Finite Group Databasebeta

← #6457519

Subgroups — #6457519

Order 512.

1508 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34815C211yesmaximal, characteristic
2C2×#2511C211yesmaximal, characteristic
3#28060C212yesmaximal, complemented
4#28054C212yesmaximal, complemented
5#28050C212yesmaximal, complemented
6#28048C212yesmaximal, complemented
7#28042C212yesmaximal, complemented
8#28040C212yesmaximal, complemented
9#28036C212yesmaximal, complemented
10#28030C212yesmaximal, complemented
11#23732C211yesmaximal, characteristic
12#23670C211yesmaximal, characteristic
13#23658C211yesmaximal, characteristic
14#23619C211yesmaximal, characteristic
15#21159C211yesmaximal, characteristic
16#21094C211yesmaximal, characteristic
17#21094C211yesmaximal, characteristic
18#21094C211yesmaximal, characteristic
19#21061C211yesmaximal, characteristic
20#21033C211yesmaximal, characteristic
21#20764C211yesmaximal, characteristic
22C4×#428C211yesmaximal, characteristic
23C4⋊C4×M16C211yesmaximal, characteristic
24C2×#428C2211yescharacteristic
25C2×#428C2211yescharacteristic
26C2×#428C2211yescharacteristic
27C2×#428C2211yescharacteristic
28C2×#423C2211yescharacteristic
29C2×#419C2211yescharacteristic
30C2×#419C2211yescharacteristic
31C2×#419C2211yescharacteristic
32C2×#419C2211yescharacteristic
33C2×C4×M16C2211yescharacteristic
34C2×C4×M16C2211yescharacteristic
35C2×C4×M16C2211yescharacteristic
36#2511—21no—
37#2511—21no—
38#2511—21no—
39#2511—21no—
40#2511C2212yes—
41#2511C2212yes—
42#2511C2212yes—
43#2511C2212yes—
44#2509C2211yescharacteristic
45#2509C2211yescharacteristic
46#2508C2211yescharacteristic
47#2508C2211yescharacteristic
48#2507C2211yescharacteristic
49#2507C2211yescharacteristic
50#2506C2211yescharacteristic
51#2506C2211yescharacteristic
52#2505—21no—
53#2505—21no—
54#2473—21no—
55#2473—21no—
56#2402—21no—
57#2402—21no—
58C2×#400—21no—
59C2×#400—21no—
60C4×#125—21no—
61C4×#125—21no—
62#2296C2211yescharacteristic
63#2296C2211yescharacteristic
64#2296C2211yescharacteristic
65#2296C2211yescharacteristic
66C2×#391C2211yescharacteristic
67C2×#391C2211yescharacteristic
68C2×#391C2211yescharacteristic
69C2×#389C2211yescharacteristic
70C2×#387—21no—
71C2×#387—21no—
72#2285C2211yescharacteristic
73C2×#384C2211yescharacteristic
74C4×#117C2211yescharacteristic
75C2×C4×C4⋊C4C2211yescharacteristic
76C2×C4×C4⋊C4C2211yescharacteristic
77#2097C2212yes—
78#2097C2212yes—
79#2096C2212yes—
80#2095C2212yes—
81#2088C2212yes—
82#2088C2212yes—
83#2087C2212yes—
84#2086C2212yes—
85#2084C2212yes—
86#2084C2212yes—
87#2083C2212yes—
88#2083C2212yes—
89#2068C2212yes—
90#2068C2212yes—
91#2066C2212yes—
92#2066C2212yes—
93#1944C2212yes—
94#1943C2212yes—
95#1942C2212yes—
96#1941C2212yes—
97#1935C2212yes—
98#1935C2212yes—
99#1935C2212yes—
100#1935C2212yes—
101#1935C2212yes—
102#1935C2212yes—
103#1933C2212yes—
104#1933C2212yes—
105#1933C2212yes—
106#1933C2212yes—
107#1933C2212yes—
108#1933C2212yes—
109#1928C2212yes—
110#1928C2212yes—
111#1927C2212yes—
112#1927C2212yes—
113#1921C2212yes—
114#1920C2212yes—
115#1919C2212yes—
116#1918C2212yes—
117#1836C2212yes—
118#1836C2212yes—
119#1834C2212yes—
120#1834C2212yes—
121#1776C2212yes—
122#1776C2212yes—
123C4×#107C2212yes—
124C4×#106C2212yes—
125#1771C2212yes—
126#1771C2212yes—
