Finite Group Databasebeta

← #10800994

Subgroups — #10800994

Order 768.

1476 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5546C211yesmaximal, characteristic, complemented
2C2×C3×#442C211yesmaximal, characteristic, complemented
3C2×#5158C211yesmaximal, characteristic
4#82396C211yesmaximal, characteristic, complemented
5C2×C4×#214C211yesmaximal, characteristic, complemented
6#72037C211yesmaximal, characteristic, complemented
7C4×#832C211yesmaximal, characteristic, complemented
8#70588C211yesmaximal, characteristic, complemented
9#70579C211yesmaximal, characteristic, complemented
10#70213C211yesmaximal, characteristic, complemented
11#70200C211yesmaximal, characteristic, complemented
12#70199C211yesmaximal, characteristic, complemented
13#70169C211yesmaximal, characteristic, complemented
14#69830C211yesmaximal, characteristic, complemented
15#69813C211yesmaximal, characteristic, complemented
16#21464—31nomaximal, Sylow
17C22×#237C2211yescharacteristic
18C22×C3×D8C2211yescharacteristic
19C2×C3×C4×D4C2211yescharacteristic
20C2×C3×C4×D4C2211yescharacteristic
21C2×#938C2211yescharacteristic
22C2×D4×Dic3C2211yescharacteristic
23C22×#214C2211yescharacteristic
24C2×C4×#67—21no—
25C22×Dic3⋊C4—21no—
26#5546—24no—
27#5546—24no—
28C2×D3×C4⋊C4C2211yescharacteristic
29C2×#887C2211yescharacteristic
30C2×#67⋊C4—21no—
31C2×#877—21no—
32C2×#872C2211yescharacteristic
33C2×C4×Dic6C2211yescharacteristic
34C3×#442—24no—
35C2×C3×#106C2211yescharacteristic
36C2×C3×#102C2211yescharacteristic
37C2×C3×#102C2211yescharacteristic
38C2×C3×#97C2211yescharacteristic
39#5221C2211yescharacteristic
40C2×#832C2211yescharacteristic
41C2×#832C2211yescharacteristic
42C2×#832C2211yescharacteristic
43#5213—21no—
44#5210—21no—
45#5158C418yescomplemented
46C2×(C2×D3)⋊C8C2211yescharacteristic
47C2×(C2×D3)⋊C8C2211yescharacteristic
48C2×#816C2211yescharacteristic
49C2×#816C2211yescharacteristic
50C4×#214—24no—
51#4987C2211yescharacteristic
52#4972C2211yescharacteristic
53C2×#810C2211yescharacteristic
54C2×#808C2211yescharacteristic
55#4957—21no—
56#4945—21no—
57C4×C4⋊Dic3C2211yescharacteristic
58C2×C4×C3⋊C8C2211yescharacteristic
59#4551C2211yescharacteristic
60#4551C2211yescharacteristic
61#4550C2211yescharacteristic
62#4550C2211yescharacteristic
63#4529C2211yescharacteristic
64#4529C2211yescharacteristic
65C2×#520—31no—
66C2×#449—31no—
67C2×#442D311yescharacteristic, complemented
68C2×C4×SD16—31no—
69#2324—31no—
70#1880—31no—
71#1879—31no—
72#1874—31no—
73#1865—31no—
74#1864—31no—
75#1853—31no—
76#1788—31no—
77#1763—31no—
78C4×#102—31no—
79#1750—31no—
80C22×C3×D4C2311yescharacteristic
81C22×C3×D4C2311yescharacteristic
82C23×C3×C4—21no—
83C23×C3×C4—21no—
84C22×#67—21no—
85C22×#67—21no—
86C23×Dic3—21no—
87C23×Dic3—21no—
88C2×#237—22no—
89C2×#237—22no—
90C2×#237—22no—
91C2×#237—22no—
92C2×#237—22no—
