Finite Group Databasebeta

← #11664201

Subgroups — #11664201

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×#3508C211yesmaximal, characteristic, complemented
2C4×#1010C211yesmaximal, characteristic, complemented
3#83439C214yesmaximal, complemented
4#83434C214yesmaximal, complemented
5#83390C212yesmaximal, complemented
6#83376C212yesmaximal, complemented
7#83367C211yesmaximal, characteristic, complemented
8#83349C211yesmaximal, characteristic, complemented
9#83316C212yesmaximal, complemented
10#83315C212yesmaximal, complemented
11#83301C212yesmaximal, complemented
12#83299C212yesmaximal, complemented
13C2×#5075C211yesmaximal, characteristic, complemented
14#83165C211yesmaximal, characteristic, complemented
15#82543C212yesmaximal, complemented
16#82537C212yesmaximal, complemented
17#82515C211yesmaximal, characteristic, complemented
18#60593—31nomaximal, Sylow
19C2×#1010C2211yescharacteristic
20C3×#559—21no—
21C3×#559—21no—
22C3×#550—21no—
23C3×#550—21no—
24C3×#546—22no—
25C3×#546—22no—
26C3×#540C2214yes—
27C3×#535C2212yes—
28C3×#533C2211yescharacteristic
29C3×#532C2212yes—
30C3×#532C2212yes—
31C2×C3×#127C2211yescharacteristic
32C3×#518C2212yes—
33C3×C4×#41C2211yescharacteristic
34#5827C2211yescharacteristic
35C22×#214C2212yes—
36C2×#932C2212yes—
37#5572—21no—
38C4×D3×Q8—21no—
39#5546—21no—
40#5546—22no—
41C4×#237—21no—
42C4×#237—22no—
43#5523C2211yescharacteristic
44#5523C2212yescomplemented
45#5516C2211yescharacteristic
46#5516C2212yescomplemented
47C4×#235C2211yescharacteristic
48C4×#235C2212yescomplemented
49C2×C4×Dic6C2211yescharacteristic
50C2×C4×Dic6C2212yescomplemented
51#5234C2212yes—
52#5215C2212yes—
53C2×#832C2212yes—
54#5094C2212yescomplemented
55#5094C2211yescharacteristic, complemented
56#5091C2212yescomplemented
57#5091C2211yescharacteristic, complemented
58#5087C2211yescharacteristic, complemented
59#5084C2211yescharacteristic, complemented
60#5075C2212yes—
61#5075C2212yes—
62#5075C2212yes—
63#5075C2212yes—
64#5075C2214yes—
65#5072C2212yes—
66#5072C2212yes—
67#5066C2212yescomplemented
68#5063C2212yescomplemented
69#5063C2214yescomplemented
70#5040C2214yescomplemented
71#5040C2214yescomplemented
72#5037C2214yescomplemented
73#5037C2214yescomplemented
74#5035C2214yescomplemented
75#5035C2214yescomplemented
76#5034C2214yescomplemented
77#5033C2214yescomplemented
78#5018C2214yescomplemented
79#5018C2214yescomplemented
80#5018C2214yescomplemented
81C4×#214C2214yescomplemented
82C4×#214C2214yescomplemented
83C4×#214C2214yescomplemented
84#5014C2214yescomplemented
85C4×#213C2214yescomplemented
86#5004C2212yes—
87#5002C2212yes—
88#5000C2214yescomplemented
89#4998C2212yes—
90#4997C2212yes—
91#4995C2212yes—
92#4926C2212yescomplemented
93#4925C2212yescomplemented
94#4924C2211yescharacteristic
95C2×C4⋊(C3⋊C8)C2211yescharacteristic
96#3508D311yescharacteristic, complemented
97C4×2−1+4—31no—
