Finite Group Databasebeta

← #34055291

Subgroups — #34055291

Order 19072.

364 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 125 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#23750159C211yesmaximal, characteristic
2#23750031C211yesmaximal, characteristic, complemented
3#23750017C211yesmaximal, characteristic, complemented
4#23749993C211yesmaximal, characteristic, complemented
5#23749987C211yesmaximal, characteristic, complemented
6#23749881C212yesmaximal, complemented
7#23749873C212yesmaximal
8C4×#14558726C212yesmaximal, complemented
9C4×#14558723C212yesmaximal, complemented
10C4×#14558720C211yesmaximal, characteristic, complemented
11#533×C149C211yesmaximal, characteristic, complemented
12C2×#14558726C2212yes—
13C2×#14558723C2212yes—
14C2×#14558720C2212yes—
15#18011905—21no—
16#18011903C2211yescharacteristic
17#18011899C2211yescharacteristic
18#18011894—21no—
19#18011890C2211yescharacteristic
20#18011885C2211yescharacteristic
21C4×Dic298C2211yescharacteristic
22C4×D596C2211yescharacteristic
23C4×C22⋊D149—21no—
24#18011868—21no—
25#18011844C2212yes—
26#18011842C2212yes—
27#18011835C2212yes—
28#18011835C2212yes—
29#18011834C2212yes—
30#18011831C2212yes—
31#18011822C2211yescharacteristic
32#18011822C2211yescharacteristic
33C4×#11924746C2212yes—
34C4⋊Q8×C149C2211yescharacteristic
35C4⋊Q8×C149C2211yescharacteristic
36#125×C149—21no—
37C22⋊Q8×C149—21no—
38C22⋊Q8×C149C2212yes—
39C4×Q8×C149—21no—
40C4×Q8×C149C2212yes—
41#117×C149—21no—
42C2×C42×C149C2211yescharacteristic
43C2×Dic298C2311yescharacteristic
44C2×D596C2311yescharacteristic
45C2×C22⋊D149—21no—
46C2×C4×D149—21no—
47#14558726—24no—
48#14558723—24no—
49#14558720—24no—
50C2×#11924746C2312yes—
51C2×#11924746C2312yes—
52C4⋊Dic149C2311yescharacteristic
53C4⋊Dic149C2311yescharacteristic
54#14558715—21no—
55#14558715—21no—
56#14558715—21no—
57#14558715—21no—
58C22⋊Dic149—21no—
59#14558713—21no—
60#14558713—21no—
61#14558713—21no—
62#14558713—21no—
63C4×Dic149—21no—
64C2×Q8×C149—21no—
65C2×Q8×C149C2312yes—
66C22×C4×C149D411yescharacteristic
67C22×C4×C149D411yescharacteristic
68C22×C4×C149C2311yescharacteristic
69C4⋊C4×C149—21no—
70C4⋊C4×C149—21no—
71C4⋊C4×C149—21no—
72C4⋊C4×C149—22no—
73C4⋊C4×C149—22no—
74C4⋊C4×C149C2312yes—
75C22⋊C4×C149—22no—
76C42×C149—22no—
77C42×C149D411yescharacteristic
78C42×C149D411yescharacteristic
79C42×C149C2311yescharacteristic
80C42×C149C2311yescharacteristic
81C22×D149—21no—
82Dic298—22no—
83D596—22no—
84C22⋊D149—42no—
85C2×Dic149—21no—
86C2×Dic149—21no—
87C2×Dic149—21no—
88C4×D149—42no—
89#11924746—22no—
90#11924746#4114yes—
91C23×C149C2×D411yescharacteristic
92Q8×C149—22no—
93Q8×C149—22no—
94Q8×C149—42no—
95C2×C4×C149—22no—
96C2×C4×C149—22no—
97C2×C4×C149—22no—
98C2×C4×C149—22no—
99C2×C4×C149—41no—
100C2×C4×C149C2×D411yescharacteristic
101C2×C4×C149C2×D411yescharacteristic
102C2×C4×C149C2×D411yescharacteristic
103C2×C4×C149C2×D411yescharacteristic
104C2×C4×C149C2×D411yescharacteristic
105C2×C4×C149C2411yescharacteristic
106C22×C149—21no—
107C22×C149—21no—
108C22×C149—21no—
109C22×C149C22×D411yescharacteristic
110C2×D149—41no—
111C2×D149—41no—
112C2×D149—41no—
113C4×C149—21no—
114C4×C149—21no—
115C4×C149—21no—
116C4×C149—21no—
117C4×C149—42no—
118C4×C149—42no—
119C4×C149#13712yes—
120C4×C149C2×#4112yes—
121Dic149—41no—
122Dic149—41no—
123Dic149—41no—
