Finite Group Databasebeta

← #44509127

Subgroups — #44509127

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#29508266C211yesmaximal, characteristic
2#29507700C212yesmaximal, complemented
3#29507515C212yesmaximal, complemented
4#29507514C211yesmaximal, characteristic, complemented
5#355×C241C211yesmaximal, characteristic, complemented
6C2×#16838771C2211yescharacteristic
7C2×#16838769C411yescharacteristic
8M16×D241—22no—
9#21440640C2211yescharacteristic
10#21440638C411yescharacteristic
11#21440630C411yescharacteristic
12#21440615—22no—
13#21440602—22no—
14C42×D241C411yescharacteristic
15#21440561C2212yes—
16#21440558—22no—
17#124×C241C2211yescharacteristic
18#101×C241C2212yes—
19#16838771—41no—
20#16838771—41no—
21#16838769—41no—
22#16838769—41no—
23C2×Dic482C2×C411yescharacteristic
24C2×D964C2×C411yescharacteristic
25C2×D964D412yes—
26C2×C22⋊D241—22no—
27C2×C22⋊D241—21no—
28C22×Dic241—21no—
29C2×C4×D241—21no—
30C2×C4×D241C2×C411yescharacteristic
31C2×C4×D241D412yes—
32#16838754—22no—
33#16838753—42no—
34C8×D241—42no—
35#16838749—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×D241C22⋊C412yes—
45C22×D241C22⋊C411yescharacteristic
46Dic482—41no—
47D964—41no—
48D964—42no—
49C22⋊D241—44no—
50C22⋊D241—42no—
51C2×Dic241—21no—
52C2×Dic241—21no—
53C2×Dic241—41no—
54C2×Dic241—41no—
55C2×Dic241C22⋊C411yescharacteristic
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—21no—
73C2×D241—22no—
74C2×D241—41no—
75C2×D241—42no—
76C4×C241—22no—
77C4×C241—21no—
78C4×C241—41no—
79Dic241—22no—
80Dic241—41no—
81Dic241#9911yescharacteristic
82Dic241#9911yescharacteristic
83C2×C241—21no—
84C2×C241—81no—
85C2×C241C2×#9911yescharacteristic
86D241—41no—
87D241—42no—
88C241#213211yescharacteristic, complemented, Sylow
89#2132—2411nomaximal, Sylow
90#532—2411no—
91#413—2412no—
92#356—2412no—
93#355—2411no—
94#355D24111yescharacteristic, complemented
95C2×#41—2411no—
96C2×#41—2411no—
97C2×M16—4822no—
98C4⋊Q8—2411no—
99#127—2411no—
100#124—2411no—
101#124C2×D24111yescharacteristic
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×Q8—2411no—
113C2×Q8C22×D24111yescharacteristic
114C2×D4—4822no—
115C2×D4—4821no—
116C2×D4—2411no—
117C2×D4—2412no—
118C2×D4C4×D24111yescharacteristic
119C22×C4—4821no—
120C22×C4—4821no—
121C22×C4—2411no—
122C22×C4—2412no—
123M16—22no—
124M16—9642no—
125M16—4822no—
126C2×C8—9642no—
127C4⋊C4—4822no—
128C22⋊C4—22no—
129C22⋊C4—4822no—
130C42—4821no—
131C42—2411no—
132C42C4×D24111yescharacteristic
133C23—21no—
134C23—2412no—
135C23—2411no—
136Q8—41no—
137Q8—9641no—
138D4—41no—
139D4—9642no—
140D4—9641no—
141D4—9642no—
142D4—9644no—
143C2×C4—21no—
144C2×C4—9642no—
145C2×C4—9641no—
146C2×C4—9641no—
147C2×C4—4822no—
148C2×C4—4822no—
149C2×C4—4821no—
150C2×C4—4821no—
151C2×C4—4821no—
152C2×C4—4821no—
153C2×C4—2411no—
154C2×C4C2×C4×D24111yescharacteristic
155C2×C4D4×D24112yes—
156C8—42no—
157C8—9642no—
158C22—42no—
159C22—41no—
160C22—9641no—
161C22—9642no—
162C22—4821no—
163C22—4822no—
164C22C22⋊C4×D24111yescharacteristic
165C4—22no—
166C4—21no—
167C4—41no—
168C4—9641no—
169C4—4822no—
170C4—2411no—
171C4—2411no—
172C2—21no—
173C2—81no—
174C2—9641no—
175C2—9642no—
176C2#99×D24111yescharacteristic
subgroupG/H
centerC2#99×D241
commutatorC2×C4×C241C22×C4
FrattiniC2×Q8C22×D241
Fitting#355×C241C2
socleC2×C241C2×#99
prime radical#29508266C2
cosocleC2×Q8×C241C23
hypercenter#355D241
hypocenterC241#2132
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. #29507700C2semidirect
3. #29507515C2semidirect
4. #29507514C2semidirect
5. #355×C241C2semidirect
88. C241#2132semidirect
94. #355D241semidirect

Maximal subgroups

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

subgroupindex
#295082662
#295077002
#295075152
#295075142
#355×C2412
#2132241