Finite Group Databasebeta

← #216822

Subgroups — #216822

Order 512.

1073 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35023C211yesmaximal, characteristic
2#21906C211yesmaximal, characteristic, complemented
3#13965C211yesmaximal, characteristic, complemented
4#9887C211yesmaximal, characteristic, complemented
5#9887C211yesmaximal, characteristic, complemented
6#9682C211yesmaximal, characteristic, complemented
7#9682C211yesmaximal, characteristic, complemented
8#9155C211yesmaximal, characteristic
9#9151C211yesmaximal, characteristic, complemented
10#9147C211yesmaximal, characteristic
11#9143C211yesmaximal, characteristic, complemented
12#8578C211yesmaximal, characteristic, complemented
13#8577C211yesmaximal, characteristic, complemented
14#8572C211yesmaximal, characteristic, complemented
15#8571C211yesmaximal, characteristic, complemented
16#2851C2211yescharacteristic
17#2850C2211yescharacteristic
18#2848C2211yescharacteristic
19#2847C2211yescharacteristic
20#2643—21no—
21#2622—21no—
22#2597—21no—
23#2595—21no—
24#2578—21no—
25#2576—21no—
26#2495C411yescharacteristic, complemented
27#2494C411yescharacteristic, complemented
28#2490C411yescharacteristic, complemented
29#2489C411yescharacteristic, complemented
30#2427C411yescharacteristic, complemented
31#2426C411yescharacteristic, complemented
32#2421C411yescharacteristic, complemented
33#2420C411yescharacteristic, complemented
34#2321—21no—
35#2318—21no—
36C4×C22⋊Q8C2211yescharacteristic
37C4×#121C2211yescharacteristic
38C2×#385—21no—
39C2×#385—21no—
40C2×#380C2211yescharacteristic
41C2×C4×C22⋊C4C2211yescharacteristic
42C22×#95C2211yescharacteristic
43#1924—21no—
44#1924—21no—
45#1924—21no—
46#1924—21no—
47#1797C2211yescharacteristic
48#1797C2211yescharacteristic
49#1779C2211yescharacteristic
50#1779C2211yescharacteristic
51#1749C2211yescharacteristic
52#1749C2211yescharacteristic
53C2×#328C2211yescharacteristic
54C2×#328C2211yescharacteristic
55C2×#328C2211yescharacteristic
56C2×#328C2211yescharacteristic
57C2×#327C2211yescharacteristic
58C2×#327C2211yescharacteristic
59C2×#327C2211yescharacteristic
60C2×#327C2211yescharacteristic
61#1444—21no—
62#1444—21no—
63C4⋊#95C2211yescharacteristic
64C4⋊#95C2211yescharacteristic
65C4⋊#95C2211yescharacteristic
66C4⋊#95C2211yescharacteristic
67#1294C2211yescharacteristic
68#1294C2211yescharacteristic
69#1294C2211yescharacteristic
70#1294C2211yescharacteristic
71#1294C2211yescharacteristic
72#1294C2211yescharacteristic
73#1294C2211yescharacteristic
74#1294C2211yescharacteristic
75C24×C4—21no—
76C24×C4C2311yescharacteristic
77C2×#125C2×C411yescharacteristic, complemented
78C2×#124C2×C411yescharacteristic, complemented
79C2×C22⋊Q8C2×C411yescharacteristic
80C2×C22⋊Q8C2×C411yescharacteristic
81C2×C22⋊Q8C2311yescharacteristic
82C2×#121C2×C411yescharacteristic
83C2×#121C2×C411yescharacteristic
84C2×#121C2311yescharacteristic
85C2×#120—21no—
86C2×C4×Q8C2×C411yescharacteristic, complemented
87C2×C4×D4—21no—
88C2×C4×D4C2×C411yescharacteristic, complemented
89C22×C4⋊C4—21no—
90C22×C4⋊C4—21no—
91C22×C4⋊C4—21no—
92C22×C4⋊C4—21no—
93C22×C4⋊C4—21no—
