Finite Group Databasebeta

← #44507892

Subgroups — #44507892

Order 30848.

358 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 83 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#29508229C211yesmaximal, characteristic
2C2×#21440599C211yesmaximal, characteristic, complemented
3C2×#21440570C211yesmaximal, characteristic, complemented
4C2×#21440568C211yesmaximal, characteristic, complemented
5#29507680C211yesmaximal, characteristic, complemented
6#29507476C211yesmaximal, characteristic, complemented
7#339×C241C211yesmaximal, characteristic, complemented
8C2×#16838770C2211yescharacteristic
9C22×C4×D241C2211yescharacteristic
10C2×#16838754C2211yescharacteristic
11#21440626—21no—
12#21440622C412yescomplemented
13#21440617C412yescomplemented
14#21440612—21no—
15C4×D964—22no—
16#21440599—22no—
17#21440599—22no—
18C2×#16838749—21no—
19C2×#16838747—21no—
20C2×C4×Dic241C2211yescharacteristic
21#21440570—22no—
22#21440568—22no—
23#21440554—22no—
24C2×M16×C241C2211yescharacteristic
25#117×C241C2211yescharacteristic
26C2×C42×C241C2211yescharacteristic
27C23×D241D411yescharacteristic
28#16838770—21no—
29#16838770—21no—
30#16838770—21no—
31#16838770—21no—
32C2×Dic482C2×C411yescharacteristic
33C2×D964—22no—
34C2×D964C2×C411yescharacteristic
35C2×C22⋊D241—21no—
36C22×Dic241—21no—
37C22×Dic241D411yescharacteristic
38C2×C4×D241—21no—
39C2×C4×D241—21no—
40C2×C4×D241—21no—
41C2×C4×D241—21no—
42C2×C4×D241—21no—
43C2×C4×D241C2×C412yes—
44C2×C4×D241D412yes—
45#16838754—21no—
46#16838754—21no—
47C2×#14515349—21no—
48C4⋊Dic241—22no—
49#16838749—24no—
50#16838747—24no—
51#16838747—22no—
52#16838747—22no—
53C4×Dic241—21no—
54C4×Dic241D412yescomplemented
55C22×C4×C241—21no—
56C22×C4×C241C2311yescharacteristic
57M16×C241—21no—
58M16×C241—21no—
59C2×C8×C241—21no—
60C4⋊C4×C241C2×C412yes—
61C22⋊C4×C241—21no—
62C42×C241—21no—
63C42×C241—21no—
64C42×C241D412yescomplemented
65C22×D241—21no—
66C22×D241—21no—
67C22×D241—21no—
68C22×D241—42no—
69C22×D241C22⋊C412yes—
70Dic482—21no—
71Dic482—21no—
72D964—21no—
73D964—21no—
74D964—44no—
75C22⋊D241—41no—
76C22⋊D241—41no—
77C2×Dic241—21no—
78C2×Dic241—21no—
79C2×Dic241—21no—
80C2×Dic241—22no—
81C2×Dic241—42no—
82C2×Dic241C22⋊C412yes—
83C4×D241—22no—
84C4×D241—22no—
85C4×D241—22no—
86C4×D241—22no—
87C4×D241—41no—
88C4×D241—41no—
89#14515349—41no—
90C23×C241C2×D411yescharacteristic
91C2×C4×C241—22no—
92C2×C4×C241—22no—
93C2×C4×C241—42no—
94C2×C4×C241C22×C411yescharacteristic
95C2×C4×C241C2×D411yescharacteristic
96C2×C4×C241C2×D411yescharacteristic
97C2×C4×C241C2×D411yescharacteristic
98C2×C4×C241#4111yescharacteristic
99C2×C4×C241#4111yescharacteristic
100C8×C241—41no—
101C22×C241—22no—
102C22×C241C2×C22⋊C411yescharacteristic
103C22×C241#12011yescharacteristic
104C22×C241#12311yescharacteristic
105C2×D241—22no—
106C2×D241—22no—
107C2×D241—22no—
108C2×D241—42no—
109C2×D241—42no—
110C2×D241—41no—
111C2×D241—42no—
112C4×C241—42no—
113C4×C241—42no—
114C4×C241C4×D411yescharacteristic
115C4×C241C4×D411yescharacteristic
116C4×C241#12111yescharacteristic
117C4×C241#12111yescharacteristic
118Dic241—22no—
119Dic241—42no—
120Dic241—41no—
121C2×C241—21no—
122C2×C241—21no—
123C2×C241#38611yescharacteristic
124C2×C241#42112yes—
125D241—42no—
126D241—81no—
127C241#189711yescharacteristic, complemented, Sylow
