Finite Group Databasebeta

← #11664340

Subgroups — #11664340

Order 768.

2046 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×2−1+4C211yesmaximal, characteristic, complemented
2#85850C211yesmaximal, characteristic, complemented
3#84114C212yesmaximal, complemented
4#82569C214yesmaximal, complemented
5#82567C212yesmaximal, complemented
6#82557C212yesmaximal, complemented
7#82552C214yesmaximal, complemented
8#82547C212yesmaximal, complemented
9#82535C212yesmaximal, complemented
10#82529C212yesmaximal, complemented
11#82525C211yesmaximal, characteristic, complemented
12#82515C211yesmaximal, characteristic, complemented
13#82508C211yesmaximal, characteristic, complemented
14#82447C212yesmaximal, complemented
15#82444C212yesmaximal, complemented
16#82441C211yesmaximal, characteristic, complemented
17C2×#5021C211yesmaximal, characteristic, complemented
18#60600—31nomaximal, Sylow
19C2×C3×2−1+4C2211yescharacteristic
20C3×#520—21no—
21C3×#520—22no—
22C3×#520C2211yescharacteristic
23C3×#520C2212yes—
24C3×#520C2211yescharacteristic
25C3×#519—21no—
26C3×#519C2211yescharacteristic
27C3×#519C2212yes—
28C3×C4×#41—21no—
29C3×C4×#41—22no—
30C3×C4×#41C2211yescharacteristic
31C3×C4×#41C2212yes—
32C3×C4×#41C2211yescharacteristic
33C2×C3×C4×Q8—21no—
34C2×C3×C4×Q8C2211yescharacteristic
35C2×C3×C4×Q8C2212yes—
36#5833C2212yes—
37C2×#950C2212yes—
38C2×#942C2212yes—
39#5584—21no—
40#5579—21no—
41#5565—22no—
42#5563—21no—
43#5552—22no—
44#5551—21no—
45#5534C2214yes—
46#5523C2212yes—
47#5477C2211yescharacteristic
48#5477C2212yes—
49#5470C2212yes—
50C2×#869C2211yescharacteristic
51#5239C2214yes—
52#5238C2214yes—
53#5234C2212yes—
54#5232C2212yes—
55#5228C2214yes—
56#5227C2214yes—
57C2×#835C2212yes—
58#5031C2212yes—
59#5031C2211yescharacteristic
60#5030C2214yes—
61C4×#216C2214yes—
62C4×#216C2214yes—
63#5028C2214yes—
64#5028C2212yes—
65#5027C2212yes—
66#5027C2211yescharacteristic
67#5026C2214yes—
68#5026C2214yes—
69C4×#215C2214yes—
70#5021C2212yes—
71#5021C2212yes—
72#5021C2212yes—
73#5021C2214yes—
74#5020C2212yes—
75#5019C2211yescharacteristic
76#5018C2214yes—
77#5016C2212yes—
78#5015C2211yescharacteristic
79C4×#213C2214yes—
80#5008C2212yes—
81#5007C2212yes—
82#5003C2214yes—
83#5002C2212yes—
84#5000C2214yes—
85#4997C2212yes—
86#4996C2214yes—
87#4995C2212yes—
88#4970C2214yes—
89#4967C2214yes—
90#4966C2212yes—
91C2×#807C2212yes—
92#4926C2212yes—
93#4925C2212yes—
94#4924C2211yescharacteristic
95C2×C4⋊(C3⋊C8)C2211yescharacteristic
96#3511—31no—
97C4×2−1+4D311yescharacteristic, complemented
98#3124—34no—
