Finite Group Databasebeta

← #44508463

Subgroups — #44508463

Order 30848.

478 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 75 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#29508286C211yesmaximal, characteristic, complemented
3C2×#21440639C211yesmaximal, characteristic, complemented
4C2×#21440570C211yesmaximal, characteristic, complemented
5#29507721C211yesmaximal, characteristic, complemented
6C2×#21440558C211yesmaximal, characteristic, complemented
7#339×C241C211yesmaximal, characteristic, complemented
8C2×#16838770C2211yescharacteristic
9C22×D964—22no—
10C22×D964C2211yescharacteristic
11C22×D964C2211yescharacteristic
12#21440670—22no—
13#21440670—22no—
14C2×#16838759—21no—
15C2×D1928—21no—
16C2×#16838754C2211yescharacteristic
17#21440639—22no—
18#21440639—21no—
19#21440639—22no—
20#21440630—21no—
21#21440617—22no—
22#21440612—22no—
23#21440570—22no—
24#21440562—22no—
25#21440558—22no—
26C2×M16×C241C2211yescharacteristic
27#117×C241C2211yescharacteristic
28C2×C42×C241C2211yescharacteristic
29C23×D241—21no—
30C23×D241D412yes—
31#16838770—21no—
32#16838770—21no—
33#16838770—21no—
34#16838770—21no—
35C2×Dic482D411yescharacteristic, complemented
36C2×D964—28no—
37C2×D964—24no—
38C2×D964—21no—
39C2×D964—21no—
40C2×D964—21no—
41C2×D964—21no—
42C2×D964—21no—
43C2×D964—21no—
44C2×D964—21no—
45C2×D964—21no—
46C2×D964—21no—
47C2×D964—21no—
48C2×D964—21no—
49C2×D964—48no—
50C2×D964D411yescharacteristic, complemented
51C2×D964D412yescomplemented
52C2×C22⋊D241—21no—
53C2×C4×D241—21no—
54#16838759—24no—
55D1928—24no—
56#16838754—21no—
57#16838754—21no—
58C2×#14515349—21no—
59#16838747—24no—
60C22×C4×C241—21no—
61C22×C4×C241C2311yescharacteristic
62M16×C241—21no—
63M16×C241D412yescomplemented
64C2×C8×C241—21no—
65C4⋊C4×C241D412yescomplemented
66C22⋊C4×C241—21no—
67C42×C241—21no—
68C42×C241—21no—
69C42×C241D412yescomplemented
70C22×D241—22no—
71C22×D241—21no—
72C22×D241—22no—
73C22×D241—22no—
74C22×D241—22no—
75C22×D241—44no—
76C22×D241—44no—
77C22×D241—41no—
78C22×D241—41no—
79Dic482—21no—
80Dic482—21no—
81D964—21no—
82D964—22no—
83D964—22no—
84D964—21no—
85D964—416no—
86D964—41no—
87D964—41no—
88D964—41no—
89D964—41no—
90D964—41no—
91D964—41no—
92D964—84no—
93C22⋊D241—41no—
94C22⋊D241—41no—
95C2×Dic241—21no—
96C4×D241—41no—
97C4×D241—41no—
98#14515349—41no—
99C23×C241C2×D411yescharacteristic
100C2×C4×C241—24no—
101C2×C4×C241—22no—
102C2×C4×C241—22no—
103C2×C4×C241C2×D411yescharacteristic
104C2×C4×C241C2×D411yescharacteristic
105C2×C4×C241C2×D411yescharacteristic
106C2×C4×C241C2×D411yescharacteristic
107C2×C4×C241C2×D411yescharacteristic
108C2×C4×C241#4111yescharacteristic
109C8×C241—22no—
110C22×C241—22no—
111C22×C241#12011yescharacteristic
112C22×C241#12011yescharacteristic
113C22×C241#12111yescharacteristic
114C2×D241—44no—
115C2×D241—44no—
116C2×D241—41no—
117C2×D241—42no—
118C2×D241—42no—
119C2×D241—42no—
120C2×D241—44no—
121C2×D241—82no—
122C2×D241—82no—
123C2×D241—82no—
124C4×C241—24no—
125C4×C241—42no—
126C4×C241#12011yescharacteristic
127C4×C241#12111yescharacteristic
128C4×C241#12111yescharacteristic
129C4×C241#12711yescharacteristic
130Dic241—41no—
131C2×C241—21no—
132C2×C241—21no—
133C2×C241#39211yescharacteristic
134C2×C241#45312yes—
135D241—81no—
136D241—82no—
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×#100—2411no—
