Finite Group Databasebeta

← #34055421

Subgroups — #34055421

Order 19072.

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

normal subgroups only

This group has 370 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#23750161C212yesmaximal, complemented
2#23750025C211yesmaximal, characteristic, complemented
3#23750010C211yesmaximal, characteristic, complemented
4#23749981C212yesmaximal, complemented
5#23749878C211yesmaximal, characteristic
6#23749873C212yesmaximal, complemented
7#23749736C211yesmaximal, characteristic, complemented
8#23749732C211yesmaximal, characteristic, complemented
9#23749728C212yesmaximal, complemented
10M16×Dic149C211yesmaximal, characteristic, complemented
11#470×C149C211yesmaximal, characteristic, complemented
12C2×#14558723C2212yes—
13C2×D1192C2211yescharacteristic
14C2×#14558720C2211yescharacteristic
15#18011906—22no—
16#18011902C2212yes—
17#18011900C2212yes—
18#18011895—22no—
19#18011885C2212yes—
20Q8×Dic149C2212yes—
21#18011873C2212yes—
22#18011871—22no—
23#18011869—22no—
24C2×C4×Dic149C2211yescharacteristic
25#18011844C2212yes—
26#18011843C2211yescharacteristic
27#18011835C2212yes—
28#18011833C2212yes—
29#18011831C2212yes—
30#18011821C2211yescharacteristic
31#18011821C2211yescharacteristic
32C8×Dic149C2211yescharacteristic
33C8×Dic149C2211yescharacteristic
34C2×Q16×C149C2211yescharacteristic
35C2×M16×C149C2211yescharacteristic
36C22⋊Q8×C149C2212yes—
37#106×C149C2211yescharacteristic
38#103×C149C2212yes—
39C2×D596C2312yes—
40C2×C22⋊D149—22no—
41C22×Dic149D412yes—
42C2×C4×D149—22no—
43#14558723—24no—
44D1192—22no—
45#14558720—22no—
46C2×#11924746C2311yescharacteristic
47C2×#11924746C2311yescharacteristic
48C4⋊Dic149—22no—
49C4⋊Dic149—22no—
50C4⋊Dic149C2312yes—
51#14558715—22no—
52#14558713—22no—
53#14558713—22no—
54#14558713—22no—
55#14558713—22no—
56C4×Dic149—22no—
57C4×Dic149D412yes—
58C4×Dic149C2311yescharacteristic
59C4×Dic149C2311yescharacteristic
60C2×Q8×C149C2312yes—
61C22×C4×C149C2311yescharacteristic
62Q16×C149—22no—
63M16×C149—22no—
64C2×C8×C149C2311yescharacteristic
65C2×C8×C149C2311yescharacteristic
66C4⋊C4×C149—22no—
67C4⋊C4×C149C2312yes—
68C22⋊C4×C149—22no—
69C22×D149—22no—
70D596—22no—
71D596—22no—
72C22⋊D149—44no—
73C2×Dic149—22no—
74C2×Dic149—42no—
75C2×Dic149C2×D412yes—
76C2×Dic149C2×D412yes—
77C4×D149—44no—
78#11924746—21no—
79#11924746#4112yes—
80C23×C149C2×D411yescharacteristic
81Q8×C149—22no—
82Q8×C149—22no—
83C2×C4×C149—21no—
84C2×C4×C149—21no—
85C2×C4×C149—22no—
86C2×C4×C149—22no—
87C2×C4×C149C2×D411yescharacteristic
88C2×C4×C149C2411yescharacteristic
89C8×C149—21no—
90C8×C149#4112yes—
91C22×C149—21no—
92C22×C149—22no—
93C22×C149C22×D411yescharacteristic
94C2×D149—42no—
95C2×D149—42no—
96C2×D149—42no—
97C4×C149—21no—
98C4×C149—42no—
99C4×C149—42no—
100C4×C149C2×#4111yescharacteristic
101C4×C149C2×#4111yescharacteristic
102Dic149—22no—
103Dic149—22no—
104Dic149—42no—
