Finite Group Databasebeta

← #10830930

Subgroups — #10830930

Order 768.

1452 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#950C211yesmaximal, characteristic, complemented
2C3×#2407C211yesmaximal, characteristic, complemented
3C2×#5052C211yesmaximal, characteristic, complemented
4C2×#5039C211yesmaximal, characteristic, complemented
5#82402C211yesmaximal, characteristic, complemented
6C2×#5011C211yesmaximal, characteristic, complemented
7#72135C211yesmaximal, characteristic, complemented
8#71699C211yesmaximal, characteristic, complemented
9#71685C211yesmaximal, characteristic, complemented
10#69680C211yesmaximal, characteristic, complemented
11#69678C211yesmaximal, characteristic, complemented
12#69651C211yesmaximal, characteristic, complemented
13#69648C211yesmaximal, characteristic, complemented
14#69522C211yesmaximal, characteristic, complemented
15#69511C211yesmaximal, characteristic, complemented
16#24271—31nomaximal, Sylow
17C22×C3×#41C2211yescharacteristic
18C22×#235C2211yescharacteristic
19C2×C3×C22⋊Q8C2211yescharacteristic
20C2×C3×#121C2211yescharacteristic
21C2×C3×C4×D4C2211yescharacteristic
22C2×#950—24no—
23C2×#950—24no—
24C2×#950—24no—
25C22×#216C2211yescharacteristic
26C22×#215C2211yescharacteristic
27C22×#214C2211yescharacteristic
28C22×#213C2211yescharacteristic
29C2×#930C2211yescharacteristic
30C2×#924C2211yescharacteristic
31C22×#208C2211yescharacteristic
32C23×C3⋊C8C2211yescharacteristic
33C3×#394—21no—
34C3×#392—21no—
35C3×#391C2211yescharacteristic
36C3×#390C2211yescharacteristic
37C3×#386—21no—
38C3×#385—21no—
39C3×#380C2211yescharacteristic
40C2×#835C2211yescharacteristic
41C2×#835C2211yescharacteristic
42#5223—21no—
43C2×#832C2211yescharacteristic
44C2×#832C2211yescharacteristic
45#5212C2211yescharacteristic
46C2×#830C2211yescharacteristic
47C2×#830C2211yescharacteristic
48#5052—24no—
49#5039—24no—
50#5011—24no—
51#4989—21no—
52C2×#810C2211yescharacteristic
53C2×#810C2211yescharacteristic
54C2×#809C2211yescharacteristic
55C2×#809C2211yescharacteristic
56C2×#808C2211yescharacteristic
57C2×#808C2211yescharacteristic
58#4959—21no—
59#4956—21no—
60#4939C2211yescharacteristic
61#4929C2211yescharacteristic
62C2×C4⋊(C3⋊C8)C2211yescharacteristic
63C2×#803C2211yescharacteristic
64#4529C2211yescharacteristic
65#4529C2211yescharacteristic
66C22×#135—31no—
67C2×#470—31no—
68C2×#469—31no—
69C2×#435—31no—
70#2407—31no—
71#2407D311yescharacteristic, complemented
72#2055—31no—
73#2055—31no—
74#2000—31no—
75#2000—31no—
76#1972—31no—
77#1971—31no—
78#1807—31no—
79#1788—31no—
80#1788—31no—
81C2×C3×#41—22no—
82C2×C3×#41—22no—
83C2×C3×#41—22no—
84C2×C3×#41—22no—
85C2×C3×#41—41no—
86C2×C3×#41—41no—
87C22×C3×Q8C2311yescharacteristic
88C22×C3×D4—21no—
89C22×C3×D4—21no—
90C22×C3×D4D411yescharacteristic
91C22×C3×D4C2311yescharacteristic
92C23×C3×C4—21no—
93C23×C3×C4C2311yescharacteristic
94C23×C3×C4C2311yescharacteristic
