Finite Group Databasebeta

← #14909623

Subgroups — #14909623

Order 2816.

584 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078271C211yesmaximal, characteristic, complemented
2#13070824C212yesmaximal, complemented
3#13070804C212yesmaximal, complemented
4#13070727C212yesmaximal, complemented
5#13070710C212yesmaximal, complemented
6#13070545C212yesmaximal, complemented
7#13070532C212yesmaximal, complemented
8#13070230C211yesmaximal, characteristic, complemented
9C11×#3058C211yesmaximal, characteristic
10C22×C11×D8C2211yescharacteristic
11C2×C11×#131C2211yescharacteristic
12C11×#535—21no—
13#10623356—21no—
14C22×Dic44C2211yescharacteristic, complemented
15C11×#469—21no—
16C11×#469—21no—
17C11×#466C2212yes—
18C11×#466C2212yes—
19C11×#427C2211yescharacteristic
20C11×#418—21no—
21C2×#66891C2212yes—
22C2×#66891C2212yes—
23#10622750—21no—
24#10622750—21no—
25#10622733—21no—
26#10622729C2212yes—
27#10622729C2212yescomplemented
28#10622719C2211yescharacteristic, complemented
29C2×#66876C2211yescharacteristic, complemented
30C22×C11⋊C16C2211yescharacteristic, complemented
31#10622200C2212yes—
32#10622200C2212yes—
33C22⋊(C11⋊C16)C2212yes—
34C22⋊(C11⋊C16)C2212yescomplemented
35#10622130C2212yescomplemented
36#10622130C2212yescomplemented
37#10622128C2212yescomplemented
38#10622127C2212yescomplemented
39C2×C11×#41D411yescharacteristic
40C22×D4×C11—21no—
41C22×Dic22—21no—
42C2×C11×D8—21no—
43C2×C11×D8—41no—
44C2×C11×D8—41no—
45C2×C11×D8C2312yes—
46C11×#131—41no—
47C11×#131—41no—
48C2×C11×M16D411yescharacteristic
49C2×C11×M16D411yescharacteristic
50C2×C11×M16D411yescharacteristic
51C22×C8×C11C2311yescharacteristic
52C22×C8×C11C2311yescharacteristic
53C22×C8×C11C2311yescharacteristic
54C11×#127—41no—
55C11×#124—41no—
56C11×#121—22no—
57C11×#121—22no—
58C11×#120—41no—
59C11×#120—41no—
60C11×#117—21no—
61#66997—41no—
62#66989—41no—
63#66988—41no—
64#66988—41no—
65#66979—21no—
66#66977—22no—
67#66977—22no—
68C2×Dic44—21no—
69C2×Dic44—41no—
70C2×Dic44—41no—
71C2×Dic44C2312yes—
72C11×#107C2312yes—
73C11×#106—21no—
74C11×#102—22no—
75C11×#102—22no—
76#66891—42no—
77#66891—42no—
78#66882C2312yes—
79#66881—21no—
80#66880—22no—
81#66880—22no—
82#66876—41no—
83C2×C11⋊C16—41no—
84C2×C11⋊C16C2312yes—
85C2×C11⋊C16C2312yes—
86#33766—111nomaximal, Sylow
87C24×C11—41no—
88C11×#41—41no—
89C11×#41—41no—
90C2×Q8×C11D811yescharacteristic
91C2×D4×C11—22no—
92C2×D4×C11—42no—
93C2×D4×C11—42no—
94C2×D4×C11—42no—
95C2×D4×C11—42no—
96C2×D4×C11—41no—
97C2×D4×C11D811yescharacteristic
98C2×D4×C11D811yescharacteristic
99C2×D4×C11D811yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C22×Dic11—41no—
104C2×Dic22—22no—
105C2×Dic22—42no—
106C2×Dic22—42no—
107C2×Dic22—41no—
108C11×D8—22no—
109C11×D8—22no—
110C11×D8—42no—
111C11×M16—41no—
112C11×M16—41no—
113C11×M16—41no—
114C2×C8×C11—21no—
115C2×C8×C11—21no—
116C2×C8×C11—21no—
117C2×C8×C11—21no—
118C2×C8×C11—21no—
119C2×C8×C11—21no—
120C2×C8×C11C2×D411yescharacteristic
121C2×C8×C11C2×D411yescharacteristic
122C2×C8×C11C2×D411yescharacteristic
123C2×C8×C11C2411yescharacteristic
124C11×C4⋊C4—22no—
125C11×C22⋊C4—41no—
126C11×C22⋊C4—42no—
