Finite Group Databasebeta

← #34056407

Subgroups — #34056407

Order 19072.

484 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 131 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×#18011930C211yesmaximal, characteristic, complemented
2#23750274C212yesmaximal, complemented
3#23750003C211yesmaximal, characteristic, complemented
4#23749866C211yesmaximal, characteristic, complemented
5#23749863C211yesmaximal, characteristic, complemented
6#23749828C212yesmaximal, complemented
7#23749787C212yesmaximal, complemented
8#23749784C212yesmaximal, complemented
9D8×Dic149C211yesmaximal, characteristic, complemented
10C8×C22⋊D149C211yesmaximal, characteristic, complemented
11C2×#135×C149C211yesmaximal, characteristic, complemented
12C2×#14558735C2212yes—
13#18011930—24no—
14C2×Dic596C2211yescharacteristic
15C2×#14558726C2212yes—
16C2×#14558724C2212yes—
17C2×C8×D149C2211yescharacteristic
18#18011909C2212yes—
19#18011894—22no—
20#18011892—22no—
21#18011890C2212yes—
22#18011887C2212yes—
23#18011883—22no—
24D4×Dic149C2212yes—
25C4×C22⋊D149C2211yescharacteristic
26C2×#14558715—22no—
27#18011845C2211yescharacteristic
28#18011840C2211yescharacteristic
29#18011836C2212yes—
30#18011835C2212yes—
31#18011832C2212yes—
32C22⋊#11924746C2211yescharacteristic
33#18011823C2211yescharacteristic
34C8×Dic149C2211yescharacteristic
35C2×#41×C149C2212yes—
36#135×C149—24no—
37C2×Q16×C149C2211yescharacteristic
38C2×SD16×C149C2212yes—
39C2×D8×C149C2211yescharacteristic
40C22×C8×C149C2211yescharacteristic
41#14558735—24no—
42#14558735—42no—
43C2×Dic298C2312yes—
44C2×C22⋊D149—22no—
45C2×C22⋊D149D411yescharacteristic
46C22×Dic149—22no—
47C22×Dic149—22no—
48C2×C4×D149C2311yescharacteristic
49Dic596—22no—
50#14558726—42no—
51#14558724—24no—
52C2×#11924746C2311yescharacteristic
53C2×#11924746C2311yescharacteristic
54C8×D149—22no—
55C4⋊Dic149C2312yes—
56#14558715—22no—
57#14558715—22no—
58#14558715—22no—
59#14558715—22no—
60#14558715D411yescharacteristic
61C22⋊Dic149—22no—
62C22⋊Dic149—22no—
63C22⋊Dic149D411yescharacteristic
64#14558713—22no—
65#14558713D411yescharacteristic
66C4×Dic149C2311yescharacteristic
67#41×C149—24no—
68#41×C149—42no—
69C2×Q8×C149C2312yes—
70C2×D4×C149—22no—
71C2×D4×C149C2312yes—
72C22×C4×C149—22no—
73C22×C4×C149C2311yescharacteristic
74Q16×C149—22no—
75SD16×C149—24no—
76D8×C149D414yescomplemented
77C2×C8×C149—22no—
78C2×C8×C149C2311yescharacteristic
79C2×C8×C149C2311yescharacteristic
80C22×D149C2×D411yescharacteristic
81Dic298—22no—
82Dic298—22no—
83C22⋊D149—22no—
84C22⋊D149—44no—
85C2×Dic149—22no—
86C2×Dic149—22no—
87C2×Dic149—44no—
88C2×Dic149—44no—
89C2×Dic149C2×D411yescharacteristic
90C2×Dic149C2×D411yescharacteristic
91C2×Dic149C2×D411yescharacteristic
92C4×D149—21no—
93C4×D149—21no—
94#11924746—21no—
95#11924746—21no—
96C23×C149—22no—
97C23×C149C2×D411yescharacteristic
98Q8×C149—22no—
99Q8×C149—22no—
100D4×C149—22no—
101D4×C149—44no—
102D4×C149C2×D414yes—
103C2×C4×C149—21no—
104C2×C4×C149—21no—
105C2×C4×C149—22no—
106C2×C4×C149—44no—
107C2×C4×C149C2×D411yescharacteristic
108C2×C4×C149C2411yescharacteristic
109C8×C149—21no—
110C8×C149C2×D412yes—
111C22×C149—21no—
112C22×C149—24no—
113C22×C149—21no—
114C22×C149—21no—
115C22×C149—42no—
116C22×C149—42no—
117C22×C149C22×D411yescharacteristic
118C2×D149—21no—
119C2×D149—21no—
120C2×D149—21no—
121C4×C149—21no—
122C4×C149—42no—
123C4×C149C22×D411yescharacteristic
124C4×C149H(5,𝔽2)11yescharacteristic
125Dic149—21no—
126Dic149—21no—
127Dic149—42no—
128Dic149—42no—
129Dic149#13512yescomplemented
