Finite Group Databasebeta

← #14739136

Subgroups — #14739136

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#13079764C211yesmaximal, characteristic
2C2×#10622634C211yesmaximal, characteristic
3#13077697C211yesmaximal, characteristic
4#13068072C214yesmaximal, complemented
5#13068018C214yesmaximal, complemented
6#13067392C211yesmaximal, characteristic
7#13067298C211yesmaximal, characteristic
8#13067273C211yesmaximal, characteristic
9C11×#3078C211yesmaximal, characteristic
10C11×#533C2211yescharacteristic
11C2×C4×Q8×C11C2211yescharacteristic
12C2×#66922C2211yescharacteristic
13C11×#479—22no—
14C11×#477C2212yes—
15C11×#475C2212yes—
16C11×#428—21no—
17C11×#423C2211yescharacteristic
18C11×#419—21no—
19C2×#66899—21no—
20#10622694C2212yes—
21#10622691C2212yes—
22#10622657—22no—
23Q8×C11⋊C8—22no—
24Q8×C11⋊C8C2214yes—
25#10622634—22no—
26#10622634—22no—
27#10622634C2214yes—
28C2×#66871—21no—
29#10622538—22no—
30#10622538C2211yescharacteristic
31#10622538C2211yescharacteristic
32C2×C4⋊(C11⋊C8)C2211yescharacteristic
33#10622185C2212yes—
34#10622184C2212yes—
35#10622119C2214yes—
36#10622117C2214yes—
37C22×Q8×C11D411yescharacteristic
38C22×Dic22—21no—
39C2×C11×M16—21no—
40C11×C4⋊Q8C2311yescharacteristic
41C11×C4⋊Q8C2311yescharacteristic
42C11×#125—21no—
43C11×C22⋊Q8—21no—
44C11×C22⋊Q8—21no—
45C4×Q8×C11—21no—
46C4×Q8×C11—21no—
47C4×Q8×C11—21no—
48C4×Q8×C11—21no—
49C4×Q8×C11D412yes—
50C4×Q8×C11C2312yes—
51C11×#117—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4D411yescharacteristic
54C2×C42×C11—21no—
55C2×C42×C11C2311yescharacteristic
56C2×C4⋊Dic11—21no—
57C2×C4⋊Dic11—21no—
58C22×C11⋊C8—21no—
59#66922—21no—
60#66922—21no—
61#66922—21no—
62#66922C2312yes—
63C11×#107—22no—
64C11×#106—22no—
65C11×C4⋊C8—21no—
66C11×C4⋊C8C2312yes—
67C11×#103—22no—
68C11×#103—22no—
69#66899—24no—
70#66899—24no—
71C22⋊(C11⋊C8)—21no—
72C22⋊(C11⋊C8)D412yes—
73#66871—24no—
74#66871—24no—
75C4⋊(C11⋊C8)—21no—
76C4⋊(C11⋊C8)—24no—
77C4⋊(C11⋊C8)D412yes—
78C4⋊(C11⋊C8)C2312yes—
79C4⋊(C11⋊C8)C2312yes—
80C4×C11⋊C8—21no—
81C4×C11⋊C8—24no—
82C4×C11⋊C8C2312yes—
83#19405—111nomaximal, Sylow
84C2×Q8×C11—21no—
85C2×Q8×C11—22no—
86C2×Q8×C11—21no—
87C2×Q8×C11—21no—
88C2×Q8×C11Q1614yes—
89C2×Q8×C11C2×D412yes—
90C22×C4×C11—21no—
91C22×C4×C11—21no—
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11#4111yescharacteristic
95C22×Dic11—41no—
96C2×Dic22—22no—
97C2×Dic22—41no—
98C2×Dic22—82no—
99C11×M16—42no—
100C2×C8×C11—22no—
101C11×C4⋊C4—22no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—22no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4—41no—
110C11×C4⋊C4C2×D412yes—
111C11×C22⋊C4—41no—
112C42×C11—22no—
113C42×C11—22no—
114C42×C11—41no—
115C42×C11C2×D411yescharacteristic
116C42×C11C2×D411yescharacteristic
117C42×C11#4111yescharacteristic
118C42×C11C2411yescharacteristic
119C4⋊Dic11—22no—
120C4⋊Dic11—22no—
121C4⋊Dic11—41no—
122C4⋊Dic11—41no—
123C2×C11⋊C8—22no—
124C2×C11⋊C8—22no—
125C2×C11⋊C8—42no—
126C2×C11⋊C8C2×D414yes—
127#3230—111no—
128#3078D1111yescharacteristic
129C2×#477—111no—
130#2982—111no—
131#1684—114no—
132#1676—114no—
133#1571—111no—
134#1548—111no—
135#1542—111no—
136C23×C11#12111yescharacteristic
137Q8×C11—22no—
138Q8×C11—24no—
139Q8×C11—42no—
140Q8×C11—81no—
141Q8×C11C2×Q1614yes—
142C2×C4×C11—22no—
143C2×C4×C11—24no—
144C2×C4×C11—22no—
145C2×C4×C11—22no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—81no—
150C2×C4×C11#12111yescharacteristic
151C2×C4×C11#12111yescharacteristic
152C2×C4×C11#12111yescharacteristic
153C2×C4×C11C2×Q1612yes—
154C2×C4×C11#13512yes—
155C2×C4×C11C22×D411yescharacteristic
156C2×C4×C11C22×D411yescharacteristic
157C2×C4×C11C2×#4111yescharacteristic
158C2×Dic11—42no—
159C2×Dic11—82no—
160Dic22—82no—
161Dic22—82no—
162C8×C11—42no—
163C11⋊C8—24no—
164C11⋊C8—42no—
165C11⋊C8—42no—
166#533C2×D1111yescharacteristic
167C2×C4⋊Q8—111no—
168C2×C4×Q8C2×D1111yescharacteristic
169#500—112no—
170#487—112no—
171#484—222no—
