Finite Group Databasebeta

← C41×#9997 #23786198

Subgroups — C41×#9997 #23786198

Order 10496.

622 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3100C211yesmaximal, characteristic
2C41×#3037C211yesmaximal, characteristic, complemented
3C41×#2536C211yesmaximal, characteristic, complemented
4C41×#1517C211yesmaximal, characteristic, complemented
5C41×#1486C211yesmaximal, characteristic, complemented
6C41×#1479C211yesmaximal, characteristic, complemented
7C41×#1286C211yesmaximal, characteristic, complemented
8C2×#137×C41—21no—
9C41×#532C2211yescharacteristic
10C2×C22⋊Q8×C41—21no—
11C2×C4×Q8×C41C2211yescharacteristic
12C2×C4×D4×C41C2211yescharacteristic
13C41×#480—21no—
14C41×#474—21no—
15C41×#464—22no—
16C41×#462—21no—
17C41×#460—21no—
18C41×#459—21no—
19C41×#447—21no—
20C4×D8×C41—22no—
21C41×#431C2211yescharacteristic
22C41×#431C2211yescharacteristic
23C41×#423C2211yescharacteristic
24C41×#417—21no—
25C41×#398—21no—
26C41×#394—21no—
27C41×#388—22no—
28C41×#382C2211yescharacteristic
29C41×#380—21no—
30C41×#327—22no—
31C41×Q8⋊C8—22no—
32C41×D4⋊C8—22no—
33C2×#41×C41—21no—
34C22×Q8×C41D411yescharacteristic
35C22×D4×C41D411yescharacteristic
36C23×C4×C41—21no—
37#137×C41—42no—
38#137×C41—42no—
39C2×Q16×C41—22no—
40C2×SD16×C41—22no—
41C2×D8×C41—22no—
42C2×M16×C41—21no—
43C4⋊Q8×C41D411yescharacteristic
44#127×C41D411yescharacteristic
45#124×C41—21no—
46C22⋊Q8×C41—42no—
47C22⋊Q8×C41—42no—
48#121×C41—21no—
49#121×C41—21no—
50C4×Q8×C41—21no—
51C4×Q8×C41—21no—
52C4×Q8×C41—21no—
53C4×Q8×C41—21no—
54C4×D4×C41—21no—
55C4×D4×C41—21no—
56C4×D4×C41—21no—
57C4×D4×C41—21no—
58C4×D4×C41—21no—
59C4×D4×C41—21no—
60C2×C4⋊C4×C41—22no—
61C2×C4⋊C4×C41—21no—
62C2×C4⋊C4×C41—21no—
63C2×C4⋊C4×C41D411yescharacteristic
64C2×C4⋊C4×C41D411yescharacteristic
65C2×C22⋊C4×C41—22no—
66C2×C22⋊C4×C41—22no—
67C2×C22⋊C4×C41—21no—
68C2×C42×C41—21no—
69C2×C42×C41C2311yescharacteristic
70#107×C41—22no—
71C4⋊C8×C41—21no—
72C4⋊C8×C41—21no—
73C4⋊C8×C41—21no—
74C4⋊C8×C41D412yes—
75#103×C41—22no—
76#102×C41—22no—
77#102×C41—22no—
78#102×C41—22no—
79C22⋊C8×C41—21no—
80C22⋊C8×C41—21no—
81C4×C8×C41—21no—
82C4×C8×C41D412yes—
83#95×C41—22no—
84#95×C41—21no—
85#95×C41D412yes—
86C24×C41—21no—
87#41×C41—41no—
88#41×C41—41no—
89#41×C41—41no—
90#41×C41—41no—
91C2×Q8×C41—21no—
92C2×Q8×C41—21no—
93C2×Q8×C41—21no—
94C2×Q8×C41—21no—
95C2×Q8×C41—21no—
96C2×Q8×C41—21no—
97C2×Q8×C41D812yescomplemented
98C2×D4×C41—21no—
99C2×D4×C41—21no—
100C2×D4×C41—21no—
101C2×D4×C41—21no—
102C2×D4×C41—21no—
103C2×D4×C41—42no—
104C2×D4×C41—41no—
105C22×C4×C41—21no—
106C22×C4×C41—22no—
107C22×C4×C41—21no—
108C22×C4×C41—21no—
109C22×C4×C41—41no—
110C22×C4×C41—41no—
111C22×C4×C41—41no—
112C22×C4×C41—41no—
113C22×C4×C41—41no—
114C22×C4×C41—41no—
