Finite Group Databasebeta

← #34054090

Subgroups — #34054090

Order 19072.

800 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 800 conjugacy classes of subgroups — too many to draw. Only its 145 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×#18011956C211yesmaximal, characteristic, complemented
2#23750187C212yesmaximal, complemented
3#23750184C211yesmaximal, characteristic, complemented
4#23749816C214yesmaximal, complemented
5#23749813C214yesmaximal, complemented
6C2×#18011825C212yesmaximal, complemented
7C2×#99×C149C211yesmaximal, characteristic, complemented
8#18011956—22no—
9#18011956—24no—
10#18011956C2214yes—
11C2×#14558736—21no—
12C2×#14558735—22no—
13C22×C22⋊D149—21no—
14C22×C22⋊D149C2212yes—
15C22×C22⋊D149C2211yescharacteristic, complemented
16C2×D4×D149—22no—
17#18011895—22no—
18#18011895C2214yescomplemented
19#18011894—21no—
20#18011892C2212yescomplemented
21#18011885—24no—
22#18011883—22no—
23#18011881—22no—
24#18011881C2214yescomplemented
25#18011880—21no—
26#18011879C2212yescomplemented
27C2×C22⋊Dic149C2211yescharacteristic, complemented
28#18011825C2218yescomplemented
29C22×D4×C149C2211yescharacteristic
30C2×C22⋊C4×C149C2212yescomplemented
31#99×C149C2214yescomplemented
32C23×D149—21no—
33C23×D149D412yescomplemented
34C23×D149C2311yescharacteristic, complemented
35#14558736—24no—
36#14558736—24no—
37#14558735—28no—
38#14558735—28no—
39C2×Dic298—21no—
40C2×D596—21no—
41C2×D596—24no—
42C2×C22⋊D149—22no—
43C2×C22⋊D149—24no—
44C2×C22⋊D149—22no—
45C2×C22⋊D149—22no—
46C2×C22⋊D149—24no—
47C2×C22⋊D149—22no—
48C2×C22⋊D149—22no—
49C2×C22⋊D149—21no—
50C2×C22⋊D149—22no—
51C2×C22⋊D149—21no—
52C2×C22⋊D149—22no—
53C2×C22⋊D149—22no—
54C2×C22⋊D149D414yescomplemented
55C2×C22⋊D149C2314yes—
56D4×D149—28no—
57D4×D149—28no—
58C22×Dic149—21no—
59C22×Dic149—21no—
60C22×Dic149D412yescomplemented
61C22×Dic149C2311yescharacteristic, complemented
62C2×C4×D149—22no—
63C4⋊Dic149—24no—
64#14558715—22no—
65C22⋊Dic149—21no—
66C22⋊Dic149—22no—
67C22⋊Dic149C2312yescomplemented
68#14558713—24no—
69#14558713—24no—
70#14558713—22no—
71C24×C149D411yescharacteristic, complemented
72C24×C149C2311yescharacteristic
73C2×D4×C149—22no—
74C2×D4×C149—22no—
75C2×D4×C149D412yescomplemented
76C2×D4×C149C2312yes—
77C22×C4×C149—22no—
78C22×C4×C149D411yescharacteristic, complemented
79C22⋊C4×C149—22no—
80C22⋊C4×C149C2314yescomplemented
81C22×D149—22no—
82C22×D149—24no—
83C22×D149—22no—
84C22×D149—21no—
85C22×D149—22no—
86C22×D149—81no—
87C22×D149—82no—
88C22×D149—82no—
89C22×D149C2×D414yes—
90Dic298—24no—
91D596—24no—
92D596—84no—
93C22⋊D149—28no—
94C22⋊D149—24no—
95C22⋊D149—24no—
96C22⋊D149—24no—
97C22⋊D149—24no—
98C22⋊D149—41no—
99C22⋊D149—41no—
100C22⋊D149—42no—
101C22⋊D149—82no—
102C2×Dic149—24no—
103C2×Dic149—22no—
