Finite Group Databasebeta

← #355×D241 #44509121

Subgroups — #355×D241 #44509121

Order 30848.

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

normal subgroups only

This group has 260 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#124×D241C211yesmaximal, characteristic
2#101×D241C212yesmaximal, complemented
3#29507514C211yesmaximal, characteristic, complemented
4#29507513C212yesmaximal, complemented
5#355×C241C211yesmaximal, characteristic, complemented
6C2×Q8×D241C2211yescharacteristic
7C2×D4×D241C411yescharacteristic
8M16×D241—22no—
9#21440631C2211yescharacteristic
10#21440630C411yescharacteristic
11#21440629C411yescharacteristic
12#21440628—22no—
13C22⋊C4×D241—22no—
14C42×D241C411yescharacteristic
15#21440561C2212yescomplemented
16#21440560—22no—
17#124×C241C2211yescharacteristic
18#101×C241C2212yescomplemented
19C23×D241—21no—
20C2×Dic482C2×C411yescharacteristic
21C2×Dic482D412yes—
22Q8×D241—41no—
23Q8×D241—41no—
24C2×D964C2×C411yescharacteristic
25C2×C22⋊D241—21no—
26D4×D241—41no—
27D4×D241—41no—
28C2×C4×D241—21no—
29C2×C4×D241C2×C411yescharacteristic
30C2×C4×D241D412yes—
31#16838754—22no—
32#16838753—42no—
33C8×D241—42no—
34C22⋊Dic241—22no—
35#16838747—22no—
36#16838747—22no—
37C4×Dic241—21no—
38C4×Dic241C2×C411yescharacteristic
39C2×Q8×C241C2311yescharacteristic
40C2×D4×C241C2×C411yescharacteristic
41M16×C241—22no—
42C22⋊C4×C241—22no—
43C42×C241C2×C411yescharacteristic
44C22×D241—21no—
45C22×D241—44no—
46C22×D241—41no—
47C22×D241—41no—
48C22×D241C22⋊C411yescharacteristic
49Dic482—41no—
50Dic482—42no—
51D964—41no—
52C22⋊D241—42no—
53C2×Dic241—21no—
54C2×Dic241C22⋊C411yescharacteristic
55C2×Dic241C22⋊C412yes—
56C4×D241—22no—
57C4×D241—22no—
58C4×D241—21no—
59C4×D241—21no—
60C4×D241—42no—
61#14515349—42no—
62C23×C241—21no—
63Q8×C241—41no—
64D4×C241—41no—
65C2×C4×C241—21no—
66C2×C4×C241C22×C411yescharacteristic
67C2×C4×C241C2×D412yes—
68C8×C241—42no—
69C22×C241—42no—
70C22×C241—41no—
71C22×C241C2×C22⋊C411yescharacteristic
72C2×D241—22no—
73C2×D241—42no—
74C2×D241—41no—
75C2×D241—82no—
76C2×D241—82no—
77C2×D241#9911yescharacteristic
78C2×D241#9911yescharacteristic
79C4×C241—22no—
80C4×C241—21no—
81C4×C241—41no—
82Dic241—21no—
83Dic241—22no—
84Dic241—41no—
85C2×C241—21no—
86C2×C241—81no—
87C2×C241C2×#9911yescharacteristic
88D241—21no—
89D241—81no—
90D241#35512yesdirect product factor
91C241C2×#35511yescharacteristic, complemented, Sylow
92C2×#355—2411nomaximal, Sylow
93C2×#124—2411no—
94C2×#101—2412no—
95#355—2411no—
96#355—2412no—
97#355D24111yescharacteristic, direct product factor
98C22×Q8—2411no—
99C22×D4—2411no—
100C2×M16—4822no—
101#124—4822no—
102#124—2411no—
103#124—2411no—
104#124—2411no—
105#124C2×D24111yescharacteristic
106C2×C22⋊C4—4822no—
107C2×C42—2411no—
108#101—4822no—
109#101—2412no—
110#101C2×D24112yescomplemented
111C24—4821no—
112C2×Q8—9641no—
113C2×Q8—9641no—
114C2×Q8—2411no—
115C2×Q8—2412no—
116C2×Q8C22×D24111yescharacteristic
117C2×D4—9641no—
118C2×D4—9641no—
119C2×D4—4821no—
120C2×D4—2411no—
121C2×D4C4×D24111yescharacteristic
122C22×C4—4821no—
123C22×C4—2411no—
124C22×C4—2412no—
125M16—22no—
126M16—9642no—
127M16—4822no—
128C2×C8—9642no—
129C22⋊C4—22no—
130C22⋊C4—4822no—
131C22⋊C4—4822no—
132C22⋊C4—4822no—
133C42—4821no—
134C42—2411no—
135C42C4×D24111yescharacteristic
136C23—21no—
137C23—9644no—
138C23—9641no—
139C23—9641no—
140C23—4821no—
141C23—2411no—
142Q8—41no—
143Q8—9642no—
144Q8—9641no—
145D4—41no—
146D4—9641no—
147D4—9642no—
148C2×C4—21no—
149C2×C4—9642no—
150C2×C4—4822no—
151C2×C4—4822no—
152C2×C4—4821no—
153C2×C4—4821no—
154C2×C4—4821no—
155C2×C4—2411no—
156C2×C4—2412no—
157C2×C4C2×C4×D24111yescharacteristic
158C2×C4D4×D24112yes—
159C8—42no—
160C8—9642no—
161C22—42no—
162C22—41no—
163C22—19282no—
164C22—19282no—
165C22—9642no—
166C22—9641no—
167C22—4822no—
168C22—2411no—
169C22—2411no—
170C22C22⋊C4×D24111yescharacteristic
171C4—22no—
172C4—21no—
173C4—41no—
174C4—9641no—
175C4—4821no—
176C4—4822no—
177C2—21no—
178C2—81no—
179C2—19281no—
180C2—4821no—
181C2—2412no—
182C2#99×D24111yescharacteristic
subgroupG/H
centerC2#99×D241
commutatorC2×C4×C241C22×C4
FrattiniC2×Q8C22×D241
Fitting#355×C241C2
socleC2×C241C2×#99
prime radicalC2×D4×D241C4
cosocleC2×Q8×C241C23
hypercenter#355D241
hypocenterC241C2×#355
LCSG ▷ C2×C4×C241 ▷ C22×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #355

Complements

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

NH ≅ G/Ntype
2. #101×D241C2semidirect
3. #29507514C2semidirect
4. #29507513C2semidirect
5. #355×C241C2semidirect
15. #21440561C22semidirect
18. #101×C241C22semidirect
90. D241#355direct (N × H)
91. C241C2×#355semidirect
97. #355D241direct (N × H)
110. #101C2×D241semidirect

Maximal subgroups

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

subgroupindex
#124×D2412
#101×D2412
#295075142
#295075132
#355×C2412
C2×#355241