Finite Group Databasebeta

← #6395754

Subgroups — #6395754

Order 512.

2178 conjugacy classes of subgroups.

The subgroup lattice has 871 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3217C211yesmaximal, characteristic
2#34364C211yesmaximal, characteristic, complemented
3#34237C211yesmaximal, characteristic, complemented
4#23231C212yesmaximal, complemented
5#23229C212yesmaximal, complemented
6#23195C212yesmaximal, complemented
7#23193C212yesmaximal, complemented
8#22884C212yesmaximal, complemented
9#22880C212yesmaximal, complemented
10#22868C212yesmaximal, complemented
11#22864C212yesmaximal, complemented
12#22160C212yesmaximal, complemented
13#22158C212yesmaximal, complemented
14#21895C211yesmaximal, characteristic, complemented
15#21515C212yesmaximal, complemented
16#21513C212yesmaximal, complemented
17#21366C211yesmaximal, characteristic, complemented
18#21260C211yesmaximal, characteristic, complemented
19#20551C211yesmaximal, characteristic, complemented
20C22×#127C2211yescharacteristic
21C2×#529C2211yescharacteristic
22#3217C4116yescomplemented
23C2×#496C2212yes—
24C2×#490C2212yes—
25C2×#460C2212yes—
26C2×#459C2212yes—
27C2×#450C2211yescharacteristic
28C2×#450C2211yescharacteristic
29C2×#447C2211yescharacteristic
30C2×#447C2211yescharacteristic
31C2×#442C2212yescomplemented
32C2×#440C2212yescomplemented
33C2×C4×SD16C2212yescomplemented
34C2×C4×D8C2212yescomplemented
35C2×#432C2211yescharacteristic
36C2×#423C2211yescharacteristic
37C2×#418C2212yes—
38C2×#418C2212yes—
39#2380—22no—
40#2370C2212yescomplemented
41#2367C2212yescomplemented
42#2366C2212yes—
43#2366C2212yes—
44#2363C2212yes—
45#2362C2212yes—
46#2357—21no—
47#2353—21no—
48#2346—21no—
49#2343—21no—
50D4×C22⋊C4—22no—
51D4×C22⋊C4C2212yes—
52D4×C22⋊C4C2212yes—
53#2335—22no—
54#2328—21no—
55#2328—21no—
56#2328C2212yes—
57#2328C2212yes—
58#2320C2211yescharacteristic, complemented
59#2319C2211yescharacteristic, complemented
60#2308—21no—
61#2308—21no—
62C4×#126—22no—
63#2283C2211yescharacteristic
64#2283C2211yescharacteristic
65#2276C2211yescharacteristic, complemented
66#2275C2211yescharacteristic, complemented
67C4×#117C2211yescharacteristic
68#1989C2211yescharacteristic, complemented
69#1989C2211yescharacteristic, complemented
70#1983C2211yescharacteristic, complemented
71#1983C2211yescharacteristic, complemented
72#1982C2212yes—
73#1982C2212yes—
74#1982C2212yes—
75#1982C2212yes—
76#1973C2212yescomplemented
77#1972C2212yescomplemented
78#1970C2212yescomplemented
79#1968C2212yescomplemented
80#1949C2212yescomplemented
81#1949C2212yescomplemented
82#1936C2212yescomplemented
83#1936C2212yescomplemented
84#1934C2212yescomplemented
85#1934C2212yescomplemented
86#1926C2212yescomplemented
87#1926C2212yescomplemented
88#1925C2212yescomplemented
89#1925C2212yescomplemented
90#1895C2212yes—
91#1894C2212yes—
92#1880C2212yescomplemented
93#1880C2212yescomplemented
94#1879C2212yescomplemented
95#1879C2212yescomplemented
96#1879C2212yescomplemented
97#1879C2212yescomplemented
98#1877C2212yescomplemented
99#1877C2212yescomplemented
