Finite Group Databasebeta

← #11792371

Subgroups — #11792371

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×#5816C211yesmaximal, characteristic, complemented
2C2×C3×#942C211yesmaximal, characteristic, complemented
3#10594786C211yesmaximal, characteristic
4#10592924C211yesmaximal, characteristic, complemented
5#10591231C211yesmaximal, characteristic, complemented
6#10591110C211yesmaximal, characteristic, complemented
7#10589170C211yesmaximal, characteristic, complemented
8#72111—31nomaximal
9#71869—31nomaximal
10C22×C32×Q8C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C2×C3×#235C2211yescharacteristic
13#64135C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15C3×#947—21no—
16C3×#946—22no—
17C3×#944—21no—
18C2×C3×#216—21no—
19C3×#942—22no—
20C3×#942—22no—
21C2×C3×#215—21no—
22C3×#929—22no—
23C3×#926C2211yescharacteristic
24C2×C3×#208C2211yescharacteristic
25#63827—21no—
26#63827—21no—
27#63823—21no—
28#63823—21no—
29#63822—22no—
30#63662—22no—
31#63580—22no—
32#63568—22no—
33C2×C3×#137—31no—
34C3×#536—31no—
35#5822—31no—
36#5822—31no—
37#5816D311yescharacteristic, complemented
38C2×#942D311yescharacteristic, complemented
39#5240—31no—
40#5236—31no—
41#5225—31no—
42#5225—31no—
43#5225—61no—
44#5139—31no—
45#5006—31no—
46#4559—31no—
47#4533—31no—
48C2×C32×Q8—21no—
49C2×C32×Q8—21no—
50C2×C32×Q8—21no—
51C2×C32×Q8—21no—
52C2×C32×Q8—21no—
53C2×C32×Q8D412yes—
54C22×C32×C4—21no—
55C22×C32×C4C2311yescharacteristic
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
72#3757—21no—
73C4⋊(C3⋊Dic3)—21no—
74C4×C3⋊Dic3—21no—
75#3748—21no—
76#3748—21no—
77C2×C3⋊(C3⋊C8)D412yes—
78C3×#217D412yes—
79C3×#216—24no—
80C3×#215—24no—
81C3×(C2×D3)⋊C4—24no—
82C3×C4⋊Dic3—21no—
83C3×Dic3⋊C4—24no—
84C3×C4×Dic3—21no—
85C3×#208—21no—
86C3×#208D412yes—
87C2×C3×C3⋊C8—21no—
88#3718—22no—
89#3715—22no—
90#3715—22no—
91#3713—22no—
92#2009—91noSylow
93C2×C3×#41—31no—
94C2×C3×#41—31no—
95C22×C3×Q8—21no—
96C22×C3×Q8C2×D311yescharacteristic
97C22×C3×Q8C2×D311yescharacteristic
98C2×#235C2×D311yescharacteristic
99C2×#235C2×D311yescharacteristic
100C3×#137—62no—
101C3×#137—62no—
102C2×C3×Q16—61no—
103C2×C3×SD16—61no—
104C2×C3×M16—31no—
105C3×C4⋊Q8—61no—
106C3×#124—61no—
107C3×#123—62no—
108C3×C22⋊Q8—62no—
109C3×#117—31no—
110#951—61no—
111#951—61no—
112#950—62no—
113#950—62no—
114#949—61no—
115#949—61no—
116#947—21no—
117#946—22no—
118#944—21no—
119C2×#216—21no—
120#942—22no—
121#942—22no—
122#942—61no—
123#942—61no—
124C2×#215—21no—
125#932—61no—
126#932—61no—
127#929—22no—
128#926—31no—
129#926—31no—
130#926—61no—
131#926C2×D311yescharacteristic
132C2×#208—31no—
133C2×#208—31no—
134C2×#208—61no—
