Finite Group Databasebeta

← #72222869

Subgroups — #72222869

Order 2304.

1408 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#83894C211yesmaximal, characteristic
2C3×#83910C211yesmaximal, characteristic, complemented
3#11860967C211yesmaximal, characteristic, complemented
4#11797969C214yesmaximal, complemented
5#11797923C214yesmaximal, complemented
6C2×#10589137C211yesmaximal, characteristic, complemented
7#11796953C211yesmaximal, characteristic, complemented
8C2×#10589432C211yesmaximal, characteristic, complemented
9#11795946C211yesmaximal, characteristic, complemented
10#10948647—31nomaximal
11#10948646—31nomaximal
12C2×C32×#135C2211yescharacteristic
13C3×#5819—21no—
14C2×C3×#904C2211yescharacteristic
15#10594992—21no—
16C2×#63644C2211yescharacteristic
17C2×#63639C2211yescharacteristic
18C3×#5236—21no—
19C3×#5197C2214yes—
20C3×#5196—22no—
21C3×#5195C2212yes—
22C3×#5194C414yescomplemented
23C3×#5193C2212yes—
24C3×#5179C412yescomplemented
25C3×#5147C412yescomplemented
26C2×C3×#819C2211yescharacteristic
27C3×#5101C2211yescharacteristic
28C2×C3×#812C2211yescharacteristic
29#10591088—21no—
30#10590812C2212yescomplemented
31#10590771C2212yescomplemented
32Dic3×#204—22no—
33#10589432C2214yes—
34#10589137C2214yescomplemented
35#10589129C2212yescomplemented
36#10589126C2212yescomplemented
37#10589105C2214yescomplemented
38C3×#3414—31no—
39C3×#2957—31no—
40#83910D311yescharacteristic, complemented
41#83899—31no—
42#83894D311yescharacteristic
43#78574—31no—
44#72081—31no—
45C2×#4566—31no—
46C2×#4566—31no—
47C2×#4566—61no—
48#71521—34no—
49#71515—34no—
50C2×#4513—31no—
51#71425—31no—
52#70929—34no—
53#70928—34no—
54#70687—31no—
55C2×#4494—31no—
56#69884—31no—
57C2×C32×#41—21no—
58C2×C3×#235—21no—
59C32×#135—21no—
60C32×#135—21no—
61C32×#135C2×C412yescomplemented
62C32×#135C2312yes—
63C2×C32×Q16C2×C411yescharacteristic, complemented
64C2×C32×SD16—21no—
65C2×C32×D8C2×C411yescharacteristic, complemented
66C22×C32×C8C2311yescharacteristic
67C2×C4⋊(C3⋊Dic3)—21no—
68C3×#948—24no—
69C3×#948—42no—
70C3×#926D411yescharacteristic
71C2×C3×#208—21no—
72C2×C3×#208—42no—
73C2×C3×#208D411yescharacteristic
74C2×C3×Dic12C2311yescharacteristic
75C3×#904—21no—
76C3×#904—21no—
77C3×#904C2×C412yes—
78C3×#904C2×C412yes—
79C2×C3×D24C2311yescharacteristic
80C2×C3×#204—21no—
81#67⋊Dic3—42no—
82Dic3×D12—22no—
83D3×C4⋊Dic3—41no—
84Dic3×Dic6—22no—
85#63841—41no—
86#63644—21no—
87#63644C2312yes—
88#63639—21no—
89#63639C2312yes—
90C2×C3⋊(C3⋊C16)—21no—
91C3×#837—24no—
92C3×#829C2×C414yescomplemented
93C3×#828C2×C414yescomplemented
