Finite Group Databasebeta

← #10846150

Subgroups — #10846150

Order 768.

1120 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#2536C211yesmaximal, characteristic, complemented
2C2×#5049C211yesmaximal, characteristic, complemented
3C2×#5048C211yesmaximal, characteristic, complemented
4C2×#5027C211yesmaximal, characteristic, complemented
5#82378C211yesmaximal, characteristic
6C2×#5011C211yesmaximal, characteristic, complemented
7#71699C211yesmaximal, characteristic, complemented
8#71699C211yesmaximal, characteristic, complemented
9#71631C211yesmaximal, characteristic, complemented
10#69553C211yesmaximal, characteristic, complemented
11#69540C211yesmaximal, characteristic, complemented
12#69524C211yesmaximal, characteristic, complemented
13#69523C211yesmaximal, characteristic, complemented
14#69517C211yesmaximal, characteristic, complemented
15#69515C211yesmaximal, characteristic, complemented
16#25402—31nomaximal, Sylow
17C2×C3×C22⋊Q8C2211yescharacteristic
18C2×C3×C22⋊Q8C2211yescharacteristic
19C2×C3×C4×Q8C2211yescharacteristic
20C2×C3×C4×D4C2211yescharacteristic
21C22×#215C2211yescharacteristic
22C22×#215C2211yescharacteristic
23C2×#940—21no—
24C2×#930C2211yescharacteristic
25C2×#930C2211yescharacteristic
26C2×#930C2211yescharacteristic
27C2×#930C2211yescharacteristic
28C22×#208C2211yescharacteristic
29C23×C3⋊C8C2211yescharacteristic
30C2×#874C2211yescharacteristic
31C3×#398—21no—
32C3×#394—21no—
33C3×#388—21no—
34C3×#388—21no—
35C3×#382C2211yescharacteristic
36C3×#380C2211yescharacteristic
37C3×#380C2211yescharacteristic
38C2×#835C2211yescharacteristic
39C2×#835C2211yescharacteristic
40C2×#830C2211yescharacteristic
41C2×#830C2211yescharacteristic
42#5049—24no—
43#5048—24no—
44#5027—24no—
45#5011—24no—
46#4988—21no—
47C2×#809C2211yescharacteristic
48C2×#809C2211yescharacteristic
49C2×#809C2211yescharacteristic
50C2×#809C2211yescharacteristic
51C2×#809C2211yescharacteristic
52C2×#809C2211yescharacteristic
53C2×#808C2211yescharacteristic
54C2×#807C2211yescharacteristic
55#4960—21no—
56#4960—21no—
57C4×C4⋊Dic3C2211yescharacteristic
58C2×C4⋊(C3⋊C8)C2211yescharacteristic
59C2×#803C2211yescharacteristic
60#4529C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#468—31no—
65C2×#465—31no—
66C2×#460—31no—
67C2×#435—31no—
68#2541—31no—
69#2536D311yescharacteristic, complemented
70#2034—31no—
71#2033—31no—
72#2000—31no—
73#2000—31no—
74#1961—31no—
75#1949—31no—
76#1895—31no—
77#1893—31no—
78#1763—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×D4D411yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C22×#67—21no—
84C22×#67—21no—
85C22×#67—21no—
86C22×#67—21no—
87C22×D12—21no—
88C22×D12—21no—
89C22×D12C2311yescharacteristic
90C22×D12C2311yescharacteristic
91C3×C22⋊Q8—22no—
92C3×C22⋊Q8—22no—
93C3×C22⋊Q8—41no—
94C3×C22⋊Q8—41no—
95C3×C4×Q8—22no—
96C3×C4×Q8—22no—
97C3×C4×D4—22no—
98C3×C4×D4—22no—
99C2×C3×C4⋊C4—21no—
100C2×C3×C4⋊C4—21no—
101C2×C3×C4⋊C4—21no—
102C2×C3×C4⋊C4D411yescharacteristic
103C2×C3×C4⋊C4C2311yescharacteristic
