Finite Group Databasebeta

← #6611244

Subgroups — #6611244

Order 512.

1526 conjugacy classes of subgroups.

The subgroup lattice has 909 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36191C211yesmaximal, characteristic
2#36134C211yesmaximal, characteristic
3#33293C211yesmaximal, characteristic, complemented
4#33218C211yesmaximal, characteristic, complemented
5#33217C211yesmaximal, characteristic, complemented
6#29211C211yesmaximal, characteristic, complemented
7#28807C212yesmaximal, complemented
8#28805C212yesmaximal, complemented
9#28783C212yesmaximal, complemented
10#28781C212yesmaximal, complemented
11#28774C212yesmaximal, complemented
12#28773C212yesmaximal, complemented
13#28694C211yesmaximal, characteristic, complemented
14#27956C211yesmaximal, characteristic, complemented
15#27955C211yesmaximal, characteristic, complemented
16#25817C211yesmaximal, characteristic, complemented
17#25817C211yesmaximal, characteristic, complemented
18#22712C212yesmaximal
19#22710C212yesmaximal
20#21731C211yesmaximal, characteristic, complemented
21#21323C211yesmaximal, characteristic, complemented
22#21321C211yesmaximal, characteristic, complemented
23#20491C211yesmaximal, characteristic
24C2×#533C2211yescharacteristic
25C2×#533C2211yescharacteristic
26C2×#501C2211yescharacteristic
27C2×#501C2211yescharacteristic
28C2×#501C2211yescharacteristic
29C2×#435C2212yes—
30C2×C4×M16C2211yescharacteristic
31C22×#97C2211yescharacteristic
32#2868C2211yescharacteristic
33#2862C2211yescharacteristic
34#2857C2211yescharacteristic
35#2857C2211yescharacteristic
36#2851C2211yescharacteristic
37#2851C2211yescharacteristic
38#2574—21no—
39#2574—21no—
40#2570C2211yescharacteristic
41#2570C2211yescharacteristic
42#2552C2212yes—
43#2542—21no—
44#2538—21no—
45#2520—21no—
46#2520—21no—
47#2450—21no—
48#2450—21no—
49#2441C2212yes—
50#2441C2212yes—
51#2440C2211yescharacteristic
52#2440C2211yescharacteristic
53#2439C2211yescharacteristic
54#2439C2211yescharacteristic
55#2429—21no—
56#2429—21no—
57#2423—21no—
58#2423—21no—
59#2368—21no—
60#2368—21no—
61#2365—21no—
62#2354C2212yes—
63#2352C2211yescharacteristic
64#2352C2211yescharacteristic
65Q8×C4⋊C4—21no—
66C4×C4⋊Q8C2211yescharacteristic
67C4×#125C2211yescharacteristic
68#2285C2211yescharacteristic
69C2×#382C2211yescharacteristic
70C42×D4C2211yescharacteristic
71#2085C2212yes—
72#2085C2212yes—
73#2084C2212yes—
74#2084C2212yes—
75#2083C2212yes—
76#2083C2212yes—
77#2059C2212yes—
78#2059C2212yes—
79#2059C2212yes—
80#2059C2212yes—
81#2058C2212yes—
82#2057C2212yes—
83#1993C2211yescharacteristic
84#1993C2211yescharacteristic
85#1993C2211yescharacteristic
86#1993C2211yescharacteristic
87#1993C2211yescharacteristic
88#1993C2211yescharacteristic
89#1993C2211yescharacteristic
