Finite Group Databasebeta

← #10594756

Subgroups — #10594756

Order 576.

526 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#64315C211yesmaximal, characteristic, complemented
2#64309C211yesmaximal, characteristic, complemented
3#64124C211yesmaximal, characteristic, complemented
4C3×#916C211yesmaximal, characteristic, complemented
5C3×#915C211yesmaximal, characteristic, complemented
6#63944C211yesmaximal, characteristic, complemented
7#63943C211yesmaximal, characteristic, complemented
8D3×#216C211yesmaximal, characteristic, complemented
9#63936C211yesmaximal, characteristic, complemented
10#63933C211yesmaximal, characteristic, complemented
11#63929C211yesmaximal, characteristic, complemented
12#63811C211yesmaximal, characteristic, complemented
13#63804C211yesmaximal, characteristic, complemented
14#63800C211yesmaximal, characteristic, complemented
15D3×Dic12C211yesmaximal, characteristic, complemented
16#5779—31nomaximal
17#5771—31nomaximal
18Q8×C3⋊D3C2211yescharacteristic
19#3830C2211yescharacteristic
20C3×#239C2211yescharacteristic
21C3×D3×Q8C2211yescharacteristic
22C3×#237C2211yescharacteristic
23C3×#237C2211yescharacteristic
24C2×#627—21no—
25#3805—21no—
26#3804—21no—
27#3804—21no—
28#3798—21no—
29#3798C2211yescharacteristic
30#3797C2211yescharacteristic
31#3796—21no—
32#3796C2211yescharacteristic
33#3795—21no—
34#3795C2211yescharacteristic
35D3×Dic6—21no—
36D3×Dic6C2211yescharacteristic
37D3×Dic6C2211yescharacteristic
38D3×Dic6C2211yescharacteristic
39C32×SD16C2211yescharacteristic
40#3756C2211yescharacteristic
41#3754C2211yescharacteristic
42#3746C2211yescharacteristic
43#3743C2211yescharacteristic
44C3×#216C2211yescharacteristic
45C3×#216C2211yescharacteristic
46C3×#214C2211yescharacteristic
47C3×#213C2211yescharacteristic
48C3×Dic12C2211yescharacteristic
49C3×#204C2211yescharacteristic
50C3×ΓL(1,𝔽25)C2211yescharacteristic
51C3×D3×C8C2211yescharacteristic
52#3719C2211yescharacteristic
53#3719C2211yescharacteristic
54#3719C2211yescharacteristic
55#3718C2211yescharacteristic
56#3716C2211yescharacteristic
57#3715C2211yescharacteristic
58#3711C2211yescharacteristic
59#3710C2211yescharacteristic
60D3×C3⋊C8C2211yescharacteristic
61#1010—31no—
62#1010—31no—
63#1010—31no—
64#1007—31no—
65C3×#137—31no—
66C3×#135—31no—
67#951—31no—
68#951—31no—
69#950—31no—
70C2×#216—31no—
71#918—31no—
72#918—31no—
73D3×Q16—31no—
74D3×Q16—31no—
75D3×Q16—31no—
76D3×Q16—31no—
77#916—31no—
78#916D311yescharacteristic, complemented
79#915—31no—
80#915—31no—
81#915—31no—
82#915—31no—
83#915—31no—
84#915—61no—
85#915D311yescharacteristic, complemented
86#912—31no—
87#912—31no—
88#909—31no—
89#907—31no—
90C2×Dic12—31no—
91#901—31no—
92C32×Q8C2311yescharacteristic
93C32×D4C2311yescharacteristic
94#638—21no—
95C2×C3⋊Dic3—21no—
96C4×C3⋊D3—21no—
97C4×C3⋊D3C2311yescharacteristic
98#634—21no—
