Finite Group Databasebeta

← #28400936

Subgroups — #28400936

Order 14464.

372 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299225C211yesmaximal, characteristic, complemented
2#20299168C211yesmaximal, characteristic
3#20298967C211yesmaximal, characteristic, complemented
4#20298965C211yesmaximal, characteristic, complemented
5#20298956C211yesmaximal, characteristic, complemented
6#20298952C211yesmaximal, characteristic, complemented
7#20298951C211yesmaximal, characteristic, complemented
8#20298950C211yesmaximal, characteristic, complemented
9#20298947C211yesmaximal, characteristic, complemented
10#20298605C211yesmaximal, characteristic, complemented
11#20298596C211yesmaximal, characteristic
12#20298591C211yesmaximal, characteristic
13#103×D113C211yesmaximal, characteristic, complemented
14#20298555C211yesmaximal, characteristic, complemented
15#489×C113C211yesmaximal, characteristic, complemented
16C2×#14268646C2211yescharacteristic
17C2×Q8×D113C2211yescharacteristic
18C2×#14268630C2211yescharacteristic
19C2×C8×D113C2211yescharacteristic
20#16813622C2211yescharacteristic
21#16813621C2211yescharacteristic
22#16813620—21no—
23#16813620C2211yescharacteristic
24#16813614C2211yescharacteristic
25#16813613C2211yescharacteristic
26#16813612—21no—
27#16813609C2211yescharacteristic
28#16813604—21no—
29#16813604—21no—
30#16813600—21no—
31#16813599—21no—
32#16813599—21no—
33#16813598—21no—
34#16813580C2211yescharacteristic
35#16813579C2211yescharacteristic
36C4⋊C4×D113C2211yescharacteristic
37#16813547C2211yescharacteristic
38#16813547C2211yescharacteristic
39#16813547C2211yescharacteristic
40#16813547C2211yescharacteristic
41#16813546C2211yescharacteristic
42#16813546C2211yescharacteristic
43#16813545C2211yescharacteristic
44#16813545C2211yescharacteristic
45#16813545C2211yescharacteristic
46#16813545C2211yescharacteristic
47#16813543C2211yescharacteristic
48#16813543C2211yescharacteristic
49#16813532C2211yescharacteristic
50C4×#11744751C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
52C4⋊Q8×C113C2211yescharacteristic
53#124×C113C2211yescharacteristic
54#103×C113C2211yescharacteristic
55#103×C113C2211yescharacteristic
56#102×C113C2211yescharacteristic
57#102×C113C2211yescharacteristic
58#97×C113C2211yescharacteristic
59#14268646—22no—
60#14268646—22no—
61C2×Dic226—21no—
62C2×Dic226—21no—
63C2×Dic226C2311yescharacteristic
64C2×Dic226C2311yescharacteristic
65Q8×D113—22no—
66Q8×D113—22no—
67C2×C22⋊D113—21no—
68C22×Dic113—21no—
69C2×C4×D113—21no—
70C2×C4×D113—21no—
71C2×C4×D113C2311yescharacteristic
72#14268630—22no—
73C2×#11744751C2311yescharacteristic
74C2×#11744751C2311yescharacteristic
75C8×D113—22no—
76C4⋊Dic113—21no—
77C4⋊Dic113—21no—
78C4⋊Dic113—21no—
79C4⋊Dic113C2311yescharacteristic
80C4⋊Dic113C2311yescharacteristic
81#14268626—21no—
82#14268626—21no—
83#14268626—21no—
84#14268626—21no—
85#14268626—21no—
86#14268626—21no—
87#14268626—21no—
88#14268626D411yescharacteristic
