Finite Group Databasebeta

← #6627672

Subgroups — #6627672

Order 512.

1455 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36608C211yesmaximal, characteristic
2C4×Q82C211yesmaximal, characteristic
3#33202C211yesmaximal, characteristic
4#33033C211yesmaximal, characteristic
5#33027C211yesmaximal, characteristic
6#29355C211yesmaximal, characteristic
7#29347C211yesmaximal, characteristic
8#29276C211yesmaximal, characteristic
9#29273C211yesmaximal, characteristic
10#29224C211yesmaximal, characteristic
11#28283C211yesmaximal, characteristic
12#27570C212yesmaximal
13#27551C212yesmaximal
14#27146C212yesmaximal
15#27131C212yesmaximal
16#25004C212yesmaximal
17#24345C212yesmaximal
18#23077C212yesmaximal
19#22823C211yesmaximal, characteristic
20#22779C212yesmaximal
21#21616C211yesmaximal, characteristic
22C4×#475C211yesmaximal, characteristic
23#21506C211yesmaximal, characteristic
24C2×Q82C2211yescharacteristic
25C2×#477C2211yescharacteristic
26C2×#475C2211yescharacteristic
27C2×#475C2212yes—
28C2×#462C2211yescharacteristic
29C2×#441C2212yes—
30#2862C2211yescharacteristic
31#2862C2211yescharacteristic
32#2862C2211yescharacteristic
33#2581—21no—
34#2581—21no—
35#2581C2212yes—
36#2514—21no—
37#2514—21no—
38#2514—21no—
39#2514—21no—
40#2514C2212yes—
41#2514C2212yes—
42#2369—21no—
43#2369—21no—
44#2369—21no—
45#2369C2211yescharacteristic
46#2369C2211yescharacteristic
47#2369C2211yescharacteristic
48#2356—21no—
49#2356—21no—
50#2356C2212yes—
51Q8×C4⋊C4—21no—
52Q8×C4⋊C4C2211yescharacteristic
53Q8×C4⋊C4C2211yescharacteristic
54Q8×C4⋊C4C2211yescharacteristic
55Q8×C4⋊C4C2211yescharacteristic
56C4×C4⋊Q8—21no—
57C4×C4⋊Q8—21no—
58C4×C4⋊Q8—21no—
59C4×C4⋊Q8C2211yescharacteristic
60C4×C4⋊Q8C2211yescharacteristic
61C4×C4⋊Q8C2211yescharacteristic
62C4×C4⋊Q8C2211yescharacteristic
63C4×C4⋊Q8C2211yescharacteristic
64C4×C4⋊Q8C2211yescharacteristic
65C42×Q8—21no—
66C42×Q8C2211yescharacteristic
67C42×Q8C2211yescharacteristic
68C42×Q8C2211yescharacteristic
69C42×Q8C2211yescharacteristic
70#2101C2212yes—
71#2101C2212yes—
72#2100C2212yes—
73#2099C2212yes—
74#2072C2212yes—
75#2072C2212yes—
76#2066C2212yes—
77#2066C2212yes—
78#2058C2212yes—
79#2058C2212yes—
80#2024C2212yes—
81#2024C2212yes—
82#1993C2212yes—
83#1988C2211yescharacteristic
84#1988C2211yescharacteristic
85#1988C2211yescharacteristic
86#1987C2211yescharacteristic
87#1987C2211yescharacteristic
88#1987C2211yescharacteristic
89#1985C2212yes—
90#1981C2211yescharacteristic
91#1981C2211yescharacteristic
92#1981C2211yescharacteristic
93#1949C2212yes—
94#1949C2212yes—
95#1948C2211yescharacteristic
96#1948C2211yescharacteristic
97#1948C2211yescharacteristic
98#1935C2212yes—
99#1935C2212yes—
100#1933C2212yes—
101#1933C2212yes—
102#1928C2212yes—
103#1928C2212yes—
104#1927C2212yes—
105#1927C2212yes—
106#1927C2212yes—
107#1920C2212yes—
108#1920C2212yes—
109#1919C2212yes—
110#1919C2212yes—
111#1919C2212yes—
112#1918C2212yes—
113#1917C2212yes—
114#1916C2212yes—
115#1878C2212yes—
116#1878C2212yes—
117#1878C2212yes—
118#1878C2212yes—
