Finite Group Databasebeta

← C41×#9371 #23785572

Subgroups — C41×#9371 #23785572

Order 10496.

442 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3214C211yesmaximal, characteristic
2C41×#2981C211yesmaximal, characteristic, complemented
3C41×#1551C211yesmaximal, characteristic, complemented
4C41×#1536C211yesmaximal, characteristic, complemented
5C41×#1480C211yesmaximal, characteristic, complemented
6C41×#1290C211yesmaximal, characteristic, complemented
7C41×#1287C211yesmaximal, characteristic, complemented
8C41×#532C2211yescharacteristic
9C41×#532C2211yescharacteristic
10C41×#496C412yes—
11C41×#489C412yes—
12C41×#461—21no—
13C41×#459—21no—
14C41×#449—22no—
15C41×#436—21no—
16C41×#435—22no—
17C8×D4×C41—21no—
18C41×#432C2211yescharacteristic
19C41×#432C2211yescharacteristic
20C41×#432C2211yescharacteristic
21C41×#431C2211yescharacteristic
22C2×C4⋊C8×C41C2211yescharacteristic
23C41×#408—22no—
24C41×#333—21no—
25C41×#331—21no—
26C41×#329—22no—
27C41×D4⋊C8—21no—
28C41×D4⋊C8—21no—
29C2×#41×C41—21no—
30C2×#41×C41D412yes—
31C2×SD16×C41—22no—
32C2×D8×C41—22no—
33C2×M16×C41—22no—
34C22×C8×C41—22no—
35C22×C8×C41—21no—
36C4⋊Q8×C41C2×C411yescharacteristic
37C4⋊Q8×C41D411yescharacteristic
38#127×C41C2×C411yescharacteristic
39#127×C41D411yescharacteristic
40#124×C41—21no—
41#124×C41C2×C412yes—
42#121×C41—21no—
43#121×C41—21no—
44#121×C41—21no—
45#121×C41—21no—
46C4×D4×C41—21no—
47C4×D4×C41—21no—
48C4×D4×C41—21no—
49C4×D4×C41—21no—
50C2×C42×C41C2311yescharacteristic
51C4⋊C8×C41—21no—
52C4⋊C8×C41—21no—
53C4⋊C8×C41—21no—
54C4⋊C8×C41—21no—
55C4⋊C8×C41—21no—
56C4⋊C8×C41—21no—
57#103×C41—22no—
58#102×C41—22no—
59C22⋊C8×C41—22no—
60C22⋊C8×C41—22no—
61C22⋊C8×C41—21no—
62C22⋊C8×C41—21no—
63C22⋊C8×C41—21no—
64C22⋊C8×C41—21no—
65#97×C41—21no—
66#97×C41C2×C412yes—
67#97×C41D412yes—
68C4×C8×C41D411yescharacteristic
69C4×C8×C41D411yescharacteristic
70#41×C41—81no—
71#41×C41—81no—
72#41×C41—82no—
73C2×Q8×C41—21no—
74C2×Q8×C41C22⋊C412yes—
75C2×D4×C41—22no—
76C2×D4×C41—21no—
77C2×D4×C41—21no—
78C2×D4×C41—21no—
79C2×D4×C41—21no—
80C2×D4×C41—21no—
81C2×D4×C41—41no—
82C2×D4×C41C22⋊C412yes—
83C22×C4×C41—22no—
84C22×C4×C41—41no—
85C22×C4×C41C2×D411yescharacteristic
86C22×C4×C41#4111yescharacteristic
87C22×C4×C41#4111yescharacteristic
88SD16×C41—82no—
89D8×C41—82no—
90M16×C41—82no—
91C2×C8×C41—22no—
92C2×C8×C41—21no—
93C2×C8×C41—21no—
94C2×C8×C41—22no—
95C2×C8×C41—41no—
96C2×C8×C41—41no—
97C2×C8×C41—82no—
98C2×C8×C41—81no—
99C4⋊C4×C41—21no—
100C4⋊C4×C41—21no—
101C4⋊C4×C41—21no—
102C4⋊C4×C41—21no—
103C22⋊C4×C41—22no—
104C22⋊C4×C41—22no—
105C22⋊C4×C41—41no—
106C22⋊C4×C41—41no—
107C42×C41C22×C411yescharacteristic
108C42×C41C2×D411yescharacteristic
109C42×C41C2×D411yescharacteristic
110C42×C41C2×D411yescharacteristic
111C23×C41—22no—
