Finite Group Databasebeta

← #6799237

Subgroups — #6799237

Order 512.

1343 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36564C211yesmaximal, characteristic
2C2×#2514C211yesmaximal, characteristic
3#33147C211yesmaximal, characteristic
4#32481C212yesmaximal, complemented
5#32444C212yesmaximal, complemented
6#32244C212yesmaximal, complemented
7#31813C212yesmaximal, complemented
8#29968C211yesmaximal, characteristic
9#29951C211yesmaximal, characteristic
10#29111C211yesmaximal, characteristic
11#29105C211yesmaximal, characteristic
12#29081C212yesmaximal, complemented
13#28124C211yesmaximal, characteristic
14#28121C211yesmaximal, characteristic
15#28059C212yesmaximal, complemented
16#27969C211yesmaximal, characteristic
17#27653C211yesmaximal, characteristic
18#27570C212yesmaximal, complemented
19#27146C212yesmaximal, complemented
20#22629C211yesmaximal, characteristic
21#22078C211yesmaximal, characteristic
22#22050C211yesmaximal, characteristic
23#21581C211yesmaximal, characteristic
24C2×#484C2211yescharacteristic
25C2×#483C2211yescharacteristic
26C2×#451C2211yescharacteristic
27#2857C2211yescharacteristic
28#2857C2211yescharacteristic
29#2857C2211yescharacteristic
30#2586—21no—
31#2586—21no—
32#2567C2211yescharacteristic
33#2551C2211yescharacteristic
34#2549—21no—
35#2549—21no—
36#2514—21no—
37#2514—21no—
38#2514—21no—
39#2514—21no—
40#2514C2212yes—
41#2514C2212yes—
42#2514C2212yes—
43#2514C2212yes—
44#2507—21no—
45#2507C2211yescharacteristic
46#2507C2211yescharacteristic
47#2451C2211yescharacteristic
48#2451C2211yescharacteristic
49#2440—21no—
50C2×#401—21no—
51C2×#400—21no—
52#2369—21no—
53#2369C2211yescharacteristic
54Q8×C4⋊C4C2211yescharacteristic
55#2345—21no—
56C4×C22⋊Q8C2211yescharacteristic
57C4×C22⋊Q8C2211yescharacteristic
58C4×C22⋊Q8C2211yescharacteristic
59C2×#391C2211yescharacteristic
60C2×#391C2211yescharacteristic
61C2×#391C2211yescharacteristic
62C2×#389C2211yescharacteristic
63C2×#387—21no—
64C2×#383—21no—
65C2×#382C2211yescharacteristic
66C2×C4×C4⋊C4C2211yescharacteristic
67C2×C4×C4⋊C4C2211yescharacteristic
68#2101C2212yes—
69#2101C2212yes—
70#2100C2212yes—
71#2096C2212yes—
72#2088C2212yes—
73#2088C2212yes—
74#2085C2212yes—
75#2074C2212yes—
76#2072C2212yes—
77#2072C2212yes—
78#2068C2212yes—
79#2066C2212yes—
80#2066C2212yes—
81#2066C2212yes—
82#2058C2212yes—
83#2056C2212yes—
84#2056C2212yes—
85#2024C2212yes—
86#2024C2212yes—
87#2024C2212yes—
88#1993C2212yes—
89#1988C2212yes—
90#1971C2212yes—
91#1949C2212yes—
92#1948C2212yes—
93#1941C2212yes—
94#1939C2212yes—
95#1935C2212yes—
96#1935C2212yes—
97#1935C2212yes—
98#1933C2212yes—
99#1933C2212yes—
100#1933C2212yes—
101#1928C2212yes—
102#1927C2212yes—
103#1927C2212yes—
104#1927C2212yes—
105#1919C2212yes—
106#1919C2212yes—
107#1919C2212yes—
108#1918C2212yes—
109#1917C2212yes—
110#1917C2212yes—
111#1878C2212yes—
112#1878C2212yes—
113#1878C2212yes—
114#1872C2211yescharacteristic
115#1865C2212yes—
116#1853C2211yescharacteristic
