Finite Group Databasebeta

← #11903644

Subgroups — #11903644

Order 1152.

2419 conjugacy classes of subgroups.

The subgroup lattice has 875 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#3830C211yesmaximal, characteristic, complemented
2C3×#5558C212yesmaximal, complemented
3#10595306C212yesmaximal, complemented
4#10595253C211yesmaximal, characteristic, complemented
5#10595134C211yesmaximal, characteristic, complemented
6#10595088C214yesmaximal, complemented
7#10594963C212yesmaximal, complemented
8C4×#3805C212yesmaximal, complemented
9D3×#892C212yesmaximal, complemented
10#10594581C211yesmaximal, characteristic, complemented
11#10594531C211yesmaximal, characteristic, complemented
12#10594276C212yesmaximal, complemented
13#10594155C212yesmaximal, complemented
14#10594112C214yesmaximal, complemented
15C4×#3802C211yesmaximal, characteristic, complemented
16#10593920C212yesmaximal, complemented
17#10593854C211yesmaximal, characteristic, complemented
18#86874—32nomaximal
19C2×#3830C2211yescharacteristic
20C2×#3805C2212yes—
21C2×#3802C2211yescharacteristic
22C2×C4×D32C2212yes—
23C32×C4×D4C2211yescharacteristic, complemented
24D4×C3⋊Dic3C2211yescharacteristic, complemented
25C4×#638C2212yes—
26C2×C4×C3⋊Dic3C2212yescomplemented
27#64101C2211yescharacteristic
28#64096C2211yescharacteristic, complemented
29#64090C2212yes—
30#64086C2212yescomplemented
31C42×C3⋊D3C2211yescharacteristic
32C4×#634C2211yescharacteristic, complemented
33C3×#938C2212yescomplemented
34C3×#938C2212yescomplemented
35C3×#929C2214yescomplemented
36C3×C4×#67C2214yescomplemented
37C3×#892C2212yescomplemented
38C3×D3×C4⋊C4C2212yescomplemented
39C3×#884C2214yes—
40C3×#879C2214yescomplemented
41C3×C4×D12C2212yes—
42C3×#870C2212yescomplemented
43#63983C2214yes—
44#63982C2212yescomplemented
45#63980C2212yes—
46#63975C2214yes—
47#67⋊Dic3C2214yescomplemented
48#67⋊Dic3C2214yescomplemented
49#63969C2214yescomplemented
50#63959C2214yescomplemented
51#63957C2212yescomplemented
52#63921C2212yes—
53D3×(C2×D3)⋊C4C2214yes—
54#63919C2211yescharacteristic, complemented
55#63919C2211yescharacteristic, complemented
56C4×#627C2212yescomplemented
57#63915C2212yes—
58#63902C2211yescharacteristic
59#63902C2211yescharacteristic
60C4×#625C2211yescharacteristic
61C4×#625C2212yes—
62C4×#625C2211yescharacteristic
63#63900C2211yescharacteristic
64#63898C2212yes—
65D3×C4⋊Dic3C2212yescomplemented