124C2×C149—41no—
125C2×C149#53211yescharacteristic
126C2×C149C2×#13711yescharacteristic
127C2×C149#57511yescharacteristic
128D149—81no—
129C149#317211yescharacteristic, complemented, Sylow
130#3172—1491nomaximal, Sylow
131#533D14911yescharacteristic, complemented
132#529—1491no—
133#501—1491no—
134#497—1491no—
135#491—1491no—
136#489—1491no—
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⋊Q8C2×D14911yescharacteristic
146C4⋊Q8C2×D14911yescharacteristic
147#126—2981no—
148#125—21no—
149#125—1491no—
150#124—1491no—
151#123—2981no—
152C22⋊Q8—21no—
153C22⋊Q8—1491no—
154C22⋊Q8C2×D14912yes—
155#121—1491no—
156C4×Q8—21no—
157C4×Q8—1491no—
158C4×Q8C2×D14912yes—
159C4×D4—2981no—
160C4×D4—1491no—
161#117—21no—
162#117—2981no—
163C2×C42C2×D14911yescharacteristic
164#107—1492no—
165#106—1492no—
166#103—1492no—
167#103—1492no—
168#103—1492no—
169#102—1492no—
170#97—1491no—
171#97—1491no—
172C4×C8—1492no—
173C2×Q8—21no—
174C2×Q8—1491no—
175C2×Q8C22×D14912yes—
176C2×D4—2981no—
177C2×D4—1491no—
178C22×C4—2981no—
179C22×C4C22⋊D14911yescharacteristic
180C22×C4C22⋊D14911yescharacteristic
181C22×C4C22×D14911yescharacteristic
182Q16—2984no—
183SD16—2984no—
184M16—2984no—
185C2×C8—1492no—
186C2×C8—1492no—
187C4⋊C4—21no—
188C4⋊C4—21no—
189C4⋊C4—21no—
190C4⋊C4—22no—
191C4⋊C4—22no—
192C4⋊C4—2981no—
193C4⋊C4—2981no—
194C4⋊C4—2981no—
195C4⋊C4—2981no—
196C4⋊C4—1491no—
197C4⋊C4—1491no—
198C4⋊C4C22×D14912yes—
199C22⋊C4—22no—
200C22⋊C4—2981no—
201C22⋊C4—2981no—
202C22⋊C4—2981no—
203C22⋊C4—2981no—
204C22⋊C4—2981no—
205C42—22no—
206C42—2981no—
207C42C22⋊D14911yescharacteristic
208C42C22⋊D14911yescharacteristic
209C42C22×D14911yescharacteristic
210C42C22×D14911yescharacteristic
211C23—2981no—
212C23C2×C22⋊D14911yescharacteristic
213Q8—22no—
214Q8—22no—
215Q8—42no—
216Q8—2982no—
217D4—2982no—
218D4—5962no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—41no—
224C2×C4—2981no—
225C2×C4—2981no—
226C2×C4—2981no—
227C2×C4—5962no—
228C2×C4C2×C22⋊D14911yescharacteristic
229C2×C4C2×C22⋊D14911yescharacteristic
230C2×C4C2×C22⋊D14911yescharacteristic
231C2×C4C2×C22⋊D14911yescharacteristic
232C2×C4C2×C22⋊D14911yescharacteristic
233C2×C4C23×D14911yescharacteristic
234C8—2982no—
235C8—1494no—
236C22—21no—
237C22—21no—
238C22—21no—
239C22—5961no—
240C22—5961no—
241C22—5961no—
242C22C22×C22⋊D14911yescharacteristic
243C4—21no—
244C4—21no—
245C4—21no—
246C4—21no—
247C4—42no—
248C4—42no—
249C4—5961no—
250C4—5961no—
251C4—5961no—
252C4#1801194212yes—
253C4#41×D14912yes—
254C2—41no—
255C2—11921no—
256C2#2375017111yescharacteristic
257C2C2×#1801194211yescharacteristic
258C2#2375042311yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#533×C149C2
socleC22×C149C22×D4
prime radical#18011885C22
hypercenter#533D149
hypocenterC149#3172
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #23750031C2semidirect
3. #23750017C2semidirect
4. #23749993C2semidirect
5. #23749987C2semidirect
6. #23749881C2semidirect
8. C4×#14558726C2semidirect
9. C4×#14558723C2semidirect
10. C4×#14558720C2semidirect
11. #533×C149C2semidirect
129. C149#3172semidirect
131. #533D149semidirect

Maximal subgroups

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

subgroupindex
#237501592
#237500312
#237500172
#237499932
#237499872
#237498812
#237498732
C4×#145587262
C4×#145587232
C4×#145587202
#533×C1492
#3172149