Finite Group Databasebeta

← #11675113

Subgroups — #11675113

Order 768.

1878 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#559C211yesmaximal, characteristic, complemented
2Q8×#235C211yesmaximal, characteristic, complemented
3#83719C212yesmaximal, complemented
4#83718C214yesmaximal, complemented
5#83717C212yesmaximal, complemented
6#83715C212yesmaximal, complemented
7#83714C214yesmaximal, complemented
8#83713C212yesmaximal, complemented
9#83165C211yesmaximal, characteristic
10#83159C211yesmaximal, characteristic, complemented
11#82945C212yesmaximal, complemented
12#82939C212yesmaximal, complemented
13Q8×#208C211yesmaximal, characteristic, complemented
14#82431C211yesmaximal, characteristic, complemented
15C4×#942C211yesmaximal, characteristic, complemented
16#82296C212yesmaximal, complemented
17C4×#932C212yesmaximal, complemented
18#61324—31nomaximal, Sylow
19C3×#559—21no—
20C3×#559—21no—
21C3×#559—22no—
22C3×#559C2212yes—
23C3×#559C2214yes—
24C3×#559C2212yes—
25C2×C3×#127C2211yescharacteristic
26C2×C3×#124—21no—
27C2×C3×#124C2212yes—
28C2×C3×#123—22no—
29C2×C3×C4×Q8C2211yescharacteristic
30C2×C3×C4×Q8C2211yescharacteristic
31C2×C3×C4×D4—21no—
32C2×C3×C4×D4C2212yes—
33Q8×#67—21no—
34C2×#942C2211yescharacteristic
35C2×#932C2212yes—
36#5579C2211yescharacteristic, complemented
37#5579C2212yescomplemented
38#5578—22no—
39#5578—21no—
40Q8×D12C2211yescharacteristic, complemented
41C4×D3×Q8—21no—
42#5567C2211yescharacteristic, complemented
43#5567C2212yescomplemented
44Q8×Dic6C2211yescharacteristic, complemented
45#5511—21no—
46#5511—22no—
47C4×#235C2212yes—
48C4×#235C2211yescharacteristic
49#5470C2212yes—
50#5470C2211yescharacteristic
51#5225C2212yes—
52#5225C2211yescharacteristic
53#5215C2212yes—
54#5215C2212yes—
55#5215C2212yes—
56#5075C2212yes—
57#5075C2212yes—
58#5072C2212yes—
59#5072C2212yes—
60#5071C2214yes—
61#5070C2212yes—
62#5070C2212yes—
63#5057C2214yescomplemented
64#5057C2214yescomplemented
65#5056C2214yescomplemented
66#5056C2214yescomplemented
67#5055C2214yescomplemented
68#5055C2214yescomplemented
69#5054C2214yescomplemented
70#5054C2214yescomplemented
71#5030C2212yescomplemented
72C4×#216C2212yescomplemented
73#5026C2212yescomplemented
74C4×#215C2212yescomplemented
75#5024C2214yescomplemented
76#5024C2212yescomplemented
77Q8×C3⋊C8C2212yescomplemented
78#5022C2214yescomplemented
79#5021C2212yescomplemented
80#5020C2212yescomplemented
81#5018C2214yescomplemented
82C4×#214C2214yescomplemented
83#5014C2214yescomplemented
84C4×#213C2214yescomplemented
85#5009C2214yescomplemented
86#5009C2214yescomplemented
87#5008C2214yescomplemented
88#5007C2214yescomplemented
89#4966C2211yescharacteristic
90#4964C2212yes—