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⋊C4D411yescharacteristic
111C2×C3×C22⋊C4D411yescharacteristic
112C2×C3×C42—21no—
113C2×C3×C42C2311yescharacteristic
114C2×#215—22no—
115C2×#215—22no—
116C2×#215—22no—
117C2×#215—22no—
118C2×#215—41no—
119C2×#215—41no—
120#940—44no—
121#930—22no—
122#930—22no—
123#930—22no—
124#930—22no—
125#930—41no—
126#930—41no—
127#930—41no—
128#930—41no—
129C2×(C2×D3)⋊C4—21no—
130C2×(C2×D3)⋊C4—21no—
131C2×(C2×D3)⋊C4—21no—
132C2×(C2×D3)⋊C4—21no—
133C2×C4⋊Dic3C2311yescharacteristic
134C2×C4⋊Dic3C2311yescharacteristic
135C2×C4×Dic3—21no—
136C2×#208—22no—
137C2×#208—22no—
138C2×#208—41no—
139C22×C3⋊C8—22no—
140C22×C3⋊C8—22no—
141C22×C3⋊C8—41no—
142C22×C3⋊C8C2311yescharacteristic
143C22×C3⋊C8C2311yescharacteristic
144C22×C3⋊C8C2311yescharacteristic
145C22×C3⋊C8C2311yescharacteristic
146#874—22no—
147#874—22no—
148C3×#95—21no—
149C3×#95—21no—
150C3×#95—21no—
151C3×#95—21no—
152#835—22no—
153#835D414yescomplemented
154C3⋊#95—21no—
155#830—22no—
156#830—22no—
157#809—22no—
158#809—22no—
159#809—22no—
160#809—22no—
161#809—41no—
162#809—41no—
163#808—22no—
164#807—22no—
165C4⋊(C3⋊C8)D414yescomplemented
166#803—22no—
167C22×SD16—31no—
168C22×SD16—31no—
169C22×M16—31no—
170C23×C8—31no—
171C2×#127—31no—
172C2×#127—61no—
173C2×C22⋊Q8C2×D311yescharacteristic
174C2×C22⋊Q8C2×D311yescharacteristic
175C2×#121—31no—
176C2×#121—31no—
177C2×#121—31no—
178C2×#121—31no—
179C2×C4×Q8C2×D311yescharacteristic
180C2×C4×D4C2×D311yescharacteristic
181#468—64no—
182#465—64no—
183#460—64no—
184#435—64no—
185C2×#107—31no—
186C2×#106—31no—
187C2×C4⋊C8—31no—
188C2×#103—31no—
189C2×#103—31no—
190C2×#102—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#398—21no—
200#394—21no—
201#392—61no—
202#392—61no—
203#390—61no—
204#388—21no—
205#388—21no—
206#382C2×D311yescharacteristic
207#380C2×D311yescharacteristic
208#380C2×D311yescharacteristic
209C4×C4⋊C4—31no—
210#340—31no—
211#340—31no—
212#340—31no—
213#340—31no—
214C24×C3C2×D411yescharacteristic
215C24×C3C2×D411yescharacteristic
216C23×D3—21no—
217C23×D3—21no—
218C2×C3×Q8—21no—
219C2×C3×Q8—21no—
220C2×C3×Q8—21no—
221C2×C3×Q8—21no—
222C2×C3×Q8—21no—
223C2×C3×Q8C2×D412yes—
224C2×C3×D4—22no—
225C2×C3×D4—22no—
226C2×C3×D4—41no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
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×C4C2×D411yescharacteristic
244C22×C3×C4C2×D411yescharacteristic
245C22×C3×C4C2×D411yescharacteristic
246C22×C3×C4C2×D411yescharacteristic
247C22×C3×C4C2411yescharacteristic
248C2×#67—42no—
249C2×#67—42no—
250C2×#67—42no—
251C2×#67—42no—
252C2×#67—42no—
253C2×#67—42no—
254C2×#67—42no—
255C2×#67—42no—
256C2×#67—81no—
257C2×#67—81no—
258C2×#67—81no—
259C2×#67—81no—
260C22×Dic3—21no—
261C22×Dic3—21no—
262C2×D12—21no—
263C2×D12—21no—
264C2×D12—21no—
265C2×D12—21no—
266C2×D12—21no—
267C2×D12—21no—
268C2×D12—21no—
269C2×D12—21no—
270C2×D12—21no—
271C2×D12—21no—
272C2×D12—21no—
273C2×D12—21no—
274C2×D12—42no—
275C2×D12—42no—
276C2×D12—42no—
