Finite Group Databasebeta

← #34078509

Subgroups — #34078509

Order 19328.

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×#18012784C211yesmaximal, characteristic, complemented
2#23752774C212yesmaximal, complemented
3#23752771C211yesmaximal, characteristic, complemented
4#23752403C214yesmaximal, complemented
5#23752400C214yesmaximal, complemented
6C2×#18012653C212yesmaximal, complemented
7C2×#99×C151C211yesmaximal, characteristic, complemented
8#18012784—22no—
9#18012784—24no—
10#18012784C2214yes—
11C2×#14559004—21no—
12C2×#14559003—22no—
13C22×C22⋊D151—21no—
14C22×C22⋊D151C2212yes—
15C22×C22⋊D151C2211yescharacteristic, complemented
16C2×D4×D151—22no—
17#18012723—22no—
18#18012723C2214yescomplemented
19#18012722—21no—
20#18012720C2212yescomplemented
21#18012713—24no—
22#18012711—22no—
23#18012709—22no—
24#18012709C2214yescomplemented
25#18012708—21no—
26#18012707C2212yescomplemented
27C2×C22⋊Dic151C2211yescharacteristic, complemented
28#18012653C2218yescomplemented
29C22×D4×C151C2211yescharacteristic
30C2×C22⋊C4×C151C2212yescomplemented
31#99×C151C2214yescomplemented
32C23×D151—21no—
33C23×D151D412yescomplemented
34C23×D151C2311yescharacteristic, complemented
35#14559004—24no—
36#14559004—24no—
37#14559003—28no—
38#14559003—28no—
39C2×Dic302—21no—
40C2×D604—21no—
41C2×D604—24no—
42C2×C22⋊D151—22no—
43C2×C22⋊D151—24no—
44C2×C22⋊D151—22no—
45C2×C22⋊D151—22no—
46C2×C22⋊D151—24no—
47C2×C22⋊D151—22no—
48C2×C22⋊D151—22no—
49C2×C22⋊D151—21no—
50C2×C22⋊D151—22no—
51C2×C22⋊D151—21no—
52C2×C22⋊D151—22no—
53C2×C22⋊D151—22no—
54C2×C22⋊D151D414yescomplemented
55C2×C22⋊D151C2314yes—
56D4×D151—28no—
57D4×D151—28no—
58C22×Dic151—21no—
59C22×Dic151—21no—
60C22×Dic151D412yescomplemented
61C22×Dic151C2311yescharacteristic, complemented
62C2×C4×D151—22no—
63C4⋊Dic151—24no—
64Dic151⋊C4—22no—
65C22⋊Dic151—21no—
66C22⋊Dic151—22no—
67C22⋊Dic151C2312yescomplemented
68(C2×D151)⋊C4—24no—
69(C2×D151)⋊C4—24no—
70(C2×D151)⋊C4—22no—
71C24×C151D411yescharacteristic, complemented
72C24×C151C2311yescharacteristic
73C2×D4×C151—22no—
74C2×D4×C151—22no—
75C2×D4×C151D412yescomplemented
76C2×D4×C151C2312yes—
77C22×C4×C151—22no—
78C22×C4×C151D411yescharacteristic, complemented
79C22⋊C4×C151—22no—
80C22⋊C4×C151C2314yescomplemented
81C22×D151—22no—
82C22×D151—24no—
83C22×D151—22no—
84C22×D151—21no—
85C22×D151—22no—
86C22×D151—81no—
87C22×D151—82no—
88C22×D151—82no—
89C22×D151C2×D414yes—
90Dic302—24no—
91D604—24no—
92D604—84no—
93C22⋊D151—28no—
94C22⋊D151—24no—
95C22⋊D151—24no—
96C22⋊D151—24no—
97C22⋊D151—24no—
98C22⋊D151—41no—
99C22⋊D151—41no—
100C22⋊D151—42no—
101C22⋊D151—82no—
102C2×Dic151—24no—
103C2×Dic151—22no—
104C2×Dic151—22no—
105C2×Dic151—22no—
106C2×Dic151—22no—
107C2×Dic151—21no—
108C2×Dic151—81no—
