Finite Group Databasebeta

← #18010547

Subgroups — #18010547

Order 4736.

316 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 78 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×#11924615C211yesmaximal, characteristic
2C2×#11924605C211yesmaximal, characteristic, complemented
3C2×#11924604C211yesmaximal, characteristic, complemented
4#14558475C211yesmaximal, characteristic
5#14558407C211yesmaximal, characteristic, complemented
6#14558407C211yesmaximal, characteristic, complemented
7C22⋊C8×D37C211yesmaximal, characteristic
8#11924615—22no—
9#11924615—22no—
10C2×C4⋊#3866C2211yescharacteristic
11C2×C4⋊#3866C2211yescharacteristic
12C2×C4⋊#3866C2211yescharacteristic
13C2×C4⋊#3866C2211yescharacteristic
14C2×C22⋊#3866—21no—
15C2×C22⋊#3866—21no—
16C2×C4×#3866—21no—
17#11924605—22no—
18#11924604—22no—
19(C2×#3866)⋊C4—21no—
20C22×C4×D37C2211yescharacteristic
21C2×C8×D37C2211yescharacteristic
22C2×C8×D37C2211yescharacteristic
23C22⋊#64436C411yescharacteristic, complemented
24#11924448C411yescharacteristic, complemented
25#11924448C411yescharacteristic, complemented
26C22⋊C8×C37C411yescharacteristic, complemented
27C23×D37D411yescharacteristic
28C22×#3866—21no—
29C22×#3866—21no—
30C22×#3866—21no—
31C22×#3866—21no—
32C22×C4×C37C2×C411yescharacteristic
33C22×Dic37Q811yescharacteristic
34C2×C4×D37—21no—
35C2×C4×D37—21no—
36C2×C4×D37—21no—
37C2×C4×D37—21no—
38C2×C4×D37C2×C411yescharacteristic
39C2×C4×D37D411yescharacteristic
40C2×C4×D37Q811yescharacteristic
41C2×C4×D37C2311yescharacteristic
42C22⋊#3866—24no—
43C22⋊#3866—42no—
44C4⋊#3866—21no—
45C4⋊#3866—21no—
46C4⋊#3866—21no—
47C4⋊#3866—21no—
48C4⋊#3866—21no—
49C4⋊#3866—21no—
50C4⋊#3866D412yes—
51C4⋊#3866D412yes—
52C4×#3866—24no—
53C2×C8×C37C2×C411yescharacteristic
54C2×C8×C37C2×C411yescharacteristic
55C2×#64436C2×C411yescharacteristic
56C2×#64436C2×C411yescharacteristic
57C8×D37—21no—
58C8×D37—21no—
59C8×D37—21no—
60C8×D37—21no—
61C23×C37C4⋊C411yescharacteristic
62C22×D37—21no—
63C22×D37—21no—
64C22×D37—21no—
65C22×D37—21no—
66C22×D37—21no—
67C22×D37—21no—
68C22×D37C4⋊C411yescharacteristic
69C22×D37C2×D411yescharacteristic
70C2×#3866—22no—
71C2×#3866—22no—
72C2×#3866—41no—
73C2×#3866—41no—
74C2×#3866—41no—
75C2×#3866—41no—
76C2×#3866—41no—
77C2×#3866—41no—
78C2×#3866—41no—
79C2×#3866—41no—
80C2×#3866—41no—
81C2×#3866—41no—
82C2×C4×C37—21no—
83C2×C4×C37—21no—
84C2×C4×C37C4⋊C411yescharacteristic
85C2×C4×C37C22×C411yescharacteristic
86C2×Dic37—21no—
87C2×Dic37—21no—
88C2×Dic37C4⋊C411yescharacteristic
89C2×Dic37C2×Q811yescharacteristic
90C4×D37—21no—
91C4×D37—21no—
92C4×D37—21no—
93C4×D37—21no—
94C4×D37—21no—
95C4×D37—21no—
96C4×D37C2×D411yescharacteristic
97C4×D37C2×D411yescharacteristic
98C4×D37#4111yescharacteristic
99C4×D37#4111yescharacteristic
100C8×C37—21no—
101C8×C37—21no—
102#64436—21no—
103#64436—21no—
104C22×C37—21no—
105C22×C37—21no—
106C22×C37—21no—
107C22×C37C2×C4⋊C411yescharacteristic
108C2×D37—21no—
109C2×D37—21no—
110C2×D37—21no—
111C2×D37—41no—
112C2×D37—41no—
113C2×D37—41no—
114C2×D37—41no—
115C2×D37#12011yescharacteristic
116C2×D37#12311yescharacteristic
117C2×D37#13511yescharacteristic
118C2×D37#13511yescharacteristic
119C2×D37AGL(1,ℤ/8)11yescharacteristic
120C2×D37#13711yescharacteristic
121#3866—42no—
122#3866—42no—
123#3866—81no—
124#3866—81no—
125C4×C37—21no—
126C4×C37C4×D411yescharacteristic
127C4×C37C4×D411yescharacteristic
128Dic37—21no—
129Dic37C22⋊Q811yescharacteristic
130Dic37C22⋊Q811yescharacteristic