94C22×C22⋊C4—21no—
95C22×C22⋊C4D411yescharacteristic
96C22×C22⋊C4D411yescharacteristic
97C22×C42C2311yescharacteristic
98C22×C42C2311yescharacteristic
99C2×C4⋊C8—21no—
100C2×C4⋊C8—21no—
101C2×C22⋊C8—21no—
102C2×C22⋊C8—21no—
103C2×C22⋊C8—21no—
104C2×C22⋊C8—21no—
105C2×C22⋊C8C2311yescharacteristic
106C2×C22⋊C8C2311yescharacteristic
107C2×C22⋊C8C2311yescharacteristic
108C2×C22⋊C8C2311yescharacteristic
109C2×#97—21no—
110C2×#97—21no—
111#401—21no—
112#400—21no—
113#400—21no—
114#400—21no—
115#397—21no—
116#397—21no—
117#397—21no—
118#397—21no—
119#397—21no—
120#397—21no—
121#397—21no—
122#396—21no—
123#394—21no—
124#394—21no—
125#394—21no—
126#394—21no—
127#391C2×C411yescharacteristic, complemented
128#391C2×C411yescharacteristic, complemented
129#390—21no—
130#390—21no—
131#390C2×C411yescharacteristic, complemented
132#390C2×C411yescharacteristic, complemented
133#389C2×C411yescharacteristic, complemented
134#389C2×C411yescharacteristic, complemented
135#389C2×C411yescharacteristic, complemented
136#389C2×C411yescharacteristic, complemented
137#388—21no—
138#388—21no—
139#388—21no—
140#388—21no—
141#388—21no—
142#388—21no—
143#388—21no—
144#388—21no—
145#388—21no—
146#387—21no—
147#387—21no—
148#387—21no—
149#387—21no—
150#387—21no—
151#386—21no—
152#386—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#385—21no—
163#385—21no—
164#385—21no—
165#385—44no—
166#385—44no—
167#383—21no—
168#382—21no—
169#382C2×C411yescharacteristic, complemented
170#382C2×C411yescharacteristic, complemented
171#381—21no—
172#380—21no—
173#380—41no—
174#380—41no—
175#380C2×C411yescharacteristic
176#380C2×C411yescharacteristic
177#380C2×C411yescharacteristic
178#380C2×C411yescharacteristic
179#380C2311yescharacteristic
180#380C2311yescharacteristic
181#379—21no—
182C4×C4⋊C4—21no—
183C4×C4⋊C4C2×C411yescharacteristic, complemented
184C4×C4⋊C4C2×C411yescharacteristic, complemented
185C4×C22⋊C4—21no—
186C4×C22⋊C4—21no—
187C4×C22⋊C4C2×C411yescharacteristic
188C4×C22⋊C4C2×C411yescharacteristic
189C4×C22⋊C4C2×C411yescharacteristic
190C4×C22⋊C4C2×C411yescharacteristic
191C4×C22⋊C4D411yescharacteristic
192C4×C22⋊C4D411yescharacteristic
193C4×C22⋊C4D411yescharacteristic
194C4×C22⋊C4D411yescharacteristic
195C2×#95—21no—
196C2×#95—21no—
197C2×#95—21no—
198C2×#95—21no—
199C2×#95—21no—
200C2×#95—41no—
201C2×#95—41no—
202C2×#95D411yescharacteristic
203C2×#95D411yescharacteristic
204C2×#95C2311yescharacteristic
205C2×#95C2311yescharacteristic
206C2×#95C2311yescharacteristic
207C2×#95C2311yescharacteristic
208#336—21no—
209#336—21no—
210#336—21no—
211#336—21no—
212#328—41no—
213#328—41no—
214#328—41no—
215#328—41no—
216#327—41no—
217#327—41no—
218#327—41no—
219#327—41no—
220C25C2×D411yescharacteristic
221C22×Q8C22×C411yescharacteristic
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—42no—
236C23×C4—42no—
237C23×C4—42no—
238C23×C4—42no—
239C23×C4—42no—
240C23×C4—81no—
241C23×C4—81no—
242C23×C4—81no—
243C23×C4—81no—
244C23×C4C22×C411yescharacteristic
245C23×C4C22×C411yescharacteristic
246C23×C4C2×D411yescharacteristic
247C23×C4C2×D411yescharacteristic
248C23×C4C2×D411yescharacteristic
