Finite Group Databasebeta

← #28402002

Subgroups — #28402002

Order 14464.

334 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299219C211yesmaximal, characteristic
2#20299210C211yesmaximal, characteristic, complemented
3#20298906C211yesmaximal, characteristic, complemented
4#20298899C211yesmaximal, characteristic, complemented
5#20298894C211yesmaximal, characteristic, complemented
6#20298884C211yesmaximal, characteristic, complemented
7#20298856C211yesmaximal, characteristic, complemented
8#20298844C211yesmaximal, characteristic
9#20298839C211yesmaximal, characteristic, complemented
10#20298827C211yesmaximal, characteristic
11#20298821C211yesmaximal, characteristic, complemented
12#20298821C211yesmaximal, characteristic, complemented
13#20298809C211yesmaximal, characteristic, complemented
14#20298804C211yesmaximal, characteristic, complemented
15#424×C113C211yesmaximal, characteristic, complemented
16C2×Dic452C2211yescharacteristic
17C2×Dic452C2211yescharacteristic
18C2×#14268636C2211yescharacteristic
19C2×#14268636C2211yescharacteristic
20#16813622C2211yescharacteristic
21#16813622C2211yescharacteristic
22#16813617—21no—
23#16813615—21no—
24#16813615—21no—
25#16813614C2211yescharacteristic
26#16813612—21no—
27#16813612—21no—
28#16813610C2211yescharacteristic
29#16813608—21no—
30#16813604—21no—
31#16813601C2211yescharacteristic
32#16813601C2211yescharacteristic
33#16813601C2211yescharacteristic
34#16813600—21no—
35#16813596C2211yescharacteristic
36C4×Dic226C2211yescharacteristic
37C4×Dic226C2211yescharacteristic
38C4×Dic226C2211yescharacteristic
39C4×D452C2211yescharacteristic
40#16813556C2211yescharacteristic
41#16813556C2211yescharacteristic
42#16813554C2211yescharacteristic
43#16813554C2211yescharacteristic
44#16813547C2211yescharacteristic
45#16813547C2211yescharacteristic
46#16813547C2211yescharacteristic
47#16813547C2211yescharacteristic
48#16813547C2211yescharacteristic
49#16813547C2211yescharacteristic
50#16813544C2211yescharacteristic
51#16813544C2211yescharacteristic
52C2×M16×C113C2211yescharacteristic
53C22×C8×C113C2211yescharacteristic
54#117×C113C2211yescharacteristic
55C4⋊C8×C113C2211yescharacteristic
56C4⋊C8×C113C2211yescharacteristic
57C4⋊C8×C113C2211yescharacteristic
58C4⋊C8×C113C2211yescharacteristic
59C2×Dic226—21no—
60C2×Dic226C2311yescharacteristic
61C2×Dic226C2311yescharacteristic
62C2×Dic226C2311yescharacteristic
63C2×D452C2311yescharacteristic
64C2×C22⋊D113—21no—
65C2×C4×D113—21no—
66Dic452—41no—
67Dic452—41no—
68#14268636—41no—
69#14268636—41no—
70C4⋊Dic113—21no—
71C4⋊Dic113—21no—
72C4⋊Dic113—21no—
73C4⋊Dic113C2311yescharacteristic
74C4⋊Dic113C2311yescharacteristic
75C4⋊Dic113C2311yescharacteristic
76C4⋊Dic113C2311yescharacteristic
77#14268626—21no—
78#14268626—21no—
79#14268626—21no—
80#14268626—21no—
81#14268626—21no—
82#14268626—21no—
83#14268626—21no—
84#14268626—21no—
85C22⋊Dic113—21no—
86C22⋊Dic113—21no—
87C22⋊Dic113—21no—
88#14268624—21no—
89#14268624—21no—
90#14268624—21no—
91#14268624—21no—