127C11×C22⋊C4—42no—
128C42×C11—41no—
129C22⋊Dic11—42no—
130C22⋊Dic11—42no—
131C22⋊Dic11—41no—
132C4⋊Dic11—22no—
133Dic11⋊C4—42no—
134Dic11⋊C4—42no—
135C4×Dic11—41no—
136Dic44—22no—
137Dic44—22no—
138Dic44—42no—
139C11⋊C16—22no—
140C11⋊C16—22no—
141#3059—111no—
142#3058D1111yescharacteristic
143#2237—112no—
144#2234—112no—
145#2220—112no—
146#2217—112no—
147#2187—112no—
148#2185—112no—
149#2113—111no—
150C23×C11—42no—
151C23×C11—82no—
152C23×C11—162no—
153C23×C11C2×D811yescharacteristic
154C23×C11C2×D811yescharacteristic
155C23×C11C2×D811yescharacteristic
156Q8×C11—41no—
157D4×C11—41no—
158D4×C11—41no—
159D4×C11—41no—
160D4×C11—42no—
161D4×C11—42no—
162D4×C11—82no—
163D4×C11—162no—
164D4×C11—162no—
165C2×C4×C11—21no—
166C2×C4×C11—21no—
167C2×C4×C11—21no—
168C2×C4×C11—21no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—42no—
172C2×C4×C11C2×D811yescharacteristic
173C2×C4×C11C2×D811yescharacteristic
174C2×C4×C11C2×D811yescharacteristic
175C2×C4×C11C22×D411yescharacteristic
176C2×Dic11—42no—
177C2×Dic11—42no—
178C2×Dic11—82no—
179Dic22—42no—
180Dic22—42no—
181Dic22—82no—
182C8×C11—21no—
183C8×C11—21no—
184C8×C11—21no—
185C8×C11H(5,𝔽2)11yescharacteristic
186C8×C11H(5,𝔽2)11yescharacteristic
187C22×Q16—111no—
188C22×D8C2×D1111yescharacteristic
189C2×#131C2×D1111yescharacteristic
190#536—221no—
191#535—21no—
192C2×SD32—112no—
193C2×SD32—112no—
194C2×M32—111no—
195C22×C16—111no—
196#470—221no—
197#470—221no—
198#469—21no—
199#469—21no—
200#467—112no—
201#467—112no—
202#466C2×D1112yes—
203#466C2×D1112yes—
204#427—111no—
205#427C2×D1111yescharacteristic
206#419—221no—
207#418—21no—
208#367—112no—
209#366—112no—
210#358—112no—
211#358—112no—
212#357—112no—
213#357—112no—
214C22⋊C16—112no—
215C22⋊C16—112no—
216C22×C11—22no—
217C22×C11—22no—
218C22×C11—22no—
219C22×C11—21no—
220C22×C11—21no—
221C22×C11—21no—
222C22×C11—82no—
223C22×C11—82no—
224C22×C11—82no—
225C22×C11—164no—
226C22×C11C22×D811yescharacteristic
227C4×C11—21no—
228C4×C11—21no—
229C4×C11—21no—
230C4×C11—82no—
231C4×C11#53411yescharacteristic
232C4×C11#57511yescharacteristic
233Dic11—82no—
234Dic11—82no—
235C2×#41C22⋊D1111yescharacteristic
236C22×Q8—221no—
237C22×D4—21no—
238C2×Q16—112no—
239C2×Q16—221no—
240C2×Q16—441no—
241C2×Q16—441no—
242C2×D8—21no—
243C2×D8—41no—
244C2×D8—41no—
245C2×D8C22×D1112yes—
246#131—41no—
247#131—41no—
248C2×M16C22⋊D1111yescharacteristic
249C2×M16C22⋊D1111yescharacteristic
250C2×M16C22⋊D1111yescharacteristic
251C22×C8C22×D1111yescharacteristic
252C22×C8C22×D1111yescharacteristic
253C22×C8C22×D1111yescharacteristic
254C4⋊Q8—441no—
255#127—41no—
256#124—41no—
257#124—441no—
258#123—441no—
259#123—441no—
260C22⋊Q8—222no—
261C22⋊Q8—222no—
262#121—22no—
263#121—22no—
264#120—41no—
265#120—41no—
266#117—21no—
267#117—221no—
268SD32—442no—
269SD32—442no—
270M32—441no—
271C2×C16—112no—
272C2×C16—112no—
273C2×C16—441no—
274#107—112no—
275#107C22×D1112yes—
276#106—21no—
277#106—221no—
278#103—222no—
279#103—222no—
280#102—22no—
281#102—22no—
282C2×C11—41no—
283C2×C11—41no—
284C2×C11—41no—
285C2×C11—162no—
286C2×C11#318611yescharacteristic
287C2×C11#341612yes—
288C24—41no—
289#41—41no—