91#4964C2211yescharacteristic
92#4924C2212yes—
93#4924C2211yescharacteristic
94C4×#208C2212yes—
95C4×#208C2211yescharacteristic
96C2×#559D311yescharacteristic, complemented
97Q8×#41—31no—
98#3375—32no—
99#3373—32no—
100#3371—34no—
101#3370—34no—
102#3365—32no—
103#3361—32no—
104#3140—32no—
105#3138—31no—
106#3078—31no—
107#3077—32no—
108#3040—32no—
109#3038—31no—
110Q8×M16—31no—
111C4×#137—31no—
112C4×AGL(1,ℤ/8)—32no—
113C22×C3×Q8D411yescharacteristic
114C22×C3×Q8C2311yescharacteristic
115C22×C3×D4—21no—
116C22×C3×D4—21no—
117C22×C3×D4C2312yes—
118C23×C3×C4—22no—
119C2×D3×Q8—21no—
120C2×#235C2311yescharacteristic
121C3×#127—21no—
122C3×#127—21no—
123C3×#127C2312yes—
124C3×#127C2312yes—
125C3×#124—22no—
126C3×#124—22no—
127C3×#124—24no—
128C3×#124—22no—
129C3×#124—22no—
130C3×#124C2314yes—
131C3×#124C2314yes—
132C3×#123—24no—
133C3×#123—24no—
134C3×#123—24no—
135C3×#123—24no—
136C3×C4×Q8—21no—
137C3×C4×Q8—21no—
138C3×C4×Q8D411yescharacteristic
139C3×C4×Q8D412yes—
140C3×C4×Q8D411yescharacteristic
141C3×C4×Q8C2312yes—
142C3×C4×Q8C2312yes—
143C3×C4×Q8C2311yescharacteristic
144C3×C4×Q8C2311yescharacteristic
145C3×C4×Q8C2312yes—
146C3×C4×D4—22no—
147C3×C4×D4—22no—
148C3×C4×D4—24no—
149C3×C4×D4—22no—
150C3×C4×D4—22no—
151C3×C4×D4C2314yes—
152C3×C4×D4C2314yes—
153C2×C3×C4⋊C4—21no—
154C2×C3×C4⋊C4D411yescharacteristic
155C2×C3×C4⋊C4D412yes—
156C2×C3×C4⋊C4C2311yescharacteristic
157C2×C3×C22⋊C4—22no—
158C2×C3×C22⋊C4—22no—
159C2×C3×C22⋊C4—22no—
160C2×C3×C42—21no—
161C2×C3×C42C2312yes—
162C2×C3×C42C2311yescharacteristic
163#946—21no—
164#946—22no—
165Q8×Dic3—21no—
166#944—21no—
167#944—22no—
168C2×#216C2312yes—
169#942—24no—
170C2×#215C2312yes—
171C2×#214C2314yes—
172#932—28no—
173C2×#213C2314yes—
174C4×#67—22no—
175C4×#67—21no—
176C4×#67—21no—
177C4×#67—22no—
178#926C2311yescharacteristic
179#926C2312yes—
180#924—22no—
181#924—21no—
182#924—21no—
183#924—22no—
184C2×#208C2311yescharacteristic
185C2×#208C2311yescharacteristic
186C2×#208C2312yes—
187#897—21no—
188#897—22no—
189#896—22no—
190#896—22no—
191#896—22no—
192D3×C4⋊C4—21no—
193D3×C4⋊C4—22no—
194#889—22no—
195#889—22no—
196#889—22no—
197#888—21no—
198#888—22no—
199#887—21no—
200#887—22no—
201C4×D12C2312yes—
202C4×D12C2312yes—
203C4×D12C2311yescharacteristic
204C4×D12C2311yescharacteristic
205#872—22no—
206#872—21no—
207C42×D3—22no—
208C42×D3—21no—
209#870C2312yes—
210#870C2312yes—
211#870C2312yes—
212#869C2312yes—
213#869C2312yes—
214#869C2311yescharacteristic
215#869C2311yescharacteristic
216C4×Dic6—22no—
217C4×Dic6—21no—
218C4×Dic6—22no—
219C4×Dic6—21no—
220C4×Dic6C2312yes—
221C4×Dic6C2312yes—
222C4×Dic6C2311yescharacteristic
223C4×Dic6C2311yescharacteristic
224#835C2314yes—
