Finite Group Databasebeta

← #11904696

Subgroups — #11904696

Order 1152.

3472 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64320C211yesmaximal, characteristic, complemented
2C2×D3×#239C211yesmaximal, characteristic, complemented
3#10596048C211yesmaximal, characteristic, complemented
4C3×#5576C211yesmaximal, characteristic, complemented
5C3×#5574C211yesmaximal, characteristic, complemented
6#10595410C211yesmaximal, characteristic, complemented
7#10595342C211yesmaximal, characteristic, complemented
8#10594629C213yesmaximal, complemented
9#10594621C213yesmaximal, complemented
10D3×#895C213yesmaximal, complemented
11#10594523C213yesmaximal, complemented
12#10594005C213yesmaximal, complemented
13D122C213yesmaximal, complemented
14#10594001C213yesmaximal, complemented
15#10593997C213yesmaximal, complemented
16#86713—31nomaximal
17#85900—31nomaximal
18C2×#3832C2211yescharacteristic, complemented
19C2×#3832C2211yescharacteristic, complemented
20C2×C3×#239C2211yescharacteristic
21C2×C3×#239C2211yescharacteristic, complemented
22C2×C3×D3×Q8C2211yescharacteristic, complemented
23#64320—28no—
24D3×#239—28no—
25C2×#3802C2213yescomplemented
26C2×D3×D12C2213yescomplemented
27C2×D3×D12C2213yescomplemented
28C2×D3×D12C2213yescomplemented
29C2×D3×D12C2216yescomplemented
30C2×C4×D32C2213yescomplemented
31C2×#3799C2213yescomplemented
32C2×#3798C2213yescomplemented
33C2×#3796C2213yescomplemented
34C32×C4×Q8C2211yescharacteristic, complemented
35#64104C2213yescomplemented
36#64104C2213yescomplemented
37#64083C2213yescomplemented
38C4×C4⋊(C3⋊D3)C2213yescomplemented
39C3×Q8×Dic3C2211yescharacteristic, complemented
40C3×#897C2213yescomplemented
41C3×#895C2213yescomplemented
42C3×#893C2213yescomplemented
43C3×D3×C4⋊C4C2213yescomplemented
44C3×#875C2213yescomplemented
45C3×C4×D12C2213yescomplemented
46C3×C4×D12C2213yescomplemented
47C3×#872C2213yescomplemented
48#63923C2216yescomplemented
49#63923C2213yescomplemented
50#63923C2216yescomplemented
51#63922C2213yescomplemented
52D3×(C2×D3)⋊C4C2216yescomplemented
53#63916C2213yescomplemented
54#63911C2213yescomplemented
55#63910C2216yescomplemented
56#63910C2213yescomplemented
57#63909C2213yescomplemented
58#63909C2216yescomplemented
59#63909C2213yescomplemented
60#63906C2216yescomplemented
61C4×#626C2213yescomplemented
62C4×#626C2213yescomplemented
63#63895C2213yescomplemented
64#63893C2211yescharacteristic, complemented
65#63891C2213yescomplemented
66#63890C2213yescomplemented
67#63886C2213yescomplemented
68#63871C2213yescomplemented
69#63864C2213yescomplemented
70C2×#1009—31no—
71C2×#1009—31no—
72C2×D3×#41—31no—
