Finite Group Databasebeta

← #34056078

Subgroups — #34056078

Order 19072.

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

normal subgroups only

This group has 386 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#23749917C212yesmaximal, complemented
3#23749905C212yesmaximal, complemented
4#23749869C214yesmaximal, complemented
5#23749830C212yesmaximal, complemented
6#23749822C212yesmaximal, complemented
7#23749649C211yesmaximal, characteristic, complemented
8#532×C149C211yesmaximal, characteristic
9C2×#14558724C2214yes—
10C2×#14558720C2212yes—
11#18011911C2211yescharacteristic
12#18011911C2211yescharacteristic
13#18011903—21no—
14#18011890—21no—
15#18011890C2212yes—
16C4×Dic298—21no—
17C4×Dic298C2212yes—
18#18011870—21no—
19#18011844C2214yes—
20C4⋊#11924746C2212yes—
21C4⋊#11924746C2212yes—
22#18011834C2214yes—
23#18011832C2214yes—
24C2×#41×C149—21no—
25C4⋊Q8×C149C2211yescharacteristic
26#127×C149C2211yescharacteristic
27#124×C149—21no—
28#121×C149—21no—
29#121×C149C2212yes—
30C4×D4×C149—21no—
31C4×D4×C149C2212yes—
32C2×C42×C149C2211yescharacteristic
33C2×Dic298—21no—
34C2×Dic298C2312yes—
35#14558724—44no—
36#14558720—42no—
37C2×#11924746C2314yes—
38C4⋊Dic149—21no—
39C4⋊Dic149—21no—
40C4⋊Dic149—21no—
41C4⋊Dic149C2312yes—
42#14558715—22no—
43#14558715—22no—
44C22⋊Dic149—22no—
45C4×Dic149—22no—
46#41×C149—44no—
47C2×Q8×C149—21no—
48C2×D4×C149—22no—
49C2×D4×C149—21no—
50C2×D4×C149—21no—
51C2×D4×C149C2312yes—
52C22×C4×C149—22no—
53C22×C4×C149D411yescharacteristic
54C22×C4×C149D411yescharacteristic
55C22×C4×C149C2311yescharacteristic
56C4⋊C4×C149—21no—
57C4⋊C4×C149C2312yes—
58C22⋊C4×C149—22no—
59C22⋊C4×C149—22no—
60C42×C149D411yescharacteristic
61C42×C149D411yescharacteristic
62C42×C149C2311yescharacteristic
63C42×C149C2311yescharacteristic
64Dic298—22no—
65Dic298—22no—
66Dic298—42no—
67C2×Dic149—22no—
68C2×Dic149—22no—
69#11924746—24no—
70C23×C149—22no—
71C23×C149C2×D411yescharacteristic
72Q8×C149—42no—
73D4×C149—22no—
74D4×C149—22no—
75D4×C149—42no—
76D4×C149—44no—
77D4×C149—42no—
78C2×C4×C149—22no—
79C2×C4×C149—22no—
80C2×C4×C149—21no—
81C2×C4×C149—21no—
82C2×C4×C149—22no—
83C2×C4×C149—44no—
84C2×C4×C149C2×D411yescharacteristic
85C2×C4×C149C2×D411yescharacteristic
86C2×C4×C149C2×D411yescharacteristic
87C2×C4×C149C2×D411yescharacteristic
88C2×C4×C149C2×D411yescharacteristic
89C2×C4×C149C2411yescharacteristic
90C22×C149—21no—
91C22×C149—21no—
92C22×C149—21no—
93C22×C149—42no—
94C22×C149—42no—
95C22×C149—42no—
96C22×C149C22×D411yescharacteristic
97C4×C149—21no—
98C4×C149—21no—
99C4×C149—21no—
100C4×C149—42no—
101C4×C149AGL(1,ℤ/8)12yes—
102C4×C149#13712yes—
103C4×C149H(5,𝔽2)11yescharacteristic
104C4×C1492−1+411yescharacteristic
105Dic149—42no—
106Dic149—42no—
107C2×C149—41no—
108C2×C149—82no—
109C2×C149#53711yescharacteristic
110C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
