Finite Group Databasebeta

← #10845961

Subgroups — #10845961

Order 768.

1052 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C8×D4C211yesmaximal, characteristic, complemented
2C2×#5116C211yesmaximal, characteristic, complemented
3C2×#5114C211yesmaximal, characteristic, complemented
4#82377C211yesmaximal, characteristic
5#82375C211yesmaximal, characteristic, complemented
6C2×#4845C211yesmaximal, characteristic, complemented
7#71973C211yesmaximal, characteristic, complemented
8#71972C211yesmaximal, characteristic, complemented
9#70455C211yesmaximal, characteristic, complemented
10#69964C211yesmaximal, characteristic, complemented
11#69962C211yesmaximal, characteristic, complemented
12#69936C211yesmaximal, characteristic, complemented
13#69934C211yesmaximal, characteristic, complemented
14#69773C211yesmaximal, characteristic, complemented
15C4×#816C211yesmaximal, characteristic, complemented
16#25389—31nomaximal, Sylow
17C23×C3×C8C2211yescharacteristic
18C23×C3×C8C2211yescharacteristic
19C2×C3×C4×D4C2211yescharacteristic
20C2×#930C2211yescharacteristic
21C2×#930C2211yescharacteristic
22C2×#924C2211yescharacteristic
23C2×#924C2211yescharacteristic
24C2×#924C2211yescharacteristic
25C2×#924C2211yescharacteristic
26C22×Dic12C2211yescharacteristic
27C22×#204C2211yescharacteristic
28C2×#875C2211yescharacteristic
29C2×C4×Dic6C2211yescharacteristic
30C3×C8×D4—24no—
31C2×C3×C4⋊C8C2211yescharacteristic
32C2×C3×C22⋊C8C2211yescharacteristic
33C2×C3×C22⋊C8C2211yescharacteristic
34C2×C3×C4×C8C2211yescharacteristic
35#5223—21no—
36#5222—21no—
37#5212C2211yescharacteristic
38#5212C2211yescharacteristic
39#5116—24no—
40#5114—24no—
41C2×#821C2211yescharacteristic
42C2×#821C2211yescharacteristic
43C2×#821C2211yescharacteristic
44C2×#818C2211yescharacteristic
45C2×#817C2211yescharacteristic
46C2×#816C2211yescharacteristic
47C2×#816C2211yescharacteristic
48C2×#816C2211yescharacteristic
49C2×#816C2211yescharacteristic
50C2×#816C2211yescharacteristic
51#4993—21no—
52#4983—21no—
53#4957—21no—
54#4957—21no—
55#4944—21no—
56#4944—21no—
57#4936C2211yescharacteristic
58C4×C4⋊Dic3C2211yescharacteristic
59#4845—24no—
60#4551C2211yescharacteristic
61#4551C2211yescharacteristic
62#4551C2211yescharacteristic
63#4551C2211yescharacteristic
64C2×#467—31no—
65C2×#465—31no—
66C2×#464—31no—
67C2×C8×D4D311yescharacteristic, complemented
68#2540—31no—
69#2536—31no—
70#2035—31no—
71#2033—31no—
72#2001—31no—
73#2000—31no—
74#1958—31no—
75#1949—31no—
76#1893—31no—
77#1892—31no—
78C4×#103—31no—