73C22×#239—31no—
74C3×#548—31no—
75C3×#520—31no—
76#5834—31no—
77#5817—31no—
78#5676—33no—
79#5674—33no—
80#5630—33no—
81#5629—33no—
82#5609—33no—
83D3×#121—33no—
84#5577—31no—
85#5577—31no—
86#5577—31no—
87#5577—61no—
88#5576—31no—
89#5576D311yescharacteristic, complemented
90#5574D311yescharacteristic, complemented
91#5554—33no—
92#5554—33no—
93D4×D12—33no—
94D4×D12—33no—
95D4×D12—33no—
96#5547—33no—
97#5525—33no—
98#5524—33no—
99#5510—33no—
100C2×#895—33no—
101C22×D32C2313yes—
102C22×D32C2316yes—
103C2×C32×Q8C2311yescharacteristic
104#3832—24no—
105#3832—24no—
106C2×C4⋊(C3⋊D3)C2313yes—
107C2×C4⋊(C3⋊D3)C2313yes—
108C2×C4⋊(C3⋊D3)C2316yes—
109C2×C4⋊(C3⋊D3)C2313yes—
110C2×C4×C3⋊D3C2313yes—
111C2×C4×C3⋊D3C2313yes—
112C3×#239—24no—
113C3×#239D418yescomplemented
114C3×D3×Q8—24no—
115C2×C3×D12C2313yes—
116C2×C3×D12C2313yes—
117C2×C3×D12C2313yes—
118C2×C3×C4×D3C2313yes—
119C2×C3×C4×D3C2313yes—
120C2×C3×C4×D3C2316yes—
121C2×C3×C4×D3C2313yes—
122C2×C3×Dic6C2313yes—
123C2×#627C2311yescharacteristic
124C2×#626C2316yes—
125C2×#626C2313yes—
126C2×#626C2313yes—
127C2×#626C2313yes—
128C2×#626C2316yes—
129C2×#626C2313yes—
130C2×#625C2313yes—
131C2×#624C2313yes—
132C2×D3×Dic3C2313yes—
133C2×D3×Dic3C2311yescharacteristic
134#3802—212no—
135D3×D12—212no—
136D3×D12—212no—
137D3×D12—212no—
138D3×D12—412no—
139C4×D32—212no—
140#3799—212no—
141#3798—212no—
142#3796—212no—
143C32×C4⋊C4C2313yes—
144C32×C42C2313yes—
145#3752C2313yes—
146#3752C2313yes—
147C4⋊(C3⋊Dic3)C2311yescharacteristic
148C3×(C2×D3)⋊C4C2313yes—
149C3×(C2×D3)⋊C4C2316yes—
150C3×(C2×D3)⋊C4C2313yes—
151C3×(C2×D3)⋊C4C2313yes—
152C3×(C2×D3)⋊C4C2311yescharacteristic
153C3×C4⋊Dic3C2313yes—
154C3×C4⋊Dic3C2313yes—
155C3×Dic3⋊C4C2313yes—
156C3×Dic3⋊C4C2311yescharacteristic
157C3×C4×Dic3C2313yes—
158Dic3⋊Dic3C2313yes—
159Dic3⋊Dic3C2311yescharacteristic
160#3722C2313yes—
161#3722C2316yes—
162#3722C2313yes—
163(C2×D3)⋊Dic3C2313yes—
164(C2×D3)⋊Dic3C2311yescharacteristic
165#3488—91noSylow
166C2×C3×#41—31no—
167C2×C3×#41—31no—
168C22×C3×Q8—31no—
169#1009—68no—
170#1009—68no—
171D3×#41—68no—
172C2×#239—31no—
173C2×#239—31no—
174C2×#239—31no—
175C2×#239—31no—
176C2×#239—33no—
177C2×#239—33no—
178C2×#239—61no—
179C2×#239—61no—
180C2×#239—68no—
181C2×#239C2×D311yescharacteristic
182C2×#239C2×D311yescharacteristic, complemented
183C2×D3×Q8C2×D311yescharacteristic, complemented
184C2×#237—33no—
185C2×D3×D4—33no—
186C2×D3×D4—33no—
187C2×D3×D4—33no—
188C2×D3×D4—33no—
189C2×D3×D4—33no—
190C2×D3×D4—36no—
191C2×#235—33no—
192C2×#235—33no—
193C2×#235—33no—
194C22×D12—33no—
195C22×D12—33no—
196C22×D12—33no—
197C22×D12—36no—
