Finite Group Databasebeta

← #14908599

Subgroups — #14908599

Order 2816.

632 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622728C211yesmaximal, characteristic
2#13070807C214yesmaximal, complemented
3#13070801C212yesmaximal, complemented
4#13070796C212yesmaximal, complemented
5#13070405C212yesmaximal, complemented
6#13070331C212yesmaximal, complemented
7#13070227C211yesmaximal, characteristic, complemented
8C2×C11×#427C211yesmaximal, characteristic, complemented
9C23×C8×C11C2211yescharacteristic
10C2×C11×#117—21no—
11C2×#66983—21no—
12C22×D88C2211yescharacteristic
13C11×#427—21no—
14C11×#427—21no—
15C11×#427C2212yes—
16C11×#427C2212yescomplemented
17C2×C11×#107C2211yescharacteristic, complemented
18C2×C11×#107C2211yescharacteristic, complemented
19C2×C11×#106—21no—
20#10622728—21no—
21#10622728—21no—
22#10622728C2212yes—
23#10622728C2212yes—
24C2×#66885—21no—
25C2×#66882C2211yescharacteristic
26C2×#66876C2212yes—
27C22⋊(C11⋊C16)C2212yescomplemented
28C22⋊(C11⋊C16)C2212yescomplemented
29#10622129C2214yescomplemented
30#10622129C2214yescomplemented
31#10622128C2214yescomplemented
32#10622127C2214yescomplemented
33C23×C4×C11D411yescharacteristic
34C22×C22⋊D11—41no—
35C22×D44—21no—
36C22×C8×C11—24no—
37C22×C8×C11D411yescharacteristic
38C22×C8×C11D411yescharacteristic
39C22×C8×C11D411yescharacteristic
40C22×C8×C11C2311yescharacteristic
41C22×C8×C11C2311yescharacteristic
42C22×C8×C11C2311yescharacteristic
43C11×#117—22no—
44C11×#117—22no—
45C11×#117—41no—
46C11×#117—41no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C22⋊C4—41no—
50C2×C42×C11—41no—
51#66983—22no—
52#66983—22no—
53#66983—41no—
54#66983—41no—
55C2×(C2×D11)⋊C4—41no—
56C2×C4⋊Dic11—21no—
57C2×D88—24no—
58C2×D88—21no—
59C2×D88C2312yes—
60C11×#107—21no—
61C11×#107—21no—
62C11×#107C2312yes—
63C11×#107C2312yes—
64C11×#106—22no—
65C11×#106—22no—
66#66885—22no—
67#66885—22no—
68#66882—21no—
69#66882C2312yes—
70#66876—24no—
71C2×C11⋊C16C2314yes—
72#33648—111nomaximal, Sylow
73C24×C11D811yescharacteristic
74C23×D11—41no—
75C22×C4×C11—22no—
76C22×C4×C11—22no—
77C22×C4×C11—41no—
78C22×C4×C11—41no—
79C22×C4×C11D811yescharacteristic
80C22×C4×C11D811yescharacteristic
81C22×C4×C11D811yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C2×C22⋊D11—42no—
86C2×C22⋊D11—42no—
87C2×C22⋊D11—84no—
88C22×Dic11—41no—
89C2×D44—22no—
90C2×D44—42no—
91C2×D44—41no—
92C2×D44—42no—
93C2×C8×C11—22no—
94C2×C8×C11—22no—
95C2×C8×C11—22no—
96C2×C8×C11—22no—
97C2×C8×C11—22no—
98C2×C8×C11C2×D411yescharacteristic
99C2×C8×C11C2×D411yescharacteristic
100C2×C8×C11C2×D411yescharacteristic
101C2×C8×C11#4114yes—
102C2×C8×C11C2411yescharacteristic
103C11×C4⋊C4—22no—
104C11×C4⋊C4—22no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—41no—
107C11×C22⋊C4—42no—
108C11×C22⋊C4—42no—
109C42×C11—42no—
110C42×C11—42no—
111(C2×D11)⋊C4—42no—
112(C2×D11)⋊C4—42no—
113C4⋊Dic11—22no—
114C4⋊Dic11—41no—
115D88—24no—
116D88—42no—
117C11⋊C16—24no—
118C2×#466—111no—
119C2×#427D1111yescharacteristic, complemented
