Finite Group Databasebeta

← #10845946

Subgroups — #10845946

Order 768.

1116 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C8×D4C211yesmaximal, characteristic, complemented
2C2×#5115C211yesmaximal, characteristic, complemented
3C2×#5114C211yesmaximal, characteristic, complemented
4#82415C211yesmaximal, characteristic, complemented
5#82377C211yesmaximal, characteristic, complemented
6C2×#4844C211yesmaximal, characteristic, complemented
7#71973C211yesmaximal, characteristic, complemented
8#71972C211yesmaximal, characteristic, complemented
9#70455C211yesmaximal, characteristic, complemented
10#69962C211yesmaximal, characteristic, complemented
11#69961C211yesmaximal, characteristic, complemented
12#69937C211yesmaximal, characteristic, complemented
13#69935C211yesmaximal, characteristic, complemented
14#69773C211yesmaximal, characteristic, complemented
15C4×#821C211yesmaximal, characteristic, complemented
16#25388—31nomaximal, Sylow
17C23×C3×C8C2211yescharacteristic
18C23×C3×C8C2211yescharacteristic
19C2×C3×C4×D4C2211yescharacteristic
20C2×#930C2211yescharacteristic
21C2×#930C2211yescharacteristic
22C2×#930C2211yescharacteristic
23C2×#930C2211yescharacteristic
24C2×#924C2211yescharacteristic
25C2×#924C2211yescharacteristic
26C22×D24C2211yescharacteristic
27C22×#204C2211yescharacteristic
28C2×#875C2211yescharacteristic
29C2×C4×D12C2211yescharacteristic
30C3×C8×D4—24no—
31C2×C3×C4⋊C8C2211yescharacteristic
32C2×C3×C22⋊C8C2211yescharacteristic
33C2×C3×C22⋊C8C2211yescharacteristic
34C2×C3×C4×C8C2211yescharacteristic
35#5223—21no—
36#5223—21no—
37#5212C2211yescharacteristic
38#5212C2211yescharacteristic
39#5115—24no—
40#5114—24no—
41C2×#821C2211yescharacteristic
42C2×#821C2211yescharacteristic
43C2×#821C2211yescharacteristic
44C2×#821C2211yescharacteristic
45C2×#821C2211yescharacteristic
46C2×#818C2211yescharacteristic
47C2×#817C2211yescharacteristic
48C2×#816C2211yescharacteristic
49C2×#816C2211yescharacteristic
50C2×#816C2211yescharacteristic
51#4993—21no—
52#4992—21no—
53#4957—21no—
54#4957—21no—
55#4956—21no—
56#4956—21no—
57#4936C2211yescharacteristic
58C4×C4⋊Dic3C2211yescharacteristic
59#4844—24no—
60#4551C2211yescharacteristic
61#4551C2211yescharacteristic
62#4551C2211yescharacteristic
63#4551C2211yescharacteristic
64C2×#466—31no—
65C2×#465—31no—
66C2×#463—31no—
67C2×C8×D4D311yescharacteristic, complemented
68#2540—31no—
69#2535—31no—
70#2036—31no—
71#2034—31no—
72#2000—31no—
73#1999—31no—
74#1958—31no—
75#1949—31no—
76#1893—31no—
77#1892—31no—
78C4×#102—31no—
79C22×C3×D4D411yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C22×#67—21no—
83C22×#67—21no—
84C22×#67—21no—
85C22×#67—21no—