104C2×Dic149—22no—
105C2×Dic149—22no—
106C2×Dic149—22no—
107C2×Dic149—21no—
108C2×Dic149—81no—
109C2×Dic149C2×D414yes—
110C4×D149—28no—
111C23×C149—21no—
112C23×C149—21no—
113C23×C149—81no—
114C23×C149—81no—
115C23×C149C2×D412yes—
116C23×C149C2×D412yes—
117C23×C149C2×D412yes—
118C23×C149C2×D411yescharacteristic
119C23×C149C2×D411yescharacteristic
120C23×C149C2411yescharacteristic
121D4×C149—24no—
122D4×C149—24no—
123C2×C4×C149—21no—
124C2×C4×C149—21no—
125C2×C4×C149—24no—
126C2×C4×C149—82no—
127C2×C4×C149C2×D412yes—
128C22×C149—22no—
129C22×C149—42no—
130C22×C149—41no—
131C22×C149—41no—
132C22×C149—42no—
133C22×C149—41no—
134C22×C149—42no—
135C22×C149—42no—
136C22×C149—81no—
137C22×C149#12011yescharacteristic
138C22×C149#12011yescharacteristic
139C22×C149#12012yes—
140C22×C149C22×D412yes—
141C22×C149C22×D411yescharacteristic
142C2×D149—24no—
143C2×D149—44no—
144C2×D149—44no—
145C2×D149—42no—
146C2×D149—44no—
147C2×D149—41no—
148C2×D149—82no—
149C2×D149—84no—
150C4×C149—22no—
151C4×C149—44no—
152Dic149—24no—
153Dic149—42no—
154Dic149—41no—
155C2×C149—21no—
156C2×C149—22no—
157C2×C149—21no—
158C2×C149—22no—
159C2×C149—21no—
160C2×C149—42no—
161C2×C149C2×#12011yescharacteristic
162D149—44no—
163D149—81no—
164C149#302611yescharacteristic, complemented, Sylow
165#3026—1491nomaximal, Sylow
166C2×H(5,𝔽2)—1491no—
167#534—1491no—
168#534—1492no—
169#458—1494no—
170B(4,𝔽2)—1494no—
171C2×#99—1492no—
172C2×#99D14911yescharacteristic, complemented
173H(5,𝔽2)—2984no—
174H(5,𝔽2)—2982no—
175H(5,𝔽2)—1494no—
176C2×#41—2982no—
177C2×#41—2981no—
178C22×D4—2982no—
179C22×D4—2981no—
180C22×D4—1491no—
181C22×D4—1492no—
182C22×D4C2×D14911yescharacteristic
183#123—2982no—
184#123—2981no—
185#123—1492no—
186#123—1494no—
187#121—2984no—
188#121—2982no—
189#120—2982no—
190#120—2981no—
191#120—1492no—
192#120—1494no—
193C2×C22⋊C4—1491no—
194C2×C22⋊C4C2×D14912yescomplemented
195#99—1498no—
196#99C2×D14914yescomplemented
197C24—2981no—
198C24—1491no—
199C24—1492no—
200C24D59611yescharacteristic, complemented
201C24C22×D14911yescharacteristic
202#41—2984no—
203#41—2988no—
204#41—2988no—
205#41—2984no—
206C2×Q8—2981no—
207C2×D4—22no—
208C2×D4—22no—
209C2×D4—2981no—
210C2×D4—2984no—
211C2×D4—2988no—
212C2×D4—2988no—
213C2×D4—2982no—
214C2×D4—2984no—
215C2×D4—2982no—
216C2×D4—2982no—
217C2×D4—2982no—
218C2×D4—2984no—
219C2×D4—2982no—
220C2×D4—2982no—
221C2×D4—2982no—
222C2×D4—2981no—
223C2×D4—2981no—
224C2×D4—2982no—
225C2×D4—1494no—
226C2×D4—1494no—
227C2×D4D59612yescomplemented
228C2×D4C22×D14912yes—
229C22×C4—22no—
230C22×C4—2982no—
231C22×C4—2981no—
232C22×C4—2981no—
233C22×C4—1491no—
234C22×C4—1492no—
235C22×C4D59611yescharacteristic, complemented
236C4⋊C4—2984no—
237C4⋊C4—2982no—
238C22⋊C4—22no—
239C22⋊C4—2984no—
240C22⋊C4—2984no—
241C22⋊C4—2981no—
