Finite Group Databasebeta

← #14670654

Subgroups — #14670654

Order 2816.

488 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081718C211yesmaximal, characteristic, complemented
2#13077310C211yesmaximal, characteristic
3#13070236C211yesmaximal, characteristic, complemented
4#13070227C211yesmaximal, characteristic, complemented
5#13066703C211yesmaximal, characteristic, complemented
6#13066701C211yesmaximal, characteristic, complemented
7C11×#2112C211yesmaximal, characteristic, complemented
8C23×C8×C11C2211yescharacteristic
9#10623322C411yescharacteristic
10C2×#66954C2211yescharacteristic
11C2×C11×M32C2211yescharacteristic
12C2×C11×M32C2211yescharacteristic
13#10622820C411yescharacteristic
14#10622724—22no—
15#10622723C411yescharacteristic
16C8×C22⋊D11—22no—
17#10622715C411yescharacteristic
18#10622714C2211yescharacteristic
19C2×#66876C2211yescharacteristic
20C2×#66876C2211yescharacteristic
21#10622520—22no—
22D11×M32—22no—
23#10622514—22no—
24C11×C22⋊C16—22no—
25C22⋊(C11⋊C16)—22no—
26#10622152—22no—
27C23×C4×C11C2×C411yescharacteristic
28C2×#4339C2×C411yescharacteristic
29C22×C8×C11—21no—
30C22×C8×C11—21no—
31C22×C8×C11—21no—
32C22×C8×C11—21no—
33C22×C8×C11—21no—
34C22×C8×C11—21no—
35C22×C8×C11C2×C411yescharacteristic
36C22×C8×C11C2311yescharacteristic
37#67006C812yes—
38#66983—21no—
39#66982C812yes—
40C4×C22⋊D11—22no—
41#66979C2×C411yescharacteristic
42#66977—21no—
43C2×#4318C2×C411yescharacteristic
44C2×#4318C2×C411yescharacteristic
45#66954—21no—
46#66954—21no—
47#66954—21no—
48#66954—21no—
49C2×#4313D412yes—
50C2×C8×D11D412yes—
51C11×M32—21no—
52C11×M32—21no—
53C11×M32—21no—
54C11×M32—21no—
55C2×C11×C16—21no—
56C2×C11×C16D412yescomplemented
57C22⋊(C11⋊C8)—22no—
58(C2×D11)⋊C8—22no—
59#66879—21no—
60Dic11⋊C8—22no—
61C8×Dic11—21no—
62#66876—21no—
63#66876—21no—
64#66876—21no—
65#66876—21no—
66C2×C11⋊C16—21no—
67C2×C11⋊C16D412yescomplemented
68#66862—24no—
69C16×D11—24no—
70#12981—111nomaximal, Sylow
71C24×C11C2×C811yescharacteristic
72C22×C4×C11—21no—
73C22×C4×C11—21no—
74C22×C4×C11—21no—
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11—21no—
78C22×C4×C11C2×C811yescharacteristic
79C22×C4×C11C22×C411yescharacteristic
80C2×C22⋊D11—22no—
81C2×C22⋊D11C2×C812yes—
82#4339—21no—
83#4339—21no—
84#4339—21no—
85#4339—21no—
86C2×D44M1611yescharacteristic
87C2×C4×D11C22⋊C412yes—
88C2×Dic22M1611yescharacteristic
89C2×C8×C11—21no—
90C2×C8×C11—21no—
91C2×C8×C11—21no—
92C2×C8×C11—41no—
93C2×C8×C11—41no—
94C2×C8×C11—41no—
95C2×C8×C11—41no—
96C2×C8×C11C2×D411yescharacteristic
97C2×C8×C11C2×D411yescharacteristic
98C2×C8×C11C2×D411yescharacteristic
99C2×C8×C11C2×D411yescharacteristic
100C2×C8×C11#4111yescharacteristic
101C2×C8×C11#4111yescharacteristic
102C22⋊Dic11—22no—
103C22⋊Dic11C2×C812yes—
104(C2×D11)⋊C4—22no—
105C4⋊Dic11—21no—
106Dic11⋊C4—22no—
107C4×Dic11—21no—
108#4318—21no—
109#4318—21no—
