Finite Group Databasebeta

← #10822729

Subgroups — #10822729

Order 768.

1482 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
1C2×#5629C211yesmaximal, characteristic
2C2×#4861C211yesmaximal, characteristic, complemented
3C2×#4803C211yesmaximal, characteristic, complemented
4C2×#4804C211yesmaximal, characteristic, complemented
5C2×#4727C211yesmaximal, characteristic, complemented
6#74003C211yesmaximal, characteristic, complemented
7C3×#2035C211yesmaximal, characteristic, complemented
8#71695C211yesmaximal, characteristic, complemented
9#70581C211yesmaximal, characteristic, complemented
10#70274C211yesmaximal, characteristic, complemented
11#70244C211yesmaximal, characteristic, complemented
12#69934C211yesmaximal, characteristic, complemented
13#69524C211yesmaximal, characteristic, complemented
14D3×#340C211yesmaximal, characteristic, complemented
15#68822C211yesmaximal, characteristic, complemented
16#23485—31nomaximal, Sylow
17C22×#239C2211yescharacteristic
18C22×#235C2211yescharacteristic
19C2×C3×C22⋊Q8C2211yescharacteristic
20C2×#946C2211yescharacteristic
21C2×#930C2211yescharacteristic
22C22×ΓL(1,𝔽25)C2211yescharacteristic
23C22×D3×C8C2211yescharacteristic
24#5629—24no—
25#5629—24no—
26C2×#896—21no—
27C2×#895—21no—
28C2×#895C2211yescharacteristic
29C2×#892C2211yescharacteristic
30C2×D3×C4⋊C4C2211yescharacteristic
31C2×D3×C4⋊C4C2211yescharacteristic
32C2×#884—21no—
33C2×#884—21no—
34C2×C3×#106C2211yescharacteristic
35C2×C3×#103C2211yescharacteristic
36C2×C3×#103C2211yescharacteristic
37C2×C3×C22⋊C8C2211yescharacteristic
38C3×#380C2211yescharacteristic
39C2×#835C2211yescharacteristic
40C2×#835C2211yescharacteristic
41#5212C2211yescharacteristic
42C2×#830C2211yescharacteristic
43C2×#821C2211yescharacteristic
44C2×#821C2211yescharacteristic
45C2×(C2×D3)⋊C8C2211yescharacteristic
46C2×(C2×D3)⋊C8C2211yescharacteristic
47C2×#818C2211yescharacteristic
48#4987C2211yescharacteristic
49#4987C2211yescharacteristic
50C2×#809C2211yescharacteristic
51C2×#809C2211yescharacteristic
52C2×#808C2211yescharacteristic
53C2×#807C2211yescharacteristic
54#4957—21no—
55#4956—21no—
56#4861—24no—
57#4804—24no—
58#4803—24no—
59#4727—24no—
60#4665—21no—
61#4646—21no—
62C3×#340C2211yescharacteristic
63#4551C2211yescharacteristic
64#4529C2211yescharacteristic
65#4529C2211yescharacteristic
66C2×#537—31no—
67C2×#428—31no—
68C2×#417—31no—
69C2×#416—31no—
70C2×#408—31no—
71#2311—31no—
72#2036—31no—
73#2036—31no—
74#2035—31no—
75#2035D311yescharacteristic, complemented
