Finite Group Databasebeta

← #34056927

Subgroups — #34056927

Order 19072.

460 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 123 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
1D4×D596C211yesmaximal, characteristic, complemented
2#23749973C211yesmaximal, characteristic, complemented
3#23749949C212yesmaximal, complemented
4#23749912C211yesmaximal, characteristic, complemented
5#23749876C212yesmaximal, complemented
6#23749820C211yesmaximal, characteristic, complemented
7#23749758C212yesmaximal, complemented
8C4×#14558721C211yesmaximal, characteristic, complemented
9#23749703C211yesmaximal, characteristic, complemented
10#23749629C212yesmaximal, complemented
11#555×C149C211yesmaximal, characteristic, complemented
12C22×D596C2212yes—
13C2×D4×D149—21no—
14C2×#14558721C2211yescharacteristic
15C2×#14558721C2212yescomplemented
16C2×#14558720C2212yescomplemented
17#18011908C2211yescharacteristic
18#18011886—21no—
19#18011885C2212yes—
20#18011881—22no—
21C4×D596C2211yescharacteristic
22#18011844C2211yescharacteristic, complemented
23#18011842C2212yescomplemented
24C4⋊#11924746C2211yescharacteristic, complemented
25#18011832C2211yescharacteristic, complemented
26#18011831C2212yes—
27#18011831C2211yescharacteristic
28#18011831C2212yescomplemented
29#18011831C2212yescomplemented
30#18011831C2212yescomplemented
31C22⋊#11924746C2212yescomplemented
32C4×#11924746C2211yescharacteristic, complemented
33C4⋊Q8×C149C2211yescharacteristic, complemented
34#124×C149—22no—
35#121×C149—21no—
36#121×C149C2212yescomplemented
37C4×D4×C149C2211yescharacteristic
38C4×D4×C149C2211yescharacteristic, complemented
39#117×C149—21no—
40#117×C149C2212yescomplemented
41C23×D149—22no—
42C2×D596—24no—
43C2×D596—21no—
44C2×D596—22no—
45C2×D596—21no—
46C2×D596—42no—
47C2×D596C2312yes—
48C2×D596C2311yescharacteristic
49C2×C22⋊D149—22no—
50D4×D149—44no—
51C2×C4×D149—21no—
52#14558721—22no—
53#14558721—42no—
54#14558720—42no—
55C2×#11924746C2311yescharacteristic
56C2×#11924746C2312yes—
57C2×#11924746C2311yescharacteristic
58C4⋊Dic149C2311yescharacteristic
59#14558713—21no—
60#14558713—22no—
61C2×Q8×C149—21no—
62C2×D4×C149—22no—
63C2×D4×C149D411yescharacteristic
64C2×D4×C149C2311yescharacteristic
65C22×C4×C149—21no—
66C22×C4×C149C2312yes—
67C4⋊C4×C149—21no—
68C4⋊C4×C149D411yescharacteristic
69C4⋊C4×C149C2311yescharacteristic
70C4⋊C4×C149C2312yes—
71C22⋊C4×C149—22no—
72C22⋊C4×C149—22no—
73C22⋊C4×C149—21no—
74C22⋊C4×C149D412yes—
75C42×C149—22no—
76C42×C149C2311yescharacteristic
77C22×D149—21no—
78C22×D149—22no—
79C22×D149—44no—
80C22×D149—44no—
81C22×D149—82no—
82D596—22no—
83D596—21no—
84D596—22no—
85D596—44no—
86D596—42no—
87D596—81no—
88D596#4112yes—
89C22⋊D149—44no—
90C2×Dic149—21no—
91C4×D149—42no—
92#11924746—21no—
93#11924746—21no—
94#11924746—22no—
95C23×C149—21no—
96C23×C149C2×D412yes—
97Q8×C149—81no—
98D4×C149—22no—
99D4×C149—21no—
100D4×C149—21no—
101D4×C149—82no—
102C2×C4×C149—22no—
103C2×C4×C149—22no—
104C2×C4×C149—21no—
105C2×C4×C149—22no—
106C2×C4×C149—42no—
107C2×C4×C149C2×D412yes—
108C2×C4×C149C2×D411yescharacteristic
109C2×C4×C149C2×D411yescharacteristic
110C2×C4×C149C2411yescharacteristic
111C22×C149—22no—
112C22×C149—22no—
113C22×C149—22no—
114C22×C149—41no—
115C22×C149—41no—
116C22×C149—41no—
117C22×C149C22×D411yescharacteristic
118C2×D149—22no—
119C2×D149—41no—
120C2×D149—41no—
121C2×D149—42no—
122C2×D149—42no—
123C2×D149—42no—
124C2×D149—88no—
125C4×C149—22no—
126C4×C149—21no—
127C4×C149—41no—
128C4×C149—42no—
129C4×C149AGL(1,ℤ/8)12yes—
130C4×C149C2×#4111yescharacteristic
131C4×C149H(5,𝔽2)11yescharacteristic
132Dic149—41no—
133C2×C149—42no—
134C2×C149—81no—
135C2×C149#54611yescharacteristic
136C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
137C2×C149#57611yescharacteristic
138D149—42no—
139D149—82no—
140C149#332511yescharacteristic, complemented, Sylow
141#3325—1491nomaximal, Sylow
142#555D14911yescharacteristic, complemented
143D42—1491no—
144#486—1491no—
145#482—1492no—
146#476—1491no—
147#469—1492no—
148#459—1491no—
149#447—1492no—
150C4×D8—1491no—
151#436—1491no—
152#418—1492no—
153C22×D4—2981no—
154C22×D4—1492no—
155C2×D8—1491no—
156C2×D8—1492no—
157C2×M16—1492no—
158C4⋊Q8C2×D14911yescharacteristic, complemented
159#127—1491no—
160#124—22no—
161#121—21no—
162#121—2981no—
163#121—1492no—
164#121C2×D14912yescomplemented
165#120—2982no—
166C4×D4—1491no—
167C4×D4C2×D14911yescharacteristic
168C4×D4C2×D14911yescharacteristic, complemented
169#117—21no—
170#117C2×D14912yescomplemented
171#107—1491no—
172#106—1492no—
173C4⋊C8—1491no—
174#102—1491no—
175#102—1491no—
176#102—1492no—
177#102—1492no—
178#102—1492no—
179#102—1492no—
180C22⋊C8—1492no—
181C4×C8—1491no—
182C24—2982no—
183C2×Q8—21no—
184C2×D4—22no—
185C2×D4—2984no—
186C2×D4—2982no—
187C2×D4—2982no—
188C2×D4—2981no—
189C2×D4—2981no—
190C2×D4—5962no—
191C2×D4—5964no—
192C2×D4—1492no—
193C2×D4—1491no—
194C2×D4C22⋊D14911yescharacteristic
195C2×D4C22×D14911yescharacteristic
196C22×C4—21no—
197C22×C4—2981no—
198C22×C4C22×D14912yes—
199D8—2982no—
200D8—5962no—
201M16—5962no—
202C2×C8—1491no—
203C2×C8—1491no—
204C2×C8—1492no—
205C4⋊C4—21no—
206C4⋊C4—1491no—
207C4⋊C4C22⋊D14911yescharacteristic
208C4⋊C4C22×D14912yes—
209C4⋊C4C22×D14911yescharacteristic
210C22⋊C4—22no—
211C22⋊C4—22no—
212C22⋊C4—21no—
213C22⋊C4—2981no—
214C22⋊C4—2982no—
215C22⋊C4C22⋊D14912yes—
216C42—22no—
217C42C22×D14911yescharacteristic
218C23—21no—
219C23—2981no—
220C23—2982no—
221C23—5964no—
222C23—5964no—
223C23—11922no—
224C23C2×C22⋊D14912yes—
225Q8—81no—
226D4—22no—
227D4—21no—
228D4—21no—
229D4—82no—
230D4—2982no—
231D4—2981no—
232D4—2982no—
233D4—5964no—
234D4—5964no—
235D4—5962no—
236D4—1492no—
237D4—11921no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—42no—
243C2×C4—2981no—
244C2×C4—5962no—
245C2×C4C2×C22⋊D14912yes—
246C2×C4C2×C22⋊D14911yescharacteristic
247C2×C4C2×C22⋊D14911yescharacteristic
248C2×C4C23×D14911yescharacteristic
249C8—2981no—
250C8—2981no—
251C8—2982no—
252C22—22no—
253C22—22no—
254C22—22no—
255C22—41no—
256C22—41no—
257C22—41no—
258C22—2982no—
259C22—5961no—
260C22—5961no—
261C22—5962no—
262C22—5962no—
263C22—5962no—
264C22—11928no—
265C22C22×C22⋊D14911yescharacteristic
266C4—21no—
267C4—22no—
268C4—41no—
269C4—42no—
270C4—5961no—
271C4#1801193612yes—
272C4#41×D14911yescharacteristic
273C4#1801195711yescharacteristic
274C2—42no—
275C2—81no—
276C2—5962no—
277C2—11922no—
278C2#2375026311yescharacteristic
279C2C2×#1801193611yescharacteristic
280C2#2375042811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#555×C149C2
socleC22×C149C22×D4
hypercenter#555D149
hypocenterC149#3325
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C4×D4 ◁ #555