94C3×#827C2×C414yescomplemented
95C3×#826C2×C414yescomplemented
96C3×#819—21no—
97C3×#819C2312yes—
98C3×#815C2312yes—
99C3×C8×Dic3D412yes—
100C3×#812C2×C412yescomplemented
101C3×#812C2312yes—
102C2×C3×C3⋊C16C2×C412yescomplemented
103#63566—22no—
104#63563—22no—
105#33469—91noSylow
106C2×C3×#135—21no—
107C2×C3×#135—31no—
108C2×C3×#135C2×D311yescharacteristic
109C2×C3×#135C2×D311yescharacteristic
110C3×#568—61no—
111#5827—61no—
112#5819—21no—
113C2×#904C2×D311yescharacteristic
114#5523—61no—
115C3×#510—32no—
116C3×#510—32no—
117C3×#509—32no—
118C3×#509—32no—
119C3×#508—34no—
120C2×C3×M32—31no—
121C3×#444—34no—
122C3×#443—62no—
123C2×C3×#108—31no—
124C3×#421—61no—
125C3×#405—31no—
126#5236—21no—
127#5232—61no—
128#5197C2×D314yes—
129#5196—22no—
130#5195C2×D312yes—
131#5194Dic314yescomplemented
132#5193C2×D312yes—
133#5184—32no—
134#5179Dic312yescomplemented
135Dic3×SD16—62no—
136#5152—32no—
137#5147Dic312yescomplemented
138#5133—61no—
139C2×#819C2×D311yescharacteristic
140C2×#817—31no—
141C2×#817—31no—
142C2×#817—61no—
143#5101C2×D311yescharacteristic
144C2×#812—31no—
145C2×#812—31no—
146C2×#812—61no—
147C2×#812C2×D311yescharacteristic
148#4716—32no—
149#4711—32no—
150C4×#204—62no—
151#4566—34no—
152#4566—34no—
153#4566—64no—
154#4565—32no—
155#4563—32no—
156#4513—34no—
157#4512—34no—
158#4496—32no—
159#4495—32no—
160#4494—34no—
161#4466—34no—
162C32×#41—22no—
163C32×#41—22no—
164C32×#41—41no—
165C32×#41—41no—
166C2×C32×Q8—21no—
167C2×C32×D4—21no—
168C2×C32×D4—41no—
169C22×C32×C4—41no—
170C22×C32×C4C2×D411yescharacteristic
171C22×C3⋊Dic3—41no—
172C2×C3×#67—41no—
173C3×#235—22no—
174C3×#235—22no—
175C3×#235—41no—
176C3×#235—41no—
177C2×C3×D12—21no—
178C2×C3×C4×D3—41no—
179C2×C3×Dic6—21no—
180C2×D3×Dic3—42no—
181C32×Q16—21no—
182C32×Q16C22×C412yes—
183C32×SD16—22no—
184C32×SD16—22no—
185C32×D8—21no—
186C32×D8C22×C412yes—
187C2×C32×C8C22×C411yescharacteristic
188C2×C32×C8C22×C411yescharacteristic
189C2×C32×C8C2×D411yescharacteristic
190C2×C32×C8#4111yescharacteristic
191C2×C32×C8#4111yescharacteristic
192C2×C32×C8C2411yescharacteristic
193C4⋊(C3⋊Dic3)—22no—
194C4⋊(C3⋊Dic3)—41no—
195C3×#217—21no—
196C3×C4⋊Dic3—21no—
197C3×C4×Dic3C2×D412yes—
198C3×#208—21no—
199C3×#208—21no—
200C3×#208—22no—
201C3×#208—44no—
202C3×#208—41no—
203C2×C3×C3⋊C8—44no—
204C2×C3×C3⋊C8—41no—
205C2×C3×C3⋊C8C2×D412yes—
206C3×Dic12—21no—
207C3×Dic12C22×C412yes—
208C3×D24—21no—
209C3×D24C22×C412yes—
210C3×#204—22no—
211C3×#204—22no—
212Dic3⋊Dic3—42no—
213(C2×D3)⋊Dic3—42no—
214Dic32—42no—
215C3⋊(C3⋊C16)—22no—