249C23×C4C2×D411yescharacteristic
250C23×C4C2×D411yescharacteristic
251C23×C4C2×D411yescharacteristic
252C23×C4C2×D411yescharacteristic
253C23×C4C2411yescharacteristic
254C22×C8—21no—
255C22×C8—21no—
256C22×C8—21no—
257C22×C8—21no—
258#125—81no—
259#124—81no—
260C22⋊Q8—21no—
261C22⋊Q8—21no—
262C22⋊Q8—21no—
263C22⋊Q8—21no—
264C22⋊Q8—81no—
265C22⋊Q8—81no—
266#121—21no—
267#121—21no—
268#121—21no—
269#121—21no—
270#121—81no—
271#121—81no—
272#120—42no—
273#120—42no—
274C4×Q8—81no—
275C4×D4—42no—
276C4×D4—42no—
277C4×D4—81no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—42no—
289C2×C4⋊C4—42no—
290C2×C4⋊C4—42no—
291C2×C4⋊C4—42no—
292C2×C4⋊C4—42no—
293C2×C4⋊C4—42no—
294C2×C4⋊C4—42no—
295C2×C4⋊C4—42no—
296C2×C4⋊C4—42no—
297C2×C4⋊C4—81no—
298C2×C4⋊C4—81no—
299C2×C4⋊C4—81no—
300C2×C4⋊C4—81no—
301C2×C4⋊C4—81no—
302C2×C4⋊C4—81no—
303C2×C4⋊C4C22×C411yescharacteristic
304C2×C4⋊C4C22×C411yescharacteristic
305C2×C4⋊C4C22×C411yescharacteristic
306C2×C4⋊C4C22×C411yescharacteristic
307C2×C4⋊C4C22×C411yescharacteristic
308C2×C4⋊C4C22×C411yescharacteristic
309C2×C22⋊C4—22no—
310C2×C22⋊C4—22no—
311C2×C22⋊C4—22no—
312C2×C22⋊C4—22no—
313C2×C22⋊C4—21no—
314C2×C22⋊C4—21no—
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⋊C4C22⋊C411yescharacteristic
336C2×C22⋊C4C22⋊C411yescharacteristic
337C2×C22⋊C4C22⋊C411yescharacteristic
338C2×C22⋊C4C22⋊C411yescharacteristic
339C2×C22⋊C4C22⋊C411yescharacteristic
340C2×C22⋊C4C22⋊C411yescharacteristic
341C2×C22⋊C4C22⋊C411yescharacteristic
342C2×C22⋊C4C22⋊C411yescharacteristic
343C2×C42—21no—
344C2×C42—21no—
345C2×C42—21no—
346C2×C42—81no—
347C2×C42—81no—
348C2×C42C22×C411yescharacteristic
349C2×C42C22×C411yescharacteristic
350C2×C42C22×C411yescharacteristic
351C2×C42C22×C411yescharacteristic
352C2×C42C2×D411yescharacteristic
353C2×C42C2×D411yescharacteristic
354C2×C42C2×D411yescharacteristic
355C2×C42C2×D411yescharacteristic
356C4⋊C8—81no—
357C4⋊C8—81no—
358C22⋊C8—21no—
359C22⋊C8—21no—
360C22⋊C8—21no—
361C22⋊C8—21no—
362C22⋊C8—21no—
363C22⋊C8—21no—
364C22⋊C8—21no—
365C22⋊C8—21no—
366C22⋊C8—81no—
367C22⋊C8—81no—
368C22⋊C8—81no—
369C22⋊C8—81no—
370#97—81no—
371#97—81no—
372#95—21no—
373#95—21no—
374#95—21no—
375#95—21no—
376#95—21no—
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—21no—
400#95—42no—
401#95—42no—
402#95—42no—
403#95—42no—
404#95—42no—
405#95C22⋊C411yescharacteristic
406#95C22⋊C411yescharacteristic
407#95C22⋊C411yescharacteristic
408#95C22⋊C411yescharacteristic
409#95C22⋊C411yescharacteristic
410#95C22⋊C411yescharacteristic
411#95C22⋊C411yescharacteristic
412#95C22⋊C411yescharacteristic
413C24—21no—
414C24—21no—
415C24—21no—
416C24—21no—
417C24—21no—
418C24—41no—
419C24—41no—
420C24—41no—
421C24—41no—
422C24C2×C22⋊C411yescharacteristic
423C24C2×C22⋊C411yescharacteristic
424C24AGL(1,ℤ/8)12yes—
425C24#13712yes—
426C24C22×D411yescharacteristic
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—41no—
430C2×Q8—41no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—41no—
434C2×D4—41no—
435C2×D4—41no—
436C2×D4—41no—
437C2×D4—41no—
438C2×D4—41no—
439C2×D4—41no—
440C2×D4—41no—
441C2×D4—42no—
442C2×D4—42no—
