Finite Group Databasebeta

← #34055300

Subgroups — #34055300

Order 19072.

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

normal subgroups only

This group has 364 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#23750180C211yesmaximal, characteristic, complemented
2#23750154C211yesmaximal, characteristic
3#23750031C211yesmaximal, characteristic, complemented
4#23750020C211yesmaximal, characteristic, complemented
5#23749994C211yesmaximal, characteristic, complemented
6#23749882C212yesmaximal, complemented
7#23749870C212yesmaximal
8#23749717C212yesmaximal, complemented
9#23749716C212yesmaximal, complemented
10#23749577C211yesmaximal, characteristic, complemented
11#489×C149C211yesmaximal, characteristic, complemented
12C2×#14558726C2212yes—
13C2×#14558724C2212yes—
14C2×#14558719C2212yes—
15#18011911C2211yescharacteristic
16#18011904—21no—
17#18011903C2211yescharacteristic
18#18011902—21no—
19#18011893—21no—
20#18011891C2212yes—
21#18011887—21no—
22#18011887C2211yescharacteristic
23#18011882C2211yescharacteristic
24Q8×Dic149—21no—
25Q8×Dic149C2211yescharacteristic
26#18011876C2212yes—
27D4×Dic149C2211yescharacteristic
28#18011871—21no—
29#18011869—21no—
30#18011867—21no—
31C42×D149C2211yescharacteristic
32#18011844C2212yes—
33#18011842C2212yes—
34#18011836C2212yes—
35#18011836C2212yes—
36#18011822C2211yescharacteristic
37C8×Dic149C2212yes—
38C4⋊Q8×C149C2211yescharacteristic
39#124×C149C2211yescharacteristic
40#103×C149C2212yes—
41#102×C149C2212yes—
42#97×C149C2211yescharacteristic
43C2×Dic298C2312yes—
44C2×C22⋊D149—21no—
45C22×Dic149—21no—
46C2×C4×D149D411yescharacteristic
47C2×C4×D149D411yescharacteristic
48C2×C4×D149C2311yescharacteristic
49#14558726—24no—
50#14558724—24no—
51#14558719—24no—
52C2×#11924746C2312yes—
53C4⋊Dic149—21no—
54C4⋊Dic149—22no—
55C4⋊Dic149—21no—
56C4⋊Dic149—21no—
57C4⋊Dic149C2311yescharacteristic
58C4⋊Dic149C2311yescharacteristic
59#14558715—21no—
60#14558715—22no—
61#14558715—21no—
62#14558715—21no—
63C22⋊Dic149—21no—
64C22⋊Dic149—21no—
65#14558713—22no—
66#14558713—21no—
67C4×Dic149—21no—
68C4×Dic149—22no—
69C4×Dic149D411yescharacteristic
70C4×Dic149D411yescharacteristic
71C4×Dic149C2311yescharacteristic
72C2×Q8×C149—21no—
73C2×Q8×C149C2311yescharacteristic
74C2×D4×C149C2311yescharacteristic
75C2×C8×C149C2312yes—
76C4⋊C4×C149—21no—
77C4⋊C4×C149C2312yes—
78C22⋊C4×C149—21no—
79C22⋊C4×C149—21no—
80C42×C149C2311yescharacteristic
81C22×D149C2×D411yescharacteristic
82Dic298—22no—
83Dic298—22no—
84C22⋊D149—42no—
85C2×Dic149—21no—
86C2×Dic149—21no—
87C2×Dic149—22no—
88C2×Dic149—42no—
89C2×Dic149C2×D411yescharacteristic
90C2×Dic149C2×D411yescharacteristic
91C2×Dic149C2×D411yescharacteristic
92C4×D149—22no—
93C4×D149—22no—
94C4×D149—41no—
95#11924746#4114yes—
96C23×C149—21no—
97Q8×C149—22no—
98Q8×C149—42no—
99D4×C149—22no—
100C2×C4×C149—21no—
101C2×C4×C149—22no—
102C2×C4×C149C2×D411yescharacteristic
103C2×C4×C149C2×D411yescharacteristic
104C2×C4×C149C2411yescharacteristic
105C8×C149—22no—
106C22×C149—41no—
107C22×C149—41no—
108C22×C149—41no—
109C22×C149C22×D411yescharacteristic
110C2×D149—21no—
111C2×D149—21no—
112C2×D149—21no—
113C4×C149—21no—
114C4×C149—21no—
115C4×C149—41no—
116C4×C149—42no—
117C4×C149C2×#4112yes—
118Dic149—21no—
119Dic149—21no—
120Dic149—42no—
121Dic149—41no—
