Finite Group Databasebeta

← #223519

Subgroups — #223519

Order 512.

1019 conjugacy classes of subgroups.

The subgroup lattice has 805 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#553C211yesmaximal, characteristic
2#22799C211yesmaximal, characteristic, complemented
3#21102C211yesmaximal, characteristic, complemented
4#9872C211yesmaximal, characteristic, complemented
5#9866C211yesmaximal, characteristic, complemented
6#9078C211yesmaximal, characteristic, complemented
7#9076C211yesmaximal, characteristic, complemented
8#8943C211yesmaximal, characteristic, complemented
9#8943C211yesmaximal, characteristic, complemented
10#8708C211yesmaximal, characteristic, complemented
11#8706C211yesmaximal, characteristic, complemented
12#8563C211yesmaximal, characteristic, complemented
13#8170C211yesmaximal, characteristic, complemented
14#7904C211yesmaximal, characteristic, complemented
15#7902C211yesmaximal, characteristic, complemented
16C2×#553C411yescharacteristic
17C2×#432C2211yescharacteristic
18C2×#432C2211yescharacteristic
19C2×#431C2211yescharacteristic
20C2×C4×M16C2211yescharacteristic
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#1954—21no—
44#1924—21no—
45#1924—21no—
46#1924—21no—
47#1917—21no—
48#1870—21no—
49#1851—21no—
50#1842C2211yescharacteristic
51#1797C2211yescharacteristic
52#1797C2211yescharacteristic
53#1770—21no—
54C4×C4⋊C8C2211yescharacteristic
55C4×C4⋊C8C2211yescharacteristic
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—
76#553—24no—
77#553—24no—
78C2×#126—21no—
79C2×#125C2×C411yescharacteristic
80C2×#123—21no—
81C2×#121—21no—
82C2×#121C2×C411yescharacteristic
83C2×#121C2×C411yescharacteristic
84C2×C4×D4—21no—
85C2×C4×D4—21no—
86C2×C4×D4—21no—
87C2×C4×D4—21no—
88C2×C4×D4C2×C411yescharacteristic
89C2×C4×D4C2×C411yescharacteristic
90C2×C4×D4C2×C411yescharacteristic
91C2×C4×D4D411yescharacteristic
92C2×C4×D4D411yescharacteristic
93C2×C4×D4C2311yescharacteristic
94C2×#117C2×C411yescharacteristic
95C2×#117C2×C411yescharacteristic
96C22×C4⋊C4C2×C411yescharacteristic
97C22×C4⋊C4C2×C411yescharacteristic
98C22×C42—21no—
99C22×C42—21no—
100C22×C42C2311yescharacteristic
101C22×C42C2311yescharacteristic
102#432—22no—
103#432—22no—
104#432—41no—
105#432—41no—
106#431—22no—
107#431—41no—
108C2×C4⋊C8—21no—
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×C22⋊C8—21no—
123C4×M16—22no—
124C4×M16—41no—
125C2×#97—21no—
126C2×#97—21no—
127C2×#97—21no—
128C2×C4×C8—21no—
129C2×C4×C8C2311yescharacteristic
130C2×C4×C8C2311yescharacteristic
131C2×C4×C8C2311yescharacteristic
132C2×C4×C8C2311yescharacteristic
133#390—21no—
134#390C2×C411yescharacteristic
135#390C2×C411yescharacteristic
136#389—21no—
137#389C2×C411yescharacteristic
138#389C2×C411yescharacteristic
139#389C2×C411yescharacteristic
140#389C2×C411yescharacteristic
141#388—21no—
142#388—21no—
143#388—21no—
144#388—21no—
145#388—21no—
146#388—21no—
147#388—21no—
148#388—21no—
149#388—21no—
150#387—21no—
151#387—21no—
152#387—21no—
153#387—21no—
154#387—21no—
155#387—21no—
156#387—21no—
157#386—21no—
158#386—21no—
159#386—21no—
160#386—21no—
161#386—21no—
162#385—21no—
163#383—21no—
164#382C2×C411yescharacteristic
165#381—21no—
166#380—21no—
167#380C2×C411yescharacteristic
168#380C2×C411yescharacteristic
169C4×C4⋊C4—21no—
170C4×C4⋊C4—21no—
171C4×C4⋊C4—21no—
172C4×C4⋊C4—21no—
173C4×C4⋊C4—21no—
174C4×C4⋊C4—21no—
175C4×C4⋊C4C2×C411yescharacteristic
176C4×C4⋊C4C2×C411yescharacteristic
177C4×C4⋊C4C2×C411yescharacteristic
178C4×C4⋊C4C2×C411yescharacteristic
179C4×C4⋊C4C2×C411yescharacteristic
180C4×C4⋊C4C2×C411yescharacteristic
181C4×C4⋊C4C2×C411yescharacteristic
182C4×C4⋊C4D411yescharacteristic
183C4×C4⋊C4D411yescharacteristic
184C4×C4⋊C4C2311yescharacteristic
185C4×C4⋊C4C2311yescharacteristic
186C4×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
