Finite Group Databasebeta

← #14670693

Subgroups — #14670693

Order 2816.

466 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081718C211yesmaximal, characteristic, complemented
2#13077332C211yesmaximal, characteristic
3#13070244C211yesmaximal, characteristic, complemented
4#13070236C211yesmaximal, characteristic, complemented
5#13066695C211yesmaximal, characteristic, complemented
6#13066695C211yesmaximal, characteristic, complemented
7C11×#2117C211yesmaximal, characteristic, complemented
8C2×C11×#131C2211yescharacteristic
9#10623363C411yescharacteristic
10C2×#66954C2211yescharacteristic
11C2×C11×M32C2211yescharacteristic
12C2×C11×M32C2211yescharacteristic
13#10622847C411yescharacteristic
14#10622742C411yescharacteristic
15#10622740—22no—
16#10622731C411yescharacteristic
17#10622724—22no—
18C2×#66879C2211yescharacteristic
19C2×#66876C2211yescharacteristic
20C2×#66876C2211yescharacteristic
21#10622520—22no—
22D11×M32—22no—
23#10622514—22no—
24C11×#350—22no—
25#10622199—22no—
26#10622152—22no—
27C2×C11×#41C2×C411yescharacteristic
28C2×#4339C2×C411yescharacteristic
29C11×#131—21no—
30C11×#131—21no—
31C11×#131—21no—
32C11×#131—21no—
33C2×C11×M16—21no—
34C2×C11×M16C2×C411yescharacteristic
35C22×C8×C11—21no—
36C22×C8×C11C2311yescharacteristic
37#67000C811yescharacteristic
38#66997C811yescharacteristic
39#66993C811yescharacteristic
40#66992—22no—
41#66989C811yescharacteristic
42C4×C22⋊D11—22no—
43C2×C4×Dic11C2×C411yescharacteristic
44C2×#4318C2×C411yescharacteristic
45C22×C11⋊C8C2×C411yescharacteristic
46#66954—21no—
47#66954—21no—
48#66954—21no—
49#66954—21no—
50C2×#4313D412yes—
51C2×C8×D11D412yes—
52C11×M32—21no—
53C11×M32—21no—
54C11×M32—21no—
55C11×M32—21no—
56C2×C11×C16—21no—
57C2×C11×C16D412yescomplemented
58C22⋊(C11⋊C8)—22no—
59(C2×D11)⋊C8—22no—
60#66879—21no—
61#66879—21no—
62Dic11⋊C8—22no—
63#66876—21no—
64#66876—21no—
65#66876—21no—
66#66876—21no—
67C2×C11⋊C16—21no—
68C2×C11⋊C16D412yescomplemented
69#66862—24no—
70C16×D11—24no—
71#12988—111nomaximal, Sylow
72C11×#41—21no—
73C11×#41—21no—
74C11×#41—21no—
75C11×#41—21no—
76C2×Q8×C11C2×C811yescharacteristic
77C2×D4×C11—21no—
78C2×D4×C11C2×C811yescharacteristic
79C22×C4×C11—21no—
80C22×C4×C11C22×C411yescharacteristic
81C2×C22⋊D11—22no—
82C2×C22⋊D11M1612yes—
83C22×Dic11—21no—
84#4339—21no—
85#4339—21no—
86#4339—21no—
87#4339—21no—
88C2×D44C2×C811yescharacteristic
89C2×C4×D11C22⋊C412yes—
90C2×Dic22C2×C811yescharacteristic
91C11×M16—21no—
92C11×M16—21no—
93C11×M16—41no—
94C11×M16—41no—
95C2×C8×C11—21no—
96C2×C8×C11—41no—
97C2×C8×C11—41no—
98C2×C8×C11C2×D411yescharacteristic
99C2×C8×C11C2×D411yescharacteristic
100C2×C8×C11C2×D411yescharacteristic
101C2×C8×C11C2×D411yescharacteristic
102C2×C8×C11#4111yescharacteristic
103C2×C8×C11#4111yescharacteristic
104C22⋊Dic11—22no—
105(C2×D11)⋊C4—22no—
106Dic11⋊C4—22no—
107C4×Dic11—21no—
