Finite Group Databasebeta

← #221773

Subgroups — #221773

Order 512.

1285 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36144C211yesmaximal, characteristic
2#22555C211yesmaximal, characteristic, complemented
3C2×#1512C211yesmaximal, characteristic, complemented
4C2×#1504C211yesmaximal, characteristic, complemented
5#13896C211yesmaximal, characteristic, complemented
6#9715C211yesmaximal, characteristic, complemented
7#9680C211yesmaximal, characteristic, complemented
8#9156C211yesmaximal, characteristic, complemented
9#9147C211yesmaximal, characteristic, complemented
10#9118C211yesmaximal, characteristic, complemented
11#9117C211yesmaximal, characteristic, complemented
12#8572C211yesmaximal, characteristic, complemented
13#8331C211yesmaximal, characteristic, complemented
14#8330C211yesmaximal, characteristic, complemented
15#8221C211yesmaximal, characteristic, complemented
16C2×#529C2211yescharacteristic
17C2×#525C2211yescharacteristic
18C2×#432C2211yescharacteristic
19C2×#407C2211yescharacteristic
20#2856C2211yescharacteristic
21#2854C2211yescharacteristic
22#2847C2211yescharacteristic
23#2554—21no—
24#2539—21no—
25#2490C411yescharacteristic, complemented
26#2471—21no—
27#2467—21no—
28#2441C411yescharacteristic, complemented
29#2431C411yescharacteristic, complemented
30#2428C411yescharacteristic, complemented
31#2426C411yescharacteristic, complemented
32#2425—21no—
33#2424—21no—
34#2423C411yescharacteristic, complemented
35#2364—21no—
36#2363—21no—
37#2363C411yescharacteristic, complemented
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—
51C4×C22⋊C8C2211yescharacteristic
52#1512—24no—
53#1504—24no—
54C2×#328C2211yescharacteristic
55C2×#328C2211yescharacteristic
56C2×#328C2211yescharacteristic
57C2×#328C2211yescharacteristic
58C2×#327C2211yescharacteristic
59C2×#327C2211yescharacteristic
60C2×#327C2211yescharacteristic
61C2×#327C2211yescharacteristic
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—
81C2×#127C2×C411yescharacteristic, complemented
82#529—22no—
83#529—22no—
84#529—41no—
85#529—41no—
86C2×#126—21no—
87C2×#125C2×C411yescharacteristic, complemented
88C2×#124C2×C411yescharacteristic, complemented
89#525—22no—
90#525—22no—
91#525—41no—
92#525—41no—
93C2×#123—21no—
94C2×#123—21no—
95C2×#123—21no—
96C2×C22⋊Q8C2×C411yescharacteristic
97C2×C22⋊Q8C2311yescharacteristic
98C2×#121—21no—
99C2×#121—21no—
100C2×#121—21no—
101C2×#121C2×C411yescharacteristic
102C2×#121C2×C411yescharacteristic
103C2×#121C2×C411yescharacteristic
104C2×#121C2311yescharacteristic
105C2×#121C2311yescharacteristic
106C2×#120—21no—
107C2×#120—21no—
108C2×C4×Q8C2×C411yescharacteristic, complemented
109C2×C4×Q8C2×C411yescharacteristic, complemented
110C2×C4×D4—21no—
111C2×C4×D4—21no—
112C2×C4×D4—21no—
113C2×C4×D4C2×C411yescharacteristic, complemented
114C2×#117—21no—
115C2×#117C2×C411yescharacteristic
116C22×C4⋊C4—21no—
117C22×C4⋊C4—21no—
118C22×C22⋊C4—21no—
119C22×C22⋊C4D411yescharacteristic
120C22×C22⋊C4D411yescharacteristic
121C22×C42C2311yescharacteristic
122C22×C42C2311yescharacteristic
123#432—22no—
124#432—41no—
125C2×C4⋊C8—21no—
126C2×C4⋊C8—21no—
127#407—22no—
128#407—41no—
129C2×C22⋊C8—21no—
130C2×C22⋊C8—21no—
131C2×C22⋊C8—21no—
132C2×C22⋊C8C2311yescharacteristic
133C2×C22⋊C8C2311yescharacteristic
134C2×C22⋊C8C2311yescharacteristic
135C2×C22⋊C8C2311yescharacteristic
