Finite Group Databasebeta

← #221523

Subgroups — #221523

Order 512.

1259 conjugacy classes of subgroups.

The subgroup lattice has 891 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#548C211yesmaximal, characteristic
2#22750C211yesmaximal, characteristic, complemented
3#21101C211yesmaximal, characteristic, complemented
4C2×#1488C211yesmaximal, characteristic, complemented
5C22×Q8⋊C8C211yesmaximal, characteristic, complemented
6#9676C211yesmaximal, characteristic, complemented
7#9645C211yesmaximal, characteristic, complemented
8#9075C211yesmaximal, characteristic, complemented
9#9072C211yesmaximal, characteristic, complemented
10#8941C211yesmaximal, characteristic, complemented
11#8939C211yesmaximal, characteristic, complemented
12#8566C211yesmaximal, characteristic, complemented
13#8312C211yesmaximal, characteristic, complemented
14#8311C211yesmaximal, characteristic, complemented
15#8175C211yesmaximal, characteristic, complemented
16C2×#548C411yescharacteristic
17C2×C4×#41C2211yescharacteristic
18C22×C4×Q8C2211yescharacteristic
19C2×#432C2211yescharacteristic
20C2×#431C2211yescharacteristic
21C22×C4⋊C8C2211yescharacteristic
22C22×C4×C8C2211yescharacteristic
23#2367—21no—
24#2367C411yescharacteristic
25#2362—21no—
26#2362C411yescharacteristic
27#2361—21no—
28#2361C411yescharacteristic
29#2352—21no—
30#2352C411yescharacteristic
31#2351C411yescharacteristic
32#2341C411yescharacteristic
33Q8×C22⋊C4C411yescharacteristic
34C4×#124—21no—
35C4×#124C2211yescharacteristic
36C4×C22⋊Q8—21no—
37C4×C22⋊Q8C2211yescharacteristic
38C4×#121—21no—
39C4×#121C2211yescharacteristic
40C42×Q8C2211yescharacteristic
41C42×D4—21no—
42C42×D4C2211yescharacteristic
43#1924—21no—
44#1923—21no—
45#1917—21no—
46#1916—21no—
47#1869—21no—
48#1869—21no—
49#1850—21no—
50#1831C2211yescharacteristic
51#1797C2211yescharacteristic
52#1797C2211yescharacteristic
53#1767C2211yescharacteristic
54C4×C4⋊C8C2211yescharacteristic
55#1752—21no—
56C4×C22⋊C8C2211yescharacteristic
57C4×C22⋊C8C2211yescharacteristic
58#1744C2211yescharacteristic
59#1488—24no—
60C2×Q8⋊C8—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×D4⋊C8C2211yescharacteristic
70C2×D4⋊C8C2211yescharacteristic
71C2×D4⋊C8C2211yescharacteristic
72C2×D4⋊C8C2211yescharacteristic
73#1279C2211yescharacteristic
74#1279C2211yescharacteristic
75#1279C2211yescharacteristic
76#1279C2211yescharacteristic
77C22×#41C2×C411yescharacteristic
78C23×Q8C2×C411yescharacteristic
79C23×C8—21no—
80C23×C8—21no—
81#548—24no—
82#548—24no—
83C2×#124—21no—
84C2×#124C2×C411yescharacteristic
85C2×C22⋊Q8—21no—
86C2×C22⋊Q8C2×C411yescharacteristic
87C2×#121—21no—
88C2×#121C2×C411yescharacteristic
89C4×#41—22no—
90C4×#41—22no—
91C4×#41—41no—
92C4×#41—41no—
93C2×C4×Q8—21no—
94C2×C4×Q8—21no—
95C2×C4×Q8—22no—
96C2×C4×Q8—22no—
97C2×C4×Q8—41no—
98C2×C4×Q8—41no—
99C2×C4×Q8C2×C411yescharacteristic
100C2×C4×Q8C2×C411yescharacteristic
101C2×C4×Q8C2×C411yescharacteristic
102C2×C4×Q8C2×C411yescharacteristic
103C2×C4×Q8C2×C411yescharacteristic
104C2×C4×Q8C2311yescharacteristic
105C2×C4×Q8C2311yescharacteristic
106C2×C4×D4—21no—
107C2×C4×D4—21no—
108C2×C4×D4—21no—
