Finite Group Databasebeta

← #72222822

Subgroups — #72222822

Order 2304.

1536 conjugacy classes of subgroups.

The subgroup lattice has 841 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10592892C211yesmaximal, characteristic
2C3×#83910C211yesmaximal, characteristic, complemented
3#11860704C211yesmaximal, characteristic, complemented
4#11797971C218yesmaximal, complemented
5#11797135C211yesmaximal, characteristic, complemented
6C2×#10589128C211yesmaximal, characteristic, complemented
7C3×#72076C211yesmaximal, characteristic, complemented
8#11795946C211yesmaximal, characteristic, complemented
9#10948662—31nomaximal
10#10948659—31nomaximal
11C2×C32×#135C2211yescharacteristic
12C22×#3745C2211yescharacteristic
13C3×#5819—21no—
14#10594996—21no—
15#10592892C414yescomplemented
16#10592892C2214yes—
17C2×#63655C412yescomplemented
18C2×#63653C412yescomplemented
19C2×#63639C2211yescharacteristic
20C3×#5236—21no—
21C3×#5197C2214yescomplemented
22C3×#5196—22no—
23C2×C3×#819C2211yescharacteristic
24C3×#5106C2211yescharacteristic
25C3×#5101C2211yescharacteristic
26C2×C3×#812C2211yescharacteristic
27#10591096—21no—
28#10590768C2214yescomplemented
29#10590763—22no—
30C3×#4566C2214yescomplemented
31#10589138C2214yescomplemented
32#10589128C2214yescomplemented
33#10589105C2214yescomplemented
34C3×#2957—31no—
35#83910D311yescharacteristic, complemented
36C2×#5193—31no—
37C2×#5193—31no—
38C2×#5193—61no—
39#79167—31no—
40#78561—31no—
41C3×#2145—31no—
42#72076D311yescharacteristic, complemented
43C2×#4516—31no—
44#71425—31no—
45#70929—38no—
46C2×#4495—31no—
47#70685—31no—
48#70650—31no—
49#69884—31no—
50#69249—38no—
51C2×C32×#41—21no—
52C22×C4⋊(C3⋊D3)—21no—
53C32×#135—21no—
54C32×#135—21no—
55C32×#135C2×C412yescomplemented
56C32×#135C2312yes—
57C2×C32×Q16C2×C411yescharacteristic, complemented
58C2×C32×SD16—21no—
59C2×C32×D8C2×C411yescharacteristic, complemented
60C22×C32×C8C2311yescharacteristic
61C2×#3745—21no—
62C2×#3745—21no—
63C2×#3745—21no—
64C2×#3745C2×C412yes—
65C2×#3745C2×C412yes—
66C2×#3745C2312yes—
67C3×#948—24no—
68C3×#948—42no—
69C3×#926—21no—
70C3×#926D411yescharacteristic
71C2×C3×#208—21no—
72C2×C3×#208—42no—
73C2×C3×#208D411yescharacteristic
74#63974—42no—
75#63894—24no—
76#63894—42no—
77#63655C2×C418yescomplemented
78#63653C2×C418yescomplemented
79#63639C2×C412yescomplemented
80#63639C2312yes—
81C2×C3⋊(C3⋊C16)C2×C412yescomplemented
82C3×#837—24no—
83C3×#819—21no—
84C3×#819C2312yes—
85C3×#818—21no—
86C3×#817C2312yes—
87C3×#815C2312yes—
88C3×C8×Dic3D412yes—
89C3×#812—21no—
90C3×#812C2312yes—
91C2×C3×C3⋊C16—21no—
92#63564—24no—
93#33471—91noSylow
94C2×C3×#135—21no—
95C2×C3×#135C2×D311yescharacteristic
96C2×C3×#135C2×D311yescharacteristic
