Finite Group Databasebeta

← #34045133

Subgroups — #34045133

Order 19072.

442 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 87 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#23750137C211yesmaximal, characteristic
2C2×C42×D149C211yesmaximal, characteristic, complemented
3C2×#18011839C211yesmaximal, characteristic, complemented
4C2×#18011837C211yesmaximal, characteristic, complemented
5#23749588C211yesmaximal, characteristic, complemented
6#23749384C211yesmaximal, characteristic, complemented
7#339×C149C211yesmaximal, characteristic, complemented
8C2×#14558736C2211yescharacteristic
9C22×C4×D149—21no—
10C22×C4×D149C2211yescharacteristic
11C2×#14558720C2211yescharacteristic
12#18011895—21no—
13#18011891C412yescomplemented
14#18011886C412yescomplemented
15#18011881—21no—
16C4×D596—22no—
17C2×C4×Dic149—21no—
18C2×C4×Dic149C2211yescharacteristic
19C42×D149—22no—
20C42×D149—22no—
21#18011839—22no—
22#18011837—22no—
23#18011823—22no—
24C2×M16×C149C2211yescharacteristic
25#117×C149C2211yescharacteristic
26C2×C42×C149C2211yescharacteristic
27C23×D149D411yescharacteristic
28#14558736—21no—
29#14558736—21no—
30#14558736—21no—
31#14558736—21no—
32C2×Dic298C2×C411yescharacteristic, complemented
33C2×D596—22no—
34C2×D596C2×C411yescharacteristic, complemented
35C2×C22⋊D149—21no—
36C22×Dic149—21no—
37C22×Dic149D411yescharacteristic
38C2×C4×D149—28no—
39C2×C4×D149—24no—
40C2×C4×D149—21no—
41C2×C4×D149—21no—
42C2×C4×D149—21no—
43C2×C4×D149—21no—
44C2×C4×D149—21no—
45C2×C4×D149C2×C412yes—
46C2×C4×D149D412yes—
47#14558720—21no—
48#14558720—21no—
49C2×#11924746—21no—
50C4⋊Dic149—22no—
51#14558713—22no—
52#14558713—22no—
53C4×Dic149—24no—
54C4×Dic149—21no—
55C4×Dic149D412yescomplemented
56C22×C4×C149—21no—
57C22×C4×C149C2311yescharacteristic
58M16×C149—21no—
59M16×C149—21no—
60C2×C8×C149—21no—
61C4⋊C4×C149C2×C412yescomplemented
62C22⋊C4×C149—21no—
63C42×C149—21no—
64C42×C149—21no—
65C42×C149D412yescomplemented
66C22×D149—21no—
67C22×D149—21no—
68C22×D149—24no—
69C22×D149—21no—
70C22×D149C22⋊C412yes—
71Dic298—21no—
72Dic298—21no—
73D596—21no—
74D596—21no—
75D596—44no—
76C22⋊D149—41no—
77C22⋊D149—41no—
78C2×Dic149—24no—
79C2×Dic149—22no—
80C2×Dic149—21no—
81C2×Dic149—21no—
82C2×Dic149—21no—
83C2×Dic149C22⋊C412yes—
84C4×D149—216no—
85C4×D149—22no—
86C4×D149—22no—
87C4×D149—22no—
88C4×D149—22no—
89C4×D149—41no—
90C4×D149—41no—
91#11924746—41no—
92C23×C149C2×D411yescharacteristic
93C2×C4×C149—24no—
94C2×C4×C149—22no—
95C2×C4×C149—22no—
96C2×C4×C149C22×C411yescharacteristic
97C2×C4×C149C2×D411yescharacteristic
98C2×C4×C149C2×D411yescharacteristic
99C2×C4×C149C2×D411yescharacteristic
100C2×C4×C149#4111yescharacteristic
101C2×C4×C149#4111yescharacteristic
102C8×C149—41no—
103C22×C149—22no—
104C22×C149C2×C22⋊C411yescharacteristic
105C22×C149#12011yescharacteristic
106C22×C149#12311yescharacteristic
107C2×D149—24no—
108C2×D149—24no—
109C2×D149—22no—
110C2×D149—22no—
111C2×D149—41no—
112C2×D149—42no—
113C2×D149#10414yescomplemented
114C4×C149—24no—
115C4×C149—42no—
116C4×C149C4×D411yescharacteristic
117C4×C149C4×D411yescharacteristic
118C4×C149#12111yescharacteristic
119C4×C149#12111yescharacteristic
120Dic149—24no—
121Dic149—22no—
122Dic149—41no—
123C2×C149—21no—
124C2×C149—21no—
125C2×C149#38611yescharacteristic
126C2×C149C2×#10412yes—
127D149—24no—
128D149—81no—
129C149#189611yescharacteristic, complemented, Sylow
130#1896—1491nomaximal, Sylow
