Finite Group Databasebeta

← #72222870

Subgroups — #72222870

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×C3×#5147C211yesmaximal, characteristic
2#11861236C211yesmaximal, characteristic, complemented
3C3×#83823C211yesmaximal, characteristic, complemented
4#11797980C218yesmaximal, complemented
5#11797136C211yesmaximal, characteristic, complemented
6C2×#10589429C211yesmaximal, characteristic, complemented
7#11796862C211yesmaximal, characteristic, complemented
8#11795946C211yesmaximal, characteristic, complemented
9#10948663—31nomaximal
10#10948660—31nomaximal
11C22×C32×D8C2211yescharacteristic
12C3×#5798—21no—
13C2×C3×#904C2211yescharacteristic
14#10594776—21no—
15C2×#63646C2211yescharacteristic
16C2×#63639C2211yescharacteristic
17C3×#5215—21no—
18C3×#5152C2214yescomplemented
19C3×Dic3×D8—22no—
20C2×C3×#827C412yescomplemented
21C3×#5147C414yescomplemented
22C3×#5147C2214yes—
23C2×C3×#826C412yescomplemented
24C3×#5106C2211yescharacteristic
25C3×#5101C2211yescharacteristic
26C2×C3×#812C2211yescharacteristic
27#10591111—21no—
28#10590916C2214yescomplemented
29#10590915—22no—
30#10589429C2214yescomplemented
31#10589136C2214yescomplemented
32#10589123C2214yescomplemented
33#10589105C2214yescomplemented
34C2×C3×#509—31no—
35C3×#2948—31no—
36#83910—31no—
37#83823D311yescharacteristic, complemented
38C2×#5147D311yescharacteristic
39#78580—31no—
40#72076—31no—
41C2×#4563—31no—
42C2×#4563—31no—
43C2×#4563—61no—
44#71515—38no—
45#71427—31no—
46#71425—31no—
47#70918—38no—
48#70656—31no—
49#70650—31no—
50#69884—31no—
51C22×C32×D4—21no—
52C2×C3×#235—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×#3748—21no—
61C2×C3×#217—42no—
62C3×D4×Dic3—24no—
63C3×D4×Dic3—42no—
64C3×#926—21no—
65C3×#926D411yescharacteristic
66C2×C3×#208D411yescharacteristic
67C2×C3×Dic12C2×C411yescharacteristic, complemented
68C3×#904—21no—
69C3×#904—21no—
70C3×#904C2×C412yescomplemented
71C3×#904C2312yes—
72C2×C3×D24C2×C411yescharacteristic, complemented
73C2×C3×#204—21no—
74#63815—42no—
75#63814—24no—
76D3×#208—42no—
77#63646—21no—
78#63646C2312yes—
79#63639—21no—
80#63639C2312yes—
81C2×C3⋊(C3⋊C16)—21no—
82C3×#832—24no—
83C3×#827C2×C418yescomplemented
84C3×#826C2×C418yescomplemented
85C3×#818—21no—
86C3×#817C2312yes—
87C3×#815C2312yes—
88C3×C8×Dic3D412yes—
89C3×#812C2×C412yescomplemented
90C3×#812C2312yes—
91C2×C3×C3⋊C16C2×C412yescomplemented
92#63569—24no—
93#33471—91noSylow
94C2×C3×#135—31no—
95C22×C3×D8—21no—
96C22×C3×D8C2×D311yescharacteristic
97C22×C3×D8C2×D311yescharacteristic
