Finite Group Databasebeta

← #6392826

Subgroups — #6392826

Order 512.

1992 conjugacy classes of subgroups.

The subgroup lattice has 851 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2988C211yesmaximal, characteristic
2#34191C211yesmaximal, characteristic
3#34127C211yesmaximal, characteristic
4#22741C211yesmaximal, characteristic, complemented
5#22739C211yesmaximal, characteristic, complemented
6#22727C211yesmaximal, characteristic, complemented
7#22725C211yesmaximal, characteristic, complemented
8#22706C212yesmaximal, complemented
9#22705C211yesmaximal, characteristic, complemented
10#22704C212yesmaximal, complemented
11#22703C211yesmaximal, characteristic, complemented
12#22656C212yesmaximal, complemented
13D4×#107C211yesmaximal, characteristic, complemented
14#22654C212yesmaximal, complemented
15D4×#106C211yesmaximal, characteristic, complemented
16#21984C211yesmaximal, characteristic, complemented
17#21983C212yesmaximal, complemented
18#21962C211yesmaximal, characteristic, complemented
19#21960C212yesmaximal, complemented
20#21361C212yesmaximal, complemented
21#21360C211yesmaximal, characteristic, complemented
22#21169C211yesmaximal, characteristic, complemented
23C2×#1949C212yesmaximal, complemented
24C2×C4×#41C2211yescharacteristic
25#2988C4116yescomplemented
26C2×C8×Q8C2211yescharacteristic
27C2×C8×Q8C2211yescharacteristic
28C2×C8×D4C2211yescharacteristic
29C2×C8×D4C2211yescharacteristic
30C2×C8×D4C2212yes—
31C2×C8×D4C2212yes—
32C2×#431C2211yescharacteristic
33C2×#431C2212yes—
34C2×#427C2212yes—
35C22×#107C2212yes—
36C22×#106C2212yes—
37C22×C4⋊C8C2212yes—
38C22×C4⋊C8C2211yescharacteristic
39#2355C2211yescharacteristic
40#2355C2211yescharacteristic
41#2355C2211yescharacteristic
42#2355C2211yescharacteristic
43#2352C2212yes—
44#2352C2212yes—
45#2352C2212yes—
46#2352C2212yes—
47D4×C4⋊C4C2211yescharacteristic
48D4×C4⋊C4C2211yescharacteristic
49D4×C4⋊C4C2211yescharacteristic
50D4×C4⋊C4C2211yescharacteristic
51#2347—21no—
52#2346—21no—
53#2343—22no—
54#2343—22no—
55#2339—21no—
56#2339—21no—
57#2320—21no—
58#2318—22no—
59#2295—21no—
60#2290—22no—
61#2285C2211yescharacteristic
62#2285C2211yescharacteristic
63#2283C2212yes—
64#2283C2211yescharacteristic
65#2283C2212yes—
66C2×#382C2212yes—
67#2275—21no—
68C42×D4—21no—
69C4×#117C2211yescharacteristic
70C2×C4×C4⋊C4C2212yes—
71#1949C2211yescharacteristic
72#1949C2211yescharacteristic
73#1949C2211yescharacteristic
74#1949C2211yescharacteristic
75#1949C2212yes—
76#1949C2212yes—
77#1949C2212yes—
78#1949C2212yes—
79#1949C2212yes—
80#1949C2212yes—
81#1949C2212yes—
82#1949C2212yes—
83#1949C2212yes—
84#1949C2212yes—
85#1949C2212yes—
86#1949C2212yes—
87#1949C2212yes—
88#1949C2212yes—
89#1948C2211yescharacteristic
90#1948C2211yescharacteristic
91#1948C2211yescharacteristic
92#1948C2211yescharacteristic
93#1947C2211yescharacteristic
94#1947C2211yescharacteristic
95#1947C2211yescharacteristic
96#1947C2211yescharacteristic
97#1854C2211yescharacteristic
98#1854C2211yescharacteristic