112C23×C41—41no—
113C23×C41#12311yescharacteristic
114Q8×C41—42no—
115Q8×C41—81no—
116D4×C41—42no—
117D4×C41—41no—
118D4×C41—41no—
119D4×C41—42no—
120D4×C41—41no—
121D4×C41—41no—
122D4×C41—81no—
123D4×C41—81no—
124D4×C41—82no—
125D4×C41—82no—
126C2×C4×C41—21no—
127C2×C4×C41—21no—
128C2×C4×C41—22no—
129C2×C4×C41—41no—
130C2×C4×C41—41no—
131C2×C4×C41—42no—
132C2×C4×C41—42no—
133C2×C4×C41—41no—
134C2×C4×C41—81no—
135C2×C4×C41—81no—
136C2×C4×C41C2×C22⋊C411yescharacteristic
137C2×C4×C41C4×D411yescharacteristic
138C2×C4×C41C4×D411yescharacteristic
139C2×C4×C41#12011yescharacteristic
140C2×C4×C41#12111yescharacteristic
141C2×C4×C41#12111yescharacteristic
142C8×C41—41no—
143C8×C41—42no—
144C8×C41—41no—
145C8×C41—42no—
146C8×C41—81no—
147C8×C41—81no—
148#9371C4111yesmaximal, characteristic, direct product factor, Sylow
149C22×C41—21no—
150C22×C41—21no—
151C22×C41—21no—
152C22×C41—42no—
153C22×C41—42no—
154C22×C41—42no—
155C22×C41—81no—
156C22×C41—81no—
157C22×C41—81no—
158C22×C41#38611yescharacteristic
159C4×C41—21no—
160C4×C41—21no—
161C4×C41—21no—
162C4×C41—21no—
163C4×C41—21no—
164C4×C41—42no—
165C4×C41—81no—
166C4×C41#47111yescharacteristic
167C4×C41#47211yescharacteristic
168#3214C2×C4111yescharacteristic
169#2981C2×C4111yescharacteristic, complemented
170#1551C2×C4111yescharacteristic, complemented
171#1536C2×C4111yescharacteristic, complemented
172#1480C2×C4111yescharacteristic, complemented
173#1290C2×C4111yescharacteristic, complemented
174#1287C2×C4111yescharacteristic, complemented
175C2×C41—41no—
176C2×C41—82no—
177C2×C41—161no—
178C2×C41#188111yescharacteristic
179C2×C41#190711yescharacteristic
180C2×C41#191111yescharacteristic
181#532C22×C4111yescharacteristic
182#532C22×C4111yescharacteristic
183#496C4×C4112yes—
184#489C4×C4112yes—
185#461—21no—
186#459—21no—
187#449—22no—
188#436—21no—
189#435—22no—
190C8×D4—21no—
191#432C22×C4111yescharacteristic
192#432C22×C4111yescharacteristic
193#432C22×C4111yescharacteristic
194#431C22×C4111yescharacteristic
195C2×C4⋊C8C22×C4111yescharacteristic
196#408—22no—
197#333—21no—
198#331—21no—
199#329—22no—
200D4⋊C8—21no—
201D4⋊C8—21no—
202C41#937111yescharacteristic, direct product factor, Sylow
203C2×#41—21no—
204C2×#41D4×C4112yes—
205C2×SD16—22no—
206C2×D8—22no—
207C2×M16—22no—
208C22×C8—22no—
209C22×C8—21no—
210C4⋊Q8C2×C4×C4111yescharacteristic
211C4⋊Q8D4×C4111yescharacteristic
212#127C2×C4×C4111yescharacteristic
213#127D4×C4111yescharacteristic
214#124—21no—
215#124C2×C4×C4112yes—
216#121—21no—
217#121—21no—
218#121—21no—
219#121—21no—
220C4×D4—21no—
221C4×D4—21no—
222C4×D4—21no—
223C4×D4—21no—
224C2×C42C23×C4111yescharacteristic
225C4⋊C8—21no—
226C4⋊C8—21no—
227C4⋊C8—21no—
228C4⋊C8—21no—
229C4⋊C8—21no—
230C4⋊C8—21no—
231#103—22no—
232#102—22no—
