Finite Group Databasebeta

← #34080883

Subgroups — #34080883

Order 19328.

448 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23753027C211yesmaximal, characteristic, complemented
2#23753026C211yesmaximal, characteristic, complemented
3#23753023C211yesmaximal, characteristic, complemented
4#23752603C211yesmaximal, characteristic, complemented
5#23752487C211yesmaximal, characteristic, complemented
6#23752485C211yesmaximal, characteristic, complemented
7#23752473C211yesmaximal, characteristic, complemented
8#23752472C211yesmaximal, characteristic, complemented
9#23752395C211yesmaximal, characteristic, complemented
10#23752393C211yesmaximal, characteristic, complemented
11#23752390C211yesmaximal, characteristic, complemented
12#23752383C211yesmaximal, characteristic, complemented
13#23752334C211yesmaximal, characteristic, complemented
14#23752332C211yesmaximal, characteristic, complemented
15#577×C151C211yesmaximal, characteristic, complemented
16#18012786C2211yescharacteristic
17#18012786C2211yescharacteristic, complemented
18#18012770—21no—
19#18012770C2211yescharacteristic, complemented
20#18012769—21no—
21#18012769—21no—
22#18012769C2211yescharacteristic
23#18012769C2211yescharacteristic
24#18012769C2211yescharacteristic
25#18012769C2211yescharacteristic, complemented
26#18012768—21no—
27#18012768—21no—
28#18012765—21no—
29#18012765C2211yescharacteristic
30#18012759—21no—
31#18012759—21no—
32#18012759C2211yescharacteristic
33#18012758—21no—
34C2×Dic604C2211yescharacteristic, complemented
35C2×#14558994—21no—
36C2×#14558994C2211yescharacteristic, complemented
37Q16×D151—21no—
38C2×#14558992—21no—
39C2×#14558992C2211yescharacteristic
40#18012746C2211yescharacteristic
41#18012746C2211yescharacteristic, complemented
42#18012745C2211yescharacteristic, complemented
43#18012737C2211yescharacteristic, complemented
44#18012726C2211yescharacteristic
45#18012675C2211yescharacteristic, complemented
46#18012674C2211yescharacteristic, complemented
47#18012666C2211yescharacteristic
48#18012666C2211yescharacteristic
49#18012666C2211yescharacteristic, complemented
50#18012665C2211yescharacteristic, complemented
51#18012658C2211yescharacteristic, complemented
52#18012657C2211yescharacteristic, complemented
53#18012657C2211yescharacteristic, complemented
54#18012656C2211yescharacteristic
55#18012649C2211yescharacteristic, complemented
562−1+4×C151C2211yescharacteristic
57H(5,𝔽2)×C151C2211yescharacteristic
58#137×C151—21no—
59#137×C151C2211yescharacteristic
60AGL(1,ℤ/8)×C151—21no—
61AGL(1,ℤ/8)×C151C2211yescharacteristic
62#135×C151—21no—
63#135×C151C2211yescharacteristic
64C2×SD16×C151—21no—
65C2×SD16×C151C2211yescharacteristic
66#131×C151C2211yescharacteristic
67#14559004—21no—
68#14559004—21no—
69#14559004C2311yescharacteristic
70#14559003—21no—
71#14559003—21no—
72#14559003—41no—
73#14559003—41no—
74C2×Dic302—21no—
75C2×Dic302—21no—
76C2×Dic302C2311yescharacteristic
77C2×Dic302C2311yescharacteristic
78Q8×D151—21no—
79Q8×D151—21no—
80Dic604—21no—
81Dic604—21no—
82#14558994—21no—
83#14558994—21no—
84#14558994—21no—
85#14558994—21no—
86#14558994—21no—
87#14558994—21no—
88#14558994—21no—
89#14558994D411yescharacteristic
90#14558992—21no—
91#14558992—21no—
92#14558992—21no—
93#14558992—21no—
94#14558992—21no—
95#14558992—21no—
96#14558992—21no—
97#14558992D411yescharacteristic
98#14558991—21no—
99#14558991D411yescharacteristic
100#14558989—21no—
101#14558989D411yescharacteristic
102#14558988—21no—
103#14558988—21no—
