Finite Group Databasebeta

← #6445950

Subgroups — #6445950

Order 512.

1572 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2507C211yesmaximal, characteristic
2#34145C211yesmaximal, characteristic
3#26886C212yesmaximal, complemented
4#26882C212yesmaximal, complemented
5#26879C212yesmaximal, complemented
6#26875C212yesmaximal, complemented
7#26871C212yesmaximal, complemented
8#26867C212yesmaximal, complemented
9#26862C212yesmaximal, complemented
10#26858C212yesmaximal, complemented
11#23670C211yesmaximal, characteristic
12#23658C211yesmaximal, characteristic
13#23554C211yesmaximal, characteristic
14#23554C211yesmaximal, characteristic
15#21171C211yesmaximal, characteristic
16#21159C211yesmaximal, characteristic
17#21034C211yesmaximal, characteristic
18#21034C211yesmaximal, characteristic
19#21034C211yesmaximal, characteristic
20#21034C211yesmaximal, characteristic
21#21033C211yesmaximal, characteristic
22#21023C211yesmaximal, characteristic
23C4×#428C211yesmaximal, characteristic
24C2×#533C2211yescharacteristic
25C2×#428C2211yescharacteristic
26C2×#428C2211yescharacteristic
27C2×#428C2211yescharacteristic
28C2×#428C2211yescharacteristic
29C2×#428C2211yescharacteristic
30C2×#428C2211yescharacteristic
31C2×#423C2211yescharacteristic
32C2×C4×M16C2211yescharacteristic
33#2507—21no—
34#2507—21no—
35#2507—21no—
36#2507—21no—
37#2507C2212yes—
38#2507C2212yes—
39#2507C2212yes—
40#2507C2212yes—
41C2×#398—21no—
42C2×#398—21no—
43#2370C2211yescharacteristic
44#2370C2211yescharacteristic
45#2370C2211yescharacteristic
46#2370C2211yescharacteristic
47#2369C2211yescharacteristic
48#2369C2211yescharacteristic
49#2368—21no—
50#2368—21no—
51#2365C2211yescharacteristic
52#2365C2211yescharacteristic
53#2360—21no—
54#2360—21no—
55#2296C2211yescharacteristic
56#2296C2211yescharacteristic
57#2295—21no—
58#2295—21no—
59#2295—21no—
60C2×#389—21no—
61C2×#389C2211yescharacteristic
62C2×#389C2211yescharacteristic
63C2×#389C2211yescharacteristic
64C2×#389C2211yescharacteristic
65C2×#387—21no—
66C2×#384C2211yescharacteristic
67C42×Q8—21no—
68C4×#117C2211yescharacteristic
69C4×#117C2211yescharacteristic
70C4×#117C2211yescharacteristic
71C2×C4×C4⋊C4C2211yescharacteristic
72C2×C4×C4⋊C4C2211yescharacteristic
73#2088C2212yes—
74#2088C2212yes—
75#2087C2212yes—
76#2086C2212yes—
77#2084C2212yes—
78#2084C2212yes—
79#2083C2212yes—
80#2083C2212yes—
81#2059C2212yes—
82#2059C2212yes—
83#2059C2212yes—
84#2059C2212yes—
85#2058C2212yes—
86#2058C2212yes—
87#2057C2212yes—
88#2057C2212yes—
89#1948C2212yes—
90#1948C2212yes—
91#1947C2212yes—
92#1947C2212yes—
93#1944C2212yes—
94#1943C2212yes—
95#1942C2212yes—
96#1941C2212yes—
97#1921C2212yes—
98#1921C2212yes—
99#1921C2212yes—
100#1921C2212yes—
101#1921C2212yes—
102#1920C2212yes—
103#1920C2212yes—
104#1920C2212yes—
105#1920C2212yes—
106#1920C2212yes—
107#1919C2212yes—
108#1919C2212yes—
109#1919C2212yes—
110#1919C2212yes—
111#1919C2212yes—
112#1918C2212yes—
113#1918C2212yes—
114#1918C2212yes—
115#1918C2212yes—
116#1918C2212yes—
117#1917C2212yes—
118#1917C2212yes—
119#1916C2212yes—
120#1916C2212yes—
121#1776C2212yes—
122#1776C2212yes—
123C4×#107C2212yes—
124C4×#106C2212yes—
125#1736C2211yescharacteristic
126#1736C2211yescharacteristic
