Finite Group Databasebeta

← #10944144

Subgroups — #10944144

Order 768.

1448 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5523C211yesmaximal, characteristic, complemented
2C3×#2620C211yesmaximal, characteristic, complemented
3C2×#5054C211yesmaximal, characteristic, complemented
4C2×#5057C211yesmaximal, characteristic, complemented
5C2×#5047C211yesmaximal, characteristic, complemented
6C2×#5037C211yesmaximal, characteristic
7#71692C211yesmaximal, characteristic, complemented
8#71677C211yesmaximal, characteristic, complemented
9#71583C211yesmaximal, characteristic, complemented
10#69690C211yesmaximal, characteristic, complemented
11#69687C211yesmaximal, characteristic, complemented
12#69660C211yesmaximal, characteristic, complemented
13#69657C211yesmaximal, characteristic, complemented
14#69588C211yesmaximal, characteristic, complemented
15#69584C211yesmaximal, characteristic, complemented
16#32919—31nomaximal, Sylow
17C22×#235C2211yescharacteristic
18C2×C3×#124C2211yescharacteristic
19C2×C3×C22⋊Q8C2211yescharacteristic
20C2×C3×#121C2211yescharacteristic
21C2×C3×#117C2211yescharacteristic
22C22×#216C2211yescharacteristic
23C22×#215C2211yescharacteristic
24C22×#214C2211yescharacteristic
25C22×#213C2211yescharacteristic
26C22×C4⋊Dic3C2211yescharacteristic
27#5523—24no—
28#5523—24no—
29C2×#892—21no—
30C2×D3×C4⋊C4—21no—
31C2×#67⋊C4—21no—
32C2×#67⋊C4—21no—
33C2×C4×D12C2211yescharacteristic
34C2×C4×D12C2211yescharacteristic
35C2×C4×Dic6C2211yescharacteristic
36C2×C4×Dic6C2211yescharacteristic
37C3×#396—21no—
38C3×#396—21no—
39C3×#394—21no—
40C3×#394—21no—
41C3×#391C2211yescharacteristic
42C3×#390C2211yescharacteristic
43C3×#384C2211yescharacteristic
44C2×#835C2211yescharacteristic
45C2×#835C2211yescharacteristic
46C2×#832C2211yescharacteristic
47C2×#832C2211yescharacteristic
48C2×#830C2211yescharacteristic
49C2×#830C2211yescharacteristic
50#5057—24no—
51#5054—24no—
52#5047—24no—
53#5037—24no—
54C2×#810C2211yescharacteristic
55C2×#810C2211yescharacteristic
56C2×#809C2211yescharacteristic
57C2×#809C2211yescharacteristic
58C2×C4⋊(C3⋊C8)C2211yescharacteristic
59C2×C4⋊(C3⋊C8)C2211yescharacteristic
60#4529C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64#4524C2211yescharacteristic
65#4524C2211yescharacteristic
66C2×#520—31no—
67C2×#464—31no—
68C2×#463—31no—
69C2×#452—31no—
70C2×#449—31no—
71#2620D311yescharacteristic, complemented
72#1880—31no—
73#1879—31no—
74#1878—31no—
75#1877—31no—
76#1874—31no—
77#1872—31no—
78#1803—31no—
79#1802—31no—
80#1798—31no—
81C22×C3×Q8C2311yescharacteristic
82C22×C3×D4—21no—
83C22×C3×D4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C22×#67—21no—
86C23×Dic3—21no—
87C2×#235—22no—
88C2×#235—22no—
89C2×#235—22no—
90C2×#235—22no—
91C2×#235—22no—
