Finite Group Databasebeta

← #10846075

Subgroups — #10846075

Order 768.

1118 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×#2537C211yesmaximal, characteristic, complemented
2C2×#5042C211yesmaximal, characteristic, complemented
3C2×#5038C211yesmaximal, characteristic, complemented
4#82377C211yesmaximal, characteristic, complemented
5C2×#5016C211yesmaximal, characteristic, complemented
6C2×#5011C211yesmaximal, characteristic, complemented
7#71685C211yesmaximal, characteristic, complemented
8#71684C211yesmaximal, characteristic, complemented
9#71609C211yesmaximal, characteristic, complemented
10#69581C211yesmaximal, characteristic, complemented
11#69567C211yesmaximal, characteristic, complemented
12#69527C211yesmaximal, characteristic, complemented
13#69523C211yesmaximal, characteristic, complemented
14#69517C211yesmaximal, characteristic, complemented
15#69514C211yesmaximal, characteristic, complemented
16#25397—31nomaximal, Sylow
17C2×C3×#121—21no—
18C2×C3×#121C2211yescharacteristic
19C2×C3×#121C2211yescharacteristic
20C2×C3×C4×D4C2211yescharacteristic
21C2×C3×C4×D4C2211yescharacteristic
22C22×#214C2211yescharacteristic
23C22×#213C2211yescharacteristic
24C2×#930C2211yescharacteristic
25C2×#930C2211yescharacteristic
26C2×#924C2211yescharacteristic
27C2×#924C2211yescharacteristic
28C22×#208C2211yescharacteristic
29C23×C3⋊C8C2211yescharacteristic
30C2×#875C2211yescharacteristic
31C3×#394—21no—
32C3×#394—21no—
33C3×#384C2211yescharacteristic
34C3×#380—21no—
35C3×#380C2211yescharacteristic
36C3×#380C2211yescharacteristic
37#5223—21no—
38C2×#832C2211yescharacteristic
39C2×#832C2211yescharacteristic
40C2×#830C2211yescharacteristic
41C2×#830C2211yescharacteristic
42#5042—24no—
43#5038—24no—
44#5016—24no—
45#5011—24no—
46#4993—21no—
47C2×#810C2211yescharacteristic
48C2×#810C2211yescharacteristic
49C2×#810C2211yescharacteristic
50C2×#809C2211yescharacteristic
51C2×#809C2211yescharacteristic
52C2×#809C2211yescharacteristic
53C2×#807C2211yescharacteristic
54C2×#807C2211yescharacteristic
55#4957—21no—
56#4957—21no—
57C4×C4⋊Dic3C2211yescharacteristic
58C2×C4⋊(C3⋊C8)C2211yescharacteristic
59C2×#803C2211yescharacteristic
60#4529C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#468—31no—
65C2×#466—31no—
66C2×#463—31no—
67C2×#435—31no—
68#2540—31no—
69#2537D311yescharacteristic, complemented
70#2036—31no—
71#2033—31no—
72#2000—31no—
73#1999—31no—
74#1959—31no—
75#1947—31no—
76#1895—31no—
77#1892—31no—
78#1762—31no—
79C22×C3×D4—21no—
80C22×C3×D4—21no—
81C22×C3×D4D411yescharacteristic
82C22×C3×D4C2311yescharacteristic
83C23×C3×C4—21no—
84C23×C3×C4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C22×#67—21no—
87C22×#67—21no—
88C22×D12C2311yescharacteristic
89C22×Dic6C2311yescharacteristic
90C3×#121—22no—
91C3×#121—22no—
92C3×#121—41no—
93C3×#121—41no—
94C3×#121—44no—
95C3×C4×D4—22no—
96C3×C4×D4—22no—
97C3×C4×D4—22no—
98C3×C4×D4—22no—
99C2×C3×C4⋊C4—21no—
100C2×C3×C4⋊C4—21no—
101C2×C3×C4⋊C4D411yescharacteristic
102C2×C3×C4⋊C4C2311yescharacteristic
103C2×C3×C4⋊C4C2311yescharacteristic
104C2×C3×C4⋊C4C2311yescharacteristic