92C4×Dic113—21no—
93C4×Dic113—21no—
94C4×Dic113—21no—
95C22×C4×C113C2311yescharacteristic
96M16×C113—41no—
97C2×C8×C113—41no—
98C2×C8×C113C2311yescharacteristic
99C2×C8×C113C2311yescharacteristic
100C2×C8×C113C2311yescharacteristic
101C2×C8×C113C2311yescharacteristic
102C4⋊C4×C113D411yescharacteristic
103C4⋊C4×C113D411yescharacteristic
104C22⋊C4×C113D411yescharacteristic
105C22⋊C4×C113D411yescharacteristic
106C42×C113C2311yescharacteristic
107C42×C113C2311yescharacteristic
108C23×C113C2×D411yescharacteristic
109C22×D113—21no—
110C2×C4×C113—21no—
111C2×C4×C113—21no—
112C2×C4×C113C2×D411yescharacteristic
113C2×C4×C113C2×D411yescharacteristic
114C2×C4×C113C2×D411yescharacteristic
115C2×C4×C113C2×D411yescharacteristic
116C2×C4×C113C2×D411yescharacteristic
117C2×C4×C113C2411yescharacteristic
118C22⋊D113—81no—
119C2×Dic113—21no—
120C2×Dic113—21no—
121C2×Dic113—21no—
122C2×Dic113—21no—
123C2×Dic113—21no—
124C2×Dic113—21no—
125C2×Dic113—21no—
126D452—21no—
127D452—21no—
128C4×D113—81no—
129Dic226—21no—
130Dic226—21no—
131Dic226—21no—
132Dic226—21no—
133Dic226—21no—
134Dic226—21no—
135Dic226—81no—
136C8×C113—21no—
137C8×C113—21no—
138C8×C113—21no—
139C8×C113—21no—
140C22×C113—21no—
141C22×C113—21no—
142C22×C113—21no—
143C22×C113C22×D411yescharacteristic
144C2×D113—41no—
145C2×D113—41no—
146C2×D113—41no—
147C4×C113—21no—
148C4×C113—21no—
149C4×C113—21no—
150C4×C113—21no—
151C4×C113—21no—
152C4×C113H(5,𝔽2)11yescharacteristic
153C4×C1132−1+411yescharacteristic
154Dic113—41no—
155Dic113—41no—
156Dic113—41no—
157Dic113—41no—
158Dic113—41no—
159Dic113—41no—
160Dic113—41no—
161C2×C113—41no—
162C2×C113#53711yescharacteristic
163C2×C113#57711yescharacteristic
164C2×C113#57811yescharacteristic
165D113—81no—
166#3258—1131nomaximal, Sylow
167C113#325811yescharacteristic, complemented, Sylow
168#542—1131no—
169#541—1131no—
170#479—1131no—
171#478—1131no—
172#477—1131no—
173#475—1131no—
174#470—1131no—
175#468—1131no—
176#467—1131no—
177#465—1131no—
178#464—1131no—
179#464—1131no—
180#462—1131no—
181#461—1131no—
182#424D11311yescharacteristic, complemented
183C2×Q16—1131no—
184C2×Q16—1131no—
185C2×SD16—1131no—
186C2×SD16—1131no—
187C2×M16C2×D11311yescharacteristic
188C22×C8C2×D11311yescharacteristic
189C4⋊Q8—1131no—
190C4⋊Q8—1131no—
191#126—2261no—
192#126—2261no—
193#126—2261no—
194#125—1131no—
195#125—2261no—
196#125—2261no—
197#124—1131no—
198#124—2261no—
199#123—2261no—
200C22⋊Q8—1131no—
201C22⋊Q8—1131no—
202C22⋊Q8—1131no—
203C22⋊Q8—2261no—
204#121—1131no—
205C4×Q8—1131no—
206C4×Q8—1131no—
207C4×Q8—1131no—
208C4×D4—1131no—
209#117C2×D11311yescharacteristic
210#107—1131no—
211#107—1131no—
212#106—1131no—
213#106—1131no—
214C4⋊C8C2×D11311yescharacteristic
215C4⋊C8C2×D11311yescharacteristic
216C4⋊C8C2×D11311yescharacteristic
217C4⋊C8C2×D11311yescharacteristic
218#103—1131no—
219#103—1131no—
220#103—1131no—
221#103—1131no—
222#103—1131no—
223#103—1131no—
224#102—1131no—
225#102—1131no—
226C2×Q8—1131no—
227C2×Q8—1131no—
228C2×Q8—1131no—
229C2×Q8—2261no—
