Finite Group Databasebeta

← #221801

Subgroups — #221801

Order 512.

1324 conjugacy classes of subgroups.

The subgroup lattice has 1007 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36107C211yesmaximal, characteristic
2#22552C211yesmaximal, characteristic, complemented
3C2×#1521C211yesmaximal, characteristic, complemented
4C22×#327C211yesmaximal, characteristic
5#13901C211yesmaximal, characteristic, complemented
6#9716C211yesmaximal, characteristic, complemented
7#9681C211yesmaximal, characteristic, complemented
8#9157C211yesmaximal, characteristic, complemented
9#9143C211yesmaximal, characteristic, complemented
10#9114C211yesmaximal, characteristic, complemented
11#9111C211yesmaximal, characteristic, complemented
12#8575C211yesmaximal, characteristic, complemented
13#8330C211yesmaximal, characteristic, complemented
14#8328C211yesmaximal, characteristic
15#8220C211yesmaximal, characteristic, complemented
16C2×#529C2211yescharacteristic
17C22×#121C2211yescharacteristic
18C2×#431C2211yescharacteristic, complemented
19C22×C22⋊C8C2211yescharacteristic
20#2854C2211yescharacteristic
21#2850C2211yescharacteristic
22#2848C2211yescharacteristic
23#2559—21no—
24#2490C411yescharacteristic, complemented
25#2480—21no—
26#2476—21no—
27#2444—21no—
28#2442C411yescharacteristic, complemented
29#2435C411yescharacteristic, complemented
30#2427C411yescharacteristic, complemented
31#2426C411yescharacteristic, complemented
32#2425—21no—
33#2420C411yescharacteristic, complemented
34#2405—21no—
35#2360C411yescharacteristic, complemented
36#2342—21no—
37D4×C22⋊C4—21no—
38D4×C22⋊C4C411yescharacteristic, complemented
39C4×#121C2211yescharacteristic
40C2×#383C2211yescharacteristic, complemented
41C2×C4×C22⋊C4C2211yescharacteristic
42C22×#95C2211yescharacteristic
43#1923—21no—
44#1923—21no—
45#1850—21no—
46#1817C2211yescharacteristic, complemented
47#1797C2211yescharacteristic, complemented
48#1779C2211yescharacteristic
49C8×C22⋊C4—21no—
50C4×C22⋊C8C2211yescharacteristic, complemented
51#1521—24no—
52C2×#328C2211yescharacteristic, complemented
53C2×#328C2211yescharacteristic, complemented
54C2×#328C2211yescharacteristic, complemented
55C2×#328C2211yescharacteristic, complemented
56C2×#327—24no—
57C2×#327C2211yescharacteristic
58C2×#327C2211yescharacteristic
59C2×#327C2211yescharacteristic
60C2×#327C2211yescharacteristic
61C2×#327C2211yescharacteristic
62C2×#327C2211yescharacteristic
63C2×#327C2211yescharacteristic
64C2×#327C2211yescharacteristic
65#1443—21no—
66#1443—21no—
67#1434C2211yescharacteristic, complemented
68#1434C2211yescharacteristic, complemented
69#1434C2211yescharacteristic, complemented
70C22⋊#95—21no—
71C22⋊#95—21no—
72C22⋊#95C2211yescharacteristic
73#1294C2211yescharacteristic, complemented
74#1294C2211yescharacteristic, complemented
75#1294C2211yescharacteristic, complemented
76#1294C2211yescharacteristic, complemented
77C23×D4—21no—
78C23×D4C2×C411yescharacteristic
79C24×C4—21no—
80C24×C4C2311yescharacteristic
81C23×C8—21no—
82#529—22no—
83#529—22no—
84#529—41no—
