Finite Group Databasebeta

← #221839

Subgroups — #221839

Order 512.

1244 conjugacy classes of subgroups.

The subgroup lattice has 963 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36148C211yesmaximal, characteristic
2#22553C211yesmaximal, characteristic, complemented
3C2×#1518C211yesmaximal, characteristic, complemented
4C2×#1504C211yesmaximal, characteristic
5#13896C211yesmaximal, characteristic, complemented
6#9716C211yesmaximal, characteristic, complemented
7#9682C211yesmaximal, characteristic, complemented
8#9156C211yesmaximal, characteristic, complemented
9#9143C211yesmaximal, characteristic, complemented
10#9115C211yesmaximal, characteristic, complemented
11#9114C211yesmaximal, characteristic, complemented
12#8578C211yesmaximal, characteristic, complemented
13#8333C211yesmaximal, characteristic, complemented
14#8331C211yesmaximal, characteristic
15#8217C211yesmaximal, characteristic, complemented
16C2×#533C2211yescharacteristic
17C2×#525C2211yescharacteristic
18C2×#431C2211yescharacteristic
19C2×#407C2211yescharacteristic
20#2854C2211yescharacteristic
21#2850C2211yescharacteristic
22#2848C2211yescharacteristic
23#2558—21no—
24#2491C411yescharacteristic, complemented
25#2472—21no—
26#2460—21no—
27#2458—21no—
28#2450—21no—
29#2439C411yescharacteristic, complemented
30#2432C411yescharacteristic, complemented
31#2429C411yescharacteristic, complemented
32#2426C411yescharacteristic, complemented
33#2421C411yescharacteristic, complemented
34#2411—21no—
35#2367—21no—
36#2362C411yescharacteristic, complemented
37#2359—21no—
38#2341C411yescharacteristic, complemented
39C4×C22⋊Q8C2211yescharacteristic
40C2×#385—21no—
41C2×#382C2211yescharacteristic
42C2×C4×C22⋊C4C2211yescharacteristic
43C22×#95C2211yescharacteristic
44#1924—21no—
45#1923—21no—
46#1851—21no—
47#1817C2211yescharacteristic
48#1797C2211yescharacteristic
49#1779C2211yescharacteristic
50#1753—21no—
51#1749C2211yescharacteristic
52#1518—24no—
53#1504—24no—
54C2×#328C2211yescharacteristic
55C2×#328C2211yescharacteristic
56C2×#328C2211yescharacteristic
57C2×#328C2211yescharacteristic
58C2×#328C2211yescharacteristic
59C2×#328C2211yescharacteristic
60C2×#328C2211yescharacteristic
61C2×#328C2211yescharacteristic
62C2×#327C2211yescharacteristic
63C2×#327C2211yescharacteristic
64C2×#327C2211yescharacteristic
65C2×#327C2211yescharacteristic
66#1442—21no—
67#1442—21no—
68C4⋊#95C2211yescharacteristic
69#1434C2211yescharacteristic
70#1434C2211yescharacteristic
71C22⋊#95—21no—
72C22⋊#95C2211yescharacteristic
73#1294C2211yescharacteristic
74#1294C2211yescharacteristic
75#1294C2211yescharacteristic
76#1294C2211yescharacteristic
77C22×#41C2×C411yescharacteristic
78C24×C4—21no—
79C24×C4C2311yescharacteristic
80C22×M16—21no—
81#533—22no—
82#533—22no—
83#533—41no—
84#533—41no—
85C2×C4⋊Q8C2×C411yescharacteristic, complemented
86C2×C4⋊Q8C2×C411yescharacteristic, complemented
87C2×#125—21no—
88C2×#124—21no—
