Finite Group Databasebeta

← #223607

Subgroups — #223607

Order 512.

1166 conjugacy classes of subgroups.

The subgroup lattice has 895 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36208C211yesmaximal, characteristic
2#22553C211yesmaximal, characteristic, complemented
3#13814C211yesmaximal, characteristic, complemented
4#9910C211yesmaximal, characteristic, complemented
5#9887C211yesmaximal, characteristic, complemented
6#9148C211yesmaximal, characteristic, complemented
7#9147C211yesmaximal, characteristic
8#9117C211yesmaximal, characteristic
9#9114C211yesmaximal, characteristic, complemented
10#8717C211yesmaximal, characteristic, complemented
11#8715C211yesmaximal, characteristic, complemented
12#8571C211yesmaximal, characteristic, complemented
13#8218C211yesmaximal, characteristic, complemented
14#8020C211yesmaximal, characteristic, complemented
15#8014C211yesmaximal, characteristic, complemented
16C2×#431C2211yescharacteristic
17C2×#407C2211yescharacteristic
18#2854C2211yescharacteristic
19#2851C2211yescharacteristic
20#2847C2211yescharacteristic
21#2576—21no—
22#2518—21no—
23#2516—21no—
24#2510—21no—
25#2500C411yescharacteristic, complemented
26#2497C411yescharacteristic, complemented
27#2494C411yescharacteristic, complemented
28#2490C411yescharacteristic, complemented
29#2441C411yescharacteristic, complemented
30#2422C411yescharacteristic, complemented
31#2418—21no—
32#2411—21no—
33#2374—21no—
34#2363C411yescharacteristic, complemented
35#2359—21no—
36#2347C411yescharacteristic, complemented
37C4×#121C2211yescharacteristic
38C2×#385—21no—
39#2285C2211yescharacteristic
40#2280C2211yescharacteristic
41C2×C4×C4⋊C4C2211yescharacteristic
42C2×C4×C22⋊C4—21no—
43C2×C4×C22⋊C4C2211yescharacteristic
44C22×#95C2211yescharacteristic
45#1924—21no—
46#1923—21no—
47#1851—21no—
48#1817C2211yescharacteristic
49#1797C2211yescharacteristic
50#1779C2211yescharacteristic
51#1753—21no—
52#1749C2211yescharacteristic
53C2×#327C2211yescharacteristic
54C2×#327C2211yescharacteristic
55C2×#327C2211yescharacteristic
56C2×#327C2211yescharacteristic
57#1436—21no—
58#1436—21no—
59C4⋊#95C2211yescharacteristic
60#1434C2211yescharacteristic
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
75C24×C4—21no—
76C24×C4C2311yescharacteristic
77C22×M16—21no—
78C2×#125C2×C411yescharacteristic, complemented
79C2×#123—21no—
80C2×#123—21no—
81C2×#121C2×C411yescharacteristic
82C2×#121C2×C411yescharacteristic
83C2×#121C2311yescharacteristic
84C2×#120—21no—
85C2×C4×D4—21no—
86C2×C4×D4C2×C411yescharacteristic, complemented
87C2×#117—21no—
88C2×#117C2×C411yescharacteristic
89C2×#117C2×C411yescharacteristic
90C22×C4⋊C4—21no—
91C22×C4⋊C4—21no—
92C22×C22⋊C4—21no—
