Finite Group Databasebeta

← #44508594

Subgroups — #44508594

Order 30848.

258 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 85 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×#21440633C211yesmaximal, characteristic
2C2×#21440566C211yesmaximal, characteristic
3#29507624C211yesmaximal, characteristic
4#29507480C211yesmaximal, characteristic
5#29507479C211yesmaximal, characteristic
6#29507471C211yesmaximal, characteristic
7C2×#103×C241C211yesmaximal, characteristic
8C22×#14515349C2211yescharacteristic
9#21440633—22no—
10#21440633—22no—
11C2×C4⋊Dic241—21no—
12C2×C4⋊Dic241C2211yescharacteristic
13C2×C4⋊Dic241C2211yescharacteristic
14C2×#16838749—21no—
15C2×C4×Dic241C2211yescharacteristic
16#21440566—22no—
17#21440549—21no—
18#21440549—21no—
19C22×Q8×C241C2211yescharacteristic
20C22×C8×C241C2211yescharacteristic
21C2×C4⋊C4×C241C2211yescharacteristic
22#103×C241—22no—
23C22×Dic241—21no—
24C22×Dic241—21no—
25C22×Dic241D411yescharacteristic
26C22×Dic241D411yescharacteristic
27C2×#14515349—21no—
28C2×#14515349—21no—
29C2×#14515349—21no—
30C4⋊Dic241—24no—
31C4⋊Dic241—21no—
32C4⋊Dic241—21no—
33C4⋊Dic241—21no—
34C4⋊Dic241D412yes—
35#16838749—24no—
36C4×Dic241—21no—
37C4×Dic241—21no—
38C2×Q8×C241—21no—
39C2×Q8×C241—21no—
40C2×Q8×C241—21no—
41C2×Q8×C241—21no—
42C2×Q8×C241—21no—
43C2×Q8×C241Q812yes—
44C22×C4×C241—21no—
45C22×C4×C241—21no—
46C22×C4×C241C2311yescharacteristic
47C2×C8×C241—21no—
48C2×C8×C241—21no—
49C2×C8×C241—21no—
50C4⋊C4×C241—21no—
51C4⋊C4×C241D412yes—
52C2×Dic241—21no—
53C2×Dic241—21no—
54C2×Dic241—22no—
55C2×Dic241—21no—
56C2×Dic241—21no—
57C2×Dic241—21no—
58C2×Dic241—21no—
59C2×Dic241—41no—
60C2×Dic241—41no—
61C2×Dic241—41no—
62C2×Dic241—41no—
63C2×Dic241—41no—
64#14515349—41no—
65C23×C241C2×D411yescharacteristic
66Q8×C241—22no—
67Q8×C241—22no—
68Q8×C241—41no—
69Q8×C241—41no—
70C2×C4×C241—22no—
71C2×C4×C241—22no—
72C2×C4×C241—41no—
73C2×C4×C241—41no—
74C2×C4×C241—41no—
75C2×C4×C241—41no—
76C2×C4×C241C2×D411yescharacteristic
77C2×C4×C241C2×D411yescharacteristic
78C2×C4×C241C2×Q811yescharacteristic
79C2×C4×C241#4111yescharacteristic
80C2×C4×C241#4111yescharacteristic
81C2×C4×C241#4111yescharacteristic
82C8×C241—41no—
83C22×C241#12011yescharacteristic
84C22×C241C22⋊Q811yescharacteristic
85C22×C241#12411yescharacteristic
86C22×C241#13511yescharacteristic
87C22×C241#13511yescharacteristic
88C22×C241#13711yescharacteristic
89C22×C241#13711yescharacteristic
90C4×C241—42no—
91C4×C241—42no—
92C4×C241C22⋊Q811yescharacteristic
93C4×C241C22⋊Q811yescharacteristic
94C4×C241#12411yescharacteristic
95C4×C241#12411yescharacteristic
96Dic241—41no—
97Dic241—41no—
98Dic241—42no—
99Dic241—81no—
100C2×C241#39311yescharacteristic
101C2×C241#45211yescharacteristic
102C2×C241#45211yescharacteristic
103C2×C241#47911yescharacteristic
104C2×C241#47911yescharacteristic
