Finite Group Databasebeta

← #11664211

Subgroups — #11664211

Order 768.

2110 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×2−1+4C211yesmaximal, characteristic, complemented
2#85848C211yesmaximal, characteristic, complemented
3#84113C212yesmaximal, complemented
4#82568C214yesmaximal, complemented
5#82566C212yesmaximal, complemented
6#82564C212yesmaximal, complemented
7#82553C214yesmaximal, complemented
8#82548C212yesmaximal, complemented
9#82531C212yesmaximal, complemented
10#82529C212yesmaximal, complemented
11#82526C211yesmaximal, characteristic, complemented
12#82515C211yesmaximal, characteristic, complemented
13#82507C211yesmaximal, characteristic, complemented
14#82444C212yesmaximal, complemented
15#82442C212yesmaximal, complemented
16C2×#5027C211yesmaximal, characteristic, complemented
17#82431C211yesmaximal, characteristic, complemented
18#60593—31nomaximal, Sylow
19C2×C3×2−1+4C2211yescharacteristic
20C3×#520—22no—
21C3×#520—21no—
22C3×#520C2211yescharacteristic
23C3×#520C2211yescharacteristic
24C3×#520C2212yescomplemented
25C3×#519—21no—
26C3×#519C2211yescharacteristic
27C3×#519C2212yescomplemented
28C3×C4×#41—22no—
29C3×C4×#41—21no—
30C3×C4×#41C2211yescharacteristic
31C3×C4×#41C2211yescharacteristic
32C3×C4×#41C2212yescomplemented
33C2×C3×C4×Q8—21no—
34C2×C3×C4×Q8C2211yescharacteristic
35C2×C3×C4×Q8C2212yescomplemented
36#5830C2212yes—
37C2×#949C2212yes—
38C22×#215C2212yes—
39#5585—21no—
40#5585—21no—
41#5553—21no—
42#5553—21no—
43#5550—22no—
44#5550—22no—
45#5535C2214yes—
46#5521C2212yes—
47#5477C2212yes—
48#5477C2212yes—
49C2×#874C2211yescharacteristic
50#5470C2211yescharacteristic
51#5238C2214yescomplemented
52#5238C2214yescomplemented
53#5234C2212yes—
54#5233C2212yes—
55#5227C2214yescomplemented
56#5227C2214yescomplemented
57#5225C2212yes—
58#5027C2212yes—
59#5027C2212yes—
60#5027C2214yes—
61#5027C2212yes—
62#5027C2212yes—
63#5026C2214yescomplemented
64#5026C2214yescomplemented
65#5026C2214yescomplemented
66C4×#215C2214yescomplemented
67C4×#215C2214yescomplemented
68C4×#215C2214yescomplemented
69#5022C2212yescomplemented
70#5022C2214yescomplemented
71#5021C2211yescharacteristic, complemented
72#5021C2212yescomplemented
73#5020C2211yescharacteristic, complemented
74#5020C2212yescomplemented
75#5015C2212yes—
76#5015C2212yes—
77#5014C2214yescomplemented
78C4×#213C2214yescomplemented
79#5009C2212yescomplemented
80#5008C2211yescharacteristic, complemented
81#5007C2211yescharacteristic, complemented
82#5003C2214yescomplemented