89C2×#124C2×C411yescharacteristic, complemented
90#525—22no—
91#525—22no—
92#525—41no—
93#525—41no—
94C2×#123—21no—
95C2×#123—21no—
96C2×C22⋊Q8—21no—
97C2×C22⋊Q8C2×C411yescharacteristic
98C2×C22⋊Q8C2×C411yescharacteristic
99C2×C22⋊Q8C2×C411yescharacteristic
100C2×C22⋊Q8C2311yescharacteristic
101C2×C22⋊Q8C2311yescharacteristic
102C2×#121C2×C411yescharacteristic
103C2×#121C2311yescharacteristic
104C2×#120—21no—
105C2×C4×Q8—21no—
106C2×C4×Q8C2×C411yescharacteristic, complemented
107C2×C4×Q8C2×C411yescharacteristic, complemented
108C2×C4×Q8C2×C411yescharacteristic, complemented
109C2×C4×D4—21no—
110C2×C4×D4—21no—
111C2×#117—21no—
112C2×#117C2×C411yescharacteristic
113C22×C4⋊C4—21no—
114C22×C4⋊C4—21no—
115C22×C22⋊C4—21no—
116C22×C22⋊C4D411yescharacteristic
117C22×C22⋊C4D411yescharacteristic
118C22×C42C2311yescharacteristic
119C22×C42C2311yescharacteristic
120#431—22no—
121#431—41no—
122C2×C4⋊C8—21no—
123C2×C4⋊C8—21no—
124#407—22no—
125#407—41no—
126C2×C22⋊C8—21no—
127C2×C22⋊C8—21no—
128C2×C22⋊C8—21no—
129C2×C22⋊C8C2311yescharacteristic
130C2×C22⋊C8C2311yescharacteristic
131C2×C22⋊C8C2311yescharacteristic
132C2×C22⋊C8C2311yescharacteristic
133C2×#97—21no—
134C2×C4×C8—21no—
135#400—21no—
136#398—21no—
137#397—21no—
138#396—21no—
139#396—21no—
140#396—21no—
141#394—21no—
142#394—21no—
143#394—21no—
144#394—21no—
145#393—21no—
146#393—21no—
147#391—21no—
148#391C2×C411yescharacteristic, complemented
149#391C2×C411yescharacteristic, complemented
150#390—21no—
151#390—21no—
152#390—21no—
153#390C2×C411yescharacteristic, complemented
154#390C2×C411yescharacteristic, complemented
155#390C2×C411yescharacteristic, complemented
156#389—21no—
157#389C2×C411yescharacteristic, complemented
158#389C2×C411yescharacteristic, complemented
159#389C2×C411yescharacteristic, complemented
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#388—21no—
169#388—21no—
170#387—21no—
171#387—21no—
172#387—21no—
173#387—21no—
174#386—21no—
175#386—21no—
176#386—21no—
177#385—21no—
178#385—21no—
179#385—21no—
180#385—21no—
181#385—21no—
182#385—21no—
183#385—44no—
184#382—22no—
185#382—41no—
186#382C2×C411yescharacteristic, complemented
187#380—21no—
188#380C2×C411yescharacteristic
189#380C2×C411yescharacteristic
190#380C2311yescharacteristic
191#379—21no—
192C4×C4⋊C4—21no—
193C4×C4⋊C4—21no—
194C4×C4⋊C4C2×C411yescharacteristic, complemented
195C4×C22⋊C4—21no—
196C4×C22⋊C4—21no—
197C4×C22⋊C4C2×C411yescharacteristic
198C4×C22⋊C4C2×C411yescharacteristic
199C4×C22⋊C4C2×C411yescharacteristic
200C4×C22⋊C4C2×C411yescharacteristic
201C4×C22⋊C4D411yescharacteristic
202C4×C22⋊C4D411yescharacteristic
203C4×C22⋊C4D411yescharacteristic
204C4×C22⋊C4D411yescharacteristic
205C2×#95—22no—
206C2×#95—21no—
207C2×#95—21no—
208C2×#95—21no—
209C2×#95—21no—
210C2×#95—21no—
211C2×#95—21no—
212C2×#95—21no—
213C2×#95—21no—
214C2×#95—41no—
215C2×#95D411yescharacteristic
216C2×#95D411yescharacteristic
217C2×#95C2311yescharacteristic
