Finite Group Databasebeta

← #28402836

Subgroups — #28402836

Order 14464.

380 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299257C211yesmaximal, characteristic
2#20298955C211yesmaximal, characteristic, complemented
3#20298933C211yesmaximal, characteristic, complemented
4#20298922C211yesmaximal, characteristic, complemented
5#20298902C211yesmaximal, characteristic, complemented
6#20298854C211yesmaximal, characteristic, complemented
7#20298846C211yesmaximal, characteristic, complemented
8#20298820C211yesmaximal, characteristic, complemented
9#20298758C211yesmaximal, characteristic, complemented
10#20298753C211yesmaximal, characteristic, complemented
11C4×#14268637C211yesmaximal, characteristic, complemented
12#20298676C211yesmaximal, characteristic, complemented
13#20298606C211yesmaximal, characteristic, complemented
14#20298597C211yesmaximal, characteristic, complemented
15#552×C113C211yesmaximal, characteristic, complemented
16C2×#14268647C2211yescharacteristic
17C22×Dic226C2211yescharacteristic
18C2×#14268637C2211yescharacteristic
19C2×#14268637C2211yescharacteristic
20C2×#14268634C2211yescharacteristic
21C2×#14268631C2211yescharacteristic
22C2×#14268631C2211yescharacteristic
23#16813610C2211yescharacteristic
24#16813608—21no—
25#16813601C2211yescharacteristic
26#16813600—21no—
27#16813596C2211yescharacteristic
28#16813594—21no—
29C4×Dic226C2211yescharacteristic
30#16813582—21no—
31#16813555C2211yescharacteristic
32#16813555C2211yescharacteristic
33#16813553C2211yescharacteristic
34C4⋊#11744751C2211yescharacteristic
35#16813546C2211yescharacteristic
36#16813545C2211yescharacteristic
37#16813545C2211yescharacteristic
38#16813545C2211yescharacteristic
39#16813545C2211yescharacteristic
40#16813545C2211yescharacteristic
41#16813545C2211yescharacteristic
42#16813542C2211yescharacteristic
43#16813542C2211yescharacteristic
44#16813542C2211yescharacteristic
45C22⋊#11744751C2211yescharacteristic
46C22⋊#11744751C2211yescharacteristic
47C4×#11744751C2211yescharacteristic
48#126×C113—21no—
49#125×C113—21no—
50#125×C113C2211yescharacteristic
51#123×C113—21no—
52C22⋊Q8×C113C2211yescharacteristic
53C22⋊Q8×C113C2211yescharacteristic
54C4×Q8×C113C2211yescharacteristic
55C4×D4×C113C2211yescharacteristic
56#117×C113—21no—
57#117×C113C2211yescharacteristic
58C2×C4⋊C4×C113C2211yescharacteristic
59#14268647—22no—
60#14268647—41no—
61C2×Dic226—22no—
62C2×Dic226—21no—
63C2×Dic226—41no—
64C2×Dic226C2311yescharacteristic
65C2×Dic226C2311yescharacteristic
66C2×D452C2311yescharacteristic
67C2×C22⋊D113—21no—
68C2×C22⋊D113—21no—
69C22×Dic113—21no—
70C2×C4×D113—21no—
71#14268637—22no—
72#14268637—41no—
73#14268634—41no—
74#14268631—41no—
75#14268631—41no—
76C2×#11744751C2311yescharacteristic
77C2×#11744751C2311yescharacteristic
78C2×#11744751C2311yescharacteristic
79C2×#11744751C2311yescharacteristic
80C4⋊Dic113C2311yescharacteristic
81#14268626—21no—
82#14268626—21no—
83C22⋊Dic113—21no—
84#14268624—21no—
85#14268624—21no—
86#14268624—21no—
87C4×Dic113—21no—
88C2×Q8×C113C2311yescharacteristic
89C2×D4×C113D411yescharacteristic
90C22×C4×C113—21no—
