Finite Group Databasebeta

← #223304

Subgroups — #223304

Order 512.

990 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2493C211yesmaximal, characteristic
2#22554C211yesmaximal, characteristic
3#22552C211yesmaximal, characteristic
4#9881C211yesmaximal, characteristic, complemented
5#9880C211yesmaximal, characteristic, complemented
6#9086C211yesmaximal, characteristic, complemented
7#9082C211yesmaximal, characteristic, complemented
8#9081C211yesmaximal, characteristic
9#9081C211yesmaximal, characteristic
10#8705C211yesmaximal, characteristic, complemented
11#8698C211yesmaximal, characteristic
12#8562C211yesmaximal, characteristic, complemented
13#8154C211yesmaximal, characteristic, complemented
14#7916C211yesmaximal, characteristic, complemented
15C2×#1280C211yesmaximal, characteristic
16C2×#432C2211yescharacteristic
17C2×#431C2211yescharacteristic
18C22×C22⋊C8C2211yescharacteristic
19C22×C22⋊C8C2211yescharacteristic
20#2493—21no—
21#2493—21no—
22#2493—21no—
23#2493—21no—
24#2493—21no—
25#2493—21no—
26#2493—21no—
27#2493—21no—
28C2×#401C411yescharacteristic
29C2×#400C411yescharacteristic
30C2×#400C411yescharacteristic
31C2×#400C411yescharacteristic
32C2×#387C2211yescharacteristic
33C2×#387C2211yescharacteristic
34C2×#387C2211yescharacteristic
35C2×#385C411yescharacteristic
36C2×#385C2211yescharacteristic
37C2×#383C2211yescharacteristic
38C2×#381C411yescharacteristic
39C2×#381C411yescharacteristic
40C2×#380C411yescharacteristic
41C2×C4×C22⋊C4C2211yescharacteristic
42C22×#95C2211yescharacteristic
43#1924—21no—
44#1924—21no—
45#1923—21no—
46#1923—21no—
47#1850—21no—
48#1850—21no—
49#1817C2211yescharacteristic
50#1817C2211yescharacteristic
51#1797C2211yescharacteristic
52#1797C2211yescharacteristic
53#1779C2211yescharacteristic
54#1779C2211yescharacteristic
55#1752—21no—
56C8×C22⋊C4—21no—
57#1749C2211yescharacteristic
58C4×C22⋊C8C2211yescharacteristic
59C2×#324C2211yescharacteristic
60C2×#324C2211yescharacteristic
61C2×#324C2211yescharacteristic
62C2×#324C2211yescharacteristic
63#1280C2211yescharacteristic
64#1280C2211yescharacteristic
65#1280C2211yescharacteristic
66#1280C2211yescharacteristic
67#1280C2211yescharacteristic
68#1280C2211yescharacteristic
69#1280C2211yescharacteristic
70#1280C2211yescharacteristic
71#1280C2211yescharacteristic
72#1280C2211yescharacteristic
73#1280C2211yescharacteristic
74#1280C2211yescharacteristic
75C24×C4C2×C411yescharacteristic
76C24×C4C2×C411yescharacteristic
77C24×C4C2311yescharacteristic
78C23×C8—21no—
79C23×C8—21no—
80C22×C4⋊C4C2×C411yescharacteristic
81C22×C4⋊C4C2×C411yescharacteristic
82C22×C4⋊C4C2×C411yescharacteristic
83C22×C4⋊C4C2×C411yescharacteristic
84C22×C4⋊C4C2×C411yescharacteristic
85C22×C4⋊C4C2311yescharacteristic
86C22×C22⋊C4C2×C411yescharacteristic
87C22×C22⋊C4C2×C411yescharacteristic