92C2×#235D414yes—
93C22×D12C2311yescharacteristic
94C22×C4×D3—21no—
95C22×C4×D3—21no—
96C22×C4×D3—21no—
97C22×Dic6C2311yescharacteristic
98C3×#124—22no—
99C3×#124—22no—
100C3×C22⋊Q8—22no—
101C3×C22⋊Q8—22no—
102C3×#121—22no—
103C3×#121—22no—
104C3×#117—22no—
105C3×#117—22no—
106C2×C3×C4⋊C4—21no—
107C2×C3×C4⋊C4—21no—
108C2×C3×C4⋊C4—21no—
109C2×C3×C4⋊C4D411yescharacteristic
110C2×C3×C4⋊C4D411yescharacteristic
111C2×C3×C4⋊C4C2311yescharacteristic
112C2×C3×C4⋊C4C2311yescharacteristic
113C2×C3×C22⋊C4—21no—
114C2×C3×C22⋊C4—21no—
115C2×C3×C22⋊C4—21no—
116C2×C3×C22⋊C4—21no—
117C2×C3×C22⋊C4—21no—
118C2×C3×C22⋊C4—21no—
119C2×C3×C22⋊C4D411yescharacteristic
120C2×C3×C22⋊C4D411yescharacteristic
121C2×C3×C42C2311yescharacteristic
122C2×C3×C42C2311yescharacteristic
123C2×#216—22no—
124C2×#216—22no—
125C2×#216—22no—
126C2×#215—22no—
127C2×#215—22no—
128C2×#215—22no—
129C2×#214—22no—
130C2×#214—22no—
131C2×#214—22no—
132C2×#213—22no—
133C2×#213—22no—
134C2×#213—22no—
135C2×(C2×D3)⋊C4—21no—
136C2×(C2×D3)⋊C4—21no—
137C2×C4⋊Dic3—21no—
138C2×C4⋊Dic3—22no—
139C2×C4⋊Dic3—22no—
140C2×C4⋊Dic3C2311yescharacteristic
141C2×C4⋊Dic3C2311yescharacteristic
142C2×Dic3⋊C4—21no—
143C2×Dic3⋊C4—21no—
144C2×C4×Dic3—21no—
145C2×C4×Dic3—21no—
146C22×C3⋊C8C2311yescharacteristic
147C22×C3⋊C8C2311yescharacteristic
148C22×C3⋊C8C2311yescharacteristic
149C22×C3⋊C8C2311yescharacteristic
150#892—28no—
151D3×C4⋊C4—28no—
152#67⋊C4—28no—
153#67⋊C4—28no—
154C4×D12—22no—
155C4×D12—22no—
156C4×D12—22no—
157C4×D12D414yescomplemented
158C4×Dic6—22no—
159C4×Dic6—22no—
160C4×Dic6—22no—
161C4×Dic6D414yescomplemented
162C3×#95—21no—
163C3×#95—21no—
164#835—22no—
165#835—22no—
166#832—22no—
167#832—22no—
168#830—22no—
169#830—22no—
170#810—22no—
171#810—22no—
172#809—22no—
173#809—22no—
174C4⋊(C3⋊C8)—22no—
175C4⋊(C3⋊C8)—22no—
176C22×#41—31no—
177C22×Q16—31no—
178C22×SD16—31no—
179C22×SD16—31no—
180C22×D8—31no—
181C2×#124C2×D311yescharacteristic
182C2×C22⋊Q8C2×D311yescharacteristic
183C2×#121C2×D311yescharacteristic
184#520—64no—
185#520—64no—
186C2×C4×Q8—31no—
187C2×C4×Q8—31no—
188C2×C4×D4—31no—
189C2×C4×D4—31no—
190C2×C4×D4—61no—
191C2×C4×D4—61no—
192C2×#117—61no—
193C2×#117C2×D311yescharacteristic
194C22×C4⋊C4—31no—
195C22×C4⋊C4—61no—
196#464—64no—
197#463—64no—
198#452—64no—
199#449—64no—
200C2×C4⋊C8—31no—
201C2×C4⋊C8—31no—
202C2×#103—31no—
203C2×#103—31no—
204C2×#103—31no—
205C2×#103—31no—
206C2×#102—31no—
207C2×#102—31no—
208C2×#102—31no—
209C2×#102—31no—
210C2×C22⋊C8—31no—
211C2×C22⋊C8—31no—
212#396—21no—
213#396—21no—
214#394—21no—
215#394—21no—
216#391C2×D311yescharacteristic
217#390C2×D311yescharacteristic
218#384C2×D311yescharacteristic
219#340—31no—
220#340—31no—
221#340—31no—
222#340—31no—
223#336—31no—
224#336—31no—
225C24×C3—21no—