95C22×#67—21no—
96C22×#67—21no—
97C2×#235—22no—
98C2×#235—22no—
99C2×#235—22no—
100C2×#235—22no—
101C2×#235—41no—
102C2×#235—41no—
103C22×D12C2311yescharacteristic
104C22×C4×D3—21no—
105C22×Dic6C2311yescharacteristic
106C3×C22⋊Q8—22no—
107C3×C22⋊Q8—41no—
108C3×#121—22no—
109C3×#121—41no—
110C3×C4×D4—22no—
111C3×C4×D4—22no—
112C2×C3×C4⋊C4—21no—
113C2×C3×C4⋊C4D411yescharacteristic
114C2×C3×C4⋊C4C2311yescharacteristic
115C2×C3×C4⋊C4C2311yescharacteristic
116C2×C3×C22⋊C4—21no—
117C2×C3×C22⋊C4—21no—
118C2×C3×C22⋊C4—21no—
119C2×C3×C22⋊C4—21no—
120C2×C3×C22⋊C4—21no—
121C2×C3×C22⋊C4D411yescharacteristic
122C2×C3×C22⋊C4D411yescharacteristic
123C2×C3×C42C2311yescharacteristic
124C2×#217—21no—
125C2×#217—21no—
126#950—232no—
127C2×#216—22no—
128C2×#216—22no—
129C2×#216D414yescomplemented
130C2×#215—22no—
131C2×#215—22no—
132C2×#215—22no—
133C2×#214—22no—
134C2×#214—22no—
135C2×#214—22no—
136C2×#213—22no—
137C2×#213—22no—
138C2×#213D414yescomplemented
139#930—22no—
140#930—41no—
141C2×(C2×D3)⋊C4—21no—
142C2×(C2×D3)⋊C4—21no—
143C2×(C2×D3)⋊C4—21no—
144C2×C4⋊Dic3C2311yescharacteristic
145C2×C4⋊Dic3C2311yescharacteristic
146#924—22no—
147#924—41no—
148C2×Dic3⋊C4—21no—
149C2×#208—22no—
150C2×#208—22no—
151C2×#208—22no—
152C22×C3⋊C8—22no—
153C22×C3⋊C8—22no—
154C22×C3⋊C8D414yescomplemented
155C22×C3⋊C8C2311yescharacteristic
156C22×C3⋊C8C2311yescharacteristic
157C22×C3⋊C8C2311yescharacteristic
158C22×C3⋊C8C2311yescharacteristic
159C3×#95—21no—
160C3×#95—21no—
161C3×#95—21no—
162#835—22no—
163#835—41no—
164#832—22no—
165#832—41no—
166C3⋊#95—21no—
167C3⋊#95—21no—
168C3⋊#95—21no—
169#830—22no—
170#830—22no—
171#810—22no—
172#810—41no—
173#809—22no—
174#809—41no—
175#808—22no—
176#808—22no—
177C4⋊(C3⋊C8)—22no—
178#803—22no—
179C22×#41—31no—
180C22×#41C2×D311yescharacteristic
181C2×#135—64no—
182C2×#135—64no—
183C2×#135—64no—
184C22×Q16—31no—
185C22×SD16—31no—
186C22×SD16—31no—
187C22×D8—31no—
188C22×M16—31no—
189C23×C8—31no—
190C2×C22⋊Q8—31no—
191C2×C22⋊Q8C2×D311yescharacteristic
192C2×#121—31no—
193C2×#121C2×D311yescharacteristic
194C2×C4×D4C2×D311yescharacteristic
195#470—64no—
196#469—64no—
197#435—64no—
198C2×#106—31no—
199C2×#106—31no—
200C2×C4⋊C8—31no—
201C2×#103—31no—
202C2×#103—31no—
203C2×#103—31no—
204C2×#103—31no—
205C2×#102—31no—
206C2×#102—31no—
207C2×#102—31no—
208C2×#102—31no—
209C2×C22⋊C8—31no—
210C2×C22⋊C8—31no—
211C2×#97—31no—
212#394—21no—
213#394—61no—
214#392—21no—
215#392—61no—
216#391—31no—
217#391C2×D311yescharacteristic
218#390—31no—
219#390C2×D311yescharacteristic
220#386—21no—
221#386—61no—
222#385—21no—
223#385—61no—
224#380—31no—
225#380C2×D311yescharacteristic
226#340—31no—
227#340—31no—
228C24×C3—21no—
229C24×C3C2×D411yescharacteristic
230C24×C3C2×D411yescharacteristic
231C23×D3—21no—
232C3×#41—28no—
233C3×#41—44no—
234C3×#41—44no—
235C3×#41—44no—
236C2×C3×Q8—21no—
237C2×C3×Q8—21no—
238C2×C3×Q8—21no—
239C2×C3×Q8—21no—
