Finite Group Databasebeta

← #11675138

Subgroups — #11675138

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
1C3×#3501C211yesmaximal, characteristic, complemented
2#86259C211yesmaximal, characteristic, complemented
3#83643C214yesmaximal, complemented
4#83639C214yesmaximal, complemented
5#83638C212yesmaximal, complemented
6#83637C212yesmaximal, complemented
7#83563C212yesmaximal, complemented
8#83562C212yesmaximal, complemented
9#83475C212yesmaximal, complemented
10#83470C212yesmaximal, complemented
11#83350C211yesmaximal, characteristic, complemented
12#83334C211yesmaximal, characteristic, complemented
13#83328C211yesmaximal, characteristic, complemented
14#82540C212yesmaximal, complemented
15#82537C212yesmaximal, complemented
16#82307C211yesmaximal, characteristic, complemented
17C2×C4×#213C211yesmaximal, characteristic, complemented
18#61325—31nomaximal, Sylow
19C3×#554—21no—
20C3×#554—22no—
21C3×#554C2212yescomplemented
22C3×#554C2214yescomplemented
23C3×D4×Q8—21no—
24C3×D4×Q8C2212yescomplemented
25C3×#544C2212yes—
26C3×#543—22no—
27C3×#533C2211yescharacteristic
28C3×#533C2211yescharacteristic
29C2×C3×C22⋊Q8—22no—
30C3×#518C2212yes—
31C2×C3×C4×D4C2211yescharacteristic
32C2×#932C2212yes—
33C22×#213C2211yescharacteristic
34#5734—21no—
35#5726—21no—
36#5695—22no—
37#5644—22no—
38#5627—22no—
39#5585C2214yescomplemented
40#5584C2212yescomplemented
41#5577C2212yescomplemented
42#5525C2212yes—
43#5523C2212yes—
44#5477C2211yescharacteristic
45C2×C4×D12C2211yescharacteristic
46C2×#832C2211yescharacteristic
47#5093C2211yescharacteristic, complemented
48#5093C2211yescharacteristic, complemented
49#5091C2214yescomplemented
50#5089C2214yescomplemented
51#5088C2214yescomplemented
52#5088C2211yescharacteristic, complemented
53#5088C2211yescharacteristic, complemented
54#5087C2214yescomplemented
55#5087C2212yescomplemented
56#5084C2212yescomplemented
57#5068C2214yescomplemented
58#5068C2212yescomplemented
59#5068C2212yescomplemented
60#5067C2214yescomplemented
61#5066C2214yescomplemented
62#5066C2214yescomplemented
63#5063C2214yescomplemented
64#5024C2212yescomplemented
65#5024C2212yescomplemented
66Q8×C3⋊C8C2212yescomplemented
67Q8×C3⋊C8C2212yescomplemented
68#5019C2212yescomplemented
69#5018C2214yescomplemented
70C4×#214C2214yescomplemented
71#5016C2214yes—
72#5016C2214yes—
73#5016C2214yescomplemented
74#5015C2214yes—
75#5015C2214yes—
76#5015C2212yescomplemented
77#5014C2214yescomplemented
78C4×#213C2212yes—
79C4×#213C2212yes—
80C4×#213C2212yes—
