Finite Group Databasebeta

← #14911517

Subgroups — #14911517

Order 2816.

518 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081589C211yesmaximal, characteristic
2#13081509C211yesmaximal, characteristic, complemented
3#13070856C212yesmaximal, complemented
4#13070775C212yesmaximal, complemented
5#13070750C211yesmaximal, characteristic, complemented
6#13070655C212yesmaximal, complemented
7#13070653C211yesmaximal, characteristic, complemented
8#13070524C211yesmaximal, characteristic, complemented
9#13070477C212yesmaximal, complemented
10C4×#66864C211yesmaximal, characteristic, complemented
11C11×#2240C211yesmaximal, characteristic, complemented
12#10623252—21no—
13#10623249—21no—
14C11×#500C2211yescharacteristic
15C11×#493C2211yescharacteristic
16#10622764C2212yes—
17#10622763—22no—
18D8×Dic11C2212yes—
19C2×#66891C2212yes—
20#10622707—21no—
21#10622685—21no—
22C2×#66864C2211yescharacteristic
23#10622491C2212yes—
24#10622490—22no—
25#10622486C2212yes—
26C4×Dic44C2211yescharacteristic
27C4×D88C2211yescharacteristic
28C8×Dic22C2211yescharacteristic
29C11×#357C2212yes—
30C11×#357C2212yes—
31C4×C11×C16C2211yescharacteristic
32#10622200C2212yes—
33#10622147C2211yescharacteristic
34#10622143C2211yescharacteristic
35#10622141C2211yescharacteristic
36#10622140C2212yes—
37Dic11⋊C16C2212yes—
38#10622129C2212yes—
39#10622127C2212yes—
40C4⋊(C11⋊C16)C2211yescharacteristic
41C2×#4341—41no—
42C2×C11×D8—21no—
43C2×C11×D8C2312yes—
44C11×C4⋊Q8—21no—
45C11×#127—21no—
46Q8×Dic11—41no—
47#66997—41no—
48#66993—22no—
49#66992—42no—
50#66991—41no—
51D4×Dic11—22no—
52C2×#4323—22no—
53C2×Dic44C2311yescharacteristic
54C2×D88C2311yescharacteristic
55#66943—22no—
56#66942—42no—
57#66940—22no—
58C4×D44—21no—
59C4×Dic22—21no—
60C4×Dic22D411yescharacteristic
61C2×C11×C16C2311yescharacteristic
62C2×C11×C16C2311yescharacteristic
63C11×#107—21no—
64C11×#107C2312yes—
65C4×C8×C11C2311yescharacteristic
66#66896—22no—
67#66891—24no—
68#66885—21no—
69#66882C2311yescharacteristic
70#66882C2311yescharacteristic
71#66880—21no—
72Dic11⋊C8D412yes—
73C8×Dic11C2312yes—
74C2×C11⋊C16C2312yes—
75#66874—22no—
76#66872—22no—
77C4⋊(C11⋊C8)D411yescharacteristic
78#66864—22no—
79#33935—111nomaximal, Sylow
80C2×Q8×C11—41no—
81C2×D4×C11—22no—
82C2×D4×C11—41no—
83C2×D4×C11—41no—
84C2×C22⋊D11—42no—
85C2×C22⋊D11—42no—
86C22×Dic11—42no—
87#4341—84no—
88C2×D44—21no—
89C2×C4×D11—41no—
90C2×Dic22—21no—
91C2×Dic22D811yescharacteristic
92C11×D8—22no—
93C11×D8—22no—
94C11×D8—81no—
95C2×C8×C11C2×D411yescharacteristic
96C2×C8×C11C2411yescharacteristic
97C11×C4⋊C4—22no—
98C11×C4⋊C4—41no—
99C42×C11C2×D411yescharacteristic
100C22⋊Dic11—42no—
101#4323—82no—
