Finite Group Databasebeta

← #34054862

Subgroups — #34054862

Order 19072.

386 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 129 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#23749960C211yesmaximal, characteristic, complemented
3#23749943C211yesmaximal, characteristic
4#23749932C212yesmaximal, complemented
5#23749847C212yesmaximal, complemented
6#23749781C211yesmaximal, characteristic, complemented
7#23749764C211yesmaximal, characteristic
8#23749730C212yesmaximal, complemented
9#23749723C212yesmaximal, complemented
10#23749682C211yesmaximal, characteristic, complemented
11C2×C4×Q8×C149C211yesmaximal, characteristic, complemented
12C2×#14558726C2212yes—
13C2×#14558723C2212yes—
14#18011905—21no—
15#18011903C2211yescharacteristic
16#18011899C2211yescharacteristic
17#18011894—21no—
18#18011890C2211yescharacteristic
19#18011885C2211yescharacteristic
20C4×Dic298C2211yescharacteristic
21C4×D596C2211yescharacteristic
22C4×C22⋊D149—21no—
23#18011868—21no—
24#18011844C2212yes—
25#18011842C2212yes—
26C4⋊#11924746C2212yes—
27#18011835C2212yes—
28#18011835C2212yes—
29#18011834C2212yes—
30#18011831C2212yes—
31C22⋊#11924746C2211yescharacteristic
32C22⋊#11924746C2211yescharacteristic
33#18011822C2212yes—
34C22×Q8×C149C2211yescharacteristic
35C4×Q8×C149—21no—
36C4×Q8×C149—21no—
37C4×Q8×C149C2212yes—
38C4×Q8×C149C2212yes—
39C2×C4⋊C4×C149—21no—
40C2×C4⋊C4×C149C2211yescharacteristic
41C2×C42×C149—21no—
42C2×C42×C149C2211yescharacteristic
43C2×Dic298C2311yescharacteristic
44C2×D596C2311yescharacteristic
45C2×C22⋊D149—21no—
46C2×C4×D149—21no—
47#14558726—24no—
48#14558723—24no—
49C2×#11924746C2312yes—
50C2×#11924746C2312yes—
51C4⋊Dic149C2311yescharacteristic
52C4⋊Dic149C2311yescharacteristic
53#14558715—21no—
54#14558715—21no—
55#14558715—21no—
56#14558715—21no—
57C22⋊Dic149—21no—
58#14558713—21no—
59#14558713—21no—
60#14558713—21no—
61#14558713—21no—
62C4×Dic149—21no—
63C2×Q8×C149—24no—
64C2×Q8×C149—21no—
65C2×Q8×C149C2312yes—
66C22×C4×C149—21no—
67C22×C4×C149—21no—
68C22×C4×C149D411yescharacteristic
69C22×C4×C149D411yescharacteristic
70C22×C4×C149C2311yescharacteristic
71C4⋊C4×C149—22no—
72C4⋊C4×C149—22no—
73C4⋊C4×C149—21no—
74C4⋊C4×C149C2312yes—
75C42×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—22no—
91C23×C149C2×D411yescharacteristic
92Q8×C149—24no—
93Q8×C149—22no—
94Q8×C149#4114yes—
95C2×C4×C149—24no—
96C2×C4×C149—22no—
97C2×C4×C149—22no—
98C2×C4×C149—22no—
99C2×C4×C149—22no—
100C2×C4×C149—41no—
101C2×C4×C149—42no—
102C2×C4×C149C2×D411yescharacteristic
103C2×C4×C149C2×D411yescharacteristic
104C2×C4×C149C2×D411yescharacteristic
105C2×C4×C149C2×D411yescharacteristic
106C2×C4×C149C2×D411yescharacteristic
107C2×C4×C149C2411yescharacteristic
108C22×C149—21no—
109C22×C149—21no—
110C22×C149#13712yes—
111C22×C149C22×D411yescharacteristic
112C2×D149—41no—
113C2×D149—41no—
114C2×D149—41no—
115C4×C149—24no—
116C4×C149—21no—
117C4×C149—21no—
118C4×C149—21no—
119C4×C149—21no—
120C4×C149—21no—
121C4×C149—42no—
122C4×C149C2×#4112yes—
123Dic149—41no—
124Dic149—41no—
125Dic149—41no—
126C2×C149—22no—
127C2×C149#52511yescharacteristic
128C2×C149C2×#13711yescharacteristic
129C2×C149#57511yescharacteristic
130D149—81no—
131C149#311711yescharacteristic, complemented, Sylow