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—
113C2×C3×#41—22no—
114C2×C3×#41—22no—
115C2×C3×#41C2311yescharacteristic
116C22×C3×D4—21no—
117C22×C3×D4—21no—
118C22×C3×D4C2312yes—
119#1010—24no—
120#1010—24no—
121C2×D3×Q8—21no—
122C2×#237—22no—
123C2×#237—21no—
124C2×#235C2312yes—
125C2×#235C2311yescharacteristic
126C22×Dic6C2312yes—
127C22×Dic6C2311yescharacteristic
128C3×C4⋊Q8C2311yescharacteristic
129C3×C4⋊Q8C2311yescharacteristic
130C3×#127—22no—
131C3×#127—21no—
132C3×#127—21no—
133C3×#127C2312yes—
134C3×#127C2312yes—
135C3×#125C2312yes—
136C3×#124—22no—
137C3×#124—22no—
138C3×#124—22no—
139C3×#123—24no—
140C3×#123—24no—
141C3×C22⋊Q8—21no—
142C3×C22⋊Q8—21no—
143C3×#121—22no—
144C3×#121—22no—
145C3×#121—24no—
146C3×#121—24no—
147C3×#121C2314yes—
148C3×#121C2314yes—
149C3×#120—24no—
150C3×C4×Q8—21no—
151C3×C4×Q8—21no—
152C3×C4×Q8D411yescharacteristic
153C3×C4×Q8D411yescharacteristic
154C3×C4×D4—22no—
155C3×C4×D4—22no—
156C3×C4×D4—22no—
157C3×C4×D4—22no—
158C3×C4×D4D412yes—
159C3×C4×D4D411yescharacteristic
160C3×C4×D4D412yes—
161C3×C4×D4D411yescharacteristic
162C3×C4×D4C2314yes—
163C3×C4×D4C2314yes—
164C3×#117C2312yes—
165C3×#117C2311yescharacteristic
166C3×#117C2312yes—
167C2×C3×C22⋊C4—24no—
168C2×C3×C42C2311yescharacteristic
169C2×C3×C42C2312yes—
170Q8×Dic3—21no—
171D4×Dic3—22no—
172D4×Dic3—21no—
173C2×#214—28no—
174C2×#214C2314yes—
175C2×#214C2314yes—
176C2×#214C2314yes—
177#932—28no—
178C2×#213C2314yes—
179C4×#67—21no—
180C4×#67—21no—
181C4×#67—22no—
182C4×#67—22no—
183#926C2311yescharacteristic
184#926C2312yes—
185C2×C4⋊Dic3C2311yescharacteristic
186C2×C4⋊Dic3C2312yes—
187C2×Dic3⋊C4—21no—
188C2×Dic3⋊C4—22no—
189C2×C4×Dic3—21no—
190C2×C4×Dic3—22no—
191C2×#208C2312yes—
192C22×C3⋊C8C2312yes—
193#892—21no—
194#892—22no—
195D3×C4⋊C4—21no—
196D3×C4⋊C4—22no—
197#887—21no—
198#887—21no—
199#887—22no—
200#887—22no—
201#67⋊C4—22no—
202#67⋊C4—22no—
203#67⋊C4—22no—
204#877—22no—
205#877—22no—
206#877—22no—
207C4×D12C2311yescharacteristic
208C4×D12C2311yescharacteristic
209C4×D12C2312yes—
210#872—21no—
211#872—22no—
212C42×D3—21no—
213C42×D3—22no—
214C4×Dic6—21no—
215C4×Dic6—21no—
216C4×Dic6—22no—
217C4×Dic6—22no—
218C4×Dic6C2312yes—
219C4×Dic6C2312yes—
220C4×Dic6C2311yescharacteristic
221C4×Dic6C2312yes—
222C4×Dic6C2312yes—
223C4×Dic6C2311yescharacteristic
224C4×Dic6C2312yes—
225#832C2314yes—
226#832C2314yes—
227#832C2314yes—
228#832C2314yes—
229#830C2314yes—
230#830C2314yes—
231#810C2312yes—
232#810C2312yes—
233#810C2314yes—
234#810C2314yes—
235#809C2312yes—
236#809C2312yes—
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+4—31no—
251C2×AGL(1,ℤ/8)—32no—
252C22×SD16—32no—
253#559—21no—
254#559—21no—
255#550—21no—
256#550—21no—
257#546—22no—
258#546—22no—
259#540C2×D314yes—
260#535C2×D312yes—
261#533C2×D311yescharacteristic
262#532C2×D312yes—
263#532C2×D312yes—
264C2×#127C2×D311yescharacteristic
265#520—31no—
266#520—32no—
267#520—31no—