91C22×C4×C113C2311yescharacteristic
92C22×C4×C113C2311yescharacteristic
93C4⋊C4×C113—21no—
94C4⋊C4×C113—21no—
95C4⋊C4×C113—21no—
96C4⋊C4×C113—21no—
97C4⋊C4×C113—21no—
98C4⋊C4×C113—21no—
99C4⋊C4×C113D411yescharacteristic
100C4⋊C4×C113C2311yescharacteristic
101C4⋊C4×C113C2311yescharacteristic
102C4⋊C4×C113C2311yescharacteristic
103C22⋊C4×C113—21no—
104C22⋊C4×C113—21no—
105C22⋊C4×C113—21no—
106C22⋊C4×C113D411yescharacteristic
107C22⋊C4×C113D411yescharacteristic
108C42×C113—21no—
109C42×C113—21no—
110C42×C113C2311yescharacteristic
111C23×C113C2×D411yescharacteristic
112C23×C113C2×D411yescharacteristic
113C22×D113—21no—
114Q8×C113—21no—
115Q8×C113—21no—
116D4×C113—41no—
117C2×C4×C113—21no—
118C2×C4×C113—21no—
119C2×C4×C113—21no—
120C2×C4×C113—21no—
121C2×C4×C113—21no—
122C2×C4×C113—21no—
123C2×C4×C113—21no—
124C2×C4×C113—21no—
125C2×C4×C113—42no—
126C2×C4×C113C2×D411yescharacteristic
127C2×C4×C113C2×D411yescharacteristic
128C2×C4×C113C2×D411yescharacteristic
129C2×C4×C113C2×D411yescharacteristic
130C2×C4×C113C2411yescharacteristic
131C22⋊D113—42no—
132C22⋊D113—42no—
133C2×Dic113—21no—
134C2×Dic113—21no—
135C2×Dic113—21no—
136C2×Dic113—42no—
137D452—21no—
138D452—21no—
139C4×D113—42no—
140Dic226—21no—
141Dic226—21no—
142Dic226—21no—
143Dic226—42no—
144Dic226#4112yes—
145#11744751—21no—
146#11744751—21no—
147#11744751—21no—
148#11744751—21no—
149C22×C113—21no—
150C22×C113—21no—
151C22×C113—21no—
152C22×C113—21no—
153C22×C113—21no—
154C22×C113—21no—
155C22×C113C22×D411yescharacteristic
156C2×D113—41no—
157C2×D113—41no—
158C2×D113—41no—
159C4×C113—21no—
160C4×C113—21no—
161C4×C113—21no—
162C4×C113—21no—
163C4×C113—41no—
164C4×C113—41no—
165C4×C113—41no—
166C4×C113—41no—
167C4×C113C2×#4111yescharacteristic
168C4×C113H(5,𝔽2)11yescharacteristic
169Dic113—22no—
170Dic113—41no—
171Dic113—41no—
172C2×C113—41no—
173C2×C113—41no—
174C2×C113#54611yescharacteristic
175C2×C113#57511yescharacteristic
176C2×C113#57811yescharacteristic
177D113—81no—
178#3327—1131nomaximal, Sylow
179C113#332711yescharacteristic, complemented, Sylow
180#552D11311yescharacteristic, complemented
181#548—1131no—
182#488—1131no—
183#484—1131no—
184#482—1131no—
185#479—1131no—
186#470—1131no—
187#468—1131no—
188#464—1131no—
189#452—1131no—
190#451—1131no—
191C4×Q16—1131no—
192#436—1131no—
193#419—1131no—
194#417—1131no—
195C2×#41—1131no—
196C22×Q8—1131no—
197C2×Q16—1131no—
198C2×Q16—1131no—
199C2×SD16—1131no—
200C2×M16—1131no—
201C2×M16—1131no—
202#126—21no—
203#125—21no—
204#125C2×D11311yescharacteristic
205#124—1131no—
206#124—2261no—
207#123—21no—
208C22⋊Q8—1131no—
209C22⋊Q8—2261no—
210C22⋊Q8C2×D11311yescharacteristic
211C22⋊Q8C2×D11311yescharacteristic
212#121—1131no—
213#121—2261no—
214C4×Q8—1131no—
215C4×Q8C2×D11311yescharacteristic
216C4×D4—2261no—
217C4×D4C2×D11311yescharacteristic
218#117—21no—
219#117C2×D11311yescharacteristic
220C2×C4⋊C4C2×D11311yescharacteristic
221#107—1131no—
222#107—1131no—
223#106—1131no—
224C4⋊C8—1131no—
225#103—1131no—
226#103—1131no—
227#103—1131no—
228#103—1131no—
229#103—1131no—
230#103—1131no—
231#103—1131no—
232#102—1131no—
233#102—1131no—
