Finite Group Databasebeta

← #28393324

Subgroups — #28393324

Order 14464.

484 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16813599C211yesmaximal, characteristic
2#20298504C211yesmaximal, characteristic, complemented
3#20298502C211yesmaximal, characteristic, complemented
4#20298491C211yesmaximal, characteristic
5#20298486C211yesmaximal, characteristic
6#20298486C211yesmaximal, characteristic
7#20298485C211yesmaximal, characteristic, complemented
8#20298483C211yesmaximal, characteristic, complemented
9#20298480C211yesmaximal, characteristic, complemented
10#20298479C211yesmaximal, characteristic, complemented
11#20298459C211yesmaximal, characteristic
12C4⋊C4×Dic113C211yesmaximal, characteristic, complemented
13C4×#14268626C211yesmaximal, characteristic, complemented
14C22⋊C4×Dic113C211yesmaximal, characteristic
15#388×C113C211yesmaximal, characteristic
16C22×Dic226C2211yescharacteristic
17C23×Dic113C2211yescharacteristic
18#16813599C418yescomplemented
19C2×C4⋊Dic113C2211yescharacteristic
20C2×C4⋊Dic113C2211yescharacteristic
21C2×#14268626C2211yescharacteristic
22C2×#14268626C2211yescharacteristic
23C2×#14268626C2211yescharacteristic
24C2×#14268626C2211yescharacteristic
25C2×C22⋊Dic113C2211yescharacteristic
26C2×C22⋊Dic113C2211yescharacteristic
27C2×C22⋊Dic113C2211yescharacteristic
28C2×C4×Dic113C2211yescharacteristic
29C2×C4×Dic113C2211yescharacteristic
30C2×C4×Dic113C2211yescharacteristic
31C2×C4×Dic113C2211yescharacteristic
32C2×C4×Dic113C2211yescharacteristic
33#16813529C2211yescharacteristic
34#16813529C2211yescharacteristic
35#16813529C2211yescharacteristic
36#16813529C2211yescharacteristic
37#16813529C2211yescharacteristic
38#16813529C2211yescharacteristic
39#16813529C2211yescharacteristic
40#16813529C2211yescharacteristic
41#16813529C2211yescharacteristic
42#16813529C2211yescharacteristic
43#16813529C2211yescharacteristic
44#16813529C2211yescharacteristic
45C2×C4⋊C4×C113C2211yescharacteristic
46C2×C22⋊C4×C113C2211yescharacteristic
47C2×C22⋊C4×C113C2211yescharacteristic
48C2×C22⋊C4×C113C2211yescharacteristic
49C2×C42×C113C2211yescharacteristic
50#95×C113C2211yescharacteristic
51#95×C113C2211yescharacteristic
52C2×Dic226—41no—
53C2×Dic226—41no—
54C2×Dic226C2×C414yes—
55C22×Dic113—41no—
56C22×Dic113—41no—
57C22×Dic113C2×C414yes—
58C22×Dic113C2311yescharacteristic
59C22×Dic113C2311yescharacteristic
60C22×Dic113C2311yescharacteristic
61C22×Dic113C2311yescharacteristic
62C22×Dic113C2311yescharacteristic
63C22×Dic113C2311yescharacteristic
64C22×Dic113C2311yescharacteristic
65C22×Dic113C2311yescharacteristic
66C4⋊Dic113—41no—
67C4⋊Dic113C2×C414yes—
68#14268626—22no—
69#14268626—41no—
70#14268626C2×C414yes—
71#14268626C2×C414yes—
72C22⋊Dic113—22no—
73C22⋊Dic113—41no—
74C22⋊Dic113C2×C414yes—
75C4×Dic113—22no—
76C4×Dic113—22no—
77C4×Dic113—41no—
78C4×Dic113—41no—
79C4×Dic113—41no—
80C24×C113C2311yescharacteristic
81C22×C4×C113C2311yescharacteristic
82C22×C4×C113C2311yescharacteristic
83C22×C4×C113C2311yescharacteristic
84C22×C4×C113C2311yescharacteristic
85C22×C4×C113C2311yescharacteristic
86C22×C4×C113C2311yescharacteristic
