Finite Group Databasebeta

← #28402745

Subgroups — #28402745

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#20299294C211yesmaximal, characteristic
2#20298966C211yesmaximal, characteristic, complemented
3#20298936C211yesmaximal, characteristic, complemented
4#20298931C211yesmaximal, characteristic, complemented
5#20298905C211yesmaximal, characteristic, complemented
6#20298846C211yesmaximal, characteristic, complemented
7#20298829C211yesmaximal, characteristic, complemented
8#20298800C211yesmaximal, characteristic, complemented
9#20298737C211yesmaximal, characteristic, complemented
10#20298737C211yesmaximal, characteristic, complemented
11#20298696C211yesmaximal, characteristic, complemented
12#20298670C211yesmaximal, characteristic, complemented
13#20298607C211yesmaximal, characteristic, complemented
14C2×#16813546C211yesmaximal, characteristic, complemented
15D4×Q8×C113C211yesmaximal, characteristic, complemented
16C2×#14268634C2211yescharacteristic
17C2×#14268634C2211yescharacteristic
18C2×#14268634C2211yescharacteristic
19C2×#14268631C2211yescharacteristic
20C22×#11744751C2211yescharacteristic
21#16813617—21no—
22#16813614C2211yescharacteristic
23#16813604—21no—
24#16813596C2211yescharacteristic
25#16813596C2211yescharacteristic
26#16813594—21no—
27C4×D452C2211yescharacteristic
28#16813582—21no—
29#16813581C2211yescharacteristic
30C2×C4⋊Dic113C2211yescharacteristic
31#16813555C2211yescharacteristic
32#16813555C2211yescharacteristic
33#16813553C2211yescharacteristic
34C4⋊#11744751C2211yescharacteristic
35#16813546C2211yescharacteristic
36#16813546C2211yescharacteristic
37#16813546C2211yescharacteristic
38#16813546C2211yescharacteristic
39#16813546C2211yescharacteristic
40#16813546C2211yescharacteristic
41#16813546C2211yescharacteristic
42#16813546C2211yescharacteristic
43#16813546C2211yescharacteristic
44#16813542C2211yescharacteristic
45C22⋊#11744751C2211yescharacteristic
46C22⋊#11744751C2211yescharacteristic
47#16813533C2211yescharacteristic
48C22×Q8×C113C2211yescharacteristic
49C22×Q8×C113C2211yescharacteristic
50C4⋊Q8×C113—21no—
51C4⋊Q8×C113C2211yescharacteristic
52C22⋊Q8×C113—21no—
53C22⋊Q8×C113—21no—
54C22⋊Q8×C113C2211yescharacteristic
55C22⋊Q8×C113C2211yescharacteristic
56C4×Q8×C113C2211yescharacteristic
57C4×D4×C113—21no—
58C4×D4×C113C2211yescharacteristic
59C2×D452C2311yescharacteristic
60C2×C22⋊D113—21no—
61C2×C22⋊D113—21no—
62C22×Dic113—21no—
63C2×C4×D113—21no—
64#14268634—22no—
65#14268634—41no—
66#14268634—41no—
67#14268631—41no—
68C2×#11744751—41no—
69C2×#11744751C2311yescharacteristic
70C2×#11744751C2311yescharacteristic
71C2×#11744751C2311yescharacteristic
72C2×#11744751C2311yescharacteristic
73C4⋊Dic113—21no—
74C4⋊Dic113C2311yescharacteristic
75C4⋊Dic113C2311yescharacteristic
76C4⋊Dic113C2311yescharacteristic
77#14268626—21no—
78#14268626—21no—
79C22⋊Dic113—21no—
80#14268624—21no—
81#14268624—21no—
82#14268624—21no—
83C4×Dic113—21no—
84C2×Q8×C113—21no—
85C2×Q8×C113—21no—
86C2×Q8×C113—22no—
87C2×Q8×C113—22no—
88C2×Q8×C113—41no—
89C2×Q8×C113—41no—
90C2×Q8×C113C2311yescharacteristic
91C2×Q8×C113C2311yescharacteristic
