Finite Group Databasebeta

← D3×#5716 #11900761

Subgroups — D3×#5716 #11900761

Order 1152.

3611 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#237C212yesmaximal, complemented
2#10596187C211yesmaximal, characteristic, complemented
3C3×#5716C211yesmaximal, characteristic, complemented
4C3×D3×#127C211yesmaximal, characteristic, complemented
5D3×#938C214yesmaximal, complemented
6#10595167C212yesmaximal, complemented
7#10595152C212yesmaximal, complemented
8D3×#936C212yesmaximal, complemented
9#10595139C214yesmaximal, complemented
10#10595133C214yesmaximal, complemented
11D3×D4×Dic3C214yesmaximal, complemented
12C42×D32C211yesmaximal, characteristic, complemented
13#10593907C211yesmaximal, characteristic, complemented
14#10593897C211yesmaximal, characteristic, complemented
15D3×#869C211yesmaximal, characteristic, complemented
16D3×#532—31nomaximal
17C2×#5716—31nomaximal
18C2×#3830C2212yescomplemented
19C2×C3×#237C2212yescomplemented
20C2×C3×D3×D4C2214yes—
21C2×C3×D3×D4C2212yes—
22C2×D3×#67C2214yes—
23C2×#3805C2214yescomplemented
24C2×#3804C2214yescomplemented
25C22×D3×Dic3C2214yes—
26D3×#237—216no—
27C2×C4×D32C2212yes—
28C2×C4×D32C2211yescharacteristic
29C2×#3796C2212yescomplemented
30C2×#3795C2212yescomplemented
31C2×D3×Dic6C2212yes—
32C32×#127C2211yescharacteristic, complemented
33#64147C2214yescomplemented
34#64145C2212yescomplemented
35D4×C3⋊Dic3C2214yescomplemented
36C42×C3⋊D3C2211yescharacteristic, complemented
37#64078C2211yescharacteristic, complemented
38C3×#940C2214yescomplemented
39C3×#940C2212yescomplemented
40C3×#938C2214yescomplemented
41C3×#936C2212yescomplemented
42C3×D4×Dic3C2214yescomplemented
43C3×#874C2211yescharacteristic, complemented
44C3×C42×D3C2211yescharacteristic
45C3×C42×D3C2211yescharacteristic, complemented
46C3×#869C2211yescharacteristic, complemented
47#67⋊Dic3C2218yescomplemented
48Dic3×#67C2218yescomplemented
49#63970C2218yescomplemented
50D3×#217C2218yes—
51#63959C2218yescomplemented
52#63958C2218yescomplemented
53#63918C2214yescomplemented
54#63916C2214yescomplemented
55#63908C2214yescomplemented
56#63898C2214yescomplemented
57Dic3×D12C2214yescomplemented
58D3×C4⋊Dic3C2214yes—
59C4×#624C2212yescomplemented
60C4×#624C2211yescharacteristic, complemented
61C4×D3×Dic3C2212yes—
62C4×D3×Dic3C2211yescharacteristic
63C4×D3×Dic3C2212yescomplemented
64C4×D3×Dic3C2211yescharacteristic, complemented
65#63866C2212yescomplemented
66#63863C2212yescomplemented
67#63860C2212yescomplemented
68C2×D3×#41—32no—
69C22×#237—32no—
70C3×#532—31no—
