Finite Group Databasebeta

← #10846321

Subgroups — #10846321

Order 768.

1120 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#2428C211yesmaximal, characteristic, complemented
2C2×#5074C211yesmaximal, characteristic, complemented
3C2×#5039C211yesmaximal, characteristic, complemented
4C2×#5042C211yesmaximal, characteristic, complemented
5C2×C4×#214C211yesmaximal, characteristic, complemented
6#73485C211yesmaximal, characteristic, complemented
7#71762C211yesmaximal, characteristic, complemented
8#71685C211yesmaximal, characteristic, complemented
9#71684C211yesmaximal, characteristic, complemented
10#71613C211yesmaximal, characteristic, complemented
11#69660C211yesmaximal, characteristic, complemented
12#69647C211yesmaximal, characteristic, complemented
13#69628C211yesmaximal, characteristic, complemented
14#69621C211yesmaximal, characteristic, complemented
15#69448C211yesmaximal, characteristic, complemented
16#25416—31nomaximal, Sylow
17C2×C3×#127C2211yescharacteristic
18C2×C3×#121—21no—
19C2×C3×#121C2211yescharacteristic
20C2×C3×#121C2211yescharacteristic
21C2×C3×C4×D4C2211yescharacteristic
22C22×#214C2211yescharacteristic
23C22×#214C2211yescharacteristic
24C22×#213C2211yescharacteristic
25C22×#213C2211yescharacteristic
26C2×#930C2211yescharacteristic
27C2×#924C2211yescharacteristic
28C22×#208C2211yescharacteristic
29C2×#875C2211yescharacteristic
30C2×C4×Dic6C2211yescharacteristic
31C3×#394—21no—
32C3×#392—21no—
33C3×#390C2211yescharacteristic
34C3×#389C2211yescharacteristic
35C3×#386—21no—
36C3×C4×C22⋊C4C2211yescharacteristic
37C2×#832C2211yescharacteristic
38C2×#832C2211yescharacteristic
39C2×#832C2211yescharacteristic
40C2×#832C2211yescharacteristic
41C2×#830C2211yescharacteristic
42#5074—24no—
43#5042—24no—
44#5039—24no—
45C4×#214—24no—
46C2×#810C2211yescharacteristic
47C2×#810C2211yescharacteristic
48C2×#809C2211yescharacteristic
49C2×#809C2211yescharacteristic
50C2×#808C2211yescharacteristic
51C2×#807C2211yescharacteristic
52#4959—21no—
53#4957—21no—
54#4939C2211yescharacteristic
55#4928C2211yescharacteristic
56C2×#803C2211yescharacteristic
57C2×C4×C3⋊C8C2211yescharacteristic
58#4676—21no—
59#4669—21no—
60#4529C2211yescharacteristic
61#4529C2211yescharacteristic
62#4524C2211yescharacteristic
63#4524C2211yescharacteristic
64C2×#496—31no—
65C2×#469—31no—
66C2×#468—31no—
67C2×C4×SD16—31no—
68#2428D311yescharacteristic, complemented
69#2426—31no—
70#2042—31no—
71#2041—31no—
72#2000—31no—
73#1999—31no—
74#1970—31no—
75#1944—31no—
76#1880—31no—
77#1879—31no—
78#1753—31no—
79C22×C3×D4—21no—
80C22×C3×D4—21no—
81C22×C3×D4—21no—
82C22×C3×D4—21no—
83C22×C3×D4C2311yescharacteristic
84C22×C3×D4C2311yescharacteristic