102(C2×D11)⋊C4—41no—
103C4⋊Dic11—21no—
104C4⋊Dic11—21no—
105C4⋊Dic11—42no—
106C4⋊Dic11D811yescharacteristic
107Dic11⋊C4—42no—
108Dic11⋊C4—42no—
109Dic11⋊C4—41no—
110Dic11⋊C4D812yes—
111C4×Dic11—42no—
112C4×Dic11—41no—
113C4×Dic11C2×D412yes—
114C2×C11⋊C8C2×D412yes—
115Dic44—21no—
116Dic44#4112yescomplemented
117D88—21no—
118D88—21no—
119C11×C16—21no—
120C11×C16—21no—
121C11⋊C16—22no—
122#3391—111no—
123#3383—111no—
124#2244—112no—
125#2240D1111yescharacteristic, complemented
126#2228—112no—
127#2224—111no—
128#2207—111no—
129#2207—112no—
130#2183—111no—
131#2175—112no—
132C4×SD32—111no—
133C23×C11—42no—
134C22×D11—41no—
135Q8×C11—82no—
136D4×C11—42no—
137D4×C11—42no—
138D4×C11—82no—
139D4×C11—161no—
140C2×C4×C11—42no—
141C2×C4×C11C2×D811yescharacteristic
142C2×C4×C11C2×D811yescharacteristic
143C2×C4×C11C22×D411yescharacteristic
144C22⋊D11—84no—
145C22⋊D11—162no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—84no—
150C2×Dic11C2×D812yes—
151C2×Dic11C2×D812yes—
152D44—41no—
153D44—41no—
154C4×D11—82no—
155Dic22—22no—
156Dic22—22no—
157Dic22—41no—
158C8×C11—21no—
159C8×C11C2×#4111yescharacteristic
160C8×C112−1+411yescharacteristic
161C11⋊C8—22no—
162#557—221no—
163#550—221no—
164C2×SD32—112no—
165C2×SD32—111no—
166#500C2×D1111yescharacteristic
167#499—112no—
168#493—112no—
169#493C2×D1111yescharacteristic
170#479—222no—
171#475—221no—
172#459—221no—
173#459—222no—
174C8×Q8—111no—
175C4×Q16—112no—
176C4×Q16—111no—
177C4×D8—112no—
178C4×D8—111no—
179#367—111no—
180#366—112no—
181C4⋊C16—112no—
182C4⋊C16—111no—
183#358—111no—
184#357—112no—
185#357—111no—
186#357—112no—
187#357C2×D1112yes—
188#357C2×D1112yes—
189#346—112no—
190C4×C16C2×D1111yescharacteristic
191C22×C11—82no—
192C22×C11—82no—
193C22×C11—82no—
194C22×C11C22×D811yescharacteristic
195C2×D11—81no—
196C2×D11—81no—
197C2×D11—81no—
198C4×C11—21no—
199C4×C11—82no—
200C4×C11#50912yes—
201C4×C11#54811yescharacteristic
202C4×C11#57711yescharacteristic
203Dic11—22no—
204Dic11—22no—
205Dic11—42no—
206Dic11—81no—
207Dic11—81no—
208C2×#41—441no—
209C2×Q16—111no—
210C2×D8—21no—
211C2×D8—111no—
212C2×D8—222no—
213C2×D8C22×D1112yes—
214C4⋊Q8—21no—
215C4⋊Q8—441no—
216#127—21no—
217#127—222no—
218#125—222no—
219#125—442no—
220#121—441no—
221#121—442no—
222C4×Q8—111no—
223C4×Q8—222no—
224C4×Q8—221no—
225C4×Q8—441no—
226C4×D4—222no—
227C4×D4—221no—
228SD32—222no—
229SD32—224no—
230C2×C16—112no—
231C2×C16C22×D1111yescharacteristic
232C2×C16C22×D1111yescharacteristic
233#107—21no—
234#107—111no—
235#107—111no—
236#107C22×D1112yes—
237#106—222no—
238C4⋊C8—112no—
239C4⋊C8—111no—
240#103—222no—
241#103—221no—
242#102—222no—
243#102—221no—
244C4×C8—112no—