83#5003C2214yescomplemented
84#5001C2212yes—
85#5000C2214yescomplemented
86#4998C2212yes—
87#4997C2212yes—
88#4968C2214yescomplemented
89#4967C2214yescomplemented
90C2×#809C2212yes—
91#4964C2212yes—
92#4926C2212yescomplemented
93#4925C2212yescomplemented
94#4924C2211yescharacteristic
95C2×C4⋊(C3⋊C8)C2211yescharacteristic
96#3508—31no—
97C4×2−1+4D311yescharacteristic, complemented
98#3126—34no—
99#3119—34no—
100#3115—32no—
101#3112—32no—
102#3106—32no—
103#3103—32no—
104#3096—32no—
105#3078—31no—
106#3076—31no—
107#3038—31no—
108C2×#460—31no—
109#3010—32no—
110#2949—32no—
111#2946—32no—
112#2925—31no—
113C3×2−1+4—24no—
114C3×2−1+4—24no—
115C2×C3×#41—22no—
116C2×C3×#41—21no—
117C2×C3×#41C2312yes—
118C2×C3×#41C2311yescharacteristic
119C2×C3×#41C2311yescharacteristic
120C22×C3×Q8—21no—
121C22×C3×Q8C2312yes—
122C22×C3×Q8C2311yescharacteristic
123C2×#235—22no—
124C2×#235—22no—
125C22×D12—21no—
126C22×D12—21no—
127C22×D12C2312yes—
128C3×C4×Q8—21no—
129C3×C4×Q8—21no—
130C3×C4×Q8—22no—
131C3×C4×Q8—21no—
132C3×C4×Q8—22no—
133C3×C4×Q8—21no—
134C3×C4×Q8—22no—
135C3×C4×Q8—21no—
136C3×C4×Q8—22no—
137C3×C4×Q8D411yescharacteristic
138C3×C4×Q8D411yescharacteristic
139C3×C4×Q8C2312yes—
140C3×C4×Q8C2311yescharacteristic
141C3×C4×Q8C2312yes—
142C3×C4×Q8C2311yescharacteristic
143C3×C4×Q8C2312yes—
144C3×C4×Q8C2312yes—
145C3×C4×Q8C2312yes—
146C3×C4×D4—22no—
147C3×C4×D4—21no—
148C3×C4×D4—21no—
149C3×C4×D4—22no—
150C3×C4×D4—21no—
151C3×C4×D4—22no—
152C3×C4×D4—22no—
153C3×C4×D4—22no—
154C3×C4×D4—22no—
155C3×C4×D4D412yes—
156C3×C4×D4D412yes—
157C3×C4×D4D411yescharacteristic
158C3×C4×D4D411yescharacteristic
159C3×C4×D4C2311yescharacteristic
160C3×C4×D4C2311yescharacteristic
161C3×C4×D4C2312yes—
162C3×#117—21no—
163C3×#117—22no—
164C3×#117—22no—
165C3×#117—22no—
166C3×#117—22no—
167C3×#117—21no—
168C3×#117—22no—
169C3×#117C2311yescharacteristic
170C3×#117C2312yes—
171C3×#117C2311yescharacteristic
172C3×#117C2312yes—
173C2×C3×C4⋊C4—21no—
174C2×C3×C4⋊C4—22no—
175C2×C3×C4⋊C4—21no—
176C2×C3×C4⋊C4—22no—
177C2×C3×C4⋊C4C2311yescharacteristic
178C2×C3×C4⋊C4C2312yes—
179C2×C3×C42—21no—
180C2×C3×C42—22no—
181C2×C3×C42—21no—
182C2×C3×C42—22no—
183C2×C3×C42C2311yescharacteristic
184C2×C3×C42C2312yes—
185#949—28no—
186#947—22no—
187C2×#215—28no—
188C2×#215C2314yes—
189C2×#215C2314yes—
190C2×#215C2314yes—
191#940—22no—
192#937—24no—
193C2×#213C2314yes—
194#930—22no—
195#930—22no—
196#930C2314yes—
197#930C2314yes—
198#926C2312yes—
199#924—21no—
200#924—21no—
201C2×#208C2312yes—
202C22×C3⋊C8C2312yes—
203#894—24no—
