Finite Group Databasebeta

← #221711

Subgroups — #221711

Order 512.

1328 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36148C211yesmaximal, characteristic
2#22553C211yesmaximal, characteristic, complemented
3C2×#1504C211yesmaximal, characteristic
4C2×#1503C211yesmaximal, characteristic, complemented
5#13814C211yesmaximal, characteristic, complemented
6#9713C211yesmaximal, characteristic, complemented
7#9682C211yesmaximal, characteristic, complemented
8#9148C211yesmaximal, characteristic, complemented
9#9143C211yesmaximal, characteristic, complemented
10#9115C211yesmaximal, characteristic, complemented
11#9114C211yesmaximal, characteristic, complemented
12#8572C211yesmaximal, characteristic, complemented
13#8333C211yesmaximal, characteristic, complemented
14#8331C211yesmaximal, characteristic
15#8219C211yesmaximal, 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×C4×C4⋊C4C2211yescharacteristic
42C2×C4×C22⋊C4—21no—
43C2×C4×C22⋊C4C2211yescharacteristic
44C22×#95C2211yescharacteristic
45#1924—21no—
46#1923—21no—
47#1851—21no—
48#1817C2211yescharacteristic
49#1797C2211yescharacteristic
50#1779C2211yescharacteristic
51#1753—21no—
52#1749C2211yescharacteristic
53#1504—24no—
54#1503—24no—
55C2×#328C2211yescharacteristic
56C2×#328C2211yescharacteristic
57C2×#328C2211yescharacteristic
58C2×#328C2211yescharacteristic
59C2×#328C2211yescharacteristic
60C2×#328C2211yescharacteristic
61C2×#328C2211yescharacteristic
62C2×#328C2211yescharacteristic
63C2×#327C2211yescharacteristic
64C2×#327C2211yescharacteristic
65C2×#327C2211yescharacteristic
66C2×#327C2211yescharacteristic
67#1436—21no—
68#1436—21no—
69C4⋊#95C2211yescharacteristic
70#1434C2211yescharacteristic
71C22⋊#95C2211yescharacteristic
72C4×#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×C42—21no—
119C22×C42—21no—
120C22×C42C2311yescharacteristic
121C22×C42C2311yescharacteristic
122#431—22no—
123#431—41no—
124C2×C4⋊C8—21no—
125C2×C4⋊C8—21no—
126#407—22no—
127#407—41no—
128C2×C22⋊C8—21no—
129C2×C22⋊C8—21no—
130C2×C22⋊C8—21no—
131C2×C22⋊C8C2311yescharacteristic
132C2×C22⋊C8C2311yescharacteristic
133C2×C22⋊C8C2311yescharacteristic
134C2×C22⋊C8C2311yescharacteristic
135C2×#97—21no—
136C2×C4×C8—21no—
137#400—21no—
138#398—21no—
139#397—21no—
140#396—21no—
141#396—21no—
142#396—21no—
143#394—21no—
144#394—21no—
145#394—21no—
146#394—21no—
147#393—21no—
148#393—21no—
149#391—21no—
150#391C2×C411yescharacteristic, complemented
151#391C2×C411yescharacteristic, complemented
152#390—21no—
153#390—21no—
154#390—21no—
155#390C2×C411yescharacteristic, complemented
156#390C2×C411yescharacteristic, complemented
157#390C2×C411yescharacteristic, complemented
158#389—21no—
159#389C2×C411yescharacteristic, complemented
160#389C2×C411yescharacteristic, complemented
161#389C2×C411yescharacteristic, complemented
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#388—21no—
171#388—21no—
172#387—21no—