98C3×#518—61no—
99#5819—61no—
100#5798—21no—
101#5745—61no—
102C2×#904C2×D311yescharacteristic
103C3×#509—34no—
104C3×#509—34no—
105C2×C3×SD32—32no—
106C2×C3×D16—32no—
107C2×C3×M32—31no—
108C3×#442—34no—
109C3×C4×D8—62no—
110C3×#427—31no—
111C3×#418—61no—
112C3×#405—31no—
113#5236—61no—
114#5215—21no—
115#5197—34no—
116#5196—62no—
117#5152C2×D314yescomplemented
118Dic3×D8—22no—
119C2×#827Dic312yescomplemented
120#5147Dic314yescomplemented
121#5147C2×D314yes—
122C2×#826Dic312yescomplemented
123C2×#819—31no—
124C2×#819—31no—
125C2×#819—61no—
126#5106C2×D311yescharacteristic
127#5101C2×D311yescharacteristic
128C2×#812—31no—
129C2×#812—31no—
130C2×#812—61no—
131C2×#812C2×D311yescharacteristic
132#5005—61no—
133#4717—34no—
134#4700—62no—
135#4566—34no—
136#4563—34no—
137#4563—34no—
138#4563—64no—
139#4513—34no—
140#4512—34no—
141#4488—34no—
142#4487—34no—
143#4466—34no—
144C24×C32—41no—
145C2×C32×D4—22no—
146C2×C32×D4—22no—
147C2×C32×D4—22no—
148C2×C32×D4—41no—
149C2×C32×D4—41no—
150C2×C32×D4—41no—
151C22×C32×C4C2×D411yescharacteristic
152C2×C3×#67—41no—
153C22×C3×Dic3—44no—
154C3×#235—22no—
155C3×#235—22no—
156C3×#235—41no—
157C3×#235—41no—
158C2×C3×D12—21no—
159C2×C3×C4×D3—41no—
160C2×C3×Dic6—21no—
161C32×D8—22no—
162C32×D8—22no—
163C32×D8—22no—
164C32×D8C22×C414yes—
165C2×C32×C8C22×C411yescharacteristic
166C2×C32×C8C22×C411yescharacteristic
167C2×C32×C8C2×D411yescharacteristic
168C2×C32×C8#4111yescharacteristic
169C2×C32×C8#4111yescharacteristic
170C2×C32×C8C2411yescharacteristic
171#3748—22no—
172#3748—41no—
173C2×C3⋊(C3⋊C8)—41no—
174C3×#217—21no—
175C3×#217—44no—
176C3×#217—41no—
177C3×C4⋊Dic3—21no—
178C3×C4⋊Dic3—22no—
179C3×C4×Dic3—41no—
180C3×C4×Dic3C2×D412yes—
181C3×#208—21no—
182C3×#208—21no—
183C2×C3×C3⋊C8C2×D412yes—
184C3×Dic12—21no—
185C3×Dic12C22×C412yes—
186C3×D24—21no—
187C3×D24C22×C412yes—
188C3×#204—22no—
189C3×#204—22no—
190#3711—44no—
191D3×C3⋊C8—44no—
192C3⋊(C3⋊C16)—22no—
193C3×C3⋊C16C22×C414yes—
194C2×#509—31no—
195#2957—91no—
196#2948—31no—
197AGL(1,ℤ/16)—98no—
198#2155—91no—
199C2×#361—91no—
200#2145—91no—
201#2110—91no—
202C2×C3×#41—61no—
203C22×C3×D4—21no—
204C22×C3×D4—21no—
205C22×C3×D4—41no—
206C2×#235—21no—
207C3×#135—32no—
208C3×#135—32no—
209C3×#135—61no—
210C3×#135—61no—
211C2×C3×Q16—31no—
212C2×C3×SD16—61no—
213C2×C3×D8—21no—
214C2×C3×D8—21no—
215C2×C3×D8—21no—
216C2×C3×D8—21no—
217C2×C3×D8—21no—
218C2×C3×D8—21no—
219C2×C3×D8—22no—
220C2×C3×D8—22no—
221C2×C3×D8—22no—
222C2×C3×D8—31no—
223C2×C3×D8—41no—
224C2×C3×D8—41no—
