Finite Group Databasebeta

← #10830650

Subgroups — #10830650

Order 768.

1424 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5552C211yesmaximal, characteristic
2C3×#2536C211yesmaximal, characteristic, complemented
3C2×#5050C211yesmaximal, characteristic, complemented
4C2×#5047C211yesmaximal, characteristic, complemented
5C2×#5028C211yesmaximal, characteristic, complemented
6C2×C4×#216C211yesmaximal, characteristic, complemented
7#71700C211yesmaximal, characteristic, complemented
8#71699C211yesmaximal, characteristic, complemented
9#71614C211yesmaximal, characteristic, complemented
10#69559C211yesmaximal, characteristic, complemented
11#69551C211yesmaximal, characteristic, complemented
12#69527C211yesmaximal, characteristic, complemented
13#69525C211yesmaximal, characteristic, complemented
14#69523C211yesmaximal, characteristic, complemented
15#69522C211yesmaximal, characteristic, complemented
16#24246—31nomaximal, Sylow
17C22×#235C2211yescharacteristic
18C23×Dic6C2211yescharacteristic
19C2×C3×C22⋊Q8C2211yescharacteristic
20C2×C3×C22⋊Q8C2211yescharacteristic
21C2×C3×C4×Q8C2211yescharacteristic
22C2×C3×C4×D4C2211yescharacteristic
23C22×#216C2211yescharacteristic
24C22×#216C2211yescharacteristic
25C22×#215C2211yescharacteristic
26C2×#939—21no—
27C2×#930C2211yescharacteristic
28C2×#924C2211yescharacteristic
29#5552—24no—
30#5552—24no—
31C2×#896—21no—
32C2×#885—21no—
33C2×#67⋊C4—21no—
34C2×#875C2211yescharacteristic
35C2×C4×Dic6C2211yescharacteristic
36C3×#398—21no—
37C3×#394—21no—
38C3×#388—21no—
39C3×#388—21no—
40C3×#382C2211yescharacteristic
41C3×#380C2211yescharacteristic
42C3×#380C2211yescharacteristic
43C2×#835C2211yescharacteristic
44C2×#830C2211yescharacteristic
45C2×#830C2211yescharacteristic
46C2×#830C2211yescharacteristic
47C2×#830C2211yescharacteristic
48#5050—24no—
49#5047—24no—
50C4×#216—24no—
51#5028—24no—
52C2×#810C2211yescharacteristic
53C2×#810C2211yescharacteristic
54C2×#810C2211yescharacteristic
55C2×#810C2211yescharacteristic
56C2×#810C2211yescharacteristic
57C2×#810C2211yescharacteristic
58C2×#809C2211yescharacteristic
59C2×#809C2211yescharacteristic
60C2×#809C2211yescharacteristic
61C2×#807C2211yescharacteristic
62C2×C4⋊(C3⋊C8)C2211yescharacteristic
63C2×C4×C3⋊C8C2211yescharacteristic
64#4529C2211yescharacteristic
65#4529C2211yescharacteristic
66C2×#548—31no—
67C2×#464—31no—
68C2×#452—31no—
69C2×#451—31no—
70C2×C4×Q16—31no—
71#2536D311yescharacteristic, complemented
72#2036—31no—
73#2033—31no—
74#2001—31no—
75#2000—31no—
76#1958—31no—
77#1954—31no—
78#1805—31no—
79#1788—31no—
80#1787—31no—
81C22×C3×Q8C2311yescharacteristic
82C22×C3×D4D411yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C22×#67—21no—
86C22×#67—21no—
87C23×Dic3—21no—
88C2×#235—22no—
89C2×#235—22no—
90C2×#235—22no—
