Finite Group Databasebeta

← #34055074

Subgroups — #34055074

Order 19072.

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

normal subgroups only

This group has 400 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#23750181C211yesmaximal, characteristic, complemented
2#124×D149C211yesmaximal, characteristic
3#23749986C212yesmaximal, complemented
4#23749983C212yesmaximal, complemented
5#23749982C211yesmaximal, characteristic, complemented
6#23749980C211yesmaximal, characteristic, complemented
7#23749979C211yesmaximal, characteristic, complemented
8#23749632C212yesmaximal, complemented
9#23749628C212yesmaximal
10C4×#14558719C211yesmaximal, characteristic, complemented
11#488×C149C211yesmaximal, characteristic, complemented
12C2×Q8×D149C2211yescharacteristic
13C2×D4×D149C2211yescharacteristic
14C2×#14558719C2212yes—
15#18011910C2212yescomplemented
16#18011903C2211yescharacteristic, complemented
17#18011900C2211yescharacteristic
18#18011899C2211yescharacteristic
19#18011898C2211yescharacteristic
20#18011897—22no—
21#18011889—22no—
22#18011876—22no—
23#18011869C2212yes—
24C22⋊C4×D149—22no—
25C42×D149C2211yescharacteristic
26#18011836C2212yescomplemented
27#18011835C2212yescomplemented
28#18011834C2212yescomplemented
29#18011833C2212yes—
30#18011832C2212yes—
31#18011831C2212yes—
32#18011821C2212yescomplemented
33C4×#11924746C2211yescharacteristic, complemented
34#125×C149C2211yescharacteristic, complemented
35#124×C149C2211yescharacteristic
36#103×C149C2212yescomplemented
37#102×C149C2212yes—
38C4×C8×C149C2211yescharacteristic, complemented
39C23×D149—21no—
40C2×Dic298—22no—
41C2×Dic298—21no—
42C2×Dic298C2311yescharacteristic
43Q8×D149—24no—
44C2×D596C2311yescharacteristic
45C2×C22⋊D149—21no—
46D4×D149—24no—
47C2×C4×D149—21no—
48C2×C4×D149D412yes—
49C2×C4×D149C2311yescharacteristic
50#14558719—24no—
51C2×#11924746C2312yes—
52C4⋊Dic149C2312yes—
53#14558715—22no—
54#14558715—22no—
55C22⋊Dic149—22no—
56#14558713—22no—
57#14558713—22no—
58#14558713—22no—
59C4×Dic149—22no—
60C4×Dic149D412yes—
61C4×Dic149C2311yescharacteristic
62C2×Q8×C149C2311yescharacteristic
63C2×D4×C149C2311yescharacteristic
64C2×C8×C149C2312yes—
65C4⋊C4×C149—22no—
66C4⋊C4×C149C2312yes—
67C22⋊C4×C149—22no—
68C42×C149C2311yescharacteristic
69C22×D149—21no—
70C22×D149—44no—
71C22×D149—42no—
72C22×D149C2×D411yescharacteristic
73Dic298—22no—
74Dic298—44no—
75Dic298—42no—
76D596—22no—
77C22⋊D149—42no—
78C2×Dic149—21no—
79C2×Dic149—22no—
80C2×Dic149C2×D412yes—
81C2×Dic149C2×D411yescharacteristic
82C4×D149—42no—
83C4×D149—42no—
84C4×D149#4114yes—
85#11924746—22no—
86C23×C149—21no—
87Q8×C149—22no—
88D4×C149—22no—
89C2×C4×C149—21no—
90C2×C4×C149—22no—
91C2×C4×C149C2×D412yes—
92C2×C4×C149C2411yescharacteristic
93C8×C149—22no—
94C22×C149—41no—
95C22×C149—42no—
96C22×C149C22×D411yescharacteristic
97C2×D149—22no—
98C2×D149—41no—
99C2×D149—42no—
100C2×D149—84no—
101C2×D149#12412yes—
102C4×C149—22no—
103C4×C149—41no—
104C4×C149—42no—
105C4×C149C2×#4112yes—
106Dic149—22no—
107Dic149—41no—
108Dic149—42no—
109Dic149#12412yes—
110C2×C149—81no—
111C2×C149C2×#12411yescharacteristic
112C2×C149#57512yes—
113D149—22no—
114D149—81no—
