Finite Group Databasebeta

← #7510578

Subgroups — #7510578

Order 512.

1620 conjugacy classes of subgroups.

The subgroup lattice has 901 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35566C211yesmaximal, characteristic, complemented
2#35338C211yesmaximal, characteristic
3#32643C212yesmaximal, complemented
4#32642C212yesmaximal, complemented
5#32639C212yesmaximal, complemented
6#32638C212yesmaximal, complemented
7#32637C212yesmaximal, complemented
8#32636C212yesmaximal, complemented
9#32633C212yesmaximal, complemented
10#32632C212yesmaximal, complemented
11#23615C211yesmaximal, characteristic, complemented
12#23612C211yesmaximal, characteristic
13#23506C211yesmaximal, characteristic
14C2×#2042C211yesmaximal, characteristic
15#23457C211yesmaximal, characteristic, complemented
16#23456C211yesmaximal, characteristic
17#21304C211yesmaximal, characteristic, complemented
18#21090C211yesmaximal, characteristic, complemented
19#21089C211yesmaximal, characteristic
20#21066C211yesmaximal, characteristic, complemented
21#21063C211yesmaximal, characteristic
22#21034C211yesmaximal, characteristic, complemented
23#21032C211yesmaximal, characteristic, complemented
24C2×#544C2211yescharacteristic
25C2×#533C2211yescharacteristic
26C22×#124C2211yescharacteristic
27C2×#428C2211yescharacteristic
28C2×#427C2211yescharacteristic
29C2×#424C2211yescharacteristic
30C2×#419C2211yescharacteristic
31C2×#419C2211yescharacteristic
32C2×#418C2211yescharacteristic
33C2×#418C2211yescharacteristic
34C22×#103C2211yescharacteristic
35C22×#103C2211yescharacteristic
36C22×#102C2211yescharacteristic
37C22×#102C2211yescharacteristic
38C2×#405C2211yescharacteristic
39#2861—21no—
40#2861—21no—
41#2640—21no—
42#2640—21no—
43#2592C2212yes—
44#2592C2212yes—
45#2592C2212yes—
46#2592C2212yes—
47#2584C2212yescomplemented
48#2584C2212yescomplemented
49#2567C2212yescomplemented
50#2561—22no—
51#2561—22no—
52#2552—21no—
53#2551—21no—
54#2550—21no—
55#2550—21no—
56#2549—22no—
57#2546C2212yescomplemented
58#2440—22no—
59#2317C2211yescharacteristic
60#2316C2211yescharacteristic
61#2310C2211yescharacteristic
62#2310C2211yescharacteristic
63#2309C2211yescharacteristic
64#2309C2211yescharacteristic
65#2296C2211yescharacteristic
66C2×#389C2211yescharacteristic
67#2274C2211yescharacteristic
68C4×#117C2211yescharacteristic
69#2068C2212yescomplemented
70#2068C2212yescomplemented
71#2067C2212yes—
72#2067C2212yes—
73#2066C2212yescomplemented
74#2066C2212yescomplemented
75#2065C2212yes—
76#2065C2212yes—
77#2042C2212yes—
78#2042C2212yes—
79#2042C2212yes—
80#2042C2212yes—
81#2042C2212yes—
82#2042C2212yes—
83#2042C2212yes—
84#2042C2212yes—
85#2026C2212yescomplemented
86#2026C2212yescomplemented
87#2025C2212yes—
88#2025C2212yes—
89#2024C2212yescomplemented
90#2024C2212yescomplemented
91#2023C2212yes—
92#2023C2212yes—
93#1985C2212yescomplemented
94#1985C2212yescomplemented
95#1984C2212yescomplemented
96#1984C2212yescomplemented
97#1936C2212yes—
98#1936C2212yes—
99#1935C2212yescomplemented