85C23×C3×C4—21no—
86C23×C3×C4C2311yescharacteristic
87C22×#67—21no—
88C22×D12C2311yescharacteristic
89C22×Dic6C2311yescharacteristic
90C3×#127—22no—
91C3×#127—41no—
92C3×#121—22no—
93C3×#121—22no—
94C3×#121—44no—
95C3×#121—41no—
96C3×#121—41no—
97C3×C4×D4—22no—
98C3×C4×D4—41no—
99C2×C3×C4⋊C4—21no—
100C2×C3×C4⋊C4C2311yescharacteristic
101C2×C3×C4⋊C4C2311yescharacteristic
102C2×C3×C22⋊C4—21no—
103C2×C3×C22⋊C4—21no—
104C2×C3×C22⋊C4—21no—
105C2×C3×C22⋊C4—21no—
106C2×C3×C22⋊C4—21no—
107C2×C3×C22⋊C4D411yescharacteristic
108C2×C3×C22⋊C4D411yescharacteristic
109C2×C3×C42C2311yescharacteristic
110C2×C3×C42C2311yescharacteristic
111C2×#217—21no—
112C2×#214—22no—
113C2×#214—22no—
114C2×#214—22no—
115C2×#214—22no—
116C2×#214—41no—
117C2×#214D414yescomplemented
118C2×#213—22no—
119C2×#213—22no—
120C2×#213—22no—
121C2×#213—22no—
122C2×#213—22no—
123C2×#213—41no—
124#930—22no—
125#930—41no—
126C2×(C2×D3)⋊C4—21no—
127C2×(C2×D3)⋊C4—21no—
128C2×(C2×D3)⋊C4—21no—
129C2×(C2×D3)⋊C4—21no—
130C2×(C2×D3)⋊C4—21no—
131C2×C4⋊Dic3C2311yescharacteristic
132C2×C4⋊Dic3C2311yescharacteristic
133#924—22no—
134#924—41no—
135C2×Dic3⋊C4—21no—
136C2×Dic3⋊C4—21no—
137C2×Dic3⋊C4—21no—
138C2×C4×Dic3—21no—
139C2×#208—22no—
140C2×#208—22no—
141C2×#208—22no—
142C22×C3⋊C8C2311yescharacteristic
143C22×C3⋊C8C2311yescharacteristic
144C22×C3⋊C8C2311yescharacteristic
145C22×C3⋊C8C2311yescharacteristic
146#875—22no—
147#875—41no—
148C4×Dic6—22no—
149C4×Dic6—41no—
150C3×#95—21no—
151C3×#95D411yescharacteristic
152C3×#95D411yescharacteristic
153#832—22no—
154#832—22no—
155#832—22no—
156#832—41no—
157C3⋊#95—21no—
158#830—22no—
159#810—22no—
160#810—22no—
161#809—22no—
162#809—41no—
163#808D414yescomplemented
164#807—22no—
165#803—22no—
166C4×C3⋊C8—22no—
167C22×SD16—31no—
168C22×SD16—31no—
169C22×D8—31no—
170C22×D8—31no—
171C22×M16—31no—
172C2×#127C2×D311yescharacteristic
173C2×#124—31no—
174C2×C22⋊Q8—31no—
175C2×#121—21no—
176C2×#121—31no—
177C2×#121C2×D311yescharacteristic
178C2×#121C2×D311yescharacteristic
179C2×C4×Q8—31no—
180C2×C4×D4C2×D311yescharacteristic
181#496—64no—
182#469—64no—
183#468—64no—
184C4×SD16—64no—
185C2×#107—31no—
186C2×#106—31no—
187C2×#103—31no—
188C2×#103—31no—
189C2×#102—31no—
190C2×#102—31no—
191C2×#102—31no—
192C2×#102—31no—
193C2×#102—31no—
194C2×#102—31no—
195C2×C22⋊C8—31no—
196C2×#97—31no—
197C2×C4×C8—31no—
198#396—61no—
199#394—21no—
200#394—61no—
201#392—21no—
202#390—31no—
203#390—61no—
204#390C2×D311yescharacteristic
205#389—31no—
206#389C2×D311yescharacteristic
207#388—61no—
208#386—21no—
209C4×C22⋊C4C2×D311yescharacteristic
210#340—31no—
211#340—31no—
212#336—31no—
213#336—31no—
214C24×C3—21no—
215C24×C3—21no—
216C24×C3C2×D411yescharacteristic
