Finite Group Databasebeta

← #34043621

Subgroups — #34043621

Order 19072.

272 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 49 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#23750220C211yesmaximal, characteristic, complemented
2#23749778C211yesmaximal, characteristic, complemented
3#23749758C211yesmaximal, characteristic
4#23749543C211yesmaximal, characteristic, complemented
5#23749361C211yesmaximal, characteristic, complemented
6#23749350C211yesmaximal, characteristic, complemented
7#327×C149C211yesmaximal, characteristic, complemented
8C22×D596C2211yescharacteristic
9C2×#14558725—21no—
10C2×#14558721—21no—
11#18011904—21no—
12#18011901—21no—
13#18011892—21no—
14#18011892—21no—
15#18011890C2211yescharacteristic
16#18011888—21no—
17D4×Dic149—21no—
18C2×#14558715C2211yescharacteristic
19C2×#14558713—21no—
20C2×#14558713—21no—
21#18011833—21no—
22#18011831—21no—
23C22⋊#11924746C2211yescharacteristic
24#121×C149C2211yescharacteristic
25C22⋊C8×C149C2211yescharacteristic
26#95×C149C2211yescharacteristic
27C23×D149—21no—
28C2×Dic298D411yescharacteristic
29C2×D596—21no—
30C2×D596—21no—
31C2×D596—42no—
32C22×Dic149—21no—
33C22×Dic149D411yescharacteristic
34C22×Dic149D411yescharacteristic
35#14558725—42no—
36#14558721—42no—
37C2×#11924746—21no—
38C4⋊Dic149—21no—
39C4⋊Dic149D411yescharacteristic
40#14558715—21no—
41#14558715—21no—
42#14558715—21no—
43#14558715—21no—
44#14558715—21no—
45C22⋊Dic149—21no—
46C22⋊Dic149—21no—
47C22⋊Dic149—21no—
48C22⋊Dic149—21no—
49#14558713—42no—
50#14558713—42no—
51C4×Dic149—21no—
52C2×D4×C149—21no—
53C2×D4×C149D411yescharacteristic
54C22×C4×C149—21no—
55C22×C4×C149C2311yescharacteristic
56C2×C8×C149—21no—
57C4⋊C4×C149D411yescharacteristic
58C22⋊C4×C149—21no—
59C22×D149—22no—
60C22×D149—41no—
61C22×D149—41no—
62C22×D149—41no—
63C22×D149—41no—
64C22×D149—41no—
65C22×D149—41no—
66Dic298—41no—
67D596—22no—
68D596—22no—
69D596—41no—
70D596—41no—
71C2×Dic149—21no—
72C2×Dic149—21no—
73C2×Dic149—21no—
74C2×Dic149—21no—
75C2×Dic149—21no—
76C2×Dic149—21no—
77C2×Dic149—41no—
78C2×Dic149—81no—
79#11924746—41no—
80C23×C149—21no—
81C23×C149C2×D411yescharacteristic
82D4×C149—41no—
83D4×C149—41no—
84D4×C149—41no—
85C2×C4×C149—21no—
86C2×C4×C149—41no—
87C2×C4×C149—41no—
88C2×C4×C149—41no—
89C2×C4×C149—41no—
90C2×C4×C149C2×D411yescharacteristic
91C2×C4×C149C2×D411yescharacteristic
92C8×C149—41no—
93C22×C149—21no—
94C22×C149—21no—
95C22×C149—41no—
96C22×C149—41no—
97C22×C149—41no—
98C22×C149#12011yescharacteristic
99C22×C149#13511yescharacteristic
100C22×C149AGL(1,ℤ/8)11yescharacteristic
101C2×D149—42no—
102C2×D149—42no—
103C2×D149—42no—
104C2×D149—81no—
105C2×D149—81no—
106C2×D149—81no—
107C2×D149—81no—
108C4×C149—21no—
109C4×C149—21no—
110C4×C149—41no—
111C4×C149—81no—
112Dic149—41no—
113Dic149—41no—
114Dic149—41no—
115Dic149—41no—
116C2×C149—21no—
117C2×C149—21no—
118C2×C149—81no—
119C2×C149#44911yescharacteristic
120C2×C149#45411yescharacteristic
121C2×C149B(4,𝔽2)11yescharacteristic
