Finite Group Databasebeta

← #6547062

Subgroups — #6547062

Order 512.

1847 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
1C2×#3375C211yesmaximal, characteristic, complemented
2C2×#2984C211yesmaximal, characteristic, complemented
3#36580C211yesmaximal, characteristic
4Q8×C22⋊Q8C211yesmaximal, characteristic, complemented
5#29853C212yesmaximal, complemented
6#29842C211yesmaximal, characteristic
7#28651C212yesmaximal, complemented
8#28640C211yesmaximal, characteristic, complemented
9#28277C212yesmaximal, complemented
10#28265C211yesmaximal, characteristic, complemented
11#25481C212yesmaximal, complemented
12#25471C211yesmaximal, characteristic, complemented
13#25307C212yesmaximal, complemented
14#25295C211yesmaximal, characteristic, complemented
15#24711C211yesmaximal, characteristic, complemented
16#24700C212yesmaximal, complemented
17#24661C211yesmaximal, characteristic
18#24655C212yesmaximal, complemented
19#23710C212yesmaximal, complemented
20#23699C211yesmaximal, characteristic, complemented
21#22728C211yesmaximal, characteristic, complemented
22#22546C211yesmaximal, characteristic, complemented
23#22525C211yesmaximal, characteristic, complemented
24C2×#559C2211yescharacteristic
25C2×Q82C2211yescharacteristic
26C22×C4×Q8C2211yescharacteristic
27#3375—28no—
28C2×#489C2212yes—
29C2×#486C2211yescharacteristic
30C2×#477C2211yescharacteristic
31C2×#474C2212yes—
32C2×#464C2212yes—
33C2×#460C2211yescharacteristic
34#2984—28no—
35C2×#446C2211yescharacteristic
36C2×#446C2212yes—
37C2×#446C2212yes—
38C2×#446C2211yescharacteristic
39C2×C8×Q8C2211yescharacteristic
40C2×C8×Q8C2211yescharacteristic
41C2×#440C2212yes—
42C2×C4×Q16C2211yescharacteristic
43C2×#432C2211yescharacteristic
44C2×#432C2212yes—
45C2×#431C2212yes—
46C2×#431C2211yescharacteristic
47#2857C2212yes—
48#2857C2211yescharacteristic
49#2856C2211yescharacteristic
50#2850C2212yes—
51#2592C2212yes—
52#2582C2211yescharacteristic
53#2582C2211yescharacteristic
54#2582C2212yes—
55#2580C2212yes—
56#2567C2211yescharacteristic
57#2567C2212yes—
58#2548C2211yescharacteristic
59#2458—22no—
60#2451—21no—
61#2451—22no—
62#2448—21no—
63#2443—22no—
64#2440—21no—
65#2440—22no—
66#2436—21no—
67#2367—21no—
68#2361—21no—
69#2355C2211yescharacteristic
70Q8×C4⋊C4—21no—
71Q8×C4⋊C4C2211yescharacteristic
72Q8×C22⋊C4—21no—
73C4×C22⋊Q8C2212yes—
74C4×C22⋊Q8C2211yescharacteristic
75C4×C22⋊Q8C2211yescharacteristic
76C4×#121C2212yes—
77#2087C2212yes—
78#2086C2211yescharacteristic
79#2075C2211yescharacteristic
80#2075C2212yes—
81#2068C2212yes—
82#2068C2212yes—
83#2068C2212yes—
84#2067C2212yes—
85#2067C2212yes—
86#2066C2211yescharacteristic
87#2066C2211yescharacteristic
88#2065C2212yes—
89#2065C2212yes—
90#2065C2212yes—
91#2056C2211yescharacteristic
92#2055C2212yes—
93#2035C2212yes—
94#2035C2211yescharacteristic
95#2035C2211yescharacteristic
96#2033C2212yes—
97#2033C2212yes—
98#2033C2212yes—
99#2001C2211yescharacteristic
100#2000C2212yes—
