Finite Group Databasebeta

← #44509108

Subgroups — #44509108

Order 30848.

258 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 65 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#29508263C211yesmaximal, characteristic
2#29507691C211yesmaximal, characteristic, complemented
3#29507511C212yesmaximal, complemented
4#29507509C212yesmaximal, complemented
5#410×C241C211yesmaximal, characteristic, complemented
6C2×#16838770C411yescharacteristic, complemented
7#21440640C411yescharacteristic, complemented
8#21440638C2211yescharacteristic
9#21440631C411yescharacteristic, complemented
10#21440629C2211yescharacteristic
11#21440614—21no—
12#21440614—21no—
13C4×C22⋊D241—21no—
14C4×C22⋊D241—21no—
15#21440601—21no—
16C2×C4×Dic241C411yescharacteristic, complemented
17#21440557—21no—
18#21440557C2212yes—
19C2×#41×C241C2211yescharacteristic
20#117×C241—21no—
21#99×C241—21no—
22#99×C241C2212yes—
23#16838770—41no—
24#16838770—41no—
25C2×Dic482C2×C411yescharacteristic
26C2×D964C2×C411yescharacteristic
27C2×C22⋊D241—21no—
28C2×C22⋊D241—21no—
29C2×C22⋊D241—21no—
30C22×Dic241—21no—
31C2×C4×D241—21no—
32C4⋊Dic241—41no—
33#16838749—21no—
34#16838749—21no—
35C22⋊Dic241—21no—
36C22⋊Dic241—21no—
37C22⋊Dic241—22no—
38#16838747—21no—
39#16838747—21no—
40C4×Dic241—21no—
41C4×Dic241—41no—
42C4×Dic241C2×C411yescharacteristic
43C4×Dic241C2×C411yescharacteristic
44#41×C241—41no—
45#41×C241—41no—
46C2×Q8×C241C2×C411yescharacteristic
47C2×D4×C241D411yescharacteristic
48C2×D4×C241D411yescharacteristic
49C2×D4×C241C2311yescharacteristic
50C22×C4×C241C2×C411yescharacteristic
51C22×C4×C241D411yescharacteristic
52C22×C4×C241D411yescharacteristic
53C4⋊C4×C241—41no—
54C22⋊C4×C241—22no—
55C42×C241—41no—
56C22×D241—21no—
57Dic482—41no—
58D964—41no—
59C22⋊D241—42no—
60C22⋊D241—42no—
61C22⋊D241—42no—
62C2×Dic241—21no—
63C2×Dic241—21no—
64C2×Dic241—21no—
65C2×Dic241—42no—
66C2×Dic241—42no—
67C4×D241—41no—
68C4×D241—41no—
69C23×C241C22⋊C411yescharacteristic
70C23×C241C2×D411yescharacteristic
71C23×C241C2×D411yescharacteristic
72Q8×C241—41no—
73D4×C241—41no—
74D4×C241—41no—
75D4×C241—41no—
76C2×C4×C241—21no—
77C2×C4×C241—21no—
78C2×C4×C241—21no—
79C2×C4×C241—21no—
80C2×C4×C241—21no—
81C2×C4×C241—21no—
82C2×C4×C241—42no—
83C2×C4×C241C22⋊C411yescharacteristic
84C2×C4×C241C22⋊C411yescharacteristic
85C2×C4×C241C22⋊C411yescharacteristic
86C2×C4×C241C22×C411yescharacteristic
87C22×C241—21no—
88C22×C241—21no—
89C22×C241—21no—
90C22×C241—41no—
91C22×C241—41no—
92C22×C241—41no—
93C22×C241C2×C22⋊C411yescharacteristic
94C2×D241—41no—
95C2×D241—41no—
96C2×D241—41no—
97C4×C241—21no—
98C4×C241—21no—
99C4×C241—21no—
100C4×C241—82no—
101C4×C241#9911yescharacteristic
102C4×C241#9911yescharacteristic
103Dic241—22no—
104Dic241—41no—
105Dic241—41no—
106Dic241—82no—
107C2×C241—21no—
108C2×C241—41no—
109C2×C241—41no—
110C2×C241—41no—
111C2×C241C2×#9911yescharacteristic
112D241—81no—
113C241#212611yescharacteristic, complemented, Sylow
