Finite Group Databasebeta

← #44505986

Subgroups — #44505986

Order 30848.

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

normal subgroups only

This group has 286 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
1#29508228C211yesmaximal, characteristic
2#29507681C211yesmaximal, characteristic, complemented
3#29507453C212yesmaximal, complemented
4#29507450C212yesmaximal, complemented
5#380×C241C211yesmaximal, characteristic, complemented
6C2×#16838770C411yescharacteristic, complemented
7C2×#16838754—21no—
8#21440625—21no—
9#21440621C411yescharacteristic, complemented
10#21440621C2211yescharacteristic
11#21440616C411yescharacteristic, complemented
12#21440616C2211yescharacteristic
13#21440611—21no—
14C4×C22⋊D241—21no—
15C4×C22⋊D241—21no—
16#21440601C411yescharacteristic, complemented
17C22⋊#14515349—21no—
18C22⋊#14515349C2212yes—
19C23×C4×C241C2211yescharacteristic
20C2×C4⋊C4×C241—21no—
21C2×C22⋊C4×C241—21no—
22#95×C241C2212yes—
23#16838770—42no—
24C2×Dic482C2×C411yescharacteristic
25C2×D964C2×C411yescharacteristic
26C2×C22⋊D241—21no—
27C2×C22⋊D241—21no—
28C2×C22⋊D241—21no—
29C2×C4×D241—21no—
30#16838754—42no—
31C2×#14515349—22no—
32C4⋊Dic241C2×C411yescharacteristic
33C4⋊Dic241C2×C411yescharacteristic
34#16838749—21no—
35#16838749—21no—
36C22⋊Dic241—21no—
37C22⋊Dic241—21no—
38C22⋊Dic241—21no—
39#16838747—21no—
40#16838747—21no—
41C4×Dic241—21no—
42C24×C241D411yescharacteristic
43C22×C4×C241—22no—
44C22×C4×C241—42no—
45C22×C4×C241C2×C411yescharacteristic
46C22×C4×C241C2×C411yescharacteristic
47C22×C4×C241D411yescharacteristic
48C22×C4×C241D411yescharacteristic
49C22×C4×C241D411yescharacteristic
50C22×C4×C241C2311yescharacteristic
51C4⋊C4×C241—42no—
52C22⋊C4×C241—42no—
53C22×D241—21no—
54Dic482—41no—
55D964—41no—
56C22⋊D241—42no—
57C22⋊D241—42no—
58C22⋊D241—41no—
59C22⋊D241—41no—
60C2×Dic241—21no—
61C2×Dic241—21no—
62C2×Dic241—21no—
63C4×D241—42no—
64#14515349—42no—
65C23×C241—21no—
66C23×C241—21no—
67C23×C241—41no—
68C23×C241—41no—
69C23×C241C22⋊C411yescharacteristic
70C23×C241C22⋊C411yescharacteristic
71C23×C241C2×D411yescharacteristic
72C2×C4×C241—22no—
73C2×C4×C241—22no—
74C2×C4×C241—22no—
75C2×C4×C241—41no—
76C2×C4×C241—41no—
77C2×C4×C241—41no—
78C2×C4×C241—42no—
79C2×C4×C241—42no—
80C2×C4×C241—42no—
81C2×C4×C241C22⋊C411yescharacteristic
82C2×C4×C241C22⋊C411yescharacteristic
83C2×C4×C241C22×C411yescharacteristic
84C2×C4×C241C2×D411yescharacteristic
85C22×C241—21no—
86C22×C241—21no—
87C22×C241—21no—
88C22×C241—21no—
89C22×C241—21no—
90C22×C241—21no—
91C22×C241—21no—
92C22×C241—21no—
93C22×C241—42no—
94C22×C241—42no—
95C22×C241C2×C22⋊C411yescharacteristic
96C22×C241AGL(1,ℤ/8)11yescharacteristic
97C22×C241#13711yescharacteristic
98C2×D241—41no—
99C2×D241—41no—
100C2×D241—41no—
101C4×C241—21no—
102C4×C241—21no—
103C4×C241—21no—
104C4×C241—82no—
105C4×C241#9912yes—
106Dic241—41no—
107Dic241—41no—
108Dic241—41no—
109C2×C241—21no—
110C2×C241—21no—
111C2×C241—41no—
112C2×C241—41no—
113C2×C241C2×#9911yescharacteristic