101#1993C2212yes—
102#1990C2211yescharacteristic
103#1988C2212yes—
104#1987C2211yescharacteristic
105#1983C2212yes—
106#1982C2211yescharacteristic
107#1973C2212yes—
108#1969C2212yes—
109#1968C2212yes—
110#1959C2212yes—
111#1957C2211yescharacteristic
112#1949C2212yes—
113#1948C2211yescharacteristic
114#1947C2211yescharacteristic
115#1947C2212yes—
116#1944C2212yes—
117#1942C2212yes—
118#1942C2212yes—
119#1936C2212yes—
120#1935C2212yes—
121#1934C2212yes—
122#1934C2212yes—
123#1934C2212yes—
124#1933C2212yes—
125#1847C2212yes—
126#1845C2211yescharacteristic
127#1805C2212yes—
128#1803C2211yescharacteristic
129#1803C2211yescharacteristic
130#1802C2212yes—
131#1776C2212yes—
132C4×#106C2211yescharacteristic
133#1763C2212yes—
134#1762C2212yes—
135C4×#103C2211yescharacteristic
136C4×#103C2211yescharacteristic
137C23×Q8D411yescharacteristic
138C22×Q16C2311yescharacteristic
139C22×SD16C2312yes—
140#559—24no—
141#559—24no—
142Q82—24no—
143Q82—24no—
144C2×C4⋊Q8—21no—
145C2×C4⋊Q8—22no—
146C2×C4⋊Q8C2311yescharacteristic
147C2×C4⋊Q8C2312yes—
148C2×#127C2311yescharacteristic
149C2×#124—21no—
150C2×#124—21no—
151C2×#124C2312yes—
152C2×#123—22no—
153C2×C22⋊Q8—22no—
154C2×C22⋊Q8—21no—
155C2×C22⋊Q8C2311yescharacteristic
156C2×C22⋊Q8C2311yescharacteristic
157C2×#121—21no—
158C2×#121—21no—
159C2×#121C2312yes—
160C2×C4×Q8—24no—
161C2×C4×Q8—24no—
162C2×C4×Q8—21no—
163C2×C4×Q8—21no—
164C2×C4×Q8D411yescharacteristic
165C2×C4×Q8D411yescharacteristic
166C2×C4×Q8D412yes—
167C2×C4×Q8C2311yescharacteristic
168C2×C4×Q8C2311yescharacteristic
169C2×C4×Q8C2312yes—
170C2×C4×Q8C2312yes—
171C2×C4×Q8C2311yescharacteristic
172C2×C4×Q8C2311yescharacteristic
173C2×C4×D4—22no—
174C2×C4×D4—21no—
175C2×C4×D4C2312yes—
176C22×C4⋊C4D411yescharacteristic
177C22×C4⋊C4D412yes—
178C22×C42C2312yes—
179C22×C42C2311yescharacteristic
180#489—28no—
181#486—24no—
182#477—24no—
183#474—28no—
184#464—28no—
185#460—24no—
186#446—24no—
187#446—28no—
188#446—28no—
189#446D418yescomplemented
190C8×Q8—24no—
191C8×Q8—24no—
192#440—28no—
193C4×Q16—24no—
194#432—24no—
195#432—28no—
196#431—28no—
197#431—24no—
198C2×#107C2312yes—
199C2×#107C2311yescharacteristic
200C2×#107C2312yes—
201C2×#107C2312yes—
202C2×#107C2312yes—
203C2×#106C2311yescharacteristic
204C2×#106C2311yescharacteristic
205C2×#106C2312yes—
206C2×C4⋊C8C2312yes—
207C2×C4⋊C8C2311yescharacteristic
208C2×C4⋊C8C2312yes—
209C2×C4⋊C8C2311yescharacteristic
210C2×C4⋊C8C2312yes—
211C2×C4⋊C8C2311yescharacteristic
212C2×C4⋊C8C2311yescharacteristic
213C2×C4⋊C8C2312yes—
214C2×#103C2312yes—
215C2×#103C2311yescharacteristic
216C2×#103C2311yescharacteristic
217C2×#103C2311yescharacteristic
218C2×#103C2311yescharacteristic
219C2×#103C2311yescharacteristic
220C2×#103C2312yes—
221C2×#103C2312yes—
222C2×#103C2311yescharacteristic
223C2×#102C2312yes—
224C2×#102C2312yes—
225C2×#102C2312yes—
226C2×#102C2312yes—
227C2×#102C2312yes—
228C2×#102C2312yes—
229C2×#102C2312yes—
230C2×C22⋊C8C2311yescharacteristic