218C2×#95C2311yescharacteristic
219C2×#95C2311yescharacteristic
220C2×#95C2311yescharacteristic
221#336—21no—
222#336—21no—
223#336—21no—
224#336—21no—
225#328—22no—
226#328—22no—
227#328—22no—
228#328—22no—
229#328—22no—
230#328—41no—
231#328—41no—
232#328D414yes—
233#327—22no—
234#327—22no—
235#327—41no—
236#327—41no—
237C25C2×D411yescharacteristic
238C2×#41—22no—
239C2×#41—41no—
240C2×#41—42no—
241C2×#41—81no—
242C22×Q8—21no—
243C22×Q8C22×C411yescharacteristic
244C22×Q8C22×C411yescharacteristic
245C22×D4—21no—
246C22×D4—21no—
247C22×D4—21no—
248C22×D4C22×C411yescharacteristic
249C23×C4—21no—
250C23×C4—21no—
251C23×C4—21no—
252C23×C4—21no—
253C23×C4—21no—
254C23×C4—21no—
255C23×C4—21no—
256C23×C4—21no—
257C23×C4—21no—
258C23×C4—42no—
259C23×C4—42no—
260C23×C4—42no—
261C23×C4—42no—
262C23×C4—42no—
263C23×C4—42no—
264C23×C4—81no—
265C23×C4—81no—
266C23×C4—81no—
267C23×C4C22×C411yescharacteristic
268C23×C4C22×C411yescharacteristic
269C23×C4C2×D411yescharacteristic
270C23×C4C2×D411yescharacteristic
271C23×C4C2×D411yescharacteristic
272C23×C4C2×D411yescharacteristic
273C23×C4C2×D411yescharacteristic
274C23×C4C2×D411yescharacteristic
275C23×C4C2×D411yescharacteristic
276C23×C4C2411yescharacteristic
277C2×M16—42no—
278C2×M16—42no—
279C2×M16—81no—
280C22×C8—21no—
281C22×C8—21no—
282C22×C8—21no—
283C22×C8—21no—
284C4⋊Q8—22no—
285C4⋊Q8—22no—
286C4⋊Q8—41no—
287C4⋊Q8—41no—
288#125—42no—
289#125—42no—
290#124—44no—
291#124—81no—
292#123—42no—
293#123—42no—
294#123—42no—
295#123—42no—
296C22⋊Q8—21no—
297C22⋊Q8—21no—
298C22⋊Q8—22no—
299C22⋊Q8—21no—
300C22⋊Q8—21no—
301C22⋊Q8—21no—
302C22⋊Q8—21no—
303C22⋊Q8—42no—
304C22⋊Q8—42no—
305C22⋊Q8—41no—
306C22⋊Q8—42no—
307C22⋊Q8—81no—
308C22⋊Q8C2×D412yes—
309C22⋊Q8#4112yes—
310#121—21no—
311#121—21no—
312#121—21no—
313#121—21no—
314#121—22no—
315#121—41no—
316#120—42no—
317#120—42no—
318C4×Q8—22no—
319C4×Q8—22no—
320C4×Q8—41no—
321C4×Q8—41no—
322C4×Q8—42no—
323C4×Q8—42no—
324C4×Q8—81no—
325C4×D4—42no—
326C4×D4—42no—
327C4×D4—42no—
328C4×D4—42no—
329#117—22no—
330#117—42no—
331#117—42no—
332#117—41no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—42no—
348C2×C4⋊C4—42no—
349C2×C4⋊C4—42no—
350C2×C4⋊C4—42no—
351C2×C4⋊C4—81no—
352C2×C4⋊C4—81no—
353C2×C4⋊C4C22×C411yescharacteristic
354C2×C4⋊C4C22×C411yescharacteristic
355C2×C4⋊C4C22×C411yescharacteristic
356C2×C4⋊C4C22×C411yescharacteristic
357C2×C4⋊C4C22×C411yescharacteristic
358C2×C22⋊C4—21no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4—42no—
382C2×C22⋊C4—42no—
383C2×C22⋊C4C22⋊C411yescharacteristic
384C2×C22⋊C4C22⋊C411yescharacteristic
385C2×C22⋊C4C22⋊C411yescharacteristic
386C2×C22⋊C4C22⋊C411yescharacteristic
387C2×C22⋊C4C22⋊C411yescharacteristic
388C2×C22⋊C4C22⋊C411yescharacteristic
389C2×C22⋊C4C22⋊C411yescharacteristic
390C2×C22⋊C4C22⋊C411yescharacteristic
391C2×C42—21no—
392C2×C42—21no—
393C2×C42—21no—
394C2×C42—21no—
395C2×C42—21no—
396C2×C42—21no—
397C2×C42—21no—
398C2×C42—21no—