86C22×D12C2311yescharacteristic
87C22×D12C2311yescharacteristic
88C22×C4×D3—21no—
89C22×Dic6C2311yescharacteristic
90C22×C3×C8—22no—
91C22×C3×C8—22no—
92C22×C3×C8—22no—
93C22×C3×C8—22no—
94C22×C3×C8—41no—
95C22×C3×C8—41no—
96C22×C3×C8C2311yescharacteristic
97C22×C3×C8C2311yescharacteristic
98C22×C3×C8C2311yescharacteristic
99C22×C3×C8C2311yescharacteristic
100C3×C4×D4—22no—
101C3×C4×D4—22no—
102C2×C3×C4⋊C4D411yescharacteristic
103C2×C3×C22⋊C4D411yescharacteristic
104C2×C3×C22⋊C4D411yescharacteristic
105C2×C3×C42C2311yescharacteristic
106C2×#217—21no—
107C2×#217—21no—
108C2×#217—21no—
109C2×#217—21no—
110#930—22no—
111#930—22no—
112#930—22no—
113#930—22no—
114#930—41no—
115#930—41no—
116#930—41no—
117#930—41no—
118C2×(C2×D3)⋊C4—21no—
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⋊Dic3C2311yescharacteristic
126C2×C4⋊Dic3C2311yescharacteristic
127C2×C4⋊Dic3C2311yescharacteristic
128C2×C4⋊Dic3C2311yescharacteristic
129C2×C4⋊Dic3C2311yescharacteristic
130#924—22no—
131#924—22no—
132#924—41no—
133#924—41no—
134C2×Dic3⋊C4—21no—
135C2×Dic3⋊C4—21no—
136C2×C4×Dic3—21no—
137C2×D24—22no—
138C2×D24—22no—
139C2×D24—41no—
140C2×#204—22no—
141C2×#204—22no—
142C2×#204—41no—
143#875—22no—
144#875—22no—
145C4×D12—22no—
146C4×D12—22no—
147C3×C4⋊C8D414yescomplemented
148C3×C22⋊C8—22no—
149C3×C22⋊C8—22no—
150C3×C4×C8—22no—
151C3⋊#95—21no—
152C3⋊#95—21no—
153C3⋊#95—21no—
154C3⋊#95—21no—
155C3⋊#95—21no—
156#821—22no—
157#821—22no—
158#821—22no—
159#821—41no—
160#821D414yescomplemented
161#818—22no—
162#817—22no—
163#816—22no—
164#816—22no—
165#816—41no—
166C22×SD16—31no—
167C22×D8—31no—
168C23×C8C2×D311yescharacteristic
169C23×C8C2×D311yescharacteristic
170C2×#124—31no—
171C2×C22⋊Q8—31no—
172C2×C22⋊Q8—31no—
173C2×#121—31no—
174C2×#121—31no—
175C2×#121—31no—
176C2×#121—31no—
177C2×C4×D4—31no—
178C2×C4×D4C2×D311yescharacteristic
179#466—64no—
180#465—64no—
181#463—64no—
182C8×D4—24no—
183C2×#107—31no—
184C2×#106—31no—
185C2×C4⋊C8C2×D311yescharacteristic
186C2×#103—31no—
187C2×#103—31no—
188C2×#103—31no—
189C2×#102—31no—
190C2×#102—31no—
191C2×#102—31no—
192C2×#102—31no—
193C2×#102—31no—
194C2×C22⋊C8C2×D311yescharacteristic
195C2×C22⋊C8C2×D311yescharacteristic
196C2×C4×C8C2×D311yescharacteristic
197#399—61no—
198#397—61no—
199#392—61no—
200#392—61no—
201#390—61no—
202#390—61no—
203#386—61no—
204#386—61no—
205#382—31no—
206#380—31no—
207#380—31no—
208C4×C4⋊C4—31no—
209#340—31no—
210#340—31no—
211#340—31no—
212#340—31no—
213C24×C3C2×D411yescharacteristic
214C24×C3C2×D411yescharacteristic
215C23×D3—21no—
216C23×D3—21no—
217C2×C3×D4—22no—
218C2×C3×D4—22no—
219C2×C3×D4—22no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4C2×D411yescharacteristic
