Finite Group Databasebeta

← #34080649

Subgroups — #34080649

Order 19328.

510 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18012763C211yesmaximal, characteristic, complemented
2C2×#18012760C211yesmaximal, characteristic, complemented
3#23752882C211yesmaximal, characteristic, complemented
4#23752855C211yesmaximal, characteristic, complemented
5#23752455C211yesmaximal, characteristic, complemented
6#23752445C211yesmaximal, characteristic, complemented
7#23752431C211yesmaximal, characteristic, complemented
8#23752404C211yesmaximal, characteristic, complemented
9#23752371C211yesmaximal, characteristic, complemented
10#23752356C211yesmaximal, characteristic, complemented
11#23752354C211yesmaximal, characteristic, complemented
12#23752344C211yesmaximal, characteristic, complemented
13#23752314C211yesmaximal, characteristic, complemented
14#23752285C211yesmaximal, characteristic, complemented
15#496×C151C211yesmaximal, characteristic, complemented
16C2×#14559005C2211yescharacteristic
17C2×#14559003C2211yescharacteristic
18C2×#14559003C2211yescharacteristic, complemented
19C2×D4×D151C2211yescharacteristic
20#18012763—24no—
21#18012760—24no—
22C2×#14558994C2211yescharacteristic, complemented
23C2×#14558993C2211yescharacteristic
24C2×#14558992C2211yescharacteristic
25C2×#14558989C2211yescharacteristic
26C2×#14558989C2211yescharacteristic
27C2×#14558987C2211yescharacteristic
28C2×C8×D151C2211yescharacteristic, complemented
29#18012735—21no—
30#18012721—21no—
31#18012715C2211yescharacteristic
32#18012712—21no—
33#18012711—21no—
34#18012711—21no—
35#18012710C2211yescharacteristic
36#18012710C2211yescharacteristic
37#18012710C2211yescharacteristic, complemented
38#18012709—21no—
39C4×Dic302C2211yescharacteristic, complemented
40C4×D604C2211yescharacteristic
41C4×D604C2211yescharacteristic
42D4×Dic151—21no—
43C22⋊C4×D151—21no—
44#18012673C2211yescharacteristic, complemented
45C4⋊(C151⋊C8)C2211yescharacteristic, complemented
46#18012664C2211yescharacteristic, complemented
47#18012663C2211yescharacteristic, complemented
48#18012661C2211yescharacteristic
49#18012660C2211yescharacteristic
50#18012660C2211yescharacteristic, complemented
51#18012660C2211yescharacteristic, complemented
52(C2×D151)⋊C8C2211yescharacteristic
53(C2×D151)⋊C8C2211yescharacteristic, complemented
54C2×SD16×C151C2211yescharacteristic, complemented
55C2×SD16×C151C2211yescharacteristic, complemented
56C2×D8×C151C2211yescharacteristic
57C2×D8×C151C2211yescharacteristic
58#127×C151C2211yescharacteristic, complemented
59#124×C151C2211yescharacteristic
60#97×C151C2211yescharacteristic, complemented
61C23×D151—21no—
62#14559005—22no—
63#14559005—41no—
64#14559003—22no—
65#14559003—22no—
66#14559003—41no—
67#14559003—41no—
68C2×Dic302C2311yescharacteristic
69C2×D604—21no—
70C2×D604D411yescharacteristic