105C2×C149—41no—
106C2×C149#53211yescharacteristic
107C2×C149#57512yes—
108D149—82no—
109C149#318311yescharacteristic, complemented, Sylow
110#3183—1491nomaximal, Sylow
111#529—1492no—
112#499—1491no—
113#495—1491no—
114#488—1492no—
115#470D14911yescharacteristic, complemented
116#469—1491no—
117#468—1492no—
118#442—1491no—
119#441—1491no—
120#440—1492no—
121C4×M16—1491no—
122C2×Q16C2×D14911yescharacteristic
123C2×SD16—1492no—
124C2×D8—1491no—
125C2×M16—1491no—
126C2×M16C2×D14911yescharacteristic
127#126—2982no—
128#125—1492no—
129#124—1492no—
130#123—2982no—
131C22⋊Q8C2×D14912yes—
132#121—1492no—
133C4×Q8—1492no—
134C4×D4—2982no—
135C4×D4—1492no—
136#117—2982no—
137C2×C42—1491no—
138#107—1492no—
139#106—1491no—
140#106C2×D14911yescharacteristic
141#103—1492no—
142#103C2×D14912yes—
143#102—1492no—
144#102—1492no—
145#97—1491no—
146#97—1491no—
147C4×C8—1491no—
148C4×C8—1491no—
149C2×Q8C22×D14912yes—
150C2×D4—2982no—
151C2×D4—1492no—
152C22×C4—2982no—
153C22×C4—1492no—
154C22×C4C22×D14911yescharacteristic
155Q16—22no—
156SD16—2984no—
157D8—2982no—
158M16—22no—
159M16—2982no—
160C2×C8—1491no—
161C2×C8—1491no—
162C2×C8C22×D14911yescharacteristic
163C2×C8C22×D14911yescharacteristic
164C4⋊C4—22no—
165C4⋊C4—2982no—
166C4⋊C4—2982no—
167C4⋊C4—2982no—
168C4⋊C4—1492no—
169C4⋊C4C22×D14912yes—
170C22⋊C4—22no—
171C22⋊C4—2982no—
172C22⋊C4—2982no—
173C22⋊C4—2982no—
174C22⋊C4—2982no—
175C42—2982no—
176C42—1492no—
177C42—1491no—
178C42—1491no—
179C23—2982no—
180C23D4×D14911yescharacteristic
181Q8—22no—
182Q8—22no—
183D4—2982no—
184D4—2982no—
185D4—5964no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—2982no—
191C2×C4—5964no—
192C2×C4—5962no—
193C2×C4—1492no—
194C2×C4—1492no—
195C2×C4D4×D14911yescharacteristic
196C2×C4C23×D14911yescharacteristic
197C8—21no—
198C8—2981no—
199C8—1492no—
200C8#1455873512yes—
201C22—22no—
202C22—21no—
203C22—5962no—
204C22—5962no—
205C22—5962no—
206C22C2×D4×D14911yescharacteristic
207C4—21no—
208C4—42no—
209C4—42no—
210C4—2982no—
211C4—2982no—
212C4—5962no—
213C4#41×D14911yescharacteristic
214C4C2×#1455873511yescharacteristic
215C2—41no—
216C2—11922no—
217C2#2375017011yescharacteristic
218C2#2375042412yes—
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#470×C149C2
socleC22×C149C22×D4
prime radical#23749878C2
hypercenter#470D149
hypocenterC149#3183
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
1. #23750161C2semidirect
2. #23750025C2semidirect
3. #23750010C2semidirect
4. #23749981C2semidirect
6. #23749873C2semidirect
7. #23749736C2semidirect
8. #23749732C2semidirect
9. #23749728C2semidirect
10. M16×Dic149C2semidirect
11. #470×C149C2semidirect
109. C149#3183semidirect
115. #470D149semidirect

Maximal subgroups

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

subgroupindex
#237501612
#237500252
#237500102
#237499812
#237498782
#237498732
#237497362
#237497322
#237497282
M16×Dic1492
#470×C1492
#3183149