Finite Group Databasebeta

← #221518

Subgroups — #221518

Order 512.

1053 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34691C211yesmaximal, characteristic
2#22795C211yesmaximal, characteristic
3#21102C211yesmaximal, characteristic
4C2×#1485C211yesmaximal, characteristic, complemented
5C2×#1479C211yesmaximal, characteristic, complemented
6#9673C211yesmaximal, characteristic, complemented
7#9643C211yesmaximal, characteristic, complemented
8#9077C211yesmaximal, characteristic, complemented
9#9073C211yesmaximal, characteristic, complemented
10#8938C211yesmaximal, characteristic, complemented
11#8938C211yesmaximal, characteristic, complemented
12#8568C211yesmaximal, characteristic, complemented
13#8314C211yesmaximal, characteristic, complemented
14#8311C211yesmaximal, characteristic, complemented
15#8182C211yesmaximal, characteristic, complemented
16C2×#533C2211yescharacteristic
17C22×C4×Q8C2211yescharacteristic
18C2×#431C2211yescharacteristic
19C2×#431C2211yescharacteristic
20C2×#431C2211yescharacteristic
21C2×C4×M16C2211yescharacteristic
22#2473—21no—
23#2465—21no—
24#2462—21no—
25#2451C411yescharacteristic
26#2449—21no—
27#2446C411yescharacteristic
28#2440C411yescharacteristic
29#2434C411yescharacteristic
30#2429C411yescharacteristic
31#2423C411yescharacteristic
32#2417C411yescharacteristic
33#2409C411yescharacteristic
34#2399—21no—
35#2396—21no—
36C4×C4⋊Q8C2211yescharacteristic
37C4×C22⋊Q8—21no—
38C4×C22⋊Q8C2211yescharacteristic
39C4×C22⋊Q8C2211yescharacteristic
40#2295C2211yescharacteristic
41#2290—21no—
42C42×D4C2211yescharacteristic
43#1954—21no—
44#1924—21no—
45#1923—21no—
46#1923—21no—
47#1917—21no—
48#1870—21no—
49#1851—21no—
50#1842C2211yescharacteristic
51#1797C2211yescharacteristic
52#1797C2211yescharacteristic
53C8×C4⋊C4—21no—
54C4×C4⋊C8C2211yescharacteristic
55C4×C4⋊C8C2211yescharacteristic
56C4×C22⋊C8C2211yescharacteristic
57C4×C22⋊C8C2211yescharacteristic
58#1744C2211yescharacteristic
59#1485—24no—
60#1479—24no—
61C2×Q8⋊C8C2211yescharacteristic
62C2×Q8⋊C8C2211yescharacteristic
63C2×Q8⋊C8C2211yescharacteristic
64C2×Q8⋊C8C2211yescharacteristic
65C2×Q8⋊C8C2211yescharacteristic
66C2×Q8⋊C8C2211yescharacteristic
67C2×Q8⋊C8C2211yescharacteristic
68C2×Q8⋊C8C2211yescharacteristic
69C2×Q8⋊C8C2211yescharacteristic
70C2×Q8⋊C8C2211yescharacteristic
71C2×Q8⋊C8C2211yescharacteristic
72C2×Q8⋊C8C2211yescharacteristic
73#1279C2211yescharacteristic
74#1279C2211yescharacteristic
75#1279C2211yescharacteristic
76#1279C2211yescharacteristic
77C23×Q8C2×C411yescharacteristic
78C22×M16—21no—
79#533—22no—
80#533—22no—
81#533—41no—
82#533—41no—
83C2×C4⋊Q8C2×C411yescharacteristic
84C2×C4⋊Q8C2×C411yescharacteristic
85C2×C4⋊Q8C2×C411yescharacteristic
86C2×#125—21no—
87C2×C22⋊Q8—21no—
88C2×C22⋊Q8—21no—
89C2×C22⋊Q8C2×C411yescharacteristic
90C2×C22⋊Q8C2×C411yescharacteristic
91C2×C22⋊Q8C2×C411yescharacteristic
92C2×C22⋊Q8C2×C411yescharacteristic
93C2×C4×Q8—21no—
94C2×C4×Q8—21no—
95C2×C4×Q8—21no—
96C2×C4×Q8—22no—
97C2×C4×Q8—22no—