100#1935C2212yescomplemented
101#1934C2212yes—
102#1934C2212yes—
103#1933C2212yescomplemented
104#1933C2212yescomplemented
105#1928C2212yescomplemented
106#1928C2212yescomplemented
107#1927C2212yescomplemented
108#1927C2212yescomplemented
109#1926C2212yes—
110#1926C2212yes—
111#1925C2212yes—
112#1925C2212yes—
113#1921C2211yescharacteristic, complemented
114#1921C2211yescharacteristic, complemented
115#1921C2212yescomplemented
116#1920C2211yescharacteristic, complemented
117#1920C2211yescharacteristic, complemented
118#1920C2212yescomplemented
119#1919C2211yescharacteristic, complemented
120#1919C2211yescharacteristic, complemented
121#1919C2212yescomplemented
122#1918C2211yescharacteristic, complemented
123#1918C2211yescharacteristic, complemented
124#1918C2212yescomplemented
125#1736C2211yescharacteristic
126#1736C2211yescharacteristic
127#1736C2211yescharacteristic
128#1735C2211yescharacteristic
129#1735C2211yescharacteristic
130#1735C2211yescharacteristic
131#1729C2211yescharacteristic
132#1729C2211yescharacteristic
133#1728C2211yescharacteristic
134C2×#336C2211yescharacteristic
135C23×Q8C2311yescharacteristic
136C23×D4C2311yescharacteristic
137C22×M16C2311yescharacteristic
138C22×M16C2311yescharacteristic
139C23×C8C2311yescharacteristic
140C23×C8C2311yescharacteristic
141#544—42no—
142#544—42no—
143#533—42no—
144#533—42no—
145C2×C4⋊Q8—22no—
146C2×C4⋊Q8—21no—
147C2×C4⋊Q8D411yescharacteristic
148C2×C4⋊Q8D411yescharacteristic
149C2×C4⋊Q8C2312yes—
150C2×#125—21no—
151C2×#125D411yescharacteristic
152C2×#125D411yescharacteristic
153C2×#125C2312yes—
154C2×#124—21no—
155C2×#124—21no—
156C2×#124—42no—
157C2×#124—42no—
158C2×#124C2312yes—
159C2×#124C2312yes—
160C2×C22⋊Q8—22no—
161C2×C22⋊Q8D412yes—
162C2×C22⋊Q8D412yes—
163C2×C4×Q8C2312yes—
164C2×C4×Q8C2312yes—
165C2×#117C2311yescharacteristic
166C2×#117C2311yescharacteristic
167C2×#117C2311yescharacteristic
168C2×#117C2311yescharacteristic
169C2×#117C2311yescharacteristic
170C2×#117C2311yescharacteristic
171C22×C4⋊C4—21no—
172C22×C4⋊C4C2311yescharacteristic
173C22×C4⋊C4C2311yescharacteristic
174C22×C22⋊C4—21no—
175C22×C22⋊C4—21no—
176C22×C42C2311yescharacteristic
177#428—24no—
178#427—24no—
179C2×#107C2311yescharacteristic
180C2×#107C2311yescharacteristic
181C2×#107C2312yes—
182C2×#106C2311yescharacteristic
183C2×#106C2311yescharacteristic
184C2×#106C2312yes—
185#424—42no—
186C2×C4⋊C8C2312yes—
187C2×C4⋊C8C2312yes—
188#419—24no—
189#419—42no—
190#418—24no—
191#418—42no—
192C2×#103—24no—
193C2×#103—42no—
194C2×#103C2312yes—
195C2×#103C2312yes—
196C2×#103C2312yes—
197C2×#103C2312yes—
198C2×#103C2312yes—
199C2×#103C2312yes—
200C2×#103C2312yes—
201C2×#103C2312yes—
202C2×#102—24no—
203C2×#102—42no—
204C2×#102C2312yes—
205C2×#102C2312yes—
206C2×#102C2312yes—
207C2×#102C2312yes—
208C2×#102C2312yes—
209C2×#102C2312yes—
210C2×#102C2312yes—
211C2×#102C2312yes—
212#405—42no—
213C2×#97C2312yes—
214C2×C4×C8C2312yes—
215#398—22no—
216#398—22no—
217#398—22no—
218#398—22no—
219#397—22no—