93C2×#237C2×C414yescomplemented
94C22×C4×D3—21no—
95C22×C4×D3C2311yescharacteristic
96C22×Dic6C2311yescharacteristic
97C2×C3×D8—22no—
98C2×C3×D8—22no—
99C2×C3×D8C2×C414yescomplemented
100C22×C3×C8C2311yescharacteristic
101C22×C3×C8C2311yescharacteristic
102C3×C4×D4—22no—
103C3×C4×D4—22no—
104C3×C4×D4—22no—
105C3×C4×D4D414yescomplemented
106C2×C3×C4⋊C4C2311yescharacteristic
107C2×C3×C4⋊C4C2311yescharacteristic
108C2×C3×C22⋊C4—21no—
109C2×C3×C22⋊C4—21no—
110C2×C3×C42C2311yescharacteristic
111C2×#217—21no—
112C2×#217—21no—
113C2×#217—21no—
114C2×#217—21no—
115#938—22no—
116#938C2×C414yescomplemented
117D4×Dic3—22no—
118D4×Dic3—22no—
119C2×#214—22no—
120C2×#214—22no—
121C2×#214C2×C414yescomplemented
122C4×#67—28no—
123C2×(C2×D3)⋊C4—21no—
124C2×(C2×D3)⋊C4D411yescharacteristic
125C2×(C2×D3)⋊C4D411yescharacteristic
126C2×C4⋊Dic3C2311yescharacteristic
127C2×C4⋊Dic3C2311yescharacteristic
128C2×C4⋊Dic3C2311yescharacteristic
129C2×Dic3⋊C4—28no—
130C2×Dic3⋊C4—21no—
131C2×Dic3⋊C4—21no—
132C2×Dic3⋊C4—21no—
133C2×Dic3⋊C4—21no—
134C2×Dic3⋊C4D411yescharacteristic
135C2×Dic3⋊C4D411yescharacteristic
136C2×C4×Dic3—21no—
137C2×C4×Dic3—21no—
138C2×C4×Dic3—21no—
139C2×C4×Dic3C2311yescharacteristic
140C22×C3⋊C8C2311yescharacteristic
141C22×C3⋊C8C2311yescharacteristic
142D3×C4⋊C4—22no—
143D3×C4⋊C4—22no—
144#887—22no—
145#887—22no—
146#67⋊C4—28no—
147#877—28no—
148#872—22no—
149#872—22no—
150C4×Dic6—22no—
151C4×Dic6D414yescomplemented
152C3×#106—22no—
153C3×#102—22no—
154C3×#102—22no—
155C3×#97—22no—
156#832—22no—
157#832—22no—
158#832C2×C414yescomplemented
159C3⋊#95—21no—
160C3⋊#95—21no—
161C3⋊#95—21no—
162(C2×D3)⋊C8—22no—
163(C2×D3)⋊C8C2×C414yescomplemented
164#816—22no—
165#816C2×C414yescomplemented
166#810—22no—
167#808—22no—
168C4×C3⋊C8—22no—
169C22×#41—31no—
170C22×SD16—31no—
171C22×D8C2×D311yescharacteristic
172C2×#121—31no—
173#520—64no—
174#520—64no—
175C2×C4×Q8—31no—
176C2×C4×Q8—31no—
177C2×C4×D4—31no—
178C2×C4×D4—61no—
179C2×C4×D4—61no—
180C2×C4×D4C2×D311yescharacteristic
181C2×C4×D4C2×D311yescharacteristic
182C2×#117—31no—
183C2×#117—61no—
184C22×C4⋊C4—31no—
185C22×C4⋊C4—61no—
186#449—38no—
187#442—24no—
188C4×SD16—64no—
189C2×#106—31no—
190C2×#106C2×D311yescharacteristic
191C2×#103—31no—
192C2×#103—31no—
193C2×#103—31no—
194C2×#102—31no—
195C2×#102—31no—
196C2×#102—31no—
197C2×#102C2×D311yescharacteristic
198C2×#102C2×D311yescharacteristic
199C2×C22⋊C8—31no—
200C2×C22⋊C8—31no—
201C2×#97C2×D311yescharacteristic
202C2×C4×C8—31no—
203#390—31no—
204#390—61no—
205#389—31no—
206#388—61no—
207#386—61no—
208#385—61no—
209#380—31no—
210C4×C4⋊C4—31no—
211#340—31no—
212#340—31no—
213#340—31no—
214#340—31no—
215#336—31no—
216#336—31no—
217C24×C3—21no—
218C24×C3—21no—
219C23×D3C2×D411yescharacteristic
220C2×C3×D4—21no—
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4C22×C412yes—
