Finite Group Databasebeta

← #28400586

Subgroups — #28400586

Order 14464.

396 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
1C4×#14268647C211yesmaximal, characteristic, complemented
2#20298936C211yesmaximal, characteristic, complemented
3#20298919C211yesmaximal, characteristic, complemented
4#20298902C211yesmaximal, characteristic, complemented
5#20298895C211yesmaximal, characteristic, complemented
6#20298817C211yesmaximal, characteristic, complemented
7#20298810C211yesmaximal, characteristic, complemented
8#20298758C211yesmaximal, characteristic, complemented
9#20298741C211yesmaximal, characteristic
10C4×#14268637C211yesmaximal, characteristic, complemented
11C4×#14268634C211yesmaximal, characteristic, complemented
12C4×#14268635C211yesmaximal, characteristic, complemented
13C4×#14268632C211yesmaximal, characteristic, complemented
14#20298651C211yesmaximal, characteristic, complemented
15#529×C113C211yesmaximal, characteristic, complemented
16C2×#14268647C2211yescharacteristic
17C2×#14268637C2211yescharacteristic
18C2×#14268635C2211yescharacteristic
19C2×#14268634C2211yescharacteristic
20C2×#14268632C2211yescharacteristic
21C4×Dic226C2211yescharacteristic
22C4×Dic226C2211yescharacteristic
23C4×D452C2211yescharacteristic
24C4×D452C2211yescharacteristic
25C4×C22⋊D113—21no—
26C4×C22⋊D113—21no—
27#16813581C2211yescharacteristic
28#16813579—21no—
29C42×D113—21no—
30#16813555C2211yescharacteristic
31#16813555C2211yescharacteristic
32#16813553C2211yescharacteristic
33#16813553C2211yescharacteristic
34C4⋊#11744751C2211yescharacteristic
35C4⋊#11744751C2211yescharacteristic
36#16813546C2211yescharacteristic
37#16813546C2211yescharacteristic
38#16813545C2211yescharacteristic
39#16813545C2211yescharacteristic
40#16813543C2211yescharacteristic
41#16813543C2211yescharacteristic
42#16813542C2211yescharacteristic
43#16813542C2211yescharacteristic
44C22⋊#11744751C2211yescharacteristic
45C22⋊#11744751C2211yescharacteristic
46C4×#11744751C2211yescharacteristic
47C4×#11744751C2211yescharacteristic
48#126×C113—21no—
49#125×C113C2211yescharacteristic
50#124×C113C2211yescharacteristic
51#123×C113—21no—
52C22⋊Q8×C113C2211yescharacteristic
53#121×C113C2211yescharacteristic
54C4×Q8×C113C2211yescharacteristic
55C4×D4×C113—21no—
56C4×D4×C113C2211yescharacteristic
57#117×C113—21no—
58C2×C42×C113C2211yescharacteristic
59#14268647—22no—
60#14268647—22no—
61C2×Dic226C2311yescharacteristic
62C2×D452C2311yescharacteristic
63C2×C22⋊D113—21no—
64C2×C4×D113—21no—
65C2×C4×D113—21no—
66C2×C4×D113—21no—
67#14268637—22no—
68#14268635—22no—
69#14268634—22no—
70#14268632—22no—
71C2×#11744751C2311yescharacteristic
72C2×#11744751C2311yescharacteristic
73C2×#11744751C2311yescharacteristic
74C2×#11744751C2311yescharacteristic
75C4⋊Dic113C2311yescharacteristic
76C4⋊Dic113C2311yescharacteristic
77#14268626—21no—
78#14268626—21no—
79C22⋊Dic113—21no—
80#14268624—21no—
81#14268624—21no—
82C4×Dic113—21no—
83C4×Dic113—21no—
84C4×Dic113—21no—
85C2×Q8×C113C2311yescharacteristic
86C2×D4×C113—21no—
87C2×D4×C113C2311yescharacteristic
