Finite Group Databasebeta

← #11904349

Subgroups — #11904349

Order 1152.

3967 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D3×D4C211yesmaximal, characteristic, complemented
2C2×#64307C211yesmaximal, characteristic, complemented
3#10596276C211yesmaximal, characteristic, complemented
4C3×#5805C211yesmaximal, characteristic, complemented
5#10595524C214yesmaximal, complemented
6D3×#953C214yesmaximal, complemented
7#10595293C214yesmaximal, complemented
8#10595288C214yesmaximal, complemented
9#10595229C214yesmaximal, complemented
10#10595228C214yesmaximal, complemented
11#10595023C211yesmaximal, characteristic, complemented
12#10595022C211yesmaximal, characteristic, complemented
13#10594982C211yesmaximal, characteristic, complemented
14#87239—31nomaximal
15#86330—31nomaximal
16C24×C3×D3C2212yescomplemented
17C22×C32×D4C2211yescharacteristic, complemented
18C2×#3828C2211yescharacteristic, complemented
19C22×C3×#67C2212yescomplemented
20C2×C3×D3×D4—28no—
21C2×C3×D3×D4C2214yescomplemented
22C2×C3×D3×D4C2214yescomplemented
23C2×C3×#235C2211yescharacteristic, complemented
24C22×C3×D12C2211yescharacteristic
25C22×C3×C4×D3C2211yescharacteristic, complemented
26C2×D3×#67C2218yescomplemented
27C2×D3×#67C2214yescomplemented
28#64307—28no—
29C2×#3802C2212yescomplemented
30C2×D3×D12C2212yescomplemented
31C2×#3796C2212yescomplemented
32C2×#3795C2212yescomplemented
33#64162C2214yescomplemented
34#64149C2212yescomplemented
35#64147C2214yescomplemented
36#64145C2212yescomplemented
37#64135C2211yescharacteristic, complemented
38C3×#953C2214yescomplemented
39C3×#940C2212yescomplemented
40C3×#938C2214yescomplemented
41C3×#936C2212yescomplemented
42C3×#926C2211yescharacteristic, complemented
43#63983C2218yescomplemented
44#63977C2212yescomplemented
45#63977C2218yescomplemented
46#63976C2212yescomplemented
47#63976C2218yescomplemented
48#63971C2218yescomplemented
49#63970C2218yescomplemented
50#63969C2218yescomplemented
51D3×#217C2218yescomplemented
52D3×#217C2214yescomplemented
53#63966C2212yescomplemented
54#63961C2212yescomplemented
55#63909C2212yescomplemented
56#63908C2212yescomplemented
57C4×#626C2214yescomplemented
58C4×#625C2214yescomplemented
59#63898C2214yescomplemented
60Dic3×D12C2214yescomplemented
61#63857C2212yescomplemented
62#63856C2212yescomplemented
63C23×C3×D4—31no—
64C2×#1009—31no—
65C2×#1004—31no—
66C22×D3×D4D311yescharacteristic, complemented
67C3×#535—31no—
68C2×#953—34no—
69#5828—31no—
70#5806—34no—
71#5806—34no—
72#5805—31no—
73#5805—31no—
74#5805—61no—
75#5805D311yescharacteristic, complemented
76#5804—34no—
77D4×#67—34no—
78D4×#67—34no—
79#5798—31no—
80#5791—31no—
81#5791—31no—
