Finite Group Databasebeta

← #14739135

Subgroups — #14739135

Order 2816.

590 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079769C211yesmaximal, characteristic
2#13078423C211yesmaximal, characteristic
3C2×#10622463C211yesmaximal, characteristic
4#13077696C211yesmaximal, characteristic
5#13068075C214yesmaximal, complemented
6#13068021C214yesmaximal, complemented
7#13067298C211yesmaximal, characteristic
8#13067274C211yesmaximal, characteristic
9C11×#1571C211yesmaximal, characteristic
10#10623001C2211yescharacteristic
11C2×#66922C2211yescharacteristic
12C2×C4×Dic22C2211yescharacteristic
13C11×#431C2211yescharacteristic
14C11×#423C2211yescharacteristic
15C2×C11×C4⋊C8C2211yescharacteristic
16#10622734—21no—
17#10622733—21no—
18C2×#66882—21no—
19C2×#66880—21no—
20#10622538C2211yescharacteristic
21#10622464C2212yes—
22#10622463—22no—
23#10622463—22no—
24#10622463C2214yes—
25#10622463C2212yes—
26#10622443—22no—
27#10622442—22no—
28#10622335—22no—
29#10622331—22no—
30#10622295C2212yes—
31#10622294C2212yes—
32C8×Dic22C2214yes—
33C11×#335C2214yes—
34#10622124C2212yes—
35#10622119C2212yes—
36#10622119C2214yes—
37C22×Dic22—21no—
38C22×Dic22D411yescharacteristic
39C2×C11×M16—21no—
40C22×C8×C11—21no—
41C2×C42×C11C2311yescharacteristic
42#66979—21no—
43C2×C4⋊Dic11—21no—
44C2×C4⋊Dic11—21no—
45C2×C4⋊Dic11D411yescharacteristic
46#66977—21no—
47#66977—21no—
48C2×Dic11⋊C4—21no—
49C2×C4×Dic11—21no—
50#66923—21no—
51#66922—21no—
52#66922—21no—
53#66922—21no—
54#66922C2311yescharacteristic
55#66922C2312yes—
56#66922C2311yescharacteristic
57C4×Dic22—21no—
58C4×Dic22—21no—
59C4×Dic22—21no—
60C4×Dic22—21no—
61C4×Dic22D412yes—
62C4×Dic22C2312yes—
63C11×C4⋊C8—21no—
64C11×C4⋊C8—21no—
65C11×C4⋊C8D412yes—
66C11×C4⋊C8C2312yes—
67C11×C4⋊C8C2312yes—
68C11×C22⋊C8D412yes—
69C4×C8×C11C2312yes—
70C22⋊(C11⋊C8)—21no—
71#66882—24no—
72#66882—22no—
73#66882—24no—
74#66881—22no—
75#66880—22no—
76#66880—22no—
77#66880—24no—
78#66880—24no—
79Dic11⋊C8—24no—
80C8×Dic11—24no—
81C4⋊(C11⋊C8)C2312yes—
82C4×C11⋊C8—21no—
83#19405—111nomaximal, Sylow
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11#4111yescharacteristic
87C22×Dic11—21no—
88C22×Dic11—21no—
89C22×Dic11—41no—
90C2×Dic22—21no—
91C2×Dic22—22no—
92C2×Dic22—21no—
93C2×Dic22—21no—
94C2×Dic22—22no—
95C2×Dic22—41no—
96C2×Dic22—82no—
97C2×Dic22Q1614yes—
98C2×Dic22C2×D412yes—
99C11×M16—42no—
100C2×C8×C11—22no—
101C2×C8×C11—22no—
102C2×C8×C11—42no—
103C2×C8×C11C2×D414yes—
104C42×C11C2×D411yescharacteristic
105C42×C11C2×D411yescharacteristic
106C42×C11#4111yescharacteristic
107C42×C11C2411yescharacteristic
108C22⋊Dic11—41no—
109C4⋊Dic11—21no—
110C4⋊Dic11—21no—
111C4⋊Dic11—22no—
