Finite Group Databasebeta

← #216853

Subgroups — #216853

Order 512.

925 conjugacy classes of subgroups.

The subgroup lattice has 797 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35083C211yesmaximal, characteristic
2#21914C211yesmaximal, characteristic, complemented
3#13783C211yesmaximal, characteristic, complemented
4#9889C211yesmaximal, characteristic, complemented
5#9884C211yesmaximal, characteristic, complemented
6#9682C211yesmaximal, characteristic
7#9681C211yesmaximal, characteristic
8#9149C211yesmaximal, characteristic
9#9148C211yesmaximal, characteristic
10#9145C211yesmaximal, characteristic, complemented
11#9144C211yesmaximal, characteristic, complemented
12#8577C211yesmaximal, characteristic
13#8575C211yesmaximal, characteristic
14#8574C211yesmaximal, characteristic, complemented
15#8572C211yesmaximal, characteristic, complemented
16#2857C2211yescharacteristic
17#2855C2211yescharacteristic
18#2854C2211yescharacteristic
19#2850C2211yescharacteristic
20#2654—21no—
21#2650—21no—
22#2512C411yescharacteristic, complemented
23#2511C411yescharacteristic, complemented
24#2509C411yescharacteristic, complemented
25#2508C411yescharacteristic, complemented
26#2488—21no—
27#2481—21no—
28#2452C411yescharacteristic, complemented
29#2451C411yescharacteristic, complemented
30#2449—21no—
31#2448C411yescharacteristic, complemented
32#2447C411yescharacteristic, complemented
33#2419—21no—
34#2334—21no—
35#2332—21no—
36C4×C22⋊Q8C2211yescharacteristic
37C4×#121C2211yescharacteristic
38C2×#389—21no—
39C2×C4×C4⋊C4C2211yescharacteristic
40C2×C4×C4⋊C4C2211yescharacteristic
41C2×#376C2211yescharacteristic
42#1917—21no—
43#1917—21no—
44#1916—21no—
45#1916—21no—
46#1817C2211yescharacteristic
47#1817C2211yescharacteristic
48#1797C2211yescharacteristic
49#1797C2211yescharacteristic
50#1749C2211yescharacteristic
51C4×C22⋊C8C2211yescharacteristic
52C2×#328C2211yescharacteristic
53C2×#328C2211yescharacteristic
54C2×#328C2211yescharacteristic
55C2×#328C2211yescharacteristic
56C2×#327C2211yescharacteristic
57C2×#327C2211yescharacteristic
58C2×#327C2211yescharacteristic
59C2×#327C2211yescharacteristic
60#1436—21no—
61#1436—21no—
62C4⋊#95—21no—
63C4⋊#95C2211yescharacteristic
64C4⋊#95C2211yescharacteristic
65#1434C2211yescharacteristic
66#1434C2211yescharacteristic
67#1294C2211yescharacteristic
68#1294C2211yescharacteristic
69#1294C2211yescharacteristic
70#1294C2211yescharacteristic
71#1294C2211yescharacteristic
72#1294C2211yescharacteristic
73#1294C2211yescharacteristic
74#1294C2211yescharacteristic
75C2×C4⋊Q8C2×C411yescharacteristic
76C2×#126—21no—
77C2×#124C2×C411yescharacteristic
78C2×#123—21no—
79C2×C22⋊Q8—21no—
80C2×C22⋊Q8—21no—
81C2×C22⋊Q8C2311yescharacteristic
82C2×#121C2311yescharacteristic
83C2×C4×Q8C2×C411yescharacteristic
84C2×C4×D4—21no—
85C2×C4×D4C2×C411yescharacteristic
86C22×C4⋊C4—21no—