225#835C2314yes—
226#835C2312yes—
227#835C2312yes—
228#832C2314yes—
229#832C2314yes—
230#832C2314yes—
231#832C2314yes—
232#832C2314yes—
233#832C2314yes—
234#810C2312yes—
235#809C2312yes—
236#808C2312yes—
237#808C2314yes—
238#807C2312yes—
239#807C2314yes—
240C4⋊(C3⋊C8)C2314yes—
241C4⋊(C3⋊C8)C2314yes—
242C4⋊(C3⋊C8)C2312yes—
243C4⋊(C3⋊C8)C2312yes—
244#803C2314yes—
245#803C2312yes—
246C4×C3⋊C8C2314yes—
247C4×C3⋊C8C2312yes—
248C2×#137—31no—
249C2×AGL(1,ℤ/8)—32no—
250#559—21no—
251#559—22no—
252#559—21no—
253#559C2×D312yes—
254#559C2×D314yes—
255#559C2×D312yes—
256Q82—31no—
257#557—31no—
258#557—32no—
259#554—31no—
260#554—32no—
261#554—61no—
262#554—62no—
263D4×Q8—31no—
264D4×Q8—61no—
265#533—32no—
266#533—31no—
267#533—62no—
268#533—61no—
269C2×#127C2×D311yescharacteristic
270C2×#124—21no—
271C2×#124C2×D312yes—
272C2×#123—22no—
273C4×#41—32no—
274C4×#41—31no—
275C2×C4×Q8—61no—
276C2×C4×Q8C2×D311yescharacteristic
277C2×C4×Q8C2×D311yescharacteristic
278C2×C4×D4—21no—
279C2×C4×D4C2×D312yes—
280#490—34no—
281#489—34no—
282#489—34no—
283#488—34no—
284#488—34no—
285#486—32no—
286#486—32no—
287#479—34no—
288#478—34no—
289#478—34no—
290#477—32no—
291#476—34no—
292#475—32no—
293#474—34no—
294#464—34no—
295#464—34no—
296#463—34no—
297#463—34no—
298#460—32no—
299#460—32no—
300#459—32no—
301#459—32no—
302#446—34no—
303#446—32no—
304C8×Q8—32no—
305#442—34no—
306#441—32no—
307#440—32no—
308#440—34no—
309C4×Q16—32no—
310C4×SD16—32no—
311C4×SD16—34no—
312C4×D8—34no—
313#428—31no—
314#428—32no—
315#423—32no—
316#423—31no—
317#419—32no—
318#419—31no—
319#418—32no—
320#418—32no—
321#418—32no—
322#417—31no—
323C4×M16—31no—
324C4×M16—32no—
325C24×C3—22no—
326C2×C3×Q8—21no—
327C2×C3×Q8—22no—
328C2×C3×Q8—22no—
329C2×C3×Q8—42no—
330C2×C3×Q8C2×D411yescharacteristic
331C2×C3×Q8C2×D411yescharacteristic
332C2×C3×Q8C2×D412yes—
333C2×C3×Q8C2412yes—
334C2×C3×D4—22no—
335C2×C3×D4—22no—
336C2×C3×D4—22no—
337C2×C3×D4—22no—
338C2×C3×D4—22no—
339C2×C3×D4—24no—
340C2×C3×D4—24no—
341C2×C3×D4—44no—
342C2×C3×D4—82no—
343C2×C3×D4C2414yes—
344C22×C3×C4—21no—
345C22×C3×C4—21no—
346C22×C3×C4—24no—
347C22×C3×C4—24no—
348C22×C3×C4—84no—
349C22×C3×C4C2×D411yescharacteristic
350C22×C3×C4C2×D412yes—
351C22×C3×C4C2×D412yes—
352C22×C3×C4C2×D411yescharacteristic
353C22×C3×C4C2411yescharacteristic
354C2×#67—21no—
355D3×Q8—44no—
356#235—22no—
357#235#4114yes—
358C2×D12C2411yescharacteristic
359C2×C4×D3—21no—
360C2×C4×D3—22no—
361C2×C4×D3—21no—
362C2×C4×D3—22no—
363C2×C4×D3—21no—
364C2×Dic6—22no—
365C2×Dic6—21no—
366C2×Dic6—22no—
367C2×Dic6—21no—
368C2×Dic6C2411yescharacteristic
369C3×C4⋊C4—22no—
370C3×C4⋊C4—22no—
371C3×C4⋊C4—21no—
372C3×C4⋊C4C2×D411yescharacteristic
373C3×C4⋊C4C2×D412yes—
