Finite Group Databasebeta

← #14738956

Subgroups — #14738956

Order 2816.

654 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078409C211yesmaximal, characteristic
2C2×#10622700C211yesmaximal, characteristic
3#13077639C211yesmaximal, characteristic
4#13068064C214yesmaximal, complemented
5#13067978C214yesmaximal, complemented
6#13067391C211yesmaximal, characteristic, complemented
7#13067301C211yesmaximal, characteristic, complemented
8#13067273C211yesmaximal, characteristic, complemented
9C11×#3209C211yesmaximal, characteristic, complemented
10C11×#533C2211yescharacteristic
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×C4×D44C2211yescharacteristic
13C11×#494C2212yescomplemented
14C11×#487C2212yescomplemented
15C11×#462—22no—
16C11×#451—22no—
17C11×#431C2211yescharacteristic
18#10622700—22no—
19#10622700C2214yes—
20#10622700C2212yes—
21#10622697C2212yes—
22#10622679—22no—
23#10622614—21no—
24#10622608—21no—
25C2×#66873—21no—
26C2×#66871—21no—
27#10622538C2211yescharacteristic
28#10622537C2211yescharacteristic
29C2×C4⋊(C11⋊C8)C2211yescharacteristic
30#10622447—22no—
31D11×C22⋊C8—22no—
32C8×D44C2214yes—
33#10622185C2212yescomplemented
34#10622185C2214yescomplemented
35#10622184C2212yescomplemented
36#10622096C2214yescomplemented
37C22×Q8×C11—21no—
38C22×D44D411yescharacteristic
39C22×C4×D11—21no—
40C2×C11×Q16—24no—
41C11×C4⋊Q8—21no—
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8—21no—
44C11×C4⋊Q8C2311yescharacteristic
45C11×C4⋊Q8C2312yes—
46C11×C4⋊Q8C2311yescharacteristic
47C11×#125—21no—
48C11×C22⋊Q8—21no—
49C11×C22⋊Q8—21no—
50C4×Q8×C11—21no—
51C4×Q8×C11—21no—
52C11×#117—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—21no—
55C2×C42×C11C2311yescharacteristic
56C2×(C2×D11)⋊C4—21no—
57C2×C4⋊Dic11D411yescharacteristic
58C2×#4318—21no—
59C22×C11⋊C8—21no—
60C2×C8×D11—24no—
61C4×D44—21no—
62C4×D44—21no—
63C4×D44D412yes—
64C4×D44C2312yes—
65C11×C4⋊C8D412yes—
66C11×#103—24no—
67C11×C22⋊C8D412yes—
68C4×C8×C11C2312yes—
69C22⋊(C11⋊C8)—21no—
70(C2×D11)⋊C8—24no—
71#66873—24no—
72#66873—22no—
73#66873—22no—
74#66872—22no—
75#66871—24no—
76#66871—22no—
77C4⋊(C11⋊C8)—21no—
78C4⋊(C11⋊C8)—21no—
79C4⋊(C11⋊C8)C2312yes—
80C4⋊(C11⋊C8)C2312yes—
81C4⋊(C11⋊C8)C2312yes—
82C4×C11⋊C8—21no—
83#19387—111nomaximal, Sylow
84C23×D11—21no—
85C2×Q8×C11—22no—
86C2×Q8×C11—21no—
87C2×Q8×C11—21no—
88C2×Q8×C11—41no—
89C2×Q8×C11—82no—
90C22×C4×C11—41no—
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11#4111yescharacteristic
94C22×Dic11—21no—
95C2×D44—21no—
96C2×D44—22no—
97C2×D44Q1614yescomplemented
98C2×D44C2×D412yes—
99C2×C4×D11—22no—
100C2×C4×D11—22no—
101C2×C4×D11—82no—
102C11×Q16—84no—
103C2×C8×C11C2×D414yes—
104C11×C4⋊C4—22no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—41no—
111C11×C4⋊C4—41no—
112C11×C4⋊C4—41no—
113C11×C4⋊C4—41no—
114C11×C22⋊C4—41no—
115C42×C11—41no—
116C42×C11C2×D411yescharacteristic
117C42×C11C2×D411yescharacteristic
118C42×C11#4111yescharacteristic
