Finite Group Databasebeta

← C41×#21557 #23797758

Subgroups — C41×#21557 #23797758

Order 10496.

906 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#471C211yesmaximal, characteristic
2C4×#137×C41C211yesmaximal, characteristic, complemented
3C4×AGL(1,ℤ/8)×C41C211yesmaximal, characteristic
4C2×C41×#440C211yesmaximal, characteristic, complemented
5C41×#2875C211yesmaximal, characteristic, complemented
6C41×#1977C211yesmaximal, characteristic, complemented
7C41×#1952C211yesmaximal, characteristic, complemented
8C41×#1931C211yesmaximal, characteristic, complemented
9C41×#1930C211yesmaximal, characteristic, complemented
10C41×#1908C211yesmaximal, characteristic, complemented
11C41×#1907C211yesmaximal, characteristic
12C41×#1816C211yesmaximal, characteristic, complemented
13C41×#1778C211yesmaximal, characteristic, complemented
14C4×#101×C41C211yesmaximal, characteristic, complemented
15C4×#100×C41C211yesmaximal, characteristic, complemented
16C2×#137×C41C2211yescharacteristic
17C2×AGL(1,ℤ/8)×C41C2211yescharacteristic
18C22×SD16×C41C2211yescharacteristic
19C2×#131×C41C2211yescharacteristic
20C2×#131×C41C2211yescharacteristic
21C4×#41×C41C2211yescharacteristic
22C2×C4×Q8×C41C2211yescharacteristic
23C2×C4×D4×C41C2211yescharacteristic
24C41×#471C418yescomplemented
25C41×#442—21no—
26C41×#441—21no—
27C41×#440—21no—
28C41×#440—21no—
29C41×#440—21no—
30C41×#440—21no—
31C41×#440—21no—
32C41×#440—21no—
33C4×Q16×C41—21no—
34C4×SD16×C41—21no—
35C4×SD16×C41—21no—
36C4×D8×C41—21no—
37C2×#108×C41C2211yescharacteristic
38C2×#108×C41C2211yescharacteristic
39C41×#428C2211yescharacteristic
40C41×#428C2211yescharacteristic
41C2×#107×C41C2211yescharacteristic
42C41×#419C2211yescharacteristic
43C41×#418C2211yescharacteristic
44C41×#417C2211yescharacteristic
45C41×#417C2211yescharacteristic
46C2×#103×C41C2211yescharacteristic
47C2×#102×C41C2211yescharacteristic
48C2×#101×C41C2211yescharacteristic
49C2×#101×C41C2211yescharacteristic
50C2×#100×C41C2211yescharacteristic
51C2×#100×C41C2211yescharacteristic
52C41×#405—21no—
53C41×#405—21no—
54C41×#405C2211yescharacteristic
55C41×#405C2211yescharacteristic
56C4×M16×C41—21no—
57C4×M16×C41C2211yescharacteristic
58C4×M16×C41C2211yescharacteristic
59C4×M16×C41C2211yescharacteristic
60C2×#97×C41—21no—
61C2×#97×C41C2211yescharacteristic
62C41×#343C2211yescharacteristic
63C41×#343C2211yescharacteristic
64C41×#343C2211yescharacteristic
65C41×#343C2211yescharacteristic
66C41×#341C2211yescharacteristic
67C41×#341C2211yescharacteristic
68C2×#41×C41C2311yescharacteristic
69C22×Q8×C41C2311yescharacteristic
70C22×D4×C41C2311yescharacteristic
71C23×C4×C41—21no—
72#137×C41—22no—
73#137×C41C2×C414yescomplemented
74AGL(1,ℤ/8)×C41—22no—
75AGL(1,ℤ/8)×C41C2×C414yes—
76C2×Q16×C41—21no—
77C2×SD16×C41—21no—
78C2×SD16×C41—21no—
79C2×SD16×C41—21no—
80C2×SD16×C41—21no—
81C2×SD16×C41—22no—
82C2×SD16×C41C2×C414yescomplemented
83C2×D8×C41—21no—
84#131×C41—22no—
85#131×C41—22no—
86#131×C41—22no—
87#131×C41C2×C414yescomplemented