229C2×C3×D4C22×C412yes—
230C2×C3×D4C2×D412yes—
231C2×C3×D4#4112yes—
232C22×C3×C4—21no—
233C22×C3×C4—24no—
234C22×C3×C4—21no—
235C22×C3×C4—42no—
236C22×C3×C4—81no—
237C22×C3×C4—81no—
238C22×C3×C4—81no—
239C22×C3×C4—81no—
240C22×C3×C4C2×D411yescharacteristic
241C22×C3×C4C2×D411yescharacteristic
242C22×C3×C4C2411yescharacteristic
243C2×#67—24no—
244C2×#67—24no—
245C2×#67—24no—
246C2×#67—24no—
247C2×#67—81no—
248C2×#67—81no—
249C22×Dic3—24no—
250C22×Dic3—24no—
251C22×Dic3—21no—
252C22×Dic3—24no—
253C22×Dic3—21no—
254C22×Dic3—21no—
255C22×Dic3—24no—
256C22×Dic3—21no—
257C22×Dic3—81no—
258C22×Dic3—81no—
259C22×Dic3C2×D411yescharacteristic
260C22×Dic3C2×D411yescharacteristic
261C22×Dic3C2×D411yescharacteristic
262#237—28no—
263#237—28no—
264#237—28no—
265#237—28no—
266C2×C4×D3—21no—
267C2×C4×D3—21no—
268C2×C4×D3—21no—
269C2×C4×D3—21no—
270C2×C4×D3—24no—
271C2×C4×D3—81no—
272C2×C4×D3—81no—
273C2×C4×D3C22×C412yes—
274C2×C4×D3#4112yes—
275C2×Dic6—21no—
276C2×Dic6—21no—
277C2×Dic6—21no—
278C2×Dic6C22×C412yes—
279C2×Dic6C2×D412yes—
280C2×Dic6#4112yes—
281C3×D8—28no—
282C2×C3×C8—21no—
283C2×C3×C8—21no—
284C2×C3×C8—21no—
285C2×C3×C8—21no—
286C2×C3×C8—21no—
287C2×C3×C8C22×C412yes—
288C3×C4⋊C4—21no—
289C3×C4⋊C4—21no—
290C3×C4⋊C4—21no—
291C3×C4⋊C4C2×D412yes—
292C3×C22⋊C4—24no—
293C3×C22⋊C4—42no—
294C3×C42C2×D412yes—
295C3×C42C2×D412yes—
296#217—24no—
297#217—24no—
298#217—81no—
299#217—81no—
300#214—28no—
301(C2×D3)⋊C4—22no—
302(C2×D3)⋊C4—22no—
303(C2×D3)⋊C4—81no—
304C4⋊Dic3—21no—
305C4⋊Dic3—21no—
306C4⋊Dic3—21no—
307C4⋊Dic3—21no—
308C4⋊Dic3C22×C412yes—
309C4⋊Dic3C2×D412yes—
310Dic3⋊C4—24no—
311Dic3⋊C4—24no—
312Dic3⋊C4—24no—
313Dic3⋊C4—22no—
314Dic3⋊C4—22no—
315Dic3⋊C4—81no—
316C4×Dic3—24no—
317C4×Dic3—24no—
318C4×Dic3—21no—
319C4×Dic3—21no—
320C4×Dic3—81no—
321C2×C3⋊C8—21no—
322C2×C3⋊C8—21no—
323C2×C3⋊C8—21no—
324C2×C3⋊C8—21no—
325C2×C3⋊C8—21no—
326C2×C3⋊C8C22×C412yes—
327C2×#41—34no—
328C2×#41—62no—
329C2×#41—62no—
330C2×#41—62no—
331C2×#41—62no—
332C2×#41—62no—
333C22×Q8—31no—
334C22×D4—61no—
335C22×D4—61no—
336C22×D4C22×D311yescharacteristic
337C22×D4C22×D311yescharacteristic
338C23×C4—21no—
339C23×C4—21no—
340C23×C4—31no—
341C23×C4—61no—
342C23×C4—61no—
343C23×C4—61no—
344C2×SD16—34no—
345C2×SD16—62no—
346C2×SD16—62no—
347C2×D8—22no—
348C2×D8—22no—
349C2×D8C4×D314yescomplemented
350C22×C8—31no—
351C22×C8—31no—
352C22×C8C22×D311yescharacteristic
353C22×C8C22×D311yescharacteristic
354#121—34no—
355#121—62no—
356C4×Q8—34no—
357C4×Q8—62no—
358C4×Q8—62no—
359C4×Q8—62no—
360C4×D4—22no—
361C4×D4—22no—
362C4×D4—22no—
363C4×D4—68no—
364C4×D4—62no—
365C4×D4—68no—
366C4×D4—62no—
367C4×D4#6714yescomplemented
368#117—68no—
369#117—62no—
370#117—62no—
371C2×C4⋊C4—31no—
372C2×C4⋊C4—31no—
373C2×C4⋊C4—31no—
374C2×C4⋊C4—31no—
375C2×C4⋊C4—31no—
376C2×C4⋊C4—62no—
377C2×C4⋊C4—61no—
