Finite Group Databasebeta

← C2×#10595464 #11918889

Subgroups — C2×#10595464 #11918889

Order 1152.

3053 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1009C211yesmaximal, characteristic, complemented
2C2×#64297C211yesmaximal, characteristic, complemented
3C2×#64159C211yesmaximal, characteristic, complemented
4C2×C3×#951C211yesmaximal, characteristic, complemented
5#10595464C2116yesmaximal, direct product factor
6C2×#63949C212yesmaximal, complemented
7C2×#63943C212yesmaximal, complemented
8C2×#63934C212yesmaximal, complemented
9C2×D3×#214C212yesmaximal, complemented
10C2×#63830C211yesmaximal, characteristic, complemented
11C22×#3715C211yesmaximal, characteristic, complemented
12C2×#63815C211yesmaximal, characteristic, complemented
13C2×#5836—31nomaximal
14C2×#5778—31nomaximal
15C2×C32×#41C2211yescharacteristic
16C2×#3828C2211yescharacteristic, complemented
17C3×#1009—24no—
18C3×#1009C2218yescomplemented
19C2×C3×#239C2212yes—
20C2×C3×D3×D4—22no—
21C2×C3×D3×D4C2212yes—
22C2×C3×#235—21no—
23C2×C3×#235C2211yescharacteristic
24C22×C3×D12—21no—
25C22×C3×D12C2211yescharacteristic
26C22×C3×Dic6C2211yescharacteristic, complemented
27C2×#3804—22no—
28C2×#3799C2212yescomplemented
29C2×#3797—21no—
30#64297—24no—
31#64297C2218yescomplemented
32C2×#3796—21no—
33C2×D3×Dic6C2212yescomplemented
34#64159C2218yescomplemented
35C2×#3756C2211yescharacteristic, complemented
36C2×#3755C2211yescharacteristic, complemented
37C2×#3754C2211yescharacteristic, complemented
38C2×#3753C2211yescharacteristic, complemented
39C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
40C3×#951C2218yescomplemented
41C2×C3×#216C2212yescomplemented
42C2×C3×#214C2212yescomplemented
43C2×C3×#208C2211yescharacteristic, complemented
44#63949C22116yescomplemented
45#63943C22116yescomplemented
46#63934C22116yescomplemented
47D3×#214C22116yescomplemented
48#63830C2218yescomplemented
49C2×#3716C2212yescomplemented
50C2×#3715C2212yescomplemented
51C2×#3715C2212yescomplemented
52C2×#3715C2218yescomplemented
53C2×#3714C2212yescomplemented
54C2×#3711C2212yescomplemented
55#63815C2218yescomplemented
56C2×D3×C3⋊C8C2212yescomplemented
57C2×C3×H(5,𝔽2)—31no—
58C2×#1010—31no—
59C2×#1009D311yescharacteristic, complemented
60C2×#1007—31no—
61C2×C3×#137—31no—
62#5836—316no—
63C2×#951—32no—
64C2×#951D311yescharacteristic, complemented
65C2×#950—31no—
66C2×#950—31no—
67C2×#950—32no—
68C2×#950—61no—
69C2×#948—31no—
70C22×#215—31no—
71C22×#214—31no—
72C22×#214—32no—
