Finite Group Databasebeta

← C2×#10595106 #11918878

Subgroups — C2×#10595106 #11918878

Order 1152.

3069 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1004C211yesmaximal, characteristic, complemented
2C2×#64298C211yesmaximal, characteristic, complemented
3C22×#3754C211yesmaximal, characteristic, complemented
4C2×C3×#932C211yesmaximal, characteristic, complemented
5C2×#63933C212yesmaximal, complemented
6C2×#63932C212yesmaximal, complemented
7#10595106C2116yesmaximal, direct product factor
8C2×#63929C212yesmaximal, complemented
9C2×D3×#214C212yesmaximal, complemented
10C2×#63831C211yesmaximal, characteristic, complemented
11C2×#63822C211yesmaximal, characteristic, complemented
12C2×#63815C211yesmaximal, characteristic, complemented
13C2×#5836—31nomaximal
14C2×#5775—31nomaximal
15C22×C32×D4C2211yescharacteristic
16C22×#634C2211yescharacteristic, complemented
17C22×C3×#67—22no—
18C3×#1004—24no—
19C3×#1004C2218yescomplemented
20C2×C3×#237—21no—
21C2×C3×#237C2212yes—
22C2×C3×D3×D4—21no—
23C2×C3×D3×D4C2212yes—
24C2×C3×#235C2211yescharacteristic
25C2×C3×#235C2211yescharacteristic
26C2×C3×#235C2211yescharacteristic, complemented
27C2×#3805—22no—
28#64298—24no—
29#64298C2218yescomplemented
30C2×#3795—21no—
31C2×#3795C2212yescomplemented
32C2×D3×Dic6—21no—
33C2×D3×Dic6C2212yescomplemented
34C2×#3754C2212yescomplemented
35C2×#3754C2212yescomplemented
36C2×#3754C2218yescomplemented
37C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
38C2×C3×#214C2212yescomplemented
39C3×#932C2218yescomplemented
40C2×C3×#213C2212yescomplemented
41C2×C3×#208C2211yescharacteristic, complemented
42#63933C22116yescomplemented
43#63932C22116yescomplemented
44#63929C22116yescomplemented
45D3×#214C22116yescomplemented
46C2×#3719C2212yescomplemented
47C2×#3718C2211yescharacteristic, complemented
48#63831C2218yescomplemented
49C2×#3716C2212yescomplemented
50C2×#3715C2211yescharacteristic, complemented
51C2×#3715C2211yescharacteristic, complemented
52#63822C2218yescomplemented
53C2×#3713C2211yescharacteristic, complemented
54C2×#3711C2212yescomplemented
55#63815C2218yescomplemented
56C2×D3×C3⋊C8C2212yescomplemented
57C2×C3×H(5,𝔽2)—31no—
58C2×#1010—31no—
59C2×#1010—31no—
60C2×#1004D311yescharacteristic, complemented
61C2×C3×AGL(1,ℤ/8)—31no—
62#5836—316no—
63C2×#951—32no—
64C2×#951—31no—
65C2×#950—31no—
66C2×#950—31no—
67C2×#950—32no—
68C2×#948—31no—
69C22×#214—31no—
70C22×#214—31no—
71C22×#214—32no—
72C22×#214—61no—