131#1854—371nomaximal, Sylow
132C2×C37—41no—
133C2×C37#38511yescharacteristic
134C2×C37#42711yescharacteristic
135C2×C37#42811yescharacteristic
136D37—41no—
137D37#44911yescharacteristic
138D37#45211yescharacteristic
139D37#48211yescharacteristic
140D37#48511yescharacteristic
141C2×#117—371no—
142C2×#107—371no—
143C2×#106—371no—
144C2×C22⋊C8—371no—
145#380—371no—
146#340—371no—
147#340—371no—
148C37#185411yescharacteristic, complemented, Sylow
149C23×C4—371no—
150C22×C8—371no—
151C22×C8—371no—
152#117—742no—
153#117—742no—
154C2×C4⋊C4—371no—
155C2×C4⋊C4—371no—
156C2×C4⋊C4—371no—
157C2×C4⋊C4—371no—
158C2×C22⋊C4—741no—
159C2×C22⋊C4—741no—
160C2×C42—741no—
161#107—742no—
162#106—742no—
163C22⋊C8—371no—
164C22⋊C8—371no—
165C22⋊C8—371no—
166C22⋊C8#386611yescharacteristic, complemented
167#95—741no—
168C24—371no—
169C22×C4—371no—
170C22×C4—371no—
171C22×C4—371no—
172C22×C4—371no—
173C22×C4—371no—
174C22×C4—741no—
175C22×C4—741no—
176C22×C4—741no—
177C22×C4—741no—
178C22×C4—741no—
179C22×C4—741no—
180C22×C4—741no—
181C22×C4—741no—
182C22×C4C2×#386611yescharacteristic
183C2×C8—371no—
184C2×C8—371no—
185C2×C8—741no—
186C2×C8—741no—
187C2×C8—741no—
188C2×C8—741no—
189C2×C8C2×#386611yescharacteristic
190C2×C8C2×#386611yescharacteristic
191C4⋊C4—372no—
192C4⋊C4—372no—
193C4⋊C4—741no—
194C4⋊C4—741no—
195C4⋊C4—741no—
196C4⋊C4—741no—
197C4⋊C4—741no—
198C4⋊C4—741no—
199C22⋊C4—744no—
200C22⋊C4—1482no—
201C42—744no—
202C23—371no—
203C23—371no—
204C23—741no—
205C23—741no—
206C23—741no—
207C23—741no—
208C23—741no—
209C23—741no—
210C23C4⋊#386611yescharacteristic
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—371no—
214C2×C4—371no—
215C2×C4—371no—
216C2×C4—371no—
217C2×C4—371no—
218C2×C4—371no—
219C2×C4—741no—
220C2×C4—741no—
221C2×C4—741no—
222C2×C4—741no—
223C2×C4—741no—
224C2×C4—741no—
225C2×C4—741no—
226C2×C4—741no—
227C2×C4—742no—
228C2×C4—742no—
229C2×C4—1481no—
230C2×C4—1481no—
231C2×C4—1481no—
232C2×C4—1481no—
233C2×C4—1481no—
234C2×C4—1481no—
235C2×C4—1481no—
236C2×C4—1481no—
237C2×C4—1481no—
238C2×C4—1481no—
239C2×C4C4⋊#386611yescharacteristic
240C2×C4C22×#386611yescharacteristic
241C8—21no—
242C8—21no—
243C8—741no—
244C8—741no—
245C22—21no—
246C22—21no—
247C22—21no—
248C22—371no—
249C22—371no—
250C22—371no—
251C22—371no—
252C22—371no—
253C22—371no—
254C22—741no—
255C22—741no—
256C22—741no—
257C22—1481no—
258C22—1481no—
259C22—1481no—
260C22—1481no—
261C22C2×C4⋊#386611yescharacteristic
262C4—21no—
263C4—371no—
264C4—371no—
265C4—2961no—
266C4—2961no—
267C4—741no—
268C4—1482no—
269C4—1482no—
270C4D4×#386611yescharacteristic
271C4D4×#386611yescharacteristic
272C2—41no—
273C2—371no—
274C2—371no—
275C2—371no—
276C2—371no—
277C2—1481no—
278C2#1455848011yescharacteristic
279C2#1455854311yescharacteristic
280C2#1455854411yescharacteristic
subgroupG/H
centerC22C2×C4⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC22⋊C8×C37C4
socleC22×C37C2×C4⋊C4
prime radicalC23×D37D4
cosocleC2×C4×D37C23
hypercenterC22⋊C8#3866
hypocenterC37#1854
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#11924605C2semidirect
3. C2×#11924604C2semidirect
5. #14558407C2semidirect
6. #14558407C2semidirect
23. C22⋊#64436C4semidirect
24. #11924448C4semidirect
25. #11924448C4semidirect
26. C22⋊C8×C37C4semidirect
148. C37#1854semidirect
166. C22⋊C8#3866semidirect

Maximal subgroups

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

subgroupindex
C2×#119246152
C2×#119246052
C2×#119246042
#145584752
#145584072
C22⋊C8×D372
#185437