Finite Group Databasebeta

← #223671

Subgroups — #223671

Order 512.

1044 conjugacy classes of subgroups.

The subgroup lattice has 881 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36208C211yesmaximal, characteristic
2#22555C211yesmaximal, characteristic, complemented
3#13901C211yesmaximal, characteristic, complemented
4#9913C211yesmaximal, characteristic, complemented
5#9886C211yesmaximal, characteristic, complemented
6#9157C211yesmaximal, characteristic, complemented
7#9147C211yesmaximal, characteristic
8#9118C211yesmaximal, characteristic, complemented
9#9117C211yesmaximal, characteristic
10#8716C211yesmaximal, characteristic, complemented
11#8715C211yesmaximal, characteristic, complemented
12#8575C211yesmaximal, characteristic, complemented
13#8220C211yesmaximal, characteristic, complemented
14#8020C211yesmaximal, characteristic, complemented
15#8018C211yesmaximal, characteristic, complemented
16C2×#432C2211yescharacteristic
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
38#2285C2211yescharacteristic
39C2×#383C2211yescharacteristic
40#2280C2211yescharacteristic
41C2×C4×C22⋊C4C2211yescharacteristic
42C22×#95C2211yescharacteristic
43#1924—21no—
44#1923—21no—
45#1851—21no—
46#1817C2211yescharacteristic
47#1797C2211yescharacteristic
48#1779C2211yescharacteristic
49#1753—21no—
50C4×C22⋊C8C2211yescharacteristic
51C2×#327C2211yescharacteristic
52C2×#327C2211yescharacteristic
53C2×#327C2211yescharacteristic
54C2×#327C2211yescharacteristic
55#1443—21no—
56#1443—21no—
57#1434C2211yescharacteristic
58#1434C2211yescharacteristic
59#1434C2211yescharacteristic
60C22⋊#95—21no—
61C22⋊#95—21no—
62C22⋊#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×C22⋊C4—21no—
91C22×C22⋊C4D411yescharacteristic
92C22×C22⋊C4D411yescharacteristic
93C22×C42C2311yescharacteristic
94C22×C42C2311yescharacteristic
95#432—22no—
96#432—41no—
97C2×C4⋊C8—21no—
98C2×C4⋊C8—21no—
99#407—22no—
100#407—41no—
101C2×C22⋊C8—21no—
102C2×C22⋊C8—21no—
103C2×C22⋊C8—21no—
104C2×C22⋊C8C2311yescharacteristic
105C2×C22⋊C8C2311yescharacteristic
106C2×C22⋊C8C2311yescharacteristic
107C2×C22⋊C8C2311yescharacteristic
108C2×#97—21no—
109C2×C4×C8—21no—
110#401—21no—
111#400—21no—
112#399—21no—
113#397—21no—
114#397—21no—
115#397—21no—
116#396—21no—
117#396—21no—
118#394—21no—
119#394—21no—
120#394—21no—
121#394—21no—
122#390—21no—
123#390—21no—
124#390C2×C411yescharacteristic, complemented
125#390C2×C411yescharacteristic, complemented
126#390C2×C411yescharacteristic, complemented
127#389—21no—
128#389C2×C411yescharacteristic, complemented
129#389C2×C411yescharacteristic, complemented
130#389C2×C411yescharacteristic, complemented
131#389C2×C411yescharacteristic, complemented
132#389C2×C411yescharacteristic, complemented
133#388—21no—
134#388—21no—
135#388—21no—
136#388—21no—
137#388—21no—
138#388—21no—
139#388—21no—
140#388—21no—
141#388—21no—
142#388—21no—
143#388—21no—
144#387—21no—
145#387—21no—
