Finite Group Databasebeta

← #10846299

Subgroups — #10846299

Order 768.

1238 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#2428C211yesmaximal, characteristic, complemented
2C2×#5073C211yesmaximal, characteristic, complemented
3C2×#5038C211yesmaximal, characteristic, complemented
4C2×#5038C211yesmaximal, characteristic, complemented
5C2×C4×#213C211yesmaximal, characteristic, complemented
6#73487C211yesmaximal, characteristic, complemented
7#71762C211yesmaximal, characteristic, complemented
8#71684C211yesmaximal, characteristic, complemented
9#71684C211yesmaximal, characteristic, complemented
10#71613C211yesmaximal, characteristic, complemented
11#69657C211yesmaximal, characteristic, complemented
12#69647C211yesmaximal, characteristic, complemented
13#69627C211yesmaximal, characteristic, complemented
14#69619C211yesmaximal, characteristic, complemented
15C22⋊C4×C3⋊C8C211yesmaximal, characteristic, complemented
16#25414—31nomaximal, Sylow
17C2×C3×#127C2211yescharacteristic
18C2×C3×#121—21no—
19C2×C3×#121C2211yescharacteristic
20C2×C3×#121C2211yescharacteristic
21C2×C3×C4×D4C2211yescharacteristic
22C22×#213C2211yescharacteristic
23C22×#213C2211yescharacteristic
24C22×#213C2211yescharacteristic
25C22×#213C2211yescharacteristic
26C2×#930C2211yescharacteristic
27C2×#930C2211yescharacteristic
28C23×C3⋊C8C2211yescharacteristic
29C2×#884—21no—
30C2×#874C2211yescharacteristic
31C2×C4×D12C2211yescharacteristic
32C3×#394—21no—
33C3×#392—21no—
34C3×#390C2211yescharacteristic
35C3×#389C2211yescharacteristic
36C3×#386—21no—
37C3×C4×C22⋊C4C2211yescharacteristic
38C2×#832C2211yescharacteristic
39C2×#832C2211yescharacteristic
40C2×#832C2211yescharacteristic
41C2×#832C2211yescharacteristic
42C2×#830C2211yescharacteristic
43#5073—24no—
44#5038—24no—
45#5038—24no—
46C4×#213—24no—
47C2×#809C2211yescharacteristic
48C2×#809C2211yescharacteristic
49C2×#809C2211yescharacteristic
50C2×#809C2211yescharacteristic
51C2×#807C2211yescharacteristic
52C2×#807C2211yescharacteristic
53#4960—21no—
54#4939C2211yescharacteristic
55#4928C2211yescharacteristic
56C2×C4×C3⋊C8C2211yescharacteristic
57C2×C4×C3⋊C8C2211yescharacteristic
58#4672—21no—
59#4665—21no—
60#4529C2211yescharacteristic
61#4529C2211yescharacteristic
62#4524C2211yescharacteristic
63#4524C2211yescharacteristic
64C2×#493—31no—
65C2×#466—31no—
66C2×#466—31no—
67C2×C4×D8—31no—
68#2428—31no—
69#2428D311yescharacteristic, complemented
70#2041—31no—
71#2041—31no—
72#1999—31no—
73#1999—31no—
74#1970—31no—
75#1942—31no—
76#1879—31no—
77#1879—31no—
78C8×C22⋊C4—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×#67—21no—
89C22×D12—21no—
90C22×D12—21no—
91C22×D12C2311yescharacteristic
92C22×D12C2311yescharacteristic
93C22×C4×D3—21no—
94C3×#127—22no—
95C3×#127—41no—
96C3×#121—22no—
97C3×#121—22no—
