Finite Group Databasebeta

← #11675142

Subgroups — #11675142

Order 768.

1870 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#86223C211yesmaximal, characteristic, complemented
2#85766C211yesmaximal, characteristic, complemented
3C3×#3036C211yesmaximal, characteristic, complemented
4#83934C212yesmaximal, complemented
5#83930C212yesmaximal, complemented
6#83281C211yesmaximal, characteristic, complemented
7C2×C4×#213C211yesmaximal, characteristic, complemented
8#80519C214yesmaximal, complemented
9#80517C214yesmaximal, complemented
10#80416C212yesmaximal, complemented
11#80415C212yesmaximal, complemented
12#80320C212yesmaximal, complemented
13#80318C212yesmaximal, complemented
14#79059C211yesmaximal, characteristic, complemented
15#79044C211yesmaximal, characteristic, complemented
16#78876C212yesmaximal, complemented
17#78872C212yesmaximal, complemented
18#61325—31nomaximal, Sylow
19C2×C3×AGL(1,ℤ/8)C2212yes—
20C3×#532C2211yescharacteristic
21C2×C3×C4×D4C2211yescharacteristic
22#5830C2212yes—
23#5827C2212yes—
24#5798C2212yes—
25C22×#213C2211yescharacteristic
26C2×#924—22no—
27#5732C2212yescomplemented
28#5718C2212yescomplemented
29#5681C2214yescomplemented
30#5617—22no—
31#5606—22no—
32#5565—22no—
33#5563—21no—
34#5555—21no—
35#5543—21no—
36#5543C2212yescomplemented
37#5539—22no—
38#5539C2214yescomplemented
39D4×Dic6—21no—
40D4×Dic6C2212yescomplemented
41#5500C2212yes—
42#5483—22no—
43C2×C4×D12C2211yescharacteristic
44#5470C2211yescharacteristic
45#5470C2211yescharacteristic
46C3×#463C2214yescomplemented
47C3×#461C2212yescomplemented
48C3×#459C2212yescomplemented
49C3×#423C2211yescharacteristic
50C3×#417C2212yes—
51#5233C2212yes—
52#5233C2212yes—
53C2×#832C2211yescharacteristic
54#5165C2214yes—
55#5165C2214yes—
56#5164C2214yescomplemented
57Dic3×SD16C2214yescomplemented
58#5152C2214yescomplemented
59#5150C2214yes—
60#5150C2214yes—
61Dic3×D8C2214yescomplemented
62#5131C2212yes—
63#5122C2212yes—
64#5121C2212yes—
65#5119C2212yes—
66#5079C2211yescharacteristic, complemented
67#5079C2211yescharacteristic, complemented
68#5070C2211yescharacteristic, complemented
69#5070C2211yescharacteristic, complemented
70#5056C2212yescomplemented
71#5056C2212yescomplemented
72C4×#213C2212yes—
73C4×#213C2212yes—
74C4×#213C2212yes—
75C4×#213C2212yes—
76C2×#809C2211yescharacteristic
77C2×#807C2211yescharacteristic
78C2×C4×C3⋊C8C2211yescharacteristic
79#4847C2214yescomplemented
80#4846C2212yescomplemented
81#4842C2212yescomplemented
82#4831C2212yescomplemented