127#1736C2211yescharacteristic
128#1736C2211yescharacteristic
129#1736C2211yescharacteristic
130#1736C2211yescharacteristic
131#1736C2211yescharacteristic
132#1736C2211yescharacteristic
133#1736C2211yescharacteristic
134#1736C2211yescharacteristic
135#1728C2211yescharacteristic
136#1728C2211yescharacteristic
137#1728C2211yescharacteristic
138#1728C2211yescharacteristic
139C22×M16C2311yescharacteristic
140C22×M16C2311yescharacteristic
141C22×M16C2311yescharacteristic
142C22×M16C2311yescharacteristic
143#533—24no—
144#533—24no—
145C2×C4⋊Q8C2311yescharacteristic
146C2×C4⋊Q8C2311yescharacteristic
147C2×#125C2311yescharacteristic
148C2×#125C2311yescharacteristic
149C2×C22⋊Q8—21no—
150C2×C22⋊Q8—21no—
151C2×C4×Q8—21no—
152C2×C4×Q8—21no—
153C2×C4×Q8—21no—
154C2×C4×Q8—21no—
155C2×#117C2311yescharacteristic
156C2×#117C2311yescharacteristic
157C2×#117C2311yescharacteristic
158C2×#117C2311yescharacteristic
159C22×C4⋊C4—21no—
160C22×C4⋊C4—21no—
161C22×C4⋊C4—21no—
162C22×C4⋊C4—21no—
163C22×C4⋊C4—21no—
164C22×C4⋊C4—21no—
165C22×C4⋊C4D411yescharacteristic
166C22×C4⋊C4D411yescharacteristic
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2311yescharacteristic
170C22×C4⋊C4C2311yescharacteristic
171C22×C42—21no—
172C22×C42C2311yescharacteristic
173C22×C42C2311yescharacteristic
174C22×C42C2311yescharacteristic
175#428—24no—
176#428—24no—
177#428—24no—
178#428—24no—
179#428—24no—
180#428Q818yescomplemented
181C2×#107C2312yes—
182C2×#107C2312yes—
183C2×#107C2312yes—
184C2×#107C2312yes—
185C2×#107C2312yes—
186C2×#107C2312yes—
187C2×#106C2312yes—
188C2×#106C2312yes—
189C2×#106C2312yes—
190C2×#106C2312yes—
191C2×#106C2312yes—
192C2×#106C2312yes—
193#423—24no—
194C2×C4⋊C8C2312yes—
195C2×C4⋊C8C2312yes—
196C4×M16—24no—
197C2×#97C2312yes—
198C2×C4×C8C2312yes—
199#398—22no—
200#398—22no—
201#398—22no—
202#398—22no—
203#398—22no—
204#398—22no—
205#398—22no—
206#398—22no—
207#391—21no—
208#391—21no—
209#391—21no—
210#391—21no—
211#391—21no—
212#391—21no—
213#389—21no—
214#389—21no—
215#389—21no—
216#389—21no—
217#389—21no—
218#389—21no—
219#389—21no—
220#389—21no—
221#389—21no—
222#389—21no—
223#389—21no—
224#389—21no—
225#389—21no—
226#389—21no—
227#389—22no—
228#389—22no—
229#389—22no—
230#389—22no—
231#389C2312yes—
232#389C2312yes—
233#389C2312yes—
234#389C2312yes—
235#389C2311yescharacteristic
236#389C2311yescharacteristic
237#389C2311yescharacteristic
238#389C2311yescharacteristic
239#389C2312yes—
240#389C2312yes—
241#389C2311yescharacteristic
242#389C2311yescharacteristic
243#389C2311yescharacteristic
244#389C2311yescharacteristic
245#389C2312yes—
246#389C2312yes—
247#387—21no—
248#387—21no—
249#387—21no—
250#387—21no—
251#387—22no—
252#387—22no—
253#387—22no—
254#387—22no—
255#387—21no—
256#387—21no—
257#387—21no—
258#387—21no—
259#387—21no—
260#387—21no—
261#387—21no—
262#387—21no—
263#385—21no—
264#385—21no—
265#385—21no—
266#385—21no—
267#384—21no—
268#384—21no—
269#384C2312yes—
270#384C2312yes—
271C4×C4⋊C4—21no—
272C4×C4⋊C4—21no—
273C4×C4⋊C4—21no—
274C4×C4⋊C4—21no—
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⋊C4D411yescharacteristic
284C4×C4⋊C4D411yescharacteristic
285C4×C4⋊C4D411yescharacteristic
286C4×C4⋊C4D411yescharacteristic
287C4×C4⋊C4C2311yescharacteristic