99#1854C2211yescharacteristic
100#1854C2211yescharacteristic
101#1854C2212yes—
102#1854C2212yes—
103#1853C2212yes—
104#1853C2212yes—
105#1853C2212yes—
106#1853C2212yes—
107#1852C2212yes—
108#1852C2212yes—
109#1852C2212yes—
110#1852C2212yes—
111#1846C2212yes—
112#1846C2212yes—
113#1845C2211yescharacteristic
114#1844C2211yescharacteristic
115#1835C2212yes—
116#1835C2212yes—
117#1834C2211yescharacteristic
118#1834C2211yescharacteristic
119#1808C2212yes—
120#1808C2212yes—
121#1808C2212yes—
122#1807C2212yes—
123#1807C2212yes—
124#1807C2212yes—
125C4×#107C2211yescharacteristic
126C4×#107C2211yescharacteristic
127C4×#107C2212yes—
128C4×#107C2212yes—
129C4×#106C2211yescharacteristic
130C4×#106C2211yescharacteristic
131C4×#106C2212yes—
132C4×#106C2212yes—
133#1735C2212yes—
134C2×#340C2212yes—
135C2×#340C2212yes—
136C22×#41D411yescharacteristic
137C23×C8C2312yes—
138C23×C8C2312yes—
139C23×C8C2312yes—
140C4×#41C2×C418yes—
141C4×#41Q818yes—
142C2×C4×Q8D411yescharacteristic
143C2×C4×Q8C2311yescharacteristic
144C2×C4×D4—21no—
145C2×C4×D4—21no—
146C2×C4×D4—21no—
147C2×C4×D4—21no—
148C2×C4×D4D412yes—
149C2×C4×D4D411yescharacteristic
150C2×C4×D4C2311yescharacteristic
151C2×C4×D4C2312yes—
152C2×#117—21no—
153C2×#117D412yes—
154C2×#117D411yescharacteristic
155C2×#117C2311yescharacteristic
156C2×#117C2311yescharacteristic
157C2×#117C2312yes—
158C22×C4⋊C4C2312yes—
159C22×C4⋊C4C2312yes—
160C22×C4⋊C4C2312yes—
161C22×C4⋊C4C2312yes—
162C22×C42—22no—
163C22×C42C2312yes—
164C22×C42C2311yescharacteristic
165C8×Q8C2×C418yescomplemented
166C8×Q8C2×C418yescomplemented
167C8×D4C2×C418yes—
168C8×D4C2×C418yes—
169C8×D4C2×C4116yescomplemented
170C8×D4C2×C4116yescomplemented
171#431C2×C418yescomplemented
172#431C2×C4116yescomplemented
173#427—44no—
174C2×#107—44no—
175C2×#107C2311yescharacteristic
176C2×#107C2312yes—
177C2×#107C2311yescharacteristic
178C2×#107C2312yes—
179C2×#107C2311yescharacteristic
180C2×#107C2312yes—
181C2×#107C2312yes—
182C2×#107C2312yes—
183C2×#107C2312yes—
184C2×#107C2311yescharacteristic
185C2×#106—44no—
186C2×#106C2311yescharacteristic
187C2×#106C2312yes—
188C2×#106C2311yescharacteristic
189C2×#106C2312yes—
190C2×#106C2311yescharacteristic
191C2×#106C2312yes—
192C2×#106C2312yes—
193C2×#106C2312yes—
194C2×#106C2312yes—
195C2×#106C2311yescharacteristic
196C2×C4⋊C8C2×C418yescomplemented
197C2×C4⋊C8C2×C4116yescomplemented
198C2×C4⋊C8C2311yescharacteristic
199C2×C4⋊C8C2312yes—
200C2×C4⋊C8C2311yescharacteristic
201C2×C4⋊C8C2311yescharacteristic
202C2×C4⋊C8C2312yes—
203C2×C4⋊C8C2312yes—
204C2×C4⋊C8C2311yescharacteristic
205C2×C22⋊C8C2312yes—
206C2×C22⋊C8C2312yes—
207C2×C22⋊C8C2311yescharacteristic
208C2×C22⋊C8C2311yescharacteristic
209C2×C4×C8C2311yescharacteristic
210C2×C4×C8C2311yescharacteristic
211C2×C4×C8C2312yes—
212C2×C4×C8C2312yes—
213#391—21no—
214#391—21no—
215#391—21no—
216#391—21no—
217#389—21no—
218#389—21no—
219#389—21no—
220#389—21no—
221#388—22no—
222#388—22no—
223#388—22no—
224#388—22no—
225#387—22no—
