Finite Group Databasebeta

← #6386206

Subgroups — #6386206

Order 512.

3037 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62815C211yesmaximal, characteristic
2#60232C211yesmaximal, characteristic, complemented
3#34086C211yesmaximal, characteristic, complemented
4#22507C214yesmaximal, complemented
5#22506C218yesmaximal, complemented
6#22505C214yesmaximal, complemented
7#21845C211yesmaximal, characteristic, complemented
8#21844C211yesmaximal, characteristic, complemented
9#21775C214yesmaximal, complemented
10#20748C211yesmaximal, characteristic, complemented
11#20747C211yesmaximal, characteristic, complemented
12#20706C214yesmaximal, complemented
13#3512C414yescomplemented
14#3511C412yescomplemented
15#3511C412yescomplemented
16#3510—22no—
17#3509—21no—
18#3508—21no—
19#3507C412yescomplemented
20#3507C412yescomplemented
21#3506C412yescomplemented
22#3506C412yescomplemented
23#3505—22no—
24#3505—22no—
25#3480—22no—
26#3480—22no—
27#3475C2214yes—
28#3475C2214yes—
29#3455—22no—
30#3449C2212yes—
31#3444—22no—
32C2×#533C2211yescharacteristic
33C2×#532C2211yescharacteristic
34#3428C2212yes—
35C2×C4×#41C2211yescharacteristic
36#2981—22no—
37#2981—22no—
38#2980—22no—
39#2979—22no—
40D4×M16C2214yescomplemented
41D4×M16C2214yescomplemented
42#2920C2211yescharacteristic
43#2920C2211yescharacteristic
44#2879C2214yes—
45#2337—22no—
46#2333—22no—
47#2331—21no—
48#2328—21no—
49#2324—22no—
50#2297C2214yes—
51#2293C2212yescomplemented
52#2290C2214yescomplemented
53#2283C2211yescharacteristic
54C42×D4C2212yescomplemented
55C4×#117C2211yescharacteristic
56#1995C2214yescomplemented
57#1994C2212yescomplemented
58#1994C2212yescomplemented
59#1986C2214yescomplemented
60#1986C2214yescomplemented
61#1897C2218yes—
62#1896C2218yes—
63#1871C2218yes—
64#1871C2218yes—
65#1826C2212yes—
66#1826C2212yes—
67#1826C2214yes—
68#1826C2214yes—
69#1826C2218yescomplemented
70#1826C2218yescomplemented
71#1806C2214yes—
72#1806C2214yes—
73#1789C2212yes—
74#1789C2212yes—
75#1759C2214yes—
76C4×#104C2212yes—
77C4×#104C2212yes—
78#1733C2218yescomplemented
79C2×#339C2218yescomplemented
80C22×#41C2311yescharacteristic
81C22×#41C2312yes—
82C22×M16C2318yes—
83#559—22no—
84#559—22no—
85#559—24no—
86#559—24no—
87#557—22no—
88#557—22no—
89#556—22no—
90#556—22no—
91#556—24no—
92#556—24no—
93#556C2×C414yescomplemented
94#556C2×C414yescomplemented
95#555C2×C414yescomplemented
96#555C2×C414yescomplemented
97#554C2×C414yescomplemented
98#554C2×C414yescomplemented
99#553—24no—
100#553—24no—
101#553—28no—
102#553—28no—
103#553C2×C418yescomplemented
104#553C2×C418yescomplemented
105#552—24no—
106#552—24no—
107#552C2×C418yescomplemented
108#552C2×C418yescomplemented
109#551—28no—
110#551—28no—
111#550—22no—
112#550—22no—
113#548—24no—