81C4×#213C2212yes—
82C4×#213C2214yescomplemented
83#5002C2212yes—
84#5002C2212yes—
85#5001C2212yes—
86#4999C2212yes—
87#4997C2212yes—
88#4995C2212yes—
89#4966C2212yes—
90C2×#809C2211yescharacteristic
91C2×#807C2211yescharacteristic
92#4924C2211yescharacteristic
93C2×C4×C3⋊C8C2211yescharacteristic
94#3506—31no—
95#3501D311yescharacteristic, complemented
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#3036—31no—
108#2960—31no—
109#2946—32no—
110C2×C4×D8—31no—
111C22×C3×Q8—22no—
112C22×C3×D4C2311yescharacteristic
113C23×C3×C4—21no—
114C2×#239—22no—
115C2×#235C2312yes—
116C22×D12C2311yescharacteristic
117C22×C4×D3—21no—
118C3×C4⋊Q8—22no—
119C3×C4⋊Q8D411yescharacteristic
120C3×C4⋊Q8D411yescharacteristic
121C3×C4⋊Q8C2311yescharacteristic
122C3×C4⋊Q8C2311yescharacteristic
123C3×C4⋊Q8C2314yes—
124C3×#125—22no—
125C3×#125D412yes—
126C3×#125C2314yes—
127C3×#125C2312yes—
128C3×C22⋊Q8—22no—
129C3×C22⋊Q8—24no—
130C3×C22⋊Q8—21no—
131C3×C22⋊Q8—21no—
132C3×C22⋊Q8—22no—
133C3×C22⋊Q8—24no—
134C3×C22⋊Q8—24no—
135C3×C22⋊Q8—24no—
136C3×C22⋊Q8—24no—
137C3×C22⋊Q8—24no—
138C3×C22⋊Q8D412yes—
139C3×C22⋊Q8D412yes—
140C3×C4×Q8—21no—
141C3×C4×Q8—21no—
142C3×C4×Q8C2312yes—
143C3×C4×Q8C2312yes—
144C3×C4×D4—22no—
145C3×C4×D4—22no—
146C3×C4×D4—21no—
147C3×C4×D4—21no—
148C3×C4×D4C2312yes—
149C3×C4×D4C2312yes—
150C3×C4×D4C2314yes—
151C3×C4×D4C2314yes—
152C3×#117C2312yes—
153C3×#117C2312yes—
154C2×C3×C4⋊C4—24no—
155C2×C3×C4⋊C4—22no—
156C2×C3×C4⋊C4C2311yescharacteristic
157C2×C3×C22⋊C4—21no—
158C2×C3×C22⋊C4—24no—
159C2×C3×C42C2311yescharacteristic
160#947—24no—
161#946—22no—
162C2×#214C2314yes—
163#932—28no—
164C2×#213—24no—
165C2×#213C2312yes—
166C2×#213C2312yes—
167C2×#213C2314yes—
168#930—21no—
169#930—21no—
170C2×(C2×D3)⋊C4—21no—
171C2×C4⋊Dic3C2311yescharacteristic
172C2×#208C2312yes—
173C22×C3⋊C8C2311yescharacteristic
174C22×C3⋊C8C2311yescharacteristic
175#898—24no—
176#895—24no—
177#895—22no—
178#895—22no—
179#895—22no—
180#894—24no—
181#894—24no—
182#893—24no—
183#892—22no—
184#892—22no—
185D3×C4⋊C4—22no—
186#882—24no—
187#67⋊C4—24no—
188#875C2312yes—
189#875C2314yes—
190#874C2311yescharacteristic
191#874C2314yes—
192C4×D12—21no—
193C4×D12—21no—
194C4×D12—21no—
195C4×D12—21no—
196C4×D12C2312yes—
197C4×D12C2312yes—
198C4×D12C2314yes—
199#869C2311yescharacteristic
200C4×Dic6C2314yes—
201#832C2312yes—
202#832C2312yes—
203#810C2314yes—
204#810C2312yes—
205#810C2312yes—
206#810C2312yes—
207#810C2312yes—
208#809C2312yes—
209#809C2312yes—
210#809C2314yes—
211#809C2314yes—
212#809C2314yes—
