Finite Group Databasebeta

← #28402742

Subgroups — #28402742

Order 14464.

388 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#20299301C211yesmaximal, characteristic
2Q8×D452C211yesmaximal, characteristic, complemented
3#20298968C211yesmaximal, characteristic, complemented
4#20298942C211yesmaximal, characteristic, complemented
5#20298935C211yesmaximal, characteristic, complemented
6#20298845C211yesmaximal, characteristic, complemented
7#20298828C211yesmaximal, characteristic, complemented
8#20298804C211yesmaximal, characteristic, complemented
9#20298738C211yesmaximal, characteristic, complemented
10#20298738C211yesmaximal, characteristic, complemented
11#20298696C211yesmaximal, characteristic, complemented
12#20298668C211yesmaximal, characteristic, complemented
13#20298605C211yesmaximal, characteristic, complemented
14#103×D113C211yesmaximal, characteristic, complemented
15#479×C113C211yesmaximal, characteristic, complemented
16C2×Q8×D113C2211yescharacteristic
17C2×Q8×D113C2211yescharacteristic
18C2×#14268636C2211yescharacteristic
19C2×#14268636C2211yescharacteristic
20C2×#14268634C2211yescharacteristic
21C2×#14268630C2211yescharacteristic
22C2×C8×D113C2211yescharacteristic
23#16813622—21no—
24#16813622C2211yescharacteristic
25#16813617—21no—
26#16813607—21no—
27#16813602—21no—
28#16813602—21no—
29#16813602C2211yescharacteristic
30#16813602C2211yescharacteristic
31#16813597—21no—
32#16813597C2211yescharacteristic
33#16813597C2211yescharacteristic
34C4×D452—21no—
35C4×D452C2211yescharacteristic
36C4×D452C2211yescharacteristic
37#16813584—21no—
38#16813580C2211yescharacteristic
39C4⋊C4×D113C2211yescharacteristic
40#16813555C2211yescharacteristic
41#16813547C2211yescharacteristic
42#16813547C2211yescharacteristic
43#16813546C2211yescharacteristic
44#16813545C2211yescharacteristic
45#16813545C2211yescharacteristic
46#16813545C2211yescharacteristic
47#16813545C2211yescharacteristic
48#16813542C2211yescharacteristic
49#16813534C2211yescharacteristic
50#16813534C2211yescharacteristic
51#16813533C2211yescharacteristic
52#125×C113C2211yescharacteristic
53C4×Q8×C113C2211yescharacteristic
54#107×C113C2211yescharacteristic
55#106×C113C2211yescharacteristic
56C4⋊C8×C113C2211yescharacteristic
57#103×C113C2211yescharacteristic
58#103×C113C2211yescharacteristic
59C2×Dic226—21no—
60C2×Dic226—21no—
61C2×Dic226C2311yescharacteristic
62C2×Dic226C2311yescharacteristic
63Q8×D113—22no—
64Q8×D113—22no—
65Q8×D113—41no—
66Q8×D113—41no—
67C2×D452—21no—
68C2×D452—21no—
69C2×D452D411yescharacteristic
70C2×D452C2311yescharacteristic
71C2×C4×D113—21no—
72C2×C4×D113—21no—
73C2×C4×D113—21no—
74C2×C4×D113—21no—
75C2×C4×D113C2311yescharacteristic
76C2×C4×D113C2311yescharacteristic
77#14268636—41no—
78#14268636—41no—
79#14268634—22no—
80#14268630—41no—
81C2×#11744751C2311yescharacteristic
82C2×#11744751C2311yescharacteristic
83C8×D113—41no—
84C4⋊Dic113—21no—
85C4⋊Dic113—21no—
86C4⋊Dic113—21no—
87C4⋊Dic113—21no—
88C4⋊Dic113D411yescharacteristic
89C4⋊Dic113C2311yescharacteristic
90#14268626—21no—
91#14268624—21no—
92#14268624—21no—