225C2×C3×D8—41no—
226C2×C3×D8C4×D312yes—
227C2×C3×D8C4×D312yes—
228C2×C3×D8C2×Dic312yes—
229C2×C3×D8C2×Dic312yes—
230C2×C3×D8C22×D312yes—
231C2×C3×D8C22×D312yes—
232C2×C3×M16—31no—
233C22×C3×C8—21no—
234C22×C3×C8C22×D311yescharacteristic
235C22×C3×C8C22×D311yescharacteristic
236C3×C4×D4—64no—
237C3×C4×D4—122no—
238C3×#117—31no—
239C3×#117—61no—
240C2×C3×C22⋊C4—122no—
241C2×#217—42no—
242#948—64no—
243#948—122no—
244D4×Dic3—24no—
245D4×Dic3—42no—
246#926—21no—
247#926#6711yescharacteristic
248C2×#208—61no—
249C2×#208—61no—
250C2×#208—121no—
251C2×#208—122no—
252C2×#208#6711yescharacteristic
253#907—122no—
254D3×M16—122no—
255C2×Dic12C2×Dic311yescharacteristic, complemented
256#904—21no—
257#904—21no—
258#904C2×Dic312yescomplemented
259#904C22×D312yes—
260C2×D24C2×Dic311yescharacteristic, complemented
261C2×#204—21no—
262#901—64no—
263C3×SD32—38no—
264C3×D16—38no—
265C3×M32—32no—
266C3×M32—32no—
267C2×C3×C16—32no—
268C3×#107—61no—
269C3×#106—32no—
270C3×#102—64no—
271C3×#97—32no—
272C3×C4×C8—32no—
273#837—64no—
274#832—24no—
275#827C2×Dic318yescomplemented
276#826C2×Dic318yescomplemented
277#819—32no—
278#819—32no—
279#819—62no—
280#819—61no—
281#819—61no—
282#819—121no—
283#818—21no—
284#817C22×D312yes—
285#815C22×D312yes—
286C8×Dic3#6712yes—
287#812—32no—
288#812—32no—
289#812—62no—
290#812—61no—
291#812—61no—
292#812—121no—
293#812C2×Dic312yescomplemented
294#812C22×D312yes—
295C2×C3⋊C16—61no—
296C2×C3⋊C16—61no—
297C2×C3⋊C16—121no—
298C2×C3⋊C16C2×Dic312yescomplemented
299#805—64no—
300C23×C32—42no—
301C23×C32—42no—
302C23×C32—42no—
303C23×C32—162no—
304C23×C32AGL(1,ℤ/8)11yescharacteristic
305C22×C3×D3—41no—
306C32×D4—24no—
307C32×D4—42no—
308C32×D4—42no—
309C32×D4—42no—
310C2×C32×C4C4×D411yescharacteristic
311C2×C32×C4C4×D411yescharacteristic
312C2×C32×C4AGL(1,ℤ/8)11yescharacteristic
313C2×C32×C4AGL(1,ℤ/8)11yescharacteristic
314C2×C32×C4AGL(1,ℤ/8)11yescharacteristic
315C2×C32×C4C22×D411yescharacteristic
316C3×#67—42no—
317C3×#67—42no—
318C2×C3×Dic3—22no—
319C2×C3×Dic3—41no—
320C2×C3×Dic3—42no—
321C2×C3×Dic3—164no—
322C3×D12—22no—
323C3×D12—41no—
324C3×C4×D3—42no—
325C3×C4×D3—42no—
326C3×Dic6—22no—
327C3×Dic6—41no—
328C32×C8C4×D411yescharacteristic
329C32×C8C4×D411yescharacteristic
330C32×C8C23×C411yescharacteristic
331C32×C8C2×#4111yescharacteristic
332C3⋊(C3⋊C8)—42no—
333C3×C3⋊C8—22no—
334C2×#135—31no—
335C22×D8D3211yescharacteristic
336#568—181no—
337#518—61no—
338#509—34no—
339#509—34no—
340C2×SD32—32no—
341C2×D16—32no—
342C2×M32—31no—
343C2×M32—91no—
