Finite Group Databasebeta

← #14737209

Subgroups — #14737209

Order 2816.

562 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079791C212yesmaximal
2#13079202C211yesmaximal, characteristic, complemented
3#13068144C211yesmaximal, characteristic, complemented
4#13068139C211yesmaximal, characteristic, complemented
5#13068110C211yesmaximal, characteristic, complemented
6#13068105C211yesmaximal, characteristic, complemented
7#13068074C212yesmaximal, complemented
8#13068067C212yesmaximal, complemented
9#13067364C211yesmaximal, characteristic, complemented
10#13067327C212yesmaximal, complemented
11C11×#2966C211yesmaximal, characteristic
12C11×#529C2211yescharacteristic
13#10623001C2212yes—
14C11×#446C2211yescharacteristic
15C8×Q8×C11C2211yescharacteristic
16C11×#436C2211yescharacteristic
17C11×#435—21no—
18C8×D4×C11—21no—
19C8×D4×C11C2211yescharacteristic
20C11×#433—21no—
21C11×#432C2211yescharacteristic
22C11×#405—21no—
23C2×C4×C8×C11C2211yescharacteristic
24#10622729—21no—
25#10622729—21no—
26#10622677—22no—
27#10622669—22no—
28#10622658—22no—
29#10622648—22no—
30#10622634C2212yes—
31#10622633C2212yes—
32#10622621C2212yes—
33#10622620C2212yes—
34#10622538C2212yes—
35#10622312C2211yescharacteristic
36C4×Dic44—21no—
37C4×Dic44—21no—
38#10622295C2211yescharacteristic
39#10622294C2212yes—
40#10622120C2212yes—
41#10622120C2212yes—
42#10622119C2212yes—
43#10622119C2212yes—
44#10622096C2212yes—
45#10622095C2211yescharacteristic
46#10622095C2211yescharacteristic
47C2×C11×M16—21no—
48C22×C8×C11—21no—
49C22×C8×C11D411yescharacteristic
50C22×C8×C11D411yescharacteristic
51C11×#126—21no—
52C11×#125D411yescharacteristic
53C11×#124D411yescharacteristic
54C11×#123—21no—
55C11×C22⋊Q8D411yescharacteristic
56C11×#121D411yescharacteristic
57C4×Q8×C11C2311yescharacteristic
58C4×D4×C11—21no—
59C4×D4×C11C2311yescharacteristic
60C11×#117—21no—
61C2×C42×C11C2311yescharacteristic
62#66979—22no—
63#66977—22no—
64#66977—22no—
65C2×Dic44—21no—
66C2×Dic44—21no—
67#66923—22no—
68#66922C2312yes—
69#66922C2312yes—
70C4×Dic22—22no—
71C4×Dic22—22no—
72C11×C4⋊C8—21no—
73C11×C4⋊C8—21no—
74C11×C4⋊C8C2311yescharacteristic
75C11×C4⋊C8C2311yescharacteristic
76C11×C22⋊C8—21no—
77C11×C22⋊C8—21no—
78C11×C22⋊C8—21no—
79C11×#97—21no—
80C11×#97—21no—
81C4×C8×C11—21no—
82C4×C8×C11D411yescharacteristic
83C4×C8×C11D411yescharacteristic
84C4×C8×C11C2311yescharacteristic
85C4×C8×C11C2311yescharacteristic
86#66899—22no—
87#66899—22no—
88#66896—22no—
89#66896—22no—
90C22⋊(C11⋊C8)—22no—
91#66882—21no—
92#66882—21no—
93#66880—22no—
94#66880—22no—
95#66872—22no—
96#66872—22no—
97#66871—22no—
98#66871—22no—
99C4⋊(C11⋊C8)C2312yes—
100C4⋊(C11⋊C8)C2312yes—
101C4×C11⋊C8—22no—
102#19226—111nomaximal, Sylow
103C2×Q8×C11C2×D411yescharacteristic
104C2×D4×C11—21no—
105C2×D4×C11C2×D411yescharacteristic
106C22×C4×C11—21no—
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11#4111yescharacteristic
110C2×Dic22—22no—
111C2×Dic22—22no—
112C11×M16—42no—
113C2×C8×C11—22no—
114C2×C8×C11—21no—
115C2×C8×C11—21no—
116C2×C8×C11—41no—
117C2×C8×C11—42no—
118C2×C8×C11C2×D411yescharacteristic
119C2×C8×C11C2×D411yescharacteristic
120C2×C8×C11C2×D411yescharacteristic
121C2×C8×C11C2×D411yescharacteristic
122C11×C4⋊C4—21no—
123C11×C4⋊C4—21no—
