Finite Group Databasebeta

← #223620

Subgroups — #223620

Order 512.

1400 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36154C211yesmaximal, characteristic
2#22399C211yesmaximal, characteristic
3#13813C211yesmaximal, characteristic
4#9909C211yesmaximal, characteristic, complemented
5#9889C211yesmaximal, characteristic, complemented
6#9146C211yesmaximal, characteristic, complemented
7#9143C211yesmaximal, characteristic, complemented
8#9115C211yesmaximal, characteristic, complemented
9#9111C211yesmaximal, characteristic, complemented
10#8713C211yesmaximal, characteristic, complemented
11#8712C211yesmaximal, characteristic, complemented
12#8574C211yesmaximal, characteristic, complemented
13#8219C211yesmaximal, characteristic, complemented
14#8019C211yesmaximal, characteristic, complemented
15C2×#1294C211yesmaximal, characteristic, complemented
16C2×#554C411yescharacteristic, complemented
17C22×C4×D4C2211yescharacteristic
18C2×#435—21no—
19C2×#407C2211yescharacteristic
20C22×C22⋊C8C2211yescharacteristic
21#2857C2211yescharacteristic
22#2848C2211yescharacteristic
23#2848C2211yescharacteristic
24#2563C411yescharacteristic, complemented
25#2538C411yescharacteristic, complemented
26#2487C411yescharacteristic, complemented
27#2487C411yescharacteristic, complemented
28#2454—21no—
29#2450—21no—
30#2450—21no—
31#2442—21no—
32#2437—21no—
33#2437—21no—
34#2417C411yescharacteristic, complemented
35#2417C411yescharacteristic, complemented
36#2349—21no—
37D4×C4⋊C4C411yescharacteristic, complemented
38D4×C22⋊C4—21no—
39C4×C22⋊Q8C2211yescharacteristic
40C2×#386—21no—
41C2×#380C2211yescharacteristic
42C2×#380C2211yescharacteristic
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#554—44no—
82C2×C4⋊Q8C2×C411yescharacteristic, complemented
83C2×#125—21no—
84C2×C22⋊Q8—21no—
85C2×C22⋊Q8—21no—
86C2×C22⋊Q8—21no—
87C2×C22⋊Q8C2×C411yescharacteristic
88C2×C22⋊Q8C2×C411yescharacteristic
89C2×C22⋊Q8C2×C411yescharacteristic, complemented
90C2×C22⋊Q8C2×C411yescharacteristic, complemented
91C2×C22⋊Q8C2311yescharacteristic
92C2×C4×Q8C2×C411yescharacteristic, complemented
93C2×C4×D4—21no—
94C2×C4×D4—21no—
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
104C22×C4⋊C4C2×C411yescharacteristic
105C22×C4⋊C4C2×C411yescharacteristic
106C22×C4⋊C4C2×C411yescharacteristic, complemented
107C22×C4⋊C4C2×C411yescharacteristic, complemented
108C22×C4⋊C4D411yescharacteristic
109C22×C22⋊C4—21no—
110C22×C22⋊C4—21no—
111C22×C22⋊C4—21no—
112C22×C22⋊C4—21no—
113C22×C22⋊C4—21no—
114C22×C22⋊C4D411yescharacteristic
115C22×C22⋊C4D411yescharacteristic
116C22×C42—21no—
117C22×C42—21no—
118C22×C42C2311yescharacteristic
119#435—44no—
120C2×C4⋊C8—21no—
121#407—22no—
122#407—41no—
123C2×C22⋊C8—22no—
124C2×C22⋊C8—21no—
125C2×C22⋊C8—21no—
126C2×C22⋊C8—21no—
127C2×C22⋊C8—21no—
128C2×C22⋊C8—21no—
129C2×C22⋊C8—21no—
130C2×C22⋊C8—41no—
131C2×C22⋊C8C2311yescharacteristic
132C2×C22⋊C8C2311yescharacteristic
133C2×C22⋊C8C2311yescharacteristic
134C2×C22⋊C8C2311yescharacteristic
135C2×#97—21no—
136#400—21no—
137#400—21no—
138#399—21no—
