Finite Group Databasebeta

← #6434896

Subgroups — #6434896

Order 512.

1444 conjugacy classes of subgroups.

The subgroup lattice has 1192 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34621C211yesmaximal, characteristic
2C4×#544C211yesmaximal, characteristic, complemented
3#30163C211yesmaximal, characteristic, complemented
4#30161C211yesmaximal, characteristic, complemented
5#30158C211yesmaximal, characteristic, complemented
6#30157C211yesmaximal, characteristic, complemented
7#30104C211yesmaximal, characteristic, complemented
8#30100C211yesmaximal, characteristic, complemented
9#30071C211yesmaximal, characteristic, complemented
10#30069C211yesmaximal, characteristic, complemented
11#29979C211yesmaximal, characteristic, complemented
12#29978C211yesmaximal, characteristic, complemented
13#29917C211yesmaximal, characteristic, complemented
14#29916C211yesmaximal, characteristic, complemented
15#29765C211yesmaximal, characteristic
16#29763C211yesmaximal, characteristic
17#29647C211yesmaximal, characteristic, complemented
18#29646C211yesmaximal, characteristic, complemented
19#23838C211yesmaximal, characteristic, complemented
20#23836C211yesmaximal, characteristic, complemented
21#23819C211yesmaximal, characteristic, complemented
22#23815C211yesmaximal, characteristic, complemented
23#23778C211yesmaximal, characteristic, complemented
24#23778C211yesmaximal, characteristic, complemented
25#23775C211yesmaximal, characteristic, complemented
26#23774C211yesmaximal, characteristic, complemented
27C4×#482C211yesmaximal, characteristic, complemented
28C4×#482C211yesmaximal, characteristic, complemented
29C4×#481C211yesmaximal, characteristic, complemented
30C4×#480C211yesmaximal, characteristic, complemented
31#20782C211yesmaximal, characteristic, complemented
32C2×#544C2211yescharacteristic
33C2×#481C2211yescharacteristic
34C2×#482C2211yescharacteristic
35C2×#482C2211yescharacteristic
36C2×#480C2211yescharacteristic
37#2651—21no—
38#2651—21no—
39#2648—21no—
40#2648—21no—
41#2647C2211yescharacteristic
42#2644C2211yescharacteristic
43#2644C2211yescharacteristic
44#2641C2211yescharacteristic
45#2629C2211yescharacteristic
46#2624C2211yescharacteristic
47#2624C2211yescharacteristic
48#2619C2211yescharacteristic
49#2395—21no—
50#2395—21no—
51#2392—21no—
52#2392—21no—
53#2331—21no—
54#2331C2211yescharacteristic
55#2331C2211yescharacteristic
56#2330—21no—
57#2330C2211yescharacteristic
58#2330C2211yescharacteristic
59#2329—21no—
60#2329—21no—
61#2317C2211yescharacteristic
62#2317C2211yescharacteristic
63#2316C2211yescharacteristic
64C4×C4⋊Q8—21no—
65C4×C4⋊Q8C2211yescharacteristic
66C4×C4⋊Q8C2211yescharacteristic
67C4×#127C2211yescharacteristic
68C4×#125—21no—
69C4×#125C2211yescharacteristic
70C4×#125C2211yescharacteristic
71C4×#125C2211yescharacteristic
72C4×C22⋊Q8—21no—
73C4×C22⋊Q8—21no—
74C4×#121C2211yescharacteristic
75C4×#121C2211yescharacteristic
76#2293C2211yescharacteristic
77#2293C2211yescharacteristic
78C4×#117C2211yescharacteristic