117#1853C2211yescharacteristic
118#1853C2211yescharacteristic
119#1836C2212yes—
120#1824C2211yescharacteristic
121#1824C2211yescharacteristic
122#1824C2211yescharacteristic
123#1823C2211yescharacteristic
124#1823C2211yescharacteristic
125#1823C2211yescharacteristic
126#1805C2212yes—
127#1797C2211yescharacteristic
128#1797C2211yescharacteristic
129#1797C2211yescharacteristic
130#1787C2211yescharacteristic
131#1787C2211yescharacteristic
132#1787C2211yescharacteristic
133#1776C2212yes—
134#1770C2212yes—
135#1763C2212yes—
136#1749C2211yescharacteristic
137#1749C2211yescharacteristic
138C4×C22⋊C8C2211yescharacteristic
139C23×Q8C2311yescharacteristic
140C22×Q16C2312yes—
141C2×C4⋊Q8—21no—
142C2×C4⋊Q8C2311yescharacteristic
143C2×C4⋊Q8C2311yescharacteristic
144C2×C4⋊Q8C2311yescharacteristic
145C2×C22⋊Q8—21no—
146C2×C22⋊Q8—21no—
147C2×C22⋊Q8—21no—
148C2×C22⋊Q8C2311yescharacteristic
149C2×C4×Q8C2311yescharacteristic
150C2×C4×Q8C2311yescharacteristic
151C2×C4×Q8C2311yescharacteristic
152C22×C4⋊C4—21no—
153C22×C4⋊C4D411yescharacteristic
154C22×C4⋊C4D411yescharacteristic
155C22×C4⋊C4C2311yescharacteristic
156C22×C4⋊C4C2311yescharacteristic
157C22×C4⋊C4C2311yescharacteristic
158C22×C42—21no—
159C22×C42C2311yescharacteristic
160C22×C42C2311yescharacteristic
161C22×C42C2311yescharacteristic
162#484—24no—
163#483—24no—
164#451—24no—
165C2×#107C2312yes—
166C2×#106C2312yes—
167C2×#106C2312yes—
168C2×#106C2312yes—
169C2×#106C2312yes—
170C2×C4⋊C8C2312yes—
171C2×C4⋊C8C2312yes—
172C2×C4⋊C8C2312yes—
173C2×#103C2312yes—
174C2×#103C2312yes—
175C2×#103C2312yes—
176C2×#103C2312yes—
177C2×#103C2312yes—
178C2×#103C2312yes—
179C2×#103C2312yes—
180C2×#103C2312yes—
181C2×#103C2312yes—
182C2×#103C2312yes—
183C2×C22⋊C8C2311yescharacteristic
184C2×C22⋊C8C2311yescharacteristic
185C2×C22⋊C8C2311yescharacteristic
186C2×C22⋊C8C2311yescharacteristic
187C2×#97C2312yes—
188C2×#97C2312yes—
189C2×C4×C8C2312yes—
190#401—22no—
191#401—22no—
192#401—22no—
193#401—22no—
194#400—22no—
195#400—22no—
196#400—22no—
197#400—22no—
198#398—21no—
199#398—21no—
200#398—21no—
201#398—21no—
202#398—21no—
203#398—21no—
204#395—21no—
205#395—21no—
206#395—21no—
207#395—21no—
208#395—21no—
209#395—21no—
210#391—21no—
211#391—21no—
212#391—21no—
213#391—21no—
214#391—21no—
215#391—21no—
216#391—21no—
217#391—21no—
218#391—21no—
219#391—21no—
220#391—21no—
221#391—21no—
222#391—21no—
223#391C2311yescharacteristic
224#391C2311yescharacteristic
225#391C2311yescharacteristic
226#391C2312yes—
227#391C2312yes—
228#391C2312yes—
229#391C2312yes—
230#391C2312yes—
231#391C2312yes—
232#389—21no—
233#389—21no—
234#389—21no—
235#389—21no—
236#389—21no—
237#389—21no—
238#389—21no—
239#389—21no—
240#389—21no—
241#389—21no—
242#389—21no—
243#389—21no—
244#389—21no—
245#389C2312yes—
246#389C2311yescharacteristic
247#389C2311yescharacteristic
248#389C2311yescharacteristic
249#389C2311yescharacteristic
250#389C2311yescharacteristic
251#389C2311yescharacteristic
252#389C2311yescharacteristic
