Finite Group Databasebeta

← #221622

Subgroups — #221622

Order 512.

1210 conjugacy classes of subgroups.

The subgroup lattice has 865 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×D4×Q8C211yesmaximal, characteristic
2#22751C211yesmaximal, characteristic
3#21102C211yesmaximal, characteristic
4C2×#1491C211yesmaximal, characteristic, complemented
5C2×#1487C211yesmaximal, characteristic, complemented
6#9673C211yesmaximal, characteristic, complemented
7#9641C211yesmaximal, characteristic, complemented
8#9077C211yesmaximal, characteristic, complemented
9#9075C211yesmaximal, characteristic, complemented
10#8942C211yesmaximal, characteristic, complemented
11#8941C211yesmaximal, characteristic, complemented
12#8566C211yesmaximal, characteristic, complemented
13#8311C211yesmaximal, characteristic, complemented
14#8311C211yesmaximal, characteristic, complemented
15#8171C211yesmaximal, characteristic, complemented
16C2×D4×Q8C411yescharacteristic
17C22×C4×Q8C2211yescharacteristic
18C22×C4×Q8C2211yescharacteristic
19C2×#432C2211yescharacteristic
20C2×#431C2211yescharacteristic
21C2×#423C2211yescharacteristic
22C2×C4×M16C2211yescharacteristic
23#2365—21no—
24#2365C411yescharacteristic
25#2360—21no—
26#2360—21no—
27#2360C411yescharacteristic
28#2360C411yescharacteristic
29Q8×C4⋊C4C411yescharacteristic
30D4×C4⋊C4—21no—
31D4×C4⋊C4C411yescharacteristic
32Q8×C22⋊C4C411yescharacteristic
33Q8×C22⋊C4C411yescharacteristic
34C4×C4⋊Q8—21no—
35C4×C4⋊Q8C2211yescharacteristic
36C4×C22⋊Q8—21no—
37C4×C22⋊Q8—21no—
38C4×C22⋊Q8C2211yescharacteristic
39C4×C22⋊Q8C2211yescharacteristic
40C42×Q8C2211yescharacteristic
41C42×D4—21no—
42C42×D4C2211yescharacteristic
43#1924—21no—
44#1923—21no—
45#1917—21no—
46#1917—21no—
47#1870—21no—
48#1870—21no—
49#1851—21no—
50#1831C2211yescharacteristic
51#1797C2211yescharacteristic
52#1797C2211yescharacteristic
53C4×C4⋊C8C2211yescharacteristic
54C4×C4⋊C8C2211yescharacteristic
55#1753—21no—
56C4×C22⋊C8C2211yescharacteristic
57C4×C22⋊C8C2211yescharacteristic
58#1744C2211yescharacteristic
59#1491—24no—
60#1487—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
78C23×Q8C2×C411yescharacteristic
79C22×M16—21no—
80C22×M16—21no—
81D4×Q8—24no—
82D4×Q8—24no—
83C2×C4⋊Q8—21no—
84C2×C4⋊Q8C2×C411yescharacteristic
85C2×C22⋊Q8—21no—
86C2×C22⋊Q8—21no—
87C2×C22⋊Q8C2×C411yescharacteristic
88C2×C22⋊Q8C2×C411yescharacteristic
89C2×C4×Q8—21no—
90C2×C4×Q8—21no—
91C2×C4×Q8—21no—
92C2×C4×Q8—21no—
93C2×C4×Q8—22no—
94C2×C4×Q8—22no—
95C2×C4×Q8—22no—
96C2×C4×Q8—22no—
97C2×C4×Q8—41no—
98C2×C4×Q8—41no—
99C2×C4×Q8—41no—
100C2×C4×Q8—41no—
101C2×C4×Q8C2×C411yescharacteristic
102C2×C4×Q8C2×C411yescharacteristic
103C2×C4×Q8C2×C411yescharacteristic
104C2×C4×Q8C2×C411yescharacteristic
105C2×C4×Q8C2×C411yescharacteristic
106C2×C4×Q8C2×C411yescharacteristic
107C2×C4×Q8C2311yescharacteristic
108C2×C4×Q8C2311yescharacteristic
109C2×C4×Q8C2311yescharacteristic
110C2×C4×D4—21no—
111C2×C4×D4—21no—
112C2×C4×D4C2×C411yescharacteristic
113C2×C4×D4D411yescharacteristic
