Finite Group Databasebeta

← #11792281

Subgroups — #11792281

Order 1152.

789 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
1C2×C3×#909C211yesmaximal, characteristic, complemented
2#10595044C211yesmaximal, characteristic
3C2×#63827C211yesmaximal, characteristic, complemented
4C2×C3×#825C211yesmaximal, characteristic, complemented
5#10591220C211yesmaximal, characteristic, complemented
6C2×#63569C211yesmaximal, characteristic, complemented
7#10589420C211yesmaximal, characteristic, complemented
8#72110—31nomaximal
9#70393—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C2×C32×M16C2211yescharacteristic
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C2×#3748C2211yescharacteristic
16C2×C3×C4×Dic3C2211yescharacteristic
17C3×#909—22no—
18C3×#909—22no—
19C2×C3×Dic12—21no—
20C2×C3×#204—21no—
21#63980—22no—
22#63908—21no—
23#63908—21no—
24#63856—21no—
25#63856—21no—
26C2×#3718—21no—
27#63827—22no—
28#63827—22no—
29C2×#3715—21no—
30C3×#825—22no—
31#63579—22no—
32#63569—22no—
33C2×C3×#137—31no—
34#5833—31no—
35#5833—31no—
36C2×#951—31no—
37C2×#942—31no—
38C2×#909D311yescharacteristic, complemented
39C2×C3×#104—31no—
40C2×#837—31no—
41#5229—31no—
42C2×#825D311yescharacteristic, complemented
43#4929—31no—
44C2×#805—31no—
45#4554—31no—
46#4554—31no—
47#4554—61no—
48C22×C32×C4C2311yescharacteristic
49C22×C3⋊Dic3D412yes—
50C2×C3×#67—21no—
51C2×C3×#67—21no—
52C22×C3×Dic3—21no—
53C22×C3×Dic3—21no—
54C3×#235—21no—
55C3×#235—21no—
56C3×#235—21no—
57C3×#235—21no—
58C3×#235—21no—
59C3×#235—21no—
60C3×#235—21no—
61C3×#235—21no—
62C2×C3×D12D411yescharacteristic
63C2×C3×D12D411yescharacteristic
64C2×C3×C4×D3—21no—
65C2×C3×C4×D3—21no—
66C2×C3×Dic6—21no—
67C2×C3×Dic6—21no—
68C2×C3×Dic6—21no—
69C2×C3×Dic6—21no—
70C2×C3×Dic6—21no—
71C2×C3×Dic6D411yescharacteristic
72C2×C3×Dic6D411yescharacteristic
73C2×C3×Dic6D412yescomplemented
74C2×#625—22no—
75C32×M16—21no—
76C32×M16D412yescomplemented
77C2×C32×C8—21no—
78C4⋊(C3⋊Dic3)—21no—
79C4⋊(C3⋊Dic3)—21no—
80#3748—21no—
81#3748D412yescomplemented
82C2×C3⋊(C3⋊C8)—21no—
83C3×C4×Dic3—21no—
84C3×C4×Dic3—21no—
85C3×Dic12—24no—
86C3×#204—24no—
87#3724—22no—
88(C2×D3)⋊Dic3—22no—
89(C2×D3)⋊Dic3—22no—
90#3718—24no—
91#3715—24no—
92#2007—91noSylow
93C2×C3×#41—31no—
94C2×C3×#41—31no—
95C22×C3×Q8—31no—
96C2×#235C2×D311yescharacteristic
97C2×#235C2×D311yescharacteristic
98C22×Dic6C2×D311yescharacteristic
99C3×#137—62no—
100C3×#137—62no—
101C2×C3×Q16—61no—
102C2×C3×SD16—61no—
103C2×C3×M16—21no—
104C2×C3×M16C2×D311yescharacteristic
105C2×C3×M16C2×D311yescharacteristic
106C2×C3×C42—31no—