82#5717—34no—
83#5676—34no—
84#5612—34no—
85#5609—34no—
86#5589—34no—
87D3×#120—34no—
88#5524—31no—
89#5521—31no—
90C24×C32C2312yes—
91C23×C3×D3—28no—
92C23×C3×D3—48no—
93C23×C3×D3C2311yescharacteristic
94C23×C3×D3C2318yes—
95C23×C3×D3C2312yes—
96C22×D32C2314yescomplemented
97C2×C32×D4—24no—
98C2×C32×D4C2312yes—
99C2×C32×D4C2312yes—
100C22×C32×C4C2311yescharacteristic
101C2×#638C2312yes—
102C2×#638C2318yescomplemented
103#3828—24no—
104C2×C4⋊(C3⋊D3)C2311yescharacteristic, complemented
105C2×C4×C3⋊D3C2312yescomplemented
106C2×#634C2311yescharacteristic, complemented
107C2×C3×#67—28no—
108C2×C3×#67C2312yes—
109C2×C3×#67C2318yes—
110C2×C3×#67C2318yescomplemented
111C22×C3×Dic3C2311yescharacteristic
112C3×D3×D4—216no—
113C3×D3×D4—216no—
114C3×#235—24no—
115C2×C3×D12D418yescomplemented
116C2×C3×D12C2312yes—
117C2×C3×D12C2312yes—
118C2×C3×D12C2311yescharacteristic, complemented
119C2×C3×C4×D3—24no—
120C2×C3×C4×D3C2312yes—
121C2×C3×C4×D3C2312yes—
122C2×C3×C4×D3C2312yescomplemented
123C2×C3×Dic6C2311yescharacteristic, complemented
124D3×#67—216no—
125D3×#67—416no—
126C2×#626C2314yes—
127C2×#626C2314yescomplemented
128C2×#625C2314yes—
129C2×#625C2314yescomplemented
130C2×D3×Dic3C2314yescomplemented
131C2×D3×Dic3C2318yescomplemented
132#3802—28no—
133D3×D12—28no—
134#3796—28no—
135#3795—28no—
136#3757C2312yes—
137#3757C2318yescomplemented
138C4⋊(C3⋊Dic3)C2312yescomplemented
139C4×C3⋊Dic3C2312yescomplemented
140C3×#217C2312yes—
141C3×#217C2318yescomplemented
142C3×C4⋊Dic3C2312yescomplemented
143C3×C4×Dic3C2312yescomplemented
144#3724C2314yescomplemented
145Dic3⋊Dic3C2314yescomplemented
146#3722C2314yescomplemented
147(C2×D3)⋊Dic3C2314yes—
148(C2×D3)⋊Dic3C2314yes—
149(C2×D3)⋊Dic3C2318yescomplemented
150(C2×D3)⋊Dic3C2314yescomplemented
151#3484—91noSylow
152C25×C3—32no—
153C24×D3C2×D312yescomplemented
154C2×C3×#41—31no—
155C22×C3×D4—21no—
156C22×C3×D4—32no—
157C22×C3×D4—34no—
158C22×C3×D4—34no—
159C22×C3×D4—31no—
160C22×C3×D4—68no—
161C22×C3×D4C2×D311yescharacteristic, complemented
162C22×C3×D4C2×D311yescharacteristic, complemented
163C23×C3×C4—31no—
164C22×#67—34no—
165C22×#67—38no—
166C22×#67C2×D312yescomplemented
167#1009—68no—
168C2×#239—32no—
169#1004—68no—
170C2×#237—32no—
171C2×#237—32no—
172C2×D3×D4—28no—
173C2×D3×D4—34no—
174C2×D3×D4—38no—
175C2×D3×D4—32no—
176C2×D3×D4—32no—
177C2×D3×D4—32no—
178C2×D3×D4C2×D314yescomplemented
179C2×D3×D4C2×D314yescomplemented
180C2×#235—31no—
181C2×#235—31no—
182C2×#235—32no—
183C2×#235—61no—
184C2×#235C2×D311yescharacteristic, complemented
185C22×D12—32no—
186C22×D12C2×D311yescharacteristic
187C22×C4×D3C2×D311yescharacteristic, complemented
188C3×#127—32no—
