Finite Group Databasebeta

← #72222871

Subgroups — #72222871

Order 2304.

1464 conjugacy classes of subgroups.

The subgroup lattice has 807 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10590634C211yesmaximal, characteristic
2C3×#79249C211yesmaximal, characteristic, complemented
3#11860704C211yesmaximal, characteristic, complemented
4#11797983C218yesmaximal, complemented
5C3×#70685C211yesmaximal, characteristic, complemented
6C2×#10589361C211yesmaximal, characteristic, complemented
7#11796862C211yesmaximal, characteristic, complemented
8#11795946C211yesmaximal, characteristic, complemented
9#10948662—31nomaximal
10#10948661—31nomaximal
11C22×#3745C2211yescharacteristic
12C3×#5745—21no—
13C2×C3×#904C2211yescharacteristic
14#10594996—21no—
15C2×C32×#108C2211yescharacteristic
16C2×#63639C2211yescharacteristic
17C3×#5139—21no—
18C3×#5106C2211yescharacteristic
19C3×#5101C2211yescharacteristic
20C2×C3×#812C2211yescharacteristic
21C3×#4895—22no—
22C3×#4894C2214yescomplemented
23#10591096—21no—
24#10590768C2214yescomplemented
25#10590763—22no—
26C2×#63549C412yescomplemented
27#10590634C414yescomplemented
28#10590634C2214yes—
29C2×#63546C412yescomplemented
30#10589361C2214yescomplemented
31C3×#4494C2214yescomplemented
32#10589123C2214yescomplemented
33#10589105C2214yescomplemented
34C3×#2957—31no—
35C2×#5193—31no—
36C2×#4908—31no—
37#79249D311yescharacteristic, complemented
38#79167—31no—
39#78561—31no—
40C3×#2155—31no—
41#72076—31no—
42#71425—31no—
43#70929—38no—
44C2×#4495—31no—
45C2×#4495—31no—
46C2×#4495—61no—
47#70685D311yescharacteristic, complemented
48#70656—31no—
49#69884—31no—
50#69310—38no—
51C22×C4⋊(C3⋊D3)—21no—
52C2×C3×#235—21no—
53C2×C32×M16—21no—
54C22×C32×C8C2311yescharacteristic
55C2×#3745—21no—
56C2×#3745—21no—
57C2×#3745—21no—
58C2×#3745C2×C412yes—
59C2×#3745C2×C412yes—
60C2×#3745C2312yes—
61C3×#926—21no—
62C3×#926D411yescharacteristic
63C2×C3×#208D411yescharacteristic
64C3×#907—24no—
65C3×D3×M16—42no—
66C2×C3×Dic12C2×C411yescharacteristic, complemented
67C3×#904—21no—
68C3×#904—21no—
69C3×#904C2×C412yescomplemented
70C3×#904C2312yes—
71C2×C3×D24C2×C411yescharacteristic, complemented
72C2×C3×#204—21no—
73C3×#901—42no—
74#63974—42no—
75#63894—24no—
76#63894—42no—
77C32×#108—21no—
78C32×#108C2312yes—
79#63639—21no—
80#63639C2312yes—
81C2×C3⋊(C3⋊C16)—21no—
82C3×#825—24no—
83C3×#818—21no—
84C3×#817C2312yes—
85C3×#815C2312yes—
86C3×C8×Dic3D412yes—
87C3×#812C2×C412yescomplemented
88C3×#812C2312yes—
89C2×C3×C3⋊C16C2×C412yescomplemented
90#63564—24no—
91#63549C2×C418yescomplemented
92#63546C2×C418yescomplemented
