Finite Group Databasebeta

← #10846257

Subgroups — #10846257

Order 768.

1104 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5175C211yesmaximal, characteristic, complemented
2#82496C211yesmaximal, characteristic, complemented
3C2×C4×#215C211yesmaximal, characteristic, complemented
4C2×#4807C211yesmaximal, characteristic, complemented
5C2×#4778C211yesmaximal, characteristic, complemented
6#76444C211yesmaximal, characteristic
7C3×#1880C211yesmaximal, characteristic, complemented
8#72054C211yesmaximal, characteristic, complemented
9#70284C211yesmaximal, characteristic, complemented
10#70177C211yesmaximal, characteristic, complemented
11#69646C211yesmaximal, characteristic, complemented
12#68887C211yesmaximal, characteristic, complemented
13#68858C211yesmaximal, characteristic, complemented
14#68672C211yesmaximal, characteristic, complemented
15#68647C211yesmaximal, characteristic, complemented
16#25410—31nomaximal, Sylow
17C22×C3×SD16C2211yescharacteristic
18C2×C3×C4×Q8C2211yescharacteristic
19C2×#946C2211yescharacteristic
20C2×#944C2211yescharacteristic
21C22×#215C2211yescharacteristic
22C2×#940C2211yescharacteristic
23C2×#938C2211yescharacteristic
24C22×#214C2211yescharacteristic
25C22×#204C2211yescharacteristic
26C22×D3×C8C2211yescharacteristic
27C2×#897C2211yescharacteristic
28C2×#895C2211yescharacteristic
29C2×#884—21no—
30C2×C4×D12C2211yescharacteristic
31C2×C3×#103C2211yescharacteristic
32C2×C3×#102C2211yescharacteristic
33C3×#390C2211yescharacteristic
34C2×#835C2211yescharacteristic
35C2×#832C2211yescharacteristic
36#5175—24no—
37C2×#821C2211yescharacteristic
38C2×(C2×D3)⋊C8C2211yescharacteristic
39C2×#816C2211yescharacteristic
40C2×C8×Dic3C2211yescharacteristic
41C4×#215—24no—
42#4994—21no—
43#4984C2211yescharacteristic
44#4981—21no—
45#4972C2211yescharacteristic
46C2×#810C2211yescharacteristic
47C2×#809C2211yescharacteristic
48C2×#808C2211yescharacteristic
49C2×#808C2211yescharacteristic
50#4960—21no—
51#4959—21no—
52#4956—21no—
53#4940—21no—
54C4×(C2×D3)⋊C4C2211yescharacteristic
55#4929C2211yescharacteristic
56#4928—21no—
57C2×C4×C3⋊C8C2211yescharacteristic
58#4807—24no—
59#4778—24no—
60C3×#340C2211yescharacteristic
61C3×#336C2211yescharacteristic
62#4551C2211yescharacteristic
63#4550C2211yescharacteristic
64C2×#492—31no—
65C2×#465—31no—
66C2×#465—31no—
67C2×C4×SD16—31no—
68#2429—31no—
69#2428—31no—
70#2043—31no—
71#2041—31no—
72#2000—31no—
73#2000—31no—
74#1968—31no—
75#1941—31no—
76#1880D311yescharacteristic, complemented
77#1877—31no—
78C8×C22⋊C4—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×D4C2311yescharacteristic
81C22×#67—21no—
82C22×#67—21no—
83C22×#67—21no—
84C22×D12—21no—
85C22×D12C2311yescharacteristic
86C22×C4×D3—21no—