109C2×Dic151C2×D414yes—
110C4×D151—28no—
111C23×C151—21no—
112C23×C151—21no—
113C23×C151—81no—
114C23×C151—81no—
115C23×C151C2×D412yes—
116C23×C151C2×D412yes—
117C23×C151C2×D412yes—
118C23×C151C2×D411yescharacteristic
119C23×C151C2×D411yescharacteristic
120C23×C151C2411yescharacteristic
121D4×C151—24no—
122D4×C151—24no—
123C2×C4×C151—21no—
124C2×C4×C151—21no—
125C2×C4×C151—24no—
126C2×C4×C151—82no—
127C2×C4×C151C2×D412yes—
128C22×C151—22no—
129C22×C151—42no—
130C22×C151—41no—
131C22×C151—41no—
132C22×C151—42no—
133C22×C151—41no—
134C22×C151—42no—
135C22×C151—42no—
136C22×C151—81no—
137C22×C151#12011yescharacteristic
138C22×C151#12011yescharacteristic
139C22×C151#12012yes—
140C22×C151C22×D412yes—
141C22×C151C22×D411yescharacteristic
142C2×D151—24no—
143C2×D151—44no—
144C2×D151—44no—
145C2×D151—42no—
146C2×D151—44no—
147C2×D151—41no—
148C2×D151—82no—
149C2×D151—84no—
150C4×C151—22no—
151C4×C151—44no—
152Dic151—24no—
153Dic151—42no—
154Dic151—41no—
155C2×C151—21no—
156C2×C151—22no—
157C2×C151—21no—
158C2×C151—22no—
159C2×C151—21no—
160C2×C151—42no—
161C2×C151C2×#12011yescharacteristic
162D151—44no—
163D151—81no—
164C151#302611yescharacteristic, complemented, Sylow
165#3026—1511nomaximal, Sylow
166C2×H(5,𝔽2)—1511no—
167#534—1511no—
168#534—1512no—
169#458—1514no—
170B(4,𝔽2)—1514no—
171C2×#99—1512no—
172C2×#99D15111yescharacteristic, complemented
173H(5,𝔽2)—3024no—
174H(5,𝔽2)—3022no—
175H(5,𝔽2)—1514no—
176C2×#41—3022no—
177C2×#41—3021no—
178C22×D4—3022no—
179C22×D4—3021no—
180C22×D4—1511no—
181C22×D4—1512no—
182C22×D4C2×D15111yescharacteristic
183#123—3022no—
184#123—3021no—
185#123—1512no—
186#123—1514no—
187#121—3024no—
188#121—3022no—
189#120—3022no—
190#120—3021no—
191#120—1512no—
192#120—1514no—
193C2×C22⋊C4—1511no—
194C2×C22⋊C4C2×D15112yescomplemented
195#99—1518no—
196#99C2×D15114yescomplemented
197C24—3021no—
198C24—1511no—
199C24—1512no—
200C24D60411yescharacteristic, complemented
201C24C22×D15111yescharacteristic
202#41—3024no—
203#41—3028no—
204#41—3028no—
205#41—3024no—
206C2×Q8—3021no—
207C2×D4—22no—
208C2×D4—22no—
209C2×D4—3021no—
210C2×D4—3024no—
211C2×D4—3028no—
212C2×D4—3028no—
213C2×D4—3022no—
214C2×D4—3024no—
215C2×D4—3022no—
216C2×D4—3022no—
217C2×D4—3022no—
218C2×D4—3024no—
219C2×D4—3022no—
220C2×D4—3022no—
221C2×D4—3022no—
222C2×D4—3021no—
223C2×D4—3021no—
224C2×D4—3022no—
225C2×D4—1514no—
226C2×D4—1514no—
227C2×D4D60412yescomplemented
228C2×D4C22×D15112yes—
229C22×C4—22no—
230C22×C4—3022no—
231C22×C4—3021no—
232C22×C4—3021no—
233C22×C4—1511no—
234C22×C4—1512no—
235C22×C4D60411yescharacteristic, complemented
236C4⋊C4—3024no—
237C4⋊C4—3022no—
238C22⋊C4—22no—
239C22⋊C4—3024no—
240C22⋊C4—3024no—
241C22⋊C4—3021no—
242C22⋊C4—3022no—
243C22⋊C4—3022no—
