Finite Group Databasebeta

← #28400778

Subgroups — #28400778

Order 14464.

396 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
1#20299204C211yesmaximal, characteristic, complemented
2#20299077C211yesmaximal, characteristic, complemented
3#20298918C211yesmaximal, characteristic, complemented
4#20298913C211yesmaximal, characteristic, complemented
5#20298902C211yesmaximal, characteristic, complemented
6#20298799C211yesmaximal, characteristic, complemented
7#20298793C211yesmaximal, characteristic, complemented
8#20298744C211yesmaximal, characteristic, complemented
9#20298744C211yesmaximal, characteristic, complemented
10#20298707C211yesmaximal, characteristic, complemented
11#20298697C211yesmaximal, characteristic, complemented
12#20298685C211yesmaximal, characteristic, complemented
13#20298678C211yesmaximal, characteristic, complemented
14#20298658C211yesmaximal, characteristic, complemented
15#478×C113C211yesmaximal, characteristic, complemented
16C2×#14268646C2211yescharacteristic
17C2×#14268636C2211yescharacteristic
18C2×#14268636C2211yescharacteristic
19C2×#14268632C2211yescharacteristic
20C2×#14268632C2211yescharacteristic
21#16813619C2211yescharacteristic
22#16813607—21no—
23#16813607—21no—
24#16813597—21no—
25#16813597—21no—
26#16813597C2211yescharacteristic
27#16813597C2211yescharacteristic
28C4×Dic226C2211yescharacteristic
29#16813587C2211yescharacteristic
30D4×Dic113C2211yescharacteristic
31#16813584C2211yescharacteristic
32#16813584C2211yescharacteristic
33C4×C22⋊D113—21no—
34#16813582—21no—
35#16813579C2211yescharacteristic
36#16813578—21no—
37C2×#14268626—21no—
38C4⋊C4×D113C2211yescharacteristic
39#16813555C2211yescharacteristic
40#16813553C2211yescharacteristic
41C4⋊#11744751C2211yescharacteristic
42#16813545C2211yescharacteristic
43#16813545C2211yescharacteristic
44#16813544C2211yescharacteristic
45#16813544C2211yescharacteristic
46#16813542C2211yescharacteristic
47#16813542C2211yescharacteristic
48#16813534C2211yescharacteristic
49#16813534C2211yescharacteristic
50#16813532C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
52#125×C113C2211yescharacteristic
53C4×D4×C113C2211yescharacteristic
54#107×C113C2211yescharacteristic
55#106×C113C2211yescharacteristic
56C4⋊C8×C113C2211yescharacteristic
57#102×C113C2211yescharacteristic
58#102×C113C2211yescharacteristic
59#14268646—22no—
60#14268646—22no—
61C2×Dic226C2311yescharacteristic
62C2×D452—21no—
63C2×D452—21no—
64C2×D452—21no—
65C2×D452—21no—
66C2×D452C2311yescharacteristic
67C2×D452C2311yescharacteristic
68C2×C22⋊D113—21no—
69C22×Dic113—21no—
70C22×Dic113—21no—
71C2×C4×D113—21no—
72C2×C4×D113—21no—
73C2×C4×D113—21no—
74C2×C4×D113C2311yescharacteristic
75#14268636—22no—
76#14268636—22no—
77#14268632—22no—
78#14268632—22no—
79C2×#11744751C2311yescharacteristic
80C2×#11744751C2311yescharacteristic
81C4⋊Dic113C2311yescharacteristic
82#14268626—21no—
83#14268626—21no—
84#14268626—21no—
85#14268626D411yescharacteristic
86#14268626D411yescharacteristic
87C22⋊Dic113—21no—
88#14268624—21no—
89#14268624—21no—
90#14268624—21no—
91#14268624—21no—
92#14268624D411yescharacteristic
