Finite Group Databasebeta

← #44508546

Subgroups — #44508546

Order 30848.

370 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 93 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
1C22×Dic964C211yesmaximal, characteristic
2C22×#16838760C211yesmaximal, characteristic
3C2×#21440640C211yesmaximal, characteristic
4C2×#21440565C211yesmaximal, characteristic
5#29507622C211yesmaximal, characteristic
6#29507471C211yesmaximal, characteristic
7C2×#103×C241C211yesmaximal, characteristic
8C22×Dic482C2211yescharacteristic
9C22×Dic482C2211yescharacteristic
10C2×Dic964—22no—
11C2×Dic964—22no—
12C2×Dic964—22no—
13C2×#16838760—22no—
14C2×#16838760—22no—
15C2×#16838760—22no—
16C22×#14515349C2211yescharacteristic
17#21440640—22no—
18#21440640—22no—
19C2×#16838749—22no—
20C2×C4×Dic241C2211yescharacteristic
21#21440565—22no—
22#21440549—22no—
23C22×Q8×C241C2211yescharacteristic
24C22×C8×C241C2211yescharacteristic
25C2×C4⋊C4×C241C2211yescharacteristic
26#103×C241—22no—
27C2×Dic482—21no—
28C2×Dic482—21no—
29C2×Dic482—21no—
30C2×Dic482—21no—
31C2×Dic482—21no—
32C2×Dic482—21no—
33C2×Dic482—21no—
34C2×Dic482—21no—
35C2×Dic482—21no—
36C2×Dic482—21no—
37C2×Dic482D412yes—
38C2×Dic482D412yes—
39C22×Dic241—21no—
40C22×Dic241—21no—
41C22×Dic241D412yes—
42Dic964—28no—
43#16838760—28no—
44C2×#14515349—21no—
45C2×#14515349—21no—
46C2×#14515349D412yes—
47#16838749—28no—
48C4×Dic241—21no—
49C4×Dic241—21no—
50C2×Q8×C241—21no—
51C2×Q8×C241—21no—
52C2×Q8×C241—21no—
53C2×Q8×C241—21no—
54C2×Q8×C241—21no—
55C2×Q8×C241D412yes—
56C22×C4×C241—21no—
57C22×C4×C241—21no—
58C22×C4×C241C2311yescharacteristic
59C2×C8×C241—21no—
60C2×C8×C241—21no—
61C2×C8×C241D412yes—
62C4⋊C4×C241—21no—
63C4⋊C4×C241—21no—
64Dic482—22no—
65Dic482—22no—
66Dic482—22no—
67Dic482—22no—
68Dic482—41no—
69Dic482—41no—
70Dic482—41no—
71Dic482—41no—
72C2×Dic241—22no—
73C2×Dic241—22no—
74C2×Dic241—22no—
75C2×Dic241—22no—
76C2×Dic241—41no—
77C2×Dic241—41no—
78C2×Dic241—41no—
79C2×Dic241—41no—
80C2×Dic241Q1614yescomplemented
81#14515349—22no—
82C23×C241C2×D411yescharacteristic
83Q8×C241—22no—
84Q8×C241—22no—
85Q8×C241—41no—
86Q8×C241—41no—
87C2×C4×C241—22no—
88C2×C4×C241—41no—
89C2×C4×C241—41no—
90C2×C4×C241—41no—
91C2×C4×C241—42no—
92C2×C4×C241C2×D411yescharacteristic
93C2×C4×C241C2×D411yescharacteristic
94C2×C4×C241C2×D411yescharacteristic
95C2×C4×C241C2×D411yescharacteristic
96C2×C4×C241C2×D411yescharacteristic
97C2×C4×C241#4111yescharacteristic
98C8×C241—22no—
99C22×C241#12011yescharacteristic
100C22×C241#12111yescharacteristic
101C22×C241#12711yescharacteristic
102C22×C241C2×Q1612yes—
103C22×C241#13712yes—
104C4×C241—42no—
105C4×C241—81no—
106C4×C241#12011yescharacteristic
107C4×C241#12011yescharacteristic
108C4×C241#12111yescharacteristic
109C4×C241#12111yescharacteristic
110Dic241—24no—
111Dic241—42no—
112Dic241—42no—
113C2×C241#39211yescharacteristic
114C2×C241#45112yes—
115C2×C241#46212yes—
116C2×C241#49411yescharacteristic