92C2×Q8×C113C2311yescharacteristic
93C2×D4×C113D411yescharacteristic
94C22×C4×C113—21no—
95C22×C4×C113—21no—
96C22×C4×C113C2311yescharacteristic
97C22×C4×C113C2311yescharacteristic
98C4⋊C4×C113—21no—
99C4⋊C4×C113—21no—
100C4⋊C4×C113—21no—
101C4⋊C4×C113—21no—
102C4⋊C4×C113—21no—
103C4⋊C4×C113D411yescharacteristic
104C4⋊C4×C113C2311yescharacteristic
105C22⋊C4×C113—21no—
106C22⋊C4×C113—21no—
107C22⋊C4×C113D411yescharacteristic
108C22⋊C4×C113D411yescharacteristic
109C42×C113—21no—
110C42×C113C2311yescharacteristic
111C23×C113C2×D411yescharacteristic
112C23×C113C2×D411yescharacteristic
113C22×D113—21no—
114Q8×C113—21no—
115Q8×C113—21no—
116Q8×C113—21no—
117Q8×C113—21no—
118Q8×C113—21no—
119Q8×C113—42no—
120Q8×C113—42no—
121Q8×C113#4112yes—
122D4×C113—22no—
123C2×C4×C113—21no—
124C2×C4×C113—21no—
125C2×C4×C113—21no—
126C2×C4×C113—21no—
127C2×C4×C113—21no—
128C2×C4×C113—21no—
129C2×C4×C113—21no—
130C2×C4×C113—21no—
131C2×C4×C113—42no—
132C2×C4×C113—42no—
133C2×C4×C113C2×D411yescharacteristic
134C2×C4×C113C2×D411yescharacteristic
135C2×C4×C113C2×D411yescharacteristic
136C2×C4×C113C2×D411yescharacteristic
137C2×C4×C113C2411yescharacteristic
138C22⋊D113—42no—
139C22⋊D113—81no—
140C2×Dic113—21no—
141C2×Dic113—21no—
142C2×Dic113—21no—
143C2×Dic113—81no—
144D452—21no—
145D452—21no—
146C4×D113—81no—
147#11744751—21no—
148#11744751—21no—
149#11744751—21no—
150#11744751—21no—
151C22×C113—21no—
152C22×C113—21no—
153C22×C113—21no—
154C22×C113—21no—
155C22×C113—21no—
156C22×C113#13712yes—
157C22×C113C22×D411yescharacteristic
158C2×D113—41no—
159C2×D113—41no—
160C2×D113—41no—
161C4×C113—21no—
162C4×C113—21no—
163C4×C113—22no—
164C4×C113—21no—
165C4×C113—21no—
166C4×C113—41no—
167C4×C113—41no—
168C4×C113—41no—
169C4×C113C2×#4111yescharacteristic
170C4×C113H(5,𝔽2)11yescharacteristic
171Dic113—41no—
172Dic113—41no—
173Dic113—41no—
174C2×C113—22no—
175C2×C113—41no—
176C2×C113#54611yescharacteristic
177C2×C113C2×#13711yescharacteristic
178C2×C113#57711yescharacteristic
179D113—81no—
180#3320—1131nomaximal, Sylow
181C113#332011yescharacteristic, complemented, Sylow
182#553—1131no—
183D4×Q8D11311yescharacteristic, complemented
184#491—1131no—
185#485—1131no—
186#484—1131no—
187#479—1131no—
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×Q8C2×D11311yescharacteristic
198C22×Q8C2×D11311yescharacteristic
199C2×SD16—1131no—
200C2×SD16—1131no—
201C2×SD16—1131no—
202C2×M16—1131no—
203C22×C8—1131no—
204C4⋊Q8—21no—
205C4⋊Q8C2×D11311yescharacteristic
206#126—2261no—
207#125—1131no—
208#123—2261no—
209C22⋊Q8—21no—
210C22⋊Q8—21no—
211C22⋊Q8C2×D11311yescharacteristic
212C22⋊Q8C2×D11311yescharacteristic
213#121—1131no—
214#121—1131no—
215#121—2261no—
216C4×Q8C2×D11311yescharacteristic
217C4×D4—21no—
218C4×D4—1131no—
219C4×D4—2261no—
220C4×D4C2×D11311yescharacteristic
221#117—1131no—
222C2×C4⋊C4—1131no—
223#107—1131no—
224#107—1131no—
225#106—1131no—
226C4⋊C8—1131no—
227#103—1131no—
228#103—1131no—
229#103—1131no—
230#103—1131no—
231#103—1131no—
232#103—1131no—
233#103—1131no—
234#103—1131no—
235#103—1131no—
236#102—1131no—
237C22⋊C8—1131no—
238C22⋊C8—1131no—
239#97—1131no—
