Finite Group Databasebeta

← #14909128

Subgroups — #14909128

Order 2816.

578 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079127C211yesmaximal, characteristic
2D11×#494C211yesmaximal, characteristic
3#13070860C214yesmaximal, complemented
4#13070845C211yesmaximal, characteristic, complemented
5#13070844C211yesmaximal, characteristic, complemented
6#13070843C211yesmaximal, characteristic, complemented
7#13070334C214yesmaximal
8C4×#66862C211yesmaximal, characteristic
9C11×#2241C211yesmaximal, characteristic, complemented
10C2×Q16×D11—21no—
11C2×Q16×D11C2212yes—
12#10623259—21no—
13D11×C4⋊Q8—21no—
14C11×#500C2211yescharacteristic
15C11×#494C2211yescharacteristic
16#10622794—21no—
17#10622794C2212yes—
18#10622705—21no—
19#10622692—21no—
20C2×#66862C2212yes—
21#10622493—21no—
22#10622493C2212yes—
23#10622491—21no—
24#10622491C2212yes—
25#10622312C2211yescharacteristic
26C4×C8×D11C2211yescharacteristic
27#10622295C2211yescharacteristic
28C11×#358C2214yes—
29C4×C11×C16C2211yescharacteristic
30#10622202C2214yes—
31#10622141C2214yes—
32#10622140C2212yes—
33#10622130C2214yes—
34C4×C11⋊C16C2211yescharacteristic
35C2×Q8×D11—22no—
36C2×C11×Q16—21no—
37C2×C11×Q16C2312yes—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8—21no—
40#66999—41no—
41Q8×Dic11—41no—
42#66997—22no—
43C2×#4326—22no—
44C2×#4326—22no—
45Q16×D11—28no—
46Q16×D11—44no—
47C2×Dic44—21no—
48C2×Dic44C2312yes—
49C2×C8×D11D411yescharacteristic
50C2×C8×D11C2311yescharacteristic
51#66950—41no—
52#66945—22no—
53C4⋊C4×D11—41no—
54C4⋊C4×D11—41no—
55#66943—22no—
56#66941—41no—
57#66941—41no—
58#66940—41no—
59C42×D11D411yescharacteristic
60#66922—21no—
61#66922—21no—
62C2×C11×C16C2312yes—
63C11×#107—21no—
64C11×#107C2312yes—
65C4×C8×C11C2311yescharacteristic
66#66882—21no—
67#66882C2312yes—
68C8×Dic11D411yescharacteristic
69C8×Dic11C2311yescharacteristic
70C2×C11⋊C16C2312yes—
71#66872—22no—
72#66872—22no—
73C4×C11⋊C8D411yescharacteristic
74#66862—24no—
75#33705—111nomaximal, Sylow
76C2×Q8×C11—22no—
77C2×Q8×C11—41no—
78Q8×D11—44no—
79Q8×D11—44no—
80C2×C4×D11—42no—
81C2×C4×D11D811yescharacteristic
82C2×C4×D11D811yescharacteristic
83C2×C4×D11C2×D411yescharacteristic
84C2×Dic22—22no—
85C2×Dic22—42no—
86C2×Dic22—41no—
87C11×Q16—24no—
88C11×Q16—42no—
89C2×C8×C11C2×D411yescharacteristic
90C2×C8×C11C2411yescharacteristic
91C11×C4⋊C4—22no—
92C11×C4⋊C4—41no—
93C11×C4⋊C4—41no—
94C11×C4⋊C4—41no—
95C42×C11C2×D411yescharacteristic
96#4326—44no—
97#4326—44no—
98(C2×D11)⋊C4—42no—
99C4⋊Dic11—22no—
100C4⋊Dic11—42no—
101C4⋊Dic11—41no—
102C4⋊Dic11—41no—
103C4⋊Dic11—41no—
104Dic11⋊C4—42no—
105Dic11⋊C4—42no—
106Dic11⋊C4—42no—
107C4×Dic11—42no—
108C4×Dic11D811yescharacteristic
109C4×Dic11D811yescharacteristic
110C4×Dic11C2×D411yescharacteristic
111C2×C11⋊C8C2×D411yescharacteristic
112C2×C11⋊C8C2×D411yescharacteristic
113Dic44—24no—
114Dic44—42no—
115C8×D11SD1614yes—
116C8×D11#4114yes—
117C11×C16—22no—
118C11⋊C16—22no—
119#3160—111no—
120C2×#494—111no—
121#2245—114no—
122#2241—111no—
123#2241—111no—
124#2241—111no—
125#2241D1111yescharacteristic, complemented
126#2141—114no—
127C4×M32—111no—
128C22×D11C2×D811yescharacteristic
129Q8×C11—42no—
130Q8×C11—42no—
131Q8×C11—82no—
132C2×C4×C11—42no—
133C2×C4×C11—42no—
134C2×C4×C11C2×D811yescharacteristic
135C2×C4×C11C2×D811yescharacteristic
136C2×C4×C11C22×D411yescharacteristic
137C2×Dic11—42no—
138C2×Dic11—42no—
139C2×Dic11C2×D811yescharacteristic
140C2×Dic11C2×D811yescharacteristic
141C2×Dic11C2×D811yescharacteristic
142C4×D11—22no—
143C4×D11—22no—
144C4×D11—84no—
145C4×D11#12412yes—
146C4×D11C2×SD1612yes—
147Dic22—42no—
148Dic22—42no—
149Dic22—82no—
150Dic22—84no—
151C8×C11C2×SD1612yes—
152C8×C11C2×#4112yes—
153C11⋊C8#12412yes—
154C11⋊C8C2×SD1612yes—
155C22×Q16—112no—
156C22×Q16—221no—
157#533—221no—
158C2×C4⋊Q8—221no—