85#529—41no—
86C2×#126—21no—
87C2×#125C2×C411yescharacteristic, complemented
88C2×#124C2×C411yescharacteristic, complemented
89C2×#124C2×C411yescharacteristic, complemented
90C2×#123—21no—
91C2×#123—21no—
92C2×C22⋊Q8C2×C411yescharacteristic
93C2×C22⋊Q8C2×C411yescharacteristic
94C2×C22⋊Q8C2311yescharacteristic
95C2×#121—21no—
96C2×#121—21no—
97C2×#121—22no—
98C2×#121—22no—
99C2×#121—41no—
100C2×#121—41no—
101C2×#121C2×C411yescharacteristic
102C2×#121C2×C411yescharacteristic
103C2×#121C2311yescharacteristic
104C2×#121C2311yescharacteristic
105C2×C4×Q8C2×C411yescharacteristic, complemented
106C2×C4×D4—21no—
107C2×C4×D4—21no—
108C2×C4×D4C2×C411yescharacteristic, complemented
109C2×C4×D4C2×C411yescharacteristic, complemented
110C2×#117—21no—
111C22×C4⋊C4C2×C411yescharacteristic
112C22×C22⋊C4—21no—
113C22×C22⋊C4—21no—
114C22×C22⋊C4—21no—
115C22×C22⋊C4D411yescharacteristic
116C22×C22⋊C4D411yescharacteristic
117C22×C42C2311yescharacteristic
118C22×C42C2311yescharacteristic
119#431—22no—
120#431—41no—
121C2×C4⋊C8—21no—
122C2×C4⋊C8—21no—
123C2×C22⋊C8—22no—
124C2×C22⋊C8—21no—
125C2×C22⋊C8—21no—
126C2×C22⋊C8—21no—
127C2×C22⋊C8—41no—
128C2×C22⋊C8C2311yescharacteristic
129C2×C22⋊C8C2311yescharacteristic
130C2×C22⋊C8C2311yescharacteristic
131C2×C22⋊C8C2311yescharacteristic
132C2×C4×C8—21no—
133C2×C4×C8—21no—
134#400—21no—
135#398—21no—
136#397—21no—
137#397—21no—
138#397—21no—
139#396—21no—
140#394—21no—
141#394—21no—
142#394—21no—
143#394—21no—
144#394—21no—
145#394—21no—
146#391C2×C411yescharacteristic, complemented
147#390—21no—
148#390—21no—
149#390C2×C411yescharacteristic, complemented
150#390C2×C411yescharacteristic, complemented
151#390C2×C411yescharacteristic, complemented
152#390C2×C411yescharacteristic, complemented
153#389—21no—
154#389C2×C411yescharacteristic, complemented
155#389C2×C411yescharacteristic, complemented
156#389C2×C411yescharacteristic, complemented
157#388—21no—
158#388—21no—
159#388—21no—
160#388—21no—
161#388—21no—
162#388—21no—
163#388—21no—
164#387—21no—
165#386—21no—
166#386—21no—
167#386—21no—
168#386—21no—
169#386—21no—
170#386—21no—
171#386—21no—
172#386—21no—
173#385—21no—
174#385—21no—
175#385—21no—
176#385—21no—
177#385—21no—
178#383—22no—
179#383—41no—
180#382C2×C411yescharacteristic, complemented
181#381—21no—
182#380—21no—
183#380—21no—
184#380C2×C411yescharacteristic
185#380C2×C411yescharacteristic
186#380C2311yescharacteristic
187#379—21no—
188#379—21no—
189#379—21no—
190#379—21no—
191C4×C4⋊C4C2×C411yescharacteristic, complemented
192C4×C22⋊C4—21no—
193C4×C22⋊C4—21no—
194C4×C22⋊C4C2×C411yescharacteristic
195C4×C22⋊C4C2×C411yescharacteristic
196C4×C22⋊C4C2×C411yescharacteristic
197C4×C22⋊C4C2×C411yescharacteristic
198C4×C22⋊C4D411yescharacteristic
199C4×C22⋊C4D411yescharacteristic
200C4×C22⋊C4D411yescharacteristic
201C4×C22⋊C4D411yescharacteristic
202C2×#95—22no—
203C2×#95—21no—
204C2×#95—21no—
205C2×#95—21no—
206C2×#95—21no—
207C2×#95—21no—
208C2×#95—21no—
209C2×#95—21no—
210C2×#95—21no—
211C2×#95—21no—
212C2×#95—21no—
213C2×#95—41no—
