Finite Group Databasebeta

← #11898304

Subgroups — #11898304

Order 1152.

872 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593902C211yesmaximal, characteristic
2#10593861C211yesmaximal, characteristic, complemented
3#10592547C211yesmaximal, characteristic, complemented
4C3×#4841C211yesmaximal, characteristic, complemented
5C3×#4830C211yesmaximal, characteristic, complemented
6#10590877C212yesmaximal, complemented
7#10590799C212yesmaximal, complemented
8#10590792C212yesmaximal, complemented
9#10590760C212yesmaximal, complemented
10#10590373C211yesmaximal, characteristic, complemented
11C4×#3716C211yesmaximal, characteristic, complemented
12#80420—31nomaximal
13#79911—31nomaximal
14C2×#3799—21no—
15C2×#3744C2212yes—
16#64083C2211yescharacteristic
17C4×#634C2211yescharacteristic
18C2×C3×#204C2212yes—
19C3×C4×D12C2211yescharacteristic
20C3×#869C2211yescharacteristic
21C3×C4×Dic6C2211yescharacteristic
22#63911C2212yes—
23#63910—22no—
24#63909—21no—
25#63894C2212yes—
26#63872—21no—
27#63866C2212yes—
28#63846—22no—
29#63843—21no—
30Dic3×Dic6C2212yes—
31C2×#3717C2212yes—
32C2×#3717C2212yes—
33C2×#3716C2211yescharacteristic
34C32×C4⋊C8C2211yescharacteristic
35#63648C2212yes—
36C3×#816C2212yes—
37C3×Dic3⋊C8C2212yes—
38C3×C8×Dic3C2212yes—
39C3×C4×C3⋊C8C2211yescharacteristic
40#63573C2211yescharacteristic
41#63567C2211yescharacteristic
42#63563C2211yescharacteristic
43#5721—31no—
44#5577—31no—
45#5570—31no—
46#5553—31no—
47C3×#461—31no—
48C3×C8×Q8—31no—
49#5175—32no—
50#5163—32no—
51#5085—31no—
52C4×#214—31no—
53#4848—32no—
54#4848—31no—
55#4848—31no—
56#4848—61no—
57#4841—32no—
58#4841D311yescharacteristic, complemented
59#4830D311yescharacteristic, complemented
60#4818—32no—
61#4788—32no—
62#4693—32no—
63#4693—31no—
64C4×#204—31no—
65C4×#204—32no—
66C2×C4⋊(C3⋊D3)—21no—
67C2×C4⋊(C3⋊D3)—21no—
68C2×C4⋊(C3⋊D3)C2312yes—
69C2×#634C2311yescharacteristic
70C2×C3×D12C2311yescharacteristic
71C2×C3×C4×D3—21no—
72C2×C3×Dic6D411yescharacteristic
73C2×C3×Dic6C2312yes—
74C2×#626—22no—
75C2×#626—22no—
76C2×#624—22no—
77#3799—44no—
78C2×C32×C8C2312yes—
79C32×C42C2311yescharacteristic
80C4⋊(C3⋊Dic3)C2311yescharacteristic
81#3750—21no—
82C4×C3⋊Dic3—21no—
83#3744—42no—
84C3×(C2×D3)⋊C4—21no—
85C3×C4⋊Dic3—21no—
86C3×C4⋊Dic3—21no—
87C3×C4⋊Dic3D411yescharacteristic
88C3×C4⋊Dic3C2311yescharacteristic
89C3×Dic3⋊C4D412yes—
90C3×C4×Dic3C2312yes—
91C2×C3×C3⋊C8C2311yescharacteristic
92C2×C3×C3⋊C8C2311yescharacteristic
93C3×#204—42no—
94Dic3⋊Dic3—22no—
95Dic3⋊Dic3—22no—
96Dic3⋊Dic3—22no—
97#3722—22no—
98Dic32—22no—
99#3717—24no—
100#3717—42no—
101#3716—22no—
102#3392—91noSylow
103C2×#239—61no—
104C2×#235—61no—
105C2×C3×SD16—32no—
106C3×C4⋊Q8—31no—
107C3×C4×Q8—31no—
108C3×C4×D4—31no—
109Q8×Dic3—32no—
110Q8×Dic3—61no—
111#944—32no—
112C2×#215—32no—
113C2×#215—32no—
114#940—32no—
115C2×#214—31no—
116#930—61no—
117C2×#204—31no—
118C2×#204—32no—
119C2×#204—32no—
120C2×#204—32no—
121C2×#204—32no—
122C2×#204—62no—
123C2×#204C2×D312yes—
