Finite Group Databasebeta

← #44506471

Subgroups — #44506471

Order 30848.

236 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 51 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#29508342C211yesmaximal, characteristic
2#29508053C211yesmaximal, characteristic, complemented
3#29508050C211yesmaximal, characteristic, complemented
4#29507654C211yesmaximal, characteristic
5#29507453C211yesmaximal, characteristic, complemented
6#29507440C211yesmaximal, characteristic
7#328×C241C211yesmaximal, characteristic, complemented
8#21440622—21no—
9#21440621C2211yescharacteristic
10#21440620—21no—
11#21440620—21no—
12#21440619—21no—
13#21440618—21no—
14C2×C4⋊Dic241—21no—
15C2×C4⋊Dic241C2211yescharacteristic
16C2×#16838747—21no—
17C2×#16838747C2211yescharacteristic
18C22⋊C4×D241—21no—
19#21440576—21no—
20#21440575—21no—
21#21440567—21no—
22#21440566—21no—
23C22⋊#14515349C2211yescharacteristic
24C22⋊Q8×C241C2211yescharacteristic
25C22⋊C8×C241C2211yescharacteristic
26#95×C241C2211yescharacteristic
27C23×D241D411yescharacteristic
28C2×Dic482—21no—
29C2×Dic482D411yescharacteristic
30C22×Dic241—21no—
31C22×Dic241D411yescharacteristic
32C2×C4×D241—21no—
33C2×C4×D241—21no—
34C2×#14515349—21no—
35C4⋊Dic241—21no—
36C4⋊Dic241—21no—
37C4⋊Dic241—21no—
38C4⋊Dic241—42no—
39C4⋊Dic241D411yescharacteristic
40#16838749—21no—
41#16838749—21no—
42#16838749—21no—
43C22⋊Dic241—21no—
44#16838747—21no—
45#16838747—21no—
46#16838747—21no—
47#16838747—21no—
48#16838747—42no—
49C2×Q8×C241D411yescharacteristic
50C22×C4×C241—21no—
51C22×C4×C241C2311yescharacteristic
52C2×C8×C241—21no—
53C4⋊C4×C241—21no—
54C4⋊C4×C241D411yescharacteristic
55C22⋊C4×C241—21no—
56C22×D241—21no—
57C22×D241—21no—
58C22×D241—41no—
59C22×D241—41no—
60C22×D241Q1612yes—
61Dic482—41no—
62Dic482—81no—
63C2×Dic241—21no—
64C2×Dic241—21no—
65C2×Dic241—21no—
66C2×Dic241—41no—
67C2×Dic241—41no—
68C2×Dic241—41no—
69C2×Dic241—41no—
70C4×D241—81no—
71C4×D241—81no—
72#14515349—41no—
73C23×C241C2×D411yescharacteristic
74Q8×C241—41no—
75C2×C4×C241—22no—
76C2×C4×C241—21no—
77C2×C4×C241—21no—
78C2×C4×C241—41no—
79C2×C4×C241—41no—
80C2×C4×C241—41no—
81C2×C4×C241C2×D411yescharacteristic
82C2×C4×C241C2×D411yescharacteristic
83C8×C241—41no—
84C22×C241—21no—
85C22×C241—21no—
86C22×C241#12011yescharacteristic
87C22×C241C2×Q1611yescharacteristic
88C22×C241#13711yescharacteristic
89C2×D241—22no—
90C2×D241—41no—
91C2×D241—41no—
92C2×D241—42no—
93C2×D241—81no—
94C4×C241—21no—
95C4×C241—21no—
96C4×C241—42no—
97C4×C241—41no—
98C4×C241—41no—
99Dic241—41no—
100Dic241—41no—
101Dic241—41no—
102Dic241—81no—
103C2×C241—21no—
104C2×C241—21no—
105C2×C241#45111yescharacteristic
106C2×C241#45311yescharacteristic
107C2×C241#45811yescharacteristic
