Finite Group Databasebeta

← #10800997

Subgroups — #10800997

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×#5827C211yesmaximal, characteristic, complemented
2C2×C3×#449C211yesmaximal, characteristic
3C2×Dic3×SD16C211yesmaximal, characteristic, complemented
4C2×#5152C211yesmaximal, characteristic, complemented
5#82633C211yesmaximal, characteristic, complemented
6#72135C211yesmaximal, characteristic, complemented
7#72048C211yesmaximal, characteristic, complemented
8#72037C211yesmaximal, characteristic, complemented
9#71677C211yesmaximal, characteristic, complemented
10#70238C211yesmaximal, characteristic, complemented
11#70220C211yesmaximal, characteristic, complemented
12#70170C211yesmaximal, characteristic, complemented
13Dic3×#102C211yesmaximal, characteristic, complemented
14#69928C211yesmaximal, characteristic, complemented
15#69907C211yesmaximal, characteristic, complemented
16#21464—31nomaximal, Sylow
17C22×C3×#41C2211yescharacteristic
18C22×C3×SD16C2211yescharacteristic
19C22×C3×D8C2211yescharacteristic
20C2×C3×#121C2211yescharacteristic
21#5827—24no—
22#5827—24no—
23C2×Q8×Dic3C2211yescharacteristic
24C2×Q8×Dic3C2211yescharacteristic
25C2×D4×Dic3—21no—
26C2×D4×Dic3—21no—
27C2×D4×Dic3C2211yescharacteristic
28C2×D4×Dic3C2211yescharacteristic
29C2×D4×Dic3C2211yescharacteristic
30C2×#926—21no—
31C2×#926C2211yescharacteristic
32C22×C4⋊Dic3—21no—
33C22×C4⋊Dic3C2211yescharacteristic
34C3×#449C418yescomplemented
35C2×C3×#103C2211yescharacteristic
36C2×C3×#102C2211yescharacteristic
37C2×C3×C22⋊C8C2211yescharacteristic
38C2×#835C2211yescharacteristic
39C2×#835C2211yescharacteristic
40#5221—21no—
41#5221C2211yescharacteristic
42#5220—21no—
43C2×#832C2211yescharacteristic
44C2×#832C2211yescharacteristic
45C2×#832C2211yescharacteristic
46C2×#832C2211yescharacteristic
47#5212C2211yescharacteristic
48C2×#830C2211yescharacteristic
49Dic3×SD16—24no—
50#5152—24no—
51C2×#817C2211yescharacteristic
52C2×#817C2211yescharacteristic
53C2×#815C2211yescharacteristic
54C2×C8×Dic3C2211yescharacteristic
55#4984C2211yescharacteristic
56Dic3×C4⋊C4C2211yescharacteristic
57#4951—21no—
58#4950—21no—
59#4551C2211yescharacteristic
60#4551C2211yescharacteristic
61#4550C2211yescharacteristic
62#4550C2211yescharacteristic
63#4529C2211yescharacteristic
64#4529C2211yescharacteristic
65C2×#520—31no—
66C2×#449D311yescharacteristic
67C2×#442—31no—
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—
80C2×C3×#41—22no—
81C2×C3×#41—22no—
82C2×C3×#41—22no—
83C2×C3×#41—22no—
84C2×C3×#41—22no—
85C2×C3×#41C2×C414yescomplemented
86C22×C3×Q8C2311yescharacteristic
87C22×C3×D4—21no—
88C22×C3×D4—21no—
89C22×C3×D4C2311yescharacteristic
90C22×C3×D4C2311yescharacteristic
91C23×C3×C4—21no—
92C23×C3×C4C2311yescharacteristic
93C23×Dic3—21no—
94C23×Dic3—21no—
95C23×Dic3—21no—
96C23×Dic3—21no—
97C2×C3×SD16—22no—