173#387—21no—
174#387—21no—
175#387—21no—
176#386—21no—
177#386—21no—
178#386—21no—
179#385—28no—
180#385—21no—
181#385—21no—
182#385—21no—
183#385—21no—
184#385—21no—
185#385—21no—
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⋊C4—22no—
195C4×C4⋊C4—41no—
196C4×C4⋊C4C2×C411yescharacteristic, complemented
197C4×C22⋊C4—21no—
198C4×C22⋊C4—21no—
199C4×C22⋊C4—44no—
200C4×C22⋊C4C2×C411yescharacteristic
201C4×C22⋊C4C2×C411yescharacteristic
202C4×C22⋊C4C2×C411yescharacteristic
203C4×C22⋊C4C2×C411yescharacteristic
204C4×C22⋊C4D411yescharacteristic
205C4×C22⋊C4D411yescharacteristic
206C4×C22⋊C4D411yescharacteristic
207C4×C22⋊C4D411yescharacteristic
208C2×#95—21no—
209C2×#95—21no—
210C2×#95—22no—
211C2×#95—21no—
212C2×#95—21no—
213C2×#95—21no—
214C2×#95—21no—
215C2×#95—41no—
216C2×#95D411yescharacteristic
217C2×#95D411yescharacteristic
218C2×#95C2311yescharacteristic
219C2×#95C2311yescharacteristic
220C2×#95C2311yescharacteristic
221C2×#95C2311yescharacteristic
222#336—21no—
223#336—21no—
224#336—21no—
225#336—21no—
226#328—22no—
227#328—22no—
228#328—22no—
229#328—22no—
230#328—22no—
231#328—41no—
232#328—41no—
233#328D414yes—
234#327—22no—
235#327—22no—
236#327—41no—
237#327—41no—
238C25C2×D411yescharacteristic
239C2×#41—22no—
240C2×#41—41no—
241C2×#41—42no—
242C2×#41—81no—
243C22×Q8—21no—
244C22×Q8C22×C411yescharacteristic
245C22×Q8C22×C411yescharacteristic
246C22×D4—21no—
247C22×D4—21no—
248C22×D4—21no—
249C22×D4C22×C411yescharacteristic
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—24no—
259C23×C4—21no—
260C23×C4—42no—
261C23×C4—42no—
262C23×C4—42no—
263C23×C4—42no—
264C23×C4—42no—
265C23×C4—81no—
266C23×C4—81no—
267C23×C4—81no—
268C23×C4C22×C411yescharacteristic
269C23×C4C22×C411yescharacteristic
270C23×C4C2×D411yescharacteristic
271C23×C4C2×D411yescharacteristic
272C23×C4C2×D411yescharacteristic
273C23×C4C2×D411yescharacteristic
274C23×C4C2×D411yescharacteristic
275C23×C4C2×D411yescharacteristic
276C23×C4C2×D411yescharacteristic
277C23×C4C2411yescharacteristic
278C2×M16—42no—
279C2×M16—42no—
280C2×M16—81no—
281C22×C8—21no—
282C22×C8—21no—
283C22×C8—21no—
284C22×C8—21no—
285C4⋊Q8—22no—
286C4⋊Q8—22no—
287C4⋊Q8—41no—
288C4⋊Q8—41no—
289#125—42no—
290#125—42no—
291#124—44no—
292#124—81no—
293#123—42no—
294#123—42no—
295#123—42no—
296#123—42no—
297C22⋊Q8—21no—
298C22⋊Q8—21no—
299C22⋊Q8—22no—
300C22⋊Q8—21no—
301C22⋊Q8—21no—
302C22⋊Q8—21no—
303C22⋊Q8—21no—
304C22⋊Q8—42no—
305C22⋊Q8—42no—
306C22⋊Q8—41no—
307C22⋊Q8—42no—
308C22⋊Q8—81no—
309C22⋊Q8C2×D412yes—
310C22⋊Q8#4112yes—
311#121—21no—
312#121—21no—
313#121—21no—
314#121—21no—
315#121—22no—
316#121—41no—
317#120—42no—
318#120—42no—
319C4×Q8—22no—
320C4×Q8—22no—
321C4×Q8—41no—
322C4×Q8—41no—
323C4×Q8—42no—
324C4×Q8—42no—
325C4×Q8—81no—
326C4×D4—42no—
327C4×D4—42no—
328C4×D4—42no—
329C4×D4—42no—
330#117—22no—
331#117—42no—
332#117—42no—
333#117—41no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—24no—