66#63884C2214yes—
67#63878C2214yescomplemented
68#63878C2214yescomplemented
69C4×D3×Dic3C2214yescomplemented
70#63870C2212yescomplemented
71#63865C2212yes—
72#63865C2212yes—
73#63862C2214yescomplemented
74#63859C2214yescomplemented
75#63857C2212yescomplemented
76#63857C2212yescomplemented
77#63851C2214yescomplemented
78#63849C2212yes—
79#63846C2214yescomplemented
80#63841C2212yescomplemented
81#63838C2212yescomplemented
82#63838C2212yescomplemented
83#63836C2214yes—
84C3×#553—32no—
85#5708—34no—
86#5706—34no—
87#5694—32no—
88#5688—32no—
89#5659—34no—
90#5649—34no—
91#5616—32no—
92#5611—32no—
93#5610—34no—
94#5606—32no—
95#5606—32no—
96#5600—34no—
97#5558D312yescomplemented
98#5556—34no—
99C4×D3×D4—32no—
100#5541—32no—
101C4×#237—32no—
102C4×#237—34no—
103C4×#237—61no—
104#5533—32no—
105D3×#117—32no—
106#5511—32no—
107C2×#892—32no—
108C22×D32C2312yes—
109C2×C32×D4C2311yescharacteristic
110C22×C32×C4C2312yes—
111C2×#638C2312yes—
112C22×C3⋊Dic3C2312yes—
113C22×C3⋊Dic3C2312yes—
114#3830—24no—
115C2×C4×C3⋊D3C2311yescharacteristic
116C2×C4×C3⋊D3C2311yescharacteristic
117C2×C4×C3⋊D3C2311yescharacteristic
118C2×#634C2311yescharacteristic
119C2×C3×#67C2314yes—
120C2×C3×#67C2314yes—
121C2×C3×D12C2312yes—
122C2×C3×C4×D3C2312yes—
123C2×C3×C4×D3C2312yes—
124C2×C3×C4×D3C2314yes—
125C2×#627C2312yes—
126C2×#627C2312yes—
127C2×#625C2311yescharacteristic
128C2×#625C2311yescharacteristic
129C2×#624C2312yes—
130#3805—28no—
131C2×D3×Dic3C2312yes—
132C2×D3×Dic3C2312yes—
133C2×D3×Dic3C2314yes—
134#3802—24no—
135C4×D32—28no—
136C32×C4⋊C4C2311yescharacteristic
137C32×C22⋊C4C2312yes—
138C32×C42C2311yescharacteristic
139#3757C2312yes—
140#3752C2312yes—
141C4⋊(C3⋊Dic3)C2311yescharacteristic
142#3750C2312yes—
143#3750C2312yes—
144C4×C3⋊Dic3C2312yes—
145C4×C3⋊Dic3C2311yescharacteristic
146C4×C3⋊Dic3C2311yescharacteristic
147C4×C3⋊Dic3C2311yescharacteristic
148C4×C3⋊Dic3C2312yes—
149C4×C3⋊Dic3C2312yes—
150C3×#217C2314yes—
151C3×#217C2314yes—
152C3×(C2×D3)⋊C4C2314yes—
153C3×(C2×D3)⋊C4C2312yes—
154C3×(C2×D3)⋊C4C2312yes—
155C3×C4⋊Dic3C2312yes—
156C3×C4⋊Dic3C2312yes—
157C3×C4⋊Dic3C2312yes—
158C3×Dic3⋊C4C2314yes—
159C3×Dic3⋊C4C2314yes—
160C3×Dic3⋊C4C2314yes—
161C3×C4×Dic3C2314yes—
162#3724C2312yes—
163#3724C2312yes—
164#3724C2311yescharacteristic
165#3724C2311yescharacteristic
166Dic3⋊Dic3C2314yes—
167Dic3⋊Dic3C2314yes—
168Dic3⋊Dic3C2314yes—
169#3722C2314yes—
170(C2×D3)⋊Dic3C2314yes—
