Finite Group Databasebeta

← #34056137

Subgroups — #34056137

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#23749929C212yesmaximal, complemented
3#23749925C212yesmaximal, complemented
4#23749869C212yesmaximal, complemented
5#23749852C212yesmaximal, complemented
6#23749830C212yesmaximal, complemented
7#23749822C212yesmaximal, complemented
8#23749652C211yesmaximal, characteristic, complemented
9#540×C149C211yesmaximal, characteristic
10C2×#14558724C2212yes—
11C2×#14558724C2212yes—
12C2×#14558720C2211yescharacteristic
13C22×#11924746C2211yescharacteristic
14#18011911C2211yescharacteristic
15#18011904—22no—
16#18011903C2211yescharacteristic
17#18011901—22no—
18#18011890C2212yes—
19C4×Dic298C2212yes—
20#18011844C2212yes—
21#18011842C2212yes—
22C4⋊#11924746C2212yes—
23C4⋊#11924746C2212yes—
24#18011834C2212yes—
25#18011834C2212yes—
26#18011832C2212yes—
27#18011832C2212yes—
28#127×C149C2211yescharacteristic
29#125×C149C2211yescharacteristic
30#123×C149—22no—
31#121×C149—22no—
32#121×C149C2212yes—
33C4×D4×C149C2212yes—
34#117×C149C2211yescharacteristic
35C2×Dic298C2312yes—
36#14558724—42no—
37#14558724—42no—
38#14558720—41no—
39C2×#11924746—41no—
40C2×#11924746C2312yes—
41C2×#11924746C2312yes—
42C4⋊Dic149—22no—
43C4⋊Dic149C2312yes—
44#14558715—22no—
45#14558715—22no—
46#14558715—22no—
47C22⋊Dic149—22no—
48C4×Dic149—22no—
49C2×D4×C149—22no—
50C2×D4×C149—22no—
51C2×D4×C149C2312yes—
52C22×C4×C149—22no—
53C22×C4×C149C2311yescharacteristic
54C4⋊C4×C149—22no—
55C4⋊C4×C149D412yes—
56C4⋊C4×C149C2312yes—
57C22⋊C4×C149—22no—
58C22⋊C4×C149—22no—
59C22⋊C4×C149D412yes—
60C42×C149C2311yescharacteristic
61C42×C149C2311yescharacteristic
62Dic298—22no—
63Dic298—22no—
64C2×Dic149—22no—
65C2×Dic149—22no—
66#11924746—22no—
67#11924746—22no—
68C23×C149—22no—
69C23×C149C2×D411yescharacteristic
70D4×C149—22no—
71D4×C149—22no—
72D4×C149—82no—
73D4×C149—82no—
74C2×C4×C149—21no—
75C2×C4×C149—21no—
76C2×C4×C149—22no—
77C2×C4×C149—82no—
78C2×C4×C149C2×D412yes—
79C2×C4×C149C2×D412yes—
80C2×C4×C149C2×D411yescharacteristic
81C2×C4×C149C2411yescharacteristic
82C22×C149—21no—
83C22×C149—22no—
84C22×C149—42no—
85C22×C149—42no—
86C22×C149—42no—
87C22×C149C22×D411yescharacteristic
88C4×C149—21no—
89C4×C149—22no—
90C4×C149—22no—
91C4×C149—42no—
92C4×C149H(5,𝔽2)11yescharacteristic
93C4×C1492−1+411yescharacteristic
94Dic149—42no—
95Dic149—42no—
96C2×C149—41no—
97C2×C149—82no—
98C2×C149#53711yescharacteristic
99C2×C149#57712yes—
100C149#326011yescharacteristic, complemented, Sylow
101#3260—1491nomaximal, Sylow
102#541—1491no—
103#540D14911yescharacteristic
104#479—1492no—
105#478—1492no—
106#468—1492no—
107#465—1492no—
108#461—1492no—
109#460—1492no—
110#424—1491no—
111C2×SD16—1492no—
112C2×SD16—1492no—
113C2×M16—1491no—
114C22×C8—1491no—
115C4⋊Q8—1491no—
116#127C2×D14911yescharacteristic
117#126—2982no—
118#125—2982no—
119#125—1491no—
120#125C2×D14911yescharacteristic
121#123—22no—
122C22⋊Q8—1492no—
123#121—22no—
124#121C2×D14912yes—
125C4×Q8—1492no—
126C4×D4C2×D14912yes—
127#117C2×D14911yescharacteristic
128#107—1492no—
129#106—1492no—
130C4⋊C8—1492no—
131C4⋊C8—1492no—
132#103—1492no—
133#103—1492no—
134#102—1492no—
135#102—1492no—
136C2×Q8—1492no—
137C2×D4—22no—
138C2×D4—22no—
139C2×D4C22×D14912yes—
140C22×C4—22no—
141C22×C4C22×D14911yescharacteristic
142SD16—5962no—
143SD16—5962no—
144M16—5961no—
145C2×C8—5961no—
146C2×C8—1492no—
147C2×C8—1492no—
148C4⋊C4—22no—
149C4⋊C4—2982no—
150C4⋊C4—2982no—
151C4⋊C4—2982no—
152C4⋊C4—2982no—
153C4⋊C4—1492no—
154C4⋊C4C22⋊D14912yes—
155C4⋊C4C22×D14912yes—
156C22⋊C4—22no—
157C22⋊C4—22no—
158C22⋊C4—2982no—
159C22⋊C4C22⋊D14912yes—
160C42—2982no—
161C42C22×D14911yescharacteristic
162C42C22×D14911yescharacteristic
163C23—22no—
164C23C2×C22⋊D14911yescharacteristic
165Q8—2982no—
166Q8—2982no—
167D4—22no—
168D4—22no—
169D4—82no—
170D4—82no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—22no—
174C2×C4—82no—
175C2×C4—2982no—
176C2×C4—2982no—
177C2×C4C2×C22⋊D14912yes—
178C2×C4C2×C22⋊D14912yes—
179C2×C4C2×C22⋊D14911yescharacteristic
180C2×C4C23×D14911yescharacteristic
181C8—2982no—
182C8—2982no—
183C22—22no—
184C22—21no—
185C22—42no—
186C22—42no—
187C22—42no—
188C22C22×C22⋊D14911yescharacteristic
189C4—22no—
190C4—22no—
191C4—21no—
192C4—42no—
193C4—5962no—
194C4—5962no—
195C4#1801195711yescharacteristic
196C4#1801195811yescharacteristic
197C2—41no—
198C2—82no—
199C2#2375020311yescharacteristic
200C2#2375043612yes—
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting, prime radical#540×C149C2
socleC22×C149C22×D4
hypercenter#540D149
hypocenterC149#3260
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #23750237C2semidirect
2. #23749929C2semidirect
3. #23749925C2semidirect
4. #23749869C2semidirect
5. #23749852C2semidirect
6. #23749830C2semidirect
7. #23749822C2semidirect
8. #23749652C2semidirect
100. C149#3260semidirect

Maximal subgroups

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

subgroupindex
#237502372
#237499292
#237499252
#237498692
#237498522
#237498302
#237498222
#237496522
#540×C1492
#3260149