Finite Group Databasebeta

← D3×#5817 #11902600

Subgroups — D3×#5817 #11902600

Order 1152.

3385 conjugacy classes of subgroups.

The subgroup lattice has 913 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D3×Q8C211yesmaximal, characteristic, complemented
2C2×D3×#239C211yesmaximal, characteristic, complemented
3#10596288C211yesmaximal, characteristic, complemented
4C3×#5817C211yesmaximal, characteristic, complemented
5D3×#947C213yesmaximal, complemented
6D3×#946C213yesmaximal, complemented
7#10595409C211yesmaximal, characteristic, complemented
8#10595402C213yesmaximal, complemented
9#10595401C213yesmaximal, complemented
10D3×Q8×Dic3C211yesmaximal, characteristic, complemented
11#10595342C211yesmaximal, characteristic, complemented
12D3×#930C213yesmaximal, complemented
13C4×D3×#67C213yesmaximal, complemented
14#10594902C213yesmaximal, complemented
15#10594900C213yesmaximal, complemented
16C2×#5817—31nomaximal
17D3×#548—31nomaximal
18C22×C32×Q8C2211yescharacteristic, complemented
19C2×#3832C2211yescharacteristic, complemented
20C2×C3×#239C2211yescharacteristic, complemented
21C2×C3×D3×Q8—28no—
22C2×C3×D3×Q8C2213yes—
23C2×C3×D3×Q8C2211yescharacteristic
24C2×C3×D3×Q8C2211yescharacteristic, complemented
25C2×C3×D3×Q8C2213yescomplemented
26C22×C3×C4×D3C2213yes—
27C22×C3×Dic6C2213yescomplemented
28C2×D3×#67C2213yes—
29D3×#239—28no—
30C2×D3×D12C2213yes—
31C2×C4×D32C2213yes—
32C2×#3799C2213yescomplemented
33C2×#3796C2213yescomplemented
34#64156C2213yescomplemented
35#64155C2213yescomplemented
36Q8×C3⋊Dic3C2211yescharacteristic, complemented
37#64139C2213yescomplemented
38C4×#638C2213yescomplemented
39C3×#947C2213yescomplemented
40C3×#946C2213yescomplemented
41C3×Q8×Dic3C2211yescharacteristic, complemented
42C3×#930C2213yescomplemented
43C3×C4×#67C2213yescomplemented
44#63978C2216yescomplemented
45Dic3×#67C2213yescomplemented
46D3×#217C2211yescharacteristic
47#63952C2213yescomplemented
48D3×(C2×D3)⋊C4C2216yes—
49D3×(C2×D3)⋊C4C2213yes—
50#63909C2213yescomplemented
51#63908C2213yescomplemented
52#63907C2216yescomplemented
53#63907C2216yescomplemented
54#63906C2216yescomplemented
55#63904C2213yescomplemented
56C4×#626C2213yescomplemented
57C4×#625C2213yescomplemented
58D3×C4⋊Dic3C2213yes—
59#63888C2216yescomplemented
60#63887C2216yescomplemented
61#63879C2213yescomplemented
62D3×Dic3⋊C4C2213yes—
63C4×D3×Dic3C2213yes—
64#63871C2213yescomplemented
65#63864C2213yescomplemented
66#63863C2213yescomplemented
67#63856C2213yescomplemented
68#63843C2213yescomplemented
69Dic3×Dic6C2213yescomplemented
70C23×C3×Q8—31no—
71C2×D3×#41—31no—
72C22×#239—31no—
73C22×D3×Q8D311yescharacteristic, complemented