240C2×C3×Q8—21no—
241C2×C3×Q8C2×D412yes—
242C2×C3×D4—22no—
243C2×C3×D4—21no—
244C2×C3×D4—21no—
245C2×C3×D4—21no—
246C2×C3×D4—21no—
247C2×C3×D4—21no—
248C2×C3×D4—41no—
249C2×C3×D4—41no—
250C2×C3×D4—42no—
251C2×C3×D4—42no—
252C2×C3×D4—42no—
253C2×C3×D4—42no—
254C2×C3×D4—42no—
255C2×C3×D4—81no—
256C2×C3×D4C2×D412yes—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—21no—
270C22×C3×C4—42no—
271C22×C3×C4—42no—
272C22×C3×C4—42no—
273C22×C3×C4C2×D412yes—
274C22×C3×C4C2×D411yescharacteristic
275C22×C3×C4C2×D411yescharacteristic
276C22×C3×C4C2×D411yescharacteristic
277C22×C3×C4C2×D411yescharacteristic
278C22×C3×C4#4112yes—
279C22×C3×C4C2411yescharacteristic
280C2×#67—42no—
281C2×#67—42no—
282C2×#67—42no—
283C2×#67—42no—
284C2×#67—42no—
285C2×#67—81no—
286C22×Dic3—21no—
287C22×Dic3—21no—
288C22×Dic3—21no—
289#235—28no—
290#235—44no—
291#235—44no—
292#235—44no—
293C2×D12—21no—
294C2×D12—21no—
295C2×D12—21no—
296C2×D12—21no—
297C2×D12—21no—
298C2×D12C2×D412yes—
299C2×C4×D3—42no—
300C2×C4×D3—42no—
301C2×C4×D3—42no—
302C2×Dic6—21no—
303C2×Dic6—21no—
304C2×Dic6—21no—
305C2×Dic6—21no—
306C2×Dic6—21no—
307C2×Dic6C2×D412yes—
308C3×C4⋊C4—22no—
309C3×C4⋊C4—21no—
310C3×C4⋊C4—21no—
311C3×C4⋊C4—21no—
312C3×C4⋊C4—21no—
313C3×C4⋊C4—42no—
314C3×C22⋊C4—22no—
315C3×C22⋊C4—22no—
316C3×C22⋊C4—42no—
317C3×C22⋊C4—42no—
318C3×C22⋊C4—42no—
319C3×C22⋊C4—81no—
320C3×C22⋊C4—81no—
321C3×C42—21no—
322C3×C42—21no—
323#217—42no—
324#217—81no—
325#216—28no—
326#215—28no—
327#214—28no—
328#213—28no—
329(C2×D3)⋊C4—42no—
330(C2×D3)⋊C4—42no—
331(C2×D3)⋊C4—81no—
332C4⋊Dic3—21no—
333C4⋊Dic3—21no—
334C4⋊Dic3—21no—
335C4⋊Dic3—21no—
336Dic3⋊C4—42no—
337#208—44no—
338C2×C3⋊C8—21no—
339C2×C3⋊C8—21no—
340C2×C3⋊C8—28no—
341C2×C3⋊C8—21no—
342C2×C3⋊C8—21no—
343C2×C3⋊C8—21no—
344C2×C3⋊C8—21no—
345C2×C3⋊C8—21no—
346C2×C3⋊C8—21no—
347C2×C3⋊C8C2×D412yes—
348C2×C3⋊C8C2×D412yes—
349C2×C3⋊C8C2×D412yes—
350C2×C3⋊C8C2×D412yes—
351C2×#41—22no—
352C2×#41—22no—
353C2×#41—22no—
354C2×#41—22no—
355C2×#41—41no—
356C2×#41—41no—
357C2×#41—62no—
358C2×#41—62no—
359C2×#41—62no—
360C2×#41—62no—
361C2×#41—121no—
362C2×#41—121no—
363C22×Q8—31no—
364C22×Q8C22×D311yescharacteristic
365C22×D4—21no—
366C22×D4—21no—
367C22×D4—31no—
368C22×D4—61no—
369C22×D4—61no—
370C22×D4#6711yescharacteristic
371C22×D4C22×D311yescharacteristic
372C23×C4—21no—
373C23×C4—61no—
374C23×C4C22×D311yescharacteristic
375C23×C4C22×D311yescharacteristic
376#135—632no—
377C2×Q16—34no—
378C2×Q16—62no—
379C2×Q16—62no—
380C2×SD16—62no—
381C2×SD16—62no—
382C2×SD16—62no—
383C2×SD16—62no—
384C2×SD16—62no—
385C2×SD16—62no—
386C2×D8—34no—
387C2×D8—62no—
388C2×D8—62no—
389C2×M16—62no—
390C2×M16—62no—
391C2×M16—62no—
392C22×C8—31no—
393C22×C8—34no—
394C22×C8—31no—
395C22×C8—31no—
396C22×C8—31no—
397C22×C8—62no—
398C22×C8—62no—
399C22⋊Q8—22no—
400C22⋊Q8—41no—
401C22⋊Q8—62no—
402C22⋊Q8—121no—
403#121—22no—
404#121—41no—
405#121—62no—
406#121—121no—
