Finite Group Databasebeta

← #34060455

Subgroups — #34060455

Order 19072.

320 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 92 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×#18011976C212yesmaximal
2C4×#14558746C211yesmaximal, characteristic, complemented
3#23750561C211yesmaximal, characteristic, complemented
4#23750495C212yesmaximal, complemented
5C4×#14558737C211yesmaximal, characteristic
6C2×#14558746C2212yes—
7C2×C4×#10597010C2212yes—
8#18011976C418yescomplemented
9#18011966—21no—
10C4×#11924753—21no—
11(C2×#10597010)⋊C4—21no—
12(C2×#10597010)⋊C4—21no—
13C2×#14558737C2211yescharacteristic
14Q8×Dic149C411yescharacteristic, complemented
15C4×D596—21no—
16C4×D596C411yescharacteristic, complemented
17#18011873—21no—
18#18011873C411yescharacteristic, complemented
19#18011869—21no—
20#18011869C2211yescharacteristic
21C42×D149—21no—
22C42×D149C2211yescharacteristic
23C4×Q8×C149C411yescharacteristic, complemented
24C22×#10597010—22no—
25#14558746—22no—
26#14558746C2×C414yescomplemented
27C2×#11924753—22no—
28C4×#10597010—22no—
29C4×#10597010C2×C414yescomplemented
30#14558737—22no—
31#14558737C2×C414yes—
32C2×D596—21no—
33C2×D596C2×C411yescharacteristic
34C2×C4×D149—21no—
35C2×C4×D149—21no—
36C2×C4×D149—21no—
37C2×C4×D149D411yescharacteristic
38C2×C4×D149D411yescharacteristic
39C2×C4×D149C2311yescharacteristic
40C4⋊Dic149—21no—
41C4⋊Dic149C2×C411yescharacteristic
42#14558713—21no—
43#14558713—21no—
44#14558713—21no—
45C4×Dic149—21no—
46C4×Dic149—21no—
47C4×Dic149C2×C411yescharacteristic
48C4×Dic149D411yescharacteristic
49C4×Dic149D411yescharacteristic
50C2×Q8×C149C2×C411yescharacteristic
51C4⋊C4×C149—21no—
52C4⋊C4×C149C2×C411yescharacteristic
53C42×C149—21no—
54C42×C149C2×C411yescharacteristic
55C2×#10597010—24no—
56C2×#10597010—42no—
57C2×#10597010—42no—
58#11924753—24no—
59C22×D149—21no—
60C22×D149C2×D411yescharacteristic
61D596—24no—
62D596—21no—
63D596C4212yes—
64C2×Dic149—21no—
65C2×Dic149C22⋊C411yescharacteristic
66C2×Dic149C22⋊C411yescharacteristic
67C2×Dic149C2×D411yescharacteristic
68C4×D149—24no—
69C4×D149—41no—
70C4×D149—41no—
71C4×D149—42no—
72C4×D149—42no—
73C4×D149C22×C412yes—
74C4×D149#4112yes—
75Q8×C149—21no—
76Q8×C149C4212yes—
77C2×C4×C149—21no—
78C2×C4×C149—21no—
79C2×C4×C149C22⋊C411yescharacteristic
80C2×C4×C149C22⋊C411yescharacteristic
81C2×C4×C149C22×C411yescharacteristic
82C22×C149C2×C22⋊C411yescharacteristic
83C2×D149—21no—
84C2×D149—21no—
85C2×D149—22no—
86C2×D149—41no—
87C2×D149—41no—
88C2×D149C4×D412yes—
89#10597010—44no—
90C4×C149—22no—
91C4×C149—21no—
92C4×C149—21no—
93C4×C149—41no—
94C4×C149C2×C4211yescharacteristic
95C4×C149#11711yescharacteristic
96Dic149—21no—
97Dic149—21no—
98Dic149—41no—
99Dic149C4×D412yes—
100C2×C149C4×C22⋊C411yescharacteristic
101C2×C149#42111yescharacteristic
102C2×C149#42111yescharacteristic
103D149—22no—
104D149—42no—