115C149#314011yescharacteristic, complemented, Sylow
116#3140—1491nomaximal, Sylow
117#533—1491no—
118C2×#124—1491no—
119#489—1492no—
120#489—1492no—
121#488—1491no—
122#488—1491no—
123#488—1491no—
124#488D14911yescharacteristic, complemented
125#419—1492no—
126#418—1492no—
127C4×M16—1491no—
128C22×Q8—1491no—
129C22×D4—1491no—
130C2×M16—1492no—
131C4⋊Q8—1492no—
132#125—1491no—
133#125C2×D14911yescharacteristic, complemented
134#124—2982no—
135#124—1491no—
136#124—1491no—
137#124—1491no—
138#124C2×D14911yescharacteristic
139C22⋊Q8—2982no—
140C4×Q8—2982no—
141#117—1492no—
142C2×C22⋊C4—2982no—
143C2×C42—1491no—
144#103—1492no—
145#103—1492no—
146#103—1492no—
147#103C2×D14912yescomplemented
148#102—1492no—
149#102—1492no—
150#102—1492no—
151#102C2×D14912yes—
152#97—1492no—
153C4×C8—1491no—
154C4×C8C2×D14911yescharacteristic, complemented
155C24—2981no—
156C2×Q8—2982no—
157C2×Q8—2981no—
158C2×Q8—2984no—
159C2×Q8—1491no—
160C2×Q8C22×D14911yescharacteristic
161C2×D4—2984no—
162C2×D4—2981no—
163C2×D4—1491no—
164C2×D4C22×D14911yescharacteristic
165C22×C4—2981no—
166C22×C4—1492no—
167C22×C4—1491no—
168M16—2984no—
169C2×C8—1492no—
170C2×C8C22×D14912yes—
171C4⋊C4—22no—
172C4⋊C4—2982no—
173C4⋊C4—2982no—
174C4⋊C4—1492no—
175C4⋊C4C22×D14912yes—
176C22⋊C4—22no—
177C22⋊C4—2982no—
178C22⋊C4—2982no—
179C22⋊C4—2982no—
180C22⋊C4—2982no—
181C42—2982no—
182C42—1492no—
183C42—1491no—
184C42C22×D14911yescharacteristic
185C23—21no—
186C23—2981no—
187C23—5964no—
188C23—5962no—
189C23—1491no—
190Q8—22no—
191Q8—2982no—
192Q8—5964no—
193Q8—5962no—
194D4—22no—
195D4—2982no—
196D4—5962no—
197C2×C4—22no—
198C2×C4—21no—
199C2×C4—2982no—
200C2×C4—2981no—
201C2×C4—5962no—
202C2×C4—5962no—
203C2×C4—1492no—
204C2×C4—1491no—
205C2×C4—1494no—
206C2×C4D4×D14912yes—
207C2×C4C23×D14911yescharacteristic
208C8—22no—
209C8—2982no—
210C22—42no—
211C22—41no—
212C22—2982no—
213C22—5962no—
214C22—5961no—
215C22—1492no—
216C22—11924no—
217C22C2×D4×D14911yescharacteristic
218C4—22no—
219C4—42no—
220C4—41no—
221C4—2982no—
222C4—5962no—
223C4—5961no—
224C4—1492no—
225C4#41×D14912yes—
226C2—81no—
227C2—2982no—
228C2—11921no—
229C2#124×D14911yescharacteristic
230C2#2375042212yes—
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#488×C149C2
socleC22×C149C22×D4
prime radicalC2×D4×D149C22
hypercenter#488D149
hypocenterC149#3140
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #23750181C2semidirect
3. #23749986C2semidirect
4. #23749983C2semidirect
5. #23749982C2semidirect
6. #23749980C2semidirect
7. #23749979C2semidirect
8. #23749632C2semidirect
10. C4×#14558719C2semidirect
11. #488×C149C2semidirect
15. #18011910C22semidirect
16. #18011903C22semidirect
26. #18011836C22semidirect
27. #18011835C22semidirect
28. #18011834C22semidirect
32. #18011821C22semidirect
33. C4×#11924746C22semidirect
34. #125×C149C22semidirect
36. #103×C149C22semidirect
38. C4×C8×C149C22semidirect
115. C149#3140semidirect
124. #488D149semidirect
133. #125C2×D149semidirect
147. #103C2×D149semidirect
154. C4×C8C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237501812
#124×D1492
#237499862
#237499832
#237499822
#237499802
#237499792
#237496322
#237496282
C4×#145587192
#488×C1492
#3140149