79C4×#117C2211yescharacteristic
80C2×C4×C4⋊C4C2211yescharacteristic
81#2101C2211yescharacteristic
82#2101C2211yescharacteristic
83#2100C2211yescharacteristic
84#2100C2211yescharacteristic
85#2100C2211yescharacteristic
86#2099C2211yescharacteristic
87#2099C2211yescharacteristic
88#2099C2211yescharacteristic
89#2094C2211yescharacteristic
90#2093C2211yescharacteristic
91#2092C2211yescharacteristic
92#2092C2211yescharacteristic
93#2088C2211yescharacteristic
94#2088C2211yescharacteristic
95#2088C2211yescharacteristic
96#2088C2211yescharacteristic
97#2087C2211yescharacteristic
98#2087C2211yescharacteristic
99#2086C2211yescharacteristic
100#2086C2211yescharacteristic
101#2085C2211yescharacteristic
102#2085C2211yescharacteristic
103#2085C2211yescharacteristic
104#2085C2211yescharacteristic
105#2085C2211yescharacteristic
106#2085C2211yescharacteristic
107#2084C2211yescharacteristic
108#2083C2211yescharacteristic
109#2073C2211yescharacteristic
110#2073C2211yescharacteristic
111#2071C2211yescharacteristic
112#2071C2211yescharacteristic
113#2067C2211yescharacteristic
114#2067C2211yescharacteristic
115#2067C2211yescharacteristic
116#2067C2211yescharacteristic
117#2065C2211yescharacteristic
118#2065C2211yescharacteristic
119#2065C2211yescharacteristic
120#2065C2211yescharacteristic
121#2059C2211yescharacteristic
122#2059C2211yescharacteristic
123#2059C2211yescharacteristic
124#2059C2211yescharacteristic
125#2059C2211yescharacteristic
126#2059C2211yescharacteristic
127#2059C2211yescharacteristic
128#2059C2211yescharacteristic
129#2058C2211yescharacteristic
130#2058C2211yescharacteristic
131#2057C2211yescharacteristic
132#2057C2211yescharacteristic
133#2041C2211yescharacteristic
134#2041C2211yescharacteristic
135#2041C2211yescharacteristic
136#2041C2211yescharacteristic
137#2025C2211yescharacteristic
138#2025C2211yescharacteristic
139#2025C2211yescharacteristic
140#2025C2211yescharacteristic
141#2023C2211yescharacteristic
142#2023C2211yescharacteristic
143#2023C2211yescharacteristic
144#2023C2211yescharacteristic
145#1926C2211yescharacteristic
146#1926C2211yescharacteristic
147#1926C2211yescharacteristic
148#1926C2211yescharacteristic
149#1925C2211yescharacteristic
150#1925C2211yescharacteristic
151#1925C2211yescharacteristic
152#1925C2211yescharacteristic
153#1921C2211yescharacteristic
154#1921C2211yescharacteristic
155#1920C2211yescharacteristic
156#1920C2211yescharacteristic
157#1919C2211yescharacteristic
158#1919C2211yescharacteristic
159#1918C2211yescharacteristic
160#1918C2211yescharacteristic
161#1875C2211yescharacteristic
162#1875C2211yescharacteristic
163#1874C2211yescharacteristic
164#1874C2211yescharacteristic
165#1854C2211yescharacteristic
166#1854C2211yescharacteristic
167#1853C2211yescharacteristic
168#1852C2211yescharacteristic
169#1840C2211yescharacteristic
170#1840C2211yescharacteristic
171#1832C2211yescharacteristic
172#1832C2211yescharacteristic
173#1825C2211yescharacteristic
174#1825C2211yescharacteristic
