Finite Group Databasebeta

← #10822712

Subgroups — #10822712

Order 768.

1418 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5628C211yesmaximal, characteristic
2C2×#4861C211yesmaximal, characteristic, complemented
3C2×#4802C211yesmaximal, characteristic, complemented
4C2×D3×#103C211yesmaximal, characteristic, complemented
5C2×#4727C211yesmaximal, characteristic
6#74003C211yesmaximal, characteristic
7C3×#2035C211yesmaximal, characteristic, complemented
8#71694C211yesmaximal, characteristic, complemented
9#70582C211yesmaximal, characteristic, complemented
10#70275C211yesmaximal, characteristic, complemented
11#70244C211yesmaximal, characteristic, complemented
12#69937C211yesmaximal, characteristic, complemented
13#69527C211yesmaximal, characteristic, complemented
14#68866C211yesmaximal, characteristic, complemented
15#68824C211yesmaximal, characteristic, complemented
16#23484—31nomaximal, Sylow
17C22×D3×Q8C2211yescharacteristic
18C22×#235C2211yescharacteristic
19C2×C3×C22⋊Q8C2211yescharacteristic
20C2×#946C2211yescharacteristic
21C2×#924C2211yescharacteristic
22C22×ΓL(1,𝔽25)C2211yescharacteristic
23C22×D3×C8C2211yescharacteristic
24#5628—24no—
25#5628—24no—
26C2×#897C2211yescharacteristic
27C2×#894—21no—
28C2×#892C2211yescharacteristic
29C2×#892C2211yescharacteristic
30C2×D3×C4⋊C4C2211yescharacteristic
31C2×#888—21no—
32C2×#885—21no—
33C2×#883—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×(C2×D3)⋊C8C2211yescharacteristic
44C2×(C2×D3)⋊C8C2211yescharacteristic
45C2×#818C2211yescharacteristic
46C2×#816C2211yescharacteristic
47C2×#816C2211yescharacteristic
48#4987C2211yescharacteristic
49#4987C2211yescharacteristic
50C2×#810C2211yescharacteristic
51C2×#810C2211yescharacteristic
52C2×#808C2211yescharacteristic
53C2×#807C2211yescharacteristic
54#4957—21no—
55#4956—21no—
56#4861—24no—
57#4802—24no—
58D3×#103—24no—
59#4727—24no—
60#4665—21no—
61#4646—21no—
62C3×#340C2211yescharacteristic
63#4551C2211yescharacteristic
64#4529C2211yescharacteristic
65#4529C2211yescharacteristic
66C2×#536—31no—
67C2×#428—31no—
68C2×#419—31no—
69C22×#103—31no—
70C2×#408—31no—
71#2311—31no—
72#2036—31no—
73#2036—31no—
74#2036—31no—
75#2036—31no—
76#2035—31no—
77#2035—31no—
78#2035—31no—
79#2035D311yescharacteristic, complemented
80#1735—31no—
81C22×C3×Q8C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C22×#67D411yescharacteristic
84C22×#67D411yescharacteristic
85C2×D3×Q8—22no—
86C2×D3×Q8—22no—
87C2×D3×Q8—22no—
88C2×D3×Q8—22no—
89C2×D3×Q8—22no—
90C2×D3×Q8D414yes—
91C2×#235—22no—
92C2×#235—22no—
93C2×#235—22no—
94C2×#235—22no—
95C2×#235—22no—
96C2×#235—22no—
97C22×D12D411yescharacteristic
98C22×C4×D3—21no—
