Finite Group Databasebeta

← #34054865

Subgroups — #34054865

Order 19072.

386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 117 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#23750161C211yesmaximal, characteristic
2C2×#18011876C211yesmaximal, characteristic, complemented
3#23749943C211yesmaximal, characteristic
4#23749931C212yesmaximal, complemented
5#23749850C212yesmaximal, complemented
6#23749780C211yesmaximal, characteristic, complemented
7#23749766C211yesmaximal, characteristic
8#23749729C212yesmaximal, complemented
9#23749724C212yesmaximal, complemented
10#23749679C211yesmaximal, characteristic, complemented
11#484×C149C211yesmaximal, characteristic, complemented
12C22×Dic298C2211yescharacteristic
13C2×#14558726C2212yes—
14C2×#14558725C2212yes—
15#18011906—21no—
16#18011902C2211yescharacteristic
17#18011900C2211yescharacteristic
18#18011895—21no—
19#18011885C2211yescharacteristic
20Q8×Dic149C2211yescharacteristic
21#18011876—21no—
22#18011876—21no—
23#18011876C2212yes—
24#18011876C2212yes—
25#18011873C2211yescharacteristic
26#18011871—21no—
27#18011869—21no—
28C2×#14558715—21no—
29C2×C4×Dic149—21no—
30C2×C4×Dic149C2211yescharacteristic
31#18011842C2212yes—
32#18011840C2212yes—
33#18011836C2212yes—
34#18011834C2212yes—
35#18011831C2212yes—
36C22⋊#11924746C2211yescharacteristic
37#18011821C2212yes—
38C22⋊Q8×C149C2211yescharacteristic
39C2×C4⋊C4×C149C2211yescharacteristic
40#107×C149C2212yes—
41#103×C149C2212yes—
42C22⋊C8×C149C2211yescharacteristic
43C2×Dic298—24no—
44C2×Dic298—21no—
45C2×Dic298C2312yes—
46C2×D596C2311yescharacteristic
47C2×C22⋊D149—21no—
48C22×Dic149—21no—
49C22×Dic149D411yescharacteristic
50C22×Dic149D411yescharacteristic
51C2×C4×D149—21no—
52#14558726—24no—
53#14558725—24no—
54C2×#11924746C2312yes—
55C4⋊Dic149—21no—
56C4⋊Dic149—21no—
57C4⋊Dic149C2311yescharacteristic
58#14558715—21no—
59#14558715—22no—
60#14558715—22no—
61#14558713—21no—
62#14558713—21no—
63#14558713—21no—
64#14558713—21no—
65C4×Dic149—22no—
66C4×Dic149—22no—
67C4×Dic149—21no—
68C4×Dic149D411yescharacteristic
69C4×Dic149D411yescharacteristic
70C4×Dic149C2311yescharacteristic
71C4×Dic149C2311yescharacteristic
72C2×Q8×C149C2311yescharacteristic
73C22×C4×C149—21no—
74C22×C4×C149C2311yescharacteristic
75C2×C8×C149C2312yes—
76C4⋊C4×C149—21no—
77C4⋊C4×C149—21no—
78C4⋊C4×C149C2312yes—
79C4⋊C4×C149C2311yescharacteristic
80C22⋊C4×C149—21no—
81C22×D149—21no—
82Dic298—24no—
83Dic298—22no—
84Dic298#4114yes—
85D596—22no—
86C22⋊D149—42no—
87C2×Dic149—24no—
88C2×Dic149—22no—
89C2×Dic149—22no—
90C2×Dic149—21no—
91C2×Dic149—41no—
92C2×Dic149C2×D411yescharacteristic
93C2×Dic149C2×D411yescharacteristic
94C2×Dic149C2×D411yescharacteristic
95C2×Dic149C2×D411yescharacteristic
96C4×D149—42no—
97#11924746—22no—
98C23×C149C2×D411yescharacteristic
99Q8×C149—22no—
100C2×C4×C149—22no—
101C2×C4×C149—21no—
102C2×C4×C149—21no—
103C2×C4×C149—22no—
104C2×C4×C149—42no—
105C2×C4×C149C2×D411yescharacteristic
106C2×C4×C149C2411yescharacteristic
107C8×C149—22no—
108C22×C149—21no—
109C22×C149—21no—
110C22×C149#13712yes—
111C22×C149C22×D411yescharacteristic
112C2×D149—41no—
113C2×D149—41no—
114C2×D149—41no—
115C4×C149—21no—