146#387—21no—
147#387—21no—
148#387—21no—
149#386—21no—
150#386—21no—
151#386—21no—
152#386—21no—
153#386—21no—
154#386—21no—
155#385—21no—
156#385—21no—
157#385—21no—
158#384C2×C411yescharacteristic, complemented
159#384C2×C411yescharacteristic, complemented
160#383—21no—
161#383—22no—
162#383—41no—
163#382—21no—
164#382C2×C411yescharacteristic, complemented
165#381—21no—
166#380—21no—
167#380C2×C411yescharacteristic
168#380C2×C411yescharacteristic
169#380C2×C411yescharacteristic
170#380C2×C411yescharacteristic
171#380C2311yescharacteristic
172#380C2311yescharacteristic
173#380C2311yescharacteristic
174#379—21no—
175C4×C4⋊C4—21no—
176C4×C4⋊C4—21no—
177C4×C4⋊C4C2×C411yescharacteristic, complemented
178C4×C4⋊C4C2×C411yescharacteristic, complemented
179C4×C4⋊C4C2×C411yescharacteristic, complemented
180C4×C22⋊C4—21no—
181C4×C22⋊C4—21no—
182C4×C22⋊C4—21no—
183C4×C22⋊C4—21no—
184C4×C22⋊C4C2×C411yescharacteristic
185C4×C22⋊C4C2×C411yescharacteristic
186C4×C22⋊C4C2×C411yescharacteristic
187C4×C22⋊C4C2×C411yescharacteristic
188C4×C22⋊C4D411yescharacteristic
189C4×C22⋊C4D411yescharacteristic
190C4×C22⋊C4D411yescharacteristic
191C4×C22⋊C4D411yescharacteristic
192C2×#95—22no—
193C2×#95—21no—
194C2×#95—21no—
195C2×#95—21no—
196C2×#95—21no—
197C2×#95—21no—
198C2×#95—21no—
199C2×#95—21no—
200C2×#95—21no—
201C2×#95—21no—
202C2×#95—21no—
203C2×#95—41no—
204C2×#95D411yescharacteristic
205C2×#95D411yescharacteristic
206C2×#95C2311yescharacteristic
207C2×#95C2311yescharacteristic
208C2×#95C2311yescharacteristic
209C2×#95C2311yescharacteristic
210#336—21no—
211#336—21no—
212#336—21no—
213#336—21no—
214#327—22no—
215#327—22no—
216#327—41no—
217#327—41no—
218C25C2×D411yescharacteristic
219C22×D4—21no—
220C22×D4—21no—
221C22×D4—21no—
222C22×D4C22×C411yescharacteristic
223C23×C4—21no—
224C23×C4—21no—
225C23×C4—21no—
226C23×C4—21no—
227C23×C4—21no—
228C23×C4—21no—
229C23×C4—21no—
230C23×C4—21no—
231C23×C4—21no—
232C23×C4—42no—
233C23×C4—42no—
234C23×C4—42no—
235C23×C4—42no—
236C23×C4—42no—
237C23×C4—42no—
238C23×C4—81no—
239C23×C4—81no—
240C23×C4—81no—
241C23×C4C22×C411yescharacteristic
242C23×C4C22×C411yescharacteristic
243C23×C4C2×D411yescharacteristic
244C23×C4C2×D411yescharacteristic
245C23×C4C2×D411yescharacteristic
246C23×C4C2×D411yescharacteristic
247C23×C4C2×D411yescharacteristic
248C23×C4C2×D411yescharacteristic
249C23×C4C2×D411yescharacteristic
250C23×C4C2411yescharacteristic
251C2×M16—42no—
252C2×M16—42no—
253C2×M16—81no—
254C22×C8—21no—
255C22×C8—21no—
256C22×C8—21no—
257C22×C8—21no—
258#125—81no—
259#123—44no—
260#123—42no—
261#123—42no—
262#121—21no—
263#121—21no—
264#121—21no—
265#121—21no—
266#121—42no—
267#121—81no—
268#120—81no—
269#120—81no—
270C4×D4—81no—
271C4×D4—81no—
272C4×D4—81no—
273#117—42no—
274#117—81no—
275#117—81no—
276#117—81no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4C22×C411yescharacteristic
289C2×C4⋊C4C22×C411yescharacteristic
