Finite Group Databasebeta

← #34054094

Subgroups — #34054094

Order 19072.

772 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 772 conjugacy classes of subgroups — too many to draw. Only its 145 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#23750461C211yesmaximal, characteristic, complemented
2#23750194C212yesmaximal, complemented
3#23750189C211yesmaximal, characteristic, complemented
4#23749813C218yesmaximal, complemented
5#23749598C212yesmaximal, complemented
6#410×C149C211yesmaximal, characteristic, complemented
7#18011959—21no—
8#18011958—22no—
9#18011957—22no—
10#18011956—21no—
11#18011956C2214yes—
12C2×#14558736—22no—
13C2×#14558736C2212yes—
14#41×D149—24no—
15C22×D596C2211yescharacteristic, complemented
16#18011908—22no—
17#18011907—21no—
18#18011900—21no—
19#18011899—22no—
20#18011886—24no—
21#18011885—22no—
22#18011881C2218yescomplemented
23#18011879C2214yescomplemented
24#18011870C2211yescharacteristic, complemented
25#18011825C2218yescomplemented
26C2×#41×C149C2211yescharacteristic
27#117×C149C2212yescomplemented
28#99×C149C2214yescomplemented
29C23×D149C2312yes—
30#14558737—24no—
31#14558736—24no—
32#14558736—24no—
33#14558736—22no—
34#14558736—22no—
35#14558736—24no—
36#14558736—22no—
37#14558736—22no—
38#14558735—24no—
39#14558735—28no—
40C2×Dic298—22no—
41C2×Dic298D412yescomplemented
42Q8×D149—24no—
43C2×D596—22no—
44C2×D596—28no—
45C2×D596—21no—
46C2×D596—22no—
47C2×D596—21no—
48C2×D596—22no—
49C2×D596D412yescomplemented
50C2×C22⋊D149—24no—
51C2×C22⋊D149—24no—
52C2×C22⋊D149C2314yes—
53D4×D149—24no—
54D4×D149—28no—
55C2×C4×D149—24no—
56C2×C4×D149D414yescomplemented
57C4⋊Dic149—21no—
58C22⋊Dic149C2312yes—
59#14558713—28no—
60#14558713—24no—
61C4×Dic149—21no—
62#41×C149—22no—
63#41×C149—22no—
64C2×Q8×C149D411yescharacteristic, complemented
65C2×D4×C149D411yescharacteristic, complemented
66C2×D4×C149C2312yes—
67C22×C4×C149D412yescomplemented
68C22×C4×C149C2311yescharacteristic
69C4⋊C4×C149—22no—
70C22⋊C4×C149C2314yes—
71C42×C149—22no—
72C22×D149—24no—
73C22×D149—22no—
74C22×D149—24no—
75C22×D149—82no—
76C22×D149C2×D414yes—
77Dic298—24no—
78Dic298—22no—
79Dic298—22no—
80D596—24no—
81D596—22no—
82D596—22no—
83D596—41no—
84D596—41no—
85D596—42no—
86D596—88no—
87C22⋊D149—28no—
88C22⋊D149—24no—
89C22⋊D149—24no—
90C22⋊D149—84no—
91C2×Dic149—24no—
92C2×Dic149—22no—
93C2×Dic149C2×D414yes—
94C4×D149—28no—
95C4×D149—24no—
96C4×D149—24no—
97C23×C149C2×D412yes—
98C23×C149C2411yescharacteristic
99Q8×C149—22no—
100D4×C149—24no—
101D4×C149—22no—
102C2×C4×C149—22no—
103C2×C4×C149—22no—
104C2×C4×C149—24no—
105C2×C4×C149C2×D412yes—
106C2×C4×C149C2×D412yes—
107C2×C4×C149C2×D412yes—
108C2×C4×C149C2×D411yescharacteristic
109C2×C4×C149C2×D411yescharacteristic
110C22×C149—22no—
111C22×C149—41no—
112C22×C149—42no—
113C22×C149C22×D412yes—
114C22×C149C22×D411yescharacteristic
115C2×D149—24no—
116C2×D149—44no—
117C2×D149—44no—
118C2×D149—48no—
119C2×D149—42no—
120C2×D149—84no—
121C4×C149—22no—
122C4×C149—44no—
123C4×C149#12011yescharacteristic
124C4×C149#12011yescharacteristic
125C4×C149#12012yes—
126Dic149—24no—
127Dic149—42no—
128C2×C149—21no—
129C2×C149—22no—
130C2×C149—42no—
131C2×C149C2×#12011yescharacteristic
132D149—44no—
133D149—82no—
134C149#302711yescharacteristic, complemented, Sylow
135#3027—1491nomaximal, Sylow
136#585—1491no—
137#535—1491no—
138#535—1492no—
139B(4,𝔽2)—1498no—
140#410—1492no—
141#410D14911yescharacteristic, complemented