216C3×C3⋊C16C22×C414yes—
217#3414—31no—
218#2957—31no—
219#2952—91no—
220AGL(1,ℤ/16)—94no—
221#2180—94no—
222C2×#365—91no—
223#2148—91no—
224C2×#360—91no—
225#2110—91no—
226C2×C3×#41—21no—
227C2×C3×#41—21no—
228C2×C3×#41—41no—
229C2×C3×#41—61no—
230C2×#235—21no—
231C3×#135—21no—
232C3×#135—21no—
233C3×#135—21no—
234C3×#135—21no—
235C3×#135—22no—
236C3×#135—22no—
237C3×#135—32no—
238C3×#135—32no—
239C3×#135—41no—
240C3×#135—41no—
241C3×#135—61no—
242C3×#135—61no—
243C3×#135C4×D312yescomplemented
244C3×#135C2×Dic312yescomplemented
245C3×#135C22×D312yes—
246C3×#135C22×D312yes—
247C2×C3×Q16—21no—
248C2×C3×Q16—31no—
249C2×C3×Q16C4×D311yescharacteristic, complemented
250C2×C3×Q16C2×Dic311yescharacteristic, complemented
251C2×C3×SD16—21no—
252C2×C3×SD16—21no—
253C2×C3×SD16—41no—
254C2×C3×SD16—61no—
255C2×C3×D8—21no—
256C2×C3×D8—31no—
257C2×C3×D8C4×D311yescharacteristic, complemented
258C2×C3×D8C2×Dic311yescharacteristic, complemented
259C3×#131—64no—
260C3×#131—122no—
261C2×C3×M16—31no—
262C2×C3×M16—61no—
263C2×C3×M16—122no—
264C22×C3×C8—21no—
265C22×C3×C8C22×D311yescharacteristic
266C22×C3×C8C22×D311yescharacteristic
267C3×#117—31no—
268#948—24no—
269#948—42no—
270Q8×Dic3—62no—
271D4×Dic3—62no—
272D4×Dic3—122no—
273#926—121no—
274#926#6711yescharacteristic
275C2×C4⋊Dic3—61no—
276C2×C4⋊Dic3—61no—
277C2×C4⋊Dic3—121no—
278C2×C4⋊Dic3—121no—
279C2×#208—21no—
280C2×#208—42no—
281C2×#208#6711yescharacteristic
282C2×Dic12C22×D311yescharacteristic
283#904—21no—
284#904—21no—
285#904C2×Dic312yes—
286#904C2×Dic312yes—
287C2×D24C22×D311yescharacteristic
288C2×#204—21no—
289#892—121no—
290D3×C4⋊C4—121no—
291#67⋊C4—122no—
292C4×D12—62no—
293C4×Dic6—62no—
294C3×Q32—34no—
295C3×SD32—34no—
296C3×SD32—34no—
297C3×D16—34no—
298C3×M32—32no—
299C3×M32—32no—
300C2×C3×C16—32no—
301C3×#108—32no—
302C3×#108—61no—
303C3×#104—64no—
304C3×#97—32no—
305C3×C4×C8—32no—
306#837—24no—
307#835—62no—
308#832—62no—
309#829C2×Dic314yescomplemented
310#828C2×Dic314yescomplemented
311#827C2×Dic314yescomplemented
312#826C2×Dic314yescomplemented
313#821—62no—
314#819—21no—
315#819C22×D312yes—
316#817—32no—
317#817—32no—
318#817—62no—
319#817—61no—
320#817—61no—
321#817—121no—
322#816—62no—
323#815C22×D312yes—
324C8×Dic3#6712yes—
325#812—32no—
326#812—32no—
327#812—62no—
328#812—61no—
329#812—61no—
330#812—121no—
331#812C2×Dic312yescomplemented
332#812C22×D312yes—
333C2×C3⋊C16—61no—
334C2×C3⋊C16—61no—
335C2×C3⋊C16—121no—
336C2×C3⋊C16C2×Dic312yescomplemented
337C23×C32—41no—
338C23×C32AGL(1,ℤ/8)11yescharacteristic
339C22×C3×D3—41no—