204#894—24no—
205#893—22no—
206#893—22no—
207#884—24no—
208#884—24no—
209D3×C22⋊C4—24no—
210#875—22no—
211#875—22no—
212#874—21no—
213#874—21no—
214#874C2312yes—
215#874C2312yes—
216C4×D12—22no—
217C4×D12—22no—
218C4×D12C2314yes—
219C4×D12C2314yes—
220#870C2312yes—
221#869C2311yescharacteristic
222#869C2311yescharacteristic
223C4×Dic6—21no—
224C4×Dic6—21no—
225#835C2314yes—
226#835C2314yes—
227#835C2312yes—
228#835C2312yes—
229#832C2312yes—
230#832C2312yes—
231#830C2314yes—
232#830C2314yes—
233#809C2314yes—
234#809C2314yes—
235#809C2314yes—
236#809C2314yes—
237#808C2314yes—
238#808C2312yes—
239#808C2312yes—
240#807C2314yes—
241#807C2312yes—
242#807C2312yes—
243C4⋊(C3⋊C8)C2311yescharacteristic
244C4⋊(C3⋊C8)C2311yescharacteristic
245C4⋊(C3⋊C8)C2312yes—
246C4⋊(C3⋊C8)C2312yes—
247C4⋊(C3⋊C8)C2312yes—
248#803C2314yes—
249C4×C3⋊C8C2314yes—
250C2×2−1+4C2×D311yescharacteristic
251C2×AGL(1,ℤ/8)—32no—
252C22×SD16—32no—
253#559—61no—
254#559—61no—
255#550—61no—
256#550—61no—
257#546—62no—
258#546—62no—
259#540—34no—
260#535—32no—
261#533—31no—
262#532—32no—
263#532—32no—
264C2×#127—31no—
265#520—22no—
266#520—21no—
267#520C2×D311yescharacteristic
268#520C2×D311yescharacteristic
269#520C2×D312yescomplemented
270#519—21no—
271#519C2×D311yescharacteristic
272#519C2×D312yescomplemented
273#518—32no—
274C4×#41—22no—
275C4×#41—21no—
276C4×#41C2×D311yescharacteristic
277C4×#41C2×D311yescharacteristic
278C4×#41C2×D312yescomplemented
279C2×C4×Q8—21no—
280C2×C4×Q8C2×D311yescharacteristic
281C2×C4×Q8C2×D312yescomplemented
282#482—34no—
283#482—34no—
284#481—34no—
285#480—34no—
286#479—32no—
287#479—34no—
288#478—32no—
289#477—31no—
290#477—32no—
291#476—31no—
292#475—31no—
293#475—32no—
294#474—31no—
295#460—32no—
296#460—32no—
297#460—32no—
298#460—34no—
299#460—32no—
300#459—32no—
301#459—32no—
302#449—34no—
303#449—34no—
304#448—34no—
305#448—34no—
306#442—34no—
307#440—34no—
308#440—34no—
309#440—34no—
310C4×SD16—34no—
311C4×SD16—34no—
312C4×SD16—34no—
313C4×D8—34no—
314#433—34no—
315#432—32no—
316#431—32no—
317#428—32no—
318#427—32no—
319#423—31no—
320C2×C4⋊C8—31no—
321#419—32no—
322#418—32no—
323#416—32no—
324C2×#102—32no—
325#408—32no—
326#405—32no—
327C23×D3—22no—
328C3×#41—216no—
329C3×#41—28no—
330C3×#41—24no—
331C3×#41—24no—
332C3×#41—22no—
333C3×#41—22no—
334C3×#41—22no—
335C3×#41#4114yescomplemented
336C2×C3×Q8—28no—
337C2×C3×Q8—24no—
338C2×C3×Q8—24no—
339C2×C3×Q8—22no—
340C2×C3×Q8—21no—
341C2×C3×Q8—22no—
342C2×C3×Q8C2×D411yescharacteristic
343C2×C3×Q8#4114yescomplemented
