Finite Group Databasebeta

← #44507845

Subgroups — #44507845

Order 30848.

344 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 83 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×#21440629C211yesmaximal, characteristic
2#29508194C211yesmaximal, characteristic, complemented
3#29507722C211yesmaximal, characteristic
4C2×#21440560C211yesmaximal, characteristic, complemented
5#29507478C211yesmaximal, characteristic, complemented
6#29507476C211yesmaximal, characteristic, complemented
7#418×C241C211yesmaximal, characteristic
8C22×Dic482C2211yescharacteristic
9C2×#16838754C2211yescharacteristic
10#21440629—22no—
11#21440629C414yescomplemented
12C4×Dic482—22no—
13#21440607—22no—
14#21440601C2211yescharacteristic
15#21440598—22no—
16C2×C22⋊Dic241—22no—
17C2×C4×Dic241C2211yescharacteristic
18#21440563—22no—
19#21440560—22no—
20C22×D4×C241C2211yescharacteristic
21C2×M16×C241C2211yescharacteristic
22#117×C241C2211yescharacteristic
23#102×C241—22no—
24C2×Dic482—21no—
25C2×Dic482—21no—
26C2×Dic482—21no—
27C2×Dic482—21no—
28C2×Dic482C2×C412yes—
29C2×Dic482D412yes—
30C22×Dic241—21no—
31C22×Dic241D412yes—
32#16838754—21no—
33#16838754—21no—
34C2×#14515349—21no—
35C4⋊Dic241D412yes—
36#16838749—24no—
37C22⋊Dic241—28no—
38C22⋊Dic241—21no—
39C4×Dic241—24no—
40C4×Dic241—21no—
41C4×Dic241—21no—
42C4×Dic241C2×C412yes—
43C24×C241—21no—
44C2×D4×C241—21no—
45C2×D4×C241—21no—
46C2×D4×C241—21no—
47C2×D4×C241—21no—
48C2×D4×C241—21no—
49C2×D4×C241C2×C412yes—
50C22×C4×C241C2311yescharacteristic
51M16×C241—21no—
52M16×C241—21no—
53C2×C8×C241—21no—
54C4⋊C4×C241D412yes—
55C22⋊C4×C241—21no—
56C42×C241—21no—
57Dic482—22no—
58Dic482—22no—
59Dic482—22no—
60Dic482—22no—
61C2×Dic241—22no—
62C2×Dic241—22no—
63C2×Dic241—22no—
64C2×Dic241—22no—
65C2×Dic241—42no—
66C2×Dic241C22⋊C414yes—
67#14515349—41no—
68C23×C241—22no—
69C23×C241—44no—
70C23×C241—41no—
71C23×C241—41no—
72C23×C241C2×D411yescharacteristic
73D4×C241—22no—
74D4×C241—22no—
75D4×C241—41no—
76D4×C241—41no—
77C2×C4×C241—22no—
78C2×C4×C241C22×C411yescharacteristic
79C2×C4×C241C2×D411yescharacteristic
80C2×C4×C241C2×D411yescharacteristic
81C2×C4×C241C2×D411yescharacteristic
82C2×C4×C241#4111yescharacteristic
83C2×C4×C241#4111yescharacteristic
84C8×C241—41no—
85C22×C241—22no—
86C22×C241—44no—
87C22×C241—42no—
88C22×C241—82no—
89C22×C241—82no—
90C22×C241C2×C22⋊C411yescharacteristic
91C22×C241#12011yescharacteristic
92C22×C241#12311yescharacteristic
93C4×C241—42no—
94C4×C241C4×D411yescharacteristic
95C4×C241C4×D411yescharacteristic
96C4×C241#12111yescharacteristic
97C4×C241#12111yescharacteristic
98Dic241—24no—
99Dic241—42no—
100Dic241—42no—
101C2×C241—21no—
102C2×C241—21no—
103C2×C241—82no—
104C2×C241#38611yescharacteristic
105C2×C241#45412yes—
