Finite Group Databasebeta

← #223659

Subgroups — #223659

Order 512.

978 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36186C211yesmaximal, characteristic
2#22601C211yesmaximal, characteristic, complemented
3#13893C211yesmaximal, characteristic, complemented
4#9911C211yesmaximal, characteristic, complemented
5#9889C211yesmaximal, characteristic, complemented
6#9157C211yesmaximal, characteristic
7#9148C211yesmaximal, characteristic
8#9118C211yesmaximal, characteristic
9#9114C211yesmaximal, characteristic
10#8717C211yesmaximal, characteristic, complemented
11#8716C211yesmaximal, characteristic, complemented
12#8575C211yesmaximal, characteristic
13#8216C211yesmaximal, characteristic
14#8018C211yesmaximal, characteristic, complemented
15#8014C211yesmaximal, characteristic, complemented
16C2×#552—21no—
17C2×#432C2211yescharacteristic
18C2×#431C2211yescharacteristic
19#2857C2211yescharacteristic
20#2854C2211yescharacteristic
21#2854C2211yescharacteristic
22#2552C411yescharacteristic, complemented
23#2542C411yescharacteristic, complemented
24#2519—21no—
25#2519—21no—
26#2512C411yescharacteristic, complemented
27#2512C411yescharacteristic, complemented
28#2506C411yescharacteristic, complemented
29#2506C411yescharacteristic, complemented
30#2498—21no—
31#2498—21no—
32#2489—21no—
33#2417—21no—
34#2365C411yescharacteristic, complemented
35#2362—21no—
36#2354C411yescharacteristic, complemented
37C4×#121C2211yescharacteristic
38#2285C2211yescharacteristic
39#2285C2211yescharacteristic
40C2×#383C2211yescharacteristic
41C2×C4×C4⋊C4C2211yescharacteristic
42C2×C4×C4⋊C4C2211yescharacteristic
43#1940—21no—
44#1917—21no—
45#1916—21no—
46#1817C2211yescharacteristic
47#1817C2211yescharacteristic
48#1797C2211yescharacteristic
49#1771—21no—
50#1749C2211yescharacteristic
51C2×#327C2211yescharacteristic
52C2×#327C2211yescharacteristic
53C2×#327C2211yescharacteristic
54C2×#327C2211yescharacteristic
55#1442—21no—
56#1441—21no—
57#1436—21no—
58#1434—21no—
59#1434C2211yescharacteristic
60#1434C2211yescharacteristic
61#1434C2211yescharacteristic
62#1434C2211yescharacteristic
63#1294C2211yescharacteristic
64#1294C2211yescharacteristic
65#1294C2211yescharacteristic
66#1294C2211yescharacteristic
67#1294C2211yescharacteristic
68#1294C2211yescharacteristic
69#1294C2211yescharacteristic
70#1294C2211yescharacteristic
71#1294C2211yescharacteristic
72#1294C2211yescharacteristic
73#1294C2211yescharacteristic
74#1294C2211yescharacteristic
75#552—44no—
76#552—44no—
77C2×C4⋊Q8C2×C411yescharacteristic
78C2×#126—21no—
79C2×#126—21no—
80C2×#125—21no—
81C2×#125—21no—
82C2×#125—21no—
83C2×#123—21no—
84C2×#123—21no—
85C2×C22⋊Q8—21no—
86C2×C22⋊Q8—21no—
87C2×C22⋊Q8—21no—
88C2×#121C2311yescharacteristic
89C2×C4×Q8—21no—
90C2×C4×D4—21no—
91C2×C4×D4C2×C411yescharacteristic
92C2×#117—21no—
93C2×#117—21no—
94C2×#117—21no—
95C22×C4⋊C4—21no—
96C22×C4⋊C4D411yescharacteristic
97C22×C4⋊C4D411yescharacteristic
98C22×C42—21no—
99C22×C42C2311yescharacteristic
100C22×C42C2311yescharacteristic
101C22×C42C2311yescharacteristic
102#432—22no—
103#432—41no—
104#431—22no—
105#431—41no—
106C2×C4⋊C8—21no—
107C2×C4⋊C8—21no—
108C2×C4⋊C8—21no—
109C2×C22⋊C8C2311yescharacteristic
110C2×C22⋊C8C2311yescharacteristic
111C2×C22⋊C8C2311yescharacteristic
112C2×C22⋊C8C2311yescharacteristic
113C2×#97—21no—
114C2×#97—21no—
115C2×C4×C8—21no—