277C2×D12—42no—
278C2×D12—81no—
279C2×D12—81no—
280C3×C4⋊C4—22no—
281C3×C4⋊C4—21no—
282C3×C4⋊C4—21no—
283C3×C4⋊C4—21no—
284C3×C4⋊C4—21no—
285C3×C4⋊C4—21no—
286C3×C4⋊C4—21no—
287C3×C4⋊C4—42no—
288C3×C4⋊C4—42no—
289C3×C4⋊C4—42no—
290C3×C22⋊C4—22no—
291C3×C22⋊C4—22no—
292C3×C22⋊C4—42no—
293C3×C22⋊C4—42no—
294C3×C22⋊C4—42no—
295C3×C22⋊C4—42no—
296C3×C42—42no—
297C3×C42C2×D412yes—
298C3×C42#4112yes—
299#215—44no—
300#215—44no—
301(C2×D3)⋊C4—42no—
302(C2×D3)⋊C4—42no—
303(C2×D3)⋊C4—42no—
304(C2×D3)⋊C4—42no—
305C4⋊Dic3—21no—
306C4⋊Dic3—21no—
307C4⋊Dic3C2×D412yes—
308C4⋊Dic3#4112yes—
309C4×Dic3—42no—
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×Q8C22×D311yescharacteristic
325C22×D4—31no—
326C22×D4—31no—
327C22×D4—61no—
328C22×D4—61no—
329C22×D4—61no—
330C22×D4—61no—
331C22×D4—61no—
332C22×D4—61no—
333C22×D4#6711yescharacteristic
334C23×C4C22×D311yescharacteristic
335C23×C4C22×D311yescharacteristic
336C2×SD16—62no—
337C2×SD16—62no—
338C2×SD16—62no—
339C2×SD16—62no—
340C2×SD16—121no—
341C2×SD16—121no—
342C2×M16—62no—
343C2×M16—62no—
344C2×M16—121no—
345C22×C8—31no—
346C22×C8—31no—
347C22×C8—31no—
348C22×C8—31no—
349C22×C8—62no—
350C22×C8—62no—
351C22×C8—121no—
352#127—62no—
353#127—62no—
354#127—124no—
355C22⋊Q8—22no—
356C22⋊Q8—22no—
357C22⋊Q8—41no—
358C22⋊Q8—41no—
359#121—62no—
360#121—62no—
361#121—62no—
362#121—62no—
363#121—121no—
364#121—121no—
365#121—121no—
366#121—121no—
367C4×Q8—22no—
368C4×Q8—22no—
369C4×D4—22no—
370C4×D4—22no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—31no—
375C2×C4⋊C4—31no—
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—61no—
385C2×C22⋊C4—61no—
386C2×C22⋊C4—61no—
387C2×C22⋊C4—61no—
388C2×C22⋊C4#6711yescharacteristic
389C2×C22⋊C4#6711yescharacteristic
390C2×C42—21no—
391C2×C42—61no—
392C2×C42C22×D311yescharacteristic
393#107—62no—
394#106—62no—
395C4⋊C8—34no—
396#103—34no—
397#103—62no—
398#102—62no—
399#102—62no—
400#102—62no—
401#102—62no—
402#102—121no—
403#102—121no—
404C22⋊C8—62no—
405C22⋊C8—62no—
406#97—62no—
407#95—21no—
408#95—21no—
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—21no—
421C23×C3—21no—
422C23×C3—21no—
423C23×C3—21no—
424C23×C3—21no—
425C23×C3AGL(1,ℤ/8)12yes—
426C23×C3C22×D411yescharacteristic
427C22×D3—41no—
428C22×D3—41no—
429C22×D3—41no—
430C22×D3—41no—
431C22×D3—41no—
432C22×D3—41no—
433C22×D3—41no—
434C22×D3—41no—
435C22×D3—41no—
436C22×D3—41no—
437C22×D3—41no—
438C22×D3—41no—
439C22×D3—41no—
440C22×D3—41no—
441C3×Q8—22no—
442C3×Q8—22no—
443C3×Q8—41no—
444C3×Q8—41no—
445C3×D4—44no—
446C2×C3×C4—21no—
447C2×C3×C4—21no—
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—22no—
455C2×C3×C4—21no—
456C2×C3×C4—21no—
457C2×C3×C4—41no—
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—41no—
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—
486#67—84no—
487#67—84no—
488C2×Dic3—22no—
489C2×Dic3—22no—
490C2×Dic3—41no—
491C2×Dic3—41no—
492C2×Dic3—41no—
493C2×Dic3—41no—
494D12—41no—
495D12—41no—
496D12—41no—
497D12—41no—
498D12—41no—
499D12—41no—