93#14268624—21no—
94#14268624—21no—
95#14268624—21no—
96#14268624—21no—
97#14268624D411yescharacteristic
98#14268624D411yescharacteristic
99C4×Dic113—21no—
100C2×Q8×C113C2311yescharacteristic
101C2×C8×C113C2311yescharacteristic
102C2×C8×C113C2311yescharacteristic
103C4⋊C4×C113—21no—
104C4⋊C4×C113—21no—
105C4⋊C4×C113—21no—
106C4⋊C4×C113C2311yescharacteristic
107C4⋊C4×C113C2311yescharacteristic
108C4⋊C4×C113C2311yescharacteristic
109C42×C113—21no—
110C42×C113C2311yescharacteristic
111C22×D113—21no—
112C22×D113C2×D411yescharacteristic
113C22×D113C2×D411yescharacteristic
114Q8×C113—21no—
115Q8×C113#4112yes—
116C2×C4×C113—21no—
117C2×C4×C113—21no—
118C2×C4×C113—21no—
119C2×C4×C113—21no—
120C2×C4×C113C2×D411yescharacteristic
121C2×C4×C113C2×D411yescharacteristic
122C2×C4×C113C2411yescharacteristic
123C2×Dic113—21no—
124C2×Dic113—21no—
125C2×Dic113—21no—
126C2×Dic113C2×D411yescharacteristic
127C2×Dic113C2×D411yescharacteristic
128D452—22no—
129D452—21no—
130D452—21no—
131D452—42no—
132D452—81no—
133C4×D113—21no—
134C4×D113—21no—
135C4×D113—21no—
136C4×D113—21no—
137C4×D113—42no—
138C4×D113—42no—
139C4×D113—81no—
140C4×D113—81no—
141Dic226—21no—
142Dic226—21no—
143Dic226—21no—
144Dic226—21no—
145Dic226—42no—
146Dic226—42no—
147C8×C113—21no—
148C8×C113—21no—
149#11744751—21no—
150#11744751—21no—
151C22×C113C22×D411yescharacteristic
152C2×D113—21no—
153C2×D113—21no—
154C2×D113—21no—
155C2×D113—21no—
156C2×D113—21no—
157C2×D113—41no—
158C2×D113—41no—
159C2×D113—41no—
160C2×D113#13712yes—
161C4×C113—22no—
162C4×C113—21no—
163C4×C113—21no—
164C4×C113—41no—
165C4×C113—41no—
166C4×C113—41no—
167C4×C113C2×#4111yescharacteristic
168C4×C113H(5,𝔽2)11yescharacteristic
169Dic113—21no—
170Dic113—21no—
171Dic113—41no—
172Dic113—41no—
173Dic113—41no—
174C2×C113#54611yescharacteristic
175C2×C113C2×#13711yescharacteristic
176C2×C113#57711yescharacteristic
177D113—22no—
178D113—41no—
179D113—81no—
180#3320—1131nomaximal, Sylow
181C113#332011yescharacteristic, complemented, Sylow
182#553—1131no—
183D4×Q8—1131no—
184#491—1131no—
185#485—1131no—
186#484—1131no—
187#479D11311yescharacteristic, complemented
188#468—1131no—
189#465—1131no—
190#461—1131no—
191#448—1131no—
192#448—1131no—
193#440—1131no—
194#435—1131no—
195#419—1131no—
196C2×#103—1131no—
197C22×Q8—1131no—
198C22×Q8—1131no—
199C2×SD16—1131no—
200C2×SD16—1131no—
201C2×SD16—1131no—
202C2×M16—1131no—
203C22×C8—1131no—
204C4⋊Q8—1131no—
205C4⋊Q8—2261no—
206#126—2261no—
207#125C2×D11311yescharacteristic
208#123—2261no—
209C22⋊Q8—1131no—
210C22⋊Q8—1131no—
211C22⋊Q8—2261no—
212C22⋊Q8—2261no—
213#121—1131no—
214#121—1131no—
215#121—2261no—
216C4×Q8C2×D11311yescharacteristic
217C4×D4—1131no—
218C4×D4—1131no—
219C4×D4—2261no—
220C4×D4—2261no—
221#117—1131no—
222C2×C4⋊C4—1131no—
223#107—1131no—
224#107C2×D11311yescharacteristic
225#106C2×D11311yescharacteristic
226C4⋊C8C2×D11311yescharacteristic
227#103—1131no—
228#103—1131no—
229#103—1131no—
230#103—1131no—
231#103—1131no—
232#103—1131no—
233#103—1131no—
234#103C2×D11311yescharacteristic
235#103C2×D11311yescharacteristic
236#102—1131no—
237C22⋊C8—1131no—
