Finite Group Databasebeta

← #34055869

Subgroups — #34055869

Order 19072.

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

normal subgroups only

This group has 332 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#23750180C211yesmaximal, characteristic, complemented
2#23750157C211yesmaximal, characteristic
3#23750025C212yesmaximal, complemented
4#23749978C212yesmaximal, complemented
5#23749969C212yesmaximal, complemented
6#23749948C212yesmaximal
7#23749917C211yesmaximal, characteristic, complemented
8#23749911C211yesmaximal, characteristic, complemented
9#23749905C211yesmaximal, characteristic, complemented
10#23749677C211yesmaximal, characteristic, complemented
11#476×C149C211yesmaximal, characteristic, complemented
12#18011911C2211yescharacteristic
13#18011904—21no—
14#18011902C2211yescharacteristic
15#18011902C2212yes—
16#18011898C2211yescharacteristic
17#18011893—21no—
18#18011891—21no—
19#18011891C2211yescharacteristic
20#18011887—21no—
21#18011882C2211yescharacteristic
22Q8×Dic149—21no—
23C4×Dic298C2211yescharacteristic
24#18011876—21no—
25C4×C22⋊D149—21no—
26#18011870—21no—
27#18011869C2212yes—
28C42×D149C2211yescharacteristic
29#18011844C2212yes—
30#18011844C2212yes—
31#18011843C2212yes—
32C4⋊#11924746C2211yescharacteristic
33#18011836C2212yes—
34#18011834C2212yes—
35#18011832C2212yes—
36#18011823C2212yes—
37C8×Dic149C2212yes—
38C4⋊Q8×C149C2211yescharacteristic
39C4×D4×C149C2211yescharacteristic
40#106×C149C2212yes—
41C4⋊C8×C149C2211yescharacteristic
42#102×C149C2212yes—
43C2×Dic298—21no—
44C2×Dic298C2311yescharacteristic
45C2×C22⋊D149—21no—
46C2×C4×D149D411yescharacteristic
47C2×C4×D149D411yescharacteristic
48C2×C4×D149C2311yescharacteristic
49C2×#11924746C2312yes—
50C4⋊Dic149—21no—
51C4⋊Dic149—21no—
52C4⋊Dic149—22no—
53C4⋊Dic149—21no—
54C4⋊Dic149C2312yes—
55C4⋊Dic149C2311yescharacteristic
56#14558715—21no—
57#14558715—22no—
58#14558715—21no—
59C22⋊Dic149—21no—
60C22⋊Dic149—21no—
61C22⋊Dic149—21no—
62#14558713—22no—
63#14558713—21no—
64C4×Dic149—22no—
65C4×Dic149—21no—
66C4×Dic149D411yescharacteristic
67C4×Dic149D411yescharacteristic
68C4×Dic149C2311yescharacteristic
69C2×Q8×C149—21no—
70C2×D4×C149C2311yescharacteristic
71C22×C4×C149—21no—
72C2×C8×C149C2312yes—
73C4⋊C4×C149—21no—
74C4⋊C4×C149C2312yes—
75C4⋊C4×C149C2311yescharacteristic
76C22⋊C4×C149—21no—
77C42×C149C2311yescharacteristic
78C22×D149C2×D411yescharacteristic
79Dic298—21no—
80Dic298—21no—
81Dic298—42no—
82C22⋊D149—42no—
83C2×Dic149—21no—
84C2×Dic149—22no—
85C2×Dic149—21no—
86C2×Dic149C2×D411yescharacteristic
87C2×Dic149C2×D411yescharacteristic
88C2×Dic149C2×D411yescharacteristic
89C4×D149—22no—
90C4×D149—21no—
91C4×D149—21no—
92C4×D149—41no—
93#11924746—22no—
94C23×C149—21no—
95Q8×C149—42no—
96D4×C149—21no—
97D4×C149—21no—
98C2×C4×C149—21no—
99C2×C4×C149—22no—
100C2×C4×C149—42no—
101C2×C4×C149C2×D411yescharacteristic
102C2×C4×C149C2×D411yescharacteristic
103C2×C4×C149C2411yescharacteristic
104C8×C149—22no—
105C22×C149—41no—
106C22×C149—41no—
107C22×C149—41no—
108C22×C149C22×D411yescharacteristic
109C2×D149—21no—
110C2×D149—21no—
111C2×D149—21no—
112C4×C149—21no—
113C4×C149—41no—
114C4×C149—42no—
115C4×C149#13512yes—
116C4×C1492−1+411yescharacteristic
117C4×C1492−1+411yescharacteristic
118Dic149—21no—
119Dic149—21no—
120Dic149—21no—
121Dic149—41no—