340C32×Q8—22no—
341C32×Q8—41no—
342C32×D4—22no—
343C32×D4—42no—
344C32×D4—42no—
345C32×D4—41no—
346C2×C32×C4—41no—
347C2×C32×C4—42no—
348C2×C32×C4—42no—
349C2×C32×C4C4×D411yescharacteristic
350C2×C32×C4C4×D411yescharacteristic
351C2×C32×C4AGL(1,ℤ/8)11yescharacteristic
352C2×C32×C4AGL(1,ℤ/8)11yescharacteristic
353C2×C32×C4AGL(1,ℤ/8)11yescharacteristic
354C2×C32×C4C22×D411yescharacteristic
355C2×C3⋊Dic3—42no—
356C2×C3⋊Dic3—161no—
357C3×#67—42no—
358C3×#67—42no—
359C2×C3×Dic3—22no—
360C2×C3×Dic3—41no—
361C3×D12—22no—
362C3×D12—41no—
363C3×C4×D3—42no—
364C3×C4×D3—42no—
365C3×Dic6—22no—
366C3×Dic6—41no—
367D3×Dic3—162no—
368C32×C8C4×D411yescharacteristic
369C32×C8C4×D411yescharacteristic
370C32×C8C23×C411yescharacteristic
371C32×C8C2×#4111yescharacteristic
372C3×C3⋊C8—22no—
373C3×C3⋊C8—42no—
374C2×#135—31no—
375C2×#135D3211yescharacteristic
376#568—61no—
377#520—181no—
378#510—32no—
379#510—32no—
380#509—32no—
381#509—32no—
382#508—34no—
383C2×M32—31no—
384C2×M32—91no—
385#444—34no—
386#443—62no—
387#442—92no—
388#441—92no—
389C4×SD16—182no—
390C2×#108—31no—
391C2×#106—91no—
392#421—61no—
393#417—181no—
394#405—31no—
395#365—94no—
396#362—92no—
397#361—92no—
398#360—94no—
399#347—94no—
400C3×#41—22no—
401C3×#41—22no—
402C3×#41—22no—
403C3×#41—22no—
404C3×#41—42no—
405C3×#41—42no—
406C3×#41—41no—
407C3×#41—41no—
408C3×#41—41no—
409C3×#41—41no—
410C3×#41—62no—
411C3×#41—62no—
412C3×#41—81no—
413C3×#41—81no—
414C3×#41—121no—
415C3×#41—121no—
416C2×C3×Q8—21no—
417C2×C3×Q8—21no—
418C2×C3×Q8—41no—
419C2×C3×Q8—61no—
420C2×C3×D4—21no—
421C2×C3×D4—21no—
422C2×C3×D4—41no—
423C2×C3×D4—41no—
424C2×C3×D4—41no—
425C2×C3×D4—61no—
426C2×C3×D4—81no—
427C2×C3×D4—121no—
428C22×C3×C4—21no—
429C22×C3×C4—41no—
430C22×C3×C4—41no—
431C22×C3×C4—81no—
432C22×C3×C4—121no—
433C22×C3×C4D3×D411yescharacteristic
434C22×C3×C4C2×#6711yescharacteristic
435C2×#67—41no—
436C22×Dic3—122no—
437C22×Dic3—121no—
438C22×Dic3—121no—
439C22×Dic3—241no—
440#235—22no—
441#235—22no—
442#235—41no—
443#235—41no—
444C2×D12—21no—
445C2×C4×D3—41no—
446C2×C4×D3—122no—
447C2×Dic6—21no—
448C3×Q16—21no—
449C3×Q16—21no—
450C3×Q16—22no—
451C3×Q16—32no—
452C3×Q16—41no—
453C3×Q16—61no—
454C3×Q16C2×C4×D312yes—
455C3×Q16C22×Dic312yes—
456C3×SD16—22no—
457C3×SD16—22no—
458C3×SD16—22no—
459C3×SD16—22no—
460C3×SD16—42no—
461C3×SD16—42no—
462C3×SD16—62no—
463C3×SD16—62no—
464C3×D8—21no—
465C3×D8—21no—
466C3×D8—22no—
467C3×D8—32no—
468C3×D8—41no—
469C3×D8—61no—
470C3×D8C2×C4×D312yes—
471C3×D8C22×Dic312yes—
472C3×M16—61no—
473C3×M16—61no—
474C3×M16—62no—
