Finite Group Databasebeta

← #14646891

Subgroups — #14646891

Order 2816.

418 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
1C2×#10622444C211yesmaximal, characteristic
2#13068743C211yesmaximal, characteristic
3#13068622C211yesmaximal, characteristic
4#13068618C211yesmaximal, characteristic
5C2×#10622118C211yesmaximal, characteristic
6#13066500C211yesmaximal, characteristic
7C11×#1296C211yesmaximal, characteristic
8C2×C4×Dic22C2211yescharacteristic
9C2×C11×C4⋊C8C2211yescharacteristic
10C2×C11×C4⋊C8C2211yescharacteristic
11C11×#384C2211yescharacteristic
12C2×#66880—21no—
13C2×#66879—21no—
14C2×Dic11⋊C8—21no—
15C2×#66874—21no—
16#10622548C2211yescharacteristic
17C2×C4⋊(C11⋊C8)C2211yescharacteristic
18C2×C4×C11⋊C8C2211yescharacteristic
19#10622444—22no—
20#10622444C414yescomplemented
21#10622189—21no—
22#10622167—21no—
23#10622167—21no—
24#10622167—21no—
25#10622118—22no—
26C22×Dic22D411yescharacteristic
27C22×C8×C11—21no—
28C22×C8×C11—21no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—21no—
32C2×C42×C11C2311yescharacteristic
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11D411yescharacteristic
37C2×Dic11⋊C4—21no—
38C2×C4×Dic11—21no—
39C22×C11⋊C8—21no—
40C22×C11⋊C8D411yescharacteristic
41C22×C11⋊C8D411yescharacteristic
42C4×Dic22—21no—
43C4×Dic22—21no—
44C4×Dic22C2×C412yes—
45C4×Dic22Q812yes—
46C11×C4⋊C8—21no—
47C11×C4⋊C8—21no—
48C11×C4⋊C8—21no—
49C11×C4⋊C8C2×C412yes—
50#66880—42no—
51#66879—24no—
52Dic11⋊C8—24no—
53#66874—42no—
54C4⋊(C11⋊C8)—21no—
55C4⋊(C11⋊C8)—21no—
56C4×C11⋊C8C2×C412yes—
57C4×C11⋊C8D412yes—
58#8657—111nomaximal, Sylow
59C22×C4×C11—41no—
60C22×C4×C11C2×D411yescharacteristic
61C22×C4×C11C2×D411yescharacteristic
62C22×C4×C11#4111yescharacteristic
63C22×Dic11—21no—
64C22×Dic11—21no—
65C22×Dic11—41no—
66C2×Dic22—21no—
67C2×Dic22—21no—
68C2×Dic22—21no—
69C2×Dic22—21no—
70C2×Dic22—21no—
71C2×Dic22C4⋊C412yes—
72C2×C8×C11—22no—
73C2×C8×C11—41no—
74C2×C8×C11—41no—
75C2×C8×C11—41no—
76C2×C8×C11—41no—
77C2×C8×C11—41no—
78C11×C4⋊C4—41no—
79C11×C4⋊C4—41no—
80C11×C4⋊C4—41no—
81C11×C4⋊C4—41no—
82C11×C4⋊C4—81no—
83C42×C11C22×C411yescharacteristic
84C42×C11C2×D411yescharacteristic
85C42×C11C2×Q811yescharacteristic
86C42×C11#4111yescharacteristic
87C4⋊Dic11—21no—
88C4⋊Dic11—41no—
89C4⋊Dic11—41no—
90C4⋊Dic11—41no—
91C4⋊Dic11—41no—
92C4⋊Dic11—81no—
93C4⋊Dic11C4⋊C412yes—
94Dic11⋊C4—22no—
95Dic11⋊C4—22no—
96C4×Dic11—22no—
97C4×Dic11—22no—
98C2×C11⋊C8—21no—
99C2×C11⋊C8—21no—
100C2×C11⋊C8—21no—
101C2×C11⋊C8—21no—
102C2×C11⋊C8—41no—
103C2×C11⋊C8—41no—
104C2×C11⋊C8—41no—
105C2×C11⋊C8C22⋊C412yes—
106C2×C11⋊C8C22⋊C412yes—
107C2×#446—111no—
108#1834—111no—
109#1803—111no—
110#1803—111no—
111C2×#334—111no—
112#1296—111no—
113#1296D1111yescharacteristic
114C23×C11#12111yescharacteristic
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—81no—
118C2×C4×C11—81no—
119C2×C4×C11—81no—
