Finite Group Databasebeta

← #34060600

Subgroups — #34060600

Order 19072.

262 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 62 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#23750611C211yesmaximal, characteristic
2#23750604C211yesmaximal, characteristic
3#23750496C212yesmaximal, complemented
4#23750492C212yesmaximal, complemented
5C4×#14558736C211yesmaximal, characteristic
6D149⋊M16C2212yes—
7#18011990C2212yes—
8#18011972—21no—
9#18011971—21no—
10#18011970—21no—
11#18011969—21no—
12C2×#14558736C2211yescharacteristic
13C4×Dic298—21no—
14C4×D596—21no—
15C4×C22⋊D149—21no—
16C4×C22⋊D149—21no—
17#18011870C411yescharacteristic, complemented
18#18011868C411yescharacteristic, complemented
19#18011868C2211yescharacteristic
20C42×D149C411yescharacteristic, complemented
21C42×D149C2211yescharacteristic
22C2×C42×C149C411yescharacteristic, complemented
23#14558746—22no—
24#14558745—22no—
25D149⋊C8—22no—
26C4⋊#10597010—22no—
27C22⋊#10597010—22no—
28C4×#10597010—22no—
29#14558736—22no—
30#14558736—22no—
31C2×Dic298D411yescharacteristic
32C2×D596D411yescharacteristic
33C2×C22⋊D149D411yescharacteristic
34C2×C22⋊D149D411yescharacteristic
35C2×C4×D149—21no—
36C2×C4×D149—21no—
37C2×C4×D149C2×C411yescharacteristic
38C2×C4×D149C2311yescharacteristic
39C4⋊Dic149—21no—
40#14558715—21no—
41#14558715—21no—
42C22⋊Dic149—21no—
43#14558713—21no—
44#14558713—21no—
45C4×Dic149—21no—
46C4×Dic149—21no—
47C4×Dic149C2×C411yescharacteristic
48C4×Dic149C2×C411yescharacteristic
49C22×C4×C149—21no—
50C22×C4×C149C2×C411yescharacteristic
51C42×C149—21no—
52C42×C149C2×C411yescharacteristic
53C42×C149C2×C411yescharacteristic
54C2×#10597010—42no—
55#11924753—42no—
56C22×D149C22⋊C411yescharacteristic
57C22×D149C2×D411yescharacteristic
58Dic298—22no—
59D596—22no—
60C22⋊D149—22no—
61C22⋊D149—22no—
62C2×Dic149—21no—
63C2×Dic149—21no—
64C2×Dic149C22⋊C411yescharacteristic
65C2×Dic149C2×D411yescharacteristic
66C4×D149—21no—
67C4×D149—21no—
68C4×D149—42no—
69C4×D149—42no—
70C4×D149#4112yes—
71C4×D149#4112yes—
72C23×C149C22⋊C411yescharacteristic
73C2×C4×C149—21no—
74C2×C4×C149—21no—
75C2×C4×C149—21no—
76C2×C4×C149—21no—
77C2×C4×C149—42no—
78C2×C4×C149C22⋊C411yescharacteristic
79C2×C4×C149C22×C411yescharacteristic
80C22×C149—21no—
81C22×C149—41no—
82C22×C149C2×C22⋊C411yescharacteristic
83C2×D149—21no—
84C2×D149—41no—
85C2×D149—41no—
86C2×D149#12312yes—
87#10597010—82no—
88C4×C149—22no—
89C4×C149—21no—
90C4×C149—41no—
91C4×C149#11711yescharacteristic
92C4×C149#11711yescharacteristic
93Dic149—21no—
94Dic149—41no—
95Dic149—41no—
96Dic149#12312yes—
97C2×C149—21no—
98C2×C149—41no—
99C2×C149#38111yescharacteristic
100D149—22no—
101D149—41no—
102C149#182711yescharacteristic, complemented, Sylow
103#1827—1491nomaximal, Sylow
104C4×#41—1491no—
105#413—1491no—
106#410—1491no—
107#339—1492no—
108H(3,ℤ/4)—1492no—
109C2×#41—1491no—
110C2×M16—1492no—
111C4×Q8—2981no—
112C4×D4—2981no—
113C4×D4—2981no—
114C4×D4—2981no—
115#117—1492no—
116#117—1491no—
117#117—1491no—
118#117—1491no—
119C2×C42—1491no—
120C2×C42—1491no—
121C2×C42#1059701011yescharacteristic, complemented
122#101—2981no—
123#100—2981no—
124#99—2981no—
125#99—2981no—
126#41—2982no—
127#41—2982no—
128C2×Q8—1491no—
129C2×D4—1491no—
130C2×D4—1491no—
131C2×D4—1491no—
132C22×C4—21no—
133C22×C4—2981no—
134C22×C4—2981no—
135C22×C4—1491no—
136C22×C4—1491no—
137C22×C4C2×#1059701011yescharacteristic
138M16—2982no—
139M16—2982no—
140C2×C8—2982no—
141C4⋊C4—2981no—
142C4⋊C4—2981no—
143C4⋊C4—2981no—
144C4⋊C4—2982no—
145C22⋊C4—2981no—
146C22⋊C4—2981no—
147C22⋊C4—2981no—
148C22⋊C4—2982no—
149C42—21no—
150C42—2981no—
151C42—2981no—
152C42—2982no—
153C42—1491no—
154C42—1491no—
155C42C2×#1059701011yescharacteristic
156C42C2×#1059701011yescharacteristic
157C23—1491no—
158C23—1491no—
159C23C22⋊#1059701011yescharacteristic
160Q8—2982no—
161D4—2982no—
162D4—2982no—
163D4—2982no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—42no—
169C2×C4—2981no—
170C2×C4—2981no—
171C2×C4—2981no—
172C2×C4—2981no—
173C2×C4—5962no—
174C2×C4—5962no—
175C2×C4—5962no—
176C2×C4—1491no—
177C2×C4—1491no—
178C2×C4—1492no—
179C2×C4—1492no—
180C2×C4C22⋊#1059701011yescharacteristic
181C2×C4C22×#1059701011yescharacteristic
182C8—5962no—
183C22—21no—
184C22—41no—
185C22—2981no—
186C22—5961no—
187C22—5961no—
188C22—1492no—
189C22C2×C22⋊#1059701011yescharacteristic
190C4—22no—
191C4—21no—
192C4—41no—
193C4—2981no—
194C4—5961no—
195C4—5961no—
196C4—1492no—
197C4—11922no—
198C4#1801199011yescharacteristic
199C4#1801199011yescharacteristic
200C2—21no—
201C2—41no—
202C2—2982no—
203C2—5961no—
204C2#2375056811yescharacteristic
subgroupG/H
centerC4#18011990
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC2×C42×C149C4
socleC2×C149#381
prime radicalC2×#14558736C22
cosocleC2×C4×D149C23
hypercenterC2×C42#10597010
hypocenterC149#1827
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C4 ◁ C42 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
3. #23750496C2semidirect
4. #23750492C2semidirect
17. #18011870C4semidirect
18. #18011868C4semidirect
20. C42×D149C4semidirect
22. C2×C42×C149C4semidirect
102. C149#1827semidirect
121. C2×C42#10597010semidirect

Maximal subgroups

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

subgroupindex
#237506112
#237506042
#237504962
#237504922
C4×#145587362
#1827149