Finite Group Databasebeta

← #224419

Subgroups — #224419

Order 512.

1007 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×C22⋊Q8C211yesmaximal, characteristic
2#22510C211yesmaximal, characteristic
3#13927C211yesmaximal, characteristic
4#9912C211yesmaximal, characteristic
5#9911C211yesmaximal, characteristic
6#9909C211yesmaximal, characteristic
7#9889C211yesmaximal, characteristic
8#9888C211yesmaximal, characteristic
9#9885C211yesmaximal, characteristic
10#8578C211yesmaximal, characteristic
11#8576C211yesmaximal, characteristic
12#8574C211yesmaximal, characteristic
13#8221C211yesmaximal, characteristic
14#8219C211yesmaximal, characteristic
15#8217C211yesmaximal, characteristic
16C2×Q82C411yescharacteristic, complemented
17C22×C4×Q8C2211yescharacteristic
18C2×#446—21no—
19#2857C2211yescharacteristic
20#2857C2211yescharacteristic
21#2857C2211yescharacteristic
22#2582C411yescharacteristic, complemented
23#2582C411yescharacteristic, complemented
24#2582C411yescharacteristic, complemented
25#2567C411yescharacteristic, complemented
26#2567C411yescharacteristic, complemented
27#2567C411yescharacteristic, complemented
28#2451—21no—
29#2451—21no—
30#2451—21no—
31#2440—21no—
32#2440—21no—
33#2440—21no—
34Q8×C4⋊C4—21no—
35Q8×C4⋊C4C411yescharacteristic, complemented
36Q8×C22⋊C4—21no—
37C4×C22⋊Q8C2211yescharacteristic
38C4×C22⋊Q8C2211yescharacteristic
39C4×C22⋊Q8C2211yescharacteristic
40C2×#387—21no—
41#1985—21no—
42#1985—21no—
43#1984—21no—
44#1797C2211yescharacteristic
45#1797C2211yescharacteristic
46#1797C2211yescharacteristic
47#1749C2211yescharacteristic
48#1749C2211yescharacteristic
49C4×C22⋊C8C2211yescharacteristic
50C2×#328C2211yescharacteristic
51C2×#328C2211yescharacteristic
52C2×#328C2211yescharacteristic
53C2×#328C2211yescharacteristic
54#1446—21no—
55#1441—21no—
56#1436—21no—
57C4⋊#95C2211yescharacteristic
58#1434C2211yescharacteristic
59#1434C2211yescharacteristic
60#1434C2211yescharacteristic
61#1434C2211yescharacteristic
62C4×#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
75C23×Q8D411yescharacteristic
76Q82—44no—
77C2×C4⋊Q8—21no—
78C2×C4⋊Q8—21no—
79C2×C4⋊Q8—21no—
80C2×C4⋊Q8C2×C411yescharacteristic
81C2×C4⋊Q8C2×C411yescharacteristic
82C2×C4⋊Q8C2×C411yescharacteristic
83C2×C22⋊Q8—21no—
84C2×C22⋊Q8—21no—
85C2×C22⋊Q8—21no—
86C2×C22⋊Q8C2311yescharacteristic
87C2×C4×Q8—21no—
88C2×C4×Q8—21no—
89C2×C4×Q8—44no—
90C2×C4×Q8C2×C411yescharacteristic
91C2×C4×Q8C2×C411yescharacteristic
92C2×C4×Q8C2×C411yescharacteristic
93C2×C4×Q8C2×C411yescharacteristic
94C2×C4×Q8C2×C411yescharacteristic
95C2×C4×Q8C2×C411yescharacteristic
96C2×C4×Q8C2×C411yescharacteristic
97C2×C4×Q8D411yescharacteristic
98C2×C4×Q8D411yescharacteristic
99C2×C4×Q8D411yescharacteristic
100C2×C4×Q8D411yescharacteristic
101C22×C4⋊C4—21no—
102C22×C4⋊C4D411yescharacteristic
103C22×C4⋊C4D411yescharacteristic
104C22×C4⋊C4D411yescharacteristic
105C22×C42—21no—
106C22×C42C2311yescharacteristic
107C22×C42C2311yescharacteristic
108C22×C42C2311yescharacteristic
109#446—44no—
110C2×C4⋊C8—21no—
111C2×C4⋊C8—21no—
112C2×C4⋊C8—21no—
113C2×C22⋊C8C2311yescharacteristic
114C2×C22⋊C8C2311yescharacteristic
115C2×C22⋊C8C2311yescharacteristic
116C2×C22⋊C8C2311yescharacteristic
117C2×#97—21no—
118C2×#97—21no—
119C2×C4×C8—21no—
120#398—21no—
121#398—21no—
122#398—21no—
123#398—21no—
124#398—21no—
125#398—21no—
