Finite Group Databasebeta

← #28400788

Subgroups — #28400788

Order 14464.

372 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299210C211yesmaximal, characteristic, complemented
2#20298933C211yesmaximal, characteristic, complemented
3#20298928C211yesmaximal, characteristic, complemented
4#20298905C211yesmaximal, characteristic, complemented
5#20298898C211yesmaximal, characteristic, complemented
6#20298808C211yesmaximal, characteristic, complemented
7#20298803C211yesmaximal, characteristic, complemented
8#20298760C211yesmaximal, characteristic
9#20298760C211yesmaximal, characteristic
10#20298703C211yesmaximal, characteristic, complemented
11#20298698C211yesmaximal, characteristic, complemented
12C4×#14268637C211yesmaximal, characteristic, complemented
13C4×#14268635C211yesmaximal, characteristic, complemented
14#20298659C211yesmaximal, characteristic, complemented
15#520×C113C211yesmaximal, characteristic
16C2×#14268637C2211yescharacteristic
17C2×#14268637C2211yescharacteristic
18C2×#14268635C2211yescharacteristic
19C2×#14268635C2211yescharacteristic
20#16813622C2211yescharacteristic
21#16813615—21no—
22#16813615—21no—
23#16813614C2211yescharacteristic
24#16813612—21no—
25#16813612—21no—
26#16813601C2211yescharacteristic
27#16813601C2211yescharacteristic
28C4×Dic226C2211yescharacteristic
29C4×Dic226C2211yescharacteristic
30#16813555C2211yescharacteristic
31#16813555C2211yescharacteristic
32#16813553C2211yescharacteristic
33#16813553C2211yescharacteristic
34C4⋊#11744751C2211yescharacteristic
35C4⋊#11744751C2211yescharacteristic
36#16813546C2211yescharacteristic
37#16813546C2211yescharacteristic
38#16813545C2211yescharacteristic
39#16813545C2211yescharacteristic
40#16813545C2211yescharacteristic
41#16813545C2211yescharacteristic
42#16813543C2211yescharacteristic
43#16813543C2211yescharacteristic
44C22⋊#11744751C2211yescharacteristic
45C22⋊#11744751C2211yescharacteristic
46#16813533C2211yescharacteristic
47C4×#11744751C2211yescharacteristic
48C2×#41×C113C2211yescharacteristic
49C4×Q8×C113C2211yescharacteristic
50C4×Q8×C113C2211yescharacteristic
51C4×D4×C113—21no—
52C4×D4×C113—21no—
53C4×D4×C113C2211yescharacteristic
54C4×D4×C113C2211yescharacteristic
55#117×C113—21no—
56#117×C113C2211yescharacteristic
57C2×C4⋊C4×C113—21no—
58C2×C4⋊C4×C113C2211yescharacteristic
59C2×Dic226C2311yescharacteristic
60C2×Dic226C2311yescharacteristic
61#14268637—22no—
62#14268637—22no—
63#14268635—22no—
64#14268635—22no—
65C2×#11744751C2311yescharacteristic
66C2×#11744751C2311yescharacteristic
67C2×#11744751C2311yescharacteristic
68C2×#11744751C2311yescharacteristic
69C4⋊Dic113—21no—
70C4⋊Dic113—21no—
71C4⋊Dic113C2311yescharacteristic
72C4⋊Dic113C2311yescharacteristic
73#14268626—21no—
74#14268626—21no—
75#14268626—21no—
76#14268626—21no—
77#14268626—21no—
78#14268626—21no—
79C22⋊Dic113—21no—
80C22⋊Dic113—21no—
81C4×Dic113—21no—
82C4×Dic113—21no—
83#41×C113—22no—
84#41×C113—22no—
85C2×Q8×C113C2311yescharacteristic
86C2×D4×C113—21no—
87C2×D4×C113C2311yescharacteristic
