Finite Group Databasebeta

← #34060831

Subgroups — #34060831

Order 19072.

408 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 74 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×#18011970C214yesmaximal, complemented
2#23750567C211yesmaximal, characteristic, complemented
3C4×C22⋊#10597010C211yesmaximal, characteristic, complemented
4C2×#18011886C211yesmaximal, characteristic
5C2×C4⋊#10597010—21no—
6C2×C22⋊#10597010C2212yes—
7C2×C22⋊#10597010C2212yes—
8C2×C4×#10597010—21no—
9#18011970—28no—
10(C2×#10597010)⋊C4—21no—
11(C2×#10597010)⋊C4—21no—
12C22×D596C411yescharacteristic, complemented
13C22×D596C2212yes—
14C22×C4×D149C2211yescharacteristic
15#18011886—21no—
16#18011886—21no—
17#18011886—21no—
18#18011886—21no—
19C2×#14558713C412yescomplemented
20C2×C4⋊C4×C149C411yescharacteristic, complemented
21C22×#10597010—22no—
22C22×#10597010—22no—
23C4⋊#10597010—42no—
24C22⋊#10597010—24no—
25C22⋊#10597010—22no—
26C22⋊#10597010D414yescomplemented
27C4×#10597010—42no—
28C23×D149C2×C412yes—
29C23×D149C2311yescharacteristic
30C2×D596—24no—
31C2×D596—22no—
32C2×D596—22no—
33C2×D596—24no—
34C2×D596—21no—
35C2×D596—21no—
36C2×D596—42no—
37C22×Dic149C2×C411yescharacteristic
38C2×C4×D149—42no—
39C2×C4×D149D411yescharacteristic
40C2×C4×D149D411yescharacteristic
41C2×C4×D149D411yescharacteristic
42C2×C4×D149D411yescharacteristic
43#14558713—22no—
44#14558713—22no—
45C22×C4×C149C2×C412yes—
46C22×C4×C149C2×C411yescharacteristic
47C4⋊C4×C149—21no—
48C4⋊C4×C149—21no—
49C2×#10597010—24no—
50C2×#10597010—42no—
51C2×#10597010—42no—
52C2×#10597010—42no—
53C2×#10597010—42no—
54C2×#10597010—42no—
55C22×D149—22no—
56C22×D149—24no—
57C22×D149—41no—
58C22×D149—41no—
59C22×D149—42no—
60C22×D149—42no—
61C22×D149C2×D411yescharacteristic
62C22×D149C2×D411yescharacteristic
63C22×D149C2×D412yes—
64C22×D149#4112yes—
65D596—42no—
66D596—44no—
67D596—42no—
68D596—42no—
69D596—42no—
70C2×Dic149—41no—
71C2×Dic149C22⋊C411yescharacteristic
72C2×Dic149C22⋊C411yescharacteristic
73C4×D149—22no—
74C4×D149—22no—
75C4×D149—41no—
76C4×D149—41no—
77C23×C149C22×C411yescharacteristic
78C2×C4×C149—22no—
79C2×C4×C149—22no—
80C2×C4×C149—24no—
81C2×C4×C149C22⋊C411yescharacteristic
82C2×C4×C149C22⋊C411yescharacteristic
83C22×C149—21no—
84C22×C149—21no—
85C22×C149C2×C22⋊C411yescharacteristic
86C22×C149C4×D412yes—
87C2×D149—21no—
88C2×D149—21no—
89C2×D149—21no—
90C2×D149—21no—
91C2×D149—42no—
92C2×D149—42no—
93C2×D149—42no—
94C2×D149—42no—
95C2×D149—42no—
96C2×D149—84no—
97C2×D149#12112yes—
98C2×D149#12411yescharacteristic
99C2×D149#12711yescharacteristic
100#10597010—44no—
101#10597010—82no—
102C4×C149—21no—
103C4×C149—42no—
104C4×C149#9912yescomplemented
105Dic149—21no—
106Dic149—21no—
107C2×C149—22no—
108C2×C149#39011yescharacteristic
109C2×C149C2×#9911yescharacteristic
110C2×C149#41011yescharacteristic
111D149—22no—
112D149—21no—
113D149—21no—
114D149—82no—
115C149#196411yescharacteristic, complemented, Sylow
