Finite Group Databasebeta

← #34055337

Subgroups — #34055337

Order 19072.

386 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 115 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#23750226C212yesmaximal, complemented
2#23750026C211yesmaximal, characteristic, complemented
3#23750000C211yesmaximal, characteristic, complemented
4#23749988C212yesmaximal, complemented
5#23749877C212yesmaximal, complemented
6#23749862C211yesmaximal, characteristic, complemented
7#23749858C211yesmaximal, characteristic, complemented
8#23749735C212yesmaximal, complemented
9C4×D1192C211yesmaximal, characteristic, complemented
10#23749579C211yesmaximal, characteristic, complemented
11C4×D8×C149C211yesmaximal, characteristic, complemented
12C2×D1192C2211yescharacteristic
13C2×#14558721C2212yes—
14C2×#14558719C2211yescharacteristic
15C2×C8×D149C2211yescharacteristic
16#18011907C2212yes—
17#18011902C2212yes—
18#18011894—22no—
19#18011893—22no—
20#18011886C2212yes—
21#18011885—22no—
22#18011884—22no—
23#18011882C2212yes—
24C4×D596C2212yes—
25#18011868C2211yescharacteristic
26#18011845C2211yescharacteristic
27#18011842C2212yes—
28#18011833C2212yes—
29#18011832C2212yes—
30#18011831C2212yes—
31#18011822C2211yescharacteristic
32#18011821C2211yescharacteristic
33C8×Dic149C2211yescharacteristic
34C2×D8×C149C2211yescharacteristic
35C4×D4×C149C2212yes—
36#107×C149C2211yescharacteristic
37#102×C149C2212yes—
38C4×C8×C149C2211yescharacteristic
39C2×D596—22no—
40C2×D596C2312yes—
41C2×C22⋊D149—22no—
42C2×C22⋊D149—22no—
43C2×C22⋊D149—22no—
44C2×C4×D149—22no—
45C2×C4×D149C2311yescharacteristic
46D1192—22no—
47#14558721—24no—
48#14558719—22no—
49C2×#11924746C2311yescharacteristic
50C2×#11924746C2311yescharacteristic
51C8×D149—22no—
52C4⋊Dic149—22no—
53C4⋊Dic149C2312yes—
54#14558715—22no—
55#14558715D411yescharacteristic
56#14558715D411yescharacteristic
57C22⋊Dic149—22no—
58#14558713—22no—
59#14558713—22no—
60#14558713D411yescharacteristic
61#14558713D411yescharacteristic
62C4×Dic149C2311yescharacteristic
63C2×D4×C149C2312yes—
64C22×C4×C149—22no—
65D8×C149—22no—
66C2×C8×C149C2311yescharacteristic
67C2×C8×C149C2311yescharacteristic
68C4⋊C4×C149C2312yes—
69C22⋊C4×C149—22no—
70C42×C149C2311yescharacteristic
71C22×D149—22no—
72C22×D149C2×D411yescharacteristic
73D596—22no—
74D596—22no—
75D596—82no—
76C22⋊D149—82no—
77C22⋊D149—82no—
78C22⋊D149—82no—
79C2×Dic149—22no—
80C2×Dic149C2×D411yescharacteristic
81C2×Dic149C2×D411yescharacteristic
82C2×Dic149C2×D411yescharacteristic
83C4×D149—21no—
84C4×D149—21no—
85C4×D149—82no—
86#11924746—21no—
87#11924746#4112yes—
88C23×C149—22no—
89D4×C149—22no—
90D4×C149—22no—
91C2×C4×C149—22no—
92C2×C4×C149—82no—
93C2×C4×C149C2×D411yescharacteristic
94C2×C4×C149C2×D411yescharacteristic
95C2×C4×C149C2411yescharacteristic
96C8×C149—21no—
97C8×C149#4112yes—
98C22×C149—42no—
99C22×C149—42no—
100C22×C149—42no—
101C22×C149C22×D411yescharacteristic
102C2×D149—21no—
103C2×D149—21no—
104C2×D149—21no—
105C2×D149—42no—
106C2×D149—42no—
107C2×D149—42no—
108C4×C149—21no—
109C4×C149—21no—
110C4×C149—42no—
111C4×C149C2×#4111yescharacteristic
112C4×C149C2×#4111yescharacteristic
113Dic149—21no—
114Dic149—21no—
115Dic149—21no—
116Dic149—42no—