245C4×C8C22×D1111yescharacteristic
246C2×C11—162no—
247C2×C11#335811yescharacteristic
248C2×C11C2×#50911yescharacteristic
249C2×C11#341611yescharacteristic
250D11—161no—
251#41—884no—
252C2×Q8—41no—
253C2×Q8—111no—
254C2×Q8—221no—
255C2×D4—22no—
256C2×D4—41no—
257C2×D4—41no—
258C2×D4—221no—
259C2×D4—442no—
260C2×D4—442no—
261C22×C4—442no—
262C22×C4—441no—
263Q16—112no—
264Q16—221no—
265D8—22no—
266D8—22no—
267D8—81no—
268D8—221no—
269D8—221no—
270D8—882no—
271C2×C8—112no—
272C2×C8D4×D1111yescharacteristic
273C2×C8C23×D1111yescharacteristic
274C4⋊C4—22no—
275C4⋊C4—41no—
276C4⋊C4—111no—
277C4⋊C4—112no—
278C4⋊C4—221no—
279C4⋊C4—221no—
280C4⋊C4—442no—
281C4⋊C4—442no—
282C4⋊C4—442no—
283C4⋊C4—441no—
284C22⋊C4—442no—
285C22⋊C4—441no—
286C42—112no—
287C42—442no—
288C42—441no—
289C42D4×D1111yescharacteristic
290C16—21no—
291C16—21no—
292C16—222no—
293C11#3393511yescharacteristic, complemented, Sylow
294C23—42no—
295C23—441no—
296Q8—82no—
297Q8—222no—
298Q8—222no—
299Q8—441no—
300D4—42no—
301D4—42no—
302D4—82no—
303D4—161no—
304D4—441no—
305D4—441no—
306D4—884no—
307D4—1762no—
308C2×C4—42no—
309C2×C4—112no—
310C2×C4—112no—
311C2×C4—441no—
312C2×C4—441no—
313C2×C4—441no—
314C2×C4—884no—
315C2×C4—882no—
316C2×C4D8×D1111yescharacteristic
317C2×C4D8×D1111yescharacteristic
318C2×C4C2×D4×D1111yescharacteristic
319C8—21no—
320C8—222no—
321C8#41×D1111yescharacteristic
322C8#6704311yescharacteristic
323C22—82no—
324C22—82no—
325C22—82no—
326C22—881no—
327C22—881no—
328C22—881no—
329C22C2×D8×D1111yescharacteristic
330C4—21no—
331C4—82no—
332C4—222no—
333C4—222no—
334C4—442no—
335C4—881no—
336C4—881no—
337C4#1062252412yes—
338C4#1062320811yescharacteristic
339C4#1062329311yescharacteristic
340C2—162no—
341C2—1761no—
342C2#1308124811yescharacteristic
343C2C2×#1062252411yescharacteristic
344C2#1308175811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2240C2
socleC22×C11C22×D8
prime radical#13081589C2
hypercenter#2240D11
hypocenterC11#33935
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2240

Complements

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

NH ≅ G/Ntype
2. #13081509C2semidirect
3. #13070856C2semidirect
4. #13070775C2semidirect
5. #13070750C2semidirect
6. #13070655C2semidirect
7. #13070653C2semidirect
8. #13070524C2semidirect
9. #13070477C2semidirect
10. C4×#66864C2semidirect
11. C11×#2240C2semidirect
116. Dic44#41semidirect
125. #2240D11semidirect
293. C11#33935semidirect

Maximal subgroups

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

subgroupindex
#130815892
#130815092
#130708562
#130707752
#130707502
#130706552
#130706532
#130705242
#130704772
C4×#668642
C11×#22402
#3393511