Finite Group Databasebeta

← #28390875

Subgroups — #28390875

Order 14464.

376 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×M16×D113C211yesmaximal, characteristic, complemented
2#20299110C211yesmaximal, characteristic
3C2×#16813550C211yesmaximal, characteristic, complemented
4C2×#16813548C211yesmaximal, characteristic, complemented
5C4×#14268624C211yesmaximal, characteristic, complemented
6#20298357C211yesmaximal, characteristic, complemented
7#339×C113C211yesmaximal, characteristic, complemented
8C2×#14268647C2211yescharacteristic
9C22×C4×D113C2211yescharacteristic
10C2×#14268631C2211yescharacteristic
11C2×#14268630—21no—
12M16×D113—22no—
13M16×D113—22no—
14C2×C8×D113—21no—
15#16813606—21no—
16#16813602C411yescharacteristic, complemented
17#16813602C411yescharacteristic, complemented
18#16813597C411yescharacteristic, complemented
19#16813597C411yescharacteristic, complemented
20#16813592—21no—
21C4×D452—21no—
22C4×D452—21no—
23C2×#14268624—21no—
24C2×C4×Dic113C2211yescharacteristic
25#16813550—22no—
26#16813548—22no—
27#16813529—21no—
28C2×M16×C113C2211yescharacteristic
29#117×C113C2211yescharacteristic
30C2×C42×C113C2211yescharacteristic
31C23×D113D411yescharacteristic
32#14268647—21no—
33#14268647—21no—
34#14268647—21no—
35#14268647—21no—
36C2×Dic226C2×C411yescharacteristic
37C2×D452—21no—
38C2×D452—21no—
39C2×D452C2×C411yescharacteristic
40C2×C22⋊D113—21no—
41C22×Dic113—21no—
42C22×Dic113D411yescharacteristic
43C2×C4×D113—21no—
44C2×C4×D113—21no—
45C2×C4×D113—21no—
46C2×C4×D113—21no—
47C2×C4×D113—21no—
48C2×C4×D113C2×C411yescharacteristic
49C2×C4×D113C2×C411yescharacteristic
50C2×C4×D113D411yescharacteristic
51C2×C4×D113D411yescharacteristic
52#14268631—21no—
53#14268631D412yescomplemented
54#14268630—24no—
55C2×#11744751—21no—
56C8×D113—24no—
57C4⋊Dic113—21no—
58C4⋊Dic113—21no—
59#14268624—24no—
60#14268624—21no—
61#14268624—21no—
62#14268624—21no—
63#14268624—21no—
64C4×Dic113—21no—
65C4×Dic113—21no—
66C22×C4×C113—21no—
67C22×C4×C113C2311yescharacteristic
68M16×C113—21no—
69M16×C113D412yescomplemented
70C2×C8×C113—21no—
71C4⋊C4×C113C2×C411yescharacteristic
72C4⋊C4×C113C2×C411yescharacteristic
73C22⋊C4×C113—21no—
74C42×C113—21no—
75C42×C113—21no—
76C42×C113—21no—
77C23×C113C2×D411yescharacteristic
78C22×D113—21no—
79C22×D113—21no—
80C22×D113—22no—
81C22×D113—21no—
82C22×D113—41no—
83C22×D113C22⋊C411yescharacteristic
84C22×D113C22⋊C411yescharacteristic
85C2×C4×C113—22no—
86C2×C4×C113—21no—
87C2×C4×C113—21no—
88C2×C4×C113—41no—
89C2×C4×C113—41no—
90C2×C4×C113C22×C411yescharacteristic
91C2×C4×C113C2×D411yescharacteristic
92C2×C4×C113C2×D411yescharacteristic
93C2×C4×C113C2×D411yescharacteristic
94C2×C4×C113#4111yescharacteristic
95C2×C4×C113#4111yescharacteristic
96C22⋊D113—41no—
97C22⋊D113—41no—
98C2×Dic113—21no—
99C2×Dic113—21no—
100C2×Dic113—22no—
101C2×Dic113—21no—
102C2×Dic113—41no—
103C2×Dic113—41no—
104C2×Dic113C22⋊C411yescharacteristic
105C2×Dic113C22⋊C411yescharacteristic
106D452—21no—
107D452—21no—
108D452—42no—
109D452—42no—
110C4×D113—21no—
111C4×D113—21no—
112C4×D113—21no—
113C4×D113—21no—
114C4×D113—21no—
115C4×D113—21no—
116C4×D113—21no—
117C4×D113—21no—
118C4×D113—41no—
119C4×D113—41no—
120Dic226—21no—
121Dic226—21no—
122C8×C113—22no—
123#11744751—22no—
124C22×C113—21no—
125C22×C113—21no—
126C22×C113C2×C22⋊C411yescharacteristic
127C22×C113#12111yescharacteristic
128C22×C113#12111yescharacteristic
129C2×D113—21no—
130C2×D113—21no—
131C2×D113—21no—
132C2×D113—21no—
133C2×D113—21no—
134C2×D113—42no—
135C2×D113—42no—
136C2×D113—41no—
137C2×D113—41no—
138C2×D113—41no—
139C2×D113#10412yescomplemented
140C4×C113—42no—
141C4×C113—41no—
142C4×C113—41no—
143C4×C113C4×D411yescharacteristic
144C4×C113C4×D411yescharacteristic
145C4×C113#12011yescharacteristic
146C4×C113#12311yescharacteristic
147Dic113—21no—
148Dic113—21no—
149Dic113—42no—
150Dic113—41no—
151C2×C113—21no—
152C2×C113—21no—
153C2×C113#38611yescharacteristic
154C2×C113C2×#10411yescharacteristic
155C2×C113#42111yescharacteristic
