Finite Group Databasebeta

← D3×#3487 #11703427

Subgroups — D3×#3487 #11703427

Order 768.

11510 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×2−1+4C211yesmaximal, characteristic, complemented
2C22×D3×#41C211yesmaximal, characteristic, complemented
3C3×#3487C211yesmaximal, characteristic, complemented
4#87290C211yesmaximal, characteristic, complemented
5#87274C211yesmaximal, characteristic, complemented
6#86783C218yesmaximal, complemented
7D3×#550C218yesmaximal, complemented
8#86736C218yesmaximal, complemented
9D3×#548C218yesmaximal, complemented
10D3×#535C216yesmaximal, complemented
11#86315C216yesmaximal, complemented
12D3×#525C216yesmaximal, complemented
13#86023C216yesmaximal, complemented
14D3×#519C211yesmaximal, characteristic, complemented
15#85874C211yesmaximal, characteristic, complemented
16C2×#3487—31nomaximal, Sylow
17C2×C3×2−1+4C2211yescharacteristic, complemented
18C22×C3×#41C2211yescharacteristic, complemented
19D3×2−1+4—216no—
20C2×#1010C2216yescomplemented
21C2×#1010C2214yescomplemented
22C2×D3×#41—216no—
23C2×D3×#41C2218yes—
24C2×D3×#41C2216yes—
25C2×D3×#41C2218yescomplemented
26C2×D3×#41C2214yescomplemented
27C2×#1007C2211yescharacteristic, complemented
28C2×#1007C2214yescomplemented
29C22×#239C2211yescharacteristic, complemented
30C22×D3×Q8C2211yescharacteristic
31C22×D3×Q8C2214yescomplemented
32C22×#237C2213yescomplemented
33C22×D3×D4C2213yes—
34C22×#235C2213yescomplemented
35C23×C4×D3C2213yes—
36C3×#550C2218yescomplemented
37C3×#548C2218yescomplemented
38C3×#535C2216yescomplemented
39C3×#525C2216yescomplemented
40C3×#519C2211yescharacteristic, complemented
41#5834C2218yescomplemented
42#5834C2218yescomplemented
43#5831C2218yescomplemented
44#5830C2216yescomplemented
45#5828C2216yescomplemented
46#5817C2218yescomplemented
47#5812C2211yescharacteristic, complemented
48#5805C2216yescomplemented
49#5791C2216yescomplemented
50#5718C22124yescomplemented
51#5715C22112yescomplemented
52D3×#127C22112yescomplemented
53#5677C22124yescomplemented
54#5674C22112yescomplemented
55D3×#124C22112yescomplemented
56#5656C22112yescomplemented
57D3×#123C2214yes—
58#5633C22124yescomplemented
59#5627C22112yescomplemented
60D3×C22⋊Q8C22112yescomplemented
61#5607C22124yescomplemented
62#5606C22112yescomplemented
63D3×#121C22112yescomplemented
64D3×#121C22124yescomplemented
65#5599C22124yescomplemented
66#5599C22124yescomplemented
67#5598C22124yescomplemented
68#5592C22124yescomplemented
69D3×#120C22112yes—
70#5586C22112yescomplemented
71#5577C2218yescomplemented
72#5576C2218yescomplemented
73#5572C2218yescomplemented
74C4×D3×Q8C2218yescomplemented
