Finite Group Databasebeta

← #223635

Subgroups — #223635

Order 512.

1158 conjugacy classes of subgroups.

The subgroup lattice has 906 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36183C211yesmaximal, characteristic
2#22554C211yesmaximal, characteristic, complemented
3#13901C211yesmaximal, characteristic, complemented
4#9911C211yesmaximal, characteristic, complemented
5#9888C211yesmaximal, characteristic, complemented
6#9157C211yesmaximal, characteristic, complemented
7#9147C211yesmaximal, characteristic
8#9118C211yesmaximal, characteristic, complemented
9#9113C211yesmaximal, characteristic
10#8717C211yesmaximal, characteristic, complemented
11#8712C211yesmaximal, characteristic, complemented
12#8573C211yesmaximal, characteristic, complemented
13#8216C211yesmaximal, characteristic, complemented
14#8018C211yesmaximal, characteristic, complemented
15C2×#1294C211yesmaximal, characteristic, complemented
16C2×#551—21no—
17C2×#432C2211yescharacteristic
18C22×C22⋊C8C2211yescharacteristic
19#2857C2211yescharacteristic
20#2854C2211yescharacteristic
21#2847C2211yescharacteristic
22#2564—21no—
23#2553—21no—
24#2521—21no—
25#2501C411yescharacteristic, complemented
26#2498—21no—
27#2496C411yescharacteristic, complemented
28#2496C411yescharacteristic, complemented
29#2491C411yescharacteristic, complemented
30#2488—21no—
31#2440C411yescharacteristic, complemented
32#2422C411yescharacteristic, complemented
33#2412—21no—
34#2361C411yescharacteristic, complemented
35#2359—21no—
36#2344C411yescharacteristic, complemented
37C4×#121C2211yescharacteristic
38#2285C2211yescharacteristic
39C2×#383C2211yescharacteristic
40C2×#380C2211yescharacteristic
41C2×C4×C22⋊C4C2211yescharacteristic
42C22×#95C2211yescharacteristic
43#1924—21no—
44#1924—21no—
45#1850—21no—
46#1817C2211yescharacteristic
47#1797C2211yescharacteristic
48#1779C2211yescharacteristic
49#1752—21no—
50#1749C2211yescharacteristic
51C2×#327C2211yescharacteristic
52C2×#327C2211yescharacteristic
53C2×#327C2211yescharacteristic
54C2×#327C2211yescharacteristic
55#1443—21no—
56#1443—21no—
57#1434C2211yescharacteristic
58#1434C2211yescharacteristic
59#1434C2211yescharacteristic
60C22⋊#95—21no—
61C22⋊#95—21no—
62C22⋊#95C2211yescharacteristic
63#1294C2211yescharacteristic
64#1294C2211yescharacteristic
65#1294C2211yescharacteristic
66#1294C2211yescharacteristic
67#1294C2211yescharacteristic
68#1294C2211yescharacteristic
69#1294C2211yescharacteristic
70#1294C2211yescharacteristic
71#1294C2211yescharacteristic
72#1294C2211yescharacteristic
73#1294C2211yescharacteristic
74#1294C2211yescharacteristic
75C24×C4—21no—
76C24×C4C2311yescharacteristic
77C23×C8—21no—
78#551—44no—
79#551—44no—
80C2×C4⋊Q8C2×C411yescharacteristic, complemented
81C2×#126—21no—
82C2×#126—21no—
83C2×#124—21no—
84C2×#123—21no—
85C2×#123—21no—
86C2×#123—21no—
87C2×#123—21no—
88C2×C22⋊Q8—21no—
89C2×C22⋊Q8—21no—