73C2×#932—32no—
74C2×#932—31no—
75#5778—316no—
76C2×#919—32no—
77C2×#918—32no—
78C2×#914—32no—
79C2×D3×SD16—32no—
80C2×#908—31no—
81C2×#907—31no—
82C23×C3×D3—21no—
83C23×C3×D3—22no—
84C32×#41—22no—
85C32×#41C2314yes—
86C2×C32×Q8C2311yescharacteristic
87C2×C32×D4—21no—
88C2×C32×D4C2311yescharacteristic
89C22×C32×C4—21no—
90C22×C32×C4C2311yescharacteristic
91C2×#638—21no—
92#3828—22no—
93#3828C2314yescomplemented
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4×C3⋊D3—21no—
96C2×#634C2311yescharacteristic
97C2×C3×#67—22no—
98C2×C3×#67D412yes—
99C22×C3×Dic3—21no—
100C3×#239—24no—
101C3×#239C2318yes—
102C3×D3×D4—216no—
103C3×D3×D4—24no—
104C3×D3×D4C2318yes—
105C3×#235—28no—
106C3×#235D414yes—
107C3×#235C2314yes—
108C2×C3×D12—22no—
109C2×C3×D12—21no—
110C2×C3×D12—22no—
111C2×C3×D12—28no—
112C2×C3×D12D411yescharacteristic
113C2×C3×D12C2312yes—
114C2×C3×D12C2314yes—
115C2×C3×C4×D3—22no—
116C2×C3×C4×D3C2312yes—
117C2×C3×Dic6—21no—
118C2×C3×Dic6—22no—
119C2×C3×Dic6D411yescharacteristic
120C2×C3×Dic6C2312yes—
121C2×C3×Dic6C2314yescomplemented
122C2×#627—22no—
123C2×#626—22no—
124C2×#624—22no—
125#3804—216no—
126C2×D3×Dic3—22no—
127#3799—24no—
128#3799C2318yescomplemented
129#3797—28no—
130#3796—28no—
131D3×Dic6—24no—
132D3×Dic6C2318yescomplemented
133#3756C2314yescomplemented
134#3755C2314yescomplemented
135#3754C2314yescomplemented
136#3753C2314yescomplemented
137C2×C3⋊(C3⋊C8)C2311yescharacteristic
138C2×C3⋊(C3⋊C8)C2311yescharacteristic
139C2×C3⋊(C3⋊C8)C2314yescomplemented
140C3×#216C2318yescomplemented
141C3×#214C2318yescomplemented
142C3×#208C2314yescomplemented
143C2×C3×C3⋊C8C2312yes—
144#3716C2318yescomplemented
145#3715C2318yescomplemented
146#3715C2318yescomplemented
147#3714C2318yescomplemented
148#3711C2318yescomplemented
149D3×C3⋊C8C2318yescomplemented
150C2×#577—91noSylow
151C3×H(5,𝔽2)—38no—
152C3×H(5,𝔽2)—64no—
153C2×C3×#41—21no—
154C2×C3×#41—31no—
155C2×C3×#41—32no—
156C2×C3×#41—61no—
157C2×C3×#41C2×D311yescharacteristic
158C2×C3×#41C2×D311yescharacteristic
159C22×C3×Q8—31no—
160C22×C3×D4—32no—
161C22×C3×D4—31no—
162C22×C3×D4—61no—
163C22×C3×D4—62no—
164#1010—38no—
165#1010—64no—
166#1009—24no—
167#1009C2×D318yescomplemented
168#1007—38no—
169#1007—64no—
170C2×#239—32no—
171C2×#239—61no—
172C2×#239C2×D312yes—
173C2×D3×Q8—32no—
174C2×D3×Q8—61no—
175C2×D3×Q8—61no—
176C2×#237—61no—
177C2×#237—62no—
178C2×D3×D4—22no—
179C2×D3×D4C2×D312yes—
180C2×#235—21no—
181C2×#235—31no—
182C2×#235—31no—
183C2×#235—32no—