93#14268624D411yescharacteristic
94C4×Dic113—21no—
95C4×Dic113—21no—
96C4×Dic113C2311yescharacteristic
97C2×D4×C113C2311yescharacteristic
98C22×C4×C113—21no—
99C2×C8×C113C2311yescharacteristic
100C2×C8×C113C2311yescharacteristic
101C4⋊C4×C113—21no—
102C4⋊C4×C113—21no—
103C4⋊C4×C113C2311yescharacteristic
104C4⋊C4×C113C2311yescharacteristic
105C4⋊C4×C113C2311yescharacteristic
106C22⋊C4×C113—21no—
107C42×C113C2311yescharacteristic
108C23×C113—21no—
109C22×D113—21no—
110C22×D113—21no—
111C22×D113C2×D411yescharacteristic
112D4×C113—21no—
113D4×C113#4112yes—
114C2×C4×C113—21no—
115C2×C4×C113—21no—
116C2×C4×C113—21no—
117C2×C4×C113—81no—
118C2×C4×C113C2×D411yescharacteristic
119C2×C4×C113C2×D411yescharacteristic
120C2×C4×C113C2411yescharacteristic
121C22⋊D113—24no—
122C2×Dic113—24no—
123C2×Dic113—21no—
124C2×Dic113—21no—
125C2×Dic113—81no—
126C2×Dic113C2×D411yescharacteristic
127C2×Dic113C2×D411yescharacteristic
128C2×Dic113C2×D411yescharacteristic
129D452—21no—
130D452—21no—
131D452—21no—
132D452—21no—
133D452—81no—
134D452—81no—
135D452—81no—
136D452—81no—
137C4×D113—21no—
138C4×D113—21no—
139C4×D113—81no—
140C4×D113—81no—
141C4×D113—81no—
142Dic226—21no—
143Dic226#4112yes—
144C8×C113—21no—
145C8×C113—21no—
146#11744751—21no—
147#11744751—21no—
148C22×C113—22no—
149C22×C113—41no—
150C22×C113—41no—
151C22×C113C22×D411yescharacteristic
152C2×D113—21no—
153C2×D113—21no—
154C2×D113—21no—
155C2×D113—41no—
156C2×D113—41no—
157C2×D113—41no—
158C2×D113—41no—
159C2×D113—41no—
160C2×D113—41no—
161C4×C113—21no—
162C4×C113—21no—
163C4×C113—41no—
164C4×C113—41no—
165C4×C113—41no—
166C4×C113C2×#4111yescharacteristic
167C4×C113C2×#4111yescharacteristic
168Dic113—22no—
169Dic113—21no—
170Dic113—21no—
171Dic113—21no—
172Dic113—41no—
173C2×C113—42no—
174C2×C113#52511yescharacteristic
175C2×C113#57611yescharacteristic
176C2×C113#57711yescharacteristic
177D113—41no—
178D113—81no—
179D113—81no—
180#3119—1131nomaximal, Sylow
181C113#311911yescharacteristic, complemented, Sylow
182#540—1131no—
183#520—1131no—
184#481—1131no—
185#480—1131no—
186#479—1131no—
187#478D11311yescharacteristic, complemented
188#460—1131no—
189#459—1131no—
190#449—1131no—
191#449—1131no—
192#442—1131no—
193#440—1131no—
194C4×SD16—1131no—
195C4×D8—1131no—
196#433—1131no—
197C2×#41—1131no—
198C2×SD16—1131no—
199C2×SD16—1131no—
200C2×D8—1131no—
201C2×D8—1131no—
202#127—1131no—
203#125C2×D11311yescharacteristic
204#123—2261no—
205#123—2261no—
206#121—1131no—
207#121—1131no—
208#121—2261no—
209#121—2261no—
210C4×Q8—1131no—
211C4×Q8—1131no—
212C4×D4—1131no—
213C4×D4—1131no—
214C4×D4—1131no—
215C4×D4—2261no—
216C4×D4—2261no—
217C4×D4C2×D11311yescharacteristic
218#117—1131no—
219#117—2261no—
220C2×C4⋊C4—1131no—
221C2×C4⋊C4—2261no—
222#107—1131no—
223#107C2×D11311yescharacteristic
224#106—1131no—
225#106C2×D11311yescharacteristic
226C4⋊C8—1131no—
227C4⋊C8C2×D11311yescharacteristic
228#103—1131no—
229#103—1131no—
230#102—1131no—
231#102—1131no—
232#102—1131no—
233#102—1131no—
234#102C2×D11311yescharacteristic
235#102C2×D11311yescharacteristic
236C22⋊C8—1131no—
237C22⋊C8—1131no—