90#1993C2211yescharacteristic
91#1993C2211yescharacteristic
92#1992C2212yes—
93#1992C2212yes—
94#1992C2211yescharacteristic
95#1991C2212yes—
96#1991C2212yes—
97#1990C2212yes—
98#1990C2212yes—
99#1949C2212yes—
100#1949C2212yes—
101#1948C2212yes—
102#1947C2212yes—
103#1944C2212yes—
104#1943C2212yes—
105#1942C2212yes—
106#1942C2212yes—
107#1941C2212yes—
108#1941C2212yes—
109#1854C2212yes—
110#1854C2212yes—
111#1854C2212yes—
112#1854C2212yes—
113#1854C2212yes—
114#1854C2212yes—
115#1853C2212yes—
116#1852C2212yes—
117#1847C2211yescharacteristic
118#1847C2211yescharacteristic
119#1847C2211yescharacteristic
120#1836C2212yes—
121#1836C2212yes—
122#1809C2212yes—
123#1809C2212yes—
124#1808C2212yes—
125#1807C2212yes—
126#1776C2212yes—
127#1776C2212yes—
128#1771C2212yes—
129#1767C2211yescharacteristic
130#1753C2212yes—
131C8×C22⋊C4C2212yes—
132#1749C2211yescharacteristic
133#1749C2211yescharacteristic
134#1736C2212yes—
135#1736C2212yes—
136#1735C2212yes—
137#1735C2212yes—
138C4×#97C2211yescharacteristic
139C22×M16C2312yes—
140C23×C8C2312yes—
141#533—24no—
142#533—24no—
143#533—42no—
144#533—42no—
145C2×C4⋊Q8—21no—
146C2×C4⋊Q8—21no—
147C2×C4⋊Q8C2311yescharacteristic
148C2×C4⋊Q8C2311yescharacteristic
149C2×C4⋊Q8C2311yescharacteristic
150C2×C4⋊Q8C2311yescharacteristic
151C2×C4⋊Q8C2311yescharacteristic
152C2×#125C2311yescharacteristic
153C2×#125C2312yes—
154C2×#125C2312yes—
155C2×C22⋊Q8—21no—
156C2×C22⋊Q8—21no—
157C2×C22⋊Q8—21no—
158C2×C22⋊Q8—21no—
159C2×C22⋊Q8—21no—
160C2×C22⋊Q8—21no—
161C2×C22⋊Q8—21no—
162C2×C22⋊Q8—21no—
163C2×C4×Q8—21no—
164C2×C4×Q8—21no—
165C2×C4×Q8—21no—
166C2×C4×Q8—21no—
167C2×C4×Q8—21no—
168C2×C4×D4D411yescharacteristic
169C2×C4×D4D411yescharacteristic
170C2×C4×D4C2311yescharacteristic
171C2×#117C2312yes—
172C2×#117C2312yes—
173C2×#117C2311yescharacteristic
174C2×#117C2311yescharacteristic
175C22×C4⋊C4C2311yescharacteristic
176C22×C4⋊C4C2311yescharacteristic
177C22×C42C2311yescharacteristic
178C22×C42C2311yescharacteristic
179#501—24no—
180#501—42no—
181#501—42no—
182#435Q8116yescomplemented
183C2×#107C2312yes—
184C2×#107C2312yes—
185C2×#107C2312yes—
186C2×#107C2312yes—
187C2×#107C2312yes—
188C2×#107C2312yes—
189C2×#106C2312yes—
190C2×#106C2312yes—
191C2×#106C2312yes—
192C2×#106C2312yes—
193C2×#106C2312yes—
194C2×#106C2312yes—
195C2×C4⋊C8C2312yes—
196C2×C22⋊C8C2312yes—
197C2×C22⋊C8C2312yes—
198C4×M16—42no—
199C2×#97—42no—
200C2×#97C2311yescharacteristic
201C2×#97C2311yescharacteristic
202C2×#97C2311yescharacteristic
203C2×#97C2311yescharacteristic
204C2×#97C2312yes—
205C2×#97C2312yes—
206C2×C4×C8C2312yes—
207C2×C4×C8C2312yes—
208#400—21no—
209#400—21no—
210#399—22no—
211#399—22no—
212#398—21no—
213#398—21no—
214#398—21no—
215#398—21no—
216#398—22no—
217#398—22no—