126#395—21no—
127#395—21no—
128#395—21no—
129#395—21no—
130#395—21no—
131#395—21no—
132#391—21no—
133#391—21no—
134#391—21no—
135#391—21no—
136#391—21no—
137#391—21no—
138#391—21no—
139#391—21no—
140#391—21no—
141#391C2×C411yescharacteristic
142#391C2×C411yescharacteristic
143#391C2×C411yescharacteristic
144#389—21no—
145#389—21no—
146#389—21no—
147#389—21no—
148#389—21no—
149#389—21no—
150#389—21no—
151#389—21no—
152#389—21no—
153#389C2×C411yescharacteristic
154#389C2×C411yescharacteristic
155#389C2×C411yescharacteristic
156#389C2×C411yescharacteristic
157#389C2×C411yescharacteristic
158#389C2×C411yescharacteristic
159#389C2×C411yescharacteristic
160#389C2×C411yescharacteristic
161#389C2×C411yescharacteristic
162#387—21no—
163#387—21no—
164#387—21no—
165#387—44no—
166#385—21no—
167#385—21no—
168#385—21no—
169#384—21no—
170#384—21no—
171#384—21no—
172#384C2×C411yescharacteristic
173#384C2×C411yescharacteristic
174#384C2×C411yescharacteristic
175#380—21no—
176#380—21no—
177#380—21no—
178#380C2311yescharacteristic
179#380C2311yescharacteristic
180#380C2311yescharacteristic
181C4×C4⋊C4—21no—
182C4×C4⋊C4—21no—
183C4×C4⋊C4—21no—
184C4×C4⋊C4C2×C411yescharacteristic
185C4×C4⋊C4C2×C411yescharacteristic
186C4×C4⋊C4C2×C411yescharacteristic
187C4×C22⋊C4—21no—
188C4×C22⋊C4—21no—
189C4×C22⋊C4—21no—
190C2×#95—21no—
191C2×#95—21no—
192C2×#95—21no—
193C2×#95—21no—
194C2×#95—21no—
195C2×#95—21no—
196C2×#95—21no—
197C2×#95—21no—
198C2×#95—21no—
199C2×#95—21no—
200C2×#95C2311yescharacteristic
201C2×#95C2311yescharacteristic
202C2×#95C2311yescharacteristic
203C2×#95C2311yescharacteristic
204#336—21no—
205#336—21no—
206#336—21no—
207#336—21no—
208#336—21no—
209#336—21no—
210#328—22no—
211#328—22no—
212#328—22no—
213#328Q814yescomplemented
214C22×Q8—21no—
215C22×Q8—21no—
216C22×Q8—21no—
217C22×Q8—22no—
218C22×Q8—22no—
219C22×Q8—42no—
220C22×Q8—42no—
221C22×Q8C22⋊C411yescharacteristic
222C22×Q8C22⋊C411yescharacteristic
223C22×Q8C22⋊C411yescharacteristic
224C22×Q8C22⋊C411yescharacteristic
225C22×Q8C22×C411yescharacteristic
226C23×C4—21no—
227C23×C4—21no—
228C23×C4—21no—
229C23×C4—21no—
230C23×C4C2×D411yescharacteristic
231C23×C4C2×D411yescharacteristic
232C23×C4C2×D411yescharacteristic
233C23×C4C2×D411yescharacteristic
234C23×C4C2×D411yescharacteristic
235C23×C4C2×D411yescharacteristic
236C23×C4C2411yescharacteristic
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—21no—
240C22×C8—21no—
241C4⋊Q8—42no—
242C4⋊Q8—42no—
243C4⋊Q8—42no—
244C4⋊Q8—44no—
245C4⋊Q8—44no—
246C4⋊Q8—44no—
247C22⋊Q8—21no—
248C22⋊Q8—21no—
249C22⋊Q8—81no—
250C22⋊Q8—81no—
251C22⋊Q8—81no—
252C22⋊Q8—81no—
253C22⋊Q8—81no—
254C22⋊Q8—81no—
255C22⋊Q8C2×Q812yes—
256C22⋊Q8#4112yes—
257C4×Q8—24no—
258C4×Q8—24no—
259C4×Q8—42no—
260C4×Q8—42no—
261C4×Q8—42no—
262C4×Q8—42no—
263C4×Q8—42no—
264C4×Q8—42no—
265C4×Q8—42no—
266C4×Q8—42no—
267C4×Q8—42no—
268C4×Q8—44no—
269C4×Q8—44no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—24no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
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—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—42no—
294C2×C4⋊C4—42no—
295C2×C4⋊C4—42no—
296C2×C4⋊C4—42no—
297C2×C4⋊C4—81no—
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×C4⋊C4C22⋊C411yescharacteristic
305C2×C4⋊C4C22⋊C411yescharacteristic
306C2×C4⋊C4C22⋊C411yescharacteristic