74C3×#548—31no—
75#5831—31no—
76#5817—31no—
77#5817—31no—
78#5817—31no—
79#5817—33no—
80#5817—33no—
81#5817—31no—
82#5817—33no—
83#5817—33no—
84#5817—61no—
85#5817D311yescharacteristic, direct product factor
86C2×#947—33no—
87C2×#946—33no—
88C2×Q8×Dic3—31no—
89C2×#930—33no—
90C2×C4×#67—33no—
91#5677—33no—
92D3×#124—33no—
93#5633—33no—
94D3×C22⋊Q8—33no—
95D3×#121—33no—
96#5598—33no—
97#5576—31no—
98C4×D3×Q8—31no—
99#5552—33no—
100C4×D3×D4—33no—
101C23×C3×D3C2311yescharacteristic
102C22×D32C2313yes—
103C2×C32×Q8—24no—
104C2×C32×Q8C2313yes—
105C2×C32×Q8C2311yescharacteristic
106C22×C32×C4C2313yes—
107C2×#638C2313yes—
108#3832—24no—
109C2×C4⋊(C3⋊D3)C2313yes—
110C2×C4×C3⋊D3C2313yes—
111C2×C3×#67C2313yes—
112C22×C3×Dic3C2313yes—
113C3×#239—24no—
114C3×D3×Q8—24no—
115C3×D3×Q8—212no—
116C3×D3×Q8—212no—
117C3×D3×Q8D418yescomplemented
118C2×C3×D12C2313yes—
119C2×C3×C4×D3—212no—
120C2×C3×C4×D3C2313yes—
121C2×C3×C4×D3C2313yes—
122C2×C3×C4×D3C2313yes—
123C2×C3×C4×D3C2313yes—
124C2×C3×C4×D3C2313yes—
125C2×C3×Dic6—212no—
126C2×C3×Dic6C2313yes—
127C2×C3×Dic6C2316yes—
128C2×C3×Dic6C2313yes—
129D3×#67—212no—
130C2×#626C2316yes—
131C2×#626C2313yes—
132C2×#625C2313yes—
133C2×#624C2313yes—
134C2×D3×Dic3C2313yes—
135C2×D3×Dic3C2311yescharacteristic
136C2×D3×Dic3C2313yes—
137C2×D3×Dic3C2311yescharacteristic
138D3×D12—212no—
139C4×D32—212no—
140#3799—212no—
141#3796—212no—
142#3757C2311yescharacteristic
143#3752C2313yes—
144#3752C2316yes—
145C4⋊(C3⋊Dic3)C2313yes—
146#3750C2313yes—
147C4×C3⋊Dic3C2313yes—
148C3×#217C2311yescharacteristic
149C3×(C2×D3)⋊C4C2313yes—
150C3×(C2×D3)⋊C4C2316yes—
151C3×C4⋊Dic3C2313yes—
152C3×Dic3⋊C4C2313yes—
153C3×C4×Dic3C2313yes—
154#3724C2313yes—
155Dic3⋊Dic3C2316yes—
156Dic3⋊Dic3C2313yes—
157#3722C2313yes—
158#3722C2316yes—
159(C2×D3)⋊Dic3C2316yes—
160(C2×D3)⋊Dic3C2313yes—
161(C2×D3)⋊Dic3C2311yescharacteristic
162(C2×D3)⋊Dic3C2311yescharacteristic
163Dic32C2313yes—
164Dic32C2313yes—
165C2×#548—91noSylow
166C2×C3×#41—31no—
167C22×C3×Q8—21no—
168C22×C3×Q8—31no—
169C22×C3×Q8—33no—
170C22×C3×Q8—33no—
171C22×C3×Q8—31no—
172C22×C3×Q8—33no—
173C22×C3×Q8—68no—
174C22×C3×Q8C2×D311yescharacteristic, complemented
175C22×C3×Q8C2×D311yescharacteristic, complemented
176C23×C3×C4—33no—
177C22×#67—33no—
178D3×#41—68no—
179C2×#239—31no—
180C2×#239—31no—
181C2×#239—33no—
182C2×#239—33no—
183C2×#239—61no—
184C2×#239—68no—
185C2×#239C2×D311yescharacteristic, complemented
186C2×D3×Q8—28no—
187C2×D3×Q8C2×D313yes—
188C2×D3×Q8C2×D311yescharacteristic
189C2×D3×Q8C2×D313yescomplemented
190C2×D3×Q8C2×D311yescharacteristic, complemented
191C2×#237—33no—
192C2×D3×D4—33no—