218#396—21no—
219#396—21no—
220#396—22no—
221#396—22no—
222#395—21no—
223#395—21no—
224#393—21no—
225#393—21no—
226#391—21no—
227#391—21no—
228#391—21no—
229#391—21no—
230#391—21no—
231#391—21no—
232#391—21no—
233#391—21no—
234#391—21no—
235#390—22no—
236#389—22no—
237#389—21no—
238#389—21no—
239#389—21no—
240#389—22no—
241#389—22no—
242#389C2311yescharacteristic
243#389C2311yescharacteristic
244#389C2312yes—
245#389C2311yescharacteristic
246#389C2311yescharacteristic
247#389C2311yescharacteristic
248#389C2311yescharacteristic
249#389C2312yes—
250#389C2312yes—
251#388—21no—
252#388—21no—
253#388—22no—
254#388—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#387—21no—
264#387—21no—
265#387—21no—
266#387—21no—
267#387—22no—
268#387—22no—
269#387—21no—
270#387—21no—
271#386—21no—
272#386—21no—
273#385—21no—
274#385—21no—
275#385—21no—
276#385—21no—
277#385—21no—
278#385—21no—
279#384—22no—
280#384—21no—
281#384—21no—
282#384C2311yescharacteristic
283#384C2311yescharacteristic
284#384C2311yescharacteristic
285#384C2312yes—
286#384C2312yes—
287#382—21no—
288#382—21no—
289#382C2311yescharacteristic
290#382C2311yescharacteristic
291#382C2311yescharacteristic
292#382C2311yescharacteristic
293#382C2311yescharacteristic
294#382C2311yescharacteristic
295#382C2311yescharacteristic
296#380—21no—
297#380—21no—
298#380—21no—
299#380—21no—
300#380C2311yescharacteristic
301#380C2312yes—
302#380C2311yescharacteristic
303#380C2311yescharacteristic
304#380C2311yescharacteristic
305#380C2312yes—
306C4×C4⋊C4—22no—
307C4×C4⋊C4—21no—
308C4×C4⋊C4—21no—
309C4×C4⋊C4—21no—
310C4×C4⋊C4—21no—
311C4×C4⋊C4—21no—
312C4×C4⋊C4D411yescharacteristic
313C4×C4⋊C4D411yescharacteristic
314C4×C4⋊C4C2311yescharacteristic
315C4×C4⋊C4C2311yescharacteristic
316C4×C4⋊C4C2312yes—
317C4×C4⋊C4C2311yescharacteristic
318C4×C22⋊C4—21no—
319C4×C22⋊C4—21no—
320C4×C22⋊C4D411yescharacteristic
321C4×C22⋊C4D411yescharacteristic
322C4×C22⋊C4D411yescharacteristic
323C4×C22⋊C4D411yescharacteristic
324C4×C22⋊C4C2311yescharacteristic
325C4×C22⋊C4C2311yescharacteristic
326C2×#95—21no—
327C2×#95—21no—
328C43C2311yescharacteristic
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#340C2312yes—
345#340C2312yes—
346#340C2312yes—
347#340C2312yes—
348#340C2312yes—
349#336C2312yes—
350#336C2312yes—
351#336C2312yes—
352C22×Q8—21no—
353C22×Q8—21no—
354C22×Q8—21no—
355C22×Q8—21no—
356C22×Q8—21no—
357C22×D4C2×D411yescharacteristic
358C23×C4—21no—
359C23×C4—21no—
360C23×C4C2×D411yescharacteristic
361C23×C4C2×D411yescharacteristic
362C23×C4C2×D411yescharacteristic
363C23×C4C2×D411yescharacteristic
364C23×C4C2411yescharacteristic
365C23×C4C2411yescharacteristic
366C2×M16—42no—
367C2×M16—42no—
368C2×M16C2×Q818yes—
369C22×C8—42no—
370C22×C8—42no—
371C22×C8C2×Q818yes—
