Finite Group Databasebeta

← #34060703

Subgroups — #34060703

Order 19072.

342 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 66 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#23750703C211yesmaximal, characteristic, complemented
2#23750612C211yesmaximal, characteristic, complemented
3#23750597C212yesmaximal, complemented
4#23750506C212yesmaximal, complemented
5#23750133C211yesmaximal, characteristic
6#18011998—24no—
7D149⋊M16—21no—
8C2×#14558745—21no—
9C2×#14558745C2212yes—
10C2×#14558745C2212yes—
11#18011972—21no—
12#18011971—21no—
13#18011968—24no—
14C2×#14558735C2211yescharacteristic
15C22×C4×D149C2211yescharacteristic
16#18011894C411yescharacteristic
17#18011889—21no—
18#18011884—21no—
19#18011881C411yescharacteristic
20#18011879C411yescharacteristic
21#18011873—21no—
22#18011871—21no—
23#18011867C2211yescharacteristic
24#123×C149C411yescharacteristic
25#14558746—22no—
26#14558745—22no—
27#14558745—22no—
28#14558745—22no—
29#14558745—22no—
30#14558745—22no—
31D149⋊C8—22no—
32C2×#11924753—22no—
33C2×#11924753—22no—
34C2×#11924753D414yescomplemented
35C23×D149C2×C411yescharacteristic
36#14558735—22no—
37#14558735—22no—
38C2×Dic298D411yescharacteristic
39C2×D596—21no—
40C2×C22⋊D149—21no—
41C2×C22⋊D149C2×C411yescharacteristic
42C2×C22⋊D149D411yescharacteristic
43C22×Dic149D411yescharacteristic
44C22×Dic149C2311yescharacteristic
45C2×C4×D149—22no—
46C2×C4×D149—21no—
47C2×C4×D149—21no—
48C2×C4×D149—22no—
49C2×C4×D149D411yescharacteristic
50#14558715—21no—
51#14558715—21no—
52C22⋊Dic149C2×C411yescharacteristic
53#14558713—21no—
54#14558713—21no—
55#14558713—21no—
56C4×Dic149—21no—
57C2×D4×C149C2×C411yescharacteristic
58C22×C4×C149C2×C411yescharacteristic
59C4⋊C4×C149—21no—
60C22⋊C4×C149—21no—
61C22⋊C4×C149C2×C411yescharacteristic
62#11924753—24no—
63#11924753—42no—
64C22×D149—21no—
65C22×D149—22no—
66C22×D149—42no—
67C22×D149C22⋊C411yescharacteristic
68Dic298—22no—
69D596—42no—
70C22⋊D149—22no—
71C22⋊D149—22no—
72C22⋊D149—42no—
73C2×Dic149—21no—
74C2×Dic149—21no—
75C2×Dic149—21no—
76C2×Dic149C22⋊C411yescharacteristic
77C2×Dic149C2×D412yes—
78C2×Dic149C2×D411yescharacteristic
79C2×Dic149C2×D411yescharacteristic
80C2×Dic149#4112yes—
81C4×D149—21no—
82C4×D149—21no—
83C4×D149—41no—
84C4×D149—42no—
85C4×D149—41no—
86C23×C149C22⋊C411yescharacteristic
87C23×C149C22×C411yescharacteristic
88D4×C149—22no—
89C2×C4×C149—21no—
90C2×C4×C149—21no—
91C2×C4×C149—22no—
92C2×C4×C149C22⋊C411yescharacteristic
93C22×C149—21no—
94C22×C149—41no—
95C22×C149—41no—
96C22×C149C2×C22⋊C411yescharacteristic
97C22×C149C4×D412yes—
98C2×D149—22no—
99C2×D149—24no—
100C2×D149—21no—
101C2×D149—41no—
102C2×D149—42no—
103C2×D149—41no—
104C2×D149—41no—
105C4×C149—21no—
106C4×C149—41no—
107C4×C149—41no—
108Dic149—21no—
109Dic149—41no—
110Dic149#12011yescharacteristic
111Dic149#12112yes—
112Dic149#12311yescharacteristic
113C2×C149—21no—
114C2×C149—22no—
115C2×C149—41no—