122Dic149—41no—
123Dic149#13712yes—
124C2×C149—81no—
125C2×C149#53211yescharacteristic
126C2×C149C2×#13711yescharacteristic
127C2×C149#57511yescharacteristic
128D149—41no—
129C149#317211yescharacteristic, complemented, Sylow
130#3172—1491nomaximal, Sylow
131#533—1491no—
132#529—1491no—
133#501—1491no—
134#497—1491no—
135#491—1491no—
136#489D14911yescharacteristic, complemented
137#470—1492no—
138#468—1492no—
139C4×Q16—1492no—
140C4×SD16—1492no—
141C4×M16—1491no—
142C2×Q16—1492no—
143C2×SD16—1492no—
144C2×M16—1492no—
145C4⋊Q8—1491no—
146C4⋊Q8C2×D14911yescharacteristic
147#126—2981no—
148#125—2981no—
149#125—1491no—
150#124C2×D14911yescharacteristic
151#123—2981no—
152C22⋊Q8—2981no—
153C22⋊Q8—1491no—
154C22⋊Q8—1492no—
155#121—1491no—
156C4×Q8—2981no—
157C4×Q8—1491no—
158C4×Q8—1492no—
159C4×D4—2981no—
160C4×D4—1491no—
161#117—2981no—
162#117—2981no—
163C2×C42—1491no—
164#107—1492no—
165#106—1492no—
166#103—1492no—
167#103—1492no—
168#103C2×D14912yes—
169#102C2×D14912yes—
170#97—1491no—
171#97C2×D14911yescharacteristic
172C4×C8—1492no—
173C2×Q8—21no—
174C2×Q8—1492no—
175C2×Q8C22×D14911yescharacteristic
176C2×D4—2981no—
177C2×D4C22×D14911yescharacteristic
178C22×C4—2981no—
179C22×C4—1491no—
180C22×C4—1491no—
181C22×C4—1491no—
182Q16—2984no—
183SD16—2984no—
184M16—2984no—
185C2×C8—1492no—
186C2×C8C22×D14912yes—
187C4⋊C4—21no—
188C4⋊C4—2981no—
189C4⋊C4—2982no—
190C4⋊C4—2982no—
191C4⋊C4—2981no—
192C4⋊C4—2981no—
193C4⋊C4—2981no—
194C4⋊C4—2981no—
195C4⋊C4—2981no—
196C4⋊C4—1491no—
197C4⋊C4—1491no—
198C4⋊C4C22×D14912yes—
199C22⋊C4—21no—
200C22⋊C4—21no—
201C22⋊C4—2982no—
202C22⋊C4—2981no—
203C22⋊C4—2981no—
204C22⋊C4—2981no—
205C42—2981no—
206C42—2982no—
207C42—1491no—
208C42—1491no—
209C42—1491no—
210C42C22×D14911yescharacteristic
211C23—21no—
212C23—1491no—
213Q8—22no—
214Q8—42no—
215Q8—2982no—
216Q8—2982no—
217D4—22no—
218D4—5962no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—2982no—
222C2×C4—2982no—
223C2×C4—2982no—
224C2×C4—2981no—
225C2×C4—2981no—
226C2×C4—5961no—
227C2×C4—5962no—
228C2×C4—1491no—
229C2×C4—1491no—
230C2×C4—1491no—
231C2×C4D4×D14911yescharacteristic
232C2×C4D4×D14911yescharacteristic
233C2×C4C23×D14911yescharacteristic
234C8—22no—
235C8—1494no—
236C22—41no—
237C22—41no—
238C22—41no—
239C22—2981no—
240C22—2981no—
241C22—2981no—
242C22C2×D4×D14911yescharacteristic
243C4—21no—
244C4—21no—
245C4—42no—
246C4—41no—
247C4—2981no—
248C4—2981no—
249C4—5961no—
250C4—5961no—
251C4—5962no—
252C4—1492no—
253C4#41×D14912yes—
254C2—81no—
255C2—5961no—
256C2#2375017411yescharacteristic
257C2#137×D14911yescharacteristic
258C2#2375042111yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#489×C149C2
socleC22×C149C22×D4
prime radical#18011882C22
hypercenter#489D149
hypocenterC149#3172
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #23750180C2semidirect
3. #23750031C2semidirect
4. #23750020C2semidirect
5. #23749994C2semidirect
6. #23749882C2semidirect
8. #23749717C2semidirect
9. #23749716C2semidirect
10. #23749577C2semidirect
11. #489×C149C2semidirect
129. C149#3172semidirect
136. #489D149semidirect

Maximal subgroups

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

subgroupindex
#237501802
#237501542
#237500312
#237500202
#237499942
#237498822
#237498702
#237497172
#237497162
#237495772
#489×C1492
#3172149