99#3121—34no—
100#3116—32no—
101#3112—32no—
102#3106—32no—
103#3104—32no—
104#3098—32no—
105#3079—31no—
106C2×#477—31no—
107#3037—31no—
108#3035—31no—
109#3013—32no—
110#2951—32no—
111#2947—32no—
112#2925—31no—
113C3×2−1+4—24no—
114C3×2−1+4—24no—
115C2×C3×#41—21no—
116C2×C3×#41—22no—
117C2×C3×#41C2312yes—
118C2×C3×#41C2311yescharacteristic
119C2×C3×#41C2311yescharacteristic
120C22×C3×Q8—21no—
121C22×C3×Q8C2312yes—
122C22×C3×Q8C2311yescharacteristic
123C2×#235—22no—
124C2×#235C2312yes—
125C22×Dic6—21no—
126C3×C4×Q8—21no—
127C3×C4×Q8—21no—
128C3×C4×Q8—22no—
129C3×C4×Q8—21no—
130C3×C4×Q8—22no—
131C3×C4×Q8—21no—
132C3×C4×Q8—22no—
133C3×C4×Q8—22no—
134C3×C4×Q8—21no—
135C3×C4×Q8D411yescharacteristic
136C3×C4×Q8D411yescharacteristic
137C3×C4×Q8C2311yescharacteristic
138C3×C4×Q8C2311yescharacteristic
139C3×C4×Q8C2312yes—
140C3×C4×Q8C2312yes—
141C3×C4×Q8C2312yes—
142C3×C4×Q8C2312yes—
143C3×C4×Q8C2312yes—
144C3×C4×D4—21no—
145C3×C4×D4—22no—
146C3×C4×D4—21no—
147C3×C4×D4—22no—
148C3×C4×D4—22no—
149C3×C4×D4—21no—
150C3×C4×D4—22no—
151C3×C4×D4—22no—
152C3×C4×D4—22no—
153C3×C4×D4D411yescharacteristic
154C3×C4×D4D412yes—
155C3×C4×D4D411yescharacteristic
156C3×C4×D4D412yes—
157C3×C4×D4C2311yescharacteristic
158C3×C4×D4C2311yescharacteristic
159C3×C4×D4C2312yes—
160C3×#117—21no—
161C3×#117—22no—
162C3×#117—22no—
163C3×#117—22no—
164C3×#117—22no—
165C3×#117—22no—
166C3×#117—21no—
167C3×#117C2311yescharacteristic
168C3×#117C2312yes—
169C3×#117C2311yescharacteristic
170C3×#117C2312yes—
171C2×C3×C4⋊C4—22no—
172C2×C3×C4⋊C4—21no—
173C2×C3×C4⋊C4—21no—
174C2×C3×C4⋊C4—22no—
175C2×C3×C4⋊C4C2311yescharacteristic
176C2×C3×C4⋊C4C2312yes—
177C2×C3×C42—21no—
178C2×C3×C42—22no—
179C2×C3×C42—21no—
180C2×C3×C42—22no—
181C2×C3×C42C2311yescharacteristic
182C2×C3×C42C2312yes—
183#950—28no—
184#946—22no—
185C2×#216C2312yes—
186C2×#216C2314yes—
187#942—28no—
188C2×#215C2312yes—
189C2×#215C2314yes—
190#939—24no—
191#938—22no—
192C2×#214C2312yes—
193C2×#213C2312yes—
194#930—21no—
195#930—22no—
196#930—21no—
197#930C2314yes—
198#926—22no—
199C2×C4⋊Dic3—21no—
200C2×C4⋊Dic3C2312yes—
201#924—22no—
202#924C2314yes—
203C2×#208C2312yes—
204C22×C3⋊C8C2312yes—
205#898—24no—
206#896—24no—
207#892—22no—
208D3×C4⋊C4—22no—
209#885—24no—
210#883—24no—
211#67⋊C4—24no—
212#875—22no—
213#875C2312yes—
214#874C2311yescharacteristic
215C4×D12—21no—
216C4×D12—21no—
217C4×D12—22no—
218C4×D12C2314yes—
219#870—22no—
220#869—21no—
221#869—21no—
222#869C2311yescharacteristic
223#869C2312yes—
224#869C2312yes—
225C4×Dic6—22no—
226C4×Dic6C2314yes—
227#835C2314yes—
