Finite Group Databasebeta

← #14911577

Subgroups — #14911577

Order 2816.

520 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#13081629C211yesmaximal, characteristic, complemented
2Q8×D88C211yesmaximal, characteristic, complemented
3#13070853C212yesmaximal, complemented
4#13070840C211yesmaximal, characteristic, complemented
5#13070764C212yesmaximal, complemented
6#13070759C211yesmaximal, characteristic, complemented
7#13070672C212yesmaximal, complemented
8#13070652C211yesmaximal, characteristic
9#13070493C212yesmaximal, complemented
10C4×#66864C211yesmaximal, characteristic, complemented
11C11×#2183C211yesmaximal, characteristic, complemented
12#10623116—21no—
13Q8×D44—21no—
14C8×Q8×C11C2211yescharacteristic
15C2×#66864C2211yescharacteristic
16C2×D176C2212yes—
17#10622461—21no—
18#10622459—22no—
19#10622459—21no—
20#10622457—22no—
21C4×Dic44C2211yescharacteristic
22#10622309C2212yes—
23#10622308C2211yescharacteristic
24C4×D88C2212yes—
25C4×D88C2211yescharacteristic
26C4×D88C2212yes—
27#10622295C2212yes—
28#10622295C2211yescharacteristic
29C11×C4⋊C16C2211yescharacteristic
30C11×C4⋊C16C2212yes—
31C11×#346C2212yes—
32C4×C11×C16C2211yescharacteristic
33#10622147C2212yes—
34#10622147C2212yes—
35#10622147C2212yes—
36#10622147C2211yescharacteristic
37#10622143C2211yescharacteristic
38#10622143C2212yes—
39#10622141C2211yescharacteristic
40#10622141C2212yes—
41C2×Q8×D11—41no—
42C4×Q8×C11D411yescharacteristic
43#67000—41no—
44C2×Dic44C2311yescharacteristic
45C2×D88—21no—
46C2×D88C2312yes—
47C2×D88C2311yescharacteristic
48C2×#4314—22no—
49#66950—41no—
50#66950—42no—
51#66947—42no—
52#66946—41no—
53#66928—22no—
54#66927—21no—
55C4×D44—21no—
56C4×D44—22no—
57C4×D44—22no—
58#66922—21no—
59#66922—22no—
60C4×Dic22—21no—
61C2×C11×C16C2311yescharacteristic
62C2×C11×C16C2311yescharacteristic
63C2×C11×C16C2312yes—
64C11×C4⋊C8D412yes—
65C11×C4⋊C8D411yescharacteristic
66C4×C8×C11C2311yescharacteristic
67C4×C8×C11C2312yes—
68#66885—22no—
69#66885—21no—
70#66885—22no—
71#66882—21no—
72#66882—22no—
73#66882C2311yescharacteristic
74#66882C2312yes—
75#66882C2311yescharacteristic
76#66880—21no—
77#66864—22no—
78D176—24no—
79#33940—111nomaximal, Sylow
80C2×Q8×C11D811yescharacteristic
81Q8×D11—84no—
82C2×D44—21no—
83C2×D44—22no—
84C2×D44—41no—
85C2×D44—41no—
86C2×C4×D11—42no—
87C2×C4×D11—41no—
88C2×C4×D11—42no—
89C2×Dic22—21no—
90C2×Dic22—42no—
91C2×Dic22—41no—
92C2×C8×C11C2×D411yescharacteristic
93C2×C8×C11C2×D412yes—
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—
101(C2×D11)⋊C4—42no—
102(C2×D11)⋊C4—42no—
103(C2×D11)⋊C4—42no—
104C4⋊Dic11—21no—
105C4⋊Dic11—22no—
106C4⋊Dic11—21no—
107C4⋊Dic11—41no—
108C4⋊Dic11—42no—
109Dic11⋊C4—41no—
110C4×Dic11—41no—
111Dic44—21no—
112Dic44—21no—
113D88—22no—
114D88—21no—
115D88—22no—
116D88—81no—
117D88#4112yes—
118#4314—82no—
119C11×C16—22no—
120C11×C16—21no—
121C11×C16—21no—
122#3396—111no—
123Q8×D8—111no—
124#2243—112no—
125#2240—111no—
126#2226—112no—
127#2225—111no—
128#2210—112no—
129#2206—111no—
130#2183D1111yescharacteristic, complemented
131#2177—112no—
132C4×SD32—111no—
133C22×D11—41no—
134C22×D11—42no—
135Q8×C11—22no—
136C2×C4×C11C2×D811yescharacteristic
137C2×C4×C11C2×D812yes—
138C2×C4×C11C2×D812yes—
139C2×C4×C11C2×D811yescharacteristic
140C2×C4×C11C22×D411yescharacteristic
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—42no—
145D44—22no—
146D44—42no—
147D44—41no—
148D44—42no—
149D44—82no—
150D44—161no—
151C4×D11—84no—
152C4×D11—82no—
153C4×D11—162no—
154Dic22—41no—
155Dic22—41no—
156Dic22—84no—
157Dic22—82no—
158C8×C11—22no—
159C8×C11—21no—
160C8×C11C2×#4111yescharacteristic
161C8×C112−1+411yescharacteristic
162#559—221no—
163D4×Q8—221no—
164C2×SD32—111no—
165C2×D16—112no—
166#500—111no—
167#500—112no—
168#495—112no—
169#493—111no—
170#474—221no—
171#474—222no—
172#463—222no—
173#460—221no—
174C8×Q8C2×D1111yescharacteristic
175C4×Q16—111no—
176C4×D8—111no—