175#1824C2211yescharacteristic
176#1823C2211yescharacteristic
177#1818C2211yescharacteristic
178#1818C2211yescharacteristic
179#1798C2211yescharacteristic
180#1798C2211yescharacteristic
181C4×#107C2211yescharacteristic
182C4×#107C2211yescharacteristic
183C4×#107C2211yescharacteristic
184C4×#107C2211yescharacteristic
185C4×#106C2211yescharacteristic
186C4×#106C2211yescharacteristic
187C4×#106C2211yescharacteristic
188C4×#106C2211yescharacteristic
189C4×C4⋊C8C2211yescharacteristic
190C4×C4⋊C8C2211yescharacteristic
191C4×#102C2211yescharacteristic
192C4×#102C2211yescharacteristic
193C4×#102C2211yescharacteristic
194C4×#102C2211yescharacteristic
195C4×#102C2211yescharacteristic
196C4×#102C2211yescharacteristic
197C4×#102C2211yescharacteristic
198C4×#102C2211yescharacteristic
199C4×C22⋊C8C2211yescharacteristic
200C4×C22⋊C8C2211yescharacteristic
201#1744C2211yescharacteristic
202#1744C2211yescharacteristic
203#544—24no—
204#544—24no—
205C2×C4⋊Q8—21no—
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×#127C2311yescharacteristic
209C2×#125—21no—
210C2×#125C2311yescharacteristic
211C2×#125C2311yescharacteristic
212C2×#125C2311yescharacteristic
213C2×C22⋊Q8—21no—
214C2×C22⋊Q8—21no—
215C2×#121C2311yescharacteristic
216C2×#121C2311yescharacteristic
217C2×C4×Q8—21no—
218C2×C4×Q8—21no—
219C2×C4×D4—21no—
220C2×C4×D4—21no—
221C2×C4×D4—21no—
222C2×C4×D4—21no—
223C2×C4×D4C2311yescharacteristic
224C2×C4×D4C2311yescharacteristic
225C2×#117—21no—
226C2×#117—21no—
227C2×#117C2311yescharacteristic
228C2×#117C2311yescharacteristic
229C2×#117C2311yescharacteristic
230C2×#117C2311yescharacteristic
231C22×C4⋊C4C2311yescharacteristic
232C22×C4⋊C4C2311yescharacteristic
233C22×C42—21no—
234C22×C42C2311yescharacteristic
235#482—24no—
236#482—24no—
237#481—24no—
238#480—24no—
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#107C2311yescharacteristic
242C2×#107C2311yescharacteristic
243C2×#107C2311yescharacteristic
244C2×#107C2311yescharacteristic
245C2×#107C2311yescharacteristic
246C2×#107C2311yescharacteristic
247C2×#106C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×#106C2311yescharacteristic
250C2×#106C2311yescharacteristic
251C2×#106C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×C4⋊C8C2311yescharacteristic
256C2×C4⋊C8C2311yescharacteristic
257C2×C4⋊C8C2311yescharacteristic
258C2×C4⋊C8C2311yescharacteristic
259C2×#102C2311yescharacteristic
260C2×#102C2311yescharacteristic
261C2×#102C2311yescharacteristic
262C2×#102C2311yescharacteristic
263C2×#102C2311yescharacteristic
264C2×#102C2311yescharacteristic
265C2×#102C2311yescharacteristic
266C2×#102C2311yescharacteristic
267C2×#102C2311yescharacteristic
268C2×#102C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×C22⋊C8C2311yescharacteristic
276C2×C22⋊C8C2311yescharacteristic
277C2×C22⋊C8C2311yescharacteristic
278C2×C22⋊C8C2311yescharacteristic
279C2×C4×C8C2311yescharacteristic
280C2×C4×C8C2311yescharacteristic
281C2×C4×C8C2311yescharacteristic
282C2×C4×C8C2311yescharacteristic
283#400—21no—