372C22×C8C2412yes—
373C22×C8C2412yes—
374C22×C8C2412yes—
375C22×C8C2412yes—
376C4⋊Q8—22no—
377C4⋊Q8—22no—
378C4⋊Q8—22no—
379C4⋊Q8—22no—
380C4⋊Q8—22no—
381C4⋊Q8—42no—
382C4⋊Q8—42no—
383C4⋊Q8—44no—
384C4⋊Q8—82no—
385C4⋊Q8#4114yes—
386#125—24no—
387#125—24no—
388#125—22no—
389#125—22no—
390#125—42no—
391#125—42no—
392C22⋊Q8—44no—
393C22⋊Q8—44no—
394C22⋊Q8—44no—
395C22⋊Q8—44no—
396C22⋊Q8—44no—
397C22⋊Q8—44no—
398C22⋊Q8—82no—
399C22⋊Q8—82no—
400C4×Q8—44no—
401C4×Q8—44no—
402C4×Q8—44no—
403C4×Q8—44no—
404C4×Q8—44no—
405C4×D4—42no—
406C4×D4—42no—
407C4×D4C2×Q818yes—
408#117—24no—
409#117—24no—
410#117—42no—
411#117—42no—
412#117—42no—
413#117—42no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—21no—
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—22no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—42no—
447C2×C4⋊C4—42no—
448C2×C4⋊C4C2×D411yescharacteristic
449C2×C4⋊C4C2×D411yescharacteristic
450C2×C4⋊C4C2×D411yescharacteristic
451C2×C4⋊C4C2411yescharacteristic
452C2×C4⋊C4C2411yescharacteristic
453C2×C4⋊C4C2411yescharacteristic
454C2×C4⋊C4C2411yescharacteristic
455C2×C4⋊C4C2412yes—
456C2×C4⋊C4C2412yes—
457C2×C4⋊C4C2411yescharacteristic
458C2×C4⋊C4C2411yescharacteristic
459C2×C4⋊C4C2411yescharacteristic
460C2×C4⋊C4C2411yescharacteristic
461C2×C4⋊C4C2412yes—
462C2×C4⋊C4C2412yes—
463C2×C22⋊C4—22no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—22no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4C2×D411yescharacteristic
474C2×C22⋊C4C2×D411yescharacteristic
475C2×C22⋊C4C2×D411yescharacteristic
476C2×C22⋊C4C2×D411yescharacteristic
477C2×C22⋊C4C2×D411yescharacteristic
478C2×C22⋊C4C2×D411yescharacteristic
479C2×C42—22no—
480C2×C42—22no—
481C2×C42—22no—
482C2×C42—22no—
483C2×C42—22no—
484C2×C42—22no—
485C2×C42—22no—
486C2×C42—21no—
487C2×C42—21no—
488C2×C42—21no—
489C2×C42—21no—
490C2×C42C2×D411yescharacteristic
491C2×C42C2×D411yescharacteristic
492C2×C42C2×D411yescharacteristic
493C2×C42C2×D411yescharacteristic
494C2×C42C2×D411yescharacteristic
495C2×C42C2×D411yescharacteristic
496C2×C42C2×D411yescharacteristic
497C2×C42C2×D411yescharacteristic
498C2×C42C2411yescharacteristic
499C2×C42C2411yescharacteristic
500C2×C42C2411yescharacteristic
501C2×C42C2411yescharacteristic
502C2×C42C2411yescharacteristic
503#107—24no—
504#107—42no—
505#107—42no—
506#107—42no—
507#107—42no—
508#107—42no—
509#106—24no—
510#106—42no—
511#106—42no—
512#106—42no—
513#106—42no—
514#106—42no—
515C4⋊C8C2×Q818yes—
516C22⋊C8C2×Q818yes—
517C22⋊C8C2×Q818yes—
518#97—22no—
519#97—22no—
520#97—22no—
521#97—22no—
522#97—42no—
523#97C2×Q818yes—
524C4×C8—42no—
525C4×C8—42no—
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—21no—
537#95—21no—
538#95—21no—
539#95—21no—
540#95—22no—
541#95—22no—