124#895—62no—
125#895—61no—
126#893—32no—
127#890—62no—
128#890—61no—
129#890—61no—
130#889—62no—
131#887—61no—
132#884—62no—
133#874—32no—
134#874—31no—
135#874—31no—
136#874—61no—
137C4×D12—32no—
138C4×D12C2×D311yescharacteristic
139#869—32no—
140#869C2×D311yescharacteristic
141C4×Dic6—32no—
142C4×Dic6—31no—
143C4×Dic6—31no—
144C4×Dic6—61no—
145C4×Dic6C2×D311yescharacteristic
146C3×C4⋊C8—21no—
147C3×C4⋊C8—32no—
148C3×C4⋊C8C2×D311yescharacteristic
149C3×C4⋊C8C2×D311yescharacteristic
150C3×#103—32no—
151C3×C4×C8—32no—
152C3×C4×C8—31no—
153#832—31no—
154#821—31no—
155#821—32no—
156#821—32no—
157#821—62no—
158#817—31no—
159#816—31no—
160#816C2×D312yes—
161Dic3⋊C8C2×D312yes—
162C8×Dic3C2×D312yes—
163#810—31no—
164#808—31no—
165C4×C3⋊C8C2×D311yescharacteristic
166C22×C3⋊D3—22no—
167C22×C3×D3—21no—
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2411yescharacteristic
171C2×C3⋊Dic3—21no—
172C2×C3⋊Dic3—21no—
173C4⋊(C3⋊D3)—22no—
174C4⋊(C3⋊D3)—22no—
175C4⋊(C3⋊D3)—42no—
176C4⋊(C3⋊D3)—81no—
177#634—21no—
178#634—21no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—21no—
181C2×C3×Dic3C2×D412yes—
182C2×C3×Dic3C2×D412yes—
183C3×D12—21no—
184C3×D12—21no—
185C3×C4×D3—42no—
186C3×Dic6—22no—
187C3×Dic6—22no—
188C3×Dic6SD1614yescomplemented
189#626—44no—
190#626—82no—
191#624—44no—
192C32×C8—22no—
193C3×C3⋊C8—21no—
194C3×C3⋊C8#4112yescomplemented
195#557—91no—
196#550—91no—
197#492—91no—
198#492—92no—
199#461—31no—
200#461—92no—
201#460—92no—
202#460—91no—
203C8×Q8—31no—
204C4×SD16—92no—
205C4×SD16—91no—
206C2×C3×Q8—31no—
207C2×C3×Q8—32no—
208C2×C3×D4—31no—
209C22×C3×C4—61no—
210C2×#67—62no—
211C2×#67—62no—
212#239—124no—
213#235—124no—
214C2×D12—32no—
215C2×D12—32no—
216C2×D12—62no—
217C2×D12—62no—
218C2×D12—61no—
219C2×D12—61no—
220C2×D12—62no—
221C2×D12—61no—
222C2×D12—61no—
223C2×D12—121no—
224C2×D12—121no—
225C2×D12C22×D311yescharacteristic
226C2×C4×D3—21no—
227C2×C4×D3—62no—
228C2×C4×D3—62no—
229C2×Dic6—31no—
230C2×Dic6—31no—
231C2×Dic6—61no—
232C2×Dic6D1211yescharacteristic
233C2×Dic6C22×D312yes—
234C3×SD16—122no—
235C2×C3×C8—22no—
236C2×C3×C8—31no—
237C2×C3×C8—31no—
238C2×C3×C8C22×D312yes—
239C2×C3×C8C22×D312yes—
240C3×C4⋊C4—32no—
241C3×C4⋊C4—31no—
242C3×C4⋊C4—31no—
243C3×C4⋊C4—61no—
244C3×C4⋊C4—61no—
245C3×C22⋊C4—61no—
246C3×C42—21no—
247C3×C42—32no—
248C3×C42C22×D311yescharacteristic
249C3×C42C22×D311yescharacteristic
250#215—64no—
251#215—122no—
252#214—62no—
253(C2×D3)⋊C4—21no—
254(C2×D3)⋊C4—62no—
255(C2×D3)⋊C4—62no—
256C4⋊Dic3—21no—
257C4⋊Dic3—21no—
258C4⋊Dic3—31no—
259C4⋊Dic3—31no—
260C4⋊Dic3—61no—
261C4⋊Dic3—62no—
262C4⋊Dic3—62no—
263C4⋊Dic3—62no—
264C4⋊Dic3D1211yescharacteristic
265C4⋊Dic3C22×D311yescharacteristic
266Dic3⋊C4—62no—
267Dic3⋊C4—61no—
268Dic3⋊C4—61no—
269Dic3⋊C4—62no—
270Dic3⋊C4—62no—
271Dic3⋊C4—121no—
272Dic3⋊C4D1212yes—
273C4×Dic3—62no—
274C4×Dic3—61no—
275C4×Dic3—61no—
276C4×Dic3—62no—
277C4×Dic3—121no—
278C4×Dic3C22×D312yes—
279C2×C3⋊C8C22×D311yescharacteristic