114#548—24no—
115#547C2×C414yescomplemented
116#547C2×C414yescomplemented
117#546—24no—
118#546—24no—
119#542—24no—
120#542—24no—
121#541—24no—
122#540—24no—
123#539—24no—
124#539—24no—
125#538—24no—
126#538—24no—
127#537C2×C414yescomplemented
128#537C2×C414yescomplemented
129#536—22no—
130#536C2×C414yescomplemented
131#535—22no—
132#535C2×C414yescomplemented
133#534—24no—
134#533—22no—
135#533—22no—
136#533—21no—
137#533—21no—
138#533—21no—
139#533—21no—
140#533C2×C412yescomplemented
141#533C2×C412yescomplemented
142#533C2312yes—
143#533C2312yes—
144#532—24no—
145#532—22no—
146#532—22no—
147#532C2×C412yes—
148#532C2×C412yes—
149#532C2×C412yes—
150#532C2×C412yes—
151#532D412yes—
152#532D412yes—
153#532D412yes—
154#532D412yes—
155C2×C4⋊Q8C2×C411yescharacteristic, complemented
156C2×C4⋊Q8C2×C411yescharacteristic, complemented
157C2×C4⋊Q8D411yescharacteristic
158C2×#127D411yescharacteristic
159#529—24no—
160#529—24no—
161#529—24no—
162#529—24no—
163#529—24no—
164#529—24no—
165#529—28no—
166#529—28no—
167C2×#125C2×C412yescomplemented
168C2×#124D412yes—
169#525—24no—
170#525—24no—
171#525—24no—
172#525C2318yes—
173C2×C22⋊Q8—21no—
174C2×C22⋊Q8—21no—
175C2×#121D412yes—
176C2×#121D412yes—
177#520C2×C414yescomplemented
178#520C2×C414yescomplemented
179#520C2×C414yescomplemented
180#520C2×C414yescomplemented
181#519—22no—
182#518—24no—
183#518—22no—
184C4×#41—24no—
185C4×#41—24no—
186C4×#41—24no—
187C4×#41—24no—
188C4×#41—21no—
189C4×#41—21no—
190C4×#41—21no—
191C4×#41—21no—
192C4×#41C2×C412yescomplemented
193C4×#41C2×C412yescomplemented
194C4×#41C2312yes—
195C4×#41C2312yes—
196C2×C4×Q8—21no—
197C2×C4×Q8—21no—
198C2×C4×Q8C2×C411yescharacteristic, complemented
199C2×C4×Q8C2×C411yescharacteristic, complemented
200C2×C4×D4—21no—
201C2×C4×D4—21no—
202C2×C4×D4—22no—
203C2×C4×D4C2×C411yescharacteristic, complemented
204C2×C4×D4C2×C411yescharacteristic, complemented
205C2×C4×D4C2312yes—
206C2×C4×D4C2312yes—
207C2×#117—21no—
208C2×#117—21no—
209C2×#117C2311yescharacteristic
210C2×#117C2312yes—
211C2×#117C2318yes—
212C2×#117C2314yes—
213C22×C42—21no—
214C22×C42C2314yes—
215C22×C42C2311yescharacteristic
216#436—24no—
217#436—24no—
218#435—28no—
219#435—28no—
220C8×D4—24no—
221C8×D4—24no—
222#432—21no—
223#432—21no—
224#432—21no—
225#432—21no—
226#431—21no—
227#431—21no—
228#431—21no—
229#431—21no—
230#423C2312yes—
231#423C2312yes—
232C2×#104C2314yes—
233C2×#104C2318yes—
234C2×#104C2314yes—
235#408—28no—
236#408—28no—
237#407C2312yes—
238#407C2312yes—
239#407C2318yes—
240C4×M16C2312yes—
241C4×M16C2312yes—
242#391—24no—
243#390—22no—
244#390—24no—
245#389—22no—
246#388—24no—
247#388—24no—
248#387—24no—
249#386—24no—
250#386—24no—
251#386—24no—
252#385—24no—
253#383—21no—
254#382—21no—
255#381—21no—
