Finite Group Databasebeta

← #223602

Subgroups — #223602

Order 512.

1409 conjugacy classes of subgroups.

The subgroup lattice has 1020 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36160C211yesmaximal, characteristic
2#22399C211yesmaximal, characteristic, complemented
3#13813C211yesmaximal, characteristic, complemented
4#9909C211yesmaximal, characteristic, complemented
5#9889C211yesmaximal, characteristic, complemented
6#9150C211yesmaximal, characteristic, complemented
7#9147C211yesmaximal, characteristic, complemented
8#9117C211yesmaximal, characteristic, complemented
9#9113C211yesmaximal, characteristic, complemented
10#8715C211yesmaximal, characteristic, complemented
11#8715C211yesmaximal, characteristic, complemented
12#8573C211yesmaximal, characteristic, complemented
13#8218C211yesmaximal, characteristic, complemented
14#8020C211yesmaximal, characteristic, complemented
15#8012C211yesmaximal, characteristic, complemented
16C2×#555C411yescharacteristic, complemented
17C22×C4×D4C2211yescharacteristic
18C2×#435—21no—
19C2×#407C2211yescharacteristic
20C22×C22⋊C8C2211yescharacteristic
21#2857C2211yescharacteristic
22#2847C2211yescharacteristic
23#2847C2211yescharacteristic
24#2563C411yescharacteristic, complemented
25#2537C411yescharacteristic, complemented
26#2485C411yescharacteristic, complemented
27#2485C411yescharacteristic, complemented
28#2472—21no—
29#2472—21no—
30#2459—21no—
31#2459—21no—
32#2420—21no—
33#2414C411yescharacteristic, complemented
34#2414C411yescharacteristic, complemented
35#2408—21no—
36#2363—21no—
37#2354C411yescharacteristic, complemented
38#2352—21no—
39C4×#121C2211yescharacteristic
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×#327C2211yescharacteristic
54C2×#327C2211yescharacteristic
55C2×#327C2211yescharacteristic
56C2×#327C2211yescharacteristic
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#555—44no—
82C2×C4⋊Q8C2×C411yescharacteristic, complemented
83C2×#124—21no—
84C2×#124—21no—
85C2×C22⋊Q8—21no—
86C2×#121—21no—
87C2×#121—21no—
88C2×#121C2×C411yescharacteristic
89C2×#121C2×C411yescharacteristic
90C2×#121C2×C411yescharacteristic, complemented
91C2×#121C2×C411yescharacteristic, complemented
92C2×#121C2311yescharacteristic
93C2×#120—21no—
94C2×#120—21no—
95C2×C4×D4—21no—
96C2×C4×D4—44no—
97C2×C4×D4C2×C411yescharacteristic
98C2×C4×D4C2×C411yescharacteristic
99C2×C4×D4C2×C411yescharacteristic
100C2×C4×D4C2×C411yescharacteristic
101C2×C4×D4C2×C411yescharacteristic, complemented
102C2×C4×D4D411yescharacteristic
103C2×C4×D4D411yescharacteristic
104C2×C4×D4D411yescharacteristic
105C2×C4×D4D411yescharacteristic
106C2×#117—21no—
107C2×#117C2×C411yescharacteristic
108C2×#117C2×C411yescharacteristic
109C2×#117C2×C411yescharacteristic, complemented
110C2×#117C2×C411yescharacteristic, complemented
111C22×C4⋊C4D411yescharacteristic
112C22×C22⋊C4—21no—
113C22×C22⋊C4—21no—
114C22×C22⋊C4—21no—
115C22×C22⋊C4D411yescharacteristic
116C22×C22⋊C4D411yescharacteristic
117C22×C42—21no—
118C22×C42—21no—
119C22×C42C2311yescharacteristic
120#435—44no—
121C2×C4⋊C8—21no—
122#407—22no—
123#407—41no—
124C2×C22⋊C8—22no—
125C2×C22⋊C8—21no—
126C2×C22⋊C8—21no—
127C2×C22⋊C8—21no—
