Finite Group Databasebeta

← #11792367

Subgroups — #11792367

Order 1152.

831 conjugacy classes of subgroups.

The subgroup lattice has 621 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596296C211yesmaximal, characteristic, complemented
2C3×#5822C211yesmaximal, characteristic
3C2×#63831C211yesmaximal, characteristic, complemented
4C3×#5236C211yesmaximal, characteristic, complemented
5#10591231C211yesmaximal, characteristic, complemented
6#10591107C211yesmaximal, characteristic, complemented
7#10589171C211yesmaximal, characteristic, complemented
8#72120—31nomaximal
9#70412—31nomaximal
10C2×C32×#41C2211yescharacteristic
11C22×#634C2211yescharacteristic
12C2×C3×#235C2211yescharacteristic
13#64153—21no—
14#64145—21no—
15#64144—22no—
16#64135C2211yescharacteristic
17#64133—22no—
18C3×#951—21no—
19C3×#950—22no—
20C3×#949—21no—
21C3×#942—21no—
22C3×#932—21no—
23C3×#926C2211yescharacteristic
24C2×C3×#208C2211yescharacteristic
25C2×C3×#208C2211yescharacteristic
26C2×#3719—21no—
27#63831—22no—
28#63831—22no—
29C2×#3716—21no—
30C3×#837—22no—
31#63580—22no—
32#63567—22no—
33C3×#575—31no—
34#5825—31no—
35#5825—31no—
36#5825—61no—
37C2×#951—31no—
38#5822D311yescharacteristic
39C2×#909—31no—
40C3×#421—31no—
41#5240—31no—
42#5236D311yescharacteristic, complemented
43#5120—31no—
44#5006—31no—
45#5004—31no—
46#4559—31no—
47#4556—31no—
48C32×#41—21no—
49C32×#41—21no—
50C32×#41—21no—
51C32×#41—21no—
52C2×C32×Q8D411yescharacteristic
53C2×C32×D4—21no—
54C2×C32×D4D411yescharacteristic
55C22×C32×C4—21no—
56C22×C32×C4C2311yescharacteristic
57C22×C3⋊Dic3—21no—
58C2×#634—21no—
59C2×#634—21no—
60C2×#634—21no—
61C2×#634—21no—
62C2×#634—21no—
63C2×#634D412yes—
64C2×C3×#67—21no—
65C3×#235—21no—
66C3×#235—21no—
67C3×#235—21no—
68C3×#235—21no—
69C2×C3×D12D411yescharacteristic
70C2×C3×C4×D3—21no—
71C2×C3×Dic6D411yescharacteristic
72#3757—24no—
73#3757D412yes—
74C4⋊(C3⋊Dic3)—21no—
75#3750—24no—
76C4×C3⋊Dic3—21no—
77C3×#217—21no—
78C3×#216—22no—
79C3×#215—22no—
80C3×#214—22no—
81C3×#213—22no—
82C3×C4⋊Dic3—21no—
83C3×C4×Dic3—21no—
84C3×#208—21no—
85C3×#208—21no—
86C3×#208—21no—
87C3×#208D412yes—
88C2×C3×C3⋊C8—21no—
89C2×C3×C3⋊C8D412yes—
90#3719—24no—
91#3716—24no—
92#2009—91noSylow
93C2×C3×#41—21no—
94C2×C3×#41—31no—
95C2×C3×#41C2×D311yescharacteristic
96C2×C3×#41C2×D311yescharacteristic
97C2×#235C2×D311yescharacteristic
98C22×Dic6—31no—
99C22×Dic6—31no—
100C22×Dic6—61no—
101C3×#137—61no—
102C3×#137—61no—
103C3×AGL(1,ℤ/8)—61no—
104C3×AGL(1,ℤ/8)—61no—
105C3×#135—62no—
106C2×C3×M16—31no—
107C2×C3×M16—31no—
