Finite Group Databasebeta

← #44508476

Subgroups — #44508476

Order 30848.

394 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 73 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×#21440675C211yesmaximal, characteristic, complemented
2#29508284C211yesmaximal, characteristic
3C2×#21440629C211yesmaximal, characteristic, complemented
4C2×#21440568C211yesmaximal, characteristic, complemented
5#29507727C211yesmaximal, characteristic, complemented
6#29507478C211yesmaximal, characteristic, complemented
7C2×#100×C241C211yesmaximal, characteristic, complemented
8C2×#16838770C2211yescharacteristic
9C22×Dic482C2211yescharacteristic
10#21440675—22no—
11#21440675—22no—
12C2×Dic964—21no—
13C2×#16838759—21no—
14#21440638—21no—
15#21440629—21no—
16#21440629—22no—
17#21440629—22no—
18#21440613—22no—
19#21440611—22no—
20#21440601C2211yescharacteristic
21C2×C22⋊Dic241—22no—
22C2×C4×Dic241C2211yescharacteristic
23#21440568—22no—
24#21440567—22no—
25C22×D4×C241C2211yescharacteristic
26C2×M16×C241C2211yescharacteristic
27C2×M16×C241C2211yescharacteristic
28#100×C241—22no—
29#16838770—21no—
30#16838770—21no—
31#16838770—21no—
32#16838770—21no—
33C2×Dic482—21no—
34C2×Dic482—21no—
35C2×Dic482—21no—
36C2×Dic482—21no—
37C2×Dic482—21no—
38C2×Dic482D411yescharacteristic
39C2×Dic482D412yescomplemented
40C2×D964D411yescharacteristic
41C2×C22⋊D241—24no—
42C2×C22⋊D241—21no—
43C22×Dic241—21no—
44C22×Dic241—21no—
45C2×C4×D241—21no—
46Dic964—24no—
47#16838759—24no—
48C4⋊Dic241D412yes—
49C22⋊Dic241—28no—
50C22⋊Dic241—24no—
51C22⋊Dic241—21no—
52C4×Dic241—21no—
53C4×Dic241—21no—
54C4×Dic241D412yescomplemented
55C24×C241D412yes—
56C2×D4×C241—21no—
57C2×D4×C241—21no—
58C2×D4×C241—21no—
59C2×D4×C241—21no—
60C2×D4×C241—21no—
61C2×D4×C241—21no—
62C22×C4×C241C2311yescharacteristic
63M16×C241—21no—
64M16×C241—21no—
65M16×C241—21no—
66M16×C241D412yescomplemented
67C2×C8×C241—21no—
68C2×C8×C241—21no—
69C22×D241—21no—
70Dic482—22no—
71Dic482—21no—
72Dic482—22no—
73Dic482—21no—
74Dic482—41no—
75Dic482—41no—
76D964—21no—
77D964—21no—
78C22⋊D241—41no—
79C22⋊D241—41no—
80C22⋊D241—84no—
81C2×Dic241—22no—
82C2×Dic241—22no—
83C2×Dic241—21no—
84C2×Dic241—22no—
85C2×Dic241—42no—
86C2×Dic241—41no—
87C2×Dic241—41no—
88C4×D241—41no—
89C4×D241—41no—
90C23×C241—22no—
91C23×C241—22no—
92C23×C241—22no—
93C23×C241—44no—
94C23×C241C2×D411yescharacteristic
95D4×C241—41no—
96D4×C241—41no—
97D4×C241—41no—
98D4×C241—41no—
99C2×C4×C241C2×D411yescharacteristic
100C2×C4×C241C2×D411yescharacteristic
101C2×C4×C241C2×D411yescharacteristic
102C2×C4×C241C2×D411yescharacteristic
103C2×C4×C241C2×D411yescharacteristic
104C2×C4×C241#4111yescharacteristic
105C8×C241—22no—
106C8×C241—41no—
107C22×C241—22no—
108C22×C241—44no—
109C22×C241—42no—
110C22×C241—44no—
111C22×C241—82no—
112C22×C241#12011yescharacteristic
113C22×C241#12011yescharacteristic
114C22×C241#12111yescharacteristic
115C2×D241—41no—
116C2×D241—42no—
117C4×C241#12011yescharacteristic
118C4×C241#12111yescharacteristic
119C4×C241#12111yescharacteristic
120C4×C241#12711yescharacteristic
121Dic241—42no—
122Dic241—41no—
123Dic241—42no—
124Dic241—42no—
125C2×C241—21no—
126C2×C241—21no—
127C2×C241—82no—
128C2×C241#39211yescharacteristic
129C2×C241#45512yes—
130D241—81no—
131C241#200411yescharacteristic, complemented, Sylow