233C22×C3×C4C2×D411yescharacteristic
234C22×C3×C4C2×D411yescharacteristic
235C22×C3×C4C2×D411yescharacteristic
236C22×C3×C4C2411yescharacteristic
237C2×#67—42no—
238C2×#67—42no—
239C2×#67—42no—
240C2×#67—42no—
241C2×#67—42no—
242C2×#67—42no—
243C2×#67—42no—
244C2×#67—42no—
245C2×#67—81no—
246C2×#67—81no—
247C2×#67—81no—
248C2×#67—81no—
249C22×Dic3—21no—
250C22×Dic3—21no—
251C22×Dic3—21no—
252C22×Dic3—21no—
253C22×Dic3—21no—
254C22×Dic3—21no—
255C2×D12—21no—
256C2×D12—21no—
257C2×D12—21no—
258C2×D12—21no—
259C2×D12—21no—
260C2×D12—21no—
261C2×D12—21no—
262C2×D12—21no—
263C2×D12—21no—
264C2×D12—21no—
265C2×D12—21no—
266C2×D12C2×D412yes—
267C2×C4×D3—42no—
268C2×C4×D3—81no—
269C2×C4×D3—81no—
270C2×Dic6—21no—
271C2×Dic6—21no—
272C2×Dic6—21no—
273C2×Dic6—21no—
274C2×Dic6—21no—
275C2×Dic6—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—21no—
283C2×C3×C8—21no—
284C2×C3×C8—21no—
285C2×C3×C8—44no—
286C2×C3×C8—44no—
287C2×C3×C8C2×D412yes—
288C2×C3×C8C2×D412yes—
289C2×C3×C8C2×D412yes—
290C3×C4⋊C4—22no—
291C3×C22⋊C4—22no—
292C3×C22⋊C4—22no—
293C3×C42C2×D412yes—
294C3×C42#4112yes—
295#217—42no—
296#217—42no—
297#217—81no—
298#217—81no—
299(C2×D3)⋊C4—42no—
300(C2×D3)⋊C4—42no—
301(C2×D3)⋊C4—42no—
302(C2×D3)⋊C4—42no—
303(C2×D3)⋊C4—42no—
304(C2×D3)⋊C4—42no—
305(C2×D3)⋊C4—42no—
306C4⋊Dic3—21no—
307C4⋊Dic3—21no—
308C4⋊Dic3—21no—
309C4⋊Dic3—21no—
310C4⋊Dic3—21no—
311C4⋊Dic3—21no—
312C4⋊Dic3—21no—
313C4⋊Dic3—21no—
314C4⋊Dic3C2×D412yes—
315C4⋊Dic3#4112yes—
316Dic3⋊C4—42no—
317Dic3⋊C4—42no—
318C4×Dic3—81no—
319D24—44no—
320#204—44no—
321C22×Q8—31no—
322C22×D4—31no—
323C22×D4—31no—
324C22×D4—61no—
325C22×D4—61no—
326C22×D4—61no—
327C22×D4—61no—
328C22×D4D1211yescharacteristic
329C23×C4—61no—
330C23×C4C22×D311yescharacteristic
331C23×C4C22×D311yescharacteristic
332C2×SD16—62no—
333C2×SD16—62no—
334C2×SD16—121no—
335C2×D8—62no—
336C2×D8—62no—
337C2×D8—121no—
338C22×C8—22no—
339C22×C8—22no—
340C22×C8—22no—
341C22×C8—22no—
342C22×C8—41no—
343C22×C8—41no—
344C22×C8C22×D311yescharacteristic
345C22×C8C22×D311yescharacteristic
346C22×C8C22×D311yescharacteristic
347C22×C8C22×D311yescharacteristic
348#124—62no—
349#124—62no—
350C22⋊Q8—62no—
351C22⋊Q8—62no—
352C22⋊Q8—121no—
353C22⋊Q8—121no—
354#121—62no—
355#121—62no—
356#121—62no—
357#121—62no—
358#121—121no—
359#121—121no—
360#121—121no—
361#121—121no—
362C4×D4—22no—
363C4×D4—22no—
364C4×D4—62no—
365C4×D4—62no—
366C2×C4⋊C4—31no—
367C2×C4⋊C4—31no—
368C2×C4⋊C4—31no—
369C2×C4⋊C4—31no—
370C2×C4⋊C4—31no—
371C2×C4⋊C4—61no—
372C2×C4⋊C4—61no—
373C2×C4⋊C4D1211yescharacteristic
374C2×C22⋊C4—61no—
375C2×C22⋊C4—61no—
376C2×C22⋊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⋊C4—61no—