500D12—41no—
501D12—41no—
502D12—84no—
503D12—84no—
504C3⋊C8—22no—
505C3⋊C8—22no—
506C3⋊C8—22no—
507C3⋊C8—41no—
508C24—61no—
509C24—61no—
510C24C2×#6711yescharacteristic
511C24C2×#6711yescharacteristic
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8D3×D412yes—
518C2×D4—22no—
519C2×D4—22no—
520C2×D4—41no—
521C2×D4—61no—
522C2×D4—61no—
523C2×D4—61no—
524C2×D4—61no—
525C2×D4—61no—
526C2×D4—61no—
527C2×D4—61no—
528C2×D4—61no—
529C2×D4—61no—
530C2×D4—61no—
531C2×D4—61no—
532C2×D4—61no—
533C2×D4—122no—
534C2×D4—122no—
535C2×D4—122no—
536C2×D4—122no—
537C2×D4—122no—
538C2×D4—122no—
539C2×D4—122no—
540C2×D4—122no—
541C2×D4—122no—
542C2×D4—122no—
543C2×D4—122no—
544C2×D4—122no—
545C2×D4—241no—
546C2×D4—241no—
547C2×D4—241no—
548C2×D4—241no—
549C2×D4—241no—
550C2×D4—241no—
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—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—61no—
568C22×C4—61no—
569C22×C4C2×#6711yescharacteristic
570C22×C4C2×#6711yescharacteristic
571C22×C4C2×#6711yescharacteristic
572C22×C4C2×#6711yescharacteristic
573C22×C4C23×D311yescharacteristic
574SD16—124no—
575SD16—124no—
576M16—124no—
577C2×C8—32no—
578C2×C8—32no—
579C2×C8—32no—
580C2×C8—61no—
581C2×C8—61no—
582C2×C8—61no—
583C2×C8—61no—
584C2×C8—61no—
585C2×C8—61no—
586C2×C8—61no—
587C2×C8—61no—
588C2×C8—61no—
589C2×C8—124no—
590C4⋊C4—22no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—32no—
598C4⋊C4—32no—
599C4⋊C4—42no—
600C4⋊C4—42no—
601C4⋊C4—42no—
602C4⋊C4—61no—
603C4⋊C4—61no—
604C22⋊C4—22no—
605C22⋊C4—22no—
606C22⋊C4—42no—
607C22⋊C4—42no—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C22⋊C4—122no—
611C22⋊C4—122no—
612C22⋊C4—122no—
613C22⋊C4—122no—
614C42—42no—
615C42—122no—
616C42D3×D412yes—
617C42#23712yes—
618C22×C3—22no—
619C22×C3—22no—
620C22×C3—22no—
621C22×C3—41no—
622C22×C3—41no—
623C22×C3—41no—
624C22×C3—41no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—41no—
629C22×C3—41no—
630C22×C3—41no—
631C22×C3—41no—
632C22×C3C2×#12111yescharacteristic
633C22×C3D4211yescharacteristic
634C22×C3#54611yescharacteristic
635C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
636C22×C3#57511yescharacteristic
637C22×C3#57711yescharacteristic
638C22×C3#57711yescharacteristic
639C2×D3—81no—
640C2×D3—81no—
641C2×D3—81no—
642C2×D3—81no—
643C2×D3—81no—
644C2×D3—81no—
645C2×D3—81no—
646C2×D3—81no—
647C2×D3—81no—
648C2×D3—81no—
649C2×D3—81no—
650C2×D3—81no—
651C2×D3—81no—
652C2×D3—81no—
653C3×C4—22no—
654C3×C4—22no—
655C3×C4—41no—
656C3×C4—41no—
657C3×C4—42no—
658C3×C4—81no—
659C3×C4—81no—
660C3×C4—81no—
661C3×C4#53211yescharacteristic
662C3×C4#54011yescharacteristic
663C3×C4D4211yescharacteristic
664C3×C4#55011yescharacteristic
665Dic3—42no—
666Dic3—42no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—121no—
681C23—121no—
682C23—121no—
683C23—121no—
684C23—121no—
685C23—121no—
686C23—121no—
687C23—121no—
688C23—121no—
689C23—121no—
690C23—121no—
691C23—121no—
692C23—121no—
693C23—121no—
694C23#94912yes—
695C23C22×#6711yescharacteristic
