Finite Group Databasebeta

← #34056346

Subgroups — #34056346

Order 19072.

476 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 121 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
1C2×#18011940C212yesmaximal, complemented
2#23750283C212yesmaximal, complemented
3#23749868C212yesmaximal, complemented
4#23749844C212yesmaximal, complemented
5#23749779C212yesmaximal, complemented
6#23749767C212yesmaximal, complemented
7C4×Dic596C211yesmaximal, characteristic, complemented
8#23749704C211yesmaximal, characteristic, complemented
9#495×C149C211yesmaximal, characteristic, complemented
10C2×#14558735C2212yes—
11C2×Q8×D149C2212yes—
12#18011940—28no—
13C2×Dic596C2211yescharacteristic
14C2×#14558726C2212yes—
15C2×#14558724C2212yes—
16C2×#14558719C2212yes—
17#18011897—22no—
18#18011888—22no—
19#18011887C2212yes—
20#18011884—22no—
21#18011882C2212yes—
22C4×Dic298C2212yes—
23C4×D596C2211yescharacteristic
24#18011871—22no—
25#18011845C2211yescharacteristic
26C4⋊#11924746C2211yescharacteristic
27#18011836C2212yes—
28#18011835C2212yes—
29#18011832C2212yes—
30#18011823C2212yes—
31C2×Q16×C149C2211yescharacteristic
32C2×SD16×C149C2212yes—
33C2×D8×C149C2211yescharacteristic
34#124×C149C2212yes—
35C4×C8×C149C2211yescharacteristic
36#14558735—24no—
37#14558735—42no—
38C2×Dic298—22no—
39C2×Dic298C2312yes—
40Q8×D149—24no—
41Q8×D149—42no—
42C2×D596D411yescharacteristic
43C2×C22⋊D149—22no—
44C2×C22⋊D149—22no—
45C22×Dic149—22no—
46C2×C4×D149—22no—
47C2×C4×D149C2312yes—
48Dic596D414yescomplemented
49#14558726—24no—
50#14558724—24no—
51#14558719—24no—
52C2×#11924746C2312yes—
53C4⋊Dic149D411yescharacteristic
54C4⋊Dic149C2312yes—
55#14558715—22no—
56#14558715—22no—
57C22⋊Dic149—22no—
58#14558713—22no—
59#14558713D412yes—
60C4×Dic149—22no—
61C2×Q8×C149C2312yes—
62C2×D4×C149C2312yes—
63Q16×C149—41no—
64SD16×C149—24no—
65D8×C149—41no—
66C2×C8×C149C2311yescharacteristic
67C2×C8×C149C2311yescharacteristic
68C22⋊C4×C149—22no—
69C22⋊C4×C149—22no—
70C42×C149C2311yescharacteristic
71C22×D149C2×D412yes—
72Dic298—22no—
73Dic298—44no—
74Dic298C2×D414yes—
75D596—41no—
76C22⋊D149—44no—
77C22⋊D149—44no—
78C2×Dic149—22no—
79C2×Dic149—22no—
80C2×Dic149—44no—
81C2×Dic149C2×D412yes—
82C4×D149—22no—
83C4×D149—22no—
84C4×D149—44no—
85#11924746—22no—
86C23×C149—22no—
87Q8×C149—22no—
88Q8×C149—22no—
89D4×C149—22no—
90D4×C149—22no—
91C2×C4×C149—22no—
92C2×C4×C149C2×D411yescharacteristic
93C2×C4×C149C2×D411yescharacteristic
94C2×C4×C149C2411yescharacteristic
95C8×C149—21no—
96C8×C149C2×D412yes—
97C22×C149—42no—
98C22×C149—42no—
99C22×C149—42no—
100C22×C149C22×D411yescharacteristic
101C2×D149—22no—
102C2×D149—22no—
103C2×D149—22no—
104C4×C149—21no—
105C4×C149—21no—
106C4×C149—42no—
107C4×C149C22×D411yescharacteristic
108C4×C149H(5,𝔽2)11yescharacteristic
109Dic149—22no—
110Dic149—24no—
111Dic149—42no—
112C2×C149—82no—
113C2×C149D4211yescharacteristic
114C2×C149#57511yescharacteristic
115C2×C149#57811yescharacteristic
116D149—42no—