189C3×#124—32no—
190C3×#121—34no—
191C3×#120—34no—
192C3×#117—31no—
193#953—34no—
194#953—34no—
195#953—32no—
196#953—38no—
197#953—32no—
198#953—38no—
199#953—64no—
200#953C2×D314yescomplemented
201C2×#217—34no—
202C2×#217—38no—
203#946—32no—
204#940—32no—
205#940—32no—
206#940—62no—
207#940C2×D312yescomplemented
208#939—38no—
209#939—38no—
210#938—34no—
211#938—34no—
212#938—38no—
213#938—32no—
214#938—64no—
215#938C2×D314yescomplemented
216#937—38no—
217#937—32no—
218#937—38no—
219#937—38no—
220#936—32no—
221#936—32no—
222#936—62no—
223#936C2×D312yescomplemented
224#935—32no—
225#935—38no—
226D4×Dic3—34no—
227D4×Dic3—34no—
228#930—32no—
229#930—32no—
230#929—32no—
231#929—32no—
232C4×#67—34no—
233C4×#67—34no—
234C4×#67—34no—
235#926—31no—
236#926—31no—
237#926—61no—
238#926C2×D311yescharacteristic, complemented
239#924—32no—
240#924—32no—
241#897—32no—
242#895—32no—
243#893—34no—
244#886—32no—
245#884—38no—
246#883—38no—
247#882—38no—
248#882—32no—
249D3×C22⋊C4—38no—
250D3×C22⋊C4—34no—
251C4×D12—34no—
252C4×D12—34no—
253C23×C32—24no—
254C23×C32—44no—
255C23×C32C2414yes—
256C23×C32C2411yescharacteristic
257C22×C3⋊D3C2412yes—
258C22×C3×D3—22no—
259C22×C3×D3—24no—
260C22×C3×D3—216no—
261C22×C3×D3—216no—
262C22×C3×D3—44no—
263C22×C3×D3—48no—
264C22×C3×D3—432no—
265C22×C3×D3C2×D418yescomplemented
266C22×C3×D3C2412yes—
267C22×C3×D3C2414yes—
268C22×C3×D3C2412yes—
269C2×D32—28no—
270C2×D32—48no—
271C32×D4—24no—
272C32×D4—24no—
273C2×C32×C4C2×D414yescomplemented
274C2×C32×C4C2411yescharacteristic
275C2×C32×C4C2411yescharacteristic
276#638—24no—
277#638—48no—
278C2×C3⋊Dic3C2412yes—
279C2×C3⋊Dic3C2414yes—
280C4⋊(C3⋊D3)—22no—
281C4×C3⋊D3—24no—
282#634—22no—
283C3×#67—24no—
284C3×#67—216no—
285C3×#67—48no—
286C2×C3×Dic3—22no—
287C2×C3×Dic3C2412yes—
288C2×C3×Dic3C2414yes—
289C2×C3×Dic3C2412yes—
290C3×D12—22no—
291C3×D12C2×D418yescomplemented
292C3×D12C2×D418yescomplemented
293C3×C4×D3—24no—
294C3×C4×D3—24no—
295C3×C4×D3—24no—
296C3×Dic6—22no—
297#626—28no—
298#626—28no—
299#625—28no—
300#625—28no—
301D3×Dic3—28no—
302D3×Dic3—48no—
303C2×H(5,𝔽2)—91no—
304C23×D4—31no—
305#546—94no—
306#546—94no—
307D42—94no—
308D42—94no—
309#535—31no—
310#535—91no—
311#534—94no—
312#525—91no—
313#525—91no—
314C2×#120—94no—
315#518—91no—
316C24×C3—22no—
317C24×C3—32no—
318C24×C3—31no—
319C24×C3—38no—
320C24×C3—68no—
321C24×C3—128no—
322C24×C3C22×D312yes—
323C24×C3C22×D312yes—
324C23×D3—28no—
325C23×D3—34no—
326C23×D3—34no—
327C23×D3—48no—
328C23×D3C22×D311yescharacteristic
329C23×D3C22×D318yes—
330C23×D3C22×D312yes—
331C3×#41—64no—
332C2×C3×Q8—31no—
333C2×C3×D4—24no—
334C2×C3×D4—24no—
335C2×C3×D4—22no—
