Finite Group Databasebeta

← #11895431

Subgroups — #11895431

Order 1152.

890 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#634C211yesmaximal, characteristic, complemented
2#10593906C211yesmaximal, characteristic
3C3×#5027C211yesmaximal, characteristic, complemented
4C3×C4×#215C211yesmaximal, characteristic, complemented
5#10591622C212yesmaximal, complemented
6#10591571C212yesmaximal, complemented
7#10590552C212yesmaximal, complemented
8#10590472C212yesmaximal, complemented
9#10590273C211yesmaximal, characteristic, complemented
10#10590268C211yesmaximal, characteristic, complemented
11#10590254C211yesmaximal, characteristic, complemented
12#80369—31nomaximal
13#79622—31nomaximal
14C2×#3795—21no—
15C32×C4×Q8C2211yescharacteristic
16Q8×C3⋊Dic3C2212yes—
17#64097—22no—
18#64097C2212yes—
19#64078—21no—
20#64078C2211yescharacteristic
21C4×#634—21no—
22C4×#634C2211yescharacteristic
23C2×C3×#215C2212yes—
24C2×C3×#215C2211yescharacteristic
25C3×#874C2211yescharacteristic
26C3×C4×D12C2211yescharacteristic
27#63914C2212yes—
28#63908—21no—
29#63898C2212yes—
30#63885—22no—
31C3×#835C2211yescharacteristic
32C3×#809C2212yes—
33C3×#809C2211yescharacteristic
34C3×#808C2211yescharacteristic
35C3×C4⋊(C3⋊C8)C2211yescharacteristic
36C3×C4×C3⋊C8C2211yescharacteristic
37#63573C2212yes—
38#63572C2212yes—
39#63563C2212yes—
40#63563C2212yes—
41#63563C2212yes—
42#63553C2212yes—
43#5718—31no—
44Q8×Dic6—31no—
45Q8×Dic6—31no—
46Q8×Dic6—61no—
47#5553—31no—
48C3×#460—31no—
49C3×C4×SD16—31no—
50#5163—32no—
51#5163—32no—
52Dic3×SD16—32no—
53#5070—31no—
54#5027D311yescharacteristic, complemented
55C4×#215D311yescharacteristic, complemented
56#5008—31no—
57#4870—32no—
58#4842—31no—
59#4830—31no—
60#4788—32no—
61#4761—32no—
62#4760—32no—
63#4760—32no—
64#4694—31no—
65C8×Dic6—31no—
66C2×C32×Q8C2311yescharacteristic
67C2×#634—21no—
68C2×#634—22no—
69C2×#634D411yescharacteristic
70C2×C3×D12—21no—
71C2×C3×D12—21no—
72C2×C3×D12C2312yes—
73C2×C3×D12C2311yescharacteristic
74C2×C3×C4×D3—21no—
75C2×#625—22no—
76C2×#625—22no—
77C2×D3×Dic3—22no—
78#3795—44no—
79C32×C4⋊C4—21no—
80C32×C4⋊C4C2311yescharacteristic
81C32×C42—21no—
82C32×C42C2311yescharacteristic
83C4⋊(C3⋊Dic3)—21no—
84C4⋊(C3⋊Dic3)—22no—
85C4⋊(C3⋊Dic3)D411yescharacteristic
86C4⋊(C3⋊Dic3)C2312yes—
87#3750—22no—
88#3750D412yes—
89C4×C3⋊Dic3—22no—
90C4×C3⋊Dic3C2312yes—
91C3×#215—22no—
92C3×#215—24no—
93C3×(C2×D3)⋊C4—21no—
94C3×C4⋊Dic3C2311yescharacteristic
95C2×C3×C3⋊C8C2312yes—
96C2×C3×C3⋊C8C2311yescharacteristic
97C2×C3×C3⋊C8C2311yescharacteristic
98(C2×D3)⋊Dic3—22no—
99#3362—91noSylow
100C2×#237—61no—
101C2×#235—61no—
102C2×C3×SD16—32no—
103C2×C3×SD16—31no—
104C3×#127—31no—
105C3×C4×Q8—21no—
106C3×C4×Q8C2×D311yescharacteristic
107C3×C4×Q8C2×D311yescharacteristic
108C3×C4×D4—31no—
109Q8×Dic3—32no—
110Q8×Dic3—32no—
111Q8×Dic3—62no—
112C2×#215C2×D311yescharacteristic
113C2×#215C2×D312yes—
114#940—32no—
115#940—32no—
116#939—62no—
117#938—61no—
118D4×Dic3—32no—
119#930—61no—
120#893—32no—
121#888—32no—