88C2×M16×C41—21no—
89C2×M16×C41—21no—
90C2×M16×C41C2311yescharacteristic
91C2×M16×C41C2311yescharacteristic
92C2×M16×C41C2311yescharacteristic
93C2×M16×C41C2311yescharacteristic
94C2×M16×C41C2311yescharacteristic
95C2×M16×C41C2311yescharacteristic
96C22×C8×C41—21no—
97C22×C8×C41—21no—
98C22×C8×C41C2311yescharacteristic
99C22×C8×C41C2311yescharacteristic
100C4×Q8×C41—21no—
101C4×Q8×C41—21no—
102C4×Q8×C41—21no—
103C4×Q8×C41—21no—
104C4×Q8×C41D411yescharacteristic
105C4×Q8×C41D411yescharacteristic
106C4×D4×C41—21no—
107C4×D4×C41—21no—
108C4×D4×C41—21no—
109C4×D4×C41—21no—
110C4×D4×C41—21no—
111C4×D4×C41—21no—
112C4×D4×C41D411yescharacteristic
113C4×D4×C41D411yescharacteristic
114#117×C41—21no—
115#117×C41C2311yescharacteristic
116C2×C4⋊C4×C41—21no—
117C2×C4⋊C4×C41C2311yescharacteristic
118C2×C4⋊C4×C41C2311yescharacteristic
119C2×C22⋊C4×C41—21no—
120C2×C42×C41—21no—
121C2×C42×C41—21no—
122C2×C42×C41C2311yescharacteristic
123#108×C41—22no—
124#108×C41C2×C414yescomplemented
125#107×C41—21no—
126#107×C41—21no—
127#107×C41—21no—
128#107×C41—21no—
129#106×C41—21no—
130#106×C41—21no—
131#103×C41—21no—
132#103×C41—21no—
133#103×C41—21no—
134#103×C41—21no—
135#103×C41—21no—
136#103×C41—21no—
137#102×C41—21no—
138#102×C41—21no—
139#102×C41—21no—
140#102×C41—21no—
141#102×C41—21no—
142#102×C41—21no—
143#101×C41—22no—
144#101×C41C2×C414yescomplemented
145#100×C41—22no—
146#100×C41C2×C414yescomplemented
147#97×C41—21no—
148#97×C41—21no—
149#97×C41—21no—
150#97×C41—21no—
151#97×C41—21no—
152#97×C41D411yescharacteristic
153#97×C41D411yescharacteristic
154#97×C41D411yescharacteristic
155#97×C41D411yescharacteristic
156C4×C8×C41—21no—
157C4×C8×C41—21no—
158C4×C8×C41—21no—
159C4×C8×C41—21no—
160C4×C8×C41—21no—
161C24×C41—21no—
162#41×C41—21no—
163#41×C41—21no—
164#41×C41C22×C412yes—
165#41×C41#4112yes—
166C2×Q8×C41—21no—
167C2×Q8×C41—21no—
168C2×Q8×C41—21no—
169C2×Q8×C41—21no—
170C2×Q8×C41—21no—
171C2×Q8×C41C22×C412yes—
172C2×Q8×C41C2×D411yescharacteristic
173C2×D4×C41—21no—
174C2×D4×C41—21no—
175C2×D4×C41—21no—
176C2×D4×C41—21no—
177C2×D4×C41—21no—
178C2×D4×C41—21no—
179C2×D4×C41C22×C412yes—
180C2×D4×C41C2×D411yescharacteristic
181C22×C4×C41—21no—
182C22×C4×C41—21no—
183C22×C4×C41—21no—
184C22×C4×C41—21no—
185C22×C4×C41—21no—
186C22×C4×C41—21no—
187C22×C4×C41—41no—
188C22×C4×C41—41no—
189C22×C4×C41—82no—
190C22×C4×C41#4111yescharacteristic
191C22×C4×C41#4111yescharacteristic
192C22×C4×C41C2411yescharacteristic
193Q16×C41—24no—
194SD16×C41—24no—
195SD16×C41—24no—
196SD16×C41—24no—
197SD16×C41—24no—
198D8×C41—24no—
199M16×C41—24no—
200M16×C41—21no—
201M16×C41—21no—
202M16×C41—21no—
203M16×C41—21no—
204M16×C41—24no—
205M16×C41—21no—
206M16×C41—21no—
207M16×C41—21no—
208M16×C41—21no—
209M16×C41C22×C412yes—
210M16×C41C22×C412yes—
211M16×C41C22×C412yes—
212M16×C41#4112yes—
213C2×C8×C41—24no—
214C2×C8×C41—21no—
215C2×C8×C41—21no—
216C2×C8×C41—21no—
217C2×C8×C41—21no—
218C2×C8×C41—21no—
219C2×C8×C41—21no—
220C2×C8×C41—24no—