97C3×#568—61no—
98#5819—21no—
99C22×D24—31no—
100C22×D24—31no—
101C22×D24—61no—
102#5521—61no—
103#5521—61no—
104C2×C3×M32—31no—
105C3×#444—34no—
106C3×#443—62no—
107C2×C3×#108—31no—
108C3×#427—31no—
109C3×#421—61no—
110C3×#405—31no—
111#5236—21no—
112#5197C2×D314yescomplemented
113#5196—22no—
114#5193—34no—
115#5193—34no—
116#5193—34no—
117#5193—34no—
118#5193—64no—
119#5193—64no—
120C2×#828—32no—
121C2×#828—32no—
122C2×#828—62no—
123C2×#826—32no—
124C2×#826—32no—
125C2×#826—62no—
126#5131—61no—
127C2×#819C2×D311yescharacteristic
128#5106C2×D311yescharacteristic
129#5101C2×D311yescharacteristic
130C2×#812—31no—
131C2×#812—31no—
132C2×#812—61no—
133C2×#812C2×D311yescharacteristic
134#5001—61no—
135#4872—62no—
136#4869—34no—
137#4711—34no—
138C4×D24—62no—
139C3×#360—34no—
140#4566C2×D314yescomplemented
141#4516—34no—
142#4512—34no—
143#4495—34no—
144#4494—34no—
145#4487—34no—
146#4466—34no—
147C23×C3⋊D3—41no—
148C32×#41—22no—
149C32×#41—22no—
150C32×#41—41no—
151C32×#41—41no—
152C2×C32×Q8—21no—
153C2×C32×D4—21no—
154C2×C32×D4—41no—
155C22×C32×C4—41no—
156C22×C32×C4C2×D411yescharacteristic
157C2×C4⋊(C3⋊D3)—22no—
158C2×C4⋊(C3⋊D3)—22no—
159C2×C4⋊(C3⋊D3)—22no—
160C2×C4⋊(C3⋊D3)—41no—
161C2×C4⋊(C3⋊D3)—41no—
162C2×C4⋊(C3⋊D3)—41no—
163C2×#624—44no—
164C32×Q16—21no—
165C32×Q16C22×C412yes—
166C32×SD16—22no—
167C32×SD16—22no—
168C32×D8—21no—
169C32×D8C22×C412yes—
170C2×C32×C8C22×C411yescharacteristic
171C2×C32×C8C22×C411yescharacteristic
172C2×C32×C8C2×D411yescharacteristic
173C2×C32×C8#4111yescharacteristic
174C2×C32×C8#4111yescharacteristic
175C2×C32×C8C2411yescharacteristic
176#3745—22no—
177#3745—22no—
178#3745—22no—
179#3745C22×C414yes—
180C3×#217—21no—
181C3×#217—41no—
182C3×C4⋊Dic3—21no—
183C3×C4⋊Dic3—22no—
184C3×C4×Dic3—41no—
185C3×C4×Dic3C2×D412yes—
186C3×#208—21no—
187C3×#208—21no—
188C3×#208—22no—
189C3×#208—44no—
190C3×#208—41no—
191C2×C3×C3⋊C8—44no—
192C2×C3×C3⋊C8—41no—
193C2×C3×C3⋊C8C2×D412yes—
194#3722—44no—
195C3⋊(C3⋊C16)C22×C414yes—
196C3×C3⋊C16—22no—
197C2×#509—91no—
198#2957—31no—
199#2948—91no—
200AGL(1,ℤ/16)—98no—
201#2155—91no—
202C2×#361—91no—
203#2145—31no—
204#2110—91no—
205C2×C3×#41—21no—
206C2×C3×#41—21no—
207C2×C3×#41—41no—
208C22×D12—61no—
209C22×D12—61no—
210C22×D12—121no—
211C3×#135—21no—
212C3×#135—21no—
213C3×#135—21no—
214C3×#135—21no—
215C3×#135—22no—
216C3×#135—22no—
217C3×#135—41no—
218C3×#135—41no—
219C3×#135C4×D312yescomplemented
220C3×#135C4×D312yescomplemented
221C3×#135C22×D312yes—
222C3×#135C22×D312yes—
223C2×C3×Q16—21no—
224C2×C3×Q16C4×D311yescharacteristic, complemented
225C2×C3×Q16C4×D311yescharacteristic, complemented
226C2×C3×SD16—21no—
227C2×C3×SD16—21no—
228C2×C3×SD16—41no—
229C2×C3×D8—21no—