108D241—42no—
109C241#161411yescharacteristic, complemented, Sylow
110#1614—2411nomaximal, Sylow
111#543—2411no—
112#484—2411no—
113#484—2411no—
114#399—2411no—
115#328—2411no—
116#328D24111yescharacteristic, complemented
117#323—2411no—
118C22⋊Q8—4821no—
119C22⋊Q8—4821no—
120C22⋊Q8—4821no—
121C22⋊Q8—4821no—
122C22⋊Q8—4821no—
123C22⋊Q8—2411no—
124C22⋊Q8C2×D24111yescharacteristic
125C2×C4⋊C4—4821no—
126C2×C4⋊C4—2411no—
127C2×C22⋊C4—4821no—
128C2×C22⋊C4—4821no—
129C2×C22⋊C4—2411no—
130#107—4821no—
131#107—4821no—
132#103—4821no—
133#103—4821no—
134C22⋊C8—2411no—
135C22⋊C8C2×D24111yescharacteristic
136#95C2×D24111yescharacteristic
137C24—2411no—
138C2×Q8—4821no—
139C2×Q8—2411no—
140C2×Q8D96411yescharacteristic
141C22×C4—21no—
142C22×C4—4821no—
143C22×C4—4821no—
144C22×C4—4821no—
145C22×C4—2411no—
146C22×C4C22×D24111yescharacteristic
147C2×C8—21no—
148C2×C8—4821no—
149C4⋊C4—21no—
150C4⋊C4—9642no—
151C4⋊C4—4821no—
152C4⋊C4—4821no—
153C4⋊C4—4821no—
154C4⋊C4—4821no—
155C4⋊C4—4821no—
156C4⋊C4—4821no—
157C4⋊C4—2411no—
158C4⋊C4D96411yescharacteristic
159C22⋊C4—21no—
160C22⋊C4—9642no—
161C22⋊C4—4821no—
162C22⋊C4—4821no—
163C22⋊C4—4821no—
164C22⋊C4—4821no—
165C22⋊C4—4821no—
166C23—9641no—
167C23—9641no—
168C23—4821no—
169C23—4821no—
170C23—2412no—
171C23D4×D24111yescharacteristic
172Q8—41no—
173Q8—19281no—
174Q8—9641no—
175C2×C4—22no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—19281no—
182C2×C4—19281no—
183C2×C4—9641no—
184C2×C4—9641no—
185C2×C4—9641no—
186C2×C4—9641no—
187C2×C4—4821no—
188C2×C4—4821no—
189C2×C4—4821no—
190C2×C4D4×D24111yescharacteristic
191C2×C4C2×D96411yescharacteristic
192C8—41no—
193C8—9641no—
194C22—21no—
195C22—21no—
196C22—19281no—
197C22—9642no—
198C22—9641no—
199C22—9641no—
200C22—4822no—
201C22#2144061211yescharacteristic
202C22Q16×D24111yescharacteristic
203C22#2144067111yescharacteristic
204C4—21no—
205C4—21no—
206C4—42no—
207C4—41no—
208C4—41no—
209C4—19281no—
210C4—9641no—
211C4—9641no—
212C4—9641no—
213C2—21no—
214C2—21no—
215C2—9642no—
216C2#2950787411yescharacteristic
217C2#2950788611yescharacteristic
218C2#2950790811yescharacteristic
subgroupG/H
centerC22#21440612
commutator, cosocleC22×C4×C241C23
FrattiniC22×C4C22×D241
Fitting#328×C241C2
socleC22×C241#120
prime radicalC23×D241D4
hypercenter#328D241
hypocenterC241#1614
LCSG ▷ C22×C4×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #29508053C2semidirect
3. #29508050C2semidirect
5. #29507453C2semidirect
7. #328×C241C2semidirect
109. C241#1614semidirect
116. #328D241semidirect

Maximal subgroups

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

subgroupindex
#295083422
#295080532
#295080502
#295076542
#295074532
#295074402
#328×C2412
#1614241