Finite Group Databasebeta

← #72222868

Subgroups — #72222868

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
1#11899652C211yesmaximal, characteristic
2#11861234C211yesmaximal, characteristic, complemented
3C3×#79106C211yesmaximal, characteristic, complemented
4#11797966C214yesmaximal, complemented
5#11797920C214yesmaximal, complemented
6C2×C3×#4487C211yesmaximal, characteristic, complemented
7#11796953C211yesmaximal, characteristic, complemented
8C2×#10589354C211yesmaximal, characteristic, complemented
9#11795946C211yesmaximal, characteristic, complemented
10#10948645—31nomaximal
11#10948644—31nomaximal
12C2×#64113C2211yescharacteristic
13C2×C3×#904C2211yescharacteristic
14C3×#5504—21no—
15#10594780—21no—
16C2×C32×#106C2211yescharacteristic
17C2×#63639C2211yescharacteristic
18C2×C3×#819C2211yescharacteristic
19C3×#5101C2211yescharacteristic
20C2×C3×#812C2211yescharacteristic
21C3×#4966—21no—
22C3×#4869C2212yescomplemented
23C3×#4853C2212yescomplemented
24C3×#4852—22no—
25#10591113—21no—
26#10590918C2214yes—
27#10590917—22no—
28#10590642C2212yes—
29#10590638C412yescomplemented
30#10590634C412yescomplemented
31#10590633C2212yes—
32#10590632C414yescomplemented
33#10589354C2214yes—
34C3×#4487C2214yescomplemented
35#10589129C2212yescomplemented
36#10589126C2212yescomplemented
37#10589105C2214yescomplemented
38C3×#2952—31no—
39#83894—31no—
40#82009—31no—
41#79249—31no—
42#79106D311yescharacteristic, complemented
43#78580—31no—
44C2×C3×#365—31no—
45#72081—31no—
46#71425—31no—
47#70918—34no—
48#70917—34no—
49#70687—31no—
50C2×#4488—31no—
51C2×#4488—31no—
52C2×#4488—61no—
53C2×#4487D311yescharacteristic, complemented
54#69884—31no—
55#69310—34no—
56#69309—34no—
57C2×#3828—21no—
58C2×C3×#235—21no—
59C22×C32×C8C2311yescharacteristic
60C2×C32×C4⋊C4—21no—
61C2×#3746C2×C411yescharacteristic, complemented
62#64113—21no—
63#64113—21no—
64#64113C2×C412yescomplemented
65#64113C2312yes—
66C2×#3745C2×C411yescharacteristic, complemented
67C2×#3744—21no—
68C3×C4×#67—42no—
69C3×#926D411yescharacteristic
70C2×C3×#208—21no—
71C2×C3×#208D411yescharacteristic
72C2×C3×Dic12C2311yescharacteristic
73C3×#904—21no—
74C3×#904—21no—
75C3×#904C2×C412yes—
76C3×#904C2×C412yes—
77C2×C3×D24C2311yescharacteristic
78C2×C3×#204—21no—
79C3×#893—22no—
80C3×#892—41no—
81C3×D3×C4⋊C4—41no—
82C3×#887—22no—
83#63818—42no—
84#63817—24no—
85#63817—42no—
86C32×#106—21no—
87C32×#106C2312yes—
88#63639—21no—
89#63639C2312yes—
90C2×C3⋊(C3⋊C16)—21no—
91C3×#819—21no—
92C3×#819C2312yes—
93C3×#815C2312yes—
94C3×C8×Dic3D412yes—
95C3×#812C2×C412yescomplemented
96C3×#812C2312yes—
97C2×C3×C3⋊C16C2×C412yescomplemented
98C3×#810—22no—
99C3×#809—22no—
100#63570—24no—