288C4×C4⋊C4C2311yescharacteristic
289C4×C4⋊C4C2311yescharacteristic
290C4×C4⋊C4C2311yescharacteristic
291C4×C4⋊C4C2311yescharacteristic
292C4×C4⋊C4C2311yescharacteristic
293C4×C4⋊C4C2311yescharacteristic
294C4×C4⋊C4C2311yescharacteristic
295C4×C4⋊C4C2311yescharacteristic
296C4×C4⋊C4C2311yescharacteristic
297C4×C4⋊C4C2311yescharacteristic
298C4×C4⋊C4C2311yescharacteristic
299C4×C4⋊C4C2312yes—
300C4×C4⋊C4C2312yes—
301C4×C4⋊C4C2311yescharacteristic
302C4×C4⋊C4C2311yescharacteristic
303C4×C4⋊C4C2311yescharacteristic
304C4×C4⋊C4C2311yescharacteristic
305C4×C22⋊C4—21no—
306C4×C22⋊C4—21no—
307C4×C22⋊C4—21no—
308C4×C22⋊C4—21no—
309C4×C22⋊C4—21no—
310C4×C22⋊C4—21no—
311#376—21no—
312#376—21no—
313#376—21no—
314C2×#95—21no—
315C2×#95—21no—
316C2×#95—21no—
317C2×#95—21no—
318C2×#95—21no—
319C2×#95D411yescharacteristic
320C2×#95D411yescharacteristic
321C43—21no—
322C43—21no—
323C43—21no—
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#340C2312yes—
340#340C2312yes—
341#340C2312yes—
342#340C2312yes—
343#340C2312yes—
344#336C2312yes—
345#336C2312yes—
346#336C2312yes—
347#336C2312yes—
348#336C2312yes—
349#336C2312yes—
350#336C2312yes—
351#336C2312yes—
352C22×Q8—21no—
353C22×Q8—21no—
354C23×C4—21no—
355C23×C4—21no—
356C23×C4—21no—
357C23×C4—21no—
358C23×C4C2×D411yescharacteristic
359C23×C4C2×D411yescharacteristic
360C23×C4C2×D411yescharacteristic
361C23×C4C2×D411yescharacteristic
362C23×C4C2×D411yescharacteristic
363C23×C4C2×D411yescharacteristic
364C23×C4C2411yescharacteristic
365C2×M16—22no—
366C2×M16—22no—
367C2×M16—22no—
368C2×M16—22no—
369C2×M16—22no—
370C2×M16—22no—
371C2×M16—22no—
372C2×M16—22no—
373C2×M16—22no—
374C2×M16—22no—
375C2×M16C2×Q814yes—
376C2×M16#4114yes—
377C22×C8C2412yes—
378C22×C8C2412yes—
379C22×C8C2412yes—
380C22×C8C2412yes—
381C4⋊Q8—22no—
382C4⋊Q8—22no—
383C4⋊Q8—22no—
384C4⋊Q8—22no—
385#125—22no—
386#125—22no—
387#125—22no—
388#125—22no—
389C22⋊Q8—28no—
390C22⋊Q8—28no—
391C4×Q8—28no—
392C4×Q8—28no—
393C4×Q8—44no—
394C4×Q8—44no—
395#117—22no—
396#117—22no—
397#117—22no—
398#117—22no—
399#117—22no—
400#117C2×Q814yes—
401#117#4114yes—
402#117#4114yes—
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—22no—
411C2×C4⋊C4—24no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—42no—
442C2×C4⋊C4—44no—
443C2×C4⋊C4—82no—
444C2×C4⋊C4—82no—
445C2×C4⋊C4—82no—
446C2×C4⋊C4—82no—
447C2×C4⋊C4—82no—
448C2×C4⋊C4C2×D411yescharacteristic
449C2×C4⋊C4C2×D411yescharacteristic
450C2×C4⋊C4C2×D411yescharacteristic
451C2×C4⋊C4C2×D411yescharacteristic
452C2×C4⋊C4C2×D411yescharacteristic
453C2×C4⋊C4C2×D411yescharacteristic
454C2×C4⋊C4C2×D411yescharacteristic
455C2×C4⋊C4C2×D411yescharacteristic
456C2×C4⋊C4C2×Q814yes—
457C2×C4⋊C4C2412yes—
458C2×C4⋊C4C2412yes—
459C2×C4⋊C4C2412yes—
460C2×C4⋊C4C2411yescharacteristic
461C2×C4⋊C4C2411yescharacteristic
462C2×C4⋊C4C2412yes—
463C2×C4⋊C4C2411yescharacteristic
464C2×C4⋊C4C2411yescharacteristic
465C2×C4⋊C4C2411yescharacteristic
466C2×C4⋊C4C2411yescharacteristic
467C2×C4⋊C4C2411yescharacteristic
468C2×C4⋊C4C2411yescharacteristic
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C42—21no—
474C2×C42—21no—
475C2×C42—21no—
476C2×C42—22no—
477C2×C42—22no—
478C2×C42—22no—
479C2×C42—22no—
480C2×C42—22no—
481C2×C42—22no—
