Finite Group Databasebeta

← #44507900

Subgroups — #44507900

Order 30848.

378 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 83 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
1C2×#21440623C211yesmaximal, characteristic
2C2×#21440598C211yesmaximal, characteristic, complemented
3C2×#21440557C211yesmaximal, characteristic
4#29507578C211yesmaximal, characteristic, complemented
5#29507483C211yesmaximal, characteristic, complemented
6#29507483C211yesmaximal, characteristic, complemented
7C2×#99×C241C211yesmaximal, characteristic
8C23×Dic241C2211yescharacteristic
9#21440623—22no—
10#21440623—21no—
11#21440623—21no—
12#21440598—22no—
13#21440598—22no—
14C2×#16838749—21no—
15C2×#16838749C412yescomplemented
16C2×C22⋊Dic241C412yescomplemented
17C2×C22⋊Dic241C2211yescharacteristic
18C2×C22⋊Dic241C2211yescharacteristic
19C2×C22⋊Dic241C2211yescharacteristic
20C2×C4×Dic241—21no—
21#21440557—22no—
22#21440549—22no—
23C22×D4×C241C2211yescharacteristic
24C2×C22⋊C4×C241C2211yescharacteristic
25C2×C22⋊C4×C241C2211yescharacteristic
26#99×C241—22no—
27C22×Dic241—21no—
28C22×Dic241—21no—
29C22×Dic241—21no—
30C22×Dic241—21no—
31C22×Dic241—21no—
32C22×Dic241—21no—
33C22×Dic241C2×C412yes—
34C22×Dic241C2×C412yes—
35C22×Dic241D412yes—
36C22×Dic241D411yescharacteristic
37C22×Dic241D411yescharacteristic
38#16838749—24no—
39#16838749—22no—
40#16838749—22no—
41C22⋊Dic241—22no—
42C22⋊Dic241—22no—
43C22⋊Dic241—21no—
44C22⋊Dic241—21no—
45C22⋊Dic241—21no—
46C22⋊Dic241—21no—
47C22⋊Dic241—21no—
48C22⋊Dic241D412yes—
49C4×Dic241—24no—
50C24×C241C2×C411yescharacteristic
51C24×C241C2311yescharacteristic
52C2×D4×C241—21no—
53C2×D4×C241—21no—
54C2×D4×C241—21no—
55C2×D4×C241—21no—
56C2×D4×C241—21no—
57C2×D4×C241—21no—
58C22×C4×C241—21no—
59C22×C4×C241—21no—
60C22×C4×C241C2×C411yescharacteristic
61C22⋊C4×C241—21no—
62C22⋊C4×C241—21no—
63C22⋊C4×C241—21no—
64C22⋊C4×C241D412yes—
65C2×Dic241—22no—
66C2×Dic241—22no—
67C2×Dic241—21no—
68C2×Dic241—21no—
69C2×Dic241—22no—
70C2×Dic241—22no—
71C2×Dic241—21no—
72C2×Dic241—21no—
73C2×Dic241—22no—
74C2×Dic241—22no—
75C2×Dic241—42no—
76C2×Dic241—42no—
77C2×Dic241—42no—
78C2×Dic241—41no—
79C2×Dic241C22⋊C412yes—
80C2×Dic241C22⋊C412yes—
81C23×C241—21no—
82C23×C241—21no—
83C23×C241—21no—
84C23×C241—42no—
85C23×C241—42no—
86C23×C241C22×C411yescharacteristic
87C23×C241C2×D411yescharacteristic
88C23×C241C2×D411yescharacteristic
89C23×C241C2×D411yescharacteristic
90C23×C241C2×D411yescharacteristic
91C23×C241#4111yescharacteristic
92C23×C241#4111yescharacteristic
93D4×C241—41no—
94D4×C241—41no—
95D4×C241—41no—
96D4×C241—41no—
97C2×C4×C241—21no—
98C2×C4×C241—21no—
99C2×C4×C241—21no—
100C2×C4×C241—22no—
101C2×C4×C241—42no—
102C2×C4×C241—42no—
103C2×C4×C241—41no—
104C22×C241—22no—
105C22×C241—22no—
106C22×C241—22no—
107C22×C241—41no—
108C22×C241—41no—
109C22×C241—41no—
110C22×C241—41no—
111C22×C241—41no—
112C22×C241—42no—
113C22×C241—81no—
114C22×C241—81no—
115C22×C241C2×C22⋊C411yescharacteristic
116C22×C241C4×D411yescharacteristic
117C22×C241C4×D411yescharacteristic
118C22×C241#12011yescharacteristic
119C22×C241#12111yescharacteristic
120C22×C241#12111yescharacteristic
121C22×C241#12311yescharacteristic
122C4×C241—42no—
123C4×C241—41no—
124C4×C241—81no—
125Dic241—22no—
126Dic241—22no—
127Dic241—42no—
128Dic241—42no—
129Dic241—81no—
130C2×C241—21no—
131C2×C241—21no—
132C2×C241—21no—
133C2×C241—21no—
134C2×C241—21no—
135C2×C241—21no—
136C2×C241—81no—