91C2×#235—22no—
92C2×#235—41no—
93C2×#235—41no—
94C22×D12C2311yescharacteristic
95C22×C4×D3—21no—
96C22×Dic6—21no—
97C22×Dic6—22no—
98C22×Dic6—22no—
99C22×Dic6—22no—
100C22×Dic6—22no—
101C22×Dic6—41no—
102C22×Dic6—41no—
103C22×Dic6C2311yescharacteristic
104C22×Dic6C2311yescharacteristic
105C3×C22⋊Q8—22no—
106C3×C22⋊Q8—22no—
107C3×C22⋊Q8—41no—
108C3×C22⋊Q8—41no—
109C3×C4×Q8—22no—
110C3×C4×Q8—22no—
111C3×C4×D4—22no—
112C3×C4×D4—22no—
113C2×C3×C4⋊C4—21no—
114C2×C3×C4⋊C4—21no—
115C2×C3×C4⋊C4—21no—
116C2×C3×C4⋊C4D411yescharacteristic
117C2×C3×C4⋊C4C2311yescharacteristic
118C2×C3×C4⋊C4C2311yescharacteristic
119C2×C3×C4⋊C4C2311yescharacteristic
120C2×C3×C22⋊C4—21no—
121C2×C3×C22⋊C4—21no—
122C2×C3×C22⋊C4—21no—
123C2×C3×C22⋊C4—21no—
124C2×C3×C22⋊C4D411yescharacteristic
125C2×C3×C22⋊C4D411yescharacteristic
126C2×C3×C42—21no—
127C2×C3×C42C2311yescharacteristic
128C2×#217—21no—
129C2×#216—22no—
130C2×#216—22no—
131C2×#216—22no—
132C2×#216—22no—
133C2×#216—41no—
134C2×#216D414yescomplemented
135C2×#215—22no—
136C2×#215—22no—
137C2×#215—41no—
138#939—28no—
139#930—22no—
140#930—22no—
141C2×(C2×D3)⋊C4—21no—
142C2×(C2×D3)⋊C4—21no—
143C2×(C2×D3)⋊C4—21no—
144C2×C4⋊Dic3C2311yescharacteristic
145#924—22no—
146#924—22no—
147C2×Dic3⋊C4—21no—
148C2×Dic3⋊C4—21no—
149C2×C4×Dic3—21no—
150C22×C3⋊C8C2311yescharacteristic
151C22×C3⋊C8C2311yescharacteristic
152C22×C3⋊C8C2311yescharacteristic
153C22×C3⋊C8C2311yescharacteristic
154#896—28no—
155#885—28no—
156#67⋊C4—28no—
157#875—22no—
158#875D414yes—
159C4×Dic6—22no—
160C4×Dic6D414yes—
161C3×#95—21no—
162C3×#95—21no—
163C3×#95—21no—
164C3×#95—21no—
165#835—22no—
166#830—22no—
167#830—22no—
168#830—41no—
169#830—41no—
170#810—22no—
171#810—22no—
172#810—22no—
173#810—22no—
174#810—22no—
175#810—41no—
176#809—22no—
177#809—22no—
178#809—41no—
179#807—22no—
180C4⋊(C3⋊C8)—22no—
181C4×C3⋊C8—22no—
182C22×#41—31no—
183C23×Q8—31no—
184C22×Q16—31no—
185C22×Q16—31no—
186C22×SD16—31no—
187#548—64no—
188#548—64no—
189C2×#124—31no—
190C2×#124—61no—
191C2×C22⋊Q8—31no—
192C2×C22⋊Q8—61no—
193C2×C22⋊Q8C2×D311yescharacteristic
194C2×C22⋊Q8C2×D311yescharacteristic
195C2×#121—31no—
196C2×#121—61no—
197C2×C4×Q8—31no—
198C2×C4×Q8C2×D311yescharacteristic
199C2×C4×D4—61no—
200C2×C4×D4C2×D311yescharacteristic
201#464—64no—
202#452—64no—
203#451—64no—
204C4×Q16—64no—
205C2×#107—31no—
206C2×C4⋊C8—31no—
207C2×#103—31no—
208C2×#103—31no—
209C2×#103—31no—
210C2×#103—31no—
211C2×#103—31no—
212C2×#103—31no—
213C2×#103—31no—
214C2×#102—31no—
215C2×#102—31no—
216C2×#102—31no—
217C2×C22⋊C8—31no—
218C2×C22⋊C8—31no—
219C2×C22⋊C8—31no—
220C2×C22⋊C8—31no—
221C2×C4×C8—31no—
222#398—21no—
223#394—21no—
224#388—21no—
225#388—21no—
226#382C2×D311yescharacteristic
227#380C2×D311yescharacteristic
228#380C2×D311yescharacteristic
