Finite Group Databasebeta

← #223422

Subgroups — #223422

Order 512.

1046 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#553C211yesmaximal, characteristic
2#22749C211yesmaximal, characteristic, complemented
3#21101C211yesmaximal, characteristic, complemented
4#9875C211yesmaximal, characteristic, complemented
5#9867C211yesmaximal, characteristic, complemented
6#9076C211yesmaximal, characteristic, complemented
7#9072C211yesmaximal, characteristic, complemented
8#8944C211yesmaximal, characteristic, complemented
9#8940C211yesmaximal, characteristic, complemented
10#8708C211yesmaximal, characteristic, complemented
11#8707C211yesmaximal, characteristic, complemented
12#8565C211yesmaximal, characteristic, complemented
13#8174C211yesmaximal, characteristic, complemented
14#7901C211yesmaximal, characteristic, complemented
15#7890C211yesmaximal, characteristic, complemented
16C2×#553C411yescharacteristic
17C2×#431C2211yescharacteristic
18C2×#431C2211yescharacteristic
19C2×#423C2211yescharacteristic
20C22×C4×C8C2211yescharacteristic
21#2374—21no—
22#2373—21no—
23#2370C411yescharacteristic
24#2364—21no—
25#2363C411yescharacteristic
26#2361C411yescharacteristic
27#2357C411yescharacteristic
28#2353—21no—
29#2352C411yescharacteristic
30#2347C411yescharacteristic
31#2345C411yescharacteristic
32C4×#125C2211yescharacteristic
33C4×#126—21no—
34C4×#123—21no—
35C4×#121—21no—
36C4×#121C2211yescharacteristic
37C4×#121C2211yescharacteristic
38C42×D4—21no—
39C42×D4C2211yescharacteristic
40C42×D4C2211yescharacteristic
41C4×#117C2211yescharacteristic
42C2×C4×C4⋊C4C2211yescharacteristic
43#1924—21no—
44#1923—21no—
45#1916—21no—
46#1916—21no—
47#1870—21no—
48#1869—21no—
49#1850—21no—
50#1831C2211yescharacteristic
51#1797C2211yescharacteristic
52#1797C2211yescharacteristic
53#1767C2211yescharacteristic
54C4×C4⋊C8C2211yescharacteristic
55#1753—21no—
56C4×C22⋊C8C2211yescharacteristic
57C4×C22⋊C8C2211yescharacteristic
58#1744C2211yescharacteristic
59C2×D4⋊C8C2211yescharacteristic
60C2×D4⋊C8C2211yescharacteristic
61C2×D4⋊C8C2211yescharacteristic
62C2×D4⋊C8C2211yescharacteristic
63#1279C2211yescharacteristic
64#1279C2211yescharacteristic
65#1279C2211yescharacteristic
66#1279C2211yescharacteristic
67#1279C2211yescharacteristic
68#1279C2211yescharacteristic
69#1279C2211yescharacteristic
70#1279C2211yescharacteristic
71#1279C2211yescharacteristic
72#1279C2211yescharacteristic
73#1279C2211yescharacteristic
74#1279C2211yescharacteristic
75C22×M16—21no—
76C23×C8—21no—
77#553—24no—
78#553—24no—
79C2×#126—21no—
80C2×#125C2×C411yescharacteristic
81C2×#123—21no—
82C2×#121—21no—
83C2×#121C2×C411yescharacteristic
84C2×#121C2×C411yescharacteristic
85C2×C4×D4—21no—
86C2×C4×D4—21no—
87C2×C4×D4—21no—
88C2×C4×D4—21no—
89C2×C4×D4C2×C411yescharacteristic
90C2×C4×D4C2×C411yescharacteristic
91C2×C4×D4C2×C411yescharacteristic
92C2×C4×D4D411yescharacteristic
93C2×C4×D4D411yescharacteristic
