Finite Group Databasebeta

← #11898308

Subgroups — #11898308

Order 1152.

869 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593900C211yesmaximal, characteristic
2#10593861C211yesmaximal, characteristic, complemented
3C4×#3744C211yesmaximal, characteristic, complemented
4C3×#4693C211yesmaximal, characteristic, complemented
5C3×C8×Dic6C211yesmaximal, characteristic, complemented
6#10590877C212yesmaximal, complemented
7#10590799C212yesmaximal, complemented
8Dic3×#204C212yesmaximal, complemented
9#10590752C212yesmaximal, complemented
10#10590379C211yesmaximal, characteristic, complemented
11#10590377C211yesmaximal, characteristic, complemented
12#81755—31nomaximal
13#79911—31nomaximal
14C2×#3796—21no—
15C2×#3744C2211yescharacteristic
16C4×C4⋊(C3⋊D3)C2211yescharacteristic
17C4×#634C2211yescharacteristic
18C2×C3×#204C2212yes—
19C2×C3×#204C2212yes—
20C3×#874C2211yescharacteristic
21C3×#869C2211yescharacteristic
22C3×C4×Dic6C2211yescharacteristic
23#63916—21no—
24#63911C2212yes—
25Dic3×D12C2212yes—
26#63886—22no—
27#63872—21no—
28#63866C2212yes—
29#63846—22no—
30#63843—21no—
31Dic3×Dic6C2212yes—
32C2×#3717C2212yes—
33C2×#3716C2212yes—
34C32×C4×C8C2211yescharacteristic
35#63648C2211yescharacteristic
36#63644C2211yescharacteristic
37#63643C2211yescharacteristic
38C3×Dic3⋊C8C2212yes—
39C3×C8×Dic3C2212yes—
40C3×C4⋊(C3⋊C8)C2211yescharacteristic
41#63566C2212yes—
42#63563C2212yes—
43#5721—31no—
44#5718—31no—
45#5577—31no—
46#5570—31no—
47C3×#492—31no—
48C3×C8×Q8—31no—
49#5175—32no—
50#5163—32no—
51#5162—32no—
52Dic3×SD16—32no—
53#5083—31no—
54#5075—31no—
55#4848—32no—
56#4848—31no—
57#4841—32no—
58#4841—31no—
59#4693—32no—
60#4693D311yescharacteristic, complemented
61C4×#204—32no—
62C4×#204—31no—
63C4×#204—31no—
64C4×#204—61no—
65C8×Dic6D311yescharacteristic, complemented
66C2×C4⋊(C3⋊D3)C2311yescharacteristic
67C2×C4×C3⋊D3—21no—
68C2×#634C2311yescharacteristic
69C2×C3×D12—21no—
70C2×C3×D12—21no—
71C2×C3×D12C2312yes—
72C2×C3×Dic6D411yescharacteristic
73C2×C3×Dic6C2312yes—
74C2×#626—22no—
75C2×#626—22no—
76C2×D3×Dic3—22no—
77#3796—44no—
78C2×C32×C8C2311yescharacteristic
79C2×C32×C8C2311yescharacteristic
80C32×C42C2311yescharacteristic
81#3752—21no—
82C4⋊(C3⋊Dic3)C2311yescharacteristic
83C4⋊(C3⋊Dic3)C2311yescharacteristic
84#3750—21no—
85C4×C3⋊Dic3—21no—
86#3744—22no—
87C3×C4⋊Dic3—21no—
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3D411yescharacteristic
90C3×Dic3⋊C4D412yes—
91C3×C4×Dic3C2312yes—
92C2×C3×C3⋊C8C2312yes—
93C3×#204—24no—
94C3×#204—42no—
95Dic3⋊Dic3—22no—
96Dic3⋊Dic3—22no—
97Dic3⋊Dic3—22no—
98(C2×D3)⋊Dic3—22no—
99Dic32—22no—
100#3717—42no—
101#3716—42no—
102#3392—91noSylow
103C2×#239—61no—
104C2×#237—61no—
105C2×C3×SD16—32no—
106C2×C3×SD16—32no—
107C3×C4⋊Q8—31no—
108C3×#127—31no—
109C3×C4×Q8—31no—
110Q8×Dic3—32no—
111Q8×Dic3—61no—
112#944—32no—
113C2×#215—32no—
114#940—32no—
115#939—62no—
116#938—61no—
117D4×Dic3—32no—
118C2×#214—32no—
119C2×#204—31no—
120C2×#204—31no—
121C2×#204—32no—
122C2×#204—32no—
123C2×#204—61no—
124C2×#204C2×D312yes—