75#5553C22124yescomplemented
76#5552C22124yescomplemented
77#5547C22124yescomplemented
78C4×D3×D4C22124yescomplemented
79#5525C2216yescomplemented
80#5524C2216yescomplemented
81D3×#117C2216yes—
82#5516C2216yescomplemented
83C22×2−1+4—31no—
84C23×#41—31no—
85#3487—31no—
86#3487—31no—
87#3487—38no—
88#3487—38no—
89#3487—36no—
90#3487—36no—
91#3487—31no—
92#3487D311yescharacteristic, direct product factor
93C2×#550—38no—
94C2×#548—38no—
95C2×#535—36no—
96C2×#525—36no—
97C2×#519—31no—
98C24×D3C2313yes—
99C3×2−1+4—28no—
100C2×C3×#41—28no—
101C2×C3×#41C2318yes—
102C2×C3×#41C2316yes—
103C2×C3×#41C2314yescomplemented
104C22×C3×Q8C2311yescharacteristic
105C22×C3×Q8C2314yescomplemented
106C22×C3×D4C2313yes—
107C23×C3×C4C2313yes—
108C22×#67C2316yes—
109C23×Dic3C2313yes—
110#1010—232no—
111#1010—248no—
112D3×#41—264no—
113D3×#41—232no—
114D3×#41—264no—
115D3×#41—248no—
116#1007—28no—
117#1007—232no—
118C2×#239—28no—
119C2×#239C2316yes—
120C2×#239C2318yes—
121C2×#239C2314yescomplemented
122C2×D3×Q8—232no—
123C2×D3×Q8D4116yescomplemented
124C2×D3×Q8C2316yes—
125C2×D3×Q8C2314yes—
126C2×D3×Q8C2314yes—
127C2×D3×Q8C23112yescomplemented
128C2×D3×Q8C2314yescomplemented
129C2×#237—224no—
130C2×#237C23112yes—
131C2×#237C23124yes—
132C2×#237C2316yes—
133C2×#237C23112yescomplemented
134C2×D3×D4—224no—
135C2×D3×D4C2314yes—
136C2×D3×D4C23112yes—
137C2×D3×D4C23112yes—
138C2×D3×D4C2316yes—
139C2×D3×D4C23124yes—
140C2×#235—224no—
141C2×#235C23124yes—
142C2×#235C2316yes—
143C2×#235C23112yes—
144C2×#235C23112yescomplemented
145C22×D12C2313yes—
146C22×C4×D3—224no—
147C22×C4×D3C2311yescharacteristic
148C22×C4×D3C2313yes—
149C22×C4×D3C2313yes—
150C22×C4×D3C23112yes—
151C22×C4×D3C23112yes—
152C22×C4×D3C23112yes—
153C22×C4×D3C2313yes—
154C22×Dic6C2313yes—
155C22×Dic6C23112yescomplemented
156C3×#127C23112yescomplemented
157C3×#124C23112yescomplemented
158C3×#123C2314yes—
159C3×C22⋊Q8C23112yescomplemented
160C3×#121C23124yescomplemented
161C3×#121C23112yescomplemented
162C3×#120C23112yes—
163C3×C4×Q8C2318yescomplemented
164C3×C4×D4C23124yescomplemented
165C3×#117C2316yes—
166#953C23112yes—
167#947C23112yescomplemented
168#946C23112yescomplemented
169Q8×Dic3C2318yescomplemented
170#940C23112yescomplemented
171#940C23112yescomplemented
172#940C23148yescomplemented
173#939C23148yescomplemented
174#939C23124yescomplemented
175#938C23124yescomplemented
176#938C23112yescomplemented
177#937C23112yes—
178#937C23124yes—
179#936C23112yescomplemented
180#935C2314yes—
181D4×Dic3C23124yescomplemented
182#930C23112yescomplemented
183#930C23124yescomplemented
184#929C2314yes—
185C4×#67C23124yescomplemented