482C2×C42—21no—
483C2×C42—21no—
484C2×C42—21no—
485C2×C42—21no—
486C2×C42—21no—
487C2×C42—21no—
488C2×C42—21no—
489C2×C42—21no—
490C2×C42—21no—
491C2×C42—21no—
492C2×C42—21no—
493C2×C42—21no—
494C2×C42—21no—
495C2×C42—22no—
496C2×C42—22no—
497C2×C42—82no—
498C2×C42C2×D411yescharacteristic
499C2×C42C2×D411yescharacteristic
500C2×C42C2×D411yescharacteristic
501C2×C42C2×D411yescharacteristic
502C2×C42C2×D411yescharacteristic
503C2×C42C2×D411yescharacteristic
504C2×C42C2411yescharacteristic
505C2×C42C2411yescharacteristic
506C2×C42C2411yescharacteristic
507C2×C42C2411yescharacteristic
508C2×C42C2411yescharacteristic
509C2×C42C2411yescharacteristic
510#107—24no—
511#107—24no—
512#107—24no—
513#107—24no—
514#107—24no—
515#107C2×Q818yes—
516#106—24no—
517#106—24no—
518#106—24no—
519#106—24no—
520#106—24no—
521#106C2×Q818yes—
522C4⋊C8—24no—
523C4⋊C8—24no—
524#97—24no—
525C4×C8—24no—
526#95—22no—
527#95—22no—
528#95—22no—
529#95—22no—
530#95—22no—
531#95—22no—
532#95—22no—
533#95—22no—
534#95—22no—
535#95—22no—
536#95—21no—
537#95—21no—
538#95—21no—
539#95—21no—
540#95—21no—
541#95—21no—
542#95—21no—
543#95—21no—
544#95—21no—
545#95—21no—
546#95—21no—
547#95—21no—
548#95—21no—
549#95—21no—
550#95—21no—
551#95—21no—
552#95—21no—
553#95—21no—
554#95—21no—
555#95—21no—
556#95C2×D411yescharacteristic
557#95C2×D411yescharacteristic
558#95C2×D411yescharacteristic
559#95C2×D411yescharacteristic
560#95C2×D411yescharacteristic
561#95C2×D411yescharacteristic
562#95C2×D411yescharacteristic
563#95C2×D411yescharacteristic
564C24C22×D411yescharacteristic
565C2×Q8—24no—
566C2×Q8—24no—
567C2×Q8—42no—
568C2×Q8—42no—
569C2×Q8—81no—
570C2×Q8—81no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—24no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—22no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
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×C4—42no—
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×C4C22×D411yescharacteristic
626C22×C4C22×Q812yes—
627C22×C4C2×#4112yes—
628C22×C4C2×#4112yes—
629C22×C4C2×#4112yes—
630C22×C42−1+412yes—
631C22×C42−1+412yes—
632C22×C4C2511yescharacteristic
633M16—28no—
634M16—28no—
635M16—44no—
636M16—44no—
637C2×C8—22no—
638C2×C8—22no—
639C2×C8—22no—
640C2×C8—22no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—22no—
646C2×C8—22no—
647C2×C8C22×Q814yes—
648C2×C8C2×#4114yes—
649C4⋊C4—24no—
650C4⋊C4—24no—
651C4⋊C4—24no—
652C4⋊C4—24no—
653C4⋊C4—24no—
654C4⋊C4—24no—
655C4⋊C4—24no—
656C4⋊C4—22no—
657C4⋊C4—22no—
658C4⋊C4—22no—
659C4⋊C4—22no—
660C4⋊C4—22no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—22no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—22no—
670C4⋊C4—22no—
671C4⋊C4—22no—
672C4⋊C4—22no—
673C4⋊C4—22no—
674C4⋊C4—21no—
675C4⋊C4—22no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—41no—
679C4⋊C4—41no—
680C4⋊C4—44no—
681C4⋊C4—42no—
682C4⋊C4—42no—
683C4⋊C4—42no—
684C4⋊C4—42no—
685C4⋊C4—42no—
686C4⋊C4—42no—
687C4⋊C4—44no—
688C4⋊C4—42no—
689C4⋊C4—81no—
690C4⋊C4—81no—
691C4⋊C4—81no—
692C4⋊C4—81no—
693C4⋊C4—82no—
694C4⋊C4—82no—
695C4⋊C4—82no—
696C4⋊C4—82no—
697C4⋊C4—82no—
698C4⋊C4—82no—
699C4⋊C4—82no—
700C4⋊C4—82no—
701C4⋊C4—82no—
702C4⋊C4—82no—
703C4⋊C4#13714yes—
704C4⋊C4C22×Q812yes—
