Finite Group Databasebeta

← #164392

Subgroups — #164392

Order 512.

1077 conjugacy classes of subgroups.

The subgroup lattice has 817 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36362C211yesmaximal, characteristic
2#22010C211yesmaximal, characteristic, complemented
3#20559C211yesmaximal, characteristic, complemented
4#7710C211yesmaximal, characteristic, complemented
5#7704C211yesmaximal, characteristic, complemented
6#7676C211yesmaximal, characteristic, complemented
7#7676C211yesmaximal, characteristic, complemented
8#7670C211yesmaximal, characteristic, complemented
9#7664C211yesmaximal, characteristic, complemented
10#7637C211yesmaximal, characteristic, complemented
11#7612C211yesmaximal, characteristic, complemented
12#7606C211yesmaximal, characteristic, complemented
13#7578C211yesmaximal, characteristic, complemented
14#7572C211yesmaximal, characteristic, complemented
15#7569C211yesmaximal, characteristic, complemented
16C2×#553C411yescharacteristic
17C2×#546C411yescharacteristic
18C2×#435—21no—
19#2861C2211yescharacteristic
20#2856C2211yescharacteristic
21#2850C2211yescharacteristic
22#2566C411yescharacteristic
23#2554—21no—
24#2554—21no—
25#2544C411yescharacteristic
26#2502C411yescharacteristic
27#2500C411yescharacteristic
28#2464—21no—
29#2464—21no—
30#2433C411yescharacteristic
31#2431C411yescharacteristic
32#2424—21no—
33#2424—21no—
34#2358—21no—
35#2358—21no—
36C4×#127C2211yescharacteristic
37#2297C2211yescharacteristic
38C2×#390C2211yescharacteristic
39C42×D4C2211yescharacteristic
40#1955—21no—
41#1940—21no—
42#1923—21no—
43#1923—21no—
44#1817C2211yescharacteristic
45#1817C2211yescharacteristic, complemented
46#1797C2211yescharacteristic
47#1797C2211yescharacteristic, complemented
48#1771—21no—
49C4×C4⋊C8C2211yescharacteristic, complemented
50C4×C4⋊C8C2211yescharacteristic, complemented
51#1753—21no—
52C8×C22⋊C4—21no—
53#1749C2211yescharacteristic, complemented
54C4×C22⋊C8C2211yescharacteristic
55#1745C2211yescharacteristic, complemented
56#1745C2211yescharacteristic, complemented
57#1728C2211yescharacteristic
58C2×#336C2211yescharacteristic, complemented
59#1272C2211yescharacteristic, complemented
60#1272C2211yescharacteristic, complemented
61#1272C2211yescharacteristic, complemented
62#1272C2211yescharacteristic, complemented
63#1270C2211yescharacteristic
64#1270C2211yescharacteristic
65#1270C2211yescharacteristic
66#1270C2211yescharacteristic
67#1270C2211yescharacteristic
68#1270C2211yescharacteristic
69#1270C2211yescharacteristic
70#1270C2211yescharacteristic
71#1270C2211yescharacteristic, complemented
72#1270C2211yescharacteristic, complemented
73#1270C2211yescharacteristic, complemented
74#1270C2211yescharacteristic, complemented
75C22×#41C2×C411yescharacteristic
76C23×D4C2×C411yescharacteristic
77C22×M16—21no—
78C23×C8—21no—
79#553—44no—
80#546—44no—
81C2×#127C2×C411yescharacteristic