71C2×C3×#127—31no—
72#5832—32no—
73C2×#938—34no—
74C2×#936—32no—
75C2×D4×Dic3—34no—
76#5725—31no—
77D3×C4⋊Q8—31no—
78#5716—32no—
79#5716—31no—
80#5716—31no—
81#5716—34no—
82#5716—32no—
83#5716—34no—
84#5716—31no—
85#5716—31no—
86#5716—61no—
87#5716D311yescharacteristic, direct product factor
88D3×#127D311yescharacteristic, complemented
89D3×#124—32no—
90#5668—32no—
91D3×#121—34no—
92#5596—34no—
93#5548—34no—
94C4×D3×D4—34no—
95#5477—31no—
96C2×C42×D3—31no—
97C2×C42×D3—31no—
98C2×#869—31no—
99C23×C3×D3C2314yes—
100C22×D32C2311yescharacteristic
101C2×C32×D4C2314yes—
102C2×C32×D4C2312yes—
103C2×#638C2314yes—
104C22×C3⋊Dic3C2314yes—
105#3830—28no—
106C2×C4×C3⋊D3C2312yes—
107C2×C4×C3⋊D3C2311yescharacteristic
108C2×#634C2312yes—
109C2×C3×#67C2314yes—
110C2×C3×#67C2314yes—
111C2×C3×#67C2318yes—
112C22×C3×Dic3C2314yes—
113C3×#237—28no—
114C3×D3×D4—28no—
115C3×D3×D4—216no—
116C2×C3×D12C2312yes—
117C2×C3×D12C2314yes—
118C2×C3×C4×D3C2312yes—
119C2×C3×C4×D3C2311yescharacteristic
120C2×C3×C4×D3C2311yescharacteristic
121C2×C3×C4×D3C2312yes—
122C2×C3×Dic6C2312yes—
123D3×#67—216no—
124C2×#627C2314yes—
125C2×#626C2314yes—
126C2×#625C2314yes—
127C2×#624C2312yes—
128C2×#624C2311yescharacteristic
129#3805—216no—
130#3804—216no—
131C2×D3×Dic3—216no—
132C2×D3×Dic3C2314yes—
133C2×D3×Dic3C2314yes—
134C2×D3×Dic3C2314yes—
135C2×D3×Dic3C2312yes—
136C2×D3×Dic3C2312yes—
137C2×D3×Dic3C2311yescharacteristic
138C2×D3×Dic3C2311yescharacteristic
139C4×D32—28no—
140C4×D32D418yescomplemented
141#3796—28no—
142#3795—28no—
143D3×Dic6—28no—
144C32×C42C2311yescharacteristic
145#3757C2318yes—
146C4⋊(C3⋊Dic3)C2314yes—
147C4×C3⋊Dic3C2311yescharacteristic
148C4×C3⋊Dic3C2312yes—
149C3×#217C2318yes—
150C3×C4⋊Dic3C2314yes—
151C3×C4×Dic3C2312yes—
152C3×C4×Dic3C2311yescharacteristic
153C3×C4×Dic3C2311yescharacteristic
154C3×C4×Dic3C2312yes—
155Dic3⋊Dic3C2318yes—
156(C2×D3)⋊Dic3C2318yes—
157(C2×D3)⋊Dic3C2318yes—
158Dic32C2312yes—
159Dic32C2312yes—
160Dic32C2312yes—
161C2×#532—91noSylow
162C2×C3×#41—32no—
163C22×C3×D4—32no—
164C22×C3×D4—34no—
165C22×#67—34no—
166C23×Dic3—34no—
167D3×#41—616no—
168C2×#239—32no—
169C2×D3×Q8—32no—
170C2×#237—32no—
171C2×#237—32no—
172C2×#237—34no—
173C2×#237—34no—
174C2×#237—34no—
175C2×#237—32no—
176C2×#237—32no—
177C2×#237—62no—
178C2×#237—616no—
179C2×#237C2×D312yescomplemented
180C2×D3×D4—34no—
181C2×D3×D4C2×D312yes—
182C2×D3×D4C2×D314yes—
183C2×#235—34no—
184C2×#235—32no—
185C22×C4×D3—31no—
186C22×C4×D3—31no—
187C22×C4×D3—34no—
188C22×C4×D3—32no—
189C22×C4×D3—32no—
190C22×Dic6—32no—
