Finite Group Databasebeta

← #34078455

Subgroups — #34078455

Order 19328.

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

normal subgroups only

This group has 724 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
1#23753047C211yesmaximal, characteristic, complemented
2#23753008C212yesmaximal, complemented
3#23752760C211yesmaximal, characteristic, complemented
4#23752396C212yesmaximal, complemented
5#23752392C211yesmaximal, characteristic, complemented
6#23752390C211yesmaximal, characteristic, complemented
7#23752383C212yesmaximal, complemented
8#23752379C211yesmaximal, characteristic, complemented
9#104×D151C212yesmaximal, complemented
10#23752193C211yesmaximal, characteristic, complemented
11#453×C151C211yesmaximal, characteristic, complemented
12#18012786—22no—
13#18012786C2212yes—
14#18012784—22no—
15#18012784—22no—
16#18012784C2211yescharacteristic
17C2×#14559003—22no—
18C2×#14559003—22no—
19C2×#14559003C2211yescharacteristic
20C2×#14559003C2211yescharacteristic, complemented
21#41×D151—22no—
22#41×D151C2212yes—
23#18012772C2212yescomplemented
24#18012769C2212yescomplemented
25#18012768—22no—
26#18012765C2212yescomplemented
27#18012763—22no—
28#18012760—22no—
29#18012758—22no—
30M16×D151C2212yescomplemented
31#18012739C2211yescharacteristic, complemented
32#18012726C2211yescharacteristic, complemented
33#18012726C2211yescharacteristic, complemented
34#18012710—22no—
35D4×Dic151—22no—
36C42×D151C2211yescharacteristic, complemented
37#18012667C2212yescomplemented
38#18012666C2212yescomplemented
39#18012665C2212yescomplemented
40#18012657C2212yescomplemented
41#18012656C2211yescharacteristic, complemented
42H(5,𝔽2)×C151C2211yescharacteristic
43AGL(1,ℤ/8)×C151C2212yescomplemented
44#127×C151C2211yescharacteristic, complemented
45#104×C151C2212yescomplemented
46#100×C151C2211yescharacteristic, complemented
47#14559005D412yescomplemented
48#14559004—24no—
49#14559004—22no—
50#14559004—22no—
51#14559004C2312yes—
52#14559003—24no—
53#14559003—24no—
54#14559003—24no—
55#14559003—22no—
56#14559003—22no—
57#14559003—24no—
58#14559003—22no—
59#14559003—22no—
60#14559003—22no—
61#14559003—22no—
62#14559003—22no—
63#14559003D412yescomplemented
64C2×Dic302—22no—
65C2×Dic302—22no—
66C2×Dic302C2311yescharacteristic
67C2×Dic302C2311yescharacteristic
68Q8×D151—22no—
69Q8×D151D412yescomplemented
70C2×C22⋊D151—24no—
71C2×C22⋊D151—22no—
72C2×C22⋊D151—21no—
73C2×C22⋊D151—22no—
74C2×C22⋊D151D412yes—
75D4×D151—24no—
76D4×D151—22no—
77D4×D151—22no—
78D4×D151D412yescomplemented
79C22×Dic151—22no—
80C22×Dic151—21no—
81C22×Dic151D412yes—
82C2×C4×D151—22no—
83C2×C4×D151—22no—
84C2×C4×D151—21no—
85C2×C4×D151C2311yescharacteristic
86Dic604—22no—
87#14558994—22no—
88#14558993—22no—
89#14558992—22no—
90#14558992—22no—
91#14558989—22no—
92#14558988C2312yes—
93#14558987—22no—
94C8×D151—22no—
95C4⋊Dic151—22no—
96C22⋊Dic151—22no—
97C22⋊Dic151—22no—
98C4×Dic151—21no—
99C4×Dic151C2311yescharacteristic
100#41×C151—22no—
101#41×C151C2312yes—
102C2×D4×C151—22no—
103C2×D4×C151—22no—
104C2×D4×C151—22no—
105C2×D4×C151C2311yescharacteristic
106C2×D4×C151C2311yescharacteristic
107SD16×C151—22no—
108D8×C151—22no—
109M16×C151C2312yes—
110C42×C151C2311yescharacteristic
111C22×D151—22no—
112C22×D151—22no—
113C22×D151C2×D411yescharacteristic
114Dic302—24no—
115Dic302—22no—
116Dic302—22no—
117Dic302—22no—
118Dic302C2×D412yes—
119D604—22no—
120D604C2×D412yes—
121C22⋊D151—24no—
122C22⋊D151—24no—
123C22⋊D151—22no—
124C22⋊D151—22no—
125C22⋊D151—24no—
126C22⋊D151—22no—
127C22⋊D151—42no—
128C2×Dic151—22no—
129C2×Dic151—24no—
130C2×Dic151—22no—
131C2×Dic151—22no—
132C2×Dic151—22no—
133C2×Dic151—21no—
134C2×Dic151—21no—
135C2×Dic151—41no—
136C2×Dic151—41no—
137C2×Dic151C2×D412yes—
138C2×Dic151C2×D411yescharacteristic
139C4×D151—24no—
140C4×D151—22no—
141C4×D151—22no—
142C4×D151—22no—
143C4×D151—42no—
144C4×D151C2×D412yes—
145C4×D151C2×D412yes—
146C151⋊C8—22no—
147C23×C151—22no—
148C23×C151—21no—
149C23×C151C2×D412yes—
150Q8×C151C2×D412yes—
151D4×C151—24no—
152D4×C151—22no—
153D4×C151—22no—
154D4×C151—22no—
155D4×C151—44no—
156D4×C151C2×D412yes—
157C2×C4×C151—22no—
158C2×C4×C151—21no—
159C2×C4×C151—22no—