268#520—62no—
269#520—61no—
270#519—32no—
271#519—31no—
272#519—61no—
273#518C2×D312yes—
274C4×#41—31no—
275C4×#41—32no—
276C4×#41—62no—
277C4×#41—61no—
278C4×#41C2×D311yescharacteristic
279C2×C4×Q8—31no—
280C2×C4×Q8—32no—
281C2×C4×Q8—61no—
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—
327C24×C3—22no—
328C3×#41—22no—
329C3×#41—22no—
330C3×#41—84no—
331C3×#41—84no—
332C2×C3×Q8—21no—
333C2×C3×Q8—21no—
334C2×C3×Q8C2×D411yescharacteristic
335C2×C3×D4—24no—
336C2×C3×D4—24no—
337C2×C3×D4—22no—
338C2×C3×D4—22no—
339C2×C3×D4—22no—
340C2×C3×D4—22no—
341C2×C3×D4—22no—
342C2×C3×D4—24no—
343C2×C3×D4—24no—
344C2×C3×D4—82no—
345C2×C3×D4—82no—
346C2×C3×D4C2×D412yes—
347C2×C3×D4C2×D411yescharacteristic
348C2×C3×D4C2414yes—
349C22×C3×C4—24no—
350C22×C3×C4—24no—
351C22×C3×C4C2×D412yes—
352C22×C3×C4C2×D411yescharacteristic
353C22×C3×C4C2×D412yes—
354C22×C3×C4C2×D411yescharacteristic
355C22×C3×C4C2412yes—
356C22×C3×C4C2411yescharacteristic
357C2×#67—22no—
358C2×#67—21no—
359C22×Dic3—22no—
360C22×Dic3—21no—
361C22×Dic3—22no—
362C22×Dic3—21no—
363D3×Q8—28no—
364#237—216no—
365#237—28no—
366#235—22no—
367#235—24no—
368#235—24no—
369#235#4114yescomplemented
370C2×D12C2411yescharacteristic
371C2×C4×D3—22no—
372C2×C4×D3—21no—
373C2×C4×D3—21no—
374C2×C4×D3—22no—
375C2×C4×D3—21no—
376C2×Dic6—22no—
377C2×Dic6—21no—
378C2×Dic6—22no—
379C2×Dic6—24no—
380C2×Dic6—24no—
381C2×Dic6#4114yescomplemented
382C2×Dic6C2411yescharacteristic
383C2×Dic6C2412yes—
384C3×C4⋊C4—21no—
385C3×C4⋊C4—21no—
386C3×C4⋊C4—22no—
387C3×C4⋊C4—22no—
388C3×C4⋊C4C2×D411yescharacteristic
389C3×C4⋊C4C2×D412yes—
390C3×C4⋊C4C2×D411yescharacteristic
391C3×C4⋊C4C2×D412yes—
392C3×C4⋊C4C2412yes—
393C3×C4⋊C4C2412yes—
394C3×C22⋊C4—22no—
395C3×C22⋊C4—24no—
396C3×C22⋊C4—24no—
397C3×C22⋊C4—24no—
398C3×C22⋊C4—24no—
399C3×C22⋊C4C2×D412yes—
400C3×C22⋊C4C2×D412yes—
401C3×C22⋊C4C2×D412yes—
402C3×C42—22no—
403C3×C42C2×D412yes—
404C3×C42C2×D411yescharacteristic
405C3×C42C2×D412yes—
406C3×C42C2×D411yescharacteristic
407C3×C42C2412yes—
408C3×C42C2411yescharacteristic
409C3×C42C2411yescharacteristic
410#217—22no—
411#217—21no—
412#214—28no—
413#214—28no—
414#214—28no—
415#213—28no—
416(C2×D3)⋊C4—21no—
417(C2×D3)⋊C4—22no—
418(C2×D3)⋊C4—21no—
419C4⋊Dic3—22no—
420C4⋊Dic3—21no—
421C4⋊Dic3C2412yes—
422C4⋊Dic3C2411yescharacteristic
423C4⋊Dic3C2411yescharacteristic
424Dic3⋊C4—22no—
425Dic3⋊C4—21no—
426Dic3⋊C4—22no—
427Dic3⋊C4—22no—
428Dic3⋊C4—22no—
429Dic3⋊C4—22no—
430Dic3⋊C4—21no—
431C4×Dic3—22no—
432C4×Dic3—21no—
433C4×Dic3—22no—
434C4×Dic3—22no—
435C4×Dic3—22no—
436C4×Dic3—22no—
437C4×Dic3—21no—
438C4×Dic3—22no—
439C4×Dic3—21no—
440#208—24no—
441C2×C3⋊C8—24no—
442C2×C3⋊C8C2412yes—
443C2×C3⋊C8C2414yes—
444C2×C3⋊C8C2412yes—
4452−1+4—64no—
4462−1+4—64no—
447C2×#41—22no—
448C2×#41—22no—
449C2×#41—31no—
450C2×#41—32no—
451C2×#41—62no—
452C2×#41—61no—
453C2×#41C22×D311yescharacteristic
454C22×Q8—31no—
