Finite Group Databasebeta

← #11664109

Subgroups — #11664109

Order 768.

2134 conjugacy classes of subgroups.

The subgroup lattice has 936 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3494C211yesmaximal, characteristic, complemented
2C2×#5523C211yesmaximal, characteristic, complemented
3#83476C212yesmaximal, complemented
4#83462C214yesmaximal, complemented
5#83434C214yesmaximal, complemented
6#83385C212yesmaximal, complemented
7#83315C212yesmaximal, complemented
8#83300C212yesmaximal, complemented
9#83153C212yesmaximal, complemented
10#83141C212yesmaximal, complemented
11#82926C211yesmaximal, characteristic, complemented
12#82914C211yesmaximal, characteristic, complemented
13#82624C211yesmaximal, characteristic, complemented
14C2×#5034C211yesmaximal, characteristic, complemented
15#82558C212yesmaximal, complemented
16#82537C212yesmaximal, complemented
17#82210C211yesmaximal, characteristic, complemented
18#60588—31nomaximal, Sylow
19C22×#235C2211yescharacteristic
20C3×#555—21no—
21C3×#553—21no—
22C3×#553—21no—
23C3×#551—22no—
24C3×#547—21no—
25C3×#546—22no—
26C3×#544C2211yescharacteristic, complemented
27C3×#542C2212yescomplemented
28C3×#540C2212yescomplemented
29C3×#535C2211yescharacteristic, complemented
30C3×#532C2212yes—
31C3×#529C2212yes—
32C3×#525C2211yescharacteristic
33C2×C3×#121C2211yescharacteristic
34C3×#520C2211yescharacteristic, complemented
35C3×#518C2211yescharacteristic, complemented
36C2×C3×#117C2211yescharacteristic
37C2×#950C2212yes—
38C2×#932C2212yes—
39C22×C4⋊Dic3C2211yescharacteristic
40#5523—22no—
41#5523—21no—
42#5523—21no—
43#5523C2212yes—
44#5523C2212yes—
45#5523C2214yescomplemented
46C2×#892—21no—
47C2×D3×C4⋊C4—21no—
48C2×#67⋊C4—22no—
49C2×C4×D12C2212yescomplemented
50C2×C4×Dic6C2212yescomplemented
51#5232C2212yescomplemented
52C2×#832C2212yescomplemented
53#5207C2211yescharacteristic
54C2×#830C2211yescharacteristic
55#5094C2214yescomplemented
56#5084C2214yescomplemented
57#5075C2214yescomplemented
58#5072C2214yescomplemented
59#5066C2214yescomplemented
60#5063C2214yescomplemented
61#5057C2214yescomplemented
62#5054C2214yescomplemented
63#5050C2211yescharacteristic, complemented
64#5047C2212yescomplemented
65#5046C2211yescharacteristic, complemented
66#5044C2212yescomplemented
67#5043C2212yescomplemented
68#5040C2212yes—
69#5040C2211yescharacteristic, complemented
70#5037C2214yes—
71#5037C2212yescomplemented
72#5036C2212yes—
73#5036C2211yescharacteristic, complemented
74#5034C2212yes—
75#5034C2212yes—
76#5034C2214yescomplemented
77#5034C2212yescomplemented
78#5033C2212yescomplemented
79#5030C2214yescomplemented