184C2×#235—61no—
185C2×#235—62no—
186C2×#235C2×D311yescharacteristic
187C22×D12—21no—
188C22×D12C2×D311yescharacteristic
189C22×Dic6—32no—
190C22×Dic6C2×D311yescharacteristic, complemented
191C3×#137—38no—
192C2×C3×Q16—32no—
193C2×C3×SD16—32no—
194C2×C3×M16—31no—
195#951—316no—
196#951C2×D318yescomplemented
197#950—38no—
198#950—38no—
199#950—316no—
200#950—68no—
201#948—38no—
202C2×#216—31no—
203C2×#216—31no—
204C2×#216—61no—
205C2×#216C2×D312yescomplemented
206C2×#215—31no—
207C2×#215—31no—
208C2×#215—32no—
209C2×#215—32no—
210C2×#215—38no—
211C2×#215—61no—
212C2×#214—31no—
213C2×#214—31no—
214C2×#214—32no—
215C2×#214—32no—
216C2×#214—38no—
217C2×#214—316no—
218C2×#214—32no—
219C2×#214—61no—
220C2×#214C2×D312yescomplemented
221#932—316no—
222#932—38no—
223C2×#213—31no—
224C2×#213—31no—
225C2×#213—32no—
226C2×#213—61no—
227C2×#208—32no—
228C2×#208C2×D311yescharacteristic, complemented
229C22×C3⋊C8—31no—
230C22×C3⋊C8—31no—
231C22×C3⋊C8—32no—
232C22×C3⋊C8—61no—
233#919—316no—
234#918—316no—
235#914—316no—
236D3×SD16—316no—
237#908—38no—
238#907—38no—
239C2×D24—32no—
240C2×#204—32no—
241C2×ΓL(1,𝔽25)—32no—
242C2×D3×C8—32no—
243C23×C32—21no—
244C23×C32C2×D411yescharacteristic
245C22×C3⋊D3—21no—
246C22×C3×D3—22no—
247C22×C3×D3—24no—
248C22×C3×D3—28no—
249C22×C3×D3—84no—
250C22×C3×D3—82no—
251C22×C3×D3C2×D412yes—
252C32×Q8—21no—
253C32×Q8C2412yes—
254C32×D4—24no—
255C32×D4—21no—
256C32×D4C2412yes—
257C2×C32×C4—21no—
258C2×C32×C4—24no—
259C2×C32×C4C2×D411yescharacteristic
260C2×C32×C4C2×D412yes—
261C2×C32×C4C2411yescharacteristic
262C2×C32×C4C2412yes—
263#638—24no—
264C2×C3⋊Dic3—21no—
265C4⋊(C3⋊D3)—21no—
266C4⋊(C3⋊D3)C2412yes—
267C4×C3⋊D3—24no—
268#634—21no—
269#634C2412yes—
270C3×#67—28no—
271C3×#67C2×D418yes—
272C2×C3×Dic3—22no—
273C2×C3×Dic3—24no—
274C2×C3×Dic3C2×D412yes—
275C3×D12—28no—
276C3×D12—24no—
277C3×D12—22no—
278C3×D12C2×D414yes—
279C3×D12C2414yes—
280C3×C4×D3—28no—
281C3×C4×D3C2×D414yes—
282C3×C4×D3C2414yes—
283C3×Dic6—22no—
284C3×Dic6—24no—
285C3×Dic6C2×D414yes—
286C3×Dic6C2414yes—
287#627—28no—
288#626—28no—
289#624—28no—
290D3×Dic3—28no—
291C3⋊(C3⋊C8)C2412yes—
292C3⋊(C3⋊C8)C2412yes—
293C3×C3⋊C8C2414yes—
294C2×2−1+4—91no—
295C2×H(5,𝔽2)—31no—
296#577—916no—
297C2×#137—31no—
298C2×#137—92no—
299C2×AGL(1,ℤ/8)—91no—
300C2×AGL(1,ℤ/8)—92no—
301C2×#135—92no—
302C2×#135—91no—
303C22×SD16—92no—
304C22×SD16—91no—
305C2×#131—91no—
306C24×C3—62no—
307C24×C3—61no—
308C23×D3—21no—
309C23×D3—22no—
310C3×#41—22no—
