Finite Group Databasebeta

← #14652174

Subgroups — #14652174

Order 2816.

386 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13069540C211yesmaximal, characteristic
2#13069372C211yesmaximal, characteristic
3#13068483C211yesmaximal, characteristic
4C2×#10622185C211yesmaximal, characteristic
5#13066499C211yesmaximal, characteristic
6#13066451C211yesmaximal, characteristic
7C11×#1990C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C4×C8×C11C2211yescharacteristic
10C11×#384C2211yescharacteristic
11C2×#66899—21no—
12C2×#66899—21no—
13C2×#66879—21no—
14C2×#66871—21no—
15C4×C4⋊Dic11C2211yescharacteristic
16C2×C4⋊(C11⋊C8)C2211yescharacteristic
17C2×C4⋊(C11⋊C8)C2211yescharacteristic
18C2×C4⋊(C11⋊C8)C2211yescharacteristic
19C11×#340—21no—
20C11×#340—21no—
21#10622188—21no—
22#10622185C414yescomplemented
23#10622167—21no—
24C22×Q8×C11—21no—
25C22×C8×C11D411yescharacteristic
26C22×C8×C11D411yescharacteristic
27C11×C4⋊Q8—21no—
28C11×C4⋊Q8—21no—
29C11×C4⋊Q8—21no—
30C11×C4⋊Q8C2×C412yes—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4—21no—
36C2×C42×C11C2311yescharacteristic
37C2×C4⋊Dic11D411yescharacteristic
38C2×C4⋊Dic11D411yescharacteristic
39C2×C4×Dic11—21no—
40C22×C11⋊C8—21no—
41C22×C11⋊C8—21no—
42C22×C11⋊C8—21no—
43C4×C8×C11—21no—
44C4×C8×C11—21no—
45#66899—42no—
46#66899—42no—
47C11⋊#95—21no—
48#66879—42no—
49#66871—42no—
50C4⋊(C11⋊C8)—21no—
51C4⋊(C11⋊C8)—21no—
52C4⋊(C11⋊C8)—21no—
53C4⋊(C11⋊C8)—21no—
54C4⋊(C11⋊C8)C2×C412yes—
55C4⋊(C11⋊C8)C2×C412yes—
56#9574—111nomaximal, Sylow
57C2×Q8×C11—22no—
58C2×Q8×C11—41no—
59C2×Q8×C11—41no—
60C2×Q8×C11—41no—
61C2×Q8×C11—41no—
62C2×Q8×C11—41no—
63C22×C4×C11—41no—
64C22×C4×C11—41no—
65C22×C4×C11C2×D411yescharacteristic
66C22×C4×C11C2×D411yescharacteristic
67C22×C4×C11#4111yescharacteristic
68C22×Dic11—21no—
69C22×Dic11—21no—
70C2×C8×C11—21no—
71C2×C8×C11—21no—
72C2×C8×C11—21no—
73C2×C8×C11—21no—
74C2×C8×C11—21no—
75C2×C8×C11Q1612yes—
76C11×C4⋊C4—22no—
77C11×C4⋊C4—22no—
78C11×C4⋊C4—41no—
79C11×C4⋊C4—41no—
80C11×C4⋊C4—41no—
81C11×C4⋊C4—41no—
82C11×C4⋊C4—41no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—81no—
85C42×C11C22×C411yescharacteristic
86C42×C11#4111yescharacteristic
87C42×C11#4111yescharacteristic
88C42×C11#4111yescharacteristic
89C4⋊Dic11—21no—
90C4⋊Dic11—21no—
91C4⋊Dic11—21no—
92C4⋊Dic11—21no—
93C4×Dic11—41no—
94C4×Dic11—41no—
95C2×C11⋊C8—22no—
96C2×C11⋊C8—22no—
97C2×C11⋊C8—41no—
98C2×C11⋊C8—41no—
99C2×C11⋊C8—41no—
100C2×C11⋊C8—41no—
101C2×C11⋊C8—41no—
102C2×C11⋊C8—41no—
103C2×C11⋊C8—41no—
104#1990D1111yescharacteristic
105#1981—111no—
106#1947—111no—
107#1770—111no—
108C2×#332—111no—
109#1296—111no—
110#1277—111no—
111C23×C11#12111yescharacteristic
112Q8×C11—42no—
113Q8×C11—42no—
114Q8×C11—81no—
115Q8×C11—81no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—42no—