197C4×C22⋊C4—21no—
198C4×C22⋊C4C2×C411yescharacteristic
199C4×C22⋊C4C2×C411yescharacteristic
200C4×C22⋊C4D411yescharacteristic
201C4×C22⋊C4D411yescharacteristic
202C4×C22⋊C4D411yescharacteristic
203C4×C22⋊C4D411yescharacteristic
204#376—21no—
205C2×#95—21no—
206C43—21no—
207C43C2311yescharacteristic
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—42no—
238C22×C8—21no—
239C22×C8—21no—
240C22×C8—21no—
241C22×C8—21no—
242C22×C8—21no—
243C22×C8—21no—
244C22×C8—21no—
245C22×C8—21no—
246#126—28no—
247#125—22no—
248#125M1614yescomplemented
249#123—28no—
250#121—28no—
251#121—22no—
252#121—22no—
253#121—22no—
254#121—22no—
255C4×D4—28no—
256C4×D4—22no—
257C4×D4—22no—
258C4×D4—22no—
259C4×D4—22no—
260C4×D4—21no—
261C4×D4—21no—
262C4×D4—21no—
263C4×D4—21no—
264C4×D4—41no—
265C4×D4—41no—
266C4×D4—41no—
267C4×D4—42no—
268C4×D4—44no—
269C4×D4—42no—
270C4×D4—42no—
271C4×D4—81no—
272C4×D4—81no—
273C4×D4M1614yescomplemented
274#117—22no—
275#117—22no—
276#117—22no—
277#117—41no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—41no—
290C2×C4⋊C4C22⋊C411yescharacteristic
291C2×C4⋊C4C22⋊C411yescharacteristic
292C2×C4⋊C4C22⋊C411yescharacteristic
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×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⋊C4C22⋊C411yescharacteristic
314C2×C22⋊C4C22⋊C411yescharacteristic
315C2×C22⋊C4C22⋊C411yescharacteristic
316C2×C22⋊C4C22⋊C411yescharacteristic
317C2×C22⋊C4C22⋊C411yescharacteristic
318C2×C22⋊C4C22⋊C411yescharacteristic
319C2×C42—21no—
320C2×C42—21no—
321C2×C42—21no—
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—81no—
339C2×C42—81no—
340C2×C42—81no—
341C2×C42—81no—
342C2×C42C22×C411yescharacteristic
343C2×C42C22×C411yescharacteristic
344C2×C42C22×C411yescharacteristic
345C2×C42C22×C411yescharacteristic
346C2×C42C2×D411yescharacteristic
347C2×C42C2×D411yescharacteristic
348C2×C42C2×D411yescharacteristic
349C2×C42C2×D411yescharacteristic
350C2×C42C2×D411yescharacteristic
351C2×C42C2×D411yescharacteristic
352C2×C42C2×D411yescharacteristic
353C2×C42C2×D411yescharacteristic
354C2×C42C2411yescharacteristic
355C4⋊C8—21no—
356C4⋊C8—21no—
357C4⋊C8—21no—
358C4⋊C8—21no—
359C4⋊C8—21no—
360C4⋊C8—21no—
361C4⋊C8—21no—
362C4⋊C8—42no—
363C4⋊C8—42no—
364C4⋊C8—42no—
365C4⋊C8—81no—
366C4⋊C8#4112yes—
367C22⋊C8—42no—
368C22⋊C8—42no—
369C22⋊C8—42no—
370C22⋊C8—42no—
371C22⋊C8—42no—
372C22⋊C8—81no—
373C22⋊C8—81no—
374#97—42no—
375#97—42no—
376#97—42no—
377C4×C8—21no—
378C4×C8—21no—
379C4×C8—21no—
380C4×C8—21no—
381C4×C8—21no—
382C4×C8—21no—
383C4×C8—21no—
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—24no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—22no—
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—22no—
432C22×C4—24no—
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—24no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—41no—
466C22×C4—41no—
467C22×C4—41no—
468C22×C4—42no—
469C22×C4—42no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4—81no—
479C22×C4—81no—
480C22×C4—81no—
481C22×C4—81no—
482C22×C4—81no—
483C22×C4—81no—
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×C22⋊C411yescharacteristic
491C22×C4C2×C22⋊C411yescharacteristic
492C22×C4C2×C22⋊C411yescharacteristic
493C22×C4C2×C22⋊C411yescharacteristic
494C22×C4C23×C411yescharacteristic
495C22×C4C22×D411yescharacteristic
496C22×C4C22×D411yescharacteristic
497M16—48no—
498C2×C8—22no—
499C2×C8—22no—
500C2×C8—22no—
501C2×C8—41no—
502C2×C8—41no—
503C2×C8—41no—
504C2×C8—41no—
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—
522C4⋊C4—24no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—24no—
528C4⋊C4—24no—
529C4⋊C4—22no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—41no—
537C4⋊C4—41no—
538C4⋊C4—42no—
539C4⋊C4—42no—
540C4⋊C4—42no—
541C4⋊C4—81no—
542C4⋊C4—81no—
