Finite Group Databasebeta

← #14911499

Subgroups — #14911499

Order 2816.

508 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081602C211yesmaximal, characteristic, complemented
2D8×Dic22C211yesmaximal, characteristic, complemented
3#13070851C212yesmaximal, complemented
4#13070844C211yesmaximal, characteristic, complemented
5#13070767C212yesmaximal, complemented
6#13070753C211yesmaximal, characteristic, complemented
7#13070669C212yesmaximal
8#13070661C211yesmaximal, characteristic, complemented
9#13070524C211yesmaximal, characteristic, complemented
10#13070477C212yesmaximal, complemented
11C4×C11×D16C211yesmaximal, characteristic
12#10623073—21no—
13D4×Dic22—21no—
14C2×C11×D16C2211yescharacteristic
15C4×C11×D8C2211yescharacteristic
16C4×C11×D8C2211yescharacteristic
17#10622768C2212yes—
18D8×Dic11C2212yes—
19C2×#66891C2212yes—
20#10622632—21no—
21#10622620—21no—
22#10622487C2212yes—
23#10622486C2212yes—
24#10622380—22no—
25#10622372—22no—
26#10622312C2211yescharacteristic
27#10622295C2211yescharacteristic
28C8×Dic22C2211yescharacteristic
29C11×#366C2211yescharacteristic
30C11×#357C2211yescharacteristic
31C11×#357C2211yescharacteristic
32C4×C11×C16C2211yescharacteristic
33#10622200C2212yes—
34#10622141C2212yes—
35#10622141C2212yes—
36#10622140C2212yes—
37Dic11⋊C16C2212yes—
38#10622130C2212yes—
39#10622127C2212yes—
40C4⋊(C11⋊C16)C2211yescharacteristic
41C22×Dic22—41no—
42C2×C11×D8C2311yescharacteristic
43C2×C11×D8C2311yescharacteristic
44C4×D4×C11—21no—
45C4×D4×C11—21no—
46#66989—22no—
47D4×Dic11—22no—
48C2×#4324—22no—
49#66979—41no—
50#66977—41no—
51#66977—41no—
52C2×Dic44—21no—
53C2×Dic44C2312yes—
54#66941—22no—
55#66940—22no—
56#66932—42no—
57#66931—42no—
58#66922—21no—
59#66922—21no—
60C4×Dic22D411yescharacteristic
61C11×D16—22no—
62C2×C11×C16C2311yescharacteristic
63C2×C11×C16C2311yescharacteristic
64C11×#107C2311yescharacteristic
65C11×#107C2311yescharacteristic
66C11×#102—21no—
67C11×#102—21no—
68C4×C8×C11C2311yescharacteristic
69#66896—22no—
70#66891—24no—
71#66882—21no—
72#66882C2312yes—
73Dic11⋊C8D412yes—
74C8×Dic11C2312yes—
75C2×C11⋊C16C2312yes—
76#66874—22no—
77#66871—22no—
78C4⋊(C11⋊C8)D411yescharacteristic
79#33934—111nomaximal, Sylow
80C2×D4×C11—21no—
81C2×D4×C11—21no—
82C22×C4×C11—41no—
83C22×C4×C11—41no—
84C22×Dic11—42no—
85C2×Dic22—22no—
86C2×Dic22—42no—
87C2×Dic22—41no—
88C2×Dic22—84no—
89C2×Dic22D811yescharacteristic
90C11×D8—21no—
91C11×D8—21no—
92C11×D8—21no—
93C11×D8#4112yes—
94C2×C8×C11C2×D411yescharacteristic
95C2×C8×C11C2411yescharacteristic
96C11×C4⋊C4—21no—
97C11×C4⋊C4—21no—
98C11×C22⋊C4—41no—
99C11×C22⋊C4—41no—
100C42×C11C2×D411yescharacteristic
101C22⋊Dic11—42no—
102C22⋊Dic11—42no—
103C22⋊Dic11—42no—
104#4324—82no—
105C4⋊Dic11—22no—
106C4⋊Dic11—41no—
107C4⋊Dic11—41no—
108C4⋊Dic11—41no—
109C4⋊Dic11D811yescharacteristic
110Dic11⋊C4—42no—
111Dic11⋊C4—42no—
112Dic11⋊C4D812yes—
113C4×Dic11—42no—
114C4×Dic11C2×D412yes—
115C2×C11⋊C8C2×D412yes—
116Dic44—22no—
117Dic44—22no—
118Dic44—81no—
119C11×C16—21no—
120C11×C16—21no—
121C11⋊C16—22no—
122#3393—111no—
123Q8×D8—111no—
124#2243—112no—
125#2241—111no—
126#2227—112no—
127#2224—111no—
128#2210—112no—
129#2208—111no—
130#2183—111no—
131#2175—112no—
132C4×D16D1111yescharacteristic
133C23×C11—41no—
134C23×C11—41no—
135D4×C11—22no—
136D4×C11—41no—
137D4×C11—41no—
138D4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—82no—
142C2×C4×C11—82no—
143C2×C4×C11C2×D811yescharacteristic
144C2×C4×C11C2×D811yescharacteristic
145C2×C4×C11C22×D411yescharacteristic
146C2×Dic11—42no—
147C2×Dic11—42no—
148C2×Dic11—84no—
149C2×Dic11C2×D812yes—
150C2×Dic11C2×D812yes—
151Dic22—22no—
152Dic22—42no—
153Dic22—42no—
154Dic22—84no—
155Dic22—82no—
156C8×C11—21no—
157C8×C11C2×#4111yescharacteristic
158C8×C112−1+411yescharacteristic
159C11⋊C8—22no—
160#556—221no—
161D4×Q8—221no—
162C2×SD32—112no—
163C2×D16C2×D1111yescharacteristic
164#500—112no—
165#500—111no—
166#495—112no—
167#494—111no—
168#474—222no—
169#474—221no—
170#464—222no—
171#461—221no—
172C8×Q8—111no—