136C2×#97—21no—
137C2×C4×C8—21no—
138#399—21no—
139#399—21no—
140#398—21no—
141#397—21no—
142#396—21no—
143#396—21no—
144#394—21no—
145#394—21no—
146#394—21no—
147#392—21no—
148#392—21no—
149#392—21no—
150#391C2×C411yescharacteristic, complemented
151#390—21no—
152#390—21no—
153#390—21no—
154#390—21no—
155#390—21no—
156#390—21no—
157#390—21no—
158#390C2×C411yescharacteristic, complemented
159#390C2×C411yescharacteristic, complemented
160#390C2×C411yescharacteristic, complemented
161#390C2×C411yescharacteristic, complemented
162#389—21no—
163#389C2×C411yescharacteristic, complemented
164#389C2×C411yescharacteristic, complemented
165#389C2×C411yescharacteristic, complemented
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#386—21no—
176#386—21no—
177#386—21no—
178#386—21no—
179#386—21no—
180#386—21no—
181#386—21no—
182#386—21no—
183#385—21no—
184#385—44no—
185#384C2×C411yescharacteristic, complemented
186#382—22no—
187#382—41no—
188#380—21no—
189#380C2×C411yescharacteristic
190#380C2×C411yescharacteristic
191#380C2311yescharacteristic
192C4×C4⋊C4—21no—
193C4×C4⋊C4C2×C411yescharacteristic, complemented
194C4×C22⋊C4—21no—
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#328D414yescomplemented
229#327—22no—
230#327—22no—
231#327—22no—
232#327—22no—
233#327—41no—
234#327—41no—
235#327—41no—
236#327—41no—
237C25C2×D411yescharacteristic
238C2×#41—22no—
239C2×#41—41no—
240C2×#41—42no—
241C2×#41—81no—
242C22×Q8C22×C411yescharacteristic
243C22×D4—21no—
244C22×D4—21no—
245C22×D4—21no—
246C22×D4—21no—
247C22×D4—21no—
248C22×D4—21no—
249C22×D4—21no—
250C22×D4—21no—
251C22×D4C22×C411yescharacteristic
252C22×D4C22×C411yescharacteristic
253C23×C4—21no—
254C23×C4—21no—
255C23×C4—21no—
256C23×C4—21no—
257C23×C4—21no—
258C23×C4—21no—
259C23×C4—21no—
260C23×C4—21no—
261C23×C4—21no—
262C23×C4—21no—
263C23×C4—42no—
264C23×C4—42no—
265C23×C4—42no—
266C23×C4—42no—
267C23×C4—42no—
268C23×C4—42no—
269C23×C4—81no—
270C23×C4—81no—
271C23×C4—81no—
272C23×C4C22×C411yescharacteristic
273C23×C4C22×C411yescharacteristic
274C23×C4C2×D411yescharacteristic
275C23×C4C2×D411yescharacteristic
276C23×C4C2×D411yescharacteristic
277C23×C4C2×D411yescharacteristic
278C23×C4C2×D411yescharacteristic
279C23×C4C2×D411yescharacteristic
280C23×C4C2×D411yescharacteristic
281C23×C4C2411yescharacteristic
282C2×M16—42no—
283C2×M16—42no—
284C2×M16—81no—
285C22×C8—21no—
286C22×C8—21no—
287C22×C8—21no—
288C22×C8—21no—
289#127—81no—
290#126—42no—
291#126—42no—
292#125—22no—
293#125—41no—
294#124—22no—
295#124—41no—
296#123—42no—
297#123—42no—
298#123—42no—
299#123—42no—
300#123—81no—
301#123—81no—
302C22⋊Q8—21no—
303C22⋊Q8—21no—
304C22⋊Q8—22no—
305C22⋊Q8—41no—
306C22⋊Q8C2×D412yes—
307C22⋊Q8#4112yes—
308#121—21no—
309#121—21no—
310#121—21no—
311#121—21no—
312#121—21no—
313#121—21no—
314#121—21no—
315#121—21no—
316#121—22no—
317#121—44no—
318#121—41no—
319#121—42no—
320#121—42no—
321#121—42no—
322#121—81no—
323#121—81no—
324#121—81no—
325#120—42no—
326#120—42no—
327#120—81no—
328#120—81no—
329C4×Q8—22no—
330C4×Q8—41no—
331C4×Q8—81no—
332C4×D4—22no—
333C4×D4—41no—
334C4×D4—42no—
335C4×D4—42no—
336C4×D4—42no—
337C4×D4—42no—
338C4×D4—42no—
339C4×D4—42no—
340#117—22no—
341#117—42no—
342#117—42no—
343#117—41no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—42no—
356C2×C4⋊C4—42no—
357C2×C4⋊C4—42no—
358C2×C4⋊C4—42no—