111C2×C149C2×#13711yescharacteristic
112C149#325411yescharacteristic, complemented, Sylow
113#3254—1491nomaximal, Sylow
114#533—1491no—
115#532D14911yescharacteristic
116#477—1492no—
117#474—1492no—
118#468—1494no—
119#461—1492no—
120#460—1492no—
121#423—1491no—
122C2×#41—21no—
123C2×SD16—1494no—
124C2×M16—1492no—
125C4⋊Q8—1491no—
126C4⋊Q8—1491no—
127C4⋊Q8C2×D14911yescharacteristic
128#127C2×D14911yescharacteristic
129#125—2981no—
130#124—21no—
131C22⋊Q8—2981no—
132C22⋊Q8—1492no—
133#121—21no—
134#121C2×D14912yes—
135C4×Q8—2981no—
136C4×Q8—1492no—
137C4×D4—21no—
138C4×D4C2×D14912yes—
139#117—2981no—
140C2×C42C2×D14911yescharacteristic
141#107—1494no—
142C4⋊C8—1492no—
143C4⋊C8—1492no—
144#103—1494no—
145#102—1494no—
146#41—44no—
147C2×Q8—21no—
148C2×Q8—2981no—
149C2×Q8—1492no—
150C2×D4—22no—
151C2×D4—21no—
152C2×D4—21no—
153C2×D4C22×D14912yes—
154C22×C4—22no—
155C22×C4C22⋊D14911yescharacteristic
156C22×C4C22⋊D14911yescharacteristic
157C22×C4C22×D14911yescharacteristic
158SD16—5964no—
159M16—5962no—
160C2×C8—1494no—
161C4⋊C4—21no—
162C4⋊C4—2981no—
163C4⋊C4—2981no—
164C4⋊C4—2981no—
165C4⋊C4—2982no—
166C4⋊C4—2982no—
167C4⋊C4—1492no—
168C4⋊C4C22×D14912yes—
169C22⋊C4—22no—
170C22⋊C4—22no—
171C22⋊C4—2982no—
172C42—2982no—
173C42C22⋊D14911yescharacteristic
174C42C22⋊D14911yescharacteristic
175C42C22×D14911yescharacteristic
176C42C22×D14911yescharacteristic
177C23—22no—
178C23C2×C22⋊D14911yescharacteristic
179Q8—42no—
180Q8—2982no—
181Q8—2982no—
182Q8—5962no—
183D4—22no—
184D4—22no—
185D4—42no—
186D4—44no—
187D4—42no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—44no—
194C2×C4—2982no—
195C2×C4—2982no—
196C2×C4C2×C22⋊D14911yescharacteristic
197C2×C4C2×C22⋊D14911yescharacteristic
198C2×C4C2×C22⋊D14911yescharacteristic
199C2×C4C2×C22⋊D14911yescharacteristic
200C2×C4C2×C22⋊D14911yescharacteristic
201C2×C4C23×D14911yescharacteristic
202C8—2984no—
203C22—21no—
204C22—21no—
205C22—21no—
206C22—42no—
207C22—42no—
208C22—42no—
209C22C22×C22⋊D14911yescharacteristic
210C4—21no—
211C4—21no—
212C4—21no—
213C4—42no—
214C4—5962no—
215C4—5962no—
216C4#1801193712yes—
217C4#1801194112yes—
218C4#1801195711yescharacteristic
219C4#1801195811yescharacteristic
220C2—41no—
221C2—82no—
222C2#2375020311yescharacteristic
223C2C2×#1801193711yescharacteristic
224C2C2×#1801194111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting, prime radical#532×C149C2
socleC22×C149C22×D4
hypercenter#532D149
hypocenterC149#3254
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. #23749917C2semidirect
3. #23749905C2semidirect
4. #23749869C2semidirect
5. #23749830C2semidirect
6. #23749822C2semidirect
7. #23749649C2semidirect
112. C149#3254semidirect

Maximal subgroups

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

subgroupindex
#237501822
#237499172
#237499052
#237498692
#237498302
#237498222
#237496492
#532×C1492
#3254149