Finite Group Databasebeta

← #11858198

Subgroups — #11858198

Order 1152.

1553 conjugacy classes of subgroups.

The subgroup lattice has 801 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5964C211yesmaximal, characteristic
2Dic3×#235C211yesmaximal, characteristic, complemented
3#10594776C211yesmaximal, characteristic, complemented
4#10592935C211yesmaximal, characteristic, complemented
5C2×C3×#837C211yesmaximal, characteristic, complemented
6#10591670C214yesmaximal, complemented
7D3×#837C214yesmaximal, complemented
8#10591110C211yesmaximal, characteristic, complemented
9C2×#63569C211yesmaximal, characteristic, complemented
10#84120—31nomaximal
11#78983—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
25#64135C2211yescharacteristic, complemented
26C2×#3748C2211yescharacteristic, complemented
27C2×C3×C4×Dic3C2211yescharacteristic, complemented
28C2×C3×#208C2211yescharacteristic, complemented
29Dic3×#67—22no—
30Dic3×D12—21no—
31C4×D3×Dic3C2212yescomplemented
32#63855C2212yescomplemented
33Dic3×Dic6—21no—
34#63815—22no—
35#63814—22no—
36D3×#208C2214yescomplemented
37#63664C2214yescomplemented
38C3×#837C2212yescomplemented
39C3×#837C2212yescomplemented
40#63569C2212yescomplemented
41#63569C2212yescomplemented
42#63568C2214yescomplemented
43C3×#585—31no—
44#5964D311yescharacteristic
45Dic3×#41—31no—
46#5819—31no—
47#5745—31no—
48C4×#235—31no—
49C2×C3×#104—31no—
50#5236—31no—
51#5236—31no—
52#5236—31no—
53#5236—34no—
54#5236—61no—
55C2×#837—31no—
56C2×#837—34no—
57C2×#837D311yescharacteristic, complemented
58#5139—31no—
59C2×#805—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
71C2×C3×#67—21no—
72C2×C3×#67—24no—
73C2×C3×#67D412yes—
74C22×C3×Dic3—21no—
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—
109#3757—21no—
110C4⋊(C3⋊Dic3)—21no—
111C4×C3⋊Dic3C2312yes—
112#3748—21no—
113#3748C2312yes—
114C2×C3⋊(C3⋊C8)—21no—
115C3×C4×Dic3—21no—
116C3×C4×Dic3C2311yescharacteristic
117C3×C4×Dic3C2311yescharacteristic
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—
155C2×C3×C42—31no—
156#948—62no—
157#948—62no—
158Q8×Dic3—61no—
159D4×Dic3—61no—
160D4×Dic3—62no—
161C4×#67—62no—
162#926—31no—
163#926—31no—
164#926—32no—
165#926—61no—
166C2×C4×Dic3—32no—
167C2×C4×Dic3C2×D311yescharacteristic, complemented
168C2×#208—31no—
169C2×#208—31no—
170C2×#208—34no—
171C2×#208—61no—
172C2×#208C2×D311yescharacteristic, complemented
173#907—62no—
174D3×M16—34no—
175#901—62no—
176C4×D12—61no—
177#872—32no—
178C42×D3—32no—
179C4×Dic6—61no—
180C3×#104—32no—
181C3×#104—32no—
182#837—34no—
183#837—34no—
184#837—32no—