108C3×#117—31no—
109#951—21no—
110#951—62no—
111#951—62no—
112#950—22no—
113#949—21no—
114#944—62no—
115#944—61no—
116#944—61no—
117C2×#216—61no—
118#942—21no—
119#936—62no—
120#936—61no—
121#936—61no—
122#935—62no—
123#935—62no—
124#935—64no—
125C2×#214—61no—
126#932—21no—
127#926—31no—
128#926—31no—
129#926—61no—
130#926C2×D311yescharacteristic
131#924—62no—
132#924—62no—
133#924—64no—
134C2×#208C2×D311yescharacteristic
135C2×#208C2×D311yescharacteristic
136#909—62no—
137#909—62no—
138C2×Dic12—61no—
139C2×#204—61no—
140C3×#104—62no—
141#837—22no—
142#834—62no—
143#816—62no—
144#810—62no—
145#806—62no—
146C23×C32—21no—
147C23×C32C2×D411yescharacteristic
148C22×C3×D3—21no—
149C32×Q8—21no—
150C32×Q8—21no—
151C32×D4—21no—
152C32×D4—21no—
153C32×D4—41no—
154C32×D4—41no—
155C2×C32×C4—21no—
156C2×C32×C4—41no—
157C2×C32×C4—41no—
158C2×C32×C4C2×D411yescharacteristic
159C2×C32×C4C2×D411yescharacteristic
160C2×C32×C4C2×D411yescharacteristic
161C2×C32×C4C2×D411yescharacteristic
162C2×C32×C4C2×D411yescharacteristic
163C2×C32×C4#4111yescharacteristic
164C2×C3⋊Dic3—22no—
165C2×C3⋊Dic3—22no—
166C2×C3⋊Dic3—41no—
167C2×C3⋊Dic3—41no—
168#634—22no—
169#634—22no—
170#634—41no—
171#634—41no—
172C3×#67—41no—
173C3×#67—41no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3—41no—
176C3×D12—21no—
177C3×D12—21no—
178C3×C4×D3—41no—
179C3×C4×D3—41no—
180C3×Dic6—21no—
181C3×Dic6—21no—
182C3×C3⋊C8—22no—
183C3×C3⋊C8—22no—
184#575—31no—
185C2×#137—91no—
186#536—91no—
187#421—31no—
188#419—91no—
189#410—91no—
190#344—91no—
191C3×#41—21no—
192C3×#41—21no—
193C3×#41—21no—
194C3×#41—21no—
195C3×#41—21no—
196C3×#41—21no—
197C3×#41—21no—
198C3×#41—21no—
199C3×#41—41no—
200C3×#41—41no—
201C3×#41—41no—
202C3×#41—41no—
203C3×#41—61no—
204C3×#41—61no—
205C3×#41—61no—
206C3×#41—61no—
207C2×C3×Q8—21no—
208C2×C3×Q8—31no—
209C2×C3×Q8D1211yescharacteristic
210C2×C3×Q8#6711yescharacteristic
211C2×C3×D4—22no—
212C2×C3×D4—21no—
213C2×C3×D4—21no—
214C2×C3×D4—21no—
215C2×C3×D4—31no—
216C2×C3×D4—61no—
217C2×C3×D4D1211yescharacteristic
218C2×C3×D4#6711yescharacteristic
219C22×C3×C4—22no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—61no—
224C22×C3×C4C22×D311yescharacteristic
225C22×C3×C4C22×D311yescharacteristic
226C2×#67—21no—
227C22×Dic3—62no—
228C22×Dic3—61no—
229C22×Dic3—61no—
230#235—21no—
231#235—21no—
232#235—21no—
233#235—21no—
234C2×D12#6711yescharacteristic
235C2×C4×D3—21no—
236C2×Dic6—32no—
237C2×Dic6—32no—
238C2×Dic6—62no—
239C2×Dic6—61no—
240C2×Dic6—61no—
241C2×Dic6—61no—
242C2×Dic6—61no—
243C2×Dic6—61no—