125C2×#204C2×D312yes—
126#895—62no—
127#895—61no—
128#890—62no—
129#890—61no—
130#890—61no—
131#889—62no—
132#887—61no—
133#874—32no—
134#874C2×D311yescharacteristic
135C4×D12—32no—
136C4×D12—31no—
137C4×D12—31no—
138C4×D12—61no—
139#869—32no—
140#869C2×D311yescharacteristic
141C4×Dic6—32no—
142C4×Dic6—31no—
143C4×Dic6—31no—
144C4×Dic6—61no—
145C4×Dic6C2×D311yescharacteristic
146C3×C4⋊C8—32no—
147C3×C4⋊C8—31no—
148C3×C4×C8—21no—
149C3×C4×C8—32no—
150C3×C4×C8C2×D311yescharacteristic
151C3×C4×C8C2×D311yescharacteristic
152#835—32no—
153#832—32no—
154#821—32no—
155#821—31no—
156#821—31no—
157#821—61no—
158#817—31no—
159#817—31no—
160#817—61no—
161#816—32no—
162#816—31no—
163#816—31no—
164#816—61no—
165Dic3⋊C8C2×D312yes—
166C8×Dic3C2×D312yes—
167C4⋊(C3⋊C8)C2×D311yescharacteristic
168C22×C3⋊D3—21no—
169C22×C3×D3—22no—
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2411yescharacteristic
173C2×C3⋊Dic3—21no—
174C2×C3⋊Dic3—21no—
175C2×C3⋊Dic3—21no—
176C4⋊(C3⋊D3)—21no—
177C4⋊(C3⋊D3)—21no—
178C4×C3⋊D3—42no—
179#634—21no—
180#634—21no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3C2×D412yes—
183C2×C3×Dic3C2×D412yes—
184C3×D12—22no—
185C3×D12—22no—
186C3×D12—42no—
187C3×D12—81no—
188C3×Dic6—22no—
189C3×Dic6—22no—
190C3×Dic6SD1614yescomplemented
191#626—44no—
192#626—82no—
193D3×Dic3—44no—
194C32×C8—21no—
195C32×C8#4112yescomplemented
196C3×C3⋊C8—22no—
197#557—91no—
198#550—91no—
199#492—31no—
200#492—92no—
201#461—91no—
202#461—92no—
203#460—91no—
204#460—92no—
205C8×Q8—31no—
206C4×SD16—92no—
207C4×SD16—91no—
208C2×C3×Q8—31no—
209C2×C3×Q8—32no—
210C2×C3×D4—32no—
211C2×C3×D4—61no—
212C2×C3×D4—61no—
213C2×#67—62no—
214C2×#67—62no—
215C22×Dic3—62no—
216#239—124no—
217#237—124no—
218C2×D12—21no—
219C2×D12—21no—
220C2×D12—31no—
221C2×D12—31no—
222C2×D12—61no—
223C2×D12—62no—
224C2×D12—62no—
225C2×D12C22×D312yes—
226C2×C4×D3—62no—
227C2×C4×D3—61no—
228C2×C4×D3—61no—
229C2×C4×D3—121no—
230C2×Dic6—31no—
231C2×Dic6—31no—
232C2×Dic6—61no—
233C2×Dic6D1211yescharacteristic
234C2×Dic6C22×D312yes—
235C3×SD16—64no—
236C3×SD16—122no—
237C2×C3×C8—21no—
238C2×C3×C8—21no—
239C2×C3×C8—32no—
240C2×C3×C8C22×D311yescharacteristic
241C2×C3×C8C22×D311yescharacteristic
242C2×C3×C8C22×D311yescharacteristic
243C2×C3×C8C22×D311yescharacteristic
244C3×C4⋊C4—32no—
245C3×C4⋊C4—31no—
246C3×C4⋊C4—61no—
247C3×C4⋊C4—61no—
248C3×C42—21no—
249C3×C42—32no—
250C3×C42C22×D311yescharacteristic
251C3×C42C22×D311yescharacteristic
252#217—62no—
253#215—122no—
254#214—122no—
255(C2×D3)⋊C4—62no—
256(C2×D3)⋊C4—61no—
257(C2×D3)⋊C4—61no—
258(C2×D3)⋊C4—121no—
259C4⋊Dic3—21no—
260C4⋊Dic3—21no—
261C4⋊Dic3—31no—
262C4⋊Dic3—31no—
263C4⋊Dic3—31no—
264C4⋊Dic3—31no—
265C4⋊Dic3—61no—
266C4⋊Dic3—61no—
267C4⋊Dic3—62no—
268C4⋊Dic3—62no—
269C4⋊Dic3—62no—
270C4⋊Dic3D1211yescharacteristic
271Dic3⋊C4—62no—
272Dic3⋊C4—61no—
273Dic3⋊C4—61no—
274Dic3⋊C4—62no—
275Dic3⋊C4—62no—
276Dic3⋊C4—121no—
277Dic3⋊C4D1212yes—
278C4×Dic3—62no—
279C4×Dic3—61no—
280C4×Dic3—61no—
281C4×Dic3—62no—
282C4×Dic3—121no—
283C4×Dic3C22×D312yes—