226C24×C3C2×D411yescharacteristic
227C23×D3—21no—
228C2×C3×Q8—21no—
229C2×C3×Q8—21no—
230C2×C3×Q8—21no—
231C2×C3×Q8—21no—
232C2×C3×Q8—21no—
233C2×C3×Q8—21no—
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—42no—
241C2×C3×D4—81no—
242C2×C3×D4—81no—
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×C4C2×D412yes—
251C22×C3×C4C2×D411yescharacteristic
252C22×C3×C4C2×D411yescharacteristic
253C22×C3×C4C2×D411yescharacteristic
254C22×C3×C4C2×D411yescharacteristic
255C22×C3×C4C2×D411yescharacteristic
256C22×C3×C4#4112yes—
257C22×C3×C4C2411yescharacteristic
258C2×#67—24no—
259C2×#67—24no—
260C2×#67—24no—
261C22×Dic3—21no—
262C22×Dic3—21no—
263C22×Dic3—21no—
264C22×Dic3—24no—
265C22×Dic3—81no—
266C22×Dic3—81no—
267#235—28no—
268#235—28no—
269#235—28no—
270#235—28no—
271C2×D12—21no—
272C2×D12—21no—
273C2×D12—21no—
274C2×D12C2×D412yes—
275C2×D12C2×D412yes—
276C2×D12#4112yes—
277C2×C4×D3—24no—
278C2×C4×D3—24no—
279C2×C4×D3—24no—
280C2×C4×D3—24no—
281C2×C4×D3—24no—
282C2×C4×D3—81no—
283C2×C4×D3—81no—
284C2×C4×D3—81no—
285C2×C4×D3—81no—
286C2×Dic6—21no—
287C2×Dic6—21no—
288C2×Dic6—21no—
289C2×Dic6C2×D412yes—
290C2×Dic6C2×D412yes—
291C2×Dic6#4112yes—
292C3×C4⋊C4—22no—
293C3×C4⋊C4—22no—
294C3×C4⋊C4—21no—
295C3×C4⋊C4—21no—
296C3×C4⋊C4—21no—
297C3×C4⋊C4—21no—
298C3×C4⋊C4—42no—
299C3×C4⋊C4—81no—
300C3×C4⋊C4—81no—
301C3×C22⋊C4—22no—
302C3×C22⋊C4—22no—
303C3×C22⋊C4—42no—
304C3×C22⋊C4—42no—
305C3×C22⋊C4—42no—
306C3×C22⋊C4—42no—
307C3×C22⋊C4—81no—
308C3×C22⋊C4—81no—
309C3×C42—21no—
310C3×C42—21no—
311C3×C42C2×D412yes—
312C3×C42C2×D412yes—
313#216—44no—
314#215—44no—
315#214—44no—
316#213—44no—
317(C2×D3)⋊C4—24no—
318(C2×D3)⋊C4—24no—
319C4⋊Dic3—24no—
320C4⋊Dic3—21no—
321C4⋊Dic3—21no—
322C4⋊Dic3C2×D412yes—
323C4⋊Dic3C2×D412yes—
324Dic3⋊C4—24no—
325Dic3⋊C4—24no—
326C4×Dic3—24no—
327C4×Dic3—24no—
328C2×C3⋊C8—21no—
329C2×C3⋊C8—21no—
330C2×C3⋊C8—21no—
331C2×C3⋊C8—21no—
332C2×C3⋊C8—21no—
333C2×C3⋊C8—21no—
334C2×C3⋊C8—21no—
335C2×C3⋊C8—21no—
336C2×C3⋊C8—21no—
337C2×C3⋊C8—21no—
338C2×C3⋊C8—21no—
339C2×C3⋊C8—21no—
340C2×#41—34no—
341C2×#41—62no—
342C2×#41—62no—
343C2×#41—62no—
344C2×#41—62no—
345C2×#41—62no—
346C22×Q8—31no—
347C22×Q8C22×D311yescharacteristic
348C22×D4—21no—
349C22×D4—31no—
350C22×D4—61no—
351C22×D4C22×D311yescharacteristic
352C23×C4—61no—
353C23×C4—61no—
354C23×C4—61no—
355C23×C4—61no—
356C23×C4C22×D311yescharacteristic
357C2×Q16—62no—
358C2×Q16—62no—
359C2×Q16—62no—
360C2×SD16—62no—
361C2×SD16—62no—
362C2×SD16—62no—
363C2×SD16—62no—
364C2×SD16—62no—
365C2×SD16—62no—
366C2×D8—62no—
367C2×D8—62no—
368C2×D8—62no—
369C22×C8—31no—
370C22×C8—31no—
371C22×C8—31no—
372C22×C8—31no—
373#124—22no—
374#124—22no—
375C22⋊Q8—22no—
376C22⋊Q8—22no—
377#121—22no—
378#121—22no—
379C4×Q8—34no—