256#380—21no—
257C4×C4⋊C4—22no—
258C4×C4⋊C4—21no—
259C4×C4⋊C4C2312yes—
260C4×C4⋊C4C2312yes—
261C4×C22⋊C4—21no—
262C4×C22⋊C4—24no—
263C4×C22⋊C4C2312yes—
264C4×C22⋊C4C2312yes—
265C4×C22⋊C4C2314yes—
266C4×C22⋊C4C2314yes—
267#376—21no—
268#376C2312yes—
269C43C2311yescharacteristic
270C43C2311yescharacteristic
271#339C2314yes—
272#339C2318yes—
273#339C2314yes—
274#339C2318yes—
275#339C2318yes—
276#339C2318yes—
277#339C2318yes—
278C2×#41—24no—
279C2×#41—24no—
280C2×#41—21no—
281C2×#41—21no—
282C2×#41—48no—
283C2×#41—44no—
284C2×#41C22×C412yes—
285C2×#41C22×C414yes—
286C2×#41C22×C414yes—
287C2×#41C2×D414yes—
288C2×#41C2×D414yes—
289C2×#41C2412yes—
290C22×Q8—21no—
291C22×Q8—21no—
292C22×Q8C22×C411yescharacteristic
293C22×Q8C2×D412yes—
294C22×D4—21no—
295C22×D4C22×C411yescharacteristic
296C22×D4C2×D412yes—
297C22×D4C2×D414yes—
298C22×D4C2×D412yes—
299C22×D4C2×D412yes—
300C23×C4—21no—
301C23×C4—21no—
302C23×C4—21no—
303C23×C4—24no—
304C23×C4C2×D411yescharacteristic
305C23×C4C2×D411yescharacteristic
306C23×C4C2414yes—
307C23×C4C2411yescharacteristic
308C2×M16—28no—
309C2×M16—48no—
310C2×M16—48no—
311C2×M16C2414yes—
312C2×M16C2414yes—
313C22×C8—28no—
314C4⋊Q8—24no—
315C4⋊Q8—21no—
316C4⋊Q8—21no—
317C4⋊Q8—21no—
318C4⋊Q8—21no—
319C4⋊Q8C22⋊C412yes—
320C4⋊Q8C22⋊C412yes—
321C4⋊Q8C22⋊C412yes—
322C4⋊Q8C22⋊C412yes—
323C4⋊Q8C22×C412yes—
324C4⋊Q8C22×C412yes—
325C4⋊Q8C22×C412yes—
326C4⋊Q8C22×C412yes—
327#127—24no—
328#127C22⋊C412yes—
329#127C22⋊C412yes—
330#127C22⋊C412yes—
331#127C22⋊C412yes—
332#126—28no—
333#126—28no—
334#126—28no—
335#126—28no—
336#126—28no—
337#126—28no—
338#125—24no—
339#125—24no—
340#125—28no—
341#125—28no—
342#125—22no—
343#125—22no—
344#125C22×C414yes—
345#125C22×C414yes—
346#124—24no—
347#124—24no—
348#124—24no—
349#124—24no—
350#124—28no—
351#124—28no—
352#124C22⋊C414yes—
353#124C22⋊C414yes—
354#124C22⋊C414yes—
355#124C22⋊C414yes—
356#123—28no—
357#123—28no—
358#123—28no—
359#123—28no—
360#123—28no—
361#123—28no—
362#123—28no—
363#123—28no—
364C22⋊Q8—24no—
365C22⋊Q8—24no—
366C22⋊Q8—22no—
367C22⋊Q8—22no—
368C22⋊Q8—22no—
369C22⋊Q8—22no—
370C22⋊Q8—22no—
371C22⋊Q8—22no—
372C22⋊Q8—22no—
373C22⋊Q8—22no—
374C22⋊Q8—24no—
375C22⋊Q8—24no—
376C22⋊Q8—28no—
377C22⋊Q8—28no—
378C22⋊Q8C22×C418yes—
379C22⋊Q8C22×C418yes—
380#121—24no—
381#121—24no—
382#121—24no—
383#121—24no—
384#121—28no—
385#121—28no—
386#121—28no—
387#121—28no—
388#121C22⋊C414yes—
389#121C22⋊C414yes—
390#121C22⋊C414yes—
391#121C22⋊C414yes—
392#121C22⋊C414yes—
393#121C22⋊C414yes—
394#121C22⋊C414yes—
395#121C22⋊C414yes—
396#121C22×C418yes—
397#121C22×C418yes—
398#120—28no—
399#120—28no—
400C4×Q8—24no—
401C4×Q8—24no—
402C4×Q8—24no—
403C4×Q8—24no—
404C4×Q8—24no—
405C4×Q8—24no—
406C4×Q8—22no—
407C4×Q8—22no—
408C4×Q8—22no—