89#14268626D411yescharacteristic
90C22⋊Dic113—21no—
91C22⋊Dic113—21no—
92#14268624—21no—
93#14268624D411yescharacteristic
94#14268624D411yescharacteristic
95C4×Dic113—21no—
96C4×Dic113C2311yescharacteristic
97C2×Q8×C113—21no—
98C2×Q8×C113C2311yescharacteristic
99C2×D4×C113C2311yescharacteristic
100C2×C8×C113C2311yescharacteristic
101C2×C8×C113C2311yescharacteristic
102C4⋊C4×C113—21no—
103C4⋊C4×C113C2311yescharacteristic
104C4⋊C4×C113C2311yescharacteristic
105C22⋊C4×C113—21no—
106C22⋊C4×C113—21no—
107C42×C113C2311yescharacteristic
108C23×C113—21no—
109C22×D113C2×D411yescharacteristic
110Q8×C113—21no—
111Q8×C113—21no—
112Q8×C113—81no—
113D4×C113—21no—
114D4×C113—21no—
115C2×C4×C113—21no—
116C2×C4×C113—21no—
117C2×C4×C113—21no—
118C2×C4×C113C2×D411yescharacteristic
119C2×C4×C113C2×D411yescharacteristic
120C2×C4×C113C2411yescharacteristic
121C22⋊D113—42no—
122C2×Dic113—21no—
123C2×Dic113—21no—
124C2×Dic113—21no—
125C2×Dic113—21no—
126C2×Dic113—42no—
127C2×Dic113C2×D411yescharacteristic
128C2×Dic113C2×D411yescharacteristic
129C2×Dic113C2×D411yescharacteristic
130C4×D113—42no—
131C4×D113—81no—
132C4×D113#4112yes—
133C4×D113#4112yes—
134Dic226—21no—
135Dic226—21no—
136Dic226—21no—
137Dic226—21no—
138Dic226—42no—
139Dic226—81no—
140C8×C113—21no—
141C8×C113—21no—
142#11744751—21no—
143#11744751—21no—
144C22×C113—41no—
145C22×C113—41no—
146C22×C113—41no—
147C22×C113C22×D411yescharacteristic
148C2×D113—21no—
149C2×D113—21no—
150C2×D113#12412yes—
151C4×C113—21no—
152C4×C113—21no—
153C4×C113—41no—
154C4×C113—41no—
155C4×C113—41no—
156C4×C113C2×#4111yescharacteristic
157C4×C113C2×#4111yescharacteristic
158Dic113—21no—
159Dic113—21no—
160Dic113—41no—
161Dic113—41no—
162Dic113—41no—
163Dic113—41no—
164Dic113#12412yes—
165C2×C113—81no—
166C2×C113C2×#12411yescharacteristic
167C2×C113#57711yescharacteristic
168C2×C113#57811yescharacteristic
169D113—22no—
170#3137—1131nomaximal, Sylow
171C113#313711yescharacteristic, complemented, Sylow
172#544—1131no—
173#536—1131no—
174#491—1131no—
175#491—1131no—
176#489—1131no—
177#489D11311yescharacteristic, complemented
178#488—1131no—
179#488—1131no—
180#487—1131no—
181#487—1131no—
182#419—1131no—
183#417—1131no—
184#416—1131no—
185C2×#103—1131no—
186#405—1131no—
187C2×#41—1131no—
188C22×Q8—1131no—
189C2×M16—1131no—
190C22×C8—1131no—
191C4⋊Q8—1131no—
192C4⋊Q8—1131no—
193C4⋊Q8—1131no—
194C4⋊Q8—2261no—
195C4⋊Q8C2×D11311yescharacteristic
196#125—1131no—
197#125—1131no—
198#125—2261no—
199#124—1131no—
200#124C2×D11311yescharacteristic
201#123—2261no—
202#123—2261no—
203C22⋊Q8—2261no—
204C22⋊Q8—2261no—
205C22⋊Q8—2261no—
206C22⋊Q8—2261no—
207#117—1131no—
208#117—1131no—
209C2×C4⋊C4—1131no—
210#103—1131no—
211#103—1131no—
212#103—1131no—
213#103—1131no—
214#103—1131no—
215#103—1131no—
216#103—1131no—
217#103—1131no—
218#103—1131no—
219#103—1131no—
220#103C2×D11311yescharacteristic
221#103C2×D11311yescharacteristic
222#102—1131no—
223#102—1131no—
224#102C2×D11311yescharacteristic
