Finite Group Databasebeta

← #34082245

Subgroups — #34082245

Order 19328.

364 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 113 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×#18012762C211yesmaximal, characteristic, complemented
2#135×D151C211yesmaximal, characteristic, complemented
3#23752654C212yesmaximal, complemented
4#23752653C211yesmaximal, characteristic, complemented
5#23752650C211yesmaximal, characteristic, complemented
6#23752649C212yesmaximal, complemented
7#23752647C211yesmaximal, characteristic, complemented
8#23752645C212yesmaximal, complemented
9#23752643C212yesmaximal, complemented
10M32×D151C211yesmaximal, characteristic, complemented
11#510×C151C211yesmaximal, characteristic, complemented
12C2×#14559005—21no—
13#41×D151—21no—
14#18012762—21no—
15#18012762—21no—
16#18012762C2212yes—
17#18012762C2211yescharacteristic, complemented
18#18012762C2212yescomplemented
19#18012761C2211yescharacteristic
20#18012760—21no—
21#18012759—21no—
22#18012758C2211yescharacteristic, complemented
23Q16×D151C2211yescharacteristic, complemented
24C2×#14558991—21no—
25SD16×D151—21no—
26C2×D1208C2211yescharacteristic, complemented
27D8×D151C2211yescharacteristic, complemented
28C2×C8×D151C2211yescharacteristic
29#18012685C2212yescomplemented
30#18012684C2212yescomplemented
31#18012682C2212yescomplemented
32#18012682C2212yescomplemented
33D2416C2212yescomplemented
34#18012680C2212yescomplemented
35#18012679C2211yescharacteristic, complemented
36#18012678C2212yescomplemented
37C16×D151C2212yescomplemented
38#135×C151C2211yescharacteristic
39C2×Q16×C151C2211yescharacteristic, complemented
40Q32×C151C2212yescomplemented
41SD32×C151C2212yescomplemented
42M32×C151C2211yescharacteristic, complemented
43#14559005—21no—
44#14559005—22no—
45#14559005—22no—
46#14559005—41no—
47#14559005—41no—
48#14559004—21no—
49#14559004—41no—
50#14559003—21no—
51#14559003—41no—
52Q8×D151—21no—
53C2×D604—21no—
54C2×D604—41no—
55D4×D151—21no—
56D4×D151—41no—
57C2×C4×D151—41no—
58C2×C4×D151—41no—
59C2×C4×D151D411yescharacteristic
60Dic604C2311yescharacteristic
61#14558994—21no—
62#14558993—21no—
63#14558992—21no—
64#14558991—21no—
65#14558991—22no—
66#14558991—22no—
67D1208—21no—
68D1208C2312yes—
69D1208C2311yescharacteristic
70#14558989—21no—
71C2×C151⋊C8D411yescharacteristic
72C8×D151D411yescharacteristic
73C8×D151D411yescharacteristic
74C8×D151C2311yescharacteristic
75C8×D151C2311yescharacteristic
76C151⋊C16C2312yes—
77#41×C151—21no—
78C2×Q8×C151—21no—
79Q16×C151—21no—
80Q16×C151C2311yescharacteristic
81Q16×C151C2312yes—
82SD16×C151—21no—
83D8×C151C2311yescharacteristic
84C2×C8×C151C2311yescharacteristic
85C16×C151C2312yes—
86C22×D151—41no—
87C22×D151—41no—
88C22×D151D811yescharacteristic
89Dic302—21no—
90Dic302—41no—
91D604—21no—
92D604—22no—
93D604—41no—
94D604—42no—
95D604—42no—
96D604—41no—
97C22⋊D151—41no—
98C22⋊D151—41no—
99C22⋊D151—41no—
100C2×Dic151—41no—
101C2×Dic151D811yescharacteristic
102C4×D151—41no—
103C4×D151—41no—
104C4×D151—41no—
105C4×D151—42no—
106C4×D151—42no—
107C4×D151D811yescharacteristic
108C4×D151D811yescharacteristic
109C4×D151C2×D411yescharacteristic
110C4×D151C2×D411yescharacteristic
111C151⋊C8C2×D411yescharacteristic
112C151⋊C8C2×D411yescharacteristic
113Q8×C151—22no—
114Q8×C151—21no—
115Q8×C151—41no—
116D4×C151—21no—
117D4×C151—41no—
118C2×C4×C151—41no—
119C2×C4×C151—41no—
120C2×C4×C151C2×D411yescharacteristic
121C8×C151C2×D411yescharacteristic
122C8×C151C2411yescharacteristic
123C22×C151—41no—
124C22×C151C2×D811yescharacteristic
125C2×D151—41no—
126C2×D151—41no—
127C2×D151—42no—
128C2×D151—82no—
129C2×D151—82no—
130C2×D151C2×D811yescharacteristic
131C2×D151C2×D811yescharacteristic
132C4×C151—41no—
133C4×C151—42no—
134C4×C151C2×D811yescharacteristic
135C4×C151C22×D411yescharacteristic
136Dic151—41no—
137Dic151C2×D811yescharacteristic
138Dic151C2×D811yescharacteristic
139C2×C151—21no—
140C2×C151—81no—
141C2×C151C22×D811yescharacteristic
142D151—21no—
143D151—21no—
144D151—81no—
145D151—82no—
146C151#341411yescharacteristic, complemented, Sylow
147#3414—1511nomaximal, Sylow
148C2×#135—1511no—
149C2×#135—1511no—
150#510—1511no—
151#510—1512no—
152#510D15111yescharacteristic, complemented
153#509—1511no—
154#509—1512no—
155#509—1511no—
156#508—1512no—
157#508—1512no—
158C2×M32—1511no—
159C2×#41—3021no—
160C2×#41—3021no—
161#135—3021no—
162#135—3021no—
163#135—3021no—
164#135—3021no—
165#135—1512no—
166#135—1511no—
167#135—1512no—
168#135—1511no—
169#135—1511no—
170#135C2×D15111yescharacteristic
171C2×Q16—1511no—
172C2×Q16C2×D15111yescharacteristic, complemented
173C2×SD16—3021no—
174C2×SD16—3021no—
175C2×D8—1511no—
176C2×D8—1511no—
177C22×C8—1511no—
178Q32—1512no—
179Q32C2×D15112yescomplemented
180SD32—1512no—
181SD32—1512no—
182SD32—1512no—
183SD32C2×D15112yescomplemented
184D16—1512no—
185D16—1512no—
186M32—1511no—
187M32—1512no—
188M32C2×D15111yescharacteristic, complemented
189C2×C16—1512no—
190#41—21no—
191#41—3021no—
192#41—3022no—
193#41—3021no—
194#41—3022no—
195#41—3021no—
196#41—6041no—
197#41—6041no—
198#41—6041no—
199#41—6041no—
200C2×Q8—21no—
201C2×Q8—3021no—
202C2×D4—3021no—
203C2×D4—3021no—
204C2×D4—6041no—
205C2×D4—6041no—
206C22×C4—6041no—
207C22×C4—6041no—
208C22×C4—1511no—
209Q16—21no—
210Q16—3021no—
211Q16—1511no—
212Q16C22×D15111yescharacteristic
213Q16C22×D15112yes—
214SD16—21no—
215SD16—3021no—
216SD16—3022no—
217SD16—3021no—
218SD16—3022no—
219SD16—3021no—
220D8—3021no—
221D8—3021no—
222D8—1512no—
223D8—1511no—
224D8C22×D15111yescharacteristic
225C2×C8—1511no—
226C2×C8—1511no—
227C2×C8—1511no—
228C2×C8—1511no—
229C2×C8—1511no—
230C2×C8C22×D15111yescharacteristic
231C16—1512no—
232C16C22×D15112yes—
233C23—6041no—
234C23—6041no—
235C23—1511no—
236Q8—21no—
237Q8—22no—
238Q8—41no—
239Q8—3021no—
240Q8—6041no—
241D4—21no—
242D4—41no—
243D4—3021no—
244D4—3022no—
245D4—6041no—
246D4—6042no—
247D4—6042no—
248D4—6041no—
249D4—6041no—
250D4—6041no—
251D4—6041no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—6041no—
255C2×C4—6041no—
256C2×C4—6042no—
257C2×C4—6042no—
258C2×C4—6041no—
259C2×C4—6041no—
260C2×C4—1511no—
261C2×C4—1511no—
262C2×C4—1511no—
263C2×C4—1511no—
264C2×C4—1511no—
265C2×C4D4×D15111yescharacteristic
266C8—1511no—
267C8—1511no—
268C8D4×D15111yescharacteristic
269C8C23×D15111yescharacteristic
270C22—41no—
271C22—6041no—
272C22—6042no—
273C22—6041no—
274C22—1511no—
275C22—1511no—
276C22—12082no—
277C22—12082no—
278C22D8×D15111yescharacteristic
279C4—41no—
280C4—42no—
281C4—6041no—
282C4—1511no—
283C4—1511no—
284C4D8×D15111yescharacteristic
285C4C2×D4×D15111yescharacteristic
286C2—21no—
287C2—81no—
288C2—3021no—
289C2—3021no—
290C2—12082no—
291C2—12081no—
292C2C2×D8×D15111yescharacteristic
subgroupG/H
centerC2C2×D8×D151
commutator, cosocleC8×C151C24
FrattiniC8C23×D151
Fitting#510×C151C2
socleC2×C151C22×D8
hypercenter#510D151
hypocenterC151#3414
LCSG ▷ C8×C151 ▷ C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #510

