Finite Group Databasebeta

← #14909112

Subgroups — #14909112

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#13079156C211yesmaximal, characteristic, complemented
2#13079105C211yesmaximal, characteristic
3#13070860C212yesmaximal, complemented
4#13070854C212yesmaximal, complemented
5#13070849C212yesmaximal, complemented
6#13070842C212yesmaximal, complemented
7#13070329C211yesmaximal, characteristic
8#13070321C211yesmaximal, characteristic
9C2×#10622202C211yesmaximal, characteristic, complemented
10#13070215C211yesmaximal, characteristic, complemented
11C11×#2141C211yesmaximal, characteristic, complemented
12C22×C11×Q16C2211yescharacteristic
13#10623347—21no—
14C2×#66995—21no—
15C2×#66957C2211yescharacteristic
16#10623050—21no—
17C2×C11×M32C2211yescharacteristic
18C11×#427C2211yescharacteristic
19#10622804C2212yes—
20#10622803—22no—
21#10622794C2212yes—
22C2×#66882C2211yescharacteristic
23#10622714C2211yescharacteristic
24C22×C11⋊C16C2211yescharacteristic
25#10622608—21no—
26#10622491C2212yes—
27#10622487C2212yes—
28#10622469—22no—
29C11×#358C2212yes—
30C11×#358C2212yes—
31#10622202C2212yes—
32#10622202C2212yes—
33#10622147C2212yes—
34#10622141C2212yes—
35#10622140C2212yes—
36C16×Dic11C2212yes—
37#10622130C2211yescharacteristic
38#10622130C2211yescharacteristic
39#10622129C2211yescharacteristic
40#10622129C2211yescharacteristic
41C22×Q8×C11—21no—
42C2×#4339—21no—
43C2×C11×Q16—21no—
44C2×C11×Q16—22no—
45C2×C11×Q16—22no—
46C2×C11×Q16C2312yes—
47C22×C8×C11C2311yescharacteristic
48C11×#117—21no—
49#67000—22no—
50#66999—41no—
51#66999—41no—
52#66997—22no—
53C2×#4326—22no—
54#66995—44no—
55C2×#4325—22no—
56#66982—42no—
57#66979D411yescharacteristic
58C2×C4⋊Dic11—21no—
59C2×#4318D411yescharacteristic
60C2×Dic44C2311yescharacteristic
61#66957—22no—
62#66957—22no—
63C2×D88C2311yescharacteristic
64C2×#4314—21no—
65#66943—22no—
66#66941—22no—
67#66931—42no—
68#66923—41no—
69#66922—41no—
70C11×M32—22no—
71C2×C11×C16C2312yes—
72C11×#107C2311yescharacteristic
73C11×#107C2311yescharacteristic
74C11×#106—21no—
75#66882—21no—
76#66882C2312yes—
77#66879D412yes—
78C8×Dic11C2312yes—
79C2×C11⋊C16—22no—
80C2×C11⋊C16C2311yescharacteristic
81C2×C11⋊C16C2311yescharacteristic
82#66872—22no—
83#66871—22no—
84#33703—111nomaximal, Sylow
85C2×Q8×C11—22no—
86C2×Q8×C11—41no—
87C2×Q8×C11—42no—
88C2×Q8×C11—42no—
89C22×C4×C11—41no—
90C22×C4×C11C2×D411yescharacteristic
91C2×C22⋊D11—41no—
92C22×Dic11—41no—
93#4339—42no—
94#4339—42no—
95C2×D44—21no—
96C2×C4×D11—41no—
97C2×Dic22—21no—
98C2×Dic22—42no—
99C11×Q16—22no—
100C11×Q16—22no—
101C11×Q16—42no—
102C2×C8×C11C2×D411yescharacteristic
103C2×C8×C11#4112yes—
104C2×C8×C11#4112yes—
105C2×C8×C11C2411yescharacteristic
106C11×C4⋊C4—21no—
107C11×C4⋊C4—21no—
108C11×C22⋊C4—41no—
109C42×C11—41no—
