Finite Group Databasebeta

← #72222813

Subgroups — #72222813

Order 2304.

1368 conjugacy classes of subgroups.

The subgroup lattice has 857 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11899653C211yesmaximal, characteristic
2#11861236C211yesmaximal, characteristic, complemented
3C3×#79106C211yesmaximal, characteristic, complemented
4#11797968C214yesmaximal, complemented
5#11797922C214yesmaximal, complemented
6C2×#10589353C211yesmaximal, characteristic, complemented
7#11796951C211yesmaximal, characteristic, complemented
8C2×C3×#4488C211yesmaximal, characteristic, complemented
9#11795946C211yesmaximal, characteristic, complemented
10#10948644—31nomaximal
11#10948642—31nomaximal
12C2×C3×#904C2211yescharacteristic
13C2×C3×#904C2211yescharacteristic
14C3×#5504—21no—
15#10594776—21no—
16C2×C32×#106C2211yescharacteristic
17C2×#63646C2211yescharacteristic
18C2×#63639C2211yescharacteristic
19C3×#5101C2211yescharacteristic
20C2×C3×#812C2211yescharacteristic
21C3×#4966—21no—
22C3×#4869C2212yescomplemented
23C3×#4853C2212yescomplemented
24C3×#4852—22no—
25#10591111—21no—
26#10590916C2214yes—
27#10590915—22no—
28#10590636C412yescomplemented
29#10590636C2212yes—
30#10590630C412yescomplemented
31#10590630C2212yes—
32#10590629C414yescomplemented
33#10589353C2214yescomplemented
34C3×#4488C2214yes—
35#10589130C2212yescomplemented
36#10589127C2212yescomplemented
37#10589105C2214yescomplemented
38C3×#2952—31no—
39#83910—31no—
40#83894—31no—
41#83894—31no—
42#79106D311yescharacteristic, complemented
43#78580—31no—
44C2×C3×#360—31no—
45#72081—31no—
46#71442—31no—
47#71425—31no—
48#70918—34no—
49#70917—34no—
50C2×#4488D311yescharacteristic, complemented
51C2×#4487—31no—
52C2×#4487—31no—
53C2×#4487—61no—
54#69884—31no—
55#69249—34no—
56#69248—34no—
57C2×C3×#235—21no—
58C2×C3×#235—21no—
59C22×C32×C8C2311yescharacteristic
60C2×C32×C4⋊C4—21no—
61C2×#3748—21no—
62C3×C4×#67—42no—
63C3×#926D411yescharacteristic
64C2×C3×#208D411yescharacteristic
65C2×C3×Dic12C2×C411yescharacteristic, complemented
66C2×C3×Dic12C2311yescharacteristic
67C3×#904—21no—
68C3×#904—21no—
69C3×#904—21no—
70C3×#904—21no—
71C3×#904C2×C412yes—
72C3×#904C2×C412yes—
73C3×#904C2×C412yescomplemented
74C3×#904C2312yes—
75C2×C3×D24C2×C411yescharacteristic, complemented
76C2×C3×D24C2311yescharacteristic
77C2×C3×#204—21no—
78C2×C3×#204—21no—
79C3×#893—22no—
80C3×#892—41no—
81C3×D3×C4⋊C4—41no—
82C3×#887—22no—
83#63815—42no—
84#63814—24no—
85D3×#208—42no—
86C32×#106—21no—
87C32×#106C2312yes—
88#63646—21no—
89#63646C2312yes—
90#63639C2×C412yescomplemented
91#63639C2312yes—
92C2×C3⋊(C3⋊C16)C2×C412yescomplemented
93C3×#815C2312yes—
94C3×C8×Dic3D412yes—
95C3×#812—21no—
96C3×#812C2312yes—
97C2×C3×C3⋊C16—21no—
98C3×#810—22no—