198C22×C4×D3—33no—
199C22×C4×D3—33no—
200C3×#124—33no—
201C3×C22⋊Q8—33no—
202C3×#121—33no—
203C3×C4×Q8—21no—
204C3×C4×Q8—31no—
205C3×C4×Q8C2×D311yescharacteristic, complemented
206C3×C4×Q8C2×D311yescharacteristic, complemented
207C3×C4×D4—33no—
208C3×C4×D4—33no—
209C3×C4×D4—33no—
210C3×#117—33no—
211C2×C3×C4⋊C4—33no—
212#947—33no—
213#946—33no—
214Q8×Dic3C2×D311yescharacteristic, complemented
215#940—33no—
216#939—33no—
217#938—33no—
218#937—33no—
219#930—36no—
220#930—36no—
221#930—33no—
222#930—33no—
223C4×#67—33no—
224C4×#67—33no—
225C2×(C2×D3)⋊C4—36no—
226#897—33no—
227#897—31no—
228#897—33no—
229#897C2×D313yescomplemented
230#896—33no—
231#895—33no—
232#895—33no—
233#895—33no—
234#895—33no—
235#895—36no—
236#895—33no—
237#895—33no—
238#895—33no—
239#895—33no—
240#895—36no—
241#895—33no—
242#895—63no—
243#895—63no—
244#895C2×D313yescomplemented
245#894—33no—
246#893C2×D313yescomplemented
247D3×C4⋊C4C2×D313yescomplemented
248#886—33no—
249#886—33no—
250#884—36no—
251#884—33no—
252#884—36no—
253#883—33no—
254#882—33no—
255#882—36no—
256#882—36no—
257#882—33no—
258#882—36no—
259#882—36no—
260#882—33no—
261D3×C22⋊C4—36no—
262#878—31no—
263#875—33no—
264#875C2×D313yescomplemented
265#874—33no—
266#874—33no—
267#874—33no—
268#874—63no—
269C4×D12—33no—
270C4×D12—33no—
271C4×D12—33no—
272C4×D12—33no—
273C4×D12—63no—
274C4×D12C2×D313yescomplemented
275C4×D12C2×D313yescomplemented
276#872C2×D313yescomplemented
277C22×C3⋊D3C2413yes—
278C22×C3⋊D3C2413yes—
279C22×C3×D3C2413yes—
280C22×C3×D3C2413yes—
281C22×C3×D3C2411yescharacteristic
282C2×D32—26no—
283C2×D32—26no—
284C2×D32—212no—
285C2×D32—43no—
286C2×D32—46no—
287C2×D32—46no—
288C32×Q8C2×D414yescomplemented
289C2×C32×C4C2413yes—
290C2×C32×C4C2411yescharacteristic
291C2×C32×C4C2413yes—
292C2×C3⋊Dic3C2411yescharacteristic
293C2×C3⋊Dic3C2411yescharacteristic
294C4⋊(C3⋊D3)—26no—
295C4⋊(C3⋊D3)—26no—
296C4⋊(C3⋊D3)—43no—
297C4⋊(C3⋊D3)—46no—
298C4×C3⋊D3—26no—
299C4×C3⋊D3—26no—
300C2×C3×Dic3C2411yescharacteristic
301C2×C3×Dic3C2413yes—
302C2×C3×Dic3C2411yescharacteristic
303C2×C3×Dic3C2413yes—
304C2×C3×Dic3C2411yescharacteristic
305C3×D12—26no—
306C3×D12—26no—
307C3×D12C2×D4112yescomplemented
308C3×C4×D3—26no—
309C3×C4×D3—26no—
310C3×C4×D3—46no—
311C3×C4×D3C2×D4112yescomplemented
312C3×Dic6—26no—
313#627—22no—
314#626—212no—
315#626—26no—
316#626—26no—
317#626—26no—
318#626—46no—
319#626—43no—
320#625—26no—
321#624—26no—
322D3×Dic3—26no—
323D3×Dic3—22no—
324C2×H(5,𝔽2)—91no—
325C22×#41—91no—
326#550—91no—
327#550—91no—
328#548—31no—
329#548—91no—
330#546—93no—
331#546—93no—
332D42—93no—
333D42—93no—
334#537—93no—