359C2×C4⋊C4—81no—
360C2×C4⋊C4—81no—
361C2×C4⋊C4C22×C411yescharacteristic
362C2×C4⋊C4C22×C411yescharacteristic
363C2×C4⋊C4C22×C411yescharacteristic
364C2×C4⋊C4C22×C411yescharacteristic
365C2×C4⋊C4C22×C411yescharacteristic
366C2×C22⋊C4—21no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—22no—
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—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—42no—
391C2×C22⋊C4—42no—
392C2×C22⋊C4—42no—
393C2×C22⋊C4—42no—
394C2×C22⋊C4C22⋊C411yescharacteristic
395C2×C22⋊C4C22⋊C411yescharacteristic
396C2×C22⋊C4C22⋊C411yescharacteristic
397C2×C22⋊C4C22⋊C411yescharacteristic
398C2×C22⋊C4C22⋊C411yescharacteristic
399C2×C22⋊C4C22⋊C411yescharacteristic
400C2×C22⋊C4C22⋊C411yescharacteristic
401C2×C22⋊C4C22⋊C411yescharacteristic
402C2×C42—21no—
403C2×C42—21no—
404C2×C42—21no—
405C2×C42—21no—
406C2×C42—21no—
407C2×C42—21no—
408C2×C42—21no—
409C2×C42—21no—
410C2×C42—81no—
411C2×C42C22×C411yescharacteristic
412C2×C42C22×C411yescharacteristic
413C2×C42C22×C411yescharacteristic
414C2×C42C22×C411yescharacteristic
415C2×C42C2×D411yescharacteristic
416C2×C42C2×D411yescharacteristic
417C2×C42C2×D411yescharacteristic
418C2×C42C2×D411yescharacteristic
419C4⋊C8—42no—
420C4⋊C8—81no—
421C22⋊C8—21no—
422C22⋊C8—21no—
423C22⋊C8—21no—
424C22⋊C8—21no—
425C22⋊C8—21no—
426C22⋊C8—21no—
427C22⋊C8—21no—
428C22⋊C8—42no—
429C22⋊C8—42no—
430C22⋊C8—81no—
431C22⋊C8C2×D412yes—
432#97—42no—
433C4×C8—81no—
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—42no—
451#95—42no—
452#95—42no—
453#95—42no—
454#95—42no—
455#95—81no—
456#95—81no—
457#95—81no—
458#95C22⋊C411yescharacteristic
459#95C22⋊C411yescharacteristic
460#95C22⋊C411yescharacteristic
461#95C22⋊C411yescharacteristic
462#95C22⋊C411yescharacteristic
463#95C22⋊C411yescharacteristic
464#95C22⋊C411yescharacteristic
465#95C22⋊C411yescharacteristic
466#95C2×D412yes—
467C24—21no—
468C24—21no—
469C24—22no—
470C24—22no—
471C24—21no—
472C24—21no—
473C24—21no—
474C24—21no—
475C24—21no—
476C24—21no—
477C24—41no—
478C24—41no—
479C24C2×C22⋊C411yescharacteristic
480C24C2×C22⋊C411yescharacteristic
481C24C22×D411yescharacteristic
482#41—84no—
483#41—84no—
484C2×Q8—21no—
485C2×Q8—41no—
486C2×Q8—41no—
487C2×Q8C4×D412yes—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—42no—
493C2×D4—42no—
494C2×D4—41no—
495C2×D4—41no—
496C2×D4—41no—
497C2×D4—41no—
498C2×D4—42no—
499C2×D4—41no—
500C2×D4—41no—
501C2×D4—41no—
502C2×D4—41no—
503C2×D4—41no—
504C2×D4—41no—
505C2×D4—41no—
506C2×D4—41no—
507C2×D4—41no—
508C2×D4—41no—
509C2×D4—41no—
510C2×D4—41no—
511C2×D4—42no—
512C2×D4—42no—
513C2×D4—42no—
514C2×D4—42no—
515C2×D4—42no—
516C2×D4—81no—
517C2×D4—81no—
518C2×D4—81no—
519C2×D4—81no—
520C2×D4—81no—
521C2×D4—81no—
522C2×D4—81no—
523C2×D4—81no—
524C2×D4—81no—
525C2×D4—81no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—22no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—22no—
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—41no—
569C22×C4—41no—
570C22×C4—41no—
571C22×C4—41no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—41no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4—41no—
580C22×C4—41no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4—48no—
584C22×C4—41no—
585C22×C4—41no—
586C22×C4—41no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—41no—
592C22×C4—41no—
593C22×C4—41no—
594C22×C4—41no—