105C2×C3×C22⋊C4—21no—
106C2×C3×C22⋊C4—21no—
107C2×C3×C22⋊C4—21no—
108C2×C3×C22⋊C4—21no—
109C2×C3×C22⋊C4—21no—
110C2×C3×C22⋊C4D411yescharacteristic
111C2×C3×C22⋊C4D411yescharacteristic
112C2×C3×C42C2311yescharacteristic
113C2×#217—21no—
114C2×#217—21no—
115C2×#214—22no—
116C2×#214—22no—
117C2×#214—41no—
118C2×#213—22no—
119C2×#213—22no—
120C2×#213—41no—
121#930—22no—
122#930—22no—
123#930—41no—
124#930—41no—
125C2×(C2×D3)⋊C4—21no—
126C2×(C2×D3)⋊C4—21no—
127C2×(C2×D3)⋊C4—21no—
128C2×(C2×D3)⋊C4—21no—
129C2×C4⋊Dic3C2311yescharacteristic
130C2×C4⋊Dic3C2311yescharacteristic
131#924—22no—
132#924—22no—
133#924—41no—
134#924—41no—
135C2×Dic3⋊C4—21no—
136C2×Dic3⋊C4—21no—
137C2×C4×Dic3—21no—
138C2×#208—22no—
139C2×#208—22no—
140C2×#208—41no—
141C22×C3⋊C8—22no—
142C22×C3⋊C8—22no—
143C22×C3⋊C8—41no—
144C22×C3⋊C8C2311yescharacteristic
145C22×C3⋊C8C2311yescharacteristic
146C22×C3⋊C8C2311yescharacteristic
147C22×C3⋊C8C2311yescharacteristic
148#875—22no—
149#875—22no—
150C3×#95—21no—
151C3×#95—21no—
152#832—22no—
153#832D414yescomplemented
154C3⋊#95—21no—
155#830—22no—
156#830—22no—
157#810—22no—
158#810—22no—
159#810—41no—
160#809—22no—
161#809—22no—
162#809—41no—
163#807—22no—
164#807—22no—
165C4⋊(C3⋊C8)D414yescomplemented
166#803—22no—
167C22×SD16—31no—
168C22×D8—31no—
169C22×M16—31no—
170C23×C8—31no—
171C2×#124—31no—
172C2×C22⋊Q8—31no—
173C2×C22⋊Q8—31no—
174C2×#121—21no—
175C2×#121—31no—
176C2×#121—31no—
177C2×#121C2×D311yescharacteristic
178C2×#121C2×D311yescharacteristic
179C2×C4×D4C2×D311yescharacteristic
180C2×C4×D4C2×D311yescharacteristic
181#468—64no—
182#466—64no—
183#463—64no—
184#435—64no—
185C2×#107—31no—
186C2×#107—31no—
187C2×C4⋊C8—31no—
188C2×#103—31no—
189C2×#103—31no—
190C2×#103—31no—
191C2×#102—31no—
192C2×#102—31no—
193C2×#102—31no—
194C2×#102—31no—
195C2×#102—31no—
196C2×C22⋊C8—31no—
197C2×C22⋊C8—31no—
198C2×#97—31no—
199#399—61no—
200#394—21no—
201#394—21no—
202#392—61no—
203#390—61no—
204#390—61no—
205#384C2×D311yescharacteristic
206#380—21no—
207#380C2×D311yescharacteristic
208#380C2×D311yescharacteristic
209C4×C4⋊C4—31no—
210#340—31no—
211#340—31no—
212#340—31no—
213#340—31no—
214C24×C3—21no—
215C24×C3C2×D411yescharacteristic
216C24×C3C2×D411yescharacteristic
217C23×D3—21no—
218C2×C3×D4—22no—
219C2×C3×D4—22no—
220C2×C3×D4—21no—
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4—41no—
226C2×C3×D4—42no—
227C2×C3×D4—42no—
228C2×C3×D4—42no—
229C2×C3×D4—42no—
230C2×C3×D4—81no—
231C2×C3×D4—81no—
232C2×C3×D4C2×D412yes—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
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—42no—
249C22×C3×C4—42no—
250C22×C3×C4—42no—
251C22×C3×C4C2×D411yescharacteristic
252C22×C3×C4C2×D411yescharacteristic
253C22×C3×C4C2×D411yescharacteristic
254C22×C3×C4C2×D411yescharacteristic
255C22×C3×C4C2411yescharacteristic
256C2×#67—42no—
257C2×#67—42no—
258C2×#67—42no—
259C2×#67—42no—
260C2×#67—81no—
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×Dic6—21no—
277C3×C4⋊C4—22no—
278C3×C4⋊C4—21no—
279C3×C4⋊C4—21no—
280C3×C4⋊C4—21no—
281C3×C4⋊C4—21no—
282C3×C4⋊C4—21no—