82C2×#127C2×C411yescharacteristic
83C2×#126—21no—
84C2×#125C2×C411yescharacteristic
85C2×#124C2×C411yescharacteristic
86C2×#124C2×C411yescharacteristic
87C2×#123—21no—
88C2×#123—21no—
89C2×C22⋊Q8C2×C411yescharacteristic
90C2×#121—21no—
91C2×#121—21no—
92C2×#121—21no—
93C2×#121—21no—
94C2×#121C2×C411yescharacteristic
95C2×#121C2×C411yescharacteristic
96C2×#121C2×C411yescharacteristic
97C2×#120—21no—
98C2×#120—21no—
99C2×#120—21no—
100C2×C4×D4—21no—
101C2×C4×D4—21no—
102C2×C4×D4—21no—
103C2×C4×D4C2×C411yescharacteristic
104C2×C4×D4C2×C411yescharacteristic
105C2×C4×D4C2×C411yescharacteristic
106C2×C4×D4D411yescharacteristic
107C2×C4×D4D411yescharacteristic
108C2×#117C2×C411yescharacteristic
109C22×C4⋊C4C2×C411yescharacteristic
110C22×C22⋊C4—21no—
111C22×C22⋊C4—21no—
112C22×C22⋊C4—21no—
113C22×C42C2311yescharacteristic
114C22×C42C2311yescharacteristic
115#435—28no—
116C2×C4⋊C8—21no—
117C2×C4⋊C8—21no—
118C2×C4⋊C8—21no—
119C2×C4⋊C8—21no—
120C2×C22⋊C8—21no—
121C2×C22⋊C8—21no—
122C2×C22⋊C8—21no—
123C2×C22⋊C8—21no—
124C2×C22⋊C8—21no—
125C2×C22⋊C8—21no—
126C2×#97—21no—
127C2×#97—21no—
128C2×#97—21no—
129C2×C4×C8—21no—
130C2×C4×C8—21no—
131C2×C4×C8—21no—
132#398—21no—
133#398—21no—
134#396—21no—
135#396—21no—
136#394—21no—
137#394—21no—
138#394—21no—
139#394—21no—
140#392—21no—
141#392—21no—
142#392—21no—
143#392—21no—
144#391C2×C411yescharacteristic
145#391C2×C411yescharacteristic
146#391C2311yescharacteristic
147#390—21no—
148#390—21no—
149#390—21no—
150#390—21no—
151#390—21no—
152#390—21no—
153#390C2×C411yescharacteristic
154#390C2×C411yescharacteristic
155#390C2×C411yescharacteristic
156#390C2×C411yescharacteristic
157#390C2311yescharacteristic
158#390C2311yescharacteristic
159#390C2311yescharacteristic
160#388—21no—
161#388—21no—
162#388—21no—
163#388—21no—
164#388—21no—
165#388—21no—
166#388—21no—
167#388—21no—
168#386—21no—
169#386—21no—
170#386—21no—
171#386—21no—
172#386—21no—
173#386—21no—
174#386—21no—
175#386—21no—
176#385—21no—
177#385—21no—
178#385—21no—
179#385—21no—
180#384C2×C411yescharacteristic
181#384C2×C411yescharacteristic
182#382C2×C411yescharacteristic
183C4×C4⋊C4C2×C411yescharacteristic
184C4×C4⋊C4D411yescharacteristic
185C4×C4⋊C4D411yescharacteristic
186C4×C22⋊C4—21no—
187C4×C22⋊C4—21no—
188C4×C22⋊C4C2×C411yescharacteristic
189C4×C22⋊C4C2×C411yescharacteristic
190C4×C22⋊C4D411yescharacteristic
191C4×C22⋊C4D411yescharacteristic
192C4×C22⋊C4D411yescharacteristic
193C4×C22⋊C4D411yescharacteristic
194C43C2311yescharacteristic
195#336—21no—
196#336—21no—
197#336—21no—
198#336—21no—
199#336—21no—
200#336—21no—
201#336C2311yescharacteristic
202#336C2311yescharacteristic
203#336C2311yescharacteristic
204#336C2311yescharacteristic
205#336C2311yescharacteristic
206#336C2311yescharacteristic
207#336C2311yescharacteristic
208#336C2311yescharacteristic
209C25—21no—
210C2×#41—22no—
211C2×#41—41no—
212C2×#41—42no—
