Finite Group Databasebeta

← #34057413

Subgroups — #34057413

Order 19072.

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

normal subgroups only

This group has 372 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#23750349C211yesmaximal, characteristic, complemented
2D4×Dic298C211yesmaximal, characteristic, complemented
3#23749986C212yesmaximal, complemented
4#23749975C211yesmaximal, characteristic, complemented
5#23749918C212yesmaximal, complemented
6#23749906C211yesmaximal, characteristic, complemented
7#23749842C212yesmaximal
8#23749752C211yesmaximal, characteristic, complemented
9#23749726C212yesmaximal, complemented
10C4×#14558721C211yesmaximal, characteristic
11#461×C149C211yesmaximal, characteristic, complemented
12C22×Dic298—21no—
13C2×#14558721C2211yescharacteristic
14#18011911C2211yescharacteristic
15#18011910C2212yes—
16#18011906—22no—
17#18011900C2212yes—
18#18011891—21no—
19#18011890—21no—
20#18011888—22no—
21Q8×Dic149C2212yes—
22C4×Dic298C2211yescharacteristic
23C4×D596C2211yescharacteristic
24D4×Dic149C2212yes—
25#18011869—21no—
26#18011845C2212yes—
27#18011844C2211yescharacteristic
28#18011840C2212yes—
29#18011835C2212yes—
30#18011835C2212yes—
31#18011833C2212yes—
32#18011832C2211yescharacteristic
33#18011831C2211yescharacteristic
34#18011821C2212yes—
35C4×#11924746C2211yescharacteristic
36C2×SD16×C149C2212yes—
37C4⋊Q8×C149C2211yescharacteristic
38C4×D4×C149C2211yescharacteristic
39C4⋊C8×C149C2211yescharacteristic
40#103×C149C2212yes—
41C2×Dic298—22no—
42C2×Dic298—21no—
43C2×Dic298—44no—
44C2×Dic298D411yescharacteristic
45C2×D596C2311yescharacteristic
46C22×Dic149—22no—
47C2×C4×D149—21no—
48#14558721—22no—
49C2×#11924746C2311yescharacteristic
50C2×#11924746C2311yescharacteristic
51C4⋊Dic149—22no—
52C4⋊Dic149—21no—
53C4⋊Dic149D411yescharacteristic
54C4⋊Dic149C2312yes—
55C4⋊Dic149C2311yescharacteristic
56#14558715—22no—
57#14558715D412yes—
58C22⋊Dic149—22no—
59#14558713—22no—
60#14558713—22no—
61#14558713—21no—
62C4×Dic149—22no—
63C4×Dic149C2312yes—
64C2×Q8×C149C2312yes—
65C2×D4×C149C2311yescharacteristic
66C22×C4×C149—21no—
67SD16×C149—24no—
68C2×C8×C149C2312yes—
69C4⋊C4×C149—21no—
70C4⋊C4×C149—21no—
71C4⋊C4×C149C2311yescharacteristic
72C22⋊C4×C149—21no—
73C42×C149C2311yescharacteristic
74C22×D149—21no—
75Dic298—22no—
76Dic298—44no—
77Dic298—42no—
78D596—21no—
79D596—21no—
80C2×Dic149—21no—
81C2×Dic149—22no—
82C2×Dic149—44no—
83C2×Dic149C2×D412yes—
84C2×Dic149C2×D412yes—
85C4×D149—42no—
86#11924746—21no—
87#11924746—21no—
88C23×C149—21no—
89Q8×C149—22no—
90Q8×C149—22no—
91D4×C149—21no—
92D4×C149#4112yes—
93C2×C4×C149—21no—
94C2×C4×C149—22no—
95C2×C4×C149—42no—
96C2×C4×C149C2×D411yescharacteristic
97C2×C4×C149C2×D411yescharacteristic
98C2×C4×C149C2411yescharacteristic
99C8×C149—22no—
100C22×C149—22no—
101C22×C149—41no—
102C22×C149—41no—
103C22×C149C22×D411yescharacteristic
104C2×D149—41no—
105C2×D149—41no—
106C2×D149—41no—
107C4×C149—21no—
108C4×C149—42no—
109C4×C149—41no—
110C4×C149AGL(1,ℤ/8)12yes—
111C4×C149C2×#4111yescharacteristic
112C4×C1492−1+411yescharacteristic
113Dic149—22no—
114Dic149—22no—
115Dic149—41no—
116Dic149—42no—
117C2×C149—42no—