87C4⋊C4×C113—22no—
88C22⋊C4×C113—22no—
89C22⋊C4×C113—41no—
90C22⋊C4×C113C2×C414yes—
91C42×C113—41no—
92C23×C113—21no—
93C23×C113—21no—
94C23×C113—21no—
95C23×C113—21no—
96C23×C113—21no—
97C23×C113—21no—
98C23×C113C22×C412yes—
99C23×C113C2411yescharacteristic
100C2×C4×C113—21no—
101C2×C4×C113—21no—
102C2×C4×C113—21no—
103C2×C4×C113—21no—
104C2×C4×C113—21no—
105C2×C4×C113—21no—
106C2×C4×C113—21no—
107C2×C4×C113—21no—
108C2×C4×C113—21no—
109C2×C4×C113—21no—
110C2×C4×C113—21no—
111C2×C4×C113—21no—
112C2×C4×C113—21no—
113C2×C4×C113—21no—
114C2×C4×C113—21no—
115C2×C4×C113C22×C412yes—
116C2×C4×C113C22×C412yes—
117C2×C4×C113#4112yes—
118C2×Dic113—21no—
119C2×Dic113—21no—
120C2×Dic113—21no—
121C2×Dic113—21no—
122C2×Dic113—21no—
123C2×Dic113—21no—
124C2×Dic113—21no—
125C2×Dic113—21no—
126C2×Dic113—21no—
127C2×Dic113—21no—
128C2×Dic113—21no—
129C2×Dic113—21no—
130C2×Dic113—21no—
131C2×Dic113—21no—
132C2×Dic113—21no—
133C2×Dic113—21no—
134C2×Dic113—21no—
135C2×Dic113—21no—
136C2×Dic113—21no—
137C2×Dic113—44no—
138C2×Dic113C22×C412yes—
139C2×Dic113C22×C412yes—
140C2×Dic113C22×C412yes—
141C2×Dic113C22×C412yes—
142C2×Dic113#4112yes—
143Dic226—44no—
144C22×C113—22no—
145C22×C113—22no—
146C22×C113—22no—
147C22×C113—41no—
148C22×C113—41no—
149C22×C113—41no—
150C22×C113—41no—
151C22×C113C23×C411yescharacteristic
152C22×C113C2×#4111yescharacteristic
153C22×C113C2×#4111yescharacteristic
154C22×C113H(5,𝔽2)11yescharacteristic
155C22×C113H(5,𝔽2)11yescharacteristic
156C22×C1132−1+411yescharacteristic
157C22×C1132−1+411yescharacteristic
158C4×C113—22no—
159C4×C113—22no—
160C4×C113—22no—
161C4×C113—41no—
162C4×C113—41no—
163C4×C113—41no—
164Dic113—22no—
165Dic113—22no—
166Dic113—22no—
167Dic113—22no—
168Dic113—22no—
169Dic113—41no—
170Dic113—41no—
171Dic113—41no—
172C2×C113—42no—
173C2×C113C4×#4111yescharacteristic
174C2×C113#51811yescharacteristic
175C2×C113#51911yescharacteristic
176C2×C113#53911yescharacteristic
177C2×C113#53911yescharacteristic
178C2×C113#54211yescharacteristic
179C2×C113#54211yescharacteristic
180#2332—1131nomaximal, Sylow
181C113#233211yescharacteristic, complemented, Sylow
182C2×C22⋊Q8—1131no—
183#391—1131no—
184#391—1131no—
185#388—1131no—
186#388—1131no—
187#388—1131no—
188#388D11311yescharacteristic
189#387—1131no—
190#387—1131no—
191#387—1131no—
192#387—1131no—
193#381—1131no—
194C4×C4⋊C4—1131no—
195C4×C4⋊C4—1131no—
196C4×C22⋊C4—1131no—
197C22×Q8—1131no—
198C23×C4—1131no—
199C22⋊Q8—1138no—
200C2×C4⋊C4—1131no—
201C2×C4⋊C4—1131no—
202C2×C4⋊C4—1131no—
203C2×C4⋊C4—1131no—
204C2×C4⋊C4—1131no—
205C2×C4⋊C4—1131no—
206C2×C4⋊C4C2×D11311yescharacteristic
207C2×C22⋊C4—1131no—
208C2×C22⋊C4—1131no—
209C2×C22⋊C4—1131no—
210C2×C22⋊C4C2×D11311yescharacteristic
211C2×C22⋊C4C2×D11311yescharacteristic
212C2×C22⋊C4C2×D11311yescharacteristic
213C2×C42—1131no—
214C2×C42—1131no—
215C2×C42—1131no—
216C2×C42—1131no—
217C2×C42—1131no—
218C2×C42C2×D11311yescharacteristic
219#95—1131no—
220#95—1131no—
221#95—1131no—
222#95—1131no—
223#95—1131no—
224#95—1131no—
225#95—1131no—
226#95—1131no—
227#95—1131no—
228#95—1131no—
229#95—1131no—
230#95—1131no—