542#95—21no—
543#95—21no—
544#95—22no—
545#95—21no—
546#95—21no—
547#95—22no—
548#95—22no—
549#95—22no—
550#95—21no—
551#95—21no—
552#95—21no—
553#95—21no—
554#95—21no—
555#95—21no—
556#95—21no—
557#95—21no—
558#95C2×D411yescharacteristic
559#95C2×D411yescharacteristic
560#95C2×D411yescharacteristic
561#95C2×D411yescharacteristic
562#95C2×D411yescharacteristic
563#95C2×D411yescharacteristic
564C24C22×D411yescharacteristic
565C24C22×D411yescharacteristic
566C2×Q8—24no—
567C2×Q8—42no—
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×Q8—42no—
577C2×Q8—81no—
578C2×Q8—81no—
579C2×Q8—81no—
580C2×Q8—81no—
581C2×D4—41no—
582C2×D4—41no—
583C2×D4C4⋊Q814yes—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—22no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—41no—
607C22×C4—41no—
608C22×C4—41no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4—41no—
613C22×C4—41no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4—81no—
617C22×C4—81no—
618C22×C4—81no—
619C22×C4—81no—
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×C4C22×Q814yes—
633C22×C4C22×Q814yes—
634C22×C4C2511yescharacteristic
635M16—48no—
636C2×C8—22no—
637C2×C8—22no—
638C2×C8—22no—
639C2×C8—22no—
640C2×C8—22no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—48no—
645C2×C8C22×Q814yes—
646C2×C8C22×Q814yes—
647C2×C8C22×Q814yes—
648C2×C8C22×Q814yes—
649C4⋊C4—24no—
650C4⋊C4—22no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—22no—
654C4⋊C4—22no—
655C4⋊C4—21no—
656C4⋊C4—22no—
657C4⋊C4—22no—
658C4⋊C4—21no—
659C4⋊C4—22no—
660C4⋊C4—22no—
661C4⋊C4—22no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—22no—
665C4⋊C4—22no—
666C4⋊C4—22no—
667C4⋊C4—41no—
668C4⋊C4—41no—
669C4⋊C4—44no—
670C4⋊C4—44no—
671C4⋊C4—44no—
672C4⋊C4—44no—
673C4⋊C4—42no—
674C4⋊C4—42no—
675C4⋊C4—42no—
676C4⋊C4—42no—
677C4⋊C4—42no—
678C4⋊C4—42no—
679C4⋊C4—44no—
680C4⋊C4—42no—
681C4⋊C4—42no—
682C4⋊C4—42no—
683C4⋊C4—42no—
684C4⋊C4—44no—
685C4⋊C4—42no—
686C4⋊C4—42no—
687C4⋊C4—44no—
688C4⋊C4—81no—
689C4⋊C4—81no—
690C4⋊C4—81no—
691C4⋊C4—81no—
692C4⋊C4—81no—
693C4⋊C4—81no—
694C4⋊C4—82no—
695C4⋊C4—82no—
696C4⋊C4—81no—
697C4⋊C4—81no—
698C4⋊C4—82no—
699C4⋊C4—82no—
700C4⋊C4C4⋊Q814yes—
701C4⋊C4C2×#4114yes—
702C22⋊C4—22no—
703C22⋊C4—22no—
704C22⋊C4—22no—
705C22⋊C4—22no—
706C22⋊C4—44no—
707C22⋊C4—44no—
708C22⋊C4—42no—
709C22⋊C4—42no—
710C22⋊C4—81no—
711C22⋊C4—81no—
712C22⋊C4—81no—
713C22⋊C4—81no—
714C22⋊C4—82no—
715C22⋊C4—82no—
716C22⋊C4C4⋊Q814yes—
717C22⋊C4C4⋊Q814yes—
718C42—22no—
719C42—22no—
720C42—22no—
721C42—22no—
722C42—22no—
723C42—22no—
724C42—21no—
725C42—21no—
726C42—21no—
727C42—21no—
728C42—22no—
729C42—41no—
730C42—41no—
731C42—44no—
732C42—44no—
733C42—44no—
734C42—81no—
735C42—81no—
736C42—81no—
737C42—81no—
738C42C22×Q814yes—