99C3×#809—22no—
100#63569—24no—
101#63550C2×C414yescomplemented
102#63547C2×C414yescomplemented
103#63547C2×C414yescomplemented
104#63545C2×C414yescomplemented
105#33469—91noSylow
106C2×C3×#135—31no—
107C2×C3×#135—31no—
108C3×#520—61no—
109#5819—61no—
110#5745—61no—
111C2×#904C2×D311yescharacteristic
112C2×#904C2×D311yescharacteristic
113#5504—21no—
114C2×C3×M32—31no—
115C3×#442—32no—
116C3×#441—32no—
117C3×C4×SD16—62no—
118C2×C3×#106—21no—
119C2×C3×#106C2×D311yescharacteristic
120C2×C3×#106C2×D311yescharacteristic
121C3×#417—61no—
122C3×#405—31no—
123#5236—61no—
124#5197—34no—
125#5196—62no—
126#5195—32no—
127#5195—32no—
128#5194—34no—
129#5194—34no—
130#5193—32no—
131#5193—32no—
132#5179—32no—
133#5179—32no—
134#5147—32no—
135#5147—32no—
136C2×#819—31no—
137C2×#819—31no—
138C2×#819—61no—
139#5101C2×D311yescharacteristic
140C2×#812—31no—
141C2×#812—31no—
142C2×#812—61no—
143C2×#812C2×D311yescharacteristic
144#5005—61no—
145#4966—21no—
146#4869C2×D312yescomplemented
147#4853C2×D312yescomplemented
148#4852—22no—
149#4717—34no—
150#4700—62no—
151C3×#360—34no—
152#4565—32no—
153#4563—32no—
154#4517—32no—
155#4516—32no—
156#4512—34no—
157#4488C2×D314yes—
158#4487—34no—
159#4487—34no—
160#4487—64no—
161#4466—34no—
162C22×C32×C4—41no—
163C22×C32×C4C2×D411yescharacteristic
164C2×C3×#67—41no—
165C2×C3×#67—41no—
166C3×#235—22no—
167C3×#235—22no—
168C3×#235—22no—
169C3×#235—22no—
170C3×#235—41no—
171C3×#235—41no—
172C3×#235—41no—
173C3×#235—41no—
174C2×C3×D12—21no—
175C2×C3×D12—21no—
176C2×C3×C4×D3—41no—
177C2×C3×C4×D3—41no—
178C2×C3×C4×D3—42no—
179C2×C3×Dic6—21no—
180C2×C3×Dic6—21no—
181C2×C32×C8C22×C411yescharacteristic
182C2×C32×C8C22×C411yescharacteristic
183C2×C32×C8C2×D411yescharacteristic
184C2×C32×C8#4111yescharacteristic
185C2×C32×C8#4111yescharacteristic
186C2×C32×C8C2411yescharacteristic
187C32×C4⋊C4—22no—
188C32×C4⋊C4—41no—
189#3748—22no—
190#3748—41no—
191C2×C3⋊(C3⋊C8)—41no—
192C3×#217—21no—
193C3×(C2×D3)⋊C4—42no—
194C3×C4⋊Dic3—21no—
195C3×Dic3⋊C4—42no—
196C3×C4×Dic3—42no—
197C3×C4×Dic3C2×D412yes—
198C3×#208—21no—
199C3×#208—21no—
200C2×C3×C3⋊C8C2×D412yes—
201C3×Dic12—21no—
202C3×Dic12—21no—
203C3×Dic12C22×C412yes—
204C3×Dic12C22×C412yes—
205C3×D24—21no—
206C3×D24—21no—
207C3×D24C22×C412yes—
208C3×D24C22×C412yes—
209C3×#204—22no—
210C3×#204—22no—
211C3×#204—22no—
212C3×#204—22no—
213#3711—44no—
214D3×C3⋊C8—44no—
215C3⋊(C3⋊C16)C22×C414yes—
216C3×C3⋊C16—22no—
217#3414—91no—
218#2957—91no—
219#2952—31no—
220AGL(1,ℤ/16)—94no—
221#2180—94no—
222C2×#365—91no—
223#2148—91no—
224C2×#360—31no—
225#2110—91no—
226C2×C3×#41—61no—
227C2×C3×#41—61no—
228C2×#235—21no—
229C2×#235—21no—
230C3×#135—32no—
231C3×#135—32no—
232C3×#135—32no—
233C3×#135—32no—
234C3×#135—61no—
235C3×#135—61no—
