Finite Group Databasebeta

← #28393875

Subgroups — #28393875

Order 14464.

432 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113⋊#401C211yesmaximal, characteristic, complemented
2#20298540C211yesmaximal, characteristic, complemented
3#20298537C211yesmaximal, characteristic, complemented
4#20298536C211yesmaximal, characteristic, complemented
5#20298527C211yesmaximal, characteristic
6#20298525C211yesmaximal, characteristic
7#20298524C211yesmaximal, characteristic
8#20298520C211yesmaximal, characteristic
9C4×#14268626C211yesmaximal, characteristic, complemented
10C4×C4⋊Dic113C211yesmaximal, characteristic, complemented
11C4×#14268624C211yesmaximal, characteristic
12C4×#14268624C211yesmaximal, characteristic
13C4×#14268624C211yesmaximal, characteristic
14#20298444C211yesmaximal, characteristic, complemented
15C4×C4⋊C4×C113C211yesmaximal, characteristic, complemented
16C22×C4×D113C2211yescharacteristic
17C2×C4⋊Dic113C2211yescharacteristic
18C2×C4⋊Dic113C2211yescharacteristic
19C2×#14268626C2211yescharacteristic
20C2×#14268626C2211yescharacteristic
21C2×#14268624C2211yescharacteristic
22C2×#14268624C2211yescharacteristic
23C2×#14268624C2211yescharacteristic
24C2×#14268624C2211yescharacteristic
25C2×#14268624C2211yescharacteristic
26C2×#14268624C2211yescharacteristic
27C2×C4×Dic113C2211yescharacteristic
28C2×C4×Dic113C2211yescharacteristic
29C2×C4×Dic113C2211yescharacteristic
30#16813529C2211yescharacteristic
31#16813529C2211yescharacteristic
32#16813529C2211yescharacteristic
33#16813529C2211yescharacteristic
34#16813529C2211yescharacteristic
35#16813529C2211yescharacteristic
36#16813529C2211yescharacteristic
37#16813529C2211yescharacteristic
38#16813529C2211yescharacteristic
39#16813529C2211yescharacteristic
40#16813529C2211yescharacteristic
41#16813529C2211yescharacteristic
42#16813529C2211yescharacteristic
43#16813529C2211yescharacteristic
44C2×C4⋊C4×C113C2211yescharacteristic
45C2×C4⋊C4×C113C2211yescharacteristic
46C2×C42×C113C2211yescharacteristic
47C2×C42×C113C2211yescharacteristic
48C2×C42×C113C2211yescharacteristic
49#95×C113C2211yescharacteristic
50#95×C113C2211yescharacteristic
51C23×D113C2311yescharacteristic
52C22×Dic113C2311yescharacteristic
53C22×Dic113C2311yescharacteristic
54C22×Dic113C2311yescharacteristic
55C22×Dic113C2311yescharacteristic
56C22×Dic113C2311yescharacteristic
57C22×Dic113C2311yescharacteristic
58C22×Dic113C2311yescharacteristic
59C2×C4×D113—22no—
60C2×C4×D113—22no—
61C2×C4×D113—22no—
62C4⋊Dic113—22no—
63C4⋊Dic113—22no—
64#14268626—22no—
65#14268626—22no—
66#14268624—22no—
67#14268624—22no—
68#14268624—22no—
69#14268624—22no—
70#14268624—22no—
71#14268624—22no—
72C4×Dic113—22no—
73C4×Dic113—22no—
74C4×Dic113—22no—
75C22×C4×C113C2311yescharacteristic
76C22×C4×C113C2311yescharacteristic
77C22×C4×C113C2311yescharacteristic
78C22×C4×C113C2311yescharacteristic
