Finite Group Databasebeta

← #34044016

Subgroups — #34044016

Order 19072.

196 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 45 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#23750369C211yesmaximal, characteristic
2#23749994C211yesmaximal, characteristic, complemented
3#23749985C211yesmaximal, characteristic, complemented
4#23749984C211yesmaximal, characteristic, complemented
5#23749366C211yesmaximal, characteristic, complemented
6#23749364C211yesmaximal, characteristic, complemented
7#329×C149C211yesmaximal, characteristic, complemented
8#18011911C2211yescharacteristic
9#18011903C2211yescharacteristic
10#18011899C2211yescharacteristic
11#18011895—21no—
12#18011893—21no—
13#18011888—21no—
14#18011887—21no—
15#18011884—21no—
16#18011883—21no—
17#18011836—21no—
18#18011836—21no—
19#18011836—21no—
20#18011835—21no—
21#18011833—21no—
22#18011832—21no—
23#18011822C2211yescharacteristic
24#124×C149C2211yescharacteristic
25#97×C149C2211yescharacteristic
26#97×C149C2211yescharacteristic
27C2×Dic298—21no—
28C2×Dic298D411yescharacteristic
29C2×D596D411yescharacteristic
30C2×C22⋊D149—21no—
31C2×C22⋊D149—21no—
32C22×Dic149—21no—
33C2×C4×D149—21no—
34C2×#11924746—21no—
35C4⋊Dic149—21no—
36C4⋊Dic149—21no—
37C4⋊Dic149—21no—
38C4⋊Dic149D411yescharacteristic
39C4⋊Dic149D411yescharacteristic
40#14558715—21no—
41#14558715—21no—
42#14558715—21no—
43C22⋊Dic149—21no—
44#14558713—21no—
45#14558713—21no—
46#14558713—21no—
47C2×Q8×C149D411yescharacteristic
48C2×D4×C149D411yescharacteristic
49C2×C8×C149—21no—
50C2×C8×C149—21no—
51C22⋊C4×C149—21no—
52C22⋊C4×C149—21no—
53C42×C149C2311yescharacteristic
54C22×D149—21no—
55Dic298—41no—
56Dic298—42no—
57D596—41no—
58C22⋊D149—81no—
59C22⋊D149—81no—
60C2×Dic149—21no—
61C2×Dic149—21no—
62C2×Dic149—21no—
63C2×Dic149—41no—
64C2×Dic149—81no—
65C4×D149—81no—
66#11924746—41no—
67C23×C149—21no—
68Q8×C149—41no—
69D4×C149—41no—
70C2×C4×C149—21no—
71C2×C4×C149C2×D411yescharacteristic
72C2×C4×C149C2×D411yescharacteristic
73C2×C4×C149C2×D411yescharacteristic
74C8×C149—41no—
75C8×C149—41no—
76C22×C149—41no—
77C22×C149—41no—
78C22×C149—41no—
79C22×C149#12011yescharacteristic
80C2×D149—41no—
81C2×D149—41no—
82C2×D149—41no—
83C4×C149—21no—
84C4×C149—21no—
85C4×C149—21no—
86C4×C149—41no—
87Dic149—41no—
88Dic149—41no—
89Dic149—41no—
90Dic149—81no—
91C2×C149—81no—
92C2×C149#45411yescharacteristic
93C2×C149#45511yescharacteristic
94C2×C149#45511yescharacteristic
95D149—81no—
96C149#166211yescharacteristic, complemented, Sylow
97#1662—1491nomaximal, Sylow
98#562—1491no—
99#491—1491no—
100#489—1491no—
101#489—1491no—
102#330—1491no—
103#329—1491no—
104#329D14911yescharacteristic, complemented
105C4⋊Q8—1491no—
106#125—1491no—
107#124—1491no—
108#124C2×D14911yescharacteristic
109#123—2981no—
110#123—2981no—
111C22⋊Q8—2981no—
112C22⋊Q8—2981no—
113#121—2981no—
114#121—2981no—
115#103—2981no—
116#103—2981no—
117#103—2981no—
118#103—2981no—
119#102—2981no—
120#102—2981no—
121#97—1491no—
122#97C2×D14911yescharacteristic
123#97C2×D14911yescharacteristic
124C2×Q8—2981no—
125C2×Q8—1491no—
126C2×Q8D59611yescharacteristic
127C2×D4—2981no—
128C2×D4—2981no—
129C2×D4—1491no—
130C2×D4D59611yescharacteristic
131C22×C4—2981no—
132C22×C4—2981no—
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—2981no—
136C4⋊C4—2981no—
137C4⋊C4—2981no—
138C4⋊C4—2981no—
139C4⋊C4—2981no—
140C4⋊C4—2981no—
141C4⋊C4—2981no—
142C4⋊C4—1491no—
143C4⋊C4—1491no—
144C22⋊C4—21no—
145C22⋊C4—21no—
146C22⋊C4—2981no—
147C22⋊C4—2981no—
148C22⋊C4—2981no—
149C22⋊C4—2981no—
150C42C22×D14911yescharacteristic
151C23—21no—
152C23—2981no—
153Q8—41no—
154Q8—5961no—
155Q8—5962no—
156D4—41no—
157D4—5961no—
158D4—11921no—
159D4—11921no—
160C2×C4—21no—
161C2×C4—2981no—
162C2×C4—2981no—
163C2×C4—2981no—
164C2×C4—5961no—
165C2×C4—11921no—
166C2×C4—11921no—
167C2×C4D4×D14911yescharacteristic
168C2×C4D4×D14911yescharacteristic
169C2×C4C2×D59611yescharacteristic
170C8—41no—
171C8—41no—
172C8—5961no—
173C22—41no—
174C22—41no—
175C22—41no—
176C22—5961no—
177C22—5961no—
178C22—5961no—
179C22#1801188111yescharacteristic
180C4—21no—
181C4—21no—
182C4—21no—
183C4—41no—
184C4—5961no—
185C4—5961no—
186C4—5961no—
187C4—11921no—
188C2—81no—
189C2—11921no—
190C2#2374979911yescharacteristic
191C2#2374980411yescharacteristic
192C2#2374980511yescharacteristic
subgroupG/H
centerC22#18011881
commutator, cosocleC42×C149C23
FrattiniC42C22×D149
Fitting#329×C149C2
socleC22×C149#120
prime radical#23750369C2
hypercenter#329D149
hypocenterC149#1662
LCSG ▷ C42×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #23749994C2semidirect
3. #23749985C2semidirect
4. #23749984C2semidirect
5. #23749366C2semidirect
6. #23749364C2semidirect
7. #329×C149C2semidirect
96. C149#1662semidirect
104. #329D149semidirect

Maximal subgroups

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

subgroupindex
#237503692
#237499942
#237499852
#237499842
#237493662
#237493642
#329×C1492
#1662149