230C2×D4—1131no—
231C2×D4—2261no—
232C22×C4—2261no—
233C22×C4C22×D11311yescharacteristic
234Q16—4521no—
235Q16—4521no—
236SD16—4521no—
237SD16—4521no—
238M16—41no—
239C2×C8—41no—
240C2×C8C22×D11311yescharacteristic
241C2×C8C22×D11311yescharacteristic
242C2×C8C22×D11311yescharacteristic
243C2×C8C22×D11311yescharacteristic
244C4⋊C4—1131no—
245C4⋊C4—1131no—
246C4⋊C4—1131no—
247C4⋊C4—1131no—
248C4⋊C4—2261no—
249C4⋊C4—2261no—
250C4⋊C4—2261no—
251C4⋊C4—2261no—
252C4⋊C4—2261no—
253C4⋊C4—2261no—
254C4⋊C4—2261no—
255C4⋊C4—2261no—
256C4⋊C4—2261no—
257C4⋊C4—2261no—
258C4⋊C4—2261no—
259C4⋊C4D45211yescharacteristic
260C4⋊C4D45211yescharacteristic
261C22⋊C4—2261no—
262C22⋊C4—2261no—
263C22⋊C4—2261no—
264C22⋊C4—2261no—
265C22⋊C4—2261no—
266C22⋊C4—2261no—
267C22⋊C4—2261no—
268C22⋊C4D45211yescharacteristic
269C22⋊C4D45211yescharacteristic
270C42—2261no—
271C42—2261no—
272C42—2261no—
273C42C22×D11311yescharacteristic
274C42C22×D11311yescharacteristic
275C23—2261no—
276C23C2×D45211yescharacteristic
277Q8—9041no—
278Q8—2261no—
279Q8—2261no—
280Q8—2261no—
281Q8—2261no—
282Q8—2261no—
283Q8—2261no—
284D4—9041no—
285D4—2261no—
286D4—2261no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—9041no—
290C2×C4—2261no—
291C2×C4—2261no—
292C2×C4—2261no—
293C2×C4—2261no—
294C2×C4—2261no—
295C2×C4—2261no—
296C2×C4—2261no—
297C2×C4C2×D45211yescharacteristic
298C2×C4C2×D45211yescharacteristic
299C2×C4C2×D45211yescharacteristic
300C2×C4C2×D45211yescharacteristic
301C2×C4C2×D45211yescharacteristic
302C2×C4C23×D11311yescharacteristic
303C8—21no—
304C8—21no—
305C8—21no—
306C8—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—4521no—
311C22—4521no—
312C22—4521no—
313C22C22×D45211yescharacteristic
314C4—21no—
315C4—21no—
316C4—21no—
317C4—21no—
318C4—21no—
319C4—4521no—
320C4—4521no—
321C4—4521no—
322C4—4521no—
323C4—4521no—
324C4—4521no—
325C4—4521no—
326C4#1681366711yescharacteristic
327C4#1681367011yescharacteristic
328C2—41no—
329C2—9041no—
330C2#2029917911yescharacteristic
331C2#2029941011yescharacteristic
332C2#2029941511yescharacteristic
subgroupG/H
centerC22C22×D452
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#424×C113C2
socleC22×C113C22×D4
prime radical#16813596C22
hypercenter#424D113
hypocenterC113#3258
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ #117 ◁ #424

Complements

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

NH ≅ G/Ntype
2. #20299210C2semidirect
3. #20298906C2semidirect
4. #20298899C2semidirect
5. #20298894C2semidirect
6. #20298884C2semidirect
7. #20298856C2semidirect
9. #20298839C2semidirect
11. #20298821C2semidirect
12. #20298821C2semidirect
13. #20298809C2semidirect
14. #20298804C2semidirect
15. #424×C113C2semidirect
167. C113#3258semidirect
182. #424D113semidirect

Maximal subgroups

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

subgroupindex
#202992192
#202992102
#202989062
#202988992
#202988942
#202988842
#202988562
#202988442
#202988392
#202988272
#202988212
#202988092
#202988042
#424×C1132
#3258113