116C4×C149—41no—
117C4×C149—42no—
118C4×C149—41no—
119C4×C149C2×#4112yes—
120Dic149—24no—
121Dic149—21no—
122Dic149—21no—
123Dic149—21no—
124Dic149—21no—
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×Q8—1491no—
135#484D14911yescharacteristic, complemented
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×Q8—1491no—
145C2×Q16—1492no—
146C2×SD16—1492no—
147#126—2981no—
148#125—1491no—
149#124—1491no—
150#123—2981no—
151C22⋊Q8C2×D14911yescharacteristic
152#121—1491no—
153C4×Q8—2981no—
154C4×Q8—2981no—
155C4×Q8—1491no—
156C4×Q8—1492no—
157C4×Q8—1492no—
158C4×D4—2981no—
159C4×D4—1491no—
160#117—2981no—
161C2×C4⋊C4—2981no—
162C2×C4⋊C4C2×D14911yescharacteristic
163C2×C42—2981no—
164C2×C42—1491no—
165#107C2×D14912yes—
166#106—1492no—
167C4⋊C8—1492no—
168#103—1492no—
169#103—1492no—
170#103C2×D14912yes—
171#102—1492no—
172C22⋊C8—1491no—
173C22⋊C8C2×D14911yescharacteristic
174#97—1492no—
175C2×Q8—2984no—
176C2×Q8—2981no—
177C2×Q8—1492no—
178C2×Q8C22×D14911yescharacteristic
179C2×D4—2981no—
180C2×D4—1491no—
181C22×C4—21no—
182C22×C4—2981no—
183C22×C4—2981no—
184C22×C4—1491no—
185C22×C4—1491no—
186C22×C4C22×D14911yescharacteristic
187Q16—2984no—
188SD16—2984no—
189C2×C8—1492no—
190C2×C8C22×D14912yes—
191C4⋊C4—21no—
192C4⋊C4—21no—
193C4⋊C4—2982no—
194C4⋊C4—2982no—
195C4⋊C4—2981no—
196C4⋊C4—2981no—
197C4⋊C4—2981no—
198C4⋊C4—1491no—
199C4⋊C4C22×D14912yes—
200C4⋊C4C22×D14911yescharacteristic
201C22⋊C4—21no—
202C22⋊C4—2981no—
203C22⋊C4—2981no—
204C22⋊C4—2981no—
205C22⋊C4—2981no—
206C42—2982no—
207C42—2982no—
208C42—2981no—
209C42—1491no—
210C42—1491no—
211C42—1491no—
212C42—1491no—
213C23—2981no—
214C23D4×D14911yescharacteristic
215Q8—22no—
216Q8—2984no—
217Q8—2982no—
218Q8—1494no—
219D4—2982no—
220D4—5962no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—42no—
226C2×C4—2984no—
227C2×C4—2982no—
228C2×C4—2982no—
229C2×C4—2981no—
230C2×C4—5962no—
231C2×C4—5961no—
232C2×C4—1491no—
233C2×C4—1491no—
234C2×C4—1491no—
235C2×C4—1491no—
236C2×C4D4×D14911yescharacteristic
237C2×C4C23×D14911yescharacteristic
238C8—22no—
239C8—2982no—
240C22—21no—
241C22—21no—
242C22—5961no—
243C22—5961no—
244C22—5961no—
245C22#1801194312yes—
246C22C2×D4×D14911yescharacteristic
247C4—21no—
248C4—42no—
249C4—41no—
250C4—41no—
251C4—2981no—
252C4—2981no—
253C4—2981no—
254C4—2981no—
255C4—2984no—
256C4—5961no—
257C4#41×D14912yes—
258C2—22no—
259C2—11921no—
260C2#2375013311yescharacteristic
261C2C2×#1801194311yescharacteristic
262C2#2375042111yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#484×C149C2
socleC22×C149C22×D4
prime radical#18011885C22
hypercenter#484D149
hypocenterC149#3117
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
2. C2×#18011876C2semidirect
4. #23749931C2semidirect
5. #23749850C2semidirect
6. #23749780C2semidirect
8. #23749729C2semidirect
9. #23749724C2semidirect
10. #23749679C2semidirect
11. #484×C149C2semidirect
131. C149#3117semidirect
135. #484D149semidirect

Maximal subgroups

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

subgroupindex
#237501612
C2×#180118762
#237499432
#237499312
#237498502
#237497802
#237497662
#237497292
#237497242
#237496792
#484×C1492
#3117149