Finite Group Databasebeta

← #10845973

Subgroups — #10845973

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
1C3×#2540C211yesmaximal, characteristic
2C2×#5054C211yesmaximal, characteristic, complemented
3C2×#5051C211yesmaximal, characteristic, complemented
4C2×#5041C211yesmaximal, characteristic, complemented
5#82375C211yesmaximal, characteristic, complemented
6C2×D4×C3⋊C8C211yesmaximal, characteristic, complemented
7#71725C211yesmaximal, characteristic, complemented
8#71700C211yesmaximal, characteristic, complemented
9#71696C211yesmaximal, characteristic, complemented
10#71694C211yesmaximal, characteristic, complemented
11#71685C211yesmaximal, characteristic, complemented
12#71681C211yesmaximal, characteristic, complemented
13#71679C211yesmaximal, characteristic, complemented
14C4×#810C211yesmaximal, characteristic, complemented
15#69468C211yesmaximal, characteristic, complemented
16#25389—31nomaximal, Sylow
17C2×C3×#124C2211yescharacteristic
18C2×C3×C22⋊Q8C2211yescharacteristic
19C2×C3×C22⋊Q8C2211yescharacteristic
20C2×C3×#121C2211yescharacteristic
21C2×C3×#121C2211yescharacteristic
22C2×C3×C4×D4C2211yescharacteristic
23C22×#216C2211yescharacteristic
24C22×#214C2211yescharacteristic
25C2×#924C2211yescharacteristic
26C2×#924C2211yescharacteristic
27C23×C3⋊C8C2211yescharacteristic
28C23×C3⋊C8C2211yescharacteristic
29C2×C4×Dic6C2211yescharacteristic
30C3×#399—21no—
31C3×#392—21no—
32C3×#390—21no—
33C3×#390—21no—
34C3×C4×C4⋊C4C2211yescharacteristic
35C2×#835C2211yescharacteristic
36C2×#835C2211yescharacteristic
37C2×#835C2211yescharacteristic
38#5222—21no—
39C2×#832C2211yescharacteristic
40C2×#832C2211yescharacteristic
41C2×#832C2211yescharacteristic
42#5212C2211yescharacteristic
43#5212C2211yescharacteristic
44C2×#830C2211yescharacteristic
45C2×#830C2211yescharacteristic
46#5054—24no—
47#5051—24no—
48#5041—24no—
49D4×C3⋊C8—24no—
50#4983—21no—
51C2×#810C2211yescharacteristic
52C2×#810C2211yescharacteristic
53C2×#808C2211yescharacteristic
54C2×#807C2211yescharacteristic
55#4944—21no—
56#4944—21no—
57#4936C2211yescharacteristic
58C2×C4⋊(C3⋊C8)C2211yescharacteristic
59C2×C4×C3⋊C8C2211yescharacteristic
60#4529C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#467—31no—
65C2×#465—31no—
66C2×#464—31no—
67C2×C8×D4—31no—
68#2540D311yescharacteristic
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×Q8C2311yescharacteristic
80C22×C3×D4—21no—
81C22×C3×D4—21no—
82C22×C3×D4D411yescharacteristic
83C22×C3×D4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C22×Dic6C2311yescharacteristic
87C3×#124—22no—
88C3×#124—22no—
89C3×C22⋊Q8—22no—
90C3×C22⋊Q8—22no—
91C3×C22⋊Q8—41no—
92C3×C22⋊Q8—41no—
93C3×#121—22no—
94C3×#121—22no—
95C3×#121—41no—
96C3×#121—41no—
97C3×C4×D4—22no—
98C3×C4×D4—22no—
99C2×C3×C4⋊C4—21no—
100C2×C3×C4⋊C4—21no—
101C2×C3×C4⋊C4D411yescharacteristic