233C22⋊C8—22no—
234C22⋊C8—22no—
235C22⋊C8—21no—
236C22⋊C8—21no—
237C22⋊C8—21no—
238C22⋊C8—21no—
239#97—21no—
240#97C2×C4×C4112yes—
241#97D4×C4112yes—
242C4×C8D4×C4111yescharacteristic
243C4×C8D4×C4111yescharacteristic
244#41—81no—
245#41—81no—
246#41—82no—
247C2×Q8—21no—
248C2×Q8C22⋊C4×C4112yes—
249C2×D4—22no—
250C2×D4—21no—
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—21no—
254C2×D4—21no—
255C2×D4—41no—
256C2×D4C22⋊C4×C4112yes—
257C22×C4—22no—
258C22×C4—41no—
259C22×C4C2×D4×C4111yescharacteristic
260C22×C4#41×C4111yescharacteristic
261C22×C4#41×C4111yescharacteristic
262SD16—82no—
263D8—82no—
264M16—82no—
265C2×C8—22no—
266C2×C8—21no—
267C2×C8—21no—
268C2×C8—22no—
269C2×C8—41no—
270C2×C8—41no—
271C2×C8—82no—
272C2×C8—81no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C22⋊C4—22no—
278C22⋊C4—22no—
279C22⋊C4—41no—
280C22⋊C4—41no—
281C42C22×C4×C4111yescharacteristic
282C42C2×D4×C4111yescharacteristic
283C42C2×D4×C4111yescharacteristic
284C42C2×D4×C4111yescharacteristic
285C23—22no—
286C23—41no—
287C23#123×C4111yescharacteristic
288Q8—42no—
289Q8—81no—
290D4—42no—
291D4—41no—
292D4—41no—
293D4—42no—
294D4—41no—
295D4—41no—
296D4—81no—
297D4—81no—
298D4—82no—
299D4—82no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—22no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—41no—
308C2×C4—81no—
309C2×C4—81no—
310C2×C4C2×C22⋊C4×C4111yescharacteristic
311C2×C4C4×D4×C4111yescharacteristic
312C2×C4C4×D4×C4111yescharacteristic
313C2×C4#120×C4111yescharacteristic
314C2×C4#121×C4111yescharacteristic
315C2×C4#121×C4111yescharacteristic
316C8—41no—
317C8—42no—
318C8—41no—
319C8—42no—
320C8—81no—
321C8—81no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—42no—
326C22—42no—
327C22—42no—
328C22—81no—
329C22—81no—
330C22—81no—
331C22C41×#38611yescharacteristic
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—21no—
337C4—42no—
338C4—81no—
339C4C41×#47111yescharacteristic
340C4C41×#47211yescharacteristic
341C2—41no—
342C2—82no—
343C2—161no—
344C2C41×#188111yescharacteristic
345C2C41×#190711yescharacteristic
346C2C41×#191111yescharacteristic
subgroupG/H
center, socleC22×C41#386
commutatorC42C22×C4×C41
Frattini, cosocleC2×C42C23×C41
prime radicalC41×#3214C2
LCSG ▷ 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×#2981C2semidirect
3. C41×#1551C2semidirect
4. C41×#1536C2semidirect
5. C41×#1480C2semidirect
6. C41×#1290C2semidirect
7. C41×#1287C2semidirect
148. #9371C41direct (N × H)
169. #2981C2×C41semidirect
170. #1551C2×C41semidirect
171. #1536C2×C41semidirect
172. #1480C2×C41semidirect
173. #1290C2×C41semidirect
174. #1287C2×C41semidirect
202. C41#9371direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#32142
C41×#29812
C41×#15512
C41×#15362
C41×#14802
C41×#12902
C41×#12872
#937141