Finite Group Databasebeta

← #223631

Subgroups — #223631

Order 512.

996 conjugacy classes of subgroups.

The subgroup lattice has 801 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36200C211yesmaximal, characteristic
2#22601C211yesmaximal, characteristic, complemented
3#13821C211yesmaximal, characteristic, complemented
4#9910C211yesmaximal, characteristic, complemented
5#9887C211yesmaximal, characteristic, complemented
6#9148C211yesmaximal, characteristic
7#9148C211yesmaximal, characteristic
8#9118C211yesmaximal, characteristic
9#9114C211yesmaximal, characteristic
10#8717C211yesmaximal, characteristic, complemented
11#8714C211yesmaximal, characteristic, complemented
12#8577C211yesmaximal, characteristic
13#8218C211yesmaximal, characteristic
14#8021C211yesmaximal, characteristic, complemented
15#8014C211yesmaximal, characteristic, complemented
16C2×#432C2211yescharacteristic
17C2×#431C2211yescharacteristic
18#2854C2211yescharacteristic
19#2854C2211yescharacteristic
20#2851C2211yescharacteristic
21#2570C411yescharacteristic, complemented
22#2566C411yescharacteristic, complemented
23#2529—21no—
24#2525—21no—
25#2515—21no—
26#2513C411yescharacteristic, complemented
27#2512C411yescharacteristic, complemented
28#2509C411yescharacteristic, complemented
29#2507C411yescharacteristic, complemented
30#2481—21no—
31#2419—21no—
32#2413—21no—
33#2373—21no—
34#2370C411yescharacteristic, complemented
35#2359—21no—
36#2357C411yescharacteristic, complemented
37C4×#121C2211yescharacteristic
38C2×#389—21no—
39#2285C2211yescharacteristic
40#2283C2211yescharacteristic
41C2×C4×C4⋊C4—21no—
42C2×C4×C4⋊C4C2211yescharacteristic
43C2×C4×C4⋊C4C2211yescharacteristic
44C2×C4×C4⋊C4C2211yescharacteristic
45#1940—21no—
46#1917—21no—
47#1916—21no—
48#1817C2211yescharacteristic
49#1817C2211yescharacteristic
50#1797C2211yescharacteristic
51#1771—21no—
52#1749C2211yescharacteristic
53C2×#327C2211yescharacteristic
54C2×#327C2211yescharacteristic
55C2×#327C2211yescharacteristic
56C2×#327C2211yescharacteristic
57#1436—21no—
58#1436—21no—
59C4⋊#95C2211yescharacteristic
60#1434C2211yescharacteristic
61#1434C2211yescharacteristic
62C4×#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
75C2×#126—21no—
76C2×#125C2×C411yescharacteristic
77C2×#123—21no—
78C2×#123—21no—
79C2×#121C2311yescharacteristic
80C2×C4×D4—21no—
81C2×C4×D4C2×C411yescharacteristic
82C2×#117—21no—
83C22×C4⋊C4—21no—
84C22×C4⋊C4—21no—
85C22×C4⋊C4—21no—
86C22×C4⋊C4D411yescharacteristic
87C22×C4⋊C4D411yescharacteristic
88C22×C42—21no—
89C22×C42—21no—
90C22×C42—21no—
91C22×C42C2311yescharacteristic
92C22×C42C2311yescharacteristic
93C22×C42C2311yescharacteristic
94#432—22no—
95#432—41no—
96#431—22no—
97#431—41no—
98C2×C4⋊C8—21no—
99C2×C4⋊C8—21no—
100C2×C4⋊C8—21no—
101C2×C22⋊C8C2311yescharacteristic
102C2×C22⋊C8C2311yescharacteristic
103C2×C22⋊C8C2311yescharacteristic
104C2×C22⋊C8C2311yescharacteristic
105C2×#97—21no—
106C2×#97—21no—
107C2×C4×C8—21no—
108#400—21no—
109#400—21no—
110#400—21no—
111#398—21no—
112#398—21no—
113#398—21no—
114#397—21no—