186C4×#67C23124yescomplemented
187#926C2316yes—
188#924C23112yescomplemented
189#897C23112yescomplemented
190#896C23124yescomplemented
191#895C23124yescomplemented
192#895C23112yescomplemented
193#894C2318yes—
194#893C23124yescomplemented
195#892C23112yes—
196D3×C4⋊C4C2318yes—
197D3×C4⋊C4C23112yes—
198#887C23124yescomplemented
199#886C2314yes—
200#885C23148yescomplemented
201#884C23148yescomplemented
202#884C23124yescomplemented
203#883C2318yes—
204#882C23112yes—
205#882C23124yes—
206#67⋊C4C23124yescomplemented
207#67⋊C4C23124yescomplemented
208D3×C22⋊C4C2314yes—
209D3×C22⋊C4C2318yes—
210D3×C22⋊C4C23124yes—
211#878C23124yescomplemented
212#877C23112yes—
213#875C23112yescomplemented
214#874C23112yescomplemented
215C4×D12C23124yescomplemented
216#872C23112yes—
217C42×D3C23112yes—
218C4×Dic6C23124yescomplemented
219C2×2−1+4—36no—
220C2×2−1+4—34no—
221C2×2−1+4—31no—
222C2×2−1+4—34no—
223C2×2−1+4—616no—
224C2×2−1+4C2×D311yescharacteristic, complemented
225C22×#41—38no—
226C22×#41—38no—
227C22×#41—36no—
228C22×#41—34no—
229C22×#41—31no—
230C22×#41—33no—
231C22×#41—33no—
232C22×#41—616no—
233C22×#41C2×D311yescharacteristic, complemented
234C23×Q8—31no—
235C23×Q8—34no—
236C23×D4—33no—
237C24×C4—33no—
238#550—38no—
239#550—38no—
240#550—324no—
241#550—324no—
242#550—324no—
243#550—38no—
244#550—324no—
245#550C2×D318yescomplemented
246#548—38no—
247#548—38no—
248#548—324no—
249#548—324no—
250#548—324no—
251#548—38no—
252#548—324no—
253#548C2×D318yescomplemented
254#535—36no—
255#535—36no—
256#535—312no—
257#535—312no—
258#535—324no—
259#535—324no—
260#535—36no—
261#535C2×D316yescomplemented
262C2×#127—312no—
263C2×#124—312no—
264#525—36no—
265#525—36no—
266#525—312no—
267#525—312no—
268#525—312no—
269#525—312no—
270#525—324no—
271#525—36no—
272#525C2×D316yescomplemented
273C2×#123—34no—
274C2×C22⋊Q8—312no—
275C2×#121—312no—
276C2×#121—324no—
277C2×#120—312no—
278#519—31no—
279#519—38no—
280#519—36no—
281#519C2×D311yescharacteristic, complemented
282C2×C4×Q8—38no—
283C2×C4×D4—324no—
284C2×#117—36no—
285C24×C3C2413yes—
286C23×D3—212no—
287C23×D3—412no—
288C23×D3C2416yes—
289C23×D3C2414yes—
290C23×D3C2411yescharacteristic
291C23×D3C2413yes—
292C23×D3C2416yes—
293C3×#41—232no—
294C3×#41—216no—
295C3×#41—224no—
296C2×C3×Q8—216no—
297C2×C3×Q8C2×D418yescomplemented
298C2×C3×Q8C2416yes—
299C2×C3×Q8C2414yes—
300C2×C3×D4—212no—
301C2×C3×D4C2414yes—
302C2×C3×D4C24112yes—
303C2×C3×D4C2416yes—
304C2×C3×D4C24124yes—
305C22×C3×C4—212no—
306C22×C3×C4C24112yes—
307C22×C3×C4C24112yes—
308C22×C3×C4C2411yescharacteristic
309C22×C3×C4C2413yes—
310C2×#67—224no—
311C2×#67C2414yes—