220#397—22no—
221#397—22no—
222#397—22no—
223#395—22no—
224#395—22no—
225#395—22no—
226#395—22no—
227#393—22no—
228#393—22no—
229#393—22no—
230#393—22no—
231#391—22no—
232#391—21no—
233#391—21no—
234#391—21no—
235#391—21no—
236#391—22no—
237#391C2312yes—
238#391C2312yes—
239#391C2312yes—
240#391C2312yes—
241#390—21no—
242#390—21no—
243#390—21no—
244#390—21no—
245#390C2312yes—
246#390C2312yes—
247#390C2312yes—
248#390C2312yes—
249#389—21no—
250#389—21no—
251#389—22no—
252#389—22no—
253#389—22no—
254#389—22no—
255#389—21no—
256#389—21no—
257#389C2311yescharacteristic
258#389C2312yes—
259#389C2312yes—
260#389C2312yes—
261#389C2312yes—
262#389C2312yes—
263#389C2311yescharacteristic
264#389C2311yescharacteristic
265#389C2312yes—
266#389C2311yescharacteristic
267#388—22no—
268#388—22no—
269#388—22no—
270#388—22no—
271#388—22no—
272#388—22no—
273#388—22no—
274#388—22no—
275#385—21no—
276#385—21no—
277#385—22no—
278#384—22no—
279#384—21no—
280#382—21no—
281#381—22no—
282#381—22no—
283#380—22no—
284#379—22no—
285#379—22no—
286C4×C4⋊C4—21no—
287C4×C4⋊C4—21no—
288C4×C4⋊C4—21no—
289C4×C4⋊C4—21no—
290C4×C4⋊C4C2312yes—
291C4×C4⋊C4C2312yes—
292C4×C4⋊C4C2311yescharacteristic
293C4×C4⋊C4C2311yescharacteristic
294C4×C4⋊C4C2311yescharacteristic
295C4×C4⋊C4C2311yescharacteristic
296C4×C22⋊C4—21no—
297C4×C22⋊C4—21no—
298C4×C22⋊C4—22no—
299#376—21no—
300C2×#95—21no—
301C43—21no—
302#340C2312yes—
303#340C2312yes—
304#340C2311yescharacteristic
305#340C2311yescharacteristic
306#340C2311yescharacteristic
307#340C2311yescharacteristic
308#340C2311yescharacteristic
309#340C2311yescharacteristic
310#340C2312yes—
311#340C2311yescharacteristic
312#340C2311yescharacteristic
313#340C2312yes—
314#340C2312yes—
315#340C2312yes—
316#340C2311yescharacteristic
317#340C2311yescharacteristic
318#340C2311yescharacteristic
319#340C2311yescharacteristic
320#336C2312yes—
321#336C2311yescharacteristic
322#336C2311yescharacteristic
323#336C2311yescharacteristic
324#336C2311yescharacteristic
325#336C2312yes—
326#336C2312yes—
327#336C2312yes—
328#336C2312yes—
329#336C2312yes—
330C25—21no—
331C22×Q8—21no—
332C22×Q8—22no—
333C22×Q8—22no—
334C22×Q8—22no—
335C22×Q8—22no—
336C22×Q8—22no—
337C22×Q8—22no—
338C22×Q8—22no—
339C22×Q8C2×D412yes—
340C22×Q8C2×D412yes—
341C22×Q8C2412yes—
342C22×D4—21no—
343C22×D4—22no—
344C22×D4—22no—
345C22×D4—22no—
346C22×D4—22no—
347C22×D4—22no—
348C22×D4—22no—
349C22×D4C2412yes—
350C23×C4—21no—
351C23×C4—21no—
352C23×C4—21no—
353C23×C4C2×D411yescharacteristic
354C23×C4C2×D411yescharacteristic
355C23×C4C2411yescharacteristic
356C2×M16—22no—
357C2×M16—22no—
358C2×M16—22no—
359C2×M16—22no—
360C2×M16—22no—
361C2×M16—22no—
362C22×C8—22no—
363C22×C8—22no—
364C22×C8—22no—
365C22×C8—22no—
366C22×C8—22no—
367C22×C8—22no—
368C22×C8C2411yescharacteristic
369C22×C8C2411yescharacteristic
370C22×C8C2411yescharacteristic
371C22×C8C2411yescharacteristic
372C22×C8C2412yes—
373C22×C8C2412yes—
374C4⋊Q8—42no—
375C4⋊Q8—42no—
376C4⋊Q8—42no—
377C4⋊Q8—42no—
378C4⋊Q8—44no—