100#1864C2212yescomplemented
101#1864C2212yescomplemented
102#1862C2212yescomplemented
103#1862C2212yescomplemented
104#1854C2212yes—
105#1854C2212yes—
106#1805C2212yescomplemented
107#1804C2212yescomplemented
108#1776C2212yescomplemented
109#1776C2212yescomplemented
110#1771C2212yescomplemented
111#1771C2212yescomplemented
112#1768C2212yescomplemented
113#1768C2212yescomplemented
114#1762C2212yescomplemented
115#1762C2212yescomplemented
116C4×#102C2212yescomplemented
117C4×#102C2212yescomplemented
118#1753C2212yes—
119#1753C2212yes—
120C23×D4—21no—
121C23×D4—21no—
122C23×D4C2311yescharacteristic
123C23×D4C2311yescharacteristic
124C22×SD16C2312yes—
125C22×SD16C2312yes—
126C22×D8C2312yes—
127C22×D8C2312yes—
128C22×M16C2312yes—
129C2×#127—21no—
130C2×#127—21no—
131C2×#127—24no—
132C2×#127C2×C418yescomplemented
133C2×#127C2312yes—
134C2×#127C2312yes—
135#529—24no—
136#529C2×C418yescomplemented
137C2×#126—21no—
138C2×#125C2311yescharacteristic
139C2×#124C2311yescharacteristic
140C2×#123—21no—
141C2×C22⋊Q8C2311yescharacteristic
142C2×#121C2311yescharacteristic
143C2×C4×Q8C2312yes—
144C2×C4×Q8C2311yescharacteristic
145C2×C4×D4—21no—
146C2×C4×D4—22no—
147C2×C4×D4—22no—
148C2×C4×D4C2312yes—
149C2×C4×D4C2311yescharacteristic
150C2×C4×D4C2312yes—
151C2×C4×D4C2312yes—
152C2×C4×D4C2312yes—
153C2×C4×D4C2312yes—
154C2×#117—21no—
155C2×#117C2312yes—
156C22×C22⋊C4—22no—
157C22×C22⋊C4—22no—
158C22×C42C2311yescharacteristic
159#496C2×C4116yescomplemented
160#490C2×C4116yescomplemented
161#460C2×C4116yescomplemented
162#459C2×C4116yescomplemented
163#450C2×C418yescomplemented
164#450C2×C418yescomplemented
165#447C2×C418yescomplemented
166#447C2×C418yescomplemented
167#442—44no—
168#440—44no—
169C4×SD16—44no—
170C4×D8—44no—
171#432C2×C418yescomplemented
172C2×#107C2312yes—
173C2×#107C2312yes—
174C2×#106C2312yes—
175C2×#106C2312yes—
176#423—24no—
177C2×C4⋊C8C2312yes—
178C2×C4⋊C8C2311yescharacteristic
179C2×C4⋊C8C2311yescharacteristic
180C2×C4⋊C8C2312yes—
181#418—44no—
182#418—44no—
183C2×#103C2312yes—
184C2×#103C2312yes—
185C2×#102C2312yes—
186C2×#102C2312yes—
187C2×#102C2312yes—
188C2×#102C2312yes—
189C2×#102C2312yes—
190C2×#102C2312yes—
191C2×#102C2312yes—
192C2×#102C2312yes—
193C2×#102C2312yes—
194C2×#102C2312yes—
195C2×#102C2312yes—
196C2×#102C2312yes—
197C2×#102C2312yes—
198C2×#102C2312yes—
199C2×C22⋊C8C2311yescharacteristic
200C2×C22⋊C8C2311yescharacteristic
201C2×#97C2312yes—
202C2×#97C2312yes—
203C2×#97C2312yes—
204C2×C4×C8C2312yes—
205C2×C4×C8C2312yes—
206#391C2312yes—
207#390—22no—
208#390—22no—
209#390—22no—
210#390C2312yes—
211#390C2312yes—
212#390C2312yes—
213#390C2312yes—
214#390C2312yes—
215#389—22no—
216#389C2312yes—
217#389C2312yes—
218#388—22no—
219#388—22no—
220#388—22no—
221#388—22no—
222#388—22no—
223#388—22no—
224#387—22no—
225#387—22no—
226#387—22no—
227#387—22no—
228#386—22no—
229#386—22no—
230#386—22no—
231#386—22no—
232#386—22no—
233#386—22no—
234#386—22no—
235#386—22no—
236#386—22no—
237#386—22no—
238#386—22no—
239#386—22no—
240#386—22no—
241#386—22no—
242#386—22no—
