Finite Group Databasebeta

← #6388818

Subgroups — #6388818

Order 512.

1908 conjugacy classes of subgroups.

The subgroup lattice has 859 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#478C211yesmaximal, characteristic
2#34378C211yesmaximal, characteristic, complemented
3#34190C211yesmaximal, characteristic
4#23071C212yesmaximal, complemented
5#23065C212yesmaximal, complemented
6#22972C212yesmaximal, complemented
7#22966C212yesmaximal, complemented
8#22617C211yesmaximal, characteristic, complemented
9#22615C211yesmaximal, characteristic, complemented
10#22611C211yesmaximal, characteristic, complemented
11#22609C211yesmaximal, characteristic, complemented
12#22574C211yesmaximal, characteristic
13#22570C211yesmaximal, characteristic
14#22566C211yesmaximal, characteristic
15#22562C211yesmaximal, characteristic
16#22126C212yesmaximal, complemented
17#22122C212yesmaximal, complemented
18#21962C211yesmaximal, characteristic, complemented
19#21836C211yesmaximal, characteristic, complemented
20#21620C212yesmaximal, complemented
21#21619C212yesmaximal, complemented
22#20732C211yesmaximal, characteristic
23#20545C211yesmaximal, characteristic, complemented
24C22×#125C2211yescharacteristic
25C22×C4×D4C2211yescharacteristic
26C2×#478C4116yescomplemented
27C2×#478C2211yescharacteristic
28C2×#478C2211yescharacteristic
29C2×#478C2211yescharacteristic
30C2×#478C2211yescharacteristic
31C2×#478C2211yescharacteristic
32C2×#478C2211yescharacteristic
33C2×#478C2211yescharacteristic
34C2×#478C2211yescharacteristic
35C2×#431C2211yescharacteristic
36C22×#107C2211yescharacteristic
37C22×#106C2211yescharacteristic
38C22×C4⋊C8C2211yescharacteristic
39C22×#102C2211yescharacteristic
40C22×#102C2211yescharacteristic
41#2382—22no—
42#2370C2212yescomplemented
43#2370C2212yescomplemented
44#2357C2212yes—
45#2353—22no—
46#2349C2212yes—
47#2345C2211yescharacteristic
48#2345C2211yescharacteristic
49#2344—21no—
50#2344—21no—
51#2344C2211yescharacteristic
52#2344C2211yescharacteristic
53#2344C2211yescharacteristic
54#2344C2211yescharacteristic
55#2342—21no—
56#2342—21no—
57D4×C22⋊C4C2211yescharacteristic
58D4×C22⋊C4C2211yescharacteristic
59#2336—22no—
60#2330C2212yescomplemented
61#2330C2212yescomplemented
62#2319C2212yes—
63#2318—22no—
64#2316—21no—
65#2313—21no—
66#2285C2211yescharacteristic
67#2283C2211yescharacteristic
68#2283C2211yescharacteristic
69#2280—21no—
70C2×#381—21no—
71#2275C2212yes—
72#1991C2212yescomplemented
73#1991C2212yescomplemented
74#1989C2212yescomplemented
75#1989C2212yescomplemented
76#1949C2212yescomplemented
77#1949C2212yescomplemented
78#1948C2212yescomplemented
79#1947C2212yescomplemented
80#1944C2212yescomplemented
81#1943C2212yescomplemented
82#1942C2212yescomplemented
83#1941C2212yescomplemented
84#1936C2212yes—
85#1936C2212yes—
86#1934C2212yes—
87#1934C2212yes—
88#1926C2212yes—
89#1926C2212yes—
90#1925C2212yes—
91#1925C2212yes—
92#1921C2212yescomplemented
93#1921C2212yescomplemented
94#1920C2212yescomplemented
95#1920C2212yescomplemented