83#4831C2212yescomplemented
84#4830C2212yescomplemented
85#4830C2212yescomplemented
86#4800C2214yescomplemented
87#4799C2214yescomplemented
88#4794C2214yescomplemented
89#4793C2214yescomplemented
90#4764C2214yescomplemented
91#4763C2214yescomplemented
92#4760C2214yescomplemented
93#4759C2214yescomplemented
94#3506—31no—
95#3501—31no—
96#3370—34no—
97#3367—32no—
98#3366—32no—
99#3361—34no—
100#3360—32no—
101#3358—32no—
102#3136—32no—
103#3131—31no—
104#3083—32no—
105#3077—31no—
106#3041—32no—
107#3036D311yescharacteristic, complemented
108#2960—31no—
109#2946—32no—
110C2×C4×D8—31no—
111C2×C3×#41C2312yes—
112C22×C3×D4C2311yescharacteristic
113C23×C3×C4—21no—
114C2×#237—22no—
115C22×D12C2311yescharacteristic
116C22×C4×D3—21no—
117C22×Dic6—22no—
118C3×AGL(1,ℤ/8)—28no—
119C2×C3×SD16C2314yes—
120C2×C3×D8C2314yes—
121C2×C3×M16C2312yes—
122C3×C4⋊Q8C2311yescharacteristic
123C3×#127C2311yescharacteristic
124C3×#124C2312yes—
125C3×#121—21no—
126C3×#121—21no—
127C3×C4×D4—21no—
128C3×C4×D4—21no—
129C3×C4×D4—21no—
130C3×C4×D4—21no—
131C3×C4×D4C2312yes—
132C3×C4×D4C2312yes—
133C2×C3×C4⋊C4C2311yescharacteristic
134C2×C3×C22⋊C4—21no—
135C2×C3×C42C2311yescharacteristic
136C2×#217—24no—
137#947C2314yes—
138Q8×Dic3C2314yes—
139#940C2314yes—
140#939—24no—
141#938—22no—
142#937—24no—
143D4×Dic3—24no—
144D4×Dic3—22no—
145D4×Dic3—22no—
146D4×Dic3C2314yes—
147D4×Dic3C2314yes—
148D4×Dic3C2314yes—
149C2×#213—24no—
150C2×#213C2312yes—
151C2×#213C2312yes—
152#930—22no—
153#930—22no—
154C2×(C2×D3)⋊C4—21no—
155#926—22no—
156#926C2312yes—
157#926C2312yes—
158C2×C4⋊Dic3—22no—
159C2×C4⋊Dic3—22no—
160C2×C4⋊Dic3C2311yescharacteristic
161#924—21no—
162#924—21no—
163#924—22no—
164#924—24no—
165#924—22no—
166#924—24no—
167#924D412yes—
168#924D412yes—
169C2×Dic3⋊C4—24no—
170C22×C3⋊C8C2311yescharacteristic
171C22×C3⋊C8C2311yescharacteristic
172#898—24no—
173#897—22no—
174#892—22no—
175#890—22no—
176#890C2314yes—
177#888—22no—
178#888C2314yes—
179#886—24no—
180#885—24no—
181#883—24no—
182#67⋊C4—24no—
183#878—24no—
184#878—24no—
185#878—24no—
186#878—24no—
187C4×D12—21no—
188C4×D12—21no—
189C4×D12C2312yes—
190C4×D12C2312yes—
191#870D412yes—
192#870C2312yes—
193#869D411yescharacteristic
194#869D411yescharacteristic
195#869C2311yescharacteristic
196#869C2311yescharacteristic
197C4×Dic6—21no—
198C4×Dic6—21no—
199C4×Dic6C2312yes—
200C4×Dic6C2312yes—
201C3×C4⋊C8C2312yes—
202C3×C4⋊C8C2312yes—
203C3×#103C2314yes—
204C3×#102C2314yes—
205#835C2312yes—
206#835C2312yes—
207#835C2312yes—
208#835C2312yes—