213#809C2312yes—
214#809C2312yes—
215#809C2312yes—
216#809C2312yes—
217#808C2314yes—
218#807C2312yes—
219#807C2312yes—
220#807C2314yes—
221C4⋊(C3⋊C8)C2312yes—
222C4⋊(C3⋊C8)C2312yes—
223C4⋊(C3⋊C8)C2314yes—
224C4⋊(C3⋊C8)C2314yes—
225#803C2314yes—
226C4×C3⋊C8C2311yescharacteristic
227C4×C3⋊C8C2311yescharacteristic
228C4×C3⋊C8C2311yescharacteristic
229C4×C3⋊C8C2311yescharacteristic
230C4×C3⋊C8C2314yes—
231C2×AGL(1,ℤ/8)—32no—
232C22×D8—31no—
233#559—34no—
234#556—32no—
235#555—61no—
236#554—21no—
237#554—22no—
238#554C2×D312yescomplemented
239#554C2×D314yescomplemented
240#553—62no—
241#550—32no—
242D4×Q8—21no—
243D4×Q8C2×D312yescomplemented
244#547—61no—
245#544C2×D312yes—
246#543—22no—
247#538—62no—
248#535—32no—
249#533C2×D311yescharacteristic
250#533C2×D311yescharacteristic
251#532—31no—
252#525—62no—
253C2×C22⋊Q8—22no—
254#520—32no—
255#518C2×D312yes—
256C2×C4×D4—31no—
257C2×C4×D4C2×D311yescharacteristic
258#490—34no—
259#489—34no—
260#488—34no—
261#488—32no—
262#488—32no—
263#487—31no—
264#487—31no—
265#486—31no—
266#486—34no—
267#486—31no—
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#463—34no—
278#461—32no—
279#459—32no—
280#459—34no—
281#459—34no—
282#446—32no—
283#446—32no—
284C8×Q8—32no—
285C8×Q8—32no—
286#442—34no—
287#440—34no—
288C4×SD16—34no—
289C4×D8—32no—
290C4×D8—34no—
291C4×D8—32no—
292C4×D8—32no—
293C4×D8—32no—
294#428—32no—
295C2×#107—31no—
296#424—32no—
297#423—31no—
298#418—32no—
299#417—32no—
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—
308C2×C3×Q8—21no—
309C2×C3×Q8—21no—
310C2×C3×Q8—24no—
311C2×C3×Q8—84no—
312C2×C3×Q8C2×D412yes—
313C2×C3×Q8C2×D412yes—
314C2×C3×D4—21no—
315C2×C3×D4—22no—
316C2×C3×D4#4114yescomplemented
317C2×C3×D4C2412yes—
318C22×C3×C4—21no—
319C22×C3×C4—22no—
320C22×C3×C4—24no—
321C22×C3×C4—24no—
322C22×C3×C4—22no—
323C22×C3×C4—82no—
324C22×C3×C4C2×D411yescharacteristic
325C22×C3×C4C2×D411yescharacteristic
326C22×C3×C4C2411yescharacteristic
327C2×#67—22no—
328C22×Dic3—21no—
329#239—84no—
330#235—24no—
331#235—24no—
332C2×D12—22no—
333C2×D12—22no—
334C2×D12—21no—
335C2×D12—21no—
336C2×D12—21no—
337C2×D12—24no—
338C2×D12—24no—
339C2×D12C2412yes—
340C2×D12C2412yes—
341C2×C4×D3—22no—
342C2×C4×D3—22no—
343C2×C4×D3—22no—
344C2×C4×D3—24no—
345C2×C4×D3—82no—
346C2×Dic6C2412yes—
347C3×C4⋊C4—22no—
348C3×C4⋊C4—21no—
349C3×C4⋊C4—24no—
350C3×C4⋊C4—24no—
351C3×C4⋊C4—24no—
352C3×C4⋊C4—21no—
353C3×C4⋊C4—22no—
354C3×C4⋊C4—21no—
355C3×C4⋊C4C2×D412yes—
356C3×C4⋊C4C2×D412yes—
357C3×C4⋊C4C2×D412yes—
358C3×C4⋊C4C2×D414yes—