344#444—94no—
345#443—182no—
346#442—34no—
347C4×D8—62no—
348C2×#108—91no—
349#427—31no—
350#421—181no—
351#418—61no—
352#405—31no—
353#365—94no—
354#361—94no—
355#360—94no—
356#347—94no—
357C24×C3—41no—
358C24×C3—41no—
359C24×C3—81no—
360C3×#41—62no—
361C3×#41—62no—
362C3×#41—121no—
363C3×#41—121no—
364C2×C3×Q8—61no—
365C2×C3×D4—22no—
366C2×C3×D4—22no—
367C2×C3×D4—22no—
368C2×C3×D4—22no—
369C2×C3×D4—22no—
370C2×C3×D4—22no—
371C2×C3×D4—42no—
372C2×C3×D4—42no—
373C2×C3×D4—42no—
374C2×C3×D4—41no—
375C2×C3×D4—41no—
376C2×C3×D4—41no—
377C2×C3×D4—41no—
378C2×C3×D4—41no—
379C2×C3×D4—41no—
380C2×C3×D4—61no—
381C2×C3×D4—81no—
382C2×C3×D4—81no—
383C2×C3×D4—81no—
384C2×C3×D4—121no—
385C22×C3×C4—21no—
386C22×C3×C4—124no—
387C22×C3×C4—121no—
388C22×C3×C4D3×D411yescharacteristic
389C22×C3×C4C2×#6711yescharacteristic
390C2×#67—41no—
391C22×Dic3—44no—
392#235—22no—
393#235—22no—
394#235—41no—
395#235—41no—
396C2×D12—21no—
397C2×C4×D3—41no—
398C2×Dic6—21no—
399C3×Q16—32no—
400C3×Q16—61no—
401C3×SD16—62no—
402C3×SD16—62no—
403C3×D8—22no—
404C3×D8—22no—
405C3×D8—22no—
406C3×D8—22no—
407C3×D8—22no—
408C3×D8—22no—
409C3×D8—24no—
410C3×D8—32no—
411C3×D8—42no—
412C3×D8—42no—
413C3×D8—42no—
414C3×D8—61no—
415C3×D8C2×C4×D314yes—
416C3×D8C22×Dic314yes—
417C3×M16—61no—
418C3×M16—61no—
419C2×C3×C8—21no—
420C2×C3×C8—21no—
421C2×C3×C8—21no—
422C2×C3×C8—21no—
423C2×C3×C8—21no—
424C2×C3×C8—21no—
425C2×C3×C8—32no—
426C2×C3×C8C2×C4×D311yescharacteristic
427C2×C3×C8C2×C4×D311yescharacteristic
428C2×C3×C8#23511yescharacteristic
429C2×C3×C8#23511yescharacteristic
430C2×C3×C8D3×D411yescharacteristic
431C2×C3×C8#23711yescharacteristic
432C2×C3×C8#23711yescharacteristic
433C2×C3×C8C22×Dic311yescharacteristic
434C2×C3×C8C22×Dic311yescharacteristic
435C2×C3×C8C2×#6711yescharacteristic
436C2×C3×C8C23×D311yescharacteristic
437C2×C3×C8C23×D311yescharacteristic
438C3×C4⋊C4—61no—
439C3×C4⋊C4—62no—
440C3×C22⋊C4—61no—
441C3×C22⋊C4—124no—
442C3×C22⋊C4—121no—
443C3×C42—32no—
444C3×C42—121no—
445#217—21no—
446#217—44no—
447#217—41no—
448C4⋊Dic3—21no—
449C4⋊Dic3—22no—
450C4×Dic3—41no—
451C4×Dic3C2×#6712yes—
452#208—21no—
453#208—21no—
454#208—62no—
455#208—62no—
456#208—122no—
457#208—124no—
458#208—121no—
459#208—121no—
460#208—241no—
461C2×C3⋊C8—124no—
462C2×C3⋊C8—121no—
463C2×C3⋊C8—121no—
464C2×C3⋊C8—241no—
465C2×C3⋊C8C2×#6712yes—
466Dic12—21no—
467Dic12C22×Dic312yes—
468D24—21no—
469D24C22×Dic312yes—
470#204—22no—
471#204—22no—
472ΓL(1,𝔽25)—124no—
473D3×C8—124no—
474C3×C16—34no—
475C3⋊C16—62no—