90C2×#121C2×C411yescharacteristic
91C2×#121C2×C411yescharacteristic
92C2×#121C2311yescharacteristic
93C2×#120—21no—
94C2×C4×D4—21no—
95C2×C4×D4—21no—
96C2×C4×D4C2×C411yescharacteristic, complemented
97C2×#117—21no—
98C2×#117—21no—
99C22×C4⋊C4C2×C411yescharacteristic
100C22×C4⋊C4C2×C411yescharacteristic
101C22×C22⋊C4—21no—
102C22×C22⋊C4—21no—
103C22×C22⋊C4D411yescharacteristic
104C22×C22⋊C4D411yescharacteristic
105C22×C42C2311yescharacteristic
106C22×C42C2311yescharacteristic
107#432—22no—
108#432—41no—
109C2×C4⋊C8—21no—
110C2×C4⋊C8—21no—
111C2×C22⋊C8—22no—
112C2×C22⋊C8—21no—
113C2×C22⋊C8—21no—
114C2×C22⋊C8—21no—
115C2×C22⋊C8—41no—
116C2×C22⋊C8C2311yescharacteristic
117C2×C22⋊C8C2311yescharacteristic
118C2×C22⋊C8C2311yescharacteristic
119C2×C22⋊C8C2311yescharacteristic
120C2×#97—21no—
121C2×#97—21no—
122#400—21no—
123#400—21no—
124#399—21no—
125#399—21no—
126#398—21no—
127#397—21no—
128#397—21no—
129#397—21no—
130#395—21no—
131#394—21no—
132#394—21no—
133#393—21no—
134#391—21no—
135#390C2×C411yescharacteristic, complemented
136#390C2×C411yescharacteristic, complemented
137#390C2×C411yescharacteristic, complemented
138#389—21no—
139#389C2×C411yescharacteristic, complemented
140#389C2×C411yescharacteristic, complemented
141#389C2×C411yescharacteristic, complemented
142#389C2×C411yescharacteristic, complemented
143#389C2×C411yescharacteristic, complemented
144#388—21no—
145#388—21no—
146#388—21no—
147#388—21no—
148#388—21no—
149#387—21no—
150#387—21no—
151#387—21no—
152#387—21no—
153#386—21no—
154#386—21no—
155#386—21no—
156#386—21no—
157#386—21no—
158#386—21no—
159#385—21no—
160#385—21no—
161#385—21no—
162#384C2×C411yescharacteristic, complemented
163#384C2×C411yescharacteristic, complemented
164#384C2×C411yescharacteristic, complemented
165#383—22no—
166#383—41no—
167#382—21no—
168#381—21no—
169#380—21no—
170#380—21no—
171#380—21no—
172#380—21no—
173#380C2×C411yescharacteristic
174#380C2×C411yescharacteristic
175#380C2×C411yescharacteristic
176#380C2×C411yescharacteristic
177#380C2311yescharacteristic
178#380C2311yescharacteristic
179#380C2311yescharacteristic
180C4×C4⋊C4—21no—
181C4×C4⋊C4C2×C411yescharacteristic, complemented
182C4×C4⋊C4C2×C411yescharacteristic, complemented
183C4×C4⋊C4C2×C411yescharacteristic, complemented
184C4×C22⋊C4—21no—
185C4×C22⋊C4C2×C411yescharacteristic
186C4×C22⋊C4C2×C411yescharacteristic
187C4×C22⋊C4C2×C411yescharacteristic
188C4×C22⋊C4C2×C411yescharacteristic
189C4×C22⋊C4D411yescharacteristic
190C4×C22⋊C4D411yescharacteristic
191C4×C22⋊C4D411yescharacteristic
192C4×C22⋊C4D411yescharacteristic
193C2×#95—21no—
194C2×#95—22no—
195C2×#95—21no—
196C2×#95—21no—
197C2×#95—21no—
198C2×#95—21no—
199C2×#95—21no—
200C2×#95—21no—
201C2×#95—21no—
202C2×#95—21no—
203C2×#95—21no—
204C2×#95—21no—
205C2×#95—41no—
206C2×#95D411yescharacteristic
207C2×#95D411yescharacteristic
208C2×#95C2311yescharacteristic
