Finite Group Databasebeta

← #34055878

Subgroups — #34055878

Order 19072.

368 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 113 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#23750170C211yesmaximal, characteristic
2C2×#18011902C211yesmaximal, characteristic, complemented
3#23750033C212yesmaximal, complemented
4#23749988C212yesmaximal, complemented
5#23749944C211yesmaximal, characteristic, complemented
6#23749941C211yesmaximal, characteristic, complemented
7#23749938C211yesmaximal, characteristic, complemented
8#23749928C212yesmaximal, complemented
9#23749927C212yesmaximal, complemented
10#23749679C211yesmaximal, characteristic, complemented
11#480×C149C211yesmaximal, characteristic, complemented
12C2×#14558735—21no—
13#18011910C2211yescharacteristic
14#18011907C2211yescharacteristic
15#18011902—21no—
16#18011902—21no—
17#18011902C2212yes—
18#18011902C2212yes—
19#18011897—21no—
20#18011885C2211yescharacteristic
21#18011883—21no—
22D4×Dic149C2211yescharacteristic
23#18011873C2211yescharacteristic
24#18011871—21no—
25C2×C4⋊Dic149—21no—
26C2×C4⋊Dic149C2211yescharacteristic
27C2×#14558715—21no—
28C2×C4×Dic149C2211yescharacteristic
29#18011844C2212yes—
30#18011843C2212yes—
31#18011842C2212yes—
32#18011840C2212yes—
33#18011833C2212yes—
34#18011832C2212yes—
35#18011831C2212yes—
36C22⋊#11924746C2211yescharacteristic
37#18011821C2212yes—
38#121×C149C2211yescharacteristic
39C2×C4⋊C4×C149C2211yescharacteristic
40#107×C149C2212yes—
41#102×C149C2212yes—
42C22⋊C8×C149C2211yescharacteristic
43#14558735—44no—
44C2×Dic298—21no—
45C2×D596C2311yescharacteristic
46C2×C22⋊D149—21no—
47C2×C22⋊D149—21no—
48C2×C22⋊D149—21no—
49C22×Dic149—21no—
50C22×Dic149—21no—
51C22×Dic149D411yescharacteristic
52C22×Dic149D411yescharacteristic
53C2×C4×D149—21no—
54C2×#11924746C2312yes—
55C4⋊Dic149—22no—
56C4⋊Dic149—22no—
57C4⋊Dic149—21no—
58C4⋊Dic149C2311yescharacteristic
59C4⋊Dic149C2312yes—
60#14558715—21no—
61#14558715—22no—
62#14558715—22no—
63C22⋊Dic149—21no—
64#14558713—21no—
65#14558713—21no—
66C4×Dic149D411yescharacteristic
67C4×Dic149D411yescharacteristic
68C4×Dic149C2311yescharacteristic
69C4×Dic149C2311yescharacteristic
70C2×D4×C149—21no—
71C2×D4×C149C2311yescharacteristic
72C22×C4×C149—21no—
73C22×C4×C149C2311yescharacteristic
74C2×C8×C149C2312yes—
75C4⋊C4×C149—21no—
76C4⋊C4×C149C2311yescharacteristic
77C4⋊C4×C149C2312yes—
78C22⋊C4×C149—21no—
79C22×D149—21no—
80Dic298—42no—
81D596—22no—
82C22⋊D149—42no—
83C22⋊D149—42no—
84C22⋊D149—42no—
85C2×Dic149—22no—
86C2×Dic149—21no—
87C2×Dic149—22no—
88C2×Dic149—41no—
89C2×Dic149—42no—
90C2×Dic149—42no—
91C2×Dic149C2×D411yescharacteristic
92C2×Dic149C2×D411yescharacteristic
93C2×Dic149C2×D411yescharacteristic
94C2×Dic149C2×D411yescharacteristic
95C4×D149—42no—
96#11924746—22no—
97C23×C149—21no—
98C23×C149C2×D411yescharacteristic
99D4×C149—22no—
100D4×C149—42no—
101C2×C4×C149—22no—
102C2×C4×C149—21no—
103C2×C4×C149—22no—
104C2×C4×C149—42no—
105C2×C4×C149C2×D411yescharacteristic
106C2×C4×C149C2411yescharacteristic
107C8×C149—22no—
108C22×C149—21no—
109C22×C149—21no—
110C22×C149—41no—
111C22×C149—41no—
112C22×C149—41no—
113C22×C149AGL(1,ℤ/8)12yes—
114C22×C149C22×D411yescharacteristic
115C2×D149—41no—
116C2×D149—41no—
117C2×D149—41no—
118C4×C149—21no—
119C4×C149—42no—
120C4×C149—41no—
121C4×C1492−1+412yes—
122Dic149—21no—
123Dic149—21no—
124Dic149—21no—
125Dic149—21no—
126Dic149—41no—
127Dic149—42no—