307C2×C4⋊C4C22⋊C411yescharacteristic
308C2×C4⋊C4C22⋊C411yescharacteristic
309C2×C4⋊C4C22⋊C411yescharacteristic
310C2×C4⋊C4C22×C411yescharacteristic
311C2×C4⋊C4C22×C411yescharacteristic
312C2×C4⋊C4C22×C411yescharacteristic
313C2×C4⋊C4C22×C411yescharacteristic
314C2×C4⋊C4C22×C411yescharacteristic
315C2×C4⋊C4C22×C411yescharacteristic
316C2×C4⋊C4C22×C411yescharacteristic
317C2×C22⋊C4—21no—
318C2×C22⋊C4—21no—
319C2×C22⋊C4—21no—
320C2×C22⋊C4—21no—
321C2×C42—21no—
322C2×C42—21no—
323C2×C42—21no—
324C2×C42—21no—
325C2×C42—21no—
326C2×C42—21no—
327C2×C42—42no—
328C2×C42—42no—
329C2×C42—42no—
330C2×C42—42no—
331C2×C42—42no—
332C2×C42—81no—
333C2×C42C22×C411yescharacteristic
334C2×C42C22×C411yescharacteristic
335C2×C42C22×C411yescharacteristic
336C2×C42C22×C411yescharacteristic
337C2×C42C22×C411yescharacteristic
338C2×C42C22×C411yescharacteristic
339C2×C42C2×D411yescharacteristic
340C2×C42C2×D411yescharacteristic
341C2×C42C2×D411yescharacteristic
342C2×C42C2×D411yescharacteristic
343C2×C42C2×D411yescharacteristic
344C2×C42C2×D411yescharacteristic
345C4⋊C8—42no—
346C4⋊C8—42no—
347C4⋊C8—42no—
348C22⋊C8—21no—
349C22⋊C8—21no—
350C22⋊C8—21no—
351C22⋊C8—21no—
352C22⋊C8—21no—
353C22⋊C8—21no—
354C22⋊C8—21no—
355C22⋊C8C2×Q812yes—
356#97—42no—
357#97—42no—
358C4×C8—42no—
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—42no—
388#95—42no—
389#95—42no—
390#95—42no—
391#95—42no—
392#95—42no—
393#95—42no—
394#95—42no—
395#95—42no—
396#95—81no—
397#95C2×Q812yes—
398C24C22×D411yescharacteristic
399C2×Q8—21no—
400C2×Q8—22no—
401C2×Q8—22no—
402C2×Q8—22no—
403C2×Q8—22no—
404C2×Q8—22no—
405C2×Q8—22no—
406C2×Q8—22no—
407C2×Q8—22no—
408C2×Q8—41no—
409C2×Q8—41no—
410C2×Q8—41no—
411C2×Q8—41no—
412C2×Q8—42no—
413C2×Q8—41no—
414C2×Q8—41no—
415C2×Q8—48no—
416C2×Q8—48no—
417C2×Q8—42no—
418C2×Q8—42no—
419C2×Q8—81no—
420C2×Q8—81no—
421C2×Q8—81no—
422C2×Q8—81no—
423C2×Q8—81no—
424C2×Q8—81no—
425C2×Q8C4×Q812yes—
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—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4—41no—
456C22×C4—41no—
457C22×C4—41no—
458C22×C4—41no—
459C22×C4—41no—
460C22×C4—41no—
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—41no—
478C22×C4—41no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4—41no—
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×C4C2×C22⋊C411yescharacteristic
495C22×C4C2×C22⋊C411yescharacteristic
496C22×C4C2×C22⋊C411yescharacteristic
497C22×C4C2×C22⋊C411yescharacteristic
498C22×C4#13712yes—
499C22×C4#13712yes—
500C22×C4C23×C411yescharacteristic
501C22×C4C22×D411yescharacteristic
502C22×C4C22×Q811yescharacteristic
503C22×C4C2×#4111yescharacteristic
504C22×C42−1+411yescharacteristic
505C22×C42−1+411yescharacteristic
506C2×C8—22no—
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—
518C4⋊C4—21no—
519C4⋊C4—22no—
520C4⋊C4—22no—
521C4⋊C4—22no—
522C4⋊C4—22no—
523C4⋊C4—22no—
524C4⋊C4—22no—
525C4⋊C4—22no—
526C4⋊C4—22no—
527C4⋊C4—22no—
528C4⋊C4—41no—
529C4⋊C4—41no—
530C4⋊C4—41no—
531C4⋊C4—41no—
532C4⋊C4—41no—
533C4⋊C4—41no—
534C4⋊C4—41no—
535C4⋊C4—41no—
536C4⋊C4—41no—
537C4⋊C4—41no—
538C4⋊C4—42no—
539C4⋊C4—42no—
540C4⋊C4—42no—
541C4⋊C4—42no—
542C4⋊C4—42no—
543C4⋊C4—42no—
544C4⋊C4—42no—
545C4⋊C4—42no—
546C4⋊C4—42no—
547C4⋊C4—81no—
548C4⋊C4—81no—
549C4⋊C4—81no—
550C4⋊C4—81no—
551C4⋊C4—81no—
552C4⋊C4—81no—
553C4⋊C4—81no—