119C42×C11C2411yescharacteristic
120(C2×D11)⋊C4—22no—
121(C2×D11)⋊C4—22no—
122C4⋊Dic11—21no—
123C4⋊Dic11C2×D412yes—
124#4318—42no—
125C2×C11⋊C8—22no—
126C2×C11⋊C8—22no—
127C2×C11⋊C8—22no—
128C2×C11⋊C8—42no—
129C8×D11—84no—
130#3209D1111yescharacteristic, complemented
131#3077—111no—
132C2×#474—111no—
133#2972—111no—
134#1683—114no—
135#1669—114no—
136#1571—111no—
137#1549—111no—
138#1542—111no—
139C23×C11#12111yescharacteristic
140C22×D11—22no—
141C22×D11—24no—
142C22×D11—81no—
143C22×D11—81no—
144Q8×C11—42no—
145Q8×C11—44no—
146Q8×C11—81no—
147Q8×C11—82no—
148C2×C4×C11—22no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—42no—
153C2×C4×C11—82no—
154C2×C4×C11#12111yescharacteristic
155C2×C4×C11#12111yescharacteristic
156C2×C4×C11#12111yescharacteristic
157C2×C4×C11C2×Q1612yes—
158C2×C4×C11#13512yes—
159C2×C4×C11C22×D411yescharacteristic
160C2×C4×C11C22×D411yescharacteristic
161C2×C4×C11C2×#4111yescharacteristic
162C2×Dic11—22no—
163C2×Dic11—81no—
164D44—22no—
165D44—24no—
166D44C2×Q1614yes—
167C4×D11—44no—
168C4×D11—82no—
169C8×C11—24no—
170C11⋊C8—42no—
171C11⋊C8—42no—
172C11⋊C8—42no—
173#533C2×D1111yescharacteristic
174C2×C4⋊Q8C2×D1111yescharacteristic
175C2×C4×D4—111no—
176#494C2×D1112yescomplemented
177#487C2×D1112yescomplemented
178#478—222no—
179#476—112no—
180#474—112no—
181#474—114no—
182#474—222no—
183#462—22no—
184#451—22no—
185C8×D4—114no—
186C8×D4—222no—
187#431—111no—
188#431C2×D1111yescharacteristic
189#428—221no—
190C2×#107—221no—
191#423—111no—
192C2×C4⋊C8—111no—
193#418—221no—
194C2×#102—221no—
195C2×C22⋊C8—222no—
196#335—114no—
197#333—112no—
198#332—112no—
199#332—114no—
200C22×C11—21no—
201C22×C11—21no—
202C22×C11#46712yes—
203C22×C11C2×#12111yescharacteristic
204C2×D11—24no—
205C2×D11—42no—
206C2×D11—42no—
207C2×D11—84no—
208C4×C11—21no—
209C4×C11—21no—
210C4×C11—21no—
211C4×C11—82no—
212C4×C11—81no—
213C4×C11—81no—
214C4×C11#46712yes—
215C4×C11C22×Q1611yescharacteristic
216C4×C11C2×#13511yescharacteristic
217C4×C11#57612yes—
218Dic11—42no—
219C22×Q8—21no—
220C22×D4—111no—
221C23×C4—221no—
222C2×Q16—24no—
223C2×M16—221no—
224C22×C8—221no—
225C22×C8—224no—
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8—21no—
229C4⋊Q8C22×D1112yes—
230C4⋊Q8C22×D1111yescharacteristic
231C4⋊Q8C22×D1111yescharacteristic
232#125—21no—
233C22⋊Q8—21no—
234C22⋊Q8—21no—
235C4×Q8—21no—
236C4×Q8—21no—
237C4×D4—112no—
238C4×D4—112no—
239C4×D4—221no—
240C4×D4—221no—
241#117—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—111no—
245C2×C22⋊C4—221no—
246C2×C42C22×D1111yescharacteristic
247#107—224no—
248#107—222no—
249#106—222no—
250C4⋊C8—112no—
251C4⋊C8—112no—
252C4⋊C8—112no—
253C4⋊C8—221no—
254C4⋊C8—221no—
255C4⋊C8C22⋊D1112yes—
256#103—24no—
257#102—224no—
258#102—222no—
259#102—222no—
260C22⋊C8—221no—
261C22⋊C8—224no—
262C22⋊C8C22⋊D1112yes—
263C4×C8—221no—
264C4×C8C22×D1112yes—
265C2×C11—22no—
266C2×C11#304111yescharacteristic
267C2×C11C2×#46711yescharacteristic