96#1919C2212yescomplemented
97#1919C2212yescomplemented
98#1918C2212yescomplemented
99#1918C2212yescomplemented
100#1864C2212yes—
101#1864C2212yes—
102#1862C2212yes—
103#1862C2212yes—
104#1824C2211yescharacteristic
105#1824C2211yescharacteristic
106#1823C2211yescharacteristic
107#1823C2211yescharacteristic
108#1823C2211yescharacteristic
109#1823C2211yescharacteristic
110#1808C2211yescharacteristic
111#1808C2211yescharacteristic
112#1807C2211yescharacteristic
113#1807C2211yescharacteristic
114#1802C2212yes—
115#1802C2212yes—
116#1786C2211yescharacteristic
117#1786C2211yescharacteristic
118#1776C2212yescomplemented
119#1776C2212yescomplemented
120C4×#107C2212yescomplemented
121C4×#106C2212yescomplemented
122#1770C2212yescomplemented
123C8×C4⋊C4C2212yescomplemented
124#1768C2212yescomplemented
125#1768C2212yescomplemented
126#1762C2212yes—
127#1762C2212yes—
128C4×#102C2212yes—
129C4×#102C2212yes—
130C4×#102C2212yes—
131C4×#102C2212yes—
132#1752C2211yescharacteristic
133#1752C2211yescharacteristic
134C8×C22⋊C4C2211yescharacteristic
135C8×C22⋊C4C2211yescharacteristic
136C23×D4C2311yescharacteristic
137C24×C4—21no—
138C23×C8C2311yescharacteristic
139C23×C8C2311yescharacteristic
140C2×#125—21no—
141C2×#125—21no—
142C2×#125—24no—
143C2×#125C2×C418yescomplemented
144C2×#125C2311yescharacteristic
145C2×#125C2311yescharacteristic
146C2×#125C2311yescharacteristic
147C2×#125C2311yescharacteristic
148C2×C4×D4—21no—
149C2×C4×D4—21no—
150C2×C4×D4—24no—
151C2×C4×D4C2×C418yes—
152C2×C4×D4C2312yes—
153C2×C4×D4C2312yes—
154C2×C4×D4C2311yescharacteristic
155C2×C4×D4C2311yescharacteristic
156C2×C4×D4C2311yescharacteristic
157C2×C4×D4C2311yescharacteristic
158C2×#117—21no—
159C2×#117—21no—
160C2×#117—21no—
161C2×#117—21no—
162C2×#117—21no—
163C22×C4⋊C4—21no—
164C22×C4⋊C4—21no—
165C22×C4⋊C4C2311yescharacteristic
166C22×C4⋊C4C2311yescharacteristic
167C22×C4⋊C4C2311yescharacteristic
168C22×C22⋊C4—21no—
169C22×C22⋊C4—21no—
170C22×C22⋊C4—21no—
171C22×C42C2311yescharacteristic
172#478C2×C418yes—
173#478C2×C418yes—
174#478C2×C418yes—
175#478C2×C418yes—
176#478C2×C418yescomplemented
177#478C2×C418yescomplemented
178#478C2×C418yescomplemented
179#478C2×C418yescomplemented
180#431—24no—
181C2×#107C2×C418yescomplemented
182C2×#107C2312yes—
183C2×#107C2312yes—
184C2×#107C2311yescharacteristic
185C2×#107C2311yescharacteristic
186C2×#107C2311yescharacteristic
187C2×#107C2311yescharacteristic
188C2×#106C2×C418yescomplemented
189C2×#106C2312yes—
190C2×#106C2312yes—
191C2×#106C2311yescharacteristic
192C2×#106C2311yescharacteristic
193C2×#106C2311yescharacteristic
194C2×#106C2311yescharacteristic
195C2×C4⋊C8C2×C418yescomplemented
196C2×C4⋊C8C2312yes—
197C2×C4⋊C8C2311yescharacteristic
198C2×C4⋊C8C2311yescharacteristic
199C2×C4⋊C8C2311yescharacteristic
200C2×C4⋊C8C2311yescharacteristic
201C2×#102C2×C418yes—
202C2×#102C2×C418yes—
203C2×#102C2312yes—
204C2×#102C2312yes—
205C2×#102C2312yes—
206C2×#102C2312yes—
207C2×#102C2311yescharacteristic
208C2×#102C2311yescharacteristic
209C2×#102C2311yescharacteristic