87C22×C4⋊C4—21no—
88C22×C4⋊C4—21no—
89C22×C4⋊C4D411yescharacteristic
90C22×C4⋊C4D411yescharacteristic
91C22×C42—21no—
92C22×C42—21no—
93C22×C42C2311yescharacteristic
94C22×C42C2311yescharacteristic
95C22×C42C2311yescharacteristic
96C2×C4⋊C8—21no—
97C2×C4⋊C8—21no—
98C2×C22⋊C8C2311yescharacteristic
99C2×C22⋊C8C2311yescharacteristic
100C2×C22⋊C8C2311yescharacteristic
101C2×C22⋊C8C2311yescharacteristic
102C2×#97—21no—
103C2×C4×C8—21no—
104#400—21no—
105#400—21no—
106#400—21no—
107#400—21no—
108#400—21no—
109#399—21no—
110#398—21no—
111#398—21no—
112#397—21no—
113#397—21no—
114#397—21no—
115#397—21no—
116#396—21no—
117#396—21no—
118#395—21no—
119#393—21no—
120#391—21no—
121#391—21no—
122#391C2×C411yescharacteristic
123#391C2×C411yescharacteristic
124#391C2×C411yescharacteristic
125#391C2×C411yescharacteristic
126#390C2×C411yescharacteristic
127#390C2×C411yescharacteristic
128#390C2×C411yescharacteristic
129#390C2×C411yescharacteristic
130#389—28no—
131#389—21no—
132#389—21no—
133#389C2×C411yescharacteristic
134#389C2×C411yescharacteristic
135#389C2×C411yescharacteristic
136#389C2×C411yescharacteristic
137#389C2×C411yescharacteristic
138#389C2×C411yescharacteristic
139#389C2×C411yescharacteristic
140#389C2×C411yescharacteristic
141#388—21no—
142#388—21no—
143#388—21no—
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#387—21no—
154#387—21no—
155#387—21no—
156#387—21no—
157#386—21no—
158#386—21no—
159#386—21no—
160#386—21no—
161#385—21no—
162#385—21no—
163#385—21no—
164#385—21no—
165#384C2×C411yescharacteristic
166#382—21no—
167#382C2×C411yescharacteristic
168#381—21no—
169#381—21no—
170#380—21no—
171#380C2311yescharacteristic
172#380C2311yescharacteristic
173C4×C4⋊C4—21no—
174C4×C4⋊C4—41no—
175C4×C4⋊C4—41no—
176C4×C4⋊C4C2×C411yescharacteristic
177C4×C4⋊C4C2×C411yescharacteristic
178C4×C4⋊C4C2×C411yescharacteristic
179C4×C4⋊C4C2×C411yescharacteristic
180C4×C4⋊C4C2×C411yescharacteristic
181C4×C4⋊C4C2×C411yescharacteristic
182C4×C4⋊C4D411yescharacteristic
183C4×C4⋊C4D411yescharacteristic
184C4×C4⋊C4D411yescharacteristic
185C4×C4⋊C4D411yescharacteristic
186C4×C22⋊C4—21no—
187C4×C22⋊C4—21no—
188#376—41no—
189#376—41no—
190C2×#95—21no—
191C2×#95—21no—
192C2×#95—21no—
193C2×#95—21no—
194C2×#95—21no—
195C2×#95—21no—
196C2×#95—21no—
197C2×#95D411yescharacteristic
198C2×#95D411yescharacteristic
199C2×#95C2311yescharacteristic
200C2×#95C2311yescharacteristic
201C2×#95C2311yescharacteristic
202C2×#95C2311yescharacteristic
203#336—21no—
204#336—21no—
205#336—21no—
206#336—21no—
207#336—21no—
208#336—21no—
209#336—21no—
210#336—21no—
211#328—41no—
212#328—41no—
213#328—41no—
214#328—41no—
215#327—41no—
216#327—41no—
217#327—41no—
218#327—41no—
219C22×Q8—21no—
220C22×Q8C22×C411yescharacteristic
221C22×D4—21no—
222C22×D4C22×C411yescharacteristic
223C23×C4—21no—
224C23×C4—21no—
225C23×C4—21no—
226C23×C4—21no—
