Finite Group Databasebeta

← #223606

Subgroups — #223606

Order 512.

1362 conjugacy classes of subgroups.

The subgroup lattice has 978 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36161C211yesmaximal, characteristic
2#22399C211yesmaximal, characteristic
3#13813C211yesmaximal, characteristic
4#9908C211yesmaximal, characteristic, complemented
5#9888C211yesmaximal, characteristic, complemented
6#9146C211yesmaximal, characteristic, complemented
7#9143C211yesmaximal, characteristic, complemented
8#9115C211yesmaximal, characteristic, complemented
9#9111C211yesmaximal, characteristic, complemented
10#8715C211yesmaximal, characteristic, complemented
11#8715C211yesmaximal, characteristic, complemented
12#8574C211yesmaximal, characteristic, complemented
13#8219C211yesmaximal, characteristic, complemented
14#8020C211yesmaximal, characteristic, complemented
15#8012C211yesmaximal, characteristic, complemented
16C2×#556C411yescharacteristic, complemented
17C22×C4×D4C2211yescharacteristic
18C2×#435—21no—
19C2×#407C2211yescharacteristic
20C22×C22⋊C8C2211yescharacteristic
21#2857C2211yescharacteristic
22#2848C2211yescharacteristic
23#2848C2211yescharacteristic
24#2547C411yescharacteristic, complemented
25#2538C411yescharacteristic, complemented
26#2485C411yescharacteristic, complemented
27#2485C411yescharacteristic, complemented
28#2480—21no—
29#2480—21no—
30#2466—21no—
31#2466—21no—
32#2447—21no—
33#2435—21no—
34#2415C411yescharacteristic, complemented
35#2415C411yescharacteristic, complemented
36#2367—21no—
37#2360—21no—
38#2354C411yescharacteristic, complemented
39C4×C22⋊Q8C2211yescharacteristic
40C2×#386—21no—
41#2280C2211yescharacteristic
42#2280C2211yescharacteristic
43C2×C4×C22⋊C4—21no—
44C2×C4×C22⋊C4C2211yescharacteristic
45C22×#95C2211yescharacteristic
46#1955—21no—
47#1870—21no—
48#1869—21no—
49#1797C2211yescharacteristic
50#1779C2211yescharacteristic
51#1779C2211yescharacteristic
52#1749C2211yescharacteristic
53C2×#328C2211yescharacteristic
54C2×#328C2211yescharacteristic
55C2×#328C2211yescharacteristic
56C2×#328C2211yescharacteristic
57#1437—21no—
58#1436—21no—
59#1434C2211yescharacteristic
60C22⋊#95C2211yescharacteristic
61C22⋊#95C2211yescharacteristic
62C4×#95C2211yescharacteristic
63#1294C2211yescharacteristic
64#1294C2211yescharacteristic
65#1294C2211yescharacteristic
66#1294C2211yescharacteristic
67#1294C2211yescharacteristic
68#1294C2211yescharacteristic
69#1294C2211yescharacteristic
70#1294C2211yescharacteristic
71#1294C2211yescharacteristic
72#1294C2211yescharacteristic
73#1294C2211yescharacteristic
74#1294C2211yescharacteristic
75C23×D4D411yescharacteristic
76C24×C4—21no—
77C24×C4C2311yescharacteristic
78C24×C4C2311yescharacteristic
79C22×M16—21no—
80C23×C8—21no—
81#556—44no—
82C2×C4⋊Q8C2×C411yescharacteristic, complemented
83C2×#126—21no—
84C2×#126—21no—
85C2×#124—21no—
86C2×#124—21no—