378C2×C4⋊C4—61no—
379C2×C4⋊C4—68no—
380C2×C4⋊C4—61no—
381C2×C4⋊C4—62no—
382C2×C4⋊C4—61no—
383C2×C4⋊C4C22×D311yescharacteristic
384C2×C4⋊C4C22×D311yescharacteristic
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—31no—
388C2×C22⋊C4—31no—
389C2×C22⋊C4—61no—
390C2×C22⋊C4—61no—
391C2×C22⋊C4—61no—
392C2×C22⋊C4—61no—
393C2×C22⋊C4—61no—
394C2×C42—31no—
395C2×C42—61no—
396C2×C42—61no—
397C2×C42—61no—
398C2×C42C22×D311yescharacteristic
399#106—22no—
400#106—62no—
401#103—34no—
402#103—62no—
403#103—62no—
404#102—22no—
405#102—22no—
406#102—34no—
407#102—62no—
408#102—62no—
409C22⋊C8—34no—
410C22⋊C8—62no—
411#97—22no—
412C4×C8—62no—
413#95—61no—
414#95—61no—
415#95—61no—
416C23×C3—22no—
417C23×C3—22no—
418C23×C3—22no—
419C23×C3—22no—
420C23×C3—41no—
421C23×C3—41no—
422C23×C3—41no—
423C23×C3—41no—
424C23×C3—41no—
425C23×C3—41no—
426C23×C3—41no—
427C23×C3—41no—
428C23×C3—41no—
429C23×C3—41no—
430C23×C3C22×D411yescharacteristic
431C22×D3—21no—
432C22×D3—21no—
433C22×D3—21no—
434C22×D3—21no—
435C22×D3—21no—
436C22×D3—21no—
437C22×D3C4×D412yes—
438C3×D4—22no—
439C3×D4—22no—
440C3×D4—22no—
441C3×D4—22no—
442C3×D4—22no—
443C3×D4—41no—
444C3×D4—41no—
445C3×D4C4×D414yes—
446C2×C3×C4—21no—
447C2×C3×C4—21no—
448C2×C3×C4—21no—
449C2×C3×C4—21no—
450C2×C3×C4—22no—
451C2×C3×C4—41no—
452C2×C3×C4—41no—
453C2×C3×C4—41no—
454C2×C3×C4—41no—
455C2×C3×C4—41no—
456C2×C3×C4—84no—
457C2×C3×C4—84no—
458C2×C3×C4#12012yes—
459C2×C3×C4#12012yes—
460C2×C3×C4C23×C411yescharacteristic
461C2×C3×C4C22×D411yescharacteristic
462C2×C3×C4C22×D411yescharacteristic
463C2×C3×C4C2×#4111yescharacteristic
464C2×C3×C4C2×#4111yescharacteristic
465C2×C3×C4C2×#4111yescharacteristic
466#67—216no—
467#67—84no—
468C2×Dic3—216no—
469C2×Dic3—22no—
470C2×Dic3—22no—
471C2×Dic3—21no—
472C2×Dic3—22no—
473C2×Dic3—21no—
474C2×Dic3—22no—
475C2×Dic3—21no—
476C2×Dic3—21no—
477C2×Dic3—22no—
478C2×Dic3—21no—
479C2×Dic3—21no—
480C2×Dic3—21no—
481C2×Dic3—21no—
482C2×Dic3—41no—
483C2×Dic3—41no—
484C2×Dic3—41no—
485C2×Dic3—41no—
486C2×Dic3—41no—
487C2×Dic3—41no—
488C2×Dic3—41no—
489C2×Dic3—84no—
490C2×Dic3C4×D412yes—
491C4×D3—22no—
492C4×D3—22no—
493C4×D3—22no—
494C4×D3—22no—
495C4×D3—84no—
496Dic6—22no—
497Dic6—22no—
498Dic6—22no—
499Dic6C4×D414yes—
500C3×C8—22no—
501C3×C8—41no—
502C3⋊C8—22no—
503C3⋊C8—41no—
504C24—21no—
505C24—21no—
506C24—31no—
507#41—68no—
508#41—68no—
509#41—68no—
510#41—68no—
511C2×Q8—32no—
512C2×Q8—32no—
513C2×Q8—32no—
514C2×Q8—61no—
515C2×Q8—61no—
516C2×Q8—61no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—64no—
526C2×D4—64no—
527C2×D4—64no—
528C2×D4—64no—
529C2×D4—241no—
530C2×D4—241no—
531C2×D4C2×C4×D312yes—
532C2×D4C2×C4×D312yes—
533C2×D4#23512yes—
534C2×D4C2×#6712yes—
535C22×C4—21no—
536C22×C4—24no—
537C22×C4—21no—
538C22×C4—31no—
539C22×C4—32no—
540C22×C4—32no—
541C22×C4—31no—