280C2×C3⋊C8C22×D311yescharacteristic
281#204—42no—
282#204—64no—
283#204—62no—
284#204—122no—
285#204—122no—
286#204—124no—
287#204—122no—
288C22×C32C22×D411yescharacteristic
289C2×C3⋊D3—42no—
290C2×C3⋊D3—42no—
291C2×C3⋊D3—42no—
292C2×C3×D3—41no—
293C2×C3×D3—41no—
294C2×C3×D3—41no—
295C32×C4—21no—
296C32×C4C2×SD1612yes—
297C32×C4C2×#4111yescharacteristic
298C32×C4H(5,𝔽2)11yescharacteristic
299C3⋊Dic3—41no—
300C3⋊Dic3—41no—
301C3×Dic3—22no—
302C3×Dic3—42no—
303C3×Dic3—41no—
304C3×Dic3C2×SD1614yes—
305C2×#41—181no—
306C2×SD16—32no—
307C2×SD16—91no—
308C2×SD16—92no—
309C2×SD16—92no—
310C2×SD16—92no—
311C4⋊Q8—31no—
312C4⋊Q8—92no—
313#127—92no—
314#127—91no—
315#125—182no—
316#125—181no—
317#121—182no—
318#121—181no—
319C4×Q8—31no—
320C4×Q8—92no—
321C4×Q8—91no—
322C4×Q8—181no—
323C4×D4—31no—
324C4×D4—92no—
325#106—91no—
326C4⋊C8—32no—
327C4⋊C8D3211yescharacteristic
328#103—32no—
329#103—91no—
330#102—91no—
331#102—92no—
332C4×C8—32no—
333C4×C8—31no—
334C23×C3—61no—
335C22×D3—21no—
336C22×D3—62no—
337C22×D3—62no—
338C22×D3—122no—
339C3×Q8—34no—
340C3×Q8—62no—
341C3×Q8—62no—
342C3×D4—61no—
343C3×D4—61no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—32no—
348C2×C3×C4—32no—
349C2×C3×C4—62no—
350C2×C3×C4—61no—
351C2×C3×C4—122no—
352C2×C3×C4C2×D1211yescharacteristic
353C2×C3×C4C2×D1211yescharacteristic
354C2×C3×C4D3×D411yescharacteristic
355C2×C3×C4D3×D411yescharacteristic
356C2×C3×C4C23×D311yescharacteristic
357C2×C3×C4C23×D311yescharacteristic
358#67—124no—
359#67—242no—
360C2×Dic3—22no—
361C2×Dic3—21no—
362C2×Dic3—61no—
363C2×Dic3—61no—
364C2×Dic3—61no—
365C2×Dic3—61no—
366C2×Dic3—121no—
367C2×Dic3—121no—
368C2×Dic3C2×D1212yes—
369C2×Dic3C2×D1212yes—
370D12—21no—
371D12—21no—
372D12—62no—
373D12—62no—
374D12—62no—
375D12—62no—
376D12—122no—
377D12—122no—
378D12—124no—
379D12—122no—
380D12—122no—
381D12—242no—
382D12—241no—
383D12—241no—
384D12—242no—
385D12—242no—
386C4×D3—42no—
387C4×D3—124no—
388C4×D3—124no—
389Dic6—22no—
390Dic6—22no—
391Dic6—62no—
392Dic6—61no—
393Dic6—61no—
394Dic6—61no—
395Dic6—61no—
396Dic6—121no—
397Dic6#20414yescomplemented
398C3×C8—22no—
399C3×C8—22no—
400C3×C8—32no—
401C3×C8—42no—
402C3×C8—61no—
403C3⋊C8—21no—
404C3⋊C8#23912yescomplemented
405C2×C32#55011yescharacteristic
406C2×C32C22×SD1611yescharacteristic
407C2×C32#57711yescharacteristic
408C3⋊D3—82no—
409C3×D3—81no—
410#41—364no—
411C2×Q8—31no—
412C2×Q8—32no—
413C2×Q8—91no—
414C2×D4—31no—
415C2×D4—92no—
416C2×D4—182no—
417C2×D4—182no—
418C2×D4—181no—
419C2×D4—181no—
420C22×C4—61no—
421C22×C4—182no—
422SD16—122no—
423SD16—182no—
424SD16—184no—
425SD16—362no—
426SD16—362no—
427C2×C8—31no—
428C2×C8—31no—
429C2×C8C2×D3212yes—
430C4⋊C4—32no—
431C4⋊C4—31no—
432C4⋊C4—31no—
433C4⋊C4—61no—
434C4⋊C4—61no—
435C4⋊C4—91no—
436C4⋊C4—182no—
437C4⋊C4—182no—
438C4⋊C4—182no—
439C4⋊C4—181no—
440C22⋊C4—61no—
441C22⋊C4—182no—
442C42—32no—
443C42—182no—
444C42—181no—
445C42C2×D3211yescharacteristic
446C22×C3—21no—
447C22×C3—121no—
448C22×C3—121no—
