Finite Group Databasebeta

← #6447304

Subgroups — #6447304

Order 512.

1806 conjugacy classes of subgroups.

The subgroup lattice has 909 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35181C211yesmaximal, characteristic, complemented
2#34211C211yesmaximal, characteristic
3#26545C212yesmaximal, complemented
4#26544C212yesmaximal, complemented
5#26543C212yesmaximal, complemented
6#26542C212yesmaximal, complemented
7#26537C212yesmaximal, complemented
8#26536C212yesmaximal, complemented
9#26535C212yesmaximal, complemented
10#26534C212yesmaximal, complemented
11#23736C211yesmaximal, characteristic, complemented
12#23735C211yesmaximal, characteristic
13#23613C211yesmaximal, characteristic, complemented
14#23612C211yesmaximal, characteristic
15C2×#1983C211yesmaximal, characteristic
16#21204C211yesmaximal, characteristic
17#21169C211yesmaximal, characteristic, complemented
18#21145C211yesmaximal, characteristic, complemented
19#20877C211yesmaximal, characteristic, complemented
20#20876C211yesmaximal, characteristic
21#20651C211yesmaximal, characteristic, complemented
22#20650C211yesmaximal, characteristic
23C4×#428C211yesmaximal, characteristic, complemented
24C22×#124C2211yescharacteristic
25C2×#519C2211yescharacteristic
26C2×#518C2211yescharacteristic
27C2×#428C2211yescharacteristic
28C2×#428C2211yescharacteristic
29C2×#427C2211yescharacteristic
30C2×#427C2211yescharacteristic
31C2×#424C2211yescharacteristic
32C2×#424C2211yescharacteristic
33C22×C4⋊C8C2211yescharacteristic
34C2×#419C2211yescharacteristic
35C2×#419C2211yescharacteristic
36C2×#418C2211yescharacteristic
37C2×#418C2211yescharacteristic
38C22×#103C2211yescharacteristic
39C22×#103C2211yescharacteristic
40C22×#102C2211yescharacteristic
41C22×#102C2211yescharacteristic
42C2×C4×M16C2211yescharacteristic
43#2851—22no—
44#2646—22no—
45#2571—21no—
46#2571C2212yescomplemented
47#2570—21no—
48#2570—21no—
49#2570C2212yescomplemented
50#2570C2212yescomplemented
51#2552—21no—
52#2552C2212yescomplemented
53#2367C2212yes—
54#2367C2212yes—
55#2367C2212yes—
56#2367C2212yes—
57#2342—22no—
58#2342—22no—
59#2326—21no—
60#2326—21no—
61#2317C2211yescharacteristic
62#2317C2211yescharacteristic
63#2317C2211yescharacteristic
64#2317C2211yescharacteristic
65#2310C2211yescharacteristic
66#2309C2211yescharacteristic
67C4×#124—21no—
68C4×#124—21no—
69#2285C2211yescharacteristic
70#2285C2211yescharacteristic
71C4×#117C2211yescharacteristic
72C2×C4×C4⋊C4C2211yescharacteristic
73#2097C2212yescomplemented
74#2097C2212yescomplemented
75#2096C2212yescomplemented
76#2095C2212yescomplemented
77#2094C2212yes—
78#2093C2212yes—
79#2092C2212yes—
80#2092C2212yes—
81#2068C2212yescomplemented
82#2068C2212yescomplemented
83#2067C2212yes—
84#2067C2212yes—
85#2066C2212yescomplemented
86#2066C2212yescomplemented
87#2065C2212yes—
88#2065C2212yes—
89#1983C2212yes—
90#1983C2212yes—
91#1983C2212yes—
92#1983C2212yes—
93#1959C2212yes—
94#1959C2212yes—
95#1958C2212yes—
96#1958C2212yes—
97#1949C2211yescharacteristic, complemented
98#1949C2211yescharacteristic, complemented