146#339D24111yescharacteristic, complemented
147C2×#41—2411no—
148C22×D4—4822no—
149C22×D4—2411no—
150C22×D4—2411no—
151AGL(1,ℤ/8)—4822no—
152AGL(1,ℤ/8)—4822no—
153C2×SD16—4821no—
154C2×D8—4821no—
155C2×M16—2411no—
156C2×M16C2×D24111yescharacteristic
157#127—4822no—
158#127—4821no—
159#127—4822no—
160#124—4821no—
161#121—4822no—
162#120—4822no—
163#117C2×D24111yescharacteristic
164C2×C42C2×D24111yescharacteristic
165#104—4822no—
166#102—4822no—
167#100—4822no—
168C24—4821no—
169C24—2412no—
170#41—4821no—
171#41—4821no—
172#41—4821no—
173#41—4821no—
174C2×Q8—2411no—
175C2×D4—9648no—
176C2×D4—4824no—
177C2×D4—4828no—
178C2×D4—4821no—
179C2×D4—4821no—
180C2×D4—4821no—
181C2×D4—4821no—
182C2×D4—4821no—
183C2×D4—4821no—
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—21no—
193C22×C4—4821no—
194C22×C4C22×D24111yescharacteristic
195SD16—4824no—
196D8—4824no—
197M16—21no—
198M16—4821no—
199M16—4821no—
200M16D96412yescomplemented
201C2×C8—21no—
202C2×C8—4821no—
203C4⋊C4D96412yescomplemented
204C22⋊C4—21no—
205C22⋊C4—4824no—
206C42—21no—
207C42—21no—
208C42D96412yescomplemented
209C23—9644no—
210C23—9644no—
211C23—9641no—
212C23—9641no—
213C23—4822no—
214C23—4822no—
215C23—4822no—
216C23—4822no—
217C23—4821no—
218C23D4×D24111yescharacteristic
219Q8—4821no—
220Q8—4821no—
221D4—19284no—
222D4—96416no—
223D4—9641no—
224D4—9641no—
225D4—9641no—
226D4—9641no—
227D4—9641no—
228D4—9641no—
229D4—9641no—
230D4—9641no—
231D4—4821no—
232D4—4822no—
233D4—4822no—
234D4—4821no—
235C2×C4—24no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—9641no—
239C2×C4—9641no—
240C2×C4—4821no—
241C2×C4D4×D24111yescharacteristic
242C2×C4D4×D24111yescharacteristic
243C2×C4C2×D96411yescharacteristic
244C2×C4C2×D96411yescharacteristic
245C2×C4C2×D96411yescharacteristic
246C2×C4#1683877111yescharacteristic
247C8—22no—
248C8—9641no—
249C22—22no—
250C22—19282no—
251C22—19282no—
252C22—19282no—
253C22—9644no—
254C22—9644no—
255C22—9641no—
256C22—9642no—
257C22—9642no—
258C22—9642no—
259C22—9644no—
260C22#2144061211yescharacteristic
261C22#2144061211yescharacteristic
262C22#2144061711yescharacteristic
263C4—24no—
264C4—42no—
265C4—9641no—
266C4#2144061211yescharacteristic
267C4#2144061711yescharacteristic
268C4#2144061711yescharacteristic
269C4#2144063911yescharacteristic
270C2—21no—
271C2—21no—
272C2—19282no—
273C2—19282no—
274C2—19281no—
275C2#2950762711yescharacteristic
276C2#2950788612yes—
subgroupG/H
centerC22#21440612
commutator, cosocleC22×C4×C241C23
FrattiniC22×C4C22×D241
Fitting#339×C241C2
socleC22×C241#120
hypercenter#339D241
hypocenterC241#2002
LCSG ▷ C22×C4×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
1. C2×#21440670C2semidirect
2. #29508286C2semidirect
3. C2×#21440639C2semidirect
4. C2×#21440570C2semidirect
5. #29507721C2semidirect
6. C2×#21440558C2semidirect
7. #339×C241C2semidirect
35. C2×Dic482D4semidirect
50. C2×D964D4semidirect
51. C2×D964D4semidirect
63. M16×C241D4semidirect
65. C4⋊C4×C241D4semidirect
69. C42×C241D4semidirect
138. C241#2002semidirect
146. #339D241semidirect
200. M16D964semidirect
203. C4⋊C4D964semidirect
208. C42D964semidirect

Maximal subgroups

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

subgroupindex
C2×#214406702
#295082862
C2×#214406392
C2×#214405702
#295077212
C2×#214405582
#339×C2412
#2002241