101#63551C2×C414yescomplemented
102#63549C2×C414yescomplemented
103#63548C2×C414yescomplemented
104#63546C2×C414yescomplemented
105#33469—91noSylow
106C2×C3×#135—31no—
107C3×#520—61no—
108#5745—61no—
109#5745—61no—
110C2×#904—31no—
111C2×#904—31no—
112C2×#904—61no—
113C2×#904C2×D311yescharacteristic
114#5504—21no—
115C2×C3×M32—31no—
116C3×#442—32no—
117C3×#441—32no—
118C3×C4×SD16—62no—
119C2×C3×#108—31no—
120C2×C3×#106—21no—
121C2×C3×#106C2×D311yescharacteristic
122C2×C3×#106C2×D311yescharacteristic
123C3×#417—61no—
124C3×#405—31no—
125#5195—32no—
126#5194—34no—
127#5193—32no—
128#5179—32no—
129#5147—32no—
130#5139—61no—
131C2×#819C2×D311yescharacteristic
132#5101C2×D311yescharacteristic
133C2×#812—31no—
134C2×#812—31no—
135C2×#812—61no—
136C2×#812C2×D311yescharacteristic
137#5005—61no—
138#4966—21no—
139#4909—32no—
140#4909—32no—
141#4908—32no—
142#4908—32no—
143#4904—34no—
144#4895—62no—
145#4894—34no—
146#4869C2×D312yescomplemented
147#4853C2×D312yescomplemented
148#4852—22no—
149#4717—34no—
150#4700—62no—
151C3×#365—34no—
152#4565—32no—
153#4563—32no—
154#4512—34no—
155#4496—32no—
156#4495—32no—
157#4488—34no—
158#4488—34no—
159#4488—64no—
160#4487C2×D314yescomplemented
161#4466—34no—
162C22×C32×C4—41no—
163C22×C32×C4C2×D411yescharacteristic
164C2×#638—41no—
165#3828—22no—
166#3828—22no—
167#3828—41no—
168#3828—41no—
169C2×C4⋊(C3⋊D3)—21no—
170C2×C4×C3⋊D3—41no—
171C2×#634—21no—
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×C4×D3—42no—
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#3746—21no—
190#3746C22×C412yes—
191#3745—21no—
192#3745C22×C412yes—
193#3744—22no—
194#3744—22no—
195C3×#217—21no—
196C3×(C2×D3)⋊C4—42no—
197C3×C4⋊Dic3—21no—
198C3×Dic3⋊C4—42no—
199C3×C4×Dic3—42no—
200C3×C4×Dic3C2×D412yes—
201C3×#208—21no—
202C3×#208—21no—
203C3×#208—22no—
204C3×#208—41no—
205C2×C3×C3⋊C8—41no—
206C2×C3×C3⋊C8C2×D412yes—
207C3×Dic12—21no—
208C3×Dic12C22×C412yes—
209C3×D24—21no—
210C3×D24C22×C412yes—
211C3×#204—22no—
212C3×#204—22no—
213#3712—44no—
214#3710—44no—
215C3⋊(C3⋊C16)—22no—
216C3×C3⋊C16C22×C414yes—
217#3414—91no—
218#2957—91no—
219#2952—31no—
220AGL(1,ℤ/16)—94no—
221#2180—94no—
222C2×#365—31no—
223#2148—91no—
224C2×#360—91no—
225#2110—91no—
226C2×C3×#41—61no—
227C2×#235—21no—
228C2×#235—61no—
229C2×#235—61no—
230C2×#235—121no—
231C3×#135—32no—
232C3×#135—32no—
233C3×#135—61no—
234C3×#135—61no—
235C2×C3×Q16—31no—
236C2×C3×SD16—61no—
237C2×C3×D8—31no—
238C2×C3×M16—31no—
239C2×C3×M16—61no—
240C22×C3×C8—21no—
241C22×C3×C8C22×D311yescharacteristic
242C22×C3×C8C22×D311yescharacteristic
243C3×C4×Q8—62no—
244C3×C4×D4—62no—
245C3×C4×D4—122no—
246C3×#117—31no—
247C3×#117—121no—
248C2×C3×C4⋊C4—21no—
249C2×C3×C4⋊C4—21no—