335#535—93no—
336#525—93no—
337C2×#121—93no—
338#520—31no—
339C23×D3—33no—
340C23×D3—33no—
341C23×D3—36no—
342C23×D3—36no—
343C3×#41—38no—
344C3×#41—64no—
345C2×C3×Q8—21no—
346C2×C3×Q8—33no—
347C2×C3×Q8—64no—
348C2×C3×Q8C22×D311yescharacteristic
349C2×C3×Q8C22×D311yescharacteristic
350C2×C3×D4—33no—
351C2×C3×D4—33no—
352C2×C3×D4—33no—
353C22×C3×C4—33no—
354C22×C3×C4—33no—
355C22×C3×C4—33no—
356C22×C3×C4—36no—
357C2×#67—33no—
358C2×#67—33no—
359C2×#67—36no—
360C2×#67—33no—
361C2×#67—33no—
362C2×#67—33no—
363C2×#67—33no—
364C2×#67—36no—
365C22×Dic3—31no—
366C22×Dic3—33no—
367#239—24no—
368#239—64no—
369#239—64no—
370#239—64no—
371#239—64no—
372#239—612no—
373#239—612no—
374#239—124no—
375#239—124no—
376#239D1218yescomplemented
377D3×Q8—24no—
378#237—612no—
379D3×D4—612no—
380D3×D4—612no—
381D3×D4—612no—
382D3×D4—612no—
383D3×D4—612no—
384D3×D4—1212no—
385#235—612no—
386#235—612no—
387#235—612no—
388C2×D12—33no—
389C2×D12—36no—
390C2×D12—33no—
391C2×D12—33no—
392C2×D12—33no—
393C2×D12—33no—
394C2×D12—33no—
395C2×D12—33no—
396C2×D12—33no—
397C2×D12—36no—
398C2×D12—33no—
399C2×D12—33no—
400C2×D12—36no—
401C2×D12—36no—
402C2×D12—63no—
403C2×D12—63no—
404C2×D12—63no—
405C2×D12—66no—
406C2×D12—612no—
407C2×D12—612no—
408C2×D12—612no—
409C2×D12—1212no—
410C2×D12C22×D313yes—
411C2×D12C22×D313yes—
412C2×D12C22×D313yes—
413C2×C4×D3—33no—
414C2×C4×D3—31no—
415C2×C4×D3—33no—
416C2×C4×D3—33no—
417C2×C4×D3—33no—
418C2×C4×D3—33no—
419C2×C4×D3—33no—
420C2×C4×D3—33no—
421C2×C4×D3—63no—
422C2×C4×D3—63no—
423C2×C4×D3—612no—
424C2×C4×D3—612no—
425C2×C4×D3C22×D313yes—
426C2×C4×D3C22×D313yes—
427C2×C4×D3C22×D316yes—
428C2×C4×D3C22×D313yes—
429C2×Dic6—31no—
430C2×Dic6—31no—
431C2×Dic6C22×D313yes—
432C3×C4⋊C4—23no—
433C3×C4⋊C4—33no—
434C3×C4⋊C4—33no—
435C3×C4⋊C4—31no—
436C3×C4⋊C4—33no—
437C3×C4⋊C4C22×D313yes—
438C3×C4⋊C4C22×D313yes—
439C3×C22⋊C4—31no—
440C3×C22⋊C4—36no—
441C3×C22⋊C4—33no—
442C3×C22⋊C4—33no—
443C3×C22⋊C4—33no—
444C3×C42—23no—
445C3×C42—33no—
446C3×C42C22×D313yes—
447C3×C42C22×D313yes—
448#217—31no—
449#217—33no—
450(C2×D3)⋊C4—31no—
451(C2×D3)⋊C4—33no—
452(C2×D3)⋊C4—33no—
453(C2×D3)⋊C4—33no—
454(C2×D3)⋊C4—33no—
455(C2×D3)⋊C4—33no—
456(C2×D3)⋊C4—33no—
457(C2×D3)⋊C4—33no—
458(C2×D3)⋊C4—36no—
459(C2×D3)⋊C4—36no—
460(C2×D3)⋊C4—33no—
461(C2×D3)⋊C4—33no—
462(C2×D3)⋊C4—63no—
463(C2×D3)⋊C4—63no—
464(C2×D3)⋊C4C22×D313yes—
465(C2×D3)⋊C4C22×D313yes—
466(C2×D3)⋊C4C22×D311yescharacteristic
467(C2×D3)⋊C4C22×D313yes—
468(C2×D3)⋊C4C22×D316yes—
469C4⋊Dic3—31no—
470C4⋊Dic3—31no—
471C4⋊Dic3—31no—
472C4⋊Dic3—33no—
473C4⋊Dic3—61no—
474C4⋊Dic3C22×D313yes—
475C4⋊Dic3C22×D313yes—