359C3×C4⋊C4C2×D412yes—
360C3×C4⋊C4C2×D414yes—
361C3×C4⋊C4C2412yes—
362C3×C4⋊C4C2412yes—
363C3×C4⋊C4C2412yes—
364C3×C22⋊C4—22no—
365C3×C22⋊C4—24no—
366C3×C22⋊C4—24no—
367C3×C22⋊C4—22no—
368C3×C22⋊C4—22no—
369C3×C22⋊C4C2×D414yes—
370C3×C42—22no—
371C3×C42C2×D411yescharacteristic
372C3×C42C2×D411yescharacteristic
373C3×C42C2411yescharacteristic
374C3×C42C2411yescharacteristic
375C3×C42C2414yes—
376#214—28no—
377#213—24no—
378#213—24no—
379#213—28no—
380(C2×D3)⋊C4—22no—
381(C2×D3)⋊C4—22no—
382(C2×D3)⋊C4—22no—
383(C2×D3)⋊C4—22no—
384(C2×D3)⋊C4—24no—
385(C2×D3)⋊C4—24no—
386(C2×D3)⋊C4—24no—
387C4⋊Dic3—21no—
388C4⋊Dic3—21no—
389C4⋊Dic3—21no—
390C4⋊Dic3C2412yes—
391Dic3⋊C4—24no—
392C4×Dic3—24no—
393#208—24no—
394C2×C3⋊C8—22no—
395C2×C3⋊C8—22no—
396C2×C3⋊C8C2411yescharacteristic
397C2×C3⋊C8C2411yescharacteristic
398C2×C3⋊C8C2411yescharacteristic
399C2×C3⋊C8C2411yescharacteristic
400C2×C3⋊C8C2414yes—
401C2×#41—32no—
402C2×#41—62no—
403C22×Q8—22no—
404C22×D4—31no—
405C22×D4C22×D311yescharacteristic
406C23×C4—21no—
407C23×C4—61no—
408AGL(1,ℤ/8)—68no—
409C2×SD16—34no—
410C2×D8—32no—
411C2×D8—32no—
412C2×D8—34no—
413C2×D8—64no—
414C2×M16—32no—
415C22×C8—31no—
416C22×C8—31no—
417C4⋊Q8—22no—
418C4⋊Q8—31no—
419C4⋊Q8#6711yescharacteristic
420C4⋊Q8#6711yescharacteristic
421C4⋊Q8C22×D311yescharacteristic
422C4⋊Q8C22×D311yescharacteristic
423C4⋊Q8C22×D314yes—
424#127—31no—
425#127—34no—
426#126—64no—
427#125—22no—
428#125#6712yes—
429#125C22×D312yes—
430#125C22×D314yes—
431#124—32no—
432#124—34no—
433#124—64no—
434#123—64no—
435#123—64no—
436C22⋊Q8—22no—
437C22⋊Q8—24no—
438C22⋊Q8—21no—
439C22⋊Q8—21no—
440C22⋊Q8—22no—
441C22⋊Q8—24no—
442C22⋊Q8—24no—
443C22⋊Q8—24no—
444C22⋊Q8—24no—
445C22⋊Q8—24no—
446C22⋊Q8—62no—
447C22⋊Q8#6712yes—
448C22⋊Q8#6712yes—
449#121—61no—
450#121—61no—
451#121—62no—
452#121—62no—
453#121—62no—
454#121—64no—
455#120—64no—
456C4×Q8—21no—
457C4×Q8—21no—
458C4×Q8—34no—
459C4×Q8C22×D312yes—
460C4×Q8C22×D312yes—
461C4×D4—22no—
462C4×D4—22no—
463C4×D4—21no—
464C4×D4—21no—
465C4×D4—32no—
466C4×D4—32no—
467C4×D4—34no—
468C4×D4—64no—
469C4×D4—64no—
470C4×D4—61no—
471C4×D4—61no—
472C4×D4—61no—
473C4×D4—61no—
474C4×D4C22×D312yes—
475C4×D4C22×D312yes—
476C4×D4C22×D314yes—
477C4×D4C22×D314yes—
478#117—62no—
479#117—62no—
480#117C22×D312yes—
481#117C22×D312yes—
482C2×C4⋊C4—24no—
483C2×C4⋊C4—22no—
484C2×C4⋊C4—31no—
485C2×C4⋊C4—62no—
486C2×C4⋊C4C22×D311yescharacteristic
487C2×C22⋊C4—21no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—61no—
