Finite Group Databasebeta

← #14826383

Subgroups — #14826383

Order 2816.

690 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13072488C211yesmaximal, characteristic
2#13071710C211yesmaximal, characteristic, complemented
3#13070003C211yesmaximal, characteristic
4#13069955C211yesmaximal, characteristic, complemented
5#13069955C211yesmaximal, characteristic, complemented
6#13069763C211yesmaximal, characteristic
7#13069571C211yesmaximal, characteristic, complemented
8#13069359C211yesmaximal, characteristic, complemented
9#13069244C211yesmaximal, characteristic
10#13069237C211yesmaximal, characteristic
11#13069195C211yesmaximal, characteristic, complemented
12#13069188C211yesmaximal, characteristic, complemented
13#13068880C211yesmaximal, characteristic
14#13068442C211yesmaximal, characteristic
15C11×#1917C211yesmaximal, characteristic, complemented
16C2×C4×D44C2211yescharacteristic
17C2×#66923C2211yescharacteristic
18C2×#66923C2211yescharacteristic
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×#97C2211yescharacteristic
21C4×C11×C4⋊C4C2211yescharacteristic
22C2×#66885C2211yescharacteristic
23C2×#66885C2211yescharacteristic
24C2×#66885C2211yescharacteristic
25C2×#66885C2211yescharacteristic
26C2×#66882C2211yescharacteristic
27C2×#66882C2211yescharacteristic
28C2×#66881C2211yescharacteristic
29C2×#66881C2211yescharacteristic
30#10622605—21no—
31#10622602—21no—
32#10622591—21no—
33#10622585—21no—
34#10622552C2211yescharacteristic
35#10622552C2211yescharacteristic
36C4×C4⋊Dic11C2211yescharacteristic
37C4×C4⋊Dic11C2211yescharacteristic
38C4×C4⋊Dic11C2211yescharacteristic
39#10622541C2211yescharacteristic
40#10622541C2211yescharacteristic
41#10622541C2211yescharacteristic
42#10622541C2211yescharacteristic
43#10622289—21no—
44#10622280—21no—
45#10622265—21no—
46#10622262—21no—
47C11×#336C2211yescharacteristic
48C11×#336C2211yescharacteristic
49C11×#336C2211yescharacteristic
50C11×#336C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59C22×D44C2311yescharacteristic
60C22×C4×D11—21no—
61C22×C8×C11C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C2×C11×C4⋊C4D411yescharacteristic
66C2×C11×C4⋊C4D411yescharacteristic
67C2×C42×C11C2311yescharacteristic
68C2×C42×C11C2311yescharacteristic
69C2×C42×C11C2311yescharacteristic
70C2×(C2×D11)⋊C4—21no—
71C2×(C2×D11)⋊C4—21no—
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—21no—
74C2×(C2×D11)⋊C4—21no—
75C2×C4⋊Dic11C2311yescharacteristic
76C2×C4⋊Dic11C2311yescharacteristic
77C2×C4⋊Dic11C2311yescharacteristic
78C2×C4⋊Dic11C2311yescharacteristic
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×C4×Dic11—21no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11—21no—
93C4×D44—22no—
94C4×D44—41no—
95#66923—22no—
96#66923—22no—
97#66923—22no—
98#66923—41no—
99C11×C4⋊C8—41no—
100C11×#97—41no—
101C11×#95D411yescharacteristic
102C11×#95D411yescharacteristic
103C11⋊#95—21no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110#66885—22no—
111#66885—22no—
112#66885—41no—
113#66885Q814yes—
114#66882—22no—
115#66882—41no—