475C3×M16—124no—
476C3×M16—121no—
477C2×C3×C8—21no—
478C2×C3×C8—21no—
479C2×C3×C8—21no—
480C2×C3×C8—21no—
481C2×C3×C8—21no—
482C2×C3×C8—21no—
483C2×C3×C8—32no—
484C2×C3×C8—124no—
485C2×C3×C8—121no—
486C2×C3×C8C2×C4×D311yescharacteristic
487C2×C3×C8C2×C4×D311yescharacteristic
488C2×C3×C8#23511yescharacteristic
489C2×C3×C8#23511yescharacteristic
490C2×C3×C8D3×D411yescharacteristic
491C2×C3×C8#23711yescharacteristic
492C2×C3×C8#23711yescharacteristic
493C2×C3×C8C22×Dic311yescharacteristic
494C2×C3×C8C22×Dic311yescharacteristic
495C2×C3×C8C2×#6711yescharacteristic
496C2×C3×C8C23×D311yescharacteristic
497C2×C3×C8C23×D311yescharacteristic
498C3×C4⋊C4—61no—
499C3×C22⋊C4—61no—
500C3×C42—32no—
501#217—21no—
502#217—122no—
503(C2×D3)⋊C4—122no—
504C4⋊Dic3—21no—
505C4⋊Dic3—62no—
506C4⋊Dic3—62no—
507C4⋊Dic3—122no—
508C4⋊Dic3—122no—
509C4⋊Dic3—121no—
510C4⋊Dic3—121no—
511C4⋊Dic3—241no—
512Dic3⋊C4—122no—
513C4×Dic3—122no—
514C4×Dic3—122no—
515C4×Dic3C2×#6712yes—
516#208—21no—
517#208—21no—
518#208—22no—
519#208—44no—
520#208—41no—
521C2×C3⋊C8—44no—
522C2×C3⋊C8—41no—
523C2×C3⋊C8C2×#6712yes—
524Dic12—21no—
525Dic12C22×Dic312yes—
526D24—21no—
527D24C22×Dic312yes—
528#204—22no—
529#204—22no—
530C3×C16—34no—
531C3⋊C16—62no—
532C3⋊C16—62no—
533C3⋊C16—122no—
534C3⋊C16C22×Dic314yes—
535C22×C32—41no—
536C22×C32—42no—
537C22×C32—161no—
538C22×C32#44211yescharacteristic
539C22×C32#44211yescharacteristic
540C22×C32C2×AGL(1,ℤ/8)11yescharacteristic
541C2×C3×D3—42no—
542C2×C3×D3—81no—
543C2×C3×D3—81no—
544C32×C4—42no—
545C32×C4#44211yescharacteristic
546C32×C4#44211yescharacteristic
547C32×C4C2×C4×D411yescharacteristic
548C32×C4C2×AGL(1,ℤ/8)11yescharacteristic
549C3⋊Dic3—82no—
550C3×Dic3—42no—
551C3×Dic3—42no—
552C2×#41—21no—
553C2×#41—61no—
554#135—21no—
555#135—21no—
556#135—32no—
557#135—32no—
558#135—61no—
559#135—61no—
560#135D3×Dic312yescomplemented
561#135C2×D3212yes—
562C2×Q16—31no—
563C2×Q16D3×Dic311yescharacteristic, complemented
564C2×SD16—21no—
565C2×SD16—61no—
566C2×D8—31no—
567C2×D8D3×Dic311yescharacteristic, complemented
568#131—64no—
569#131—122no—
570C2×M16—31no—
571C2×M16—61no—
572C2×M16—122no—
573C22×C8C2×D3211yescharacteristic
574C4×Q8—182no—
575C4×D4—182no—
576C4×D4—362no—
577#117—31no—
578#117—361no—
579C2×C4⋊C4—181no—
580C2×C4⋊C4—361no—
581Q32—34no—
582SD32—34no—
583SD32—34no—
584D16—34no—
585M32—32no—
586M32—32no—
587M32—92no—
588M32—181no—
589C2×C16—32no—
590C2×C16—181no—
591#108—32no—
592#108—61no—
593#106—92no—
594#106—181no—
595#104—64no—
596#103—182no—
597#102—182no—
598#97—32no—
