Finite Group Databasebeta

← #44508492

Subgroups — #44508492

Order 30848.

370 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 75 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
1C2×#21440672C212yesmaximal, complemented
2C2×#21440569C212yesmaximal, complemented
3#29507622C211yesmaximal, characteristic, complemented
4#29507486C211yesmaximal, characteristic, complemented
5#537×C241C211yesmaximal, characteristic
6C22×Dic482C2211yescharacteristic
7#21440672—24no—
8#21440672—24no—
9C2×#16838760—22no—
10C2×#16838758—22no—
11C2×#16838754C2212yes—
12C2×C4×Dic241C2211yescharacteristic
13#21440569—24no—
14#21440549—22no—
15C2×#41×C241C2212yes—
16C22⋊Q8×C241—22no—
17#121×C241—22no—
18#121×C241—22no—
19C2×C4⋊C4×C241C2211yescharacteristic
20C2×Dic482—22no—
21C2×Dic482—22no—
22C2×Dic482—21no—
23C2×Dic482D412yescomplemented
24C22×Dic241—21no—
25C22×Dic241—21no—
26#16838760—28no—
27#16838758—28no—
28#16838754—22no—
29#16838754D414yescomplemented
30C2×#14515349—22no—
31C4×Dic241—22no—
32#41×C241—22no—
33#41×C241—22no—
34#41×C241—22no—
35#41×C241—22no—
36C2×Q8×C241D412yes—
37C2×D4×C241—22no—
38C2×D4×C241—22no—
39C2×D4×C241D412yes—
40C22×C4×C241—22no—
41C22×C4×C241D412yes—
42C22×C4×C241C2311yescharacteristic
43C4⋊C4×C241—22no—
44C4⋊C4×C241—22no—
45C22⋊C4×C241—24no—
46Dic482—24no—
47Dic482—42no—
48C2×Dic241—22no—
49C2×Dic241—22no—
50C2×Dic241—41no—
51C2×Dic241—41no—
52C2×Dic241—41no—
53C2×Dic241—41no—
54#14515349—24no—
55C23×C241—22no—
56C23×C241C2×D411yescharacteristic
57Q8×C241—22no—
58Q8×C241—22no—
59D4×C241—22no—
60D4×C241—22no—
61D4×C241—42no—
62D4×C241—42no—
63D4×C241—82no—
64C2×C4×C241—22no—
65C2×C4×C241—22no—
66C2×C4×C241—42no—
67C2×C4×C241—42no—
68C2×C4×C241—42no—
69C2×C4×C241C2×D411yescharacteristic
70C2×C4×C241C2×D412yes—
71C2×C4×C241C2×D412yes—
72C2×C4×C241#4111yescharacteristic
73C22×C241—21no—
74C22×C241—21no—
75C22×C241—42no—
76C22×C241—42no—
77C22×C241—42no—
78C22×C241#12011yescharacteristic
79C22×C241#12111yescharacteristic
80C22×C241#12711yescharacteristic
81C4×C241—42no—
82C4×C241—42no—
83C4×C241#12012yes—
84C4×C241#12112yes—
85Dic241—42no—
86Dic241—42no—
87C2×C241—21no—
88C2×C241—21no—
89C2×C241—82no—
90C2×C241#39211yescharacteristic
91C2×C241#45511yescharacteristic
92C2×C241#45611yescharacteristic
93C241#200711yescharacteristic, complemented, Sylow
94#2007—2411nomaximal, Sylow
95C2×#137—2412no—
96#537D24111yescharacteristic
97C2×#104—2412no—
98#391—2411no—
99#343—2411no—
100C2×#41C2×D24112yes—
101C22×Q8—2411no—
102#137—4824no—
103#137—4824no—
104C2×Q16—4822no—
105C2×SD16—4822no—
106C2×M16—2412no—
107C22⋊Q8—22no—
108#121—22no—
109#121—22no—
110C2×C4⋊C4C2×D24111yescharacteristic
111C2×C42—2411no—
112#104—4824no—
113#95—4822no—
114#41—22no—
115#41—22no—
116#41—22no—
117#41—22no—
118C2×Q8—4822no—
119C2×Q8—4822no—
120C2×Q8—4821no—
121C2×Q8—2412no—
122C2×Q8C22⋊D24112yes—
123C2×D4—22no—
124C2×D4—22no—
125C2×D4C22⋊D24112yes—
126C22×C4—22no—
127C22×C4—4821no—
128C22×C4—4821no—
129C22×C4C22⋊D24112yes—
130C22×C4C22×D24111yescharacteristic
131Q16—4828no—
132SD16—4828no—
133M16—4822no—
134M16—2414no—
135C2×C8—4822no—
136C4⋊C4—22no—
137C4⋊C4—22no—
138C22⋊C4—24no—
139C42—4822no—
140C23—22no—
141C23C2×C22⋊D24111yescharacteristic
142Q8—22no—
143Q8—22no—
144Q8—9642no—
145Q8—4824no—
146D4—22no—
147D4—22no—
148D4—42no—
149D4—42no—
150D4—82no—
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—42no—
154C2×C4—42no—
155C2×C4—42no—
156C2×C4—9641no—
157C2×C4—9641no—
158C2×C4—9641no—
159C2×C4—9641no—
160C2×C4—4822no—
161C2×C4—4822no—
162C2×C4D4×D24111yescharacteristic
163C2×C4D4×D24112yes—
164C2×C4C2×C22⋊D24112yes—
165C2×C4#1683876911yescharacteristic
166C8—4824no—
167C22—21no—
168C22—21no—
169C22—42no—
170C22—42no—
171C22—42no—
172C22#2144061111yescharacteristic
173C22#2144061311yescharacteristic
174C22#2144063811yescharacteristic
175C4—42no—
176C4—42no—
177C4—9642no—
178C4—9642no—
179C4#2144061012yes—
180C4#2144061412yes—
181C2—21no—
182C2—21no—
183C2—82no—
184C2#2950762511yescharacteristic
185C2#2950789511yescharacteristic
186C2#2950790011yescharacteristic
subgroupG/H
centerC22#21440611
commutator, cosocleC22×C4×C241C23
FrattiniC22×C4C22×D241
Fitting, prime radical#537×C241C2
socleC22×C241#120
hypercenter#537D241
hypocenterC241#2007
LCSG ▷ C22×C4×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C22 ◁ C22×C4 ◁ #537

Complements

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

NH ≅ G/Ntype
1. C2×#21440672C2semidirect
2. C2×#21440569C2semidirect
3. #29507622C2semidirect
4. #29507486C2semidirect
23. C2×Dic482D4semidirect
29. #16838754D4semidirect
93. C241#2007semidirect

Maximal subgroups

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

subgroupindex
C2×#214406722
C2×#214405692
#295076222
#295074862
#537×C2412
#2007241