214C2×#95D411yescharacteristic
215C2×#95D411yescharacteristic
216C2×#95C2311yescharacteristic
217C2×#95C2311yescharacteristic
218C2×#95C2311yescharacteristic
219C2×#95C2311yescharacteristic
220#336—21no—
221#336—21no—
222#336—21no—
223#336—21no—
224#328—22no—
225#328—22no—
226#328—41no—
227#328—41no—
228#327—22no—
229#327—22no—
230#327—22no—
231#327—22no—
232#327—22no—
233#327—41no—
234#327—41no—
235#327D414yes—
236C25—21no—
237C25C2×D411yescharacteristic
238C22×Q8C22×C411yescharacteristic
239C22×D4—21no—
240C22×D4—22no—
241C22×D4—21no—
242C22×D4—21no—
243C22×D4—21no—
244C22×D4—21no—
245C22×D4—41no—
246C22×D4—42no—
247C22×D4—42no—
248C22×D4—42no—
249C22×D4—42no—
250C22×D4—42no—
251C22×D4—81no—
252C22×D4—81no—
253C22×D4—81no—
254C22×D4C22×C411yescharacteristic
255C22×D4C22×C411yescharacteristic
256C23×C4—21no—
257C23×C4—21no—
258C23×C4—21no—
259C23×C4—21no—
260C23×C4—21no—
261C23×C4—21no—
262C23×C4—21no—
263C23×C4—21no—
264C23×C4—21no—
265C23×C4—21no—
266C23×C4—21no—
267C23×C4—42no—
268C23×C4—42no—
269C23×C4—42no—
270C23×C4—42no—
271C23×C4—42no—
272C23×C4—42no—
273C23×C4—81no—
274C23×C4—81no—
275C23×C4—81no—
276C23×C4C22×C411yescharacteristic
277C23×C4C22×C411yescharacteristic
278C23×C4C2×D411yescharacteristic
279C23×C4C2×D411yescharacteristic
280C23×C4C2×D411yescharacteristic
281C23×C4C2×D411yescharacteristic
282C23×C4C2×D411yescharacteristic
283C23×C4C2×D411yescharacteristic
284C23×C4C2×D411yescharacteristic
285C23×C4C2411yescharacteristic
286C22×C8—21no—
287C22×C8—21no—
288C22×C8—21no—
289C22×C8—21no—
290C22×C8—42no—
291C22×C8—42no—
292C22×C8—81no—
293#126—42no—
294#126—42no—
295#125—22no—
296#125—41no—
297#124—22no—
298#124—41no—
299#124—81no—
300#123—42no—
301#123—42no—
302#123—81no—
303#123—81no—
304C22⋊Q8—21no—
305C22⋊Q8—21no—
306C22⋊Q8—21no—
307C22⋊Q8—21no—
308C22⋊Q8—42no—
309C22⋊Q8—81no—
310#121—21no—
311#121—21no—
312#121—22no—
313#121—21no—
314#121—21no—
315#121—21no—
316#121—21no—
317#121—22no—
318#121—42no—
319#121—42no—
320#121—41no—
321#121—41no—
322#121—42no—
323#121—42no—
324#121C2×D412yes—
325#121#4112yes—
326C4×Q8—22no—
327C4×Q8—41no—
328C4×D4—22no—
329C4×D4—41no—
330C4×D4—42no—
331C4×D4—42no—
332C4×D4—81no—
333C4×D4—81no—
334C4×D4—81no—
335#117—42no—
336#117—42no—
337C2×C4⋊C4—22no—
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—21no—
348C2×C4⋊C4—41no—
349C2×C4⋊C4C22×C411yescharacteristic
350C2×C4⋊C4C22×C411yescharacteristic
351C2×C4⋊C4C22×C411yescharacteristic
352C2×C4⋊C4C22×C411yescharacteristic
353C2×C4⋊C4C22×C411yescharacteristic
354C2×C22⋊C4—22no—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—21no—
357C2×C22⋊C4—21no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—21no—
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—21no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4—42no—
382C2×C22⋊C4—42no—
383C2×C22⋊C4—44no—
384C2×C22⋊C4—42no—
385C2×C22⋊C4—42no—
386C2×C22⋊C4—42no—
387C2×C22⋊C4C22⋊C411yescharacteristic
388C2×C22⋊C4C22⋊C411yescharacteristic
389C2×C22⋊C4C22⋊C411yescharacteristic
390C2×C22⋊C4C22⋊C411yescharacteristic
