Finite Group Databasebeta

← #6855567

Subgroups — #6855567

Order 512.

1433 conjugacy classes of subgroups.

The subgroup lattice has 902 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36598C211yesmaximal, characteristic, complemented
2#34929C211yesmaximal, characteristic
3#33026C211yesmaximal, characteristic
4#32566C212yesmaximal, complemented
5#32546C212yesmaximal
6#32428C212yesmaximal
7#32228C212yesmaximal, complemented
8#29868C211yesmaximal, characteristic
9#29828C211yesmaximal, characteristic
10#29347C211yesmaximal, characteristic, complemented
11#29347C211yesmaximal, characteristic, complemented
12#29287C211yesmaximal, characteristic, complemented
13#29273C211yesmaximal, characteristic, complemented
14#29255C211yesmaximal, characteristic, complemented
15#29218C211yesmaximal, characteristic, complemented
16#29075C212yesmaximal
17#28030C212yesmaximal, complemented
18#27426C212yesmaximal
19#27362C212yesmaximal, complemented
20#22821C211yesmaximal, characteristic, complemented
21#22146C211yesmaximal, characteristic
22#22111C211yesmaximal, characteristic
23C4×#476C211yesmaximal, characteristic
24C2×#533—21no—
25C2×#476C2211yescharacteristic
26C2×#476C2211yescharacteristic
27C2×#461C2211yescharacteristic
28#2868C2211yescharacteristic
29#2862C2211yescharacteristic
30#2862C2211yescharacteristic
31#2582C2212yes—
32#2571—21no—
33#2570—21no—
34#2570—21no—
35#2568—21no—
36#2556—21no—
37#2556—21no—
38#2551C2211yescharacteristic
39#2546C2211yescharacteristic
40#2542C2211yescharacteristic
41#2538C2211yescharacteristic
42#2511C2212yes—
43#2511C2212yes—
44#2506C2211yescharacteristic
45#2506C2211yescharacteristic
46#2492—21no—
47#2452C2211yescharacteristic
48#2452C2211yescharacteristic
49#2446—21no—
50#2446—21no—
51#2429—21no—
52#2396—21no—
53#2396—21no—
54#2365—21no—
55#2355—21no—
56#2355C2212yes—
57C4×C4⋊Q8C2211yescharacteristic
58C4×C4⋊Q8C2211yescharacteristic
59C4×C4⋊Q8C2211yescharacteristic
60C4×C4⋊Q8C2211yescharacteristic
61C4×C4⋊Q8C2211yescharacteristic
62C4×C4⋊Q8C2211yescharacteristic
63C4×C22⋊Q8—21no—
64#2293C2211yescharacteristic
65#2293C2211yescharacteristic
66C42×Q8C2211yescharacteristic
67C42×D4C2211yescharacteristic
68#2100C2212yes—
69#2100C2212yes—
70#2099C2212yes—
71#2096C2212yes—
72#2088C2212yes—
73#2088C2212yes—
74#2084C2212yes—
75#2084C2212yes—
76#2072C2212yes—
77#2072C2212yes—
78#2071C2212yes—
79#2071C2212yes—
80#2066C2212yes—
81#2066C2212yes—
82#2058C2212yes—
83#2055C2212yes—
84#2055C2212yes—
85#2024C2212yes—
86#2024C2212yes—
87#2024C2212yes—
88#1990C2212yes—
89#1988C2212yes—
90#1987C2211yescharacteristic
91#1987C2211yescharacteristic
92#1987C2211yescharacteristic
93#1987C2211yescharacteristic
94#1987C2211yescharacteristic
95#1987C2211yescharacteristic
96#1984C2212yes—
97#1981C2211yescharacteristic
98#1981C2211yescharacteristic
99#1981C2211yescharacteristic
100#1968C2212yes—
101#1948C2211yescharacteristic
102#1948C2211yescharacteristic
103#1948C2211yescharacteristic
104#1948C2212yes—
105#1941C2212yes—