490C2×C42C22×D311yescharacteristic
491#107—32no—
492#107—32no—
493#107—34no—
494#106—34no—
495C4⋊C8—32no—
496C4⋊C8—32no—
497C4⋊C8—34no—
498C4⋊C8—34no—
499#103—32no—
500#103—32no—
501#103—32no—
502#103—32no—
503#103—34no—
504#102—32no—
505#102—32no—
506#102—32no—
507#102—32no—
508#102—32no—
509#102—32no—
510#102—32no—
511#102—32no—
512#102—34no—
513#102—34no—
514#102—34no—
515#97—34no—
516C4×C8—31no—
517C4×C8—31no—
518C4×C8—31no—
519C4×C8—31no—
520C4×C8—34no—
521C23×C3—22no—
522C23×C3—24no—
523C23×C3—81no—
524C23×C3—81no—
525C23×C3C22×D411yescharacteristic
526C22×D3—22no—
527C22×D3—22no—
528C22×D3—42no—
529C22×D3—81no—
530C22×D3—81no—
531C3×Q8—24no—
532C3×Q8—42no—
533C3×Q8—42no—
534C3×Q8—81no—
535C3×Q8—84no—
536C3×D4—24no—
537C3×D4—22no—
538C3×D4C2×#4114yes—
539C2×C3×C4—22no—
540C2×C3×C4—22no—
541C2×C3×C4—22no—
542C2×C3×C4—22no—
543C2×C3×C4—41no—
544C2×C3×C4—44no—
545C2×C3×C4—84no—
546C2×C3×C4—82no—
547C2×C3×C4—84no—
548C2×C3×C4—81no—
549C2×C3×C4C22×D414yes—
550C2×C3×C4C22×D414yes—
551C2×C3×C4C22×D411yescharacteristic
552C2×C3×C4C22×D411yescharacteristic
553C2×C3×C4C22×D411yescharacteristic
554C2×C3×C4C22×D411yescharacteristic
555C2×C3×C4C22×D411yescharacteristic
556C2×C3×C4C2×#4112yes—
557C2×C3×C42−1+412yes—
558C2×C3×C4C2511yescharacteristic
559#67—44no—
560C2×Dic3—22no—
561C2×Dic3—22no—
562C2×Dic3—81no—
563D12—22no—
564D12—22no—
565D12—22no—
566D12—22no—
567D12—42no—
568D12—42no—
569D12—81no—
570D12—84no—
571D12—84no—
572C4×D3—44no—
573C4×D3—44no—
574C4×D3—82no—
575C4×D3—84no—
576Dic6—22no—
577Dic6—22no—
578C3⋊C8—21no—
579C3⋊C8—21no—
580C3⋊C8—24no—
581C3⋊C8—21no—
582C3⋊C8—21no—
583C24—21no—
584C24—61no—
585#41—64no—
586#41—64no—
587#41—244no—
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8—24no—
591C2×Q8—32no—
592C2×Q8—84no—
593C2×Q8C2×#6712yes—
594C2×Q8C2×#6712yes—
595C2×D4—22no—
596C2×D4—21no—
597C2×D4—32no—
598C2×D4—32no—
599C2×D4—62no—
600C2×D4—62no—
601C2×D4—62no—
602C2×D4—61no—
603C2×D4—61no—
604C2×D4—64no—
605C2×D4—61no—
606C2×D4—64no—
607C2×D4#23914yescomplemented
608C2×D4C23×D312yes—
609C22×C4—21no—
610C22×C4—22no—
611C22×C4—24no—
612C22×C4—24no—
613C22×C4—22no—
614C22×C4—61no—
615C22×C4—62no—
616C22×C4—62no—
617C22×C4—64no—
618C22×C4—62no—
619C22×C4—82no—
620C22×C4—242no—
621C22×C4C2×#6711yescharacteristic
622C22×C4C2×#6711yescharacteristic
623C22×C4C23×D311yescharacteristic
624SD16—68no—
625D8—64no—
626D8—64no—
627D8—68no—
628M16—64no—
629C2×C8—31no—
630C2×C8—31no—
631C2×C8—31no—
632C2×C8—31no—
633C2×C8—34no—
634C2×C8—62no—
635C2×C8—62no—