344C2×C3×Q8C2411yescharacteristic
345C2×C3×Q8C2412yes—
346C2×C3×D4—22no—
347C2×C3×D4—21no—
348C2×C3×D4C2×D412yes—
349C2×C3×D4C2×D411yescharacteristic
350C2×C3×D4C2411yescharacteristic
351C22×C3×C4—22no—
352C22×C3×C4—21no—
353C22×C3×C4—22no—
354C22×C3×C4—21no—
355C22×C3×C4—22no—
356C22×C3×C4—21no—
357C22×C3×C4—21no—
358C22×C3×C4—21no—
359C22×C3×C4—22no—
360C22×C3×C4C2×D411yescharacteristic
361C22×C3×C4C2×D412yes—
362C22×C3×C4C2×D411yescharacteristic
363C22×C3×C4C2×D412yes—
364C22×C3×C4C2412yes—
365C22×C3×C4C2411yescharacteristic
366C2×#67—24no—
367C2×#67—24no—
368#235—84no—
369#235—84no—
370C2×D12—24no—
371C2×D12—24no—
372C2×D12—22no—
373C2×D12—22no—
374C2×D12—22no—
375C2×D12—22no—
376C2×D12—22no—
377C2×D12—82no—
378C2×D12—82no—
379C2×D12C2414yes—
380C2×C4×D3—24no—
381C2×C4×D3—24no—
382C2×Dic6—21no—
383C2×Dic6—21no—
384C3×C4⋊C4—22no—
385C3×C4⋊C4—22no—
386C3×C4⋊C4—21no—
387C3×C4⋊C4—22no—
388C3×C4⋊C4—22no—
389C3×C4⋊C4—22no—
390C3×C4⋊C4—21no—
391C3×C4⋊C4—21no—
392C3×C4⋊C4—22no—
393C3×C4⋊C4C2×D411yescharacteristic
394C3×C4⋊C4C2×D411yescharacteristic
395C3×C4⋊C4C2×D412yes—
396C3×C4⋊C4C2×D412yes—
397C3×C4⋊C4C2412yes—
398C3×C4⋊C4C2411yescharacteristic
399C3×C4⋊C4C2411yescharacteristic
400C3×C22⋊C4—22no—
401C3×C22⋊C4—21no—
402C3×C22⋊C4—21no—
403C3×C22⋊C4—21no—
404C3×C22⋊C4—22no—
405C3×C22⋊C4C2×D412yes—
406C3×C22⋊C4C2×D412yes—
407C3×C22⋊C4C2×D412yes—
408C3×C42—22no—
409C3×C42—21no—
410C3×C42—21no—
411C3×C42—22no—
412C3×C42—22no—
413C3×C42—22no—
414C3×C42—22no—
415C3×C42—22no—
416C3×C42—21no—
417C3×C42C2×D411yescharacteristic
418C3×C42C2×D411yescharacteristic
419C3×C42C2×D412yes—
420C3×C42C2×D412yes—
421C3×C42C2412yes—
422C3×C42C2411yescharacteristic
423C3×C42C2411yescharacteristic
424#217—22no—
425#215—28no—
426#215—28no—
427#215—28no—
428#213—28no—
429(C2×D3)⋊C4—24no—
430(C2×D3)⋊C4—24no—
431(C2×D3)⋊C4—24no—
432(C2×D3)⋊C4—24no—
433C4⋊Dic3—21no—
434C4⋊Dic3—21no—
435C4⋊Dic3C2412yes—
436C4⋊Dic3C2412yes—
437Dic3⋊C4—22no—
438Dic3⋊C4—22no—
439C4×Dic3—22no—
440#208—24no—
441C2×C3⋊C8—24no—
442C2×C3⋊C8C2412yes—
443C2×C3⋊C8C2414yes—
444C2×C3⋊C8C2412yes—
4452−1+4—24no—
4462−1+4—24no—
447C2×#41—22no—
448C2×#41—21no—
449C2×#41—62no—
450C2×#41—62no—
451C2×#41C22×D312yes—
452C2×#41C22×D311yescharacteristic
453C2×#41C22×D311yescharacteristic
454C22×Q8—21no—
455C22×Q8C22×D312yes—
456C22×Q8C22×D311yescharacteristic
457C22×D4—32no—
458C22×D4—61no—
459C22×D4—61no—
460AGL(1,ℤ/8)—68no—
461C2×SD16—34no—
462C2×SD16—34no—
463C2×SD16—34no—
464C2×SD16—68no—
465C2×D8—34no—
466C2×M16—32no—