76#2034—31no—
77#2034—31no—
78#2033—31no—
79#2033—31no—
80C2×#340—31no—
81C22×C3×Q8C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C22×#67—21no—
84C22×#67D411yescharacteristic
85C22×#67D411yescharacteristic
86C2×#239—22no—
87C2×#239—22no—
88C2×#239—22no—
89C2×#239—22no—
90C2×#239—22no—
91C2×#239D414yes—
92C2×#235—22no—
93C2×#235—22no—
94C2×#235—22no—
95C2×#235—22no—
96C2×#235—22no—
97C2×#235—22no—
98C22×D12—21no—
99C22×D12—21no—
100C22×D12D411yescharacteristic
101C22×D12C2311yescharacteristic
102C22×C4×D3—21no—
103C22×C4×D3—21no—
104C22×C4×D3—21no—
105C22×C4×D3C2311yescharacteristic
106C22×C4×D3C2311yescharacteristic
107C22×Dic6D411yescharacteristic
108C22×C3×C8C2311yescharacteristic
109C22×C3×C8C2311yescharacteristic
110C3×C22⋊Q8—22no—
111C3×C22⋊Q8—22no—
112C2×C3×C4⋊C4—21no—
113C2×C3×C4⋊C4C2311yescharacteristic
114C2×C3×C4⋊C4C2311yescharacteristic
115C2×C3×C4⋊C4C2311yescharacteristic
116C2×C3×C22⋊C4—21no—
117C2×C3×C22⋊C4—21no—
118C2×#217—21no—
119#946—22no—
120#946—22no—
121#930—22no—
122#930—22no—
123C2×(C2×D3)⋊C4—21no—
124C2×(C2×D3)⋊C4—21no—
125C2×(C2×D3)⋊C4—21no—
126C2×(C2×D3)⋊C4—21no—
127C2×(C2×D3)⋊C4—21no—
128C2×(C2×D3)⋊C4—21no—
129C2×C4⋊Dic3C2311yescharacteristic
130C2×C4⋊Dic3C2311yescharacteristic
131C2×C4⋊Dic3C2311yescharacteristic
132C2×Dic3⋊C4—21no—
133C2×Dic3⋊C4—21no—
134C2×Dic3⋊C4—21no—
135C2×C4×Dic3—21no—
136C22×C3⋊C8C2311yescharacteristic
137C22×C3⋊C8C2311yescharacteristic
138C2×ΓL(1,𝔽25)—22no—
139C2×ΓL(1,𝔽25)—22no—
140C2×ΓL(1,𝔽25)D414yescomplemented
141C2×D3×C8—22no—
142C2×D3×C8—22no—
143C2×D3×C8—22no—
144#896—28no—
145#895—28no—
146#895—22no—
147#895—22no—
148#892—22no—
149#892—22no—
150D3×C4⋊C4—22no—
151D3×C4⋊C4—22no—
152D3×C4⋊C4—22no—
153D3×C4⋊C4D414yes—
154#884—28no—
155#884—28no—
156C3×#106—22no—
157C3×#103—22no—
158C3×#103—22no—
159C3×C22⋊C8—22no—
160C3×#95—21no—
161#835—22no—
162#835—22no—
163C3⋊#95—21no—
164C3⋊#95—21no—
165C3⋊#95—21no—
166#830—22no—
167#821—22no—
168#821—22no—
169(C2×D3)⋊C8—22no—
170(C2×D3)⋊C8—22no—
171#818—22no—
172#809—22no—
173#809—22no—
174#808—22no—
175#807—22no—
176C22×#41—31no—
177C22×#41—31no—
178C22×M16—31no—
179C23×C8—31no—
180#537—64no—
181#537—64no—
182C2×C22⋊Q8—31no—
183C2×C22⋊Q8—61no—
184C2×C22⋊Q8C2×D311yescharacteristic
185C2×#121—31no—
186C2×#121—31no—
187C2×#121—61no—
188C2×#121—61no—
189C2×#121—61no—
190C2×#117—31no—
191C22×C4⋊C4—31no—
192C22×C4⋊C4—31no—
193#428—64no—
194C2×#107—31no—
195C2×#107—31no—
196C2×#106—31no—
197C2×#106C2×D311yescharacteristic
198#417—64no—