290#41—41no—
291C2×Q8—222no—
292C2×Q8—442no—
293C2×Q8—442no—
294C2×Q8—441no—
295C2×Q8#432311yescharacteristic
296C2×D4—22no—
297C2×D4—42no—
298C2×D4—42no—
299C2×D4—42no—
300C2×D4—42no—
301C2×D4—41no—
302C2×D4#432311yescharacteristic
303C2×D4#432311yescharacteristic
304C2×D4#432311yescharacteristic
305C22×C4—441no—
306C22×C4C2×C22⋊D1111yescharacteristic
307C22×C4C2×C22⋊D1111yescharacteristic
308C22×C4C2×C22⋊D1111yescharacteristic
309Q16—222no—
310Q16—222no—
311Q16—442no—
312D8—22no—
313D8—22no—
314D8—42no—
315M16—41no—
316M16—41no—
317M16—41no—
318C2×C8—21no—
319C2×C8—21no—
320C2×C8—21no—
321C2×C8—21no—
322C2×C8—21no—
323C2×C8—21no—
324C2×C8C2×C22⋊D1111yescharacteristic
325C2×C8C2×C22⋊D1111yescharacteristic
326C2×C8C2×C22⋊D1111yescharacteristic
327C2×C8C23×D1111yescharacteristic
328C4⋊C4—22no—
329C4⋊C4—222no—
330C4⋊C4—442no—
331C4⋊C4—442no—
332C22⋊C4—41no—
333C22⋊C4—42no—
334C22⋊C4—42no—
335C22⋊C4—441no—
336C22⋊C4—442no—
337C22⋊C4—442no—
338C42—41no—
339C42—441no—
340C16—222no—
341C16—222no—
342C11#3376611yescharacteristic, complemented, Sylow
343C23—42no—
344C23—82no—
345C23—162no—
346C23C2×#432311yescharacteristic
347C23C2×#432311yescharacteristic
348C23C2×#432311yescharacteristic
349Q8—41no—
350Q8—442no—
351Q8—442no—
352Q8—882no—
353D4—41no—
354D4—41no—
355D4—41no—
356D4—42no—
357D4—42no—
358D4—82no—
359D4—162no—
360D4—162no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—42no—
368C2×C4—442no—
369C2×C4—442no—
370C2×C4—882no—
371C2×C4C2×#432311yescharacteristic
372C2×C4C2×#432311yescharacteristic
373C2×C4C2×#432311yescharacteristic
374C2×C4C22×C22⋊D1111yescharacteristic
375C8—21no—
376C8—21no—
377C8—21no—
378C8#6703711yescharacteristic
379C8#6703711yescharacteristic
380C22—21no—
381C22—21no—
382C22—21no—
383C22—22no—
384C22—22no—
385C22—22no—
386C22—82no—
387C22—82no—
388C22—82no—
389C22—164no—
390C22C22×#432311yescharacteristic
391C4—21no—
392C4—21no—
393C4—21no—
394C4—82no—
395C4—882no—
396C4—882no—
397C4#1062333511yescharacteristic
398C4#1062335311yescharacteristic
399C2—41no—
400C2—41no—
401C2—41no—
402C2—162no—
403C2#1307936411yescharacteristic
404C2#1308176312yes—
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
Fitting, prime radicalC11×#3058C2
socleC22×C11C22×D8
hypercenter#3058D11
hypocenterC11#33766
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#131 ◁ #3058

Complements

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

NH ≅ G/Ntype
1. #13078271C2semidirect
2. #13070824C2semidirect
3. #13070804C2semidirect
4. #13070727C2semidirect
5. #13070710C2semidirect
6. #13070545C2semidirect
7. #13070532C2semidirect
8. #13070230C2semidirect
14. C22×Dic44C22semidirect
27. #10622729C22semidirect
28. #10622719C22semidirect
29. C2×#66876C22semidirect
30. C22×C11⋊C16C22semidirect
34. C22⋊(C11⋊C16)C22semidirect
35. #10622130C22semidirect
36. #10622130C22semidirect
37. #10622128C22semidirect
38. #10622127C22semidirect
342. C11#33766semidirect

Maximal subgroups

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

subgroupindex
#130782712
#130708242
#130708042
#130707272
#130707102
#130705452
#130705322
#130702302
C11×#30582
#3376611