107#951—62no—
108#951—62no—
109#946—61no—
110#946—61no—
111C2×#216—61no—
112C2×#216—61no—
113#942—62no—
114#942—62no—
115C2×#215—61no—
116#939—62no—
117#939—62no—
118#938—61no—
119#938—61no—
120C2×#214—61no—
121#930—61no—
122#930—61no—
123C2×C4⋊Dic3—31no—
124C2×C4⋊Dic3—31no—
125C2×C4⋊Dic3—61no—
126#924—61no—
127#924—61no—
128C2×C4×Dic3C2×D311yescharacteristic
129C2×#208—31no—
130C2×#208—31no—
131C2×#208—61no—
132#909—22no—
133#909—22no—
134C2×Dic12—21no—
135C2×#204—21no—
136C3×#104—62no—
137#837—62no—
138C3⋊#95—62no—
139C3⋊#95—62no—
140#825—22no—
141#805—62no—
142C23×C32C2×D411yescharacteristic
143C22×C3×D3—21no—
144C22×C3×D3—21no—
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4C2×D411yescharacteristic
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4#4111yescharacteristic
151C2×C3⋊Dic3—22no—
152C2×C3⋊Dic3—42no—
153C3×#67—41no—
154C3×#67—41no—
155C3×#67—41no—
156C3×#67—41no—
157C2×C3×Dic3—22no—
158C2×C3×Dic3—21no—
159C2×C3×Dic3—21no—
160C2×C3×Dic3—22no—
161C2×C3×Dic3—41no—
162C2×C3×Dic3—41no—
163C2×C3×Dic3—41no—
164C2×C3×Dic3—41no—
165C3×D12—21no—
166C3×D12—21no—
167C3×D12—21no—
168C3×D12—21no—
169C3×C4×D3—41no—
170C3×C4×D3—41no—
171C3×C4×D3—41no—
172C3×C4×D3—41no—
173C3×Dic6—22no—
174C3×Dic6—21no—
175C3×Dic6—22no—
176C3×Dic6—21no—
177C3×Dic6—21no—
178C3×Dic6—21no—
179C3×Dic6—41no—
180C3×Dic6—41no—
181#625—82no—
182C32×C8—22no—
183C3⋊(C3⋊C8)—22no—
184C2×#137—31no—
185C2×#137—91no—
186#537—91no—
187C2×#104—31no—
188C2×#104—91no—
189#391—91no—
190#343—91no—
191C3×#41—61no—
192C3×#41—61no—
193C3×#41—61no—
194C3×#41—61no—
195C3×#41—61no—
196C3×#41—61no—
197C3×#41—61no—
198C3×#41—61no—
199C2×C3×Q8—32no—
200C2×C3×Q8—31no—
201C2×C3×Q8—31no—
202C2×C3×Q8—61no—
203C2×C3×Q8—61no—
204C2×C3×Q8—61no—
205C2×C3×Q8—61no—
206C2×C3×Q8—61no—
207C2×C3×D4—31no—
208C2×C3×D4—31no—
209C2×C3×D4—61no—
210C2×C3×D4—61no—
211C22×C3×C4—21no—
212C22×C3×C4—61no—
213C22×C3×C4—61no—
214C22×C3×C4—61no—
215C22×C3×C4—61no—
216C22×C3×C4C22×D311yescharacteristic
217C22×C3×C4C22×D311yescharacteristic
218C2×#67—21no—
219C2×#67—21no—
220C2×#67—62no—
221C2×#67—62no—
222C22×Dic3—21no—
223C22×Dic3—21no—
224C22×Dic3—32no—
225C22×Dic3—32no—
226C22×Dic3—62no—
227#235—21no—
228#235—21no—
229#235—21no—
230#235—21no—
231#235—21no—
232#235—21no—
233#235—21no—
234#235—21no—
235C2×D12D1211yescharacteristic
236C2×D12#6711yescharacteristic
237C2×C4×D3—21no—
238C2×C4×D3—21no—
239C2×Dic6—21no—
240C2×Dic6—21no—
241C2×Dic6—21no—
242C2×Dic6—21no—
243C2×Dic6—21no—
244C2×Dic6D1211yescharacteristic
245C2×Dic6#6711yescharacteristic
246C2×Dic6#6712yescomplemented