399C2×C42—21no—
400C2×C42—81no—
401C2×C42C22×C411yescharacteristic
402C2×C42C22×C411yescharacteristic
403C2×C42C22×C411yescharacteristic
404C2×C42C22×C411yescharacteristic
405C2×C42C2×D411yescharacteristic
406C2×C42C2×D411yescharacteristic
407C2×C42C2×D411yescharacteristic
408C2×C42C2×D411yescharacteristic
409C4⋊C8—42no—
410C4⋊C8—81no—
411C22⋊C8—21no—
412C22⋊C8—21no—
413C22⋊C8—21no—
414C22⋊C8—21no—
415C22⋊C8—21no—
416C22⋊C8—21no—
417C22⋊C8—21no—
418C22⋊C8—42no—
419C22⋊C8—42no—
420C22⋊C8—81no—
421C22⋊C8C2×D412yes—
422#97—81no—
423C4×C8—42no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95—21no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—21no—
434#95—21no—
435#95—21no—
436#95—21no—
437#95—21no—
438#95—21no—
439#95—21no—
440#95—21no—
441#95—21no—
442#95—21no—
443#95—21no—
444#95—42no—
445#95—42no—
446#95—42no—
447#95—42no—
448#95—42no—
449#95—81no—
450#95—81no—
451#95—81no—
452#95C22⋊C411yescharacteristic
453#95C22⋊C411yescharacteristic
454#95C22⋊C411yescharacteristic
455#95C22⋊C411yescharacteristic
456#95C22⋊C411yescharacteristic
457#95C22⋊C411yescharacteristic
458#95C22⋊C411yescharacteristic
459#95C22⋊C411yescharacteristic
460#95C2×D412yes—
461C24—21no—
462C24—21no—
463C24—22no—
464C24—22no—
465C24—21no—
466C24—21no—
467C24—21no—
468C24—21no—
469C24—21no—
470C24—41no—
471C24—41no—
472C24C2×C22⋊C411yescharacteristic
473C24C2×C22⋊C411yescharacteristic
474C24C22×D411yescharacteristic
475#41—84no—
476#41—84no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—42no—
481C2×Q8—42no—
482C2×Q8—41no—
483C2×Q8—41no—
484C2×Q8—41no—
485C2×Q8—41no—
486C2×Q8—81no—
487C2×Q8C4×D412yes—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—42no—
491C2×D4—42no—
492C2×D4—41no—
493C2×D4—41no—
494C2×D4—41no—
495C2×D4—41no—
496C2×D4—41no—
497C2×D4—41no—
498C2×D4—41no—
499C2×D4—41no—
500C2×D4—42no—
501C2×D4—42no—
502C2×D4—81no—
503C2×D4—81no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—22no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—22no—
535C22×C4—41no—
536C22×C4—41no—
537C22×C4—41no—
538C22×C4—41no—
539C22×C4—41no—
540C22×C4—41no—
541C22×C4—41no—
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—41no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—41no—
554C22×C4—41no—
555C22×C4—41no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4—41no—
559C22×C4—41no—
560C22×C4—48no—
561C22×C4—41no—
562C22×C4—41no—
563C22×C4—41no—
564C22×C4—41no—
565C22×C4—41no—
566C22×C4—41no—
567C22×C4—41no—
568C22×C4—41no—
569C22×C4—41no—
570C22×C4—41no—
571C22×C4—41no—
572C22×C4—41no—
573C22×C4—41no—
574C22×C4—41no—
575C22×C4—41no—
576C22×C4—41no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4—41no—
580C22×C4—81no—
581C22×C4—82no—
582C22×C4—82no—
583C22×C4—82no—
584C22×C4—82no—
585C22×C4—84no—
586C22×C4—84no—
587C22×C4—84no—
588C22×C4—84no—
589C22×C4—84no—
590C22×C4—84no—
591C22×C4C2×C22⋊C411yescharacteristic
592C22×C4C2×C22⋊C411yescharacteristic
593C22×C4C2×C22⋊C411yescharacteristic