122#888—32no—
123#888—62no—
124#888—62no—
125#888—62no—
126#888—64no—
127#884—62no—
128#874C2×D311yescharacteristic
129C4×D12C2×D311yescharacteristic
130#869—31no—
131#869—31no—
132#869—61no—
133#869—61no—
134#869—61no—
135#869—62no—
136C4×Dic6—31no—
137C4×Dic6—31no—
138C4×Dic6—61no—
139C4×Dic6—61no—
140C4×Dic6—61no—
141C4×Dic6—62no—
142C3×#106—31no—
143C3×C4⋊C8—31no—
144C3×#103—31no—
145C3×#102—31no—
146C3×#102—32no—
147C3×C4×C8—31no—
148#835C2×D311yescharacteristic
149#832—32no—
150#832—32no—
151#832—32no—
152#821—32no—
153#821—32no—
154#821—32no—
155#817—32no—
156Dic3⋊C8—32no—
157Dic3⋊C8—32no—
158C8×Dic3—32no—
159C8×Dic3—32no—
160#809C2×D312yes—
161#809C2×D311yescharacteristic
162#808—32no—
163#808C2×D311yescharacteristic
164C4⋊(C3⋊C8)C2×D311yescharacteristic
165C4×C3⋊C8C2×D311yescharacteristic
166C22×C3×D3—22no—
167C22×C3×D3—21no—
168C32×Q8—21no—
169C32×Q8#4112yescomplemented
170C2×C32×C4—21no—
171C2×C32×C4—21no—
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2×D411yescharacteristic
174C2×C32×C4C2411yescharacteristic
175C2×C3⋊Dic3—22no—
176C2×C3⋊Dic3C2×D412yes—
177C2×C3⋊Dic3C2×D412yes—
178#634—82no—
179#634—81no—
180#634SD1614yescomplemented
181C2×C3×Dic3—21no—
182C3×D12—21no—
183C3×D12—22no—
184C3×D12—22no—
185C3×D12—21no—
186C3×D12—42no—
187C3×D12—81no—
188C3×C4×D3—42no—
189#625—44no—
190#625—82no—
191D3×Dic3—44no—
192C3×C3⋊C8—21no—
193C3×C3⋊C8—22no—
194C3×C3⋊C8—21no—
195Q82—91no—
196#550—91no—
197#486—91no—
198#486—92no—
199#476—92no—
200#476—91no—
201#460—31no—
202#460—92no—
203C8×Q8—91no—
204C4×SD16—31no—
205C4×SD16—92no—
206C2×C3×Q8—21no—
207C2×C3×Q8C22×D311yescharacteristic
208C2×C3×Q8C22×D311yescharacteristic
209C2×C3×D4—32no—
210C2×C3×D4—31no—
211C2×C3×D4—61no—
212C2×C3×D4—61no—
213C22×C3×C4—61no—
214C2×#67—62no—
215C2×#67—62no—
216C2×#67—62no—
217C2×#67—62no—
218C22×Dic3—62no—
219#237—124no—
220#235—124no—
221C2×D12—21no—
222C2×D12—21no—
223C2×D12C22×D311yescharacteristic
224C2×D12C22×D312yes—
225C2×C4×D3—21no—
226C2×C4×D3—62no—
227C2×Dic6—31no—
228C2×Dic6—31no—
229C2×Dic6—61no—
230C2×Dic6—62no—
231C2×Dic6—62no—
232C2×Dic6—64no—
233C2×Dic6—62no—
234C2×Dic6—61no—
235C2×Dic6—61no—
236C3×SD16—64no—
237C3×SD16—62no—
238C2×C3×C8—31no—
239C2×C3×C8—32no—
240C2×C3×C8—31no—
241C3×C4⋊C4—22no—
242C3×C4⋊C4—21no—
243C3×C4⋊C4—21no—
244C3×C4⋊C4—21no—
245C3×C4⋊C4—31no—
246C3×C4⋊C4C22×D311yescharacteristic
247C3×C4⋊C4C22×D311yescharacteristic
248C3×C22⋊C4—61no—
249C3×C42—22no—
250C3×C42—21no—
251C3×C42—21no—
252C3×C42—21no—
253C3×C42C22×D311yescharacteristic
254C3×C42C22×D311yescharacteristic
255#217—62no—
256#215—22no—
257#215—24no—
258(C2×D3)⋊C4—21no—
259(C2×D3)⋊C4—62no—
260C4⋊Dic3—31no—
261C4⋊Dic3—31no—
262C4⋊Dic3—32no—
263C4⋊Dic3—32no—
264C4⋊Dic3—61no—
265C4⋊Dic3—62no—
266C4⋊Dic3—62no—
267C4⋊Dic3—62no—
268C4⋊Dic3—62no—
269C4⋊Dic3—64no—
270C4⋊Dic3—61no—
271C4⋊Dic3—61no—
272C4⋊Dic3C22×D311yescharacteristic
273Dic3⋊C4—32no—
274Dic3⋊C4—32no—
275Dic3⋊C4—62no—
276Dic3⋊C4—62no—
277Dic3⋊C4—62no—
278Dic3⋊C4—64no—
