Finite Group Databasebeta

← #2027×C179 #37505249

Subgroups — #2027×C179 #37505249

Order 22912.

282 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 84 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#544×C179C211yesmaximal, characteristic, complemented
2#418×C179C212yesmaximal
3#390×C179C211yesmaximal, characteristic
4#343×C179C211yesmaximal, characteristic, complemented
5#339×C179C212yesmaximal, complemented
6C22×D4×C179C2211yescharacteristic
7C2×M16×C179C2212yes—
8C4⋊Q8×C179—22no—
9#125×C179—22no—
10C22⋊Q8×C179—22no—
11#117×C179C2212yes—
12C2×C4⋊C4×C179C2211yescharacteristic
13C2×C22⋊C4×C179—22no—
14C2×C42×C179C2211yescharacteristic
15#102×C179—22no—
16#102×C179—22no—
17C24×C179—21no—
18C2×Q8×C179—22no—
19C2×D4×C179—22no—
20C2×D4×C179—22no—
21C2×D4×C179—21no—
22C2×D4×C179Q812yescomplemented
23C22×C4×C179—21no—
24C22×C4×C179D412yes—
25C22×C4×C179C2311yescharacteristic
26M16×C179—22no—
27M16×C179—22no—
28C2×C8×C179—22no—
29C4⋊C4×C179—22no—
30C4⋊C4×C179—24no—
31C4⋊C4×C179—22no—
32C4⋊C4×C179D412yes—
33C4⋊C4×C179D412yes—
34C22⋊C4×C179—22no—
35C22⋊C4×C179—44no—
36C42×C179—22no—
37C42×C179—22no—
38C23×C179—22no—
39C23×C179—42no—
40C23×C179—42no—
41C23×C179—41no—
42C23×C179—41no—
43C23×C179C2×D411yescharacteristic
44Q8×C179—82no—
45D4×C179—24no—
46D4×C179—42no—
47C2×C4×C179—22no—
48C2×C4×C179—22no—
49C2×C4×C179—22no—
50C2×C4×C179—22no—
51C2×C4×C179—41no—
52C2×C4×C179—41no—
53C2×C4×C179—42no—
54C2×C4×C179C2×D412yes—
55C2×C4×C179C2×Q811yescharacteristic
56C2×C4×C179#4112yes—
57C2×C4×C179#4111yescharacteristic
58C8×C179—42no—
59C22×C179—21no—
60C22×C179—21no—
61C22×C179—44no—
62C22×C179—42no—
63C22×C179—82no—
64C22×C179—81no—
65C22×C179—81no—
66C22×C179#12011yescharacteristic
67C22×C179C22⋊Q811yescharacteristic
68C22×C179#12411yescharacteristic
69C4×C179—42no—
70C4×C179—42no—
71C4×C179—42no—
72C4×C179—42no—
73C4×C179C22⋊Q812yes—
74C4×C179#12412yes—
75C2×C179—21no—
76C2×C179—21no—
77C2×C179—82no—
78C2×C179#39311yescharacteristic
79C2×C179#45311yescharacteristic
80C2×C179#45411yescharacteristic
81C179#202711yescharacteristic, direct product factor, Sylow
82#2027C17911yesmaximal, characteristic, direct product factor, Sylow
83#544C2×C17911yescharacteristic, complemented
84#418C2×C17912yes—
85#390C2×C17911yescharacteristic
86#343C2×C17911yescharacteristic, complemented
87#339C2×C17912yescomplemented
88C22×D4C22×C17911yescharacteristic
89C2×M16C22×C17912yes—
90C4⋊Q8—22no—
91#125—22no—
92C22⋊Q8—22no—
93#117C22×C17912yes—
94C2×C4⋊C4C22×C17911yescharacteristic
95C2×C22⋊C4—22no—
96C2×C42C22×C17911yescharacteristic
97#102—22no—
98#102—22no—
99C24—21no—
100C2×Q8—22no—
101C2×D4—22no—
102C2×D4—22no—
103C2×D4—21no—
104C2×D4Q8×C17912yescomplemented
105C22×C4—21no—
106C22×C4D4×C17912yes—
107C22×C4C23×C17911yescharacteristic
108M16—22no—
109M16—22no—
110C2×C8—22no—
111C4⋊C4—22no—
112C4⋊C4—24no—
113C4⋊C4—22no—
114C4⋊C4D4×C17912yes—
115C4⋊C4D4×C17912yes—
116C22⋊C4—22no—
117C22⋊C4—44no—
118C42—22no—
119C42—22no—
120C23—22no—
121C23—42no—
122C23—42no—
123C23—41no—
124C23—41no—
125C23C2×D4×C17911yescharacteristic
126Q8—82no—
127D4—24no—
128D4—42no—
129C2×C4—22no—
130C2×C4—22no—
131C2×C4—22no—
132C2×C4—22no—
133C2×C4—41no—
134C2×C4—41no—
135C2×C4—42no—
136C2×C4C2×D4×C17912yes—
137C2×C4C2×Q8×C17911yescharacteristic
138C2×C4#41×C17912yes—
139C2×C4#41×C17911yescharacteristic
140C8—42no—
141C22—21no—
142C22—21no—
143C22—44no—
144C22—42no—
145C22—82no—
146C22—81no—
147C22—81no—
148C22#120×C17911yescharacteristic
149C22C22⋊Q8×C17911yescharacteristic
150C22#124×C17911yescharacteristic
151C4—42no—
152C4—42no—
153C4—42no—
154C4—42no—
155C4C22⋊Q8×C17912yes—
156C4#124×C17912yes—
157C2—21no—
158C2—21no—
159C2—82no—
160C2#393×C17911yescharacteristic
161C2#453×C17911yescharacteristic
162C2#454×C17911yescharacteristic
subgroupG/H
center, socleC22×C179#120
commutator, Frattini, cosocleC22×C4C23×C179
prime radicalC22×D4×C179C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C179 ◁ C22×C4×C179 ◁ G

Complements

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

NH ≅ G/Ntype
1. #544×C179C2semidirect
4. #343×C179C2semidirect
5. #339×C179C2semidirect
22. C2×D4×C179Q8semidirect
81. C179#2027direct (N × H)
82. #2027C179direct (N × H)
83. #544C2×C179semidirect
86. #343C2×C179semidirect
87. #339C2×C179semidirect
104. C2×D4Q8×C179semidirect

Maximal subgroups

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

subgroupindex
#544×C1792
#418×C1792
#390×C1792
#343×C1792
#339×C1792
#2027179