71C2×D604C2311yescharacteristic
72C2×C22⋊D151—21no—
73C2×C22⋊D151—21no—
74C2×C22⋊D151—21no—
75C2×C22⋊D151—21no—
76C2×C22⋊D151—21no—
77C2×C22⋊D151—21no—
78D4×D151—22no—
79D4×D151—41no—
80C22×Dic151—21no—
81C22×Dic151—21no—
82C2×C4×D151—21no—
83C2×C4×D151—21no—
84C2×C4×D151C2311yescharacteristic
85C2×C4×D151C2311yescharacteristic
86#14558994—22no—
87#14558993D414yescomplemented
88#14558992—22no—
89#14558989—22no—
90#14558989—22no—
91#14558987—22no—
92C2×C151⋊C8C2311yescharacteristic
93C2×C151⋊C8C2311yescharacteristic
94C8×D151—22no—
95C4⋊Dic151D411yescharacteristic
96C4⋊Dic151C2311yescharacteristic
97C4⋊Dic151C2311yescharacteristic
98Dic151⋊C4—21no—
99Dic151⋊C4—21no—
100C22⋊Dic151—21no—
101C22⋊Dic151—21no—
102C22⋊Dic151—21no—
103(C2×D151)⋊C4—21no—
104(C2×D151)⋊C4—21no—
105(C2×D151)⋊C4D411yescharacteristic
106(C2×D151)⋊C4D411yescharacteristic
107C4×Dic151—21no—
108C2×Q8×C151C2311yescharacteristic
109C2×D4×C151—21no—
110C2×D4×C151—21no—
111C2×D4×C151C2311yescharacteristic
112C2×D4×C151C2311yescharacteristic
113C2×D4×C151C2311yescharacteristic
114SD16×C151—22no—
115SD16×C151—41no—
116D8×C151—22no—
117D8×C151—41no—
118C2×C8×C151C2311yescharacteristic
119C2×C8×C151C2311yescharacteristic
120C22⋊C4×C151—21no—
121C22⋊C4×C151—21no—
122C42×C151C2311yescharacteristic
123C22×D151—21no—
124C22×D151—42no—
125C22×D151—42no—
126C22×D151—81no—
127C22×D151C2×D411yescharacteristic
128C22×D151C2×D411yescharacteristic
129Dic302—21no—
130Dic302C2×D412yes—
131D604—21no—
132D604—41no—
133D604—42no—
134D604C2×D412yes—
135C22⋊D151—42no—
136C22⋊D151—42no—
137C22⋊D151—42no—
138C22⋊D151—81no—
139C22⋊D151—81no—
140C22⋊D151—81no—
141C2×Dic151—21no—
142C2×Dic151—21no—
143C2×Dic151—21no—
144C2×Dic151—42no—
145C2×Dic151—42no—
146C2×Dic151C2×D411yescharacteristic
147C2×Dic151C2×D411yescharacteristic
148C4×D151—21no—
149C4×D151—21no—
150C4×D151—21no—
151C4×D151—21no—
152C4×D151—42no—
153C4×D151—81no—
154C151⋊C8—21no—
155C151⋊C8—21no—
156C23×C151—21no—
157C23×C151—21no—
158C23×C151—21no—
159Q8×C151—21no—
160Q8×C151—21no—
161D4×C151—21no—
162D4×C151—21no—
163D4×C151—21no—
164D4×C151—21no—
165D4×C151—21no—
166D4×C151—21no—
167D4×C151—42no—
168D4×C151—81no—
169C2×C4×C151—21no—
170C2×C4×C151C2×D411yescharacteristic
171C2×C4×C151C2×D411yescharacteristic
172C2×C4×C151C2411yescharacteristic
173C8×C151—21no—
174C8×C151C2×D412yes—
175C22×C151—41no—
176C22×C151—41no—
177C22×C151—41no—
178C22×C151—41no—
179C22×C151—41no—
180C22×C151—41no—
181C22×C151—41no—
182C22×C151—41no—
183C22×C151—41no—
184C22×C151C22×D411yescharacteristic
185C2×D151—21no—
186C2×D151—21no—
187C2×D151—22no—
188C2×D151—21no—
189C2×D151—21no—
190C2×D151—21no—
191C2×D151—21no—
192C2×D151—41no—
193C2×D151—41no—
194C2×D151—84no—
195C4×C151—21no—
196C4×C151—21no—
197C4×C151—41no—
198C4×C151C22×D411yescharacteristic