213C2×#41—81no—
214C22×Q8C22×C411yescharacteristic
215C22×D4—22no—
216C22×D4—21no—
217C22×D4—21no—
218C22×D4—21no—
219C22×D4—21no—
220C22×D4—21no—
221C22×D4—21no—
222C22×D4—21no—
223C22×D4—21no—
224C22×D4—21no—
225C22×D4—41no—
226C22×D4—42no—
227C22×D4—81no—
228C22×D4C22⋊C411yescharacteristic
229C22×D4C22×C411yescharacteristic
230C22×D4C22×C411yescharacteristic
231C22×D4C22×C411yescharacteristic
232C23×C4—21no—
233C23×C4—21no—
234C23×C4—21no—
235C23×C4—21no—
236C23×C4C22×C411yescharacteristic
237C23×C4C22×C411yescharacteristic
238C23×C4C2×D411yescharacteristic
239C23×C4C2×D411yescharacteristic
240C23×C4C2×D411yescharacteristic
241C23×C4C2×D411yescharacteristic
242C2×M16—24no—
243C2×M16—81no—
244C2×M16—81no—
245C22×C8—21no—
246C22×C8—21no—
247C22×C8—21no—
248C22×C8—21no—
249C22×C8—24no—
250C22×C8—21no—
251C22×C8—21no—
252C22×C8—21no—
253C22×C8—21no—
254C22×C8—81no—
255C22×C8—81no—
256#127—22no—
257#127—41no—
258#127—81no—
259#126—44no—
260#125—42no—
261#124—42no—
262#124—81no—
263#123—44no—
264#123—44no—
265C22⋊Q8—42no—
266#121—42no—
267#121—42no—
268#121—44no—
269#121—44no—
270#121—42no—
271#121—81no—
272#121—81no—
273#121—81no—
274#121—81no—
275#120—44no—
276#120—44no—
277#120—44no—
278C4×D4—24no—
279C4×D4—24no—
280C4×D4—42no—
281C4×D4—42no—
282C4×D4—42no—
283C4×D4—44no—
284C4×D4—81no—
285C4×D4—81no—
286C4×D4—81no—
287C4×D4—81no—
288#117—42no—
289C2×C4⋊C4—21no—
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—42no—
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×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—44no—
331C2×C22⋊C4—81no—
332C2×C22⋊C4—81no—
333C2×C22⋊C4—81no—
334C2×C22⋊C4—81no—
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×C42—21no—
342C2×C42—81no—
343C2×C42—81no—
344C2×C42C22×C411yescharacteristic
345C2×C42C22×C411yescharacteristic
346C2×C42C22×C411yescharacteristic
347C2×C42C22×C411yescharacteristic
348C2×C42C2×D411yescharacteristic
349C2×C42C2×D411yescharacteristic
350C2×C42C2×D411yescharacteristic
351C2×C42C2×D411yescharacteristic
352C2×C42C2×D411yescharacteristic
353C2×C42C2×D411yescharacteristic
354C2×C42C2×D411yescharacteristic
355C2×C42C2×D411yescharacteristic
356C2×C42C2411yescharacteristic
357C4⋊C8—24no—
358C4⋊C8—42no—
359C4⋊C8—81no—
360C4⋊C8—81no—
361C22⋊C8—24no—
362C22⋊C8—24no—
363C22⋊C8—81no—
364C22⋊C8—81no—
365C22⋊C8—81no—
366C22⋊C8—81no—
367#97—24no—
368#97—42no—
369#97—81no—
370C4×C8—81no—
371C4×C8—81no—
372C4×C8—81no—
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#95C22⋊C411yescharacteristic
382#95C22⋊C411yescharacteristic
383#95C22⋊C411yescharacteristic
384#95C22⋊C411yescharacteristic
385#95C22⋊C411yescharacteristic
386#95C22⋊C411yescharacteristic
387C24—21no—
388C24—21no—
389C24—21no—
390C24—42no—
391C24—42no—
392C24—42no—
393C24—42no—
394C24—81no—
395C24—81no—
396C24—81no—
397C24C2×C22⋊C411yescharacteristic
398C24C2×C22⋊C411yescharacteristic