243#386—22no—
244#386—22no—
245#385—22no—
246#383—21no—
247#383—21no—
248#383D412yes—
249#382—21no—
250#382D411yescharacteristic
251#382D411yescharacteristic
252#382C2312yes—
253#381—21no—
254#381—21no—
255#381D411yescharacteristic
256#381D411yescharacteristic
257#380—21no—
258#380D412yes—
259#380C2312yes—
260#379—22no—
261#379—22no—
262C4×C4⋊C4—22no—
263C4×C4⋊C4—22no—
264C4×C4⋊C4—22no—
265C4×C4⋊C4—21no—
266C4×C4⋊C4C2311yescharacteristic
267C4×C4⋊C4C2312yes—
268C4×C4⋊C4C2312yes—
269C4×C4⋊C4C2311yescharacteristic
270C4×C4⋊C4C2311yescharacteristic
271C4×C4⋊C4C2312yes—
272C4×C4⋊C4C2311yescharacteristic
273C4×C4⋊C4C2312yes—
274C4×C22⋊C4—21no—
275C4×C22⋊C4—21no—
276C4×C22⋊C4—21no—
277C4×C22⋊C4—22no—
278C4×C22⋊C4—22no—
279C4×C22⋊C4—22no—
280C4×C22⋊C4—21no—
281C4×C22⋊C4C2312yes—
282#376—21no—
283#376—21no—
284#376—21no—
285#376C2311yescharacteristic
286#376C2311yescharacteristic
287C2×#95—21no—
288C43—21no—
289#340C2312yes—
290#340C2312yes—
291#340C2312yes—
292#340C2312yes—
293#340C2312yes—
294#340C2312yes—
295#340C2312yes—
296#340C2312yes—
297#336C2312yes—
298#336C2312yes—
299#336C2312yes—
300#336C2312yes—
301C25—21no—
302C25—21no—
303C22×Q8C2411yescharacteristic
304C22×D4—21no—
305C22×D4—28no—
306C22×D4—28no—
307C22×D4—22no—
308C22×D4—21no—
309C22×D4—21no—
310C22×D4—22no—
311C22×D4—22no—
312C22×D4—22no—
313C22×D4—22no—
314C22×D4—22no—
315C22×D4—42no—
316C22×D4—42no—
317C22×D4—42no—
318C22×D4—42no—
319C22×D4—82no—
320C22×D4—82no—
321C22×D4—84no—
322C22×D4C22×C414yes—
323C22×D4C22×C414yes—
324C22×D4C2411yescharacteristic
325C22×D4C2412yes—
326C22×D4C2412yes—
327C23×C4—21no—
328C23×C4—22no—
329C23×C4—22no—
330C23×C4—22no—
331C23×C4—22no—
332C23×C4—22no—
333C23×C4C2×D411yescharacteristic
334C23×C4C2×D411yescharacteristic
335C23×C4C2411yescharacteristic
336C2×SD16—42no—
337C2×SD16—42no—
338C2×SD16—42no—
339C2×SD16—42no—
340C2×SD16C22×C418yes—
341C2×SD16C22×C418yes—
342C2×D8—42no—
343C2×D8—42no—
344C2×D8—42no—
345C2×D8—42no—
346C2×D8C22×C418yes—
347C2×D8C22×C418yes—
348C2×M16—24no—
349C2×M16—42no—
350C2×M16—42no—
351C22×C8C2412yes—
352C22×C8C2412yes—
353C22×C8C2412yes—
354C22×C8C2412yes—
355#127—28no—
356#127—28no—
357#127—24no—
358#127—24no—
359#127C22×C418yes—
360#127C22×C418yes—
361#126—28no—
362#125—22no—
363#125C22×C414yes—
364#124—22no—
365#124C22×C414yes—
366#123—28no—
367C22⋊Q8—22no—
368C22⋊Q8C22×C414yes—
369#121—22no—
370#121C22×C414yes—
371C4×Q8—22no—
372C4×Q8—24no—
373C4×Q8—42no—
374C4×Q8C22×C414yes—
375C4×D4—28no—
376C4×D4—24no—
377C4×D4—22no—
378C4×D4—42no—
379C4×D4—42no—
380C4×D4—42no—
381C4×D4—42no—
382C4×D4—42no—
383C4×D4—42no—
384C4×D4—42no—
385C4×D4—42no—
386C4×D4—42no—
387C4×D4—84no—
388C4×D4—84no—
389C4×D4C22×C414yes—
390#117—28no—
391#117—24no—
392#117—42no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4C2×D412yes—
401C2×C4⋊C4C2×D412yes—
402C2×C4⋊C4C2412yes—
403C2×C4⋊C4C2412yes—
404C2×C4⋊C4C2412yes—
405C2×C4⋊C4C2411yescharacteristic
406C2×C4⋊C4C2411yescharacteristic
407C2×C4⋊C4C2412yes—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—22no—
415C2×C22⋊C4—22no—
