Finite Group Databasebeta

← #14911514

Subgroups — #14911514

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#13081591C211yesmaximal, characteristic
2#13081508C211yesmaximal, characteristic, complemented
3#13070858C212yesmaximal, complemented
4#13070840C211yesmaximal, characteristic, complemented
5#13070774C212yesmaximal, complemented
6#13070754C211yesmaximal, characteristic, complemented
7#13070657C211yesmaximal, characteristic, complemented
8#13070657C212yesmaximal, complemented
9#13070482C212yesmaximal, complemented
10C4×#66864C211yesmaximal, characteristic, complemented
11C11×#2183C211yesmaximal, characteristic, complemented
12#10623108—21no—
13#10623098—21no—
14C8×Q8×C11C2211yescharacteristic
15C2×#66864C2211yescharacteristic
16C2×#66864C2212yes—
17#10622464—21no—
18#10622456—21no—
19#10622456—22no—
20#10622442—22no—
21C4×Dic44C2211yescharacteristic
22C4×Dic44C2212yes—
23#10622308C2212yes—
24#10622308C2211yescharacteristic
25C4×D88C2211yescharacteristic
26C4×D88C2212yes—
27#10622296C2212yes—
28#10622295C2211yescharacteristic
29C11×C4⋊C16C2211yescharacteristic
30C11×C4⋊C16C2212yes—
31C11×#346C2212yes—
32C4×C11×C16C2211yescharacteristic
33#10622147C2211yescharacteristic
34#10622147C2212yes—
35#10622147C2212yes—
36#10622147C2212yes—
37#10622147C2212yes—
38#10622143C2211yescharacteristic
39#10622142C2212yes—
40#10622141C2211yescharacteristic
41C2×#4343—41no—
42C4×Q8×C11D411yescharacteristic
43#66997—41no—
44C2×Dic44C2311yescharacteristic
45C2×D88—22no—
46C2×D88—21no—
47C2×D88C2311yescharacteristic
48C2×D88C2312yes—
49#66948—41no—
50#66948—42no—
51#66942—42no—
52#66940—41no—
53#66927—21no—
54#66927—22no—
55C4×D44—21no—
56C4×D44—22no—
57#66923—22no—
58#66922—21no—
59C4×Dic22—21no—
60C4×Dic22—22no—
61C2×C11×C16C2311yescharacteristic
62C2×C11×C16C2311yescharacteristic
63C2×C11×C16C2312yes—
64C11×C4⋊C8D411yescharacteristic
65C11×C4⋊C8D412yes—
66C4×C8×C11C2311yescharacteristic
67C4×C8×C11C2312yes—
68#66885—22no—
69#66885—21no—
70#66882—21no—
71#66882C2312yes—
72#66882C2311yescharacteristic
73#66882C2311yescharacteristic
74#66881—22no—
75#66880—22no—
76#66880—21no—
77#66864—22no—
78#66864—24no—
79#33935—111nomaximal, Sylow
80C2×Q8×C11D811yescharacteristic
81#4343—84no—
82C2×D44—22no—
83C2×D44—21no—
84C2×D44—42no—
85C2×D44—41no—
86C2×D44—42no—
87C2×D44—41no—
88C2×C4×D11—42no—
89C2×C4×D11—41no—
90C2×Dic22—21no—
91C2×Dic22—41no—
92C2×C8×C11C2×D412yes—
93C2×C8×C11C2×D411yescharacteristic
94C2×C8×C11C2411yescharacteristic
95C11×C4⋊C4D811yescharacteristic
96C11×C4⋊C4D812yes—
97C42×C11C2×D411yescharacteristic
98C42×C11C2×D412yes—
99(C2×D11)⋊C4—42no—
100(C2×D11)⋊C4—41no—
101C4⋊Dic11—21no—
102C4⋊Dic11—22no—