250C2×C3×C4⋊C4—41no—
251C2×C3×C4⋊C4—121no—
252C4×#67—42no—
253#926#6711yescharacteristic
254C2×#208—21no—
255C2×#208#6711yescharacteristic
256#907—64no—
257#907—122no—
258D3×M16—122no—
259D3×M16—122no—
260C2×Dic12—31no—
261C2×Dic12—31no—
262C2×Dic12—61no—
263C2×Dic12C22×D311yescharacteristic
264#904—21no—
265#904—21no—
266#904—32no—
267#904—32no—
268#904—32no—
269#904—32no—
270#904—62no—
271#904—62no—
272#904—61no—
273#904—61no—
274#904—61no—
275#904—61no—
276#904—121no—
277#904—121no—
278#904C4×D312yes—
279#904C4×D312yes—
280C2×D24—31no—
281C2×D24—31no—
282C2×D24—61no—
283C2×D24C22×D311yescharacteristic
284C2×#204—21no—
285C2×#204—61no—
286C2×#204—61no—
287C2×#204—121no—
288#901—64no—
289#901—122no—
290#893—22no—
291#892—41no—
292D3×C4⋊C4—41no—
293#887—22no—
294C3×M32—32no—
295C3×M32—32no—
296C2×C3×C16—32no—
297C3×#108—32no—
298C3×#108—61no—
299C3×#106—21no—
300C3×#106—21no—
301C3×#106—22no—
302C3×#106—41no—
303C3×#106C22×D312yes—
304C3×#106C22×D312yes—
305C3×#103—62no—
306C3×#102—62no—
307C3×#97—32no—
308C3×C4×C8—32no—
309#829—34no—
310#828—34no—
311#827—34no—
312#826—34no—
313#825—64no—
314#819—21no—
315#819C22×D312yes—
316#815C22×D312yes—
317C8×Dic3#6712yes—
318#812—32no—
319#812—32no—
320#812—62no—
321#812—61no—
322#812—61no—
323#812—121no—
324#812C4×D312yescomplemented
325#812C22×D312yes—
326C2×C3⋊C16—61no—
327C2×C3⋊C16—61no—
328C2×C3⋊C16—121no—
329C2×C3⋊C16C4×D312yescomplemented
330#810—22no—
331#809—22no—
332#805—64no—
333Dic24—34no—
334#800—34no—
335#800—34no—
336D48—34no—
337C23×C32AGL(1,ℤ/8)11yescharacteristic
338C22×C3⋊D3—41no—
339C22×C3×D3—41no—
340C2×C32×C4—42no—
341C2×C32×C4—161no—
342C2×C32×C4C4×D411yescharacteristic
343C2×C32×C4C4×D411yescharacteristic
344C2×C32×C4AGL(1,ℤ/8)11yescharacteristic
345C2×C32×C4AGL(1,ℤ/8)11yescharacteristic
346C2×C32×C4AGL(1,ℤ/8)11yescharacteristic
347C2×C32×C4C22×D411yescharacteristic
348#638—42no—
349#638—42no—
350C2×C3⋊Dic3—41no—
351C4⋊(C3⋊D3)—22no—
352C4⋊(C3⋊D3)—41no—
353C4×C3⋊D3—42no—
354C4×C3⋊D3—42no—
355#634—22no—
356#634—41no—
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×C4×D3—162no—
366C3×Dic6—22no—
367C3×Dic6—41no—
368C32×C8C4×D411yescharacteristic
369C32×C8C4×D411yescharacteristic
370C32×C8C23×C411yescharacteristic
371C32×C8C2×#4111yescharacteristic
372C3×C3⋊C8—22no—
373C3×C3⋊C8—42no—
374C2×#135—31no—
375C2×#135—91no—
376#568—181no—
377#520—61no—
378#510—92no—
379#510—92no—
380#509—92no—
381#509—92no—
382#508—94no—
383C2×M32—31no—
384C2×M32—91no—
385#444—94no—
386#443—182no—
387#442—32no—
388#441—32no—
389C4×SD16—62no—
390C2×#108—31no—
391C2×#106D3211yescharacteristic
392#421—181no—
393#417—61no—
394#405—31no—
395#365—34no—
396#362—92no—
397#361—92no—