191C3×C4⋊Q8—31no—
192C3×#127—21no—
193C3×#127—32no—
194C3×#127—34no—
195C3×#127—31no—
196C3×#127C2×D311yescharacteristic, complemented
197C3×#127C2×D311yescharacteristic, complemented
198C3×#124—32no—
199C3×#121—34no—
200C3×C4×D4—34no—
201C2×C3×C42—31no—
202C2×C3×C42—31no—
203C2×#217—38no—
204#947—32no—
205#944—32no—
206#940C2×D312yescomplemented
207#940C2×D314yescomplemented
208#939—38no—
209#938—34no—
210#938—34no—
211#938—38no—
212#938—34no—
213#938—38no—
214#938—34no—
215#938—64no—
216#938C2×D314yescomplemented
217#936—32no—
218#936—32no—
219#936—32no—
220#936—38no—
221#936—32no—
222#936—62no—
223#936C2×D312yescomplemented
224D4×Dic3—34no—
225D4×Dic3—34no—
226D4×Dic3—38no—
227D4×Dic3—38no—
228D4×Dic3—34no—
229D4×Dic3—34no—
230D4×Dic3—64no—
231D4×Dic3C2×D314yescomplemented
232#930—34no—
233C4×#67—38no—
234C2×C4⋊Dic3—34no—
235C2×C4×Dic3—32no—
236C2×C4×Dic3—31no—
237C2×C4×Dic3—31no—
238C2×C4×Dic3—32no—
239#895—34no—
240#893—34no—
241D3×C4⋊C4—34no—
242#888—34no—
243#885—38no—
244#884—38no—
245#67⋊C4—38no—
246D3×C22⋊C4—38no—
247#875—32no—
248#874C2×D311yescharacteristic, complemented
249C4×D12—34no—
250C42×D3—31no—
251C42×D3—32no—
252C42×D3—31no—
253C42×D3—32no—
254C42×D3—31no—
255C42×D3—31no—
256C42×D3—31no—
257C42×D3—31no—
258C42×D3—32no—
259C42×D3—32no—
260C42×D3—61no—
261C42×D3C2×D311yescharacteristic
262C42×D3C2×D311yescharacteristic, complemented
263#869—32no—
264#869—31no—
265#869—31no—
266#869—34no—
267#869—61no—
268#869C2×D311yescharacteristic, complemented
269C23×C32C2414yes—
270C22×C3⋊D3C2411yescharacteristic
271C22×C3×D3—28no—
272C22×C3×D3—216no—
273C22×C3×D3C2414yes—
274C22×C3×D3C2411yescharacteristic
275C22×C3×D3C2411yescharacteristic
276C2×D32—24no—
277C2×D32C2×D414yes—
278C32×D4—24no—
279C32×D4—28no—
280C2×C32×C4C2411yescharacteristic
281C2×C32×C4C2412yes—
282#638—28no—
283C2×C3⋊Dic3—28no—
284C2×C3⋊Dic3C2412yes—
285C2×C3⋊Dic3C2414yes—
286C2×C3⋊Dic3C2411yescharacteristic
287C4×C3⋊D3—24no—
288C4×C3⋊D3C2×D414yescomplemented
289#634—24no—
290C3×#67—28no—
291C3×#67—28no—
292C3×#67—216no—
293C2×C3×Dic3—28no—
294C2×C3×Dic3C2412yes—
295C2×C3×Dic3C2414yes—
296C2×C3×Dic3C2411yescharacteristic
297C2×C3×Dic3C2411yescharacteristic
298C2×C3×Dic3C2412yes—
299C3×D12—24no—
300C3×D12—28no—
301C3×C4×D3—24no—
302C3×C4×D3C2×D414yes—
303C3×C4×D3C2×D414yescomplemented
304C3×C4×D3#4118yescomplemented
305C3×Dic6—24no—
306#627—28no—
307#626—28no—
308#625—28no—
309#624—24no—
310#624C2×D414yescomplemented
311D3×Dic3—28no—
312D3×Dic3—24no—
313D3×Dic3—28no—
314D3×Dic3—28no—