103C4⋊Dic11—21no—
104C4⋊Dic11—41no—
105Dic11⋊C4—41no—
106Dic11⋊C4—42no—
107Dic11⋊C4—42no—
108Dic11⋊C4—42no—
109C4×Dic11—42no—
110C4×Dic11—41no—
111Dic44—21no—
112Dic44#4112yescomplemented
113D88—21no—
114D88—22no—
115D88—21no—
116D88—22no—
117D88—82no—
118D88—81no—
119C11×C16—21no—
120C11×C16—22no—
121C11×C16—21no—
122#3391—111no—
123#3383—111no—
124#2244—112no—
125#2240—111no—
126#2228—112no—
127#2224—111no—
128#2207—112no—
129#2207—111no—
130#2183D1111yescharacteristic, complemented
131#2175—112no—
132C4×SD32—111no—
133C22×D11—42no—
134C22×D11—41no—
135Q8×C11—22no—
136C2×C4×C11C2×D812yes—
137C2×C4×C11C2×D812yes—
138C2×C4×C11C2×D811yescharacteristic
139C2×C4×C11C2×D811yescharacteristic
140C2×C4×C11C22×D411yescharacteristic
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—42no—
144C2×Dic11—41no—
145D44—41no—
146D44—42no—
147D44—41no—
148D44—42no—
149D44—84no—
150D44—82no—
151D44—162no—
152D44—161no—
153C4×D11—84no—
154C4×D11—82no—
155Dic22—22no—
156Dic22—41no—
157Dic22—82no—
158C8×C11—22no—
159C8×C11—21no—
160C8×C11C2×#4111yescharacteristic
161C8×C112−1+411yescharacteristic
162#557—221no—
163#550—221no—
164C2×SD32—111no—
165C2×SD32—112no—
166#500—111no—
167#499—112no—
168#493—111no—
169#493—112no—
170#479—222no—
171#475—221no—
172#459—221no—
173#459—222no—
174C8×Q8C2×D1111yescharacteristic
175C4×Q16—111no—
176C4×Q16—112no—
177C4×D8—111no—
178C4×D8—112no—
179#367—111no—
180#366—112no—
181C4⋊C16C2×D1111yescharacteristic
182C4⋊C16C2×D1112yes—
183#358—111no—
184#357—111no—
185#357—112no—
186#357—112no—
187#357—112no—
188#357—112no—
189#346C2×D1112yes—
190C4×C16C2×D1111yescharacteristic
191C22×C11C22×D811yescharacteristic
192C2×D11—82no—
193C2×D11—81no—
194C2×D11—82no—
195C2×D11—81no—
196C2×D11—82no—
197C2×D11—81no—
198C4×C11—22no—
199C4×C11—22no—
200C4×C11—21no—
201C4×C11#50912yes—
202C4×C11#54811yescharacteristic
203C4×C11#57711yescharacteristic
204Dic11—42no—
205Dic11—82no—
206Dic11—81no—
207Dic11—81no—
208C2×#41—441no—
209C2×Q16—111no—
210C2×D8—111no—
211C2×D8—112no—
212C2×D8—222no—
213C2×D8—221no—
214C4⋊Q8—221no—
215C4⋊Q8—441no—
216#127—222no—
217#127—221no—
218#125—222no—
219#125—442no—
220#121—441no—
221#121—442no—
222C4×Q8—221no—
223C4×Q8—222no—
224C4×Q8—441no—
225C4×Q8D4411yescharacteristic
226C4×D4—222no—
227C4×D4—221no—
228SD32—222no—
229SD32—224no—
230C2×C16C22×D1111yescharacteristic
231C2×C16C22×D1111yescharacteristic
232C2×C16C22×D1112yes—
233#107—112no—
234#107—111no—
235#107—111no—
236#107—221no—
237#106—222no—
238C4⋊C8D4411yescharacteristic
239C4⋊C8D4412yes—
240#103—222no—
241#103—221no—
242#102—222no—
243#102—221no—
244C4×C8C22×D1111yescharacteristic
245C4×C8C22×D1112yes—
246C2×C11#335811yescharacteristic