139#399—21no—
140#398—21no—
141#398—21no—
142#396—21no—
143#396—21no—
144#396—21no—
145#396—21no—
146#393—21no—
147#393—21no—
148#391—21no—
149#391C2×C411yescharacteristic, complemented
150#390—21no—
151#390—21no—
152#389—21no—
153#389—21no—
154#389—21no—
155#389C2×C411yescharacteristic, complemented
156#389C2×C411yescharacteristic, complemented
157#389C2×C411yescharacteristic, complemented
158#387—21no—
159#386—28no—
160#386—21no—
161#386—21no—
162#386—21no—
163#386—21no—
164#385—21no—
165#385—21no—
166#385—21no—
167#385—21no—
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#382—21no—
177#380—21no—
178#380—21no—
179#380—21no—
180#380—21no—
181#380—21no—
182#380—21no—
183#380—21no—
184#380C2×C411yescharacteristic
185#380C2×C411yescharacteristic
186#380C2×C411yescharacteristic
187#380C2×C411yescharacteristic
188#380C2×C411yescharacteristic, complemented
189#380C2×C411yescharacteristic, complemented
190#380C2×C411yescharacteristic, complemented
191#380C2×C411yescharacteristic, complemented
192#380C2311yescharacteristic
193#380C2311yescharacteristic
194#380C2311yescharacteristic
195#379—21no—
196#379—21no—
197C4×C4⋊C4—21no—
198C4×C4⋊C4C2×C411yescharacteristic, complemented
199C4×C22⋊C4—21no—
200C4×C22⋊C4—22no—
201C4×C22⋊C4—41no—
202C4×C22⋊C4—44no—
203C2×#95—21no—
204C2×#95—21no—
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—22no—
228C22×D4—22no—
229C22×D4—24no—
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—21no—
249C23×C4—21no—
250C23×C4—21no—
251C23×C4—21no—
252C23×C4—42no—
253C23×C4—42no—
254C23×C4—42no—
255C23×C4—42no—
256C23×C4—42no—
257C23×C4—42no—
258C23×C4—81no—
259C23×C4—81no—
260C23×C4—81no—
261C23×C4—81no—
262C23×C4C22×C411yescharacteristic
263C23×C4C22×C411yescharacteristic
264C23×C4C22×C411yescharacteristic
265C23×C4C22×C411yescharacteristic
266C23×C4C2×D411yescharacteristic
267C23×C4C2×D411yescharacteristic
268C23×C4C2×D411yescharacteristic
269C23×C4C2×D411yescharacteristic
270C23×C4C2×D411yescharacteristic
271C23×C4C2×D411yescharacteristic
272C23×C4C2×D411yescharacteristic
273C23×C4C2×D411yescharacteristic
274C23×C4C2411yescharacteristic
275C2×M16—42no—
276C2×M16—42no—
277C2×M16—81no—
278C22×C8—21no—
279C22×C8—21no—
280C22×C8—21no—
281C22×C8—21no—
282C22×C8—42no—
283C22×C8—42no—
284C22×C8—81no—
285C4⋊Q8—42no—
286#125—44no—
287C22⋊Q8—21no—
288C22⋊Q8—21no—
289C22⋊Q8—21no—
290C22⋊Q8—21no—
291C22⋊Q8—44no—
292C22⋊Q8—42no—
293C22⋊Q8—44no—
294C22⋊Q8—42no—
295C22⋊Q8—81no—
296C22⋊Q8—81no—
297C22⋊Q8—81no—
298C22⋊Q8—81no—
299C4×Q8—42no—
300C4×D4—24no—
301C4×D4—24no—
302C4×D4—42no—
303C4×D4—42no—
304C4×D4—42no—
305C4×D4—42no—
306C4×D4—42no—
307C4×D4—42no—
308C4×D4—44no—
309C4×D4—44no—
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—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—42no—
327C2×C4⋊C4—42no—
328C2×C4⋊C4—42no—
329C2×C4⋊C4—81no—
330C2×C4⋊C4—81no—
331C2×C4⋊C4C22⋊C411yescharacteristic
332C2×C4⋊C4C22⋊C411yescharacteristic
333C2×C4⋊C4C22⋊C411yescharacteristic
334C2×C4⋊C4C22⋊C411yescharacteristic
335C2×C4⋊C4C22×C411yescharacteristic
