Finite Group Databasebeta

← #34080882

Subgroups — #34080882

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#23753029C211yesmaximal, characteristic, complemented
2#23753028C211yesmaximal, characteristic, complemented
3#23753022C211yesmaximal, characteristic, complemented
4#23753018C211yesmaximal, characteristic, complemented
5#23752603C211yesmaximal, characteristic, complemented
6#23752488C211yesmaximal, characteristic, complemented
7#23752486C211yesmaximal, characteristic, complemented
8#23752474C211yesmaximal, characteristic, complemented
9#23752397C211yesmaximal, characteristic, complemented
10#23752393C211yesmaximal, characteristic, complemented
11#23752392C211yesmaximal, characteristic, complemented
12#23752383C211yesmaximal, characteristic, complemented
13#23752333C211yesmaximal, characteristic, complemented
14#23752332C211yesmaximal, characteristic, complemented
15#471×C151C211yesmaximal, characteristic, complemented
16#18012787C2211yescharacteristic
17#18012786C2211yescharacteristic
18#18012786C2211yescharacteristic, complemented
19#18012784C2211yescharacteristic
20#18012772—21no—
21#18012772—21no—
22#18012772C2211yescharacteristic
23#18012772C2211yescharacteristic
24#18012772C2211yescharacteristic
25#18012772C2211yescharacteristic, complemented
26#18012771—21no—
27#18012770C2211yescharacteristic
28#18012768—21no—
29#18012768—21no—
30#18012768—21no—
31#18012766—21no—
32#18012765C2211yescharacteristic
33#18012763—21no—
34#18012761—21no—
35#18012761C2211yescharacteristic
36#18012760—21no—
37#18012760—21no—
38#18012759C2211yescharacteristic
39#18012758—21no—
40C2×Dic604—21no—
41C2×Dic604C2211yescharacteristic, complemented
42C2×#14558994C2211yescharacteristic, complemented
43Q16×D151—21no—
44C2×#14558992C2211yescharacteristic
45SD16×D151—21no—
46SD16×D151—21no—
47#18012747C2211yescharacteristic
48#18012747C2211yescharacteristic, complemented
49#18012745C2211yescharacteristic
50#18012737C2211yescharacteristic, complemented
51#18012726C2211yescharacteristic
52#18012674C2211yescharacteristic, complemented
53#18012666C2211yescharacteristic, complemented
54#18012665C2211yescharacteristic
55#18012665C2211yescharacteristic
56#18012665C2211yescharacteristic, complemented
57#18012657C2211yescharacteristic, complemented
58#18012657C2211yescharacteristic, complemented
59#18012649C2211yescharacteristic, complemented
60#137×C151C2211yescharacteristic, complemented
61AGL(1,ℤ/8)×C151C2211yescharacteristic
62C2×SD16×C151C2211yescharacteristic
63#131×C151C2211yescharacteristic, complemented
64#108×C151C2211yescharacteristic, complemented
65#101×C151C2211yescharacteristic, complemented
66#100×C151C2211yescharacteristic
67#14559005—21no—
68#14559005—21no—
69#14559004—21no—
70#14559004—21no—
71#14559004—41no—
72#14559004C2311yescharacteristic
73#14559004C2311yescharacteristic
74#14559004C2311yescharacteristic
75#14559003—21no—
76#14559003—21no—
77#14559003—21no—
78#14559003—21no—
79#14559003—41no—
80#14559003—41no—
81C2×Dic302—21no—
82C2×Dic302—21no—
83C2×Dic302C2311yescharacteristic
84C2×Dic302C2311yescharacteristic
85Q8×D151—21no—
86Q8×D151—21no—
87Q8×D151—21no—
88Q8×D151—21no—
89C2×C22⋊D151—41no—
90D4×D151—21no—
91D4×D151—21no—
92Dic604—21no—
93Dic604—21no—
94Dic604—21no—
95Dic604—21no—
96Dic604—21no—
97Dic604—21no—
98Dic604D411yescharacteristic
99#14558994—21no—
100#14558994—21no—
101#14558994—21no—
102#14558994D411yescharacteristic
103#14558993—21no—
104#14558993—21no—
105#14558993—21no—
106#14558993—21no—
107#14558993D411yescharacteristic
108#14558993D411yescharacteristic
109#14558992—21no—
110#14558992—21no—
111#14558992—21no—
112#14558992D411yescharacteristic
113#14558991—21no—
114#14558991D411yescharacteristic
115D1208D411yescharacteristic
116#14558989—21no—
117#14558989D411yescharacteristic
118#14558988C2311yescharacteristic
119#14558987—21no—
120#14558987—21no—
121#14558987—21no—
122C2×C151⋊C8C2311yescharacteristic
123C8×D151—21no—
124C8×D151—21no—
125C8×D151—21no—
126Dic151⋊C4—41no—
127C22⋊Dic151—41no—
128C4×Dic151C2311yescharacteristic
129#41×C151C2311yescharacteristic
130C2×Q8×C151C2311yescharacteristic
131C2×D4×C151C2311yescharacteristic
132Q16×C151—21no—
133SD16×C151—21no—
134SD16×C151—21no—
135SD16×C151—21no—
136SD16×C151—21no—
137D8×C151—21no—
138M16×C151—21no—
139M16×C151C2311yescharacteristic
140M16×C151C2311yescharacteristic
141M16×C151C2311yescharacteristic
142C2×C8×C151—21no—
143C2×C8×C151C2311yescharacteristic
144C22×D151—41no—
145Dic302—21no—
146Dic302—21no—
147Dic302—21no—
148Dic302—21no—
149Dic302—41no—
150Dic302—41no—
151Dic302—41no—
152Dic302C2×D411yescharacteristic
153Dic302C2×D411yescharacteristic
154Dic302C2×D411yescharacteristic
155D604—41no—
156D604C2×D411yescharacteristic
157D604C2×D411yescharacteristic
158D604C2×D411yescharacteristic
159C22⋊D151—21no—
160C22⋊D151—21no—
161C22⋊D151—21no—