132#3117—1491nomaximal, Sylow
133#529—1491no—
134C2×C4×Q8D14911yescharacteristic, complemented
135#484—1491no—
136#481—1491no—
137#479—1492no—
138#464—1492no—
139#451—1491no—
140#448—1491no—
141#441—1492no—
142#440—1492no—
143#432—1491no—
144C22×Q8C2×D14911yescharacteristic
145C2×Q16—1492no—
146C2×SD16—1492no—
147#126—2981no—
148#125—1491no—
149#124—1491no—
150#123—2981no—
151C22⋊Q8—1491no—
152#121—1491no—
153C4×Q8—21no—
154C4×Q8—21no—
155C4×Q8—1491no—
156C4×Q8C2×D14912yes—
157C4×Q8C2×D14912yes—
158C4×D4—2981no—
159C4×D4—1491no—
160#117—2981no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4C2×D14911yescharacteristic
163C2×C42—21no—
164C2×C42C2×D14911yescharacteristic
165#107—1492no—
166#106—1492no—
167C4⋊C8—1492no—
168#103—1492no—
169#103—1492no—
170#103—1492no—
171#102—1492no—
172C22⋊C8—1491no—
173C22⋊C8—1491no—
174#97—1492no—
175C2×Q8—24no—
176C2×Q8—21no—
177C2×Q8—1491no—
178C2×Q8C22×D14912yes—
179C2×D4—2981no—
180C2×D4—1491no—
181C22×C4—21no—
182C22×C4—21no—
183C22×C4—2981no—
184C22×C4C22⋊D14911yescharacteristic
185C22×C4C22⋊D14911yescharacteristic
186C22×C4C22×D14911yescharacteristic
187Q16—2984no—
188SD16—2984no—
189C2×C8—1492no—
190C2×C8—1492no—
191C4⋊C4—22no—
192C4⋊C4—22no—
193C4⋊C4—21no—
194C4⋊C4—2981no—
195C4⋊C4—2981no—
196C4⋊C4—2981no—
197C4⋊C4—2981no—
198C4⋊C4—1491no—
199C4⋊C4—1491no—
200C4⋊C4C22×D14912yes—
201C22⋊C4—2981no—
202C22⋊C4—2981no—
203C22⋊C4—2981no—
204C22⋊C4—2981no—
205C22⋊C4—2981no—
206C42—22no—
207C42—22no—
208C42—2981no—
209C42C22⋊D14911yescharacteristic
210C42C22⋊D14911yescharacteristic
211C42C22×D14911yescharacteristic
212C42C22×D14911yescharacteristic
213C23—2981no—
214C23C2×C22⋊D14911yescharacteristic
215Q8—24no—
216Q8—22no—
217Q8—2982no—
218Q8#1455873614yes—
219D4—2982no—
220D4—5962no—
221C2×C4—24no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—2981no—
229C2×C4—2981no—
230C2×C4—2981no—
231C2×C4—5962no—
232C2×C4C2×C22⋊D14911yescharacteristic
233C2×C4C2×C22⋊D14911yescharacteristic
234C2×C4C2×C22⋊D14911yescharacteristic
235C2×C4C2×C22⋊D14911yescharacteristic
236C2×C4C2×C22⋊D14911yescharacteristic
237C2×C4C23×D14911yescharacteristic
238C8—2982no—
239C8—2982no—
240C22—21no—
241C22—21no—
242C22—5961no—
243C22—5961no—
244C22—5961no—
245C22#1801194212yes—
246C22C22×C22⋊D14911yescharacteristic
247C4—21no—
248C4—21no—
249C4—21no—
250C4—21no—
251C4—24no—
252C4—21no—
253C4—42no—
254C4—5961no—
255C4—5961no—
256C4—5961no—
257C4C2×#1455873612yes—
258C2—22no—
259C2—11921no—
260C2#2375013611yescharacteristic
261C2C2×#1801194211yescharacteristic
262C2#2375042311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC2×C4×Q8×C149C2
socleC22×C149C22×D4
prime radical#18011885C22
hypercenterC2×C4×Q8D149
hypocenterC149#3117
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
2. #23749960C2semidirect
4. #23749932C2semidirect
5. #23749847C2semidirect
6. #23749781C2semidirect
8. #23749730C2semidirect
9. #23749723C2semidirect
10. #23749682C2semidirect
11. C2×C4×Q8×C149C2semidirect
131. C149#3117semidirect
134. C2×C4×Q8D149semidirect

Maximal subgroups

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

subgroupindex
#237501592
#237499602
#237499432
#237499322
#237498472
#237497812
#237497642
#237497302
#237497232
#237496822
C2×C4×Q8×C1492
#3117149