88C22×C4×C113—21no—
89C22×C4×C113—21no—
90C22×C4×C113—21no—
91C22×C4×C113—21no—
92C22×C4×C113C2311yescharacteristic
93C4⋊C4×C113—21no—
94C4⋊C4×C113—21no—
95C4⋊C4×C113—21no—
96C4⋊C4×C113D411yescharacteristic
97C4⋊C4×C113D411yescharacteristic
98C4⋊C4×C113C2311yescharacteristic
99C4⋊C4×C113C2311yescharacteristic
100C22⋊C4×C113—21no—
101C22⋊C4×C113—21no—
102C22⋊C4×C113D411yescharacteristic
103C22⋊C4×C113D411yescharacteristic
104C42×C113—21no—
105C42×C113—21no—
106C42×C113C2311yescharacteristic
107C42×C113C2311yescharacteristic
108C23×C113—21no—
109C23×C113C2×D411yescharacteristic
110Q8×C113—21no—
111Q8×C113#4112yes—
112D4×C113—24no—
113D4×C113—21no—
114D4×C113#4112yes—
115C2×C4×C113—24no—
116C2×C4×C113—21no—
117C2×C4×C113—21no—
118C2×C4×C113—21no—
119C2×C4×C113—21no—
120C2×C4×C113—21no—
121C2×C4×C113—81no—
122C2×C4×C113—81no—
123C2×C4×C113—81no—
124C2×C4×C113C2×D411yescharacteristic
125C2×C4×C113C2×D411yescharacteristic
126C2×C4×C113C2×D411yescharacteristic
127C2×C4×C113C2×D411yescharacteristic
128C2×C4×C113C2×D411yescharacteristic
129C2×C4×C113C2411yescharacteristic
130C2×Dic113—21no—
131C2×Dic113—21no—
132C2×Dic113—21no—
133C2×Dic113—21no—
134Dic226—21no—
135Dic226—21no—
136Dic226—21no—
137Dic226—21no—
138#11744751—21no—
139#11744751—21no—
140#11744751—21no—
141#11744751—21no—
142C22×C113—21no—
143C22×C113—22no—
144C22×C113—21no—
145C22×C113—21no—
146C22×C113—41no—
147C22×C113—41no—
148C22×C113C22×D411yescharacteristic
149C4×C113—21no—
150C4×C113—22no—
151C4×C113—21no—
152C4×C113—21no—
153C4×C113—21no—
154C4×C113—21no—
155C4×C113—41no—
156C4×C113—41no—
157C4×C113C2×#4111yescharacteristic
158C4×C113C2×#4111yescharacteristic
159Dic113—41no—
160Dic113—41no—
161Dic113—41no—
162Dic113—41no—
163C2×C113—41no—
164C2×C113—42no—
165C2×C113#52511yescharacteristic
166C2×C113#57711yescharacteristic
167C2×C113#57811yescharacteristic
168#3120—1131nomaximal, Sylow
169C113#312011yescharacteristic, complemented, Sylow
170#541—1131no—
171#520D11311yescharacteristic
172#484—1131no—
173#483—1131no—
174#479—1131no—
175#478—1131no—
176#462—1131no—
177#461—1131no—
178#452—1131no—
179#452—1131no—
180#441—1131no—
181#440—1131no—
182C4×Q16—1131no—
183C4×SD16—1131no—
184#433—1131no—
185C2×#41C2×D11311yescharacteristic
186C2×Q16—1131no—
187C2×Q16—1131no—
188C2×SD16—1131no—
189C2×SD16—1131no—
190C4⋊Q8—1131no—
191#126—2261no—
192#126—2261no—
193#125—1131no—
194#125—2261no—
195#125—2261no—
196C22⋊Q8—1131no—
197C22⋊Q8—1131no—
198C4×Q8—1131no—
199C4×Q8—1131no—
200C4×Q8C2×D11311yescharacteristic
201C4×Q8C2×D11311yescharacteristic
202C4×D4—21no—
203C4×D4—21no—
204C4×D4C2×D11311yescharacteristic
205C4×D4C2×D11311yescharacteristic
206#117—21no—
207#117C2×D11311yescharacteristic
208C2×C4⋊C4—21no—
209C2×C4⋊C4C2×D11311yescharacteristic
210#107—1131no—
211#107—1131no—
212#106—1131no—
213#106—1131no—
214C4⋊C8—1131no—
215C4⋊C8—1131no—
216#103—1131no—
217#103—1131no—
218#103—1131no—
219#103—1131no—
220#103—1131no—
221#103—1131no—
222#102—1131no—
223#102—1131no—
224C22⋊C8—1131no—
225C22⋊C8—1131no—