102C2×C3×C4⋊C4C2311yescharacteristic
103C2×C3×C4⋊C4C2311yescharacteristic
104C2×C3×C22⋊C4—21no—
105C2×C3×C22⋊C4—21no—
106C2×C3×C22⋊C4—21no—
107C2×C3×C22⋊C4—21no—
108C2×C3×C22⋊C4—21no—
109C2×C3×C22⋊C4—21no—
110C2×C3×C22⋊C4D411yescharacteristic
111C2×C3×C22⋊C4D411yescharacteristic
112C2×C3×C42—21no—
113C2×C3×C42C2311yescharacteristic
114C2×#217—21no—
115C2×#217—21no—
116C2×#217—21no—
117C2×#217—21no—
118C2×#216—22no—
119C2×#216—22no—
120C2×#216—41no—
121C2×#214—22no—
122C2×#214—22no—
123C2×#214—41no—
124C2×C4⋊Dic3C2311yescharacteristic
125C2×C4⋊Dic3C2311yescharacteristic
126C2×C4⋊Dic3C2311yescharacteristic
127#924—22no—
128#924—22no—
129#924—41no—
130#924—41no—
131C2×Dic3⋊C4—21no—
132C2×Dic3⋊C4—21no—
133C2×Dic3⋊C4—21no—
134C2×C4×Dic3—21no—
135C22×C3⋊C8—22no—
136C22×C3⋊C8—22no—
137C22×C3⋊C8—22no—
138C22×C3⋊C8—22no—
139C22×C3⋊C8—41no—
140C22×C3⋊C8—41no—
141C22×C3⋊C8C2311yescharacteristic
142C22×C3⋊C8C2311yescharacteristic
143C22×C3⋊C8C2311yescharacteristic
144C22×C3⋊C8C2311yescharacteristic
145C4×Dic6—22no—
146C4×Dic6—22no—
147C3×#95—21no—
148#835—22no—
149#835—22no—
150#835—41no—
151#832—22no—
152#832—22no—
153#832—41no—
154C3⋊#95—21no—
155C3⋊#95—21no—
156C3⋊#95—21no—
157C3⋊#95—21no—
158#830—22no—
159#830—22no—
160#810—22no—
161#810D414yescomplemented
162#808—22no—
163#807—22no—
164C4⋊(C3⋊C8)D414yescomplemented
165C4×C3⋊C8—22no—
166C22×Q16—31no—
167C22×SD16—31no—
168C23×C8—31no—
169C23×C8—31no—
170C2×#124C2×D311yescharacteristic
171C2×C22⋊Q8—31no—
172C2×C22⋊Q8—31no—
173C2×C22⋊Q8C2×D311yescharacteristic
174C2×C22⋊Q8C2×D311yescharacteristic
175C2×#121C2×D311yescharacteristic
176C2×#121C2×D311yescharacteristic
177C2×C4×Q8—31no—
178C2×C4×D4C2×D311yescharacteristic
179#467—64no—
180#465—64no—
181#464—64no—
182C8×D4—64no—
183C2×#107—31no—
184C2×#106—31no—
185C2×C4⋊C8—31no—
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⋊C8—31no—
195C2×C22⋊C8—31no—
196C2×C4×C8—31no—
197#399—21no—
198#398—61no—
199#394—61no—
200#392—21no—
201#390—21no—
202#390—21no—
203#388—61no—
204#388—61no—
205#382—31no—
206#380—31no—
207#380—31no—
208C4×C4⋊C4C2×D311yescharacteristic
209#340—31no—
210#340—31no—
211#340—31no—
212#340—31no—
213C24×C3—21no—
214C24×C3C2×D411yescharacteristic
215C24×C3C2×D411yescharacteristic
216C2×C3×Q8—21no—
217C2×C3×Q8—21no—
218C2×C3×Q8—21no—
219C2×C3×Q8—21no—
220C2×C3×Q8—21no—
221C2×C3×Q8—21no—
222C2×C3×D4—22no—
223C2×C3×D4—22no—
224C2×C3×D4—22no—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4—21no—
231C2×C3×D4—42no—
232C2×C3×D4—42no—
233C2×C3×D4—42no—
234C2×C3×D4—42no—
235C2×C3×D4—81no—
236C2×C3×D4—81no—
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×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4C2×D411yescharacteristic
253C22×C3×C4C2×D411yescharacteristic
254C22×C3×C4C2×D411yescharacteristic