135C2×#208C2×D311yescharacteristic
136#837—62no—
137#835—62no—
138#835—62no—
139#835—64no—
140#834—62no—
141#825—62no—
142#806—62no—
143C23×C32C2×D411yescharacteristic
144C22×C3×D3—21no—
145C22×C3×D3—21no—
146C32×Q8—22no—
147C32×Q8—22no—
148C32×Q8—41no—
149C32×Q8—41no—
150C2×C32×C4—22no—
151C2×C32×C4—41no—
152C2×C32×C4—41no—
153C2×C32×C4C2×D411yescharacteristic
154C2×C32×C4C2×D411yescharacteristic
155C2×C32×C4C2×D411yescharacteristic
156C2×C32×C4C2×D411yescharacteristic
157C2×C32×C4C2×D411yescharacteristic
158C2×C32×C4#4111yescharacteristic
159C2×C3⋊Dic3—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—31no—
183#536—31no—
184#421—91no—
185#419—91no—
186#410—91no—
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—21no—
197C2×C3×Q8—21no—
198C2×C3×Q8—22no—
199C2×C3×Q8—22no—
200C2×C3×Q8—21no—
201C2×C3×Q8—21no—
202C2×C3×Q8—21no—
203C2×C3×Q8—21no—
204C2×C3×Q8—21no—
205C2×C3×Q8—21no—
206C2×C3×Q8—21no—
207C2×C3×Q8—21no—
208C2×C3×Q8—22no—
209C2×C3×Q8—31no—
210C2×C3×Q8—31no—
211C2×C3×Q8—41no—
212C2×C3×Q8—41no—
213C2×C3×Q8—41no—
214C2×C3×Q8#6712yes—
215C2×C3×Q8#6712yes—
216C2×C3×D4—31no—
217C2×C3×D4—31no—
218C2×C3×D4—61no—
219C2×C3×D4—61no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—41no—
224C22×C3×C4—61no—
225C22×C3×C4—61no—
226C22×C3×C4C22×D311yescharacteristic
227C22×C3×C4C22×D311yescharacteristic
228C2×#67—21no—
229C2×#67—21no—
230#235—21no—
231#235—21no—
232#235—21no—
233#235—21no—
234#235—21no—
235#235—21no—
236#235—21no—
237#235—21no—
238C2×D12#6711yescharacteristic
239C2×D12#6711yescharacteristic
240C2×C4×D3—21no—
241C2×C4×D3—21no—
242C2×Dic6#6711yescharacteristic
243C2×Dic6#6711yescharacteristic
244C3×Q16—64no—
245C3×SD16—64no—
246C3×M16—32no—
247C3×M16—61no—
248C2×C3×C8—61no—
249C3×C4⋊C4—64no—
250C3×C4⋊C4—61no—
251C3×C22⋊C4—32no—
252C3×C22⋊C4—64no—
253C3×C42—61no—
254#217—61no—
255#217—61no—
256#217—121no—
257#217#6712yes—
258#216—24no—
259#216—62no—
260#216—62no—
261#215—24no—
262#215—62no—
263#215—62no—
264#214—62no—
265#214—62no—
266#213—62no—
267#213—62no—
268(C2×D3)⋊C4—24no—
269C4⋊Dic3—21no—
270C4⋊Dic3—62no—
271C4⋊Dic3—61no—
272C4⋊Dic3—61no—
273Dic3⋊C4—24no—
274C4×Dic3—21no—
275C4×Dic3—61no—
276C4×Dic3—61no—
277C4×Dic3—121no—
278#208—21no—
279#208—61no—
280#208—61no—
281#208—61no—
282#208—61no—
283#208—121no—
284#208—121no—
285#208#6712yes—
286C2×C3⋊C8—21no—
287C2×C3⋊C8—32no—
288C2×C3⋊C8—32no—
289C2×C3⋊C8—62no—
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—42no—
299C32×C4#12011yescharacteristic
300C32×C4#12011yescharacteristic
301C32×C4#12111yescharacteristic
302C32×C4#12111yescharacteristic
303C3⋊Dic3—81no—
304C3×Dic3—42no—
305C3×Dic3—41no—