315D3×Dic3—24no—
316D3×Dic3C2×D414yes—
317D3×Dic3C2×D414yescomplemented
318C22×#41—92no—
319#532—31no—
320#532—91no—
321#532—94no—
322#532—94no—
323#532—92no—
324#532—91no—
325#532—92no—
326#532—91no—
327C2×C4⋊Q8—91no—
328C2×#127—31no—
329C2×#124—92no—
330C2×#121—94no—
331C2×C4×D4—94no—
332C22×C42—91no—
333C24×C3—34no—
334C23×D3—31no—
335C23×D3—31no—
336C23×D3C22×D314yes—
337C3×#41—68no—
338C2×C3×Q8—32no—
339C2×C3×D4—24no—
340C2×C3×D4—22no—
341C2×C3×D4—38no—
342C2×C3×D4—34no—
343C2×C3×D4—34no—
344C2×C3×D4—34no—
345C2×C3×D4—32no—
346C2×C3×D4—68no—
347C2×C3×D4—616no—
348C2×C3×D4C22×D314yes—
349C2×C3×D4C22×D314yes—
350C2×C3×D4C22×D312yes—
351C2×C3×D4C22×D312yes—
352C22×C3×C4—32no—
353C22×C3×C4—31no—
354C22×C3×C4—31no—
355C22×C3×C4—34no—
356C22×C3×C4—32no—
357C2×#67—34no—
358C2×#67—34no—
359C2×#67—34no—
360C2×#67—34no—
361C2×#67—34no—
362C2×#67—64no—
363C2×#67—616no—
364C2×#67C22×D318yes—
365C2×#67C22×D314yes—
366C2×#67C22×D314yes—
367C22×Dic3—31no—
368C22×Dic3—31no—
369C22×Dic3—34no—
370C22×Dic3—34no—
371C22×Dic3—32no—
372C22×Dic3—32no—
373C22×Dic3—34no—
374C22×Dic3—34no—
375C22×Dic3—34no—
376C22×Dic3—64no—
377C22×Dic3—616no—
378C22×Dic3C22×D314yes—
379#239—68no—
380D3×Q8—68no—
381#237—28no—
382#237—68no—
383#237—616no—
384#237—616no—
385#237—68no—
386#237—68no—
387#237—616no—
388#237—68no—
389#237—128no—
390D3×D4—28no—
391D3×D4—216no—
392D3×D4—616no—
393#235—616no—
394#235—68no—
395C2×D12—34no—
396C2×D12C22×D314yes—
397C2×D12C22×D312yes—
398C2×C4×D3—31no—
399C2×C4×D3—31no—
400C2×C4×D3—31no—
401C2×C4×D3—31no—
402C2×C4×D3—31no—
403C2×C4×D3—31no—
404C2×C4×D3—38no—
405C2×C4×D3—38no—
406C2×C4×D3—32no—
407C2×C4×D3—32no—
408C2×C4×D3—34no—
409C2×C4×D3—34no—
410C2×C4×D3—34no—
411C2×C4×D3—32no—
412C2×C4×D3—32no—
413C2×C4×D3—32no—
414C2×C4×D3—32no—
415C2×C4×D3—61no—
416C2×C4×D3—62no—
417C2×C4×D3—68no—
418C2×C4×D3—616no—
419C2×C4×D3—68no—
420C2×C4×D3C22×D312yes—
421C2×C4×D3C22×D311yescharacteristic
422C2×C4×D3C22×D311yescharacteristic
423C2×C4×D3C22×D312yes—
424C2×Dic6—32no—
425C2×Dic6—32no—
426C2×Dic6—34no—
427C2×Dic6—34no—
428C2×Dic6—62no—
429C2×Dic6—68no—
430C2×Dic6C22×D312yes—
431C3×C4⋊C4—34no—
432C3×C22⋊C4—38no—
433C3×C42—21no—
434C3×C42—31no—
435C3×C42—32no—
436C3×C42—32no—
437C3×C42—31no—
438C3×C42C22×D311yescharacteristic
439C3×C42C22×D311yescharacteristic
440#217—38no—
441#217—38no—
442#217—38no—
443#217—38no—
444#217—68no—
445#217C22×D318yes—
446(C2×D3)⋊C4—38no—
447(C2×D3)⋊C4—38no—
448C4⋊Dic3—34no—
449C4⋊Dic3—34no—
450C4⋊Dic3—38no—
451C4⋊Dic3—64no—
452C4⋊Dic3C22×D314yes—
