Finite Group Databasebeta

← #34046359

Subgroups — #34046359

Order 19072.

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

normal subgroups only

This group has 286 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#23750193C211yesmaximal, characteristic
2#99×D149C212yesmaximal, complemented
3#23749420C211yesmaximal, characteristic, complemented
4#23749417C212yesmaximal, complemented
5#354×C149C211yesmaximal, characteristic, complemented
6C2×#14558737C411yescharacteristic, complemented
7C2×D4×D149C2211yescharacteristic
8#18011908C411yescharacteristic, complemented
9#18011907C2211yescharacteristic
10#18011900C411yescharacteristic, complemented
11#18011884—22no—
12#18011881—22no—
13#18011868C411yescharacteristic, complemented
14C22⋊C4×D149—22no—
15#18011826C2212yes—
16#18011825—22no—
17#124×C149C2211yescharacteristic
18#99×C149C2212yes—
19C23×D149D412yes—
20#14558737—42no—
21C2×D596—21no—
22C2×D596—22no—
23C2×D596C2×C411yescharacteristic
24C2×D596C2×C411yescharacteristic, complemented
25C2×C22⋊D149—22no—
26C2×C22⋊D149D412yes—
27D4×D149—42no—
28C2×C4×D149—21no—
29C2×C4×D149—42no—
30C2×C4×D149C2×C411yescharacteristic
31#14558715—21no—
32C22⋊Dic149—22no—
33#14558713—21no—
34#14558713—22no—
35#14558713—42no—
36C4×Dic149C2×C411yescharacteristic, complemented
37C2×Q8×C149C2×C411yescharacteristic, complemented
38C2×D4×C149C2311yescharacteristic
39C22⋊C4×C149—22no—
40C22⋊C4×C149—22no—
41C42×C149C2×C411yescharacteristic, complemented
42C22×D149—22no—
43C22×D149—22no—
44C22×D149—21no—
45C22×D149—82no—
46C22×D149C22⋊C412yes—
47C22×D149C22⋊C411yescharacteristic
48D596—41no—
49D596—41no—
50D596—42no—
51D596—82no—
52C22⋊D149—42no—
53C22⋊D149—82no—
54C2×Dic149—21no—
55C2×Dic149—42no—
56C2×Dic149C22⋊C411yescharacteristic
57C4×D149—22no—
58C4×D149—42no—
59C4×D149—84no—
60C23×C149C2×D412yes—
61Q8×C149—41no—
62D4×C149—41no—
63C2×C4×C149—21no—
64C2×C4×C149—21no—
65C2×C4×C149—42no—
66C2×C4×C149C22×C411yescharacteristic
67C22×C149—22no—
68C22×C149—42no—
69C22×C149C2×C22⋊C411yescharacteristic
70C2×D149—22no—
71C2×D149—41no—
72C2×D149—44no—
73C2×D149—42no—
74C2×D149—42no—
75C2×D149—41no—
76C2×D149—82no—
77C2×D149#9912yes—
78C4×C149—21no—
79C4×C149—41no—
80C4×C149—41no—
81C4×C149—82no—
82Dic149—21no—
83Dic149—41no—
84Dic149—82no—
85C2×C149—21no—
86C2×C149—42no—
87C2×C149C2×#9911yescharacteristic
88D149—22no—
89D149—42no—
90D149—81no—
91C149#212711yescharacteristic, complemented, Sylow
92#2127—1491nomaximal, Sylow
93#535—1491no—
94C2×#99—1492no—
95#354—1491no—
96#354D14911yescharacteristic, complemented
97#353—1492no—
98C2×#41—1491no—
99C22×D4—1491no—
100#127—1491no—
101#127—1491no—
102#124—1491no—
103#124C2×D14911yescharacteristic
104#121—2982no—
105#120—2982no—
106#117—1491no—
107C2×C22⋊C4—2982no—
108#99—2982no—
109#99—1492no—
110#99C2×D14912yes—
111C24—1492no—
112#41—5962no—
113C2×Q8C4×D14911yescharacteristic, complemented
114C2×D4—2981no—
115C2×D4—2982no—
116C2×D4—2982no—
117C2×D4—5962no—
118C2×D4—1492no—
119C2×D4—1491no—
120C2×D4—1491no—
121C2×D4C22×D14911yescharacteristic
122C22×C4—2981no—
123C22×C4—5962no—
124C22×C4—1491no—
125C4⋊C4—2981no—
126C22⋊C4—22no—
127C22⋊C4—22no—
128C22⋊C4—2981no—
129C22⋊C4—2982no—
130C22⋊C4—2982no—
131C22⋊C4—5962no—
132C42—1491no—
133C42C4×D14911yescharacteristic, complemented
134C23—2982no—
135C23—2982no—
136C23—2981no—
137C23—1492no—
138C23—1491no—
139C23—11922no—
140C23D4×D14912yes—
141Q8—41no—
142D4—41no—
143D4—5961no—
144D4—5961no—
145D4—5962no—
146D4—5962no—
147D4—11922no—
148D4—11922no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—42no—
152C2×C4—2982no—
153C2×C4—2981no—
154C2×C4—5962no—
155C2×C4—5962no—
156C2×C4—1491no—
157C2×C4—11924no—
158C2×C4C2×C4×D14911yescharacteristic
159C22—22no—
160C22—42no—
161C22—2982no—
162C22—5961no—
163C22—5962no—
164C22—5962no—
165C22—5964no—
166C22—5961no—
167C22—1492no—
168C22—11922no—
169C22C22⋊C4×D14911yescharacteristic
170C4—21no—
171C4—41no—
172C4—41no—
173C4—82no—
174C4—2981no—
175C4—5961no—
176C4—11922no—
177C2—21no—
178C2—42no—
179C2—2982no—
180C2—5962no—
181C2—11921no—
182C2#99×D14911yescharacteristic
subgroupG/H
centerC2#99×D149
commutatorC2×C4×C149C22×C4
FrattiniC2×D4C22×D149
Fitting#354×C149C2
socleC2×C149C2×#99
prime radical#23750193C2
cosocleC2×D4×C149C23
hypercenter#354D149
hypocenterC149#2127
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #354

Complements

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

NH ≅ G/Ntype
2. #99×D149C2semidirect
3. #23749420C2semidirect
4. #23749417C2semidirect
5. #354×C149C2semidirect
6. C2×#14558737C4semidirect
8. #18011908C4semidirect
10. #18011900C4semidirect
13. #18011868C4semidirect
24. C2×D596C2×C4semidirect
36. C4×Dic149C2×C4semidirect
37. C2×Q8×C149C2×C4semidirect
41. C42×C149C2×C4semidirect
91. C149#2127semidirect
96. #354D149semidirect
113. C2×Q8C4×D149semidirect
133. C42C4×D149semidirect

Maximal subgroups

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

subgroupindex
#237501932
#99×D1492
#237494202
#237494172
#354×C1492
#2127149