117C2×C149—82no—
118C2×C149#53211yescharacteristic
119C2×C149#57611yescharacteristic
120C2×C149#57611yescharacteristic
121D149—41no—
122D149—82no—
123C149#317611yescharacteristic, complemented, Sylow
124#3176—1491nomaximal, Sylow
125#540—1492no—
126#499—1491no—
127#493—1491no—
128#490—1492no—
129#469—1492no—
130#466—1491no—
131#466—1491no—
132#442—1492no—
133C4×D8—1491no—
134C4×D8D14911yescharacteristic, complemented
135#405—1491no—
136C2×D8—1492no—
137C2×D8—1491no—
138C2×D8C2×D14911yescharacteristic
139C2×M16—1491no—
140C22×C8—1491no—
141#127—1492no—
142#125—1492no—
143#123—2982no—
144#123—2982no—
145#121—2982no—
146#121—2982no—
147#121—1492no—
148#121—1492no—
149C4×D4—1492no—
150C4×D4C2×D14912yes—
151#117—1491no—
152#107—1491no—
153#107C2×D14911yescharacteristic
154#106—1492no—
155#102—1492no—
156#102—1492no—
157#102—1492no—
158#102C2×D14912yes—
159#97—1491no—
160#97—1491no—
161C4×C8—1491no—
162C4×C8C2×D14911yescharacteristic
163C2×D4—2982no—
164C2×D4—2982no—
165C2×D4—2982no—
166C2×D4—2982no—
167C2×D4—1492no—
168C2×D4C22×D14912yes—
169C22×C4—22no—
170C22×C4—2982no—
171C22×C4—1491no—
172D8—22no—
173D8—2984no—
174D8—2982no—
175M16—2982no—
176C2×C8—2982no—
177C2×C8—1491no—
178C2×C8—1491no—
179C2×C8C22×D14911yescharacteristic
180C2×C8C22×D14911yescharacteristic
181C4⋊C4—2982no—
182C4⋊C4—2982no—
183C4⋊C4—1492no—
184C4⋊C4—1491no—
185C4⋊C4—1491no—
186C4⋊C4C22×D14912yes—
187C22⋊C4—22no—
188C22⋊C4—2982no—
189C22⋊C4—2982no—
190C22⋊C4—2982no—
191C22⋊C4—1491no—
192C22⋊C4—1491no—
193C42—1491no—
194C42C22×D14911yescharacteristic
195C23—22no—
196C23—2982no—
197C23—1491no—
198D4—22no—
199D4—22no—
200D4—2982no—
201D4—2982no—
202D4—11922no—
203D4—11922no—
204D4—11922no—
205D4—11922no—
206C2×C4—22no—
207C2×C4—82no—
208C2×C4—2981no—
209C2×C4—2981no—
210C2×C4—2982no—
211C2×C4—1491no—
212C2×C4—1491no—
213C2×C4—1491no—
214C2×C4—11922no—
215C2×C4D4×D14911yescharacteristic
216C2×C4D4×D14911yescharacteristic
217C2×C4C23×D14911yescharacteristic
218C8—21no—
219C8—2981no—
220C8—1492no—
221C8#1455873612yes—
222C22—42no—
223C22—42no—
224C22—42no—
225C22—2981no—
226C22—2981no—
227C22—2981no—
228C22—5962no—
229C22—5962no—
230C22—5962no—
231C22C2×D4×D14911yescharacteristic
232C4—21no—
233C4—21no—
234C4—42no—
235C4—2981no—
236C4—2981no—
237C4—2981no—
238C4—5962no—
239C4#41×D14911yescharacteristic
240C4C2×#1455873611yescharacteristic
241C2—82no—
242C2—5961no—
243C2—11922no—
244C2#2375017211yescharacteristic
245C2#2375042611yescharacteristic
246C2#2375042711yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC4×D8×C149C2
socleC22×C149C22×D4
hypercenterC4×D8D149
hypocenterC149#3176
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #23750226C2semidirect
2. #23750026C2semidirect
3. #23750000C2semidirect
4. #23749988C2semidirect
5. #23749877C2semidirect
6. #23749862C2semidirect
7. #23749858C2semidirect
8. #23749735C2semidirect
9. C4×D1192C2semidirect
10. #23749579C2semidirect
11. C4×D8×C149C2semidirect
123. C149#3176semidirect
134. C4×D8D149semidirect

Maximal subgroups

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

subgroupindex
#237502262
#237500262
#237500002
#237499882
#237498772
#237498622
#237498582
#237497352
C4×D11922
#237495792
C4×D8×C1492
#3176149