636C4⋊C4—22no—
637C4⋊C4—21no—
638C4⋊C4—24no—
639C4⋊C4—24no—
640C4⋊C4—24no—
641C4⋊C4—21no—
642C4⋊C4—22no—
643C4⋊C4—21no—
644C4⋊C4—32no—
645C4⋊C4—61no—
646C4⋊C4—64no—
647C4⋊C4—61no—
648C4⋊C4—61no—
649C4⋊C4C2×#6712yes—
650C4⋊C4C2×#6714yes—
651C4⋊C4C2×#6712yes—
652C4⋊C4C2×#6712yes—
653C4⋊C4C2×#6714yes—
654C4⋊C4C2×#6712yes—
655C4⋊C4C23×D312yes—
656C4⋊C4C23×D312yes—
657C4⋊C4C23×D312yes—
658C22⋊C4—22no—
659C22⋊C4—24no—
660C22⋊C4—24no—
661C22⋊C4—22no—
662C22⋊C4—22no—
663C22⋊C4—62no—
664C22⋊C4—62no—
665C22⋊C4—64no—
666C22⋊C4—64no—
667C22⋊C4—62no—
668C22⋊C4—64no—
669C22⋊C4—62no—
670C22⋊C4C2×#6714yes—
671C42—22no—
672C42—64no—
673C42C2×#6711yescharacteristic
674C42C2×#6711yescharacteristic
675C42C23×D311yescharacteristic
676C42C23×D311yescharacteristic
677C42C23×D314yes—
678C22×C3—21no—
679C22×C3—21no—
680C22×C3—24no—
681C22×C3—42no—
682C22×C3—42no—
683C22×C3—84no—
684C22×C3#54812yes—
685C22×C3C23×D411yescharacteristic
686C2×D3—42no—
687C2×D3—42no—
688C2×D3—42no—
689C2×D3—42no—
690C2×D3—42no—
691C2×D3—42no—
692C2×D3—84no—
693C3×C4—21no—
694C3×C4—24no—
695C3×C4—21no—
696C3×C4—21no—
697C3×C4—24no—
698C3×C4—42no—
699C3×C4—42no—
700C3×C4—42no—
701C3×C4#54812yes—
702C3×C4#57612yes—
703C3×C4C22×#4111yescharacteristic
704C3×C4C2×2−1+411yescharacteristic
705Dic3—42no—
706Dic3—42no—
707C23—22no—
708C23—24no—
709C23—62no—
710C23—62no—
711C23—81no—
712C23—81no—
713C23—122no—
714C23—241no—
715C23—241no—
716C23C22×#6711yescharacteristic
717Q8—24no—
718Q8—42no—
719Q8—42no—
720Q8—62no—
721Q8—62no—
722Q8—84no—
723Q8—81no—
724D4—22no—
725D4—24no—
726D4—62no—
727D4—62no—
728D4—62no—
729D4—62no—
730D4—124no—
731D4—122no—
732D4—122no—
733D4—244no—
734D4—241no—
735D4—244no—
736D4C2×#23914yes—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—41no—
742C2×C4—44no—
743C2×C4—62no—
744C2×C4—62no—
745C2×C4—82no—
746C2×C4—84no—
747C2×C4—84no—
748C2×C4—81no—
749C2×C4—124no—
750C2×C4—124no—
751C2×C4—242no—
752C2×C4—244no—
753C2×C4—241no—
754C2×C4C2×#23912yes—
755C2×C4#100712yes—
756C2×C4C22×#6714yes—
757C2×C4C22×#6711yescharacteristic
758C2×C4C22×#6711yescharacteristic
759C2×C4C22×#6711yescharacteristic
760C2×C4C22×#6714yes—
761C2×C4C22×#6711yescharacteristic
762C2×C4C22×#6711yescharacteristic
763C2×C4C24×D311yescharacteristic
764C8—61no—
765C8—61no—
766C8—64no—
767C8—61no—
768C8—61no—
769C2×C3—22no—
770C2×C3—44no—
771C2×C3C2×#54811yescharacteristic
772C2×C3C2×#57611yescharacteristic
773C2×C3#358411yescharacteristic
774D3—82no—
775D3—82no—
776C22—21no—
777C22—21no—
778C22—24no—
779C22—42no—