228#835C2314yes—
229#835C2314yes—
230#832C2314yes—
231#830C2314yes—
232#830C2314yes—
233#810C2314yes—
234#810C2312yes—
235#810C2312yes—
236#809C2314yes—
237#809C2312yes—
238#809C2312yes—
239#808C2314yes—
240#807C2314yes—
241#807C2314yes—
242#807C2314yes—
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×#137—32no—
252C2×#135—32no—
253#556—61no—
254#555—61no—
255#554—61no—
256#553—62no—
257#548—62no—
258#547—61no—
259#542—34no—
260#537—32no—
261#533—32no—
262#532—32no—
263#532—31no—
264C2×C4⋊Q8—31no—
265#520—21no—
266#520—22no—
267#520—32no—
268#520C2×D312yes—
269#520C2×D311yescharacteristic
270#520C2×D311yescharacteristic
271#519—21no—
272#519C2×D312yes—
273#519C2×D311yescharacteristic
274C4×#41—22no—
275C4×#41—21no—
276C4×#41C2×D311yescharacteristic
277C4×#41C2×D312yes—
278C4×#41C2×D311yescharacteristic
279C2×C4×Q8—21no—
280C2×C4×Q8C2×D311yescharacteristic
281C2×C4×Q8C2×D312yes—
282#485—34no—
283#484—34no—
284#482—34no—
285#480—34no—
286#477—32no—
287#477—32no—
288#477—34no—
289#477—32no—
290#476—32no—
291#475—32no—
292#474—32no—
293#464—32no—
294#464—34no—
295#463—32no—
296#462—31no—
297#462—32no—
298#461—31no—
299#460—32no—
300#460—31no—
301#459—31no—
302#452—34no—
303#451—34no—
304#449—34no—
305#448—34no—
306#441—34no—
307#440—34no—
308#440—34no—
309#440—34no—
310C4×Q16—34no—
311C4×Q16—34no—
312C4×SD16—34no—
313C4×D8—34no—
314#433—34no—
315#432—32no—
316#431—32no—
317#428—32no—
318C2×#107—32no—
319#423—31no—
320C2×C4⋊C8—31no—
321#417—32no—
322#417—32no—
323#416—32no—
324C2×#103—32no—
325#408—32no—
326#405—32no—
327C3×#41—216no—
328C3×#41—28no—
329C3×#41—24no—
330C3×#41—24no—
331C3×#41—22no—
332C3×#41—22no—
333C3×#41—22no—
334C3×#41#4114yescomplemented
335C2×C3×Q8—28no—
336C2×C3×Q8—24no—
337C2×C3×Q8—24no—
338C2×C3×Q8—22no—
339C2×C3×Q8—21no—
340C2×C3×Q8—22no—
341C2×C3×Q8C2×D411yescharacteristic
342C2×C3×Q8#4114yescomplemented
343C2×C3×Q8C2411yescharacteristic
344C2×C3×Q8C2412yes—
345C2×C3×D4—22no—
346C2×C3×D4—21no—
347C2×C3×D4C2×D411yescharacteristic
348C2×C3×D4C2×D412yes—
349C2×C3×D4C2411yescharacteristic
350C22×C3×C4—22no—
351C22×C3×C4—21no—
352C22×C3×C4—22no—
353C22×C3×C4—21no—
354C22×C3×C4—22no—
355C22×C3×C4—21no—
356C22×C3×C4—21no—
357C22×C3×C4—22no—
358C22×C3×C4—21no—
359C22×C3×C4C2×D411yescharacteristic
360C22×C3×C4C2×D412yes—
361C22×C3×C4C2×D412yes—
362C22×C3×C4C2×D411yescharacteristic
363C22×C3×C4C2412yes—
364C22×C3×C4C2411yescharacteristic
365C2×#67—22no—
366C2×#67—24no—
367C22×Dic3—22no—
368#235—24no—
369#235—24no—
370#235—84no—
371C2×D12—21no—
372C2×D12—21no—