380C4×Q8—62no—
381C4×Q8—62no—
382C4×Q8—62no—
383C4×D4—34no—
384C4×D4—62no—
385C4×D4—62no—
386C4×D4—68no—
387C4×D4—68no—
388C4×D4—62no—
389#117—22no—
390#117—22no—
391#117—68no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—31no—
396C2×C4⋊C4—31no—
397C2×C4⋊C4—68no—
398C2×C4⋊C4—62no—
399C2×C4⋊C4—62no—
400C2×C4⋊C4—61no—
401C2×C4⋊C4—61no—
402C2×C4⋊C4—61no—
403C2×C4⋊C4#6711yescharacteristic
404C2×C4⋊C4#6711yescharacteristic
405C2×C4⋊C4C22×D311yescharacteristic
406C2×C4⋊C4C22×D311yescharacteristic
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—61no—
414C2×C22⋊C4—61no—
415C2×C22⋊C4#6711yescharacteristic
416C2×C22⋊C4#6711yescharacteristic
417C2×C42—61no—
418C2×C42—61no—
419C2×C42C22×D311yescharacteristic
420C2×C42C22×D311yescharacteristic
421C4⋊C8—62no—
422C4⋊C8—62no—
423#103—62no—
424#103—62no—
425#103—62no—
426#103—62no—
427#102—62no—
428#102—62no—
429#102—62no—
430#102—62no—
431C22⋊C8—62no—
432C22⋊C8—62no—
433#95—21no—
434#95—21no—
435C23×C3—21no—
436C23×C3—21no—
437C23×C3—21no—
438C23×C3—21no—
439C23×C3—21no—
440C23×C3—21no—
441C23×C3—41no—
442C23×C3—41no—
443C23×C3—41no—
444C23×C3—41no—
445C23×C3—41no—
446C23×C3—41no—
447C23×C3—41no—
448C23×C3#12112yes—
449C23×C3C22×D411yescharacteristic
450C22×D3—22no—
451C22×D3—22no—
452C22×D3—22no—
453C22×D3—41no—
454C22×D3—41no—
455C22×D3—41no—
456C22×D3—41no—
457C3×Q8—41no—
458C3×Q8—41no—
459C3×Q8—41no—
460C3×Q8—41no—
461C3×D4—41no—
462C3×D4—41no—
463C3×D4—41no—
464C3×D4—41no—
465C3×D4—84no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—22no—
473C2×C3×C4—22no—
474C2×C3×C4—22no—
475C2×C3×C4—22no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—41no—
483C2×C3×C4—41no—
484C2×C3×C4—41no—
485C2×C3×C4—41no—
486C2×C3×C4—41no—
487C2×C3×C4—41no—
488C2×C3×C4—41no—
489C2×C3×C4—41no—
490C2×C3×C4—41no—
491C2×C3×C4#12012yes—
492C2×C3×C4#12012yes—
493C2×C3×C4#12112yes—
494C2×C3×C4C22×D411yescharacteristic
495C2×C3×C4C22×D411yescharacteristic
496C2×C3×C4C22×D411yescharacteristic
497C2×C3×C4C2×#4111yescharacteristic
498C2×C3×C4C2×#4111yescharacteristic
499C2×C3×C4C2×#4111yescharacteristic
500#67—216no—
501C2×Dic3—22no—
502C2×Dic3—22no—
503C2×Dic3—22no—
504C2×Dic3—22no—
505C2×Dic3—22no—
506C2×Dic3—41no—
507C2×Dic3—41no—
508C2×Dic3—41no—
509C2×Dic3—41no—
510C2×Dic3—84no—
511D12—22no—
512D12—22no—
513D12—22no—
514D12#12114yes—
515C4×D3—216no—
516C4×D3—84no—
517C4×D3—84no—
518Dic6—22no—
519Dic6—22no—
520Dic6—22no—
521Dic6#12114yes—
522C3⋊C8—41no—
523C3⋊C8—41no—
524C3⋊C8—41no—
525C3⋊C8—41no—
526C24—21no—
527C24—61no—
528C24C2×#6711yescharacteristic
529#41—68no—
530#41—68no—
531#41—68no—
532#41—68no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—32no—
540C2×Q8—32no—
541C2×Q8—32no—
542C2×Q8—61no—
543C2×Q8—61no—
