Finite Group Databasebeta

← #223430

Subgroups — #223430

Order 512.

998 conjugacy classes of subgroups.

The subgroup lattice has 779 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#554C211yesmaximal, characteristic
2#22749C211yesmaximal, characteristic
3#21265C211yesmaximal, characteristic
4#9877C211yesmaximal, characteristic, complemented
5#9869C211yesmaximal, characteristic, complemented
6#9075C211yesmaximal, characteristic, complemented
7#9073C211yesmaximal, characteristic, complemented
8#8942C211yesmaximal, characteristic, complemented
9#8938C211yesmaximal, characteristic, complemented
10#8707C211yesmaximal, characteristic, complemented
11#8706C211yesmaximal, characteristic, complemented
12#8566C211yesmaximal, characteristic, complemented
13#8173C211yesmaximal, characteristic, complemented
14#7901C211yesmaximal, characteristic, complemented
15#7892C211yesmaximal, characteristic, complemented
16C2×#554C411yescharacteristic
17C2×#431C2211yescharacteristic
18C2×#431C2211yescharacteristic
19C2×#431C2211yescharacteristic
20C2×#423C2211yescharacteristic
21#2370—21no—
22#2369C411yescharacteristic
23#2368—21no—
24#2368—21no—
25#2360C411yescharacteristic
26#2360C411yescharacteristic
27#2355C411yescharacteristic
28#2349—21no—
29D4×C4⋊C4C411yescharacteristic
30#2345C411yescharacteristic
31#2345C411yescharacteristic
32C4×C4⋊Q8C2211yescharacteristic
33C4×#125—21no—
34C4×C22⋊Q8—21no—
35C4×C22⋊Q8—21no—
36C4×C22⋊Q8C2211yescharacteristic
37C4×C22⋊Q8C2211yescharacteristic
38C42×Q8C2211yescharacteristic
39C42×D4—21no—
40C42×D4C2211yescharacteristic
41C2×C4×C4⋊C4C2211yescharacteristic
42C2×C4×C4⋊C4C2211yescharacteristic
43#1955—21no—
44#1940—21no—
45#1924—21no—
46#1924—21no—
47#1924—21no—
48#1916—21no—
49#1870—21no—
50#1831C2211yescharacteristic
51#1797C2211yescharacteristic
52#1797C2211yescharacteristic
53#1767C2211yescharacteristic
54C4×C4⋊C8C2211yescharacteristic
55#1753—21no—
56C4×C22⋊C8C2211yescharacteristic
57C4×C22⋊C8C2211yescharacteristic
58C4×#97C2211yescharacteristic
59C2×Q8⋊C8C2211yescharacteristic
60C2×Q8⋊C8C2211yescharacteristic
61C2×Q8⋊C8C2211yescharacteristic
62C2×Q8⋊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#554—24no—
77#554—24no—
78C2×C4⋊Q8C2×C411yescharacteristic
79C2×#125—21no—
80C2×C22⋊Q8—21no—
81C2×C22⋊Q8—21no—
82C2×C22⋊Q8C2×C411yescharacteristic
83C2×C22⋊Q8C2×C411yescharacteristic
84C2×C4×Q8—21no—
85C2×C4×Q8C2×C411yescharacteristic
86C2×C4×Q8C2×C411yescharacteristic
87C2×C4×Q8C2311yescharacteristic
88C2×C4×D4—21no—
89C2×C4×D4—21no—
90C2×C4×D4C2×C411yescharacteristic
91C2×C4×D4D411yescharacteristic
92C2×C4×D4D411yescharacteristic
93C22×C4⋊C4C2×C411yescharacteristic
94C22×C4⋊C4C2×C411yescharacteristic
95C22×C4⋊C4C2×C411yescharacteristic
96C22×C4⋊C4C2×C411yescharacteristic
97C22×C42—21no—
98C22×C42—21no—
99C22×C42C2311yescharacteristic
100C22×C42C2311yescharacteristic
101#431—22no—
102#431—22no—
103#431—22no—
104#431—41no—
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⋊C8—21no—
113C2×C4⋊C8C2311yescharacteristic
114C2×C4⋊C8C2311yescharacteristic
115C2×C4⋊C8C2311yescharacteristic
116C2×C4⋊C8C2311yescharacteristic
117C2×C22⋊C8—21no—
118C2×C22⋊C8—21no—
119C2×C22⋊C8—21no—
120C2×C22⋊C8—21no—
121C2×C22⋊C8—21no—
122C2×C22⋊C8—21no—
123C2×C22⋊C8—21no—
124C2×#97—21no—
125C2×#97—21no—
126C2×#97—21no—
127C2×C4×C8—21no—
