Finite Group Databasebeta

← #20244602

Subgroups — #20244602

Order 6016.

278 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 71 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#15689166C211yesmaximal, characteristic, complemented
2C2×#13093951C211yesmaximal, characteristic
3#15689124C211yesmaximal, characteristic
4C2×#13093943C211yesmaximal, characteristic, complemented
5#15689030C211yesmaximal, characteristic, complemented
6#15688882C211yesmaximal, characteristic, complemented
7C47×#536C211yesmaximal, characteristic
8C2×#10625329C2211yescharacteristic
9C2×#10625329C2211yescharacteristic
10C2×C4⋊Dic47C2211yescharacteristic
11C2×C4×Dic47C2211yescharacteristic
12#13093957—21no—
13#13093955—21no—
14#13093951—22no—
15#13093948—21no—
16#13093945—21no—
17#13093943—22no—
18C47⋊#95—22no—
19C2×#41×C47C2211yescharacteristic
20C22×Q8×C47C2211yescharacteristic
21C4⋊Q8×C47—21no—
22#124×C47—21no—
23#123×C47—22no—
24C22⋊Q8×C47—21no—
25C22⋊Q8×C47—21no—
26#117×C47C2211yescharacteristic
27#41×C47—21no—
28#41×C47—21no—
29#41×C47—21no—
30#41×C47—21no—
31C2×Q8×C47—21no—
32C2×Q8×C47—21no—
33C2×Q8×C47—21no—
34C2×Q8×C47—21no—
35C2×Q8×C47—21no—
36C2×Q8×C47—21no—
37C2×Q8×C47D411yescharacteristic
38C2×D4×C47—21no—
39C2×D4×C47D411yescharacteristic
40C22×C4×C47—21no—
41C22×C4×C47D412yes—
42C22×C4×C47C2311yescharacteristic
43C22×Dic47—21no—
44C22×Dic47—21no—
45C4⋊C4×C47—22no—
46C4⋊C4×C47—22no—
47C4⋊C4×C47D411yescharacteristic
48C4⋊C4×C47D411yescharacteristic
49C22⋊C4×C47—22no—
50C22⋊C4×C47—22no—
51C22⋊C4×C47—21no—
52C42×C47—21no—
53C4⋊Dic47—21no—
54C4⋊Dic47—21no—
55C4×Dic47—21no—
56C4×Dic47—21no—
57#10625329—21no—
58#10625329—21no—
59#10625329—21no—
60#10625329D412yes—
61C2×C47⋊C8—21no—
62C2×C47⋊C8—21no—
63C23×C47—21no—
64C23×C47C2×D411yescharacteristic
65Q8×C47—21no—
66Q8×C47—21no—
67Q8×C47—41no—
68Q8×C47—41no—
69Q8×C47—41no—
70Q8×C47—41no—
71D4×C47—21no—
72D4×C47—21no—
73D4×C47—41no—
74D4×C47—41no—
75C2×C4×C47—21no—
76C2×C4×C47—21no—
77C2×C4×C47—22no—
78C2×C4×C47—21no—
79C2×C4×C47—22no—
80C2×C4×C47—22no—
81C2×C4×C47—41no—
82C2×C4×C47—41no—
83C2×C4×C47C2×D411yescharacteristic
84C2×C4×C47C2×D411yescharacteristic
85C2×C4×C47C2×D411yescharacteristic
86C2×C4×C47#4111yescharacteristic
87C2×C4×C47#4111yescharacteristic
88C2×C4×C47#4111yescharacteristic
89C2×Dic47—22no—
90C2×Dic47—41no—
91C2×Dic47—41no—
92C2×Dic47—42no—
93C2×Dic47—41no—
94C47⋊C8—22no—
95C47⋊C8—41no—
96C22×C47—21no—
97C22×C47—21no—
98C22×C47—41no—
99C22×C47—41no—
100C22×C47—41no—
101C22×C47#12011yescharacteristic
102C22×C47#12111yescharacteristic
103C22×C47#12311yescharacteristic
104C4×C47—42no—
105C4×C47—41no—
106C4×C47—41no—
107C4×C47—41no—
108C4×C47#12111yescharacteristic
109C4×C47#12111yescharacteristic
110C4×C47#12311yescharacteristic
111C4×C47#12411yescharacteristic
112Dic47—42no—
113Dic47—81no—
114#2038—471nomaximal, Sylow
115C2×C47—21no—