199C4×C151H(5,𝔽2)11yescharacteristic
200Dic151—21no—
201Dic151—21no—
202Dic151—22no—
203Dic151—41no—
204Dic151—41no—
205C2×C151—81no—
206C2×C151—81no—
207C2×C151—81no—
208C2×C151D4211yescharacteristic
209C2×C151#57511yescharacteristic
210C2×C151#57611yescharacteristic
211D151—41no—
212D151—41no—
213D151—42no—
214C151#326811yescharacteristic, complemented, Sylow
215#3268—1511nomaximal, Sylow
216C2×AGL(1,ℤ/8)—1511no—
217C2×#135—1511no—
218#550—1511no—
219#546—1511no—
220#496D15111yescharacteristic, complemented
221#468—1511no—
222#466—1511no—
223#464—1511no—
224#459—1511no—
225#452—1511no—
226#449—1511no—
227#449—1511no—
228#447—1511no—
229#440—1511no—
230#435—1511no—
231C2×#41—1511no—
232C2×#41—1511no—
233C2×#41—1511no—
234C22×D4—1511no—
235AGL(1,ℤ/8)—3024no—
236#135—3024no—
237C2×Q16—1511no—
238C2×SD16—1511no—
239C2×SD16—1511no—
240C2×SD16C2×D15111yescharacteristic, complemented
241C2×SD16C2×D15111yescharacteristic, complemented
242C2×D8—1511no—
243C2×D8—1511no—
244C2×D8C2×D15111yescharacteristic
245C2×D8C2×D15111yescharacteristic
246C2×M16—1511no—
247C22×C8—1511no—
248#127—3021no—
249#127C2×D15111yescharacteristic, complemented
250#124C2×D15111yescharacteristic
251#123—3021no—
252C22⋊Q8—1511no—
253#121—3021no—
254#121—3021no—
255#121—3021no—
256#121—1511no—
257#121—1511no—
258#121—1511no—
259#120—3021no—
260C4×Q8—1511no—
261C4×D4—3021no—
262C4×D4—1511no—
263C4×D4—1511no—
264C2×C22⋊C4—3021no—
265#107—1511no—
266C4⋊C8—1511no—
267#103—1511no—
268#103—1511no—
269#102—1511no—
270#102—1511no—
271#102—1511no—
272#102—1511no—
273C22⋊C8—1511no—
274C22⋊C8—1511no—
275#97C2×D15111yescharacteristic, complemented
276C24—3021no—
277#41—3022no—
278#41—3022no—
279#41—3022no—
280#41—6041no—
281#41—6041no—
282#41—6041no—
283C2×Q8—1511no—
284C2×Q8C22×D15111yescharacteristic
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—3021no—
288C2×D4—3022no—
289C2×D4—3021no—
290C2×D4—3021no—
291C2×D4—3021no—
292C2×D4—3021no—
293C2×D4—3021no—
294C2×D4—3021no—
295C2×D4—6041no—
296C2×D4—1511no—
297C2×D4—1511no—
298C2×D4C22×D15111yescharacteristic
299C2×D4C22×D15111yescharacteristic
300C2×D4C22×D15111yescharacteristic
301C22×C4—3021no—
302C22×C4—3021no—
303C22×C4—3021no—
304C22×C4—3021no—
305C22×C4—1511no—
306C22×C4—1511no—
307Q16—3022no—
308SD16—22no—
309SD16—41no—
310SD16—3022no—
311SD16—1514no—
312D8—22no—
313D8—41no—
314D8—3022no—
315D8—3022no—
316M16—3022no—
317C2×C8—3022no—
318C2×C8—1511no—
319C2×C8—1511no—
320C2×C8C22×D15111yescharacteristic
321C2×C8C22×D15111yescharacteristic
322C4⋊C4—3021no—
323C4⋊C4—3021no—
324C4⋊C4—1511no—
325C4⋊C4—1511no—
326C4⋊C4—1511no—
327C22⋊C4—21no—
328C22⋊C4—21no—
329C22⋊C4—3021no—
330C22⋊C4—3021no—
331C22⋊C4—3021no—
332C22⋊C4—3021no—
333C22⋊C4—3021no—
334C22⋊C4—1511no—
335C22⋊C4—1511no—
336C42—3021no—
337C42C22×D15111yescharacteristic
338C23—21no—