99C22×C4×D3—21no—
100C22×C4×D3C2311yescharacteristic
101C22×C4×D3C2311yescharacteristic
102C22×Dic6—21no—
103C22×Dic6D411yescharacteristic
104C22×Dic6C2311yescharacteristic
105C22×C3×C8C2311yescharacteristic
106C22×C3×C8C2311yescharacteristic
107C3×C22⋊Q8—22no—
108C3×C22⋊Q8—22no—
109C2×C3×C4⋊C4—21no—
110C2×C3×C4⋊C4C2311yescharacteristic
111C2×C3×C4⋊C4C2311yescharacteristic
112C2×C3×C4⋊C4C2311yescharacteristic
113C2×C3×C22⋊C4—21no—
114C2×C3×C22⋊C4—21no—
115C2×#217—21no—
116C2×#217—21no—
117#946—22no—
118#946—22no—
119C2×(C2×D3)⋊C4—21no—
120C2×(C2×D3)⋊C4—21no—
121C2×(C2×D3)⋊C4—21no—
122C2×(C2×D3)⋊C4—21no—
123C2×(C2×D3)⋊C4—21no—
124C2×(C2×D3)⋊C4—21no—
125C2×C4⋊Dic3—21no—
126C2×C4⋊Dic3C2311yescharacteristic
127C2×C4⋊Dic3C2311yescharacteristic
128C2×C4⋊Dic3C2311yescharacteristic
129#924—22no—
130#924—22no—
131C2×Dic3⋊C4—21no—
132C2×Dic3⋊C4—21no—
133C2×Dic3⋊C4—21no—
134C2×C4×Dic3—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)D414yes—
141C2×D3×C8—22no—
142C2×D3×C8—22no—
143C2×D3×C8—22no—
144#897—22no—
145#897—22no—
146#894—28no—
147#892—22no—
148#892—22no—
149#892—22no—
150#892D414yes—
151D3×C4⋊C4—22no—
152D3×C4⋊C4—22no—
153#888—28no—
154#885—28no—
155#883—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(C2×D3)⋊C8—22no—
168(C2×D3)⋊C8—22no—
169#818—22no—
170#816—22no—
171#816—22no—
172#810—22no—
173#810—22no—
174#808—22no—
175#807—22no—
176C22×#41—31no—
177C23×Q8—31no—
178C22×M16—31no—
179C23×C8—31no—
180#536—64no—
181#536—64no—
182C2×C4⋊Q8—61no—
183C2×#124—61no—
184C2×#123—61no—
185C2×#123—61no—
186C2×C22⋊Q8—31no—
187C2×C22⋊Q8—31no—
188C2×C22⋊Q8—31no—
189C2×C22⋊Q8C2×D311yescharacteristic
190C2×#117—31no—
191C2×#117—31no—
192C22×C4⋊C4—31no—
193#428—64no—
194C2×#107—31no—
195C2×#107—31no—
196C2×#106—31no—
197C2×#106C2×D311yescharacteristic
198#419—64no—
199C2×#103—31no—
200C2×#103—31no—
201C2×#103—31no—
202C2×#103—31no—
203C2×#103—31no—
204C2×#103—31no—
205C2×#103—64no—
206C2×#103C2×D311yescharacteristic
207C2×#103C2×D311yescharacteristic
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×D3C2×D411yescharacteristic
227C23×D3C2×D411yescharacteristic
228C2×C3×Q8—21no—
229C2×C3×Q8—21no—
230C2×C3×Q8—21no—
231C2×C3×Q8—21no—
232C2×C3×Q8—21no—
233C2×C3×Q8C2×D412yes—
234C22×C3×C4—21no—
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×C4C2×D411yescharacteristic
245C22×C3×C4C2411yescharacteristic
246C2×#67—22no—
247C2×#67—22no—
248C2×#67—22no—
249C2×#67—22no—
250C2×#67—22no—
251C2×#67—22no—
252C22×Dic3—21no—
253C22×Dic3—21no—
254C22×Dic3—21no—
255C22×Dic3—21no—
256C22×Dic3C2×D411yescharacteristic
257C22×Dic3C2×D411yescharacteristic
258D3×Q8—28no—
259D3×Q8—28no—
260D3×Q8—44no—
261D3×Q8—44no—
