Finite Group Databasebeta

← #34078718

Subgroups — #34078718

Order 19328.

500 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 133 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×#18012759C211yesmaximal, characteristic, complemented
2C22×#14558987C211yesmaximal, characteristic, complemented
3#23752724C211yesmaximal, characteristic, complemented
4#23752719C211yesmaximal, characteristic, complemented
5#23752469C212yesmaximal, complemented
6#23752464C212yesmaximal, complemented
7#23752461C212yesmaximal, complemented
8#23752457C212yesmaximal, complemented
9#23752248C211yesmaximal, characteristic, complemented
10#23752209C211yesmaximal, characteristic, complemented
11#416×C151C211yesmaximal, characteristic, complemented
12C2×#14559004C2211yescharacteristic
13C22×C4×D151C2211yescharacteristic
14#18012759—24no—
15C2×#14558994C2211yescharacteristic, complemented
16C2×#14558992C2211yescharacteristic, complemented
17C2×#14558991C2211yescharacteristic, complemented
18C2×#14558989C2211yescharacteristic, complemented
19C2×#14558987—24no—
20C2×#14558987C2212yes—
21C2×#14558987C2212yes—
22C22×C151⋊C8C2211yescharacteristic
23#18012723—21no—
24#18012720—21no—
25#18012719C2212yes—
26#18012715C2212yes—
27#18012714C2212yes—
28#18012710C2212yes—
29#18012709—21no—
30#18012707—21no—
31C4×D604—22no—
32C4×C22⋊D151—22no—
33#18012698C2211yescharacteristic
34#18012672C2212yescomplemented
35#18012670C2212yescomplemented
36#18012664C2212yescomplemented
37#18012661C2212yescomplemented
38C2×#41×C151C2211yescharacteristic
39C22×C8×C151C2211yescharacteristic
40#117×C151C2211yescharacteristic
41#103×C151C2212yescomplemented
42#102×C151C2212yescomplemented
43C23×D151D411yescharacteristic
44#14559004—22no—
45#14559004—22no—
46C2×Dic302C2311yescharacteristic
47C2×D604—22no—
48C2×D604C2311yescharacteristic
49C2×C22⋊D151—22no—
50C2×C22⋊D151—21no—
51C22×Dic151D411yescharacteristic
52C2×C4×D151—22no—
53C2×C4×D151—21no—
54C2×C4×D151—22no—
55C2×C4×D151D412yes—
56C2×C4×D151C2312yes—
57#14558994—22no—
58#14558992—22no—
59#14558991—22no—
60#14558989—22no—
61#14558987—24no—
62#14558987—24no—
63C2×C151⋊C8D414yescomplemented
64C2×C151⋊C8C2311yescharacteristic
65C2×C151⋊C8C2311yescharacteristic
66C4⋊Dic151—22no—
67C4⋊Dic151C2312yes—
68Dic151⋊C4—22no—
69C22⋊Dic151—22no—
70C22⋊Dic151—21no—
71(C2×D151)⋊C4—22no—
72(C2×D151)⋊C4—22no—
73(C2×D151)⋊C4—22no—
74C4×Dic151—21no—
75#41×C151—22no—
76#41×C151—22no—
77C2×Q8×C151C2311yescharacteristic
78C2×D4×C151—21no—
79C2×D4×C151C2311yescharacteristic
80C22×C4×C151—21no—
81C22×C4×C151C2311yescharacteristic
82C2×C8×C151—22no—
83C2×C8×C151C2312yes—
84C4⋊C4×C151C2312yes—
85C22⋊C4×C151—21no—
86C42×C151—21no—
87C22×D151—22no—
88C22×D151—21no—
89C22×D151—42no—
90C22×D151C2×D412yes—
91Dic302—21no—
92Dic302—21no—
93D604—21no—
94D604—21no—
95D604—44no—
96C22⋊D151—44no—
97C22⋊D151—42no—
98C2×Dic151—22no—
99C2×Dic151—22no—
100C2×Dic151—21no—
101C2×Dic151C2×D412yes—
102C4×D151—24no—
103C4×D151—22no—
104C4×D151—22no—
105C4×D151—42no—
106C151⋊C8C2×D412yes—
107C151⋊C8C2×D412yes—
108C23×C151—21no—
109C23×C151C2×D411yescharacteristic
110Q8×C151—21no—
111Q8×C151—21no—
112D4×C151—21no—
113D4×C151—21no—
114D4×C151—42no—
115C2×C4×C151—21no—
116C2×C4×C151—22no—
117C2×C4×C151—42no—
118C2×C4×C151C2×D412yes—
119C2×C4×C151C2×D411yescharacteristic
120C2×C4×C151#4112yes—
121C2×C4×C151C2411yescharacteristic
122C8×C151—22no—
123C22×C151—22no—
124C22×C151—41no—
125C22×C151—42no—
126C22×C151#12112yes—
127C22×C151C22×D411yescharacteristic
128C2×D151—22no—
129C2×D151—22no—
130C2×D151—22no—
131C2×D151—44no—
132C2×D151—41no—
133C2×D151—42no—
134C4×C151—41no—
135C4×C151—42no—
136C4×C151#12112yes—
137C4×C151C22×D411yescharacteristic
138C4×C151C2×#4111yescharacteristic
139Dic151—22no—
140Dic151—41no—
141Dic151—42no—
142C2×C151—22no—
143C2×C151—81no—
144C2×C151C2×#12111yescharacteristic
145C2×C151#57512yes—