199#416—64no—
200C2×#103—31no—
201C2×#103—31no—
202C2×#103C2×D311yescharacteristic
203C2×#103C2×D311yescharacteristic
204C2×#102—31no—
205C2×#102—31no—
206C2×#102—31no—
207C2×#102—31no—
208#408—64no—
209C2×C22⋊C8—31no—
210C2×C22⋊C8—31no—
211C2×C22⋊C8—31no—
212C2×C22⋊C8C2×D311yescharacteristic
213#391—61no—
214#390—61no—
215#386—61no—
216#386—61no—
217#380—31no—
218#380—31no—
219#380—31no—
220#380C2×D311yescharacteristic
221#340—31no—
222#340—31no—
223#340—31no—
224#340C2×D311yescharacteristic
225C24×C3C2×D411yescharacteristic
226C23×D3—21no—
227C23×D3C2×D411yescharacteristic
228C23×D3C2×D411yescharacteristic
229C2×C3×Q8—21no—
230C2×C3×Q8—21no—
231C2×C3×Q8—21no—
232C2×C3×Q8—21no—
233C2×C3×Q8—21no—
234C2×C3×Q8C2×D412yes—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4C2×D411yescharacteristic
246C22×C3×C4C2411yescharacteristic
247C2×#67—22no—
248C2×#67—22no—
249C2×#67—22no—
250C2×#67—24no—
251C2×#67—22no—
252C2×#67—22no—
253C2×#67—22no—
254C2×#67—81no—
255C2×#67—81no—
256C22×Dic3—21no—
257C22×Dic3—21no—
258C22×Dic3—21no—
259C22×Dic3C2×D411yescharacteristic
260C22×Dic3C2×D411yescharacteristic
261#239—28no—
262#239—28no—
263#239—44no—
264#239—44no—
265#235—44no—
266#235—44no—
267#235—44no—
268#235—44no—
269C2×D12—21no—
270C2×D12—21no—
271C2×D12—21no—
272C2×D12—21no—
273C2×D12—24no—
274C2×D12—22no—
275C2×D12—22no—
276C2×D12—22no—
277C2×D12—21no—
278C2×D12—24no—
279C2×D12—42no—
280C2×D12—42no—
281C2×D12—81no—
282C2×D12—81no—
283C2×D12C2×D412yes—
284C2×C4×D3—21no—
285C2×C4×D3—21no—
286C2×C4×D3—21no—
287C2×C4×D3—21no—
288C2×C4×D3—21no—
289C2×C4×D3—21no—
290C2×C4×D3—24no—
291C2×C4×D3—24no—
292C2×C4×D3—42no—
293C2×C4×D3—42no—
294C2×C4×D3—42no—
295C2×C4×D3—81no—
296C2×C4×D3—81no—
297C2×C4×D3—81no—
298C2×C4×D3—81no—
299C2×C4×D3C2×D412yes—
300C2×C4×D3C2×D412yes—
301C2×C4×D3C2×D412yes—
302C2×C4×D3#4112yes—
303C2×C4×D3#4112yes—
304C2×C4×D3#4112yes—
305C2×Dic6—22no—
306C2×Dic6—22no—
307C2×Dic6—22no—
308C2×C3×C8—21no—
309C2×C3×C8—21no—
310C2×C3×C8—21no—
311C2×C3×C8—21no—
312C2×C3×C8—21no—
313C2×C3×C8C2×D412yes—
314C3×C4⋊C4—24no—
315C3×C4⋊C4—21no—
316C3×C4⋊C4—21no—
317C3×C4⋊C4—21no—
318C3×C4⋊C4—21no—
319C3×C4⋊C4—21no—
320C3×C4⋊C4C2×D412yes—
321C3×C22⋊C4—24no—
322C3×C22⋊C4—81no—
323#217—81no—
324(C2×D3)⋊C4—24no—
325(C2×D3)⋊C4—24no—
326(C2×D3)⋊C4—24no—
327(C2×D3)⋊C4—42no—
328(C2×D3)⋊C4—81no—
329(C2×D3)⋊C4—81no—
330C4⋊Dic3—21no—
331C4⋊Dic3—21no—
332C4⋊Dic3—21no—
333C4⋊Dic3—21no—
334C4⋊Dic3—21no—
335C4⋊Dic3C2×D412yes—
336Dic3⋊C4—24no—
337Dic3⋊C4—24no—
338Dic3⋊C4—42no—
