Finite Group Databasebeta

← #34055602

Subgroups — #34055602

Order 19072.

402 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 109 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#23750204C212yesmaximal, complemented
2#23749957C212yesmaximal, complemented
3#23749942C212yesmaximal, complemented
4#23749883C211yesmaximal, characteristic, complemented
5#23749852C212yesmaximal, complemented
6#23749788C212yesmaximal, complemented
7#23749767C212yesmaximal, complemented
8#23749593C211yesmaximal, characteristic, complemented
9#469×C149C211yesmaximal, characteristic, complemented
10C2×#14558736C2211yescharacteristic
11C2×#14558735C2212yes—
12C2×Dic596C2211yescharacteristic
13C2×#14558724C2212yes—
14C22×#11924746C2211yescharacteristic
15#18011891C2212yes—
16#18011890C2212yes—
17#18011888—22no—
18#18011884—22no—
19#18011883—22no—
20#18011882—22no—
21#18011882C2212yes—
22C4⋊C4×D149C2212yes—
23#18011843C2211yescharacteristic
24#18011842C2212yes—
25#18011836C2212yes—
26#18011834C2212yes—
27#18011832C2212yes—
28#18011823C2212yes—
29#18011823C2212yes—
30C2×D8×C149C2211yescharacteristic
31C2×M16×C149C2211yescharacteristic
32#121×C149C2212yes—
33#106×C149C2211yescharacteristic
34#102×C149C2212yes—
35#14558736—41no—
36#14558736—41no—
37#14558735—42no—
38#14558735—42no—
39C2×Dic298D411yescharacteristic
40C2×Dic298C2312yes—
41C2×D596D411yescharacteristic
42C2×C22⋊D149—22no—
43C2×C22⋊D149—22no—
44C2×C22⋊D149D412yes—
45C22×Dic149—22no—
46C2×C4×D149—22no—
47C2×C4×D149C2312yes—
48Dic596—41no—
49#14558724—42no—
50C2×#11924746—41no—
51C2×#11924746C2312yes—
52C4⋊Dic149—22no—
53C4⋊Dic149C2312yes—
54#14558715—22no—
55#14558715—22no—
56C22⋊Dic149—22no—
57C22⋊Dic149—22no—
58#14558713—22no—
59C2×D4×C149—22no—
60C2×D4×C149C2312yes—
61C22×C4×C149C2311yescharacteristic
62D8×C149—41no—
63M16×C149—41no—
64C2×C8×C149C2311yescharacteristic
65C2×C8×C149C2311yescharacteristic
66C4⋊C4×C149C2312yes—
67C22⋊C4×C149—22no—
68C22×D149C2×D412yes—
69Dic298—22no—
70Dic298—22no—
71Dic298—41no—
72D596—41no—
73C22⋊D149—42no—
74C22⋊D149—44no—
75C22⋊D149—82no—
76C2×Dic149—22no—
77C2×Dic149—22no—
78C2×Dic149—44no—
79C2×Dic149C2×D412yes—
80C4×D149—22no—
81C4×D149—22no—
82C4×D149—82no—
83#11924746—22no—
84C23×C149—22no—
85C23×C149C2×D411yescharacteristic
86D4×C149—22no—
87D4×C149—22no—
88D4×C149—82no—
89C2×C4×C149—21no—
90C2×C4×C149—21no—
91C2×C4×C149—22no—
92C2×C4×C149C2×D411yescharacteristic
93C2×C4×C149C2411yescharacteristic
94C8×C149—21no—
95C8×C149—21no—
96C22×C149—21no—
97C22×C149—22no—
98C22×C149—42no—
99C22×C149—42no—
100C22×C149—42no—
101C22×C149C22×D411yescharacteristic
102C2×D149—22no—
103C2×D149—22no—
104C2×D149—22no—
105C4×C149—21no—
106C4×C149—42no—
107C4×C149H(5,𝔽2)11yescharacteristic
108C4×C149H(5,𝔽2)11yescharacteristic
109Dic149—22no—
110Dic149—42no—
111Dic149—42no—
112C2×C149—41no—
113C2×C149—82no—
114C2×C149#53411yescharacteristic
115C2×C149#57712yes—