106#1934C2212yes—
107#1933C2212yes—
108#1933C2212yes—
109#1933C2212yes—
110#1933C2212yes—
111#1933C2212yes—
112#1927C2212yes—
113#1927C2212yes—
114#1926C2212yes—
115#1920C2212yes—
116#1919C2212yes—
117#1919C2212yes—
118#1919C2212yes—
119#1916C2212yes—
120#1916C2212yes—
121#1880C2212yes—
122#1877C2212yes—
123#1877C2212yes—
124#1865C2212yes—
125#1865C2212yes—
126#1865C2212yes—
127#1864C2212yes—
128#1842C2211yescharacteristic
129#1834C2212yes—
130#1831C2211yescharacteristic
131#1831C2211yescharacteristic
132#1802C2211yescharacteristic
133C4×#106C2212yes—
134C8×C4⋊C4C2212yes—
135C4×C4⋊C8C2211yescharacteristic
136C4×C4⋊C8C2211yescharacteristic
137C4×C4⋊C8C2211yescharacteristic
138C4×#102C2212yes—
139C22×SD16C2312yes—
140#533—48no—
141C2×C4⋊Q8—21no—
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×#125—21no—
152C2×#125—21no—
153C2×C22⋊Q8—21no—
154C2×C22⋊Q8—21no—
155C2×C22⋊Q8—21no—
156C2×C22⋊Q8—21no—
157C2×C22⋊Q8—21no—
158C2×C4×Q8—21no—
159C2×C4×Q8—21no—
160C2×C4×Q8—21no—
161C2×C4×Q8—21no—
162C2×C4×Q8—21no—
163C2×C4×Q8D411yescharacteristic
164C2×C4×Q8D411yescharacteristic
165C2×C4×Q8C2312yes—
166C2×C4×Q8C2311yescharacteristic
167C2×C4×D4C2311yescharacteristic
168C2×C4×D4C2311yescharacteristic
169C2×C4×D4C2311yescharacteristic
170C2×#117—21no—
171C2×#117—21no—
172C22×C42—21no—
173#476—24no—
174#476—24no—
175#461—24no—
176C2×#106C2312yes—
177C2×#106C2312yes—
178C2×#106C2312yes—
179C2×#106C2312yes—
180C2×#106C2312yes—
181C2×C4⋊C8C2311yescharacteristic
182C2×C4⋊C8C2311yescharacteristic
183C2×C4⋊C8C2311yescharacteristic
184C2×C4⋊C8C2311yescharacteristic
185C2×C4⋊C8C2312yes—
186C2×C4⋊C8C2312yes—
187C2×#103C2312yes—
188C2×#103C2312yes—
189C2×#103C2312yes—
190C2×#103C2312yes—
191C2×#103C2312yes—
192C2×#103C2312yes—
193C2×#103C2312yes—
194C2×#102C2312yes—
195C2×#102C2312yes—
196C2×#102C2312yes—
197C2×C4×C8C2312yes—
198C2×C4×C8C2312yes—
199C2×C4×C8C2312yes—
200#400—22no—
201#400—22no—
202#400—22no—
203#400—22no—
204#400—21no—
205#400—21no—
206#399—21no—
207#399—21no—
208#398—22no—
209#398—22no—
210#398—21no—
211#398—21no—
212#398—21no—
213#398—21no—
214#396—21no—
215#396—21no—
216#396—21no—
217#396—21no—
218#395—21no—
219#395—21no—
220#393—21no—
221#393—21no—
222#391—22no—
223#391—21no—
224#391—21no—
225#391—21no—
226#391—21no—
227#391—21no—
228#391—21no—
229#391—21no—
230#391—21no—
231#391—21no—
232#391—21no—
233#391C2312yes—
234#391C2312yes—
235#391C2312yes—
236#391C2312yes—
237#391C2312yes—
238#390C2311yescharacteristic
239#390C2311yescharacteristic
240#390C2311yescharacteristic
241#390C2311yescharacteristic
242#389—22no—
243#389—21no—
244#389—21no—
245#389—21no—
246#389—21no—
247#389—21no—
248#389—21no—
249#389—21no—
250#389—21no—
251#389C2312yes—
252#389C2312yes—
253#389C2311yescharacteristic
254#389C2311yescharacteristic
255#389C2311yescharacteristic
256#389C2311yescharacteristic
257#389C2311yescharacteristic
258#389C2311yescharacteristic
259#389C2311yescharacteristic
260#389C2311yescharacteristic
261#389C2311yescharacteristic