193C2×D3×D4—33no—
194C2×#235—33no—
195C22×D12—33no—
196C22×C4×D3—33no—
197C22×C4×D3—33no—
198C22×C4×D3C2×D313yes—
199C22×Dic6C2×D313yescomplemented
200C3×#124—33no—
201C3×C22⋊Q8—33no—
202C3×#121—33no—
203C3×C4×Q8—31no—
204C3×C4×D4—33no—
205C2×#217—31no—
206#947—33no—
207#947—33no—
208#947—33no—
209#947—36no—
210#947—36no—
211#947—33no—
212#947—63no—
213#947C2×D313yescomplemented
214#946—33no—
215#946—33no—
216#946—33no—
217#946—36no—
218#946—33no—
219#946—36no—
220#946—63no—
221#946C2×D313yescomplemented
222Q8×Dic3—31no—
223Q8×Dic3—31no—
224Q8×Dic3—33no—
225Q8×Dic3—33no—
226Q8×Dic3—61no—
227Q8×Dic3C2×D311yescharacteristic, complemented
228#939—36no—
229#938—33no—
230#936—33no—
231D4×Dic3—33no—
232#930—33no—
233#930—33no—
234#930—36no—
235#930—33no—
236#930—36no—
237#930—33no—
238#930—63no—
239#930C2×D313yescomplemented
240C4×#67—33no—
241C4×#67—33no—
242C4×#67—33no—
243C4×#67—33no—
244C4×#67—33no—
245C4×#67—33no—
246C4×#67—33no—
247C4×#67—33no—
248C4×#67—33no—
249C4×#67—63no—
250C4×#67C2×D313yescomplemented
251C2×(C2×D3)⋊C4—33no—
252C2×(C2×D3)⋊C4—36no—
253C2×C4⋊Dic3—33no—
254#924—33no—
255C2×Dic3⋊C4—33no—
256C2×C4×Dic3—33no—
257#897—33no—
258#896—36no—
259#895—33no—
260#893—33no—
261D3×C4⋊C4—33no—
262D3×C4⋊C4—33no—
263#887—33no—
264#885—36no—
265#885—36no—
266#884—36no—
267#67⋊C4—33no—
268#67⋊C4—33no—
269D3×C22⋊C4—31no—
270D3×C22⋊C4—33no—
271D3×C22⋊C4—36no—
272#878—36no—
273#875—33no—
274C4×D12—33no—
275C42×D3—33no—
276C4×Dic6—33no—
277C23×C32C2411yescharacteristic
278C22×C3⋊D3C2413yes—
279C22×C3×D3—22no—
280C22×C3×D3—22no—
281C22×C3×D3#4114yescomplemented
282C22×C3×D3C2413yes—
283C22×C3×D3C2411yescharacteristic
284C22×C3×D3C2411yescharacteristic
285C2×D32—26no—
286C2×D32—26no—
287C2×D32—26no—
288C32×Q8—26no—
289C32×Q8C2×D414yescomplemented
290C2×C32×C4—26no—
291C2×C32×C4C2413yes—
292C2×C32×C4C2413yes—
293#638—26no—
294C2×C3⋊Dic3C2411yescharacteristic
295C2×C3⋊Dic3C2413yes—
296C2×C3⋊Dic3C2411yescharacteristic
297C4⋊(C3⋊D3)—26no—
298C4×C3⋊D3—26no—
299C3×#67—26no—
300C2×C3×Dic3—26no—
301C2×C3×Dic3C2411yescharacteristic
302C2×C3×Dic3C2413yes—
303C2×C3×Dic3C2413yes—
304C2×C3×Dic3C2411yescharacteristic
305C2×C3×Dic3C2413yes—
306C3×D12—26no—
307C3×C4×D3—26no—
308C3×C4×D3—26no—
309C3×C4×D3—26no—
310C3×C4×D3—26no—
311C3×C4×D3C2×D4112yes—
312C3×Dic6—26no—
313C3×Dic6—212no—
314C3×Dic6C2×D4112yescomplemented
315#626—26no—
316#626—212no—
317#625—26no—
318#624—26no—
319D3×Dic3—22no—
320D3×Dic3—26no—
321D3×Dic3—22no—
322D3×Dic3—26no—
323C22×#41—91no—
324C23×Q8—31no—
325#548—31no—
326#548—93no—
327#548—91no—
328#548—93no—
329#548—93no—
330#548—93no—
331#548—91no—
332#548—91no—