339C4×Dic3—42no—
340C2×C3⋊C8—21no—
341C2×C3⋊C8—21no—
342C2×C3⋊C8—21no—
343C2×C3⋊C8—21no—
344C2×C3⋊C8—21no—
345C2×C3⋊C8C2×D412yes—
346ΓL(1,𝔽25)—28no—
347D3×C8—44no—
348C2×#41—34no—
349C2×#41—62no—
350C2×#41—62no—
351C2×#41—62no—
352C2×#41—62no—
353C2×#41—62no—
354C2×#41—62no—
355C2×#41—62no—
356C2×#41—62no—
357C2×#41—62no—
358C2×#41—62no—
359C2×#41—62no—
360C22×Q8—31no—
361C22×Q8C22×D311yescharacteristic
362C22×D4—31no—
363C22×D4—31no—
364C22×D4—31no—
365C22×D4—31no—
366C22×D4—61no—
367C22×D4—61no—
368C22×D4—61no—
369C23×C4—31no—
370C23×C4—31no—
371C23×C4—61no—
372C23×C4—61no—
373C23×C4—61no—
374C23×C4C22×D311yescharacteristic
375C2×M16—34no—
376C2×M16—62no—
377C2×M16—62no—
378C22×C8—31no—
379C22×C8—31no—
380C22×C8—62no—
381C22×C8—62no—
382C22×C8—62no—
383C22×C8C22×D311yescharacteristic
384C22×C8C22×D311yescharacteristic
385C22⋊Q8—22no—
386C22⋊Q8—22no—
387C22⋊Q8—68no—
388C22⋊Q8—62no—
389C22⋊Q8—62no—
390#121—68no—
391#121—68no—
392#121—62no—
393#121—68no—
394#121—62no—
395#121—62no—
396#121—62no—
397#117—62no—
398#117—62no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—31no—
401C2×C4⋊C4—34no—
402C2×C4⋊C4—31no—
403C2×C4⋊C4—31no—
404C2×C4⋊C4—62no—
405C2×C4⋊C4—62no—
406C2×C4⋊C4—62no—
407C2×C4⋊C4—61no—
408C2×C4⋊C4—61no—
409C2×C4⋊C4—61no—
410C2×C4⋊C4C22×D311yescharacteristic
411C2×C4⋊C4C22×D311yescharacteristic
412C2×C4⋊C4C22×D311yescharacteristic
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—61no—
416C2×C22⋊C4—61no—
417C2×C22⋊C4—61no—
418C2×C22⋊C4—61no—
419C2×C22⋊C4—61no—
420C2×C22⋊C4—61no—
421C2×C22⋊C4—61no—
422C2×C42—61no—
423#107—62no—
424#107—62no—
425#106—22no—
426#106—62no—
427#103—22no—
428#103—22no—
429#103—62no—
430#103—62no—
431#102—62no—
432#102—62no—
433#102—62no—
434#102—62no—
435C22⋊C8—22no—
436C22⋊C8—62no—
437C22⋊C8—62no—
438C22⋊C8—62no—
439#95—21no—
440#95—61no—
441#95—61no—
442#95—61no—
443C23×C3—21no—
444C23×C3—21no—
445C23×C3—21no—
446C23×C3—21no—
447C23×C3—21no—
448C23×C3—21no—
449C23×C3—21no—
450C23×C3C22×D411yescharacteristic
451C22×D3—21no—
452C22×D3—21no—
453C22×D3—21no—
454C22×D3—21no—
455C22×D3—21no—
456C22×D3—22no—
457C22×D3—21no—
458C22×D3—21no—
459C22×D3—21no—
460C22×D3—21no—
461C22×D3—21no—
462C22×D3—21no—
463C22×D3—41no—
464C22×D3—41no—
465C22×D3—41no—
466C22×D3—41no—
467C22×D3—41no—
468C22×D3—41no—
469C22×D3#12012yes—
470C22×D3#12112yes—
471C22×D3#12312yes—
472C3×Q8—22no—
473C3×Q8—22no—
474C3×Q8—41no—
475C3×Q8—41no—
476C2×C3×C4—22no—
477C2×C3×C4—22no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—41no—