599C4×C8—32no—
600C23×C3—21no—
601C23×C3—41no—
602C23×C3—41no—
603C23×C3—81no—
604C23×C3—121no—
605C23×C3#91111yescharacteristic
606C23×C3#94911yescharacteristic
607C22×D3—41no—
608C3×Q8—22no—
609C3×Q8—22no—
610C3×Q8—42no—
611C3×Q8—41no—
612C3×Q8—41no—
613C3×Q8—62no—
614C3×Q8—81no—
615C3×Q8—121no—
616C3×D4—22no—
617C3×D4—22no—
618C3×D4—42no—
619C3×D4—42no—
620C3×D4—42no—
621C3×D4—42no—
622C3×D4—42no—
623C3×D4—41no—
624C3×D4—41no—
625C3×D4—62no—
626C3×D4—81no—
627C3×D4—82no—
628C3×D4—82no—
629C3×D4—122no—
630C3×D4—122no—
631C3×D4—121no—
632C2×C3×C4—21no—
633C2×C3×C4—21no—
634C2×C3×C4—21no—
635C2×C3×C4—21no—
636C2×C3×C4—21no—
637C2×C3×C4—21no—
638C2×C3×C4—41no—
639C2×C3×C4—41no—
640C2×C3×C4—42no—
641C2×C3×C4—42no—
642C2×C3×C4—42no—
643C2×C3×C4—42no—
644C2×C3×C4—62no—
645C2×C3×C4—82no—
646C2×C3×C4—82no—
647C2×C3×C4—81no—
648C2×C3×C4—121no—
649C2×C3×C4—122no—
650C2×C3×C4—122no—
651C2×C3×C4#91111yescharacteristic
652C2×C3×C4#91111yescharacteristic
653C2×C3×C4#91111yescharacteristic
654C2×C3×C4C4×#6711yescharacteristic
655C2×C3×C4C4×#6711yescharacteristic
656C2×C3×C4#93211yescharacteristic
657C2×C3×C4#93211yescharacteristic
658C2×C3×C4D4×Dic311yescharacteristic
659C2×C3×C4D4×Dic311yescharacteristic
660C2×C3×C4#94911yescharacteristic
661C2×C3×C4C2×D3×D411yescharacteristic
662C2×C3×C4C22×#6711yescharacteristic
663#67—42no—
664#67—42no—
665C2×Dic3—22no—
666C2×Dic3—41no—
667C2×Dic3—122no—
668C2×Dic3—122no—
669C2×Dic3—242no—
670C2×Dic3—482no—
671C2×Dic3—481no—
672C2×Dic3—481no—
673C2×Dic3—482no—
674D12—22no—
675D12—41no—
676C4×D3—42no—
677C4×D3—42no—
678C4×D3—482no—
679Dic6—22no—
680Dic6—41no—
681C3×C8—21no—
682C3×C8—21no—
683C3×C8—21no—
684C3×C8—21no—
685C3×C8—62no—
686C3×C8—122no—
687C3×C8C4×#6711yescharacteristic
688C3×C8C4×#6711yescharacteristic
689C3×C8D4×Dic311yescharacteristic
690C3×C8D4×Dic311yescharacteristic
691C3×C8C22×C4×D311yescharacteristic
692C3×C8C2×#23511yescharacteristic
693C3×C8C2×#23711yescharacteristic
694C3×C8C23×Dic311yescharacteristic
695C3⋊C8—22no—
696C3⋊C8—42no—
697C2×C32—21no—
698C2×C32—21no—
699C2×C32—21no—
700C2×C32—82no—
701C2×C32C2×#44211yescharacteristic
702C3×D3—82no—
703#41—22no—
704#41—22no—
705#41—41no—
706#41—41no—
707#41—62no—
708#41—62no—
709#41—121no—
710#41—121no—
711C2×Q8—21no—
712C2×Q8—61no—
713C2×D4—21no—
714C2×D4—41no—
715C2×D4—61no—
716C2×D4—121no—
717C22×C4—41no—
718C22×C4—121no—
719C22×C4—362no—
720C22×C4—361no—
721C22×C4D3×#6711yescharacteristic
722Q16—21no—
723Q16—32no—
724Q16—61no—
725Q16C2×D3×Dic312yes—
726SD16—22no—
727SD16—22no—
728SD16—62no—