244C2×Dic6—61no—
245C2×Dic6—61no—
246C2×Dic6—61no—
247C2×Dic6—62no—
248C2×Dic6—61no—
249C2×Dic6—61no—
250C2×Dic6—121no—
251C2×Dic6—121no—
252C2×Dic6—121no—
253C2×Dic6—121no—
254C2×Dic6#6711yescharacteristic
255C3×Q16—62no—
256C3×SD16—62no—
257C3×SD16—62no—
258C3×D8—62no—
259C3×M16—32no—
260C3×M16—61no—
261C3×M16—61no—
262C3×M16—61no—
263C2×C3×C8—32no—
264C2×C3×C8—61no—
265C3×C4⋊C4—61no—
266C3×C22⋊C4—61no—
267C3×C42—61no—
268#217—21no—
269#217—32no—
270#217—32no—
271#217—62no—
272#217—68no—
273#217—64no—
274#217—64no—
275#216—22no—
276#216—64no—
277#215—22no—
278#214—22no—
279#214—64no—
280#213—22no—
281C4⋊Dic3—21no—
282C4⋊Dic3—62no—
283C4⋊Dic3—61no—
284C4⋊Dic3—61no—
285Dic3⋊C4—68no—
286Dic3⋊C4—64no—
287Dic3⋊C4—64no—
288C4×Dic3—21no—
289C4×Dic3—62no—
290C4×Dic3—61no—
291C4×Dic3—61no—
292#208—21no—
293#208—21no—
294#208—21no—
295#208#6712yes—
296C2×C3⋊C8—21no—
297C2×C3⋊C8#6712yes—
298Dic12—64no—
299#204—64no—
300C22×C32—41no—
301C22×C32—42no—
302C22×C32—41no—
303C22×C32#12011yescharacteristic
304C22×C32#12111yescharacteristic
305C22×C32#12711yescharacteristic
306C2×C3×D3—41no—
307C2×C3×D3—81no—
308C32×C4—41no—
309C32×C4#12011yescharacteristic
310C32×C4#12011yescharacteristic
311C32×C4#12111yescharacteristic
312C32×C4#12111yescharacteristic
313C3⋊Dic3—42no—
314C3⋊Dic3—42no—
315C3×Dic3—41no—
316C3×Dic3—81no—
317C2×#41—31no—
318C2×#41D3211yescharacteristic
319C22×Q8—91no—
320#137—61no—
321#137—61no—
322#137—182no—
323#137—182no—
324AGL(1,ℤ/8)—61no—
325AGL(1,ℤ/8)—61no—
326#135—62no—
327C2×Q16—181no—
328C2×SD16—181no—
329C2×M16—31no—
330C2×M16—31no—
331C4⋊Q8—181no—
332#124—181no—
333#123—182no—
334C22⋊Q8—182no—
335#117—31no—
336#117—91no—
337#104—62no—
338#103—182no—
339#99—182no—
340C23×C3—22no—
341C23×C3—21no—
342C23×C3—21no—
343C23×C3—21no—
344C23×C3—61no—
345C23×C3D3×D411yescharacteristic
346C23×C3D3×D411yescharacteristic
347C22×D3—21no—
348C3×Q8—21no—
349C3×Q8—21no—
350C3×Q8—21no—
351C3×Q8—21no—
352C3×Q8—41no—
353C3×Q8—41no—
354C3×Q8—61no—
355C3×Q8—61no—
356C3×D4—21no—
357C3×D4—21no—
358C3×D4—21no—
359C3×D4—21no—
360C3×D4—41no—
361C3×D4—41no—
362C3×D4—42no—
363C3×D4—42no—
364C3×D4—41no—
365C3×D4—41no—
366C3×D4—41no—
367C3×D4—41no—
368C3×D4—61no—
369C3×D4—61no—
370C3×D4—121no—
371C3×D4—121no—
372C2×C3×C4—22no—
373C2×C3×C4—21no—
374C2×C3×C4—21no—
375C2×C3×C4—21no—
376C2×C3×C4—21no—
377C2×C3×C4—21no—
378C2×C3×C4—21no—
379C2×C3×C4—21no—
380C2×C3×C4—21no—
381C2×C3×C4—42no—
382C2×C3×C4—42no—
383C2×C3×C4—41no—
384C2×C3×C4—41no—
385C2×C3×C4—41no—
386C2×C3×C4—41no—
387C2×C3×C4—61no—