114C2×C4×D4D411yescharacteristic
115C22×C4⋊C4—21no—
116C22×C4⋊C4—21no—
117C22×C4⋊C4C2×C411yescharacteristic
118C22×C4⋊C4C2×C411yescharacteristic
119C22×C42—21no—
120C22×C42—21no—
121C22×C42C2311yescharacteristic
122C22×C42C2311yescharacteristic
123#432—22no—
124#432—41no—
125#431—22no—
126#431—41no—
127#423—22no—
128#423—41no—
129C2×C4⋊C8—21no—
130C2×C4⋊C8—21no—
131C2×C4⋊C8—21no—
132C2×C4⋊C8C2311yescharacteristic
133C2×C4⋊C8C2311yescharacteristic
134C2×C4⋊C8C2311yescharacteristic
135C2×C4⋊C8C2311yescharacteristic
136C2×C22⋊C8—21no—
137C2×C22⋊C8—21no—
138C2×C22⋊C8—21no—
139C2×C22⋊C8—21no—
140C2×C22⋊C8—21no—
141C2×C22⋊C8—21no—
142C4×M16—22no—
143C4×M16—41no—
144C2×#97—21no—
145C2×#97—21no—
146C2×C4×C8—21no—
147C2×C4×C8C2311yescharacteristic
148C2×C4×C8C2311yescharacteristic
149C2×C4×C8C2311yescharacteristic
150C2×C4×C8C2311yescharacteristic
151#391—21no—
152#391—21no—
153#391—21no—
154#391—21no—
155#391C2×C411yescharacteristic
156#391C2×C411yescharacteristic
157#391C2×C411yescharacteristic
158#391C2×C411yescharacteristic
159#389—21no—
160#389—21no—
161#389—21no—
162#389—21no—
163#389—21no—
164#389—21no—
165#389—21no—
166#389—21no—
167#389C2×C411yescharacteristic
168#389C2×C411yescharacteristic
169#387—21no—
170#387—21no—
171#387—21no—
172#387—21no—
173#387—21no—
174#387—21no—
175#385—21no—
176#385—21no—
177#385—21no—
178#385—21no—
179#385—21no—
180#385—21no—
181#384—21no—
182#384C2×C411yescharacteristic
183#380—21no—
184#380—21no—
185#380C2×C411yescharacteristic
186#380C2×C411yescharacteristic
187C4×C4⋊C4—21no—
188C4×C4⋊C4—21no—
189C4×C4⋊C4—21no—
190C4×C4⋊C4—21no—
191C4×C4⋊C4—21no—
192C4×C4⋊C4—21no—
193C4×C4⋊C4—21no—
194C4×C4⋊C4—21no—
195C4×C4⋊C4—21no—
196C4×C4⋊C4C2×C411yescharacteristic
197C4×C4⋊C4C2×C411yescharacteristic
198C4×C4⋊C4C2×C411yescharacteristic
199C4×C4⋊C4D411yescharacteristic
200C4×C4⋊C4D411yescharacteristic
201C4×C4⋊C4C2311yescharacteristic
202C4×C22⋊C4—21no—
203C4×C22⋊C4—21no—
204C4×C22⋊C4—21no—
205C4×C22⋊C4—21no—
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
214C43—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—
224#336—21no—
225#336—21no—
226Q8⋊C8—22no—
227Q8⋊C8—22no—
228Q8⋊C8—22no—
229Q8⋊C8—22no—
230Q8⋊C8—22no—
231Q8⋊C8—22no—
232Q8⋊C8—22no—
233Q8⋊C8—41no—
234Q8⋊C8—41no—
235Q8⋊C8—41no—
236Q8⋊C8—41no—
237Q8⋊C8D414yescomplemented
238C22×Q8—22no—
239C22×Q8—22no—
240C22×Q8—22no—
241C22×Q8—22no—
242C22×Q8—21no—
243C22×Q8—21no—
244C22×Q8—22no—
245C22×Q8—22no—
246C22×Q8—22no—
247C22×Q8—22no—
248C22×Q8—41no—
249C22×Q8—41no—
250C22×Q8—41no—
251C22×Q8—41no—
252C22×Q8C22×C411yescharacteristic
253C22×Q8C22×C411yescharacteristic
254C22×Q8C22×C411yescharacteristic
255C22×D4C22⋊C411yescharacteristic
256C23×C4—21no—
257C23×C4—21no—
258C23×C4—21no—
259C23×C4—21no—
260C23×C4C22×C411yescharacteristic
261C23×C4C22×C411yescharacteristic
262C23×C4C2×D411yescharacteristic
263C23×C4C2×D411yescharacteristic
264C23×C4C2×D411yescharacteristic
265C23×C4C2×D411yescharacteristic
266C2×M16—42no—
267C2×M16—42no—