80C4×#215C2214yescomplemented
81#5018C2214yescomplemented
82C4×#214C2214yescomplemented
83C4×#214C2214yescomplemented
84#5014C2214yescomplemented
85#5014C2214yescomplemented
86C4×#213C2214yescomplemented
87#5002C2212yes—
88#5000C2214yescomplemented
89#4999C2212yescomplemented
90#4997C2212yescomplemented
91#4995C2212yescomplemented
92#4966C2212yes—
93C2×#808C2212yescomplemented
94#4926C2212yescomplemented
95#4925C2212yescomplemented
96#3494D311yescharacteristic, complemented
97C2×#520—31no—
98#3125—34no—
99#3119—34no—
100#3117—32no—
101#3109—32no—
102#3105—32no—
103#3103—32no—
104#3092—31no—
105C2×#481—31no—
106#3084—32no—
107#3045—32no—
108#3006—31no—
109#3002—31no—
110#2952—32no—
111#2946—32no—
112#2924—31no—
113C2×C3×#41—22no—
114C2×C3×#41C2311yescharacteristic
115C22×C3×D4—21no—
116C22×C3×D4C2311yescharacteristic
117C23×C3×C4C2311yescharacteristic
118C22×#67—21no—
119C23×Dic3—21no—
120C2×#235—21no—
121C2×#235—21no—
122C2×#235—28no—
123C2×#235C2312yes—
124C2×#235C2312yes—
125C22×D12C2311yescharacteristic
126C22×C4×D3—21no—
127C22×C4×D3—22no—
128C22×Dic6C2311yescharacteristic
129C3×C4⋊Q8—21no—
130C3×C4⋊Q8C2312yes—
131C3×#127C2312yes—
132C3×#126—22no—
133C3×#126—22no—
134C3×#125—21no—
135C3×#125C2312yes—
136C3×#124—22no—
137C3×#124—22no—
138C3×#124C2312yes—
139C3×#123—21no—
140C3×#123—22no—
141C3×#123—22no—
142C3×#123—22no—
143C3×#123—22no—
144C3×C22⋊Q8—22no—
145C3×C22⋊Q8—22no—
146C3×C22⋊Q8C2311yescharacteristic
147C3×C22⋊Q8C2311yescharacteristic
148C3×#121—21no—
149C3×#121—21no—
150C3×#121—22no—
151C3×#121—21no—
152C3×#121—21no—
153C3×#121—22no—
154C3×#121—22no—
155C3×#121C2311yescharacteristic
156C3×#121C2312yes—
157C3×#121C2311yescharacteristic
158C3×#121C2312yes—
159C3×#120—21no—
160C3×#120—22no—
161C3×C4×Q8C2312yes—
162C3×C4×D4—21no—
163C3×C4×D4—21no—
164C3×C4×D4—22no—
165C3×C4×D4—21no—
166C3×C4×D4—21no—
167C3×C4×D4—22no—
168C3×C4×D4—22no—
169C3×C4×D4C2312yes—
170C3×C4×D4C2312yes—
171C3×C4×D4C2312yes—
172C3×#117—21no—
173C3×#117—22no—
174C3×#117D412yes—
175C3×#117D411yescharacteristic
176C3×#117D411yescharacteristic
177C3×#117C2311yescharacteristic
178C3×#117C2311yescharacteristic
179C3×#117C2311yescharacteristic
180C3×#117C2312yes—
181C2×C3×C4⋊C4—21no—
182C2×C3×C4⋊C4D411yescharacteristic
183C2×C3×C4⋊C4D411yescharacteristic
184C2×C3×C4⋊C4C2311yescharacteristic
185C2×C3×C22⋊C4—21no—
186C2×C3×C22⋊C4—22no—
187C2×C3×C22⋊C4D412yes—
188C2×C3×C42C2312yes—
189#950—28no—
190C2×#216C2312yes—
191C2×#215C2312yes—
192C2×#214C2312yes—
193C2×#214C2314yes—
194#932—28no—
195C2×#213C2314yes—
196C2×#213C2312yes—
197C2×(C2×D3)⋊C4—22no—
198C2×C4⋊Dic3—21no—