146D151—42no—
147D151—81no—
148C151#305411yescharacteristic, complemented, Sylow
149#3054—1511nomaximal, Sylow
150C2×#135—1511no—
151C22×M16—1511no—
152#525—1511no—
153#525—1511no—
154#470—1512no—
155#469—1512no—
156#468—1512no—
157#468—1512no—
158#427—1511no—
159#416—1511no—
160#416D15111yescharacteristic, complemented
161C2×#41—1511no—
162C2×#41C2×D15111yescharacteristic
163C23×C4—1511no—
164#135—3024no—
165C2×Q16—1511no—
166C2×SD16—1511no—
167C2×SD16—1511no—
168C2×D8—1511no—
169C2×M16—3024no—
170C2×M16—1512no—
171C2×M16—1512no—
172C22×C8—1511no—
173C22×C8C2×D15111yescharacteristic
174#123—3021no—
175#123—3021no—
176C22⋊Q8—1512no—
177C22⋊Q8—1512no—
178#121—1512no—
179#121—1512no—
180#120—3021no—
181#120—3021no—
182C4×D4—3022no—
183C4×D4—3022no—
184#117—1511no—
185#117C2×D15111yescharacteristic
186#107—1512no—
187#106—1512no—
188#103—1512no—
189#103C2×D15112yescomplemented
190#102—1512no—
191#102C2×D15112yescomplemented
192C24—1511no—
193#41—22no—
194#41—22no—
195#41—3022no—
196#41—3022no—
197C2×Q8—1511no—
198C2×Q8C22×D15111yescharacteristic
199C2×D4—21no—
200C2×D4—3022no—
201C2×D4—3022no—
202C2×D4—3021no—
203C2×D4—1511no—
204C2×D4C22×D15111yescharacteristic
205C22×C4—21no—
206C22×C4—3022no—
207C22×C4—3022no—
208C22×C4—3021no—
209C22×C4—1511no—
210C22×C4—1512no—
211C22×C4—1512no—
212C22×C4C22×D15111yescharacteristic
213Q16—3022no—
214SD16—3022no—
215SD16—3022no—
216D8—3022no—
217M16—3024no—
218M16—3024no—
219C2×C8—22no—
220C2×C8—1514no—
221C2×C8—1511no—
222C2×C8—1511no—
223C2×C8C22×D15112yes—
224C4⋊C4—3022no—
225C4⋊C4—3022no—
226C4⋊C4—1512no—
227C4⋊C4C22×D15112yes—
228C22⋊C4—21no—
229C22⋊C4—3022no—
230C22⋊C4—3022no—
231C22⋊C4—3022no—
232C22⋊C4—3021no—
233C22⋊C4—3022no—
234C42—21no—
235C42—3021no—
236C23—21no—
237C23—3022no—
238C23—3021no—
239C23—6042no—
240C23—1512no—
241C23D4×D15111yescharacteristic
242Q8—21no—
243Q8—21no—
244Q8—3021no—
245Q8—3021no—
246D4—21no—
247D4—21no—
248D4—42no—
249D4—3021no—
250D4—3021no—
251D4—6044no—
252D4—6044no—
253D4—6042no—
254C2×C4—22no—
255C2×C4—21no—
256C2×C4—42no—
257C2×C4—3022no—
258C2×C4—3024no—
259C2×C4—3022no—
260C2×C4—3022no—
261C2×C4—3022no—
262C2×C4—3021no—
263C2×C4—6042no—
264C2×C4—1512no—
265C2×C4D4×D15112yes—
266C2×C4D4×D15111yescharacteristic
267C2×C4#1455900412yes—
268C2×C4C23×D15111yescharacteristic
269C8—22no—
270C8—1512no—
271C8—1512no—
272C22—22no—
273C22—42no—
274C22—41no—
275C22—3022no—
276C22—3022no—
277C22—3022no—
278C22—6044no—
279C22—6042no—
280C22—6041no—
281C22#1801271212yes—
282C22C2×D4×D15111yescharacteristic
283C4—42no—
284C4—41no—
285C4—3022no—
286C4—6042no—
287C4—6041no—
288C4#1801271212yes—
289C4C2×D4×D15111yescharacteristic
290C4C2×#1455900411yescharacteristic
291C2—22no—
292C2—81no—
293C2—6042no—
294C2—12081no—
295C2C2×#1801271211yescharacteristic
296C2#2375300912yes—
subgroupG/H
centerC2×C4D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#416×C151C2
socleC22×C151C22×D4
hypercenter#416D151
hypocenterC151#3054
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. C2×#18012759C2semidirect
2. C22×#14558987C2semidirect
3. #23752724C2semidirect
4. #23752719C2semidirect
5. #23752469C2semidirect
6. #23752464C2semidirect
7. #23752461C2semidirect
8. #23752457C2semidirect
9. #23752248C2semidirect
10. #23752209C2semidirect
11. #416×C151C2semidirect
15. C2×#14558994C22semidirect
16. C2×#14558992C22semidirect
17. C2×#14558991C22semidirect
18. C2×#14558989C22semidirect
34. #18012672C22semidirect
35. #18012670C22semidirect
36. #18012664C22semidirect
37. #18012661C22semidirect
41. #103×C151C22semidirect
42. #102×C151C22semidirect
63. C2×C151⋊C8D4semidirect
148. C151#3054semidirect
160. #416D151semidirect
189. #103C2×D151semidirect
191. #102C2×D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127592
C22×#145589872
#237527242
#237527192
#237524692
#237524642
#237524612
#237524572
#237522482
#237522092
#416×C1512
#3054151