284#400—21no—
285#399—21no—
286#399—21no—
287#398—21no—
288#398—21no—
289#398—21no—
290#398—21no—
291#397—21no—
292#397—21no—
293#397—21no—
294#397—21no—
295#397—21no—
296#397—21no—
297#397—21no—
298#397—21no—
299#396—21no—
300#396—21no—
301#396—21no—
302#396—21no—
303#394—21no—
304#394—21no—
305#394—21no—
306#394—21no—
307#394—21no—
308#394—21no—
309#394—21no—
310#394—21no—
311#394—21no—
312#394—21no—
313#392—21no—
314#392—21no—
315#391—21no—
316#391—21no—
317#391—21no—
318#391—21no—
319#391—21no—
320#391—21no—
321#390—21no—
322#390—21no—
323#390C2311yescharacteristic
324#390C2311yescharacteristic
325#390C2311yescharacteristic
326#390C2311yescharacteristic
327#390C2311yescharacteristic
328#390C2311yescharacteristic
329#390C2311yescharacteristic
330#390C2311yescharacteristic
331#389—21no—
332#389—21no—
333#389—21no—
334#389—21no—
335#389—21no—
336#389—21no—
337#389—21no—
338#389—21no—
339#389—21no—
340#389—21no—
341#389C2311yescharacteristic
342#389C2311yescharacteristic
343#389C2311yescharacteristic
344#389C2311yescharacteristic
345#389C2311yescharacteristic
346#389C2311yescharacteristic
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#388—21no—
358#388—21no—
359#388—21no—
360#388—21no—
361#388—21no—
362#388—21no—
363#387—21no—
364#387—21no—
365#387—21no—
366#387—21no—
367#387—21no—
368#387—21no—
369#387—21no—
370#387—21no—
371#387—21no—
372#387—21no—
373#387—21no—
374#387—21no—
375#387—21no—
376#387—21no—
377#386—21no—
378#386—21no—
379#385—21no—
380#385—21no—
381#385—21no—
382#385—21no—
383#384—21no—
384#384C2311yescharacteristic
385#384C2311yescharacteristic
386#384C2311yescharacteristic
387#382—21no—
388#382C2311yescharacteristic
389#382C2311yescharacteristic
390#382C2311yescharacteristic
391#380—21no—
392#380—21no—
393#380C2311yescharacteristic
394#380C2311yescharacteristic
395C4×C4⋊C4—21no—
396C4×C4⋊C4—21no—
397C4×C4⋊C4—21no—
398C4×C4⋊C4—21no—
399C4×C4⋊C4—21no—
400C4×C4⋊C4—21no—
401C4×C4⋊C4—21no—
402C4×C4⋊C4—21no—
403C4×C4⋊C4—21no—
404C4×C4⋊C4—21no—
405C4×C4⋊C4D411yescharacteristic
406C4×C4⋊C4D411yescharacteristic
407C4×C4⋊C4D411yescharacteristic
408C4×C4⋊C4D411yescharacteristic
409C4×C4⋊C4C2311yescharacteristic
410C4×C4⋊C4C2311yescharacteristic
411C4×C4⋊C4C2311yescharacteristic
412C4×C4⋊C4C2311yescharacteristic
413C4×C4⋊C4C2311yescharacteristic
414C4×C4⋊C4C2311yescharacteristic
415C4×C4⋊C4C2311yescharacteristic
416C4×C4⋊C4C2311yescharacteristic
417C4×C4⋊C4C2311yescharacteristic
418C4×C4⋊C4C2311yescharacteristic
419C4×C22⋊C4—21no—
420C4×C22⋊C4—21no—
421C4×C22⋊C4—21no—
422C4×C22⋊C4—21no—
423C4×C22⋊C4—21no—
424C4×C22⋊C4—21no—
425C4×C22⋊C4D411yescharacteristic
426C4×C22⋊C4D411yescharacteristic
427C4×C22⋊C4D411yescharacteristic
428C4×C22⋊C4D411yescharacteristic
429#376—21no—
430#376C2311yescharacteristic
431#376C2311yescharacteristic
432C2×#95—21no—
433C43—21no—
434C43C2311yescharacteristic
435C43C2311yescharacteristic
436#340C2311yescharacteristic
437#340C2311yescharacteristic
438#340C2311yescharacteristic