240C2×Q8—21no—
241C2×Q8—21no—
242C2×Q8—22no—
243C2×Q8—22no—
244C2×Q8—41no—
245C2×Q8—41no—
246C2×Q8C22×D11311yescharacteristic
247C2×Q8C22×D11311yescharacteristic
248C2×Q8C22×D11311yescharacteristic
249C2×D4—1131no—
250C2×D4—2261no—
251C2×D4—2261no—
252C2×D4C22⋊D11311yescharacteristic
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—2261no—
256C22×C4—2261no—
257C22×C4C22×D11311yescharacteristic
258C22×C4C22×D11311yescharacteristic
259SD16—4521no—
260SD16—4521no—
261SD16—2262no—
262M16—4521no—
263C2×C8—1131no—
264C2×C8—1131no—
265C2×C8—1131no—
266C2×C8—1131no—
267C2×C8—4521no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—1131no—
274C4⋊C4—1131no—
275C4⋊C4—1131no—
276C4⋊C4—2261no—
277C4⋊C4—2261no—
278C4⋊C4—2261no—
279C4⋊C4C22⋊D11311yescharacteristic
280C4⋊C4C22×D11311yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—2261no—
284C22⋊C4—2261no—
285C22⋊C4—2261no—
286C22⋊C4—2261no—
287C22⋊C4C22⋊D11311yescharacteristic
288C22⋊C4C22⋊D11311yescharacteristic
289C42—21no—
290C42—2261no—
291C42C22×D11311yescharacteristic
292C23—2261no—
293C23C2×C22⋊D11311yescharacteristic
294C23C2×C22⋊D11311yescharacteristic
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—21no—
299Q8—21no—
300Q8—42no—
301Q8—42no—
302Q8#1426864612yes—
303D4—22no—
304D4—9041no—
305D4—4522no—
306D4—2261no—
307D4—2261no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—9041no—
319C2×C4—9041no—
320C2×C4—2261no—
321C2×C4—2261no—
322C2×C4—2261no—
323C2×C4C2×C22⋊D11311yescharacteristic
324C2×C4C2×C22⋊D11311yescharacteristic
325C2×C4C2×C22⋊D11311yescharacteristic
326C2×C4C2×C22⋊D11311yescharacteristic
327C2×C4C23×D11311yescharacteristic
328C8—2261no—
329C8—2261no—
330C8—2261no—
331C8—2261no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—4521no—
338C22—4521no—
339C22—4521no—
340C22#1681365312yes—
341C22C22×C22⋊D11311yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—22no—
347C4—41no—
348C4—41no—
349C4—41no—
350C4—4521no—
351C4—4521no—
352C4—4521no—
353C4C2×#1426864611yescharacteristic
354C4#1681366711yescharacteristic
355C2—22no—
356C2—41no—
357C2—9041no—
358C2#2029924211yescharacteristic
359C2C2×#1681365311yescharacteristic
360C2#2029940611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingD4×Q8×C113C2
socleC22×C113C22×D4
prime radical#20299294C2
hypercenterD4×Q8D113
hypocenterC113#3320
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C4×D4 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
2. #20298966C2semidirect
3. #20298936C2semidirect
4. #20298931C2semidirect
5. #20298905C2semidirect
6. #20298846C2semidirect
7. #20298829C2semidirect
8. #20298800C2semidirect
9. #20298737C2semidirect
10. #20298737C2semidirect
11. #20298696C2semidirect
12. #20298670C2semidirect
13. #20298607C2semidirect
14. C2×#16813546C2semidirect
15. D4×Q8×C113C2semidirect
181. C113#3320semidirect
183. D4×Q8D113semidirect

Maximal subgroups

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

subgroupindex
#202992942
#202989662
#202989362
#202989312
#202989052
#202988462
#202988292
#202988002
#202987372
#202986962
#202986702
#202986072
C2×#168135462
D4×Q8×C1132
#3320113