467C22×C8—32no—
468C4⋊Q8—31no—
469C4⋊Q8—31no—
470#127—32no—
471#127—32no—
472#127—62no—
473#127—61no—
474#127—61no—
475#125—32no—
476#124—62no—
477#124—62no—
478#124—62no—
479#123—64no—
480#123—64no—
481C22⋊Q8—61no—
482C22⋊Q8—61no—
483#121—34no—
484#121—34no—
485#121—62no—
486#121—62no—
487#121—64no—
488#121—64no—
489#120—64no—
490C4×Q8—21no—
491C4×Q8—21no—
492C4×Q8—22no—
493C4×Q8—21no—
494C4×Q8—22no—
495C4×Q8—21no—
496C4×Q8—22no—
497C4×Q8—21no—
498C4×Q8—22no—
499C4×Q8—61no—
500C4×Q8—61no—
501C4×Q8#6711yescharacteristic
502C4×Q8#6711yescharacteristic
503C4×Q8C22×D312yes—
504C4×Q8C22×D312yes—
505C4×Q8C22×D311yescharacteristic
506C4×Q8C22×D312yes—
507C4×Q8C22×D312yes—
508C4×Q8C22×D311yescharacteristic
509C4×Q8C22×D312yes—
510C4×D4—22no—
511C4×D4—21no—
512C4×D4—21no—
513C4×D4—22no—
514C4×D4—21no—
515C4×D4—22no—
516C4×D4—22no—
517C4×D4—22no—
518C4×D4—22no—
519C4×D4—34no—
520C4×D4—34no—
521C4×D4—62no—
522C4×D4—62no—
523C4×D4—62no—
524C4×D4—62no—
525C4×D4#6712yes—
526C4×D4#6711yescharacteristic
527C4×D4#6712yes—
528C4×D4#6711yescharacteristic
529C4×D4C22×D311yescharacteristic
530C4×D4C22×D311yescharacteristic
531C4×D4C22×D312yes—
532#117—21no—
533#117—22no—
534#117—22no—
535#117—22no—
536#117—22no—
537#117—21no—
538#117—22no—
539#117—32no—
540#117C22×D311yescharacteristic
541#117C22×D312yes—
542#117C22×D311yescharacteristic
543#117C22×D312yes—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—22no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—22no—
548C2×C4⋊C4C22×D311yescharacteristic
549C2×C4⋊C4C22×D312yes—
550C2×C22⋊C4—64no—
551C2×C42—21no—
552C2×C42—22no—
553C2×C42—21no—
554C2×C42—22no—
555C2×C42C22×D311yescharacteristic
556C2×C42C22×D312yes—
557#107—32no—
558#107—32no—
559#107—34no—
560#106—32no—
561#106—32no—
562#106—34no—
563C4⋊C8—31no—
564C4⋊C8—31no—
565C4⋊C8—32no—
566C4⋊C8—32no—
567C4⋊C8—32no—
568#103—32no—
569#103—32no—
570#103—34no—
571#103—34no—
572#102—32no—
573#102—32no—
574#102—34no—
575#102—34no—
576#102—34no—
577#102—34no—
578C22⋊C8—34no—
579C22⋊C8—34no—
580#97—34no—
581C4×C8—34no—
582C23×C3—21no—
583C23×C3C22×D412yes—
584C23×C3C22×D411yescharacteristic
585C22×D3—24no—
586C22×D3—44no—
587C22×D3—82no—
588C22×D3—82no—
589C3×Q8—28no—
590C3×Q8—22no—
591C3×Q8—24no—
592C3×Q8—21no—
593C3×Q8—22no—
594C3×Q8C2×#4112yes—
595C3×Q8C2×#4114yes—
596C3×D4—28no—
597C3×D4—24no—
598C3×D4—24no—
599C3×D4—22no—
600C3×D4—21no—
601C3×D4C2×#4112yes—
602C2×C3×C4—28no—
603C2×C3×C4—28no—
604C2×C3×C4—24no—
605C2×C3×C4—22no—
606C2×C3×C4—21no—
607C2×C3×C4—24no—