115#397—21no—
116#397—21no—
117#396—21no—
118#396—21no—
119#396—21no—
120#390C2×C411yescharacteristic
121#390C2×C411yescharacteristic
122#390C2×C411yescharacteristic
123#390C2×C411yescharacteristic
124#390C2×C411yescharacteristic
125#389—28no—
126#389—21no—
127#389—21no—
128#389—21no—
129#389C2×C411yescharacteristic
130#389C2×C411yescharacteristic
131#389C2×C411yescharacteristic
132#389C2×C411yescharacteristic
133#389C2×C411yescharacteristic
134#389C2×C411yescharacteristic
135#389C2×C411yescharacteristic
136#388—21no—
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#387—21no—
152#387—21no—
153#387—21no—
154#386—21no—
155#386—21no—
156#386—21no—
157#385—21no—
158#385—21no—
159#385—21no—
160#385—21no—
161#384C2×C411yescharacteristic
162#384C2×C411yescharacteristic
163#383—21no—
164#382—21no—
165#382C2×C411yescharacteristic
166#382C2×C411yescharacteristic
167#382C2×C411yescharacteristic
168#381—21no—
169#381—21no—
170#380—21no—
171#380C2311yescharacteristic
172#380C2311yescharacteristic
173#380C2311yescharacteristic
174C4×C4⋊C4—21no—
175C4×C4⋊C4—21no—
176C4×C4⋊C4—22no—
177C4×C4⋊C4—22no—
178C4×C4⋊C4—41no—
179C4×C4⋊C4—41no—
180C4×C4⋊C4—44no—
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⋊C4C2×C411yescharacteristic
190C4×C4⋊C4D411yescharacteristic
191C4×C4⋊C4D411yescharacteristic
192C4×C4⋊C4D411yescharacteristic
193C4×C4⋊C4D411yescharacteristic
194C4×C22⋊C4—21no—
195C4×C22⋊C4—21no—
196C4×C22⋊C4—21no—
197#376—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×D4—21no—
221C22×D4C22×C411yescharacteristic
222C23×C4—21no—
223C23×C4—21no—
224C23×C4—21no—
225C23×C4—21no—
226C23×C4—21no—
227C23×C4C2×D411yescharacteristic
228C23×C4C2×D411yescharacteristic
229C23×C4C2×D411yescharacteristic
230C23×C4C2×D411yescharacteristic
231C23×C4C2×D411yescharacteristic
232C23×C4C2×D411yescharacteristic
233C23×C4C2411yescharacteristic
234C22×C8—21no—
235C22×C8—21no—
236C22×C8—21no—
237C22×C8—21no—
238#126—44no—
239#125—42no—
240#123—42no—
241#123—42no—
242#123—81no—
243#123—81no—
244#121—21no—
245#121—21no—
246#121—21no—
247#121—21no—
248C4×D4—42no—
249C4×D4—81no—
250C4×D4—81no—
251#117—81no—
252#117—81no—
253C2×C4⋊C4—22no—
254C2×C4⋊C4—22no—
255C2×C4⋊C4—24no—
256C2×C4⋊C4—24no—
257C2×C4⋊C4—24no—
258C2×C4⋊C4—24no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—42no—
273C2×C4⋊C4—42no—
274C2×C4⋊C4—42no—
275C2×C4⋊C4—42no—
276C2×C4⋊C4—42no—
277C2×C4⋊C4—42no—
278C2×C4⋊C4C22⋊C411yescharacteristic
279C2×C4⋊C4C22⋊C411yescharacteristic
280C2×C4⋊C4C22⋊C411yescharacteristic
281C2×C4⋊C4C22⋊C411yescharacteristic
282C2×C4⋊C4C22⋊C411yescharacteristic
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×C22⋊C4—21no—
294C2×C22⋊C4—21no—
295C2×C22⋊C4—21no—
296C2×C22⋊C4—21no—
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×C42—21no—
309C2×C42—21no—
310C2×C42—21no—
311C2×C42—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—21no—
321C2×C42—21no—
322C2×C42—42no—
323C2×C42—42no—
324C2×C42—42no—
325C2×C42—42no—
326C2×C42—42no—
327C2×C42—42no—
328C2×C42—42no—
329C2×C42—81no—
330C2×C42—81no—