544C2×Q8—61no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—32no—
552C2×D4—32no—
553C2×D4—32no—
554C2×D4—42no—
555C2×D4—64no—
556C2×D4—64no—
557C2×D4—64no—
558C2×D4—61no—
559C2×D4—61no—
560C2×D4—61no—
561C2×D4—81no—
562C2×D4—81no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—64no—
571C22×C4—64no—
572C22×C4—64no—
573C22×C4—61no—
574C22×C4—64no—
575C22×C4—61no—
576C22×C4—61no—
577C22×C4—64no—
578C22×C4—64no—
579C22×C4—241no—
580C22×C4—241no—
581C22×C4—241no—
582C22×C4—241no—
583C22×C4—241no—
584C22×C4—241no—
585C22×C4D3×D412yes—
586C22×C4#23712yes—
587C22×C4C2×#6711yescharacteristic
588C22×C4C2×#6711yescharacteristic
589C22×C4C2×#6711yescharacteristic
590C22×C4C2×#6711yescharacteristic
591C22×C4C2×#6711yescharacteristic
592C22×C4C23×D311yescharacteristic
593Q16—124no—
594SD16—124no—
595SD16—124no—
596D8—124no—
597C2×C8—61no—
598C2×C8—61no—
599C2×C8—61no—
600C2×C8—61no—
601C2×C8—61no—
602C2×C8—61no—
603C2×C8—61no—
604C2×C8—61no—
605C2×C8—61no—
606C2×C8—61no—
607C2×C8—61no—
608C2×C8—61no—
609C4⋊C4—22no—
610C4⋊C4—22no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—32no—
616C4⋊C4—32no—
617C4⋊C4—42no—
618C4⋊C4—64no—
619C4⋊C4—64no—
620C4⋊C4—64no—
621C4⋊C4—61no—
622C4⋊C4—61no—
623C4⋊C4—81no—
624C4⋊C4—81no—
625C22⋊C4—22no—
626C22⋊C4—22no—
627C22⋊C4—42no—
628C22⋊C4—42no—
629C22⋊C4—42no—
630C22⋊C4—42no—
631C22⋊C4—64no—
632C22⋊C4—64no—
633C22⋊C4—81no—
634C22⋊C4—81no—
635C42—21no—
636C42—21no—
637C42—64no—
638C42—64no—
639C42D3×D412yes—
640C42D3×D412yes—
641C22×C3—22no—
642C22×C3—22no—
643C22×C3—22no—
644C22×C3—41no—
645C22×C3—41no—
646C22×C3—41no—
647C22×C3—41no—
648C22×C3—81no—
649C22×C3—81no—
650C22×C3—81no—
651C22×C3—81no—
652C22×C3—81no—
653C22×C3—81no—
654C22×C3—81no—
655C22×C3C2×#12011yescharacteristic
656C22×C3C2×#12111yescharacteristic
657C22×C3#52511yescharacteristic
658C22×C3#57611yescharacteristic
659C22×C3#57711yescharacteristic
660C22×C3#57711yescharacteristic
661C22×C3#57811yescharacteristic
662C2×D3—24no—
663C2×D3—42no—
664C2×D3—42no—
665C2×D3—42no—
666C2×D3—42no—
667C2×D3—42no—
668C2×D3—42no—
669C3×C4—22no—
670C3×C4—22no—
671C3×C4—22no—
672C3×C4—41no—
673C3×C4—41no—
674C3×C4—81no—
675C3×C4—81no—
676C3×C4—81no—
677C3×C4C2×#12111yescharacteristic
678C3×C4C2×#12111yescharacteristic
679C3×C4#52511yescharacteristic
680C3×C4#52511yescharacteristic
681Dic3—24no—
682Dic3—42no—
683Dic3—42no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—62no—
698C23—62no—
699C23—62no—
700C23—121no—
701C23—121no—
702C23—121no—
703C23—121no—
704C23#93812yes—
705C23C22×#6711yescharacteristic
706Q8—34no—
707Q8—41no—
708Q8—41no—
709Q8—41no—
710Q8—41no—
711Q8—62no—
712Q8—62no—
713Q8—62no—
714D4—34no—
715D4—41no—
716D4—41no—
717D4—41no—
718D4—41no—
719D4—616no—
720D4—62no—
721D4—62no—
722D4—62no—
