Finite Group Databasebeta

← #11792373

Subgroups — #11792373

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
1C3×#5748C211yesmaximal, characteristic
2#10594856C211yesmaximal, characteristic, complemented
3C2×#63831C211yesmaximal, characteristic, complemented
4#10592819C211yesmaximal, characteristic, complemented
5#10591231C211yesmaximal, characteristic, complemented
6#10591110C211yesmaximal, characteristic, complemented
7C3×#4556C211yesmaximal, characteristic, complemented
8#72120—31nomaximal
9#69031—31nomaximal
10C22×#634C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C2×C3×#235C2211yescharacteristic
13C2×C32×M16C2211yescharacteristic
14#64135C2211yescharacteristic
15C3×#926C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C3×#909—21no—
18C3×#909—21no—
19C3×#908—21no—
20C3×#908—21no—
21C3×#904—22no—
22#63962—22no—
23#63866—21no—
24#63860—21no—
25#63857—22no—
26C2×#3719—21no—
27#63831—22no—
28#63831—22no—
29C2×#3716—21no—
30#63643—22no—
31#63580—22no—
32#63568—22no—
33C3×#575—31no—
34#5825—31no—
35C2×#951—31no—
36#5748D311yescharacteristic
37C2×#909—31no—
38#5526—31no—
39#5240—31no—
40#5236—31no—
41#5139—31no—
42#5120—31no—
43#5120—31no—
44#5120—61no—
45#5006—31no—
46C3×#344—31no—
47#4556D311yescharacteristic, complemented
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×M16—21no—
73C32×M16—21no—
74C2×C32×C8D412yes—
75#3757—21no—
76C4⋊(C3⋊Dic3)—21no—
77C4×C3⋊Dic3—21no—
78C3×#217D412yes—
79C3×C4⋊Dic3—21no—
80C3×C4×Dic3—21no—
81C3×#208—21no—
82C3×#208D412yes—
83C2×C3×C3⋊C8—21no—
84C3×Dic12—22no—
85C3×D24—22no—
86C3×#204—22no—
87C3×#204—22no—
88Dic3⋊Dic3—24no—
89(C2×D3)⋊Dic3—24no—
90#3719—24no—
91#3716—24no—
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—
100C3×#137—61no—
101C3×#137—61no—
102C3×AGL(1,ℤ/8)—61no—
103C3×AGL(1,ℤ/8)—61no—
104C3×#135—62no—
105C2×C3×M16—21no—
106C2×C3×M16—31no—
107C2×C3×M16C2×D311yescharacteristic
108C2×C3×M16C2×D311yescharacteristic
109C3×#117—31no—
110#951—62no—
111#951—62no—
112#944—61no—
113C2×#216—61no—
114#936—61no—
115#935—62no—
116C2×#214—61no—
117#926—31no—
118#926—31no—
119#926—61no—
120#926C2×D311yescharacteristic
121#924—62no—
122C2×#208C2×D311yescharacteristic
123#909—21no—
124#909—21no—
125#909—62no—
126#909—62no—
127#908—21no—
128#908—21no—
129C2×Dic12—61no—
130#904—22no—
131C2×#204—61no—
132#897—62no—
133#886—62no—
134#875—61no—
135#869—61no—
136#837—62no—
137#834—62no—
138#825—62no—
139#816—64no—
140#816—62no—
141#816—62no—
142#806—62no—
143C23×C32C2×D411yescharacteristic
144C22×C3×D3—21no—
145C22×C3×D3—21no—
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4C2×D411yescharacteristic
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4C2×D411yescharacteristic
151C2×C32×C4#4111yescharacteristic
152C2×C3⋊Dic3—22no—
153C2×C3⋊Dic3—41no—
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—
179C32×C8—22no—
180C3×C3⋊C8—22no—
181#575—31no—