217C23×D3—21no—
218C2×C3×D4—21no—
219C2×C3×D4—21no—
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×D4—21no—
229C2×C3×D4—42no—
230C2×C3×D4—42no—
231C2×C3×D4—42no—
232C2×C3×D4—42no—
233C2×C3×D4—42no—
234C2×C3×D4—42no—
235C2×C3×D4—42no—
236C2×C3×D4—42no—
237C2×C3×D4—81no—
238C2×C3×D4—81no—
239C2×C3×D4—81no—
240C2×C3×D4—81no—
241C2×C3×D4C2×D412yes—
242C22×C3×C4—21no—
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—42no—
251C22×C3×C4—42no—
252C22×C3×C4—81no—
253C22×C3×C4C2×D411yescharacteristic
254C22×C3×C4C2×D411yescharacteristic
255C22×C3×C4C2×D411yescharacteristic
256C22×C3×C4C2×D411yescharacteristic
257C22×C3×C4C2×D411yescharacteristic
258C22×C3×C4C2411yescharacteristic
259C2×#67—42no—
260C2×#67—42no—
261C2×#67—81no—
262C22×Dic3—21no—
263C22×Dic3—21no—
264C22×Dic3—21no—
265C2×D12—21no—
266C2×D12—21no—
267C2×D12—21no—
268C2×D12—21no—
269C2×D12—21no—
270C2×D12—21no—
271C2×Dic6—21no—
272C2×Dic6—21no—
273C2×Dic6—21no—
274C2×Dic6—21no—
275C2×Dic6—21no—
276C2×Dic6C2×D412yes—
277C3×C4⋊C4—21no—
278C3×C4⋊C4—21no—
279C3×C4⋊C4—21no—
280C3×C4⋊C4—42no—
281C3×C4⋊C4C2×D412yes—
282C3×C22⋊C4—22no—
283C3×C22⋊C4—41no—
284C3×C22⋊C4—42no—
285C3×C22⋊C4—42no—
286C3×C22⋊C4—42no—
287C3×C22⋊C4—42no—
288C3×C22⋊C4—81no—
289C3×C42—21no—
290C3×C42—21no—
291C3×C42—21no—
292C3×C42—21no—
293#217—42no—
294#214—28no—
295#214—44no—
296#213—44no—
297#213—44no—
298(C2×D3)⋊C4—42no—
299(C2×D3)⋊C4—42no—
300(C2×D3)⋊C4—42no—
301(C2×D3)⋊C4—42no—
302(C2×D3)⋊C4—81no—
303C4⋊Dic3—21no—
304C4⋊Dic3—21no—
305C4⋊Dic3—21no—
306C4⋊Dic3C2×D412yes—
307Dic3⋊C4—42no—
308Dic3⋊C4—42no—
309Dic3⋊C4—81no—
310C4×Dic3—42no—
311#208—44no—
312C2×C3⋊C8—21no—
313C2×C3⋊C8—21no—
314C2×C3⋊C8—21no—
315C2×C3⋊C8—21no—
316C2×C3⋊C8—21no—
317C2×C3⋊C8—21no—
318C2×C3⋊C8—21no—
319C2×C3⋊C8—21no—
320C2×C3⋊C8C2×D412yes—
321C2×C3⋊C8C2×D412yes—
322C2×C3⋊C8#4112yes—
323C2×C3⋊C8#4112yes—
324C22×Q8—31no—
325C22×D4—21no—
326C22×D4—21no—
327C22×D4—21no—
328C22×D4—21no—
329C22×D4—31no—
330C22×D4—61no—
331C22×D4C22×D311yescharacteristic
332C22×D4C22×D311yescharacteristic
333C23×C4—21no—
334C23×C4C22×D311yescharacteristic
335C2×SD16—34no—
336C2×SD16—62no—
337C2×SD16—62no—
338C2×SD16—62no—
339C2×SD16—62no—
340C2×SD16—121no—
341C2×D8—62no—
342C2×D8—62no—
343C2×D8—62no—
344C2×D8—62no—
345C2×D8—62no—
346C2×D8—121no—
347C2×M16—62no—
348C2×M16—62no—
349C2×M16—62no—
350C22×C8—31no—
351C22×C8—31no—
352C22×C8—31no—
353C22×C8—31no—
354#127—22no—
355#127—41no—
356#124—62no—
357#124—121no—
358C22⋊Q8—62no—
359C22⋊Q8—121no—
360#121—22no—
361#121—22no—
362#121—44no—
363#121—41no—
364#121—41no—
365#121—62no—
366#121—121no—
367C4×Q8—62no—
368C4×Q8—121no—
369C4×D4—22no—
370C4×D4—41no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—31no—
