Finite Group Databasebeta

← #44507641

Subgroups — #44507641

Order 30848.

316 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 99 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×#21440600C211yesmaximal, characteristic
2C2×#21440573C211yesmaximal, characteristic, complemented
3C2×#21440554C211yesmaximal, characteristic
4#29507574C211yesmaximal, characteristic
5#29507480C211yesmaximal, characteristic, complemented
6#29507479C211yesmaximal, characteristic, complemented
7C2×#107×C241C211yesmaximal, characteristic, complemented
8C22×C4×D241C2211yescharacteristic
9C22×#14515349C2211yescharacteristic
10#21440600—22no—
11#21440600—22no—
12C2×C4⋊Dic241C2211yescharacteristic
13C2×C4⋊Dic241C2211yescharacteristic
14C2×#16838747—21no—
15C2×#16838747—21no—
16C2×C4×Dic241—21no—
17#21440573—22no—
18#21440554C414yescomplemented
19#21440549—21no—
20C22×C8×C241C2211yescharacteristic
21C2×C4⋊C4×C241C2211yescharacteristic
22C2×C4⋊C4×C241C2211yescharacteristic
23#107×C241—22no—
24C23×D241D411yescharacteristic
25C22×Dic241—21no—
26C22×Dic241—21no—
27C22×Dic241D411yescharacteristic
28C2×C4×D241—21no—
29C2×C4×D241—21no—
30C2×C4×D241—21no—
31C2×C4×D241—21no—
32C2×C4×D241C2×C412yes—
33C2×C4×D241Q812yes—
34C2×#14515349—21no—
35C2×#14515349—21no—
36C2×#14515349C2×C412yes—
37C4⋊Dic241—21no—
38C4⋊Dic241—21no—
39C4⋊Dic241—21no—
40C4⋊Dic241D412yes—
41#16838747—24no—
42#16838747—42no—
43C4×Dic241—24no—
44C22×C4×C241—21no—
45C22×C4×C241—21no—
46C22×C4×C241C2311yescharacteristic
47C2×C8×C241—21no—
48C2×C8×C241—21no—
49C2×C8×C241C2×C412yes—
50C4⋊C4×C241—21no—
51C4⋊C4×C241—21no—
52C4⋊C4×C241—21no—
53C4⋊C4×C241D412yes—
54C22×D241—21no—
55C22×D241—21no—
56C22×D241—21no—
57C22×D241—21no—
58C22×D241—21no—
59C22×D241—21no—
60C22×D241C4⋊C412yes—
61C2×Dic241—21no—
62C2×Dic241—21no—
63C2×Dic241—22no—
64C2×Dic241—41no—
65C2×Dic241—41no—
66C2×Dic241—41no—
67C2×Dic241—41no—
68C2×Dic241—41no—
69C2×Dic241C4⋊C412yes—
70C4×D241—22no—
71C4×D241—22no—
72C4×D241—22no—
73C4×D241—22no—
74#14515349—22no—
75C23×C241C2×D411yescharacteristic
76C2×C4×C241—22no—
77C2×C4×C241—41no—
78C2×C4×C241—41no—
79C2×C4×C241—41no—
80C2×C4×C241—41no—
81C2×C4×C241—41no—
82C2×C4×C241C22×C411yescharacteristic
83C2×C4×C241C2×D411yescharacteristic
84C2×C4×C241C2×D411yescharacteristic
85C2×C4×C241C2×Q811yescharacteristic
86C2×C4×C241#4111yescharacteristic
87C2×C4×C241#4111yescharacteristic
88C8×C241—22no—
89C22×C241C2×C4⋊C411yescharacteristic
90C22×C241#12011yescharacteristic
91C22×C241#12311yescharacteristic
92C22×C241#13511yescharacteristic
93C22×C241#13511yescharacteristic
94C22×C241AGL(1,ℤ/8)11yescharacteristic
95C22×C241#13711yescharacteristic
96C2×D241—22no—
97C2×D241—22no—
98C2×D241—22no—
99C2×D241—41no—
100C2×D241—41no—
101C2×D241—41no—
102C2×D241—41no—
103C4×C241—42no—
104C4×C241—81no—
105C4×C241C4×D411yescharacteristic
106C4×C241C4×D411yescharacteristic
107C4×C241C22⋊Q811yescharacteristic
108C4×C241C22⋊Q811yescharacteristic
109Dic241—22no—
110Dic241—42no—
111Dic241—81no—
112C2×C241#38511yescharacteristic
113C2×C241#42711yescharacteristic
114C2×C241#42811yescharacteristic
115C2×C241#44911yescharacteristic
116C2×C241#45211yescharacteristic
117C2×C241#48211yescharacteristic
118C2×C241#48511yescharacteristic
119D241—42no—
