Finite Group Databasebeta

← #14658356

Subgroups — #14658356

Order 2816.

370 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13069578C211yesmaximal, characteristic
2#13069565C211yesmaximal, characteristic
3#13069380C211yesmaximal, characteristic
4#13069332C211yesmaximal, characteristic
5C2×#10622118C211yesmaximal, characteristic
6#13066500C211yesmaximal, characteristic
7C2×C11×#333C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C11×C4⋊C8C2211yescharacteristic
10C2×C11×C4⋊C8C2211yescharacteristic
11C2×#66881—21no—
12C2×Dic11⋊C8—21no—
13#10622548C2211yescharacteristic
14C4×C4⋊Dic11C2211yescharacteristic
15C2×C4⋊(C11⋊C8)C2211yescharacteristic
16C2×C4×C11⋊C8C2211yescharacteristic
17C11×#333—22no—
18#10622189—21no—
19#10622188—21no—
20#10622167—21no—
21#10622167—21no—
22#10622167—21no—
23#10622167—21no—
24#10622118—22no—
25C22×Q8×C11—21no—
26C22×C8×C11—21no—
27C22×C8×C11—21no—
28C11×C4⋊Q8—21no—
29C11×C4⋊Q8—21no—
30C11×C4⋊Q8—21no—
31C11×C4⋊Q8Q812yes—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—21no—
34C2×C42×C11C2311yescharacteristic
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11—21no—
38C2×C4⋊Dic11D411yescharacteristic
39C2×C4⋊Dic11D411yescharacteristic
40C2×C4×Dic11—21no—
41C22×C11⋊C8—21no—
42C22×C11⋊C8D411yescharacteristic
43C22×C11⋊C8D411yescharacteristic
44C11×C4⋊C8—21no—
45C11×C4⋊C8—21no—
46C11×C4⋊C8—21no—
47C11×C4⋊C8D412yes—
48C11⋊#95—21no—
49#66881—42no—
50Dic11⋊C8—42no—
51C4⋊(C11⋊C8)—21no—
52C4⋊(C11⋊C8)—21no—
53C4×C11⋊C8—21no—
54C4×C11⋊C8—21no—
55#10597—111nomaximal, Sylow
56C2×Q8×C11—22no—
57C2×Q8×C11—41no—
58C2×Q8×C11—81no—
59C2×Q8×C11—81no—
60C22×C4×C11—41no—
61C22×C4×C11C2×D411yescharacteristic
62C22×C4×C11C2×D411yescharacteristic
63C22×C4×C11#4111yescharacteristic
64C22×Dic11—21no—
65C22×Dic11—21no—
66C22×Dic11—41no—
67C2×C8×C11—22no—
68C2×C8×C11—41no—
69C2×C8×C11—41no—
70C2×C8×C11—41no—
71C2×C8×C11—41no—
72C2×C8×C11—41no—
73C11×C4⋊C4—22no—
74C11×C4⋊C4—22no—
75C11×C4⋊C4—41no—
76C11×C4⋊C4—41no—
77C42×C11C2×D411yescharacteristic
78C42×C11C2×Q811yescharacteristic
79C42×C11#4111yescharacteristic
80C42×C11#4111yescharacteristic
81C4⋊Dic11—21no—
82C4⋊Dic11—21no—
83C4⋊Dic11—21no—
84C4⋊Dic11—41no—
85C4⋊Dic11—41no—
86C4⋊Dic11—41no—
87C4⋊Dic11—41no—
88C4⋊Dic11—81no—
89C4⋊Dic11SD1612yes—
90C4×Dic11—41no—
91C4×Dic11—41no—
92C2×C11⋊C8—21no—
93C2×C11⋊C8—21no—
94C2×C11⋊C8—21no—
95C2×C11⋊C8—21no—
96C2×C11⋊C8—21no—
97C2×C11⋊C8—41no—
98C2×C11⋊C8—41no—
99C2×C11⋊C8—41no—
100C2×C11⋊C8SD1612yes—
101#1990—111no—
102#1987—111no—
103#1948—111no—
104#1939—111no—
105C2×#334—111no—
106C2×#333D1111yescharacteristic
107#1296—111no—
108C23×C11#12111yescharacteristic
109Q8×C11—82no—
110Q8×C11—82no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—42no—
114C2×C4×C11—81no—
115C2×C4×C11—81no—