238C22⋊C8—1131no—
239#97—1131no—
240C2×Q8—1131no—
241C2×Q8—1131no—
242C2×Q8—4521no—
243C2×Q8—4521no—
244C2×Q8—2261no—
245C2×Q8—2261no—
246C2×Q8—2262no—
247C2×Q8—2262no—
248C2×Q8C22×D11311yescharacteristic
249C2×D4—1131no—
250C2×D4—1131no—
251C2×D4—2261no—
252C2×D4—2261no—
253C22×C4—1131no—
254C22×C4—1131no—
255C22×C4—2261no—
256C22×C4—2261no—
257C22×C4—2261no—
258C22×C4—2261no—
259SD16—4521no—
260SD16—4521no—
261SD16—2262no—
262M16—4521no—
263C2×C8—1131no—
264C2×C8—1131no—
265C2×C8—4521no—
266C2×C8C22×D11311yescharacteristic
267C2×C8C22×D11311yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—1131no—
272C4⋊C4—1131no—
273C4⋊C4—2261no—
274C4⋊C4—2261no—
275C4⋊C4—2261no—
276C4⋊C4—2261no—
277C4⋊C4—2261no—
278C4⋊C4C22×D11311yescharacteristic
279C4⋊C4C22×D11311yescharacteristic
280C4⋊C4C22×D11311yescharacteristic
281C22⋊C4—1131no—
282C22⋊C4—1131no—
283C22⋊C4—2261no—
284C22⋊C4—2261no—
285C22⋊C4—2261no—
286C22⋊C4—2261no—
287C22⋊C4—2261no—
288C22⋊C4—2261no—
289C42—21no—
290C42—2261no—
291C42C22×D11311yescharacteristic
292C23—1131no—
293C23—1131no—
294C23—2261no—
295Q8—21no—
296Q8—4522no—
297Q8—4522no—
298Q8—2261no—
299Q8—2261no—
300Q8—2261no—
301Q8—2261no—
302Q8#1426864812yes—
303D4—9041no—
304D4—4522no—
305D4—2262no—
306D4—2261no—
307D4—2261no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—1131no—
313C2×C4—1131no—
314C2×C4—9041no—
315C2×C4—9041no—
316C2×C4—4522no—
317C2×C4—4522no—
318C2×C4—2261no—
319C2×C4—2261no—
320C2×C4—2261no—
321C2×C4—2261no—
322C2×C4—2261no—
323C2×C4—2261no—
324C2×C4—2261no—
325C2×C4D4×D11311yescharacteristic
326C2×C4D4×D11311yescharacteristic
327C2×C4C23×D11311yescharacteristic
328C8—21no—
329C8—21no—
330C8—2261no—
331C8—2261no—
332C22—1132no—
333C22—4521no—
334C22—4521no—
335C22—4521no—
336C22—2261no—
337C22—2261no—
338C22—2261no—
339C22—2261no—
340C22—2261no—
341C22C2×D4×D11311yescharacteristic
342C4—21no—
343C4—21no—
344C4—22no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—4521no—
349C4—4521no—
350C4—4521no—
351C4—2261no—
352C4—2261no—
353C4C2×#1426864811yescharacteristic
354C4#1681366811yescharacteristic
355C2—9041no—
356C2—4521no—
357C2—2262no—
358C2#2029923911yescharacteristic
359C2#137×D11311yescharacteristic
360C2#2029940511yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#479×C113C2
socleC22×C113C22×D4
prime radical#20299301C2
hypercenter#479D113
hypocenterC113#3320
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
2. Q8×D452C2semidirect
3. #20298968C2semidirect
4. #20298942C2semidirect
5. #20298935C2semidirect
6. #20298845C2semidirect
7. #20298828C2semidirect
8. #20298804C2semidirect
9. #20298738C2semidirect
10. #20298738C2semidirect
11. #20298696C2semidirect
12. #20298668C2semidirect
13. #20298605C2semidirect
14. #103×D113C2semidirect
15. #479×C113C2semidirect
181. C113#3320semidirect
187. #479D113semidirect

Maximal subgroups

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

subgroupindex
#202993012
Q8×D4522
#202989682
#202989422
#202989352
#202988452
#202988282
#202988042
#202987382
#202986962
#202986682
#202986052
#103×D1132
#479×C1132
#3320113