594C22×C4C2×C22⋊C411yescharacteristic
595C22×C4C2×C22⋊C411yescharacteristic
596C22×C4C2×C22⋊C411yescharacteristic
597C22×C4C2×C22⋊C411yescharacteristic
598C22×C4C2×C22⋊C411yescharacteristic
599C22×C4C2×C22⋊C411yescharacteristic
600C22×C4C2×C22⋊C411yescharacteristic
601C22×C4AGL(1,ℤ/8)12yes—
602C22×C4#13712yes—
603C22×C4C23×C411yescharacteristic
604C22×C4C22×D411yescharacteristic
605C22×C4C22×D411yescharacteristic
606C22×C4C2×#4111yescharacteristic
607C22×C4H(5,𝔽2)11yescharacteristic
608C22×C4H(5,𝔽2)11yescharacteristic
609M16—84no—
610C2×C8—22no—
611C2×C8—41no—
612C2×C8—41no—
613C2×C8—41no—
614C2×C8—41no—
615C2×C8—41no—
616C2×C8—41no—
617C2×C8—41no—
618C2×C8—41no—
619C2×C8—41no—
620C2×C8—41no—
621C2×C8—41no—
622C4⋊C4—21no—
623C4⋊C4—22no—
624C4⋊C4—22no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—42no—
630C4⋊C4—42no—
631C4⋊C4—42no—
632C4⋊C4—42no—
633C4⋊C4—42no—
634C4⋊C4—42no—
635C4⋊C4—41no—
636C4⋊C4—41no—
637C4⋊C4—42no—
638C4⋊C4—41no—
639C4⋊C4—41no—
640C4⋊C4—42no—
641C4⋊C4—42no—
642C4⋊C4—81no—
643C4⋊C4—81no—
644C4⋊C4—81no—
645C4⋊C4—84no—
646C4⋊C4—84no—
647C4⋊C4C4×D412yes—
648C22⋊C4—22no—
649C22⋊C4—22no—
650C22⋊C4—22no—
651C22⋊C4—22no—
652C22⋊C4—22no—
653C22⋊C4—22no—
654C22⋊C4—22no—
655C22⋊C4—22no—
656C22⋊C4—41no—
657C22⋊C4—41no—
658C22⋊C4—42no—
659C22⋊C4—42no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—41no—
664C22⋊C4—41no—
665C22⋊C4—41no—
666C22⋊C4—41no—
667C22⋊C4—42no—
668C22⋊C4—42no—
669C22⋊C4—41no—
670C22⋊C4—41no—
671C22⋊C4—42no—
672C22⋊C4—42no—
673C22⋊C4—81no—
674C22⋊C4—81no—
675C22⋊C4—81no—
676C22⋊C4—81no—
677C22⋊C4—81no—
678C22⋊C4—81no—
679C22⋊C4—84no—
680C42—21no—
681C42—21no—
682C42—21no—
683C42—21no—
684C42—21no—
685C42—21no—
686C42—21no—
687C42—21no—
688C42—41no—
689C42—41no—
690C42—41no—
691C42—41no—
692C42—42no—
693C42—42no—
694C42—42no—
695C42—42no—
696C42—81no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—24no—
702C23—24no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23#41012yes—
737C23#42112yes—
738C23C22×C22⋊C411yescharacteristic
739C23D4211yescharacteristic
740C23#54611yescharacteristic
741C23C2×AGL(1,ℤ/8)11yescharacteristic
742C23C2×#13711yescharacteristic
743C23#57711yescharacteristic
744C23#57811yescharacteristic
745Q8—42no—
746Q8—42no—
747Q8—81no—
748Q8—81no—
749Q8—84no—
750D4—81no—
751D4—81no—
752D4—84no—
753D4—84no—
754D4—81no—
755D4—81no—
756D4—81no—
757D4—81no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—21no—
774C2×C4—22no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—42no—
831C2×C4—81no—
832C2×C4—81no—
833C2×C4—81no—
834C2×C4—81no—
835C2×C4—81no—
836C2×C4—81no—
837C2×C4—81no—
838C2×C4—81no—
839C2×C4—81no—
840C2×C4—81no—
841C2×C4—84no—
842C2×C4—81no—
843C2×C4—81no—
844C2×C4—81no—
845C2×C4—81no—
846C2×C4—81no—
847C2×C4—81no—
848C2×C4—81no—
849C2×C4—816no—
850C2×C4—81no—
851C2×C4—81no—
852C2×C4—81no—
853C2×C4—81no—
854C2×C4—81no—
855C2×C4—81no—
856C2×C4—81no—
857C2×C4—81no—
858C2×C4—81no—