185#837—32no—
186#837—34no—
187#837—64no—
188#837C2×D312yescomplemented
189#837C2×D312yescomplemented
190#825—34no—
191#805—32no—
192#805—32no—
193C23×C32—21no—
194C23×C32C2×D411yescharacteristic
195C22×C3×D3—21no—
196C22×C3×D3—24no—
197C22×C3×D3C2×D412yes—
198C32×Q8—21no—
199C32×Q8C22×C412yes—
200C32×D4—22no—
201C32×D4—22no—
202C32×D4—21no—
203C32×D4C22×C412yes—
204C2×C32×C4—21no—
205C2×C32×C4—22no—
206C2×C32×C4—22no—
207C2×C32×C4C22×C411yescharacteristic
208C2×C32×C4C22×C411yescharacteristic
209C2×C32×C4C2×D411yescharacteristic
210C2×C32×C4C2×D411yescharacteristic
211C2×C32×C4C2×D411yescharacteristic
212C2×C32×C4C2411yescharacteristic
213C2×C3⋊Dic3—22no—
214C3×#67—22no—
215C3×#67—22no—
216C3×#67—24no—
217C3×#67—24no—
218C3×#67C22⋊C414yes—
219C3×#67C22⋊C414yes—
220C2×C3×Dic3—21no—
221C2×C3×Dic3—21no—
222C2×C3×Dic3—24no—
223C2×C3×Dic3—21no—
224C2×C3×Dic3—42no—
225C2×C3×Dic3C2×D412yes—
226C3×D12—24no—
227C3×D12—21no—
228C3×D12C22⋊C412yes—
229C3×D12C22⋊C412yes—
230C3×D12C22×C412yes—
231C3×C4×D3—24no—
232C3×C4×D3—22no—
233C3×C4×D3—22no—
234C3×C4×D3—24no—
235C3×C4×D3C22×C414yes—
236C3×C4×D3C2×D414yes—
237C3×Dic6—21no—
238C3×Dic6—24no—
239C3×Dic6C22⋊C412yes—
240C3×Dic6C22⋊C412yes—
241C3×Dic6C22×C412yes—
242D3×Dic3—44no—
243C3⋊(C3⋊C8)—22no—
244C3×C3⋊C8—22no—
245#585—31no—
246#568—91no—
247C4×#41—91no—
248#421—94no—
249#421—91no—
250#421—91no—
251C2×#104—31no—
252C2×#104—94no—
253C2×#104—91no—
254C3×#41—21no—
255C3×#41—21no—
256C3×#41—21no—
257C3×#41—21no—
258C3×#41—22no—
259C3×#41—22no—
260C3×#41—32no—
261C3×#41—32no—
262C3×#41—32no—
263C3×#41—32no—
264C3×#41—34no—
265C3×#41—34no—
266C3×#41—32no—
267C3×#41—32no—
268C3×#41—41no—
269C3×#41—41no—
270C3×#41—64no—
271C3×#41—64no—
272C3×#41—62no—
273C3×#41—62no—
274C3×#41—64no—
275C3×#41—64no—
276C3×#41—62no—
277C3×#41—62no—
278C3×#41—61no—
279C3×#41—61no—
280C3×#41C4×D312yescomplemented
281C3×#41C2×Dic312yescomplemented
282C3×#41C22×D312yes—
283C3×#41C22×D312yes—
284C2×C3×Q8—21no—
285C2×C3×Q8—31no—
286C2×C3×Q8—34no—
287C2×C3×Q8—31no—
288C2×C3×Q8—62no—
289C2×C3×Q8—62no—
290C2×C3×Q8C4×D311yescharacteristic, complemented
291C2×C3×Q8C2×Dic311yescharacteristic, complemented
292C2×C3×D4—21no—
293C2×C3×D4—21no—
294C2×C3×D4—21no—
295C2×C3×D4—32no—
296C2×C3×D4—34no—
297C2×C3×D4—31no—
298C2×C3×D4—31no—
299C2×C3×D4—41no—
300C2×C3×D4—62no—
301C2×C3×D4—64no—
302C2×C3×D4—62no—
303C2×C3×D4—64no—
304C2×C3×D4—64no—
305C2×C3×D4—61no—
306C2×C3×D4C4×D311yescharacteristic, complemented
307C2×C3×D4C2×Dic311yescharacteristic, complemented
308C22×C3×C4—21no—
309C22×C3×C4—21no—
310C22×C3×C4—21no—