608C2×C3×C4—22no—
609C2×C3×C4—24no—
610C2×C3×C4—22no—
611C2×C3×C4—22no—
612C2×C3×C4—21no—
613C2×C3×C4—22no—
614C2×C3×C4—21no—
615C2×C3×C4—41no—
616C2×C3×C4—42no—
617C2×C3×C4—42no—
618C2×C3×C4—82no—
619C2×C3×C4—81no—
620C2×C3×C4—81no—
621C2×C3×C4—82no—
622C2×C3×C4C22×D411yescharacteristic
623C2×C3×C4C22×D411yescharacteristic
624C2×C3×C4C22×D411yescharacteristic
625C2×C3×C4C22×D412yes—
626C2×C3×C4C22×D412yes—
627C2×C3×C4C22×D412yes—
628C2×C3×C4C22×D411yescharacteristic
629C2×C3×C4C22×D411yescharacteristic
630C2×C3×C4C2×#4112yes—
631C2×C3×C4C2×#4112yes—
632C2×C3×C4C2511yescharacteristic
633#67—84no—
634#67—84no—
635C2×Dic3—22no—
636C2×Dic3—22no—
637D12—24no—
638D12—24no—
639D12—44no—
640D12—44no—
641D12—44no—
642D12—82no—
643D12—82no—
644C4×D3—84no—
645C4×D3—84no—
646Dic6—42no—
647Dic6—42no—
648C3⋊C8—22no—
649C3⋊C8—22no—
650C3⋊C8—24no—
651C24—62no—
652#41—216no—
653#41—28no—
654#41—24no—
655#41—24no—
656#41—22no—
657#41—22no—
658#41—22no—
659#41—244no—
660#41—244no—
661#41#23514yescomplemented
662C2×Q8—28no—
663C2×Q8—24no—
664C2×Q8—24no—
665C2×Q8—22no—
666C2×Q8—22no—
667C2×Q8—21no—
668C2×Q8—61no—
669C2×Q8—61no—
670C2×Q8#23514yescomplemented
671C2×Q8C2×#6711yescharacteristic
672C2×Q8C23×D311yescharacteristic
673C2×Q8C23×D312yes—
674C2×D4—22no—
675C2×D4—21no—
676C2×D4—34no—
677C2×D4—64no—
678C2×D4—64no—
679C2×D4—64no—
680C2×D4—64no—
681C2×D4—62no—
682C2×D4—62no—
683C2×D4—62no—
684C2×D4—62no—
685C2×D4—62no—
686C2×D4—242no—
687C2×D4—242no—
688C2×D4C2×#6712yes—
689C2×D4C2×#6711yescharacteristic
690C2×D4C23×D311yescharacteristic
691C22×C4—22no—
692C22×C4—21no—
693C22×C4—22no—
694C22×C4—21no—
695C22×C4—22no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—22no—
699C22×C4—21no—
700C22×C4—64no—
701C22×C4—64no—
702C22×C4C2×#6712yes—
703C22×C4C2×#6711yescharacteristic
704C22×C4C2×#6712yes—
705C22×C4C2×#6711yescharacteristic
706C22×C4C23×D312yes—
707C22×C4C23×D311yescharacteristic
708SD16—68no—
709SD16—68no—
710SD16—68no—
711D8—68no—
712M16—64no—
713C2×C8—32no—
714C2×C8—34no—
715C2×C8—32no—
716C2×C8—64no—
717C4⋊C4—22no—
718C4⋊C4—22no—
719C4⋊C4—22no—
720C4⋊C4—22no—
721C4⋊C4—21no—
722C4⋊C4—22no—
723C4⋊C4—21no—
724C4⋊C4—22no—
725C4⋊C4—21no—
726C4⋊C4—32no—
727C4⋊C4—32no—
728C4⋊C4—61no—
729C4⋊C4—61no—
730C4⋊C4—62no—
731C4⋊C4—62no—
732C4⋊C4C2×#6711yescharacteristic
733C4⋊C4C2×#6712yes—
734C4⋊C4C2×#6711yescharacteristic
735C4⋊C4C2×#6712yes—
736C4⋊C4C23×D312yes—
737C4⋊C4C23×D311yescharacteristic
738C4⋊C4C23×D311yescharacteristic
739C22⋊C4—22no—
740C22⋊C4—21no—
741C22⋊C4—21no—