116#400—21no—
117#400—21no—
118#399—21no—
119#399—21no—
120#398—21no—
121#398—21no—
122#398—21no—
123#398—21no—
124#397—21no—
125#397—21no—
126#396—21no—
127#396—21no—
128#391—21no—
129#391—21no—
130#390C2×C411yescharacteristic
131#390C2×C411yescharacteristic
132#390C2×C411yescharacteristic
133#390C2×C411yescharacteristic
134#390C2×C411yescharacteristic
135#389—21no—
136#389—21no—
137#389C2×C411yescharacteristic
138#389C2×C411yescharacteristic
139#389C2×C411yescharacteristic
140#389C2×C411yescharacteristic
141#389C2×C411yescharacteristic
142#389C2×C411yescharacteristic
143#389C2×C411yescharacteristic
144#388—21no—
145#388—21no—
146#388—21no—
147#388—21no—
148#388—21no—
149#388—21no—
150#388—21no—
151#388—21no—
152#388—21no—
153#387—21no—
154#387—21no—
155#387—21no—
156#387—21no—
157#386—21no—
158#386—21no—
159#386—21no—
160#384C2×C411yescharacteristic
161#384C2×C411yescharacteristic
162#384C2×C411yescharacteristic
163#384C2×C411yescharacteristic
164#384C2×C411yescharacteristic
165#383—22no—
166#383—41no—
167#382—21no—
168#382—21no—
169#380—21no—
170#380—21no—
171#380—21no—
172#380—21no—
173#380C2311yescharacteristic
174#380C2311yescharacteristic
175#380C2311yescharacteristic
176C4×C4⋊C4—21no—
177C4×C4⋊C4—21no—
178C4×C4⋊C4—22no—
179C4×C4⋊C4—41no—
180C4×C4⋊C4C2×C411yescharacteristic
181C4×C4⋊C4C2×C411yescharacteristic
182C4×C4⋊C4C2×C411yescharacteristic
183C4×C4⋊C4C2×C411yescharacteristic
184C4×C4⋊C4C2×C411yescharacteristic
185C4×C4⋊C4C2×C411yescharacteristic
186C4×C4⋊C4C2×C411yescharacteristic
187C4×C4⋊C4C2×C411yescharacteristic
188C4×C4⋊C4C2×C411yescharacteristic
189C4×C4⋊C4D411yescharacteristic
190C4×C4⋊C4D411yescharacteristic
191C4×C4⋊C4D411yescharacteristic
192C4×C4⋊C4D411yescharacteristic
193C4×C22⋊C4—21no—
194C2×#95—21no—
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×#95D411yescharacteristic
205C2×#95D411yescharacteristic
206C2×#95C2311yescharacteristic
207C2×#95C2311yescharacteristic
208C2×#95C2311yescharacteristic
209C2×#95C2311yescharacteristic
210#336—21no—
211#336—21no—
212#336—21no—
213#336—21no—
214#336—21no—
215#336—21no—
216#327—22no—
217#327—22no—
218#327—41no—
219#327—41no—
220C22×Q8—21no—
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—42no—
240#126—44no—
241#126—44no—
242#125—44no—
243#125—44no—
244#125—44no—
245#123—42no—
246#123—42no—
247#123—42no—
248#123—42no—
249C22⋊Q8—44no—
250C22⋊Q8—44no—
251C22⋊Q8—42no—
252C22⋊Q8—42no—
253#121—21no—
254#121—21no—
255#121—21no—
256#121—21no—
257C4×Q8—44no—
258C4×D4—42no—
259C4×D4—42no—
260C4×D4—42no—
261#117—44no—
262#117—42no—
263#117—42no—
264#117—42no—
265#117—42no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—22no—
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—21no—
277C2×C4⋊C4—21no—
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—42no—
287C2×C4⋊C4—42no—
288C2×C4⋊C4—42no—
289C2×C4⋊C4—42no—
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×C4⋊C4C22⋊C411yescharacteristic
298C2×C4⋊C4C22×C411yescharacteristic
299C2×C4⋊C4C22×C411yescharacteristic
300C2×C4⋊C4C22×C411yescharacteristic
301C2×C4⋊C4C22×C411yescharacteristic
302C2×C4⋊C4C22×C411yescharacteristic
303C2×C4⋊C4C22×C411yescharacteristic
304C2×C4⋊C4C22×C411yescharacteristic
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×C22⋊C4—21no—
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×C42—21no—
321C2×C42—21no—