79C22×C3×D4D411yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C22×#67—21no—
83C22×#67—21no—
84C22×D12C2311yescharacteristic
85C22×Dic6C2311yescharacteristic
86C22×Dic6C2311yescharacteristic
87C22×C3×C8—22no—
88C22×C3×C8—22no—
89C22×C3×C8—22no—
90C22×C3×C8—22no—
91C22×C3×C8—41no—
92C22×C3×C8—41no—
93C22×C3×C8C2311yescharacteristic
94C22×C3×C8C2311yescharacteristic
95C22×C3×C8C2311yescharacteristic
96C22×C3×C8C2311yescharacteristic
97C3×C4×D4—22no—
98C3×C4×D4—22no—
99C2×C3×C4⋊C4D411yescharacteristic
100C2×C3×C22⋊C4D411yescharacteristic
101C2×C3×C22⋊C4D411yescharacteristic
102C2×C3×C42C2311yescharacteristic
103C2×#217—21no—
104C2×#217—21no—
105C2×#217—21no—
106C2×#217—21no—
107C2×#217—21no—
108C2×#217—21no—
109#930—22no—
110#930—22no—
111#930—41no—
112#930—41no—
113C2×(C2×D3)⋊C4—21no—
114C2×(C2×D3)⋊C4—21no—
115C2×(C2×D3)⋊C4—21no—
116C2×(C2×D3)⋊C4—21no—
117C2×C4⋊Dic3C2311yescharacteristic
118C2×C4⋊Dic3C2311yescharacteristic
119C2×C4⋊Dic3C2311yescharacteristic
120C2×C4⋊Dic3C2311yescharacteristic
121C2×C4⋊Dic3C2311yescharacteristic
122#924—22no—
123#924—22no—
124#924—22no—
125#924—22no—
126#924—41no—
127#924—41no—
128#924—41no—
129#924—41no—
130C2×Dic3⋊C4—21no—
131C2×Dic3⋊C4—21no—
132C2×Dic3⋊C4—21no—
133C2×Dic3⋊C4—21no—
134C2×Dic3⋊C4—21no—
135C2×C4×Dic3—21no—
136C2×C4×Dic3—21no—
137C2×Dic12—22no—
138C2×Dic12—22no—
139C2×Dic12—41no—
140C2×#204—22no—
141C2×#204—22no—
142C2×#204—41no—
143#875—22no—
144#875—22no—
145C4×Dic6—22no—
146C4×Dic6—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—41no—
159#818—22no—
160#817—22no—
161#816—22no—
162#816—22no—
163#816—22no—
164#816—41no—
165#816D414yescomplemented
166C22×Q16—31no—
167C22×SD16—31no—
168C23×C8C2×D311yescharacteristic
169C23×C8C2×D311yescharacteristic
170C2×#124—31no—
171C2×C22⋊Q8—31no—
172C2×C22⋊Q8—31no—
173C2×C22⋊Q8—31no—
174C2×C22⋊Q8—31no—
175C2×#121—31no—
176C2×#121—31no—
177C2×C4×Q8—31no—
178C2×C4×D4C2×D311yescharacteristic
179#467—64no—
180#465—64no—
181#464—64no—
182C8×D4—24no—
183C2×#107—31no—
184C2×#106—31no—
185C2×C4⋊C8C2×D311yescharacteristic
186C2×#103—31no—
187C2×#103—31no—
188C2×#103—31no—
189C2×#103—31no—
190C2×#103—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#398—61no—
199#394—61no—
200#392—61no—
201#390—61no—
202#390—61no—
203#388—61no—
204#388—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—
216C2×C3×D4—22no—
217C2×C3×D4—22no—
218C2×C3×D4—22no—
219C22×C3×C4—21no—
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×C4C2×D411yescharacteristic
232C22×C3×C4C2×D411yescharacteristic
