Finite Group Databasebeta

← #34055605

Subgroups — #34055605

Order 19072.

532 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 125 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#23750173C211yesmaximal, characteristic, complemented
2#127×D149C211yesmaximal, characteristic, complemented
3#23750001C211yesmaximal, characteristic, complemented
4#23749972C211yesmaximal, characteristic, complemented
5#23749971C211yesmaximal, characteristic, complemented
6#23749818C214yesmaximal, complemented
7#23749757C214yesmaximal, complemented
8#23749676C211yesmaximal, characteristic, complemented
9#493×C149C211yesmaximal, characteristic, complemented
10C2×#14558735—21no—
11C2×D4×D149—21no—
12C2×D4×D149—21no—
13C2×D4×D149C2212yes—
14C2×#14558721C2214yescomplemented
15#18011911C2211yescharacteristic, complemented
16#18011908C2211yescharacteristic
17#18011907—21no—
18#18011907—21no—
19#18011907C2212yes—
20#18011898—21no—
21#18011882—21no—
22#18011882C2212yes—
23D4×Dic149—21no—
24D4×Dic149C2212yescomplemented
25C42×D149C2211yescharacteristic
26#18011840C2212yescomplemented
27#18011833C2214yescomplemented
28#18011832C2214yescomplemented
29#18011823C2212yes—
30C4×#11924746C2211yescharacteristic, complemented
31C2×D8×C149C2214yescomplemented
32#127×C149C2211yescharacteristic
33#127×C149C2211yescharacteristic, complemented
34C4×C8×C149C2211yescharacteristic, complemented
35C23×D149—22no—
36#14558735—44no—
37C2×Dic298—21no—
38C2×D596—21no—
39C2×D596—21no—
40C2×D596C2312yes—
41C2×C22⋊D149—22no—
42C2×C22⋊D149—22no—
43C2×C22⋊D149—22no—
44C2×C22⋊D149—22no—
45D4×D149—44no—
46D4×D149—44no—
47D4×D149—44no—
48C22×Dic149—22no—
49C2×C4×D149D411yescharacteristic
50C2×C4×D149D411yescharacteristic
51C2×C4×D149C2311yescharacteristic
52#14558721—44no—
53C2×#11924746C2312yes—
54C4⋊Dic149—21no—
55C4⋊Dic149C2312yes—
56C22⋊Dic149—22no—
57C22⋊Dic149—22no—
58C4×Dic149D411yescharacteristic
59C4×Dic149D411yescharacteristic
60C4×Dic149C2311yescharacteristic
61C2×D4×C149—21no—
62C2×D4×C149—21no—
63C2×D4×C149—21no—
64C2×D4×C149—21no—
65C2×D4×C149C2312yes—
66C2×D4×C149C2312yes—
67D8×C149—44no—
68C2×C8×C149C2312yes—
69C42×C149C2311yescharacteristic
70C22×D149—22no—
71C22×D149—44no—
72C22×D149—44no—
73C22×D149—44no—
74C22×D149C2×D411yescharacteristic
75Dic298—42no—
76D596—24no—
77D596—42no—
78D596—42no—
79C22⋊D149—44no—
80C22⋊D149—44no—
81C22⋊D149—44no—
82C22⋊D149—44no—
83C2×Dic149—22no—
84C2×Dic149—44no—
85C2×Dic149C2×D411yescharacteristic
86C2×Dic149C2×D411yescharacteristic
87C2×Dic149C2×D411yescharacteristic
88C4×D149—22no—
89C4×D149—22no—
90C4×D149D814yescomplemented
91#11924746—22no—
92C23×C149—22no—
93C23×C149—22no—
94D4×C149—24no—
95D4×C149—24no—
96D4×C149—42no—
97D4×C149—42no—
98D4×C149—42no—
99D4×C149—42no—
100C2×C4×C149C2×D411yescharacteristic
101C2×C4×C149C2×D411yescharacteristic
102C2×C4×C149C2411yescharacteristic
103C8×C149—22no—
104C22×C149—42no—
105C22×C149—42no—
106C22×C149—42no—
107C22×C149—42no—
108C22×C149—42no—
109C22×C149—42no—
110C22×C149C22×D411yescharacteristic
111C2×D149—21no—
112C2×D149—21no—
113C2×D149—42no—
114C2×D149—42no—
115C2×D149—42no—
116C2×D149—88no—
117C2×D149C2×D812yes—
118C4×C149C2×D812yes—
119C4×C149AGL(1,ℤ/8)12yes—
120C4×C149H(5,𝔽2)12yes—
121Dic149—21no—
122Dic149—21no—
123Dic149—42no—
124Dic149C2×D812yes—
125C2×C149—82no—
126C2×C149—82no—
127C2×C149#53511yescharacteristic
128C2×C149C22×D811yescharacteristic
129C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
130D149—22no—
131D149—82no—