322C2×C42—21no—
323C2×C42—21no—
324C2×C42—21no—
325C2×C42—21no—
326C2×C42—21no—
327C2×C42—21no—
328C2×C42—21no—
329C2×C42—21no—
330C2×C42—21no—
331C2×C42—21no—
332C2×C42—21no—
333C2×C42—42no—
334C2×C42—42no—
335C2×C42—42no—
336C2×C42—81no—
337C2×C42C22×C411yescharacteristic
338C2×C42C22×C411yescharacteristic
339C2×C42C22×C411yescharacteristic
340C2×C42C22×C411yescharacteristic
341C2×C42C22×C411yescharacteristic
342C2×C42C22×C411yescharacteristic
343C2×C42C2×D411yescharacteristic
344C2×C42C2×D411yescharacteristic
345C2×C42C2×D411yescharacteristic
346C2×C42C2×D411yescharacteristic
347C2×C42C2×D411yescharacteristic
348C2×C42C2×D411yescharacteristic
349C4⋊C8—42no—
350C4⋊C8—42no—
351C4⋊C8—42no—
352C22⋊C8—21no—
353C22⋊C8—21no—
354C22⋊C8—21no—
355C22⋊C8—21no—
356C22⋊C8—21no—
357C22⋊C8—21no—
358C22⋊C8—21no—
359C22⋊C8#4112yes—
360#97—42no—
361#97—42no—
362C4×C8—42no—
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—21no—
384#95—21no—
385#95—42no—
386#95—42no—
387#95—42no—
388#95—42no—
389#95—42no—
390#95—42no—
391#95—42no—
392#95—42no—
393#95—81no—
394#95—81no—
395#95C22⋊C411yescharacteristic
396#95C22⋊C411yescharacteristic
397#95C22⋊C411yescharacteristic
398#95C22⋊C411yescharacteristic
399#95C22⋊C411yescharacteristic
400#95C22⋊C411yescharacteristic
401#95C22⋊C411yescharacteristic
402#95C22⋊C411yescharacteristic
403#95#4112yes—
404C24—21no—
405C24C22×D411yescharacteristic
406C2×Q8—42no—
407C2×Q8—42no—
408C2×Q8—42no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—41no—
412C2×D4—41no—
413C2×D4—41no—
414C2×D4—41no—
415C2×D4—41no—
416C2×D4—41no—
417C2×D4—41no—
418C2×D4—41no—
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—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4—41no—
456C22×C4—42no—
457C22×C4—42no—
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—42no—
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—41no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—41no—
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×C4C2×C22⋊C411yescharacteristic
494C22×C4C2×C22⋊C411yescharacteristic
495C22×C4C2×C22⋊C411yescharacteristic
496C22×C4C2×C22⋊C411yescharacteristic
497C22×C4AGL(1,ℤ/8)12yes—
498C22×C4AGL(1,ℤ/8)12yes—
499C22×C4C23×C411yescharacteristic
500C22×C4C22×D411yescharacteristic
501C22×C4C2×#4111yescharacteristic
502C22×C4C2×#4111yescharacteristic
503C22×C4H(5,𝔽2)11yescharacteristic
504C22×C42−1+411yescharacteristic
505C2×C8—22no—
506C2×C8—41no—
507C2×C8—41no—
508C2×C8—41no—
509C2×C8—41no—
510C2×C8—41no—
511C2×C8—41no—
512C2×C8—41no—
513C2×C8—41no—
514C2×C8—41no—
515C2×C8—41no—
516C2×C8—41no—
517C4⋊C4—22no—
518C4⋊C4—22no—
519C4⋊C4—22no—
520C4⋊C4—22no—
521C4⋊C4—22no—
522C4⋊C4—22no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—41no—
526C4⋊C4—41no—
527C4⋊C4—41no—
528C4⋊C4—41no—
529C4⋊C4—41no—
530C4⋊C4—41no—
531C4⋊C4—41no—
532C4⋊C4—41no—
533C4⋊C4—42no—
534C4⋊C4—42no—
535C4⋊C4—42no—
536C4⋊C4—42no—
537C4⋊C4—42no—
538C4⋊C4—42no—
539C4⋊C4—42no—
540C4⋊C4—42no—
541C4⋊C4—42no—
542C4⋊C4—42no—
543C4⋊C4—48no—
544C4⋊C4—42no—
545C4⋊C4—42no—
546C4⋊C4—42no—
547C4⋊C4—42no—
548C4⋊C4—42no—
549C4⋊C4—81no—
550C4⋊C4—81no—
551C4⋊C4—81no—
552C22⋊C4—42no—
553C22⋊C4—42no—
554C22⋊C4—42no—
555C22⋊C4—42no—
556C22⋊C4—42no—
557C22⋊C4—41no—
558C22⋊C4—41no—
559C22⋊C4—41no—
560C22⋊C4—41no—
561C22⋊C4—41no—
562C22⋊C4—41no—
563C22⋊C4—41no—
564C22⋊C4—41no—
565C22⋊C4—42no—
