Finite Group Databasebeta

← #14738987

Subgroups — #14738987

Order 2816.

674 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078409C211yesmaximal, characteristic
2C2×#10622696C211yesmaximal, characteristic
3#13077639C211yesmaximal, characteristic
4#13068036C214yesmaximal, complemented
5#13067988C214yesmaximal, complemented
6#13067387C211yesmaximal, characteristic, complemented
7#13067288C211yesmaximal, characteristic, complemented
8#13067273C211yesmaximal, characteristic, complemented
9C11×#3229C211yesmaximal, characteristic, complemented
10C11×#533C2211yescharacteristic
11C2×C11×C4⋊Q8C2211yescharacteristic
12C22×#4325—21no—
13C2×C4×D44C2211yescharacteristic
14C11×#498C2212yescomplemented
15C11×#487C2212yescomplemented
16C11×#483—22no—
17C11×#475—22no—
18C11×#431C2211yescharacteristic
19C2×#66899—21no—
20#10622700C2212yes—
21#10622697C2212yes—
22#10622696—22no—
23#10622696C2214yes—
24#10622679—22no—
25#10622614—21no—
26#10622608—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#10622095C2214yescomplemented
37C22×Q8×C11—21no—
38C22×D44D411yescharacteristic
39C22×C4×D11—21no—
40C11×C4⋊Q8—21no—
41C11×C4⋊Q8—21no—
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8C2311yescharacteristic
44C11×C4⋊Q8C2312yes—
45C11×C4⋊Q8C2311yescharacteristic
46C11×#125—21no—
47C11×C22⋊Q8—21no—
48C11×C22⋊Q8—21no—
49C4×Q8×C11—21no—
50C4×Q8×C11—21no—
51C11×#117—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C42×C11C2311yescharacteristic
55C2×#4325—24no—
56C2×#4325—44no—
57C2×(C2×D11)⋊C4—21no—
58C2×C4⋊Dic11D411yescharacteristic
59C2×#4318—21no—
60C22×C11⋊C8—21no—
61C2×C8×D11—24no—
62C4×D44—21no—
63C4×D44—21no—
64C4×D44D412yes—
65C4×D44C2312yes—
66C11×#106—24no—
67C11×C4⋊C8D412yes—
68C11×#103—24no—
69C11×C22⋊C8D412yes—
70C4×C8×C11C2312yes—
71#66899—24no—
72C22⋊(C11⋊C8)—21no—
73(C2×D11)⋊C8—24no—
74#66873—22no—
75#66873—22no—
76#66872—22no—
77#66871—22no—
78C4⋊(C11⋊C8)—21no—
79C4⋊(C11⋊C8)—21no—
80C4⋊(C11⋊C8)C2312yes—
81C4⋊(C11⋊C8)C2312yes—
82C4⋊(C11⋊C8)C2312yes—
83C4×C11⋊C8—21no—
84#19390—111nomaximal, Sylow
85C23×D11—21no—
86C2×Q8×C11—22no—
87C2×Q8×C11—21no—
88C2×Q8×C11—21no—
89C2×Q8×C11—41no—
90C2×Q8×C11—42no—
91C2×Q8×C11—42no—
92C22×C4×C11—41no—
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11#4111yescharacteristic
96C22×Dic11—21no—
97C2×D44—21no—
98C2×D44—22no—
99C2×D44SD1614yes—
100C2×D44C2×D412yes—
101C2×C4×D11—22no—
102C2×C4×D11—22no—
103C2×C4×D11—82no—
104C2×C8×C11C2×D414yes—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—22no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—21no—
111C11×C4⋊C4—41no—
112C11×C4⋊C4—41no—
113C11×C4⋊C4—41no—
114C11×C4⋊C4—41no—
115C11×C22⋊C4—41no—
116C42×C11—41no—
117C42×C11C2×D411yescharacteristic
118C42×C11C2×D411yescharacteristic
119C42×C11#4111yescharacteristic
120C42×C11C2411yescharacteristic
121#4325—48no—
122(C2×D11)⋊C4—22no—
123(C2×D11)⋊C4—22no—
124C4⋊Dic11—21no—
125C4⋊Dic11C2×D412yes—