595C22×C4—41no—
596C22×C4—41no—
597C22×C4—41no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4—41no—
601C22×C4—41no—
602C22×C4—41no—
603C22×C4—81no—
604C22×C4—81no—
605C22×C4—82no—
606C22×C4—82no—
607C22×C4—82no—
608C22×C4—82no—
609C22×C4—84no—
610C22×C4—84no—
611C22×C4—84no—
612C22×C4—84no—
613C22×C4—84no—
614C22×C4—84no—
615C22×C4C2×C22⋊C411yescharacteristic
616C22×C4C2×C22⋊C411yescharacteristic
617C22×C4C2×C22⋊C411yescharacteristic
618C22×C4C2×C22⋊C411yescharacteristic
619C22×C4C2×C22⋊C411yescharacteristic
620C22×C4C2×C22⋊C411yescharacteristic
621C22×C4C2×C22⋊C411yescharacteristic
622C22×C4C2×C22⋊C411yescharacteristic
623C22×C4C2×C22⋊C411yescharacteristic
624C22×C4C2×C22⋊C411yescharacteristic
625C22×C4AGL(1,ℤ/8)12yes—
626C22×C4#13712yes—
627C22×C4C23×C411yescharacteristic
628C22×C4C22×D411yescharacteristic
629C22×C4C22×D411yescharacteristic
630C22×C4C2×#4111yescharacteristic
631C22×C4H(5,𝔽2)11yescharacteristic
632C22×C4H(5,𝔽2)11yescharacteristic
633M16—84no—
634C2×C8—22no—
635C2×C8—41no—
636C2×C8—41no—
637C2×C8—41no—
638C2×C8—41no—
639C2×C8—41no—
640C2×C8—41no—
641C2×C8—41no—
642C2×C8—41no—
643C2×C8—41no—
644C2×C8—41no—
645C2×C8—41no—
646C4⋊C4—21no—
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—42no—
654C4⋊C4—42no—
655C4⋊C4—42no—
656C4⋊C4—42no—
657C4⋊C4—41no—
658C4⋊C4—41no—
659C4⋊C4—42no—
660C4⋊C4—42no—
661C4⋊C4—81no—
662C4⋊C4—81no—
663C4⋊C4—81no—
664C4⋊C4—81no—
665C4⋊C4—84no—
666C4⋊C4—84no—
667C4⋊C4C4×D412yes—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—22no—
672C22⋊C4—22no—
673C22⋊C4—22no—
674C22⋊C4—22no—
675C22⋊C4—22no—
676C22⋊C4—41no—
677C22⋊C4—41no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C22⋊C4—42no—
686C22⋊C4—41no—
687C22⋊C4—41no—
688C22⋊C4—41no—
689C22⋊C4—41no—
690C22⋊C4—41no—
691C22⋊C4—41no—
692C22⋊C4—42no—
693C22⋊C4—42no—
694C22⋊C4—81no—
695C22⋊C4—81no—
696C22⋊C4—81no—
697C22⋊C4—81no—
698C22⋊C4—81no—
699C22⋊C4—81no—
700C22⋊C4—81no—
701C22⋊C4—81no—
702C22⋊C4—84no—
703C42—21no—
704C42—21no—
705C42—21no—
706C42—21no—
707C42—21no—
708C42—21no—
709C42—21no—
710C42—21no—
711C42—41no—
712C42—41no—
713C42—41no—
714C42—41no—
715C42—42no—
716C42—42no—
717C42—81no—
718C42—81no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—24no—
724C23—24no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—42no—
744C23—42no—
745C23—42no—
746C23—42no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23#41012yes—
766C23#42112yes—
767C23C22×C22⋊C411yescharacteristic
768C23D4211yescharacteristic
769C23#54611yescharacteristic
770C23C2×AGL(1,ℤ/8)11yescharacteristic
771C23C2×#13711yescharacteristic
772C23#57611yescharacteristic
773C23#57711yescharacteristic
774Q8—42no—
775Q8—42no—
776D4—81no—
777D4—81no—
778D4—81no—
779D4—81no—
780D4—84no—
781D4—84no—
782D4—81no—
783D4—81no—
784D4—81no—
785D4—81no—
786D4—81no—
787D4—81no—
788D4—81no—
789D4—81no—
790D4—162no—
791D4—162no—
792D4—162no—
793D4—162no—
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—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—42no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
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—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—42no—
864C2×C4—81no—
865C2×C4—81no—
866C2×C4—81no—
867C2×C4—81no—
868C2×C4—81no—
869C2×C4—81no—
870C2×C4—81no—
871C2×C4—81no—
872C2×C4—81no—
873C2×C4—81no—
874C2×C4—84no—
875C2×C4—84no—
