Finite Group Databasebeta

← #11858196

Subgroups — #11858196

Order 1152.

1561 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5964C211yesmaximal, characteristic
2#10594958C211yesmaximal, characteristic, complemented
3#10594776C211yesmaximal, characteristic, complemented
4C2×#63664C211yesmaximal, characteristic, complemented
5C3×#5236C211yesmaximal, characteristic, complemented
6#10591670C214yesmaximal, complemented
7D3×#837C214yesmaximal, complemented
8#10591111C211yesmaximal, characteristic, complemented
9C2×#63568C211yesmaximal, characteristic, complemented
10#84120—31nomaximal
11#78992—31nomaximal
12C2×C32×#41C2211yescharacteristic
13C3×#1010—21no—
14C3×#1010C412yescomplemented
15C3×#1009—21no—
16C3×#1009C412yescomplemented
17C3×D3×#41—22no—
18C3×D3×#41C2214yes—
19C3×#1007C412yescomplemented
20C3×#1004—22no—
21C3×#1004C412yescomplemented
22C2×C3×#235—22no—
23C2×C3×#235C2211yescharacteristic
24C2×C3×#235C2211yescharacteristic
25C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
26C2×#3748C2211yescharacteristic, complemented
27C3×#926C2211yescharacteristic, complemented
28C2×C3×#208C2211yescharacteristic, complemented
29#67⋊Dic3—22no—
30#63898—21no—
31C4×D3×Dic3C2212yescomplemented
32#63855C2212yescomplemented
33#63843—21no—
34#63815—22no—
35#63814—22no—
36D3×#208C2214yescomplemented
37#63664C2212yescomplemented
38#63664C2212yescomplemented
39C3×#837C2214yescomplemented
40#63569C2214yescomplemented
41#63568C2212yescomplemented
42#63568C2212yescomplemented
43C3×#585—31no—
44#5964D311yescharacteristic
45Dic3×#41—31no—
46#5819—31no—
47#5745—31no—
48#5522—31no—
49C3×#421—31no—
50#5236—31no—
51#5236—34no—
52#5236D311yescharacteristic, complemented
53C2×#837—31no—
54C2×#837—31no—
55C2×#837—31no—
56C2×#837—34no—
57C2×#837—61no—
58C2×#825—31no—
59#5005—31no—
60#4821—34no—
61D3×#104—34no—
62C32×#41—21no—
63C32×#41—21no—
64C32×#41C2×C412yescomplemented
65C32×#41C2312yes—
66C2×C32×Q8C2×C411yescharacteristic, complemented
67C2×C32×D4—21no—
68C2×C32×D4C2×C411yescharacteristic, complemented
69C22×C32×C4—21no—
70C22×C32×C4C2311yescharacteristic
71C22×C3⋊Dic3—21no—
72C2×C3×#67—21no—
73C2×C3×#67—24no—
74C2×C3×#67D412yes—
75C3×#239—22no—
76C3×#239C2×C414yescomplemented
77C3×D3×Q8—22no—
78C3×D3×Q8C2×C414yescomplemented
79C3×#237—24no—
80C3×#237—24no—
81C3×#237—22no—
82C3×#237C2×C414yescomplemented
83C3×D3×D4—24no—
84C3×D3×D4—24no—
85C3×D3×D4—22no—
86C3×D3×D4C2×C414yescomplemented
87C3×#235—21no—
88C3×#235—21no—
89C3×#235—24no—
90C3×#235—22no—
91C3×#235—24no—
92C3×#235—22no—
93C3×#235C2×C412yes—
94C3×#235C2×C412yes—
95C3×#235C2×C412yescomplemented
96C3×#235D412yes—
97C3×#235D412yes—