373C2×C4⋊C4—31no—
374C2×C4⋊C4—61no—
375C2×C4⋊C4—61no—
376C2×C4⋊C4—61no—
377C2×C4⋊C4C22×D311yescharacteristic
378C2×C4⋊C4C22×D311yescharacteristic
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—61no—
385C2×C22⋊C4—61no—
386C2×C22⋊C4—61no—
387C2×C22⋊C4—61no—
388C2×C22⋊C4—61no—
389C2×C22⋊C4—61no—
390C2×C22⋊C4#6711yescharacteristic
391C2×C22⋊C4#6711yescharacteristic
392C2×C42—61no—
393C2×C42C22×D311yescharacteristic
394C2×C42C22×D311yescharacteristic
395#107—62no—
396#106—34no—
397#103—62no—
398#103—62no—
399#102—62no—
400#102—62no—
401#102—62no—
402#102—62no—
403#102—121no—
404#102—121no—
405C22⋊C8—62no—
406#97—62no—
407C4×C8—62no—
408#95—21no—
409#95—61no—
410#95#6711yescharacteristic
411#95#6711yescharacteristic
412C23×C3—21no—
413C23×C3—21no—
414C23×C3—22no—
415C23×C3—21no—
416C23×C3—21no—
417C23×C3—21no—
418C23×C3—21no—
419C23×C3—21no—
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×C3—41no—
431C23×C3—41no—
432C23×C3—41no—
433C23×C3C22×D411yescharacteristic
434C22×D3—41no—
435C22×D3—41no—
436C22×D3—41no—
437C22×D3—41no—
438C22×D3—41no—
439C22×D3—41no—
440C22×D3—41no—
441C3×D4—22no—
442C3×D4—22no—
443C3×D4—41no—
444C3×D4—41no—
445C3×D4—41no—
446C3×D4—41no—
447C3×D4—41no—
448C3×D4—41no—
449C3×D4—84no—
450C3×D4—84no—
451C3×D4—84no—
452C3×D4—84no—
453C2×C3×C4—21no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—22no—
462C2×C3×C4—21no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—41no—
469C2×C3×C4—41no—
470C2×C3×C4—41no—
471C2×C3×C4—41no—
472C2×C3×C4—41no—
473C2×C3×C4—41no—
474C2×C3×C4—41no—
475C2×C3×C4—41no—
476C2×C3×C4—41no—
477C2×C3×C4—84no—
478C2×C3×C4AGL(1,ℤ/8)12yes—
479C2×C3×C4C22×D411yescharacteristic
480C2×C3×C4C22×D411yescharacteristic
481C2×C3×C4C2×#4111yescharacteristic
482C2×C3×C4C2×#4111yescharacteristic
483C2×C3×C4H(5,𝔽2)11yescharacteristic
484C2×C3×C4H(5,𝔽2)11yescharacteristic
485#67—84no—
486C2×Dic3—22no—
487C2×Dic3—22no—
488C2×Dic3—41no—
489C2×Dic3—41no—
490C2×Dic3—41no—
491C2×Dic3—41no—
492C2×Dic3—41no—
493C2×Dic3—41no—
494C2×Dic3—41no—
495D12—41no—
496D12—41no—
497D12—41no—
498D12—41no—
499Dic6—22no—
500Dic6—22no—
501Dic6—41no—
502Dic6—41no—
503C3⋊C8—22no—
504C3⋊C8—41no—
505C3⋊C8—41no—
506C3⋊C8#12114yescomplemented
507C24—21no—
508C24—21no—
509C24—61no—
510C24C2×#6711yescharacteristic
511C2×Q8—32no—
512C2×Q8—61no—
513C2×Q8—61no—
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—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—42no—
529C2×D4—42no—
530C2×D4—42no—
531C2×D4—42no—
532C2×D4—42no—
533C2×D4—42no—
534C2×D4—42no—
535C2×D4—42no—
536C2×D4—61no—
537C2×D4—61no—
538C2×D4—61no—
539C2×D4—61no—
540C2×D4—61no—
541C2×D4—61no—
542C2×D4—81no—
543C2×D4—81no—
544C2×D4—81no—