374C3×C4⋊C4C2×D411yescharacteristic
375C3×C4⋊C4C2×D412yes—
376C3×C4⋊C4C2×D412yes—
377C3×C4⋊C4C2×D412yes—
378C3×C4⋊C4C2×D412yes—
379C3×C4⋊C4C2412yes—
380C3×C22⋊C4—24no—
381C3×C22⋊C4—24no—
382C3×C22⋊C4—24no—
383C3×C22⋊C4—24no—
384C3×C22⋊C4—24no—
385C3×C22⋊C4—24no—
386C3×C42—22no—
387C3×C42—22no—
388C3×C42C2×D412yes—
389C3×C42C2×D411yescharacteristic
390C3×C42C2×D412yes—
391C3×C42C2×D411yescharacteristic
392C3×C42C2411yescharacteristic
393C3×C42C2412yes—
394C3×C42C2412yes—
395C3×C42C2411yescharacteristic
396#217—21no—
397#217—22no—
398#216—24no—
399#215—24no—
400#214—28no—
401#213—28no—
402(C2×D3)⋊C4—22no—
403(C2×D3)⋊C4—21no—
404(C2×D3)⋊C4—21no—
405(C2×D3)⋊C4—22no—
406C4⋊Dic3—22no—
407C4⋊Dic3—21no—
408C4⋊Dic3—22no—
409C4⋊Dic3—21no—
410C4⋊Dic3C2411yescharacteristic
411C4⋊Dic3C2412yes—
412C4⋊Dic3C2411yescharacteristic
413C4⋊Dic3C2412yes—
414Dic3⋊C4—22no—
415Dic3⋊C4—22no—
416Dic3⋊C4—22no—
417Dic3⋊C4—22no—
418Dic3⋊C4—22no—
419Dic3⋊C4—22no—
420Dic3⋊C4—22no—
421Dic3⋊C4—21no—
422Dic3⋊C4—21no—
423Dic3⋊C4—22no—
424C4×Dic3—21no—
425C4×Dic3—22no—
426C4×Dic3—22no—
427C4×Dic3—21no—
428C4×Dic3—22no—
429C4×Dic3—21no—
430#208—24no—
431#208—22no—
432#208—22no—
433C2×C3⋊C8C2412yes—
434C2×C3⋊C8C2412yes—
435C2×C3⋊C8C2414yes—
436C2×#41—31no—
437C22×Q8—61no—
438C22×Q8#6711yescharacteristic
439C22×Q8C22×D311yescharacteristic
440C22×D4—21no—
441C22×D4—21no—
442C22×D4C22×D312yes—
443C23×C4—22no—
444#137—64no—
445AGL(1,ℤ/8)—68no—
446C2×Q16—32no—
447C2×SD16—32no—
448C2×SD16—34no—
449C2×D8—34no—
450C2×M16—32no—
451C2×M16—31no—
452C2×M16—31no—
453C4⋊Q8—31no—
454C4⋊Q8—32no—
455C4⋊Q8—32no—
456C4⋊Q8—31no—
457C4⋊Q8—61no—
458C4⋊Q8—62no—
459C4⋊Q8—61no—
460C4⋊Q8—62no—
461#127—21no—
462#127—21no—
463#127C22×D312yes—
464#127C22×D312yes—
465#125—32no—
466#125—32no—
467#125—32no—
468#125—62no—
469#125—62no—
470#125—62no—
471#124—22no—
472#124—22no—
473#124—24no—
474#124—22no—
475#124—22no—
476#124C22×D314yes—
477#124C22×D314yes—
478#123—24no—
479#123—24no—
480#123—24no—
481#123—24no—
482C22⋊Q8—61no—
483C22⋊Q8—62no—
484C22⋊Q8—61no—
485C22⋊Q8—62no—
486C22⋊Q8—62no—
487C22⋊Q8—61no—
488C22⋊Q8—61no—
489C22⋊Q8—62no—
490C22⋊Q8—62no—
491C22⋊Q8—62no—
492C22⋊Q8—62no—
493C4×Q8—21no—
494C4×Q8—21no—
495C4×Q8—32no—
496C4×Q8—31no—
497C4×Q8—31no—
498C4×Q8—32no—
499C4×Q8—61no—
500C4×Q8—61no—
501C4×Q8—62no—
502C4×Q8—62no—
503C4×Q8—61no—
504C4×Q8—62no—
505C4×Q8—61no—
506C4×Q8#6711yescharacteristic
507C4×Q8#6712yes—
508C4×Q8#6711yescharacteristic
509C4×Q8C22×D312yes—
510C4×Q8C22×D312yes—
511C4×Q8C22×D311yescharacteristic
512C4×Q8C22×D311yescharacteristic
513C4×Q8C22×D312yes—
514C4×D4—22no—
515C4×D4—24no—
516C4×D4—22no—
517C4×D4—22no—
518C4×D4—22no—
519C4×D4—31no—
520C4×D4—32no—