416C2×C22⋊C4—22no—
417C2×C22⋊C4—22no—
418C2×C22⋊C4—22no—
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—22no—
426C2×C22⋊C4—22no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—22no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—84no—
431C2×C22⋊C4—84no—
432C2×C22⋊C4C2×D412yes—
433C2×C22⋊C4C2×D412yes—
434C2×C42—21no—
435C2×C42—22no—
436C2×C42—21no—
437C2×C42—21no—
438C2×C42—22no—
439C2×C42—21no—
440C2×C42—22no—
441C2×C42—21no—
442C2×C42—22no—
443C2×C42—22no—
444C2×C42C22×C414yes—
445C2×C42C2×D411yescharacteristic
446C2×C42C2×D411yescharacteristic
447C2×C42#4114yes—
448C2×C42C2412yes—
449C2×C42C2412yes—
450C2×C42C2411yescharacteristic
451C2×C42C2411yescharacteristic
452#107—24no—
453#107—42no—
454#106—24no—
455#106—42no—
456C4⋊C8—24no—
457C4⋊C8—22no—
458C4⋊C8—22no—
459C4⋊C8C22×C418yes—
460#103—42no—
461#103—42no—
462#102—24no—
463#102—24no—
464#102—24no—
465#102—24no—
466#102—42no—
467#102—42no—
468#102—42no—
469#102—42no—
470#102—42no—
471#102—42no—
472#102C22×C418yes—
473#102C22×C418yes—
474#102C22×C418yes—
475#102C22×C418yes—
476C22⋊C8C22×C414yes—
477C22⋊C8C22×C414yes—
478#97—42no—
479#97—42no—
480#97C22×C418yes—
481C4×C8—42no—
482C4×C8—42no—
483#95—21no—
484#95—22no—
485#95—21no—
486#95—22no—
487#95—22no—
488#95—22no—
489#95—22no—
490#95—22no—
491#95—22no—
492#95—22no—
493#95—22no—
494#95—22no—
495#95—21no—
496#95—21no—
497#95C2×D411yescharacteristic
498#95C2×D411yescharacteristic
499#95C2×D412yes—
500#95C2×D411yescharacteristic
501#95C2×D412yes—
502#95C2×D411yescharacteristic
503#95C2×D412yes—
504#95C2×D412yes—
505#95C2×D412yes—
506#95C2×D412yes—
507C24—21no—
508C24—22no—
509C24—22no—
510C24—24no—
511C24—24no—
512C24—44no—
513C24—44no—
514C24—82no—
515C24—82no—
516C24—81no—
517C24—81no—
518C24—81no—
519C24—81no—
520C24C22×D411yescharacteristic
521C2×Q8—21no—
522C2×Q8—22no—
523C2×Q8—22no—
524C2×Q8C23×C412yes—
525C2×D4—24no—
526C2×D4—28no—
527C2×D4—24no—
528C2×D4—24no—
529C2×D4—28no—
530C2×D4—28no—
531C2×D4—28no—
532C2×D4—21no—
533C2×D4—22no—
534C2×D4—22no—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—22no—
538C2×D4—22no—
539C2×D4—22no—
540C2×D4—22no—
541C2×D4—22no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—22no—
545C2×D4—48no—
546C2×D4—48no—
547C2×D4—44no—
548C2×D4—44no—
549C2×D4—82no—
550C2×D4—82no—
551C2×D4—82no—
552C2×D4—82no—
553C2×D4—82no—
554C2×D4—82no—
555C2×D4—82no—
556C2×D4—82no—
557C2×D4—82no—
558C2×D4—82no—
559C2×D4—82no—
560C2×D4—82no—
561C2×D4—816no—
562C2×D4—81no—
563C2×D4—81no—
564C2×D4—816no—
565C2×D4C23×C414yes—
566C2×D4C23×C414yes—
567C2×D4C23×C412yes—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—24no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—41no—
579C22×C4—41no—
580C22×C4—42no—
581C22×C4—44no—
582C22×C4—82no—
583C22×C4—82no—
584C22×C4—82no—
585C22×C4—82no—
586C22×C4—82no—
587C22×C4—82no—
588C22×C4—82no—
589C22×C4—82no—
590C22×C4—82no—
591C22×C4—82no—
592C22×C4—82no—
593C22×C4—82no—
594C22×C4—82no—
595C22×C4—82no—
596C22×C4—82no—
597C22×C4C4×D414yes—
598C22×C4C4×D414yes—
599C22×C4C23×C412yes—
600C22×C4C22×D412yes—
