Finite Group Databasebeta

← #44508604

Subgroups — #44508604

Order 30848.

246 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 69 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#29508345C211yesmaximal, characteristic
2#29507726C211yesmaximal, characteristic
3#29507624C211yesmaximal, characteristic
4#29507485C211yesmaximal, characteristic
5#29507478C211yesmaximal, characteristic
6#29507476C211yesmaximal, characteristic
7#419×C241C211yesmaximal, characteristic
8C2×#16838754C2211yescharacteristic
9#21440642—21no—
10#21440641—21no—
11#21440634—21no—
12#21440633—21no—
13#21440619—22no—
14#21440601C2211yescharacteristic
15C2×C4⋊Dic241C2211yescharacteristic
16C2×C4×Dic241C2211yescharacteristic
17#21440566—21no—
18#21440566—21no—
19#21440549—22no—
20C22×Q8×C241C2211yescharacteristic
21C2×M16×C241C2211yescharacteristic
22#117×C241C2211yescharacteristic
23#103×C241—21no—
24#103×C241—21no—
25C2×Dic482—22no—
26C22×Dic241—21no—
27C22×Dic241D412yes—
28#16838754—21no—
29#16838754—21no—
30C2×#14515349—21no—
31C4⋊Dic241—22no—
32C4⋊Dic241—21no—
33C4⋊Dic241—21no—
34C4⋊Dic241D411yescharacteristic
35C4⋊Dic241D411yescharacteristic
36#16838749—22no—
37#16838749—22no—
38C22⋊Dic241—21no—
39C4×Dic241—21no—
40C4×Dic241—21no—
41C4×Dic241—21no—
42C2×Q8×C241—21no—
43C2×Q8×C241—21no—
44C2×Q8×C241—21no—
45C2×Q8×C241—21no—
46C2×Q8×C241—21no—
47C2×Q8×C241Q812yescomplemented
48C22×C4×C241—21no—
49C22×C4×C241C2311yescharacteristic
50M16×C241—21no—
51M16×C241—21no—
52C2×C8×C241—21no—
53C4⋊C4×C241D411yescharacteristic
54C4⋊C4×C241D411yescharacteristic
55C22⋊C4×C241—21no—
56C42×C241—21no—
57Dic482—82no—
58C2×Dic241—22no—
59C2×Dic241—21no—
60C2×Dic241—21no—
61C2×Dic241—22no—
62C2×Dic241—41no—
63C2×Dic241—41no—
64C2×Dic241—42no—
65#14515349—41no—
66C23×C241C2×D411yescharacteristic
67Q8×C241—22no—
68Q8×C241—22no—
69Q8×C241—41no—
70Q8×C241—41no—
71C2×C4×C241—21no—
72C2×C4×C241—21no—
73C2×C4×C241—22no—
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—21no—
84C22×C241—21no—
85C22×C241#12011yescharacteristic
86C22×C241C22⋊Q811yescharacteristic
87C22×C241#12411yescharacteristic
88C4×C241—42no—
89C4×C241—41no—
90C4×C241—41no—
91C4×C241C22⋊Q811yescharacteristic
92C4×C241C22⋊Q811yescharacteristic
93C4×C241#12411yescharacteristic
94C4×C241#12411yescharacteristic
95Dic241—42no—
96Dic241—42no—
97Dic241—41no—
98Dic241—41no—
99C2×C241—21no—
100C2×C241—21no—
101C2×C241#39311yescharacteristic
102C2×C241#45511yescharacteristic
103C2×C241#45611yescharacteristic
104C241#202811yescharacteristic, complemented, Sylow
105#2028—2411nomaximal, Sylow
106#544—2411no—
107#419—2411no—
108#419D24111yescharacteristic
109#391—2411no—
110#343—2411no—
111#339—2411no—
112#339—2411no—
113C22×Q8C2×D24111yescharacteristic
114C2×M16—2411no—
115C2×M16C2×D24111yescharacteristic
116C4⋊Q8—4821no—
117C4⋊Q8—4821no—
118#125—4821no—
119#125—4821no—
120C22⋊Q8—4822no—
121#117—2411no—
122#117C2×D24111yescharacteristic
123C2×C4⋊C4—2411no—
124C2×C42—2411no—
125#103—21no—
126#103—21no—
127#103—4821no—
128#103—4821no—
129#95—4822no—
130C2×Q8—21no—
131C2×Q8—21no—
132C2×Q8—21no—
133C2×Q8—21no—
134C2×Q8—21no—
135C2×Q8—4822no—
136C2×Q8Dic48212yescomplemented
137C22×C4—21no—
138C22×C4—4821no—
139C22×C4—2412no—
140C22×C4C22×D24111yescharacteristic
141M16—21no—
142M16—21no—
143M16—4821no—
144M16—4821no—
145C2×C8—21no—
146C2×C8—4821no—
147C4⋊C4—4822no—
148C4⋊C4—4822no—
149C4⋊C4—4822no—
150C4⋊C4—4821no—
151C4⋊C4—4821no—
152C4⋊C4—2411no—
153C4⋊C4—2411no—
154C4⋊C4C22⋊D24111yescharacteristic
155C4⋊C4C22⋊D24111yescharacteristic
156C22⋊C4—21no—
157C22⋊C4—4821no—
158C42—21no—
159C42—4821no—
160C42—4821no—
161C42—4821no—
162C23D4×D24111yescharacteristic
163Q8—22no—
164Q8—22no—
165Q8—41no—
166Q8—41no—
167Q8—19282no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—22no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—9641no—
174C2×C4—9641no—
175C2×C4—9642no—
176C2×C4—4822no—
177C2×C4—4821no—
178C2×C4—4821no—
179C2×C4—4822no—
180C2×C4D4×D24111yescharacteristic
181C2×C4C2×C22⋊D24111yescharacteristic
182C2×C4C2×Dic48211yescharacteristic
183C2×C4#1683876911yescharacteristic
184C2×C4#1683876911yescharacteristic
185C2×C4#1683877011yescharacteristic
186C8—41no—
187C8—9641no—
188C22—21no—
189C22—21no—
190C22#2144061011yescharacteristic
191C22#2144061911yescharacteristic
192C22#2144062811yescharacteristic
193C4—42no—
194C4—41no—
195C4—41no—
196C4—9642no—
197C4—9642no—
198C4—9641no—
199C4—9641no—
200C4#2144061911yescharacteristic
201C4#2144062111yescharacteristic
202C4#2144062811yescharacteristic
203C4#2144062911yescharacteristic
204C2—21no—
205C2—21no—
206C2#2950762911yescharacteristic
207C2#2950789311yescharacteristic
208C2#2950789811yescharacteristic
subgroupG/H
centerC22#21440610
commutator, cosocleC22×C4×C241C23
FrattiniC22×C4C22×D241
Fitting#419×C241C2
socleC22×C241#120
prime radicalC23×C241C2×D4
hypercenter#419D241
hypocenterC241#2028
LCSG ▷ C22×C4×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
47. C2×Q8×C241Q8semidirect
104. C241#2028semidirect
136. C2×Q8Dic482semidirect

Maximal subgroups

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

subgroupindex
#295083452
#295077262
#295076242
#295074852
#295074782
#295074762
#419×C2412
#2028241