230C2×C3×D8C4×D311yescharacteristic, complemented
231C2×C3×D8C4×D311yescharacteristic, complemented
232C3×#131—64no—
233C3×#131—122no—
234C2×C3×M16—31no—
235C2×C3×M16—61no—
236C2×C3×M16—122no—
237C22×C3×C8—21no—
238C22×C3×C8C22×D311yescharacteristic
239C22×C3×C8C22×D311yescharacteristic
240C3×#117—31no—
241C3×#117—61no—
242#948—24no—
243#948—42no—
244#926—21no—
245#926#6711yescharacteristic
246C2×#208—21no—
247C2×#208—42no—
248C2×#208#6711yescharacteristic
249C2×D24—32no—
250C2×D24—32no—
251C2×D24—32no—
252C2×D24—32no—
253C2×D24—32no—
254C2×D24—32no—
255C2×D24—62no—
256C2×D24—62no—
257C2×D24—62no—
258C2×D24—61no—
259C2×D24—61no—
260C2×D24—61no—
261C2×D24—61no—
262C2×D24—61no—
263C2×D24—61no—
264C2×D24—121no—
265C2×D24—121no—
266C2×D24—121no—
267#893—64no—
268#893—122no—
269D3×C22⋊C4—122no—
270D3×C22⋊C4—122no—
271C4×D12—64no—
272C4×D12—122no—
273C3×M32—32no—
274C3×M32—61no—
275C2×C3×C16—61no—
276C3×#108—32no—
277C3×#108—61no—
278C3×#107—61no—
279C3×#106—32no—
280C3×#104—64no—
281C3×#97—32no—
282C3×C4×C8—32no—
283#837—24no—
284#828—38no—
285#828—38no—
286#828—68no—
287#826—38no—
288#826—38no—
289#826—68no—
290#821—64no—
291#819—21no—
292#819C22×D312yes—
293#818—21no—
294#817C22×D312yes—
295#815C22×D312yes—
296C8×Dic3#6712yes—
297#812—21no—
298#812—32no—
299#812—32no—
300#812—32no—
301#812—32no—
302#812—62no—
303#812—62no—
304#812C22×D312yes—
305C2×C3⋊C16—21no—
306C2×C3⋊C16—32no—
307C2×C3⋊C16—32no—
308C2×C3⋊C16—62no—
309#809—64no—
310C23×C32—41no—
311C23×C32AGL(1,ℤ/8)11yescharacteristic
312C22×C3⋊D3—42no—
313C22×C3⋊D3—42no—
314C22×C3⋊D3—42no—
315C22×C3⋊D3—162no—
316C32×Q8—22no—
317C32×Q8—41no—
318C32×D4—22no—
319C32×D4—42no—
320C32×D4—42no—
321C32×D4—41no—
322C2×C32×C4—41no—
323C2×C32×C4—42no—
324C2×C32×C4—42no—
325C2×C32×C4C4×D411yescharacteristic
326C2×C32×C4C4×D411yescharacteristic
327C2×C32×C4AGL(1,ℤ/8)11yescharacteristic
328C2×C32×C4AGL(1,ℤ/8)11yescharacteristic
329C2×C32×C4AGL(1,ℤ/8)11yescharacteristic
330C2×C32×C4C22×D411yescharacteristic
331C4⋊(C3⋊D3)—24no—
332C4⋊(C3⋊D3)—42no—
333C4⋊(C3⋊D3)—42no—
334C4⋊(C3⋊D3)—42no—
335C2×C3×Dic3—22no—
336C2×C3×Dic3—42no—
337#624—164no—
338C32×C8C4×D411yescharacteristic
339C32×C8C4×D411yescharacteristic
340C32×C8C23×C411yescharacteristic
341C32×C8C2×#4111yescharacteristic
342C3×C3⋊C8—22no—
343C3×C3⋊C8—42no—
344C2×#135D3211yescharacteristic
345C22×D8—91no—
346#568—61no—
347#518—181no—
348#509—94no—
349#509—94no—
350C2×SD32—92no—
351C2×D16—92no—
352C2×M32—31no—
353C2×M32—91no—
354#444—34no—
355#443—62no—
356#442—94no—
357C4×D8—182no—
358C2×#108—31no—
359#427—31no—
360#421—61no—
361#418—181no—
362#405—31no—
363#365—94no—
364#361—94no—
365#360—34no—
366#347—94no—
367C23×D3—121no—
368C23×D3—121no—
369C23×D3—241no—