601C22×C4C22×D412yes—
602C22×C4C22×D412yes—
603C22×C4C22×D412yes—
604C22×C4C22×D411yescharacteristic
605C22×C4C22×D411yescharacteristic
606C22×C4C22×D411yescharacteristic
607C22×C4C22×D411yescharacteristic
608C22×C4C22×D411yescharacteristic
609C22×C4C2×#4112yes—
610C22×C4C2511yescharacteristic
611SD16—48no—
612SD16—48no—
613D8—48no—
614D8—48no—
615M16—84no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—22no—
620C2×C8—22no—
621C2×C8—22no—
622C2×C8—22no—
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8C23×C414yes—
627C2×C8C23×C414yes—
628C4⋊C4—24no—
629C4⋊C4—24no—
630C4⋊C4—24no—
631C4⋊C4—24no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—42no—
642C4⋊C4—42no—
643C4⋊C4—44no—
644C4⋊C4—82no—
645C4⋊C4—82no—
646C4⋊C4C23×C412yes—
647C4⋊C4C23×C412yes—
648C4⋊C4H(5,𝔽2)14yes—
649C22⋊C4—24no—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—24no—
653C22⋊C4—24no—
654C22⋊C4—42no—
655C22⋊C4—42no—
656C22⋊C4—44no—
657C22⋊C4—44no—
658C22⋊C4—44no—
659C22⋊C4—82no—
660C22⋊C4—82no—
661C22⋊C4—82no—
662C22⋊C4—82no—
663C22⋊C4—82no—
664C22⋊C4—82no—
665C22⋊C4—82no—
666C22⋊C4—82no—
667C22⋊C4—82no—
668C22⋊C4—82no—
669C22⋊C4—82no—
670C22⋊C4—82no—
671C22⋊C4—82no—
672C22⋊C4—82no—
673C42—24no—
674C42—22no—
675C42—22no—
676C42—22no—
677C42—22no—
678C42—44no—
679C42—44no—
680C42—42no—
681C42—42no—
682C42—81no—
683C42—82no—
684C42—81no—
685C42—82no—
686C42—82no—
687C42C4×D414yes—
688C42C4×D414yes—
689C42C23×C412yes—
690C42C23×C412yes—
691C42C2×#4112yes—
692C42C2×#4112yes—
693C23—22no—
694C23—21no—
695C23—21no—
696C23—22no—
697C23—22no—
698C23—24no—
699C23—24no—
700C23—48no—
701C23—48no—
702C23—42no—
703C23—42no—
704C23—41no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—41no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—84no—
719C23—84no—
720C23—84no—
721C23—84no—
722C23—164no—
723C23—164no—
724C23—164no—
725C23—164no—
726C23C2×C4×D412yes—
727C23C23×D411yescharacteristic
728Q8—24no—
729Q8—41no—
730Q8—41no—
731D4—24no—
732D4—24no—
733D4—24no—
734D4—24no—
735D4—24no—
736D4—416no—
737D4—41no—
738D4—42no—
739D4—42no—
740D4—41no—
741D4—42no—
742D4—42no—
743D4—84no—
744D4—84no—
745D4—88no—
746D4—88no—
747D4—88no—
748D4—84no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—22no—
753C2×C4—21no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—24no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—24no—
775C2×C4—44no—
776C2×C4—44no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—41no—
780C2×C4—42no—
781C2×C4—41no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—84no—
793C2×C4—164no—
794C2×C4—164no—
795C2×C4—164no—
796C2×C4—164no—
797C2×C4—164no—
798C2×C4C2×C4×D412yes—
799C2×C4C2×C4×D412yes—
800C2×C4C2×C4×D412yes—
801C2×C4C2×C4×D412yes—
802C2×C4C2×C4×D412yes—
803C2×C4C24×C411yescharacteristic
804C2×C4C22×#4111yescharacteristic
805C2×C4C2×H(5,𝔽2)12yes—
806C2×C4#58512yes—
807C8—24no—
808C8—24no—
809C8—42no—
810C8—42no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—42no—
815C22—42no—
816C22—42no—
817C22—44no—
818C22—44no—
819C22—44no—
820C22—44no—
821C22—42no—
822C22—44no—