93#33471—91noSylow
94C2×C3×#135—31no—
95C3×#568—61no—
96#5745—21no—
97C2×#904C2×D311yescharacteristic
98C22×D24—31no—
99C22×D24—31no—
100C22×D24—61no—
101#5521—61no—
102#5521—61no—
103C2×C3×M32—31no—
104C3×#444—34no—
105C3×#443—62no—
106C2×C3×#108—21no—
107C2×C3×#108C2×D311yescharacteristic
108C2×C3×#108C2×D311yescharacteristic
109C3×#427—31no—
110C3×#421—61no—
111C3×#405—31no—
112#5193—34no—
113#5193—34no—
114C2×#828—32no—
115C2×#826—32no—
116#5139—21no—
117#5131—61no—
118#5106C2×D311yescharacteristic
119#5101C2×D311yescharacteristic
120C2×#812—31no—
121C2×#812—31no—
122C2×#812—61no—
123C2×#812C2×D311yescharacteristic
124#5001—61no—
125#4908—34no—
126#4908—34no—
127C2×#800—32no—
128C2×D48—32no—
129#4895—22no—
130#4894C2×D314yescomplemented
131#4872—62no—
132#4869—34no—
133#4711—34no—
134C4×D24—62no—
135C3×#365—34no—
136#4566—34no—
137#4512—34no—
138#4495—34no—
139#4495—34no—
140#4495—64no—
141#4494C2×D314yescomplemented
142#4488—34no—
143#4466—34no—
144C23×C3⋊D3—41no—
145C22×C32×C4C2×D411yescharacteristic
146C2×C4⋊(C3⋊D3)—22no—
147C2×C4⋊(C3⋊D3)—22no—
148C2×C4⋊(C3⋊D3)—22no—
149C2×C4⋊(C3⋊D3)—41no—
150C2×C4⋊(C3⋊D3)—41no—
151C2×C4⋊(C3⋊D3)—41no—
152C2×C3×#67—41no—
153C3×#235—22no—
154C3×#235—22no—
155C3×#235—41no—
156C3×#235—41no—
157C2×C3×D12—21no—
158C2×C3×C4×D3—41no—
159C2×C3×Dic6—21no—
160C2×#624—44no—
161C32×M16—22no—
162C32×M16—41no—
163C2×C32×C8—41no—
164C2×C32×C8C22×C411yescharacteristic
165C2×C32×C8C22×C411yescharacteristic
166C2×C32×C8C2×D411yescharacteristic
167C2×C32×C8#4111yescharacteristic
168C2×C32×C8#4111yescharacteristic
169C2×C32×C8C2411yescharacteristic
170#3745—22no—
171#3745—22no—
172#3745—22no—
173#3745C22×C414yes—
174C3×#217—21no—
175C3×#217—41no—
176C3×C4⋊Dic3—21no—
177C3×C4⋊Dic3—22no—
178C3×C4×Dic3—41no—
179C3×C4×Dic3C2×D412yes—
180C3×#208—21no—
181C3×#208—21no—
182C2×C3×C3⋊C8C2×D412yes—
183C3×Dic12—21no—
184C3×Dic12C22×C412yes—
185C3×D24—21no—
186C3×D24C22×C412yes—
187C3×#204—22no—
188C3×#204—22no—
189C3×ΓL(1,𝔽25)—44no—
190C3×D3×C8—44no—
191#3722—44no—
192C3⋊(C3⋊C16)—22no—
193C3×C3⋊C16C22×C414yes—
194C2×#509—91no—
195#2957—31no—
196#2948—91no—
197AGL(1,ℤ/16)—98no—
198#2155—31no—
199C2×#361—91no—
200#2145—91no—
201#2110—91no—
202C2×C3×#41—61no—
203C2×#235—21no—
204C22×D12—61no—
205C22×D12—61no—
206C22×D12—121no—
207C3×#135—32no—
208C3×#135—32no—
209C3×#135—61no—
210C3×#135—61no—
211C2×C3×Q16—31no—
212C2×C3×SD16—61no—
213C2×C3×D8—31no—
214C3×#131—64no—
215C3×#131—122no—
216C2×C3×M16—21no—
217C2×C3×M16—21no—
218C2×C3×M16—31no—
219C2×C3×M16—41no—
220C2×C3×M16—122no—
221C22×C3×C8—21no—
222C22×C3×C8C22×D311yescharacteristic
