Finite Group Databasebeta

← #10846120

Subgroups — #10846120

Order 768.

1048 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#2535C211yesmaximal, characteristic
2C2×#5042C211yesmaximal, characteristic, complemented
3C2×#5041C211yesmaximal, characteristic, complemented
4#82379C211yesmaximal, characteristic, complemented
5C2×#5019C211yesmaximal, characteristic, complemented
6C2×#5011C211yesmaximal, characteristic, complemented
7#71685C211yesmaximal, characteristic, complemented
8#71685C211yesmaximal, characteristic, complemented
9#71609C211yesmaximal, characteristic, complemented
10#69552C211yesmaximal, characteristic, complemented
11#69540C211yesmaximal, characteristic, complemented
12#69527C211yesmaximal, characteristic, complemented
13#69526C211yesmaximal, characteristic, complemented
14#69516C211yesmaximal, characteristic, complemented
15#69514C211yesmaximal, characteristic, complemented
16#25400—31nomaximal, Sylow
17C2×C3×#121C2211yescharacteristic
18C2×C3×#121C2211yescharacteristic
19C2×C3×C4×D4C2211yescharacteristic
20C2×C3×C4×D4C2211yescharacteristic
21C22×#214C2211yescharacteristic
22C22×#214C2211yescharacteristic
23C2×#924C2211yescharacteristic
24C2×#924C2211yescharacteristic
25C2×#924C2211yescharacteristic
26C2×#924C2211yescharacteristic
27C22×#208C2211yescharacteristic
28C23×C3⋊C8C2211yescharacteristic
29C2×#869C2211yescharacteristic
30C3×#397—21no—
31C3×#392—21no—
32C3×#386—21no—
33C3×#386—21no—
34C3×#382C2211yescharacteristic
35C3×#380C2211yescharacteristic
36C3×#380C2211yescharacteristic
37#5221—21no—
38C2×#832C2211yescharacteristic
39C2×#832C2211yescharacteristic
40C2×#830C2211yescharacteristic
41C2×#830C2211yescharacteristic
42#5042—24no—
43#5041—24no—
44#5019—24no—
45#5011—24no—
46#4975—21no—
47C2×#810C2211yescharacteristic
48C2×#810C2211yescharacteristic
49C2×#810C2211yescharacteristic
50C2×#810C2211yescharacteristic
51C2×#810C2211yescharacteristic
52C2×#810C2211yescharacteristic
53C2×#808C2211yescharacteristic
54C2×#807C2211yescharacteristic
55#4949—21no—
56#4949—21no—
57C4×C4⋊Dic3C2211yescharacteristic
58C2×C4⋊(C3⋊C8)C2211yescharacteristic
59C2×#803C2211yescharacteristic
60#4529C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#468—31no—
65C2×#465—31no—
66C2×#461—31no—
67C2×#435—31no—
68#2542—31no—
69#2535D311yescharacteristic
70#2036—31no—
71#2035—31no—
72#2000—31no—
73#2000—31no—
74#1960—31no—
75#1949—31no—
76#1894—31no—
77#1892—31no—
78#1762—31no—
79C22×C3×D4—21no—
80C22×C3×D4—21no—
81C22×C3×D4D411yescharacteristic
82C22×C3×D4C2311yescharacteristic
83C23×C3×C4—21no—
84C23×C3×C4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C22×Dic6C2311yescharacteristic
87C22×Dic6C2311yescharacteristic
88C3×#121—22no—
89C3×#121—22no—
90C3×#121—41no—
91C3×#121—41no—
92C3×C4×D4—22no—
93C3×C4×D4—22no—
94C3×C4×D4—22no—
95C3×C4×D4—22no—
96C2×C3×C4⋊C4D411yescharacteristic
97C2×C3×C4⋊C4C2311yescharacteristic