98C3×#235C2312yes—
99C2×C3×D12—22no—
100C2×C3×D12C2×C411yescharacteristic, complemented
101C2×C3×D12D411yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3—24no—
104C2×C3×C4×D3C2312yes—
105C2×C3×Dic6—22no—
106C2×C3×Dic6C2×C411yescharacteristic, complemented
107C2×C3×Dic6D411yescharacteristic
108C2×D3×Dic3—22no—
109C4×C3⋊Dic3—21no—
110C4×C3⋊Dic3C2311yescharacteristic
111C4×C3⋊Dic3C2311yescharacteristic
112#3748—21no—
113#3748C2312yes—
114C2×C3⋊(C3⋊C8)—21no—
115C3×#217—21no—
116C3×C4⋊Dic3—21no—
117C3×C4×Dic3C2312yes—
118C3×#208—21no—
119C3×#208C2312yes—
120C2×C3×C3⋊C8—21no—
121Dic3⋊Dic3—22no—
122(C2×D3)⋊Dic3—22no—
123Dic32—22no—
124#3711—24no—
125D3×C3⋊C8—24no—
126#2901—91noSylow
127C3×2−1+4—32no—
128C3×2−1+4—32no—
129C3×2−1+4—61no—
130C3×H(5,𝔽2)—32no—
131C3×H(5,𝔽2)—32no—
132C3×H(5,𝔽2)—62no—
133C3×H(5,𝔽2)—61no—
134C2×C3×#41—21no—
135C2×C3×#41—31no—
136C2×C3×#41—34no—
137C2×C3×#41—31no—
138C2×C3×#41—62no—
139C2×C3×#41—62no—
140C2×C3×#41C2×D311yescharacteristic
141C2×C3×#41C2×D311yescharacteristic
142#1010—21no—
143#1010Dic312yescomplemented
144#1009—21no—
145#1009Dic312yescomplemented
146D3×#41—22no—
147D3×#41C2×D314yes—
148#1007Dic312yescomplemented
149#1004—22no—
150#1004Dic312yescomplemented
151C2×#235—22no—
152C2×#235C2×D311yescharacteristic
153C2×#235C2×D311yescharacteristic
154C2×C3×M16—31no—
155C3×#117—31no—
156#948—62no—
157#948—62no—
158Q8×Dic3—61no—
159D4×Dic3—61no—
160D4×Dic3—62no—
161#926—32no—
162#926C2×D311yescharacteristic, complemented
163C2×C4×Dic3—31no—
164C2×C4×Dic3—31no—
165C2×C4×Dic3—32no—
166C2×C4×Dic3—61no—
167C2×#208—31no—
168C2×#208—31no—
169C2×#208—34no—
170C2×#208—61no—
171C2×#208C2×D311yescharacteristic, complemented
172#907—62no—
173D3×M16—34no—
174#901—62no—
175#893—61no—
176#887—61no—
177#67⋊C4—62no—
178#872—32no—
179C42×D3—32no—
180C3×#104—34no—
181#837—32no—
182#837—32no—
183#837—32no—
184#837—32no—
185#837—34no—
186#837—32no—
187#837—32no—
188#837—62no—
189#837—62no—
190#837C2×D314yescomplemented
191#825—32no—
192#825—32no—
193#805—34no—
194C23×C32—21no—
195C23×C32C2×D411yescharacteristic
196C22×C3×D3—21no—
197C22×C3×D3—24no—
198C22×C3×D3C2×D412yes—
199C32×Q8—21no—
200C32×Q8C22×C412yes—
201C32×D4—22no—
202C32×D4—22no—
203C32×D4—21no—
204C32×D4C22×C412yes—
205C2×C32×C4—21no—
206C2×C32×C4—22no—
207C2×C32×C4—22no—
208C2×C32×C4C22×C411yescharacteristic
209C2×C32×C4C22×C411yescharacteristic
210C2×C32×C4C2×D411yescharacteristic
211C2×C32×C4C2×D411yescharacteristic
212C2×C32×C4C2×D411yescharacteristic
213C2×C32×C4C2411yescharacteristic
214C2×C3⋊Dic3—21no—
215C2×C3⋊Dic3—21no—
216C2×C3⋊Dic3—42no—
217C3×#67—22no—
218C3×#67—22no—
219C3×#67—24no—