128C2×C4×C8C2311yescharacteristic
129C2×C4×C8C2311yescharacteristic
130C2×C4×C8C2311yescharacteristic
131C2×C4×C8C2311yescharacteristic
132#391—21no—
133#391—21no—
134#391—21no—
135#391C2×C411yescharacteristic
136#391C2×C411yescharacteristic
137#389—21no—
138#389—21no—
139#389—21no—
140#389—21no—
141#389—21no—
142#389C2×C411yescharacteristic
143#389C2×C411yescharacteristic
144#389C2×C411yescharacteristic
145#389C2×C411yescharacteristic
146#387—21no—
147#387—21no—
148#387—21no—
149#387—21no—
150#387—21no—
151#387—21no—
152#387—21no—
153#387—21no—
154#387—21no—
155#387—21no—
156#385—21no—
157#385—21no—
158#385—21no—
159#385—21no—
160#385—21no—
161#385—21no—
162#384C2×C411yescharacteristic
163#382—21no—
164#380—21no—
165#380—21no—
166#380C2×C411yescharacteristic
167#380C2×C411yescharacteristic
168C4×C4⋊C4—21no—
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⋊C4—21no—
176C4×C4⋊C4—21no—
177C4×C4⋊C4—21no—
178C4×C4⋊C4—21no—
179C4×C4⋊C4—21no—
180C4×C4⋊C4C2×C411yescharacteristic
181C4×C4⋊C4C2×C411yescharacteristic
182C4×C4⋊C4C2×C411yescharacteristic
183C4×C4⋊C4C2×C411yescharacteristic
184C4×C4⋊C4C2×C411yescharacteristic
185C4×C4⋊C4C2×C411yescharacteristic
186C4×C4⋊C4C2×C411yescharacteristic
187C4×C4⋊C4D411yescharacteristic
188C4×C4⋊C4D411yescharacteristic
189C4×C4⋊C4C2311yescharacteristic
190C4×C4⋊C4C2311yescharacteristic
191C4×C4⋊C4C2311yescharacteristic
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
204C2×#95—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—
216Q8⋊C8—22no—
217Q8⋊C8—22no—
218Q8⋊C8—41no—
219Q8⋊C8—41no—
220C22×Q8—21no—
221C22×Q8C22×C411yescharacteristic
222C22×D4C22⋊C411yescharacteristic
223C23×C4—21no—
224C23×C4—21no—
225C23×C4—21no—
226C23×C4—21no—
227C23×C4C22×C411yescharacteristic
228C23×C4C22×C411yescharacteristic
229C23×C4C2×D411yescharacteristic
230C23×C4C2×D411yescharacteristic
231C23×C4C2×D411yescharacteristic
232C23×C4C2×D411yescharacteristic
233C2×M16—42no—
234C2×M16—42no—
235C2×M16—81no—
236C22×C8—21no—
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—21no—
240C22×C8—21no—
241C22×C8—21no—
242C22×C8—21no—
243C22×C8—21no—
244C4⋊Q8—22no—
245C4⋊Q8—22no—
246#125—28no—
247C22⋊Q8—28no—
248C22⋊Q8—28no—
249C22⋊Q8—22no—
250C22⋊Q8—22no—
251C22⋊Q8—22no—
252C22⋊Q8M1614yescomplemented
253C4×Q8—22no—
254C4×Q8—22no—
255C4×Q8—22no—
256C4×Q8—21no—
257C4×Q8—21no—
258C4×Q8—21no—
259C4×Q8—21no—
260C4×Q8—41no—
261C4×Q8—81no—
262C4×Q8—81no—
263C4×D4—28no—
264C4×D4—22no—
265C4×D4—22no—
266C4×D4—22no—
267C4×D4—22no—
268C4×D4—42no—
269C4×D4—44no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—22no—
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⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—41no—
292C2×C4⋊C4—41no—
293C2×C4⋊C4C22⋊C411yescharacteristic
294C2×C4⋊C4C22⋊C411yescharacteristic
295C2×C4⋊C4C22⋊C411yescharacteristic
296C2×C4⋊C4M1614yescomplemented
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×C4⋊C4C22×C411yescharacteristic
304C2×C22⋊C4—21no—
305C2×C22⋊C4—21no—
306C2×C22⋊C4—21no—
307C2×C22⋊C4—21no—
308C2×C22⋊C4C22⋊C411yescharacteristic
309C2×C22⋊C4C22⋊C411yescharacteristic
310C2×C22⋊C4C22⋊C411yescharacteristic
311C2×C22⋊C4C22⋊C411yescharacteristic
312C2×C22⋊C4C22⋊C411yescharacteristic
313C2×C22⋊C4C22⋊C411yescharacteristic
314C2×C42—21no—
315C2×C42—21no—
316C2×C42—21no—
317C2×C42—21no—
318C2×C42—21no—