542C22×C4—31no—
543C22×C4—42no—
544C22×C4—64no—
545C22×C4—64no—
546C22×C4—64no—
547C22×C4—64no—
548C22×C4—61no—
549C22×C4—61no—
550C22×C4—61no—
551C22×C4—61no—
552C22×C4—61no—
553C22×C4—61no—
554C22×C4—61no—
555C22×C4—64no—
556C22×C4—61no—
557C22×C4—81no—
558C22×C4—81no—
559C22×C4—81no—
560C22×C4—81no—
561C22×C4—241no—
562C22×C4—241no—
563C22×C4—241no—
564C22×C4—241no—
565C22×C4D3×D411yescharacteristic
566C22×C4D3×D411yescharacteristic
567C22×C4C23×D311yescharacteristic
568SD16—68no—
569D8—28no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—32no—
576C2×C8—61no—
577C2×C8—61no—
578C2×C8—61no—
579C2×C8—61no—
580C2×C8—61no—
581C2×C8C2×C4×D312yes—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—32no—
586C4⋊C4—32no—
587C4⋊C4—64no—
588C4⋊C4—64no—
589C4⋊C4—62no—
590C4⋊C4—62no—
591C4⋊C4—64no—
592C4⋊C4—61no—
593C4⋊C4—61no—
594C4⋊C4—61no—
595C4⋊C4—61no—
596C4⋊C4—241no—
597C4⋊C4C2×#6712yes—
598C22⋊C4—24no—
599C22⋊C4—42no—
600C22⋊C4—64no—
601C22⋊C4—64no—
602C22⋊C4—62no—
603C22⋊C4—62no—
604C22⋊C4—241no—
605C22⋊C4—241no—
606C22⋊C4—241no—
607C42—64no—
608C42—64no—
609C42—61no—
610C42—61no—
611C42—241no—
612C42D3×D412yes—
613C42C2×#6712yes—
614C22×C3—24no—
615C22×C3—42no—
616C22×C3—42no—
617C22×C3—42no—
618C22×C3—42no—
619C22×C3—42no—
620C22×C3—42no—
621C22×C3—42no—
622C22×C3—42no—
623C22×C3—42no—
624C22×C3—81no—
625C22×C3—81no—
626C22×C3—81no—
627C22×C3—81no—
628C22×C3C2×C4×D411yescharacteristic
629C22×C3C2×#12011yescharacteristic
630C22×C3#52511yescharacteristic
631C22×C3#57611yescharacteristic
632C22×C3#57711yescharacteristic
633C22×C3#57711yescharacteristic
634C22×C3#57711yescharacteristic
635C2×D3—22no—
636C2×D3—22no—
637C2×D3—22no—
638C2×D3—41no—
639C2×D3—41no—
640C2×D3—41no—
641C2×D3—41no—
642C3×C4—22no—
643C3×C4—22no—
644C3×C4—42no—
645C3×C4—81no—
646C3×C4C2×C4×D411yescharacteristic
647C3×C4C2×C4×D411yescharacteristic
648C3×C4#52511yescharacteristic
649C3×C4#52511yescharacteristic
650Dic3—24no—
651Dic3—22no—
652Dic3—42no—
653Dic3—41no—
654Dic3—42no—
655Dic3—41no—
656Dic3—81no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—32no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—61no—
673C23—61no—
674C23—61no—
675C23—61no—
676C23—61no—
677C23—61no—
678C23C2×D3×D411yescharacteristic
679Q8—34no—
680Q8—62no—
681Q8—62no—
682Q8—62no—
683D4—22no—
684D4—22no—
685D4—22no—
686D4—22no—
687D4—22no—
688D4—41no—
689D4—41no—
690D4—616no—
691D4—244no—
692D4C4×#6714yes—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—32no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—616no—
705C2×C4—62no—
706C2×C4—61no—
707C2×C4—62no—
708C2×C4—61no—
709C2×C4—62no—
710C2×C4—62no—
711C2×C4—62no—
712C2×C4—62no—
713C2×C4—62no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—62no—
720C2×C4—61no—
721C2×C4—62no—
722C2×C4—84no—
723C2×C4—84no—
724C2×C4—121no—
725C2×C4—121no—
