Finite Group Databasebeta

← #44508462

Subgroups — #44508462

Order 30848.

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

normal subgroups only

This group has 478 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
1C2×#21440670C211yesmaximal, characteristic, complemented
2#29508284C211yesmaximal, characteristic, complemented
3C2×#21440638C211yesmaximal, characteristic, complemented
4C2×#21440568C211yesmaximal, characteristic, complemented
5#29507723C211yesmaximal, characteristic, complemented
6#29507478C211yesmaximal, characteristic, complemented
7C2×#100×C241C211yesmaximal, characteristic, complemented
8C2×#16838770C2211yescharacteristic
9C22×D964C2211yescharacteristic
10C22×C22⋊D241—22no—
11#21440670—22no—
12#21440670—22no—
13C2×#16838759—21no—
14C2×D1928—21no—
15#21440638—22no—
16#21440638—21no—
17#21440638—22no—
18#21440629—21no—
19#21440613—22no—
20#21440611—22no—
21#21440601C2211yescharacteristic
22C2×C4×Dic241C2211yescharacteristic
23#21440568—22no—
24#21440564—22no—
25C22×D4×C241C2211yescharacteristic
26C2×M16×C241C2211yescharacteristic
27C2×M16×C241C2211yescharacteristic
28#100×C241—22no—
29C23×D241—21no—
30#16838770—21no—
31#16838770—21no—
32#16838770—21no—
33#16838770—21no—
34C2×Dic482D411yescharacteristic, complemented
35C2×D964—21no—
36C2×D964—21no—
37C2×D964—21no—
38C2×D964—21no—
39C2×D964—21no—
40C2×D964D411yescharacteristic, complemented
41C2×D964D412yescomplemented
42C2×C22⋊D241—28no—
43C2×C22⋊D241—24no—
44C2×C22⋊D241—21no—
45C2×C22⋊D241—48no—
46C22×Dic241—21no—
47C2×C4×D241—21no—
48#16838759—24no—
49D1928—24no—
50C4⋊Dic241D412yescomplemented
51C22⋊Dic241—24no—
52C22⋊Dic241—21no—
53C4×Dic241—21no—
54C4×Dic241—21no—
55C4×Dic241D412yescomplemented
56C24×C241D412yes—
57C2×D4×C241—21no—
58C2×D4×C241—21no—
59C2×D4×C241—21no—
60C2×D4×C241—21no—
61C2×D4×C241—21no—
62C2×D4×C241—21no—
63C22×C4×C241C2311yescharacteristic
64M16×C241—21no—
65M16×C241—21no—
66M16×C241—21no—
67M16×C241D412yescomplemented
68C2×C8×C241—21no—
69C2×C8×C241—21no—
70C22×D241—21no—
71C22×D241—22no—
72C22×D241—44no—
73C22×D241—41no—
74C22×D241—41no—
75Dic482—21no—
76Dic482—21no—
77D964—21no—
78D964—22no—
79D964—22no—
80D964—21no—
81D964—41no—
82D964—41no—
83C22⋊D241—416no—
84C22⋊D241—41no—
85C22⋊D241—41no—
86C22⋊D241—84no—
87C2×Dic241—24no—
88C2×Dic241—22no—
89C2×Dic241—22no—
90C2×Dic241—21no—
91C4×D241—41no—
92C4×D241—41no—
93C23×C241—22no—
94C23×C241—22no—
95C23×C241—22no—
96C23×C241—44no—
97C23×C241C2×D411yescharacteristic
98D4×C241—41no—
99D4×C241—41no—
100D4×C241—41no—
101D4×C241—41no—
102C2×C4×C241C2×D411yescharacteristic
103C2×C4×C241C2×D411yescharacteristic
104C2×C4×C241C2×D411yescharacteristic
105C2×C4×C241C2×D411yescharacteristic
106C2×C4×C241C2×D411yescharacteristic
107C2×C4×C241#4111yescharacteristic
108C8×C241—22no—
109C8×C241—41no—
110C22×C241—22no—
111C22×C241—44no—
112C22×C241—42no—
113C22×C241—44no—
114C22×C241—82no—
115C22×C241#12011yescharacteristic
116C22×C241#12011yescharacteristic
117C22×C241#12111yescharacteristic
118C2×D241—44no—
119C2×D241—41no—
120C2×D241—42no—
121C2×D241—42no—
122C2×D241—82no—
123C2×D241—82no—
124C4×C241#12011yescharacteristic
125C4×C241#12111yescharacteristic
126C4×C241#12111yescharacteristic
127C4×C241#12711yescharacteristic
128Dic241—24no—
129Dic241—41no—
130Dic241—42no—
131C2×C241—21no—
132C2×C241—21no—
133C2×C241—82no—
134C2×C241#39211yescharacteristic
135C2×C241#45312yes—
136D241—81no—
137D241—82no—
138C241#200211yescharacteristic, complemented, Sylow
