Finite Group Databasebeta

← #44508529

Subgroups — #44508529

Order 30848.

406 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 93 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
1C22×#16838759C211yesmaximal, characteristic
2C22×#16838757C211yesmaximal, characteristic
3C2×#21440640C211yesmaximal, characteristic, complemented
4C2×#21440565C211yesmaximal, characteristic, complemented
5#29507618C211yesmaximal, characteristic
6#29507471C211yesmaximal, characteristic, complemented
7C2×#103×C241C211yesmaximal, characteristic, complemented
8C22×Dic482C2211yescharacteristic
9C22×D964C2211yescharacteristic
10C2×#16838759—22no—
11C2×#16838759—22no—
12C2×#16838759—22no—
13C2×#16838757—22no—
14C2×#16838757—22no—
15C2×#16838757—22no—
16C22×#14515349C2211yescharacteristic
17#21440640—22no—
18#21440640—22no—
19C2×#16838749—22no—
20C2×#16838747—22no—
21C2×C4×Dic241C2211yescharacteristic
22#21440565—22no—
23C22×Q8×C241C2211yescharacteristic
24C22×C8×C241C2211yescharacteristic
25C2×C4⋊C4×C241C2211yescharacteristic
26#103×C241—22no—
27C23×D241—21no—
28C2×Dic482—21no—
29C2×Dic482—21no—
30C2×Dic482—21no—
31C2×Dic482—21no—
32C2×Dic482—21no—
33C2×Dic482D412yes—
34C2×D964—21no—
35C2×D964—21no—
36C2×D964—21no—
37C2×D964—21no—
38C2×D964—21no—
39C2×D964D412yes—
40C22×Dic241—21no—
41C22×Dic241D412yes—
42#16838759—28no—
43#16838757—28no—
44C2×#14515349—21no—
45C2×#14515349—21no—
46C2×#14515349D412yes—
47#16838749—28no—
48#16838747—44no—
49C4×Dic241—21no—
50C4×Dic241—21no—
51C2×Q8×C241—21no—
52C2×Q8×C241—21no—
53C2×Q8×C241—21no—
54C2×Q8×C241—21no—
55C2×Q8×C241—21no—
56C2×Q8×C241D412yes—
57C22×C4×C241—21no—
58C22×C4×C241—21no—
59C22×C4×C241C2311yescharacteristic
60C2×C8×C241—21no—
61C2×C8×C241—21no—
62C2×C8×C241D412yes—
63C4⋊C4×C241—21no—
64C4⋊C4×C241—21no—
65C22×D241—22no—
66C22×D241—41no—
67C22×D241—41no—
68C22×D241—42no—
69C22×D241—42no—
70Dic482—22no—
71Dic482—22no—
72Dic482—41no—
73Dic482—41no—
74D964—22no—
75D964—22no—
76D964—41no—
77D964—41no—
78C2×Dic241—22no—
79C2×Dic241—22no—
80C2×Dic241—22no—
81C2×Dic241—41no—
82C2×Dic241—41no—
83C2×Dic241SD1614yescomplemented
84#14515349—22no—
85C23×C241C2×D411yescharacteristic
86Q8×C241—22no—
87Q8×C241—22no—
88Q8×C241—41no—
89Q8×C241—41no—
90C2×C4×C241—22no—
91C2×C4×C241—41no—
92C2×C4×C241—41no—
93C2×C4×C241—41no—
94C2×C4×C241—42no—
95C2×C4×C241C2×D411yescharacteristic
96C2×C4×C241C2×D411yescharacteristic
97C2×C4×C241C2×D411yescharacteristic
98C2×C4×C241C2×D411yescharacteristic
99C2×C4×C241C2×D411yescharacteristic
100C2×C4×C241#4111yescharacteristic
101C8×C241—22no—
102C22×C241#12011yescharacteristic
103C22×C241#12111yescharacteristic
104C22×C241#12711yescharacteristic
105C22×C241C2×SD1612yes—
106C22×C241#13712yes—
107C2×D241—42no—
108C2×D241—44no—
109C2×D241—82no—
110C2×D241—81no—
111C2×D241—81no—
112C4×C241—42no—
113C4×C241—81no—
114C4×C241#12011yescharacteristic
115C4×C241#12011yescharacteristic
116C4×C241#12111yescharacteristic
117C4×C241#12111yescharacteristic
118Dic241—24no—
119Dic241—42no—
120C2×C241#39211yescharacteristic
121C2×C241#44812yes—
122C2×C241#46112yes—
123C2×C241#49211yescharacteristic
124C2×C241#49711yescharacteristic
125D241—82no—
126C241#201311yescharacteristic, complemented, Sylow