312C2×#67C2414yes—
313C2×#67C24124yes—
314C2×#67C24112yes—
315C2×#67C24124yes—
316C2×#67C24124yes—
317C22×Dic3—212no—
318C22×Dic3C24112yes—
319C22×Dic3C24112yes—
320C22×Dic3C2411yescharacteristic
321C22×Dic3C2413yes—
322#239—232no—
323#239—216no—
324#239—224no—
325D3×Q8—216no—
326D3×Q8—224no—
327D3×Q8—248no—
328D3×Q8C2×D4132yes—
329D3×Q8C2×D4132yescomplemented
330#237—248no—
331#237—224no—
332#237—296no—
333#237—248no—
334D3×D4—216no—
335D3×D4—248no—
336D3×D4—248no—
337D3×D4—224no—
338D3×D4—448no—
339#235—224no—
340#235—248no—
341#235—296no—
342#235—248no—
343C2×D12—212no—
344C2×D12C2416yes—
345C2×D12C24112yes—
346C2×D12C2414yes—
347C2×D12C24124yes—
348C2×C4×D3—24no—
349C2×C4×D3—212no—
350C2×C4×D3—212no—
351C2×C4×D3—248no—
352C2×C4×D3—248no—
353C2×C4×D3—248no—
354C2×C4×D3C2×D4124yes—
355C2×C4×D3C2418yes—
356C2×C4×D3C24112yes—
357C2×C4×D3C24112yes—
358C2×C4×D3C2414yes—
359C2×C4×D3C2412yes—
360C2×C4×D3C24112yes—
361C2×C4×D3C24112yes—
362C2×C4×D3C2412yes—
363C2×C4×D3C2416yes—
364C2×C4×D3C2416yes—
365C2×Dic6—248no—
366C2×Dic6C2×D4124yescomplemented
367C2×Dic6C2416yes—
368C2×Dic6C24112yes—
369C2×Dic6C24112yes—
370C3×C4⋊C4C24112yes—
371C3×C4⋊C4C2418yes—
372C3×C22⋊C4C2414yes—
373C3×C22⋊C4C24124yes—
374C3×C22⋊C4C2418yes—
375C3×C42C24112yes—
376#217C2414yes—
377#217C24124yes—
378#217C2418yes—
379(C2×D3)⋊C4C2418yes—
380(C2×D3)⋊C4C2418yes—
381(C2×D3)⋊C4C24124yes—
382(C2×D3)⋊C4C24124yes—
383(C2×D3)⋊C4C2418yes—
384C4⋊Dic3C24112yes—
385C4⋊Dic3C2418yes—
386Dic3⋊C4C24124yes—
387Dic3⋊C4C2418yes—
388Dic3⋊C4C2418yes—
389C4×Dic3C24124yes—
390C4×Dic3C24112yes—
391C25—33no—
3922−1+4—28no—
3932−1+4—632no—
3942−1+4—632no—
3952−1+4—648no—
3962−1+4—68no—
397C2×#41—28no—
398C2×#41—36no—
399C2×#41—38no—
400C2×#41—34no—
401C2×#41—312no—
402C2×#41—36no—
403C2×#41—324no—
404C2×#41—312no—
405C2×#41—312no—
406C2×#41—36no—
407C2×#41—324no—
408C2×#41—312no—
409C2×#41—624no—
410C2×#41—648no—
411C2×#41—624no—
412C2×#41—664no—
413C2×#41—664no—
414C2×#41—632no—
415C2×#41—68no—
416C2×#41C22×D316yes—
417C2×#41C22×D318yes—
418C2×#41C22×D314yescomplemented
419C22×Q8—316no—
420C22×Q8—34no—
421C22×Q8—34no—
422C22×Q8—36no—
423C22×Q8—312no—
424C22×Q8—34no—
425C22×Q8—33no—
426C22×Q8—312no—
427C22×Q8—632no—
428C22×Q8C22×D311yescharacteristic
429C22×Q8C22×D314yescomplemented
430C22×D4—36no—
431C22×D4—34no—
432C22×D4—312no—
433C22×D4—36no—
434C22×D4—312no—
435C22×D4—324no—
436C22×D4—33no—
437C22×D4—624no—
438C22×D4C22×D313yes—
439C23×C4—33no—
440C23×C4—33no—
441C23×C4—312no—
442C23×C4—312no—
443C23×C4—31no—
444C23×C4—33no—
445C23×C4—312no—
446C23×C4—33no—
447C23×C4—624no—
448C23×C4C22×D313yes—