262#235—44no—
263#235—44no—
264#235—44no—
265#235—44no—
266C2×D12—22no—
267C2×D12—22no—
268C2×D12—22no—
269C2×C4×D3—24no—
270C2×C4×D3—21no—
271C2×C4×D3—21no—
272C2×C4×D3—21no—
273C2×C4×D3—21no—
274C2×C4×D3—21no—
275C2×C4×D3—21no—
276C2×C4×D3—42no—
277C2×C4×D3—42no—
278C2×C4×D3—42no—
279C2×C4×D3—81no—
280C2×C4×D3—81no—
281C2×C4×D3C2×D412yes—
282C2×C4×D3C2×D412yes—
283C2×C4×D3C2×D412yes—
284C2×C4×D3#4112yes—
285C2×C4×D3#4112yes—
286C2×C4×D3#4112yes—
287C2×Dic6—21no—
288C2×Dic6—21no—
289C2×Dic6—21no—
290C2×Dic6—21no—
291C2×Dic6—21no—
292C2×Dic6—24no—
293C2×Dic6—22no—
294C2×Dic6—22no—
295C2×Dic6—22no—
296C2×Dic6—42no—
297C2×Dic6—42no—
298C2×Dic6C2×D412yes—
299C2×C3×C8—21no—
300C2×C3×C8—21no—
301C2×C3×C8—21no—
302C2×C3×C8—21no—
303C2×C3×C8—21no—
304C2×C3×C8C2×D412yes—
305C3×C4⋊C4—24no—
306C3×C4⋊C4—21no—
307C3×C4⋊C4—21no—
308C3×C4⋊C4—21no—
309C3×C4⋊C4—21no—
310C3×C4⋊C4—21no—
311C3×C4⋊C4C2×D412yes—
312C3×C22⋊C4—24no—
313C3×C22⋊C4—81no—
314#217—24no—
315#217—81no—
316(C2×D3)⋊C4—24no—
317(C2×D3)⋊C4—24no—
318(C2×D3)⋊C4—24no—
319(C2×D3)⋊C4—42no—
320(C2×D3)⋊C4—81no—
321(C2×D3)⋊C4—81no—
322C4⋊Dic3—24no—
323C4⋊Dic3—21no—
324C4⋊Dic3—21no—
325C4⋊Dic3—21no—
326C4⋊Dic3—21no—
327C4⋊Dic3—21no—
328C4⋊Dic3C2×D412yes—
329Dic3⋊C4—24no—
330Dic3⋊C4—24no—
331Dic3⋊C4—42no—
332C4×Dic3—24no—
333C4×Dic3—42no—
334C2×C3⋊C8—21no—
335C2×C3⋊C8—21no—
336C2×C3⋊C8—21no—
337C2×C3⋊C8—21no—
338C2×C3⋊C8—21no—
339C2×C3⋊C8C2×D412yes—
340ΓL(1,𝔽25)—28no—
341D3×C8—44no—
342C2×#41—62no—
343C2×#41—62no—
344C2×#41—62no—
345C2×#41—62no—
346C2×#41—62no—
347C2×#41—62no—
348C22×Q8—31no—
349C22×Q8—34no—
350C22×Q8—31no—
351C22×Q8—61no—
352C22×Q8—62no—
353C22×Q8—62no—
354C22×Q8—62no—
355C22×Q8—62no—
356C22×Q8—62no—
357C22×Q8C22×D311yescharacteristic
358C22×D4—31no—
359C22×D4—31no—
360C22×D4—31no—
361C23×C4—31no—
362C23×C4—31no—
363C23×C4—61no—
364C23×C4—61no—
365C23×C4C22×D311yescharacteristic
366C2×M16—34no—
367C2×M16—62no—
368C2×M16—62no—
369C22×C8—31no—
370C22×C8—31no—
371C22×C8—62no—
372C22×C8—62no—
373C22×C8—62no—
374C22×C8C22×D311yescharacteristic
375C22×C8C22×D311yescharacteristic
376C4⋊Q8—68no—
377#124—68no—
378#123—68no—
379#123—68no—
380C22⋊Q8—22no—
381C22⋊Q8—22no—
382C22⋊Q8—62no—
383C22⋊Q8—62no—
384C22⋊Q8—62no—
385C22⋊Q8—62no—
386C22⋊Q8—62no—
387C22⋊Q8—62no—
388#117—34no—
389#117—62no—
390#117—62no—
391#117—62no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—31no—
394C2×C4⋊C4—31no—
395C2×C4⋊C4—31no—
396C2×C4⋊C4—62no—
397C2×C4⋊C4—62no—
398C2×C4⋊C4—61no—
399C2×C4⋊C4—61no—
400C2×C4⋊C4—61no—
401C2×C4⋊C4—61no—
402C2×C4⋊C4C22×D311yescharacteristic
403C2×C4⋊C4C22×D311yescharacteristic
404C2×C4⋊C4C22×D311yescharacteristic