108C4×Dic11C2×C811yescharacteristic
109C4×Dic11C2×C811yescharacteristic
110#4318—21no—
111#4318—21no—
112C2×C11⋊C8—21no—
113C2×C11⋊C8—21no—
114C2×C11⋊C8—21no—
115C2×C11⋊C8C22⋊C412yes—
116#4313—22no—
117#4313—22no—
118C8×D11—22no—
119C8×D11—22no—
120C11×C16—22no—
121C11×C16—41no—
122C11⋊C16—22no—
123C11⋊C16—41no—
124#3407—111no—
125#2932—111no—
126#2117—111no—
127#2117D1111yescharacteristic, complemented
128#2115—111no—
129#1375—111no—
130#1375—111no—
131C23×C11—21no—
132C23×C11C2×M1611yescharacteristic
133C22×D11C22⋊C812yes—
134Q8×C11—21no—
135Q8×C11—21no—
136D4×C11—21no—
137D4×C11—21no—
138D4×C11—41no—
139D4×C11—41no—
140C2×C4×C11—21no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11C2×C22⋊C411yescharacteristic
144C2×C4×C11C4×D411yescharacteristic
145C2×C4×C11C4×D411yescharacteristic
146C2×C4×C11C22×C811yescharacteristic
147C2×C4×C11#13111yescharacteristic
148C2×C4×C11#13111yescharacteristic
149C22⋊D11—22no—
150C22⋊D11—22no—
151C22⋊D11—82no—
152C2×Dic11—21no—
153C2×Dic11—21no—
154C2×Dic11—81no—
155C2×Dic11C22⋊C812yes—
156D44—21no—
157D44—21no—
158C4×D11—22no—
159C4×D11—22no—
160Dic22—21no—
161Dic22—21no—
162C8×C11—41no—
163C8×C11#12011yescharacteristic
164C8×C11#12111yescharacteristic
165C8×C11#12111yescharacteristic
166C8×C11#12311yescharacteristic
167C11⋊C8—22no—
168C11⋊C8—41no—
169C2×#131—111no—
170C2×#131C2×D1111yescharacteristic
171#532—111no—
172#504—222no—
173#504—222no—
174C2×M32—111no—
175C2×M32—111no—
176C2×M32—222no—
177C2×M32C2×D1111yescharacteristic
178C2×M32C2×D1111yescharacteristic
179#435—222no—
180#435—222no—
181#423—111no—
182#408—111no—
183#408—111no—
184C2×#97—111no—
185#350—22no—
186#350—222no—
187#349—222no—
188C22×C11—41no—
189C22×C11—42no—
190C22×C11—41no—
191C22×C11C2×C22⋊C811yescharacteristic
192C22×C11#43511yescharacteristic
193C22×C11#43511yescharacteristic
194C2×D11—22no—
195C2×D11—42no—
196C4×C11—41no—
197C4×C11#38611yescharacteristic
198C4×C11#40811yescharacteristic
199C4×C11C8×D411yescharacteristic
200C4×C11C8×D411yescharacteristic
201Dic11—22no—
202Dic11—41no—
203Dic11—41no—
204C2×#41—111no—
205C2×#41C4×D1111yescharacteristic
206#131—21no—
207#131—21no—
208#131—21no—
209#131—21no—
210#131—221no—
211#131—221no—
212#131—221no—
213#131—221no—
214C2×M16—21no—
215C2×M16—111no—
216C2×M16—112no—
217C2×M16C4×D1111yescharacteristic
218C22×C8—21no—
219C22×C8—112no—
220C22×C8—111no—
221C22×C8C22×D1111yescharacteristic
222C4⋊Q8—111no—
223#127—111no—
224#124—111no—
225#124—111no—
226#121—222no—
227C4×D4—222no—
228C2×C42—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—
247#97—221no—
248C2×C11—21no—
249C2×C11—21no—
250C2×C11—21no—
251C2×C11—81no—
252C2×C11#186911yescharacteristic
253D11—42no—
254#41—21no—
255#41—21no—
256#41—21no—
257#41—21no—
258#41—221no—
259#41—221no—
260#41—221no—
261#41—221no—
262C2×Q8—111no—
263C2×Q8C8×D1111yescharacteristic
264C2×D4—21no—
265C2×D4—112no—