311C22×C3×C4—32no—
312C22×C3×C4—41no—
313C22×C3×C4—64no—
314C22×C3×C4—61no—
315C22×C3×C4—61no—
316C22×C3×C4C22×D311yescharacteristic
317C22×C3×C4C22×D311yescharacteristic
318C2×#67—21no—
319C2×#67—24no—
320C2×#67#6712yes—
321C22×Dic3—21no—
322C22×Dic3—62no—
323#239—22no—
324#239C2×Dic314yescomplemented
325D3×Q8—22no—
326D3×Q8C2×Dic314yescomplemented
327#237—24no—
328#237—24no—
329#237—22no—
330#237C2×Dic314yescomplemented
331D3×D4—24no—
332D3×D4—24no—
333D3×D4—22no—
334D3×D4C2×Dic314yescomplemented
335#235—21no—
336#235—21no—
337#235—24no—
338#235—22no—
339#235—24no—
340#235—22no—
341#235C2×Dic312yes—
342#235C2×Dic312yes—
343#235C2×Dic312yescomplemented
344#235#6712yes—
345#235#6712yes—
346#235C22×D312yes—
347C2×D12—22no—
348C2×D12C2×Dic311yescharacteristic, complemented
349C2×D12#6711yescharacteristic
350C2×C4×D3—21no—
351C2×C4×D3—24no—
352C2×C4×D3—62no—
353C2×C4×D3C22×D312yes—
354C2×Dic6—22no—
355C2×Dic6C2×Dic311yescharacteristic, complemented
356C2×Dic6#6711yescharacteristic
357C3×M16—32no—
358C3×M16—61no—
359C2×C3×C8—61no—
360C3×C42—31no—
361C3×C42—31no—
362C3×C42—61no—
363#217—62no—
364#217—61no—
365#217—61no—
366#217—121no—
367(C2×D3)⋊C4—62no—
368C4⋊Dic3—62no—
369C4⋊Dic3—61no—
370C4⋊Dic3—61no—
371C4⋊Dic3—121no—
372Dic3⋊C4—62no—
373C4×Dic3—21no—
374C4×Dic3—32no—
375C4×Dic3—32no—
376C4×Dic3—62no—
377C4×Dic3—62no—
378C4×Dic3—62no—
379C4×Dic3C22×D311yescharacteristic
380C4×Dic3C22×D311yescharacteristic
381#208—21no—
382#208—32no—
383#208—32no—
384#208—62no—
385#208—64no—
386#208—61no—
387#208—61no—
388#208—121no—
389#208C22×D312yes—
390C2×C3⋊C8—21no—
391C2×C3⋊C8—64no—
392C2×C3⋊C8—61no—
393C2×C3⋊C8—61no—
394C2×C3⋊C8—121no—
395ΓL(1,𝔽25)—64no—
396D3×C8—64no—
397C22×C32—22no—
398C22×C32—41no—
399C22×C32—81no—
400C22×C32C2×C22⋊C411yescharacteristic
401C22×C32C2×C22⋊C411yescharacteristic
402C22×C32C22×D411yescharacteristic
403C2×C3×D3—22no—
404C2×C3×D3—42no—
405C2×C3×D3—84no—
406C2×C3×D3—81no—
407C2×C3×D3C2×C22⋊C414yes—
408C32×C4—22no—
409C32×C4C2×C22⋊C411yescharacteristic
410C32×C4C2×C22⋊C411yescharacteristic
411C32×C4C23×C411yescharacteristic
412C32×C4C22×D411yescharacteristic
413C3⋊Dic3—42no—
414C3×Dic3—22no—
415C3×Dic3—22no—
416C3×Dic3—41no—
417C3×Dic3C2×C22⋊C414yes—
4182−1+4—32no—
4192−1+4—32no—
4202−1+4—61no—
421H(5,𝔽2)—32no—
422H(5,𝔽2)—32no—
423H(5,𝔽2)—62no—
424H(5,𝔽2)—61no—
425C2×#41—31no—
426C2×#41—34no—
427C2×#41—31no—
428C2×#41—62no—
429C2×#41—62no—
430C2×#41D3211yescharacteristic
431#131—182no—
432#131—182no—
433C2×M16—31no—
434C2×M16—94no—
435C2×M16—91no—
436C4×Q8—181no—
437C4×D4—181no—
438C4×D4—182no—