729SD16—62no—
730D8—21no—
731D8—32no—
732D8—61no—
733D8C2×D3×Dic312yes—
734M16—61no—
735M16—61no—
736M16—62no—
737M16—124no—
738M16—121no—
739C2×C8—32no—
740C2×C8—124no—
741C2×C8—121no—
742C2×C8C2×D3×Dic311yescharacteristic
743C2×C8C2×D3×Dic311yescharacteristic
744C2×C8#380411yescharacteristic
745C2×C8#380411yescharacteristic
746C2×C8D3×#6711yescharacteristic
747C2×C8C22×D3211yescharacteristic
748C4⋊C4—61no—
749C4⋊C4—182no—
750C4⋊C4—362no—
751C4⋊C4—361no—
752C22⋊C4—61no—
753C22⋊C4—362no—
754C42—32no—
755C42—362no—
756C16—34no—
757C16—182no—
758C22×C3—21no—
759C22×C3—21no—
760C22×C3—21no—
761C22×C3—41no—
762C22×C3—41no—
763C22×C3—42no—
764C22×C3—42no—
765C22×C3—42no—
766C22×C3—82no—
767C22×C3—122no—
768C22×C3—161no—
769C22×C3—161no—
770C22×C3—162no—
771C22×C3—241no—
772C22×C3—241no—
773C22×C3#501411yescharacteristic
774C22×C3#501411yescharacteristic
775C22×C3#515211yescharacteristic
776C22×C3#515211yescharacteristic
777C22×C3C2×#91111yescharacteristic
778C22×C3C2×#94911yescharacteristic
779C2×D3—42no—
780C2×D3—81no—
781C2×D3—81no—
782C3×C4—21no—
783C3×C4—21no—
784C3×C4—21no—
785C3×C4—21no—
786C3×C4—42no—
787C3×C4—42no—
788C3×C4—82no—
789C3×C4—122no—
790C3×C4—122no—
791C3×C4#501411yescharacteristic
792C3×C4#501411yescharacteristic
793C3×C4#515211yescharacteristic
794C3×C4#515211yescharacteristic
795C3×C4C2×#91111yescharacteristic
796C3×C4C2×C4×#6711yescharacteristic
797C3×C4C2×#93211yescharacteristic
798C3×C4C2×D4×Dic311yescharacteristic
799Dic3—42no—
800Dic3—42no—
801Dic3—242no—
802Dic3—242no—
803Dic3—482no—
804C32#3346911yescharacteristic, complemented, Sylow
805C23—41no—
806C23—121no—
807C23#6392511yescharacteristic
808Q8—22no—
809Q8—41no—
810Q8—62no—
811Q8—121no—
812D4—22no—
813D4—42no—
814D4—42no—
815D4—41no—
816D4—62no—
817D4—122no—
818D4—122no—
819D4—121no—
820C2×C4—41no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—62no—
824C2×C4—121no—
825C2×C4—122no—
826C2×C4—122no—
827C2×C4—362no—
828C2×C4—1442no—
829C2×C4—1441no—
830C2×C4#6392511yescharacteristic
831C2×C4#6393211yescharacteristic
832C2×C4#6393211yescharacteristic
833C2×C4Dic3×#6711yescharacteristic
834C2×C4Dic3×#6711yescharacteristic
835C2×C4C2×D3×#6711yescharacteristic
836C8—62no—
837C8—122no—
838C8Dic3×#6711yescharacteristic
839C8Dic3×#6711yescharacteristic
840C8C22×D3×Dic311yescharacteristic
841C8C2×#380411yescharacteristic
842C2×C3—22no—
843C2×C3—21no—
844C2×C3—21no—
845C2×C3—21no—
846C2×C3—21no—
847C2×C3—21no—
848C2×C3—21no—
849C2×C3—21no—
850C2×C3—41no—
851C2×C3—41no—
852C2×C3—82no—
853C2×C3—82no—
854C2×C3—162no—