171(C2×D3)⋊Dic3C2312yes—
172(C2×D3)⋊Dic3C2314yes—
173(C2×D3)⋊Dic3C2314yes—
174(C2×D3)⋊Dic3C2312yes—
175Dic32C2314yes—
176Dic32C2314yes—
177#3475—91noSylow
178C2×#237—32no—
179C2×#237—34no—
180C2×#237—61no—
181C2×D3×D4—32no—
182C22×C4×D3—32no—
183C22×C4×D3—32no—
184C3×#126—34no—
185C3×#125—32no—
186C3×#123—34no—
187C3×#121—32no—
188C3×#121—32no—
189C3×#121—34no—
190C3×C4×D4—21no—
191C3×C4×D4—34no—
192C3×C4×D4—32no—
193C3×C4×D4C2×D312yescomplemented
194C3×#117—32no—
195C2×C3×C4⋊C4—32no—
196#939—34no—
197#938C2×D312yescomplemented
198#938C2×D312yescomplemented
199#937—34no—
200#937—34no—
201#936—34no—
202#935—34no—
203#935—34no—
204D4×Dic3—32no—
205D4×Dic3—34no—
206D4×Dic3—34no—
207D4×Dic3—32no—
208D4×Dic3—61no—
209#929C2×D314yescomplemented
210C4×#67—34no—
211C4×#67—34no—
212C4×#67—32no—
213C4×#67—32no—
214C4×#67—62no—
215C4×#67C2×D314yescomplemented
216C2×(C2×D3)⋊C4—34no—
217#926—32no—
218C2×C4⋊Dic3—32no—
219#924—32no—
220#924—32no—
221#924—34no—
222C2×C4×Dic3—34no—
223C2×C4×Dic3—34no—
224C2×C4×Dic3—62no—
225#898—34no—
226#897—32no—
227#897—32no—
228#896—34no—
229#896—34no—
230#896—34no—
231#894—34no—
232#893—32no—
233#892—32no—
234#892—32no—
235#892—34no—
236#892—34no—
237#892—32no—
238#892—32no—
239#892—34no—
240#892—61no—
241#892C2×D312yescomplemented
242D3×C4⋊C4—32no—
243D3×C4⋊C4—32no—
244D3×C4⋊C4C2×D312yescomplemented
245#890—34no—
246#889—34no—
247#889—34no—
248#888—32no—
249#888—32no—
250#887—32no—
251#887—34no—
252#887—34no—
253#887—61no—
254#885—34no—
255#885—34no—
256#884C2×D314yes—
257#883—34no—
258#883—34no—
259#883—34no—
260#67⋊C4—34no—
261#67⋊C4—34no—
262#67⋊C4—34no—
263#67⋊C4—32no—
264#67⋊C4—32no—
265#67⋊C4—62no—
266D3×C22⋊C4—34no—
267D3×C22⋊C4—32no—
268D3×C22⋊C4—32no—
269#879—34no—
270#879—34no—
271#879C2×D314yescomplemented
272#878—34no—
273#877—34no—
274#877—34no—
275#877—34no—
276#877—34no—
277#877—62no—
278#876—34no—
279C4×D12C2×D312yes—
280#872—34no—
281C42×D3—34no—
282C42×D3—32no—
283C42×D3—61no—
284#870C2×D312yescomplemented
285C4×Dic6—32no—
286C4×Dic6—34no—
287C4×Dic6—61no—
288C23×C32C2412yes—
289C22×C3⋊D3C2411yescharacteristic
290C22×C3×D3C2412yes—
291C22×C3×D3C2412yes—
292C2×D32—24no—
293C2×D32—24no—
294C2×D32—42no—
295C32×D4—22no—
296C2×C32×C4—42no—
297C2×C32×C4C2412yes—
298C2×C32×C4C2411yescharacteristic
299C2×C32×C4C2411yescharacteristic
300C2×C32×C4C2411yescharacteristic
301#638—24no—
302C2×C3⋊Dic3—24no—