127#1770C2212yes—
128C8×C4⋊C4C2212yes—
129#1736C2211yescharacteristic
130#1736C2211yescharacteristic
131#1736C2211yescharacteristic
132#1736C2211yescharacteristic
133#1736C2211yescharacteristic
134#1736C2211yescharacteristic
135#1736C2211yescharacteristic
136#1736C2211yescharacteristic
137#1728C2211yescharacteristic
138#1728C2211yescharacteristic
139C23×Q8C2311yescharacteristic
140C22×M16C2311yescharacteristic
141C22×M16C2311yescharacteristic
142C22×M16C2311yescharacteristic
143C22×M16C2311yescharacteristic
144C2×#125—21no—
145C2×#125—21no—
146C2×#117C2311yescharacteristic
147C2×#117C2311yescharacteristic
148C2×#117C2311yescharacteristic
149C2×#117C2311yescharacteristic
150C22×C4⋊C4—21no—
151C22×C4⋊C4—21no—
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#428—24no—
163#428—24no—
164#428—24no—
165#428—24no—
166C2×#107C2312yes—
167C2×#107C2312yes—
168C2×#107C2312yes—
169C2×#107C2312yes—
170C2×#106C2312yes—
171C2×#106C2312yes—
172C2×#106C2312yes—
173C2×#106C2312yes—
174#423—24no—
175C2×C4⋊C8C2312yes—
176C2×C4⋊C8C2312yes—
177#419—24no—
178#419—24no—
179#419—24no—
180#419—24no—
181C2×#103C2312yes—
182C2×#103C2312yes—
183C2×#103C2312yes—
184C2×#103C2312yes—
185C2×#103C2312yes—
186C2×#103C2312yes—
187C2×#103C2312yes—
188C2×#103C2312yes—
189C4×M16—24no—
190C4×M16—24no—
191C4×M16—24no—
192C2×#97C2312yes—
193C2×#97C2312yes—
194C2×#97C2312yes—
195C2×C4×C8C2312yes—
196C2×C4×C8C2312yes—
197C2×C4×C8C2312yes—
198#400—22no—
199#400—22no—
200#400—22no—
201#400—22no—
202#400—21no—
203#400—21no—
204#400—22no—
205#400—22no—
206#400—22no—
207#400—22no—
208#400—21no—
209#400—21no—
210#400—21no—
211#400—21no—
212#400—21no—
213#400—21no—
214#398—21no—
215#398—21no—
216#398—21no—
217#398—21no—
218#398—21no—
219#398—21no—
220#398—21no—
221#398—21no—
222#391—21no—
223#391—21no—
224#391—21no—
225#391—21no—
226#391—21no—
227#391—21no—
228#391C2312yes—
229#391C2312yes—
230#391C2312yes—
231#391C2312yes—
232#391C2312yes—
233#391C2312yes—
234#389—21no—
235#389—21no—
236#389—21no—
237#389—21no—
238#389—21no—
239#389—21no—
240#389C2311yescharacteristic
241#389C2311yescharacteristic
242#389C2311yescharacteristic
243#389C2311yescharacteristic
244#389C2311yescharacteristic
245#389C2311yescharacteristic
246#389C2311yescharacteristic
247#389C2311yescharacteristic
248#389C2311yescharacteristic
249#389C2312yes—
250#389C2311yescharacteristic
251#389C2312yes—
252#389C2311yescharacteristic
253#389C2311yescharacteristic
254#389C2311yescharacteristic
255#389C2311yescharacteristic
256#389C2311yescharacteristic
257#389C2311yescharacteristic
258#387—21no—
259#387—21no—
260#387—21no—
261#387—21no—
262#387—22no—
263#387—22no—
264#387—22no—
265#387—22no—
266#387—21no—
267#387—21no—
268#387—21no—
269#387—21no—
270#387—22no—
271#387—22no—
272#387—22no—
273#387—22no—
274#385—21no—
275#385—21no—
276#385—21no—
277#385—21no—
278#385—21no—
279#385—21no—
280#385—21no—
281#385—21no—
282#384—21no—
283#384—21no—
284#384C2312yes—
285#384C2312yes—
286#384C2311yescharacteristic
287#384C2311yescharacteristic
288#382—21no—
289#382—21no—
290#382C2311yescharacteristic
291#382C2311yescharacteristic
292#380—21no—
293#380—21no—
294C4×C4⋊C4—21no—
295C4×C4⋊C4—21no—
296C4×C4⋊C4—21no—
297C4×C4⋊C4—21no—
298C4×C4⋊C4—21no—
299C4×C4⋊C4—21no—
300C4×C4⋊C4—21no—
