Finite Group Databasebeta

← #34078733

Subgroups — #34078733

Order 19328.

496 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18012768C211yesmaximal, characteristic, complemented
2C22×#14558987C211yesmaximal, characteristic, complemented
3#23752722C211yesmaximal, characteristic
4C22⋊Q8×D151C211yesmaximal, characteristic, complemented
5#23752471C211yesmaximal, characteristic, complemented
6#23752469C211yesmaximal, characteristic, complemented
7#23752457C211yesmaximal, characteristic, complemented
8#23752455C211yesmaximal, characteristic, complemented
9#23752453C211yesmaximal, characteristic, complemented
10#23752451C211yesmaximal, characteristic, complemented
11#23752439C211yesmaximal, characteristic, complemented
12#23752251C211yesmaximal, characteristic, complemented
13#23752219C211yesmaximal, characteristic, complemented
14#23752210C211yesmaximal, characteristic, complemented
15#465×C151C211yesmaximal, characteristic, complemented
16C2×#14559003C2211yescharacteristic
17C2×Q8×D151C2211yescharacteristic
18C22×C4×D151C2211yescharacteristic
19#18012768—24no—
20C2×Dic604C2211yescharacteristic, complemented
21C2×#14558994C2211yescharacteristic, complemented
22C2×#14558992C2211yescharacteristic, complemented
23C2×#14558987—24no—
24C2×#14558987C2211yescharacteristic
25C2×#14558987C2211yescharacteristic
26C2×#14558987C2211yescharacteristic
27C2×#14558987C2211yescharacteristic
28C22×C151⋊C8C2211yescharacteristic
29#18012721—21no—
30#18012719C2211yescharacteristic
31#18012719C2211yescharacteristic
32#18012718C2211yescharacteristic
33#18012718C2211yescharacteristic
34#18012717—21no—
35#18012716—21no—
36#18012715C2211yescharacteristic
37#18012710C2211yescharacteristic
38#18012707—21no—
39D4×Dic151—21no—
40(C22⋊D151)⋊C4—21no—
41#18012697C2211yescharacteristic
42C4⋊C4×D151—21no—
43C4⋊C4×D151C2211yescharacteristic
44C22⋊C4×D151—21no—
45#18012673C2211yescharacteristic, complemented
46#18012672C2211yescharacteristic, complemented
47#18012670C2211yescharacteristic, complemented
48#18012664C2211yescharacteristic, complemented
49#18012664C2211yescharacteristic, complemented
50#18012663C2211yescharacteristic, complemented
51#18012662C2211yescharacteristic, complemented
52#18012662C2211yescharacteristic, complemented
53#18012660C2211yescharacteristic, complemented
54C2×SD16×C151C2211yescharacteristic, complemented
55C22×C8×C151C2211yescharacteristic
56C22⋊Q8×C151C2211yescharacteristic
57#121×C151C2211yescharacteristic
58#106×C151C2211yescharacteristic, complemented
59#103×C151C2211yescharacteristic, complemented
60#102×C151C2211yescharacteristic, complemented
61C23×D151D411yescharacteristic
62#14559003—22no—
63#14559003—22no—
64C2×Dic302—21no—
65C2×Dic302C2311yescharacteristic
66C2×Dic302C2311yescharacteristic