696Q8—22no—
697Q8—22no—
698Q8—41no—
699Q8—41no—
700D4—44no—
701D4—121no—
702D4—121no—
703D4—121no—
704D4—121no—
705D4—121no—
706D4—121no—
707D4—121no—
708D4—121no—
709D4—244no—
710D4—244no—
711D4—244no—
712D4—244no—
713D4—244no—
714D4—244no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—22no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
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—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—62no—
746C2×C4—62no—
747C2×C4—121no—
748C2×C4—121no—
749C2×C4—121no—
750C2×C4—121no—
751C2×C4#93912yes—
752C2×C4#93912yes—
753C2×C4C2×D3×D411yescharacteristic
754C2×C4C2×D3×D411yescharacteristic
755C2×C4C2×#23711yescharacteristic
756C2×C4#100411yescharacteristic
757C2×C4D3×#4111yescharacteristic
758C2×C4#100911yescharacteristic
759C8—62no—
760C8—62no—
761C8—62no—
762C8—121no—
763C2×C3—42no—
764C2×C3—81no—
765C2×C3#242811yescharacteristic
766C2×C3#305511yescharacteristic
767C2×C3#305711yescharacteristic
768C2×C3#326511yescharacteristic
769C2×C3#327111yescharacteristic
770C2×C3#331011yescharacteristic
771C2×C3#331711yescharacteristic
772D3—161no—
773D3—161no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—241no—
789C22—241no—
790C22—241no—
791C22—241no—
792C22—241no—
793C22—241no—
794C22—241no—
795C22—241no—
796C22—241no—
797C22—241no—
798C22—241no—
799C22—241no—
800C22—241no—
801C22—241no—
802C22D4×#6711yescharacteristic
803C22C2×#93911yescharacteristic
804C22C2×#94911yescharacteristic
805C22#582211yescharacteristic
806C22#582911yescharacteristic
807C22#583711yescharacteristic
808C22#583711yescharacteristic
809C4—22no—
810C4—22no—
811C4—41no—
812C4—41no—
813C4—42no—
814C4—81no—
815C4—81no—
816C4—81no—
817C4—122no—
818C4—122no—
819C4#559611yescharacteristic
820C4#559911yescharacteristic
821C4#560911yescharacteristic
822C4#561911yescharacteristic
823C3#2540211yescharacteristic, complemented, Sylow
824C2—42no—
825C2—81no—
826C2—481no—
827C2—481no—
828C2#8264911yescharacteristic
829C2#8292411yescharacteristic
830C2#8339811yescharacteristic
831C2#8354211yescharacteristic
832C2#8354711yescharacteristic
833C2#8359911yescharacteristic
834C2#8360411yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2536C2
socleC23×C3C22×D4
prime radical#82378C2
hypercenter#2536D3
hypocenterC3#25402
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
1. C3×#2536C2semidirect
2. C2×#5049C2semidirect
3. C2×#5048C2semidirect
4. C2×#5027C2semidirect
6. C2×#5011C2semidirect
7. #71699C2semidirect
8. #71699C2semidirect
9. #71631C2semidirect
10. #69553C2semidirect
11. #69540C2semidirect
12. #69524C2semidirect
13. #69523C2semidirect
14. #69517C2semidirect
15. #69515C2semidirect
69. #2536D3semidirect
153. #835D4semidirect
165. C4⋊(C3⋊C8)D4semidirect
823. C3#25402semidirect

Maximal subgroups

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

subgroupindex
C3×#25362
C2×#50492
C2×#50482
C2×#50272
#823782
C2×#50112
#716992
#716312
#695532
#695402
#695242
#695232
#695172
#695152
#254023