399#41—84no—
400#41—84no—
401C2×Q8—21no—
402C2×Q8—21no—
403C2×Q8—41no—
404C2×Q8—41no—
405C2×D4—22no—
406C2×D4—22no—
407C2×D4—21no—
408C2×D4—21no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4—41no—
413C2×D4—41no—
414C2×D4—41no—
415C2×D4—42no—
416C2×D4—42no—
417C2×D4—42no—
418C2×D4—41no—
419C2×D4—41no—
420C2×D4—41no—
421C2×D4—41no—
422C2×D4—42no—
423C2×D4—42no—
424C2×D4—42no—
425C2×D4—42no—
426C2×D4—42no—
427C2×D4—42no—
428C2×D4—42no—
429C2×D4—42no—
430C2×D4—42no—
431C2×D4—42no—
432C2×D4—42no—
433C2×D4—42no—
434C2×D4—81no—
435C2×D4—81no—
436C2×D4—81no—
437C2×D4—81no—
438C2×D4—81no—
439C2×D4—81no—
440C2×D4—81no—
441C2×D4—84no—
442C2×D4—84no—
443C2×D4—81no—
444C2×D4—81no—
445C2×D4—81no—
446C2×D4—81no—
447C2×D4—81no—
448C2×D4#13112yes—
449C22×C4—22no—
450C22×C4—22no—
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—22no—
460C22×C4—22no—
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—41no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4—42no—
479C22×C4—42no—
480C22×C4—42no—
481C22×C4—42no—
482C22×C4—42no—
483C22×C4—81no—
484C22×C4—81no—
485C22×C4—81no—
486C22×C4—81no—
487C22×C4—81no—
488C22×C4—81no—
489C22×C4—81no—
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×C4C2×C22⋊C411yescharacteristic
498C22×C4C2×C22⋊C411yescharacteristic
499C22×C4C2×C22⋊C411yescharacteristic
500C22×C4C23×C411yescharacteristic
501C22×C4C22×D411yescharacteristic
502C22×C4C22×D411yescharacteristic
503M16—84no—
504C2×C8—22no—
505C2×C8—22no—
506C2×C8—22no—
507C2×C8—22no—
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—
517C2×C8—41no—
518C2×C8—41no—
519C2×C8—41no—
520C2×C8—41no—
521C2×C8—41no—
522C2×C8—41no—
523C2×C8—41no—
524C2×C8—41no—
525C2×C8—41no—
526C2×C8—41no—
527C2×C8—41no—
528C2×C8—84no—
529C4⋊C4—22no—
530C4⋊C4—22no—
531C4⋊C4—41no—
532C4⋊C4—41no—
533C4⋊C4—41no—
534C4⋊C4—41no—
535C4⋊C4—41no—
536C4⋊C4—42no—
537C4⋊C4—42no—
538C4⋊C4—42no—
539C4⋊C4—42no—
540C4⋊C4—81no—
541C4⋊C4—81no—
542C4⋊C4—81no—
543C4⋊C4—81no—
544C22⋊C4—22no—
545C22⋊C4—22no—
546C22⋊C4—22no—
547C22⋊C4—22no—
548C22⋊C4—42no—
549C22⋊C4—42no—
550C22⋊C4—42no—
551C22⋊C4—42no—
552C22⋊C4—42no—
553C22⋊C4—42no—
554C22⋊C4—42no—
555C22⋊C4—42no—
556C22⋊C4—41no—
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—41no—
566C22⋊C4—41no—
567C22⋊C4—41no—
568C22⋊C4—42no—
569C22⋊C4—42no—
570C22⋊C4—42no—
571C22⋊C4—42no—
572C22⋊C4—42no—
573C22⋊C4—81no—
574C22⋊C4—81no—
575C22⋊C4—81no—
576C22⋊C4—81no—
577C22⋊C4—81no—
578C22⋊C4—81no—
579C22⋊C4#10014yes—
580C22⋊C4#10414yes—
581C42—21no—
582C42—21no—
583C42—21no—
584C42—21no—
585C42—21no—
586C42—21no—
587C42—22no—
588C42—22no—
589C42—22no—
590C42—41no—
591C42—41no—
592C42—41no—
593C42—41no—
594C42—41no—
595C42—41no—
596C42—41no—
597C42—42no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—22no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—84no—
632C23—84no—
633C23—84no—
634C23—84no—
635C23—162no—