388C2×C3×C4—121no—
389C2×C3×C4—121no—
390C2×C3×C4—121no—
391C2×C3×C4C2×D1211yescharacteristic
392C2×C3×C4#23511yescharacteristic
393C2×C3×C4D3×D411yescharacteristic
394C2×C3×C4D3×D411yescharacteristic
395C2×C3×C4D3×D411yescharacteristic
396C2×C3×C4D3×D411yescharacteristic
397C2×C3×C4D3×D411yescharacteristic
398C2×C3×C4#23711yescharacteristic
399C2×C3×C4C2×#6711yescharacteristic
400C2×C3×C4C2×#6711yescharacteristic
401C2×C3×C4C2×#6711yescharacteristic
402C2×C3×C4C2×#6711yescharacteristic
403#67—41no—
404#67—41no—
405C2×Dic3—21no—
406C2×Dic3—41no—
407C2×Dic3—64no—
408C2×Dic3—64no—
409C2×Dic3—62no—
410C2×Dic3—62no—
411C2×Dic3—62no—
412C2×Dic3—62no—
413C2×Dic3—122no—
414C2×Dic3—122no—
415C2×Dic3—121no—
416C2×Dic3—121no—
417C2×Dic3—121no—
418C2×Dic3—121no—
419D12—21no—
420D12—21no—
421C4×D3—41no—
422C4×D3—41no—
423Dic6—21no—
424Dic6—21no—
425Dic6—62no—
426Dic6—62no—
427Dic6—62no—
428Dic6—62no—
429Dic6—122no—
430Dic6—122no—
431Dic6—122no—
432Dic6—122no—
433Dic6—121no—
434Dic6—121no—
435Dic6—121no—
436Dic6—121no—
437C3×C8—62no—
438C3×C8—62no—
439C3⋊C8—22no—
440C3⋊C8—22no—
441C2×C32—21no—
442C2×C32—21no—
443C2×C32—21no—
444C2×C32—81no—
445C2×C32#39211yescharacteristic
446C3×D3—81no—
447#41—21no—
448#41—21no—
449#41—21no—
450#41—21no—
451#41—61no—
452#41—61no—
453#41—61no—
454#41—61no—
455C2×Q8—31no—
456C2×Q8—92no—
457C2×Q8—181no—
458C2×Q8—181no—
459C2×Q8—181no—
460C2×Q8—181no—
461C2×Q8—181no—
462C2×Q8#62611yescharacteristic
463C2×D4—21no—
464C2×D4—31no—
465C2×D4—61no—
466C2×D4#62611yescharacteristic
467C22×C4—21no—
468C22×C4—61no—
469C22×C4—181no—
470C22×C4C2×D3211yescharacteristic
471Q16—62no—
472Q16—184no—
473SD16—62no—
474SD16—62no—
475SD16—184no—
476D8—62no—
477M16—32no—
478M16—61no—
479M16—61no—
480M16—61no—
481C2×C8—32no—
482C2×C8—61no—
483C4⋊C4—61no—
484C4⋊C4—184no—
485C4⋊C4—181no—
486C22⋊C4—61no—
487C22⋊C4—92no—
488C22⋊C4—184no—
489C42—61no—
490C42—181no—
491C22×C3—21no—
492C22×C3—21no—
493C22×C3—21no—
494C22×C3—41no—
495C22×C3—41no—
496C22×C3—42no—
497C22×C3—42no—
498C22×C3—44no—
499C22×C3—42no—
500C22×C3—42no—
501C22×C3—41no—
502C22×C3—41no—
503C22×C3—121no—
504C22×C3—241no—
505C22×C3#88211yescharacteristic
506C22×C3#88411yescharacteristic
507C22×C3#93711yescharacteristic
508C22×C3#93911yescharacteristic
509C22×C3#94011yescharacteristic
510C22×C3#94011yescharacteristic
511C2×D3—41no—
512C2×D3—81no—
513C3×C4—21no—
514C3×C4—21no—
515C3×C4—21no—
516C3×C4—21no—
517C3×C4—42no—
518C3×C4—41no—
519C3×C4—41no—
520C3×C4—121no—
521C3×C4—241no—
522C3×C4#88211yescharacteristic
523C3×C4#88411yescharacteristic