290C2×C4⋊C4C22×C411yescharacteristic
291C2×C4⋊C4C22×C411yescharacteristic
292C2×C4⋊C4C22×C411yescharacteristic
293C2×C4⋊C4C22×C411yescharacteristic
294C2×C4⋊C4C22×C411yescharacteristic
295C2×C22⋊C4—21no—
296C2×C22⋊C4—21no—
297C2×C22⋊C4—21no—
298C2×C22⋊C4—21no—
299C2×C22⋊C4—21no—
300C2×C22⋊C4—21no—
301C2×C22⋊C4—21no—
302C2×C22⋊C4—21no—
303C2×C22⋊C4—21no—
304C2×C22⋊C4—21no—
305C2×C22⋊C4—21no—
306C2×C22⋊C4—21no—
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—42no—
315C2×C22⋊C4—41no—
316C2×C22⋊C4—41no—
317C2×C22⋊C4—42no—
318C2×C22⋊C4—42no—
319C2×C22⋊C4—42no—
320C2×C22⋊C4C22⋊C411yescharacteristic
321C2×C22⋊C4C22⋊C411yescharacteristic
322C2×C22⋊C4C22⋊C411yescharacteristic
323C2×C22⋊C4C22⋊C411yescharacteristic
324C2×C22⋊C4C22⋊C411yescharacteristic
325C2×C22⋊C4C22⋊C411yescharacteristic
326C2×C22⋊C4C22⋊C411yescharacteristic
327C2×C22⋊C4C22⋊C411yescharacteristic
328C2×C42—21no—
329C2×C42—21no—
330C2×C42—21no—
331C2×C42—21no—
332C2×C42—21no—
333C2×C42—21no—
334C2×C42—21no—
335C2×C42—21no—
336C2×C42—21no—
337C2×C42—81no—
338C2×C42C22×C411yescharacteristic
339C2×C42C22×C411yescharacteristic
340C2×C42C22×C411yescharacteristic
341C2×C42C22×C411yescharacteristic
342C2×C42C2×D411yescharacteristic
343C2×C42C2×D411yescharacteristic
344C2×C42C2×D411yescharacteristic
345C2×C42C2×D411yescharacteristic
346C4⋊C8—42no—
347C4⋊C8—81no—
348C22⋊C8—21no—
349C22⋊C8—21no—
350C22⋊C8—21no—
351C22⋊C8—21no—
352C22⋊C8—21no—
353C22⋊C8—21no—
354C22⋊C8—21no—
355C22⋊C8—42no—
356C22⋊C8—42no—
357C22⋊C8—81no—
358C22⋊C8#4112yes—
359#97—42no—
360C4×C8—81no—
361#95—21no—
362#95—21no—
363#95—21no—
364#95—21no—
365#95—21no—
366#95—21no—
367#95—21no—
368#95—21no—
369#95—21no—
370#95—21no—
371#95—21no—
372#95—21no—
373#95—21no—
374#95—21no—
375#95—21no—
376#95—21no—
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—42no—
386#95—42no—
387#95—42no—
388#95—42no—
389#95—42no—
390#95—81no—
391#95—81no—
392#95—81no—
393#95—81no—
394#95—81no—
395#95C22⋊C411yescharacteristic
396#95C22⋊C411yescharacteristic
397#95C22⋊C411yescharacteristic
398#95C22⋊C411yescharacteristic
399#95C22⋊C411yescharacteristic
400#95C22⋊C411yescharacteristic
401#95C22⋊C411yescharacteristic
402#95C22⋊C411yescharacteristic
403#95#4112yes—
404C24—21no—
405C24—21no—
406C24—22no—
407C24—22no—
408C24—21no—
409C24—21no—
410C24—21no—
411C24—21no—
412C24—21no—
413C24—41no—
414C24—41no—
415C24C2×C22⋊C411yescharacteristic
416C24C2×C22⋊C411yescharacteristic
417C24C22×D411yescharacteristic
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—41no—
421C2×D4—41no—
422C2×D4—41no—
423C2×D4—41no—
424C2×D4—41no—
425C2×D4—41no—
426C2×D4—41no—
427C2×D4—41no—
428C2×D4—42no—
429C2×D4—42no—
430C2×D4—81no—
431C2×D4—81no—
432C2×D4—81no—
433C2×D4—81no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4—41no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4—42no—
484C22×C4—41no—
485C22×C4—41no—
486C22×C4—41no—
487C22×C4—41no—
488C22×C4—41no—