110#4318—21no—
111#4318—21no—
112C2×C11⋊C8—21no—
113C2×C11⋊C8C22⋊C412yes—
114#4313—22no—
115#4313—22no—
116C8×D11—22no—
117C8×D11—22no—
118C11×C16—22no—
119C11×C16—41no—
120C11⋊C16—22no—
121C11⋊C16—41no—
122#3407—111no—
123#2929—111no—
124#2115—111no—
125#2112—111no—
126#2112D1111yescharacteristic, complemented
127#1378—111no—
128#1378—111no—
129C23×C11—21no—
130C23×C11—21no—
131C23×C11—21no—
132C23×C11—42no—
133C23×C11C22×C811yescharacteristic
134C22×D11C22⋊C812yes—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11C2×C22⋊C411yescharacteristic
143C2×C4×C11C4×D411yescharacteristic
144C2×C4×C11C4×D411yescharacteristic
145C2×C4×C11C2×M1611yescharacteristic
146C2×C4×C11#13111yescharacteristic
147C2×C4×C11#13111yescharacteristic
148C22⋊D11—22no—
149C22⋊D11—22no—
150C22⋊D11—44no—
151C2×Dic11—22no—
152C2×Dic11C22⋊C812yes—
153D44—21no—
154D44—21no—
155C4×D11—22no—
156C4×D11—22no—
157Dic22—21no—
158Dic22—21no—
159C8×C11—41no—
160C8×C11#12011yescharacteristic
161C8×C11#12111yescharacteristic
162C8×C11#12111yescharacteristic
163C8×C11#12311yescharacteristic
164C11⋊C8—22no—
165C11⋊C8—41no—
166C2×#131—111no—
167C23×C8C2×D1111yescharacteristic
168#525—111no—
169#504—222no—
170#504—222no—
171C2×M32—111no—
172C2×M32—111no—
173C2×M32—222no—
174C2×M32C2×D1111yescharacteristic
175C2×M32C2×D1111yescharacteristic
176#435—222no—
177C8×D4—222no—
178#424—111no—
179#408—111no—
180#407—111no—
181#405—111no—
182#349—222no—
183C22⋊C16—22no—
184C22⋊C16—222no—
185C22×C11—22no—
186C22×C11—22no—
187C22×C11—22no—
188C22×C11—41no—
189C22×C11—41no—
190C22×C11—41no—
191C22×C11—41no—
192C22×C11—41no—
193C22×C11C2×C22⋊C811yescharacteristic
194C22×C11C8×D411yescharacteristic
195C22×C11C8×D411yescharacteristic
196C2×D11—22no—
197C2×D11—42no—
198C4×C11—41no—
199C4×C11#38611yescharacteristic
200C4×C11#40811yescharacteristic
201C4×C11#43511yescharacteristic
202C4×C11#43511yescharacteristic
203Dic11—22no—
204Dic11—42no—
205C2×#41—111no—
206C23×C4C4×D1111yescharacteristic
207#131—221no—
208#131—221no—
209#131—221no—
210#131—221no—
211C2×M16—111no—
212C2×M16—112no—
213C2×M16—111no—
214C22×C8—21no—
215C22×C8—21no—
216C22×C8—21no—
217C22×C8—21no—
218C22×C8—21no—
219C22×C8—21no—
220C22×C8—112no—
221C22×C8C4×D1111yescharacteristic
222C22×C8C22×D1111yescharacteristic
223#123—112no—
224C22⋊Q8—221no—
225#121—221no—
226#120—112no—
227C4×D4—222no—
228#117—111no—
229M32—21no—
230M32—21no—
231M32—21no—
232M32—21no—
233M32—224no—
234M32—221no—
235M32—221no—
236M32—221no—
237M32—221no—
238C2×C16—21no—
239C2×C16—112no—
240C2×C16—224no—
241C2×C16—221no—
242C2×C16C22⋊D1112yescomplemented
243C4⋊C8—222no—
244C22⋊C8—222no—
245C22⋊C8—222no—
246#97—221no—
247C4×C8—221no—
248C2×C11—21no—
249C2×C11—21no—
250C2×C11—21no—
251C2×C11—42no—
252C2×C11#186911yescharacteristic
253D11—42no—
254C24C8×D1111yescharacteristic
255#41—221no—
256#41—221no—