88C22×C22⋊C4C2×C411yescharacteristic
89C22×C22⋊C4C2×C411yescharacteristic
90C22×C42C2311yescharacteristic
91C22×C42C2311yescharacteristic
92#432—22no—
93#432—41no—
94#431—22no—
95#431—41no—
96C2×C4⋊C8—21no—
97C2×C4⋊C8—21no—
98C2×C4⋊C8—21no—
99C2×C4⋊C8—21no—
100C2×C22⋊C8—22no—
101C2×C22⋊C8—22no—
102C2×C22⋊C8—21no—
103C2×C22⋊C8—21no—
104C2×C22⋊C8—21no—
105C2×C22⋊C8—21no—
106C2×C22⋊C8—21no—
107C2×C22⋊C8—21no—
108C2×C22⋊C8—41no—
109C2×C22⋊C8—41no—
110C2×C22⋊C8C2311yescharacteristic
111C2×C22⋊C8C2311yescharacteristic
112C2×C22⋊C8C2311yescharacteristic
113C2×C22⋊C8C2311yescharacteristic
114C2×C22⋊C8C2311yescharacteristic
115C2×C22⋊C8C2311yescharacteristic
116C2×C22⋊C8C2311yescharacteristic
117C2×C22⋊C8C2311yescharacteristic
118C2×#97—21no—
119C2×#97—21no—
120C2×C4×C8—21no—
121C2×C4×C8—21no—
122#401—21no—
123#401—21no—
124#401—21no—
125#401—21no—
126#400—21no—
127#400—21no—
128#400—21no—
129#400—21no—
130#400—21no—
131#400—21no—
132#400—21no—
133#400—21no—
134#400—21no—
135#400—21no—
136#400—21no—
137#400—21no—
138#387—21no—
139#387—21no—
140#387—21no—
141#387—21no—
142#387—21no—
143#387—21no—
144#387—21no—
145#387—21no—
146#387—21no—
147#387—21no—
148#387—21no—
149#387—21no—
150#385—21no—
151#385—21no—
152#385—21no—
153#385—21no—
154#385—21no—
155#385—21no—
156#385—21no—
157#385—21no—
158#383—21no—
159#383—21no—
160#383—21no—
161#383—21no—
162#381—21no—
163#381—21no—
164#381—21no—
165#381—21no—
166#381—21no—
167#381—21no—
168#381—21no—
169#381—21no—
170#380—21no—
171#380—21no—
172#380—21no—
173#380—21no—
174C4×C22⋊C4D411yescharacteristic
175C4×C22⋊C4D411yescharacteristic
176C4×C22⋊C4D411yescharacteristic
177C4×C22⋊C4D411yescharacteristic
178C4×C22⋊C4D411yescharacteristic
179C4×C22⋊C4D411yescharacteristic
180C4×C22⋊C4D411yescharacteristic
181C4×C22⋊C4D411yescharacteristic
182C2×#95—21no—
183C2×#95—21no—
184C2×#95—21no—
185C2×#95—21no—
186C2×#95C2×C411yescharacteristic
187C2×#95C2×C411yescharacteristic
188C2×#95C2×C411yescharacteristic
189C2×#95C2×C411yescharacteristic
190C2×#95C2×C411yescharacteristic
191C2×#95C2×C411yescharacteristic
192C2×#95C2×C411yescharacteristic
193C2×#95C2×C411yescharacteristic
194C2×#95C2×C411yescharacteristic
195C2×#95C2×C411yescharacteristic
196C2×#95C2×C411yescharacteristic
197C2×#95C2×C411yescharacteristic
198C2×#95C2×C411yescharacteristic
199C2×#95C2×C411yescharacteristic
200C2×#95C2×C411yescharacteristic
201C2×#95C2×C411yescharacteristic
202C2×#95C2×C411yescharacteristic
203C2×#95C2311yescharacteristic
204C2×#95C2311yescharacteristic
205C2×#95C2311yescharacteristic
206#336—21no—
207#336—21no—
208#336—21no—
209#336—21no—
210#336—21no—
211#336—21no—
212#336—21no—
213#336—21no—
214#324—22no—
215#324—22no—
216#324—41no—
217#324—41no—
218C25C22×C411yescharacteristic
219C23×C4—21no—
220C23×C4—21no—
221C23×C4—21no—
222C23×C4—21no—
223C23×C4—21no—