482C2×C3×C4—41no—
483C2×C3×C4—41no—
484C2×C3×C4—41no—
485C2×C3×C4—41no—
486C2×C3×C4—41no—
487C2×C3×C4—41no—
488C2×C3×C4—41no—
489C2×C3×C4—41no—
490C2×C3×C4—41no—
491C2×C3×C4—41no—
492C2×C3×C4—41no—
493C2×C3×C4—41no—
494C2×C3×C4—41no—
495C2×C3×C4C22×D411yescharacteristic
496C2×C3×C4C22×D411yescharacteristic
497C2×C3×C4C22×D411yescharacteristic
498C2×C3×C4C2×#4111yescharacteristic
499C2×C3×C4C2×#4111yescharacteristic
500C2×C3×C4C2×#4111yescharacteristic
501#67—44no—
502#67—44no—
503#67—84no—
504C2×Dic3—22no—
505C2×Dic3—21no—
506C2×Dic3—21no—
507C2×Dic3—21no—
508C2×Dic3—41no—
509C2×Dic3—41no—
510C2×Dic3—41no—
511C2×Dic3—41no—
512C2×Dic3—41no—
513C2×Dic3—41no—
514C2×Dic3—41no—
515C2×Dic3—41no—
516C2×Dic3#12012yes—
517C2×Dic3#12112yes—
518C2×Dic3#12312yes—
519D12—22no—
520D12—22no—
521D12—44no—
522D12—48no—
523D12—41no—
524D12—41no—
525D12—84no—
526C4×D3—41no—
527C4×D3—41no—
528C4×D3—41no—
529C4×D3—41no—
530C4×D3—48no—
531C4×D3—84no—
532C4×D3—84no—
533C4×D3#12114yes—
534C4×D3#12114yes—
535C4×D3#12314yes—
536C4×D3#12414yes—
537Dic6—44no—
538C3×C8—22no—
539C3×C8—41no—
540C3⋊C8—22no—
541C3⋊C8—41no—
542C24—31no—
543C24—31no—
544C24—61no—
545C24D3×D411yescharacteristic
546#41—68no—
547#41—68no—
548#41—124no—
549#41—124no—
550#41—124no—
551#41—124no—
552#41—124no—
553#41—124no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—62no—
560C2×Q8—62no—
561C2×Q8—62no—
562C2×Q8D3×D412yes—
563C2×D4—32no—
564C2×D4—62no—
565C2×D4—64no—
566C2×D4—62no—
567C2×D4—62no—
568C2×D4—64no—
569C2×D4—62no—
570C2×D4—62no—
571C2×D4—62no—
572C2×D4—62no—
573C2×D4—62no—
574C2×D4—62no—
575C2×D4—64no—
576C2×D4—61no—
577C2×D4—61no—
578C2×D4—61no—
579C2×D4—61no—
580C2×D4—61no—
581C2×D4—122no—
582C2×D4—122no—
583C2×D4—241no—
584C2×D4—241no—
585C2×D4—241no—
586C2×D4—241no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—31no—
598C22×C4—32no—
599C22×C4—32no—
600C22×C4—32no—
601C22×C4—32no—
602C22×C4—32no—
603C22×C4—32no—
604C22×C4—31no—
605C22×C4—64no—
606C22×C4—64no—
607C22×C4—61no—
608C22×C4—61no—
609C22×C4—61no—
610C22×C4—61no—
611C22×C4—61no—
612C22×C4—61no—
613C22×C4—61no—
614C22×C4—61no—
615C22×C4—61no—
616C22×C4—122no—
617C22×C4—122no—
618C22×C4—122no—
619C22×C4—241no—
620C22×C4—241no—
621C22×C4—241no—
622C22×C4—241no—
623C22×C4D3×D411yescharacteristic
624C22×C4C23×D311yescharacteristic
625M16—68no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—32no—
632C2×C8—61no—
633C2×C8—61no—
634C2×C8—61no—
635C2×C8—61no—
636C2×C8—61no—
637C2×C8—124no—