453Dic3⋊C4—38no—
454C4×Dic3—32no—
455C4×Dic3—32no—
456C4×Dic3—31no—
457C4×Dic3—31no—
458C4×Dic3—32no—
459C4×Dic3—32no—
460C4×Dic3—32no—
461C4×Dic3—32no—
462C4×Dic3—32no—
463C4×Dic3—32no—
464C4×Dic3—62no—
465C4×Dic3—61no—
466C4×Dic3C22×D312yes—
467C4×Dic3C22×D311yescharacteristic
468C4×Dic3C22×D312yes—
469C4×Dic3C22×D311yescharacteristic
470C22×C32—24no—
471C22×C32—28no—
472C22×C32C2511yescharacteristic
473C2×C3⋊D3—22no—
474C2×C3⋊D3C22×D412yes—
475C2×C3×D3—22no—
476C2×C3×D3—24no—
477C2×C3×D3—28no—
478C2×C3×D3—416no—
479C2×C3×D3C22×D412yes—
480C2×C3×D3C22×D412yes—
481C2×C3×D3C2×#4114yes—
482D32—28no—
483C32×C4C22×D412yes—
484C32×C4C2×#4114yescomplemented
485C3⋊Dic3—24no—
486C3⋊Dic3—22no—
487C3⋊Dic3C22×D412yes—
488C3×Dic3—24no—
489C3×Dic3—22no—
490C3×Dic3C22×D412yes—
491C3×Dic3C22×D412yes—
492C3×Dic3C2×#4114yescomplemented
493C2×#41—32no—
494C2×#41—92no—
495C2×#41—94no—
496C2×#41—94no—
497C2×#41—92no—
498C2×#41—92no—
499C2×#41—1816no—
500C22×Q8—92no—
501C22×D4—34no—
502C22×D4—32no—
503C22×D4—94no—
504C23×C4—91no—
505C23×C4—92no—
506C23×C4—94no—
507C4⋊Q8—31no—
508C4⋊Q8—94no—
509C4⋊Q8—92no—
510C4⋊Q8—91no—
511#127—32no—
512#127—34no—
513#127—31no—
514#127D3211yescharacteristic, complemented
515#124—32no—
516#124—92no—
517#124—98no—
518#124—92no—
519#124—92no—
520#121—34no—
521#121—98no—
522#121—94no—
523#121—94no—
524#121—98no—
525#121—94no—
526C4×D4—34no—
527C4×D4—94no—
528C4×D4—98no—
529C4×D4—94no—
530C4×D4—98no—
531C4×D4—94no—
532C2×C4⋊C4—94no—
533C2×C22⋊C4—98no—
534C2×C42—31no—
535C2×C42—31no—
536C2×C42—92no—
537C2×C42—91no—
538C2×C42—92no—
539C2×C42—91no—
540C2×C42—91no—
541C2×C42—92no—
542C2×C42—91no—
543C23×C3—24no—
544C23×C3—31no—
545C23×C3—31no—
546C23×C3—34no—
547C23×C3—68no—
548C23×C3—616no—
549C23×C3C23×D314yes—
550C23×C3C23×D314yes—
551C22×D3—28no—
552C22×D3—216no—
553C22×D3—31no—
554C22×D3—31no—
555C22×D3—34no—
556C22×D3—34no—
557C22×D3—61no—
558C22×D3—64no—
559C22×D3—64no—
560C22×D3C23×D314yes—
561C22×D3C23×D311yescharacteristic
562C22×D3C23×D311yescharacteristic
563C3×Q8—64no—
564C3×D4—24no—
565C3×D4—24no—
566C3×D4—28no—
567C3×D4—28no—
568C3×D4—44no—
569C3×D4—48no—
570C3×D4—68no—
571C3×D4—616no—
572C3×D4—68no—
573C3×D4—64no—
574C3×D4—68no—
575C2×C3×C4—22no—
576C2×C3×C4—21no—
577C2×C3×C4—32no—
578C2×C3×C4—31no—
579C2×C3×C4—31no—
580C2×C3×C4—34no—
581C2×C3×C4—34no—
582C2×C3×C4—38no—
583C2×C3×C4—32no—
584C2×C3×C4—34no—
585C2×C3×C4—68no—
586C2×C3×C4—64no—
587C2×C3×C4C23×D311yescharacteristic
588C2×C3×C4C23×D311yescharacteristic
589C2×C3×C4C23×D312yes—