253#389C2312yes—
254#389C2311yescharacteristic
255#389C2311yescharacteristic
256#387—21no—
257#387—21no—
258#387—21no—
259#387—21no—
260#387—22no—
261#387—22no—
262#387—22no—
263#387—22no—
264#387—21no—
265#387—21no—
266#387—21no—
267#385—21no—
268#385—21no—
269#385—21no—
270#384—21no—
271#384C2311yescharacteristic
272#384C2311yescharacteristic
273#384C2311yescharacteristic
274#383—22no—
275#383—22no—
276#383—22no—
277#383—22no—
278#382—21no—
279#382—21no—
280#382C2312yes—
281#382C2312yes—
282#380—21no—
283#380—21no—
284#380—21no—
285#380C2311yescharacteristic
286#380C2311yescharacteristic
287#380C2311yescharacteristic
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⋊C4—21no—
295C4×C4⋊C4D411yescharacteristic
296C4×C4⋊C4D411yescharacteristic
297C4×C4⋊C4D411yescharacteristic
298C4×C4⋊C4D411yescharacteristic
299C4×C4⋊C4C2311yescharacteristic
300C4×C4⋊C4C2311yescharacteristic
301C4×C4⋊C4C2311yescharacteristic
302C4×C4⋊C4C2312yes—
303C4×C4⋊C4C2312yes—
304C4×C4⋊C4C2311yescharacteristic
305C4×C4⋊C4C2311yescharacteristic
306C4×C4⋊C4C2311yescharacteristic
307C4×C4⋊C4C2311yescharacteristic
308C4×C22⋊C4—21no—
309C4×C22⋊C4—21no—
310C4×C22⋊C4—21no—
311C2×#95—21no—
312C2×#95—21no—
313C2×#95—21no—
314C2×#95—21no—
315C2×#95—21no—
316C2×#95—21no—
317C2×#95—21no—
318C2×#95—21no—
319C2×#95—21no—
320C2×#95—21no—
321C2×#95D411yescharacteristic
322C2×#95D411yescharacteristic
323#340C2312yes—
324#340C2312yes—
325#340C2312yes—
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#336C2312yes—
340#336C2312yes—
341#336C2312yes—
342#336C2312yes—
343#336C2312yes—
344#336C2312yes—
345C22×Q8—21no—
346C22×Q8—21no—
347C22×Q8—21no—
348C22×Q8—21no—
349C22×Q8—22no—
350C22×Q8—22no—
351C22×Q8—42no—
352C22×Q8—42no—
353C22×Q8C2412yes—
354C22×Q8C2411yescharacteristic
355C23×C4—21no—
356C23×C4—21no—
357C23×C4—21no—
358C23×C4—21no—
359C23×C4C2×D411yescharacteristic
360C23×C4C2×D411yescharacteristic
361C23×C4C2×D411yescharacteristic
362C23×C4C2×D411yescharacteristic
363C23×C4C2×D411yescharacteristic
364C23×C4C2×D411yescharacteristic
365C23×C4C2411yescharacteristic
366C2×Q16—24no—
367C2×Q16—42no—
368C2×Q16—42no—
369C22×C8C2412yes—
370C22×C8C2412yes—
371C22×C8C2412yes—
372C22×C8C2412yes—
373C4⋊Q8—42no—
374C4⋊Q8—42no—
375C4⋊Q8—42no—
376C4⋊Q8—44no—
377C22⋊Q8—22no—
378C22⋊Q8—82no—
379C22⋊Q8—82no—
380C22⋊Q8—82no—
381C22⋊Q8#4114yes—
382C4×Q8—42no—
383C4×Q8—42no—
384C4×Q8—42no—
385C2×C4⋊C4—24no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
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—42no—
418C2×C4⋊C4—42no—
419C2×C4⋊C4—44no—
420C2×C4⋊C4C2×D411yescharacteristic
421C2×C4⋊C4C2×D411yescharacteristic
422C2×C4⋊C4C2×D411yescharacteristic
423C2×C4⋊C4C2×D411yescharacteristic
424C2×C4⋊C4C2×D411yescharacteristic
425C2×C4⋊C4C2×D411yescharacteristic
426C2×C4⋊C4C2×D411yescharacteristic
427C2×C4⋊C4C2×D411yescharacteristic
428C2×C4⋊C4C2412yes—
429C2×C4⋊C4C2412yes—
430C2×C4⋊C4C2412yes—
431C2×C4⋊C4C2411yescharacteristic
432C2×C4⋊C4C2411yescharacteristic
