Finite Group Databasebeta

← #34060104

Subgroups — #34060104

Order 19072.

222 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 56 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#23750648C211yesmaximal, characteristic, complemented
2#23750569C211yesmaximal, characteristic, complemented
3#23750479C212yesmaximal, complemented
4#23750477C212yesmaximal
5#23750162C211yesmaximal, characteristic
6C2×C4⋊#10597010—21no—
7#18011978—21no—
8#18011968C2212yes—
9#18011966—21no—
10(C2×#10597010)⋊C4—21no—
11(C2×#10597010)⋊C4C2212yes—
12#18011906—21no—
13#18011902C411yescharacteristic, complemented
14#18011900C411yescharacteristic, complemented
15#18011896—21no—
16#18011887C2211yescharacteristic
17#18011886C2211yescharacteristic
18C4×D596—21no—
19C4×D596C411yescharacteristic, complemented
20#18011868—21no—
21C42×D149C2211yescharacteristic
22C4×Q8×C149C411yescharacteristic, complemented
23C22×#10597010—22no—
24C2×#11924753—22no—
25C4⋊#10597010—42no—
26C2×D596—21no—
27C2×D596C2×C411yescharacteristic
28C2×C4×D149—21no—
29C2×C4×D149D411yescharacteristic
30C2×C4×D149D411yescharacteristic
31C2×C4×D149C2311yescharacteristic
32C4⋊Dic149—21no—
33C4⋊Dic149C2×C411yescharacteristic
34#14558715—21no—
35#14558715—21no—
36#14558713—21no—
37#14558713—21no—
38#14558713—21no—
39#14558713—21no—
40#14558713—21no—
41C4×Dic149C2×C411yescharacteristic
42C4×Dic149D411yescharacteristic
43C4×Dic149D411yescharacteristic
44C2×Q8×C149C2×C411yescharacteristic
45C4⋊C4×C149—21no—
46C4⋊C4×C149C2×C411yescharacteristic
47C42×C149—21no—
48C42×C149C2×C411yescharacteristic
49C2×#10597010—42no—
50C2×#10597010—42no—
51C2×#10597010—42no—
52#11924753—42no—
53C22×D149—21no—
54C22×D149C2×D411yescharacteristic
55D596—41no—
56D596—41no—
57D596—41no—
58C2×Dic149—21no—
59C2×Dic149C22⋊C411yescharacteristic
60C2×Dic149C22⋊C411yescharacteristic
61C2×Dic149C2×D411yescharacteristic
62C4×D149—21no—
63C4×D149—21no—
64C4×D149—41no—
65C4×D149—41no—
66C4×D149—42no—
67Q8×C149—41no—
68C2×C4×C149—21no—
69C2×C4×C149—21no—
70C2×C4×C149C22⋊C411yescharacteristic
71C2×C4×C149C22⋊C411yescharacteristic
72C2×C4×C149C22×C411yescharacteristic
73C22×C149C2×C22⋊C411yescharacteristic
74C2×D149—21no—
75C2×D149—21no—
76C2×D149—41no—
77C2×D149—41no—
78C2×D149—41no—
79C2×D149AGL(1,ℤ/8)11yescharacteristic
80C2×D149#13711yescharacteristic
81#10597010—82no—
82C4×C149—21no—
83C4×C149—21no—
84C4×C149—21no—
85C4×C149—41no—
86C4×C149—41no—
87Dic149—21no—
88Dic149—21no—
89Dic149—21no—
90Dic149—41no—
91C2×C149#41011yescharacteristic
92C2×C149#41711yescharacteristic
93C2×C149#42111yescharacteristic
94D149—21no—
95D149—21no—
96D149—81no—
97C149#151211yescharacteristic, complemented, Sylow
98#1512—1491nomaximal, Sylow
99#529—1491no—
100#432—1491no—
101#382—1491no—
102#328—1492no—
103#327—1492no—
104#126—2981no—
105#125—1491no—
106#124—1491no—
107#123—2981no—
108C22⋊Q8—1491no—
109#121—1491no—
110C4×Q8#1059701011yescharacteristic, complemented
111C4×D4—2981no—
112C4×D4—1491no—
113#117—2981no—
114C2×C4⋊C4—2981no—
115C2×C42—1491no—
116C4⋊C8—2981no—
117C22⋊C8—1492no—
118#97—2981no—
119#95—2981no—
120#95—1492no—
121C2×Q8C2×#1059701011yescharacteristic
122C2×D4—2981no—
123C2×D4—1491no—
124C22×C4—2981no—
125C22×C4—2982no—
126C22×C4—1491no—
127C22×C4—1491no—
128C22×C4—1491no—
129C2×C8—2982no—
130C4⋊C4—21no—
131C4⋊C4—2981no—
132C4⋊C4—2981no—
133C4⋊C4—2981no—
134C4⋊C4—5962no—
135C4⋊C4—1491no—
136C4⋊C4C2×#1059701011yescharacteristic
137C22⋊C4—2981no—
138C22⋊C4—2981no—
139C22⋊C4—2981no—
140C22⋊C4—2981no—
141C22⋊C4—2981no—
142C42—21no—
143C42—1491no—
144C42—1491no—
145C42—1491no—
146C42C2×#1059701011yescharacteristic
147C23—2981no—
148C23—1491no—
149Q8—41no—
150D4—5961no—
151D4—5961no—
152D4—5961no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—2981no—
156C2×C4—2981no—
157C2×C4—2981no—
158C2×C4—5961no—
159C2×C4—5961no—
160C2×C4—5962no—
161C2×C4—5962no—
162C2×C4—5962no—
163C2×C4—5962no—
164C2×C4—1491no—
165C2×C4—1491no—
166C2×C4—1491no—
167C2×C4C22⋊#1059701011yescharacteristic
168C2×C4C22⋊#1059701011yescharacteristic
169C2×C4C22×#1059701011yescharacteristic
170C8—5962no—
171C22—2981no—
172C22—2981no—
173C22—5961no—
174C22—5961no—
175C22—5961no—
176C22—1491no—
177C22—1491no—
178C22C2×C22⋊#1059701011yescharacteristic
179C4—21no—
180C4—21no—
181C4—21no—
182C4—41no—
183C4—41no—
184C4—2981no—
185C4—2981no—
186C4—2981no—
187C4—5961no—
188C4—11922no—
189C2—2981no—
190C2—2981no—
191C2—11921no—
192C2#2375060411yescharacteristic
193C2#2375061611yescharacteristic
194C2#2375062411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC4×Q8×C149C4
socleC22×C149C2×C22⋊C4
prime radical#18011886C22
cosocleC2×C4×D149C23
hypercenterC4×Q8#10597010
hypocenterC149#1512
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #23750648C2semidirect
2. #23750569C2semidirect
3. #23750479C2semidirect
13. #18011902C4semidirect
14. #18011900C4semidirect
19. C4×D596C4semidirect
22. C4×Q8×C149C4semidirect
97. C149#1512semidirect
110. C4×Q8#10597010semidirect

Maximal subgroups

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

subgroupindex
#237506482
#237505692
#237504792
#237504772
#237501622
#1512149