116#1964—1491nomaximal, Sylow
117C2×#121—1491no—
118C2×#99—1494no—
119#380—1491no—
120C4×C22⋊C4—1491no—
121C22×D4—1492no—
122C22×D4—1491no—
123C23×C4—1491no—
124#121—2981no—
125#121—2981no—
126#121—2981no—
127#121—2981no—
128C2×C4⋊C4—2981no—
129C2×C4⋊C4#1059701011yescharacteristic, complemented
130C2×C22⋊C4—1492no—
131C2×C22⋊C4—1492no—
132C2×C22⋊C4—1492no—
133C2×C42—2981no—
134#99—2988no—
135#95—2981no—
136#95—2981no—
137C24—1492no—
138C24—1491no—
139C2×D4—2984no—
140C2×D4—2982no—
141C2×D4—2982no—
142C2×D4—2984no—
143C2×D4—2981no—
144C2×D4—2981no—
145C2×D4—5962no—
146C22×C4—2982no—
147C22×C4—2982no—
148C22×C4—5962no—
149C22×C4—1491no—
150C22×C4—1491no—
151C22×C4—1491no—
152C22×C4—1491no—
153C22×C4—1491no—
154C22×C4C2×#1059701012yes—
155C22×C4C2×#1059701011yescharacteristic
156C4⋊C4—21no—
157C4⋊C4—21no—
158C4⋊C4—5962no—
159C22⋊C4—2982no—
160C22⋊C4—2982no—
161C22⋊C4—2982no—
162C22⋊C4—2984no—
163C22⋊C4—1494no—
164C42—5962no—
165C23—2982no—
166C23—2984no—
167C23—5961no—
168C23—5961no—
169C23—5962no—
170C23—5962no—
171C23—1491no—
172C23—1491no—
173C23—1492no—
174C23—1492no—
175C23C22×#1059701011yescharacteristic
176D4—5962no—
177D4—5964no—
178D4—5962no—
179D4—5962no—
180D4—5962no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—24no—
184C2×C4—2982no—
185C2×C4—2982no—
186C2×C4—2984no—
187C2×C4—5961no—
188C2×C4—5961no—
189C2×C4—5961no—
190C2×C4—5962no—
191C2×C4—5962no—
192C2×C4—5962no—
193C2×C4—5962no—
194C2×C4—5962no—
195C2×C4—1491no—
196C2×C4—1491no—
197C2×C4C22⋊#1059701011yescharacteristic
198C2×C4C22⋊#1059701011yescharacteristic
199C22—21no—
200C22—21no—
201C22—2981no—
202C22—2981no—
203C22—2981no—
204C22—2981no—
205C22—5962no—
206C22—5962no—
207C22—5962no—
208C22—5962no—
209C22—5962no—
210C22—1492no—
211C22—1491no—
212C22—1491no—
213C22—11924no—
214C22C2×C22⋊#1059701011yescharacteristic
215C22D4×#1059701012yes—
216C4—21no—
217C4—42no—
218C4—2981no—
219C4—2981no—
220C4—5964no—
221C4—11922no—
222C4#1801197012yescomplemented
223C2—22no—
224C2—2982no—
225C2—2981no—
226C2—2981no—
227C2—11922no—
228C2#2375057711yescharacteristic
229C2C2×#1801197011yescharacteristic
230C2#2375060611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC23×C149C22×C4
FrattiniC23C22×#10597010
FittingC2×C4⋊C4×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC2×#18011886C2
cosocleC23×D149C23
hypercenterC2×C4⋊C4#10597010
hypocenterC149#1964
LCSG ▷ C23×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#18011970C2semidirect
2. #23750567C2semidirect
3. C4×C22⋊#10597010C2semidirect
12. C22×D596C4semidirect
19. C2×#14558713C4semidirect
20. C2×C4⋊C4×C149C4semidirect
26. C22⋊#10597010D4semidirect
104. C4×C149#99semidirect
115. C149#1964semidirect
129. C2×C4⋊C4#10597010semidirect
222. C4#18011970semidirect

Maximal subgroups

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

subgroupindex
C2×#180119702
#237505672
C4×C22⋊#105970102
C2×#180118862
#1964149