104#14558988C2311yescharacteristic
105#14558988C2311yescharacteristic
106#14558988C2311yescharacteristic
107#14558987—21no—
108C2×C151⋊C8—21no—
109C2×C151⋊C8—21no—
110C2×C151⋊C8C2311yescharacteristic
111C8×D151—21no—
112Dic151⋊C4—41no—
113C22⋊Dic151—41no—
114C4×Dic151C2311yescharacteristic
115#41×C151—21no—
116#41×C151—21no—
117#41×C151—21no—
118#41×C151—21no—
119#41×C151—41no—
120#41×C151C2311yescharacteristic
121#41×C151C2311yescharacteristic
122#41×C151C2311yescharacteristic
123C2×Q8×C151—21no—
124C2×Q8×C151—21no—
125C2×Q8×C151C2311yescharacteristic
126C2×D4×C151—21no—
127C2×D4×C151—21no—
128C2×D4×C151—41no—
129C2×D4×C151C2311yescharacteristic
130Q16×C151—21no—
131Q16×C151D411yescharacteristic
132SD16×C151—21no—
133SD16×C151—21no—
134SD16×C151—21no—
135SD16×C151—21no—
136SD16×C151D411yescharacteristic
137SD16×C151D411yescharacteristic
138D8×C151—21no—
139D8×C151D411yescharacteristic
140M16×C151—21no—
141M16×C151C2311yescharacteristic
142C2×C8×C151—21no—
143C2×C8×C151C2311yescharacteristic
144Dic302—21no—
145Dic302—21no—
146Dic302—21no—
147Dic302—21no—
148Dic302—41no—
149Dic302—41no—
150Dic302C2×D411yescharacteristic
151D604C2×D411yescharacteristic
152C22⋊D151—21no—
153C22⋊D151—41no—
154C22⋊D151—41no—
155C2×Dic151—21no—
156C2×Dic151—21no—
157C2×Dic151—21no—
158C2×Dic151—41no—
159C2×Dic151—41no—
160C4×D151—21no—
161C4×D151—41no—
162C4×D151—41no—
163C151⋊C8—21no—
164C151⋊C8—21no—
165C151⋊C8—21no—
166C151⋊C8C2×D411yescharacteristic
167C151⋊C8C2×D411yescharacteristic
168C23×C151—21no—
169C23×C151—41no—
170Q8×C151—21no—
171Q8×C151—21no—
172Q8×C151—41no—
173Q8×C151C2×D411yescharacteristic
174Q8×C151C2×D411yescharacteristic
175Q8×C151C2×D411yescharacteristic
176D4×C151—21no—
177D4×C151—21no—
178D4×C151—21no—
179D4×C151—21no—
180D4×C151—21no—
181D4×C151—41no—
182D4×C151—41no—
183D4×C151—41no—
184D4×C151C2×D411yescharacteristic
185D4×C151C2×D411yescharacteristic
186D4×C151C2×D411yescharacteristic
187C2×C4×C151—21no—
188C2×C4×C151—21no—
189C2×C4×C151—21no—
190C2×C4×C151—21no—
191C2×C4×C151—41no—
192C2×C4×C151—41no—
193C2×C4×C151—41no—
194C2×C4×C151C2411yescharacteristic
195C8×C151—21no—
196C8×C151C2×D411yescharacteristic
197C8×C151C2×D411yescharacteristic
198C22×C151—21no—
199C22×C151—21no—
200C22×C151—21no—
201C22×C151—41no—
202C22×C151—81no—
203C22×C151—161no—
204C22×C151H(5,𝔽2)11yescharacteristic
205C2×D151—21no—
206C4×C151—21no—
207C4×C151—21no—
208C4×C151—21no—
209C4×C151—41no—
210C4×C151C22×D411yescharacteristic
211C4×C151C22×D411yescharacteristic
212Dic151—21no—
213Dic151—41no—
214Dic151—41no—
215Dic151—41no—
216C2×C151—21no—
217C2×C151—41no—
218C2×C151—41no—
219C2×C151—41no—
220C2×C151—81no—
221C2×C151D4211yescharacteristic
222D151—41no—
223C151#328911yescharacteristic, complemented, Sylow
224#3289—1511nomaximal, Sylow
225#578—1511no—
226#578—1511no—
227#577—1511no—
228#577D15111yescharacteristic, complemented
229#497—1511no—
230#473—1511no—
231#473—1511no—
232#471—1511no—
233#471—1511no—
234#456—1511no—
235#456—1511no—
236#455—1511no—
237#454—1511no—
238#444—1511no—
239#444—1511no—
2402−1+4—1511no—
2412−1+4—1511no—
2422−1+4C2×D15111yescharacteristic
243H(5,𝔽2)C2×D15111yescharacteristic
244#137—21no—
245#137—3021no—
246#137—3021no—
247#137—3021no—
248#137—3021no—
249#137—3021no—
250#137—1511no—
251#137—1511no—
252#137—1511no—
253#137—1511no—
254#137—1511no—
255#137C2×D15111yescharacteristic
256AGL(1,ℤ/8)—21no—
257AGL(1,ℤ/8)—3021no—
258AGL(1,ℤ/8)—1511no—
259AGL(1,ℤ/8)C2×D15111yescharacteristic