120#2234—114no—
121#2233—112no—
122#2232—112no—
123#2159—112no—
124#2140—112no—
125#2112—111no—
126C23×C11—22no—
127C23×C11—22no—
128C23×C11—41no—
129C23×C11C2×D811yescharacteristic
130C23×C11C2×D811yescharacteristic
131C23×C11C2×D811yescharacteristic
132C22×D11—42no—
133C22×D11—82no—
134C22×D11—82no—
135C22×D11—82no—
136C2×C4×C11—22no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—22no—
142C2×C4×C11—22no—
143C2×C4×C11—42no—
144C2×C4×C11—42no—
145C2×C4×C11—82no—
146C2×C4×C11—82no—
147C2×C4×C11#12312yes—
148C2×C4×C11C2×D811yescharacteristic
149C2×C4×C11C2×D811yescharacteristic
150C2×C4×C11C2×D811yescharacteristic
151C2×C4×C11#13712yes—
152C2×C4×C11C22×D411yescharacteristic
153C22⋊D11—84no—
154C22⋊D11—84no—
155C2×Dic11—42no—
156C2×Dic11—82no—
157D44—42no—
158D44—42no—
159D44—82no—
160C8×C11—21no—
161C8×C11—21no—
162C8×C11#12312yes—
163C8×C11C2×#4112yes—
164C22×D8—111no—
165C23×C8C2×D1111yescharacteristic
166C2×#121—221no—
167C2×#117—21no—
168C2×M32—112no—
169#466—112no—
170#466—112no—
171#466—221no—
172#466—221no—
173#427—21no—
174#427—21no—
175#427C2×D1112yes—
176#427C2×D1112yescomplemented
177C2×#107—111no—
178C2×#107C2×D1111yescharacteristic, complemented
179C2×#107C2×D1111yescharacteristic, complemented
180C2×#106—21no—
181C2×#102—221no—
182#367—114no—
183#366—114no—
184#357—114no—
185#357—114no—
186C22⋊C16—112no—
187C22⋊C16—112no—
188C22×C11—21no—
189C22×C11—21no—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11—21no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—44no—
196C22×C11#48012yes—
197C22×C11#50912yes—
198C22×C11C22×D811yescharacteristic
199C2×D11—82no—
200C2×D11—82no—
201C2×D11—82no—
202C2×D11—164no—
203C4×C11—21no—
204C4×C11—21no—
205C4×C11—82no—
206C4×C11—82no—
207C4×C11#48012yes—
208C4×C11C2×#12311yescharacteristic
209C4×C11C2×#13711yescharacteristic
210Dic11—82no—
211C22×D4—221no—
212C22×D4—441no—
213C23×C4C22⋊D1111yescharacteristic
214C2×D8—112no—
215C2×D8—224no—
216C2×D8—221no—
217C22×C8—24no—
218C22×C8C22⋊D1111yescharacteristic
219C22×C8C22⋊D1111yescharacteristic
220C22×C8C22⋊D1111yescharacteristic
221C22×C8C22×D1111yescharacteristic
222C22×C8C22×D1111yescharacteristic
223C22×C8C22×D1111yescharacteristic
224#121—222no—
225#121—222no—
226#121—441no—
227#121—441no—
228#117—22no—
229#117—22no—
230#117—41no—
231#117—41no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—221no—
235C2×C22⋊C4—41no—
236C2×C22⋊C4—441no—
237C2×C42—41no—
238M32—224no—
239C2×C16—114no—
240#107—21no—
241#107—21no—
242#107—112no—
243#107—221no—
244#107C22×D1112yes—
245#107C22×D1112yes—
246#106—22no—
247#106—22no—
248#102—222no—
249#102—222no—
250C2×C11—22no—
251C2×C11—22no—
252C2×C11—41no—
253C2×C11C2×#48011yescharacteristic
254C2×C11C2×#50911yescharacteristic
255C2×C11#341411yescharacteristic
256D11—162no—
257C24—441no—
258C24#432311yescharacteristic
259C2×D4—222no—
260C2×D4—442no—
261C2×D4—442no—
262C2×D4—442no—
263C2×D4—441no—
264C2×D4—442no—
265C2×D4—884no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—441no—