373C2×D12C2412yes—
374C2×C4×D3—22no—
375C2×C4×D3—24no—
376C2×Dic6—22no—
377C2×Dic6—22no—
378C2×Dic6—82no—
379C2×Dic6C2412yes—
380C3×C4⋊C4—22no—
381C3×C4⋊C4—22no—
382C3×C4⋊C4—21no—
383C3×C4⋊C4—22no—
384C3×C4⋊C4—22no—
385C3×C4⋊C4—22no—
386C3×C4⋊C4—21no—
387C3×C4⋊C4—22no—
388C3×C4⋊C4—21no—
389C3×C4⋊C4C2×D411yescharacteristic
390C3×C4⋊C4C2×D411yescharacteristic
391C3×C4⋊C4C2×D412yes—
392C3×C4⋊C4C2×D412yes—
393C3×C4⋊C4C2412yes—
394C3×C4⋊C4C2411yescharacteristic
395C3×C4⋊C4C2411yescharacteristic
396C3×C22⋊C4—22no—
397C3×C22⋊C4—21no—
398C3×C22⋊C4—21no—
399C3×C22⋊C4—22no—
400C3×C22⋊C4—21no—
401C3×C22⋊C4C2×D412yes—
402C3×C22⋊C4C2×D412yes—
403C3×C22⋊C4C2×D412yes—
404C3×C42—22no—
405C3×C42—21no—
406C3×C42—22no—
407C3×C42—21no—
408C3×C42—22no—
409C3×C42—22no—
410C3×C42—22no—
411C3×C42—22no—
412C3×C42—21no—
413C3×C42C2×D412yes—
414C3×C42C2×D411yescharacteristic
415C3×C42C2×D411yescharacteristic
416C3×C42C2×D412yes—
417C3×C42C2412yes—
418C3×C42C2411yescharacteristic
419C3×C42C2411yescharacteristic
420#217—24no—
421#216—28no—
422#216—24no—
423#215—28no—
424#215—24no—
425#214—24no—
426#213—24no—
427(C2×D3)⋊C4—24no—
428(C2×D3)⋊C4—22no—
429(C2×D3)⋊C4—22no—
430(C2×D3)⋊C4—24no—
431C4⋊Dic3—21no—
432C4⋊Dic3—22no—
433C4⋊Dic3—22no—
434C4⋊Dic3—22no—
435C4⋊Dic3—21no—
436C4⋊Dic3C2414yes—
437Dic3⋊C4—24no—
438Dic3⋊C4—24no—
439C4×Dic3—24no—
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—21no—
448C2×#41—22no—
449C2×#41—32no—
450C2×#41—62no—
451C2×#41C22×D312yes—
452C2×#41C22×D311yescharacteristic
453C2×#41C22×D311yescharacteristic
454C22×Q8—21no—
455C22×Q8—61no—
456C22×Q8C22×D312yes—
457C22×Q8C22×D311yescharacteristic
458#137—68no—
459#135—68no—
460C2×Q16—32no—
461C2×Q16—34no—
462C2×SD16—32no—
463C2×SD16—34no—
464C2×SD16—32no—
465C2×D8—32no—
466C2×M16—32no—
467C22×C8—32no—
468C4⋊Q8—32no—
469C4⋊Q8—32no—
470C4⋊Q8—31no—
471C4⋊Q8—61no—
472C4⋊Q8—61no—
473#127—31no—
474#126—64no—
475#125—62no—
476#124—32no—
477#124—64no—
478#124—62no—
479#123—64no—
480C22⋊Q8—34no—
481C22⋊Q8—62no—
482C22⋊Q8—62no—
483C22⋊Q8—64no—
484#121—34no—
485#121—62no—
486#121—64no—
487#121—61no—
488#121—61no—
489#121—62no—
490C4×Q8—21no—
491C4×Q8—21no—
492C4×Q8—22no—
493C4×Q8—21no—
494C4×Q8—22no—
495C4×Q8—22no—
496C4×Q8—21no—
497C4×Q8—21no—
498C4×Q8—22no—
499C4×Q8—34no—
500C4×Q8—62no—
501C4×Q8#6711yescharacteristic
502C4×Q8#6711yescharacteristic
503C4×Q8C22×D312yes—
504C4×Q8C22×D311yescharacteristic
505C4×Q8C22×D312yes—
506C4×Q8C22×D312yes—
507C4×Q8C22×D312yes—
508C4×Q8C22×D312yes—
509C4×Q8C22×D311yescharacteristic
