Finite Group Databasebeta

← #72222819

Subgroups — #72222819

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×#10592846C211yesmaximal, characteristic
2#11861234C211yesmaximal, characteristic, complemented
3C3×#83823C211yesmaximal, characteristic, complemented
4#11797978C218yesmaximal, complemented
5#11797135C211yesmaximal, characteristic, complemented
6C2×C3×#4563C211yesmaximal, characteristic, complemented
7#11796861C211yesmaximal, characteristic, complemented
8#11795946C211yesmaximal, characteristic, complemented
9#10948665—31nomaximal
10#10948660—31nomaximal
11C22×C32×D8C2211yescharacteristic
12C2×#64113C2211yescharacteristic
13C3×#5798—21no—
14#10594780—21no—
15C2×#63654C412yescomplemented
16#10592846C414yescomplemented
17#10592846C2214yes—
18C2×#63653C412yescomplemented
19C2×#63639C2211yescharacteristic
20C3×#5215—21no—
21C3×#5152C2214yescomplemented
22C3×Dic3×D8—22no—
23C2×C3×#819C2211yescharacteristic
24C3×#5106C2211yescharacteristic
25C3×#5101C2211yescharacteristic
26C2×C3×#812C2211yescharacteristic
27#10591113—21no—
28#10590918C2214yescomplemented
29#10590917—22no—
30C3×#4563C2214yescomplemented
31#10589138C2214yescomplemented
32#10589125C2214yescomplemented
33#10589105C2214yescomplemented
34C3×#2948—31no—
35#83823D311yescharacteristic, complemented
36C2×#5147—31no—
37C2×#5147—31no—
38C2×#5147—61no—
39#79249—31no—
40#78580—31no—
41C2×C3×#361—31no—
42C2×#4563D311yescharacteristic, complemented
43#71450—31no—
44#71425—31no—
45#70918—38no—
46#70685—31no—
47#70656—31no—
48#70650—31no—
49#69884—31no—
50#69254—38no—
51C22×C32×D4—21no—
52C2×#3828—21no—
53C2×C32×D8—21no—
54C2×C32×D8—21no—
55C2×C32×D8—21no—
56C2×C32×D8C2×C412yes—
57C2×C32×D8C2×C412yes—
58C2×C32×D8C2312yes—
59C22×C32×C8C2311yescharacteristic
60C2×#3746C2×C411yescharacteristic, complemented
61#64113—21no—
62#64113—21no—
63#64113C2×C412yescomplemented
64#64113C2312yes—
65C2×#3745C2×C411yescharacteristic, complemented
66C2×#3744—21no—
67C2×C3×#217—42no—
68C3×D4×Dic3—24no—
69C3×D4×Dic3—42no—
70C3×#926—21no—
71C3×#926D411yescharacteristic
72C2×C3×#208—21no—
73C2×C3×#208D411yescharacteristic
74#63818—42no—
75#63817—24no—
76#63817—42no—
77#63654C2×C418yescomplemented
78#63653C2×C418yescomplemented
79#63639C2×C412yescomplemented
80#63639C2312yes—
81C2×C3⋊(C3⋊C16)C2×C412yescomplemented
82C3×#832—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#63570—24no—
93#33471—91noSylow
94C22×C3×D8—21no—
95C22×C3×D8C2×D311yescharacteristic
96C22×C3×D8C2×D311yescharacteristic
97C3×#518—61no—
98#5798—21no—
99#5745—61no—
100#5745—61no—
101C2×#904—31no—
102C2×#904—31no—
103C2×#904—61no—
104C2×C3×M32—31no—
105C3×#442—34no—
106C3×C4×D8—62no—
107C2×C3×#108—31no—
108C3×#427—31no—
109C3×#418—61no—
110C3×#405—31no—
111#5215—21no—
112#5152C2×D314yescomplemented