112C4⋊Dic11—22no—
113C4⋊Dic11—21no—
114C4⋊Dic11—21no—
115C4⋊Dic11—21no—
116C4⋊Dic11—41no—
117C4⋊Dic11—41no—
118C4⋊Dic11C2×D412yes—
119Dic11⋊C4—22no—
120Dic11⋊C4—22no—
121Dic11⋊C4—41no—
122Dic11⋊C4—41no—
123C4×Dic11—22no—
124C4×Dic11—22no—
125C4×Dic11—41no—
126C2×C11⋊C8—22no—
127#3230—111no—
128#3078—111no—
129C2×#477—111no—
130#2982—111no—
131#1684—114no—
132#1676—114no—
133#1571D1111yescharacteristic
134#1548—111no—
135#1542—111no—
136C23×C11#12111yescharacteristic
137C2×C4×C11—22no—
138C2×C4×C11—41no—
139C2×C4×C11#12111yescharacteristic
140C2×C4×C11#12111yescharacteristic
141C2×C4×C11#12111yescharacteristic
142C2×C4×C11C2×Q1612yes—
143C2×C4×C11#13512yes—
144C2×C4×C11C22×D411yescharacteristic
145C2×C4×C11C22×D411yescharacteristic
146C2×C4×C11C2×#4111yescharacteristic
147C2×Dic11—22no—
148C2×Dic11—24no—
149C2×Dic11—22no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—42no—
153C2×Dic11—81no—
154C2×Dic11—82no—
155Dic22—22no—
156Dic22—24no—
157Dic22—42no—
158Dic22—82no—
159Dic22—81no—
160Dic22—82no—
161Dic22C2×Q1614yes—
162C8×C11—24no—
163C8×C11—42no—
164C8×C11—42no—
165C11⋊C8—42no—
166#533—111no—
167C2×C4⋊Q8—111no—
168C2×C4×Q8—111no—
169#500—112no—
170#487—112no—
171#484—222no—
172#479—222no—
173#477—114no—
174#477—112no—
175#477—222no—
176#477—222no—
177#475—112no—
178C8×Q8—114no—
179C8×Q8—222no—
180#431—111no—
181#431—222no—
182#431C2×D1111yescharacteristic
183#428—221no—
184C2×#107—221no—
185#423C2×D1111yescharacteristic
186C2×C4⋊C8C2×D1111yescharacteristic
187#419—221no—
188C2×#103—221no—
189#335C2×D1114yes—
190#333—112no—
191#333—114no—
192#332—112no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11#46712yes—
196C22×C11C2×#12111yescharacteristic
197C4×C11—21no—
198C4×C11—21no—
199C4×C11—21no—
200C4×C11#46712yes—
201C4×C11C22×Q1611yescharacteristic
202C4×C11C2×#13511yescharacteristic
203C4×C11#57812yes—
204Dic11—24no—
205Dic11—42no—
206Dic11—81no—
207Dic11—82no—
208Dic11—81no—
209C22×Q8—111no—
210C22×Q8—221no—
211C2×M16—21no—
212C22×C8—21no—
213C4⋊Q8—112no—
214C4⋊Q8—111no—
215C4⋊Q8—111no—
216C4⋊Q8—221no—
217C4⋊Q8—221no—
218C4⋊Q8—221no—
219#125—221no—
220C22⋊Q8—221no—
221C22⋊Q8—221no—
222C4×Q8—112no—
223C4×Q8—112no—
224C4×Q8—221no—
225C4×Q8—221no—
226C4×Q8—221no—
227C4×Q8—221no—
228#117—221no—
229C2×C4⋊C4—111no—
230C2×C4⋊C4—221no—
231C2×C4⋊C4—221no—
232C2×C4⋊C4—221no—
233C2×C42—221no—
234C2×C42C22×D1111yescharacteristic
235#107—224no—
236#107—222no—
237#107—224no—
238#106—222no—
239C4⋊C8—21no—
240C4⋊C8—21no—
241C4⋊C8—112no—
242C4⋊C8—224no—
243C4⋊C8D4412yes—
244C4⋊C8C22×D1112yes—
245C4⋊C8C22×D1112yes—
246#103—224no—
247#103—222no—
248#103—222no—
249#103—224no—
250C22⋊C8—221no—