385C2×C22⋊C4D1211yescharacteristic
386C2×C22⋊C4D1211yescharacteristic
387C2×C42—61no—
388C2×C42C22×D311yescharacteristic
389#107—62no—
390#106—62no—
391C4⋊C8#6714yescomplemented
392#103—62no—
393#103—62no—
394#103—121no—
395#102—34no—
396#102—62no—
397#102—62no—
398#102—62no—
399#102—121no—
400C22⋊C8—22no—
401C22⋊C8—22no—
402C4×C8—22no—
403#95—61no—
404#95—61no—
405#95—61no—
406#95—61no—
407#95—61no—
408C23×C3—21no—
409C23×C3—21no—
410C23×C3—21no—
411C23×C3—21no—
412C23×C3—21no—
413C23×C3—21no—
414C23×C3—21no—
415C23×C3—21no—
416C23×C3—21no—
417C23×C3—21no—
418C23×C3—21no—
419C23×C3—21no—
420C23×C3#13512yes—
421C23×C3#13512yes—
422C23×C3C22×D411yescharacteristic
423C22×D3—22no—
424C22×D3—41no—
425C22×D3—41no—
426C22×D3—41no—
427C22×D3—41no—
428C22×D3—41no—
429C22×D3—41no—
430C22×D3—41no—
431C22×D3—41no—
432C22×D3—41no—
433C22×D3—41no—
434C22×D3—41no—
435C22×D3—41no—
436C22×D3—41no—
437C3×D4—28no—
438C2×C3×C4—21no—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
441C2×C3×C4—21no—
442C2×C3×C4—21no—
443C2×C3×C4—21no—
444C2×C3×C4—21no—
445C2×C3×C4—21no—
446C2×C3×C4—21no—
447C2×C3×C4—21no—
448C2×C3×C4—41no—
449C2×C3×C4—41no—
450C2×C3×C4—41no—
451C2×C3×C4—41no—
452C2×C3×C4—41no—
453C2×C3×C4—41no—
454C2×C3×C4—41no—
455C2×C3×C4—41no—
456C2×C3×C4#12112yes—
457C2×C3×C4#12112yes—
458C2×C3×C4C22×D411yescharacteristic
459C2×C3×C4C22×D411yescharacteristic
460C2×C3×C4C2×#4111yescharacteristic
461C2×C3×C4C2×#4111yescharacteristic
462C2×C3×C4H(5,𝔽2)11yescharacteristic
463C2×C3×C4H(5,𝔽2)11yescharacteristic
464#67—84no—
465#67—84no—
466#67—84no—
467#67—84no—
468C2×Dic3—22no—
469C2×Dic3—22no—
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×Dic3—41no—
479C2×Dic3—41no—
480C2×Dic3—41no—
481C2×Dic3—41no—
482C2×Dic3—41no—
483C2×Dic3—41no—
484C2×Dic3—41no—
485C2×Dic3—41no—
486D12—22no—
487D12—22no—
488D12—41no—
489D12—41no—
490D12—41no—
491D12—41no—
492D12—41no—
493D12—41no—
494C4×D3—84no—
495Dic6—41no—
496Dic6—41no—
497Dic6—41no—
498Dic6—41no—
499C3×C8—22no—
500C3×C8—22no—
501C3×C8—22no—
502C3×C8—41no—
503C24—61no—
504C24—61no—
505C24C2×D1211yescharacteristic
506C24C2×D1211yescharacteristic
507C2×Q8—61no—
508C2×Q8—61no—
509C2×Q8—61no—
510C2×Q8—61no—
511C2×Q8—61no—
512C2×Q8—61no—
513C2×D4—22no—
514C2×D4—22no—
515C2×D4—22no—
516C2×D4—32no—
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—61no—
526C2×D4—61no—
527C2×D4—61no—
528C2×D4—122no—
529C2×D4—122no—
530C2×D4—122no—
531C2×D4—122no—
532C2×D4—122no—
533C2×D4—122no—
534C2×D4—122no—
535C2×D4—122no—
536C2×D4—241no—
537C2×D4—241no—
538C2×D4—241no—
539C2×D4—241no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—61no—
553C22×C4—61no—
554C22×C4—61no—