128C2×C22⋊C8—21no—
129C2×C22⋊C8—21no—
130C2×C22⋊C8—21no—
131C2×C22⋊C8—41no—
132C2×C22⋊C8C2311yescharacteristic
133C2×C22⋊C8C2311yescharacteristic
134C2×C22⋊C8C2311yescharacteristic
135C2×C22⋊C8C2311yescharacteristic
136C2×#97—21no—
137#397—21no—
138#397—21no—
139#394—21no—
140#394—21no—
141#394—21no—
142#394—21no—
143#394—21no—
144#394—21no—
145#393—21no—
146#393—21no—
147#392—21no—
148#392—21no—
149#391—21no—
150#390—21no—
151#390—21no—
152#390—21no—
153#390—21no—
154#390C2×C411yescharacteristic, complemented
155#389—21no—
156#389C2×C411yescharacteristic, complemented
157#389C2×C411yescharacteristic, complemented
158#389C2×C411yescharacteristic, complemented
159#388—21no—
160#388—21no—
161#388—21no—
162#388—21no—
163#388—21no—
164#388—21no—
165#388—21no—
166#387—21no—
167#387—21no—
168#386—28no—
169#386—21no—
170#386—21no—
171#386—21no—
172#386—21no—
173#386—21no—
174#386—21no—
175#386—21no—
176#384C2×C411yescharacteristic, complemented
177#382—21no—
178#381—21no—
179#381—21no—
180#380—21no—
181#380—21no—
182#380C2×C411yescharacteristic
183#380C2×C411yescharacteristic
184#380C2×C411yescharacteristic
185#380C2×C411yescharacteristic
186#380C2×C411yescharacteristic, complemented
187#380C2×C411yescharacteristic, complemented
188#380C2×C411yescharacteristic, complemented
189#380C2×C411yescharacteristic, complemented
190#380C2311yescharacteristic
191#380C2311yescharacteristic
192#380C2311yescharacteristic
193#379—21no—
194#379—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#327—22no—
220#327—22no—
221#327—41no—
222#327—41no—
223C25C2×D411yescharacteristic
224C25C2×D411yescharacteristic
225C22×Q8—21no—
226C22×D4—24no—
227C22×D4—21no—
228C22×D4—21no—
229C22×D4—21no—
230C22×D4—21no—
231C22×D4—21no—
232C22×D4—41no—
233C22×D4—41no—
234C22×D4—42no—
235C22×D4C22⋊C411yescharacteristic
236C22×D4C22⋊C411yescharacteristic
237C22×D4C22⋊C411yescharacteristic
238C22×D4C22⋊C411yescharacteristic
239C22×D4C22×C411yescharacteristic
240C23×C4—21no—
241C23×C4—21no—
242C23×C4—21no—
243C23×C4—21no—
244C23×C4—21no—
245C23×C4—21no—
246C23×C4—21no—
247C23×C4—21no—
248C23×C4—21no—
249C23×C4—21no—
250C23×C4—21no—
251C23×C4—21no—
252C23×C4—24no—
253C23×C4—21no—
254C23×C4—42no—
255C23×C4—42no—
256C23×C4—42no—
257C23×C4—42no—
258C23×C4—42no—
259C23×C4—42no—
260C23×C4—81no—
261C23×C4—81no—
262C23×C4—81no—
263C23×C4—81no—
264C23×C4C22×C411yescharacteristic
265C23×C4C22×C411yescharacteristic
266C23×C4C22×C411yescharacteristic
267C23×C4C22×C411yescharacteristic
268C23×C4C2×D411yescharacteristic
269C23×C4C2×D411yescharacteristic
270C23×C4C2×D411yescharacteristic
271C23×C4C2×D411yescharacteristic
272C23×C4C2×D411yescharacteristic
273C23×C4C2×D411yescharacteristic
274C23×C4C2×D411yescharacteristic
275C23×C4C2×D411yescharacteristic
276C23×C4C2411yescharacteristic
277C2×M16—42no—
278C2×M16—42no—
279C2×M16—81no—
280C22×C8—21no—
281C22×C8—21no—
282C22×C8—21no—
283C22×C8—21no—
284C22×C8—42no—
285C22×C8—42no—
286C22×C8—81no—
287C4⋊Q8—42no—
288#124—44no—
289#124—44no—
290C22⋊Q8—81no—
291C22⋊Q8—81no—
292#121—21no—
293#121—21no—
294#121—21no—
295#121—21no—
296#121—42no—
297#121—44no—
298#121—44no—
299#121—42no—
300#121—81no—
301#121—81no—