224C23×C4—21no—
225C23×C4—21no—
226C23×C4—21no—
227C23×C4—22no—
228C23×C4—22no—
229C23×C4—22no—
230C23×C4—41no—
231C23×C4—42no—
232C23×C4—42no—
233C23×C4—42no—
234C23×C4—42no—
235C23×C4—81no—
236C23×C4—81no—
237C23×C4C22×C411yescharacteristic
238C23×C4C22×C411yescharacteristic
239C23×C4C22×C411yescharacteristic
240C23×C4C22×C411yescharacteristic
241C23×C4C22×C411yescharacteristic
242C23×C4C22×C411yescharacteristic
243C23×C4C22×C411yescharacteristic
244C23×C4C22×C411yescharacteristic
245C23×C4C22×C411yescharacteristic
246C23×C4C22×C411yescharacteristic
247C23×C4C22×C411yescharacteristic
248C23×C4C22×C411yescharacteristic
249C23×C4C22×C411yescharacteristic
250C23×C4C2×D411yescharacteristic
251C23×C4C2×D411yescharacteristic
252C23×C4C2×D411yescharacteristic
253C23×C4C2×D411yescharacteristic
254C23×C4C2411yescharacteristic
255C22×C8—21no—
256C22×C8—21no—
257C22×C8—21no—
258C22×C8—21no—
259C22×C8—21no—
260C22×C8—21no—
261C22×C8—21no—
262C22×C8—21no—
263C22×C8—42no—
264C22×C8—42no—
265C22×C8—42no—
266C22×C8—42no—
267C22×C8—81no—
268C22×C8—81no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
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—41no—
288C2×C4⋊C4—41no—
289C2×C4⋊C4—81no—
290C2×C4⋊C4—81no—
291C2×C4⋊C4—81no—
292C2×C22⋊C4—22no—
293C2×C22⋊C4—22no—
294C2×C22⋊C4—21no—
295C2×C22⋊C4—21no—
296C2×C22⋊C4—21no—
297C2×C22⋊C4—21no—
298C2×C22⋊C4—22no—
299C2×C22⋊C4—22no—
300C2×C22⋊C4—42no—
301C2×C22⋊C4—42no—
302C2×C22⋊C4C22⋊C411yescharacteristic
303C2×C22⋊C4C22⋊C411yescharacteristic
304C2×C22⋊C4C22⋊C411yescharacteristic
305C2×C22⋊C4C22⋊C411yescharacteristic
306C2×C22⋊C4C22⋊C411yescharacteristic
307C2×C22⋊C4C22⋊C411yescharacteristic
308C2×C22⋊C4C22⋊C411yescharacteristic
309C2×C22⋊C4C22⋊C411yescharacteristic
310C2×C42—21no—
311C2×C42—21no—
312C2×C42—21no—
313C2×C42—21no—
314C2×C42—81no—
315C2×C42C2×D411yescharacteristic
316C2×C42C2×D411yescharacteristic
317C2×C42C2×D411yescharacteristic
318C2×C42C2×D411yescharacteristic
319C2×C42C2×D411yescharacteristic
320C2×C42C2×D411yescharacteristic
321C2×C42C2×D411yescharacteristic
322C2×C42C2×D411yescharacteristic
323C4⋊C8—42no—
324C4⋊C8—42no—
325C4⋊C8—81no—
326C4⋊C8—81no—
327C22⋊C8—21no—
328C22⋊C8—21no—
329C22⋊C8—21no—
330C22⋊C8—21no—
331C22⋊C8—21no—
332C22⋊C8—21no—
333C22⋊C8—21no—
334C22⋊C8—21no—
335C22⋊C8—21no—
336C22⋊C8—21no—
337C22⋊C8—21no—
338C22⋊C8—21no—
339C22⋊C8—21no—
340C22⋊C8—21no—
341C22⋊C8—42no—
342C22⋊C8—42no—
343C22⋊C8—42no—
344C22⋊C8—42no—
345C22⋊C8—81no—
346C22⋊C8—81no—
347C22⋊C8#4112yes—
348C22⋊C8#4112yes—
349#97—42no—
350#97—81no—
351C4×C8—42no—
352C4×C8—81no—
353#95—21no—
354#95—21no—
355#95—21no—
356#95—21no—
357#95—21no—
358#95—21no—
359#95—21no—
360#95—21no—
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—21no—
386#95—21no—
387#95—21no—
388#95—21no—
389#95C22⋊C411yescharacteristic