236C3×#135—61no—
237C3×#135—61no—
238C2×C3×Q16—31no—
239C2×C3×Q16—31no—
240C2×C3×SD16—61no—
241C2×C3×SD16—61no—
242C2×C3×D8—31no—
243C2×C3×D8—31no—
244C2×C3×M16—31no—
245C22×C3×C8—21no—
246C22×C3×C8C22×D311yescharacteristic
247C22×C3×C8C22×D311yescharacteristic
248C3×C4×Q8—62no—
249C3×C4×D4—62no—
250C3×C4×D4—122no—
251C3×#117—31no—
252C3×#117—121no—
253C2×C3×C4⋊C4—21no—
254C2×C3×C4⋊C4—21no—
255C2×C3×C4⋊C4—41no—
256C2×C3×C4⋊C4—121no—
257#948—64no—
258#948—122no—
259C4×#67—42no—
260#926#6711yescharacteristic
261C2×#208—61no—
262C2×#208—61no—
263C2×#208—121no—
264C2×#208—122no—
265C2×#208#6711yescharacteristic
266#907—122no—
267D3×M16—122no—
268C2×Dic12C4×D311yescharacteristic, complemented
269C2×Dic12C22×D311yescharacteristic
270#904—21no—
271#904—21no—
272#904—21no—
273#904—21no—
274#904C4×D312yes—
275#904C4×D312yes—
276#904C4×D312yescomplemented
277#904C22×D312yes—
278C2×D24C4×D311yescharacteristic, complemented
279C2×D24C22×D311yescharacteristic
280C2×#204—21no—
281C2×#204—21no—
282#901—64no—
283#893—22no—
284#892—41no—
285D3×C4⋊C4—41no—
286#887—22no—
287C3×M32—32no—
288C3×M32—61no—
289C2×C3×C16—61no—
290C3×#106—21no—
291C3×#106—21no—
292C3×#106—22no—
293C3×#106—41no—
294C3×#106C22×D312yes—
295C3×#106C22×D312yes—
296C3×#103—62no—
297C3×#102—62no—
298C3×#97—32no—
299C3×C4×C8—32no—
300#837—64no—
301#829—34no—
302#829—34no—
303#828—34no—
304#828—34no—
305#827—34no—
306#827—34no—
307#826—34no—
308#826—34no—
309#819—32no—
310#819—32no—
311#819—62no—
312#819—61no—
313#819—61no—
314#819—121no—
315#815C22×D312yes—
316C8×Dic3#6712yes—
317#812—21no—
318#812—32no—
319#812—32no—
320#812—32no—
321#812—32no—
322#812—62no—
323#812—62no—
324#812C22×D312yes—
325C2×C3⋊C16—21no—
326C2×C3⋊C16—32no—
327C2×C3⋊C16—32no—
328C2×C3⋊C16—62no—
329#810—22no—
330#809—22no—
331#805—64no—
332C23×C32AGL(1,ℤ/8)11yescharacteristic
333C22×C3×D3—41no—
334C22×C3×D3—41no—
335C2×C32×C4—42no—
336C2×C32×C4—161no—
337C2×C32×C4C4×D411yescharacteristic
338C2×C32×C4C4×D411yescharacteristic
339C2×C32×C4AGL(1,ℤ/8)11yescharacteristic
340C2×C32×C4AGL(1,ℤ/8)11yescharacteristic
341C2×C32×C4AGL(1,ℤ/8)11yescharacteristic
342C2×C32×C4C22×D411yescharacteristic
343C3×#67—42no—
344C3×#67—42no—
345C3×#67—42no—
346C3×#67—42no—
347C2×C3×Dic3—22no—
348C2×C3×Dic3—41no—
349C2×C3×Dic3—41no—
350C3×D12—22no—
351C3×D12—22no—
352C3×D12—41no—
353C3×D12—41no—
354C3×C4×D3—42no—
355C3×C4×D3—42no—
356C3×C4×D3—42no—
357C3×C4×D3—42no—
358C3×C4×D3—162no—
359C3×Dic6—22no—
360C3×Dic6—22no—
361C3×Dic6—41no—
362C3×Dic6—41no—
363C32×C8C4×D411yescharacteristic
364C32×C8C4×D411yescharacteristic
365C32×C8C23×C411yescharacteristic
366C32×C8C2×#4111yescharacteristic
367C3⋊(C3⋊C8)—42no—
368C3×C3⋊C8—22no—
369C2×#135—31no—
370C2×#135—31no—
371#568—181no—
372#520—61no—