302#120—81no—
303#120—81no—
304#120—81no—
305#120—81no—
306C4×D4—24no—
307C4×D4—24no—
308C4×D4—42no—
309C4×D4—42no—
310C4×D4—42no—
311C4×D4—42no—
312C4×D4—42no—
313C4×D4—42no—
314C4×D4—42no—
315C4×D4—42no—
316C4×D4—42no—
317#117—44no—
318#117—42no—
319#117—42no—
320#117—81no—
321#117—81no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—42no—
329C2×C4⋊C4C22⋊C411yescharacteristic
330C2×C4⋊C4C22⋊C411yescharacteristic
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×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
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—21no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—21no—
354C2×C22⋊C4—21no—
355C2×C22⋊C4—24no—
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—42no—
368C2×C22⋊C4—42no—
369C2×C22⋊C4—42no—
370C2×C22⋊C4—42no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4—81no—
373C2×C22⋊C4—81no—
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×C22⋊C4C22⋊C411yescharacteristic
382C2×C42—21no—
383C2×C42—21no—
384C2×C42—21no—
385C2×C42—21no—
386C2×C42—21no—
387C2×C42—42no—
388C2×C42—42no—
389C2×C42—42no—
390C2×C42—42no—
391C2×C42—42no—
392C2×C42—81no—
393C2×C42—81no—
394C2×C42C22×C411yescharacteristic
395C2×C42C22×C411yescharacteristic
396C2×C42C2×D411yescharacteristic
397C2×C42C2×D411yescharacteristic
398C4⋊C8—42no—
399C22⋊C8—21no—
400C22⋊C8—21no—
401C22⋊C8—21no—
402C22⋊C8—21no—
403C22⋊C8—21no—
404C22⋊C8—21no—
405C22⋊C8—21no—
406C22⋊C8—42no—
407C22⋊C8—42no—
408C22⋊C8—42no—
409C22⋊C8—42no—
410C22⋊C8—81no—
411C22⋊C8—81no—
412C22⋊C8#4112yes—
413#97—42no—
414#95—24no—
415#95—24no—
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—21no—
437#95—21no—
438#95—42no—
439#95—42no—
440#95—42no—
441#95—81no—
442#95#4112yes—
443C24—21no—
444C24—21no—
445C24—22no—
446C24—22no—
447C24—21no—
448C24—21no—
449C24—21no—
450C24—21no—
451C24—22no—
452C24—21no—
453C24—21no—
454C24—21no—
455C24—21no—
456C24—21no—
457C24—21no—
458C24—21no—
459C24—41no—
460C24—41no—
461C24—41no—
462C24—41no—
463C24—41no—
464C24C2×C22⋊C411yescharacteristic
465C24C2×C22⋊C411yescharacteristic
466C24C2×C22⋊C411yescharacteristic
467C24C2×C22⋊C411yescharacteristic
468C24C22×D411yescharacteristic
469C2×Q8—42no—
470C2×Q8—81no—
471C2×Q8—81no—
472C2×D4—22no—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—22no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—22no—
479C2×D4—41no—
480C2×D4—41no—
481C2×D4—41no—
482C2×D4—41no—
483C2×D4—41no—
484C2×D4—41no—
485C2×D4—41no—
486C2×D4—41no—
487C2×D4—48no—
488C2×D4—48no—
489C2×D4—41no—
490C2×D4—41no—
491C2×D4—41no—
492C2×D4—41no—
493C2×D4—41no—
494C2×D4—41no—
495C2×D4—42no—
496C2×D4—42no—
497C2×D4—42no—
498C2×D4—42no—
499C2×D4—81no—
500C2×D4—81no—
501C2×D4—81no—
502C2×D4—81no—
503C2×D4—81no—
504C2×D4—81no—
505C2×D4—81no—
506C2×D4—81no—
507C2×D4#10414yes—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
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—21no—
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—21no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
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—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