116C2×C4×C11#12111yescharacteristic
117C2×C4×C11#12111yescharacteristic
118C2×C4×C11C22⋊Q811yescharacteristic
119C2×C4×C11C22⋊Q811yescharacteristic
120C2×C4×C11C22⋊Q811yescharacteristic
121C2×C4×C11#12611yescharacteristic
122C2×C4×C11C2×SD1611yescharacteristic
123C2×C4×C11C2×SD1611yescharacteristic
124C2×C4×C11#13511yescharacteristic
125C2×C4×C11#13511yescharacteristic
126C2×C4×C11#13711yescharacteristic
127C2×C4×C11#13711yescharacteristic
128C2×C4×C11#13711yescharacteristic
129C2×C4×C11#13711yescharacteristic
130C2×Dic11—22no—
131C2×Dic11—41no—
132C2×Dic11—41no—
133C2×Dic11—41no—
134C2×Dic11—41no—
135C2×Dic11—41no—
136C2×Dic11—81no—
137C2×Dic11—81no—
138C2×Dic11—81no—
139C8×C11—42no—
140C8×C11—81no—
141C11⋊C8—22no—
142C11⋊C8—41no—
143C11⋊C8—81no—
144C2×C4⋊Q8C2×D1111yescharacteristic
145C2×#106—221no—
146C2×C4⋊C8—111no—
147C2×C4⋊C8—221no—
148C2×C4⋊C8C2×D1111yescharacteristic
149C2×C4⋊C8C2×D1111yescharacteristic
150C2×C4×C8—111no—
151#384—111no—
152C4×C4⋊C4—111no—
153#340—221no—
154#340—221no—
155#340—221no—
156#340—221no—
157#340—221no—
158#336—221no—
159#334—222no—
160#333—22no—
161C22×C11#39611yescharacteristic
162C22×C11#46111yescharacteristic
163C22×C11#46411yescharacteristic
164C22×C11#46511yescharacteristic
165C22×C11#47011yescharacteristic
166C22×C11#47111yescharacteristic
167C22×C11#47211yescharacteristic
168C4×C11—21no—
169C4×C11—21no—
170C4×C11—82no—
171C4×C11#46111yescharacteristic
172C4×C11#46411yescharacteristic
173C4×C11#46511yescharacteristic
174C4×C11#47011yescharacteristic
175C4×C11#47511yescharacteristic
176C4×C11#47511yescharacteristic
177C4×C11#47911yescharacteristic
178C4×C11#47911yescharacteristic
179Dic11—42no—
180Dic11—81no—
181Dic11—161no—
182C22×Q8—21no—
183C22×C8—21no—
184C22×C8—21no—
185C22×C8—111no—
186C22×C8—111no—
187C22×C8—221no—
188C4⋊Q8—21no—
189C4⋊Q8—21no—
190C4⋊Q8—21no—
191C4⋊Q8Dic2212yes—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—111no—
195C2×C4⋊C4—111no—
196C2×C4⋊C4—221no—
197C2×C4⋊C4—221no—
198C2×C4⋊C4—221no—
199C2×C42—221no—
200C2×C42C22×D1111yescharacteristic
201#106—442no—
202C4⋊C8—21no—
203C4⋊C8—21no—
204C4⋊C8—21no—
205C4⋊C8—221no—
206C4⋊C8—221no—
207C4⋊C8—442no—
208C4⋊C8C22⋊D1112yes—
209C4×C8—221no—
210C4×C8—221no—
211#95—221no—
212C2×C11#167111yescharacteristic
213C2×C11#167811yescharacteristic
214C2×C11#169511yescharacteristic
215C2×C11#170411yescharacteristic
216C2×C11#206311yescharacteristic
217C2×C11#206611yescharacteristic
218C2×C11#206611yescharacteristic
219C2×Q8—22no—
220C2×Q8—41no—
221C2×Q8—81no—
222C2×Q8—81no—
223C22×C4—41no—
224C22×C4—221no—
225C22×C4—221no—
226C22×C4—441no—
227C22×C4#433911yescharacteristic
228C22×C4D4×D1111yescharacteristic
229C22×C4D4×D1111yescharacteristic
230C2×C8—22no—
231C2×C8—41no—
232C2×C8—41no—
233C2×C8—41no—
234C2×C8—41no—