109C2×C4×D4—21no—
110C2×C4×D4—21no—
111C2×C4×D4C2×C411yescharacteristic
112C2×C4×D4C2×C411yescharacteristic
113C2×C4×D4D411yescharacteristic
114C2×C4×D4D411yescharacteristic
115C2×C4×D4C2311yescharacteristic
116C2×#117—21no—
117C2×#117C2×C411yescharacteristic
118C22×C4⋊C4—21no—
119C22×C4⋊C4C2×C411yescharacteristic
120C22×C42—21no—
121C22×C42—21no—
122C22×C42C2311yescharacteristic
123C22×C42C2311yescharacteristic
124#432—22no—
125#432—41no—
126#431—22no—
127#431—41no—
128C2×C4⋊C8—22no—
129C2×C4⋊C8—21no—
130C2×C4⋊C8—21no—
131C2×C4⋊C8—21no—
132C2×C4⋊C8—41no—
133C2×C4⋊C8C2311yescharacteristic
134C2×C4⋊C8C2311yescharacteristic
135C2×C4⋊C8C2311yescharacteristic
136C2×C4⋊C8C2311yescharacteristic
137C2×C22⋊C8—21no—
138C2×C22⋊C8—21no—
139C2×C22⋊C8—21no—
140C2×C22⋊C8—21no—
141C2×C22⋊C8—21no—
142C2×C22⋊C8—21no—
143C2×#97—21no—
144C2×#97—21no—
145C2×C4×C8—22no—
146C2×C4×C8—21no—
147C2×C4×C8—41no—
148C2×C4×C8C2311yescharacteristic
149C2×C4×C8C2311yescharacteristic
150C2×C4×C8C2311yescharacteristic
151C2×C4×C8C2311yescharacteristic
152#391—21no—
153#391—21no—
154#391C2×C411yescharacteristic
155#391C2×C411yescharacteristic
156#390—21no—
157#390—21no—
158#390C2×C411yescharacteristic
159#390C2×C411yescharacteristic
160#389—21no—
161#389—21no—
162#389C2×C411yescharacteristic
163#389C2×C411yescharacteristic
164#388—21no—
165#388—21no—
166#388—21no—
167#388—21no—
168#388—21no—
169#388—21no—
170#388—21no—
171#388—21no—
172#388—21no—
173#387—21no—
174#387—21no—
175#387—21no—
176#386—21no—
177#386—21no—
178#386—21no—
179#385—21no—
180#385—21no—
181#385—21no—
182#382—21no—
183#382C2×C411yescharacteristic
184#380—21no—
185#380—21no—
186#380C2×C411yescharacteristic
187#380C2×C411yescharacteristic
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⋊C4C2×C411yescharacteristic
195C4×C4⋊C4C2×C411yescharacteristic
196C4×C4⋊C4C2×C411yescharacteristic
197C4×C4⋊C4D411yescharacteristic
198C4×C4⋊C4D411yescharacteristic
199C4×C4⋊C4C2311yescharacteristic
200C4×C22⋊C4—21no—
201C4×C22⋊C4—21no—
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—41no—
232Q8⋊C8—41no—
233Q8⋊C8D414yescomplemented
234D4⋊C8—22no—
235D4⋊C8—22no—
236D4⋊C8—41no—
237D4⋊C8—41no—
238C2×#41—22no—
239C2×#41—22no—
240C2×#41—22no—
241C2×#41—22no—
242C2×#41—41no—
243C2×#41—41no—
244C22×Q8—21no—
245C22×Q8—22no—
246C22×Q8—22no—
247C22×Q8—22no—
248C22×Q8—41no—
249C22×Q8—41no—
250C22×Q8M1614yes—
251C22×Q8C22×C411yescharacteristic
252C22×Q8C22×C411yescharacteristic
253C22×D4—21no—
254C22×D4—21no—
255C22×D4C22⋊C411yescharacteristic
256C22×D4C22×C411yescharacteristic
257C23×C4—21no—
258C23×C4—21no—
259C23×C4—21no—
260C23×C4—21no—
261C23×C4—21no—
262C23×C4C22×C411yescharacteristic
263C23×C4C22×C411yescharacteristic
264C23×C4C2×D411yescharacteristic
265C23×C4C2×D411yescharacteristic
266C23×C4C2×D411yescharacteristic
267C23×C4C2×D411yescharacteristic
268C22×C8—21no—
269C22×C8—21no—
270C22×C8—21no—
271C22×C8—21no—
272C22×C8—21no—
273C22×C8—21no—
274C22×C8—21no—
275C22×C8—21no—
276C22×C8—42no—
277C22×C8—42no—
278C22×C8—42no—
279C22×C8—42no—
280C22×C8—42no—
281C22×C8—81no—
282#124—28no—
283#124—22no—
284#124—22no—
285C22⋊Q8—28no—
286C22⋊Q8—22no—