126#4318—42no—
127C2×C11⋊C8—22no—
128C2×C11⋊C8—22no—
129C2×C11⋊C8—22no—
130C2×C11⋊C8—42no—
131C8×D11—84no—
132#3229D1111yescharacteristic, complemented
133#3077—111no—
134C2×#461—111no—
135#2972—111no—
136#1679—114no—
137#1671—114no—
138#1570—111no—
139#1546—111no—
140#1542—111no—
141C23×C11#12111yescharacteristic
142C22×D11—22no—
143C22×D11—24no—
144C22×D11—81no—
145C22×D11—81no—
146Q8×C11—42no—
147Q8×C11—42no—
148Q8×C11—42no—
149Q8×C11—81no—
150Q8×C11—82no—
151C2×C4×C11—22no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—42no—
156C2×C4×C11—82no—
157C2×C4×C11#12111yescharacteristic
158C2×C4×C11#12111yescharacteristic
159C2×C4×C11#12111yescharacteristic
160C2×C4×C11C2×SD1612yes—
161C2×C4×C11#13512yes—
162C2×C4×C11C22×D411yescharacteristic
163C2×C4×C11C22×D411yescharacteristic
164C2×C4×C11C2×#4111yescharacteristic
165C2×Dic11—22no—
166C2×Dic11—81no—
167D44—22no—
168D44—24no—
169D44C2×SD1614yes—
170C4×D11—44no—
171C4×D11—82no—
172C8×C11—24no—
173C11⋊C8—42no—
174C11⋊C8—42no—
175C11⋊C8—42no—
176C22×SD16—221no—
177#533C2×D1111yescharacteristic
178C2×C4⋊Q8C2×D1111yescharacteristic
179C2×C4×D4—111no—
180#498C2×D1112yescomplemented
181#487C2×D1112yescomplemented
182#483—22no—
183#478—222no—
184#476—112no—
185#475—22no—
186#474—112no—
187#461—114no—
188#461—222no—
189C8×D4—114no—
190C8×D4—222no—
191#431—111no—
192#431C2×D1111yescharacteristic
193#428—221no—
194#423—111no—
195C2×C4⋊C8—111no—
196#418—221no—
197C2×#103—221no—
198C2×C22⋊C8—222no—
199#334—114no—
200#333—112no—
201#332—112no—
202#332—114no—
203C22×C11—21no—
204C22×C11—21no—
205C22×C11#46512yes—
206C22×C11C2×#12111yescharacteristic
207C2×D11—24no—
208C2×D11—42no—
209C2×D11—42no—
210C2×D11—84no—
211C4×C11—21no—
212C4×C11—21no—
213C4×C11—21no—
214C4×C11—81no—
215C4×C11—82no—
216C4×C11—81no—
217C4×C11#46512yes—
218C4×C11C22×SD1611yescharacteristic
219C4×C11C2×#13511yescharacteristic
220C4×C11#57712yes—
221Dic11—42no—
222C22×Q8—21no—
223C22×D4—111no—
224C23×C4—221no—
225C2×SD16—224no—
226C2×SD16—444no—
227C2×M16—221no—
228C22×C8—221no—
229C22×C8—224no—
230C4⋊Q8—21no—
231C4⋊Q8—21no—
232C4⋊Q8—21no—
233C4⋊Q8C22×D1112yes—
234C4⋊Q8C22×D1111yescharacteristic
235C4⋊Q8C22×D1111yescharacteristic
236#125—21no—
237C22⋊Q8—21no—
238C22⋊Q8—21no—
239C4×Q8—21no—
240C4×Q8—21no—
241C4×D4—112no—
242C4×D4—112no—
243C4×D4—221no—
244C4×D4—221no—
245#117—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—111no—
249C2×C22⋊C4—221no—
250C2×C42C22×D1111yescharacteristic
251#107—222no—
252#106—24no—
253#106—222no—
254C4⋊C8—112no—
255C4⋊C8—112no—
256C4⋊C8—112no—
257C4⋊C8—221no—
258C4⋊C8—221no—
259C4⋊C8C22⋊D1112yes—
260#103—24no—
261#103—224no—
262#102—222no—
263#102—222no—
264C22⋊C8—221no—
265C22⋊C8—224no—
266C22⋊C8C22⋊D1112yes—
267C4×C8—221no—
268C4×C8C22×D1112yes—
269C2×C11—22no—
270C2×C11#304211yescharacteristic
271C2×C11C2×#46511yescharacteristic
272C2×C11#306911yescharacteristic
273D11—44no—
274C24—221no—