705C4⋊C4C22×Q814yes—
706C4⋊C4C22×Q812yes—
707C4⋊C4C2×#4112yes—
708C4⋊C4C2×#4112yes—
709C4⋊C4C2×#4112yes—
710C4⋊C4C2×#4112yes—
711C22⋊C4—24no—
712C22⋊C4—24no—
713C22⋊C4—24no—
714C22⋊C4—42no—
715C42—22no—
716C42—22no—
717C42—24no—
718C42—24no—
719C42—22no—
720C42—22no—
721C42—22no—
722C42—22no—
723C42—24no—
724C42—21no—
725C42—21no—
726C42—21no—
727C42—21no—
728C42—21no—
729C42—21no—
730C42—21no—
731C42—21no—
732C42—21no—
733C42—21no—
734C42—21no—
735C42—21no—
736C42—42no—
737C42—42no—
738C42—42no—
739C42—42no—
740C42—42no—
741C42—42no—
742C42—42no—
743C42—81no—
744C42—81no—
745C42—81no—
746C42—81no—
747C42—81no—
748C42—81no—
749C42—82no—
750C42—82no—
751C23—21no—
752C23—21no—
753C23—21no—
754C23—21no—
755C23#52512yes—
756C23#54712yes—
757C23D4×Q812yes—
758C23C23×D411yescharacteristic
759Q8—48no—
760Q8—84no—
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—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—24no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—44no—
801C2×C4—44no—
802C2×C4—44no—
803C2×C4—44no—
804C2×C4—48no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—42no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—42no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—42no—
834C2×C4—82no—
835C2×C4—82no—
836C2×C4—84no—
837C2×C4—84no—
838C2×C4—84no—
839C2×C4#52512yes—
840C2×C4#53314yes—
841C2×C4#54114yes—
842C2×C4#54712yes—
843C2×C4D4×Q812yes—
844C2×C4#55214yes—
845C2×C4#55714yes—
846C2×C4C2×#13712yes—
847C2×C4C2×#13712yes—
848C2×C4C2×#13712yes—
849C2×C4#57512yes—
850C2×C4C23×Q811yescharacteristic
851C2×C4C22×#4111yescharacteristic
852C2×C4C22×#4111yescharacteristic
853C2×C4C22×#4111yescharacteristic
854C2×C4C2×2−1+411yescharacteristic
855C2×C4C2×2−1+411yescharacteristic
856C8—24no—
857C8—24no—
858C8—42no—
859C8—42no—
860C22—22no—
861C22—22no—
862C22—22no—
863C22—22no—
864C22—22no—
865C22—22no—
866C22#246214yes—
867C22C2×#52511yescharacteristic
868C22C2×#54711yescharacteristic
869C22C2×D4×Q811yescharacteristic
870C22C22×#13711yescharacteristic
871C22C2×#57511yescharacteristic
872C22#358511yescharacteristic
873C22#358511yescharacteristic
874C4—22no—
875C4—22no—
876C4—22no—
877C4—22no—
878C4—41no—
879C4—41no—
880C4—41no—
881C4—41no—
882C4—41no—
883C4—41no—
884C4—42no—
885C4—42no—
886C4—41no—
887C4—41no—
888C4—42no—
889C4—42no—
890C4—42no—
891C4—44no—
892C4—42no—
893C4—81no—
894C4—81no—
895C4—82no—
896C4—82no—
897C4—82no—
898C4#246214yes—
899C4C2×#53311yescharacteristic
900C4C2×#54111yescharacteristic
901C4C2×#55211yescharacteristic
902C4C2×#55711yescharacteristic
903C2—24no—
904C2C2×#246211yescharacteristic
905C2#6056211yescharacteristic
906C2#6056811yescharacteristic
907C2#6125411yescharacteristic
908C2#6125511yescharacteristic
909C2#6136711yescharacteristic
910C2Q8×#13711yescharacteristic
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
3. #26886C2semidirect
4. #26882C2semidirect
5. #26879C2semidirect
6. #26875C2semidirect
7. #26871C2semidirect
8. #26867C2semidirect
9. #26862C2semidirect
10. #26858C2semidirect
180. #428Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#25072
#341452
#268862
#268822
#268792
#268752
#268712
#268672
#268622
#268582
#236702
#236582
#235542
#211712
#211592
#210342
#210332
#210232
C4×#4282