Finite Group Databasebeta

← #34056138

Subgroups — #34056138

Order 19072.

346 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 117 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#23750237C211yesmaximal, characteristic, complemented
2#23750230C211yesmaximal, characteristic
3#23749933C212yesmaximal, complemented
4#23749926C212yesmaximal, complemented
5#23749871C212yesmaximal, complemented
6#23749854C212yesmaximal, complemented
7#23749831C212yesmaximal, complemented
8#23749826C212yesmaximal, complemented
9#424×C149C211yesmaximal, characteristic, complemented
10C2×#14558725C2212yes—
11C2×#14558725C2212yes—
12#18011911C2211yescharacteristic
13#18011908C2211yescharacteristic
14#18011904—22no—
15#18011903C2211yescharacteristic
16#18011903C2211yescharacteristic
17#18011901—22no—
18#18011896—22no—
19#18011890C2212yes—
20#18011885C2212yes—
21#18011884—22no—
22C4×Dic298C2212yes—
23C4×D596C2212yes—
24#18011845C2212yes—
25#18011843C2212yes—
26#18011836C2212yes—
27#18011836C2212yes—
28#18011833C2212yes—
29#18011833C2212yes—
30C2×M16×C149C2211yescharacteristic
31C22×C8×C149C2211yescharacteristic
32#117×C149C2211yescharacteristic
33C4⋊C8×C149C2212yes—
34C4⋊C8×C149C2212yes—
35C2×Dic298C2312yes—
36C2×D596—22no—
37C2×D596C2312yes—
38C2×C22⋊D149—22no—
39C2×C4×D149—22no—
40#14558725—42no—
41#14558725—42no—
42C4⋊Dic149—22no—
43C4⋊Dic149C2312yes—
44C4⋊Dic149C2312yes—
45#14558715—22no—
46#14558715—22no—
47#14558715—22no—
48#14558715—22no—
49C22⋊Dic149—22no—
50#14558713—22no—
51#14558713—22no—
52C4×Dic149—22no—
53C22×C4×C149C2311yescharacteristic
54M16×C149—41no—
55C2×C8×C149—41no—
56C2×C8×C149C2312yes—
57C2×C8×C149C2312yes—
58C4⋊C4×C149D412yes—
59C22⋊C4×C149D412yes—
60C42×C149C2311yescharacteristic
61C42×C149C2311yescharacteristic
62C22×D149—22no—
63Dic298—22no—
64Dic298—22no—
65D596—22no—
66D596—22no—
67D596—82no—
68C22⋊D149—82no—
69C2×Dic149—22no—
70C2×Dic149—22no—
71C2×Dic149—22no—
72C4×D149—82no—
73C23×C149C2×D411yescharacteristic
74C2×C4×C149—21no—
75C2×C4×C149—21no—
76C2×C4×C149C2×D412yes—
77C2×C4×C149C2×D412yes—
78C2×C4×C149C2×D411yescharacteristic
79C2×C4×C149C2411yescharacteristic
80C8×C149—22no—
81C8×C149—22no—
82C22×C149—21no—
83C22×C149—22no—
84C22×C149C22×D411yescharacteristic
85C2×D149—42no—
86C2×D149—42no—
87C2×D149—42no—
88C4×C149—21no—
89C4×C149—22no—
90C4×C149—22no—
91C4×C149H(5,𝔽2)11yescharacteristic
92C4×C1492−1+411yescharacteristic
93Dic149—42no—
94Dic149—42no—
95Dic149—42no—
96C2×C149—41no—
97C2×C149#53711yescharacteristic
98C2×C149#57712yes—
99D149—82no—
100C149#326011yescharacteristic, complemented, Sylow
101#3260—1491nomaximal, Sylow
102#541—1491no—
103#540—1491no—
104#479—1492no—
105#478—1492no—
106#468—1492no—
107#465—1492no—
108#461—1492no—
109#460—1492no—
110#424D14911yescharacteristic, complemented
111C2×SD16—1492no—
112C2×SD16—1492no—
113C2×M16C2×D14911yescharacteristic
114C22×C8C2×D14911yescharacteristic
115C4⋊Q8—1491no—
116#127—1491no—
117#126—2982no—
118#125—2982no—
119#125—1491no—
120#125—1491no—
121#123—2982no—
122C22⋊Q8—1492no—
123#121—2982no—
124#121—1492no—
125C4×Q8—1492no—
126C4×D4—1492no—
127#117C2×D14911yescharacteristic
128#107—1492no—
129#106—1492no—
130C4⋊C8C2×D14912yes—
131C4⋊C8C2×D14912yes—
132#103—1492no—
133#103—1492no—
134#102—1492no—
135#102—1492no—
136C2×Q8—1492no—
137C2×D4—2982no—
138C2×D4—2982no—
139C2×D4—1492no—
140C22×C4—2982no—
141C22×C4C22×D14911yescharacteristic
142SD16—5962no—
143SD16—5962no—
144M16—41no—
145C2×C8—41no—
146C2×C8C22×D14912yes—
147C2×C8C22×D14912yes—
148C4⋊C4—2982no—
149C4⋊C4—2982no—
150C4⋊C4—2982no—
151C4⋊C4—2982no—
152C4⋊C4—2982no—
153C4⋊C4—1492no—
154C4⋊C4—1492no—
155C4⋊C4D59612yes—
156C22⋊C4—2982no—
157C22⋊C4—2982no—
158C22⋊C4—2982no—
159C22⋊C4D59612yes—
160C42—2982no—
161C42C22×D14911yescharacteristic
162C42C22×D14911yescharacteristic
163C23—2982no—
164C23C2×D59611yescharacteristic
165Q8—2982no—
166Q8—2982no—
167D4—2982no—
168D4—2982no—
169D4—11922no—
170D4—11922no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—2982no—
174C2×C4—2982no—
175C2×C4—2982no—
176C2×C4—11922no—
177C2×C4C2×D59612yes—
178C2×C4C2×D59612yes—
179C2×C4C2×D59611yescharacteristic
180C2×C4C23×D14911yescharacteristic
181C8—22no—
182C8—22no—
183C22—22no—
184C22—21no—
185C22—5962no—
186C22—5962no—
187C22—5962no—
188C22C22×D59611yescharacteristic
189C4—22no—
190C4—22no—
191C4—21no—
192C4—5962no—
193C4—5962no—
194C4—5962no—
195C4#1801195611yescharacteristic
196C4#1801195911yescharacteristic
197C2—41no—
198C2—11922no—
199C2#2375020611yescharacteristic
200C2#2375043712yes—
subgroupG/H
centerC22C22×D596
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#424×C149C2
socleC22×C149C22×D4
prime radical#23750230C2
hypercenter#424D149
hypocenterC149#3260
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ #117 ◁ #424

Complements

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

NH ≅ G/Ntype
1. #23750237C2semidirect
3. #23749933C2semidirect
4. #23749926C2semidirect
5. #23749871C2semidirect
6. #23749854C2semidirect
7. #23749831C2semidirect
8. #23749826C2semidirect
9. #424×C149C2semidirect
100. C149#3260semidirect
110. #424D149semidirect

Maximal subgroups

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

subgroupindex
#237502372
#237502302
#237499332
#237499262
#237498712
#237498542
#237498312
#237498262
#424×C1492
#3260149