67Q8×D151—22no—
68Q8×D151—22no—
69C2×C22⋊D151—21no—
70C2×C22⋊D151—21no—
71C22×Dic151—21no—
72C22×Dic151D411yescharacteristic
73C2×C4×D151—22no—
74C2×C4×D151—22no—
75C2×C4×D151—21no—
76C2×C4×D151—21no—
77C2×C4×D151D411yescharacteristic
78C2×C4×D151D411yescharacteristic
79C2×C4×D151C2311yescharacteristic
80C2×C4×D151C2311yescharacteristic
81Dic604—22no—
82#14558994—22no—
83#14558992—22no—
84#14558987—22no—
85#14558987—22no—
86#14558987—22no—
87#14558987D414yescomplemented
88C2×C151⋊C8—22no—
89C2×C151⋊C8C2311yescharacteristic
90C2×C151⋊C8C2311yescharacteristic
91C4⋊Dic151—21no—
92C4⋊Dic151—21no—
93C4⋊Dic151C2311yescharacteristic
94C4⋊Dic151C2311yescharacteristic
95Dic151⋊C4—21no—
96Dic151⋊C4—21no—
97Dic151⋊C4—21no—
98Dic151⋊C4—21no—
99C22⋊Dic151—21no—
100C22⋊Dic151—21no—
101C22⋊Dic151—21no—
102(C2×D151)⋊C4—21no—
103(C2×D151)⋊C4—21no—
104(C2×D151)⋊C4—21no—
105(C2×D151)⋊C4—21no—
106C4×Dic151—21no—
107C2×Q8×C151C2311yescharacteristic
108C2×D4×C151—21no—
109C2×D4×C151C2311yescharacteristic
110C22×C4×C151C2311yescharacteristic
111SD16×C151—22no—
112C2×C8×C151—22no—
113C2×C8×C151C2311yescharacteristic
114C2×C8×C151C2311yescharacteristic
115C4⋊C4×C151—21no—
116C4⋊C4×C151C2311yescharacteristic
117C4⋊C4×C151C2311yescharacteristic
118C22⋊C4×C151—21no—
119C22⋊C4×C151—21no—
120C22×D151—22no—
121C22×D151—22no—
122C22×D151—41no—
123C22×D151C2×D411yescharacteristic
124C22×D151C2×D411yescharacteristic
125Dic302—21no—
126Dic302—21no—
127Dic302—21no—
128Dic302—21no—
129Dic302—42no—
130C22⋊D151—42no—
131C22⋊D151—42no—
132C2×Dic151—22no—
133C2×Dic151—21no—
134C2×Dic151—21no—
135C2×Dic151—21no—
136C2×Dic151—21no—
137C2×Dic151—42no—
138C2×Dic151C2×D411yescharacteristic
139C2×Dic151C2×D411yescharacteristic
140C4×D151—22no—
141C4×D151—21no—
142C4×D151—21no—
143C4×D151—22no—
144C4×D151—42no—
145C4×D151—42no—
146C4×D151C2×D412yes—
147C4×D151#4112yes—
148C151⋊C8—21no—
149C151⋊C8C2×D412yes—
150C23×C151—21no—
151C23×C151C2×D411yescharacteristic
152Q8×C151—21no—
153Q8×C151—21no—
154D4×C151—21no—
155D4×C151—21no—
156D4×C151—42no—
157C2×C4×C151—21no—
158C2×C4×C151—21no—
159C2×C4×C151—21no—
160C2×C4×C151—21no—
161C2×C4×C151—21no—
162C2×C4×C151C2×D411yescharacteristic
163C2×C4×C151C2411yescharacteristic
164C8×C151—21no—
165C8×C151C2×D412yes—
166C22×C151—21no—
167C22×C151—21no—
168C22×C151—41no—
169C22×C151—41no—
170C22×C151—41no—
171C22×C151#13712yescomplemented
172C22×C151C22×D411yescharacteristic
173C2×D151—21no—
174C2×D151—21no—
175C2×D151—21no—
176C2×D151—21no—
177C2×D151—21no—
178C2×D151—44no—
179C2×D151#12112yes—
180C4×C151—21no—
181C4×C151—41no—
182C4×C151—41no—
183C4×C151—41no—
184C4×C151C22×D411yescharacteristic
185C4×C151C2×#4111yescharacteristic
186Dic151—21no—
187Dic151—41no—
188Dic151—41no—
189Dic151—41no—
