Finite Group Databasebeta

← #34078644

Subgroups — #34078644

Order 19328.

504 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18012763C211yesmaximal, characteristic, complemented
2C2×#18012758C211yesmaximal, characteristic, complemented
3#23752775C211yesmaximal, characteristic, complemented
4#23752691C211yesmaximal, characteristic, complemented
5#23752435C211yesmaximal, characteristic, complemented
6#23752433C211yesmaximal, characteristic, complemented
7#23752427C211yesmaximal, characteristic, complemented
8#23752425C211yesmaximal, characteristic, complemented
9#23752411C211yesmaximal, characteristic, complemented
10#23752409C211yesmaximal, characteristic, complemented
11#23752405C211yesmaximal, characteristic, complemented
12#23752237C211yesmaximal, characteristic, complemented
13#23752210C211yesmaximal, characteristic, complemented
14#102×D151C211yesmaximal, characteristic, complemented
15#459×C151C211yesmaximal, characteristic, complemented
16C2×#14559003C2211yescharacteristic
17C2×#14559003C2211yescharacteristic
18C2×D4×D151C2211yescharacteristic
19#18012763—24no—
20#18012758—24no—
21C2×Dic604C2211yescharacteristic, complemented
22C2×#14558993C2211yescharacteristic
23C2×#14558992C2211yescharacteristic
24C2×#14558992C2211yescharacteristic, complemented
25C2×#14558992C2211yescharacteristic, complemented
26C2×#14558989C2211yescharacteristic
27C2×#14558987C2211yescharacteristic
28C2×C8×D151C2211yescharacteristic
29#18012735C2211yescharacteristic
30#18012727C2211yescharacteristic
31#18012726C2211yescharacteristic
32#18012711—21no—
33#18012711—21no—
34#18012707—21no—
35#18012707—21no—
36C4×Dic302C2211yescharacteristic, complemented
37#18012704C2211yescharacteristic, complemented
38D4×Dic151C2211yescharacteristic, complemented
39C4×C22⋊D151—21no—
40(C22⋊D151)⋊C4—21no—
41#18012696C2211yescharacteristic
42#18012695—21no—
43C2×Dic151⋊C4—21no—
44C4⋊C4×D151C2211yescharacteristic
45C4⋊(C151⋊C8)C2211yescharacteristic, complemented
46Dic151⋊C8C2211yescharacteristic, complemented
47Dic151⋊C8C2211yescharacteristic, complemented
48#18012664C2211yescharacteristic, complemented
49#18012662C2211yescharacteristic, complemented
50#18012661C2211yescharacteristic
51#18012660C2211yescharacteristic
52#18012660C2211yescharacteristic, complemented
53#18012659C2211yescharacteristic
54C2×D8×C151C2211yescharacteristic
55C2×D8×C151C2211yescharacteristic, complemented
56#127×C151C2211yescharacteristic
57C4×D4×C151C2211yescharacteristic, complemented
58C4⋊C8×C151C2211yescharacteristic, complemented
59#102×C151C2211yescharacteristic
60#102×C151C2211yescharacteristic, complemented
61C23×D151—21no—
62#14559003—22no—
63#14559003—22no—
64#14559003—22no—
65#14559003D414yescomplemented
66C2×Dic302C2311yescharacteristic