524C3×C4#93011yescharacteristic
525C3×C4#93711yescharacteristic
526C3×C4#93711yescharacteristic
527C3×C4#93811yescharacteristic
528C3×C4#93911yescharacteristic
529C3×C4#95311yescharacteristic
530Dic3—41no—
531Dic3—81no—
532Dic3—124no—
533Dic3—124no—
534Dic3—122no—
535Dic3—122no—
536Dic3—122no—
537Dic3—122no—
538C32#200911yescharacteristic, complemented, Sylow
539C23—21no—
540C23—61no—
541C23#381111yescharacteristic
542Q8—21no—
543Q8—21no—
544Q8—61no—
545Q8—61no—
546Q8—182no—
547Q8—182no—
548Q8—361no—
549Q8—361no—
550D4—21no—
551D4—21no—
552D4—41no—
553D4—41no—
554D4—61no—
555D4—61no—
556D4—121no—
557D4—121no—
558C2×C4—21no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—61no—
562C2×C4—121no—
563C2×C4—121no—
564C2×C4—121no—
565C2×C4—182no—
566C2×C4—182no—
567C2×C4—361no—
568C2×C4—361no—
569C2×C4#380411yescharacteristic
570C2×C4C2×#62611yescharacteristic
571C2×C4D3×#6711yescharacteristic
572C2×C4D3×#6711yescharacteristic
573C2×C4D3×#6711yescharacteristic
574C2×C4#381111yescharacteristic
575C8—62no—
576C8—62no—
577C2×C3—22no—
578C2×C3—21no—
579C2×C3—21no—
580C2×C3—21no—
581C2×C3—21no—
582C2×C3—21no—
583C2×C3—21no—
584C2×C3—21no—
585C2×C3—41no—
586C2×C3—41no—
587C2×C3—82no—
588C2×C3—81no—
589C2×C3—81no—
590C2×C3—241no—
591C2×C3#496011yescharacteristic
592C2×C3#522311yescharacteristic
593D3—81no—
594C22—41no—
595C22—42no—
596C22—41no—
597C22—121no—
598C22—241no—
599C22#6397111yescharacteristic
600C22#6397911yescharacteristic
601C22#6398111yescharacteristic
602C4—41no—
603C4—121no—
604C4—241no—
605C4—362no—
606C4—362no—
607C4#6395811yescharacteristic
608C4#6397711yescharacteristic
609C4#6397811yescharacteristic
610C4#6398311yescharacteristic
611C3—21no—
612C3#7041211yescharacteristic, complemented
613C3#7212011yescharacteristic, complemented
614C2—21no—
615C2—21no—
616C2—21no—
617C2—81no—
618C2—241no—
619C2#1059172411yescharacteristic
subgroupG/H
centerC2#10591724
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×#41C22
socleC2×C32#392
prime radicalC3×#5822C2
hypercenterC2×#41D32
hypocenterC32#2009
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #10596296C2semidirect
3. C2×#63831C2semidirect
4. C3×#5236C2semidirect
5. #10591231C2semidirect
6. #10591107C2semidirect
7. #10589171C2semidirect
42. #5236D3semidirect
538. C32#2009semidirect
612. C3#70412semidirect
613. C3#72120semidirect

Maximal subgroups

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

subgroupindex
#105962962
C3×#58222
C2×#638312
C3×#52362
#105912312
#105911072
#105891712
#721203
#704123