Finite Group Databasebeta

← #6627686

Subgroups — #6627686

Order 512.

1429 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36608C211yesmaximal, characteristic
2C4×#557C211yesmaximal, characteristic
3#33202C211yesmaximal, characteristic
4#33033C211yesmaximal, characteristic
5#33027C211yesmaximal, characteristic
6#29357C211yesmaximal, characteristic
7#29349C211yesmaximal, characteristic
8#29275C211yesmaximal, characteristic
9#29274C211yesmaximal, characteristic
10#29224C211yesmaximal, characteristic
11#28284C211yesmaximal, characteristic
12#27575C212yesmaximal
13#27562C212yesmaximal
14#27151C212yesmaximal
15#27134C212yesmaximal
16#25005C212yesmaximal
17#24344C212yesmaximal
18#23073C212yesmaximal
19#22823C211yesmaximal, characteristic
20#22779C212yesmaximal
21#21615C211yesmaximal, characteristic
22C4×#477C211yesmaximal, characteristic
23#21506C211yesmaximal, characteristic
24C2×#557C2211yescharacteristic
25C2×#477C2211yescharacteristic
26C2×#477C2212yes—
27C2×#475C2211yescharacteristic
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#2370—21no—
43#2370—21no—
44#2370C2211yescharacteristic
45#2370C2211yescharacteristic
46#2365—21no—
47#2365C2211yescharacteristic
48#2356—21no—
49#2356—21no—
50#2356C2212yes—
51#2355—21no—
52#2355C2211yescharacteristic
53#2351C2211yescharacteristic
54#2351C2211yescharacteristic
55Q8×C4⋊C4C2211yescharacteristic
56C4×C4⋊Q8—21no—
57C4×C4⋊Q8C2211yescharacteristic
58C4×C4⋊Q8C2211yescharacteristic
59C4×C4⋊Q8C2211yescharacteristic
60C4×C4⋊Q8C2211yescharacteristic
61C4×#125—21no—
62C4×#125—21no—
63C4×#125C2211yescharacteristic
64C4×#125C2211yescharacteristic
65C42×Q8—21no—
66C42×Q8C2211yescharacteristic
67C42×Q8C2211yescharacteristic
68C42×Q8C2211yescharacteristic
69C42×Q8C2211yescharacteristic
70#2101C2212yes—
71#2101C2212yes—
72#2101C2212yes—
73#2101C2212yes—
74#2074C2212yes—
75#2074C2212yes—
76#2068C2212yes—
77#2068C2212yes—
78#2059C2212yes—
79#2059C2212yes—
80#2026C2212yes—
81#2026C2212yes—
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#1947C2211yescharacteristic
97#1947C2211yescharacteristic
98#1935C2212yes—
99#1935C2212yes—
100#1933C2212yes—
101#1933C2212yes—
102#1928C2212yes—
103#1928C2212yes—
104#1927C2212yes—
105#1927C2212yes—
106#1927C2212yes—
107#1921C2212yes—
108#1921C2212yes—
109#1920C2212yes—
110#1920C2212yes—
111#1919C2212yes—
112#1918C2212yes—
113#1917C2212yes—
114#1916C2212yes—
115#1878C2212yes—
116#1878C2212yes—
117#1878C2212yes—
118#1878C2212yes—
119#1878C2212yes—
120#1863C2212yes—
121#1863C2212yes—
122#1842C2211yescharacteristic
123#1836C2212yes—
124#1831C2211yescharacteristic
125#1831C2211yescharacteristic
126#1805C2212yes—
127#1805C2212yes—
128#1803C2211yescharacteristic
129#1803C2212yes—
130#1776C2212yes—
131C4×#107C2212yes—
132#1771C2212yes—
133#1767C2211yescharacteristic
134#1767C2211yescharacteristic
135C4×C4⋊C8C2211yescharacteristic
136#1763C2212yes—
137#1763C2212yes—
138C4×#103C2212yes—
139C22×Q16C2312yes—
140#557—24no—
141#557—24no—
142C2×C4⋊Q8—21no—
143C2×C4⋊Q8C2311yescharacteristic
144C2×C4⋊Q8C2311yescharacteristic
145C2×C4⋊Q8C2311yescharacteristic
146C2×C4⋊Q8C2311yescharacteristic
147C2×#125—21no—
148C2×#125—21no—
149C2×#125C2311yescharacteristic
150C2×#125C2311yescharacteristic
151C2×C4×Q8—21no—
152C2×C4×Q8—21no—
153C2×C4×Q8—21no—
154C2×C4×Q8—21no—