223C22×C3×C8C22×D311yescharacteristic
224C3×#117—31no—
225C3×#117—61no—
226#926—21no—
227#926#6711yescharacteristic
228C2×#208#6711yescharacteristic
229#907—24no—
230D3×M16—42no—
231C2×Dic12C4×D311yescharacteristic, complemented
232#904—21no—
233#904—21no—
234#904C4×D312yescomplemented
235#904C22×D312yes—
236C2×D24—32no—
237C2×D24—32no—
238C2×D24—32no—
239C2×D24—32no—
240C2×D24—32no—
241C2×D24—32no—
242C2×D24—62no—
243C2×D24—62no—
244C2×D24—62no—
245C2×D24—61no—
246C2×D24—61no—
247C2×D24—61no—
248C2×D24—61no—
249C2×D24—61no—
250C2×D24—61no—
251C2×D24—121no—
252C2×D24—121no—
253C2×D24—121no—
254C2×D24C4×D311yescharacteristic, complemented
255C2×#204—21no—
256#901—42no—
257#893—64no—
258#893—122no—
259D3×C22⋊C4—122no—
260D3×C22⋊C4—122no—
261C4×D12—64no—
262C4×D12—122no—
263C3×M32—32no—
264C3×M32—32no—
265C2×C3×C16—32no—
266C3×#108—21no—
267C3×#108—21no—
268C3×#108—22no—
269C3×#108—41no—
270C3×#108C22×D312yes—
271C3×#108C22×D312yes—
272C3×#107—61no—
273C3×#106—32no—
274C3×#104—64no—
275C3×#97—32no—
276C3×C4×C8—32no—
277#828—38no—
278#826—38no—
279#825—24no—
280#821—64no—
281#818—21no—
282#817C22×D312yes—
283#815C22×D312yes—
284C8×Dic3#6712yes—
285#812—32no—
286#812—32no—
287#812—62no—
288#812—61no—
289#812—61no—
290#812—121no—
291#812C4×D312yescomplemented
292#812C22×D312yes—
293C2×C3⋊C16—61no—
294C2×C3⋊C16—61no—
295C2×C3⋊C16—121no—
296C2×C3⋊C16C4×D312yescomplemented
297#809—64no—
298#800—38no—
299D48—38no—
300C23×C32AGL(1,ℤ/8)11yescharacteristic
301C22×C3⋊D3—42no—
302C22×C3⋊D3—42no—
303C22×C3⋊D3—42no—
304C22×C3⋊D3—162no—
305C22×C3×D3—41no—
306C2×C32×C4C4×D411yescharacteristic
307C2×C32×C4C4×D411yescharacteristic
308C2×C32×C4AGL(1,ℤ/8)11yescharacteristic
309C2×C32×C4AGL(1,ℤ/8)11yescharacteristic
310C2×C32×C4AGL(1,ℤ/8)11yescharacteristic
311C2×C32×C4C22×D411yescharacteristic
312C4⋊(C3⋊D3)—24no—
313C4⋊(C3⋊D3)—42no—
314C4⋊(C3⋊D3)—42no—
315C4⋊(C3⋊D3)—42no—
316C3×#67—42no—
317C3×#67—42no—
318C2×C3×Dic3—22no—
319C2×C3×Dic3—41no—
320C2×C3×Dic3—42no—
321C3×D12—22no—
322C3×D12—41no—
323C3×C4×D3—42no—
324C3×C4×D3—42no—
325C3×Dic6—22no—
326C3×Dic6—41no—
327#624—164no—
328C32×C8—42no—
329C32×C8C4×D411yescharacteristic
330C32×C8C4×D411yescharacteristic
331C32×C8C23×C411yescharacteristic
332C32×C8C2×#4111yescharacteristic
333C3×C3⋊C8—22no—
334C2×#135—31no—
335C22×D8—91no—
336#568—61no—
337#518—181no—
338#509—94no—
339#509—94no—
340C2×SD32—92no—
341C2×D16—92no—
342C2×M32—31no—
343C2×M32—91no—
344#444—34no—
345#443—62no—
346#442—94no—
347C4×D8—182no—
348C2×#108D3211yescharacteristic
349#427—31no—
350#421—61no—
351#418—181no—
352#405—31no—
