Finite Group Databasebeta

← #34045792

Subgroups — #34045792

Order 19072.

370 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 93 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
1C22×Dic596C211yesmaximal, characteristic
2C22×#14558726C211yesmaximal, characteristic
3C2×#18011909C211yesmaximal, characteristic
4C2×#18011834C211yesmaximal, characteristic
5#23749530C211yesmaximal, characteristic
6#23749379C211yesmaximal, characteristic
7C2×#103×C149C211yesmaximal, characteristic
8C22×Dic298C2211yescharacteristic
9C22×Dic298C2211yescharacteristic
10C2×Dic596—22no—
11C2×Dic596—22no—
12C2×Dic596—22no—
13C2×#14558726—22no—
14C2×#14558726—22no—
15C2×#14558726—22no—
16C22×#11924746C2211yescharacteristic
17#18011909—22no—
18#18011909—22no—
19C2×#14558715—22no—
20C2×C4×Dic149C2211yescharacteristic
21#18011834—22no—
22#18011818—22no—
23C22×Q8×C149C2211yescharacteristic
24C22×C8×C149C2211yescharacteristic
25C2×C4⋊C4×C149C2211yescharacteristic
26#103×C149—22no—
27C2×Dic298—21no—
28C2×Dic298—21no—
29C2×Dic298—21no—
30C2×Dic298—21no—
31C2×Dic298—21no—
32C2×Dic298—21no—
33C2×Dic298—21no—
34C2×Dic298—21no—
35C2×Dic298—21no—
36C2×Dic298—21no—
37C2×Dic298D412yes—
38C2×Dic298D412yes—
39C22×Dic149—21no—
40C22×Dic149—21no—
41C22×Dic149D412yes—
42Dic596—28no—
43#14558726—28no—
44C2×#11924746—21no—
45C2×#11924746—21no—
46C2×#11924746D412yes—
47#14558715—28no—
48C4×Dic149—21no—
49C4×Dic149—21no—
50C2×Q8×C149—21no—
51C2×Q8×C149—21no—
52C2×Q8×C149—21no—
53C2×Q8×C149—21no—
54C2×Q8×C149—21no—
55C2×Q8×C149D412yes—
56C22×C4×C149—21no—
57C22×C4×C149—21no—
58C22×C4×C149C2311yescharacteristic
59C2×C8×C149—21no—
60C2×C8×C149—21no—
61C2×C8×C149D412yes—
62C4⋊C4×C149—21no—
63C4⋊C4×C149—21no—
64Dic298—22no—
65Dic298—22no—
66Dic298—22no—
67Dic298—22no—
68Dic298—41no—
69Dic298—41no—
70Dic298—41no—
71Dic298—41no—
72C2×Dic149—22no—
73C2×Dic149—22no—
74C2×Dic149—22no—
75C2×Dic149—22no—
76C2×Dic149—41no—
77C2×Dic149—41no—
78C2×Dic149—41no—
79C2×Dic149—41no—
80C2×Dic149Q1614yescomplemented
81#11924746—22no—
82C23×C149C2×D411yescharacteristic
83Q8×C149—22no—
84Q8×C149—22no—
85Q8×C149—41no—
86Q8×C149—41no—
87C2×C4×C149—22no—
88C2×C4×C149—41no—
89C2×C4×C149—41no—
90C2×C4×C149—41no—
91C2×C4×C149—42no—
92C2×C4×C149C2×D411yescharacteristic
93C2×C4×C149C2×D411yescharacteristic
94C2×C4×C149C2×D411yescharacteristic
95C2×C4×C149C2×D411yescharacteristic
96C2×C4×C149C2×D411yescharacteristic
97C2×C4×C149#4111yescharacteristic
98C8×C149—22no—
99C22×C149#12011yescharacteristic
100C22×C149#12111yescharacteristic
101C22×C149#12711yescharacteristic
102C22×C149C2×Q1612yes—
103C22×C149#13712yes—
104C4×C149—42no—
105C4×C149—81no—
106C4×C149#12011yescharacteristic
107C4×C149#12011yescharacteristic
108C4×C149#12111yescharacteristic
109C4×C149#12111yescharacteristic
110Dic149—24no—
111Dic149—42no—
112Dic149—42no—
113C2×C149#39211yescharacteristic
114C2×C149#45112yes—
115C2×C149#46212yes—
116C2×C149#49411yescharacteristic
117C2×C149#49711yescharacteristic