122D149—82no—
123C149#159711yescharacteristic, complemented, Sylow
124#1597—1491nomaximal, Sylow
125#539—1491no—
126#450—1491no—
127#447—1491no—
128#394—1491no—
129#328—1491no—
130#327D14911yescharacteristic, complemented
131#324—1491no—
132C22×D4—1491no—
133C2×SD16—2981no—
134C2×D8—2981no—
135#126—2981no—
136#125—2981no—
137#123—2981no—
138#123—2981no—
139C22⋊Q8—2981no—
140C22⋊Q8—1491no—
141#121C2×D14911yescharacteristic
142C4×D4—2981no—
143C2×C4⋊C4—1491no—
144C2×C22⋊C4—2981no—
145C2×C22⋊C4—2981no—
146#102—2981no—
147#102—2981no—
148C22⋊C8—1491no—
149C22⋊C8C2×D14911yescharacteristic
150#95C2×D14911yescharacteristic
151C24—2981no—
152C2×Q8—1491no—
153C2×D4—21no—
154C2×D4—2981no—
155C2×D4—2981no—
156C2×D4—5962no—
157C2×D4D59611yescharacteristic
158C22×C4—21no—
159C22×C4—2981no—
160C22×C4—1491no—
161C22×C4—1491no—
162C22×C4C22×D14911yescharacteristic
163SD16—5962no—
164D8—5962no—
165C2×C8—21no—
166C2×C8—2981no—
167C4⋊C4—2981no—
168C4⋊C4—2981no—
169C4⋊C4—2981no—
170C4⋊C4—2981no—
171C4⋊C4—2981no—
172C4⋊C4—2981no—
173C4⋊C4—1491no—
174C4⋊C4D59611yescharacteristic
175C22⋊C4—21no—
176C22⋊C4—2981no—
177C22⋊C4—2981no—
178C22⋊C4—2981no—
179C22⋊C4—2981no—
180C22⋊C4—5962no—
181C22⋊C4—5962no—
182C42—2981no—
183C23—21no—
184C23—2982no—
185C23—5961no—
186C23—5961no—
187C23—5961no—
188C23—5961no—
189C23—5961no—
190C23—5961no—
191C23D4×D14911yescharacteristic
192Q8—5961no—
193D4—41no—
194D4—41no—
195D4—41no—
196D4—2982no—
197D4—2982no—
198D4—5961no—
199D4—5961no—
200C2×C4—21no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—2981no—
206C2×C4—2981no—
207C2×C4—2981no—
208C2×C4—2981no—
209C2×C4—2981no—
210C2×C4—2981no—
211C2×C4—5961no—
212C2×C4—11921no—
213C2×C4D4×D14911yescharacteristic
214C2×C4C2×D59611yescharacteristic
215C8—41no—
216C8—5961no—
217C22—21no—
218C22—21no—
219C22—41no—
220C22—41no—
221C22—41no—
222C22—5962no—
223C22—5962no—
224C22—5962no—
225C22—11921no—
226C22—11921no—
227C22—11921no—
228C22—11921no—
229C22#1801188111yescharacteristic
230C22#1801193211yescharacteristic
231C22#1801193511yescharacteristic
232C4—21no—
233C4—21no—
234C4—41no—
235C4—81no—
236C4—5961no—
237C4—5961no—
238C4—5961no—
239C4—5961no—
240C2—21no—
241C2—21no—
242C2—81no—
243C2—11922no—
244C2#2374977111yescharacteristic
245C2#2374979911yescharacteristic
246C2#2374981311yescharacteristic
subgroupG/H
centerC22#18011881
commutator, cosocleC22×C4×C149C23
FrattiniC22×C4C22×D149
Fitting#327×C149C2
socleC22×C149#120
prime radical#23749758C2
hypercenter#327D149
hypocenterC149#1597
LCSG ▷ C22×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
1. #23750220C2semidirect
2. #23749778C2semidirect
4. #23749543C2semidirect
5. #23749361C2semidirect
6. #23749350C2semidirect
7. #327×C149C2semidirect
123. C149#1597semidirect
130. #327D149semidirect

Maximal subgroups

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

subgroupindex
#237502202
#237497782
#237497582
#237495432
#237493612
#237493502
#327×C1492
#1597149