Finite Group Databasebeta

← #34078652

Subgroups — #34078652

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×#18012766C211yesmaximal, characteristic, complemented
2C2×#18012762C211yesmaximal, characteristic, complemented
3#23752780C211yesmaximal, characteristic, complemented
4#23752694C211yesmaximal, characteristic, complemented
5#23752436C211yesmaximal, characteristic, complemented
6#23752430C211yesmaximal, characteristic, complemented
7#23752424C211yesmaximal, characteristic, complemented
8#23752412C211yesmaximal, characteristic, complemented
9#23752410C211yesmaximal, characteristic, complemented
10#23752408C211yesmaximal, characteristic, complemented
11#23752406C211yesmaximal, characteristic, complemented
12#23752237C211yesmaximal, characteristic, complemented
13#23752212C211yesmaximal, characteristic, complemented
14#102×D151C211yesmaximal, characteristic, complemented
15#464×C151C211yesmaximal, characteristic, complemented
16C2×#14559005C2211yescharacteristic
17C2×#14559005C2211yescharacteristic
18C2×D4×D151C2211yescharacteristic
19#18012766—24no—
20#18012762—24no—
21C2×#14558991C2211yescharacteristic
22C2×#14558991C2211yescharacteristic, complemented
23C2×#14558991C2211yescharacteristic, complemented
24C2×D1208C2211yescharacteristic
25C2×D1208C2211yescharacteristic, complemented
26C2×#14558989C2211yescharacteristic
27C2×#14558987C2211yescharacteristic
28C2×C8×D151C2211yescharacteristic
29#18012736C2211yescharacteristic
30#18012735C2211yescharacteristic
31#18012728C2211yescharacteristic
32#18012712—21no—
33#18012712—21no—
34#18012709—21no—
35#18012709—21no—
36Q8×Dic151C2211yescharacteristic, complemented
37C4×D604—21no—
38C4×D604C2211yescharacteristic, complemented
39#18012701—21no—
40#18012701C2211yescharacteristic, complemented
41#18012696—21no—
42#18012696C2211yescharacteristic
43C4⋊C4×D151—21no—
44C4⋊C4×D151C2211yescharacteristic
45C4⋊(C151⋊C8)C2211yescharacteristic, complemented
46Dic151⋊C8C2211yescharacteristic, complemented
47Dic151⋊C8C2211yescharacteristic, complemented
48#18012663C2211yescharacteristic, complemented
49#18012661C2211yescharacteristic
50#18012661C2211yescharacteristic, complemented
51#18012660C2211yescharacteristic
52#18012659C2211yescharacteristic
53#18012659C2211yescharacteristic, complemented
54C2×Q16×C151C2211yescharacteristic, complemented
55C2×SD16×C151C2211yescharacteristic
56#124×C151C2211yescharacteristic
57C4×Q8×C151C2211yescharacteristic, complemented
58C4⋊C8×C151C2211yescharacteristic, complemented
59#103×C151C2211yescharacteristic, complemented
60#102×C151C2211yescharacteristic
61C23×D151—21no—
62#14559005—22no—
63#14559005—22no—
64#14559005—22no—
65#14559005D414yescomplemented
66C2×D604—21no—
67C2×D604—21no—
68C2×D604—21no—
69C2×D604—21no—
70C2×D604C2311yescharacteristic
71C2×D604C2311yescharacteristic
72C2×D604C2311yescharacteristic
73C2×C22⋊D151—21no—
74C2×C22⋊D151—21no—
75C2×C22⋊D151—21no—
76D4×D151—22no—
77D4×D151—22no—
78C2×C4×D151—21no—
79C2×C4×D151—21no—
80C2×C4×D151—21no—
81C2×C4×D151—21no—
82C2×C4×D151—21no—
83C2×C4×D151C2311yescharacteristic
84#14558991—22no—
85#14558991—22no—
86#14558991—22no—
87D1208—22no—
88D1208—22no—
89#14558989—22no—
90#14558987—22no—
91C2×C151⋊C8C2311yescharacteristic
92C2×C151⋊C8C2311yescharacteristic
93C8×D151—22no—
94C4⋊Dic151—21no—
95C4⋊Dic151C2311yescharacteristic
96Dic151⋊C4—21no—
97Dic151⋊C4D411yescharacteristic
98Dic151⋊C4D411yescharacteristic
99(C2×D151)⋊C4—21no—
100(C2×D151)⋊C4—21no—
101(C2×D151)⋊C4—21no—
102(C2×D151)⋊C4—21no—
103(C2×D151)⋊C4D411yescharacteristic