199C2×C4⋊Dic3—21no—
200C2×C4⋊Dic3—21no—
201C2×C4⋊Dic3C2312yes—
202C2×C4⋊Dic3C2312yes—
203C2×C4⋊Dic3C2312yes—
204C2×Dic3⋊C4—22no—
205C2×C4×Dic3—22no—
206C2×#208C2312yes—
207C22×C3⋊C8C2312yes—
208#892—22no—
209#892—22no—
210#892—24no—
211D3×C4⋊C4—22no—
212D3×C4⋊C4—22no—
213D3×C4⋊C4—24no—
214#67⋊C4—24no—
215#67⋊C4—24no—
216#67⋊C4—24no—
217#67⋊C4—24no—
218C4×D12—22no—
219C4×D12—22no—
220C4×D12C2314yes—
221C4×D12C2314yes—
222C4×Dic6—22no—
223C4×Dic6—22no—
224C4×Dic6C2314yes—
225C4×Dic6C2314yes—
226#835C2314yes—
227#832C2314yes—
228#832C2314yes—
229#832C2314yes—
230#830C2311yescharacteristic
231#830C2312yes—
232#830C2311yescharacteristic
233#830C2312yes—
234#830C2312yes—
235#810C2314yes—
236#810C2312yes—
237#810C2312yes—
238#809C2314yes—
239#809C2312yes—
240#809C2312yes—
241#808C2314yes—
242#808C2314yes—
243#808C2314yes—
244#807C2314yes—
245C4⋊(C3⋊C8)C2314yes—
246C4⋊(C3⋊C8)C2314yes—
247#803C2314yes—
248C4×C3⋊C8C2314yes—
249C22×#41—31no—
250C2×AGL(1,ℤ/8)—32no—
251C2×#135—32no—
252#555—21no—
253#553—21no—
254#553—21no—
255#551—22no—
256#547—21no—
257#546—22no—
258#544C2×D311yescharacteristic, complemented
259#542C2×D312yescomplemented
260#540C2×D312yescomplemented
261#535C2×D311yescharacteristic, complemented
262#532C2×D312yes—
263#529C2×D312yes—
264#525C2×D311yescharacteristic
265C2×#121C2×D311yescharacteristic
266#520—32no—
267#520—34no—
268#520—32no—
269#520—62no—
270#520—61no—
271#520—61no—
272#520C2×D311yescharacteristic, complemented
273#518C2×D311yescharacteristic, complemented
274C2×C4×Q8—32no—
275C2×C4×D4—32no—
276C2×C4×D4—62no—
277C2×#117—61no—
278C2×#117C2×D311yescharacteristic
279C22×C4⋊C4—31no—
280C22×C4⋊C4—61no—
281#484—32no—
282#483—32no—
283#481—32no—
284#481—32no—
285#481—34no—
286#481—32no—
287#480—32no—
288#479—34no—
289#478—34no—
290#476—34no—
291#475—34no—
292#464—34no—
293#463—34no—
294#460—34no—
295#459—34no—
296#452—32no—
297#451—31no—
298#450—31no—
299#449—32no—
300#449—34no—
301#448—31no—
302#448—32no—
303#447—32no—
304#447—31no—
305#442—34no—
306#442—34no—
307#441—34no—
308#440—34no—
309C4×SD16—34no—
310C4×SD16—34no—
311C4×SD16—34no—
312C4×D8—34no—
313#433—34no—
314#432—32no—
315#431—32no—
316#428—32no—
317C2×#106—32no—
318#424—32no—
319#417—32no—
320#417—32no—
321#416—32no—
322C2×#102—32no—
323#407—31no—
324C2×C22⋊C8—31no—
325#405—32no—
326C24×C3—21no—
327C24×C3C2×D411yescharacteristic
328C23×D3—21no—
329C3×#41—24no—
330C3×#41—84no—
331C2×C3×Q8—22no—
332C2×C3×Q8C2411yescharacteristic
333C2×C3×D4—21no—
334C2×C3×D4—21no—
335C2×C3×D4—22no—
336C2×C3×D4—21no—
337C2×C3×D4—22no—
338C2×C3×D4—21no—
339C2×C3×D4—22no—
340C2×C3×D4—22no—