221C2×C8×C41—21no—
222C2×C8×C41—21no—
223C2×C8×C41C22×C412yes—
224C2×C8×C41C2×D411yescharacteristic
225C2×C8×C41C2×D411yescharacteristic
226C2×C8×C41C2×D411yescharacteristic
227C2×C8×C41C2×D411yescharacteristic
228C2×C8×C41#4112yes—
229C4⋊C4×C41—21no—
230C4⋊C4×C41—21no—
231C4⋊C4×C41—21no—
232C4⋊C4×C41—21no—
233C4⋊C4×C41—21no—
234C4⋊C4×C41—21no—
235C4⋊C4×C41—41no—
236C4⋊C4×C41—41no—
237C4⋊C4×C41C2×D411yescharacteristic
238C4⋊C4×C41C2×D411yescharacteristic
239C22⋊C4×C41—21no—
240C22⋊C4×C41—21no—
241C22⋊C4×C41—21no—
242C22⋊C4×C41—41no—
243C22⋊C4×C41—41no—
244C42×C41—21no—
245C42×C41—21no—
246C42×C41—21no—
247C42×C41—41no—
248C42×C41—41no—
249C42×C41C2×D411yescharacteristic
250C42×C41C2×D411yescharacteristic
251C42×C41C2×D411yescharacteristic
252C42×C41C2×D411yescharacteristic
253C23×C41—21no—
254C23×C41—22no—
255C23×C41—41no—
256C23×C41—41no—
257C23×C41—81no—
258C23×C41—81no—
259C23×C41C2×#4111yescharacteristic
260Q8×C41—21no—
261Q8×C41—22no—
262Q8×C41—22no—
263Q8×C41—41no—
264Q8×C41—41no—
265Q8×C41C4×D412yes—
266D4×C41—22no—
267D4×C41—22no—
268D4×C41—22no—
269D4×C41—22no—
270D4×C41—21no—
271D4×C41—41no—
272D4×C41—41no—
273D4×C41C4×D412yes—
274C2×C4×C41—21no—
275C2×C4×C41—22no—
276C2×C4×C41—22no—
277C2×C4×C41—22no—
278C2×C4×C41—21no—
279C2×C4×C41—21no—
280C2×C4×C41—41no—
281C2×C4×C41—41no—
282C2×C4×C41—41no—
283C2×C4×C41—41no—
284C2×C4×C41—41no—
285C2×C4×C41—41no—
286C2×C4×C41—81no—
287C2×C4×C41—81no—
288C2×C4×C41—82no—
289C2×C4×C41—82no—
290C2×C4×C41—81no—
291C2×C4×C41—81no—
292C2×C4×C41#12111yescharacteristic
293C2×C4×C41#12111yescharacteristic
294C2×C4×C41#12111yescharacteristic
295C2×C4×C41#12111yescharacteristic
296C2×C4×C41C23×C411yescharacteristic
297C2×C4×C41C22×D411yescharacteristic
298C2×C4×C41C22×D411yescharacteristic
299C2×C4×C41C2×#4111yescharacteristic
300C2×C4×C41C2×#4111yescharacteristic
301C2×C4×C41C2×#4111yescharacteristic
302C8×C41—22no—
303C8×C41—22no—
304C8×C41—22no—
305C8×C41—21no—
306C8×C41—22no—
307C8×C41—21no—
308C8×C41—41no—
309C8×C41—41no—
310C8×C41C4×D412yes—
311C8×C41C4×D412yes—
312#21557C4111yesmaximal, characteristic, direct product factor, Sylow
313C22×C41—21no—
314C22×C41—21no—
315C22×C41—22no—
316C22×C41—41no—
317C22×C41—41no—
318C22×C41—42no—
319C22×C41—82no—
320C22×C41—82no—
321C22×C41—81no—
322C22×C41—81no—
323C22×C41C4×#4111yescharacteristic
324C22×C41C2×#12111yescharacteristic
325C22×C41#52911yescharacteristic
326C4×C41—22no—
327C4×C41—21no—
328C4×C41—21no—
329C4×C41—21no—
330C4×C41—21no—
331C4×C41—42no—
332C4×C41—41no—
333C4×C41—41no—
334C4×C41—81no—
335C4×C41—81no—
336C4×C41C2×C4×D411yescharacteristic
337C4×C41C2×C4×D411yescharacteristic
338C4×C41#52511yescharacteristic
339C4×C41#53211yescharacteristic
340C2×#471C2×C4111yescharacteristic
341C4×#137C2×C4111yescharacteristic, complemented
342C4×AGL(1,ℤ/8)C2×C4111yescharacteristic
343C2×#440C2×C4111yescharacteristic, complemented
344#2875C2×C4111yescharacteristic, complemented
345#1977C2×C4111yescharacteristic, complemented