220C3×#67—24no—
221C3×#67C22⋊C414yes—
222C3×#67C22⋊C414yes—
223C2×C3×Dic3—21no—
224C2×C3×Dic3—24no—
225C2×C3×Dic3—22no—
226C2×C3×Dic3C2×D412yes—
227C3×D12—24no—
228C3×D12—21no—
229C3×D12C22⋊C412yes—
230C3×D12C22⋊C412yes—
231C3×D12C22×C412yes—
232C3×C4×D3—24no—
233C3×C4×D3—22no—
234C3×C4×D3—22no—
235C3×C4×D3—24no—
236C3×C4×D3C22×C414yes—
237C3×C4×D3C2×D414yes—
238C3×Dic6—21no—
239C3×Dic6—24no—
240C3×Dic6C22⋊C412yes—
241C3×Dic6C22⋊C412yes—
242C3×Dic6C22×C412yes—
243D3×Dic3—44no—
244C3⋊(C3⋊C8)—22no—
245C3×C3⋊C8—22no—
246#585—31no—
247#568—91no—
248C4×#41—91no—
249#421—31no—
250#421—94no—
251#421—91no—
252C2×#104—94no—
253C2×#104—91no—
254C2×#104—91no—
255C3×#41—21no—
256C3×#41—21no—
257C3×#41—21no—
258C3×#41—21no—
259C3×#41—22no—
260C3×#41—22no—
261C3×#41—32no—
262C3×#41—32no—
263C3×#41—32no—
264C3×#41—32no—
265C3×#41—34no—
266C3×#41—34no—
267C3×#41—32no—
268C3×#41—32no—
269C3×#41—41no—
270C3×#41—41no—
271C3×#41—64no—
272C3×#41—64no—
273C3×#41—62no—
274C3×#41—62no—
275C3×#41—64no—
276C3×#41—64no—
277C3×#41—62no—
278C3×#41—62no—
279C3×#41—61no—
280C3×#41—61no—
281C3×#41C4×D312yescomplemented
282C3×#41C2×Dic312yescomplemented
283C3×#41C22×D312yes—
284C3×#41C22×D312yes—
285C2×C3×Q8—21no—
286C2×C3×Q8—31no—
287C2×C3×Q8—34no—
288C2×C3×Q8—31no—
289C2×C3×Q8—62no—
290C2×C3×Q8—62no—
291C2×C3×Q8C4×D311yescharacteristic, complemented
292C2×C3×Q8C2×Dic311yescharacteristic, complemented
293C2×C3×D4—21no—
294C2×C3×D4—21no—
295C2×C3×D4—21no—
296C2×C3×D4—32no—
297C2×C3×D4—34no—
298C2×C3×D4—31no—
299C2×C3×D4—31no—
300C2×C3×D4—41no—
301C2×C3×D4—62no—
302C2×C3×D4—64no—
303C2×C3×D4—62no—
304C2×C3×D4—64no—
305C2×C3×D4—64no—
306C2×C3×D4—61no—
307C2×C3×D4C4×D311yescharacteristic, complemented
308C2×C3×D4C2×Dic311yescharacteristic, complemented
309C22×C3×C4—21no—
310C22×C3×C4—21no—
311C22×C3×C4—21no—
312C22×C3×C4—32no—
313C22×C3×C4—41no—
314C22×C3×C4—64no—
315C22×C3×C4—61no—
316C22×C3×C4C22×D311yescharacteristic
317C22×C3×C4C22×D311yescharacteristic
318C2×#67—21no—
319C2×#67—24no—
320C2×#67#6712yes—
321C22×Dic3—62no—
322C22×Dic3—61no—
323C22×Dic3—61no—
324C22×Dic3—121no—
325#239—22no—
326#239C2×Dic314yescomplemented
327D3×Q8—22no—
328D3×Q8C2×Dic314yescomplemented
329#237—24no—
330#237—24no—
331#237—22no—
332#237C2×Dic314yescomplemented
333D3×D4—24no—
334D3×D4—24no—
335D3×D4—22no—
336D3×D4C2×Dic314yescomplemented
337#235—21no—
338#235—21no—
339#235—24no—
340#235—22no—
341#235—24no—
342#235—22no—
343#235C2×Dic312yes—
344#235C2×Dic312yes—
345#235C2×Dic312yescomplemented
346#235#6712yes—
347#235#6712yes—
348#235C22×D312yes—
349C2×D12—22no—
350C2×D12C2×Dic311yescharacteristic, complemented