476C3⋊C16—62no—
477C3⋊C16—122no—
478C3⋊C16C22×Dic314yes—
479C22×C32—41no—
480C22×C32—44no—
481C22×C32—84no—
482C22×C32—162no—
483C22×C32—162no—
484C22×C32#44211yescharacteristic
485C22×C32#44211yescharacteristic
486C22×C32C2×AGL(1,ℤ/8)11yescharacteristic
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—21no—
498#135—32no—
499#135—32no—
500#135—61no—
501#135—61no—
502C2×Q16—31no—
503C2×SD16—61no—
504C2×D8—21no—
505C2×D8—21no—
506C2×D8—21no—
507C2×D8—31no—
508C2×D8D3×Dic312yes—
509C2×D8D3×Dic312yes—
510C2×D8C2×D3212yes—
511#131—184no—
512#131—362no—
513C2×M16—31no—
514C2×M16—181no—
515C2×M16—362no—
516C22×C8C2×D3211yescharacteristic
517C4×D4—64no—
518C4×D4—122no—
519#117—31no—
520#117—61no—
521C2×C22⋊C4—122no—
522SD32—38no—
523D16—38no—
524M32—32no—
525M32—32no—
526M32—92no—
527M32—181no—
528C2×C16—32no—
529C2×C16—181no—
530#108—92no—
531#108—181no—
532#107—61no—
533#106—32no—
534#104—184no—
535#102—64no—
536#97—32no—
537C4×C8—32no—
538C23×C3—21no—
539C23×C3—42no—
540C23×C3—42no—
541C23×C3—42no—
542C23×C3—42no—
543C23×C3—42no—
544C23×C3—42no—
545C23×C3—82no—
546C23×C3—82no—
547C23×C3—82no—
548C23×C3—121no—
549C23×C3—162no—
550C23×C3—162no—
551C23×C3—164no—
552C23×C3#91111yescharacteristic
553C23×C3#93211yescharacteristic
554C22×D3—41no—
555C3×Q8—62no—
556C3×Q8—121no—
557C3×D4—24no—
558C3×D4—24no—
559C3×D4—44no—
560C3×D4—42no—
561C3×D4—42no—
562C3×D4—42no—
563C3×D4—42no—
564C3×D4—42no—
565C3×D4—42no—
566C3×D4—62no—
567C3×D4—82no—
568C3×D4—82no—
569C3×D4—82no—
570C3×D4—122no—
571C3×D4—122no—
572C3×D4—121no—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—62no—
580C2×C3×C4—121no—
581C2×C3×C4—122no—
582C2×C3×C4—122no—
583C2×C3×C4—122no—
584C2×C3×C4—484no—
585C2×C3×C4#91111yescharacteristic
586C2×C3×C4#91111yescharacteristic
587C2×C3×C4#91111yescharacteristic
588C2×C3×C4C4×#6711yescharacteristic
589C2×C3×C4C4×#6711yescharacteristic
590C2×C3×C4#93211yescharacteristic
591C2×C3×C4D4×Dic311yescharacteristic
592C2×C3×C4D4×Dic311yescharacteristic
593C2×C3×C4#94911yescharacteristic
594C2×C3×C4#94911yescharacteristic
595C2×C3×C4C2×D3×D411yescharacteristic
596C2×C3×C4C22×#6711yescharacteristic
597#67—42no—
598#67—42no—
599C2×Dic3—22no—
600C2×Dic3—41no—
601C2×Dic3—42no—
602C2×Dic3—164no—
603D12—22no—
604D12—41no—
605C4×D3—42no—
606C4×D3—42no—
607Dic6—22no—
608Dic6—41no—
609C3×C8—21no—
610C3×C8—21no—
611C3×C8—21no—
612C3×C8—21no—
613C3×C8—62no—
614C3×C8C4×#6711yescharacteristic
615C3×C8C4×#6711yescharacteristic
616C3×C8D4×Dic311yescharacteristic