87C22×C4×D3C2311yescharacteristic
88C22×Dic6C2311yescharacteristic
89C2×C3×SD16—22no—
90C2×C3×SD16—22no—
91C2×C3×SD16—41no—
92C22×C3×C8C2311yescharacteristic
93C22×C3×C8C2311yescharacteristic
94C3×C4×Q8—22no—
95C3×C4×Q8—41no—
96C2×C3×C4⋊C4—21no—
97C2×C3×C4⋊C4C2311yescharacteristic
98C2×C3×C4⋊C4C2311yescharacteristic
99C2×C3×C22⋊C4—21no—
100C2×C3×C22⋊C4—21no—
101C2×C3×C42—21no—
102C2×C3×C42C2311yescharacteristic
103C2×#217—21no—
104#946—22no—
105#946—41no—
106#944—22no—
107#944—41no—
108C2×#215—22no—
109C2×#215—22no—
110C2×#215D414yescomplemented
111#940—22no—
112#940—41no—
113#938—22no—
114#938—41no—
115C2×#214—22no—
116C2×#214—22no—
117C2×#214—22no—
118C2×(C2×D3)⋊C4—21no—
119C2×(C2×D3)⋊C4—21no—
120C2×(C2×D3)⋊C4—21no—
121C2×(C2×D3)⋊C4—21no—
122C2×(C2×D3)⋊C4D411yescharacteristic
123C2×(C2×D3)⋊C4D411yescharacteristic
124C2×C4⋊Dic3—21no—
125C2×C4⋊Dic3—21no—
126C2×C4⋊Dic3C2311yescharacteristic
127C2×C4⋊Dic3C2311yescharacteristic
128C2×Dic3⋊C4—21no—
129C2×Dic3⋊C4—21no—
130C2×Dic3⋊C4—21no—
131C2×Dic3⋊C4—21no—
132C2×C4×Dic3C2311yescharacteristic
133C22×C3⋊C8C2311yescharacteristic
134C22×C3⋊C8C2311yescharacteristic
135C2×#204—22no—
136C2×#204—22no—
137C2×#204—41no—
138C2×D3×C8—22no—
139C2×D3×C8—22no—
140C2×D3×C8—22no—
141#897—22no—
142#897—41no—
143#895—22no—
144#895—41no—
145#884—44no—
146C4×D12—22no—
147C4×D12—41no—
148C3×#103—22no—
149C3×#102—22no—
150#835—22no—
151#832—41no—
152C3⋊#95—21no—
153C3⋊#95—21no—
154C3⋊#95—21no—
155C3⋊#95—21no—
156C3⋊#95D411yescharacteristic
157C3⋊#95D411yescharacteristic
158#821—22no—
159(C2×D3)⋊C8—22no—
160#816—22no—
161C8×Dic3—22no—
162#810—41no—
163#809—22no—
164#808—22no—
165#808D414yescomplemented
166C4×C3⋊C8—22no—
167C22×SD16—31no—
168C22×SD16—31no—
169C22×SD16—31no—
170C22×SD16C2×D311yescharacteristic
171C23×C8—31no—
172C2×C4⋊Q8—31no—
173C2×#127—31no—
174C2×C22⋊Q8—31no—
175C2×C22⋊Q8—31no—
176C2×#121—31no—
177C2×#121—31no—
178C2×#121—61no—
179C2×C4×Q8C2×D311yescharacteristic
180C2×C4×D4—31no—
181#492—64no—
182#465—64no—
183#465—64no—
184C4×SD16—64no—
185C2×#106—31no—
186C2×#106—31no—
187C2×#103—31no—
188C2×#103—31no—
189C2×#103—31no—
190C2×#103C2×D311yescharacteristic
191C2×#102—31no—
192C2×#102—31no—
193C2×#102—31no—
194C2×#102C2×D311yescharacteristic
195C2×C22⋊C8—31no—
196C2×C4×C8—31no—
197C2×C4×C8—31no—
198#398—61no—
199#396—61no—
200#394—61no—
201#392—61no—
202#391—31no—
203#390C2×D311yescharacteristic
204#389—31no—
205#389—31no—
206#389—61no—
207#388—61no—
208#386—61no—
209C4×C22⋊C4—31no—
210#340—31no—
211#340C2×D311yescharacteristic
212#336—31no—
213#336C2×D311yescharacteristic
214C24×C3—21no—
215C23×D3—21no—
216C23×D3C2×D411yescharacteristic
217C2×C3×Q8—21no—
218C2×C3×Q8—21no—
219C2×C3×Q8—21no—
220C2×C3×Q8—21no—
221C2×C3×Q8—21no—