99#1949C2211yescharacteristic, complemented
100#1949C2211yescharacteristic, complemented
101#1948C2211yescharacteristic, complemented
102#1948C2211yescharacteristic, complemented
103#1947C2211yescharacteristic, complemented
104#1947C2211yescharacteristic, complemented
105#1940C2212yescomplemented
106#1940C2212yescomplemented
107#1939C2212yescomplemented
108#1939C2212yescomplemented
109#1865C2212yescomplemented
110#1865C2212yescomplemented
111#1864C2212yes—
112#1864C2212yes—
113#1863C2212yescomplemented
114#1863C2212yescomplemented
115#1862C2212yes—
116#1862C2212yes—
117#1805C2212yescomplemented
118#1805C2212yescomplemented
119#1804C2212yes—
120#1804C2212yes—
121#1803C2212yescomplemented
122#1803C2212yescomplemented
123#1802C2212yes—
124#1802C2212yes—
125#1776C2212yescomplemented
126#1776C2212yescomplemented
127C4×#107C2212yescomplemented
128C4×#106C2212yescomplemented
129#1736C2211yescharacteristic
130#1736C2211yescharacteristic
131#1735C2211yescharacteristic
132#1735C2211yescharacteristic
133#1729C2211yescharacteristic
134#1729C2211yescharacteristic
135C23×Q8C2311yescharacteristic
136C23×D4C2311yescharacteristic
137C22×M16C2311yescharacteristic
138C22×M16C2311yescharacteristic
139C23×C8C2311yescharacteristic
140C23×C8C2311yescharacteristic
141C2×#125—22no—
142C2×#124—21no—
143C2×#124—21no—
144C2×#124—24no—
145C2×#124Q818yes—
146C2×#124C2312yes—
147C2×#124C2312yes—
148#519—24no—
149#519—42no—
150#518—24no—
151#518—42no—
152C2×C4×Q8—21no—
153C2×C4×Q8—21no—
154C2×C4×Q8C2312yes—
155C2×C4×Q8C2312yes—
156C2×C4×D4—21no—
157C2×C4×D4—21no—
158C2×C4×D4C2312yes—
159C2×C4×D4C2312yes—
160C2×#117—22no—
161C2×#117C2311yescharacteristic
162C2×#117C2311yescharacteristic
163C2×#117C2311yescharacteristic
164C2×#117C2311yescharacteristic
165C2×#117C2311yescharacteristic
166C2×#117C2311yescharacteristic
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2311yescharacteristic
169C22×C22⋊C4—21no—
170C22×C22⋊C4—21no—
171C22×C22⋊C4—22no—
172C22×C42—21no—
173C22×C42C2311yescharacteristic
174#428—24no—
175#428—24no—
176#427—42no—
177#427—42no—
178C2×#107C2312yes—
179C2×#107C2312yes—
180C2×#107C2311yescharacteristic
181C2×#107C2311yescharacteristic
182C2×#107C2311yescharacteristic
183C2×#107C2311yescharacteristic
184C2×#106C2312yes—
185C2×#106C2312yes—
186C2×#106C2311yescharacteristic
187C2×#106C2311yescharacteristic
188C2×#106C2311yescharacteristic
189C2×#106C2311yescharacteristic
190#424—42no—
191#424—42no—
192C2×C4⋊C8—24no—
193C2×C4⋊C8C2311yescharacteristic
194C2×C4⋊C8C2311yescharacteristic
195C2×C4⋊C8C2311yescharacteristic
196C2×C4⋊C8C2311yescharacteristic
197C2×C4⋊C8C2312yes—
198C2×C4⋊C8C2312yes—
199C2×C4⋊C8C2312yes—
200C2×C4⋊C8C2312yes—
201#419—24no—
202#419—42no—
203#418—24no—
204#418—42no—
205C2×#103—42no—
206C2×#103—42no—
207C2×#103C2312yes—
208C2×#103C2312yes—
209C2×#103C2312yes—
210C2×#103C2312yes—
211C2×#103C2312yes—
212C2×#103C2312yes—
213C2×#103C2312yes—
214C2×#103C2312yes—
215C2×#102—42no—
216C2×#102—42no—
217C2×#102C2312yes—
218C2×#102C2312yes—
219C2×#102C2312yes—
220C2×#102C2312yes—
221C2×#102C2312yes—