341C2×C3×D4—24no—
342C2×C3×D4—82no—
343C2×C3×D4C2412yes—
344C2×C3×D4C2411yescharacteristic
345C22×C3×C4—24no—
346C22×C3×C4—21no—
347C22×C3×C4—21no—
348C22×C3×C4—22no—
349C22×C3×C4—22no—
350C22×C3×C4—22no—
351C22×C3×C4C2×D412yes—
352C22×C3×C4C2×D411yescharacteristic
353C22×C3×C4C2×D411yescharacteristic
354C22×C3×C4C2×D411yescharacteristic
355C22×C3×C4C2×D412yes—
356C22×C3×C4C2411yescharacteristic
357C22×C3×C4C2411yescharacteristic
358C22×C3×C4C2411yescharacteristic
359C2×#67—28no—
360C2×#67—22no—
361C2×#67—22no—
362C22×Dic3—21no—
363C22×Dic3—22no—
364C22×Dic3—22no—
365C22×Dic3—22no—
366C22×Dic3—82no—
367#235—28no—
368#235—28no—
369#235—24no—
370#235—24no—
371#235—24no—
372#235#4118yescomplemented
373C2×D12—21no—
374C2×D12—24no—
375C2×D12C2412yes—
376C2×C4×D3—28no—
377C2×C4×D3—22no—
378C2×C4×D3—22no—
379C2×C4×D3—24no—
380C2×C4×D3—24no—
381C2×C4×D3—84no—
382C2×Dic6—21no—
383C2×Dic6—24no—
384C2×Dic6C2412yes—
385C3×C4⋊C4—21no—
386C3×C4⋊C4—22no—
387C3×C4⋊C4—21no—
388C3×C4⋊C4—22no—
389C3×C4⋊C4—22no—
390C3×C4⋊C4—22no—
391C3×C4⋊C4—21no—
392C3×C4⋊C4C2×D411yescharacteristic
393C3×C4⋊C4C2×D411yescharacteristic
394C3×C4⋊C4C2×D412yes—
395C3×C4⋊C4C2×D411yescharacteristic
396C3×C4⋊C4C2×D411yescharacteristic
397C3×C4⋊C4C2×D412yes—
398C3×C4⋊C4C2411yescharacteristic
399C3×C4⋊C4C2412yes—
400C3×C4⋊C4C2411yescharacteristic
401C3×C22⋊C4—21no—
402C3×C22⋊C4—21no—
403C3×C22⋊C4—21no—
404C3×C22⋊C4—22no—
405C3×C22⋊C4—22no—
406C3×C22⋊C4—22no—
407C3×C22⋊C4—22no—
408C3×C22⋊C4—22no—
409C3×C22⋊C4—22no—
410C3×C22⋊C4—21no—
411C3×C22⋊C4—22no—
412C3×C22⋊C4—21no—
413C3×C22⋊C4C2×D412yes—
414C3×C22⋊C4C2×D412yes—
415C3×C22⋊C4C2×D412yes—
416C3×C22⋊C4C2×D412yes—
417C3×C42—22no—
418C3×C42—21no—
419C3×C42C2×D412yes—
420C3×C42C2×D412yes—
421C3×C42C2412yes—
422C3×C42C2412yes—
423#216—24no—
424#215—24no—
425#214—28no—
426#214—24no—
427#213—28no—
428#213—24no—
429(C2×D3)⋊C4—24no—
430(C2×D3)⋊C4—24no—
431C4⋊Dic3—22no—
432C4⋊Dic3—22no—
433C4⋊Dic3—22no—
434C4⋊Dic3C2414yes—
435Dic3⋊C4—24no—
436Dic3⋊C4—24no—
437C4×Dic3—24no—
438C4×Dic3—24no—
439#208—24no—
440C2×C3⋊C8—24no—
441C2×C3⋊C8C2412yes—
442C2×C3⋊C8C2414yes—
443C2×C3⋊C8C2412yes—
444C2×#41—22no—
445C2×#41—32no—
446C2×#41—32no—
447C2×#41—68no—
448C2×#41—61no—
449C2×#41—61no—
450C2×#41C22×D311yescharacteristic
451C22×Q8—31no—
452C22×D4—21no—
453C22×D4—31no—
454C22×D4—61no—
455C22×D4C22×D311yescharacteristic
456C23×C4—61no—
457C23×C4—61no—
458C23×C4—62no—
459C23×C4C22×D311yescharacteristic
460AGL(1,ℤ/8)—68no—
461#135—68no—
462C2×Q16—32no—
463C2×SD16—32no—
464C2×SD16—32no—
465C2×SD16—34no—
466C2×D8—32no—
467C2×D8—34no—
468C2×M16—32no—
469C22×C8—32no—