98C2×C3×SD16—22no—
99C2×C3×SD16C2×C414yescomplemented
100C2×C3×D8—22no—
101C2×C3×D8—22no—
102C2×C3×D8C2×C414yescomplemented
103C22×C3×C8C2311yescharacteristic
104C22×C3×C8C2311yescharacteristic
105C3×#121—22no—
106C3×#121C2×C414yescomplemented
107C2×C3×C4⋊C4C2311yescharacteristic
108C2×C3×C22⋊C4—21no—
109C2×#217—21no—
110C2×#217—21no—
111C2×#217—21no—
112C2×#217—21no—
113C2×#217—21no—
114C2×#217—21no—
115C2×#217D411yescharacteristic
116C2×#217D411yescharacteristic
117Q8×Dic3—22no—
118Q8×Dic3—22no—
119Q8×Dic3—22no—
120Q8×Dic3D414yescomplemented
121D4×Dic3—28no—
122D4×Dic3—28no—
123D4×Dic3—22no—
124D4×Dic3—22no—
125D4×Dic3—22no—
126D4×Dic3—22no—
127D4×Dic3—22no—
128D4×Dic3D414yescomplemented
129#926—28no—
130#926—22no—
131#926—22no—
132C2×C4⋊Dic3—28no—
133C2×C4⋊Dic3—21no—
134C2×C4⋊Dic3—21no—
135C2×C4⋊Dic3—21no—
136C2×C4⋊Dic3—22no—
137C2×C4⋊Dic3—22no—
138C2×C4⋊Dic3—21no—
139C2×C4⋊Dic3D411yescharacteristic
140C2×C4⋊Dic3D411yescharacteristic
141C2×C4⋊Dic3C2311yescharacteristic
142C2×C4⋊Dic3C2311yescharacteristic
143C2×C4⋊Dic3C2311yescharacteristic
144C2×C4⋊Dic3C2311yescharacteristic
145C2×C4×Dic3—21no—
146C2×C4×Dic3—21no—
147C2×C4×Dic3—21no—
148C2×C4×Dic3C2311yescharacteristic
149C2×C4×Dic3C2311yescharacteristic
150C22×C3⋊C8C2311yescharacteristic
151C22×C3⋊C8C2311yescharacteristic
152C3×#103C2×C414yescomplemented
153C3×#102C2×C414yescomplemented
154C3×C22⋊C8C2×C414yescomplemented
155#835—22no—
156#835—22no—
157#832—22no—
158#832—22no—
159#832—22no—
160#832—22no—
161C3⋊#95—21no—
162C3⋊#95—21no—
163C3⋊#95—21no—
164#830—22no—
165#817—22no—
166#817—22no—
167#815—22no—
168C8×Dic3—22no—
169C22×#41C2×D311yescharacteristic
170C22×SD16C2×D311yescharacteristic
171C22×D8C2×D311yescharacteristic
172C2×#121C2×D311yescharacteristic
173#520—64no—
174#520—64no—
175C2×C4×Q8—31no—
176C2×C4×Q8—31no—
177C2×C4×D4—31no—
178C2×C4×D4—31no—
179C2×C4×D4—31no—
180C2×C4×D4—61no—
181C2×C4×D4—61no—
182C2×#117—31no—
183C2×#117—61no—
184C22×C4⋊C4—31no—
185C22×C4⋊C4—61no—
186#449Dic318yescomplemented
187#442—64no—
188C4×SD16—64no—
189C2×#106—31no—
190C2×#106—31no—
191C2×#103—31no—
192C2×#103—31no—
193C2×#103C2×D311yescharacteristic
194C2×#102—31no—
195C2×#102—31no—
196C2×#102—31no—
197C2×#102—31no—
198C2×#102C2×D311yescharacteristic
199C2×C22⋊C8—31no—
200C2×C22⋊C8C2×D311yescharacteristic
201C2×#97—31no—
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—
219C24×C3C2×D411yescharacteristic
220C3×#41—28no—
221C3×#41—28no—
222C3×#41—28no—
223C3×#41—28no—
224C2×C3×Q8—21no—
225C2×C3×Q8—21no—
226C2×C3×Q8—21no—
227C2×C3×Q8C22×C412yes—
228C2×C3×Q8C2×D412yes—
229C2×C3×Q8#4112yes—
230C2×C3×D4—24no—
231C2×C3×D4—24no—
232C2×C3×D4—24no—
233C2×C3×D4—24no—
234C2×C3×D4—21no—
235C2×C3×D4—21no—
236C2×C3×D4—21no—
237C2×C3×D4—21no—
238C2×C3×D4—21no—
239C2×C3×D4—21no—
240C2×C3×D4—21no—
241C2×C3×D4—21no—
242C2×C3×D4—81no—