190Dic151—41no—
191Dic151#12112yes—
192C2×C151—22no—
193C2×C151—81no—
194C2×C151C2×#12111yescharacteristic
195C2×C151C2×#13711yescharacteristic
196C2×C151#57511yescharacteristic
197D151—22no—
198D151—41no—
199C151#305611yescharacteristic, complemented, Sylow
200#3056—1511nomaximal, Sylow
201C2×#137—1511no—
202C22×M16—1511no—
203#525—1511no—
204C2×C22⋊Q8—1511no—
205#470—1511no—
206#470—1511no—
207#468—1511no—
208#468—1511no—
209#467—1511no—
210#467—1511no—
211#465—1511no—
212#465D15111yescharacteristic, complemented
213#428—1511no—
214#419—1511no—
215#417—1511no—
216C2×#41—1511no—
217C22×Q8—1511no—
218C23×C4—1511no—
219#137—3024no—
220C2×Q16—1511no—
221C2×Q16—1511no—
222C2×SD16—1511no—
223C2×SD16C2×D15111yescharacteristic, complemented
224C2×M16—3024no—
225C2×M16—1511no—
226C2×M16—1511no—
227C2×M16—1511no—
228C2×M16—1511no—
229C22×C8—1511no—
230C22×C8C2×D15111yescharacteristic
231#123—3021no—
232C22⋊Q8—3021no—
233C22⋊Q8—3021no—
234C22⋊Q8—1511no—
235C22⋊Q8—1511no—
236C22⋊Q8—1511no—
237C22⋊Q8—1511no—
238C22⋊Q8—1511no—
239C22⋊Q8C2×D15111yescharacteristic
240#121—1511no—
241#121C2×D15111yescharacteristic
242#120—3021no—
243C4×D4—3021no—
244C4×D4—3021no—
245#117—1511no—
246C2×C4⋊C4—3021no—
247C2×C4⋊C4—1511no—
248C2×C22⋊C4—3021no—
249#107—1511no—
250#107—1511no—
251#106—1511no—
252#106C2×D15111yescharacteristic, complemented
253#103—1511no—
254#103—1511no—
255#103—1511no—
256#103—1511no—
257#103—1511no—
258#103C2×D15111yescharacteristic, complemented
259#102—1511no—
260#102C2×D15111yescharacteristic, complemented
261C24—1511no—
262#41—3022no—
263#41—3022no—
264C2×Q8—3021no—
265C2×Q8—3022no—
266C2×Q8—3022no—
267C2×Q8—1511no—
268C2×Q8—1511no—
269C2×Q8C22×D15111yescharacteristic
270C2×D4—21no—
271C2×D4—3021no—
272C2×D4—3021no—
273C2×D4C22×D15111yescharacteristic
274C22×C4—3022no—
275C22×C4—3022no—
276C22×C4—3021no—
277C22×C4—3021no—
278C22×C4—3021no—
279C22×C4—1511no—
280C22×C4—1511no—
281C22×C4—1511no—
282C22×C4—1511no—
283C22×C4—1511no—
284C22×C4C22×D15111yescharacteristic
285Q16—3022no—
286Q16—3022no—
287SD16—22no—
288SD16—3022no—
289M16—3022no—
290M16—3022no—
291M16—3022no—
292M16—1514no—
293C2×C8—22no—
294C2×C8—3022no—
295C2×C8—1511no—
296C2×C8—1511no—
297C2×C8C22×D15111yescharacteristic
298C2×C8C22×D15111yescharacteristic
299C4⋊C4—21no—
300C4⋊C4—3021no—
301C4⋊C4—3021no—
302C4⋊C4—3021no—
303C4⋊C4—3021no—
304C4⋊C4—3021no—
305C4⋊C4—3021no—
306C4⋊C4—1511no—
307C4⋊C4—1511no—
308C4⋊C4C22×D15111yescharacteristic
309C4⋊C4C22×D15111yescharacteristic
310C22⋊C4—21no—
311C22⋊C4—21no—
312C22⋊C4—3021no—
313C22⋊C4—3021no—
314C22⋊C4—3021no—
315C22⋊C4—3021no—
316C22⋊C4—3021no—
317C22⋊C4—3021no—
318C22⋊C4—3021no—
319C42—3021no—
320C23—21no—
321C23—3022no—
322C23—3022no—
323C23—6041no—
324C23—1511no—
325C23—1511no—