268C2×M16—42no—
269C2×M16—42no—
270C2×M16—42no—
271C2×M16—81no—
272C22×C8—21no—
273C22×C8—21no—
274C22×C8—21no—
275C22×C8—21no—
276C22×C8—21no—
277C22×C8—21no—
278C22×C8—21no—
279C22×C8—21no—
280C4⋊Q8—28no—
281C4⋊Q8—22no—
282C4⋊Q8M1614yescomplemented
283C22⋊Q8—28no—
284C22⋊Q8—28no—
285C22⋊Q8—22no—
286C22⋊Q8—22no—
287C22⋊Q8—22no—
288C22⋊Q8—22no—
289C4×Q8—22no—
290C4×Q8—21no—
291C4×Q8—21no—
292C4×Q8—22no—
293C4×Q8—22no—
294C4×Q8—22no—
295C4×Q8—22no—
296C4×Q8—22no—
297C4×Q8—21no—
298C4×Q8—21no—
299C4×Q8—21no—
300C4×Q8—21no—
301C4×Q8—21no—
302C4×Q8—21no—
303C4×Q8—21no—
304C4×Q8—21no—
305C4×Q8—42no—
306C4×Q8—42no—
307C4×Q8—42no—
308C4×Q8—42no—
309C4×Q8—41no—
310C4×Q8—41no—
311C4×Q8—41no—
312C4×Q8—41no—
313C4×Q8—41no—
314C4×Q8—42no—
315C4×Q8—42no—
316C4×Q8—42no—
317C4×Q8—42no—
318C4×Q8M1614yescomplemented
319C4×Q8C2×D412yes—
320C4×Q8#4112yes—
321C4×D4—28no—
322C4×D4—22no—
323C4×D4—22no—
324C4×D4—22no—
325C4×D4—22no—
326C4×D4—42no—
327C4×D4—44no—
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—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—41no—
350C2×C4⋊C4—41no—
351C2×C4⋊C4—42no—
352C2×C4⋊C4—42no—
353C2×C4⋊C4—42no—
354C2×C4⋊C4—42no—
355C2×C4⋊C4C22⋊C411yescharacteristic
356C2×C4⋊C4C22⋊C411yescharacteristic
357C2×C4⋊C4C22⋊C411yescharacteristic
358C2×C4⋊C4C22×C411yescharacteristic
359C2×C4⋊C4C22×C411yescharacteristic
360C2×C4⋊C4C22×C411yescharacteristic
361C2×C4⋊C4C22×C411yescharacteristic
362C2×C4⋊C4C22×C411yescharacteristic
363C2×C22⋊C4—21no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4C22⋊C411yescharacteristic
368C2×C22⋊C4C22⋊C411yescharacteristic
369C2×C22⋊C4C22⋊C411yescharacteristic
370C2×C22⋊C4C22⋊C411yescharacteristic
371C2×C22⋊C4C22⋊C411yescharacteristic
372C2×C22⋊C4C22⋊C411yescharacteristic
373C2×C42—21no—
374C2×C42—21no—
375C2×C42—21no—
376C2×C42—21no—
377C2×C42—21no—
378C2×C42—21no—
379C2×C42—21no—
380C2×C42—21no—
381C2×C42—21no—
382C2×C42—21no—
383C2×C42—21no—
384C2×C42—21no—
385C2×C42—21no—
386C2×C42—21no—
387C2×C42—21no—
388C2×C42—21no—
389C2×C42—21no—
390C2×C42—21no—
391C2×C42—21no—
392C2×C42—21no—
393C2×C42—42no—
394C2×C42—42no—
395C2×C42—42no—
396C2×C42—42no—
397C2×C42C22×C411yescharacteristic
398C2×C42C22×C411yescharacteristic
399C2×C42C22×C411yescharacteristic
400C2×C42C22×C411yescharacteristic
401C2×C42C2×D411yescharacteristic
402C2×C42C2×D411yescharacteristic
403C2×C42C2×D411yescharacteristic
404C2×C42C2×D411yescharacteristic
405C2×C42C2×D411yescharacteristic
406C2×C42C2×D411yescharacteristic
407C2×C42C2×D411yescharacteristic
408C2×C42C2×D411yescharacteristic
409C2×C42C2411yescharacteristic
410C4⋊C8—21no—
411C4⋊C8—21no—
412C4⋊C8—21no—
413C4⋊C8—21no—
414C4⋊C8—21no—
415C4⋊C8—21no—
416C4⋊C8—21no—
417C4⋊C8—42no—
418C4⋊C8—42no—
419C4⋊C8—42no—
420C4⋊C8C2×D412yes—
421C22⋊C8—42no—
422C22⋊C8—42no—
423C22⋊C8—42no—
424C22⋊C8—42no—
425C22⋊C8—42no—
426C22⋊C8—81no—
427#97—42no—
428#97—42no—
429C4×C8—21no—
430C4×C8—21no—
431C4×C8—21no—
432C4×C8—21no—
433C4×C8—21no—
434C4×C8—21no—
435C4×C8—21no—