209#832C2312yes—
210#832C2312yes—
211#832C2312yes—
212#832C2312yes—
213#832C2312yes—
214#832C2312yes—
215#821C2314yes—
216#821C2314yes—
217#818C2314yes—
218#817C2314yes—
219#815C2314yes—
220Dic3⋊C8C2314yes—
221Dic3⋊C8C2314yes—
222C8×Dic3C2314yes—
223#809C2312yes—
224#809C2312yes—
225#807C2312yes—
226#807C2312yes—
227C4×C3⋊C8C2311yescharacteristic
228C4×C3⋊C8C2311yescharacteristic
229C4×C3⋊C8C2311yescharacteristic
230C4×C3⋊C8C2311yescharacteristic
231C2×AGL(1,ℤ/8)C2×D312yes—
232C22×D8—31no—
233#559—34no—
234#556—32no—
235#555—61no—
236#554—32no—
237#554—34no—
238#554—62no—
239#554—61no—
240#553—62no—
241#550—32no—
242D4×Q8—32no—
243D4×Q8—61no—
244#547—61no—
245#544—32no—
246#543—62no—
247#538—62no—
248#535—32no—
249#533—31no—
250#533—31no—
251#532C2×D311yescharacteristic
252#525—62no—
253C2×C22⋊Q8—62no—
254#520—32no—
255#518—32no—
256C2×C4×D4—31no—
257C2×C4×D4C2×D311yescharacteristic
258#490—34no—
259#489—34no—
260#488—32no—
261#488—32no—
262#488—34no—
263#487—31no—
264#487—31no—
265#486—31no—
266#486—31no—
267#486—34no—
268#479—34no—
269#478—34no—
270#478—34no—
271#477—34no—
272#476—32no—
273#474—32no—
274#474—34no—
275#463—34no—
276#463—34no—
277#463C2×D314yescomplemented
278#461C2×D312yescomplemented
279#459—34no—
280#459—34no—
281#459C2×D312yescomplemented
282#446—32no—
283#446—32no—
284C8×Q8—32no—
285C8×Q8—32no—
286#442—34no—
287#440—34no—
288C4×SD16—34no—
289C4×D8—34no—
290C4×D8—32no—
291C4×D8—32no—
292C4×D8—32no—
293C4×D8—32no—
294#428—32no—
295C2×#107—31no—
296#424—32no—
297#423C2×D311yescharacteristic
298#418—32no—
299#417C2×D312yes—
300#416—32no—
301#416—32no—
302C2×#102—31no—
303C2×#102—31no—
304#405—32no—
305C2×C4×C8—31no—
306C24×C3—21no—
307C23×D3—21no—
308C3×#41—24no—
309C3×#41—24no—
310C2×C3×Q8C2412yes—
311C2×C3×D4—22no—
312C2×C3×D4—21no—
313C2×C3×D4—21no—
314C2×C3×D4—21no—
315C2×C3×D4—22no—
316C2×C3×D4#4114yescomplemented
317C2×C3×D4C2412yes—
318C2×C3×D4C2412yes—
319C22×C3×C4—21no—
320C22×C3×C4—22no—
321C22×C3×C4—22no—
322C22×C3×C4—22no—
323C22×C3×C4—82no—
324C22×C3×C4C2×D411yescharacteristic
325C22×C3×C4C2×D411yescharacteristic
326C22×C3×C4C2411yescharacteristic
327C2×#67—24no—
328C2×#67—24no—
329C22×Dic3—21no—
330C22×Dic3—24no—
331C22×Dic3—24no—
332C22×Dic3—24no—
333#237—84no—
334C2×D12—22no—
335C2×D12—22no—
336C2×D12—21no—
337C2×D12C2412yes—
338C2×C4×D3—22no—
339C2×C4×D3—22no—
340C2×C4×D3—82no—
341C2×Dic6—21no—
342C2×Dic6—21no—
343C2×Dic6—24no—
344C2×Dic6—84no—
345C2×Dic6C2×D412yes—
346C2×Dic6C2×D412yes—
347C3×SD16—28no—