73C2×#932—32no—
74C2×#932D311yescharacteristic, complemented
75#5775—316no—
76C2×#915—32no—
77C2×D3×SD16—32no—
78C2×#912—32no—
79C2×#911—32no—
80C2×#909—31no—
81C2×#907—31no—
82C24×C32—21no—
83C23×C3×D3—22no—
84C2×C32×D4—21no—
85C2×C32×D4—22no—
86C2×C32×D4C2312yes—
87C2×C32×D4C2314yes—
88C22×C32×C4C2311yescharacteristic
89C22×C3⋊Dic3—21no—
90C2×#634—21no—
91C2×#634—22no—
92C2×#634C2312yes—
93C2×#634C2314yescomplemented
94C2×C3×#67—21no—
95C2×C3×#67—21no—
96C2×C3×#67—22no—
97C2×C3×#67—216no—
98C2×C3×#67—22no—
99C2×C3×#67D412yes—
100C22×C3×Dic3—22no—
101C3×#237—24no—
102C3×#237—28no—
103C3×#237C2318yes—
104C3×D3×D4—28no—
105C3×D3×D4—24no—
106C3×D3×D4C2318yes—
107C3×#235—22no—
108C3×#235—22no—
109C3×#235D414yes—
110C3×#235C2314yes—
111C3×#235C2314yes—
112C3×#235C2314yescomplemented
113C2×C3×D12D411yescharacteristic
114C2×C3×D12C2311yescharacteristic
115C2×C3×D12C2311yescharacteristic
116C2×C3×C4×D3—21no—
117C2×C3×C4×D3—21no—
118C2×C3×C4×D3C2312yes—
119C2×C3×Dic6D411yescharacteristic
120C2×C3×Dic6C2311yescharacteristic
121C2×C3×Dic6C2311yescharacteristic
122C2×#627—22no—
123C2×#625—22no—
124#3805—216no—
125C2×D3×Dic3—22no—
126C2×D3×Dic3—22no—
127#3795—28no—
128#3795—24no—
129#3795C2318yescomplemented
130D3×Dic6—24no—
131D3×Dic6—28no—
132D3×Dic6C2318yescomplemented
133#3754C2318yescomplemented
134#3754C2318yescomplemented
135C2×C3⋊(C3⋊C8)C2311yescharacteristic
136C2×C3⋊(C3⋊C8)C2311yescharacteristic
137C2×C3⋊(C3⋊C8)C2314yescomplemented
138C3×#214C2318yescomplemented
139C3×#213C2318yescomplemented
140C3×#208C2314yescomplemented
141C2×C3×C3⋊C8C2312yes—
142#3719C2318yescomplemented
143#3718C2314yescomplemented
144#3716C2318yescomplemented
145#3715C2314yescomplemented
146#3715C2314yescomplemented
147#3713C2314yescomplemented
148#3711C2318yescomplemented
149D3×C3⋊C8C2318yescomplemented
150C2×#577—91noSylow
151C3×H(5,𝔽2)—38no—
152C3×H(5,𝔽2)—64no—
153C2×C3×#41—31no—
154C2×C3×#41—32no—
155C2×C3×#41—31no—
156C2×C3×#41—31no—
157C2×C3×#41—61no—
158C22×C3×D4—21no—
159C22×C3×D4—32no—
160C22×C3×D4—61no—
161C22×C3×D4—62no—
162C22×C3×D4C2×D311yescharacteristic
163C22×C3×D4C2×D311yescharacteristic
164C22×#67—22no—
165#1010—38no—
166#1010—38no—
167#1010—64no—
168#1010—64no—
169C2×D3×Q8—32no—
170C2×D3×Q8—61no—
171#1004—24no—
172#1004C2×D318yescomplemented
173C2×#237—21no—
174C2×#237—32no—
175C2×#237—61no—
176C2×#237—62no—
177C2×#237—62no—
178C2×#237C2×D312yes—
179C2×D3×D4—21no—
180C2×D3×D4C2×D312yes—