105C149#175911yescharacteristic, complemented, Sylow
106#1759—1491nomaximal, Sylow
107C4×#41—1491no—
108C2×#104—1492no—
109C4×M16—1491no—
110#376—1491no—
111#339—1492no—
112C2×#41—1491no—
113C2×M16—1492no—
114C4×Q8—1491no—
115C4×Q8#1059701011yescharacteristic, complemented
116C4×D4—2981no—
117C4×D4—2981no—
118C4×D4—1491no—
119C4×D4—1491no—
120#117—2981no—
121#117—1491no—
122C2×C42—2981no—
123C2×C42—1492no—
124C2×C42—1491no—
125#104—1498no—
126#97—2981no—
127C4×C8—2981no—
128#95—2981no—
129#95—2981no—
130#41—2982no—
131#41—1494no—
132C2×Q8C2×#1059701011yescharacteristic
133C2×D4—2981no—
134C2×D4—1491no—
135C22×C4—2981no—
136C22×C4—2981no—
137C22×C4—2982no—
138C22×C4—2981no—
139C22×C4—1491no—
140C22×C4—1491no—
141C22×C4—1491no—
142M16—2982no—
143M16—1494no—
144C2×C8—2982no—
145C4⋊C4—21no—
146C4⋊C4—2981no—
147C4⋊C4—1491no—
148C4⋊C4C2×#1059701011yescharacteristic
149C22⋊C4—2981no—
150C22⋊C4—2981no—
151C22⋊C4—2981no—
152C42—21no—
153C42—2981no—
154C42—2981no—
155C42—2982no—
156C42—1494no—
157C42—1491no—
158C42—1491no—
159C42—1491no—
160C42C2×#1059701011yescharacteristic
161C23—2981no—
162C23—1491no—
163Q8—21no—
164Q8C4×#1059701012yes—
165D4—2984no—
166D4—2981no—
167D4—1492no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—2984no—
171C2×C4—2984no—
172C2×C4—2981no—
173C2×C4—5961no—
174C2×C4—5961no—
175C2×C4—5962no—
176C2×C4—5962no—
177C2×C4—5962no—
178C2×C4—5962no—
179C2×C4—1491no—
180C2×C4—1491no—
181C2×C4—1491no—
182C2×C4—1492no—
183C2×C4—1492no—
184C2×C4C22⋊#1059701011yescharacteristic
185C2×C4C22⋊#1059701011yescharacteristic
186C2×C4C22×#1059701011yescharacteristic
187C8—2984no—
188C22—2981no—
189C22—2981no—
190C22—2982no—
191C22—5961no—
192C22—5961no—
193C22—1492no—
194C22C2×C22⋊#1059701011yescharacteristic
195C4—22no—
196C4—21no—
197C4—21no—
198C4—41no—
199C4—2981no—
200C4—2981no—
201C4—5964no—
202C4—5961no—
203C4—1492no—
204C4C2×C4×#1059701011yescharacteristic
205C4#1801199011yescharacteristic
206C2—2982no—
207C2—5962no—
208C2C4×C22⋊#1059701011yescharacteristic
209C2#2375062211yescharacteristic
210C2#2375062411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC4×C149C2×C42
FrattiniC2×C4C22×#10597010
FittingC4×Q8×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC2×#14558737C22
cosocleC2×C4×D149C23
hypercenterC4×Q8#10597010
hypocenterC149#1759
LCSG ▷ C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
2. C4×#14558746C2semidirect
3. #23750561C2semidirect
4. #23750495C2semidirect
8. #18011976C4semidirect
14. Q8×Dic149C4semidirect
16. C4×D596C4semidirect
18. #18011873C4semidirect
23. C4×Q8×C149C4semidirect
26. #14558746C2×C4semidirect
29. C4×#10597010C2×C4semidirect
105. C149#1759semidirect
115. C4×Q8#10597010semidirect

Maximal subgroups

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

subgroupindex
C2×#180119762
C4×#145587462
#237505612
#237504952
C4×#145587372
#1759149