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—24no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—42no—
351C2×C4⋊C4—42no—
352C2×C4⋊C4—81no—
353C2×C4⋊C4—81no—
354C2×C4⋊C4C22×C411yescharacteristic
355C2×C4⋊C4C22×C411yescharacteristic
356C2×C4⋊C4C22×C411yescharacteristic
357C2×C4⋊C4C22×C411yescharacteristic
358C2×C4⋊C4C22×C411yescharacteristic
359C2×C22⋊C4—21no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
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—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—42no—
383C2×C22⋊C4—42no—
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×C22⋊C4C22⋊C411yescharacteristic
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—21no—
401C2×C42—42no—
402C2×C42—42no—
403C2×C42—42no—
404C2×C42—42no—
405C2×C42—81no—
406C2×C42—81no—
407C2×C42—81no—
408C2×C42C22×C411yescharacteristic
409C2×C42C22×C411yescharacteristic
410C2×C42C22×C411yescharacteristic
411C2×C42C22×C411yescharacteristic
412C2×C42C2×D411yescharacteristic
413C2×C42C2×D411yescharacteristic
414C2×C42C2×D411yescharacteristic
415C2×C42C2×D411yescharacteristic
416C4⋊C8—42no—
417C4⋊C8—81no—
418C22⋊C8—21no—
419C22⋊C8—21no—
420C22⋊C8—21no—
421C22⋊C8—21no—
422C22⋊C8—21no—
423C22⋊C8—21no—
424C22⋊C8—21no—
425C22⋊C8—42no—
426C22⋊C8—42no—
427C22⋊C8—81no—
428C22⋊C8C2×D412yes—
429#97—81no—
430C4×C8—42no—
431#95—24no—
432#95—24no—
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—21no—
445#95—21no—
446#95—21no—
447#95—21no—
448#95—21no—
449#95—21no—
450#95—21no—
451#95—21no—
452#95—21no—
453#95—42no—
454#95—42no—
455#95—42no—
456#95—81no—
457#95C22⋊C411yescharacteristic
458#95C22⋊C411yescharacteristic
459#95C22⋊C411yescharacteristic
460#95C22⋊C411yescharacteristic
461#95C22⋊C411yescharacteristic
462#95C22⋊C411yescharacteristic
463#95C22⋊C411yescharacteristic
464#95C22⋊C411yescharacteristic
465#95C2×D412yes—
466C24—21no—
467C24—21no—
468C24—22no—
469C24—22no—
470C24—21no—
471C24—21no—
472C24—21no—
473C24—21no—
474C24—21no—
475C24—41no—
476C24—41no—
477C24C2×C22⋊C411yescharacteristic
478C24C2×C22⋊C411yescharacteristic
479C24C22×D411yescharacteristic
480#41—84no—
481#41—84no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—42no—
486C2×Q8—41no—
487C2×Q8—41no—
488C2×Q8—41no—
489C2×Q8—41no—
490C2×Q8—42no—
491C2×Q8—81no—
492C2×Q8C4×D412yes—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—42no—
496C2×D4—42no—
497C2×D4—41no—
498C2×D4—41no—
499C2×D4—41no—
500C2×D4—41no—
501C2×D4—41no—
502C2×D4—41no—
503C2×D4—41no—
504C2×D4—41no—
505C2×D4—42no—
506C2×D4—42no—
507C2×D4—81no—
508C2×D4—81no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—41no—
547C22×C4—41no—
548C22×C4—41no—
549C22×C4—41no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—41no—
555C22×C4—41no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4—41no—
559C22×C4—41no—
560C22×C4—42no—
561C22×C4—48no—
562C22×C4—42no—
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—48no—