113Dic3×D8—22no—
114C2×#827—32no—
115C2×#827—32no—
116C2×#827—62no—
117#5147—34no—
118#5147—34no—
119#5147—34no—
120#5147—34no—
121#5147—64no—
122#5147—64no—
123C2×#826—32no—
124C2×#826—32no—
125C2×#826—62no—
126#5139—61no—
127C2×#819C2×D311yescharacteristic
128#5106C2×D311yescharacteristic
129#5101C2×D311yescharacteristic
130C2×#812—31no—
131C2×#812—31no—
132C2×#812—61no—
133C2×#812C2×D311yescharacteristic
134#5005—61no—
135#4895—62no—
136#4894—34no—
137#4717—34no—
138#4700—62no—
139C3×#361—34no—
140#4563C2×D314yescomplemented
141#4518—34no—
142#4512—34no—
143#4494—34no—
144#4488—34no—
145#4487—34no—
146#4466—34no—
147C24×C32—41no—
148C2×C32×D4—22no—
149C2×C32×D4—22no—
150C2×C32×D4—22no—
151C2×C32×D4—41no—
152C2×C32×D4—41no—
153C2×C32×D4—41no—
154C22×C32×C4C2×D411yescharacteristic
155C2×#638—41no—
156#3828—22no—
157#3828—22no—
158#3828—41no—
159#3828—41no—
160C2×C4⋊(C3⋊D3)—21no—
161C2×C4×C3⋊D3—41no—
162C2×#634—21no—
163C22×C3×Dic3—44no—
164C32×D8—22no—
165C32×D8—22no—
166C32×D8—22no—
167C32×D8C22×C414yes—
168C2×C32×C8C22×C411yescharacteristic
169C2×C32×C8C22×C411yescharacteristic
170C2×C32×C8C2×D411yescharacteristic
171C2×C32×C8#4111yescharacteristic
172C2×C32×C8#4111yescharacteristic
173C2×C32×C8C2411yescharacteristic
174#3746—21no—
175#3746C22×C412yes—
176#3745—21no—
177#3745C22×C412yes—
178#3744—22no—
179#3744—22no—
180C3×#217—21no—
181C3×#217—44no—
182C3×#217—41no—
183C3×C4⋊Dic3—21no—
184C3×C4⋊Dic3—22no—
185C3×C4×Dic3—41no—
186C3×C4×Dic3C2×D412yes—
187C3×#208—21no—
188C3×#208—21no—
189C3×#208—22no—
190C3×#208—41no—
191C2×C3×C3⋊C8—41no—
192C2×C3×C3⋊C8C2×D412yes—
193#3712—44no—
194#3710—44no—
195C3⋊(C3⋊C16)C22×C414yes—
196C3×C3⋊C16—22no—
197C2×#509—91no—
198#2957—91no—
199#2948—31no—
200AGL(1,ℤ/16)—98no—
201#2155—91no—
202C2×#361—31no—
203#2145—91no—
204#2110—91no—
205C22×C3×D4—21no—
206C22×C3×D4—21no—
207C22×C3×D4—41no—
208C2×#235—61no—
209C2×#235—61no—
210C2×#235—121no—
211C2×C3×D8—21no—
212C2×C3×D8—21no—
213C2×C3×D8—21no—
214C2×C3×D8—21no—
215C2×C3×D8—21no—
216C2×C3×D8—21no—
217C2×C3×D8—22no—
218C2×C3×D8—22no—
219C2×C3×D8—22no—
220C2×C3×D8—41no—
221C2×C3×D8—41no—
222C2×C3×D8—41no—
223C2×C3×D8C4×D312yes—
224C2×C3×D8C4×D312yes—
225C2×C3×D8C4×D312yes—
226C2×C3×D8C4×D312yes—
227C2×C3×D8C22×D312yes—
228C2×C3×D8C22×D312yes—
229C2×C3×M16—31no—
230C2×C3×M16—61no—
231C22×C3×C8—21no—
232C22×C3×C8C22×D311yescharacteristic
233C22×C3×C8C22×D311yescharacteristic
234C3×C4×D4—64no—
235C3×C4×D4—122no—
236C3×#117—31no—
237C3×#117—61no—
238C2×C3×C22⋊C4—122no—
239C2×#217—42no—
240D4×Dic3—24no—
241D4×Dic3—42no—
242#926—21no—
243#926#6711yescharacteristic
244C2×#208—21no—
245C2×#208#6711yescharacteristic
246#907—64no—
247#907—122no—
248D3×M16—122no—
249D3×M16—122no—
250C2×Dic12—31no—
251C2×Dic12—31no—
252C2×Dic12—61no—
253#904—32no—