407C4×D4—22no—
408C4×D4—22no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—31no—
411C2×C4⋊C4—31no—
412C2×C4⋊C4—61no—
413C2×C4⋊C4#6711yescharacteristic
414C2×C4⋊C4C22×D311yescharacteristic
415C2×C4⋊C4C22×D311yescharacteristic
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—61no—
422C2×C22⋊C4—61no—
423C2×C22⋊C4—61no—
424C2×C22⋊C4—61no—
425C2×C22⋊C4—61no—
426C2×C22⋊C4#6711yescharacteristic
427C2×C22⋊C4#6711yescharacteristic
428C2×C42C22×D311yescharacteristic
429#106—62no—
430#106—62no—
431C4⋊C8—62no—
432#103—62no—
433#103—62no—
434#103—121no—
435#103—121no—
436#102—62no—
437#102—62no—
438#102—121no—
439#102—121no—
440C22⋊C8—62no—
441C22⋊C8—62no—
442#97—62no—
443#95—21no—
444#95—21no—
445#95—21no—
446#95—61no—
447#95—61no—
448#95—61no—
449C23×C3—21no—
450C23×C3—21no—
451C23×C3—21no—
452C23×C3—21no—
453C23×C3—21no—
454C23×C3—21no—
455C23×C3—21no—
456C23×C3—21no—
457C23×C3—22no—
458C23×C3—21no—
459C23×C3—21no—
460C23×C3—21no—
461C23×C3—21no—
462C23×C3—21no—
463C23×C3—41no—
464C23×C3—41no—
465C23×C3—41no—
466C23×C3—41no—
467C23×C3—41no—
468C23×C3—41no—
469C23×C3#12112yes—
470C23×C3C22×D411yescharacteristic
471C22×D3—22no—
472C22×D3—41no—
473C22×D3—41no—
474C22×D3—41no—
475C22×D3—41no—
476C22×D3—41no—
477C22×D3—41no—
478C3×Q8—22no—
479C3×Q8—22no—
480C3×Q8—41no—
481C3×Q8—41no—
482C3×D4—22no—
483C3×D4—22no—
484C3×D4—44no—
485C3×D4—48no—
486C3×D4—41no—
487C3×D4—41no—
488C3×D4—84no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—22no—
492C2×C3×C4—22no—
493C2×C3×C4—22no—
494C2×C3×C4—22no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—22no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—48no—
506C2×C3×C4—41no—
507C2×C3×C4—41no—
508C2×C3×C4—41no—
509C2×C3×C4—41no—
510C2×C3×C4—41no—
511C2×C3×C4—41no—
512C2×C3×C4—41no—
513C2×C3×C4—41no—
514C2×C3×C4—41no—
515C2×C3×C4—41no—
516C2×C3×C4—41no—
517C2×C3×C4—41no—
518C2×C3×C4#12112yes—
519C2×C3×C4C22×D411yescharacteristic
520C2×C3×C4C22×D411yescharacteristic
521C2×C3×C4C22×D411yescharacteristic
522C2×C3×C4C2×#4111yescharacteristic
523C2×C3×C4H(5,𝔽2)11yescharacteristic
524C2×C3×C4H(5,𝔽2)11yescharacteristic
525#67—48no—
526#67—84no—
527C2×Dic3—22no—
528C2×Dic3—41no—
529C2×Dic3—41no—
530C2×Dic3—41no—
531C2×Dic3—41no—
532C2×Dic3—41no—
533C2×Dic3—41no—
534C2×Dic3—41no—
535C2×Dic3—41no—
536D12—22no—
537D12—22no—
538D12—41no—
539D12—41no—
540C4×D3—48no—
541Dic6—22no—
542Dic6—22no—
543Dic6—41no—
544Dic6—41no—
545C3⋊C8—22no—
546C3⋊C8—41no—
547C3⋊C8—41no—
548C3⋊C8#12014yes—
549C24—21no—
550C24—61no—
551C24C2×#6711yescharacteristic
552C24C2×#6711yescharacteristic
553#41—28no—
554#41—44no—
555#41—44no—
556#41—44no—
557#41—68no—
558#41—124no—
559#41—124no—
560#41—124no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—32no—
567C2×Q8—61no—
568C2×Q8—61no—
569C2×Q8—61no—
570C2×Q8—61no—
571C2×Q8—61no—
572C2×Q8D3×D412yes—
573C2×D4—22no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—32no—
