Finite Group Databasebeta

← C41×#8969 #23785170

Subgroups — C41×#8969 #23785170

Order 10496.

516 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3106C211yesmaximal, characteristic
2C41×#2990C211yesmaximal, characteristic, complemented
3C41×#1962C211yesmaximal, characteristic, complemented
4C4×#104×C41C211yesmaximal, characteristic, complemented
5C41×#1484C211yesmaximal, characteristic, complemented
6C41×#1299C211yesmaximal, characteristic, complemented
7C41×#1276C211yesmaximal, characteristic, complemented
8C41×#532C2211yescharacteristic
9C4×#41×C41C2211yescharacteristic
10C41×#482—21no—
11C41×#477C411yescharacteristic, complemented
12C41×#476C411yescharacteristic, complemented
13C41×#460C411yescharacteristic, complemented
14C41×#459C411yescharacteristic, complemented
15C41×#449—21no—
16C41×#446—21no—
17C4×SD16×C41—21no—
18C4×D8×C41—21no—
19C41×#435—22no—
20C8×D4×C41—21no—
21C41×#432—21no—
22C41×#431C2211yescharacteristic
23C41×#431C2211yescharacteristic
24C41×#423C2211yescharacteristic
25C2×C4⋊C8×C41—21no—
26C2×#104×C41—21no—
27C2×#104×C41—22no—
28C4×M16×C41C2211yescharacteristic
29C43×C41C2211yescharacteristic
30C41×#339—21no—
31C41×D4⋊C8—21no—
32C41×D4⋊C8—21no—
33C2×#41×C41—21no—
34C2×#41×C41D411yescharacteristic
35C2×SD16×C41—21no—
36C2×D8×C41—21no—
37C2×M16×C41—21no—
38C2×M16×C41D412yes—
39C22×C8×C41—22no—
40C4⋊Q8×C41C2×C411yescharacteristic
41#127×C41C2×C411yescharacteristic
42#124×C41—21no—
43#121×C41—21no—
44#121×C41—21no—
45C4×Q8×C41C2×C411yescharacteristic
46C4×Q8×C41D411yescharacteristic
47C4×D4×C41—21no—
48C4×D4×C41—21no—
49C4×D4×C41—21no—
50C4×D4×C41—21no—
51C4×D4×C41C2×C411yescharacteristic
52C4×D4×C41D411yescharacteristic
53#117×C41—21no—
54#117×C41D411yescharacteristic
55C2×C42×C41—21no—
56C2×C42×C41—21no—
57C2×C42×C41—21no—
58C2×C42×C41—21no—
59C2×C42×C41C2311yescharacteristic
60#107×C41—21no—
61#106×C41—21no—
62C4⋊C8×C41—22no—
63C4⋊C8×C41—21no—
64C4⋊C8×C41—21no—
65C4⋊C8×C41C2×C411yescharacteristic
66C4⋊C8×C41C2×C411yescharacteristic
67C4⋊C8×C41D411yescharacteristic
68C4⋊C8×C41D411yescharacteristic
69#104×C41—24no—
70#104×C41—44no—
71#103×C41—21no—
72#102×C41—21no—
73#102×C41—21no—
74#102×C41—21no—
75C22⋊C8×C41—22no—
76C22⋊C8×C41—21no—
77C22⋊C8×C41—21no—
78#97×C41—22no—
79#97×C41—21no—
80C4×C8×C41—21no—
81C4×C8×C41—21no—
82C4×C8×C41—21no—
83#41×C41—22no—
84#41×C41—41no—
85#41×C41—42no—
86#41×C41—42no—
87C2×Q8×C41—21no—
88C2×Q8×C41C22⋊C411yescharacteristic
89C2×D4×C41—21no—
90C2×D4×C41—21no—
91C2×D4×C41—21no—
92C2×D4×C41—21no—
93C2×D4×C41—41no—
94C2×D4×C41C22⋊C411yescharacteristic
95C22×C4×C41—21no—
96C22×C4×C41—21no—
97C22×C4×C41—21no—
98C22×C4×C41—41no—