409C4×Q8—22no—
410C4×Q8—21no—
411C4×Q8—21no—
412C4×Q8—21no—
413C4×Q8—21no—
414C4×Q8—22no—
415C4×Q8—22no—
416C4×Q8—22no—
417C4×Q8—22no—
418C4×Q8C22×C412yes—
419C4×Q8C22×C412yes—
420C4×Q8C22×C412yes—
421C4×Q8C22×C412yes—
422C4×D4—28no—
423C4×D4—28no—
424C4×D4—24no—
425C4×D4—24no—
426C4×D4—28no—
427C4×D4—28no—
428C4×D4—24no—
429C4×D4—24no—
430C4×D4—24no—
431C4×D4—24no—
432C4×D4—22no—
433C4×D4—22no—
434C4×D4—22no—
435C4×D4—22no—
436C4×D4—22no—
437C4×D4—22no—
438C4×D4—22no—
439C4×D4—22no—
440C4×D4—28no—
441C4×D4—28no—
442C4×D4—28no—
443C4×D4—28no—
444C4×D4—21no—
445C4×D4—21no—
446C4×D4—21no—
447C4×D4—21no—
448C4×D4—48no—
449C4×D4C22×C412yes—
450C4×D4C22×C412yes—
451C4×D4C22×C412yes—
452C4×D4C22×C412yes—
453C4×D4C22×C414yes—
454C4×D4C22×C414yes—
455C4×D4C22×C414yes—
456C4×D4C22×C414yes—
457C4×D4C2×D414yes—
458C4×D4C2×D414yes—
459C4×D4C2×D414yes—
460C4×D4C2×D414yes—
461#117—21no—
462#117—21no—
463#117—22no—
464#117—28no—
465#117—22no—
466#117—28no—
467#117—24no—
468#117—24no—
469#117—28no—
470#117—28no—
471#117—22no—
472#117—22no—
473#117—22no—
474#117—22no—
475#117—48no—
476#117—44no—
477#117C22×C412yes—
478#117C22×C414yes—
479#117C22×C418yes—
480#117C22×C418yes—
481#117C2412yes—
482#117C2414yes—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—22no—
486C2×C4⋊C4—22no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—22no—
490C2×C4⋊C4—22no—
491C2×C4⋊C4—24no—
492C2×C4⋊C4C22×C411yescharacteristic
493C2×C4⋊C4C22×C411yescharacteristic
494C2×C4⋊C4C22×C412yes—
495C2×C4⋊C4C22×C412yes—
496C2×C4⋊C4C22×C418yes—
497C2×C4⋊C4C22×C418yes—
498C2×C4⋊C4C2×D412yes—
499C2×C4⋊C4C2×D412yes—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—28no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4C2×D414yes—
511C2×C22⋊C4C2×D414yes—
512C2×C42—21no—
513C2×C42—21no—
514C2×C42—21no—
515C2×C42—21no—
516C2×C42—22no—
517C2×C42—28no—
518C2×C42—22no—
519C2×C42—22no—
520C2×C42—22no—
521C2×C42—22no—
522C2×C42—21no—
523C2×C42—21no—
524C2×C42—21no—
525C2×C42—24no—
526C2×C42—48no—
527C2×C42C22×C411yescharacteristic
528C2×C42C22×C411yescharacteristic
529C2×C42C22×C411yescharacteristic
530C2×C42C22×C411yescharacteristic
531C2×C42C2×D411yescharacteristic
532C2×C42C2×D411yescharacteristic
533C2×C42C2×D411yescharacteristic
534C2×C42C2×D411yescharacteristic
535C2×C42C2×D411yescharacteristic
536C2×C42C2×D411yescharacteristic
537C2×C42C2412yes—
538C2×C42C2414yes—
539C2×C42C2412yes—
540C2×C42C2411yescharacteristic
541C2×C42C2411yescharacteristic
542C4⋊C8—22no—
543C4⋊C8—22no—
544C4⋊C8—22no—
545C4⋊C8—22no—
546#104—44no—
547#104—48no—
548#104—44no—
549C22⋊C8—22no—
550C22⋊C8—22no—
551C22⋊C8—22no—
552C22⋊C8—22no—
553C22⋊C8—28no—
554C22⋊C8—28no—
555#97—22no—
556#97—22no—
557C4×C8—22no—
558C4×C8—22no—
559#95—22no—
560#95—22no—