742C22⋊C4—22no—
743C22⋊C4—21no—
744C22⋊C4—62no—
745C22⋊C4—64no—
746C22⋊C4—64no—
747C22⋊C4—64no—
748C22⋊C4—64no—
749C22⋊C4C2×#6712yes—
750C22⋊C4C2×#6712yes—
751C22⋊C4C2×#6712yes—
752C42—22no—
753C42—21no—
754C42—22no—
755C42—21no—
756C42—22no—
757C42—22no—
758C42—22no—
759C42—22no—
760C42—21no—
761C42—62no—
762C42C2×#6712yes—
763C42C2×#6711yescharacteristic
764C42C2×#6712yes—
765C42C2×#6711yescharacteristic
766C42C23×D312yes—
767C42C23×D311yescharacteristic
768C42C23×D311yescharacteristic
769C22×C3—21no—
770C22×C3—21no—
771C22×C3—22no—
772C22×C3—22no—
773C22×C3—22no—
774C22×C3—22no—
775C22×C3—41no—
776C22×C3—41no—
777C22×C3#52512yes—
778C22×C3C23×D411yescharacteristic
779C2×D3—44no—
780C2×D3—44no—
781C2×D3—44no—
782C2×D3—164no—
783C3×C4—21no—
784C3×C4—22no—
785C3×C4—21no—
786C3×C4—24no—
787C3×C4—22no—
788C3×C4—22no—
789C3×C4—22no—
790C3×C4—21no—
791C3×C4—42no—
792C3×C4—41no—
793C3×C4—41no—
794C3×C4#52512yes—
795C3×C4#57712yes—
796C3×C4C22×#4111yescharacteristic
797C3×C4C22×#4111yescharacteristic
798Dic3—42no—
799Dic3—42no—
800C23—21no—
801C23—64no—
802C23—124no—
803C23—242no—
804C23—242no—
805C23C22×#6712yes—
806C23C22×#6711yescharacteristic
807Q8—28no—
808Q8—21no—
809Q8—22no—
810Q8—24no—
811Q8—22no—
812Q8—122no—
813Q8—122no—
814Q8C2×#23512yes—
815Q8C2×#23514yes—
816D4—28no—
817D4—24no—
818D4—24no—
819D4—21no—
820D4—22no—
821D4—64no—
822D4—64no—
823D4—124no—
824D4—124no—
825D4—124no—
826D4—242no—
827D4—242no—
828D4—244no—
829D4—244no—
830D4C2×#23512yes—
831C2×C4—28no—
832C2×C4—28no—
833C2×C4—22no—
834C2×C4—21no—
835C2×C4—24no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—24no—
839C2×C4—22no—
840C2×C4—24no—
841C2×C4—21no—
842C2×C4—22no—
843C2×C4—21no—
844C2×C4—41no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—62no—
848C2×C4—62no—
849C2×C4—82no—
850C2×C4—81no—
851C2×C4—81no—
852C2×C4—82no—
853C2×C4—244no—
854C2×C4—244no—
855C2×C4C2×#23512yes—
856C2×C4C2×#23512yes—
857C2×C4C22×#6712yes—
858C2×C4C22×#6711yescharacteristic
859C2×C4C22×#6712yes—
860C2×C4C22×#6712yes—
861C2×C4C22×#6711yescharacteristic
862C2×C4C22×#6711yescharacteristic
863C2×C4C22×#6711yescharacteristic
864C2×C4C22×#6711yescharacteristic
865C2×C4C24×D311yescharacteristic
866C8—62no—
867C8—62no—
868C8—64no—
869C2×C3—22no—
870C2×C3—42no—
871C2×C3—42no—
872C2×C3C2×#52511yescharacteristic
873C2×C3C2×#57711yescharacteristic
874C2×C3#358511yescharacteristic
875D3—84no—
876C22—21no—
877C22—21no—
878C22—22no—
879C22—22no—
880C22—22no—
881C22—22no—
882C22—41no—
883C22—41no—
884C22—124no—