160C2×C4×C151C2411yescharacteristic
161C8×C151—22no—
162C22×C151—22no—
163C22×C151—22no—
164C22×C151—42no—
165C22×C151—42no—
166C22×C151—41no—
167C22×C151—82no—
168C22×C151C22×D411yescharacteristic
169C2×D151—22no—
170C2×D151—41no—
171C2×D151—82no—
172C2×D151—82no—
173C2×D151#12012yes—
174C4×C151—22no—
175C4×C151—22no—
176C4×C151C22×D412yes—
177Dic151—22no—
178Dic151—22no—
179Dic151—41no—
180Dic151—41no—
181Dic151#12011yescharacteristic
182Dic151#12011yescharacteristic
183C2×C151—21no—
184C2×C151—42no—
185C2×C151—42no—
186C2×C151—81no—
187C2×C151C2×#12011yescharacteristic
188D151—22no—
189D151—42no—
190C151#301811yescharacteristic, complemented, Sylow
191#3018—1511nomaximal, Sylow
192#585—1511no—
193#575—1512no—
194#532—1511no—
195#456—1512no—
196#455—1511no—
197#455—1511no—
198#454—1512no—
199#453—1511no—
200#453D15111yescharacteristic, complemented
201C2×#104—1512no—
202#413—1511no—
2032−1+4—3022no—
2042−1+4—1512no—
205H(5,𝔽2)—3022no—
206H(5,𝔽2)—3022no—
207H(5,𝔽2)—1511no—
208H(5,𝔽2)C2×D15111yescharacteristic
209C2×#41—3022no—
210C2×#41—3022no—
211C2×#41—3022no—
212C2×#41—1512no—
213C2×#41—1511no—
214C2×#41—1511no—
215#137—3022no—
216#137—1512no—
217#137—1512no—
218AGL(1,ℤ/8)—3022no—
219AGL(1,ℤ/8)—1512no—
220AGL(1,ℤ/8)C2×D15112yescomplemented
221#135—3022no—
222#135—3022no—
223C2×M16—1512no—
224C4⋊Q8—1511no—
225#127C2×D15111yescharacteristic, complemented
226#124—1511no—
227#124—1511no—
228#121—3022no—
229C4×D4—3022no—
230C2×C42—1511no—
231#104—1512no—
232#104—1512no—
233#104—1512no—
234#104C2×D15112yescomplemented
235#101—1512no—
236#100—1511no—
237#100C2×D15111yescharacteristic, complemented
238#41—22no—
239#41—3024no—
240#41—3022no—
241#41—3022no—
242#41—3024no—
243#41—3024no—
244#41—3024no—
245#41—3022no—
246#41—3022no—
247#41—3022no—
248#41—3022no—
249#41—3024no—
250#41—3022no—
251#41—3022no—
252#41—3022no—
253#41—1512no—
254#41—1512no—
255#41—1512no—
256#41C22×D15112yes—
257C2×Q8—3022no—
258C2×Q8—3022no—
259C2×Q8—3022no—
260C2×Q8—1512no—
261C2×Q8—1511no—
262C2×Q8—1511no—
263C2×D4—22no—
264C2×D4—22no—
265C2×D4—22no—
266C2×D4—3024no—
267C2×D4—3022no—
268C2×D4—3022no—
269C2×D4—3024no—
270C2×D4—3022no—
271C2×D4—3022no—
272C2×D4—3021no—
273C2×D4—1512no—
274C2×D4—1512no—
275C2×D4C22×D15111yescharacteristic
276C2×D4C22×D15111yescharacteristic
277C22×C4—3022no—
278C22×C4—3022no—
279C22×C4—3021no—
280C22×C4—3022no—
281C22×C4—3021no—
282C22×C4—1512no—
283C22×C4—1511no—
284Q16—3022no—
285Q16—3022no—
286SD16—22no—
287SD16—3022no—
288SD16—3022no—
289SD16—3022no—
290D8—22no—
291D8—3022no—
292M16—3022no—
293M16—1512no—
294M16C22×D15112yes—
295C2×C8—3022no—
296C4⋊C4—3022no—
297C22⋊C4—3022no—
298C22⋊C4—3022no—
299C42—3021no—
300C42—1511no—
301C42C22×D15111yescharacteristic
302C23—22no—
303C23—21no—
304C23—3022no—
305C23—3022no—
306C23—1511no—
307C23D4×D15112yes—
308Q8—3024no—
309Q8—3022no—
310Q8—3022no—
311Q8—3022no—
312Q8—1512no—
313Q8D4×D15112yes—
314D4—24no—
315D4—22no—
316D4—22no—
317D4—22no—
318D4—44no—
319D4—3022no—
320D4—3024no—
321D4—3024no—
322D4—3022no—
323D4—3024no—
324D4—3022no—
325D4—3022no—
326D4—6042no—
327D4—1512no—
328D4D4×D15112yes—
329C2×C4—22no—
330C2×C4—21no—
331C2×C4—22no—
332C2×C4—3024no—
333C2×C4—3022no—
334C2×C4—3022no—
335C2×C4—3022no—
336C2×C4—3024no—
337C2×C4—3022no—
338C2×C4—3022no—
339C2×C4—3022no—
340C2×C4—3022no—
341C2×C4—3021no—
342C2×C4—3021no—
343C2×C4—6042no—
344C2×C4—6041no—
345C2×C4—6041no—
346C2×C4—1512no—
347C2×C4—1511no—
348C2×C4—1512no—
349C2×C4—1512no—
350C2×C4C23×D15111yescharacteristic
351C8—22no—
352C8—3022no—
353C22—22no—
354C22—22no—
355C22—42no—
356C22—42no—
357C22—41no—
358C22—82no—
359C22—3022no—
360C22—6041no—
361C22—1512no—
362C22—12082no—
363C22—12082no—
364C22C2×D4×D15111yescharacteristic
365C4—22no—
366C4—22no—
367C4—3022no—
368C4—3022no—
369C4—6041no—
370C4—6041no—
371C4—1511no—
372C4—1511no—
373C4C2×D4×D15112yes—
374C2—21no—
375C2—42no—
376C2—42no—
377C2—81no—
378C2—3022no—
379C2—6042no—
380C2#120×D15111yescharacteristic
subgroupG/H
centerC2#120×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#453×C151C2
socleC2×C151C2×#120
hypercenter#453D151
hypocenterC151#3018
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C2×C4 ◁ #453

