Finite Group Databasebeta

← #34079588

Subgroups — #34079588

Order 19328.

564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 149 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×#18012770C211yesmaximal, characteristic, complemented
2C2×#18012764C211yesmaximal, characteristic, complemented
3C2×#18012759C211yesmaximal, characteristic, complemented
4C22×#14558991C211yesmaximal, characteristic, complemented
5#23752781C211yesmaximal, characteristic, complemented
6#23752604C212yesmaximal, complemented
7#23752602C212yesmaximal, complemented
8#23752594C212yesmaximal, complemented
9#23752586C212yesmaximal, complemented
10#23752168C211yesmaximal, characteristic, complemented
11#536×C151C211yesmaximal, characteristic, complemented
12C2×#14559004C2211yescharacteristic
13C22×D604C2211yescharacteristic
14#18012770—24no—
15#18012764—24no—
16#18012759—24no—
17C2×#14558994C2211yescharacteristic, complemented
18C2×#14558994C2212yescomplemented
19C2×#14558992C2211yescharacteristic, complemented
20C2×#14558991—24no—
21C2×#14558991C2212yes—
22C2×#14558991C2212yes—
23C2×#14558991C2212yes—
24C2×#14558991C2211yescharacteristic, complemented
25C2×#14558991C2212yescomplemented
26C2×#14558989C2212yes—
27C2×#14558989C2211yescharacteristic, complemented
28C2×#14558988C2211yescharacteristic
29C22×C151⋊C8C2211yescharacteristic
30#18012736C2212yes—
31#18012727C2212yes—
32#18012714—22no—
33#18012709—22no—
34#18012650C2212yescomplemented
35C4×C151⋊C8C2212yescomplemented
36C2×#41×C151C2211yescharacteristic
37C22×Q8×C151C2211yescharacteristic
38C4⋊Q8×C151C2212yescomplemented
39#124×C151C2212yescomplemented
40#123×C151—22no—
41C22⋊Q8×C151—22no—
42#117×C151C2211yescharacteristic
43C23×D151—21no—
44#14559004—22no—
45#14559004—22no—
46C2×Dic302C2311yescharacteristic
47C2×D604—22no—
48C2×D604—22no—
49C2×D604—21no—
50C2×D604—24no—
51C2×D604C2312yes—
52C2×D604C2311yescharacteristic
53C2×C22⋊D151—21no—
54C2×C4×D151—21no—
55#14558994—22no—
56#14558994—24no—
57#14558992—22no—
58#14558991—24no—
59#14558991—24no—
60#14558991—24no—
61#14558991—22no—
62#14558991—24no—
63#14558989—24no—
64#14558989—22no—
65#14558988D414yescomplemented
66C2×C151⋊C8D414yescomplemented
67C2×C151⋊C8C2311yescharacteristic
68C2×C151⋊C8C2311yescharacteristic
69C2×C151⋊C8C2312yes—
70(C2×D151)⋊C4—24no—
71#41×C151—22no—
72#41×C151—22no—
73C2×Q8×C151—21no—
74C2×Q8×C151—22no—
75C2×Q8×C151—22no—
76C2×Q8×C151C2312yes—
77C2×Q8×C151C2311yescharacteristic
78C2×D4×C151—21no—
79C2×D4×C151C2311yescharacteristic
80C22×C4×C151—21no—
81C22×C4×C151—21no—
82C22×C4×C151C2311yescharacteristic
83C4⋊C4×C151—24no—
84C4⋊C4×C151D412yes—
85C22⋊C4×C151—24no—
86C22⋊C4×C151D412yes—
87C42×C151C2312yes—
88C22×D151—22no—
89C22×D151—21no—
90C22×D151—42no—
91C22×D151—82no—
92Dic302—21no—
93Dic302—21no—
94D604—22no—
95D604—21no—
96D604—22no—
97D604—21no—
98D604—42no—
99D604—84no—
100C22⋊D151—42no—
101C2×Dic151—21no—
102C4×D151—42no—
103C151⋊C8C2×D412yes—
104C151⋊C8C2×D412yes—
105C151⋊C8C2×D414yes—
106C23×C151—21no—
107C23×C151C2×D411yescharacteristic
108Q8×C151—22no—
109Q8×C151—22no—
110Q8×C151—21no—
111Q8×C151—21no—
112Q8×C151—42no—
113D4×C151—21no—
114D4×C151—21no—
115D4×C151—42no—
116C2×C4×C151—22no—
117C2×C4×C151—21no—
118C2×C4×C151—42no—
119C2×C4×C151—42no—
120C2×C4×C151C2×D412yes—
121C2×C4×C151C2×D412yes—
122C2×C4×C151C2×D414yes—
123C2×C4×C151C2×D411yescharacteristic
124C2×C4×C151C2411yescharacteristic
125C22×C151—22no—
126C22×C151—41no—
127C22×C151—42no—
128C22×C151#12712yes—
129C22×C151C22×D411yescharacteristic
130C2×D151—41no—
131C2×D151—42no—
132C2×D151—42no—
133C2×D151—44no—
134C2×D151—84no—
135C4×C151—24no—
136C4×C151—41no—
137C4×C151—42no—
138C4×C151#12712yes—
139C4×C151C22×D411yescharacteristic
140C4×C151C22×D411yescharacteristic
141Dic151—41no—
142C2×C151—22no—
143C2×C151—81no—
144C2×C151C2×#12711yescharacteristic
145C2×C151#57712yes—
146D151—81no—
147D151—82no—
148C151#315411yescharacteristic, complemented, Sylow