226#97—1131no—
227C4×C8—1131no—
228#41—22no—
229#41—22no—
230C2×Q8—1131no—
231C2×Q8—1131no—
232C2×Q8C22×D11311yescharacteristic
233C2×D4—21no—
234C2×D4C22×D11311yescharacteristic
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4C22×D11311yescharacteristic
240Q16—2262no—
241Q16—2262no—
242SD16—2262no—
243SD16—2262no—
244C2×C8—1131no—
245C2×C8—1131no—
246C2×C8—1131no—
247C2×C8—1131no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—1131no—
252C4⋊C4—1131no—
253C4⋊C4—2261no—
254C4⋊C4—2261no—
255C4⋊C4—2261no—
256C4⋊C4—2261no—
257C4⋊C4—2261no—
258C4⋊C4—2261no—
259C4⋊C4—2261no—
260C4⋊C4—2261no—
261C4⋊C4C22⋊D11311yescharacteristic
262C4⋊C4C22⋊D11311yescharacteristic
263C4⋊C4C22×D11311yescharacteristic
264C4⋊C4C22×D11311yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—2261no—
268C22⋊C4—2261no—
269C22⋊C4C22⋊D11311yescharacteristic
270C22⋊C4C22⋊D11311yescharacteristic
271C42—21no—
272C42—21no—
273C42—2261no—
274C42—2261no—
275C42C22×D11311yescharacteristic
276C42C22×D11311yescharacteristic
277C23—21no—
278C23C2×C22⋊D11311yescharacteristic
279Q8—21no—
280Q8—2261no—
281Q8—2261no—
282Q8—2261no—
283Q8—2261no—
284Q8#1426864712yes—
285D4—24no—
286D4—21no—
287D4#1426864712yes—
288C2×C4—24no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—81no—
295C2×C4—81no—
296C2×C4—81no—
297C2×C4—2261no—
298C2×C4—2261no—
299C2×C4—2261no—
300C2×C4—2261no—
301C2×C4C2×C22⋊D11311yescharacteristic
302C2×C4C2×C22⋊D11311yescharacteristic
303C2×C4C2×C22⋊D11311yescharacteristic
304C2×C4C2×C22⋊D11311yescharacteristic
305C2×C4C2×C22⋊D11311yescharacteristic
306C2×C4C23×D11311yescharacteristic
307C8—2261no—
308C8—2261no—
309C8—2261no—
310C8—2261no—
311C22—21no—
312C22—22no—
313C22—21no—
314C22—21no—
315C22—41no—
316C22—41no—
317C22C22×C22⋊D11311yescharacteristic
318C4—21no—
319C4—22no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—41no—
325C4—41no—
326C4—4521no—
327C4—4521no—
328C4—4521no—
329C4—4521no—
330C4C2×#1426864711yescharacteristic
331C4C2×#1426864711yescharacteristic
332C2—41no—
333C2—42no—
334C2#2029910911yescharacteristic
335C2#2029940911yescharacteristic
336C2#2029941311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#520×C113C2
socleC22×C113C22×D4
prime radicalC2×#41×C113C22
hypercenter#520D113
hypocenterC113#3120
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ #117 ◁ #520

Complements

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

NH ≅ G/Ntype
1. #20299210C2semidirect
2. #20298933C2semidirect
3. #20298928C2semidirect
4. #20298905C2semidirect
5. #20298898C2semidirect
6. #20298808C2semidirect
7. #20298803C2semidirect
10. #20298703C2semidirect
11. #20298698C2semidirect
12. C4×#14268637C2semidirect
13. C4×#14268635C2semidirect
14. #20298659C2semidirect
169. C113#3120semidirect

Maximal subgroups

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

subgroupindex
#202992102
#202989332
#202989282
#202989052
#202988982
#202988082
#202988032
#202987602
#202987032
#202986982
C4×#142686372
C4×#142686352
#202986592
#520×C1132
#3120113