79C22×C4×C113C2311yescharacteristic
80C22×C4×C113C2311yescharacteristic
81C22×C4×C113C2311yescharacteristic
82C4⋊C4×C113—22no—
83C4⋊C4×C113—22no—
84C42×C113—22no—
85C42×C113—22no—
86C42×C113—22no—
87C23×C113C2411yescharacteristic
88C22×D113—21no—
89C22×D113—21no—
90C22×D113—21no—
91C22×D113—21no—
92C22×D113—21no—
93C22×D113—21no—
94C22×D113#4112yes—
95C2×C4×C113—21no—
96C2×C4×C113—21no—
97C2×C4×C113—21no—
98C2×C4×C113—21no—
99C2×C4×C113—21no—
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#4112yes—
112C2×C4×C113#4112yes—
113C2×C4×C113#4112yes—
114C2×C4×C113#4112yes—
115C2×C4×C113#4112yes—
116C2×Dic113—21no—
117C2×Dic113—21no—
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#4112yes—
137C4×D113—44no—
138C22×C113C2×#4111yescharacteristic
139C22×C113C2×#4111yescharacteristic
140C22×C113C2×#4111yescharacteristic
141C22×C113C2×#4111yescharacteristic
142C22×C113C2×#4111yescharacteristic
143C22×C113C2×#4111yescharacteristic
144C22×C113C2×#4111yescharacteristic
145C2×D113—22no—
146C2×D113—22no—
147C2×D113—22no—
148C2×D113—41no—
149C2×D113—41no—
150C2×D113—41no—
151C2×D113—41no—
152C4×C113—22no—
153C4×C113—22no—
154C4×C113—41no—
155C4×C113—41no—
156C4×C113—41no—
157C4×C113—41no—
158C4×C113#12614yes—
159Dic113—22no—
160Dic113—41no—
161Dic113—41no—
162Dic113—41no—
163Dic113—41no—
164Dic113—41no—
165Dic113—41no—
166C2×C113C2×#12611yescharacteristic
167C2×C113#52911yescharacteristic
168C2×C113#52911yescharacteristic
169C2×C113#52911yescharacteristic
170C2×C113#52911yescharacteristic
171C2×C113#52911yescharacteristic
172C2×C113#52911yescharacteristic
173D113—42no—
174#2401—1131nomaximal, Sylow
175C113#240111yescharacteristic, complemented, Sylow
176#401—1131no—
177#400—1131no—
178#400—1131no—
179#400—1131no—
180#397—1131no—
181#397—1131no—
182#397—1131no—
183#396—1131no—
184C4×C4⋊C4—1131no—
185C4×C4⋊C4—1131no—
186C4×C4⋊C4D11311yescharacteristic, complemented
187C4×C22⋊C4—1131no—
188C4×C22⋊C4—1131no—
189C4×C22⋊C4—1131no—
190#376—1131no—
191C23×C4—1131no—
192C2×C4⋊C4—1131no—
193C2×C4⋊C4—1131no—
194C2×C4⋊C4—1131no—
195C2×C4⋊C4—1131no—
196C2×C4⋊C4C2×D11311yescharacteristic
197C2×C4⋊C4C2×D11311yescharacteristic
198C2×C22⋊C4—1131no—
199C2×C22⋊C4—1131no—
200C2×C22⋊C4—1131no—
201C2×C22⋊C4—1131no—
202C2×C22⋊C4—1131no—
203C2×C22⋊C4—1131no—
204C2×C42—1131no—
205C2×C42—1131no—
206C2×C42—1131no—
207C2×C42C2×D11311yescharacteristic
208C2×C42C2×D11311yescharacteristic
209C2×C42C2×D11311yescharacteristic
210#95—1131no—
211#95—1131no—
212#95—1131no—
213#95—1131no—
214#95—1131no—
215#95—1131no—
216#95—1131no—
217#95—1131no—
218#95—1131no—
219#95—1131no—
220#95—1131no—
221#95—1131no—
222#95—1131no—
223#95—1131no—
224#95C2×D11311yescharacteristic
225#95C2×D11311yescharacteristic
226C24—1131no—
227C22×C4—1131no—
228C22×C4—1131no—
229C22×C4—1131no—
230C22×C4—1131no—
231C22×C4—1131no—
232C22×C4—1131no—
233C22×C4—1131no—
234C22×C4—2262no—
