Finite Group Databasebeta

← #34045897

Subgroups — #34045897

Order 19072.

316 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 85 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
1C2×#18011891C211yesmaximal, characteristic
2C2×#18011844C211yesmaximal, characteristic, complemented
3C2×#18011836C211yesmaximal, characteristic, complemented
4C2×#18011834C211yesmaximal, characteristic, complemented
5C2×#18011823C211yesmaximal, characteristic
6#23749482C211yesmaximal, characteristic
7#340×C149C211yesmaximal, characteristic, complemented
8C22×Dic298C2211yescharacteristic
9C22×C4×D149C2211yescharacteristic
10C22×#11924746C2211yescharacteristic
11#18011891—22no—
12#18011891—22no—
13C2×C4⋊Dic149—21no—
14C2×C4⋊Dic149C2211yescharacteristic
15C2×#14558713—21no—
16C2×#14558713—21no—
17#18011844—22no—
18#18011836—22no—
19#18011834—22no—
20#18011823—22no—
21#18011818—21no—
22C22×C8×C149C2211yescharacteristic
23C2×C4⋊C4×C149C2211yescharacteristic
24C2×C4⋊C4×C149C2211yescharacteristic
25C23×D149D411yescharacteristic
26C2×Dic298—21no—
27C2×Dic298—21no—
28C2×Dic298—21no—
29C2×Dic298—21no—
30C2×Dic298—21no—
31C2×Dic298D412yes—
32C22×Dic149—21no—
33C22×Dic149—21no—
34C22×Dic149D411yescharacteristic
35C2×C4×D149—21no—
36C2×C4×D149—21no—
37C2×C4×D149—21no—
38C2×C4×D149—21no—
39C2×C4×D149—21no—
40C2×C4×D149—21no—
41C2×#11924746—21no—
42C2×#11924746—21no—
43C2×#11924746D412yes—
44C4⋊Dic149—24no—
45C4⋊Dic149—21no—
46C4⋊Dic149—21no—
47#14558713—24no—
48#14558713—42no—
49C22×C4×C149—21no—
50C22×C4×C149—21no—
51C22×C4×C149C2311yescharacteristic
52C2×C8×C149—21no—
53C2×C8×C149—21no—
54C2×C8×C149—21no—
55C4⋊C4×C149—21no—
56C4⋊C4×C149—21no—
57C4⋊C4×C149—21no—
58C4⋊C4×C149D412yes—
59C22×D149—21no—
60C22×D149—21no—
61C22×D149—21no—
62C22×D149—21no—
63C22×D149—21no—
64C22×D149—21no—
65C22×D149Q1612yes—
66Dic298—22no—
67Dic298—22no—
68Dic298—41no—
69Dic298—41no—
70C2×Dic149—21no—
71C2×Dic149—22no—
72C2×Dic149—21no—
73C2×Dic149—21no—
74C2×Dic149—41no—
75C2×Dic149—41no—
76C2×Dic149—41no—
77C2×Dic149—41no—
78C2×Dic149—41no—
79C4×D149—41no—
80C4×D149—41no—
81C4×D149—41no—
82C4×D149—41no—
83#11924746—22no—
84C23×C149C2×D411yescharacteristic
85C2×C4×C149—22no—
86C2×C4×C149—41no—
87C2×C4×C149—41no—
88C2×C4×C149—41no—
89C2×C4×C149—41no—
90C2×C4×C149—41no—
91C2×C4×C149C2×D411yescharacteristic
92C2×C4×C149C2×D411yescharacteristic
93C2×C4×C149C2×D411yescharacteristic
94C2×C4×C149#4111yescharacteristic
95C2×C4×C149#4111yescharacteristic
96C2×C4×C149#4111yescharacteristic
97C8×C149—41no—
98C22×C149#12011yescharacteristic
99C22×C149#12111yescharacteristic
100C22×C149#12311yescharacteristic
101C22×C149C2×Q1611yescharacteristic
102C22×C149#13511yescharacteristic
103C22×C149AGL(1,ℤ/8)11yescharacteristic
104C22×C149#13711yescharacteristic
105C2×D149—22no—
106C2×D149—22no—
107C2×D149—22no—
108C2×D149—41no—
109C2×D149—41no—
110C2×D149—41no—
111C2×D149—41no—
112C4×C149—42no—
113C4×C149—81no—
114C4×C149#12111yescharacteristic
115C4×C149#12111yescharacteristic
116C4×C149#12311yescharacteristic
117C4×C149#12411yescharacteristic
118Dic149—41no—
119Dic149—42no—
120Dic149—81no—
121C2×C149#39411yescharacteristic
122C2×C149#44911yescharacteristic
123C2×C149#45111yescharacteristic
124C2×C149#46711yescharacteristic
125C2×C149#46811yescharacteristic
126C2×C149#48411yescharacteristic