257#41—221no—
258#41—221no—
259C2×Q8—111no—
260C2×D4—112no—
261C2×D4—111no—
262C2×D4—222no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—112no—
270C22×C4C8×D1111yescharacteristic
271C22×C4C2×C4×D1111yescharacteristic
272M16—221no—
273M16—221no—
274M16—222no—
275M16—222no—
276M16—221no—
277M16—221no—
278C2×C8—21no—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8—41no—
285C2×C8—112no—
286C2×C8—222no—
287C2×C8—222no—
288C2×C8—221no—
289C2×C8#433911yescharacteristic
290C2×C8D4×D1111yescharacteristic
291C2×C8D4×D1111yescharacteristic
292C2×C8D4×D1111yescharacteristic
293C2×C8#434111yescharacteristic
294C2×C8C2×C22⋊D1111yescharacteristic
295C4⋊C4—222no—
296C4⋊C4—221no—
297C22⋊C4—112no—
298C22⋊C4—222no—
299C22⋊C4—222no—
300C42—221no—
301C16—22no—
302C16—41no—
303C16—222no—
304C16—441no—
305C11#1298111yescharacteristic, complemented, Sylow
306C23—21no—
307C23—21no—
308C23—21no—
309C23—42no—
310C23—112no—
311C23C2×C8×D1111yescharacteristic
312Q8—221no—
313Q8—221no—
314D4—222no—
315D4—222no—
316D4—221no—
317D4—221no—
318D4—444no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—112no—
327C2×C4—222no—
328C2×C4—222no—
329C2×C4—222no—
330C2×C4C22⋊C4×D1111yescharacteristic
331C2×C4(C22⋊D11)⋊C411yescharacteristic
332C2×C4#6695411yescharacteristic
333C2×C4M16×D1111yescharacteristic
334C2×C4#6696011yescharacteristic
335C2×C4C4×C22⋊D1111yescharacteristic
336C8—41no—
337C8—222no—
338C8—441no—
339C8#6693611yescharacteristic
340C8#6693711yescharacteristic
341C8#6699011yescharacteristic
342C8#6699111yescharacteristic
343C22—22no—
344C22—22no—
345C22—22no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—222no—
352C22—442no—
353C22D11×C22⋊C811yescharacteristic
354C22(C22⋊D11)⋊C811yescharacteristic
355C22C8×C22⋊D1111yescharacteristic
356C4—41no—
357C4—222no—
358C4—442no—
359C4#1062234011yescharacteristic
360C4#1062234111yescharacteristic
361C4#1062256911yescharacteristic
362C4#1062274011yescharacteristic
363C2—21no—
364C2—21no—
365C2—21no—
366C2—42no—
367C2—442no—
368C2#1306890511yescharacteristic
subgroupG/H
centerC8#66990
commutatorC23×C11C22×C8
FrattiniC22×C8C22×D11
FittingC11×#2112C2
socleC2×C11#1869
prime radical#10623322C4
cosocleC22×C8×C11C23
hypercenter#2112D11
hypocenterC11#12981
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C8 ◁ C22×C8 ◁ #2112

Complements

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

NH ≅ G/Ntype
1. #13081718C2semidirect
3. #13070236C2semidirect
4. #13070227C2semidirect
5. #13066703C2semidirect
6. #13066701C2semidirect
7. C11×#2112C2semidirect
56. C2×C11×C16D4semidirect
67. C2×C11⋊C16D4semidirect
126. #2112D11semidirect
242. C2×C16C22⋊D11semidirect
305. C11#12981semidirect

Maximal subgroups

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

subgroupindex
#130817182
#130773102
#130702362
#130702272
#130667032
#130667012
C11×#21122
#1298111