Finite Group Databasebeta

← #10846250

Subgroups — #10846250

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×#5114C211yesmaximal, characteristic, complemented
2C2×#5114C211yesmaximal, characteristic, complemented
3C2×C4×#204C211yesmaximal, characteristic, complemented
4C2×#4693C211yesmaximal, characteristic, complemented
5#73488C211yesmaximal, characteristic, complemented
6#73487C211yesmaximal, characteristic
7C3×C8×C22⋊C4C211yesmaximal, characteristic, complemented
8#69962C211yesmaximal, characteristic, complemented
9#69962C211yesmaximal, characteristic, complemented
10#69774C211yesmaximal, characteristic, complemented
11#69769C211yesmaximal, characteristic, complemented
12#68686C211yesmaximal, characteristic, complemented
13#68672C211yesmaximal, characteristic, complemented
14#68631C211yesmaximal, characteristic, complemented
15#68629C211yesmaximal, characteristic, complemented
16#25410—31nomaximal, Sylow
17C23×C3×C8C2211yescharacteristic
18C2×#930C2211yescharacteristic
19C2×#930C2211yescharacteristic
20C2×#924C2211yescharacteristic
21C2×#924C2211yescharacteristic
22C22×#204C2211yescharacteristic
23C22×#204C2211yescharacteristic
24C22×#204C2211yescharacteristic
25C22×#204C2211yescharacteristic
26C2×#884—21no—
27C2×#874C2211yescharacteristic
28C2×C4×D12C2211yescharacteristic
29C2×#869C2211yescharacteristic
30C2×C4×Dic6C2211yescharacteristic
31C2×C3×C22⋊C8C2211yescharacteristic
32C2×C3×C4×C8C2211yescharacteristic
33C2×C3×C4×C8C2211yescharacteristic
34C3×C4×C22⋊C4C2211yescharacteristic
35#5114—24no—
36#5114—24no—
37C2×#821C2211yescharacteristic
38C2×#821C2211yescharacteristic
39C2×#821C2211yescharacteristic
40C2×#821C2211yescharacteristic
41C2×#817C2211yescharacteristic
42C2×#817C2211yescharacteristic
43C2×#816C2211yescharacteristic
44C2×#816C2211yescharacteristic
45C2×#816C2211yescharacteristic
46C2×#816C2211yescharacteristic
47#4960—21no—
48#4951—21no—
49#4948—21no—
50#4939C2211yescharacteristic
51#4929C2211yescharacteristic
52#4928C2211yescharacteristic
53#4928C2211yescharacteristic
54#4693—24no—
55C4×#204—24no—
56#4672—21no—
57#4665—21no—
58#4657—21no—
59#4647—21no—
60C3×#336C2211yescharacteristic
61C3×#336C2211yescharacteristic
62#4551C2211yescharacteristic
63#4551C2211yescharacteristic
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#1880—31no—
77#1877—31no—
78C8×C22⋊C4D311yescharacteristic, complemented
79C23×C3×C4C2311yescharacteristic
80C22×#67—21no—
81C22×#67—21no—
82C22×D12—21no—
83C22×D12—21no—
84C22×D12C2311yescharacteristic
85C22×D12C2311yescharacteristic
86C22×C4×D3—21no—
87C22×Dic6C2311yescharacteristic
88C22×Dic6C2311yescharacteristic