222C2×#102C2312yes—
223C2×#102C2312yes—
224C2×#102C2312yes—
225C4×M16—24no—
226C2×#97C2312yes—
227C2×C4×C8C2312yes—
228#400—22no—
229#400—22no—
230#400—22no—
231#400—22no—
232#398—22no—
233#398—22no—
234#398—22no—
235#398—22no—
236#391—21no—
237#391—21no—
238#391C2312yes—
239#391C2312yes—
240#390—21no—
241#390—21no—
242#390C2312yes—
243#390C2312yes—
244#389—21no—
245#389—21no—
246#389—21no—
247#389—21no—
248#389—22no—
249#389—22no—
250#389C2312yes—
251#389C2312yes—
252#389C2312yes—
253#389C2312yes—
254#388—22no—
255#388—22no—
256#388—22no—
257#388—22no—
258#388—22no—
259#388—22no—
260#388—22no—
261#388—22no—
262#387—22no—
263#387—22no—
264#387—22no—
265#387—22no—
266#385—22no—
267#385—22no—
268#385—22no—
269#385—22no—
270#385—22no—
271#385—22no—
272#385—22no—
273#385—22no—
274#384—21no—
275#384—21no—
276#384D411yescharacteristic
277#384D411yescharacteristic
278#384C2312yes—
279#384C2312yes—
280#384C2311yescharacteristic
281#384C2311yescharacteristic
282#382—21no—
283#382—21no—
284#382—22no—
285#382D411yescharacteristic
286#382D411yescharacteristic
287#382C2311yescharacteristic
288#382C2311yescharacteristic
289#382C2312yes—
290#382C2312yes—
291#381—22no—
292#380—21no—
293#380—21no—
294#380D412yes—
295#380D412yes—
296#379—22no—
297C4×C4⋊C4—21no—
298C4×C4⋊C4—21no—
299C4×C4⋊C4—21no—
300C4×C4⋊C4—21no—
301C4×C4⋊C4C2312yes—
302C4×C4⋊C4C2312yes—
303C4×C4⋊C4C2311yescharacteristic
304C4×C4⋊C4C2311yescharacteristic
305C4×C4⋊C4C2311yescharacteristic
306C4×C4⋊C4C2311yescharacteristic
307C4×C4⋊C4C2312yes—
308C4×C4⋊C4C2312yes—
309C4×C22⋊C4—21no—
310C4×C22⋊C4—21no—
311C4×C22⋊C4—22no—
312C4×C22⋊C4—22no—
313C4×C22⋊C4—22no—
314C4×C22⋊C4—22no—
315#376—21no—
316C2×#95—21no—
317C43—21no—
318#340C2311yescharacteristic
319#340C2311yescharacteristic
320#340C2312yes—
321#340C2312yes—
322#340C2311yescharacteristic
323#340C2311yescharacteristic
324#340C2311yescharacteristic
325#340C2311yescharacteristic
326#340C2311yescharacteristic
327#340C2311yescharacteristic
328#340C2312yes—
329#340C2312yes—
330#336C2312yes—
331#336C2312yes—
332#336C2312yes—
333#336C2312yes—
334C25—21no—
335C22×Q8—21no—
336C22×Q8—22no—
337C22×Q8—22no—
338C22×Q8—22no—
339C22×Q8—22no—
340C22×Q8—22no—
341C22×Q8C2×Q814yes—
342C22×Q8C2412yes—
343C22×D4—21no—
344C22×D4—22no—
345C22×D4—22no—
346C22×D4—22no—
347C22×D4—22no—
348C22×D4—22no—
349C22×D4C2×Q814yes—
350C22×D4C2412yes—
351C23×C4—21no—
352C23×C4—21no—
353C23×C4—21no—
354C23×C4—22no—
355C23×C4—22no—
356C23×C4C2×D411yescharacteristic
357C23×C4C2×D411yescharacteristic
358C23×C4C2411yescharacteristic
359C2×M16—22no—
360C2×M16—22no—
361C2×M16—22no—
362C2×M16—22no—
363C2×M16—22no—
364C2×M16#4114yes—
365C22×C8—22no—
366C22×C8—22no—
367C22×C8—22no—
368C22×C8—22no—
369C22×C8—22no—
370C22×C8—22no—
371C22×C8C2411yescharacteristic
372C22×C8C2411yescharacteristic
373C22×C8C2411yescharacteristic
374C22×C8C2411yescharacteristic
375C22×C8C2412yes—
376C22×C8C2412yes—
377#125—84no—
378#124—28no—
379#124—28no—
380#124—24no—
381#124—24no—
382#124C2×Q818yes—
383#124C2×Q818yes—
384C4×Q8—24no—
385C4×Q8—24no—
386C4×Q8—42no—