638C2×C8D3×D412yes—
639C4⋊C4—24no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—32no—
646C4⋊C4—64no—
647C4⋊C4—64no—
648C4⋊C4—61no—
649C4⋊C4—61no—
650C4⋊C4—61no—
651C4⋊C4—61no—
652C4⋊C4—61no—
653C4⋊C4—122no—
654C4⋊C4D3×D412yes—
655C22⋊C4—24no—
656C22⋊C4—64no—
657C22⋊C4—64no—
658C22⋊C4—64no—
659C22⋊C4—81no—
660C22⋊C4—122no—
661C22⋊C4—241no—
662C22⋊C4—241no—
663C22⋊C4—241no—
664C42—122no—
665C22×C3—41no—
666C22×C3—41no—
667C22×C3—41no—
668C22×C3—41no—
669C22×C3—41no—
670C22×C3—41no—
671C22×C3—41no—
672C22×C3C2×#12011yescharacteristic
673C22×C3C2×#12111yescharacteristic
674C22×C3C2×#12311yescharacteristic
675C22×C3#57611yescharacteristic
676C22×C3#57711yescharacteristic
677C22×C3#57711yescharacteristic
678C22×C3#57811yescharacteristic
679C2×D3—22no—
680C2×D3—22no—
681C2×D3—22no—
682C2×D3—22no—
683C2×D3—22no—
684C2×D3—22no—
685C2×D3—41no—
686C2×D3—41no—
687C2×D3—42no—
688C2×D3—41no—
689C2×D3—41no—
690C2×D3—42no—
691C2×D3—41no—
692C2×D3—42no—
693C2×D3—41no—
694C2×D3—41no—
695C2×D3—81no—
696C2×D3—81no—
697C2×D3—81no—
698C2×D3—81no—
699C2×D3#39414yes—
700C3×C4—41no—
701C3×C4—42no—
702C3×C4—42no—
703C3×C4—81no—
704C3×C4—81no—
705C3×C4C2×#12111yescharacteristic
706C3×C4C2×#12111yescharacteristic
707C3×C4C2×#12311yescharacteristic
708C3×C4C2×#12411yescharacteristic
709Dic3—41no—
710Dic3—42no—
711Dic3—81no—
712Dic3—81no—
713Dic3#39414yes—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—32no—
722C23—32no—
723C23—32no—
724C23—61no—
725C23—61no—
726C23—61no—
727C23—61no—
728C23—61no—
729C23—61no—
730C23—61no—
731C23—61no—
732C23—61no—
733C23—62no—
734C23—61no—
735C23—61no—
736C23—121no—
737C23—121no—
738C23—121no—
739C23—121no—
740C23—121no—
741C23—121no—
742C23C2×D3×D411yescharacteristic
743Q8—22no—
744Q8—22no—
745Q8—41no—
746Q8—41no—
747Q8—124no—
748D4—62no—
749D4—62no—
750D4—124no—
751D4—124no—
752D4—128no—
753D4—124no—
754D4—121no—
755D4—121no—
756D4—244no—
757D4—244no—
758C2×C4—21no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—32no—
764C2×C4—32no—
765C2×C4—32no—
766C2×C4—34no—
767C2×C4—34no—
768C2×C4—34no—
769C2×C4—34no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—61no—
785C2×C4—62no—
786C2×C4—61no—
787C2×C4—61no—
788C2×C4—128no—
789C2×C4—121no—
790C2×C4—121no—
791C2×C4—121no—
792C2×C4—121no—
793C2×C4—121no—
794C2×C4—121no—
795C2×C4—121no—
796C2×C4—121no—
797C2×C4—121no—
798C2×C4—121no—
799C2×C4—121no—
800C2×C4—121no—
801C2×C4—244no—
802C2×C4—244no—
803C2×C4C2×D3×D411yescharacteristic
804C2×C4C2×D3×D411yescharacteristic