225#102C2×D11311yescharacteristic
226#97—1131no—
227#97C2×D11311yescharacteristic
228C4×C8—1131no—
229C4×C8—1131no—
230#41—2262no—
231#41—2262no—
232C2×Q8—21no—
233C2×Q8—1131no—
234C2×Q8—1131no—
235C2×Q8—2261no—
236C2×Q8—2261no—
237C2×Q8—2262no—
238C2×Q8—2262no—
239C2×Q8C22×D11311yescharacteristic
240C2×D4—2261no—
241C2×D4C22×D11311yescharacteristic
242C22×C4—1131no—
243C22×C4—2261no—
244C22×C4—2261no—
245C22×C4—2261no—
246M16—2262no—
247C2×C8—1131no—
248C2×C8—1131no—
249C2×C8—2262no—
250C2×C8C22×D11311yescharacteristic
251C2×C8C22×D11311yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—1131no—
254C4⋊C4—1131no—
255C4⋊C4—1131no—
256C4⋊C4—1131no—
257C4⋊C4—2261no—
258C4⋊C4—2261no—
259C4⋊C4—2261no—
260C4⋊C4—2261no—
261C4⋊C4—2261no—
262C4⋊C4—2261no—
263C4⋊C4—2261no—
264C4⋊C4—2261no—
265C4⋊C4—2261no—
266C4⋊C4—2261no—
267C4⋊C4C22×D11311yescharacteristic
268C4⋊C4C22×D11311yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—1131no—
272C22⋊C4—1131no—
273C22⋊C4—2261no—
274C22⋊C4—2261no—
275C22⋊C4—2261no—
276C42—1131no—
277C42—2261no—
278C42C22×D11311yescharacteristic
279C23—21no—
280C23—1131no—
281Q8—21no—
282Q8—21no—
283Q8—81no—
284Q8—9041no—
285Q8—4522no—
286Q8—2261no—
287Q8—2261no—
288Q8—2261no—
289Q8—2261no—
290D4—21no—
291D4—21no—
292D4—4522no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—1131no—
297C2×C4—1132no—
298C2×C4—1132no—
299C2×C4—1131no—
300C2×C4—1131no—
301C2×C4—9041no—
302C2×C4—4522no—
303C2×C4—4522no—
304C2×C4—2261no—
305C2×C4—2261no—
306C2×C4—2261no—
307C2×C4—2261no—
308C2×C4D4×D11311yescharacteristic
309C2×C4D4×D11311yescharacteristic
310C2×C4C23×D11311yescharacteristic
311C8—21no—
312C8—21no—
313C8—2261no—
314C8—2261no—
315C22—41no—
316C22—41no—
317C22—41no—
318C22—1132no—
319C22—2261no—
320C22—2261no—
321C22C2×D4×D11311yescharacteristic
322C4—21no—
323C4—21no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—1132no—
328C4—4521no—
329C4—4521no—
330C4—4521no—
331C4—4521no—
332C4—2261no—
333C4—2261no—
334C4#41×D11311yescharacteristic
335C4#41×D11311yescharacteristic
336C2—81no—
337C2—2262no—
338C2#124×D11311yescharacteristic
339C2#2029940811yescharacteristic
340C2#2029941411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#489×C113C2
socleC22×C113C22×D4
prime radicalC2×#14268646C22
hypercenter#489D113
hypocenterC113#3137
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #20299225C2semidirect
3. #20298967C2semidirect
4. #20298965C2semidirect
5. #20298956C2semidirect
6. #20298952C2semidirect
7. #20298951C2semidirect
8. #20298950C2semidirect
9. #20298947C2semidirect
10. #20298605C2semidirect
13. #103×D113C2semidirect
14. #20298555C2semidirect
15. #489×C113C2semidirect
171. C113#3137semidirect
177. #489D113semidirect

Maximal subgroups

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

subgroupindex
#202992252
#202991682
#202989672
#202989652
#202989562
#202989522
#202989512
#202989502
#202989472
#202986052
#202985962
#202985912
#103×D1132
#202985552
#489×C1132
#3137113