543C4⋊C4C2×M1612yes—
544C4⋊C4C2×M1612yes—
545C4⋊C4C2×M1612yes—
546C4⋊C4#13112yes—
547C22⋊C4—24no—
548C22⋊C4—24no—
549C22⋊C4—24no—
550C22⋊C4—22no—
551C22⋊C4—24no—
552C22⋊C4—22no—
553C22⋊C4—22no—
554C22⋊C4—41no—
555C22⋊C4—41no—
556C22⋊C4—41no—
557C22⋊C4—42no—
558C22⋊C4—42no—
559C22⋊C4—42no—
560C22⋊C4—42no—
561C22⋊C4—42no—
562C22⋊C4—41no—
563C22⋊C4—41no—
564C22⋊C4—81no—
565C22⋊C4—81no—
566C22⋊C4—81no—
567C42—24no—
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—41no—
587C42—41no—
588C42—42no—
589C42—42no—
590C42—41no—
591C42—41no—
592C42—41no—
593C42—41no—
594C42—41no—
595C42—41no—
596C42—81no—
597C42—81no—
598C42—81no—
599C42—81no—
600C42—81no—
601C42C2×M1612yes—
602C42C2×M1612yes—
603C42C2×#4111yescharacteristic
604C42C2×#4111yescharacteristic
605C42H(5,𝔽2)11yescharacteristic
606C422−1+411yescharacteristic
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—22no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23#42112yes—
628C23C22×C22⋊C411yescharacteristic
629D4—22no—
630D4—22no—
631D4—44no—
632D4—48no—
633D4—41no—
634D4—41no—
635D4—84no—
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—21no—
648C2×C4—21no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—21no—
652C2×C4—22no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—22no—
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—21no—
669C2×C4—21no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
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#40712yes—
717C2×C4C4×#4111yescharacteristic
718C2×C4#52011yescharacteristic
719C2×C4#54611yescharacteristic
720C2×C4#54611yescharacteristic
721C2×C4#54711yescharacteristic
722C2×C4#54711yescharacteristic
723C2×C4C22×M1611yescharacteristic
724C2×C4C22×M1611yescharacteristic
725C2×C4C2×#13111yescharacteristic
726C2×C4#56811yescharacteristic
727C2×C4#57511yescharacteristic
728C2×C4#57511yescharacteristic
729C2×C4#57611yescharacteristic
730C2×C4#57711yescharacteristic
731C8—42no—
732C8—42no—
733C8—42no—
734C8—81no—
735C8—81no—
736C8—81no—
737C8—81no—
738C8—81no—
739C22—22no—
740C22—22no—
741C22—22no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—42no—
748C22—42no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—42no—
754C22—41no—
755C22—41no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22#233911yescharacteristic
761C22C2×#40711yescharacteristic
762C22#288011yescharacteristic
763C22#289611yescharacteristic
764C22#289711yescharacteristic
765C22C2×#42111yescharacteristic
766C22#290111yescharacteristic
767C4—22no—
768C4—22no—
769C4—21no—
770C4—21no—
771C4—42no—
772C4—42no—
773C4—42no—
774C4—41no—
775C4—41no—
776C4—42no—
777C4—41no—
778C4—41no—
779C4—41no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—81no—
784C4—81no—
785C4—81no—
786C4#296511yescharacteristic
787C4#297111yescharacteristic
788C4#298911yescharacteristic
789C4#299111yescharacteristic
790C4#330711yescharacteristic
791C4#330911yescharacteristic
792C4#334711yescharacteristic
793C4#335011yescharacteristic
794C2—42no—
795C2—81no—
796C2—82no—
797C2#1745211yescharacteristic
798C2#1745311yescharacteristic
799C2#1751611yescharacteristic
800C2#1752111yescharacteristic
801C2#2247311yescharacteristic
802C2#2249811yescharacteristic
803C2#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. #22799C2semidirect
3. #21102C2semidirect
4. #9872C2semidirect
5. #9866C2semidirect
6. #9078C2semidirect
7. #9076C2semidirect
8. #8943C2semidirect
9. #8943C2semidirect
10. #8708C2semidirect
11. #8706C2semidirect
12. #8563C2semidirect
13. #8170C2semidirect
14. #7904C2semidirect
15. #7902C2semidirect
248. #125M16semidirect
273. C4×D4M16semidirect

Maximal subgroups

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

subgroupindex
C4×#5532
#227992
#211022
#98722
#98662
#90782
#90762
#89432
#87082
#87062
#85632
#81702
#79042
#79022