Finite Group Databasebeta

← #34043321

Subgroups — #34043321

Order 19072.

200 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 57 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#23750160C211yesmaximal, characteristic
2#23749680C211yesmaximal, characteristic, complemented
3#23749680C211yesmaximal, characteristic, complemented
4#23749367C211yesmaximal, characteristic, complemented
5#23749364C211yesmaximal, characteristic, complemented
6#23749364C211yesmaximal, characteristic, complemented
7#330×C149C211yesmaximal, characteristic, complemented
8#18011906—21no—
9#18011899C2211yescharacteristic
10#18011896—21no—
11#18011891C411yescharacteristic
12#18011886C411yescharacteristic
13#18011876C411yescharacteristic
14#18011873—21no—
15#18011873C411yescharacteristic
16#18011869—21no—
17C42×D149C2211yescharacteristic
18#18011840—21no—
19#18011840—21no—
20#18011823—21no—
21#18011823—21no—
22#18011822C2211yescharacteristic
23#18011822C2211yescharacteristic
24#125×C149C2211yescharacteristic
25#97×C149C2211yescharacteristic
26#97×C149C2211yescharacteristic
27C2×Dic298C2×C411yescharacteristic
28C2×D596—21no—
29C2×D596C2×C411yescharacteristic
30C2×C4×D149—21no—
31C2×C4×D149C2×C411yescharacteristic
32C2×C4×D149D411yescharacteristic
33C2×C4×D149D411yescharacteristic
34C2×#11924746—21no—
35C2×#11924746—21no—
36C4⋊Dic149—21no—
37#14558715—21no—
38#14558713—21no—
39#14558713—21no—
40#14558713—21no—
41#14558713—21no—
42#14558713—21no—
43C4×Dic149—21no—
44C4×Dic149C2×C411yescharacteristic
45C4×Dic149D411yescharacteristic
46C4×Dic149D411yescharacteristic
47C2×C8×C149—21no—
48C2×C8×C149—21no—
49C4⋊C4×C149—21no—
50C4⋊C4×C149—21no—
51C4⋊C4×C149C2×C411yescharacteristic
52C4⋊C4×C149C2×C411yescharacteristic
53C42×C149C2311yescharacteristic
54C22×D149—21no—
55C22×D149C22⋊C411yescharacteristic
56Dic298—41no—
57D596—41no—
58D596—42no—
59C2×Dic149—21no—
60C2×Dic149C22⋊C411yescharacteristic
61C2×Dic149C22⋊C411yescharacteristic
62C2×Dic149C22⋊C411yescharacteristic
63C4×D149—41no—
64C4×D149—41no—
65C4×D149—41no—
66C4×D149—42no—
67#11924746—41no—
68#11924746—41no—
69C2×C4×C149—21no—
70C2×C4×C149—21no—
71C2×C4×C149C22×C411yescharacteristic
72C2×C4×C149C2×D411yescharacteristic
73C2×C4×C149C2×D411yescharacteristic
74C8×C149—41no—
75C8×C149—41no—
76C22×C149C2×C22⋊C411yescharacteristic
77C2×D149—21no—
78C2×D149—21no—
79C2×D149—21no—
80C2×D149—41no—
81C2×D149—41no—
82C2×D149—41no—
83C4×C149—21no—
84C4×C149—21no—
85C4×C149—21no—
86C4×C149—41no—
87C4×C149—41no—
88Dic149—21no—
89Dic149—21no—
90Dic149—21no—
91Dic149—41no—
92C2×C149#41311yescharacteristic
93C2×C149#42111yescharacteristic
94C2×C149#42111yescharacteristic
95D149—41no—
96D149—81no—
97C149#153511yescharacteristic, complemented, Sylow
98#1535—1491nomaximal, Sylow
99#529—1491no—
100#432—1491no—
101#432—1491no—
102#330—1491no—
103#330D14911yescharacteristic, complemented
104#329—1491no—
105#329—1491no—
106#126—2981no—
107#125C2×D14911yescharacteristic
108#124—1491no—
109#123—2981no—
110C22⋊Q8—1491no—
111#121—1491no—
112C4×Q8—1491no—
113C4×D4—2981no—
114C4×D4—1491no—
115#117—2981no—
116C2×C42—1491no—
117C4⋊C8—2981no—
118C4⋊C8—2981no—
119C22⋊C8—2981no—
120C22⋊C8—2981no—
121#97—1491no—
122#97—1491no—
123#97C2×D14911yescharacteristic
124#97C2×D14911yescharacteristic
125C2×Q8—1491no—
126C2×D4—2981no—
127C2×D4—1491no—
128C22×C4—2981no—
129C22×C4—1491no—
130C22×C4—1491no—
131C22×C4—1491no—
132C2×C8—21no—
133C2×C8—21no—
134C2×C8—2981no—
135C2×C8—2981no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C4⋊C4—2981no—
139C4⋊C4—2981no—
140C4⋊C4C4×D14911yescharacteristic
141C4⋊C4C4×D14911yescharacteristic
142C22⋊C4—2981no—
143C22⋊C4—2981no—
144C22⋊C4—2981no—
145C22⋊C4—2981no—
146C22⋊C4—2981no—
147C42—2981no—
148C42—1491no—
149C42—1491no—
150C42—1491no—
151C42C22×D14911yescharacteristic
152C23—2981no—
153C23—1491no—
154Q8—5961no—
155D4—5961no—
156D4—5962no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—2981no—
160C2×C4—5961no—
161C2×C4—5961no—
162C2×C4—5961no—
163C2×C4—5962no—
164C2×C4—1491no—
165C2×C4—1491no—
166C2×C4—1491no—
167C2×C4C2×C4×D14911yescharacteristic
168C2×C4D4×D14911yescharacteristic
169C2×C4D4×D14911yescharacteristic
170C8—41no—
171C8—41no—
172C8—5961no—
173C8—5961no—
174C22—2981no—
175C22—2981no—
176C22—2981no—
177C22—5961no—
178C22—5961no—
179C22—5961no—
180C22C22⋊C4×D14911yescharacteristic
181C4—21no—
182C4—21no—
183C4—21no—
184C4—41no—
185C4—41no—
186C4—2981no—
187C4—2981no—
188C4—2981no—
189C4—5961no—
190C2—5961no—
191C2—11921no—
192C2#2374960811yescharacteristic
193C2#2374964011yescharacteristic
194C2#2374964011yescharacteristic
subgroupG/H
centerC22C22⋊C4×D149
commutatorC2×C4×C149C22×C4
FrattiniC42C22×D149
Fitting#330×C149C2
socleC22×C149C2×C22⋊C4
prime radical#18011886C4
cosocleC42×C149C23
hypercenter#330D149
hypocenterC149#1535
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
2. #23749680C2semidirect
3. #23749680C2semidirect
4. #23749367C2semidirect
5. #23749364C2semidirect
6. #23749364C2semidirect
7. #330×C149C2semidirect
97. C149#1535semidirect
103. #330D149semidirect

Maximal subgroups

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

subgroupindex
#237501602
#237496802
#237493672
#237493642
#330×C1492
#1535149