575C22×C4—41no—
576C22×C4—41no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4—41no—
580C22×C4—41no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4—41no—
584C22×C4—41no—
585C22×C4—41no—
586C22×C4—81no—
587C22×C4—82no—
588C22×C4—82no—
589C22×C4—82no—
590C22×C4—82no—
591C22×C4—84no—
592C22×C4—84no—
593C22×C4—84no—
594C22×C4—84no—
595C22×C4—84no—
596C22×C4C2×C22⋊C411yescharacteristic
597C22×C4C2×C22⋊C411yescharacteristic
598C22×C4C2×C22⋊C411yescharacteristic
599C22×C4C2×C22⋊C411yescharacteristic
600C22×C4C2×C22⋊C411yescharacteristic
601C22×C4C2×C22⋊C411yescharacteristic
602C22×C4C2×C22⋊C411yescharacteristic
603C22×C4C2×C22⋊C411yescharacteristic
604C22×C4C2×C22⋊C411yescharacteristic
605C22×C4C2×C22⋊C411yescharacteristic
606C22×C4AGL(1,ℤ/8)12yes—
607C22×C4#13712yes—
608C22×C4C23×C411yescharacteristic
609C22×C4C22×D411yescharacteristic
610C22×C4C22×D411yescharacteristic
611C22×C4C2×#4111yescharacteristic
612C22×C4H(5,𝔽2)11yescharacteristic
613C22×C4H(5,𝔽2)11yescharacteristic
614M16—84no—
615C2×C8—22no—
616C2×C8—41no—
617C2×C8—41no—
618C2×C8—41no—
619C2×C8—41no—
620C2×C8—41no—
621C2×C8—41no—
622C2×C8—41no—
623C2×C8—41no—
624C2×C8—41no—
625C2×C8—41no—
626C2×C8—41no—
627C4⋊C4—21no—
628C4⋊C4—22no—
629C4⋊C4—22no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—42no—
635C4⋊C4—42no—
636C4⋊C4—42no—
637C4⋊C4—42no—
638C4⋊C4—42no—
639C4⋊C4—42no—
640C4⋊C4—41no—
641C4⋊C4—41no—
642C4⋊C4—48no—
643C4⋊C4—42no—
644C4⋊C4—41no—
645C4⋊C4—41no—
646C4⋊C4—42no—
647C4⋊C4—42no—
648C4⋊C4—81no—
649C4⋊C4—81no—
650C4⋊C4—81no—
651C4⋊C4—84no—
652C4⋊C4C4×D412yes—
653C22⋊C4—22no—
654C22⋊C4—22no—
655C22⋊C4—22no—
656C22⋊C4—22no—
657C22⋊C4—22no—
658C22⋊C4—22no—
659C22⋊C4—22no—
660C22⋊C4—22no—
661C22⋊C4—22no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—42no—
665C22⋊C4—48no—
666C22⋊C4—41no—
667C22⋊C4—41no—
668C22⋊C4—41no—
669C22⋊C4—41no—
670C22⋊C4—42no—
671C22⋊C4—42no—
672C22⋊C4—41no—
673C22⋊C4—41no—
674C22⋊C4—42no—
675C22⋊C4—42no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C22⋊C4—81no—
679C22⋊C4—81no—
680C22⋊C4—81no—
681C22⋊C4—81no—
682C22⋊C4—81no—
683C22⋊C4—81no—
684C22⋊C4#10414yes—
685C42—21no—
686C42—21no—
687C42—21no—
688C42—21no—
689C42—21no—
690C42—21no—
691C42—21no—
692C42—21no—
693C42—41no—
694C42—41no—
695C42—41no—
696C42—41no—
697C42—42no—
698C42—42no—
699C42—42no—
700C42—42no—
701C42—81no—
702C42—84no—
703C42—84no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—24no—
709C23—24no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23#41012yes—
744C23C2×#10412yes—
745C23C22×C22⋊C411yescharacteristic
746C23D4211yescharacteristic
747C23#54611yescharacteristic
748C23C2×AGL(1,ℤ/8)11yescharacteristic
749C23C2×#13711yescharacteristic
750C23#57711yescharacteristic
751C23#57811yescharacteristic
752Q8—42no—
753Q8—42no—
754Q8—84no—
755Q8—81no—
756Q8—81no—
757D4—81no—
758D4—81no—
759D4—84no—
760D4—84no—
761D4—81no—
762D4—81no—