254#904—32no—
255#904—32no—
256#904—32no—
257#904—62no—
258#904—62no—
259#904—61no—
260#904—61no—
261#904—61no—
262#904—61no—
263#904—121no—
264#904—121no—
265C2×D24—31no—
266C2×D24—31no—
267C2×D24—61no—
268C2×#204—61no—
269C2×#204—61no—
270C2×#204—121no—
271#901—64no—
272#901—122no—
273C3×M32—32no—
274C3×M32—61no—
275C2×C3×C16—61no—
276C3×#108—32no—
277C3×#108—61no—
278C3×#107—61no—
279C3×#106—32no—
280C3×#102—64no—
281C3×#97—32no—
282C3×C4×C8—32no—
283#832—24no—
284#827—38no—
285#827—38no—
286#827—68no—
287#826—38no—
288#826—38no—
289#826—68no—
290#825—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#805—64no—
310C23×C32—42no—
311C23×C32—42no—
312C23×C32—42no—
313C23×C32—162no—
314C23×C32AGL(1,ℤ/8)11yescharacteristic
315C22×C3⋊D3—41no—
316C32×D4—24no—
317C32×D4—42no—
318C32×D4—42no—
319C32×D4—42no—
320C2×C32×C4C4×D411yescharacteristic
321C2×C32×C4C4×D411yescharacteristic
322C2×C32×C4AGL(1,ℤ/8)11yescharacteristic
323C2×C32×C4AGL(1,ℤ/8)11yescharacteristic
324C2×C32×C4AGL(1,ℤ/8)11yescharacteristic
325C2×C32×C4C22×D411yescharacteristic
326#638—42no—
327#638—42no—
328C2×C3⋊Dic3—41no—
329C4⋊(C3⋊D3)—22no—
330C4⋊(C3⋊D3)—41no—
331C4×C3⋊D3—42no—
332C4×C3⋊D3—42no—
333#634—22no—
334#634—41no—
335C2×C3×Dic3—22no—
336C2×C3×Dic3—42no—
337C2×C3×Dic3—164no—
338C32×C8C4×D411yescharacteristic
339C32×C8C4×D411yescharacteristic
340C32×C8C23×C411yescharacteristic
341C32×C8C2×#4111yescharacteristic
342C3×C3⋊C8—22no—
343C3×C3⋊C8—42no—
344C2×#135—91no—
345C22×D8D3211yescharacteristic
346#568—181no—
347#518—61no—
348#509—94no—
349#509—94no—
350C2×SD32—92no—
351C2×D16—92no—
352C2×M32—31no—
353C2×M32—91no—
354#444—94no—
355#443—182no—
356#442—34no—
357C4×D8—62no—
358C2×#108—31no—
359#427—31no—
360#421—181no—
361#418—61no—
362#405—31no—
363#365—94no—
364#361—34no—
365#360—94no—
366#347—94no—
367C24×C3—41no—
368C24×C3—41no—
369C24×C3—81no—
370C2×C3×D4—22no—
371C2×C3×D4—22no—
372C2×C3×D4—22no—
373C2×C3×D4—22no—
374C2×C3×D4—22no—
375C2×C3×D4—22no—
376C2×C3×D4—42no—
377C2×C3×D4—42no—
378C2×C3×D4—42no—
379C2×C3×D4—41no—
380C2×C3×D4—41no—
381C2×C3×D4—41no—
382C2×C3×D4—41no—
383C2×C3×D4—41no—
384C2×C3×D4—41no—
385C2×C3×D4—81no—
386C2×C3×D4—81no—
387C2×C3×D4—81no—
388C22×C3×C4—21no—
389C22×C3×C4—124no—
390C22×C3×C4D3×D411yescharacteristic
391C22×C3×C4C2×#6711yescharacteristic
392C2×#67—121no—
393C2×#67—121no—
394C2×#67—241no—
395C22×Dic3—44no—
396#235—62no—
397#235—62no—
398#235—62no—
399#235—62no—
400#235—122no—
401#235—122no—
402#235—121no—
403#235—121no—
404#235—121no—
405#235—121no—
406#235—241no—
407#235—241no—
408C2×D12—61no—
409C2×D12—61no—
410C2×D12—121no—
411C2×C4×D3—121no—
412C2×C4×D3—121no—
413C2×C4×D3—241no—
414C2×Dic6—61no—
415C2×Dic6—61no—
416C2×Dic6—121no—
417C3×D8—22no—
418C3×D8—22no—
419C3×D8—22no—
420C3×D8—22no—
421C3×D8—22no—