120C2×C4×C11C2×C22⋊C411yescharacteristic
121C2×C4×C11C2×C4⋊C411yescharacteristic
122C2×C4×C11#11711yescharacteristic
123C2×C4×C11#12111yescharacteristic
124C2×C4×C11C22⋊Q811yescharacteristic
125C2×C4×C11C22⋊Q811yescharacteristic
126C2×C4×C11#13511yescharacteristic
127C2×C4×C11#13511yescharacteristic
128C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
129C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
130C2×C4×C11#13711yescharacteristic
131C2×C4×C11#13711yescharacteristic
132C2×C4×C11#13711yescharacteristic
133C2×C4×C11#13711yescharacteristic
134C2×Dic11—22no—
135C2×Dic11—22no—
136C2×Dic11—41no—
137C2×Dic11—41no—
138C2×Dic11—41no—
139C2×Dic11—41no—
140C2×Dic11—81no—
141C2×Dic11—81no—
142C2×Dic11—81no—
143Dic22—22no—
144Dic22—22no—
145Dic22—41no—
146Dic22—41no—
147C8×C11—42no—
148C8×C11—81no—
149C11⋊C8—22no—
150C11⋊C8—22no—
151C11⋊C8—81no—
152C2×C4×Q8—111no—
153#446—114no—
154#446—222no—
155C2×C4⋊C8—111no—
156C2×C4⋊C8—221no—
157C2×C4⋊C8C2×D1111yescharacteristic
158C2×C4⋊C8C2×D1111yescharacteristic
159C2×#103—221no—
160C2×#103—221no—
161C2×#97—221no—
162C2×C4×C8—111no—
163#384—111no—
164#384C2×D1111yescharacteristic
165#340—221no—
166#340—221no—
167#340—221no—
168#340—221no—
169#334—222no—
170C22×C11#38011yescharacteristic
171C22×C11#46411yescharacteristic
172C22×C11#46411yescharacteristic
173C22×C11#46911yescharacteristic
174C22×C11#47011yescharacteristic
175C22×C11#47111yescharacteristic
176C22×C11#47111yescharacteristic
177C4×C11—21no—
178C4×C11—21no—
179C4×C11—161no—
180C4×C11#41611yescharacteristic
181C4×C11#41911yescharacteristic
182C4×C11#42811yescharacteristic
183C4×C11#42811yescharacteristic
184C4×C11#46811yescharacteristic
185C4×C11#46811yescharacteristic
186C4×C11#47911yescharacteristic
187C4×C11#47911yescharacteristic
188Dic11—42no—
189Dic11—42no—
190Dic11—161no—
191C22×Q8—111no—
192C22×C8—21no—
193C22×C8—21no—
194C22×C8—111no—
195C22×C8—111no—
196C22×C8—221no—
197C4×Q8—112no—
198C4×Q8—112no—
199C4×Q8—221no—
200C4×Q8—221no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—111no—
205C2×C4⋊C4—221no—
206C2×C4⋊C4—221no—
207C2×C4⋊C4—221no—
208C2×C4⋊C4—221no—
209C2×C42—221no—
210C2×C42C22×D1111yescharacteristic
211C4⋊C8—21no—
212C4⋊C8—21no—
213C4⋊C8—21no—
214C4⋊C8—224no—
215C4⋊C8—221no—
216C4⋊C8—221no—
217C4⋊C8C4×D1112yes—
218#103—442no—
219#103—442no—
220#97—224no—
221C4×C8—112no—
222C4×C8—112no—
223C2×C11#170211yescharacteristic
224C2×C11#170211yescharacteristic
225C2×C11#170411yescharacteristic
226C2×C11#170411yescharacteristic
227C2×C11#180511yescharacteristic
228C2×C11#180911yescharacteristic
229C2×C11#181511yescharacteristic
230C2×Q8—112no—
231C2×Q8—221no—
232C2×Q8—221no—
233C2×Q8—221no—
234C2×Q8—221no—
235C2×Q8—221no—
236C22×C4—41no—
237C22×C4—221no—
238C22×C4—221no—
239C22×C4—441no—
240C22×C4#433911yescharacteristic
241C22×C4D4×D1111yescharacteristic