303C2×C3⋊Dic3—24no—
304C2×C3⋊Dic3C2412yes—
305C2×C3⋊Dic3C2412yes—
306C2×C3⋊Dic3C2411yescharacteristic
307C2×C3⋊Dic3C2411yescharacteristic
308C2×C3⋊Dic3C2411yescharacteristic
309C4×C3⋊D3—22no—
310C4×C3⋊D3—41no—
311C4×C3⋊D3#4114yescomplemented
312#634—22no—
313C3×#67—28no—
314C3×#67—44no—
315C2×C3×Dic3C2414yes—
316C2×C3×Dic3C2412yes—
317C2×C3×Dic3C2414yes—
318C2×C3×Dic3C2412yes—
319C3×D12—24no—
320C3×C4×D3—24no—
321C3×C4×D3—24no—
322C3×C4×D3—44no—
323#627—24no—
324#627—42no—
325#625—22no—
326#625#4114yescomplemented
327#624—24no—
328D3×Dic3—28no—
329D3×Dic3—24no—
330D3×Dic3—24no—
331#556—91no—
332#555—91no—
333#554—91no—
334#553—32no—
335#552—92no—
336#552—92no—
337#551—94no—
338#547—91no—
339#546—92no—
340#533—91no—
341#529—94no—
342#529—92no—
343#525—92no—
344C4×#41—92no—
345C4×#41—91no—
346C2×C4×D4—91no—
347C2×#117—92no—
348C23×D3—32no—
349C23×D3—32no—
350C2×C3×D4—21no—
351C2×C3×D4—34no—
352C2×C3×D4—34no—
353C2×C3×D4—32no—
354C2×C3×D4C22×D312yes—
355C22×C3×C4—22no—
356C22×C3×C4—32no—
357C22×C3×C4—32no—
358C22×C3×C4—34no—
359C22×C3×C4C22×D314yes—
360C2×#67—32no—
361C2×#67—34no—
362C2×#67—32no—
363C2×#67—62no—
364C2×#67C22×D314yes—
365C2×#67C22×D314yes—
366C22×Dic3—34no—
367C22×Dic3—34no—
368C22×Dic3—32no—
369C22×Dic3—34no—
370C22×Dic3—32no—
371C22×Dic3—62no—
372C22×Dic3—62no—
373#237—68no—
374#237—616no—
375#237—68no—
376D3×D4—68no—
377C2×D12C22×D312yes—
378C2×C4×D3—32no—
379C2×C4×D3—32no—
380C2×C4×D3—34no—
381C2×C4×D3—32no—
382C2×C4×D3—32no—
383C2×C4×D3—32no—
384C2×C4×D3—32no—
385C2×C4×D3—32no—
386C2×C4×D3—61no—
387C2×C4×D3—61no—
388C2×C4×D3—61no—
389C2×C4×D3—68no—
390C2×C4×D3—68no—
391C2×C4×D3C22×D312yes—
392C2×C4×D3C22×D312yes—
393C2×C4×D3C22×D314yes—
394C2×Dic6—32no—
395C2×Dic6—34no—
396C2×Dic6—34no—
397C2×Dic6—61no—
398C3×C4⋊C4—21no—
399C3×C4⋊C4—34no—
400C3×C4⋊C4—34no—
401C3×C4⋊C4—32no—
402C3×C4⋊C4—32no—
403C3×C4⋊C4—32no—
404C3×C4⋊C4—34no—
405C3×C4⋊C4C22×D312yes—
406C3×C22⋊C4—22no—
407C3×C22⋊C4—34no—
408C3×C22⋊C4—34no—
409C3×C22⋊C4—32no—
410C3×C22⋊C4—34no—
411C3×C22⋊C4—32no—
412C3×C22⋊C4C22×D314yes—
413C3×C42—21no—
414C3×C42—34no—
415C3×C42C22×D312yes—
416#217—34no—
417#217—34no—
418#217—34no—
419#217—32no—
420#217—34no—
421#217—32no—
422#217—62no—
423#217C22×D314yes—
424#217C22×D314yes—
425(C2×D3)⋊C4—32no—
426(C2×D3)⋊C4—34no—
427(C2×D3)⋊C4—32no—
428(C2×D3)⋊C4—34no—
429(C2×D3)⋊C4—34no—
430(C2×D3)⋊C4—34no—
431(C2×D3)⋊C4—34no—
