Finite Group Databasebeta

← #37510171

Subgroups — #37510171

Order 22912.

244 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 63 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#26038992C211yesmaximal, characteristic, complemented
2#26038457C211yesmaximal, characteristic
3C2×#19153039C211yesmaximal, characteristic
4#26038412C211yesmaximal, characteristic
5#26038211C211yesmaximal, characteristic, complemented
6#26038198C211yesmaximal, characteristic, complemented
7H(3,ℤ/4)×C179C211yesmaximal, characteristic, complemented
8C2×#15668259C2211yescharacteristic
9C2×#15668243C2211yescharacteristic
10#19153112—21no—
11#19153104—21no—
12#19153090—22no—
13C4×Dic358—22no—
14#19153072C2211yescharacteristic
15C2×C4×Dic179C2211yescharacteristic
16#19153041—22no—
17#19153039—21no—
18#19153039—21no—
19#19153027—22no—
20C2×M16×C179C2211yescharacteristic
21#117×C179C2211yescharacteristic
22#117×C179C2211yescharacteristic
23#15668259—21no—
24#15668259—21no—
25#15668259—21no—
26#15668259—21no—
27C2×Dic358—22no—
28C2×Dic358Q811yescharacteristic, complemented
29C2×D716Q811yescharacteristic, complemented
30C2×C22⋊D179—21no—
31C22×Dic179—21no—
32C2×C4×D179—21no—
33#15668243—21no—
34#15668243—21no—
35C2×C179⋊C8—21no—
36C4⋊Dic179—22no—
37C4⋊Dic179—21no—
38Dic179⋊C4—22no—
39Dic179⋊C4—22no—
40C22⋊Dic179D412yes—
41C4×Dic179—21no—
42C4×Dic179—21no—
43C4×Dic179D411yescharacteristic
44C4×Dic179D411yescharacteristic
45C22×C4×C179C2311yescharacteristic
46M16×C179—21no—
47M16×C179—21no—
48C2×C8×C179—21no—
49C4⋊C4×C179—21no—
50C4⋊C4×C179—21no—
51C22⋊C4×C179—21no—
52C22⋊C4×C179—21no—
53C42×C179—21no—
54C42×C179D412yes—
55C22×D179—21no—
56Dic358—21no—
57Dic358—21no—
58Dic358—44no—
59D716—21no—
60D716—21no—
61C22⋊D179—41no—
62C22⋊D179—41no—
63C2×Dic179—21no—
64C2×Dic179—21no—
65C2×Dic179—22no—
66C2×Dic179—21no—
67C2×Dic179—42no—
68C4×D179—41no—
69C4×D179—41no—
70C179⋊C8—41no—
71C23×C179C2×D411yescharacteristic
72C2×C4×C179—22no—
73C2×C4×C179—41no—
74C2×C4×C179C2×D411yescharacteristic
75C2×C4×C179C2×D411yescharacteristic
76C2×C4×C179C2×Q811yescharacteristic
77C2×C4×C179#4111yescharacteristic
78C2×C4×C179#4111yescharacteristic
79C2×C4×C179#4111yescharacteristic
80C8×C179—41no—
81C22×C179—41no—
82C22×C179#12011yescharacteristic
83C22×C179C22⋊Q811yescharacteristic
84C22×C179#12411yescharacteristic
85C2×D179—41no—
86C2×D179—81no—
87C4×C179—42no—
88C4×C179—81no—
89C4×C179C22⋊Q811yescharacteristic
90C4×C179C22⋊Q811yescharacteristic
91C4×C179#12411yescharacteristic
92C4×C179#12411yescharacteristic
93Dic179—22no—
94Dic179—41no—
95Dic179—42no—
96Dic179—41no—
97C2×C179—21no—
98C2×C179—21no—
99C2×C179—21no—
100C2×C179#39311yescharacteristic
101D179—81no—
102C179#203111yescharacteristic, complemented, Sylow