255C22×C3×C4C2×D411yescharacteristic
256C22×C3×C4C2411yescharacteristic
257C22×Dic3—21no—
258C22×Dic3—21no—
259C22×Dic3—21no—
260C22×Dic3—21no—
261C2×Dic6—21no—
262C2×Dic6—21no—
263C2×Dic6—21no—
264C2×Dic6—21no—
265C2×Dic6—21no—
266C2×Dic6C2×D412yes—
267C3×C4⋊C4—22no—
268C3×C4⋊C4—21no—
269C3×C4⋊C4—21no—
270C3×C4⋊C4—42no—
271C3×C4⋊C4—42no—
272C3×C4⋊C4C2×D412yes—
273C3×C4⋊C4#4112yes—
274C3×C22⋊C4—22no—
275C3×C22⋊C4—22no—
276C3×C22⋊C4—42no—
277C3×C22⋊C4—42no—
278C3×C22⋊C4—42no—
279C3×C22⋊C4—42no—
280C3×C22⋊C4—42no—
281C3×C22⋊C4—42no—
282C3×C42—81no—
283C3×C42C2×D412yes—
284C3×C42#4112yes—
285#217—42no—
286#217—42no—
287#217—42no—
288#217—42no—
289#216—44no—
290#214—44no—
291C4⋊Dic3—21no—
292C4⋊Dic3—21no—
293C4⋊Dic3—21no—
294C4⋊Dic3—21no—
295C4⋊Dic3—21no—
296C4⋊Dic3—21no—
297Dic3⋊C4—42no—
298Dic3⋊C4—42no—
299Dic3⋊C4—42no—
300C4×Dic3—42no—
301C2×C3⋊C8—21no—
302C2×C3⋊C8—21no—
303C2×C3⋊C8—21no—
304C2×C3⋊C8—21no—
305C2×C3⋊C8—21no—
306C2×C3⋊C8—21no—
307C2×C3⋊C8—21no—
308C2×C3⋊C8—21no—
309C2×C3⋊C8—21no—
310C2×C3⋊C8—44no—
311C2×C3⋊C8—44no—
312C2×C3⋊C8C2×D412yes—
313C2×C3⋊C8C2×D412yes—
314C2×C3⋊C8C2×D412yes—
315C22×Q8—31no—
316C22×Q8C22×D311yescharacteristic
317C22×D4—21no—
318C22×D4—21no—
319C22×D4#6711yescharacteristic
320C22×D4C22×D311yescharacteristic
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—31no—
330C22×C8—31no—
331C22×C8—31no—
332C22×C8—31no—
333C22×C8—62no—
334C22×C8—62no—
335C22×C8—62no—
336C22×C8—62no—
337C22×C8—121no—
338C22×C8—121no—
339#124—22no—
340#124—22no—
341C22⋊Q8—22no—
342C22⋊Q8—22no—
343C22⋊Q8—41no—
344C22⋊Q8—41no—
345C22⋊Q8—62no—
346C22⋊Q8—62no—
347C22⋊Q8—121no—
348C22⋊Q8—121no—
349#121—22no—
350#121—22no—
351#121—41no—
352#121—41no—
353C4×Q8—62no—
354C4×Q8—62no—
355C4×D4—22no—
356C4×D4—22no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
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#6711yescharacteristic
366C2×C4⋊C4C22×D311yescharacteristic
367C2×C4⋊C4C22×D311yescharacteristic
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—61no—
375C2×C22⋊C4—61no—
376C2×C22⋊C4—61no—
377C2×C22⋊C4—61no—
378C2×C22⋊C4#6711yescharacteristic
379C2×C22⋊C4#6711yescharacteristic
380C2×C42—21no—
381C2×C42—61no—
382C2×C42C22×D311yescharacteristic
383#107—62no—
384#106—62no—
385C4⋊C8—34no—
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—62no—
395C22⋊C8—62no—
396C4×C8—62no—
397#95—21no—
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—41no—
415C23×C3—41no—
416C23×C3—41no—
417C23×C3—41no—
418C23×C3—41no—
419C23×C3—41no—
420C23×C3—41no—
421C23×C3#13512yes—
422C23×C3#13512yes—
423C23×C3C22×D411yescharacteristic
424C3×Q8—41no—
425C3×Q8—41no—
426C3×Q8—41no—
427C3×Q8—41no—
428C3×D4—28no—
429C3×D4—41no—
430C3×D4—41no—
431C3×D4—41no—
432C3×D4—41no—
433C3×D4—84no—
434C3×D4—84no—
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—21no—
443C2×C3×C4—22no—