763D4—81no—
764D4—81no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—24no—
782C2×C4—21no—
783C2×C4—22no—
784C2×C4—21no—
785C2×C4—22no—
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—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—81no—
851C2×C4—81no—
852C2×C4—81no—
853C2×C4—81no—
854C2×C4—81no—
855C2×C4—81no—
856C2×C4—84no—
857C2×C4—816no—
858C2×C4—81no—
859C2×C4—81no—
860C2×C4—81no—
861C2×C4—81no—
862C2×C4—81no—
863C2×C4—81no—
864C2×C4—81no—
865C2×C4—81no—
866C2×C4—81no—
867C2×C4—81no—
868C2×C4—81no—
869C2×C4—81no—
870C2×C4#41712yes—
871C2×C4#41712yes—
872C2×C4C2×#10412yes—
873C2×C4C2×#10412yes—
874C2×C4C2×C4×D411yescharacteristic
875C2×C4#51811yescharacteristic
876C2×C4D4211yescharacteristic
877C2×C4#54611yescharacteristic
878C8—42no—
879C8—81no—
880C8—81no—
881C8—81no—
882C22—21no—
883C22—21no—
884C22—21no—
885C22—21no—
886C22—21no—
887C22—21no—
888C22—21no—
889C22—21no—
890C22—21no—
891C22—21no—
892C22—21no—
893C22—21no—
894C22—22no—
895C22—22no—
896C22—22no—
897C22—22no—
898C22—22no—
899C22—22no—
900C22—44no—
901C22—44no—
902C22—44no—
903C22—44no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—41no—
910C22—41no—
911C22—41no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22D4×C22⋊C411yescharacteristic
920C22C2×#41011yescharacteristic
921C22#288311yescharacteristic
922C22C2×#41711yescharacteristic
923C22#289811yescharacteristic
924C22C22×#10411yescharacteristic
925C22#290111yescharacteristic
926C22#326511yescharacteristic
927C22#327011yescharacteristic
928C22#330811yescharacteristic
929C22#331611yescharacteristic
930C4—21no—
931C4—21no—
932C4—21no—
933C4—21no—
934C4—22no—
935C4—22no—
936C4—22no—
937C4—22no—
938C4—44no—
939C4—41no—
940C4—41no—
941C4—42no—
942C4—41no—
943C4—41no—
944C4—42no—
945C4—41no—
946C4—41no—
947C4—82no—
948C4—82no—
949C4—82no—
950C4—81no—
951C4—81no—
952C4—81no—
953C4—81no—
954C4—81no—
955C2—21no—
956C2—21no—
957C2—21no—
958C2—21no—
959C2—42no—
960C2—42no—
961C2—161no—
962C2#1754611yescharacteristic
963C2#1754811yescharacteristic
964C2#1760911yescharacteristic
965C2#1763011yescharacteristic
966C2#2240511yescharacteristic
967C2#2242111yescharacteristic
968C2D4×#10411yescharacteristic
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
4. C2×#1503C2semidirect
5. #13814C2semidirect
6. #9713C2semidirect
7. #9682C2semidirect
8. #9148C2semidirect
9. #9143C2semidirect
10. #9115C2semidirect
11. #9114C2semidirect
12. #8572C2semidirect
13. #8333C2semidirect
15. #8219C2semidirect
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
150. #391C2×C4semidirect
151. #391C2×C4semidirect
155. #390C2×C4semidirect
156. #390C2×C4semidirect
157. #390C2×C4semidirect
159. #389C2×C4semidirect
160. #389C2×C4semidirect
161. #389C2×C4semidirect
186. #382C2×C4semidirect
196. 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×#15042
C2×#15032
#138142
#97132
#96822
#91482
#91432
#91152
#91142
#85722
#83332
#83312
#82192