561#95—22no—
562#95—22no—
563#95—22no—
564#95—24no—
565#95—22no—
566#95—24no—
567C24—21no—
568C24C22×D411yescharacteristic
569C24C22×D414yes—
570#41—24no—
571#41—24no—
572#41—48no—
573#41—48no—
574#41—44no—
575#41—48no—
576#41—44no—
577#41—42no—
578#41—42no—
579#41—44no—
580#41—44no—
581#41—88no—
582#41—88no—
583C2×Q8—22no—
584C2×Q8—22no—
585C2×Q8—21no—
586C2×Q8—22no—
587C2×Q8—22no—
588C2×Q8—44no—
589C2×Q8—42no—
590C2×Q8—82no—
591C2×Q8—82no—
592C2×Q8C2×C22⋊C414yes—
593C2×Q8C2×C22⋊C414yes—
594C2×Q8C23×C412yes—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—28no—
598C2×D4—28no—
599C2×D4—21no—
600C2×D4—44no—
601C2×D4—42no—
602C2×D4—44no—
603C2×D4—44no—
604C2×D4—44no—
605C2×D4—44no—
606C2×D4—82no—
607C2×D4C2×C22⋊C414yes—
608C2×D4C2×C22⋊C418yes—
609C2×D4C2×C22⋊C418yes—
610C2×D4C2×C22⋊C414yes—
611C2×D4C2×C22⋊C414yes—
612C2×D4C2×C22⋊C414yes—
613C2×D4C2×C22⋊C414yes—
614C2×D4C2×C22⋊C414yes—
615C2×D4C23×C412yes—
616C22×C4—28no—
617C22×C4—28no—
618C22×C4—24no—
619C22×C4—21no—
620C22×C4—22no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—28no—
626C22×C4—28no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—24no—
634C22×C4—22no—
635C22×C4—42no—
636C22×C4—44no—
637C22×C4—48no—
638C22×C4—82no—
639C22×C4—81no—
640C22×C4—82no—
641C22×C4—84no—
642C22×C4—84no—
643C22×C4C2×C22⋊C411yescharacteristic
644C22×C4C2×C22⋊C411yescharacteristic
645C22×C4C2×C22⋊C411yescharacteristic
646C22×C4C2×C22⋊C411yescharacteristic
647C22×C4C2×C22⋊C411yescharacteristic
648C22×C4C2×C22⋊C411yescharacteristic
649C22×C4C2×C22⋊C411yescharacteristic
650C22×C4C2×C22⋊C411yescharacteristic
651C22×C4C23×C411yescharacteristic
652C22×C4C23×C411yescharacteristic
653C22×C4C23×C418yes—
654C22×C4C22×D411yescharacteristic
655C22×C4C22×D414yes—
656C22×C4C22×D411yescharacteristic
657C22×C4C22×D411yescharacteristic
658C22×C4C22×D411yescharacteristic
659C22×C4C22×D418yes—
660C22×C4C22×D411yescharacteristic
661C22×C4C22×D411yescharacteristic
662C22×C4C22×D411yescharacteristic
663C22×C4C2511yescharacteristic
664M16—24no—
665M16—28no—
666M16—24no—
667M16—88no—
668C2×C8—24no—
669C2×C8—24no—
670C2×C8—88no—
671C4⋊C4—22no—
672C4⋊C4—22no—
673C4⋊C4—24no—
674C4⋊C4—24no—
675C4⋊C4—22no—
676C4⋊C4—22no—
677C4⋊C4—22no—
678C4⋊C4—22no—
679C4⋊C4—24no—
680C4⋊C4—24no—
681C4⋊C4—22no—
682C4⋊C4—22no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—22no—
686C4⋊C4—22no—
687C4⋊C4—28no—
688C4⋊C4—28no—
689C4⋊C4—28no—
690C4⋊C4—28no—
691C4⋊C4—44no—
692C4⋊C4—44no—
693C4⋊C4—84no—
694C4⋊C4C2×C22⋊C414yes—
695C4⋊C4C2×C22⋊C414yes—
696C4⋊C4C2×C22⋊C414yes—
697C4⋊C4C2×C22⋊C414yes—
698C4⋊C4C23×C412yes—
699C4⋊C4C23×C412yes—
700C4⋊C4C23×C414yes—
701C4⋊C4C23×C414yes—
702C22⋊C4—22no—
703C22⋊C4—24no—
704C22⋊C4—28no—
705C22⋊C4—28no—
706C22⋊C4—28no—
707C22⋊C4—28no—