98C2×C3×C4⋊C4C2311yescharacteristic
99C2×C3×C4⋊C4C2311yescharacteristic
100C2×C3×C22⋊C4—21no—
101C2×C3×C22⋊C4—21no—
102C2×C3×C22⋊C4—21no—
103C2×C3×C22⋊C4—21no—
104C2×C3×C22⋊C4—21no—
105C2×C3×C22⋊C4D411yescharacteristic
106C2×C3×C22⋊C4D411yescharacteristic
107C2×C3×C42C2311yescharacteristic
108C2×#217—21no—
109C2×#217—21no—
110C2×#217—21no—
111C2×#217—21no—
112C2×#214—22no—
113C2×#214—22no—
114C2×#214—22no—
115C2×#214—22no—
116C2×#214—41no—
117C2×#214—41no—
118C2×C4⋊Dic3—21no—
119C2×C4⋊Dic3—21no—
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×C4×Dic3—21no—
135C2×#208—22no—
136C2×#208—22no—
137C2×#208—41no—
138C22×C3⋊C8—22no—
139C22×C3⋊C8—22no—
140C22×C3⋊C8—41no—
141C22×C3⋊C8C2311yescharacteristic
142C22×C3⋊C8C2311yescharacteristic
143C22×C3⋊C8C2311yescharacteristic
144C22×C3⋊C8C2311yescharacteristic
145#869—22no—
146#869—22no—
147C3×#95—21no—
148C3×#95—21no—
149C3×#95—21no—
150C3×#95—21no—
151#832—22no—
152#832D414yescomplemented
153C3⋊#95—21no—
154#830—22no—
155#830—22no—
156#810—22no—
157#810—22no—
158#810—22no—
159#810—22no—
160#810—41no—
161#810—41no—
162#808—22no—
163#807—22no—
164C4⋊(C3⋊C8)D414yescomplemented
165#803—22no—
166C22×SD16—31no—
167C22×SD16—31no—
168C22×M16—31no—
169C23×C8—31no—
170C2×C4⋊Q8—31no—
171C2×C22⋊Q8—31no—
172C2×C22⋊Q8—31no—
173C2×C22⋊Q8—31no—
174C2×C22⋊Q8—31no—
175C2×#121C2×D311yescharacteristic
176C2×#121C2×D311yescharacteristic
177C2×C4×D4C2×D311yescharacteristic
178C2×C4×D4C2×D311yescharacteristic
179#468—64no—
180#465—64no—
181#461—64no—
182#435—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×#103—31no—
192C2×#102—31no—
193C2×#102—31no—
194C2×C22⋊C8—31no—
195C2×C22⋊C8—31no—
196C2×#97—31no—
197#399—61no—
198#399—61no—
199#397—21no—
200#392—21no—
201#390—61no—
202#386—21no—
203#386—21no—
204#384—61no—
205#382C2×D311yescharacteristic
206#380C2×D311yescharacteristic
207#380C2×D311yescharacteristic
208C4×C4⋊C4—31no—
209#340—31no—
210#340—31no—
211#340—31no—
212#340—31no—
213C24×C3—21no—
214C24×C3C2×D411yescharacteristic
215C24×C3C2×D411yescharacteristic
216C2×C3×D4—22no—
217C2×C3×D4—22no—
218C2×C3×D4—21no—
219C2×C3×D4—21no—
220C2×C3×D4—21no—
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4—41no—
224C2×C3×D4—42no—
225C2×C3×D4—42no—
226C2×C3×D4—42no—
227C2×C3×D4—42no—
228C2×C3×D4—81no—
229C2×C3×D4—81no—
230C2×C3×D4C2×D412yes—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
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—42no—
247C22×C3×C4—81no—
248C22×C3×C4—81no—
249C22×C3×C4C2×D411yescharacteristic
250C22×C3×C4C2×D411yescharacteristic
251C22×C3×C4C2×D411yescharacteristic
252C22×C3×C4C2×D411yescharacteristic
253C22×C3×C4C2411yescharacteristic
254C22×Dic3—21no—
255C22×Dic3—21no—
256C22×Dic3—21no—
257C22×Dic3—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×Dic6—21no—
267C2×Dic6—21no—
268C2×Dic6—21no—
269C2×Dic6—21no—
270C3×C4⋊C4—22no—
271C3×C4⋊C4—21no—
272C3×C4⋊C4—21no—
273C3×C4⋊C4—21no—