311C3×#41—22no—
312C3×#41—24no—
313C3×#41—34no—
314C3×#41—34no—
315C3×#41—38no—
316C3×#41—42no—
317C3×#41—68no—
318C3×#41—64no—
319C3×#41C22×D314yes—
320C3×#41C22×D314yes—
321C2×C3×Q8—21no—
322C2×C3×Q8—31no—
323C2×C3×Q8—32no—
324C2×C3×Q8—34no—
325C2×C3×Q8—61no—
326C2×C3×Q8—62no—
327C2×C3×Q8C22×D311yescharacteristic
328C2×C3×Q8C22×D311yescharacteristic
329C2×C3×D4—21no—
330C2×C3×D4—21no—
331C2×C3×D4—21no—
332C2×C3×D4—32no—
333C2×C3×D4—38no—
334C2×C3×D4—31no—
335C2×C3×D4—32no—
336C2×C3×D4—34no—
337C2×C3×D4—41no—
338C2×C3×D4—68no—
339C2×C3×D4—62no—
340C2×C3×D4—64no—
341C2×C3×D4—62no—
342C2×C3×D4—616no—
343C2×C3×D4—61no—
344C2×C3×D4—62no—
345C2×C3×D4C22×D311yescharacteristic
346C2×C3×D4C22×D311yescharacteristic
347C22×C3×C4—21no—
348C22×C3×C4—21no—
349C22×C3×C4—21no—
350C22×C3×C4—32no—
351C22×C3×C4—41no—
352C22×C3×C4—62no—
353C22×C3×C4—61no—
354C22×C3×C4C22×D311yescharacteristic
355C22×C3×C4C22×D311yescharacteristic
356C2×#67—22no—
357C2×#67—62no—
358C2×#67—61no—
359C2×#67—61no—
360C2×#67—121no—
361C2×#67#6712yes—
362C22×Dic3—21no—
363C22×Dic3—62no—
364#239—24no—
365#239—38no—
366#239—68no—
367#239—64no—
368#239C22×D318yes—
369D3×Q8—38no—
370D3×Q8—68no—
371D3×Q8—64no—
372D3×Q8—68no—
373#237—68no—
374#237—616no—
375D3×D4—216no—
376D3×D4—24no—
377D3×D4C22×D318yes—
378#235—28no—
379#235—34no—
380#235—34no—
381#235—38no—
382#235—64no—
383#235—64no—
384#235—62no—
385#235—62no—
386#235—616no—
387#235—122no—
388#235#6714yes—
389#235C22×D314yes—
390C2×D12—22no—
391C2×D12—21no—
392C2×D12—22no—
393C2×D12—28no—
394C2×D12—31no—
395C2×D12—31no—
396C2×D12—61no—
397C2×D12—62no—
398C2×D12#6711yescharacteristic
399C2×D12C22×D312yes—
400C2×D12C22×D314yes—
401C2×C4×D3—22no—
402C2×C4×D3—62no—
403C2×C4×D3—62no—
404C2×C4×D3—61no—
405C2×C4×D3—61no—
406C2×C4×D3—62no—
407C2×C4×D3—121no—
408C2×C4×D3C22×D312yes—
409C2×Dic6—21no—
410C2×Dic6—22no—
411C2×Dic6—31no—
412C2×Dic6—31no—
413C2×Dic6—38no—
414C2×Dic6—61no—
415C2×Dic6—64no—
416C2×Dic6—62no—
417C2×Dic6—62no—
418C2×Dic6#6711yescharacteristic
419C2×Dic6C22×D312yes—
420C2×Dic6C22×D314yescomplemented
421C3×Q16—38no—
422C3×SD16—38no—
423C3×M16—34no—
424C2×C3×C8—32no—
425#216—34no—
426#216—34no—
427#216—64no—
428#216C22×D318yescomplemented
429#215—34no—
430#215—34no—
431#215—38no—
432#215—38no—
433#215—64no—
434#214—34no—
435#214—34no—
436#214—38no—
437#214—38no—
438#214—38no—
439#214—64no—
440#214C22×D318yescomplemented
441#213—34no—
442#213—34no—
443#213—38no—
444#213—64no—
445#208—38no—