98C2×C4×Q8—41no—
99C2×C4×Q8—41no—
100C2×C4×Q8C2×C411yescharacteristic
101C2×C4×Q8C2×C411yescharacteristic
102C2×C4×Q8C2311yescharacteristic
103C2×C4×Q8C2311yescharacteristic
104C2×C4×Q8C2311yescharacteristic
105C2×C4×D4C2×C411yescharacteristic
106C2×C4×D4D411yescharacteristic
107C2×C4×D4D411yescharacteristic
108C2×#117—21no—
109C22×C4⋊C4—21no—
110C22×C4⋊C4C2×C411yescharacteristic
111C22×C42—21no—
112C22×C42C2311yescharacteristic
113C22×C42C2311yescharacteristic
114#431—22no—
115#431—22no—
116#431—22no—
117#431—41no—
118#431—41no—
119#431—41no—
120C2×C4⋊C8—21no—
121C2×C4⋊C8—21no—
122C2×C4⋊C8—21no—
123C2×C4⋊C8—21no—
124C2×C4⋊C8C2311yescharacteristic
125C2×C4⋊C8C2311yescharacteristic
126C2×C4⋊C8C2311yescharacteristic
127C2×C4⋊C8C2311yescharacteristic
128C2×C22⋊C8—21no—
129C2×C22⋊C8—21no—
130C2×C22⋊C8—21no—
131C2×C22⋊C8—21no—
132C2×C22⋊C8—21no—
133C2×C22⋊C8—21no—
134C2×C22⋊C8—21no—
135C4×M16—22no—
136C4×M16—41no—
137C2×#97—21no—
138C2×C4×C8—21no—
139C2×C4×C8—21no—
140C2×C4×C8—21no—
141C2×C4×C8C2311yescharacteristic
142C2×C4×C8C2311yescharacteristic
143C2×C4×C8C2311yescharacteristic
144C2×C4×C8C2311yescharacteristic
145#400—21no—
146#399—21no—
147#398—21no—
148#398—21no—
149#398—21no—
150#398—21no—
151#398—21no—
152#398—21no—
153#396—21no—
154#396—21no—
155#395—21no—
156#395—21no—
157#395—21no—
158#395—21no—
159#395—21no—
160#393—21no—
161#391—21no—
162#391C2×C411yescharacteristic
163#391C2×C411yescharacteristic
164#391C2×C411yescharacteristic
165#391C2×C411yescharacteristic
166#391C2×C411yescharacteristic
167#391C2×C411yescharacteristic
168#389—21no—
169#389—21no—
170#389—21no—
171#389C2×C411yescharacteristic
172#389C2×C411yescharacteristic
173#389C2×C411yescharacteristic
174#389C2×C411yescharacteristic
175#388—21no—
176#388—21no—
177#387—21no—
178#387—21no—
179#387—21no—
180#387—21no—
181#387—21no—
182#387—21no—
183#387—21no—
184#387—21no—
185#386—21no—
186#386—21no—
187#385—21no—
188#385—21no—
189#385—21no—
190#385—21no—
191#385—21no—
192#385—21no—
193#384C2×C411yescharacteristic
194#380—21no—
195#380C2×C411yescharacteristic
196#380C2×C411yescharacteristic
197C4×C4⋊C4—21no—
198C4×C4⋊C4—21no—
199C4×C4⋊C4—21no—
200C4×C4⋊C4—21no—
201C4×C4⋊C4—21no—
202C4×C4⋊C4C2×C411yescharacteristic
203C4×C4⋊C4D411yescharacteristic
204C4×C4⋊C4D411yescharacteristic
205C4×C4⋊C4C2311yescharacteristic
206C4×C22⋊C4—21no—
207C4×C22⋊C4—21no—
208C4×C22⋊C4C2×C411yescharacteristic
209C4×C22⋊C4C2×C411yescharacteristic
210C4×C22⋊C4D411yescharacteristic
211C4×C22⋊C4D411yescharacteristic
212C4×C22⋊C4D411yescharacteristic
213C4×C22⋊C4D411yescharacteristic
214#376—21no—
215C43C2311yescharacteristic
216#336—21no—
217#336—21no—
218#336—21no—
219#336—21no—
220#336—21no—
221#336—21no—
222#336—21no—
223#336—21no—
224Q8⋊C8—22no—
225Q8⋊C8—22no—
226Q8⋊C8—22no—
227Q8⋊C8—22no—
228Q8⋊C8—22no—
229Q8⋊C8—22no—
230Q8⋊C8—22no—
231Q8⋊C8—41no—
232Q8⋊C8—41no—
233Q8⋊C8—41no—
234Q8⋊C8—41no—
235Q8⋊C8D414yescomplemented
236C22×Q8—21no—
237C22×Q8—21no—
238C22×Q8—22no—