172#479—22no—
173#477—114no—
174#477—222no—
175#477—222no—
176#477C2×D1112yes—
177#475C2×D1112yes—
178C8×Q8—114no—
179C8×Q8—222no—
180#431—111no—
181#431—111no—
182#431—222no—
183#428—21no—
184C2×#107—221no—
185#423C2×D1111yescharacteristic
186C2×C4⋊C8—111no—
187#419—21no—
188C2×#103—221no—
189#335—114no—
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—24no—
199C4×C11—21no—
200C4×C11—21no—
201C4×C11—42no—
202C4×C11—81no—
203C4×C11—81no—
204C4×C11#46712yes—
205C4×C11C22×Q1611yescharacteristic
206C4×C11C2×#13511yescharacteristic
207C4×C11#57812yes—
208Dic11—82no—
209C22×Q8—221no—
210C22×Q8C22⋊D1111yescharacteristic
211C2×M16—21no—
212C22×C8—221no—
213C4⋊Q8—112no—
214C4⋊Q8—221no—
215C4⋊Q8—221no—
216C4⋊Q8—221no—
217C4⋊Q8C22×D1111yescharacteristic
218C4⋊Q8C22×D1111yescharacteristic
219#125—21no—
220C22⋊Q8—21no—
221C22⋊Q8—21no—
222C4×Q8—21no—
223C4×Q8—21no—
224C4×Q8—21no—
225C4×Q8—21no—
226C4×Q8C22⋊D1112yes—
227C4×Q8C22×D1112yes—
228#117—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—221no—
231C2×C4⋊C4—221no—
232C2×C4⋊C4C22⋊D1111yescharacteristic
233C2×C42—21no—
234C2×C42C22×D1111yescharacteristic
235#107—22no—
236#107—224no—
237#107—224no—
238#106—22no—
239C4⋊C8—21no—
240C4⋊C8—112no—
241C4⋊C8—112no—
242C4⋊C8—112no—
243C4⋊C8—224no—
244C4⋊C8—221no—
245C4⋊C8C22×D1112yes—
246#103—22no—
247#103—22no—
248#103—224no—
249#103—224no—
250C22⋊C8—112no—
251C22⋊C8—221no—
252C4×C8—112no—
253C4×C8—224no—
254C4×C8—221no—
255C2×C11—22no—
256C2×C11#304411yescharacteristic
257C2×C11C2×#46711yescharacteristic
258C2×C11#306811yescharacteristic
259C2×Q8—21no—
260C2×Q8—22no—
261C2×Q8—21no—
262C2×Q8—21no—
263C2×Q8—222no—
264C2×Q8—441no—
265C2×Q8—882no—
266C2×Q8#432614yes—
267C2×Q8C2×C22⋊D1112yes—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—441no—
271C22×C4D4×D1111yescharacteristic
272C22×C4#434111yescharacteristic
273C22×C4C2×C22⋊D1111yescharacteristic
274M16—42no—
275C2×C8—22no—
276C2×C8—114no—
277C2×C8—222no—
278C2×C8—222no—
279C2×C8—442no—
280C4⋊C4—22no—
281C4⋊C4—21no—
282C4⋊C4—22no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—222no—
290C4⋊C4—222no—
291C4⋊C4—441no—
292C4⋊C4—441no—
293C4⋊C4C2×C22⋊D1112yes—
294C22⋊C4—41no—
295C42—22no—
296C42—22no—
297C42—41no—
298C42D4×D1111yescharacteristic
299C42#434111yescharacteristic
300C42C2×C22⋊D1111yescharacteristic
301C42C23×D1111yescharacteristic
302C11#1940511yescharacteristic, complemented, Sylow
303C23#6699211yescharacteristic
304Q8—22no—
305Q8—24no—
306Q8—42no—
307Q8—81no—
308Q8—882no—
309Q8—882no—
310Q8C2×#432614yes—
311C2×C4—22no—
312C2×C4—24no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—81no—
319C2×C4—442no—
320C2×C4—882no—
321C2×C4#6699211yescharacteristic
322C2×C4#6699211yescharacteristic
323C2×C4#6699211yescharacteristic
324C2×C4C2×#432612yes—
325C2×C4#6700312yes—
326C2×C4C2×D4×D1111yescharacteristic
327C2×C4C2×#434111yescharacteristic
328C2×C4C22×C22⋊D1111yescharacteristic
329C8—42no—
330C8—224no—
331C8—442no—
332C8—442no—
333C22—21no—
334C22—21no—
335C22#1062266412yes—
336C22C2×#6699211yescharacteristic
337C4—21no—
338C4—21no—
339C4—21no—
340C4—24no—
341C4—42no—
342C4—81no—
343C4—81no—
344C4—882no—
345C4#1062266412yes—
346C4#1062331012yes—
347C4C22×#432611yescharacteristic
348C4C2×#6700311yescharacteristic
349C2—22no—
350C2#1307814811yescharacteristic
351C2C2×#1062266411yescharacteristic
352C2#1307834611yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3078C2
socleC22×C11C2×#121
prime radicalC23×C11#121
hypercenter#3078D11
hypocenterC11#19405
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3078

Complements

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

NH ≅ G/Ntype
4. #13068072C2semidirect
5. #13068018C2semidirect
302. C11#19405semidirect

Maximal subgroups

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

subgroupindex
#130797642
C2×#106226342
#130776972
#130680722
#130680182
#130673922
#130672982
#130672732
C11×#30782
#1940511