373#510—92no—
374#510—92no—
375#509—92no—
376#509—92no—
377#508—94no—
378C2×M32—31no—
379C2×M32—91no—
380#444—94no—
381#443—182no—
382#442—32no—
383#441—32no—
384C4×SD16—62no—
385C2×#108—91no—
386C2×#106D3211yescharacteristic
387#421—181no—
388#417—61no—
389#405—31no—
390#365—94no—
391#362—92no—
392#361—92no—
393#360—34no—
394#347—94no—
395C3×#41—62no—
396C3×#41—62no—
397C3×#41—62no—
398C3×#41—62no—
399C3×#41—121no—
400C3×#41—121no—
401C3×#41—121no—
402C3×#41—121no—
403C2×C3×Q8—61no—
404C2×C3×Q8—61no—
405C2×C3×D4—61no—
406C2×C3×D4—61no—
407C2×C3×D4—121no—
408C2×C3×D4—121no—
409C22×C3×C4—21no—
410C22×C3×C4—41no—
411C22×C3×C4—41no—
412C22×C3×C4—81no—
413C22×C3×C4—122no—
414C22×C3×C4—121no—
415C22×C3×C4—121no—
416C22×C3×C4D3×D411yescharacteristic
417C22×C3×C4C2×#6711yescharacteristic
418C2×#67—41no—
419C2×#67—41no—
420#235—22no—
421#235—22no—
422#235—22no—
423#235—22no—
424#235—41no—
425#235—41no—
426#235—41no—
427#235—41no—
428C2×D12—21no—
429C2×D12—21no—
430C2×C4×D3—41no—
431C2×C4×D3—41no—
432C2×C4×D3—42no—
433C2×Dic6—21no—
434C2×Dic6—21no—
435C3×Q16—32no—
436C3×Q16—32no—
437C3×Q16—61no—
438C3×Q16—61no—
439C3×SD16—62no—
440C3×SD16—62no—
441C3×SD16—62no—
442C3×SD16—62no—
443C3×D8—32no—
444C3×D8—32no—
445C3×D8—61no—
446C3×D8—61no—
447C3×M16—61no—
448C3×M16—61no—
449C2×C3×C8—21no—
450C2×C3×C8—21no—
451C2×C3×C8—21no—
452C2×C3×C8—21no—
453C2×C3×C8—21no—
454C2×C3×C8—21no—
455C2×C3×C8—32no—
456C2×C3×C8C2×C4×D311yescharacteristic
457C2×C3×C8C2×C4×D311yescharacteristic
458C2×C3×C8C2×C4×D311yescharacteristic
459C2×C3×C8C2×C4×D311yescharacteristic
460C2×C3×C8#23511yescharacteristic
461C2×C3×C8#23511yescharacteristic
462C2×C3×C8D3×D411yescharacteristic
463C2×C3×C8#23711yescharacteristic
464C2×C3×C8#23711yescharacteristic
465C2×C3×C8C2×#6711yescharacteristic
466C2×C3×C8C23×D311yescharacteristic
467C2×C3×C8C23×D311yescharacteristic
468C3×C4⋊C4—22no—
469C3×C4⋊C4—22no—
470C3×C4⋊C4—42no—
471C3×C4⋊C4—41no—
472C3×C4⋊C4—41no—
473C3×C4⋊C4—61no—
474C3×C4⋊C4—81no—
475C3×C4⋊C4—122no—
476C3×C22⋊C4—61no—
477C3×C22⋊C4—122no—
478C3×C42—32no—
479C3×C42—122no—
480#217—21no—
481(C2×D3)⋊C4—42no—
482C4⋊Dic3—21no—
483Dic3⋊C4—42no—
484C4×Dic3—42no—
485C4×Dic3C2×#6712yes—
486#208—21no—
487#208—21no—
488#208—62no—
489#208—62no—
490#208—122no—
491#208—124no—
492#208—121no—
493#208—121no—
494#208—241no—
495C2×C3⋊C8—124no—
496C2×C3⋊C8—121no—
497C2×C3⋊C8—121no—
498C2×C3⋊C8—241no—
499C2×C3⋊C8C2×#6712yes—
500Dic12—21no—
501Dic12—21no—
502Dic12C2×C4×D312yes—
503Dic12C2×C4×D312yes—
504D24—21no—
505D24—21no—
506D24C2×C4×D312yes—
507D24C2×C4×D312yes—
508#204—22no—
509#204—22no—
510#204—22no—
511#204—22no—
512ΓL(1,𝔽25)—124no—
513D3×C8—124no—
514C3×C16—62no—
515C3⋊C16—22no—
516C3⋊C16—34no—
517C3⋊C16—34no—