88C22×C4×C113—21no—
89C22×C4×C113D411yescharacteristic
90C22×C4×C113D411yescharacteristic
91C22×C4×C113C2311yescharacteristic
92C4⋊C4×C113—21no—
93C4⋊C4×C113—21no—
94C4⋊C4×C113—21no—
95C4⋊C4×C113—21no—
96C4⋊C4×C113C2311yescharacteristic
97C4⋊C4×C113C2311yescharacteristic
98C22⋊C4×C113—21no—
99C22⋊C4×C113—21no—
100C22⋊C4×C113—21no—
101C22⋊C4×C113—21no—
102C22⋊C4×C113—21no—
103C42×C113—21no—
104C42×C113D411yescharacteristic
105C42×C113D411yescharacteristic
106C42×C113C2311yescharacteristic
107C42×C113C2311yescharacteristic
108C23×C113—21no—
109C23×C113C2×D411yescharacteristic
110C22×D113—21no—
111Q8×C113—21no—
112Q8×C113—21no—
113D4×C113—21no—
114D4×C113—21no—
115D4×C113—42no—
116C2×C4×C113—22no—
117C2×C4×C113—21no—
118C2×C4×C113—21no—
119C2×C4×C113—21no—
120C2×C4×C113—21no—
121C2×C4×C113—21no—
122C2×C4×C113—41no—
123C2×C4×C113—42no—
124C2×C4×C113C2×D411yescharacteristic
125C2×C4×C113C2×D411yescharacteristic
126C2×C4×C113C2×D411yescharacteristic
127C2×C4×C113C2×D411yescharacteristic
128C2×C4×C113C2×D411yescharacteristic
129C2×C4×C113C2411yescharacteristic
130C22⋊D113—24no—
131C2×Dic113—21no—
132C2×Dic113—21no—
133C2×Dic113—21no—
134D452—21no—
135D452#4112yes—
136C4×D113—24no—
137C4×D113—42no—
138C4×D113—42no—
139Dic226—21no—
140Dic226#4112yes—
141#11744751—21no—
142#11744751—21no—
143#11744751—21no—
144#11744751—21no—
145C22×C113—21no—
146C22×C113—21no—
147C22×C113—21no—
148C22×C113—41no—
149C22×C113—41no—
150C22×C113—41no—
151C22×C113C22×D411yescharacteristic
152C2×D113—22no—
153C2×D113—41no—
154C2×D113—41no—
155C4×C113—21no—
156C4×C113—21no—
157C4×C113—21no—
158C4×C113—21no—
159C4×C113—41no—
160C4×C113—41no—
161C4×C113—41no—
162C4×C113#13512yes—
163C4×C113C2×#4111yescharacteristic
164C4×C113C2×#4111yescharacteristic
165Dic113—22no—
166Dic113—41no—
167Dic113—41no—
168C2×C113—41no—
169C2×C113—81no—
170C2×C113#52511yescharacteristic
171C2×C113C2×#13511yescharacteristic
172C2×C113#57511yescharacteristic
173D113—42no—
174#3102—1131nomaximal, Sylow
175C113#310211yescharacteristic, complemented, Sylow
176#529D11311yescharacteristic, complemented
177C4×#41—1131no—
178#485—1131no—
179#482—1131no—
180#479—1131no—
181#478—1131no—
182#464—1131no—
183#463—1131no—
184#452—1131no—
185#449—1131no—
186C4×Q16—1131no—
187C4×SD16—1131no—
188C4×SD16—1131no—
189C4×D8—1131no—
190#431—1131no—
191C2×#41—1131no—
192C2×Q16—1131no—
193C2×SD16—1131no—
194C2×SD16—1131no—
195C2×D8—1131no—
196#126—21no—
197#125C2×D11311yescharacteristic
198#124C2×D11311yescharacteristic
199#123—21no—
200C22⋊Q8C2×D11311yescharacteristic
201#121C2×D11311yescharacteristic
202C4×Q8—1131no—
203C4×Q8—1131no—
204C4×Q8C2×D11311yescharacteristic
205C4×D4—21no—
206C4×D4—1131no—
207C4×D4—1131no—
208C4×D4—2261no—
209C4×D4—2261no—
210C4×D4C2×D11311yescharacteristic
211#117—21no—
212#117—1131no—
213#117—2261no—
214C2×C42—2261no—
215C2×C42C2×D11311yescharacteristic
216#107—1131no—
217#107—1131no—
218#106—1131no—
219#106—1131no—
220C4⋊C8—1131no—
221C4⋊C8—1131no—
222#103—1131no—
223#103—1131no—
224#103—1131no—
225#103—1131no—
226#102—1131no—
227#102—1131no—