439#117—92no—
440#117—91no—
441C2×C42—31no—
442C2×C42—92no—
443#104—32no—
444#104—32no—
445#104—92no—
446#104—92no—
447#104—94no—
448#104—94no—
449C23×C3—21no—
450C23×C3—21no—
451C23×C3—21no—
452C23×C3—32no—
453C23×C3—41no—
454C23×C3—64no—
455C23×C3—61no—
456C23×C3D3×D411yescharacteristic
457C23×C3C2×#6711yescharacteristic
458C22×D3—21no—
459C22×D3—24no—
460C22×D3C2×#6712yes—
461C3×Q8—21no—
462C3×Q8—21no—
463C3×Q8—22no—
464C3×Q8—32no—
465C3×Q8—32no—
466C3×Q8—32no—
467C3×Q8—41no—
468C3×Q8—64no—
469C3×Q8—61no—
470C3×Q8C2×C4×D312yes—
471C3×Q8C22×Dic312yes—
472C3×D4—22no—
473C3×D4—22no—
474C3×D4—22no—
475C3×D4—22no—
476C3×D4—21no—
477C3×D4—21no—
478C3×D4—22no—
479C3×D4—34no—
480C3×D4—34no—
481C3×D4—32no—
482C3×D4—32no—
483C3×D4—32no—
484C3×D4—41no—
485C3×D4—42no—
486C3×D4—42no—
487C3×D4—64no—
488C3×D4—64no—
489C3×D4—64no—
490C3×D4—62no—
491C3×D4—62no—
492C3×D4—61no—
493C3×D4C2×C4×D312yes—
494C3×D4C22×Dic312yes—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—22no—
498C2×C3×C4—22no—
499C2×C3×C4—22no—
500C2×C3×C4—22no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—32no—
508C2×C3×C4—34no—
509C2×C3×C4—34no—
510C2×C3×C4—42no—
511C2×C3×C4—42no—
512C2×C3×C4—41no—
513C2×C3×C4—64no—
514C2×C3×C4—64no—
515C2×C3×C4—64no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—62no—
519C2×C3×C4—62no—
520C2×C3×C4—61no—
521C2×C3×C4—122no—
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—21no—
542C2×Dic3—24no—
543C2×Dic3—21no—
544C2×Dic3—42no—
545C2×Dic3—62no—
546C2×Dic3—62no—
547C2×Dic3—122no—
548C2×Dic3—124no—
549C2×Dic3C2×#6712yes—
550D12—24no—
551D12—21no—
552D12#21712yes—
553D12#21712yes—
554D12C22×Dic312yes—
555C4×D3—24no—
556C4×D3—22no—
557C4×D3—22no—
558C4×D3—24no—
559C4×D3—124no—
560C4×D3C22×Dic314yes—
561C4×D3C2×#6714yes—
562Dic6—21no—
563Dic6—24no—
564Dic6#21712yes—
565Dic6#21712yes—
566Dic6C22×Dic312yes—
567C3×C8—62no—
568C3⋊C8—22no—
569C3⋊C8—62no—
570C3⋊C8—62no—
571C3⋊C8—122no—
572C2×C32—21no—
573C2×C32—21no—
574C2×C32—21no—
575C2×C32—42no—
576C2×C32C22×C22⋊C411yescharacteristic
577C3×D3—24no—
578C3×D3—42no—
579#41—21no—
580#41—21no—
581#41—32no—
582#41—32no—
583#41—32no—
584#41—32no—
585#41—34no—
586#41—34no—
587#41—32no—
588#41—32no—
589#41—64no—
590#41—64no—
591#41—62no—
592#41—62no—
593#41—64no—
594#41—64no—
595#41—62no—
596#41—62no—
597#41—61no—
598#41—61no—
599#41D3×Dic312yescomplemented
600#41C2×D3212yes—
601C2×Q8—31no—
602C2×Q8—34no—
603C2×Q8—31no—
604C2×Q8—62no—
605C2×Q8—62no—
606C2×Q8D3×Dic311yescharacteristic, complemented
607C2×D4—21no—
608C2×D4—32no—
609C2×D4—34no—
610C2×D4—31no—
611C2×D4—31no—