229#340—31no—
230#340—31no—
231C24×C3C2×D411yescharacteristic
232C24×C3C2×D411yescharacteristic
233C23×D3—21no—
234C2×C3×Q8—21no—
235C2×C3×Q8—21no—
236C2×C3×Q8—21no—
237C2×C3×Q8—21no—
238C2×C3×Q8—21no—
239C2×C3×Q8C2×D412yes—
240C2×C3×D4—22no—
241C2×C3×D4—22no—
242C2×C3×D4—41no—
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×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4C2×D411yescharacteristic
260C22×C3×C4C2×D411yescharacteristic
261C22×C3×C4C2×D411yescharacteristic
262C22×C3×C4C2×D411yescharacteristic
263C22×C3×C4C2411yescharacteristic
264C2×#67—24no—
265C2×#67—24no—
266C2×#67—42no—
267C2×#67—42no—
268C2×#67—42no—
269C2×#67—42no—
270C22×Dic3—21no—
271C22×Dic3—24no—
272C22×Dic3—21no—
273C22×Dic3—21no—
274C22×Dic3—42no—
275C22×Dic3—42no—
276#235—44no—
277#235—44no—
278#235—44no—
279#235—44no—
280C2×D12—21no—
281C2×D12—21no—
282C2×D12—21no—
283C2×D12—21no—
284C2×D12—21no—
285C2×D12C2×D412yes—
286C2×C4×D3—24no—
287C2×C4×D3—42no—
288C2×C4×D3—42no—
289C2×Dic6—21no—
290C2×Dic6—21no—
291C2×Dic6—21no—
292C2×Dic6—21no—
293C2×Dic6—21no—
294C2×Dic6—21no—
295C2×Dic6—21no—
296C2×Dic6—24no—
297C2×Dic6—21no—
298C2×Dic6—44no—
299C2×Dic6—44no—
300C2×Dic6—44no—
301C2×Dic6—42no—
302C2×Dic6—42no—
303C2×Dic6—44no—
304C2×Dic6C2×D412yes—
305C2×Dic6C2×D412yes—
306C2×Dic6C2×D412yes—
307C2×Dic6#4112yes—
308C3×C4⋊C4—22no—
309C3×C4⋊C4—21no—
310C3×C4⋊C4—21no—
311C3×C4⋊C4—21no—
312C3×C4⋊C4—21no—
313C3×C4⋊C4—21no—
314C3×C4⋊C4—21no—
315C3×C4⋊C4—42no—
316C3×C4⋊C4—42no—
317C3×C4⋊C4—42no—
318C3×C22⋊C4—22no—
319C3×C22⋊C4—22no—
320C3×C22⋊C4—42no—
321C3×C22⋊C4—42no—
322C3×C22⋊C4—42no—
323C3×C22⋊C4—42no—
324C3×C42—42no—
325C3×C42C2×D412yes—
326C3×C42C2×D412yes—
327#217—24no—
328#216—28no—
329#216—44no—
330#215—44no—
331(C2×D3)⋊C4—24no—
332(C2×D3)⋊C4—24no—
333(C2×D3)⋊C4—24no—
334C4⋊Dic3—21no—
335C4⋊Dic3C2×D412yes—
336Dic3⋊C4—24no—
337Dic3⋊C4—24no—
338C4×Dic3—24no—
339C2×C3⋊C8—21no—
340C2×C3⋊C8—21no—
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⋊C8—21no—
348C2×C3⋊C8—21no—
349C2×C3⋊C8—21no—
350C2×C3⋊C8C2×D412yes—
351C2×#41—62no—
352C2×#41—62no—
353C2×#41—62no—
354C2×#41—62no—
355C2×#41—121no—
356C2×#41—121no—
357C22×Q8—31no—
358C22×Q8—31no—
359C22×Q8—62no—
360C22×Q8—62no—
361C22×Q8—62no—
362C22×Q8—62no—
363C22×Q8—61no—
364C22×Q8—121no—
365C22×Q8—121no—
366C22×Q8C22×D311yescharacteristic
367C22×D4—31no—
368C22×D4—61no—
369C22×D4—61no—
370C22×D4#6711yescharacteristic
371C23×C4—61no—
372C23×C4—61no—
373C23×C4C22×D311yescharacteristic
374C23×C4C22×D311yescharacteristic
375C2×Q16—34no—
376C2×Q16—62no—
377C2×Q16—62no—
378C2×Q16—62no—
379C2×Q16—62no—
380C2×Q16—121no—
381C2×SD16—62no—
382C2×SD16—62no—
383C2×SD16—121no—
384C22×C8—31no—
385C22×C8—31no—
386C22×C8—31no—
387C22×C8—31no—
388#124—34no—
389#124—68no—
390#124—62no—
391C22⋊Q8—22no—
