Finite Group Databasebeta

← #34060723

Subgroups — #34060723

Order 19072.

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

normal subgroups only

This group has 324 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#23750705C211yesmaximal, characteristic, complemented
2#23750624C211yesmaximal, characteristic, complemented
3#23750617C211yesmaximal, characteristic, complemented
4D149⋊#100C211yesmaximal, characteristic, complemented
5#23750507C211yesmaximal, characteristic, complemented
6#23750494C211yesmaximal, characteristic, complemented
7C2×#18011938C211yesmaximal, characteristic
8#18011999—22no—
9#18011999—22no—
10D149⋊M16—22no—
11D149⋊M16C2211yescharacteristic
12D149⋊M16C2211yescharacteristic
13D149⋊M16C2211yescharacteristic
14#18011990C2211yescharacteristic
15#18011976—22no—
16#18011973—22no—
17#18011971—22no—
18C2×#14558737C2211yescharacteristic
19C2×D4×D149C2211yescharacteristic
20#18011938—22no—
21#18011938—22no—
22C2×#14558723C411yescharacteristic, complemented
23C2×D1192C411yescharacteristic, complemented
24C2×#14558721C411yescharacteristic, complemented
25C2×#14558719C2211yescharacteristic
26C2×SD16×C149C411yescharacteristic, complemented
27#14558746—24no—
28#14558746—21no—
29#14558746—21no—
30#14558746—21no—
31#14558745—21no—
32#14558745—21no—
33#14558745D412yes—
34D149⋊C8—24no—
35D149⋊C8—21no—
36D149⋊C8—21no—
37D149⋊C8D412yes—
38C4⋊#10597010—21no—
39C22⋊#10597010—21no—
40C4×#10597010—21no—
41C23×D149—21no—
42#14558737—21no—
43#14558737—21no—
44#14558737D412yes—
45#14558737D412yes—
46C2×D596—21no—
47C2×D596C2×C411yescharacteristic
48C2×D596C2×C411yescharacteristic
49C2×C22⋊D149—21no—
50D4×D149—21no—
51D4×D149—21no—
52D4×D149—21no—
53D4×D149—21no—
54C2×C4×D149—21no—
55C2×C4×D149C2311yescharacteristic
56#14558723—22no—
57D1192—22no—
58#14558721—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—21no—
71C22×D149—21no—
72C22×D149—41no—
73C22×D149—41no—
74C22×D149—82no—
75C22×D149#4111yescharacteristic
76D596—22no—
77D596—22no—
78D596—21no—
79D596—21no—
80D596—21no—
81D596C22⋊C412yes—
82C22⋊D149—41no—
83C22⋊D149—41no—
84C2×Dic149C2×D411yescharacteristic
85C4×D149—22no—
86C4×D149—22no—
87C4×D149C2×D411yescharacteristic
88C4×D149C2×D411yescharacteristic
89C4×D149C2×D411yescharacteristic
90C4×D149#4111yescharacteristic
91#11924746—21no—
92C23×C149—21no—
93Q8×C149—21no—
94Q8×C149C22⋊C412yes—
95D4×C149—21no—
96D4×C149—21no—
97C2×C4×C149—21no—
98C2×C4×C149C22×C411yescharacteristic
99C8×C149—21no—
100C22×C149—41no—
101C22×C149—81no—
102C22×C149C4×D411yescharacteristic
103C2×D149—22no—
104C2×D149—41no—
105C2×D149—41no—
106C2×D149—82no—
107C2×D149—82no—
108C2×D149—81no—
109C2×D149—81no—
110C2×D149#12111yescharacteristic
111C2×D149#12311yescharacteristic
112#10597010—81no—
113C4×C149—22no—
114C4×C149C2×C22⋊C411yescharacteristic
115C4×C149C4×D411yescharacteristic
116Dic149#12011yescharacteristic
117Dic149#12111yescharacteristic
118C2×C149—21no—
119C2×C149—81no—
120C2×C149#38611yescharacteristic
121D149—21no—
122D149—21no—
123D149—42no—
124D149—81no—