283C3×C4⋊C4—21no—
284C3×C4⋊C4—42no—
285C3×C4⋊C4—81no—
286C3×C22⋊C4—22no—
287C3×C22⋊C4—22no—
288C3×C22⋊C4—42no—
289C3×C22⋊C4—42no—
290C3×C22⋊C4—42no—
291C3×C22⋊C4—42no—
292C3×C22⋊C4—42no—
293C3×C42C2×D412yes—
294C3×C42#4112yes—
295#217—42no—
296#217—42no—
297#214—44no—
298#213—44no—
299(C2×D3)⋊C4—42no—
300(C2×D3)⋊C4—42no—
301(C2×D3)⋊C4—42no—
302(C2×D3)⋊C4—42no—
303C4⋊Dic3—21no—
304C4⋊Dic3—21no—
305C4⋊Dic3C2×D412yes—
306C4⋊Dic3#4112yes—
307Dic3⋊C4—42no—
308Dic3⋊C4—42no—
309C4×Dic3—81no—
310#208—44no—
311C2×C3⋊C8—21no—
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⋊C8—44no—
321C2×C3⋊C8C2×D412yes—
322C2×C3⋊C8C2×D412yes—
323C2×C3⋊C8C2×D412yes—
324C22×Q8—31no—
325C22×D4—21no—
326C22×D4—21no—
327C22×D4—31no—
328C22×D4—61no—
329C22×D4—61no—
330C22×D4#6711yescharacteristic
331C22×D4C22×D311yescharacteristic
332C23×C4—21no—
333C23×C4C22×D311yescharacteristic
334C23×C4C22×D311yescharacteristic
335C2×SD16—62no—
336C2×SD16—62no—
337C2×SD16—121no—
338C2×D8—62no—
339C2×D8—62no—
340C2×D8—121no—
341C2×M16—62no—
342C2×M16—62no—
343C2×M16—121no—
344C22×C8—31no—
345C22×C8—31no—
346C22×C8—31no—
347C22×C8—31no—
348C22×C8—62no—
349C22×C8—62no—
350C22×C8—121no—
351#124—62no—
352#124—62no—
353C22⋊Q8—62no—
354C22⋊Q8—62no—
355C22⋊Q8—121no—
356C22⋊Q8—121no—
357#121—22no—
358#121—22no—
359#121—41no—
360#121—41no—
361#121—44no—
362#121—62no—
363#121—62no—
364#121—121no—
365#121—121no—
366C4×D4—22no—
367C4×D4—22no—
368C4×D4—22no—
369C4×D4—22no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—31no—
373C2×C4⋊C4—31no—
374C2×C4⋊C4—61no—
375C2×C4⋊C4—61no—
376C2×C4⋊C4#6711yescharacteristic
377C2×C4⋊C4C22×D311yescharacteristic
378C2×C4⋊C4C22×D311yescharacteristic
379C2×C4⋊C4C22×D311yescharacteristic
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—61no—
386C2×C22⋊C4—61no—
387C2×C22⋊C4—61no—
388C2×C22⋊C4—61no—
389C2×C22⋊C4—61no—
390C2×C22⋊C4—61no—
391C2×C22⋊C4#6711yescharacteristic
392C2×C22⋊C4#6711yescharacteristic
393C2×C42—61no—
394C2×C42C22×D311yescharacteristic
395#107—62no—
396#107—62no—
397C4⋊C8—34no—
398#103—62no—
399#103—62no—
400#103—121no—
401#102—34no—
402#102—62no—
403#102—62no—
404#102—62no—
405#102—121no—
406C22⋊C8—62no—
407C22⋊C8—62no—
408#97—62no—
409#95—21no—
410#95—21no—
411#95—61no—
412C23×C3—21no—
413C23×C3—21no—
414C23×C3—21no—
415C23×C3—21no—
416C23×C3—21no—
417C23×C3—21no—
418C23×C3—21no—
419C23×C3—21no—
420C23×C3—22no—
421C23×C3—21no—
422C23×C3—21no—
423C23×C3—21no—
424C23×C3—21no—
425C23×C3—21no—
426C23×C3—41no—
427C23×C3—41no—
428C23×C3—41no—
429C23×C3—41no—
430C23×C3—41no—
431C23×C3—41no—
432C23×C3AGL(1,ℤ/8)12yes—
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—44no—
444C3×D4—41no—
445C3×D4—41no—
446C3×D4—84no—
447C3×D4—84no—
448C2×C3×C4—21no—
449C2×C3×C4—21no—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
452C2×C3×C4—21no—
453C2×C3×C4—21no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
458C2×C3×C4—41no—
459C2×C3×C4—41no—
460C2×C3×C4—41no—
461C2×C3×C4—41no—
462C2×C3×C4—41no—
463C2×C3×C4—41no—
464C2×C3×C4—41no—
465C2×C3×C4—41no—
466C2×C3×C4—41no—
467C2×C3×C4—41no—