708C22⋊C4—22no—
709C22⋊C4—24no—
710C22⋊C4—22no—
711C22⋊C4—22no—
712C22⋊C4—22no—
713C22⋊C4—22no—
714C22⋊C4—28no—
715C22⋊C4—28no—
716C22⋊C4—44no—
717C22⋊C4—48no—
718C22⋊C4—84no—
719C22⋊C4—84no—
720C22⋊C4—82no—
721C22⋊C4C2×C22⋊C418yes—
722C22⋊C4C2×C22⋊C418yes—
723C22⋊C4C2×C22⋊C418yes—
724C22⋊C4C2×C22⋊C418yes—
725C42—24no—
726C42—22no—
727C42—22no—
728C42—22no—
729C42—22no—
730C42—22no—
731C42—28no—
732C42—28no—
733C42—24no—
734C42—22no—
735C42—24no—
736C42—24no—
737C42—28no—
738C42—24no—
739C42—42no—
740C42—84no—
741C42—81no—
742C42—81no—
743C42C2×C22⋊C411yescharacteristic
744C42C2×C22⋊C411yescharacteristic
745C42C2×C22⋊C411yescharacteristic
746C42C2×C22⋊C411yescharacteristic
747C42C2×C22⋊C411yescharacteristic
748C42C2×C22⋊C411yescharacteristic
749C42C2×C22⋊C411yescharacteristic
750C42C2×C22⋊C411yescharacteristic
751C42C23×C411yescharacteristic
752C42C23×C411yescharacteristic
753C42C23×C411yescharacteristic
754C42C23×C411yescharacteristic
755C42C22×D411yescharacteristic
756C42C22×D411yescharacteristic
757C42C22×D411yescharacteristic
758C42C22×D411yescharacteristic
759C23—24no—
760C23—24no—
761C23—22no—
762C23—22no—
763C23—41no—
764C23—44no—
765C23—41no—
766C23—44no—
767C23—42no—
768C23—81no—
769C23—81no—
770C23C22×C22⋊C418yes—
771C23C22×C22⋊C411yescharacteristic
772C23C22×C22⋊C411yescharacteristic
773C23C23×D411yescharacteristic
774Q8—22no—
775Q8—22no—
776Q8—44no—
777Q8—44no—
778Q8—42no—
779Q8—44no—
780Q8—44no—
781Q8—82no—
782Q8—82no—
783D4—28no—
784D4—22no—
785D4—22no—
786D4—44no—
787D4—44no—
788D4—44no—
789D4—48no—
790D4—48no—
791D4—44no—
792D4—44no—
793D4—42no—
794D4—44no—
795D4—44no—
796D4—88no—
797D4—88no—
798C2×C4—24no—
799C2×C4—24no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—216no—
806C2×C4—22no—
807C2×C4—28no—
808C2×C4—28no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—24no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—24no—
816C2×C4—24no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—44no—
827C2×C4—44no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—44no—
832C2×C4—44no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—44no—
836C2×C4—44no—
837C2×C4—44no—
838C2×C4—42no—
839C2×C4—82no—
840C2×C4—82no—
841C2×C4—81no—
842C2×C4—81no—
843C2×C4—82no—
844C2×C4—82no—
845C2×C4—88no—
846C2×C4—88no—
847C2×C4—816no—
848C2×C4C22×C22⋊C411yescharacteristic
849C2×C4C22×C22⋊C411yescharacteristic
850C2×C4C22×C22⋊C411yescharacteristic
851C2×C4C22×C22⋊C411yescharacteristic
852C2×C4C22×C22⋊C411yescharacteristic
853C2×C4C22×C22⋊C418yes—
854C2×C4C22×C22⋊C411yescharacteristic
855C2×C4C22×C22⋊C411yescharacteristic
856C2×C4C22×C22⋊C411yescharacteristic
857C2×C4C22×C22⋊C411yescharacteristic
858C2×C4C22×C22⋊C411yescharacteristic
859C2×C4C24×C411yescharacteristic