379C4⋊Q8—84no—
380#125—42no—
381#125—42no—
382#125—42no—
383#125—42no—
384#125—44no—
385#124—42no—
386#124—42no—
387#124—42no—
388#124—42no—
389#124—44no—
390#124—44no—
391C22⋊Q8—44no—
392C22⋊Q8—44no—
393C22⋊Q8—48no—
394C4×Q8—42no—
395C4×Q8—42no—
396C4×Q8—42no—
397C4×Q8—42no—
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—22no—
408#117—22no—
409#117#4114yes—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—82no—
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⋊C4C2×D412yes—
438C2×C4⋊C4C2×D412yes—
439C2×C4⋊C4#4114yes—
440C2×C4⋊C4C2412yes—
441C2×C4⋊C4C2411yescharacteristic
442C2×C4⋊C4C2411yescharacteristic
443C2×C4⋊C4C2411yescharacteristic
444C2×C4⋊C4C2411yescharacteristic
445C2×C4⋊C4C2411yescharacteristic
446C2×C4⋊C4C2411yescharacteristic
447C2×C4⋊C4C2412yes—
448C2×C4⋊C4C2411yescharacteristic
449C2×C4⋊C4C2411yescharacteristic
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—22no—
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—22no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—44no—
467C2×C22⋊C4—44no—
468C2×C22⋊C4C2×D412yes—
469C2×C22⋊C4C2×D412yes—
470C2×C42—21no—
471C2×C42—22no—
472C2×C42—22no—
473C2×C42—21no—
474C2×C42—21no—
475C2×C42—21no—
476C2×C42—22no—
477C2×C42—21no—
478C2×C42—21no—
479C2×C42—21no—
480C2×C42—21no—
481C2×C42—22no—
482C2×C42C2×D411yescharacteristic
483C2×C42C2×D411yescharacteristic
484C2×C42C2412yes—
485C2×C42C2412yes—
486C2×C42C2411yescharacteristic
487C2×C42C2411yescharacteristic
488#107—22no—
489#107—22no—
490#107—24no—
491#106—22no—
492#106—22no—
493#106—24no—
494C4⋊C8—42no—
495C4⋊C8—42no—
496#103—24no—
497#103—24no—
498#103—24no—
499#103—24no—
500#103—42no—
501#103—42no—
502#103—42no—
503#103—42no—
504#102—24no—
505#102—24no—
506#102—24no—
507#102—24no—
508#102—42no—
509#102—42no—
510#102—42no—
511#102—42no—
512#97—42no—
513C4×C8—42no—
514#95—22no—
515#95—22no—
516#95—21no—
517#95—21no—
518#95—21no—
519#95—21no—
520#95—22no—
521#95—22no—
522#95—21no—
523#95—21no—
524#95—21no—
525#95—21no—
526#95—22no—
527#95—22no—
528#95—22no—
529#95—22no—
530#95—22no—
531#95—22no—
532#95—22no—
533#95—22no—
534#95—22no—
535#95—22no—
536#95—22no—
537#95—22no—
538C24—22no—
539C24—42no—
540C24—42no—
541C24—42no—
542C24—81no—
543C24—81no—
544C24—81no—
545C24—81no—
546C24C22×D411yescharacteristic
547C2×Q8—22no—
548C2×Q8—22no—
549C2×Q8—22no—
550C2×Q8—22no—
551C2×Q8—22no—
552C2×Q8—22no—
553C2×Q8—42no—
554C2×Q8—42no—
555C2×Q8—42no—
556C2×Q8—42no—
557C2×Q8—42no—
558C2×Q8—42no—
559C2×Q8—44no—
560C2×Q8—42no—
561C2×Q8—42no—
562C2×Q8—42no—
563C2×Q8—44no—
564C2×Q8—44no—
565C2×Q8—44no—
566C2×Q8—44no—
567C2×Q8—82no—
568C2×Q8—82no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—42no—
576C2×D4—44no—
577C2×D4—44no—
578C2×D4—42no—
579C2×D4—42no—
580C2×D4—44no—
581C2×D4—44no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—24no—
588C22×C4—22no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—22no—
596C22×C4—41no—
597C22×C4—41no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—81no—