823C22—44no—
824C22—42no—
825C22—82no—
826C22—82no—
827C22—82no—
828C22—82no—
829C22—82no—
830C22—82no—
831C22—82no—
832C22—82no—
833C22—82no—
834C22—82no—
835C22—168no—
836C22—168no—
837C22C22×C4×D411yescharacteristic
838C22#348812yes—
839C22#358511yescharacteristic
840C22#358512yes—
841C22#358511yescharacteristic
842C4—22no—
843C4—22no—
844C4—22no—
845C4—22no—
846C4—22no—
847C4—42no—
848C4—42no—
849C4—42no—
850C4—42no—
851C4—44no—
852C4—42no—
853C4—42no—
854C4—42no—
855C4—82no—
856C4—82no—
857C4—82no—
858C4C4×H(5,𝔽2)12yes—
859C4#350811yescharacteristic
860C4#351011yescharacteristic
861C2—42no—
862C2—82no—
863C2—84no—
864C2—84no—
865C2#3426911yescharacteristic
866C2#6016811yescharacteristic
867C2#6016811yescharacteristic
868C2#6207912yes—
869C2#6208112yes—
subgroupG/H
center, socleC23C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC2×#3217C2
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. #34364C2semidirect
3. #34237C2semidirect
4. #23231C2semidirect
5. #23229C2semidirect
6. #23195C2semidirect
7. #23193C2semidirect
8. #22884C2semidirect
9. #22880C2semidirect
10. #22868C2semidirect
11. #22864C2semidirect
12. #22160C2semidirect
13. #22158C2semidirect
14. #21895C2semidirect
15. #21515C2semidirect
16. #21513C2semidirect
17. #21366C2semidirect
18. #21260C2semidirect
19. #20551C2semidirect
22. #3217C4semidirect
31. C2×#442C22semidirect
32. C2×#440C22semidirect
33. C2×C4×SD16C22semidirect
34. C2×C4×D8C22semidirect
40. #2370C22semidirect
41. #2367C22semidirect
58. #2320C22semidirect
59. #2319C22semidirect
65. #2276C22semidirect
66. #2275C22semidirect
68. #1989C22semidirect
69. #1989C22semidirect
70. #1983C22semidirect
71. #1983C22semidirect
76. #1973C22semidirect
77. #1972C22semidirect
78. #1970C22semidirect
79. #1968C22semidirect
80. #1949C22semidirect
81. #1949C22semidirect
82. #1936C22semidirect
83. #1936C22semidirect
84. #1934C22semidirect
85. #1934C22semidirect
86. #1926C22semidirect
87. #1926C22semidirect
88. #1925C22semidirect
89. #1925C22semidirect
92. #1880C22semidirect
93. #1880C22semidirect
94. #1879C22semidirect
95. #1879C22semidirect
96. #1879C22semidirect
97. #1879C22semidirect
98. #1877C22semidirect
99. #1877C22semidirect
100. #1864C22semidirect
101. #1864C22semidirect
102. #1862C22semidirect
103. #1862C22semidirect
106. #1805C22semidirect
107. #1804C22semidirect
108. #1776C22semidirect
109. #1776C22semidirect
110. #1771C22semidirect
111. #1771C22semidirect
112. #1768C22semidirect
113. #1768C22semidirect
114. #1762C22semidirect
115. #1762C22semidirect
116. C4×#102C22semidirect
117. C4×#102C22semidirect
132. C2×#127C2×C4semidirect
136. #529C2×C4semidirect
159. #496C2×C4semidirect
160. #490C2×C4semidirect
161. #460C2×C4semidirect
162. #459C2×C4semidirect
163. #450C2×C4semidirect
164. #450C2×C4semidirect
165. #447C2×C4semidirect
166. #447C2×C4semidirect
171. #432C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#32172
#343642
#342372
#232312
#232292
#231952
#231932
#228842
#228802
#228682
#228642
#221602
#221582
#218952
#215152
#215132
#213662
#212602
#205512