580C2×D4—41no—
581C2×D4—41no—
582C2×D4—42no—
583C2×D4—42no—
584C2×D4—42no—
585C2×D4—42no—
586C2×D4—42no—
587C2×D4—61no—
588C2×D4—61no—
589C2×D4—61no—
590C2×D4—61no—
591C2×D4—61no—
592C2×D4—81no—
593C2×D4—122no—
594C2×D4—122no—
595C2×D4—122no—
596C2×D4—122no—
597C2×D4—122no—
598C2×D4—241no—
599C2×D4D3×D412yes—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—42no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4—61no—
617C22×C4—61no—
618C22×C4—61no—
619C22×C4—122no—
620C22×C4—122no—
621C22×C4—122no—
622C22×C4D3×D412yes—
623C22×C4#23712yes—
624C22×C4C2×#6711yescharacteristic
625C22×C4C2×#6711yescharacteristic
626C22×C4C2×#6711yescharacteristic
627C22×C4C2×#6711yescharacteristic
628C22×C4C23×D311yescharacteristic
629Q16—68no—
630SD16—68no—
631SD16—68no—
632D8—68no—
633M16—124no—
634C2×C8—32no—
635C2×C8—32no—
636C2×C8—32no—
637C2×C8—32no—
638C2×C8—68no—
639C2×C8—61no—
640C2×C8—61no—
641C2×C8—61no—
642C2×C8—61no—
643C2×C8—61no—
644C2×C8—61no—
645C2×C8—61no—
646C2×C8—61no—
647C4⋊C4—22no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—42no—
653C4⋊C4—61no—
654C4⋊C4—61no—
655C4⋊C4—61no—
656C4⋊C4—61no—
657C4⋊C4—122no—
658C22⋊C4—22no—
659C22⋊C4—22no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—81no—
664C22⋊C4—81no—
665C22⋊C4—122no—
666C22⋊C4—122no—
667C22⋊C4—122no—
668C22⋊C4—241no—
669C22⋊C4—241no—
670C42—21no—
671C42—21no—
672C22×C3—22no—
673C22×C3—22no—
674C22×C3—22no—
675C22×C3—41no—
676C22×C3—41no—
677C22×C3—41no—
678C22×C3—41no—
679C22×C3—42no—
680C22×C3—41no—
681C22×C3—41no—
682C22×C3—41no—
683C22×C3—42no—
684C22×C3—42no—
685C22×C3—41no—
686C22×C3—41no—
687C22×C3—41no—
688C22×C3—41no—
689C22×C3—81no—
690C22×C3—81no—
691C22×C3—81no—
692C22×C3—81no—
693C22×C3C2×#12111yescharacteristic
694C22×C3D4211yescharacteristic
695C22×C3D4211yescharacteristic
696C22×C3#57511yescharacteristic
697C22×C3#57511yescharacteristic
698C22×C3#57711yescharacteristic
699C22×C3#57711yescharacteristic
700C2×D3—42no—
701C2×D3—42no—
702C2×D3—42no—
703C2×D3—81no—
704C2×D3—81no—
705C2×D3—81no—
706C2×D3—81no—
707C3×C4—22no—
708C3×C4—41no—
709C3×C4—42no—
710C3×C4—41no—
711C3×C4—41no—
712C3×C4—81no—
713C3×C4—81no—
714C3×C4C2×#12011yescharacteristic
715C3×C4#53511yescharacteristic
716C3×C4#54611yescharacteristic
717C3×C4#54611yescharacteristic
718Dic3—42no—
719Dic3—81no—
720Dic3—81no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—22no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—62no—
742C23—121no—
743C23—121no—
744C23—121no—
745C23—121no—
746C23—121no—
747C23—121no—
748C23#93912yes—
749C23C22×#6711yescharacteristic
750Q8—22no—
751Q8—22no—
752Q8—41no—
753Q8—41no—
754Q8—62no—
755Q8—62no—
756Q8—121no—
757Q8—121no—
758D4—22no—
759D4—22no—
760D4—44no—
761D4—48no—
762D4—41no—
763D4—41no—
764D4—62no—
765D4—62no—
766D4—84no—
767D4—128no—
768D4—121no—
769D4—121no—
770D4—244no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—21no—