331C2×C42C22×C411yescharacteristic
332C2×C42C22×C411yescharacteristic
333C2×C42C22×C411yescharacteristic
334C2×C42C22×C411yescharacteristic
335C2×C42C22×C411yescharacteristic
336C2×C42C22×C411yescharacteristic
337C2×C42C2×D411yescharacteristic
338C2×C42C2×D411yescharacteristic
339C2×C42C2×D411yescharacteristic
340C2×C42C2×D411yescharacteristic
341C2×C42C2×D411yescharacteristic
342C2×C42C2×D411yescharacteristic
343C4⋊C8—42no—
344C4⋊C8—42no—
345C4⋊C8—42no—
346C22⋊C8—21no—
347C22⋊C8—21no—
348C22⋊C8—21no—
349C22⋊C8—21no—
350C22⋊C8—21no—
351C22⋊C8—21no—
352C22⋊C8—21no—
353C22⋊C8#4112yes—
354#97—42no—
355#97—42no—
356C4×C8—42no—
357#95—24no—
358#95—24no—
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—21no—
384#95—21no—
385#95—21no—
386#95—21no—
387#95—42no—
388#95—42no—
389#95—42no—
390#95—81no—
391#95C22⋊C411yescharacteristic
392#95C22⋊C411yescharacteristic
393#95C22⋊C411yescharacteristic
394#95C22⋊C411yescharacteristic
395#95C22⋊C411yescharacteristic
396#95C22⋊C411yescharacteristic
397#95C22⋊C411yescharacteristic
398#95C22⋊C411yescharacteristic
399#95#4112yes—
400C24—21no—
401C24C22×D411yescharacteristic
402C2×D4—21no—
403C2×D4—21no—
404C2×D4—41no—
405C2×D4—41no—
406C2×D4—41no—
407C2×D4—41no—
408C2×D4—41no—
409C2×D4—41no—
410C2×D4—41no—
411C2×D4—41no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
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—22no—
436C22×C4—22no—
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—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—42no—
454C22×C4—41no—
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—81no—
477C22×C4—81no—
478C22×C4C2×C22⋊C411yescharacteristic
479C22×C4C2×C22⋊C411yescharacteristic
480C22×C4C2×C22⋊C411yescharacteristic
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×C4AGL(1,ℤ/8)12yes—
491C22×C4#13712yes—
492C22×C4C23×C411yescharacteristic
493C22×C4C22×D411yescharacteristic
494C22×C4C2×#4111yescharacteristic
495C22×C4C2×#4111yescharacteristic
496C22×C4H(5,𝔽2)11yescharacteristic
497C22×C42−1+411yescharacteristic
498C2×C8—22no—
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—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—22no—
514C4⋊C4—22no—
515C4⋊C4—22no—
516C4⋊C4—22no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—41no—
520C4⋊C4—41no—
521C4⋊C4—41no—
522C4⋊C4—41no—
523C4⋊C4—41no—
524C4⋊C4—41no—
525C4⋊C4—48no—
526C4⋊C4—48no—
527C4⋊C4—48no—
528C4⋊C4—42no—
529C4⋊C4—42no—
530C4⋊C4—42no—
531C4⋊C4—42no—
532C4⋊C4—42no—
533C4⋊C4—42no—
534C4⋊C4—81no—
535C4⋊C4—81no—
536C4⋊C4—81no—
537C4⋊C4—81no—
538C4⋊C4—81no—
539C4⋊C4—81no—
540C4⋊C4—81no—
541C4⋊C4#10414yes—
542C22⋊C4—41no—
543C22⋊C4—41no—
544C22⋊C4—41no—
545C22⋊C4—41no—
546C22⋊C4—41no—
547C22⋊C4—41no—
548C22⋊C4—41no—
549C22⋊C4—41no—
550C22⋊C4—42no—
551C22⋊C4—42no—
552C22⋊C4—42no—
553C22⋊C4—42no—
554C22⋊C4—42no—
555C22⋊C4—42no—
556C22⋊C4—81no—
557C22⋊C4—81no—
558C22⋊C4—81no—
559C22⋊C4—81no—
560C22⋊C4—81no—
561C42—21no—
562C42—21no—
563C42—21no—
564C42—21no—
565C42—21no—
566C42—21no—
567C42—21no—
568C42—21no—
569C42—21no—
570C42—21no—
571C42—21no—