247C3×Q16—64no—
248C3×SD16—64no—
249C3×M16—21no—
250C3×M16—21no—
251C3×M16—22no—
252C3×M16—41no—
253C3×M16#6712yescomplemented
254C3×M16#6712yescomplemented
255C2×C3×C8—21no—
256C2×C3×C8—21no—
257C2×C3×C8—41no—
258C3×C42—61no—
259C3×C42—61no—
260#217—62no—
261#217—62no—
262#216—64no—
263#216—64no—
264#215—64no—
265#214—64no—
266(C2×D3)⋊C4—62no—
267(C2×D3)⋊C4—62no—
268C4⋊Dic3—61no—
269C4⋊Dic3—61no—
270C4⋊Dic3—61no—
271C4⋊Dic3—61no—
272C4⋊Dic3—121no—
273C4⋊Dic3—121no—
274Dic3⋊C4—62no—
275Dic3⋊C4—62no—
276C4×Dic3—21no—
277C4×Dic3—21no—
278#208—32no—
279#208—32no—
280#208—62no—
281#208—61no—
282#208—61no—
283#208—121no—
284C2×C3⋊C8—61no—
285C2×C3⋊C8—61no—
286C2×C3⋊C8—121no—
287Dic12—24no—
288#204—24no—
289C22×C32—21no—
290C22×C32—21no—
291C22×C32#12011yescharacteristic
292C22×C32#12111yescharacteristic
293C22×C32#12711yescharacteristic
294C2×C3×D3—41no—
295C2×C3×D3—41no—
296C2×C3×D3—41no—
297C2×C3×D3—41no—
298C2×C3×D3—41no—
299C2×C3×D3—41no—
300C32×C4#12011yescharacteristic
301C32×C4#12011yescharacteristic
302C32×C4#12111yescharacteristic
303C32×C4#12111yescharacteristic
304C3⋊Dic3—42no—
305C3×Dic3—42no—
306C3×Dic3—42no—
307C3×Dic3—41no—
308C3×Dic3—41no—
309C2×#41—31no—
310C2×#41—31no—
311C22×Q8—31no—
312#137—62no—
313#137—62no—
314#137—182no—
315#137—182no—
316C2×Q16—61no—
317C2×Q16—181no—
318C2×SD16—61no—
319C2×SD16—181no—
320C2×M16—91no—
321C2×M16D3211yescharacteristic
322C22⋊Q8—181no—
323C22⋊Q8—181no—
324#121—181no—
325#121—181no—
326#121—182no—
327C2×C4⋊C4—91no—
328C2×C42—31no—
329#104—62no—
330#104—182no—
331#95—182no—
332C23×C3—21no—
333C23×C3—61no—
334C23×C3—61no—
335C23×C3D3×D411yescharacteristic
336C23×C3D3×D411yescharacteristic
337C22×D3—21no—
338C22×D3—21no—
339C3×Q8—62no—
340C3×Q8—61no—
341C3×Q8—61no—
342C3×Q8—62no—
343C3×Q8—61no—
344C3×Q8—61no—
345C3×Q8—121no—
346C3×Q8—121no—
347C3×D4—61no—
348C3×D4—61no—
349C3×D4—61no—
350C3×D4—61no—
351C3×D4—121no—
352C3×D4—121no—
353C3×D4—121no—
354C3×D4—121no—
355C2×C3×C4—21no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—21no—
360C2×C3×C4—21no—
361C2×C3×C4—62no—
362C2×C3×C4—61no—
363C2×C3×C4—62no—
364C2×C3×C4—61no—
365C2×C3×C4—121no—
366C2×C3×C4—121no—
367C2×C3×C4—121no—
368C2×C3×C4—121no—
369C2×C3×C4—121no—
370C2×C3×C4—121no—
371C2×C3×C4—121no—
372C2×C3×C4—121no—
373C2×C3×C4C2×D1211yescharacteristic
374C2×C3×C4#23511yescharacteristic
375C2×C3×C4D3×D411yescharacteristic
376C2×C3×C4D3×D411yescharacteristic
377C2×C3×C4D3×D411yescharacteristic
378C2×C3×C4D3×D411yescharacteristic
379C2×C3×C4D3×D411yescharacteristic
380C2×C3×C4#23711yescharacteristic