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—81no—
335C2×C42—81no—
336C2×C42—81no—
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
346C2×C42C2×D411yescharacteristic
347C2×C42C2×D411yescharacteristic
348C2×C42C2×D411yescharacteristic
349C2×C42C2×D411yescharacteristic
350C2×C42C2411yescharacteristic
351C4⋊C8—21no—
352C4⋊C8—21no—
353C4⋊C8—21no—
354C4⋊C8—21no—
355C4⋊C8—21no—
356C4⋊C8—21no—
357C4⋊C8—21no—
358C4⋊C8—42no—
359C4⋊C8—42no—
360C4⋊C8—42no—
361C4⋊C8—42no—
362C4⋊C8#4112yes—
363C22⋊C8—42no—
364C22⋊C8—42no—
365C22⋊C8—42no—
366C22⋊C8—42no—
367C22⋊C8—42no—
368C22⋊C8—42no—
369C22⋊C8—81no—
370#97—42no—
371#97—42no—
372#97—81no—
373C4×C8—21no—
374C4×C8—21no—
375C4×C8—21no—
376C4×C8—21no—
377C4×C8—21no—
378C4×C8—21no—
379C4×C8—21no—
380C4×C8—42no—
381C4×C8#4112yes—
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#95C22⋊C411yescharacteristic
402#95C22⋊C411yescharacteristic
403#95C22⋊C411yescharacteristic
404#95C22⋊C411yescharacteristic
405#95C22⋊C411yescharacteristic
406#95C22⋊C411yescharacteristic
407C24C2×C22⋊C411yescharacteristic
408C24C2×C22⋊C411yescharacteristic
409C2×Q8—24no—
410C2×Q8—21no—
411C2×Q8—21no—
412C2×Q8—21no—
413C2×Q8—21no—
414C2×Q8—21no—
415C2×Q8—81no—
416C2×Q8—81no—
417C2×Q8C2×M1612yes—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—22no—
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—24no—
435C22×C4—24no—
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—41no—
456C22×C4—41no—
457C22×C4—41no—
458C22×C4—41no—
459C22×C4—42no—
460C22×C4—42no—
461C22×C4—42no—
462C22×C4—42no—
463C22×C4—81no—
464C22×C4—81no—
465C22×C4—81no—
466C22×C4—81no—
467C22×C4—81no—
468C22×C4—81no—
469C22×C4C2×C22⋊C411yescharacteristic
470C22×C4C2×C22⋊C411yescharacteristic
471C22×C4C2×C22⋊C411yescharacteristic
472C22×C4C2×C22⋊C411yescharacteristic
473C22×C4C2×C22⋊C411yescharacteristic
474C22×C4C2×C22⋊C411yescharacteristic
475C22×C4C2×C22⋊C411yescharacteristic
476C22×C4C2×C22⋊C411yescharacteristic
477C22×C4C2×C22⋊C411yescharacteristic
478C22×C4C2×C22⋊C411yescharacteristic
479C22×C4C2×M1612yes—
480C22×C4C2×M1612yes—
481C22×C4#13712yes—
482C22×C4#13712yes—
483C22×C4C23×C411yescharacteristic
484C22×C4C22×D411yescharacteristic
485C22×C4C22×D411yescharacteristic
486M16—84no—
487C2×C8—22no—
488C2×C8—22no—
489C2×C8—22no—
490C2×C8—41no—
491C2×C8—41no—
492C2×C8—41no—
493C2×C8—41no—
494C2×C8—41no—
495C2×C8—41no—
496C2×C8—41no—
497C2×C8—41no—
498C2×C8—41no—
499C2×C8—41no—
500C2×C8—41no—
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—
511C4⋊C4—24no—
512C4⋊C4—24no—
513C4⋊C4—24no—
514C4⋊C4—24no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—24no—
520C4⋊C4—24no—
521C4⋊C4—22no—
522C4⋊C4—22no—
523C4⋊C4—22no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—42no—
531C4⋊C4—42no—
532C4⋊C4—42no—
533C4⋊C4—41no—
534C4⋊C4—41no—
535C4⋊C4—42no—
536C4⋊C4—81no—
537C4⋊C4—81no—
538C4⋊C4—81no—
539C4⋊C4—81no—
540C4⋊C4—81no—
541C4⋊C4C2×M1612yes—
542C4⋊C4C2×M1612yes—
543C4⋊C4C2×M1612yes—
544C4⋊C4#13112yes—
545C22⋊C4—24no—
546C22⋊C4—24no—
547C22⋊C4—22no—
548C22⋊C4—22no—
549C22⋊C4—22no—
550C22⋊C4—22no—
551C22⋊C4—41no—
552C22⋊C4—41no—
553C22⋊C4—42no—
554C22⋊C4—42no—
555C42—24no—
556C42—21no—
557C42—21no—
558C42—21no—
559C42—21no—
560C42—21no—
561C42—21no—
562C42—21no—
563C42—21no—
564C42—21no—
565C42—21no—
566C42—21no—
567C42—21no—
568C42—21no—
569C42—21no—
570C42—21no—