209C2×#95C2311yescharacteristic
210C2×#95C2311yescharacteristic
211C2×#95C2311yescharacteristic
212#336—21no—
213#336—21no—
214#336—21no—
215#336—21no—
216#327—22no—
217#327—22no—
218#327—41no—
219#327—41no—
220C25C2×D411yescharacteristic
221C22×Q8—21no—
222C22×D4—21no—
223C22×D4—21no—
224C22×D4—21no—
225C22×D4C22×C411yescharacteristic
226C23×C4—21no—
227C23×C4—21no—
228C23×C4—21no—
229C23×C4—21no—
230C23×C4—21no—
231C23×C4—21no—
232C23×C4—21no—
233C23×C4—21no—
234C23×C4—21no—
235C23×C4—21no—
236C23×C4—21no—
237C23×C4—42no—
238C23×C4—42no—
239C23×C4—42no—
240C23×C4—42no—
241C23×C4—42no—
242C23×C4—42no—
243C23×C4—81no—
244C23×C4—81no—
245C23×C4—81no—
246C23×C4C22×C411yescharacteristic
247C23×C4C22×C411yescharacteristic
248C23×C4C2×D411yescharacteristic
249C23×C4C2×D411yescharacteristic
250C23×C4C2×D411yescharacteristic
251C23×C4C2×D411yescharacteristic
252C23×C4C2×D411yescharacteristic
253C23×C4C2×D411yescharacteristic
254C23×C4C2×D411yescharacteristic
255C23×C4C2411yescharacteristic
256C22×C8—21no—
257C22×C8—21no—
258C22×C8—21no—
259C22×C8—21no—
260C22×C8—42no—
261C22×C8—42no—
262C22×C8—81no—
263C4⋊Q8—81no—
264#126—44no—
265#126—44no—
266#124—44no—
267#123—44no—
268#123—44no—
269#123—44no—
270#123—42no—
271#123—42no—
272C22⋊Q8—44no—
273C22⋊Q8—42no—
274C22⋊Q8—42no—
275#121—21no—
276#121—21no—
277#121—21no—
278#121—21no—
279#121—42no—
280#121—81no—
281#120—42no—
282#120—42no—
283C4×D4—44no—
284C4×D4—42no—
285C4×D4—42no—
286C4×D4—81no—
287#117—44no—
288#117—42no—
289#117—42no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—42no—
305C2×C4⋊C4—81no—
306C2×C4⋊C4C22×C411yescharacteristic
307C2×C4⋊C4C22×C411yescharacteristic
308C2×C4⋊C4C22×C411yescharacteristic
309C2×C4⋊C4C22×C411yescharacteristic
310C2×C4⋊C4C22×C411yescharacteristic
311C2×C4⋊C4C22×C411yescharacteristic
312C2×C4⋊C4C22×C411yescharacteristic
313C2×C22⋊C4—22no—
314C2×C22⋊C4—22no—
315C2×C22⋊C4—21no—
316C2×C22⋊C4—21no—
317C2×C22⋊C4—21no—
318C2×C22⋊C4—21no—
319C2×C22⋊C4—21no—
320C2×C22⋊C4—21no—
321C2×C22⋊C4—21no—
322C2×C22⋊C4—21no—
323C2×C22⋊C4—21no—
324C2×C22⋊C4—21no—
325C2×C22⋊C4—21no—
326C2×C22⋊C4—21no—
327C2×C22⋊C4—21no—
328C2×C22⋊C4—21no—
329C2×C22⋊C4—21no—
330C2×C22⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—42no—
333C2×C22⋊C4—42no—
334C2×C22⋊C4—42no—
335C2×C22⋊C4—42no—
336C2×C22⋊C4—42no—
337C2×C22⋊C4—42no—
338C2×C22⋊C4C22⋊C411yescharacteristic
339C2×C22⋊C4C22⋊C411yescharacteristic
340C2×C22⋊C4C22⋊C411yescharacteristic
341C2×C22⋊C4C22⋊C411yescharacteristic
342C2×C22⋊C4C22⋊C411yescharacteristic
343C2×C22⋊C4C22⋊C411yescharacteristic
344C2×C22⋊C4C22⋊C411yescharacteristic
345C2×C22⋊C4C22⋊C411yescharacteristic
346C2×C42—21no—
347C2×C42—21no—
348C2×C42—21no—
349C2×C42—21no—
350C2×C42—21no—
351C2×C42—21no—
352C2×C42—21no—
353C2×C42—81no—
354C2×C42C22×C411yescharacteristic
355C2×C42C22×C411yescharacteristic
356C2×C42C22×C411yescharacteristic
357C2×C42C22×C411yescharacteristic
