Finite Group Databasebeta

← #14909121

Subgroups — #14909121

Order 2816.

570 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079110C211yesmaximal, characteristic
2#13070863C212yesmaximal, complemented
3#13070855C212yesmaximal, complemented
4#13070850C212yesmaximal, complemented
5#13070845C212yesmaximal, complemented
6#13070335C211yesmaximal, characteristic, complemented
7#13070326C211yesmaximal, characteristic
8#13070321C211yesmaximal, characteristic
9C2×#10622130C211yesmaximal, characteristic, complemented
10#13070213C211yesmaximal, characteristic, complemented
11C11×#3164C211yesmaximal, characteristic, complemented
12C11×#544—21no—
13C2×#66962—21no—
14C22×Dic44C2211yescharacteristic
15C2×#66957C2211yescharacteristic
16#10623057—21no—
17C11×#501—22no—
18C11×#500C2212yes—
19C11×#499C2212yes—
20C11×#428—21no—
21C11×#427C2211yescharacteristic
22C2×C11×#107C2211yescharacteristic
23C11×#405C2211yescharacteristic
24C2×#66876C2211yescharacteristic
25C22×C11⋊C16C2211yescharacteristic
26#10622328—22no—
27#10622312C2212yes—
28#10622309C2212yes—
29#10622130C2212yes—
30#10622130C2212yes—
31#10622130C2212yes—
32#10622130C2212yes—
33#10622130C2211yescharacteristic
34#10622130C2212yes—
35#10622130C2211yescharacteristic
36#10622129C2211yescharacteristic
37#10622129C2212yes—
38#10622129C2211yescharacteristic
39#10622099C2212yes—
40C4×C11⋊C16C2212yes—
41C2×#4339—21no—
42C22×Dic22—21no—
43C2×C11×M16D411yescharacteristic
44C22×C8×C11C2311yescharacteristic
45C11×C4⋊Q8—22no—
46C11×C4⋊Q8—41no—
47C11×#125—22no—
48C11×#125—41no—
49C11×C22⋊Q8—42no—
50C11×#117—21no—
51C11×#117D411yescharacteristic
52C2×C11×C4⋊C4—21no—
53#66962—44no—
54C2×Dic44—22no—
55C2×Dic44—22no—
56C2×Dic44—21no—
57C2×Dic44—22no—
58C2×Dic44C2311yescharacteristic
59C2×Dic44C2312yes—
60#66957—22no—
61#66957—22no—
62C2×D88C2311yescharacteristic
63C2×#4314—21no—
64C2×#4314—22no—
65#66950—41no—
66#66950—41no—
67#66939—42no—
68#66928—22no—
69#66922—22no—
70C11×#107—22no—
71C11×#107—21no—
72C11×#107C2311yescharacteristic
73C11×#107C2312yes—
74C11×#107C2311yescharacteristic
75C11×#106—22no—
76C11×#106—21no—
77C11×#97D412yes—
78C4×C8×C11C2312yes—
79#66876—22no—
80C2×C11⋊C16—22no—
81C2×C11⋊C16C2311yescharacteristic
82C2×C11⋊C16C2312yes—
83C2×C11⋊C16C2311yescharacteristic
84#33703—111nomaximal, Sylow
85C2×Q8×C11—42no—
86C22×C4×C11—41no—
87C22×C4×C11C2×D411yescharacteristic
88C2×C22⋊D11—41no—
89C22×Dic11—41no—
90#4339—42no—
91#4339—42no—
92C2×D44—21no—
93C2×C4×D11—41no—
94C2×Dic22—21no—
95C2×Dic22—22no—
96C2×Dic22—42no—
97C2×Dic22—41no—
98C2×Dic22—42no—
99C11×M16SD1614yes—
100C2×C8×C11C2×D411yescharacteristic
101C2×C8×C11C2×D412yes—
102C2×C8×C11#4112yes—
103C2×C8×C11#4112yes—
104C2×C8×C11C2411yescharacteristic
105C11×C4⋊C4—21no—
106C11×C4⋊C4—22no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4—42no—
110C11×C4⋊C4—42no—
111C11×C4⋊C4—42no—
112C11×C4⋊C4D811yescharacteristic