446#208C22×D314yescomplemented
447C2×C3⋊C8—31no—
448C2×C3⋊C8—31no—
449C2×C3⋊C8—34no—
450C2×C3⋊C8—31no—
451C2×C3⋊C8—31no—
452C2×C3⋊C8—34no—
453C2×C3⋊C8—38no—
454C2×C3⋊C8—61no—
455C2×C3⋊C8—61no—
456C2×C3⋊C8—64no—
457C2×C3⋊C8C22×D312yes—
458D24—38no—
459#204—38no—
460ΓL(1,𝔽25)—38no—
461D3×C8—38no—
462C22×C32—22no—
463C22×C32—22no—
464C22×C32—42no—
465C22×C32C22×D412yes—
466C22×C32C22×D411yescharacteristic
467C2×C3⋊D3—22no—
468C2×C3⋊D3—42no—
469C2×C3×D3—24no—
470C2×C3×D3—24no—
471C2×C3×D3—44no—
472C2×C3×D3—88no—
473C2×C3×D3—84no—
474C2×C3×D3C22×D414yes—
475C32×C4—22no—
476C32×C4C22×D412yes—
477C32×C4C22×D411yescharacteristic
478C32×C4C2511yescharacteristic
479C3⋊Dic3—22no—
480C3×Dic3—24no—
481C3×Dic3C22×D414yes—
4822−1+4—98no—
4832−1+4—184no—
484H(5,𝔽2)—38no—
485H(5,𝔽2)—64no—
486C2×#41—31no—
487C2×#41—32no—
488C2×#41—61no—
489C2×#41—92no—
490C2×#41—91no—
491C2×#41—182no—
492C2×#41—181no—
493C2×#41D3211yescharacteristic
494C22×Q8—31no—
495C22×Q8—92no—
496C22×Q8—181no—
497C22×D4—32no—
498C22×D4—31no—
499C22×D4—61no—
500C22×D4—62no—
501#137—38no—
502#137—916no—
503AGL(1,ℤ/8)—98no—
504AGL(1,ℤ/8)—916no—
505#135—916no—
506#135—98no—
507C2×Q16—32no—
508C2×Q16—91no—
509C2×SD16—32no—
510C2×SD16—92no—
511C2×SD16—916no—
512C2×SD16—92no—
513C2×SD16—92no—
514C2×SD16—98no—
515C2×SD16—91no—
516C2×SD16—91no—
517C2×D8—92no—
518C2×D8—91no—
519#131—98no—
520C2×M16—31no—
521C2×M16—92no—
522C22×C8—92no—
523C22×C8—91no—
524C23×C3—21no—
525C23×C3—21no—
526C23×C3—21no—
527C23×C3—32no—
528C23×C3—41no—
529C23×C3—68no—
530C23×C3—62no—
531C23×C3—64no—
532C23×C3—242no—
533C23×C3—244no—
534C23×C3D3×D411yescharacteristic
535C23×C3C2×#6711yescharacteristic
536C22×D3—22no—
537C22×D3—24no—
538C22×D3—28no—
539C22×D3—61no—
540C22×D3—61no—
541C22×D3—84no—
542C22×D3—82no—
543C22×D3—121no—
544C22×D3C2×#6712yes—
545C3×Q8—21no—
546C3×Q8—21no—
547C3×Q8—22no—
548C3×Q8—34no—
549C3×Q8—34no—
550C3×Q8—41no—
551C3×Q8—62no—
552C3×Q8—64no—
553C3×Q8C23×D312yes—
554C3×Q8C23×D312yes—
555C3×D4—24no—
556C3×D4—24no—
557C3×D4—21no—
558C3×D4—21no—
559C3×D4—22no—
560C3×D4—38no—
561C3×D4—34no—
562C3×D4—34no—
563C3×D4—41no—
564C3×D4—44no—
565C3×D4—68no—
566C3×D4—68no—
567C3×D4—62no—
568C3×D4—64no—
569C3×D4C23×D312yes—
570C3×D4C23×D312yes—
571C2×C3×C4—21no—
572C2×C3×C4—21no—
573C2×C3×C4—24no—
574C2×C3×C4—24no—
575C2×C3×C4—21no—
576C2×C3×C4—22no—
577C2×C3×C4—21no—
578C2×C3×C4—22no—
579C2×C3×C4—32no—
580C2×C3×C4—34no—
581C2×C3×C4—34no—
582C2×C3×C4—44no—
583C2×C3×C4—41no—
