Finite Group Databasebeta

← #14737624

Subgroups — #14737624

Order 2816.

602 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079202C211yesmaximal, characteristic
2#13078421C212yesmaximal
3#13068074C214yesmaximal, complemented
4#13068020C212yesmaximal, complemented
5#13067986C212yesmaximal, complemented
6#13067375C211yesmaximal, characteristic
7#13067304C212yesmaximal
8C2×C8×Q8×C11C211yesmaximal, characteristic
9C2×C4×Q8×C11C2211yescharacteristic
10#10623001C2212yes—
11C8×Q8×C11—21no—
12C8×Q8×C11—21no—
13C8×Q8×C11C2212yes—
14C8×Q8×C11C2212yes—
15C2×C11×C4⋊C8—21no—
16C2×C11×C4⋊C8C2211yescharacteristic
17C2×C4×C8×C11—21no—
18C2×C4×C8×C11C2211yescharacteristic
19#10622838—22no—
20#10622729—21no—
21#10622729—21no—
22#10622635—24no—
23#10622634C2214yes—
24#10622633C2214yes—
25#10622577—22no—
26#10622537C2212yes—
27#10622312C2211yescharacteristic
28C4×Dic44—21no—
29C4×Dic44—21no—
30#10622295C2211yescharacteristic
31#10622294C2212yes—
32#10622120C2214yes—
33#10622119C2214yes—
34#10622096C2212yes—
35#10622096C2212yes—
36C22×Q8×C11D411yescharacteristic
37C22×C8×C11—21no—
38C22×C8×C11D411yescharacteristic
39C22×C8×C11D411yescharacteristic
40C4×Q8×C11—21no—
41C4×Q8×C11—21no—
42C4×Q8×C11D412yes—
43C4×Q8×C11C2312yes—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4D411yescharacteristic
46C2×C42×C11—21no—
47C2×C42×C11C2311yescharacteristic
48#66979—22no—
49#66977—22no—
50#66977—22no—
51C2×#4318—22no—
52C2×Dic44—21no—
53C2×Dic44—21no—
54#66923—22no—
55#66922C2312yes—
56#66922C2312yes—
57C4×Dic22—22no—
58C4×Dic22—22no—
59C11×C4⋊C8—22no—
60C11×C4⋊C8—22no—
61C11×C4⋊C8—21no—
62C11×C4⋊C8C2312yes—
63C4×C8×C11—22no—
64C4×C8×C11—22no—
65C4×C8×C11D411yescharacteristic
66C4×C8×C11D411yescharacteristic
67C4×C8×C11C2311yescharacteristic
68C4×C8×C11C2311yescharacteristic
69#66899—24no—
70#66899—24no—
71#66882—21no—
72#66882—21no—
73#66880—22no—
74#66880—22no—
75#66872—24no—
76#66871—24no—
77C4⋊(C11⋊C8)—22no—
78C4⋊(C11⋊C8)C2314yes—
79#19262—111nomaximal, Sylow
80C2×Q8×C11—21no—
81C2×Q8×C11—22no—
82C2×Q8×C11Q1614yescomplemented
83C2×Q8×C11C2×D412yes—
84C22×C4×C11—21no—
85C22×C4×C11—21no—
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11#4111yescharacteristic
89C2×Dic22—22no—
90C2×Dic22—22no—
91C2×C8×C11—22no—
92C2×C8×C11—22no—
93C2×C8×C11—41no—
94C2×C8×C11—42no—
95C2×C8×C11C2×D411yescharacteristic
96C2×C8×C11C2×D411yescharacteristic
97C2×C8×C11C2×D411yescharacteristic
98C2×C8×C11C2×D411yescharacteristic
99C11×C4⋊C4—22no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—22no—
102C11×C4⋊C4C2×D412yes—
103C42×C11—22no—
104C42×C11—22no—
105C42×C11C2×D411yescharacteristic
106C42×C11C2×D411yescharacteristic
107C42×C11#4111yescharacteristic
108C42×C11C2411yescharacteristic
109C22⋊Dic11—42no—
110C4⋊Dic11—22no—