351C2×D12#6711yescharacteristic
352C2×C4×D3—21no—
353C2×C4×D3—24no—
354C2×C4×D3—62no—
355C2×C4×D3C22×D312yes—
356C2×Dic6—22no—
357C2×Dic6C2×Dic311yescharacteristic, complemented
358C2×Dic6#6711yescharacteristic
359C3×M16—32no—
360C3×M16—61no—
361C2×C3×C8—61no—
362C3×C4⋊C4—61no—
363C3×C22⋊C4—61no—
364C3×C42—32no—
365#217—21no—
366#217—62no—
367(C2×D3)⋊C4—62no—
368C4⋊Dic3—21no—
369C4⋊Dic3—62no—
370Dic3⋊C4—62no—
371C4×Dic3—31no—
372C4×Dic3—31no—
373C4×Dic3—31no—
374C4×Dic3—31no—
375C4×Dic3—61no—
376C4×Dic3—61no—
377C4×Dic3—62no—
378C4×Dic3—61no—
379C4×Dic3—61no—
380C4×Dic3—62no—
381C4×Dic3—121no—
382C4×Dic3C22×D312yes—
383#208—21no—
384#208—32no—
385#208—32no—
386#208—62no—
387#208—64no—
388#208—61no—
389#208—61no—
390#208—121no—
391#208C22×D312yes—
392C2×C3⋊C8—21no—
393C2×C3⋊C8—64no—
394C2×C3⋊C8—61no—
395C2×C3⋊C8—61no—
396C2×C3⋊C8—121no—
397ΓL(1,𝔽25)—64no—
398D3×C8—64no—
399C22×C32—22no—
400C22×C32—41no—
401C22×C32—81no—
402C22×C32C2×C22⋊C411yescharacteristic
403C22×C32C2×C22⋊C411yescharacteristic
404C22×C32C22×D411yescharacteristic
405C2×C3×D3—22no—
406C2×C3×D3—42no—
407C2×C3×D3—84no—
408C2×C3×D3—81no—
409C2×C3×D3C2×C22⋊C414yes—
410C32×C4—22no—
411C32×C4C2×C22⋊C411yescharacteristic
412C32×C4C2×C22⋊C411yescharacteristic
413C32×C4C23×C411yescharacteristic
414C32×C4C22×D411yescharacteristic
415C3⋊Dic3—22no—
416C3⋊Dic3—41no—
417C3×Dic3—22no—
418C3×Dic3—42no—
419C3×Dic3C2×C22⋊C414yes—
4202−1+4—32no—
4212−1+4—32no—
4222−1+4—61no—
423H(5,𝔽2)—32no—
424H(5,𝔽2)—32no—
425H(5,𝔽2)—62no—
426H(5,𝔽2)—61no—
427C2×#41—31no—
428C2×#41—34no—
429C2×#41—31no—
430C2×#41—62no—
431C2×#41—62no—
432C2×#41D3211yescharacteristic
433#131—182no—
434#131—182no—
435C2×M16—31no—
436C2×M16—94no—
437C2×M16—91no—
438C4×Q8—181no—
439C4×D4—182no—
440C4×D4—181no—
441#117—31no—
442#117—92no—
443C2×C42—92no—
444C2×C42—91no—
445#104—34no—
446#104—94no—
447#104—92no—
448#104—92no—
449#104—92no—
450#104—92no—
451C23×C3—21no—
452C23×C3—21no—
453C23×C3—21no—
454C23×C3—32no—
455C23×C3—41no—
456C23×C3—64no—
457C23×C3—61no—
458C23×C3D3×D411yescharacteristic
459C23×C3C2×#6711yescharacteristic
460C22×D3—21no—
461C22×D3—24no—
462C22×D3C2×#6712yes—
463C3×Q8—21no—
464C3×Q8—21no—
465C3×Q8—22no—
466C3×Q8—32no—
467C3×Q8—32no—
468C3×Q8—32no—
469C3×Q8—41no—
470C3×Q8—64no—
471C3×Q8—61no—
472C3×Q8C2×C4×D312yes—
473C3×Q8C22×Dic312yes—
474C3×D4—22no—
475C3×D4—22no—
476C3×D4—22no—
477C3×D4—22no—
478C3×D4—21no—
479C3×D4—21no—
480C3×D4—22no—
481C3×D4—34no—
482C3×D4—34no—
483C3×D4—32no—
484C3×D4—32no—
485C3×D4—32no—
486C3×D4—41no—
487C3×D4—42no—
488C3×D4—42no—
489C3×D4—64no—
490C3×D4—64no—
491C3×D4—64no—
492C3×D4—62no—
493C3×D4—62no—
494C3×D4—61no—