390#95C22⋊C411yescharacteristic
391#95C22⋊C411yescharacteristic
392#95C22⋊C411yescharacteristic
393#95C22⋊C411yescharacteristic
394#95C22⋊C411yescharacteristic
395#95C22⋊C411yescharacteristic
396#95C22⋊C411yescharacteristic
397C24—21no—
398C24—21no—
399C24—21no—
400C24—21no—
401C24—22no—
402C24—22no—
403C24—41no—
404C24—41no—
405C24C2×C22⋊C411yescharacteristic
406C24C2×C22⋊C411yescharacteristic
407C24#13112yes—
408C24#13112yes—
409C24C23×C411yescharacteristic
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
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—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—41no—
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—42no—
478C22×C4—42no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—42no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4—41no—
490C22×C4—41no—
491C22×C4—41no—
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—82no—
502C22×C4—82no—
503C22×C4—82no—
504C22×C4—82no—
505C22×C4—81no—
506C22×C4—81no—
507C22×C4—84no—
508C22×C4—84no—
509C22×C4—84no—
510C22×C4—84no—
511C22×C4C2×C22⋊C411yescharacteristic
512C22×C4C2×C22⋊C411yescharacteristic
513C22×C4C2×C22⋊C411yescharacteristic
514C22×C4C2×C22⋊C411yescharacteristic
515C22×C4C2×C22⋊C411yescharacteristic
516C22×C4C2×C22⋊C411yescharacteristic
517C22×C4C2×C22⋊C411yescharacteristic
518C22×C4C2×C22⋊C411yescharacteristic
519C22×C4C2×C22⋊C411yescharacteristic
520C22×C4C2×C22⋊C411yescharacteristic
521C22×C4#13112yes—
522C22×C4C22×D411yescharacteristic
523C22×C4C22×D411yescharacteristic
524C22×C4C2×#4111yescharacteristic
525C22×C4C2×#4111yescharacteristic
526C22×C4H(5,𝔽2)11yescharacteristic
527C22×C42−1+411yescharacteristic
528C2×C8—22no—
529C2×C8—22no—
530C2×C8—41no—
531C2×C8—41no—
532C2×C8—41no—
533C2×C8—41no—
534C2×C8—41no—
535C2×C8—41no—
536C2×C8—41no—
537C2×C8—41no—
538C2×C8—41no—
539C2×C8—41no—
540C2×C8—41no—
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—
552C2×C8—84no—
553C2×C8—84no—
554C4⋊C4—42no—
555C4⋊C4—42no—
556C4⋊C4—42no—
557C4⋊C4—42no—
558C4⋊C4—41no—
559C4⋊C4—41no—
560C4⋊C4—41no—
561C4⋊C4—41no—
562C4⋊C4—81no—
563C4⋊C4—81no—
564C4⋊C4—81no—
565C4⋊C4—81no—
566C4⋊C4—81no—
567C4⋊C4—81no—
568C22⋊C4—22no—
569C22⋊C4—22no—
570C22⋊C4—22no—
571C22⋊C4—22no—
572C22⋊C4—22no—
573C22⋊C4—22no—
574C22⋊C4—41no—
575C22⋊C4—41no—
576C22⋊C4—42no—
577C22⋊C4—42no—
578C22⋊C4—42no—
579C22⋊C4—42no—
580C42—21no—
581C42—21no—
582C42—21no—
583C42—21no—
584C42—21no—
585C42—21no—
586C42—21no—
587C42—21no—
588C42—41no—
589C42—41no—
590C42—41no—
591C42—41no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—22no—
610C23—24no—
611C23—24no—
612C23—42no—
613C23—42no—
614C23—42no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23#40812yes—
623C23#40812yes—
624C23#41012yes—
625C23#41312yes—
626C23C22×C22⋊C411yescharacteristic
627C23C4×#4111yescharacteristic
