Finite Group Databasebeta

← #6624359

Subgroups — #6624359

Order 512.

1521 conjugacy classes of subgroups.

The subgroup lattice has 877 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36571C211yesmaximal, characteristic
2C2×#2356C211yesmaximal, characteristic
3#33151C211yesmaximal, characteristic
4#33149C211yesmaximal, characteristic
5#32960C211yesmaximal, characteristic
6#29112C211yesmaximal, characteristic
7#29111C211yesmaximal, characteristic
8#28124C211yesmaximal, characteristic
9#28121C211yesmaximal, characteristic
10#27964C211yesmaximal, characteristic
11#27653C211yesmaximal, characteristic
12#27453C212yesmaximal, complemented
13#27448C212yesmaximal, complemented
14#27389C212yesmaximal, complemented
15#27382C212yesmaximal, complemented
16#26031C212yesmaximal, complemented
17#24687C212yesmaximal, complemented
18#23070C212yesmaximal, complemented
19#22761C212yesmaximal, complemented
20#22629C211yesmaximal, characteristic
21#21581C211yesmaximal, characteristic
22#21579C211yesmaximal, characteristic
23C4×#451C211yesmaximal, characteristic
24C22×C4×Q8C2211yescharacteristic
25C2×#484C2211yescharacteristic
26C2×#483C2211yescharacteristic
27C2×#479C2212yes—
28C2×#451C2211yescharacteristic
29C2×C4×Q16C2212yes—
30#2857C2211yescharacteristic
31#2851C2211yescharacteristic
32#2851C2211yescharacteristic
33#2588—21no—
34#2585—21no—
35#2583—21no—
36#2565C2211yescharacteristic
37#2550C2211yescharacteristic
38#2520—21no—
39#2509C2211yescharacteristic
40#2506C2211yescharacteristic
41#2505—21no—
42#2473—21no—
43#2453C2211yescharacteristic
44#2451C2211yescharacteristic
45#2370—21no—
46#2370C2211yescharacteristic
47#2368—21no—
48#2356—21no—
49#2356—21no—
50#2356—21no—
51#2356—21no—
52#2356C2212yes—
53#2356C2212yes—
54#2356C2212yes—
55#2356C2212yes—
56#2351C2211yescharacteristic
57C4×C22⋊Q8C2211yescharacteristic
58C4×C22⋊Q8C2211yescharacteristic
59C4×C22⋊Q8C2211yescharacteristic
60C2×#391C2211yescharacteristic
61C2×#391C2211yescharacteristic
62C2×#387—21no—
63C2×#387—21no—
64C2×#383—21no—
65C2×#382C2211yescharacteristic
66C2×C4×C4⋊C4C2211yescharacteristic
67C2×C4×C4⋊C4C2211yescharacteristic
68C2×C4×C4⋊C4C2211yescharacteristic
69C2×#376—21no—
70#2101C2212yes—
71#2101C2212yes—
72#2085C2212yes—
73#2074C2212yes—
74#2074C2212yes—
75#2072C2212yes—
76#2068C2212yes—
77#2066C2212yes—
78#2056C2212yes—
79#2056C2212yes—
80#2026C2212yes—
81#2024C2212yes—
82#1991C2212yes—
83#1989C2212yes—
84#1987C2212yes—
85#1949C2212yes—
86#1949C2212yes—
87#1947C2212yes—
88#1939C2212yes—
89#1935C2212yes—
90#1935C2212yes—
91#1935C2212yes—
92#1935C2212yes—
93#1928C2212yes—
94#1928C2212yes—
95#1927C2212yes—
96#1927C2212yes—
97#1921C2212yes—
98#1921C2212yes—
99#1921C2212yes—
100#1919C2212yes—
101#1919C2212yes—
102#1918C2212yes—
103#1917C2212yes—
104#1917C2212yes—
105#1878C2212yes—
106#1878C2212yes—
107#1878C2212yes—
108#1872C2211yescharacteristic
109#1865C2212yes—
110#1863C2212yes—
111#1863C2212yes—
112#1853C2211yescharacteristic
113#1852C2211yescharacteristic
114#1852C2211yescharacteristic
115#1835C2212yes—
116#1824C2211yescharacteristic
117#1824C2211yescharacteristic
118#1824C2211yescharacteristic
119#1823C2211yescharacteristic
120#1823C2211yescharacteristic
121#1823C2211yescharacteristic
