Finite Group Databasebeta

← #34043059

Subgroups — #34043059

Order 19072.

214 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 61 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
1C2×#18011906C211yesmaximal, characteristic
2#23749679C211yesmaximal, characteristic, complemented
3#23749675C211yesmaximal, characteristic, complemented
4#23749351C211yesmaximal, characteristic, complemented
5#23749348C211yesmaximal, characteristic
6#23749348C211yesmaximal, characteristic
7#324×C149C211yesmaximal, characteristic, complemented
8#18011906—21no—
9#18011906—21no—
10#18011906—21no—
11#18011906—21no—
12C2×C4⋊Dic149C411yescharacteristic
13C2×#14558715C411yescharacteristic
14C2×#14558713C411yescharacteristic
15C2×#14558713C411yescharacteristic
16C2×#14558713C2211yescharacteristic
17C2×C4×Dic149C2211yescharacteristic
18#18011840—21no—
19#18011840—21no—
20C22⋊#11924746C2211yescharacteristic
21C22⋊#11924746C2211yescharacteristic
22#18011821—21no—
23C8×Dic149—21no—
24C2×C4⋊C4×C149C2211yescharacteristic
25C22⋊C8×C149C2211yescharacteristic
26C22⋊C8×C149C2211yescharacteristic
27C23×D149C2×C411yescharacteristic
28C22×Dic149C2×C411yescharacteristic
29C22×Dic149C2×C411yescharacteristic
30C22×Dic149C2×C411yescharacteristic
31C2×#11924746—21no—
32C2×#11924746—21no—
33C4⋊Dic149—21no—
34C4⋊Dic149—21no—
35#14558715—21no—
36#14558715—21no—
37#14558713—21no—
38#14558713—21no—
39#14558713—21no—
40#14558713—21no—
41#14558713—21no—
42#14558713—21no—
43C4×Dic149D411yescharacteristic
44C4×Dic149D411yescharacteristic
45C4×Dic149D411yescharacteristic
46C4×Dic149D411yescharacteristic
47C22×C4×C149C2×C411yescharacteristic
48C22×C4×C149C2×C411yescharacteristic
49C22×C4×C149C2311yescharacteristic
50C2×C8×C149—21no—
51C2×C8×C149—21no—
52C4⋊C4×C149—21no—
53C4⋊C4×C149—21no—
54C22×D149—21no—
55C22×D149—21no—
56C22×D149—21no—
57C22×D149—41no—
58C22×D149—41no—
59C2×Dic149—21no—
60C2×Dic149—21no—
61C2×Dic149—21no—
62C2×Dic149—41no—
63C2×Dic149—41no—
64C2×Dic149C22⋊C411yescharacteristic
65C2×Dic149C22⋊C411yescharacteristic
66C2×Dic149C22⋊C411yescharacteristic
67C2×Dic149C22⋊C411yescharacteristic
68#11924746—41no—
69#11924746—41no—
70C23×C149C22×C411yescharacteristic
71C2×C4×C149—21no—
72C2×C4×C149—21no—
73C2×C4×C149—21no—
74C2×C4×C149—21no—
75C2×C4×C149—41no—
76C2×C4×C149—41no—
77C2×C4×C149C2×D411yescharacteristic
78C2×C4×C149C2×D411yescharacteristic
79C8×C149—41no—
80C8×C149—41no—
81C22×C149—21no—
82C22×C149—21no—
83C22×C149C2×C22⋊C411yescharacteristic
84C22×C149#13111yescharacteristic
85C22×C149#13111yescharacteristic
86C2×D149—41no—
87C2×D149—41no—
88C2×D149—41no—
89C2×D149—81no—
90C2×D149—81no—
91C4×C149—21no—
92C4×C149—21no—
93C4×C149—41no—
94C4×C149—41no—
95Dic149—21no—
96Dic149—21no—
97Dic149—21no—
98Dic149—21no—