348C3×D8—28no—
349C3×M16—24no—
350C2×C3×C8C2414yes—
351C3×C4⋊C4—21no—
352C3×C4⋊C4—21no—
353C3×C4⋊C4—21no—
354C3×C4⋊C4C2412yes—
355C3×C22⋊C4—22no—
356C3×C22⋊C4—22no—
357C3×C22⋊C4—22no—
358C3×C22⋊C4—22no—
359C3×C42C2×D411yescharacteristic
360C3×C42C2×D411yescharacteristic
361C3×C42C2411yescharacteristic
362C3×C42C2411yescharacteristic
363#217—22no—
364#217—24no—
365#217—24no—
366#217—24no—
367#217C2×D414yes—
368#213—24no—
369#213—24no—
370(C2×D3)⋊C4—22no—
371(C2×D3)⋊C4—22no—
372(C2×D3)⋊C4—24no—
373(C2×D3)⋊C4—24no—
374C4⋊Dic3—21no—
375C4⋊Dic3—21no—
376C4⋊Dic3—21no—
377C4⋊Dic3—24no—
378C4⋊Dic3—24no—
379C4⋊Dic3C2×D412yes—
380C4⋊Dic3C2×D412yes—
381C4⋊Dic3C2×D412yes—
382C4⋊Dic3C2×D412yes—
383C4⋊Dic3C2412yes—
384C4⋊Dic3C2412yes—
385C4⋊Dic3C2412yes—
386Dic3⋊C4—22no—
387Dic3⋊C4—22no—
388Dic3⋊C4—24no—
389Dic3⋊C4—24no—
390Dic3⋊C4C2×D414yes—
391Dic3⋊C4C2×D414yes—
392C4×Dic3—22no—
393C4×Dic3—24no—
394C4×Dic3C2414yes—
395C2×C3⋊C8—22no—
396C2×C3⋊C8—22no—
397C2×C3⋊C8C2411yescharacteristic
398C2×C3⋊C8C2411yescharacteristic
399C2×C3⋊C8C2411yescharacteristic
400C2×C3⋊C8C2411yescharacteristic
401C2×#41—62no—
402C2×#41C22×D312yes—
403C22×Q8—62no—
404C22×D4—31no—
405C22×D4C22×D311yescharacteristic
406C23×C4—21no—
407C23×C4—61no—
408AGL(1,ℤ/8)—28no—
409C2×SD16C22×D314yes—
410C2×D8—32no—
411C2×D8—32no—
412C2×D8—64no—
413C2×D8C22×D314yes—
414C2×M16C22×D312yes—
415C22×C8—31no—
416C22×C8—31no—
417C4⋊Q8—34no—
418C4⋊Q8—31no—
419C4⋊Q8—31no—
420C4⋊Q8—31no—
421C4⋊Q8—31no—
422C4⋊Q8—62no—
423C4⋊Q8C22×D311yescharacteristic
424#127—34no—
425#127C22×D311yescharacteristic
426#126—64no—
427#125—34no—
428#125—32no—
429#125—32no—
430#125—62no—
431#124—34no—
432#124—64no—
433#124C22×D312yes—
434#123—64no—
435#123—64no—
436C22⋊Q8—32no—
437C22⋊Q8—32no—
438C22⋊Q8—64no—
439C22⋊Q8—64no—
440C22⋊Q8—64no—
441C22⋊Q8—64no—
442C22⋊Q8—64no—
443C22⋊Q8—62no—
444C22⋊Q8—62no—
445C22⋊Q8—64no—
446C22⋊Q8—62no—
447C22⋊Q8—61no—
448C22⋊Q8—61no—
449#121—21no—
450#121—21no—
451#121—62no—
452#121—62no—
453#121—62no—
454#121—64no—
455#120—64no—
456C4×Q8—32no—
457C4×Q8—32no—
458C4×Q8—34no—
459C4×Q8—61no—
460C4×Q8—61no—
461C4×D4—21no—
462C4×D4—21no—
463C4×D4—21no—
464C4×D4—21no—
465C4×D4—34no—
466C4×D4—34no—
467C4×D4—34no—
468C4×D4—32no—
469C4×D4—32no—
470C4×D4—64no—
471C4×D4—64no—
472C4×D4—62no—
473C4×D4—62no—
474C4×D4—61no—
475C4×D4—61no—
476C4×D4C22×D312yes—
477C4×D4C22×D312yes—
478#117—32no—
479#117—32no—
480#117—62no—
481#117—62no—
482C2×C4⋊C4—31no—
483C2×C4⋊C4—62no—
484C2×C4⋊C4—64no—
485C2×C4⋊C4—62no—