131#525—1491no—
132C22×C42—1491no—
133C2×#104—1491no—
134C2×#104—1491no—
135#407—1491no—
136#339—1491no—
137#339D14911yescharacteristic, complemented
138C2×#41—1491no—
139C23×C4—2981no—
140C23×C4—1491no—
141C2×M16—1491no—
142C2×M16C2×D14911yescharacteristic
143#123—2981no—
144C22⋊Q8—1492no—
145#121—1492no—
146#120—2981no—
147C4×D4—2982no—
148#117C2×D14911yescharacteristic
149C2×C42—2982no—
150C2×C42—2981no—
151C2×C42—2982no—
152C2×C42—1491no—
153C2×C42C2×D14911yescharacteristic
154#104—2982no—
155#104—2982no—
156C22⋊C8—2982no—
157C24—1491no—
158#41—2981no—
159#41—2981no—
160#41—2981no—
161#41—2981no—
162C2×Q8—1491no—
163C2×D4—2982no—
164C2×D4—2981no—
165C2×D4—1491no—
166C22×C4—21no—
167C22×C4—2984no—
168C22×C4—2988no—
169C22×C4—2981no—
170C22×C4—2981no—
171C22×C4—2981no—
172C22×C4—2981no—
173C22×C4—2981no—
174C22×C4—2981no—
175C22×C4—1491no—
176C22×C4—1492no—
177C22×C4—1492no—
178C22×C4C22×D14911yescharacteristic
179M16—21no—
180M16—21no—
181M16—2981no—
182M16—2981no—
183C2×C8—21no—
184C2×C8—2981no—
185C4⋊C4—2982no—
186C4⋊C4C4×D14912yescomplemented
187C22⋊C4—21no—
188C22⋊C4—2982no—
189C22⋊C4—2982no—
190C42—21no—
191C42—21no—
192C42—2984no—
193C42—2981no—
194C42—1492no—
195C42D59612yescomplemented
196C23—2984no—
197C23—2981no—
198C23—2981no—
199C23—2981no—
200C23—1492no—
201C23D4×D14911yescharacteristic
202Q8—2981no—
203Q8—2981no—
204D4—2981no—
205D4—2981no—
206D4—5964no—
207D4—5961no—
208D4—5961no—
209C2×C4—24no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—29816no—
213C2×C4—2984no—
214C2×C4—2981no—
215C2×C4—2982no—
216C2×C4—2981no—
217C2×C4—2982no—
218C2×C4—2982no—
219C2×C4—2982no—
220C2×C4—2982no—
221C2×C4—2981no—
222C2×C4—5961no—
223C2×C4—5961no—
224C2×C4—1492no—
225C2×C4C2×C4×D14911yescharacteristic
226C2×C4D4×D14911yescharacteristic
227C2×C4D4×D14911yescharacteristic
228C2×C4C2×D59611yescharacteristic
229C2×C4#1455873611yescharacteristic
230C2×C4#1455873711yescharacteristic
231C8—41no—
232C8—5961no—
233C22—22no—
234C22—2984no—
235C22—2984no—
236C22—2982no—
237C22—2982no—
238C22—5962no—
239C22—5961no—
240C22—1494no—
241C22C22⋊C4×D14911yescharacteristic
242C22#1801188111yescharacteristic
243C22#1801189611yescharacteristic
244C4—24no—
245C4—42no—
246C4—2984no—
247C4—2982no—
248C4—5961no—
249C4#1801187311yescharacteristic
250C4C4×D59611yescharacteristic
251C4#1801188411yescharacteristic
252C4#1801188611yescharacteristic
253C2—21no—
254C2—21no—
255C2—2984no—
256C2—11921no—
257C2#2374950311yescharacteristic
258C2#104×D14912yes—
subgroupG/H
centerC2×C4D4×D149
commutatorC2×C4×C149C22×C4
FrattiniC22×C4C22×D149
Fitting#339×C149C2
socleC22×C149C2×C22⋊C4
prime radical#23750137C2
cosocleC22×C4×C149C23
hypercenter#339D149
hypocenterC149#1896
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
2. C2×C42×D149C2semidirect
3. C2×#18011839C2semidirect
4. C2×#18011837C2semidirect
5. #23749588C2semidirect
6. #23749384C2semidirect
7. #339×C149C2semidirect
13. #18011891C4semidirect
14. #18011886C4semidirect
32. C2×Dic298C2×C4semidirect
34. C2×D596C2×C4semidirect
55. C4×Dic149D4semidirect
61. C4⋊C4×C149C2×C4semidirect
65. C42×C149D4semidirect
113. C2×D149#104semidirect
129. C149#1896semidirect
137. #339D149semidirect
186. C4⋊C4C4×D149semidirect
195. C42D596semidirect

Maximal subgroups

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

subgroupindex
#237501372
C2×C42×D1492
C2×#180118392
C2×#180118372
#237495882
#237493842
#339×C1492
#1896149