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—84no—
476C2×C3×C4#12112yes—
477C2×C3×C4#12112yes—
478C2×C3×C4C22×D411yescharacteristic
479C2×C3×C4C22×D411yescharacteristic
480C2×C3×C4C2×#4111yescharacteristic
481C2×C3×C4C2×#4111yescharacteristic
482C2×C3×C4H(5,𝔽2)11yescharacteristic
483C2×C3×C4H(5,𝔽2)11yescharacteristic
484#67—84no—
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—41no—
500Dic6—41no—
501Dic6—41no—
502Dic6—41no—
503C3⋊C8—22no—
504C3⋊C8—22no—
505C3⋊C8—22no—
506C3⋊C8—41no—
507C24—21no—
508C24—61no—
509C24C2×#6711yescharacteristic
510C24C2×#6711yescharacteristic
511C2×Q8—61no—
512C2×Q8—61no—
513C2×Q8—61no—
514C2×Q8—61no—
515C2×Q8—61no—
516C2×Q8—61no—
517C2×D4—22no—
518C2×D4—22no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—41no—
525C2×D4—42no—
526C2×D4—42no—
527C2×D4—42no—
528C2×D4—42no—
529C2×D4—61no—
530C2×D4—61no—
531C2×D4—61no—
532C2×D4—61no—
533C2×D4—61no—
534C2×D4—61no—
535C2×D4—81no—
536C2×D4—81no—
537C2×D4—122no—
538C2×D4—122no—
539C2×D4—122no—
540C2×D4—122no—
541C2×D4—241no—
542C2×D4—241no—
543C2×D4D3×D412yes—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
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—21no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—61no—
563C22×C4—61no—
564C22×C4—61no—
565C22×C4C2×#6711yescharacteristic
566C22×C4C2×#6711yescharacteristic
567C22×C4C2×#6711yescharacteristic
568C22×C4C2×#6711yescharacteristic
569C22×C4C23×D311yescharacteristic
570SD16—124no—
571D8—124no—
572M16—124no—
573C2×C8—32no—
574C2×C8—32no—
575C2×C8—32no—
576C2×C8—61no—
577C2×C8—61no—
578C2×C8—61no—
579C2×C8—61no—
580C2×C8—61no—
581C2×C8—61no—
582C2×C8—61no—
583C2×C8—61no—
584C2×C8—61no—
585C2×C8—124no—
586C4⋊C4—22no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—32no—
594C4⋊C4—32no—
595C4⋊C4—42no—
596C4⋊C4—61no—
597C4⋊C4—61no—
598C4⋊C4—81no—
599C4⋊C4—122no—
600C4⋊C4—122no—
601C22⋊C4—22no—
602C22⋊C4—22no—
603C22⋊C4—42no—
604C22⋊C4—42no—
605C22⋊C4—42no—
606C22⋊C4—42no—
607C22⋊C4—42no—
608C22⋊C4—122no—
609C22⋊C4—122no—
610C22⋊C4—122no—
611C22⋊C4—122no—
612C22⋊C4—122no—
613C22⋊C4—122no—
614C42—241no—
615C42D3×D412yes—
616C42#23712yes—
617C22×C3—22no—
618C22×C3—22no—
619C22×C3—22no—
620C22×C3—41no—
621C22×C3—41no—
622C22×C3—41no—
623C22×C3—41no—
624C22×C3—41no—
625C22×C3—42no—
626C22×C3—41no—
627C22×C3—42no—
628C22×C3—41no—
629C22×C3—42no—
630C22×C3—41no—
631C22×C3—41no—
632C22×C3—41no—
633C22×C3—41no—
634C22×C3—81no—
635C22×C3—81no—
636C22×C3—81no—
637C22×C3—81no—
638C22×C3C2×#12111yescharacteristic
639C22×C3D4211yescharacteristic
640C22×C3#54611yescharacteristic
641C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
642C22×C3#57511yescharacteristic
643C22×C3#57611yescharacteristic
644C22×C3#57811yescharacteristic
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—22no—
654C3×C4—41no—
655C3×C4—41no—
656C3×C4—81no—
657C3×C4—81no—
658C3×C4—81no—
659C3×C4#53211yescharacteristic
660C3×C4#54011yescharacteristic
661C3×C4D4211yescharacteristic
662C3×C4#55011yescharacteristic
663Dic3—42no—
664Dic3—42no—
665Dic3—81no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—22no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—121no—