301C4×C4⋊C4—21no—
302C4×C4⋊C4—21no—
303C4×C4⋊C4—21no—
304C4×C4⋊C4—21no—
305C4×C4⋊C4—21no—
306C4×C4⋊C4D411yescharacteristic
307C4×C4⋊C4D411yescharacteristic
308C4×C4⋊C4D411yescharacteristic
309C4×C4⋊C4D411yescharacteristic
310C4×C4⋊C4C2312yes—
311C4×C4⋊C4C2312yes—
312C4×C4⋊C4C2311yescharacteristic
313C4×C4⋊C4C2311yescharacteristic
314C4×C4⋊C4C2311yescharacteristic
315C4×C4⋊C4C2311yescharacteristic
316C4×C4⋊C4C2311yescharacteristic
317C4×C4⋊C4C2311yescharacteristic
318C4×C4⋊C4C2311yescharacteristic
319C4×C4⋊C4C2311yescharacteristic
320C4×C22⋊C4—21no—
321C4×C22⋊C4—21no—
322#376—21no—
323C2×#95—21no—
324C2×#95—21no—
325C2×#95—21no—
326C2×#95—21no—
327C2×#95—21no—
328C2×#95—21no—
329C2×#95—21no—
330C2×#95—21no—
331C2×#95D411yescharacteristic
332C2×#95D411yescharacteristic
333C43—21no—
334#340C2312yes—
335#340C2312yes—
336#340C2312yes—
337#340C2312yes—
338#340C2312yes—
339#340C2312yes—
340#340C2312yes—
341#340C2312yes—
342#340C2312yes—
343#340C2312yes—
344#340C2312yes—
345#340C2312yes—
346#340C2312yes—
347#340C2312yes—
348#340C2312yes—
349#340C2312yes—
350#336C2312yes—
351#336C2312yes—
352#336C2312yes—
353#336C2312yes—
354C22×Q8—21no—
355C22×Q8—22no—
356C22×Q8—22no—
357C22×Q8—22no—
358C22×Q8—22no—
359C22×Q8—22no—
360C22×Q8—22no—
361C22×Q8C2412yes—
362C23×C4—21no—
363C23×C4—21no—
364C23×C4—21no—
365C23×C4—21no—
366C23×C4C2×D411yescharacteristic
367C23×C4C2×D411yescharacteristic
368C23×C4C2×D411yescharacteristic
369C23×C4C2×D411yescharacteristic
370C23×C4C2×D411yescharacteristic
371C23×C4C2×D411yescharacteristic
372C23×C4C2411yescharacteristic
373C2×M16—22no—
374C2×M16—22no—
375C2×M16—22no—
376C2×M16—22no—
377C2×M16—22no—
378C2×M16—22no—
379C2×M16—22no—
380C2×M16—22no—
381C2×M16—22no—
382C2×M16#4114yes—
383C2×M16#4114yes—
384C2×M16#4114yes—
385C22×C8C2412yes—
386C22×C8C2412yes—
387C22×C8C2412yes—
388C22×C8C2412yes—
389#125—44no—
390#125—44no—
391#117—22no—
392#117—22no—
393#117—22no—
394#117—22no—
395#117—22no—
396#117—22no—
397#117—22no—
398#117#4114yes—
399C2×C4⋊C4—24no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—22no—
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—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
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—42no—
436C2×C4⋊C4—44no—
437C2×C4⋊C4—82no—
438C2×C4⋊C4—82no—
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⋊C4C2×D411yescharacteristic
447C2×C4⋊C4C2412yes—
448C2×C4⋊C4C2412yes—
449C2×C4⋊C4C2412yes—
450C2×C4⋊C4C2411yescharacteristic
451C2×C4⋊C4C2411yescharacteristic
452C2×C4⋊C4C2411yescharacteristic
453C2×C4⋊C4C2411yescharacteristic
454C2×C4⋊C4C2411yescharacteristic
455C2×C4⋊C4C2411yescharacteristic
456C2×C4⋊C4C2411yescharacteristic
457C2×C4⋊C4C2411yescharacteristic
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C42—21no—
463C2×C42—22no—
464C2×C42—22no—
465C2×C42—22no—
466C2×C42—22no—
467C2×C42—22no—
468C2×C42—22no—
469C2×C42—21no—
470C2×C42—21no—
471C2×C42—21no—
472C2×C42—21no—
473C2×C42—21no—
474C2×C42—21no—
475C2×C42—21no—
476C2×C42—22no—
477C2×C42—22no—
478C2×C42—82no—
479C2×C42C2×D411yescharacteristic
480C2×C42C2×D411yescharacteristic
481C2×C42C2×D411yescharacteristic
482C2×C42C2×D411yescharacteristic
483C2×C42C2×D411yescharacteristic
484C2×C42C2×D411yescharacteristic
485C2×C42C2411yescharacteristic