113C11×C4⋊C4D811yescharacteristic
114C11×C22⋊C4—41no—
115C11×C22⋊C4D812yes—
116C42×C11—41no—
117C42×C11C2×D412yes—
118(C2×D11)⋊C4—42no—
119(C2×D11)⋊C4—42no—
120C4⋊Dic11—42no—
121C4⋊Dic11—42no—
122Dic44—21no—
123Dic44—21no—
124Dic44—22no—
125Dic44—22no—
126Dic44—42no—
127Dic44—44no—
128D88—21no—
129D88—21no—
130#4314—42no—
131#4314—44no—
132C11⋊C16—21no—
133C11⋊C16—21no—
134C11⋊C16—22no—
135#3164D1111yescharacteristic, complemented
136#3156—111no—
137#2245—112no—
138#2243—112no—
139#2242—112no—
140#2241—112no—
141#2141—111no—
142#2139—111no—
143#2138—111no—
144C2×#358—111no—
145#2108—111no—
146C23×C11C2×D811yescharacteristic
147C22×D11—41no—
148Q8×C11—162no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—42no—
152C2×C4×C11—161no—
153C2×C4×C11#12412yes—
154C2×C4×C11C2×D812yes—
155C2×C4×C11C2×D812yes—
156C2×C4×C11C2×D811yescharacteristic
157C2×C4×C11C2×SD1612yes—
158C2×C4×C11C22×D411yescharacteristic
159C22⋊D11—82no—
160C2×Dic11—41no—
161C2×Dic11—42no—
162C2×Dic11—82no—
163D44—41no—
164D44—41no—
165C4×D11—82no—
166Dic22—41no—
167Dic22—42no—
168Dic22—42no—
169Dic22—41no—
170Dic22—82no—
171C8×C11#12412yes—
172C8×C11C2×SD1614yes—
173C8×C11C2×#4111yescharacteristic
174C8×C11C2×#4111yescharacteristic
175C2×#137—221no—
176C2×#135—111no—
177C22×Q16—111no—
178#544—21no—
179#536—221no—
180C2×M32—111no—
181C22×C16—111no—
182#501—22no—
183#500C2×D1112yes—
184#499C2×D1112yes—
185#497—222no—
186#495—112no—
187#494—112no—
188#428—21no—
189#427C2×D1111yescharacteristic
190C2×#107C2×D1111yescharacteristic
191#405C2×D1111yescharacteristic
192#358—112no—
193#358—112no—
194#358—111no—
195#358—111no—
196#358—112no—
197#358—112no—
198#358—112no—
199#357—111no—
200#357—111no—
201#357—112no—
202#346—112no—
203C4×C16—112no—
204C22×C11—21no—
205C22×C11—21no—
206C22×C11#48612yes—
207C22×C11C22×D811yescharacteristic
208C2×D11—81no—
209C2×D11—81no—
210C2×D11—81no—
211C4×C11—22no—
212C4×C11—22no—
213C4×C11—82no—
214C4×C11—81no—
215C4×C11—81no—
216C4×C11#48612yes—
217C4×C11C2×#12411yescharacteristic
218C4×C11C22×SD1611yescharacteristic
219Dic11—82no—
220Dic11—81no—
221C2×#41—221no—
222C22×Q8—221no—
223#137—444no—
224#135—222no—
225#135—222no—
226C2×Q16—112no—
227C2×Q16—111no—
228C2×Q16—222no—
229C2×Q16—222no—
230C2×Q16—221no—
231C2×Q16—222no—
232C2×SD16—221no—
233C2×SD16—222no—
234C2×D8—111no—
235C2×M16C22⋊D1111yescharacteristic
236C22×C8C22×D1111yescharacteristic
237C4⋊Q8—22no—
238C4⋊Q8—41no—
239C4⋊Q8—222no—
240#125—22no—
241#125—41no—
242#124—222no—
243#123—442no—
244C22⋊Q8—42no—
245C22⋊Q8—441no—
246C22⋊Q8—441no—
247#117—21no—
248#117C22⋊D1111yescharacteristic
249C2×C4⋊C4—21no—
250M32—222no—
251C2×C16—111no—
252C2×C16—112no—
253C2×C16—111no—
254C2×C16—222no—
255#107—21no—
256#107—22no—
257#107C22×D1112yes—
258#107C22×D1111yescharacteristic
259#107C22×D1111yescharacteristic
260#106—21no—
261#106—22no—
262#97C22⋊D1112yes—