122Dic149—42no—
123Dic149—41no—
124C2×C149—81no—
125C2×C149#53611yescharacteristic
126C2×C149C2×#13511yescharacteristic
127C2×C149#57511yescharacteristic
128D149—41no—
129C149#323311yescharacteristic, complemented, Sylow
130#3233—1491nomaximal, Sylow
131#533—1491no—
132#529—1491no—
133#499—1492no—
134#488—1492no—
135#485—1492no—
136#482—1492no—
137#477—1491no—
138#476D14911yescharacteristic, complemented
139#475—1491no—
140#474—1491no—
141#431—1491no—
142C4⋊Q8—1491no—
143C4⋊Q8C2×D14911yescharacteristic
144#126—2981no—
145#125—1491no—
146#125—1492no—
147#124—1491no—
148#123—2981no—
149C22⋊Q8—2981no—
150C22⋊Q8—2981no—
151C22⋊Q8—1491no—
152#121—1491no—
153C4×Q8—2981no—
154C4×Q8—2981no—
155C4×Q8—1491no—
156C4×D4—2981no—
157C4×D4C2×D14911yescharacteristic
158#117—2981no—
159#117—1492no—
160C2×C42—1491no—
161#107—1492no—
162#107—1492no—
163#106—1492no—
164#106C2×D14912yes—
165C4⋊C8—1491no—
166C4⋊C8C2×D14911yescharacteristic
167#103—1492no—
168#103—1492no—
169#102—1492no—
170#102C2×D14912yes—
171C22⋊C8—1492no—
172C4×C8—1492no—
173C2×Q8—21no—
174C2×Q8—2981no—
175C2×Q8—1491no—
176C2×D4—2981no—
177C2×D4C22×D14911yescharacteristic
178C22×C4—21no—
179C22×C4—1491no—
180C22×C4—1491no—
181C22×C4—1491no—
182C2×C8—1492no—
183C2×C8C22×D14912yes—
184C4⋊C4—21no—
185C4⋊C4—2981no—
186C4⋊C4—2981no—
187C4⋊C4—2981no—
188C4⋊C4—2982no—
189C4⋊C4—2982no—
190C4⋊C4—2981no—
191C4⋊C4—2981no—
192C4⋊C4—1492no—
193C4⋊C4—1491no—
194C4⋊C4C22×D14912yes—
195C4⋊C4C22×D14911yescharacteristic
196C22⋊C4—21no—
197C22⋊C4—2982no—
198C22⋊C4—2981no—
199C22⋊C4—2981no—
200C22⋊C4—2981no—
201C22⋊C4—2981no—
202C42—2982no—
203C42—2981no—
204C42—1491no—
205C42—1491no—
206C42—1491no—
207C42C22×D14911yescharacteristic
208C23—21no—
209C23—1491no—
210Q8—42no—
211Q8—2981no—
212Q8—2981no—
213Q8—5962no—
214D4—21no—
215D4—21no—
216D4—5962no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—42no—
220C2×C4—2982no—
221C2×C4—2981no—
222C2×C4—2981no—
223C2×C4—2981no—
224C2×C4—2981no—
225C2×C4—2982no—
226C2×C4—5961no—
227C2×C4—1491no—
228C2×C4—1491no—
229C2×C4—1491no—
230C2×C4D4×D14911yescharacteristic
231C2×C4D4×D14911yescharacteristic
232C2×C4C23×D14911yescharacteristic
233C8—22no—
234C8—2982no—
235C22—41no—
236C22—41no—
237C22—41no—
238C22—2981no—
239C22—2981no—
240C22—2981no—
241C22C2×D4×D14911yescharacteristic
242C4—21no—
243C4—41no—
244C4—42no—
245C4—2981no—
246C4—2981no—
247C4—2981no—
248C4—5962no—
249C4—5961no—
250C4—5961no—
251C4#1801193212yes—
252C4#1801195811yescharacteristic
253C4#1801195911yescharacteristic
254C2—81no—
255C2—5961no—
256C2#2375019811yescharacteristic
257C2C2×#1801193211yescharacteristic
258C2#2375042111yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#476×C149C2
socleC22×C149C22×D4
prime radical#18011882C22
hypercenter#476D149
hypocenterC149#3233
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #23750180C2semidirect
3. #23750025C2semidirect
4. #23749978C2semidirect
5. #23749969C2semidirect
7. #23749917C2semidirect
8. #23749911C2semidirect
9. #23749905C2semidirect
10. #23749677C2semidirect
11. #476×C149C2semidirect
129. C149#3233semidirect
138. #476D149semidirect

Maximal subgroups

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

subgroupindex
#237501802
#237501572
#237500252
#237499782
#237499692
#237499482
#237499172
#237499112
#237499052
#237496772
#476×C1492
#3233149