Finite Group Databasebeta

← #11792382

Subgroups — #11792382

Order 1152.

771 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594856C211yesmaximal, characteristic, complemented
2C2×#63831C211yesmaximal, characteristic, complemented
3#10594786C211yesmaximal, characteristic
4#10592703C211yesmaximal, characteristic, complemented
5C3×#5006C211yesmaximal, characteristic, complemented
6C3×#5005C211yesmaximal, characteristic, complemented
7#10589170C211yesmaximal, characteristic, complemented
8#70412—31nomaximal
9#70053—31nomaximal
10C22×#634C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C2×C3×#235C2211yescharacteristic
13C32×#117C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15C3×#926C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17#63962—22no—
18#63866—21no—
19#63860—21no—
20#63857—22no—
21C2×#3719—21no—
22#63831—22no—
23#63831—22no—
24C2×#3716—21no—
25#63827—21no—
26#63827—21no—
27#63823—21no—
28#63823—21no—
29#63822—22no—
30#63637—22no—
31C3×#806—22no—
32C3×#805—22no—
33#5825—31no—
34C2×#951—31no—
35#5822—31no—
36#5822—31no—
37C2×#909—31no—
38#5526—31no—
39C3×#421—31no—
40C3×#410—31no—
41#5006D311yescharacteristic, complemented
42#5005D311yescharacteristic, complemented
43#5004—31no—
44#5004—31no—
45#5004—61no—
46#4559—31no—
47#4533—31no—
48C22×C32×C4C2311yescharacteristic
49C22×C3⋊Dic3—21no—
50C2×#634—21no—
51C2×#634—21no—
52C2×#634—21no—
53C2×#634—21no—
54C2×#634—21no—
55C2×#634D412yes—
56C2×C3×#67—21no—
57C2×C3×#67—21no—
58C3×#235—21no—
59C3×#235—21no—
60C3×#235—21no—
61C3×#235—21no—
62C3×#235—21no—
63C3×#235—21no—
64C3×#235—21no—
65C3×#235—21no—
66C2×C3×D12D411yescharacteristic
67C2×C3×D12D411yescharacteristic
68C2×C3×C4×D3—21no—
69C2×C3×C4×D3—21no—
70C2×C3×Dic6D411yescharacteristic
71C2×C3×Dic6D411yescharacteristic
72C32×C4⋊C4—21no—
73C32×C22⋊C4—21no—
74C32×C42—21no—
75#3748—21no—
76#3748—21no—
77C2×C3⋊(C3⋊C8)D412yes—
78C3×#217D412yes—
79C3×C4⋊Dic3—21no—
80C3×C4×Dic3—21no—
81C3×#208—21no—
82C3×#208D412yes—
83C2×C3×C3⋊C8—21no—
84Dic3⋊Dic3—24no—
85(C2×D3)⋊Dic3—24no—
86#3719—24no—
87#3718—22no—
88#3716—24no—
89#3715—22no—
90#3715—22no—
91#3713—22no—
92#2009—91noSylow
93C2×C3×#41—31no—
94C2×C3×#41—31no—
95C2×#235C2×D311yescharacteristic
96C2×#235C2×D311yescharacteristic
97C22×Dic6—31no—
98C22×Dic6—31no—
99C22×Dic6—61no—
100C2×C3×M16—31no—
101C3×#117—21no—
102C3×#117—31no—
103C3×#117C2×D311yescharacteristic
104C3×#117C2×D311yescharacteristic
105#951—62no—
106#951—61no—
107#951—61no—
108#951—62no—
109#950—62no—
110#950—62no—
111#949—61no—
112#949—61no—
113#944—61no—
114C2×#216—61no—
115#942—61no—
116#942—61no—
117#936—61no—
118#935—62no—
119C2×#214—61no—
120#932—61no—
121#932—61no—
122#926C2×D311yescharacteristic
123#924—62no—
124C2×#208—31no—
125C2×#208—31no—
126C2×#208—61no—
127C2×#208C2×D311yescharacteristic
128#909—62no—
129#909—62no—
130C2×Dic12—61no—
131C2×#204—61no—
132#897—62no—
133#886—62no—
134#875—61no—
135#869—61no—
136C3×#104—62no—
137C3×#99—62no—
138#810—62no—
139#810—62no—
140#810—64no—
141#806—22no—
142#805—22no—