231C2×C22⋊C8C2312yes—
232C2×C22⋊C8C2311yescharacteristic
233C2×#97C2312yes—
234C2×#97C2312yes—
235C2×#97C2312yes—
236C2×C4×C8C2312yes—
237C2×C4×C8C2312yes—
238C2×C4×C8C2311yescharacteristic
239C2×C4×C8C2311yescharacteristic
240#399—22no—
241#398—22no—
242#398—22no—
243#398—22no—
244#398—22no—
245#397—22no—
246#395—22no—
247#395—22no—
248#395—22no—
249#394—22no—
250#393—22no—
251#393—22no—
252#391—22no—
253#391—21no—
254#391—22no—
255#391—21no—
256#391—21no—
257#391—21no—
258#391—22no—
259#391—21no—
260#391C2312yes—
261#391C2311yescharacteristic
262#391C2311yescharacteristic
263#391C2312yes—
264#390—21no—
265#390—21no—
266#390—21no—
267#390C2312yes—
268#390C2312yes—
269#390C2312yes—
270#389—21no—
271#389—22no—
272#389—21no—
273#389—21no—
274#389—22no—
275#389—21no—
276#389—22no—
277#389C2312yes—
278#389C2311yescharacteristic
279#389C2312yes—
280#389C2312yes—
281#389C2312yes—
282#389C2311yescharacteristic
283#389C2312yes—
284#388—22no—
285#388—22no—
286#388—22no—
287#388—22no—
288#388—22no—
289#387—22no—
290#387—22no—
291#387—21no—
292#387—21no—
293#386—22no—
294#386—22no—
295#386—22no—
296#385—22no—
297#385—21no—
298#385—21no—
299#385—22no—
300#385—22no—
301#384—21no—
302#384—22no—
303#384C2312yes—
304#384C2311yescharacteristic
305#384C2311yescharacteristic
306#382C2312yes—
307#380—21no—
308#380—22no—
309#380C2311yescharacteristic
310#380C2311yescharacteristic
311#380C2312yes—
312C4×C4⋊C4—21no—
313C4×C4⋊C4—21no—
314C4×C4⋊C4—22no—
315C4×C4⋊C4—21no—
316C4×C4⋊C4C2311yescharacteristic
317C4×C4⋊C4C2312yes—
318C4×C4⋊C4C2312yes—
319C4×C4⋊C4C2311yescharacteristic
320C4×C22⋊C4—21no—
321C4×C22⋊C4—22no—
322C4×C22⋊C4—21no—
323C4×C22⋊C4—22no—
324#340C2312yes—
325#340C2311yescharacteristic
326#340C2311yescharacteristic
327#340C2312yes—
328#340C2312yes—
329#340C2312yes—
330#340C2312yes—
331#340C2311yescharacteristic
332#340C2312yes—
333#340C2311yescharacteristic
334#340C2312yes—
335#340C2311yescharacteristic
336#340C2311yescharacteristic
337#340C2312yes—
338C22×Q8—24no—
339C22×Q8—24no—
340C22×Q8—22no—
341C22×Q8—21no—
342C22×Q8—42no—
343C22×Q8C2×D412yes—
344C22×Q8C2×D411yescharacteristic
345C22×Q8C2×D411yescharacteristic
346C22×Q8C2411yescharacteristic
347C22×Q8C2411yescharacteristic
348C22×D4—22no—
349C22×D4—21no—
350C22×D4—21no—
351C22×D4C2412yes—
352C23×C4—22no—
353C23×C4C2×D411yescharacteristic
354C23×C4C2×D412yes—
355C23×C4C2×D411yescharacteristic
356C23×C4C2×D412yes—
357C23×C4C2411yescharacteristic
358C2×Q16—22no—
359C2×Q16—22no—
360C2×Q16—41no—
361C2×SD16—24no—
362C2×SD16—24no—
363C2×SD16—42no—
364C22×C8C2411yescharacteristic
365C22×C8C2412yes—
366C22×C8C2411yescharacteristic
367C22×C8C2412yes—
368C22×C8C2411yescharacteristic
369C22×C8C2411yescharacteristic
370C4⋊Q8—24no—
371C4⋊Q8—22no—
372C4⋊Q8—24no—
373C4⋊Q8—22no—
374C4⋊Q8—44no—
375C4⋊Q8—48no—
376#127—22no—
377#127—22no—
378#124—24no—
379#124—24no—
380#124—44no—
381#124—44no—
382#123—48no—
383C22⋊Q8—22no—
384C22⋊Q8—22no—
385C22⋊Q8—41no—
