Finite Group Databasebeta

← #34055069

Subgroups — #34055069

Order 19072.

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

normal subgroups only

This group has 380 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#23750178C211yesmaximal, characteristic
2C2×#18011909C211yesmaximal, characteristic
3#23749992C214yesmaximal, complemented
4#23749974C214yesmaximal, complemented
5#23749635C211yesmaximal, characteristic
6#23749634C211yesmaximal, characteristic
7#23749633C211yesmaximal, characteristic
8M16×Dic149C211yesmaximal, characteristic
9#419×C149C211yesmaximal, characteristic
10C22×Dic298C2211yescharacteristic
11C2×#14558720C2211yescharacteristic
12#18011910C2212yes—
13#18011909—22no—
14#18011909C2212yes—
15#18011909C2212yes—
16#18011902C2212yes—
17#18011888—22no—
18C4×Dic298—22no—
19#18011870C2211yescharacteristic
20C2×#14558715—22no—
21C2×C4×Dic149C2211yescharacteristic
22#18011836C2214yes—
23#18011835C2214yes—
24#18011834C2214yes—
25#18011821C2212yes—
26C8×Dic149C2212yes—
27C22×Q8×C149C2211yescharacteristic
28C2×M16×C149C2211yescharacteristic
29#117×C149C2211yescharacteristic
30#103×C149C2214yes—
31C2×Dic298—22no—
32C2×Dic298—21no—
33C2×Dic298—22no—
34C2×Dic298—22no—
35C2×Dic298C2312yes—
36C22×Dic149—21no—
37C22×Dic149D412yes—
38#14558720—22no—
39C2×#11924746C2312yes—
40C4⋊Dic149—22no—
41C4⋊Dic149C2312yes—
42#14558715—24no—
43#14558715—24no—
44#14558715—22no—
45#14558715—22no—
46C22⋊Dic149—21no—
47C4×Dic149—21no—
48C4×Dic149D412yes—
49C4×Dic149C2311yescharacteristic
50C4×Dic149C2311yescharacteristic
51C2×Q8×C149—21no—
52C2×Q8×C149—22no—
53C2×Q8×C149—22no—
54C2×Q8×C149C2312yes—
55C22×C4×C149—21no—
56C22×C4×C149C2311yescharacteristic
57M16×C149—22no—
58C2×C8×C149C2312yes—
59C4⋊C4×C149C2312yes—
60C22⋊C4×C149—21no—
61C42×C149—21no—
62Dic298—22no—
63Dic298—22no—
64Dic298—42no—
65Dic298—44no—
66C2×Dic149—24no—
67C2×Dic149—22no—
68C2×Dic149—22no—
69C2×Dic149—42no—
70C2×Dic149C2×D412yes—
71C2×Dic149C2×D412yes—
72#11924746—22no—
73C23×C149C2×D411yescharacteristic
74Q8×C149—22no—
75Q8×C149—22no—
76Q8×C149—42no—
77C2×C4×C149—22no—
78C2×C4×C149—22no—
79C2×C4×C149—42no—
80C2×C4×C149C2×D411yescharacteristic
81C2×C4×C149#4112yes—
82C2×C4×C149#4112yes—
83C2×C4×C149C2411yescharacteristic
84C8×C149—22no—
85C22×C149—22no—
86C22×C149#12412yes—
87C22×C149C22×D411yescharacteristic
88C4×C149—42no—
89C4×C149—42no—
90C4×C149#12412yes—
91C4×C149C2×#4111yescharacteristic
92C4×C149C2×#4111yescharacteristic
93Dic149—22no—
94Dic149—42no—
95Dic149—42no—
96Dic149#13714yes—
97C2×C149—22no—
98C2×C149C2×#12411yescharacteristic
99C2×C149C2×#13712yes—
100C149#313911yescharacteristic, complemented, Sylow
101#3139—1491nomaximal, Sylow
102#533—1491no—
103C2×C4⋊Q8—1491no—
104#491—1494no—
105#487—1494no—
106#419—1491no—
107#419—1491no—
108#419—1491no—
109#419D14911yescharacteristic
110C4×M16—1491no—
111C22×Q8—1491no—
112C22×Q8C2×D14911yescharacteristic
113C2×M16—1491no—
114C2×M16C2×D14911yescharacteristic
115C4⋊Q8—2982no—
116C4⋊Q8—1492no—
117C4⋊Q8—1492no—
118C4⋊Q8—1492no—
119#125—1492no—
120C22⋊Q8—2982no—
121C4×Q8—2982no—
122#117—1491no—
123#117C2×D14911yescharacteristic
124C2×C4⋊C4—2982no—
125C2×C42—1491no—
126#103—1494no—
127#103—1494no—
128#103—1494no—
129#103C2×D14914yes—
130#97—1492no—
131C4×C8—1492no—
132C2×Q8—21no—
133C2×Q8—22no—
134C2×Q8—22no—
135C2×Q8—2982no—
136C2×Q8—2981no—
137C2×Q8—2982no—
138C2×Q8—2982no—
139C2×Q8—1492no—
140C2×Q8C22×D14912yes—
141C22×C4—21no—
142C22×C4—2981no—
143C22×C4—1492no—
144C22×C4C22×D14911yescharacteristic
145M16—22no—
146M16—2982no—
147C2×C8—1492no—
148C2×C8C22×D14912yes—
149C4⋊C4—2984no—
150C4⋊C4—2984no—
151C4⋊C4—2982no—
152C4⋊C4—2982no—
153C4⋊C4—2982no—
154C4⋊C4—1492no—
155C4⋊C4C22×D14912yes—
156C22⋊C4—21no—
157C22⋊C4—2981no—
158C42—21no—
159C42—2981no—
160C42—1492no—
161C42—1491no—
162C42—1491no—
163C23D4×D14911yescharacteristic
164Q8—22no—
165Q8—22no—
166Q8—42no—
167Q8—2982no—
168Q8—2982no—
169Q8—5964no—
170Q8—5962no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—42no—
174C2×C4—2984no—
175C2×C4—2982no—
176C2×C4—2982no—
177C2×C4—5962no—
178C2×C4—1492no—
179C2×C4—1492no—
180C2×C4D4×D14911yescharacteristic
181C2×C4#1455873512yes—
182C2×C4#1455873612yes—
183C2×C4C23×D14911yescharacteristic
184C8—22no—
185C8—2982no—
186C22—22no—
187C22#1801189712yes—
188C22C2×D4×D14911yescharacteristic
189C4—42no—
190C4—42no—
191C4—2982no—
192C4—5962no—
193C4—5962no—
194C4—1494no—
195C4#1801189712yes—
196C4C2×#1455873511yescharacteristic
197C4C2×#1455873611yescharacteristic
198C2—22no—
199C2C2×#1801189711yescharacteristic
200C2#137×D14912yes—
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#419×C149C2
socleC22×C149C22×D4
prime radicalC23×C149C2×D4
hypercenter#419D149
hypocenterC149#3139
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
3. #23749992C2semidirect
4. #23749974C2semidirect
100. C149#3139semidirect

Maximal subgroups

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

subgroupindex
#237501782
C2×#180119092
#237499922
#237499742
#237496352
#237496342
#237496332
M16×Dic1492
#419×C1492
#3139149