859C2×C4—81no—
860C2×C4—81no—
861C2×C4—81no—
862C2×C4—81no—
863C2×C4—81no—
864C2×C4—81no—
865C2×C4#41712yes—
866C2×C4#41712yes—
867C2×C4C2×C4×D411yescharacteristic
868C2×C4#51811yescharacteristic
869C2×C4D4211yescharacteristic
870C2×C4#54611yescharacteristic
871C8—42no—
872C8—81no—
873C8—81no—
874C8—81no—
875C22—21no—
876C22—21no—
877C22—21no—
878C22—21no—
879C22—21no—
880C22—21no—
881C22—21no—
882C22—21no—
883C22—21no—
884C22—21no—
885C22—21no—
886C22—21no—
887C22—22no—
888C22—22no—
889C22—22no—
890C22—22no—
891C22—22no—
892C22—22no—
893C22—44no—
894C22—44no—
895C22—44no—
896C22—44no—
897C22—41no—
898C22—41no—
899C22—41no—
900C22—41no—
901C22—41no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—81no—
906C22—81no—
907C22—81no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—81no—
912C22D4×C22⋊C411yescharacteristic
913C22C2×#41011yescharacteristic
914C22#288311yescharacteristic
915C22C2×#41711yescharacteristic
916C22#289811yescharacteristic
917C22C2×#42111yescharacteristic
918C22#290111yescharacteristic
919C22#326511yescharacteristic
920C22#327011yescharacteristic
921C22#330811yescharacteristic
922C22#331611yescharacteristic
923C4—21no—
924C4—21no—
925C4—21no—
926C4—21no—
927C4—22no—
928C4—22no—
929C4—41no—
930C4—41no—
931C4—42no—
932C4—41no—
933C4—41no—
934C4—42no—
935C4—41no—
936C4—41no—
937C4—41no—
938C4—41no—
939C4—82no—
940C4—82no—
941C4—81no—
942C4—81no—
943C4—81no—
944C4—81no—
945C4—81no—
946C4—161no—
947C4—161no—
948C2—21no—
949C2—21no—
950C2—21no—
951C2—21no—
952C2—42no—
953C2—42no—
954C2—161no—
955C2#1758811yescharacteristic
956C2#1759811yescharacteristic
957C2#1760911yescharacteristic
958C2#1763011yescharacteristic
959C2#2240511yescharacteristic
960C2#2242111yescharacteristic
961C2#2243411yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC2×#525C22
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. #22553C2semidirect
3. C2×#1518C2semidirect
5. #13896C2semidirect
6. #9716C2semidirect
7. #9682C2semidirect
8. #9156C2semidirect
9. #9143C2semidirect
10. #9115C2semidirect
11. #9114C2semidirect
12. #8578C2semidirect
13. #8333C2semidirect
15. #8217C2semidirect
24. #2491C4semidirect
29. #2439C4semidirect
30. #2432C4semidirect
31. #2429C4semidirect
32. #2426C4semidirect
33. #2421C4semidirect
36. #2362C4semidirect
38. #2341C4semidirect
85. C2×C4⋊Q8C2×C4semidirect
86. C2×C4⋊Q8C2×C4semidirect
89. C2×#124C2×C4semidirect
106. C2×C4×Q8C2×C4semidirect
107. C2×C4×Q8C2×C4semidirect
108. C2×C4×Q8C2×C4semidirect
148. #391C2×C4semidirect
149. #391C2×C4semidirect
153. #390C2×C4semidirect
154. #390C2×C4semidirect
155. #390C2×C4semidirect
157. #389C2×C4semidirect
158. #389C2×C4semidirect
159. #389C2×C4semidirect
186. #382C2×C4semidirect
194. C4×C4⋊C4C2×C4semidirect

Maximal subgroups

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

subgroupindex
#361482
#225532
C2×#15182
C2×#15042
#138962
#97162
#96822
#91562
#91432
#91152
#91142
#85782
#83332
#83312
#82172