436C4×C8—81no—
437C4×C8C2×D412yes—
438#95—21no—
439#95—21no—
440#95—21no—
441#95—21no—
442#95—21no—
443#95—21no—
444#95—21no—
445#95—21no—
446#95—21no—
447#95—21no—
448#95—21no—
449#95—21no—
450#95—21no—
451#95—21no—
452#95—21no—
453#95C22⋊C411yescharacteristic
454#95C22⋊C411yescharacteristic
455#95C22⋊C411yescharacteristic
456#95C22⋊C411yescharacteristic
457#95C22⋊C411yescharacteristic
458#95C22⋊C411yescharacteristic
459C24C2×C22⋊C411yescharacteristic
460C24C2×C22⋊C411yescharacteristic
461C2×Q8—24no—
462C2×Q8—24no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—42no—
477C2×Q8—42no—
478C2×Q8—42no—
479C2×Q8—42no—
480C2×Q8—44no—
481C2×Q8—44no—
482C2×Q8—44no—
483C2×Q8—44no—
484C2×Q8—44no—
485C2×Q8—44no—
486C2×Q8—44no—
487C2×Q8—44no—
488C2×Q8C4×D412yes—
489C2×Q8C2×M1612yes—
490C2×Q8C2×M1612yes—
491C2×Q8C2×M1612yes—
492C2×Q8#13112yes—
493C2×D4—22no—
494C2×D4—22no—
495C2×D4—22no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—41no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—81no—
545C22×C4—81no—
546C22×C4C2×C22⋊C411yescharacteristic
547C22×C4C2×C22⋊C411yescharacteristic
548C22×C4C2×C22⋊C411yescharacteristic
549C22×C4C2×C22⋊C411yescharacteristic
550C22×C4C2×C22⋊C411yescharacteristic
551C22×C4C2×C22⋊C411yescharacteristic
552C22×C4C2×C22⋊C411yescharacteristic
553C22×C4C2×C22⋊C411yescharacteristic
554C22×C4C2×C22⋊C411yescharacteristic
555C22×C4C2×C22⋊C411yescharacteristic
556C22×C4#13712yes—
557C22×C4#13712yes—
558C22×C4C23×C411yescharacteristic
559C22×C4C22×D411yescharacteristic
560C22×C4C22×D411yescharacteristic
561M16—48no—
562M16—84no—
563C2×C8—22no—
564C2×C8—22no—
565C2×C8—22no—
566C2×C8—41no—
567C2×C8—41no—
568C2×C8—41no—
569C2×C8—41no—
570C2×C8—41no—
571C2×C8—41no—
572C2×C8—41no—
573C2×C8—41no—
574C2×C8—41no—
575C2×C8—41no—
576C2×C8—41no—
577C2×C8—41no—
578C2×C8—41no—
579C2×C8—41no—
580C2×C8—41no—
581C2×C8—41no—
582C2×C8—41no—
583C2×C8—41no—
584C2×C8—41no—
585C2×C8—41no—
586C2×C8—41no—
587C4⋊C4—24no—
588C4⋊C4—24no—
589C4⋊C4—21no—
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—21no—
593C4⋊C4—24no—
594C4⋊C4—24no—
595C4⋊C4—24no—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—41no—
605C4⋊C4—42no—
606C4⋊C4—42no—
607C4⋊C4—42no—
608C4⋊C4—42no—
609C4⋊C4—42no—
610C4⋊C4—42no—
611C4⋊C4—42no—
612C4⋊C4—42no—
613C4⋊C4—41no—
614C4⋊C4—41no—
615C4⋊C4—41no—
616C4⋊C4—41no—
617C4⋊C4—81no—
618C4⋊C4—81no—
619C4⋊C4—81no—
620C4⋊C4C4×D412yes—
621C4⋊C4C2×M1612yes—
622C22⋊C4—24no—
623C22⋊C4—24no—
624C22⋊C4—22no—
625C22⋊C4—22no—
626C22⋊C4—22no—
627C22⋊C4—22no—
628C22⋊C4—22no—
629C22⋊C4—41no—
630C22⋊C4—42no—
631C22⋊C4—42no—
632C42—21no—
633C42—21no—
634C42—21no—
635C42—21no—
636C42—21no—
637C42—21no—
638C42—21no—
639C42—21no—
640C42—22no—
641C42—21no—
642C42—21no—
643C42—21no—
644C42—21no—
645C42—22no—
646C42—21no—
647C42—21no—
648C42—21no—
649C42—21no—
650C42—21no—
651C42—21no—
652C42—24no—
653C42—41no—
654C42—41no—
655C42—42no—
656C42—42no—
657C42—42no—
658C42—42no—
659C42—42no—
660C42—42no—
661C42—41no—
662C42—41no—
