Finite Group Databasebeta

← #34055552

Subgroups — #34055552

Order 19072.

442 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 117 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#23750189C211yesmaximal, characteristic, complemented
2#23749949C212yesmaximal, complemented
3#23749946C212yesmaximal, complemented
4#23749876C212yesmaximal, complemented
5#23749859C212yesmaximal, complemented
6#23749759C212yesmaximal, complemented
7#23749758C212yesmaximal, complemented
8#23749592C211yesmaximal, characteristic, complemented
9#535×C149C211yesmaximal, characteristic, complemented
10C22×D596C2211yescharacteristic, complemented
11C2×#14558721C2212yes—
12C2×#14558721C2212yes—
13C2×#14558720C2211yescharacteristic, complemented
14C22×#11924746C2211yescharacteristic, complemented
15#18011907—21no—
16#18011900—21no—
17#18011885C2212yes—
18#18011885C2212yescomplemented
19#18011879—21no—
20#18011879—21no—
21#18011870C2211yescharacteristic, complemented
22#18011844C2212yescomplemented
23#18011842C2212yescomplemented
24#18011832C2212yescomplemented
25#18011832C2212yescomplemented
26#18011831C2212yescomplemented
27#18011831C2212yescomplemented
28C22⋊#11924746C2212yescomplemented
29C22⋊#11924746C2212yescomplemented
30C2×#41×C149C2211yescharacteristic
31C22×D4×C149C2211yescharacteristic, complemented
32#127×C149—21no—
33#124×C149—21no—
34#121×C149C2212yes—
35#121×C149C2212yescomplemented
36#120×C149—21no—
37#120×C149—21no—
38#117×C149C2211yescharacteristic, complemented
39C23×D149—21no—
40C2×D596—21no—
41C2×D596—41no—
42C2×D596—41no—
43C2×D596C2312yes—
44C2×C22⋊D149—22no—
45C2×C22⋊D149—22no—
46#14558721—42no—
47#14558721—42no—
48#14558720—41no—
49C2×#11924746—41no—
50C2×#11924746C2312yes—
51C2×#11924746C2312yes—
52C4⋊Dic149C2312yes—
53C22⋊Dic149—21no—
54#14558713—22no—
55#14558713—22no—
56C4×Dic149—21no—
57C24×C149—21no—
58#41×C149—41no—
59#41×C149—41no—
60C2×Q8×C149D411yescharacteristic
61C2×D4×C149—22no—
62C2×D4×C149—22no—
63C2×D4×C149—21no—
64C2×D4×C149—41no—
65C2×D4×C149—41no—
66C2×D4×C149D411yescharacteristic
67C2×D4×C149D411yescharacteristic
68C2×D4×C149D411yescharacteristic
69C2×D4×C149C2312yes—
70C22×C4×C149C2311yescharacteristic
71C22×C4×C149C2311yescharacteristic
72C22×C4×C149C2311yescharacteristic
73C4⋊C4×C149C2312yes—
74C22⋊C4×C149—21no—
75C22⋊C4×C149—22no—
76C22⋊C4×C149—22no—
77C42×C149—21no—
78C22×D149—22no—
79C22×D149—42no—
80C22×D149—82no—
81D596—22no—
82D596—22no—
83D596—42no—
84C22⋊D149—82no—
85C22⋊D149—82no—
86C2×Dic149—22no—
87#11924746—22no—
88#11924746—22no—
89C23×C149—22no—
90C23×C149—42no—
91C23×C149—82no—
92C23×C149C2×D411yescharacteristic
93C23×C149C2×D411yescharacteristic
94C23×C149C2×D411yescharacteristic
95Q8×C149—41no—
96D4×C149—22no—
97D4×C149—22no—
98D4×C149—41no—
99D4×C149—41no—
100D4×C149—41no—
101D4×C149—42no—
102D4×C149—82no—
103D4×C149—82no—
104C2×C4×C149—21no—
105C2×C4×C149—21no—
106C2×C4×C149—21no—
107C2×C4×C149—21no—
108C2×C4×C149—21no—
109C2×C4×C149—21no—
110C2×C4×C149—22no—
111C2×C4×C149C2×D411yescharacteristic
112C2×C4×C149C2×D411yescharacteristic
113C2×C4×C149C2×D411yescharacteristic
114C2×C4×C149C2411yescharacteristic
115C22×C149—21no—
116C22×C149—21no—
117C22×C149—21no—
118C22×C149—22no—
119C22×C149—22no—
120C22×C149—22no—
121C22×C149—42no—
122C22×C149—42no—
123C22×C149—42no—
124C22×C149—84no—
125C22×C149C22×D411yescharacteristic
126C2×D149—42no—
127C2×D149—42no—
128C2×D149—42no—
129C2×D149—84no—
130C4×C149—21no—
131C4×C149—21no—
132C4×C149—21no—
133C4×C149—42no—
134C4×C149H(5,𝔽2)11yescharacteristic
135C4×C149H(5,𝔽2)11yescharacteristic
136Dic149—42no—
137C2×C149—41no—
138C2×C149—41no—
139C2×C149—41no—
140C2×C149—82no—
141C2×C149#53411yescharacteristic
142C2×C149#57612yes—
143D149—82no—
144C149#319911yescharacteristic, complemented, Sylow
145#3199—1491nomaximal, Sylow
146#535—1491no—