98C3×#121—41no—
99C3×#121—41no—
100C3×#121—44no—
101C3×C4×D4—22no—
102C3×C4×D4—41no—
103C2×C3×C4⋊C4—21no—
104C2×C3×C4⋊C4C2311yescharacteristic
105C2×C3×C4⋊C4C2311yescharacteristic
106C2×C3×C22⋊C4—21no—
107C2×C3×C22⋊C4—21no—
108C2×C3×C22⋊C4—21no—
109C2×C3×C22⋊C4—21no—
110C2×C3×C22⋊C4—21no—
111C2×C3×C22⋊C4D411yescharacteristic
112C2×C3×C22⋊C4D411yescharacteristic
113C2×C3×C42C2311yescharacteristic
114C2×C3×C42C2311yescharacteristic
115C2×#213—22no—
116C2×#213—22no—
117C2×#213—22no—
118C2×#213—22no—
119C2×#213—22no—
120C2×#213—22no—
121C2×#213—22no—
122C2×#213—22no—
123C2×#213—22no—
124C2×#213—41no—
125C2×#213—41no—
126C2×#213D414yescomplemented
127#930—22no—
128#930—22no—
129#930—41no—
130#930—41no—
131C2×(C2×D3)⋊C4—21no—
132C2×(C2×D3)⋊C4—21no—
133C2×(C2×D3)⋊C4—21no—
134C2×(C2×D3)⋊C4—21no—
135C2×(C2×D3)⋊C4—21no—
136C2×C4⋊Dic3C2311yescharacteristic
137C2×C4⋊Dic3C2311yescharacteristic
138C2×Dic3⋊C4—21no—
139C22×C3⋊C8—22no—
140C22×C3⋊C8—22no—
141C22×C3⋊C8—22no—
142C22×C3⋊C8C2311yescharacteristic
143C22×C3⋊C8C2311yescharacteristic
144C22×C3⋊C8C2311yescharacteristic
145C22×C3⋊C8C2311yescharacteristic
146#884—44no—
147#874—22no—
148#874—41no—
149C4×D12—22no—
150C4×D12—41no—
151C3×#95—21no—
152C3×#95D411yescharacteristic
153C3×#95D411yescharacteristic
154#832—22no—
155#832—22no—
156#832—22no—
157#832—41no—
158C3⋊#95—21no—
159#830—22no—
160#809—22no—
161#809—22no—
162#809—22no—
163#809—41no—
164#807—22no—
165#807D414yescomplemented
166C4×C3⋊C8—22no—
167C4×C3⋊C8—22no—
168C22×D8—31no—
169C22×D8—31no—
170C22×D8—31no—
171C22×D8—31no—
172C23×C8—31no—
173C2×#127—31no—
174C2×#127C2×D311yescharacteristic
175C2×#121—21no—
176C2×#121—31no—
177C2×#121—31no—
178C2×#121—61no—
179C2×#121C2×D311yescharacteristic
180C2×#121C2×D311yescharacteristic
181C2×C4×D4—31no—
182C2×C4×D4C2×D311yescharacteristic
183#493—64no—
184#466—64no—
185#466—64no—
186C4×D8—64no—
187C2×#107—31no—
188C2×#107—31no—
189C2×#102—31no—
190C2×#102—31no—
191C2×#102—31no—
192C2×#102—31no—
193C2×#102—31no—
194C2×#102—31no—
195C2×#102—31no—
196C2×#102—31no—
197C2×C22⋊C8—31no—
198C2×C4×C8—31no—
199C2×C4×C8—31no—
200#394—21no—
201#394—61no—
202#392—21no—
203#392—61no—
204#390—31no—
205#390C2×D311yescharacteristic
206#389—31no—
207#389C2×D311yescharacteristic
208#386—21no—
209#386—61no—
210C4×C22⋊C4C2×D311yescharacteristic
211#340—31no—
212#340—31no—
213#336—31no—
214#336—31no—
215C24×C3—21no—
216C24×C3—21no—
217C24×C3C2×D411yescharacteristic
218C23×D3—21no—
219C23×D3—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—21no—
230C2×C3×D4—21no—
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—42no—
238C2×C3×D4—42no—
239C2×C3×D4—81no—
240C2×C3×D4—81no—
241C2×C3×D4—81no—
242C2×C3×D4—81no—
243C2×C3×D4C2×D412yes—
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—42no—
253C22×C3×C4—42no—