279C4×Dic3—32no—
280C4×Dic3—32no—
281C4×Dic3—62no—
282C4×Dic3—62no—
283C4×Dic3—62no—
284C4×Dic3—64no—
285C2×C3⋊C8C22×D311yescharacteristic
286C2×C3⋊C8C22×D311yescharacteristic
287C2×C3⋊C8C22×D312yes—
288C22×C32C22×D411yescharacteristic
289C2×C3×D3—41no—
290C2×C3×D3—42no—
291C2×C3×D3—42no—
292C2×C3×D3—41no—
293C2×C3×D3—41no—
294C2×C3×D3—42no—
295C32×C4—22no—
296C32×C4—21no—
297C32×C4—41no—
298C32×C4C2×SD1612yes—
299C32×C4C2×#4111yescharacteristic
300C32×C42−1+411yescharacteristic
301C3⋊Dic3—22no—
302C3⋊Dic3—42no—
303C3⋊Dic3C2×SD1614yes—
304C3×Dic3—41no—
305C2×#41—181no—
306C2×SD16—31no—
307C2×SD16—32no—
308C4⋊Q8—92no—
309C4⋊Q8—91no—
310C4⋊Q8—181no—
311C4⋊Q8—182no—
312#127—31no—
313#127—92no—
314#121—182no—
315#121—181no—
316C4×Q8—91no—
317C4×Q8—92no—
318C4×Q8—181no—
319C4×Q8D3211yescharacteristic
320C4×D4—31no—
321C4×D4—92no—
322#106—31no—
323#106—92no—
324C4⋊C8—31no—
325C4⋊C8—92no—
326#103—31no—
327#102—31no—
328#102—32no—
329#102—92no—
330#102—92no—
331#102—92no—
332C4×C8—31no—
333C4×C8—92no—
334C23×C3—62no—
335C23×C3—61no—
336C22×D3—21no—
337C22×D3—22no—
338C3×Q8—22no—
339C3×Q8—21no—
340C3×Q8—21no—
341C3×Q8—22no—
342C3×Q8#23512yescomplemented
343C3×Q8#23712yescomplemented
344C3×D4—62no—
345C3×D4—61no—
346C3×D4—62no—
347C3×D4—61no—
348C3×D4—122no—
349C3×D4—241no—
350C2×C3×C4—22no—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4—22no—
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—61no—
360C2×C3×C4—122no—
361C2×C3×C4D3×D411yescharacteristic
362C2×C3×C4D3×D411yescharacteristic
363C2×C3×C4D3×D411yescharacteristic
364C2×C3×C4D3×D411yescharacteristic
365C2×C3×C4C23×D311yescharacteristic
366C2×C3×C4C23×D311yescharacteristic
367#67—124no—
368#67—124no—
369#67—242no—
370#67—242no—
371C2×Dic3—21no—
372C2×Dic3—32no—
373C2×Dic3—32no—
374C2×Dic3—32no—
375C2×Dic3—32no—
376C2×Dic3—62no—
377C2×Dic3—62no—
378C2×Dic3—64no—
379C2×Dic3—62no—
380C2×Dic3—62no—
381C2×Dic3—124no—
382D12—21no—
383D12—22no—
384D12—21no—
385D12—22no—
386D12—42no—
387D12—81no—
388C4×D3—42no—
389C4×D3—124no—
390Dic6—34no—
391Dic6—34no—
392Dic6—64no—
393Dic6—242no—
394Dic6—242no—
395Dic6—241no—
396Dic6—241no—
397Dic6—242no—
398Dic6—244no—
399C3×C8—62no—
400C3×C8—61no—
401C3×C8—61no—
402C3⋊C8—21no—
403C3⋊C8—22no—
404C3⋊C8—21no—
405C2×C32#54811yescharacteristic
406C2×C32C22×SD1611yescharacteristic
407C2×C32#57611yescharacteristic
408C3×D3—81no—
409C3×D3—82no—
410#41—364no—
411C2×Q8—91no—
412C2×Q8—182no—
413C2×Q8—181no—
414C2×Q8C2×D3211yescharacteristic
415C2×D4—31no—
416C2×D4—32no—
417C2×D4—61no—
418C2×D4—61no—
419C2×D4—182no—
420C2×D4—182no—
421C22×C4—61no—
422C22×C4—182no—
423SD16—62no—
424SD16—64no—
425C2×C8—31no—
426C2×C8—31no—
427C2×C8—32no—
428C4⋊C4—21no—
429C4⋊C4—31no—
430C4⋊C4—92no—
431C4⋊C4—91no—
432C4⋊C4—92no—
433C4⋊C4—182no—
434C4⋊C4—182no—
435C4⋊C4—181no—
436C4⋊C4C2×D3211yescharacteristic
437C22⋊C4—61no—
438C22⋊C4—182no—
439C42—21no—
440C42—92no—
441C42—182no—
442C42C2×D3211yescharacteristic
443C22×C3—21no—
444C22×C3—122no—
445C22×C3—121no—
