Finite Group Databasebeta

← #44509129

Subgroups — #44509129

Order 30848.

250 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 55 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#29508268C211yesmaximal, characteristic
2#29507700C212yesmaximal, complemented
3#29507516C211yesmaximal, characteristic, complemented
4#29507513C212yesmaximal, complemented
5#356×C241C211yesmaximal, characteristic, complemented
6C2×#16838771C411yescharacteristic
7C2×#16838771C2211yescharacteristic
8M16×D241—22no—
9#21440639C411yescharacteristic
10#21440631C411yescharacteristic
11#21440631C2211yescharacteristic
12#21440617—22no—
13#21440604—22no—
14C42×D241C411yescharacteristic
15#21440561C2212yes—
16#21440558—22no—
17C4⋊Q8×C241C2211yescharacteristic
18#101×C241C2212yes—
19#16838771—41no—
20#16838771—41no—
21#16838771—41no—
22#16838771—41no—
23C2×D964—22no—
24C2×D964—21no—
25C2×D964C2×C411yescharacteristic
26C2×D964C2×C411yescharacteristic
27C2×D964D412yes—
28C2×C4×D241—21no—
29C2×C4×D241—21no—
30C2×C4×D241C2×C411yescharacteristic
31C2×C4×D241D412yes—
32#16838754—22no—
33#16838753—42no—
34C8×D241—42no—
35#16838747—22no—
36#16838747—22no—
37C4×Dic241—21no—
38C4×Dic241C2×C411yescharacteristic
39C2×Q8×C241C2×C411yescharacteristic
40C2×Q8×C241C2311yescharacteristic
41M16×C241—22no—
42C4⋊C4×C241—22no—
43C42×C241C2×C411yescharacteristic
44C22×D241—21no—
45C22×D241C22⋊C412yes—
46C22×D241C22⋊C411yescharacteristic
47D964—41no—
48D964—42no—
49D964—41no—
50D964—44no—
51D964—42no—
52C2×Dic241—21no—
53C2×Dic241C22⋊C411yescharacteristic
54C4×D241—22no—
55C4×D241—22no—
56C4×D241—21no—
57C4×D241—21no—
58C4×D241—42no—
59C4×D241—41no—
60C4×D241—41no—
61#14515349—42no—
62Q8×C241—41no—
63Q8×C241—41no—
64C2×C4×C241—21no—
65C2×C4×C241—21no—
66C2×C4×C241C22×C411yescharacteristic
67C2×C4×C241C2×D412yes—
68C8×C241—42no—
69C22×C241C2×C22⋊C411yescharacteristic
70C2×D241—21no—
71C2×D241—22no—
72C2×D241—41no—
73C2×D241—42no—
74C2×D241—42no—
75C2×D241—41no—
76C4×C241—22no—
77C4×C241—22no—
78C4×C241—21no—
79C4×C241—41no—
80Dic241—41no—
81Dic241#9911yescharacteristic
82Dic241#9911yescharacteristic
83C2×C241—21no—
84C2×C241C2×#9911yescharacteristic
85D241—41no—
86D241—42no—
87D241—81no—
88C241#213211yescharacteristic, complemented, Sylow
89#2132—2411nomaximal, Sylow
90#532—2411no—
91#413—2412no—
92#356—2411no—
93#356D24111yescharacteristic, complemented
94#355—2412no—
95C2×#41—2411no—
96C2×#41—2411no—
97C2×M16—4822no—
98C4⋊Q8C2×D24111yescharacteristic
99#127—2411no—
100#124—2411no—
101#124—2411no—
102#121—4822no—
103C4×D4—4822no—
104C2×C42—2411no—
105#101—2412no—
106#101C2×D24112yes—
107#100—4822no—
108#41—9641no—
109#41—9641no—
110#41—9641no—
111#41—9641no—
112C2×Q8C4×D24111yescharacteristic
113C2×Q8C22×D24111yescharacteristic
114C2×D4—4822no—
115C2×D4—4821no—
116C2×D4—2411no—
117C2×D4—2411no—
118C2×D4—2412no—
119C22×C4—4821no—
120C22×C4—4821no—
121C22×C4—2411no—
122C22×C4—2412no—
123M16—22no—
124M16—9642no—
125M16—4822no—
126C2×C8—9642no—
127C4⋊C4—22no—
128C22⋊C4—4822no—
129C22⋊C4—4822no—
130C42—4821no—
131C42—2411no—
132C42C4×D24111yescharacteristic
133C23—4821no—
134C23—2412no—
135C23—2411no—
136Q8—41no—
137Q8—41no—
138D4—9641no—
139D4—9644no—
140D4—9642no—
141D4—9641no—
142D4—9642no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—9642no—
146C2×C4—9641no—
147C2×C4—9641no—
148C2×C4—4822no—
149C2×C4—4822no—
150C2×C4—4821no—
151C2×C4—4821no—
152C2×C4—4821no—
153C2×C4—2411no—
154C2×C4C2×C4×D24111yescharacteristic
155C2×C4D4×D24112yes—
156C8—42no—
157C8—9642no—
158C22—9642no—
159C22—9641no—
160C22—9642no—
161C22—9641no—
162C22—4821no—
163C22—4822no—
164C22C22⋊C4×D24111yescharacteristic
165C4—22no—
166C4—22no—
167C4—21no—
168C4—41no—
169C4—9641no—
170C4—2411no—
171C4—2411no—
172C2—21no—
173C2—19281no—
174C2—9641no—
175C2—9642no—
176C2#99×D24111yescharacteristic
subgroupG/H
centerC2#99×D241
commutatorC2×C4×C241C22×C4
FrattiniC2×Q8C22×D241
Fitting#356×C241C2
socleC2×C241C2×#99
prime radical#29508268C2
cosocleC2×Q8×C241C23
hypercenter#356D241
hypocenterC241#2132
LCSG ▷ C2×C4×C241 ▷ C22×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #356

Complements

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

NH ≅ G/Ntype
2. #29507700C2semidirect
3. #29507516C2semidirect
4. #29507513C2semidirect
5. #356×C241C2semidirect
88. C241#2132semidirect
93. #356D241semidirect

Maximal subgroups

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

subgroupindex
#295082682
#295077002
#295075162
#295075132
#356×C2412
#2132241