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—64no—
521C4×D4—61no—
522C4×D4—62no—
523C4×D4—61no—
524C4×D4#6712yes—
525C4×D4#6711yescharacteristic
526C4×D4#6711yescharacteristic
527C4×D4#6712yes—
528C4×D4C22×D311yescharacteristic
529C4×D4C22×D312yes—
530C4×D4C22×D311yescharacteristic
531#117—21no—
532#117—22no—
533#117—22no—
534#117—22no—
535#117—22no—
536#117—21no—
537#117—22no—
538#117—62no—
539#117—62no—
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⋊C4—32no—
549C2×C4⋊C4—61no—
550C2×C4⋊C4—62no—
551C2×C4⋊C4C22×D311yescharacteristic
552C2×C4⋊C4C22×D312yes—
553C2×C42—21no—
554C2×C42—22no—
555C2×C42—22no—
556C2×C42—21no—
557C2×C42C22×D311yescharacteristic
558C2×C42C22×D312yes—
559#107—34no—
560#107—34no—
561#107—34no—
562#106—34no—
563C4⋊C8—31no—
564C4⋊C8—31no—
565C4⋊C8—32no—
566C4⋊C8—32no—
567C4⋊C8—32no—
568#103—34no—
569#103—34no—
570#103—34no—
571#103—32no—
572#103—32no—
573#103—34no—
574#102—34no—
575#102—32no—
576#102—32no—
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—22no—
586C3×Q8—28no—
587C3×Q8—22no—
588C3×Q8—24no—
589C3×Q8—21no—
590C3×Q8—22no—
591C3×Q8C2×#4112yes—
592C3×Q8C2×#4114yes—
593C3×D4—28no—
594C3×D4—24no—
595C3×D4—24no—
596C3×D4—22no—
597C3×D4—21no—
598C3×D4C2×#4112yes—
599C2×C3×C4—28no—
600C2×C3×C4—28no—
601C2×C3×C4—24no—
602C2×C3×C4—22no—
603C2×C3×C4—21no—
604C2×C3×C4—24no—
605C2×C3×C4—22no—
606C2×C3×C4—24no—
607C2×C3×C4—22no—
608C2×C3×C4—22no—
609C2×C3×C4—21no—
610C2×C3×C4—21no—
611C2×C3×C4—22no—
612C2×C3×C4—41no—
613C2×C3×C4—42no—
614C2×C3×C4—42no—
615C2×C3×C4—81no—
616C2×C3×C4—82no—
617C2×C3×C4—81no—
618C2×C3×C4—82no—
619C2×C3×C4C22×D412yes—
620C2×C3×C4C22×D412yes—
621C2×C3×C4C22×D412yes—
622C2×C3×C4C22×D411yescharacteristic
623C2×C3×C4C22×D411yescharacteristic
624C2×C3×C4C22×D411yescharacteristic
625C2×C3×C4C22×D411yescharacteristic
626C2×C3×C4C22×D411yescharacteristic
627C2×C3×C4C2×#4112yes—
628C2×C3×C4C2×#4112yes—
629C2×C3×C4C2511yescharacteristic
630#67—44no—
631#67—84no—
632C2×Dic3—22no—
633C2×Dic3—24no—
634C2×Dic3—82no—
635D12—22no—
636D12—22no—
637D12—42no—
638D12—42no—
639C4×D3—44no—
640C4×D3—84no—
641Dic6—22no—
642Dic6—22no—
643Dic6—44no—
644Dic6—82no—
645C3⋊C8—22no—
646C3⋊C8—22no—
647C3⋊C8—24no—
648#41—216no—
649#41—28no—
650#41—24no—
651#41—24no—
652#41—22no—
653#41—22no—
654#41—22no—
655#41—64no—
656#41—64no—
657#41—244no—
658#41#23514yescomplemented
659C2×Q8—28no—
660C2×Q8—24no—
661C2×Q8—24no—
662C2×Q8—22no—
663C2×Q8—22no—
664C2×Q8—21no—
665C2×Q8—32no—
666C2×Q8—62no—
667C2×Q8—62no—
668C2×Q8—242no—
669C2×Q8#23514yescomplemented
670C2×Q8C2×#6711yescharacteristic