358C2×C42C2×D411yescharacteristic
359C2×C42C2×D411yescharacteristic
360C2×C42C2×D411yescharacteristic
361C2×C42C2×D411yescharacteristic
362C4⋊C8—42no—
363C4⋊C8—81no—
364C22⋊C8—21no—
365C22⋊C8—21no—
366C22⋊C8—21no—
367C22⋊C8—21no—
368C22⋊C8—21no—
369C22⋊C8—21no—
370C22⋊C8—21no—
371C22⋊C8—42no—
372C22⋊C8—42no—
373C22⋊C8—81no—
374C22⋊C8#4112yes—
375#97—42no—
376#97—81no—
377#95—21no—
378#95—21no—
379#95—21no—
380#95—21no—
381#95—21no—
382#95—21no—
383#95—21no—
384#95—21no—
385#95—21no—
386#95—21no—
387#95—21no—
388#95—21no—
389#95—21no—
390#95—21no—
391#95—21no—
392#95—21no—
393#95—21no—
394#95—21no—
395#95—21no—
396#95—21no—
397#95—21no—
398#95—21no—
399#95—42no—
400#95—42no—
401#95—42no—
402#95—42no—
403#95—42no—
404#95—81no—
405#95—81no—
406#95—81no—
407#95—81no—
408#95—81no—
409#95C22⋊C411yescharacteristic
410#95C22⋊C411yescharacteristic
411#95C22⋊C411yescharacteristic
412#95C22⋊C411yescharacteristic
413#95C22⋊C411yescharacteristic
414#95C22⋊C411yescharacteristic
415#95C22⋊C411yescharacteristic
416#95C22⋊C411yescharacteristic
417#95#4112yes—
418C24—21no—
419C24—21no—
420C24—21no—
421C24—21no—
422C24—22no—
423C24—22no—
424C24—21no—
425C24—41no—
426C24—41no—
427C24C2×C22⋊C411yescharacteristic
428C24C2×C22⋊C411yescharacteristic
429C24AGL(1,ℤ/8)12yes—
430C24AGL(1,ℤ/8)12yes—
431C24C22×D411yescharacteristic
432C2×Q8—42no—
433C2×Q8—81no—
434C2×Q8—81no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—41no—
438C2×D4—41no—
439C2×D4—41no—
440C2×D4—41no—
441C2×D4—41no—
442C2×D4—41no—
443C2×D4—41no—
444C2×D4—41no—
445C2×D4—42no—
446C2×D4—42no—
447C2×D4—42no—
448C2×D4—42no—
449C2×D4—81no—
450C2×D4—81no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—22no—
484C22×C4—41no—
485C22×C4—41no—
486C22×C4—41no—
487C22×C4—41no—
488C22×C4—41no—
489C22×C4—41no—
490C22×C4—41no—
491C22×C4—41no—
492C22×C4—41no—
493C22×C4—41no—
494C22×C4—41no—
495C22×C4—41no—
496C22×C4—41no—
497C22×C4—41no—
498C22×C4—41no—
499C22×C4—41no—
500C22×C4—42no—
501C22×C4—41no—
502C22×C4—41no—
503C22×C4—41no—
504C22×C4—41no—
505C22×C4—41no—
506C22×C4—41no—
507C22×C4—41no—
508C22×C4—48no—
509C22×C4—41no—
510C22×C4—41no—
511C22×C4—41no—
512C22×C4—41no—
513C22×C4—41no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—41no—
519C22×C4—41no—
520C22×C4—41no—
521C22×C4—41no—
522C22×C4—41no—
523C22×C4—41no—
524C22×C4—41no—
525C22×C4—41no—
526C22×C4—41no—
527C22×C4—41no—
528C22×C4—41no—
529C22×C4—41no—
530C22×C4—41no—
531C22×C4—41no—
532C22×C4—81no—
533C22×C4—81no—
534C22×C4—82no—
535C22×C4—82no—
536C22×C4—82no—
537C22×C4—82no—
538C22×C4—81no—
539C22×C4—81no—
540C22×C4—84no—
541C22×C4—84no—
542C22×C4—84no—
543C22×C4—84no—
544C22×C4—84no—
545C22×C4—84no—
546C22×C4C2×C22⋊C411yescharacteristic
547C22×C4C2×C22⋊C411yescharacteristic
548C22×C4C2×C22⋊C411yescharacteristic
549C22×C4C2×C22⋊C411yescharacteristic
550C22×C4C2×C22⋊C411yescharacteristic
551C22×C4C2×C22⋊C411yescharacteristic