105C2×C241#48811yescharacteristic
106C2×C241#49111yescharacteristic
107C241#202611yescharacteristic, complemented, Sylow
108#2026—2411nomaximal, Sylow
109C2×#125—2411no—
110C2×#103—2411no—
111C2×#103D24111yescharacteristic
112#391—2411no—
113#340—2411no—
114#340—2411no—
115#336—2411no—
116C22×Q8C2×D24111yescharacteristic
117C22×C8—2411no—
118C22×C8C2×D24111yescharacteristic
119#125—4822no—
120#125—4822no—
121C2×C4⋊C4—4821no—
122C2×C4⋊C4—4821no—
123C2×C4⋊C4—2411no—
124C2×C4⋊C4—2411no—
125C2×C4⋊C4C2×D24111yescharacteristic
126C2×C42—2411no—
127#103—22no—
128#103—4822no—
129#95—4821no—
130#95—4821no—
131C2×Q8—21no—
132C2×Q8—21no—
133C2×Q8—21no—
134C2×Q8—21no—
135C2×Q8—21no—
136C2×Q8Dic48212yes—
137C22×C4—21no—
138C22×C4—21no—
139C22×C4—4821no—
140C22×C4—4821no—
141C22×C4—2411no—
142C22×C4—2411no—
143C22×C4C22×D24111yescharacteristic
144C2×C8—21no—
145C2×C8—21no—
146C2×C8—21no—
147C2×C8—4821no—
148C2×C8—4821no—
149C2×C8—4821no—
150C4⋊C4—21no—
151C4⋊C4—4824no—
152C4⋊C4—4824no—
153C4⋊C4—4821no—
154C4⋊C4—4821no—
155C4⋊C4—4821no—
156C4⋊C4—2412no—
157C4⋊C4C22⋊D24112yes—
158C42—4821no—
159C42—4821no—
160C23D4×D24111yescharacteristic
161Q8—22no—
162Q8—22no—
163Q8—41no—
164Q8—41no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—9641no—
172C2×C4—9641no—
173C2×C4—9641no—
174C2×C4—9641no—
175C2×C4—9641no—
176C2×C4—4821no—
177C2×C4—4821no—
178C2×C4—4822no—
179C2×C4—4821no—
180C2×C4—4821no—
181C2×C4—4821no—
182C2×C4—4821no—
183C2×C4D4×D24111yescharacteristic
184C2×C4C2×C22⋊D24111yescharacteristic
185C2×C4C2×Dic48211yescharacteristic
186C2×C4#1683876911yescharacteristic
187C2×C4#1683876911yescharacteristic
188C2×C4#1683877011yescharacteristic
189C8—41no—
190C8—9641no—
191C22#2144061011yescharacteristic
192C22#2144061911yescharacteristic
193C22#2144062811yescharacteristic
194C22#2144066311yescharacteristic
195C22#2144066511yescharacteristic
196C22#2144067111yescharacteristic
197C22#2144067411yescharacteristic
198C4—42no—
199C4—42no—
200C4—19281no—
201C4—9641no—
202C4—9642no—
203C4—9641no—
204C4#2144061911yescharacteristic
205C4#2144062111yescharacteristic
206C4#2144062811yescharacteristic
207C4#2144062911yescharacteristic
208C2#2950762911yescharacteristic
209C2#2950787611yescharacteristic
210C2#2950787811yescharacteristic
211C2#2950802211yescharacteristic
212C2#2950802611yescharacteristic
213C2#2950807311yescharacteristic
214C2#2950808411yescharacteristic
subgroupG/H
centerC23D4×D241
commutator, cosocleC22×C4×C241C23
FrattiniC22×C4C22×D241
FittingC2×#103×C241C2
socle, prime radicalC23×C241C2×D4
hypercenterC2×#103D241
hypocenterC241#2026
LCSG ▷ C22×C4×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
107. C241#2026semidirect

Maximal subgroups

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

subgroupindex
C2×#214406332
C2×#214405662
#295076242
#295074802
#295074792
#295074712
C2×#103×C2412
#2026241