89C22×C3×C8—22no—
90C22×C3×C8—22no—
91C22×C3×C8—22no—
92C22×C3×C8C2311yescharacteristic
93C22×C3×C8C2311yescharacteristic
94C22×C3×C8C2311yescharacteristic
95C22×C3×C8C2311yescharacteristic
96C2×C3×C22⋊C4D411yescharacteristic
97C2×C3×C22⋊C4D411yescharacteristic
98C2×C3×C42C2311yescharacteristic
99C2×C3×C42C2311yescharacteristic
100C2×#217—21no—
101C2×#217—21no—
102#930—22no—
103#930—22no—
104#930—41no—
105#930—41no—
106C2×(C2×D3)⋊C4—21no—
107C2×(C2×D3)⋊C4—21no—
108C2×(C2×D3)⋊C4—21no—
109C2×(C2×D3)⋊C4—21no—
110C2×(C2×D3)⋊C4—21no—
111C2×C4⋊Dic3—21no—
112C2×C4⋊Dic3—21no—
113C2×C4⋊Dic3C2311yescharacteristic
114C2×C4⋊Dic3C2311yescharacteristic
115C2×C4⋊Dic3C2311yescharacteristic
116C2×C4⋊Dic3C2311yescharacteristic
117#924—22no—
118#924—22no—
119#924—41no—
120#924—41no—
121C2×Dic3⋊C4—21no—
122C2×Dic3⋊C4—21no—
123C2×Dic3⋊C4—21no—
124C2×Dic3⋊C4—21no—
125C2×Dic3⋊C4—21no—
126C2×C4×Dic3—21no—
127C2×#204—22no—
128C2×#204—22no—
129C2×#204—22no—
130C2×#204—22no—
131C2×#204—22no—
132C2×#204—22no—
133C2×#204—22no—
134C2×#204—22no—
135C2×#204—22no—
136C2×#204—41no—
137C2×#204—41no—
138C2×#204D414yescomplemented
139#884—44no—
140#874—22no—
141#874—41no—
142C4×D12—22no—
143C4×D12—41no—
144#869—22no—
145#869—41no—
146C4×Dic6—22no—
147C4×Dic6—41no—
148C3×C22⋊C8—22no—
149C3×C4×C8—22no—
150C3×C4×C8—22no—
151C3×#95D411yescharacteristic
152C3×#95D411yescharacteristic
153C3⋊#95—21no—
154C3⋊#95—21no—
155C3⋊#95—21no—
156C3⋊#95—21no—
157#821—22no—
158#821—22no—
159#821—22no—
160#821—41no—
161#817—22no—
162#817D414yescomplemented
163#816—22no—
164#816—22no—
165#816—22no—
166#816—41no—
167C22×SD16—31no—
168C22×SD16—31no—
169C22×SD16—31no—
170C22×SD16—31no—
171C23×C8C2×D311yescharacteristic
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×Q8—31no—
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×#103—31no—
191C2×#102—31no—
192C2×#102—31no—
193C2×#102—31no—
194C2×#102—31no—
195C2×C22⋊C8C2×D311yescharacteristic
196C2×C4×C8C2×D311yescharacteristic
197C2×C4×C8C2×D311yescharacteristic
198#398—61no—
199#396—61no—
200#394—61no—
201#392—61no—
202#391—31no—
203#390—31no—
204#389—31no—
205#389—31no—
206#389—61no—
207#388—61no—
208#386—61no—
209C4×C22⋊C4C2×D311yescharacteristic
210#340—31no—
211#340—31no—
212#336C2×D311yescharacteristic
213#336C2×D311yescharacteristic
214C24×C3C2×D411yescharacteristic
215C23×D3—21no—
216C23×D3—21no—
217C22×C3×C4—21no—
218C22×C3×C4—21no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4C2×D411yescharacteristic
224C22×C3×C4C2×D411yescharacteristic
225C22×C3×C4C2×D411yescharacteristic
226C22×C3×C4C2×D411yescharacteristic