284C2×C3⋊C8C22×D312yes—
285#204—24no—
286#204—42no—
287#204—64no—
288#204—62no—
289#204—62no—
290#204—122no—
291#204—122no—
292C22×C32C22×D411yescharacteristic
293C2×C3⋊D3—41no—
294C2×C3⋊D3—41no—
295C2×C3⋊D3—41no—
296C2×C3×D3—42no—
297C2×C3×D3—42no—
298C2×C3×D3—42no—
299C32×C4—21no—
300C32×C4C2×SD1612yes—
301C32×C4C2×#4111yescharacteristic
302C32×C4H(5,𝔽2)11yescharacteristic
303C3⋊Dic3—41no—
304C3⋊Dic3—41no—
305C3⋊Dic3—41no—
306C3×Dic3—22no—
307C3×Dic3—42no—
308C3×Dic3C2×SD1614yes—
309C2×#41—181no—
310C2×SD16—32no—
311C2×SD16—32no—
312C2×SD16—92no—
313C2×SD16—92no—
314C2×SD16—91no—
315C4⋊Q8—31no—
316C4⋊Q8—92no—
317#127—31no—
318#127—92no—
319#125—182no—
320#125—181no—
321#121—181no—
322#121—182no—
323C4×Q8—31no—
324C4×Q8—92no—
325C4×Q8—91no—
326C4×Q8—181no—
327C4×D4—92no—
328C4×D4—91no—
329#106—91no—
330C4⋊C8—32no—
331C4⋊C8—31no—
332#103—92no—
333#103—91no—
334#102—92no—
335#102—91no—
336C4×C8—32no—
337C4×C8D3211yescharacteristic
338C23×C3—62no—
339C22×D3—22no—
340C22×D3—61no—
341C22×D3—61no—
342C22×D3—121no—
343C3×Q8—34no—
344C3×Q8—62no—
345C3×Q8—62no—
346C3×D4—62no—
347C3×D4—62no—
348C3×D4—122no—
349C3×D4—241no—
350C2×C3×C4—21no—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4—32no—
354C2×C3×C4—32no—
355C2×C3×C4—62no—
356C2×C3×C4C2×D1211yescharacteristic
357C2×C3×C4C2×D1211yescharacteristic
358C2×C3×C4D3×D411yescharacteristic
359C2×C3×C4D3×D411yescharacteristic
360C2×C3×C4C23×D311yescharacteristic
361C2×C3×C4C23×D311yescharacteristic
362#67—124no—
363#67—242no—
364C2×Dic3—22no—
365C2×Dic3—61no—
366C2×Dic3—61no—
367C2×Dic3—61no—
368C2×Dic3—61no—
369C2×Dic3—61no—
370C2×Dic3—61no—
371C2×Dic3—121no—
372C2×Dic3—121no—
373C2×Dic3—121no—
374C2×Dic3—124no—
375C2×Dic3C2×D1212yes—
376C2×Dic3C2×D1212yes—
377D12—22no—
378D12—22no—
379D12—42no—
380D12—62no—
381D12—61no—
382D12—61no—
383D12—61no—
384D12—61no—
385D12—81no—
386D12—121no—
387D12—124no—
388D12—242no—
389C4×D3—124no—
390C4×D3—122no—
391C4×D3—122no—
392C4×D3—242no—
393Dic6—22no—
394Dic6—22no—
395Dic6—62no—
396Dic6—61no—
397Dic6—61no—
398Dic6—61no—
399Dic6—61no—
400Dic6—121no—
401Dic6#20414yescomplemented
402C3×C8—21no—
403C3×C8—21no—
404C3×C8—22no—
405C3×C8—41no—
406C3×C8—62no—
407C3×C8#23712yescomplemented
408C3×C8#23912yescomplemented
409C3⋊C8—22no—
410C2×C32#55011yescharacteristic
411C2×C32C22×SD1611yescharacteristic
412C2×C32#57711yescharacteristic
413C3⋊D3—81no—
414C3×D3—82no—
415#41—364no—
416C2×Q8—31no—
417C2×Q8—32no—
418C2×Q8—91no—
419C2×D4—32no—
420C2×D4—61no—
421C2×D4—61no—
422C2×D4—91no—
423C2×D4—182no—
424C2×D4—182no—
425C22×C4—182no—
426C22×C4—181no—
427SD16—64no—
428SD16—122no—
429SD16—182no—
430SD16—362no—
431SD16—362no—
432C2×C8—32no—
433C2×C8C2×D3211yescharacteristic
434C2×C8C2×D3211yescharacteristic
435C4⋊C4—32no—
436C4⋊C4—31no—
437C4⋊C4—61no—
438C4⋊C4—61no—
439C4⋊C4—91no—
440C4⋊C4—91no—
441C4⋊C4—182no—
442C4⋊C4—182no—
443C4⋊C4—182no—
444C4⋊C4—181no—
445C22⋊C4—182no—
446C22⋊C4—181no—
447C42—32no—
448C42—182no—
449C42—181no—
450C42C2×D3211yescharacteristic
451C22×C3—21no—
