Finite Group Databasebeta

← #34060851

Subgroups — #34060851

Order 19072.

296 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 68 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
1D149⋊#108C211yesmaximal, characteristic, complemented
2#23750618C211yesmaximal, characteristic, complemented
3#23750617C211yesmaximal, characteristic
4D149⋊#101C211yesmaximal, characteristic, complemented
5D149⋊#100C211yesmaximal, characteristic
6#23750588C211yesmaximal, characteristic, complemented
7C2×SD16×D149C211yesmaximal, characteristic
8D149⋊M16C2211yescharacteristic
9D149⋊M16C2211yescharacteristic
10D149⋊M16C2211yescharacteristic
11#18011990C2211yescharacteristic
12#18011982—21no—
13#18011981—21no—
14#18011974—22no—
15#18011973—22no—
16#18011972—22no—
17#18011971—22no—
18#18011965—21no—
19C8×#10597010—21no—
20C2×Q8×D149C2211yescharacteristic
21C2×D4×D149C2211yescharacteristic
22C2×#14558725C411yescharacteristic, complemented
23C2×#14558724C411yescharacteristic, complemented
24C2×#14558723C411yescharacteristic, complemented
25SD16×D149—21no—
26SD16×D149—21no—
27SD16×D149—21no—
28SD16×D149—21no—
29C2×C8×D149C2211yescharacteristic
30C2×SD16×C149C411yescharacteristic, complemented
31#14558746—21no—
32#14558746—21no—
33#14558746—21no—
34#14558745—21no—
35#14558745—21no—
36#14558745D412yes—
37D149⋊C8—21no—
38D149⋊C8—21no—
39D149⋊C8—21no—
40C4⋊#10597010D412yes—
41C22⋊#10597010—21no—
42C4×#10597010—21no—
43C23×D149—21no—
44C2×Dic298—21no—
45C2×Dic298C2×C411yescharacteristic
46Q8×D149—21no—
47Q8×D149—21no—
48Q8×D149—21no—
49Q8×D149—21no—
50C2×D596C2×C411yescharacteristic
51C2×C22⋊D149—21no—
52D4×D149—21no—
53D4×D149—21no—
54D4×D149—21no—
55D4×D149—21no—
56C2×C4×D149—21no—
57C2×C4×D149C2311yescharacteristic
58#14558725—21no—
59#14558725—21no—
60#14558724—21no—
61#14558724—21no—
62#14558723—21no—
63#14558723—21no—
64C2×#11924746C2×C411yescharacteristic
65C8×D149D411yescharacteristic
66C8×D149D411yescharacteristic
67C8×D149D411yescharacteristic
68C8×D149D411yescharacteristic
69C2×Q8×C149C2×C411yescharacteristic
70C2×D4×C149C2×C411yescharacteristic
71SD16×C149—21no—
72SD16×C149—21no—
73C2×C8×C149C2×C411yescharacteristic
74C2×#10597010—22no—
75#11924753—22no—
76#11924753—41no—
77#11924753—41no—
78C22×D149—21no—
79C22×D149—41no—
80C22×D149—41no—
81C22×D149—82no—
82C22×D149#4111yescharacteristic
83Dic298—21no—
84Dic298—21no—
85Dic298—41no—
86Dic298—41no—
87D596—21no—
88D596—21no—
89C22⋊D149—41no—
90C22⋊D149—41no—
91C2×Dic149—21no—
92C2×Dic149C2×D411yescharacteristic
93C4×D149—41no—
94C4×D149—41no—
95C4×D149C2×D411yescharacteristic
96C4×D149C2×D411yescharacteristic
97C4×D149C2×D411yescharacteristic
98C4×D149#4111yescharacteristic
99#11924746C22⋊C411yescharacteristic
100#11924746C22⋊C411yescharacteristic
101C23×C149—21no—
102Q8×C149—21no—
103Q8×C149—21no—
104D4×C149—21no—
105D4×C149—21no—
106C2×C4×C149—21no—
107C2×C4×C149C22×C411yescharacteristic
108C8×C149C22⋊C411yescharacteristic
109C8×C149C22⋊C411yescharacteristic
110C22×C149—41no—
111C22×C149—81no—
112C22×C149C4×D411yescharacteristic
113C2×D149—22no—
114C2×D149—41no—
115C2×D149—82no—
116C2×D149—82no—
117C2×D149—81no—
118C2×D149#12111yescharacteristic
119C2×D149#12411yescharacteristic
120#10597010—42no—
121C4×C149—41no—
122C4×C149C2×C22⋊C411yescharacteristic
123C4×C149C4×D411yescharacteristic
124Dic149—41no—
125Dic149#12111yescharacteristic