156D113—22no—
157D113—41no—
158D113—81no—
159#1871—1131nomaximal, Sylow
160C113#187111yescharacteristic, complemented, Sylow
161C22×M16—1131no—
162#525—1131no—
163C2×#104—1131no—
164C2×#104—1131no—
165C4×C22⋊C4—1131no—
166#339—1131no—
167#339D11311yescharacteristic, complemented
168C2×#41—1131no—
169C23×C4—1131no—
170C2×M16—1131no—
171C2×M16—2261no—
172C2×M16—2262no—
173C2×M16—2262no—
174C2×M16C2×D11311yescharacteristic
175C22×C8—2261no—
176#123—2261no—
177C22⋊Q8—1131no—
178C22⋊Q8—1131no—
179#121—1131no—
180#121—1131no—
181#120—2261no—
182C4×D4—2261no—
183C4×D4—2261no—
184#117C2×D11311yescharacteristic
185C2×C22⋊C4—2261no—
186C2×C42—1131no—
187C2×C42C2×D11311yescharacteristic
188#104—2262no—
189#104—2262no—
190#95—2261no—
191C24—1131no—
192#41—2261no—
193#41—2261no—
194#41—2261no—
195#41—2261no—
196C2×Q8—1131no—
197C2×D4—1131no—
198C2×D4—2261no—
199C2×D4—2261no—
200C2×D4—2261no—
201C22×C4—21no—
202C22×C4—1131no—
203C22×C4—1131no—
204C22×C4—1131no—
205C22×C4—1131no—
206C22×C4—1131no—
207C22×C4—2261no—
208C22×C4—2261no—
209C22×C4—2261no—
210C22×C4—2261no—
211C22×C4—2261no—
212C22×C4—2261no—
213C22×C4C22×D11311yescharacteristic
214M16—21no—
215M16—1132no—
216M16—2264no—
217M16—2261no—
218M16D45212yescomplemented
219C2×C8—21no—
220C2×C8—2264no—
221C2×C8—2261no—
222C4⋊C4—2261no—
223C4⋊C4—2261no—
224C4⋊C4C4×D11311yescharacteristic
225C4⋊C4C4×D11311yescharacteristic
226C22⋊C4—21no—
227C22⋊C4—2261no—
228C22⋊C4—2261no—
229C22⋊C4—2261no—
230C22⋊C4—2261no—
231C22⋊C4—2264no—
232C42—21no—
233C42—21no—
234C42—21no—
235C42—2261no—
236C42—2261no—
237C23—1131no—
238C23—1131no—
239C23—4521no—
240C23—2262no—
241C23—2261no—
242C23—2261no—
243C23—2261no—
244C23D4×D11311yescharacteristic
245Q8—2261no—
246Q8—2261no—
247D4—4522no—
248D4—4522no—
249D4—4521no—
250D4—4521no—
251D4—2261no—
252D4—2261no—
253C2×C4—22no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—1131no—
259C2×C4—1131no—
260C2×C4—4521no—
261C2×C4—4521no—
262C2×C4—4521no—
263C2×C4—4521no—
264C2×C4—2262no—
265C2×C4—2261no—
266C2×C4—2261no—
267C2×C4—2261no—
268C2×C4—2261no—
269C2×C4—2261no—
270C2×C4—2261no—
271C2×C4—2261no—
272C2×C4—2261no—
273C2×C4—2261no—
274C2×C4—2261no—
275C2×C4—2261no—
276C2×C4C2×C4×D11311yescharacteristic
277C2×C4D4×D11311yescharacteristic
278C2×C4D4×D11311yescharacteristic
279C2×C4C2×D45211yescharacteristic
280C2×C4#1426864711yescharacteristic
281C2×C4#1426864811yescharacteristic
282C8—22no—
283C8—2262no—
284C22—21no—
285C22—21no—
286C22—1132no—
287C22—4522no—
288C22—4522no—
289C22—4521no—
290C22—4521no—
291C22—4521no—
292C22—2261no—
293C22—2261no—
294C22—2261no—
295C22—2261no—
296C22—2261no—
297C22C22⋊C4×D11311yescharacteristic
298C22#1681359511yescharacteristic
299C22#1681359711yescharacteristic
300C4—42no—
301C4—41no—
302C4—41no—
303C4—4522no—
304C4—4521no—
305C4—2261no—
306C4—2261no—
307C4#1681358411yescharacteristic
308C4C4×D45211yescharacteristic
309C4#1681359211yescharacteristic
310C4#1681360711yescharacteristic
311C2—21no—
312C2—21no—
313C2—9041no—
314C2—4521no—
315C2—2262no—
316C2#2029847611yescharacteristic
317C2#104×D11311yescharacteristic
318C2#2029861311yescharacteristic
subgroupG/H
centerC2×C4D4×D113
commutatorC2×C4×C113C22×C4
FrattiniC22×C4C22×D113
Fitting#339×C113C2
socleC22×C113C2×C22⋊C4
prime radical#20299110C2
cosocleC22×C4×C113C23
hypercenter#339D113
hypocenterC113#1871
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
1. C2×M16×D113C2semidirect
3. C2×#16813550C2semidirect
4. C2×#16813548C2semidirect
5. C4×#14268624C2semidirect
6. #20298357C2semidirect
7. #339×C113C2semidirect
16. #16813602C4semidirect
17. #16813602C4semidirect
18. #16813597C4semidirect
19. #16813597C4semidirect
53. #14268631D4semidirect
69. M16×C113D4semidirect
139. C2×D113#104semidirect
160. C113#1871semidirect
167. #339D113semidirect
218. M16D452semidirect

Maximal subgroups

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

subgroupindex
C2×M16×D1132
#202991102
C2×#168135502
C2×#168135482
C4×#142686242
#202983572
#339×C1132
#1871113