605C22×C4—81no—
606C22×C4—81no—
607C22×C4—81no—
608C22×C4C22×D411yescharacteristic
609C22×C4C22×D412yes—
610C22×C4C22×D411yescharacteristic
611C22×C4C22×D412yes—
612C22×C4C22×D412yes—
613C22×C4C22×D411yescharacteristic
614C22×C4C22×D412yes—
615C22×C4C22×D411yescharacteristic
616C22×C4C22×D411yescharacteristic
617C22×C4C2×#4112yes—
618C22×C4C2×#4112yes—
619C22×C4H(5,𝔽2)12yes—
620C22×C4H(5,𝔽2)12yes—
621C22×C42−1+412yes—
622C22×C42−1+412yes—
623C22×C4C2511yescharacteristic
624M16—44no—
625M16—44no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—22no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—22no—
632C2×C8—21no—
633C2×C8—22no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—22no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—22no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—22no—
644C2×C8—44no—
645C2×C8—44no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—24no—
651C4⋊C4—22no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—22no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—22no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—42no—
669C4⋊C4—42no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4—42no—
673C4⋊C4—42no—
674C4⋊C4—42no—
675C4⋊C4—44no—
676C4⋊C4—44no—
677C4⋊C4—44no—
678C4⋊C4—44no—
679C4⋊C4—42no—
680C4⋊C4—42no—
681C4⋊C4—81no—
682C4⋊C4—81no—
683C4⋊C4—82no—
684C4⋊C4—82no—
685C4⋊C4—82no—
686C4⋊C4—82no—
687C4⋊C4—82no—
688C4⋊C4C2×#4114yes—
689C4⋊C4C2×#4112yes—
690C4⋊C4C2×#4112yes—
691C22⋊C4—24no—
692C22⋊C4—24no—
693C22⋊C4—24no—
694C22⋊C4—44no—
695C22⋊C4—44no—
696C22⋊C4—44no—
697C22⋊C4—44no—
698C22⋊C4—42no—
699C22⋊C4—42no—
700C22⋊C4—42no—
701C22⋊C4—82no—
702C22⋊C4—82no—
703C22⋊C4—82no—
704C22⋊C4—82no—
705C22⋊C4—82no—
706C22⋊C4—82no—
707C22⋊C4—82no—
708C22⋊C4—82no—
709C42—22no—
710C42—22no—
711C42—24no—
712C42—22no—
713C42—22no—
714C42—21no—
715C42—21no—
716C42—21no—
717C42—21no—
718C42—22no—
719C42—22no—
720C42—42no—
721C42—42no—
722C42—42no—
723C42—82no—
724C42—81no—
725C42—81no—
726C42—81no—
727C42—81no—
728C42—82no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—42no—
734C23—42no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—84no—
741C23—84no—
742C23—84no—
743C23—162no—
744C23—162no—
745C23—162no—
746C23—162no—
747C23#53412yes—
748C23#54812yes—
749C23#54812yes—
750C23C23×D411yescharacteristic
751Q8—42no—
752Q8—42no—
753Q8—42no—
754Q8—42no—
755Q8—84no—
756Q8—84no—
757Q8—84no—
758Q8—164no—
759D4—42no—
760D4—42no—
761D4—42no—
762D4—42no—
763D4—84no—
764C2×C4—22no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—21no—
774C2×C4—22no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—24no—
791C2×C4—41no—
792C2×C4—42no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—42no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—42no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—42no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—82no—
822C2×C4—82no—
823C2×C4—84no—
824C2×C4—84no—
825C2×C4—162no—
826C2×C4#53412yes—
827C2×C4#54214yes—