243C2×C3×D4—81no—
244C2×C3×D4C22×C412yes—
245C2×C3×D4C22×C412yes—
246C2×C3×D4C2×D412yes—
247C2×C3×D4#4112yes—
248C22×C3×C4—24no—
249C22×C3×C4—24no—
250C22×C3×C4—21no—
251C22×C3×C4—24no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4C22×C412yes—
258C22×C3×C4C2×D411yescharacteristic
259C22×C3×C4#4112yes—
260C22×C3×C4C2411yescharacteristic
261C22×Dic3—21no—
262C22×Dic3—21no—
263C22×Dic3—24no—
264C22×Dic3—24no—
265C22×Dic3—24no—
266C22×Dic3—21no—
267C22×Dic3—21no—
268C22×Dic3—42no—
269C22×Dic3—81no—
270C22×Dic3—81no—
271C22×Dic3—81no—
272C22×Dic3—81no—
273C22×Dic3—81no—
274C22×Dic3—81no—
275C22×Dic3—81no—
276C22×Dic3—81no—
277C22×Dic3C2×D411yescharacteristic
278C22×Dic3C2×D411yescharacteristic
279C22×Dic3C2×D411yescharacteristic
280C22×Dic3C2×D411yescharacteristic
281C3×SD16—28no—
282C3×D8—28no—
283C2×C3×C8—21no—
284C2×C3×C8—21no—
285C2×C3×C8—21no—
286C2×C3×C8—21no—
287C2×C3×C8C22×C412yes—
288C2×C3×C8C22×C412yes—
289C3×C4⋊C4—21no—
290C3×C4⋊C4C22×C412yes—
291C3×C22⋊C4—24no—
292#217—24no—
293#217—22no—
294#217—22no—
295#217—24no—
296#217—42no—
297#217—81no—
298#217—81no—
299#217—81no—
300C4⋊Dic3—24no—
301C4⋊Dic3—24no—
302C4⋊Dic3—21no—
303C4⋊Dic3—21no—
304C4⋊Dic3—22no—
305C4⋊Dic3—24no—
306C4⋊Dic3—22no—
307C4⋊Dic3—21no—
308C4⋊Dic3—21no—
309C4⋊Dic3—21no—
310C4⋊Dic3—21no—
311C4⋊Dic3—81no—
312C4⋊Dic3C2×D412yes—
313C4⋊Dic3C2×D412yes—
314C4×Dic3—24no—
315C4×Dic3—21no—
316C4×Dic3—21no—
317C4×Dic3—24no—
318C4×Dic3—81no—
319C4×Dic3C2×D412yes—
320C4×Dic3C2×D412yes—
321C2×C3⋊C8—21no—
322C2×C3⋊C8—21no—
323C2×C3⋊C8—21no—
324C2×C3⋊C8—21no—
325C2×C3⋊C8—21no—
326C2×C3⋊C8—21no—
327C2×#41—22no—
328C2×#41—22no—
329C2×#41—22no—
330C2×#41—22no—
331C2×#41—22no—
332C2×#41C2×Dic314yescomplemented
333C22×Q8C22×D311yescharacteristic
334C22×D4—21no—
335C22×D4—21no—
336C22×D4C22×D311yescharacteristic
337C22×D4C22×D311yescharacteristic
338C23×C4—21no—
339C23×C4—61no—
340C23×C4—61no—
341C23×C4—61no—
342C23×C4—61no—
343C23×C4C22×D311yescharacteristic
344C2×SD16—22no—
345C2×SD16—22no—
346C2×SD16C2×Dic314yescomplemented
347C2×D8—22no—
348C2×D8—22no—
349C2×D8C2×Dic314yescomplemented
350C22×C8—31no—
351C22×C8—31no—
352C22×C8C22×D311yescharacteristic
353C22×C8C22×D311yescharacteristic
354#121—22no—
355#121C2×Dic314yescomplemented
356C4×Q8—34no—
357C4×Q8—62no—
358C4×Q8—62no—
359C4×Q8—62no—
360C4×D4—34no—
361C4×D4—62no—
362C4×D4—62no—
363C4×D4—62no—
364C4×D4—62no—
365C4×D4—68no—
366C4×D4—68no—
367C4×D4—62no—
368#117—62no—
369#117—62no—
370#117—68no—
371C2×C4⋊C4—31no—
372C2×C4⋊C4—31no—
373C2×C4⋊C4—31no—
374C2×C4⋊C4—31no—
375C2×C4⋊C4—31no—
376C2×C4⋊C4—31no—
377C2×C4⋊C4—62no—
378C2×C4⋊C4—62no—
379C2×C4⋊C4—61no—
380C2×C4⋊C4—61no—
381C2×C4⋊C4—68no—
382C2×C4⋊C4—61no—
383C2×C4⋊C4—61no—
384C2×C4⋊C4C22×D311yescharacteristic
385C2×C22⋊C4—21no—
386C2×C22⋊C4—31no—
387C2×C22⋊C4—31no—
388C2×C22⋊C4—61no—
