Finite Group Databasebeta

← #34045720

Subgroups — #34045720

Order 19072.

394 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 75 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
1C2×#18011942C211yesmaximal, characteristic, complemented
2#23750192C211yesmaximal, characteristic
3C2×#18011839C211yesmaximal, characteristic, complemented
4#23749634C211yesmaximal, characteristic, complemented
5C2×#18011828C211yesmaximal, characteristic, complemented
6#23749385C211yesmaximal, characteristic, complemented
7C2×#124×C149C211yesmaximal, characteristic, complemented
8C2×#14558736C2211yescharacteristic
9#18011942—22no—
10#18011942—22no—
11C2×#14558726—21no—
12C2×#14558723—21no—
13C2×#14558720C2211yescharacteristic
14C2×#14558720C2211yescharacteristic
15#18011907—21no—
16#18011898—21no—
17#18011882—22no—
18#18011880—22no—
19#18011870C2211yescharacteristic
20#18011839—22no—
21#18011835—22no—
22#18011828—22no—
23C22×Q8×C149C2211yescharacteristic
24C22×D4×C149C2211yescharacteristic
25#124×C149—22no—
26#124×C149—22no—
27C2×C22⋊C4×C149—22no—
28C2×C42×C149C2211yescharacteristic
29#14558736—21no—
30#14558736—21no—
31#14558736—21no—
32#14558736—21no—
33C2×Dic298D411yescharacteristic
34C2×D596D411yescharacteristic
35C2×C22⋊D149—24no—
36C2×C22⋊D149—21no—
37C2×C4×D149—21no—
38#14558726—24no—
39#14558723—24no—
40#14558720—21no—
41#14558720—21no—
42#14558720—21no—
43#14558720D412yescomplemented
44C2×#11924746—21no—
45C2×#11924746—21no—
46C4⋊Dic149D412yes—
47C22⋊Dic149—24no—
48C22⋊Dic149—21no—
49C4×Dic149—21no—
50C24×C149D412yes—
51C2×Q8×C149—21no—
52C2×Q8×C149—21no—
53C2×Q8×C149—21no—
54C2×Q8×C149—21no—
55C2×Q8×C149—21no—
56C2×Q8×C149D412yescomplemented
57C2×D4×C149—21no—
58C2×D4×C149—21no—
59C2×D4×C149—21no—
60C2×D4×C149—21no—
61C2×D4×C149—21no—
62C2×D4×C149—21no—
63C22×C4×C149—21no—
64C22×C4×C149—21no—
65C22×C4×C149C2311yescharacteristic
66C22⋊C4×C149—28no—
67C42×C149—21no—
68C42×C149D412yescomplemented
69C22×D149—21no—
70Dic298—21no—
71Dic298—21no—
72D596—21no—
73D596—21no—
74C22⋊D149—41no—
75C22⋊D149—41no—
76C22⋊D149—84no—
77C2×Dic149—21no—
78C2×Dic149—22no—
79C4×D149—41no—
80C4×D149—41no—
81#11924746—22no—
82#11924746—41no—
83C23×C149—22no—
84C23×C149—22no—
85C23×C149—22no—
86C23×C149—44no—
87C23×C149C2×D411yescharacteristic
88Q8×C149—22no—
89Q8×C149—22no—
90Q8×C149—41no—
91Q8×C149—41no—
92D4×C149—41no—
93D4×C149—41no—
94D4×C149—41no—
95D4×C149—41no—
96C2×C4×C149—22no—
97C2×C4×C149—22no—
98C2×C4×C149—42no—
99C2×C4×C149—41no—
100C2×C4×C149—41no—
101C2×C4×C149C2×D411yescharacteristic
102C2×C4×C149C2×D411yescharacteristic
103C2×C4×C149C2×D411yescharacteristic
104C2×C4×C149C2×D411yescharacteristic
105C2×C4×C149C2×D411yescharacteristic
106C2×C4×C149#4111yescharacteristic
107C22×C149—22no—
108C22×C149—44no—
109C22×C149—42no—
110C22×C149—44no—
111C22×C149—82no—
112C22×C149#12011yescharacteristic
113C22×C149#12011yescharacteristic
114C22×C149#12111yescharacteristic
115C2×D149—41no—
116C2×D149—42no—
117C4×C149—42no—
118C4×C149—42no—
119C4×C149#12011yescharacteristic
120C4×C149#12111yescharacteristic
121C4×C149#12111yescharacteristic
122C4×C149#12711yescharacteristic
123Dic149—41no—
124Dic149—42no—
125C2×C149—21no—
126C2×C149—21no—
127C2×C149—82no—
128C2×C149#39211yescharacteristic
129C2×C149#45512yes—
130D149—81no—