432(C2×D3)⋊C4—34no—
433(C2×D3)⋊C4—62no—
434(C2×D3)⋊C4C22×D312yes—
435(C2×D3)⋊C4C22×D312yes—
436(C2×D3)⋊C4C22×D314yes—
437C4⋊Dic3—32no—
438C4⋊Dic3—34no—
439C4⋊Dic3—34no—
440C4⋊Dic3—34no—
441C4⋊Dic3—61no—
442C4⋊Dic3C22×D312yes—
443C4⋊Dic3C22×D312yes—
444C4⋊Dic3C22×D312yes—
445Dic3⋊C4—34no—
446Dic3⋊C4—34no—
447Dic3⋊C4—32no—
448Dic3⋊C4—34no—
449Dic3⋊C4—34no—
450Dic3⋊C4—34no—
451Dic3⋊C4—34no—
452Dic3⋊C4—32no—
453Dic3⋊C4—34no—
454Dic3⋊C4—62no—
455Dic3⋊C4—62no—
456Dic3⋊C4C22×D314yes—
457Dic3⋊C4C22×D314yes—
458Dic3⋊C4C22×D314yes—
459C4×Dic3—34no—
460C4×Dic3—34no—
461C4×Dic3—32no—
462C4×Dic3—34no—
463C4×Dic3—32no—
464C4×Dic3—32no—
465C4×Dic3—34no—
466C4×Dic3—34no—
467C4×Dic3—34no—
468C4×Dic3—34no—
469C4×Dic3—62no—
470C4×Dic3—61no—
471C4×Dic3—61no—
472C4×Dic3—61no—
473C4×Dic3—62no—
474C4×Dic3—62no—
475C4×Dic3C22×D314yes—
476C22×C32—22no—
477C22×C32—22no—
478C22×C32—22no—
479C22×C32C2511yescharacteristic
480C2×C3⋊D3—21no—
481C2×C3⋊D3—21no—
482C2×C3⋊D3C2×#4112yes—
483C2×C3×D3—22no—
484C2×C3×D3—22no—
485C2×C3×D3—22no—
486C2×C3×D3—22no—
487C2×C3×D3—22no—
488C2×C3×D3C2×#4114yes—
489D32—48no—
490C32×C4—21no—
491C32×C4—21no—
492C32×C4—22no—
493C32×C4C2×#4112yes—
494C3⋊Dic3—22no—
495C3⋊Dic3—22no—
496C3⋊Dic3—21no—
497C3⋊Dic3C2×#4112yes—
498C3⋊Dic3C2×#4112yes—
499C3×Dic3—22no—
500C3×Dic3—22no—
501C3×Dic3—24no—
502C3×Dic3—24no—
503C2×#41—92no—
504C2×#41—91no—
505C22×D4—91no—
506C23×C4—92no—
507C4⋊Q8—91no—
508C4⋊Q8—91no—
509#126—34no—
510#126—94no—
511#126—94no—
512#125—32no—
513#125—94no—
514#125—92no—
515#124—92no—
516#124—94no—
517#123—34no—
518#123—94no—
519#123—94no—
520#123—94no—
521C22⋊Q8—92no—
522C22⋊Q8—92no—
523C22⋊Q8—92no—
524C22⋊Q8—92no—
525C22⋊Q8—92no—
526C22⋊Q8—94no—
527#121—32no—
528#121—32no—
529#121—34no—
530#121—92no—
531#120—94no—
532C4×Q8—92no—
533C4×Q8—92no—
534C4×Q8—92no—
535C4×Q8—91no—
536C4×Q8—91no—
537C4×D4—34no—
538C4×D4—32no—
539C4×D4—91no—
540C4×D4—91no—
541C4×D4—94no—
542C4×D4—94no—
543C4×D4—92no—
544C4×D4—91no—
545C4×D4—91no—
546C4×D4—92no—
547C4×D4—91no—
548C4×D4—92no—
549C4×D4—92no—
550C4×D4D3211yescharacteristic, complemented
551#117—32no—
552#117—94no—
553#117—92no—
554#117—94no—
555#117—94no—
556#117—92no—
557#117—92no—
558#117—91no—
559#117—92no—
560C2×C4⋊C4—32no—
561C2×C4⋊C4—91no—
562C2×C4⋊C4—92no—
563C2×C22⋊C4—92no—
564C2×C22⋊C4—94no—
565C2×C42—94no—
566C2×C42—92no—
567C2×C42—91no—
568C23×C3—22no—
569C23×C3—32no—
570C23×C3—32no—