521C4×D4—32no—
522C4×D4—31no—
523C4×D4—61no—
524C4×D4—62no—
525C4×D4—62no—
526C4×D4—61no—
527C4×D4C22×D314yes—
528C4×D4C22×D314yes—
529#117—32no—
530#117—31no—
531#117—62no—
532#117—61no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—61no—
535C2×C4⋊C4—62no—
536C2×C4⋊C4#6711yescharacteristic
537C2×C4⋊C4#6712yes—
538C2×C4⋊C4C22×D311yescharacteristic
539C2×C22⋊C4—22no—
540C2×C22⋊C4—22no—
541C2×C22⋊C4—22no—
542C2×C42—21no—
543C2×C42—62no—
544C2×C42—61no—
545C2×C42C22×D312yes—
546C2×C42C22×D311yescharacteristic
547#107—34no—
548#107—32no—
549#106—32no—
550#106—34no—
551C4⋊C8—32no—
552C4⋊C8—34no—
553C4⋊C8—32no—
554C4⋊C8—34no—
555#103—32no—
556#103—32no—
557#103—34no—
558#103—34no—
559#103—32no—
560#102—34no—
561#102—34no—
562#102—34no—
563#102—34no—
564#102—34no—
565#102—34no—
566#102—32no—
567#97—32no—
568#97—34no—
569C4×C8—34no—
570C4×C8—32no—
571C23×C3—24no—
572C23×C3—44no—
573C23×C3—44no—
574C23×C3—44no—
575C23×C3C22×D411yescharacteristic
576C22×D3—21no—
577C3×Q8—22no—
578C3×Q8—22no—
579C3×Q8—22no—
580C3×Q8—22no—
581C3×Q8—42no—
582C3×Q8—42no—
583C3×D4—24no—
584C3×D4—24no—
585C3×D4—44no—
586C3×D4—44no—
587C3×D4—44no—
588C3×D4—82no—
589C3×D4—82no—
590C2×C3×C4—22no—
591C2×C3×C4—22no—
592C2×C3×C4—22no—
593C2×C3×C4—42no—
594C2×C3×C4—41no—
595C2×C3×C4—42no—
596C2×C3×C4—42no—
597C2×C3×C4—42no—
598C2×C3×C4—84no—
599C2×C3×C4—84no—
600C2×C3×C4C22×D412yes—
601C2×C3×C4C22×D411yescharacteristic
602C2×C3×C4C22×D412yes—
603C2×C3×C4C22×D411yescharacteristic
604C2×C3×C4C22×D412yes—
605C2×C3×C4C22×D412yes—
606C2×C3×C4C22×D411yescharacteristic
607C2×C3×C4C22×D411yescharacteristic
608C2×C3×C4C22×D411yescharacteristic
609C2×C3×C4C2×#4112yes—
610C2×C3×C42−1+412yes—
611C2×C3×C4C2511yescharacteristic
612#67—24no—
613C2×Dic3—21no—
614C2×Dic3—22no—
615C2×Dic3—21no—
616C2×Dic3—21no—
617C2×Dic3—22no—
618D12—21no—
619D12C2×#4112yes—
620C4×D3—24no—
621C4×D3—44no—
622C4×D3—42no—
623C4×D3—82no—
624C4×D3—81no—
625Dic6—21no—
626Dic6—44no—
627Dic6—42no—
628Dic6—82no—
629Dic6—81no—
630Dic6C2×#4112yes—
631C3⋊C8—24no—
632C3⋊C8—22no—
633C3⋊C8—22no—
634C24—22no—
635#41—34no—
636#41—62no—
637C2×Q8—21no—
638C2×Q8—22no—
639C2×Q8—22no—
640C2×Q8—31no—
641C2×Q8—42no—
642C2×Q8—62no—
643C2×Q8—61no—
644C2×Q8—62no—
645C2×Q8—61no—
646C2×Q8—124no—
647C2×Q8C2×#6711yescharacteristic
648C2×Q8C2×#6711yescharacteristic
649C2×Q8C2×#6712yes—
650C2×Q8C23×D312yes—
651C2×D4—24no—
652C2×D4—24no—
653C2×D4—22no—
654C2×D4—22no—
655C2×D4—22no—
656C2×D4—22no—
657C2×D4—22no—
658C2×D4—31no—
659C2×D4—44no—
660C2×D4—61no—
661C2×D4—82no—
662C2×D4C23×D314yes—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—24no—
666C22×C4—24no—
667C22×C4—61no—
668C22×C4—62no—
669C22×C4—61no—