422C3×D8—22no—
423C3×D8—24no—
424C3×D8—42no—
425C3×D8—42no—
426C3×D8—42no—
427C3×D8C2×C4×D314yes—
428C3×D8C2×C4×D314yes—
429C3×M16—61no—
430C3×M16—61no—
431C3×M16—62no—
432C3×M16—121no—
433C2×C3×C8—21no—
434C2×C3×C8—21no—
435C2×C3×C8—21no—
436C2×C3×C8—21no—
437C2×C3×C8—21no—
438C2×C3×C8—21no—
439C2×C3×C8—32no—
440C2×C3×C8—121no—
441C2×C3×C8C2×C4×D311yescharacteristic
442C2×C3×C8C2×C4×D311yescharacteristic
443C2×C3×C8C2×C4×D311yescharacteristic
444C2×C3×C8C2×C4×D311yescharacteristic
445C2×C3×C8#23511yescharacteristic
446C2×C3×C8#23511yescharacteristic
447C2×C3×C8D3×D411yescharacteristic
448C2×C3×C8#23711yescharacteristic
449C2×C3×C8#23711yescharacteristic
450C2×C3×C8C2×#6711yescharacteristic
451C2×C3×C8C23×D311yescharacteristic
452C2×C3×C8C23×D311yescharacteristic
453C3×C4⋊C4—61no—
454C3×C4⋊C4—62no—
455C3×C22⋊C4—61no—
456C3×C22⋊C4—124no—
457C3×C22⋊C4—121no—
458C3×C42—32no—
459C3×C42—121no—
460#217—21no—
461#217—44no—
462#217—41no—
463C4⋊Dic3—21no—
464C4⋊Dic3—22no—
465C4×Dic3—41no—
466C4×Dic3C2×#6712yes—
467#208—21no—
468#208—21no—
469#208—22no—
470#208—41no—
471C2×C3⋊C8—41no—
472C2×C3⋊C8C2×#6712yes—
473Dic12—32no—
474Dic12—32no—
475Dic12—62no—
476Dic12—61no—
477Dic12—61no—
478Dic12—121no—
479D24—32no—
480D24—32no—
481D24—62no—
482D24—61no—
483D24—61no—
484D24—121no—
485#204—62no—
486#204—62no—
487#204—62no—
488#204—62no—
489#204—122no—
490#204—122no—
491ΓL(1,𝔽25)—124no—
492ΓL(1,𝔽25)—124no—
493D3×C8—124no—
494D3×C8—124no—
495C3×C16—62no—
496C3⋊C16—22no—
497C3⋊C16—34no—
498C3⋊C16—34no—
499C3⋊C16—64no—
500C22×C32—41no—
501C22×C32—44no—
502C22×C32—84no—
503C22×C32—162no—
504C22×C32—162no—
505C22×C32#44211yescharacteristic
506C22×C32#44211yescharacteristic
507C22×C32C2×AGL(1,ℤ/8)11yescharacteristic
508C2×C3⋊D3—42no—
509C2×C3⋊D3—161no—
510C32×C4#44211yescharacteristic
511C32×C4#44211yescharacteristic
512C32×C4C2×C4×D411yescharacteristic
513C32×C4C2×AGL(1,ℤ/8)11yescharacteristic
514C3⋊Dic3—42no—
515C3×Dic3—42no—
516C3×Dic3—82no—
517C2×#41—181no—
518C22×D4—21no—
519#135—92no—
520#135—92no—
521#135—181no—
522#135—181no—
523C2×Q16—91no—
524C2×SD16—181no—
525C2×D8—21no—
526C2×D8—21no—
527C2×D8—21no—
528C2×D8—91no—
529C2×D8#62412yes—
530C2×D8#62412yes—
531C2×D8C2×D3212yes—
532#131—184no—
533#131—362no—
534C2×M16—31no—
535C2×M16—61no—
536C2×M16—362no—
537C22×C8C2×D3211yescharacteristic
538C4×D4—64no—
539C4×D4—122no—
540#117—31no—
541#117—61no—
542C2×C22⋊C4—122no—
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—184no—
556#102—64no—
557#97—32no—
558C4×C8—32no—
559C23×C3—21no—
560C23×C3—42no—
561C23×C3—42no—
562C23×C3—42no—
563C23×C3—42no—
564C23×C3—42no—
565C23×C3—42no—
566C23×C3—82no—
567C23×C3—82no—
568C23×C3—82no—
569C23×C3—162no—
570C23×C3—162no—
571C23×C3—164no—
572C23×C3#91411yescharacteristic
573C23×C3#93211yescharacteristic