99C22×C4×C41—41no—
100C22×C4×C41C2×D411yescharacteristic
101C22×C4×C41C2×D411yescharacteristic
102C22×C4×C41#4111yescharacteristic
103SD16×C41—42no—
104D8×C41—42no—
105M16×C41—22no—
106M16×C41—41no—
107M16×C41—42no—
108C2×C8×C41—21no—
109C2×C8×C41—21no—
110C2×C8×C41—21no—
111C2×C8×C41—21no—
112C2×C8×C41—22no—
113C2×C8×C41—41no—
114C2×C8×C41—82no—
115C4⋊C4×C41—21no—
116C4⋊C4×C41—21no—
117C4⋊C4×C41—21no—
118C4⋊C4×C41—21no—
119C4⋊C4×C41C22⋊C411yescharacteristic
120C4⋊C4×C41C22⋊C411yescharacteristic
121C22⋊C4×C41—21no—
122C22⋊C4×C41—21no—
123C22⋊C4×C41—21no—
124C22⋊C4×C41—41no—
125C22⋊C4×C41—41no—
126C42×C41—21no—
127C42×C41—21no—
128C42×C41—21no—
129C42×C41—22no—
130C42×C41—22no—
131C42×C41—22no—
132C42×C41—41no—
133C42×C41—41no—
134C42×C41—41no—
135C42×C41C22×C411yescharacteristic
136C42×C41C2×D411yescharacteristic
137C42×C41C2×D411yescharacteristic
138C42×C41#4111yescharacteristic
139C23×C41—21no—
140C23×C41—41no—
141C23×C41#12111yescharacteristic
142Q8×C41—21no—
143Q8×C41—21no—
144Q8×C41—42no—
145D4×C41—21no—
146D4×C41—42no—
147D4×C41—42no—
148D4×C41—41no—
149D4×C41—41no—
150D4×C41—41no—
151D4×C41—41no—
152D4×C41—82no—
153D4×C41#10412yescomplemented
154C2×C4×C41—21no—
155C2×C4×C41—21no—
156C2×C4×C41—21no—
157C2×C4×C41—21no—
158C2×C4×C41—21no—
159C2×C4×C41—21no—
160C2×C4×C41—21no—
161C2×C4×C41—21no—
162C2×C4×C41—21no—
163C2×C4×C41—42no—
164C2×C4×C41—42no—
165C2×C4×C41—42no—
166C2×C4×C41—42no—
167C2×C4×C41—41no—
168C2×C4×C41—41no—
169C2×C4×C41—41no—
170C2×C4×C41—41no—
171C2×C4×C41—41no—
172C2×C4×C41—81no—
173C2×C4×C41—81no—
174C2×C4×C41C2×C22⋊C411yescharacteristic
175C2×C4×C41C4×D411yescharacteristic
176C2×C4×C41C4×D411yescharacteristic
177C2×C4×C41#12011yescharacteristic
178C2×C4×C41#12111yescharacteristic
179C2×C4×C41#12311yescharacteristic
180C8×C41—42no—
181C8×C41—41no—
182C8×C41—41no—
183C8×C41—41no—
184C8×C41—42no—
185C8×C41—41no—
186#8969C4111yesmaximal, characteristic, direct product factor, Sylow
187C22×C41—21no—
188C22×C41—22no—
189C22×C41—21no—
190C22×C41—21no—
191C22×C41—41no—
192C22×C41—41no—
193C22×C41—81no—
194C22×C41—81no—
195C22×C41—81no—
196C22×C41#38611yescharacteristic
197C4×C41—21no—
198C4×C41—21no—
199C4×C41—21no—
200C4×C41—44no—
201C4×C41—41no—
202C4×C41—41no—
203C4×C41—41no—
204C4×C41—81no—
205C4×C41C2×#10411yescharacteristic
206C4×C41#42111yescharacteristic
207C4×C41#44311yescharacteristic
208C4×C41#44411yescharacteristic
209C4×C41#45311yescharacteristic
210C4×C41#45411yescharacteristic
211#3106C2×C4111yescharacteristic
212#2990C2×C4111yescharacteristic, complemented
213#1962C2×C4111yescharacteristic, complemented
214C4×#104C2×C4111yescharacteristic, complemented