227C23×C4—21no—
228C23×C4C2×D411yescharacteristic
229C23×C4C2×D411yescharacteristic
230C23×C4C2×D411yescharacteristic
231C23×C4C2×D411yescharacteristic
232C23×C4C2×D411yescharacteristic
233C23×C4C2×D411yescharacteristic
234C23×C4C2411yescharacteristic
235C22×C8—21no—
236C22×C8—21no—
237C22×C8—21no—
238C22×C8—21no—
239C4⋊Q8—81no—
240#126—44no—
241#124—81no—
242#123—81no—
243#123—81no—
244C22⋊Q8—21no—
245C22⋊Q8—21no—
246C22⋊Q8—21no—
247C22⋊Q8—21no—
248C22⋊Q8—44no—
249C22⋊Q8—81no—
250C22⋊Q8—81no—
251#121—21no—
252#121—21no—
253#121—21no—
254#121—21no—
255C4×Q8—81no—
256C4×D4—81no—
257C4×D4—81no—
258C4×D4—81no—
259C2×C4⋊C4—24no—
260C2×C4⋊C4—24no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—24no—
267C2×C4⋊C4—24no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—42no—
277C2×C4⋊C4—42no—
278C2×C4⋊C4—42no—
279C2×C4⋊C4—81no—
280C2×C4⋊C4—81no—
281C2×C4⋊C4—81no—
282C2×C4⋊C4—81no—
283C2×C4⋊C4C22⋊C411yescharacteristic
284C2×C4⋊C4C22⋊C411yescharacteristic
285C2×C4⋊C4C22⋊C411yescharacteristic
286C2×C4⋊C4C22⋊C411yescharacteristic
287C2×C4⋊C4C22⋊C411yescharacteristic
288C2×C4⋊C4C22⋊C411yescharacteristic
289C2×C4⋊C4C22⋊C411yescharacteristic
290C2×C4⋊C4C22⋊C411yescharacteristic
291C2×C4⋊C4C22×C411yescharacteristic
292C2×C4⋊C4C22×C411yescharacteristic
293C2×C4⋊C4C22×C411yescharacteristic
294C2×C4⋊C4C22×C411yescharacteristic
295C2×C4⋊C4C22×C411yescharacteristic
296C2×C4⋊C4C22×C411yescharacteristic
297C2×C22⋊C4—21no—
298C2×C22⋊C4—21no—
299C2×C22⋊C4—21no—
300C2×C22⋊C4—21no—
301C2×C22⋊C4—21no—
302C2×C22⋊C4—21no—
303C2×C22⋊C4—21no—
304C2×C22⋊C4—21no—
305C2×C22⋊C4—21no—
306C2×C22⋊C4—21no—
307C2×C22⋊C4—21no—
308C2×C22⋊C4—21no—
309C2×C22⋊C4—21no—
310C2×C22⋊C4—21no—
311C2×C22⋊C4—21no—
312C2×C42—21no—
313C2×C42—21no—
314C2×C42—21no—
315C2×C42—21no—
316C2×C42—24no—
317C2×C42—21no—
318C2×C42—21no—
319C2×C42—21no—
320C2×C42—42no—
321C2×C42—42no—
322C2×C42—42no—
323C2×C42—81no—
324C2×C42—81no—
325C2×C42—81no—
326C2×C42—81no—
327C2×C42C22×C411yescharacteristic
328C2×C42C22×C411yescharacteristic
329C2×C42C22×C411yescharacteristic
330C2×C42C22×C411yescharacteristic
331C2×C42C22×C411yescharacteristic
332C2×C42C22×C411yescharacteristic
333C2×C42C2×D411yescharacteristic
334C2×C42C2×D411yescharacteristic
335C2×C42C2×D411yescharacteristic
336C2×C42C2×D411yescharacteristic
337C2×C42C2×D411yescharacteristic
338C2×C42C2×D411yescharacteristic
339C4⋊C8—81no—
340C4⋊C8—81no—
341C22⋊C8—21no—
342C22⋊C8—21no—
343C22⋊C8—21no—
344C22⋊C8—21no—
345C22⋊C8—21no—
346C22⋊C8—21no—
347C22⋊C8—21no—
348C22⋊C8—21no—
349#97—81no—
350C4×C8—81no—
351#95—24no—
352#95—24no—
353#95—21no—
354#95—21no—
355#95—21no—
356#95—21no—
357#95—21no—
358#95—21no—
359#95—21no—
360#95—21no—
361#95—21no—
362#95—21no—
363#95—21no—
364#95—21no—
365#95—21no—
366#95—21no—
367#95—21no—
368#95—21no—
369#95—21no—
370#95—21no—
371#95—21no—