663C42—41no—
664C42—41no—
665C42—41no—
666C42—41no—
667C42—81no—
668C42C2×M1612yes—
669C42C2×M1612yes—
670C42C22×D411yescharacteristic
671C42C2×#4111yescharacteristic
672C42H(5,𝔽2)11yescharacteristic
673C42H(5,𝔽2)11yescharacteristic
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23#41912yes—
687C23#42112yes—
688C23C22×C22⋊C411yescharacteristic
689Q8—22no—
690Q8—22no—
691Q8—22no—
692Q8—22no—
693Q8—22no—
694Q8—22no—
695Q8—22no—
696Q8—48no—
697Q8—48no—
698Q8—41no—
699Q8—41no—
700Q8—41no—
701Q8—41no—
702Q8#43614yes—
703D4—28no—
704C2×C4—21no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—48no—
747C2×C4—48no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—81no—
778C2×C4—81no—
779C2×C4—84no—
780C2×C4—84no—
781C2×C4#40712yes—
782C2×C4#40712yes—
783C2×C4#41912yes—
784C2×C4C2×C4×D411yescharacteristic
785C2×C4#51811yescharacteristic
786C2×C4D4211yescharacteristic
787C2×C4D4211yescharacteristic
788C2×C4#54611yescharacteristic
789C2×C4#54611yescharacteristic
790C2×C4C22×M1611yescharacteristic
791C2×C4C22×M1611yescharacteristic
792C2×C4C2×#13111yescharacteristic
793C2×C4#56811yescharacteristic
794C2×C4C2×#13711yescharacteristic
795C2×C4C2×#13711yescharacteristic
796C2×C4#57711yescharacteristic
797C2×C4#57811yescharacteristic
798C8—42no—
799C8—42no—
800C8—42no—
801C8—81no—
802C8—81no—
803C8—81no—
804C8—81no—
805C8—81no—
806C22—22no—
807C22—22no—
808C22—22no—
809C22—22no—
810C22—22no—
811C22—22no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22D4×C22⋊C411yescharacteristic
821C22C2×#40711yescharacteristic
822C22#288011yescharacteristic
823C22C2×#41911yescharacteristic
824C22#289811yescharacteristic
825C22C2×#42111yescharacteristic
826C22#290111yescharacteristic
827C4—22no—
828C4—22no—
829C4—24no—
830C4—22no—
831C4—21no—
832C4—21no—
833C4—42no—
834C4—41no—
835C4—41no—
836C4—41no—
837C4—41no—
838C4—42no—
839C4—42no—
840C4—41no—
841C4—41no—
842C4—41no—
843C4—42no—
844C4—81no—
845C4—81no—
846C4—81no—
847C4C2×#43611yescharacteristic
848C4D4×M1611yescharacteristic
849C4#297411yescharacteristic
850C4#297511yescharacteristic
851C4#326611yescharacteristic
852C4#327011yescharacteristic
853C4#331211yescharacteristic
854C4#332011yescharacteristic
855C2—42no—
856C2—42no—
857C2#1744911yescharacteristic
858C2#1745411yescharacteristic
859C2#1751411yescharacteristic
860C2#1752411yescharacteristic
861C2#2240111yescharacteristic
862C2#2242511yescharacteristic
863C2#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×#1491C2semidirect
5. C2×#1487C2semidirect
6. #9673C2semidirect
7. #9641C2semidirect
8. #9077C2semidirect
9. #9075C2semidirect
10. #8942C2semidirect
11. #8941C2semidirect
12. #8566C2semidirect
13. #8311C2semidirect
14. #8311C2semidirect
15. #8171C2semidirect
237. Q8⋊C8D4semidirect
282. C4⋊Q8M16semidirect
318. C4×Q8M16semidirect

Maximal subgroups

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

subgroupindex
C4×D4×Q82
#227512
#211022
C2×#14912
C2×#14872
#96732
#96412
#90772
#90752
#89422
#89412
#85662
#83112
#81712