386C22⋊Q8—41no—
387C22⋊Q8—84no—
388C22⋊Q8—82no—
389#121—42no—
390#121—42no—
391#121—44no—
392#121—82no—
393C4×Q8—24no—
394C4×Q8—24no—
395C4×Q8—28no—
396C4×Q8—22no—
397C4×Q8—24no—
398C4×Q8—24no—
399C4×Q8—22no—
400C4×Q8—22no—
401C4×Q8—24no—
402C4×Q8—22no—
403C4×Q8—24no—
404C4×Q8—22no—
405C4×Q8—22no—
406C4×Q8—44no—
407C4×Q8—44no—
408C4×Q8C2×D414yes—
409C4×Q8#4114yes—
410C4×D4—24no—
411C4×D4—24no—
412C4×D4—44no—
413C4×D4—84no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—24no—
416C2×C4⋊C4—28no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4C2×D411yescharacteristic
437C2×C4⋊C4C2×D412yes—
438C2×C4⋊C4C2×D412yes—
439C2×C4⋊C4C2×D412yes—
440C2×C4⋊C4C2×D412yes—
441C2×C4⋊C4C2×D411yescharacteristic
442C2×C4⋊C4C2×D412yes—
443C2×C4⋊C4C2411yescharacteristic
444C2×C4⋊C4C2411yescharacteristic
445C2×C4⋊C4C2412yes—
446C2×C4⋊C4C2412yes—
447C2×C4⋊C4C2411yescharacteristic
448C2×C4⋊C4C2411yescharacteristic
449C2×C4⋊C4C2411yescharacteristic
450C2×C4⋊C4C2412yes—
451C2×C4⋊C4C2411yescharacteristic
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—22no—
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—22no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—22no—
467C2×C42—24no—
468C2×C42—22no—
469C2×C42—24no—
470C2×C42—22no—
471C2×C42—21no—
472C2×C42—22no—
473C2×C42—21no—
474C2×C42—22no—
475C2×C42—21no—
476C2×C42—21no—
477C2×C42—22no—
478C2×C42C2×D412yes—
479C2×C42C2×D411yescharacteristic
480C2×C42C2×D412yes—
481C2×C42C2×D411yescharacteristic
482C2×C42C2412yes—
483C2×C42C2411yescharacteristic
484C2×C42C2412yes—
485C2×C42C2411yescharacteristic
486#107—22no—
487#107—24no—
488#107—42no—
489#107—42no—
490#107—42no—
491#106—22no—
492#106—41no—
493#106—42no—
494C4⋊C8—22no—
495C4⋊C8—22no—
496C4⋊C8—24no—
497C4⋊C8—24no—
498C4⋊C8—24no—
499C4⋊C8—22no—
500C4⋊C8C2×D418yes—
501C4⋊C8C2×D414yes—
502#103—22no—
503#103—22no—
504#103—22no—
505#103—24no—
506#103—22no—
507#103—42no—
508#103—41no—
509#103—41no—
510#103—42no—
511#102—24no—
512#102—24no—
513#102—24no—
514#102—24no—
515#102—42no—
516#102—42no—
517#102—42no—
518C22⋊C8—22no—
519C22⋊C8—24no—
520C22⋊C8—22no—
521#97—24no—
522#97—24no—
523#97C2×D418yes—
524C4×C8—24no—
525C4×C8—24no—
526C4×C8—22no—
527C4×C8C2×D414yes—
528#95—21no—
529#95—21no—
530#95—22no—
531#95—21no—
532#95—21no—
533#95—22no—
534#95—21no—
535#95—22no—
536#95—21no—
537#95—22no—
538#95—22no—
539#95—21no—
540#95—22no—
541#95—21no—
542#95—21no—
543#95—22no—
544#95—21no—
545#95—22no—
546#95—22no—
547#95—22no—
548#95—22no—
549#95—22no—
550#95—22no—
551#95—22no—
552C24—22no—
553C24C22×D411yescharacteristic
554C2×Q8—22no—
555C2×Q8—24no—
556C2×Q8—22no—
557C2×Q8—24no—
558C2×Q8—22no—
559C2×Q8—22no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—42no—
572C2×Q8—416no—
573C2×Q8—44no—
574C2×Q8—42no—
575C2×Q8—82no—
576C2×Q8—81no—
577C2×Q8—82no—
578C2×Q8—81no—
579C2×Q8#12114yes—
580C2×Q8#13714yes—
581C2×Q82−1+412yes—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—22no—
587C2×D4—22no—