574C22×D3—121no—
575C22×D3—121no—
576C22×D3—241no—
577C3×D4—24no—
578C3×D4—24no—
579C3×D4—44no—
580C3×D4—42no—
581C3×D4—42no—
582C3×D4—42no—
583C3×D4—42no—
584C3×D4—42no—
585C3×D4—42no—
586C3×D4—82no—
587C3×D4—82no—
588C3×D4—82no—
589C2×C3×C4—21no—
590C2×C3×C4—21no—
591C2×C3×C4—21no—
592C2×C3×C4—21no—
593C2×C3×C4—21no—
594C2×C3×C4—21no—
595C2×C3×C4—62no—
596C2×C3×C4—122no—
597C2×C3×C4—484no—
598C2×C3×C4#67⋊C411yescharacteristic
599C2×C3×C4#67⋊C411yescharacteristic
600C2×C3×C4#91111yescharacteristic
601C2×C3×C4#91111yescharacteristic
602C2×C3×C4#91411yescharacteristic
603C2×C3×C4C4×#6711yescharacteristic
604C2×C3×C4C4×#6711yescharacteristic
605C2×C3×C4#93211yescharacteristic
606C2×C3×C4#94911yescharacteristic
607C2×C3×C4#94911yescharacteristic
608C2×C3×C4C2×D3×D411yescharacteristic
609C2×C3×C4C22×#6711yescharacteristic
610#67—122no—
611#67—122no—
612#67—122no—
613#67—122no—
614#67—242no—
615#67—242no—
616C2×Dic3—22no—
617C2×Dic3—42no—
618C2×Dic3—121no—
619C2×Dic3—121no—
620C2×Dic3—164no—
621C2×Dic3—241no—
622D12—62no—
623D12—62no—
624D12—122no—
625D12—121no—
626D12—121no—
627D12—241no—
628C4×D3—122no—
629C4×D3—122no—
630C4×D3—122no—
631C4×D3—122no—
632C4×D3—242no—
633C4×D3—242no—
634Dic6—62no—
635Dic6—62no—
636Dic6—122no—
637Dic6—121no—
638Dic6—121no—
639Dic6—241no—
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—84no—
660C2×C32C2×#44211yescharacteristic
661C3⋊D3—82no—
662C24—41no—
663#41—182no—
664#41—182no—
665#41—361no—
666#41—361no—
667C2×Q8—181no—
668C2×D4—22no—
669C2×D4—22no—
670C2×D4—22no—
671C2×D4—41no—
672C2×D4—41no—
673C2×D4—41no—
674C2×D4—181no—
675C2×D4—361no—
676C22×C4—124no—
677C22×C4—361no—
678C22×C4D3×#6711yescharacteristic
679Q16—92no—
680Q16—181no—
681SD16—182no—
682SD16—182no—
683D8—22no—
684D8—22no—
685D8—22no—
686D8—92no—
687D8—181no—
688D8C2×#62414yes—
689M16—61no—
690M16—61no—
691M16—62no—
692M16—121no—
693M16—364no—
694C2×C8—32no—
695C2×C8—121no—
696C2×C8—364no—
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—124no—
707C22⋊C4—121no—
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—44no—
719C22×C3—44no—
720C22×C3—84no—
721C22×C3—84no—
722C22×C3—84no—
723C22×C3—164no—
724C22×C3—162no—
725C22×C3—162no—
726C22×C3—162no—
727C22×C3—162no—
728C22×C3—164no—
729C22×C3—164no—
730C22×C3#478511yescharacteristic
731C22×C3#478511yescharacteristic
732C22×C3#501411yescharacteristic
733C22×C3#501411yescharacteristic
734C22×C3C2×#91411yescharacteristic
735C22×C3C2×#93211yescharacteristic
736C2×D3—122no—
737C2×D3—122no—
738C2×D3—242no—
739C2×D3—481no—
740C2×D3—481no—
741C2×D3—482no—
742C3×C4—21no—
743C3×C4—21no—
744C3×C4—21no—
745C3×C4—21no—
746C3×C4—122no—
747C3×C4—242no—
748C3×C4#478511yescharacteristic
749C3×C4#478511yescharacteristic
750C3×C4#501411yescharacteristic
751C3×C4#501411yescharacteristic