67C2×Dic302C2311yescharacteristic
68C2×D604C2311yescharacteristic
69C2×C22⋊D151—21no—
70C2×C22⋊D151—21no—
71C2×C22⋊D151—21no—
72C2×C22⋊D151—21no—
73C2×C22⋊D151—21no—
74D4×D151—22no—
75D4×D151—22no—
76C22×Dic151—21no—
77C22×Dic151—21no—
78C22×Dic151—21no—
79C2×C4×D151—21no—
80C2×C4×D151C2311yescharacteristic
81Dic604—22no—
82#14558993—22no—
83#14558992—22no—
84#14558992—22no—
85#14558992—22no—
86#14558989—22no—
87#14558987—22no—
88C2×C151⋊C8C2311yescharacteristic
89C2×C151⋊C8C2311yescharacteristic
90C8×D151—22no—
91C4⋊Dic151C2311yescharacteristic
92Dic151⋊C4—21no—
93Dic151⋊C4—21no—
94Dic151⋊C4—21no—
95Dic151⋊C4D411yescharacteristic
96Dic151⋊C4D411yescharacteristic
97C22⋊Dic151—21no—
98C22⋊Dic151—21no—
99C22⋊Dic151—21no—
100(C2×D151)⋊C4—21no—
101(C2×D151)⋊C4—21no—
102(C2×D151)⋊C4D411yescharacteristic
103(C2×D151)⋊C4D411yescharacteristic
104C4×Dic151—21no—
105C4×Dic151—21no—
106C4×Dic151C2311yescharacteristic
107C2×D4×C151—21no—
108C2×D4×C151—21no—
109C2×D4×C151C2311yescharacteristic
110C2×D4×C151C2311yescharacteristic
111C2×D4×C151C2311yescharacteristic
112C22×C4×C151—21no—
113D8×C151—22no—
114D8×C151—22no—
115C2×C8×C151C2311yescharacteristic
116C2×C8×C151C2311yescharacteristic
117C4⋊C4×C151C2311yescharacteristic
118C22⋊C4×C151—21no—
119C42×C151C2311yescharacteristic
120C22×D151—21no—
121C22×D151—42no—
122C22×D151—81no—
123C22×D151—81no—
124C22×D151C2×D411yescharacteristic
125Dic302—21no—
126Dic302—21no—
127Dic302—21no—
128Dic302C2×D412yes—
129D604—21no—
130D604—21no—
131C22⋊D151—24no—
132C22⋊D151—42no—
133C22⋊D151—42no—
134C22⋊D151—81no—
135C22⋊D151—81no—
136C2×Dic151—21no—
137C2×Dic151—24no—
138C2×Dic151—21no—
139C2×Dic151—21no—
140C2×Dic151—42no—
141C2×Dic151—81no—
142C2×Dic151C2×D411yescharacteristic
143C2×Dic151C2×D411yescharacteristic
144C2×Dic151C2×D411yescharacteristic
145C4×D151—81no—
146C4×D151C2×D412yes—
147C4×D151#4112yes—
148C151⋊C8—21no—
149C151⋊C8—21no—
150C23×C151—21no—
151C23×C151—21no—
152C23×C151—21no—
153D4×C151—21no—
154D4×C151—21no—
155D4×C151—21no—
156D4×C151—21no—
157D4×C151—21no—
158D4×C151—81no—
159D4×C151—81no—
160D4×C151C2×D412yes—
161C2×C4×C151—21no—
162C2×C4×C151—81no—
163C2×C4×C151C2×D411yescharacteristic
164C2×C4×C151C2×D411yescharacteristic
165C2×C4×C151C2411yescharacteristic
166C8×C151—21no—
167C8×C151—21no—
168C22×C151—22no—
169C22×C151—41no—
170C22×C151—41no—
171C22×C151—41no—
172C22×C151—41no—
173C22×C151—41no—
174C22×C151—41no—
175C22×C151—41no—
176C22×C151—41no—
177C22×C151C22×D411yescharacteristic
178C2×D151—21no—
179C2×D151—21no—
180C2×D151—41no—
181C2×D151—41no—
182C2×D151—41no—
183C2×D151—84no—
184C2×D151#12112yes—
185C4×C151—21no—
186C4×C151—21no—
187C4×C151—41no—
188C4×C151C22×D411yescharacteristic
189C4×C151C2×#4111yescharacteristic