210C2×#102C2311yescharacteristic
211C2×#102C2311yescharacteristic
212C2×#102C2311yescharacteristic
213C2×#102C2311yescharacteristic
214C2×#102C2311yescharacteristic
215C2×C22⋊C8C2311yescharacteristic
216C2×C22⋊C8C2311yescharacteristic
217C2×#97C2312yes—
218C2×#97C2312yes—
219C2×C4×C8C2312yes—
220C2×C4×C8C2312yes—
221C2×C4×C8C2312yes—
222#390C2312yes—
223#390C2312yes—
224#389—22no—
225#389—22no—
226#389—22no—
227#389—22no—
228#389—22no—
229#389—22no—
230#389C2312yes—
231#389C2312yes—
232#389C2312yes—
233#389C2312yes—
234#389C2312yes—
235#389C2312yes—
236#388—22no—
237#388—22no—
238#388—22no—
239#388—22no—
240#387—22no—
241#387—22no—
242#387—22no—
243#387—22no—
244#387—22no—
245#387—22no—
246#387—22no—
247#387—22no—
248#387—22no—
249#387—22no—
250#387—22no—
251#387—22no—
252#387—22no—
253#387—22no—
254#386—22no—
255#386—22no—
256#385—22no—
257#385—22no—
258#384C2312yes—
259#383—21no—
260#383D412yes—
261#382—21no—
262#382D412yes—
263#382C2312yes—
264#381—21no—
265#381—21no—
266#381—21no—
267#381—21no—
268#381—21no—
269#381—22no—
270#381—22no—
271#381D411yescharacteristic
272#381D411yescharacteristic
273#380—21no—
274#380—21no—
275#380—21no—
276#380—22no—
277#380—22no—
278#380D411yescharacteristic
279#380D411yescharacteristic
280#380C2311yescharacteristic
281#380C2311yescharacteristic
282#380C2311yescharacteristic
283#380C2311yescharacteristic
284#379—21no—
285#379—21no—
286C4×C4⋊C4—21no—
287C4×C4⋊C4—22no—
288C4×C4⋊C4—22no—
289C4×C4⋊C4C2312yes—
290C4×C4⋊C4C2312yes—
291C4×C4⋊C4C2312yes—
292C4×C4⋊C4C2312yes—
293C4×C4⋊C4C2312yes—
294C4×C4⋊C4C2312yes—
295C4×C4⋊C4C2312yes—
296C4×C4⋊C4C2312yes—
297C4×C4⋊C4C2312yes—
298C4×C22⋊C4—21no—
299C4×C22⋊C4—21no—
300C4×C22⋊C4—21no—
301C4×C22⋊C4—22no—
302C4×C22⋊C4—22no—
303C4×C22⋊C4—22no—
304C4×C22⋊C4—22no—
305C4×C22⋊C4C2311yescharacteristic
306C4×C22⋊C4C2311yescharacteristic
307#376—21no—
308#376C2312yes—
309C2×#95—22no—
310C2×#95—22no—
311#340C2312yes—
312#340C2312yes—
313#340C2312yes—
314#340C2312yes—
315#340C2312yes—
316#340C2312yes—
317#340C2312yes—
318#340C2312yes—
319#340C2312yes—
320#340C2312yes—
321#340C2312yes—
322#340C2312yes—
323#340C2312yes—
324#340C2312yes—
325#340C2312yes—
326#340C2312yes—
327#336C2312yes—
328#336C2312yes—
329#336C2312yes—
330#336C2312yes—
331C25—21no—
332C22×D4—24no—
333C22×D4—21no—
334C22×D4—22no—
335C22×D4—42no—
336C22×D4C22×C414yes—
337C22×D4C2411yescharacteristic
338C22×D4C2411yescharacteristic
339C23×C4—21no—
340C23×C4—21no—
341C23×C4—21no—
342C23×C4—28no—
343C23×C4—21no—
344C23×C4—21no—
345C23×C4—21no—
346C23×C4—21no—
347C23×C4—22no—
348C23×C4—22no—
349C23×C4—82no—
350C23×C4—82no—
351C23×C4C2×D411yescharacteristic
352C23×C4C2×D411yescharacteristic
353C23×C4C2411yescharacteristic
354C22×C8—42no—
355C22×C8—42no—
356C22×C8C22×C414yes—
357C22×C8C22×C414yes—
358C22×C8C2412yes—
359C22×C8C2412yes—
360C22×C8C2411yescharacteristic
361C22×C8C2411yescharacteristic
362C22×C8C2411yescharacteristic
363C22×C8C2411yescharacteristic
364#125—28no—
365#125—28no—
366#125—22no—
367#125—22no—