149#3154—1511nomaximal, Sylow
150C2×#137—1511no—
151C2×AGL(1,ℤ/8)—1511no—
152C2×#135—1511no—
153C22×SD16—1511no—
154#536D15111yescharacteristic, complemented
155#535—1511no—
156#497—1512no—
157#496—1512no—
158#495—1512no—
159#492—1512no—
160#405—1511no—
161C2×#41—1511no—
162C2×#41C2×D15111yescharacteristic
163C22×Q8C2×D15111yescharacteristic
164C22×D4—1511no—
165#137—3024no—
166AGL(1,ℤ/8)—3024no—
167#135—3024no—
168C2×Q16—1511no—
169C2×Q16—1512no—
170C2×SD16—3024no—
171C2×SD16—1512no—
172C2×SD16—1512no—
173C2×SD16—1511no—
174C2×SD16—1512no—
175C2×SD16—1512no—
176C2×SD16—1511no—
177C2×D8—1511no—
178C2×D8—1512no—
179C2×M16—1511no—
180C22×C8—1511no—
181C4⋊Q8C2×D15112yescomplemented
182#127—1512no—
183#124—1512no—
184#124C2×D15112yescomplemented
185#123—22no—
186C22⋊Q8—22no—
187#121—3022no—
188#120—3022no—
189#117C2×D15111yescharacteristic
190#97—1512no—
191C4×C8—1512no—
192C24—3021no—
193#41—22no—
194#41—22no—
195#41—3022no—
196#41—3022no—
197C2×Q8—21no—
198C2×Q8—22no—
199C2×Q8—22no—
200C2×Q8—1511no—
201C2×Q8C22×D15112yes—
202C2×Q8C22×D15111yescharacteristic
203C2×D4—21no—
204C2×D4—3021no—
205C2×D4—3022no—
206C2×D4—3022no—
207C2×D4—3021no—
208C2×D4—3024no—
209C2×D4—1512no—
210C2×D4—1511no—
211C2×D4C22×D15111yescharacteristic
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—3021no—
215C22×C4C22×D15111yescharacteristic
216Q16—3022no—
217Q16—3024no—
218SD16—3022no—
219SD16—3024no—
220SD16—3024no—
221SD16—3022no—
222SD16—3024no—
223SD16—3024no—
224D8—3022no—
225D8—3024no—
226M16—1514no—
227C2×C8—1514no—
228C2×C8—1511no—
229C2×C8—1512no—
230C2×C8—1511no—
231C4⋊C4—24no—
232C4⋊C4C22⋊D15112yes—
233C22⋊C4—24no—
234C22⋊C4—3024no—
235C22⋊C4C22⋊D15112yes—
236C42C22×D15112yes—
237C23—21no—
238C23—3022no—
239C23—3021no—
240C23—6042no—
241C23—12082no—
242C23C2×C22⋊D15111yescharacteristic
243Q8—22no—
244Q8—21no—
245Q8—22no—
246Q8—21no—
247Q8—42no—
248Q8—3021no—
249Q8—3021no—
250D4—21no—
251D4—21no—
252D4—42no—
253D4—3022no—
254D4—3021no—
255D4—3022no—
256D4—3021no—
257D4—6042no—
258D4—6042no—
259D4—12084no—
260C2×C4—22no—
261C2×C4—21no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—3021no—
265C2×C4—6042no—
266C2×C4D4×D15112yes—
267C2×C4D4×D15112yes—
268C2×C4C2×C22⋊D15114yes—
269C2×C4C2×C22⋊D15111yescharacteristic
270C2×C4C23×D15111yescharacteristic
271C8—1512no—
272C8—1512no—
273C8—1514no—
274C22—22no—
275C22—41no—
276C22—42no—
277C22—6041no—
278C22—6042no—
279C22—6042no—
280C22—6044no—
281C22—12084no—
282C22#1801273512yes—
283C22C22×C22⋊D15111yescharacteristic
284C4—24no—
285C4—41no—
286C4—42no—
287C4—6041no—
288C4#1801273512yes—
289C4C2×D4×D15111yescharacteristic
290C4C2×D4×D15111yescharacteristic
291C2—22no—
292C2—81no—
293C2—12082no—
294C2—12081no—
295C2C2×#1801273511yescharacteristic
296C2#2375302012yes—
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#536×C151C2
socleC22×C151C22×D4
hypercenter#536D151
hypocenterC151#3154
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ #117 ◁ #536

Complements

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

NH ≅ G/Ntype
1. C2×#18012770C2semidirect
2. C2×#18012764C2semidirect
3. C2×#18012759C2semidirect
4. C22×#14558991C2semidirect
5. #23752781C2semidirect
6. #23752604C2semidirect
7. #23752602C2semidirect
8. #23752594C2semidirect
9. #23752586C2semidirect
10. #23752168C2semidirect
11. #536×C151C2semidirect
17. C2×#14558994C22semidirect
18. C2×#14558994C22semidirect
19. C2×#14558992C22semidirect
24. C2×#14558991C22semidirect
25. C2×#14558991C22semidirect
27. C2×#14558989C22semidirect
34. #18012650C22semidirect
35. C4×C151⋊C8C22semidirect
38. C4⋊Q8×C151C22semidirect
39. #124×C151C22semidirect
65. #14558988D4semidirect
66. C2×C151⋊C8D4semidirect
148. C151#3154semidirect
154. #536D151semidirect
181. C4⋊Q8C2×D151semidirect
184. #124C2×D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127702
C2×#180127642
C2×#180127592
C22×#145589912
#237527812
#237526042
#237526022
#237525942
#237525862
#237521682
#536×C1512
#3154151