571C23×C3C23×D314yes—
572C22×D3—32no—
573C22×D3—61no—
574C22×D3—64no—
575C22×D3—64no—
576C22×D3—64no—
577C22×D3—64no—
578C22×D3—122no—
579C22×D3—122no—
580C22×D3C23×D312yes—
581C22×D3C23×D312yes—
582C3×D4—24no—
583C3×D4—24no—
584C3×D4—64no—
585C3×D4—68no—
586C3×D4—124no—
587C2×C3×C4—21no—
588C2×C3×C4—21no—
589C2×C3×C4—22no—
590C2×C3×C4—21no—
591C2×C3×C4—32no—
592C2×C3×C4—34no—
593C2×C3×C4—34no—
594C2×C3×C4—32no—
595C2×C3×C4—44no—
596C2×C3×C4—44no—
597C2×C3×C4—64no—
598C2×C3×C4—64no—
599C2×C3×C4—124no—
600C2×C3×C4C23×D312yes—
601C2×C3×C4C23×D314yes—
602C2×C3×C4C23×D312yes—
603C2×C3×C4C23×D312yes—
604#67—28no—
605#67—38no—
606#67—44no—
607#67—64no—
608#67—68no—
609#67—68no—
610C2×Dic3—32no—
611C2×Dic3—32no—
612C2×Dic3—34no—
613C2×Dic3—34no—
614C2×Dic3—32no—
615C2×Dic3—61no—
616C2×Dic3—61no—
617C2×Dic3—62no—
618C2×Dic3—61no—
619C2×Dic3—62no—
620C2×Dic3—64no—
621C2×Dic3—64no—
622C2×Dic3—68no—
623C2×Dic3—68no—
624C2×Dic3—68no—
625C2×Dic3—68no—
626C2×Dic3—124no—
627C2×Dic3C23×D312yes—
628C2×Dic3C23×D314yes—
629C2×Dic3C23×D314yes—
630C2×Dic3C23×D312yes—
631D12—24no—
632C4×D3—24no—
633C4×D3—24no—
634C4×D3—38no—
635C4×D3—44no—
636C4×D3—64no—
637C4×D3—64no—
638C4×D3—64no—
639C4×D3—64no—
640C4×D3—64no—
641C4×D3—64no—
642C4×D3—68no—
643C4×D3—122no—
644C4×D3—122no—
645C4×D3—122no—
646Dic6—68no—
647Dic6—64no—
648Dic6—64no—
649Dic6—124no—
650C2×C32—42no—
651C2×C32C22×#4111yescharacteristic
652C2×C32C22×#4111yescharacteristic
653C2×C32#58511yescharacteristic
654C3⋊D3—22no—
655C3×D3—24no—
656C3×D3—42no—
657C24—92no—
658#41—184no—
659#41—188no—
660C2×Q8—92no—
661C2×Q8—92no—
662C2×Q8—91no—
663C2×D4—34no—
664C2×D4—34no—
665C2×D4—32no—
666C2×D4—91no—
667C2×D4—91no—
668C2×D4—92no—
669C2×D4—184no—
670C2×D4C2×D3211yescharacteristic
671C22×C4—32no—
672C22×C4—32no—
673C22×C4—34no—
674C22×C4—92no—
675C22×C4—92no—
676C22×C4—94no—
677C22×C4—92no—
678C22×C4—91no—
679C22×C4—92no—
680C22×C4—92no—
681C22×C4—91no—
682C22×C4—91no—
683C22×C4—188no—
684C22×C4C2×D3212yes—
685C4⋊C4—32no—
686C4⋊C4—34no—
687C4⋊C4—32no—
688C4⋊C4—32no—
689C4⋊C4—34no—
690C4⋊C4—34no—
691C4⋊C4—91no—
692C4⋊C4—94no—
693C4⋊C4—91no—
694C4⋊C4—92no—
695C4⋊C4—94no—
696C4⋊C4—94no—
697C4⋊C4—92no—
698C4⋊C4—91no—
699C4⋊C4—92no—
700C4⋊C4—92no—
701C4⋊C4C2×D3211yescharacteristic
702C22⋊C4—34no—
703C22⋊C4—34no—
704C22⋊C4—34no—
705C22⋊C4—32no—
706C22⋊C4—32no—
707C22⋊C4—94no—
708C22⋊C4—94no—
709C22⋊C4—92no—