336C2×C3×D4—22no—
337C2×C3×D4—38no—
338C2×C3×D4—32no—
339C2×C3×D4—38no—
340C2×C3×D4—38no—
341C2×C3×D4—32no—
342C2×C3×D4—32no—
343C2×C3×D4—31no—
344C2×C3×D4—44no—
345C2×C3×D4—616no—
346C2×C3×D4—616no—
347C2×C3×D4—68no—
348C2×C3×D4C22×D312yes—
349C2×C3×D4C22×D312yes—
350C2×C3×D4C22×D312yes—
351C2×C3×D4C22×D312yes—
352C22×C3×C4—21no—
353C22×C3×C4—31no—
354C22×C3×C4—32no—
355C22×C3×C4—32no—
356C22×C3×C4—32no—
357C22×C3×C4—64no—
358C22×C3×C4C22×D311yescharacteristic
359C22×C3×C4C22×D311yescharacteristic
360C2×#67—28no—
361C2×#67—32no—
362C2×#67—32no—
363C2×#67—34no—
364C2×#67—34no—
365C2×#67—34no—
366C2×#67—34no—
367C2×#67—38no—
368C2×#67—38no—
369C2×#67—34no—
370C2×#67—34no—
371C2×#67—62no—
372C2×#67—68no—
373C2×#67—616no—
374C2×#67—1216no—
375C2×#67C22×D318yes—
376C2×#67C22×D312yes—
377C2×#67C22×D318yescomplemented
378C22×Dic3—34no—
379C22×Dic3—38no—
380C22×Dic3C22×D311yescharacteristic
381#239—68no—
382#237—68no—
383#237—68no—
384D3×D4—216no—
385D3×D4—216no—
386D3×D4—68no—
387D3×D4—68no—
388D3×D4—616no—
389D3×D4—68no—
390D3×D4—1216no—
391#235—24no—
392#235—64no—
393#235—64no—
394#235—68no—
395#235—124no—
396C2×D12—34no—
397C2×D12—34no—
398C2×D12—31no—
399C2×D12—31no—
400C2×D12—61no—
401C2×D12—68no—
402C2×D12#6718yescomplemented
403C2×D12C22×D312yes—
404C2×D12C22×D312yes—
405C2×D12C22×D311yescharacteristic, complemented
406C2×C4×D3—24no—
407C2×C4×D3—34no—
408C2×C4×D3—32no—
409C2×C4×D3—32no—
410C2×C4×D3—38no—
411C2×C4×D3—62no—
412C2×C4×D3C22×D312yes—
413C2×C4×D3C22×D312yes—
414C2×C4×D3C22×D312yescomplemented
415C2×Dic6—31no—
416C2×Dic6—31no—
417C2×Dic6—61no—
418C2×Dic6C22×D311yescharacteristic, complemented
419C3×C4⋊C4—32no—
420C3×C22⋊C4—32no—
421C3×C22⋊C4—38no—
422C3×C42—32no—
423#217—32no—
424#217—38no—
425#217—32no—
426#217—38no—
427#217—34no—
428#217—34no—
429#217—34no—
430#217—38no—
431#217—62no—
432#217—68no—
433#217C22×D312yes—
434#217C22×D318yescomplemented
435(C2×D3)⋊C4—34no—
436(C2×D3)⋊C4—38no—
437(C2×D3)⋊C4—34no—
438(C2×D3)⋊C4—34no—
439(C2×D3)⋊C4—34no—
440(C2×D3)⋊C4—34no—
441C4⋊Dic3—32no—
442C4⋊Dic3—32no—
443C4⋊Dic3—34no—
444C4⋊Dic3—62no—
445C4⋊Dic3C22×D312yescomplemented
446Dic3⋊C4—34no—
447Dic3⋊C4—34no—
448Dic3⋊C4—34no—
449C4×Dic3—32no—
450C4×Dic3—32no—
451C4×Dic3—62no—
452C4×Dic3C22×D312yescomplemented
453C22×C32—22no—
454C22×C32—24no—
455C22×C32—28no—
456C22×C32—48no—
457C22×C32C22×D412yes—
458C22×C32C2511yescharacteristic
459C2×C3⋊D3—22no—
460C2×C3⋊D3—24no—
461C2×C3×D3—28no—
462C2×C3×D3—22no—
463C2×C3×D3—28no—
464C2×C3×D3—22no—
465C2×C3×D3—22no—
466C2×C3×D3—24no—
467C2×C3×D3—48no—
468C2×C3×D3—432no—
469C2×C3×D3C22×D418yes—
470C2×C3×D3H(5,𝔽2)14yescomplemented
471D32—88no—