115C22×C4×C41—41no—
116C22×C4×C41C2×D411yescharacteristic
117C22×C4×C41C2×D411yescharacteristic
118C22×C4×C41C2×D411yescharacteristic
119Q16×C41—44no—
120SD16×C41—44no—
121D8×C41—44no—
122M16×C41—41no—
123M16×C41—41no—
124C2×C8×C41—22no—
125C2×C8×C41—22no—
126C2×C8×C41—41no—
127C4⋊C4×C41—21no—
128C4⋊C4×C41—21no—
129C4⋊C4×C41—21no—
130C4⋊C4×C41—21no—
131C4⋊C4×C41—21no—
132C4⋊C4×C41—21no—
133C4⋊C4×C41—44no—
134C4⋊C4×C41—41no—
135C4⋊C4×C41—41no—
136C4⋊C4×C41—41no—
137C4⋊C4×C41—41no—
138C22⋊C4×C41—44no—
139C22⋊C4×C41—44no—
140C22⋊C4×C41—41no—
141C22⋊C4×C41—41no—
142C22⋊C4×C41—41no—
143C22⋊C4×C41—41no—
144C42×C41—41no—
145C42×C41—41no—
146C42×C41C2×D411yescharacteristic
147C42×C41C2×D411yescharacteristic
148C42×C41C2×D411yescharacteristic
149C42×C41#4111yescharacteristic
150C23×C41—22no—
151C23×C41—41no—
152C23×C41—41no—
153C23×C41—41no—
154C23×C41—41no—
155C23×C41—41no—
156C23×C41—41no—
157C23×C41—41no—
158C23×C41#12011yescharacteristic
159Q8×C41—22no—
160Q8×C41—22no—
161Q8×C41—41no—
162Q8×C41—41no—
163Q8×C41—41no—
164Q8×C41—41no—
165D4×C41—22no—
166D4×C41—22no—
167D4×C41—41no—
168D4×C41—41no—
169D4×C41—42no—
170D4×C41—41no—
171D4×C41—41no—
172D4×C41—81no—
173D4×C41—81no—
174D4×C41—81no—
175C2×C4×C41—22no—
176C2×C4×C41—41no—
177C2×C4×C41—41no—
178C2×C4×C41—41no—
179C2×C4×C41—41no—
180C2×C4×C41—42no—
181C2×C4×C41—42no—
182C2×C4×C41—42no—
183C2×C4×C41—41no—
184C2×C4×C41—41no—
185C2×C4×C41—41no—
186C2×C4×C41—42no—
187C2×C4×C41—41no—
188C2×C4×C41—41no—
189C2×C4×C41—81no—
190C2×C4×C41—81no—
191C2×C4×C41—81no—
192C2×C4×C41—81no—
193C2×C4×C41—81no—
194C2×C4×C41—81no—
195C2×C4×C41#12011yescharacteristic
196C2×C4×C41#12011yescharacteristic
197C2×C4×C41#12111yescharacteristic
198C2×C4×C41#12111yescharacteristic
199C2×C4×C41#12111yescharacteristic
200C2×C4×C41#12711yescharacteristic
201C2×C4×C41C2×D811yescharacteristic
202C2×C4×C41#13511yescharacteristic
203C2×C4×C41AGL(1,ℤ/8)11yescharacteristic
204C2×C4×C41AGL(1,ℤ/8)11yescharacteristic
205C8×C41—42no—
206C8×C41—42no—
207C8×C41—81no—
208#9997C4111yesmaximal, characteristic, direct product factor, Sylow
209C22×C41—21no—
210C22×C41—21no—
211C22×C41—42no—
212C22×C41—42no—
213C22×C41—42no—
214C22×C41—81no—
215C22×C41—81no—
216C22×C41—81no—
217C22×C41—81no—
218C22×C41—81no—
219C22×C41—81no—
220C22×C41—81no—
221C22×C41#39211yescharacteristic
222C22×C41#44711yescharacteristic
223C22×C41#44911yescharacteristic
224C4×C41—21no—
225C4×C41—21no—
226C4×C41—21no—
227C4×C41—21no—
228C4×C41—42no—
229C4×C41—82no—
230C4×C41—81no—
231C4×C41—81no—
232C4×C41—81no—
233C4×C41#44711yescharacteristic
234C4×C41#44911yescharacteristic
235C4×C41#46611yescharacteristic
236C4×C41#46911yescharacteristic
237#3100C2×C4111yescharacteristic
238#3037C2×C4111yescharacteristic, complemented