87C2×C22⋊Q8—21no—
88C2×C22⋊Q8C2×C411yescharacteristic
89C2×C22⋊Q8C2×C411yescharacteristic
90C2×C22⋊Q8C2×C411yescharacteristic, complemented
91C2×C22⋊Q8C2×C411yescharacteristic, complemented
92C2×C22⋊Q8C2311yescharacteristic
93C2×C4×Q8—21no—
94C2×C4×Q8C2×C411yescharacteristic, complemented
95C2×C4×D4—44no—
96C2×C4×D4C2×C411yescharacteristic
97C2×C4×D4C2×C411yescharacteristic
98C2×C4×D4C2×C411yescharacteristic
99C2×C4×D4C2×C411yescharacteristic
100C2×C4×D4D411yescharacteristic
101C2×C4×D4D411yescharacteristic
102C2×C4×D4D411yescharacteristic
103C2×C4×D4D411yescharacteristic
104C2×#117C2×C411yescharacteristic
105C2×#117C2×C411yescharacteristic
106C2×#117C2×C411yescharacteristic, complemented
107C2×#117C2×C411yescharacteristic, complemented
108C22×C4⋊C4D411yescharacteristic
109C22×C22⋊C4—21no—
110C22×C22⋊C4—21no—
111C22×C22⋊C4—21no—
112C22×C22⋊C4D411yescharacteristic
113C22×C22⋊C4D411yescharacteristic
114C22×C42—21no—
115C22×C42—21no—
116C22×C42C2311yescharacteristic
117#435—44no—
118C2×C4⋊C8—21no—
119#407—22no—
120#407—41no—
121C2×C22⋊C8—22no—
122C2×C22⋊C8—21no—
123C2×C22⋊C8—21no—
124C2×C22⋊C8—21no—
125C2×C22⋊C8—21no—
126C2×C22⋊C8—21no—
127C2×C22⋊C8—21no—
128C2×C22⋊C8—41no—
129C2×C22⋊C8C2311yescharacteristic
130C2×C22⋊C8C2311yescharacteristic
131C2×C22⋊C8C2311yescharacteristic
132C2×C22⋊C8C2311yescharacteristic
133C2×#97—21no—
134#397—21no—
135#397—21no—
136#397—21no—
137#397—21no—
138#397—21no—
139#397—21no—
140#396—21no—
141#396—21no—
142#394—21no—
143#394—21no—
144#394—21no—
145#394—21no—
146#391—21no—
147#391—21no—
148#391C2×C411yescharacteristic, complemented
149#390—21no—
150#390—21no—
151#389—21no—
152#389—21no—
153#389—21no—
154#389—21no—
155#389C2×C411yescharacteristic, complemented
156#389C2×C411yescharacteristic, complemented
157#389C2×C411yescharacteristic, complemented
158#388—21no—
159#388—21no—
160#388—21no—
161#388—21no—
162#388—21no—
163#388—21no—
164#387—21no—
165#387—21no—
166#387—21no—
167#386—28no—
168#385—21no—
169#385—21no—
170#385—21no—
171#385—21no—
172#385—21no—
173#385—21no—
174#385—21no—
175#384C2×C411yescharacteristic, complemented
176#381—21no—
177#381—21no—
178#380—21no—
179#380C2×C411yescharacteristic
180#380C2×C411yescharacteristic
181#380C2×C411yescharacteristic
182#380C2×C411yescharacteristic
183#380C2×C411yescharacteristic, complemented
184#380C2×C411yescharacteristic, complemented
185#380C2×C411yescharacteristic, complemented
186#380C2×C411yescharacteristic, complemented
187#380C2311yescharacteristic
188#380C2311yescharacteristic
189#380C2311yescharacteristic
190#379—21no—
191#379—21no—
192#379—21no—
193#379—21no—
194C4×C4⋊C4—21no—
195C4×C4⋊C4—21no—
196C4×C4⋊C4C2×C411yescharacteristic, complemented
197C4×C22⋊C4—21no—
198C4×C22⋊C4—21no—
199C4×C22⋊C4—21no—
200C4×C22⋊C4—21no—
201C4×C22⋊C4—21no—
202C4×C22⋊C4—22no—
203C4×C22⋊C4—41no—
204C4×C22⋊C4—44no—
205C2×#95—21no—
