Finite Group Databasebeta

← #34043639

Subgroups — #34043639

Order 19072.

320 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 49 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#23750213C211yesmaximal, characteristic, complemented
2#23749778C211yesmaximal, characteristic, complemented
3#23749761C211yesmaximal, characteristic, complemented
4#23749534C211yesmaximal, characteristic, complemented
5#23749363C211yesmaximal, characteristic, complemented
6#23749360C211yesmaximal, characteristic, complemented
7#323×C149C211yesmaximal, characteristic, complemented
8C22×D596C2211yescharacteristic
9C22×C22⋊D149—21no—
10C2×#14558725—21no—
11C2×D1192—21no—
12#18011904—21no—
13#18011897—21no—
14#18011893—21no—
15#18011890C2211yescharacteristic
16#18011885C2211yescharacteristic
17#18011884—21no—
18#18011880—21no—
19C4×C22⋊D149—21no—
20C2×#14558713—21no—
21#18011833—21no—
22#18011833—21no—
23#18011818C2211yescharacteristic
24C2×C22⋊C4×C149C2211yescharacteristic
25C22⋊C8×C149C2211yescharacteristic
26C22⋊C8×C149C2211yescharacteristic
27C23×D149—21no—
28C2×Dic298D411yescharacteristic, complemented
29C2×D596—21no—
30C2×D596—21no—
31C2×D596—42no—
32C2×D596D411yescharacteristic, complemented
33C2×C22⋊D149—21no—
34C2×C22⋊D149—21no—
35C2×C22⋊D149—21no—
36C2×C22⋊D149—42no—
37C2×C22⋊D149—42no—
38C2×C22⋊D149—42no—
39C22×Dic149—21no—
40C2×C4×D149—21no—
41#14558725—42no—
42D1192—42no—
43C4⋊Dic149D411yescharacteristic, complemented
44C4⋊Dic149D411yescharacteristic, complemented
45#14558715—21no—
46#14558715—21no—
47C22⋊Dic149—21no—
48C22⋊Dic149—21no—
49C22⋊Dic149—21no—
50#14558713—21no—
51#14558713—21no—
52#14558713—42no—
53C4×Dic149—21no—
54C24×C149D411yescharacteristic
55C22×C4×C149D411yescharacteristic
56C22×C4×C149C2311yescharacteristic
57C2×C8×C149—21no—
58C2×C8×C149—21no—
59C22⋊C4×C149—21no—
60C22⋊C4×C149—21no—
61C22×D149—22no—
62C22×D149—21no—
63C22×D149—41no—
64C22×D149—41no—
65C22×D149—41no—
66C22×D149—41no—
67C22×D149—41no—
68C22×D149—41no—
69Dic298—41no—
70D596—22no—
71D596—22no—
72D596—41no—
73D596—41no—
74D596—41no—
75C22⋊D149—48no—
76C22⋊D149—41no—
77C22⋊D149—41no—
78C22⋊D149—81no—
79C22⋊D149—81no—
80C2×Dic149—22no—
81C2×Dic149—21no—
82C2×Dic149—21no—
83C2×Dic149—21no—
84C2×Dic149—41no—
85C2×Dic149—41no—
86C4×D149—81no—
87C23×C149—21no—
88C23×C149—21no—
89C23×C149—21no—
90C23×C149—41no—
91C23×C149—41no—
92C23×C149C2×D411yescharacteristic
93C2×C4×C149—21no—
94C2×C4×C149—41no—
95C2×C4×C149—41no—
96C2×C4×C149C2×D411yescharacteristic
97C2×C4×C149C2×D411yescharacteristic
98C8×C149—41no—
99C8×C149—41no—
100C22×C149—21no—
101C22×C149—21no—
102C22×C149—42no—
103C22×C149—41no—
104C22×C149—41no—
105C22×C149—41no—
106C22×C149—81no—
107C22×C149#12011yescharacteristic
108C22×C149#13511yescharacteristic
109C22×C149AGL(1,ℤ/8)11yescharacteristic
110C2×D149—42no—
111C2×D149—42no—
112C2×D149—41no—
113C2×D149—41no—
114C2×D149—41no—
115C2×D149—42no—
116C2×D149—81no—
117C2×D149—81no—
118C2×D149—81no—
119C2×D149—81no—
120C4×C149—21no—
121C4×C149—21no—
122C4×C149—41no—
123Dic149—42no—
124Dic149—41no—
125Dic149—41no—
126Dic149—41no—
127C2×C149—21no—
128C2×C149—21no—
129C2×C149—81no—
130C2×C149#44911yescharacteristic
131C2×C149#45311yescharacteristic
132C2×C149B(4,𝔽2)11yescharacteristic
133D149—81no—