227C22×C3×C4C2×D411yescharacteristic
228C22×C3×C4C2411yescharacteristic
229C2×#67—42no—
230C2×#67—42no—
231C2×#67—42no—
232C2×#67—42no—
233C2×#67—81no—
234C2×#67—81no—
235C22×Dic3—21no—
236C22×Dic3—21no—
237C22×Dic3—21no—
238C22×Dic3—21no—
239C22×Dic3—21no—
240C22×Dic3—21no—
241C2×D12—21no—
242C2×D12—21no—
243C2×D12—21no—
244C2×D12—21no—
245C2×D12—21no—
246C2×D12—21no—
247C2×D12—21no—
248C2×D12—21no—
249C2×D12—21no—
250C2×D12—21no—
251C2×D12—21no—
252C2×D12—42no—
253C2×D12—42no—
254C2×D12—42no—
255C2×D12—42no—
256C2×D12—81no—
257C2×D12—81no—
258C2×D12C2×D412yes—
259C2×C4×D3—42no—
260C2×C4×D3—42no—
261C2×C4×D3—81no—
262C2×Dic6—21no—
263C2×Dic6—21no—
264C2×Dic6—21no—
265C2×Dic6—21no—
266C2×Dic6—21no—
267C2×Dic6—21no—
268C2×Dic6—21no—
269C2×Dic6—21no—
270C2×Dic6—21no—
271C2×Dic6—21no—
272C2×Dic6—21no—
273C2×Dic6C2×D412yes—
274C2×C3×C8—21no—
275C2×C3×C8—21no—
276C2×C3×C8—21no—
277C2×C3×C8—21no—
278C2×C3×C8—21no—
279C2×C3×C8—21no—
280C2×C3×C8—21no—
281C2×C3×C8—21no—
282C2×C3×C8—44no—
283C2×C3×C8C2×D412yes—
284C2×C3×C8C2×D412yes—
285C2×C3×C8#4112yes—
286C2×C3×C8#4112yes—
287C3×C22⋊C4—22no—
288C3×C22⋊C4SD1614yescomplemented
289C3×C42—21no—
290C3×C42—21no—
291C3×C42—21no—
292C3×C42—21no—
293#217—42no—
294#217—42no—
295(C2×D3)⋊C4—42no—
296(C2×D3)⋊C4—42no—
297(C2×D3)⋊C4—42no—
298(C2×D3)⋊C4—42no—
299(C2×D3)⋊C4—81no—
300C4⋊Dic3—21no—
301C4⋊Dic3—21no—
302C4⋊Dic3—21no—
303C4⋊Dic3—21no—
304C4⋊Dic3—21no—
305C4⋊Dic3—21no—
306C4⋊Dic3—42no—
307C4⋊Dic3—42no—
308C4⋊Dic3C2×D412yes—
309C4⋊Dic3C2×D412yes—
310Dic3⋊C4—42no—
311Dic3⋊C4—42no—
312Dic3⋊C4—42no—
313Dic3⋊C4—42no—
314Dic3⋊C4—42no—
315C4×Dic3—42no—
316#204—28no—
317#204—44no—
318#204—44no—
319#204—44no—
320C22×Q8—31no—
321C22×Q8—31no—
322C22×D4—31no—
323C22×D4—31no—
324C22×D4—61no—
325C22×D4—61no—
326C22×D4—61no—
327C22×D4—61no—
328C23×C4—61no—
329C23×C4C22×D311yescharacteristic
330C2×SD16—34no—
331C2×SD16—62no—
332C2×SD16—62no—
333C2×SD16—62no—
334C2×SD16—62no—
335C2×SD16—62no—
336C2×SD16—62no—
337C2×SD16—62no—
338C2×SD16—62no—
339C2×SD16—62no—
340C2×SD16—121no—
341C2×SD16—121no—
342C22×C8—22no—
343C22×C8—22no—
344C22×C8—22no—
345C22×C8C22×D311yescharacteristic
346C22×C8C22×D311yescharacteristic
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—121no—
360#121—121no—
361#121—124no—
362C4×Q8—62no—
363C4×Q8—121no—
364C4×D4—62no—
365C4×D4—121no—
366C2×C4⋊C4—31no—
367C2×C4⋊C4—31no—
368C2×C4⋊C4—31no—
369C2×C4⋊C4—31no—
370C2×C4⋊C4—61no—
371C2×C4⋊C4—61no—
372C2×C4⋊C4—61no—
373C2×C4⋊C4—61no—
374C2×C4⋊C4—61no—
375C2×C4⋊C4—61no—
376C2×C4⋊C4—61no—
377C2×C22⋊C4—61no—
378C2×C22⋊C4—61no—
379C2×C22⋊C4—61no—
380C2×C22⋊C4—61no—