387C4×Q8—42no—
388C4×Q8—44no—
389C4×Q8—44no—
390C4×D4—24no—
391C4×D4—24no—
392C4×D4—42no—
393C4×D4—42no—
394C4×D4—44no—
395C4×D4—44no—
396#117—22no—
397#117—22no—
398#117—22no—
399#117—22no—
400#117—22no—
401#117—22no—
402#117—22no—
403#117—22no—
404#117—22no—
405#117—22no—
406#117—22no—
407#117—48no—
408#117#4114yes—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4C2×D411yescharacteristic
430C2×C4⋊C4C2×D411yescharacteristic
431C2×C4⋊C4C2×D411yescharacteristic
432C2×C4⋊C4C2×D411yescharacteristic
433C2×C4⋊C4C2×D412yes—
434C2×C4⋊C4C2×D412yes—
435C2×C4⋊C4C2×D412yes—
436C2×C4⋊C4C2×D412yes—
437C2×C4⋊C4C2412yes—
438C2×C4⋊C4C2412yes—
439C2×C4⋊C4C2411yescharacteristic
440C2×C4⋊C4C2411yescharacteristic
441C2×C4⋊C4C2411yescharacteristic
442C2×C4⋊C4C2411yescharacteristic
443C2×C4⋊C4C2411yescharacteristic
444C2×C4⋊C4C2411yescharacteristic
445C2×C4⋊C4C2411yescharacteristic
446C2×C4⋊C4C2411yescharacteristic
447C2×C22⋊C4—21no—
448C2×C22⋊C4—28no—
449C2×C22⋊C4—28no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—22no—
452C2×C22⋊C4—22no—
453C2×C22⋊C4—22no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4—22no—
462C2×C22⋊C4—22no—
463C2×C22⋊C4—48no—
464C2×C22⋊C4C2×D412yes—
465C2×C22⋊C4C2×D412yes—
466C2×C42—21no—
467C2×C42—22no—
468C2×C42—22no—
469C2×C42—21no—
470C2×C42—21no—
471C2×C42—21no—
472C2×C42—22no—
473C2×C42—21no—
474C2×C42—21no—
475C2×C42—21no—
476C2×C42—21no—
477C2×C42—22no—
478C2×C42—82no—
479C2×C42C2×D411yescharacteristic
480C2×C42C2×D411yescharacteristic
481C2×C42C2×Q814yes—
482C2×C42#4114yes—
483C2×C42C2412yes—
484C2×C42C2412yes—
485C2×C42C2411yescharacteristic
486C2×C42C2411yescharacteristic
487#107—24no—
488#107—24no—
489#107—41no—
490#107—41no—
491#107—41no—
492#107—41no—
493#106—24no—
494#106—24no—
495#106—41no—
496#106—41no—
497#106—41no—
498#106—41no—
499C4⋊C8—22no—
500C4⋊C8—22no—
501C4⋊C8—22no—
502C4⋊C8—22no—
503C4⋊C8—42no—
504C4⋊C8—42no—
505C4⋊C8—42no—
506C4⋊C8—42no—
507#103—24no—
508#103—24no—
509#103—42no—
510#103—42no—
511#103—42no—
512#103—42no—
513#103—42no—
514#103—42no—
515#102—24no—
516#102—24no—
517#102—42no—
518#102—42no—
519#102—42no—
520#102—42no—
521#102—42no—
522#102—42no—
523#97—24no—
524C4×C8—24no—
525#95—22no—
526#95—22no—
527#95—21no—
528#95—21no—
529#95—21no—
530#95—21no—
531#95—22no—
532#95—22no—
533#95—22no—
534#95—22no—
535#95—21no—
536#95—21no—
537#95—21no—
538#95—21no—
539#95—22no—
540#95—22no—
541#95—22no—
542#95—22no—
543#95—22no—
544#95—22no—
545#95—22no—
546#95—22no—
547#95C2×D412yes—
548#95C2×D412yes—
549#95C2×D412yes—
550#95C2×D412yes—
551C24—22no—
552C24—24no—
553C24—42no—
554C24—42no—
555C24—81no—
556C24—81no—
557C24—81no—
558C24—81no—
559C24C22×D411yescharacteristic
560C2×Q8—24no—
561C2×Q8—22no—
562C2×Q8—28no—
563C2×Q8—28no—
564C2×Q8—22no—
565C2×Q8—22no—
566C2×Q8—22no—
567C2×Q8—22no—
568C2×Q8—44no—
569C2×Q8—44no—
570C2×Q8—42no—
571C2×Q8—42no—
572C2×Q8C22×Q814yes—
573C2×D4—24no—
574C2×D4—28no—
575C2×D4—28no—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—44no—
582C2×D4—44no—
583C2×D4—42no—
584C2×D4—42no—
585C2×D4C22×Q814yes—
586C22×C4—24no—
