Finite Group Databasebeta

← #18010369

Subgroups — #18010369

Order 4736.

324 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 98 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×Q8×#3866C211yesmaximal, characteristic
2C2×#11924599C211yesmaximal, characteristic
3C2×#11924590C211yesmaximal, characteristic
4C4⋊C4×#3866C211yesmaximal, characteristic
5#14558407C211yesmaximal, characteristic
6#14558406C211yesmaximal, characteristic
7#103×D37C211yesmaximal, characteristic
8C2×D37⋊C8C2211yescharacteristic
9Q8×#3866—22no—
10Q8×#3866C414yescomplemented
11C2×C4⋊#3866—21no—
12C2×C4⋊#3866C2211yescharacteristic
13C2×C4⋊#3866C2211yescharacteristic
14C2×C4×#3866—21no—
15C2×C4×#3866—21no—
16C2×C4×#3866C2211yescharacteristic
17#11924599C414yescomplemented
18#11924590—22no—
19(C2×#3866)⋊C4—21no—
20C2×Q8×D37C2211yescharacteristic
21C2×C8×D37C2211yescharacteristic
22C4⋊C4×D37C2211yescharacteristic
23#11924461C411yescharacteristic, complemented
24#11924460C411yescharacteristic, complemented
25#11924459C411yescharacteristic, complemented
26#103×C37C411yescharacteristic, complemented
27C22×#3866—21no—
28C22×#3866—21no—
29C22×#3866D411yescharacteristic
30C22×#3866D411yescharacteristic
31C2×Q8×C37C2×C411yescharacteristic
32Q8×D37—21no—
33Q8×D37—21no—
34Q8×D37C2×C412yes—
35Q8×D37C2×C412yes—
36C2×C4×D37—21no—
37C2×C4×D37—21no—
38C2×C4×D37C2311yescharacteristic
39C2×Dic74—21no—
40C2×Dic74C2×C411yescharacteristic
41C2×#64438—21no—
42C4⋊#3866—24no—
43C4⋊#3866—21no—
44C4⋊#3866—21no—
45C4⋊#3866C2×C412yes—
46C4⋊#3866C2×C412yes—
47C4×#3866—24no—
48C4×#3866—42no—
49C4×#3866C2×C412yes—
50C4×#3866D412yes—
51D37⋊C8—21no—
52D37⋊C8C2×C412yes—
53C2×C8×C37C2×C411yescharacteristic
54C4⋊C4×C37C2×C411yescharacteristic
55C4⋊Dic37C2×C411yescharacteristic
56#10596936—21no—
57C2×#64436C2×C411yescharacteristic
58C8×D37—21no—
59C8×D37—21no—
60C22×D37C2×D411yescharacteristic
61C2×#3866—21no—
62C2×#3866—21no—
63C2×#3866—21no—
64C2×#3866—21no—
65C2×#3866—22no—
66C2×#3866—22no—
67C2×#3866—41no—
68C2×#3866—41no—
69C2×#3866—41no—
70C2×#3866—41no—
71C2×#3866C22⋊C412yes—
72C2×#3866C22⋊C412yes—
73Q8×C37—21no—
74Q8×C37C4212yescomplemented
75C2×C4×C37—21no—
76C2×C4×C37—21no—
77C2×C4×C37C22×C411yescharacteristic
78C2×Dic37—21no—
79C2×Dic37—21no—
80C2×Dic37#4111yescharacteristic
81C4×D37—22no—
82C4×D37—22no—
83C4×D37—41no—
84C4×D37—41no—
85C4×D37C22×C411yescharacteristic
86C4×D37C22×C411yescharacteristic
87C4×D37C2×D411yescharacteristic
88C4×D37#4111yescharacteristic
89Dic74—21no—
90Dic74—22no—
91Dic74—22no—
92Dic74C4212yescomplemented
93#64438—22no—
94C8×C37—21no—
95#64436—21no—
96C22×C37C4×D411yescharacteristic
97C2×D37C2×C22⋊C411yescharacteristic
98C2×D37C4×D411yescharacteristic
99C2×D37AGL(1,ℤ/8)11yescharacteristic
100C2×D37#13711yescharacteristic
101C2×D37#13711yescharacteristic
102C2×D37#13711yescharacteristic
103#3866—22no—
104#3866—22no—
105#3866—42no—
106#3866—42no—
107C4×C37—22no—
108C4×C37—41no—
109C4×C37C2×C4211yescharacteristic
110C4×C37C4×D411yescharacteristic
111Dic37—22no—
112Dic37—41no—
113Dic37#11711yescharacteristic
114Dic37C4×D411yescharacteristic
115#1763—371nomaximal, Sylow