251C22⋊C8D4412yes—
252C4×C8—224no—
253C4×C8—221no—
254C4×C8C22×D1112yes—
255C2×C11—22no—
256C2×C11#304411yescharacteristic
257C2×C11C2×#46711yescharacteristic
258C2×C11#306811yescharacteristic
259C2×Q8—114no—
260C2×Q8—112no—
261C2×Q8—221no—
262C2×Q8—222no—
263C2×Q8—221no—
264C2×Q8—221no—
265C2×Q8—222no—
266C2×Q8—441no—
267C2×Q8—882no—
268C22×C4—221no—
269C22×C4—221no—
270C22×C4—441no—
271C22×C4C2×D4411yescharacteristic
272C22×C4D4×D1111yescharacteristic
273C22×C4#434311yescharacteristic
274M16—42no—
275C2×C8—22no—
276C2×C8—22no—
277C2×C8—42no—
278C2×C8—222no—
279C2×C8C2×D4414yes—
280C4⋊C4—112no—
281C4⋊C4—221no—
282C4⋊C4—222no—
283C4⋊C4—222no—
284C4⋊C4—222no—
285C4⋊C4—221no—
286C4⋊C4—221no—
287C4⋊C4—222no—
288C4⋊C4—221no—
289C4⋊C4—221no—
290C4⋊C4—441no—
291C4⋊C4—441no—
292C4⋊C4—441no—
293C4⋊C4—441no—
294C22⋊C4—441no—
295C42—222no—
296C42—222no—
297C42—441no—
298C42C2×D4411yescharacteristic
299C42D4×D1111yescharacteristic
300C42#434311yescharacteristic
301C42C23×D1111yescharacteristic
302C11#1940511yescharacteristic, complemented, Sylow
303C23#6694811yescharacteristic
304Q8—114no—
305Q8—224no—
306Q8—222no—
307Q8—442no—
308Q8—882no—
309Q8—881no—
310Q8—882no—
311C2×C4—22no—
312C2×C4—41no—
313C2×C4—224no—
314C2×C4—222no—
315C2×C4—222no—
316C2×C4—441no—
317C2×C4—441no—
318C2×C4—442no—
319C2×C4—881no—
320C2×C4—882no—
321C2×C4#6694811yescharacteristic
322C2×C4#6694811yescharacteristic
323C2×C4#6694811yescharacteristic
324C2×C4#6696512yes—
325C2×C4Q16×D1112yes—
326C2×C4C22×D4411yescharacteristic
327C2×C4C2×D4×D1111yescharacteristic
328C2×C4C2×#434311yescharacteristic
329C8—24no—
330C8—42no—
331C8—42no—
332C8—442no—
333C22—21no—
334C22—21no—
335C22#1062250012yes—
336C22C2×#6694811yescharacteristic
337C4—21no—
338C4—21no—
339C4—21no—
340C4—224no—
341C4—442no—
342C4—882no—
343C4—881no—
344C4—881no—
345C4#1062250012yes—
346C4#1062328412yes—
347C4C2×#6696511yescharacteristic
348C4C2×Q16×D1111yescharacteristic
349C2—22no—
350C2#1307814711yescharacteristic
351C2C2×#1062250011yescharacteristic
352C2#1307834511yescharacteristic
subgroupG/H
centerC22C2×#66948
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1571C2
socleC22×C11C2×#121
prime radicalC23×C11#121
hypercenter#1571D11
hypocenterC11#19405
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1571

Complements

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

NH ≅ G/Ntype
5. #13068075C2semidirect
6. #13068021C2semidirect
302. C11#19405semidirect

Maximal subgroups

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

subgroupindex
#130797692
#130784232
C2×#106224632
#130776962
#130680752
#130680212
#130672982
#130672742
C11×#15712
#1940511