584C2×C3×C4—68no—
585C2×C3×C4—62no—
586C2×C3×C4—64no—
587C2×C3×C4D3×D411yescharacteristic
588C2×C3×C4D3×D412yes—
589C2×C3×C4C2×#6711yescharacteristic
590C2×C3×C4C2×#6712yes—
591C2×C3×C4C23×D311yescharacteristic
592C2×C3×C4C23×D312yes—
593C2×C3×C4C23×D311yescharacteristic
594C2×C3×C4C23×D312yes—
595#67—28no—
596#67—68no—
597#67—64no—
598#67—64no—
599#67—124no—
600#67C2×#6718yes—
601C2×Dic3—22no—
602C2×Dic3—24no—
603C2×Dic3—68no—
604C2×Dic3—61no—
605C2×Dic3—61no—
606C2×Dic3—121no—
607C2×Dic3C2×#6712yes—
608D12—28no—
609D12—24no—
610D12—22no—
611D12—32no—
612D12—32no—
613D12—62no—
614D12—68no—
615D12—61no—
616D12—61no—
617D12—121no—
618D12C2×#6714yes—
619D12C23×D314yes—
620C4×D3—28no—
621C4×D3—68no—
622C4×D3—68no—
623C4×D3—64no—
624C4×D3—64no—
625C4×D3—68no—
626C4×D3—124no—
627C4×D3C2×#6714yes—
628C4×D3C23×D314yes—
629Dic6—22no—
630Dic6—24no—
631Dic6—32no—
632Dic6—32no—
633Dic6—62no—
634Dic6—68no—
635Dic6—61no—
636Dic6—61no—
637Dic6—68no—
638Dic6—121no—
639Dic6C2×#6714yes—
640Dic6C23×D314yes—
641C3×C8—34no—
642C3⋊C8—32no—
643C3⋊C8—32no—
644C3⋊C8—32no—
645C3⋊C8—32no—
646C3⋊C8—62no—
647C3⋊C8—62no—
648C3⋊C8C23×D314yes—
649C2×C32—22no—
650C2×C32—42no—
651C2×C32#57712yescomplemented
652C2×C32C23×D411yescharacteristic
653C3⋊D3—42no—
654C3×D3—24no—
655C3×D3—44no—
656C24—62no—
657C24—61no—
658#41—22no—
659#41—34no—
660#41—34no—
661#41—38no—
662#41—68no—
663#41—64no—
664#41—98no—
665#41—94no—
666#41—184no—
667#41—1816no—
668#41—188no—
669#41—182no—
670#41C2×D3214yes—
671C2×Q8—31no—
672C2×Q8—32no—
673C2×Q8—34no—
674C2×Q8—61no—
675C2×Q8—62no—
676C2×Q8—98no—
677C2×Q8—91no—
678C2×Q8—182no—
679C2×Q8—184no—
680C2×Q8—188no—
681C2×Q8C2×D3211yescharacteristic
682C2×D4—21no—
683C2×D4—32no—
684C2×D4—38no—
685C2×D4—32no—
686C2×D4—34no—
687C2×D4—31no—
688C2×D4—68no—
689C2×D4—62no—
690C2×D4—64no—
691C2×D4—62no—
692C2×D4—616no—
693C2×D4—61no—
694C2×D4—62no—
695C2×D4—91no—
696C2×D4—182no—
697C2×D4—181no—
698C2×D4C2×D3211yescharacteristic
699C22×C4—21no—
700C22×C4—32no—
701C22×C4—62no—
702C22×C4—61no—
703C22×C4—182no—
704C22×C4—182no—
705C22×C4—181no—
706C22×C4C2×D3211yescharacteristic
707Q16—38no—
708Q16—94no—
709SD16—38no—
710SD16—98no—
711SD16—98no—
712SD16—98no—
713SD16—94no—
714SD16—94no—
715D8—98no—
716D8—94no—
717M16—34no—
718M16—98no—
719C2×C8—32no—
720C2×C8—98no—
721C2×C8—91no—
722C2×C8—91no—
723C2×C8—94no—
724C22×C3—22no—
725C22×C3—22no—
726C22×C3—22no—
727C22×C3—22no—
728C22×C3—22no—
729C22×C3—21no—
730C22×C3—34no—
731C22×C3—42no—
