Finite Group Databasebeta

← #34078485

Subgroups — #34078485

Order 19328.

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

normal subgroups only

This group has 704 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
2#137×D151C212yesmaximal, complemented
3#23752782C211yesmaximal, characteristic, complemented
4#23752396C212yesmaximal, complemented
5#23752393C212yesmaximal, complemented
6#23752392C211yesmaximal, characteristic, complemented
7#23752390C211yesmaximal, characteristic, complemented
8#23752389C211yesmaximal, characteristic, complemented
9#23752227C212yesmaximal, complemented
10#23752193C211yesmaximal, characteristic, complemented
11#455×C151C211yesmaximal, characteristic, complemented
12#18012786—22no—
13#18012786C2212yes—
14#18012784—22no—
15#18012784—22no—
16#18012784C2211yescharacteristic
17C2×#14559003—22no—
18C2×#14559003—22no—
19C2×#14559003C2211yescharacteristic
20#41×D151—22no—
21#41×D151C2212yes—
22C2×Q8×D151C2211yescharacteristic, complemented
23#18012772C2212yescomplemented
24#18012771—22no—
25#18012770C2212yescomplemented
26#18012769C2212yescomplemented
27#18012768—22no—
28Q16×D151—22no—
29SD16×D151—22no—
30M16×D151C2212yescomplemented
31#18012739C2211yescharacteristic, complemented
32#18012737C2211yescharacteristic, complemented
33#18012726C2211yescharacteristic, complemented
34#18012721—22no—
35#18012716—22no—
36#18012696C2211yescharacteristic, complemented
37#18012667C2212yescomplemented
38#18012666C2212yescomplemented
39#18012665C2212yescomplemented
40#18012657C2212yescomplemented
41#18012656C2211yescharacteristic, complemented
42H(5,𝔽2)×C151C2211yescharacteristic
43#137×C151C2212yescomplemented
44#124×C151C2211yescharacteristic, complemented
45#104×C151C2212yescomplemented
46#100×C151C2211yescharacteristic, complemented
47#14559005D412yes—
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#14559003D412yes—
62C2×Dic302—22no—
63C2×Dic302—22no—
64C2×Dic302—21no—
65C2×Dic302C2311yescharacteristic
66C2×Dic302C2311yescharacteristic
67Q8×D151—22no—
68Q8×D151—22no—
69Q8×D151—22no—
70Q8×D151D412yes—
71C2×C22⋊D151—24no—
72C2×C22⋊D151—22no—
73C2×C22⋊D151—22no—
74C2×C22⋊D151D412yes—
75D4×D151—24no—
76D4×D151—22no—
77D4×D151—22no—
78D4×D151D412yes—
79C22×Dic151—22no—
80C22×Dic151D412yes—
81C2×C4×D151—22no—
82C2×C4×D151—22no—
83C2×C4×D151—21no—
84C2×C4×D151C2311yescharacteristic
85Dic604—22no—
86#14558994—22no—
87#14558994—22no—
88#14558993—22no—
89#14558992—22no—
90#14558991—22no—
91#14558988C2312yes—
92#14558987—22no—
93C8×D151—22no—
94C4⋊Dic151—22no—
95Dic151⋊C4—21no—
96Dic151⋊C4—22no—
97C22⋊Dic151—22no—
98(C2×D151)⋊C4—21no—
99C4×Dic151C2311yescharacteristic
100#41×C151—22no—
101#41×C151C2312yes—
102C2×Q8×C151C2311yescharacteristic
103C2×D4×C151—22no—
104C2×D4×C151—22no—
105C2×D4×C151C2311yescharacteristic
106Q16×C151—22no—
107SD16×C151—22no—
108M16×C151C2312yes—
109C22⋊C4×C151—22no—
110C42×C151C2311yescharacteristic
111C22×D151—22no—
112C22×D151—22no—
113C22×D151C2×D411yescharacteristic
114Dic302—24no—
115Dic302—22no—
116Dic302—22no—
117Dic302—22no—
118Dic302—41no—
119Dic302—41no—
120Dic302C2×D412yes—
121D604—22no—
122D604C2×D412yes—
123C22⋊D151—24no—
124C22⋊D151—24no—
125C22⋊D151—22no—
126C22⋊D151—22no—
127C22⋊D151—24no—
128C22⋊D151—22no—
129C2×Dic151—22no—
130C2×Dic151—24no—
131C2×Dic151—22no—
132C2×Dic151—22no—
133C2×Dic151—22no—
134C2×Dic151—21no—
135C2×Dic151—21no—
136C2×Dic151C2×D412yes—
137C2×Dic151C2×D411yescharacteristic
138C4×D151—24no—
139C4×D151—22no—
140C4×D151—22no—
141C4×D151—22no—
142C4×D151—42no—
143C4×D151C2×D412yes—
144C4×D151C2×D412yes—
145C151⋊C8—22no—
146C23×C151—22no—
147C23×C151C2×D412yes—
148Q8×C151—22no—
149Q8×C151C2×D412yes—
150D4×C151—24no—
151D4×C151—22no—
152D4×C151—22no—
153D4×C151C2×D412yes—
154C2×C4×C151—22no—
155C2×C4×C151—22no—
156C2×C4×C151—21no—
157C2×C4×C151—21no—
158C2×C4×C151C2411yescharacteristic
159C8×C151—22no—
160C22×C151—22no—
161C22×C151—22no—
162C22×C151—42no—
163C22×C151—82no—