122#1805C2212yes—
123#1805C2212yes—
124#1797C2211yescharacteristic
125#1797C2211yescharacteristic
126#1797C2211yescharacteristic
127#1787C2211yescharacteristic
128#1787C2211yescharacteristic
129#1787C2211yescharacteristic
130#1776C2212yes—
131#1776C2212yes—
132#1770C2212yes—
133#1763C2212yes—
134#1763C2212yes—
135C4×#103C2212yes—
136#1749C2211yescharacteristic
137#1749C2211yescharacteristic
138C4×C22⋊C8C2211yescharacteristic
139C23×Q8C2311yescharacteristic
140C22×Q16C2312yes—
141C2×C4⋊Q8C2311yescharacteristic
142C2×#125—21no—
143C2×#125C2311yescharacteristic
144C2×#125C2311yescharacteristic
145C2×C22⋊Q8—21no—
146C2×C22⋊Q8C2311yescharacteristic
147C2×C4×Q8—28no—
148C2×C4×Q8—21no—
149C2×C4×Q8—21no—
150C2×C4×Q8C2311yescharacteristic
151C2×C4×Q8C2312yes—
152C2×C4×Q8C2312yes—
153C2×C4×Q8C2311yescharacteristic
154C2×C4×Q8C2311yescharacteristic
155C22×C4⋊C4—21no—
156C22×C4⋊C4D411yescharacteristic
157C22×C4⋊C4D411yescharacteristic
158C22×C4⋊C4C2311yescharacteristic
159C22×C4⋊C4C2311yescharacteristic
160C22×C4⋊C4C2311yescharacteristic
161C22×C42—21no—
162C22×C42—21no—
163C22×C42—21no—
164C22×C42C2311yescharacteristic
165C22×C42C2311yescharacteristic
166C22×C42C2311yescharacteristic
167#484—24no—
168#483—24no—
169#479—28no—
170#451—24no—
171C4×Q16—28no—
172C2×#107C2312yes—
173C2×#107C2312yes—
174C2×#107C2312yes—
175C2×#106C2312yes—
176C2×#106C2312yes—
177C2×C4⋊C8C2312yes—
178C2×C4⋊C8C2312yes—
179C2×C4⋊C8C2312yes—
180C2×#103C2312yes—
181C2×#103C2312yes—
182C2×#103C2312yes—
183C2×#103C2312yes—
184C2×#103C2312yes—
185C2×#103C2312yes—
186C2×#103C2312yes—
187C2×#103C2312yes—
188C2×#103C2312yes—
189C2×#103C2312yes—
190C2×C22⋊C8C2311yescharacteristic
191C2×C22⋊C8C2311yescharacteristic
192C2×C22⋊C8C2311yescharacteristic
193C2×C22⋊C8C2311yescharacteristic
194C2×#97C2312yes—
195C2×#97C2312yes—
196C2×C4×C8C2312yes—
197#400—21no—
198#400—21no—
199#400—21no—
200#400—21no—
201#398—21no—
202#398—21no—
203#398—21no—
204#398—21no—
205#398—21no—
206#398—21no—
207#395—21no—
208#395—21no—
209#391—21no—
210#391—21no—
211#391—21no—
212#391—21no—
213#391—21no—
214#391—21no—
215#391—21no—
216#391C2311yescharacteristic
217#391C2311yescharacteristic
218#391C2312yes—
219#391C2312yes—
220#391C2311yescharacteristic
221#391C2312yes—
222#391C2312yes—
223#389—21no—
224#389—21no—
225#389—21no—
226#389—21no—
227#389—21no—
228#389—21no—
229#389—21no—
230#389C2311yescharacteristic
231#389C2311yescharacteristic
232#389C2311yescharacteristic
233#389C2311yescharacteristic
234#389C2311yescharacteristic
235#389C2311yescharacteristic
236#389C2311yescharacteristic
237#389C2311yescharacteristic
238#389C2311yescharacteristic
239#387—21no—
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—21no—
249#387—21no—
250#387—21no—
251#387—21no—
252#387—21no—
253#387—21no—
254#387—21no—
255#387—21no—
256#387—21no—
257#387—21no—
258#387—21no—
259#387—21no—
260#387—21no—
261#387—21no—
262#385—21no—
263#385—21no—
264#385—21no—
265#385—21no—
266#385—21no—
267#385—21no—
268#385—21no—
269#384C2311yescharacteristic
270#383—22no—
271#383—22no—
272#383—22no—
273#383—22no—
274#382—21no—
275#382—21no—
276#382—21no—
277#382C2311yescharacteristic
278#382C2311yescharacteristic
279#382C2312yes—
280#382C2312yes—
281#380—21no—
282#380C2311yescharacteristic