486C2×C4⋊C4C22×D311yescharacteristic
487C2×C22⋊C4—21no—
488C2×C22⋊C4—64no—
489C2×C22⋊C4—61no—
490C2×C42C22×D311yescharacteristic
491#107—34no—
492#107—32no—
493#107—32no—
494#106—34no—
495C4⋊C8—34no—
496C4⋊C8—34no—
497C4⋊C8C22×D312yes—
498C4⋊C8C22×D312yes—
499#103—32no—
500#103—32no—
501#103—32no—
502#103—32no—
503#103C22×D314yes—
504#102—32no—
505#102—32no—
506#102—32no—
507#102—32no—
508#102—32no—
509#102—32no—
510#102—34no—
511#102—34no—
512#102—32no—
513#102—32no—
514#102C22×D314yes—
515#97—34no—
516C4×C8—34no—
517C4×C8—31no—
518C4×C8—31no—
519C4×C8—31no—
520C4×C8—31no—
521C23×C3—22no—
522C23×C3—24no—
523C23×C3—22no—
524C23×C3—81no—
525C23×C3—81no—
526C23×C3C22×D411yescharacteristic
527C22×D3—22no—
528C22×D3—42no—
529C22×D3—81no—
530C22×D3—81no—
531C3×Q8—22no—
532C3×Q8—22no—
533C3×D4—24no—
534C3×D4—22no—
535C3×D4—22no—
536C3×D4—22no—
537C3×D4—44no—
538C3×D4—42no—
539C3×D4—81no—
540C3×D4C2×#4114yes—
541C2×C3×C4—22no—
542C2×C3×C4—22no—
543C2×C3×C4—22no—
544C2×C3×C4—41no—
545C2×C3×C4—44no—
546C2×C3×C4—44no—
547C2×C3×C4—82no—
548C2×C3×C4—81no—
549C2×C3×C4C22×D411yescharacteristic
550C2×C3×C4C22×D411yescharacteristic
551C2×C3×C4C22×D411yescharacteristic
552C2×C3×C4C22×D411yescharacteristic
553C2×C3×C4C22×D411yescharacteristic
554C2×C3×C4C2×#4112yes—
555C2×C3×C42−1+412yes—
556C2×C3×C4C2511yescharacteristic
557#67—84no—
558#67—84no—
559C2×Dic3—22no—
560C2×Dic3—22no—
561C2×Dic3—22no—
562C2×Dic3—84no—
563C2×Dic3—84no—
564C2×Dic3—84no—
565C2×Dic3—81no—
566C2×Dic3C22×D414yes—
567C2×Dic3C22×D414yes—
568D12—22no—
569D12—22no—
570D12—42no—
571C4×D3—44no—
572C4×D3—82no—
573Dic6—24no—
574Dic6—42no—
575Dic6—42no—
576Dic6—84no—
577Dic6—81no—
578C3×C8—24no—
579C3⋊C8—21no—
580C3⋊C8—21no—
581C3⋊C8—21no—
582C3⋊C8—21no—
583C24—21no—
584C24—61no—
585#41—24no—
586#41—24no—
587#41—244no—
588C2×Q8—32no—
589C2×Q8—32no—
590C2×Q8—64no—
591C2×Q8—61no—
592C2×Q8—61no—
593C2×Q8—244no—
594C2×Q8C23×D312yes—
595C2×D4—22no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—22no—
600C2×D4—32no—
601C2×D4—64no—
602C2×D4—64no—
603C2×D4—61no—
604C2×D4—62no—
605C2×D4—62no—
606C2×D4#23714yescomplemented
607C2×D4C23×D312yes—
608C2×D4C23×D312yes—
609C22×C4—21no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—64no—
614C22×C4—64no—
615C22×C4—64no—
616C22×C4—61no—
617C22×C4—62no—
618C22×C4—62no—
619C22×C4—82no—
620C22×C4—242no—
621C22×C4D3×D411yescharacteristic
622C22×C4D3×D411yescharacteristic
623C22×C4C23×D311yescharacteristic
624SD16—28no—
625D8—28no—
626D8—64no—
627D8—64no—
628M16—24no—