353#365—34no—
354#361—94no—
355#360—94no—
356#347—94no—
357C23×D3—121no—
358C23×D3—121no—
359C23×D3—241no—
360C3×#41—62no—
361C3×#41—62no—
362C3×#41—121no—
363C3×#41—121no—
364C2×C3×Q8—61no—
365C2×C3×D4—61no—
366C2×C3×D4—121no—
367C22×C3×C4—21no—
368C22×C3×C4—121no—
369C22×C3×C4D3×D411yescharacteristic
370C22×C3×C4C2×#6711yescharacteristic
371C2×#67—41no—
372#235—22no—
373#235—22no—
374#235—41no—
375#235—41no—
376C2×D12—21no—
377C2×D12—62no—
378C2×D12—62no—
379C2×D12—62no—
380C2×D12—62no—
381C2×D12—62no—
382C2×D12—62no—
383C2×D12—122no—
384C2×D12—122no—
385C2×D12—122no—
386C2×D12—121no—
387C2×D12—121no—
388C2×D12—121no—
389C2×D12—121no—
390C2×D12—121no—
391C2×D12—121no—
392C2×D12—241no—
393C2×D12—241no—
394C2×D12—241no—
395C2×C4×D3—41no—
396C2×C4×D3—124no—
397C2×C4×D3—124no—
398C2×Dic6—21no—
399C3×Q16—32no—
400C3×Q16—61no—
401C3×SD16—62no—
402C3×SD16—62no—
403C3×D8—32no—
404C3×D8—61no—
405C3×M16—22no—
406C3×M16—22no—
407C3×M16—42no—
408C3×M16—41no—
409C3×M16—41no—
410C3×M16—61no—
411C3×M16—61no—
412C3×M16—81no—
413C3×M16—124no—
414C2×C3×C8—21no—
415C2×C3×C8—21no—
416C2×C3×C8—21no—
417C2×C3×C8—21no—
418C2×C3×C8—21no—
419C2×C3×C8—21no—
420C2×C3×C8—32no—
421C2×C3×C8—41no—
422C2×C3×C8—41no—
423C2×C3×C8—81no—
424C2×C3×C8—124no—
425C2×C3×C8C2×C4×D311yescharacteristic
426C2×C3×C8C2×C4×D311yescharacteristic
427C2×C3×C8C2×C4×D311yescharacteristic
428C2×C3×C8C2×C4×D311yescharacteristic
429C2×C3×C8#23511yescharacteristic
430C2×C3×C8#23511yescharacteristic
431C2×C3×C8D3×D411yescharacteristic
432C2×C3×C8#23911yescharacteristic
433C2×C3×C8#23911yescharacteristic
434C2×C3×C8C2×#6711yescharacteristic
435C2×C3×C8C23×D311yescharacteristic
436C2×C3×C8C23×D311yescharacteristic
437C3×C4⋊C4—61no—
438C3×C4⋊C4—62no—
439C3×C22⋊C4—61no—
440C3×C22⋊C4—121no—
441C3×C42—32no—
442C3×C42—121no—
443#217—21no—
444#217—41no—
445(C2×D3)⋊C4—124no—
446(C2×D3)⋊C4—124no—
447C4⋊Dic3—21no—
448C4⋊Dic3—22no—
449C4×Dic3—41no—
450C4×Dic3C2×#6712yes—
451#208—21no—
452#208—21no—
453C2×C3⋊C8C2×#6712yes—
454Dic12—21no—
455Dic12C2×C4×D312yes—
456D24—21no—
457D24—34no—
458D24—34no—
459D24—64no—
460D24—62no—
461D24—62no—
462D24—62no—
463D24—62no—
464D24—62no—
465D24—62no—
466D24—122no—
467D24—122no—
468D24—122no—
469D24C2×C4×D312yes—
470#204—22no—
471#204—22no—
472ΓL(1,𝔽25)—44no—
473D3×C8—44no—
474C3×C16—34no—
475C3⋊C16—62no—
476C3⋊C16—62no—
477C3⋊C16—122no—
478C3⋊C16C2×C4×D314yes—
479C22×C32—41no—
480C22×C32#44211yescharacteristic
481C22×C32#44211yescharacteristic
482C22×C32C2×AGL(1,ℤ/8)11yescharacteristic
483C2×C3⋊D3—44no—
484C2×C3⋊D3—84no—
485C2×C3⋊D3—162no—
486C2×C3⋊D3—162no—