119C2×C4×C11—81no—
120C2×C4×C11—81no—
121C2×C4×C11—81no—
122C2×C4×C11—81no—
123C2×C4×C11—81no—
124C2×C4×C11#11711yescharacteristic
125C2×C4×C11C4×D411yescharacteristic
126C2×C4×C11C4×D411yescharacteristic
127C2×C4×C11#12311yescharacteristic
128C2×C4×C11#12411yescharacteristic
129C2×C4×C11#12611yescharacteristic
130C2×C4×C11C2×Q1611yescharacteristic
131C2×C4×C11#13511yescharacteristic
132C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
134C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C11#13711yescharacteristic
137C2×C4×C11#13711yescharacteristic
138C2×Dic11—41no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C8×C11—22no—
145C8×C11—41no—
146C11⋊C8—42no—
147C11⋊C8—42no—
148C11⋊C8—81no—
149C2×C4⋊Q8C2×D1111yescharacteristic
150C2×#107—221no—
151C2×C4⋊C8—111no—
152C2×C4⋊C8—111no—
153C2×C4⋊C8—111no—
154C2×#103—221no—
155C2×#103—221no—
156C2×#97—221no—
157C2×C4×C8C2×D1111yescharacteristic
158#384C2×D1111yescharacteristic
159C4×C4⋊C4—111no—
160#340—21no—
161#340—21no—
162#340—221no—
163#336—221no—
164#332—114no—
165C22×C11#38811yescharacteristic
166C22×C11#46211yescharacteristic
167C22×C11#46311yescharacteristic
168C22×C11#46811yescharacteristic
169C22×C11#46911yescharacteristic
170C22×C11#47111yescharacteristic
171C22×C11#47311yescharacteristic
172C4×C11—21no—
173C4×C11—21no—
174C4×C11—82no—
175C4×C11—161no—
176C4×C11C4×Q1611yescharacteristic
177C4×C11#44011yescharacteristic
178C4×C11#44011yescharacteristic
179C4×C11#44211yescharacteristic
180C4×C11#48411yescharacteristic
181C4×C11#48511yescharacteristic
182C4×C11#48911yescharacteristic
183C4×C11#49011yescharacteristic
184Dic11—81no—
185Dic11—81no—
186C22×Q8—21no—
187C22×C8—221no—
188C22×C8—221no—
189C22×C8—221no—
190C22×C8C22⋊D1111yescharacteristic
191C22×C8C22⋊D1111yescharacteristic
192C4⋊Q8—21no—
193C4⋊Q8—21no—
194C4⋊Q8—21no—
195C4⋊Q8C4×D1112yes—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—111no—
202C2×C4⋊C4—111no—
203C2×C42—221no—
204C2×C42C22×D1111yescharacteristic
205#107—442no—
206C4⋊C8—112no—
207C4⋊C8—112no—
208C4⋊C8—221no—
209C4⋊C8—221no—
210C4⋊C8—221no—
211C4⋊C8—221no—
212#103—442no—
213#103—442no—
214#97—442no—
215C4×C8—21no—
216C4×C8—21no—
217#95—221no—
218C2×C11#169211yescharacteristic
219C2×C11#169411yescharacteristic
220C2×C11#169911yescharacteristic
221C2×C11#170111yescharacteristic
222C2×C11#192811yescharacteristic
223C2×C11#193011yescharacteristic
224C2×C11#193611yescharacteristic
225C2×Q8—22no—
226C2×Q8—41no—
227C2×Q8—41no—
228C2×Q8—41no—
229C2×Q8—41no—
230C2×Q8—41no—
231C22×C4—41no—
232C22×C4—41no—
233C22×C4—221no—
234C22×C4—221no—
235C22×C4D4×D1111yescharacteristic
236C22×C4#434111yescharacteristic
237C22×C4C2×C22⋊D1111yescharacteristic
238C2×C8—21no—
239C2×C8—21no—
240C2×C8—21no—
241C2×C8—21no—
242C2×C8—21no—