552C22×C4C2×C22⋊C411yescharacteristic
553C22×C4C2×C22⋊C411yescharacteristic
554C22×C4C2×C22⋊C411yescharacteristic
555C22×C4C2×C22⋊C411yescharacteristic
556C22×C4C23×C411yescharacteristic
557C22×C4C22×D411yescharacteristic
558C22×C4C2×#4111yescharacteristic
559C22×C4C2×#4111yescharacteristic
560C22×C4H(5,𝔽2)11yescharacteristic
561C22×C42−1+411yescharacteristic
562C2×C8—22no—
563C2×C8—41no—
564C2×C8—41no—
565C2×C8—41no—
566C2×C8—41no—
567C2×C8—41no—
568C2×C8—41no—
569C2×C8—41no—
570C2×C8—41no—
571C2×C8—41no—
572C2×C8—41no—
573C2×C8—41no—
574C2×C8—84no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—41no—
578C4⋊C4—41no—
579C4⋊C4—41no—
580C4⋊C4—41no—
581C4⋊C4—41no—
582C4⋊C4—41no—
583C4⋊C4—42no—
584C4⋊C4—42no—
585C4⋊C4—42no—
586C4⋊C4—42no—
587C4⋊C4—42no—
588C4⋊C4—42no—
589C4⋊C4—42no—
590C4⋊C4—42no—
591C4⋊C4—42no—
592C4⋊C4—42no—
593C4⋊C4—42no—
594C4⋊C4—81no—
595C4⋊C4—81no—
596C4⋊C4—81no—
597C22⋊C4—22no—
598C22⋊C4—22no—
599C22⋊C4—22no—
600C22⋊C4—22no—
601C22⋊C4—22no—
602C22⋊C4—22no—
603C22⋊C4—41no—
604C22⋊C4—41no—
605C22⋊C4—42no—
606C22⋊C4—42no—
607C22⋊C4—42no—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C22⋊C4—42no—
611C22⋊C4—41no—
612C22⋊C4—41no—
613C22⋊C4—41no—
614C22⋊C4—41no—
615C22⋊C4—41no—
616C22⋊C4—41no—
617C22⋊C4—42no—
618C22⋊C4—42no—
619C22⋊C4—42no—
620C22⋊C4—42no—
621C22⋊C4—41no—
622C22⋊C4—41no—
623C22⋊C4—81no—
624C22⋊C4—81no—
625C22⋊C4—81no—
626C22⋊C4—84no—
627C42—21no—
628C42—21no—
629C42—21no—
630C42—21no—
631C42—21no—
632C42—21no—
633C42—21no—
634C42—21no—
635C42—41no—
636C42—41no—
637C42—41no—
638C42—41no—
639C42—42no—
640C42—42no—
641C42—42no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—22no—
651C23—22no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—24no—
659C23—24no—
660C23—22no—
661C23—22no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23#41012yes—
680C23#41812yes—
681C23#41812yes—
682C23#42112yes—
683C23C22×C22⋊C411yescharacteristic
684C23#54611yescharacteristic
685C23#54711yescharacteristic
686C23C2×AGL(1,ℤ/8)11yescharacteristic
687C23C2×AGL(1,ℤ/8)11yescharacteristic
688C23#57711yescharacteristic
689C23#57811yescharacteristic
690Q8—162no—
691D4—81no—
692D4—81no—
693D4—81no—
694D4—81no—
695D4—84no—
696D4—81no—
697D4—81no—
698D4—162no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
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—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—42no—
772C2×C4—81no—
773C2×C4—81no—
774C2×C4—81no—
775C2×C4—81no—
776C2×C4—81no—
777C2×C4—81no—
778C2×C4—81no—
779C2×C4—81no—
780C2×C4—81no—
781C2×C4—81no—
782C2×C4—81no—
783C2×C4—81no—
784C2×C4—81no—
785C2×C4—81no—
786C2×C4—81no—
787C2×C4—81no—
788C2×C4—81no—
789C2×C4—81no—
790C2×C4—81no—
791C2×C4—816no—
792C2×C4—84no—
793C2×C4—81no—
794C2×C4—81no—
795C2×C4—81no—
796C2×C4—81no—
797C2×C4—81no—
798C2×C4—81no—
799C2×C4—81no—
800C2×C4—81no—
801C2×C4—81no—
802C2×C4—81no—