392C22⋊Q8—22no—
393C22⋊Q8—41no—
394C22⋊Q8—41no—
395C22⋊Q8—68no—
396C22⋊Q8—62no—
397C22⋊Q8—62no—
398#121—62no—
399#121—62no—
400#121—68no—
401C4×Q8—22no—
402C4×Q8—22no—
403C4×Q8—34no—
404C4×Q8—62no—
405C4×D4—22no—
406C4×D4—22no—
407C4×D4—68no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—31no—
412C2×C4⋊C4—61no—
413C2×C4⋊C4—61no—
414C2×C4⋊C4#6711yescharacteristic
415C2×C4⋊C4C22×D311yescharacteristic
416C2×C4⋊C4C22×D311yescharacteristic
417C2×C4⋊C4C22×D311yescharacteristic
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
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×C42—21no—
429C2×C42—61no—
430C2×C42C22×D311yescharacteristic
431#107—62no—
432C4⋊C8—62no—
433#103—62no—
434#103—62no—
435#103—62no—
436#103—62no—
437#103—62no—
438#103—62no—
439#103—121no—
440#102—62no—
441#102—62no—
442#102—121no—
443C22⋊C8—62no—
444C22⋊C8—62no—
445C22⋊C8—121no—
446C22⋊C8—121no—
447C4×C8—62no—
448#95—21no—
449#95—21no—
450#95—21no—
451#95—21no—
452C23×C3—21no—
453C23×C3—21no—
454C23×C3—21no—
455C23×C3—21no—
456C23×C3—21no—
457C23×C3—21no—
458C23×C3—21no—
459C23×C3—21no—
460C23×C3—21no—
461C23×C3—21no—
462C23×C3—21no—
463C23×C3—21no—
464C23×C3—21no—
465C23×C3#13512yes—
466C23×C3C22×D411yescharacteristic
467C22×D3—22no—
468C22×D3—41no—
469C22×D3—41no—
470C22×D3—41no—
471C22×D3—41no—
472C22×D3—41no—
473C22×D3—41no—
474C3×Q8—22no—
475C3×Q8—22no—
476C3×Q8—41no—
477C3×Q8—41no—
478C3×D4—44no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—22no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—41no—
491C2×C3×C4—41no—
492C2×C3×C4—41no—
493C2×C3×C4—41no—
494C2×C3×C4—41no—
495C2×C3×C4—41no—
496C2×C3×C4—41no—
497C2×C3×C4—41no—
498C2×C3×C4—41no—
499C2×C3×C4—41no—
500C2×C3×C4—41no—
501C2×C3×C4—41no—
502C2×C3×C4—41no—
503C2×C3×C4—41no—
504C2×C3×C4—41no—
505C2×C3×C4—41no—
506C2×C3×C4—41no—
507C2×C3×C4—41no—
508C2×C3×C4—41no—
509C2×C3×C4#12012yes—
510C2×C3×C4#12012yes—
511C2×C3×C4C22×D411yescharacteristic
512C2×C3×C4C22×D411yescharacteristic
513C2×C3×C4C22×D411yescharacteristic
514C2×C3×C4C2×#4111yescharacteristic
515C2×C3×C4H(5,𝔽2)11yescharacteristic
516C2×C3×C4H(5,𝔽2)11yescharacteristic
517#67—48no—
518#67—48no—
519C2×Dic3—22no—
520C2×Dic3—22no—
521C2×Dic3—22no—
522C2×Dic3—22no—
523C2×Dic3—22no—
524C2×Dic3—48no—
525C2×Dic3—41no—
526C2×Dic3—41no—
527C2×Dic3—41no—
528C2×Dic3—41no—
529D12—22no—
530D12—22no—
531D12—41no—
532D12—41no—
533C4×D3—48no—
534Dic6—22no—
535Dic6—22no—
536Dic6—22no—
537Dic6—22no—
538Dic6—22no—
539Dic6—48no—
540Dic6—41no—
541Dic6—41no—
542Dic6#12114yes—
543C3⋊C8—22no—
544C3⋊C8—41no—
545C3⋊C8—41no—
546C3⋊C8—41no—
547C24—61no—
548C24C2×#6711yescharacteristic
549C24C2×#6711yescharacteristic
550#41—124no—
551#41—124no—
552#41—124no—
553#41—124no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—32no—