336C2×C4⋊C4C22×C411yescharacteristic
337C2×C4⋊C4C22×C411yescharacteristic
338C2×C4⋊C4C22×C411yescharacteristic
339C2×C4⋊C4C22×C411yescharacteristic
340C2×C4⋊C4C22×C411yescharacteristic
341C2×C4⋊C4C22×C411yescharacteristic
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—21no—
346C2×C22⋊C4—21no—
347C2×C22⋊C4—21no—
348C2×C22⋊C4—21no—
349C2×C22⋊C4—21no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—21no—
355C2×C22⋊C4—21no—
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—42no—
363C2×C22⋊C4—42no—
364C2×C22⋊C4—42no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4—81no—
368C2×C22⋊C4—81no—
369C2×C22⋊C4—81no—
370C2×C22⋊C4—81no—
371C2×C22⋊C4—81no—
372C2×C22⋊C4—81no—
373C2×C22⋊C4C22⋊C411yescharacteristic
374C2×C22⋊C4C22⋊C411yescharacteristic
375C2×C22⋊C4C22⋊C411yescharacteristic
376C2×C22⋊C4C22⋊C411yescharacteristic
377C2×C22⋊C4C22⋊C411yescharacteristic
378C2×C22⋊C4C22⋊C411yescharacteristic
379C2×C22⋊C4C22⋊C411yescharacteristic
380C2×C22⋊C4C22⋊C411yescharacteristic
381C2×C42—21no—
382C2×C42—21no—
383C2×C42—42no—
384C2×C42—42no—
385C2×C42—42no—
386C2×C42—42no—
387C2×C42—42no—
388C2×C42—81no—
389C2×C42—81no—
390C2×C42C22×C411yescharacteristic
391C2×C42C22×C411yescharacteristic
392C2×C42C2×D411yescharacteristic
393C2×C42C2×D411yescharacteristic
394C4⋊C8—42no—
395C22⋊C8—21no—
396C22⋊C8—21no—
397C22⋊C8—21no—
398C22⋊C8—21no—
399C22⋊C8—21no—
400C22⋊C8—21no—
401C22⋊C8—21no—
402C22⋊C8—42no—
403C22⋊C8—42no—
404C22⋊C8—42no—
405C22⋊C8—42no—
406C22⋊C8—81no—
407C22⋊C8—81no—
408C22⋊C8#4112yes—
409#97—42no—
410#95—24no—
411#95—24no—
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—21no—
433#95—21no—
434#95—21no—
435#95—21no—
436#95—42no—
437#95—42no—
438#95—42no—
439#95—81no—
440#95#4112yes—
441C24—21no—
442C24—21no—
443C24—21no—
444C24—21no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—21no—
449C24—21no—
450C24—21no—
451C24—21no—
452C24—21no—
453C24—21no—
454C24—41no—
455C24—41no—
456C24—41no—
457C24—41no—
458C24—41no—
459C24C2×C22⋊C411yescharacteristic
460C24C2×C22⋊C411yescharacteristic
461C24C2×C22⋊C411yescharacteristic
462C24C2×C22⋊C411yescharacteristic
463C24#13712yes—
464C24#13712yes—
465C24C22×D411yescharacteristic
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—41no—
469C2×Q8—41no—
470C2×Q8—42no—
471C2×Q8—81no—
472C2×Q8—81no—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—22no—
476C2×D4—22no—
477C2×D4—22no—
478C2×D4—22no—
479C2×D4—22no—
480C2×D4—22no—
481C2×D4—22no—
482C2×D4—41no—
483C2×D4—41no—
484C2×D4—48no—
485C2×D4—48no—
486C2×D4#10414yes—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
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—41no—
548C22×C4—41no—
549C22×C4—41no—
550C22×C4—41no—
551C22×C4—48no—
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—41no—
561C22×C4—41no—
562C22×C4—41no—
563C22×C4—41no—
564C22×C4—48no—
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—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—82no—
580C22×C4—82no—
581C22×C4—82no—
582C22×C4—82no—
583C22×C4—82no—
584C22×C4—82no—
585C22×C4—82no—
