Finite Group Databasebeta

← #44537345

Subgroups — #44537345

Order 31424.

216 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 93 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
1#30628335C211yesmaximal, characteristic, complemented
2#30628332C211yesmaximal, characteristic, complemented
3#30628330C211yesmaximal, characteristic, complemented
4#30628326C211yesmaximal, characteristic, complemented
5#30628323C211yesmaximal, characteristic, complemented
6#30628323C211yesmaximal, characteristic, complemented
7#30628322C211yesmaximal, characteristic, complemented
8#30628320C211yesmaximal, characteristic, complemented
9#30628315C211yesmaximal, characteristic, complemented
10#30628315C211yesmaximal, characteristic, complemented
11#30628310C211yesmaximal, characteristic
12#30628302C211yesmaximal, characteristic, complemented
13C4×C22⋊D491C211yesmaximal, characteristic, complemented
14#30628295C211yesmaximal, characteristic, complemented
15C22⋊Q8×C491C211yesmaximal, characteristic, complemented
16C2×Dic982C2211yescharacteristic
17C2×Dic982C2211yescharacteristic
18C2×D1964C2211yescharacteristic
19C2×C22⋊D491C2211yescharacteristic
20C2×C22⋊D491C2211yescharacteristic
21C2×C4×D491C2211yescharacteristic
22C2×C4×D491C2211yescharacteristic
23C4⋊Dic491C2211yescharacteristic
24Dic491⋊C4C2211yescharacteristic
25Dic491⋊C4C2211yescharacteristic
26Dic491⋊C4C2211yescharacteristic
27Dic491⋊C4C2211yescharacteristic
28Dic491⋊C4C2211yescharacteristic
29Dic491⋊C4C2211yescharacteristic
30C22⋊Dic491C2211yescharacteristic
31C22⋊Dic491C2211yescharacteristic
32(C2×D491)⋊C4C2211yescharacteristic
33(C2×D491)⋊C4C2211yescharacteristic
34(C2×D491)⋊C4C2211yescharacteristic
35(C2×D491)⋊C4C2211yescharacteristic
36(C2×D491)⋊C4C2211yescharacteristic
37(C2×D491)⋊C4C2211yescharacteristic
38(C2×D491)⋊C4C2211yescharacteristic
39(C2×D491)⋊C4C2211yescharacteristic
40C4×Dic491C2211yescharacteristic
41C4×Dic491C2211yescharacteristic
42C4×Dic491C2211yescharacteristic
43C4×Dic491C2211yescharacteristic
44C2×Q8×C491C2211yescharacteristic
45C22×C4×C491C2211yescharacteristic
46C4⋊C4×C491C2211yescharacteristic
47C4⋊C4×C491C2211yescharacteristic
48C4⋊C4×C491C2211yescharacteristic
49C22⋊C4×C491C2211yescharacteristic
50C22⋊C4×C491C2211yescharacteristic
51C22×D491C2311yescharacteristic
52C22×D491C2311yescharacteristic
53Dic982—22no—
54Dic982—41no—
55D1964—41no—
56C22⋊D491—22no—
57C22⋊D491—41no—
58C2×Dic491C2311yescharacteristic
59C2×Dic491C2311yescharacteristic
60C2×Dic491C2311yescharacteristic
61C2×Dic491C2311yescharacteristic
62C2×Dic491C2311yescharacteristic
63C2×Dic491C2311yescharacteristic
64C4×D491—22no—
65C4×D491—41no—
66C23×C491C2311yescharacteristic
67Q8×C491—41no—
68C2×C4×C491—41no—
69C2×C4×C491C2311yescharacteristic
70C2×C4×C491C2311yescharacteristic
71C2×C4×C491C2311yescharacteristic
72C2×C4×C491C2311yescharacteristic
73C2×C4×C491C2311yescharacteristic
74C2×C4×C491C2311yescharacteristic
75C22×C491—21no—
76C22×C491—21no—
77C22×C491—21no—
78C22×C491C2411yescharacteristic
79C2×D491—21no—
80C2×D491—21no—
81C2×D491—21no—
82C2×D491—21no—
83C2×D491—21no—
84C2×D491—21no—
85C4×C491—21no—
86C4×C491—21no—
87C4×C491—21no—
88C4×C491—21no—
89C4×C491—21no—
90C4×C491—21no—
91Dic491—21no—
