Finite Group Databasebeta

← #44508584

Subgroups — #44508584

Order 30848.

290 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 89 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×#21440641C211yesmaximal, characteristic
2C2×#21440566C211yesmaximal, characteristic
3#29507624C211yesmaximal, characteristic
4#29507480C211yesmaximal, characteristic
5#29507479C211yesmaximal, characteristic
6#29507471C211yesmaximal, characteristic
7C2×#103×C241C211yesmaximal, characteristic
8C22×Dic482—21no—
9C22×#14515349C2211yescharacteristic
10#21440641—22no—
11#21440641—22no—
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—
23C2×Dic482—24no—
24C2×Dic482—42no—
25C2×Dic482—42no—
26C22×Dic241—21no—
27C22×Dic241—21no—
28C22×Dic241D411yescharacteristic
29C22×Dic241D411yescharacteristic
30C2×#14515349—21no—
31C2×#14515349—21no—
32C2×#14515349—21no—
33C4⋊Dic241—21no—
34C4⋊Dic241—21no—
35C4⋊Dic241—21no—
36C4⋊Dic241D412yes—
37#16838749—24no—
38C4×Dic241—21no—
39C4×Dic241—21no—
40C2×Q8×C241—21no—
41C2×Q8×C241—21no—
42C2×Q8×C241—21no—
43C2×Q8×C241—21no—
44C2×Q8×C241—21no—
45C2×Q8×C241Q812yescomplemented
46C22×C4×C241—21no—
47C22×C4×C241—21no—
48C22×C4×C241C2311yescharacteristic
49C2×C8×C241—21no—
50C2×C8×C241—21no—
51C2×C8×C241—21no—
52C4⋊C4×C241—21no—
53C4⋊C4×C241D412yes—
54Dic482—48no—
55C2×Dic241—21no—
56C2×Dic241—21no—
57C2×Dic241—21no—
58C2×Dic241—21no—
59C2×Dic241—22no—
60C2×Dic241—41no—
61C2×Dic241—41no—
62C2×Dic241—41no—
63C2×Dic241—41no—
64C2×Dic241—41no—
65C2×Dic241SD1612yes—
66C2×Dic241Q1612yes—
67#14515349—41no—
68C23×C241C2×D411yescharacteristic
69Q8×C241—22no—
70Q8×C241—22no—
71Q8×C241—41no—
72Q8×C241—41no—
73C2×C4×C241—22no—
74C2×C4×C241—22no—
75C2×C4×C241—41no—
76C2×C4×C241—41no—
77C2×C4×C241—41no—
78C2×C4×C241—41no—
79C2×C4×C241C2×D411yescharacteristic
80C2×C4×C241C2×D411yescharacteristic
81C2×C4×C241C2×Q811yescharacteristic
82C2×C4×C241#4111yescharacteristic
83C2×C4×C241#4111yescharacteristic
84C2×C4×C241#4111yescharacteristic
85C8×C241—41no—
86C22×C241#12011yescharacteristic
87C22×C241C22⋊Q811yescharacteristic
88C22×C241#12411yescharacteristic
89C22×C241C2×SD1611yescharacteristic
90C22×C241C2×Q1611yescharacteristic
91C22×C241AGL(1,ℤ/8)11yescharacteristic
92C22×C241#13711yescharacteristic
93C4×C241—42no—
94C4×C241—42no—
95C4×C241C22⋊Q811yescharacteristic
96C4×C241C22⋊Q811yescharacteristic
97C4×C241#12411yescharacteristic
98C4×C241#12411yescharacteristic
99Dic241—22no—
100Dic241—22no—
101Dic241—42no—
102Dic241—81no—
103C2×C241#39311yescharacteristic
104C2×C241#45011yescharacteristic
105C2×C241#45111yescharacteristic
106C2×C241#47511yescharacteristic
107C2×C241#47711yescharacteristic
108C2×C241#48711yescharacteristic
109C2×C241#48911yescharacteristic
110C241#202411yescharacteristic, complemented, Sylow
111#2024—2411nomaximal, Sylow
112C2×C4⋊Q8—2411no—