206C2×#95—21no—
207C2×#95—22no—
208C2×#95—21no—
209C2×#95—21no—
210C2×#95—21no—
211C2×#95—21no—
212C2×#95—41no—
213C2×#95C2311yescharacteristic
214C2×#95C2311yescharacteristic
215C2×#95C2311yescharacteristic
216C2×#95C2311yescharacteristic
217#336—21no—
218#336—21no—
219#328—22no—
220#328—22no—
221#328—41no—
222#328—41no—
223C25C2×D411yescharacteristic
224C25C2×D411yescharacteristic
225C22×Q8—21no—
226C22×Q8C22×C411yescharacteristic
227C22×D4—24no—
228C22×D4—41no—
229C22×D4—41no—
230C22×D4—42no—
231C22×D4C22⋊C411yescharacteristic
232C22×D4C22⋊C411yescharacteristic
233C22×D4C22⋊C411yescharacteristic
234C22×D4C22⋊C411yescharacteristic
235C23×C4—21no—
236C23×C4—21no—
237C23×C4—21no—
238C23×C4—21no—
239C23×C4—21no—
240C23×C4—21no—
241C23×C4—21no—
242C23×C4—21no—
243C23×C4—21no—
244C23×C4—21no—
245C23×C4—21no—
246C23×C4—21no—
247C23×C4—24no—
248C23×C4—42no—
249C23×C4—42no—
250C23×C4—42no—
251C23×C4—42no—
252C23×C4—42no—
253C23×C4—42no—
254C23×C4—81no—
255C23×C4—81no—
256C23×C4—81no—
257C23×C4—81no—
258C23×C4C22×C411yescharacteristic
259C23×C4C22×C411yescharacteristic
260C23×C4C22×C411yescharacteristic
261C23×C4C22×C411yescharacteristic
262C23×C4C2×D411yescharacteristic
263C23×C4C2×D411yescharacteristic
264C23×C4C2×D411yescharacteristic
265C23×C4C2×D411yescharacteristic
266C23×C4C2×D411yescharacteristic
267C23×C4C2×D411yescharacteristic
268C23×C4C2×D411yescharacteristic
269C23×C4C2×D411yescharacteristic
270C23×C4C2411yescharacteristic
271C2×M16—42no—
272C2×M16—42no—
273C2×M16—81no—
274C22×C8—21no—
275C22×C8—21no—
276C22×C8—21no—
277C22×C8—21no—
278C22×C8—42no—
279C22×C8—42no—
280C22×C8—81no—
281C4⋊Q8—42no—
282#126—44no—
283#126—44no—
284#124—44no—
285#124—44no—
286C22⋊Q8—21no—
287C22⋊Q8—21no—
288C22⋊Q8—21no—
289C22⋊Q8—21no—
290C22⋊Q8—42no—
291C22⋊Q8—42no—
292C22⋊Q8—42no—
293C22⋊Q8—42no—
294C22⋊Q8—81no—
295C22⋊Q8—81no—
296C4×Q8—42no—
297C4×Q8—44no—
298C4×D4—24no—
299C4×D4—24no—
300C4×D4—42no—
301C4×D4—42no—
302C4×D4—42no—
303C4×D4—42no—
304C4×D4—42no—
305C4×D4—42no—
306#117—42no—
307#117—42no—
308#117—81no—
309#117—81no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—42no—
323C2×C4⋊C4C22⋊C411yescharacteristic
324C2×C4⋊C4C22⋊C411yescharacteristic
325C2×C4⋊C4C22⋊C411yescharacteristic
326C2×C4⋊C4C22⋊C411yescharacteristic
327C2×C4⋊C4C22×C411yescharacteristic
328C2×C4⋊C4C22×C411yescharacteristic
329C2×C4⋊C4C22×C411yescharacteristic
330C2×C4⋊C4C22×C411yescharacteristic
331C2×C4⋊C4C22×C411yescharacteristic
332C2×C4⋊C4C22×C411yescharacteristic
333C2×C4⋊C4C22×C411yescharacteristic
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—21no—
338C2×C22⋊C4—21no—
339C2×C22⋊C4—21no—
340C2×C22⋊C4—21no—
341C2×C22⋊C4—21no—
342C2×C22⋊C4—21no—
343C2×C22⋊C4—21no—
344C2×C22⋊C4—21no—
345C2×C22⋊C4—21no—
346C2×C22⋊C4—21no—
347C2×C22⋊C4—21no—
348C2×C22⋊C4—21no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—21no—
354C2×C22⋊C4—21no—