111C4⋊Dic11—22no—
112C4⋊Dic11—22no—
113C4⋊Dic11—22no—
114Dic11⋊C4—42no—
115Dic11⋊C4—42no—
116C4×Dic11—42no—
117#4318—44no—
118C2×C11⋊C8—24no—
119Dic44—42no—
120Dic44—42no—
121#3170—111no—
122#3078—112no—
123C2×C8×Q8D1111yescharacteristic
124#1684—114no—
125#1676—112no—
126#1670—112no—
127#1567—111no—
128#1550—112no—
129C23×C11#12111yescharacteristic
130Q8×C11—22no—
131Q8×C11—24no—
132Q8×C11C2×Q1614yes—
133C2×C4×C11—22no—
134C2×C4×C11—24no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—22no—
138C2×C4×C11—41no—
139C2×C4×C11—42no—
140C2×C4×C11#12111yescharacteristic
141C2×C4×C11#12111yescharacteristic
142C2×C4×C11#12111yescharacteristic
143C2×C4×C11C2×Q1612yes—
144C2×C4×C11#13512yes—
145C2×C4×C11C22×D411yescharacteristic
146C2×C4×C11C22×D411yescharacteristic
147C2×C4×C11C2×#4111yescharacteristic
148C2×Dic11—42no—
149C2×Dic11—42no—
150Dic22—42no—
151Dic22—42no—
152Dic22—82no—
153C8×C11—21no—
154C8×C11—21no—
155C8×C11—21no—
156C8×C11—42no—
157C8×C11#13712yes—
158C11⋊C8—44no—
159#533—112no—
160C2×C4×Q8C2×D1111yescharacteristic
161#500—111no—
162#494—111no—
163#487—112no—
164#479—224no—
165#477—114no—
166#475—114no—
167#467—221no—
168#467—221no—
169C8×Q8—21no—
170C8×Q8—21no—
171C8×Q8C2×D1112yes—
172C8×Q8C2×D1112yes—
173C4×Q16—221no—
174C4×Q16—221no—
175#428—222no—
176#423—112no—
177C2×C4⋊C8—21no—
178C2×C4⋊C8C2×D1111yescharacteristic
179#419—222no—
180C2×C4×C8—21no—
181C2×C4×C8C2×D1111yescharacteristic
182#335—112no—
183#335—112no—
184#333—114no—
185#332—114no—
186C22×C11—21no—
187C22×C11—21no—
188C22×C11#46712yes—
189C22×C11C2×#12111yescharacteristic
190C4×C11—21no—
191C4×C11—24no—
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—42no—
195C4×C11#46712yes—
196C4×C11C22×Q1611yescharacteristic
197C4×C11C2×#13511yescharacteristic
198C4×C11C2×#13711yescharacteristic
199C4×C11#57511yescharacteristic
200Dic11—82no—
201Dic11—82no—
202C22×Q8D4411yescharacteristic
203C2×Q16—221no—
204C2×Q16—221no—
205C2×M16—222no—
206C22×C8—21no—
207C22×C8C22⋊D1111yescharacteristic
208C22×C8C22⋊D1111yescharacteristic
209C4⋊Q8—112no—
210C4⋊Q8—112no—
211#125—222no—
212C22⋊Q8—222no—
213C22⋊Q8—222no—
214C4×Q8—21no—
215C4×Q8—21no—
216C4×Q8—222no—
217C4×Q8—222no—
218C4×Q8D4412yes—
219C4×Q8C22×D1112yes—
220#117—222no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4D4411yescharacteristic
223C2×C42—21no—
224C2×C42C22×D1111yescharacteristic
225#107—221no—
226#107—221no—
227#107—224no—
228#106—224no—
229C4⋊C8—22no—
230C4⋊C8—22no—
231C4⋊C8—21no—
232C4⋊C8—114no—
233C4⋊C8—222no—
234C4⋊C8C22×D1112yes—
235#103—224no—
236#103—224no—
237#103—222no—
238#103—222no—
239C4×C8—22no—
240C4×C8—22no—
241C4×C8C22⋊D1111yescharacteristic
242C4×C8C22⋊D1111yescharacteristic
243C4×C8C22×D1111yescharacteristic
244C4×C8C22×D1111yescharacteristic