346#1952C2×C4111yescharacteristic, complemented
347#1931C2×C4111yescharacteristic, complemented
348#1930C2×C4111yescharacteristic, complemented
349#1908C2×C4111yescharacteristic, complemented
350#1907C2×C4111yescharacteristic
351#1816C2×C4111yescharacteristic, complemented
352#1778C2×C4111yescharacteristic, complemented
353C4×#101C2×C4111yescharacteristic, complemented
354C4×#100C2×C4111yescharacteristic, complemented
355C2×C41—21no—
356C2×C41—21no—
357C2×C41—42no—
358C2×C41—82no—
359C2×C41C4×#12111yescharacteristic
360C2×C41#306811yescharacteristic
361C2×C41#306911yescharacteristic
362C2×#137C22×C4111yescharacteristic
363C2×AGL(1,ℤ/8)C22×C4111yescharacteristic
364C22×SD16C22×C4111yescharacteristic
365C2×#131C22×C4111yescharacteristic
366C2×#131C22×C4111yescharacteristic
367C4×#41C22×C4111yescharacteristic
368C2×C4×Q8C22×C4111yescharacteristic
369C2×C4×D4C22×C4111yescharacteristic
370#471C4×C4118yescomplemented
371#442—21no—
372#441—21no—
373#440—21no—
374#440—21no—
375#440—21no—
376#440—21no—
377#440—21no—
378#440—21no—
379C4×Q16—21no—
380C4×SD16—21no—
381C4×SD16—21no—
382C4×D8—21no—
383C2×#108C22×C4111yescharacteristic
384C2×#108C22×C4111yescharacteristic
385#428C22×C4111yescharacteristic
386#428C22×C4111yescharacteristic
387C2×#107C22×C4111yescharacteristic
388#419C22×C4111yescharacteristic
389#418C22×C4111yescharacteristic
390#417C22×C4111yescharacteristic
391#417C22×C4111yescharacteristic
392C2×#103C22×C4111yescharacteristic
393C2×#102C22×C4111yescharacteristic
394C2×#101C22×C4111yescharacteristic
395C2×#101C22×C4111yescharacteristic
396C2×#100C22×C4111yescharacteristic
397C2×#100C22×C4111yescharacteristic
398#405—21no—
399#405—21no—
400#405C22×C4111yescharacteristic
401#405C22×C4111yescharacteristic
402C4×M16—21no—
403C4×M16C22×C4111yescharacteristic
404C4×M16C22×C4111yescharacteristic
405C4×M16C22×C4111yescharacteristic
406C2×#97—21no—
407C2×#97C22×C4111yescharacteristic
408#343C22×C4111yescharacteristic
409#343C22×C4111yescharacteristic
410#343C22×C4111yescharacteristic
411#343C22×C4111yescharacteristic
412#341C22×C4111yescharacteristic
413#341C22×C4111yescharacteristic
414C41#2155711yescharacteristic, direct product factor, Sylow
415C2×#41C23×C4111yescharacteristic
416C22×Q8C23×C4111yescharacteristic
417C22×D4C23×C4111yescharacteristic
418C23×C4—21no—
419#137—22no—
420#137C2×C4×C4114yescomplemented
421AGL(1,ℤ/8)—22no—
422AGL(1,ℤ/8)C2×C4×C4114yes—
423C2×Q16—21no—
424C2×SD16—21no—
425C2×SD16—21no—
426C2×SD16—21no—
427C2×SD16—21no—
428C2×SD16—22no—
429C2×SD16C2×C4×C4114yescomplemented
430C2×D8—21no—
431#131—22no—
432#131—22no—
433#131—22no—
434#131C2×C4×C4114yescomplemented
435C2×M16—21no—
436C2×M16—21no—
437C2×M16C23×C4111yescharacteristic
438C2×M16C23×C4111yescharacteristic
439C2×M16C23×C4111yescharacteristic
440C2×M16C23×C4111yescharacteristic
441C2×M16C23×C4111yescharacteristic
442C2×M16C23×C4111yescharacteristic
443C22×C8—21no—
444C22×C8—21no—
445C22×C8C23×C4111yescharacteristic
446C22×C8C23×C4111yescharacteristic