590C2×C3×C4C23×D312yes—
591#67—28no—
592#67—28no—
593#67—216no—
594#67—68no—
595#67—68no—
596#67—68no—
597#67—68no—
598#67—68no—
599#67—128no—
600C2×Dic3—28no—
601C2×Dic3—31no—
602C2×Dic3—31no—
603C2×Dic3—34no—
604C2×Dic3—34no—
605C2×Dic3—32no—
606C2×Dic3—32no—
607C2×Dic3—34no—
608C2×Dic3—34no—
609C2×Dic3—61no—
610C2×Dic3—62no—
611C2×Dic3—64no—
612C2×Dic3—68no—
613C2×Dic3—68no—
614C2×Dic3—64no—
615C2×Dic3—68no—
616C2×Dic3—68no—
617C2×Dic3—68no—
618C2×Dic3—64no—
619C2×Dic3—128no—
620C2×Dic3C23×D312yes—
621C2×Dic3C23×D314yes—
622C2×Dic3C23×D311yescharacteristic
623C2×Dic3C23×D311yescharacteristic
624C2×Dic3C23×D312yes—
625D12—24no—
626D12—28no—
627D12—68no—
628C4×D3—24no—
629C4×D3—34no—
630C4×D3—34no—
631C4×D3—34no—
632C4×D3—34no—
633C4×D3—34no—
634C4×D3—34no—
635C4×D3—64no—
636C4×D3—64no—
637C4×D3—68no—
638C4×D3—64no—
639C4×D3—68no—
640C4×D3—68no—
641C4×D3—64no—
642C4×D3—64no—
643C4×D3—64no—
644C4×D3—64no—
645C4×D3—124no—
646C4×D3D3×D414yes—
647C4×D3D3×D414yescomplemented
648C4×D3#23718yescomplemented
649Dic6—24no—
650Dic6—68no—
651Dic6—64no—
652Dic6—64no—
653Dic6—68no—
654Dic6—124no—
655C2×C32—44no—
656C2×C32C23×D411yescharacteristic
657C2×C32C22×#4112yes—
658C3⋊D3—22no—
659C3×D3—22no—
660C3×D3—44no—
661C3×D3#53214yescomplemented
662C24—34no—
663C24—91no—
664#41—68no—
665#41—188no—
666#41—1816no—
667#41—188no—
668#41—1816no—
669#41—188no—
670C2×Q8—32no—
671C2×Q8—94no—
672C2×Q8—92no—
673C2×Q8—188no—
674C2×D4—38no—
675C2×D4—34no—
676C2×D4—34no—
677C2×D4—34no—
678C2×D4—32no—
679C2×D4—68no—
680C2×D4—616no—
681C2×D4—94no—
682C2×D4—94no—
683C2×D4—94no—
684C2×D4—1816no—
685C2×D4C2×D3214yes—
686C2×D4C2×D3212yes—
687C22×C4—32no—
688C22×C4—31no—
689C22×C4—31no—
690C22×C4—34no—
691C22×C4—32no—
692C22×C4—91no—
693C22×C4—98no—
694C22×C4—92no—
695C22×C4—91no—
696C22×C4—91no—
697C22×C4—92no—
698C22×C4—92no—
699C22×C4—94no—
700C22×C4—94no—
701C22×C4—94no—
702C22×C4—91no—
703C22×C4—94no—
704C22×C4—92no—
705C22×C4—188no—
706C22×C4—1816no—
707C4⋊C4—34no—
708C4⋊C4—98no—
709C4⋊C4—94no—
710C22⋊C4—38no—
711C22⋊C4—98no—
712C22⋊C4—98no—
713C22⋊C4—98no—
714C42—32no—
715C42—31no—
716C42—31no—
717C42—32no—
718C42—92no—
719C42—92no—
720C42—92no—
721C42—92no—
722C42—91no—
723C42C2×D3211yescharacteristic
724C22×C3—24no—
725C22×C3—24no—
726C22×C3—28no—
727C22×C3—28no—
728C22×C3—21no—
729C22×C3—32no—
730C22×C3—34no—
731C22×C3—32no—
732C22×C3—44no—
733C22×C3—48no—
734C22×C3—62no—
735C22×C3—64no—
736C22×C3—68no—
737C22×C3—1216no—
738C22×C3C24×D311yescharacteristic
739C22×C3C24×D311yescharacteristic