287C22⋊Q8—22no—
288#121—28no—
289#121—22no—
290#121M1614yes—
291C4×Q8—22no—
292C4×Q8—22no—
293C4×Q8—21no—
294C4×Q8—21no—
295C4×Q8—22no—
296C4×Q8—22no—
297C4×Q8—22no—
298C4×Q8—22no—
299C4×Q8—21no—
300C4×Q8—21no—
301C4×Q8—21no—
302C4×Q8—21no—
303C4×Q8—42no—
304C4×Q8—42no—
305C4×Q8—41no—
306C4×Q8—41no—
307C4×Q8—41no—
308C4×Q8—41no—
309C4×Q8—42no—
310C4×Q8—42no—
311C4×Q8C2×D412yes—
312C4×Q8#4112yes—
313C4×D4—28no—
314C4×D4—22no—
315C4×D4—22no—
316C4×D4—22no—
317C4×D4—22no—
318C4×D4—22no—
319C4×D4—21no—
320C4×D4—21no—
321C4×D4—21no—
322C4×D4—21no—
323C4×D4—41no—
324C4×D4—42no—
325C4×D4—42no—
326C4×D4—42no—
327C4×D4—44no—
328C4×D4—42no—
329C4×D4—42no—
330C4×D4—42no—
331C4×D4—42no—
332#117—22no—
333#117—42no—
334#117—42no—
335#117—41no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—22no—
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—41no—
349C2×C4⋊C4—42no—
350C2×C4⋊C4—42no—
351C2×C4⋊C4C22⋊C411yescharacteristic
352C2×C4⋊C4C22⋊C411yescharacteristic
353C2×C4⋊C4C22⋊C411yescharacteristic
354C2×C4⋊C4C22×C411yescharacteristic
355C2×C4⋊C4C22×C411yescharacteristic
356C2×C4⋊C4C22×C411yescharacteristic
357C2×C4⋊C4C22×C411yescharacteristic
358C2×C4⋊C4C22×C411yescharacteristic
359C2×C22⋊C4—21no—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4C22⋊C411yescharacteristic
373C2×C22⋊C4C22⋊C411yescharacteristic
374C2×C22⋊C4C22⋊C411yescharacteristic
375C2×C22⋊C4C22⋊C411yescharacteristic
376C2×C22⋊C4C22⋊C411yescharacteristic
377C2×C22⋊C4C22⋊C411yescharacteristic
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—21no—
394C2×C42—21no—
395C2×C42—21no—
396C2×C42—21no—
397C2×C42—42no—
398C2×C42—42no—
399C2×C42—42no—
400C2×C42—42no—
401C2×C42C22×C411yescharacteristic
402C2×C42C22×C411yescharacteristic
403C2×C42C22×C411yescharacteristic
404C2×C42C22×C411yescharacteristic
405C2×C42C2×D411yescharacteristic
406C2×C42C2×D411yescharacteristic
407C2×C42C2×D411yescharacteristic
408C2×C42C2×D411yescharacteristic
409C2×C42C2×D411yescharacteristic
410C2×C42C2×D411yescharacteristic
411C2×C42C2×D411yescharacteristic
412C2×C42C2×D411yescharacteristic
413C2×C42C2411yescharacteristic
414C4⋊C8—21no—
415C4⋊C8—21no—
416C4⋊C8—21no—
417C4⋊C8—21no—
418C4⋊C8—21no—
419C4⋊C8—21no—
420C4⋊C8—21no—
421C4⋊C8—42no—
422C4⋊C8—42no—
423C4⋊C8—42no—
424C4⋊C8C2×D412yes—
425C22⋊C8—42no—
426C22⋊C8—42no—
427C22⋊C8—42no—
428C22⋊C8—42no—
429C22⋊C8—42no—
430C22⋊C8—81no—
431#97—42no—
432#97—81no—
433C4×C8—21no—
434C4×C8—21no—
435C4×C8—21no—
436C4×C8—21no—
437C4×C8—21no—
438C4×C8—21no—
439C4×C8—21no—
440C4×C8—42no—
441C4×C8C2×D412yes—
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#95—21no—
454#95—21no—
455#95C22⋊C411yescharacteristic
456#95C22⋊C411yescharacteristic
457#95C22⋊C411yescharacteristic
458#95C22⋊C411yescharacteristic
459#95C22⋊C411yescharacteristic
460#95C22⋊C411yescharacteristic
461C24—21no—
462C24C2×C22⋊C411yescharacteristic
463C24C2×C22⋊C411yescharacteristic
464#41—44no—
465#41—44no—
466#41—44no—
467#41—44no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—24no—
473C2×Q8—28no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—42no—
479C2×Q8—42no—
480C2×Q8—44no—
481C2×Q8—44no—