143C23×C32C2×D411yescharacteristic
144C22×C3×D3—21no—
145C22×C3×D3—21no—
146C2×C32×C4—41no—
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4C2×D411yescharacteristic
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4C2×D411yescharacteristic
151C2×C32×C4C2×D411yescharacteristic
152C2×C32×C4#4111yescharacteristic
153C2×C3⋊Dic3—22no—
154C2×C3⋊Dic3—41no—
155C2×C3⋊Dic3—41no—
156#634—22no—
157#634—22no—
158#634—41no—
159#634—41no—
160C3×#67—41no—
161C3×#67—41no—
162C3×#67—41no—
163C3×#67—41no—
164C2×C3×Dic3—22no—
165C2×C3×Dic3—21no—
166C2×C3×Dic3—21no—
167C3×D12—21no—
168C3×D12—21no—
169C3×D12—21no—
170C3×D12—21no—
171C3×C4×D3—41no—
172C3×C4×D3—41no—
173C3×C4×D3—41no—
174C3×C4×D3—41no—
175C3×Dic6—21no—
176C3×Dic6—21no—
177C3×Dic6—21no—
178C3×Dic6—21no—
179C3⋊(C3⋊C8)—22no—
180C3×C3⋊C8—22no—
181#575—91no—
182C2×#137—91no—
183#536—91no—
184#421—31no—
185#419—91no—
186#410—31no—
187#344—91no—
188C3×#41—61no—
189C3×#41—61no—
190C3×#41—61no—
191C3×#41—61no—
192C3×#41—61no—
193C3×#41—61no—
194C3×#41—61no—
195C3×#41—61no—
196C2×C3×Q8—31no—
197C2×C3×Q8—31no—
198C2×C3×D4—31no—
199C2×C3×D4—31no—
200C2×C3×D4—61no—
201C2×C3×D4—61no—
202C22×C3×C4—21no—
203C22×C3×C4—61no—
204C22×C3×C4—61no—
205C22×C3×C4C22×D311yescharacteristic
206C22×C3×C4C22×D311yescharacteristic
207C2×#67—21no—
208C2×#67—21no—
209C22×Dic3—61no—
210C22×Dic3—61no—
211C22×Dic3—121no—
212#235—21no—
213#235—21no—
214#235—21no—
215#235—21no—
216#235—21no—
217#235—21no—
218#235—21no—
219#235—21no—
220C2×D12D1211yescharacteristic
221C2×D12D1211yescharacteristic
222C2×C4×D3—21no—
223C2×C4×D3—21no—
224C2×Dic6—32no—
225C2×Dic6—32no—
226C2×Dic6—62no—
227C2×Dic6—62no—
228C2×Dic6—62no—
229C2×Dic6—61no—
230C2×Dic6—61no—
231C2×Dic6—61no—
232C2×Dic6—61no—
233C2×Dic6—61no—
234C2×Dic6—61no—
235C2×Dic6—61no—
236C2×Dic6—61no—
237C2×Dic6—61no—
238C2×Dic6—61no—
239C2×Dic6—121no—
240C2×Dic6—121no—
241C2×Dic6—121no—
242C2×Dic6D1211yescharacteristic
243C2×Dic6D1211yescharacteristic
244C3×M16—32no—
245C3×M16—61no—
246C2×C3×C8—61no—
247C3×C4⋊C4—22no—
248C3×C4⋊C4—21no—
249C3×C4⋊C4—21no—
250C3×C4⋊C4—61no—
251C3×C22⋊C4—21no—
252C3×C22⋊C4—21no—
253C3×C22⋊C4—32no—
254C3×C22⋊C4—41no—
255C3×C42—21no—
256C3×C42—21no—
257C3×C42—41no—
258C3×C42—61no—
259#217—64no—
260#217#6712yes—
261#216—64no—
262#216—62no—
263#216—62no—
264#215—62no—
265#215—62no—
266#214—64no—
267#214—62no—
268#214—62no—
269#213—62no—
270#213—62no—
271(C2×D3)⋊C4—64no—
272C4⋊Dic3—21no—
273C4⋊Dic3—64no—
274Dic3⋊C4—64no—
275C4×Dic3—21no—
276#208—21no—
277#208—61no—
278#208—61no—
279#208—61no—
280#208—61no—
281#208—121no—
282#208—121no—
283#208#6712yes—
284C2×C3⋊C8—21no—
285C2×C3⋊C8—32no—
286C2×C3⋊C8—32no—
287C2×C3⋊C8—62no—
288Dic12—64no—
289#204—64no—
290C22×C32—41no—
291C22×C32#12011yescharacteristic
292C22×C32#12111yescharacteristic
293C22×C32#12711yescharacteristic
294C2×C3×D3—42no—
295C2×C3×D3—41no—
296C2×C3×D3—41no—
297C2×C3×D3—81no—
298C32×C4—81no—
299C32×C4#12011yescharacteristic
300C32×C4#12011yescharacteristic
301C32×C4#12111yescharacteristic
302C32×C4#12111yescharacteristic