495C3×D4C2×C4×D312yes—
496C3×D4C22×Dic312yes—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—22no—
500C2×C3×C4—22no—
501C2×C3×C4—22no—
502C2×C3×C4—22no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—32no—
510C2×C3×C4—34no—
511C2×C3×C4—34no—
512C2×C3×C4—42no—
513C2×C3×C4—42no—
514C2×C3×C4—41no—
515C2×C3×C4—64no—
516C2×C3×C4—64no—
517C2×C3×C4—64no—
518C2×C3×C4—61no—
519C2×C3×C4—62no—
520C2×C3×C4—62no—
521C2×C3×C4—62no—
522C2×C3×C4C2×C4×D311yescharacteristic
523C2×C3×C4C2×C4×D311yescharacteristic
524C2×C3×C4D3×D411yescharacteristic
525C2×C3×C4D3×D411yescharacteristic
526C2×C3×C4D3×D411yescharacteristic
527C2×C3×C4C22×Dic311yescharacteristic
528C2×C3×C4C22×Dic311yescharacteristic
529C2×C3×C4C2×#6711yescharacteristic
530C2×C3×C4C2×#6711yescharacteristic
531C2×C3×C4C2×#6711yescharacteristic
532C2×C3×C4C23×D311yescharacteristic
533C2×C3×C4C23×D311yescharacteristic
534#67—22no—
535#67—22no—
536#67—24no—
537#67—24no—
538#67#21714yes—
539#67#21714yes—
540C2×Dic3—21no—
541C2×Dic3—24no—
542C2×Dic3—22no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—61no—
546C2×Dic3—61no—
547C2×Dic3—121no—
548C2×Dic3—121no—
549C2×Dic3—124no—
550C2×Dic3—122no—
551C2×Dic3—122no—
552C2×Dic3—124no—
553C2×Dic3C2×#6712yes—
554D12—24no—
555D12—21no—
556D12#21712yes—
557D12#21712yes—
558D12C22×Dic312yes—
559C4×D3—24no—
560C4×D3—22no—
561C4×D3—22no—
562C4×D3—24no—
563C4×D3—124no—
564C4×D3C22×Dic314yes—
565C4×D3C2×#6714yes—
566Dic6—21no—
567Dic6—24no—
568Dic6#21712yes—
569Dic6#21712yes—
570Dic6C22×Dic312yes—
571C3×C8—62no—
572C3⋊C8—22no—
573C3⋊C8—62no—
574C3⋊C8—62no—
575C3⋊C8—122no—
576C2×C32—21no—
577C2×C32—21no—
578C2×C32—21no—
579C2×C32—42no—
580C2×C32C22×C22⋊C411yescharacteristic
581C3×D3—24no—
582C3×D3—42no—
583#41—21no—
584#41—21no—
585#41—32no—
586#41—32no—
587#41—32no—
588#41—32no—
589#41—34no—
590#41—34no—
591#41—32no—
592#41—32no—
593#41—64no—
594#41—64no—
595#41—62no—
596#41—62no—
597#41—64no—
598#41—64no—
599#41—62no—
600#41—62no—
601#41—61no—
602#41—61no—
603#41D3×Dic312yescomplemented
604#41C2×D3212yes—
605C2×Q8—31no—
606C2×Q8—34no—
607C2×Q8—31no—
608C2×Q8—62no—
609C2×Q8—62no—
610C2×Q8D3×Dic311yescharacteristic, complemented
611C2×D4—21no—
612C2×D4—32no—
613C2×D4—34no—
614C2×D4—31no—
615C2×D4—31no—
616C2×D4—62no—
617C2×D4—64no—
618C2×D4—62no—
619C2×D4—64no—
620C2×D4—64no—
621C2×D4—61no—
622C2×D4D3×Dic311yescharacteristic, complemented
623C22×C4—21no—
624C22×C4—32no—
625C22×C4—64no—
626C22×C4—61no—
627C22×C4—182no—
628C22×C4—181no—
629C22×C4C2×D3211yescharacteristic
630M16—32no—
631M16—61no—
632M16—92no—
633M16—184no—
634M16—181no—
635C2×C8—61no—
636C2×C8—184no—
637C2×C8—181no—