391C2×C22⋊C4C22⋊C411yescharacteristic
392C2×C22⋊C4C22⋊C411yescharacteristic
393C2×C22⋊C4C22⋊C411yescharacteristic
394C2×C22⋊C4C22⋊C411yescharacteristic
395C2×C42—21no—
396C2×C42—21no—
397C2×C42—21no—
398C2×C42—21no—
399C2×C42—21no—
400C2×C42—21no—
401C2×C42—81no—
402C2×C42C22×C411yescharacteristic
403C2×C42C22×C411yescharacteristic
404C2×C42C22×C411yescharacteristic
405C2×C42C22×C411yescharacteristic
406C2×C42C2×D411yescharacteristic
407C2×C42C2×D411yescharacteristic
408C2×C42C2×D411yescharacteristic
409C2×C42C2×D411yescharacteristic
410C4⋊C8—42no—
411C4⋊C8—81no—
412C22⋊C8—21no—
413C22⋊C8—21no—
414C22⋊C8—21no—
415C22⋊C8—21no—
416C22⋊C8—21no—
417C22⋊C8—21no—
418C22⋊C8—21no—
419C22⋊C8—42no—
420C22⋊C8—42no—
421C22⋊C8—81no—
422C22⋊C8C2×D412yes—
423C4×C8—42no—
424C4×C8—81no—
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—42no—
444#95—42no—
445#95—42no—
446#95—42no—
447#95—42no—
448#95—81no—
449#95—81no—
450#95—81no—
451#95—81no—
452#95—81no—
453#95C22⋊C411yescharacteristic
454#95C22⋊C411yescharacteristic
455#95C22⋊C411yescharacteristic
456#95C22⋊C411yescharacteristic
457#95C22⋊C411yescharacteristic
458#95C22⋊C411yescharacteristic
459#95C22⋊C411yescharacteristic
460#95C22⋊C411yescharacteristic
461#95C2×D412yes—
462C24—21no—
463C24—21no—
464C24—21no—
465C24—21no—
466C24—22no—
467C24—22no—
468C24—21no—
469C24—21no—
470C24—41no—
471C24—41no—
472C24—42no—
473C24—42no—
474C24—42no—
475C24—42no—
476C24—81no—
477C24—81no—
478C24—81no—
479C24C2×C22⋊C411yescharacteristic
480C24C2×C22⋊C411yescharacteristic
481C24#13512yes—
482C24#13512yes—
483C24C22×D411yescharacteristic
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—41no—
487C2×Q8—41no—
488C2×D4—22no—
489C2×D4—22no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—41no—
494C2×D4—41no—
495C2×D4—42no—
496C2×D4—42no—
497C2×D4—41no—
498C2×D4—41no—
499C2×D4—42no—
500C2×D4—41no—
501C2×D4—41no—
502C2×D4—41no—
503C2×D4—41no—
504C2×D4—42no—
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—81no—
514C2×D4—84no—
515C2×D4—84no—
516C2×D4—81no—
517C2×D4—81no—
518C2×D4—84no—
519C2×D4—84no—
520C2×D4—84no—
521C2×D4—84no—
522C2×D4C4×D412yes—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
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—22no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—22no—
555C22×C4—41no—
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—42no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—41no—
576C22×C4—41no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4—41no—
580C22×C4—41no—
581C22×C4—41no—
582C22×C4—48no—
583C22×C4—41no—
584C22×C4—41no—
585C22×C4—41no—
586C22×C4—41no—
587C22×C4—41no—
588C22×C4—42no—
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—81no—
606C22×C4—82no—
607C22×C4—82no—
608C22×C4—82no—
609C22×C4—82no—
610C22×C4—81no—
611C22×C4—84no—
612C22×C4—84no—
613C22×C4—84no—
614C22×C4—84no—
615C22×C4—84no—
616C22×C4—84no—
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×C4C2×C22⋊C411yescharacteristic
626C22×C4C2×C22⋊C411yescharacteristic
627C22×C4C23×C411yescharacteristic