398#360—94no—
399#347—94no—
400C3×#41—62no—
401C3×#41—62no—
402C3×#41—121no—
403C3×#41—121no—
404C2×C3×Q8—61no—
405C2×C3×D4—61no—
406C2×C3×D4—121no—
407C22×C3×C4—21no—
408C22×C3×C4—41no—
409C22×C3×C4—41no—
410C22×C3×C4—81no—
411C22×C3×C4—122no—
412C22×C3×C4—121no—
413C22×C3×C4D3×D411yescharacteristic
414C22×C3×C4C2×#6711yescharacteristic
415C2×#67—41no—
416C2×#67—121no—
417C2×#67—121no—
418C2×#67—241no—
419#235—22no—
420#235—22no—
421#235—41no—
422#235—41no—
423#235—62no—
424#235—62no—
425#235—62no—
426#235—62no—
427#235—122no—
428#235—122no—
429#235—121no—
430#235—121no—
431#235—121no—
432#235—121no—
433#235—241no—
434#235—241no—
435C2×D12—21no—
436C2×D12—61no—
437C2×D12—61no—
438C2×D12—121no—
439C2×C4×D3—41no—
440C2×C4×D3—42no—
441C2×C4×D3—121no—
442C2×C4×D3—121no—
443C2×C4×D3—241no—
444C2×Dic6—21no—
445C2×Dic6—61no—
446C2×Dic6—61no—
447C2×Dic6—121no—
448C3×Q16—32no—
449C3×Q16—61no—
450C3×SD16—62no—
451C3×SD16—62no—
452C3×D8—32no—
453C3×D8—61no—
454C3×M16—61no—
455C3×M16—61no—
456C3×M16—62no—
457C3×M16—121no—
458C2×C3×C8—21no—
459C2×C3×C8—21no—
460C2×C3×C8—21no—
461C2×C3×C8—21no—
462C2×C3×C8—21no—
463C2×C3×C8—21no—
464C2×C3×C8—32no—
465C2×C3×C8—121no—
466C2×C3×C8C2×C4×D311yescharacteristic
467C2×C3×C8C2×C4×D311yescharacteristic
468C2×C3×C8C2×C4×D311yescharacteristic
469C2×C3×C8C2×C4×D311yescharacteristic
470C2×C3×C8#23511yescharacteristic
471C2×C3×C8#23511yescharacteristic
472C2×C3×C8D3×D411yescharacteristic
473C2×C3×C8#23911yescharacteristic
474C2×C3×C8#23911yescharacteristic
475C2×C3×C8C2×#6711yescharacteristic
476C2×C3×C8C23×D311yescharacteristic
477C2×C3×C8C23×D311yescharacteristic
478C3×C4⋊C4—22no—
479C3×C4⋊C4—22no—
480C3×C4⋊C4—42no—
481C3×C4⋊C4—41no—
482C3×C4⋊C4—41no—
483C3×C4⋊C4—61no—
484C3×C4⋊C4—81no—
485C3×C4⋊C4—122no—
486C3×C22⋊C4—61no—
487C3×C22⋊C4—122no—
488C3×C42—32no—
489C3×C42—122no—
490#217—21no—
491(C2×D3)⋊C4—42no—
492C4⋊Dic3—21no—
493Dic3⋊C4—42no—
494C4×Dic3—42no—
495C4×Dic3C2×#6712yes—
496#208—21no—
497#208—21no—
498#208—22no—
499#208—41no—
500C2×C3⋊C8—41no—
501C2×C3⋊C8C2×#6712yes—
502Dic12—21no—
503Dic12—32no—
504Dic12—32no—
505Dic12—62no—
506Dic12—61no—
507Dic12—61no—
508Dic12—121no—
509Dic12C2×C4×D312yes—
510D24—21no—
511D24—32no—
512D24—32no—
513D24—62no—
514D24—61no—
515D24—61no—
516D24—121no—
517D24C2×C4×D312yes—
518#204—22no—
519#204—22no—
520#204—62no—
521#204—62no—
522#204—62no—
523#204—62no—
524#204—122no—
525#204—122no—
526ΓL(1,𝔽25)—124no—
527ΓL(1,𝔽25)—124no—
528D3×C8—124no—
529D3×C8—124no—
530C3×C16—34no—
531C3⋊C16—62no—
532C3⋊C16—62no—
533C3⋊C16—122no—
534C3⋊C16C2×C4×D314yes—
535C22×C32—41no—
536C22×C32#44211yescharacteristic
537C22×C32#44211yescharacteristic
538C22×C32C2×AGL(1,ℤ/8)11yescharacteristic