226#387—22no—
227#387—22no—
228#387—22no—
229#387—22no—
230#387—22no—
231#387—22no—
232#387—22no—
233#386—22no—
234#386—22no—
235#386—22no—
236#386—22no—
237#385—22no—
238#385—22no—
239#385—22no—
240#385—22no—
241#384C2311yescharacteristic
242#384C2311yescharacteristic
243#384C2311yescharacteristic
244#384C2311yescharacteristic
245#383—22no—
246#383—21no—
247#383—22no—
248#382—22no—
249#382—21no—
250#382—22no—
251#382C2312yes—
252#382C2312yes—
253#382C2312yes—
254#382C2312yes—
255#382C2311yescharacteristic
256#382C2312yes—
257#382C2311yescharacteristic
258#381—21no—
259#381—22no—
260#381—22no—
261#380—21no—
262#380—21no—
263#380—21no—
264#380C2311yescharacteristic
265#380C2312yes—
266#380C2312yes—
267#380C2312yes—
268#380C2312yes—
269#380C2312yes—
270#380C2311yescharacteristic
271C4×C4⋊C4—21no—
272C4×C4⋊C4—21no—
273C4×C4⋊C4—21no—
274C4×C4⋊C4—21no—
275C4×C4⋊C4—21no—
276C4×C4⋊C4—21no—
277C4×C4⋊C4—22no—
278C4×C4⋊C4—22no—
279C4×C4⋊C4—21no—
280C4×C4⋊C4C2311yescharacteristic
281C4×C4⋊C4C2311yescharacteristic
282C4×C4⋊C4C2311yescharacteristic
283C4×C4⋊C4C2311yescharacteristic
284C4×C4⋊C4C2312yes—
285C4×C4⋊C4C2312yes—
286C4×C4⋊C4C2312yes—
287C4×C4⋊C4C2312yes—
288C4×C4⋊C4C2311yescharacteristic
289C4×C4⋊C4C2312yes—
290C4×C4⋊C4C2311yescharacteristic
291C4×C22⋊C4—22no—
292C4×C22⋊C4—21no—
293C4×C22⋊C4—21no—
294C4×C22⋊C4—21no—
295C4×C22⋊C4—22no—
296C4×C22⋊C4—22no—
297C4×C22⋊C4—22no—
298C4×C22⋊C4—22no—
299C4×C22⋊C4—22no—
300#376—21no—
301#376—21no—
302#376—22no—
303#376—22no—
304C2×#95—22no—
305C2×#95—22no—
306C2×#95—22no—
307C43—21no—
308#340C2311yescharacteristic
309#340C2312yes—
310#340C2312yes—
311#340C2312yes—
312#340C2312yes—
313#340C2312yes—
314#340C2311yescharacteristic
315#340C2312yes—
316#340C2312yes—
317#340C2312yes—
318#340C2312yes—
319#340C2312yes—
320#340C2311yescharacteristic
321#340C2311yescharacteristic
322#340C2311yescharacteristic
323#340C2312yes—
324#340C2311yescharacteristic
325#340C2312yes—
326#340C2311yescharacteristic
327#340C2311yescharacteristic
328C2×#41—24no—
329C2×#41—24no—
330C2×#41C4⋊C418yes—
331C22×Q8C2×D411yescharacteristic
332C22×D4C2×D412yes—
333C22×D4C2×D411yescharacteristic
334C23×C4—22no—
335C23×C4—22no—
336C23×C4—22no—
337C23×C4—22no—
338C23×C4C2×D412yes—
339C23×C4C2×D411yescharacteristic
340C23×C4C2×D411yescharacteristic
341C23×C4C2×D412yes—
342C23×C4C2412yes—
343C23×C4C2411yescharacteristic
344C22×C8—42no—
345C22×C8—42no—
346C22×C8—42no—
347C22×C8—42no—
348C22×C8—42no—
349C22×C8—42no—
350C22×C8C22×C418yes—
351C22×C8C22×C418yes—
352C22×C8C22×C418yes—
353C22×C8C2411yescharacteristic
354C22×C8C2412yes—
355C22×C8C2412yes—
356C22×C8C2411yescharacteristic
357C22×C8C2411yescharacteristic
358C22×C8C2411yescharacteristic
359C4×Q8C4⋊C418yes—
360C4×Q8C22×C414yes—
361C4×Q8C2×Q814yes—
362C4×D4—44no—
363C4×D4—44no—
364C4×D4—44no—
365C4×D4—44no—
366C4×D4C4⋊C4116yes—
367C4×D4C4⋊C418yes—
368C4×D4C22×C414yes—
369C4×D4C22×C418yes—
370C4×D4C2×Q818yes—
371C4×D4C2×Q814yes—
372#117—22no—
373#117—22no—
374#117—41no—