752C3×C4C2×#67⋊C411yescharacteristic
753C3×C4C2×#91111yescharacteristic
754C3×C4C2×C4×#6711yescharacteristic
755C3×C4C2×#94911yescharacteristic
756Dic3—42no—
757Dic3—82no—
758Dic3—122no—
759Dic3—122no—
760Dic3—242no—
761C32#3347111yescharacteristic, complemented, Sylow
762C23—42no—
763C23—42no—
764C23—42no—
765C23—162no—
766C23—361no—
767C23#6393411yescharacteristic
768Q8—182no—
769Q8—361no—
770D4—24no—
771D4—42no—
772D4—42no—
773D4—42no—
774D4—182no—
775D4—362no—
776D4—362no—
777D4—361no—
778C2×C4—62no—
779C2×C4—122no—
780C2×C4—361no—
781C2×C4—362no—
782C2×C4—362no—
783C2×C4—484no—
784C2×C4#6392511yescharacteristic
785C2×C4#6392511yescharacteristic
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—84no—
807C2×C3—84no—
808C2×C3—164no—
809C2×C3C2×#478511yescharacteristic
810C2×C3C2×#501411yescharacteristic
811D3—242no—
812D3—242no—
813D3—482no—
814C22—41no—
815C22—44no—
816C22—84no—
817C22—162no—
818C22—162no—
819C22—362no—
820C22—1441no—
821C22#1059140411yescharacteristic
822C22#1059140411yescharacteristic
823C22C2×#6393411yescharacteristic
824C4—122no—
825C4—242no—
826C4—362no—
827C4#1059140411yescharacteristic
828C4#1059140411yescharacteristic
829C4C2×#6392511yescharacteristic
830C4C2×#6395211yescharacteristic
831C3—21no—
832C3#1094866011yescharacteristic, complemented
833C3#1094866511yescharacteristic, complemented
834C2—21no—
835C2—21no—
836C2—21no—
837C2—84no—
838C2—722no—
839C2C2×#1059140411yescharacteristic
subgroupG/H
centerC2C2×#10591404
commutatorC32×C8C23×C4
FrattiniC2×C8C22×D32
FittingC22×C32×D8C22
socleC2×C32C2×#442
prime radicalC2×#10592846C2
cosocleC2×C32×C8C24
hypercenterC22×D8D32
hypocenterC32#33471
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ C22×C8 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
2. #11861234C2semidirect
3. C3×#83823C2semidirect
4. #11797978C2semidirect
5. #11797135C2semidirect
6. C2×C3×#4563C2semidirect
7. #11796861C2semidirect
8. #11795946C2semidirect
15. C2×#63654C4semidirect
16. #10592846C4semidirect
18. C2×#63653C4semidirect
21. C3×#5152C22semidirect
28. #10590918C22semidirect
30. C3×#4563C22semidirect
31. #10589138C22semidirect
32. #10589125C22semidirect
33. #10589105C22semidirect
35. #83823D3semidirect
42. C2×#4563D3semidirect
60. C2×#3746C2×C4semidirect
63. #64113C2×C4semidirect
65. C2×#3745C2×C4semidirect
77. #63654C2×C4semidirect
78. #63653C2×C4semidirect
79. #63639C2×C4semidirect
81. C2×C3⋊(C3⋊C16)C2×C4semidirect
112. #5152C2×D3semidirect
140. #4563C2×D3semidirect
761. C32#33471semidirect
832. C3#10948660semidirect
833. C3#10948665semidirect

Maximal subgroups

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

subgroupindex
C2×#105928462
#118612342
C3×#838232
#117979782
#117971352
C2×C3×#45632
#117968612
#117959462
#109486653
#109486603