355C2×C22⋊C4—21no—
356C2×C22⋊C4—21no—
357C2×C22⋊C4—21no—
358C2×C22⋊C4—42no—
359C2×C22⋊C4—42no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4—42no—
362C2×C22⋊C4—42no—
363C2×C22⋊C4—81no—
364C2×C22⋊C4—81no—
365C2×C22⋊C4C22⋊C411yescharacteristic
366C2×C22⋊C4C22⋊C411yescharacteristic
367C2×C22⋊C4C22⋊C411yescharacteristic
368C2×C22⋊C4C22⋊C411yescharacteristic
369C2×C22⋊C4C22⋊C411yescharacteristic
370C2×C22⋊C4C22⋊C411yescharacteristic
371C2×C22⋊C4C22⋊C411yescharacteristic
372C2×C22⋊C4C22⋊C411yescharacteristic
373C2×C42—21no—
374C2×C42—21no—
375C2×C42—21no—
376C2×C42—21no—
377C2×C42—21no—
378C2×C42—21no—
379C2×C42—42no—
380C2×C42—42no—
381C2×C42—42no—
382C2×C42—42no—
383C2×C42—42no—
384C2×C42—81no—
385C2×C42—81no—
386C2×C42C22×C411yescharacteristic
387C2×C42C22×C411yescharacteristic
388C2×C42C2×D411yescharacteristic
389C2×C42C2×D411yescharacteristic
390C4⋊C8—42no—
391C22⋊C8—21no—
392C22⋊C8—21no—
393C22⋊C8—21no—
394C22⋊C8—21no—
395C22⋊C8—21no—
396C22⋊C8—21no—
397C22⋊C8—21no—
398C22⋊C8—42no—
399C22⋊C8—42no—
400C22⋊C8—42no—
401C22⋊C8—42no—
402C22⋊C8—81no—
403C22⋊C8—81no—
404C22⋊C8#4112yes—
405#97—42no—
406#95—24no—
407#95—24no—
408#95—21no—
409#95—21no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95—21no—
421#95—21no—
422#95—21no—
423#95—21no—
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—42no—
433#95—42no—
434#95—42no—
435#95—81no—
436#95#4112yes—
437C24—21no—
438C24—21no—
439C24—22no—
440C24—22no—
441C24—21no—
442C24—21no—
443C24—21no—
444C24—21no—
445C24—22no—
446C24—21no—
447C24—21no—
448C24—21no—
449C24—21no—
450C24—21no—
451C24—21no—
452C24—41no—
453C24—41no—
454C24—41no—
455C24—41no—
456C24—41no—
457C24C2×C22⋊C411yescharacteristic
458C24C2×C22⋊C411yescharacteristic
459C24C2×C22⋊C411yescharacteristic
460C24C2×C22⋊C411yescharacteristic
461C24C22×D411yescharacteristic
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—42no—
465C2×Q8—42no—
466C2×Q8—41no—
467C2×Q8—41no—
468C2×Q8—42no—
469C2×D4—22no—
470C2×D4—22no—
471C2×D4—22no—
472C2×D4—22no—
473C2×D4—22no—
474C2×D4—41no—
475C2×D4—41no—
476C2×D4—41no—
477C2×D4—41no—
478C2×D4—41no—
479C2×D4—41no—
480C2×D4—48no—
481C2×D4—48no—
482C2×D4#10414yes—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
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—41no—
529C22×C4—41no—
530C22×C4—41no—
531C22×C4—41no—
532C22×C4—41no—
533C22×C4—41no—
534C22×C4—41no—
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—48no—
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—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—82no—
572C22×C4—82no—
573C22×C4—82no—
574C22×C4—82no—
575C22×C4—82no—
576C22×C4—82no—
577C22×C4—82no—
578C22×C4—82no—
579C22×C4—84no—
580C22×C4—84no—
581C22×C4—84no—
582C22×C4—84no—
583C22×C4—84no—
584C22×C4C2×C22⋊C411yescharacteristic
585C22×C4C2×C22⋊C411yescharacteristic
586C22×C4C2×C22⋊C411yescharacteristic