439#340C2311yescharacteristic
440#340C2311yescharacteristic
441#340C2311yescharacteristic
442#340C2311yescharacteristic
443#340C2311yescharacteristic
444#340C2311yescharacteristic
445#340C2311yescharacteristic
446#340C2311yescharacteristic
447#340C2311yescharacteristic
448#340C2311yescharacteristic
449#340C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#336C2311yescharacteristic
469#336C2311yescharacteristic
470#336C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484C22×Q8—21no—
485C22×Q8—21no—
486C22×D4—21no—
487C22×D4—21no—
488C22×D4—21no—
489C22×D4—21no—
490C22×D4C2411yescharacteristic
491C22×D4C2411yescharacteristic
492C23×C4—21no—
493C23×C4—21no—
494C23×C4—21no—
495C23×C4—21no—
496C23×C4C2×D411yescharacteristic
497C23×C4C2×D411yescharacteristic
498C23×C4C2411yescharacteristic
499C22×C8C2411yescharacteristic
500C22×C8C2411yescharacteristic
501C22×C8C2411yescharacteristic
502C22×C8C2411yescharacteristic
503C22×C8C2411yescharacteristic
504C22×C8C2411yescharacteristic
505C22×C8C2411yescharacteristic
506C22×C8C2411yescharacteristic
507C4⋊Q8—28no—
508C4⋊Q8—22no—
509C4⋊Q8—22no—
510C4⋊Q8—22no—
511C4⋊Q8—22no—
512#127—41no—
513#127—41no—
514#125—28no—
515#125—22no—
516#125—22no—
517#125—22no—
518#125—22no—
519#125—41no—
520#125—41no—
521C22⋊Q8—28no—
522C22⋊Q8—28no—
523#121—22no—
524#121—22no—
525#121—22no—
526#121—22no—
527C4×Q8—82no—
528C4×Q8—82no—
529C4×D4—22no—
530C4×D4—22no—
531C4×D4—22no—
532C4×D4—22no—
533C4×D4—82no—
534C4×D4—82no—
535C4×D4—82no—
536C4×D4—82no—
537#117—22no—
538#117—22no—
539#117—22no—
540#117—41no—
541#117—41no—
542#117—41no—
543#117—41no—
544#117—82no—
545#117—82no—
546#117#4114yes—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—22no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—41no—
581C2×C4⋊C4—41no—
582C2×C4⋊C4C2×D411yescharacteristic
583C2×C4⋊C4C2×D411yescharacteristic
584C2×C4⋊C4C2×D411yescharacteristic
585C2×C4⋊C4C2×D411yescharacteristic
586C2×C4⋊C4#4114yes—
587C2×C4⋊C4C2411yescharacteristic
588C2×C4⋊C4C2411yescharacteristic
589C2×C4⋊C4C2411yescharacteristic
590C2×C4⋊C4C2411yescharacteristic
591C2×C4⋊C4C2411yescharacteristic
592C2×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2411yescharacteristic
594C2×C4⋊C4C2411yescharacteristic
595C2×C4⋊C4C2411yescharacteristic
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2411yescharacteristic
599C2×C4⋊C4C2411yescharacteristic
600C2×C4⋊C4C2411yescharacteristic
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4C2×D411yescharacteristic
626C2×C22⋊C4C2×D411yescharacteristic
627C2×C22⋊C4C2×D411yescharacteristic
628C2×C22⋊C4C2×D411yescharacteristic
629C2×C42—21no—
630C2×C42—22no—
631C2×C42—22no—
632C2×C42—21no—
633C2×C42—21no—
634C2×C42—21no—
635C2×C42—21no—
636C2×C42—21no—
637C2×C42—21no—
638C2×C42—21no—
639C2×C42—21no—
640C2×C42—21no—
641C2×C42—21no—
642C2×C42—21no—
643C2×C42—82no—
644C2×C42C2×D411yescharacteristic
645C2×C42C2×D411yescharacteristic
646C2×C42C2×D411yescharacteristic
647C2×C42C2×D411yescharacteristic