333C2×#124—93no—
334C2×C22⋊Q8—93no—
335C2×#121—93no—
336C2×C4×Q8—91no—
337C2×C4×D4—93no—
338C24×C3—31no—
339C23×D3—33no—
340C23×D3—33no—
341C23×D3C22×D311yescharacteristic
342C3×#41—64no—
343C2×C3×Q8—24no—
344C2×C3×Q8—24no—
345C2×C3×Q8—21no—
346C2×C3×Q8—23no—
347C2×C3×Q8—38no—
348C2×C3×Q8—33no—
349C2×C3×Q8—36no—
350C2×C3×Q8—33no—
351C2×C3×Q8—44no—
352C2×C3×Q8—612no—
353C2×C3×Q8—612no—
354C2×C3×Q8—612no—
355C2×C3×Q8—64no—
356C2×C3×Q8C22×D313yes—
357C2×C3×Q8C22×D313yes—
358C2×C3×Q8C22×D311yescharacteristic
359C2×C3×Q8C22×D311yescharacteristic
360C2×C3×D4—33no—
361C2×C3×D4—33no—
362C22×C3×C4—23no—
363C22×C3×C4—33no—
364C22×C3×C4—33no—
365C22×C3×C4—33no—
366C22×C3×C4—33no—
367C22×C3×C4—33no—
368C22×C3×C4—33no—
369C22×C3×C4—612no—
370C22×C3×C4C22×D313yes—
371C22×C3×C4C22×D313yes—
372C2×#67—33no—
373C2×#67—33no—
374C2×#67—33no—
375C2×#67—33no—
376C2×#67—36no—
377C2×#67—33no—
378C2×#67—63no—
379C2×#67—612no—
380C2×#67C22×D313yes—
381C22×Dic3—33no—
382C22×Dic3—31no—
383C22×Dic3—33no—
384C22×Dic3—31no—
385C22×Dic3C22×D313yes—
386#239—24no—
387#239—612no—
388#239—612no—
389#239—64no—
390#239—64no—
391#239—124no—
392D3×Q8—24no—
393D3×Q8—212no—
394D3×Q8—212no—
395D3×Q8#6718yescomplemented
396#237—612no—
397D3×D4—612no—
398D3×D4—612no—
399#235—612no—
400C2×D12—33no—
401C2×D12—36no—
402C2×D12—33no—
403C2×D12—33no—
404C2×D12—63no—
405C2×D12—612no—
406C2×D12C22×D313yes—
407C2×C4×D3—212no—
408C2×C4×D3—31no—
409C2×C4×D3—33no—
410C2×C4×D3—31no—
411C2×C4×D3—33no—
412C2×C4×D3—33no—
413C2×C4×D3—33no—
414C2×C4×D3—33no—
415C2×C4×D3—33no—
416C2×C4×D3—63no—
417C2×C4×D3—612no—
418C2×C4×D3—612no—
419C2×C4×D3C22×D313yes—
420C2×C4×D3C22×D313yes—
421C2×C4×D3C22×D313yes—
422C2×C4×D3C22×D313yes—
423C2×C4×D3C22×D313yes—
424C2×Dic6—212no—
425C2×Dic6C22×D313yes—
426C2×Dic6C22×D316yes—
427C2×Dic6C22×D313yes—
428C3×C4⋊C4—33no—
429C3×C4⋊C4—33no—
430C3×C22⋊C4—31no—
431C3×C22⋊C4—36no—
432C3×C22⋊C4—33no—
433C3×C42—33no—
434#217—31no—
435#217—31no—
436#217—36no—
437#217—33no—
438#217—31no—
439#217—31no—
440#217—61no—
441#217C22×D311yescharacteristic
442(C2×D3)⋊C4—31no—
443(C2×D3)⋊C4—31no—
444(C2×D3)⋊C4—33no—
445(C2×D3)⋊C4—36no—
446(C2×D3)⋊C4—36no—
447(C2×D3)⋊C4—33no—
448(C2×D3)⋊C4—33no—
449(C2×D3)⋊C4—36no—
450(C2×D3)⋊C4—33no—
451(C2×D3)⋊C4—36no—
452(C2×D3)⋊C4—33no—
453(C2×D3)⋊C4—36no—
454(C2×D3)⋊C4—63no—
455(C2×D3)⋊C4—66no—
456(C2×D3)⋊C4C22×D313yes—
457(C2×D3)⋊C4C22×D316yes—
458C4⋊Dic3—33no—
459C4⋊Dic3—33no—
460C4⋊Dic3—33no—
461C4⋊Dic3—36no—
462C4⋊Dic3—63no—
463C4⋊Dic3C22×D313yes—
464Dic3⋊C4—33no—
465Dic3⋊C4—33no—
466Dic3⋊C4—36no—
467Dic3⋊C4—33no—
468Dic3⋊C4—33no—
469Dic3⋊C4—33no—
470Dic3⋊C4—63no—