233C22×C3×C4C2×D411yescharacteristic
234C22×C3×C4C2×D411yescharacteristic
235C22×C3×C4C2411yescharacteristic
236C2×#67—42no—
237C2×#67—42no—
238C2×#67—42no—
239C2×#67—42no—
240C2×#67—81no—
241C2×#67—81no—
242C22×Dic3—21no—
243C22×Dic3—21no—
244C22×Dic3—21no—
245C22×Dic3—21no—
246C22×Dic3—21no—
247C22×Dic3—21no—
248C22×Dic3—21no—
249C2×D12—21no—
250C2×D12—21no—
251C2×D12—21no—
252C2×D12—21no—
253C2×D12—21no—
254C2×D12—21no—
255C2×Dic6—21no—
256C2×Dic6—21no—
257C2×Dic6—21no—
258C2×Dic6—21no—
259C2×Dic6—21no—
260C2×Dic6—21no—
261C2×Dic6—21no—
262C2×Dic6—21no—
263C2×Dic6—21no—
264C2×Dic6—21no—
265C2×Dic6—21no—
266C2×Dic6C2×D412yes—
267C2×C3×C8—21no—
268C2×C3×C8—21no—
269C2×C3×C8—21no—
270C2×C3×C8—21no—
271C2×C3×C8—21no—
272C2×C3×C8—21no—
273C2×C3×C8—21no—
274C2×C3×C8—21no—
275C2×C3×C8—21no—
276C2×C3×C8—44no—
277C2×C3×C8—44no—
278C2×C3×C8C2×D412yes—
279C2×C3×C8C2×D412yes—
280C2×C3×C8C2×D412yes—
281C3×C4⋊C4—22no—
282C3×C22⋊C4—22no—
283C3×C22⋊C4—22no—
284C3×C42C2×D412yes—
285C3×C42#4112yes—
286#217—42no—
287#217—42no—
288#217—42no—
289#217—42no—
290#217—42no—
291#217—42no—
292(C2×D3)⋊C4—42no—
293(C2×D3)⋊C4—42no—
294(C2×D3)⋊C4—42no—
295(C2×D3)⋊C4—42no—
296C4⋊Dic3—21no—
297C4⋊Dic3—21no—
298C4⋊Dic3—21no—
299C4⋊Dic3—21no—
300C4⋊Dic3—21no—
301C4⋊Dic3—21no—
302C4⋊Dic3—21no—
303C4⋊Dic3—21no—
304C4⋊Dic3C2×D412yes—
305C4⋊Dic3#4112yes—
306Dic3⋊C4—42no—
307Dic3⋊C4—42no—
308Dic3⋊C4—42no—
309Dic3⋊C4—42no—
310Dic3⋊C4—42no—
311C4×Dic3—42no—
312C4×Dic3—81no—
313Dic12—44no—
314#204—44no—
315C22×Q8—31no—
316C22×Q8—31no—
317C22×D4—31no—
318C22×D4—61no—
319C22×D4—61no—
320C22×D4D1211yescharacteristic
321C23×C4C22×D311yescharacteristic
322C23×C4C22×D311yescharacteristic
323C2×Q16—62no—
324C2×Q16—62no—
325C2×Q16—121no—
326C2×SD16—62no—
327C2×SD16—62no—
328C2×SD16—121no—
329C22×C8—22no—
330C22×C8—22no—
331C22×C8—22no—
332C22×C8—22no—
333C22×C8—41no—
334C22×C8—41no—
335C22×C8C22×D311yescharacteristic
336C22×C8C22×D311yescharacteristic
337C22×C8C22×D311yescharacteristic
338C22×C8C22×D311yescharacteristic
339#124—62no—
340#124—62no—
341C22⋊Q8—62no—
342C22⋊Q8—62no—
343C22⋊Q8—62no—
344C22⋊Q8—62no—
345C22⋊Q8—121no—
346C22⋊Q8—121no—
347C22⋊Q8—121no—
348C22⋊Q8—121no—
349#121—62no—
350#121—62no—
351#121—121no—
352#121—121no—
353C4×Q8—62no—
354C4×Q8—62no—
355C4×D4—22no—
356C4×D4—22no—
357C2×C4⋊C4—31no—
358C2×C4⋊C4—31no—
359C2×C4⋊C4—31no—
360C2×C4⋊C4—31no—
361C2×C4⋊C4—31no—
362C2×C4⋊C4—61no—
363C2×C4⋊C4—61no—
364C2×C4⋊C4—61no—
365C2×C4⋊C4—61no—
366C2×C4⋊C4—61no—
367C2×C4⋊C4D1211yescharacteristic
368C2×C22⋊C4—61no—