235C2×C8—41no—
236C2×C8—112no—
237C2×C8—221no—
238C2×C8—221no—
239C2×C8—221no—
240C2×C8—221no—
241C2×C8—221no—
242C2×C8—441no—
243C2×C8—441no—
244C2×C8—441no—
245C4⋊C4—22no—
246C4⋊C4—22no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—112no—
250C4⋊C4—221no—
251C4⋊C4—221no—
252C4⋊C4—221no—
253C4⋊C4—441no—
254C4⋊C4—441no—
255C4⋊C4—441no—
256C4⋊C4—441no—
257C4⋊C4—881no—
258C42—441no—
259C42—441no—
260C42C2×Dic2211yescharacteristic
261C42#434111yescharacteristic
262C42#434111yescharacteristic
263C42C2×C22⋊D1111yescharacteristic
264C11#1059711yescharacteristic, complemented, Sylow
265C23#6693711yescharacteristic
266Q8—82no—
267Q8—82no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—42no—
271C2×C4—81no—
272C2×C4—81no—
273C2×C4—222no—
274C2×C4—441no—
275C2×C4—441no—
276C2×C4—441no—
277C2×C4—441no—
278C2×C4—441no—
279C2×C4—881no—
280C2×C4—881no—
281C2×C4—881no—
282C2×C4#6693111yescharacteristic
283C2×C4#6693111yescharacteristic
284C2×C4#6693211yescharacteristic
285C2×C4SD16×D1111yescharacteristic
286C2×C4SD16×D1111yescharacteristic
287C2×C4#6696811yescharacteristic
288C2×C4#6696911yescharacteristic
289C2×C4#6697111yescharacteristic
290C2×C4#6697111yescharacteristic
291C2×C4#6697111yescharacteristic
292C2×C4#6697211yescharacteristic
293C2×C4#6697711yescharacteristic
294C2×C4#6699111yescharacteristic
295C2×C4#6699211yescharacteristic
296C8—42no—
297C8—81no—
298C8—222no—
299C8—441no—
300C8—881no—
301C22#1062236111yescharacteristic
302C22#1062236211yescharacteristic
303C22#1062241111yescharacteristic
304C22#1062242011yescharacteristic
305C22#1062242911yescharacteristic
306C22#1062243111yescharacteristic
307C22#1062256111yescharacteristic
308C4—21no—
309C4—21no—
310C4—82no—
311C4—442no—
312C4—881no—
313C4—1761no—
314C4#1062240411yescharacteristic
315C4#1062240411yescharacteristic
316C4#1062240911yescharacteristic
317C4#1062241211yescharacteristic
318C4#1062277511yescharacteristic
319C4#1062278411yescharacteristic
320C4#1062279811yescharacteristic
321C4#1062280211yescharacteristic
322C2#1306799411yescharacteristic
323C2#1306803511yescharacteristic
324C2#1306813811yescharacteristic
325C2#1306820111yescharacteristic
326C2#1306997211yescharacteristic
327C2#1306999311yescharacteristic
328C2#1306999511yescharacteristic
subgroupG/H
centerC23#66937
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#333C2
socle, prime radicalC23×C11#121
hypercenterC2×#333D11
hypocenterC11#10597
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#333

Complements

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

NH ≅ G/Ntype
264. C11#10597semidirect

Maximal subgroups

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

subgroupindex
#130695782
#130695652
#130693802
#130693322
C2×#106221182
#130665002
C2×C11×#3332
#1059711