181C2×#235—32no—
182C2×#235—61no—
183C2×#235C2×D311yescharacteristic
184C2×#235C2×D311yescharacteristic
185C2×#235C2×D311yescharacteristic, complemented
186C22×Dic6—31no—
187C22×Dic6—31no—
188C22×Dic6—32no—
189C22×Dic6—61no—
190C22×Dic6—61no—
191C3×AGL(1,ℤ/8)—38no—
192C2×C3×SD16—32no—
193C2×C3×D8—32no—
194C2×C3×M16—31no—
195#951—316no—
196#951—38no—
197#950—38no—
198#950—38no—
199#950—316no—
200#948—38no—
201C2×#216—31no—
202C2×#216—31no—
203C2×#216—32no—
204C2×#215—31no—
205C2×#215—31no—
206C2×#214—32no—
207C2×#214—32no—
208C2×#214—38no—
209C2×#214—32no—
210C2×#214—32no—
211C2×#214—38no—
212C2×#214—31no—
213C2×#214—31no—
214C2×#214—316no—
215C2×#214—32no—
216C2×#214—62no—
217C2×#214—62no—
218C2×#214—68no—
219C2×#214C2×D312yescomplemented
220#932—316no—
221#932C2×D318yescomplemented
222C2×#213—31no—
223C2×#213—31no—
224C2×#213C2×D312yescomplemented
225C2×#208—32no—
226C2×#208C2×D311yescharacteristic, complemented
227C22×C3⋊C8—31no—
228C22×C3⋊C8—31no—
229C22×C3⋊C8—32no—
230C22×C3⋊C8—61no—
231#915—316no—
232D3×SD16—316no—
233#912—316no—
234#911—316no—
235#909—38no—
236#907—38no—
237C2×Dic12—32no—
238C2×#204—32no—
239C2×ΓL(1,𝔽25)—32no—
240C2×D3×C8—32no—
241C23×C32—22no—
242C23×C32—24no—
243C23×C32—82no—
244C23×C32C2×D411yescharacteristic
245C22×C3×D3—21no—
246C22×C3×D3—21no—
247C22×C3×D3—28no—
248C22×C3×D3—84no—
249C22×C3×D3C2×D412yes—
250C32×D4—22no—
251C32×D4—24no—
252C32×D4C2414yes—
253C2×C32×C4C2×D411yescharacteristic
254C2×C32×C4C2×D412yes—
255C2×C32×C4C2411yescharacteristic
256C2×C32×C4C2412yes—
257C2×C3⋊Dic3—22no—
258C2×C3⋊Dic3—24no—
259#634—22no—
260#634—24no—
261#634C2414yes—
262C3×#67—24no—
263C3×#67—24no—
264C3×#67—28no—
265C3×#67—28no—
266C3×#67C2×D418yes—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3—28no—
270C2×C3×Dic3C2×D412yes—
271C3×D12—21no—
272C3×D12—21no—
273C3×D12C2×D414yes—
274C3×D12C2412yes—
275C3×D12C2412yes—
276C3×C4×D3—24no—
277C3×C4×D3—24no—
278C3×C4×D3C2×D414yes—
279C3×C4×D3C2414yes—
280C3×Dic6—21no—
281C3×Dic6—21no—
282C3×Dic6C2×D414yes—
283C3×Dic6C2412yes—
284C3×Dic6C2412yes—
285#627—28no—
286#625—28no—
287D3×Dic3—28no—
288D3×Dic3—28no—
289C3⋊(C3⋊C8)C2412yes—
290C3⋊(C3⋊C8)C2412yes—
291C3×C3⋊C8C2414yes—
292C2×2−1+4—91no—
293C2×H(5,𝔽2)—31no—
294#577—916no—
295C2×#137—91no—
296C2×#137—92no—
297C2×AGL(1,ℤ/8)—31no—
298C2×AGL(1,ℤ/8)—92no—
299C2×#135—92no—
300C2×#135—91no—
301C22×SD16—92no—
302C22×SD16—91no—
303C2×#131—91no—
304C24×C3—21no—
305C24×C3—21no—
