Finite Group Databasebeta

← #37560168

Subgroups — #37560168

Order 23872.

220 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 91 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#26045782C211yesmaximal, characteristic, complemented
2#26045781C211yesmaximal, characteristic, complemented
3#26045778C211yesmaximal, characteristic, complemented
4#26045777C211yesmaximal, characteristic, complemented
5#26045777C211yesmaximal, characteristic, complemented
6#26045775C211yesmaximal, characteristic, complemented
7#26045774C211yesmaximal, characteristic, complemented
8#26045772C211yesmaximal, characteristic, complemented
9#26045770C211yesmaximal, characteristic, complemented
10#26045768C211yesmaximal, characteristic, complemented
11#26045767C211yesmaximal, characteristic, complemented
12#26045766C211yesmaximal, characteristic, complemented
13#26045765C211yesmaximal, characteristic, complemented
14#26045765C211yesmaximal, characteristic, complemented
15C22⋊Q8×C373C211yesmaximal, characteristic, complemented
16C2×Dic746C2211yescharacteristic
17C2×D1492C2211yescharacteristic
18C2×D1492C2211yescharacteristic
19C2×D1492C2211yescharacteristic
20C2×C22⋊D373C2211yescharacteristic
21C2×C22⋊D373C2211yescharacteristic
22C2×C22⋊D373C2211yescharacteristic
23C2×C4×D373C2211yescharacteristic
24C2×C4×D373C2211yescharacteristic
25C2×C4×D373C2211yescharacteristic
26C4⋊Dic373C2211yescharacteristic
27C4⋊Dic373C2211yescharacteristic
28#20238589C2211yescharacteristic
29#20238589C2211yescharacteristic
30#20238589C2211yescharacteristic
31#20238589C2211yescharacteristic
32#20238589C2211yescharacteristic
33C22⋊Dic373C2211yescharacteristic
34#20238587C2211yescharacteristic
35#20238587C2211yescharacteristic
36#20238587C2211yescharacteristic
37#20238587C2211yescharacteristic
38#20238587C2211yescharacteristic
39#20238587C2211yescharacteristic
40#20238587C2211yescharacteristic
41#20238587C2211yescharacteristic
42#20238587C2211yescharacteristic
43C4×Dic373C2211yescharacteristic
44C2×Q8×C373C2211yescharacteristic
45C22×C4×C373C2211yescharacteristic
46C4⋊C4×C373C2211yescharacteristic
47C4⋊C4×C373C2211yescharacteristic
48C4⋊C4×C373C2211yescharacteristic
49C22⋊C4×C373C2211yescharacteristic
50C22⋊C4×C373C2211yescharacteristic
51C22×D373C2311yescharacteristic
52C22×D373C2311yescharacteristic
53C22×D373C2311yescharacteristic
54Dic746—41no—
55D1492—41no—
56D1492—41no—
57D1492—41no—
58C22⋊D373—41no—
59C22⋊D373—41no—
60C22⋊D373—41no—
61C2×Dic373C2311yescharacteristic
62C2×Dic373C2311yescharacteristic
63C2×Dic373C2311yescharacteristic
64C2×Dic373C2311yescharacteristic
65C2×Dic373C2311yescharacteristic
66C4×D373—41no—
67C4×D373—41no—
68C4×D373—41no—
69C23×C373C2311yescharacteristic
70Q8×C373—41no—
71C2×C4×C373—41no—
72C2×C4×C373C2311yescharacteristic
73C2×C4×C373C2311yescharacteristic
74C2×C4×C373C2311yescharacteristic
75C2×C4×C373C2311yescharacteristic
76C2×C4×C373C2311yescharacteristic
77C2×C4×C373C2311yescharacteristic
78C22×C373—21no—
79C22×C373—21no—
80C22×C373—21no—
81C22×C373C2411yescharacteristic
82C2×D373—21no—
83C2×D373—21no—
84C2×D373—21no—
85C2×D373—21no—
86C2×D373—21no—
87C2×D373—21no—
88C2×D373—21no—
89C2×D373—21no—
90C2×D373—21no—
91C4×C373—21no—
92C4×C373—21no—
93C4×C373—21no—
94C4×C373—21no—
95C4×C373—21no—
96C4×C373—21no—
97Dic373—21no—
98Dic373—21no—