103#2031—1791nomaximal, Sylow
104#533—1791no—
105#421—1791no—
106C2×#104—1791no—
107#410—1791no—
108#344—1791no—
109#339—1791no—
110H(3,ℤ/4)D17911yescharacteristic, complemented
111C2×#41—1791no—
112C2×M16—1791no—
113C2×M16C2×D17911yescharacteristic
114C4⋊Q8—3581no—
115#125—3581no—
116C22⋊Q8—3582no—
117C4×Q8—3582no—
118#117—1791no—
119#117C2×D17911yescharacteristic
120#117C2×D17911yescharacteristic
121C2×C42—1791no—
122#104—3581no—
123#104—3581no—
124#104—3582no—
125#99—3582no—
126#41—3581no—
127#41—3581no—
128#41—3581no—
129#41—3581no—
130C2×Q8—3582no—
131C2×Q8—1791no—
132C2×D4—3581no—
133C2×D4—1791no—
134C22×C4—3581no—
135C22×C4—3581no—
136C22×C4C22×D17911yescharacteristic
137M16—21no—
138M16—21no—
139M16—3581no—
140M16—3581no—
141C2×C8—21no—
142C2×C8—3581no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—3582no—
146C4⋊C4—3582no—
147C4⋊C4—3582no—
148C4⋊C4—3581no—
149C22⋊C4—21no—
150C22⋊C4—21no—
151C22⋊C4—1792no—
152C42—21no—
153C42—3581no—
154C42—3581no—
155C42—1791no—
156C42—1791no—
157C42D71612yes—
158C23—3581no—
159C23D4×D17911yescharacteristic
160Q8—3581no—
161Q8—3581no—
162Q8—7164no—
163D4—3581no—
164D4—3581no—
165D4—7161no—
166D4—7161no—
167C2×C4—22no—
168C2×C4—41no—
169C2×C4—3581no—
170C2×C4—3581no—
171C2×C4—3582no—
172C2×C4—3581no—
173C2×C4—7162no—
174C2×C4—7161no—
175C2×C4—7161no—
176C2×C4D4×D17911yescharacteristic
177C2×C4C2×D71611yescharacteristic
178C2×C4Q8×D17911yescharacteristic
179C2×C4#1566825811yescharacteristic
180C2×C4#1566825911yescharacteristic
181C2×C4#1566825911yescharacteristic
182C8—41no—
183C8—7161no—
184C22—41no—
185C22—14321no—
186C22—7161no—
187C22#1915308311yescharacteristic
188C22#1915309111yescharacteristic
189C22#1915309911yescharacteristic
190C4—42no—
191C4—81no—
192C4—3582no—
193C4—7161no—
194C4—7162no—
195C4—7161no—
196C4#1915309111yescharacteristic
197C4#1915309311yescharacteristic
198C4#1915309911yescharacteristic
199C4#1915310111yescharacteristic
200C2—21no—
201C2—21no—
202C2—21no—
203C2—14321no—
204C2#2603835211yescharacteristic
subgroupG/H
centerC4#19153101
commutator, cosocleC22×C4×C179C23
FrattiniC22×C4C22×D179
FittingH(3,ℤ/4)×C179C2
socleC2×C179#393
prime radicalC2×#15668259C22
hypercenterH(3,ℤ/4)D179
hypocenterC179#2031
LCSG ▷ C22×C4×C179 ▷ C2×C179 ▷ C179
UCSC1 ◁ C4 ◁ C22×C4 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
1. #26038992C2semidirect
5. #26038211C2semidirect
6. #26038198C2semidirect
7. H(3,ℤ/4)×C179C2semidirect
28. C2×Dic358Q8semidirect
29. C2×D716Q8semidirect
102. C179#2031semidirect
110. H(3,ℤ/4)D179semidirect

Maximal subgroups

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

subgroupindex
#260389922
#260384572
C2×#191530392
#260384122
#260382112
#260381982
H(3,ℤ/4)×C1792
#2031179