368#125—22no—
369#125—22no—
370#125C22×C414yes—
371#125C22×C414yes—
372#125C22×C414yes—
373#125C22×C414yes—
374C4×D4—24no—
375C4×D4—24no—
376C4×D4—28no—
377C4×D4—28no—
378C4×D4—22no—
379C4×D4—22no—
380C4×D4—22no—
381C4×D4—22no—
382C4×D4—42no—
383C4×D4—42no—
384C4×D4C22×C414yes—
385C4×D4C22×C414yes—
386C4×D4C22×C414yes—
387C4×D4C22×C414yes—
388#117—82no—
389#117—82no—
390#117—82no—
391#117—82no—
392#117—82no—
393C2×C4⋊C4—28no—
394C2×C4⋊C4—28no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4C22×C414yes—
418C2×C4⋊C4C22×C414yes—
419C2×C4⋊C4C22×C414yes—
420C2×C4⋊C4C2×D412yes—
421C2×C4⋊C4C2×D412yes—
422C2×C4⋊C4C2412yes—
423C2×C4⋊C4C2412yes—
424C2×C4⋊C4C2412yes—
425C2×C4⋊C4C2412yes—
426C2×C4⋊C4C2411yescharacteristic
427C2×C4⋊C4C2411yescharacteristic
428C2×C4⋊C4C2411yescharacteristic
429C2×C4⋊C4C2411yescharacteristic
430C2×C4⋊C4C2411yescharacteristic
431C2×C4⋊C4C2411yescharacteristic
432C2×C22⋊C4—28no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—22no—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—22no—
444C2×C22⋊C4—22no—
445C2×C22⋊C4—22no—
446C2×C22⋊C4—22no—
447C2×C22⋊C4—82no—
448C2×C22⋊C4—82no—
449C2×C22⋊C4C2×D411yescharacteristic
450C2×C22⋊C4C2×D411yescharacteristic
451C2×C22⋊C4C2×D411yescharacteristic
452C2×C22⋊C4C2×D411yescharacteristic
453C2×C42—22no—
454C2×C42—22no—
455C2×C42—22no—
456C2×C42—22no—
457C2×C42—22no—
458C2×C42—22no—
459C2×C42—22no—
460C2×C42—22no—
461C2×C42C22×C414yes—
462C2×C42C2×D411yescharacteristic
463C2×C42C2×D411yescharacteristic
464C2×C42#4114yes—
465C2×C42C2412yes—
466C2×C42C2412yes—
467C2×C42C2411yescharacteristic
468C2×C42C2411yescharacteristic
469#107—42no—
470#107—42no—
471#107C22×C414yes—
472#107C22×C414yes—
473#107C22×C414yes—
474#107C22×C414yes—
475#106—42no—
476#106—42no—
477#106C22×C414yes—
478#106C22×C414yes—
479#106C22×C414yes—
480#106C22×C414yes—
481C4⋊C8—24no—
482C4⋊C8C22×C414yes—
483C4⋊C8C22×C414yes—
484C4⋊C8C22×C414yes—
485C4⋊C8C22×C414yes—
486#102—24no—
487#102—24no—
488#102—42no—
489#102—42no—
490#102C22×C414yes—
491#102C22×C414yes—
492#102C22×C414yes—
493#102C22×C414yes—
494#102C22×C414yes—
495#102C22×C414yes—
496#102C22×C414yes—
497#102C22×C414yes—
498C22⋊C8—22no—
499C22⋊C8—22no—
500#97—42no—
501#97—42no—
502C4×C8—24no—
503C4×C8—42no—
504C4×C8—42no—
505#95—22no—
506#95—22no—
507#95—22no—
508#95—22no—
509#95—22no—
510#95—22no—
511#95—21no—
512#95—21no—
513#95—22no—
514#95—22no—
515#95—22no—
516#95—21no—
517#95—21no—
518#95—22no—
519#95—22no—
520#95—22no—
521#95—22no—
522#95—22no—
523#95—22no—
524#95—22no—
525#95C2×D412yes—
526#95C2×D412yes—
527#95C2×D412yes—
528#95C2×D412yes—
529#95C2×D412yes—
530#95C2×D412yes—
531#95C2×D412yes—
532#95C2×D412yes—
533C24—21no—
534C24—21no—
535C24—24no—
536C24—44no—
537C24—42no—
538C24—42no—
539C24—82no—
540C24C22×D411yescharacteristic
541C2×D4—28no—
542C2×D4—24no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—44no—
549C2×D4—48no—
550C2×D4—44no—
551C2×D4C23×C412yes—
552C2×D4C23×C412yes—
553C2×D42−1+414yes—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—24no—