260#135—21no—
261#135—3021no—
262#135—3021no—
263#135—3021no—
264#135—1511no—
265#135C2×D15111yescharacteristic
266C2×Q16—3021no—
267C2×Q16—3021no—
268C2×Q16—1511no—
269C2×Q16—1511no—
270C2×SD16—21no—
271C2×SD16—3021no—
272C2×SD16—1511no—
273C2×SD16C2×D15111yescharacteristic
274#131—1511no—
275#131—1511no—
276#131—1511no—
277#131C2×D15111yescharacteristic
278C4⋊Q8—1511no—
279#124—1511no—
280#108—1511no—
281#108—1511no—
282#104—1511no—
283#104—1511no—
284#104—1511no—
285#104—1511no—
286#101—1511no—
287#101—1511no—
288#101—1511no—
289#100—1511no—
290#97—1511no—
291#41—21no—
292#41—21no—
293#41—21no—
294#41—21no—
295#41—41no—
296#41—3021no—
297#41—3021no—
298#41—3021no—
299#41—3021no—
300#41—6041no—
301#41—6041no—
302#41—1511no—
303#41C22×D15111yescharacteristic
304#41C22×D15111yescharacteristic
305#41C22×D15111yescharacteristic
306C2×Q8—21no—
307C2×Q8—21no—
308C2×Q8—3021no—
309C2×Q8—3021no—
310C2×Q8—3021no—
311C2×Q8—3021no—
312C2×Q8—1511no—
313C2×Q8—1511no—
314C2×Q8C22×D15111yescharacteristic
315C2×D4—21no—
316C2×D4—21no—
317C2×D4—41no—
318C2×D4C22×D15111yescharacteristic
319Q16—21no—
320Q16—3021no—
321Q16—3021no—
322Q16—3021no—
323Q16—3021no—
324Q16—3021no—
325Q16—3021no—
326Q16—3021no—
327Q16—3021no—
328Q16—3021no—
329Q16—1511no—
330Q16C22⋊D15111yescharacteristic
331SD16—21no—
332SD16—21no—
333SD16—21no—
334SD16—21no—
335SD16—3021no—
336SD16—3021no—
337SD16—3021no—
338SD16—3021no—
339SD16—3021no—
340SD16—3021no—
341SD16—3021no—
342SD16—3021no—
343SD16—1511no—
344SD16—1511no—
345SD16C22⋊D15111yescharacteristic
346SD16C22⋊D15111yescharacteristic
347D8—21no—
348D8—3021no—
349D8—1511no—
350D8C22⋊D15111yescharacteristic
351M16—21no—
352M16—3021no—
353M16—3021no—
354M16—3021no—
355M16—1511no—
356M16—1511no—
357M16—1511no—
358M16C22×D15111yescharacteristic
359C2×C8—21no—
360C2×C8—3021no—
361C2×C8—3021no—
362C2×C8—3021no—
363C2×C8—1511no—
364C2×C8C22×D15111yescharacteristic
365C4⋊C4—6041no—
366C22⋊C4—6041no—
367C42—1511no—
368C23—21no—
369C23—41no—
370Q8—21no—
371Q8—21no—
372Q8—41no—
373Q8—3021no—
374Q8—3021no—
375Q8—3021no—
376Q8—3021no—
377Q8—6041no—
378Q8—6041no—
379Q8—1511no—
380Q8D4×D15111yescharacteristic
381Q8C2×C22⋊D15111yescharacteristic
382Q8C2×C22⋊D15111yescharacteristic
383D4—21no—
384D4—21no—
385D4—21no—
386D4—21no—
387D4—21no—
388D4—41no—
389D4—41no—
390D4—41no—
391D4—3021no—
392D4—6041no—
393D4—6041no—
394D4—1511no—
395D4D4×D15111yescharacteristic
396D4C2×C22⋊D15111yescharacteristic
397D4C2×C22⋊D15111yescharacteristic
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—3021no—
406C2×C4—3021no—
407C2×C4—3021no—
408C2×C4—3021no—
409C2×C4—6041no—
410C2×C4—6041no—
411C2×C4—6041no—
412C2×C4—6041no—
413C2×C4C23×D15111yescharacteristic
414C8—21no—
415C8—3021no—
416C8—3021no—
417C8—3021no—
418C8—1511no—
419C8—1511no—
420C8C2×C22⋊D15111yescharacteristic
421C8C2×C22⋊D15111yescharacteristic
422C22—21no—
423C22—21no—
424C22—21no—
425C22—41no—
426C22—81no—
427C22—161no—
428C22—3021no—
429C22#1801278411yescharacteristic
430C4—21no—
431C4—21no—
432C4—21no—
433C4—41no—
434C4—3021no—
435C4—6041no—
436C4—6041no—
437C4—6041no—
438C4C2×D4×D15111yescharacteristic
439C4C22×C22⋊D15111yescharacteristic
440C2—21no—
441C2—41no—
442C2—41no—
443C2—41no—
444C2—81no—
445C2—6041no—
446C2D4×C22⋊D15111yescharacteristic
subgroupG/H
centerC2D4×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#577×C151C2
socleC2×C151D42
hypercenter#577D151
hypocenterC151#3289
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C2×C4 ◁ #577