370C3×#41—22no—
371C3×#41—22no—
372C3×#41—22no—
373C3×#41—22no—
374C3×#41—42no—
375C3×#41—42no—
376C3×#41—41no—
377C3×#41—41no—
378C3×#41—41no—
379C3×#41—41no—
380C3×#41—81no—
381C3×#41—81no—
382C2×C3×Q8—21no—
383C2×C3×Q8—21no—
384C2×C3×Q8—41no—
385C2×C3×D4—21no—
386C2×C3×D4—21no—
387C2×C3×D4—41no—
388C2×C3×D4—41no—
389C2×C3×D4—41no—
390C2×C3×D4—81no—
391C22×C3×C4—21no—
392C22×C3×C4—41no—
393C22×C3×C4—41no—
394C22×C3×C4—81no—
395C22×C3×C4D3×D411yescharacteristic
396C22×C3×C4C2×#6711yescharacteristic
397C2×D12—62no—
398C2×D12—62no—
399C2×D12—62no—
400C2×D12—62no—
401C2×D12—62no—
402C2×D12—62no—
403C2×D12—122no—
404C2×D12—122no—
405C2×D12—122no—
406C2×D12—121no—
407C2×D12—121no—
408C2×D12—121no—
409C2×D12—121no—
410C2×D12—121no—
411C2×D12—121no—
412C2×D12—241no—
413C2×D12—241no—
414C2×D12—241no—
415C2×C4×D3—124no—
416C2×C4×D3—124no—
417C3×Q16—21no—
418C3×Q16—21no—
419C3×Q16—22no—
420C3×Q16—41no—
421C3×Q16C2×C4×D312yes—
422C3×Q16C2×C4×D312yes—
423C3×SD16—22no—
424C3×SD16—22no—
425C3×SD16—22no—
426C3×SD16—22no—
427C3×SD16—42no—
428C3×SD16—42no—
429C3×D8—21no—
430C3×D8—21no—
431C3×D8—22no—
432C3×D8—41no—
433C3×D8C2×C4×D312yes—
434C3×D8C2×C4×D312yes—
435C3×M16—61no—
436C3×M16—61no—
437C3×M16—62no—
438C3×M16—124no—
439C3×M16—121no—
440C2×C3×C8—21no—
441C2×C3×C8—21no—
442C2×C3×C8—21no—
443C2×C3×C8—21no—
444C2×C3×C8—21no—
445C2×C3×C8—21no—
446C2×C3×C8—32no—
447C2×C3×C8—124no—
448C2×C3×C8—121no—
449C2×C3×C8C2×C4×D311yescharacteristic
450C2×C3×C8C2×C4×D311yescharacteristic
451C2×C3×C8C2×C4×D311yescharacteristic
452C2×C3×C8C2×C4×D311yescharacteristic
453C2×C3×C8#23511yescharacteristic
454C2×C3×C8#23511yescharacteristic
455C2×C3×C8D3×D411yescharacteristic
456C2×C3×C8#23711yescharacteristic
457C2×C3×C8#23711yescharacteristic
458C2×C3×C8C2×#6711yescharacteristic
459C2×C3×C8C23×D311yescharacteristic
460C2×C3×C8C23×D311yescharacteristic
461C3×C4⋊C4—61no—
462C3×C4⋊C4—62no—
463C3×C22⋊C4—61no—
464C3×C22⋊C4—121no—
465C3×C42—32no—
466C3×C42—121no—
467#217—21no—
468#217—41no—
469(C2×D3)⋊C4—124no—
470(C2×D3)⋊C4—124no—
471C4⋊Dic3—21no—
472C4⋊Dic3—22no—
473C4×Dic3—41no—
474C4×Dic3C2×#6712yes—
475#208—21no—
476#208—21no—
477#208—22no—
478#208—44no—
479#208—41no—
480C2×C3⋊C8—44no—
481C2×C3⋊C8—41no—
482C2×C3⋊C8C2×#6712yes—
483D24—34no—
484D24—34no—
485D24—64no—
486D24—62no—
487D24—62no—
488D24—62no—
489D24—62no—
490D24—62no—
491D24—62no—
492D24—122no—
493D24—122no—
494D24—122no—
495C3×C16—62no—
496C3⋊C16—22no—
497C3⋊C16—34no—
498C3⋊C16—34no—
499C3⋊C16—64no—
500C22×C32—41no—
501C22×C32—42no—
502C22×C32—161no—
503C22×C32#44211yescharacteristic
504C22×C32#44211yescharacteristic
505C22×C32C2×AGL(1,ℤ/8)11yescharacteristic
506C2×C3⋊D3—44no—
507C2×C3⋊D3—84no—
508C2×C3⋊D3—162no—