671C2×Q8C23×D311yescharacteristic
672C2×Q8C23×D312yes—
673C2×D4—22no—
674C2×D4—21no—
675C2×D4—32no—
676C2×D4—62no—
677C2×D4—64no—
678C2×D4—61no—
679C2×D4—61no—
680C2×D4C2×#6712yes—
681C2×D4C2×#6711yescharacteristic
682C2×D4C23×D311yescharacteristic
683C22×C4—22no—
684C22×C4—21no—
685C22×C4—22no—
686C22×C4—21no—
687C22×C4—22no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—22no—
692C22×C4—62no—
693C22×C4—62no—
694C22×C4—64no—
695C22×C4C2×#6711yescharacteristic
696C22×C4C2×#6712yes—
697C22×C4C2×#6711yescharacteristic
698C22×C4C2×#6712yes—
699C22×C4C23×D312yes—
700C22×C4C23×D311yescharacteristic
701Q16—64no—
702Q16—68no—
703SD16—64no—
704SD16—68no—
705SD16—64no—
706D8—64no—
707M16—64no—
708C2×C8—32no—
709C2×C8—34no—
710C2×C8—32no—
711C2×C8—64no—
712C4⋊C4—22no—
713C4⋊C4—22no—
714C4⋊C4—22no—
715C4⋊C4—22no—
716C4⋊C4—21no—
717C4⋊C4—22no—
718C4⋊C4—21no—
719C4⋊C4—22no—
720C4⋊C4—21no—
721C4⋊C4—34no—
722C4⋊C4—62no—
723C4⋊C4—62no—
724C4⋊C4—64no—
725C4⋊C4—62no—
726C4⋊C4—61no—
727C4⋊C4—61no—
728C4⋊C4—64no—
729C4⋊C4C2×#6711yescharacteristic
730C4⋊C4C2×#6712yes—
731C4⋊C4C2×#6711yescharacteristic
732C4⋊C4C2×#6712yes—
733C4⋊C4C23×D311yescharacteristic
734C4⋊C4C23×D311yescharacteristic
735C4⋊C4C23×D312yes—
736C22⋊C4—22no—
737C22⋊C4—21no—
738C22⋊C4—21no—
739C22⋊C4—22no—
740C22⋊C4—21no—
741C22⋊C4—64no—
742C22⋊C4—64no—
743C22⋊C4—64no—
744C22⋊C4—62no—
745C22⋊C4—62no—
746C22⋊C4C2×#6712yes—
747C22⋊C4C2×#6712yes—
748C22⋊C4C2×#6712yes—
749C42—22no—
750C42—21no—
751C42—21no—
752C42—22no—
753C42—22no—
754C42—22no—
755C42—22no—
756C42—22no—
757C42—21no—
758C42—64no—
759C42C2×#6712yes—
760C42C2×#6711yescharacteristic
761C42C2×#6711yescharacteristic
762C42C2×#6712yes—
763C42C23×D312yes—
764C42C23×D311yescharacteristic
765C42C23×D311yescharacteristic
766C22×C3—21no—
767C22×C3—21no—
768C22×C3—22no—
769C22×C3—22no—
770C22×C3—22no—
771C22×C3—22no—
772C22×C3—41no—
773C22×C3—41no—
774C22×C3#52512yes—
775C22×C3C23×D411yescharacteristic
776C2×D3—42no—
777C2×D3—42no—
778C2×D3—42no—
779C3×C4—21no—
780C3×C4—21no—
781C3×C4—22no—
782C3×C4—24no—
783C3×C4—22no—
784C3×C4—22no—
785C3×C4—22no—
786C3×C4—21no—
787C3×C4—41no—
788C3×C4—42no—
789C3×C4—41no—
790C3×C4#52512yes—
791C3×C4#57812yes—
792C3×C4C22×#4111yescharacteristic
793C3×C4C22×#4111yescharacteristic
794Dic3—44no—
795Dic3—42no—
796C23—21no—
797C23—62no—
798C23C22×#6712yes—
799C23C22×#6711yescharacteristic
800Q8—28no—
801Q8—21no—
802Q8—22no—
803Q8—24no—
804Q8—22no—
805Q8—62no—
806Q8—62no—
807Q8—124no—
808Q8—242no—
809Q8C2×#23512yes—
810Q8C2×#23514yes—