99#634C2311yescharacteristic
100#634C2311yescharacteristic
101C3×#67—21no—
102C3×#67—21no—
103C2×C3×Dic3—21no—
104C2×C3×Dic3—21no—
105C3×D12—21no—
106C3×D12C2311yescharacteristic
107C3×C4×D3—21no—
108C3×C4×D3—21no—
109C3×C4×D3C2311yescharacteristic
110C3×C4×D3C2311yescharacteristic
111C3×Dic6—21no—
112C3×Dic6C2311yescharacteristic
113C3×Dic6C2311yescharacteristic
114C3×Dic6C2311yescharacteristic
115#627—21no—
116#627—21no—
117#627—21no—
118#627—21no—
119#627D411yescharacteristic
120#626—21no—
121#626D411yescharacteristic
122#626D411yescharacteristic
123#625—21no—
124#625D411yescharacteristic
125#624—21no—
126D3×Dic3—21no—
127D3×Dic3—21no—
128D3×Dic3—21no—
129D3×Dic3—21no—
130D3×Dic3—21no—
131C32×C8C2311yescharacteristic
132C3⋊(C3⋊C8)C2311yescharacteristic
133C3×C3⋊C8C2311yescharacteristic
134C3×C3⋊C8C2311yescharacteristic
135#578—91noSylow
136C3×#41—31no—
137C3×#41—31no—
138C3×#41—31no—
139C2×C3×Q8—31no—
140#239—31no—
141#239—61no—
142#239C2×D311yescharacteristic
143D3×Q8—31no—
144D3×Q8—31no—
145D3×Q8—31no—
146D3×Q8—31no—
147D3×Q8—31no—
148D3×Q8—31no—
149D3×Q8—31no—
150D3×Q8—61no—
151D3×Q8—61no—
152D3×Q8C2×D311yescharacteristic
153#237—31no—
154#237—31no—
155#237—31no—
156#237—31no—
157#237—61no—
158#237—61no—
159#237—61no—
160#237—61no—
161#237—61no—
162#237—61no—
163#237—61no—
164#237C2×D311yescharacteristic
165#237C2×D311yescharacteristic
166#235—31no—
167#235—31no—
168#235—31no—
169#235—61no—
170#235—61no—
171#235—61no—
172#235—61no—
173#235—61no—
174C2×Dic6—31no—
175C2×Dic6—31no—
176C2×Dic6—31no—
177C2×Dic6—61no—
178C2×Dic6—61no—
179C2×Dic6—61no—
180C3×Q16—31no—
181C3×Q16—31no—
182C3×Q16—31no—
183C3×SD16—21no—
184C3×SD16—31no—
185C3×SD16—31no—
186C3×SD16C2×D311yescharacteristic
187C3×SD16C2×D311yescharacteristic
188C3×D8—31no—
189C3×M16—31no—
190C2×C3×C8—31no—
191#216—31no—
192#216—31no—
193#216—31no—
194#216—31no—
195#216—31no—
196#216—31no—
197#216—31no—
198#216—61no—
199#216C2×D311yescharacteristic
200#216C2×D311yescharacteristic
201#215—31no—
202#214—31no—
203#214—31no—
204#214—31no—
205#214—31no—
206#214—61no—
207#214C2×D311yescharacteristic
208#213C2×D311yescharacteristic
209#208—31no—
210C2×C3⋊C8—31no—
211Dic12—31no—
212Dic12—31no—
213Dic12—31no—
214Dic12—31no—
215Dic12—31no—
216Dic12—61no—
217Dic12C2×D311yescharacteristic
218#204—31no—
219#204C2×D311yescharacteristic
220ΓL(1,𝔽25)—31no—
221ΓL(1,𝔽25)—31no—
222ΓL(1,𝔽25)—31no—
223ΓL(1,𝔽25)—61no—
224ΓL(1,𝔽25)C2×D311yescharacteristic
225D3×C8—31no—
226D3×C8—31no—
227D3×C8—31no—
228D3×C8C2×D311yescharacteristic
229C22×C32—21no—
230C2×C3⋊D3C2×D411yescharacteristic
231C2×C3×D3—21no—
232C2×C3×D3C2×D411yescharacteristic
233C2×C3×D3C2×D411yescharacteristic
234C32×C4—21no—
235C32×C4C2411yescharacteristic
236C3⋊Dic3—21no—
237C3⋊Dic3—21no—
238C3⋊Dic3C2×D411yescharacteristic
239C3×Dic3—21no—
240C3×Dic3—21no—
241C3×Dic3—21no—
242C3×Dic3C2×D411yescharacteristic