283#380C2311yescharacteristic
284#380C2311yescharacteristic
285C4×C4⋊C4—21no—
286C4×C4⋊C4—21no—
287C4×C4⋊C4—21no—
288C4×C4⋊C4—21no—
289C4×C4⋊C4—21no—
290C4×C4⋊C4—21no—
291C4×C4⋊C4—21no—
292C4×C4⋊C4—21no—
293C4×C4⋊C4—21no—
294C4×C4⋊C4D411yescharacteristic
295C4×C4⋊C4D411yescharacteristic
296C4×C4⋊C4D411yescharacteristic
297C4×C4⋊C4D411yescharacteristic
298C4×C4⋊C4C2312yes—
299C4×C4⋊C4C2312yes—
300C4×C4⋊C4C2312yes—
301C4×C4⋊C4C2312yes—
302C4×C4⋊C4C2311yescharacteristic
303C4×C4⋊C4C2311yescharacteristic
304C4×C4⋊C4C2311yescharacteristic
305C4×C4⋊C4C2311yescharacteristic
306C4×C4⋊C4C2311yescharacteristic
307C4×C4⋊C4C2311yescharacteristic
308C4×C4⋊C4C2311yescharacteristic
309C4×C22⋊C4—21no—
310C4×C22⋊C4—21no—
311C4×C22⋊C4—21no—
312#376—22no—
313#376—22no—
314#376—22no—
315#376—22no—
316C2×#95—21no—
317C2×#95—21no—
318C2×#95—21no—
319C2×#95—21no—
320C2×#95—21no—
321C2×#95—21no—
322C2×#95—21no—
323C2×#95—21no—
324C2×#95D411yescharacteristic
325C2×#95D411yescharacteristic
326#340C2312yes—
327#340C2312yes—
328#340C2312yes—
329#340C2312yes—
330#340C2312yes—
331#340C2312yes—
332#340C2312yes—
333#340C2312yes—
334#340C2312yes—
335#340C2312yes—
336#340C2312yes—
337#340C2312yes—
338#340C2312yes—
339#340C2312yes—
340#340C2312yes—
341#340C2312yes—
342#336C2312yes—
343#336C2312yes—
344#336C2312yes—
345#336C2312yes—
346#336C2312yes—
347#336C2312yes—
348C22×Q8—24no—
349C22×Q8—21no—
350C22×Q8—21no—
351C22×Q8—22no—
352C22×Q8—22no—
353C22×Q8—42no—
354C22×Q8C2411yescharacteristic
355C22×Q8C2412yes—
356C23×C4—21no—
357C23×C4—21no—
358C23×C4—21no—
359C23×C4—21no—
360C23×C4C2×D411yescharacteristic
361C23×C4C2×D411yescharacteristic
362C23×C4C2×D411yescharacteristic
363C23×C4C2×D411yescharacteristic
364C23×C4C2×D411yescharacteristic
365C23×C4C2×D411yescharacteristic
366C23×C4C2411yescharacteristic
367C2×Q16—24no—
368C2×Q16—24no—
369C2×Q16—42no—
370C22×C8C2412yes—
371C22×C8C2412yes—
372C22×C8C2412yes—
373C22×C8C2412yes—
374C4⋊Q8—42no—
375#125—24no—
376#125—42no—
377#125—44no—
378C22⋊Q8—22no—
379C22⋊Q8—44no—
380C22⋊Q8#4114yes—
381C4×Q8—28no—
382C4×Q8—28no—
383C4×Q8—24no—
384C4×Q8—24no—
385C4×Q8—24no—
386C4×Q8—24no—
387C4×Q8—42no—
388C4×Q8—42no—
389C4×Q8#4118yes—
390C2×C4⋊C4—28no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—24no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
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—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—42no—
422C2×C4⋊C4—42no—
423C2×C4⋊C4C2×D411yescharacteristic
424C2×C4⋊C4C2×D411yescharacteristic
425C2×C4⋊C4C2×D411yescharacteristic
426C2×C4⋊C4C2×D411yescharacteristic
427C2×C4⋊C4C2×D411yescharacteristic
428C2×C4⋊C4C2×D411yescharacteristic
429C2×C4⋊C4C2×D411yescharacteristic
430C2×C4⋊C4C2×D411yescharacteristic
431C2×C4⋊C4C2412yes—
432C2×C4⋊C4C2412yes—
433C2×C4⋊C4C2411yescharacteristic
434C2×C4⋊C4C2411yescharacteristic
435C2×C4⋊C4C2411yescharacteristic
436C2×C4⋊C4C2411yescharacteristic
437C2×C4⋊C4C2411yescharacteristic
438C2×C4⋊C4C2411yescharacteristic
439C2×C4⋊C4C2412yes—
440C2×C4⋊C4C2411yescharacteristic
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C42—28no—
446C2×C42—22no—
447C2×C42—22no—
448C2×C42—24no—
449C2×C42—21no—
450C2×C42—21no—
451C2×C42—22no—
452C2×C42—22no—
