Finite Group Databasebeta

← #34060720

Subgroups — #34060720

Order 19072.

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

normal subgroups only

This group has 304 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
2#23750623C211yesmaximal, characteristic
3#23750618C211yesmaximal, characteristic, complemented
4D149⋊#101C211yesmaximal, characteristic, complemented
5#23750507C211yesmaximal, characteristic, complemented
6#23750494C211yesmaximal, characteristic, complemented
7C2×#18011940C211yesmaximal, characteristic
8#18011998—22no—
9#18011998—22no—
10D149⋊M16C2211yescharacteristic
11D149⋊M16C2211yescharacteristic
12D149⋊M16C2211yescharacteristic
13C2×#14558745—22no—
14#18011990C2211yescharacteristic
15#18011975—22no—
16#18011974—22no—
17#18011972—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#14558746—21no—
29#14558746—21no—
30#14558745—24no—
31#14558745—21no—
32#14558745—21no—
33#14558745D412yes—
34D149⋊C8—21no—
35D149⋊C8—21no—
36D149⋊C8D412yes—
37C2×#11924753—24no—
38C4⋊#10597010—21no—
39C22⋊#10597010—21no—
40C4×#10597010—21no—
41#14558735—21no—
42#14558735—21no—
43#14558735D412yes—
44#14558735D412yes—
45C2×Dic298—21no—
46C2×Dic298C2×C411yescharacteristic
47C2×Dic298C2×C411yescharacteristic
48Q8×D149—21no—
49Q8×D149—21no—
50Q8×D149—21no—
51Q8×D149—21no—
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—41no—
67#11924753—22no—
68#11924753—22no—
69#11924753—41no—
70C22×D149#4111yescharacteristic
71Dic298—21no—
72Dic298—21no—
73Dic298—21no—
74Dic298—41no—
75Dic298—41no—
76Dic298C22⋊C412yes—
77C22⋊D149—22no—
78C22⋊D149—22no—
79C2×Dic149—21no—
80C2×Dic149—22no—
81C2×Dic149—22no—
82C2×Dic149—21no—
83C2×Dic149C2×D411yescharacteristic
84C4×D149—41no—
85C4×D149—41no—
86C4×D149C2×D411yescharacteristic
87C4×D149C2×D411yescharacteristic
88C4×D149C2×D411yescharacteristic
89C4×D149#4111yescharacteristic
90#11924746—21no—
91C23×C149—21no—
92Q8×C149—21no—
93Q8×C149—21no—
94D4×C149—21no—
95D4×C149C22⋊C412yes—
96C2×C4×C149—21no—
97C2×C4×C149C22×C411yescharacteristic
98C8×C149—21no—
99C22×C149—22no—
100C22×C149—81no—
101C22×C149C4×D411yescharacteristic
102C2×D149—41no—
103C2×D149#12111yescharacteristic
104C2×D149#12311yescharacteristic
105#10597010—81no—
106C4×C149—41no—
107C4×C149C2×C22⋊C411yescharacteristic
108C4×C149C4×D411yescharacteristic
109Dic149—22no—
110Dic149—41no—
111Dic149#12011yescharacteristic
112Dic149#12111yescharacteristic
113C2×C149—21no—
114C2×C149—42no—
115C2×C149#38611yescharacteristic
116D149—21no—
117D149—21no—
118C149#190211yescharacteristic, complemented, Sylow
119#1902—1491nomaximal, Sylow
120C2×#137—1491no—
121#568—1491no—
122#421—1491no—
123#419—1491no—
124C2×#101—1491no—
125#344—1491no—
126#338—1491no—
127C2×#41—1491no—
128C22×Q8—1491no—
129#137—2982no—
130#137—2982no—
131C2×Q16—1491no—
132C2×Q16—1491no—
133C2×SD16—1491no—
134C2×SD16#1059701011yescharacteristic, complemented
135#131—2982no—
136#131—2982no—
137C2×M16—2982no—
138C2×M16—1491no—
139C2×M16—1491no—
140C2×M16—1491no—
141C2×M16—1491no—
142#117—1491no—
143#104—2982no—
144#103—2982no—
145#101—2982no—
146#41—2981no—
147#41—2981no—
148#41—1492no—
149#41—1492no—
150C2×Q8—2981no—
151C2×Q8—2981no—
152C2×Q8—2981no—
153C2×Q8—2981no—
154C2×Q8—2981no—
155C2×Q8—1491no—
156C2×Q8—1491no—
157C2×Q8C2×#1059701011yescharacteristic
158C2×D4—2981no—
159C2×D4C2×#1059701011yescharacteristic
160C22×C4—2981no—
161C22×C4—2981no—
162C22×C4—1491no—
163Q16—2982no—
164Q16—2982no—
165SD16—22no—
166SD16—2982no—
167M16—2981no—
168M16—2981no—
169M16—2984no—
170M16—2981no—
171M16—2981no—
172M16—2981no—
173M16—2981no—
174M16—2981no—
175M16—1492no—
176C2×C8—2984no—
177C2×C8—2981no—
178C2×C8—2981no—
179C2×C8—1492no—
180C2×C8—1491no—
181C2×C8C2×#1059701011yescharacteristic
182C4⋊C4—2981no—
183C22⋊C4—2981no—
184C42—2981no—
185C23—21no—
186C23—1491no—
187Q8—21no—
188Q8—21no—
189Q8—2981no—
190Q8—2981no—
191Q8—2981no—
192Q8—5961no—
193Q8—5961no—
194Q8—1492no—
195D4—21no—
196D4—2982no—
197D4—2982no—
198D4C22⋊#1059701012yes—
199C2×C4—21no—
200C2×C4—2981no—
201C2×C4—2982no—
202C2×C4—2982no—
203C2×C4—2981no—
204C2×C4—5961no—
205C2×C4—5961no—
206C2×C4—5961no—
207C2×C4—1491no—
208C2×C4—1491no—
209C2×C4—1491no—
210C2×C4—1491no—
211C2×C4—1491no—
212C2×C4C22×#1059701011yescharacteristic
213C8—21no—
214C8—2982no—
215C8—2982no—
216C8—2981no—
217C8—5961no—
218C22—22no—
219C22—81no—
220C22—5961no—
221C22—1491no—
222C22—1491no—
223C22D4×#1059701011yescharacteristic
224C4—41no—
225C4—2982no—
226C4—5961no—
227C4—1491no—
228C4—1491no—
229C4—11921no—
230C4C2×C22⋊#1059701011yescharacteristic
231C4D4×#1059701011yescharacteristic
232C2—21no—
233C2—42no—
234C2—2981no—
235C2—2981no—
236C2#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#1902
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
3. #23750618C2semidirect
4. D149⋊#101C2semidirect
5. #23750507C2semidirect
6. #23750494C2semidirect
22. C2×Dic596C4semidirect
23. C2×#14558726C4semidirect
24. C2×#14558724C4semidirect
26. C2×SD16×C149C4semidirect
118. C149#1902semidirect
134. C2×SD16#10597010semidirect

Maximal subgroups

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

subgroupindex
#237507032
#237506232
#237506182
D149⋊#1012
#237505072
#237504942
C2×#180119402
#1902149