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—31no—
396C2×C42—61no—
397C2×C42—61no—
398C2×C42—61no—
399#106—62no—
400#106—62no—
401#103—62no—
402#103—62no—
403#103C2×Dic314yescomplemented
404#102—62no—
405#102—62no—
406#102—62no—
407#102—62no—
408#102C2×Dic314yescomplemented
409C22⋊C8—62no—
410C22⋊C8C2×Dic314yescomplemented
411#97—62no—
412C4×C8—62no—
413#95—61no—
414#95—61no—
415#95—61no—
416C23×C3—22no—
417C23×C3—21no—
418C23×C3—22no—
419C23×C3—21no—
420C23×C3—22no—
421C23×C3—21no—
422C23×C3—21no—
423C23×C3—21no—
424C23×C3—21no—
425C23×C3—22no—
426C23×C3—41no—
427C23×C3—41no—
428C23×C3—41no—
429C23×C3—41no—
430C23×C3—41no—
431C23×C3—41no—
432C23×C3—41no—
433C23×C3—41no—
434C23×C3—41no—
435C23×C3—41no—
436C23×C3C4×D412yes—
437C23×C3C22×D411yescharacteristic
438C3×Q8—22no—
439C3×Q8—22no—
440C3×Q8—22no—
441C3×Q8C4×D414yes—
442C3×D4—216no—
443C3×D4—22no—
444C3×D4—22no—
445C3×D4—22no—
446C3×D4—22no—
447C3×D4—22no—
448C3×D4—41no—
449C3×D4—41no—
450C3×D4—84no—
451C3×D4C4×D414yes—
452C2×C3×C4—216no—
453C2×C3×C4—22no—
454C2×C3×C4—22no—
455C2×C3×C4—21no—
456C2×C3×C4—21no—
457C2×C3×C4—22no—
458C2×C3×C4—22no—
459C2×C3×C4—22no—
460C2×C3×C4—22no—
461C2×C3×C4—22no—
462C2×C3×C4—22no—
463C2×C3×C4—41no—
464C2×C3×C4—41no—
465C2×C3×C4C4×D412yes—
466C2×C3×C4C23×C411yescharacteristic
467C2×C3×C4C22×D411yescharacteristic
468C2×C3×C4C22×D411yescharacteristic
469C2×C3×C4C2×#4111yescharacteristic
470C2×C3×C4C2×#4111yescharacteristic
471C2×C3×C4C2×#4111yescharacteristic
472C2×Dic3—21no—
473C2×Dic3—21no—
474C2×Dic3—21no—
475C2×Dic3—21no—
476C2×Dic3—21no—
477C2×Dic3—21no—
478C2×Dic3—22no—
479C2×Dic3—22no—
480C2×Dic3—21no—
481C2×Dic3—21no—
482C2×Dic3—21no—
483C2×Dic3—21no—
484C2×Dic3—41no—
485C2×Dic3—41no—
486C2×Dic3—41no—
487C2×Dic3—41no—
488C2×Dic3—41no—
489C2×Dic3—41no—
490C2×Dic3—41no—
491C2×Dic3—41no—
492C2×Dic3—41no—
493C2×Dic3—41no—
494C2×Dic3—84no—
495C2×Dic3—84no—
496C2×Dic3—84no—
497C2×Dic3—84no—
498C2×Dic3#12012yes—
499C2×Dic3#12012yes—
500C3×C8—22no—
501C3×C8—22no—
502C3⋊C8—41no—
503C3⋊C8—41no—
504C24—21no—
505C24—21no—
506C24D3×D411yescharacteristic
507#41—28no—
508#41—28no—
509#41—28no—
510#41—28no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8D3×D412yes—
515C2×Q8#23712yes—
516C2×Q8C22×Dic312yes—
517C2×D4—24no—
518C2×D4—24no—
519C2×D4—24no—
520C2×D4—24no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—81no—
530C2×D4—81no—
531C2×D4D3×D412yes—
532C2×D4#23712yes—
533C2×D4C22×Dic312yes—
534C2×D4C22×Dic312yes—
535C22×C4—24no—
536C22×C4—24no—
537C22×C4—21no—
538C22×C4—24no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—31no—
545C22×C4—31no—
546C22×C4—31no—
547C22×C4—31no—
548C22×C4—64no—
549C22×C4—61no—
550C22×C4—61no—
551C22×C4—64no—
552C22×C4—64no—
553C22×C4—61no—
554C22×C4—61no—
555C22×C4—122no—
556C22×C4—241no—
557C22×C4—241no—
558C22×C4—241no—
559C22×C4—241no—