449#127—348no—
450#127—312no—
451#127—312no—
452#127—312no—
453#127C22×D3112yescomplemented
454#124—312no—
455#124—312no—
456#124—348no—
457#124—312no—
458#124C22×D3112yescomplemented
459#123—34no—
460#123—34no—
461#123—38no—
462#123—38no—
463#123—34no—
464#123C22×D314yes—
465C22⋊Q8—312no—
466C22⋊Q8—312no—
467C22⋊Q8—324no—
468C22⋊Q8—312no—
469C22⋊Q8—324no—
470C22⋊Q8C22×D3112yescomplemented
471#121—312no—
472#121—324no—
473#121—324no—
474#121—348no—
475#121—312no—
476#121—324no—
477#121—312no—
478#121—324no—
479#121—324no—
480#121—348no—
481#121C22×D3112yescomplemented
482#121C22×D3124yescomplemented
483#120—312no—
484#120—312no—
485#120—324no—
486#120—324no—
487#120—312no—
488#120C22×D3112yes—
489C4×Q8—38no—
490C4×Q8—324no—
491C4×Q8—324no—
492C4×Q8C22×D318yescomplemented
493C4×D4—324no—
494C4×D4—324no—
495C4×D4—324no—
496C4×D4—324no—
497C4×D4—324no—
498C4×D4—324no—
499C4×D4—324no—
500C4×D4C22×D3124yescomplemented
501#117—36no—
502#117—312no—
503#117—312no—
504#117—312no—
505#117C22×D316yes—
506C2×C4⋊C4—312no—
507C2×C4⋊C4—38no—
508C2×C22⋊C4—34no—
509C2×C22⋊C4—38no—
510C2×C22⋊C4—324no—
511C2×C42—312no—
512C23×C3—26no—
513C23×C3—46no—
514C23×C3C2516yes—
515C23×C3C2514yes—
516C23×C3C2511yescharacteristic
517C22×D3—24no—
518C22×D3—26no—
519C22×D3—28no—
520C22×D3—212no—
521C22×D3—212no—
522C22×D3—216no—
523C22×D3—224no—
524C22×D3—412no—
525C22×D3—46no—
526C22×D3—448no—
527C22×D3C22×D414yes—
528C22×D3C2516yes—
529C22×D3C2514yes—
530C22×D3C2511yescharacteristic
531C22×D3C2511yescharacteristic
532C3×Q8—212no—
533C3×Q8C22×D4116yes—
534C3×D4—28no—
535C3×D4—224no—
536C3×D4—212no—
537C3×D4—424no—
538C2×C3×C4—22no—
539C2×C3×C4—224no—
540C2×C3×C4—224no—
541C2×C3×C4C22×D4112yes—
542C2×C3×C4C2518yes—
543C2×C3×C4C2512yes—
544C2×C3×C4C2514yes—
545C2×C3×C4C2516yes—
546#67—28no—
547#67—28no—
548#67—224no—
549#67—248no—
550#67—424no—
551#67—424no—
552C2×Dic3—22no—
553C2×Dic3—224no—
554C2×Dic3—224no—
555C2×Dic3C22×D4112yes—
556C2×Dic3C2518yes—
557C2×Dic3C2512yes—
558C2×Dic3C2514yes—
559C2×Dic3C2516yes—
560D12—28no—
561D12—224no—
562D12—212no—
563D12—424no—
564C4×D3—24no—
565C4×D3—24no—
566C4×D3—28no—
567C4×D3—216no—
568C4×D3—224no—
569C4×D3—224no—
570C4×D3—224no—
571C4×D3—224no—
572C4×D3C22×D4124yes—
573C4×D3C22×D4124yes—
574Dic6—212no—
575Dic6—224no—
576Dic6C22×D4148yes—
577C24—31no—
578C24—36no—
579C24—34no—
580C24—36no—
581C24—33no—
582C24—612no—
583C24—1212no—
584C24C23×D313yes—
585#41—232no—
586#41—216no—
587#41—224no—
588#41—648no—
589#41—696no—
590#41—648no—
591#41—648no—
592#41—624no—
593#41—624no—
594#41—696no—
595#41—648no—
596#41—632no—
597#41—616no—
598#41—624no—