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—61no—
408C2×C22⋊C4—61no—
409C2×C22⋊C4—61no—
410C2×C22⋊C4—61no—
411C2×C22⋊C4—61no—
412C2×C22⋊C4—61no—
413C2×C22⋊C4—61no—
414C2×C22⋊C4—61no—
415C2×C42—61no—
416C2×C42—61no—
417#107—62no—
418#107—62no—
419#106—22no—
420#106—62no—
421#103—22no—
422#103—22no—
423#103—62no—
424#103—62no—
425#103—62no—
426#103—62no—
427#103—62no—
428#103—62no—
429C22⋊C8—22no—
430C22⋊C8—62no—
431C22⋊C8—62no—
432C22⋊C8—62no—
433#95—21no—
434#95—61no—
435#95—61no—
436#95—61no—
437C23×C3—21no—
438C23×C3—21no—
439C23×C3—21no—
440C23×C3—21no—
441C23×C3—21no—
442C23×C3—21no—
443C23×C3—21no—
444C23×C3C22×D411yescharacteristic
445C22×D3—21no—
446C22×D3—21no—
447C22×D3—21no—
448C22×D3—21no—
449C22×D3—21no—
450C22×D3—21no—
451C22×D3—21no—
452C22×D3—21no—
453C22×D3—21no—
454C22×D3—21no—
455C22×D3—21no—
456C22×D3#12012yes—
457C22×D3#12112yes—
458C22×D3#12312yes—
459C3×Q8—22no—
460C3×Q8—22no—
461C3×Q8—41no—
462C3×Q8—41no—
463C2×C3×C4—22no—
464C2×C3×C4—21no—
465C2×C3×C4—22no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—41no—
469C2×C3×C4—41no—
470C2×C3×C4—41no—
471C2×C3×C4—41no—
472C2×C3×C4—41no—
473C2×C3×C4—41no—
474C2×C3×C4—41no—
475C2×C3×C4—41no—
476C2×C3×C4—41no—
477C2×C3×C4—41no—
478C2×C3×C4—41no—
479C2×C3×C4—41no—
480C2×C3×C4—41no—
481C2×C3×C4—41no—
482C2×C3×C4C22×D411yescharacteristic
483C2×C3×C4C22×D411yescharacteristic
484C2×C3×C4C22×D411yescharacteristic
485C2×C3×C4C2×#4111yescharacteristic
486C2×C3×C4C2×#4111yescharacteristic
487C2×C3×C4C2×#4111yescharacteristic
488#67—44no—
489#67—44no—
490C2×Dic3—22no—
491C2×Dic3—21no—
492C2×Dic3—22no—
493C2×Dic3—21no—
494C2×Dic3—21no—
495C2×Dic3—41no—
496C2×Dic3—41no—
497C2×Dic3—41no—
498C2×Dic3—41no—
499C2×Dic3—41no—
500C2×Dic3—41no—
501C2×Dic3—41no—
502C2×Dic3—41no—
503C2×Dic3—41no—
504C2×Dic3—41no—
505C2×Dic3#12012yes—
506C2×Dic3#12112yes—
507C2×Dic3#12312yes—
508D12—44no—
509C4×D3—48no—
510C4×D3—41no—
511C4×D3—41no—
512C4×D3—41no—
513C4×D3—41no—
514C4×D3—84no—
515C4×D3#12114yes—
516C4×D3#12114yes—
517C4×D3#12314yes—
518C4×D3#12414yes—
519Dic6—22no—
520Dic6—22no—
521Dic6—41no—
522Dic6—41no—
523Dic6—44no—
524Dic6—48no—
525C3×C8—22no—
526C3×C8—41no—
527C3⋊C8—22no—
528C3⋊C8—41no—
529C24—31no—
530C24—31no—
531C24D3×D411yescharacteristic
532#41—124no—
533#41—124no—
534#41—124no—
535#41—124no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—32no—
542C2×Q8—64no—
543C2×Q8—62no—
544C2×Q8—62no—
545C2×Q8—62no—
546C2×Q8—68no—
547C2×Q8—68no—
548C2×Q8—61no—
549C2×Q8—61no—
550C2×Q8—61no—
551C2×Q8—61no—
552C2×Q8—61no—
553C2×Q8—122no—
554C2×Q8—122no—
555C2×Q8—124no—
556C2×Q8—124no—
557C2×Q8D3×D412yes—
558C2×D4—62no—
559C2×D4—62no—
560C2×D4—62no—
561C2×D4—62no—