476Dic3⋊C4—31no—
477Dic3⋊C4—33no—
478Dic3⋊C4C22×D311yescharacteristic
479Dic3⋊C4C22×D313yes—
480C4×Dic3C22×D313yes—
481C22×C32C2511yescharacteristic
482C2×C3⋊D3—23no—
483C2×C3⋊D3—23no—
484C2×C3⋊D3—23no—
485C2×C3⋊D3—23no—
486C2×C3⋊D3—23no—
487C2×C3⋊D3—23no—
488C2×C3×D3—21no—
489C2×C3×D3—23no—
490C2×C3×D3—21no—
491C2×C3×D3—23no—
492C2×C3×D3—23no—
493C2×C3×D3—23no—
494C2×C3×D3—23no—
495C2×C3×D3C22×D416yes—
496C2×C3×D3H(5,𝔽2)12yescomplemented
497D32—412no—
498D32—812no—
499C32×C4—21no—
500C32×C4—23no—
501C32×C4C22×D416yes—
502C3⋊Dic3—21no—
503C3⋊Dic3—21no—
504C3×Dic3—23no—
505C3×Dic3—21no—
506C3×Dic3—23no—
507C3×Dic3—21no—
508C3×Dic3C22×D412yes—
509H(5,𝔽2)—188no—
510C2×#41—31no—
511C2×#41—31no—
512C2×#41—93no—
513C2×#41—93no—
514C2×#41—93no—
515C2×#41—91no—
516C2×#41—91no—
517C2×#41—188no—
518C22×Q8—31no—
519C22×D4—93no—
520C22×D4—93no—
521C22×D4—93no—
522C22×D4—96no—
523C22×D4—93no—
524C23×C4—93no—
525#127—93no—
526#127—93no—
527#124—33no—
528#124—93no—
529#123—93no—
530#123—93no—
531C22⋊Q8—33no—
532C22⋊Q8—91no—
533C22⋊Q8—93no—
534C22⋊Q8—93no—
535#121—33no—
536#121—96no—
537#121—93no—
538#121—96no—
539#121—93no—
540#121—96no—
541#121—93no—
542#121—93no—
543#121—93no—
544#121—93no—
545#121—93no—
546#120—93no—
547#120—96no—
548#120—96no—
549#120—93no—
550C4×Q8—31no—
551C4×Q8D3211yescharacteristic, complemented
552C4×D4—33no—
553C4×D4—33no—
554C4×D4—33no—
555C4×D4—93no—
556C4×D4—93no—
557C4×D4—93no—
558#117—33no—
559C2×C4⋊C4—33no—
560C2×C22⋊C4—96no—
561C23×C3—31no—
562C23×C3—33no—
563C23×C3—33no—
564C22×D3—33no—
565C22×D3—33no—
566C22×D3—33no—
567C22×D3—33no—
568C22×D3—63no—
569C22×D3—63no—
570C22×D3—66no—
571C22×D3—66no—
572C22×D3—612no—
573C22×D3—66no—
574C22×D3—66no—
575C22×D3—612no—
576C22×D3—123no—
577C22×D3—123no—
578C22×D3—126no—
579C22×D3—126no—
580C22×D3—126no—
581C22×D3—126no—
582C22×D3C23×D313yes—
583C22×D3C23×D313yes—
584C22×D3C23×D311yescharacteristic
585C3×Q8—24no—
586C3×Q8—66no—
587C3×Q8C2×D1214yescomplemented
588C3×Q8D3×D414yescomplemented
589C3×D4—312no—
590C3×D4—66no—
591C3×D4—66no—
592C2×C3×C4—21no—
593C2×C3×C4—23no—
594C2×C3×C4—23no—
595C2×C3×C4—31no—
596C2×C3×C4—312no—
597C2×C3×C4—33no—
598C2×C3×C4—31no—
599C2×C3×C4—31no—
600C2×C3×C4—33no—
601C2×C3×C4—66no—
602C2×C3×C4—66no—
603C2×C3×C4—126no—
604C2×C3×C4C23×D311yescharacteristic
605C2×C3×C4C23×D313yes—
606C2×C3×C4C23×D311yescharacteristic
607C2×C3×C4C23×D313yes—
608C2×C3×C4C23×D313yes—
609C2×C3×C4C23×D313yes—
610#67—66no—
611#67—612no—
612#67—66no—
613#67—66no—
614#67—66no—
615#67—66no—
616#67—126no—
617#67—123no—
618C2×Dic3—31no—
619C2×Dic3—31no—
620C2×Dic3—31no—
621C2×Dic3—31no—