455C22×Q8—32no—
456C22×Q8—61no—
457C22×D4—21no—
458C22×D4—21no—
459C22×D4C22×D312yes—
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⋊Q8C22×D311yescharacteristic
469C4⋊Q8C22×D311yescharacteristic
470#127—22no—
471#127—21no—
472#127—21no—
473#127C22×D312yes—
474#127C22×D312yes—
475#125C22×D312yes—
476#124—22no—
477#124—22no—
478#124—22no—
479#123—24no—
480#123—24no—
481C22⋊Q8—21no—
482C22⋊Q8—21no—
483#121—22no—
484#121—22no—
485#121—24no—
486#121—24no—
487#121C22×D314yes—
488#121C22×D314yes—
489#120—24no—
490C4×Q8—21no—
491C4×Q8—21no—
492C4×Q8—32no—
493C4×Q8—31no—
494C4×Q8—32no—
495C4×Q8—32no—
496C4×Q8—32no—
497C4×Q8—32no—
498C4×Q8—31no—
499C4×Q8—61no—
500C4×Q8—61no—
501C4×Q8—62no—
502C4×Q8—61no—
503C4×Q8—62no—
504C4×Q8—62no—
505C4×Q8—61no—
506C4×Q8—62no—
507C4×Q8—61no—
508C4×Q8#6711yescharacteristic
509C4×Q8#6711yescharacteristic
510C4×D4—22no—
511C4×D4—22no—
512C4×D4—22no—
513C4×D4—22no—
514C4×D4—31no—
515C4×D4—32no—
516C4×D4—31no—
517C4×D4—62no—
518C4×D4—61no—
519C4×D4—62no—
520C4×D4—61no—
521C4×D4—62no—
522C4×D4—61no—
523C4×D4—62no—
524C4×D4—62no—
525C4×D4—62no—
526C4×D4#6712yes—
527C4×D4#6711yescharacteristic
528C4×D4#6712yes—
529C4×D4#6711yescharacteristic
530C4×D4C22×D314yes—
531C4×D4C22×D314yes—
532#117—31no—
533#117—32no—
534#117—61no—
535#117—62no—
536#117—62no—
537#117—62no—
538#117—62no—
539#117—62no—
540#117—61no—
541#117C22×D312yes—
542#117C22×D311yescharacteristic
543#117C22×D312yes—
544C2×C4⋊C4—31no—
545C2×C4⋊C4—32no—
546C2×C4⋊C4—62no—
547C2×C4⋊C4—61no—
548C2×C4⋊C4—61no—
549C2×C4⋊C4—62no—
550C2×C22⋊C4—24no—
551C2×C42—62no—
552C2×C42—61no—
553C2×C42—62no—
554C2×C42—61no—
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—34no—
573#102—34no—
574#102—34no—
575#102—34no—
576#102—32no—
577#102—32no—
578C22⋊C8—34no—
579C22⋊C8—34no—
580#97—34no—
581C4×C8—34no—
582C23×C3—24no—
583C23×C3—44no—
584C23×C3—82no—
585C23×C3—82no—
586C23×C3C22×D412yes—
587C23×C3C22×D411yescharacteristic
588C22×D3—21no—
589C3×Q8—22no—
590C3×Q8—42no—
591C3×Q8—42no—
592C3×D4—24no—
593C3×D4—22no—
594C3×D4—24no—
595C3×D4—24no—
596C3×D4—44no—
597C3×D4—44no—
598C3×D4—44no—
599C3×D4—82no—
600C3×D4—82no—
601C3×D4—84no—
602C3×D4—84no—
603C2×C3×C4—22no—
604C2×C3×C4—24no—
605C2×C3×C4—22no—
606C2×C3×C4—22no—
607C2×C3×C4—22no—
608C2×C3×C4—22no—
609C2×C3×C4—41no—
610C2×C3×C4—42no—
611C2×C3×C4—84no—
612C2×C3×C4—84no—
613C2×C3×C4C22×D412yes—
614C2×C3×C4C22×D411yescharacteristic
615C2×C3×C4C22×D412yes—
616C2×C3×C4C22×D411yescharacteristic
617C2×C3×C4C22×D412yes—
618C2×C3×C4C22×D411yescharacteristic
619C2×C3×C4C22×D411yescharacteristic
620C2×C3×C4C22×D411yescharacteristic
621C2×C3×C4C2×#4112yes—
622C2×C3×C4C2×#4112yes—
623C2×C3×C4C2511yescharacteristic
624#67—28no—
625#67—24no—
626C2×Dic3—28no—
627C2×Dic3—24no—
628C2×Dic3—21no—
629C2×Dic3—22no—
630C2×Dic3—21no—
631C2×Dic3—22no—
632C2×Dic3—21no—
633C2×Dic3—81no—
634C2×Dic3—82no—
635D12—21no—