132C149#320511yescharacteristic, complemented, Sylow
133#3205—1491nomaximal, Sylow
134#532—1491no—
135C2×#127—1491no—
136#493—1491no—
137#493D14911yescharacteristic, complemented
138#486—1491no—
139#486—1491no—
140#459—1494no—
141#447—1494no—
142#431—1491no—
143C2×#41—2981no—
144C22×D4—2981no—
145C22×D4—2981no—
146C22×D4—1492no—
147C2×D8—1494no—
148C2×D8C2×D14914yescomplemented
149C4⋊Q8—1491no—
150#127—2981no—
151#127—2981no—
152#127—1492no—
153#127—1491no—
154#127C2×D14911yescharacteristic
155#127C2×D14911yescharacteristic, complemented
156#124—2981no—
157#121—2981no—
158#121—1492no—
159C4×D4—2981no—
160C4×D4—1492no—
161C2×C42—1491no—
162C4⋊C8—1492no—
163#102—1494no—
164#102—1494no—
165C22⋊C8—1492no—
166C4×C8—1491no—
167C4×C8C2×D14911yescharacteristic, complemented
168C24—2982no—
169#41—5964no—
170C2×Q8—2981no—
171C2×D4—21no—
172C2×D4—21no—
173C2×D4—21no—
174C2×D4—21no—
175C2×D4—2982no—
176C2×D4—2982no—
177C2×D4—2982no—
178C2×D4—2982no—
179C2×D4—2981no—
180C2×D4—2981no—
181C2×D4—5964no—
182C2×D4—5964no—
183C2×D4—5964no—
184C2×D4—1492no—
185C2×D4C22×D14912yes—
186C2×D4C22×D14912yes—
187C22×C4—2982no—
188C22×C4—1491no—
189C22×C4—1491no—
190C22×C4—1491no—
191D8—44no—
192D8—5964no—
193C2×C8—1492no—
194C2×C8C22×D14912yes—
195C4⋊C4—2981no—
196C4⋊C4—1492no—
197C22⋊C4—2982no—
198C22⋊C4—2982no—
199C42—1491no—
200C42—1491no—
201C42—1491no—
202C42C22×D14911yescharacteristic
203C23—22no—
204C23—22no—
205C23—2982no—
206C23—5964no—
207C23—5964no—
208C23—5964no—
209C23—1491no—
210Q8—5962no—
211D4—24no—
212D4—24no—
213D4—42no—
214D4—42no—
215D4—42no—
216D4—42no—
217D4—2984no—
218D4—5964no—
219D4—5964no—
220D4—5964no—
221D4—5964no—
222D4—5962no—
223D4—5962no—
224C2×C4—2982no—
225C2×C4—2982no—
226C2×C4—2982no—
227C2×C4—5964no—
228C2×C4—1491no—
229C2×C4—1491no—
230C2×C4—1491no—
231C2×C4—1494no—
232C2×C4D4×D14911yescharacteristic
233C2×C4D4×D14911yescharacteristic
234C2×C4C23×D14911yescharacteristic
235C8—22no—
236C8—2982no—
237C22—42no—
238C22—42no—
239C22—42no—
240C22—42no—
241C22—42no—
242C22—42no—
243C22—2981no—
244C22—2981no—
245C22—5962no—
246C22—5962no—
247C22—5962no—
248C22—1492no—
249C22—11928no—
250C22C2×D4×D14911yescharacteristic
251C4—2981no—
252C4—2981no—
253C4—5962no—
254C4—1492no—
255C4D8×D14912yes—
256C4#1801193512yes—
257C4#1801195612yes—
258C2—82no—
259C2—82no—
260C2—2982no—
261C2—11922no—
262C2#2375018811yescharacteristic
263C2C2×D8×D14911yescharacteristic
264C2C2×#1801193511yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#493×C149C2
socleC22×C149C22×D4
hypercenter#493D149
hypocenterC149#3205
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #493

Complements

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

NH ≅ G/Ntype
1. #23750173C2semidirect
2. #127×D149C2semidirect
3. #23750001C2semidirect
4. #23749972C2semidirect
5. #23749971C2semidirect
6. #23749818C2semidirect
7. #23749757C2semidirect
8. #23749676C2semidirect
9. #493×C149C2semidirect
14. C2×#14558721C22semidirect
15. #18011911C22semidirect
24. D4×Dic149C22semidirect
26. #18011840C22semidirect
27. #18011833C22semidirect
28. #18011832C22semidirect
30. C4×#11924746C22semidirect
31. C2×D8×C149C22semidirect
33. #127×C149C22semidirect
34. C4×C8×C149C22semidirect
90. C4×D149D8semidirect
132. C149#3205semidirect
137. #493D149semidirect
148. C2×D8C2×D149semidirect
155. #127C2×D149semidirect
167. C4×C8C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237501732
#127×D1492
#237500012
#237499722
#237499712
#237498182
#237497572
#237496762
#493×C1492
#3205149