222C2×C3×Q8C2×D412yes—
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4C2×D411yescharacteristic
233C22×C3×C4C2×D411yescharacteristic
234C22×C3×C4C2411yescharacteristic
235C2×#67—42no—
236C2×#67—42no—
237C2×#67—42no—
238C2×#67—42no—
239C2×#67—42no—
240C2×#67—42no—
241C2×#67—81no—
242C2×#67—81no—
243C2×#67—81no—
244C22×Dic3—21no—
245C22×Dic3—21no—
246C22×Dic3—21no—
247C22×Dic3C2×D411yescharacteristic
248C22×Dic3C2×D411yescharacteristic
249C22×Dic3C2×D411yescharacteristic
250C2×D12—21no—
251C2×D12—21no—
252C2×D12—21no—
253C2×D12—21no—
254C2×D12—21no—
255C2×D12—42no—
256C2×D12—42no—
257C2×D12—81no—
258C2×D12C2×D412yes—
259C2×C4×D3—21no—
260C2×C4×D3—21no—
261C2×C4×D3—21no—
262C2×C4×D3—21no—
263C2×C4×D3—21no—
264C2×C4×D3—21no—
265C2×C4×D3—42no—
266C2×C4×D3—42no—
267C2×C4×D3—81no—
268C2×Dic6—21no—
269C2×Dic6—21no—
270C2×Dic6—21no—
271C2×Dic6—21no—
272C2×Dic6—21no—
273C2×Dic6—21no—
274C3×SD16—44no—
275C2×C3×C8—21no—
276C2×C3×C8—21no—
277C2×C3×C8—21no—
278C2×C3×C8—21no—
279C2×C3×C8—21no—
280C2×C3×C8#4112yes—
281C3×C4⋊C4—21no—
282C3×C4⋊C4—21no—
283C3×C4⋊C4—21no—
284C3×C4⋊C4—42no—
285C3×C4⋊C4C2×D412yes—
286C3×C22⋊C4—42no—
287C3×C22⋊C4—81no—
288C3×C42—21no—
289C3×C42—21no—
290C3×C42—42no—
291#217—42no—
292#215—28no—
293#214—44no—
294(C2×D3)⋊C4—22no—
295(C2×D3)⋊C4—42no—
296(C2×D3)⋊C4—42no—
297(C2×D3)⋊C4—42no—
298(C2×D3)⋊C4—42no—
299(C2×D3)⋊C4SD1614yescomplemented
300C4⋊Dic3—21no—
301C4⋊Dic3—21no—
302C4⋊Dic3—21no—
303C4⋊Dic3—42no—
304C4⋊Dic3—42no—
305C4⋊Dic3C2×D412yes—
306Dic3⋊C4—42no—
307Dic3⋊C4—42no—
308Dic3⋊C4—42no—
309Dic3⋊C4—42no—
310C4×Dic3—21no—
311C4×Dic3—21no—
312C2×C3⋊C8—21no—
313C2×C3⋊C8—21no—
314C2×C3⋊C8—21no—
315C2×C3⋊C8C2×D412yes—
316C2×C3⋊C8C2×D412yes—
317C2×C3⋊C8#4112yes—
318#204—44no—
319D3×C8—44no—
320C22×Q8—31no—
321C22×Q8C22×D311yescharacteristic
322C22×D4—31no—
323C22×D4—61no—
324C22×D4—61no—
325C22×D4—61no—
326C22×D4—61no—
327C22×D4C22×D311yescharacteristic
328C23×C4—31no—
329C23×C4—61no—
330C2×SD16—22no—
331C2×SD16—22no—
332C2×SD16—34no—
333C2×SD16—41no—
334C2×SD16—62no—
335C2×SD16—62no—
336C2×SD16—62no—
337C2×SD16—62no—
338C2×SD16—62no—
339C2×SD16—62no—
340C2×SD16—62no—
341C2×SD16—121no—
342C22×C8—31no—
343C22×C8—31no—
344C22×C8—62no—
345C22×C8—62no—
346C22×C8—62no—
347C22×C8C22×D311yescharacteristic
348C22×C8C22×D311yescharacteristic
349C4⋊Q8—62no—
350C4⋊Q8—121no—
351#127—62no—
352#127—121no—
353C22⋊Q8—62no—
354C22⋊Q8—62no—
355C22⋊Q8—121no—
356C22⋊Q8—121no—
357#121—62no—
358#121—62no—
359#121—124no—
360#121—121no—
361#121—121no—
362C4×Q8—22no—
363C4×Q8—41no—
364C4×D4—62no—
365C4×D4—121no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—31no—
368C2×C4⋊C4—31no—
369C2×C4⋊C4—61no—
370C2×C4⋊C4—61no—
371C2×C4⋊C4—61no—
372C2×C4⋊C4—61no—