117C149#327711yescharacteristic, complemented, Sylow
118#3277—1491nomaximal, Sylow
119C2×#137—1492no—
120#548—1492no—
121#495D14911yescharacteristic, complemented
122#468—1492no—
123#464—1492no—
124#451—1492no—
125#449—1492no—
126C4×Q16—1491no—
127#436—1491no—
128C2×#41—1492no—
129C22×Q8—1492no—
130#137—2988no—
131C2×Q16—1492no—
132C2×Q16—1491no—
133C2×Q16C2×D14911yescharacteristic
134C2×SD16—1492no—
135C2×SD16C2×D14912yes—
136C2×D8C2×D14911yescharacteristic
137C2×M16—1492no—
138#124—2982no—
139#124C2×D14912yes—
140C22⋊Q8—2982no—
141C22⋊Q8—1492no—
142#121—2982no—
143#121—1492no—
144C4×Q8—1492no—
145C4×D4—2982no—
146C4×D4—1491no—
147#107—1491no—
148C4⋊C8—1491no—
149#103—1492no—
150#103—1492no—
151#102—1492no—
152C22⋊C8—1492no—
153C4×C8C2×D14911yescharacteristic
154#41—2984no—
155#41—5962no—
156C2×Q8—2982no—
157C2×Q8—2984no—
158C2×Q8—5962no—
159C2×Q8—1492no—
160C2×Q8C22×D14912yes—
161C2×D4—2982no—
162C2×D4—2982no—
163C2×D4—1491no—
164C2×D4C22×D14912yes—
165C22×C4—2982no—
166C22×C4—2982no—
167C22×C4—1492no—
168Q16—41no—
169Q16—2984no—
170Q16—1494no—
171SD16—24no—
172SD16—2984no—
173D8—41no—
174M16—2984no—
175C2×C8—1492no—
176C2×C8C22×D14911yescharacteristic
177C2×C8C22×D14911yescharacteristic
178C4⋊C4—2982no—
179C4⋊C4—2982no—
180C4⋊C4—1492no—
181C4⋊C4—1491no—
182C22⋊C4—22no—
183C22⋊C4—22no—
184C22⋊C4—2982no—
185C22⋊C4—2982no—
186C22⋊C4—1492no—
187C42—2982no—
188C42C22×D14911yescharacteristic
189C23—22no—
190C23—1492no—
191Q8—22no—
192Q8—22no—
193Q8—2982no—
194Q8—5964no—
195Q8—1494no—
196D4—22no—
197D4—22no—
198D4—5961no—
199D4—5964no—
200D4—5964no—
201C2×C4—22no—
202C2×C4—2982no—
203C2×C4—2982no—
204C2×C4—2982no—
205C2×C4—2982no—
206C2×C4—5964no—
207C2×C4—5964no—
208C2×C4—1492no—
209C2×C4D4×D14911yescharacteristic
210C2×C4D4×D14911yescharacteristic
211C2×C4C23×D14911yescharacteristic
212C8—21no—
213C8—2982no—
214C8D4×D14912yes—
215C22—42no—
216C22—42no—
217C22—42no—
218C22—2982no—
219C22—2982no—
220C22—2982no—
221C22C2×D4×D14911yescharacteristic
222C4—21no—
223C4—21no—
224C4—42no—
225C4—2982no—
226C4—2984no—
227C4—5962no—
228C4C2×D4×D14911yescharacteristic
229C4#1801195611yescharacteristic
230C2—82no—
231C2—5962no—
232C2#2375026011yescharacteristic
233C2#2375042211yescharacteristic
234C2#2375043911yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#495×C149C2
socleC22×C149C22×D4
hypercenter#495D149
hypocenterC149#3277
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #495

Complements

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

NH ≅ G/Ntype
1. C2×#18011940C2semidirect
2. #23750283C2semidirect
3. #23749868C2semidirect
4. #23749844C2semidirect
5. #23749779C2semidirect
6. #23749767C2semidirect
7. C4×Dic596C2semidirect
8. #23749704C2semidirect
9. #495×C149C2semidirect
48. Dic596D4semidirect
117. C149#3277semidirect
121. #495D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119402
#237502832
#237498682
#237498442
#237497792
#237497672
C4×Dic5962
#237497042
#495×C1492
#3277149