381C2×C3×C4C2×#6711yescharacteristic
382C2×C3×C4C2×#6711yescharacteristic
383C2×C3×C4C2×#6711yescharacteristic
384C2×C3×C4C2×#6711yescharacteristic
385#67—41no—
386#67—41no—
387#67—41no—
388#67—41no—
389#67—242no—
390#67—242no—
391C2×Dic3—22no—
392C2×Dic3—21no—
393C2×Dic3—21no—
394C2×Dic3—22no—
395C2×Dic3—41no—
396C2×Dic3—41no—
397C2×Dic3—41no—
398C2×Dic3—41no—
399C2×Dic3—62no—
400C2×Dic3—62no—
401C2×Dic3—122no—
402C2×Dic3—122no—
403C2×Dic3—122no—
404C2×Dic3—242no—
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—22no—
416Dic6—21no—
417Dic6—22no—
418Dic6—21no—
419Dic6—41no—
420Dic6—41no—
421C3×C8—22no—
422C3×C8—22no—
423C3×C8—42no—
424C3⋊C8—62no—
425C3⋊C8—62no—
426C3⋊C8—122no—
427C2×C32—21no—
428C2×C32—21no—
429C2×C32#39211yescharacteristic
430C2×C32#45511yescharacteristic
431C2×C32#45611yescharacteristic
432C3×D3—81no—
433C3×D3—81no—
434#41—61no—
435#41—61no—
436#41—61no—
437#41—61no—
438#41—61no—
439#41—61no—
440#41—61no—
441#41—61no—
442C2×Q8—31no—
443C2×Q8—31no—
444C2×Q8—32no—
445C2×Q8—61no—
446C2×Q8—61no—
447C2×Q8—61no—
448C2×Q8—61no—
449C2×Q8—61no—
450C2×D4—31no—
451C2×D4—31no—
452C2×D4—61no—
453C2×D4—61no—
454C2×D4—182no—
455C22×C4—61no—
456C22×C4—61no—
457C22×C4—61no—
458C22×C4—61no—
459C22×C4—92no—
460C22×C4C2×D3211yescharacteristic
461Q16—64no—
462Q16—184no—
463SD16—64no—
464SD16—184no—
465M16—21no—
466M16—92no—
467M16—181no—
468M16#62512yescomplemented
469C2×C8—21no—
470C2×C8—181no—
471C4⋊C4—182no—
472C4⋊C4—181no—
473C4⋊C4—181no—
474C22⋊C4—182no—
475C22⋊C4—182no—
476C42—61no—
477C42—61no—
478C22×C3—21no—
479C22×C3—21no—
480C22×C3—21no—
481C22×C3—21no—
482C22×C3—21no—
483C22×C3—21no—
484C22×C3—21no—
485C22×C3—41no—
486C22×C3—41no—
487C22×C3—121no—
488C22×C3—121no—
489C22×C3—121no—
490C22×C3—121no—
491C22×C3—121no—
492C22×C3—121no—
493C22×C3#88211yescharacteristic
494C22×C3#88411yescharacteristic
495C22×C3#93711yescharacteristic
496C22×C3#93911yescharacteristic
497C22×C3#94011yescharacteristic
498C22×C3#94011yescharacteristic
499C2×D3—41no—
500C2×D3—41no—
501C2×D3—41no—
502C2×D3—41no—
503C2×D3—41no—
504C2×D3—41no—
505C3×C4—21no—
506C3×C4—21no—
507C3×C4—21no—
508C3×C4—21no—
509C3×C4—122no—
510C3×C4—121no—
511C3×C4—122no—
512C3×C4—121no—
513C3×C4#88211yescharacteristic
514C3×C4#88411yescharacteristic
515C3×C4#93011yescharacteristic
516C3×C4#93711yescharacteristic
517C3×C4#93711yescharacteristic
518C3×C4#93811yescharacteristic
519C3×C4#93911yescharacteristic
520C3×C4#95311yescharacteristic
521Dic3—42no—
522Dic3—41no—
523Dic3—42no—
524Dic3—41no—
525Dic3—122no—
526Dic3—122no—
527Dic3—242no—