518C3⋊C16—64no—
519C22×C32—41no—
520C22×C32#44211yescharacteristic
521C22×C32#44211yescharacteristic
522C22×C32C2×AGL(1,ℤ/8)11yescharacteristic
523C2×C3×D3—42no—
524C2×C3×D3—42no—
525C2×C3×D3—81no—
526C2×C3×D3—81no—
527C2×C3×D3—161no—
528C32×C4—82no—
529C32×C4#44211yescharacteristic
530C32×C4#44211yescharacteristic
531C32×C4C2×C4×D411yescharacteristic
532C32×C4C2×AGL(1,ℤ/8)11yescharacteristic
533C3×Dic3—42no—
534C3×Dic3—42no—
535C3×Dic3—42no—
536C2×#41—61no—
537C2×#41—61no—
538#135—32no—
539#135—32no—
540#135—32no—
541#135—32no—
542#135—61no—
543#135—61no—
544#135—61no—
545#135—61no—
546C2×Q16—31no—
547C2×Q16—31no—
548C2×SD16—61no—
549C2×SD16—61no—
550C2×D8—31no—
551C2×D8—31no—
552#131—184no—
553#131—362no—
554C2×M16—31no—
555C2×M16—181no—
556C2×M16—362no—
557C22×C8C2×D3211yescharacteristic
558C4×Q8—62no—
559C4×D4—62no—
560C4×D4—122no—
561#117—31no—
562#117—121no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—121no—
565Q32—94no—
566SD32—94no—
567SD32—94no—
568D16—94no—
569M32—32no—
570M32—61no—
571M32—92no—
572M32—92no—
573C2×C16—61no—
574C2×C16—92no—
575#108—92no—
576#108—181no—
577#106—21no—
578#106C2×D3212yes—
579#104—184no—
580#103—62no—
581#102—62no—
582#97—32no—
583C4×C8—32no—
584C23×C3—21no—
585C23×C3—121no—
586C23×C3—121no—
587C23×C3#91111yescharacteristic
588C23×C3#93211yescharacteristic
589C22×D3—41no—
590C22×D3—41no—
591C3×Q8—62no—
592C3×Q8—62no—
593C3×Q8—121no—
594C3×Q8—121no—
595C3×D4—62no—
596C3×D4—62no—
597C3×D4—122no—
598C3×D4—122no—
599C3×D4—122no—
600C3×D4—122no—
601C3×D4—121no—
602C3×D4—121no—
603C2×C3×C4—21no—
604C2×C3×C4—21no—
605C2×C3×C4—21no—
606C2×C3×C4—21no—
607C2×C3×C4—21no—
608C2×C3×C4—21no—
609C2×C3×C4—42no—
610C2×C3×C4—42no—
611C2×C3×C4—62no—
612C2×C3×C4—82no—
613C2×C3×C4—121no—
614C2×C3×C4—121no—
615C2×C3×C4—122no—
616C2×C3×C4—122no—
617C2×C3×C4—122no—
618C2×C3×C4—122no—
619C2×C3×C4—161no—
620C2×C3×C4—161no—
621C2×C3×C4—162no—
622C2×C3×C4—482no—
623C2×C3×C4#67⋊C411yescharacteristic
624C2×C3×C4#67⋊C411yescharacteristic
625C2×C3×C4#91111yescharacteristic
626C2×C3×C4#91411yescharacteristic
627C2×C3×C4#91411yescharacteristic
628C2×C3×C4C4×#6711yescharacteristic
629C2×C3×C4C4×#6711yescharacteristic
630C2×C3×C4#93211yescharacteristic
631C2×C3×C4#94911yescharacteristic
632C2×C3×C4#94911yescharacteristic
633C2×C3×C4C2×D3×D411yescharacteristic
634C2×C3×C4C22×#6711yescharacteristic
635#67—42no—
636#67—42no—
637#67—42no—
638#67—42no—
639C2×Dic3—22no—
640C2×Dic3—41no—
641C2×Dic3—41no—
642D12—22no—
643D12—22no—
644D12—41no—
645D12—41no—
646C4×D3—42no—
647C4×D3—42no—
648C4×D3—42no—
649C4×D3—42no—
650C4×D3—162no—
651Dic6—22no—
652Dic6—22no—
653Dic6—41no—
654Dic6—41no—
655C3×C8—21no—
656C3×C8—21no—
657C3×C8—21no—
658C3×C8—21no—
659C3×C8—62no—