471Dic3⋊C4C22×D313yes—
472C4×Dic3—33no—
473C4×Dic3—33no—
474C4×Dic3—33no—
475C4×Dic3—33no—
476C4×Dic3—33no—
477C4×Dic3—33no—
478C4×Dic3—63no—
479C4×Dic3C22×D313yes—
480C22×C32—21no—
481C22×C32—21no—
482C22×C32C2×#4112yescomplemented
483C22×C32C2511yescharacteristic
484C2×C3⋊D3—23no—
485C2×C3⋊D3—23no—
486C2×C3⋊D3—23no—
487C2×C3×D3—21no—
488C2×C3×D3—21no—
489C2×C3×D3—28no—
490C2×C3×D3—23no—
491C2×C3×D3—23no—
492C2×C3×D3—23no—
493C2×C3×D3C22×D412yes—
494C2×C3×D3C2×#4112yes—
495C2×C3×D3C2×#4112yescomplemented
496C2×C3×D32−1+412yes—
497D32—412no—
498C32×C4—23no—
499C32×C4C22×D416yes—
500C3⋊Dic3—21no—
501C3⋊Dic3—23no—
502C3⋊Dic3—21no—
503C3×Dic3—21no—
504C3×Dic3—23no—
505C3×Dic3—23no—
506C3×Dic3—21no—
507C3×Dic3C22×D416yes—
508C2×#41—31no—
509C2×#41—93no—
510C2×#41—93no—
511C2×#41—91no—
512C2×#41—188no—
513C22×Q8—31no—
514C22×Q8—33no—
515C22×Q8—33no—
516C22×Q8—31no—
517C22×Q8—33no—
518C22×Q8—68no—
519C22×Q8D3211yescharacteristic, complemented
520C22×D4—93no—
521C22×D4—93no—
522C23×C4—33no—
523C23×C4—93no—
524#124—33no—
525#124—93no—
526#124—96no—
527#124—96no—
528#124—93no—
529#124—93no—
530C22⋊Q8—33no—
531C22⋊Q8—96no—
532C22⋊Q8—96no—
533C22⋊Q8—93no—
534C22⋊Q8—93no—
535C22⋊Q8—93no—
536#121—33no—
537#121—96no—
538#121—93no—
539#121—93no—
540#121—96no—
541#121—93no—
542C4×Q8—31no—
543C4×Q8—93no—
544C4×Q8—93no—
545C4×Q8—91no—
546C4×D4—33no—
547C4×D4—93no—
548C4×D4—93no—
549C4×D4—93no—
550C4×D4—93no—
551C4×D4—93no—
552C4×D4—93no—
553C4×D4—93no—
554C2×C4⋊C4—93no—
555C2×C4⋊C4—93no—
556C2×C22⋊C4—93no—
557C2×C22⋊C4—96no—
558C2×C22⋊C4—91no—
559C2×C42—93no—
560C23×C3—21no—
561C23×C3—31no—
562C23×C3—34no—
563C23×C3—31no—
564C23×C3—33no—
565C23×C3—62no—
566C23×C3—62no—
567C23×C3C23×D311yescharacteristic
568C23×C3C23×D311yescharacteristic
569C22×D3—22no—
570C22×D3—22no—
571C22×D3—33no—
572C22×D3—33no—
573C22×D3—63no—
574C22×D3—66no—
575C22×D3—66no—
576C22×D3—66no—
577C22×D3—66no—
578C22×D3—66no—
579C22×D3—66no—
580C22×D3#23914yescomplemented
581C22×D3C23×D313yes—
582C22×D3C23×D311yescharacteristic
583C22×D3C23×D311yescharacteristic
584C3×Q8—26no—
585C3×Q8—26no—
586C3×Q8—24no—
587C3×Q8—312no—
588C3×Q8—46no—
589C3×Q8—612no—
590C3×Q8—66no—
591C3×Q8D3×D414yescomplemented
592C3×Q8C2×#6714yescomplemented
593C3×D4—66no—
594C3×D4—66no—
595C2×C3×C4—26no—
596C2×C3×C4—26no—
597C2×C3×C4—23no—
598C2×C3×C4—23no—
599C2×C3×C4—33no—
600C2×C3×C4—312no—
601C2×C3×C4—31no—
602C2×C3×C4—33no—
603C2×C3×C4—31no—
604C2×C3×C4—33no—
605C2×C3×C4—46no—
606C2×C3×C4—66no—
607C2×C3×C4—66no—
608C2×C3×C4—66no—
609C2×C3×C4—66no—
610C2×C3×C4—66no—
611C2×C3×C4C23×D313yes—
612C2×C3×C4C23×D313yes—
613C2×C3×C4C23×D313yes—