636D12C2×#4112yes—
637C4×D3—28no—
638C4×D3—24no—
639C4×D3—42no—
640C4×D3—82no—
641C4×D3—81no—
642Dic6—28no—
643Dic6—24no—
644Dic6—22no—
645Dic6—21no—
646Dic6C2×#4112yes—
647Dic6C2×#4114yes—
648C3⋊C8—22no—
649C3⋊C8—22no—
650C3⋊C8—24no—
651C24—22no—
652#41—22no—
653#41—22no—
654#41—34no—
655#41—64no—
656#41—64no—
657#41—616no—
658#41—68no—
659#41—62no—
660#41—84no—
661#41—84no—
662C2×Q8—21no—
663C2×Q8—21no—
664C2×Q8—34no—
665C2×Q8—32no—
666C2×Q8—31no—
667C2×Q8—64no—
668C2×Q8—64no—
669C2×Q8—68no—
670C2×Q8—62no—
671C2×Q8—62no—
672C2×Q8—61no—
673C2×Q8C2×#6711yescharacteristic
674C2×D4—24no—
675C2×D4—24no—
676C2×D4—24no—
677C2×D4—24no—
678C2×D4—22no—
679C2×D4—22no—
680C2×D4—22no—
681C2×D4—22no—
682C2×D4—22no—
683C2×D4—31no—
684C2×D4—62no—
685C2×D4—61no—
686C2×D4—82no—
687C2×D4—82no—
688C2×D4C2×#6712yes—
689C2×D4C2×#6711yescharacteristic
690C2×D4C23×D314yes—
691C22×C4—24no—
692C22×C4—24no—
693C22×C4—62no—
694C22×C4—61no—
695C22×C4—62no—
696C22×C4—61no—
697C22×C4—62no—
698C22×C4—61no—
699C22×C4—61no—
700C22×C4—62no—
701C22×C4—61no—
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—21no—
718C4⋊C4—21no—
719C4⋊C4—22no—
720C4⋊C4—22no—
721C4⋊C4—32no—
722C4⋊C4—31no—
723C4⋊C4—31no—
724C4⋊C4—62no—
725C4⋊C4—61no—
726C4⋊C4—62no—
727C4⋊C4—62no—
728C4⋊C4—62no—
729C4⋊C4—61no—
730C4⋊C4—62no—
731C4⋊C4—62no—
732C4⋊C4—61no—
733C4⋊C4C2×#6711yescharacteristic
734C4⋊C4C2×#6712yes—
735C4⋊C4C2×#6711yescharacteristic
736C4⋊C4C2×#6712yes—
737C4⋊C4C23×D312yes—
738C4⋊C4C23×D312yes—
739C22⋊C4—22no—
740C22⋊C4—24no—
741C22⋊C4—24no—
742C22⋊C4—24no—
743C22⋊C4—24no—
744C22⋊C4—62no—
745C22⋊C4—61no—
746C22⋊C4—61no—
747C22⋊C4—62no—
748C22⋊C4—61no—
749C22⋊C4C2×#6712yes—
750C22⋊C4C2×#6712yes—
751C22⋊C4C2×#6712yes—
752C42—22no—
753C42—61no—
754C42—62no—
755C42—62no—
756C42—61no—
757C42—62no—
758C42—61no—
759C42—62no—
760C42—62no—
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—44no—
775C22×C3—44no—
776C22×C3—44no—
777C22×C3—164no—
778C22×C3#52512yes—
779C22×C3C23×D411yescharacteristic
780C2×D3—22no—
781C2×D3—41no—
782C2×D3—41no—
783C3×C4—22no—
784C3×C4—21no—
785C3×C4—21no—
786C3×C4—22no—
787C3×C4—22no—
788C3×C4—21no—
789C3×C4—42no—
790C3×C4—42no—
791C3×C4#52512yes—
792C3×C4#57712yes—
793C3×C4C22×#4111yescharacteristic
794C3×C4C22×#4111yescharacteristic
795Dic3—22no—
796Dic3—24no—
797Dic3—42no—
798Dic3—41no—
799Dic3—41no—
800C23—24no—
801C23—44no—
802C23—61no—
803C23—82no—
804C23—82no—
805C23C22×#6712yes—
806C23C22×#6711yescharacteristic
807Q8—22no—
808Q8—34no—
809Q8—32no—
810Q8—42no—
811Q8—42no—
812Q8—68no—
813Q8—62no—
814Q8—61no—
815Q8—64no—
816D4—24no—
817D4—24no—
818D4—24no—
819D4—22no—
820D4—32no—
821D4—44no—
822D4—44no—
823D4—44no—
824D4—68no—
825D4—64no—
826D4—61no—
827D4—82no—
828D4—82no—
829D4—84no—
830D4—84no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—24no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—41no—
838C2×C4—42no—
839C2×C4—68no—