648C2×C42C2×D411yescharacteristic
649C2×C42C2×D411yescharacteristic
650C2×C42C2×D411yescharacteristic
651C2×C42C2×D411yescharacteristic
652C2×C42C2×D411yescharacteristic
653C2×C42C2×D411yescharacteristic
654C2×C42C2411yescharacteristic
655C2×C42C2411yescharacteristic
656C2×C42C2411yescharacteristic
657C2×C42C2411yescharacteristic
658C2×C42C2411yescharacteristic
659C2×C42C2411yescharacteristic
660#107—22no—
661#107—22no—
662#107—22no—
663#107—22no—
664#107—41no—
665#107—41no—
666#107—41no—
667#107—41no—
668#106—22no—
669#106—22no—
670#106—22no—
671#106—22no—
672#106—41no—
673#106—41no—
674#106—41no—
675#106—41no—
676C4⋊C8—41no—
677C4⋊C8—41no—
678C4⋊C8—41no—
679C4⋊C8—41no—
680#102—22no—
681#102—22no—
682#102—22no—
683#102—22no—
684#102—22no—
685#102—22no—
686#102—22no—
687#102—22no—
688#102—41no—
689#102—41no—
690#102—41no—
691#102—41no—
692#102—41no—
693#102—41no—
694#102—41no—
695#102—41no—
696C22⋊C8—22no—
697C22⋊C8—22no—
698C22⋊C8—22no—
699C22⋊C8—22no—
700C4×C8—22no—
701C4×C8—22no—
702C4×C8—22no—
703C4×C8—22no—
704#95—21no—
705#95—21no—
706#95—21no—
707#95—21no—
708#95—21no—
709#95—21no—
710#95—21no—
711#95—21no—
712#95—21no—
713#95—21no—
714#95—21no—
715#95—21no—
716#95—21no—
717#95—21no—
718#95—21no—
719#95—21no—
720#95—21no—
721#95—21no—
722#95—21no—
723#95—21no—
724#95—21no—
725#95—21no—
726#95—21no—
727#95—21no—
728#95—21no—
729#95—21no—
730#95—21no—
731#95—21no—
732#95—21no—
733#95—21no—
734#95—21no—
735#95—21no—
736#95—21no—
737#95—21no—
738#95C2×D411yescharacteristic
739#95C2×D411yescharacteristic
740#95C2×D411yescharacteristic
741#95C2×D411yescharacteristic
742#95C2×D411yescharacteristic
743#95C2×D411yescharacteristic
744#95C2×D411yescharacteristic
745#95C2×D411yescharacteristic
746C24—21no—
747C24—21no—
748C24C22×D411yescharacteristic
749C2×Q8—24no—
750C2×Q8—24no—
751C2×Q8—81no—
752C2×Q8—81no—
753C2×Q8—81no—
754C2×Q8—81no—
755C2×D4—21no—
756C2×D4—21no—
757C2×D4—21no—
758C2×D4—21no—
759C2×D4—21no—
760C2×D4—21no—
761C2×D4—21no—
762C2×D4—21no—
763C2×D4—21no—
764C2×D4—21no—
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—42no—
768C2×D4—42no—
769C2×D4—42no—
770C2×D4—42no—
771C2×D4—81no—
772C2×D4—81no—
773C2×D4—81no—
774C2×D4—81no—
775C2×D4—81no—
776C2×D4—81no—
777C2×D4—81no—
778C2×D4—81no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—24no—
788C22×C4—22no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—41no—
803C22×C4—41no—
804C22×C4—42no—
805C22×C4—42no—
806C22×C4—42no—
807C22×C4—42no—
808C22×C4—42no—
809C22×C4—42no—
810C22×C4—42no—
811C22×C4—81no—
812C22×C4—81no—
813C22×C4—81no—
814C22×C4—81no—
815C22×C4C22×D411yescharacteristic
816C22×C4C22×D411yescharacteristic
817C22×C4C22×D411yescharacteristic
818C22×C4C22×D411yescharacteristic
819C22×C4C22×D411yescharacteristic
820C22×C4C22×D411yescharacteristic
821C22×C4C22×D411yescharacteristic
822C22×C4C22×D411yescharacteristic
823C22×C4C22×D411yescharacteristic
824C22×C4C22×D411yescharacteristic
825C22×C4C22×D411yescharacteristic
826C22×C4C22×D411yescharacteristic