373C2×C4⋊C4—61no—
374C2×C4⋊C4—61no—
375C2×C4⋊C4C22×D311yescharacteristic
376C2×C4⋊C4C22×D311yescharacteristic
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—31no—
380C2×C22⋊C4—31no—
381C2×C22⋊C4—61no—
382C2×C22⋊C4—61no—
383C2×C22⋊C4—61no—
384C2×C22⋊C4—61no—
385C2×C22⋊C4—61no—
386C2×C42—21no—
387C2×C42—31no—
388C2×C42C22×D311yescharacteristic
389#106—34no—
390#106—62no—
391#103—22no—
392#103—62no—
393#103—62no—
394#103—121no—
395#102—22no—
396#102—62no—
397#102—62no—
398#102—121no—
399C22⋊C8—62no—
400C4×C8—62no—
401C4×C8—62no—
402#95—31no—
403#95—31no—
404#95—61no—
405#95—61no—
406#95—61no—
407#95—61no—
408C23×C3—41no—
409C23×C3—41no—
410C23×C3—41no—
411C23×C3—41no—
412C23×C3—41no—
413C23×C3—41no—
414C23×C3—41no—
415C23×C3C22×D411yescharacteristic
416C22×D3—21no—
417C22×D3—21no—
418C22×D3—21no—
419C22×D3—21no—
420C22×D3—21no—
421C22×D3—21no—
422C22×D3—22no—
423C22×D3—41no—
424C22×D3—41no—
425C22×D3—41no—
426C22×D3—41no—
427C22×D3—41no—
428C22×D3—41no—
429C22×D3C2×SD1612yes—
430C3×Q8—22no—
431C3×Q8—22no—
432C3×Q8—41no—
433C3×Q8—41no—
434C3×D4—41no—
435C3×D4—41no—
436C3×D4—41no—
437C3×D4—41no—
438C2×C3×C4—21no—
439C2×C3×C4—21no—
440C2×C3×C4—22no—
441C2×C3×C4—22no—
442C2×C3×C4—21no—
443C2×C3×C4—21no—
444C2×C3×C4—21no—
445C2×C3×C4—41no—
446C2×C3×C4—41no—
447C2×C3×C4—41no—
448C2×C3×C4—41no—
449C2×C3×C4—41no—
450C2×C3×C4—41no—
451C2×C3×C4—41no—
452C2×C3×C4C2×SD1612yes—
453C2×C3×C4C22×D411yescharacteristic
454C2×C3×C4C22×D411yescharacteristic
455C2×C3×C4C2×#4111yescharacteristic
456C2×C3×C4C2×#4111yescharacteristic
457C2×C3×C4H(5,𝔽2)11yescharacteristic
458C2×C3×C4H(5,𝔽2)11yescharacteristic
459#67—84no—
460#67—84no—
461#67—84no—
462C2×Dic3—21no—
463C2×Dic3—21no—
464C2×Dic3—21no—
465C2×Dic3—21no—
466C2×Dic3—21no—
467C2×Dic3—21no—
468C2×Dic3—22no—
469C2×Dic3—21no—
470C2×Dic3—41no—
471C2×Dic3—41no—
472C2×Dic3—41no—
473C2×Dic3—41no—
474C2×Dic3—41no—
475C2×Dic3—41no—
476C2×Dic3—41no—
477C2×Dic3—41no—
478C2×Dic3C2×SD1612yes—
479C2×Dic3#13512yes—
480D12—22no—
481D12—22no—
482D12—41no—
483D12—41no—
484D12—84no—
485C4×D3—41no—
486C4×D3—41no—
487C4×D3—41no—
488C4×D3—41no—
489C4×D3—84no—
490Dic6—41no—
491Dic6—41no—
492Dic6—41no—
493Dic6—41no—
494C3×C8—22no—
495C3×C8—41no—
496C3⋊C8—41no—
497C3⋊C8#12114yescomplemented
498C24—21no—
499C24—31no—
500C24—61no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—61no—
507C2×Q8—61no—
508C2×Q8—61no—
509C2×Q8—61no—
510C2×Q8—61no—
511C2×Q8—61no—
512C2×Q8D3×D412yes—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—32no—
520C2×D4—61no—
521C2×D4—61no—
522C2×D4—61no—
523C2×D4—61no—
524C2×D4—61no—
525C2×D4—122no—
526C2×D4—122no—
527C2×D4—122no—
528C2×D4—122no—
529C2×D4—122no—
530C2×D4—122no—
531C2×D4—122no—
532C2×D4—122no—
533C2×D4—241no—