93C22×C22⋊C4D411yescharacteristic
94C22×C22⋊C4D411yescharacteristic
95C22×C42—21no—
96C22×C42—21no—
97C22×C42C2311yescharacteristic
98C22×C42C2311yescharacteristic
99#431—22no—
100#431—41no—
101C2×C4⋊C8—21no—
102C2×C4⋊C8—21no—
103#407—22no—
104#407—41no—
105C2×C22⋊C8—21no—
106C2×C22⋊C8—21no—
107C2×C22⋊C8—21no—
108C2×C22⋊C8C2311yescharacteristic
109C2×C22⋊C8C2311yescharacteristic
110C2×C22⋊C8C2311yescharacteristic
111C2×C22⋊C8C2311yescharacteristic
112C2×#97—21no—
113C2×C4×C8—21no—
114#401—21no—
115#400—21no—
116#399—21no—
117#397—21no—
118#397—21no—
119#397—21no—
120#396—21no—
121#396—21no—
122#394—21no—
123#394—21no—
124#394—21no—
125#394—21no—
126#390—21no—
127#390—21no—
128#390C2×C411yescharacteristic, complemented
129#390C2×C411yescharacteristic, complemented
130#390C2×C411yescharacteristic, complemented
131#389—21no—
132#389C2×C411yescharacteristic, complemented
133#389C2×C411yescharacteristic, complemented
134#389C2×C411yescharacteristic, complemented
135#389C2×C411yescharacteristic, complemented
136#389C2×C411yescharacteristic, complemented
137#388—21no—
138#388—21no—
139#388—21no—
140#388—21no—
141#388—21no—
142#388—21no—
143#388—21no—
144#388—21no—
145#388—21no—
146#388—21no—
147#388—21no—
148#387—21no—
149#387—21no—
150#387—21no—
151#387—21no—
152#387—21no—
153#386—21no—
154#386—21no—
155#386—21no—
156#386—21no—
157#386—21no—
158#386—21no—
159#385—28no—
160#385—21no—
161#385—21no—
162#385—21no—
163#384C2×C411yescharacteristic, complemented
164#384C2×C411yescharacteristic, complemented
165#383—21no—
166#382—21no—
167#382C2×C411yescharacteristic, complemented
168#381—21no—
169#380—21no—
170#380C2×C411yescharacteristic
171#380C2×C411yescharacteristic
172#380C2×C411yescharacteristic
173#380C2×C411yescharacteristic
174#380C2311yescharacteristic
175#380C2311yescharacteristic
176#380C2311yescharacteristic
177#379—21no—
178C4×C4⋊C4—21no—
179C4×C4⋊C4—21no—
180C4×C4⋊C4—22no—
181C4×C4⋊C4—41no—
182C4×C4⋊C4C2×C411yescharacteristic, complemented
183C4×C4⋊C4C2×C411yescharacteristic, complemented
184C4×C4⋊C4C2×C411yescharacteristic, complemented
185C4×C22⋊C4—21no—
186C4×C22⋊C4—21no—
187C4×C22⋊C4—21no—
188C4×C22⋊C4—21no—
189C4×C22⋊C4—44no—
190C4×C22⋊C4C2×C411yescharacteristic
191C4×C22⋊C4C2×C411yescharacteristic
192C4×C22⋊C4C2×C411yescharacteristic
193C4×C22⋊C4C2×C411yescharacteristic
194C4×C22⋊C4D411yescharacteristic
195C4×C22⋊C4D411yescharacteristic
196C4×C22⋊C4D411yescharacteristic
197C4×C22⋊C4D411yescharacteristic
198C2×#95—21no—
199C2×#95—21no—
200C2×#95—22no—
201C2×#95—21no—
202C2×#95—21no—
203C2×#95—21no—
204C2×#95—21no—
205C2×#95—41no—
206C2×#95D411yescharacteristic
207C2×#95D411yescharacteristic
208C2×#95C2311yescharacteristic
209C2×#95C2311yescharacteristic