242C22×C4D4×D1111yescharacteristic
243C2×C8—22no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—41no—
248C2×C8—41no—
249C2×C8—112no—
250C2×C8—112no—
251C2×C8—221no—
252C2×C8—221no—
253C2×C8—221no—
254C2×C8—221no—
255C2×C8—441no—
256C2×C8—441no—
257C2×C8—441no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—81no—
263C4⋊C4—112no—
264C4⋊C4—222no—
265C4⋊C4—221no—
266C4⋊C4—222no—
267C4⋊C4—441no—
268C4⋊C4—441no—
269C4⋊C4—441no—
270C4⋊C4—441no—
271C4⋊C4—881no—
272C42—222no—
273C42—222no—
274C42C2×C4×D1111yescharacteristic
275C42#433911yescharacteristic
276C42D4×D1111yescharacteristic
277C42Q8×D1111yescharacteristic
278C11#865711yescharacteristic, complemented, Sylow
279C23#6693711yescharacteristic
280Q8—222no—
281Q8—222no—
282Q8—441no—
283Q8—441no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—81no—
287C2×C4—81no—
288C2×C4—81no—
289C2×C4—222no—
290C2×C4—222no—
291C2×C4—441no—
292C2×C4—441no—
293C2×C4—441no—
294C2×C4—441no—
295C2×C4—881no—
296C2×C4—881no—
297C2×C4—881no—
298C2×C4#6692511yescharacteristic
299C2×C4C22⋊C4×D1111yescharacteristic
300C2×C4#6693711yescharacteristic
301C2×C4C4⋊C4×D1111yescharacteristic
302C2×C4#6694911yescharacteristic
303C2×C4#6694911yescharacteristic
304C2×C4#6696411yescharacteristic
305C2×C4#6696511yescharacteristic
306C2×C4#6696711yescharacteristic
307C2×C4#6696811yescharacteristic
308C2×C4#6696811yescharacteristic
309C2×C4#6696911yescharacteristic
310C2×C4#6697111yescharacteristic
311C2×C4#6697111yescharacteristic
312C8—42no—
313C8—81no—
314C8—222no—
315C8—222no—
316C8—881no—
317C22#1062228011yescharacteristic
318C22#1062236111yescharacteristic
319C22#1062236711yescharacteristic
320C22#1062238011yescharacteristic
321C22#1062239511yescharacteristic
322C22#1062241111yescharacteristic
323C22#1062242911yescharacteristic
324C4—21no—
325C4—21no—
326C4—161no—
327C4—442no—
328C4—442no—
329C4—1761no—
330C4#1062238511yescharacteristic
331C4#1062239311yescharacteristic
332C4#1062241511yescharacteristic
333C4#1062242511yescharacteristic
334C4#1062247011yescharacteristic
335C4#1062247411yescharacteristic
336C4#1062249011yescharacteristic
337C4#1062249411yescharacteristic
338C2#1306818311yescharacteristic
339C2#1306818711yescharacteristic
340C2#1306819711yescharacteristic
341C2#1306820111yescharacteristic
342C2#1306863011yescharacteristic
343C2#1306864811yescharacteristic
344C2#1306867411yescharacteristic
subgroupG/H
centerC23#66937
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1296C2
socle, prime radicalC23×C11#121
cosocleC2×C42×C11C23
hypercenter#1296D11
hypocenterC11#8657
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
20. #10622444C4semidirect
278. C11#8657semidirect

Maximal subgroups

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

subgroupindex
C2×#106224442
#130687432
#130686222
#130686182
C2×#106221182
#130665002
C11×#12962
#865711