235C22×C4—2262no—
236C22×C4—2262no—
237C22×C4C22×D11311yescharacteristic
238C22×C4C22×D11311yescharacteristic
239C22×C4C22×D11311yescharacteristic
240C22×C4C22×D11311yescharacteristic
241C22×C4C22×D11311yescharacteristic
242C22×C4C22×D11311yescharacteristic
243C22×C4C22×D11311yescharacteristic
244C4⋊C4—22no—
245C4⋊C4—22no—
246C4⋊C4—2262no—
247C4⋊C4—2262no—
248C4⋊C4—2262no—
249C4⋊C4—2262no—
250C22⋊C4—2262no—
251C22⋊C4—2262no—
252C22⋊C4—2262no—
253C22⋊C4—2262no—
254C22⋊C4—2262no—
255C22⋊C4—2262no—
256C42—22no—
257C42—22no—
258C42—22no—
259C42—2262no—
260C42—2262no—
261C42—2262no—
262C23—1132no—
263C23—2261no—
264C23—2261no—
265C23—2261no—
266C23—2261no—
267C23—2261no—
268C23—2261no—
269C23C23×D11311yescharacteristic
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—1132no—
287C2×C4—4524no—
288C2×C4—2261no—
289C2×C4—2261no—
290C2×C4—2261no—
291C2×C4—2261no—
292C2×C4—2261no—
293C2×C4—2261no—
294C2×C4—2261no—
295C2×C4—2261no—
296C2×C4—2261no—
297C2×C4—2261no—
298C2×C4—2261no—
299C2×C4—2261no—
300C2×C4—2261no—
301C2×C4—2261no—
302C2×C4—2261no—
303C2×C4—2261no—
304C2×C4—2261no—
305C2×C4—2261no—
306C2×C4—2261no—
307C2×C4—2261no—
308C2×C4#1426864612yes—
309C2×C4#1426864712yes—
310C2×C4#1426864712yes—
311C2×C4#1426864712yes—
312C2×C4#1426864812yes—
313C22—4521no—
314C22—4521no—
315C22—4521no—
316C22—4521no—
317C22—2262no—
318C22—2262no—
319C22—2262no—
320C22#41×D11311yescharacteristic
321C22#41×D11311yescharacteristic
322C22C2×#1426864611yescharacteristic
323C22C2×#1426864711yescharacteristic
324C22C2×#1426864711yescharacteristic
325C22C2×#1426864711yescharacteristic
326C22C2×#1426864811yescharacteristic
327C4—22no—
328C4—22no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—4521no—
334C4—4521no—
335C4—4521no—
336C4—4521no—
337C4—4521no—
338C4—4521no—
339C4—2262no—
340C4#1681361714yes—
341C2—4522no—
342C2C2×#1681361711yescharacteristic
343C2#2029912611yescharacteristic
344C2#2029912811yescharacteristic
345C2#2029913011yescharacteristic
346C2#2029913211yescharacteristic
347C2#2029913511yescharacteristic
348C2#2029913511yescharacteristic
subgroupG/H
centerC22×C4C22×D113
commutator, socle, cosocleC23×C113C24
FrattiniC23C23×D113
FittingC4×C4⋊C4×C113C2
prime radicalC23×D113C23
hypercenterC4×C4⋊C4D113
hypocenterC113#2401
LCSG ▷ C23×C113 ▷ C113
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C113⋊#401C2semidirect
2. #20298540C2semidirect
3. #20298537C2semidirect
4. #20298536C2semidirect
9. C4×#14268626C2semidirect
10. C4×C4⋊Dic113C2semidirect
14. #20298444C2semidirect
15. C4×C4⋊C4×C113C2semidirect
175. C113#2401semidirect
186. C4×C4⋊C4D113semidirect

Maximal subgroups

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

subgroupindex
C113⋊#4012
#202985402
#202985372
#202985362
#202985272
#202985252
#202985242
#202985202
C4×#142686262
C4×C4⋊Dic1132
C4×#142686242
#202984442
C4×C4⋊C4×C1132
#2401113