155C2×C4×Q8—21no—
156C2×C4×Q8D411yescharacteristic
157C2×C4×Q8D411yescharacteristic
158C2×C4×Q8C2312yes—
159C2×C4×Q8C2311yescharacteristic
160C2×C4×Q8C2311yescharacteristic
161C2×C4×Q8C2311yescharacteristic
162C2×C4×Q8C2311yescharacteristic
163C2×C4×Q8C2311yescharacteristic
164C2×C4×Q8C2311yescharacteristic
165C2×C4×Q8C2311yescharacteristic
166C2×C4×Q8C2311yescharacteristic
167#477—28no—
168#477—24no—
169#475—24no—
170#462—24no—
171#441—28no—
172C2×#107C2312yes—
173C2×#107C2312yes—
174C2×#107C2312yes—
175C2×#106C2312yes—
176C2×#106C2312yes—
177C2×C4⋊C8C2311yescharacteristic
178C2×C4⋊C8C2312yes—
179C2×C4⋊C8C2311yescharacteristic
180C2×C4⋊C8C2311yescharacteristic
181C2×C4⋊C8C2311yescharacteristic
182C2×C4⋊C8C2312yes—
183C2×#103C2312yes—
184C2×#103C2312yes—
185C2×#103C2312yes—
186C2×#103C2312yes—
187C2×#103C2312yes—
188C2×#103C2312yes—
189C2×#103C2312yes—
190C2×#103C2312yes—
191C2×#103C2312yes—
192C2×#103C2312yes—
193C2×#97C2312yes—
194C2×#97C2312yes—
195C2×C4×C8C2312yes—
196#401—22no—
197#401—22no—
198#400—22no—
199#400—22no—
200#400—22no—
201#395—22no—
202#391—21no—
203#391—21no—
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#391C2312yes—
216#391C2312yes—
217#391C2312yes—
218#391C2312yes—
219#391C2312yes—
220#389—21no—
221#389—21no—
222#389—21no—
223#389—21no—
224#389—21no—
225#389—21no—
226#389—21no—
227#389—21no—
228#389—21no—
229#389—21no—
230#389—21no—
231#389—21no—
232#389—21no—
233#389C2311yescharacteristic
234#389C2311yescharacteristic
235#389C2311yescharacteristic
236#389C2311yescharacteristic
237#389C2312yes—
238#389C2312yes—
239#389C2311yescharacteristic
240#389C2311yescharacteristic
241#387—21no—
242#387—21no—
243#387—21no—
244#387—21no—
245#387—22no—
246#387—22no—
247#387—22no—
248#387—22no—
249#387—22no—
250#387—22no—
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#384—21no—
260#384C2311yescharacteristic
261#384C2311yescharacteristic
262#383—22no—
263#383—22no—
264#383—22no—
265#382—21no—
266#382—21no—
267#382—21no—
268#382—21no—
269#382—21no—
270#382—21no—
271#382C2311yescharacteristic
272#382C2311yescharacteristic
273#382C2312yes—
274#382C2312yes—
275C4×C4⋊C4—21no—
276C4×C4⋊C4—21no—
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×Q8C2×D411yescharacteristic
353C22×Q8C2412yes—
354C22×Q8C2411yescharacteristic
355C2×Q16—24no—
356C2×Q16—24no—
357C2×Q16—24no—
358C22×C8C2412yes—
359C22×C8C2412yes—
360C22×C8C2412yes—
361C22×C8C2412yes—
362C4⋊Q8—28no—
363C4⋊Q8—22no—
364C4⋊Q8—22no—
365C4⋊Q8—22no—
366C4⋊Q8—22no—
367C4⋊Q8—22no—
368C4⋊Q8—22no—
369C4⋊Q8—22no—
370C4⋊Q8#4114yes—
371#125—28no—
372#125—28no—
373#125—22no—
374#125—22no—
375#125—22no—
376#125—22no—
377C4×Q8—28no—
378C4×Q8—22no—
379C4×Q8—22no—
380C4×Q8—22no—
381C4×Q8—22no—
382C4×Q8—22no—
383C4×Q8—22no—
384C4×Q8—22no—
385C4×Q8—22no—
386C4×Q8—22no—
387C4×Q8—22no—
388C4×Q8—22no—
389C4×Q8—24no—
390C4×Q8—24no—
391C4×Q8—42no—
392C4×Q8—42no—
393C4×Q8—41no—
394C4×Q8—41no—
395C4×Q8—41no—
396C4×Q8—44no—
397C4×Q8—44no—
398C4×Q8—44no—
399C4×Q8—44no—
400C4×Q8#4114yes—
401C4×Q8#4114yes—
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—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⋊C4C2×D411yescharacteristic
432C2×C4⋊C4C2×D411yescharacteristic
433C2×C4⋊C4C2×D411yescharacteristic
434C2×C4⋊C4C2×D411yescharacteristic
435C2×C4⋊C4C2×D411yescharacteristic