306C3×Dic3—41no—
307C2×#41—31no—
308C2×#41—31no—
309C22×Q8D3211yescharacteristic
310#137—62no—
311#137—62no—
312#137—181no—
313#137—181no—
314AGL(1,ℤ/8)—181no—
315AGL(1,ℤ/8)—181no—
316#135—182no—
317C2×Q16—61no—
318C2×SD16—61no—
319C2×M16—31no—
320C2×M16—91no—
321C4⋊Q8—61no—
322#124—61no—
323#123—62no—
324C22⋊Q8—62no—
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×C3D3×D411yescharacteristic
334C23×C3C2×#6711yescharacteristic
335C22×D3—21no—
336C22×D3—21no—
337C3×Q8—24no—
338C3×Q8—22no—
339C3×Q8—22no—
340C3×Q8—22no—
341C3×Q8—22no—
342C3×Q8—42no—
343C3×Q8—42no—
344C3×Q8—42no—
345C3×Q8—41no—
346C3×Q8—41no—
347C3×Q8—41no—
348C3×Q8—41no—
349C3×Q8—61no—
350C3×Q8—61no—
351C3×Q8—61no—
352C3×Q8—61no—
353C3×D4—61no—
354C3×D4—61no—
355C3×D4—61no—
356C3×D4—61no—
357C3×D4—121no—
358C3×D4—121no—
359C3×D4—121no—
360C3×D4—121no—
361C2×C3×C4—22no—
362C2×C3×C4—22no—
363C2×C3×C4—21no—
364C2×C3×C4—21no—
365C2×C3×C4—21no—
366C2×C3×C4—21no—
367C2×C3×C4—21no—
368C2×C3×C4—21no—
369C2×C3×C4—42no—
370C2×C3×C4—42no—
371C2×C3×C4—42no—
372C2×C3×C4—41no—
373C2×C3×C4—41no—
374C2×C3×C4—41no—
375C2×C3×C4—41no—
376C2×C3×C4—62no—
377C2×C3×C4—61no—
378C2×C3×C4—61no—
379C2×C3×C4—121no—
380C2×C3×C4—121no—
381C2×C3×C4—121no—
382C2×C3×C4—121no—
383C2×C3×C4D3×D411yescharacteristic
384C2×C3×C4D3×D411yescharacteristic
385C2×C3×C4D3×D411yescharacteristic
386C2×C3×C4D3×D411yescharacteristic
387C2×C3×C4D3×D411yescharacteristic
388C2×C3×C4#23711yescharacteristic
389C2×C3×C4#23711yescharacteristic
390C2×C3×C4C2×#6711yescharacteristic
391C2×C3×C4C2×#6711yescharacteristic
392C2×C3×C4C2×#6711yescharacteristic
393C2×C3×C4C2×#6711yescharacteristic
394C2×C3×C4C2×#6711yescharacteristic
395#67—41no—
396#67—41no—
397#67—41no—
398#67—41no—
399C2×Dic3—21no—
400C2×Dic3—22no—
401C2×Dic3—21no—
402C2×Dic3—122no—
403C2×Dic3—121no—
404C2×Dic3—121no—
405D12—21no—
406D12—21no—
407D12—21no—
408D12—21no—
409C4×D3—41no—
410C4×D3—41no—
411C4×D3—41no—
412C4×D3—41no—
413Dic6—21no—
414Dic6—21no—
415Dic6—21no—
416Dic6—21no—
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—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—31no—
442C2×Q8—31no—
443C2×Q8#62512yes—
444C2×D4—31no—
445C2×D4—31no—
446C2×D4—61no—
447C2×D4—61no—
448C22×C4—21no—
449C22×C4—61no—
450C22×C4—61no—
451C22×C4C2×D3211yescharacteristic
452Q16—64no—
453Q16—182no—
454SD16—64no—
455SD16—182no—
456SD16—182no—
457D8—182no—
458M16—32no—
459M16—61no—
460M16—181no—
461M16—181no—
462C2×C8—61no—
463C2×C8—92no—
464C4⋊C4—64no—
465C4⋊C4—61no—
466C4⋊C4—181no—
467C22⋊C4—32no—
468C22⋊C4—64no—
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#93711yescharacteristic
