Finite Group Databasebeta

← #34056126

Subgroups — #34056126

Order 19072.

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

normal subgroups only

This group has 370 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#23750230C211yesmaximal, characteristic, complemented
2#23749925C212yesmaximal, complemented
3#23749922C212yesmaximal, complemented
4#23749876C212yesmaximal, complemented
5#23749859C212yesmaximal, complemented
6#23749820C212yesmaximal, complemented
7#23749817C212yesmaximal, complemented
8#23749652C211yesmaximal, characteristic, complemented
9#540×C149C211yesmaximal, characteristic, complemented
10C2×#14558721C2212yes—
11C2×#14558721C2212yes—
12C2×#14558720C2211yescharacteristic
13C22×#11924746C2211yescharacteristic
14#18011908C2211yescharacteristic
15#18011903C2211yescharacteristic
16#18011896—22no—
17#18011885C2212yes—
18#18011884—22no—
19C4×D596C2212yes—
20#18011844C2212yes—
21#18011842C2212yes—
22C4⋊#11924746C2212yes—
23C4⋊#11924746C2212yes—
24#18011832C2212yes—
25#18011832C2212yes—
26#18011831C2212yes—
27#18011831C2212yes—
28#127×C149C2211yescharacteristic
29#125×C149C2211yescharacteristic
30#123×C149—22no—
31#121×C149—22no—
32#121×C149C2212yes—
33C4×D4×C149C2212yes—
34#117×C149C2211yescharacteristic
35C2×D596—22no—
36C2×D596C2312yes—
37C2×C22⋊D149—22no—
38C2×C4×D149—22no—
39#14558721—42no—
40#14558721—42no—
41#14558720—41no—
42C2×#11924746—41no—
43C2×#11924746C2312yes—
44C2×#11924746C2312yes—
45C4⋊Dic149C2312yes—
46#14558715—22no—
47#14558713—22no—
48#14558713—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
62C22×D149—22no—
63D596—22no—
64D596—22no—
65D596—82no—
66C22⋊D149—82no—
67C2×Dic149—22no—
68C4×D149—82no—
69#11924746—22no—
70#11924746—22no—
71C23×C149—22no—
72C23×C149C2×D411yescharacteristic
73D4×C149—22no—
74D4×C149—22no—
75D4×C149—82no—
76D4×C149—82no—
77C2×C4×C149—21no—
78C2×C4×C149—21no—
79C2×C4×C149—22no—
80C2×C4×C149—82no—
81C2×C4×C149C2×D412yes—
82C2×C4×C149C2×D412yes—
83C2×C4×C149C2×D411yescharacteristic
84C2×C4×C149C2411yescharacteristic
85C22×C149—21no—
86C22×C149—22no—
87C22×C149—42no—
88C22×C149—42no—
89C22×C149—42no—
90C22×C149C22×D411yescharacteristic
91C2×D149—42no—
92C2×D149—42no—
93C2×D149—42no—
94C4×C149—21no—
95C4×C149—22no—
96C4×C149—22no—
97C4×C149—42no—
98C4×C149H(5,𝔽2)11yescharacteristic
99C4×C1492−1+411yescharacteristic
100Dic149—42no—
101C2×C149—41no—
102C2×C149—82no—
103C2×C149#53711yescharacteristic
104C2×C149#57612yes—
105D149—82no—
106C149#325911yescharacteristic, complemented, Sylow
107#3259—1491nomaximal, Sylow
108#540—1491no—
109#540D14911yescharacteristic, complemented
110#478—1492no—
111#478—1492no—
112#469—1492no—
113#466—1492no—
114#459—1492no—
115#459—1492no—
116#424—1491no—
117C2×D8—1492no—
118C2×D8—1492no—
119C2×M16—1491no—
120C22×C8—1491no—
121#127—1491no—
122#127C2×D14911yescharacteristic
123#125—1491no—
124#125C2×D14911yescharacteristic
125#123—22no—
126#123—2982no—
127#121—22no—
128#121—2982no—
129#121—1492no—
130#121C2×D14912yes—
131C4×D4—1492no—
132C4×D4C2×D14912yes—
133#117C2×D14911yescharacteristic
134#107—1492no—
135#106—1492no—
136C4⋊C8—1492no—
137C4⋊C8—1492no—
138#102—1492no—
139#102—1492no—
140#102—1492no—
141#102—1492no—
142C2×D4—22no—
143C2×D4—22no—
144C2×D4—2982no—
145C2×D4—2982no—
146C2×D4—1492no—
147C2×D4C22×D14912yes—
148C22×C4—22no—
149C22×C4—2982no—
150C22×C4C22×D14911yescharacteristic
151D8—5962no—
152D8—5962no—
153M16—5961no—
154C2×C8—5961no—
155C2×C8—1492no—
156C2×C8—1492no—
157C4⋊C4—22no—
158C4⋊C4—2982no—
159C4⋊C4—1492no—
160C4⋊C4C22⋊D14912yes—
161C4⋊C4C22×D14912yes—
162C22⋊C4—22no—
163C22⋊C4—22no—
164C22⋊C4—2982no—
165C22⋊C4—2982no—
166C22⋊C4C22⋊D14912yes—
167C42C22×D14911yescharacteristic
168C42C22×D14911yescharacteristic
169C23—22no—
170C23—2982no—
171C23C2×C22⋊D14911yescharacteristic
172D4—22no—
173D4—22no—
174D4—82no—
175D4—82no—
176D4—2982no—
177D4—2982no—
178D4—11922no—
179D4—11922no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—22no—
183C2×C4—82no—
184C2×C4—2982no—
185C2×C4—11922no—
186C2×C4C2×C22⋊D14912yes—
187C2×C4C2×C22⋊D14912yes—
188C2×C4C2×C22⋊D14911yescharacteristic
189C2×C4C23×D14911yescharacteristic
190C8—2982no—
191C8—2982no—
192C22—22no—
193C22—21no—
194C22—42no—
195C22—42no—
196C22—42no—
197C22—5962no—
198C22—5962no—
199C22—5962no—
200C22C22×C22⋊D14911yescharacteristic
201C4—22no—
202C4—22no—
203C4—21no—
204C4—42no—
205C4—5962no—
206C4#1801195711yescharacteristic
207C4#1801195811yescharacteristic
208C2—41no—
209C2—82no—
210C2—11922no—
211C2#2375020311yescharacteristic
212C2#2375042812yes—
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#540×C149C2
socleC22×C149C22×D4
hypercenter#540D149
hypocenterC149#3259
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. #23750230C2semidirect
2. #23749925C2semidirect
3. #23749922C2semidirect
4. #23749876C2semidirect
5. #23749859C2semidirect
6. #23749820C2semidirect
7. #23749817C2semidirect
8. #23749652C2semidirect
9. #540×C149C2semidirect
106. C149#3259semidirect
109. #540D149semidirect

Maximal subgroups

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

subgroupindex
#237502302
#237499252
#237499222
#237498762
#237498592
#237498202
#237498172
#237496522
#540×C1492
#3259149