586C22×C4—82no—
587C22×C4—84no—
588C22×C4—81no—
589C22×C4—81no—
590C22×C4—81no—
591C22×C4—81no—
592C22×C4—81no—
593C22×C4—81no—
594C22×C4—81no—
595C22×C4—81no—
596C22×C4—84no—
597C22×C4—84no—
598C22×C4—84no—
599C22×C4—84no—
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×C4C2×C22⋊C411yescharacteristic
607C22×C4C2×C22⋊C411yescharacteristic
608C22×C4C23×C411yescharacteristic
609C22×C4C22×D411yescharacteristic
610C22×C4C2×#4111yescharacteristic
611C22×C4C2×#4111yescharacteristic
612C22×C4H(5,𝔽2)11yescharacteristic
613C22×C42−1+411yescharacteristic
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—
627C2×C8—84no—
628C4⋊C4—22no—
629C4⋊C4—22no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—41no—
633C4⋊C4—41no—
634C4⋊C4—41no—
635C4⋊C4—41no—
636C4⋊C4—41no—
637C4⋊C4—41no—
638C4⋊C4—41no—
639C4⋊C4—41no—
640C4⋊C4—42no—
641C4⋊C4—42no—
642C4⋊C4—42no—
643C4⋊C4—41no—
644C4⋊C4—41no—
645C4⋊C4—42no—
646C4⋊C4—42no—
647C4⋊C4—42no—
648C4⋊C4—42no—
649C4⋊C4—81no—
650C4⋊C4—81no—
651C4⋊C4—81no—
652C4⋊C4—81no—
653C4⋊C4—81no—
654C4⋊C4—81no—
655C4⋊C4—81no—
656C4⋊C4—81no—
657C22⋊C4—22no—
658C22⋊C4—22no—
659C22⋊C4—22no—
660C22⋊C4—22no—
661C22⋊C4—22no—
662C22⋊C4—41no—
663C22⋊C4—41no—
664C22⋊C4—48no—
665C22⋊C4—48no—
666C22⋊C4—42no—
667C22⋊C4—41no—
668C22⋊C4—41no—
669C22⋊C4—41no—
670C22⋊C4—41no—
671C22⋊C4—41no—
672C22⋊C4—41no—
673C22⋊C4—41no—
674C22⋊C4—41no—
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—81no—
685C22⋊C4—81no—
686C22⋊C4—84no—
687C22⋊C4#9914yes—
688C42—22no—
689C42—22no—
690C42—41no—
691C42—41no—
692C42—42no—
693C42—42no—
694C42—84no—
695C42—84no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—22no—
705C23—22no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—24no—
719C23—24no—
720C23—22no—
721C23—22no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—42no—
733C23—42no—
734C23—42no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—42no—
744C23—42no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—81no—
750C23—81no—
751C23—81no—
752C23—81no—
753C23—81no—
754C23—81no—
755C23C2×#9912yes—
756C23#41912yes—
757C23#41912yes—
758C23C2×#10412yes—
759C23C2×#10412yes—
760C23C22×C22⋊C411yescharacteristic
761C23#54611yescharacteristic
762C23#54711yescharacteristic
763C23C2×#13711yescharacteristic
764C23C2×#13711yescharacteristic
765C23#57611yescharacteristic
766C23#57711yescharacteristic
767Q8—81no—
768Q8—81no—
769Q8—162no—
770D4—28no—
771D4—44no—
772D4—44no—
773D4—44no—
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—24no—
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—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
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—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
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—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—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
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—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—816no—
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—81no—