306C24×C3—41no—
307C24×C3—62no—
308C23×D3—22no—
309C3×#41—34no—
310C3×#41—34no—
311C3×#41—38no—
312C3×#41—34no—
313C3×#41—34no—
314C3×#41—64no—
315C3×#41—68no—
316C3×#41—62no—
317C3×#41—62no—
318C2×C3×Q8—31no—
319C2×C3×Q8—31no—
320C2×C3×Q8—31no—
321C2×C3×D4—21no—
322C2×C3×D4—22no—
323C2×C3×D4—21no—
324C2×C3×D4—22no—
325C2×C3×D4—22no—
326C2×C3×D4—24no—
327C2×C3×D4—32no—
328C2×C3×D4—38no—
329C2×C3×D4—31no—
330C2×C3×D4—31no—
331C2×C3×D4—31no—
332C2×C3×D4—41no—
333C2×C3×D4—42no—
334C2×C3×D4—64no—
335C2×C3×D4—62no—
336C2×C3×D4—68no—
337C2×C3×D4—616no—
338C2×C3×D4—62no—
339C2×C3×D4—61no—
340C2×C3×D4—61no—
341C2×C3×D4C22×D312yes—
342C2×C3×D4C22×D314yes—
343C2×C3×D4C22×D312yes—
344C2×C3×D4C22×D314yes—
345C22×C3×C4—21no—
346C22×C3×C4—32no—
347C22×C3×C4—62no—
348C22×C3×C4—61no—
349C22×C3×C4—61no—
350C22×C3×C4C22×D311yescharacteristic
351C22×C3×C4C22×D311yescharacteristic
352C2×#67—21no—
353C2×#67—21no—
354C2×#67—22no—
355C2×#67—216no—
356C2×#67—22no—
357C2×#67—62no—
358C2×#67—62no—
359C2×#67#6712yes—
360C22×Dic3—22no—
361C22×Dic3—62no—
362C22×Dic3—61no—
363C22×Dic3—61no—
364C22×Dic3—62no—
365C22×Dic3—121no—
366D3×Q8—38no—
367D3×Q8—68no—
368D3×Q8—64no—
369#237—24no—
370#237—28no—
371#237—38no—
372#237—68no—
373#237—616no—
374#237—616no—
375#237—64no—
376#237C22×D318yes—
377D3×D4—28no—
378D3×D4—24no—
379D3×D4C22×D318yes—
380#235—22no—
381#235—22no—
382#235—38no—
383#235—64no—
384#235—68no—
385#235#6714yes—
386#235C22×D314yes—
387#235C22×D314yes—
388#235C22×D314yescomplemented
389C2×D12#6711yescharacteristic
390C2×D12C22×D311yescharacteristic
391C2×D12C22×D311yescharacteristic
392C2×C4×D3—21no—
393C2×C4×D3—21no—
394C2×C4×D3—62no—
395C2×C4×D3—62no—
396C2×C4×D3C22×D312yes—
397C2×Dic6—32no—
398C2×Dic6—34no—
399C2×Dic6—32no—
400C2×Dic6—34no—
401C2×Dic6—38no—
402C2×Dic6—62no—
403C2×Dic6—64no—
404C2×Dic6—64no—
405C2×Dic6—62no—
406C2×Dic6—61no—
407C2×Dic6—62no—
408C2×Dic6—61no—
409C2×Dic6—62no—
410C2×Dic6—62no—
411C2×Dic6—68no—
412C2×Dic6—121no—
413C2×Dic6—122no—
414C2×Dic6#6711yescharacteristic
415C2×Dic6C22×D311yescharacteristic
416C2×Dic6C22×D311yescharacteristic
417C3×SD16—38no—
418C3×D8—38no—
419C3×M16—34no—
420C2×C3×C8—32no—
421#216—34no—
422#216—34no—
423#216—38no—
424#215—34no—
425#215—34no—
426#214—38no—
427#214—38no—
428#214—38no—
429#214—38no—
430#214—34no—
431#214—34no—
432#214—38no—
433#214—68no—
434#214—68no—
435#214C22×D318yescomplemented
436#213—34no—
437#213—34no—
438#213C22×D318yescomplemented