263C4×C8C22×D1112yes—
264C2×C11—22no—
265C2×C11C2×#48611yescharacteristic
266C2×C11#341611yescharacteristic
267C2×C11#341711yescharacteristic
268D11—161no—
269#41—442no—
270#41—442no—
271C2×Q8—42no—
272C2×Q8—222no—
273C2×Q8—221no—
274C2×Q8—441no—
275C2×Q8—442no—
276C2×Q8—442no—
277C2×D4—221no—
278C2×D4—441no—
279C22×C4—41no—
280C22×C4—441no—
281C22×C4—441no—
282C22×C4C2×C22⋊D1111yescharacteristic
283Q16—222no—
284Q16—222no—
285Q16—221no—
286Q16—221no—
287Q16—444no—
288Q16—442no—
289SD16—444no—
290SD16—442no—
291D8—221no—
292D8—221no—
293M16#432514yes—
294C2×C8#434312yes—
295C2×C8#434312yes—
296C2×C8C2×C22⋊D1112yes—
297C2×C8C2×C22⋊D1111yescharacteristic
298C2×C8C23×D1111yescharacteristic
299C4⋊C4—21no—
300C4⋊C4—22no—
301C4⋊C4—21no—
302C4⋊C4—41no—
303C4⋊C4—42no—
304C4⋊C4—42no—
305C4⋊C4—42no—
306C4⋊C4—442no—
307C4⋊C4—442no—
308C4⋊C4#432311yescharacteristic
309C4⋊C4#432311yescharacteristic
310C22⋊C4—41no—
311C22⋊C4—442no—
312C22⋊C4—442no—
313C22⋊C4#432312yes—
314C42—41no—
315C42C2×C22⋊D1112yes—
316C16—221no—
317C16—221no—
318C16—222no—
319C11#3370311yescharacteristic, complemented, Sylow
320C23—441no—
321C23C2×#432311yescharacteristic
322Q8—162no—
323Q8—442no—
324Q8—441no—
325Q8—441no—
326Q8—442no—
327Q8—882no—
328D4—441no—
329D4—441no—
330D4—882no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—42no—
334C2×C4—161no—
335C2×C4—442no—
336C2×C4—441no—
337C2×C4—882no—
338C2×C4—882no—
339C2×C4C2×#432312yes—
340C2×C4C2×#432312yes—
341C2×C4C2×#432311yescharacteristic
342C2×C4C2×#432512yes—
343C2×C4#6700012yes—
344C2×C4C22×C22⋊D1111yescharacteristic
345C8C2×#432514yes—
346C8#6700012yes—
347C8C2×#434311yescharacteristic
348C8C2×#434311yescharacteristic
349C22—21no—
350C22—21no—
351C22—881no—
352C22—881no—
353C22—881no—
354C22#1062270112yes—
355C22C22×#432311yescharacteristic
356C4—22no—
357C4—22no—
358C4—82no—
359C4—81no—
360C4—81no—
361C4—881no—
362C4—882no—
363C4#1062270112yes—
364C4C22×#432511yescharacteristic
365C4C2×#6700011yescharacteristic
366C2—22no—
367C2—1761no—
368C2C2×#1062270111yescharacteristic
369C2#1308176311yescharacteristic
370C2#1308176711yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3164C2
socleC22×C11C22×D8
prime radicalC2×#66957C22
hypercenter#3164D11
hypocenterC11#33703
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #3164

Complements

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

NH ≅ G/Ntype
2. #13070863C2semidirect
3. #13070855C2semidirect
4. #13070850C2semidirect
5. #13070845C2semidirect
6. #13070335C2semidirect
9. C2×#10622130C2semidirect
10. #13070213C2semidirect
11. C11×#3164C2semidirect
135. #3164D11semidirect
319. C11#33703semidirect

Maximal subgroups

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

subgroupindex
#130791102
#130708632
#130708552
#130708502
#130708452
#130703352
#130703262
#130703212
C2×#106221302
#130702132
C11×#31642
#3370311