638C4⋊C4—61no—
639C4⋊C4—182no—
640C22⋊C4—61no—
641C22⋊C4—182no—
642C42—32no—
643C42—91no—
644C42—91no—
645C42—182no—
646C42—181no—
647C22×C3—22no—
648C22×C3—22no—
649C22×C3—21no—
650C22×C3—21no—
651C22×C3—21no—
652C22×C3—34no—
653C22×C3—42no—
654C22×C3—41no—
655C22×C3—41no—
656C22×C3—42no—
657C22×C3—62no—
658C22×C3—81no—
659C22×C3—81no—
660C22×C3—82no—
661C22×C3—122no—
662C22×C3—241no—
663C22×C3—244no—
664C22×C3D3×C22⋊C411yescharacteristic
665C22×C3D3×C22⋊C411yescharacteristic
666C22×C3C2×#21711yescharacteristic
667C22×C3C2×#21711yescharacteristic
668C22×C3C2×D3×D411yescharacteristic
669C22×C3C22×#6711yescharacteristic
670C2×D3—22no—
671C2×D3—42no—
672C2×D3—84no—
673C2×D3—81no—
674C2×D3C2×#21714yes—
675C3×C4—22no—
676C3×C4—22no—
677C3×C4—21no—
678C3×C4—21no—
679C3×C4—21no—
680C3×C4—21no—
681C3×C4—34no—
682C3×C4—42no—
683C3×C4—62no—
684C3×C4—122no—
685C3×C4D3×C22⋊C411yescharacteristic
686C3×C4D3×C22⋊C411yescharacteristic
687C3×C4C2×#21711yescharacteristic
688C3×C4C2×#21711yescharacteristic
689C3×C4C22×C4×D311yescharacteristic
690C3×C4C2×D3×D411yescharacteristic
691C3×C4C23×Dic311yescharacteristic
692C3×C4C22×#6711yescharacteristic
693Dic3—22no—
694Dic3—42no—
695Dic3—62no—
696Dic3—62no—
697Dic3—122no—
698Dic3—121no—
699Dic3—121no—
700Dic3—122no—
701Dic3C2×#21714yes—
702C32#290111yescharacteristic, complemented, Sylow
703C23—21no—
704C23—32no—
705C23—64no—
706C23—61no—
707C23D3×#6711yescharacteristic
708Q8—21no—
709Q8—32no—
710Q8—32no—
711Q8—32no—
712Q8—64no—
713Q8—61no—
714Q8C2×D3×Dic312yes—
715D4—22no—
716D4—22no—
717D4—21no—
718D4—34no—
719D4—34no—
720D4—32no—
721D4—32no—
722D4—32no—
723D4—64no—
724D4—64no—
725D4—64no—
726D4—62no—
727D4—62no—
728D4—61no—
729D4C2×D3×Dic312yes—
730C2×C4—21no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—32no—
734C2×C4—34no—
735C2×C4—34no—
736C2×C4—64no—
737C2×C4—64no—
738C2×C4—64no—
739C2×C4—61no—
740C2×C4—62no—
741C2×C4—62no—
742C2×C4—62no—
743C2×C4—181no—
744C2×C4—181no—
745C2×C4—364no—
746C2×C4—362no—
747C2×C4C2×D3×Dic311yescharacteristic
748C2×C4C2×D3×Dic311yescharacteristic
749C2×C4D3×#6711yescharacteristic
750C2×C4D3×#6711yescharacteristic
751C2×C4D3×#6711yescharacteristic
752C2×C4C22×D3211yescharacteristic
753C8—62no—
754C8—182no—
755C2×C3—22no—
756C2×C3—21no—
757C2×C3—21no—
758C2×C3—21no—
759C2×C3—21no—
760C2×C3—21no—
761C2×C3—21no—
762C2×C3—21no—
763C2×C3—41no—
764C2×C3—41no—
765C2×C3—42no—
766C2×C3—42no—
767C2×C3—64no—
768C2×C3—82no—
769C2×C3—122no—
770C2×C3C2×D3×C22⋊C411yescharacteristic
771C2×C3C22×#21711yescharacteristic
772D3—24no—
773D3—42no—
774C22—22no—
775C22—34no—
776C22—41no—
777C22—62no—
778C22—81no—
779C22—122no—