215#1484C2×C4111yescharacteristic, complemented
216#1299C2×C4111yescharacteristic, complemented
217#1276C2×C4111yescharacteristic, complemented
218C2×C41—41no—
219C2×C41—42no—
220C2×C41—161no—
221C2×C41#187111yescharacteristic
222C2×C41#187611yescharacteristic
223C2×C41#188311yescharacteristic
224#532C22×C4111yescharacteristic
225C4×#41C22×C4111yescharacteristic
226#482—21no—
227#477C4×C4111yescharacteristic, complemented
228#476C4×C4111yescharacteristic, complemented
229#460C4×C4111yescharacteristic, complemented
230#459C4×C4111yescharacteristic, complemented
231#449—21no—
232#446—21no—
233C4×SD16—21no—
234C4×D8—21no—
235#435—22no—
236C8×D4—21no—
237#432—21no—
238#431C22×C4111yescharacteristic
239#431C22×C4111yescharacteristic
240#423C22×C4111yescharacteristic
241C2×C4⋊C8—21no—
242C2×#104—21no—
243C2×#104—22no—
244C4×M16C22×C4111yescharacteristic
245C43C22×C4111yescharacteristic
246#339—21no—
247D4⋊C8—21no—
248D4⋊C8—21no—
249C41#896911yescharacteristic, direct product factor, Sylow
250C2×#41—21no—
251C2×#41D4×C4111yescharacteristic
252C2×SD16—21no—
253C2×D8—21no—
254C2×M16—21no—
255C2×M16D4×C4112yes—
256C22×C8—22no—
257C4⋊Q8C2×C4×C4111yescharacteristic
258#127C2×C4×C4111yescharacteristic
259#124—21no—
260#121—21no—
261#121—21no—
262C4×Q8C2×C4×C4111yescharacteristic
263C4×Q8D4×C4111yescharacteristic
264C4×D4—21no—
265C4×D4—21no—
266C4×D4—21no—
267C4×D4—21no—
268C4×D4C2×C4×C4111yescharacteristic
269C4×D4D4×C4111yescharacteristic
270#117—21no—
271#117D4×C4111yescharacteristic
272C2×C42—21no—
273C2×C42—21no—
274C2×C42—21no—
275C2×C42—21no—
276C2×C42C23×C4111yescharacteristic
277#107—21no—
278#106—21no—
279C4⋊C8—22no—
280C4⋊C8—21no—
281C4⋊C8—21no—
282C4⋊C8C2×C4×C4111yescharacteristic
283C4⋊C8C2×C4×C4111yescharacteristic
284C4⋊C8D4×C4111yescharacteristic
285C4⋊C8D4×C4111yescharacteristic
286#104—24no—
287#104—44no—
288#103—21no—
289#102—21no—
290#102—21no—
291#102—21no—
292C22⋊C8—22no—
293C22⋊C8—21no—
294C22⋊C8—21no—
295#97—22no—
296#97—21no—
297C4×C8—21no—
298C4×C8—21no—
299C4×C8—21no—
300#41—22no—
301#41—41no—
302#41—42no—
303#41—42no—
304C2×Q8—21no—
305C2×Q8C22⋊C4×C4111yescharacteristic
306C2×D4—21no—
307C2×D4—21no—
308C2×D4—21no—
309C2×D4—21no—
310C2×D4—41no—
311C2×D4C22⋊C4×C4111yescharacteristic
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4C2×D4×C4111yescharacteristic
318C22×C4C2×D4×C4111yescharacteristic
319C22×C4#41×C4111yescharacteristic
320SD16—42no—
321D8—42no—
322M16—22no—
323M16—41no—
324M16—42no—
325C2×C8—21no—
326C2×C8—21no—
327C2×C8—21no—
328C2×C8—21no—
329C2×C8—22no—
330C2×C8—41no—
331C2×C8—82no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4C22⋊C4×C4111yescharacteristic