614C2×C3×C4C23×D313yes—
615#67—26no—
616#67—66no—
617#67—66no—
618#67—66no—
619#67—66no—
620#67—66no—
621#67—612no—
622#67—126no—
623C2×Dic3—26no—
624C2×Dic3—31no—
625C2×Dic3—31no—
626C2×Dic3—33no—
627C2×Dic3—33no—
628C2×Dic3—31no—
629C2×Dic3—31no—
630C2×Dic3—61no—
631C2×Dic3—63no—
632C2×Dic3—61no—
633C2×Dic3—62no—
634C2×Dic3—62no—
635C2×Dic3—66no—
636C2×Dic3—66no—
637C2×Dic3C23×D311yescharacteristic
638C2×Dic3C23×D313yes—
639C2×Dic3C23×D311yescharacteristic
640C2×Dic3C23×D313yes—
641C2×Dic3C23×D313yes—
642D12—26no—
643D12—612no—
644D12—66no—
645D12—66no—
646D12—66no—
647D12—126no—
648C4×D3—26no—
649C4×D3—26no—
650C4×D3—26no—
651C4×D3—26no—
652C4×D3—66no—
653C4×D3—66no—
654C4×D3—66no—
655C4×D3—62no—
656C4×D3—62no—
657C4×D3—66no—
658C4×D3—66no—
659C4×D3—66no—
660C4×D3—126no—
661C4×D3C2×#67112yes—
662Dic6—26no—
663Dic6—212no—
664Dic6C2×#67112yescomplemented
665C2×C32—22no—
666C2×C32C23×D411yescharacteristic
667C2×C32C22×#4111yescharacteristic
668C2×C32C2×2−1+411yescharacteristic
669C3⋊D3—43no—
670C3×D3—22no—
671C3×D3—43no—
672C3×D3#54814yescomplemented
673C24—31no—
674C24—93no—
675#41—64no—
676#41—1812no—
677#41—1812no—
678#41—184no—
679C2×Q8—24no—
680C2×Q8—38no—
681C2×Q8—33no—
682C2×Q8—36no—
683C2×Q8—33no—
684C2×Q8—612no—
685C2×Q8—612no—
686C2×Q8—612no—
687C2×Q8—64no—
688C2×Q8C2×D3213yes—
689C2×Q8C2×D3211yescharacteristic
690C2×D4—33no—
691C2×D4—33no—
692C2×D4—93no—
693C2×D4—96no—
694C2×D4—93no—
695C2×D4—93no—
696C2×D4—93no—
697C2×D4—1812no—
698C2×D4—1812no—
699C22×C4—33no—
700C22×C4—33no—
701C22×C4—33no—
702C22×C4—33no—
703C22×C4—33no—
704C22×C4—33no—
705C22×C4—612no—
706C22×C4—93no—
707C22×C4—91no—
708C22×C4—93no—
709C22×C4—91no—
710C22×C4—93no—
711C22×C4—93no—
712C22×C4—1812no—
713C22×C4C2×D3213yes—
714C4⋊C4—33no—
715C4⋊C4—33no—
716C4⋊C4—93no—
717C4⋊C4—93no—
718C4⋊C4—96no—
719C4⋊C4—93no—
720C4⋊C4—93no—
721C22⋊C4—31no—
722C22⋊C4—33no—
723C22⋊C4—36no—
724C22⋊C4—93no—
725C22⋊C4—96no—
726C22⋊C4—91no—
727C22⋊C4—91no—
728C22⋊C4—93no—
729C22⋊C4—96no—
730C22⋊C4—91no—
731C22⋊C4—93no—
732C22⋊C4—96no—
733C42—33no—
734C42—93no—
735C42—93no—
736C42—93no—
737C22×C3—21no—
738C22×C3—21no—
739C22×C3—21no—
740C22×C3—21no—
741C22×C3—22no—
742C22×C3—21no—
743C22×C3—32no—
744C22×C3—32no—
745C22×C3—32no—
746C22×C3—32no—
747C22×C3—41no—
748C22×C3—41no—
749C22×C3—68no—
750C22×C3—61no—
751C22×C3—61no—
752C22×C3—63no—
753C22×C3—63no—
754C22×C3—63no—
755C22×C3C2×#23912yescomplemented
756C22×C3D3×#4112yescomplemented
757C22×C3C24×D311yescharacteristic
758C22×C3C24×D311yescharacteristic
759C2×D3—21no—
760C2×D3—21no—
761C2×D3—28no—
762C2×D3—23no—
763C2×D3—23no—
764C2×D3—23no—
765C2×D3—63no—
