Finite Group Databasebeta

← #37508124

Subgroups — #37508124

Order 22912.

256 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 55 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#26039109C211yesmaximal, characteristic
2#26038731C211yesmaximal, characteristic, complemented
3#26038726C211yesmaximal, characteristic, complemented
4#26038183C211yesmaximal, characteristic, complemented
5#26038171C211yesmaximal, characteristic, complemented
6#26038168C211yesmaximal, characteristic, complemented
7#492×C179C211yesmaximal, characteristic, complemented
8C2×#15668258—21no—
9#19153109—21no—
10#19153085—22no—
11#19153084—21no—
12C4×Dic358C2211yescharacteristic
13C4×D716C2211yescharacteristic
14D4×Dic179—21no—
15#19153046—21no—
16#19153044—21no—
17C4⋊(C179⋊C8)C2211yescharacteristic
18C4⋊(C179⋊C8)C2211yescharacteristic
19#19153036—21no—
20#19153033—21no—
21C2×SD16×C179—22no—
22C4⋊Q8×C179C2211yescharacteristic
23#127×C179C2211yescharacteristic
24C4×C8×C179C2211yescharacteristic
25#15668258—42no—
26#15668258—42no—
27C2×Dic358D411yescharacteristic
28C2×D716D411yescharacteristic
29C2×C22⋊D179—22no—
30C2×C22⋊D179—22no—
31C22×Dic179—22no—
32C2×C4×D179—21no—
33C2×C179⋊C8—21no—
34C2×C179⋊C8—21no—
35C4⋊Dic179D411yescharacteristic
36C4⋊Dic179D411yescharacteristic
37Dic179⋊C4—21no—
38C22⋊Dic179—22no—
39(C2×D179)⋊C4—21no—
40C4×Dic179—21no—
41C2×Q8×C179—21no—
42C2×D4×C179—21no—
43C2×D4×C179—21no—
44C2×D4×C179D412yes—
45SD16×C179—44no—
46C2×C8×C179—21no—
47C4⋊C4×C179—21no—
48C4⋊C4×C179—21no—
49C42×C179C2311yescharacteristic
50C22×D179—21no—
51Dic358—21no—
52Dic358SD1612yescomplemented
53D716—21no—
54D716—21no—
55C22⋊D179—44no—
56C22⋊D179—82no—
57C2×Dic179—21no—
58C2×Dic179—21no—
59C2×Dic179—21no—
60C2×Dic179—44no—
61C4×D179—41no—
62C4×D179—41no—
63C179⋊C8—41no—
64C179⋊C8—41no—
65C23×C179—22no—
66Q8×C179—42no—
67D4×C179—42no—
68D4×C179—41no—
69D4×C179—41no—
70D4×C179—41no—
71D4×C179—41no—
72C2×C4×C179—41no—
73C2×C4×C179C2×D411yescharacteristic
74C2×C4×C179C2×D411yescharacteristic
75C2×C4×C179C2×D411yescharacteristic
76C8×C179—22no—
77C22×C179—42no—
78C22×C179—42no—
79C22×C179—42no—
80C22×C179#12011yescharacteristic
81C2×D179—41no—
82C2×D179—41no—
83C2×D179—41no—
84C4×C179—21no—
85C4×C179—81no—
86C4×C179C2×SD1611yescharacteristic
87C4×C179#13511yescharacteristic
88C4×C179AGL(1,ℤ/8)11yescharacteristic
89C4×C179#13711yescharacteristic
90Dic179—22no—
91Dic179—41no—
92Dic179—41no—
93C2×C179—82no—
94C2×C179#45011yescharacteristic
95C2×C179#45211yescharacteristic
96C2×C179#45311yescharacteristic
97D179—81no—
98C179#163111yescharacteristic, complemented, Sylow
99#1631—1791nomaximal, Sylow
100#550—1791no—
101#492D17911yescharacteristic, complemented
102#477—1791no—
103#476—1791no—
104#331—1791no—
105Q8⋊C8—1791no—
106D4⋊C8—1791no—
107C2×#41—3581no—
108C2×SD16—22no—
109C4⋊Q8C2×D17911yescharacteristic
110#127—3581no—
111#127C2×D17911yescharacteristic
112#121—3582no—
113#121—3581no—
114C4×Q8—1791no—
115C4×D4—3581no—
116C4×D4—1791no—
117#107—3581no—
118#106—3581no—
119C4⋊C8—1791no—
120C4⋊C8—1791no—
121#103—3581no—
122#102—3581no—
123C4×C8C2×D17911yescharacteristic
124#41—7162no—
125#41—7162no—
126C2×Q8—21no—
127C2×Q8—1791no—
128C2×D4—21no—
129C2×D4—21no—
130C2×D4—3582no—
131C2×D4—3582no—
132C2×D4—1791no—
133C2×D4C22⋊D17912yes—
134C22×C4—3582no—
135C22×C4—3581no—
136SD16—44no—
137C2×C8—21no—
138C2×C8—3581no—
139C2×C8—3581no—
140C4⋊C4—21no—
141C4⋊C4—21no—
142C4⋊C4—3581no—
143C4⋊C4—1791no—
144C4⋊C4—1791no—
145C22⋊C4—3582no—
146C22⋊C4—3581no—
147C42—3581no—
148C42C22×D17911yescharacteristic
149C23—22no—
150C23—3581no—
151Q8—42no—
152Q8—3581no—
153Q8—1792no—
154D4—42no—
155D4—41no—
156D4—41no—
157D4—41no—
158D4—41no—
159D4—3581no—
160D4—3581no—
161D4—14322no—
162D4—7164no—
163C2×C4—41no—
164C2×C4—3581no—
165C2×C4—3581no—
166C2×C4—3581no—
167C2×C4—7164no—
168C2×C4—7161no—
169C2×C4—7161no—
170C2×C4D4×D17911yescharacteristic
171C2×C4D4×D17911yescharacteristic
172C2×C4C2×C22⋊D17911yescharacteristic
173C8—22no—
174C8—7161no—
175C8—7161no—
176C22—42no—
177C22—42no—
178C22—42no—
179C22—7161no—
180C22—7161no—
181C22—7161no—
182C22#1915308111yescharacteristic
183C4—21no—
184C4—81no—
185C4—3582no—
186C4—7161no—
187C4—7161no—
188C4SD16×D17911yescharacteristic
189C4#1915313411yescharacteristic
190C4#1915314011yescharacteristic
191C4#1915314211yescharacteristic
192C2—82no—
193C2—14321no—
194C2#2603858811yescharacteristic
195C2#2603859811yescharacteristic
196C2#2603860611yescharacteristic
subgroupG/H
centerC22#19153081
commutator, cosocleC42×C179C23
FrattiniC42C22×D179
Fitting#492×C179C2
socleC22×C179#120
prime radical#26039109C2
hypercenter#492D179
hypocenterC179#1631
LCSG ▷ C42×C179 ▷ C22×C179 ▷ C179
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
2. #26038731C2semidirect
3. #26038726C2semidirect
4. #26038183C2semidirect
5. #26038171C2semidirect
6. #26038168C2semidirect
7. #492×C179C2semidirect
52. Dic358SD16semidirect
98. C179#1631semidirect
101. #492D179semidirect

Maximal subgroups

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

subgroupindex
#260391092
#260387312
#260387262
#260381832
#260381712
#260381682
#492×C1792
#1631179