628C22×C4C22×D411yescharacteristic
629C22×C4C22×D411yescharacteristic
630C22×C4C2×#4111yescharacteristic
631C22×C4H(5,𝔽2)11yescharacteristic
632C22×C4H(5,𝔽2)11yescharacteristic
633C2×C8—22no—
634C2×C8—41no—
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—84no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—42no—
652C4⋊C4—42no—
653C4⋊C4—42no—
654C4⋊C4—42no—
655C4⋊C4—41no—
656C4⋊C4—41no—
657C4⋊C4—42no—
658C4⋊C4—41no—
659C4⋊C4—41no—
660C4⋊C4—81no—
661C4⋊C4—81no—
662C4⋊C4—81no—
663C4⋊C4—81no—
664C4⋊C4C4×D412yes—
665C22⋊C4—22no—
666C22⋊C4—22no—
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—22no—
672C22⋊C4—22no—
673C22⋊C4—41no—
674C22⋊C4—41no—
675C22⋊C4—42no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—41no—
683C22⋊C4—41no—
684C22⋊C4—41no—
685C22⋊C4—41no—
686C22⋊C4—42no—
687C22⋊C4—42no—
688C22⋊C4—41no—
689C22⋊C4—41no—
690C22⋊C4—81no—
691C22⋊C4—81no—
692C22⋊C4—81no—
693C22⋊C4—81no—
694C22⋊C4—81no—
695C22⋊C4—81no—
696C22⋊C4—81no—
697C22⋊C4—81no—
698C22⋊C4—81no—
699C22⋊C4—81no—
700C22⋊C4—81no—
701C22⋊C4—84no—
702C42—21no—
703C42—21no—
704C42—21no—
705C42—21no—
706C42—21no—
707C42—21no—
708C42—21no—
709C42—21no—
710C42—41no—
711C42—41no—
712C42—41no—
713C42—41no—
714C42—42no—
715C42—81no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—24no—
735C23—24no—
736C23—22no—
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—84no—
761C23—84no—
762C23—84no—
763C23—84no—
764C23—162no—
765C23—162no—
766C23—162no—
767C23#41012yes—
768C23#41612yes—
769C23#41612yes—
770C23#42112yes—
771C23C22×C22⋊C411yescharacteristic
772C23D4211yescharacteristic
773C23#54611yescharacteristic
774C23C2×#13511yescharacteristic
775C23C2×#13511yescharacteristic
776C23#57611yescharacteristic
777C23#57711yescharacteristic
778Q8—81no—
779Q8—81no—
780D4—42no—
781D4—42no—
782D4—42no—
783D4—42no—
784D4—42no—
785D4—42no—
786D4—81no—
787D4—81no—
788D4—84no—
789D4—84no—
790D4—84no—
791D4—81no—
792D4—81no—
793D4—81no—
794D4—81no—
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—22no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
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—21no—
829C2×C4—21no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
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—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—41no—
850C2×C4—41no—
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—41no—
864C2×C4—42no—
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—81no—
875C2×C4—81no—
876C2×C4—81no—
877C2×C4—84no—
878C2×C4—84no—
879C2×C4—81no—
880C2×C4—81no—
881C2×C4—81no—
882C2×C4—81no—
883C2×C4—81no—
884C2×C4—81no—
885C2×C4—81no—
886C2×C4—816no—
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—81no—
900C2×C4—81no—
901C2×C4—81no—
902C2×C4—162no—
903C2×C4C2×C4×D411yescharacteristic
904C2×C4#51811yescharacteristic
905C2×C4D4211yescharacteristic
906C2×C4#54611yescharacteristic
907C8—42no—
908C8—81no—
909C8—81no—
910C8—81no—
911C22—21no—
912C22—22no—
913C22—21no—
914C22—22no—
915C22—21no—
916C22—21no—
917C22—21no—
918C22—21no—
919C22—22no—