231#95C2×D11311yescharacteristic
232#95C2×D11311yescharacteristic
233C24C22×D11311yescharacteristic
234C2×Q8—1134no—
235C2×Q8—4521no—
236C2×Q8—4521no—
237C22×C4—1134no—
238C22×C4—1131no—
239C22×C4—1131no—
240C22×C4—1131no—
241C22×C4—1131no—
242C22×C4—1131no—
243C22×C4—1131no—
244C22×C4—1131no—
245C22×C4—1131no—
246C22×C4—4521no—
247C22×C4—4521no—
248C22×C4C22×D11311yescharacteristic
249C22×C4C22×D11311yescharacteristic
250C22×C4C22×D11311yescharacteristic
251C22×C4C22×D11311yescharacteristic
252C22×C4C22×D11311yescharacteristic
253C22×C4C22×D11311yescharacteristic
254C4⋊C4—22no—
255C4⋊C4—1134no—
256C4⋊C4—1134no—
257C4⋊C4—1134no—
258C4⋊C4—4521no—
259C4⋊C4—4521no—
260C4⋊C4—2262no—
261C22⋊C4—22no—
262C22⋊C4—41no—
263C22⋊C4—1134no—
264C22⋊C4—4521no—
265C22⋊C4—2262no—
266C22⋊C4C4×D11314yes—
267C42—41no—
268C42—4521no—
269C42—4521no—
270C42—4521no—
271C42—2262no—
272C42—2262no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23—21no—
279C23C2×C4×D11312yes—
280C23C23×D11311yescharacteristic
281Q8—4524no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—1132no—
298C2×C4—1132no—
299C2×C4—1132no—
300C2×C4—1132no—
301C2×C4—1132no—
302C2×C4—4524no—
303C2×C4—2261no—
304C2×C4—2261no—
305C2×C4—2261no—
306C2×C4—2261no—
307C2×C4—2261no—
308C2×C4—2261no—
309C2×C4—2261no—
310C2×C4—2261no—
311C2×C4—2261no—
312C2×C4—2261no—
313C2×C4—2261no—
314C2×C4—2261no—
315C2×C4—2261no—
316C2×C4—2261no—
317C2×C4—2261no—
318C2×C4—2261no—
319C2×C4—2261no—
320C2×C4—2261no—
321C2×C4—2261no—
322C2×C4C2×C4×D11312yes—
323C2×C4C2×C4×D11312yes—
324C2×C4#1426864612yes—
325C22—22no—
326C22—22no—
327C22—22no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22C22×C4×D11311yescharacteristic
333C22#41×D11311yescharacteristic
334C22C2×#1426864611yescharacteristic
335C22#1681366711yescharacteristic
336C22#1681366811yescharacteristic
337C22#1681366911yescharacteristic
338C22#1681366911yescharacteristic
339C4—22no—
340C4—22no—
341C4—22no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—4521no—
346C4—4521no—
347C4—4521no—
348C4—2262no—
349C4—2262no—
350C4—2262no—
351C4—2262no—
352C4—2262no—
353C2—42no—
354C2C4×#1426864611yescharacteristic
355C2#2029907011yescharacteristic
356C2#2029907511yescharacteristic
357C2#2029919111yescharacteristic
358C2#2029919311yescharacteristic
359C2#2029921411yescharacteristic
360C2#2029921711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D113
commutatorC22×C113C23×C4
Fitting#388×C113C2
socle, cosocleC23×C113C24
prime radicalC24×C113C23
hypercenter#388D113
hypocenterC113#2332
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. #20298504C2semidirect
3. #20298502C2semidirect
7. #20298485C2semidirect
8. #20298483C2semidirect
9. #20298480C2semidirect
10. #20298479C2semidirect
12. C4⋊C4×Dic113C2semidirect
13. C4×#14268626C2semidirect
18. #16813599C4semidirect
181. C113#2332semidirect

Maximal subgroups

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

subgroupindex
C2×#168135992
#202985042
#202985022
#202984912
#202984862
#202984852
#202984832
#202984802
#202984792
#202984592
C4⋊C4×Dic1132
C4×#142686262
C22⋊C4×Dic1132
#388×C1132
#2332113