599C2×Q8—216no—
600C2×Q8—332no—
601C2×Q8—332no—
602C2×Q8—324no—
603C2×Q8—312no—
604C2×Q8—312no—
605C2×Q8—36no—
606C2×Q8—648no—
607C2×Q8—624no—
608C2×Q8—648no—
609C2×Q8—616no—
610C2×Q8D3×D418yescomplemented
611C2×Q8C23×D316yes—
612C2×Q8C23×D314yes—
613C2×D4—212no—
614C2×D4—34no—
615C2×D4—34no—
616C2×D4—324no—
617C2×D4—312no—
618C2×D4—324no—
619C2×D4—324no—
620C2×D4—34no—
621C2×D4—312no—
622C2×D4—36no—
623C2×D4—324no—
624C2×D4—648no—
625C2×D4—648no—
626C2×D4—624no—
627C2×D4—624no—
628C2×D4—616no—
629C2×D4—612no—
630C2×D4—1248no—
631C2×D4C23×D314yes—
632C2×D4C23×D3112yes—
633C2×D4C23×D316yes—
634C2×D4C23×D3124yes—
635C22×C4—212no—
636C22×C4—33no—
637C22×C4—324no—
638C22×C4—36no—
639C22×C4—36no—
640C22×C4—312no—
641C22×C4—312no—
642C22×C4—31no—
643C22×C4—38no—
644C22×C4—34no—
645C22×C4—32no—
646C22×C4—312no—
647C22×C4—312no—
648C22×C4—312no—
649C22×C4—312no—
650C22×C4—32no—
651C22×C4—612no—
652C22×C4—648no—
653C22×C4—648no—
654C22×C4—648no—
655C22×C4—64no—
656C22×C4—612no—
657C22×C4—612no—
658C22×C4C23×D3112yes—
659C22×C4C23×D3112yes—
660C22×C4C23×D311yescharacteristic
661C22×C4C23×D313yes—
662C4⋊C4—324no—
663C4⋊C4—312no—
664C4⋊C4—38no—
665C4⋊C4—38no—
666C4⋊C4—38no—
667C4⋊C4C23×D3112yes—
668C4⋊C4C23×D318yes—
669C22⋊C4—34no—
670C22⋊C4—38no—
671C22⋊C4—324no—
672C22⋊C4—38no—
673C22⋊C4—38no—
674C22⋊C4—38no—
675C22⋊C4—324no—
676C22⋊C4—324no—
677C22⋊C4C23×D314yes—
678C22⋊C4C23×D318yes—
679C22⋊C4C23×D3124yes—
680C42—324no—
681C42—312no—
682C42C23×D3112yes—
683C22×C3—22no—
684C22×C3—24no—
685C22×C3—26no—
686C22×C3—28no—
687C22×C3—212no—
688C22×C3—412no—
689C22×C3C23×D412yes—
690C22×C3C2611yescharacteristic
691C2×D3—22no—
692C2×D3—28no—
693C2×D3—24no—
694C2×D3—26no—
695C2×D3—28no—
696C2×D3—212no—
697C2×D3—424no—
698C2×D3—412no—
699C2×D3—416no—
700C2×D3—424no—
701C2×D3C23×D412yes—
702C2×D3C23×D412yes—
703C2×D3#58514yes—
704C3×C4—24no—
705C3×C4—22no—
706C3×C4—28no—
707C3×C4C23×D4112yes—
708Dic3—24no—
709Dic3—22no—
710Dic3—28no—
711Dic3C23×D4112yes—
712C23—26no—
713C23—31no—
714C23—34no—
715C23—31no—
716C23—36no—
717C23—34no—
718C23—46no—
719C23—64no—
720C23—68no—
721C23—612no—
722C23—612no—
723C23—616no—
724C23—624no—
725C23—66no—
726C23—126no—
727C23—1212no—
728C23—1248no—
729C23C24×D316yes—
730C23C24×D314yes—
731C23C24×D311yescharacteristic
732Q8—212no—
733Q8—348no—
734Q8—624no—
735Q8—612no—
736Q8C2×D3×D4116yes—
737D4—28no—
738D4—224no—
739D4—212no—
740D4—424no—
741D4—68no—
742D4—648no—
743D4—624no—
744D4—68no—
745D4—68no—
746D4—624no—
747D4—612no—
748D4—1224no—
749D4—1224no—
750D4—1224no—
751C2×C4—22no—
752C2×C4—224no—
753C2×C4—224no—
754C2×C4—312no—