247C2×C11C2×#50911yescharacteristic
248C2×C11#341611yescharacteristic
249D11—162no—
250D11—161no—
251#41—884no—
252C2×Q8—221no—
253C2×Q8—441no—
254C2×Q8D8811yescharacteristic
255C2×D4—222no—
256C2×D4—221no—
257C2×D4—442no—
258C2×D4—441no—
259C2×D4—442no—
260C2×D4—441no—
261C22×C4—442no—
262C22×C4—441no—
263Q16—112no—
264Q16—221no—
265D8—221no—
266D8—222no—
267D8—221no—
268D8—222no—
269D8—882no—
270D8—881no—
271C2×C8C2×D4412yes—
272C2×C8C2×D4411yescharacteristic
273C2×C8C23×D1111yescharacteristic
274C4⋊C4—221no—
275C4⋊C4—221no—
276C4⋊C4—222no—
277C4⋊C4—441no—
278C4⋊C4—442no—
279C4⋊C4—442no—
280C4⋊C4—442no—
281C4⋊C4—441no—
282C4⋊C4D8811yescharacteristic
283C4⋊C4D8812yes—
284C22⋊C4—442no—
285C22⋊C4—441no—
286C42—442no—
287C42—441no—
288C42C2×D4412yes—
289C42C2×D4411yescharacteristic
290C16—21no—
291C16—21no—
292C16—22no—
293C11#3393511yescharacteristic, complemented, Sylow
294C23—442no—
295C23—441no—
296Q8—22no—
297Q8—222no—
298Q8—441no—
299Q8—882no—
300D4—441no—
301D4—442no—
302D4—441no—
303D4—442no—
304D4—884no—
305D4—882no—
306D4—1762no—
307D4—1761no—
308C2×C4—441no—
309C2×C4—441no—
310C2×C4—442no—
311C2×C4—441no—
312C2×C4—884no—
313C2×C4—882no—
314C2×C4C2×D8812yes—
315C2×C4C2×D8811yescharacteristic
316C2×C4C2×D8812yes—
317C2×C4C2×D8811yescharacteristic
318C2×C4C22×D4411yescharacteristic
319C8—22no—
320C8—21no—
321C8#6704011yescharacteristic
322C8#41×D1111yescharacteristic
323C22—882no—
324C22—881no—
325C22—882no—
326C22—881no—
327C22—882no—
328C22—881no—
329C22C22×D8811yescharacteristic
330C4—22no—
331C4—22no—
332C4—21no—
333C4—442no—
334C4—881no—
335C4—882no—
336C4—881no—
337C4#1062252112yes—
338C4#1062310711yescharacteristic
339C4#1062328211yescharacteristic
340C2—1762no—
341C2—1761no—
342C2#1308125211yescharacteristic
343C2C2×#1062252111yescharacteristic
344C2#1308176411yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2183C2
socleC22×C11C22×D8
prime radical#13081591C2
hypercenter#2183D11
hypocenterC11#33935
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×Q8 ◁ C8×Q8 ◁ #2183

Complements

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

NH ≅ G/Ntype
2. #13081508C2semidirect
3. #13070858C2semidirect
4. #13070840C2semidirect
5. #13070774C2semidirect
6. #13070754C2semidirect
7. #13070657C2semidirect
8. #13070657C2semidirect
9. #13070482C2semidirect
10. C4×#66864C2semidirect
11. C11×#2183C2semidirect
112. Dic44#41semidirect
130. #2183D11semidirect
293. C11#33935semidirect

Maximal subgroups

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

subgroupindex
#130815912
#130815082
#130708582
#130708402
#130707742
#130707542
#130706572
#130704822
C4×#668642
C11×#21832
#3393511