Finite Group Databasebeta

← #44507847

Subgroups — #44507847

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×#21440630C211yesmaximal, characteristic
2#29508194C211yesmaximal, characteristic, complemented
3#29507723C211yesmaximal, characteristic
4#29507721C211yesmaximal, characteristic
5C2×#21440560C211yesmaximal, characteristic, complemented
6#29507477C211yesmaximal, characteristic, complemented
7#339×C241C211yesmaximal, characteristic, complemented
8C22×Dic482C2211yescharacteristic
9C22×D964C2211yescharacteristic
10C2×#16838754C2211yescharacteristic
11#21440630—22no—
12#21440630C414yescomplemented
13C4×Dic482—22no—
14#21440607—22no—
15#21440601C2211yescharacteristic
16#21440598—22no—
17C2×#16838747—22no—
18#21440564—22no—
19#21440562—22no—
20#21440560—22no—
21C2×M16×C241C2211yescharacteristic
22#117×C241C2211yescharacteristic
23C2×C42×C241C2211yescharacteristic
24C23×D241—21no—
25C2×Dic482—21no—
26C2×Dic482—21no—
27C2×Dic482—21no—
28C2×Dic482—21no—
29C2×Dic482C2×C412yes—
30C2×Dic482D412yes—
31C2×D964—21no—
32C2×D964—21no—
33C2×D964—21no—
34C2×D964—21no—
35C2×D964—21no—
36C2×D964C2×C412yes—
37C22×Dic241D412yes—
38#16838754—21no—
39#16838754—21no—
40C2×#14515349—21no—
41C4⋊Dic241D412yes—
42#16838749—24no—
43C22⋊Dic241—21no—
44#16838747—28no—
45C4×Dic241—24no—
46C4×Dic241—21no—
47C22×C4×C241—21no—
48C22×C4×C241C2311yescharacteristic
49M16×C241—21no—
50M16×C241—21no—
51C2×C8×C241—21no—
52C4⋊C4×C241D412yes—
53C22⋊C4×C241—21no—
54C42×C241—21no—
55C42×C241—21no—
56C42×C241C2×C412yes—
57C22×D241—22no—
58C22×D241—44no—
59C22×D241—41no—
60C22×D241—41no—
61Dic482—22no—
62Dic482—22no—
63Dic482—22no—
64Dic482—22no—
65D964—22no—
66D964—22no—
67D964—41no—
68D964—41no—
69C2×Dic241—22no—
70C2×Dic241—22no—
71C2×Dic241—22no—
72C2×Dic241C22⋊C414yes—
73#14515349—41no—
74C23×C241C2×D411yescharacteristic
75C2×C4×C241—22no—
76C2×C4×C241—22no—
77C2×C4×C241—42no—
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×C241C2×C22⋊C411yescharacteristic
87C22×C241#12011yescharacteristic
88C22×C241#12311yescharacteristic
89C2×D241—44no—
90C2×D241—42no—
91C2×D241—82no—
92C2×D241—82no—
93C4×C241—42no—
94C4×C241—42no—
95C4×C241C4×D411yescharacteristic
96C4×C241C4×D411yescharacteristic
97C4×C241#12111yescharacteristic
98C4×C241#12111yescharacteristic
99Dic241—24no—
100Dic241—42no—
101C2×C241—21no—
102C2×C241—21no—
103C2×C241#38611yescharacteristic
104C2×C241#45412yes—
105D241—82no—
106C241#188811yescharacteristic, complemented, Sylow
107#1888—2411nomaximal, Sylow
108C2×#124—2411no—
109#519—2411no—
110#418—2411no—
111#418—2411no—
112C2×#101—2411no—
113#339—2411no—
114#339D24111yescharacteristic, complemented
115C22×Q8—2411no—
116C22×D4—2411no—
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×C42C2×D24111yescharacteristic
128#102—4822no—
129#102—4822no—
130#101—4822no—
131C24—4821no—
132C2×Q8—4821no—
133C2×Q8—4821no—
134C2×Q8—4821no—
135C2×Q8—4821no—
136C2×Q8—2412no—
137C2×Q8—2412no—
138C2×D4—4821no—
139C2×D4—4821no—
140C2×D4—4821no—
141C2×D4—4821no—
142C2×D4—4821no—
143C2×D4—2412no—
144C22×C4—21no—
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⋊C4D96412yes—
156C22⋊C4—21no—
157C22⋊C4—4828no—
158C22⋊C4—4821no—
159C42—21no—
160C42—21no—
161C42—4824no—
162C42—4821no—
163C42C4×D24112yes—
164C23—9644no—
165C23—9641no—
166C23—9641no—
167C23—4822no—
168C23D4×D24111yescharacteristic
169Q8—4822no—
170Q8—4822no—
171Q8—4822no—
172Q8—4822no—
173D4—9641no—
174D4—9641no—
175D4—4822no—
176D4—4822no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—42no—
180C2×C4—4822no—
181C2×C4—4822no—
182C2×C4—4822no—
183C2×C4—2414no—
184C2×C4C2×C4×D24111yescharacteristic
185C2×C4D4×D24111yescharacteristic
186C2×C4D4×D24111yescharacteristic
187C2×C4C2×D96411yescharacteristic
188C2×C4#1683877011yescharacteristic
189C2×C4#1683877111yescharacteristic
190C8—41no—
191C8—9641no—
192C22—22no—
193C22—19282no—
194C22—19282no—
195C22—9644no—
196C22—9642no—
197C22C22⋊C4×D24111yescharacteristic
198C22#2144061211yescharacteristic
199C22#2144062711yescharacteristic
200C4—42no—
201C4—42no—
202C4—9642no—
203C4—4824no—
204C4#2144060411yescharacteristic
205C4C4×D96411yescharacteristic
206C4#2144061511yescharacteristic
207C4#2144061711yescharacteristic
208C2—21no—
209C2—21no—
210C2—19282no—
211C2#2950759511yescharacteristic
212C2#2950789112yes—
subgroupG/H
centerC22#21440612
commutatorC2×C4×C241C22×C4
FrattiniC22×C4C22×D241
Fitting#339×C241C2
socleC22×C241#120
prime radicalC22×D964C22
cosocleC22×C4×C241C23
hypercenter#339D241
hypocenterC241#1888
LCSG ▷ C2×C4×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
2. #29508194C2semidirect
5. C2×#21440560C2semidirect
6. #29507477C2semidirect
7. #339×C241C2semidirect
12. #21440630C4semidirect
106. C241#1888semidirect
114. #339D241semidirect

Maximal subgroups

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

subgroupindex
C2×#214406302
#295081942
#295077232
#295077212
C2×#214405602
#295074772
#339×C2412
#1888241