337C4⋊C4C22⋊C4×C4111yescharacteristic
338C22⋊C4—21no—
339C22⋊C4—21no—
340C22⋊C4—21no—
341C22⋊C4—41no—
342C22⋊C4—41no—
343C42—21no—
344C42—21no—
345C42—21no—
346C42—22no—
347C42—22no—
348C42—22no—
349C42—41no—
350C42—41no—
351C42—41no—
352C42C22×C4×C4111yescharacteristic
353C42C2×D4×C4111yescharacteristic
354C42C2×D4×C4111yescharacteristic
355C42#41×C4111yescharacteristic
356C23—21no—
357C23—41no—
358C23#121×C4111yescharacteristic
359Q8—21no—
360Q8—21no—
361Q8—42no—
362D4—21no—
363D4—42no—
364D4—42no—
365D4—41no—
366D4—41no—
367D4—41no—
368D4—41no—
369D4—82no—
370D4#104×C4112yescomplemented
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—81no—
390C2×C4—81no—
391C2×C4C2×C22⋊C4×C4111yescharacteristic
392C2×C4C4×D4×C4111yescharacteristic
393C2×C4C4×D4×C4111yescharacteristic
394C2×C4#120×C4111yescharacteristic
395C2×C4#121×C4111yescharacteristic
396C2×C4#123×C4111yescharacteristic
397C8—42no—
398C8—41no—
399C8—41no—
400C8—41no—
401C8—42no—
402C8—41no—
403C22—21no—
404C22—22no—
405C22—21no—
406C22—21no—
407C22—41no—
408C22—41no—
409C22—81no—
410C22—81no—
411C22—81no—
412C22C41×#38611yescharacteristic
413C4—21no—
414C4—21no—
415C4—21no—
416C4—44no—
417C4—41no—
418C4—41no—
419C4—41no—
420C4—81no—
421C4C2×#104×C4111yescharacteristic
422C4C41×#42111yescharacteristic
423C4C41×#44311yescharacteristic
424C4C41×#44411yescharacteristic
425C4C41×#45311yescharacteristic
426C4C41×#45411yescharacteristic
427C2—41no—
428C2—42no—
429C2—161no—
430C2C41×#187111yescharacteristic
431C2C41×#187611yescharacteristic
432C2C41×#188311yescharacteristic
subgroupG/H
centerC2×C4×C41#120
commutatorC42C22×C4×C41
Frattini, cosocleC2×C42C23×C41
socleC22×C41#386
prime radicalC41×#3106C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C41 ◁ C2×C42×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C41×#2990C2semidirect
3. C41×#1962C2semidirect
4. C4×#104×C41C2semidirect
5. C41×#1484C2semidirect
6. C41×#1299C2semidirect
7. C41×#1276C2semidirect
11. C41×#477C4semidirect
12. C41×#476C4semidirect
13. C41×#460C4semidirect
14. C41×#459C4semidirect
153. D4×C41#104semidirect
186. #8969C41direct (N × H)
212. #2990C2×C41semidirect
213. #1962C2×C41semidirect
214. C4×#104C2×C41semidirect
215. #1484C2×C41semidirect
216. #1299C2×C41semidirect
217. #1276C2×C41semidirect
227. #477C4×C41semidirect
228. #476C4×C41semidirect
229. #460C4×C41semidirect
230. #459C4×C41semidirect
249. C41#8969direct (N × H)
370. D4#104×C41semidirect

Maximal subgroups

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

subgroupindex
C41×#31062
C41×#29902
C41×#19622
C4×#104×C412
C41×#14842
C41×#12992
C41×#12762
#896941