876C2×C4—81no—
877C2×C4—81no—
878C2×C4—81no—
879C2×C4—81no—
880C2×C4—81no—
881C2×C4—81no—
882C2×C4—81no—
883C2×C4—816no—
884C2×C4—81no—
885C2×C4—81no—
886C2×C4—81no—
887C2×C4—81no—
888C2×C4—81no—
889C2×C4—81no—
890C2×C4—81no—
891C2×C4—81no—
892C2×C4—81no—
893C2×C4—81no—
894C2×C4—81no—
895C2×C4—81no—
896C2×C4—81no—
897C2×C4—81no—
898C2×C4—81no—
899C2×C4#41712yes—
900C2×C4#41712yes—
901C2×C4C2×C4×D411yescharacteristic
902C2×C4#51811yescharacteristic
903C2×C4D4211yescharacteristic
904C2×C4#54611yescharacteristic
905C8—42no—
906C8—81no—
907C8—81no—
908C8—81no—
909C22—21no—
910C22—21no—
911C22—21no—
912C22—21no—
913C22—21no—
914C22—21no—
915C22—21no—
916C22—21no—
917C22—21no—
918C22—21no—
919C22—21no—
920C22—21no—
921C22—22no—
922C22—22no—
923C22—22no—
924C22—22no—
925C22—22no—
926C22—22no—
927C22—44no—
928C22—44no—
929C22—44no—
930C22—44no—
931C22—41no—
932C22—41no—
933C22—41no—
934C22—41no—
935C22—41no—
936C22—41no—
937C22—41no—
938C22—41no—
939C22—81no—
940C22—81no—
941C22—81no—
942C22—81no—
943C22—81no—
944C22—81no—
945C22—81no—
946C22—81no—
947C22—81no—
948C22—81no—
949C22—81no—
950C22—81no—
951C22—81no—
952C22—81no—
953C22D4×C22⋊C411yescharacteristic
954C22C2×#41011yescharacteristic
955C22#288311yescharacteristic
956C22C2×#41711yescharacteristic
957C22#289711yescharacteristic
958C22C2×#42111yescharacteristic
959C22#290111yescharacteristic
960C22#327411yescharacteristic
961C22#327811yescharacteristic
962C22#333211yescharacteristic
963C22#333311yescharacteristic
964C4—21no—
965C4—21no—
966C4—21no—
967C4—21no—
968C4—22no—
969C4—22no—
970C4—41no—
971C4—41no—
972C4—42no—
973C4—41no—
974C4—41no—
975C4—41no—
976C4—41no—
977C4—42no—
978C4—41no—
979C4—41no—
980C4—82no—
981C4—82no—
982C4—81no—
983C4—81no—
984C4—81no—
985C4—81no—
986C4—161no—
987C4—161no—
988C2—21no—
989C2—21no—
990C2—21no—
991C2—21no—
992C2—42no—
993C2—42no—
994C2—161no—
995C2—161no—
996C2#1758811yescharacteristic
997C2#1759711yescharacteristic
998C2#1760411yescharacteristic
999C2#1762211yescharacteristic
1000C2#2240511yescharacteristic
1001C2#2243211yescharacteristic
1002C2#2243411yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radical#36144C2
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. #22555C2semidirect
3. C2×#1512C2semidirect
4. C2×#1504C2semidirect
5. #13896C2semidirect
6. #9715C2semidirect
7. #9680C2semidirect
8. #9156C2semidirect
9. #9147C2semidirect
10. #9118C2semidirect
11. #9117C2semidirect
12. #8572C2semidirect
13. #8331C2semidirect
14. #8330C2semidirect
15. #8221C2semidirect
25. #2490C4semidirect
28. #2441C4semidirect
29. #2431C4semidirect
30. #2428C4semidirect
31. #2426C4semidirect
34. #2423C4semidirect
37. #2363C4semidirect
38. #2341C4semidirect
81. C2×#127C2×C4semidirect
87. C2×#125C2×C4semidirect
88. C2×#124C2×C4semidirect
108. C2×C4×Q8C2×C4semidirect
109. C2×C4×Q8C2×C4semidirect
113. C2×C4×D4C2×C4semidirect
150. #391C2×C4semidirect
158. #390C2×C4semidirect
159. #390C2×C4semidirect
160. #390C2×C4semidirect
161. #390C2×C4semidirect
163. #389C2×C4semidirect
164. #389C2×C4semidirect
165. #389C2×C4semidirect
185. #384C2×C4semidirect
193. C4×C4⋊C4C2×C4semidirect
228. #328D4semidirect

Maximal subgroups

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

subgroupindex
#361442
#225552
C2×#15122
C2×#15042
#138962
#97152
#96802
#91562
#91472
#91182
#91172
#85722
#83312
#83302
#82212