629C2×C8—31no—
630C2×C8—31no—
631C2×C8—31no—
632C2×C8—31no—
633C2×C8—62no—
634C2×C8—62no—
635C2×C8C23×D314yes—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—32no—
640C4⋊C4—32no—
641C4⋊C4—34no—
642C4⋊C4—32no—
643C4⋊C4—34no—
644C4⋊C4—32no—
645C4⋊C4—32no—
646C4⋊C4—32no—
647C4⋊C4—32no—
648C4⋊C4—64no—
649C4⋊C4—64no—
650C4⋊C4—64no—
651C4⋊C4—64no—
652C4⋊C4—61no—
653C4⋊C4—62no—
654C4⋊C4—61no—
655C4⋊C4—62no—
656C4⋊C4—61no—
657C4⋊C4C23×D312yes—
658C22⋊C4—22no—
659C22⋊C4—22no—
660C22⋊C4—22no—
661C22⋊C4—22no—
662C22⋊C4—34no—
663C22⋊C4—64no—
664C22⋊C4—64no—
665C22⋊C4—64no—
666C22⋊C4—64no—
667C22⋊C4—64no—
668C22⋊C4—62no—
669C22⋊C4—62no—
670C22⋊C4—62no—
671C42—34no—
672C42—64no—
673C42—62no—
674C42D3×D411yescharacteristic
675C42D3×D411yescharacteristic
676C42C23×D311yescharacteristic
677C42C23×D311yescharacteristic
678C22×C3—21no—
679C22×C3—21no—
680C22×C3—24no—
681C22×C3—42no—
682C22×C3—42no—
683C22×C3—42no—
684C22×C3—42no—
685C22×C3—42no—
686C22×C3—84no—
687C22×C3#54812yes—
688C22×C3C23×D411yescharacteristic
689C2×D3—42no—
690C2×D3—42no—
691C2×D3—42no—
692C2×D3—84no—
693C3×C4—21no—
694C3×C4—21no—
695C3×C4—21no—
696C3×C4—42no—
697C3×C4—42no—
698C3×C4#54812yes—
699C3×C4#57612yes—
700C3×C4C22×#4111yescharacteristic
701C3×C4C2×2−1+411yescharacteristic
702Dic3—24no—
703Dic3—24no—
704Dic3—42no—
705Dic3—42no—
706Dic3—42no—
707C23—22no—
708C23—24no—
709C23—22no—
710C23—62no—
711C23—81no—
712C23—81no—
713C23—122no—
714C23—241no—
715C23—241no—
716C23C2×D3×D411yescharacteristic
717Q8—22no—
718Q8—22no—
719Q8—64no—
720Q8—122no—
721Q8—122no—
722Q8—241no—
723Q8—244no—
724D4—22no—
725D4—22no—
726D4—22no—
727D4—24no—
728D4—44no—
729D4—42no—
730D4—62no—
731D4—62no—
732D4—81no—
733D4—122no—
734D4—244no—
735D4—244no—
736D4C2×#23714yes—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—34no—
741C2×C4—34no—
742C2×C4—41no—
743C2×C4—44no—
744C2×C4—44no—
745C2×C4—62no—
746C2×C4—62no—
747C2×C4—62no—
748C2×C4—82no—
749C2×C4—81no—
750C2×C4—124no—
751C2×C4—242no—
752C2×C4—244no—
753C2×C4—244no—
754C2×C4—244no—
755C2×C4—241no—
756C2×C4C2×D3×D411yescharacteristic
757C2×C4C2×D3×D411yescharacteristic
758C2×C4C2×D3×D411yescharacteristic
759C2×C4C2×D3×D411yescharacteristic
760C2×C4C2×D3×D411yescharacteristic
761C2×C4C2×#23712yes—
762C2×C4#101012yes—
763C2×C4C24×D311yescharacteristic
764C8—24no—
765C8—61no—
766C8—61no—
767C8—61no—
768C8—61no—
769C2×C3—22no—
770C2×C3—44no—
771C2×C3—82no—
772C2×C3C2×#54811yescharacteristic
773C2×C3C2×#57611yescharacteristic
774C2×C3#358411yescharacteristic