99Dic149—41no—
100C2×C149—21no—
101C2×C149—21no—
102C2×C149#40811yescharacteristic
103C2×C149#41011yescharacteristic
104C2×C149#41311yescharacteristic
105D149—81no—
106C149#147311yescharacteristic, complemented, Sylow
107#1473—1491nomaximal, Sylow
108C2×#126—1491no—
109#432—1491no—
110#431—1491no—
111#324—1491no—
112#324D14911yescharacteristic, complemented
113#323—1491no—
114#323—1491no—
115#126—2981no—
116#126—2981no—
117#126—2981no—
118#126—2981no—
119C2×C4⋊C4—1491no—
120C2×C4⋊C4—1491no—
121C2×C4⋊C4C2×D14911yescharacteristic
122C2×C22⋊C4—1491no—
123C2×C22⋊C4—1491no—
124C2×C22⋊C4—1491no—
125C2×C42—1491no—
126C4⋊C8—2981no—
127C4⋊C8—2981no—
128C22⋊C8—1491no—
129C22⋊C8—1491no—
130C22⋊C8C2×D14911yescharacteristic
131C22⋊C8C2×D14911yescharacteristic
132#97—2981no—
133C4×C8—2981no—
134C24—1491no—
135C22×C4—1491no—
136C22×C4—1491no—
137C22×C4—1491no—
138C22×C4C4×D14911yescharacteristic
139C22×C4C4×D14911yescharacteristic
140C22×C4C22×D14911yescharacteristic
141C2×C8—21no—
142C2×C8—21no—
143C2×C8—2981no—
144C2×C8—2981no—
145C4⋊C4—21no—
146C4⋊C4—21no—
147C4⋊C4—2981no—
148C4⋊C4—2981no—
149C4⋊C4—2981no—
150C4⋊C4—2981no—
151C22⋊C4—2981no—
152C22⋊C4—2981no—
153C22⋊C4—2981no—
154C22⋊C4—2981no—
155C22⋊C4—2981no—
156C22⋊C4—2981no—
157C42—1491no—
158C42—1491no—
159C42—1491no—
160C42—1491no—
161C23—2981no—
162C23—2981no—
163C23—2981no—
164C23—5961no—
165C23—5961no—
166C23C2×C4×D14911yescharacteristic
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—2981no—
174C2×C4—2981no—
175C2×C4—2981no—
176C2×C4—5961no—
177C2×C4—5961no—
178C2×C4—1491no—
179C2×C4—1491no—
180C2×C4—1491no—
181C2×C4—1491no—
182C2×C4D4×D14911yescharacteristic
183C2×C4D4×D14911yescharacteristic
184C8—41no—
185C8—41no—
186C8—5961no—
187C8—5961no—
188C22—21no—
189C22—21no—
190C22—5961no—
191C22—5961no—
192C22—5961no—
193C22—11921no—
194C22—11921no—
195C22C22⋊C4×D14911yescharacteristic
196C22#1801191711yescharacteristic
197C22#1801191911yescharacteristic
198C4—21no—
199C4—21no—
200C4—41no—
201C4—41no—
202C4—2981no—
203C4—2981no—
204C4—2981no—
205C4—2981no—
206C4—5961no—
207C2—21no—
208C2—21no—
209C2—11921no—
210C2#2374959011yescharacteristic
211C2#2374959711yescharacteristic
212C2#2374960811yescharacteristic
subgroupG/H
centerC22C22⋊C4×D149
commutatorC23×C149C22×C4
FrattiniC22×C4C22×D149
Fitting#324×C149C2
socleC22×C149C2×C22⋊C4
prime radicalC23×D149C2×C4
cosocleC22×C4×C149C23
hypercenter#324D149
hypocenterC149#1473
LCSG ▷ C23×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #23749679C2semidirect
3. #23749675C2semidirect
4. #23749351C2semidirect
7. #324×C149C2semidirect
106. C149#1473semidirect
112. #324D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119062
#237496792
#237496752
#237493512
#237493482
#324×C1492
#1473149