275C2×Q8—22no—
276C2×Q8—21no—
277C2×Q8—21no—
278C2×Q8—41no—
279C2×Q8—42no—
280C2×Q8—42no—
281C2×D4—114no—
282C2×D4—112no—
283C2×D4—222no—
284C2×D4—221no—
285C22×C4—41no—
286C22×C4—221no—
287C22×C4—222no—
288C22×C4—222no—
289C22×C4—882no—
290C22×C4D4×D1111yescharacteristic
291C22×C4#434111yescharacteristic
292C22×C4C2×C22⋊D1111yescharacteristic
293SD16—448no—
294M16—442no—
295C2×C8—222no—
296C2×C8—222no—
297C2×C8—222no—
298C2×C8—442no—
299C2×C8—884no—
300C2×C8C2×C22⋊D1114yes—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—22no—
304C4⋊C4—21no—
305C4⋊C4—22no—
306C4⋊C4—21no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—112no—
312C4⋊C4—221no—
313C22⋊C4—41no—
314C22⋊C4—222no—
315C22⋊C4—222no—
316C42—41no—
317C42D4×D1111yescharacteristic
318C42#434111yescharacteristic
319C42C2×C22⋊D1111yescharacteristic
320C42C23×D1111yescharacteristic
321C11#1939011yescharacteristic, complemented, Sylow
322C23—222no—
323C23—224no—
324C23—881no—
325C23—881no—
326C23#6699111yescharacteristic
327Q8—42no—
328Q8—42no—
329Q8—42no—
330Q8—81no—
331Q8—82no—
332D4—114no—
333D4—222no—
334D4—224no—
335C2×C4—22no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—82no—
341C2×C4—222no—
342C2×C4—444no—
343C2×C4—882no—
344C2×C4—881no—
345C2×C4SD16×D1112yes—
346C2×C4#6696912yes—
347C2×C4#6699111yescharacteristic
348C2×C4#6699111yescharacteristic
349C2×C4#6699111yescharacteristic
350C2×C4C2×D4×D1111yescharacteristic
351C2×C4C2×#434111yescharacteristic
352C2×C4C22×C22⋊D1111yescharacteristic
353C8—24no—
354C8—442no—
355C8—442no—
356C8—442no—
357C22—21no—
358C22—21no—
359C22—224no—
360C22—442no—
361C22—442no—
362C22—884no—
363C22#1062278412yes—
364C22C2×#6699111yescharacteristic
365C4—21no—
366C4—21no—
367C4—21no—
368C4—81no—
369C4—81no—
370C4—82no—
371C4—442no—
372C4#1062278412yes—
373C4C2×SD16×D1111yescharacteristic
374C4C2×#6696911yescharacteristic
375C4#1062336812yes—
376C2—22no—
377C2—444no—
378C2#1307812411yescharacteristic
379C2C2×#1062278411yescharacteristic
380C2#1307834911yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3229C2
socleC22×C11C2×#121
prime radicalC22×D44D4
hypercenter#3229D11
hypocenterC11#19390
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3229

Complements

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

NH ≅ G/Ntype
4. #13068036C2semidirect
5. #13067988C2semidirect
6. #13067387C2semidirect
7. #13067288C2semidirect
8. #13067273C2semidirect
9. C11×#3229C2semidirect
14. C11×#498C22semidirect
15. C11×#487C22semidirect
33. #10622185C22semidirect
34. #10622185C22semidirect
35. #10622184C22semidirect
36. #10622095C22semidirect
132. #3229D11semidirect
180. #498C2×D11semidirect
181. #487C2×D11semidirect
321. C11#19390semidirect

Maximal subgroups

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

subgroupindex
#130784092
C2×#106226962
#130776392
#130680362
#130679882
#130673872
#130672882
#130672732
C11×#32292
#1939011