243C3×Dic3C2×D411yescharacteristic
2442−1+4—91no—
2452−1+4—91no—
246#137—31no—
247#137—91no—
248#137—91no—
249#137—91no—
250#137—91no—
251#137—91no—
252#135—31no—
253#135—91no—
254#135—91no—
255C2×Q16—91no—
256C2×Q16—91no—
257C2×Q16—91no—
258#131—91no—
259C3×Q8—21no—
260C3×Q8—31no—
261C3×Q8—31no—
262C3×Q8—31no—
263C3×Q8—61no—
264C3×Q8C22×D311yescharacteristic
265C3×Q8C22×D311yescharacteristic
266C3×D4—21no—
267C3×D4—31no—
268C3×D4—61no—
269C3×D4—61no—
270C3×D4—61no—
271C3×D4C22×D311yescharacteristic
272C3×D4C22×D311yescharacteristic
273C2×C3×C4—31no—
274C2×C3×C4—31no—
275C2×C3×C4—61no—
276C2×C3×C4—61no—
277C2×C3×C4—61no—
278C2×C3×C4—61no—
279#67—21no—
280#67—21no—
281#67—31no—
282#67—31no—
283#67—31no—
284#67—31no—
285#67—61no—
286#67—61no—
287#67—61no—
288#67—61no—
289#67—61no—
290#67—121no—
291C2×Dic3—21no—
292C2×Dic3—21no—
293C2×Dic3—61no—
294C2×Dic3—61no—
295C2×Dic3—61no—
296C2×Dic3—61no—
297C2×Dic3—61no—
298C2×Dic3—61no—
299C2×Dic3—61no—
300C2×Dic3—121no—
301D12—21no—
302D12—31no—
303D12—31no—
304D12—61no—
305D12C22×D311yescharacteristic
306C4×D3—21no—
307C4×D3—21no—
308C4×D3—31no—
309C4×D3—31no—
310C4×D3—61no—
311C4×D3—61no—
312C4×D3—61no—
313C4×D3—61no—
314C4×D3—61no—
315C4×D3—61no—
316C4×D3—61no—
317C4×D3—61no—
318C4×D3—61no—
319C4×D3—61no—
320C4×D3—121no—
321C4×D3C22×D311yescharacteristic
322C4×D3C22×D311yescharacteristic
323Dic6—21no—
324Dic6—31no—
325Dic6—31no—
326Dic6—31no—
327Dic6—31no—
328Dic6—31no—
329Dic6—31no—
330Dic6—61no—
331Dic6—61no—
332Dic6—61no—
333Dic6—61no—
334Dic6—61no—
335Dic6—61no—
336Dic6—61no—
337Dic6—61no—
338Dic6—61no—
339Dic6—61no—
340Dic6—61no—
341Dic6—61no—
342Dic6—121no—
343Dic6C22×D311yescharacteristic
344Dic6C22×D311yescharacteristic
345Dic6C22×D311yescharacteristic
346C3×C8—21no—
347C3×C8—31no—
348C3×C8—31no—
349C3×C8C22×D311yescharacteristic
350C3×C8C22×D311yescharacteristic
351C3⋊C8—31no—
352C3⋊C8—31no—
353C3⋊C8—61no—
354C3⋊C8C22×D311yescharacteristic
355C3⋊C8C22×D311yescharacteristic
356C2×C32—41no—
357C2×C32C22×D411yescharacteristic
358C3⋊D3—21no—
359C3×D3—21no—
360C3×D3—21no—
361C3×D3—41no—
362#41—31no—
363#41—31no—
364#41—31no—
365#41—91no—
366#41—91no—
367#41—91no—
368#41—91no—
369#41—181no—
370#41—181no—
371#41—181no—
372#41—181no—
373#41—181no—
374#41—181no—
375C2×Q8—31no—
376C2×Q8—91no—
377C2×Q8—91no—
378C2×Q8—91no—
379C2×Q8—91no—
380C2×Q8—91no—
381C2×Q8—181no—
382C2×Q8—181no—
383Q16—31no—
384Q16—31no—
385Q16—31no—
386Q16—91no—
387Q16—91no—
388Q16—91no—
389Q16—91no—
390Q16—91no—
391Q16—91no—
392SD16—31no—
393SD16—31no—
394SD16—91no—
395SD16—91no—
396SD16—91no—
397SD16D3211yescharacteristic
398D8—31no—
399M16—31no—
400M16—91no—
401M16—91no—
402C2×C8—31no—
403C2×C8—91no—
404C2×C8—91no—
405C22×C3—21no—
406C22×C3—21no—
407C22×C3—31no—
408C22×C3—31no—
409C22×C3—41no—
410C22×C3—61no—
411C2×D3—21no—
412C2×D3—31no—
413C2×D3—31no—