124C11×C4⋊C4—21no—
125C11×C4⋊C4—21no—
126C11×C4⋊C4C2×D411yescharacteristic
127C11×C4⋊C4C2×D411yescharacteristic
128C11×C22⋊C4—21no—
129C11×C22⋊C4—21no—
130C11×C22⋊C4—21no—
131C11×C22⋊C4—21no—
132C11×C22⋊C4—21no—
133C42×C11—21no—
134C42×C11C2×D411yescharacteristic
135C42×C11C2×D411yescharacteristic
136C42×C11#4111yescharacteristic
137C42×C11C2411yescharacteristic
138C22⋊Dic11—42no—
139C4⋊Dic11—22no—
140C4⋊Dic11—22no—
141C4⋊Dic11—22no—
142C4⋊Dic11—22no—
143Dic11⋊C4—42no—
144Dic11⋊C4—42no—
145C4×Dic11—42no—
146C2×C11⋊C8—22no—
147C2×C11⋊C8—22no—
148Dic44—42no—
149Dic44—42no—
150#3233—112no—
151#3170—111no—
152#2966D1111yescharacteristic
153#1696—111no—
154#1695—111no—
155#1690—111no—
156#1689—111no—
157#1684—112no—
158#1683—112no—
159#1564—111no—
160#1554—112no—
161C23×C11—21no—
162C23×C11#12111yescharacteristic
163Q8×C11—22no—
164D4×C11—22no—
165D4×C11—42no—
166C2×C4×C11—21no—
167C2×C4×C11—21no—
168C2×C4×C11—22no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11#12111yescharacteristic
176C2×C4×C11#12111yescharacteristic
177C2×C4×C11#12111yescharacteristic
178C2×C4×C11C22×D411yescharacteristic
179C2×C4×C11C22×D411yescharacteristic
180C2×C4×C11C2×#4111yescharacteristic
181C2×Dic11—42no—
182C2×Dic11—42no—
183Dic22—42no—
184Dic22—42no—
185Dic22—82no—
186C8×C11—21no—
187C8×C11—21no—
188C8×C11—21no—
189C8×C11—41no—
190C8×C11—41no—
191C8×C11#13512yes—
192C11⋊C8—42no—
193C11⋊C8—42no—
194#533—112no—
195#529C2×D1111yescharacteristic
196#500—111no—
197#499—222no—
198#494—111no—
199#488—222no—
200#487—112no—
201#485—222no—
202#482—222no—
203#477—112no—
204#476—112no—
205#475—112no—
206#474—112no—
207#467—221no—
208#467—221no—
209#446C2×D1111yescharacteristic
210C8×Q8C2×D1111yescharacteristic
211C4×Q16—221no—
212C4×Q16—221no—
213#436C2×D1111yescharacteristic
214#435—21no—
215C8×D4—21no—
216C8×D4C2×D1111yescharacteristic
217#433—21no—
218#432C2×D1111yescharacteristic
219#431—112no—
220#405—21no—
221C2×C4×C8C2×D1111yescharacteristic
222#335—112no—
223#334—111no—
224#334—111no—
225#333—112no—
226#333—112no—
227#332—112no—
228#332—112no—
229C22×C11—21no—
230C22×C11—21no—
231C22×C11—21no—
232C22×C11—41no—
233C22×C11—41no—
234C22×C11—41no—
235C22×C11C2×#12111yescharacteristic
236C4×C11—21no—
237C4×C11—21no—
238C4×C11—21no—
239C4×C11—21no—
240C4×C11—41no—
241C4×C11—41no—
242C4×C11—41no—
243C4×C11C2×#13511yescharacteristic
244C4×C11#57511yescharacteristic
245C4×C11#57812yes—
246Dic11—82no—
247Dic11—82no—
248C2×Q16—221no—
249C2×Q16—221no—
250C2×M16—21no—
251C22×C8—21no—
252C22×C8C22⋊D1111yescharacteristic
253C22×C8C22⋊D1111yescharacteristic
254C4⋊Q8—112no—
255C4⋊Q8—112no—
256#126—21no—
257#125—222no—
258#125D4411yescharacteristic
259#124D4411yescharacteristic
260#123—21no—
261C22⋊Q8—222no—
262C22⋊Q8—222no—
263C22⋊Q8D4411yescharacteristic
264#121D4411yescharacteristic
265C4×Q8—222no—
266C4×Q8—222no—
267C4×Q8C22×D1111yescharacteristic
268C4×D4—21no—
269C4×D4C22×D1111yescharacteristic
270#117—21no—
271#117—222no—
272C2×C42C22×D1111yescharacteristic
273#107—221no—
274#107—221no—
275#107—222no—
276#107—222no—
277#106—222no—
278#106—222no—
279C4⋊C8—21no—
280C4⋊C8—21no—
281C4⋊C8—112no—
282C4⋊C8—112no—
283C4⋊C8C22×D1111yescharacteristic
284C4⋊C8C22×D1111yescharacteristic
285#103—222no—