117C2×C241#49711yescharacteristic
118C241#201611yescharacteristic, complemented, Sylow
119#2016—2411nomaximal, Sylow
120C22×Q16—2411no—
121C22×Q16—2411no—
122C2×C4⋊Q8—2411no—
123C2×#103—2411no—
124C2×#103D24111yescharacteristic
125#391—2411no—
126#336—2411no—
127C22×Q8—2411no—
128C22×Q8—2411no—
129C22×Q8C2×D24111yescharacteristic
130C2×Q16—4822no—
131C2×Q16—4822no—
132C2×Q16—4822no—
133C2×Q16—4822no—
134C2×Q16—4822no—
135C2×Q16—4822no—
136C22×C8—2411no—
137C22×C8C2×D24111yescharacteristic
138C4⋊Q8—4822no—
139C4⋊Q8—4822no—
140C2×C4⋊C4—4822no—
141C2×C4⋊C4C2×D24111yescharacteristic
142C2×C42—2411no—
143#103—22no—
144#103—4822no—
145#95—4822no—
146C2×Q8—21no—
147C2×Q8—21no—
148C2×Q8—21no—
149C2×Q8—21no—
150C2×Q8—21no—
151C2×Q8—4821no—
152C2×Q8—4821no—
153C2×Q8—4821no—
154C2×Q8—4821no—
155C2×Q8—4821no—
156C2×Q8—4821no—
157C2×Q8—4821no—
158C2×Q8—4821no—
159C2×Q8—4821no—
160C2×Q8—4821no—
161C2×Q8—2412no—
162C2×Q8—2412no—
163C2×Q8D96412yes—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—4821no—
167C22×C4—4821no—
168C22×C4—2412no—
169C22×C4C22×D24111yescharacteristic
170Q16—4828no—
171Q16—4828no—
172C2×C8—21no—
173C2×C8—21no—
174C2×C8—4821no—
175C2×C8—4821no—
176C2×C8—2412no—
177C2×C8C22⋊D24112yes—
178C4⋊C4—21no—
179C4⋊C4—21no—
180C4⋊C4—4828no—
181C42—4821no—
182C42—4821no—
183C23D4×D24111yescharacteristic
184Q8—22no—
185Q8—22no—
186Q8—41no—
187Q8—41no—
188Q8—9641no—
189Q8—9641no—
190Q8—9641no—
191Q8—9641no—
192Q8—4822no—
193Q8—4822no—
194Q8—4822no—
195Q8—4822no—
196C2×C4—22no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—41no—
200C2×C4—42no—
201C2×C4—9641no—
202C2×C4—9641no—
203C2×C4—9641no—
204C2×C4—9641no—
205C2×C4—4822no—
206C2×C4—4822no—
207C2×C4—4822no—
208C2×C4—4822no—
209C2×C4—2414no—
210C2×C4D4×D24111yescharacteristic
211C2×C4D4×D24111yescharacteristic
212C2×C4D4×D24111yescharacteristic
213C2×C4C2×C22⋊D24111yescharacteristic
214C2×C4C2×D96411yescharacteristic
215C2×C4#1683877011yescharacteristic
216C8—22no—
217C8—4822no—
218C22#2144061211yescharacteristic
219C22#2144061511yescharacteristic
220C22#2144063811yescharacteristic
221C22Q16×D24112yes—
222C22#2144067112yes—
223C4—42no—
224C4—81no—
225C4—9642no—
226C4—9642no—
227C4—4824no—
228C4#2144061011yescharacteristic
229C4#2144061211yescharacteristic
230C4#2144061511yescharacteristic
231C4#2144061611yescharacteristic
232C2#2950762611yescharacteristic
233C2#2950787412yes—
234C2#2950792612yes—
235C2#2950809511yescharacteristic
236C2#2950810811yescharacteristic
subgroupG/H
centerC23D4×D241
commutator, cosocleC22×C4×C241C23
FrattiniC22×C4C22×D241
FittingC2×#103×C241C2
socle, prime radicalC23×C241C2×D4
hypercenterC2×#103D241
hypocenterC241#2016
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
80. C2×Dic241Q16semidirect
118. C241#2016semidirect

Maximal subgroups

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

subgroupindex
C22×Dic9642
C22×#168387602
C2×#214406402
C2×#214405652
#295076222
#295074712
C2×#103×C2412
#2016241