472C32×C4C22×D412yes—
473C32×C4C22×D412yes—
474C3⋊Dic3—22no—
475C3⋊Dic3—24no—
476C3×Dic3—22no—
477C3×Dic3—22no—
478C3×Dic3—24no—
479C25—32no—
480H(5,𝔽2)—188no—
481C2×#41—31no—
482C2×#41—92no—
483C2×#41—92no—
484C2×#41—91no—
485C22×D4—32no—
486C22×D4—34no—
487C22×D4—34no—
488C22×D4—31no—
489C22×D4—68no—
490C22×D4—92no—
491C22×D4—92no—
492C22×D4—94no—
493C22×D4—98no—
494C22×D4D3211yescharacteristic, complemented
495C23×C4—31no—
496#127—32no—
497#127—92no—
498#124—32no—
499#124—92no—
500#123—92no—
501#123—98no—
502#123—92no—
503C22⋊Q8—92no—
504C22⋊Q8—92no—
505#121—34no—
506#121—98no—
507#121—92no—
508#121—92no—
509#121—98no—
510#121—94no—
511#120—34no—
512#120—92no—
513#120—98no—
514#120—98no—
515#120—92no—
516#120—98no—
517#120—94no—
518C4×D4—94no—
519C4×D4—94no—
520C4×D4—94no—
521C4×D4—94no—
522#117—31no—
523#117—91no—
524C2×C22⋊C4—94no—
525C2×C22⋊C4—98no—
526C23×C3—24no—
527C23×C3—24no—
528C23×C3—21no—
529C23×C3—24no—
530C23×C3—32no—
531C23×C3—34no—
532C23×C3—38no—
533C23×C3—32no—
534C23×C3—44no—
535C23×C3—44no—
536C23×C3—44no—
537C23×C3—64no—
538C23×C3—616no—
539C23×C3—616no—
540C23×C3—62no—
541C23×C3—84no—
542C23×C3—124no—
543C23×C3—128no—
544C23×C3—1232no—
545C23×C3C23×D314yes—
546C23×C3C23×D314yes—
547C23×C3C23×D311yescharacteristic
548C23×C3C23×D311yescharacteristic
549C22×D3—22no—
550C22×D3—24no—
551C22×D3—216no—
552C22×D3—216no—
553C22×D3—32no—
554C22×D3—32no—
555C22×D3—44no—
556C22×D3—48no—
557C22×D3—432no—
558C22×D3—62no—
559C22×D3—68no—
560C22×D3—68no—
561C22×D3—128no—
562C22×D3—128no—
563C22×D3C2×#6718yescomplemented
564C22×D3C23×D312yes—
565C22×D3C23×D312yes—
566C22×D3C23×D314yes—
567C3×Q8—62no—
568C3×D4—24no—
569C3×D4—24no—
570C3×D4—24no—
571C3×D4—24no—
572C3×D4—38no—
573C3×D4—38no—
574C3×D4—44no—
575C3×D4—44no—
576C3×D4—616no—
577C3×D4—64no—
578C3×D4—62no—
579C3×D4—128no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—24no—
583C2×C3×C4—32no—
584C2×C3×C4—32no—
585C2×C3×C4—34no—
586C2×C3×C4—62no—
587C2×C3×C4—64no—
588C2×C3×C4—64no—
589C2×C3×C4—64no—
590C2×C3×C4D3×D414yescomplemented
591C2×C3×C4C2×#6714yescomplemented
592C2×C3×C4C23×D311yescharacteristic
593C2×C3×C4C23×D311yescharacteristic
594C2×C3×C4C23×D311yescharacteristic
595C2×C3×C4C23×D311yescharacteristic
596#67—24no—
597#67—216no—
598#67—48no—
599#67—68no—
600#67—68no—
601#67—68no—
602#67—68no—
603#67—64no—
604#67—64no—
605#67—68no—
606#67—68no—
607#67—124no—
608#67—128no—
609#67—128no—
610#67—248no—
611C2×Dic3—22no—
612C2×Dic3—34no—
613C2×Dic3—34no—
614C2×Dic3—32no—
615C2×Dic3—32no—
616C2×Dic3—64no—
617C2×Dic3—62no—
618C2×Dic3—68no—
619C2×Dic3—128no—
620C2×Dic3C23×D314yes—
621C2×Dic3C23×D312yes—
622C2×Dic3C23×D312yes—