486C2×C42C2411yescharacteristic
487C2×C42C2411yescharacteristic
488C2×C42C2411yescharacteristic
489C2×C42C2411yescharacteristic
490C2×C42C2411yescharacteristic
491#107—24no—
492#107—24no—
493#107—24no—
494#107—24no—
495#106—24no—
496#106—24no—
497#106—24no—
498#106—24no—
499C4⋊C8—24no—
500C4⋊C8—24no—
501#103—24no—
502#103—24no—
503#103—24no—
504#103—24no—
505#103—24no—
506#103—24no—
507#103—24no—
508#103—24no—
509#97—24no—
510#97—24no—
511#97—24no—
512C4×C8—24no—
513C4×C8—24no—
514C4×C8—24no—
515#95—22no—
516#95—22no—
517#95—22no—
518#95—22no—
519#95—22no—
520#95—22no—
521#95—22no—
522#95—22no—
523#95—22no—
524#95—22no—
525#95—22no—
526#95—22no—
527#95—22no—
528#95—22no—
529#95—22no—
530#95—22no—
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#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#95C2×D411yescharacteristic
556#95C2×D411yescharacteristic
557#95C2×D411yescharacteristic
558#95C2×D411yescharacteristic
559#95C2×D411yescharacteristic
560#95C2×D411yescharacteristic
561#95C2×D411yescharacteristic
562#95C2×D411yescharacteristic
563C24C22×D411yescharacteristic
564C2×Q8—22no—
565C2×Q8—22no—
566C2×Q8—22no—
567C2×Q8—22no—
568C2×Q8—22no—
569C2×Q8—22no—
570C2×Q8—42no—
571C2×Q8—42no—
572C2×Q8—42no—
573C2×Q8—44no—
574C2×Q8—44no—
575C2×Q8—44no—
576C2×Q8—44no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
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—22no—
590C22×C4—22no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—22no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—22no—
599C22×C4—41no—
600C22×C4—41no—
601C22×C4—41no—
602C22×C4—41no—
603C22×C4—41no—
604C22×C4—41no—
605C22×C4—41no—
606C22×C4—41no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4—42no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4C22×D411yescharacteristic
620C22×C4C22×D411yescharacteristic
621C22×C4C22×D411yescharacteristic
622C22×C4C22×D411yescharacteristic
623C22×C4C22×D411yescharacteristic
624C22×C4C22×D411yescharacteristic
625C22×C4C22×D411yescharacteristic
626C22×C4C22×D411yescharacteristic
627C22×C4C22×D411yescharacteristic
628C22×C4C22×D411yescharacteristic
629C22×C4C22×D411yescharacteristic
630C22×C4C22×D411yescharacteristic
631C22×C4C22×D411yescharacteristic
632C22×C4C2×#4112yes—
633C22×C4C2×#4112yes—
634C22×C4C2×#4112yes—
635C22×C4C2×#4112yes—
636C22×C42−1+412yes—
637C22×C42−1+412yes—
638C22×C4C2511yescharacteristic
639M16—28no—
640M16—28no—
641M16—28no—
642M16—44no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—22no—
646C2×C8—22no—
647C2×C8—22no—
648C2×C8—22no—
649C2×C8—22no—
650C2×C8—22no—
651C2×C8—22no—
652C2×C8C2×#4114yes—
653C2×C8C2×#4114yes—
654C2×C8C2×#4114yes—
655C4⋊C4—22no—
656C4⋊C4—22no—
657C4⋊C4—22no—
658C4⋊C4—22no—
659C4⋊C4—22no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—22no—
671C4⋊C4—22no—
672C4⋊C4—22no—
673C4⋊C4—22no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—22no—
677C4⋊C4—22no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—41no—
681C4⋊C4—41no—
682C4⋊C4—44no—
683C4⋊C4—42no—
684C4⋊C4—42no—
685C4⋊C4—42no—
686C4⋊C4—42no—
687C4⋊C4—42no—
688C4⋊C4—42no—
689C4⋊C4—42no—
690C4⋊C4—42no—
691C4⋊C4—42no—
692C4⋊C4—42no—
693C4⋊C4—42no—
694C4⋊C4—44no—
695C4⋊C4—42no—
696C4⋊C4—42no—
697C4⋊C4—81no—
698C4⋊C4—81no—