482C2×Q8—44no—
483C2×Q8C4×D412yes—
484C2×Q8C2×M1612yes—
485C2×Q8C2×M1612yes—
486C2×Q8#13112yes—
487C2×D4—24no—
488C2×D4—22no—
489C2×D4—24no—
490C2×D4—22no—
491C2×D4—22no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—42no—
498C2×D4—42no—
499C2×D4—42no—
500C2×D4—42no—
501C2×D4C2×M1612yes—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—24no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—24no—
516C22×C4—22no—
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—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—41no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—41no—
540C22×C4—41no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—41no—
548C22×C4—41no—
549C22×C4—41no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—81no—
554C22×C4—81no—
555C22×C4C2×C22⋊C411yescharacteristic
556C22×C4C2×C22⋊C411yescharacteristic
557C22×C4C2×C22⋊C411yescharacteristic
558C22×C4C2×C22⋊C411yescharacteristic
559C22×C4C2×C22⋊C411yescharacteristic
560C22×C4C2×C22⋊C411yescharacteristic
561C22×C4C2×C22⋊C411yescharacteristic
562C22×C4C2×C22⋊C411yescharacteristic
563C22×C4C2×C22⋊C411yescharacteristic
564C22×C4C2×C22⋊C411yescharacteristic
565C22×C4C2×M1612yes—
566C22×C4C2×M1612yes—
567C22×C4#13512yes—
568C22×C4#13512yes—
569C22×C4C23×C411yescharacteristic
570C22×C4C22×D411yescharacteristic
571C22×C4C22×D411yescharacteristic
572C2×C8—22no—
573C2×C8—22no—
574C2×C8—22no—
575C2×C8—41no—
576C2×C8—41no—
577C2×C8—41no—
578C2×C8—48no—
579C2×C8—41no—
580C2×C8—41no—
581C2×C8—41no—
582C2×C8—41no—
583C2×C8—41no—
584C2×C8—41no—
585C2×C8—41no—
586C2×C8—41no—
587C2×C8—41no—
588C2×C8—41no—
589C2×C8—41no—
590C2×C8—41no—
591C2×C8—41no—
592C2×C8—41no—
593C2×C8—41no—
594C2×C8—41no—
595C2×C8—41no—
596C2×C8—41no—
597C2×C8—84no—
598C4⋊C4—24no—
599C4⋊C4—24no—
600C4⋊C4—21no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—21no—
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—41no—
613C4⋊C4—42no—
614C4⋊C4—42no—
615C4⋊C4—42no—
616C4⋊C4—42no—
617C4⋊C4—42no—
618C4⋊C4—42no—
619C4⋊C4—41no—
620C4⋊C4—41no—
621C4⋊C4—42no—
622C4⋊C4C4×D412yes—
623C4⋊C4C2×M1612yes—
624C22⋊C4—24no—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—22no—
628C22⋊C4—22no—
629C22⋊C4—22no—
630C22⋊C4—24no—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—41no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—41no—
639C22⋊C4—41no—
640C22⋊C4—42no—
641C22⋊C4—81no—
642C22⋊C4—81no—
643C22⋊C4—81no—
644C42—24no—
645C42—21no—
646C42—21no—
647C42—21no—
648C42—21no—
649C42—21no—
650C42—21no—
651C42—21no—
652C42—21no—
653C42—22no—
654C42—21no—
655C42—21no—
656C42—21no—
657C42—21no—
658C42—22no—
659C42—21no—
660C42—21no—
661C42—21no—
662C42—21no—
663C42—21no—
664C42—21no—
665C42—21no—
666C42—21no—
667C42—41no—
668C42—41no—
669C42—42no—
670C42—42no—
671C42—42no—
672C42—42no—
673C42—42no—
674C42—42no—
675C42—41no—
676C42—41no—
677C42—41no—
678C42—41no—
679C42—81no—
680C42C22×D411yescharacteristic
681C42C2×#4111yescharacteristic
682C42H(5,𝔽2)11yescharacteristic
683C42H(5,𝔽2)11yescharacteristic
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—22no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23#40712yes—