369C2×C22⋊C4—61no—
370C2×C22⋊C4—61no—
371C2×C22⋊C4—61no—
372C2×C22⋊C4—61no—
373C2×C22⋊C4—61no—
374C2×C22⋊C4—61no—
375C2×C22⋊C4—61no—
376C2×C22⋊C4—61no—
377C2×C22⋊C4—61no—
378C2×C22⋊C4D1211yescharacteristic
379C2×C22⋊C4D1211yescharacteristic
380C2×C42—61no—
381C2×C42—61no—
382C2×C42C22×D311yescharacteristic
383#107—62no—
384#106—62no—
385C4⋊C8#6714yescomplemented
386#103—34no—
387#103—62no—
388#103—62no—
389#103—62no—
390#103—121no—
391#102—62no—
392#102—62no—
393#102—121no—
394C22⋊C8—22no—
395C22⋊C8—22no—
396C4×C8—22no—
397#95—61no—
398#95—61no—
399#95—61no—
400#95—61no—
401#95—61no—
402C23×C3—21no—
403C23×C3—21no—
404C23×C3—21no—
405C23×C3—21no—
406C23×C3—21no—
407C23×C3—21no—
408C23×C3—21no—
409C23×C3—21no—
410C23×C3—21no—
411C23×C3—21no—
412C23×C3—21no—
413C23×C3—21no—
414C23×C3#13512yes—
415C23×C3#13512yes—
416C23×C3C22×D411yescharacteristic
417C22×D3—41no—
418C22×D3—41no—
419C22×D3—41no—
420C22×D3—41no—
421C22×D3—41no—
422C22×D3—41no—
423C22×D3—41no—
424C3×D4—28no—
425C2×C3×C4—21no—
426C2×C3×C4—21no—
427C2×C3×C4—21no—
428C2×C3×C4—21no—
429C2×C3×C4—21no—
430C2×C3×C4—21no—
431C2×C3×C4—21no—
432C2×C3×C4—21no—
433C2×C3×C4—21no—
434C2×C3×C4—21no—
435C2×C3×C4—41no—
436C2×C3×C4—41no—
437C2×C3×C4—41no—
438C2×C3×C4—41no—
439C2×C3×C4—41no—
440C2×C3×C4—41no—
441C2×C3×C4—41no—
442C2×C3×C4—41no—
443C2×C3×C4#12112yes—
444C2×C3×C4#12112yes—
445C2×C3×C4C22×D411yescharacteristic
446C2×C3×C4C22×D411yescharacteristic
447C2×C3×C4C2×#4111yescharacteristic
448C2×C3×C4C2×#4111yescharacteristic
449C2×C3×C4H(5,𝔽2)11yescharacteristic
450C2×C3×C4H(5,𝔽2)11yescharacteristic
451#67—84no—
452#67—84no—
453C2×Dic3—22no—
454C2×Dic3—22no—
455C2×Dic3—22no—
456C2×Dic3—41no—
457C2×Dic3—41no—
458C2×Dic3—41no—
459C2×Dic3—41no—
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—
474D12—41no—
475D12—41no—
476D12—41no—
477D12—41no—
478Dic6—22no—
479Dic6—22no—
480Dic6—41no—
481Dic6—41no—
482Dic6—41no—
483Dic6—41no—
484Dic6—41no—
485Dic6—41no—
486C3×C8—22no—
487C3×C8—22no—
488C3×C8—22no—
489C3×C8—41no—
490C24—61no—
491C24C2×D1211yescharacteristic
492C24C2×D1211yescharacteristic
493C2×Q8—32no—
494C2×Q8—61no—
495C2×Q8—61no—
496C2×Q8—61no—
497C2×Q8—61no—
498C2×Q8—61no—
499C2×Q8—61no—
500C2×Q8—61no—
501C2×Q8—61no—
502C2×Q8—61no—
503C2×Q8—61no—
504C2×Q8—61no—
505C2×D4—22no—
506C2×D4—22no—
507C2×D4—22no—
508C2×D4—61no—
509C2×D4—61no—
510C2×D4—61no—
511C2×D4—61no—
512C2×D4—61no—
513C2×D4—61no—
514C2×D4—122no—
515C2×D4—122no—
516C2×D4—122no—
517C2×D4—122no—
518C2×D4—241no—