487C2×C3×D3—42no—
488C2×C3×D3—161no—
489C32×C4#44211yescharacteristic
490C32×C4#44211yescharacteristic
491C32×C4C2×C4×D411yescharacteristic
492C32×C4C2×AGL(1,ℤ/8)11yescharacteristic
493C3×Dic3—42no—
494C3×Dic3—42no—
495C3×Dic3—82no—
496C2×#41—61no—
497C22×D4—181no—
498#135—32no—
499#135—32no—
500#135—61no—
501#135—61no—
502C2×Q16—31no—
503C2×SD16—61no—
504C2×D8—31no—
505C2×D8—92no—
506C2×D8—92no—
507C2×D8—92no—
508C2×D8—181no—
509C2×D8—181no—
510C2×D8—181no—
511#131—64no—
512#131—122no—
513C2×M16—21no—
514C2×M16—31no—
515C2×M16—122no—
516C22×C8C2×D3211yescharacteristic
517C4×D4—184no—
518C4×D4—362no—
519#117—31no—
520#117—61no—
521C2×C22⋊C4—362no—
522SD32—98no—
523D16—98no—
524M32—32no—
525M32—32no—
526M32—92no—
527M32—181no—
528C2×C16—32no—
529C2×C16—181no—
530#108—21no—
531#108C2×D3212yes—
532#107—61no—
533#106—32no—
534#104—64no—
535#102—184no—
536#97—32no—
537C4×C8—32no—
538C23×C3—21no—
539C23×C3—121no—
540C23×C3#91411yescharacteristic
541C23×C3#94911yescharacteristic
542C22×D3—41no—
543C22×D3—122no—
544C22×D3—122no—
545C22×D3—122no—
546C22×D3—122no—
547C22×D3—122no—
548C22×D3—122no—
549C22×D3—242no—
550C22×D3—242no—
551C22×D3—242no—
552C22×D3—482no—
553C22×D3—482no—
554C22×D3—484no—
555C3×Q8—62no—
556C3×Q8—121no—
557C3×D4—62no—
558C3×D4—122no—
559C3×D4—122no—
560C3×D4—121no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—21no—
567C2×C3×C4—62no—
568C2×C3×C4—121no—
569C2×C3×C4—122no—
570C2×C3×C4—122no—
571C2×C3×C4—122no—
572C2×C3×C4#89311yescharacteristic
573C2×C3×C4#89311yescharacteristic
574C2×C3×C4#91411yescharacteristic
575C2×C3×C4#91411yescharacteristic
576C2×C3×C4#91411yescharacteristic
577C2×C3×C4C4×#6711yescharacteristic
578C2×C3×C4C4×#6711yescharacteristic
579C2×C3×C4#93211yescharacteristic
580C2×C3×C4#93211yescharacteristic
581C2×C3×C4#94911yescharacteristic
582C2×C3×C4C2×D3×D411yescharacteristic
583C2×C3×C4C22×#6711yescharacteristic
584#67—42no—
585#67—42no—
586C2×Dic3—22no—
587C2×Dic3—41no—
588C2×Dic3—42no—
589D12—22no—
590D12—41no—
591D12—64no—
592D12—64no—
593D12—124no—
594D12—122no—
595D12—122no—
596D12—122no—
597D12—122no—
598D12—122no—
599D12—122no—
600D12—242no—
601D12—242no—
602D12—242no—
603C4×D3—42no—
604C4×D3—42no—
605C4×D3—484no—
606C4×D3—484no—
607Dic6—22no—
608Dic6—41no—
609C3×C8—21no—
610C3×C8—21no—
611C3×C8—21no—
612C3×C8—21no—
613C3×C8—42no—
614C3×C8—42no—
615C3×C8—62no—
616C3×C8—82no—
617C3×C8#89311yescharacteristic
618C3×C8#89311yescharacteristic
619C3×C8C4×#6711yescharacteristic
620C3×C8C4×#6711yescharacteristic
621C3×C8C22×C4×D311yescharacteristic
622C3×C8C22×C4×D311yescharacteristic