190Dic151—22no—
191Dic151—21no—
192Dic151—21no—
193Dic151—41no—
194Dic151—41no—
195Dic151#12112yes—
196C2×C151—42no—
197C2×C151—81no—
198C2×C151—81no—
199C2×C151C2×#12111yescharacteristic
200C2×C151#57611yescharacteristic
201C2×C151#57711yescharacteristic
202D151—22no—
203D151—81no—
204C151#304511yescharacteristic, complemented, Sylow
205#3045—1511nomaximal, Sylow
206C2×AGL(1,ℤ/8)—1511no—
207C2×#135—1511no—
208#535—1511no—
209#520—1511no—
210#464—1511no—
211#464—1511no—
212#463—1511no—
213#463—1511no—
214#460—1511no—
215#460—1511no—
216#459—1511no—
217#459D15111yescharacteristic, complemented
218#424—1511no—
219#417—1511no—
220C2×#102—1511no—
221C2×#41—1511no—
222C2×#41—1511no—
223C22×D4—1511no—
224AGL(1,ℤ/8)—3024no—
225#135—3024no—
226C2×Q16—1511no—
227C2×SD16—1511no—
228C2×SD16—1511no—
229C2×SD16—1511no—
230C2×SD16—1511no—
231C2×D8—1511no—
232C2×D8C2×D15111yescharacteristic
233C2×D8C2×D15111yescharacteristic, complemented
234C2×M16—1511no—
235C22×C8—1511no—
236#127—1511no—
237#127C2×D15111yescharacteristic
238#124—1511no—
239#124—1511no—
240#121—3021no—
241#121—3021no—
242#120—3021no—
243#120—3021no—
244C4×Q8—1511no—
245C4×Q8—1511no—
246C4×D4—3021no—
247C4×D4—3021no—
248C4×D4—1511no—
249C4×D4C2×D15111yescharacteristic, complemented
250#117—3021no—
251#117—1511no—
252C2×C4⋊C4—3021no—
253C2×C4⋊C4—1511no—
254C4⋊C8—1511no—
255C4⋊C8—1511no—
256C4⋊C8—1511no—
257C4⋊C8C2×D15111yescharacteristic, complemented
258#103—1511no—
259#103—1511no—
260#102—1511no—
261#102—1511no—
262#102—1511no—
263#102—1511no—
264#102C2×D15111yescharacteristic
265#102C2×D15111yescharacteristic, complemented
266C24—3021no—
267#41—3022no—
268#41—3022no—
269#41—3022no—
270#41—1514no—
271C2×Q8—1511no—
272C2×Q8—1511no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4—3021no—
276C2×D4—3021no—
277C2×D4—3022no—
278C2×D4—3022no—
279C2×D4—3021no—
280C2×D4—3021no—
281C2×D4—3021no—
282C2×D4—1511no—
283C2×D4C22×D15111yescharacteristic
284C2×D4C22×D15111yescharacteristic
285C2×D4C22×D15111yescharacteristic
286C22×C4—21no—
287C22×C4—3021no—
288C22×C4—3021no—
289C22×C4—3021no—
290C22×C4—3021no—
291C22×C4—1511no—
292Q16—3022no—
293SD16—3022no—
294SD16—3022no—
295SD16—3022no—
296SD16—3022no—
297D8—22no—
298D8—22no—
299D8—3022no—
300M16—3022no—
301C2×C8—3022no—
302C2×C8—1511no—
303C2×C8—1511no—
304C2×C8C22×D15111yescharacteristic
305C2×C8C22×D15111yescharacteristic
306C4⋊C4—3021no—
307C4⋊C4—3021no—
308C4⋊C4—3021no—
309C4⋊C4—1511no—
310C4⋊C4—1511no—
311C4⋊C4—1511no—
312C4⋊C4C22×D15111yescharacteristic
313C22⋊C4—21no—
314C22⋊C4—3021no—
315C22⋊C4—3021no—
316C22⋊C4—3021no—
317C22⋊C4—3021no—
318C22⋊C4—3021no—
319C22⋊C4—1511no—
320C22⋊C4—1511no—
321C42—3021no—
322C42—3021no—
323C42—1511no—
324C42C22×D15111yescharacteristic