116C2×C47—21no—
117C2×C47—81no—
118C2×C47#39411yescharacteristic
119C2×C47#45411yescharacteristic
120C2×C47#45611yescharacteristic
121#536D4711yescharacteristic
122#428—471no—
123C2×#104—471no—
124#417—471no—
125C2×#101—471no—
126#391—471no—
127#339—471no—
128C47#203811yescharacteristic, complemented, Sylow
129C2×#41C2×D4711yescharacteristic
130C22×Q8C2×D4711yescharacteristic
131C2×M16—471no—
132C2×M16—471no—
133C4⋊Q8—21no—
134#124—21no—
135#123—22no—
136C22⋊Q8—21no—
137C22⋊Q8—21no—
138#117C2×D4711yescharacteristic
139C2×C4⋊C4—471no—
140C2×C42—471no—
141#107—941no—
142#106—941no—
143#104—942no—
144#103—941no—
145#102—941no—
146#101—942no—
147#95—942no—
148#41—21no—
149#41—21no—
150#41—21no—
151#41—21no—
152C2×Q8—21no—
153C2×Q8—21no—
154C2×Q8—21no—
155C2×Q8—21no—
156C2×Q8—21no—
157C2×Q8—21no—
158C2×Q8C22⋊D4711yescharacteristic
159C2×D4—21no—
160C2×D4C22⋊D4711yescharacteristic
161C22×C4—21no—
162C22×C4—941no—
163C22×C4—941no—
164C22×C4C22⋊D4712yes—
165C22×C4C22×D4711yescharacteristic
166M16—472no—
167M16—941no—
168M16—941no—
169M16—941no—
170C2×C8—941no—
171C2×C8—941no—
172C4⋊C4—22no—
173C4⋊C4—22no—
174C4⋊C4—941no—
175C4⋊C4—941no—
176C4⋊C4C22⋊D4711yescharacteristic
177C4⋊C4C22⋊D4711yescharacteristic
178C22⋊C4—22no—
179C22⋊C4—22no—
180C22⋊C4—21no—
181C42—21no—
182C42—941no—
183C42—941no—
184C23—21no—
185C23C2×C22⋊D4711yescharacteristic
186Q8—21no—
187Q8—21no—
188Q8—41no—
189Q8—41no—
190Q8—41no—
191Q8—41no—
192D4—21no—
193D4—21no—
194D4—41no—
195D4—41no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—22no—
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—942no—
205C2×C4—1882no—
206C2×C4—1881no—
207C2×C4—1881no—
208C2×C4—1881no—
209C2×C4D4×D4711yescharacteristic
210C2×C4#1062535211yescharacteristic
211C2×C4#1062535211yescharacteristic
212C2×C4#1062535211yescharacteristic
213C2×C4C2×C22⋊D4711yescharacteristic
214C2×C4C2×C22⋊D4711yescharacteristic
215C8—942no—
216C8—1881no—
217C22—21no—
218C22—21no—
219C22—41no—
220C22—41no—
221C22—41no—
222C22#1309399311yescharacteristic
223C22#1309399611yescharacteristic
224C22#1309400511yescharacteristic
225C4—42no—
226C4—41no—
227C4—41no—
228C4—41no—
229C4—3761no—
230C4—1882no—
231C4#1309399511yescharacteristic
232C4#1309399611yescharacteristic
233C4#1309400511yescharacteristic
234C4#1309401111yescharacteristic
235C2—21no—
236C2—21no—
237C2—81no—
238C2#1568903711yescharacteristic
239C2#1568929611yescharacteristic
240C2#1568930611yescharacteristic
subgroupG/H
centerC22#13093993
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#536C2
socleC22×C47#120
hypercenter#536D47
hypocenterC47#2038
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #536

Complements

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

NH ≅ G/Ntype
1. #15689166C2semidirect
4. C2×#13093943C2semidirect
5. #15689030C2semidirect
6. #15688882C2semidirect
128. C47#2038semidirect