528C32#200711yescharacteristic, complemented, Sylow
529C23—61no—
530C23—61no—
531C23#380211yescharacteristic
532Q8—61no—
533Q8—61no—
534Q8—62no—
535Q8—61no—
536Q8—62no—
537Q8—61no—
538Q8—121no—
539Q8—121no—
540D4—61no—
541D4—61no—
542D4—61no—
543D4—61no—
544D4—121no—
545D4—121no—
546D4—121no—
547D4—121no—
548D4—722no—
549C2×C4—62no—
550C2×C4—62no—
551C2×C4—61no—
552C2×C4—61no—
553C2×C4—121no—
554C2×C4—121no—
555C2×C4—121no—
556C2×C4—121no—
557C2×C4—121no—
558C2×C4—121no—
559C2×C4—121no—
560C2×C4—121no—
561C2×C4—182no—
562C2×C4—362no—
563C2×C4#379511yescharacteristic
564C2×C4D3×D1211yescharacteristic
565C2×C4#380211yescharacteristic
566C2×C4C2×#62511yescharacteristic
567C2×C4D3×#6711yescharacteristic
568C2×C4D3×#6711yescharacteristic
569C8—22no—
570C8—182no—
571C2×C3—21no—
572C2×C3—21no—
573C2×C3—21no—
574C2×C3—21no—
575C2×C3—21no—
576C2×C3—21no—
577C2×C3—21no—
578C2×C3—41no—
579C2×C3—41no—
580C2×C3—241no—
581C2×C3—241no—
582C2×C3#482511yescharacteristic
583C2×C3#482611yescharacteristic
584C2×C3#496011yescharacteristic
585C2×C3#520211yescharacteristic
586C2×C3#520511yescharacteristic
587C2×C3#522311yescharacteristic
588D3—81no—
589D3—81no—
590C22—21no—
591C22—21no—
592C22—121no—
593C22—121no—
594C22—121no—
595C22—121no—
596C22—121no—
597C22—121no—
598C22#6388511yescharacteristic
599C22#6391411yescharacteristic
600C22#6392211yescharacteristic
601C4—122no—
602C4—121no—
603C4—121no—
604C4—122no—
605C4—362no—
606C4#6388511yescharacteristic
607C4#6390811yescharacteristic
608C4#6392211yescharacteristic
609C4#6397611yescharacteristic
610C3—21no—
611C3#7039311yescharacteristic, complemented
612C3#7211011yescharacteristic, complemented
613C2—21no—
614C2—21no—
615C2—241no—
616C2—241no—
617C2#1059101111yescharacteristic
618C2#1059101711yescharacteristic
619C2#1059138911yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32#120
prime radical#10595044C2
hypercenterC2×M16D32
hypocenterC32#2007
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C2×C3×#909C2semidirect
3. C2×#63827C2semidirect
4. C2×C3×#825C2semidirect
5. #10591220C2semidirect
6. C2×#63569C2semidirect
7. #10589420C2semidirect
38. C2×#909D3semidirect
42. C2×#825D3semidirect
73. C2×C3×Dic6D4semidirect
76. C32×M16D4semidirect
81. #3748D4semidirect
246. C2×Dic6#67semidirect
253. C3×M16#67semidirect
254. C3×M16#67semidirect
468. M16#625semidirect
528. C32#2007semidirect
611. C3#70393semidirect
612. C3#72110semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9092
#105950442
C2×#638272
C2×C3×#8252
#105912202
C2×#635692
#105894202
#721103
#703933