210C2×#95C2311yescharacteristic
211C2×#95C2311yescharacteristic
212#336—21no—
213#336—21no—
214#336—21no—
215#336—21no—
216#327—22no—
217#327—22no—
218#327—41no—
219#327—41no—
220C25C2×D411yescharacteristic
221C22×D4—21no—
222C22×D4—21no—
223C22×D4—21no—
224C22×D4C22×C411yescharacteristic
225C23×C4—21no—
226C23×C4—21no—
227C23×C4—21no—
228C23×C4—21no—
229C23×C4—21no—
230C23×C4—21no—
231C23×C4—21no—
232C23×C4—21no—
233C23×C4—24no—
234C23×C4—21no—
235C23×C4—42no—
236C23×C4—42no—
237C23×C4—42no—
238C23×C4—42no—
239C23×C4—42no—
240C23×C4—81no—
241C23×C4—81no—
242C23×C4—81no—
243C23×C4C22×C411yescharacteristic
244C23×C4C22×C411yescharacteristic
245C23×C4C2×D411yescharacteristic
246C23×C4C2×D411yescharacteristic
247C23×C4C2×D411yescharacteristic
248C23×C4C2×D411yescharacteristic
249C23×C4C2×D411yescharacteristic
250C23×C4C2×D411yescharacteristic
251C23×C4C2×D411yescharacteristic
252C23×C4C2411yescharacteristic
253C2×M16—42no—
254C2×M16—42no—
255C2×M16—81no—
256C22×C8—21no—
257C22×C8—21no—
258C22×C8—21no—
259C22×C8—21no—
260#125—81no—
261#123—42no—
262#123—42no—
263#123—44no—
264#121—21no—
265#121—21no—
266#121—21no—
267#121—21no—
268#121—42no—
269#121—81no—
270#120—81no—
271#120—81no—
272C4×D4—81no—
273C4×D4—81no—
274C4×D4—81no—
275#117—42no—
276#117—81no—
277#117—81no—
278#117—81no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—42no—
293C2×C4⋊C4—42no—
294C2×C4⋊C4—81no—
295C2×C4⋊C4—81no—
296C2×C4⋊C4C22×C411yescharacteristic
297C2×C4⋊C4C22×C411yescharacteristic
298C2×C4⋊C4C22×C411yescharacteristic
299C2×C4⋊C4C22×C411yescharacteristic
300C2×C4⋊C4C22×C411yescharacteristic
301C2×C4⋊C4C22×C411yescharacteristic
302C2×C4⋊C4C22×C411yescharacteristic
303C2×C22⋊C4—22no—
304C2×C22⋊C4—22no—
305C2×C22⋊C4—24no—
306C2×C22⋊C4—24no—
307C2×C22⋊C4—21no—
308C2×C22⋊C4—21no—
309C2×C22⋊C4—21no—
310C2×C22⋊C4—21no—
311C2×C22⋊C4—21no—
312C2×C22⋊C4—21no—
313C2×C22⋊C4—21no—
314C2×C22⋊C4—21no—
315C2×C22⋊C4—21no—
316C2×C22⋊C4—21no—
317C2×C22⋊C4—21no—
318C2×C22⋊C4—21no—
319C2×C22⋊C4—21no—
320C2×C22⋊C4—21no—
321C2×C22⋊C4—21no—
322C2×C22⋊C4—21no—
323C2×C22⋊C4—21no—
324C2×C22⋊C4—21no—
325C2×C22⋊C4—21no—
326C2×C22⋊C4—42no—
327C2×C22⋊C4—42no—
328C2×C22⋊C4C22⋊C411yescharacteristic
329C2×C22⋊C4C22⋊C411yescharacteristic
330C2×C22⋊C4C22⋊C411yescharacteristic
331C2×C22⋊C4C22⋊C411yescharacteristic
332C2×C22⋊C4C22⋊C411yescharacteristic
333C2×C22⋊C4C22⋊C411yescharacteristic
334C2×C22⋊C4C22⋊C411yescharacteristic
335C2×C22⋊C4C22⋊C411yescharacteristic
336C2×C42—21no—
337C2×C42—21no—
338C2×C42—21no—
339C2×C42—21no—
340C2×C42—21no—
341C2×C42—21no—
342C2×C42—21no—
343C2×C42—21no—
344C2×C42—21no—
345C2×C42—42no—
346C2×C42—42no—
347C2×C42—42no—
348C2×C42—42no—
349C2×C42—81no—