828C2×C4#54214yes—
829C2×C4#54812yes—
830C2×C4#54812yes—
831C2×C4#55514yes—
832C2×C4#56314yes—
833C2×C4C22×#4111yescharacteristic
834C2×C4C22×#4111yescharacteristic
835C2×C4C2×H(5,𝔽2)11yescharacteristic
836C2×C4C2×H(5,𝔽2)11yescharacteristic
837C2×C4C2×2−1+411yescharacteristic
838C2×C4C2×2−1+411yescharacteristic
839C8—41no—
840C8—41no—
841C8—42no—
842C8—41no—
843C8—41no—
844C8—42no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—22no—
851C22—82no—
852C22—82no—
853C22—82no—
854C22—82no—
855C22—82no—
856C22—82no—
857C22—82no—
858C22—168no—
859C22#273114yes—
860C22C2×#53411yescharacteristic
861C22C2×#54811yescharacteristic
862C22C2×#54811yescharacteristic
863C22#358411yescharacteristic
864C22#358411yescharacteristic
865C22#358511yescharacteristic
866C22#358611yescharacteristic
867C4—41no—
868C4—41no—
869C4—42no—
870C4—42no—
871C4—41no—
872C4—41no—
873C4—42no—
874C4—42no—
875C4—42no—
876C4—42no—
877C4—44no—
878C4—82no—
879C4—81no—
880C4—81no—
881C4—81no—
882C4—81no—
883C4—81no—
884C4—81no—
885C4—82no—
886C4#273114yes—
887C4C2×#54211yescharacteristic
888C4C2×#54211yescharacteristic
889C4C2×#55511yescharacteristic
890C4C2×#56311yescharacteristic
891C2—24no—
892C2—162no—
893C2C2×#273111yescharacteristic
894C2#6076011yescharacteristic
895C2#6076111yescharacteristic
896C2#6133111yescharacteristic
897C2#6133611yescharacteristic
898C2#6134311yescharacteristic
899C2#6134411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×#533 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #35566C2semidirect
3. #32643C2semidirect
4. #32642C2semidirect
5. #32639C2semidirect
6. #32638C2semidirect
7. #32637C2semidirect
8. #32636C2semidirect
9. #32633C2semidirect
10. #32632C2semidirect
11. #23615C2semidirect
15. #23457C2semidirect
17. #21304C2semidirect
18. #21090C2semidirect
20. #21066C2semidirect
22. #21034C2semidirect
23. #21032C2semidirect
47. #2584C22semidirect
48. #2584C22semidirect
49. #2567C22semidirect
57. #2546C22semidirect
69. #2068C22semidirect
70. #2068C22semidirect
73. #2066C22semidirect
74. #2066C22semidirect
85. #2026C22semidirect
86. #2026C22semidirect
89. #2024C22semidirect
90. #2024C22semidirect
93. #1985C22semidirect
94. #1985C22semidirect
95. #1984C22semidirect
96. #1984C22semidirect
99. #1935C22semidirect
100. #1935C22semidirect
103. #1933C22semidirect
104. #1933C22semidirect
105. #1928C22semidirect
106. #1928C22semidirect
107. #1927C22semidirect
108. #1927C22semidirect
113. #1921C22semidirect
114. #1921C22semidirect
115. #1921C22semidirect
116. #1920C22semidirect
117. #1920C22semidirect
118. #1920C22semidirect
119. #1919C22semidirect
120. #1919C22semidirect
121. #1919C22semidirect
122. #1918C22semidirect
123. #1918C22semidirect
124. #1918C22semidirect

Maximal subgroups

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

subgroupindex
#355662
#353382
#326432
#326422
#326392
#326382
#326372
#326362
#326332
#326322
#236152
#236122
#235062
C2×#20422
#234572
#234562
#213042
#210902
#210892
#210662
#210632
#210342
#210322