545C2×D4—81no—
546C2×D4—122no—
547C2×D4—122no—
548C2×D4—241no—
549C2×D4D3×D412yes—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—61no—
561C22×C4—61no—
562C22×C4—61no—
563C22×C4—81no—
564C22×C4C2×#6711yescharacteristic
565C22×C4C2×#6711yescharacteristic
566C22×C4C2×#6711yescharacteristic
567C22×C4C2×#6711yescharacteristic
568C22×C4C2×#6711yescharacteristic
569C22×C4C23×D311yescharacteristic
570SD16—68no—
571SD16—124no—
572D8—124no—
573D8—124no—
574M16—124no—
575C2×C8—32no—
576C2×C8—32no—
577C2×C8—32no—
578C2×C8—32no—
579C2×C8—61no—
580C2×C8—61no—
581C2×C8—61no—
582C2×C8—61no—
583C2×C8—61no—
584C2×C8—61no—
585C2×C8—61no—
586C2×C8—61no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—32no—
591C4⋊C4—42no—
592C4⋊C4—61no—
593C4⋊C4—61no—
594C4⋊C4—61no—
595C4⋊C4—122no—
596C4⋊C4—122no—
597C4⋊C4—241no—
598C4⋊C4D3×D412yes—
599C22⋊C4—22no—
600C22⋊C4—41no—
601C22⋊C4—42no—
602C22⋊C4—42no—
603C22⋊C4—42no—
604C22⋊C4—42no—
605C22⋊C4—81no—
606C22⋊C4—122no—
607C22⋊C4—122no—
608C22⋊C4—122no—
609C22⋊C4—122no—
610C22⋊C4—122no—
611C22⋊C4—241no—
612C42—21no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—122no—
617C22×C3—41no—
618C22×C3—41no—
619C22×C3—41no—
620C22×C3—42no—
621C22×C3—41no—
622C22×C3—41no—
623C22×C3—41no—
624C22×C3—42no—
625C22×C3—42no—
626C22×C3—41no—
627C22×C3—81no—
628C22×C3—81no—
629C22×C3—81no—
630C22×C3—81no—
631C22×C3—81no—
632C22×C3—81no—
633C22×C3—81no—
634C22×C3—81no—
635C22×C3—81no—
636C22×C3—81no—
637C22×C3—81no—
638C22×C3#53211yescharacteristic
639C22×C3D4211yescharacteristic
640C22×C3D4211yescharacteristic
641C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
642C22×C3#57511yescharacteristic
643C22×C3#57611yescharacteristic
644C22×C3#57711yescharacteristic
645C2×D3—81no—
646C2×D3—81no—
647C2×D3—81no—
648C2×D3—81no—
649C2×D3—81no—
650C2×D3—81no—
651C2×D3—81no—
652C3×C4—22no—
653C3×C4—41no—
654C3×C4—42no—
655C3×C4—41no—
656C3×C4—41no—
657C3×C4—41no—
658C3×C4—81no—
659C3×C4C2×#12111yescharacteristic
660C3×C4#54011yescharacteristic
661C3×C4#54611yescharacteristic
662C3×C4#55011yescharacteristic
663Dic3—42no—
664Dic3—42no—
665Dic3—81no—
666C23—21no—
667C23—22no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—121no—
688C23—121no—
689C23—121no—
690C23—121no—
691C23—121no—
692C23—121no—
693C23—121no—
694C23C22×#6711yescharacteristic
695Q8—62no—
696Q8—62no—
697Q8—121no—
698Q8—121no—
699D4—22no—
700D4—22no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—84no—
708D4—84no—
709D4—84no—
710D4—84no—
711D4—121no—
712D4—121no—
713D4—121no—
714D4—121no—
715D4—244no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—22no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—62no—
741C2×C4—62no—