710C22⋊C4—92no—
711C22⋊C4—94no—
712C22⋊C4—94no—
713C22⋊C4—92no—
714C22⋊C4—92no—
715C22⋊C4C2×D3212yes—
716C42—34no—
717C42—94no—
718C42—94no—
719C42—92no—
720C42—91no—
721C42—91no—
722C42—92no—
723C42—91no—
724C42—92no—
725C42C2×D3211yescharacteristic
726C22×C3—24no—
727C22×C3—24no—
728C22×C3—24no—
729C22×C3—24no—
730C22×C3—21no—
731C22×C3—34no—
732C22×C3—42no—
733C22×C3—42no—
734C22×C3—62no—
735C22×C3—62no—
736C22×C3—62no—
737C22×C3—62no—
738C22×C3—62no—
739C22×C3C24×D312yes—
740C2×D3—22no—
741C2×D3—22no—
742C2×D3—22no—
743C2×D3—22no—
744C2×D3—22no—
745C2×D3—34no—
746C2×D3—62no—
747C2×D3—62no—
748C2×D3—62no—
749C2×D3—121no—
750C2×D3—121no—
751C2×D3—128no—
752C2×D3—128no—
753C2×D3D3×#4114yes—
754C3×C4—22no—
755C3×C4—22no—
756C3×C4—24no—
757C3×C4—22no—
758C3×C4—22no—
759C3×C4—41no—
760C3×C4—42no—
761C3×C4—64no—
762C3×C4—62no—
763C3×C4—62no—
764C3×C4—64no—
765C3×C4D3×#4114yes—
766Dic3—24no—
767Dic3—22no—
768Dic3—22no—
769Dic3—24no—
770Dic3—34no—
771Dic3—34no—
772Dic3—62no—
773Dic3—62no—
774Dic3—64no—
775Dic3—64no—
776Dic3—64no—
777Dic3—62no—
778Dic3—121no—
779Dic3—122no—
780C32#347511yescharacteristic, complemented, Sylow
781C23—32no—
782C23—32no—
783C23—91no—
784C23—184no—
785C23—184no—
786C23—362no—
787C23C22×D3212yes—
788Q8—184no—
789Q8—182no—
790Q8—362no—
791D4—22no—
792D4—64no—
793D4—68no—
794D4—94no—
795D4—124no—
796D4—182no—
797D4—184no—
798C2×C4—32no—
799C2×C4—34no—
800C2×C4—34no—
801C2×C4—32no—
802C2×C4—42no—
803C2×C4—64no—
804C2×C4—64no—
805C2×C4—91no—
806C2×C4—91no—
807C2×C4—94no—
808C2×C4—92no—
809C2×C4—91no—
810C2×C4—92no—
811C2×C4—124no—
812C2×C4—182no—
813C2×C4—184no—
814C2×C4—184no—
815C2×C4—184no—
816C2×C4—188no—
817C2×C4—184no—
818C2×C4—184no—
819C2×C4—361no—
820C2×C4C22×D3212yes—
821C2×C4C22×D3211yescharacteristic
822C2×C4C22×D3211yescharacteristic
823C2×C4C22×D3211yescharacteristic
824C2×C3—21no—
825C2×C3—21no—
826C2×C3—21no—
827C2×C3—44no—
828C2×C3—44no—
829C2×C3—64no—
830C2×C3—122no—
831C2×C3C2×D3×#4112yes—
832C2×C3C2×D3×#4112yes—
833C2×C3#596612yes—
834D3—24no—
835D3—42no—
836D3—64no—
837D3—122no—
838C22—22no—
839C22—22no—
840C22—22no—
841C22—34no—
842C22—62no—
843C22—62no—
844C22—62no—
845C22—62no—
846C22—62no—
847C22—92no—
848C22—181no—
849C22—181no—
850C22—368no—
851C22C23×D3211yescharacteristic
852C4—21no—
853C4—22no—
854C4—21no—
855C4—62no—
856C4—62no—
857C4—64no—
858C4—64no—
859C4—92no—
860C4—92no—
861C4—182no—