159C2×M32—112no—
160#500—111no—
161#500C2×D1111yescharacteristic
162#499—112no—
163#499—221no—
164#498—221no—
165#494—112no—
166#494—111no—
167#494—221no—
168#494—221no—
169#494C2×D1111yescharacteristic
170#427—112no—
171#427—221no—
172C2×C4×C8—111no—
173#358—114no—
174#358—114no—
175#358—114no—
176#358C2×D1114yes—
177#346—112no—
178C4×C16—111no—
179C4×C16C2×D1111yescharacteristic
180C22×C11C22×D811yescharacteristic
181C2×D11—21no—
182C2×D11—21no—
183C2×D11#48612yes—
184C4×C11—82no—
185C4×C11—82no—
186C4×C11#51012yes—
187C4×C11#51012yes—
188C4×C11C2×#12411yescharacteristic
189C4×C11C22×SD1611yescharacteristic
190Dic11—21no—
191Dic11—21no—
192Dic11—82no—
193Dic11—82no—
194Dic11#48612yes—
195C22×Q8—222no—
196C2×Q16—21no—
197C2×Q16—112no—
198C2×Q16—228no—
199C2×Q16—222no—
200C2×Q16—222no—
201C2×Q16—221no—
202C2×Q16—444no—
203C2×Q16C22×D1112yes—
204C22×C8—111no—
205C22×C8—111no—
206C4⋊Q8—21no—
207C4⋊Q8—21no—
208C4⋊Q8—222no—
209C4⋊Q8—221no—
210C4⋊Q8—221no—
211C4⋊Q8—441no—
212C4⋊Q8—441no—
213#125—222no—
214C22⋊Q8—441no—
215C22⋊Q8—441no—
216C4×Q8—441no—
217C4×Q8—441no—
218#117—222no—
219C2×C4⋊C4—441no—
220C2×C4⋊C4—441no—
221C2×C42—111no—
222M32—224no—
223C2×C16—112no—
224C2×C16C22×D1112yes—
225#107—21no—
226#107—112no—
227#107—221no—
228#107C22×D1112yes—
229#106—222no—
230#106—222no—
231C4×C8—111no—
232C4×C8—111no—
233C4×C8—111no—
234C4×C8C22×D1111yescharacteristic
235C2×C11C2×#48611yescharacteristic
236C2×C11C2×#51011yescharacteristic
237C2×C11C2×#51011yescharacteristic
238D11—22no—
239C2×Q8—22no—
240C2×Q8—41no—
241C2×Q8—222no—
242C2×Q8—442no—
243C2×Q8—444no—
244C2×Q8—444no—
245C2×Q8—441no—
246C22×C4—111no—
247C22×C4—111no—
248C22×C4—111no—
249C22×C4—442no—
250Q16—24no—
251Q16—42no—
252Q16—224no—
253Q16—444no—
254Q16—444no—
255Q16—442no—
256C2×C8—111no—
257C2×C8—111no—
258C2×C8—114no—
259C2×C8—114no—
260C2×C8D4×D1111yescharacteristic
261C2×C8C23×D1111yescharacteristic
262C4⋊C4—22no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—222no—
267C4⋊C4—442no—
268C4⋊C4—442no—
269C4⋊C4—442no—
270C4⋊C4—442no—
271C4⋊C4—441no—
272C4⋊C4—441no—
273C4⋊C4—441no—
274C22⋊C4—442no—
275C42—111no—
276C42—111no—
277C42—111no—
278C42—442no—
279C42D4×D1111yescharacteristic
280C16—22no—
281C16—222no—
282C11#3370511yescharacteristic, complemented, Sylow
283C23—111no—
284Q8—42no—
285Q8—42no—
286Q8—82no—
287Q8—442no—
288Q8—442no—
289Q8—884no—
290Q8—882no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—111no—
294C2×C4—112no—
295C2×C4—112no—
296C2×C4—111no—
297C2×C4—111no—
298C2×C4—222no—
299C2×C4—222no—
300C2×C4—442no—
301C2×C4—442no—
302C2×C4—884no—
303C2×C4D8×D1111yescharacteristic
304C2×C4D8×D1111yescharacteristic
305C2×C4C2×D4×D1111yescharacteristic
306C8—112no—
307C8—112no—
308C8SD16×D1112yes—
309C8#41×D1112yes—
310C22—112no—
311C22—221no—
312C22—221no—
313C22C2×D8×D1111yescharacteristic
314C4—82no—
315C4—82no—
316C4—112no—
317C4—221no—
318C4—221no—
319C4—882no—
320C4—882no—
321C4#1062252812yes—
322C4#1062253112yes—
323C4D11×#12411yescharacteristic
324C4C2×SD16×D1111yescharacteristic
325C2—222no—
326C2D11×#48611yescharacteristic
327C2C2×#1062252811yescharacteristic
328C2C2×#1062253111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2241C2
socleC22×C11C22×D8
prime radicalC22×D11C2×D8
hypercenter#2241D11
hypocenterC11#33705
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2241

Complements

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

NH ≅ G/Ntype
3. #13070860C2semidirect
4. #13070845C2semidirect
5. #13070844C2semidirect
6. #13070843C2semidirect
9. C11×#2241C2semidirect
125. #2241D11semidirect
282. C11#33705semidirect

Maximal subgroups

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

subgroupindex
#130791272
D11×#4942
#130708602
#130708452
#130708442
#130708432
#130703342
C4×#668622
C11×#22412
#3370511