381C2×C22⋊C4—61no—
382C2×C22⋊C4—61no—
383C2×C22⋊C4—61no—
384C2×C22⋊C4D1211yescharacteristic
385C2×C22⋊C4D1211yescharacteristic
386C2×C42—61no—
387C2×C42C22×D311yescharacteristic
388C2×C42C22×D311yescharacteristic
389#106—34no—
390#106—62no—
391#103—62no—
392#103—62no—
393#103—62no—
394#103—121no—
395#102—62no—
396#102—62no—
397#102—62no—
398#102—121no—
399C22⋊C8—22no—
400C4×C8—22no—
401C4×C8—22no—
402#95—61no—
403#95—61no—
404#95—61no—
405#95—61no—
406#95D1211yescharacteristic
407#95D1211yescharacteristic
408C23×C3—21no—
409C23×C3—21no—
410C23×C3—21no—
411C23×C3—21no—
412C23×C3—21no—
413C23×C3—21no—
414C23×C3C2×SD1612yes—
415C23×C3C22×D411yescharacteristic
416C22×D3—22no—
417C22×D3—41no—
418C22×D3—41no—
419C22×D3—41no—
420C22×D3—41no—
421C22×D3—41no—
422C22×D3—41no—
423C22×D3—41no—
424C22×D3—41no—
425C22×D3—41no—
426C22×D3—41no—
427C22×D3—41no—
428C22×D3—41no—
429C22×D3—41no—
430C2×C3×C4—21no—
431C2×C3×C4—21no—
432C2×C3×C4—21no—
433C2×C3×C4—21no—
434C2×C3×C4—21no—
435C2×C3×C4—21no—
436C2×C3×C4—21no—
437C2×C3×C4—21no—
438C2×C3×C4—21no—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
441C2×C3×C4—21no—
442C2×C3×C4—41no—
443C2×C3×C4—41no—
444C2×C3×C4—41no—
445C2×C3×C4—41no—
446C2×C3×C4C2×SD1612yes—
447C2×C3×C4C2×SD1612yes—
448C2×C3×C4#13512yes—
449C2×C3×C4C22×D411yescharacteristic
450C2×C3×C4C22×D411yescharacteristic
451C2×C3×C4C2×#4111yescharacteristic
452C2×C3×C4C2×#4111yescharacteristic
453C2×C3×C4H(5,𝔽2)11yescharacteristic
454C2×C3×C4H(5,𝔽2)11yescharacteristic
455#67—84no—
456#67—84no—
457C2×Dic3—22no—
458C2×Dic3—22no—
459C2×Dic3—22no—
460C2×Dic3—41no—
461C2×Dic3—41no—
462C2×Dic3—41no—
463C2×Dic3—41no—
464C2×Dic3—41no—
465C2×Dic3—41no—
466C2×Dic3—41no—
467C2×Dic3—41no—
468C2×Dic3—41no—
469C2×Dic3—41no—
470C2×Dic3—41no—
471C2×Dic3—41no—
472C2×Dic3—41no—
473C2×Dic3—41no—
474C2×Dic3—41no—
475D12—22no—
476D12—22no—
477D12—41no—
478D12—41no—
479D12—41no—
480D12—41no—
481D12—41no—
482D12—41no—
483D12—84no—
484D12—84no—
485C4×D3—84no—
486Dic6—22no—
487Dic6—22no—
488Dic6—41no—
489Dic6—41no—
490Dic6—41no—
491Dic6—41no—
492Dic6—41no—
493Dic6—41no—
494C3×C8—22no—
495C3×C8—41no—
496C3×C8—41no—
497C3×C8#12114yescomplemented
498C24—61no—
499C24—61no—
500C24C2×D1211yescharacteristic
501C2×Q8—32no—
502C2×Q8—61no—
503C2×Q8—61no—
504C2×Q8—61no—
505C2×Q8—61no—
506C2×Q8—61no—
507C2×Q8—61no—
508C2×Q8—61no—
509C2×Q8—61no—
510C2×Q8—61no—
511C2×Q8—61no—
512C2×Q8—61no—
513C2×D4—32no—
514C2×D4—61no—
515C2×D4—61no—
516C2×D4—61no—
517C2×D4—61no—
518C2×D4—61no—
519C2×D4—61no—
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—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—61no—