560C2×Q8—32no—
561C2×Q8—32no—
562C2×Q8—32no—
563C2×Q8—64no—
564C2×Q8—61no—
565C2×Q8—61no—
566C2×Q8—61no—
567C2×Q8—61no—
568C2×Q8—61no—
569C2×Q8—61no—
570C2×Q8—61no—
571C2×Q8—61no—
572C2×Q8—122no—
573C2×Q8—122no—
574C2×Q8—124no—
575C2×Q8—124no—
576C2×Q8—124no—
577C2×Q8—124no—
578C2×Q8D3×D412yes—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—32no—
582C2×D4—41no—
583C2×D4—64no—
584C2×D4—64no—
585C2×D4—61no—
586C2×D4—61no—
587C2×D4—61no—
588C2×D4—61no—
589C2×D4—61no—
590C2×D4—122no—
591C2×D4—122no—
592C2×D4—122no—
593C2×D4—122no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
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—64no—
611C22×C4—61no—
612C22×C4—64no—
613C22×C4—61no—
614C22×C4—61no—
615C22×C4—122no—
616C22×C4—122no—
617C22×C4—122no—
618C22×C4—122no—
619C22×C4C2×#6711yescharacteristic
620C22×C4C2×#6711yescharacteristic
621C22×C4C2×#6711yescharacteristic
622C22×C4C2×#6711yescharacteristic
623C22×C4C23×D311yescharacteristic
624Q16—68no—
625Q16—124no—
626SD16—124no—
627C2×C8—32no—
628C2×C8—61no—
629C2×C8—61no—
630C2×C8—61no—
631C2×C8—61no—
632C2×C8—61no—
633C2×C8—61no—
634C2×C8—61no—
635C2×C8—61no—
636C2×C8—61no—
637C2×C8—61no—
638C2×C8—61no—
639C4⋊C4—22no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—32no—
647C4⋊C4—42no—
648C4⋊C4—42no—
649C4⋊C4—42no—
650C4⋊C4—64no—
651C4⋊C4—64no—
652C4⋊C4—61no—
653C22⋊C4—22no—
654C22⋊C4—22no—
655C22⋊C4—42no—
656C22⋊C4—42no—
657C22⋊C4—42no—
658C22⋊C4—42no—
659C22⋊C4—64no—
660C22⋊C4—64no—
661C22⋊C4—64no—
662C22⋊C4—64no—
663C42—42no—
664C42—64no—
665C42D3×D412yes—
666C42D3×D412yes—
667C22×C3—22no—
668C22×C3—22no—
669C22×C3—22no—
670C22×C3—41no—
671C22×C3—41no—
672C22×C3—41no—
673C22×C3—41no—
674C22×C3—41no—
675C22×C3—41no—
676C22×C3—41no—
677C22×C3—41no—
678C22×C3—41no—
679C22×C3—41no—
680C22×C3—41no—
681C22×C3C2×#12011yescharacteristic
682C22×C3D4211yescharacteristic
683C22×C3#54611yescharacteristic
684C22×C3C2×#13511yescharacteristic
685C22×C3#57511yescharacteristic
686C22×C3#57811yescharacteristic
687C22×C3#57811yescharacteristic
688C2×D3—42no—
689C2×D3—42no—
690C2×D3—42no—
691C2×D3—81no—
692C2×D3—81no—
693C2×D3—81no—
694C2×D3—81no—
695C3×C4—22no—
696C3×C4—22no—
697C3×C4—41no—
698C3×C4—41no—
699C3×C4—42no—
700C3×C4—81no—
701C3×C4—81no—
702C3×C4—81no—
703C3×C4C2×#12111yescharacteristic
704C3×C4#53511yescharacteristic
705C3×C4D4211yescharacteristic
706C3×C4#54611yescharacteristic
707Dic3—24no—
708Dic3—42no—
709Dic3—42no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—62no—
724C23—121no—
725C23—121no—
726C23—121no—
727C23—121no—
728C23—121no—
729C23—121no—
730C23#95012yes—
731C23C22×#6711yescharacteristic
732Q8—22no—
733Q8—22no—
734Q8—34no—
735Q8—41no—
736Q8—41no—
737Q8—62no—
738Q8—62no—
739Q8—62no—
740Q8—62no—
741Q8—62no—
742Q8—128no—
743Q8—121no—