559C22×C4—24no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—24no—
567C22×C4—24no—
568C22×C4—24no—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—42no—
576C22×C4—44no—
577C22×C4—44no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4—816no—
583C22×C4—81no—
584C22×C4—81no—
585C22×C4—81no—
586C22×C4—81no—
587C22×C4—81no—
588C22×C4—81no—
589C22×C4—81no—
590C22×C4—81no—
591C22×C4—82no—
592C22×C4—82no—
593C22×C4—82no—
594C22×C4—82no—
595C22×C4—82no—
596C22×C4C4×D414yes—
597C22×C4C4×D414yes—
598C22×C4C23×C412yes—
599C22×C4C22×D412yes—
600C22×C4C22×D412yes—
601C22×C4C22×D412yes—
602C22×C4C22×D412yes—
603C22×C4C22×D411yescharacteristic
604C22×C4C22×D411yescharacteristic
605C22×C4C22×D411yescharacteristic
606C22×C4C22×D411yescharacteristic
607C22×C4C22×D411yescharacteristic
608C22×C4C2×#4112yes—
609C22×C4C2511yescharacteristic
610C2×C8—22no—
611C2×C8—22no—
612C2×C8—22no—
613C2×C8—22no—
614C2×C8—22no—
615C2×C8—22no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—22no—
620C2×C8—44no—
621C2×C8—44no—
622C2×C8C23×C412yes—
623C2×C8C23×C412yes—
624C2×C8C23×C412yes—
625C2×C8C23×C412yes—
626C4⋊C4—24no—
627C4⋊C4—24no—
628C4⋊C4—24no—
629C4⋊C4—24no—
630C4⋊C4—24no—
631C4⋊C4—24no—
632C4⋊C4—24no—
633C4⋊C4—24no—
634C4⋊C4—24no—
635C4⋊C4—24no—
636C4⋊C4—24no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—22no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—22no—
651C4⋊C4—42no—
652C4⋊C4—42no—
653C4⋊C4—82no—
654C4⋊C4—82no—
655C4⋊C4—82no—
656C4⋊C4—82no—
657C4⋊C4—82no—
658C4⋊C4—82no—
659C4⋊C4—82no—
660C4⋊C4—82no—
661C4⋊C4C23×C412yes—
662C4⋊C4C23×C412yes—
663C4⋊C4C23×C412yes—
664C4⋊C4C23×C412yes—
665C4⋊C4C23×C412yes—
666C4⋊C4C23×C412yes—
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—24no—
672C22⋊C4—24no—
673C22⋊C4—24no—
674C22⋊C4—24no—
675C22⋊C4—44no—
676C22⋊C4—44no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—82no—
682C22⋊C4—82no—
683C22⋊C4—82no—
684C22⋊C4—82no—
685C42—22no—
686C42—22no—
687C42—22no—
688C42—22no—
689C42—82no—
690C42—82no—
691C42—82no—
692C42—82no—
693C42—82no—
694C42—82no—
695C42—82no—
696C42—82no—
697C42C4×D414yes—
698C42C4×D414yes—
699C42C23×C412yes—
700C42C23×C412yes—
701C42C2×#4112yes—
702C42C2×#4112yes—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—24no—
707C23—22no—
708C23—48no—
709C23—42no—
710C23—41no—
711C23—41no—
712C23—42no—
713C23—48no—
714C23—42no—
715C23—41no—
716C23—41no—
717C23—84no—
718C23—88no—
719C23—88no—
720C23C2×C4×D412yes—
721C23#57612yes—
722C23#57712yes—
723C23C23×D411yescharacteristic
724D4—22no—
725D4—22no—
726D4—22no—
727D4—24no—
728D4—48no—
729D4—42no—
730D4#51914yes—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—28no—
734C2×C4—22no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—24no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—44no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—48no—
764C2×C4—48no—
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—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—84no—
786C2×C4—84no—
787C2×C4—84no—