739C42C2×#4112yes—
740C42H(5,𝔽2)12yes—
741C23—21no—
742C23—21no—
743C23—21no—
744C23—21no—
745C23—21no—
746C23—21no—
747C23—21no—
748C23—21no—
749C23—21no—
750C23—21no—
751C23—21no—
752C23—21no—
753C23C2×C4⋊Q812yes—
754C23C2×C4⋊Q812yes—
755C23C23×D411yescharacteristic
756Q8—48no—
757Q8—84no—
758Q8—84no—
759Q8—162no—
760Q8—162no—
761D4—44no—
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—24no—
779C2×C4—24no—
780C2×C4—24no—
781C2×C4—24no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—24no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—42no—
809C2×C4—42no—
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—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—82no—
831C2×C4—82no—
832C2×C4—82no—
833C2×C4—82no—
834C2×C4—162no—
835C2×C4—162no—
836C2×C4C2×C4⋊Q812yes—
837C2×C4C2×C4⋊Q812yes—
838C2×C4C2×C4⋊Q812yes—
839C2×C4C2×C4⋊Q812yes—
840C2×C4#54612yes—
841C2×C4#54612yes—
842C2×C4#57512yes—
843C2×C4#57512yes—
844C2×C4C23×Q812yes—
845C2×C4C22×#4111yescharacteristic
846C2×C4C2×H(5,𝔽2)11yescharacteristic
847C2×C4#58512yes—
848C8—24no—
849C8—24no—
850C8—24no—
851C8—24no—
852C22—22no—
853C22—22no—
854C22—22no—
855C22—22no—
856C22—22no—
857C22—22no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22C22×C4⋊Q811yescharacteristic
867C22C2×#54611yescharacteristic
868C22#350011yescharacteristic
869C22C2×#57511yescharacteristic
870C22C2×#57511yescharacteristic
871C22#358511yescharacteristic
872C22#358611yescharacteristic
873C4—22no—
874C4—22no—
875C4—22no—
876C4—22no—
877C4—22no—
878C4—22no—
879C4—22no—
880C4—22no—
881C4—41no—
882C4—41no—
883C4—44no—
884C4—41no—
885C4—41no—
886C4—82no—
887C4—81no—
888C4—81no—
889C4—81no—
890C4—81no—
891C4—81no—
892C4—81no—
893C4—81no—
894C4—81no—
895C4—82no—
896C4—82no—
897C4Q8×#4112yes—
898C4#350112yes—
899C2—42no—
900C2—42no—
901C2#3627611yescharacteristic
902C2#6066311yescharacteristic
903C2#6066811yescharacteristic
904C2#6115911yescharacteristic
905C2#6116011yescharacteristic
906C2#6258411yescharacteristic
907C2#6258511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #33293C2semidirect
4. #33218C2semidirect
5. #33217C2semidirect
6. #29211C2semidirect
7. #28807C2semidirect
8. #28805C2semidirect
9. #28783C2semidirect
10. #28781C2semidirect
11. #28774C2semidirect
12. #28773C2semidirect
13. #28694C2semidirect
14. #27956C2semidirect
15. #27955C2semidirect
16. #25817C2semidirect
17. #25817C2semidirect
20. #21731C2semidirect
21. #21323C2semidirect
22. #21321C2semidirect
182. #435Q8semidirect

Maximal subgroups

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

subgroupindex
#361912
#361342
#332932
#332182
#332172
#292112
#288072
#288052
#287832
#287812
#287742
#287732
#286942
#279562
#279552
#258172
#227122
#227102
#217312
#213232
#213212
#204912