118C2×C149#54811yescharacteristic
119C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
120C2×C149#57811yescharacteristic
121D149—81no—
122C149#336711yescharacteristic, complemented, Sylow
123#3367—1491nomaximal, Sylow
124#556—1491no—
125D4×Q8—1491no—
126#489—1492no—
127#487—1491no—
128#477—1492no—
129#474—1491no—
130#463—1492no—
131#461D14911yescharacteristic, complemented
132#446—1491no—
133#440—1492no—
134C4×D8—1491no—
135C22×Q8—2981no—
136C2×SD16C2×D14912yes—
137C2×D8—1491no—
138C4⋊Q8—1492no—
139C4⋊Q8—1491no—
140C4⋊Q8C2×D14911yescharacteristic
141#126—2982no—
142#124—1492no—
143C22⋊Q8—2982no—
144C22⋊Q8—2981no—
145C22⋊Q8—2981no—
146C4×Q8—1492no—
147C4×Q8—1491no—
148C4×D4—1492no—
149C4×D4—1491no—
150C4×D4C2×D14911yescharacteristic
151#117—2981no—
152#107—1492no—
153#107—1491no—
154C4⋊C8—1492no—
155C4⋊C8C2×D14911yescharacteristic
156#103—1492no—
157#103—1492no—
158#103C2×D14912yes—
159#102—1491no—
160#102—1492no—
161#102—1491no—
162#97—1492no—
163C4×C8—1491no—
164C2×Q8—2982no—
165C2×Q8—2981no—
166C2×Q8—5964no—
167C2×Q8—1491no—
168C2×Q8C22×D14912yes—
169C2×D4—1491no—
170C2×D4C22×D14911yescharacteristic
171C22×C4—21no—
172C22×C4—2982no—
173C22×C4—2981no—
174SD16—24no—
175D8—2982no—
176C2×C8—1491no—
177C2×C8—1491no—
178C2×C8C22×D14912yes—
179C4⋊C4—21no—
180C4⋊C4—21no—
181C4⋊C4—2982no—
182C4⋊C4—2982no—
183C4⋊C4—2981no—
184C4⋊C4—1492no—
185C4⋊C4—1491no—
186C4⋊C4—1491no—
187C4⋊C4—1492no—
188C4⋊C4C22×D14911yescharacteristic
189C22⋊C4—21no—
190C22⋊C4—2982no—
191C22⋊C4—2982no—
192C22⋊C4—2982no—
193C22⋊C4—2981no—
194C42—2982no—
195C42—1492no—
196C42C22×D14911yescharacteristic
197C23—21no—
198C23—2981no—
199Q8—22no—
200Q8—22no—
201Q8—2982no—
202Q8—5964no—
203Q8—5962no—
204D4—21no—
205D4—2981no—
206D4—2981no—
207D4#1455873512yes—
208C2×C4—22no—
209C2×C4—21no—
210C2×C4—42no—
211C2×C4—2981no—
212C2×C4—2982no—
213C2×C4—5964no—
214C2×C4—5962no—
215C2×C4—1492no—
216C2×C4—1492no—
217C2×C4D4×D14911yescharacteristic
218C2×C4D4×D14911yescharacteristic
219C2×C4C23×D14911yescharacteristic
220C8—22no—
221C8—2981no—
222C8—2981no—
223C22—22no—
224C22—41no—
225C22—41no—
226C22—5961no—
227C22—5961no—
228C22—5961no—
229C22C2×D4×D14911yescharacteristic
230C4—21no—
231C4—41no—
232C4—42no—
233C4—2982no—
234C4—2982no—
235C4—5962no—
236C4—5961no—
237C4#1801193812yes—
238C4C2×#1455873511yescharacteristic
239C4#1801195811yescharacteristic
240C2—42no—
241C2—11921no—
242C2#2375028111yescharacteristic
243C2C2×#1801193811yescharacteristic
244C2#2375044111yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#461×C149C2
socleC22×C149C22×D4
prime radicalC2×#14558721C22
hypercenter#461D149
hypocenterC149#3367
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. #23750349C2semidirect
2. D4×Dic298C2semidirect
3. #23749986C2semidirect
4. #23749975C2semidirect
5. #23749918C2semidirect
6. #23749906C2semidirect
8. #23749752C2semidirect
9. #23749726C2semidirect
11. #461×C149C2semidirect
122. C149#3367semidirect
131. #461D149semidirect

Maximal subgroups

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

subgroupindex
#237503492
D4×Dic2982
#237499862
#237499752
#237499182
#237499062
#237498422
#237497522
#237497262
C4×#145587212
#461×C1492
#3367149