699C4⋊C4—81no—
700C4⋊C4—81no—
701C4⋊C4—81no—
702C4⋊C4—81no—
703C4⋊C4—81no—
704C4⋊C4—81no—
705C4⋊C4—81no—
706C4⋊C4—81no—
707C4⋊C4—82no—
708C4⋊C4—82no—
709C4⋊C4—82no—
710C4⋊C4—82no—
711C4⋊C4#13714yes—
712C4⋊C4C2×#4112yes—
713C4⋊C4C2×#4112yes—
714C22⋊C4—24no—
715C22⋊C4—42no—
716C22⋊C4—42no—
717C22⋊C4—42no—
718C42—22no—
719C42—22no—
720C42—22no—
721C42—22no—
722C42—22no—
723C42—22no—
724C42—24no—
725C42—21no—
726C42—21no—
727C42—21no—
728C42—21no—
729C42—21no—
730C42—21no—
731C42—21no—
732C42—21no—
733C42—21no—
734C42—21no—
735C42—21no—
736C42—21no—
737C42—42no—
738C42—42no—
739C42—42no—
740C42—42no—
741C42—42no—
742C42—81no—
743C42—81no—
744C42—82no—
745C42—82no—
746C23—21no—
747C23—21no—
748C23—21no—
749C23—21no—
750C23#53212yes—
751C23#54712yes—
752C23#54812yes—
753C23C23×D411yescharacteristic
754Q8—42no—
755Q8—42no—
756Q8—42no—
757Q8—42no—
758Q8—84no—
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—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—44no—
794C2×C4—44no—
795C2×C4—44no—
796C2×C4—44no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—41no—
804C2×C4—42no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—42no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—82no—
832C2×C4—82no—
833C2×C4—84no—
834C2×C4—84no—
835C2×C4—84no—
836C2×C4—84no—
837C2×C4#52914yes—
838C2×C4#53212yes—
839C2×C4#54114yes—
840C2×C4#54712yes—
841C2×C4#54812yes—
842C2×C4#55214yes—
843C2×C4#55214yes—
844C2×C4C2×#13712yes—
845C2×C4C2×#13712yes—
846C2×C4C2×#13712yes—
847C2×C4#57512yes—
848C2×C4C22×#4111yescharacteristic
849C2×C4C22×#4111yescharacteristic
850C2×C4C22×#4111yescharacteristic
851C2×C4C22×#4111yescharacteristic
852C2×C4C2×2−1+411yescharacteristic
853C2×C4C2×2−1+411yescharacteristic
854C8—24no—
855C8—24no—
856C8—24no—
857C8—42no—
858C22—22no—
859C22—22no—
860C22—22no—
861C22—22no—
862C22—22no—
863C22—22no—
864C22#251914yes—
865C22C2×#53211yescharacteristic
866C22C2×#54711yescharacteristic
867C22C2×#54811yescharacteristic
868C22C22×#13711yescharacteristic
869C22C2×#57511yescharacteristic
870C22#358511yescharacteristic
871C22#358611yescharacteristic
872C4—22no—
873C4—22no—
874C4—22no—
875C4—22no—
876C4—41no—
877C4—41no—
878C4—41no—
879C4—41no—
880C4—41no—
881C4—41no—
882C4—41no—
883C4—41no—
884C4—42no—
885C4—42no—
886C4—81no—
887C4—81no—
888C4—81no—
889C4—81no—
890C4—82no—
891C4—81no—
892C4—81no—
893C4—82no—
894C4—82no—
895C4—82no—
896C4#251914yes—
897C4C2×#52911yescharacteristic
898C4C2×#54111yescharacteristic
899C4C2×#55211yescharacteristic
900C4C2×#55211yescharacteristic
901C2—24no—
902C2C2×#251911yescharacteristic
903C2#6070111yescharacteristic
904C2#6070311yescharacteristic
905C2#6125311yescharacteristic
906C2#6125411yescharacteristic
907C2#6132211yescharacteristic
908C2#6132411yescharacteristic
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. #28060C2semidirect
4. #28054C2semidirect
5. #28050C2semidirect
6. #28048C2semidirect
7. #28042C2semidirect
8. #28040C2semidirect
9. #28036C2semidirect
10. #28030C2semidirect

Maximal subgroups

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

subgroupindex
#348152
C2×#25112
#280602
#280542
#280502
#280482
#280422
#280402
#280362
#280302
#237322
#236702
#236582
#236192
#211592
#210942
#210612
#210332
#207642
C4×#4282
C4⋊C4×M162