104(C2×D151)⋊C4D411yescharacteristic
105C4×Dic151—21no—
106C4×Dic151C2311yescharacteristic
107C2×Q8×C151C2311yescharacteristic
108C2×Q8×C151C2311yescharacteristic
109C2×D4×C151C2311yescharacteristic
110Q16×C151—22no—
111SD16×C151—22no—
112C2×C8×C151C2311yescharacteristic
113C2×C8×C151C2311yescharacteristic
114C4⋊C4×C151—21no—
115C4⋊C4×C151C2311yescharacteristic
116C22⋊C4×C151—21no—
117C22⋊C4×C151—21no—
118C42×C151—21no—
119C42×C151C2311yescharacteristic
120C22×D151—21no—
121C22×D151—21no—
122C22×D151—21no—
123C22×D151—42no—
124C22×D151—81no—
125C22×D151—81no—
126C22×D151C2×D411yescharacteristic
127D604—24no—
128D604—21no—
129D604—21no—
130D604—21no—
131D604—21no—
132D604—21no—
133D604—42no—
134D604—81no—
135D604—81no—
136D604C2×D412yes—
137C22⋊D151—42no—
138C22⋊D151—81no—
139C22⋊D151—81no—
140C2×Dic151—21no—
141C2×Dic151C2×D411yescharacteristic
142C2×Dic151C2×D411yescharacteristic
143C2×Dic151C2×D411yescharacteristic
144C4×D151—24no—
145C4×D151—42no—
146C4×D151—81no—
147C4×D151—81no—
148C4×D151—81no—
149C4×D151C2×D412yes—
150C4×D151#4112yes—
151C151⋊C8—21no—
152C151⋊C8—21no—
153C23×C151—21no—
154Q8×C151—21no—
155Q8×C151—21no—
156Q8×C151—21no—
157Q8×C151C2×D412yes—
158D4×C151—21no—
159D4×C151—21no—
160C2×C4×C151—21no—
161C2×C4×C151—21no—
162C2×C4×C151—21no—
163C2×C4×C151C2×D411yescharacteristic
164C2×C4×C151C2×D411yescharacteristic
165C2×C4×C151C2411yescharacteristic
166C8×C151—21no—
167C8×C151—21no—
168C22×C151—41no—
169C22×C151—41no—
170C22×C151—41no—
171C22×C151C22×D411yescharacteristic
172C2×D151—21no—
173C2×D151—21no—
174C2×D151—22no—
175C2×D151—41no—
176C2×D151—41no—
177C2×D151—41no—
178C2×D151—41no—
179C2×D151—41no—
180C2×D151—41no—
181C2×D151—41no—
182C2×D151—41no—
183C2×D151—84no—
184C2×D151#12112yes—
185C4×C151—22no—
186C4×C151—21no—
187C4×C151—21no—
188C4×C151—41no—
189C4×C151—41no—
190C4×C151C22×D411yescharacteristic
191C4×C151C2×#4111yescharacteristic
192Dic151—21no—
193Dic151—21no—
194Dic151—41no—
195Dic151#12112yes—
196C2×C151—81no—
197C2×C151C2×#12111yescharacteristic
198C2×C151#57611yescharacteristic
199C2×C151#57711yescharacteristic
200D151—22no—
201D151—42no—
202D151—81no—
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#464D15111yescharacteristic, complemented
212#463—1511no—
213#463—1511no—
214#460—1511no—
215#460—1511no—
216#459—1511no—
217#459—1511no—
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×Q16C2×D15111yescharacteristic, complemented
227C2×SD16—1511no—
228C2×SD16—1511no—
229C2×SD16—1511no—
230C2×SD16C2×D15111yescharacteristic
231C2×D8—1511no—
232C2×D8—1511no—
233C2×D8—1511no—
234C2×M16—1511no—
235C22×C8—1511no—
236#127—1511no—
237#127—1511no—
238#124—1511no—
239#124C2×D15111yescharacteristic
240#121—3021no—
241#121—3021no—
242#120—3021no—
243#120—3021no—
244C4×Q8—1511no—
245C4×Q8C2×D15111yescharacteristic, complemented
246C4×D4—3021no—
247C4×D4—3021no—
248C4×D4—1511no—
249C4×D4—1511no—
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#103C2×D15111yescharacteristic, complemented
260#102—1511no—
261#102—1511no—
262#102—1511no—
263#102—1511no—
264#102—1511no—
265#102C2×D15111yescharacteristic
266C24—3021no—
267#41—3022no—
268#41—3022no—
269#41—3022no—
270#41—1514no—
271C2×Q8C22×D15111yescharacteristic
272C2×Q8C22×D15111yescharacteristic
273C2×D4—3021no—
274C2×D4—3021no—
275C2×D4—3022no—
276C2×D4—3022no—
277C2×D4—3021no—
278C2×D4—3021no—
279C2×D4—3021no—
280C2×D4—3021no—
281C2×D4—3021no—
282C2×D4—1511no—
283C2×D4—1511no—
284C2×D4—1511no—
285C2×D4C22×D15111yescharacteristic