182C2×#137—91no—
183#536—91no—
184#421—91no—
185#419—91no—
186#410—91no—
187#344—31no—
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×D12#6711yescharacteristic
221C2×D12#6711yescharacteristic
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×Dic6#6711yescharacteristic
243C2×Dic6#6711yescharacteristic
244C3×Q16—62no—
245C3×SD16—62no—
246C3×SD16—62no—
247C3×D8—62no—
248C3×M16—21no—
249C3×M16—21no—
250C3×M16—21no—
251C3×M16—21no—
252C3×M16—32no—
253C3×M16—41no—
254C3×M16—41no—
255C3×M16—61no—
256C2×C3×C8—22no—
257C2×C3×C8—61no—
258C2×C3×C8D1212yes—
259C2×C3×C8#6712yes—
260C3×C4⋊C4—61no—
261C3×C22⋊C4—32no—
262C3×C42—61no—
263#217—64no—
264#217—61no—
265#217—61no—
266#217—121no—
267#217D1212yes—
268#216—64no—
269#214—64no—
270(C2×D3)⋊C4—64no—
271C4⋊Dic3—21no—
272C4⋊Dic3—64no—
273C4⋊Dic3—62no—
274C4⋊Dic3—61no—
275C4⋊Dic3—61no—
276Dic3⋊C4—64no—
277C4×Dic3—21no—
278C4×Dic3—61no—
279C4×Dic3—61no—
280C4×Dic3—121no—
281#208—21no—
282#208D1212yes—
283C2×C3⋊C8—21no—
284Dic12—22no—
285Dic12—64no—
286D24—22no—
287#204—22no—
288#204—22no—
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#12011yescharacteristic
299C32×C4#12011yescharacteristic
300C32×C4#12111yescharacteristic
301C32×C4#12111yescharacteristic
302C3⋊Dic3—42no—
303C3⋊Dic3—81no—
304C3×Dic3—42no—
305C3×Dic3—41no—
306C3×Dic3—41no—
307C2×#41—31no—
308C2×#41—31no—
309C22×Q8—91no—
310#137—61no—
311#137—61no—
312#137—182no—
313#137—182no—
314AGL(1,ℤ/8)—61no—
315AGL(1,ℤ/8)—61no—
316#135—62no—
317C2×Q16—181no—
318C2×SD16—181no—
319C2×M16—31no—
320C2×M16D3211yescharacteristic
321C4⋊Q8—181no—
322#124—181no—
323#123—182no—
324C22⋊Q8—182no—
325#117—31no—
326#117—91no—
327#104—182no—
328#103—182no—
329#99—182no—
330C23×C3—21no—
331C23×C3—61no—
332C23×C3—61no—
333C23×C3C2×D1211yescharacteristic
334C23×C3D3×D411yescharacteristic
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—61no—
356C2×C3×C4—61no—
357C2×C3×C4—62no—
358C2×C3×C4—121no—
359C2×C3×C4—121no—
360C2×C3×C4—121no—
361C2×C3×C4—121no—
362C2×C3×C4C2×D1211yescharacteristic
363C2×C3×C4C2×D1211yescharacteristic
364C2×C3×C4D3×D411yescharacteristic
365C2×C3×C4D3×D411yescharacteristic
366C2×C3×C4D3×D411yescharacteristic
367C2×C3×C4D3×D411yescharacteristic
368C2×C3×C4D3×D411yescharacteristic
369C2×C3×C4#23711yescharacteristic
370C2×C3×C4#23911yescharacteristic
371C2×C3×C4C2×#6711yescharacteristic
372C2×C3×C4C2×#6711yescharacteristic
373C2×C3×C4C2×#6711yescharacteristic
374#67—41no—
375#67—41no—
376#67—41no—
377#67—41no—
378C2×Dic3—22no—
379C2×Dic3—21no—
380C2×Dic3—21no—
381C2×Dic3—62no—
382C2×Dic3—62no—
383C2×Dic3—122no—
384C2×Dic3—122no—
385C2×Dic3—122no—
386C2×Dic3—121no—
387C2×Dic3—121no—
388C2×Dic3—121no—
389C2×Dic3—121no—
390C2×Dic3—122no—
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—22no—
418C3×C8—22no—
419C3×C8—42no—
420C3×C8—62no—
421C3⋊C8—22no—
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—62no—