375#117—41no—
376#117—42no—
377#117—42no—
378#117—82no—
379#117C4⋊C4116yes—
380#117C4⋊C418yes—
381C2×C4⋊C4—24no—
382C2×C4⋊C4—24no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—42no—
396C2×C4⋊C4—42no—
397C2×C4⋊C4—42no—
398C2×C4⋊C4—42no—
399C2×C4⋊C4—42no—
400C2×C4⋊C4—42no—
401C2×C4⋊C4C2×D411yescharacteristic
402C2×C4⋊C4C2×D412yes—
403C2×C4⋊C4C2×D412yes—
404C2×C4⋊C4C2×D411yescharacteristic
405C2×C4⋊C4C2411yescharacteristic
406C2×C4⋊C4C2411yescharacteristic
407C2×C4⋊C4C2412yes—
408C2×C4⋊C4C2412yes—
409C2×C4⋊C4C2412yes—
410C2×C4⋊C4C2412yes—
411C2×C4⋊C4C2411yescharacteristic
412C2×C4⋊C4C2411yescharacteristic
413C2×C4⋊C4C2411yescharacteristic
414C2×C4⋊C4C2411yescharacteristic
415C2×C4⋊C4C2411yescharacteristic
416C2×C4⋊C4C2411yescharacteristic
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—22no—
420C2×C22⋊C4—22no—
421C2×C22⋊C4—22no—
422C2×C22⋊C4—22no—
423C2×C22⋊C4—22no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4C2×D412yes—
428C2×C22⋊C4C2×D412yes—
429C2×C22⋊C4C2×D412yes—
430C2×C42—22no—
431C2×C42—21no—
432C2×C42—21no—
433C2×C42—21no—
434C2×C42—21no—
435C2×C42—21no—
436C2×C42—21no—
437C2×C42—21no—
438C2×C42—21no—
439C2×C42—22no—
440C2×C42—22no—
441C2×C42—22no—
442C2×C42—22no—
443C2×C42—22no—
444C2×C42—84no—
445C2×C42C22×C418yes—
446C2×C42C22×C414yes—
447C2×C42C2×D411yescharacteristic
448C2×C42C2×D412yes—
449C2×C42C2×D411yescharacteristic
450C2×C42C2×D412yes—
451C2×C42C2×Q818yes—
452C2×C42C2×Q814yes—
453C2×C42C2412yes—
454C2×C42C2411yescharacteristic
455C2×C42C2411yescharacteristic
456#107—22no—
457#107—24no—
458#107—22no—
459#107—42no—
460#107—42no—
461#107—41no—
462#107—42no—
463#107—42no—
464#107—41no—
465#107—42no—
466#106—22no—
467#106—24no—
468#106—22no—
469#106—42no—
470#106—42no—
471#106—42no—
472#106—41no—
473#106—42no—
474#106—41no—
475#106—42no—
476C4⋊C8C22×C414yes—
477C4⋊C8C22×C418yes—
478C4⋊C8C22×C414yes—
479C4⋊C8C22×C414yes—
480C4⋊C8C22×C418yes—
481C4⋊C8C22×C418yes—
482C4⋊C8C22×C414yes—
483C22⋊C8C22×C418yes—
484C22⋊C8C22×C418yes—
485C22⋊C8C22×C414yes—
486C22⋊C8C22×C414yes—
487C4×C8C22×C414yes—
488C4×C8C22×C414yes—
489C4×C8C22×C418yes—
490C4×C8C22×C418yes—
491#95—21no—
492#95—21no—
493#95—21no—
494#95—22no—
495#95—22no—
496#95—22no—
497#95—22no—
498#95—22no—
499#95—22no—
500#95—22no—
501#95—22no—
502#95—22no—
503#95—21no—
504#95—21no—
505#95—21no—
506#95—21no—
507#95—21no—
508#95—21no—
509#95—21no—
510#95—22no—
511#95—22no—
512#95—22no—
513#95—22no—
514#95—22no—
515#95—22no—
516#95—22no—
517#95—22no—
518#95—22no—
519#95—21no—
520#95—21no—
521#95—22no—
522#95—22no—
523C24C22×D411yescharacteristic
524C24C22×D412yes—
525#41—232no—
526C2×Q8—22no—
527C2×Q8—22no—
528C2×Q8C2×C4⋊C414yes—
529C2×D4—24no—
530C2×D4—24no—
531C2×D4C2×C4⋊C418yes—
532C2×D4C2×C4⋊C414yes—
533C2×D4#13514yes—
534C2×D4#13514yes—
535C22×C4—24no—
536C22×C4—24no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—21no—
541C22×C4—22no—
542C22×C4—21no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—42no—
560C22×C4—41no—