483C22×C3#93811yescharacteristic
484C22×C3#93911yescharacteristic
485C22×C3#94011yescharacteristic
486C22×C3#94011yescharacteristic
487C22×C3#95311yescharacteristic
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—44no—
497C3×C4—42no—
498C3×C4—42no—
499C3×C4—122no—
500C3×C4—121no—
501C3×C4—121no—
502C3×C4#93711yescharacteristic
503C3×C4#93711yescharacteristic
504C3×C4#93711yescharacteristic
505C3×C4#93811yescharacteristic
506C3×C4#93911yescharacteristic
507C3×C4#93911yescharacteristic
508C3×C4#93911yescharacteristic
509C3×C4#95311yescharacteristic
510Dic3—42no—
511Dic3—41no—
512Dic3—41no—
513Dic3—242no—
514Dic3—241no—
515Dic3—241no—
516C32#200911yescharacteristic, complemented, Sylow
517C23—61no—
518C23—61no—
519C23D3×#6711yescharacteristic
520Q8—22no—
521Q8—22no—
522Q8—41no—
523Q8—41no—
524Q8—61no—
525Q8—61no—
526Q8—61no—
527Q8—61no—
528D4—61no—
529D4—61no—
530D4—61no—
531D4—61no—
532D4—121no—
533D4—121no—
534D4—121no—
535D4—121no—
536C2×C4—22no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—61no—
540C2×C4—62no—
541C2×C4—61no—
542C2×C4—121no—
543C2×C4—121no—
544C2×C4—121no—
545C2×C4—121no—
546C2×C4—361no—
547C2×C4#380511yescharacteristic
548C2×C4C2×#62511yescharacteristic
549C2×C4D3×#6711yescharacteristic
550C2×C4D3×#6711yescharacteristic
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#522311yescharacteristic
568C2×C3#522311yescharacteristic
569D3—81no—
570D3—81no—
571C22—41no—
572C22—122no—
573C22—121no—
574C22—121no—
575C22—241no—
576C22#6397011yescharacteristic
577C22#6397611yescharacteristic
578C22#6397911yescharacteristic
579C4—42no—
580C4—122no—
581C4—121no—
582C4—121no—
583C4—721no—
584C4#6397011yescharacteristic
585C4#6397611yescharacteristic
586C4#6398011yescharacteristic
587C4#6398311yescharacteristic
588C3—21no—
589C3#7186911yescharacteristic, complemented
590C3#7211111yescharacteristic, complemented
591C2—21no—
592C2—21no—
593C2—21no—
594C2—241no—
595C2—241no—
596C2#1059172311yescharacteristic
subgroupG/H
centerC2#10591723
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×Q8C22
socleC2×C32#392
prime radical#10594786C2
hypercenterC22×Q8D32
hypocenterC32#2009
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5816C2semidirect
2. C2×C3×#942C2semidirect
4. #10592924C2semidirect
5. #10591231C2semidirect
6. #10591110C2semidirect
7. #10589170C2semidirect
37. #5816D3semidirect
38. C2×#942D3semidirect
516. C32#2009semidirect
589. C3#71869semidirect
590. C3#72111semidirect

Maximal subgroups

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

subgroupindex
C3×#58162
C2×C3×#9422
#105947862
#105929242
#105912312
#105911102
#105891702
#721113
#718693