436C2×C4⋊C4C2×D411yescharacteristic
437C2×C4⋊C4C2×D411yescharacteristic
438C2×C4⋊C4C2×D411yescharacteristic
439C2×C4⋊C4C2×D411yescharacteristic
440C2×C4⋊C4C2411yescharacteristic
441C2×C4⋊C4C2411yescharacteristic
442C2×C4⋊C4C2411yescharacteristic
443C2×C4⋊C4C2412yes—
444C2×C4⋊C4C2412yes—
445C2×C4⋊C4C2412yes—
446C2×C4⋊C4C2411yescharacteristic
447C2×C4⋊C4C2411yescharacteristic
448C2×C4⋊C4C2411yescharacteristic
449C2×C4⋊C4C2411yescharacteristic
450C2×C42—21no—
451C2×C42—21no—
452C2×C42—21no—
453C2×C42—21no—
454C2×C42—21no—
455C2×C42—21no—
456C2×C42—21no—
457C2×C42—21no—
458C2×C42—21no—
459C2×C42—22no—
460C2×C42—22no—
461C2×C42—21no—
462C2×C42—21no—
463C2×C42—21no—
464C2×C42—22no—
465C2×C42—21no—
466C2×C42—21no—
467C2×C42—21no—
468C2×C42—21no—
469C2×C42C2×D411yescharacteristic
470C2×C42C2×D411yescharacteristic
471C2×C42C2×D411yescharacteristic
472C2×C42C2×D411yescharacteristic
473C2×C42C2×D411yescharacteristic
474C2×C42C2×D411yescharacteristic
475C2×C42C2×D411yescharacteristic
476C2×C42C2×D411yescharacteristic
477C2×C42C2×D411yescharacteristic
478C2×C42C2×D411yescharacteristic
479C2×C42C2×D411yescharacteristic
480C2×C42C2×D411yescharacteristic
481C2×C42C2411yescharacteristic
482C2×C42C2411yescharacteristic
483C2×C42C2411yescharacteristic
484C2×C42C2411yescharacteristic
485C2×C42C2411yescharacteristic
486C2×C42C2411yescharacteristic
487C2×C42C2411yescharacteristic
488#107—24no—
489#107—24no—
490#107—24no—
491#106—24no—
492#106—24no—
493C4⋊C8—22no—
494C4⋊C8—22no—
495C4⋊C8—24no—
496C4⋊C8—22no—
497C4⋊C8—22no—
498C4⋊C8—42no—
499#103—24no—
500#103—24no—
501#103—24no—
502#103—24no—
503#103—24no—
504#103—24no—
505#103—24no—
506#103—42no—
507#103—42no—
508#103—42no—
509#97—24no—
510#97—42no—
511C4×C8—42no—
512#95—22no—
513#95—22no—
514#95—22no—
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#95—21no—
533#95—21no—
534#95—22no—
535#95—22no—
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#95C2×D411yescharacteristic
550#95C2×D411yescharacteristic
551#95C2×D411yescharacteristic
552#95C2×D411yescharacteristic
553#95C2×D411yescharacteristic
554#95C2×D411yescharacteristic
555C2×Q8—22no—
556C2×Q8—24no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—22no—
561C2×Q8—22no—
562C2×Q8—22no—
563C2×Q8—22no—
564C2×Q8—22no—
565C2×Q8—22no—
566C2×Q8—41no—
567C2×Q8—41no—
568C2×Q8—42no—
569C2×Q8—42no—
570C2×Q8—42no—
571C2×Q8—42no—
572C2×Q8—42no—
573C2×Q8—42no—
574C2×Q8—42no—
575C2×Q8—42no—
576C2×Q8C2×#4112yes—
577C2×Q8C2×#4112yes—
578C2×Q82−1+412yes—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—22no—
591C22×C4C22×D411yescharacteristic
592C22×C4C22×D411yescharacteristic
593C22×C4C22×D411yescharacteristic
594C22×C4C22×D411yescharacteristic
595C22×C4C22×D411yescharacteristic
596C22×C4C22×D411yescharacteristic
597C22×C4C22×D411yescharacteristic
598C22×C4C22×D411yescharacteristic
599C22×C4C22×D411yescharacteristic
600C22×C4C22×D411yescharacteristic
601C22×C4C22×D411yescharacteristic
602C22×C4C22×D411yescharacteristic
603C22×C4C22×D411yescharacteristic
604C22×C4C22×D411yescharacteristic
605C22×C4C2511yescharacteristic
606Q16—48no—
607C2×C8—22no—
608C2×C8—22no—
609C2×C8—22no—
610C2×C8—22no—
611C2×C8—22no—
612C2×C8—22no—
613C2×C8—22no—
614C2×C8—22no—
615C2×C8—22no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—22no—
619C4⋊C4—24no—