131C149#200411yescharacteristic, complemented, Sylow
132#2004—1491nomaximal, Sylow
133C2×#137—1491no—
134#535—1491no—
135C2×#124D14911yescharacteristic, complemented
136C2×#104—1491no—
137#419—1491no—
138C2×#100—1491no—
139#339—1491no—
140C2×#41—1491no—
141C22×Q8C2×D14911yescharacteristic
142C22×D4C2×D14911yescharacteristic
143#137—2982no—
144#137—2982no—
145C2×Q16—2981no—
146C2×SD16—2981no—
147C2×M16—1491no—
148C2×M16—1491no—
149#127—2981no—
150#124—22no—
151#124—22no—
152#124—2981no—
153#121—2982no—
154#120—2982no—
155#117—1491no—
156C2×C22⋊C4—22no—
157C2×C42C2×D14911yescharacteristic
158#104—2982no—
159#103—2982no—
160#100—2982no—
161C24C22⋊D14912yes—
162#41—2981no—
163#41—2981no—
164#41—2981no—
165#41—2981no—
166C2×Q8—21no—
167C2×Q8—21no—
168C2×Q8—21no—
169C2×Q8—21no—
170C2×Q8—21no—
171C2×Q8—1491no—
172C2×Q8C22⋊D14912yescomplemented
173C2×D4—21no—
174C2×D4—21no—
175C2×D4—21no—
176C2×D4—21no—
177C2×D4—21no—
178C2×D4—21no—
179C2×D4—2981no—
180C2×D4—2984no—
181C2×D4—1491no—
182C22×C4—21no—
183C22×C4—21no—
184C22×C4—2981no—
185C22×C4C22×D14911yescharacteristic
186Q16—2984no—
187SD16—2984no—
188M16—2981no—
189M16—2981no—
190M16—2981no—
191M16—1492no—
192C2×C8—2981no—
193C2×C8—2981no—
194C4⋊C4—1492no—
195C22⋊C4—28no—
196C22⋊C4—2984no—
197C22⋊C4—2981no—
198C42—21no—
199C42—2981no—
200C42C22⋊D14912yescomplemented
201C23—22no—
202C23—22no—
203C23—22no—
204C23—44no—
205C23—2981no—
206C23C2×C22⋊D14911yescharacteristic
207Q8—22no—
208Q8—22no—
209Q8—41no—
210Q8—41no—
211Q8—2981no—
212Q8—2981no—
213D4—41no—
214D4—41no—
215D4—41no—
216D4—41no—
217D4—2981no—
218D4—2981no—
219D4—5961no—
220D4—5961no—
221D4—11924no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—42no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—2982no—
228C2×C4—2981no—
229C2×C4—5961no—
230C2×C4—5961no—
231C2×C4D4×D14911yescharacteristic
232C2×C4D4×D14911yescharacteristic
233C2×C4D4×D14911yescharacteristic
234C2×C4C2×C22⋊D14911yescharacteristic
235C2×C4C2×C22⋊D14911yescharacteristic
236C2×C4#1455873511yescharacteristic
237C8—2982no—
238C8—5961no—
239C22—22no—
240C22—44no—
241C22—42no—
242C22—44no—
243C22—82no—
244C22—5961no—
245C22—5962no—
246C22#1801187911yescharacteristic
247C22#1801188011yescharacteristic
248C22#1801188311yescharacteristic
249C4—42no—
250C4—42no—
251C4—5961no—
252C4—5962no—
253C4#1801187911yescharacteristic
254C4#1801188211yescharacteristic
255C4#1801188311yescharacteristic
256C4#1801190711yescharacteristic
257C2—21no—
258C2—21no—
259C2—82no—
260C2—11921no—
261C2#2374953311yescharacteristic
262C2#2374980212yes—
subgroupG/H
centerC22#18011879
commutator, cosocleC22×C4×C149C23
FrattiniC22×C4C22×D149
FittingC2×#124×C149C2
socleC22×C149#120
prime radical#23750192C2
hypercenterC2×#124D149
hypocenterC149#2004
LCSG ▷ C22×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×#18011942C2semidirect
3. C2×#18011839C2semidirect
4. #23749634C2semidirect
5. C2×#18011828C2semidirect
6. #23749385C2semidirect
7. C2×#124×C149C2semidirect
43. #14558720D4semidirect
56. C2×Q8×C149D4semidirect
68. C42×C149D4semidirect
131. C149#2004semidirect
135. C2×#124D149semidirect
172. C2×Q8C22⋊D149semidirect
200. C42C22⋊D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119422
#237501922
C2×#180118392
#237496342
C2×#180118282
#237493852
C2×#124×C1492
#2004149