878C2×C4—81no—
879C2×C4—81no—
880C2×C4—162no—
881C2×C4—162no—
882C2×C4—162no—
883C2×C4—162no—
884C2×C4C2×#9912yes—
885C2×C4C2×#9912yes—
886C2×C4C2×#10412yes—
887C2×C4C4×#4111yescharacteristic
888C2×C4#52011yescharacteristic
889C2×C4#54611yescharacteristic
890C2×C4#54711yescharacteristic
891C8—42no—
892C8—81no—
893C8—81no—
894C8—81no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—22no—
900C22—21no—
901C22—21no—
902C22—22no—
903C22—21no—
904C22—21no—
905C22—22no—
906C22—21no—
907C22—21no—
908C22—22no—
909C22—22no—
910C22—21no—
911C22—21no—
912C22—22no—
913C22—22no—
914C22—22no—
915C22—22no—
916C22—22no—
917C22—22no—
918C22—22no—
919C22—44no—
920C22—44no—
921C22—44no—
922C22—44no—
923C22—41no—
924C22—41no—
925C22—41no—
926C22—41no—
927C22—41no—
928C22—41no—
929C22—41no—
930C22—41no—
931C22—41no—
932C22—41no—
933C22—41no—
934C22—41no—
935C22—41no—
936C22—41no—
937C22—41no—
938C22—82no—
939C22—82no—
940C22—82no—
941C22—82no—
942C22#150814yes—
943C22#233911yescharacteristic
944C22C22×#9911yescharacteristic
945C22#288311yescharacteristic
946C22C2×#41911yescharacteristic
947C22#289711yescharacteristic
948C22C22×#10411yescharacteristic
949C22#290111yescharacteristic
950C22#331411yescharacteristic
951C22#331611yescharacteristic
952C22#334411yescharacteristic
953C22#334611yescharacteristic
954C4—22no—
955C4—22no—
956C4—21no—
957C4—21no—
958C4—21no—
959C4—21no—
960C4—22no—
961C4—44no—
962C4—41no—
963C4—41no—
964C4—41no—
965C4—41no—
966C4—41no—
967C4—82no—
968C4—82no—
969C4—82no—
970C4—81no—
971C4—81no—
972C4—81no—
973C4—81no—
974C4—81no—
975C4—81no—
976C4—81no—
977C4—81no—
978C2—21no—
979C2—21no—
980C2—21no—
981C2—21no—
982C2—24no—
983C2—42no—
984C2—42no—
985C2—81no—
986C2C2×#150811yescharacteristic
987C2#1754711yescharacteristic
988C2#1760311yescharacteristic
989C2#1762111yescharacteristic
990C2#2247611yescharacteristic
991C2#2249711yescharacteristic
992C2#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. #9909C2semidirect
5. #9889C2semidirect
6. #9146C2semidirect
7. #9143C2semidirect
8. #9115C2semidirect
9. #9111C2semidirect
10. #8713C2semidirect
11. #8712C2semidirect
12. #8574C2semidirect
13. #8219C2semidirect
14. #8019C2semidirect
15. C2×#1294C2semidirect
16. C2×#554C4semidirect
24. #2563C4semidirect
25. #2538C4semidirect
26. #2487C4semidirect
27. #2487C4semidirect
34. #2417C4semidirect
35. #2417C4semidirect
37. D4×C4⋊C4C4semidirect
82. C2×C4⋊Q8C2×C4semidirect
89. C2×C22⋊Q8C2×C4semidirect
90. C2×C22⋊Q8C2×C4semidirect
92. C2×C4×Q8C2×C4semidirect
106. C22×C4⋊C4C2×C4semidirect
107. C22×C4⋊C4C2×C4semidirect
149. #391C2×C4semidirect
155. #389C2×C4semidirect
156. #389C2×C4semidirect
157. #389C2×C4semidirect
175. #384C2×C4semidirect
188. #380C2×C4semidirect
189. #380C2×C4semidirect
190. #380C2×C4semidirect
191. #380C2×C4semidirect
198. C4×C4⋊C4C2×C4semidirect

Maximal subgroups

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

subgroupindex
#361542
#223992
#138132
#99092
#98892
#91462
#91432
#91152
#91112
#87132
#87122
#85742
#82192
#80192
C2×#12942