239C22×Q8—22no—
240C22×Q8—22no—
241C22×Q8—22no—
242C22×Q8—41no—
243C22×Q8—41no—
244C22×Q8C22×C411yescharacteristic
245C22×Q8C22×C411yescharacteristic
246C22×Q8C22×C411yescharacteristic
247C22×D4C22⋊C411yescharacteristic
248C23×C4—21no—
249C23×C4—21no—
250C23×C4C22×C411yescharacteristic
251C23×C4C22×C411yescharacteristic
252C23×C4C2×D411yescharacteristic
253C23×C4C2×D411yescharacteristic
254C23×C4C2×D411yescharacteristic
255C23×C4C2×D411yescharacteristic
256C2×M16—42no—
257C2×M16—42no—
258C2×M16—42no—
259C22×C8—21no—
260C22×C8—21no—
261C22×C8—21no—
262C22×C8—21no—
263C22×C8—21no—
264C22×C8—21no—
265C22×C8—21no—
266C22×C8—21no—
267C4⋊Q8—22no—
268C4⋊Q8—22no—
269C4⋊Q8—22no—
270C4⋊Q8—41no—
271C4⋊Q8—41no—
272C4⋊Q8—41no—
273#125—42no—
274#125—42no—
275C22⋊Q8—22no—
276C22⋊Q8—22no—
277C22⋊Q8—22no—
278C22⋊Q8—22no—
279C22⋊Q8—22no—
280C22⋊Q8—44no—
281C22⋊Q8—41no—
282C22⋊Q8—41no—
283C22⋊Q8—41no—
284C22⋊Q8—42no—
285C22⋊Q8—42no—
286C4×Q8—21no—
287C4×Q8—21no—
288C4×Q8—22no—
289C4×Q8—22no—
290C4×Q8—21no—
291C4×Q8—21no—
292C4×Q8—21no—
293C4×Q8—21no—
294C4×Q8—21no—
295C4×Q8—21no—
296C4×Q8—21no—
297C4×Q8—21no—
298C4×Q8—42no—
299C4×Q8—42no—
300C4×Q8—42no—
301C4×Q8—42no—
302C4×Q8—41no—
303C4×Q8—41no—
304C4×Q8—42no—
305C4×Q8—42no—
306C4×Q8C2×D412yes—
307C4×Q8#4112yes—
308C4×D4—22no—
309C4×D4—22no—
310C4×D4—22no—
311C4×D4—22no—
312C4×D4—42no—
313#117—42no—
314#117—42no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—41no—
338C2×C4⋊C4—42no—
339C2×C4⋊C4—42no—
340C2×C4⋊C4C22⋊C411yescharacteristic
341C2×C4⋊C4C22⋊C411yescharacteristic
342C2×C4⋊C4C22⋊C411yescharacteristic
343C2×C4⋊C4C22×C411yescharacteristic
344C2×C4⋊C4C22×C411yescharacteristic
345C2×C4⋊C4C22×C411yescharacteristic
346C2×C4⋊C4C22×C411yescharacteristic
347C2×C4⋊C4C22×C411yescharacteristic
348C2×C22⋊C4—21no—
349C2×C22⋊C4—21no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—21no—
354C2×C22⋊C4C22⋊C411yescharacteristic
355C2×C22⋊C4C22⋊C411yescharacteristic
356C2×C22⋊C4C22⋊C411yescharacteristic
357C2×C22⋊C4C22⋊C411yescharacteristic
358C2×C22⋊C4C22⋊C411yescharacteristic
359C2×C22⋊C4C22⋊C411yescharacteristic
360C2×C42—21no—
361C2×C42—21no—
362C2×C42—21no—
363C2×C42—21no—
364C2×C42—21no—
365C2×C42—21no—
366C2×C42—21no—
367C2×C42—21no—
368C2×C42—21no—
369C2×C42—21no—
370C2×C42—21no—
371C2×C42—21no—
372C2×C42—21no—
373C2×C42—21no—
374C2×C42—42no—
375C2×C42—42no—
376C2×C42C22×C411yescharacteristic
377C2×C42C22×C411yescharacteristic
378C2×C42C22×C411yescharacteristic
379C2×C42C22×C411yescharacteristic
380C2×C42C2×D411yescharacteristic
381C2×C42C2×D411yescharacteristic
382C2×C42C2×D411yescharacteristic
383C2×C42C2×D411yescharacteristic
384C2×C42C2×D411yescharacteristic
385C2×C42C2×D411yescharacteristic
386C2×C42C2×D411yescharacteristic
387C2×C42C2×D411yescharacteristic
388C2×C42C2411yescharacteristic
389C4⋊C8—21no—
390C4⋊C8—21no—
391C4⋊C8—21no—
392C4⋊C8—21no—
393C4⋊C8—21no—
394C4⋊C8—21no—
395C4⋊C8—21no—
396C4⋊C8—42no—
397C4⋊C8—42no—
398C4⋊C8—42no—
399C4⋊C8—81no—
400C4⋊C8C2×D412yes—