534C2×D4—241no—
535C2×D4—241no—
536C2×D4—241no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—31no—
541C22×C4—31no—
542C22×C4—31no—
543C22×C4—61no—
544C22×C4—61no—
545C22×C4—61no—
546C22×C4—61no—
547C22×C4—61no—
548C22×C4—61no—
549C22×C4—61no—
550C22×C4—61no—
551C22×C4—61no—
552C22×C4—122no—
553C22×C4—122no—
554C22×C4—241no—
555C22×C4D3×D411yescharacteristic
556C22×C4D3×D411yescharacteristic
557C22×C4C23×D311yescharacteristic
558SD16—44no—
559SD16—68no—
560SD16—124no—
561SD16—124no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—32no—
568C2×C8—32no—
569C2×C8—32no—
570C2×C8—61no—
571C2×C8—61no—
572C2×C8—61no—
573C2×C8—124no—
574C2×C8#23512yes—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—32no—
579C4⋊C4—42no—
580C4⋊C4—61no—
581C4⋊C4—61no—
582C4⋊C4—61no—
583C4⋊C4—122no—
584C4⋊C4—122no—
585C4⋊C4—122no—
586C4⋊C4—122no—
587C4⋊C4—122no—
588C4⋊C4—122no—
589C4⋊C4D3×D412yes—
590C22⋊C4—34no—
591C22⋊C4—42no—
592C22⋊C4—62no—
593C22⋊C4—81no—
594C22⋊C4—122no—
595C22⋊C4—122no—
596C22⋊C4—122no—
597C22⋊C4—122no—
598C22⋊C4—122no—
599C42—21no—
600C42—21no—
601C42—42no—
602C42—61no—
603C42—61no—
604C22×C3—81no—
605C22×C3—81no—
606C22×C3—81no—
607C22×C3—81no—
608C22×C3—81no—
609C22×C3—81no—
610C22×C3—81no—
611C22×C3#53211yescharacteristic
612C22×C3D4211yescharacteristic
613C22×C3D4211yescharacteristic
614C22×C3C22×SD1611yescharacteristic
615C22×C3C2×#13511yescharacteristic
616C22×C3#57711yescharacteristic
617C22×C3#57711yescharacteristic
618C2×D3—22no—
619C2×D3—22no—
620C2×D3—22no—
621C2×D3—41no—
622C2×D3—41no—
623C2×D3—41no—
624C2×D3—41no—
625C2×D3—42no—
626C2×D3—42no—
627C2×D3—42no—
628C2×D3—81no—
629C2×D3—81no—
630C2×D3—81no—
631C2×D3—81no—
632C3×C4—22no—
633C3×C4—42no—
634C3×C4—41no—
635C3×C4—42no—
636C3×C4—81no—
637C3×C4C2×#12111yescharacteristic
638C3×C4#54011yescharacteristic
639C3×C4#54611yescharacteristic
640C3×C4#55011yescharacteristic
641Dic3—22no—
642Dic3—22no—
643Dic3—41no—
644Dic3—42no—
645Dic3—81no—
646Dic3—81no—
647C23—32no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—61no—
656C23—61no—
657C23—61no—
658C23—61no—
659C23—61no—
660C23—61no—
661C23—62no—
662C23—121no—
663C23—121no—
664C23—121no—
665C23—121no—
666C23—121no—
667C23—121no—
668C23C2×D3×D411yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—41no—
672Q8—41no—
673Q8—121no—
674Q8—121no—
675Q8—121no—
676Q8—121no—
677D4—41no—
678D4—41no—
679D4—41no—
680D4—41no—
681D4—62no—
682D4—62no—
683D4—121no—
684D4—121no—
685D4—244no—
686D4—244no—
687D4—244no—
688D4—244no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—32no—
697C2×C4—32no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—62no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—121no—
714C2×C4—121no—
715C2×C4—121no—