660C3×C8#67⋊C411yescharacteristic
661C3×C8#67⋊C411yescharacteristic
662C3×C8C4×#6711yescharacteristic
663C3×C8C4×#6711yescharacteristic
664C3×C8C22×C4×D311yescharacteristic
665C3×C8C22×C4×D311yescharacteristic
666C3×C8C2×#23511yescharacteristic
667C3×C8C2×#23711yescharacteristic
668C3⋊C8—22no—
669C3⋊C8—122no—
670C3⋊C8—122no—
671C3⋊C8—242no—
672C2×C32—21no—
673C2×C32—21no—
674C2×C32—21no—
675C2×C32C2×#44211yescharacteristic
676C3×D3—82no—
677C3×D3—82no—
678#41—62no—
679#41—62no—
680#41—62no—
681#41—62no—
682#41—121no—
683#41—121no—
684#41—121no—
685#41—121no—
686C2×Q8—61no—
687C2×Q8—61no—
688C2×D4—61no—
689C2×D4—61no—
690C2×D4—121no—
691C2×D4—121no—
692C22×C4—41no—
693C22×C4—122no—
694C22×C4—121no—
695C22×C4—121no—
696C22×C4D3×#6711yescharacteristic
697Q16—32no—
698Q16—32no—
699Q16—61no—
700Q16—61no—
701SD16—62no—
702SD16—62no—
703SD16—62no—
704SD16—62no—
705D8—32no—
706D8—32no—
707D8—61no—
708D8—61no—
709M16—61no—
710M16—61no—
711M16—182no—
712M16—364no—
713M16—361no—
714C2×C8—32no—
715C2×C8—364no—
716C2×C8—361no—
717C2×C8#379511yescharacteristic
718C2×C8#379511yescharacteristic
719C2×C8C4×D3211yescharacteristic
720C2×C8C4×D3211yescharacteristic
721C2×C8D3×#6711yescharacteristic
722C2×C8C22×D3211yescharacteristic
723C4⋊C4—22no—
724C4⋊C4—41no—
725C4⋊C4—61no—
726C4⋊C4—122no—
727C22⋊C4—61no—
728C22⋊C4—122no—
729C42—32no—
730C42—122no—
731C16—62no—
732C16—94no—
733C22×C3—21no—
734C22×C3—21no—
735C22×C3—21no—
736C22×C3—41no—
737C22×C3—41no—
738C22×C3—42no—
739C22×C3—122no—
740C22×C3—122no—
741C22×C3—241no—
742C22×C3—241no—
743C22×C3—481no—
744C22×C3#478511yescharacteristic
745C22×C3#478511yescharacteristic
746C22×C3#501411yescharacteristic
747C22×C3#501411yescharacteristic
748C22×C3C2×#91111yescharacteristic
749C22×C3C2×#93211yescharacteristic
750C2×D3—42no—
751C2×D3—42no—
752C2×D3—81no—
753C2×D3—81no—
754C2×D3—161no—
755C3×C4—21no—
756C3×C4—21no—
757C3×C4—21no—
758C3×C4—21no—
759C3×C4—82no—
760C3×C4—82no—
761C3×C4—122no—
762C3×C4—122no—
763C3×C4—122no—
764C3×C4—162no—
765C3×C4#478511yescharacteristic
766C3×C4#478511yescharacteristic
767C3×C4#501411yescharacteristic
768C3×C4#501411yescharacteristic
769C3×C4C2×#67⋊C411yescharacteristic
770C3×C4C2×#91411yescharacteristic
771C3×C4C2×C4×#6711yescharacteristic
772C3×C4C2×#94911yescharacteristic
773Dic3—42no—
774Dic3—42no—
775Dic3—42no—
776C32#3346911yescharacteristic, complemented, Sylow
777C23—121no—
778C23—121no—
779C23#6393211yescharacteristic
780Q8—62no—
781Q8—62no—
782Q8—121no—
783Q8—121no—
784D4—62no—
785D4—62no—
786D4—122no—
787D4—122no—
788D4—122no—
789D4—122no—
790D4—121no—
791D4—121no—
792C2×C4—42no—
793C2×C4—62no—
794C2×C4—121no—
795C2×C4—121no—
796C2×C4—122no—
797C2×C4—122no—
798C2×C4—122no—
799C2×C4—122no—
800C2×C4—161no—
801C2×C4—482no—