723D4—84no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—616no—
750C2×C4—62no—
751C2×C4—62no—
752C2×C4—62no—
753C2×C4—62no—
754C2×C4—62no—
755C2×C4—121no—
756C2×C4—121no—
757C2×C4—121no—
758C2×C4—121no—
759C2×C4—244no—
760C2×C4—244no—
761C2×C4—244no—
762C2×C4#93712yes—
763C2×C4#93712yes—
764C2×C4#93812yes—
765C2×C4C2×D3×D411yescharacteristic
766C2×C4C2×D3×D411yescharacteristic
767C2×C4C2×D3×D411yescharacteristic
768C2×C4C2×#23711yescharacteristic
769C2×C4D3×#4111yescharacteristic
770C2×C4D3×#4111yescharacteristic
771C8—121no—
772C8—121no—
773C8—121no—
774C8—121no—
775C2×C3—42no—
776C2×C3—161no—
777C2×C3#284711yescharacteristic
778C2×C3#301211yescharacteristic
779C2×C3#301311yescharacteristic
780C2×C3#304511yescharacteristic
781C2×C3#304611yescharacteristic
782C2×C3#312411yescharacteristic
783C2×C3#312511yescharacteristic
784D3—44no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—64no—
793C22—81no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—122no—
801C22—122no—
802C22—122no—
803C22—122no—
804C22—122no—
805C22—122no—
806C22C2×#93711yescharacteristic
807C22C2×#93811yescharacteristic
808C22#582811yescharacteristic
809C22#583511yescharacteristic
810C22#583611yescharacteristic
811C22#583711yescharacteristic
812C22#583811yescharacteristic
813C4—22no—
814C4—22no—
815C4—22no—
816C4—41no—
817C4—41no—
818C4—64no—
819C4—81no—
820C4—81no—
821C4—81no—
822C4—122no—
823C4—122no—
824C4D3×#12111yescharacteristic
825C4D3×#12111yescharacteristic
826C4#560611yescharacteristic
827C4#560611yescharacteristic
828C3#3291911yescharacteristic, complemented, Sylow
829C2—42no—
830C2—124no—
831C2—161no—
832C2#8272311yescharacteristic
833C2#8338511yescharacteristic
834C2#8340611yescharacteristic
835C2#8342411yescharacteristic
836C2#8342711yescharacteristic
837C2#8346111yescharacteristic
838C2#8346211yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2620C2
socleC23×C3C22×D4
prime radicalC2×#5037C2
hypercenter#2620D3
hypocenterC3#32919
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2620

Complements

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

NH ≅ G/Ntype
1. C2×#5523C2semidirect
2. C3×#2620C2semidirect
3. C2×#5054C2semidirect
4. C2×#5057C2semidirect
5. C2×#5047C2semidirect
7. #71692C2semidirect
8. #71677C2semidirect
9. #71583C2semidirect
10. #69690C2semidirect
11. #69687C2semidirect
12. #69660C2semidirect
13. #69657C2semidirect
14. #69588C2semidirect
15. #69584C2semidirect
71. #2620D3semidirect
157. C4×D12D4semidirect
161. C4×Dic6D4semidirect
828. C3#32919semidirect

Maximal subgroups

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

subgroupindex
C2×#55232
C3×#26202
C2×#50542
C2×#50572
C2×#50472
C2×#50372
#716922
#716772
#715832
#696902
#696872
#696602
#696572
#695882
#695842
#329193