612C2×D4—62no—
613C2×D4—64no—
614C2×D4—62no—
615C2×D4—64no—
616C2×D4—64no—
617C2×D4—61no—
618C2×D4D3×Dic311yescharacteristic, complemented
619C22×C4—21no—
620C22×C4—32no—
621C22×C4—64no—
622C22×C4—61no—
623C22×C4—61no—
624C22×C4—182no—
625C22×C4C2×D3211yescharacteristic
626M16—32no—
627M16—61no—
628M16—92no—
629M16—184no—
630M16—181no—
631C2×C8—61no—
632C2×C8—184no—
633C2×C8—181no—
634C4⋊C4—182no—
635C4⋊C4—181no—
636C22⋊C4—182no—
637C22⋊C4—181no—
638C42—31no—
639C42—31no—
640C42—61no—
641C42—92no—
642C42—182no—
643C22×C3—22no—
644C22×C3—22no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—34no—
649C22×C3—42no—
650C22×C3—41no—
651C22×C3—41no—
652C22×C3—62no—
653C22×C3—81no—
654C22×C3—81no—
655C22×C3—81no—
656C22×C3—82no—
657C22×C3—122no—
658C22×C3—241no—
659C22×C3—244no—
660C22×C3D3×C22⋊C411yescharacteristic
661C22×C3D3×C22⋊C411yescharacteristic
662C22×C3C2×#21711yescharacteristic
663C22×C3C2×#21711yescharacteristic
664C22×C3C2×D3×D411yescharacteristic
665C22×C3C22×#6711yescharacteristic
666C2×D3—22no—
667C2×D3—42no—
668C2×D3—84no—
669C2×D3—81no—
670C2×D3C2×#21714yes—
671C3×C4—22no—
672C3×C4—22no—
673C3×C4—21no—
674C3×C4—21no—
675C3×C4—21no—
676C3×C4—21no—
677C3×C4—34no—
678C3×C4—42no—
679C3×C4—62no—
680C3×C4—62no—
681C3×C4—121no—
682C3×C4D3×C22⋊C411yescharacteristic
683C3×C4D3×C22⋊C411yescharacteristic
684C3×C4C2×#21711yescharacteristic
685C3×C4C2×#21711yescharacteristic
686C3×C4C22×C4×D311yescharacteristic
687C3×C4C2×D3×D411yescharacteristic
688C3×C4C23×Dic311yescharacteristic
689C3×C4C22×#6711yescharacteristic
690Dic3—22no—
691Dic3—22no—
692Dic3—41no—
693Dic3—122no—
694Dic3—122no—
695Dic3—242no—
696Dic3C2×#21714yes—
697C32#290111yescharacteristic, complemented, Sylow
698C23—21no—
699C23—32no—
700C23—64no—
701C23—61no—
702C23D3×#6711yescharacteristic
703Q8—21no—
704Q8—32no—
705Q8—32no—
706Q8—32no—
707Q8—64no—
708Q8—61no—
709Q8C2×D3×Dic312yes—
710D4—22no—
711D4—22no—
712D4—21no—
713D4—34no—
714D4—34no—
715D4—32no—
716D4—32no—
717D4—32no—
718D4—64no—
719D4—64no—
720D4—64no—
721D4—62no—
722D4—62no—
723D4—61no—
724D4C2×D3×Dic312yes—
725C2×C4—21no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—32no—
729C2×C4—34no—
730C2×C4—34no—
731C2×C4—64no—
732C2×C4—64no—
733C2×C4—64no—
734C2×C4—61no—
735C2×C4—61no—
736C2×C4—62no—
737C2×C4—62no—
738C2×C4—61no—
739C2×C4—122no—
740C2×C4—182no—
741C2×C4—364no—
742C2×C4C2×D3×Dic311yescharacteristic
743C2×C4C2×D3×Dic311yescharacteristic
744C2×C4D3×#6711yescharacteristic
745C2×C4D3×#6711yescharacteristic
746C2×C4D3×#6711yescharacteristic
747C2×C4C22×D3211yescharacteristic
