Finite Group Databasebeta

← #353×D241 #44509101

Subgroups — #353×D241 #44509101

Order 30848.

368 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 57 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#127×D241C211yesmaximal, characteristic
2#99×D241C212yesmaximal, complemented
3#29507510C211yesmaximal, characteristic, complemented
4#29507509C212yesmaximal, complemented
5#353×C241C211yesmaximal, characteristic, complemented
6C2×D4×D241—22no—
7C2×D4×D241C411yescharacteristic, complemented
8C2×D4×D241C2211yescharacteristic
9#21440639C411yescharacteristic, complemented
10#21440638—22no—
11#21440638C411yescharacteristic, complemented
12#21440638C2211yescharacteristic
13C22⋊C4×D241—22no—
14C42×D241C411yescharacteristic, complemented
15#21440557C2212yescomplemented
16#21440556—22no—
17#127×C241C2211yescharacteristic
18#99×C241C2212yescomplemented
19C23×D241—21no—
20C23×D241D412yes—
21C2×D964—22no—
22C2×D964C2×C411yescharacteristic
23C2×D964C2×C411yescharacteristic, complemented
24C2×C22⋊D241—22no—
25C2×C22⋊D241—21no—
26C2×C22⋊D241—22no—
27C2×C22⋊D241D412yes—
28D4×D241—41no—
29D4×D241—41no—
30D4×D241—41no—
31D4×D241—41no—
32D4×D241—48no—
33C2×C4×D241—21no—
34C2×C4×D241—42no—
35C2×C4×D241C2×C411yescharacteristic
36C22⋊Dic241—22no—
37#16838747—42no—
38C4×Dic241—21no—
39C4×Dic241C2×C411yescharacteristic, complemented
40C2×D4×C241—22no—
41C2×D4×C241C2×C411yescharacteristic, complemented
42C2×D4×C241C2311yescharacteristic
43C22⋊C4×C241—22no—
44C42×C241C2×C411yescharacteristic, complemented
45C22×D241—22no—
46C22×D241—22no—
47C22×D241—21no—
48C22×D241—44no—
49C22×D241—44no—
50C22×D241—41no—
51C22×D241—41no—
52C22×D241C22⋊C411yescharacteristic
53C22×D241C22⋊C412yes—
54D964—41no—
55D964—41no—
56D964—44no—
57C22⋊D241—42no—
58C22⋊D241—44no—
59C22⋊D241—44no—
60C22⋊D241—42no—
61C2×Dic241—21no—
62C2×Dic241—42no—
63C2×Dic241C22⋊C411yescharacteristic
64C4×D241—24no—
65C4×D241—21no—
66C4×D241—21no—
67C4×D241—84no—
68C23×C241—21no—
69C23×C241C2×D412yes—
70D4×C241—41no—
71D4×C241—41no—
72D4×C241—44no—
73C2×C4×C241—21no—
74C2×C4×C241—42no—
75C2×C4×C241C22×C411yescharacteristic
76C22×C241—22no—
77C22×C241—42no—
78C22×C241—42no—
79C22×C241—41no—
80C22×C241C2×C22⋊C411yescharacteristic
81C2×D241—22no—
82C2×D241—22no—
83C2×D241—44no—
84C2×D241—42no—
85C2×D241—42no—
86C2×D241—41no—
87C2×D241—82no—
88C2×D241—82no—
89C2×D241—82no—
90C2×D241#9911yescharacteristic
91C2×D241#9911yescharacteristic
92C4×C241—22no—
93C4×C241—21no—
94C4×C241—82no—
95Dic241—22no—
96Dic241—21no—
97Dic241—82no—
98C2×C241—21no—
99C2×C241—42no—
100C2×C241—81no—
101C2×C241C2×#9911yescharacteristic
102D241—21no—
103D241—42no—
104D241—81no—
105D241#35312yesdirect product factor
106C241C2×#35311yescharacteristic, complemented, Sylow
107C2×#353—2411nomaximal, Sylow
108C2×#127—2411no—
109C2×#99—2412no—
110#353—2411no—
111#353—2412no—
