2×D1111yescharacteristic
316#340C2×D1111yescharacteristic
317#336—111no—
318#336—111no—
319C22×C11—22no—
320C22×C11—22no—
321C22×C11—22no—
322C22×C11—41no—
323C22×C11—41no—
324C22×C11—41no—
325C22×C11—41no—
326C22×C11#52511yescharacteristic
327C22×C11#54611yescharacteristic
328C22×C11#54711yescharacteristic
329C22×C11C2×#13511yescharacteristic
330C22×C11C2×#13711yescharacteristic
331C22×C11#57711yescharacteristic
332C22×C11#57711yescharacteristic
333C4×C11—41no—
334C4×C11—42no—
335C4×C11—81no—
336C4×C11—81no—
337C4×C11—81no—
338C4×C11#52911yescharacteristic
339C4×C11#53911yescharacteristic
340C4×C11#55311yescharacteristic
341C4×C11#55611yescharacteristic
342Dic11—22no—
343Dic11—41no—
344Dic11—41no—
345Dic11—42no—
346Dic11—42no—
347Dic11—41no—
348Dic11—81no—
349Dic11—81no—
350C22×Q8—111no—
351C23×C4—21no—
352C23×C4C22×D1111yescharacteristic
353C22×C8—111no—
354C22×C8—111no—
355C22×C8C22×D1111yescharacteristic
356C22×C8C22×D1111yescharacteristic
357C22⋊Q8—222no—
358C22⋊Q8—222no—
359C4×Q8—222no—
360C4×Q8—441no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—41no—
364C2×C4⋊C4—111no—
365C2×C4⋊C4—111no—
366C2×C4⋊C4—111no—
367C2×C4⋊C4—221no—
368C2×C4⋊C4—221no—
369C2×C4⋊C4—221no—
370C2×C4⋊C4—221no—
371C2×C4⋊C4—221no—
372C2×C4⋊C4C22×D1111yescharacteristic
373C2×C4⋊C4C22×D1111yescharacteristic
374C2×C4⋊C4C22×D1111yescharacteristic
375C2×C4⋊C4C22×D1111yescharacteristic
376C2×C22⋊C4—21no—
377C2×C22⋊C4—111no—
378C2×C22⋊C4—111no—
379C2×C22⋊C4—221no—
380C2×C22⋊C4—221no—
381C2×C42—111no—
382C2×C42—111no—
383C2×C42—221no—
384C2×C42—221no—
385C2×C42—221no—
386#107—222no—
387#106—222no—
388#106—222no—
389#106—441no—
390C4⋊C8—222no—
391#103—222no—
392#103—222no—
393#103—222no—
394#103—441no—
395C22⋊C8—41no—
396C22⋊C8—222no—
397C4×C8—441no—
398#95—21no—
399#95—111no—
400#95—111no—
401#95—221no—
402#95—221no—
403#95—221no—
404#95—221no—
405#95—221no—
406#95—221no—
407#95—221no—
408#95—221no—
409#95—221no—
410#95—221no—
411C2×C11—42no—
412C2×C11#246611yescharacteristic
413C2×C11#310811yescharacteristic
414C2×C11#312511yescharacteristic
415C2×C11#329611yescharacteristic
416C2×C11#332011yescharacteristic
417C2×C11#333711yescharacteristic
418C2×C11#335611yescharacteristic
419C24D4×D1111yescharacteristic
420C2×Q8—112no—
421C2×Q8—221no—
422C2×Q8—221no—
423C2×Q8—221no—
424C2×Q8—221no—
425C2×Q8—221no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—42no—
437C22×C4—42no—
438C22×C4—81no—
439C22×C4—111no—
440C22×C4—111no—
441C22×C4—111no—
442C22×C4—111no—
443C22×C4—221no—
444C22×C4—221no—
445C22×C4—221no—
446C22×C4—221no—
447C22×C4D4×D1111yescharacteristic
448C22×C4C23×D1111yescharacteristic
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—112no—
456C2×C8—221no—
457C2×C8—221no—
458C2×C8—221no—
459C2×C8—221no—
460C2×C8—221no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—42no—
469C4⋊C4—112no—
470C4⋊C4—224no—
471C4⋊C4—221no—
472C4⋊C4—221no—
473C4⋊C4—221no—