623D12—22no—
624D12—68no—
625D12—68no—
626D12—62no—
627D12—62no—
628D12—122no—
629D12C2×#6718yescomplemented
630D12C2×#6718yescomplemented
631C4×D3—24no—
632C4×D3—24no—
633C4×D3—24no—
634C4×D3—68no—
635C4×D3—64no—
636C4×D3—64no—
637C4×D3—124no—
638C4×D3—128no—
639Dic6—22no—
640Dic6—62no—
641Dic6—62no—
642Dic6—122no—
643C2×C32—22no—
644C2×C32—44no—
645C2×C32C23×D411yescharacteristic
646C2×C32C2×H(5,𝔽2)12yes—
647C3⋊D3—42no—
648C3×D3—28no—
649C3×D3—24no—
650C3×D3—42no—
651C24—32no—
652C24—31no—
653C24—38no—
654C24—68no—
655C24—94no—
656C24—128no—
657C24C2×D3212yes—
658#41—64no—
659#41—188no—
660#41—188no—
661#41—184no—
662C2×Q8—31no—
663C2×Q8—91no—
664C2×D4—24no—
665C2×D4—32no—
666C2×D4—38no—
667C2×D4—38no—
668C2×D4—32no—
669C2×D4—32no—
670C2×D4—31no—
671C2×D4—38no—
672C2×D4—616no—
673C2×D4—616no—
674C2×D4—68no—
675C2×D4—94no—
676C2×D4—94no—
677C2×D4—94no—
678C2×D4—94no—
679C2×D4—92no—
680C2×D4—98no—
681C2×D4—91no—
682C2×D4—188no—
683C2×D4—188no—
684C2×D4—1816no—
685C2×D4—3616no—
686C2×D4C2×D3212yes—
687C2×D4C2×D3212yes—
688C22×C4—31no—
689C22×C4—32no—
690C22×C4—32no—
691C22×C4—32no—
692C22×C4—64no—
693C22×C4—94no—
694C22×C4—98no—
695C22×C4—92no—
696C22×C4C2×D3211yescharacteristic
697C4⋊C4—32no—
698C4⋊C4—94no—
699C4⋊C4—94no—
700C4⋊C4—92no—
701C22⋊C4—32no—
702C22⋊C4—38no—
703C22⋊C4—94no—
704C22⋊C4—94no—
705C22⋊C4—94no—
706C22⋊C4—98no—
707C22⋊C4—94no—
708C22⋊C4—92no—
709C22⋊C4—98no—
710C42—32no—
711C42—92no—
712C22×C3—22no—
713C22×C3—22no—
714C22×C3—24no—
715C22×C3—28no—
716C22×C3—28no—
717C22×C3—24no—
718C22×C3—22no—
719C22×C3—21no—
720C22×C3—38no—
721C22×C3—34no—
722C22×C3—42no—
723C22×C3—48no—
724C22×C3—44no—
725C22×C3—48no—
726C22×C3—48no—
727C22×C3—68no—
728C22×C3—62no—
729C22×C3—68no—
730C22×C3—62no—
731C22×C3—64no—
732C22×C3—62no—
733C22×C3—88no—
734C22×C3—128no—
735C22×C3—1232no—
736C22×C3C2×D3×D412yes—
737C22×C3C22×#6712yes—
738C22×C3C24×D311yescharacteristic
739C22×C3C24×D311yescharacteristic
740C2×D3—28no—
741C2×D3—28no—
742C2×D3—22no—
743C2×D3—22no—
744C2×D3—22no—
745C2×D3—24no—
746C2×D3—48no—
747C2×D3—432no—
748C2×D3—62no—
749C2×D3—64no—
750C2×D3—64no—
751C2×D3—62no—
752C2×D3—122no—
753C2×D3—124no—
754C2×D3—248no—
755C2×D3—248no—
756C2×D3#100414yescomplemented
757C2×D3C22×#6718yes—
758C3×C4—22no—
759C3×C4—22no—
760C3×C4—62no—
761C3×C4—64no—
762C3×C4—62no—
763C3×C4C2×D3×D412yes—
764C3×C4C2×D3×D412yes—
765C3×C4C22×#6712yes—
766C3×C4C22×#6712yes—
767Dic3—22no—
768Dic3—24no—
769Dic3—22no—
770Dic3—62no—
771Dic3—64no—
772Dic3—64no—
773Dic3—62no—
774Dic3—122no—
775Dic3—124no—
776C32#348411yescharacteristic, complemented, Sylow
777C23—24no—
778C23—32no—
779C23—34no—
780C23—38no—
781C23—32no—