127C2×C149#48511yescharacteristic
128D149—42no—
129C149#203611yescharacteristic, complemented, Sylow
130#2036—1491nomaximal, Sylow
131C2×C22⋊Q8—1491no—
132C2×#107—1491no—
133C2×#103—1491no—
134C2×#103—1491no—
135C2×C22⋊C8—1491no—
136#380—1491no—
137#340D14911yescharacteristic, complemented
138C22×Q8—1491no—
139C23×C4—1491no—
140C22×C8—1491no—
141C22×C8C2×D14911yescharacteristic
142C22⋊Q8—2982no—
143C22⋊Q8—2982no—
144C2×C4⋊C4—2981no—
145C2×C4⋊C4—1491no—
146C2×C4⋊C4C2×D14911yescharacteristic
147C2×C4⋊C4C2×D14911yescharacteristic
148C2×C22⋊C4—2981no—
149C2×C22⋊C4—2981no—
150#107—2982no—
151#103—2982no—
152#103—2982no—
153C22⋊C8—2982no—
154#95—2981no—
155C24—1491no—
156C2×Q8—2981no—
157C2×Q8—2981no—
158C2×Q8—2981no—
159C2×Q8—2981no—
160C2×Q8—2981no—
161C2×Q8—1492no—
162C22×C4—21no—
163C22×C4—21no—
164C22×C4—2981no—
165C22×C4—2981no—
166C22×C4—2981no—
167C22×C4—2981no—
168C22×C4—2981no—
169C22×C4—2981no—
170C22×C4—2981no—
171C22×C4—2981no—
172C22×C4—1491no—
173C22×C4C22×D14911yescharacteristic
174C2×C8—21no—
175C2×C8—21no—
176C2×C8—21no—
177C2×C8—2981no—
178C2×C8—2981no—
179C2×C8—1492no—
180C4⋊C4—21no—
181C4⋊C4—21no—
182C4⋊C4—21no—
183C4⋊C4—2984no—
184C4⋊C4—2981no—
185C4⋊C4—2981no—
186C4⋊C4D59612yes—
187C22⋊C4—2984no—
188C22⋊C4—5962no—
189C23—2981no—
190C23—2981no—
191C23—2981no—
192C23—2981no—
193C23—2981no—
194C23—2981no—
195C23—1492no—
196C23D4×D14911yescharacteristic
197Q8—2982no—
198Q8—2982no—
199Q8—5961no—
200Q8—5961no—
201C2×C4—22no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—2982no—
208C2×C4—2981no—
209C2×C4—2981no—
210C2×C4—2981no—
211C2×C4—5961no—
212C2×C4—5961no—
213C2×C4—5961no—
214C2×C4—5961no—
215C2×C4—5961no—
216C2×C4—5961no—
217C2×C4—5961no—
218C2×C4—5961no—
219C2×C4—5961no—
220C2×C4D4×D14911yescharacteristic
221C2×C4D4×D14911yescharacteristic
222C2×C4C2×D59611yescharacteristic
223C2×C4#1455873611yescharacteristic
224C2×C4#1455873611yescharacteristic
225C2×C4#1455873711yescharacteristic
226C8—41no—
227C8—2982no—
228C22—2982no—
229C22—2982no—
230C22—2982no—
231C22—5961no—
232C22—5961no—
233C22—5961no—
234C22—5961no—
235C22#1801188111yescharacteristic
236C22#1801188411yescharacteristic
237C22#1801189611yescharacteristic
238C22Q16×D14911yescharacteristic
239C22#1801193211yescharacteristic
240C22#1801193511yescharacteristic
241C22#1801194011yescharacteristic
242C4—42no—
243C4—81no—
244C4—5961no—
245C4—5962no—
246C4—11921no—
247C4#1801188411yescharacteristic
248C4#1801188611yescharacteristic
249C4#1801189611yescharacteristic
250C4#1801189911yescharacteristic
251C2—5962no—
252C2#2374954311yescharacteristic
253C2#2374977111yescharacteristic
254C2#2374978211yescharacteristic
255C2#2374986511yescharacteristic
256C2#2374987011yescharacteristic
257C2#2374996211yescharacteristic
258C2#2374996911yescharacteristic
subgroupG/H
centerC23D4×D149
commutator, cosocleC22×C4×C149C23
FrattiniC22×C4C22×D149
Fitting#340×C149C2
socleC23×C149C2×D4
prime radicalC23×D149D4
hypercenter#340D149
hypocenterC149#2036
LCSG ▷ C22×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
2. C2×#18011844C2semidirect
3. C2×#18011836C2semidirect
4. C2×#18011834C2semidirect
7. #340×C149C2semidirect
129. C149#2036semidirect
137. #340D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180118912
C2×#180118442
C2×#180118362
C2×#180118342
C2×#180118232
#237494822
#340×C1492
#2036149