555C22×C4—61no—
556C22×C4—61no—
557C22×C4—61no—
558C22×C4—122no—
559C22×C4—241no—
560C22×C4—241no—
561C22×C4C2×D1211yescharacteristic
562C22×C4C2×D1211yescharacteristic
563C22×C4C2×D1211yescharacteristic
564C22×C4C2×D1211yescharacteristic
565C22×C4C23×D311yescharacteristic
566SD16—124no—
567D8—124no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—44no—
578C2×C8—44no—
579C2×C8D3×D412yes—
580C2×C8C2×#6712yes—
581C2×C8C2×#6712yes—
582C4⋊C4—22no—
583C4⋊C4—32no—
584C4⋊C4—32no—
585C4⋊C4—61no—
586C4⋊C4—61no—
587C4⋊C4—61no—
588C4⋊C4—61no—
589C4⋊C4—61no—
590C4⋊C4—61no—
591C4⋊C4—61no—
592C4⋊C4—61no—
593C4⋊C4—122no—
594C4⋊C4—122no—
595C22⋊C4—22no—
596C22⋊C4—22no—
597C22⋊C4—122no—
598C22⋊C4—122no—
599C22⋊C4—122no—
600C22⋊C4—122no—
601C22⋊C4—122no—
602C22⋊C4—122no—
603C22⋊C4—122no—
604C22⋊C4—122no—
605C22⋊C4—122no—
606C22⋊C4—241no—
607C22⋊C4—241no—
608C42—241no—
609C42#23512yes—
610C42C2×#6712yes—
611C22×C3—22no—
612C22×C3—22no—
613C22×C3—22no—
614C22×C3—22no—
615C22×C3—22no—
616C22×C3—22no—
617C22×C3—41no—
618C22×C3—41no—
619C22×C3—41no—
620C22×C3—41no—
621C22×C3—41no—
622C22×C3—41no—
623C22×C3—41no—
624C22×C3—41no—
625C22×C3C2×#12111yescharacteristic
626C22×C3D4211yescharacteristic
627C22×C3#54611yescharacteristic
628C22×C3C2×#13511yescharacteristic
629C22×C3C2×#13511yescharacteristic
630C22×C3#57611yescharacteristic
631C22×C3#57711yescharacteristic
632C2×D3—42no—
633C2×D3—42no—
634C2×D3—42no—
635C2×D3—81no—
636C2×D3—81no—
637C2×D3—81no—
638C2×D3—81no—
639C2×D3—81no—
640C2×D3—81no—
641C2×D3—81no—
642C2×D3—81no—
643C2×D3—81no—
644C2×D3—81no—
645C2×D3—81no—
646C3×C4—22no—
647C3×C4—22no—
648C3×C4—41no—
649C3×C4—41no—
650C3×C4#53211yescharacteristic
651C3×C4#54011yescharacteristic
652C3×C4D4211yescharacteristic
653C3×C4#55011yescharacteristic
654Dic3—42no—
655Dic3—42no—
656Dic3—81no—
657Dic3—81no—
658Dic3—81no—
659Dic3—81no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—62no—
673C23—121no—
674C23—121no—
675C23—121no—
676C23—121no—
677C23—121no—
678C23—121no—
679C23—121no—
680C23—121no—
681C23—121no—
682C23—121no—
683C23—121no—
684C23—121no—
685C23—121no—
686C23#90412yes—
687C23#90412yes—
688C23C22×D1211yescharacteristic
689Q8—121no—
690Q8—121no—
691Q8—121no—
692Q8—121no—
693D4—28no—
694D4—62no—
695D4—62no—
696D4—121no—
697D4—121no—
698D4—121no—
699D4—121no—
700D4—121no—
701D4—121no—
702D4—244no—
703D4—244no—
704D4—244no—
705D4—244no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—62no—
725C2×C4—62no—
726C2×C4—121no—
727C2×C4—121no—
728C2×C4—121no—
729C2×C4—121no—
730C2×C4—121no—
731C2×C4—121no—
732C2×C4—121no—
733C2×C4—121no—
734C2×C4—121no—
735C2×C4—121no—
736C2×C4—121no—
737C2×C4—121no—
738C2×C4—121no—