827C22×C4C22×D411yescharacteristic
828C22×C4C2×#4112yes—
829C22×C4C2×#4112yes—
830C22×C4C2511yescharacteristic
831C2×C8—21no—
832C2×C8—21no—
833C2×C8—21no—
834C2×C8—21no—
835C2×C8—21no—
836C2×C8—21no—
837C2×C8—21no—
838C2×C8—21no—
839C2×C8—21no—
840C2×C8—21no—
841C2×C8—21no—
842C2×C8—21no—
843C2×C8—21no—
844C2×C8—21no—
845C2×C8—21no—
846C2×C8—21no—
847C2×C8—21no—
848C2×C8—21no—
849C2×C8—21no—
850C2×C8—21no—
851C2×C8—21no—
852C2×C8—21no—
853C2×C8—21no—
854C2×C8—21no—
855C4⋊C4—24no—
856C4⋊C4—24no—
857C4⋊C4—24no—
858C4⋊C4—24no—
859C4⋊C4—24no—
860C4⋊C4—24no—
861C4⋊C4—24no—
862C4⋊C4—22no—
863C4⋊C4—22no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—21no—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—21no—
871C4⋊C4—21no—
872C4⋊C4—21no—
873C4⋊C4—21no—
874C4⋊C4—21no—
875C4⋊C4—21no—
876C4⋊C4—21no—
877C4⋊C4—21no—
878C4⋊C4—21no—
879C4⋊C4—21no—
880C4⋊C4—21no—
881C4⋊C4—21no—
882C4⋊C4—21no—
883C4⋊C4—21no—
884C4⋊C4—21no—
885C4⋊C4—21no—
886C4⋊C4—21no—
887C4⋊C4—21no—
888C4⋊C4—41no—
889C4⋊C4—41no—
890C4⋊C4—42no—
891C4⋊C4—42no—
892C4⋊C4—42no—
893C4⋊C4—81no—
894C4⋊C4—81no—
895C4⋊C4—81no—
896C4⋊C4—81no—
897C4⋊C4—81no—
898C4⋊C4—81no—
899C4⋊C4—81no—
900C4⋊C4—81no—
901C4⋊C4—81no—
902C4⋊C4—81no—
903C4⋊C4—81no—
904C4⋊C4—81no—
905C4⋊C4—81no—
906C4⋊C4—81no—
907C4⋊C4—81no—
908C4⋊C4—81no—
909C4⋊C4—81no—
910C4⋊C4—81no—
911C4⋊C4—81no—
912C4⋊C4—81no—
913C4⋊C4—81no—
914C4⋊C4—81no—
915C4⋊C4C2×#4112yes—
916C4⋊C4C2×#4112yes—
917C4⋊C4C2×#4112yes—
918C4⋊C4C2×#4112yes—
919C22⋊C4—24no—
920C22⋊C4—22no—
921C22⋊C4—22no—
922C22⋊C4—41no—
923C22⋊C4—41no—
924C22⋊C4—42no—
925C22⋊C4—42no—
926C22⋊C4—42no—
927C22⋊C4—42no—
928C22⋊C4—42no—
929C22⋊C4—81no—
930C22⋊C4—81no—
931C22⋊C4—81no—
932C22⋊C4—81no—
933C22⋊C4—81no—
934C22⋊C4—81no—
935C22⋊C4—81no—
936C22⋊C4—81no—
937C22⋊C4—81no—
938C22⋊C4—81no—
939C22⋊C4—81no—
940C22⋊C4—81no—
941C22⋊C4—81no—
942C22⋊C4—81no—
943C22⋊C4—81no—
944C22⋊C4—81no—
945C22⋊C4—81no—
946C22⋊C4—81no—
947C42—24no—
948C42—22no—
949C42—22no—
950C42—22no—
951C42—22no—
952C42—22no—
953C42—22no—
954C42—21no—
955C42—21no—
956C42—21no—
957C42—21no—
958C42—21no—
959C42—21no—
960C42—21no—
961C42—21no—
962C42—21no—
963C42—21no—
964C42—41no—
965C42—41no—
966C42—41no—
967C42—41no—
968C42—42no—
969C42—42no—
970C42—42no—
971C42—42no—
972C42—42no—
973C42—42no—
974C42—42no—
975C42—81no—
976C42—81no—
977C42—81no—
978C42—81no—
979C422−1+412yes—
980C422−1+412yes—
981C23—21no—
982C23—21no—
983C23—21no—
984C23—21no—
985C23—21no—
986C23—21no—
987C23—41no—
988C23—41no—
989C23—41no—
990C23—41no—
991C23—41no—
992C23—41no—
993C23—41no—
994C23—41no—
995C23—41no—
996C23—41no—
997C23—41no—
998C23—41no—
999C23—41no—
1000C23—41no—
1001C23#52512yes—
1002C23C23×D411yescharacteristic
1003Q8—84no—
1004Q8—84no—
1005D4—41no—
1006D4—41no—
1007D4—41no—
1008D4—41no—
1009D4—41no—
1010D4—41no—
1011D4—41no—
1012D4—41no—
1013D4—84no—
1014D4—84no—
1015D4—84no—
1016D4—84no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—22no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—44no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—82no—