326C23D4×D15111yescharacteristic
327Q8—21no—
328Q8—21no—
329Q8—3021no—
330Q8—3021no—
331Q8—3021no—
332Q8—3021no—
333Q8—6042no—
334D4—21no—
335D4—21no—
336D4—42no—
337D4—6042no—
338D4—6042no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—3022no—
345C2×C4—3022no—
346C2×C4—3022no—
347C2×C4—3021no—
348C2×C4—3021no—
349C2×C4—3021no—
350C2×C4—3021no—
351C2×C4—3021no—
352C2×C4—3021no—
353C2×C4—6042no—
354C2×C4—6042no—
355C2×C4—6042no—
356C2×C4—1511no—
357C2×C4—1511no—
358C2×C4—1512no—
359C2×C4—1512no—
360C2×C4D4×D15111yescharacteristic
361C2×C4C23×D15111yescharacteristic
362C8—21no—
363C8—3021no—
364C8—1512no—
365C8D4×D15112yes—
366C22—21no—
367C22—21no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—3021no—
372C22—3021no—
373C22—3021no—
374C22—3021no—
375C22—3021no—
376C22—6044no—
377C22—1512no—
378C22#1801276812yescomplemented
379C22C2×D4×D15111yescharacteristic
380C4—21no—
381C4—41no—
382C4—41no—
383C4—41no—
384C4—3021no—
385C4—6041no—
386C4—6041no—
387C4—6041no—
388C4—6041no—
389C4—1512no—
390C4C2×D4×D15111yescharacteristic
391C4#41×D15111yescharacteristic
392C2—22no—
393C2—81no—
394C2—3022no—
395C2—6041no—
396C2#121×D15111yescharacteristic
397C2C2×#1801276811yescharacteristic
398C2#2375300911yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#465×C151C2
socleC22×C151C22×D4
prime radical#23752722C2
hypercenter#465D151
hypocenterC151#3056
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. C2×#18012768C2semidirect
2. C22×#14558987C2semidirect
4. C22⋊Q8×D151C2semidirect
5. #23752471C2semidirect
6. #23752469C2semidirect
7. #23752457C2semidirect
8. #23752455C2semidirect
9. #23752453C2semidirect
10. #23752451C2semidirect
11. #23752439C2semidirect
12. #23752251C2semidirect
13. #23752219C2semidirect
14. #23752210C2semidirect
15. #465×C151C2semidirect
20. C2×Dic604C22semidirect
21. C2×#14558994C22semidirect
22. C2×#14558992C22semidirect
45. #18012673C22semidirect
46. #18012672C22semidirect
47. #18012670C22semidirect
48. #18012664C22semidirect
49. #18012664C22semidirect
50. #18012663C22semidirect
51. #18012662C22semidirect
52. #18012662C22semidirect
53. #18012660C22semidirect
54. C2×SD16×C151C22semidirect
58. #106×C151C22semidirect
59. #103×C151C22semidirect
60. #102×C151C22semidirect
87. #14558987D4semidirect
171. C22×C151#137semidirect
199. C151#3056semidirect
212. #465D151semidirect
223. C2×SD16C2×D151semidirect
252. #106C2×D151semidirect
258. #103C2×D151semidirect
260. #102C2×D151semidirect
378. C22#18012768semidirect

Maximal subgroups

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

subgroupindex
C2×#180127682
C22×#145589872
#237527222
C22⋊Q8×D1512
#237524712
#237524692
#237524572
#237524552
#237524532
#237524512
#237524392
#237522512
#237522192
#237522102
#465×C1512
#3056151