239#2536C2×C4111yescharacteristic, complemented
240#1517C2×C4111yescharacteristic, complemented
241#1486C2×C4111yescharacteristic, complemented
242#1479C2×C4111yescharacteristic, complemented
243#1286C2×C4111yescharacteristic, complemented
244C2×C41—21no—
245C2×C41—21no—
246C2×C41—82no—
247C2×C41—161no—
248C2×C41#199911yescharacteristic
249C2×C41#200911yescharacteristic
250C2×C41#201011yescharacteristic
251C2×#137—21no—
252#532C22×C4111yescharacteristic
253C2×C22⋊Q8—21no—
254C2×C4×Q8C22×C4111yescharacteristic
255C2×C4×D4C22×C4111yescharacteristic
256#480—21no—
257#474—21no—
258#464—22no—
259#462—21no—
260#460—21no—
261#459—21no—
262#447—21no—
263C4×D8—22no—
264#431C22×C4111yescharacteristic
265#431C22×C4111yescharacteristic
266#423C22×C4111yescharacteristic
267#417—21no—
268#398—21no—
269#394—21no—
270#388—22no—
271#382C22×C4111yescharacteristic
272#380—21no—
273#327—22no—
274Q8⋊C8—22no—
275D4⋊C8—22no—
276C41#999711yescharacteristic, direct product factor, Sylow
277C2×#41—21no—
278C22×Q8D4×C4111yescharacteristic
279C22×D4D4×C4111yescharacteristic
280C23×C4—21no—
281#137—42no—
282#137—42no—
283C2×Q16—22no—
284C2×SD16—22no—
285C2×D8—22no—
286C2×M16—21no—
287C4⋊Q8D4×C4111yescharacteristic
288#127D4×C4111yescharacteristic
289#124—21no—
290C22⋊Q8—42no—
291C22⋊Q8—42no—
292#121—21no—
293#121—21no—
294C4×Q8—21no—
295C4×Q8—21no—
296C4×Q8—21no—
297C4×Q8—21no—
298C4×D4—21no—
299C4×D4—21no—
300C4×D4—21no—
301C4×D4—21no—
302C4×D4—21no—
303C4×D4—21no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4D4×C4111yescharacteristic
308C2×C4⋊C4D4×C4111yescharacteristic
309C2×C22⋊C4—22no—
310C2×C22⋊C4—22no—
311C2×C22⋊C4—21no—
312C2×C42—21no—
313C2×C42C23×C4111yescharacteristic
314#107—22no—
315C4⋊C8—21no—
316C4⋊C8—21no—
317C4⋊C8—21no—
318C4⋊C8D4×C4112yes—
319#103—22no—
320#102—22no—
321#102—22no—
322#102—22no—
323C22⋊C8—21no—
324C22⋊C8—21no—
325C4×C8—21no—
326C4×C8D4×C4112yes—
327#95—22no—
328#95—21no—
329#95D4×C4112yes—
330C24—21no—
331#41—41no—
332#41—41no—
333#41—41no—
334#41—41no—
335C2×Q8—21no—
336C2×Q8—21no—
337C2×Q8—21no—
338C2×Q8—21no—
339C2×Q8—21no—
340C2×Q8—21no—
341C2×Q8D8×C4112yescomplemented
342C2×D4—21no—
343C2×D4—21no—
344C2×D4—21no—
345C2×D4—21no—
346C2×D4—21no—
347C2×D4—42no—
348C2×D4—41no—
349C22×C4—21no—
350C22×C4—22no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—41no—
354C22×C4—41no—
355C22×C4—41no—
356C22×C4—41no—
357C22×C4—41no—
358C22×C4—41no—
359C22×C4—41no—
360C22×C4C2×D4×C4111yescharacteristic
361C22×C4C2×D4×C4111yescharacteristic
362C22×C4C2×D4×C4111yescharacteristic
363Q16—44no—
364SD16—44no—
365D8—44no—
366M16—41no—
367M16—41no—
368C2×C8—22no—
369C2×C8—22no—
370C2×C8—41no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—44no—
378C4⋊C4—41no—