414C2×D3—61no—
415C2×D3D3×D411yescharacteristic
416C2×D3D3×D411yescharacteristic
417C3×C4—21no—
418C3×C4—21no—
419C3×C4—21no—
420C3×C4—31no—
421C3×C4—31no—
422C3×C4—41no—
423C3×C4—61no—
424C3×C4—61no—
425C3×C4—61no—
426C3×C4C23×D311yescharacteristic
427C3×C4C23×D311yescharacteristic
428Dic3—21no—
429Dic3—21no—
430Dic3—21no—
431Dic3—31no—
432Dic3—31no—
433Dic3—61no—
434Dic3—61no—
435Dic3—61no—
436Dic3—61no—
437Dic3—61no—
438Dic3—121no—
439Dic3—121no—
440Dic3D3×D411yescharacteristic
441Dic3D3×D411yescharacteristic
442C32#57811yescharacteristic, complemented, Sylow
443Q8—31no—
444Q8—31no—
445Q8—31no—
446Q8—61no—
447Q8—91no—
448Q8—91no—
449Q8—91no—
450Q8—181no—
451Q8—181no—
452Q8—181no—
453Q8—181no—
454Q8—181no—
455Q8C2×D3211yescharacteristic
456D4—31no—
457D4—61no—
458D4—61no—
459D4—61no—
460D4—91no—
461D4—91no—
462D4—91no—
463D4—181no—
464D4—181no—
465D4—181no—
466D4C2×D3211yescharacteristic
467C2×C4—31no—
468C2×C4—31no—
469C2×C4—61no—
470C2×C4—61no—
471C2×C4—61no—
472C2×C4—61no—
473C2×C4—91no—
474C2×C4—181no—
475C2×C4—181no—
476C2×C4—181no—
477C2×C4—181no—
478C2×C4—181no—
479C2×C4—181no—
480C2×C4—181no—
481C2×C4—181no—
482C8—31no—
483C8—31no—
484C8—91no—
485C8C2×D3211yescharacteristic
486C2×C3—21no—
487C2×C3—41no—
488C2×C3—41no—
489C2×C3—61no—
490C2×C3—61no—
491C2×C3—81no—
492C2×C3—121no—
493C2×C3C2×D3×D411yescharacteristic
494C2×C3C2×D3×D411yescharacteristic
495D3—21no—
496D3—21no—
497D3—41no—
498D3—61no—
499D3—61no—
500D3—121no—
501C22—21no—
502C22—31no—
503C22—31no—
504C22—61no—
505C22—91no—
506C4—21no—
507C4—31no—
508C4—31no—
509C4—61no—
510C4—61no—
511C4—61no—
512C4—91no—
513C4—181no—
514C4—181no—
515C4C22×D3211yescharacteristic
516C3—21no—
517C3#577111yescharacteristic, complemented
518C3#577911yescharacteristic, complemented
519C2—41no—
520C2—61no—
521C2—61no—
522C2—121no—
523C2—181no—
524C2D32×D411yescharacteristic
subgroupG/H
centerC2D32×D4
commutator, cosocleC32×C4C24
FrattiniC4C22×D32
FittingC32×SD16C22
socleC2×C32C22×D4
hypercenterSD16D32
hypocenterC32#578
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C4 ◁ SD16

Complements

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

NH ≅ G/Ntype
1. #64315C2semidirect
2. #64309C2semidirect
3. #64124C2semidirect
4. C3×#916C2semidirect
5. C3×#915C2semidirect
6. #63944C2semidirect
7. #63943C2semidirect
8. D3×#216C2semidirect
9. #63936C2semidirect
10. #63933C2semidirect
11. #63929C2semidirect
12. #63811C2semidirect
13. #63804C2semidirect
14. #63800C2semidirect
15. D3×Dic12C2semidirect
78. #916D3semidirect
85. #915D3semidirect
442. C32#578semidirect
517. C3#5771semidirect
518. C3#5779semidirect

Maximal subgroups

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

subgroupindex
#643152
#643092
#641242
C3×#9162
C3×#9152
#639442
#639432
D3×#2162
#639362
#639332
#639292
#638112
#638042
#638002
D3×Dic122
#57793
#57713