94C2×C4×D4C2311yescharacteristic
95C2×#117C2×C411yescharacteristic
96C2×#117C2×C411yescharacteristic
97C22×C4⋊C4C2×C411yescharacteristic
98C22×C4⋊C4C2×C411yescharacteristic
99C22×C42—21no—
100C22×C42—21no—
101C22×C42C2311yescharacteristic
102C22×C42C2311yescharacteristic
103#431—22no—
104#431—22no—
105#431—41no—
106#431—41no—
107#423—22no—
108#423—41no—
109C2×C4⋊C8—21no—
110C2×C4⋊C8—21no—
111C2×C4⋊C8—21no—
112C2×C4⋊C8C2311yescharacteristic
113C2×C4⋊C8C2311yescharacteristic
114C2×C4⋊C8C2311yescharacteristic
115C2×C4⋊C8C2311yescharacteristic
116C2×C22⋊C8—21no—
117C2×C22⋊C8—21no—
118C2×C22⋊C8—21no—
119C2×C22⋊C8—21no—
120C2×C22⋊C8—21no—
121C2×C22⋊C8—21no—
122C2×#97—21no—
123C2×C4×C8—22no—
124C2×C4×C8—21no—
125C2×C4×C8—21no—
126C2×C4×C8—41no—
127C2×C4×C8C2311yescharacteristic
128C2×C4×C8C2311yescharacteristic
129C2×C4×C8C2311yescharacteristic
130C2×C4×C8C2311yescharacteristic
131#390—21no—
132#390C2×C411yescharacteristic
133#390C2×C411yescharacteristic
134#389—21no—
135#389C2×C411yescharacteristic
136#389C2×C411yescharacteristic
137#389C2×C411yescharacteristic
138#389C2×C411yescharacteristic
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#387—21no—
154#387—21no—
155#386—21no—
156#386—21no—
157#386—21no—
158#386—21no—
159#386—21no—
160#385—21no—
161#383—21no—
162#382C2×C411yescharacteristic
163#381—21no—
164#380—21no—
165#380C2×C411yescharacteristic
166#380C2×C411yescharacteristic
167C4×C4⋊C4—21no—
168C4×C4⋊C4—21no—
169C4×C4⋊C4—21no—
170C4×C4⋊C4—21no—
171C4×C4⋊C4—21no—
172C4×C4⋊C4—21no—
173C4×C4⋊C4C2×C411yescharacteristic
174C4×C4⋊C4C2×C411yescharacteristic
175C4×C4⋊C4C2×C411yescharacteristic
176C4×C4⋊C4C2×C411yescharacteristic
177C4×C4⋊C4C2×C411yescharacteristic
178C4×C4⋊C4C2×C411yescharacteristic
179C4×C4⋊C4C2×C411yescharacteristic
180C4×C4⋊C4D411yescharacteristic
181C4×C4⋊C4D411yescharacteristic
182C4×C4⋊C4C2311yescharacteristic
183C4×C4⋊C4C2311yescharacteristic
184C4×C4⋊C4C2311yescharacteristic
185C4×C22⋊C4—21no—
186C4×C22⋊C4—21no—
187C4×C22⋊C4—21no—
188C4×C22⋊C4—21no—
189C4×C22⋊C4—21no—
190C4×C22⋊C4—21no—
191C4×C22⋊C4—21no—
192C4×C22⋊C4—21no—
193C4×C22⋊C4—21no—
194C4×C22⋊C4—21no—
195C4×C22⋊C4—21no—
196C4×C22⋊C4C2×C411yescharacteristic
197C4×C22⋊C4C2×C411yescharacteristic
198C4×C22⋊C4D411yescharacteristic
199C4×C22⋊C4D411yescharacteristic
200C4×C22⋊C4D411yescharacteristic
201C4×C22⋊C4D411yescharacteristic
202#376—21no—
203C2×#95—21no—
204C43—21no—
205C43C2311yescharacteristic
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#336—21no—
215#336—21no—
216D4⋊C8—22no—
217D4⋊C8—22no—
218D4⋊C8—41no—
219D4⋊C8—41no—
220C22×D4—21no—
221C22×D4—21no—
222C22×D4C22⋊C411yescharacteristic
223C22×D4C22×C411yescharacteristic
224C23×C4—21no—
225C23×C4—21no—
226C23×C4—21no—
227C23×C4—21no—
228C23×C4—21no—
229C23×C4C22×C411yescharacteristic
230C23×C4C22×C411yescharacteristic
231C23×C4C2×D411yescharacteristic
232C23×C4C2×D411yescharacteristic