439#208—38no—
440#208C22×D314yescomplemented
441C2×C3⋊C8—31no—
442C2×C3⋊C8—31no—
443C2×C3⋊C8—34no—
444C2×C3⋊C8—31no—
445C2×C3⋊C8—31no—
446C2×C3⋊C8—34no—
447C2×C3⋊C8—38no—
448C2×C3⋊C8—61no—
449C2×C3⋊C8—61no—
450C2×C3⋊C8—64no—
451C2×C3⋊C8C22×D312yes—
452Dic12—38no—
453#204—38no—
454ΓL(1,𝔽25)—38no—
455D3×C8—38no—
456C22×C32—22no—
457C22×C32—24no—
458C22×C32—44no—
459C22×C32—84no—
460C22×C32C22×D412yes—
461C22×C32C22×D411yescharacteristic
462C2×C3×D3—24no—
463C2×C3×D3—22no—
464C2×C3×D3—22no—
465C2×C3×D3—42no—
466C2×C3×D3—42no—
467C2×C3×D3—88no—
468C2×C3×D3C22×D414yes—
469C32×C4C22×D411yescharacteristic
470C32×C4C22×D412yes—
471C32×C4C2511yescharacteristic
472C3⋊Dic3—24no—
473C3×Dic3—22no—
474C3×Dic3—22no—
475C3×Dic3C22×D414yes—
4762−1+4—98no—
4772−1+4—184no—
478H(5,𝔽2)—38no—
479H(5,𝔽2)—64no—
480C2×#41—31no—
481C2×#41—32no—
482C2×#41—31no—
483C2×#41—31no—
484C2×#41—61no—
485C2×#41—92no—
486C2×#41—181no—
487C2×#41—182no—
488C22×Q8—92no—
489C22×Q8—91no—
490C22×Q8—181no—
491C22×D4—32no—
492C22×D4—61no—
493C22×D4—62no—
494C22×D4D3211yescharacteristic
495#137—98no—
496#137—916no—
497AGL(1,ℤ/8)—38no—
498AGL(1,ℤ/8)—916no—
499#135—916no—
500#135—98no—
501C2×Q16—92no—
502C2×Q16—91no—
503C2×SD16—32no—
504C2×SD16—92no—
505C2×SD16—916no—
506C2×SD16—91no—
507C2×SD16—91no—
508C2×SD16—92no—
509C2×SD16—92no—
510C2×SD16—98no—
511C2×D8—32no—
512C2×D8—91no—
513#131—98no—
514C2×M16—31no—
515C2×M16—92no—
516C22×C8—92no—
517C22×C8—91no—
518C23×C3—22no—
519C23×C3—22no—
520C23×C3—24no—
521C23×C3—24no—
522C23×C3—21no—
523C23×C3—32no—
524C23×C3—42no—
525C23×C3—44no—
526C23×C3—68no—
527C23×C3—61no—
528C23×C3—61no—
529C23×C3—82no—
530C23×C3—82no—
531C23×C3—84no—
532C23×C3—244no—
533C23×C3D3×D411yescharacteristic
534C23×C3C2×#6711yescharacteristic
535C22×D3—21no—
536C22×D3—21no—
537C22×D3—28no—
538C22×D3—84no—
539C22×D3C2×#6712yes—
540C3×Q8—34no—
541C3×Q8—32no—
542C3×Q8—32no—
543C3×Q8—61no—
544C3×Q8—61no—
545C3×D4—22no—
546C3×D4—24no—
547C3×D4—22no—
548C3×D4—24no—
549C3×D4—24no—
550C3×D4—38no—
551C3×D4—34no—
552C3×D4—32no—
553C3×D4—32no—
554C3×D4—42no—
555C3×D4—44no—
556C3×D4—68no—
557C3×D4—68no—
558C3×D4—64no—
559C3×D4—64no—
560C3×D4—61no—
561C3×D4—61no—
562C3×D4C23×D314yes—
563C3×D4C23×D314yes—
564C2×C3×C4—22no—
565C2×C3×C4—21no—
566C2×C3×C4—22no—
567C2×C3×C4—21no—
568C2×C3×C4—32no—
569C2×C3×C4—34no—
570C2×C3×C4—34no—
571C2×C3×C4—68no—
572C2×C3×C4—61no—
573C2×C3×C4—61no—
574C2×C3×C4—64no—
575C2×C3×C4—64no—