128C2×C149—22no—
129C2×C149—81no—
130C2×C149#53611yescharacteristic
131C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
132C2×C149#57511yescharacteristic
133D149—81no—
134C149#323411yescharacteristic, complemented, Sylow
135#3234—1491nomaximal, Sylow
136#532—1491no—
137C2×#125—1491no—
138#501—1492no—
139#490—1492no—
140#481—1491no—
141#481—1491no—
142#480—1491no—
143#480D14911yescharacteristic, complemented
144#478—1492no—
145#478—1492no—
146#432—1491no—
147C2×#41—2981no—
148C4⋊Q8—1491no—
149#127—1491no—
150#125—2981no—
151#125—2981no—
152#125—1492no—
153#125—1492no—
154#124—2981no—
155#121—2981no—
156#121—1491no—
157#121C2×D14911yescharacteristic
158C4×D4—2981no—
159C4×D4—1491no—
160C4×D4—1491no—
161C2×C4⋊C4—2981no—
162C2×C4⋊C4—2981no—
163C2×C4⋊C4—1491no—
164C2×C4⋊C4C2×D14911yescharacteristic
165C2×C42—1491no—
166#107—1492no—
167#107C2×D14912yes—
168#106—1492no—
169#106—1492no—
170C4⋊C8—1492no—
171#102—1492no—
172#102—1492no—
173#102—1492no—
174#102C2×D14912yes—
175C22⋊C8—1491no—
176C22⋊C8C2×D14911yescharacteristic
177#97—1492no—
178#41—5964no—
179C2×Q8—2981no—
180C2×D4—21no—
181C2×D4—2981no—
182C2×D4—2981no—
183C2×D4—2981no—
184C2×D4—1491no—
185C2×D4C22×D14911yescharacteristic
186C22×C4—21no—
187C22×C4—2981no—
188C22×C4—2981no—
189C22×C4—2981no—
190C22×C4—1491no—
191C22×C4—1491no—
192C22×C4C22×D14911yescharacteristic
193C2×C8—1492no—
194C2×C8C22×D14912yes—
195C4⋊C4—21no—
196C4⋊C4—2982no—
197C4⋊C4—2982no—
198C4⋊C4—2982no—
199C4⋊C4—2982no—
200C4⋊C4—2981no—
201C4⋊C4—2981no—
202C4⋊C4—1492no—
203C4⋊C4—1491no—
204C4⋊C4C22×D14912yes—
205C4⋊C4C22×D14911yescharacteristic
206C22⋊C4—21no—
207C22⋊C4—2981no—
208C22⋊C4—2981no—
209C22⋊C4—2981no—
210C42—1491no—
211C42—1491no—
212C42—1491no—
213C42—1491no—
214C23—21no—
215C23—2981no—
216C23D4×D14911yescharacteristic
217Q8—5962no—
218D4—22no—
219D4—42no—
220D4—2982no—
221D4—5962no—
222D4—5962no—
223D4—5962no—
224C2×C4—22no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—42no—
228C2×C4—2982no—
229C2×C4—2981no—
230C2×C4—2982no—
231C2×C4—5962no—
232C2×C4—5961no—
233C2×C4—5962no—
234C2×C4—5962no—
235C2×C4—1491no—
236C2×C4—1491no—
237C2×C4—1491no—
238C2×C4—1491no—
239C2×C4D4×D14911yescharacteristic
240C2×C4C23×D14911yescharacteristic
241C8—22no—
242C8—2982no—
243C22—21no—
244C22—21no—
245C22—41no—
246C22—41no—
247C22—41no—
248C22—5961no—
249C22—5961no—
250C22—5961no—
251C22#1801193512yes—
252C22C2×D4×D14911yescharacteristic
253C4—21no—
254C4—42no—
255C4—41no—
256C4—2981no—
257C4—2981no—
258C4—2981no—
259C4—2981no—
260C4—5961no—
261C4—5962no—
262C4#1801195812yes—
263C2—22no—
264C2—81no—
265C2—11921no—
266C2#2375019711yescharacteristic
267C2C2×#1801193511yescharacteristic
268C2#2375042411yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#480×C149C2
socleC22×C149C22×D4
prime radical#23750170C2
hypercenter#480D149
hypocenterC149#3234
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. C2×#18011902C2semidirect
3. #23750033C2semidirect
4. #23749988C2semidirect
5. #23749944C2semidirect
6. #23749941C2semidirect
7. #23749938C2semidirect
8. #23749928C2semidirect
9. #23749927C2semidirect
10. #23749679C2semidirect
11. #480×C149C2semidirect
134. C149#3234semidirect
143. #480D149semidirect

Maximal subgroups

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

subgroupindex
#237501702
C2×#180119022
#237500332
#237499882
#237499442
#237499412
#237499382
#237499282
#237499272
#237496792
#480×C1492
#3234149