238#97—1131no—
239C4×C8—1131no—
240#41—2262no—
241#41—2262no—
242C2×Q8—1131no—
243C2×D4—1131no—
244C2×D4—1131no—
245C2×D4—2261no—
246C2×D4—2261no—
247C2×D4—2261no—
248C2×D4—2261no—
249C2×D4—2261no—
250C2×D4C22×D11311yescharacteristic
251C22×C4—21no—
252C22×C4—1131no—
253C22×C4—2261no—
254C22×C4—2261no—
255C22×C4—2261no—
256C22×C4—2261no—
257C22×C4—2261no—
258SD16—2262no—
259SD16—2262no—
260D8—2262no—
261D8—2262no—
262C2×C8—1131no—
263C2×C8—1131no—
264C2×C8C22×D11311yescharacteristic
265C2×C8C22×D11311yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—1131no—
269C4⋊C4—1131no—
270C4⋊C4—1131no—
271C4⋊C4—2261no—
272C4⋊C4—2261no—
273C4⋊C4—2261no—
274C4⋊C4C22×D11311yescharacteristic
275C4⋊C4C22×D11311yescharacteristic
276C4⋊C4C22×D11311yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—1131no—
279C22⋊C4—1131no—
280C22⋊C4—2261no—
281C22⋊C4—2261no—
282C22⋊C4—2261no—
283C22⋊C4—2261no—
284C22⋊C4—2261no—
285C42—1131no—
286C42—2261no—
287C42—2261no—
288C42C22×D11311yescharacteristic
289C23—21no—
290C23—1131no—
291C23—2261no—
292C23—2261no—
293Q8—1132no—
294Q8—2261no—
295D4—21no—
296D4—9041no—
297D4—9041no—
298D4—9041no—
299D4—9041no—
300D4—2264no—
301D4—2261no—
302D4—2261no—
303D4—2261no—
304D4—2261no—
305D4#1426864812yes—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—81no—
310C2×C4—1131no—
311C2×C4—1131no—
312C2×C4—1131no—
313C2×C4—9041no—
314C2×C4—9041no—
315C2×C4—9041no—
316C2×C4—9041no—
317C2×C4—2261no—
318C2×C4—2264no—
319C2×C4—2261no—
320C2×C4—2261no—
321C2×C4—2261no—
322C2×C4D4×D11311yescharacteristic
323C2×C4D4×D11311yescharacteristic
324C2×C4C23×D11311yescharacteristic
325C8—21no—
326C8—21no—
327C8—2261no—
328C8—2261no—
329C22—22no—
330C22—41no—
331C22—41no—
332C22—4521no—
333C22—4521no—
334C22—4521no—
335C22—4521no—
336C22—4521no—
337C22—4521no—
338C22—2261no—
339C22—2261no—
340C22—2261no—
341C22C2×D4×D11311yescharacteristic
342C4—21no—
343C4—21no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—4521no—
348C4—2261no—
349C4—2262no—
350C4—2261no—
351C4—2261no—
352C4#41×D11311yescharacteristic
353C4C2×#1426864811yescharacteristic
354C2—42no—
355C2—9041no—
356C2—9041no—
357C2—4521no—
358C2#2029911111yescharacteristic
359C2#2029940211yescharacteristic
360C2#2029940511yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#478×C113C2
socleC22×C113C22×D4
hypercenter#478D113
hypocenterC113#3119
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #20299204C2semidirect
2. #20299077C2semidirect
3. #20298918C2semidirect
4. #20298913C2semidirect
5. #20298902C2semidirect
6. #20298799C2semidirect
7. #20298793C2semidirect
8. #20298744C2semidirect
9. #20298744C2semidirect
10. #20298707C2semidirect
11. #20298697C2semidirect
12. #20298685C2semidirect
13. #20298678C2semidirect
14. #20298658C2semidirect
15. #478×C113C2semidirect
181. C113#3119semidirect
187. #478D113semidirect

Maximal subgroups

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

subgroupindex
#202992042
#202990772
#202989182
#202989132
#202989022
#202987992
#202987932
#202987442
#202987072
#202986972
#202986852
#202986782
#202986582
#478×C1132
#3119113