636C23—162no—
637C23—162no—
638C23C2×#10012yes—
639C23C2×#10412yes—
640C23C22×C22⋊C411yescharacteristic
641Q8—81no—
642Q8—81no—
643D4—42no—
644D4—42no—
645D4—44no—
646D4—84no—
647D4—84no—
648D4—84no—
649D4—81no—
650D4—81no—
651D4—81no—
652D4—81no—
653D4—84no—
654D4—84no—
655D4—162no—
656D4—162no—
657D4—162no—
658D4—162no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—81no—
714C2×C4—81no—
715C2×C4—81no—
716C2×C4—81no—
717C2×C4—84no—
718C2×C4—162no—
719C2×C4—162no—
720C2×C4—162no—
721C2×C4C2×#10012yes—
722C2×C4C2×#10012yes—
723C2×C4C2×#10412yes—
724C2×C4C2×#10412yes—
725C2×C4#42112yes—
726C2×C4C2×#13111yescharacteristic
727C2×C4#56811yescharacteristic
728C2×C4#57611yescharacteristic
729C2×C4#57611yescharacteristic
730C2×C4#57711yescharacteristic
731C2×C4#57711yescharacteristic
732C8—42no—
733C8—42no—
734C8—42no—
735C8—42no—
736C8—81no—
737C8—81no—
738C8—81no—
739C8—81no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22—81no—
768C22—81no—
769C22—81no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—168no—
776C22#288011yescharacteristic
777C22#288311yescharacteristic
778C22C22×#10011yescharacteristic
779C22#289711yescharacteristic
780C22#289711yescharacteristic
781C22C22×#10411yescharacteristic
782C22C2×#42111yescharacteristic
783C4—21no—
784C4—21no—
785C4—22no—
786C4—22no—
787C4—22no—
788C4—22no—
789C4—21no—
790C4—21no—
791C4—22no—
792C4—21no—
793C4—21no—
794C4—41no—
795C4—41no—
796C4—41no—
797C4—41no—
798C4—41no—
799C4—81no—
800C4—81no—
801C4—81no—
802C4—81no—
803C4—81no—
804C2—42no—
805C2—42no—
806C2—82no—
807C2—161no—
808C2—161no—
809C2#1742111yescharacteristic
810C2#1751711yescharacteristic
811C2#1752111yescharacteristic
812C2#1754711yescharacteristic
813C2#1759911yescharacteristic
814C2#1764711yescharacteristic
815C2#1777011yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC22×C4C23×C4
Frattini, cosocleC2×C42C24
prime radical#36362C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C2×C42 ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #22010C2semidirect
3. #20559C2semidirect
4. #7710C2semidirect
5. #7704C2semidirect
6. #7676C2semidirect
7. #7676C2semidirect
8. #7670C2semidirect
9. #7664C2semidirect
10. #7637C2semidirect
11. #7612C2semidirect
12. #7606C2semidirect
13. #7578C2semidirect
14. #7572C2semidirect
15. #7569C2semidirect
45. #1817C22semidirect
47. #1797C22semidirect
49. C4×C4⋊C8C22semidirect
50. C4×C4⋊C8C22semidirect
53. #1749C22semidirect
55. #1745C22semidirect
56. #1745C22semidirect
58. C2×#336C22semidirect
59. #1272C22semidirect
60. #1272C22semidirect
61. #1272C22semidirect
62. #1272C22semidirect
71. #1270C22semidirect
72. #1270C22semidirect
73. #1270C22semidirect
74. #1270C22semidirect

Maximal subgroups

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

subgroupindex
#363622
#220102
#205592
#77102
#77042
#76762
#76702
#76642
#76372
#76122
#76062
#75782
#75722
#75692