554C4⋊C4—81no—
555C4⋊C4—81no—
556C4⋊C4—81no—
557C4⋊C4—81no—
558C4⋊C4—81no—
559C4⋊C4—84no—
560C4⋊C4#9914yes—
561C4⋊C4C4×Q812yes—
562C22⋊C4—22no—
563C22⋊C4—22no—
564C22⋊C4—41no—
565C22⋊C4—41no—
566C22⋊C4—41no—
567C22⋊C4—41no—
568C22⋊C4—41no—
569C22⋊C4—41no—
570C42—22no—
571C42—22no—
572C42—22no—
573C42—22no—
574C42—22no—
575C42—22no—
576C42—41no—
577C42—41no—
578C42—41no—
579C42—41no—
580C42—41no—
581C42—41no—
582C42—42no—
583C42—42no—
584C42—42no—
585C42—42no—
586C42—42no—
587C42—42no—
588C42—84no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23C22×C22⋊C411yescharacteristic
594C23#54811yescharacteristic
595C23D4×Q811yescharacteristic
596C23C2×#13711yescharacteristic
597C23C2×#13711yescharacteristic
598C23#57611yescharacteristic
599C23#57711yescharacteristic
600Q8—28no—
601Q8—44no—
602Q8—44no—
603Q8—42no—
604Q8—42no—
605Q8—44no—
606Q8—162no—
607Q8—162no—
608Q8—162no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
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—42no—
646C2×C4—42no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
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—81no—
692C2×C4—81no—
693C2×C4—81no—
694C2×C4—81no—
695C2×C4—81no—
696C2×C4—81no—
697C2×C4—81no—
698C2×C4—81no—
699C2×C4—81no—
700C2×C4—81no—
701C2×C4—81no—
702C2×C4—81no—
703C2×C4—81no—
704C2×C4—81no—
705C2×C4—81no—
706C2×C4—81no—
707C2×C4—81no—
708C2×C4—81no—
709C2×C4—81no—
710C2×C4—81no—
711C2×C4C2×#9912yes—
712C2×C4C2×#9912yes—
713C2×C4C2×#9912yes—
714C2×C4#41912yes—
715C2×C4#41912yes—
716C2×C4#42112yes—
717C2×C4C2×C4×Q811yescharacteristic
718C2×C4#51911yescharacteristic
719C2×C4#54811yescharacteristic
720C2×C4D4×Q811yescharacteristic
721C8—42no—
722C8—81no—
723C8—81no—
724C8—81no—
725C22—21no—
726C22—21no—
727C22—21no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22Q8×C22⋊C411yescharacteristic
738C22C22×#9911yescharacteristic
739C22#288411yescharacteristic
740C22C2×#41911yescharacteristic
741C22#289711yescharacteristic
742C22C2×#42111yescharacteristic
743C22#290111yescharacteristic
744C22#336911yescharacteristic
745C22#337511yescharacteristic
746C22#338511yescharacteristic
747C22#338711yescharacteristic
748C4—22no—
749C4—22no—
750C4—22no—
751C4—22no—
752C4—22no—
753C4—22no—
754C4—21no—
755C4—21no—
756C4—21no—
757C4—21no—
758C4—42no—
759C4—41no—
760C4—41no—
761C4—41no—
762C4—41no—
763C4—41no—
764C4—41no—
765C4—42no—
766C4—82no—
767C4—82no—
768C4—81no—
769C4—81no—
770C4—81no—
771C4—81no—
772C4—81no—
773C4—81no—
774C4—161no—
775C4—161no—
776C2—21no—
777C2—21no—
778C2—21no—
779C2—21no—
780C2#1757811yescharacteristic
781C2#1760211yescharacteristic
782C2#1760311yescharacteristic
783C2#1763211yescharacteristic
784C2Q8×#9911yescharacteristic
785C2#2252511yescharacteristic
786C2#2252911yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC24C22×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C22×C4×Q8 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
16. C2×Q82C4semidirect
22. #2582C4semidirect
23. #2582C4semidirect
24. #2582C4semidirect
25. #2567C4semidirect
26. #2567C4semidirect
27. #2567C4semidirect
35. Q8×C4⋊C4C4semidirect
213. #328Q8semidirect

Maximal subgroups

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

subgroupindex
Q8×C22⋊Q82
#225102
#139272
#99122
#99112
#99092
#98892
#98882
#98852
#85782
#85762
#85742
#82212
#82192
#82172