544C22×C4—61no—
545C22×C4—61no—
546C22×C4—61no—
547C22×C4—61no—
548C22×C4—61no—
549C22×C4—122no—
550C22×C4—122no—
551C22×C4—241no—
552C22×C4C2×D1211yescharacteristic
553C22×C4C2×D1211yescharacteristic
554C22×C4C2×D1211yescharacteristic
555C22×C4C2×D1211yescharacteristic
556C22×C4C2×D1211yescharacteristic
557C22×C4C23×D311yescharacteristic
558SD16—68no—
559SD16—124no—
560SD16—124no—
561SD16—124no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—44no—
571C2×C8#23512yes—
572C2×C8#23512yes—
573C2×C8D3×D412yes—
574C2×C8D3×D412yes—
575C4⋊C4—32no—
576C4⋊C4—32no—
577C4⋊C4—61no—
578C4⋊C4—61no—
579C4⋊C4—61no—
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⋊C4—122no—
590C22⋊C4—22no—
591C22⋊C4—122no—
592C22⋊C4—122no—
593C22⋊C4—122no—
594C22⋊C4—122no—
595C22⋊C4—122no—
596C22⋊C4—122no—
597C22⋊C4—241no—
598C22⋊C4#20414yescomplemented
599C42—21no—
600C42—21no—
601C42—21no—
602C42—21no—
603C42—122no—
604C22×C3—22no—
605C22×C3—22no—
606C22×C3—22no—
607C22×C3—41no—
608C22×C3—41no—
609C22×C3—41no—
610C22×C3—41no—
611C22×C3#53211yescharacteristic
612C22×C3D4211yescharacteristic
613C22×C3D4211yescharacteristic
614C22×C3C22×SD1611yescharacteristic
615C22×C3C2×#13511yescharacteristic
616C22×C3#57711yescharacteristic
617C22×C3#57711yescharacteristic
618C2×D3—42no—
619C2×D3—42no—
620C2×D3—42no—
621C2×D3—81no—
622C2×D3—81no—
623C2×D3—81no—
624C2×D3—81no—
625C2×D3—81no—
626C2×D3—81no—
627C2×D3—81no—
628C2×D3—81no—
629C2×D3—81no—
630C2×D3—81no—
631C2×D3—81no—
632C3×C4—22no—
633C3×C4—22no—
634C3×C4—22no—
635C3×C4—41no—
636C3×C4—41no—
637C3×C4C2×#12111yescharacteristic
638C3×C4#54011yescharacteristic
639C3×C4#54611yescharacteristic
640C3×C4#55011yescharacteristic
641Dic3—42no—
642Dic3—42no—
643Dic3—42no—
644Dic3—81no—
645Dic3—81no—
646Dic3—81no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—62no—
654C23—121no—
655C23—121no—
656C23—121no—
657C23—121no—
658C23—121no—
659C23—121no—
660C23—121no—
661C23—121no—
662C23—121no—
663C23—121no—
664C23—121no—
665C23—121no—
666C23—121no—
667C23C2×#20412yes—
668C23C22×D1211yescharacteristic
669Q8—62no—
670Q8—62no—
671Q8—121no—
672Q8—121no—
673Q8—121no—
674Q8—121no—
675Q8—121no—
676Q8—121no—
677D4—62no—
678D4—62no—
679D4—121no—
680D4—121no—
681D4—121no—
682D4—121no—
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—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—62no—
706C2×C4—62no—
707C2×C4—62no—
708C2×C4—121no—
709C2×C4—121no—
710C2×C4—121no—
711C2×C4—121no—
712C2×C4—121no—
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—244no—
724C2×C4C2×#20412yes—
725C2×C4C2×#20412yes—
726C2×C4#90412yes—