110C22⋊Dic11D812yes—
111#4326—44no—
112#4325—44no—
113(C2×D11)⋊C4—42no—
114(C2×D11)⋊C4—42no—
115C4⋊Dic11—22no—
116C4⋊Dic11—42no—
117C4⋊Dic11—41no—
118C4⋊Dic11D811yescharacteristic
119C4⋊Dic11D811yescharacteristic
120Dic11⋊C4—42no—
121Dic11⋊C4—42no—
122Dic11⋊C4—42no—
123Dic11⋊C4—42no—
124C4×Dic11C2×D412yes—
125#4318SD1614yes—
126C2×C11⋊C8C2×D412yes—
127Dic44—21no—
128Dic44—21no—
129D88—21no—
130D88—21no—
131#4314—42no—
132C11×C16—22no—
133C11⋊C16—21no—
134C11⋊C16—21no—
135#3164—111no—
136#3156—111no—
137#2245—112no—
138#2243—112no—
139#2242—112no—
140#2241—112no—
141#2141D1111yescharacteristic, complemented
142#2139—111no—
143#2138—111no—
144C2×#358—111no—
145#2108—111no—
146C23×C11C2×D811yescharacteristic
147C22×D11—41no—
148Q8×C11—42no—
149Q8×C11—42no—
150Q8×C11—82no—
151C2×C4×C11—41no—
152C2×C4×C11—42no—
153C2×C4×C11—41no—
154C2×C4×C11—82no—
155C2×C4×C11#12412yes—
156C2×C4×C11C2×D811yescharacteristic
157C2×C4×C11C2×SD1612yes—
158C2×C4×C11C22×D411yescharacteristic
159C22⋊D11—82no—
160C2×Dic11—41no—
161C2×Dic11—42no—
162C2×Dic11—161no—
163C2×Dic11C2×D812yes—
164C2×Dic11C2×D812yes—
165D44—41no—
166D44—41no—
167C4×D11—82no—
168Dic22—41no—
169Dic22—41no—
170Dic22—162no—
171C8×C11#12412yes—
172C8×C11C2×#4111yescharacteristic
173C8×C11C2×#4111yescharacteristic
174C11⋊C8C2×SD1614yes—
175C2×#137—221no—
176C2×#135—111no—
177C22×Q16C2×D1111yescharacteristic
178#544—221no—
179#536—221no—
180C2×M32C2×D1111yescharacteristic
181C22×C16—111no—
182#501—222no—
183#500—112no—
184#499—112no—
185#497—222no—
186#495—112no—
187#494—112no—
188#428—221no—
189#427C2×D1111yescharacteristic
190C2×#107—111no—
191#405—111no—
192#358—112no—
193#358—112no—
194#358—112no—
195#358—111no—
196#358—111no—
197#358C2×D1112yes—
198#358C2×D1112yes—
199#357—112no—
200#357—111no—
201#357—111no—
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—82no—
212C4×C11—81no—
213C4×C11—81no—
214C4×C11#48612yes—
215C4×C11C2×#12411yescharacteristic
216C4×C11C22×SD1611yescharacteristic
217Dic11—22no—
218Dic11—22no—
219Dic11—81no—
220Dic11—82no—
221C2×#41—221no—
222C22×Q8—21no—
223#137—444no—
224#135—222no—
225#135—222no—
226C2×Q16—22no—
227C2×Q16—21no—
228C2×Q16—22no—
229C2×Q16—111no—
230C2×Q16—222no—
231C2×Q16C22×D1112yes—
232C2×SD16—222no—
233C2×SD16—221no—
234C2×D8—111no—
235C2×M16—111no—
236C22×C8C22×D1111yescharacteristic
237C4⋊Q8—222no—
238C4⋊Q8—222no—
239C4⋊Q8—441no—
240#125—222no—
241#125—441no—
242#124—222no—
243#123—442no—
244C22⋊Q8—442no—
245C22⋊Q8—441no—
246C22⋊Q8—441no—
247#117—21no—
248#117—111no—
249C2×C4⋊C4—221no—
250M32—22no—
251C2×C16—111no—
252C2×C16—111no—
253C2×C16—222no—
254C2×C16C22×D1112yes—
255#107—112no—
256#107—222no—
257#107—221no—
258#107C22×D1111yescharacteristic
259#107C22×D1111yescharacteristic
260#106—21no—
261#106—222no—
262#97—112no—