703C23#41612yes—
704C23#42112yes—
705C23C22×C22⋊C411yescharacteristic
706Q8—22no—
707Q8—22no—
708Q8—22no—
709Q8—22no—
710Q8—22no—
711Q8—48no—
712Q8—41no—
713Q8—41no—
714Q8#43514yes—
715D4—22no—
716D4—22no—
717D4—48no—
718D4—44no—
719D4—48no—
720D4—41no—
721D4—41no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—22no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—48no—
769C2×C4—48no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—81no—
794C2×C4—81no—
795C2×C4—84no—
796C2×C4—84no—
797C2×C4—81no—
798C2×C4—81no—
799C2×C4—81no—
800C2×C4—81no—
801C2×C4#40712yes—
802C2×C4#41612yes—
803C2×C4C2×C4×D411yescharacteristic
804C2×C4#51811yescharacteristic
805C2×C4D4211yescharacteristic
806C2×C4D4211yescharacteristic
807C2×C4#54611yescharacteristic
808C2×C4#54611yescharacteristic
809C2×C4C22×M1611yescharacteristic
810C2×C4C22×M1611yescharacteristic
811C2×C4C2×#13111yescharacteristic
812C2×C4#56811yescharacteristic
813C2×C4C2×#13511yescharacteristic
814C2×C4C2×#13511yescharacteristic
815C2×C4#57711yescharacteristic
816C2×C4#57811yescharacteristic
817C8—42no—
818C8—42no—
819C8—42no—
820C8—81no—
821C8—81no—
822C8—81no—
823C8—81no—
824C8—81no—
825C22—22no—
826C22—22no—
827C22—22no—
828C22—22no—
829C22—22no—
830C22—22no—
831C22—41no—
832C22—42no—
833C22—41no—
834C22—42no—
835C22—41no—
836C22—41no—
837C22—42no—
838C22—41no—
839C22—41no—
840C22—41no—
841C22—81no—
842C22—81no—
843C22—81no—
844C22—81no—
845C22#148814yescomplemented
846C22D4×C22⋊C411yescharacteristic
847C22C2×#40711yescharacteristic
848C22#288011yescharacteristic
849C22C2×#41611yescharacteristic
850C22#289811yescharacteristic
851C22C2×#42111yescharacteristic
852C22#290111yescharacteristic
853C4—22no—
854C4—24no—
855C4—22no—
856C4—21no—
857C4—21no—
858C4—41no—
859C4—42no—
860C4—41no—
861C4—41no—
862C4—41no—
863C4—41no—
864C4—42no—
865C4—41no—
866C4—41no—
867C4—41no—
868C4—42no—
869C4—81no—
870C4—81no—
871C4—81no—
872C4C2×#43511yescharacteristic
873C4D4×M1611yescharacteristic
874C4#297311yescharacteristic
875C4#297411yescharacteristic
876C4#328211yescharacteristic
877C4#328511yescharacteristic
878C4#330011yescharacteristic
879C4#330111yescharacteristic
880C2—24no—
881C2—81no—
882C2—82no—
883C2C2×#148811yescharacteristic
884C2#1745411yescharacteristic
885C2#1751011yescharacteristic
886C2#1752411yescharacteristic
887C2#2239911yescharacteristic
888C2#2241611yescharacteristic
889C2#2243411yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC2×C42C24
socleC23C22×C22⋊C4
prime radicalC2×#548C4
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. #22750C2semidirect
3. #21101C2semidirect
4. C2×#1488C2semidirect
5. C22×Q8⋊C8C2semidirect
6. #9676C2semidirect
7. #9645C2semidirect
8. #9075C2semidirect
9. #9072C2semidirect
10. #8941C2semidirect
11. #8939C2semidirect
12. #8566C2semidirect
13. #8312C2semidirect
14. #8311C2semidirect
15. #8175C2semidirect
233. Q8⋊C8D4semidirect
845. C22#1488semidirect

Maximal subgroups

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

subgroupindex
C4×#5482
#227502
#211012
C2×#14882
C22×Q8⋊C82
#96762
#96452
#90752
#90722
#89412
#89392
#85662
#83122
#83112
#81752