139#2002—2411nomaximal, Sylow
140C2×AGL(1,ℤ/8)—2411no—
141#535—2411no—
142C2×#127—2411no—
143C2×#104—2411no—
144#418—2411no—
145C2×#100D24111yescharacteristic, complemented
146#339—2411no—
147C2×#41—2411no—
148C22×D4—4822no—
149C22×D4—2411no—
150C22×D4C2×D24111yescharacteristic
151AGL(1,ℤ/8)—4822no—
152AGL(1,ℤ/8)—4822no—
153C2×SD16—4821no—
154C2×D8—4821no—
155C2×M16C2×D24111yescharacteristic
156C2×M16C2×D24111yescharacteristic
157#127—4822no—
158#127—4821no—
159#127—4822no—
160#124—4821no—
161#121—4822no—
162#120—4822no—
163#117—2411no—
164C2×C42—2411no—
165#104—4822no—
166#102—4822no—
167#100—22no—
168C24—4821no—
169C24D96412yes—
170#41—4821no—
171#41—4821no—
172#41—4821no—
173#41—4821no—
174C2×Q8—2411no—
175C2×D4—21no—
176C2×D4—21no—
177C2×D4—21no—
178C2×D4—21no—
179C2×D4—21no—
180C2×D4—21no—
181C2×D4—9648no—
182C2×D4—4824no—
183C2×D4—4828no—
184C2×D4—4821no—
185C2×D4—4821no—
186C2×D4—4821no—
187C2×D4—4821no—
188C2×D4—4821no—
189C2×D4—4821no—
190C2×D4—2411no—
191C2×D4—2412no—
192C22×C4—4821no—
193C22×C4—4821no—
194C22×C4C22×D24111yescharacteristic
195SD16—4824no—
196D8—4824no—
197M16—21no—
198M16—21no—
199M16—21no—
200M16C22⋊D24112yescomplemented
201C2×C8—21no—
202C2×C8—21no—
203C4⋊C4—2412no—
204C22⋊C4—4824no—
205C22⋊C4—4821no—
206C42—4821no—
207C42—4821no—
208C42—2412no—
209C23—22no—
210C23—22no—
211C23—22no—
212C23—44no—
213C23—9644no—
214C23—9641no—
215C23—9641no—
216C23—4822no—
217C23—4821no—
218C23C2×D96411yescharacteristic
219Q8—4821no—
220Q8—4821no—
221D4—41no—
222D4—41no—
223D4—41no—
224D4—41no—
225D4—19284no—
226D4—9641no—
227D4—9641no—
228D4—96416no—
229D4—9641no—
230D4—9641no—
231D4—4821no—
232D4—4822no—
233D4—4822no—
234D4—4821no—
235C2×C4—9641no—
236C2×C4—9641no—
237C2×C4—4822no—
238C2×C4—4821no—
239C2×C4—4824no—
240C2×C4—4822no—
241C2×C4D4×D24111yescharacteristic
242C2×C4D4×D24111yescharacteristic
243C2×C4D4×D24111yescharacteristic
244C2×C4D4×D24111yescharacteristic
245C2×C4C2×C22⋊D24111yescharacteristic
246C2×C4#1683877011yescharacteristic
247C8—22no—
248C8—41no—
249C22—22no—
250C22—44no—
251C22—42no—
252C22—44no—
253C22—82no—
254C22—19282no—
255C22—19282no—
256C22—9644no—
257C22—9641no—
258C22—9642no—
259C22—9642no—
260C22#2144061211yescharacteristic
261C22#2144061211yescharacteristic
262C22#2144061611yescharacteristic
263C4—9641no—
264C4—9642no—
265C4—4824no—
266C4#2144061011yescharacteristic
267C4#2144061511yescharacteristic
268C4#2144061511yescharacteristic
269C4#2144063811yescharacteristic
270C2—21no—
271C2—21no—
272C2—82no—
273C2—19282no—
274C2—19281no—
275C2#2950762611yescharacteristic
276C2#2950788712yes—
subgroupG/H
centerC22#21440612
commutator, cosocleC22×C4×C241C23
FrattiniC22×C4C22×D241
FittingC2×#100×C241C2
socleC22×C241#120
hypercenterC2×#100D241
hypocenterC241#2002
LCSG ▷ C22×C4×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
1. C2×#21440670C2semidirect
2. #29508284C2semidirect
3. C2×#21440638C2semidirect
4. C2×#21440568C2semidirect
5. #29507723C2semidirect
6. #29507478C2semidirect
7. C2×#100×C241C2semidirect
34. C2×Dic482D4semidirect
40. C2×D964D4semidirect
41. C2×D964D4semidirect
50. C4⋊Dic241D4semidirect
55. C4×Dic241D4semidirect
67. M16×C241D4semidirect
138. C241#2002semidirect
145. C2×#100D241semidirect
200. M16C22⋊D241semidirect

Maximal subgroups

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

subgroupindex
C2×#214406702
#295082842
C2×#214406382
C2×#214405682
#295077232
#295074782
C2×#100×C2412
#2002241