748C8—62no—
749C8—182no—
750C2×C3—21no—
751C2×C3—21no—
752C2×C3—21no—
753C2×C3—21no—
754C2×C3—21no—
755C2×C3—21no—
756C2×C3—21no—
757C2×C3—41no—
758C2×C3—41no—
759C2×C3—41no—
760C2×C3—42no—
761C2×C3—42no—
762C2×C3—64no—
763C2×C3—82no—
764C2×C3—122no—
765C2×C3C2×D3×C22⋊C411yescharacteristic
766C2×C3C22×#21711yescharacteristic
767D3—24no—
768D3—42no—
769C22—22no—
770C22—34no—
771C22—41no—
772C22—62no—
773C22—81no—
774C22—122no—
775C22—241no—
776C22—244no—
777C22D3×#21711yescharacteristic
778C22D3×#21711yescharacteristic
779C22C2×D3×#6711yescharacteristic
780C4—22no—
781C4—34no—
782C4—62no—
783C4—62no—
784C4—121no—
785C4—362no—
786C4D3×#21711yescharacteristic
787C4D3×#21711yescharacteristic
788C4C22×D3×Dic311yescharacteristic
789C4C2×D3×#6711yescharacteristic
790C3—21no—
791C3#7898311yescharacteristic, complemented
792C3#8412011yescharacteristic, complemented
793C2—21no—
794C2—21no—
795C2—21no—
796C2—42no—
797C2—64no—
798C2—122no—
799C2C2×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. Dic3×#235C2semidirect
3. #10594776C2semidirect
4. #10592935C2semidirect
5. C2×C3×#837C2semidirect
6. #10591670C2semidirect
7. D3×#837C2semidirect
8. #10591110C2semidirect
9. C2×#63569C2semidirect
14. C3×#1010C4semidirect
16. C3×#1009C4semidirect
19. C3×#1007C4semidirect
21. C3×#1004C4semidirect
25. #64135C22semidirect
26. C2×#3748C22semidirect
27. C2×C3×C4×Dic3C22semidirect
28. C2×C3×#208C22semidirect
31. C4×D3×Dic3C22semidirect
32. #63855C22semidirect
36. D3×#208C22semidirect
37. #63664C22semidirect
38. C3×#837C22semidirect
39. C3×#837C22semidirect
40. #63569C22semidirect
41. #63569C22semidirect
42. #63568C22semidirect
57. C2×#837D3semidirect
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
167. C2×C4×Dic3C2×D3semidirect
172. C2×#208C2×D3semidirect
188. #837C2×D3semidirect
189. #837C2×D3semidirect
280. C3×#41C4×D3semidirect
281. C3×#41C2×Dic3semidirect
290. C2×C3×Q8C4×D3semidirect
291. C2×C3×Q8C2×Dic3semidirect
306. C2×C3×D4C4×D3semidirect
307. C2×C3×D4C2×Dic3semidirect
324. #239C2×Dic3semidirect
326. D3×Q8C2×Dic3semidirect
330. #237C2×Dic3semidirect
334. D3×D4C2×Dic3semidirect
343. #235C2×Dic3semidirect
348. C2×D12C2×Dic3semidirect
355. C2×Dic6C2×Dic3semidirect
599. #41D3×Dic3semidirect
606. C2×Q8D3×Dic3semidirect
618. C2×D4D3×Dic3semidirect
697. C32#2901semidirect
791. C3#78983semidirect
792. C3#84120semidirect

Maximal subgroups

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

subgroupindex
C3×#59642
Dic3×#2352
#105947762
#105929352
C2×C3×#8372
#105916702
D3×#8372
#105911102
C2×#635692
#841203
#789833