286C22×C4—3021no—
287C22×C4—3021no—
288C22×C4—3021no—
289C22×C4—3021no—
290C22×C4—3021no—
291C22×C4—1511no—
292Q16—22no—
293SD16—22no—
294SD16—3022no—
295SD16—3022no—
296SD16—3022no—
297D8—3022no—
298D8—3022no—
299D8—3022no—
300M16—3022no—
301C2×C8—3022no—
302C2×C8—1511no—
303C2×C8—1511no—
304C2×C8C22×D15111yescharacteristic
305C2×C8C22×D15111yescharacteristic
306C4⋊C4—21no—
307C4⋊C4—3021no—
308C4⋊C4—3021no—
309C4⋊C4—1511no—
310C4⋊C4—1511no—
311C4⋊C4—1511no—
312C4⋊C4C22×D15111yescharacteristic
313C22⋊C4—21no—
314C22⋊C4—21no—
315C22⋊C4—3021no—
316C22⋊C4—3021no—
317C22⋊C4—3021no—
318C22⋊C4—3021no—
319C22⋊C4—1511no—
320C22⋊C4—1511no—
321C42—21no—
322C42—3021no—
323C42—1511no—
324C42C22×D15111yescharacteristic
325C23—21no—
326C23—3021no—
327C23—3021no—
328C23—3021no—
329C23—6042no—
330C23—1511no—
331C23—12081no—
332C23—12081no—
333Q8—21no—
334Q8—21no—
335Q8—21no—
336Q8D4×D15112yes—
337D4—21no—
338D4—21no—
339D4—3024no—
340D4—3021no—
341D4—3021no—
342D4—3021no—
343D4—3021no—
344D4—3021no—
345D4—6042no—
346D4—6042no—
347D4—1512no—
348D4—12081no—
349D4—12081no—
350D4—12081no—
351D4—12081no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—3024no—
356C2×C4—3021no—
357C2×C4—6042no—
358C2×C4—1511no—
359C2×C4—1511no—
360C2×C4—1511no—
361C2×C4—1512no—
362C2×C4—1512no—
363C2×C4—12081no—
364C2×C4—12081no—
365C2×C4—12081no—
366C2×C4D4×D15111yescharacteristic
367C2×C4D4×D15111yescharacteristic
368C2×C4C23×D15111yescharacteristic
369C8—21no—
370C8—21no—
371C8—3021no—
372C8—3021no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—3021no—
377C22—3021no—
378C22—3022no—
379C22—6041no—
380C22—6041no—
381C22—6041no—
382C22—6041no—
383C22—6041no—
384C22—6041no—
385C22—6041no—
386C22—6041no—
387C22—1512no—
388C22—12084no—
389C22C2×D4×D15111yescharacteristic
390C4—21no—
391C4—21no—
392C4—22no—
393C4—41no—
394C4—41no—
395C4—3021no—
396C4—3021no—
397C4—6041no—
398C4—1512no—
399C4C2×D4×D15111yescharacteristic
400C4#41×D15111yescharacteristic
401C2—81no—
402C2—3022no—
403C2—6042no—
404C2—12081no—
405C2—12081no—
406C2#121×D15111yescharacteristic
407C2#2375301411yescharacteristic
408C2#2375302111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#464×C151C2
socleC22×C151C22×D4
hypercenter#464D151
hypocenterC151#3045
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. C2×#18012766C2semidirect
2. C2×#18012762C2semidirect
3. #23752780C2semidirect
4. #23752694C2semidirect
5. #23752436C2semidirect
6. #23752430C2semidirect
7. #23752424C2semidirect
8. #23752412C2semidirect
9. #23752410C2semidirect
10. #23752408C2semidirect
11. #23752406C2semidirect
12. #23752237C2semidirect
13. #23752212C2semidirect
14. #102×D151C2semidirect
15. #464×C151C2semidirect
22. C2×#14558991C22semidirect
23. C2×#14558991C22semidirect
25. C2×D1208C22semidirect
36. Q8×Dic151C22semidirect
38. C4×D604C22semidirect
40. #18012701C22semidirect
45. C4⋊(C151⋊C8)C22semidirect
46. Dic151⋊C8C22semidirect
47. Dic151⋊C8C22semidirect
48. #18012663C22semidirect
50. #18012661C22semidirect
53. #18012659C22semidirect
54. C2×Q16×C151C22semidirect
57. C4×Q8×C151C22semidirect
58. C4⋊C8×C151C22semidirect
59. #103×C151C22semidirect
65. #14559005D4semidirect
204. C151#3045semidirect
211. #464D151semidirect
226. C2×Q16C2×D151semidirect
245. C4×Q8C2×D151semidirect
257. C4⋊C8C2×D151semidirect
259. #103C2×D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127662
C2×#180127622
#237527802
#237526942
#237524362
#237524302
#237524242
#237524122
#237524102
#237524082
#237524062
#237522372
#237522122
#102×D1512
#464×C1512
#3045151