470C4⋊Q8—21no—
471C4⋊Q8C22×D312yes—
472#127C22×D312yes—
473#126—22no—
474#126—22no—
475#125—21no—
476#125C22×D312yes—
477#124—22no—
478#124—22no—
479#124C22×D312yes—
480#123—21no—
481#123—22no—
482#123—22no—
483#123—22no—
484#123—22no—
485C22⋊Q8—22no—
486C22⋊Q8—22no—
487C22⋊Q8C22×D311yescharacteristic
488C22⋊Q8C22×D311yescharacteristic
489#121—21no—
490#121—21no—
491#121—22no—
492#121—21no—
493#121—21no—
494#121—22no—
495#121—22no—
496#121C22×D312yes—
497#121C22×D312yes—
498#121C22×D311yescharacteristic
499#121C22×D311yescharacteristic
500#120—21no—
501#120—22no—
502C4×Q8—34no—
503C4×Q8—34no—
504C4×Q8—62no—
505C4×Q8—62no—
506C4×Q8C22×D312yes—
507C4×D4—21no—
508C4×D4—21no—
509C4×D4—22no—
510C4×D4—21no—
511C4×D4—21no—
512C4×D4—22no—
513C4×D4—22no—
514C4×D4—34no—
515C4×D4—34no—
516C4×D4—64no—
517C4×D4—64no—
518C4×D4—64no—
519C4×D4—64no—
520C4×D4—62no—
521C4×D4—62no—
522C4×D4C22×D312yes—
523C4×D4C22×D312yes—
524C4×D4C22×D312yes—
525#117—21no—
526#117—22no—
527#117—62no—
528#117—62no—
529#117—64no—
530#117#6712yes—
531#117#6711yescharacteristic
532#117#6711yescharacteristic
533#117C22×D311yescharacteristic
534#117C22×D311yescharacteristic
535#117C22×D311yescharacteristic
536#117C22×D312yes—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—32no—
539C2×C4⋊C4—32no—
540C2×C4⋊C4—32no—
541C2×C4⋊C4—61no—
542C2×C4⋊C4—61no—
543C2×C4⋊C4—61no—
544C2×C4⋊C4—62no—
545C2×C4⋊C4—62no—
546C2×C4⋊C4—62no—
547C2×C4⋊C4—64no—
548C2×C4⋊C4#6711yescharacteristic
549C2×C4⋊C4#6711yescharacteristic
550C2×C4⋊C4C22×D311yescharacteristic
551C2×C22⋊C4—21no—
552C2×C22⋊C4—22no—
553C2×C22⋊C4—62no—
554C2×C22⋊C4#6712yes—
555C2×C42—62no—
556C2×C42C22×D312yes—
557#107—34no—
558#106—34no—
559#106—34no—
560#106—34no—
561C4⋊C8—34no—
562C4⋊C8—34no—
563#103—34no—
564#103—32no—
565#103—32no—
566#103—34no—
567#102—34no—
568#102—34no—
569#102—34no—
570#102—32no—
571#102—32no—
572#102—34no—
573C22⋊C8—31no—
574C22⋊C8—31no—
575C22⋊C8—32no—
576C22⋊C8—32no—
577C22⋊C8—32no—
578#97—34no—
579C4×C8—34no—
580C23×C3—22no—
581C23×C3—22no—
582C23×C3—22no—
583C23×C3—21no—
584C23×C3—41no—
585C23×C3—42no—
586C23×C3—81no—
587C23×C3—81no—
588C23×C3C22×D411yescharacteristic
589C23×C3C22×D411yescharacteristic
590C23×C3C22×D411yescharacteristic
591C22×D3—24no—
592C22×D3—22no—
593C22×D3—42no—
594C22×D3—42no—
595C3×Q8—22no—
596C3×Q8—82no—
597C3×D4—24no—
598C3×D4—22no—
599C3×D4—42no—
600C3×D4—44no—
601C3×D4—42no—
602C3×D4—42no—
603C3×D4—82no—
604C3×D4—82no—
605C3×D4—81no—
606C3×D4—82no—
607C2×C3×C4—22no—
608C2×C3×C4—24no—
609C2×C3×C4—22no—
610C2×C3×C4—22no—
611C2×C3×C4—22no—
612C2×C3×C4—22no—
613C2×C3×C4—21no—