576C2×C3×C4D3×D411yescharacteristic
577C2×C3×C4D3×D412yes—
578C2×C3×C4C2×#6711yescharacteristic
579C2×C3×C4C2×#6712yes—
580C2×C3×C4C23×D311yescharacteristic
581C2×C3×C4C23×D312yes—
582C2×C3×C4C23×D311yescharacteristic
583C2×C3×C4C23×D312yes—
584#67—24no—
585#67—24no—
586#67—28no—
587#67—28no—
588#67—68no—
589#67—68no—
590#67C2×#6718yes—
591C2×Dic3—21no—
592C2×Dic3—21no—
593C2×Dic3—28no—
594C2×Dic3—68no—
595C2×Dic3—62no—
596C2×Dic3—64no—
597C2×Dic3—62no—
598C2×Dic3—64no—
599C2×Dic3—68no—
600C2×Dic3—124no—
601C2×Dic3—122no—
602C2×Dic3C2×#6712yes—
603D12—21no—
604D12—21no—
605D12C2×#6714yes—
606D12C23×D312yes—
607D12C23×D312yes—
608C4×D3—24no—
609C4×D3—24no—
610C4×D3—68no—
611C4×D3—68no—
612C4×D3C2×#6714yes—
613C4×D3C23×D314yes—
614Dic6—21no—
615Dic6—21no—
616Dic6—34no—
617Dic6—34no—
618Dic6—64no—
619Dic6—68no—
620Dic6—62no—
621Dic6—64no—
622Dic6—64no—
623Dic6—62no—
624Dic6—68no—
625Dic6—122no—
626Dic6—124no—
627Dic6C2×#6714yes—
628Dic6C23×D312yes—
629Dic6C23×D312yes—
630C3×C8—34no—
631C3⋊C8—32no—
632C3⋊C8—32no—
633C3⋊C8—32no—
634C3⋊C8—32no—
635C3⋊C8—62no—
636C3⋊C8—62no—
637C3⋊C8C23×D314yes—
638C2×C32—22no—
639C2×C32—44no—
640C2×C32#57712yescomplemented
641C2×C32C23×D411yescharacteristic
642C3×D3—24no—
643C3×D3—42no—
644C3×D3—42no—
645C24—21no—
646C24—62no—
647#41—34no—
648#41—34no—
649#41—38no—
650#41—34no—
651#41—34no—
652#41—64no—
653#41—68no—
654#41—62no—
655#41—62no—
656#41—98no—
657#41—184no—
658#41—188no—
659#41—1816no—
660C2×Q8—31no—
661C2×Q8—31no—
662C2×Q8—31no—
663C2×Q8—98no—
664C2×Q8—92no—
665C2×Q8—94no—
666C2×Q8—182no—
667C2×Q8—184no—
668C2×Q8—188no—
669C2×Q8—181no—
670C2×Q8—182no—
671C2×D4—21no—
672C2×D4—22no—
673C2×D4—32no—
674C2×D4—38no—
675C2×D4—31no—
676C2×D4—31no—
677C2×D4—31no—
678C2×D4—64no—
679C2×D4—62no—
680C2×D4—68no—
681C2×D4—616no—
682C2×D4—62no—
683C2×D4—61no—
684C2×D4—61no—
685C2×D4—182no—
686C2×D4C2×D3212yes—
687C2×D4C2×D3214yes—
688C22×C4—32no—
689C22×C4—62no—
690C22×C4—61no—
691C22×C4—61no—
692C22×C4—182no—
693C22×C4—182no—
694C22×C4—181no—
695C22×C4C2×D3211yescharacteristic
696Q16—98no—
697Q16—94no—
698SD16—38no—
699SD16—98no—
700SD16—94no—
701SD16—94no—
702SD16—98no—
703SD16—98no—
704D8—38no—
705D8—94no—
706M16—34no—
707M16—98no—
708C2×C8—32no—
709C2×C8—98no—
710C2×C8—91no—
711C2×C8—91no—
712C2×C8—94no—
713C22×C3—24no—
714C22×C3—22no—
715C22×C3—22no—
716C22×C3—24no—
717C22×C3—24no—
718C22×C3—22no—
719C22×C3—21no—
720C22×C3—34no—
721C22×C3—44no—
722C22×C3—44no—