233C23×C4C2×D411yescharacteristic
234C23×C4C2×D411yescharacteristic
235C2×M16—42no—
236C2×M16—42no—
237C2×M16—81no—
238C22×C8—21no—
239C22×C8—21no—
240C22×C8—21no—
241C22×C8—21no—
242C22×C8—21no—
243C22×C8—21no—
244C22×C8—21no—
245C22×C8—21no—
246C22×C8—42no—
247C22×C8—42no—
248C22×C8—42no—
249#126—28no—
250#125—22no—
251#125—22no—
252#123—28no—
253#121—28no—
254#121—22no—
255#121—22no—
256#121—22no—
257#121M1614yescomplemented
258C4×D4—28no—
259C4×D4—22no—
260C4×D4—22no—
261C4×D4—22no—
262C4×D4—22no—
263C4×D4—22no—
264C4×D4—22no—
265C4×D4—22no—
266C4×D4—21no—
267C4×D4—21no—
268C4×D4—21no—
269C4×D4—21no—
270C4×D4—41no—
271C4×D4—42no—
272C4×D4—44no—
273C4×D4—42no—
274C4×D4—42no—
275C4×D4—81no—
276C4×D4—81no—
277#117—22no—
278#117—22no—
279#117—41no—
280#117M1614yescomplemented
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—41no—
293C2×C4⋊C4C22⋊C411yescharacteristic
294C2×C4⋊C4C22⋊C411yescharacteristic
295C2×C4⋊C4C22⋊C411yescharacteristic
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—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—21no—
315C2×C22⋊C4—21no—
316C2×C22⋊C4C22⋊C411yescharacteristic
317C2×C22⋊C4C22⋊C411yescharacteristic
318C2×C22⋊C4C22⋊C411yescharacteristic
319C2×C22⋊C4C22⋊C411yescharacteristic
320C2×C22⋊C4C22⋊C411yescharacteristic
321C2×C22⋊C4C22⋊C411yescharacteristic
322C2×C42—21no—
323C2×C42—21no—
324C2×C42—21no—
325C2×C42—21no—
326C2×C42—21no—
327C2×C42—21no—
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—21no—
338C2×C42—21no—
339C2×C42—21no—
340C2×C42—21no—
341C2×C42—81no—
342C2×C42—81no—
343C2×C42—81no—
344C2×C42—81no—
345C2×C42C22×C411yescharacteristic
346C2×C42C22×C411yescharacteristic
347C2×C42C22×C411yescharacteristic
348C2×C42C22×C411yescharacteristic
349C2×C42C2×D411yescharacteristic
350C2×C42C2×D411yescharacteristic
351C2×C42C2×D411yescharacteristic
352C2×C42C2×D411yescharacteristic
353C2×C42C2×D411yescharacteristic
354C2×C42C2×D411yescharacteristic
355C2×C42C2×D411yescharacteristic
356C2×C42C2×D411yescharacteristic
357C2×C42C2411yescharacteristic
358C4⋊C8—21no—
359C4⋊C8—21no—
360C4⋊C8—21no—
361C4⋊C8—21no—
362C4⋊C8—21no—
363C4⋊C8—21no—
364C4⋊C8—21no—
365C4⋊C8—42no—
366C4⋊C8—42no—
367C4⋊C8—42no—
368C4⋊C8#4112yes—
369C22⋊C8—42no—
370C22⋊C8—42no—
371C22⋊C8—42no—
372C22⋊C8—42no—
373C22⋊C8—42no—
374C22⋊C8—81no—
375#97—81no—
376C4×C8—21no—
377C4×C8—21no—
378C4×C8—21no—
379C4×C8—21no—
380C4×C8—21no—
381C4×C8—21no—
382C4×C8—21no—
383C4×C8—42no—
384C4×C8—42no—
385C4×C8#4112yes—
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—21no—
402#95—21no—
403#95C22⋊C411yescharacteristic
404#95C22⋊C411yescharacteristic
405#95C22⋊C411yescharacteristic
406#95C22⋊C411yescharacteristic
407#95C22⋊C411yescharacteristic
408#95C22⋊C411yescharacteristic
409C24—21no—
410C24C2×C22⋊C411yescharacteristic
411C24C2×C22⋊C411yescharacteristic
412C2×D4—24no—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—24no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—41no—