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—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—48no—
574C22×C4—41no—
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—48no—
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—42no—
598C22×C4—82no—
599C22×C4—82no—
600C22×C4—82no—
601C22×C4—82no—
602C22×C4—82no—
603C22×C4—82no—
604C22×C4—82no—
605C22×C4—82no—
606C22×C4—84no—
607C22×C4—84no—
608C22×C4—84no—
609C22×C4—84no—
610C22×C4—84no—
611C22×C4C2×C22⋊C411yescharacteristic
612C22×C4C2×C22⋊C411yescharacteristic
613C22×C4C2×C22⋊C411yescharacteristic
614C22×C4C2×C22⋊C411yescharacteristic
615C22×C4C2×C22⋊C411yescharacteristic
616C22×C4C2×C22⋊C411yescharacteristic
617C22×C4C2×C22⋊C411yescharacteristic
618C22×C4C2×C22⋊C411yescharacteristic
619C22×C4C23×C411yescharacteristic
620C22×C4C22×D411yescharacteristic
621C22×C4C2×#4111yescharacteristic
622C22×C4C2×#4111yescharacteristic
623C22×C4H(5,𝔽2)11yescharacteristic
624C22×C42−1+411yescharacteristic
625M16—84no—
626C2×C8—22no—
627C2×C8—41no—
628C2×C8—41no—
629C2×C8—41no—
630C2×C8—41no—
631C2×C8—41no—
632C2×C8—41no—
633C2×C8—41no—
634C2×C8—41no—
635C2×C8—41no—
636C2×C8—41no—
637C2×C8—41no—
638C2×C8—84no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—41no—
644C4⋊C4—41no—
645C4⋊C4—41no—
646C4⋊C4—41no—
647C4⋊C4—41no—
648C4⋊C4—41no—
649C4⋊C4—41no—
650C4⋊C4—41no—
651C4⋊C4—42no—
652C4⋊C4—42no—
653C4⋊C4—42no—
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—42no—
666C22⋊C4—42no—
667C22⋊C4—48no—
668C22⋊C4—42no—
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—41no—
679C22⋊C4—41no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—81no—
683C22⋊C4—81no—
684C22⋊C4—81no—
685C22⋊C4—81no—
686C22⋊C4—81no—
687C22⋊C4—81no—
688C22⋊C4—81no—
689C22⋊C4—81no—
690C22⋊C4—81no—
691C22⋊C4—81no—
692C22⋊C4—81no—
693C22⋊C4—84no—
694C22⋊C4#9914yes—
695C42—22no—
696C42—22no—
697C42—41no—
698C42—41no—
699C42—42no—
700C42—42no—
701C42—42no—
702C42—81no—
703C42—81no—
704C42—84no—
705C42—84no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—24no—
711C23—24no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
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—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—42no—
748C23—42no—
749C23—42no—
750C23—42no—
751C23—42no—
752C23—42no—
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—41no—
766C23—41no—
767C23—41no—
768C23—81no—
769C23—81no—
770C23—81no—
771C23—81no—
772C23—81no—
773C23—81no—
774C23C2×#9912yes—
775C23C2×#10412yes—
776C23C2×#10412yes—
777C23C22×C22⋊C411yescharacteristic
778C23#54611yescharacteristic
779C23#54711yescharacteristic
780C23#57511yescharacteristic
781C23#57511yescharacteristic
782C23#57611yescharacteristic
783C23#57711yescharacteristic
784Q8—162no—
785D4—44no—
786D4—44no—
787D4—44no—
788D4—44no—
789D4—81no—
790D4—81no—
791D4—81no—
792D4—81no—
793D4—81no—
794D4—81no—
795D4—162no—
796D4—162no—
797D4—162no—
798D4—162no—
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—21no—
808C2×C4—21no—
809C2×C4—24no—
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—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—81no—
880C2×C4—81no—
881C2×C4—81no—
882C2×C4—81no—
883C2×C4—81no—
884C2×C4—81no—
885C2×C4—81no—
886C2×C4—81no—