622C2×Dic3—61no—
623C2×Dic3—61no—
624C2×Dic3—66no—
625C2×Dic3—62no—
626C2×Dic3C23×D311yescharacteristic
627C2×Dic3C23×D313yes—
628C2×Dic3C23×D311yescharacteristic
629C2×Dic3C23×D313yes—
630C2×Dic3C23×D311yescharacteristic
631D12—26no—
632D12—26no—
633D12—66no—
634D12—66no—
635D12—612no—
636D12—66no—
637D12—66no—
638D12—66no—
639D12—66no—
640D12—66no—
641D12—126no—
642D12—126no—
643D12—123no—
644D12—123no—
645D12—126no—
646D12—126no—
647D12—126no—
648D12—123no—
649D12—126no—
650D12—246no—
651D12C2×D12112yescomplemented
652C4×D3—26no—
653C4×D3—26no—
654C4×D3—46no—
655C4×D3—66no—
656C4×D3—62no—
657C4×D3—66no—
658C4×D3—66no—
659C4×D3—66no—
660C4×D3—66no—
661C4×D3—66no—
662C4×D3—66no—
663C4×D3—126no—
664C4×D3—126no—
665C4×D3C2×D12112yescomplemented
666Dic6—26no—
667Dic6—62no—
668Dic6—62no—
669C2×C32C23×D411yescharacteristic
670C2×C32C2×H(5,𝔽2)11yescharacteristic
671C2×C32#58511yescharacteristic
672C3⋊D3—43no—
673C3⋊D3—43no—
674C3×D3—22no—
675C3×D3—26no—
676C3×D3—43no—
677C24—93no—
678C24—96no—
679#41—38no—
680#41—64no—
681#41—1812no—
682#41—1812no—
683#41—1812no—
684#41—184no—
685#41—184no—
686C2×Q8—33no—
687C2×Q8—64no—
688C2×Q8—91no—
689C2×Q8C2×D3211yescharacteristic
690C2×D4—33no—
691C2×D4—33no—
692C2×D4—33no—
693C2×D4—93no—
694C2×D4—96no—
695C2×D4—93no—
696C2×D4—93no—
697C2×D4—93no—
698C2×D4—96no—
699C2×D4—93no—
700C2×D4—93no—
701C2×D4—93no—
702C2×D4—93no—
703C2×D4—96no—
704C2×D4—1812no—
705C2×D4—1812no—
706C2×D4—1812no—
707C2×D4—1812no—
708C2×D4—3612no—
709C22×C4—33no—
710C22×C4—33no—
711C22×C4—33no—
712C22×C4—36no—
713C22×C4—93no—
714C22×C4—93no—
715C22×C4—91no—
716C22×C4—93no—
717C22×C4—93no—
718C22×C4—1812no—
719C4⋊C4—33no—
720C4⋊C4—33no—
721C4⋊C4—31no—
722C4⋊C4—33no—
723C4⋊C4—91no—
724C4⋊C4—93no—
725C4⋊C4—91no—
726C4⋊C4C2×D3213yes—
727C22⋊C4—36no—
728C22⋊C4—33no—
729C22⋊C4—33no—
730C22⋊C4—31no—
731C22⋊C4—33no—
732C22⋊C4—96no—
733C22⋊C4—93no—
734C22⋊C4—93no—
735C22⋊C4—93no—
736C22⋊C4—91no—
737C22⋊C4—93no—
738C22⋊C4—93no—
739C42—33no—
740C42C2×D3213yes—
741C22×C3—21no—
742C22×C3—36no—
743C22×C3—32no—
744C22×C3—61no—
745C22×C3—63no—
746C22×C3—61no—
747C22×C3—63no—
748C22×C3—63no—
749C22×C3—63no—
750C22×C3—63no—
751C22×C3C24×D311yescharacteristic
752C22×C3C24×D311yescharacteristic
753C2×D3—21no—
754C2×D3—23no—
755C2×D3—23no—
756C2×D3—21no—
757C2×D3—23no—
758C2×D3—23no—
759C2×D3—23no—
760C2×D3—63no—
761C2×D3—63no—
762C2×D3—63no—
763C2×D3—63no—
764C2×D3—63no—
765C2×D3—63no—
766C2×D3—63no—
767C2×D3—63no—
768C2×D3—63no—
769C2×D3—63no—
770C2×D3—63no—
771C2×D3—63no—
772C2×D3—123no—
773C2×D3—123no—
774C2×D3—123no—
775C2×D3—123no—
776C2×D3—123no—