254C22×C3×C4—81no—
255C22×C3×C4C2×D411yescharacteristic
256C22×C3×C4C2×D411yescharacteristic
257C22×C3×C4C2×D411yescharacteristic
258C22×C3×C4C2×D411yescharacteristic
259C22×C3×C4C2×D411yescharacteristic
260C22×C3×C4C2411yescharacteristic
261C2×#67—42no—
262C2×#67—42no—
263C2×#67—42no—
264C2×#67—42no—
265C2×#67—81no—
266C2×#67—81no—
267C22×Dic3—21no—
268C22×Dic3—21no—
269C2×D12—21no—
270C2×D12—21no—
271C2×D12—21no—
272C2×D12—21no—
273C2×D12—21no—
274C2×D12—21no—
275C2×D12—21no—
276C2×D12—21no—
277C2×D12—21no—
278C2×D12—21no—
279C2×D12—21no—
280C2×D12—42no—
281C2×D12—42no—
282C2×D12—42no—
283C2×D12—42no—
284C2×D12—81no—
285C2×D12—81no—
286C2×D12C2×D412yes—
287C2×C4×D3—42no—
288C2×C4×D3—42no—
289C2×C4×D3—81no—
290C3×C4⋊C4—21no—
291C3×C4⋊C4—21no—
292C3×C4⋊C4—21no—
293C3×C4⋊C4—42no—
294C3×C4⋊C4C2×D412yes—
295C3×C22⋊C4—22no—
296C3×C22⋊C4—42no—
297C3×C22⋊C4—42no—
298C3×C22⋊C4—42no—
299C3×C22⋊C4—42no—
300C3×C22⋊C4—81no—
301C3×C22⋊C4D814yescomplemented
302C3×C42—21no—
303C3×C42—21no—
304C3×C42—21no—
305C3×C42—21no—
306#213—28no—
307#213—44no—
308#213—44no—
309#213—44no—
310(C2×D3)⋊C4—42no—
311(C2×D3)⋊C4—42no—
312(C2×D3)⋊C4—42no—
313(C2×D3)⋊C4—42no—
314(C2×D3)⋊C4—81no—
315C4⋊Dic3—21no—
316C4⋊Dic3—21no—
317C4⋊Dic3—21no—
318C4⋊Dic3C2×D412yes—
319Dic3⋊C4—42no—
320C2×C3⋊C8—21no—
321C2×C3⋊C8—21no—
322C2×C3⋊C8—21no—
323C2×C3⋊C8—21no—
324C2×C3⋊C8—21no—
325C2×C3⋊C8—21no—
326C2×C3⋊C8—21no—
327C2×C3⋊C8—21no—
328C2×C3⋊C8—44no—
329C2×C3⋊C8C2×D412yes—
330C2×C3⋊C8C2×D412yes—
331C2×C3⋊C8#4112yes—
332C2×C3⋊C8#4112yes—
333C22×D4—21no—
334C22×D4—21no—
335C22×D4—21no—
336C22×D4—21no—
337C22×D4—31no—
338C22×D4—31no—
339C22×D4—61no—
340C22×D4—61no—
341C22×D4—61no—
342C22×D4—61no—
343C22×D4C22×D311yescharacteristic
344C22×D4C22×D311yescharacteristic
345C23×C4—21no—
346C23×C4—61no—
347C23×C4C22×D311yescharacteristic
348C2×D8—34no—
349C2×D8—62no—
350C2×D8—62no—
351C2×D8—62no—
352C2×D8—62no—
353C2×D8—62no—
354C2×D8—62no—
355C2×D8—62no—
356C2×D8—62no—
357C2×D8—62no—
358C2×D8—121no—
359C2×D8—121no—
360C22×C8—31no—
361C22×C8—31no—
362C22×C8—31no—
363C22×C8—31no—
364C22×C8—62no—
365C22×C8—62no—
366C22×C8—62no—
367#127—22no—
368#127—41no—
369#127—62no—
370#127—121no—
371#121—22no—
372#121—22no—
373#121—41no—
374#121—41no—
375#121—44no—
376#121—62no—
377#121—62no—
378#121—121no—
379#121—121no—
380#121—124no—
381C4×D4—22no—
382C4×D4—41no—
383C4×D4—62no—
384C4×D4—121no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—31no—
387C2×C4⋊C4—31no—
388C2×C4⋊C4—61no—
389C2×C4⋊C4C22×D311yescharacteristic
390C2×C4⋊C4C22×D311yescharacteristic
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—61no—
397C2×C22⋊C4—61no—
398C2×C22⋊C4—61no—
399C2×C22⋊C4—61no—
400C2×C22⋊C4—61no—
401C2×C22⋊C4#6711yescharacteristic
402C2×C22⋊C4#6711yescharacteristic
403C2×C42C22×D311yescharacteristic