453C2×C42—22no—
454C2×C42—22no—
455C2×C42—21no—
456C2×C42—21no—
457C2×C42—21no—
458C2×C42—21no—
459C2×C42—42no—
460C2×C42—42no—
461C2×C42—44no—
462C2×C42—44no—
463C2×C42C2×D411yescharacteristic
464C2×C42C2×D411yescharacteristic
465C2×C42C2×D411yescharacteristic
466C2×C42C2×D411yescharacteristic
467C2×C42C2×D411yescharacteristic
468C2×C42C2×D411yescharacteristic
469C2×C42C2411yescharacteristic
470C2×C42C2411yescharacteristic
471C2×C42C2411yescharacteristic
472C2×C42C2411yescharacteristic
473C2×C42C2411yescharacteristic
474C2×C42C2411yescharacteristic
475#107—24no—
476#107—24no—
477#107—24no—
478#106—24no—
479#106—24no—
480C4⋊C8—24no—
481C4⋊C8—42no—
482C4⋊C8—42no—
483#103—24no—
484#103—24no—
485#103—24no—
486#103—24no—
487#103—24no—
488#103—24no—
489#103—24no—
490#103—42no—
491#103—42no—
492#103—42no—
493C22⋊C8—22no—
494C22⋊C8—22no—
495C22⋊C8—22no—
496C22⋊C8—22no—
497#97—42no—
498#97—42no—
499C4×C8—24no—
500#95—22no—
501#95—22no—
502#95—22no—
503#95—22no—
504#95—22no—
505#95—22no—
506#95—22no—
507#95—22no—
508#95—22no—
509#95—22no—
510#95—22no—
511#95—22no—
512#95—22no—
513#95—22no—
514#95—22no—
515#95—22no—
516#95—21no—
517#95—21no—
518#95—21no—
519#95—21no—
520#95—21no—
521#95—21no—
522#95—21no—
523#95—21no—
524#95—21no—
525#95—21no—
526#95—21no—
527#95—21no—
528#95—21no—
529#95—21no—
530#95—21no—
531#95—21no—
532#95—21no—
533#95—21no—
534#95—21no—
535#95—21no—
536#95—21no—
537#95—21no—
538#95—21no—
539#95—21no—
540#95—21no—
541#95C2×D411yescharacteristic
542#95C2×D411yescharacteristic
543#95C2×D411yescharacteristic
544#95C2×D411yescharacteristic
545#95C2×D411yescharacteristic
546#95C2×D411yescharacteristic
547#95C2×D411yescharacteristic
548#95C2×D411yescharacteristic
549C24C22×D411yescharacteristic
550C2×Q8—24no—
551C2×Q8—22no—
552C2×Q8—21no—
553C2×Q8—22no—
554C2×Q8—22no—
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—22no—
558C2×Q8—22no—
559C2×Q8—48no—
560C2×Q8—48no—
561C2×Q8—42no—
562C2×Q8—42no—
563C2×Q8—42no—
564C2×Q8—81no—
565C2×Q8—81no—
566C2×Q8C2×#4112yes—
567C2×Q8C2×#4114yes—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—24no—
571C22×C4—24no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—41no—
594C22×C4—41no—
595C22×C4—41no—
596C22×C4—41no—
597C22×C4—41no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4—41no—
601C22×C4—41no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4C22×D411yescharacteristic
613C22×C4C22×D411yescharacteristic
614C22×C4C22×D411yescharacteristic
615C22×C4C22×D411yescharacteristic
616C22×C4C22×D411yescharacteristic
617C22×C4C22×D411yescharacteristic
618C22×C4C22×D411yescharacteristic
619C22×C4C22×D411yescharacteristic
620C22×C4C22×D411yescharacteristic
621C22×C4C22×D411yescharacteristic
622C22×C4C22×D411yescharacteristic
623C22×C4C22×D411yescharacteristic
624C22×C4C22×D411yescharacteristic
625C22×C4C2×#4112yes—
626C22×C42−1+412yes—
627C22×C4C2511yescharacteristic
628Q16—48no—
629C2×C8—22no—
630C2×C8—22no—
631C2×C8—22no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—22no—
638C2×C8—22no—
639C2×C8—22no—
640C2×C8—22no—
641C4⋊C4—24no—
642C4⋊C4—28no—
643C4⋊C4—28no—
644C4⋊C4—24no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—21no—
649C4⋊C4—22no—
650C4⋊C4—22no—
651C4⋊C4—22no—
652C4⋊C4—22no—
653C4⋊C4—22no—