116D149—42no—
117C149#320411yescharacteristic, complemented, Sylow
118#3204—1491nomaximal, Sylow
119#537—1492no—
120#483—1492no—
121#481—1492no—
122#470—1491no—
123#469D14911yescharacteristic, complemented
124#465—1492no—
125#452—1492no—
126#449—1492no—
127#408—1491no—
128C2×#41—1492no—
129C2×#41—1491no—
130C2×Q16—1491no—
131C2×SD16—1492no—
132C2×D8C2×D14911yescharacteristic
133C2×M16C2×D14911yescharacteristic
134C22×C8—1491no—
135C22⋊Q8—2982no—
136C22⋊Q8—1492no—
137C22⋊Q8—1492no—
138#121—2982no—
139#121—2982no—
140#121—2982no—
141#121—1492no—
142#121C2×D14912yes—
143C2×C4⋊C4—1492no—
144#106—1491no—
145#106—1492no—
146#106C2×D14911yescharacteristic
147#103—1492no—
148#103—1492no—
149#102—1492no—
150#102C2×D14912yes—
151C22⋊C8—1492no—
152C22⋊C8—1492no—
153#41—5961no—
154#41—5961no—
155#41—5962no—
156#41—5962no—
157C2×Q8—1492no—
158C2×Q8—1491no—
159C2×D4—22no—
160C2×D4—2982no—
161C2×D4—2982no—
162C2×D4—1492no—
163C2×D4—1491no—
164C2×D4C22×D14912yes—
165C22×C4—2982no—
166C22×C4—2982no—
167C22×C4—1492no—
168C22×C4C22×D14911yescharacteristic
169Q16—5961no—
170SD16—5962no—
171D8—41no—
172M16—41no—
173C2×C8—5961no—
174C2×C8—1492no—
175C2×C8C22×D14911yescharacteristic
176C2×C8C22×D14911yescharacteristic
177C4⋊C4—2982no—
178C4⋊C4—2982no—
179C4⋊C4—2982no—
180C4⋊C4—1492no—
181C4⋊C4C22×D14912yes—
182C22⋊C4—22no—
183C22⋊C4—2982no—
184C22⋊C4—2982no—
185C22⋊C4—2982no—
186C23—22no—
187C23—1492no—
188C23D4×D14911yescharacteristic
189Q8—2982no—
190Q8—2982no—
191Q8—5961no—
192D4—22no—
193D4—22no—
194D4—82no—
195D4—5961no—
196D4—5962no—
197D4—5964no—
198D4—11922no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—2982no—
203C2×C4—2982no—
204C2×C4—2982no—
205C2×C4—2982no—
206C2×C4—5964no—
207C2×C4—1492no—
208C2×C4—11922no—
209C2×C4D4×D14911yescharacteristic
210C2×C4C23×D14911yescharacteristic
211C8—21no—
212C8—21no—
213C8—2982no—
214C22—22no—
215C22—21no—
216C22—42no—
217C22—42no—
218C22—42no—
219C22—2982no—
220C22—2982no—
221C22—2982no—
222C22C2×D4×D14911yescharacteristic
223C4—21no—
224C4—42no—
225C4—2982no—
226C4—5962no—
227C4—5962no—
228C4#1801195611yescharacteristic
229C4#1801195711yescharacteristic
230C2—41no—
231C2—82no—
232C2—5962no—
233C2#2375018311yescharacteristic
234C2#2375043512yes—
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#469×C149C2
socleC22×C149C22×D4
hypercenter#469D149
hypocenterC149#3204
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #23750204C2semidirect
2. #23749957C2semidirect
3. #23749942C2semidirect
4. #23749883C2semidirect
5. #23749852C2semidirect
6. #23749788C2semidirect
7. #23749767C2semidirect
8. #23749593C2semidirect
9. #469×C149C2semidirect
117. C149#3204semidirect
123. #469D149semidirect

Maximal subgroups

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

subgroupindex
#237502042
#237499572
#237499422
#237498832
#237498522
#237497882
#237497672
#237495932
#469×C1492
#3204149