670C22×C4—62no—
671C22×C4—61no—
672C22×C4—84no—
673C22×C4C2×#6711yescharacteristic
674C22×C4C2×#6712yes—
675C22×C4C2×#6712yes—
676C22×C4C2×#6711yescharacteristic
677C22×C4C23×D311yescharacteristic
678Q16—64no—
679SD16—68no—
680SD16—64no—
681D8—68no—
682M16—64no—
683M16—62no—
684M16—62no—
685C2×C8—32no—
686C2×C8—32no—
687C2×C8—34no—
688C4⋊C4—22no—
689C4⋊C4—22no—
690C4⋊C4—21no—
691C4⋊C4—32no—
692C4⋊C4—31no—
693C4⋊C4—32no—
694C4⋊C4—31no—
695C4⋊C4—62no—
696C4⋊C4—62no—
697C4⋊C4—62no—
698C4⋊C4—62no—
699C4⋊C4—61no—
700C4⋊C4—61no—
701C4⋊C4—62no—
702C4⋊C4—62no—
703C4⋊C4—61no—
704C4⋊C4—62no—
705C4⋊C4—62no—
706C4⋊C4—62no—
707C4⋊C4—62no—
708C4⋊C4—61no—
709C4⋊C4C2×#6711yescharacteristic
710C4⋊C4C2×#6712yes—
711C4⋊C4C2×#6712yes—
712C4⋊C4C2×#6711yescharacteristic
713C4⋊C4C2×#6712yes—
714C4⋊C4C2×#6712yes—
715C4⋊C4C2×#6712yes—
716C4⋊C4C23×D312yes—
717C22⋊C4—24no—
718C22⋊C4—24no—
719C22⋊C4—24no—
720C22⋊C4—24no—
721C22⋊C4—24no—
722C22⋊C4—24no—
723C22⋊C4—62no—
724C22⋊C4—61no—
725C22⋊C4—61no—
726C22⋊C4—62no—
727C22⋊C4—62no—
728C22⋊C4—61no—
729C42—22no—
730C42—22no—
731C42—62no—
732C42—61no—
733C42—62no—
734C42—61no—
735C42—62no—
736C42—61no—
737C42C2×#6712yes—
738C42C2×#6711yescharacteristic
739C42C2×#6712yes—
740C42C2×#6711yescharacteristic
741C42C23×D312yes—
742C42C23×D311yescharacteristic
743C42C23×D312yes—
744C42C23×D311yescharacteristic
745C22×C3—21no—
746C22×C3—21no—
747C22×C3—44no—
748C22×C3—44no—
749C22×C3—44no—
750C22×C3—88no—
751C22×C3#54812yes—
752C22×C3C23×D411yescharacteristic
753C2×D3—22no—
754C2×D3—41no—
755C2×D3—41no—
756C3×C4—22no—
757C3×C4—21no—
758C3×C4—22no—
759C3×C4—21no—
760C3×C4—22no—
761C3×C4—21no—
762C3×C4—22no—
763C3×C4—42no—
764C3×C4—42no—
765C3×C4#54812yes—
766C3×C4#57512yes—
767C3×C4C22×#4111yescharacteristic
768C3×C4C2×2−1+411yescharacteristic
769Dic3—22no—
770Dic3—41no—
771Dic3—42no—
772Dic3—41no—
773Dic3—42no—
774C23—24no—
775C23—44no—
776C23—44no—
777C23—44no—
778C23—61no—
779C23C22×#6711yescharacteristic
780Q8—22no—
781Q8—22no—
782Q8—22no—
783Q8—22no—
784Q8—32no—
785Q8—42no—
786Q8—42no—
787Q8—61no—
788Q8—124no—
789Q8—122no—
790Q8—242no—
791Q8—241no—
792D4—24no—
793D4—24no—
794D4—32no—
795D4—44no—
796D4—44no—
797D4—44no—
798D4—64no—
799D4—61no—
800D4—82no—
801D4—82no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—42no—
806C2×C4—41no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—61no—
811C2×C4—64no—
812C2×C4—62no—
813C2×C4—61no—
814C2×C4—62no—
815C2×C4—61no—
816C2×C4—84no—
817C2×C4—84no—
818C2×C4—124no—
819C2×C4—122no—
820C2×C4—242no—
821C2×C4—241no—
822C2×C4D3×#4112yes—
823C2×C4#101012yes—
824C2×C4C22×#6711yescharacteristic
825C2×C4C22×#6712yes—
826C2×C4C22×#6712yes—
827C2×C4C22×#6711yescharacteristic