623C3×C8C2×#23511yescharacteristic
624C3×C8C2×#23911yescharacteristic
625C3⋊C8—22no—
626C2×C32—21no—
627C2×C32—21no—
628C2×C32—21no—
629C2×C32C2×#44211yescharacteristic
630C3⋊D3—84no—
631C3×D3—82no—
632C24—361no—
633#41—62no—
634#41—62no—
635#41—121no—
636#41—121no—
637C2×Q8—61no—
638C2×D4—61no—
639C2×D4—121no—
640C2×D4—182no—
641C2×D4—182no—
642C2×D4—182no—
643C2×D4—361no—
644C2×D4—361no—
645C2×D4—361no—
646C22×C4—121no—
647C22×C4—364no—
648C22×C4D3×#6711yescharacteristic
649Q16—32no—
650Q16—61no—
651SD16—62no—
652SD16—62no—
653D8—32no—
654D8—61no—
655D8—94no—
656D8—182no—
657D8—182no—
658D8—182no—
659M16—22no—
660M16—41no—
661M16—61no—
662M16—61no—
663M16—124no—
664C2×C8—32no—
665C2×C8—41no—
666C2×C8—124no—
667C2×C8#379911yescharacteristic
668C2×C8#379911yescharacteristic
669C2×C8C4×D3211yescharacteristic
670C2×C8C4×D3211yescharacteristic
671C2×C8D3×#6711yescharacteristic
672C2×C8C22×D3211yescharacteristic
673C4⋊C4—61no—
674C4⋊C4—62no—
675C22⋊C4—61no—
676C22⋊C4—121no—
677C22⋊C4—364no—
678C42—32no—
679C42—121no—
680C16—34no—
681C16—182no—
682C22×C3—21no—
683C22×C3—21no—
684C22×C3—21no—
685C22×C3—41no—
686C22×C3—41no—
687C22×C3—42no—
688C22×C3—122no—
689C22×C3—481no—
690C22×C3#486911yescharacteristic
691C22×C3#486911yescharacteristic
692C22×C3#501411yescharacteristic
693C22×C3#501411yescharacteristic
694C22×C3C2×#91411yescharacteristic
695C22×C3C2×#94911yescharacteristic
696C2×D3—42no—
697C2×D3—124no—
698C2×D3—124no—
699C2×D3—161no—
700C2×D3—244no—
701C2×D3—244no—
702C2×D3—244no—
703C2×D3—484no—
704C2×D3—482no—
705C2×D3—482no—
706C2×D3—482no—
707C2×D3—482no—
708C2×D3—484no—
709C2×D3—484no—
710C3×C4—21no—
711C3×C4—21no—
712C3×C4—21no—
713C3×C4—21no—
714C3×C4—122no—
715C3×C4—122no—
716C3×C4—242no—
717C3×C4#486911yescharacteristic
718C3×C4#486911yescharacteristic
719C3×C4#501411yescharacteristic
720C3×C4#501411yescharacteristic
721C3×C4C2×#89311yescharacteristic
722C3×C4C2×#91411yescharacteristic
723C3×C4C2×C4×#6711yescharacteristic
724C3×C4C2×#93211yescharacteristic
725Dic3—42no—
726Dic3—42no—
727Dic3—82no—
728C32#3347111yescharacteristic, complemented, Sylow
729C23—121no—
730C23—362no—
731C23—362no—
732C23—362no—
733C23—1442no—
734C23#6393911yescharacteristic
735Q8—62no—
736Q8—121no—
737D4—62no—
738D4—122no—
739D4—122no—
740D4—121no—
741D4—184no—
742D4—362no—
743D4—362no—
744D4—362no—
745C2×C4—62no—
746C2×C4—121no—
747C2×C4—122no—
748C2×C4—122no—
749C2×C4—122no—
750C2×C4—1444no—
751C2×C4#6390411yescharacteristic
752C2×C4#6390411yescharacteristic
753C2×C4#6393411yescharacteristic
754C2×C4#6393411yescharacteristic
755C2×C4#6393911yescharacteristic