245C2×C11—22no—
246C2×C11#303711yescharacteristic
247C2×C11C2×#46711yescharacteristic
248C2×C11#306711yescharacteristic
249C2×Q8—22no—
250C2×Q8—21no—
251C2×Q8—222no—
252C2×Q8—222no—
253C2×Q8Dic4414yescomplemented
254C2×Q8C2×D4412yes—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4C2×D4411yescharacteristic
258C22×C4#433911yescharacteristic
259C22×C4C2×C22⋊D1111yescharacteristic
260Q16—442no—
261Q16—442no—
262M16—444no—
263C2×C8—22no—
264C2×C8—22no—
265C2×C8—41no—
266C2×C8—42no—
267C2×C8—224no—
268C2×C8C2×C22⋊D1111yescharacteristic
269C2×C8C2×C22⋊D1111yescharacteristic
270C2×C8C2×C22⋊D1111yescharacteristic
271C2×C8C2×C22⋊D1111yescharacteristic
272C4⋊C4—22no—
273C4⋊C4—21no—
274C4⋊C4—22no—
275C4⋊C4—222no—
276C4⋊C4—222no—
277C4⋊C4—222no—
278C4⋊C4—222no—
279C4⋊C4—442no—
280C4⋊C4—442no—
281C4⋊C4C2×D4412yes—
282C22⋊C4—442no—
283C42—22no—
284C42—22no—
285C42—442no—
286C42C2×D4411yescharacteristic
287C42#433911yescharacteristic
288C42C2×C22⋊D1111yescharacteristic
289C42C23×D1111yescharacteristic
290C11#1926211yescharacteristic, complemented, Sylow
291C23#6698311yescharacteristic
292Q8—24no—
293Q8—22no—
294Q8—442no—
295Q8—442no—
296Q8—882no—
297Q8C2×Dic4414yes—
298C2×C4—24no—
299C2×C4—22no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—22no—
303C2×C4—41no—
304C2×C4—42no—
305C2×C4—442no—
306C2×C4—442no—
307C2×C4#6695712yes—
308C2×C4C2×Dic4412yes—
309C2×C4#6698311yescharacteristic
310C2×C4#6698311yescharacteristic
311C2×C4#6698311yescharacteristic
312C2×C4C22×D4411yescharacteristic
313C2×C4C2×#433911yescharacteristic
314C2×C4C22×C22⋊D1111yescharacteristic
315C8—21no—
316C8—21no—
317C8—21no—
318C8—42no—
319C8—444no—
320C8#6699512yes—
321C22—21no—
322C22—21no—
323C22#1062272912yes—
324C22C2×#6698311yescharacteristic
325C4—21no—
326C4—21no—
327C4—21no—
328C4—24no—
329C4—42no—
330C4—882no—
331C4—882no—
332C4#1062272912yes—
333C4C2×#6695711yescharacteristic
334C4C22×Dic4411yescharacteristic
335C4C2×#6699511yescharacteristic
336C4#1062335311yescharacteristic
337C2—22no—
338C2#1307808811yescharacteristic
339C2C2×#1062272911yescharacteristic
340C2#1307833611yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C8×Q8×C11C2
socleC22×C11C2×#121
prime radicalC23×C11#121
hypercenterC2×C8×Q8D11
hypocenterC11#19262
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C8×Q8

Complements

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

NH ≅ G/Ntype
3. #13068074C2semidirect
4. #13068020C2semidirect
5. #13067986C2semidirect
82. C2×Q8×C11Q16semidirect
253. C2×Q8Dic44semidirect
290. C11#19262semidirect

Maximal subgroups

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

subgroupindex
#130792022
#130784212
#130680742
#130680202
#130679862
#130673752
#130673042
C2×C8×Q8×C112
#1926211