242C22⋊C4—2982no—
243C22⋊C4—2982no—
244C22⋊C4—1492no—
245C22⋊C4C22×D14914yescomplemented
246C23—21no—
247C23—21no—
248C23—81no—
249C23—81no—
250C23—2984no—
251C23—2982no—
252C23—2982no—
253C23—2982no—
254C23—2981no—
255C23—1494no—
256C23—11921no—
257C23—11922no—
258C23—11922no—
259C23D4×D14912yes—
260C23D4×D14912yes—
261C23C2×D59612yes—
262C23C2×D59611yescharacteristic
263C23C2×D59611yescharacteristic
264C23C23×D14911yescharacteristic
265Q8—2984no—
266D4—24no—
267D4—24no—
268D4—2984no—
269D4—2988no—
270D4—2984no—
271D4—2984no—
272D4—2984no—
273D4—2984no—
274D4—5961no—
275D4—5961no—
276D4—5962no—
277D4—11924no—
278D4—11922no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—24no—
282C2×C4—82no—
283C2×C4—2988no—
284C2×C4—2984no—
285C2×C4—2982no—
286C2×C4—2982no—
287C2×C4—2982no—
288C2×C4—2982no—
289C2×C4—2981no—
290C2×C4—1494no—
291C2×C4—11921no—
292C2×C4C2×D59612yes—
293C22—22no—
294C22—42no—
295C22—41no—
296C22—41no—
297C22—42no—
298C22—41no—
299C22—42no—
300C22—42no—
301C22—81no—
302C22—2984no—
303C22—5964no—
304C22—5964no—
305C22—5964no—
306C22—5962no—
307C22—5961no—
308C22—11922no—
309C22—11924no—
310C22#1801188111yescharacteristic
311C22#1801188111yescharacteristic
312C22#1801188112yes—
313C22C2×D4×D14912yes—
314C22C22×D59611yescharacteristic
315C4—22no—
316C4—44no—
317C4—2984no—
318C4—5962no—
319C4—5961no—
320C2—22no—
321C2—21no—
322C2—21no—
323C2—21no—
324C2—22no—
325C2—42no—
326C2—5964no—
327C2—11921no—
328C2C2×#1801188111yescharacteristic
subgroupG/H
centerC2C2×#18011881
commutator, cosocleC23×C149C24
FrattiniC23C23×D149
FittingC2×#99×C149C2
socleC2×C149C2×#120
hypercenterC2×#99D149
hypocenterC149#3026
LCSG ▷ C23×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
1. C2×#18011956C2semidirect
2. #23750187C2semidirect
3. #23750184C2semidirect
4. #23749816C2semidirect
5. #23749813C2semidirect
6. C2×#18011825C2semidirect
7. C2×#99×C149C2semidirect
15. C22×C22⋊D149C22semidirect
18. #18011895C22semidirect
20. #18011892C22semidirect
24. #18011881C22semidirect
26. #18011879C22semidirect
27. C2×C22⋊Dic149C22semidirect
28. #18011825C22semidirect
30. C2×C22⋊C4×C149C22semidirect
31. #99×C149C22semidirect
33. C23×D149D4semidirect
34. C23×D149C23semidirect
54. C2×C22⋊D149D4semidirect
60. C22×Dic149D4semidirect
61. C22×Dic149C23semidirect
67. C22⋊Dic149C23semidirect
71. C24×C149D4semidirect
75. C2×D4×C149D4semidirect
78. C22×C4×C149D4semidirect
80. C22⋊C4×C149C23semidirect
164. C149#3026semidirect
172. C2×#99D149semidirect
194. C2×C22⋊C4C2×D149semidirect
196. #99C2×D149semidirect
200. C24D596semidirect
227. C2×D4D596semidirect
235. C22×C4D596semidirect
245. C22⋊C4C22×D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119562
#237501872
#237501842
#237498162
#237498132
C2×#180118252
C2×#99×C1492
#3026149