404C2×C42C22×D311yescharacteristic
405#107—34no—
406#107—62no—
407#102—62no—
408#102—62no—
409#102—62no—
410#102—62no—
411#102—62no—
412#102—62no—
413#102—121no—
414#102—121no—
415C22⋊C8—62no—
416C4×C8—62no—
417C4×C8—62no—
418#95—21no—
419#95—61no—
420#95#6711yescharacteristic
421#95#6711yescharacteristic
422C23×C3—21no—
423C23×C3—21no—
424C23×C3—21no—
425C23×C3—21no—
426C23×C3—21no—
427C23×C3—21no—
428C23×C3—22no—
429C23×C3—41no—
430C23×C3—41no—
431C23×C3—41no—
432C23×C3—41no—
433C23×C3—41no—
434C23×C3—41no—
435C23×C3—41no—
436C23×C3—41no—
437C23×C3—41no—
438C23×C3—41no—
439C23×C3—41no—
440C23×C3—41no—
441C23×C3—41no—
442C23×C3C2×D812yes—
443C23×C3C22×D411yescharacteristic
444C22×D3—22no—
445C22×D3—41no—
446C22×D3—41no—
447C22×D3—41no—
448C22×D3—41no—
449C22×D3—41no—
450C22×D3—41no—
451C22×D3—41no—
452C22×D3—41no—
453C22×D3—41no—
454C22×D3—41no—
455C22×D3—41no—
456C22×D3—41no—
457C22×D3—41no—
458C3×D4—22no—
459C3×D4—22no—
460C3×D4—41no—
461C3×D4—41no—
462C3×D4—41no—
463C3×D4—41no—
464C3×D4—41no—
465C3×D4—41no—
466C3×D4—84no—
467C3×D4—84no—
468C3×D4—84no—
469C3×D4—84no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—22no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
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—41no—
492C2×C3×C4—84no—
493C2×C3×C4C2×D812yes—
494C2×C3×C4C2×D812yes—
495C2×C3×C4#13512yes—
496C2×C3×C4C22×D411yescharacteristic
497C2×C3×C4C22×D411yescharacteristic
498C2×C3×C4C2×#4111yescharacteristic
499C2×C3×C4C2×#4111yescharacteristic
500C2×C3×C4H(5,𝔽2)11yescharacteristic
501C2×C3×C4H(5,𝔽2)11yescharacteristic
502#67—84no—
503#67—84no—
504C2×Dic3—22no—
505C2×Dic3—41no—
506C2×Dic3—41no—
507C2×Dic3—41no—
508C2×Dic3—41no—
509C2×Dic3—41no—
510D12—22no—
511D12—22no—
512D12—41no—
513D12—41no—
514D12—41no—
515D12—41no—
516D12—41no—
517D12—41no—
518D12—84no—
519D12—84no—
520C4×D3—84no—
521C3⋊C8—22no—
522C3⋊C8—41no—
523C3⋊C8—41no—
524C3⋊C8#12114yescomplemented
525C24—21no—
526C24—21no—
527C24—61no—
528C24—61no—
529C24C2×#6711yescharacteristic
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—32no—
542C2×D4—42no—
543C2×D4—42no—
544C2×D4—42no—
545C2×D4—42no—
546C2×D4—42no—
547C2×D4—42no—
548C2×D4—42no—
549C2×D4—42no—
550C2×D4—61no—
551C2×D4—61no—
552C2×D4—61no—
553C2×D4—61no—
554C2×D4—61no—
555C2×D4—61no—
556C2×D4—61no—
557C2×D4—61no—
558C2×D4—61no—
559C2×D4—61no—
560C2×D4—61no—
561C2×D4—81no—
562C2×D4—81no—
563C2×D4—81no—
564C2×D4—81no—
565C2×D4—122no—
566C2×D4—122no—
567C2×D4—122no—
568C2×D4—122no—
569C2×D4—122no—
570C2×D4—122no—
571C2×D4—122no—
572C2×D4—122no—
573C2×D4—241no—
574C2×D4—241no—
575C2×D4—241no—
576C2×D4—241no—
577C2×D4D3×D412yes—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—61no—
589C22×C4—61no—
590C22×C4—81no—
591C22×C4—122no—
592C22×C4—122no—
593C22×C4—241no—
