Finite Group Databasebeta

← #34055823

Subgroups — #34055823

Order 19072.

370 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 125 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#23750182C211yesmaximal, characteristic, complemented
2#23750028C211yesmaximal, characteristic, complemented
3#23750021C211yesmaximal, characteristic, complemented
4#23749971C211yesmaximal, characteristic, complemented
5#23749971C211yesmaximal, characteristic, complemented
6#23749946C214yesmaximal, complemented
7#23749925C214yesmaximal, complemented
8#23749678C211yesmaximal, characteristic, complemented
9#532×C149C211yesmaximal, characteristic
10#18011911C2211yescharacteristic
11#18011911C2211yescharacteristic
12#18011903C2212yes—
13#18011890—21no—
14#18011890—21no—
15C4×Dic298—21no—
16C4×Dic298—21no—
17#18011870C2212yes—
18#18011844C2214yes—
19#18011842C2214yes—
20C4⋊#11924746C2212yes—
21#18011832C2214yes—
22#18011832C2214yes—
23C22⋊#11924746C2212yes—
24C4×#11924746C2211yescharacteristic
25C4×#11924746C2211yescharacteristic
26C2×#41×C149—21no—
27C4⋊Q8×C149C2211yescharacteristic
28#127×C149C2211yescharacteristic
29#124×C149—21no—
30#121×C149—21no—
31#121×C149C2212yes—
32C4×D4×C149—21no—
33C4×D4×C149C2212yes—
34C2×C42×C149C2211yescharacteristic
35C2×Dic298—21no—
36C2×Dic298—21no—
37C2×#11924746C2312yes—
38C2×#11924746C2312yes—
39C4⋊Dic149—21no—
40C4⋊Dic149—21no—
41C4⋊Dic149C2312yes—
42C4⋊Dic149C2312yes—
43#14558715—22no—
44#14558715—22no—
45C22⋊Dic149—22no—
46C4×Dic149—22no—
47#41×C149—44no—
48C2×Q8×C149—21no—
49C2×D4×C149—22no—
50C2×D4×C149—21no—
51C2×D4×C149—21no—
52C2×D4×C149C2312yes—
53C22×C4×C149—22no—
54C22×C4×C149D411yescharacteristic
55C22×C4×C149D411yescharacteristic
56C22×C4×C149C2311yescharacteristic
57C4⋊C4×C149—21no—
58C4⋊C4×C149C2312yes—
59C22⋊C4×C149—22no—
60C22⋊C4×C149—22no—
61C42×C149D411yescharacteristic
62C42×C149D411yescharacteristic
63C42×C149C2311yescharacteristic
64C42×C149C2311yescharacteristic
65Dic298—42no—
66Dic298—42no—
67C2×Dic149—22no—
68C2×Dic149—22no—
69#11924746—22no—
70#11924746—22no—
71C23×C149—22no—
72C23×C149C2×D411yescharacteristic
73Q8×C149—42no—
74D4×C149—24no—
75D4×C149—44no—
76D4×C149—42no—
77D4×C149—42no—
78C2×C4×C149—22no—
79C2×C4×C149—22no—
80C2×C4×C149—22no—
81C2×C4×C149—22no—
82C2×C4×C149—44no—
83C2×C4×C149C2×D411yescharacteristic
84C2×C4×C149C2×D411yescharacteristic
85C2×C4×C149C2×D411yescharacteristic
86C2×C4×C149C2×D411yescharacteristic
87C2×C4×C149C2×D411yescharacteristic
88C2×C4×C149C2411yescharacteristic
89C22×C149—21no—
90C22×C149—21no—
91C22×C149—21no—
92C22×C149—42no—
93C22×C149—42no—
94C22×C149—42no—
95C22×C149C22×D411yescharacteristic
96C4×C149—21no—
97C4×C149—21no—
98C4×C149—21no—
99C4×C149—42no—
100C4×C149#13512yes—
101C4×C149AGL(1,ℤ/8)12yes—
102C4×C1492−1+412yes—
103Dic149—42no—
104Dic149—42no—
105C2×C149—41no—
106C2×C149—82no—
107C2×C149#53611yescharacteristic
108C2×C149C2×#13511yescharacteristic
109C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