560C22×C4—241no—
561C22×C4—241no—
562C22×C4—241no—
563C22×C4—241no—
564C22×C4D3×D411yescharacteristic
565C22×C4#23712yes—
566C22×C4C22×Dic312yes—
567C22×C4C23×D311yescharacteristic
568SD16—28no—
569D8—28no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—61no—
575C2×C8—61no—
576C2×C8—61no—
577C2×C8—61no—
578C2×C8—61no—
579C2×C8—61no—
580C2×C8C22×Dic312yes—
581C2×C8C22×Dic312yes—
582C4⋊C4—21no—
583C4⋊C4—32no—
584C4⋊C4—32no—
585C4⋊C4—62no—
586C4⋊C4—62no—
587C4⋊C4—64no—
588C4⋊C4—64no—
589C4⋊C4—64no—
590C4⋊C4—61no—
591C4⋊C4—61no—
592C4⋊C4—61no—
593C4⋊C4—61no—
594C4⋊C4—61no—
595C4⋊C4—61no—
596C4⋊C4—241no—
597C4⋊C4C22×Dic312yes—
598C22⋊C4—24no—
599C22⋊C4—62no—
600C22⋊C4—62no—
601C22⋊C4—64no—
602C22⋊C4—64no—
603C22⋊C4—122no—
604C22⋊C4—241no—
605C22⋊C4—241no—
606C22⋊C4—241no—
607C42—32no—
608C42—32no—
609C42—64no—
610C42—64no—
611C42—61no—
612C42—61no—
613C42—241no—
614C22×C3—22no—
615C22×C3—22no—
616C22×C3—22no—
617C22×C3—24no—
618C22×C3—41no—
619C22×C3—42no—
620C22×C3—41no—
621C22×C3—42no—
622C22×C3—42no—
623C22×C3—42no—
624C22×C3—41no—
625C22×C3—42no—
626C22×C3—41no—
627C22×C3—42no—
628C22×C3—42no—
629C22×C3—42no—
630C22×C3—42no—
631C22×C3—81no—
632C22×C3—81no—
633C22×C3—81no—
634C22×C3—81no—
635C22×C3C2×C4×D411yescharacteristic
636C22×C3C2×#12011yescharacteristic
637C22×C3#52511yescharacteristic
638C22×C3#57611yescharacteristic
639C22×C3#57711yescharacteristic
640C22×C3#57711yescharacteristic
641C22×C3#57711yescharacteristic
642C3×C4—22no—
643C3×C4—24no—
644C3×C4—42no—
645C3×C4C2×C4×D411yescharacteristic
646C3×C4C2×C4×D411yescharacteristic
647C3×C4#52511yescharacteristic
648C3×C4#52511yescharacteristic
649Dic3—22no—
650Dic3—22no—
651Dic3—41no—
652Dic3—41no—
653Dic3—42no—
654Dic3—42no—
655Dic3—81no—
656Dic3—81no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—22no—
662C23—21no—
663C23—22no—
664C23—21no—
665C23—22no—
666C23—22no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23D4×Dic312yes—
678C23C2×D3×D411yescharacteristic
679Q8—22no—
680Q8—22no—
681Q8—22no—
682Q8D4×Dic314yes—
683D4—216no—
684D4—22no—
685D4—22no—
686D4—22no—
687D4—22no—
688D4—22no—
689D4—41no—
690D4—41no—
691D4—84no—
692D4D4×Dic314yes—
693C2×C4—216no—
694C2×C4—22no—
695C2×C4—21no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—21no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—32no—
705C2×C4—32no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—61no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—61no—
717C2×C4—62no—
718C2×C4—62no—
719C2×C4—61no—
720C2×C4—121no—
721C2×C4—121no—
722C2×C4—121no—
723C2×C4—121no—
724C2×C4—121no—
725C2×C4—121no—
726C2×C4—121no—
727C2×C4—121no—
728C2×C4—121no—
729C2×C4—121no—
730C2×C4—244no—
731C2×C4—244no—
732C2×C4—244no—
733C2×C4—244no—
734C2×C4D4×Dic312yes—
735C2×C4C2×D3×D411yescharacteristic
736C2×C4C2×D3×D411yescharacteristic
