Finite Group Databasebeta

← #44507464

Subgroups — #44507464

Order 30848.

312 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 87 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#29508185C211yesmaximal, characteristic
2#29507740C211yesmaximal, characteristic, complemented
3C2×#21440570C211yesmaximal, characteristic
4C2×#21440568C211yesmaximal, characteristic
5C4×#16838749C211yesmaximal, characteristic, complemented
6#29507476C211yesmaximal, characteristic, complemented
7#339×C241C211yesmaximal, characteristic, complemented
8C2×#16838770C2211yescharacteristic
9C2×#16838754C2211yescharacteristic
10#21440607C411yescharacteristic, complemented
11#21440607C411yescharacteristic, complemented
12#21440604C411yescharacteristic, complemented
13#21440604C411yescharacteristic, complemented
14#21440602—21no—
15#21440602—21no—
16#21440599—21no—
17C2×#16838749—21no—
18C2×C4×Dic241C2211yescharacteristic
19C2×C4×Dic241C2211yescharacteristic
20C42×D241—21no—
21#21440571—21no—
22#21440571—21no—
23#21440570—22no—
24#21440568—22no—
25#21440549—21no—
26C2×M16×C241C2211yescharacteristic
27#117×C241C2211yescharacteristic
28C2×C42×C241C2211yescharacteristic
29#16838770—21no—
30#16838770—21no—
31#16838770D412yes—
32#16838770Q812yes—
33C2×Dic482C2×C411yescharacteristic
34C2×D964C2×C411yescharacteristic
35C2×C22⋊D241—21no—
36C22×Dic241—21no—
37C22×Dic241D411yescharacteristic
38C22×Dic241D411yescharacteristic
39C2×C4×D241—21no—
40C2×C4×D241—21no—
41C2×C4×D241—21no—
42#16838754—21no—
43#16838754—21no—
44C2×#14515349—21no—
45#16838749—24no—
46#16838749—21no—
47#16838749—21no—
48#16838747—21no—
49#16838747—21no—
50C4×Dic241—21no—
51C4×Dic241—21no—
52C4×Dic241—21no—
53C4×Dic241—21no—
54C4×Dic241C2×C411yescharacteristic
55C4×Dic241C2×C411yescharacteristic
56C4×Dic241D411yescharacteristic
57C4×Dic241D411yescharacteristic
58C22×C4×C241—21no—
59C22×C4×C241C2311yescharacteristic
60M16×C241—21no—
61M16×C241—21no—
62C2×C8×C241—21no—
63C4⋊C4×C241C2×C411yescharacteristic
64C4⋊C4×C241C2×C411yescharacteristic
65C22⋊C4×C241—21no—
66C42×C241—21no—
67C42×C241—21no—
68C42×C241—21no—
69C22×D241—21no—
70Dic482—21no—
71Dic482C4⋊C412yescomplemented
72D964—21no—
73D964C4⋊C412yescomplemented
74C22⋊D241—22no—
75C22⋊D241—22no—
76C2×Dic241—21no—
77C2×Dic241—22no—
78C2×Dic241—22no—
79C2×Dic241—41no—
80C2×Dic241—41no—
81C2×Dic241—41no—
82C2×Dic241C22⋊C411yescharacteristic
83C2×Dic241C22⋊C411yescharacteristic
84C2×Dic241C22⋊C411yescharacteristic
85C2×Dic241C22⋊C411yescharacteristic
86C4×D241—22no—
87C4×D241—22no—
88C4×D241—42no—
89C4×D241—42no—
90#14515349—41no—
91C23×C241C2×D411yescharacteristic
92C2×C4×C241—22no—
93C2×C4×C241—21no—
94C2×C4×C241—21no—
95C2×C4×C241—41no—
96C2×C4×C241—41no—
97C2×C4×C241C22×C411yescharacteristic
98C2×C4×C241C2×D411yescharacteristic
99C2×C4×C241C2×D411yescharacteristic
100C2×C4×C241C2×Q811yescharacteristic
101C2×C4×C241#4111yescharacteristic
102C2×C4×C241#4111yescharacteristic
103C8×C241—41no—
104C22×C241—21no—
105C22×C241—21no—
106C22×C241C2×C22⋊C411yescharacteristic
107C22×C241#12111yescharacteristic
108C22×C241C22⋊Q811yescharacteristic
109C2×D241—22no—
110C2×D241—41no—
111C2×D241—41no—
112C4×C241—42no—
113C4×C241—41no—
114C4×C241—41no—
115C4×C241C2×C4⋊C411yescharacteristic
116C4×C241#11711yescharacteristic
117C4×C241#12111yescharacteristic
118C4×C241C22⋊Q811yescharacteristic
119Dic241—22no—
120Dic241—21no—
121Dic241—21no—
122Dic241—21no—
123Dic241—42no—
124Dic241#10412yescomplemented
125C2×C241—21no—
126C2×C241—21no—