447C4×Q8—21no—
448C4×Q8—21no—
449C4×Q8—21no—
450C4×Q8—21no—
451C4×Q8D4×C4111yescharacteristic
452C4×Q8D4×C4111yescharacteristic
453C4×D4—21no—
454C4×D4—21no—
455C4×D4—21no—
456C4×D4—21no—
457C4×D4—21no—
458C4×D4—21no—
459C4×D4D4×C4111yescharacteristic
460C4×D4D4×C4111yescharacteristic
461#117—21no—
462#117C23×C4111yescharacteristic
463C2×C4⋊C4—21no—
464C2×C4⋊C4C23×C4111yescharacteristic
465C2×C4⋊C4C23×C4111yescharacteristic
466C2×C22⋊C4—21no—
467C2×C42—21no—
468C2×C42—21no—
469C2×C42C23×C4111yescharacteristic
470#108—22no—
471#108C2×C4×C4114yescomplemented
472#107—21no—
473#107—21no—
474#107—21no—
475#107—21no—
476#106—21no—
477#106—21no—
478#103—21no—
479#103—21no—
480#103—21no—
481#103—21no—
482#103—21no—
483#103—21no—
484#102—21no—
485#102—21no—
486#102—21no—
487#102—21no—
488#102—21no—
489#102—21no—
490#101—22no—
491#101C2×C4×C4114yescomplemented
492#100—22no—
493#100C2×C4×C4114yescomplemented
494#97—21no—
495#97—21no—
496#97—21no—
497#97—21no—
498#97—21no—
499#97D4×C4111yescharacteristic
500#97D4×C4111yescharacteristic
501#97D4×C4111yescharacteristic
502#97D4×C4111yescharacteristic
503C4×C8—21no—
504C4×C8—21no—
505C4×C8—21no—
506C4×C8—21no—
507C4×C8—21no—
508C24—21no—
509#41—21no—
510#41—21no—
511#41C22×C4×C4112yes—
512#41#41×C4112yes—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8C22×C4×C4112yes—
519C2×Q8C2×D4×C4111yescharacteristic
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4C22×C4×C4112yes—
527C2×D4C2×D4×C4111yescharacteristic
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—82no—
537C22×C4#41×C4111yescharacteristic
538C22×C4#41×C4111yescharacteristic
539C22×C4C24×C4111yescharacteristic
540Q16—24no—
541SD16—24no—
542SD16—24no—
543SD16—24no—
544SD16—24no—
545D8—24no—
546M16—24no—
547M16—21no—
548M16—21no—
549M16—21no—
550M16—21no—
551M16—24no—
552M16—21no—
553M16—21no—
554M16—21no—
555M16—21no—
556M16C22×C4×C4112yes—
557M16C22×C4×C4112yes—
558M16C22×C4×C4112yes—
559M16#41×C4112yes—
560C2×C8—24no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—24no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8C22×C4×C4112yes—
571C2×C8C2×D4×C4111yescharacteristic
572C2×C8C2×D4×C4111yescharacteristic
573C2×C8C2×D4×C4111yescharacteristic
574C2×C8C2×D4×C4111yescharacteristic
575C2×C8#41×C4112yes—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—41no—
583C4⋊C4—41no—
584C4⋊C4C2×D4×C4111yescharacteristic
585C4⋊C4C2×D4×C4111yescharacteristic
586C22⋊C4—21no—
587C22⋊C4—21no—
588C22⋊C4—21no—
589C22⋊C4—41no—
590C22⋊C4—41no—
591C42—21no—
592C42—21no—
593C42—21no—
594C42—41no—
595C42—41no—
596C42C2×D4×C4111yescharacteristic
597C42C2×D4×C4111yescharacteristic
598C42C2×D4×C4111yescharacteristic
599C42C2×D4×C4111yescharacteristic
600C23—21no—
601C23—22no—
602C23—41no—
603C23—41no—
604C23—81no—
605C23—81no—
606C23C2×#41×C4111yescharacteristic
607Q8—21no—
608Q8—22no—
609Q8—22no—
610Q8—41no—
611Q8—41no—
612Q8C4×D4×C4112yes—
613D4—22no—
614D4—22no—
615D4—22no—
616D4—22no—
617D4—21no—
618D4—41no—