732C22×C3—42no—
733C22×C3—42no—
734C22×C3—42no—
735C22×C3—64no—
736C22×C3—64no—
737C22×C3—82no—
738C22×C3—124no—
739C22×C3—244no—
740C22×C3—248no—
741C22×C3C2×D3×D412yes—
742C22×C3C2×D3×D411yescharacteristic
743C22×C3C22×#6712yes—
744C22×C3C22×#6711yescharacteristic
745C2×D3—24no—
746C2×D3—24no—
747C2×D3—44no—
748C2×D3—62no—
749C2×D3—62no—
750C2×D3—88no—
751C2×D3—84no—
752C2×D3—122no—
753C2×D3—122no—
754C2×D3—122no—
755C2×D3—242no—
756C2×D3C22×#6714yes—
757C3×C4—22no—
758C3×C4—22no—
759C3×C4—21no—
760C3×C4—22no—
761C3×C4—21no—
762C3×C4—34no—
763C3×C4—42no—
764C3×C4—64no—
765C3×C4C2×D3×D411yescharacteristic
766C3×C4C2×D3×D412yes—
767C3×C4C22×#6711yescharacteristic
768C3×C4C22×#6712yes—
769C3×C4C24×D311yescharacteristic
770C3×C4C24×D311yescharacteristic
771Dic3—24no—
772Dic3—62no—
773Dic3—62no—
774Dic3—122no—
775Dic3C22×#6714yes—
776C32C2×#57711yescharacteristic, complemented, Sylow
777C23—21no—
778C23—32no—
779C23—68no—
780C23—62no—
781C23—64no—
782C23—181no—
783C23—242no—
784C23—244no—
785C23D3×#6711yescharacteristic
786Q8—21no—
787Q8—34no—
788Q8—34no—
789Q8—64no—
790Q8—62no—
791Q8—92no—
792Q8—188no—
793Q8—181no—
794Q8C22×D3212yes—
795D4—24no—
796D4—21no—
797D4—38no—
798D4—34no—
799D4—34no—
800D4—68no—
801D4—68no—
802D4—64no—
803D4—62no—
804D4—92no—
805D4—188no—
806D4—184no—
807D4—181no—
808D4C22×D3212yes—
809C2×C4—21no—
810C2×C4—24no—
811C2×C4—32no—
812C2×C4—34no—
813C2×C4—34no—
814C2×C4—68no—
815C2×C4—64no—
816C2×C4—62no—
817C2×C4—188no—
818C2×C4—188no—
819C2×C4—181no—
820C2×C4—184no—
821C2×C4D3×#6712yes—
822C2×C4D3×#6711yescharacteristic
823C2×C4C22×D3212yes—
824C2×C4C22×D3211yescharacteristic
825C8—34no—
826C8—92no—
827C8—92no—
828C2×C3—22no—
829C2×C3—22no—
830C2×C3—21no—
831C2×C3—22no—
832C2×C3—42no—
833C2×C3—42no—
834C2×C3—42no—
835C2×C3—64no—
836C2×C3—82no—
837C2×C3—124no—
838C2×C3#577812yescomplemented
839C2×C3#583612yescomplemented
840C2×C3C22×D3×D411yescharacteristic
841C2×C3C23×#6711yescharacteristic
842D3—24no—
843D3—44no—
844D3—122no—
845D3—122no—
846D3—242no—
847C22—22no—
848C22—22no—
849C22—34no—
850C22—42no—
851C22—64no—
852C22—64no—
853C22—124no—
854C22—182no—
855C22—244no—
856C22—248no—
857C22—362no—
858C22C2×D3×#6712yes—
859C22C2×D3×#6711yescharacteristic
860C4—22no—
861C4—34no—
862C4—64no—
863C4—182no—
864C4C2×D3×#6712yes—
865C4C2×D3×#6711yescharacteristic
866C4C23×D3211yescharacteristic
867C3—21no—
868C3C2×#577811yescharacteristic, complemented
869C3C2×#583611yescharacteristic, complemented