775D3—82no—
776C22—21no—
777C22—21no—
778C22—24no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—84no—
785C22—122no—
786C22—122no—
787C22—122no—
788C22—244no—
789C22#559812yes—
790C22C22×D3×D411yescharacteristic
791C4—21no—
792C4—21no—
793C4—21no—
794C4—42no—
795C4—42no—
796C4—64no—
797C4—64no—
798C4—122no—
799C4—122no—
800C4—122no—
801C4#559812yes—
802C4#577412yes—
803C4C22×#23711yescharacteristic
804C4C2×#101011yescharacteristic
805C3#6132511yescharacteristic, complemented, Sylow
806C2—22no—
807C2—44no—
808C2—82no—
809C2—242no—
810C2C2×#559811yescharacteristic
811C2C2×#577411yescharacteristic
812C2#8719911yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3036C2
socleC22×C3C23×D4
hypercenter#3036D3
hypocenterC3#61325
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3036

Complements

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

NH ≅ G/Ntype
1. #86223C2semidirect
2. #85766C2semidirect
3. C3×#3036C2semidirect
4. #83934C2semidirect
5. #83930C2semidirect
6. #83281C2semidirect
7. C2×C4×#213C2semidirect
8. #80519C2semidirect
9. #80517C2semidirect
10. #80416C2semidirect
11. #80415C2semidirect
12. #80320C2semidirect
13. #80318C2semidirect
14. #79059C2semidirect
15. #79044C2semidirect
16. #78876C2semidirect
17. #78872C2semidirect
27. #5732C22semidirect
28. #5718C22semidirect
29. #5681C22semidirect
36. #5543C22semidirect
38. #5539C22semidirect
40. D4×Dic6C22semidirect
46. C3×#463C22semidirect
47. C3×#461C22semidirect
48. C3×#459C22semidirect
56. #5164C22semidirect
57. Dic3×SD16C22semidirect
58. #5152C22semidirect
61. Dic3×D8C22semidirect
66. #5079C22semidirect
67. #5079C22semidirect
68. #5070C22semidirect
69. #5070C22semidirect
70. #5056C22semidirect
71. #5056C22semidirect
79. #4847C22semidirect
80. #4846C22semidirect
81. #4842C22semidirect
82. #4831C22semidirect
83. #4831C22semidirect
84. #4830C22semidirect
85. #4830C22semidirect
86. #4800C22semidirect
87. #4799C22semidirect
88. #4794C22semidirect
89. #4793C22semidirect
90. #4764C22semidirect
91. #4763C22semidirect
92. #4760C22semidirect
93. #4759C22semidirect
107. #3036D3semidirect
277. #463C2×D3semidirect
278. #461C2×D3semidirect
281. #459C2×D3semidirect
316. C2×C3×D4#41semidirect
606. C2×D4#237semidirect
805. C3#61325semidirect

Maximal subgroups

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

subgroupindex
#862232
#857662
C3×#30362
#839342
#839302
#832812
C2×C4×#2132
#805192
#805172
#804162
#804152
#803202
#803182
#790592
#790442
#788762
#788722
#613253