509C2×C3⋊D3—162no—
510C32×C4—42no—
511C32×C4#44211yescharacteristic
512C32×C4#44211yescharacteristic
513C32×C4C2×C4×D411yescharacteristic
514C32×C4C2×AGL(1,ℤ/8)11yescharacteristic
515C3×Dic3—42no—
516C3×Dic3—82no—
517C2×#41—21no—
518C22×D4—181no—
519#135—21no—
520#135—21no—
521#135#62412yescomplemented
522#135C2×D3212yes—
523C2×Q16#62411yescharacteristic, complemented
524C2×SD16—21no—
525C2×D8—92no—
526C2×D8—92no—
527C2×D8—92no—
528C2×D8—181no—
529C2×D8—181no—
530C2×D8—181no—
531C2×D8#62411yescharacteristic, complemented
532#131—64no—
533#131—122no—
534C2×M16—31no—
535C2×M16—61no—
536C2×M16—122no—
537C22×C8C2×D3211yescharacteristic
538C4×D4—184no—
539C4×D4—362no—
540#117—31no—
541#117—61no—
542C2×C22⋊C4—362no—
543SD32—98no—
544D16—98no—
545M32—32no—
546M32—61no—
547M32—92no—
548M32—92no—
549C2×C16—61no—
550C2×C16—92no—
551#108—32no—
552#108—61no—
553#107—61no—
554#106—32no—
555#104—64no—
556#102—184no—
557#97—32no—
558C4×C8—32no—
559C23×C3—21no—
560C23×C3—41no—
561C23×C3—41no—
562C23×C3—81no—
563C23×C3#91111yescharacteristic
564C23×C3#94911yescharacteristic
565C22×D3—122no—
566C22×D3—122no—
567C22×D3—122no—
568C22×D3—122no—
569C22×D3—122no—
570C22×D3—122no—
571C22×D3—242no—
572C22×D3—242no—
573C22×D3—242no—
574C22×D3—482no—
575C22×D3—482no—
576C22×D3—484no—
577C3×Q8—22no—
578C3×Q8—22no—
579C3×Q8—42no—
580C3×Q8—41no—
581C3×Q8—41no—
582C3×Q8—81no—
583C3×D4—22no—
584C3×D4—22no—
585C3×D4—42no—
586C3×D4—42no—
587C3×D4—42no—
588C3×D4—42no—
589C3×D4—42no—
590C3×D4—41no—
591C3×D4—41no—
592C3×D4—81no—
593C3×D4—82no—
594C3×D4—82no—
595C2×C3×C4—21no—
596C2×C3×C4—21no—
597C2×C3×C4—21no—
598C2×C3×C4—21no—
599C2×C3×C4—21no—
600C2×C3×C4—21no—
601C2×C3×C4—41no—
602C2×C3×C4—41no—
603C2×C3×C4—42no—
604C2×C3×C4—42no—
605C2×C3×C4—42no—
606C2×C3×C4—42no—
607C2×C3×C4—62no—
608C2×C3×C4—82no—
609C2×C3×C4—82no—
610C2×C3×C4—81no—
611C2×C3×C4—122no—
612C2×C3×C4#67⋊C411yescharacteristic
613C2×C3×C4#67⋊C411yescharacteristic
614C2×C3×C4#91111yescharacteristic
615C2×C3×C4#91411yescharacteristic
616C2×C3×C4#91411yescharacteristic
617C2×C3×C4C4×#6711yescharacteristic
618C2×C3×C4C4×#6711yescharacteristic
619C2×C3×C4#93211yescharacteristic
620C2×C3×C4#93211yescharacteristic
621C2×C3×C4#94911yescharacteristic
622C2×C3×C4C2×D3×D411yescharacteristic
623C2×C3×C4C22×#6711yescharacteristic
624C2×Dic3—22no—
625C2×Dic3—42no—
626D12—64no—
627D12—64no—
628D12—124no—
629D12—122no—
630D12—122no—
631D12—122no—
632D12—122no—
633D12—122no—
634D12—122no—
635D12—242no—
636D12—242no—
637D12—242no—
638C4×D3—484no—
639C4×D3—484no—
640C3×C8—21no—
641C3×C8—21no—
642C3×C8—21no—
643C3×C8—21no—
644C3×C8—62no—
645C3×C8—122no—
646C3×C8#67⋊C411yescharacteristic
647C3×C8#67⋊C411yescharacteristic