723C22×C3—44no—
724C22×C3—64no—
725C22×C3—62no—
726C22×C3—62no—
727C22×C3—84no—
728C22×C3—84no—
729C22×C3—84no—
730C22×C3—88no—
731C22×C3—122no—
732C22×C3—122no—
733C22×C3—248no—
734C22×C3C2×D3×D412yes—
735C22×C3C2×D3×D411yescharacteristic
736C22×C3C22×#6712yes—
737C22×C3C22×#6711yescharacteristic
738C2×D3—24no—
739C2×D3—22no—
740C2×D3—22no—
741C2×D3—42no—
742C2×D3—42no—
743C2×D3—88no—
744C2×D3C22×#6714yes—
745C3×C4—21no—
746C3×C4—22no—
747C3×C4—21no—
748C3×C4—34no—
749C3×C4—62no—
750C3×C4—62no—
751C3×C4C2×D3×D411yescharacteristic
752C3×C4C2×D3×D412yes—
753C3×C4C22×#6711yescharacteristic
754C3×C4C22×#6712yes—
755C3×C4C24×D311yescharacteristic
756C3×C4C24×D311yescharacteristic
757Dic3—22no—
758Dic3—22no—
759Dic3—64no—
760Dic3—64no—
761Dic3—124no—
762Dic3C22×#6714yes—
763C32C2×#57711yescharacteristic, complemented, Sylow
764C23—22no—
765C23—24no—
766C23—32no—
767C23—68no—
768C23—61no—
769C23—61no—
770C23—82no—
771C23—244no—
772C23D3×#6711yescharacteristic
773Q8—34no—
774Q8—32no—
775Q8—32no—
776Q8—61no—
777Q8—61no—
778Q8—94no—
779Q8—188no—
780Q8—182no—
781Q8—184no—
782D4—22no—
783D4—24no—
784D4—38no—
785D4—34no—
786D4—32no—
787D4—32no—
788D4—68no—
789D4—68no—
790D4—64no—
791D4—64no—
792D4—61no—
793D4—61no—
794D4—188no—
795D4C22×D3214yes—
796C2×C4—32no—
797C2×C4—34no—
798C2×C4—34no—
799C2×C4—68no—
800C2×C4—61no—
801C2×C4—61no—
802C2×C4—64no—
803C2×C4—64no—
804C2×C4—188no—
805C2×C4—188no—
806C2×C4—184no—
807C2×C4—182no—
808C2×C4D3×#6712yes—
809C2×C4D3×#6711yescharacteristic
810C2×C4C22×D3212yes—
811C2×C4C22×D3211yescharacteristic
812C8—34no—
813C8—92no—
814C8—92no—
815C2×C3—24no—
816C2×C3—22no—
817C2×C3—22no—
818C2×C3—22no—
819C2×C3—21no—
820C2×C3—44no—
821C2×C3—44no—
822C2×C3—64no—
823C2×C3—84no—
824C2×C3—122no—
825C2×C3—122no—
826C2×C3#577512yescomplemented
827C2×C3#583612yescomplemented
828C2×C3C22×D3×D411yescharacteristic
829C2×C3C23×#6711yescharacteristic
830D3—24no—
831D3—42no—
832D3—42no—
833C22—22no—
834C22—24no—
835C22—34no—
836C22—44no—
837C22—64no—
838C22—62no—
839C22—62no—
840C22—84no—
841C22—122no—
842C22—122no—
843C22—248no—
844C22C2×D3×#6712yes—
845C22C2×D3×#6711yescharacteristic
846C4—34no—
847C4—62no—
848C4—62no—
849C4—184no—
850C4C2×D3×#6711yescharacteristic
851C4C2×D3×#6712yes—
852C4C23×D3211yescharacteristic
853C3—21no—
854C3C2×#577511yescharacteristic, complemented
855C3C2×#583611yescharacteristic, complemented
856C2—22no—
857C2—44no—
858C2—64no—
859C2—122no—