788C2×C4—84no—
789C2×C4—84no—
790C2×C4—164no—
791C2×C4—164no—
792C2×C4C2×C4×D412yes—
793C2×C4C2×C4×D412yes—
794C2×C4C2×C4×D412yes—
795C2×C4C2×C4×D412yes—
796C2×C4C2×C4×D412yes—
797C2×C4C24×C411yescharacteristic
798C2×C4C22×#4111yescharacteristic
799C2×C4C2×2−1+412yes—
800C2×C4#58512yes—
801C8—22no—
802C8—22no—
803C8—22no—
804C8—22no—
805C8—42no—
806C8—42no—
807C22—24no—
808C22—24no—
809C22—22no—
810C22—22no—
811C22—24no—
812C22—44no—
813C22—44no—
814C22—42no—
815C22—42no—
816C22—42no—
817C22—42no—
818C22—42no—
819C22—816no—
820C22—82no—
821C22—82no—
822C22#294614yes—
823C22C22×C4×D411yescharacteristic
824C22#348912yes—
825C22C2×#57611yescharacteristic
826C22C2×#57711yescharacteristic
827C22#358412yes—
828C4—22no—
829C4—22no—
830C4—22no—
831C4—22no—
832C4—22no—
833C4—42no—
834C4—42no—
835C4—42no—
836C4—42no—
837C4—42no—
838C4—42no—
839C4—42no—
840C4—42no—
841C4—42no—
842C4—42no—
843C4—82no—
844C4—82no—
845C4—82no—
846C4—82no—
847C4C2×#51911yescharacteristic
848C4#342811yescharacteristic
849C4#349512yes—
850C2—24no—
851C2—44no—
852C2—82no—
853C2#3420311yescharacteristic
854C2C2×#294611yescharacteristic
855C2#6016711yescharacteristic
856C2#6221112yes—
857C2#6221212yes—
subgroupG/H
center, socleC23C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC23×D4C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2283 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34378C2semidirect
4. #23071C2semidirect
5. #23065C2semidirect
6. #22972C2semidirect
7. #22966C2semidirect
8. #22617C2semidirect
9. #22615C2semidirect
10. #22611C2semidirect
11. #22609C2semidirect
16. #22126C2semidirect
17. #22122C2semidirect
18. #21962C2semidirect
19. #21836C2semidirect
20. #21620C2semidirect
21. #21619C2semidirect
23. #20545C2semidirect
26. C2×#478C4semidirect
42. #2370C22semidirect
43. #2370C22semidirect
60. #2330C22semidirect
61. #2330C22semidirect
72. #1991C22semidirect
73. #1991C22semidirect
74. #1989C22semidirect
75. #1989C22semidirect
76. #1949C22semidirect
77. #1949C22semidirect
78. #1948C22semidirect
79. #1947C22semidirect
80. #1944C22semidirect
81. #1943C22semidirect
82. #1942C22semidirect
83. #1941C22semidirect
92. #1921C22semidirect
93. #1921C22semidirect
94. #1920C22semidirect
95. #1920C22semidirect
96. #1919C22semidirect
97. #1919C22semidirect
98. #1918C22semidirect
99. #1918C22semidirect
118. #1776C22semidirect
119. #1776C22semidirect
120. C4×#107C22semidirect
121. C4×#106C22semidirect
122. #1770C22semidirect
123. C8×C4⋊C4C22semidirect
124. #1768C22semidirect
125. #1768C22semidirect
143. C2×#125C2×C4semidirect
176. #478C2×C4semidirect
177. #478C2×C4semidirect
178. #478C2×C4semidirect
179. #478C2×C4semidirect
181. C2×#107C2×C4semidirect
188. C2×#106C2×C4semidirect
195. C2×C4⋊C8C2×C4semidirect

Maximal subgroups

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

subgroupindex
C22×#4782
#343782
#341902
#230712
#230652
#229722
#229662
#226172
#226152
#226112
#226092
#225742
#225702
#225662
#225622
#221262
#221222
#219622
#218362
#216202
#216192
#207322
#205452