130C2×C149—41no—
131C2×C149—44no—
132C2×C149D4211yescharacteristic
133C2×C149C2×#13511yescharacteristic
134C2×C149#57811yescharacteristic
135D149—41no—
136C149#328311yescharacteristic, complemented, Sylow
137#3283—1491nomaximal, Sylow
138C2×#135—1491no—
139C2×#135D14911yescharacteristic, complemented
140#547—1492no—
141#494—1491no—
142#467—1491no—
143#467—1491no—
144#461—1492no—
145#452—1492no—
146#452—1492no—
147C4×D8—1491no—
148C8×D4—1491no—
149C2×#41—1492no—
150C2×#41C2×D14912yes—
151#135—24no—
152#135—2984no—
153C2×Q16—1492no—
154C2×Q16—1491no—
155C2×Q16C2×D14911yescharacteristic
156C2×SD16—1492no—
157C2×SD16C2×D14912yes—
158C2×D8C2×D14911yescharacteristic
159C22×C8—1491no—
160C22×C8C2×D14911yescharacteristic
161C4⋊Q8—1492no—
162#123—2982no—
163#123—2982no—
164C22⋊Q8—1492no—
165C22⋊Q8—1492no—
166#121—2982no—
167C4×D4—1492no—
168C4×D4—1491no—
169C2×C4⋊C4—2982no—
170#107—1491no—
171C4⋊C8—1491no—
172#103—1492no—
173#103—1492no—
174#102—1492no—
175C22⋊C8—1491no—
176C22⋊C8—1491no—
177C4×C8—1491no—
178#41—24no—
179#41—42no—
180#41—2984no—
181#41—5962no—
182C2×Q8—1492no—
183C2×Q8C22×D14912yes—
184C2×D4—22no—
185C2×D4—2982no—
186C2×D4—1491no—
187C2×D4C22×D14912yes—
188C22×C4—22no—
189C22×C4—2982no—
190C22×C4—2982no—
191C22×C4—1491no—
192C22×C4C22×D14911yescharacteristic
193Q16—22no—
194Q16—2982no—
195Q16—5962no—
196SD16—24no—
197SD16—2984no—
198D8C22⋊D14914yescomplemented
199C2×C8—22no—
200C2×C8—2982no—
201C2×C8—1491no—
202C2×C8—1491no—
203C2×C8C22×D14911yescharacteristic
204C2×C8C22×D14911yescharacteristic
205C4⋊C4—2982no—
206C4⋊C4—2982no—
207C4⋊C4—2982no—
208C4⋊C4—2982no—
209C4⋊C4—1492no—
210C4⋊C4—1491no—
211C22⋊C4—2982no—
212C22⋊C4—2982no—
213C22⋊C4—2982no—
214C22⋊C4—1491no—
215C22⋊C4—1491no—
216C42—1491no—
217C23—22no—
218C23—1491no—
219C23D4×D14911yescharacteristic
220Q8—22no—
221Q8—22no—
222Q8—2982no—
223Q8—2982no—
224D4—22no—
225D4—44no—
226D4—2982no—
227D4—5964no—
228D4C2×C22⋊D14914yes—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—22no—
232C2×C4—44no—
233C2×C4—2981no—
234C2×C4—2981no—
235C2×C4—2982no—
236C2×C4—2982no—
237C2×C4—5964no—
238C2×C4—5964no—
239C2×C4—1491no—
240C2×C4—1491no—
241C2×C4—1491no—
242C2×C4D4×D14911yescharacteristic
243C2×C4C23×D14911yescharacteristic
244C8—21no—
245C8—2981no—
246C8—2981no—
247C8C2×C22⋊D14912yes—
248C22—21no—
249C22—21no—
250C22—21no—
251C22—24no—
252C22—42no—
253C22—42no—
254C22—2981no—
255C22—2981no—
256C22—2981no—
257C22C2×D4×D14911yescharacteristic
258C4—21no—
259C4—42no—
260C4—2981no—
261C4—2981no—
262C4—5962no—
263C4—5962no—
264C4—1492no—
265C4C22×C22⋊D14911yescharacteristic
266C4#1801195611yescharacteristic
267C2—41no—
268C2—44no—
269C2—5961no—
270C2D4×C22⋊D14911yescharacteristic
271C2#135×D14911yescharacteristic
272C2#2375043911yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC2×#135×C149C2
socleC22×C149C22×D4
hypercenterC2×#135D149
hypocenterC149#3283
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×#18011930C2semidirect
2. #23750274C2semidirect
3. #23750003C2semidirect
4. #23749866C2semidirect
5. #23749863C2semidirect
6. #23749828C2semidirect
7. #23749787C2semidirect
8. #23749784C2semidirect
9. D8×Dic149C2semidirect
10. C8×C22⋊D149C2semidirect
11. C2×#135×C149C2semidirect
76. D8×C149D4semidirect
129. Dic149#135semidirect
136. C149#3283semidirect
139. C2×#135D149semidirect
198. D8C22⋊D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119302
#237502742
#237500032
#237498662
#237498632
#237498282
#237497872
#237497842
D8×Dic1492
C8×C22⋊D1492
C2×#135×C1492
#3283149