Finite Group Databasebeta

← #34060727

Subgroups — #34060727

Order 19072.

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

normal subgroups only

This group has 310 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#23750693C211yesmaximal, characteristic, complemented
2#23750623C211yesmaximal, characteristic
3#23750618C211yesmaximal, characteristic, complemented
4#23750605C211yesmaximal, characteristic
5#23750507C211yesmaximal, characteristic, complemented
6#23750493C211yesmaximal, characteristic, complemented
7C2×#18011940C211yesmaximal, characteristic
8D149⋊M16C2211yescharacteristic
9Q8×#10597010—22no—
10Q8×#10597010—22no—
11#18011990—22no—
12#18011990C2211yescharacteristic
13#18011990C2211yescharacteristic
14#18011990C2211yescharacteristic
15#18011975—22no—
16#18011974—22no—
17#18011969—22no—
18C2×#14558735C2211yescharacteristic
19C2×Q8×D149C2211yescharacteristic
20#18011940—22no—
21#18011940—22no—
22C2×Dic596C411yescharacteristic, complemented
23C2×#14558726C411yescharacteristic, complemented
24C2×#14558724C411yescharacteristic, complemented
25C2×#14558719C2211yescharacteristic
26C2×SD16×C149C411yescharacteristic, complemented
27#14558746—21no—
28#14558745—21no—
29D149⋊C8—21no—
30C4⋊#10597010—24no—
31C4⋊#10597010—21no—
32C4⋊#10597010—21no—
33C4⋊#10597010—21no—
34C22⋊#10597010—21no—
35C22⋊#10597010—21no—
36C22⋊#10597010D412yes—
37C4×#10597010—24no—
38C4×#10597010—21no—
39C4×#10597010—21no—
40C4×#10597010D412yes—
41#14558735—21no—
42#14558735—21no—
43#14558735—21no—
44#14558735—21no—
45C2×Dic298—21no—
46C2×Dic298C2×C411yescharacteristic
47C2×Dic298C2×C411yescharacteristic
48Q8×D149—21no—
49Q8×D149—21no—
50Q8×D149D412yes—
51Q8×D149D412yes—
52C2×C22⋊D149—21no—
53C22×Dic149—21no—
54C2×C4×D149—21no—
55C2×C4×D149C2311yescharacteristic
56Dic596—22no—
57#14558726—22no—
58#14558724—22no—
59#14558719—21no—
60#14558719—21no—
61C2×#11924746C2×C411yescharacteristic
62C2×Q8×C149C2×C411yescharacteristic
63C2×D4×C149C2×C411yescharacteristic
64SD16×C149—22no—
65C2×C8×C149C2×C411yescharacteristic
66C2×#10597010—22no—
67C2×#10597010—22no—
68C2×#10597010—41no—
69#11924753—41no—
70C22×D149C2×D411yescharacteristic
71Dic298—21no—
72Dic298—22no—
73Dic298—22no—
74Dic298—21no—
75Dic298—21no—
76Dic298C22⋊C412yes—
77C22⋊D149—41no—
78C22⋊D149—41no—
79C2×Dic149—21no—
80C2×Dic149—21no—
81C2×Dic149—41no—
82C2×Dic149—41no—
83C2×Dic149#4111yescharacteristic
84C4×D149—22no—
85C4×D149—22no—
86C4×D149C2×D411yescharacteristic
87C4×D149C2×D411yescharacteristic
88C4×D149C2×D411yescharacteristic
89C4×D149#4111yescharacteristic
90#11924746—21no—
91C23×C149—21no—
92Q8×C149—21no—
93Q8×C149C22⋊C412yes—
94D4×C149—21no—
95D4×C149—21no—
96C2×C4×C149—21no—
97C2×C4×C149C22×C411yescharacteristic
98C8×C149—21no—
99C22×C149—41no—
100C22×C149—81no—
101C22×C149C4×D411yescharacteristic
102C2×D149—41no—
103C2×D149#12011yescharacteristic
104C2×D149#12111yescharacteristic
105#10597010—42no—
106#10597010—42no—
107#10597010—81no—
108C4×C149—22no—
109C4×C149C2×C22⋊C411yescharacteristic
110C4×C149C4×D411yescharacteristic
111Dic149—22no—
112Dic149—41no—