828C2×C4C22×#6712yes—
829C2×C4C22×#6712yes—
830C2×C4C22×#6711yescharacteristic
831C2×C4C22×#6711yescharacteristic
832C2×C4C22×#6711yescharacteristic
833C2×C4C24×D311yescharacteristic
834C8—64no—
835C8—62no—
836C8—62no—
837C2×C3—22no—
838C2×C3—84no—
839C2×C3C2×#54811yescharacteristic
840C2×C3C2×#57511yescharacteristic
841C2×C3#358511yescharacteristic
842D3—42no—
843C22—21no—
844C22—21no—
845C22—44no—
846C22—44no—
847C22—44no—
848C22—62no—
849C22—88no—
850C22—121no—
851C22—121no—
852C22#583112yes—
853C22C23×#6711yescharacteristic
854C4—21no—
855C4—22no—
856C4—22no—
857C4—22no—
858C4—22no—
859C4—21no—
860C4—21no—
861C4—42no—
862C4—42no—
863C4—62no—
864C4—122no—
865C4—121no—
866C4—122no—
867C4—121no—
868C4#582212yes—
869C4#583112yes—
870C4C2×D3×#4111yescharacteristic
871C4C2×#101011yescharacteristic
872C3#6132411yescharacteristic, complemented, Sylow
873C2—22no—
874C2—84no—
875C2—122no—
876C2C2×#582211yescharacteristic
877C2C2×#583111yescharacteristic
878C2#8727711yescharacteristic
subgroupG/H
centerC22C23×#67
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#559C2
socleC22×C3C23×D4
prime radical#83165C2
hypercenterC2×#559D3
hypocenterC3#61324
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C4×Q8 ◁ C2×#559

Complements

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

NH ≅ G/Ntype
1. C2×C3×#559C2semidirect
2. Q8×#235C2semidirect
3. #83719C2semidirect
4. #83718C2semidirect
5. #83717C2semidirect
6. #83715C2semidirect
7. #83714C2semidirect
8. #83713C2semidirect
10. #83159C2semidirect
11. #82945C2semidirect
12. #82939C2semidirect
13. Q8×#208C2semidirect
14. #82431C2semidirect
15. C4×#942C2semidirect
16. #82296C2semidirect
17. C4×#932C2semidirect
36. #5579C22semidirect
37. #5579C22semidirect
40. Q8×D12C22semidirect
42. #5567C22semidirect
43. #5567C22semidirect
44. Q8×Dic6C22semidirect
63. #5057C22semidirect
64. #5057C22semidirect
65. #5056C22semidirect
66. #5056C22semidirect
67. #5055C22semidirect
68. #5055C22semidirect
69. #5054C22semidirect
70. #5054C22semidirect
71. #5030C22semidirect
72. C4×#216C22semidirect
73. #5026C22semidirect
74. C4×#215C22semidirect
75. #5024C22semidirect
76. #5024C22semidirect
77. Q8×C3⋊C8C22semidirect
78. #5022C22semidirect
79. #5021C22semidirect
80. #5020C22semidirect
81. #5018C22semidirect
82. C4×#214C22semidirect
83. #5014C22semidirect
84. C4×#213C22semidirect
85. #5009C22semidirect
86. #5009C22semidirect
87. #5008C22semidirect
88. #5007C22semidirect
96. C2×#559D3semidirect
872. C3#61324semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#5592
Q8×#2352
#837192
#837182
#837172
#837152
#837142
#837132
#831652
#831592
#829452
#829392
Q8×#2082
#824312
C4×#9422
#822962
C4×#9322
#613243