401C22⋊C8—42no—
402C22⋊C8—42no—
403C22⋊C8—42no—
404C22⋊C8—42no—
405C22⋊C8—42no—
406C22⋊C8—81no—
407C22⋊C8—81no—
408#97—42no—
409C4×C8—21no—
410C4×C8—21no—
411C4×C8—21no—
412C4×C8—21no—
413C4×C8—21no—
414C4×C8—21no—
415C4×C8—21no—
416C4×C8—42no—
417C4×C8—42no—
418C4×C8—42no—
419C4×C8C2×D412yes—
420#95—21no—
421#95—21no—
422#95—21no—
423#95—21no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95—21no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—21no—
434#95—21no—
435#95—21no—
436#95—21no—
437#95—21no—
438#95—21no—
439#95C22⋊C411yescharacteristic
440#95C22⋊C411yescharacteristic
441#95C22⋊C411yescharacteristic
442#95C22⋊C411yescharacteristic
443#95C22⋊C411yescharacteristic
444#95C22⋊C411yescharacteristic
445C24C2×C22⋊C411yescharacteristic
446C24C2×C22⋊C411yescharacteristic
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—28no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—42no—
465C2×Q8—42no—
466C2×Q8—42no—
467C2×Q8—44no—
468C2×Q8—44no—
469C2×Q8—44no—
470C2×Q8—42no—
471C2×Q8—42no—
472C2×Q8—81no—
473C2×Q8C4×D412yes—
474C2×Q8#13112yes—
475C2×D4—22no—
476C2×D4—22no—
477C2×D4—41no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—41no—
514C22×C4—41no—
515C22×C4—41no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—81no—
522C22×C4C2×C22⋊C411yescharacteristic
523C22×C4C2×C22⋊C411yescharacteristic
524C22×C4C2×C22⋊C411yescharacteristic
525C22×C4C2×C22⋊C411yescharacteristic
526C22×C4C2×C22⋊C411yescharacteristic
527C22×C4C2×C22⋊C411yescharacteristic
528C22×C4C2×C22⋊C411yescharacteristic
529C22×C4C2×C22⋊C411yescharacteristic
530C22×C4C2×C22⋊C411yescharacteristic
531C22×C4C2×C22⋊C411yescharacteristic
532C22×C4#13112yes—
533C22×C4#13112yes—
534C22×C4C23×C411yescharacteristic
535C22×C4C22×D411yescharacteristic
536C22×C4C22×D411yescharacteristic
537M16—48no—
538C2×C8—22no—
539C2×C8—22no—
540C2×C8—22no—
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—41no—
553C2×C8—41no—
554C2×C8—41no—
555C2×C8—41no—
556C2×C8—41no—
557C2×C8—41no—
558C2×C8—41no—
559C2×C8—41no—
560C2×C8—41no—
561C2×C8—41no—
562C4⋊C4—21no—
563C4⋊C4—22no—
564C4⋊C4—22no—
565C4⋊C4—22no—
566C4⋊C4—22no—
567C4⋊C4—22no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—42no—
577C4⋊C4—42no—
578C4⋊C4—42no—
579C4⋊C4—42no—
580C4⋊C4—42no—
581C4⋊C4—42no—
582C4⋊C4—42no—
583C4⋊C4—42no—
584C4⋊C4—42no—
585C4⋊C4—42no—
586C4⋊C4—42no—
587C4⋊C4—42no—
588C4⋊C4—42no—
589C4⋊C4—41no—
590C4⋊C4—41no—
591C4⋊C4—41no—
592C4⋊C4—41no—
593C4⋊C4—42no—
594C4⋊C4—42no—
595C4⋊C4—81no—
596C4⋊C4—81no—
597C4⋊C4—81no—
598C4⋊C4C4×D412yes—
599C22⋊C4—22no—
600C22⋊C4—22no—
601C22⋊C4—22no—
602C22⋊C4—22no—
603C22⋊C4—22no—
604C22⋊C4—41no—
605C22⋊C4—42no—
606C22⋊C4—42no—
607C22⋊C4—42no—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C22⋊C4—81no—
611C42—21no—
612C42—21no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—21no—
617C42—21no—
618C42—21no—
619C42—22no—
620C42—21no—
621C42—21no—
622C42—21no—
623C42—21no—
624C42—22no—
625C42—21no—
626C42—21no—
627C42—21no—
628C42—21no—