339C23—21no—
340C23—21no—
341C23—3021no—
342C23—6042no—
343C23—6042no—
344C23—1511no—
345C23—1511no—
346C23—12081no—
347Q8—21no—
348Q8—21no—
349Q8—3021no—
350Q8—1512no—
351D4—21no—
352D4—21no—
353D4—21no—
354D4—21no—
355D4—21no—
356D4—21no—
357D4—42no—
358D4—81no—
359D4—3021no—
360D4—6041no—
361D4—6042no—
362D4—6042no—
363D4—6042no—
364D4—6042no—
365D4—1512no—
366D4—12081no—
367D4—12081no—
368D4—12081no—
369C2×C4—21no—
370C2×C4—3021no—
371C2×C4—3021no—
372C2×C4—3021no—
373C2×C4—3021no—
374C2×C4—3021no—
375C2×C4—3021no—
376C2×C4—3021no—
377C2×C4—6042no—
378C2×C4—6042no—
379C2×C4—6042no—
380C2×C4—1511no—
381C2×C4—1511no—
382C2×C4—12081no—
383C2×C4D4×D15111yescharacteristic
384C2×C4D4×D15111yescharacteristic
385C2×C4C23×D15111yescharacteristic
386C8—21no—
387C8—3021no—
388C8—3021no—
389C8D4×D15112yes—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—3021no—
400C22—3021no—
401C22—3021no—
402C22—3021no—
403C22—3021no—
404C22—3021no—
405C22—3022no—
406C22—6041no—
407C22—6041no—
408C22—12084no—
409C22C2×D4×D15111yescharacteristic
410C4—21no—
411C4—21no—
412C4—41no—
413C4—3021no—
414C4—3021no—
415C4—3022no—
416C4—6041no—
417C4—6041no—
418C4C2×D4×D15111yescharacteristic
419C4#1801278411yescharacteristic
420C2—81no—
421C2—81no—
422C2—81no—
423C2—6041no—
424C2—6041no—
425C2—6042no—
426C2#2375284711yescharacteristic
427C2#2375300811yescharacteristic
428C2#2375301611yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#496×C151C2
socleC22×C151C22×D4
hypercenter#496D151
hypocenterC151#3268
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. C2×#18012763C2semidirect
2. C2×#18012760C2semidirect
3. #23752882C2semidirect
4. #23752855C2semidirect
5. #23752455C2semidirect
6. #23752445C2semidirect
7. #23752431C2semidirect
8. #23752404C2semidirect
9. #23752371C2semidirect
10. #23752356C2semidirect
11. #23752354C2semidirect
12. #23752344C2semidirect
13. #23752314C2semidirect
14. #23752285C2semidirect
15. #496×C151C2semidirect
18. C2×#14559003C22semidirect
22. C2×#14558994C22semidirect
28. C2×C8×D151C22semidirect
37. #18012710C22semidirect
39. C4×Dic302C22semidirect
44. #18012673C22semidirect
45. C4⋊(C151⋊C8)C22semidirect
46. #18012664C22semidirect
47. #18012663C22semidirect
50. #18012660C22semidirect
51. #18012660C22semidirect
53. (C2×D151)⋊C8C22semidirect
54. C2×SD16×C151C22semidirect
55. C2×SD16×C151C22semidirect
58. #127×C151C22semidirect
60. #97×C151C22semidirect
87. #14558993D4semidirect
214. C151#3268semidirect
220. #496D151semidirect
240. C2×SD16C2×D151semidirect
241. C2×SD16C2×D151semidirect
249. #127C2×D151semidirect
275. #97C2×D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127632
C2×#180127602
#237528822
#237528552
#237524552
#237524452
#237524312
#237524042
#237523712
#237523562
#237523542
#237523442
#237523142
#237522852
#496×C1512
#3268151