116#66881—22no—
117#66881—22no—
118#27027—111nomaximal, Sylow
119C23×D11—21no—
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2411yescharacteristic
127C22×Dic11—21no—
128C22×Dic11—21no—
129C22×Dic11—21no—
130C22×Dic11—21no—
131C22×Dic11—21no—
132C22×Dic11—21no—
133C22×Dic11—21no—
134C2×D44—21no—
135C2×D44—21no—
136C2×D44—21no—
137C2×D44—21no—
138C2×D44—21no—
139C2×D44C2×Q812yes—
140C2×C4×D11—42no—
141C2×C4×D11—42no—
142C2×C4×D11—81no—
143C2×C8×C11—21no—
144C2×C8×C11—21no—
145C2×C8×C11—21no—
146C2×C8×C11—21no—
147C2×C8×C11—21no—
148C2×C8×C11—21no—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11C2×Q812yes—
155C11×C4⋊C4—41no—
156C11×C4⋊C4—41no—
157C42×C11—21no—
158C42×C11—21no—
159C42×C11—21no—
160C42×C11—21no—
161C42×C11—21no—
162C42×C11—21no—
163(C2×D11)⋊C4—42no—
164(C2×D11)⋊C4—42no—
165(C2×D11)⋊C4—81no—
166(C2×D11)⋊C4—81no—
167(C2×D11)⋊C4—81no—
168C4⋊Dic11—21no—
169C4⋊Dic11—21no—
170C4⋊Dic11—21no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11C2×Q812yes—
179C4⋊Dic11#4112yes—
180C4⋊Dic11#4112yes—
181C4⋊Dic11#4112yes—
182Dic11⋊C4—24no—
183Dic11⋊C4—24no—
184Dic11⋊C4—42no—
185Dic11⋊C4—42no—
186Dic11⋊C4—42no—
187Dic11⋊C4—81no—
188Dic11⋊C4—81no—
189Dic11⋊C4—81no—
190C4×Dic11—42no—
191C4×Dic11—81no—
192C4×Dic11—81no—
193#2454—111no—
194#2370—111no—
195#2067—111no—
196#2059—111no—
197#2059—111no—
198#2025—111no—
199#1989—111no—
200#1944—111no—
201#1926—111no—
202#1925—111no—
203#1919—111no—
204#1918—111no—
205#1917D1111yescharacteristic, complemented
206#1864—111no—
207#1762—111no—
208C23×C11C22×D411yescharacteristic
209C22×D11—22no—
210C22×D11—41no—
211C22×D11—41no—
212C22×D11—41no—
213C22×D11—41no—
214C22×D11—41no—
215C22×D11—41no—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11C22×Q811yescharacteristic
235C2×C4×C11C2×#4111yescharacteristic
236C2×C4×C11C2×#4111yescharacteristic
237C2×C4×C11C2×#4111yescharacteristic
238C2×C4×C11H(5,𝔽2)11yescharacteristic
239C2×C4×C112−1+411yescharacteristic
240C2×Dic11—22no—
241C2×Dic11—22no—
242C2×Dic11—22no—
243C2×Dic11—22no—
244C2×Dic11—41no—
245C2×Dic11—41no—
246C2×Dic11—41no—
247C2×Dic11—41no—
248C2×Dic11—41no—
249C2×Dic11—41no—
250C2×Dic11—41no—
251C2×Dic11—41no—
252C2×Dic11—41no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261D44—22no—
262D44—22no—
263D44—41no—
264D44—41no—
265C4×D11—84no—
266C8×C11—22no—
267C8×C11—41no—
268C8×C11—41no—
269C8×C11—41no—
270C2×#125—111no—
271C2×#125—111no—
272C2×C4×D4—111no—
273C2×#107—111no—
274C2×#107—111no—
275C2×#106—111no—
276C2×#106—111no—
277C2×C4⋊C8C2×D1111yescharacteristic
278C2×#102—111no—
279C2×#102—111no—
280C2×#102—111no—
281C2×#102—111no—
282C2×#97C2×D1111yescharacteristic
283#399—221no—
284#396—221no—
285#390—111no—
286#390—111no—
287#389—111no—
288#389—111no—
289#389—111no—
290#389—111no—
291#389—221no—
292#387—221no—
293#387—221no—
294#385—221no—
295#380—221no—
296C4×C4⋊C4—111no—
297C4×C4⋊C4—111no—
298C4×C4⋊C4—111no—
299C4×C4⋊C4—221no—
300C4×C4⋊C4C2×D1111yescharacteristic
301#340—111no—
302#340—111no—
303#340—111no—
304#340—111no—
305#340—111no—