654C4⋊C4—22no—
655C4⋊C4—22no—
656C4⋊C4—22no—
657C4⋊C4—22no—
658C4⋊C4—22no—
659C4⋊C4—41no—
660C4⋊C4—41no—
661C4⋊C4—41no—
662C4⋊C4—41no—
663C4⋊C4—41no—
664C4⋊C4—41no—
665C4⋊C4—42no—
666C4⋊C4—42no—
667C4⋊C4—42no—
668C4⋊C4—42no—
669C4⋊C4—42no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4—42no—
673C4⋊C4—42no—
674C4⋊C4—42no—
675C4⋊C4—42no—
676C4⋊C4—42no—
677C4⋊C4—42no—
678C4⋊C4—81no—
679C4⋊C4—81no—
680C4⋊C4—81no—
681C4⋊C4—81no—
682C4⋊C4—81no—
683C4⋊C4—81no—
684C4⋊C4—81no—
685C4⋊C4—81no—
686C4⋊C4C2×#4112yes—
687C4⋊C4C2×#4114yes—
688C22⋊C4—24no—
689C22⋊C4—42no—
690C22⋊C4—42no—
691C22⋊C4—42no—
692C42—28no—
693C42—28no—
694C42—22no—
695C42—22no—
696C42—22no—
697C42—22no—
698C42—22no—
699C42—22no—
700C42—22no—
701C42—41no—
702C42—41no—
703C42—41no—
704C42—41no—
705C42—44no—
706C42—44no—
707C42—44no—
708C42—42no—
709C42—42no—
710C42—44no—
711C42—81no—
712C42—81no—
713C42—81no—
714C42—81no—
715C42C2×#4114yes—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23#54812yes—
721C23#57512yes—
722C23#57812yes—
723C23C23×D411yescharacteristic
724Q8—24no—
725Q8—24no—
726Q8—24no—
727Q8—48no—
728Q8—42no—
729Q8—42no—
730Q8—42no—
731Q8—162no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—44no—
774C2×C4—44no—
775C2×C4—44no—
776C2×C4—44no—
777C2×C4—48no—
778C2×C4—48no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—42no—
782C2×C4—41no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—42no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—42no—
811C2×C4—82no—
812C2×C4—82no—
813C2×C4—84no—
814C2×C4—84no—
815C2×C4#52512yes—
816C2×C4#52512yes—
817C2×C4#54812yes—
818C2×C4#57512yes—
819C2×C4C22×#4111yescharacteristic
820C2×C4C22×#4112yes—
821C2×C4C2×2−1+411yescharacteristic
822C2×C4#58512yes—
823C8—42no—
824C8—42no—
825C8—42no—
826C8—42no—
827C22—22no—
828C22—22no—
829C22—22no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22#337714yes—
834C22C2×#52511yescharacteristic
835C22C2×#54811yescharacteristic
836C22#348511yescharacteristic
837C22C2×#57511yescharacteristic
838C22C2×#57511yescharacteristic
839C22C2×#57811yescharacteristic
840C22#358611yescharacteristic
841C4—22no—
842C4—22no—
843C4—22no—
844C4—22no—
845C4—41no—
846C4—41no—
847C4—41no—
848C4—41no—
849C4—41no—
850C4—41no—
851C4—41no—
852C4—41no—
853C4—44no—
854C4—42no—
855C4—44no—
856C4—42no—
857C4—41no—
858C4—81no—
859C4—81no—
860C4—81no—
861C4—81no—
862C4—81no—
863C4—82no—
864C4—82no—
865C4—81no—
866C4#347512yes—
867C4#349512yes—
868C2—24no—
869C2#3651611yescharacteristic
870C2#6054611yescharacteristic
871C2#6058311yescharacteristic
872C2C2×#337711yescharacteristic
873C2#6132311yescharacteristic
874C2#6171611yescharacteristic
875C2#6173811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24C22×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
12. #27453C2semidirect
13. #27448C2semidirect
14. #27389C2semidirect
15. #27382C2semidirect
16. #26031C2semidirect
17. #24687C2semidirect
18. #23070C2semidirect
19. #22761C2semidirect

Maximal subgroups

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

subgroupindex
#365712
C2×#23562
#331512
#331492
#329602
#291122
#291112
#281242
#281212
#279642
#276532
#274532
#274482
#273892
#273822
#260312
#246872
#230702
#227612
#226292
#215812
#215792
C4×#4512