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—42no—
384#95—81no—
385#95—81no—
386#95—81no—
387#95—81no—
388#95C22⋊C411yescharacteristic
389#95C22⋊C411yescharacteristic
390#95C22⋊C411yescharacteristic
391#95C22⋊C411yescharacteristic
392#95C22⋊C411yescharacteristic
393#95C22⋊C411yescharacteristic
394#95C22⋊C411yescharacteristic
395#95C22⋊C411yescharacteristic
396C24—21no—
397C24C22×D411yescharacteristic
398C2×Q8—21no—
399C2×Q8—21no—
400C2×Q8—42no—
401C2×Q8—41no—
402C2×Q8—41no—
403C2×Q8—81no—
404C2×Q8—81no—
405C2×D4—21no—
406C2×D4—21no—
407C2×D4—41no—
408C2×D4—41no—
409C2×D4—41no—
410C2×D4—41no—
411C2×D4—41no—
412C2×D4—41no—
413C2×D4—41no—
414C2×D4—41no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—41no—
454C22×C4—42no—
455C22×C4—41no—
456C22×C4—41no—
457C22×C4—41no—
458C22×C4—41no—
459C22×C4—41no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—41no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4—41no—
479C22×C4—81no—
480C22×C4—81no—
481C22×C4C2×C22⋊C411yescharacteristic
482C22×C4C2×C22⋊C411yescharacteristic
483C22×C4C2×C22⋊C411yescharacteristic
484C22×C4C2×C22⋊C411yescharacteristic
485C22×C4C2×C22⋊C411yescharacteristic
486C22×C4C2×C22⋊C411yescharacteristic
487C22×C4C2×C22⋊C411yescharacteristic
488C22×C4C2×C22⋊C411yescharacteristic
489C22×C4C2×C22⋊C411yescharacteristic
490C22×C4C2×C22⋊C411yescharacteristic
491C22×C4C2×C22⋊C411yescharacteristic
492C22×C4C2×C22⋊C411yescharacteristic
493C22×C4C23×C411yescharacteristic
494C22×C4C22×D411yescharacteristic
495C22×C4H(5,𝔽2)11yescharacteristic
496C22×C4H(5,𝔽2)11yescharacteristic
497C22×C42−1+411yescharacteristic
498C22×C42−1+411yescharacteristic
499C2×C8—41no—
500C2×C8—41no—
501C2×C8—41no—
502C2×C8—41no—
503C2×C8—41no—
504C2×C8—41no—
505C2×C8—41no—
506C2×C8—41no—
507C2×C8—41no—
508C2×C8—41no—
509C2×C8—41no—
510C2×C8—41no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—22no—
514C4⋊C4—22no—
515C4⋊C4—22no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—41no—
521C4⋊C4—41no—
522C4⋊C4—41no—
523C4⋊C4—41no—
524C4⋊C4—41no—
525C4⋊C4—41no—
526C4⋊C4—48no—
527C4⋊C4—42no—
528C4⋊C4—41no—
529C4⋊C4—41no—
530C4⋊C4—42no—
531C4⋊C4—42no—
532C4⋊C4—42no—
533C4⋊C4—81no—
534C4⋊C4—81no—
535C4⋊C4—81no—
536C4⋊C4—81no—
537C4⋊C4—81no—
538C4⋊C4—81no—
539C4⋊C4—81no—
540C4⋊C4—81no—
541C4⋊C4—84no—
542C4⋊C4—84no—
543C4⋊C4#10414yes—
544C22⋊C4—42no—
545C22⋊C4—41no—
546C22⋊C4—41no—
547C22⋊C4—41no—
548C22⋊C4—41no—
549C22⋊C4—41no—
550C22⋊C4—41no—
551C22⋊C4—41no—
552C22⋊C4—41no—
553C22⋊C4—42no—
554C22⋊C4—42no—
555C22⋊C4—42no—
556C22⋊C4—42no—
557C22⋊C4—81no—
558C22⋊C4—81no—
559C22⋊C4—81no—
560C22⋊C4—81no—
561C22⋊C4—81no—
562C22⋊C4—81no—
563C42—21no—
564C42—21no—
565C42—21no—
566C42—21no—
567C42—21no—
568C42—21no—
569C42—21no—
570C42—21no—
571C42—41no—
572C42—41no—
573C42—41no—
574C42—41no—
575C42—41no—
576C42—41no—
577C42—41no—
578C42—41no—
579C42—48no—
580C42—42no—