444C2×C3×C4—22no—
445C2×C3×C4—21no—
446C2×C3×C4—21no—
447C2×C3×C4—41no—
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—41no—
457C2×C3×C4—41no—
458C2×C3×C4—41no—
459C2×C3×C4—41no—
460C2×C3×C4—41no—
461C2×C3×C4—41no—
462C2×C3×C4#12112yes—
463C2×C3×C4#12112yes—
464C2×C3×C4C22×D411yescharacteristic
465C2×C3×C4C22×D411yescharacteristic
466C2×C3×C4C2×#4111yescharacteristic
467C2×C3×C4C2×#4111yescharacteristic
468C2×C3×C4H(5,𝔽2)11yescharacteristic
469C2×C3×C4H(5,𝔽2)11yescharacteristic
470C2×Dic3—22no—
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—
482Dic6—22no—
483Dic6—22no—
484Dic6—41no—
485Dic6—41no—
486C3⋊C8—22no—
487C3⋊C8—22no—
488C3⋊C8—22no—
489C3⋊C8—41no—
490C24—21no—
491C24C2×#6711yescharacteristic
492C24C2×#6711yescharacteristic
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—32no—
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—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—42no—
515C2×D4—42no—
516C2×D4—42no—
517C2×D4—42no—
518C2×D4—81no—
519C2×D4—81no—
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—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—61no—
536C22×C4—61no—
537C22×C4—61no—
538C22×C4—61no—
539C22×C4C2×#6711yescharacteristic
540C22×C4C2×#6711yescharacteristic
541C22×C4C2×#6711yescharacteristic
542C22×C4C2×#6711yescharacteristic
543C22×C4C23×D311yescharacteristic
544Q16—124no—
545SD16—124no—
546C2×C8—32no—
547C2×C8—32no—
548C2×C8—32no—
549C2×C8—61no—
550C2×C8—61no—
551C2×C8—61no—
552C2×C8—61no—
553C2×C8—61no—
554C2×C8—61no—
555C2×C8—61no—
556C2×C8—61no—
557C2×C8—61no—
558C2×C8—124no—
559C2×C8—124no—
560C4⋊C4—22no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—42no—
564C4⋊C4—42no—
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⋊C4D3×D412yes—
575C4⋊C4#23712yes—
576C22⋊C4—22no—
577C22⋊C4—22no—
578C22⋊C4—42no—
579C22⋊C4—42no—
580C22⋊C4—42no—
581C22⋊C4—42no—
582C22⋊C4—42no—
583C22⋊C4—42no—
584C22⋊C4—122no—
585C22⋊C4—122no—
586C22⋊C4—122no—
587C22⋊C4—122no—
588C42—81no—
589C42—122no—
590C42D3×D412yes—
591C42#23712yes—
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×C3—81no—
607C22×C3—81no—
608C22×C3—81no—
609C22×C3—81no—
610C22×C3—81no—
611C22×C3—81no—
612C22×C3—81no—
613C22×C3C2×#12111yescharacteristic
614C22×C3D4211yescharacteristic
615C22×C3#54611yescharacteristic
616C22×C3C2×#13511yescharacteristic
617C22×C3C2×#13511yescharacteristic
618C22×C3#57711yescharacteristic
619C22×C3#57811yescharacteristic
620C3×C4—22no—
621C3×C4—22no—
622C3×C4—41no—
623C3×C4—41no—
624C3×C4—42no—
625C3×C4—42no—
626C3×C4—81no—
627C3×C4#53211yescharacteristic
628C3×C4#54011yescharacteristic
629C3×C4D4211yescharacteristic
630C3×C4#55011yescharacteristic
631Dic3—42no—
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—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23#95012yes—
655C23#95012yes—