350C2×C42—81no—
351C2×C42—81no—
352C2×C42C22×C411yescharacteristic
353C2×C42C22×C411yescharacteristic
354C2×C42C22×C411yescharacteristic
355C2×C42C22×C411yescharacteristic
356C2×C42C2×D411yescharacteristic
357C2×C42C2×D411yescharacteristic
358C2×C42C2×D411yescharacteristic
359C2×C42C2×D411yescharacteristic
360C4⋊C8—42no—
361C4⋊C8—81no—
362C22⋊C8—21no—
363C22⋊C8—21no—
364C22⋊C8—21no—
365C22⋊C8—21no—
366C22⋊C8—21no—
367C22⋊C8—21no—
368C22⋊C8—21no—
369C22⋊C8—42no—
370C22⋊C8—42no—
371C22⋊C8—81no—
372C22⋊C8#4112yes—
373#97—81no—
374C4×C8—42no—
375#95—24no—
376#95—24no—
377#95—21no—
378#95—21no—
379#95—21no—
380#95—21no—
381#95—21no—
382#95—21no—
383#95—21no—
384#95—21no—
385#95—21no—
386#95—21no—
387#95—21no—
388#95—21no—
389#95—21no—
390#95—21no—
391#95—21no—
392#95—21no—
393#95—21no—
394#95—21no—
395#95—21no—
396#95—21no—
397#95—21no—
398#95—21no—
399#95—21no—
400#95—21no—
401#95—42no—
402#95—42no—
403#95—42no—
404#95—81no—
405#95C22⋊C411yescharacteristic
406#95C22⋊C411yescharacteristic
407#95C22⋊C411yescharacteristic
408#95C22⋊C411yescharacteristic
409#95C22⋊C411yescharacteristic
410#95C22⋊C411yescharacteristic
411#95C22⋊C411yescharacteristic
412#95C22⋊C411yescharacteristic
413#95#4112yes—
414C24—21no—
415C24—21no—
416C24—22no—
417C24—22no—
418C24—21no—
419C24—21no—
420C24—21no—
421C24—21no—
422C24—21no—
423C24—41no—
424C24—41no—
425C24C2×C22⋊C411yescharacteristic
426C24C2×C22⋊C411yescharacteristic
427C24C22×D411yescharacteristic
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—41no—
431C2×D4—41no—
432C2×D4—41no—
433C2×D4—41no—
434C2×D4—41no—
435C2×D4—41no—
436C2×D4—41no—
437C2×D4—41no—
438C2×D4—42no—
439C2×D4—42no—
440C2×D4—81no—
441C2×D4—81no—
442C2×D4—81no—
443C2×D4—81no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4—41no—
486C22×C4—41no—
487C22×C4—41no—
488C22×C4—41no—
489C22×C4—41no—
490C22×C4—41no—
491C22×C4—41no—
492C22×C4—41no—
493C22×C4—41no—
494C22×C4—41no—
495C22×C4—48no—
496C22×C4—41no—
497C22×C4—41no—
498C22×C4—41no—
499C22×C4—41no—
500C22×C4—41no—
501C22×C4—41no—
502C22×C4—41no—
503C22×C4—41no—
504C22×C4—41no—
505C22×C4—41no—
506C22×C4—41no—
507C22×C4—48no—
508C22×C4—41no—
509C22×C4—41no—
510C22×C4—41no—
511C22×C4—41no—
512C22×C4—41no—
513C22×C4—41no—
514C22×C4—41no—
515C22×C4—41no—
516C22×C4—41no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4—42no—
520C22×C4—81no—
521C22×C4—81no—
522C22×C4—82no—
523C22×C4—82no—
524C22×C4—82no—
525C22×C4—82no—
526C22×C4—84no—
527C22×C4—84no—
528C22×C4—84no—
529C22×C4—84no—
530C22×C4—84no—
531C22×C4C2×C22⋊C411yescharacteristic
532C22×C4C2×C22⋊C411yescharacteristic
533C22×C4C2×C22⋊C411yescharacteristic
534C22×C4C2×C22⋊C411yescharacteristic
535C22×C4C2×C22⋊C411yescharacteristic