325C23—21no—
326C23—21no—
327C23—21no—
328C23—3021no—
329C23—6042no—
330C23—1511no—
331C23—12081no—
332C23—12081no—
333Q8—3021no—
334Q8—3021no—
335Q8—3021no—
336Q8—1512no—
337D4—21no—
338D4—21no—
339D4—21no—
340D4—21no—
341D4—21no—
342D4—81no—
343D4—81no—
344D4—3024no—
345D4—3021no—
346D4—3021no—
347D4—6042no—
348D4—6042no—
349D4—12081no—
350D4—12081no—
351D4D4×D15112yes—
352C2×C4—21no—
353C2×C4—81no—
354C2×C4—3021no—
355C2×C4—3024no—
356C2×C4—3021no—
357C2×C4—3021no—
358C2×C4—6042no—
359C2×C4—1511no—
360C2×C4—1511no—
361C2×C4—1511no—
362C2×C4—1512no—
363C2×C4—1512no—
364C2×C4—12081no—
365C2×C4—12081no—
366C2×C4D4×D15111yescharacteristic
367C2×C4D4×D15111yescharacteristic
368C2×C4C23×D15111yescharacteristic
369C8—21no—
370C8—21no—
371C8—3021no—
372C8—3021no—
373C22—22no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—3021no—
383C22—3021no—
384C22—6041no—
385C22—6041no—
386C22—6041no—
387C22—1512no—
388C22—12084no—
389C22C2×D4×D15111yescharacteristic
390C4—21no—
391C4—21no—
392C4—41no—
393C4—3021no—
394C4—3021no—
395C4—3022no—
396C4—6041no—
397C4—6041no—
398C4—1512no—
399C4C2×D4×D15111yescharacteristic
400C4#41×D15111yescharacteristic
401C2—42no—
402C2—81no—
403C2—81no—
404C2—3022no—
405C2—12081no—
406C2#121×D15111yescharacteristic
407C2#2375301311yescharacteristic
408C2#2375302211yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#459×C151C2
socleC22×C151C22×D4
hypercenter#459D151
hypocenterC151#3045
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. C2×#18012763C2semidirect
2. C2×#18012758C2semidirect
3. #23752775C2semidirect
4. #23752691C2semidirect
5. #23752435C2semidirect
6. #23752433C2semidirect
7. #23752427C2semidirect
8. #23752425C2semidirect
9. #23752411C2semidirect
10. #23752409C2semidirect
11. #23752405C2semidirect
12. #23752237C2semidirect
13. #23752210C2semidirect
14. #102×D151C2semidirect
15. #459×C151C2semidirect
21. C2×Dic604C22semidirect
24. C2×#14558992C22semidirect
25. C2×#14558992C22semidirect
36. C4×Dic302C22semidirect
37. #18012704C22semidirect
38. D4×Dic151C22semidirect
45. C4⋊(C151⋊C8)C22semidirect
46. Dic151⋊C8C22semidirect
47. Dic151⋊C8C22semidirect
48. #18012664C22semidirect
49. #18012662C22semidirect
52. #18012660C22semidirect
55. C2×D8×C151C22semidirect
57. C4×D4×C151C22semidirect
58. C4⋊C8×C151C22semidirect
60. #102×C151C22semidirect
65. #14559003D4semidirect
204. C151#3045semidirect
217. #459D151semidirect
233. C2×D8C2×D151semidirect
249. C4×D4C2×D151semidirect
257. C4⋊C8C2×D151semidirect
265. #102C2×D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127632
C2×#180127582
#237527752
#237526912
#237524352
#237524332
#237524272
#237524252
#237524112
#237524092
#237524052
#237522372
#237522102
#102×D1512
#459×C1512
#3045151