120C241#185411yescharacteristic, complemented, Sylow
121#1854—2411nomaximal, Sylow
122C2×#117—2411no—
123C2×#107D24111yescharacteristic, complemented
124C2×#106—2411no—
125C2×C22⋊C8—2411no—
126#380—2411no—
127#340—2411no—
128#340—2411no—
129C23×C4—2411no—
130C22×C8—2411no—
131C22×C8C2×D24111yescharacteristic
132#117—4822no—
133#117—4822no—
134C2×C4⋊C4—2411no—
135C2×C4⋊C4—2411no—
136C2×C4⋊C4C2×D24111yescharacteristic
137C2×C4⋊C4C2×D24111yescharacteristic
138C2×C22⋊C4—4821no—
139C2×C22⋊C4—4821no—
140C2×C42—4821no—
141#107—22no—
142#106—4822no—
143C22⋊C8—2414no—
144#95—4821no—
145C24—2411no—
146C22×C4—21no—
147C22×C4—21no—
148C22×C4—4821no—
149C22×C4—4821no—
150C22×C4—4821no—
151C22×C4—4821no—
152C22×C4—4821no—
153C22×C4—4821no—
154C22×C4—2411no—
155C22×C4—2412no—
156C22×C4—2412no—
157C22×C4C22×D24111yescharacteristic
158C2×C8—21no—
159C2×C8—21no—
160C2×C8—4821no—
161C2×C8—4821no—
162C2×C8—2412no—
163C2×C8C4×D24112yes—
164C4⋊C4—21no—
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—4821no—
168C4⋊C4—4821no—
169C4⋊C4—4821no—
170C4⋊C4—2412no—
171C4⋊C4C22⋊D24112yes—
172C22⋊C4—9642no—
173C22⋊C4—4824no—
174C42—4824no—
175C23—4821no—
176C23—4821no—
177C23—4821no—
178C23—4821no—
179C23—4821no—
180C23—4821no—
181C23—2412no—
182C23D4×D24111yescharacteristic
183C2×C4—22no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—9641no—
190C2×C4—9641no—
191C2×C4—9641no—
192C2×C4—9641no—
193C2×C4—9641no—
194C2×C4—4822no—
195C2×C4—4821no—
196C2×C4—4821no—
197C2×C4—4822no—
198C2×C4—4822no—
199C2×C4—4822no—
200C2×C4—4822no—
201C2×C4—2412no—
202C2×C4C2×C4×D24111yescharacteristic
203C2×C4D4×D24111yescharacteristic
204C2×C4C2×C22⋊D24111yescharacteristic
205C2×C4Q8×D24111yescharacteristic
206C2×C4#1683877011yescharacteristic
207C2×C4#1683877111yescharacteristic
208C8—22no—
209C8—4822no—
210C22—9641no—
211C22—9641no—
212C22—9641no—
213C22—9641no—
214C22—4822no—
215C22—4822no—
216C22—4822no—
217C22C4⋊C4×D24111yescharacteristic
218C22#2144061011yescharacteristic
219C22#2144062711yescharacteristic
220C22#2144066111yescharacteristic
221C22#2144066511yescharacteristic
222C22#2144066611yescharacteristic
223C22#2144067411yescharacteristic
224C4—42no—
225C4—81no—
226C4—19281no—
227C4—9642no—
228C4—4822no—
229C4C4×C22⋊D24111yescharacteristic
230C4#2144060411yescharacteristic
231C4#2144061811yescharacteristic
232C4#2144062011yescharacteristic
233C2—9642no—
234C2#2950758811yescharacteristic
235C2#2950775411yescharacteristic
236C2#2950775811yescharacteristic
237C2#2950785911yescharacteristic
238C2#2950787811yescharacteristic
239C2#2950804411yescharacteristic
240C2#2950806011yescharacteristic
subgroupG/H
centerC23D4×D241
commutatorC2×C4×C241C22×C4
FrattiniC22×C4C22×D241
FittingC2×#107×C241C2
socleC23×C241C2×D4
prime radicalC23×D241D4
cosocleC22×C4×C241C23
hypercenterC2×#107D241
hypocenterC241#1854
LCSG ▷ C2×C4×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
2. C2×#21440573C2semidirect
5. #29507480C2semidirect
6. #29507479C2semidirect
7. C2×#107×C241C2semidirect
18. #21440554C4semidirect
120. C241#1854semidirect
123. C2×#107D241semidirect

Maximal subgroups

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

subgroupindex
C2×#214406002
C2×#214405732
C2×#214405542
#295075742
#295074802
#295074792
C2×#107×C2412
#1854241