113Dic149#12111yescharacteristic
114Dic149#12311yescharacteristic
115C2×C149—21no—
116C2×C149—81no—
117C2×C149#38611yescharacteristic
118D149—21no—
119D149—21no—
120C149#190511yescharacteristic, complemented, Sylow
121#1905—1491nomaximal, Sylow
122C2×#137—1491no—
123#519—1491no—
124#421—1491no—
125#419—1491no—
126#410—1491no—
127#344—1491no—
128H(3,ℤ/4)—1491no—
129C2×#41—1491no—
130C22×Q8—1491no—
131#137—2982no—
132#137—2982no—
133C2×Q16—1491no—
134C2×Q16—1491no—
135C2×SD16—1491no—
136C2×SD16#1059701011yescharacteristic, complemented
137C2×M16—1491no—
138C2×M16—1491no—
139C4×Q8—2982no—
140C4×Q8—2982no—
141#117—2982no—
142#117—1491no—
143#117—1491no—
144#117—1491no—
145#104—2982no—
146#103—2982no—
147#99—2982no—
148#41—2981no—
149#41—2981no—
150#41—2981no—
151#41—2981no—
152C2×Q8—2981no—
153C2×Q8—2981no—
154C2×Q8—2981no—
155C2×Q8—1492no—
156C2×Q8—1492no—
157C2×Q8—1491no—
158C2×Q8—1491no—
159C2×Q8C2×#1059701011yescharacteristic
160C2×D4—2981no—
161C2×D4C2×#1059701011yescharacteristic
162C22×C4—2981no—
163C22×C4—2981no—
164C22×C4—1491no—
165Q16—2982no—
166Q16—2982no—
167SD16—22no—
168SD16—2982no—
169M16—2981no—
170M16—2981no—
171M16—2981no—
172M16—2981no—
173C2×C8—2981no—
174C2×C8—1491no—
175C2×C8C2×#1059701011yescharacteristic
176C4⋊C4—2984no—
177C4⋊C4—2981no—
178C4⋊C4—2981no—
179C4⋊C4—2981no—
180C22⋊C4—2981no—
181C22⋊C4—2981no—
182C22⋊C4—1492no—
183C42—2984no—
184C42—2981no—
185C42—2981no—
186C42—1492no—
187C23—21no—
188C23—1491no—
189Q8—21no—
190Q8—2982no—
191Q8—2982no—
192Q8—2981no—
193Q8—2981no—
194Q8—2981no—
195Q8—1492no—
196Q8C22⋊#1059701012yes—
197D4—21no—
198D4—21no—
199D4—5961no—
200D4—5961no—
201C2×C4—21no—
202C2×C4—2982no—
203C2×C4—2982no—
204C2×C4—2981no—
205C2×C4—2982no—
206C2×C4—2982no—
207C2×C4—2981no—
208C2×C4—5961no—
209C2×C4—5961no—
210C2×C4—5961no—
211C2×C4—1491no—
212C2×C4—1491no—
213C2×C4—1491no—
214C2×C4—1491no—
215C2×C4—1491no—
216C2×C4C22×#1059701011yescharacteristic
217C8—21no—
218C8—2981no—
219C8—5961no—
220C22—41no—
221C22—81no—
222C22—5961no—
223C22—1491no—
224C22—1491no—
225C22D4×#1059701011yescharacteristic
226C4—22no—
227C4—2982no—
228C4—5962no—
229C4—5962no—
230C4—5961no—
231C4—1491no—
232C4—1491no—
233C4—11921no—
234C4C2×C22⋊#1059701011yescharacteristic
235C4D4×#1059701011yescharacteristic
236C2—21no—
237C2—81no—
238C2—2981no—
239C2—2981no—
240C2#2375057311yescharacteristic
subgroupG/H
centerC2#23750573
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC2×SD16×C149C4
socleC2×C149#386
prime radicalC2×#14558735C22
cosocleC2×C4×D149C23
hypercenterC2×SD16#10597010
hypocenterC149#1905
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. #23750693C2semidirect
3. #23750618C2semidirect
5. #23750507C2semidirect
6. #23750493C2semidirect
22. C2×Dic596C4semidirect
23. C2×#14558726C4semidirect
24. C2×#14558724C4semidirect
26. C2×SD16×C149C4semidirect
120. C149#1905semidirect
136. C2×SD16#10597010semidirect

Maximal subgroups

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

subgroupindex
#237506932
#237506232
#237506182
#237506052
#237505072
#237504932
C2×#180119402
#1905149