Complements

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

NH ≅ G/Ntype
1. #23753027C2semidirect
2. #23753026C2semidirect
3. #23753023C2semidirect
4. #23752603C2semidirect
5. #23752487C2semidirect
6. #23752485C2semidirect
7. #23752473C2semidirect
8. #23752472C2semidirect
9. #23752395C2semidirect
10. #23752393C2semidirect
11. #23752390C2semidirect
12. #23752383C2semidirect
13. #23752334C2semidirect
14. #23752332C2semidirect
15. #577×C151C2semidirect
17. #18012786C22semidirect
19. #18012770C22semidirect
25. #18012769C22semidirect
34. C2×Dic604C22semidirect
36. C2×#14558994C22semidirect
41. #18012746C22semidirect
42. #18012745C22semidirect
43. #18012737C22semidirect
45. #18012675C22semidirect
46. #18012674C22semidirect
49. #18012666C22semidirect
50. #18012665C22semidirect
51. #18012658C22semidirect
52. #18012657C22semidirect
53. #18012657C22semidirect
55. #18012649C22semidirect
223. C151#3289semidirect
228. #577D151semidirect

Maximal subgroups

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

subgroupindex
#237530272
#237530262
#237530232
#237526032
#237524872
#237524852
#237524732
#237524722
#237523952
#237523932
#237523902
#237523832
#237523342
#237523322
#577×C1512
#3289151