286#103—222no—
287#103—222no—
288#103—222no—
289#102—222no—
290#102—222no—
291C22⋊C8—21no—
292C22⋊C8—21no—
293C22⋊C8—21no—
294C22⋊C8—222no—
295#97—21no—
296#97—21no—
297C4×C8—21no—
298C4×C8—222no—
299C4×C8C22⋊D1111yescharacteristic
300C4×C8C22⋊D1111yescharacteristic
301C4×C8C22×D1111yescharacteristic
302C4×C8C22×D1111yescharacteristic
303C2×C11—41no—
304C2×C11—81no—
305C2×C11#303511yescharacteristic
306C2×C11#305911yescharacteristic
307C2×C11#306711yescharacteristic
308C2×Q8—222no—
309C2×Q8—222no—
310C2×Q8C2×D4411yescharacteristic
311C2×D4—21no—
312C2×D4C2×D4411yescharacteristic
313C22×C4—21no—
314C22×C4C2×D4411yescharacteristic
315C22×C4#433911yescharacteristic
316C22×C4C2×C22⋊D1111yescharacteristic
317Q16—442no—
318Q16—442no—
319M16—42no—
320C2×C8—22no—
321C2×C8—21no—
322C2×C8—21no—
323C2×C8—41no—
324C2×C8—42no—
325C2×C8—222no—
326C2×C8—222no—
327C2×C8C2×C22⋊D1111yescharacteristic
328C2×C8C2×C22⋊D1111yescharacteristic
329C2×C8C2×C22⋊D1111yescharacteristic
330C2×C8C2×C22⋊D1111yescharacteristic
331C4⋊C4—21no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—222no—
336C4⋊C4—222no—
337C4⋊C4—222no—
338C4⋊C4—222no—
339C4⋊C4—442no—
340C4⋊C4—442no—
341C4⋊C4C2×D4411yescharacteristic
342C4⋊C4C2×D4411yescharacteristic
343C22⋊C4—21no—
344C22⋊C4—21no—
345C22⋊C4—21no—
346C22⋊C4—21no—
347C22⋊C4—21no—
348C22⋊C4—442no—
349C42—21no—
350C42—442no—
351C42C2×D4411yescharacteristic
352C42#433911yescharacteristic
353C42C2×C22⋊D1111yescharacteristic
354C42C23×D1111yescharacteristic
355C11#1922611yescharacteristic, complemented, Sylow
356C23—21no—
357C23#6698311yescharacteristic
358Q8—22no—
359Q8—442no—
360Q8—442no—
361Q8—882no—
362D4—22no—
363D4—42no—
364C2×C4—22no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—442no—
374C2×C4—442no—
375C2×C4#6698311yescharacteristic
376C2×C4#6698311yescharacteristic
377C2×C4#6698311yescharacteristic
378C2×C4C22×D4411yescharacteristic
379C2×C4C2×#433911yescharacteristic
380C2×C4C22×C22⋊D1111yescharacteristic
381C8—21no—
382C8—21no—
383C8—21no—
384C8—41no—
385C8—41no—
386C8—442no—
387C8—442no—
388C8#6700312yes—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22C2×#6698311yescharacteristic
396C4—21no—
397C4—21no—
398C4—21no—
399C4—21no—
400C4—41no—
401C4—41no—
402C4—41no—
403C4—882no—
404C4—882no—
405C4#1062328412yes—
406C4C2×#6700311yescharacteristic
407C4#1062335311yescharacteristic
408C2—41no—
409C2—81no—
410C2#1307807111yescharacteristic
411C2#1307827111yescharacteristic
412C2#1307833611yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2966C2
socleC22×C11C2×#121
prime radicalC11×#121D4
hypercenter#2966D11
hypocenterC11#19226
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2966

Complements

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

NH ≅ G/Ntype
2. #13079202C2semidirect
3. #13068144C2semidirect
4. #13068139C2semidirect
5. #13068110C2semidirect
6. #13068105C2semidirect
7. #13068074C2semidirect
8. #13068067C2semidirect
9. #13067364C2semidirect
10. #13067327C2semidirect
355. C11#19226semidirect

Maximal subgroups

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

subgroupindex
#130797912
#130792022
#130681442
#130681392
#130681102
#130681052
#130680742
#130680672
#130673642
#130673272
C11×#29662
#1922611