648C3×C8C4×#6711yescharacteristic
649C3×C8C4×#6711yescharacteristic
650C3×C8C22×C4×D311yescharacteristic
651C3×C8C22×C4×D311yescharacteristic
652C3×C8C2×#23511yescharacteristic
653C3×C8C2×#23711yescharacteristic
654C3⋊C8—22no—
655C3⋊C8—42no—
656C2×C32—21no—
657C2×C32—21no—
658C2×C32—21no—
659C2×C32—82no—
660C2×C32C2×#44211yescharacteristic
661C3⋊D3—84no—
662C24—361no—
663#41—22no—
664#41—22no—
665#41—41no—
666#41—41no—
667C2×Q8—21no—
668C2×D4—21no—
669C2×D4—41no—
670C2×D4—182no—
671C2×D4—182no—
672C2×D4—182no—
673C2×D4—361no—
674C2×D4—361no—
675C2×D4—361no—
676C22×C4—41no—
677C22×C4—364no—
678C22×C4D3×#6711yescharacteristic
679Q16—21no—
680Q16C2×#62412yes—
681SD16—22no—
682SD16—22no—
683D8—21no—
684D8—94no—
685D8—182no—
686D8—182no—
687D8—182no—
688D8C2×#62412yes—
689M16—61no—
690M16—61no—
691M16—62no—
692M16—124no—
693M16—121no—
694C2×C8—32no—
695C2×C8—124no—
696C2×C8—121no—
697C2×C8#380411yescharacteristic
698C2×C8#380411yescharacteristic
699C2×C8C2×#62411yescharacteristic
700C2×C8C2×#62411yescharacteristic
701C2×C8D3×#6711yescharacteristic
702C2×C8C22×D3211yescharacteristic
703C4⋊C4—61no—
704C4⋊C4—62no—
705C22⋊C4—61no—
706C22⋊C4—121no—
707C22⋊C4—364no—
708C42—32no—
709C42—121no—
710C16—62no—
711C16—94no—
712C22×C3—21no—
713C22×C3—21no—
714C22×C3—21no—
715C22×C3—41no—
716C22×C3—41no—
717C22×C3—42no—
718C22×C3—42no—
719C22×C3—42no—
720C22×C3—82no—
721C22×C3—161no—
722C22×C3—161no—
723C22×C3—162no—
724C22×C3#478511yescharacteristic
725C22×C3#478511yescharacteristic
726C22×C3#501411yescharacteristic
727C22×C3#501411yescharacteristic
728C22×C3C2×#91111yescharacteristic
729C22×C3C2×#94911yescharacteristic
730C2×D3—124no—
731C2×D3—124no—
732C2×D3—244no—
733C2×D3—244no—
734C2×D3—244no—
735C2×D3—484no—
736C2×D3—482no—
737C2×D3—482no—
738C2×D3—482no—
739C2×D3—482no—
740C2×D3—484no—
741C2×D3—484no—
742C3×C4—21no—
743C3×C4—21no—
744C3×C4—21no—
745C3×C4—21no—
746C3×C4—42no—
747C3×C4—42no—
748C3×C4—82no—
749C3×C4—122no—
750C3×C4—242no—
751C3×C4#478511yescharacteristic
752C3×C4#478511yescharacteristic
753C3×C4#501411yescharacteristic
754C3×C4#501411yescharacteristic
755C3×C4C2×#67⋊C411yescharacteristic
756C3×C4C2×#91411yescharacteristic
757C3×C4C2×C4×#6711yescharacteristic
758C3×C4C2×#93211yescharacteristic
759Dic3—42no—
760Dic3—82no—
761C32#3347111yescharacteristic, complemented, Sylow
762C23—41no—
763C23—362no—
764C23—362no—
765C23—362no—
766C23—1442no—
767C23#6392511yescharacteristic
768Q8—22no—
769Q8—41no—
770D4—22no—
771D4—42no—
772D4—42no—
773D4—41no—
774D4—184no—
775D4—362no—
776D4—362no—
777D4—362no—
778C2×C4—41no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—62no—
782C2×C4—122no—
783C2×C4—1444no—
784C2×C4#6392511yescharacteristic