306#340—111no—
307#340—111no—
308#340—111no—
309#336C2×D1111yescharacteristic
310#336C2×D1111yescharacteristic
311#336C2×D1111yescharacteristic
312#336C2×D1111yescharacteristic
313C22×C11#52511yescharacteristic
314C22×C11#54611yescharacteristic
315C22×C11D4×Q811yescharacteristic
316C22×C11#57511yescharacteristic
317C22×C11#57511yescharacteristic
318C22×C11#57611yescharacteristic
319C22×C11#57711yescharacteristic
320C2×D11—42no—
321C2×D11—42no—
322C2×D11—42no—
323C2×D11—81no—
324C2×D11—81no—
325C2×D11—81no—
326C2×D11—81no—
327C4×C11—41no—
328C4×C11—41no—
329C4×C11—41no—
330C4×C11—41no—
331C4×C11—41no—
332C4×C11—41no—
333C4×C11#53311yescharacteristic
334C4×C11#54211yescharacteristic
335C4×C11#55411yescharacteristic
336C4×C11#55611yescharacteristic
337Dic11—42no—
338Dic11—42no—
339Dic11—42no—
340Dic11—42no—
341Dic11—81no—
342Dic11—81no—
343Dic11—81no—
344C22×D4—111no—
345C23×C4—221no—
346C22×C8C22×D1111yescharacteristic
347C22×C8C22×D1111yescharacteristic
348C22×C8C22×D1111yescharacteristic
349C22×C8C22×D1111yescharacteristic
350#125—222no—
351#125—222no—
352#125—222no—
353#125—441no—
354C4×D4—222no—
355C4×D4—441no—
356C2×C4⋊C4—111no—
357C2×C4⋊C4—111no—
358C2×C4⋊C4—111no—
359C2×C4⋊C4—111no—
360C2×C4⋊C4—111no—
361C2×C4⋊C4—111no—
362C2×C4⋊C4—111no—
363C2×C4⋊C4—221no—
364C2×C4⋊C4—221no—
365C2×C4⋊C4—221no—
366C2×C4⋊C4—221no—
367C2×C4⋊C4—221no—
368C2×C4⋊C4—221no—
369C2×C4⋊C4—221no—
370C2×C4⋊C4—221no—
371C2×C4⋊C4D4411yescharacteristic
372C2×C4⋊C4D4411yescharacteristic
373C2×C22⋊C4—221no—
374C2×C22⋊C4—221no—
375C2×C22⋊C4—221no—
376C2×C22⋊C4—221no—
377C2×C22⋊C4—221no—
378C2×C42—221no—
379C2×C42—221no—
380C2×C42—221no—
381C2×C42C22×D1111yescharacteristic
382C2×C42C22×D1111yescharacteristic
383C2×C42C22×D1111yescharacteristic
384#107—222no—
385#107—441no—
386#106—222no—
387#106—222no—
388C4⋊C8—41no—
389#102—114no—
390#102—222no—
391#102—222no—
392#102—441no—
393#97—41no—
394#95—221no—
395#95—221no—
396#95—221no—
397#95—221no—
398#95—221no—
399#95—221no—
400#95—221no—
401#95D4411yescharacteristic
402#95D4411yescharacteristic
403C2×C11#246511yescharacteristic
404C2×C11#311111yescharacteristic
405C2×C11#311911yescharacteristic
406C2×C11#330911yescharacteristic
407C2×C11#332311yescharacteristic
408C2×C11#338811yescharacteristic
409C2×C11#338911yescharacteristic
410D11—82no—
411C24—221no—
412C2×D4—112no—
413C2×D4—221no—
414C2×D4—221no—
415C2×D4—221no—
416C2×D4—221no—
417C2×D4—221no—
418C22×C4—221no—
419C22×C4—221no—
420C22×C4—221no—
421C22×C4—221no—
422C22×C4—221no—
423C22×C4—221no—
424C22×C4—221no—
425C22×C4—442no—
426C22×C4—442no—
427C22×C4—881no—
428C22×C4C2×D4411yescharacteristic
429C22×C4C2×D4411yescharacteristic
430C22×C4C2×D4411yescharacteristic
431C22×C4C2×D4411yescharacteristic
432C22×C4C2×D4411yescharacteristic
433C22×C4C2×D4411yescharacteristic
434C22×C4C23×D1111yescharacteristic
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8Q8×D1112yes—
447C4⋊C4—41no—
448C4⋊C4—41no—
449C4⋊C4—112no—
450C4⋊C4—112no—
451C4⋊C4—112no—
452C4⋊C4—112no—
453C4⋊C4—224no—
454C4⋊C4—224no—