614C2×C3×C4—21no—
615C2×C3×C4—21no—
616C2×C3×C4—22no—
617C2×C3×C4—42no—
618C2×C3×C4—42no—
619C2×C3×C4—82no—
620C2×C3×C4—82no—
621C2×C3×C4—82no—
622C2×C3×C4—81no—
623C2×C3×C4C22×D412yes—
624C2×C3×C4C22×D412yes—
625C2×C3×C4C22×D412yes—
626C2×C3×C4C22×D412yes—
627C2×C3×C4C22×D411yescharacteristic
628C2×C3×C4C22×D411yescharacteristic
629C2×C3×C4C22×D411yescharacteristic
630C2×C3×C4C2×#4114yes—
631C2×C3×C4C2511yescharacteristic
632#67—28no—
633#67—28no—
634C2×Dic3—24no—
635C2×Dic3—22no—
636C2×Dic3—24no—
637C2×Dic3—44no—
638C2×Dic3—82no—
639C2×Dic3—82no—
640D12—24no—
641D12—22no—
642D12C2×#4114yes—
643C4×D3—28no—
644C4×D3—28no—
645C4×D3—84no—
646C4×D3—84no—
647Dic6—24no—
648Dic6—22no—
649Dic6C2×#4114yes—
650C3⋊C8—22no—
651C3⋊C8—22no—
652C3⋊C8—24no—
653C24—21no—
654C24—61no—
655C24C2×#6711yescharacteristic
656#41—24no—
657#41—38no—
658#41—64no—
659#41—64no—
660#41—68no—
661#41—68no—
662#41—64no—
663#41—84no—
664C2×Q8—22no—
665C2×Q8—32no—
666C2×Q8—64no—
667C2×Q8—61no—
668C2×Q8C23×D311yescharacteristic
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—22no—
672C2×D4—21no—
673C2×D4—22no—
674C2×D4—24no—
675C2×D4—21no—
676C2×D4—22no—
677C2×D4—22no—
678C2×D4—32no—
679C2×D4—64no—
680C2×D4—68no—
681C2×D4—62no—
682C2×D4—62no—
683C2×D4—61no—
684C2×D4—82no—
685C2×D4C23×D312yes—
686C2×D4C23×D311yescharacteristic
687C22×C4—24no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—22no—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—68no—
694C22×C4—61no—
695C22×C4—62no—
696C22×C4—62no—
697C22×C4—62no—
698C22×C4—62no—
699C22×C4—62no—
700C22×C4—64no—
701C22×C4—64no—
702C22×C4—244no—
703C22×C4—242no—
704C22×C4C2×#6712yes—
705C22×C4C2×#6711yescharacteristic
706C22×C4C2×#6711yescharacteristic
707C22×C4C2×#6711yescharacteristic
708C22×C4C2×#6712yes—
709C22×C4C23×D311yescharacteristic
710C22×C4C23×D311yescharacteristic
711C22×C4C23×D311yescharacteristic
712Q16—64no—
713SD16—64no—
714SD16—68no—
715SD16—64no—
716D8—64no—
717D8—68no—
718M16—64no—
719C2×C8—32no—
720C2×C8—34no—
721C2×C8—32no—
722C2×C8—64no—
723C4⋊C4—21no—
724C4⋊C4—22no—
725C4⋊C4—21no—
726C4⋊C4—22no—
727C4⋊C4—22no—
728C4⋊C4—22no—
729C4⋊C4—21no—
730C4⋊C4—34no—
731C4⋊C4—62no—
732C4⋊C4—62no—
733C4⋊C4—62no—
734C4⋊C4—64no—
735C4⋊C4—64no—
736C4⋊C4C2×#6711yescharacteristic
737C4⋊C4C2×#6711yescharacteristic
738C4⋊C4C2×#6711yescharacteristic
739C4⋊C4C2×#6712yes—
740C4⋊C4C2×#6711yescharacteristic
741C4⋊C4C2×#6712yes—
742C4⋊C4C23×D312yes—
743C4⋊C4C23×D311yescharacteristic
744C4⋊C4C23×D311yescharacteristic
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—22no—
749C22⋊C4—22no—
750C22⋊C4—22no—
751C22⋊C4—22no—