785C2×C4#6393411yescharacteristic
786C2×C4#6393411yescharacteristic
787C2×C4#6395211yescharacteristic
788C2×C4#6395211yescharacteristic
789C2×C4C2×D3×#6711yescharacteristic
790C8—62no—
791C8—122no—
792C8#6395211yescharacteristic
793C8#6395211yescharacteristic
794C8C2×#380411yescharacteristic
795C8C22×#62411yescharacteristic
796C2×C3—22no—
797C2×C3—21no—
798C2×C3—21no—
799C2×C3—21no—
800C2×C3—21no—
801C2×C3—21no—
802C2×C3—21no—
803C2×C3—21no—
804C2×C3—41no—
805C2×C3—41no—
806C2×C3—82no—
807C2×C3—82no—
808C2×C3—162no—
809C2×C3C2×#478511yescharacteristic
810C2×C3C2×#501411yescharacteristic
811D3—244no—
812D3—244no—
813D3—484no—
814C22—41no—
815C22—42no—
816C22—161no—
817C22—364no—
818C22—724no—
819C22—1442no—
820C22—1442no—
821C22#1059140411yescharacteristic
822C22#1059140411yescharacteristic
823C22C2×#6392511yescharacteristic
824C4—42no—
825C4—122no—
826C4—242no—
827C4#1059140411yescharacteristic
828C4#1059140411yescharacteristic
829C4C2×#6393411yescharacteristic
830C4C2×#6395211yescharacteristic
831C3—21no—
832C3#1094865911yescharacteristic, complemented
833C3#1094866211yescharacteristic, complemented
834C2—21no—
835C2—21no—
836C2—21no—
837C2—82no—
838C2—724no—
839C2C2×#1059140411yescharacteristic
subgroupG/H
centerC2C2×#10591404
commutatorC32×C8C23×C4
FrattiniC2×C8C22×D32
FittingC2×C32×#135C22
socleC2×C32C2×#442
prime radicalC2×#10592892C2
cosocleC2×C32×C8C24
hypercenterC2×#135D32
hypocenterC32#33471
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. #11860704C2semidirect
4. #11797971C2semidirect
5. #11797135C2semidirect
6. C2×#10589128C2semidirect
7. C3×#72076C2semidirect
8. #11795946C2semidirect
15. #10592892C4semidirect
17. C2×#63655C4semidirect
18. C2×#63653C4semidirect
21. C3×#5197C22semidirect
28. #10590768C22semidirect
30. C3×#4566C22semidirect
31. #10589138C22semidirect
32. #10589128C22semidirect
33. #10589105C22semidirect
35. #83910D3semidirect
42. #72076D3semidirect
55. C32×#135C2×C4semidirect
57. C2×C32×Q16C2×C4semidirect
59. C2×C32×D8C2×C4semidirect
77. #63655C2×C4semidirect
78. #63653C2×C4semidirect
79. #63639C2×C4semidirect
81. C2×C3⋊(C3⋊C16)C2×C4semidirect
112. #5197C2×D3semidirect
140. #4566C2×D3semidirect
219. C3×#135C4×D3semidirect
220. C3×#135C4×D3semidirect
224. C2×C3×Q16C4×D3semidirect
225. C2×C3×Q16C4×D3semidirect
230. C2×C3×D8C4×D3semidirect
231. C2×C3×D8C4×D3semidirect
521. #135#624semidirect
523. C2×Q16#624semidirect
531. C2×D8#624semidirect
761. C32#33471semidirect
832. C3#10948659semidirect
833. C3#10948662semidirect

Maximal subgroups

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

subgroupindex
C2×#105928922
C3×#839102
#118607042
#117979712
#117971352
C2×#105891282
C3×#720762
#117959462
#109486623
#109486593