656C23C22×#6711yescharacteristic
657Q8—41no—
658Q8—41no—
659Q8—41no—
660Q8—41no—
661Q8—62no—
662Q8—62no—
663Q8—121no—
664Q8—121no—
665D4—28no—
666D4—41no—
667D4—41no—
668D4—41no—
669D4—41no—
670D4—84no—
671D4—84no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—22no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—22no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—62no—
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#93912yes—
712C2×C4#93912yes—
713C2×C4C2×D3×D411yescharacteristic
714C2×C4C2×D3×D411yescharacteristic
715C2×C4C2×#23711yescharacteristic
716C2×C4C2×#23711yescharacteristic
717C2×C4#100411yescharacteristic
718C2×C4#100411yescharacteristic
719C8—62no—
720C8—62no—
721C8—62no—
722C8—121no—
723C2×C3—42no—
724C2×C3—42no—
725C2×C3—161no—
726C2×C3#242811yescharacteristic
727C2×C3#305011yescharacteristic
728C2×C3#306311yescharacteristic
729C2×C3#328211yescharacteristic
730C2×C3#328511yescharacteristic
731C2×C3#329611yescharacteristic
732C2×C3#330011yescharacteristic
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—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22D4×#6711yescharacteristic
755C22C2×#93911yescharacteristic
756C22#580611yescharacteristic
757C22C2×#95011yescharacteristic
758C22C2×#95011yescharacteristic
759C22#583611yescharacteristic
760C22#583811yescharacteristic
761C4—22no—
762C4—22no—
763C4—42no—
764C4—42no—
765C4—41no—
766C4—41no—
767C4—81no—
768C4—122no—
769C4—241no—
770C4—241no—
771C4—241no—
772C4#571611yescharacteristic
773C4#571711yescharacteristic
774C4#571811yescharacteristic
775C4#571911yescharacteristic
776C3#2538911yescharacteristic, complemented, Sylow
777C2—42no—
778C2—42no—
779C2—161no—
780C2#8292211yescharacteristic
781C2#8318611yescharacteristic
782C2#8342311yescharacteristic
783C2#8349411yescharacteristic
784C2#8350911yescharacteristic
785C2#8353411yescharacteristic
786C2#8354911yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
Fitting, prime radicalC3×#2540C2
socleC23×C3C22×D4
hypercenter#2540D3
hypocenterC3#25389
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2540

Complements

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

NH ≅ G/Ntype
2. C2×#5054C2semidirect
3. C2×#5051C2semidirect
4. C2×#5041C2semidirect
5. #82375C2semidirect
6. C2×D4×C3⋊C8C2semidirect
7. #71725C2semidirect
8. #71700C2semidirect
9. #71696C2semidirect
10. #71694C2semidirect
11. #71685C2semidirect
12. #71681C2semidirect
13. #71679C2semidirect
14. C4×#810C2semidirect
15. #69468C2semidirect
161. #810D4semidirect
164. C4⋊(C3⋊C8)D4semidirect
776. C3#25389semidirect

Maximal subgroups

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

subgroupindex
C3×#25402
C2×#50542
C2×#50512
C2×#50412
#823752
C2×D4×C3⋊C82
#717252
#717002
#716962
#716942
#716852
#716812
#716792
C4×#8102
#694682
#253893