519C2×D4—241no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—61no—
533C22×C4—61no—
534C22×C4—61no—
535C22×C4—61no—
536C22×C4—61no—
537C22×C4—61no—
538C22×C4—61no—
539C22×C4C2×D1211yescharacteristic
540C22×C4C2×D1211yescharacteristic
541C22×C4C2×D1211yescharacteristic
542C22×C4C2×D1211yescharacteristic
543C22×C4C23×D311yescharacteristic
544Q16—124no—
545SD16—124no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—44no—
556C2×C8—44no—
557C2×C8D3×D412yes—
558C2×C8C2×#6712yes—
559C2×C8C2×#6712yes—
560C4⋊C4—22no—
561C4⋊C4—32no—
562C4⋊C4—32no—
563C4⋊C4—61no—
564C4⋊C4—61no—
565C4⋊C4—61no—
566C4⋊C4—61no—
567C4⋊C4—61no—
568C4⋊C4—61no—
569C4⋊C4—61no—
570C4⋊C4—61no—
571C4⋊C4—122no—
572C4⋊C4—122no—
573C4⋊C4—122no—
574C4⋊C4—122no—
575C4⋊C4—122no—
576C22⋊C4—22no—
577C22⋊C4—22no—
578C22⋊C4—122no—
579C22⋊C4—122no—
580C22⋊C4—122no—
581C22⋊C4—122no—
582C22⋊C4—122no—
583C22⋊C4—122no—
584C22⋊C4—122no—
585C22⋊C4—122no—
586C22⋊C4—122no—
587C22⋊C4—122no—
588C42—122no—
589C42—241no—
590C42#23512yes—
591C42C2×#6712yes—
592C22×C3—22no—
593C22×C3—22no—
594C22×C3—22no—
595C22×C3—22no—
596C22×C3—22no—
597C22×C3—22no—
598C22×C3—41no—
599C22×C3—41no—
600C22×C3—41no—
601C22×C3—41no—
602C22×C3—41no—
603C22×C3—41no—
604C22×C3—41no—
605C22×C3—41no—
606C22×C3C2×#12111yescharacteristic
607C22×C3D4211yescharacteristic
608C22×C3#54611yescharacteristic
609C22×C3C2×#13511yescharacteristic
610C22×C3C2×#13511yescharacteristic
611C22×C3#57711yescharacteristic
612C22×C3#57811yescharacteristic
613C2×D3—81no—
614C2×D3—81no—
615C2×D3—81no—
616C2×D3—81no—
617C2×D3—81no—
618C2×D3—81no—
619C2×D3—81no—
620C3×C4—22no—
621C3×C4—22no—
622C3×C4—41no—
623C3×C4—41no—
624C3×C4#53211yescharacteristic
625C3×C4#54011yescharacteristic
626C3×C4D4211yescharacteristic
627C3×C4#55011yescharacteristic
628Dic3—42no—
629Dic3—42no—
630Dic3—42no—
631Dic3—81no—
632Dic3—81no—
633Dic3—81no—
634Dic3—81no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—121no—
648C23—121no—
649C23—121no—
650C23—121no—
651C23—121no—
652C23—121no—
653C23—121no—
654C23#90412yes—
655C23#90412yes—
656C23C22×D1211yescharacteristic
657Q8—62no—
658Q8—62no—
659Q8—121no—
660Q8—121no—
661Q8—121no—
662Q8—121no—
663Q8—121no—
664Q8—121no—
665D4—28no—
666D4—121no—
667D4—121no—
668D4—121no—
669D4—121no—
670D4—244no—
671D4—244no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—62no—
691C2×C4—62no—
692C2×C4—62no—
693C2×C4—121no—
694C2×C4—121no—
695C2×C4—121no—
696C2×C4—121no—
697C2×C4—121no—
698C2×C4—121no—
699C2×C4—121no—
700C2×C4—121no—
701C2×C4—121no—
702C2×C4—121no—
703C2×C4—121no—