587C22×C4C2×C22⋊C411yescharacteristic
588C22×C4C2×C22⋊C411yescharacteristic
589C22×C4C2×C22⋊C411yescharacteristic
590C22×C4C2×C22⋊C411yescharacteristic
591C22×C4C2×C22⋊C411yescharacteristic
592C22×C4C23×C411yescharacteristic
593C22×C4C22×D411yescharacteristic
594C22×C4C2×#4111yescharacteristic
595C22×C4C2×#4111yescharacteristic
596C22×C4H(5,𝔽2)11yescharacteristic
597C22×C42−1+411yescharacteristic
598M16—84no—
599C2×C8—22no—
600C2×C8—41no—
601C2×C8—41no—
602C2×C8—41no—
603C2×C8—41no—
604C2×C8—41no—
605C2×C8—41no—
606C2×C8—41no—
607C2×C8—41no—
608C2×C8—41no—
609C2×C8—41no—
610C2×C8—41no—
611C2×C8—84no—
612C4⋊C4—22no—
613C4⋊C4—22no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—41no—
617C4⋊C4—41no—
618C4⋊C4—41no—
619C4⋊C4—41no—
620C4⋊C4—41no—
621C4⋊C4—41no—
622C4⋊C4—41no—
623C4⋊C4—41no—
624C4⋊C4—42no—
625C4⋊C4—42no—
626C4⋊C4—42no—
627C4⋊C4—42no—
628C4⋊C4—41no—
629C4⋊C4—41no—
630C4⋊C4—42no—
631C4⋊C4—42no—
632C4⋊C4—42no—
633C4⋊C4—81no—
634C4⋊C4—81no—
635C4⋊C4—81no—
636C4⋊C4—81no—
637C22⋊C4—22no—
638C22⋊C4—22no—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—22no—
642C22⋊C4—41no—
643C22⋊C4—41no—
644C22⋊C4—48no—
645C22⋊C4—48no—
646C22⋊C4—42no—
647C22⋊C4—42no—
648C22⋊C4—41no—
649C22⋊C4—41no—
650C22⋊C4—41no—
651C22⋊C4—41no—
652C22⋊C4—41no—
653C22⋊C4—41no—
654C22⋊C4—41no—
655C22⋊C4—41no—
656C22⋊C4—42no—
657C22⋊C4—42no—
658C22⋊C4—42no—
659C22⋊C4—42no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—81no—
663C22⋊C4—81no—
664C22⋊C4—81no—
665C22⋊C4—81no—
666C22⋊C4—81no—
667C22⋊C4—81no—
668C22⋊C4—81no—
669C22⋊C4—81no—
670C22⋊C4—84no—
671C22⋊C4#9914yes—
672C42—22no—
673C42—22no—
674C42—41no—
675C42—41no—
676C42—42no—
677C42—42no—
678C42—42no—
679C42—42no—
680C42—81no—
681C42—81no—
682C42—84no—
683C42—84no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—24no—
689C23—24no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
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—42no—
726C23—42no—
727C23—42no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—81no—
740C23—81no—
741C23—81no—
742C23—81no—
743C23—81no—
744C23—81no—
745C23C2×#9912yes—
746C23C2×#10412yes—
747C23C2×#10412yes—
748C23C22×C22⋊C411yescharacteristic
749C23#54611yescharacteristic
750C23#54711yescharacteristic
751C23#57511yescharacteristic
752C23#57511yescharacteristic
753C23#57711yescharacteristic
754C23#57811yescharacteristic
755Q8—81no—
756Q8—81no—
757Q8—84no—
758D4—44no—
759D4—44no—
760D4—44no—
761D4—44no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—24no—
773C2×C4—21no—
774C2×C4—21no—
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—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
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—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
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—81no—
846C2×C4—81no—
847C2×C4—81no—
848C2×C4—81no—
849C2×C4—81no—
850C2×C4—81no—