164C22×C151C22×D411yescharacteristic
165C2×D151—22no—
166C2×D151—41no—
167C2×D151—82no—
168C2×D151—82no—
169C2×D151#12012yes—
170C4×C151—22no—
171C4×C151—41no—
172C4×C151—41no—
173C4×C151C22×D412yes—
174Dic151—22no—
175Dic151—22no—
176Dic151—41no—
177Dic151—41no—
178Dic151#12011yescharacteristic
179Dic151#12011yescharacteristic
180C2×C151—21no—
181C2×C151—42no—
182C2×C151—42no—
183C2×C151C2×#12011yescharacteristic
184D151—22no—
185D151—42no—
186C151#302211yescharacteristic, complemented, Sylow
187#3022—1511nomaximal, Sylow
188#585—1511no—
189C2×#137—1512no—
190#536—1511no—
191#456—1512no—
192#456—1512no—
193#455—1511no—
194#455—1511no—
195#455—1511no—
196#455D15111yescharacteristic, complemented
197#421—1512no—
198#413—1511no—
1992−1+4—3022no—
2002−1+4—1512no—
201H(5,𝔽2)—3022no—
202H(5,𝔽2)—3022no—
203H(5,𝔽2)—1511no—
204H(5,𝔽2)C2×D15111yescharacteristic
205C2×#41—3022no—
206C2×#41—3022no—
207C2×#41—3022no—
208C2×#41—1512no—
209C2×#41—1511no—
210C22×Q8—1511no—
211#137—3022no—
212#137—3022no—
213#137—1512no—
214#137—1512no—
215#137—1512no—
216#137C2×D15112yescomplemented
217C2×Q16—3022no—
218C2×SD16—3022no—
219C2×M16—1512no—
220C4⋊Q8—1511no—
221C4⋊Q8—1511no—
222#124—1511no—
223#124C2×D15111yescharacteristic, complemented
224#123—3022no—
225C22⋊Q8—3022no—
226#117—1511no—
227#104—1512no—
228#104—1512no—
229#104—1512no—
230#104C2×D15112yescomplemented
231#101—1512no—
232#100—1511no—
233#100C2×D15111yescharacteristic, complemented
234#41—22no—
235#41—3024no—
236#41—3022no—
237#41—3022no—
238#41—3024no—
239#41—3024no—
240#41—3024no—
241#41—3022no—
242#41—3022no—
243#41—3022no—
244#41—3022no—
245#41—3024no—
246#41—3022no—
247#41—1512no—
248#41—1512no—
249#41—1512no—
250#41C22×D15112yes—
251C2×Q8—3022no—
252C2×Q8—3022no—
253C2×Q8—3021no—
254C2×Q8—3022no—
255C2×Q8—3022no—
256C2×Q8—3022no—
257C2×Q8—1512no—
258C2×Q8—1511no—
259C2×Q8—1511no—
260C2×Q8C22×D15111yescharacteristic
261C2×D4—22no—
262C2×D4—22no—
263C2×D4—3024no—
264C2×D4—3022no—
265C2×D4—3022no—
266C2×D4—3024no—
267C2×D4—3022no—
268C2×D4—3022no—
269C2×D4—1512no—
270C2×D4—1512no—
271C2×D4C22×D15111yescharacteristic
272C22×C4—3022no—
273C22×C4—3022no—
274C22×C4—3021no—
275C22×C4—3022no—
276C22×C4—1512no—
277C22×C4—1511no—
278Q16—22no—
279Q16—3022no—
280Q16—3022no—
281Q16—3022no—
282SD16—22no—
283SD16—3022no—
284SD16—3022no—
285SD16—3022no—
286M16—3022no—
287M16—1512no—
288M16C22×D15112yes—
289C2×C8—3022no—
290C4⋊C4—3021no—
291C4⋊C4—3022no—
292C4⋊C4—3022no—
293C22⋊C4—22no—
294C22⋊C4—3021no—
295C22⋊C4—3022no—
296C42—1511no—
297C42C22×D15111yescharacteristic
298C23—22no—
299C23—3022no—
300C23—3022no—
301C23—1511no—
302C23D4×D15112yes—
303Q8—22no—
304Q8—3024no—
305Q8—3022no—
306Q8—3022no—
307Q8—3022no—
308Q8—6041no—
309Q8—6041no—
310Q8—1512no—
311Q8D4×D15112yes—
312D4—24no—
313D4—22no—
314D4—22no—
315D4—3022no—
316D4—3024no—
317D4—3024no—
318D4—3022no—
319D4—3024no—
320D4—3022no—
321D4—3022no—
322D4—1512no—
323D4D4×D15112yes—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—3024no—
329C2×C4—3022no—
330C2×C4—3022no—
331C2×C4—3022no—
332C2×C4—3024no—
333C2×C4—3022no—
334C2×C4—3022no—
335C2×C4—3022no—
336C2×C4—3022no—
337C2×C4—3021no—
338C2×C4—3021no—
339C2×C4—6042no—
340C2×C4—1512no—
341C2×C4—1511no—
342C2×C4—1512no—
343C2×C4—1512no—
344C2×C4C23×D15111yescharacteristic
345C8—22no—
346C8—3022no—
347C22—22no—
348C22—22no—
349C22—42no—
350C22—82no—
351C22—3022no—
352C22—6041no—
353C22—1512no—
354C22—12082no—
355C22—12082no—
356C22C2×D4×D15111yescharacteristic
357C4—22no—
358C4—41no—
359C4—41no—
360C4—3022no—
361C4—3022no—
362C4—6041no—
363C4—6041no—
364C4—1511no—
365C4—1511no—
366C4C2×D4×D15112yes—
367C2—21no—
368C2—42no—
369C2—42no—
370C2—3022no—
371C2—6042no—
372C2#120×D15111yescharacteristic
subgroupG/H
centerC2#120×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#455×C151C2
socleC2×C151C2×#120
prime radical#23753047C2
hypercenter#455D151
hypocenterC151#3022
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C2×C4 ◁ #455