125C149#190311yescharacteristic, complemented, Sylow
126#1903—1491nomaximal, Sylow
127C2×AGL(1,ℤ/8)—1491no—
128#568—1491no—
129#421—1491no—
130#418—1491no—
131C2×#100—1491no—
132#344—1491no—
133#338—1491no—
134C2×#41—1491no—
135C22×D4—1491no—
136AGL(1,ℤ/8)—2982no—
137AGL(1,ℤ/8)—2982no—
138C2×SD16—1491no—
139C2×SD16#1059701011yescharacteristic, complemented
140C2×D8—1491no—
141C2×D8—1491no—
142#131—2982no—
143#131—2982no—
144C2×M16—2982no—
145C2×M16—1491no—
146C2×M16—1491no—
147C2×M16—1491no—
148C2×M16—1491no—
149#117—1491no—
150#104—2982no—
151#102—2982no—
152#100—2982no—
153C24—2981no—
154#41—2981no—
155#41—2981no—
156#41—1492no—
157#41—1492no—
158C2×Q8C2×#1059701011yescharacteristic
159C2×D4—2981no—
160C2×D4—2981no—
161C2×D4—2981no—
162C2×D4—2981no—
163C2×D4—2981no—
164C2×D4—2981no—
165C2×D4—1491no—
166C2×D4—1491no—
167C2×D4C2×#1059701011yescharacteristic
168C22×C4—2981no—
169C22×C4—1491no—
170SD16—22no—
171SD16—2982no—
172D8—2982no—
173D8—2982no—
174M16—2981no—
175M16—2981no—
176M16—2984no—
177M16—2981no—
178M16—2981no—
179M16—2981no—
180M16—2981no—
181M16—2981no—
182M16—1492no—
183C2×C8—2984no—
184C2×C8—2981no—
185C2×C8—2981no—
186C2×C8—1492no—
187C2×C8—1491no—
188C2×C8C2×#1059701011yescharacteristic
189C4⋊C4—2981no—
190C22⋊C4—2981no—
191C42—2981no—
192C23—21no—
193C23—2981no—
194C23—2981no—
195C23—5961no—
196C23—5961no—
197C23—1491no—
198C23—11922no—
199Q8—21no—
200Q8C22⋊#1059701012yes—
201D4—21no—
202D4—21no—
203D4—2982no—
204D4—2982no—
205D4—2981no—
206D4—2981no—
207D4—2981no—
208D4—5961no—
209D4—5961no—
210D4—1492no—
211C2×C4—21no—
212C2×C4—2982no—
213C2×C4—2982no—
214C2×C4—5961no—
215C2×C4—1491no—
216C2×C4—1491no—
217C2×C4—1491no—
218C2×C4—1491no—
219C2×C4—1491no—
220C2×C4C22×#1059701011yescharacteristic
221C8—21no—
222C8—2982no—
223C8—2982no—
224C8—2981no—
225C8—5961no—
226C22—41no—
227C22—81no—
228C22—2982no—
229C22—5961no—
230C22—5961no—
231C22—1491no—
232C22—1491no—
233C22—11921no—
234C22—11921no—
235C22—11922no—
236C22—11922no—
237C22D4×#1059701011yescharacteristic
238C4—22no—
239C4—1491no—
240C4—1491no—
241C4—11921no—
242C4C2×C22⋊#1059701011yescharacteristic
243C4D4×#1059701011yescharacteristic
244C2—21no—
245C2—81no—
246C2—2981no—
247C2—2981no—
248C2—5962no—
249C2—11921no—
250C2#2375057311yescharacteristic
subgroupG/H
centerC2#23750573
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC2×SD16×C149C4
socleC2×C149#386
prime radicalC2×#18011938C2
cosocleC2×C4×D149C23
hypercenterC2×SD16#10597010
hypocenterC149#1903
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. #23750705C2semidirect
2. #23750624C2semidirect
3. #23750617C2semidirect
4. D149⋊#100C2semidirect
5. #23750507C2semidirect
6. #23750494C2semidirect
22. C2×#14558723C4semidirect
23. C2×D1192C4semidirect
24. C2×#14558721C4semidirect
26. C2×SD16×C149C4semidirect
125. C149#1903semidirect
139. C2×SD16#10597010semidirect

Maximal subgroups

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

subgroupindex
#237507052
#237506242
#237506172
D149⋊#1002
#237505072
#237504942
C2×#180119382
#1903149