740C2×D3—22no—
741C2×D3—24no—
742C2×D3—28no—
743C2×D3—32no—
744C2×D3—32no—
745C2×D3—416no—
746C2×D3—62no—
747C2×D3—68no—
748C2×D3—62no—
749C2×D3—62no—
750C2×D3—68no—
751C2×D3—122no—
752C2×D3C2×D3×D412yes—
753C2×D3C2×D3×D412yes—
754C2×D3C2×#23714yes—
755C3×C4—22no—
756C3×C4—24no—
757C3×C4—32no—
758C3×C4—32no—
759C3×C4—34no—
760C3×C4—64no—
761C3×C4—62no—
762C3×C4C2×D3×D412yes—
763C3×C4C2×D3×D412yes—
764C3×C4C2×#23714yescomplemented
765C3×C4D3×#4114yescomplemented
766Dic3—24no—
767Dic3—22no—
768Dic3—32no—
769Dic3—32no—
770Dic3—62no—
771Dic3—64no—
772Dic3—64no—
773Dic3—62no—
774Dic3—62no—
775Dic3—124no—
776Dic3—122no—
777Dic3C2×D3×D412yes—
778Dic3C2×D3×D412yes—
779Dic3C2×#23714yescomplemented
780C32C2×#53211yescharacteristic, complemented, Sylow
781C23—31no—
782C23—31no—
783C23—34no—
784C23—68no—
785C23—616no—
786C23—94no—
787C23—91no—
788C23—184no—
789C23C22×D3214yes—
790Q8—64no—
791Q8—188no—
792Q8—184no—
793D4—24no—
794D4—28no—
795D4—68no—
796D4—616no—
797D4—68no—
798D4—64no—
799D4—68no—
800D4—188no—
801D4—188no—
802D4—188no—
803C2×C4—32no—
804C2×C4—31no—
805C2×C4—31no—
806C2×C4—34no—
807C2×C4—34no—
808C2×C4—38no—
809C2×C4—32no—
810C2×C4—34no—
811C2×C4—68no—
812C2×C4—64no—
813C2×C4—94no—
814C2×C4—94no—
815C2×C4—94no—
816C2×C4—91no—
817C2×C4—94no—
818C2×C4—92no—
819C2×C4—94no—
820C2×C4—184no—
821C2×C4—188no—
822C2×C4—184no—
823C2×C4—188no—
824C2×C4—188no—
825C2×C4—184no—
826C2×C4—188no—
827C2×C4—184no—
828C2×C4C22×D3211yescharacteristic
829C2×C4C22×D3212yes—
830C2×C3—21no—
831C2×C3—22no—
832C2×C3—34no—
833C2×C3—44no—
834C2×C3—44no—
835C2×C3—62no—
836C2×C3—84no—
837C2×C3—124no—
838C2×C3C22×D3×D411yescharacteristic
839C2×C3C22×D3×D411yescharacteristic
840C2×C3C22×#23712yes—
841C2×C3C2×D3×#4112yes—
842D3—22no—
843D3—44no—
844D3—62no—
845D3—62no—
846D3—122no—
847D3#571614yesdirect product factor
848C22—24no—
849C22—28no—
850C22—32no—
851C22—34no—
852C22—32no—
853C22—62no—
854C22—64no—
855C22—68no—
856C22—92no—
857C22—1216no—
858C22—188no—
859C22—182no—
860C22C23×D3211yescharacteristic
861C4—32no—
862C4—32no—
863C4—34no—
864C4—64no—
865C4—62no—
866C4—92no—
867C4—184no—
868C4—182no—
869C4D32×D412yes—
870C4D3×#23714yescomplemented
871C3—21no—
872C3C2×#571611yescharacteristic, complemented
873C3D3×#53211yescharacteristic, complemented
874C2—34no—
875C2—44no—
876C2—62no—
877C2—124no—
878C2—182no—
879C2C2×D32×D411yescharacteristic
880C2C2×D3×#23712yes—
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#127C22
hypercenter#127D32
hypocenterC32C2×#532