422C2×D4—42no—
423C2×D4—42no—
424C2×D4—81no—
425C2×D4—81no—
426C2×D4C2×M1612yes—
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—24no—
440C22×C4—24no—
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—22no—
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—42no—
465C22×C4—42no—
466C22×C4—42no—
467C22×C4—42no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—81no—
475C22×C4—81no—
476C22×C4—81no—
477C22×C4—81no—
478C22×C4—81no—
479C22×C4—81no—
480C22×C4C2×C22⋊C411yescharacteristic
481C22×C4C2×C22⋊C411yescharacteristic
482C22×C4C2×C22⋊C411yescharacteristic
483C22×C4C2×C22⋊C411yescharacteristic
484C22×C4C2×C22⋊C411yescharacteristic
485C22×C4C2×C22⋊C411yescharacteristic
486C22×C4C2×C22⋊C411yescharacteristic
487C22×C4C2×C22⋊C411yescharacteristic
488C22×C4C2×C22⋊C411yescharacteristic
489C22×C4C2×C22⋊C411yescharacteristic
490C22×C4C2×M1612yes—
491C22×C4C2×M1612yes—
492C22×C4#13512yes—
493C22×C4#13512yes—
494C22×C4C23×C411yescharacteristic
495C22×C4C22×D411yescharacteristic
496C22×C4C22×D411yescharacteristic
497M16—84no—
498C2×C8—22no—
499C2×C8—22no—
500C2×C8—22no—
501C2×C8—41no—
502C2×C8—41no—
503C2×C8—41no—
504C2×C8—48no—
505C2×C8—41no—
506C2×C8—41no—
507C2×C8—41no—
508C2×C8—41no—
509C2×C8—41no—
510C2×C8—41no—
511C2×C8—41no—
512C2×C8—41no—
513C2×C8—41no—
514C2×C8—41no—
515C2×C8—41no—
516C2×C8—41no—
517C2×C8—41no—
518C2×C8—41no—
519C2×C8—41no—
520C2×C8—41no—
521C2×C8—41no—
522C2×C8—41no—
523C4⋊C4—24no—
524C4⋊C4—24no—
525C4⋊C4—24no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—22no—
531C4⋊C4—22no—
532C4⋊C4—22no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—42no—
540C4⋊C4—42no—
541C4⋊C4—42no—
542C4⋊C4—81no—
543C4⋊C4—81no—
544C4⋊C4C2×M1612yes—
545C4⋊C4C2×M1612yes—
546C4⋊C4C2×M1612yes—
547C4⋊C4#13112yes—
548C22⋊C4—24no—
549C22⋊C4—24no—
550C22⋊C4—24no—
551C22⋊C4—22no—
552C22⋊C4—22no—
553C22⋊C4—24no—
554C22⋊C4—22no—
555C22⋊C4—22no—
556C22⋊C4—22no—
557C22⋊C4—41no—
558C22⋊C4—42no—
559C22⋊C4—42no—
560C22⋊C4—42no—
561C22⋊C4—41no—
562C22⋊C4—41no—
563C22⋊C4—42no—
564C22⋊C4—42no—
565C22⋊C4—81no—
566C22⋊C4—81no—
567C22⋊C4—81no—
568C42—21no—
569C42—21no—
570C42—21no—
571C42—21no—
572C42—21no—
573C42—21no—
574C42—21no—
575C42—21no—
576C42—21no—
577C42—21no—
578C42—21no—
579C42—21no—
580C42—21no—
581C42—21no—
582C42—21no—
583C42—21no—
584C42—21no—
585C42—21no—
586C42—21no—
587C42—21no—
588C42—24no—
589C42—41no—
590C42—41no—
591C42—42no—
592C42—41no—
593C42—41no—
594C42—41no—
595C42—41no—
596C42—41no—
597C42—41no—
598C42—42no—
599C42—81no—
600C42—81no—
601C42—81no—
602C42—81no—
603C42—81no—
604C42C2×#4111yescharacteristic
605C42C2×#4111yescharacteristic
606C42H(5,𝔽2)11yescharacteristic
607C422−1+411yescharacteristic
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—22no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23#40712yes—
628C23#41612yes—
629C23C22×C22⋊C411yescharacteristic
630D4—22no—
631D4—22no—