112#353D24111yescharacteristic, direct product factor
113C22×D4—4822no—
114C22×D4—2411no—
115C22×D4—2411no—
116#127—4822no—
117#127—2411no—
118#127—2411no—
119#127—2411no—
120#127C2×D24111yescharacteristic
121C2×C22⋊C4—4822no—
122C2×C42—2411no—
123#99—4822no—
124#99—2412no—
125#99C2×D24112yescomplemented
126C24—4821no—
127C24—2412no—
128C2×D4—22no—
129C2×D4—9641no—
130C2×D4—9641no—
131C2×D4—9648no—
132C2×D4—9641no—
133C2×D4—9641no—
134C2×D4—4822no—
135C2×D4—4822no—
136C2×D4—4822no—
137C2×D4—4821no—
138C2×D4—2412no—
139C2×D4—2411no—
140C2×D4—2411no—
141C2×D4C4×D24111yescharacteristic, complemented
142C2×D4C22×D24111yescharacteristic
143C22×C4—9642no—
144C22×C4—4821no—
145C22×C4—2411no—
146C22⋊C4—22no—
147C22⋊C4—9642no—
148C22⋊C4—4822no—
149C42—4821no—
150C42—2411no—
151C42C4×D24111yescharacteristic, complemented
152C23—21no—
153C23—9644no—
154C23—9641no—
155C23—9641no—
156C23—9644no—
157C23—4822no—
158C23—4822no—
159C23—4821no—
160C23—2412no—
161C23—2411no—
162C23D4×D24112yes—
163D4—41no—
164D4—41no—
165D4—44no—
166D4—9641no—
167D4—9644no—
168D4—9641no—
169D4—9642no—
170D4—9644no—
171D4—9644no—
172D4—9642no—
173C2×C4—21no—
174C2×C4—42no—
175C2×C4—19284no—
176C2×C4—9642no—
177C2×C4—4824no—
178C2×C4—4821no—
179C2×C4—4821no—
180C2×C4—4821no—
181C2×C4—2411no—
182C2×C4C2×C4×D24111yescharacteristic
183C22—22no—
184C22—42no—
185C22—42no—
186C22—41no—
187C22—19282no—
188C22—19282no—
189C22—19282no—
190C22—9642no—
191C22—9642no—
192C22—9644no—
193C22—9641no—
194C22—4822no—
195C22—4822no—
196C22—2411no—
197C22—2411no—
198C22C22⋊C4×D24111yescharacteristic
199C4—22no—
200C4—21no—
201C4—82no—
202C4—19282no—
203C4—4822no—
204C4—4821no—
205C2—21no—
206C2—42no—
207C2—81no—
208C2—19281no—
209C2—9642no—
210C2—4821no—
211C2—2412no—
212C2#99×D24111yescharacteristic
subgroupG/H
centerC2#99×D241
commutatorC2×C4×C241C22×C4
FrattiniC2×D4C22×D241
Fitting#353×C241C2
socleC2×C241C2×#99
prime radical#127×D241C2
cosocleC2×D4×C241C23
hypercenter#353D241
hypocenterC241C2×#353
LCSG ▷ C2×C4×C241 ▷ C22×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #353

Complements

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

NH ≅ G/Ntype
2. #99×D241C2semidirect
3. #29507510C2semidirect
4. #29507509C2semidirect
5. #353×C241C2semidirect
7. C2×D4×D241C4semidirect
9. #21440639C4semidirect
11. #21440638C4semidirect
14. C42×D241C4semidirect
15. #21440557C22semidirect
18. #99×C241C22semidirect
23. C2×D964C2×C4semidirect
39. C4×Dic241C2×C4semidirect
41. C2×D4×C241C2×C4semidirect
44. C42×C241C2×C4semidirect
105. D241#353direct (N × H)
106. C241C2×#353semidirect
112. #353D241direct (N × H)
125. #99C2×D241semidirect
141. C2×D4C4×D241semidirect
151. C42C4×D241semidirect

Maximal subgroups

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

subgroupindex
#127×D2412
#99×D2412
#295075102
#295075092
#353×C2412
C2×#353241