455C4⋊C4—221no—
456C4⋊C4—221no—
457C4⋊C4—221no—
458C4⋊C4—221no—
459C4⋊C4—221no—
460C4⋊C4—221no—
461C4⋊C4—221no—
462C4⋊C4—221no—
463C4⋊C4—221no—
464C4⋊C4—221no—
465C4⋊C4—442no—
466C4⋊C4—442no—
467C4⋊C4—442no—
468C4⋊C4—881no—
469C4⋊C4—881no—
470C4⋊C4—881no—
471C22⋊C4—442no—
472C22⋊C4—442no—
473C22⋊C4—881no—
474C22⋊C4—881no—
475C22⋊C4—881no—
476C42—21no—
477C42—21no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—442no—
483C42—881no—
484C42—881no—
485C11#2702711yescharacteristic, complemented, Sylow
486C23—222no—
487C23—441no—
488C23—441no—
489C23—441no—
490C23—441no—
491C23—441no—
492C23—441no—
493C23C22×D4411yescharacteristic
494D4—222no—
495D4—222no—
496D4—441no—
497D4—441no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—222no—
517C2×C4—222no—
518C2×C4—222no—
519C2×C4—222no—
520C2×C4—441no—
521C2×C4—441no—
522C2×C4—441no—
523C2×C4—441no—
524C2×C4—441no—
525C2×C4—441no—
526C2×C4—441no—
527C2×C4—441no—
528C2×C4—441no—
529C2×C4—441no—
530C2×C4—441no—
531C2×C4—441no—
532C2×C4—441no—
533C2×C4—441no—
534C2×C4—441no—
535C2×C4—441no—
536C2×C4—441no—
537C2×C4—884no—
538C2×C4#6703711yescharacteristic
539C2×C4C2×Q8×D1111yescharacteristic
540C2×C4#41×D1111yescharacteristic
541C2×C4#41×D1111yescharacteristic
542C2×C4#41×D1111yescharacteristic
543C2×C4#6704311yescharacteristic
544C8—22no—
545C8—41no—
546C8—41no—
547C8—41no—
548C22—442no—
549C22—442no—
550C22—442no—
551C22—881no—
552C22—881no—
553C22—881no—
554C22—881no—
555C22#1062305511yescharacteristic
556C22#1062308511yescharacteristic
557C22Q8×D4411yescharacteristic
558C22#1062327911yescharacteristic
559C22#1062327911yescharacteristic
560C22#1062328211yescharacteristic
561C22#1062328311yescharacteristic
562C4—41no—
563C4—41no—
564C4—41no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—442no—
569C4—442no—
570C4—442no—
571C4—442no—
572C4—881no—
573C4—881no—
574C4—881no—
575C4#1062316711yescharacteristic
576C4#1062319311yescharacteristic
577C4#1062321911yescharacteristic
578C4#1062323311yescharacteristic
579C2—882no—
580C2#1307263511yescharacteristic
581C2#1307872711yescharacteristic
582C2#1307881711yescharacteristic
583C2#1308062411yescharacteristic
584C2#1308083411yescharacteristic
585C2#1308156311yescharacteristic
586C2#1308157611yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1917C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#1917D11
hypocenterC11#27027
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #1917

Complements

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

NH ≅ G/Ntype
2. #13071710C2semidirect
4. #13069955C2semidirect
5. #13069955C2semidirect
7. #13069571C2semidirect
8. #13069359C2semidirect
11. #13069195C2semidirect
12. #13069188C2semidirect
15. C11×#1917C2semidirect
205. #1917D11semidirect
485. C11#27027semidirect

Maximal subgroups

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

subgroupindex
#130724882
#130717102
#130700032
#130699552
#130697632
#130695712
#130693592
#130692442
#130692372
#130691952
#130691882
#130688802
#130684422
C11×#19172
#2702711