619D4—41no—
620D4C4×D4×C4112yes—
621C2×C4—21no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—81no—
634C2×C4—81no—
635C2×C4—82no—
636C2×C4—82no—
637C2×C4—81no—
638C2×C4—81no—
639C2×C4#121×C4111yescharacteristic
640C2×C4#121×C4111yescharacteristic
641C2×C4#121×C4111yescharacteristic
642C2×C4#121×C4111yescharacteristic
643C2×C4C23×C4×C4111yescharacteristic
644C2×C4C22×D4×C4111yescharacteristic
645C2×C4C22×D4×C4111yescharacteristic
646C2×C4C2×#41×C4111yescharacteristic
647C2×C4C2×#41×C4111yescharacteristic
648C2×C4C2×#41×C4111yescharacteristic
649C8—22no—
650C8—22no—
651C8—22no—
652C8—21no—
653C8—22no—
654C8—21no—
655C8—41no—
656C8—41no—
657C8C4×D4×C4112yes—
658C8C4×D4×C4112yes—
659C22—21no—
660C22—21no—
661C22—22no—
662C22—41no—
663C22—41no—
664C22—42no—
665C22—82no—
666C22—82no—
667C22—81no—
668C22—81no—
669C22C4×#41×C4111yescharacteristic
670C22C2×#121×C4111yescharacteristic
671C22C41×#52911yescharacteristic
672C4—22no—
673C4—21no—
674C4—21no—
675C4—21no—
676C4—21no—
677C4—42no—
678C4—41no—
679C4—41no—
680C4—81no—
681C4—81no—
682C4C2×C4×D4×C4111yescharacteristic
683C4C2×C4×D4×C4111yescharacteristic
684C4C41×#52511yescharacteristic
685C4C41×#53211yescharacteristic
686C2—21no—
687C2—21no—
688C2—42no—
689C2—82no—
690C2C4×#121×C4111yescharacteristic
691C2C41×#306811yescharacteristic
692C2C41×#306911yescharacteristic
subgroupG/H
center, socleC22×C41C2×#121
commutatorC2×C4C23×C4×C41
Frattini, cosocleC22×C4C24×C41
prime radicalC2×AGL(1,ℤ/8)×C41C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C41 ◁ C2×C42×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×#137×C41C2semidirect
4. C2×C41×#440C2semidirect
5. C41×#2875C2semidirect
6. C41×#1977C2semidirect
7. C41×#1952C2semidirect
8. C41×#1931C2semidirect
9. C41×#1930C2semidirect
10. C41×#1908C2semidirect
12. C41×#1816C2semidirect
13. C41×#1778C2semidirect
14. C4×#101×C41C2semidirect
15. C4×#100×C41C2semidirect
24. C41×#471C4semidirect
73. #137×C41C2×C4semidirect
82. C2×SD16×C41C2×C4semidirect
87. #131×C41C2×C4semidirect
124. #108×C41C2×C4semidirect
144. #101×C41C2×C4semidirect
146. #100×C41C2×C4semidirect
312. #21557C41direct (N × H)
341. C4×#137C2×C41semidirect
343. C2×#440C2×C41semidirect
344. #2875C2×C41semidirect
345. #1977C2×C41semidirect
346. #1952C2×C41semidirect
347. #1931C2×C41semidirect
348. #1930C2×C41semidirect
349. #1908C2×C41semidirect
351. #1816C2×C41semidirect
352. #1778C2×C41semidirect
353. C4×#101C2×C41semidirect
354. C4×#100C2×C41semidirect
370. #471C4×C41semidirect
414. C41#21557direct (N × H)
420. #137C2×C4×C41semidirect
429. C2×SD16C2×C4×C41semidirect
434. #131C2×C4×C41semidirect
471. #108C2×C4×C41semidirect
491. #101C2×C4×C41semidirect
493. #100C2×C4×C41semidirect

Maximal subgroups

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

subgroupindex
C2×C41×#4712
C4×#137×C412
C4×AGL(1,ℤ/8)×C412
C2×C41×#4402
C41×#28752
C41×#19772
C41×#19522
C41×#19312
C41×#19302
C41×#19082
C41×#19072
C41×#18162
C41×#17782
C4×#101×C412
C4×#100×C412
#2155741