562C2×D4—62no—
563C2×D4—62no—
564C2×D4—62no—
565C2×D4—62no—
566C2×D4—62no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—31no—
578C22×C4—32no—
579C22×C4—32no—
580C22×C4—32no—
581C22×C4—32no—
582C22×C4—32no—
583C22×C4—32no—
584C22×C4—31no—
585C22×C4—64no—
586C22×C4—61no—
587C22×C4—61no—
588C22×C4—61no—
589C22×C4—61no—
590C22×C4—61no—
591C22×C4—61no—
592C22×C4—61no—
593C22×C4—61no—
594C22×C4—61no—
595C22×C4—61no—
596C22×C4—122no—
597C22×C4—122no—
598C22×C4—122no—
599C22×C4—241no—
600C22×C4—241no—
601C22×C4D3×D411yescharacteristic
602C22×C4C23×D311yescharacteristic
603M16—68no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—32no—
610C2×C8—61no—
611C2×C8—61no—
612C2×C8—61no—
613C2×C8—61no—
614C2×C8—61no—
615C2×C8—124no—
616C2×C8D3×D412yes—
617C4⋊C4—24no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—32no—
624C4⋊C4—64no—
625C4⋊C4—64no—
626C4⋊C4—64no—
627C4⋊C4—61no—
628C4⋊C4—61no—
629C4⋊C4—61no—
630C4⋊C4—61no—
631C4⋊C4—61no—
632C4⋊C4—122no—
633C4⋊C4D3×D412yes—
634C22⋊C4—24no—
635C22⋊C4—64no—
636C22⋊C4—64no—
637C22⋊C4—64no—
638C22⋊C4—64no—
639C22⋊C4—81no—
640C22⋊C4—122no—
641C22⋊C4—241no—
642C22⋊C4—241no—
643C22⋊C4—241no—
644C42—64no—
645C42—122no—
646C22×C3—41no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—41no—
650C22×C3—41no—
651C22×C3—41no—
652C22×C3—41no—
653C22×C3C2×#12011yescharacteristic
654C22×C3C2×#12111yescharacteristic
655C22×C3C2×#12311yescharacteristic
656C22×C3#57711yescharacteristic
657C22×C3#57711yescharacteristic
658C22×C3#57811yescharacteristic
659C22×C3#57811yescharacteristic
660C2×D3—22no—
661C2×D3—22no—
662C2×D3—22no—
663C2×D3—22no—
664C2×D3—22no—
665C2×D3—22no—
666C2×D3—41no—
667C2×D3—41no—
668C2×D3—41no—
669C2×D3—41no—
670C2×D3—41no—
671C2×D3—41no—
672C2×D3—41no—
673C2×D3#39414yes—
674C3×C4—42no—
675C3×C4—41no—
676C3×C4—42no—
677C3×C4—81no—
678C3×C4—81no—
679C3×C4C2×#12111yescharacteristic
680C3×C4C2×#12111yescharacteristic
681C3×C4C2×#12311yescharacteristic
682C3×C4C2×#12411yescharacteristic
683Dic3—42no—
684Dic3—41no—
685Dic3—42no—
686Dic3—81no—
687Dic3—81no—
688Dic3#39414yes—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—32no—
697C23—32no—
698C23—32no—
699C23—61no—
700C23—61no—
701C23—61no—
702C23—61no—
703C23—61no—
704C23—61no—
705C23—61no—
706C23—61no—
707C23—61no—
708C23—61no—
709C23—61no—
710C23C2×D3×D411yescharacteristic
711Q8—22no—
712Q8—22no—
713Q8—41no—
714Q8—41no—
715Q8—62no—
716Q8—62no—
717Q8—128no—
718Q8—124no—
719Q8—121no—
720Q8—121no—
721D4—124no—
722D4—124no—
723D4—124no—
724C2×C4—21no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—32no—
730C2×C4—32no—
731C2×C4—32no—
732C2×C4—34no—
733C2×C4—34no—
734C2×C4—34no—