752C22⋊C4—22no—
753C22⋊C4—22no—
754C22⋊C4—21no—
755C22⋊C4—22no—
756C22⋊C4—21no—
757C22⋊C4—64no—
758C22⋊C4—64no—
759C22⋊C4C2×#6712yes—
760C22⋊C4C2×#6712yes—
761C22⋊C4C2×#6712yes—
762C22⋊C4C2×#6712yes—
763C42—22no—
764C42—21no—
765C42—64no—
766C42—64no—
767C42C2×#6712yes—
768C42C2×#6712yes—
769C42C23×D312yes—
770C42C23×D312yes—
771C22×C3—21no—
772C22×C3—21no—
773C22×C3—21no—
774C22×C3—21no—
775C22×C3—21no—
776C22×C3—21no—
777C22×C3—21no—
778C22×C3—44no—
779C22×C3—42no—
780C22×C3—41no—
781C22×C3—41no—
782C22×C3—42no—
783C22×C3—41no—
784C22×C3—42no—
785C22×C3—162no—
786C22×C3#52512yes—
787C22×C3#57712yes—
788C22×C3C23×D411yescharacteristic
789C2×D3—24no—
790C2×D3—48no—
791C2×D3—42no—
792C2×D3—42no—
793C3×C4—22no—
794C3×C4—22no—
795C3×C4—21no—
796C3×C4—21no—
797C3×C4—22no—
798C3×C4—22no—
799C3×C4—41no—
800C3×C4—41no—
801C3×C4—42no—
802C3×C4—41no—
803C3×C4#52512yes—
804C3×C4C22×#4112yes—
805Dic3—24no—
806Dic3—44no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—21no—
811C23—41no—
812C23—42no—
813C23—64no—
814C23—62no—
815C23—81no—
816C23—81no—
817C23—122no—
818C23—122no—
819C23C22×#6711yescharacteristic
820C23C22×#6711yescharacteristic
821C23C22×#6711yescharacteristic
822Q8—22no—
823Q8—34no—
824Q8—64no—
825Q8—62no—
826Q8—82no—
827D4—24no—
828D4—22no—
829D4—34no—
830D4—42no—
831D4—44no—
832D4—42no—
833D4—42no—
834D4—64no—
835D4—68no—
836D4—68no—
837D4—62no—
838D4—82no—
839D4—82no—
840D4—82no—
841D4—81no—
842C2×C4—22no—
843C2×C4—24no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—22no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—68no—
855C2×C4—64no—
856C2×C4—62no—
857C2×C4—68no—
858C2×C4—64no—
859C2×C4—82no—
860C2×C4—82no—
861C2×C4—82no—
862C2×C4—81no—
863C2×C4—124no—
864C2×C4—244no—
865C2×C4—244no—
866C2×C4—242no—
867C2×C4—242no—
868C2×C4D3×#4114yes—
869C2×C4C22×#6712yes—
870C2×C4C22×#6712yes—
871C2×C4C22×#6712yes—
872C2×C4C22×#6711yescharacteristic
873C2×C4C22×#6712yes—
874C2×C4C22×#6711yescharacteristic
875C2×C4C22×#6711yescharacteristic
876C2×C4C24×D311yescharacteristic
877C8—62no—
878C8—62no—
879C8—64no—
880C2×C3—22no—
881C2×C3—22no—
882C2×C3—41no—
883C2×C3—81no—
884C2×C3—82no—
885C2×C3C2×#52511yescharacteristic
886C2×C3C2×#57711yescharacteristic
887C2×C3#358511yescharacteristic
888D3—44no—
889C22—21no—
890C22—21no—
891C22—21no—
892C22—21no—
893C22—21no—
894C22—21no—
895C22—21no—
896C22—44no—
897C22—42no—
898C22—41no—
899C22—41no—
900C22—42no—
901C22—41no—
902C22—42no—
903C22—64no—
904C22—128no—
905C22—122no—
906C22—122no—
907C22—162no—
908C22#582812yes—
909C22#583612yes—
910C22C23×#6711yescharacteristic
911C4—22no—
912C4—22no—