126Dic149#12711yescharacteristic
127C2×C149—21no—
128C2×C149—81no—
129C2×C149#39011yescharacteristic
130D149—21no—
131D149—81no—
132D149#47112yes—
133C149#197711yescharacteristic, complemented, Sylow
134#1977—1491nomaximal, Sylow
135C22×SD16—1491no—
136C2×#108—1491no—
137#419—1491no—
138#418—1491no—
139C2×#101—1491no—
140C2×#100—1491no—
141#405—1491no—
142C22×Q8—1491no—
143C22×D4—1491no—
144C2×SD16—2981no—
145C2×SD16—2981no—
146C2×SD16—2981no—
147C2×SD16—2981no—
148C2×SD16—1491no—
149C2×SD16—1491no—
150C2×SD16—1491no—
151C2×SD16#1059701011yescharacteristic, complemented
152C2×M16—1491no—
153C2×M16—1491no—
154C2×M16—1491no—
155C22×C8—1491no—
156#117—1491no—
157#108—2981no—
158#108—2981no—
159#103—2982no—
160#102—2982no—
161#101—2982no—
162#100—2982no—
163#97—2981no—
164C4×C8—2981no—
165C24—2981no—
166C2×Q8—2981no—
167C2×Q8—2981no—
168C2×Q8—2981no—
169C2×Q8—2981no—
170C2×Q8—2981no—
171C2×Q8—1491no—
172C2×Q8C2×#1059701011yescharacteristic
173C2×D4—2981no—
174C2×D4—2981no—
175C2×D4—2981no—
176C2×D4—2981no—
177C2×D4—2981no—
178C2×D4—1491no—
179C2×D4C2×#1059701011yescharacteristic
180C22×C4—2981no—
181C22×C4—1491no—
182SD16—21no—
183SD16—21no—
184SD16—2981no—
185SD16—2981no—
186SD16—2981no—
187SD16—2981no—
188SD16—2981no—
189SD16—2981no—
190M16—2981no—
191M16—2981no—
192M16—2981no—
193M16—2981no—
194M16—2981no—
195M16—1492no—
196C2×C8—2981no—
197C2×C8—2981no—
198C2×C8—2981no—
199C2×C8—1491no—
200C2×C8—1491no—
201C2×C8—1491no—
202C2×C8—1491no—
203C2×C8—1491no—
204C2×C8C2×#1059701011yescharacteristic
205C4⋊C4—1492no—
206C22⋊C4—2981no—
207C42—2981no—
208C23—21no—
209C23—2981no—
210C23—5961no—
211C23—5961no—
212C23—1491no—
213C23—11922no—
214Q8—21no—
215Q8—21no—
216Q8—2981no—
217Q8—2981no—
218Q8—5961no—
219Q8—5961no—
220D4—21no—
221D4—21no—
222D4—2981no—
223D4—2981no—
224D4—5961no—
225D4—5961no—
226C2×C4—21no—
227C2×C4—2982no—
228C2×C4—2981no—
229C2×C4—5961no—
230C2×C4—5961no—
231C2×C4—1491no—
232C2×C4—1491no—
233C2×C4—1491no—
234C2×C4—1491no—
235C2×C4—1491no—
236C2×C4C22×#1059701011yescharacteristic
237C8—2982no—
238C8—5961no—
239C8—5961no—
240C8—1491no—
241C8—1491no—
242C8C22⋊#1059701011yescharacteristic
243C8C22⋊#1059701011yescharacteristic
244C22—41no—
245C22—81no—
246C22—2982no—
247C22—5961no—
248C22—1491no—
249C22—1491no—
250C22—11921no—
251C22—11922no—
252C22—11922no—
253C22D4×#1059701011yescharacteristic
254C4—41no—
255C4—5962no—
256C4—5961no—
257C4—1491no—
258C4—1491no—
259C4C2×C22⋊#1059701011yescharacteristic
260C4D4×#1059701011yescharacteristic
261C2—21no—
262C2—81no—
263C2—2981no—
264C2—1492no—
265C2—11921no—
266C2#2375057711yescharacteristic
subgroupG/H
centerC2#23750577
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC2×SD16×C149C4
socleC2×C149#390
prime radicalC2×D4×D149C22
cosocleC2×C4×D149C23
hypercenterC2×SD16#10597010
hypocenterC149#1977
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. D149⋊#108C2semidirect
2. #23750618C2semidirect
4. D149⋊#101C2semidirect
6. #23750588C2semidirect
22. C2×#14558725C4semidirect
23. C2×#14558724C4semidirect
24. C2×#14558723C4semidirect
30. C2×SD16×C149C4semidirect
133. C149#1977semidirect
151. C2×SD16#10597010semidirect

Maximal subgroups

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

subgroupindex
D149⋊#1082
#237506182
#237506172
D149⋊#1012
D149⋊#1002
#237505882
C2×SD16×D1492
#1977149