581C42—81no—
582C42—81no—
583C42—84no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23C22×C22⋊C411yescharacteristic
596C23#53511yescharacteristic
597C23#53611yescharacteristic
598C23#57611yescharacteristic
599C23#57711yescharacteristic
600C23#57711yescharacteristic
601C23#57811yescharacteristic
602Q8—81no—
603Q8—81no—
604Q8—162no—
605D4—81no—
606D4—81no—
607D4—81no—
608D4—81no—
609D4—81no—
610D4—81no—
611C2×C4—24no—
612C2×C4—24no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—81no—
695C2×C4—81no—
696C2×C4—81no—
697C2×C4—81no—
698C2×C4—81no—
699C2×C4—81no—
700C2×C4—81no—
701C2×C4—81no—
702C2×C4—81no—
703C2×C4—81no—
704C2×C4—81no—
705C2×C4—81no—
706C2×C4—81no—
707C2×C4—81no—
708C2×C4—81no—
709C2×C4—81no—
710C2×C4—81no—
711C2×C4—81no—
712C2×C4—81no—
713C2×C4—81no—
714C2×C4—162no—
715C2×C4C2×#10412yes—
716C2×C4C2×#10412yes—
717C2×C4C2×#10412yes—
718C2×C4#42112yes—
719C2×C4#52011yescharacteristic
720C2×C4#52011yescharacteristic
721C2×C4#53711yescharacteristic
722C2×C4#53711yescharacteristic
723C8—81no—
724C8—81no—
725C8—81no—
726C8—81no—
727C22—21no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—21no—
738C22—21no—
739C22—81no—
740C22—81no—
741C22—81no—
742C22—81no—
743C22—81no—
744C22—81no—
745C22—81no—
746C22#231111yescharacteristic
747C22#288311yescharacteristic
748C22#288411yescharacteristic
749C22#289711yescharacteristic
750C22#289811yescharacteristic
751C22C22×#10411yescharacteristic
752C22C2×#42111yescharacteristic
753C22#322411yescharacteristic
754C22#322511yescharacteristic
755C22#324311yescharacteristic
756C22#324411yescharacteristic
757C4—21no—
758C4—21no—
759C4—21no—
760C4—21no—
761C4—22no—
762C4—22no—
763C4—22no—
764C4—22no—
765C4—41no—
766C4—41no—
767C4—41no—
768C4—41no—
769C4—41no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—82no—
774C4—82no—
775C4—82no—
776C4—82no—
777C4—81no—
778C4—81no—
779C4—81no—
780C4—81no—
781C4—81no—
782C4—81no—
783C4—81no—
784C2—21no—
785C2—21no—
786C2—21no—
787C2—21no—
788C2—161no—
789C2#1754811yescharacteristic
790C2#1755011yescharacteristic
791C2#1759911yescharacteristic
792C2#1760111yescharacteristic
793C2#2187111yescharacteristic
794C2#2187711yescharacteristic
795C2#2189911yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC2×#121C23
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #21914C2semidirect
3. #13783C2semidirect
4. #9889C2semidirect
5. #9884C2semidirect
10. #9145C2semidirect
11. #9144C2semidirect
14. #8574C2semidirect
15. #8572C2semidirect
22. #2512C4semidirect
23. #2511C4semidirect
24. #2509C4semidirect
25. #2508C4semidirect
28. #2452C4semidirect
29. #2451C4semidirect
31. #2448C4semidirect
32. #2447C4semidirect

Maximal subgroups

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

subgroupindex
#350832
#219142
#137832
#98892
#98842
#96822
#96812
#91492
#91482
#91452
#91442
#85772
#85752
#85742
#85722