1099C2×C4—84no—
1100C2×C4—84no—
1101C2×C4—84no—
1102C2×C4—84no—
1103C2×C4#52512yes—
1104C2×C4#53612yes—
1105C2×C4#53612yes—
1106C2×C4#57612yes—
1107C2×C4#57712yes—
1108C2×C4C22×#4111yescharacteristic
1109C2×C4C22×#4111yescharacteristic
1110C2×C4C2×2−1+411yescharacteristic
1111C2×C4C2×2−1+411yescharacteristic
1112C2×C4#58511yescharacteristic
1113C2×C4#58511yescharacteristic
1114C8—41no—
1115C8—41no—
1116C8—41no—
1117C8—41no—
1118C8—41no—
1119C8—41no—
1120C8—41no—
1121C8—41no—
1122C22—22no—
1123C22—22no—
1124C22—22no—
1125C22—41no—
1126C22—41no—
1127C22—41no—
1128C22—41no—
1129C22—81no—
1130C22—81no—
1131C22—81no—
1132C22—81no—
1133C22—81no—
1134C22—81no—
1135C22—81no—
1136C22—81no—
1137C22—81no—
1138C22—81no—
1139C22—81no—
1140C22—81no—
1141C22—81no—
1142C22—81no—
1143C22C2×#52511yescharacteristic
1144C22C2×#53611yescharacteristic
1145C22#344911yescharacteristic
1146C22C2×#57611yescharacteristic
1147C22C2×#57711yescharacteristic
1148C22#358411yescharacteristic
1149C22#358411yescharacteristic
1150C4—22no—
1151C4—22no—
1152C4—41no—
1153C4—41no—
1154C4—41no—
1155C4—41no—
1156C4—41no—
1157C4—41no—
1158C4—42no—
1159C4—42no—
1160C4—42no—
1161C4—41no—
1162C4—41no—
1163C4—42no—
1164C4—41no—
1165C4—41no—
1166C4—81no—
1167C4—81no—
1168C4—81no—
1169C4—81no—
1170C4—81no—
1171C4—81no—
1172C4—81no—
1173C4—81no—
1174C4—81no—
1175C4—81no—
1176C4#324114yes—
1177C4#346111yescharacteristic
1178C4#346111yescharacteristic
1179C4#346111yescharacteristic
1180C4#346111yescharacteristic
1181C2—42no—
1182C2—161no—
1183C2—161no—
1184C2#3460211yescharacteristic
1185C2#6057011yescharacteristic
1186C2#6057211yescharacteristic
1187C2C2×#324111yescharacteristic
1188C2#6085911yescharacteristic
1189C2#6095511yescharacteristic
1190C2#6095611yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutator, Frattini, cosocleC22×C4C25
socleC23C23×D4
prime radical#2619C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C4×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C4×#544C2semidirect
3. #30163C2semidirect
4. #30161C2semidirect
5. #30158C2semidirect
6. #30157C2semidirect
7. #30104C2semidirect
8. #30100C2semidirect
9. #30071C2semidirect
10. #30069C2semidirect
11. #29979C2semidirect
12. #29978C2semidirect
13. #29917C2semidirect
14. #29916C2semidirect
17. #29647C2semidirect
18. #29646C2semidirect
19. #23838C2semidirect
20. #23836C2semidirect
21. #23819C2semidirect
22. #23815C2semidirect
23. #23778C2semidirect
24. #23778C2semidirect
25. #23775C2semidirect
26. #23774C2semidirect
27. C4×#482C2semidirect
28. C4×#482C2semidirect
29. C4×#481C2semidirect
30. C4×#480C2semidirect
31. #20782C2semidirect

Maximal subgroups

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

subgroupindex
#346212
C4×#5442
#301632
#301612
#301582
#301572
#301042
#301002
#300712
#300692
#299792
#299782
#299172
#299162
#297652
#297632
#296472
#296462
#238382
#238362
#238192
#238152
#237782
#237752
#237742
C4×#4822
C4×#4812
C4×#4802
#207822