860C2×C4C23×D411yescharacteristic
861C2×C4#58514yes—
862C8—44no—
863C8—44no—
864C22—21no—
865C22—21no—
866C22—21no—
867C22—21no—
868C22—28no—
869C22—21no—
870C22—21no—
871C22—28no—
872C22—21no—
873C22—21no—
874C22—28no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—84no—
879C22—84no—
880C22—82no—
881C22—84no—
882C22C23×C22⋊C411yescharacteristic
883C22#348512yes—
884C4—21no—
885C4—21no—
886C4—28no—
887C4—21no—
888C4—21no—
889C4—21no—
890C4—21no—
891C4—21no—
892C4—21no—
893C4—21no—
894C4—44no—
895C4—42no—
896C4—42no—
897C4—44no—
898C4—42no—
899C4—44no—
900C4—82no—
901C4—84no—
902C4#290112yes—
903C4#342812yes—
904C4#348512yes—
905C2—22no—
906C2—41no—
907C2—48no—
908C2—41no—
909C2—82no—
910C2#3417211yescharacteristic
911C2C2×#290111yescharacteristic
912C2#6009311yescharacteristic
subgroupG/H
centerC2×C4C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
socleC22C23×C22⋊C4
prime radical#62815C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C2×#532 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60232C2semidirect
3. #34086C2semidirect
4. #22507C2semidirect
5. #22506C2semidirect
6. #22505C2semidirect
7. #21845C2semidirect
8. #21844C2semidirect
9. #21775C2semidirect
10. #20748C2semidirect
11. #20747C2semidirect
12. #20706C2semidirect
13. #3512C4semidirect
14. #3511C4semidirect
15. #3511C4semidirect
19. #3507C4semidirect
20. #3507C4semidirect
21. #3506C4semidirect
22. #3506C4semidirect
40. D4×M16C22semidirect
41. D4×M16C22semidirect
51. #2293C22semidirect
52. #2290C22semidirect
54. C42×D4C22semidirect
56. #1995C22semidirect
57. #1994C22semidirect
58. #1994C22semidirect
59. #1986C22semidirect
60. #1986C22semidirect
69. #1826C22semidirect
70. #1826C22semidirect
78. #1733C22semidirect
79. C2×#339C22semidirect
93. #556C2×C4semidirect
94. #556C2×C4semidirect
95. #555C2×C4semidirect
96. #555C2×C4semidirect
97. #554C2×C4semidirect
98. #554C2×C4semidirect
103. #553C2×C4semidirect
104. #553C2×C4semidirect
107. #552C2×C4semidirect
108. #552C2×C4semidirect
115. #547C2×C4semidirect
116. #547C2×C4semidirect
127. #537C2×C4semidirect
128. #537C2×C4semidirect
130. #536C2×C4semidirect
132. #535C2×C4semidirect
140. #533C2×C4semidirect
141. #533C2×C4semidirect
155. C2×C4⋊Q8C2×C4semidirect
156. C2×C4⋊Q8C2×C4semidirect
167. C2×#125C2×C4semidirect
177. #520C2×C4semidirect
178. #520C2×C4semidirect
179. #520C2×C4semidirect
180. #520C2×C4semidirect
192. C4×#41C2×C4semidirect
193. C4×#41C2×C4semidirect
198. C2×C4×Q8C2×C4semidirect
199. C2×C4×Q8C2×C4semidirect
203. C2×C4×D4C2×C4semidirect
204. C2×C4×D4C2×C4semidirect

Maximal subgroups

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

subgroupindex
#628152
#602322
#340862
#225072
#225062
#225052
#218452
#218442
#217752
#207482
#207472
#207062