147#535D14911yescharacteristic, complemented
148#482—1492no—
149#482—1492no—
150#469—1492no—
151#466—1492no—
152#447—1492no—
153#447—1492no—
154#408—1491no—
155C2×#41C2×D14911yescharacteristic
156C22×D4—1491no—
157C22×D4C2×D14911yescharacteristic, complemented
158C2×D8—1492no—
159C2×D8—1492no—
160C2×M16—1491no—
161C22×C8—1491no—
162#127—21no—
163#127—2981no—
164#124—21no—
165#124—2981no—
166#121—1492no—
167#121—1492no—
168#121C2×D14912yes—
169#121C2×D14912yescomplemented
170#120—21no—
171#120—21no—
172#120—2981no—
173#120—2981no—
174#117—1491no—
175#117C2×D14911yescharacteristic, complemented
176#107—1492no—
177#106—1492no—
178#102—1492no—
179#102—1492no—
180#102—1492no—
181#102—1492no—
182C22⋊C8—1492no—
183C22⋊C8—1492no—
184C24—21no—
185C24—2981no—
186#41—41no—
187#41—41no—
188C2×Q8C22⋊D14911yescharacteristic
189C2×D4—22no—
190C2×D4—22no—
191C2×D4—21no—
192C2×D4—41no—
193C2×D4—41no—
194C2×D4—2982no—
195C2×D4—2982no—
196C2×D4—2981no—
197C2×D4—5961no—
198C2×D4—5961no—
199C2×D4—1492no—
200C2×D4C22⋊D14911yescharacteristic
201C2×D4C22⋊D14911yescharacteristic
202C2×D4C22⋊D14911yescharacteristic
203C2×D4C22×D14912yes—
204C22×C4C22×D14911yescharacteristic
205C22×C4C22×D14911yescharacteristic
206C22×C4C22×D14911yescharacteristic
207D8—5962no—
208D8—5962no—
209M16—5961no—
210C2×C8—5961no—
211C2×C8—1492no—
212C2×C8—1492no—
213C4⋊C4—1492no—
214C4⋊C4C22×D14912yes—
215C22⋊C4—21no—
216C22⋊C4—22no—
217C22⋊C4—22no—
218C22⋊C4—2981no—
219C22⋊C4—2982no—
220C22⋊C4—2982no—
221C42—21no—
222C42—2981no—
223C23—22no—
224C23—42no—
225C23—82no—
226C23—2982no—
227C23—5962no—
228C23—11922no—
229C23C2×C22⋊D14911yescharacteristic
230C23C2×C22⋊D14911yescharacteristic
231C23C2×C22⋊D14911yescharacteristic
232Q8—41no—
233D4—22no—
234D4—22no—
235D4—41no—
236D4—41no—
237D4—41no—
238D4—42no—
239D4—82no—
240D4—82no—
241D4—2982no—
242D4—2982no—
243D4—5962no—
244D4—11922no—
245D4—11922no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—22no—
253C2×C4—2982no—
254C2×C4C2×C22⋊D14911yescharacteristic
255C2×C4C2×C22⋊D14911yescharacteristic
256C2×C4C2×C22⋊D14911yescharacteristic
257C2×C4C23×D14911yescharacteristic
258C8—2982no—
259C8—2982no—
260C22—22no—
261C22—22no—
262C22—22no—
263C22—21no—
264C22—21no—
265C22—21no—
266C22—42no—
267C22—42no—
268C22—42no—
269C22—84no—
270C22—5962no—
271C22—5962no—
272C22—5962no—
273C22—11924no—
274C22C22×C22⋊D14911yescharacteristic
275C4—21no—
276C4—21no—
277C4—21no—
278C4—42no—
279C4—5962no—
280C4#1801195611yescharacteristic
281C4#1801195611yescharacteristic
282C2—41no—
283C2—41no—
284C2—41no—
285C2—82no—
286C2—11922no—
287C2#2375018411yescharacteristic
288C2#2375042812yes—
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#535×C149C2
socleC22×C149C22×D4
hypercenter#535D149
hypocenterC149#3199
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C2×#41 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #23750189C2semidirect
2. #23749949C2semidirect
3. #23749946C2semidirect
4. #23749876C2semidirect
5. #23749859C2semidirect
6. #23749759C2semidirect
7. #23749758C2semidirect
8. #23749592C2semidirect
9. #535×C149C2semidirect
10. C22×D596C22semidirect
13. C2×#14558720C22semidirect
14. C22×#11924746C22semidirect
18. #18011885C22semidirect
21. #18011870C22semidirect
22. #18011844C22semidirect
23. #18011842C22semidirect
24. #18011832C22semidirect
25. #18011832C22semidirect
26. #18011831C22semidirect
27. #18011831C22semidirect
28. C22⋊#11924746C22semidirect
29. C22⋊#11924746C22semidirect
31. C22×D4×C149C22semidirect
35. #121×C149C22semidirect
38. #117×C149C22semidirect
144. C149#3199semidirect
147. #535D149semidirect
157. C22×D4C2×D149semidirect
169. #121C2×D149semidirect
175. #117C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237501892
#237499492
#237499462
#237498762
#237498592
#237497592
#237497582
#237495922
#535×C1492
#3199149