266C2×D4—111no—
267C2×D4—222no—
268C2×D4C8×D1111yescharacteristic
269C22×C4—21no—
270C22×C4—112no—
271C22×C4—221no—
272C22×C4C2×C4×D1111yescharacteristic
273M16—21no—
274M16—21no—
275M16—41no—
276M16—41no—
277M16—221no—
278M16—221no—
279M16—222no—
280M16—222no—
281C2×C8—21no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8—112no—
285C2×C8—222no—
286C2×C8—222no—
287C2×C8—221no—
288C2×C8—221no—
289C2×C8—221no—
290C2×C8#433911yescharacteristic
291C2×C8D4×D1111yescharacteristic
292C2×C8D4×D1111yescharacteristic
293C2×C8D4×D1111yescharacteristic
294C2×C8#434111yescharacteristic
295C2×C8C2×C22⋊D1111yescharacteristic
296C4⋊C4—222no—
297C22⋊C4—222no—
298C22⋊C4—222no—
299C42—111no—
300C42—111no—
301C42—221no—
302C16—22no—
303C16—41no—
304C16—222no—
305C16—441no—
306C11#1298811yescharacteristic, complemented, Sylow
307C23—21no—
308C23—112no—
309C23M16×D1111yescharacteristic
310Q8—21no—
311Q8—21no—
312Q8—221no—
313Q8—221no—
314D4—21no—
315D4—21no—
316D4—41no—
317D4—41no—
318D4—222no—
319D4—222no—
320D4—221no—
321D4—221no—
322D4—882no—
323C2×C4—21no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—112no—
327C2×C4—222no—
328C2×C4—222no—
329C2×C4—221no—
330C2×C4—221no—
331C2×C4—881no—
332C2×C4C22⋊C4×D1111yescharacteristic
333C2×C4(C22⋊D11)⋊C411yescharacteristic
334C2×C4C2×C8×D1111yescharacteristic
335C2×C4#6695411yescharacteristic
336C2×C4#6696011yescharacteristic
337C2×C4C4×C22⋊D1111yescharacteristic
338C8—41no—
339C8—222no—
340C8—441no—
341C8#6693611yescharacteristic
342C8#6693711yescharacteristic
343C8#6699011yescharacteristic
344C8#6699111yescharacteristic
345C22—41no—
346C22—42no—
347C22—41no—
348C22—222no—
349C22—442no—
350C22D11×C22⋊C811yescharacteristic
351C22#1062234111yescharacteristic
352C22#1062274011yescharacteristic
353C4—41no—
354C4—222no—
355C4—441no—
356C4—441no—
357C4(C22⋊D11)⋊C811yescharacteristic
358C4#1062234011yescharacteristic
359C4#1062256911yescharacteristic
360C4C8×C22⋊D1111yescharacteristic
361C2—21no—
362C2—21no—
363C2—21no—
364C2—81no—
365C2—442no—
366C2#1306890511yescharacteristic
subgroupG/H
centerC4#10622569
commutatorC2×C4×C11C22×C8
FrattiniC22×C8C22×D11
FittingC11×#2117C2
socleC2×C11#1869
prime radical#10623363C4
cosocleC22×C8×C11C23
hypercenter#2117D11
hypocenterC11#12988
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C22×C8 ◁ #2117

Complements

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

NH ≅ G/Ntype
1. #13081718C2semidirect
3. #13070244C2semidirect
4. #13070236C2semidirect
5. #13066695C2semidirect
6. #13066695C2semidirect
7. C11×#2117C2semidirect
57. C2×C11×C16D4semidirect
68. C2×C11⋊C16D4semidirect
127. #2117D11semidirect
242. C2×C16C22⋊D11semidirect
306. C11#12988semidirect

Maximal subgroups

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

subgroupindex
#130817182
#130773322
#130702442
#130702362
#130666952
C11×#21172
#1298811