755C2×C4—36no—
756C2×C4—324no—
757C2×C4—324no—
758C2×C4—38no—
759C2×C4—34no—
760C2×C4—32no—
761C2×C4—624no—
762C2×C4—624no—
763C2×C4—64no—
764C2×C4—64no—
765C2×C4—68no—
766C2×C4—616no—
767C2×C4—624no—
768C2×C4—624no—
769C2×C4—62no—
770C2×C4—624no—
771C2×C4—624no—
772C2×C4C2×D3×D4112yes—
773C2×C4C24×D318yes—
774C2×C4C24×D314yes—
775C2×C4C24×D312yes—
776C2×C4C24×D316yes—
777C2×C3—22no—
778C2×C3—46no—
779C2×C3—44no—
780C2×C3C24×D411yescharacteristic
781C2×C3C2×#58512yes—
782D3—22no—
783D3—44no—
784D3—46no—
785D3#348714yesdirect product factor
786C22—22no—
787C22—24no—
788C22—26no—
789C22—28no—
790C22—212no—
791C22—32no—
792C22—34no—
793C22—32no—
794C22—412no—
795C22—68no—
796C22—62no—
797C22—64no—
798C22—66no—
799C22—68no—
800C22—612no—
801C22—1212no—
802C22—1224no—
803C22—1216no—
804C22—1224no—
805C22C22×D3×D412yes—
806C22C25×D311yescharacteristic
807C4—22no—
808C4—24no—
809C4—28no—
810C4—312no—
811C4—62no—
812C4—64no—
813C4—68no—
814C4C22×D3×D4112yes—
815C3C2×#348711yescharacteristic, complemented, Sylow
816C2—22no—
817C2—34no—
818C2—46no—
819C2—44no—
820C2—62no—
821C2—126no—
822C2—124no—
823C2C23×D3×D411yescharacteristic
824C2D3×#58512yes—
subgroupG/H
center, FrattiniC22C25×D3
commutator, socle, cosocleC22×C3C26
FittingC3×#3487C2
hypercenter#3487D3
hypocenterC3C2×#3487
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ #3487

Complements

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

NH ≅ G/Ntype
1. C2×D3×2−1+4C2semidirect
2. C22×D3×#41C2semidirect
3. C3×#3487C2semidirect
4. #87290C2semidirect
5. #87274C2semidirect
6. #86783C2semidirect
7. D3×#550C2semidirect
8. #86736C2semidirect
9. D3×#548C2semidirect
10. D3×#535C2semidirect
11. #86315C2semidirect
12. D3×#525C2semidirect
13. #86023C2semidirect
14. D3×#519C2semidirect
15. #85874C2semidirect
17. C2×C3×2−1+4C22semidirect
18. C22×C3×#41C22semidirect
20. C2×#1010C22semidirect
21. C2×#1010C22semidirect
25. C2×D3×#41C22semidirect
26. C2×D3×#41C22semidirect
27. C2×#1007C22semidirect
28. C2×#1007C22semidirect
29. C22×#239C22semidirect
31. C22×D3×Q8C22semidirect
32. C22×#237C22semidirect
34. C22×#235C22semidirect
36. C3×#550C22semidirect
37. C3×#548C22semidirect
38. C3×#535C22semidirect
39. C3×#525C22semidirect
40. C3×#519C22semidirect
41. #5834C22semidirect
42. #5834C22semidirect
43. #5831C22semidirect
44. #5830C22semidirect
45. #5828C22semidirect
46. #5817C22semidirect
47. #5812C22semidirect
48. #5805C22semidirect
49. #5791C22semidirect
50. #5718C22semidirect
51. #5715C22semidirect
52. D3×#127C22semidirect
53. #5677C22semidirect
54. #5674C22semidirect
55. D3×#124C22semidirect
56. #5656C22semidirect