119#1878C2212yes—
120#1865C2212yes—
121#1865C2212yes—
122#1842C2211yescharacteristic
123#1836C2212yes—
124#1831C2211yescharacteristic
125#1831C2211yescharacteristic
126#1805C2212yes—
127#1805C2212yes—
128#1803C2211yescharacteristic
129#1803C2212yes—
130#1776C2212yes—
131C4×#106C2212yes—
132#1771C2212yes—
133#1767C2211yescharacteristic
134#1767C2211yescharacteristic
135C4×C4⋊C8C2211yescharacteristic
136#1763C2212yes—
137#1763C2212yes—
138C4×#103C2212yes—
139C22×Q16C2312yes—
140Q82—24no—
141Q82—24no—
142C2×C4⋊Q8—21no—
143C2×C4⋊Q8—21no—
144C2×C4⋊Q8—21no—
145C2×C4⋊Q8C2311yescharacteristic
146C2×C4⋊Q8C2311yescharacteristic
147C2×C4⋊Q8C2311yescharacteristic
148C2×C4⋊Q8C2311yescharacteristic
149C2×C4⋊Q8C2311yescharacteristic
150C2×C4⋊Q8C2311yescharacteristic
151C2×C4×Q8—21no—
152C2×C4×Q8—21no—
153C2×C4×Q8—21no—
154C2×C4×Q8—21no—
155C2×C4×Q8—21no—
156C2×C4×Q8—21no—
157C2×C4×Q8—21no—
158C2×C4×Q8D411yescharacteristic
159C2×C4×Q8D411yescharacteristic
160C2×C4×Q8C2312yes—
161C2×C4×Q8C2311yescharacteristic
162C2×C4×Q8C2311yescharacteristic
163C2×C4×Q8C2311yescharacteristic
164C2×C4×Q8C2311yescharacteristic
165C2×C4×Q8C2311yescharacteristic
166C2×C4×Q8C2311yescharacteristic
167C2×C4×Q8C2311yescharacteristic
168C2×C4×Q8C2311yescharacteristic
169#477—24no—
170#475—28no—
171#475—24no—
172#462—24no—
173#441—28no—
174C2×#107C2312yes—
175C2×#106C2312yes—
176C2×#106C2312yes—
177C2×#106C2312yes—
178C2×#106C2312yes—
179C2×C4⋊C8C2312yes—
180C2×C4⋊C8C2311yescharacteristic
181C2×C4⋊C8C2311yescharacteristic
182C2×C4⋊C8C2311yescharacteristic
183C2×C4⋊C8C2311yescharacteristic
184C2×C4⋊C8C2312yes—
185C2×#103C2312yes—
186C2×#103C2312yes—
187C2×#103C2312yes—
188C2×#103C2312yes—
189C2×#103C2312yes—
190C2×#103C2312yes—
191C2×#103C2312yes—
192C2×#103C2312yes—
193C2×#103C2312yes—
194C2×#103C2312yes—
195C2×#97C2312yes—
196C2×#97C2312yes—
197C2×C4×C8C2312yes—
198#401—22no—
199#401—22no—
200#400—22no—
201#400—22no—
202#400—22no—
203#395—22no—
204#391—21no—
205#391—21no—
206#391—21no—
207#391—21no—
208#391—21no—
209#391—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#391C2312yes—
224#391C2312yes—
225#391C2312yes—
226#391C2312yes—
227#391C2312yes—
228#389—21no—
229#389—21no—
230#389—21no—
231#389—21no—
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#389—21no—
246#389—21no—
247#389C2312yes—
248#389C2312yes—
249#389C2311yescharacteristic
250#389C2311yescharacteristic
251#389C2311yescharacteristic
252#389C2311yescharacteristic
253#389C2311yescharacteristic
254#389C2311yescharacteristic
255#387—22no—
256#387—22no—
257#387—22no—
258#387—22no—
259#387—22no—
260#387—22no—
261#384—21no—
262#384—21no—
263#384—21no—
264#384C2311yescharacteristic
265#384C2311yescharacteristic
266#384C2311yescharacteristic
267#384C2311yescharacteristic
268#383—22no—
269#383—22no—
270#383—22no—
271#382—21no—
272#382—21no—
273#382—21no—
274#382—21no—
275#382C2312yes—
276#382C2312yes—
277C4×C4⋊C4—21no—
278C4×C4⋊C4—21no—
279C4×C4⋊C4—21no—
280C4×C4⋊C4—21no—
281C4×C4⋊C4—21no—
282C4×C4⋊C4—21no—