474C4⋊C4—221no—
475C4⋊C4—221no—
476C4⋊C4—442no—
477C4⋊C4—442no—
478C4⋊C4—881no—
479C4⋊C4—881no—
480C4⋊C4#433912yes—
481C22⋊C4—42no—
482C22⋊C4—222no—
483C22⋊C4—224no—
484C22⋊C4—222no—
485C22⋊C4—881no—
486C42—221no—
487C42—221no—
488C42—221no—
489C42—221no—
490C42—442no—
491C42—881no—
492C42—881no—
493C11#2703711yescharacteristic, complemented, Sylow
494C23—21no—
495C23—21no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—21no—
500C23#6696512yes—
501C23C2×D4×D1111yescharacteristic
502Q8—222no—
503Q8—222no—
504Q8—441no—
505Q8—441no—
506C2×C4—22no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—84no—
526C2×C4—112no—
527C2×C4—221no—
528C2×C4—221no—
529C2×C4—221no—
530C2×C4—221no—
531C2×C4—221no—
532C2×C4—221no—
533C2×C4—221no—
534C2×C4—221no—
535C2×C4—221no—
536C2×C4—221no—
537C2×C4—221no—
538C2×C4—222no—
539C2×C4—222no—
540C2×C4—441no—
541C2×C4—441no—
542C2×C4—441no—
543C2×C4—441no—
544C2×C4—441no—
545C2×C4—441no—
546C2×C4—441no—
547C2×C4—441no—
548C2×C4—441no—
549C2×C4—441no—
550C2×C4C2×#433911yescharacteristic
551C2×C4#6703711yescharacteristic
552C2×C4#41×D1111yescharacteristic
553C2×C4#41×D1111yescharacteristic
554C2×C4#41×D1111yescharacteristic
555C2×C4#6704311yescharacteristic
556C8—41no—
557C8—41no—
558C8—222no—
559C8—441no—
560C22—22no—
561C22—22no—
562C22—22no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22#1062302111yescharacteristic
568C22#1062318611yescharacteristic
569C22#1062318711yescharacteristic
570C22C2×#6696511yescharacteristic
571C22#1062329311yescharacteristic
572C22D11×#13711yescharacteristic
573C22#1062330911yescharacteristic
574C4—41no—
575C4—42no—
576C4—81no—
577C4—81no—
578C4—81no—
579C4—222no—
580C4—442no—
581C4—442no—
582C4—441no—
583C4—441no—
584C4—441no—
585C4—881no—
586C4—881no—
587C4#1062305911yescharacteristic
588C4#1062306411yescharacteristic
589C4#1062319111yescharacteristic
590C4#1062319211yescharacteristic
591C2—42no—
592C2#1307265111yescharacteristic
593C2#1307869311yescharacteristic
594C2#1307888811yescharacteristic
595C2#1308044711yescharacteristic
596C2#1308078811yescharacteristic
597C2#1308099911yescharacteristic
598C2#1308122411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1823C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#1823D11
hypocenterC11#27037
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1823

Complements

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

NH ≅ G/Ntype
3. #13070038C2semidirect
4. #13069998C2semidirect
7. #13069387C2semidirect
8. #13069343C2semidirect
10. #13069207C2semidirect
11. #13069199C2semidirect
12. #13068885C2semidirect
14. #13068435C2semidirect
493. C11#27037semidirect

Maximal subgroups

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

subgroupindex
#130730122
#130716212
#130700382
#130699982
#130698202
#130698122
#130693872
#130693432
#130692192
#130692072
#130691992
#130688852
#130688092
#130684352
C11×#18232
#2703711