132#2004—2411nomaximal, Sylow
133C2×#137—2411no—
134#535—2411no—
135C2×#124—2411no—
136C2×#104—2411no—
137#419—2411no—
138C2×#100D24111yescharacteristic, complemented
139#339—2411no—
140C2×#41—2411no—
141C22×Q8—2411no—
142C22×D4C2×D24111yescharacteristic
143#137—4822no—
144#137—4822no—
145C2×Q16—4821no—
146C2×SD16—4821no—
147C2×M16C2×D24111yescharacteristic
148C2×M16C2×D24111yescharacteristic
149#127—4821no—
150#124—4822no—
151#124—4821no—
152#124—4822no—
153#121—4822no—
154#120—4822no—
155#117—2411no—
156C2×C22⋊C4—4822no—
157C2×C42—2411no—
158#104—4822no—
159#103—4822no—
160#100—22no—
161C24D96412yes—
162#41—4821no—
163#41—4821no—
164#41—4821no—
165#41—4821no—
166C2×Q8—4821no—
167C2×Q8—4821no—
168C2×Q8—4821no—
169C2×Q8—4821no—
170C2×Q8—4821no—
171C2×Q8—2411no—
172C2×Q8—2412no—
173C2×D4—21no—
174C2×D4—21no—
175C2×D4—21no—
176C2×D4—21no—
177C2×D4—21no—
178C2×D4—21no—
179C2×D4—4824no—
180C2×D4—4821no—
181C2×D4—2411no—
182C22×C4—4821no—
183C22×C4—4821no—
184C22×C4—4821no—
185C22×C4C22×D24111yescharacteristic
186Q16—4824no—
187SD16—4824no—
188M16—21no—
189M16—21no—
190M16—21no—
191M16C22⋊D24112yescomplemented
192C2×C8—21no—
193C2×C8—21no—
194C4⋊C4—2412no—
195C22⋊C4—4828no—
196C22⋊C4—4824no—
197C22⋊C4—4821no—
198C42—4821no—
199C42—4821no—
200C42—2412no—
201C23—22no—
202C23—22no—
203C23—22no—
204C23—44no—
205C23—4821no—
206C23C2×D96411yescharacteristic
207Q8—9641no—
208Q8—9641no—
209Q8—4822no—
210Q8—4821no—
211Q8—4822no—
212Q8—4821no—
213D4—41no—
214D4—41no—
215D4—41no—
216D4—41no—
217D4—19284no—
218D4—9641no—
219D4—9641no—
220D4—4821no—
221D4—4821no—
222C2×C4—9642no—
223C2×C4—9641no—
224C2×C4—9641no—
225C2×C4—9641no—
226C2×C4—9641no—
227C2×C4—4822no—
228C2×C4—4822no—
229C2×C4—4822no—
230C2×C4—4821no—
231C2×C4D4×D24111yescharacteristic
232C2×C4D4×D24111yescharacteristic
233C2×C4D4×D24111yescharacteristic
234C2×C4D4×D24111yescharacteristic
235C2×C4C2×C22⋊D24111yescharacteristic
236C2×C4#1683877011yescharacteristic
237C8—22no—
238C8—41no—
239C22—22no—
240C22—44no—
241C22—42no—
242C22—44no—
243C22—82no—
244C22—9641no—
245C22—9642no—
246C22#2144061211yescharacteristic
247C22#2144061211yescharacteristic
248C22#2144061611yescharacteristic
249C4—9642no—
250C4—9641no—
251C4—9642no—
252C4—9642no—
253C4#2144061011yescharacteristic
254C4#2144061511yescharacteristic
255C4#2144061511yescharacteristic
256C4#2144063811yescharacteristic
257C2—21no—
258C2—21no—
259C2—82no—
260C2—19281no—
261C2#2950762611yescharacteristic
262C2#2950789712yes—
subgroupG/H
centerC22#21440612
commutator, cosocleC22×C4×C241C23
FrattiniC22×C4C22×D241
FittingC2×#100×C241C2
socleC22×C241#120
prime radical#29508284C2
hypercenterC2×#100D241
hypocenterC241#2004
LCSG ▷ C22×C4×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
1. C2×#21440675C2semidirect
3. C2×#21440629C2semidirect
4. C2×#21440568C2semidirect
5. #29507727C2semidirect
6. #29507478C2semidirect
7. C2×#100×C241C2semidirect
39. C2×Dic482D4semidirect
54. C4×Dic241D4semidirect
66. M16×C241D4semidirect
131. C241#2004semidirect
138. C2×#100D241semidirect
191. M16C22⋊D241semidirect

Maximal subgroups

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

subgroupindex
C2×#214406752
#295082842
C2×#214406292
C2×#214405682
#295077272
#295074782
C2×#100×C2412
#2004241