704C2×C4—121no—
705C2×C4—121no—
706C2×C4—121no—
707C2×C4—121no—
708C2×C4—121no—
709C2×C4—121no—
710C2×C4—121no—
711C2×C4#93012yes—
712C2×C4#93012yes—
713C2×C4C2×#23511yescharacteristic
714C2×C4C2×D3×D411yescharacteristic
715C2×C4#100411yescharacteristic
716C2×C4D3×#4111yescharacteristic
717C2×C4#100911yescharacteristic
718C2×C4C22×#6711yescharacteristic
719C8—22no—
720C8—22no—
721C8—22no—
722C8—41no—
723C2×C3—42no—
724C2×C3—42no—
725C2×C3#242811yescharacteristic
726C2×C3#305011yescharacteristic
727C2×C3#306311yescharacteristic
728C2×C3#328211yescharacteristic
729C2×C3#328511yescharacteristic
730C2×C3#329611yescharacteristic
731C2×C3#330011yescharacteristic
732D3—161no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—22no—
737C22—22no—
738C22—22no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—241no—
748C22—241no—
749C22—241no—
750C22—241no—
751C22—241no—
752C22—241no—
753C22—241no—
754C22D4×D1211yescharacteristic
755C22#555411yescharacteristic
756C22C2×#90411yescharacteristic
757C22C2×#90411yescharacteristic
758C22#575111yescharacteristic
759C22#575311yescharacteristic
760C22C2×#93011yescharacteristic
761C4—22no—
762C4—22no—
763C4—41no—
764C4—41no—
765C4—122no—
766C4—122no—
767C4—122no—
768C4—241no—
769C4—241no—
770C4—241no—
771C4—241no—
772C4#554811yescharacteristic
773C4#556211yescharacteristic
774C4D4×#6711yescharacteristic
775C4#583411yescharacteristic
776C3#2538911yescharacteristic, complemented, Sylow
777C2—42no—
778C2—42no—
779C2—481no—
780C2#7943511yescharacteristic
781C2#7944011yescharacteristic
782C2#7944411yescharacteristic
783C2#7944911yescharacteristic
784C2#8240911yescharacteristic
785C2#8374211yescharacteristic
786C2#8380811yescharacteristic
subgroupG/H
centerC23C22×D12
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×C8×D4C2
socleC23×C3C22×D4
prime radical#82377C2
hypercenterC2×C8×D4D3
hypocenterC3#25389
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×#5116C2semidirect
3. C2×#5114C2semidirect
5. #82375C2semidirect
6. C2×#4845C2semidirect
7. #71973C2semidirect
8. #71972C2semidirect
9. #70455C2semidirect
10. #69964C2semidirect
11. #69962C2semidirect
12. #69936C2semidirect
13. #69934C2semidirect
14. #69773C2semidirect
15. C4×#816C2semidirect
67. C2×C8×D4D3semidirect
147. C3×C4⋊C8D4semidirect
165. #816D4semidirect
385. C4⋊C8#67semidirect
776. C3#25389semidirect

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×#51162
C2×#51142
#823772
#823752
C2×#48452
#719732
#719722
#704552
#699642
#699622
#699362
#699342
#697732
C4×#8162
#253893