Finite Group Databasebeta

← #44507745

Subgroups — #44507745

Order 30848.

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

normal subgroups only

This group has 376 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×#16838754C211yesmaximal, characteristic, complemented
2#29508228C211yesmaximal, characteristic
3C2×#21440570C212yesmaximal, complemented
4#29507477C212yesmaximal, complemented
5C4×C22⋊C4×C241C211yesmaximal, characteristic, complemented
6C2×#16838770C2211yescharacteristic
7C2×#16838754—24no—
8C2×#16838754—21no—
9C2×#16838754C2212yes—
10C22×#14515349—21no—
11#21440625—21no—
12#21440621C411yescharacteristic, complemented
13#21440621C411yescharacteristic, complemented
14#21440616C411yescharacteristic, complemented
15#21440616C411yescharacteristic, complemented
16#21440611—21no—
17C4×C22⋊D241—21no—
18C4×C22⋊D241—21no—
19#21440601C2211yescharacteristic
20#21440570—24no—
21C23×C4×C241C2211yescharacteristic
22C2×C22⋊C4×C241—21no—
23C2×C42×C241C2212yes—
24#95×C241—21no—
25#16838770—22no—
26#16838770—22no—
27C2×Dic482C2×C411yescharacteristic
28C2×D964C2×C411yescharacteristic
29C2×C22⋊D241—21no—
30C2×C22⋊D241—21no—
31C2×C22⋊D241—21no—
32C2×C4×D241—21no—
33#16838754—24no—
34#16838754—22no—
35#16838754D414yescomplemented
36C2×#14515349—24no—
37C2×#14515349—22no—
38C4⋊Dic241C2×C411yescharacteristic
39C4⋊Dic241C2×C411yescharacteristic
40#16838749—21no—
41#16838749—21no—
42C22⋊Dic241—21no—
43C22⋊Dic241—21no—
44C22⋊Dic241—21no—
45#16838747—21no—
46#16838747—21no—
47C4×Dic241—21no—
48C24×C241D411yescharacteristic
49C22×C4×C241—22no—
50C22×C4×C241—22no—
51C22×C4×C241—22no—
52C22×C4×C241C2×C411yescharacteristic
53C22×C4×C241C2×C411yescharacteristic
54C22×C4×C241D411yescharacteristic
55C22×C4×C241D411yescharacteristic
56C22×C4×C241D411yescharacteristic
57C22×C4×C241C2311yescharacteristic
58C22⋊C4×C241—24no—
59C42×C241—22no—
60C42×C241—22no—
61C22×D241—21no—
62Dic482—22no—
63D964—22no—
64C22⋊D241—42no—
65C22⋊D241—42no—
66C22⋊D241—42no—
67C2×Dic241—21no—
68C2×Dic241—21no—
69C2×Dic241—21no—
70C4×D241—41no—
71C4×D241—41no—
72#14515349—24no—
73C23×C241—22no—
74C23×C241—22no—
75C23×C241—41no—
76C23×C241C22⋊C411yescharacteristic
77C23×C241C22⋊C411yescharacteristic
78C23×C241C2×D411yescharacteristic
79C2×C4×C241—22no—
80C2×C4×C241—22no—
81C2×C4×C241—22no—
82C2×C4×C241—21no—
83C2×C4×C241—21no—
84C2×C4×C241—21no—
85C2×C4×C241—21no—
86C2×C4×C241—24no—
87C2×C4×C241—42no—
88C2×C4×C241—42no—
89C2×C4×C241C22⋊C411yescharacteristic
90C2×C4×C241C22⋊C411yescharacteristic
91C2×C4×C241C22×C411yescharacteristic
92C2×C4×C241C2×D412yes—
93C2×C4×C241C2×D411yescharacteristic
94C2×C4×C241#4112yes—
95C22×C241—21no—
96C22×C241—21no—
97C22×C241—21no—
98C22×C241—21no—
99C22×C241—21no—
100C22×C241—21no—
101C22×C241—21no—
102C22×C241—44no—
103C22×C241#10412yescomplemented
104C22×C241C2×C22⋊C411yescharacteristic
105C22×C241#12112yes—
106C2×D241—41no—
107C2×D241—41no—
108C2×D241—41no—
109C4×C241—21no—
110C4×C241—21no—
111C4×C241—44no—
112C4×C241C4×D412yes—
113C4×C241#12011yescharacteristic
114C4×C241#12311yescharacteristic
115Dic241—41no—
116Dic241—41no—
117Dic241—41no—
118C2×C241—22no—
119C2×C241—22no—
120C2×C241—41no—
121C2×C241#38611yescharacteristic
122C2×C241C2×#10411yescharacteristic
123C2×C241#42111yescharacteristic
124D241—81no—