744Q8—121no—
745D4—44no—
746D4—62no—
747D4—62no—
748D4—128no—
749D4—128no—
750D4—121no—
751D4—121no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—22no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—62no—
783C2×C4—62no—
784C2×C4—62no—
785C2×C4—62no—
786C2×C4—62no—
787C2×C4—128no—
788C2×C4—128no—
789C2×C4—121no—
790C2×C4—121no—
791C2×C4—121no—
792C2×C4—121no—
793C2×C4#93712yes—
794C2×C4#93712yes—
795C2×C4C2×D3×D411yescharacteristic
796C2×C4C2×D3×D411yescharacteristic
797C2×C4C2×D3×D411yescharacteristic
798C2×C4#100411yescharacteristic
799C2×C4D3×#4111yescharacteristic
800C2×C4#100911yescharacteristic
801C8—62no—
802C8—121no—
803C8—121no—
804C8—121no—
805C2×C3—42no—
806C2×C3—81no—
807C2×C3#240811yescharacteristic
808C2×C3#300211yescharacteristic
809C2×C3#301111yescharacteristic
810C2×C3#327711yescharacteristic
811C2×C3#328511yescharacteristic
812C2×C3#330011yescharacteristic
813C2×C3#332711yescharacteristic
814D3—82no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—122no—
830C22—122no—
831C22—122no—
832C22—241no—
833C22—241no—
834C22—241no—
835C22—241no—
836C22C2×#93711yescharacteristic
837C22D4×#6711yescharacteristic
838C22C2×#95011yescharacteristic
839C22#582211yescharacteristic
840C22#582911yescharacteristic
841C22#583811yescharacteristic
842C22#583811yescharacteristic
843C4—22no—
844C4—22no—
845C4—41no—
846C4—41no—
847C4—42no—
848C4—64no—
849C4—81no—
850C4—81no—
851C4—81no—
852C4—122no—
853C4—122no—
854C4D3×#12111yescharacteristic
855C4#560711yescharacteristic
856C4#560911yescharacteristic
857C4#561211yescharacteristic
858C3#2424611yescharacteristic, complemented, Sylow
859C2—42no—
860C2—81no—
861C2—242no—
862C2#8264011yescharacteristic
863C2#8292611yescharacteristic
864C2#8341111yescharacteristic
865C2#8354811yescharacteristic
866C2#8354911yescharacteristic
867C2#8360211yescharacteristic
868C2#8360511yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2536C2
socleC23×C3C22×D4
prime radicalC2×#5552C2
hypercenter#2536D3
hypocenterC3#24246
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2536

Complements

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

NH ≅ G/Ntype
2. C3×#2536C2semidirect
3. C2×#5050C2semidirect
4. C2×#5047C2semidirect
5. C2×#5028C2semidirect
6. C2×C4×#216C2semidirect
7. #71700C2semidirect
8. #71699C2semidirect
9. #71614C2semidirect
10. #69559C2semidirect
11. #69551C2semidirect
12. #69527C2semidirect
13. #69525C2semidirect
14. #69523C2semidirect
15. #69522C2semidirect
71. #2536D3semidirect
134. C2×#216D4semidirect
858. C3#24246semidirect

Maximal subgroups

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

subgroupindex
C2×#55522
C3×#25362
C2×#50502
C2×#50472
C2×#50282
C2×C4×#2162
#717002
#716992
#716142
#695592
#695512
#695272
#695252
#695232
#695222
#242463