571C42—21no—
572C42—21no—
573C42—21no—
574C42—21no—
575C42—21no—
576C42—22no—
577C42—41no—
578C42—42no—
579C42—41no—
580C42—41no—
581C42—41no—
582C42—41no—
583C42—41no—
584C42—41no—
585C42—41no—
586C42—41no—
587C42—42no—
588C42—81no—
589C42—81no—
590C42—81no—
591C42—81no—
592C42—81no—
593C42C2×#4111yescharacteristic
594C42C2×#4111yescharacteristic
595C42H(5,𝔽2)11yescharacteristic
596C422−1+411yescharacteristic
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23#40712yes—
610C23#41912yes—
611C23C22×C22⋊C411yescharacteristic
612Q8—22no—
613Q8—22no—
614Q8—41no—
615Q8—41no—
616Q8—84no—
617D4—28no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—22no—
639C2×C4—21no—
640C2×C4—22no—
641C2×C4—21no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—22no—
647C2×C4—21no—
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—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
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—81no—
688C2×C4—81no—
689C2×C4—81no—
690C2×C4—81no—
691C2×C4—84no—
692C2×C4—84no—
693C2×C4—84no—
694C2×C4—84no—
695C2×C4#40712yes—
696C2×C4#41912yes—
697C2×C4#42112yes—
698C2×C4C4×#4111yescharacteristic
699C2×C4#52011yescharacteristic
700C2×C4#54611yescharacteristic
701C2×C4#54611yescharacteristic
702C2×C4#54711yescharacteristic
703C2×C4#54711yescharacteristic
704C2×C4C22×M1611yescharacteristic
705C2×C4C22×M1611yescharacteristic
706C2×C4C2×#13111yescharacteristic
707C2×C4#56811yescharacteristic
708C2×C4C2×#13711yescharacteristic
709C2×C4C2×#13711yescharacteristic
710C2×C4#57611yescharacteristic
711C2×C4#57711yescharacteristic
712C8—42no—
713C8—42no—
714C8—42no—
715C8—81no—
716C8—81no—
717C8—81no—
718C8—81no—
719C8—81no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22#233911yescharacteristic
735C22C2×#40711yescharacteristic
736C22#288011yescharacteristic
737C22C2×#41911yescharacteristic
738C22#289711yescharacteristic
739C22C2×#42111yescharacteristic
740C22#290111yescharacteristic
741C4—22no—
742C4—22no—
743C4—22no—
744C4—21no—
745C4—21no—
746C4—41no—
747C4—42no—
748C4—42no—
749C4—42no—
750C4—41no—
751C4—41no—
752C4—42no—
753C4—41no—
754C4—42no—
755C4—41no—
756C4—41no—
757C4—41no—
758C4—81no—
759C4—81no—
760C4—81no—
761C4#296511yescharacteristic
762C4#297011yescharacteristic
763C4#298911yescharacteristic
764C4#299011yescharacteristic
765C4#331411yescharacteristic
766C4#331611yescharacteristic
767C4#334411yescharacteristic
768C4#334611yescharacteristic
769C2—42no—
770C2—42no—
771C2#1744911yescharacteristic
772C2#1745311yescharacteristic
773C2#1751411yescharacteristic
774C2#1752211yescharacteristic
775C2#2247111yescharacteristic
776C2#2249711yescharacteristic
777C2#2250711yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC2×C42C24
socleC23C22×C22⋊C4
prime radicalC22×D4C22⋊C4
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
4. #9877C2semidirect
5. #9869C2semidirect
6. #9075C2semidirect
7. #9073C2semidirect
8. #8942C2semidirect
9. #8938C2semidirect
10. #8707C2semidirect
11. #8706C2semidirect
12. #8566C2semidirect
13. #8173C2semidirect
14. #7901C2semidirect
15. #7892C2semidirect
252. C22⋊Q8M16semidirect
296. C2×C4⋊C4M16semidirect

Maximal subgroups

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

subgroupindex
C4×#5542
#227492
#212652
#98772
#98692
#90752
#90732
#89422
#89382
#87072
#87062
#85662
#81732
#79012
#78922