536C22×C4C2×C22⋊C411yescharacteristic
537C22×C4C2×C22⋊C411yescharacteristic
538C22×C4C2×C22⋊C411yescharacteristic
539C22×C4C2×C22⋊C411yescharacteristic
540C22×C4C2×C22⋊C411yescharacteristic
541C22×C4AGL(1,ℤ/8)12yes—
542C22×C4#13712yes—
543C22×C4C23×C411yescharacteristic
544C22×C4C22×D411yescharacteristic
545C22×C4C2×#4111yescharacteristic
546C22×C4C2×#4111yescharacteristic
547C22×C4H(5,𝔽2)11yescharacteristic
548C22×C42−1+411yescharacteristic
549M16—84no—
550C2×C8—22no—
551C2×C8—41no—
552C2×C8—41no—
553C2×C8—41no—
554C2×C8—41no—
555C2×C8—41no—
556C2×C8—41no—
557C2×C8—41no—
558C2×C8—41no—
559C2×C8—41no—
560C2×C8—41no—
561C2×C8—41no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—41no—
565C4⋊C4—41no—
566C4⋊C4—41no—
567C4⋊C4—41no—
568C4⋊C4—41no—
569C4⋊C4—41no—
570C4⋊C4—48no—
571C4⋊C4—42no—
572C4⋊C4—42no—
573C4⋊C4—42no—
574C4⋊C4—42no—
575C4⋊C4—81no—
576C4⋊C4—81no—
577C4⋊C4—81no—
578C4⋊C4—81no—
579C4⋊C4—81no—
580C4⋊C4—81no—
581C4⋊C4—81no—
582C4⋊C4—84no—
583C22⋊C4—22no—
584C22⋊C4—22no—
585C22⋊C4—22no—
586C22⋊C4—22no—
587C22⋊C4—22no—
588C22⋊C4—22no—
589C22⋊C4—22no—
590C22⋊C4—42no—
591C22⋊C4—48no—
592C22⋊C4—41no—
593C22⋊C4—41no—
594C22⋊C4—41no—
595C22⋊C4—41no—
596C22⋊C4—41no—
597C22⋊C4—41no—
598C22⋊C4—42no—
599C22⋊C4—42no—
600C22⋊C4—41no—
601C22⋊C4—41no—
602C22⋊C4—42no—
603C22⋊C4—42no—
604C22⋊C4—42no—
605C22⋊C4—81no—
606C22⋊C4—81no—
607C22⋊C4—81no—
608C22⋊C4—81no—
609C22⋊C4—81no—
610C22⋊C4—81no—
611C22⋊C4—81no—
612C22⋊C4—81no—
613C22⋊C4—81no—
614C22⋊C4#10414yes—
615C42—21no—
616C42—21no—
617C42—21no—
618C42—21no—
619C42—21no—
620C42—21no—
621C42—21no—
622C42—21no—
623C42—41no—
624C42—41no—
625C42—41no—
626C42—41no—
627C42—42no—
628C42—81no—
629C42—81no—
630C42—81no—
631C42—81no—
632C42—84no—
633C42—84no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—24no—
639C23—24no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23#41012yes—
674C23C2×#10412yes—
675C23C22×C22⋊C411yescharacteristic
676C23#54611yescharacteristic
677C23#54711yescharacteristic
678C23C2×AGL(1,ℤ/8)11yescharacteristic
679C23C2×#13711yescharacteristic
680C23#57611yescharacteristic
681C23#57711yescharacteristic
682D4—81no—
683D4—81no—
684D4—81no—
685D4—81no—
686D4—81no—
687D4—81no—
688D4—162no—
689D4—162no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—24no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—81no—
776C2×C4—81no—
777C2×C4—81no—
778C2×C4—81no—
779C2×C4—81no—
780C2×C4—81no—
781C2×C4—816no—
782C2×C4—81no—
783C2×C4—81no—
784C2×C4—81no—
785C2×C4—81no—
786C2×C4—81no—
787C2×C4—81no—
788C2×C4—81no—
789C2×C4—81no—
790C2×C4—81no—
791C2×C4—81no—
792C2×C4—81no—
793C2×C4—81no—
794C2×C4—162no—
795C2×C4#41712yes—
796C2×C4#41712yes—
797C2×C4C2×#10412yes—
798C2×C4C2×#10412yes—