742C2×C4—84no—
743C2×C4—121no—
744C2×C4—121no—
745C2×C4—121no—
746C2×C4—121no—
747C2×C4—121no—
748C2×C4—121no—
749C2×C4—121no—
750C2×C4#93212yes—
751C2×C4C2×D3×D411yescharacteristic
752C2×C4C2×D3×D411yescharacteristic
753C2×C4#100411yescharacteristic
754C2×C4#100411yescharacteristic
755C2×C4D3×#4111yescharacteristic
756C2×C4D3×#4111yescharacteristic
757C8—34no—
758C8—62no—
759C8—121no—
760C8—121no—
761C2×C3—81no—
762C2×C3—82no—
763C2×C3—161no—
764C2×C3#242811yescharacteristic
765C2×C3#317111yescharacteristic
766C2×C3#317911yescharacteristic
767C2×C3#326511yescharacteristic
768C2×C3#326811yescharacteristic
769C2×C3#327411yescharacteristic
770C2×C3#327511yescharacteristic
771D3—161no—
772C22—41no—
773C22—41no—
774C22—42no—
775C22—42no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—42no—
781C22—41no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22—241no—
794C22—241no—
795C22—241no—
796C22—241no—
797C22—241no—
798C22—241no—
799C22—241no—
800C22C2×#93211yescharacteristic
801C22D4×#6711yescharacteristic
802C22D4×#6711yescharacteristic
803C22#582211yescharacteristic
804C22#583211yescharacteristic
805C22#583511yescharacteristic
806C22#583611yescharacteristic
807C4—22no—
808C4—42no—
809C4—41no—
810C4—41no—
811C4—41no—
812C4—41no—
813C4—81no—
814C4—122no—
815C4—122no—
816C4—241no—
817C4#559911yescharacteristic
818C4D3×#12111yescharacteristic
819C4#561011yescharacteristic
820C4#561511yescharacteristic
821C3#2541611yescharacteristic, complemented, Sylow
822C2—81no—
823C2—82no—
824C2—161no—
825C2—481no—
826C2#8265011yescharacteristic
827C2#8329211yescharacteristic
828C2#8343311yescharacteristic
829C2#8349111yescharacteristic
830C2#8349211yescharacteristic
831C2#8350811yescharacteristic
832C2#8357711yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2428C2
socleC23×C3C22×D4
hypercenter#2428D3
hypocenterC3#25416
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2428

Complements

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

NH ≅ G/Ntype
1. C3×#2428C2semidirect
2. C2×#5074C2semidirect
3. C2×#5039C2semidirect
4. C2×#5042C2semidirect
5. C2×C4×#214C2semidirect
6. #73485C2semidirect
7. #71762C2semidirect
8. #71685C2semidirect
9. #71684C2semidirect
10. #71613C2semidirect
11. #69660C2semidirect
12. #69647C2semidirect
13. #69628C2semidirect
14. #69621C2semidirect
15. #69448C2semidirect
68. #2428D3semidirect
117. C2×#214D4semidirect
163. #808D4semidirect
506. C3⋊C8#121semidirect
821. C3#25416semidirect

Maximal subgroups

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

subgroupindex
C3×#24282
C2×#50742
C2×#50392
C2×#50422
C2×C4×#2142
#734852
#717622
#716852
#716842
#716132
#696602
#696472
#696282
#696212
#694482
#254163