173C4×Q16—112no—
174C4×D8—112no—
175C4×D8C2×D1111yescharacteristic
176C4×D8C2×D1111yescharacteristic
177#366—112no—
178#366C2×D1111yescharacteristic
179C4⋊C16—112no—
180C4⋊C16—111no—
181#358—112no—
182#358—112no—
183#358—112no—
184#357—112no—
185#357C2×D1111yescharacteristic
186#357C2×D1111yescharacteristic
187#346—112no—
188C4×C16C2×D1111yescharacteristic
189C22×C11—42no—
190C22×C11—81no—
191C22×C11—81no—
192C22×C11—81no—
193C22×C11—81no—
194C22×C11—81no—
195C22×C11C22×D811yescharacteristic
196C4×C11—21no—
197C4×C11—81no—
198C4×C11—81no—
199C4×C11#50912yes—
200C4×C11#54811yescharacteristic
201C4×C11#57711yescharacteristic
202Dic11—22no—
203Dic11—22no—
204Dic11—82no—
205Dic11—82no—
206C22×Q8—441no—
207C2×Q16—112no—
208C2×Q16—221no—
209C2×SD16—222no—
210C2×D8C22×D1111yescharacteristic
211C2×D8C22×D1111yescharacteristic
212C4⋊Q8—222no—
213C4⋊Q8—221no—
214C4⋊Q8—221no—
215#126—442no—
216#124—222no—
217C22⋊Q8—442no—
218C22⋊Q8—441no—
219C22⋊Q8—441no—
220C4×Q8—111no—
221C4×Q8—222no—
222C4×D4—21no—
223C4×D4—21no—
224C4×D4—222no—
225#117—441no—
226SD32—224no—
227D16—22no—
228C2×C16—112no—
229C2×C16C22×D1111yescharacteristic
230C2×C16C22×D1111yescharacteristic
231#107—112no—
232#107—222no—
233#107—221no—
234#107C22×D1111yescharacteristic
235#107C22×D1111yescharacteristic
236C4⋊C8—112no—
237C4⋊C8—111no—
238#103—222no—
239#102—21no—
240#102—21no—
241#102—222no—
242C4×C8—112no—
243C4×C8C22×D1111yescharacteristic
244C2×C11—82no—
245C2×C11—161no—
246C2×C11#335811yescharacteristic
247C2×C11C2×#50911yescharacteristic
248C2×C11#341711yescharacteristic
249C2×Q8—111no—
250C2×Q8—222no—
251C2×Q8—442no—
252C2×Q8—441no—
253C2×Q8—884no—
254C2×D4—21no—
255C2×D4—21no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4—442no—
259Q16—222no—
260Q16—222no—
261Q16—881no—
262SD16—882no—
263D8—21no—
264D8—21no—
265D8—21no—
266D8#433912yes—
267C2×C8—112no—
268C2×C8D4×D1111yescharacteristic
269C2×C8C23×D1111yescharacteristic
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—111no—
273C4⋊C4—112no—
274C4⋊C4—222no—
275C4⋊C4—442no—
276C4⋊C4—442no—
277C4⋊C4—441no—
278C4⋊C4—441no—
279C4⋊C4—441no—
280C22⋊C4—41no—
281C22⋊C4—41no—
282C22⋊C4—442no—
283C22⋊C4—442no—
284C22⋊C4—442no—
285C42—112no—
286C42—442no—
287C42D4×D1111yescharacteristic
288C16—21no—
289C16—21no—
290C16—222no—
291C11#3393411yescharacteristic, complemented, Sylow
292C23—41no—
293C23—41no—
294Q8—222no—
295Q8—442no—
296Q8—442no—
297Q8—884no—
298Q8—882no—
299D4—22no—
300D4—41no—
301D4—41no—
302D4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—82no—
306C2×C4—82no—
307C2×C4—112no—
308C2×C4—112no—
309C2×C4—442no—
310C2×C4—442no—
311C2×C4—884no—
312C2×C4D8×D1111yescharacteristic
313C2×C4D8×D1111yescharacteristic
314C2×C4C2×D4×D1111yescharacteristic
315C8—21no—
316C8—222no—
317C8C2×#433911yescharacteristic
318C8#6704311yescharacteristic
319C22—42no—
320C22—81no—
321C22—81no—
322C22—81no—
323C22—81no—
324C22—81no—
325C22C2×D8×D1111yescharacteristic
326C4—21no—
327C4—81no—
328C4—81no—
329C4—222no—
330C4—222no—
331C4—882no—
332C4—882no—
333C4#1062252412yes—
334C4#1062308311yescharacteristic
335C4#1062330111yescharacteristic
336C2—82no—
337C2—161no—
338C2#1308124911yescharacteristic
339C2C2×#1062252411yescharacteristic
340C2#1308176611yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC4×C11×D16C2
socleC22×C11C22×D8
prime radicalC2×C11×D16C22
hypercenterC4×D16D11
hypocenterC11#33934
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ C4×D16

Complements

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

NH ≅ G/Ntype
1. #13081602C2semidirect
2. D8×Dic22C2semidirect
3. #13070851C2semidirect
4. #13070844C2semidirect
5. #13070767C2semidirect
6. #13070753C2semidirect
8. #13070661C2semidirect
9. #13070524C2semidirect
10. #13070477C2semidirect
291. C11#33934semidirect

Maximal subgroups

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

subgroupindex
#130816022
D8×Dic222
#130708512
#130708442
#130707672
#130707532
#130706692
#130706612
#130705242
#130704772
C4×C11×D162
#3393411