443C2×D4—81no—
444C2×D4—81no—
445C2×D4—81no—
446C2×D4—81no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4—41no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4—41no—
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—48no—
499C22×C4—41no—
500C22×C4—41no—
501C22×C4—41no—
502C22×C4—41no—
503C22×C4—41no—
504C22×C4—41no—
505C22×C4—42no—
506C22×C4—41no—
507C22×C4—41no—
508C22×C4—41no—
509C22×C4—41no—
510C22×C4—41no—
511C22×C4—41no—
512C22×C4—41no—
513C22×C4—41no—
514C22×C4—41no—
515C22×C4—41no—
516C22×C4—41no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4—41no—
520C22×C4—81no—
521C22×C4—81no—
522C22×C4—82no—
523C22×C4—82no—
524C22×C4—82no—
525C22×C4—82no—
526C22×C4—84no—
527C22×C4—84no—
528C22×C4—84no—
529C22×C4—84no—
530C22×C4—84no—
531C22×C4—84no—
532C22×C4C2×C22⋊C411yescharacteristic
533C22×C4C2×C22⋊C411yescharacteristic
534C22×C4C2×C22⋊C411yescharacteristic
535C22×C4C2×C22⋊C411yescharacteristic
536C22×C4C2×C22⋊C411yescharacteristic
537C22×C4C2×C22⋊C411yescharacteristic
538C22×C4C2×C22⋊C411yescharacteristic
539C22×C4C2×C22⋊C411yescharacteristic
540C22×C4C2×C22⋊C411yescharacteristic
541C22×C4C2×C22⋊C411yescharacteristic
542C22×C4AGL(1,ℤ/8)12yes—
543C22×C4#13712yes—
544C22×C4C23×C411yescharacteristic
545C22×C4C22×D411yescharacteristic
546C22×C4H(5,𝔽2)11yescharacteristic
547C22×C4H(5,𝔽2)11yescharacteristic
548C22×C42−1+411yescharacteristic
549C22×C42−1+411yescharacteristic
550C2×C8—41no—
551C2×C8—41no—
552C2×C8—41no—
553C2×C8—41no—
554C2×C8—41no—
555C2×C8—41no—
556C2×C8—41no—
557C2×C8—41no—
558C2×C8—41no—
559C2×C8—41no—
560C2×C8—41no—
561C2×C8—41no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—41no—
567C4⋊C4—41no—
568C4⋊C4—41no—
569C4⋊C4—41no—
570C4⋊C4—41no—
571C4⋊C4—41no—
572C4⋊C4—42no—
573C4⋊C4—81no—
574C4⋊C4—81no—
575C4⋊C4—81no—
576C4⋊C4—81no—
577C4⋊C4—81no—
578C4⋊C4—81no—
579C4⋊C4—81no—
580C4⋊C4—81no—
581C4⋊C4—84no—
582C4⋊C4—84no—
583C4⋊C4—84no—
584C4⋊C4—84no—
585C4⋊C4—84no—
586C22⋊C4—22no—
587C22⋊C4—22no—
588C22⋊C4—22no—
589C22⋊C4—22no—
590C22⋊C4—22no—
591C22⋊C4—22no—
592C22⋊C4—22no—
593C22⋊C4—22no—
594C22⋊C4—41no—
595C22⋊C4—41no—
596C22⋊C4—41no—
597C22⋊C4—41no—
598C22⋊C4—41no—
599C22⋊C4—41no—
600C22⋊C4—42no—
601C22⋊C4—42no—
602C22⋊C4—41no—
603C22⋊C4—41no—
604C22⋊C4—42no—
605C22⋊C4—81no—
606C22⋊C4—81no—
607C22⋊C4—81no—
608C22⋊C4—81no—
609C22⋊C4—81no—
610C22⋊C4—81no—
611C22⋊C4—81no—
612C22⋊C4—81no—
613C22⋊C4—81no—
614C22⋊C4—81no—
615C22⋊C4—81no—
616C22⋊C4—81no—
617C22⋊C4—84no—
618C42—41no—
619C42—41no—
620C42—41no—
621C42—41no—
622C42—41no—
623C42—41no—
624C42—41no—
625C42—41no—
626C42—42no—
627C42—81no—
628C42—81no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23#41712yes—
669C23#41712yes—
670C23C22×C22⋊C411yescharacteristic
671C23#53511yescharacteristic
672C23#53611yescharacteristic
673C23C2×AGL(1,ℤ/8)11yescharacteristic
674C23C2×AGL(1,ℤ/8)11yescharacteristic
675C23C2×#13711yescharacteristic
676C23C2×#13711yescharacteristic
677Q8—81no—
678Q8—81no—
679D4—81no—
680D4—81no—
681D4—81no—
682D4—81no—
683D4—81no—
684D4—81no—
685D4—162no—
686D4—162no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