Complements

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

NH ≅ G/Ntype
1. #23753047C2semidirect
2. #23753008C2semidirect
3. #23752760C2semidirect
4. #23752396C2semidirect
5. #23752392C2semidirect
6. #23752390C2semidirect
7. #23752383C2semidirect
8. #23752379C2semidirect
9. #104×D151C2semidirect
10. #23752193C2semidirect
11. #453×C151C2semidirect
20. C2×#14559003C22semidirect
23. #18012772C22semidirect
24. #18012769C22semidirect
26. #18012765C22semidirect
30. M16×D151C22semidirect
31. #18012739C22semidirect
32. #18012726C22semidirect
33. #18012726C22semidirect
36. C42×D151C22semidirect
37. #18012667C22semidirect
38. #18012666C22semidirect
39. #18012665C22semidirect
40. #18012657C22semidirect
41. #18012656C22semidirect
43. AGL(1,ℤ/8)×C151C22semidirect
44. #127×C151C22semidirect
45. #104×C151C22semidirect
46. #100×C151C22semidirect
47. #14559005D4semidirect
63. #14559003D4semidirect
69. Q8×D151D4semidirect
78. D4×D151D4semidirect
190. C151#3018semidirect
200. #453D151semidirect
220. AGL(1,ℤ/8)C2×D151semidirect
225. #127C2×D151semidirect
234. #104C2×D151semidirect
237. #100C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237530472
#237530082
#237527602
#237523962
#237523922
#237523902
#237523832
#237523792
#104×D1512
#237521932
#453×C1512
#3018151