128#1897—2411nomaximal, Sylow
129#525—2411no—
130C2×#117—2411no—
131C2×#104—2411no—
132C2×#104—2411no—
133#407—2411no—
134#339—2411no—
135#339D24111yescharacteristic, complemented
136C2×#41—2411no—
137C23×C4—2411no—
138C2×M16—2411no—
139C2×M16C2×D24111yescharacteristic
140#123—4821no—
141C22⋊Q8—2412no—
142#121—2412no—
143#120—4821no—
144C4×D4—4822no—
145#117—4822no—
146#117—4822no—
147#117C2×D24111yescharacteristic
148C2×C4⋊C4—4821no—
149C2×C22⋊C4—4821no—
150C2×C42—2411no—
151C2×C42C2×D24111yescharacteristic
152#104—4822no—
153#104—4822no—
154C22⋊C8—4822no—
155C24—2411no—
156#41—4821no—
157#41—4821no—
158#41—4821no—
159#41—4821no—
160C2×Q8—2411no—
161C2×D4—4822no—
162C2×D4—4821no—
163C2×D4—2411no—
164C22×C4—21no—
165C22×C4—4821no—
166C22×C4—4821no—
167C22×C4—4821no—
168C22×C4—4821no—
169C22×C4—4821no—
170C22×C4—4821no—
171C22×C4—2411no—
172C22×C4—2412no—
173C22×C4—2412no—
174C22×C4C22×D24111yescharacteristic
175M16—21no—
176M16—21no—
177M16—4821no—
178M16—4821no—
179C2×C8—21no—
180C2×C8—4821no—
181C4⋊C4—4824no—
182C4⋊C4—4822no—
183C4⋊C4C4×D24112yes—
184C22⋊C4—21no—
185C22⋊C4—4824no—
186C22⋊C4—4822no—
187C22⋊C4—4822no—
188C42—21no—
189C42—21no—
190C42—4821no—
191C42—2412no—
192C42D96412yescomplemented
193C23—9642no—
194C23—4821no—
195C23—4821no—
196C23—4821no—
197C23—2412no—
198C23D4×D24111yescharacteristic
199Q8—4821no—
200Q8—4821no—
201D4—9644no—
202D4—9641no—
203D4—9641no—
204D4—4821no—
205D4—4821no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—42no—
209C2×C4—9642no—
210C2×C4—9641no—
211C2×C4—9641no—
212C2×C4—4821no—
213C2×C4—4822no—
214C2×C4—4821no—
215C2×C4—4821no—
216C2×C4—4822no—
217C2×C4—4822no—
218C2×C4—4822no—
219C2×C4—4822no—
220C2×C4—2412no—
221C2×C4C2×C4×D24111yescharacteristic
222C2×C4D4×D24111yescharacteristic
223C2×C4D4×D24111yescharacteristic
224C2×C4C2×D96411yescharacteristic
225C2×C4#1683877011yescharacteristic
226C2×C4#1683877111yescharacteristic
227C8—41no—
228C8—9641no—
229C22—22no—
230C22—9642no—
231C22—9642no—
232C22—9641no—
233C22—9642no—
234C22—4822no—
235C22—4822no—
236C22—4822no—
237C22C22⋊C4×D24111yescharacteristic
238C22#2144061211yescharacteristic
239C22#2144062711yescharacteristic
240C4—42no—
241C4—42no—
242C4—9642no—
243C4—9641no—
244C4—4822no—
245C4#2144060411yescharacteristic
246C4C4×D96411yescharacteristic
247C4#2144061511yescharacteristic
248C4#2144061711yescharacteristic
249C2—21no—
250C2—21no—
251C2—19281no—
252C2—9642no—
253C2#2950759511yescharacteristic
254C2#2950773212yes—
subgroupG/H
centerC2×C4D4×D241
commutatorC2×C4×C241C22×C4
FrattiniC22×C4C22×D241
Fitting#339×C241C2
socleC22×C241C2×C22⋊C4
prime radical#29508229C2
cosocleC22×C4×C241C23
hypercenter#339D241
hypocenterC241#1897
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. C2×#21440599C2semidirect
3. C2×#21440570C2semidirect
4. C2×#21440568C2semidirect
5. #29507680C2semidirect
6. #29507476C2semidirect
7. #339×C241C2semidirect
12. #21440622C4semidirect
13. #21440617C4semidirect
54. C4×Dic241D4semidirect
64. C42×C241D4semidirect
127. C241#1897semidirect
135. #339D241semidirect
192. C42D964semidirect

Maximal subgroups

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

subgroupindex
#295082292
C2×#214405992
C2×#214405702
C2×#214405682
#295076802
#295074762
#339×C2412
#1897241