735C2×C4—34no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—61no—
751C2×C4—62no—
752C2×C4—62no—
753C2×C4—61no—
754C2×C4—61no—
755C2×C4—128no—
756C2×C4—121no—
757C2×C4—121no—
758C2×C4—121no—
759C2×C4—121no—
760C2×C4—121no—
761C2×C4—121no—
762C2×C4—121no—
763C2×C4—121no—
764C2×C4—121no—
765C2×C4—121no—
766C2×C4—121no—
767C2×C4—121no—
768C2×C4—121no—
769C2×C4—121no—
770C2×C4—244no—
771C2×C4C2×D3×D411yescharacteristic
772C2×C4C2×D3×D411yescharacteristic
773C2×C4C2×D3×D411yescharacteristic
774C2×C4D3×#4111yescharacteristic
775C2×C4D3×#4111yescharacteristic
776C2×C4D3×#4111yescharacteristic
777C8—22no—
778C8—41no—
779C8—62no—
780C8—121no—
781C2×C3—81no—
782C2×C3C2×#39411yescharacteristic
783C2×C3#301011yescharacteristic
784C2×C3#301111yescharacteristic
785C2×C3#306311yescharacteristic
786C2×C3#306311yescharacteristic
787C2×C3#309711yescharacteristic
788C2×C3#309711yescharacteristic
789D3—24no—
790D3—81no—
791C22—34no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—62no—
800C22—62no—
801C22—62no—
802C22—62no—
803C22—62no—
804C22—62no—
805C22—121no—
806C22—121no—
807C22—121no—
808C22—121no—
809C22—121no—
810C22—121no—
811C22—121no—
812C22D3×#12011yescharacteristic
813C22D3×#12111yescharacteristic
814C22D3×#12311yescharacteristic
815C22#576211yescharacteristic
816C22#577111yescharacteristic
817C22#577811yescharacteristic
818C22#577911yescharacteristic
819C4—34no—
820C4—41no—
821C4—42no—
822C4—42no—
823C4—81no—
824C4—81no—
825C4—121no—
826C4—122no—
827C4—122no—
828C4—241no—
829C4—241no—
830C4D3×#12111yescharacteristic
831C4D3×#12111yescharacteristic
832C4D3×#12311yescharacteristic
833C4D3×#12411yescharacteristic
834C3#2348411yescharacteristic, complemented, Sylow
835C2—64no—
836C2—81no—
837C2—241no—
838C2D3×#39411yescharacteristic
839C2#8004111yescharacteristic
840C2#8023011yescharacteristic
841C2#8066211yescharacteristic
842C2#8090711yescharacteristic
843C2#8142911yescharacteristic
844C2#8151911yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2035C2
socleC23×C3C22×D4
prime radicalC22×#235C22
hypercenter#2035D3
hypocenterC3#23484
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×#4802C2semidirect
4. C2×D3×#103C2semidirect
7. C3×#2035C2semidirect
8. #71694C2semidirect
9. #70582C2semidirect
10. #70275C2semidirect
11. #70244C2semidirect
12. #69937C2semidirect
13. #69527C2semidirect
14. #68866C2semidirect
15. #68824C2semidirect
79. #2035D3semidirect
834. C3#23484semidirect

Maximal subgroups

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

subgroupindex
C2×#56282
C2×#48612
C2×#48022
C2×D3×#1032
C2×#47272
#740032
C3×#20352
#716942
#705822
#702752
#702442
#699372
#695272
#688662
#688242
#234843