92Dic491—21no—
93Dic491—21no—
94Dic491—21no—
95Dic491—21no—
96Dic491#4112yes—
97C2×C491—41no—
98C2×C491C2×#4111yescharacteristic
99C2×C491H(5,𝔽2)11yescharacteristic
100C2×C4912−1+411yescharacteristic
101D491—41no—
102D491—41no—
103C491#54211yescharacteristic, complemented, Sylow
104#542—4911nomaximal, Sylow
105C4⋊Q8—4911no—
106#126—4911no—
107#126—4911no—
108#124—4911no—
109#124—4911no—
110#124—4911no—
111#123—4911no—
112#123—4911no—
113C22⋊Q8—4911no—
114C22⋊Q8—4911no—
115C22⋊Q8D49111yescharacteristic, complemented
116#121—4911no—
117C4×Q8—4911no—
118C4×D4—4911no—
119#117—4911no—
120C2×Q8—4911no—
121C2×Q8—4911no—
122C2×Q8C2×D49111yescharacteristic
123C2×D4—4911no—
124C2×D4—4911no—
125C2×D4—4911no—
126C22×C4—4911no—
127C22×C4—4911no—
128C22×C4C2×D49111yescharacteristic
129C4⋊C4—4911no—
130C4⋊C4—4911no—
131C4⋊C4—4911no—
132C4⋊C4—4911no—
133C4⋊C4—4911no—
134C4⋊C4—4911no—
135C4⋊C4—4911no—
136C4⋊C4C2×D49111yescharacteristic
137C4⋊C4C2×D49111yescharacteristic
138C4⋊C4C2×D49111yescharacteristic
139C22⋊C4—4911no—
140C22⋊C4—4911no—
141C22⋊C4—4911no—
142C22⋊C4—4911no—
143C22⋊C4—4911no—
144C22⋊C4—4911no—
145C22⋊C4—4911no—
146C22⋊C4—4911no—
147C22⋊C4—4911no—
148C22⋊C4—4911no—
149C22⋊C4C2×D49111yescharacteristic
150C22⋊C4C2×D49111yescharacteristic
151C42—4911no—
152C42—4911no—
153C42—4911no—
154C42—4911no—
155C23—4911no—
156C23—4911no—
157C23C22×D49111yescharacteristic
158Q8—41no—
159Q8—19641no—
160Q8—9822no—
161D4—19641no—
162D4—19641no—
163D4—9822no—
164C2×C4—41no—
165C2×C4—19641no—
166C2×C4—9822no—
167C2×C4—4911no—
168C2×C4—4911no—
169C2×C4—4911no—
170C2×C4—4911no—
171C2×C4—4911no—
172C2×C4—4911no—
173C2×C4C22×D49111yescharacteristic
174C2×C4C22×D49111yescharacteristic
175C2×C4C22×D49111yescharacteristic
176C2×C4C22×D49111yescharacteristic
177C2×C4C22×D49111yescharacteristic
178C2×C4C22×D49111yescharacteristic
179C22—21no—
180C22—21no—
181C22—21no—
182C22—9821no—
183C22—9821no—
184C22—9821no—
185C22—9821no—
186C22—9821no—
187C22—9821no—
188C22C23×D49111yescharacteristic
189C4—21no—
190C4—21no—
191C4—21no—
192C4—21no—
193C4—21no—
194C4—21no—
195C4—9821no—
196C4—9821no—
197C4—9821no—
198C4—9821no—
199C4—9821no—
200C4—4912no—
201C2—41no—
202C2—19641no—
203C2—19641no—
204C2#41×D49111yescharacteristic
205C2#3062838211yescharacteristic
206C2#3062838511yescharacteristic
subgroupG/H
center, FrattiniC22C23×D491
commutator, socle, cosocleC22×C491C24
FittingC22⋊Q8×C491C2
prime radical#30628310C2
hypercenterC22⋊Q8D491
hypocenterC491#542
LCSG ▷ C22×C491 ▷ C491
UCSC1 ◁ C22 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. #30628335C2semidirect
2. #30628332C2semidirect
3. #30628330C2semidirect
4. #30628326C2semidirect
5. #30628323C2semidirect
6. #30628323C2semidirect
7. #30628322C2semidirect
8. #30628320C2semidirect
9. #30628315C2semidirect
10. #30628315C2semidirect
12. #30628302C2semidirect
13. C4×C22⋊D491C2semidirect
14. #30628295C2semidirect
15. C22⋊Q8×C491C2semidirect
103. C491#542semidirect
115. C22⋊Q8D491semidirect

Maximal subgroups

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

subgroupindex
#306283352
#306283322
#306283302
#306283262
#306283232
#306283222
#306283202
#306283152
#306283102
#306283022
C4×C22⋊D4912
#306282952
C22⋊Q8×C4912
#542491