778C2×C4—22no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—48no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—62no—
801C2×C4—128no—
802C2×C4—121no—
803C2×C4—121no—
804C2×C4—121no—
805C2×C4—121no—
806C2×C4—121no—
807C2×C4—121no—
808C2×C4—121no—
809C2×C4—121no—
810C2×C4#93912yes—
811C2×C4C2×D3×D411yescharacteristic
812C2×C4C2×D3×D411yescharacteristic
813C2×C4C2×D3×D411yescharacteristic
814C2×C4C2×#23711yescharacteristic
815C2×C4#100411yescharacteristic
816C2×C4#100411yescharacteristic
817C8—34no—
818C8—62no—
819C8—121no—
820C8—121no—
821C2×C3—42no—
822C2×C3—81no—
823C2×C3—82no—
824C2×C3#240811yescharacteristic
825C2×C3#305411yescharacteristic
826C2×C3#306011yescharacteristic
827C2×C3#326711yescharacteristic
828C2×C3#326711yescharacteristic
829C2×C3#327111yescharacteristic
830C2×C3#327111yescharacteristic
831D3—82no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—42no—
841C22—41no—
842C22—42no—
843C22—41no—
844C22—41no—
845C22—42no—
846C22—41no—
847C22—41no—
848C22—41no—
849C22—81no—
850C22—81no—
851C22—81no—
852C22—81no—
853C22—122no—
854C22—122no—
855C22—122no—
856C22—241no—
857C22—241no—
858C22—241no—
859C22—241no—
860C22D4×#6711yescharacteristic
861C22D4×#6711yescharacteristic
862C22C2×#93911yescharacteristic
863C22#582211yescharacteristic
864C22#582211yescharacteristic
865C22#583611yescharacteristic
866C22#583711yescharacteristic
867C4—22no—
868C4—41no—
869C4—42no—
870C4—41no—
871C4—41no—
872C4—81no—
873C4—81no—
874C4—122no—
875C4—241no—
876C4—241no—
877C4D3×#12011yescharacteristic
878C4#559111yescharacteristic
879C4#559111yescharacteristic
880C4#559211yescharacteristic
881C3#2427111yescharacteristic, complemented, Sylow
882C2—42no—
883C2—81no—
884C2—82no—
885C2—242no—
886C2#8258211yescharacteristic
887C2#8292311yescharacteristic
888C2#8342011yescharacteristic
889C2#8350311yescharacteristic
890C2#8352211yescharacteristic
891C2#8354711yescharacteristic
892C2#8358311yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2407C2
socleC23×C3C22×D4
hypercenter#2407D3
hypocenterC3#24271
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2407

Complements

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

NH ≅ G/Ntype
1. C22×#950C2semidirect
2. C3×#2407C2semidirect
3. C2×#5052C2semidirect
4. C2×#5039C2semidirect
5. #82402C2semidirect
6. C2×#5011C2semidirect
7. #72135C2semidirect
8. #71699C2semidirect
9. #71685C2semidirect
10. #69680C2semidirect
11. #69678C2semidirect
12. #69651C2semidirect
13. #69648C2semidirect
14. #69522C2semidirect
15. #69511C2semidirect
71. #2407D3semidirect
129. C2×#216D4semidirect
138. C2×#213D4semidirect
154. C22×C3⋊C8D4semidirect
881. C3#24271semidirect

Maximal subgroups

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

subgroupindex
C22×#9502
C3×#24072
C2×#50522
C2×#50392
#824022
C2×#50112
#721352
#716992
#716852
#696802
#696782
#696512
#696482
#695222
#695112
#242713