127#2013—2411nomaximal, Sylow
128C22×SD16—2411no—
129C22×SD16—2411no—
130C2×C4⋊Q8—2411no—
131C2×#103—2411no—
132C2×#103D24111yescharacteristic, complemented
133#390—2411no—
134#336—2411no—
135C22×Q8—2411no—
136C22×Q8C2×D24111yescharacteristic
137C22×D4—2411no—
138C2×SD16—4822no—
139C2×SD16—4822no—
140C2×SD16—4822no—
141C2×SD16—4822no—
142C2×SD16—4822no—
143C2×SD16—4822no—
144C22×C8—2411no—
145C22×C8C2×D24111yescharacteristic
146C4⋊Q8—4822no—
147C4⋊Q8—4822no—
148C2×C4⋊C4—4822no—
149C2×C4⋊C4C2×D24111yescharacteristic
150C2×C22⋊C4—4822no—
151C2×C42—2411no—
152#103—22no—
153#103—4822no—
154C24—4821no—
155C2×Q8—21no—
156C2×Q8—21no—
157C2×Q8—21no—
158C2×Q8—21no—
159C2×Q8—21no—
160C2×Q8—4821no—
161C2×Q8—4821no—
162C2×Q8—4821no—
163C2×Q8—4821no—
164C2×Q8—4821no—
165C2×Q8—2412no—
166C2×Q8D96412yes—
167C2×D4—4821no—
168C2×D4—4821no—
169C2×D4—4821no—
170C2×D4—4821no—
171C2×D4—4821no—
172C2×D4—2412no—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—4821no—
176C22×C4—2412no—
177C22×C4C22×D24111yescharacteristic
178SD16—4828no—
179SD16—4828no—
180C2×C8—21no—
181C2×C8—21no—
182C2×C8—4821no—
183C2×C8—4821no—
184C2×C8—2412no—
185C2×C8C22⋊D24112yes—
186C4⋊C4—21no—
187C4⋊C4—21no—
188C4⋊C4—4828no—
189C22⋊C4—9644no—
190C42—4821no—
191C42—4821no—
192C23—9641no—
193C23—9641no—
194C23—9642no—
195C23—9642no—
196C23—4822no—
197C23D4×D24111yescharacteristic
198Q8—22no—
199Q8—22no—
200Q8—41no—
201Q8—41no—
202Q8—9641no—
203Q8—9641no—
204Q8—4822no—
205Q8—4822no—
206D4—9641no—
207D4—9641no—
208D4—4822no—
209D4—4822no—
210C2×C4—22no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—42no—
215C2×C4—9641no—
216C2×C4—9641no—
217C2×C4—4822no—
218C2×C4—4822no—
219C2×C4—4822no—
220C2×C4—2414no—
221C2×C4D4×D24111yescharacteristic
222C2×C4D4×D24111yescharacteristic
223C2×C4D4×D24111yescharacteristic
224C2×C4C2×C22⋊D24111yescharacteristic
225C2×C4C2×D96411yescharacteristic
226C2×C4#1683877011yescharacteristic
227C8—22no—
228C8—4822no—
229C22—19281no—
230C22—19282no—
231C22—19281no—
232C22—9642no—
233C22—9644no—
234C22#2144061211yescharacteristic
235C22#2144061511yescharacteristic
236C22#2144063811yescharacteristic
237C22SD16×D24112yes—
238C22#2144067412yes—
239C4—42no—
240C4—81no—
241C4—9642no—
242C4—4824no—
243C4#2144061011yescharacteristic
244C4#2144061211yescharacteristic
245C4#2144061511yescharacteristic
246C4#2144061611yescharacteristic
247C2—19282no—
248C2#2950762611yescharacteristic
249C2#2950785712yes—
250C2#2950792112yes—
251C2#2950808811yescharacteristic
252C2#2950811011yescharacteristic
subgroupG/H
centerC23D4×D241
commutator, cosocleC22×C4×C241C23
FrattiniC22×C4C22×D241
FittingC2×#103×C241C2
socleC23×C241C2×D4
prime radicalC22×D964C22
hypercenterC2×#103D241
hypocenterC241#2013
LCSG ▷ C22×C4×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
3. C2×#21440640C2semidirect
4. C2×#21440565C2semidirect
6. #29507471C2semidirect
7. C2×#103×C241C2semidirect
83. C2×Dic241SD16semidirect
126. C241#2013semidirect
132. C2×#103D241semidirect

Maximal subgroups

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

subgroupindex
C22×#168387592
C22×#168387572
C2×#214406402
C2×#214405652
#295076182
#295074712
C2×#103×C2412
#2013241