263C4×C8—112no—
264C2×C11—22no—
265C2×C11C2×#48611yescharacteristic
266C2×C11#341611yescharacteristic
267C2×C11#341711yescharacteristic
268D11—161no—
269#41—442no—
270#41—442no—
271C2×Q8—22no—
272C2×Q8—41no—
273C2×Q8—42no—
274C2×Q8—42no—
275C2×Q8—221no—
276C2×Q8—442no—
277C2×D4—221no—
278C2×D4—441no—
279C22×C4—41no—
280C22×C4—441no—
281C22×C4—441no—
282C22×C4D4×D1111yescharacteristic
283Q16—22no—
284Q16—22no—
285Q16—42no—
286Q16—221no—
287Q16—221no—
288Q16—444no—
289SD16—444no—
290SD16—442no—
291D8—221no—
292D8—221no—
293M16—114no—
294C2×C8—112no—
295C2×C8#433912yes—
296C2×C8D4×D1111yescharacteristic
297C2×C8#434112yes—
298C2×C8C23×D1111yescharacteristic
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—111no—
302C4⋊C4—111no—
303C4⋊C4—222no—
304C4⋊C4—442no—
305C4⋊C4—442no—
306C4⋊C4—442no—
307C4⋊C4—442no—
308C4⋊C4—442no—
309C4⋊C4—441no—
310C22⋊C4—41no—
311C22⋊C4—112no—
312C22⋊C4—442no—
313C22⋊C4—442no—
314C42—41no—
315C42—112no—
316C16—22no—
317C16—221no—
318C16—221no—
319C11#3370311yescharacteristic, complemented, Sylow
320C23—441no—
321C23D8×D1111yescharacteristic
322Q8—42no—
323Q8—42no—
324Q8—82no—
325Q8—441no—
326Q8—441no—
327Q8—1762no—
328D4—441no—
329D4—441no—
330D4—882no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—42no—
334C2×C4—82no—
335C2×C4—112no—
336C2×C4—112no—
337C2×C4—442no—
338C2×C4—441no—
339C2×C4—882no—
340C2×C4—1761no—
341C2×C4#6693812yes—
342C2×C4D8×D1111yescharacteristic
343C2×C4SD16×D1112yes—
344C2×C4C2×D4×D1111yescharacteristic
345C8—114no—
346C8#6693812yes—
347C8C2×#433911yescharacteristic
348C8C2×#434111yescharacteristic
349C22—21no—
350C22—21no—
351C22—881no—
352C22—881no—
353C22—881no—
354C22#1062237312yes—
355C22C2×D8×D1111yescharacteristic
356C4—82no—
357C4—81no—
358C4—81no—
359C4—222no—
360C4—222no—
361C4—881no—
362C4—882no—
363C4#1062237312yes—
364C4C2×#6693811yescharacteristic
365C4C2×SD16×D1111yescharacteristic
366C2—22no—
367C2—1761no—
368C2C2×#1062237311yescharacteristic
369C2#1308176111yescharacteristic
370C2#1308176811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2141C2
socleC22×C11C22×D8
prime radicalC2×#66957C22
hypercenter#2141D11
hypocenterC11#33703
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2141

Complements

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

NH ≅ G/Ntype
1. #13079156C2semidirect
3. #13070860C2semidirect
4. #13070854C2semidirect
5. #13070849C2semidirect
6. #13070842C2semidirect
9. C2×#10622202C2semidirect
10. #13070215C2semidirect
11. C11×#2141C2semidirect
141. #2141D11semidirect
319. C11#33703semidirect

Maximal subgroups

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

subgroupindex
#130791562
#130791052
#130708602
#130708542
#130708492
#130708422
#130703292
#130703212
C2×#106222022
#130702152
C11×#21412
#3370311