234#102—1131no—
235C22⋊C8—1131no—
236C22⋊C8—1131no—
237C4×C8—1131no—
238#41—4521no—
239#41—2262no—
240C2×Q8—1131no—
241C2×Q8—1131no—
242C2×Q8—4521no—
243C2×Q8—2262no—
244C2×Q8—2261no—
245C2×Q8C22×D11311yescharacteristic
246C2×D4—1131no—
247C2×D4—2261no—
248C2×D4—2261no—
249C2×D4C22⋊D11311yescharacteristic
250C22×C4—21no—
251C22×C4—2261no—
252C22×C4—2261no—
253C22×C4C22×D11311yescharacteristic
254C22×C4C22×D11311yescharacteristic
255Q16—4521no—
256Q16—2262no—
257SD16—4521no—
258M16—4521no—
259M16—4521no—
260C2×C8—1131no—
261C2×C8—1131no—
262C2×C8—1131no—
263C2×C8—1131no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—1131no—
271C4⋊C4—2261no—
272C4⋊C4—2261no—
273C4⋊C4C22⋊D11311yescharacteristic
274C4⋊C4C22×D11311yescharacteristic
275C4⋊C4C22×D11311yescharacteristic
276C4⋊C4C22×D11311yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—21no—
280C22⋊C4—2261no—
281C22⋊C4—2261no—
282C22⋊C4—2261no—
283C22⋊C4—2261no—
284C22⋊C4C22⋊D11311yescharacteristic
285C22⋊C4C22⋊D11311yescharacteristic
286C42—21no—
287C42—21no—
288C42—2261no—
289C42C22×D11311yescharacteristic
290C23—2261no—
291C23C2×C22⋊D11311yescharacteristic
292C23C2×C22⋊D11311yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—1132no—
296Q8—4522no—
297Q8—2261no—
298Q8—2261no—
299Q8—2261no—
300D4—41no—
301D4—4522no—
302D4—4522no—
303D4—2261no—
304D4—2261no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—42no—
314C2×C4—4522no—
315C2×C4—4522no—
316C2×C4—2261no—
317C2×C4—2261no—
318C2×C4—2261no—
319C2×C4C2×C22⋊D11311yescharacteristic
320C2×C4C2×C22⋊D11311yescharacteristic
321C2×C4C2×C22⋊D11311yescharacteristic
322C2×C4C2×C22⋊D11311yescharacteristic
323C2×C4C23×D11311yescharacteristic
324C8—2261no—
325C8—2261no—
326C8—2261no—
327C8—2261no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—4521no—
335C22—4521no—
336C22—4521no—
337C22C22×C22⋊D11311yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—4521no—
347C4—4521no—
348C4—2262no—
349C4#41×D11311yescharacteristic
350C4#1681366811yescharacteristic
351C2—41no—
352C2—41no—
353C2—9041no—
354C2#2029923611yescharacteristic
355C2#2029939611yescharacteristic
356C2#2029941311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#552×C113C2
socleC22×C113C22×D4
prime radical#20299257C2
hypercenter#552D113
hypocenterC113#3327
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C4×D4 ◁ #552

Complements

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

NH ≅ G/Ntype
2. #20298955C2semidirect
3. #20298933C2semidirect
4. #20298922C2semidirect
5. #20298902C2semidirect
6. #20298854C2semidirect
7. #20298846C2semidirect
8. #20298820C2semidirect
9. #20298758C2semidirect
10. #20298753C2semidirect
11. C4×#14268637C2semidirect
12. #20298676C2semidirect
13. #20298606C2semidirect
14. #20298597C2semidirect
15. #552×C113C2semidirect
179. C113#3327semidirect
180. #552D113semidirect

Maximal subgroups

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

subgroupindex
#202992572
#202989552
#202989332
#202989222
#202989022
#202988542
#202988462
#202988202
#202987582
#202987532
C4×#142686372
#202986762
#202986062
#202985972
#552×C1132
#3327113