58. #5633C22semidirect
59. #5627C22semidirect
60. D3×C22⋊Q8C22semidirect
61. #5607C22semidirect
62. #5606C22semidirect
63. D3×#121C22semidirect
64. D3×#121C22semidirect
65. #5599C22semidirect
66. #5599C22semidirect
67. #5598C22semidirect
68. #5592C22semidirect
70. #5586C22semidirect
71. #5577C22semidirect
72. #5576C22semidirect
73. #5572C22semidirect
74. C4×D3×Q8C22semidirect
75. #5553C22semidirect
76. #5552C22semidirect
77. #5547C22semidirect
78. C4×D3×D4C22semidirect
79. #5525C22semidirect
80. #5524C22semidirect
82. #5516C22semidirect
92. #3487D3direct (N × H)
103. C2×C3×#41C23semidirect
105. C22×C3×Q8C23semidirect
121. C2×#239C23semidirect
123. C2×D3×Q8D4semidirect
127. C2×D3×Q8C23semidirect
128. C2×D3×Q8C23semidirect
133. C2×#237C23semidirect
144. C2×#235C23semidirect
155. C22×Dic6C23semidirect
156. C3×#127C23semidirect
157. C3×#124C23semidirect
159. C3×C22⋊Q8C23semidirect
160. C3×#121C23semidirect
161. C3×#121C23semidirect
163. C3×C4×Q8C23semidirect
164. C3×C4×D4C23semidirect
167. #947C23semidirect
168. #946C23semidirect
169. Q8×Dic3C23semidirect
170. #940C23semidirect
171. #940C23semidirect
172. #940C23semidirect
173. #939C23semidirect
174. #939C23semidirect
175. #938C23semidirect
176. #938C23semidirect
179. #936C23semidirect
181. D4×Dic3C23semidirect
182. #930C23semidirect
183. #930C23semidirect
185. C4×#67C23semidirect
186. C4×#67C23semidirect
188. #924C23semidirect
189. #897C23semidirect
190. #896C23semidirect
191. #895C23semidirect
192. #895C23semidirect
194. #893C23semidirect
198. #887C23semidirect
200. #885C23semidirect
201. #884C23semidirect
202. #884C23semidirect
206. #67⋊C4C23semidirect
207. #67⋊C4C23semidirect
211. #878C23semidirect
213. #875C23semidirect
214. #874C23semidirect
215. C4×D12C23semidirect
218. C4×Dic6C23semidirect
224. C2×2−1+4C2×D3semidirect
233. C22×#41C2×D3semidirect
245. #550C2×D3semidirect
253. #548C2×D3semidirect
261. #535C2×D3semidirect
272. #525C2×D3semidirect
281. #519C2×D3semidirect
297. C2×C3×Q8C2×D4semidirect
329. D3×Q8C2×D4semidirect
366. C2×Dic6C2×D4semidirect
418. C2×#41C22×D3semidirect
429. C22×Q8C22×D3semidirect
453. #127C22×D3semidirect
458. #124C22×D3semidirect
470. C22⋊Q8C22×D3semidirect
481. #121C22×D3semidirect
482. #121C22×D3semidirect
492. C4×Q8C22×D3semidirect
500. C4×D4C22×D3semidirect
610. C2×Q8D3×D4semidirect
785. D3#3487direct (N × H)
815. C3C2×#3487semidirect

Maximal subgroups

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

subgroupindex
C2×D3×2−1+42
C22×D3×#412
C3×#34872
#872902
#872742
#867832
D3×#5502
#867362
D3×#5482
D3×#5352
#863152
D3×#5252
#860232
D3×#5192
#858742
C2×#34873