262#389C2311yescharacteristic
263#388—21no—
264#388—21no—
265#388—21no—
266#388—21no—
267#387—22no—
268#387—22no—
269#387—22no—
270#387—22no—
271#387—22no—
272#387—22no—
273#387—21no—
274#387—21no—
275#385—21no—
276#385—21no—
277#384—21no—
278#384—21no—
279#384C2311yescharacteristic
280#384C2311yescharacteristic
281#384C2311yescharacteristic
282#384C2311yescharacteristic
283#384C2312yes—
284#384C2312yes—
285#382—22no—
286#382—21no—
287#382—21no—
288#382—21no—
289#382—21no—
290#380—21no—
291C4×C4⋊C4—22no—
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×C22⋊C4—21no—
316C4×C22⋊C4—21no—
317C4×C22⋊C4—21no—
318C4×C22⋊C4—21no—
319C4×C22⋊C4—21no—
320C43C2311yescharacteristic
321C43C2311yescharacteristic
322C43C2311yescharacteristic
323#340C2312yes—
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#336C2312yes—
340#336C2312yes—
341#336C2312yes—
342#336C2312yes—
343#336C2312yes—
344#336C2312yes—
345#336C2312yes—
346C22×Q8—21no—
347C22×Q8—21no—
348C22×Q8—21no—
349C22×Q8—21no—
350C22×Q8—21no—
351C22×Q8C2×D411yescharacteristic
352C22×Q8C2412yes—
353C22×D4C2411yescharacteristic
354C23×C4—21no—
355C23×C4—21no—
356C23×C4—21no—
357C2×SD16—24no—
358C2×SD16—42no—
359C2×SD16—42no—
360C22×C8C2412yes—
361C22×C8C2412yes—
362C22×C8C2412yes—
363C22×C8C2412yes—
364C4⋊Q8—22no—
365C4⋊Q8—22no—
366C4⋊Q8—22no—
367C4⋊Q8—22no—
368C4⋊Q8—22no—
369C4⋊Q8—22no—
370C4⋊Q8—22no—
371C4⋊Q8—22no—
372C4⋊Q8—41no—
373C4⋊Q8—41no—
374C4⋊Q8—41no—
375C4⋊Q8—41no—
376C4⋊Q8—44no—
377C4⋊Q8—44no—
378C4⋊Q8—44no—
379C4⋊Q8—82no—
380#125—44no—
381#125—44no—
382C22⋊Q8—44no—
383C22⋊Q8—44no—
384C22⋊Q8—44no—
385C22⋊Q8—44no—
386C22⋊Q8—44no—
387C4×Q8—41no—
388C4×Q8—41no—
389C4×Q8—42no—
390C4×Q8—42no—
391C4×Q8—42no—
392C4×Q8—44no—
393C4×Q8—44no—
394C4×Q8—44no—
395C4×Q8—82no—
396C4×Q8—82no—
397C4×Q8SD1618yescomplemented
398C4×D4—22no—
399C4×D4—22no—
400C4×D4—41no—
401C4×D4—41no—
402C4×D4—41no—
403C4×D4#4114yes—
404#117—44no—
405#117—44no—
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—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
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—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
447C2×C4⋊C4C2411yescharacteristic
448C2×C4⋊C4C2412yes—
449C2×C4⋊C4C2412yes—
450C2×C4⋊C4C2412yes—
451C2×C4⋊C4C2411yescharacteristic
452C2×C4⋊C4C2411yescharacteristic
453C2×C4⋊C4C2411yescharacteristic
454C2×C4⋊C4C2411yescharacteristic
455C2×C4⋊C4C2411yescharacteristic
456C2×C4⋊C4C2411yescharacteristic
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C42—21no—
469C2×C42—21no—
470C2×C42—21no—
471C2×C42—22no—
472C2×C42—21no—
473C2×C42—21no—
474C2×C42—22no—
475C2×C42—22no—
476C2×C42—44no—
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×C42C2×D411yescharacteristic
488C2×C42C2×D411yescharacteristic
489C2×C42C2411yescharacteristic
490C2×C42C2411yescharacteristic
491C2×C42C2411yescharacteristic
492C2×C42C2411yescharacteristic
493C2×C42C2411yescharacteristic
494C2×C42C2411yescharacteristic
495C2×C42C2411yescharacteristic