887C2×C4—84no—
888C2×C4—81no—
889C2×C4—81no—
890C2×C4—816no—
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—81no—
903C2×C4C2×#9912yes—
904C2×C4C2×#9912yes—
905C2×C4C2×#10412yes—
906C2×C4C4×#4111yescharacteristic
907C2×C4#52011yescharacteristic
908C2×C4#54611yescharacteristic
909C2×C4#54711yescharacteristic
910C8—42no—
911C8—81no—
912C8—81no—
913C8—81no—
914C22—21no—
915C22—21no—
916C22—21no—
917C22—21no—
918C22—21no—
919C22—21no—
920C22—21no—
921C22—21no—
922C22—21no—
923C22—21no—
924C22—21no—
925C22—21no—
926C22—22no—
927C22—22no—
928C22—22no—
929C22—22no—
930C22—22no—
931C22—22no—
932C22—22no—
933C22—22no—
934C22—22no—
935C22—44no—
936C22—44no—
937C22—44no—
938C22—44no—
939C22—41no—
940C22—41no—
941C22—41no—
942C22—41no—
943C22—41no—
944C22—41no—
945C22—41no—
946C22—41no—
947C22—41no—
948C22—41no—
949C22—41no—
950C22—41no—
951C22—41no—
952C22—41no—
953C22—41no—
954C22—41no—
955C22—41no—
956C22—41no—
957C22—41no—
958C22—82no—
959C22—82no—
960C22—82no—
961C22—82no—
962C22—81no—
963C22—81no—
964C22—81no—
965C22—81no—
966C22—81no—
967C22—81no—
968C22—81no—
969C22#233911yescharacteristic
970C22C22×#9911yescharacteristic
971C22#288311yescharacteristic
972C22#289611yescharacteristic
973C22#289711yescharacteristic
974C22C22×#10411yescharacteristic
975C22#290111yescharacteristic
976C22#331911yescharacteristic
977C22#332111yescharacteristic
978C22#334711yescharacteristic
979C22#334811yescharacteristic
980C4—22no—
981C4—22no—
982C4—21no—
983C4—21no—
984C4—21no—
985C4—21no—
986C4—22no—
987C4—44no—
988C4—41no—
989C4—41no—
990C4—41no—
991C4—41no—
992C4—41no—
993C4—82no—
994C4—82no—
995C4—82no—
996C4—81no—
997C4—81no—
998C4—81no—
999C4—81no—
1000C4—81no—
1001C4—81no—
1002C4—81no—
1003C2—21no—
1004C2—21no—
1005C2—21no—
1006C2—21no—
1007C2—42no—
1008C2—42no—
1009C2—42no—
1010C2—81no—
1011C2—161no—
1012C2#1754211yescharacteristic
1013C2#1754711yescharacteristic
1014C2#1760311yescharacteristic
1015C2#1762911yescharacteristic
1016C2#2247611yescharacteristic
1017C2#2249211yescharacteristic
1018C2#2250511yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radical#36160C2
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
2. #22399C2semidirect
3. #13813C2semidirect
4. #9909C2semidirect
5. #9889C2semidirect
6. #9150C2semidirect
7. #9147C2semidirect
8. #9117C2semidirect
9. #9113C2semidirect
10. #8715C2semidirect
11. #8715C2semidirect
12. #8573C2semidirect
13. #8218C2semidirect
14. #8020C2semidirect
15. #8012C2semidirect
16. C2×#555C4semidirect
24. #2563C4semidirect
25. #2537C4semidirect
26. #2485C4semidirect
27. #2485C4semidirect
33. #2414C4semidirect
34. #2414C4semidirect
37. #2354C4semidirect
82. C2×C4⋊Q8C2×C4semidirect
90. C2×#121C2×C4semidirect
91. C2×#121C2×C4semidirect
101. C2×C4×D4C2×C4semidirect
109. C2×#117C2×C4semidirect
110. C2×#117C2×C4semidirect
154. #390C2×C4semidirect
156. #389C2×C4semidirect
157. #389C2×C4semidirect
158. #389C2×C4semidirect
176. #384C2×C4semidirect
186. #380C2×C4semidirect
187. #380C2×C4semidirect
188. #380C2×C4semidirect
189. #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
#361602
#223992
#138132
#99092
#98892
#91502
#91472
#91172
#91132
#87152
#85732
#82182
#80202
#80122