860C2—122no—
861C2#1059510612yesdirect product factor
862C2C22×D3×#6711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
hypercenterC22×D4D32
hypocenterC32C2×#577
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1004C2semidirect
2. C2×#64298C2semidirect
3. C22×#3754C2semidirect
4. C2×C3×#932C2semidirect
5. C2×#63933C2semidirect
6. C2×#63932C2semidirect
7. #10595106C2direct (N × H)
8. C2×#63929C2semidirect
9. C2×D3×#214C2semidirect
10. C2×#63831C2semidirect
11. C2×#63822C2semidirect
12. C2×#63815C2semidirect
16. C22×#634C22semidirect
19. C3×#1004C22semidirect
26. C2×C3×#235C22semidirect
29. #64298C22semidirect
31. C2×#3795C22semidirect
33. C2×D3×Dic6C22semidirect
34. C2×#3754C22semidirect
35. C2×#3754C22semidirect
36. C2×#3754C22semidirect
37. C22×C3⋊(C3⋊C8)C22semidirect
38. C2×C3×#214C22semidirect
39. C3×#932C22semidirect
40. C2×C3×#213C22semidirect
41. C2×C3×#208C22semidirect
42. #63933C22semidirect
43. #63932C22semidirect
44. #63929C22semidirect
45. D3×#214C22semidirect
46. C2×#3719C22semidirect
47. C2×#3718C22semidirect
48. #63831C22semidirect
49. C2×#3716C22semidirect
50. C2×#3715C22semidirect
51. C2×#3715C22semidirect
52. #63822C22semidirect
53. C2×#3713C22semidirect
54. C2×#3711C22semidirect
55. #63815C22semidirect
56. C2×D3×C3⋊C8C22semidirect
60. C2×#1004D3semidirect
74. C2×#932D3semidirect
93. C2×#634C23semidirect
112. C3×#235C23semidirect
129. #3795C23semidirect
132. D3×Dic6C23semidirect
133. #3754C23semidirect
134. #3754C23semidirect
137. C2×C3⋊(C3⋊C8)C23semidirect
138. C3×#214C23semidirect
139. C3×#213C23semidirect
140. C3×#208C23semidirect
142. #3719C23semidirect
143. #3718C23semidirect
144. #3716C23semidirect
145. #3715C23semidirect
146. #3715C23semidirect
147. #3713C23semidirect
148. #3711C23semidirect
149. D3×C3⋊C8C23semidirect
172. #1004C2×D3semidirect
185. C2×#235C2×D3semidirect
219. C2×#214C2×D3semidirect
221. #932C2×D3semidirect
224. C2×#213C2×D3semidirect
226. C2×#208C2×D3semidirect
388. #235C22×D3semidirect
435. #214C22×D3semidirect
438. #213C22×D3semidirect
440. #208C22×D3semidirect
640. C2×C32#577semidirect
763. C32C2×#577semidirect
826. C2×C3#5775semidirect
827. C2×C3#5836semidirect
854. C3C2×#5775semidirect
855. C3C2×#5836semidirect
861. C2#10595106direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#10042
C2×#642982
C22×#37542
C2×C3×#9322
C2×#639332
C2×#639322
#105951062
C2×#639292
C2×D3×#2142
C2×#638312
C2×#638222
C2×#638152
C2×#58363
C2×#57753