274C3×C4⋊C4—21no—
275C3×C4⋊C4—21no—
276C3×C4⋊C4—21no—
277C3×C22⋊C4—22no—
278C3×C22⋊C4—22no—
279C3×C22⋊C4—42no—
280C3×C22⋊C4—42no—
281C3×C22⋊C4—42no—
282C3×C22⋊C4—81no—
283C3×C22⋊C4—81no—
284C3×C42C2×D412yes—
285C3×C42#4112yes—
286#217—42no—
287#217—42no—
288#217—42no—
289#217—42no—
290#214—44no—
291#214—44no—
292C4⋊Dic3—21no—
293C4⋊Dic3—21no—
294C4⋊Dic3—42no—
295C4⋊Dic3—42no—
296C4⋊Dic3C2×D412yes—
297C4⋊Dic3#4112yes—
298Dic3⋊C4—42no—
299Dic3⋊C4—42no—
300Dic3⋊C4—42no—
301Dic3⋊C4—42no—
302C4×Dic3—42no—
303#208—44no—
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—21no—
311C2×C3⋊C8—21no—
312C2×C3⋊C8—21no—
313C2×C3⋊C8—44no—
314C2×C3⋊C8C2×D412yes—
315C2×C3⋊C8C2×D412yes—
316C2×C3⋊C8C2×D412yes—
317C22×Q8—31no—
318C22×Q8—31no—
319C22×D4—21no—
320C22×D4—21no—
321C22×D4#6711yescharacteristic
322C22×D4C22×D311yescharacteristic
323C23×C4—21no—
324C23×C4C22×D311yescharacteristic
325C23×C4C22×D311yescharacteristic
326C2×SD16—62no—
327C2×SD16—62no—
328C2×SD16—62no—
329C2×SD16—62no—
330C2×SD16—121no—
331C2×SD16—121no—
332C2×M16—62no—
333C2×M16—62no—
334C2×M16—121no—
335C22×C8—31no—
336C22×C8—31no—
337C22×C8—31no—
338C22×C8—31no—
339C22×C8—62no—
340C22×C8—62no—
341C22×C8—121no—
342C4⋊Q8—62no—
343C4⋊Q8—62no—
344C22⋊Q8—62no—
345C22⋊Q8—62no—
346C22⋊Q8—62no—
347C22⋊Q8—62no—
348C22⋊Q8—121no—
349C22⋊Q8—121no—
350C22⋊Q8—121no—
351C22⋊Q8—121no—
352#121—22no—
353#121—22no—
354#121—41no—
355#121—41no—
356C4×D4—22no—
357C4×D4—22no—
358C4×D4—22no—
359C4×D4—22no—
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⋊C4—61no—
368C2×C4⋊C4#6711yescharacteristic
369C2×C4⋊C4C22×D311yescharacteristic
370C2×C4⋊C4C22×D311yescharacteristic
371C2×C4⋊C4C22×D311yescharacteristic
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—61no—
378C2×C22⋊C4—61no—
379C2×C22⋊C4—61no—
380C2×C22⋊C4—61no—
381C2×C22⋊C4#6711yescharacteristic
382C2×C22⋊C4#6711yescharacteristic
383C2×C42—61no—
384C2×C42C22×D311yescharacteristic
385#107—62no—
386#106—62no—
387C4⋊C8—34no—
388#103—62no—
389#103—62no—
390#103—62no—
391#103—62no—
392#103—121no—
393#103—121no—
394#102—34no—
395#102—62no—
396C22⋊C8—62no—
397C22⋊C8—62no—
398#97—62no—
399#95—21no—
400#95—21no—
401#95—21no—
402#95—21no—
403#95—61no—
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—22no—
413C23×C3—21no—
414C23×C3—21no—
415C23×C3—21no—
416C23×C3—21no—
417C23×C3—21no—
418C23×C3—41no—
419C23×C3—41no—
420C23×C3—41no—
421C23×C3—41no—
422C23×C3—41no—
423C23×C3—41no—
424C23×C3#13712yes—
425C23×C3C22×D411yescharacteristic
426C3×D4—22no—
427C3×D4—22no—
428C3×D4—44no—
429C3×D4—41no—
430C3×D4—41no—
431C3×D4—84no—
432C3×D4—84no—
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—21no—
443C2×C3×C4—41no—
444C2×C3×C4—41no—
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×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—84no—
461C2×C3×C4#12112yes—
462C2×C3×C4#12112yes—
463C2×C3×C4C22×D411yescharacteristic