114C2×C241#41711yescharacteristic
115C2×C241#42111yescharacteristic
116D241—81no—
117C241#151311yescharacteristic, complemented, Sylow
118#1513—2411nomaximal, Sylow
119#525—2411no—
120#407—2411no—
121#380D24111yescharacteristic, complemented
122#328—2412no—
123#327—2412no—
124C2×#41—2411no—
125C23×C4C2×D24111yescharacteristic
126C2×M16—4821no—
127#123—4821no—
128C22⋊Q8—2411no—
129C22⋊Q8—2411no—
130#121—2411no—
131#121—2411no—
132#120—4821no—
133C4×D4—4821no—
134C4×D4—4821no—
135#117—2411no—
136C2×C4⋊C4—21no—
137C2×C22⋊C4—21no—
138C22⋊C8—4821no—
139C22⋊C8—2412no—
140#95C2×D24112yes—
141C24C22⋊D24111yescharacteristic
142#41—9642no—
143C2×Q8—2411no—
144C2×D4—4821no—
145C2×D4—4821no—
146C2×D4—4821no—
147C2×D4—2411no—
148C22×C4—22no—
149C22×C4—42no—
150C22×C4—4821no—
151C22×C4C4×D24111yescharacteristic
152C22×C4C4×D24111yescharacteristic
153C22×C4C22⋊D24111yescharacteristic
154C22×C4D96411yescharacteristic
155C22×C4D96411yescharacteristic
156C22×C4C22×D24111yescharacteristic
157M16—9642no—
158C2×C8—4822no—
159C4⋊C4—42no—
160C4⋊C4—4821no—
161C4⋊C4—4821no—
162C4⋊C4—2411no—
163C4⋊C4—2411no—
164C22⋊C4—42no—
165C22⋊C4—4821no—
166C22⋊C4—4821no—
167C22⋊C4—4821no—
168C22⋊C4—4821no—
169C22⋊C4—4821no—
170C42—4821no—
171C23—21no—
172C23—21no—
173C23—41no—
174C23—41no—
175C23—4821no—
176C23#1683874711yescharacteristic
177C23#1683874711yescharacteristic
178C23C2×C22⋊D24111yescharacteristic
179Q8—9641no—
180D4—9641no—
181D4—9642no—
182D4—9642no—
183D4—9641no—
184D4—9641no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—9642no—
195C2×C4—4821no—
196C2×C4—4821no—
197C2×C4—4821no—
198C2×C4#1683874711yescharacteristic
199C2×C4#1683874711yescharacteristic
200C2×C4C2×C4×D24111yescharacteristic
201C2×C4C2×D96411yescharacteristic
202C8—9642no—
203C22—21no—
204C22—21no—
205C22—21no—
206C22—21no—
207C22—21no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22—42no—
212C22—42no—
213C22—9641no—
214C22—9641no—
215C22—9641no—
216C22C2×#1683874711yescharacteristic
217C22#2144066811yescharacteristic
218C22#2144067311yescharacteristic
219C4—21no—
220C4—21no—
221C4—21no—
222C4—82no—
223C4—9641no—
224C4—9641no—
225C4—9641no—
226C4#2144055612yes—
227C2—21no—
228C2—21no—
229C2—41no—
230C2—41no—
231C2—19281no—
232C2C2×#2144055611yescharacteristic
233C2#2950771611yescharacteristic
234C2#2950773511yescharacteristic
subgroupG/H
centerC22C2×#16838747
commutatorC2×C4×C241C22×C4
FrattiniC22×C4C22×D241
Fitting#380×C241C2
socleC22×C241C2×C22⋊C4
prime radical#29508228C2
cosocleC22×C4×C241C23
hypercenter#380D241
hypocenterC241#1513
LCSG ▷ C2×C4×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
2. #29507681C2semidirect
3. #29507453C2semidirect
4. #29507450C2semidirect
5. #380×C241C2semidirect
6. C2×#16838770C4semidirect
9. #21440621C4semidirect
11. #21440616C4semidirect
16. #21440601C4semidirect
117. C241#1513semidirect
121. #380D241semidirect

Maximal subgroups

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

subgroupindex
#295082282
#295076812
#295074532
#295074502
#380×C2412
#1513241