920C22—21no—
921C22—21no—
922C22—22no—
923C22—21no—
924C22—21no—
925C22—22no—
926C22—21no—
927C22—21no—
928C22—22no—
929C22—22no—
930C22—22no—
931C22—22no—
932C22—44no—
933C22—44no—
934C22—44no—
935C22—44no—
936C22—41no—
937C22—41no—
938C22—41no—
939C22—41no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—81no—
944C22—81no—
945C22—81no—
946C22—81no—
947C22—81no—
948C22—81no—
949C22—81no—
950C22—81no—
951C22—81no—
952C22—81no—
953C22—81no—
954C22—168no—
955C22#152114yescomplemented
956C22D4×C22⋊C411yescharacteristic
957C22C2×#41011yescharacteristic
958C22#288311yescharacteristic
959C22C2×#41611yescharacteristic
960C22#289711yescharacteristic
961C22C2×#42111yescharacteristic
962C22#290111yescharacteristic
963C22#328011yescharacteristic
964C22#328211yescharacteristic
965C22#329611yescharacteristic
966C22#329711yescharacteristic
967C4—21no—
968C4—21no—
969C4—21no—
970C4—21no—
971C4—41no—
972C4—41no—
973C4—41no—
974C4—41no—
975C4—42no—
976C4—41no—
977C4—41no—
978C4—41no—
979C4—41no—
980C4—41no—
981C4—41no—
982C4—82no—
983C4—82no—
984C4—81no—
985C4—81no—
986C4—81no—
987C4—81no—
988C4—81no—
989C4—161no—
990C4—161no—
991C2—21no—
992C2—21no—
993C2—21no—
994C2—24no—
995C2—21no—
996C2—42no—
997C2—82no—
998C2—161no—
999C2C2×#152111yescharacteristic
1000C2#1759711yescharacteristic
1001C2#1760411yescharacteristic
1002C2#1761511yescharacteristic
1003C2#2240511yescharacteristic
1004C2#2241411yescharacteristic
1005C2#2243411yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC22×#121C22
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. #22552C2semidirect
3. C2×#1521C2semidirect
5. #13901C2semidirect
6. #9716C2semidirect
7. #9681C2semidirect
8. #9157C2semidirect
9. #9143C2semidirect
10. #9114C2semidirect
11. #9111C2semidirect
12. #8575C2semidirect
13. #8330C2semidirect
15. #8220C2semidirect
18. C2×#431C22semidirect
24. #2490C4semidirect
28. #2442C4semidirect
29. #2435C4semidirect
30. #2427C4semidirect
31. #2426C4semidirect
33. #2420C4semidirect
35. #2360C4semidirect
38. D4×C22⋊C4C4semidirect
40. C2×#383C22semidirect
46. #1817C22semidirect
47. #1797C22semidirect
50. C4×C22⋊C8C22semidirect
52. C2×#328C22semidirect
53. C2×#328C22semidirect
54. C2×#328C22semidirect
55. C2×#328C22semidirect
67. #1434C22semidirect
68. #1434C22semidirect
69. #1434C22semidirect
73. #1294C22semidirect
74. #1294C22semidirect
75. #1294C22semidirect
76. #1294C22semidirect
87. C2×#125C2×C4semidirect
88. C2×#124C2×C4semidirect
89. C2×#124C2×C4semidirect
105. C2×C4×Q8C2×C4semidirect
108. C2×C4×D4C2×C4semidirect
109. C2×C4×D4C2×C4semidirect
146. #391C2×C4semidirect
149. #390C2×C4semidirect
150. #390C2×C4semidirect
151. #390C2×C4semidirect
152. #390C2×C4semidirect
154. #389C2×C4semidirect
155. #389C2×C4semidirect
156. #389C2×C4semidirect
180. #382C2×C4semidirect
191. C4×C4⋊C4C2×C4semidirect
955. C22#1521semidirect

Maximal subgroups

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

subgroupindex
#361072
#225522
C2×#15212
C22×#3272
#139012
#97162
#96812
#91572
#91432
#91142
#91112
#85752
#83302
#83282
#82202