303C3⋊Dic3—42no—
304C3×Dic3—42no—
305C3×Dic3—41no—
306C3×Dic3—41no—
307C2×#41—31no—
308C2×#41—31no—
309C22×Q8—91no—
310#137—182no—
311#137—182no—
312#137—181no—
313#137—181no—
314AGL(1,ℤ/8)—181no—
315AGL(1,ℤ/8)—181no—
316#135—182no—
317C2×Q16—181no—
318C2×SD16—181no—
319C2×M16—31no—
320C2×M16—91no—
321C4⋊Q8—181no—
322#124—181no—
323#123—182no—
324C22⋊Q8—182no—
325#117—31no—
326#117D3211yescharacteristic
327#104—62no—
328#103—182no—
329#99—62no—
330C23×C3—21no—
331C23×C3—61no—
332C23×C3—61no—
333C23×C3D3×D411yescharacteristic
334C23×C3C2×#6711yescharacteristic
335C22×D3—21no—
336C22×D3—21no—
337C3×Q8—61no—
338C3×Q8—61no—
339C3×Q8—61no—
340C3×Q8—61no—
341C3×D4—61no—
342C3×D4—61no—
343C3×D4—61no—
344C3×D4—61no—
345C3×D4—121no—
346C3×D4—121no—
347C3×D4—121no—
348C3×D4—121no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4—21no—
354C2×C3×C4—21no—
355C2×C3×C4—42no—
356C2×C3×C4—41no—
357C2×C3×C4—41no—
358C2×C3×C4—62no—
359C2×C3×C4—61no—
360C2×C3×C4—61no—
361C2×C3×C4—121no—
362C2×C3×C4—121no—
363C2×C3×C4—121no—
364C2×C3×C4—121no—
365C2×C3×C4C2×D1211yescharacteristic
366C2×C3×C4C2×D1211yescharacteristic
367C2×C3×C4#23511yescharacteristic
368C2×C3×C4#23511yescharacteristic
369C2×C3×C4D3×D411yescharacteristic
370C2×C3×C4D3×D411yescharacteristic
371C2×C3×C4D3×D411yescharacteristic
372C2×C3×C4D3×D411yescharacteristic
373C2×C3×C4D3×D411yescharacteristic
374C2×C3×C4D3×D411yescharacteristic
375C2×C3×C4D3×D411yescharacteristic
376C2×C3×C4C2×#6711yescharacteristic
377#67—41no—
378#67—41no—
379#67—41no—
380#67—41no—
381C2×Dic3—21no—
382C2×Dic3—21no—
383C2×Dic3—22no—
384C2×Dic3—62no—
385C2×Dic3—62no—
386C2×Dic3—122no—
387C2×Dic3—122no—
388C2×Dic3—122no—
389C2×Dic3—121no—
390C2×Dic3—121no—
391C2×Dic3—121no—
392C2×Dic3—121no—
393D12—21no—
394D12—21no—
395D12—21no—
396D12—21no—
397C4×D3—41no—
398C4×D3—41no—
399C4×D3—41no—
400C4×D3—41no—
401Dic6—21no—
402Dic6—21no—
403Dic6—21no—
404Dic6—21no—
405Dic6—64no—
406Dic6—62no—
407Dic6—62no—
408Dic6—62no—
409Dic6—62no—
410Dic6—122no—
411Dic6—122no—
412Dic6—122no—
413Dic6—121no—
414Dic6—121no—
415Dic6—121no—
416Dic6—121no—
417C3×C8—62no—
418C3⋊C8—22no—
419C3⋊C8—62no—
420C3⋊C8—62no—
421C3⋊C8—122no—
422C2×C32—21no—
423C2×C32—21no—
424C2×C32—21no—
425C2×C32#39211yescharacteristic
426C3×D3—81no—
427C3×D3—81no—
428#41—61no—
429#41—61no—
430#41—61no—
431#41—61no—
432#41—61no—
433#41—61no—
434#41—61no—
435#41—61no—
436C2×Q8—31no—
437C2×Q8—31no—
438C2×Q8—92no—
439C2×Q8—181no—
440C2×Q8—181no—
441C2×Q8—181no—
442C2×Q8—181no—
443C2×Q8—181no—
444C2×D4—31no—
445C2×D4—31no—
446C2×D4—61no—
447C2×D4—61no—
448C22×C4—61no—
449C22×C4—61no—
450C22×C4—181no—
451C22×C4C2×D3211yescharacteristic
452Q16—184no—
453Q16—182no—
454SD16—184no—
455SD16—182no—
456SD16—182no—
457D8—182no—
458M16—32no—
459M16—61no—
460M16—181no—
461M16—181no—
462C2×C8—61no—
463C2×C8—92no—
464C4⋊C4—21no—
465C4⋊C4—61no—
466C4⋊C4—184no—
467C22⋊C4—21no—
468C22⋊C4—32no—
469C22⋊C4—184no—
470C42—21no—
471C42—61no—
472C22×C3—21no—
473C22×C3—21no—
474C22×C3—21no—
475C22×C3—41no—
476C22×C3—41no—