271C22×C4#432311yescharacteristic
272C22×C4#432311yescharacteristic
273C22×C4#432311yescharacteristic
274C22×C4C2×C22⋊D1111yescharacteristic
275C22×C4C2×C22⋊D1111yescharacteristic
276C22×C4C2×C22⋊D1111yescharacteristic
277D8—224no—
278D8—442no—
279C2×C8—22no—
280C2×C8—22no—
281C2×C8—22no—
282C2×C8—22no—
283C2×C8—22no—
284C2×C8#433914yes—
285C2×C8C2×C22⋊D1111yescharacteristic
286C2×C8C2×C22⋊D1111yescharacteristic
287C2×C8C2×C22⋊D1111yescharacteristic
288C2×C8C23×D1111yescharacteristic
289C4⋊C4—22no—
290C4⋊C4—22no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—222no—
294C4⋊C4—441no—
295C22⋊C4—42no—
296C22⋊C4—42no—
297C22⋊C4—442no—
298C22⋊C4—442no—
299C42—42no—
300C42—42no—
301C16—224no—
302C11#3364811yescharacteristic, complemented, Sylow
303C23—22no—
304C23—22no—
305C23—41no—
306C23—442no—
307C23—882no—
308C23—882no—
309C23—882no—
310C23C2×#432311yescharacteristic
311C23C2×#432311yescharacteristic
312C23C2×#432311yescharacteristic
313D4—442no—
314D4—442no—
315D4—884no—
316D4—884no—
317D4—882no—
318C2×C4—22no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—82no—
328C2×C4—82no—
329C2×C4—442no—
330C2×C4—882no—
331C2×C4#6698212yes—
332C2×C4C2×#432311yescharacteristic
333C2×C4C2×#432311yescharacteristic
334C2×C4C2×#432311yescharacteristic
335C2×C4#6699512yes—
336C2×C4C22×C22⋊D1111yescharacteristic
337C8—21no—
338C8—21no—
339C8#6698212yes—
340C8C2×#433912yes—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—44no—
349C22—882no—
350C22—882no—
351C22—882no—
352C22—1764no—
353C22#1062258012yes—
354C22#1062280612yes—
355C22C22×#432311yescharacteristic
356C4—21no—
357C4—21no—
358C4—82no—
359C4—82no—
360C4—882no—
361C4#1062258012yes—
362C4C2×#6698211yescharacteristic
363C4C2×#6699511yescharacteristic
364C2—22no—
365C2—22no—
366C2—41no—
367C2—1762no—
368C2C2×#1062258011yescharacteristic
369C2C2×#1062280611yescharacteristic
370C2#1308175011yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#427C2
socleC22×C11C22×D8
prime radicalC2×#10622728C2
hypercenterC2×#427D11
hypocenterC11#33648
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C23×C8 ◁ C2×#427

Complements

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

NH ≅ G/Ntype
2. #13070807C2semidirect
3. #13070801C2semidirect
4. #13070796C2semidirect
5. #13070405C2semidirect
6. #13070331C2semidirect
7. #13070227C2semidirect
8. C2×C11×#427C2semidirect
16. C11×#427C22semidirect
17. C2×C11×#107C22semidirect
18. C2×C11×#107C22semidirect
27. C22⋊(C11⋊C16)C22semidirect
28. C22⋊(C11⋊C16)C22semidirect
29. #10622129C22semidirect
30. #10622129C22semidirect
31. #10622128C22semidirect
32. #10622127C22semidirect
119. C2×#427D11semidirect
176. #427C2×D11semidirect
178. C2×#107C2×D11semidirect
179. C2×#107C2×D11semidirect
302. C11#33648semidirect

Maximal subgroups

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

subgroupindex
C2×#106227282
#130708072
#130708012
#130707962
#130704052
#130703312
#130702272
C2×C11×#4272
#3364811