Finite Group Databasebeta

← #14739103

Subgroups — #14739103

Order 2816.

622 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078417C211yesmaximal, characteristic
2C2×#10622703C211yesmaximal, characteristic
3#13077696C211yesmaximal, characteristic
4#13068043C214yesmaximal, complemented
5#13067995C214yesmaximal, complemented
6#13067387C211yesmaximal, characteristic
7#13067288C211yesmaximal, characteristic
8#13067273C211yesmaximal, characteristic
9C11×#3229C211yesmaximal, characteristic
10C11×#533C2211yescharacteristic
11C2×C11×C4⋊Q8C2211yescharacteristic
12C22×#4326—21no—
13C2×C4×Dic22C2211yescharacteristic
14C11×#498C2212yes—
15C11×#487C2212yes—
16C11×#483—22no—
17C11×#475—22no—
18C11×#431C2211yescharacteristic
19C2×#66899—21no—
20#10622707C2212yes—
21#10622704C2212yes—
22#10622703—22no—
23#10622703C2214yes—
24#10622676—22no—
25#10622617—21no—
26#10622608—21no—
27#10622538C2211yescharacteristic
28#10622537C2211yescharacteristic
29C2×C4⋊(C11⋊C8)C2211yescharacteristic
30#10622443—22no—
31#10622331—22no—
32C8×Dic22C2214yes—
33#10622185C2212yes—
34#10622185C2214yes—
35#10622184C2212yes—
36#10622095C2214yes—
37C22×Q8×C11—21no—
38C22×Dic22D411yescharacteristic
39C11×C4⋊Q8—21no—
40C11×C4⋊Q8—21no—
41C11×C4⋊Q8—21no—
42C11×C4⋊Q8C2311yescharacteristic
43C11×C4⋊Q8C2312yes—
44C11×C4⋊Q8C2311yescharacteristic
45C11×#125—21no—
46C11×C22⋊Q8—21no—
47C11×C22⋊Q8—21no—
48C4×Q8×C11—21no—
49C4×Q8×C11—21no—
50C11×#117—21no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C42×C11C2311yescharacteristic
54C2×#4326—24no—
55C2×#4326—44no—
56C2×C4⋊Dic11D411yescharacteristic
57C2×Dic11⋊C4—21no—
58C2×C4×Dic11—21no—
59C2×#4318—21no—
60C22×C11⋊C8—21no—
61C4×Dic22—21no—
62C4×Dic22—21no—
63C4×Dic22D412yes—
64C4×Dic22C2312yes—
65C11×#106—24no—
66C11×C4⋊C8D412yes—
67C11×#103—24no—
68C11×C22⋊C8D412yes—
69C4×C8×C11C2312yes—
70#66899—24no—
71C22⋊(C11⋊C8)—21no—
72Dic11⋊C8—24no—
73C8×Dic11—24no—
74#66874—22no—
75#66874—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#19402—111nomaximal, Sylow
85C2×Q8×C11—22no—
86C2×Q8×C11—21no—
87C2×Q8×C11—21no—
88C2×Q8×C11—41no—
89C2×Q8×C11—42no—
90C2×Q8×C11—42no—
91C22×C4×C11—41no—
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11#4111yescharacteristic
95C22×Dic11—21no—
96C22×Dic11—21no—
97C2×Dic22—21no—
98C2×Dic22—22no—
99C2×Dic22SD1614yes—
100C2×Dic22C2×D412yes—
101C2×C8×C11C2×D414yes—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—22no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—22no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4—41no—
110C11×C4⋊C4—41no—
111C11×C4⋊C4—41no—
112C11×C22⋊C4—41no—
113C42×C11—41no—
114C42×C11C2×D411yescharacteristic
115C42×C11C2×D411yescharacteristic
116C42×C11#4111yescharacteristic
117C42×C11C2411yescharacteristic
118#4326—48no—
119C4⋊Dic11—21no—
120C4⋊Dic11C2×D412yes—
121Dic11⋊C4—22no—
122Dic11⋊C4—22no—
123C4×Dic11—22no—
124C4×Dic11—22no—
125#4318—42no—
126C2×C11⋊C8—22no—
127C2×C11⋊C8—22no—
128C2×C11⋊C8—22no—
129C2×C11⋊C8—42no—
130#3229D1111yescharacteristic
131#3078—111no—
132C2×#462—111no—
133#2982—111no—
134#1680—114no—
135#1672—114no—
136#1570—111no—
137#1546—111no—
138#1542—111no—
139C23×C11#12111yescharacteristic
140Q8×C11—42no—
141Q8×C11—42no—
142Q8×C11—42no—
143Q8×C11—81no—
144Q8×C11—82no—
145C2×C4×C11—22no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—42no—
150C2×C4×C11—82no—
151C2×C4×C11#12111yescharacteristic
152C2×C4×C11#12111yescharacteristic
153C2×C4×C11#12111yescharacteristic
154C2×C4×C11C2×SD1612yes—
155C2×C4×C11#13512yes—
156C2×C4×C11C22×D411yescharacteristic
157C2×C4×C11C22×D411yescharacteristic
158C2×C4×C11C2×#4111yescharacteristic
159C2×Dic11—22no—
160C2×Dic11—24no—
161C2×Dic11—22no—
162C2×Dic11—81no—
163Dic22—22no—
164Dic22—24no—
165Dic22C2×SD1614yes—
166C8×C11—24no—
167C11⋊C8—42no—
168C11⋊C8—42no—
169C11⋊C8—42no—
170C22×Q16—221no—
171#533C2×D1111yescharacteristic
172C2×C4⋊Q8C2×D1111yescharacteristic
173C2×C4×Q8—111no—
174#498C2×D1112yes—
175#487C2×D1112yes—
176#483—22no—