114#2126—2411nomaximal, Sylow
115#532—2411no—
116#410—2411no—
117#410D24111yescharacteristic, complemented
118#354—2412no—
119#353—2412no—
120C2×#41—2411no—
121C2×#41C2×D24111yescharacteristic
122C4⋊Q8—2411no—
123#127—2411no—
124#124—2411no—
125#124—2411no—
126#121—4821no—
127#121—4821no—
128C4×D4—4821no—
129C4×D4—4821no—
130#117—21no—
131#117—4821no—
132C2×C42—2411no—
133#99—21no—
134#99—4821no—
135#99—2412no—
136#99C2×D24112yes—
137#41—41no—
138#41—41no—
139#41—9641no—
140#41—9641no—
141C2×Q8—2411no—
142C2×Q8C4×D24111yescharacteristic
143C2×D4—4821no—
144C2×D4—4821no—
145C2×D4—4821no—
146C2×D4—2411no—
147C2×D4C22⋊D24111yescharacteristic
148C2×D4D96411yescharacteristic
149C2×D4C22×D24111yescharacteristic
150C22×C4—4821no—
151C22×C4—4821no—
152C22×C4C4×D24111yescharacteristic
153C22×C4C22⋊D24111yescharacteristic
154C22×C4D96411yescharacteristic
155C4⋊C4—41no—
156C4⋊C4—9641no—
157C4⋊C4—4821no—
158C4⋊C4—4821no—
159C22⋊C4—22no—
160C22⋊C4—4822no—
161C22⋊C4—4821no—
162C22⋊C4—4821no—
163C22⋊C4—4821no—
164C22⋊C4—4821no—
165C42—41no—
166C42—9641no—
167C42—4821no—
168C42—2411no—
169C42—2411no—
170C23—4821no—
171C23#1683874711yescharacteristic
172C23C2×C22⋊D24111yescharacteristic
173C23C2×D96411yescharacteristic
174Q8—41no—
175Q8—9641no—
176D4—41no—
177D4—41no—
178D4—41no—
179D4—9641no—
180D4—9642no—
181D4—9642no—
182D4—9642no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—42no—
190C2×C4—9642no—
191C2×C4—9642no—
192C2×C4—9641no—
193C2×C4—9641no—
194C2×C4—4821no—
195C2×C4—4821no—
196C2×C4—4821no—
197C2×C4#1683874711yescharacteristic
198C2×C4#1683874711yescharacteristic
199C2×C4#1683874711yescharacteristic
200C2×C4C2×C4×D24111yescharacteristic
201C22—21no—
202C22—21no—
203C22—21no—
204C22—41no—
205C22—41no—
206C22—41no—
207C22—9641no—
208C22—9641no—
209C22—9641no—
210C22C2×#1683874711yescharacteristic
211C4—21no—
212C4—21no—
213C4—21no—
214C4—82no—
215C4—19282no—
216C4—9641no—
217C4—9641no—
218C4—4822no—
219C4#2144055611yescharacteristic
220C4#2144055611yescharacteristic
221C2—21no—
222C2—41no—
223C2—41no—
224C2—41no—
225C2—19281no—
226C2C2×#2144055611yescharacteristic
subgroupG/H
centerC4#21440556
commutatorC2×C4×C241C22×C4
FrattiniC2×D4C22×D241
Fitting#410×C241C2
socleC2×C241C2×#99
prime radical#29508263C2
cosocleC2×D4×C241C23
hypercenter#410D241
hypocenterC241#2126
LCSG ▷ C2×C4×C241 ▷ C22×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #410

Complements

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

NH ≅ G/Ntype
2. #29507691C2semidirect
3. #29507511C2semidirect
4. #29507509C2semidirect
5. #410×C241C2semidirect
6. C2×#16838770C4semidirect
7. #21440640C4semidirect
9. #21440631C4semidirect
16. C2×C4×Dic241C4semidirect
113. C241#2126semidirect
117. #410D241semidirect

Maximal subgroups

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

subgroupindex
#295082632
#295076912
#295075112
#295075092
#410×C2412
#2126241