244C22⋊C4—1512no—
245C22⋊C4C22×D15114yescomplemented
246C23—21no—
247C23—21no—
248C23—81no—
249C23—81no—
250C23—3024no—
251C23—3022no—
252C23—3022no—
253C23—3022no—
254C23—3021no—
255C23—1514no—
256C23—12081no—
257C23—12082no—
258C23—12082no—
259C23D4×D15112yes—
260C23D4×D15112yes—
261C23C2×D60412yes—
262C23C2×D60411yescharacteristic
263C23C2×D60411yescharacteristic
264C23C23×D15111yescharacteristic
265Q8—3024no—
266D4—24no—
267D4—24no—
268D4—3024no—
269D4—3028no—
270D4—3024no—
271D4—3024no—
272D4—3024no—
273D4—3024no—
274D4—6041no—
275D4—6041no—
276D4—6042no—
277D4—12084no—
278D4—12082no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—24no—
282C2×C4—82no—
283C2×C4—3028no—
284C2×C4—3024no—
285C2×C4—3022no—
286C2×C4—3022no—
287C2×C4—3022no—
288C2×C4—3022no—
289C2×C4—3021no—
290C2×C4—1514no—
291C2×C4—12081no—
292C2×C4C2×D60412yes—
293C22—22no—
294C22—42no—
295C22—41no—
296C22—41no—
297C22—42no—
298C22—41no—
299C22—42no—
300C22—42no—
301C22—81no—
302C22—3024no—
303C22—6044no—
304C22—6044no—
305C22—6044no—
306C22—6042no—
307C22—6041no—
308C22—12082no—
309C22—12084no—
310C22#1801270911yescharacteristic
311C22#1801270911yescharacteristic
312C22#1801270912yes—
313C22C2×D4×D15112yes—
314C22C22×D60411yescharacteristic
315C4—22no—
316C4—44no—
317C4—3024no—
318C4—6042no—
319C4—6041no—
320C2—22no—
321C2—21no—
322C2—21no—
323C2—21no—
324C2—22no—
325C2—42no—
326C2—6044no—
327C2—12081no—
328C2C2×#1801270911yescharacteristic
subgroupG/H
centerC2C2×#18012709
commutator, cosocleC23×C151C24
FrattiniC23C23×D151
FittingC2×#99×C151C2
socleC2×C151C2×#120
hypercenterC2×#99D151
hypocenterC151#3026
LCSG ▷ C23×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
1. C2×#18012784C2semidirect
2. #23752774C2semidirect
3. #23752771C2semidirect
4. #23752403C2semidirect
5. #23752400C2semidirect
6. C2×#18012653C2semidirect
7. C2×#99×C151C2semidirect
15. C22×C22⋊D151C22semidirect
18. #18012723C22semidirect
20. #18012720C22semidirect
24. #18012709C22semidirect
26. #18012707C22semidirect
27. C2×C22⋊Dic151C22semidirect
28. #18012653C22semidirect
30. C2×C22⋊C4×C151C22semidirect
31. #99×C151C22semidirect
33. C23×D151D4semidirect
34. C23×D151C23semidirect
54. C2×C22⋊D151D4semidirect
60. C22×Dic151D4semidirect
61. C22×Dic151C23semidirect
67. C22⋊Dic151C23semidirect
71. C24×C151D4semidirect
75. C2×D4×C151D4semidirect
78. C22×C4×C151D4semidirect
80. C22⋊C4×C151C23semidirect
164. C151#3026semidirect
172. C2×#99D151semidirect
194. C2×C22⋊C4C2×D151semidirect
196. #99C2×D151semidirect
200. C24D604semidirect
227. C2×D4D604semidirect
235. C22×C4D604semidirect
245. C22⋊C4C22×D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127842
#237527742
#237527712
#237524032
#237524002
C2×#180126532
C2×#99×C1512
#3026151