Complements

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

NH ≅ G/Ntype
2. #137×D151C2semidirect
3. #23752782C2semidirect
4. #23752396C2semidirect
5. #23752393C2semidirect
6. #23752392C2semidirect
7. #23752390C2semidirect
8. #23752389C2semidirect
9. #23752227C2semidirect
10. #23752193C2semidirect
11. #455×C151C2semidirect
22. C2×Q8×D151C22semidirect
23. #18012772C22semidirect
25. #18012770C22semidirect
26. #18012769C22semidirect
30. M16×D151C22semidirect
31. #18012739C22semidirect
32. #18012737C22semidirect
33. #18012726C22semidirect
36. #18012696C22semidirect
37. #18012667C22semidirect
38. #18012666C22semidirect
39. #18012665C22semidirect
40. #18012657C22semidirect
41. #18012656C22semidirect
43. #137×C151C22semidirect
44. #124×C151C22semidirect
45. #104×C151C22semidirect
46. #100×C151C22semidirect
186. C151#3022semidirect
196. #455D151semidirect
216. #137C2×D151semidirect
223. #124C2×D151semidirect
230. #104C2×D151semidirect
233. #100C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237530472
#137×D1512
#237527822
#237523962
#237523932
#237523922
#237523902
#237523892
#237522272
#237521932
#455×C1512
#3022151