632D4—44no—
633D4—48no—
634D4—41no—
635D4—41no—
636D4—84no—
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—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—22no—
658C2×C4—21no—
659C2×C4—22no—
660C2×C4—21no—
661C2×C4—22no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—22no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
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—81no—
706C2×C4—81no—
707C2×C4—84no—
708C2×C4—84no—
709C2×C4—84no—
710C2×C4—84no—
711C2×C4—81no—
712C2×C4—81no—
713C2×C4—81no—
714C2×C4—81no—
715C2×C4#40712yes—
716C2×C4#41612yes—
717C2×C4#42112yes—
718C2×C4C4×#4111yescharacteristic
719C2×C4#52011yescharacteristic
720C2×C4#54611yescharacteristic
721C2×C4#54611yescharacteristic
722C2×C4#54711yescharacteristic
723C2×C4#54711yescharacteristic
724C2×C4C22×M1611yescharacteristic
725C2×C4C22×M1611yescharacteristic
726C2×C4C2×#13111yescharacteristic
727C2×C4#56811yescharacteristic
728C2×C4C2×#13511yescharacteristic
729C2×C4C2×#13511yescharacteristic
730C2×C4#57611yescharacteristic
731C2×C4#57711yescharacteristic
732C8—42no—
733C8—42no—
734C8—42no—
735C8—81no—
736C8—81no—
737C8—81no—
738C8—81no—
739C8—81no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22#233911yescharacteristic
762C22C2×#40711yescharacteristic
763C22#288011yescharacteristic
764C22C2×#41611yescharacteristic
765C22#289711yescharacteristic
766C22C2×#42111yescharacteristic
767C22#290111yescharacteristic
768C4—22no—
769C4—22no—
770C4—21no—
771C4—21no—
772C4—22no—
773C4—41no—
774C4—42no—
775C4—41no—
776C4—42no—
777C4—42no—
778C4—41no—
779C4—41no—
780C4—42no—
781C4—41no—
782C4—41no—
783C4—41no—
784C4—81no—
785C4—81no—
786C4—81no—
787C4#296511yescharacteristic
788C4#297011yescharacteristic
789C4#298911yescharacteristic
790C4#299011yescharacteristic
791C4#329711yescharacteristic
792C4#330111yescharacteristic
793C4#333711yescharacteristic
794C4#333911yescharacteristic
795C2—42no—
796C2—42no—
797C2—82no—
798C2#1744311yescharacteristic
799C2#1745311yescharacteristic
800C2#1751011yescharacteristic
801C2#1752211yescharacteristic
802C2#2247111yescharacteristic
803C2#2248811yescharacteristic
804C2#2250611yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC2×C42C24
socleC23C22×C22⋊C4
prime radicalC2×#553C4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C42×D4 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #22749C2semidirect
3. #21101C2semidirect
4. #9875C2semidirect
5. #9867C2semidirect
6. #9076C2semidirect
7. #9072C2semidirect
8. #8944C2semidirect
9. #8940C2semidirect
10. #8708C2semidirect
11. #8707C2semidirect
12. #8565C2semidirect
13. #8174C2semidirect
14. #7901C2semidirect
15. #7890C2semidirect
257. #121M16semidirect
280. #117M16semidirect

Maximal subgroups

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

subgroupindex
C4×#5532
#227492
#211012
#98752
#98672
#90762
#90722
#89442
#89402
#87082
#87072
#85652
#81742
#79012
#78902