594C22×C4C2×#6711yescharacteristic
595C22×C4C2×#6711yescharacteristic
596C22×C4C2×#6711yescharacteristic
597C22×C4C2×#6711yescharacteristic
598C22×C4C2×#6711yescharacteristic
599C22×C4C23×D311yescharacteristic
600D8—68no—
601D8—124no—
602D8—124no—
603D8—124no—
604C2×C8—32no—
605C2×C8—32no—
606C2×C8—32no—
607C2×C8—32no—
608C2×C8—61no—
609C2×C8—61no—
610C2×C8—61no—
611C2×C8—61no—
612C2×C8—61no—
613C2×C8—61no—
614C2×C8—61no—
615C2×C8—61no—
616C2×C8—124no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—32no—
621C4⋊C4—42no—
622C4⋊C4—61no—
623C4⋊C4—61no—
624C4⋊C4—61no—
625C4⋊C4—122no—
626C4⋊C4D3×D412yes—
627C22⋊C4—22no—
628C22⋊C4—42no—
629C22⋊C4—42no—
630C22⋊C4—42no—
631C22⋊C4—42no—
632C22⋊C4—81no—
633C22⋊C4—122no—
634C22⋊C4—122no—
635C22⋊C4—122no—
636C22⋊C4—122no—
637C22⋊C4—241no—
638C22⋊C4#21314yescomplemented
639C42—21no—
640C42—21no—
641C42—21no—
642C42—21no—
643C22×C3—22no—
644C22×C3—22no—
645C22×C3—22no—
646C22×C3—41no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—41no—
650C22×C3—42no—
651C22×C3—42no—
652C22×C3—42no—
653C22×C3—81no—
654C22×C3—81no—
655C22×C3—81no—
656C22×C3—81no—
657C22×C3—81no—
658C22×C3—81no—
659C22×C3—81no—
660C22×C3—81no—
661C22×C3—81no—
662C22×C3—81no—
663C22×C3—81no—
664C22×C3#53211yescharacteristic
665C22×C3D4211yescharacteristic
666C22×C3D4211yescharacteristic
667C22×C3C22×D811yescharacteristic
668C22×C3C2×#13511yescharacteristic
669C22×C3#57611yescharacteristic
670C22×C3#57611yescharacteristic
671C2×D3—42no—
672C2×D3—42no—
673C2×D3—42no—
674C2×D3—81no—
675C2×D3—81no—
676C2×D3—81no—
677C2×D3—81no—
678C2×D3—81no—
679C2×D3—81no—
680C2×D3—81no—
681C2×D3—81no—
682C2×D3—81no—
683C2×D3—81no—
684C2×D3—81no—
685C3×C4—22no—
686C3×C4—22no—
687C3×C4—22no—
688C3×C4—41no—
689C3×C4—42no—
690C3×C4—41no—
691C3×C4—81no—
692C3×C4C2×#12111yescharacteristic
693C3×C4#54011yescharacteristic
694C3×C4#54611yescharacteristic
695C3×C4#55011yescharacteristic
696Dic3—42no—
697Dic3—81no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—22no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—62no—
719C23—121no—
720C23—121no—
721C23—121no—
722C23—121no—
723C23—121no—
724C23—121no—
725C23—121no—
726C23—121no—
727C23—121no—
728C23—121no—
729C23—121no—
730C23—121no—
731C23—121no—
732C23C2×#21312yes—
733C23C22×#6711yescharacteristic
734D4—22no—
735D4—22no—
736D4—41no—
737D4—41no—
738D4—41no—
739D4—41no—
740D4—41no—
741D4—41no—
742D4—62no—
743D4—62no—
744D4—84no—
745D4—84no—
746D4—84no—
747D4—84no—
748D4—121no—
749D4—121no—
750D4—121no—
751D4—121no—
752D4—121no—
753D4—121no—
754D4—244no—
755D4—244no—
756D4—244no—
757D4—244no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—22no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
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—62no—
781C2×C4—84no—
782C2×C4—121no—