870C2—22no—
871C2—42no—
872C2—64no—
873C2—124no—
874C2—362no—
875C2#1059546412yesdirect product factor
876C2C22×D3×#6711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32C2×#577
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1009C2semidirect
2. C2×#64297C2semidirect
3. C2×#64159C2semidirect
4. C2×C3×#951C2semidirect
5. #10595464C2direct (N × H)
6. C2×#63949C2semidirect
7. C2×#63943C2semidirect
8. C2×#63934C2semidirect
9. C2×D3×#214C2semidirect
10. C2×#63830C2semidirect
11. C22×#3715C2semidirect
12. C2×#63815C2semidirect
16. C2×#3828C22semidirect
18. C3×#1009C22semidirect
26. C22×C3×Dic6C22semidirect
28. C2×#3799C22semidirect
31. #64297C22semidirect
33. C2×D3×Dic6C22semidirect
34. #64159C22semidirect
35. C2×#3756C22semidirect
36. C2×#3755C22semidirect
37. C2×#3754C22semidirect
38. C2×#3753C22semidirect
39. C22×C3⋊(C3⋊C8)C22semidirect
40. C3×#951C22semidirect
41. C2×C3×#216C22semidirect
42. C2×C3×#214C22semidirect
43. C2×C3×#208C22semidirect
44. #63949C22semidirect
45. #63943C22semidirect
46. #63934C22semidirect
47. D3×#214C22semidirect
48. #63830C22semidirect
49. C2×#3716C22semidirect
50. C2×#3715C22semidirect
51. C2×#3715C22semidirect
52. C2×#3715C22semidirect
53. C2×#3714C22semidirect
54. C2×#3711C22semidirect
55. #63815C22semidirect
56. C2×D3×C3⋊C8C22semidirect
59. C2×#1009D3semidirect
64. C2×#951D3semidirect
93. #3828C23semidirect
121. C2×C3×Dic6C23semidirect
128. #3799C23semidirect
132. D3×Dic6C23semidirect
133. #3756C23semidirect
134. #3755C23semidirect
135. #3754C23semidirect
136. #3753C23semidirect
139. C2×C3⋊(C3⋊C8)C23semidirect
140. C3×#216C23semidirect
141. C3×#214C23semidirect
142. C3×#208C23semidirect
144. #3716C23semidirect
145. #3715C23semidirect
146. #3715C23semidirect
147. #3714C23semidirect
148. #3711C23semidirect
149. D3×C3⋊C8C23semidirect
167. #1009C2×D3semidirect
190. C22×Dic6C2×D3semidirect
196. #951C2×D3semidirect
205. C2×#216C2×D3semidirect
220. C2×#214C2×D3semidirect
228. C2×#208C2×D3semidirect
420. C2×Dic6C22×D3semidirect
428. #216C22×D3semidirect
440. #214C22×D3semidirect
446. #208C22×D3semidirect
651. C2×C32#577semidirect
776. C32C2×#577semidirect
838. C2×C3#5778semidirect
839. C2×C3#5836semidirect
868. C3C2×#5778semidirect
869. C3C2×#5836semidirect
875. C2#10595464direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#10092
C2×#642972
C2×#641592
C2×C3×#9512
#105954642
C2×#639492
C2×#639432
C2×#639342
C2×D3×#2142
C2×#638302
C22×#37152
C2×#638152
C2×#58363
C2×#57783