561C22×C4—42no—
562C22×C4—41no—
563C22×C4—44no—
564C22×C4—44no—
565C22×C4—44no—
566C22×C4—44no—
567C22×C4—44no—
568C22×C4—44no—
569C22×C4—82no—
570C22×C4—82no—
571C22×C4—82no—
572C22×C4—82no—
573C22×C4—82no—
574C22×C4—82no—
575C22×C4C2×C4⋊C418yes—
576C22×C4C2×C4⋊C414yes—
577C22×C4C2×C4⋊C414yes—
578C22×C4C2×C4⋊C418yes—
579C22×C4C23×C412yes—
580C22×C4C23×C414yes—
581C22×C4C22×D411yescharacteristic
582C22×C4C22×D412yes—
583C22×C4C22×D411yescharacteristic
584C22×C4C22×D411yescharacteristic
585C22×C4C22×D412yes—
586C22×C4C22×D412yes—
587C22×C4C22×D411yescharacteristic
588C22×C4C22×D411yescharacteristic
589C22×C4C22×Q812yes—
590C22×C4C22×Q814yes—
591C22×C4C2511yescharacteristic
592C2×C8—21no—
593C2×C8—22no—
594C2×C8—21no—
595C2×C8—22no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—22no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—22no—
604C2×C8—48no—
605C2×C8—48no—
606C2×C8—48no—
607C2×C8C23×C412yes—
608C2×C8C23×C412yes—
609C2×C8C23×C412yes—
610C2×C8C23×C412yes—
611C2×C8C23×C414yes—
612C2×C8C23×C414yes—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—22no—
617C4⋊C4—22no—
618C4⋊C4—21no—
619C4⋊C4—22no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—22no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—22no—
628C4⋊C4—22no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—22no—
633C4⋊C4—21no—
634C4⋊C4—22no—
635C4⋊C4—44no—
636C4⋊C4—44no—
637C4⋊C4—42no—
638C4⋊C4—42no—
639C4⋊C4—42no—
640C4⋊C4—42no—
641C4⋊C4—81no—
642C4⋊C4—81no—
643C4⋊C4—82no—
644C4⋊C4—82no—
645C4⋊C4—81no—
646C4⋊C4—81no—
647C4⋊C4C2×C4⋊C418yes—
648C4⋊C4C2×C4⋊C414yes—
649C4⋊C4C2×C4⋊C418yes—
650C4⋊C4C2×C4⋊C414yes—
651C4⋊C4H(5,𝔽2)12yes—
652C4⋊C42−1+412yes—
653C22⋊C4—42no—
654C22⋊C4—42no—
655C22⋊C4—44no—
656C22⋊C4—44no—
657C22⋊C4—44no—
658C22⋊C4—44no—
659C22⋊C4—81no—
660C22⋊C4—81no—
661C22⋊C4—82no—
662C22⋊C4—82no—
663C22⋊C4C2×C4⋊C418yes—
664C22⋊C4C2×C4⋊C418yes—
665C22⋊C4C2×C4⋊C418yes—
666C42—42no—
667C42—42no—
668C42—42no—
669C42—42no—
670C42—44no—
671C42—42no—
672C42—42no—
673C42—42no—
674C42—42no—
675C42—82no—
676C42—82no—
677C42—82no—
678C42—82no—
679C42—82no—
680C42C2×C4⋊C414yes—
681C42C2×C4⋊C418yes—
682C42C2×C4⋊C418yes—
683C42C2×C4⋊C414yes—
684C42C23×C414yes—
685C42C23×C412yes—
686C42C23×C412yes—
687C42C22×Q812yes—
688C42C22×Q814yes—
689C42C22×Q812yes—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23C22×C4⋊C412yes—
701C23C22×C4⋊C414yes—
702C23C2×#13514yes—
703C23C2×#13514yes—
704C23C23×D411yescharacteristic
705Q8—28no—
706D4—216no—
707D4#427116yescomplemented
708C2×C4—21no—
709C2×C4—22no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—22no—
713C2×C4—21no—
714C2×C4—216no—
715C2×C4—21no—
716C2×C4—22no—
717C2×C4—21no—
718C2×C4—22no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—28no—
724C2×C4—24no—
725C2×C4—22no—
726C2×C4—24no—
727C2×C4—22no—
728C2×C4—24no—
729C2×C4—22no—
730C2×C4—24no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—48no—
735C2×C4—44no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—41no—