628C23#52011yescharacteristic
629C23C2×#13111yescharacteristic
630C23C2×#13111yescharacteristic
631C23C2×#13111yescharacteristic
632C23#56811yescharacteristic
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—22no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—42no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—81no—
710C2×C4—81no—
711C2×C4—81no—
712C2×C4—81no—
713C2×C4—81no—
714C2×C4—81no—
715C2×C4—81no—
716C2×C4—81no—
717C2×C4—81no—
718C2×C4—81no—
719C2×C4—81no—
720C2×C4—81no—
721C2×C4—84no—
722C2×C4—84no—
723C2×C4—84no—
724C2×C4—84no—
725C2×C4—81no—
726C2×C4—81no—
727C2×C4—81no—
728C2×C4—81no—
729C2×C4—81no—
730C2×C4—81no—
731C2×C4—81no—
732C2×C4—81no—
733C2×C4—81no—
734C2×C4—81no—
735C2×C4—81no—
736C2×C4—81no—
737C2×C4#54611yescharacteristic
738C2×C4#54611yescharacteristic
739C2×C4#54711yescharacteristic
740C2×C4#54711yescharacteristic
741C8—42no—
742C8—42no—
743C8—81no—
744C8—81no—
745C8—81no—
746C8—81no—
747C8—81no—
748C8—81no—
749C22—21no—
750C22—21no—
751C22—22no—
752C22—21no—
753C22—21no—
754C22—22no—
755C22—22no—
756C22—22no—
757C22—21no—
758C22—21no—
759C22—21no—
760C22—21no—
761C22—22no—
762C22—21no—
763C22—21no—
764C22—21no—
765C22—21no—
766C22—22no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—44no—
771C22—44no—
772C22—44no—
773C22—44no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22#147314yes—
779C22#233911yescharacteristic
780C22C2×#40811yescharacteristic
781C22#288011yescharacteristic
782C22C2×#41011yescharacteristic
783C22#288311yescharacteristic
784C22C2×#41311yescharacteristic
785C22#288911yescharacteristic
786C22#296611yescharacteristic
787C22#296811yescharacteristic
788C22#299211yescharacteristic
789C22#299411yescharacteristic
790C4—21no—
791C4—21no—
792C4—21no—
793C4—21no—
794C4—41no—
795C4—41no—
796C4—42no—
797C4—41no—
798C4—41no—
799C4—41no—
800C4—41no—
801C4—41no—
802C4—41no—
803C4—41no—
804C4—41no—
805C4—81no—
806C4—81no—
807C4—81no—
808C4—81no—
809C4—81no—
810C4—81no—
811C4—81no—
812C2—21no—
813C2—21no—
814C2—21no—
815C2—21no—
816C2—24no—
817C2—42no—
818C2C2×#147311yescharacteristic
819C2#1738711yescharacteristic
820C2#1741711yescharacteristic
821C2#1742211yescharacteristic
822C2#2247011yescharacteristic
823C2#2247711yescharacteristic
824C2#2248011yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC24C23×C4
Frattini, cosocleC23×C4C24
prime radicalC25C22×C4
LCSG ▷ C24 ▷ C2 ▷ 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
4. #9881C2semidirect
5. #9880C2semidirect
6. #9086C2semidirect
7. #9082C2semidirect
10. #8705C2semidirect
12. #8562C2semidirect
13. #8154C2semidirect
14. #7916C2semidirect

Maximal subgroups

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

subgroupindex
C2×#24932
#225542
#225522
#98812
#98802
#90862
#90822
#90812
#87052
#86982
#85622
#81542
#79162
C2×#12802