1422−1+4—2982no—
1432−1+4—2981no—
144H(5,𝔽2)—2982no—
145H(5,𝔽2)—2981no—
146H(5,𝔽2)—1494no—
147C2×#41—2984no—
148C2×#41—2982no—
149C2×#41—1492no—
150C2×#41C2×D14911yescharacteristic
151C22×D4—1491no—
152#127—2982no—
153#127—2981no—
154#124—2982no—
155#124—2981no—
156#121—2984no—
157#121—2982no—
158#120—1494no—
159#120—1498no—
160#117—1491no—
161#117C2×D14912yescomplemented
162#99—1498no—
163#99C2×D14914yescomplemented
164C24—1492no—
165#41—22no—
166#41—22no—
167#41—2984no—
168#41—2984no—
169#41—2984no—
170#41—2984no—
171#41—2988no—
172#41—2982no—
173#41—2982no—
174#41—2982no—
175#41—2984no—
176#41—2982no—
177C2×Q8—2982no—
178C2×Q8—2984no—
179C2×Q8—1492no—
180C2×Q8D59611yescharacteristic, complemented
181C2×D4—2982no—
182C2×D4—2988no—
183C2×D4—2984no—
184C2×D4—2988no—
185C2×D4—2984no—
186C2×D4—2984no—
187C2×D4—2982no—
188C2×D4—2982no—
189C2×D4—2981no—
190C2×D4—2981no—
191C2×D4—1494no—
192C2×D4—1492no—
193C2×D4D59611yescharacteristic, complemented
194C2×D4C22×D14912yes—
195C22×C4—2984no—
196C22×C4—1494no—
197C22×C4D59612yescomplemented
198C22×C4C22×D14911yescharacteristic
199C4⋊C4—22no—
200C4⋊C4—2981no—
201C22⋊C4—2988no—
202C22⋊C4—2984no—
203C22⋊C4—1492no—
204C22⋊C4C22×D14914yes—
205C42—22no—
206C42—2981no—
207C23—2984no—
208C23—2984no—
209C23—2982no—
210C23—1494no—
211C23—11922no—
212C23C2×D59612yes—
213C23C23×D14911yescharacteristic
214Q8—22no—
215Q8—2984no—
216Q8—2982no—
217Q8—2982no—
218D4—24no—
219D4—22no—
220D4—2984no—
221D4—2988no—
222D4—2984no—
223D4—2984no—
224D4—2982no—
225D4—2982no—
226D4—5961no—
227D4—5961no—
228D4—5962no—
229D4—11928no—
230D4—11924no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—24no—
234C2×C4—2988no—
235C2×C4—2984no—
236C2×C4—2984no—
237C2×C4—2984no—
238C2×C4—2982no—
239C2×C4—1494no—
240C2×C4D4×D14912yes—
241C2×C4D4×D14912yes—
242C2×C4C2×D59612yes—
243C2×C4C2×D59611yescharacteristic
244C2×C4C2×D59611yescharacteristic
245C22—22no—
246C22—41no—
247C22—42no—
248C22—2984no—
249C22—5964no—
250C22—5968no—
251C22—5964no—
252C22—5962no—
253C22—11924no—
254C22C2×D4×D14912yes—
255C22C22×D59611yescharacteristic
256C4—22no—
257C4—44no—
258C4—2984no—
259C4—5962no—
260C4#1801188111yescharacteristic
261C4#1801188111yescharacteristic
262C4#1801188112yes—
263C2—22no—
264C2—21no—
265C2—42no—
266C2—5964no—
267C2—11922no—
268C2C2×#1801188111yescharacteristic
subgroupG/H
centerC2C2×#18011881
commutator, cosocleC23×C149C24
FrattiniC23C23×D149
Fitting#410×C149C2
socleC2×C149C2×#120
hypercenter#410D149
hypocenterC149#3027
LCSG ▷ C23×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
1. #23750461C2semidirect
2. #23750194C2semidirect
3. #23750189C2semidirect
4. #23749813C2semidirect
5. #23749598C2semidirect
6. #410×C149C2semidirect
15. C22×D596C22semidirect
22. #18011881C22semidirect
23. #18011879C22semidirect
24. #18011870C22semidirect
25. #18011825C22semidirect
27. #117×C149C22semidirect
28. #99×C149C22semidirect
41. C2×Dic298D4semidirect
49. C2×D596D4semidirect
56. C2×C4×D149D4semidirect
64. C2×Q8×C149D4semidirect
65. C2×D4×C149D4semidirect
67. C22×C4×C149D4semidirect
134. C149#3027semidirect
141. #410D149semidirect
161. #117C2×D149semidirect
163. #99C2×D149semidirect
180. C2×Q8D596semidirect
193. C2×D4D596semidirect
197. C22×C4D596semidirect

Maximal subgroups

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

subgroupindex
#237504612
#237501942
#237501892
#237498132
#237495982
#410×C1492
#3027149