Finite Group Databasebeta

← #34060694

Subgroups — #34060694

Order 19072.

332 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 66 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#23750703C211yesmaximal, characteristic, complemented
2#23750623C212yesmaximal, complemented
3#23750605C211yesmaximal, characteristic, complemented
4#23750496C212yesmaximal, complemented
5#23750173C211yesmaximal, characteristic
6#18011998—24no—
7D149⋊M16C2212yes—
8C2×#14558745—22no—
9#18011990C2212yes—
10#18011975—24no—
11#18011969—22no—
12C2×#14558735C2211yescharacteristic
13C2×#14558735C2211yescharacteristic
14#18011911C411yescharacteristic, complemented
15#18011898C411yescharacteristic, complemented
16#18011898C411yescharacteristic, complemented
17#18011882—22no—
18D4×Dic149—22no—
19C42×D149C2211yescharacteristic
20#127×C149C411yescharacteristic, complemented
21#14558746D414yescomplemented
22#14558745—24no—
23#14558745—22no—
24D149⋊C8—22no—
25C2×#11924753—24no—
26C4⋊#10597010—22no—
27C22⋊#10597010—22no—
28C4×#10597010—22no—
29#14558735—22no—
30#14558735—22no—
31#14558735—22no—
32#14558735—22no—
33C2×Dic298C2×C411yescharacteristic
34C2×Dic298C2×C411yescharacteristic
35C2×C22⋊D149—21no—
36C2×C22⋊D149D412yes—
37C22×Dic149—21no—
38C22×Dic149D412yes—
39C2×C4×D149—21no—
40C2×C4×D149C2311yescharacteristic
41C4⋊Dic149—22no—
42C22⋊Dic149—22no—
43C22⋊Dic149—22no—
44C4×Dic149—21no—
45C4×Dic149C2×C411yescharacteristic
46C2×D4×C149—22no—
47C2×D4×C149C2×C411yescharacteristic
48C2×D4×C149C2×C411yescharacteristic
49C42×C149C2×C411yescharacteristic
50C2×#10597010—42no—
51#11924753—24no—
52C22×D149C2×D411yescharacteristic
53Dic298—22no—
54Dic298—22no—
55C22⋊D149—24no—
56C22⋊D149—42no—
57C2×Dic149—22no—
58C2×Dic149—22no—
59C2×Dic149—21no—
60C2×Dic149—21no—
61C2×Dic149—41no—
62C2×Dic149—41no—
63C2×Dic149C22⋊C412yes—
64C2×Dic149C2×D411yescharacteristic
65C4×D149—42no—
66C4×D149C2×D412yes—
67C4×D149#4112yes—
68C23×C149—21no—
69C23×C149C22⋊C412yes—
70D4×C149—22no—
71D4×C149—22no—
72D4×C149—44no—
73C2×C4×C149—21no—
74C2×C4×C149C22×C411yescharacteristic
75C22×C149—22no—
76C22×C149—42no—
77C22×C149—42no—
78C22×C149—41no—
79C22×C149C2×C22⋊C411yescharacteristic
80C2×D149—41no—
81C2×D149#12112yes—
82#10597010—82no—
83C4×C149—22no—
84C4×C149C4×D412yes—
85Dic149—22no—
86Dic149—41no—
87Dic149—41no—
88Dic149#12011yescharacteristic
89Dic149#12311yescharacteristic
90C2×C149—21no—
91C2×C149—42no—
92C2×C149—81no—
93C2×C149#38611yescharacteristic
94D149—22no—
95C149#188411yescharacteristic, complemented, Sylow
96#1884—1491nomaximal, Sylow
97#568—1491no—
98#532—1491no—
99#421—1492no—
100#410—1491no—
101#339—1492no—
102C2×#41—1491no—
103C2×#41—1491no—
104#131—2984no—
105C2×M16—2982no—
106C2×M16—1492no—
107C4⋊Q8—1491no—
108#127#1059701011yescharacteristic, complemented
109#124—1491no—
110#124—1491no—
111#121—2982no—
112C4×D4—2982no—
113#117—1492no—
114C2×C42—1491no—
115#104—2984no—
116#99—2982no—
117#41—2982no—
118#41—2982no—
119#41—2982no—
120#41—2982no—
121C2×Q8—1491no—
122C2×Q8—1491no—
123C2×D4—22no—
124C2×D4—2981no—
125C2×D4—1492no—
126C2×D4C2×#1059701011yescharacteristic
127C2×D4C2×#1059701011yescharacteristic
128C22×C4—2981no—
129C22×C4—2981no—
130C22×C4—1492no—
131C22×C4—1491no—
132M16—2984no—
133M16—2982no—
134M16—1494no—
135C2×C8—2984no—
136C2×C8—2982no—
137C4⋊C4—2982no—
138C4⋊C4—2982no—
139C22⋊C4—2982no—
140C22⋊C4—2982no—
141C22⋊C4—2982no—
142C42—2981no—
143C42—2982no—
144C42—1491no—
145C42C2×#1059701011yescharacteristic
146C23—21no—
147C23—1491no—
148C23C22⋊#1059701012yes—
149Q8—2982no—
150Q8—2982no—
151D4—22no—
152D4—22no—
153D4—44no—
154D4—2984no—
155D4—5962no—
156C2×C4—21no—
157C2×C4—2982no—
158C2×C4—2982no—
159C2×C4—2981no—
160C2×C4—2981no—
161C2×C4—5962no—
162C2×C4—5961no—
163C2×C4—5961no—
164C2×C4—5962no—
165C2×C4—1492no—
166C2×C4—1491no—
167C2×C4—1492no—
168C2×C4—1492no—
169C2×C4C22×#1059701011yescharacteristic
170C8—2984no—
171C22—22no—
172C22—42no—
173C22—42no—
174C22—41no—
175C22—5961no—
176C22—1492no—
177C22C2×C22⋊#1059701011yescharacteristic
178C4—22no—
179C4—2982no—
180C4—5961no—
181C4—5961no—
182C4—1491no—
183C4—1491no—
184C4—11922no—
185C4D4×#1059701012yes—
186C2—21no—
187C2—42no—
188C2—81no—
189C2—2982no—
190C2#2375057311yescharacteristic
subgroupG/H
centerC2#23750573
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
Fitting#127×C149C4
socleC2×C149#386
prime radical#23750173C2
cosocleC2×C4×D149C23
hypercenter#127#10597010
hypocenterC149#1884
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C2×C4 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #23750703C2semidirect
2. #23750623C2semidirect
3. #23750605C2semidirect
4. #23750496C2semidirect
14. #18011911C4semidirect
15. #18011898C4semidirect
16. #18011898C4semidirect
20. #127×C149C4semidirect
21. #14558746D4semidirect
95. C149#1884semidirect
108. #127#10597010semidirect

Maximal subgroups

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

subgroupindex
#237507032
#237506232
#237506052
#237504962
#237501732
#1884149