805C2×C4C2×D3×D411yescharacteristic
806C2×C4D3×#4111yescharacteristic
807C2×C4D3×#4111yescharacteristic
808C2×C4D3×#4111yescharacteristic
809C8—22no—
810C8—41no—
811C8—62no—
812C8—121no—
813C2×C3—81no—
814C2×C3C2×#39411yescharacteristic
815C2×C3#301211yescharacteristic
816C2×C3#301311yescharacteristic
817C2×C3#306211yescharacteristic
818C2×C3#306311yescharacteristic
819C2×C3#309811yescharacteristic
820C2×C3#309911yescharacteristic
821D3—24no—
822D3—81no—
823D3—82no—
824C22—34no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—62no—
833C22—62no—
834C22—62no—
835C22—62no—
836C22—62no—
837C22—62no—
838C22—121no—
839C22—121no—
840C22—121no—
841C22—122no—
842C22—121no—
843C22—121no—
844C22—122no—
845C22—121no—
846C22—121no—
847C22—122no—
848C22—241no—
849C22—241no—
850C22—241no—
851C22—241no—
852C22D3×#12011yescharacteristic
853C22D3×#12111yescharacteristic
854C22D3×#12311yescharacteristic
855C22#576211yescharacteristic
856C22#576911yescharacteristic
857C22#577811yescharacteristic
858C22#577911yescharacteristic
859C4—34no—
860C4—41no—
861C4—42no—
862C4—42no—
863C4—81no—
864C4—81no—
865C4—121no—
866C4—122no—
867C4—241no—
868C4—241no—
869C4D3×#12111yescharacteristic
870C4D3×#12111yescharacteristic
871C4D3×#12311yescharacteristic
872C4D3×#12411yescharacteristic
873C3#2348511yescharacteristic, complemented, Sylow
874C2—64no—
875C2—81no—
876C2—241no—
877C2—242no—
878C2D3×#39411yescharacteristic
879C2#8004211yescharacteristic
880C2#8023111yescharacteristic
881C2#8066111yescharacteristic
882C2#8090711yescharacteristic
883C2#8143011yescharacteristic
884C2#8152011yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2035C2
socleC23×C3C22×D4
prime radicalC2×#5629C2
hypercenter#2035D3
hypocenterC3#23485
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2035

Complements

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

NH ≅ G/Ntype
2. C2×#4861C2semidirect
3. C2×#4803C2semidirect
4. C2×#4804C2semidirect
5. C2×#4727C2semidirect
6. #74003C2semidirect
7. C3×#2035C2semidirect
8. #71695C2semidirect
9. #70581C2semidirect
10. #70274C2semidirect
11. #70244C2semidirect
12. #69934C2semidirect
13. #69524C2semidirect
14. D3×#340C2semidirect
15. #68822C2semidirect
75. #2035D3semidirect
140. C2×ΓL(1,𝔽25)D4semidirect
873. C3#23485semidirect

Maximal subgroups

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

subgroupindex
C2×#56292
C2×#48612
C2×#48032
C2×#48042
C2×#47272
#740032
C3×#20352
#716952
#705812
#702742
#702442
#699342
#695242
D3×#3402
#688222
#234853