118C149#201611yescharacteristic, complemented, Sylow
119#2016—1491nomaximal, Sylow
120C22×Q16—1491no—
121C22×Q16—1491no—
122C2×C4⋊Q8—1491no—
123C2×#103—1491no—
124C2×#103D14911yescharacteristic
125#391—1491no—
126#336—1491no—
127C22×Q8—1491no—
128C22×Q8—1491no—
129C22×Q8C2×D14911yescharacteristic
130C2×Q16—2982no—
131C2×Q16—2982no—
132C2×Q16—2982no—
133C2×Q16—2982no—
134C2×Q16—2982no—
135C2×Q16—2982no—
136C22×C8—1491no—
137C22×C8C2×D14911yescharacteristic
138C4⋊Q8—2982no—
139C4⋊Q8—2982no—
140C2×C4⋊C4—2982no—
141C2×C4⋊C4C2×D14911yescharacteristic
142C2×C42—1491no—
143#103—22no—
144#103—2982no—
145#95—2982no—
146C2×Q8—21no—
147C2×Q8—21no—
148C2×Q8—21no—
149C2×Q8—21no—
150C2×Q8—21no—
151C2×Q8—2981no—
152C2×Q8—2981no—
153C2×Q8—2981no—
154C2×Q8—2981no—
155C2×Q8—2981no—
156C2×Q8—2981no—
157C2×Q8—2981no—
158C2×Q8—2981no—
159C2×Q8—2981no—
160C2×Q8—2981no—
161C2×Q8—1492no—
162C2×Q8—1492no—
163C2×Q8D59612yes—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—2981no—
167C22×C4—2981no—
168C22×C4—1492no—
169C22×C4C22×D14911yescharacteristic
170Q16—2988no—
171Q16—2988no—
172C2×C8—21no—
173C2×C8—21no—
174C2×C8—2981no—
175C2×C8—2981no—
176C2×C8—1492no—
177C2×C8C22⋊D14912yes—
178C4⋊C4—21no—
179C4⋊C4—21no—
180C4⋊C4—2988no—
181C42—2981no—
182C42—2981no—
183C23D4×D14911yescharacteristic
184Q8—22no—
185Q8—22no—
186Q8—41no—
187Q8—41no—
188Q8—2982no—
189Q8—2982no—
190Q8—2982no—
191Q8—2982no—
192Q8—5961no—
193Q8—5961no—
194Q8—5961no—
195Q8—5961no—
196C2×C4—22no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—41no—
200C2×C4—42no—
201C2×C4—2982no—
202C2×C4—2982no—
203C2×C4—2982no—
204C2×C4—2982no—
205C2×C4—5961no—
206C2×C4—5961no—
207C2×C4—5961no—
208C2×C4—5961no—
209C2×C4—1494no—
210C2×C4D4×D14911yescharacteristic
211C2×C4D4×D14911yescharacteristic
212C2×C4D4×D14911yescharacteristic
213C2×C4C2×C22⋊D14911yescharacteristic
214C2×C4C2×D59611yescharacteristic
215C2×C4#1455873611yescharacteristic
216C8—22no—
217C8—2982no—
218C22#1801188111yescharacteristic
219C22#1801188411yescharacteristic
220C22#1801190711yescharacteristic
221C22Q16×D14912yes—
222C22#1801194012yes—
223C4—42no—
224C4—81no—
225C4—2984no—
226C4—5962no—
227C4—5962no—
228C4#1801187911yescharacteristic
229C4#1801188111yescharacteristic
230C4#1801188411yescharacteristic
231C4#1801188511yescharacteristic
232C2#2374953411yescharacteristic
233C2#2374978212yes—
234C2#2374983412yes—
235C2#2375000311yescharacteristic
236C2#2375001611yescharacteristic
subgroupG/H
centerC23D4×D149
commutator, cosocleC22×C4×C149C23
FrattiniC22×C4C22×D149
FittingC2×#103×C149C2
socle, prime radicalC23×C149C2×D4
hypercenterC2×#103D149
hypocenterC149#2016
LCSG ▷ C22×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
80. C2×Dic149Q16semidirect
118. C149#2016semidirect

Maximal subgroups

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

subgroupindex
C22×Dic5962
C22×#145587262
C2×#180119092
C2×#180118342
#237495302
#237493792
C2×#103×C1492
#2016149