162C22⋊D151—41no—
163C22⋊D151—41no—
164C22⋊D151—41no—
165C22⋊D151—41no—
166C2×Dic151—21no—
167C2×Dic151—21no—
168C2×Dic151—21no—
169C2×Dic151—41no—
170C2×Dic151—41no—
171C2×Dic151—41no—
172C4×D151—21no—
173C4×D151—21no—
174C4×D151—21no—
175C4×D151—41no—
176C4×D151—41no—
177C4×D151—41no—
178C4×D151—41no—
179C151⋊C8—21no—
180C151⋊C8C2×D411yescharacteristic
181C151⋊C8C2×D411yescharacteristic
182C23×C151—21no—
183Q8×C151—21no—
184Q8×C151—21no—
185Q8×C151C2×D411yescharacteristic
186D4×C151—21no—
187D4×C151—21no—
188D4×C151—21no—
189D4×C151C2×D411yescharacteristic
190C2×C4×C151—21no—
191C2×C4×C151—21no—
192C2×C4×C151C2411yescharacteristic
193C8×C151—21no—
194C8×C151—21no—
195C8×C151—21no—
196C8×C151C2×D411yescharacteristic
197C8×C151C2×D411yescharacteristic
198C22×C151—21no—
199C22×C151—41no—
200C22×C151—81no—
201C22×C151H(5,𝔽2)11yescharacteristic
202C2×D151—21no—
203C2×D151—21no—
204C2×D151—21no—
205C2×D151—161no—
206C4×C151—21no—
207C4×C151—41no—
208C4×C151C22×D411yescharacteristic
209C4×C151C22×D411yescharacteristic
210Dic151—21no—
211Dic151—21no—
212Dic151—21no—
213Dic151—41no—
214Dic151—41no—
215Dic151—41no—
216C2×C151—21no—
217C2×C151—41no—
218C2×C151—81no—
219C2×C151D4211yescharacteristic
220D151—41no—
221D151—41no—
222D151—41no—
223C151#328911yescharacteristic, complemented, Sylow
224#3289—1511nomaximal, Sylow
225#578—1511no—
226#578—1511no—
227#577—1511no—
228#577—1511no—
229#497—1511no—
230#473—1511no—
231#473—1511no—
232#471—1511no—
233#471D15111yescharacteristic, complemented
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+4—1511no—
243H(5,𝔽2)—1511no—
244#137—3021no—
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, complemented
256AGL(1,ℤ/8)—3021no—
257AGL(1,ℤ/8)—3021no—
258AGL(1,ℤ/8)—1511no—
259AGL(1,ℤ/8)C2×D15111yescharacteristic
260#135—3021no—
261#135—3021no—
262#135—3021no—
263#135—3021no—
264#135—1511no—
265#135—1511no—
266C2×Q16—3021no—
267C2×Q16—3021no—
268C2×Q16—1511no—
269C2×Q16—1511no—
270C2×SD16—3021no—
271C2×SD16—3021no—
272C2×SD16—1511no—
273C2×SD16C2×D15111yescharacteristic
274#131—1511no—
275#131—1511no—
276#131—1511no—
277#131C2×D15111yescharacteristic, complemented
278C4⋊Q8—1511no—
279#124—1511no—
280#108—1511no—
281#108C2×D15111yescharacteristic, complemented
282#104—1511no—
283#104—1511no—
284#104—1511no—
285#104—1511no—
286#101—1511no—
287#101—1511no—
288#101C2×D15111yescharacteristic, complemented
289#100C2×D15111yescharacteristic
290#97—1511no—
291#41—3021no—
292#41—3021no—
293#41—3021no—
294#41—3021no—
295#41—3021no—
296#41—3021no—
297#41—3021no—
298#41—3021no—
299#41—6041no—
300#41—6041no—
301#41—6041no—
302#41—1511no—
303#41—1511no—
304#41—1511no—
305#41C22×D15111yescharacteristic
306C2×Q8—3021no—
307C2×Q8—3021no—
308C2×Q8—3021no—
309C2×Q8—3021no—
310C2×Q8—3021no—
311C2×Q8—3021no—
312C2×Q8—1511no—
313C2×Q8—1511no—
314C2×Q8C22×D15111yescharacteristic
315C2×D4—3021no—
316C2×D4—3021no—
317C2×D4—6041no—
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—
330Q16—1511no—
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—
345SD16—1511no—
346SD16—1511no—
347D8—21no—
348D8—3021no—
349D8—1511no—
350D8—1511no—
351M16—21no—
352M16—3021no—
353M16—3021no—
354M16—3021no—
355M16—1511no—
356M16C22×D15111yescharacteristic
357M16C22×D15111yescharacteristic
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—6041no—
370Q8—21no—
371Q8—21no—
372Q8—3021no—
373Q8—3021no—
374Q8—3021no—
375Q8—3021no—
376Q8—6041no—
377Q8—6041no—
378Q8—6041no—
379Q8—1511no—
380Q8—1511no—
381Q8—1511no—
382Q8D4×D15111yescharacteristic
383D4—21no—
384D4—21no—
385D4—21no—
386D4—3021no—
387D4—3021no—
388D4—3021no—
389D4—6041no—
390D4—6041no—
391D4—6041no—
392D4—6041no—
393D4—6041no—
394D4—1511no—
395D4—1511no—
396D4—1511no—
397D4D4×D15111yescharacteristic
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—3021no—
401C2×C4—3021no—
402C2×C4—3021no—
403C2×C4—3021no—
404C2×C4—3021no—
405C2×C4—3021no—
406C2×C4—6041no—
407C2×C4—6041no—
408C2×C4—6041no—
409C2×C4—6041no—
410C2×C4—6041no—
411C2×C4—6041no—
412C2×C4—6041no—
413C2×C4C23×D15111yescharacteristic
414C8—21no—
415C8—21no—
416C8—21no—
417C8—3021no—
418C8—1511no—
419C8—1511no—
420C8D4×D15111yescharacteristic
421C8D4×D15111yescharacteristic
422C22—21no—
423C22—41no—
424C22—81no—
425C22—3021no—
426C22—3021no—
427C22—3021no—
428C22—24161no—
429C22#1801278511yescharacteristic
430C4—21no—
431C4—41no—
432C4—3021no—
433C4—3021no—
434C4—3021no—
435C4—6041no—
436C4—6041no—
437C4—6041no—
438C4C2×D4×D15111yescharacteristic
439C4C2×D4×D15111yescharacteristic
440C2—21no—
441C2—41no—
442C2—81no—
443C2—6041no—
444C2—6041no—
445C2—6041no—
446C2#2375284611yescharacteristic
subgroupG/H
centerC2#23752846
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#471×C151C2
socleC2×C151D42
hypercenter#471D151
hypocenterC151#3289
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C2×C4 ◁ #471