588C2×D4—44no—
589C2×D4—44no—
590C2×D4—44no—
591C2×D4—42no—
592C2×D4—42no—
593C2×D4—42no—
594C2×D4—42no—
595C2×D4—81no—
596C2×D4—81no—
597C22×C4—24no—
598C22×C4—22no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—24no—
602C22×C4—22no—
603C22×C4—24no—
604C22×C4—22no—
605C22×C4—24no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—22no—
618C22×C4—21no—
619C22×C4—22no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—22no—
623C22×C4—42no—
624C22×C4—41no—
625C22×C4—42no—
626C22×C4—44no—
627C22×C4—82no—
628C22×C4—82no—
629C22×C4C22×D411yescharacteristic
630C22×C4C22×D411yescharacteristic
631C22×C4C22×D412yes—
632C22×C4C22×D411yescharacteristic
633C22×C4C22×D412yes—
634C22×C4C22×D412yes—
635C22×C4C22×D411yescharacteristic
636C22×C4C22×D412yes—
637C22×C4C22×D411yescharacteristic
638C22×C4C2511yescharacteristic
639Q16—44no—
640SD16—48no—
641C2×C8—21no—
642C2×C8—22no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—22no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—22no—
650C2×C8—22no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—22no—
656C2×C8C22×D412yes—
657C2×C8C22×D414yes—
658C2×C8C22×D412yes—
659C4⋊C4—24no—
660C4⋊C4—24no—
661C4⋊C4—24no—
662C4⋊C4—24no—
663C4⋊C4—22no—
664C4⋊C4—24no—
665C4⋊C4—21no—
666C4⋊C4—22no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—22no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—22no—
676C4⋊C4—22no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—22no—
680C4⋊C4—21no—
681C4⋊C4—22no—
682C4⋊C4—44no—
683C4⋊C4—42no—
684C4⋊C4—42no—
685C4⋊C4—44no—
686C4⋊C4—42no—
687C4⋊C4—44no—
688C4⋊C4—42no—
689C4⋊C4—42no—
690C4⋊C4—42no—
691C4⋊C4—82no—
692C4⋊C4—81no—
693C4⋊C4—81no—
694C4⋊C4—82no—
695C4⋊C4—81no—
696C4⋊C4—82no—
697C4⋊C4—81no—
698C4⋊C4—82no—
699C4⋊C4—82no—
700C4⋊C4—82no—
701C4⋊C4#12114yes—
702C4⋊C4#12118yes—
703C4⋊C42−1+412yes—
704C22⋊C4—24no—
705C22⋊C4—44no—
706C22⋊C4—44no—
707C22⋊C4—42no—
708C22⋊C4—42no—
709C22⋊C4—42no—
710C22⋊C4—44no—
711C22⋊C4—44no—
712C22⋊C4—44no—
713C22⋊C4—44no—
714C22⋊C4—44no—
715C22⋊C4—44no—
716C22⋊C4—82no—
717C22⋊C4—82no—
718C22⋊C4—82no—
719C42—24no—
720C42—24no—
721C42—22no—
722C42—22no—
723C42—22no—
724C42—21no—
725C42—22no—
726C42—21no—
727C42—44no—
728C42—42no—
729C42—44no—
730C42—42no—
731C42—42no—
732C42—42no—
733C42—82no—
734C42C22×D412yes—
735C42C22×D414yes—
736C42C2×#4114yes—
737C42C2×#4112yes—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—21no—
744C23—42no—
745C23—42no—
746C23—42no—
747C23—42no—
748C23—42no—
749C23—42no—
750C23—42no—
751C23#57612yes—
752C23C23×D411yescharacteristic
753Q8—28no—
754Q8—28no—
755Q8—22no—
756Q8—22no—
757Q8—48no—
758Q8—41no—
759Q8—41no—
760Q8—41no—
761Q8—41no—
762Q8—41no—
763Q8—41no—
764Q8—164no—
765Q8—162no—
766D4—42no—
767D4—42no—
768D4—42no—
769D4—42no—
770D4—88no—
771D4—84no—
772D4—162no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—21no—
781C2×C4—22no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—22no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—22no—