885C22—124no—
886C22—124no—
887C22—484no—
888C22#579112yes—
889C22C23×#6711yescharacteristic
890C4—21no—
891C4—22no—
892C4—21no—
893C4—24no—
894C4—22no—
895C4—22no—
896C4—22no—
897C4—21no—
898C4—42no—
899C4—41no—
900C4—41no—
901C4—122no—
902C4—122no—
903C4#579112yes—
904C4#583712yes—
905C4C22×#23511yescharacteristic
906C4C22×#23511yescharacteristic
907C3#6059311yescharacteristic, complemented, Sylow
908C2—22no—
909C2—42no—
910C2—42no—
911C2—244no—
912C2C2×#579111yescharacteristic
913C2C2×#583711yescharacteristic
914C2#8729811yescharacteristic
subgroupG/H
centerC22C23×#67
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×C4×2−1+4C2
socleC22×C3C23×D4
hypercenterC4×2−1+4D3
hypocenterC3#60593
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C4×#41 ◁ C4×2−1+4

Complements

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

NH ≅ G/Ntype
1. C3×C4×2−1+4C2semidirect
2. #85848C2semidirect
3. #84113C2semidirect
4. #82568C2semidirect
5. #82566C2semidirect
6. #82564C2semidirect
7. #82553C2semidirect
8. #82548C2semidirect
9. #82531C2semidirect
10. #82529C2semidirect
11. #82526C2semidirect
12. #82515C2semidirect
13. #82507C2semidirect
14. #82444C2semidirect
15. #82442C2semidirect
16. C2×#5027C2semidirect
17. #82431C2semidirect
24. C3×#520C22semidirect
27. C3×#519C22semidirect
32. C3×C4×#41C22semidirect
35. C2×C3×C4×Q8C22semidirect
51. #5238C22semidirect
52. #5238C22semidirect
55. #5227C22semidirect
56. #5227C22semidirect
63. #5026C22semidirect
64. #5026C22semidirect
65. #5026C22semidirect
66. C4×#215C22semidirect
67. C4×#215C22semidirect
68. C4×#215C22semidirect
69. #5022C22semidirect
70. #5022C22semidirect
71. #5021C22semidirect
72. #5021C22semidirect
73. #5020C22semidirect
74. #5020C22semidirect
77. #5014C22semidirect
78. C4×#213C22semidirect
79. #5009C22semidirect
80. #5008C22semidirect
81. #5007C22semidirect
82. #5003C22semidirect
83. #5003C22semidirect
85. #5000C22semidirect
88. #4968C22semidirect
89. #4967C22semidirect
92. #4926C22semidirect
93. #4925C22semidirect
97. C4×2−1+4D3semidirect
269. #520C2×D3semidirect
272. #519C2×D3semidirect
278. C4×#41C2×D3semidirect
281. C2×C4×Q8C2×D3semidirect
335. C3×#41#41semidirect
343. C2×C3×Q8#41semidirect
661. #41#235semidirect
670. C2×Q8#235semidirect
907. C3#60593semidirect

Maximal subgroups

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

subgroupindex
C3×C4×2−1+42
#858482
#841132
#825682
#825662
#825642
#825532
#825482
#825312
#825292
#825262
#825152
#825072
#824442
#824422
C2×#50272
#824312
#605933