106C241#188811yescharacteristic, complemented, Sylow
107#1888—2411nomaximal, Sylow
108C2×#124—2411no—
109#519—2411no—
110#418—2411no—
111#418D24111yescharacteristic
112C2×#101—2411no—
113#339—2411no—
114#339—2411no—
115C22×Q8—2411no—
116C22×D4C2×D24111yescharacteristic
117C2×M16—2411no—
118C2×M16C2×D24111yescharacteristic
119#124—4822no—
120#124—2414no—
121C4×Q8—4822no—
122C4×Q8—4822no—
123#117—4822no—
124#117—2411no—
125#117C2×D24111yescharacteristic
126C2×C22⋊C4—4822no—
127C2×C42—2411no—
128#102—22no—
129#102—4822no—
130#101—4822no—
131C24—21no—
132C2×Q8—4821no—
133C2×Q8—4821no—
134C2×Q8—4821no—
135C2×Q8—4821no—
136C2×Q8—2412no—
137C2×Q8—2412no—
138C2×D4—21no—
139C2×D4—21no—
140C2×D4—21no—
141C2×D4—21no—
142C2×D4—21no—
143C2×D4C4×D24112yes—
144C22×C4—4821no—
145C22×C4—2412no—
146C22×C4C22×D24111yescharacteristic
147M16—21no—
148M16—21no—
149M16—4821no—
150M16—4821no—
151C2×C8—21no—
152C2×C8—4821no—
153C4⋊C4—4824no—
154C4⋊C4—2412no—
155C4⋊C4C22⋊D24112yes—
156C22⋊C4—21no—
157C22⋊C4—4821no—
158C22⋊C4—4828no—
159C42—21no—
160C42—4824no—
161C42—4821no—
162C42—4821no—
163C42—2412no—
164C23—22no—
165C23—44no—
166C23—41no—
167C23—41no—
168C23D4×D24111yescharacteristic
169Q8—4822no—
170Q8—4822no—
171Q8—4822no—
172Q8—4822no—
173D4—22no—
174D4—22no—
175D4—41no—
176D4—41no—
177C2×C4—22no—
178C2×C4—9642no—
179C2×C4—4822no—
180C2×C4—4822no—
181C2×C4—4822no—
182C2×C4—4822no—
183C2×C4—2414no—
184C2×C4C2×C4×D24111yescharacteristic
185C2×C4D4×D24111yescharacteristic
186C2×C4D4×D24111yescharacteristic
187C2×C4C2×C22⋊D24111yescharacteristic
188C2×C4#1683876911yescharacteristic
189C2×C4#1683877011yescharacteristic
190C8—41no—
191C8—9641no—
192C22—22no—
193C22—44no—
194C22—42no—
195C22—82no—
196C22—82no—
197C22C22⋊C4×D24111yescharacteristic
198C22#2144061011yescharacteristic
199C22#2144062411yescharacteristic
200C4—42no—
201C4—9642no—
202C4—9642no—
203C4—4824no—
204C4#2144060211yescharacteristic
205C4C4×C22⋊D24111yescharacteristic
206C4#2144061311yescharacteristic
207C4#2144061511yescharacteristic
208C2—21no—
209C2—21no—
210C2—82no—
211C2#2950759311yescharacteristic
212C2#2950788812yes—
subgroupG/H
centerC22#21440610
commutatorC2×C4×C241C22×C4
FrattiniC22×C4C22×D241
Fitting#418×C241C2
socleC22×C241#120
prime radicalC22×D4×C241C22
cosocleC22×C4×C241C23
hypercenter#418D241
hypocenterC241#1888
LCSG ▷ C2×C4×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
2. #29508194C2semidirect
4. C2×#21440560C2semidirect
5. #29507478C2semidirect
6. #29507476C2semidirect
11. #21440629C4semidirect
106. C241#1888semidirect

Maximal subgroups

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

subgroupindex
C2×#214406292
#295081942
#295077222
C2×#214405602
#295074782
#295074762
#418×C2412
#1888241