Complements

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

NH ≅ G/Ntype
1. D4×D596C2semidirect
2. #23749973C2semidirect
3. #23749949C2semidirect
4. #23749912C2semidirect
5. #23749876C2semidirect
6. #23749820C2semidirect
7. #23749758C2semidirect
8. C4×#14558721C2semidirect
9. #23749703C2semidirect
10. #23749629C2semidirect
11. #555×C149C2semidirect
15. C2×#14558721C22semidirect
16. C2×#14558720C22semidirect
22. #18011844C22semidirect
23. #18011842C22semidirect
24. C4⋊#11924746C22semidirect
25. #18011832C22semidirect
28. #18011831C22semidirect
29. #18011831C22semidirect
30. #18011831C22semidirect
31. C22⋊#11924746C22semidirect
32. C4×#11924746C22semidirect
33. C4⋊Q8×C149C22semidirect
36. #121×C149C22semidirect
38. C4×D4×C149C22semidirect
40. #117×C149C22semidirect
140. C149#3325semidirect
142. #555D149semidirect
158. C4⋊Q8C2×D149semidirect
164. #121C2×D149semidirect
168. C4×D4C2×D149semidirect
170. #117C2×D149semidirect

Maximal subgroups

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

subgroupindex
D4×D5962
#237499732
#237499492
#237499122
#237498762
#237498202
#237497582
C4×#145587212
#237497032
#237496292
#555×C1492
#3325149