449C22×C3—121no—
450C22×C3C22×D1211yescharacteristic
451C22×C3C2×D3×D411yescharacteristic
452C2×D3—41no—
453C2×D3—41no—
454C2×D3—41no—
455C2×D3—122no—
456C2×D3—122no—
457C2×D3—122no—
458C2×D3—122no—
459C2×D3—122no—
460C2×D3—122no—
461C2×D3—242no—
462C2×D3—242no—
463C2×D3—242no—
464C3×C4—21no—
465C3×C4—21no—
466C3×C4—22no—
467C3×C4—21no—
468C3×C4—21no—
469C3×C4—34no—
470C3×C4—41no—
471C3×C4—62no—
472C3×C4—121no—
473C3×C4—122no—
474C3×C4C2×#20412yes—
475C3×C4D3×SD1612yes—
476C3×C4#100411yescharacteristic
477C3×C4C2×#23911yescharacteristic
478C3×C4D3×#4111yescharacteristic
479C3×C4#100911yescharacteristic
480Dic3—22no—
481Dic3—41no—
482Dic3—42no—
483Dic3—122no—
484Dic3—121no—
485Dic3—121no—
486Dic3—121no—
487Dic3—121no—
488Dic3—241no—
489Dic3C2×#20414yes—
490C32#339211yescharacteristic, complemented, Sylow
491C23—61no—
492C23—182no—
493Q8—34no—
494Q8—62no—
495Q8—62no—
496Q8—181no—
497Q8—181no—
498D4—61no—
499D4—61no—
500D4—182no—
501D4—182no—
502D4—364no—
503D4—362no—
504D4—721no—
505D4—722no—
506C2×C4—32no—
507C2×C4—32no—
508C2×C4—62no—
509C2×C4—61no—
510C2×C4—122no—
511C2×C4—181no—
512C2×C4—181no—
513C2×C4—364no—
514C2×C4D3×D1211yescharacteristic
515C2×C4D3×D1211yescharacteristic
516C2×C4C22×D3211yescharacteristic
517C8—22no—
518C8—32no—
519C8—61no—
520C2×C3—21no—
521C2×C3—21no—
522C2×C3—21no—
523C2×C3—241no—
524C2×C3#557711yescharacteristic
525C2×C3#559911yescharacteristic
526C2×C3C22×#20411yescharacteristic
527C2×C3#575111yescharacteristic
528C2×C3C2×D3×SD1611yescharacteristic
529C2×C3#577811yescharacteristic
530D3—81no—
531D3—242no—
532D3—242no—
533D3—482no—
534C22—121no—
535C22—121no—
536C22—121no—
537C22—362no—
538C22—362no—
539C22—362no—
540C22C2×D3×D1211yescharacteristic
541C4—21no—
542C4—34no—
543C4—62no—
544C4—121no—
545C4—122no—
546C4—361no—
547C4—361no—
548C4D3×#20412yes—
549C4#6431411yescharacteristic
550C4D3×#23911yescharacteristic
551C3—21no—
552C3#7991111yescharacteristic, complemented
553C3#8042011yescharacteristic, complemented
554C2—241no—
555C2—722no—
556C2#1059452411yescharacteristic
557C2C2×D3×#20411yescharacteristic
558C2#1059471511yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radical#10593902C2
hypercenterC4⋊C8D32
hypocenterC32#3392
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #10593861C2semidirect
3. #10592547C2semidirect
4. C3×#4841C2semidirect
5. C3×#4830C2semidirect
6. #10590877C2semidirect
7. #10590799C2semidirect
8. #10590792C2semidirect
9. #10590760C2semidirect
10. #10590373C2semidirect
11. C4×#3716C2semidirect
58. #4841D3semidirect
59. #4830D3semidirect
188. C3×Dic6SD16semidirect
194. C3×C3⋊C8#41semidirect
397. Dic6#204semidirect
404. C3⋊C8#239semidirect
490. C32#3392semidirect
552. C3#79911semidirect
553. C3#80420semidirect

Maximal subgroups

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

subgroupindex
#105939022
#105938612
#105925472
C3×#48412
C3×#48302
#105908772
#105907992
#105907922
#105907602
#105903732
C4×#37162
#804203
#799113