782C23—44no—
783C23—64no—
784C23—616no—
785C23—616no—
786C23—62no—
787C23—92no—
788C23—124no—
789C23—128no—
790C23—1232no—
791C23—188no—
792C23—368no—
793C23C22×D3214yes—
794C23C22×D3211yescharacteristic
795Q8—62no—
796Q8—182no—
797D4—24no—
798D4—24no—
799D4—38no—
800D4—38no—
801D4—616no—
802D4—64no—
803D4—62no—
804D4—128no—
805D4—188no—
806D4—188no—
807D4—188no—
808D4—188no—
809D4—184no—
810D4—182no—
811D4—368no—
812C2×C4—34no—
813C2×C4—32no—
814C2×C4—32no—
815C2×C4—62no—
816C2×C4—64no—
817C2×C4—64no—
818C2×C4—64no—
819C2×C4—94no—
820C2×C4—92no—
821C2×C4—188no—
822C2×C4—184no—
823C2×C4—368no—
824C2×C4D3×#6714yescomplemented
825C2×C4C22×D3211yescharacteristic
826C2×C4C22×D3211yescharacteristic
827C2×C3—22no—
828C2×C3—22no—
829C2×C3—22no—
830C2×C3—21no—
831C2×C3—42no—
832C2×C3—44no—
833C2×C3—44no—
834C2×C3—68no—
835C2×C3—64no—
836C2×C3—84no—
837C2×C3—122no—
838C2×C3C22×D3×D411yescharacteristic
839C2×C3C2×#100412yes—
840C2×C3D3×H(5,𝔽2)12yes—
841C2×C3C23×#6711yescharacteristic
842D3—24no—
843D3—28no—
844D3—42no—
845D3—122no—
846D3—122no—
847D3—242no—
848C22—22no—
849C22—28no—
850C22—24no—
851C22—34no—
852C22—38no—
853C22—48no—
854C22—68no—
855C22—68no—
856C22—62no—
857C22—62no—
858C22—64no—
859C22—62no—
860C22—128no—
861C22—1232no—
862C22—184no—
863C22—182no—
864C22—728no—
865C22C2×D3×#6712yes—
866C22C23×D3211yescharacteristic
867C4—64no—
868C4—62no—
869C4—62no—
870C4—184no—
871C4—182no—
872C4C2×D3×#6712yes—
873C4C2×D3×#6712yes—
874C3—21no—
875C3#8633011yescharacteristic, complemented
876C3#8723911yescharacteristic, complemented
877C2—22no—
878C2—44no—
879C2—64no—
880C2—68no—
881C2—122no—
882C2—362no—
883C2D3×#100412yes—
884C2C22×D3×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC22×C32×D4C22
hypercenterC22×D4D32
hypocenterC32#3484
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×C3×D3×D4C2semidirect
2. C2×#64307C2semidirect
3. #10596276C2semidirect
4. C3×#5805C2semidirect
5. #10595524C2semidirect
6. D3×#953C2semidirect
7. #10595293C2semidirect
8. #10595288C2semidirect
9. #10595229C2semidirect
10. #10595228C2semidirect
11. #10595023C2semidirect
12. #10595022C2semidirect
13. #10594982C2semidirect
16. C24×C3×D3C22semidirect
17. C22×C32×D4C22semidirect
18. C2×#3828C22semidirect
19. C22×C3×#67C22semidirect
21. C2×C3×D3×D4C22semidirect
22. C2×C3×D3×D4C22semidirect
23. C2×C3×#235C22semidirect
25. C22×C3×C4×D3C22semidirect
26. C2×D3×#67C22semidirect
27. C2×D3×#67C22semidirect
29. C2×#3802C22semidirect
30. C2×D3×D12C22semidirect
31. C2×#3796C22semidirect
32. C2×#3795C22semidirect
33. #64162C22semidirect
34. #64149C22semidirect
35. #64147C22semidirect
36. #64145C22semidirect