756C2×C4C2×D3×#6711yescharacteristic
757C8—42no—
758C8—62no—
759C8#6390411yescharacteristic
760C8#6390411yescharacteristic
761C8C2×#379911yescharacteristic
762C8C2×C4×D3211yescharacteristic
763C2×C3—22no—
764C2×C3—21no—
765C2×C3—21no—
766C2×C3—21no—
767C2×C3—21no—
768C2×C3—21no—
769C2×C3—21no—
770C2×C3—21no—
771C2×C3—41no—
772C2×C3—41no—
773C2×C3—242no—
774C2×C3C2×#486911yescharacteristic
775C2×C3C2×#501411yescharacteristic
776D3—82no—
777D3—244no—
778D3—244no—
779D3—484no—
780C22—41no—
781C22—122no—
782C22—364no—
783C22—481no—
784C22—724no—
785C22—1442no—
786C22—1442no—
787C22#1059058911yescharacteristic
788C22#1059058911yescharacteristic
789C22C2×#6393911yescharacteristic
790C4—122no—
791C4—122no—
792C4—242no—
793C4#1059058911yescharacteristic
794C4#1059058911yescharacteristic
795C4C2×#6390411yescharacteristic
796C4C2×#6393411yescharacteristic
797C3—21no—
798C3#1094866111yescharacteristic, complemented
799C3#1094866211yescharacteristic, complemented
800C2—21no—
801C2—21no—
802C2—21no—
803C2—242no—
804C2—724no—
805C2C2×#1059058911yescharacteristic
subgroupG/H
centerC2C2×#10590589
commutatorC32×C8C23×C4
FrattiniC2×C8C22×D32
FittingC2×C32×#108C22
socleC2×C32C2×#442
prime radicalC2×#10590634C2
cosocleC2×C32×C8C24
hypercenterC2×#108D32
hypocenterC32#33471
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ C22×C8 ◁ C2×#108

Complements

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

NH ≅ G/Ntype
2. C3×#79249C2semidirect
3. #11860704C2semidirect
4. #11797983C2semidirect
5. C3×#70685C2semidirect
6. C2×#10589361C2semidirect
7. #11796862C2semidirect
8. #11795946C2semidirect
22. C3×#4894C22semidirect
24. #10590768C22semidirect
26. C2×#63549C4semidirect
27. #10590634C4semidirect
29. C2×#63546C4semidirect
30. #10589361C22semidirect
31. C3×#4494C22semidirect
32. #10589123C22semidirect
33. #10589105C22semidirect
37. #79249D3semidirect
47. #70685D3semidirect
66. C2×C3×Dic12C2×C4semidirect
69. C3×#904C2×C4semidirect
71. C2×C3×D24C2×C4semidirect
87. C3×#812C2×C4semidirect
89. C2×C3×C3⋊C16C2×C4semidirect
91. #63549C2×C4semidirect
92. #63546C2×C4semidirect
130. #4894C2×D3semidirect
141. #4494C2×D3semidirect
231. C2×Dic12C4×D3semidirect
234. #904C4×D3semidirect
254. C2×D24C4×D3semidirect
291. #812C4×D3semidirect
296. C2×C3⋊C16C4×D3semidirect
728. C32#33471semidirect
798. C3#10948661semidirect
799. C3#10948662semidirect

Maximal subgroups

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

subgroupindex
C2×#105906342
C3×#792492
#118607042
#117979832
C3×#706852
C2×#105893612
#117968622
#117959462
#109486623
#109486613