283C4×C4⋊C4—21no—
284C4×C4⋊C4—21no—
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⋊C4—21no—
295C4×C4⋊C4—21no—
296C4×C4⋊C4—21no—
297C4×C4⋊C4—21no—
298C4×C4⋊C4—21no—
299C4×C4⋊C4D411yescharacteristic
300C4×C4⋊C4D411yescharacteristic
301C4×C4⋊C4D411yescharacteristic
302C4×C4⋊C4D411yescharacteristic
303C4×C4⋊C4D411yescharacteristic
304C4×C4⋊C4D411yescharacteristic
305C4×C4⋊C4C2311yescharacteristic
306C4×C4⋊C4C2311yescharacteristic
307C4×C4⋊C4C2311yescharacteristic
308C4×C4⋊C4C2312yes—
309C4×C4⋊C4C2312yes—
310C4×C4⋊C4C2311yescharacteristic
311C4×C4⋊C4C2311yescharacteristic
312C4×C4⋊C4C2311yescharacteristic
313C4×C4⋊C4C2311yescharacteristic
314C4×C4⋊C4C2311yescharacteristic
315C4×C4⋊C4C2311yescharacteristic
316C4×C4⋊C4C2311yescharacteristic
317C4×C4⋊C4C2311yescharacteristic
318C4×C4⋊C4C2311yescharacteristic
319#376—22no—
320C43—21no—
321C43—21no—
322C43—21no—
323C43C2311yescharacteristic
324C43C2311yescharacteristic
325C43C2311yescharacteristic
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—
348#336C2312yes—
349C22×Q8—21no—
350C22×Q8—21no—
351C22×Q8—21no—
352C22×Q8—21no—
353C22×Q8—21no—
354C22×Q8C2×D411yescharacteristic
355C22×Q8C2412yes—
356C22×Q8C2411yescharacteristic
357C2×Q16—24no—
358C2×Q16—24no—
359C2×Q16—24no—
360C22×C8C2412yes—
361C22×C8C2412yes—
362C22×C8C2412yes—
363C22×C8C2412yes—
364C4⋊Q8—28no—
365C4⋊Q8—28no—
366C4⋊Q8—28no—
367C4⋊Q8—22no—
368C4⋊Q8—22no—
369C4⋊Q8—22no—
370C4⋊Q8—22no—
371C4⋊Q8—22no—
372C4⋊Q8—22no—
373C4⋊Q8—22no—
374C4⋊Q8—22no—
375C4⋊Q8—22no—
376C4⋊Q8—22no—
377C4⋊Q8—22no—
378C4⋊Q8#4114yes—
379C4×Q8—28no—
380C4×Q8—22no—
381C4×Q8—22no—
382C4×Q8—22no—
383C4×Q8—22no—
384C4×Q8—24no—
385C4×Q8—22no—
386C4×Q8—22no—
387C4×Q8—22no—
388C4×Q8—22no—
389C4×Q8—22no—
390C4×Q8—22no—
391C4×Q8—22no—
392C4×Q8—24no—
393C4×Q8—24no—
394C4×Q8—42no—
395C4×Q8—41no—
396C4×Q8—41no—
397C4×Q8—41no—
398C4×Q8—44no—
399C4×Q8—44no—
400C4×Q8—44no—
401C4×Q8—82no—
402C4×Q8—82no—
403C4×Q8—82no—
404C4×Q8#4114yes—
405C4×Q8#4114yes—
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—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4C2×D411yescharacteristic
438C2×C4⋊C4C2×D411yescharacteristic
439C2×C4⋊C4C2×D411yescharacteristic
440C2×C4⋊C4C2×D411yescharacteristic
441C2×C4⋊C4C2×D411yescharacteristic
442C2×C4⋊C4C2×D411yescharacteristic
443C2×C4⋊C4C2×D411yescharacteristic
444C2×C4⋊C4C2×D411yescharacteristic
445C2×C4⋊C4C2×D411yescharacteristic
446C2×C4⋊C4C2411yescharacteristic
447C2×C4⋊C4C2411yescharacteristic
448C2×C4⋊C4C2411yescharacteristic
449C2×C4⋊C4C2412yes—
450C2×C4⋊C4C2412yes—
451C2×C4⋊C4C2412yes—
452C2×C4⋊C4C2411yescharacteristic
453C2×C4⋊C4C2411yescharacteristic
454C2×C4⋊C4C2411yescharacteristic
455C2×C4⋊C4C2411yescharacteristic
456C2×C42—21no—
457C2×C42—21no—
458C2×C42—21no—
459C2×C42—21no—
460C2×C42—21no—
461C2×C42—21no—
462C2×C42—21no—
463C2×C42—21no—
464C2×C42—21no—
465C2×C42—21no—
466C2×C42—22no—
467C2×C42—22no—
468C2×C42—21no—
469C2×C42—21no—
470C2×C42—21no—
471C2×C42—22no—
472C2×C42—21no—
473C2×C42—21no—
474C2×C42—21no—