37. #64135C22semidirect
38. C3×#953C22semidirect
39. C3×#940C22semidirect
40. C3×#938C22semidirect
41. C3×#936C22semidirect
42. C3×#926C22semidirect
43. #63983C22semidirect
44. #63977C22semidirect
45. #63977C22semidirect
46. #63976C22semidirect
47. #63976C22semidirect
48. #63971C22semidirect
49. #63970C22semidirect
50. #63969C22semidirect
51. D3×#217C22semidirect
52. D3×#217C22semidirect
53. #63966C22semidirect
54. #63961C22semidirect
55. #63909C22semidirect
56. #63908C22semidirect
57. C4×#626C22semidirect
58. C4×#625C22semidirect
59. #63898C22semidirect
60. Dic3×D12C22semidirect
61. #63857C22semidirect
62. #63856C22semidirect
66. C22×D3×D4D3semidirect
75. #5805D3semidirect
96. C22×D32C23semidirect
102. C2×#638C23semidirect
104. C2×C4⋊(C3⋊D3)C23semidirect
105. C2×C4×C3⋊D3C23semidirect
106. C2×#634C23semidirect
110. C2×C3×#67C23semidirect
115. C2×C3×D12D4semidirect
118. C2×C3×D12C23semidirect
122. C2×C3×C4×D3C23semidirect
123. C2×C3×Dic6C23semidirect
127. C2×#626C23semidirect
129. C2×#625C23semidirect
130. C2×D3×Dic3C23semidirect
131. C2×D3×Dic3C23semidirect
137. #3757C23semidirect
138. C4⋊(C3⋊Dic3)C23semidirect
139. C4×C3⋊Dic3C23semidirect
141. C3×#217C23semidirect
142. C3×C4⋊Dic3C23semidirect
143. C3×C4×Dic3C23semidirect
144. #3724C23semidirect
145. Dic3⋊Dic3C23semidirect
146. #3722C23semidirect
149. (C2×D3)⋊Dic3C23semidirect
150. (C2×D3)⋊Dic3C23semidirect
153. C24×D3C2×D3semidirect
161. C22×C3×D4C2×D3semidirect
162. C22×C3×D4C2×D3semidirect
166. C22×#67C2×D3semidirect
178. C2×D3×D4C2×D3semidirect
179. C2×D3×D4C2×D3semidirect
184. C2×#235C2×D3semidirect
187. C22×C4×D3C2×D3semidirect
200. #953C2×D3semidirect
207. #940C2×D3semidirect
215. #938C2×D3semidirect
223. #936C2×D3semidirect
238. #926C2×D3semidirect
265. C22×C3×D3C2×D4semidirect
273. C2×C32×C4C2×D4semidirect
291. C3×D12C2×D4semidirect
292. C3×D12C2×D4semidirect
377. C2×#67C22×D3semidirect
402. C2×D12#67semidirect
405. C2×D12C22×D3semidirect
414. C2×C4×D3C22×D3semidirect
418. C2×Dic6C22×D3semidirect
434. #217C22×D3semidirect
445. C4⋊Dic3C22×D3semidirect
452. C4×Dic3C22×D3semidirect
470. C2×C3×D3H(5,𝔽2)semidirect
494. C22×D4D32semidirect
563. C22×D3C2×#67semidirect
590. C2×C3×C4D3×D4semidirect
591. C2×C3×C4C2×#67semidirect
629. D12C2×#67semidirect
630. D12C2×#67semidirect
756. C2×D3#1004semidirect
776. C32#3484semidirect
824. C2×C4D3×#67semidirect
875. C3#86330semidirect
876. C3#87239semidirect

Maximal subgroups

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

subgroupindex
C22×C3×D3×D42
C2×#643072
#105962762
C3×#58052
#105955242
D3×#9532
#105952932
#105952882
#105952292
#105952282
#105950232
#105950222
#105949822
#872393
#863303