620C4⋊C4—24no—
621C4⋊C4—24no—
622C4⋊C4—24no—
623C4⋊C4—24no—
624C4⋊C4—24no—
625C4⋊C4—24no—
626C4⋊C4—24no—
627C4⋊C4—22no—
628C4⋊C4—22no—
629C4⋊C4—22no—
630C4⋊C4—24no—
631C4⋊C4—22no—
632C4⋊C4—22no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—41no—
650C4⋊C4—41no—
651C4⋊C4—41no—
652C4⋊C4—41no—
653C4⋊C4—42no—
654C4⋊C4—42no—
655C4⋊C4—42no—
656C4⋊C4—42no—
657C4⋊C4—42no—
658C4⋊C4—42no—
659C4⋊C4—42no—
660C4⋊C4—44no—
661C4⋊C4—44no—
662C4⋊C4—42no—
663C4⋊C4—44no—
664C4⋊C4—42no—
665C4⋊C4—42no—
666C4⋊C4—42no—
667C4⋊C4—42no—
668C4⋊C4—42no—
669C4⋊C4—42no—
670C4⋊C4—81no—
671C4⋊C4—81no—
672C4⋊C4—81no—
673C4⋊C4C2×#4112yes—
674C4⋊C4C2×#4112yes—
675C4⋊C4C2×#4112yes—
676C4⋊C4C2×#4112yes—
677C42—24no—
678C42—24no—
679C42—24no—
680C42—24no—
681C42—22no—
682C42—22no—
683C42—22no—
684C42—22no—
685C42—22no—
686C42—22no—
687C42—22no—
688C42—21no—
689C42—21no—
690C42—21no—
691C42—21no—
692C42—21no—
693C42—21no—
694C42—21no—
695C42—21no—
696C42—21no—
697C42—21no—
698C42—41no—
699C42—41no—
700C42—41no—
701C42—41no—
702C42—41no—
703C42—42no—
704C42—42no—
705C42—42no—
706C42—42no—
707C42—44no—
708C42—42no—
709C42—44no—
710C42—42no—
711C42—42no—
712C42—42no—
713C42—44no—
714C42—42no—
715C42—81no—
716C42—81no—
717C42—81no—
718C42C2×#4112yes—
719C42C2×#4112yes—
720C42C2×#4112yes—
721C422−1+412yes—
722C23C23×D411yescharacteristic
723Q8—22no—
724Q8—22no—
725Q8—22no—
726Q8—44no—
727Q8—48no—
728Q8—42no—
729Q8—42no—
730Q8—42no—
731Q8—42no—
732Q8—84no—
733Q8—84no—
734Q8#55614yes—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—21no—
740C2×C4—22no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—22no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
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—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—41no—
805C2×C4—42no—
806C2×C4#52512yes—
807C2×C4#52512yes—
808C2×C4#54812yes—
809C2×C4#54812yes—
810C2×C4#57512yes—
811C2×C4#57512yes—
812C2×C4#57812yes—
813C2×C4C22×#4111yescharacteristic
814C2×C4C22×#4111yescharacteristic
815C2×C4C22×#4111yescharacteristic
816C2×C4C2×2−1+411yescharacteristic
817C2×C4C2×2−1+411yescharacteristic
818C2×C4#58511yescharacteristic
819C8—42no—
820C8—42no—
821C8—42no—
822C8—42no—
823C22C2×#52511yescharacteristic
824C22C2×#54811yescharacteristic
825C22#348911yescharacteristic
826C22C2×#57511yescharacteristic
827C22C2×#57511yescharacteristic
828C22C2×#57811yescharacteristic
829C22#358611yescharacteristic
830C4—22no—
831C4—22no—
832C4—22no—
833C4—22no—
834C4—24no—
835C4—42no—
836C4—41no—
837C4—41no—
838C4—42no—
839C4—42no—
840C4—41no—
841C4—41no—
842C4—41no—
843C4—41no—
844C4—41no—
845C4—42no—
846C4—41no—
847C4—41no—
848C4—82no—
849C4—82no—
850C4—82no—
851C4—81no—
852C4—81no—
853C4—81no—
854C4—82no—
855C4#337714yes—
856C4C2×#55611yescharacteristic
857C4#348011yescharacteristic
858C4#350711yescharacteristic
859C4#352311yescharacteristic
860C2#3657911yescharacteristic
861C2#6055911yescharacteristic
862C2#6059411yescharacteristic
863C2C2×#337711yescharacteristic
864C2#6132311yescharacteristic
865C2#6211811yescharacteristic
866C2#6213011yescharacteristic
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×#5572
#332022
#330332
#330272
#293572
#293492
#292752
#292742
#292242
#282842
#275752
#275622
#271512
#271342
#250052
#243442
#230732
#228232
#227792
#216152
C4×#4772
#215062