727C2×C4C2×#23511yescharacteristic
728C2×C4C2×#23511yescharacteristic
729C2×C4C2×D3×D411yescharacteristic
730C2×C4C2×D3×D411yescharacteristic
731C2×C4#100911yescharacteristic
732C2×C4#100911yescharacteristic
733C8—22no—
734C8—41no—
735C8—41no—
736C8#88414yescomplemented
737C2×C3—42no—
738C2×C3#242811yescharacteristic
739C2×C3#316711yescharacteristic
740C2×C3#317411yescharacteristic
741C2×C3D4×SD1611yescharacteristic
742C2×C3D4×SD1611yescharacteristic
743C2×C3#328211yescharacteristic
744C2×C3#328411yescharacteristic
745D3—82no—
746D3—161no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—122no—
755C22—122no—
756C22—122no—
757C22—241no—
758C22—241no—
759C22—241no—
760C22—241no—
761C22—241no—
762C22—241no—
763C22—241no—
764C22—241no—
765C22—241no—
766C22—241no—
767C22—241no—
768C22#547711yescharacteristic
769C22D4×D1211yescharacteristic
770C22D4×D1211yescharacteristic
771C22C22×#20411yescharacteristic
772C22C2×#90411yescharacteristic
773C22#575111yescharacteristic
774C22#575111yescharacteristic
775C4—22no—
776C4—22no—
777C4—22no—
778C4—41no—
779C4—41no—
780C4—122no—
781C4—122no—
782C4—122no—
783C4—241no—
784C4—241no—
785C4—241no—
786C4C2×#88411yescharacteristic
787C4#553511yescharacteristic
788C4#555011yescharacteristic
789C4#555311yescharacteristic
790C3#2541011yescharacteristic, complemented, Sylow
791C2—42no—
792C2—242no—
793C2—481no—
794C2#7348711yescharacteristic
795C2#7846811yescharacteristic
796C2#7856711yescharacteristic
797C2D4×#20411yescharacteristic
798C2D4×#20411yescharacteristic
799C2#7943511yescharacteristic
800C2#7943711yescharacteristic
subgroupG/H
centerC23C22×D12
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×C8×C22⋊C4C2
socleC23×C3C22×D4
prime radical#73487C2
hypercenterC8×C22⋊C4D3
hypocenterC3#25410
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ C8×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#5114C2semidirect
2. C2×#5114C2semidirect
3. C2×C4×#204C2semidirect
4. C2×#4693C2semidirect
5. #73488C2semidirect
7. C3×C8×C22⋊C4C2semidirect
8. #69962C2semidirect
9. #69962C2semidirect
10. #69774C2semidirect
11. #69769C2semidirect
12. #68686C2semidirect
13. #68672C2semidirect
14. #68631C2semidirect
15. #68629C2semidirect
78. C8×C22⋊C4D3semidirect
138. C2×#204D4semidirect
162. #817D4semidirect
288. C3×C22⋊C4SD16semidirect
497. C3×C8#121semidirect
598. C22⋊C4#204semidirect
736. C8#884semidirect
790. C3#25410semidirect

Maximal subgroups

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

subgroupindex
C2×#51142
C2×C4×#2042
C2×#46932
#734882
#734872
C3×C8×C22⋊C42
#699622
#697742
#697692
#686862
#686722
#686312
#686292
#254103