127C2×C241#38011yescharacteristic
128C2×C241C2×#10411yescharacteristic
129C2×C241#42111yescharacteristic
130D241—42no—
131C241#180611yescharacteristic, complemented, Sylow
132#1806—2411nomaximal, Sylow
133C4×#41—2411no—
134#423—2411no—
135C2×#104—2411no—
136C2×#104—2411no—
137C4×C4⋊C4—2411no—
138#339—2411no—
139#339D24111yescharacteristic, complemented
140C2×#41—2411no—
141C2×M16—2411no—
142C2×M16C2×D24111yescharacteristic
143C4×Q8—2411no—
144C4×Q8—2411no—
145C4×D4—4821no—
146C4×D4—4821no—
147C4×D4—2411no—
148C4×D4—2411no—
149#117—4821no—
150#117C2×D24111yescharacteristic
151C2×C4⋊C4—4821no—
152C2×C42—4821no—
153C2×C42—2411no—
154C2×C42—2411no—
155C2×C42C2×D24111yescharacteristic
156C4⋊C8—4821no—
157C4⋊C8—4821no—
158#104—4822no—
159#104—4822no—
160#95—4821no—
161#41—4821no—
162#41—4821no—
163#41—2412no—
164#41—2412no—
165C2×Q8—2411no—
166C2×D4—4821no—
167C2×D4—2411no—
168C22×C4—21no—
169C22×C4—4821no—
170C22×C4—4821no—
171C22×C4—4821no—
172C22×C4—4821no—
173C22×C4—2411no—
174C22×C4—2411no—
175C22×C4C22×D24111yescharacteristic
176M16—21no—
177M16—21no—
178M16—4821no—
179M16—4821no—
180C2×C8—21no—
181C2×C8—4821no—
182C4⋊C4—4824no—
183C4⋊C4—4821no—
184C4⋊C4—4821no—
185C4⋊C4C4×D24111yescharacteristic
186C4⋊C4C4×D24111yescharacteristic
187C22⋊C4—21no—
188C22⋊C4—4821no—
189C22⋊C4—4821no—
190C42—21no—
191C42—21no—
192C42—21no—
193C42—4821no—
194C42—4821no—
195C42—4821no—
196C42—4821no—
197C42—2411no—
198C42—2411no—
199C42—2411no—
200C42—2411no—
201C23—4821no—
202C23D4×D24111yescharacteristic
203Q8—4821no—
204Q8—2412no—
205D4—4822no—
206D4—4822no—
207D4—4821no—
208D4—2412no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—9642no—
215C2×C4—9642no—
216C2×C4—9641no—
217C2×C4—9641no—
218C2×C4—9641no—
219C2×C4—4822no—
220C2×C4—4821no—
221C2×C4—4822no—
222C2×C4—4822no—
223C2×C4—4822no—
224C2×C4—2411no—
225C2×C4—2411no—
226C2×C4—2411no—
227C2×C4—2411no—
228C2×C4C2×C4×D24111yescharacteristic
229C2×C4D4×D24111yescharacteristic
230C2×C4D4×D24111yescharacteristic
231C2×C4Q8×D24111yescharacteristic
232C2×C4#1683877011yescharacteristic
233C2×C4#1683877011yescharacteristic
234C8—41no—
235C8—9641no—
236C22—21no—
237C22—21no—
238C22—9641no—
239C22—9641no—
240C22—4822no—
241C22C22⋊C4×D24111yescharacteristic
242C22#2144061511yescharacteristic
243C22#2144062011yescharacteristic
244C4—42no—
245C4—41no—
246C4—41no—
247C4—9642no—
248C4—4821no—
249C4—4821no—
250C4—4821no—
251C4—4822no—
252C4—2412no—
253C4C4⋊C4×D24111yescharacteristic
254C4#2144059911yescharacteristic
255C4#2144061511yescharacteristic
256C4#2144062011yescharacteristic
257C2—21no—
258C2—21no—
259C2—9642no—
260C2#2950757611yescharacteristic
261C2#104×D24111yescharacteristic
262C2#2950773211yescharacteristic
subgroupG/H
centerC2×C4D4×D241
commutatorC2×C4×C241C22×C4
FrattiniC22×C4C22×D241
Fitting#339×C241C2
socleC22×C241C2×C22⋊C4
prime radicalC2×#16838770C22
cosocleC22×C4×C241C23
hypercenter#339D241
hypocenterC241#1806
LCSG ▷ C2×C4×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
2. #29507740C2semidirect
5. C4×#16838749C2semidirect
6. #29507476C2semidirect
7. #339×C241C2semidirect
10. #21440607C4semidirect
11. #21440607C4semidirect
12. #21440604C4semidirect
13. #21440604C4semidirect
71. Dic482C4⋊C4semidirect
73. D964C4⋊C4semidirect
124. Dic241#104semidirect
131. C241#1806semidirect
139. #339D241semidirect

Maximal subgroups

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

subgroupindex
#295081852
#295077402
C2×#214405702
C2×#214405682
C4×#168387492
#295074762
#339×C2412
#1806241