777C2×D3—123no—
778C2×D3—1212no—
779C2×D3—1212no—
780C2×D3—2412no—
781C2×D3—2412no—
782C2×D3C22×D1216yes—
783C2×D3#100912yescomplemented
784C3×C4—22no—
785C3×C4—23no—
786C3×C4—23no—
787C3×C4—21no—
788C3×C4—21no—
789C3×C4—26no—
790C3×C4—32no—
791C3×C4—43no—
792C3×C4—61no—
793C3×C4—63no—
794C3×C4—63no—
795C3×C4—61no—
796C3×C4C22×D1216yes—
797C3×C4C2×D3×D416yes—
798Dic3—23no—
799Dic3—21no—
800Dic3—23no—
801Dic3—21no—
802Dic3—61no—
803Dic3—61no—
804Dic3—61no—
805Dic3—61no—
806Dic3—121no—
807Dic3—121no—
808Dic3C22×D1212yes—
809C32#348811yescharacteristic, complemented, Sylow
810C23—33no—
811C23—31no—
812C23—33no—
813C23—93no—
814C23—93no—
815C23—186no—
816C23—186no—
817C23—1812no—
818C23—363no—
819C23—366no—
820C23—366no—
821Q8—66no—
822Q8—182no—
823Q8D3×D1214yescomplemented
824D4—312no—
825D4—66no—
826D4—66no—
827D4—186no—
828D4—186no—
829D4—1812no—
830D4—186no—
831D4—186no—
832D4—186no—
833D4—186no—
834D4—366no—
835D4—363no—
836D4—366no—
837D4—363no—
838C2×C4—31no—
839C2×C4—312no—
840C2×C4—31no—
841C2×C4—33no—
842C2×C4—33no—
843C2×C4—31no—
844C2×C4—66no—
845C2×C4—66no—
846C2×C4—91no—
847C2×C4—91no—
848C2×C4—126no—
849C2×C4—186no—
850C2×C4—182no—
851C2×C4—186no—
852C2×C4—186no—
853C2×C4—186no—
854C2×C4C22×D3211yescharacteristic
855C2×C4C22×D3213yes—
856C2×C4C22×D3213yes—
857C2×C3—21no—
858C2×C3—21no—
859C2×C3—21no—
860C2×C3—62no—
861C2×C3—66no—
862C2×C3—123no—
863C2×C3C23×D1211yescharacteristic
864C2×C3C22×D3×D411yescharacteristic
865C2×C3C2×#100911yescharacteristic
866C2×C3D3×H(5,𝔽2)11yescharacteristic
867C2×C3#596811yescharacteristic
868C2×C3#596811yescharacteristic
869D3—26no—
870D3—22no—
871D3—43no—
872D3—123no—
873D3—123no—
874D3—123no—
875D3—123no—
876D3—243no—
877D3—243no—
878C22—36no—
879C22—32no—
880C22—61no—
881C22—61no—
882C22—63no—
883C22—63no—
884C22—63no—
885C22—63no—
886C22—63no—
887C22—183no—
888C22—183no—
889C22—183no—
890C22—183no—
891C22—183no—
892C22—183no—
893C22—3612no—
894C22—7212no—
895C22C23×D3211yescharacteristic
896C4—21no—
897C4—23no—
898C4—32no—
899C4—61no—
900C4—63no—
901C4—61no—
902C4—63no—
903C4—181no—
904C4—181no—
905C4C2×D3×D1216yes—
906C3—21no—
907C3#8590011yescharacteristic, complemented
908C3#8671311yescharacteristic, complemented
909C2—62no—
910C2—66no—
911C2—123no—
912C2—363no—
913C2—363no—
914C2C22×D3×D1211yescharacteristic
915C2#1059668911yescharacteristic
916C2D3×#100911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×Q8C22
hypercenterC4×Q8D32
hypocenterC32#3488
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#64320C2semidirect
2. C2×D3×#239C2semidirect
3. #10596048C2semidirect
4. C3×#5576C2semidirect