116C2×C37C4×C22⋊C411yescharacteristic
117C2×C37#44011yescharacteristic
118C2×C37#44111yescharacteristic
119D37#41711yescharacteristic
120D37#41911yescharacteristic
121D37#44011yescharacteristic
122D37#44111yescharacteristic
123C2×C4×Q8—371no—
124C2×#103—371no—
125C2×#103—371no—
126C2×#97—371no—
127C4×C4⋊C4—371no—
128#340—371no—
129#340—371no—
130C37#176311yescharacteristic, complemented, Sylow
131C22×Q8—371no—
132C22×C8—371no—
133C22×C8—371no—
134C4×Q8—374no—
135C4×Q8—742no—
136C2×C4⋊C4—371no—
137C2×C4⋊C4—371no—
138C2×C4⋊C4—371no—
139C2×C4⋊C4—741no—
140C2×C42—371no—
141C2×C42—741no—
142C2×C42—741no—
143#103—374no—
144#103—371no—
145#103—371no—
146#103—371no—
147#103#386611yescharacteristic, complemented
148#97—742no—
149#95—741no—
150C2×Q8—372no—
151C2×Q8—372no—
152C2×Q8—371no—
153C2×Q8—741no—
154C2×Q8—741no—
155C2×Q8—741no—
156C2×Q8C2×#386611yescharacteristic
157C22×C4—371no—
158C22×C4—371no—
159C22×C4—371no—
160C22×C4—741no—
161C22×C4—741no—
162C22×C4—741no—
163C22×C4—741no—
164C2×C8—372no—
165C2×C8—371no—
166C2×C8—741no—
167C2×C8—741no—
168C2×C8—741no—
169C2×C8—741no—
170C2×C8C2×#386611yescharacteristic
171C4⋊C4—372no—
172C4⋊C4—372no—
173C4⋊C4—371no—
174C4⋊C4—741no—
175C4⋊C4—741no—
176C4⋊C4—741no—
177C4⋊C4—744no—
178C4⋊C4C2×#386611yescharacteristic
179C42—372no—
180C42—372no—
181C42—744no—
182C42—1482no—
183C23—371no—
184Q8—21no—
185Q8—372no—
186Q8—742no—
187Q8—742no—
188Q8—741no—
189Q8C4×#386612yescomplemented
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—371no—
193C2×C4—371no—
194C2×C4—371no—
195C2×C4—371no—
196C2×C4—371no—
197C2×C4—372no—
198C2×C4—372no—
199C2×C4—742no—
200C2×C4—742no—
201C2×C4—741no—
202C2×C4—741no—
203C2×C4—741no—
204C2×C4—741no—
205C2×C4—741no—
206C2×C4—742no—
207C2×C4—742no—
208C2×C4—741no—
209C2×C4—1481no—
210C2×C4—1481no—
211C2×C4—1481no—
212C2×C4—1481no—
213C2×C4—1481no—
214C2×C4—1481no—
215C2×C4C22×#386611yescharacteristic
216C8—21no—
217C8—742no—
218C8—741no—
219C22—371no—
220C22—371no—
221C22—371no—
222C22—371no—
223C22—371no—
224C22—371no—
225C22D4×#386611yescharacteristic
226C4—22no—
227C4—41no—
228C4—371no—
229C4—371no—
230C4—742no—
231C4—742no—
232C4—742no—
233C4—1482no—
234C4—1482no—
235C4—1481no—
236C4C2×C4×#386611yescharacteristic
237C4D4×#386611yescharacteristic
238C2—371no—
239C2—371no—
240C2—371no—
241C2—371no—
242C2C22⋊C4×#386611yescharacteristic
243C2#1455857211yescharacteristic
244C2#1455857311yescharacteristic
subgroupG/H
centerC22D4×#3866
commutatorC4×C37C2×C42
FrattiniC2×C4C22×#3866
Fitting#103×C37C4
socleC22×C37C4×D4
prime radicalC22×D37C2×D4
cosocleC2×C4×D37C23
hypercenter#103#3866
hypocenterC37#1763
LCSG ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
10. Q8×#3866C4semidirect
17. #11924599C4semidirect
23. #11924461C4semidirect
24. #11924460C4semidirect
25. #11924459C4semidirect
26. #103×C37C4semidirect
74. Q8×C37C42semidirect
92. Dic74C42semidirect
130. C37#1763semidirect
147. #103#3866semidirect
189. Q8C4×#3866semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×#38662
C2×#119245992
C2×#119245902
C4⋊C4×#38662
#145584072
#145584062
#103×D372
#176337