177#479—222no—
178#477—112no—
179#475—22no—
180#475—112no—
181#462—114no—
182#462—222no—
183C8×Q8—114no—
184C8×Q8—222no—
185#431—111no—
186#431—222no—
187#431C2×D1111yescharacteristic
188#428—221no—
189#423—111no—
190C2×C4⋊C8—111no—
191#419—221no—
192C2×#103—221no—
193#334—114no—
194#333—112no—
195#332—112no—
196#332—114no—
197C22×C11—21no—
198C22×C11—21no—
199C22×C11#46512yes—
200C22×C11C2×#12111yescharacteristic
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—81no—
205C4×C11—82no—
206C4×C11—81no—
207C4×C11#46512yes—
208C4×C11C22×SD1611yescharacteristic
209C4×C11C2×#13511yescharacteristic
210C4×C11#57812yes—
211Dic11—24no—
212Dic11—42no—
213C22×Q8—21no—
214C22×Q8—111no—
215C2×Q16—224no—
216C2×Q16—444no—
217C2×M16—221no—
218C22×C8—221no—
219C4⋊Q8—21no—
220C4⋊Q8—21no—
221C4⋊Q8—21no—
222C4⋊Q8C22×D1112yes—
223C4⋊Q8C22×D1111yescharacteristic
224C4⋊Q8C22×D1111yescharacteristic
225#125—21no—
226C22⋊Q8—21no—
227C22⋊Q8—21no—
228C4×Q8—21no—
229C4×Q8—21no—
230C4×Q8—112no—
231C4×Q8—112no—
232C4×Q8—221no—
233C4×Q8—221no—
234#117—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—111no—
238C2×C4⋊C4—221no—
239C2×C42—221no—
240C2×C42C22×D1111yescharacteristic
241#107—222no—
242#106—24no—
243#106—222no—
244C4⋊C8—112no—
245C4⋊C8—112no—
246C4⋊C8—112no—
247C4⋊C8—224no—
248C4⋊C8—221no—
249C4⋊C8—221no—
250C4⋊C8C22⋊D1112yes—
251#103—24no—
252#103—222no—
253#103—222no—
254#103—224no—
255C22⋊C8—221no—
256C22⋊C8C22⋊D1112yes—
257C4×C8—224no—
258C4×C8—221no—
259C4×C8C22×D1112yes—
260C2×C11—22no—
261C2×C11#304411yescharacteristic
262C2×C11C2×#46511yescharacteristic
263C2×C11#306911yescharacteristic
264C2×Q8—22no—
265C2×Q8—21no—
266C2×Q8—21no—
267C2×Q8—41no—
268C2×Q8—42no—
269C2×Q8—42no—
270C2×Q8—114no—
271C2×Q8—112no—
272C2×Q8—222no—
273C2×Q8—221no—
274C22×C4—41no—
275C22×C4—221no—
276C22×C4—221no—
277C22×C4D4×D1111yescharacteristic
278C22×C4#434111yescharacteristic
279C22×C4C2×C22⋊D1111yescharacteristic
280Q16—448no—
281M16—442no—
282C2×C8—222no—
283C2×C8—222no—
284C2×C8—222no—
285C2×C8—442no—
286C2×C8C2×C22⋊D1114yes—
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—22no—
290C4⋊C4—21no—
291C4⋊C4—22no—
292C4⋊C4—21no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—112no—
298C4⋊C4—221no—
299C4⋊C4—222no—
300C4⋊C4—222no—
301C22⋊C4—41no—
302C42—41no—
303C42—222no—
304C42—222no—
305C42D4×D1111yescharacteristic
306C42#434111yescharacteristic
307C42C2×C22⋊D1111yescharacteristic
308C42C23×D1111yescharacteristic
309C11#1940211yescharacteristic, complemented, Sylow
310C23#6699111yescharacteristic
311Q8—42no—
312Q8—42no—
313Q8—42no—
314Q8—81no—
315Q8—82no—
316Q8—114no—
317Q8—222no—
318Q8—224no—
319C2×C4—22no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—42no—
324C2×C4—82no—
325C2×C4—224no—
326C2×C4—222no—
327C2×C4—222no—
328C2×C4—881no—
329C2×C4SD16×D1112yes—
330C2×C4#6696912yes—
331C2×C4#6699111yescharacteristic
332C2×C4#6699111yescharacteristic
333C2×C4#6699111yescharacteristic
334C2×C4C2×D4×D1111yescharacteristic
335C2×C4C2×#434111yescharacteristic
336C2×C4C22×C22⋊D1111yescharacteristic
337C8—24no—
338C8—442no—
339C8—442no—
340C8—442no—
341C22—21no—
342C22—21no—
343C22#1062278412yes—
344C22C2×#6699111yescharacteristic
345C4—21no—
346C4—21no—
347C4—21no—
348C4—81no—
349C4—81no—
350C4—82no—
351C4—224no—
352C4—442no—
353C4#1062278412yes—
354C4C2×SD16×D1111yescharacteristic
355C4C2×#6696911yescharacteristic
356C4#1062336912yes—
357C2—22no—
358C2#1307814211yescharacteristic
359C2C2×#1062278411yescharacteristic
360C2#1307834911yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3229C2
socleC22×C11C2×#121
prime radicalC23×C11#121
hypercenter#3229D11
hypocenterC11#19402
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. #13068043C2semidirect
5. #13067995C2semidirect
309. C11#19402semidirect

Maximal subgroups

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

subgroupindex
#130784172
C2×#106227032
#130776962
#130680432
#130679952
#130673872
#130672882
#130672732
C11×#32292
#1940211