Complements

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

NH ≅ G/Ntype
1. #23753029C2semidirect
2. #23753028C2semidirect
3. #23753022C2semidirect
4. #23753018C2semidirect
5. #23752603C2semidirect
6. #23752488C2semidirect
7. #23752486C2semidirect
8. #23752474C2semidirect
9. #23752397C2semidirect
10. #23752393C2semidirect
11. #23752392C2semidirect
12. #23752383C2semidirect
13. #23752333C2semidirect
14. #23752332C2semidirect
15. #471×C151C2semidirect
18. #18012786C22semidirect
25. #18012772C22semidirect
41. C2×Dic604C22semidirect
42. C2×#14558994C22semidirect
48. #18012747C22semidirect
50. #18012737C22semidirect
52. #18012674C22semidirect
53. #18012666C22semidirect
56. #18012665C22semidirect
57. #18012657C22semidirect
58. #18012657C22semidirect
59. #18012649C22semidirect
60. #137×C151C22semidirect
63. #131×C151C22semidirect
64. #108×C151C22semidirect
65. #101×C151C22semidirect
223. C151#3289semidirect
233. #471D151semidirect
255. #137C2×D151semidirect
277. #131C2×D151semidirect
281. #108C2×D151semidirect
288. #101C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237530292
#237530282
#237530222
#237530182
#237526032
#237524882
#237524862
#237524742
#237523972
#237523932
#237523922
#237523832
#237523332
#237523322
#471×C1512
#3289151