464C2×C3×C4C22×D411yescharacteristic
465C2×C3×C4C2×#4111yescharacteristic
466C2×C3×C4C2×#4111yescharacteristic
467C2×C3×C4H(5,𝔽2)11yescharacteristic
468C2×C3×C4H(5,𝔽2)11yescharacteristic
469C2×Dic3—22no—
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—
481Dic6—41no—
482Dic6—41no—
483Dic6—41no—
484Dic6—41no—
485Dic6—41no—
486Dic6—41no—
487Dic6—41no—
488Dic6—41no—
489C3⋊C8—22no—
490C3⋊C8—22no—
491C3⋊C8—22no—
492C3⋊C8—41no—
493C24—21no—
494C24C2×#6711yescharacteristic
495C24C2×#6711yescharacteristic
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×Q8—61no—
506C2×Q8—61no—
507C2×Q8—61no—
508C2×D4—22no—
509C2×D4—22no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—41no—
516C2×D4—42no—
517C2×D4—42no—
518C2×D4—42no—
519C2×D4—42no—
520C2×D4—81no—
521C2×D4—81no—
522C2×D4D3×D412yes—
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—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—42no—
539C22×C4—61no—
540C22×C4—61no—
541C22×C4—61no—
542C22×C4—61no—
543C22×C4—81no—
544C22×C4—81no—
545C22×C4C2×#6711yescharacteristic
546C22×C4C2×#6711yescharacteristic
547C22×C4C2×#6711yescharacteristic
548C22×C4C2×#6711yescharacteristic
549C22×C4C23×D311yescharacteristic
550SD16—124no—
551SD16—124no—
552M16—124no—
553C2×C8—32no—
554C2×C8—32no—
555C2×C8—32no—
556C2×C8—61no—
557C2×C8—61no—
558C2×C8—61no—
559C2×C8—61no—
560C2×C8—61no—
561C2×C8—61no—
562C2×C8—61no—
563C2×C8—61no—
564C2×C8—61no—
565C2×C8—124no—
566C4⋊C4—22no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—32no—
574C4⋊C4—32no—
575C4⋊C4—61no—
576C4⋊C4—61no—
577C4⋊C4—122no—
578C4⋊C4—122no—
579C4⋊C4—122no—
580C4⋊C4—122no—
581C4⋊C4—122no—
582C4⋊C4—122no—
583C22⋊C4—22no—
584C22⋊C4—22no—
585C22⋊C4—42no—
586C22⋊C4—42no—
587C22⋊C4—42no—
588C22⋊C4—81no—
589C22⋊C4—81no—
590C22⋊C4—122no—
591C22⋊C4—122no—
592C22⋊C4—122no—
593C22⋊C4—122no—
594C42—122no—
595C42D3×D412yes—
596C42#23712yes—
597C22×C3—22no—
598C22×C3—22no—
599C22×C3—22no—
600C22×C3—41no—
601C22×C3—41no—
602C22×C3—41no—
603C22×C3—41no—
604C22×C3—41no—
605C22×C3—42no—
606C22×C3—42no—
607C22×C3—41no—
608C22×C3—41no—
609C22×C3—42no—
610C22×C3—41no—
611C22×C3—41no—
612C22×C3—41no—
613C22×C3—41no—
614C22×C3—81no—
615C22×C3—81no—
616C22×C3—81no—
617C22×C3—81no—
618C22×C3C2×#12111yescharacteristic
619C22×C3D4211yescharacteristic
620C22×C3#54611yescharacteristic
621C22×C3C2×#13711yescharacteristic
622C22×C3#57511yescharacteristic
623C22×C3#57711yescharacteristic
624C22×C3#57711yescharacteristic
625C3×C4—22no—
626C3×C4—22no—
627C3×C4—41no—
628C3×C4—41no—
629C3×C4—81no—
630C3×C4—81no—
631C3×C4—81no—
632C3×C4#53211yescharacteristic
633C3×C4#54011yescharacteristic
634C3×C4D4211yescharacteristic
635C3×C4#55011yescharacteristic
636Dic3—42no—
637Dic3—42no—
638Dic3—81no—
639Dic3—81no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—22no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23#95112yes—
661C23C22×#6711yescharacteristic
662Q8—121no—
663Q8—121no—