617C3×C8D4×Dic311yescharacteristic
618C3×C8C22×C4×D311yescharacteristic
619C3×C8C2×#23511yescharacteristic
620C3×C8C2×#23711yescharacteristic
621C3×C8C23×Dic311yescharacteristic
622C3⋊C8—22no—
623C3⋊C8—122no—
624C3⋊C8—122no—
625C3⋊C8—242no—
626C2×C32—21no—
627C2×C32—21no—
628C2×C32—21no—
629C2×C32—84no—
630C2×C32C2×#44211yescharacteristic
631C3×D3—82no—
632C24—41no—
633#41—62no—
634#41—62no—
635#41—121no—
636#41—121no—
637C2×Q8—61no—
638C2×D4—22no—
639C2×D4—22no—
640C2×D4—22no—
641C2×D4—41no—
642C2×D4—41no—
643C2×D4—41no—
644C2×D4—61no—
645C2×D4—121no—
646C22×C4—124no—
647C22×C4—121no—
648C22×C4D3×#6711yescharacteristic
649Q16—32no—
650Q16—61no—
651SD16—62no—
652SD16—62no—
653D8—22no—
654D8—22no—
655D8—22no—
656D8—32no—
657D8—61no—
658D8C2×D3×Dic314yes—
659M16—61no—
660M16—61no—
661M16—182no—
662M16—364no—
663M16—361no—
664C2×C8—32no—
665C2×C8—364no—
666C2×C8—361no—
667C2×C8C2×D3×Dic311yescharacteristic
668C2×C8C2×D3×Dic311yescharacteristic
669C2×C8#380411yescharacteristic
670C2×C8#380411yescharacteristic
671C2×C8D3×#6711yescharacteristic
672C2×C8C22×D3211yescharacteristic
673C4⋊C4—61no—
674C4⋊C4—62no—
675C22⋊C4—61no—
676C22⋊C4—124no—
677C22⋊C4—121no—
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—44no—
689C22×C3—44no—
690C22×C3—84no—
691C22×C3—84no—
692C22×C3—84no—
693C22×C3—122no—
694C22×C3—164no—
695C22×C3—162no—
696C22×C3—162no—
697C22×C3—162no—
698C22×C3—162no—
699C22×C3—164no—
700C22×C3—164no—
701C22×C3—481no—
702C22×C3#501411yescharacteristic
703C22×C3#501411yescharacteristic
704C22×C3#515211yescharacteristic
705C22×C3#515211yescharacteristic
706C22×C3C2×#91111yescharacteristic
707C22×C3C2×#93211yescharacteristic
708C2×D3—42no—
709C2×D3—161no—
710C3×C4—21no—
711C3×C4—21no—
712C3×C4—21no—
713C3×C4—21no—
714C3×C4—122no—
715C3×C4—122no—
716C3×C4—242no—
717C3×C4#501411yescharacteristic
718C3×C4#501411yescharacteristic
719C3×C4#515211yescharacteristic
720C3×C4#515211yescharacteristic
721C3×C4C2×#91111yescharacteristic
722C3×C4C2×C4×#6711yescharacteristic
723C3×C4C2×D4×Dic311yescharacteristic
724C3×C4C2×#94911yescharacteristic
725Dic3—42no—
726Dic3—42no—
727Dic3—82no—
728C32#3347111yescharacteristic, complemented, Sylow
729C23—42no—
730C23—42no—
731C23—42no—
732C23—121no—
733C23—162no—
734C23#6393211yescharacteristic
735Q8—62no—
736Q8—121no—
737D4—24no—
738D4—42no—
739D4—42no—
740D4—42no—
741D4—62no—
742D4—122no—
743D4—122no—
744D4—121no—
745C2×C4—62no—
746C2×C4—121no—
747C2×C4—122no—
748C2×C4—122no—
749C2×C4—122no—
750C2×C4—484no—
751C2×C4#6392511yescharacteristic