743C2×C4—42no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—42no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—42no—
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—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—88no—
771C2×C4—88no—
772C2×C4—164no—
773C2×C4—164no—
774C2×C4C22×C4⋊C412yes—
775C2×C4C22×C4⋊C412yes—
776C2×C4C22×C4⋊C412yes—
777C2×C4C22×C4⋊C414yes—
778C2×C4C22×C4⋊C414yes—
779C2×C4C22×C4⋊C412yes—
780C2×C4C22×C4⋊C414yes—
781C2×C4C22×C4⋊C412yes—
782C2×C4C2×#13512yes—
783C2×C4C2×#13512yes—
784C2×C4C24×C411yescharacteristic
785C2×C4C23×Q811yescharacteristic
786C2×C4C2×H(5,𝔽2)11yescharacteristic
787C2×C4C2×2−1+411yescharacteristic
788C2×C4#58511yescharacteristic
789C2×C4#58511yescharacteristic
790C8—22no—
791C8—24no—
792C8—22no—
793C8—24no—
794C8—22no—
795C8—22no—
796C22—24no—
797C22—24no—
798C22—24no—
799C22—24no—
800C22—24no—
801C22—24no—
802C22—22no—
803C22—22no—
804C22—22no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22C2×#42718yes—
810C22C23×C4⋊C411yescharacteristic
811C22#348811yescharacteristic
812C22#348911yescharacteristic
813C22C22×#13511yescharacteristic
814C22C22×#13511yescharacteristic
815C22#358511yescharacteristic
816C22#358611yescharacteristic
817C4—22no—
818C4—24no—
819C4—22no—
820C4—24no—
821C4—22no—
822C4—24no—
823C4—22no—
824C4—42no—
825C4—42no—
826C4—82no—
827C4—82no—
828C4—81no—
829C4—81no—
830C4—82no—
831C4—81no—
832C4—81no—
833C4—82no—
834C4—81no—
835C4—81no—
836C4C2×#42714yes—
837C4C4×H(5,𝔽2)11yescharacteristic
838C4C4×2−1+411yescharacteristic
839C4#350311yescharacteristic
840C4#350411yescharacteristic
841C2—28no—
842C2—42no—
843C2#3425011yescharacteristic
844C2C22×#42711yescharacteristic
845C2#6010911yescharacteristic
846C2#6195511yescharacteristic
847C2#6195611yescharacteristic
848C2#6210311yescharacteristic
849C2#6210411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC22×#41D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×#41 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #22741C2semidirect
5. #22739C2semidirect
6. #22727C2semidirect
7. #22725C2semidirect
8. #22706C2semidirect
9. #22705C2semidirect
10. #22704C2semidirect
11. #22703C2semidirect
12. #22656C2semidirect
13. D4×#107C2semidirect
14. #22654C2semidirect
15. D4×#106C2semidirect
16. #21984C2semidirect
17. #21983C2semidirect
18. #21962C2semidirect
19. #21960C2semidirect
20. #21361C2semidirect
21. #21360C2semidirect
22. #21169C2semidirect
23. C2×#1949C2semidirect
25. #2988C4semidirect
165. C8×Q8C2×C4semidirect
166. C8×Q8C2×C4semidirect
169. C8×D4C2×C4semidirect
170. C8×D4C2×C4semidirect
171. #431C2×C4semidirect
172. #431C2×C4semidirect
196. C2×C4⋊C8C2×C4semidirect
197. C2×C4⋊C8C2×C4semidirect
707. D4#427semidirect

Maximal subgroups

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

subgroupindex
C2×#29882
#341912
#341272
#227412
#227392
#227272
#227252
#227062
#227052
#227042
#227032
#226562
D4×#1072
#226542
D4×#1062
#219842
#219832
#219622
#219602
#213612
#213602
#211692
C2×#19492