137C2×C241#38611yescharacteristic
138C2×C241#41012yes—
139C241#189911yescharacteristic, complemented, Sylow
140#1899—2411nomaximal, Sylow
141C2×#123—2411no—
142C2×#117—2411no—
143C2×#99—2411no—
144C2×#99D24111yescharacteristic
145#381—2411no—
146#342—2411no—
147#342—2411no—
148C22×D4C2×D24111yescharacteristic
149C23×C4—2411no—
150#123—4822no—
151#123—4821no—
152#123—4821no—
153#117—4822no—
154#117—4822no—
155C2×C4⋊C4—4821no—
156C2×C4⋊C4—2412no—
157C2×C22⋊C4—2411no—
158C2×C22⋊C4—2412no—
159C2×C22⋊C4—2411no—
160C2×C22⋊C4—2411no—
161C2×C22⋊C4C2×D24111yescharacteristic
162C2×C22⋊C4C2×D24111yescharacteristic
163C2×C42—4821no—
164#99—22no—
165#99—4822no—
166#95—4822no—
167C24C4×D24111yescharacteristic
168C24C22×D24111yescharacteristic
169C2×D4—21no—
170C2×D4—21no—
171C2×D4—21no—
172C2×D4—21no—
173C2×D4—21no—
174C2×D4—21no—
175C22×C4—21no—
176C22×C4—21no—
177C22×C4—4821no—
178C22×C4—4821no—
179C22×C4—4821no—
180C22×C4—4821no—
181C22×C4—4821no—
182C22×C4—4821no—
183C22×C4—2412no—
184C22×C4—2412no—
185C22×C4—2412no—
186C22×C4—2411no—
187C22×C4—2411no—
188C22×C4C4×D24111yescharacteristic
189C4⋊C4—4824no—
190C4⋊C4—4822no—
191C4⋊C4—4822no—
192C22⋊C4—21no—
193C22⋊C4—21no—
194C22⋊C4—21no—
195C22⋊C4—4821no—
196C22⋊C4—4821no—
197C22⋊C4—4821no—
198C22⋊C4—4821no—
199C22⋊C4—4821no—
200C22⋊C4—4822no—
201C22⋊C4—4822no—
202C22⋊C4—2412no—
203C22⋊C4C22⋊D24112yes—
204C42—4824no—
205C23—21no—
206C23—21no—
207C23—21no—
208C23—42no—
209C23—42no—
210C23C2×C4×D24111yescharacteristic
211C23D4×D24111yescharacteristic
212C23D4×D24111yescharacteristic
213C23D4×D24111yescharacteristic
214C23C2×C22⋊D24111yescharacteristic
215C23#1683876911yescharacteristic
216C23#1683877011yescharacteristic
217D4—41no—
218D4—41no—
219D4—41no—
220D4—41no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—22no—
225C2×C4—42no—
226C2×C4—42no—
227C2×C4—41no—
228C2×C4—9642no—
229C2×C4—9641no—
230C2×C4—9642no—
231C2×C4—9642no—
232C2×C4—4822no—
233C2×C4—4822no—
234C2×C4—4822no—
235C2×C4—4822no—
236C2×C4—4821no—
237C2×C4—4821no—
238C2×C4—4822no—
239C2×C4—4822no—
240C2×C4—4821no—
241C2×C4—4821no—
242C2×C4—2412no—
243C2×C4—2412no—
244C22—22no—
245C22—22no—
246C22—22no—
247C22—41no—
248C22—41no—
249C22—41no—
250C22—41no—
251C22—41no—
252C22—42no—
253C22—81no—
254C22—81no—
255C22C22⋊C4×D24111yescharacteristic
256C22#2144060211yescharacteristic
257C22C4×C22⋊D24111yescharacteristic
258C22#2144061011yescharacteristic
259C22#2144061311yescharacteristic
260C22#2144061511yescharacteristic
261C22#2144062411yescharacteristic
262C4—42no—
263C4—41no—
264C4—81no—
265C4—19281no—
266C4—9642no—
267C4—9642no—
268C4—4822no—
269C4—4822no—
270C2—21no—
271C2—21no—
272C2—21no—
273C2—21no—
274C2—21no—
275C2—21no—
276C2—81no—
277C2#2950759311yescharacteristic
278C2#2950768912yes—
subgroupG/H
centerC22C22⋊C4×D241
commutatorC23×C241C22×C4
FrattiniC24C22×D241
FittingC2×#99×C241C2
socleC22×C241C2×C22⋊C4
prime radicalC22×D4×C241C22
cosocleC24×C241C23
hypercenterC2×#99D241
hypocenterC241#1899
LCSG ▷ C23×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C22 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
2. C2×#21440598C2semidirect
4. #29507578C2semidirect
5. #29507483C2semidirect
6. #29507483C2semidirect
15. C2×#16838749C4semidirect
16. C2×C22⋊Dic241C4semidirect
139. C241#1899semidirect

Maximal subgroups

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

subgroupindex
C2×#214406232
C2×#214405982
C2×#214405572
#295075782
#295074832
C2×#99×C2412
#1899241