799C2×C4C4×#4111yescharacteristic
800C2×C4#52011yescharacteristic
801C2×C4#54611yescharacteristic
802C2×C4#54711yescharacteristic
803C8—42no—
804C8—81no—
805C8—81no—
806C8—81no—
807C22—21no—
808C22—21no—
809C22—21no—
810C22—21no—
811C22—21no—
812C22—21no—
813C22—21no—
814C22—21no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—22no—
820C22—22no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—44no—
826C22—44no—
827C22—44no—
828C22—44no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—81no—
838C22—81no—
839C22—81no—
840C22—81no—
841C22—81no—
842C22—81no—
843C22—81no—
844C22#233911yescharacteristic
845C22C2×#41011yescharacteristic
846C22#288311yescharacteristic
847C22C2×#41711yescharacteristic
848C22#289711yescharacteristic
849C22C22×#10411yescharacteristic
850C22#290111yescharacteristic
851C22#331811yescharacteristic
852C22#332011yescharacteristic
853C22#334511yescharacteristic
854C22#334611yescharacteristic
855C4—22no—
856C4—21no—
857C4—21no—
858C4—21no—
859C4—21no—
860C4—22no—
861C4—22no—
862C4—22no—
863C4—44no—
864C4—41no—
865C4—41no—
866C4—41no—
867C4—41no—
868C4—41no—
869C4—41no—
870C4—82no—
871C4—82no—
872C4—82no—
873C4—81no—
874C4—81no—
875C4—81no—
876C4—81no—
877C4—81no—
878C4—81no—
879C4—81no—
880C2—21no—
881C2—21no—
882C2—21no—
883C2—21no—
884C2—42no—
885C2—42no—
886C2—161no—
887C2#1754611yescharacteristic
888C2#1754711yescharacteristic
889C2#1760411yescharacteristic
890C2#1763011yescharacteristic
891C2#2247711yescharacteristic
892C2#2249311yescharacteristic
893C2#2250511yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radical#2847C22
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. #22553C2semidirect
3. #13814C2semidirect
4. #9910C2semidirect
5. #9887C2semidirect
6. #9148C2semidirect
9. #9114C2semidirect
10. #8717C2semidirect
11. #8715C2semidirect
12. #8571C2semidirect
13. #8218C2semidirect
14. #8020C2semidirect
15. #8014C2semidirect
25. #2500C4semidirect
26. #2497C4semidirect
27. #2494C4semidirect
28. #2490C4semidirect
29. #2441C4semidirect
30. #2422C4semidirect
34. #2363C4semidirect
36. #2347C4semidirect
78. C2×#125C2×C4semidirect
86. C2×C4×D4C2×C4semidirect
128. #390C2×C4semidirect
129. #390C2×C4semidirect
130. #390C2×C4semidirect
132. #389C2×C4semidirect
133. #389C2×C4semidirect
134. #389C2×C4semidirect
135. #389C2×C4semidirect
136. #389C2×C4semidirect
163. #384C2×C4semidirect
164. #384C2×C4semidirect
167. #382C2×C4semidirect
182. C4×C4⋊C4C2×C4semidirect
183. C4×C4⋊C4C2×C4semidirect
184. C4×C4⋊C4C2×C4semidirect

Maximal subgroups

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

subgroupindex
#362082
#225532
#138142
#99102
#98872
#91482
#91472
#91172
#91142
#87172
#87152
#85712
#82182
#80202
#80142