113C2×#103—2411no—
114C2×#103D24111yescharacteristic
115#391—2411no—
116#340—2411no—
117#340—2411no—
118#336—2411no—
119C22×Q8—4821no—
120C22×Q8C2×D24111yescharacteristic
121C22×C8—2411no—
122C22×C8C2×D24111yescharacteristic
123C4⋊Q8—4822no—
124C4⋊Q8—4822no—
125C2×C4⋊C4—4821no—
126C2×C4⋊C4—2411no—
127C2×C4⋊C4—2411no—
128C2×C4⋊C4C2×D24111yescharacteristic
129C2×C42—2411no—
130#103—22no—
131#103—4822no—
132#95—4821no—
133#95—4821no—
134C2×Q8—21no—
135C2×Q8—21no—
136C2×Q8—21no—
137C2×Q8—21no—
138C2×Q8—21no—
139C2×Q8—9642no—
140C2×Q8—9642no—
141C2×Q8—4824no—
142C2×Q8Dic48212yescomplemented
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—4821no—
146C22×C4—4821no—
147C22×C4—2411no—
148C22×C4—2411no—
149C22×C4C22×D24111yescharacteristic
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—21no—
153C2×C8—4821no—
154C2×C8—4821no—
155C2×C8—4821no—
156C4⋊C4—21no—
157C4⋊C4—4824no—
158C4⋊C4—4821no—
159C4⋊C4—4821no—
160C4⋊C4—4821no—
161C4⋊C4—2412no—
162C4⋊C4C22⋊D24112yes—
163C42—4821no—
164C42—4821no—
165C23D4×D24111yescharacteristic
166Q8—22no—
167Q8—22no—
168Q8—41no—
169Q8—41no—
170Q8—9648no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—9641no—
178C2×C4—9641no—
179C2×C4—9641no—
180C2×C4—9641no—
181C2×C4—9641no—
182C2×C4—4822no—
183C2×C4—4821no—
184C2×C4—4821no—
185C2×C4—4821no—
186C2×C4—4821no—
187C2×C4—2412no—
188C2×C4—2412no—
189C2×C4D4×D24111yescharacteristic
190C2×C4C2×C22⋊D24111yescharacteristic
191C2×C4C2×Dic48211yescharacteristic
192C2×C4#1683876911yescharacteristic
193C2×C4#1683876911yescharacteristic
194C2×C4#1683877011yescharacteristic
195C8—41no—
196C8—9641no—
197C22#2144061011yescharacteristic
198C22#2144061911yescharacteristic
199C22#2144062811yescharacteristic
200C22SD16×D24111yescharacteristic
201C22Q16×D24111yescharacteristic
202C22#2144066911yescharacteristic
203C22#2144067411yescharacteristic
204C4—42no—
205C4—42no—
206C4—19281no—
207C4—9642no—
208C4—4822no—
209C4—4822no—
210C4#2144061911yescharacteristic
211C4#2144062111yescharacteristic
212C4#2144062811yescharacteristic
213C4#2144062911yescharacteristic
214C2#2950762911yescharacteristic
215C2#2950786611yescharacteristic
216C2#2950787111yescharacteristic
217C2#2950800011yescharacteristic
218C2#2950801011yescharacteristic
219C2#2950806611yescharacteristic
220C2#2950807811yescharacteristic
subgroupG/H
centerC23D4×D241
commutator, cosocleC22×C4×C241C23
FrattiniC22×C4C22×D241
FittingC2×#103×C241C2
socle, prime radicalC23×C241C2×D4
hypercenterC2×#103D241
hypocenterC241#2024
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
45. C2×Q8×C241Q8semidirect
110. C241#2024semidirect
142. C2×Q8Dic482semidirect

Maximal subgroups

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

subgroupindex
C2×#214406412
C2×#214405662
#295076242
#295074802
#295074792
#295074712
C2×#103×C2412
#2024241