752C2×C4#6392511yescharacteristic
753C2×C4#6393211yescharacteristic
754C2×C4Dic3×#6711yescharacteristic
755C2×C4Dic3×#6711yescharacteristic
756C2×C4C2×D3×#6711yescharacteristic
757C8—62no—
758C8—362no—
759C8Dic3×#6711yescharacteristic
760C8Dic3×#6711yescharacteristic
761C8C22×D3×Dic311yescharacteristic
762C8C2×#380411yescharacteristic
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—84no—
774C2×C3—84no—
775C2×C3—164no—
776C2×C3—242no—
777C2×C3C2×#501411yescharacteristic
778C2×C3C2×#515211yescharacteristic
779D3—82no—
780C22—41no—
781C22—44no—
782C22—84no—
783C22—122no—
784C22—162no—
785C22—162no—
786C22—481no—
787C22#1059143011yescharacteristic
788C22#1059143011yescharacteristic
789C22C2×#6393211yescharacteristic
790C4—122no—
791C4—122no—
792C4—242no—
793C4#1059143011yescharacteristic
794C4#1059143011yescharacteristic
795C4C2×#6392511yescharacteristic
796C4C2×Dic3×#6711yescharacteristic
797C3—21no—
798C3#1094866011yescharacteristic, complemented
799C3#1094866311yescharacteristic, complemented
800C2—21no—
801C2—21no—
802C2—21no—
803C2—84no—
804C2—242no—
805C2C2×#1059143011yescharacteristic
subgroupG/H
centerC2C2×#10591430
commutatorC32×C8C23×C4
FrattiniC2×C8C22×D32
FittingC22×C32×D8C22
socleC2×C32C2×#442
prime radicalC2×C3×#5147C2
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. #11861236C2semidirect
3. C3×#83823C2semidirect
4. #11797980C2semidirect
5. #11797136C2semidirect
6. C2×#10589429C2semidirect
7. #11796862C2semidirect
8. #11795946C2semidirect
18. C3×#5152C22semidirect
20. C2×C3×#827C4semidirect
21. C3×#5147C4semidirect
23. C2×C3×#826C4semidirect
28. #10590916C22semidirect
30. #10589429C22semidirect
31. #10589136C22semidirect
32. #10589123C22semidirect
33. #10589105C22semidirect
37. #83823D3semidirect
67. C2×C3×Dic12C2×C4semidirect
70. C3×#904C2×C4semidirect
72. C2×C3×D24C2×C4semidirect
83. C3×#827C2×C4semidirect
84. C3×#826C2×C4semidirect
89. C3×#812C2×C4semidirect
91. C2×C3×C3⋊C16C2×C4semidirect
117. #5152C2×D3semidirect
119. C2×#827Dic3semidirect
120. #5147Dic3semidirect
122. C2×#826Dic3semidirect
255. C2×Dic12C2×Dic3semidirect
258. #904C2×Dic3semidirect
260. C2×D24C2×Dic3semidirect
275. #827C2×Dic3semidirect
276. #826C2×Dic3semidirect
293. #812C2×Dic3semidirect
298. C2×C3⋊C16C2×Dic3semidirect
728. C32#33471semidirect
798. C3#10948660semidirect
799. C3#10948663semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#51472
#118612362
C3×#838232
#117979802
#117971362
C2×#105894292
#117968622
#117959462
#109486633
#109486603