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #127

Complements

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

NH ≅ G/Ntype
1. C2×D3×#237C2semidirect
2. #10596187C2semidirect
3. C3×#5716C2semidirect
4. C3×D3×#127C2semidirect
5. D3×#938C2semidirect
6. #10595167C2semidirect
7. #10595152C2semidirect
8. D3×#936C2semidirect
9. #10595139C2semidirect
10. #10595133C2semidirect
11. D3×D4×Dic3C2semidirect
12. C42×D32C2semidirect
13. #10593907C2semidirect
14. #10593897C2semidirect
15. D3×#869C2semidirect
18. C2×#3830C22semidirect
19. C2×C3×#237C22semidirect
23. C2×#3805C22semidirect
24. C2×#3804C22semidirect
29. C2×#3796C22semidirect
30. C2×#3795C22semidirect
32. C32×#127C22semidirect
33. #64147C22semidirect
34. #64145C22semidirect
35. D4×C3⋊Dic3C22semidirect
36. C42×C3⋊D3C22semidirect
37. #64078C22semidirect
38. C3×#940C22semidirect
39. C3×#940C22semidirect
40. C3×#938C22semidirect
41. C3×#936C22semidirect
42. C3×D4×Dic3C22semidirect
43. C3×#874C22semidirect
45. C3×C42×D3C22semidirect
46. C3×#869C22semidirect
47. #67⋊Dic3C22semidirect
48. Dic3×#67C22semidirect
49. #63970C22semidirect
51. #63959C22semidirect
52. #63958C22semidirect
53. #63918C22semidirect
54. #63916C22semidirect
55. #63908C22semidirect
56. #63898C22semidirect
57. Dic3×D12C22semidirect
59. C4×#624C22semidirect
60. C4×#624C22semidirect
63. C4×D3×Dic3C22semidirect
64. C4×D3×Dic3C22semidirect
65. #63866C22semidirect
66. #63863C22semidirect
67. #63860C22semidirect
87. #5716D3direct (N × H)
88. D3×#127D3semidirect
140. C4×D32D4semidirect
179. C2×#237C2×D3semidirect
196. C3×#127C2×D3semidirect
197. C3×#127C2×D3semidirect
206. #940C2×D3semidirect
207. #940C2×D3semidirect
216. #938C2×D3semidirect
223. #936C2×D3semidirect
231. D4×Dic3C2×D3semidirect
248. #874C2×D3semidirect
262. C42×D3C2×D3semidirect
268. #869C2×D3semidirect
288. C4×C3⋊D3C2×D4semidirect
303. C3×C4×D3C2×D4semidirect
304. C3×C4×D3#41semidirect
310. #624C2×D4semidirect
317. D3×Dic3C2×D4semidirect
484. C32×C4C2×#41semidirect
492. C3×Dic3C2×#41semidirect
514. #127D32semidirect
647. C4×D3D3×D4semidirect
648. C4×D3#237semidirect
661. C3×D3#532semidirect
764. C3×C4C2×#237semidirect
765. C3×C4D3×#41semidirect
779. Dic3C2×#237semidirect
780. C32C2×#532semidirect
847. D3#5716direct (N × H)
870. C4D3×#237semidirect
872. C3C2×#5716semidirect
873. C3D3×#532semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2372
#105961872
C3×#57162
C3×D3×#1272
D3×#9382
#105951672
#105951522
D3×#9362
#105951392
#105951332
D3×D4×Dic32
C42×D322
#105939072
#105938972
D3×#8692
D3×#5323
C2×#57163