228#102—1131no—
229#102—1131no—
230C22⋊C8—1131no—
231C22⋊C8—1131no—
232C4×C8—1131no—
233C4×C8—1131no—
234#41—2262no—
235#41—2262no—
236C2×Q8—1131no—
237C2×Q8C22×D11311yescharacteristic
238C2×D4—21no—
239C2×D4—1131no—
240C2×D4—2261no—
241C2×D4C22×D11311yescharacteristic
242C22×C4—21no—
243C22×C4—2261no—
244C22×C4—2261no—
245C22×C4—2261no—
246C22×C4C22⋊D11311yescharacteristic
247C22×C4C22⋊D11311yescharacteristic
248C22×C4C22×D11311yescharacteristic
249Q16—2262no—
250SD16—2262no—
251SD16—2262no—
252D8—2262no—
253C2×C8—1131no—
254C2×C8—1131no—
255C2×C8—1131no—
256C2×C8—1131no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—1131no—
262C4⋊C4—1131no—
263C4⋊C4—2261no—
264C4⋊C4—2261no—
265C4⋊C4C22×D11311yescharacteristic
266C4⋊C4C22×D11311yescharacteristic
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—21no—
272C22⋊C4—2261no—
273C22⋊C4—2261no—
274C22⋊C4—2261no—
275C42—21no—
276C42—2261no—
277C42—2261no—
278C42—2261no—
279C42C22⋊D11311yescharacteristic
280C42C22⋊D11311yescharacteristic
281C42C22×D11311yescharacteristic
282C42C22×D11311yescharacteristic
283C23—21no—
284C23—2261no—
285C23C2×C22⋊D11311yescharacteristic
286Q8—21no—
287Q8—21no—
288Q8—1132no—
289Q8—2261no—
290D4—21no—
291D4—21no—
292D4—42no—
293D4—1132no—
294D4—2264no—
295D4—2261no—
296C2×C4—22no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—41no—
303C2×C4—42no—
304C2×C4—4522no—
305C2×C4—4522no—
306C2×C4—2264no—
307C2×C4—2261no—
308C2×C4—2261no—
309C2×C4—2261no—
310C2×C4C2×C22⋊D11311yescharacteristic
311C2×C4C2×C22⋊D11311yescharacteristic
312C2×C4C2×C22⋊D11311yescharacteristic
313C2×C4C2×C22⋊D11311yescharacteristic
314C2×C4C2×C22⋊D11311yescharacteristic
315C2×C4C23×D11311yescharacteristic
316C8—2261no—
317C8—2261no—
318C8—2261no—
319C8—2261no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—4521no—
327C22—4521no—
328C22—2262no—
329C22C22×C22⋊D11311yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—4521no—
338C4—4521no—
339C4—2262no—
340C4#1681364212yes—
341C4#41×D11311yescharacteristic
342C4#41×D11311yescharacteristic
343C2—41no—
344C2—81no—
345C2—4522no—
346C2#2029910511yescharacteristic
347C2C2×#1681364211yescharacteristic
348C2#2029939611yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#529×C113C2
socleC22×C113C22×D4
prime radical#20298741C2
hypercenter#529D113
hypocenterC113#3102
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. C4×#14268647C2semidirect
2. #20298936C2semidirect
3. #20298919C2semidirect
4. #20298902C2semidirect
5. #20298895C2semidirect
6. #20298817C2semidirect
7. #20298810C2semidirect
8. #20298758C2semidirect
10. C4×#14268637C2semidirect
11. C4×#14268634C2semidirect
12. C4×#14268635C2semidirect
13. C4×#14268632C2semidirect
14. #20298651C2semidirect
15. #529×C113C2semidirect
175. C113#3102semidirect
176. #529D113semidirect

Maximal subgroups

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

subgroupindex
C4×#142686472
#202989362
#202989192
#202989022
#202988952
#202988172
#202988102
#202987582
#202987412
C4×#142686372
C4×#142686342
C4×#142686352
C4×#142686322
#202986512
#529×C1132
#3102113