664Q8—121no—
665Q8—121no—
666Q8—121no—
667Q8—121no—
668Q8—121no—
669Q8—121no—
670D4—22no—
671D4—22no—
672D4—44no—
673D4—41no—
674D4—41no—
675D4—84no—
676D4—84no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
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—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—62no—
705C2×C4—62no—
706C2×C4—84no—
707C2×C4—121no—
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#93912yes—
718C2×C4#93912yes—
719C2×C4C2×D3×D411yescharacteristic
720C2×C4C2×D3×D411yescharacteristic
721C2×C4C2×#23711yescharacteristic
722C2×C4#100411yescharacteristic
723C2×C4D3×#4111yescharacteristic
724C2×C4#100911yescharacteristic
725C8—62no—
726C8—62no—
727C8—62no—
728C8—121no—
729C2×C3—42no—
730C2×C3—81no—
731C2×C3—82no—
732C2×C3#242811yescharacteristic
733C2×C3#305611yescharacteristic
734C2×C3#305711yescharacteristic
735C2×C3#326611yescharacteristic
736C2×C3#326711yescharacteristic
737C2×C3#330711yescharacteristic
738C2×C3#332011yescharacteristic
739C22—22no—
740C22—22no—
741C22—22no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—42no—
748C22—42no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—42no—
755C22—41no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22D4×#6711yescharacteristic
761C22C2×#93911yescharacteristic
762C22#582211yescharacteristic
763C22C2×#95111yescharacteristic
764C22#582911yescharacteristic
765C22#583611yescharacteristic
766C22#583611yescharacteristic
767C4—22no—
768C4—22no—
769C4—41no—
770C4—41no—
771C4—81no—
772C4—81no—
773C4—81no—
774C4—122no—
775C4—122no—
776C4—241no—
777C4—241no—
778C4#559611yescharacteristic
779C4#559911yescharacteristic
780C4#560911yescharacteristic
781C4#561911yescharacteristic
782C3#2540011yescharacteristic, complemented, Sylow
783C2—42no—
784C2—81no—
785C2—82no—
786C2#8264911yescharacteristic
787C2#8292511yescharacteristic
788C2#8337711yescharacteristic
789C2#8350311yescharacteristic
790C2#8350611yescharacteristic
791C2#8361511yescharacteristic
792C2#8362011yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
Fitting, prime radicalC3×#2535C2
socleC23×C3C22×D4
hypercenter#2535D3
hypocenterC3#25400
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2535

Complements

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

NH ≅ G/Ntype
2. C2×#5042C2semidirect
3. C2×#5041C2semidirect
4. #82379C2semidirect
5. C2×#5019C2semidirect
6. C2×#5011C2semidirect
7. #71685C2semidirect
8. #71685C2semidirect
9. #71609C2semidirect
10. #69552C2semidirect
11. #69540C2semidirect
12. #69527C2semidirect
13. #69526C2semidirect
14. #69516C2semidirect
15. #69514C2semidirect
152. #832D4semidirect
164. C4⋊(C3⋊C8)D4semidirect
782. C3#25400semidirect

Maximal subgroups

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

subgroupindex
C3×#25352
C2×#50422
C2×#50412
#823792
C2×#50192
C2×#50112
#716852
#716092
#695522
#695402
#695272
#695262
#695162
#695142
#254003