716C2×C4—121no—
717C2×C4—121no—
718C2×C4—121no—
719C2×C4—121no—
720C2×C4—121no—
721C2×C4—121no—
722C2×C4—121no—
723C2×C4—121no—
724C2×C4—121no—
725C2×C4—244no—
726C2×C4D3×SD1612yes—
727C2×C4C2×#23511yescharacteristic
728C2×C4C2×D3×D411yescharacteristic
729C2×C4C2×D3×D411yescharacteristic
730C2×C4#100411yescharacteristic
731C2×C4D3×#4111yescharacteristic
732C2×C4#100911yescharacteristic
733C8—22no—
734C8—34no—
735C8—41no—
736C8—121no—
737C2×C3—161no—
738C2×C3#242811yescharacteristic
739C2×C3#316711yescharacteristic
740C2×C3#317411yescharacteristic
741C2×C3D4×SD1611yescharacteristic
742C2×C3D4×SD1611yescharacteristic
743C2×C3#328211yescharacteristic
744C2×C3#328411yescharacteristic
745D3—42no—
746D3—82no—
747C22—62no—
748C22—62no—
749C22—62no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22—121no—
758C22—121no—
759C22—121no—
760C22—121no—
761C22—122no—
762C22—122no—
763C22—122no—
764C22—241no—
765C22—241no—
766C22—241no—
767C22—241no—
768C22#554811yescharacteristic
769C22#559011yescharacteristic
770C22#560911yescharacteristic
771C22C2×D3×SD1611yescharacteristic
772C22D3×#13511yescharacteristic
773C22#577511yescharacteristic
774C22#577811yescharacteristic
775C4—22no—
776C4—41no—
777C4—42no—
778C4—42no—
779C4—62no—
780C4—62no—
781C4—81no—
782C4—122no—
783C4—121no—
784C4—241no—
785C4—241no—
786C4#549011yescharacteristic
787C4#555311yescharacteristic
788C4D3×#12111yescharacteristic
789C4#566311yescharacteristic
790C3#2541011yescharacteristic, complemented, Sylow
791C2—122no—
792C2—161no—
793C2—242no—
794C2#7469811yescharacteristic
795C2#7966211yescharacteristic
796C2#7976711yescharacteristic
797C2#8006311yescharacteristic
798C2#8013011yescharacteristic
799C2#8040611yescharacteristic
800C2#8063011yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1880C2
socleC23×C3C22×D4
prime radical#76444C2
hypercenter#1880D3
hypocenterC3#25410
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1880

Complements

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

NH ≅ G/Ntype
1. C2×#5175C2semidirect
2. #82496C2semidirect
3. C2×C4×#215C2semidirect
4. C2×#4807C2semidirect
5. C2×#4778C2semidirect
7. C3×#1880C2semidirect
8. #72054C2semidirect
9. #70284C2semidirect
10. #70177C2semidirect
11. #69646C2semidirect
12. #68887C2semidirect
13. #68858C2semidirect
14. #68672C2semidirect
15. #68647C2semidirect
76. #1880D3semidirect
110. C2×#215D4semidirect
165. #808D4semidirect
299. (C2×D3)⋊C4SD16semidirect
497. C3⋊C8#121semidirect
790. C3#25410semidirect

Maximal subgroups

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

subgroupindex
C2×#51752
#824962
C2×C4×#2152
C2×#48072
C2×#47782
#764442
C3×#18802
#720542
#702842
#701772
#696462
#688872
#688582
#686722
#686472
#254103