802C2×C4#6387911yescharacteristic
803C2×C4#6387911yescharacteristic
804C2×C4#6393211yescharacteristic
805C2×C4#6393911yescharacteristic
806C2×C4#6393911yescharacteristic
807C2×C4C2×D3×#6711yescharacteristic
808C8—62no—
809C8—362no—
810C8#6387911yescharacteristic
811C8#6387911yescharacteristic
812C8C2×#379511yescharacteristic
813C8C2×C4×D3211yescharacteristic
814C2×C3—22no—
815C2×C3—21no—
816C2×C3—21no—
817C2×C3—21no—
818C2×C3—21no—
819C2×C3—21no—
820C2×C3—21no—
821C2×C3—21no—
822C2×C3—41no—
823C2×C3—41no—
824C2×C3—242no—
825C2×C3—242no—
826C2×C3C2×#478511yescharacteristic
827C2×C3C2×#501411yescharacteristic
828D3—82no—
829D3—82no—
830C22—41no—
831C22—122no—
832C22—122no—
833C22—241no—
834C22—241no—
835C22—481no—
836C22#1059045511yescharacteristic
837C22#1059045511yescharacteristic
838C22C2×#6393211yescharacteristic
839C4—82no—
840C4—122no—
841C4—122no—
842C4—122no—
843C4#1059045511yescharacteristic
844C4#1059045511yescharacteristic
845C4C2×#6387911yescharacteristic
846C4C2×#6393911yescharacteristic
847C3—21no—
848C3#1094864211yescharacteristic, complemented
849C3#1094864411yescharacteristic, complemented
850C2—21no—
851C2—21no—
852C2—21no—
853C2—242no—
854C2—242no—
855C2C2×#1059045511yescharacteristic
subgroupG/H
centerC2C2×#10590455
commutatorC32×C8C23×C4
FrattiniC2×C8C22×D32
FittingC2×C32×#106C22
socleC2×C32C2×#442
prime radical#11899653C2
cosocleC2×C32×C8C24
hypercenterC2×#106D32
hypocenterC32#33469
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ C22×C8 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
2. #11861236C2semidirect
3. C3×#79106C2semidirect
4. #11797968C2semidirect
5. #11797922C2semidirect
6. C2×#10589353C2semidirect
7. #11796951C2semidirect
8. C2×C3×#4488C2semidirect
9. #11795946C2semidirect
22. C3×#4869C22semidirect
23. C3×#4853C22semidirect
28. #10590636C4semidirect
30. #10590630C4semidirect
32. #10590629C4semidirect
33. #10589353C22semidirect
35. #10589130C22semidirect
36. #10589127C22semidirect
37. #10589105C22semidirect
42. #79106D3semidirect
50. C2×#4488D3semidirect
65. C2×C3×Dic12C2×C4semidirect
73. C3×#904C2×C4semidirect
75. C2×C3×D24C2×C4semidirect
90. #63639C2×C4semidirect
92. C2×C3⋊(C3⋊C16)C2×C4semidirect
101. #63550C2×C4semidirect
102. #63547C2×C4semidirect
103. #63547C2×C4semidirect
104. #63545C2×C4semidirect
146. #4869C2×D3semidirect
147. #4853C2×D3semidirect
268. C2×Dic12C4×D3semidirect
276. #904C4×D3semidirect
278. C2×D24C4×D3semidirect
776. C32#33469semidirect
848. C3#10948642semidirect
849. C3#10948644semidirect

Maximal subgroups

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

subgroupindex
#118996532
#118612362
C3×#791062
#117979682
#117979222
C2×#105893532
#117969512
C2×C3×#44882
#117959462
#109486443
#109486423