780C22—42no—
781C22—84no—
782C22—122no—
783C22—122no—
784C22—122no—
785C22—122no—
786C22—122no—
787C22—122no—
788C22—244no—
789C22#581712yes—
790C22C23×#6711yescharacteristic
791C4—21no—
792C4—21no—
793C4—24no—
794C4—21no—
795C4—24no—
796C4—42no—
797C4—42no—
798C4—42no—
799C4—122no—
800C4—122no—
801C4#581712yes—
802C4#583512yes—
803C4C22×#23911yescharacteristic
804C4C2×#100711yescharacteristic
805C3#6132511yescharacteristic, complemented, Sylow
806C2—22no—
807C2—44no—
808C2—242no—
809C2—242no—
810C2C2×#581711yescharacteristic
811C2C2×#583511yescharacteristic
812C2#8729711yescharacteristic
subgroupG/H
centerC22C23×#67
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3501C2
socleC22×C3C23×D4
hypercenter#3501D3
hypocenterC3#61325
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ #533 ◁ #3501

Complements

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

NH ≅ G/Ntype
1. C3×#3501C2semidirect
2. #86259C2semidirect
3. #83643C2semidirect
4. #83639C2semidirect
5. #83638C2semidirect
6. #83637C2semidirect
7. #83563C2semidirect
8. #83562C2semidirect
9. #83475C2semidirect
10. #83470C2semidirect
11. #83350C2semidirect
12. #83334C2semidirect
13. #83328C2semidirect
14. #82540C2semidirect
15. #82537C2semidirect
16. #82307C2semidirect
17. C2×C4×#213C2semidirect
21. C3×#554C22semidirect
22. C3×#554C22semidirect
24. C3×D4×Q8C22semidirect
39. #5585C22semidirect
40. #5584C22semidirect
41. #5577C22semidirect
47. #5093C22semidirect
48. #5093C22semidirect
49. #5091C22semidirect
50. #5089C22semidirect
51. #5088C22semidirect
52. #5088C22semidirect
53. #5088C22semidirect
54. #5087C22semidirect
55. #5087C22semidirect
56. #5084C22semidirect
57. #5068C22semidirect
58. #5068C22semidirect
59. #5068C22semidirect
60. #5067C22semidirect
61. #5066C22semidirect
62. #5066C22semidirect
63. #5063C22semidirect
64. #5024C22semidirect
65. #5024C22semidirect
66. Q8×C3⋊C8C22semidirect
67. Q8×C3⋊C8C22semidirect
68. #5019C22semidirect
69. #5018C22semidirect
70. C4×#214C22semidirect
73. #5016C22semidirect
76. #5015C22semidirect
77. #5014C22semidirect
82. C4×#213C22semidirect
95. #3501D3semidirect
238. #554C2×D3semidirect
239. #554C2×D3semidirect
243. D4×Q8C2×D3semidirect
316. C2×C3×D4#41semidirect
607. C2×D4#239semidirect
805. C3#61325semidirect

Maximal subgroups

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

subgroupindex
C3×#35012
#862592
#836432
#836392
#836382
#836372
#835632
#835622
#834752
#834702
#833502
#833342
#833282
#825402
#825372
#823072
C2×C4×#2132
#613253