811D4—28no—
812D4—24no—
813D4—24no—
814D4—21no—
815D4—22no—
816D4—62no—
817D4—62no—
818D4—122no—
819D4—124no—
820D4—122no—
821D4—244no—
822D4C2×#23512yes—
823C2×C4—28no—
824C2×C4—28no—
825C2×C4—22no—
826C2×C4—21no—
827C2×C4—24no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—24no—
831C2×C4—22no—
832C2×C4—24no—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—22no—
836C2×C4—41no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—62no—
840C2×C4—64no—
841C2×C4—82no—
842C2×C4—81no—
843C2×C4—81no—
844C2×C4—82no—
845C2×C4—124no—
846C2×C4—244no—
847C2×C4—242no—
848C2×C4C2×#23512yes—
849C2×C4C2×#23512yes—
850C2×C4C22×#6712yes—
851C2×C4C22×#6711yescharacteristic
852C2×C4C22×#6712yes—
853C2×C4C22×#6711yescharacteristic
854C2×C4C22×#6712yes—
855C2×C4C22×#6711yescharacteristic
856C2×C4C22×#6711yescharacteristic
857C2×C4C22×#6711yescharacteristic
858C2×C4C24×D311yescharacteristic
859C8—62no—
860C8—62no—
861C8—64no—
862C2×C3—22no—
863C2×C3—42no—
864C2×C3—42no—
865C2×C3C2×#52511yescharacteristic
866C2×C3C2×#57811yescharacteristic
867C2×C3#358511yescharacteristic
868D3—82no—
869C22—21no—
870C22—21no—
871C22—22no—
872C22—22no—
873C22—22no—
874C22—22no—
875C22—41no—
876C22—41no—
877C22—122no—
878C22—122no—
879C22—122no—
880C22#579112yes—
881C22C23×#6711yescharacteristic
882C4—21no—
883C4—22no—
884C4—21no—
885C4—24no—
886C4—22no—
887C4—22no—
888C4—22no—
889C4—21no—
890C4—42no—
891C4—41no—
892C4—41no—
893C4—124no—
894C4—122no—
895C4#579112yes—
896C4#583812yes—
897C4C22×#23511yescharacteristic
898C4C22×#23511yescharacteristic
899C3#6060011yescharacteristic, complemented, Sylow
900C2—22no—
901C2—42no—
902C2—42no—
903C2—242no—
904C2C2×#579111yescharacteristic
905C2C2×#583811yescharacteristic
906C2#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#60600
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. #85850C2semidirect
3. #84114C2semidirect
4. #82569C2semidirect
5. #82567C2semidirect
6. #82557C2semidirect
7. #82552C2semidirect
8. #82547C2semidirect
9. #82535C2semidirect
10. #82529C2semidirect
11. #82525C2semidirect
12. #82515C2semidirect
13. #82508C2semidirect
14. #82447C2semidirect
15. #82444C2semidirect
16. #82441C2semidirect
17. C2×#5021C2semidirect
97. C4×2−1+4D3semidirect
334. C3×#41#41semidirect
342. C2×C3×Q8#41semidirect
658. #41#235semidirect
669. C2×Q8#235semidirect
899. C3#60600semidirect

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
#858502
#841142
#825692
#825672
#825572
#825522
#825472
#825352
#825292
#825252
#825152
#825082
#824472
#824442
#824412
C2×#50212
#606003