Finite Group Databasebeta

← #34059784

Subgroups — #34059784

Order 19072.

232 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 40 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
1D149⋊#99C211yesmaximal, characteristic
2#23750577C211yesmaximal, characteristic
3#99×D149C211yesmaximal, characteristic
4C2×C4⋊#10597010C411yescharacteristic, complemented
5C2×C22⋊#10597010—21no—
6C2×C22⋊#10597010—21no—
7C2×C22⋊#10597010—21no—
8C2×C4×#10597010C411yescharacteristic, complemented
9#18011970C412yescomplemented
10#18011969—21no—
11C2×D4×D149C2211yescharacteristic
12C22⋊C4×D149—21no—
13#18011826C411yescharacteristic, complemented
14#18011825—21no—
15#99×C149C411yescharacteristic, complemented
16C22×#10597010—21no—
17C22×#10597010—21no—
18C22×#10597010—41no—
19C4⋊#10597010—41no—
20C22⋊#10597010—22no—
21C22⋊#10597010—41no—
22C22⋊#10597010—42no—
23C22⋊#10597010—42no—
24C4×#10597010—41no—
25C23×D149D411yescharacteristic
26C23×D149D411yescharacteristic
27C2×D596C2×C411yescharacteristic
28C2×C22⋊D149D411yescharacteristic
29C2×C22⋊D149Q811yescharacteristic
30D4×D149—41no—
31D4×D149—41no—
32C2×C4×D149—41no—
33C2×C4×D149C2×C411yescharacteristic
34C22⋊Dic149—21no—
35#14558713—41no—
36C2×D4×C149C2×C411yescharacteristic
37C22⋊C4×C149—21no—
38C2×#10597010—22no—
39C2×#10597010—41no—
40C2×#10597010—41no—
41C2×#10597010—42no—
42C2×#10597010—41no—
43C2×#10597010—41no—
44C2×#10597010—41no—
45C2×#10597010—81no—
46C2×#10597010—81no—
47C22×D149—21no—
48C22×D149—21no—
49C22×D149—21no—
50C22×D149—21no—
51C22×D149—41no—
52C22×D149—41no—
53C22×D149—41no—
54C22×D149—41no—
55C22×D149C22⋊C411yescharacteristic
56C22×D149C22⋊C411yescharacteristic
57C22×D149C4⋊C411yescharacteristic
58D596—41no—
59C22⋊D149—41no—
60C22⋊D149—41no—
61C2×Dic149—41no—
62C2×Dic149C4⋊C411yescharacteristic
63C4×D149—21no—
64C4×D149—21no—
65C4×D149—81no—
66C4×D149—81no—
67C23×C149C22⋊C411yescharacteristic
68C23×C149C4⋊C411yescharacteristic
69D4×C149—41no—
70C2×C4×C149—41no—
71C2×C4×C149C4211yescharacteristic
72C22×C149—21no—
73C22×C149—21no—
74C22×C149—41no—
75C22×C149—41no—
76C22×C149#9511yescharacteristic
77C2×D149—21no—
78C2×D149—21no—
79C2×D149—21no—
80C2×D149—21no—
81C2×D149—41no—
82C2×D149—41no—
83C2×D149—41no—
84C2×D149—41no—
85C2×D149—41no—
86C2×D149—41no—
87C2×D149—81no—
88C2×D149—81no—
89C2×D149#9911yescharacteristic
90C2×D149#9911yescharacteristic
91#10597010—42no—
92#10597010—82no—
93#10597010—81no—
94C4×C149—21no—
95C4×C149—81no—
96Dic149—21no—
97Dic149—81no—
98C2×C149—21no—
99C2×C149—41no—
100C2×C149—41no—
101C2×C149#34211yescharacteristic
102D149—21no—
103D149—41no—
104D149—41no—
105D149#35311yescharacteristic
106D149#35411yescharacteristic
107C149#139311yescharacteristic, complemented, Sylow
108#1393—1491nomaximal, Sylow
109C2×#99—1491no—
110C2×#99—1491no—
111#390—1491no—
112C22×D4—1491no—
113C2×C4⋊C4—1491no—
114C2×C22⋊C4—2981no—
115C2×C22⋊C4—2981no—
116C2×C22⋊C4—2981no—
117C2×C22⋊C4—2981no—
118C2×C42—1491no—
119#99—2981no—
120#99—2981no—
121#99—1492no—
122#99—1491no—
123#99#1059701011yescharacteristic, complemented
124C24—1491no—
125C24—1491no—
126C2×D4—5961no—
127C2×D4—5961no—
128C2×D4—1491no—
129C2×D4—1491no—
130C2×D4—1491no—
131C2×D4C2×#1059701011yescharacteristic
132C22×C4—2981no—
133C22×C4—2981no—
134C22×C4—5961no—
135C22×C4—5961no—
136C22×C4—1491no—
137C4⋊C4—5961no—
138C22⋊C4—21no—
139C22⋊C4—2982no—
140C22⋊C4—2981no—
141C22⋊C4—5961no—
142C22⋊C4—5962no—
143C22⋊C4—5962no—
144C22⋊C4—5961no—
145C42—5961no—
146C23—2981no—
147C23—2981no—
148C23—2981no—
149C23—2981no—
150C23—5961no—
151C23—5961no—
152C23—5961no—
153C23—5961no—
154C23—1491no—
155C23—1491no—
156C23—1491no—
157C23C22⋊#1059701011yescharacteristic
158C23C4⋊#1059701011yescharacteristic
159D4—41no—
160D4—5961no—
161D4—5961no—
162D4—5961no—
163C2×C4—41no—
164C2×C4—2981no—
165C2×C4—2981no—
166C2×C4—2982no—
167C2×C4—5961no—
168C2×C4—5961no—
169C2×C4—5961no—
170C2×C4—5962no—
171C2×C4—5961no—
172C2×C4—5961no—
173C2×C4—5961no—
174C2×C4—1491no—
175C2×C4—11921no—
176C2×C4—11921no—
177C2×C4—11921no—
178C2×C4—11921no—
179C2×C4C4×#1059701011yescharacteristic
180C22—21no—
181C22—21no—
182C22—41no—
183C22—41no—
184C22—2981no—
185C22—2981no—
186C22—2981no—
187C22—2981no—
188C22—5961no—
189C22—5961no—
190C22—5961no—
191C22—5961no—
192C22—5961no—
193C22—5961no—
194C22—1491no—
195C22—1491no—
196C22—11921no—
197C22—11921no—
198C22(C2×#10597010)⋊C411yescharacteristic
199C4—21no—
200C4—81no—
201C4—2981no—
202C4—5962no—
203C4—11921no—
204C4—11922no—
205C4—11921no—
206C2—21no—
207C2—41no—
208C2—41no—
209C2—2981no—
210C2—5961no—
211C2—5961no—
212C2—1491no—
213C2—1491no—
214C2#2375050211yescharacteristic
subgroupG/H
centerC2#23750502
commutatorC2×C4×C149C42
FrattiniC2×D4C2×#10597010
Fitting#99×C149C4
socleC2×C149#342
prime radical, cosocleC2×D4×D149C22
hypercenter#99#10597010
hypocenterC149#1393
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #99

Complements

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

NH ≅ G/Ntype
4. C2×C4⋊#10597010C4semidirect
8. C2×C4×#10597010C4semidirect
9. #18011970C4semidirect
13. #18011826C4semidirect
15. #99×C149C4semidirect
107. C149#1393semidirect
123. #99#10597010semidirect

Maximal subgroups

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

subgroupindex
D149⋊#992
#237505772
#99×D1492
#1393149