496#106—24no—
497#106—24no—
498#106—42no—
499#106—42no—
500#106—42no—
501C4⋊C8—22no—
502C4⋊C8—22no—
503C4⋊C8—22no—
504C4⋊C8—22no—
505C4⋊C8—42no—
506C4⋊C8—42no—
507#103—24no—
508#103—24no—
509#103—42no—
510#103—42no—
511#103—42no—
512#103—42no—
513#103—42no—
514#102—24no—
515#102—24no—
516#102—42no—
517C4×C8—42no—
518C4×C8—42no—
519C4×C8—42no—
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—22no—
530#95—22no—
531#95—21no—
532#95—21no—
533#95—22no—
534#95—22no—
535#95—22no—
536#95—22no—
537#95—21no—
538#95—21no—
539#95—22no—
540#95—22no—
541#95—21no—
542#95—21no—
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
555C24—21no—
556C2×Q8—22no—
557C2×Q8—22no—
558C2×Q8—22no—
559C2×Q8—22no—
560C2×Q8—22no—
561C2×Q8—22no—
562C2×Q8—41no—
563C2×Q8—41no—
564C2×Q8—42no—
565C2×Q8—42no—
566C2×Q8—42no—
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×Q8C2×SD1614yes—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4C2×#4112yes—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—24no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—81no—
606C22×C4C22×D411yescharacteristic
607C22×C4C22×D411yescharacteristic
608C22×C4C22×D411yescharacteristic
609C22×C4C22×D411yescharacteristic
610C22×C4C22×D411yescharacteristic
611C22×C4C22×D411yescharacteristic
612C22×C4C22×D411yescharacteristic
613C22×C4C22×D411yescharacteristic
614C22×C4C22×D411yescharacteristic
615C22×C4C22×D411yescharacteristic
616C22×C4C22×D411yescharacteristic
617C22×C4C22×D411yescharacteristic
618C22×C4C22×D411yescharacteristic
619C22×C4C22×D411yescharacteristic
620C22×C4C2511yescharacteristic
621SD16—84no—
622C2×C8—22no—
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—22no—
627C2×C8—22no—
628C2×C8—22no—
629C2×C8—22no—
630C2×C8—22no—
631C2×C8—22no—
632C2×C8—22no—
633C2×C8—22no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—22no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—22no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—22no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—22no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—41no—
655C4⋊C4—41no—
656C4⋊C4—41no—
657C4⋊C4—41no—
658C4⋊C4—42no—
659C4⋊C4—42no—
660C4⋊C4—44no—
661C4⋊C4—42no—
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—42no—
671C4⋊C4—42no—
672C4⋊C4—42no—
673C4⋊C4—42no—
674C4⋊C4—42no—
675C4⋊C4—42no—
676C4⋊C4—42no—
677C4⋊C4—42no—
678C4⋊C4—42no—
679C4⋊C4—42no—
680C4⋊C4—42no—
681C4⋊C4—42no—
682C4⋊C4—42no—
683C4⋊C4—44no—
684C4⋊C4—42no—
685C4⋊C4—81no—
686C4⋊C4—82no—
687C4⋊C4—82no—
688C4⋊C4—82no—
689C4⋊C4—82no—
690C4⋊C4C2×SD1614yes—
691C4⋊C4C2×SD1614yes—
692C4⋊C4C2×SD1614yes—
693C4⋊C4C2×#4112yes—
694C4⋊C42−1+412yes—
695C22⋊C4—24no—
696C22⋊C4—42no—
697C22⋊C4—42no—
698C22⋊C4—42no—
699C22⋊C4—42no—
700C22⋊C4—42no—
701C22⋊C4—42no—
702C22⋊C4—42no—
703C22⋊C4—42no—
704C22⋊C4—81no—
705C22⋊C4—81no—
706C42—22no—
707C42—22no—
708C42—22no—
709C42—22no—
710C42—21no—
711C42—21no—
712C42—21no—
713C42—21no—
714C42—21no—
715C42—21no—
716C42—21no—
717C42—21no—