475C2×C42C2×D411yescharacteristic
476C2×C42C2×D411yescharacteristic
477C2×C42C2×D411yescharacteristic
478C2×C42C2×D411yescharacteristic
479C2×C42C2×D411yescharacteristic
480C2×C42C2×D411yescharacteristic
481C2×C42C2×D411yescharacteristic
482C2×C42C2×D411yescharacteristic
483C2×C42C2×D411yescharacteristic
484C2×C42C2×D411yescharacteristic
485C2×C42C2×D411yescharacteristic
486C2×C42C2×D411yescharacteristic
487C2×C42C2411yescharacteristic
488C2×C42C2411yescharacteristic
489C2×C42C2411yescharacteristic
490C2×C42C2411yescharacteristic
491C2×C42C2411yescharacteristic
492C2×C42C2411yescharacteristic
493C2×C42C2411yescharacteristic
494#107—24no—
495#106—24no—
496#106—24no—
497#106—24no—
498#106—24no—
499C4⋊C8—22no—
500C4⋊C8—24no—
501C4⋊C8—22no—
502C4⋊C8—22no—
503C4⋊C8—22no—
504C4⋊C8—42no—
505#103—24no—
506#103—24no—
507#103—24no—
508#103—24no—
509#103—24no—
510#103—24no—
511#103—24no—
512#103—42no—
513#103—42no—
514#103—42no—
515#97—24no—
516#97—42no—
517C4×C8—42no—
518#95—22no—
519#95—22no—
520#95—22no—
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—22no—
537#95—22no—
538#95—22no—
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#95—22no—
548#95—22no—
549#95—22no—
550#95—22no—
551#95C2×D411yescharacteristic
552#95C2×D411yescharacteristic
553#95C2×D411yescharacteristic
554#95C2×D411yescharacteristic
555#95C2×D411yescharacteristic
556#95C2×D411yescharacteristic
557C2×Q8—24no—
558C2×Q8—24no—
559C2×Q8—22no—
560C2×Q8—24no—
561C2×Q8—22no—
562C2×Q8—22no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—22no—
567C2×Q8—22no—
568C2×Q8—22no—
569C2×Q8—22no—
570C2×Q8—22no—
571C2×Q8—22no—
572C2×Q8—42no—
573C2×Q8—42no—
574C2×Q8—42no—
575C2×Q8—42no—
576C2×Q8—42no—
577C2×Q8—42no—
578C2×Q8—81no—
579C2×Q8—81no—
580C2×Q8—81no—
581C2×Q8—81no—
582C2×Q8—81no—
583C2×Q8—81no—
584C2×Q8C2×#4112yes—
585C2×Q8C2×#4112yes—
586C2×Q82−1+412yes—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4C22×D411yescharacteristic
600C22×C4C22×D411yescharacteristic
601C22×C4C22×D411yescharacteristic
602C22×C4C22×D411yescharacteristic
603C22×C4C22×D411yescharacteristic
604C22×C4C22×D411yescharacteristic
605C22×C4C22×D411yescharacteristic
606C22×C4C22×D411yescharacteristic
607C22×C4C22×D411yescharacteristic
608C22×C4C22×D411yescharacteristic
609C22×C4C22×D411yescharacteristic
610C22×C4C22×D411yescharacteristic
611C22×C4C22×D411yescharacteristic
612C22×C4C22×D411yescharacteristic
613C22×C4C2511yescharacteristic
614Q16—48no—
615C2×C8—22no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—22no—
620C2×C8—22no—
621C2×C8—22no—
622C2×C8—22no—
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—22no—
627C4⋊C4—24no—
628C4⋊C4—24no—
629C4⋊C4—24no—
630C4⋊C4—24no—
631C4⋊C4—24no—
632C4⋊C4—24no—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—24no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—22no—
653C4⋊C4—22no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—41no—
658C4⋊C4—41no—
659C4⋊C4—42no—
660C4⋊C4—42no—
661C4⋊C4—42no—
662C4⋊C4—42no—
663C4⋊C4—42no—
664C4⋊C4—42no—
665C4⋊C4—44no—