587C22×C4—22no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4—41no—
601C22×C4—41no—
602C22×C4—44no—
603C22×C4—44no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—82no—
609C22×C4—82no—
610C22×C4—82no—
611C22×C4—82no—
612C22×C4—81no—
613C22×C4—81no—
614C22×C4—81no—
615C22×C4—81no—
616C22×C4C22⋊Q814yes—
617C22×C4C22⋊Q814yes—
618C22×C4C22×D412yes—
619C22×C4C22×D412yes—
620C22×C4C22×D412yes—
621C22×C4C22×D412yes—
622C22×C4C22×D411yescharacteristic
623C22×C4C22×D411yescharacteristic
624C22×C4C22×D411yescharacteristic
625C22×C4C22×D411yescharacteristic
626C22×C4C22×D411yescharacteristic
627C22×C4C22×Q812yes—
628C22×C4C2×#4112yes—
629C22×C4C2×#4112yes—
630C22×C4C2×#4112yes—
631C22×C4H(5,𝔽2)12yes—
632C22×C4H(5,𝔽2)12yes—
633C22×C4C2511yescharacteristic
634M16—28no—
635M16—44no—
636C2×C8—22no—
637C2×C8—22no—
638C2×C8—22no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—22no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—22no—
653C2×C8—44no—
654C2×C8—44no—
655C2×C8C2×#4114yes—
656C4⋊C4—22no—
657C4⋊C4—22no—
658C4⋊C4—22no—
659C4⋊C4—22no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—22no—
668C4⋊C4—22no—
669C4⋊C4—21no—
670C4⋊C4—22no—
671C4⋊C4—22no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—42no—
679C4⋊C4—42no—
680C4⋊C4—42no—
681C4⋊C4—42no—
682C4⋊C4—44no—
683C4⋊C4—44no—
684C4⋊C4—42no—
685C4⋊C4—42no—
686C4⋊C4—42no—
687C4⋊C4—42no—
688C4⋊C4—81no—
689C4⋊C4—81no—
690C4⋊C4—82no—
691C4⋊C4—82no—
692C4⋊C4—82no—
693C4⋊C4—82no—
694C4⋊C4—82no—
695C4⋊C4—82no—
696C4⋊C4—82no—
697C4⋊C4—82no—
698C4⋊C4C2×#4112yes—
699C4⋊C4C2×#4112yes—
700C22⋊C4—24no—
701C22⋊C4—24no—
702C22⋊C4—24no—
703C22⋊C4—28no—
704C22⋊C4—28no—
705C22⋊C4—28no—
706C22⋊C4—28no—
707C22⋊C4—44no—
708C22⋊C4—44no—
709C22⋊C4—42no—
710C22⋊C4—42no—
711C22⋊C4—42no—
712C22⋊C4—82no—
713C22⋊C4—82no—
714C22⋊C4—82no—
715C22⋊C4—82no—
716C42—24no—
717C42—22no—
718C42—22no—
719C42—22no—
720C42—22no—
721C42—44no—
722C42—44no—
723C42—44no—
724C42—42no—
725C42—42no—
726C42—42no—
727C42—81no—
728C42—81no—
729C42—81no—
730C42—81no—
731C42—82no—
732C42C22⋊Q814yes—
733C42C22⋊Q814yes—
734C42C22×Q812yes—
735C42C22×Q812yes—
736C42C2×#4112yes—
737C42C2×#4112yes—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—24no—
743C23—42no—
744C23—42no—
745C23—42no—
746C23—42no—
747C23—42no—
748C23—42no—
749C23—48no—
750C23—84no—
751C23—84no—
752C23—162no—
753C23—162no—
754C23—162no—
755C23—162no—
756C23C2×C22⋊Q812yes—
757C23#54612yes—
758C23#55012yes—
759C23C23×D411yescharacteristic
760Q8—24no—
761Q8—24no—
762Q8—42no—
763Q8—42no—
764Q8—48no—
765D4—24no—
766D4—24no—
767D4—42no—
768D4—42no—
769D4—48no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—24no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—44no—
794C2×C4—44no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—48no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—42no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—42no—
826C2×C4—84no—
827C2×C4—84no—
828C2×C4—164no—
829C2×C4—164no—
830C2×C4C2×C22⋊Q812yes—
831C2×C4C2×C22⋊Q812yes—
832C2×C4C2×C22⋊Q812yes—
833C2×C4C2×C22⋊Q812yes—