840C2×C4—68no—
841C2×C4—62no—
842C2×C4—61no—
843C2×C4—64no—
844C2×C4—64no—
845C2×C4—61no—
846C2×C4—62no—
847C2×C4—61no—
848C2×C4—84no—
849C2×C4—84no—
850C2×C4—122no—
851C2×C4—242no—
852C2×C4—241no—
853C2×C4—241no—
854C2×C4—242no—
855C2×C4D3×#4112yes—
856C2×C4D3×#4112yes—
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—84no—
872C2×C3C2×#52511yescharacteristic
873C2×C3C2×#57711yescharacteristic
874C2×C3#358511yescharacteristic
875D3—42no—
876C22—21no—
877C22—21no—
878C22—22no—
879C22—22no—
880C22—22no—
881C22—44no—
882C22—44no—
883C22—44no—
884C22—62no—
885C22—121no—
886C22—121no—
887C22—164no—
888C22#582812yes—
889C22C23×#6711yescharacteristic
890C4—22no—
891C4—21no—
892C4—22no—
893C4—21no—
894C4—22no—
895C4—21no—
896C4—42no—
897C4—42no—
898C4—64no—
899C4—62no—
900C4—122no—
901C4—121no—
902C4—121no—
903C4#582812yes—
904C4#583612yes—
905C4C2×D3×#4111yescharacteristic
906C4C2×D3×#4111yescharacteristic
907C3#6059311yescharacteristic, complemented, Sylow
908C2—22no—
909C2—42no—
910C2—84no—
911C2—122no—
912C2C2×#582811yescharacteristic
913C2#8727711yescharacteristic
914C2C2×#583611yescharacteristic
subgroupG/H
centerC22C23×#67
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3508C2
socleC22×C3C23×D4
hypercenter#3508D3
hypocenterC3#60593
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3508

Complements

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

NH ≅ G/Ntype
1. C3×#3508C2semidirect
2. C4×#1010C2semidirect
3. #83439C2semidirect
4. #83434C2semidirect
5. #83390C2semidirect
6. #83376C2semidirect
7. #83367C2semidirect
8. #83349C2semidirect
9. #83316C2semidirect
10. #83315C2semidirect
11. #83301C2semidirect
12. #83299C2semidirect
13. C2×#5075C2semidirect
14. #83165C2semidirect
15. #82543C2semidirect
16. #82537C2semidirect
17. #82515C2semidirect
44. #5523C22semidirect
46. #5516C22semidirect
48. C4×#235C22semidirect
50. C2×C4×Dic6C22semidirect
54. #5094C22semidirect
55. #5094C22semidirect
56. #5091C22semidirect
57. #5091C22semidirect
58. #5087C22semidirect
59. #5084C22semidirect
67. #5066C22semidirect
68. #5063C22semidirect
69. #5063C22semidirect
70. #5040C22semidirect
71. #5040C22semidirect
72. #5037C22semidirect
73. #5037C22semidirect
74. #5035C22semidirect
75. #5035C22semidirect
76. #5034C22semidirect
77. #5033C22semidirect
78. #5018C22semidirect
79. #5018C22semidirect
80. #5018C22semidirect
81. C4×#214C22semidirect
82. C4×#214C22semidirect
83. C4×#214C22semidirect
84. #5014C22semidirect
85. C4×#213C22semidirect
88. #5000C22semidirect
92. #4926C22semidirect
93. #4925C22semidirect
96. #3508D3semidirect
369. #235#41semidirect
381. C2×Dic6#41semidirect
907. C3#60593semidirect

Maximal subgroups

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

subgroupindex
C3×#35082
C4×#10102
#834392
#834342
#833902
#833762
#833672
#833492
#833162
#833152
#833012
#832992
C2×#50752
#831652
#825432
#825372
#825152
#605933