452C22×C3—122no—
453C22×C3—122no—
454C22×C3—122no—
455C22×C3C22×D1211yescharacteristic
456C22×C3C2×D3×D411yescharacteristic
457C2×D3—42no—
458C2×D3—42no—
459C2×D3—42no—
460C2×D3—122no—
461C2×D3—121no—
462C2×D3—121no—
463C2×D3—121no—
464C2×D3—121no—
465C2×D3—121no—
466C2×D3—121no—
467C2×D3—241no—
468C2×D3—241no—
469C3×C4—21no—
470C3×C4—21no—
471C3×C4—21no—
472C3×C4—22no—
473C3×C4—21no—
474C3×C4—34no—
475C3×C4—41no—
476C3×C4—62no—
477C3×C4—122no—
478C3×C4C2×#20412yes—
479C3×C4D3×SD1612yes—
480C3×C4C2×#23711yescharacteristic
481C3×C4#100411yescharacteristic
482C3×C4C2×#23911yescharacteristic
483C3×C4#100911yescharacteristic
484Dic3—22no—
485Dic3—42no—
486Dic3—122no—
487Dic3—121no—
488Dic3—121no—
489Dic3—121no—
490Dic3—121no—
491Dic3—121no—
492Dic3—121no—
493Dic3—241no—
494Dic3—241no—
495Dic3C2×#20414yes—
496C32#339211yescharacteristic, complemented, Sylow
497C23—62no—
498C23—181no—
499Q8—34no—
500Q8—62no—
501Q8—62no—
502Q8—181no—
503Q8—181no—
504D4—62no—
505D4—62no—
506D4—122no—
507D4—181no—
508D4—181no—
509D4—241no—
510D4—364no—
511D4—722no—
512C2×C4—32no—
513C2×C4—32no—
514C2×C4—62no—
515C2×C4—181no—
516C2×C4—181no—
517C2×C4—181no—
518C2×C4—364no—
519C2×C4—362no—
520C2×C4D3×D1211yescharacteristic
521C2×C4D3×D1211yescharacteristic
522C2×C4C22×D3211yescharacteristic
523C8—21no—
524C8—62no—
525C8#379612yescomplemented
526C2×C3—21no—
527C2×C3—21no—
528C2×C3—21no—
529C2×C3—242no—
530C2×C3#557711yescharacteristic
531C2×C3#571811yescharacteristic
532C2×C3C22×#20411yescharacteristic
533C2×C3#575111yescharacteristic
534C2×C3C2×D3×SD1611yescharacteristic
535C2×C3#576211yescharacteristic
536D3—82no—
537D3—242no—
538D3—241no—
539D3—241no—
540C22—122no—
541C22—122no—
542C22—122no—
543C22—361no—
544C22—361no—
545C22—361no—
546C22C2×D3×D1211yescharacteristic
547C4—21no—
548C4—34no—
549C4—62no—
550C4—122no—
551C4—361no—
552C4—361no—
553C4—361no—
554C4D3×#20412yes—
555C4C2×#379611yescharacteristic
556C4#6430711yescharacteristic
557C3—21no—
558C3#7991111yescharacteristic, complemented
559C3#8175511yescharacteristic, complemented
560C2—242no—
561C2—721no—
562C2#1059390011yescharacteristic
563C2C2×D3×#20411yescharacteristic
564C2#1059467711yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radical#10593900C2
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. C4×#3744C2semidirect
4. C3×#4693C2semidirect
5. C3×C8×Dic6C2semidirect
6. #10590877C2semidirect
7. #10590799C2semidirect
8. Dic3×#204C2semidirect
9. #10590752C2semidirect
10. #10590379C2semidirect
11. #10590377C2semidirect
60. #4693D3semidirect
65. C8×Dic6D3semidirect
190. C3×Dic6SD16semidirect
195. C32×C8#41semidirect
401. Dic6#204semidirect
407. C3×C8#237semidirect
408. C3×C8#239semidirect
496. C32#3392semidirect
525. C8#3796semidirect
558. C3#79911semidirect
559. C3#81755semidirect

Maximal subgroups

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

subgroupindex
#105939002
#105938612
C4×#37442
C3×#46932
C3×C8×Dic62
#105908772
#105907992
Dic3×#2042
#105907522
#105903792
#105903772
#817553
#799113