629C42—21no—
630C42—21no—
631C42—41no—
632C42—41no—
633C42—42no—
634C42—42no—
635C42—41no—
636C42—41no—
637C42—41no—
638C42—41no—
639C42—41no—
640C42—41no—
641C42#13712yes—
642C42#13712yes—
643C42C22×D411yescharacteristic
644C42C2×#4111yescharacteristic
645C42H(5,𝔽2)11yescharacteristic
646C42H(5,𝔽2)11yescharacteristic
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23#40812yes—
661C23C22×C22⋊C411yescharacteristic
662Q8—22no—
663Q8—22no—
664Q8—22no—
665Q8—22no—
666Q8—48no—
667Q8—41no—
668Q8—41no—
669Q8—41no—
670Q8—41no—
671Q8—41no—
672Q8—41no—
673Q8—41no—
674Q8—41no—
675Q8—84no—
676D4—44no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—22no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—48no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—81no—
749C2×C4—81no—
750C2×C4—84no—
751C2×C4#40812yes—
752C2×C4#41912yes—
753C2×C4#41912yes—
754C2×C4#42112yes—
755C2×C4C2×C4×D411yescharacteristic
756C2×C4#51811yescharacteristic
757C2×C4D4211yescharacteristic
758C2×C4D4211yescharacteristic
759C2×C4#54611yescharacteristic
760C2×C4#54611yescharacteristic
761C2×C4C2×#13111yescharacteristic
762C2×C4C2×#13111yescharacteristic
763C2×C4C2×#13111yescharacteristic
764C2×C4#56811yescharacteristic
765C2×C4C2×#13711yescharacteristic
766C2×C4C2×#13711yescharacteristic
767C2×C4#57711yescharacteristic
768C2×C4#57811yescharacteristic
769C8—42no—
770C8—42no—
771C8—42no—
772C8—81no—
773C8—81no—
774C8—81no—
775C8—81no—
776C8—81no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22D4×C22⋊C411yescharacteristic
792C22C2×#40811yescharacteristic
793C22#288011yescharacteristic
794C22C2×#41911yescharacteristic
795C22#289811yescharacteristic
796C22C2×#42111yescharacteristic
797C22#290111yescharacteristic
798C4—22no—
799C4—22no—
800C4—22no—
801C4—21no—
802C4—21no—
803C4—22no—
804C4—41no—
805C4—41no—
806C4—41no—
807C4—42no—
808C4—42no—
809C4—41no—
810C4—41no—
811C4—41no—
812C4—42no—
813C4—81no—
814C4—81no—
815C4—81no—
816C4—81no—
817C4—81no—
818C4#292911yescharacteristic
819C4#293311yescharacteristic
820C4#297611yescharacteristic
821C4#297711yescharacteristic
822C4#327611yescharacteristic
823C4#327811yescharacteristic
824C4#332811yescharacteristic
825C4#332911yescharacteristic
826C2—42no—
827C2—81no—
828C2#1746411yescharacteristic
829C2#1746911yescharacteristic
830C2#1751411yescharacteristic
831C2#1752511yescharacteristic
832C2#2239811yescharacteristic
833C2#2243011yescharacteristic
834C2#2243411yescharacteristic
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. C2×#1485C2semidirect
5. C2×#1479C2semidirect
6. #9673C2semidirect
7. #9643C2semidirect
8. #9077C2semidirect
9. #9073C2semidirect
10. #8938C2semidirect
11. #8938C2semidirect
12. #8568C2semidirect
13. #8314C2semidirect
14. #8311C2semidirect
15. #8182C2semidirect
235. Q8⋊C8D4semidirect

Maximal subgroups

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

subgroupindex
#346912
#227952
#211022
C2×#14852
C2×#14792
#96732
#96432
#90772
#90732
#89382
#85682
#83142
#83112
#81822