726C2×C4—121no—
727C2×C4—121no—
728C2×C4—121no—
729C2×C4—121no—
730C2×C4—121no—
731C2×C4—244no—
732C2×C4—244no—
733C2×C4#93712yes—
734C2×C4#93712yes—
735C2×C4C22×C4×D311yescharacteristic
736C2×C4C2×#23511yescharacteristic
737C2×C4C2×D3×D411yescharacteristic
738C2×C4D3×#4111yescharacteristic
739C2×C4D3×#4111yescharacteristic
740C2×C4C22×#6711yescharacteristic
741C8—22no—
742C8—41no—
743C8—62no—
744C8—121no—
745C2×C3—44no—
746C2×C3—82no—
747C2×C3C4×#12011yescharacteristic
748C2×C3#294611yescharacteristic
749C2×C3#295211yescharacteristic
750C2×C3#301011yescharacteristic
751C2×C3#301211yescharacteristic
752C2×C3#311911yescharacteristic
753C2×C3#312511yescharacteristic
754D3—42no—
755C22—24no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—62no—
766C22—62no—
767C22—62no—
768C22—81no—
769C22—81no—
770C22—81no—
771C22—81no—
772C22—121no—
773C22—121no—
774C22—121no—
775C22—121no—
776C22C4×D3×D411yescharacteristic
777C22#554711yescharacteristic
778C22#577411yescharacteristic
779C22#577511yescharacteristic
780C22#577511yescharacteristic
781C22#577511yescharacteristic
782C22C2×#93711yescharacteristic
783C4—22no—
784C4—22no—
785C4—42no—
786C4—62no—
787C4—64no—
788C4—81no—
789C4—121no—
790C4—121no—
791C4—122no—
792C4—122no—
793C4—241no—
794C4C4×D3×D411yescharacteristic
795C4#554711yescharacteristic
796C4C2×C4×#6711yescharacteristic
797C4#582811yescharacteristic
798C3#2146411yescharacteristic, complemented, Sylow
799C2—44no—
800C2—82no—
801C2—122no—
802C2#7986611yescharacteristic
803C2#7986811yescharacteristic
804C2#7987311yescharacteristic
805C2#7987511yescharacteristic
806C2C4×#93711yescharacteristic
807C2#8394811yescharacteristic
808C2#8394911yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
FittingC2×C3×#442C2
socleC23×C3C22×D4
prime radicalC2×#5158C2
cosocleC22×C3×C4C24
hypercenterC2×#442D3
hypocenterC3#21464
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
1. C2×#5546C2semidirect
2. C2×C3×#442C2semidirect
4. #82396C2semidirect
5. C2×C4×#214C2semidirect
6. #72037C2semidirect
7. C4×#832C2semidirect
8. #70588C2semidirect
9. #70579C2semidirect
10. #70213C2semidirect
11. #70200C2semidirect
12. #70199C2semidirect
13. #70169C2semidirect
14. #69830C2semidirect
15. #69813C2semidirect
45. #5158C4semidirect
67. C2×#442D3semidirect
93. C2×#237C2×C4semidirect
99. C2×C3×D8C2×C4semidirect
105. C3×C4×D4D4semidirect
116. #938C2×C4semidirect
121. C2×#214C2×C4semidirect
151. C4×Dic6D4semidirect
158. #832C2×C4semidirect
163. (C2×D3)⋊C8C2×C4semidirect
165. #816C2×C4semidirect
349. C2×D8C4×D3semidirect
367. C4×D4#67semidirect
798. C3#21464semidirect

Maximal subgroups

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

subgroupindex
C2×#55462
C2×C3×#4422
C2×#51582
#823962
C2×C4×#2142
#720372
C4×#8322
#705882
#705792
#702132
#702002
#701992
#701692
#698302
#698132
#214643