477C22×C3—42no—
478C22×C3—122no—
479C22×C3—121no—
480C22×C3—121no—
481C22×C3—241no—
482C22×C3#88211yescharacteristic
483C22×C3#88411yescharacteristic
484C22×C3#93011yescharacteristic
485C22×C3#93711yescharacteristic
486C22×C3#94011yescharacteristic
487C22×C3#94011yescharacteristic
488C2×D3—42no—
489C2×D3—41no—
490C2×D3—41no—
491C2×D3—81no—
492C3×C4—21no—
493C3×C4—21no—
494C3×C4—21no—
495C3×C4—21no—
496C3×C4—82no—
497C3×C4—81no—
498C3×C4—81no—
499C3×C4—122no—
500C3×C4—121no—
501C3×C4—121no—
502C3×C4#88211yescharacteristic
503C3×C4#88211yescharacteristic
504C3×C4#88211yescharacteristic
505C3×C4#88411yescharacteristic
506C3×C4#88411yescharacteristic
507C3×C4#88411yescharacteristic
508C3×C4#93011yescharacteristic
509C3×C4#93711yescharacteristic
510Dic3—42no—
511Dic3—41no—
512Dic3—41no—
513Dic3—124no—
514Dic3—122no—
515Dic3—122no—
516C32#200911yescharacteristic, complemented, Sylow
517C23—61no—
518C23—61no—
519C23D3×#6711yescharacteristic
520Q8—61no—
521Q8—61no—
522Q8—61no—
523Q8—61no—
524Q8—182no—
525Q8—182no—
526Q8—361no—
527Q8—361no—
528D4—61no—
529D4—61no—
530D4—61no—
531D4—61no—
532D4—121no—
533D4—121no—
534D4—121no—
535D4—121no—
536C2×C4—41no—
537C2×C4—61no—
538C2×C4—62no—
539C2×C4—61no—
540C2×C4—121no—
541C2×C4—121no—
542C2×C4—121no—
543C2×C4—121no—
544C2×C4—182no—
545C2×C4—361no—
546C2×C4—361no—
547C2×C4#379811yescharacteristic
548C2×C4D3×D1211yescharacteristic
549C2×C4D3×D1211yescharacteristic
550C2×C4#380211yescharacteristic
551C2×C4D3×#6711yescharacteristic
552C2×C4#381111yescharacteristic
553C8—62no—
554C8—182no—
555C2×C3—22no—
556C2×C3—21no—
557C2×C3—21no—
558C2×C3—21no—
559C2×C3—21no—
560C2×C3—21no—
561C2×C3—21no—
562C2×C3—21no—
563C2×C3—41no—
564C2×C3—41no—
565C2×C3—241no—
566C2×C3—241no—
567C2×C3#496011yescharacteristic
568C2×C3#496011yescharacteristic
569D3—81no—
570D3—81no—
571C22—41no—
572C22—122no—
573C22—121no—
574C22—121no—
575C22—241no—
576C22#6390611yescharacteristic
577C22#6392211yescharacteristic
578C22#6397911yescharacteristic
579C4—81no—
580C4—122no—
581C4—121no—
582C4—121no—
583C4—362no—
584C4#6390611yescharacteristic
585C4#6391211yescharacteristic
586C4#6392211yescharacteristic
587C4#6392311yescharacteristic
588C3—21no—
589C3#7005311yescharacteristic, complemented
590C3#7041211yescharacteristic, complemented
591C2—21no—
592C2—21no—
593C2—21no—
594C2—241no—
595C2—241no—
596C2#1059139311yescharacteristic
subgroupG/H
centerC2#10591393
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC2×C32#392
prime radical#10594786C2
hypercenter#117D32
hypocenterC32#2009
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #10594856C2semidirect
2. C2×#63831C2semidirect
4. #10592703C2semidirect
5. C3×#5006C2semidirect
6. C3×#5005C2semidirect
7. #10589170C2semidirect
41. #5006D3semidirect
42. #5005D3semidirect
516. C32#2009semidirect
589. C3#70053semidirect
590. C3#70412semidirect

Maximal subgroups

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

subgroupindex
#105948562
C2×#638312
#105947862
#105927032
C3×#50062
C3×#50052
#105891702
#704123
#700533