666C4⋊C4—42no—
667C4⋊C4—42no—
668C4⋊C4—42no—
669C4⋊C4—42no—
670C4⋊C4—42no—
671C4⋊C4—44no—
672C4⋊C4—42no—
673C4⋊C4—44no—
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⋊C4C2×#4112yes—
684C4⋊C4C2×#4112yes—
685C4⋊C4C2×#4112yes—
686C4⋊C4C2×#4112yes—
687C42—24no—
688C42—24no—
689C42—24no—
690C42—24no—
691C42—22no—
692C42—22no—
693C42—22no—
694C42—22no—
695C42—22no—
696C42—22no—
697C42—21no—
698C42—21no—
699C42—21no—
700C42—21no—
701C42—21no—
702C42—21no—
703C42—21no—
704C42—21no—
705C42—21no—
706C42—21no—
707C42—41no—
708C42—41no—
709C42—41no—
710C42—41no—
711C42—41no—
712C42—42no—
713C42—42no—
714C42—42no—
715C42—42no—
716C42—42no—
717C42—44no—
718C42—44no—
719C42—44no—
720C42—42no—
721C42—42no—
722C42—42no—
723C42—42no—
724C42—81no—
725C42—81no—
726C42—81no—
727C42#13714yes—
728C42C2×#4112yes—
729C42C2×#4112yes—
730C42C2×#4112yes—
731C422−1+412yes—
732C23C23×D411yescharacteristic
733Q8—28no—
734Q8—22no—
735Q8—22no—
736Q8—22no—
737Q8—42no—
738Q8—42no—
739Q8—42no—
740Q8—42no—
741Q8—84no—
742Q8—84no—
743Q8—84no—
744Q8—84no—
745Q8—84no—
746Q8#55614yes—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—22no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—22no—
754C2×C4—21no—
755C2×C4—22no—
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—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—42no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—42no—
816C2×C4#52512yes—
817C2×C4#52512yes—
818C2×C4#54812yes—
819C2×C4#54812yes—
820C2×C4C2×#13712yes—
821C2×C4C2×#13712yes—
822C2×C4C2×#13712yes—
823C2×C4#57512yes—
824C2×C4#57712yes—
825C2×C4C22×#4111yescharacteristic
826C2×C4C22×#4111yescharacteristic
827C2×C4C22×#4111yescharacteristic
828C2×C4C2×2−1+411yescharacteristic
829C2×C4C2×2−1+411yescharacteristic
830C2×C4#58511yescharacteristic
831C8—42no—
832C8—42no—
833C8—42no—
834C8—42no—
835C22C2×#52511yescharacteristic
836C22C2×#54811yescharacteristic
837C22#348911yescharacteristic
838C22C22×#13711yescharacteristic
839C22C2×#57511yescharacteristic
840C22C2×#57711yescharacteristic
841C22#358611yescharacteristic
842C4—22no—
843C4—22no—
844C4—22no—
845C4—22no—
846C4—22no—
847C4—22no—
848C4—24no—
849C4—42no—
850C4—41no—
851C4—41no—
852C4—41no—
853C4—41no—
854C4—42no—
855C4—42no—
856C4—42no—
857C4—41no—
858C4—41no—
859C4—41no—
860C4—82no—
861C4—82no—
862C4—82no—
863C4—81no—
864C4—81no—
865C4—81no—
866C4—82no—
867C4#336914yes—
868C4C2×#55611yescharacteristic
869C4#348011yescharacteristic
870C4#350711yescharacteristic
871C4#352311yescharacteristic
872C2#3657911yescharacteristic
873C2#6056011yescharacteristic
874C2#6059111yescharacteristic
875C2C2×#336911yescharacteristic
876C2#6132311yescharacteristic
877C2#6211311yescharacteristic
878C2#6213511yescharacteristic
subgroupG/H
center, socle, prime radicalC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
#366082
C4×Q822
#332022
#330332
#330272
#293552
#293472
#292762
#292732
#292242
#282832
#275702
#275512
#271462
#271312
#250042
#243452
#230772
#228232
#227792
#216162
C4×#4752
#215062