566C22⋊C4—42no—
567C22⋊C4—42no—
568C22⋊C4—81no—
569C22⋊C4—81no—
570C22⋊C4—81no—
571C42—21no—
572C42—21no—
573C42—21no—
574C42—21no—
575C42—21no—
576C42—21no—
577C42—21no—
578C42—21no—
579C42—21no—
580C42—21no—
581C42—21no—
582C42—21no—
583C42—21no—
584C42—21no—
585C42—21no—
586C42—21no—
587C42—22no—
588C42—22no—
589C42—41no—
590C42—41no—
591C42—42no—
592C42—42no—
593C42—42no—
594C42—42no—
595C42—42no—
596C42—84no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23C22×C22⋊C411yescharacteristic
609C23#54611yescharacteristic
610C23#54711yescharacteristic
611C23C2×AGL(1,ℤ/8)11yescharacteristic
612C23C2×AGL(1,ℤ/8)11yescharacteristic
613C23#57711yescharacteristic
614C23#57811yescharacteristic
615Q8—84no—
616D4—81no—
617D4—81no—
618D4—81no—
619D4—81no—
620D4—81no—
621D4—81no—
622C2×C4—22no—
623C2×C4—22no—
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—22no—
637C2×C4—22no—
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—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
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—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—42no—
701C2×C4—84no—
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—81no—
715C2×C4—81no—
716C2×C4—81no—
717C2×C4—81no—
718C2×C4—81no—
719C2×C4—81no—
720C2×C4—81no—
721C2×C4—81no—
722C2×C4—81no—
723C2×C4—81no—
724C2×C4—81no—
725C2×C4—81no—
726C2×C4—81no—
727C2×C4—81no—
728C2×C4#41012yes—
729C2×C4#41812yes—
730C2×C4#41812yes—
731C2×C4#42112yes—
732C2×C4C4×#4111yescharacteristic
733C2×C4#52011yescharacteristic
734C2×C4#54611yescharacteristic
735C2×C4#54711yescharacteristic
736C8—42no—
737C8—81no—
738C8—81no—
739C8—81no—
740C22—21no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—21no—
745C22—21no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22#233911yescharacteristic
760C22C2×#41011yescharacteristic
761C22#288411yescharacteristic
762C22C2×#41811yescharacteristic
763C22#289811yescharacteristic
764C22C2×#42111yescharacteristic
765C22#290111yescharacteristic
766C22#330611yescharacteristic
767C22#330811yescharacteristic
768C22#334311yescharacteristic
769C22#334511yescharacteristic
770C4—22no—
771C4—21no—
772C4—21no—
773C4—21no—
774C4—21no—
775C4—22no—
776C4—22no—
777C4—22no—
778C4—41no—
779C4—41no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—41no—
784C4—41no—
785C4—41no—
786C4—82no—
787C4—82no—
788C4—81no—
789C4—81no—
790C4—81no—
791C4—81no—
792C4—81no—
793C4—81no—
794C4—81no—
795C4—161no—
796C4—161no—
797C2—21no—
798C2—21no—
799C2—21no—
800C2—21no—
801C2—161no—
802C2#1756111yescharacteristic
803C2#1760111yescharacteristic
804C2#1761211yescharacteristic
805C2#1763111yescharacteristic
806C2#2247811yescharacteristic
807C2#2249511yescharacteristic
808C2#2250611yescharacteristic
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. #22601C2semidirect
3. #13893C2semidirect
4. #9911C2semidirect
5. #9889C2semidirect
10. #8717C2semidirect
11. #8716C2semidirect
14. #8018C2semidirect
15. #8014C2semidirect
22. #2552C4semidirect
23. #2542C4semidirect
26. #2512C4semidirect
27. #2512C4semidirect
28. #2506C4semidirect
29. #2506C4semidirect
34. #2365C4semidirect
36. #2354C4semidirect

Maximal subgroups

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

subgroupindex
#361862
#226012
#138932
#99112
#98892
#91572
#91482
#91182
#91142
#87172
#87162
#85752
#82162
#80182
#80142