116C2×C149#38611yescharacteristic
117D149—42no—
118D149—41no—
119C149#189111yescharacteristic, complemented, Sylow
120#1891—1491nomaximal, Sylow
121#568—1491no—
122#525—1491no—
123#413—1491no—
124#407—1492no—
125#344—1492no—
126C2×#41—1491no—
127C23×C4—1491no—
128#131—2984no—
129C2×M16—2981no—
130C2×M16—2981no—
131C2×M16—1492no—
132C2×M16—1492no—
133#123—1491no—
134#123#1059701011yescharacteristic
135C22⋊Q8—2981no—
136#121—2981no—
137#120—1491no—
138#120—1491no—
139C4×D4—2981no—
140C4×D4—2981no—
141#117—1491no—
142#101—2981no—
143#100—2981no—
144C22⋊C8—2984no—
145C24—1491no—
146#41—2982no—
147#41—2982no—
148C2×Q8—1491no—
149C2×D4—2981no—
150C2×D4—2981no—
151C2×D4—1491no—
152C2×D4—1491no—
153C2×D4C2×#1059701011yescharacteristic
154C22×C4—2982no—
155C22×C4—2981no—
156C22×C4—2981no—
157C22×C4—2982no—
158C22×C4—1491no—
159C22×C4—1491no—
160C22×C4—1491no—
161C22×C4C2×#1059701011yescharacteristic
162M16—2982no—
163M16—2982no—
164M16—2982no—
165M16—2982no—
166M16—2982no—
167M16—2982no—
168C2×C8—2982no—
169C2×C8—2982no—
170C2×C8—2982no—
171C2×C8—1494no—
172C4⋊C4—21no—
173C4⋊C4—2981no—
174C4⋊C4—2981no—
175C22⋊C4—21no—
176C22⋊C4—2981no—
177C22⋊C4—2981no—
178C22⋊C4—2981no—
179C22⋊C4—1491no—
180C22⋊C4C2×#1059701011yescharacteristic
181C42—2981no—
182C23—2981no—
183C23—2982no—
184C23—5962no—
185C23—1491no—
186C23C22⋊#1059701011yescharacteristic
187C23C22×#1059701011yescharacteristic
188Q8—2982no—
189D4—22no—
190D4—2982no—
191D4—2982no—
192D4—5962no—
193D4—5962no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—22no—
197C2×C4—2981no—
198C2×C4—2981no—
199C2×C4—2981no—
200C2×C4—2981no—
201C2×C4—2981no—
202C2×C4—5961no—
203C2×C4—5962no—
204C2×C4—5961no—
205C2×C4—1491no—
206C2×C4—1491no—
207C2×C4—1491no—
208C2×C4—1492no—
209C2×C4—1492no—
210C2×C4C22⋊#1059701011yescharacteristic
211C8—2984no—
212C8—5962no—
213C22—21no—
214C22—41no—
215C22—41no—
216C22—2982no—
217C22—2984no—
218C22—2981no—
219C22—5961no—
220C22—5961no—
221C22—5962no—
222C22—5961no—
223C22C2×C22⋊#1059701011yescharacteristic
224C22D4×#1059701012yes—
225C4—21no—
226C4—41no—
227C4—41no—
228C4—2981no—
229C4—5961no—
230C4—1491no—
231C4—1492no—
232C4—1491no—
233C2—21no—
234C2—22no—
235C2—41no—
236C2—5962no—
237C2—5961no—
238C2#2375057311yescharacteristic
subgroupG/H
centerC2#23750573
commutatorC23×C149C22×C4
FrattiniC23C22×#10597010
Fitting#123×C149C4
socleC2×C149#386
prime radical#23750133C2
cosocleC22×Dic149C23
hypercenter#123#10597010
hypocenterC149#1891
LCSG ▷ C23×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C23 ◁ #123

Complements

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

NH ≅ G/Ntype
1. #23750703C2semidirect
2. #23750612C2semidirect
3. #23750597C2semidirect
4. #23750506C2semidirect
34. C2×#11924753D4semidirect
119. C149#1891semidirect

Maximal subgroups

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

subgroupindex
#237507032
#237506122
#237505972
#237505062
#237501332
#1891149