687C23—121no—
688C23—121no—
689C23—121no—
690C23—121no—
691C23—121no—
692C23—121no—
693C23#93212yes—
694C23C22×#6711yescharacteristic
695Q8—121no—
696Q8—121no—
697Q8—121no—
698Q8—121no—
699D4—22no—
700D4—22no—
701D4—44no—
702D4—41no—
703D4—41no—
704D4—84no—
705D4—84no—
706D4—121no—
707D4—121no—
708D4—121no—
709D4—121no—
710D4—244no—
711D4—244no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
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—62no—
740C2×C4—62no—
741C2×C4—84no—
742C2×C4—121no—
743C2×C4—121no—
744C2×C4—121no—
745C2×C4—121no—
746C2×C4—121no—
747C2×C4—121no—
748C2×C4—121no—
749C2×C4#93912yes—
750C2×C4#93912yes—
751C2×C4C2×D3×D411yescharacteristic
752C2×C4C2×D3×D411yescharacteristic
753C2×C4C2×#23711yescharacteristic
754C2×C4#100411yescharacteristic
755C2×C4D3×#4111yescharacteristic
756C2×C4#100911yescharacteristic
757C8—62no—
758C8—62no—
759C8—62no—
760C8—121no—
761C2×C3—42no—
762C2×C3—81no—
763C2×C3—82no—
764C2×C3#242811yescharacteristic
765C2×C3#305511yescharacteristic
766C2×C3#306111yescharacteristic
767C2×C3#326411yescharacteristic
768C2×C3#326911yescharacteristic
769C2×C3#330811yescharacteristic
770C2×C3#331911yescharacteristic
771D3—161no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—42no—
781C22—41no—
782C22—42no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—42no—
788C22—41no—
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
802C22C2×#93911yescharacteristic
803C22#582211yescharacteristic
804C22#582911yescharacteristic
805C22#583511yescharacteristic
806C22#583811yescharacteristic
807C4—22no—
808C4—22no—
809C4—41no—
810C4—41no—
811C4—81no—
812C4—81no—
813C4—81no—
814C4—122no—
815C4—122no—
816C4—241no—
817C4#559611yescharacteristic
818C4#559911yescharacteristic
819C4#560911yescharacteristic
820C4#561911yescharacteristic
821C3#2539711yescharacteristic, complemented, Sylow
822C2—42no—
823C2—81no—
824C2—82no—
825C2—481no—
826C2#8262111yescharacteristic
827C2#8264911yescharacteristic
828C2#8342111yescharacteristic
829C2#8348811yescharacteristic
830C2#8352811yescharacteristic
831C2#8353211yescharacteristic
832C2#8365311yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2537C2
socleC23×C3C22×D4
hypercenter#2537D3
hypocenterC3#25397
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2537

Complements

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

NH ≅ G/Ntype
1. C3×#2537C2semidirect
2. C2×#5042C2semidirect
3. C2×#5038C2semidirect
4. #82377C2semidirect
5. C2×#5016C2semidirect
6. C2×#5011C2semidirect
7. #71685C2semidirect
8. #71684C2semidirect
9. #71609C2semidirect
10. #69581C2semidirect
11. #69567C2semidirect
12. #69527C2semidirect
13. #69523C2semidirect
14. #69517C2semidirect
15. #69514C2semidirect
69. #2537D3semidirect
153. #832D4semidirect
165. C4⋊(C3⋊C8)D4semidirect
821. C3#25397semidirect

Maximal subgroups

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

subgroupindex
C3×#25372
C2×#50422
C2×#50382
#823772
C2×#50162
C2×#50112
#716852
#716842
#716092
#695812
#695672
#695272
#695232
#695172
#695142
#253973