572C42—21no—
573C42—21no—
574C42—21no—
575C42—21no—
576C42—21no—
577C42—22no—
578C42—22no—
579C42—41no—
580C42—41no—
581C42—48no—
582C42—42no—
583C42—81no—
584C42—81no—
585C42—81no—
586C42—81no—
587C42—84no—
588C42—84no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23C22×C22⋊C411yescharacteristic
601C23#54611yescharacteristic
602C23#54711yescharacteristic
603C23C2×AGL(1,ℤ/8)11yescharacteristic
604C23C2×#13711yescharacteristic
605C23#57611yescharacteristic
606C23#57711yescharacteristic
607D4—81no—
608D4—81no—
609D4—81no—
610D4—81no—
611D4—81no—
612D4—81no—
613C2×C4—24no—
614C2×C4—24no—
615C2×C4—22no—
616C2×C4—22no—
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—22no—
634C2×C4—22no—
635C2×C4—24no—
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—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—42no—
671C2×C4—41no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
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—41no—
701C2×C4—41no—
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—162no—
717C2×C4#41012yes—
718C2×C4#41712yes—
719C2×C4#41712yes—
720C2×C4C2×#10412yes—
721C2×C4C2×#10412yes—
722C2×C4C2×#10412yes—
723C2×C4C4×#4111yescharacteristic
724C2×C4#52011yescharacteristic
725C2×C4#54611yescharacteristic
726C2×C4#54711yescharacteristic
727C8—42no—
728C8—81no—
729C8—81no—
730C8—81no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—21no—
738C22—21no—
739C22—21no—
740C22—21no—
741C22—21no—
742C22—21no—
743C22—81no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22#233911yescharacteristic
751C22C2×#41011yescharacteristic
752C22#288411yescharacteristic
753C22C2×#41711yescharacteristic
754C22#289711yescharacteristic
755C22C22×#10411yescharacteristic
756C22#290111yescharacteristic
757C22#331811yescharacteristic
758C22#332011yescharacteristic
759C22#334511yescharacteristic
760C22#334611yescharacteristic
761C4—22no—
762C4—22no—
763C4—21no—
764C4—21no—
765C4—21no—
766C4—21no—
767C4—22no—
768C4—22no—
769C4—22no—
770C4—22no—
771C4—44no—
772C4—41no—
773C4—41no—
774C4—41no—
775C4—41no—
776C4—41no—
777C4—41no—
778C4—82no—
779C4—82no—
780C4—82no—
781C4—81no—
782C4—81no—
783C4—81no—
784C4—81no—
785C4—81no—
786C4—81no—
787C4—81no—
788C2—21no—
789C2—21no—
790C2—21no—
791C2—21no—
792C2—161no—
793C2#1754611yescharacteristic
794C2#1755011yescharacteristic
795C2#1760711yescharacteristic
796C2#1762811yescharacteristic
797C2#2247811yescharacteristic
798C2#2249311yescharacteristic
799C2#2250511yescharacteristic
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. #13821C2semidirect
4. #9910C2semidirect
5. #9887C2semidirect
10. #8717C2semidirect
11. #8714C2semidirect
14. #8021C2semidirect
15. #8014C2semidirect
21. #2570C4semidirect
22. #2566C4semidirect
26. #2513C4semidirect
27. #2512C4semidirect
28. #2509C4semidirect
29. #2507C4semidirect
34. #2370C4semidirect
36. #2357C4semidirect

Maximal subgroups

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

subgroupindex
#362002
#226012
#138212
#99102
#98872
#91482
#91182
#91142
#87172
#87142
#85772
#82182
#80212
#80142