834C2×C4C2×C22⋊Q812yes—
835C2×C4#52914yes—
836C2×C4#54014yes—
837C2×C4#54612yes—
838C2×C4#55012yes—
839C2×C4#55414yes—
840C2×C4#55414yes—
841C2×C4C23×Q811yescharacteristic
842C2×C4C22×#4111yescharacteristic
843C2×C4C22×#4111yescharacteristic
844C2×C4C22×#4111yescharacteristic
845C2×C4C2×H(5,𝔽2)11yescharacteristic
846C2×C4C2×H(5,𝔽2)11yescharacteristic
847C8—24no—
848C8—41no—
849C8—41no—
850C8—41no—
851C8—41no—
852C8—42no—
853C22—22no—
854C22—22no—
855C22—22no—
856C22—22no—
857C22—22no—
858C22—22no—
859C22—44no—
860C22—44no—
861C22—44no—
862C22—82no—
863C22—82no—
864C22—82no—
865C22—82no—
866C22—168no—
867C22#245414yes—
868C22C22×C22⋊Q811yescharacteristic
869C22C2×#54611yescharacteristic
870C22C2×#55011yescharacteristic
871C22#358411yescharacteristic
872C22#358411yescharacteristic
873C22#358511yescharacteristic
874C22#358611yescharacteristic
875C4—22no—
876C4—22no—
877C4—22no—
878C4—22no—
879C4—42no—
880C4—42no—
881C4—42no—
882C4—42no—
883C4—42no—
884C4—42no—
885C4—44no—
886C4—82no—
887C4—81no—
888C4—81no—
889C4—81no—
890C4—81no—
891C4—81no—
892C4—81no—
893C4—82no—
894C4#245414yes—
895C4C2×#52911yescharacteristic
896C4C2×#54011yescharacteristic
897C4C2×#55411yescharacteristic
898C4C2×#55411yescharacteristic
899C2—24no—
900C2—84no—
901C2C2×#245411yescharacteristic
902C2#6048911yescharacteristic
903C2#6049311yescharacteristic
904C2#6120711yescharacteristic
905C2#6120811yescharacteristic
906C2#6142311yescharacteristic
907C2#6142411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2285 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #35181C2semidirect
3. #26545C2semidirect
4. #26544C2semidirect
5. #26543C2semidirect
6. #26542C2semidirect
7. #26537C2semidirect
8. #26536C2semidirect
9. #26535C2semidirect
10. #26534C2semidirect
11. #23736C2semidirect
13. #23613C2semidirect
17. #21169C2semidirect
18. #21145C2semidirect
19. #20877C2semidirect
21. #20651C2semidirect
23. C4×#428C2semidirect
46. #2571C22semidirect
49. #2570C22semidirect
50. #2570C22semidirect
52. #2552C22semidirect
73. #2097C22semidirect
74. #2097C22semidirect
75. #2096C22semidirect
76. #2095C22semidirect
81. #2068C22semidirect
82. #2068C22semidirect
85. #2066C22semidirect
86. #2066C22semidirect
97. #1949C22semidirect
98. #1949C22semidirect
99. #1949C22semidirect
100. #1949C22semidirect
101. #1948C22semidirect
102. #1948C22semidirect
103. #1947C22semidirect
104. #1947C22semidirect
105. #1940C22semidirect
106. #1940C22semidirect
107. #1939C22semidirect
108. #1939C22semidirect
109. #1865C22semidirect
110. #1865C22semidirect
113. #1863C22semidirect
114. #1863C22semidirect
117. #1805C22semidirect
118. #1805C22semidirect
121. #1803C22semidirect
122. #1803C22semidirect
125. #1776C22semidirect
126. #1776C22semidirect
127. C4×#107C22semidirect
128. C4×#106C22semidirect

Maximal subgroups

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

subgroupindex
#351812
#342112
#265452
#265442
#265432
#265422
#265372
#265362
#265352
#265342
#237362
#237352
#236132
#236122
C2×#19832
#212042
#211692
#211452
#208772
#208762
#206512
#206502
C4×#4282