855C2×C3—242no—
856C2×C3C2×#501411yescharacteristic
857C2×C3C2×#515211yescharacteristic
858D3—82no—
859C22—41no—
860C22—42no—
861C22—122no—
862C22—161no—
863C22—241no—
864C22—241no—
865C22#1059143011yescharacteristic
866C22#1059143011yescharacteristic
867C22C2×#6392511yescharacteristic
868C4—42no—
869C4—122no—
870C4—122no—
871C4—722no—
872C4#1059143011yescharacteristic
873C4#1059143011yescharacteristic
874C4C2×#6393211yescharacteristic
875C4C2×Dic3×#6711yescharacteristic
876C3—21no—
877C3#1094864611yescharacteristic, complemented
878C3#1094864711yescharacteristic, complemented
879C2—21no—
880C2—21no—
881C2—21no—
882C2—82no—
883C2—242no—
884C2C2×#1059143011yescharacteristic
subgroupG/H
centerC2C2×#10591430
commutatorC32×C8C23×C4
FrattiniC2×C8C22×D32
FittingC2×C32×#135C22
socleC2×C32C2×#442
prime radicalC3×#83894C2
cosocleC2×C32×C8C24
hypercenterC2×#135D32
hypocenterC32#33469
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ C22×C8 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
2. C3×#83910C2semidirect
3. #11860967C2semidirect
4. #11797969C2semidirect
5. #11797923C2semidirect
6. C2×#10589137C2semidirect
7. #11796953C2semidirect
8. C2×#10589432C2semidirect
9. #11795946C2semidirect
22. C3×#5194C4semidirect
24. C3×#5179C4semidirect
25. C3×#5147C4semidirect
30. #10590812C22semidirect
31. #10590771C22semidirect
34. #10589137C22semidirect
35. #10589129C22semidirect
36. #10589126C22semidirect
37. #10589105C22semidirect
40. #83910D3semidirect
61. C32×#135C2×C4semidirect
63. C2×C32×Q16C2×C4semidirect
65. C2×C32×D8C2×C4semidirect
92. C3×#829C2×C4semidirect
93. C3×#828C2×C4semidirect
94. C3×#827C2×C4semidirect
95. C3×#826C2×C4semidirect
100. C3×#812C2×C4semidirect
102. C2×C3×C3⋊C16C2×C4semidirect
131. #5194Dic3semidirect
134. #5179Dic3semidirect
137. #5147Dic3semidirect
243. C3×#135C4×D3semidirect
244. C3×#135C2×Dic3semidirect
249. C2×C3×Q16C4×D3semidirect
250. C2×C3×Q16C2×Dic3semidirect
257. C2×C3×D8C4×D3semidirect
258. C2×C3×D8C2×Dic3semidirect
309. #829C2×Dic3semidirect
310. #828C2×Dic3semidirect
311. #827C2×Dic3semidirect
312. #826C2×Dic3semidirect
331. #812C2×Dic3semidirect
336. C2×C3⋊C16C2×Dic3semidirect
560. #135D3×Dic3semidirect
563. C2×Q16D3×Dic3semidirect
567. C2×D8D3×Dic3semidirect
804. C32#33469semidirect
877. C3#10948646semidirect
878. C3#10948647semidirect

Maximal subgroups

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

subgroupindex
C3×#838942
C3×#839102
#118609672
#117979692
#117979232
C2×#105891372
#117969532
C2×#105894322
#117959462
#109486473
#109486463