783C2×C4—121no—
784C2×C4—121no—
785C2×C4—121no—
786C2×C4—121no—
787C2×C4—244no—
788C2×C4C2×#21312yes—
789C2×C4C2×#21312yes—
790C2×C4#95012yes—
791C2×C4C2×D3×D411yescharacteristic
792C2×C4C2×D3×D411yescharacteristic
793C2×C4#100411yescharacteristic
794C2×C4#100411yescharacteristic
795C2×C4D3×#4111yescharacteristic
796C2×C4D3×#4111yescharacteristic
797C8—34no—
798C8—62no—
799C8—121no—
800C8—121no—
801C2×C3—42no—
802C2×C3—82no—
803C2×C3—161no—
804C2×C3#242811yescharacteristic
805C2×C3#316911yescharacteristic
806C2×C3#317611yescharacteristic
807C2×C3D4×D811yescharacteristic
808C2×C3D4×D811yescharacteristic
809C2×C3#328011yescharacteristic
810C2×C3#328711yescharacteristic
811D3—82no—
812D3—161no—
813C22—22no—
814C22—22no—
815C22—22no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22—81no—
824C22—81no—
825C22—81no—
826C22—81no—
827C22—81no—
828C22—81no—
829C22—81no—
830C22—81no—
831C22—81no—
832C22—81no—
833C22—81no—
834C22—122no—
835C22—122no—
836C22—122no—
837C22—241no—
838C22—241no—
839C22—241no—
840C22—241no—
841C22—241no—
842C22—241no—
843C22—241no—
844C22—241no—
845C22—241no—
846C22—241no—
847C22—241no—
848C22C22×#21311yescharacteristic
849C22D4×#6711yescharacteristic
850C22D4×#6711yescharacteristic
851C22C2×#95011yescharacteristic
852C22#583211yescharacteristic
853C22#583511yescharacteristic
854C22#583511yescharacteristic
855C4—22no—
856C4—22no—
857C4—22no—
858C4—42no—
859C4—41no—
860C4—41no—
861C4—81no—
862C4—122no—
863C4—241no—
864C4#559911yescharacteristic
865C4D3×#12111yescharacteristic
866C4#561011yescharacteristic
867C4#561511yescharacteristic
868C3#2541411yescharacteristic, complemented, Sylow
869C2—42no—
870C2—82no—
871C2—161no—
872C2—242no—
873C2—481no—
874C2#8265011yescharacteristic
875C2#8329111yescharacteristic
876C2#8343211yescharacteristic
877C2D4×#21311yescharacteristic
878C2D4×#21311yescharacteristic
879C2#8350511yescharacteristic
880C2#8358511yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2428C2
socleC23×C3C22×D4
hypercenter#2428D3
hypocenterC3#25414
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×#5073C2semidirect
3. C2×#5038C2semidirect
4. C2×#5038C2semidirect
5. C2×C4×#213C2semidirect
6. #73487C2semidirect
7. #71762C2semidirect
8. #71684C2semidirect
9. #71684C2semidirect
10. #71613C2semidirect
11. #69657C2semidirect
12. #69647C2semidirect
13. #69627C2semidirect
14. #69619C2semidirect
15. C22⋊C4×C3⋊C8C2semidirect
69. #2428D3semidirect
126. C2×#213D4semidirect
165. #807D4semidirect
301. C3×C22⋊C4D8semidirect
524. C3⋊C8#121semidirect
638. C22⋊C4#213semidirect
868. C3#25414semidirect

Maximal subgroups

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

subgroupindex
C3×#24282
C2×#50732
C2×#50382
C2×C4×#2132
#734872
#717622
#716842
#716132
#696572
#696472
#696272
#696192
C22⋊C4×C3⋊C82
#254143