379C4⋊C4—41no—
380C4⋊C4—41no—
381C4⋊C4—41no—
382C22⋊C4—44no—
383C22⋊C4—44no—
384C22⋊C4—41no—
385C22⋊C4—41no—
386C22⋊C4—41no—
387C22⋊C4—41no—
388C42—41no—
389C42—41no—
390C42C2×D4×C4111yescharacteristic
391C42C2×D4×C4111yescharacteristic
392C42C2×D4×C4111yescharacteristic
393C42#41×C4111yescharacteristic
394C23—22no—
395C23—41no—
396C23—41no—
397C23—41no—
398C23—41no—
399C23—41no—
400C23—41no—
401C23—41no—
402C23#120×C4111yescharacteristic
403Q8—22no—
404Q8—22no—
405Q8—41no—
406Q8—41no—
407Q8—41no—
408Q8—41no—
409D4—22no—
410D4—22no—
411D4—41no—
412D4—41no—
413D4—42no—
414D4—41no—
415D4—41no—
416D4—81no—
417D4—81no—
418D4—81no—
419C2×C4—22no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—42no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—81no—
434C2×C4—81no—
435C2×C4—81no—
436C2×C4—81no—
437C2×C4—81no—
438C2×C4—81no—
439C2×C4#120×C4111yescharacteristic
440C2×C4#120×C4111yescharacteristic
441C2×C4#121×C4111yescharacteristic
442C2×C4#121×C4111yescharacteristic
443C2×C4#121×C4111yescharacteristic
444C2×C4#127×C4111yescharacteristic
445C2×C4C2×D8×C4111yescharacteristic
446C2×C4#135×C4111yescharacteristic
447C2×C4AGL(1,ℤ/8)×C4111yescharacteristic
448C2×C4AGL(1,ℤ/8)×C4111yescharacteristic
449C8—42no—
450C8—42no—
451C8—81no—
452C22—21no—
453C22—21no—
454C22—42no—
455C22—42no—
456C22—42no—
457C22—81no—
458C22—81no—
459C22—81no—
460C22—81no—
461C22—81no—
462C22—81no—
463C22—81no—
464C22C41×#39211yescharacteristic
465C22C41×#44711yescharacteristic
466C22C41×#44911yescharacteristic
467C4—21no—
468C4—21no—
469C4—21no—
470C4—21no—
471C4—42no—
472C4—82no—
473C4—81no—
474C4—81no—
475C4—81no—
476C4C41×#44711yescharacteristic
477C4C41×#44911yescharacteristic
478C4C41×#46611yescharacteristic
479C4C41×#46911yescharacteristic
480C2—21no—
481C2—21no—
482C2—82no—
483C2—161no—
484C2C41×#199911yescharacteristic
485C2C41×#200911yescharacteristic
486C2C41×#201011yescharacteristic
subgroupG/H
center, socleC22×C41#392
commutator, Frattini, cosocleC2×C42C23×C41
prime radicalC41×#3100C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C41 ◁ C2×C42×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C41×#3037C2semidirect
3. C41×#2536C2semidirect
4. C41×#1517C2semidirect
5. C41×#1486C2semidirect
6. C41×#1479C2semidirect
7. C41×#1286C2semidirect
97. C2×Q8×C41D8semidirect
208. #9997C41direct (N × H)
238. #3037C2×C41semidirect
239. #2536C2×C41semidirect
240. #1517C2×C41semidirect
241. #1486C2×C41semidirect
242. #1479C2×C41semidirect
243. #1286C2×C41semidirect
276. C41#9997direct (N × H)
341. C2×Q8D8×C41semidirect

Maximal subgroups

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

subgroupindex
C41×#31002
C41×#30372
C41×#25362
C41×#15172
C41×#14862
C41×#14792
C41×#12862
#999741