Complements

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

NH ≅ G/Ntype
1. C2×#18012762C2semidirect
2. #135×D151C2semidirect
3. #23752654C2semidirect
4. #23752653C2semidirect
5. #23752650C2semidirect
6. #23752649C2semidirect
7. #23752647C2semidirect
8. #23752645C2semidirect
9. #23752643C2semidirect
10. M32×D151C2semidirect
11. #510×C151C2semidirect
17. #18012762C22semidirect
18. #18012762C22semidirect
22. #18012758C22semidirect
23. Q16×D151C22semidirect
26. C2×D1208C22semidirect
27. D8×D151C22semidirect
29. #18012685C22semidirect
30. #18012684C22semidirect
31. #18012682C22semidirect
32. #18012682C22semidirect
33. D2416C22semidirect
34. #18012680C22semidirect
35. #18012679C22semidirect
36. #18012678C22semidirect
37. C16×D151C22semidirect
39. C2×Q16×C151C22semidirect
40. Q32×C151C22semidirect
41. SD32×C151C22semidirect
42. M32×C151C22semidirect
146. C151#3414semidirect
152. #510D151semidirect
172. C2×Q16C2×D151semidirect
179. Q32C2×D151semidirect
183. SD32C2×D151semidirect
188. M32C2×D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127622
#135×D1512
#237526542
#237526532
#237526502
#237526492
#237526472
#237526452
#237526432
M32×D1512
#510×C1512
#3414151