851C2×C4—81no—
852C2×C4—81no—
853C2×C4—81no—
854C2×C4—81no—
855C2×C4—816no—
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—81no—
866C2×C4—81no—
867C2×C4—81no—
868C2×C4C2×#9912yes—
869C2×C4C2×#9912yes—
870C2×C4C2×#10412yes—
871C2×C4C4×#4111yescharacteristic
872C2×C4#52011yescharacteristic
873C2×C4#54611yescharacteristic
874C2×C4#54711yescharacteristic
875C8—42no—
876C8—81no—
877C8—81no—
878C8—81no—
879C22—21no—
880C22—21no—
881C22—21no—
882C22—21no—
883C22—21no—
884C22—21no—
885C22—21no—
886C22—21no—
887C22—21no—
888C22—21no—
889C22—21no—
890C22—21no—
891C22—22no—
892C22—22no—
893C22—22no—
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—41no—
913C22—41no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—82no—
924C22—82no—
925C22—82no—
926C22—82no—
927C22#233911yescharacteristic
928C22C22×#9911yescharacteristic
929C22#288311yescharacteristic
930C22#289611yescharacteristic
931C22#289811yescharacteristic
932C22C22×#10411yescharacteristic
933C22#290111yescharacteristic
934C22#331111yescharacteristic
935C22#331311yescharacteristic
936C22#334911yescharacteristic
937C22#335011yescharacteristic
938C4—22no—
939C4—22no—
940C4—21no—
941C4—21no—
942C4—21no—
943C4—21no—
944C4—22no—
945C4—44no—
946C4—41no—
947C4—41no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—82no—
952C4—82no—
953C4—82no—
954C4—81no—
955C4—81no—
956C4—81no—
957C4—81no—
958C4—81no—
959C4—81no—
960C4—81no—
961C4—81no—
962C2—21no—
963C2—21no—
964C2—21no—
965C2—21no—
966C2—42no—
967C2—42no—
968C2—42no—
969C2—81no—
970C2#1754211yescharacteristic
971C2#1754811yescharacteristic
972C2#1760811yescharacteristic
973C2#1762911yescharacteristic
974C2#2247611yescharacteristic
975C2#2249411yescharacteristic
976C2#2250511yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC23×D4D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C22×C4×D4 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #9908C2semidirect
5. #9888C2semidirect
6. #9146C2semidirect
7. #9143C2semidirect
8. #9115C2semidirect
9. #9111C2semidirect
10. #8715C2semidirect
11. #8715C2semidirect
12. #8574C2semidirect
13. #8219C2semidirect
14. #8020C2semidirect
15. #8012C2semidirect
16. C2×#556C4semidirect
24. #2547C4semidirect
25. #2538C4semidirect
26. #2485C4semidirect
27. #2485C4semidirect
34. #2415C4semidirect
35. #2415C4semidirect
38. #2354C4semidirect
82. C2×C4⋊Q8C2×C4semidirect
90. C2×C22⋊Q8C2×C4semidirect
91. C2×C22⋊Q8C2×C4semidirect
94. C2×C4×Q8C2×C4semidirect
106. C2×#117C2×C4semidirect
107. C2×#117C2×C4semidirect
148. #391C2×C4semidirect
155. #389C2×C4semidirect
156. #389C2×C4semidirect
157. #389C2×C4semidirect
175. #384C2×C4semidirect
183. #380C2×C4semidirect
184. #380C2×C4semidirect
185. #380C2×C4semidirect
186. #380C2×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
#361612
#223992
#138132
#99082
#98882
#91462
#91432
#91152
#91112
#87152
#85742
#82192
#80202
#80122