243C2×C8—222no—
244C2×C8—222no—
245C2×C8—441no—
246C2×C8—441no—
247C2×C8—441no—
248C2×C8—441no—
249C2×C8—441no—
250C2×C8—441no—
251C2×C8—441no—
252C2×C8#432612yes—
253C4⋊C4—22no—
254C4⋊C4—22no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—81no—
262C4⋊C4—221no—
263C4⋊C4—221no—
264C4⋊C4—221no—
265C4⋊C4—221no—
266C42—441no—
267C42—441no—
268C42C2×C4×D1111yescharacteristic
269C42#433911yescharacteristic
270C42#434111yescharacteristic
271C42#434111yescharacteristic
272C11#957411yescharacteristic, complemented, Sylow
273C23#6699111yescharacteristic
274Q8—42no—
275Q8—42no—
276Q8—81no—
277Q8—81no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—42no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4—81no—
284C2×C4—81no—
285C2×C4—81no—
286C2×C4—441no—
287C2×C4—441no—
288C2×C4—441no—
289C2×C4—441no—
290C2×C4—441no—
291C2×C4—441no—
292C2×C4#6693011yescharacteristic
293C2×C4#6693211yescharacteristic
294C2×C4(C22⋊D11)⋊C411yescharacteristic
295C2×C4#6693811yescharacteristic
296C2×C4#6696411yescharacteristic
297C2×C4#6696411yescharacteristic
298C2×C4#6696711yescharacteristic
299C2×C4#6696811yescharacteristic
300C2×C4C4×C22⋊D1111yescharacteristic
301C2×C4#6698811yescharacteristic
302C2×C4#6699511yescharacteristic
303C2×C4C2×#432611yescharacteristic
304C2×C4#6700211yescharacteristic
305C2×C4#6700311yescharacteristic
306C8—22no—
307C8—41no—
308C8—442no—
309C8—442no—
310C8—881no—
311C22#1062255711yescharacteristic
312C22#1062267011yescharacteristic
313C22#1062270311yescharacteristic
314C22#1062277211yescharacteristic
315C22#1062278711yescharacteristic
316C22#1062279011yescharacteristic
317C22#1062280511yescharacteristic
318C4—21no—
319C4—21no—
320C4—82no—
321C4—161no—
322C4—881no—
323C4—881no—
324C4#1062237011yescharacteristic
325C4#1062237711yescharacteristic
326C4#1062237811yescharacteristic
327C4#1062239811yescharacteristic
328C4#1062263911yescharacteristic
329C4C4×#432611yescharacteristic
330C4#1062265711yescharacteristic
331C4#1062265811yescharacteristic
332C2#1306811911yescharacteristic
333C2#1306813111yescharacteristic
334C2#1306816011yescharacteristic
335C2#1306817411yescharacteristic
336C2#1306925411yescharacteristic
337C2#1306926811yescharacteristic
338C2#1306931011yescharacteristic
subgroupG/H
centerC23#66991
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1990C2
socle, prime radicalC23×C11#121
cosocleC2×C42×C11C23
hypercenter#1990D11
hypocenterC11#9574
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1990

Complements

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

NH ≅ G/Ntype
22. #10622185C4semidirect
272. C11#9574semidirect

Maximal subgroups

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

subgroupindex
#130695402
#130693722
#130684832
C2×#106221852
#130664992
#130664512
C11×#19902
#957411