539C2×C3⋊D3—42no—
540C2×C3⋊D3—161no—
541C2×C3×D3—42no—
542C2×C3×D3—81no—
543C2×C3×D3—81no—
544C32×C4—82no—
545C32×C4#44211yescharacteristic
546C32×C4#44211yescharacteristic
547C32×C4C2×C4×D411yescharacteristic
548C32×C4C2×AGL(1,ℤ/8)11yescharacteristic
549C3⋊Dic3—42no—
550C3×Dic3—42no—
551C3×Dic3—42no—
552C2×#41—61no—
553C2×#41—181no—
554#135—32no—
555#135—32no—
556#135—61no—
557#135—61no—
558#135—92no—
559#135—92no—
560#135—181no—
561#135—181no—
562C2×Q16—31no—
563C2×Q16—91no—
564C2×SD16—61no—
565C2×SD16—181no—
566C2×D8—31no—
567C2×D8—91no—
568#131—184no—
569#131—362no—
570C2×M16—31no—
571C2×M16—61no—
572C2×M16—362no—
573C22×C8C2×D3211yescharacteristic
574C4×Q8—62no—
575C4×D4—62no—
576C4×D4—122no—
577#117—31no—
578#117—121no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—121no—
581Q32—94no—
582SD32—94no—
583SD32—94no—
584D16—94no—
585M32—32no—
586M32—32no—
587M32—92no—
588M32—181no—
589C2×C16—32no—
590C2×C16—181no—
591#108—32no—
592#108—61no—
593#106—21no—
594#106C2×D3212yes—
595#104—184no—
596#103—62no—
597#102—62no—
598#97—32no—
599C4×C8—32no—
600C23×C3—21no—
601C23×C3—121no—
602C23×C3#91411yescharacteristic
603C23×C3#93211yescharacteristic
604C22×D3—41no—
605C22×D3—121no—
606C22×D3—121no—
607C22×D3—241no—
608C3×Q8—62no—
609C3×Q8—121no—
610C3×D4—62no—
611C3×D4—122no—
612C3×D4—122no—
613C3×D4—121no—
614C2×C3×C4—21no—
615C2×C3×C4—21no—
616C2×C3×C4—21no—
617C2×C3×C4—21no—
618C2×C3×C4—21no—
619C2×C3×C4—21no—
620C2×C3×C4—42no—
621C2×C3×C4—42no—
622C2×C3×C4—62no—
623C2×C3×C4—82no—
624C2×C3×C4—121no—
625C2×C3×C4—122no—
626C2×C3×C4—122no—
627C2×C3×C4—161no—
628C2×C3×C4—161no—
629C2×C3×C4—162no—
630C2×C3×C4—482no—
631C2×C3×C4#89311yescharacteristic
632C2×C3×C4#89311yescharacteristic
633C2×C3×C4#91411yescharacteristic
634C2×C3×C4#91411yescharacteristic
635C2×C3×C4#91411yescharacteristic
636C2×C3×C4C4×#6711yescharacteristic
637C2×C3×C4C4×#6711yescharacteristic
638C2×C3×C4#93211yescharacteristic
639C2×C3×C4#94911yescharacteristic
640C2×C3×C4#94911yescharacteristic
641C2×C3×C4C2×D3×D411yescharacteristic
642C2×C3×C4C22×#6711yescharacteristic
643#67—42no—
644#67—42no—
645#67—122no—
646#67—122no—
647#67—122no—
648#67—122no—
649#67—242no—
650#67—242no—
651C2×Dic3—22no—
652C2×Dic3—41no—
653C2×Dic3—121no—
654C2×Dic3—121no—
655C2×Dic3—241no—
656D12—22no—
657D12—41no—
658D12—62no—
659D12—62no—
660D12—122no—
661D12—121no—
662D12—121no—
663D12—241no—
664C4×D3—42no—
665C4×D3—42no—
666C4×D3—122no—
667C4×D3—122no—
668C4×D3—122no—
669C4×D3—122no—
670C4×D3—162no—
671C4×D3—242no—
672C4×D3—242no—
673Dic6—22no—
674Dic6—41no—
675Dic6—62no—
676Dic6—62no—
677Dic6—122no—
678Dic6—121no—
679Dic6—121no—
680Dic6—241no—