739C2×C4—121no—
740C2×C4—121no—
741C2×C4—121no—
742C2×C4—244no—
743C2×C4#93012yes—
744C2×C4#93012yes—
745C2×C4C2×#23511yescharacteristic
746C2×C4C2×D3×D411yescharacteristic
747C2×C4#100411yescharacteristic
748C2×C4D3×#4111yescharacteristic
749C2×C4#100911yescharacteristic
750C2×C4C22×#6711yescharacteristic
751C8—22no—
752C8—22no—
753C8—22no—
754C8—41no—
755C2×C3—42no—
756C2×C3—42no—
757C2×C3#242811yescharacteristic
758C2×C3#305011yescharacteristic
759C2×C3#306211yescharacteristic
760C2×C3#328011yescharacteristic
761C2×C3#328211yescharacteristic
762C2×C3#329711yescharacteristic
763C2×C3#330111yescharacteristic
764D3—82no—
765D3—161no—
766C22—22no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—22no—
771C22—22no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—122no—
781C22—122no—
782C22—122no—
783C22—241no—
784C22—241no—
785C22—241no—
786C22—241no—
787C22—241no—
788C22—241no—
789C22—241no—
790C22—241no—
791C22—241no—
792C22—241no—
793C22—241no—
794C22D4×D1211yescharacteristic
795C22#555411yescharacteristic
796C22C2×#90411yescharacteristic
797C22C2×#90411yescharacteristic
798C22#575111yescharacteristic
799C22#575211yescharacteristic
800C22C2×#93011yescharacteristic
801C4—22no—
802C4—22no—
803C4—41no—
804C4—41no—
805C4—122no—
806C4—122no—
807C4—241no—
808C4—241no—
809C4—241no—
810C4—241no—
811C4#554811yescharacteristic
812C4#556211yescharacteristic
813C4D4×#6711yescharacteristic
814C4#583411yescharacteristic
815C3#2538811yescharacteristic, complemented, Sylow
816C2—42no—
817C2—42no—
818C2—242no—
819C2—481no—
820C2#7943311yescharacteristic
821C2#7943511yescharacteristic
822C2#7944111yescharacteristic
823C2#7945011yescharacteristic
824C2#8240911yescharacteristic
825C2#8374211yescharacteristic
826C2#8380211yescharacteristic
subgroupG/H
centerC23C22×D12
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×C8×D4C2
socleC23×C3C22×D4
hypercenterC2×C8×D4D3
hypocenterC3#25388
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×C8×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×C8×D4C2semidirect
2. C2×#5115C2semidirect
3. C2×#5114C2semidirect
4. #82415C2semidirect
5. #82377C2semidirect
6. C2×#4844C2semidirect
7. #71973C2semidirect
8. #71972C2semidirect
9. #70455C2semidirect
10. #69962C2semidirect
11. #69961C2semidirect
12. #69937C2semidirect
13. #69935C2semidirect
14. #69773C2semidirect
15. C4×#821C2semidirect
67. C2×C8×D4D3semidirect
147. C3×C4⋊C8D4semidirect
160. #821D4semidirect
391. C4⋊C8#67semidirect
815. C3#25388semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C8×D42
C2×#51152
C2×#51142
#824152
#823772
C2×#48442
#719732
#719722
#704552
#699622
#699612
#699372
#699352
#697732
C4×#8212
#253883