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—42no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
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—81no—
761C2×C4—81no—
762C2×C4—81no—
763C2×C4—81no—
764C2×C4—81no—
765C2×C4—81no—
766C2×C4—81no—
767C2×C4—81no—
768C2×C4—81no—
769C2×C4—81no—
770C2×C4—81no—
771C2×C4—81no—
772C2×C4—81no—
773C2×C4—81no—
774C2×C4—816no—
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—162no—
792C2×C4#41712yes—
793C2×C4#41712yes—
794C2×C4#52011yescharacteristic
795C2×C4#52011yescharacteristic
796C2×C4#53711yescharacteristic
797C2×C4#53711yescharacteristic
798C8—81no—
799C8—81no—
800C8—81no—
801C8—81no—
802C22—21no—
803C22—21no—
804C22—21no—
805C22—21no—
806C22—21no—
807C22—21no—
808C22—21no—
809C22—21no—
810C22—21no—
811C22—21no—
812C22—21no—
813C22—21no—
814C22—22no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—22no—
820C22—44no—
821C22—44no—
822C22—44no—
823C22—44no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—81no—
833C22—81no—
834C22—81no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22#231111yescharacteristic
840C22#288311yescharacteristic
841C22#288311yescharacteristic
842C22C2×#41711yescharacteristic
843C22C2×#41711yescharacteristic
844C22#290111yescharacteristic
845C22#290111yescharacteristic
846C22#321711yescharacteristic
847C22#321811yescharacteristic
848C22#323811yescharacteristic
849C22#323911yescharacteristic
850C4—21no—
851C4—21no—
852C4—21no—
853C4—21no—
854C4—22no—
855C4—22no—
856C4—41no—
857C4—41no—
858C4—41no—
859C4—41no—
860C4—41no—
861C4—41no—
862C4—41no—
863C4—41no—
864C4—82no—
865C4—82no—
866C4—81no—
867C4—81no—
868C4—81no—
869C4—81no—
870C4—81no—
871C4—81no—
872C4—81no—
873C4—161no—
874C4—161no—
875C2—21no—
876C2—21no—
877C2—21no—
878C2—21no—
879C2—42no—
880C2—42no—
881C2—161no—
882C2#1762211yescharacteristic
883C2#1762211yescharacteristic
884C2#1762211yescharacteristic
885C2#1763011yescharacteristic
886C2#2186711yescharacteristic
887C2#2187611yescharacteristic
888C2#2190111yescharacteristic
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. #21906C2semidirect
3. #13965C2semidirect
4. #9887C2semidirect
5. #9887C2semidirect
6. #9682C2semidirect
7. #9682C2semidirect
9. #9151C2semidirect
11. #9143C2semidirect
12. #8578C2semidirect
13. #8577C2semidirect
14. #8572C2semidirect
15. #8571C2semidirect
26. #2495C4semidirect
27. #2494C4semidirect
28. #2490C4semidirect
29. #2489C4semidirect
30. #2427C4semidirect
31. #2426C4semidirect
32. #2421C4semidirect
33. #2420C4semidirect
77. C2×#125C2×C4semidirect
78. C2×#124C2×C4semidirect
86. C2×C4×Q8C2×C4semidirect
88. C2×C4×D4C2×C4semidirect
127. #391C2×C4semidirect
128. #391C2×C4semidirect
131. #390C2×C4semidirect
132. #390C2×C4semidirect
133. #389C2×C4semidirect
134. #389C2×C4semidirect
135. #389C2×C4semidirect
136. #389C2×C4semidirect
169. #382C2×C4semidirect
170. #382C2×C4semidirect
183. C4×C4⋊C4C2×C4semidirect
184. C4×C4⋊C4C2×C4semidirect

Maximal subgroups

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

subgroupindex
#350232
#219062
#139652
#98872
#96822
#91552
#91512
#91472
#91432
#85782
#85772
#85722
#85712