681C3×C8—21no—
682C3×C8—21no—
683C3×C8—21no—
684C3×C8—21no—
685C3×C8—62no—
686C3×C8—122no—
687C3×C8#89311yescharacteristic
688C3×C8#89311yescharacteristic
689C3×C8C4×#6711yescharacteristic
690C3×C8C4×#6711yescharacteristic
691C3×C8C22×C4×D311yescharacteristic
692C3×C8C22×C4×D311yescharacteristic
693C3×C8C2×#23511yescharacteristic
694C3×C8C2×#23911yescharacteristic
695C3⋊C8—22no—
696C3⋊C8—42no—
697C2×C32—21no—
698C2×C32—21no—
699C2×C32—21no—
700C2×C32C2×#44211yescharacteristic
701C3⋊D3—82no—
702C3×D3—82no—
703#41—62no—
704#41—62no—
705#41—121no—
706#41—121no—
707#41—182no—
708#41—182no—
709#41—361no—
710#41—361no—
711C2×Q8—61no—
712C2×Q8—181no—
713C2×D4—61no—
714C2×D4—121no—
715C2×D4—181no—
716C2×D4—361no—
717C22×C4—41no—
718C22×C4—122no—
719C22×C4—121no—
720C22×C4—361no—
721C22×C4D3×#6711yescharacteristic
722Q16—32no—
723Q16—61no—
724Q16—92no—
725Q16—181no—
726SD16—62no—
727SD16—62no—
728SD16—182no—
729SD16—182no—
730D8—32no—
731D8—61no—
732D8—92no—
733D8—181no—
734M16—61no—
735M16—61no—
736M16—62no—
737M16—121no—
738M16—364no—
739C2×C8—32no—
740C2×C8—121no—
741C2×C8—364no—
742C2×C8#379911yescharacteristic
743C2×C8#379911yescharacteristic
744C2×C8C4×D3211yescharacteristic
745C2×C8C4×D3211yescharacteristic
746C2×C8D3×#6711yescharacteristic
747C2×C8C22×D3211yescharacteristic
748C4⋊C4—22no—
749C4⋊C4—41no—
750C4⋊C4—61no—
751C4⋊C4—122no—
752C22⋊C4—61no—
753C22⋊C4—122no—
754C42—32no—
755C42—122no—
756C16—34no—
757C16—182no—
758C22×C3—21no—
759C22×C3—21no—
760C22×C3—21no—
761C22×C3—41no—
762C22×C3—41no—
763C22×C3—42no—
764C22×C3—122no—
765C22×C3—241no—
766C22×C3—241no—
767C22×C3#486911yescharacteristic
768C22×C3#486911yescharacteristic
769C22×C3#501411yescharacteristic
770C22×C3#501411yescharacteristic
771C22×C3C2×#91411yescharacteristic
772C22×C3C2×#93211yescharacteristic
773C2×D3—42no—
774C2×D3—81no—
775C2×D3—81no—
776C2×D3—122no—
777C2×D3—122no—
778C2×D3—242no—
779C2×D3—481no—
780C2×D3—481no—
781C2×D3—482no—
782C3×C4—21no—
783C3×C4—21no—
784C3×C4—21no—
785C3×C4—21no—
786C3×C4—82no—
787C3×C4—82no—
788C3×C4—122no—
789C3×C4—122no—
790C3×C4—162no—
791C3×C4#486911yescharacteristic
792C3×C4#486911yescharacteristic
793C3×C4#501411yescharacteristic
794C3×C4#501411yescharacteristic
795C3×C4C2×#89311yescharacteristic
796C3×C4C2×#91411yescharacteristic
797C3×C4C2×C4×#6711yescharacteristic
798C3×C4C2×#94911yescharacteristic
799Dic3—42no—
800Dic3—42no—
801Dic3—122no—
802Dic3—122no—
803Dic3—242no—
804C32#3346911yescharacteristic, complemented, Sylow
805C23—121no—
806C23—361no—
807C23#6393411yescharacteristic
808Q8—62no—
809Q8—121no—
810Q8—182no—
811Q8—361no—
812D4—62no—
813D4—122no—
814D4—122no—
815D4—121no—
816D4—182no—
817D4—362no—
818D4—362no—