489C22×C4—41no—
490C22×C4—41no—
491C22×C4—48no—
492C22×C4—41no—
493C22×C4—41no—
494C22×C4—41no—
495C22×C4—41no—
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—41no—
508C22×C4—41no—
509C22×C4—41no—
510C22×C4—41no—
511C22×C4—81no—
512C22×C4—81no—
513C22×C4—82no—
514C22×C4—82no—
515C22×C4—82no—
516C22×C4—82no—
517C22×C4—84no—
518C22×C4—84no—
519C22×C4—84no—
520C22×C4—84no—
521C22×C4—84no—
522C22×C4—84no—
523C22×C4C2×C22⋊C411yescharacteristic
524C22×C4C2×C22⋊C411yescharacteristic
525C22×C4C2×C22⋊C411yescharacteristic
526C22×C4C2×C22⋊C411yescharacteristic
527C22×C4C2×C22⋊C411yescharacteristic
528C22×C4C2×C22⋊C411yescharacteristic
529C22×C4C2×C22⋊C411yescharacteristic
530C22×C4C2×C22⋊C411yescharacteristic
531C22×C4C2×C22⋊C411yescharacteristic
532C22×C4C2×C22⋊C411yescharacteristic
533C22×C4C23×C411yescharacteristic
534C22×C4C22×D411yescharacteristic
535C22×C4C2×#4111yescharacteristic
536C22×C4C2×#4111yescharacteristic
537C22×C4H(5,𝔽2)11yescharacteristic
538C22×C42−1+411yescharacteristic
539M16—84no—
540C2×C8—22no—
541C2×C8—41no—
542C2×C8—41no—
543C2×C8—41no—
544C2×C8—41no—
545C2×C8—41no—
546C2×C8—41no—
547C2×C8—41no—
548C2×C8—41no—
549C2×C8—41no—
550C2×C8—41no—
551C2×C8—41no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—41no—
555C4⋊C4—41no—
556C4⋊C4—41no—
557C4⋊C4—41no—
558C4⋊C4—41no—
559C4⋊C4—41no—
560C4⋊C4—42no—
561C4⋊C4—42no—
562C4⋊C4—42no—
563C4⋊C4—42no—
564C4⋊C4—81no—
565C4⋊C4—81no—
566C4⋊C4—81no—
567C4⋊C4—81no—
568C4⋊C4—81no—
569C4⋊C4—81no—
570C4⋊C4—81no—
571C22⋊C4—22no—
572C22⋊C4—22no—
573C22⋊C4—41no—
574C22⋊C4—41no—
575C22⋊C4—41no—
576C22⋊C4—41no—
577C22⋊C4—41no—
578C22⋊C4—41no—
579C22⋊C4—42no—
580C22⋊C4—42no—
581C22⋊C4—42no—
582C22⋊C4—42no—
583C22⋊C4—41no—
584C22⋊C4—41no—
585C22⋊C4—41no—
586C22⋊C4—41no—
587C22⋊C4—41no—
588C22⋊C4—41no—
589C22⋊C4—42no—
590C22⋊C4—42no—
591C22⋊C4—41no—
592C22⋊C4—41no—
593C22⋊C4—81no—
594C22⋊C4—81no—
595C22⋊C4—81no—
596C22⋊C4—81no—
597C22⋊C4—81no—
598C22⋊C4—81no—
599C22⋊C4—81no—
600C22⋊C4—81no—
601C22⋊C4—81no—
602C22⋊C4—84no—
603C42—21no—
604C42—21no—
605C42—21no—
606C42—21no—
607C42—21no—
608C42—21no—
609C42—21no—
610C42—21no—
611C42—41no—
612C42—41no—
613C42—41no—
614C42—41no—
615C42—42no—
616C42—81no—
617C42—81no—
618C42—81no—
619C42—81no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—24no—
625C23—24no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23#41012yes—
660C23#42112yes—
661C23C22×C22⋊C411yescharacteristic
662C23#54611yescharacteristic
663C23#54711yescharacteristic
664C23#57511yescharacteristic
665C23#57511yescharacteristic
666C23#57611yescharacteristic
667C23#57711yescharacteristic
668D4—81no—
669D4—81no—
670D4—81no—
671D4—81no—
672D4—81no—
673D4—81no—
674D4—162no—
675D4—162no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
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—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—42no—
749C2×C4—81no—
750C2×C4—81no—
751C2×C4—81no—