110C149#322811yescharacteristic, complemented, Sylow
111#3228—1491nomaximal, Sylow
112#533—1491no—
113#532D14911yescharacteristic
114#500—1491no—
115#498—1491no—
116#486—1491no—
117#486—1491no—
118#482—1494no—
119#478—1494no—
120#431—1491no—
121C2×#41—21no—
122C4⋊Q8—1491no—
123C4⋊Q8—1491no—
124C4⋊Q8C2×D14911yescharacteristic
125#127C2×D14911yescharacteristic
126#125—1492no—
127#124—21no—
128C22⋊Q8—2981no—
129C22⋊Q8—2981no—
130#121—21no—
131#121C2×D14912yes—
132C4×Q8—2981no—
133C4×Q8—2981no—
134C4×D4—21no—
135C4×D4C2×D14912yes—
136#117—1492no—
137C2×C42C2×D14911yescharacteristic
138#107—1494no—
139#106—1494no—
140C4⋊C8—1492no—
141#102—1494no—
142#102—1494no—
143C22⋊C8—1492no—
144C4×C8—1491no—
145C4×C8—1491no—
146#41—44no—
147C2×Q8—21no—
148C2×Q8—2981no—
149C2×Q8—2981no—
150C2×D4—22no—
151C2×D4—21no—
152C2×D4—21no—
153C2×D4C22×D14912yes—
154C22×C4—22no—
155C22×C4C22⋊D14911yescharacteristic
156C22×C4C22⋊D14911yescharacteristic
157C22×C4C22×D14911yescharacteristic
158C2×C8—1492no—
159C2×C8—1492no—
160C4⋊C4—21no—
161C4⋊C4—2982no—
162C4⋊C4—2982no—
163C4⋊C4—2981no—
164C4⋊C4—2981no—
165C4⋊C4—1492no—
166C4⋊C4—1492no—
167C4⋊C4C22×D14912yes—
168C22⋊C4—22no—
169C22⋊C4—22no—
170C22⋊C4—2982no—
171C42—2982no—
172C42C22⋊D14911yescharacteristic
173C42C22⋊D14911yescharacteristic
174C42C22×D14911yescharacteristic
175C42C22×D14911yescharacteristic
176C23—22no—
177C23C2×C22⋊D14911yescharacteristic
178Q8—42no—
179Q8—5962no—
180Q8—5962no—
181D4—24no—
182D4—44no—
183D4—42no—
184D4—42no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—44no—
190C2×C4—2982no—
191C2×C4—2982no—
192C2×C4C2×C22⋊D14911yescharacteristic
193C2×C4C2×C22⋊D14911yescharacteristic
194C2×C4C2×C22⋊D14911yescharacteristic
195C2×C4C2×C22⋊D14911yescharacteristic
196C2×C4C2×C22⋊D14911yescharacteristic
197C2×C4C23×D14911yescharacteristic
198C8—2982no—
199C8—2982no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—42no—
204C22—42no—
205C22—42no—
206C22C22×C22⋊D14911yescharacteristic
207C4—21no—
208C4—21no—
209C4—21no—
210C4—42no—
211C4—5962no—
212C4—5962no—
213C4#1801193112yes—
214C4#1801193712yes—
215C4#1801195812yes—
216C2—41no—
217C2—82no—
218C2#2375019611yescharacteristic
219C2C2×#1801193111yescharacteristic
220C2C2×#1801193711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting, prime radical#532×C149C2
socleC22×C149C22×D4
hypercenter#532D149
hypocenterC149#3228
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C2×C42 ◁ #532

Complements

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

NH ≅ G/Ntype
1. #23750182C2semidirect
2. #23750028C2semidirect
3. #23750021C2semidirect
4. #23749971C2semidirect
5. #23749971C2semidirect
6. #23749946C2semidirect
7. #23749925C2semidirect
8. #23749678C2semidirect
110. C149#3228semidirect

Maximal subgroups

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

subgroupindex
#237501822
#237500282
#237500212
#237499712
#237499462
#237499252
#237496782
#532×C1492
#3228149