819D4—361no—
820C2×C4—42no—
821C2×C4—62no—
822C2×C4—121no—
823C2×C4—122no—
824C2×C4—122no—
825C2×C4—161no—
826C2×C4—361no—
827C2×C4—362no—
828C2×C4—362no—
829C2×C4—482no—
830C2×C4#6390411yescharacteristic
831C2×C4#6390411yescharacteristic
832C2×C4#6393411yescharacteristic
833C2×C4#6393911yescharacteristic
834C2×C4#6393911yescharacteristic
835C2×C4C2×D3×#6711yescharacteristic
836C8—62no—
837C8—122no—
838C8#6390411yescharacteristic
839C8#6390411yescharacteristic
840C8C2×#379911yescharacteristic
841C8C2×C4×D3211yescharacteristic
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—242no—
853C2×C3C2×#486911yescharacteristic
854C2×C3C2×#501411yescharacteristic
855D3—82no—
856D3—242no—
857D3—242no—
858D3—482no—
859C22—41no—
860C22—122no—
861C22—241no—
862C22—241no—
863C22—362no—
864C22—1441no—
865C22#1059058911yescharacteristic
866C22#1059058911yescharacteristic
867C22C2×#6393411yescharacteristic
868C4—82no—
869C4—122no—
870C4—122no—
871C4—362no—
872C4#1059058911yescharacteristic
873C4#1059058911yescharacteristic
874C4C2×#6390411yescharacteristic
875C4C2×#6393911yescharacteristic
876C3—21no—
877C3#1094864411yescharacteristic, complemented
878C3#1094864511yescharacteristic, complemented
879C2—21no—
880C2—21no—
881C2—21no—
882C2—242no—
883C2—722no—
884C2C2×#1059058911yescharacteristic
subgroupG/H
centerC2C2×#10590589
commutatorC32×C8C23×C4
FrattiniC2×C8C22×D32
FittingC2×C32×#106C22
socleC2×C32C2×#442
prime radical#11899652C2
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. #11861234C2semidirect
3. C3×#79106C2semidirect
4. #11797966C2semidirect
5. #11797920C2semidirect
6. C2×C3×#4487C2semidirect
7. #11796953C2semidirect
8. C2×#10589354C2semidirect
9. #11795946C2semidirect
22. C3×#4869C22semidirect
23. C3×#4853C22semidirect
29. #10590638C4semidirect
30. #10590634C4semidirect
32. #10590632C4semidirect
34. C3×#4487C22semidirect
35. #10589129C22semidirect
36. #10589126C22semidirect
37. #10589105C22semidirect
42. #79106D3semidirect
53. C2×#4487D3semidirect
61. C2×#3746C2×C4semidirect
64. #64113C2×C4semidirect
66. C2×#3745C2×C4semidirect
95. C3×#812C2×C4semidirect
97. C2×C3×C3⋊C16C2×C4semidirect
101. #63551C2×C4semidirect
102. #63549C2×C4semidirect
103. #63548C2×C4semidirect
104. #63546C2×C4semidirect
146. #4869C2×D3semidirect
147. #4853C2×D3semidirect
160. #4487C2×D3semidirect
324. #812C4×D3semidirect
329. C2×C3⋊C16C4×D3semidirect
804. C32#33469semidirect
877. C3#10948644semidirect
878. C3#10948645semidirect

Maximal subgroups

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

subgroupindex
#118996522
#118612342
C3×#791062
#117979662
#117979202
C2×C3×#44872
#117969532
C2×#105893542
#117959462
#109486453
#109486443