268C2×C11#306911yescharacteristic
269D11—44no—
270C24—221no—
271C2×Q8—21no—
272C2×Q8—22no—
273C2×Q8—21no—
274C2×Q8—41no—
275C2×Q8—82no—
276C2×D4—114no—
277C2×D4—112no—
278C2×D4—222no—
279C2×D4—221no—
280C22×C4—41no—
281C22×C4—221no—
282C22×C4—222no—
283C22×C4—222no—
284C22×C4—882no—
285C22×C4D4×D1111yescharacteristic
286C22×C4#434111yescharacteristic
287C22×C4C2×C22⋊D1111yescharacteristic
288Q16—84no—
289M16—442no—
290C2×C8—222no—
291C2×C8—222no—
292C2×C8—222no—
293C2×C8—442no—
294C2×C8—884no—
295C2×C8C2×C22⋊D1114yes—
296C4⋊C4—21no—
297C4⋊C4—22no—
298C4⋊C4—21no—
299C4⋊C4—22no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—112no—
307C4⋊C4—221no—
308C22⋊C4—41no—
309C22⋊C4—222no—
310C22⋊C4—222no—
311C42—41no—
312C42D4×D1111yescharacteristic
313C42#434111yescharacteristic
314C42C2×C22⋊D1111yescharacteristic
315C42C23×D1111yescharacteristic
316C11#1938711yescharacteristic, complemented, Sylow
317C23—222no—
318C23—224no—
319C23—881no—
320C23—881no—
321C23#6699111yescharacteristic
322Q8—42no—
323Q8—44no—
324Q8—81no—
325Q8—82no—
326D4—114no—
327D4—222no—
328D4—224no—
329C2×C4—22no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—42no—
334C2×C4—82no—
335C2×C4—222no—
336C2×C4—444no—
337C2×C4—882no—
338C2×C4—881no—
339C2×C4Q16×D1112yes—
340C2×C4#6697212yes—
341C2×C4#6699111yescharacteristic
342C2×C4#6699111yescharacteristic
343C2×C4#6699111yescharacteristic
344C2×C4C2×D4×D1111yescharacteristic
345C2×C4C2×#434111yescharacteristic
346C2×C4C22×C22⋊D1111yescharacteristic
347C8—24no—
348C8—442no—
349C8—442no—
350C8—442no—
351C22—21no—
352C22—21no—
353C22—224no—
354C22—442no—
355C22—442no—
356C22—884no—
357C22#1062280112yes—
358C22C2×#6699111yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—81no—
363C4—82no—
364C4—81no—
365C4—442no—
366C4#1062280112yes—
367C4C2×Q16×D1111yescharacteristic
368C4C2×#6697211yescharacteristic
369C4#1062336612yes—
370C2—22no—
371C2—444no—
372C2#1307811511yescharacteristic
373C2C2×#1062280111yescharacteristic
374C2#1307834911yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3209C2
socleC22×C11C2×#121
prime radicalC22×D44D4
hypercenter#3209D11
hypocenterC11#19387
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3209

Complements

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

NH ≅ G/Ntype
4. #13068064C2semidirect
5. #13067978C2semidirect
6. #13067391C2semidirect
7. #13067301C2semidirect
8. #13067273C2semidirect
9. C11×#3209C2semidirect
13. C11×#494C22semidirect
14. C11×#487C22semidirect
33. #10622185C22semidirect
34. #10622185C22semidirect
35. #10622184C22semidirect
36. #10622096C22semidirect
97. C2×D44Q16semidirect
130. #3209D11semidirect
176. #494C2×D11semidirect
177. #487C2×D11semidirect
316. C11#19387semidirect

Maximal subgroups

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

subgroupindex
#130784092
C2×#106227002
#130776392
#130680642
#130679782
#130673912
#130673012
#130672732
C11×#32092
#1938711