795C2×C4—48no—
796C2×C4—48no—
797C2×C4—44no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—44no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—42no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—42no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—42no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—42no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—42no—
825C2×C4—41no—
826C2×C4—42no—
827C2×C4—41no—
828C2×C4—42no—
829C2×C4—41no—
830C2×C4—42no—
831C2×C4—41no—
832C2×C4—42no—
833C2×C4—41no—
834C2×C4—164no—
835C2×C4C2×#12114yes—
836C2×C4C2×#12114yes—
837C2×C4C2×#12112yes—
838C2×C4C2×#12112yes—
839C2×C4C2×#13714yes—
840C2×C4C2×#13712yes—
841C2×C4#57512yes—
842C2×C4C23×D411yescharacteristic
843C2×C4C22×#4111yescharacteristic
844C2×C4C2×2−1+411yescharacteristic
845C2×C4C2×2−1+411yescharacteristic
846C2×C4#58511yescharacteristic
847C2×C4#58511yescharacteristic
848C8—24no—
849C8—22no—
850C8—22no—
851C8—41no—
852C8—41no—
853C8—42no—
854C22—22no—
855C22—22no—
856C22—22no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—82no—
862C22—82no—
863C22—82no—
864C22—82no—
865C22—82no—
866C22—82no—
867C22—82no—
868C22C22×#12111yescharacteristic
869C22#348611yescharacteristic
870C22#348711yescharacteristic
871C22C22×#13711yescharacteristic
872C22C2×#57511yescharacteristic
873C22C2×#57611yescharacteristic
874C22#358411yescharacteristic
875C4—24no—
876C4—24no—
877C4—24no—
878C4—22no—
879C4—41no—
880C4—42no—
881C4—41no—
882C4—42no—
883C4—41no—
884C4—42no—
885C4—81no—
886C4—81no—
887C4—82no—
888C4—81no—
889C4—81no—
890C4—81no—
891C4—82no—
892C4—82no—
893C4—81no—
894C4#305614yes—
895C4#348911yescharacteristic
896C4#349711yescharacteristic
897C4#351611yescharacteristic
898C4#351811yescharacteristic
899C2—42no—
900C2—162no—
901C2#3577111yescharacteristic
902C2C2×#305611yescharacteristic
903C2#6045811yescharacteristic
904C2#6184411yescharacteristic
905C2#6184511yescharacteristic
906C2#6189811yescharacteristic
907C2#6190911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2856C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×C4×Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3375C2semidirect
2. C2×#2984C2semidirect
4. Q8×C22⋊Q8C2semidirect
5. #29853C2semidirect
7. #28651C2semidirect
8. #28640C2semidirect
9. #28277C2semidirect
10. #28265C2semidirect
11. #25481C2semidirect
12. #25471C2semidirect
13. #25307C2semidirect
14. #25295C2semidirect
15. #24711C2semidirect
16. #24700C2semidirect
18. #24655C2semidirect
19. #23710C2semidirect
20. #23699C2semidirect
21. #22728C2semidirect
22. #22546C2semidirect
23. #22525C2semidirect
189. #446D4semidirect

Maximal subgroups

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

subgroupindex
C2×#33752
C2×#29842
#365802
Q8×C22⋊Q82
#298532
#298422
#286512
#286402
#282772
#282652
#254812
#254712
#253072
#252952
#247112
#247002
#246612
#246552
#237102
#236992
#227282
#225462
#225252