718C42—21no—
719C42—21no—
720C42—21no—
721C42—21no—
722C42—41no—
723C42—41no—
724C42—41no—
725C42—41no—
726C42—41no—
727C42—44no—
728C42—42no—
729C42—42no—
730C42—42no—
731C42—42no—
732C42—42no—
733C42—82no—
734C42—82no—
735C42C2×SD1614yes—
736C42C2×SD1614yes—
737C42C2×SD1614yes—
738C42C2×#4112yes—
739C422−1+412yes—
740C23—22no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23C23×D411yescharacteristic
748Q8—44no—
749Q8—42no—
750Q8—42no—
751Q8—42no—
752Q8—42no—
753Q8—84no—
754Q8—84no—
755Q8—84no—
756Q8—84no—
757Q8—84no—
758D4—22no—
759D4—22no—
760D4—41no—
761D4—41no—
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—21no—
786C2×C4—21no—
787C2×C4—22no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—48no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—42no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—84no—
828C2×C4—84no—
829C2×C4#54812yes—
830C2×C4#54812yes—
831C2×C4C22×SD1612yes—
832C2×C4C22×SD1612yes—
833C2×C4C22×SD1612yes—
834C2×C4C22×SD1612yes—
835C2×C4C22×SD1612yes—
836C2×C4C22×SD1612yes—
837C2×C4C22×SD1612yes—
838C2×C4#57512yes—
839C2×C4#57812yes—
840C2×C4C22×#4111yescharacteristic
841C2×C4C2×2−1+411yescharacteristic
842C2×C4C2×2−1+411yescharacteristic
843C2×C4#58511yescharacteristic
844C2×C4#58511yescharacteristic
845C2×C4#58511yescharacteristic
846C8—42no—
847C8—42no—
848C8—42no—
849C8—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—81no—
854C22—81no—
855C22—81no—
856C22—81no—
857C22#344911yescharacteristic
858C22C2×#54811yescharacteristic
859C22#348911yescharacteristic
860C22C23×SD1611yescharacteristic
861C22C2×#57511yescharacteristic
862C22C2×#57811yescharacteristic
863C22#358511yescharacteristic
864C4—22no—
865C4—22no—
866C4—22no—
867C4—22no—
868C4—22no—
869C4—22no—
870C4—22no—
871C4—22no—
872C4—41no—
873C4—41no—
874C4—41no—
875C4—42no—
876C4—42no—
877C4—41no—
878C4—41no—
879C4—81no—
880C4—81no—
881C4—81no—
882C4—82no—
883C4—82no—
884C4—82no—
885C4—82no—
886C4—81no—
887C4—81no—
888C4#335914yes—
889C4#350711yescharacteristic
890C4#351011yescharacteristic
891C4#355511yescharacteristic
892C4#355711yescharacteristic
893C2—82no—
894C2#3971911yescharacteristic
895C2#6094111yescharacteristic
896C2#6099311yescharacteristic
897C2C2×#335911yescharacteristic
898C2#6132411yescharacteristic
899C2#6209611yescharacteristic
900C2#6213011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C24
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36598C2semidirect
4. #32566C2semidirect
7. #32228C2semidirect
10. #29347C2semidirect
11. #29347C2semidirect
12. #29287C2semidirect
13. #29273C2semidirect
14. #29255C2semidirect
15. #29218C2semidirect
17. #28030C2semidirect
19. #27362C2semidirect
20. #22821C2semidirect
397. C4×Q8SD16semidirect

Maximal subgroups

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

subgroupindex
#365982
#349292
#330262
#325662
#325462
#324282
#322282
#298682
#298282
#293472
#292872
#292732
#292552
#292182
#290752
#280302
#274262
#273622
#228212
#221462
#221112
C4×#4762