737C2×C4C2×#23711yescharacteristic
738C2×C4C2×#23711yescharacteristic
739C2×C4C2×#23711yescharacteristic
740C2×C4C23×Dic311yescharacteristic
741C8—22no—
742C8—22no—
743C8—121no—
744C8—121no—
745C2×C3—42no—
746C2×C3—44no—
747C2×C3—82no—
748C2×C3C4×#12011yescharacteristic
749C2×C3#294611yescharacteristic
750C2×C3#295211yescharacteristic
751C2×C3#301011yescharacteristic
752C2×C3#301211yescharacteristic
753C2×C3#311911yescharacteristic
754C2×C3#312511yescharacteristic
755C22—22no—
756C22—24no—
757C22—22no—
758C22—22no—
759C22—42no—
760C22—41no—
761C22—42no—
762C22—41no—
763C22—42no—
764C22—41no—
765C22—42no—
766C22—41no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—42no—
771C22—42no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22#558611yescharacteristic
777C22D3×#12011yescharacteristic
778C22#577011yescharacteristic
779C22#577011yescharacteristic
780C22#577411yescharacteristic
781C22#577511yescharacteristic
782C22C2×D4×Dic311yescharacteristic
783C4—22no—
784C4—24no—
785C4—42no—
786C4—62no—
787C4—62no—
788C4—121no—
789C4—121no—
790C4—122no—
791C4—122no—
792C4—241no—
793C4—241no—
794C4#558611yescharacteristic
795C4#558611yescharacteristic
796C4C2×D4×Dic311yescharacteristic
797C4C2×D4×Dic311yescharacteristic
798C3#2146411yescharacteristic, complemented, Sylow
799C2—42no—
800C2—44no—
801C2—82no—
802C2#8007311yescharacteristic
803C2#8007511yescharacteristic
804C2#8008611yescharacteristic
805C2#8008711yescharacteristic
806C2Dic3×#12011yescharacteristic
807C2#8389911yescharacteristic
808C2#8393011yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
Fitting, prime radicalC2×C3×#449C2
socleC23×C3C22×D4
cosocleC22×C3×C4C24
hypercenterC2×#449D3
hypocenterC3#21464
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. C2×#5827C2semidirect
3. C2×Dic3×SD16C2semidirect
4. C2×#5152C2semidirect
5. #82633C2semidirect
6. #72135C2semidirect
7. #72048C2semidirect
8. #72037C2semidirect
9. #71677C2semidirect
10. #70238C2semidirect
11. #70220C2semidirect
12. #70170C2semidirect
13. Dic3×#102C2semidirect
14. #69928C2semidirect
15. #69907C2semidirect
34. C3×#449C4semidirect
85. C2×C3×#41C2×C4semidirect
99. C2×C3×SD16C2×C4semidirect
102. C2×C3×D8C2×C4semidirect
106. C3×#121C2×C4semidirect
120. Q8×Dic3D4semidirect
128. D4×Dic3D4semidirect
152. C3×#103C2×C4semidirect
153. C3×#102C2×C4semidirect
154. C3×C22⋊C8C2×C4semidirect
186. #449Dic3semidirect
332. C2×#41C2×Dic3semidirect
346. C2×SD16C2×Dic3semidirect
349. C2×D8C2×Dic3semidirect
355. #121C2×Dic3semidirect
403. #103C2×Dic3semidirect
408. #102C2×Dic3semidirect
410. C22⋊C8C2×Dic3semidirect
798. C3#21464semidirect

Maximal subgroups

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

subgroupindex
C2×#58272
C2×C3×#4492
C2×Dic3×SD162
C2×#51522
#826332
#721352
#720482
#720372
#716772
#702382
#702202
#701702
Dic3×#1022
#699282
#699072
#214643