862C4—181no—
863C4—182no—
864C4#6430612yes—
865C3—21no—
866C3#8687412yescomplemented
867C2—42no—
868C2—64no—
869C2—122no—
870C2—182no—
871C2C2×#6430611yescharacteristic
872C2#1059667911yescharacteristic
873C2D32×#4111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×D4C22
hypercenterC4×D4D32
hypocenterC32#3475
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C4×#3830C2semidirect
2. C3×#5558C2semidirect
3. #10595306C2semidirect
4. #10595253C2semidirect
5. #10595134C2semidirect
6. #10595088C2semidirect
7. #10594963C2semidirect
8. C4×#3805C2semidirect
9. D3×#892C2semidirect
10. #10594581C2semidirect
11. #10594531C2semidirect
12. #10594276C2semidirect
13. #10594155C2semidirect
14. #10594112C2semidirect
15. C4×#3802C2semidirect
16. #10593920C2semidirect
17. #10593854C2semidirect
23. C32×C4×D4C22semidirect
24. D4×C3⋊Dic3C22semidirect
26. C2×C4×C3⋊Dic3C22semidirect
28. #64096C22semidirect
30. #64086C22semidirect
32. C4×#634C22semidirect
33. C3×#938C22semidirect
34. C3×#938C22semidirect
35. C3×#929C22semidirect
36. C3×C4×#67C22semidirect
37. C3×#892C22semidirect
38. C3×D3×C4⋊C4C22semidirect
40. C3×#879C22semidirect
42. C3×#870C22semidirect
44. #63982C22semidirect
47. #67⋊Dic3C22semidirect
48. #67⋊Dic3C22semidirect
49. #63969C22semidirect
50. #63959C22semidirect
51. #63957C22semidirect
54. #63919C22semidirect
55. #63919C22semidirect
56. C4×#627C22semidirect
65. D3×C4⋊Dic3C22semidirect
67. #63878C22semidirect
68. #63878C22semidirect
69. C4×D3×Dic3C22semidirect
70. #63870C22semidirect
73. #63862C22semidirect
74. #63859C22semidirect
75. #63857C22semidirect
76. #63857C22semidirect
77. #63851C22semidirect
79. #63846C22semidirect
80. #63841C22semidirect
81. #63838C22semidirect
82. #63838C22semidirect
97. #5558D3semidirect
193. C3×C4×D4C2×D3semidirect
197. #938C2×D3semidirect
198. #938C2×D3semidirect
209. #929C2×D3semidirect
215. C4×#67C2×D3semidirect
241. #892C2×D3semidirect
244. D3×C4⋊C4C2×D3semidirect
271. #879C2×D3semidirect
284. #870C2×D3semidirect
311. C4×C3⋊D3#41semidirect
326. #625#41semidirect
550. C4×D4D32semidirect
780. C32#3475semidirect
866. C3#86874semidirect

Maximal subgroups

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

subgroupindex
C4×#38302
C3×#55582
#105953062
#105952532
#105951342
#105950882
#105949632
C4×#38052
D3×#8922
#105945812
#105945312
#105942762
#105941552
#105941122
C4×#38022
#105939202
#105938542
#868743