125C241#187111yescharacteristic, complemented, Sylow
126#1871—2411nomaximal, Sylow
127C22×M16—2411no—
128#525—2411no—
129C2×#104—2412no—
130C4×C22⋊C4D24111yescharacteristic, complemented
131#339—2412no—
132C2×#41—2411no—
133C23×C4C2×D24111yescharacteristic
134C2×M16—4821no—
135C2×M16—4824no—
136C2×M16—2412no—
137C22×C8—4821no—
138#123—4821no—
139C22⋊Q8—2411no—
140C22⋊Q8—2411no—
141#121—2411no—
142#121—2411no—
143#120—4821no—
144C4×D4—4821no—
145C4×D4—4821no—
146#117—2411no—
147C2×C22⋊C4—21no—
148C2×C42C2×D24112yes—
149#104—4824no—
150#95—21no—
151C24C22⋊D24111yescharacteristic
152#41—4822no—
153#41—4822no—
154C2×Q8—2411no—
155C2×D4—4821no—
156C2×D4—4821no—
157C2×D4—4821no—
158C2×D4—2411no—
159C22×C4—22no—
160C22×C4—22no—
161C22×C4—22no—
162C22×C4—4821no—
163C22×C4C4×D24111yescharacteristic
164C22×C4C4×D24111yescharacteristic
165C22×C4C22⋊D24111yescharacteristic
166C22×C4D96411yescharacteristic
167C22×C4D96411yescharacteristic
168C22×C4C22×D24111yescharacteristic
169M16—4824no—
170M16—4822no—
171M16—2414no—
172C2×C8—4824no—
173C2×C8—4822no—
174C4⋊C4—4821no—
175C4⋊C4—4821no—
176C4⋊C4—2411no—
177C4⋊C4—2411no—
178C22⋊C4—24no—
179C22⋊C4—4821no—
180C22⋊C4—4821no—
181C22⋊C4—4821no—
182C22⋊C4—4821no—
183C22⋊C4—4821no—
184C42—22no—
185C42—22no—
186C42—4821no—
187C23—22no—
188C23—22no—
189C23—41no—
190C23—4821no—
191C23#1683874711yescharacteristic
192C23#1683874711yescharacteristic
193C23C2×C22⋊D24111yescharacteristic
194Q8—4822no—
195D4—9642no—
196D4—9642no—
197D4—9642no—
198D4—4822no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—24no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—9641no—
210C2×C4—9641no—
211C2×C4—4821no—
212C2×C4—4821no—
213C2×C4—4821no—
214C2×C4#1683874711yescharacteristic
215C2×C4#1683874711yescharacteristic
216C2×C4C2×C4×D24111yescharacteristic
217C2×C4D4×D24112yes—
218C2×C4C2×D96411yescharacteristic
219C2×C4#1683876912yes—
220C8—4824no—
221C22—21no—
222C22—21no—
223C22—21no—
224C22—21no—
225C22—21no—
226C22—21no—
227C22—21no—
228C22—44no—
229C22—9641no—
230C22—9641no—
231C22—9641no—
232C22#2144057012yescomplemented
233C22C2×#1683874711yescharacteristic
234C22#2144061412yes—
235C4—21no—
236C4—21no—
237C4—44no—
238C4—9641no—
239C4—9641no—
240C4—9641no—
241C4#2144060212yes—
242C4#2144061211yescharacteristic
243C4#2144062611yescharacteristic
244C2—22no—
245C2—22no—
246C2—41no—
247C2—19281no—
248C2#2950759411yescharacteristic
249C2C2×#2144057011yescharacteristic
250C2#2950773511yescharacteristic
subgroupG/H
centerC2×C4C2×D964
commutatorC2×C4×C241C22×C4
FrattiniC22×C4C22×D241
FittingC4×C22⋊C4×C241C2
socleC22×C241C2×C22⋊C4
prime radical#29508228C2
cosocleC22×C4×C241C23
hypercenterC4×C22⋊C4D241
hypocenterC241#1871
LCSG ▷ C2×C4×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#16838754C2semidirect
3. C2×#21440570C2semidirect
4. #29507477C2semidirect
5. C4×C22⋊C4×C241C2semidirect
12. #21440621C4semidirect
13. #21440621C4semidirect
14. #21440616C4semidirect
15. #21440616C4semidirect
35. #16838754D4semidirect
103. C22×C241#104semidirect
125. C241#1871semidirect
130. C4×C22⋊C4D241semidirect
232. C22#21440570semidirect

Maximal subgroups

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

subgroupindex
C22×#168387542
#295082282
C2×#214405702
#295074772
C4×C22⋊C4×C2412
#1871241