134D149—82no—
135C149#160011yescharacteristic, complemented, Sylow
136#1600—1491nomaximal, Sylow
137#538—1491no—
138#450—1491no—
139#447—1491no—
140#392—1491no—
141#328—1491no—
142#327—1491no—
143#323D14911yescharacteristic, complemented
144C22×D4—2981no—
145C22×D4—1491no—
146C2×SD16—2981no—
147C2×D8—2981no—
148#126—2981no—
149#124—2981no—
150#123—2981no—
151C22⋊Q8—1491no—
152#121—2981no—
153#121—1491no—
154#120—2981no—
155C4×D4—2981no—
156C2×C22⋊C4—2981no—
157C2×C22⋊C4C2×D14911yescharacteristic
158#102—2981no—
159#102—2981no—
160C22⋊C8C2×D14911yescharacteristic
161C22⋊C8C2×D14911yescharacteristic
162#95—1491no—
163C24—2981no—
164C24D59611yescharacteristic
165C2×Q8—1491no—
166C2×D4—2981no—
167C2×D4—2981no—
168C2×D4—2981no—
169C2×D4—2981no—
170C2×D4—2981no—
171C2×D4—5962no—
172C2×D4—5962no—
173C2×D4—5962no—
174C2×D4—5962no—
175C2×D4—1491no—
176C22×C4—2981no—
177C22×C4—2981no—
178C22×C4D59611yescharacteristic
179C22×C4C22×D14911yescharacteristic
180SD16—5962no—
181D8—5962no—
182C2×C8—21no—
183C2×C8—21no—
184C4⋊C4—2981no—
185C4⋊C4—2981no—
186C4⋊C4—1491no—
187C4⋊C4—1491no—
188C22⋊C4—21no—
189C22⋊C4—21no—
190C22⋊C4—2981no—
191C22⋊C4—2981no—
192C22⋊C4—2981no—
193C22⋊C4—2981no—
194C22⋊C4—2981no—
195C22⋊C4—5962no—
196C42—2981no—
197C23—21no—
198C23—21no—
199C23—21no—
200C23—41no—
201C23—41no—
202C23—2982no—
203C23—2981no—
204C23—5961no—
205C23—5961no—
206C23—5961no—
207C23—5961no—
208C23—5961no—
209C23—5961no—
210C23C2×D59611yescharacteristic
211Q8—5961no—
212D4—2982no—
213D4—2982no—
214D4—5961no—
215D4—5961no—
216D4—5961no—
217D4—5968no—
218D4—5961no—
219D4—5961no—
220D4—11921no—
221D4—11921no—
222C2×C4—21no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—2982no—
226C2×C4—2981no—
227C2×C4—2981no—
228C2×C4—2981no—
229C2×C4—5961no—
230C2×C4—5961no—
231C2×C4—11921no—
232C2×C4D4×D14911yescharacteristic
233C2×C4D4×D14911yescharacteristic
234C8—41no—
235C8—41no—
236C22—21no—
237C22—21no—
238C22—42no—
239C22—41no—
240C22—41no—
241C22—41no—
242C22—81no—
243C22—5962no—
244C22—5962no—
245C22—5961no—
246C22—5961no—
247C22—5962no—
248C22—5961no—
249C22—11921no—
250C22—11921no—
251C22—11921no—
252C22—11921no—
253C22#1801188111yescharacteristic
254C22#1801193311yescharacteristic
255C22#1801193911yescharacteristic
256C4—21no—
257C4—21no—
258C4—41no—
259C4—5962no—
260C4—5961no—
261C4—5961no—
262C4—5961no—
263C2—21no—
264C2—21no—
265C2—81no—
266C2—11922no—
267C2—11921no—
268C2#2374977211yescharacteristic
269C2#2374979511yescharacteristic
270C2#2374981311yescharacteristic
subgroupG/H
centerC22#18011881
commutator, cosocleC22×C4×C149C23
FrattiniC22×C4C22×D149
Fitting#323×C149C2
socleC22×C149#120
hypercenter#323D149
hypocenterC149#1600
LCSG ▷ C22×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
1. #23750213C2semidirect
2. #23749778C2semidirect
3. #23749761C2semidirect
4. #23749534C2semidirect
5. #23749363C2semidirect
6. #23749360C2semidirect
7. #323×C149C2semidirect
28. C2×Dic298D4semidirect
32. C2×D596D4semidirect
43. C4⋊Dic149D4semidirect
44. C4⋊Dic149D4semidirect
135. C149#1600semidirect
143. #323D149semidirect

Maximal subgroups

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

subgroupindex
#237502132
#237497782
#237497612
#237495342
#237493632
#237493602
#323×C1492
#1600149