766C2×D3—63no—
767C2×D3—63no—
768C2×D3—63no—
769C2×D3—63no—
770C2×D3—63no—
771C2×D3—123no—
772C2×D3—123no—
773C2×D3—123no—
774C2×D3—1212no—
775C2×D3—1212no—
776C2×D3C2×#23912yes—
777C2×D3C2×#23912yescomplemented
778C2×D3#100712yes—
779C2×D3C22×#6712yes—
780C3×C4—23no—
781C3×C4—23no—
782C3×C4—26no—
783C3×C4—36no—
784C3×C4—43no—
785C3×C4—63no—
786C3×C4—63no—
787C3×C4—61no—
788C3×C4—61no—
789C3×C4C2×D3×D416yes—
790C3×C4C22×#6716yes—
791Dic3—21no—
792Dic3—23no—
793Dic3—21no—
794Dic3—23no—
795Dic3—61no—
796Dic3—63no—
797Dic3—61no—
798Dic3—63no—
799Dic3—61no—
800Dic3—61no—
801Dic3—121no—
802Dic3—123no—
803Dic3—121no—
804Dic3C22×#6716yes—
805C32C2×#54811yescharacteristic, complemented, Sylow
806C23—31no—
807C23—34no—
808C23—31no—
809C23—33no—
810C23—62no—
811C23—62no—
812C23—93no—
813C23—186no—
814C23—186no—
815C23—186no—
816C23C22×D3211yescharacteristic
817Q8—26no—
818Q8—312no—
819Q8—612no—
820Q8—66no—
821Q8D3×#6714yescomplemented
822D4—66no—
823D4—66no—
824D4—1812no—
825D4—186no—
826D4—186no—
827D4—186no—
828D4—186no—
829C2×C4—26no—
830C2×C4—33no—
831C2×C4—312no—
832C2×C4—31no—
833C2×C4—33no—
834C2×C4—31no—
835C2×C4—33no—
836C2×C4—66no—
837C2×C4—66no—
838C2×C4—66no—
839C2×C4—66no—
840C2×C4—66no—
841C2×C4—91no—
842C2×C4—93no—
843C2×C4—91no—
844C2×C4—186no—
845C2×C4—186no—
846C2×C4—182no—
847C2×C4—186no—
848C2×C4—182no—
849C2×C4—186no—
850C2×C4C22×D3213yes—
851C2×C4C22×D3213yes—
852C2×C3—22no—
853C2×C3—22no—
854C2×C3—21no—
855C2×C3—21no—
856C2×C3—21no—
857C2×C3—34no—
858C2×C3—42no—
859C2×C3—62no—
860C2×C3—123no—
861C2×C3C22×D3×D411yescharacteristic
862C2×C3C22×#23911yescharacteristic
863C2×C3C2×#100711yescharacteristic
864C2×C3C2×D3×#4111yescharacteristic
865C2×C3D3×2−1+411yescharacteristic
866C2×C3C23×#6711yescharacteristic
867D3—22no—
868D3—43no—
869D3—123no—
870D3—123no—
871D3—243no—
872D3#581714yesdirect product factor
873C22—21no—
874C22—21no—
875C22—32no—
876C22—32no—
877C22—32no—
878C22—32no—
879C22—68no—
880C22—61no—
881C22—61no—
882C22—63no—
883C22—63no—
884C22—63no—
885C22—183no—
886C22—183no—
887C22—183no—
888C22—3612no—
889C22D3×#23912yescomplemented
890C22C23×D3211yescharacteristic
891C4—23no—
892C4—36no—
893C4—63no—
894C4—61no—
895C4—61no—
896C4—63no—
897C4—183no—
898C4—181no—
899C4—181no—
900C4C2×D3×#6716yes—
901C3—21no—
902C3D3×#54811yescharacteristic, complemented
903C3C2×#581711yescharacteristic, complemented
904C2—22no—
905C2—34no—
906C2—62no—
907C2—123no—
908C2—363no—
909C2C2×D3×#23911yescharacteristic
910C2D3×#100711yescharacteristic
911C2C22×D3×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC22×C32×Q8C22
hypercenterC22×Q8D32
hypocenterC32C2×#548