99Dic373—21no—
100Dic373—21no—
101Dic373—21no—
102C2×C373—41no—
103C2×C373H(5,𝔽2)11yescharacteristic
104C2×C373H(5,𝔽2)11yescharacteristic
105C2×C3732−1+411yescharacteristic
106D373—41no—
107D373—41no—
108D373—41no—
109C373#56211yescharacteristic, complemented, Sylow
110#562—3731nomaximal, Sylow
111#125—3731no—
112#124—3731no—
113#124—3731no—
114#123—3731no—
115#123—3731no—
116#123—3731no—
117#123—3731no—
118C22⋊Q8—3731no—
119C22⋊Q8—3731no—
120C22⋊Q8—3731no—
121C22⋊Q8D37311yescharacteristic, complemented
122#121—3731no—
123#121—3731no—
124#121—3731no—
125#121—3731no—
126C2×Q8—3731no—
127C2×Q8C2×D37311yescharacteristic
128C2×D4—3731no—
129C2×D4—3731no—
130C2×D4—3731no—
131C2×D4—3731no—
132C2×D4—3731no—
133C2×D4—3731no—
134C22×C4—3731no—
135C22×C4—3731no—
136C22×C4—3731no—
137C22×C4C2×D37311yescharacteristic
138C4⋊C4—3731no—
139C4⋊C4—3731no—
140C4⋊C4—3731no—
141C4⋊C4—3731no—
142C4⋊C4—3731no—
143C4⋊C4—3731no—
144C4⋊C4—3731no—
145C4⋊C4C2×D37311yescharacteristic
146C4⋊C4C2×D37311yescharacteristic
147C4⋊C4C2×D37311yescharacteristic
148C22⋊C4—3731no—
149C22⋊C4—3731no—
150C22⋊C4—3731no—
151C22⋊C4—3731no—
152C22⋊C4—3731no—
153C22⋊C4—3731no—
154C22⋊C4—3731no—
155C22⋊C4—3731no—
156C22⋊C4—3731no—
157C22⋊C4—3731no—
158C22⋊C4C2×D37311yescharacteristic
159C22⋊C4C2×D37311yescharacteristic
160C42—3731no—
161C23—3731no—
162C23—3731no—
163C23—3731no—
164C23C22×D37311yescharacteristic
165Q8—41no—
166Q8—14921no—
167D4—14921no—
168D4—14921no—
169D4—14921no—
170D4—14921no—
171D4—14921no—
172D4—14921no—
173C2×C4—41no—
174C2×C4—3731no—
175C2×C4—3731no—
176C2×C4—3731no—
177C2×C4—3731no—
178C2×C4—3731no—
179C2×C4—14921no—
180C2×C4—14921no—
181C2×C4—14921no—
182C2×C4C22×D37311yescharacteristic
183C2×C4C22×D37311yescharacteristic
184C2×C4C22×D37311yescharacteristic
185C2×C4C22×D37311yescharacteristic
186C2×C4C22×D37311yescharacteristic
187C2×C4C22×D37311yescharacteristic
188C22—21no—
189C22—21no—
190C22—21no—
191C22—7461no—
192C22—7461no—
193C22—7461no—
194C22—7461no—
195C22—7461no—
196C22—7461no—
197C22—7461no—
198C22—7461no—
199C22—7461no—
200C22C23×D37311yescharacteristic
201C4—21no—
202C4—21no—
203C4—21no—
204C4—21no—
205C4—21no—
206C4—21no—
207C4—7461no—
208C4—7461no—
209C4—7461no—
210C4—7461no—
211C4—7461no—
212C2—41no—
213C2—14921no—
214C2—14921no—
215C2—14921no—
216C2#2604583711yescharacteristic
217C2#2604583811yescharacteristic
218C2#2604584011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D373
commutator, socle, cosocleC22×C373C24
FittingC22⋊Q8×C373C2
hypercenterC22⋊Q8D373
hypocenterC373#562
LCSG ▷ C22×C373 ▷ C373
UCSC1 ◁ C22 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. #26045782C2semidirect
2. #26045781C2semidirect
3. #26045778C2semidirect
4. #26045777C2semidirect
5. #26045777C2semidirect
6. #26045775C2semidirect
7. #26045774C2semidirect
8. #26045772C2semidirect
9. #26045770C2semidirect
10. #26045768C2semidirect
11. #26045767C2semidirect
12. #26045766C2semidirect
13. #26045765C2semidirect
14. #26045765C2semidirect
15. C22⋊Q8×C373C2semidirect
109. C373#562semidirect
121. C22⋊Q8D373semidirect

Maximal subgroups

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

subgroupindex
#260457822
#260457812
#260457782
#260457772
#260457752
#260457742
#260457722
#260457702
#260457682
#260457672
#260457662
#260457652
C22⋊Q8×C3732
#562373