446C22×C3—122no—
447C22×C3—121no—
448C22×C3—122no—
449C22×C3—121no—
450C22×C3C2×D3×D411yescharacteristic
451C22×C3C2×D3×D411yescharacteristic
452C2×D3—41no—
453C2×D3—42no—
454C2×D3—41no—
455C2×D3—42no—
456C2×D3—41no—
457C2×D3—42no—
458C3×C4—24no—
459C3×C4—21no—
460C3×C4—21no—
461C3×C4—22no—
462C3×C4—22no—
463C3×C4—21no—
464C3×C4—21no—
465C3×C4—22no—
466C3×C4—41no—
467C3×C4—42no—
468C3×C4—41no—
469C3×C4—41no—
470C3×C4—121no—
471C3×C4D3×SD1612yes—
472C3×C4D3×SD1612yes—
473C3×C4C2×#23511yescharacteristic
474C3×C4C2×#23711yescharacteristic
475C3×C4#101011yescharacteristic
476C3×C4#101011yescharacteristic
477Dic3—34no—
478Dic3—34no—
479Dic3—41no—
480Dic3—64no—
481Dic3—62no—
482Dic3—62no—
483Dic3—122no—
484Dic3—124no—
485Dic3—122no—
486Dic3—122no—
487C32#336211yescharacteristic, complemented, Sylow
488C23—61no—
489C23—62no—
490Q8—21no—
491Q8—94no—
492Q8—721no—
493Q8—722no—
494Q8#379512yescomplemented
495D4—61no—
496D4—62no—
497D4—61no—
498D4—62no—
499D4—122no—
500D4—241no—
501D4—364no—
502D4—722no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—61no—
506C2×C4—92no—
507C2×C4—92no—
508C2×C4—122no—
509C2×C4—182no—
510C2×C4—364no—
511C2×C4#381111yescharacteristic
512C2×C4#381111yescharacteristic
513C2×C4C22×D3211yescharacteristic
514C8—61no—
515C8—62no—
516C8—61no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—21no—
520C2×C3—242no—
521C2×C3—241no—
522C2×C3#555211yescharacteristic
523C2×C3#559811yescharacteristic
524C2×C3C2×D3×SD1611yescharacteristic
525C2×C3C2×D3×SD1611yescharacteristic
526C2×C3#576911yescharacteristic
527C2×C3#577411yescharacteristic
528D3—81no—
529D3—82no—
530C22—121no—
531C22—122no—
532C22—122no—
533C22—121no—
534C22—121no—
535C22—122no—
536C22C2×#381111yescharacteristic
537C4—22no—
538C4—21no—
539C4—41no—
540C4—94no—
541C4—121no—
542C4—182no—
543C4—362no—
544C4#6394012yes—
545C4C2×#379511yescharacteristic
546C4#6429811yescharacteristic
547C3—21no—
548C3#7962211yescharacteristic, complemented
549C3#8036911yescharacteristic, complemented
550C2—242no—
551C2—241no—
552C2#1059491811yescharacteristic
553C2C2×#6394011yescharacteristic
554C2#1059546111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radical#10593906C2
hypercenterC4×Q8D32
hypocenterC32#3362
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. Q8×#634C2semidirect
3. C3×#5027C2semidirect
4. C3×C4×#215C2semidirect
5. #10591622C2semidirect
6. #10591571C2semidirect
7. #10590552C2semidirect
8. #10590472C2semidirect
9. #10590273C2semidirect
10. #10590268C2semidirect
11. #10590254C2semidirect
54. #5027D3semidirect
55. C4×#215D3semidirect
169. C32×Q8#41semidirect
180. #634SD16semidirect
342. C3×Q8#235semidirect
343. C3×Q8#237semidirect
487. C32#3362semidirect
494. Q8#3795semidirect
548. C3#79622semidirect
549. C3#80369semidirect

Maximal subgroups

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

subgroupindex
Q8×#6342
#105939062
C3×#50272
C3×C4×#2152
#105916222
#105915712
#105905522
#105904722
#105902732
#105902682
#105902542
#803693
#796223