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C22×C3×D3×Q8C2semidirect
2. C2×D3×#239C2semidirect
3. #10596288C2semidirect
4. C3×#5817C2semidirect
5. D3×#947C2semidirect
6. D3×#946C2semidirect
7. #10595409C2semidirect
8. #10595402C2semidirect
9. #10595401C2semidirect
10. D3×Q8×Dic3C2semidirect
11. #10595342C2semidirect
12. D3×#930C2semidirect
13. C4×D3×#67C2semidirect
14. #10594902C2semidirect
15. #10594900C2semidirect
18. C22×C32×Q8C22semidirect
19. C2×#3832C22semidirect
20. C2×C3×#239C22semidirect
24. C2×C3×D3×Q8C22semidirect
25. C2×C3×D3×Q8C22semidirect
27. C22×C3×Dic6C22semidirect
32. C2×#3799C22semidirect
33. C2×#3796C22semidirect
34. #64156C22semidirect
35. #64155C22semidirect
36. Q8×C3⋊Dic3C22semidirect
37. #64139C22semidirect
38. C4×#638C22semidirect
39. C3×#947C22semidirect
40. C3×#946C22semidirect
41. C3×Q8×Dic3C22semidirect
42. C3×#930C22semidirect
43. C3×C4×#67C22semidirect
44. #63978C22semidirect
45. Dic3×#67C22semidirect
47. #63952C22semidirect
50. #63909C22semidirect
51. #63908C22semidirect
52. #63907C22semidirect
53. #63907C22semidirect
54. #63906C22semidirect
55. #63904C22semidirect
56. C4×#626C22semidirect
57. C4×#625C22semidirect
59. #63888C22semidirect
60. #63887C22semidirect
61. #63879C22semidirect
64. #63871C22semidirect
65. #63864C22semidirect
66. #63863C22semidirect
67. #63856C22semidirect
68. #63843C22semidirect
69. Dic3×Dic6C22semidirect
73. C22×D3×Q8D3semidirect
85. #5817D3direct (N × H)
117. C3×D3×Q8D4semidirect
174. C22×C3×Q8C2×D3semidirect
175. C22×C3×Q8C2×D3semidirect
185. C2×#239C2×D3semidirect
189. C2×D3×Q8C2×D3semidirect
190. C2×D3×Q8C2×D3semidirect
199. C22×Dic6C2×D3semidirect
213. #947C2×D3semidirect
221. #946C2×D3semidirect
227. Q8×Dic3C2×D3semidirect
239. #930C2×D3semidirect
250. C4×#67C2×D3semidirect
281. C22×C3×D3#41semidirect
289. C32×Q8C2×D4semidirect
314. C3×Dic6C2×D4semidirect
395. D3×Q8#67semidirect
482. C22×C32C2×#41semidirect
495. C2×C3×D3C2×#41semidirect
519. C22×Q8D32semidirect
580. C22×D3#239semidirect
591. C3×Q8D3×D4semidirect
592. C3×Q8C2×#67semidirect
664. Dic6C2×#67semidirect
672. C3×D3#548semidirect
755. C22×C3C2×#239semidirect
756. C22×C3D3×#41semidirect
777. C2×D3C2×#239semidirect
805. C32C2×#548semidirect
821. Q8D3×#67semidirect
872. D3#5817direct (N × H)
889. C22D3×#239semidirect
902. C3D3×#548semidirect
903. C3C2×#5817semidirect

Maximal subgroups

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

subgroupindex
C22×C3×D3×Q82
C2×D3×#2392
#105962882
C3×#58172
D3×#9472
D3×#9462
#105954092
#105954022
#105954012
D3×Q8×Dic32
#105953422
D3×#9302
C4×D3×#672
#105949022
#105949002
C2×#58173
D3×#5483