803C2×C4—81no—
804C2×C4—81no—
805C2×C4—81no—
806C2×C4—81no—
807C2×C4—81no—
808C2×C4—162no—
809C2×C4—162no—
810C2×C4C4×#4111yescharacteristic
811C2×C4#52011yescharacteristic
812C2×C4#54611yescharacteristic
813C2×C4#54711yescharacteristic
814C8—42no—
815C8—81no—
816C8—81no—
817C8—81no—
818C22—21no—
819C22—21no—
820C22—21no—
821C22—21no—
822C22—22no—
823C22—21no—
824C22—21no—
825C22—22no—
826C22—21no—
827C22—22no—
828C22—21no—
829C22—21no—
830C22—21no—
831C22—22no—
832C22—22no—
833C22—21no—
834C22—21no—
835C22—22no—
836C22—22no—
837C22—22no—
838C22—22no—
839C22—44no—
840C22—44no—
841C22—44no—
842C22—44no—
843C22—41no—
844C22—41no—
845C22—41no—
846C22—41no—
847C22—81no—
848C22—81no—
849C22—81no—
850C22—81no—
851C22—81no—
852C22—81no—
853C22—81no—
854C22#151414yes—
855C22#233911yescharacteristic
856C22C2×#41011yescharacteristic
857C22#288311yescharacteristic
858C22C2×#41811yescharacteristic
859C22#289811yescharacteristic
860C22C2×#42111yescharacteristic
861C22#290111yescharacteristic
862C22#330611yescharacteristic
863C22#330811yescharacteristic
864C22#334311yescharacteristic
865C22#334511yescharacteristic
866C4—21no—
867C4—21no—
868C4—21no—
869C4—21no—
870C4—41no—
871C4—41no—
872C4—41no—
873C4—41no—
874C4—41no—
875C4—41no—
876C4—41no—
877C4—41no—
878C4—41no—
879C4—41no—
880C4—82no—
881C4—82no—
882C4—81no—
883C4—81no—
884C4—81no—
885C4—81no—
886C4—81no—
887C4—81no—
888C4—81no—
889C4—161no—
890C4—161no—
891C2—21no—
892C2—21no—
893C2—21no—
894C2—21no—
895C2—24no—
896C2—42no—
897C2—161no—
898C2C2×#151411yescharacteristic
899C2#1759811yescharacteristic
900C2#1760911yescharacteristic
901C2#1762011yescharacteristic
902C2#2247711yescharacteristic
903C2#2249511yescharacteristic
904C2#2250611yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radical#2847C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #22554C2semidirect
3. #13901C2semidirect
4. #9911C2semidirect
5. #9888C2semidirect
6. #9157C2semidirect
8. #9118C2semidirect
10. #8717C2semidirect
11. #8712C2semidirect
12. #8573C2semidirect
13. #8216C2semidirect
14. #8018C2semidirect
15. C2×#1294C2semidirect
25. #2501C4semidirect
27. #2496C4semidirect
28. #2496C4semidirect
29. #2491C4semidirect
31. #2440C4semidirect
32. #2422C4semidirect
34. #2361C4semidirect
36. #2344C4semidirect
80. C2×C4⋊Q8C2×C4semidirect
96. C2×C4×D4C2×C4semidirect
135. #390C2×C4semidirect
136. #390C2×C4semidirect
137. #390C2×C4semidirect
139. #389C2×C4semidirect
140. #389C2×C4semidirect
141. #389C2×C4semidirect
142. #389C2×C4semidirect
143. #389C2×C4semidirect
162. #384C2×C4semidirect
163. #384C2×C4semidirect
164. #384C2×C4semidirect
181. C4×C4⋊C4C2×C4semidirect
182. C4×C4⋊C4C2×C4semidirect
183. C4×C4⋊C4C2×C4semidirect

Maximal subgroups

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

subgroupindex
#361832
#225542
#139012
#99112
#98882
#91572
#91472
#91182
#91132
#87172
#87122
#85732
#82162
#80182
C2×#12942