177C4×D8—112no—
178C4×D8—112no—
179#367—111no—
180#367—112no—
181C4⋊C16C2×D1111yescharacteristic
182C4⋊C16C2×D1112yes—
183#358—111no—
184#358—112no—
185#357—111no—
186#357—112no—
187#357—112no—
188#357—112no—
189#346C2×D1112yes—
190C4×C16C2×D1111yescharacteristic
191C22×C11C22×D811yescharacteristic
192C2×D11—42no—
193C2×D11—81no—
194C2×D11—81no—
195C2×D11—82no—
196C2×D11—82no—
197C2×D11—82no—
198C4×C11—22no—
199C4×C11—22no—
200C4×C11—21no—
201C4×C11#50912yes—
202C4×C11#54811yescharacteristic
203C4×C11#57711yescharacteristic
204Dic11—81no—
205Dic11—81no—
206Dic11—82no—
207Dic11—81no—
208C22×Q8—441no—
209C2×Q16—111no—
210C2×SD16—222no—
211C2×D8—111no—
212C2×D8—112no—
213C2×D8—221no—
214C4⋊Q8—222no—
215C4⋊Q8—221no—
216#127—221no—
217#124—222no—
218#124—441no—
219#123—442no—
220C22⋊Q8—441no—
221C22⋊Q8—442no—
222C4×Q8—221no—
223C4×Q8D4411yescharacteristic
224C4×D4—222no—
225C4×D4—221no—
226C4×D4—222no—
227C4×D4—441no—
228SD32—222no—
229D16—224no—
230C2×C16C22×D1111yescharacteristic
231C2×C16C22×D1111yescharacteristic
232C2×C16C22×D1112yes—
233#107—112no—
234#107—111no—
235#107—111no—
236#107—222no—
237#107—221no—
238C4⋊C8D4411yescharacteristic
239C4⋊C8D4412yes—
240#103—221no—
241#102—222no—
242#102—222no—
243#102—221no—
244C4×C8C22×D1111yescharacteristic
245C4×C8C22×D1112yes—
246C2×C11#335811yescharacteristic
247C2×C11C2×#50911yescharacteristic
248C2×C11#341611yescharacteristic
249D11—82no—
250D11—162no—
251C2×Q8—221no—
252C2×Q8—442no—
253C2×Q8—441no—
254C2×Q8—884no—
255C2×Q8D8811yescharacteristic
256C2×D4—221no—
257C2×D4—222no—
258C2×D4—441no—
259C2×D4—441no—
260C22×C4—442no—
261C22×C4—441no—
262C22×C4—442no—
263Q16—221no—
264Q16—221no—
265SD16—882no—
266D8—112no—
267D8—221no—
268D8—222no—
269D8—222no—
270D8—881no—
271C2×C8C2×D4412yes—
272C2×C8C2×D4411yescharacteristic
273C2×C8C23×D1111yescharacteristic
274C4⋊C4—221no—
275C4⋊C4—222no—
276C4⋊C4—221no—
277C4⋊C4—441no—
278C4⋊C4—442no—
279C4⋊C4—441no—
280C4⋊C4D8811yescharacteristic
281C4⋊C4D8812yes—
282C22⋊C4—442no—
283C22⋊C4—441no—
284C22⋊C4—442no—
285C22⋊C4—442no—
286C22⋊C4—442no—
287C42—441no—
288C42C2×D4412yes—
289C42C2×D4411yescharacteristic
290C16—21no—
291C16—22no—
292C16—21no—
293C11#3394011yescharacteristic, complemented, Sylow
294C23—441no—
295C23—442no—
296Q8—22no—
297Q8—441no—
298Q8—441no—
299Q8—884no—
300Q8—882no—
301D4—222no—
302D4—441no—
303D4—442no—
304D4—442no—
305D4—882no—
306D4—1761no—
307C2×C4—441no—
308C2×C4—441no—
309C2×C4—442no—
310C2×C4—441no—
311C2×C4—884no—
312C2×C4—882no—
313C2×C4—1762no—
314C2×C4C2×D8812yes—
315C2×C4C2×D8812yes—
316C2×C4C2×D8811yescharacteristic
317C2×C4C2×D8811yescharacteristic
318C2×C4C22×D4411yescharacteristic
319C8—21no—
320C8—22no—
321C8#6704011yescharacteristic
322C8#41×D1111yescharacteristic
323C22—442no—
324C22—881no—
325C22—881no—
326C22—882no—
327C22—882no—
328C22—882no—
329C22C22×D8811yescharacteristic
330C4—22no—
331C4—22no—
332C4—21no—
333C4—882no—
334C4—881no—
335C4—881no—
336C4—881no—
337C4#1062252112yes—
338C4#1062310711yescharacteristic
339C4#1062328211yescharacteristic
340C2—882no—
341C2—1762no—
342C2#1308125211yescharacteristic
343C2C2×#1062252111yescharacteristic
344C2#1308176411yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2183C2
socleC22×C11C22×D8
prime radical#13070652C2
hypercenter#2183D11
hypocenterC11#33940
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
1. #13081629C2semidirect
2. Q8×D88C2semidirect
3. #13070853C2semidirect
4. #13070840C2semidirect
5. #13070764C2semidirect
6. #13070759C2semidirect
7. #13070672C2semidirect
9. #13070493C2semidirect
10. C4×#66864C2semidirect
11. C11×#2183C2semidirect
130. #2183D11semidirect
293. C11#33940semidirect

Maximal subgroups

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

subgroupindex
#130816292
Q8×D882
#130708532
#130708402
#130707642
#130707592
#130706722
#130706522
#130704932
C4×#668642
C11×#21832
#3394011