913C4—21no—
914C4—21no—
915C4—22no—
916C4—22no—
917C4—41no—
918C4—41no—
919C4—42no—
920C4—41no—
921C4—64no—
922C4—124no—
923C4#582812yes—
924C4C2×D3×#4112yes—
925C3#6058811yescharacteristic, complemented, Sylow
926C2—22no—
927C2—22no—
928C2—41no—
929C2—82no—
930C2—81no—
931C2—124no—
932C2C2×#582811yescharacteristic
933C2C2×#583611yescharacteristic
934C2#8729811yescharacteristic
subgroupG/H
centerC22C23×#67
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3494C2
socleC22×C3C23×D4
hypercenter#3494D3
hypocenterC3#60588
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×#117 ◁ #3494

Complements

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

NH ≅ G/Ntype
1. C3×#3494C2semidirect
2. C2×#5523C2semidirect
3. #83476C2semidirect
4. #83462C2semidirect
5. #83434C2semidirect
6. #83385C2semidirect
7. #83315C2semidirect
8. #83300C2semidirect
9. #83153C2semidirect
10. #83141C2semidirect
11. #82926C2semidirect
12. #82914C2semidirect
13. #82624C2semidirect
14. C2×#5034C2semidirect
15. #82558C2semidirect
16. #82537C2semidirect
17. #82210C2semidirect
26. C3×#544C22semidirect
27. C3×#542C22semidirect
28. C3×#540C22semidirect
29. C3×#535C22semidirect
34. C3×#520C22semidirect
35. C3×#518C22semidirect
45. #5523C22semidirect
49. C2×C4×D12C22semidirect
50. C2×C4×Dic6C22semidirect
51. #5232C22semidirect
52. C2×#832C22semidirect
55. #5094C22semidirect
56. #5084C22semidirect
57. #5075C22semidirect
58. #5072C22semidirect
59. #5066C22semidirect
60. #5063C22semidirect
61. #5057C22semidirect
62. #5054C22semidirect
63. #5050C22semidirect
64. #5047C22semidirect
65. #5046C22semidirect
66. #5044C22semidirect
67. #5043C22semidirect
69. #5040C22semidirect
71. #5037C22semidirect
73. #5036C22semidirect
76. #5034C22semidirect
77. #5034C22semidirect
78. #5033C22semidirect
79. #5030C22semidirect
80. C4×#215C22semidirect
81. #5018C22semidirect
82. C4×#214C22semidirect
83. C4×#214C22semidirect
84. #5014C22semidirect
85. #5014C22semidirect
86. C4×#213C22semidirect
88. #5000C22semidirect
89. #4999C22semidirect
90. #4997C22semidirect
91. #4995C22semidirect
93. C2×#808C22semidirect
94. #4926C22semidirect
95. #4925C22semidirect
96. #3494D3semidirect
258. #544C2×D3semidirect
259. #542C2×D3semidirect
260. #540C2×D3semidirect
261. #535C2×D3semidirect
272. #520C2×D3semidirect
273. #518C2×D3semidirect
372. #235#41semidirect
925. C3#60588semidirect

Maximal subgroups

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

subgroupindex
C3×#34942
C2×#55232
#834762
#834622
#834342
#833852
#833152
#833002
#831532
#831412
#829262
#829142
#826242
C2×#50342
#825582
#825372
#822102
#605883