Finite Group Databasebeta

← #37509431

Subgroups — #37509431

Order 22912.

360 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 105 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
1C22×#15668243C211yesmaximal, characteristic
2C2×#19153092C211yesmaximal, characteristic
3C2×#19153036C212yesmaximal, complemented
4#26038201C212yesmaximal, complemented
5#380×C179C211yesmaximal, characteristic
6C22×Dic358C2211yescharacteristic
7C2×#15668243—24no—
8C2×#15668243—22no—
9C22×C179⋊C8C2212yes—
10#19153092—22no—
11#19153092C414yescomplemented
12C2×C4⋊Dic179C2211yescharacteristic
13C2×Dic179⋊C4—21no—
14C2×C22⋊Dic179—21no—
15#19153036—24no—
16C23×C4×C179C2211yescharacteristic
17C2×C4⋊C4×C179C2212yes—
18C2×C22⋊C4×C179—21no—
19#95×C179—21no—
20C2×Dic358—21no—
21C2×Dic358—22no—
22C2×Dic358—22no—
23C2×Dic358C2×C412yes—
24C22×Dic179—21no—
25C22×Dic179—21no—
26#15668243—28no—
27C2×C179⋊C8—22no—
28C2×C179⋊C8—22no—
29C2×C179⋊C8D414yes—
30C4⋊Dic179—21no—
31C4⋊Dic179C2×C412yes—
32Dic179⋊C4—24no—
33C22⋊Dic179—24no—
34C24×C179D411yescharacteristic
35C22×C4×C179—22no—
36C22×C4×C179—22no—
37C22×C4×C179—22no—
38C22×C4×C179C2×C412yes—
39C22×C4×C179D411yescharacteristic
40C22×C4×C179D412yes—
41C22×C4×C179C2311yescharacteristic
42C4⋊C4×C179—22no—
43C4⋊C4×C179—22no—
44C22⋊C4×C179—42no—
45Dic358—24no—
46Dic358—41no—
47Dic358—41no—
48C2×Dic179—22no—
49C2×Dic179—22no—
50C2×Dic179—42no—
51C2×Dic179—41no—
52C2×Dic179—41no—
53C179⋊C8—24no—
54C23×C179—22no—
55C23×C179—21no—
56C23×C179—22no—
57C23×C179—21no—
58C23×C179C22⋊C412yes—
59C23×C179C2×D411yescharacteristic
60C2×C4×C179—22no—
61C2×C4×C179—24no—
62C2×C4×C179—22no—
63C2×C4×C179—22no—
64C2×C4×C179—42no—
65C2×C4×C179—42no—
66C2×C4×C179—42no—
67C2×C4×C179C22⋊C412yes—
68C2×C4×C179C22×C411yescharacteristic
69C2×C4×C179C2×D412yes—
70C2×C4×C179C2×D411yescharacteristic
71C2×C4×C179#4112yes—
72C22×C179—22no—
73C22×C179—22no—
74C22×C179—22no—
75C22×C179—42no—
76C22×C179—42no—
77C22×C179C2×C22⋊C411yescharacteristic
78C22×C179#12112yes—
79C22×C179AGL(1,ℤ/8)11yescharacteristic
80C22×C179#13712yes—
81C22×C179#13711yescharacteristic
82C4×C179—22no—
83C4×C179—82no—
84C4×C179C4×D412yes—
85C4×C179#12011yescharacteristic
86C4×C179#12311yescharacteristic
87Dic179—42no—
88Dic179—42no—
89C2×C179—42no—
90C2×C179#38611yescharacteristic
91C2×C179#41711yescharacteristic
92C2×C179#41911yescharacteristic
93C2×C179#46812yes—
94C2×C179#47012yes—
95C179#189411yescharacteristic, complemented, Sylow
96#1894—1791nomaximal, Sylow
97C22×M16—1791no—
98C2×C22⋊Q8—1791no—
99C2×#103—1792no—
100#380D17911yescharacteristic
101#340—1792no—
102C22×Q8—1791no—
103C23×C4C2×D17911yescharacteristic
104C2×M16—3582no—
105C2×M16—3584no—
106C22×C8—1792no—
107C22⋊Q8—3582no—
108C22⋊Q8—1794no—
109C2×C4⋊C4—3581no—
110C2×C4⋊C4—1791no—
111C2×C4⋊C4C2×D17912yes—
112C2×C22⋊C4—21no—
113C2×C22⋊C4—3581no—
114#103—3584no—
115#95—21no—
116C24C22⋊D17911yescharacteristic
117C2×Q8—3581no—
118C2×Q8—3582no—
119C2×Q8—3582no—
120C2×Q8—1792no—
121C22×C4—22no—
122C22×C4—22no—
123C22×C4—22no—
124C22×C4—3581no—
125C22×C4—3581no—
126C22×C4C4×D17912yes—
127C22×C4C22⋊D17911yescharacteristic
128C22×C4D71612yes—
129C22×C4C22×D17911yescharacteristic
130M16—3588no—
131C2×C8—3582no—
132C2×C8—3582no—
133C2×C8—1794no—
134C4⋊C4—22no—
135C4⋊C4—22no—
136C4⋊C4—3584no—
137C4⋊C4—3581no—
138C4⋊C4—1792no—
139C22⋊C4—42no—
140C22⋊C4—3584no—
141C23—22no—
142C23—21no—
143C23—22no—
144C23—21no—
145C23(C2×D179)⋊C412yes—
146C23C2×C22⋊D17911yescharacteristic
147Q8—3584no—
148Q8—7161no—
149Q8—7161no—
150C2×C4—22no—
151C2×C4—24no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—42no—
155C2×C4—42no—
156C2×C4—42no—
157C2×C4—3582no—
158C2×C4—3582no—
159C2×C4—7162no—
160C2×C4—7161no—
161C2×C4—7161no—
162C2×C4(C2×D179)⋊C412yes—
163C2×C4C2×C4×D17911yescharacteristic
164C2×C4D4×D17912yes—
165C2×C4C2×D71611yescharacteristic
166C2×C4#1566825812yes—
167C8—3584no—
168C22—22no—
169C22—22no—
170C22—22no—
171C22—42no—
172C22—42no—
173C22C2×(C2×D179)⋊C411yescharacteristic
174C22#1915308512yes—
175C22#1915313911yescharacteristic
176C22#1915314312yes—
177C22#1915314411yescharacteristic
178C4—22no—
179C4—82no—
180C4—7162no—
181C4—7162no—
182C4(C22⋊D179)⋊C412yes—
183C4#1915308311yescharacteristic
184C4#1915309711yescharacteristic
185C2—42no—
186C2#2603831611yescharacteristic
187C2#2603843811yescharacteristic
188C2#2603844711yescharacteristic
189C2#2603868312yes—
190C2#2603869512yes—
subgroupG/H
centerC23C2×C22⋊D179
commutatorC2×C4×C179C22×C4
FrattiniC22×C4C22×D179
Fitting#380×C179C2
socleC23×C179C2×D4
prime radicalC24×C179D4
cosocleC22×C4×C179C23
hypercenter#380D179
hypocenterC179#1894
LCSG ▷ C2×C4×C179 ▷ C2×C179 ▷ C179
UCSC1 ◁ C23 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
3. C2×#19153036C2semidirect
4. #26038201C2semidirect
11. #19153092C4semidirect
95. C179#1894semidirect

Maximal subgroups

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

subgroupindex
C22×#156682432
C2×#191530922
C2×#191530362
#260382012
#380×C1792
#1894179