433C2×C4⋊C4C2411yescharacteristic
434C2×C4⋊C4C2411yescharacteristic
435C2×C4⋊C4C2411yescharacteristic
436C2×C4⋊C4C2411yescharacteristic
437C2×C4⋊C4C2411yescharacteristic
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C42—21no—
443C2×C42—21no—
444C2×C42—22no—
445C2×C42—22no—
446C2×C42—21no—
447C2×C42—21no—
448C2×C42—21no—
449C2×C42—21no—
450C2×C42—42no—
451C2×C42—42no—
452C2×C42—42no—
453C2×C42—44no—
454C2×C42C2×D411yescharacteristic
455C2×C42C2×D411yescharacteristic
456C2×C42C2×D411yescharacteristic
457C2×C42C2×D411yescharacteristic
458C2×C42C2×D411yescharacteristic
459C2×C42C2×D411yescharacteristic
460C2×C42C2411yescharacteristic
461C2×C42C2411yescharacteristic
462C2×C42C2411yescharacteristic
463C2×C42C2411yescharacteristic
464C2×C42C2411yescharacteristic
465C2×C42C2411yescharacteristic
466#107—24no—
467#106—24no—
468#106—42no—
469#106—42no—
470#106—42no—
471C4⋊C8—42no—
472C4⋊C8—42no—
473C4⋊C8—42no—
474#103—24no—
475#103—24no—
476#103—24no—
477#103—42no—
478#103—42no—
479#103—42no—
480#103—42no—
481#103—42no—
482#103—42no—
483#103—42no—
484C22⋊C8—22no—
485C22⋊C8—22no—
486C22⋊C8—22no—
487C22⋊C8—22no—
488#97—42no—
489#97—42no—
490C4×C8—42no—
491#95—22no—
492#95—22no—
493#95—22no—
494#95—22no—
495#95—22no—
496#95—22no—
497#95—22no—
498#95—22no—
499#95—22no—
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—21no—
512#95—21no—
513#95—21no—
514#95—21no—
515#95—21no—
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#95C2×D411yescharacteristic
533#95C2×D411yescharacteristic
534#95C2×D411yescharacteristic
535#95C2×D411yescharacteristic
536#95C2×D411yescharacteristic
537#95C2×D411yescharacteristic
538#95C2×D411yescharacteristic
539#95C2×D411yescharacteristic
540C24C22×D411yescharacteristic
541C2×Q8—21no—
542C2×Q8—22no—
543C2×Q8—22no—
544C2×Q8—22no—
545C2×Q8—22no—
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8—22no—
549C2×Q8—22no—
550C2×Q8—42no—
551C2×Q8—42no—
552C2×Q8—42no—
553C2×Q8—42no—
554C2×Q8—42no—
555C2×Q8—42no—
556C2×Q8—81no—
557C2×Q8—81no—
558C2×Q8—81no—
559C2×Q8—81no—
560C2×Q8—81no—
561C2×Q8—81no—
562C2×Q8—84no—
563C2×Q8—84no—
564C2×Q8C2×#4112yes—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—41no—
586C22×C4—41no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—41no—
592C22×C4—41no—
593C22×C4—41no—
594C22×C4—41no—
595C22×C4—41no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4#13714yes—
609C22×C4C22×D411yescharacteristic
610C22×C4C22×D411yescharacteristic
611C22×C4C22×D411yescharacteristic
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×C4C2×#4112yes—
623C22×C42−1+412yes—
624C22×C4C2511yescharacteristic
625Q16—84no—
626C2×C8—22no—
627C2×C8—22no—
628C2×C8—22no—
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—
638C4⋊C4—24no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—22no—
642C4⋊C4—22no—
643C4⋊C4—22no—
644C4⋊C4—22no—
645C4⋊C4—21no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—22no—
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—41no—