453Q16—184no—
454SD16—62no—
455SD16—62no—
456SD16—184no—
457D8—62no—
458M16—21no—
459M16—21no—
460M16—32no—
461M16—61no—
462C2×C8—61no—
463C2×C8#62612yes—
464C4⋊C4—61no—
465C4⋊C4—184no—
466C4⋊C4—181no—
467C22⋊C4—32no—
468C22⋊C4—184no—
469C22⋊C4—181no—
470C42—61no—
471C42—181no—
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#87411yescharacteristic
483C22×C3#88211yescharacteristic
484C22×C3#89511yescharacteristic
485C22×C3#93711yescharacteristic
486C22×C3#93911yescharacteristic
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—122no—
497C3×C4—121no—
498C3×C4—121no—
499C3×C4#88211yescharacteristic
500C3×C4#88211yescharacteristic
501C3×C4#89511yescharacteristic
502C3×C4#89511yescharacteristic
503C3×C4#93711yescharacteristic
504C3×C4#93811yescharacteristic
505C3×C4#93911yescharacteristic
506C3×C4#95311yescharacteristic
507Dic3—42no—
508Dic3—41no—
509Dic3—41no—
510Dic3—124no—
511Dic3—122no—
512Dic3—122no—
513Dic3—242no—
514Dic3—241no—
515Dic3—241no—
516C32#200911yescharacteristic, complemented, Sylow
517C23—61no—
518C23—61no—
519C23D3×D1211yescharacteristic
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—61no—
537C2×C4—62no—
538C2×C4—61no—
539C2×C4—121no—
540C2×C4—121no—
541C2×C4—121no—
542C2×C4—121no—
543C2×C4—182no—
544C2×C4—361no—
545C2×C4—361no—
546C2×C4—361no—
547C2×C4#379611yescharacteristic
548C2×C4D3×D1211yescharacteristic
549C2×C4#380211yescharacteristic
550C2×C4C2×#62611yescharacteristic
551C2×C4D3×#6711yescharacteristic
552C2×C4D3×#6711yescharacteristic
553C8—22no—
554C8—62no—
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#467111yescharacteristic
568C2×C3#522311yescharacteristic
569D3—81no—
570D3—81no—
571C22—41no—
572C22—122no—
573C22—121no—
574C22—121no—
575C22—241no—
576C22#6388611yescharacteristic
577C22#6391111yescharacteristic
578C22#6392211yescharacteristic
579C4—122no—
580C4—121no—
581C4—121no—
582C4—362no—
583C4—721no—
584C4#6388611yescharacteristic
585C4#6391611yescharacteristic
586C4#6392211yescharacteristic
587C4#6397711yescharacteristic
588C3—21no—
589C3#6903111yescharacteristic, complemented
590C3#7212011yescharacteristic, complemented
591C2—21no—
592C2—21no—
593C2—21no—
594C2—241no—
595C2—241no—
596C2#1059139111yescharacteristic
subgroupG/H
centerC2#10591391
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC2×C32#392
prime radicalC3×#5748C2
hypercenterC2×M16D32
hypocenterC32#2009
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. #10594856C2semidirect
3. C2×#63831C2semidirect
4. #10592819C2semidirect
5. #10591231C2semidirect
6. #10591110C2semidirect
7. C3×#4556C2semidirect
47. #4556D3semidirect
516. C32#2009semidirect
589. C3#69031semidirect
590. C3#72120semidirect

Maximal subgroups

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

subgroupindex
C3×#57482
#105948562
C2×#638312
#105928192
#105912312
#105911102
C3×#45562
#721203
#690313