752C2×C4—81no—
753C2×C4—81no—
754C2×C4—81no—
755C2×C4—81no—
756C2×C4—81no—
757C2×C4—81no—
758C2×C4—81no—
759C2×C4—81no—
760C2×C4—81no—
761C2×C4—81no—
762C2×C4—81no—
763C2×C4—81no—
764C2×C4—81no—
765C2×C4—81no—
766C2×C4—81no—
767C2×C4—81no—
768C2×C4—816no—
769C2×C4—81no—
770C2×C4—81no—
771C2×C4—81no—
772C2×C4—81no—
773C2×C4—81no—
774C2×C4—81no—
775C2×C4—81no—
776C2×C4—81no—
777C2×C4—81no—
778C2×C4—81no—
779C2×C4—81no—
780C2×C4—81no—
781C2×C4—81no—
782C2×C4—81no—
783C2×C4—81no—
784C2×C4—162no—
785C2×C4C4×#4111yescharacteristic
786C2×C4#52011yescharacteristic
787C2×C4#54611yescharacteristic
788C2×C4#54711yescharacteristic
789C8—42no—
790C8—81no—
791C8—81no—
792C8—81no—
793C22—21no—
794C22—21no—
795C22—21no—
796C22—21no—
797C22—21no—
798C22—21no—
799C22—21no—
800C22—21no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—21no—
805C22—22no—
806C22—22no—
807C22—22no—
808C22—22no—
809C22—22no—
810C22—22no—
811C22—44no—
812C22—44no—
813C22—44no—
814C22—44no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—81no—
824C22—81no—
825C22—81no—
826C22—81no—
827C22—81no—
828C22—81no—
829C22—81no—
830C22#233911yescharacteristic
831C22C2×#41011yescharacteristic
832C22#288311yescharacteristic
833C22#289611yescharacteristic
834C22#289711yescharacteristic
835C22C2×#42111yescharacteristic
836C22#290111yescharacteristic
837C22#332211yescharacteristic
838C22#332611yescharacteristic
839C22#335111yescharacteristic
840C22#335511yescharacteristic
841C4—21no—
842C4—21no—
843C4—21no—
844C4—21no—
845C4—41no—
846C4—41no—
847C4—41no—
848C4—41no—
849C4—41no—
850C4—41no—
851C4—41no—
852C4—41no—
853C4—41no—
854C4—41no—
855C4—82no—
856C4—82no—
857C4—81no—
858C4—81no—
859C4—81no—
860C4—81no—
861C4—81no—
862C4—81no—
863C4—81no—
864C4—161no—
865C4—161no—
866C2—21no—
867C2—21no—
868C2—21no—
869C2—21no—
870C2—42no—
871C2—42no—
872C2—161no—
873C2#1759311yescharacteristic
874C2#1759711yescharacteristic
875C2#1760411yescharacteristic
876C2#1762911yescharacteristic
877C2#2247711yescharacteristic
878C2#2250111yescharacteristic
879C2#2250611yescharacteristic
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. #22555C2semidirect
3. #13901C2semidirect
4. #9913C2semidirect
5. #9886C2semidirect
6. #9157C2semidirect
8. #9118C2semidirect
10. #8716C2semidirect
11. #8715C2semidirect
12. #8575C2semidirect
13. #8220C2semidirect
14. #8020C2semidirect
15. #8018C2semidirect
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
124. #390C2×C4semidirect
125. #390C2×C4semidirect
126. #390C2×C4semidirect
128. #389C2×C4semidirect
129. #389C2×C4semidirect
130. #389C2×C4semidirect
131. #389C2×C4semidirect
132. #389C2×C4semidirect
158. #384C2×C4semidirect
159. #384C2×C4semidirect
164. #382C2×C4semidirect
177. C4×C4⋊C4C2×C4semidirect
178. C4×C4⋊C4C2×C4semidirect
179. 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
#225552
#139012
#99132
#98862
#91572
#91472
#91182
#91172
#87162
#87152
#85752
#82202
#80202
#80182