659C4⋊C4—41no—
660C4⋊C4—42no—
661C4⋊C4—42no—
662C4⋊C4—42no—
663C4⋊C4—42no—
664C4⋊C4—42no—
665C4⋊C4—42no—
666C4⋊C4—42no—
667C4⋊C4—44no—
668C4⋊C4—44no—
669C4⋊C4—42no—
670C4⋊C4—81no—
671C4⋊C4—81no—
672C4⋊C4—81no—
673C4⋊C4—81no—
674C4⋊C4—81no—
675C4⋊C4—81no—
676C4⋊C4—81no—
677C4⋊C4—81no—
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—
687C22⋊C4—24no—
688C22⋊C4—42no—
689C22⋊C4—42no—
690C22⋊C4—42no—
691C42—22no—
692C42—22no—
693C42—22no—
694C42—22no—
695C42—22no—
696C42—22no—
697C42—41no—
698C42—41no—
699C42—41no—
700C42—41no—
701C42—41no—
702C42—41no—
703C42—44no—
704C42—42no—
705C42—42no—
706C42—44no—
707C42—81no—
708C42—81no—
709C42—81no—
710C42—81no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23#54812yes—
716C23C2×#13712yes—
717C23#57712yes—
718C23C23×D411yescharacteristic
719Q8—24no—
720Q8—42no—
721Q8—42no—
722Q8—42no—
723Q8—42no—
724Q8—42no—
725Q8—84no—
726Q8—162no—
727Q8—162no—
728Q8—162no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
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—44no—
769C2×C4—44no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—42no—
778C2×C4—41no—
779C2×C4—42no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—42no—
804C2×C4—82no—
805C2×C4—82no—
806C2×C4—82no—
807C2×C4—82no—
808C2×C4—84no—
809C2×C4—84no—
810C2×C4—84no—
811C2×C4—84no—
812C2×C4#54812yes—
813C2×C4C2×#13712yes—
814C2×C4C2×#13712yes—
815C2×C4#57512yes—
816C2×C4C22×#4111yescharacteristic
817C2×C4C2×2−1+411yescharacteristic
818C2×C4#58512yes—
819C2×C4#58512yes—
820C8—42no—
821C8—42no—
822C8—42no—
823C8—42no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—22no—
828C22—22no—
829C22—22no—
830C22#336914yes—
831C22#344911yescharacteristic
832C22C2×#54811yescharacteristic
833C22#348511yescharacteristic
834C22C22×#13711yescharacteristic
835C22C2×#57511yescharacteristic
836C22C2×#57711yescharacteristic
837C22#358611yescharacteristic
838C4—22no—
839C4—22no—
840C4—22no—
841C4—22no—
842C4—41no—
843C4—41no—
844C4—41no—
845C4—41no—
846C4—41no—
847C4—41no—
848C4—41no—
849C4—41no—
850C4—41no—
851C4—42no—
852C4—42no—
853C4—82no—
854C4—81no—
855C4—81no—
856C4—81no—
857C4—81no—
858C4—81no—
859C4—81no—
860C4—82no—
861C4—82no—
862C4—82no—
863C4#352112yes—
864C4#356412yes—
865C2—24no—
866C2#3911711yescharacteristic
867C2#6096011yescharacteristic
868C2#6098211yescharacteristic
869C2C2×#336911yescharacteristic
870C2#6132311yescharacteristic
871C2#6172311yescharacteristic
872C2#6172911yescharacteristic
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
4. #32481C2semidirect
5. #32444C2semidirect
6. #32244C2semidirect
7. #31813C2semidirect
12. #29081C2semidirect
15. #28059C2semidirect
18. #27570C2semidirect
19. #27146C2semidirect

Maximal subgroups

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

subgroupindex
#365642
C2×#25142
#331472
#324812
#324442
#322442
#318132
#299682
#299512
#291112
#291052
#290812
#281242
#281212
#280592
#279692
#276532
#275702
#271462
#226292
#220782
#220502
#215812