780C22—241no—
781C22—244no—
782C22D3×#21711yescharacteristic
783C22D3×#21711yescharacteristic
784C22C2×D3×#6711yescharacteristic
785C4—22no—
786C4—34no—
787C4—62no—
788C4—122no—
789C4—182no—
790C4—361no—
791C4D3×#21711yescharacteristic
792C4D3×#21711yescharacteristic
793C4C22×D3×Dic311yescharacteristic
794C4C2×D3×#6711yescharacteristic
795C3—21no—
796C3#7899211yescharacteristic, complemented
797C3#8412011yescharacteristic, complemented
798C2—21no—
799C2—21no—
800C2—21no—
801C2—42no—
802C2—64no—
803C2—122no—
804C2C2×D3×#21711yescharacteristic
subgroupG/H
centerC4C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC2×C32C22×C22⋊C4
prime radicalC3×#5964C2
cosocleC2×C32×C4C24
hypercenterC2×#41D32
hypocenterC32#2901
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. #10594958C2semidirect
3. #10594776C2semidirect
4. C2×#63664C2semidirect
5. C3×#5236C2semidirect
6. #10591670C2semidirect
7. D3×#837C2semidirect
8. #10591111C2semidirect
9. C2×#63568C2semidirect
14. C3×#1010C4semidirect
16. C3×#1009C4semidirect
19. C3×#1007C4semidirect
21. C3×#1004C4semidirect
25. C2×C4×C3⋊Dic3C22semidirect
26. C2×#3748C22semidirect
27. C3×#926C22semidirect
28. C2×C3×#208C22semidirect
31. C4×D3×Dic3C22semidirect
32. #63855C22semidirect
36. D3×#208C22semidirect
37. #63664C22semidirect
38. #63664C22semidirect
39. C3×#837C22semidirect
40. #63569C22semidirect
41. #63568C22semidirect
42. #63568C22semidirect
52. #5236D3semidirect
64. C32×#41C2×C4semidirect
66. C2×C32×Q8C2×C4semidirect
68. C2×C32×D4C2×C4semidirect
76. C3×#239C2×C4semidirect
78. C3×D3×Q8C2×C4semidirect
82. C3×#237C2×C4semidirect
86. C3×D3×D4C2×C4semidirect
95. C3×#235C2×C4semidirect
100. C2×C3×D12C2×C4semidirect
106. C2×C3×Dic6C2×C4semidirect
143. #1010Dic3semidirect
145. #1009Dic3semidirect
148. #1007Dic3semidirect
150. #1004Dic3semidirect
162. #926C2×D3semidirect
171. C2×#208C2×D3semidirect
190. #837C2×D3semidirect
281. C3×#41C4×D3semidirect
282. C3×#41C2×Dic3semidirect
291. C2×C3×Q8C4×D3semidirect
292. C2×C3×Q8C2×Dic3semidirect
307. C2×C3×D4C4×D3semidirect
308. C2×C3×D4C2×Dic3semidirect
326. #239C2×Dic3semidirect
328. D3×Q8C2×Dic3semidirect
332. #237C2×Dic3semidirect
336. D3×D4C2×Dic3semidirect
345. #235C2×Dic3semidirect
350. C2×D12C2×Dic3semidirect
357. C2×Dic6C2×Dic3semidirect
603. #41D3×Dic3semidirect
610. C2×Q8D3×Dic3semidirect
622. C2×D4D3×Dic3semidirect
702. C32#2901semidirect
796. C3#78992semidirect
797. C3#84120semidirect

Maximal subgroups

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

subgroupindex
C3×#59642
#105949582
#105947762
C2×#636642
C3×#52362
#105916702
D3×#8372
#105911112
C2×#635682
#841203
#789923