5. C3×#5574C2semidirect
6. #10595410C2semidirect
7. #10595342C2semidirect
8. #10594629C2semidirect
9. #10594621C2semidirect
10. D3×#895C2semidirect
11. #10594523C2semidirect
12. #10594005C2semidirect
13. D122C2semidirect
14. #10594001C2semidirect
15. #10593997C2semidirect
18. C2×#3832C22semidirect
19. C2×#3832C22semidirect
21. C2×C3×#239C22semidirect
22. C2×C3×D3×Q8C22semidirect
25. C2×#3802C22semidirect
26. C2×D3×D12C22semidirect
27. C2×D3×D12C22semidirect
28. C2×D3×D12C22semidirect
29. C2×D3×D12C22semidirect
30. C2×C4×D32C22semidirect
31. C2×#3799C22semidirect
32. C2×#3798C22semidirect
33. C2×#3796C22semidirect
34. C32×C4×Q8C22semidirect
35. #64104C22semidirect
36. #64104C22semidirect
37. #64083C22semidirect
38. C4×C4⋊(C3⋊D3)C22semidirect
39. C3×Q8×Dic3C22semidirect
40. C3×#897C22semidirect
41. C3×#895C22semidirect
42. C3×#893C22semidirect
43. C3×D3×C4⋊C4C22semidirect
44. C3×#875C22semidirect
45. C3×C4×D12C22semidirect
46. C3×C4×D12C22semidirect
47. C3×#872C22semidirect
48. #63923C22semidirect
49. #63923C22semidirect
50. #63923C22semidirect
51. #63922C22semidirect
52. D3×(C2×D3)⋊C4C22semidirect
53. #63916C22semidirect
54. #63911C22semidirect
55. #63910C22semidirect
56. #63910C22semidirect
57. #63909C22semidirect
58. #63909C22semidirect
59. #63909C22semidirect
60. #63906C22semidirect
61. C4×#626C22semidirect
62. C4×#626C22semidirect
63. #63895C22semidirect
64. #63893C22semidirect
65. #63891C22semidirect
66. #63890C22semidirect
67. #63886C22semidirect
68. #63871C22semidirect
69. #63864C22semidirect
89. #5576D3semidirect
90. #5574D3semidirect
113. C3×#239D4semidirect
182. C2×#239C2×D3semidirect
183. C2×D3×Q8C2×D3semidirect
205. C3×C4×Q8C2×D3semidirect
206. C3×C4×Q8C2×D3semidirect
214. Q8×Dic3C2×D3semidirect
229. #897C2×D3semidirect
244. #895C2×D3semidirect
246. #893C2×D3semidirect
247. D3×C4⋊C4C2×D3semidirect
264. #875C2×D3semidirect
274. C4×D12C2×D3semidirect
275. C4×D12C2×D3semidirect
276. #872C2×D3semidirect
288. C32×Q8C2×D4semidirect
307. C3×D12C2×D4semidirect
311. C3×C4×D3C2×D4semidirect
376. #239D12semidirect
496. C2×C3×D3H(5,𝔽2)semidirect
551. C4×Q8D32semidirect
587. C3×Q8C2×D12semidirect
588. C3×Q8D3×D4semidirect
651. D12C2×D12semidirect
665. C4×D3C2×D12semidirect
783. C2×D3#1009semidirect
809. C32#3488semidirect
823. Q8D3×D12semidirect
907. C3#85900semidirect
908. C3#86713semidirect

Maximal subgroups

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

subgroupindex
C2×#643202
C2×D3×#2392
#105960482
C3×#55762
C3×#55742
#105954102
#105953422
#105946292
#105946212
D3×#8952
#105945232
#105940052
D1222
#105940012
#105939972
#867133
#859003