Finite Group Databasebeta

← #34045755

Subgroups — #34045755

Order 19072.

394 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 71 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#23750132C212yesmaximal, complemented
2#23749642C212yesmaximal, complemented
3#23749588C211yesmaximal, characteristic, complemented
4#23749382C211yesmaximal, characteristic, complemented
5#575×C149C211yesmaximal, characteristic, complemented
6C22×C4×D149C2211yescharacteristic
7C2×#14558720C2211yescharacteristic
8#18011892—22no—
9#18011887—22no—
10#18011882—22no—
11#18011879—22no—
12C4×C22⋊D149—24no—
13#18011870C2212yes—
14#18011838—24no—
15#18011823—22no—
16C2×#41×C149C2212yes—
17#137×C149—22no—
18AGL(1,ℤ/8)×C149—22no—
19#135×C149—22no—
20C2×M16×C149C2211yescharacteristic
21C23×D149D411yescharacteristic
22C2×C22⋊D149—24no—
23C22×Dic149D411yescharacteristic
24C2×C4×D149—21no—
25C2×C4×D149—22no—
26C2×C4×D149—22no—
27C2×C4×D149—21no—
28#14558720—22no—
29C2×#11924746—21no—
30C4⋊Dic149—22no—
31#14558715—24no—
32C22⋊Dic149—24no—
33C22⋊Dic149—22no—
34#14558713—24no—
35C4×Dic149D414yescomplemented
36#41×C149—22no—
37#41×C149—22no—
38#41×C149—22no—
39#41×C149—22no—
40C2×Q8×C149D412yescomplemented
41C2×D4×C149—22no—
42C2×D4×C149D412yescomplemented
43C22×C4×C149—22no—
44C22×C4×C149C2311yescharacteristic
45Q16×C149—22no—
46SD16×C149—24no—
47D8×C149—22no—
48M16×C149—22no—
49C2×C8×C149D412yescomplemented
50C22×D149—22no—
51C22×D149—21no—
52C22×D149—42no—
53C22⋊D149—48no—
54C2×Dic149—22no—
55C2×Dic149—24no—
56C2×Dic149—21no—
57C4×D149—41no—
58C4×D149—42no—
59C4×D149—41no—
60#11924746—41no—
61C23×C149—22no—
62C23×C149C2×D411yescharacteristic
63Q8×C149—22no—
64Q8×C149—22no—
65D4×C149—22no—
66D4×C149—22no—
67D4×C149—42no—
68D4×C149—42no—
69C2×C4×C149—22no—
70C2×C4×C149—42no—
71C2×C4×C149—42no—
72C2×C4×C149C2×D412yes—
73C2×C4×C149C2×D412yes—
74C2×C4×C149C2×D411yescharacteristic
75C2×C4×C149#4111yescharacteristic
76C8×C149—22no—
77C22×C149—41no—
78C22×C149—44no—
79C22×C149—42no—
80C22×C149#12012yes—
81C22×C149#12111yescharacteristic
82C2×D149—24no—
83C2×D149—22no—
84C2×D149—42no—
85C2×D149—41no—
86C2×D149—41no—
87C4×C149—42no—
88C4×C149#12011yescharacteristic
89C4×C149#12112yes—
90C4×C149#12711yescharacteristic
91Dic149—44no—
92Dic149—41no—
93C2×C149—22no—
94C2×C149—21no—
95C2×C149—82no—
96C2×C149#39211yescharacteristic
97D149—42no—
98C149#201011yescharacteristic, complemented, Sylow
99#2010—1491nomaximal, Sylow
100#575D14911yescharacteristic, complemented
101#525—1492no—
102#421—1492no—
103#407—1491no—
104H(3,ℤ/4)—1491no—
105C2×#41C2×D14912yes—
106C23×C4—1491no—
107#137—22no—
108AGL(1,ℤ/8)—22no—
109#135—22no—
110C2×M16—1491no—
111C2×M16C2×D14911yescharacteristic
112#123—2982no—
113C22⋊Q8—2982no—
114#121—2982no—
115#120—2982no—
116C4×D4—2984no—
117#117—1492no—
118#104—2984no—
119C22⋊C8—2982no—
120C24—1491no—
121#41—22no—
122#41—22no—
123#41—22no—
124#41—22no—
125C2×Q8C22⋊D14912yescomplemented
126C2×D4—22no—
127C2×D4—2984no—
128C2×D4C22⋊D14912yescomplemented
129C22×C4—22no—
130C22×C4—2982no—
131C22×C4—2981no—
132C22×C4—2982no—
133C22×C4—2981no—
134C22×C4—1491no—
135C22×C4C22×D14911yescharacteristic
136Q16—22no—
137SD16—24no—
138D8—22no—
139M16—22no—
140M16—2982no—
141C2×C8—2981no—
142C2×C8C22⋊D14912yescomplemented
143C4⋊C4—2984no—
144C4⋊C4—2982no—
145C22⋊C4—2984no—
146C22⋊C4—2984no—
147C22⋊C4—2982no—
148C42—1494no—
149C23—22no—
150C23—2982no—
151C23—2981no—
152C23—5962no—
153C23D4×D14911yescharacteristic
154Q8—22no—
155Q8—22no—
156D4—22no—
157D4—22no—
158D4—42no—
159D4—42no—
160D4—5968no—
161C2×C4—22no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—2984no—
165C2×C4—2982no—
166C2×C4—2981no—
167C2×C4—5961no—
168C2×C4—5961no—
169C2×C4—5962no—
170C2×C4D4×D14912yes—
171C2×C4C2×C22⋊D14911yescharacteristic
172C2×C4C2×C22⋊D14912yes—
173C2×C4#1455873511yescharacteristic
174C8—22no—
175C8—5961no—
176C22—41no—
177C22—44no—
178C22—42no—
179C22—2984no—
180C22—2982no—
181C22—5962no—
182C22—5961no—
183C22—5961no—
184C22#1801187912yes—
185C22#1801188211yescharacteristic
186C4—42no—
187C4—5964no—
188C4—5961no—
189C4#1801188011yescharacteristic
190C4#1801188312yes—
191C4#1801190711yescharacteristic
192C2—22no—
193C2—21no—
194C2—82no—
195C2—5962no—
196C2#2374953311yescharacteristic
subgroupG/H
centerC4#18011907
commutator, cosocleC22×C4×C149C23
FrattiniC22×C4C22×D149
Fitting#575×C149C2
socleC2×C149#392
hypercenter#575D149
hypocenterC149#2010
LCSG ▷ C22×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C4 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. #23750132C2semidirect
2. #23749642C2semidirect
3. #23749588C2semidirect
4. #23749382C2semidirect
5. #575×C149C2semidirect
35. C4×Dic149D4semidirect
40. C2×Q8×C149D4semidirect
42. C2×D4×C149D4semidirect
49. C2×C8×C149D4semidirect
98. C149#2010semidirect
100. #575D149semidirect
125. C2×Q8C22⋊D149semidirect
128. C2×D4C22⋊D149semidirect
142. C2×C8C22⋊D149semidirect

Maximal subgroups

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

subgroupindex
#237501322
#237496422
#237495882
#237493822
#575×C1492
#2010149