Finite Group Databasebeta

← C41×#33897 #23810098

Subgroups — C41×#33897 #23810098

Order 10496.

580 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3334C211yesmaximal, characteristic, complemented
2C41×#3283C211yesmaximal, characteristic, complemented
3C41×#2241C211yesmaximal, characteristic, complemented
4C41×#2236C212yesmaximal, complemented
5C41×#2224C211yesmaximal, characteristic, complemented
6C41×#2220C212yesmaximal, complemented
7C41×#2208C211yesmaximal, characteristic, complemented
8C41×#2186C212yesmaximal, complemented
9C4×D16×C41C211yesmaximal, characteristic, complemented
10C41×#2169C211yesmaximal, characteristic, complemented
11C41×#2139C212yesmaximal, complemented
12C2×#135×C41C2212yes—
13C41×#547—21no—
14C41×#547—21no—
15C2×SD32×C41C2212yes—
16C2×D16×C41C2211yescharacteristic
17C2×M32×C41C2212yes—
18C41×#500C2211yescharacteristic
19C41×#494C2211yescharacteristic
20C41×#480—22no—
21C41×#474—21no—
22C41×#467C2212yes—
23C41×#466C2212yes—
24C41×#461—21no—
25C41×#452—22no—
26C4×D8×C41C2211yescharacteristic
27C4×D8×C41C2211yescharacteristic
28C8×D4×C41C2211yescharacteristic
29C2×#107×C41C2212yes—
30C41×#366C2211yescharacteristic
31C41×#366C2212yes—
32C41×C4⋊C16C2211yescharacteristic
33C41×#358C2212yes—
34C41×#358C2212yes—
35C41×#358C2212yes—
36C41×#357C2211yescharacteristic
37C41×#357C2212yes—
38C41×#357C2211yescharacteristic
39C41×C22⋊C16C2212yes—
40C4×C16×C41C2211yescharacteristic
41C2×#41×C41—22no—
42C2×#41×C41—41no—
43#135×C41—24no—
44#135×C41—42no—
45C2×Q16×C41—21no—
46C2×Q16×C41C2312yes—
47C2×SD16×C41—22no—
48C2×D8×C41C2311yescharacteristic
49C2×D8×C41C2311yescharacteristic
50C22×C8×C41C2312yes—
51C4⋊Q8×C41—21no—
52C4⋊Q8×C41—21no—
53#123×C41—42no—
54#123×C41—42no—
55C22⋊Q8×C41—22no—
56C22⋊Q8×C41—41no—
57#121×C41—22no—
58#121×C41—41no—
59C4×D4×C41—21no—
60C4×D4×C41—21no—
61C4×D4×C41D411yescharacteristic
62C2×C4⋊C4×C41—22no—
63C2×C4⋊C4×C41—41no—
64SD32×C41—42no—
65D16×C41—22no—
66M32×C41—42no—
67C2×C16×C41C2311yescharacteristic
68C2×C16×C41C2312yes—
69C2×C16×C41C2311yescharacteristic
70#107×C41—21no—
71#107×C41—22no—
72#107×C41C2312yes—
73#107×C41C2311yescharacteristic
74#107×C41C2311yescharacteristic
75C4⋊C8×C41D411yescharacteristic
76#103×C41—22no—
77#102×C41—21no—
78#102×C41—21no—
79#102×C41—22no—
80C22⋊C8×C41D412yes—
81C4×C8×C41C2311yescharacteristic
82#41×C41—44no—
83#41×C41—82no—
84#41×C41—84no—
85C2×Q8×C41—22no—
86C2×Q8×C41—41no—
87C2×D4×C41—21no—
88C2×D4×C41—21no—
89C2×D4×C41—42no—
90C2×D4×C41—42no—
91C2×D4×C41D811yescharacteristic
92C22×C4×C41—42no—
93C22×C4×C41—41no—
94C22×C4×C41—42no—
95C22×C4×C41—41no—
96C22×C4×C41C2×D412yes—
97Q16×C41—22no—
98Q16×C41—22no—
99Q16×C41—81no—
100SD16×C41—44no—
101D8×C41—21no—
102D8×C41—21no—
103D8×C41—21no—
104D8×C41#4112yescomplemented
105C2×C8×C41—22no—
106C2×C8×C41—22no—
107C2×C8×C41C2×D411yescharacteristic
108C2×C8×C41C2×D412yes—
109C2×C8×C41C2411yescharacteristic
110C4⋊C4×C41—21no—
111C4⋊C4×C41—21no—
112C4⋊C4×C41—22no—
113C4⋊C4×C41—42no—
114C4⋊C4×C41—41no—
115C4⋊C4×C41—42no—
116C4⋊C4×C41—41no—
117C4⋊C4×C41—41no—
118C4⋊C4×C41D811yescharacteristic
119C22⋊C4×C41—42no—
120C22⋊C4×C41—41no—
121C22⋊C4×C41—41no—
122C22⋊C4×C41—42no—
123C22⋊C4×C41D812yes—
124C42×C41C2×D411yescharacteristic
125C16×C41—21no—
126C16×C41—21no—
127C16×C41—22no—
128C23×C41—41no—
129C23×C41—41no—
130C23×C41C2×D812yes—
131Q8×C41—42no—
132Q8×C41—42no—
133Q8×C41—82no—
134D4×C41—22no—
135D4×C41—22no—
136D4×C41—41no—
137D4×C41—41no—
138D4×C41—41no—
139D4×C41—84no—
140D4×C41—84no—
141C2×C4×C41—22no—
142C2×C4×C41—22no—
143C2×C4×C41—41no—
144C2×C4×C41—41no—
145C2×C4×C41—42no—
146C2×C4×C41—42no—
147C2×C4×C41—84no—
148C2×C4×C41—84no—
149C2×C4×C41—82no—
150C2×C4×C41—82no—
151C2×C4×C41C2×D811yescharacteristic
152C2×C4×C41C2×D812yes—
153C2×C4×C41C2×D811yescharacteristic
154C2×C4×C41C22×D411yescharacteristic
155C8×C41—22no—
156C8×C41—21no—
157C8×C41C2×#4111yescharacteristic
158C8×C41H(5,𝔽2)11yescharacteristic
159#33897C4111yesmaximal, characteristic, direct product factor, Sylow
160C22×C41—22no—
161C22×C41—22no—
162C22×C41—22no—
163C22×C41—42no—
164C22×C41—81no—
165C22×C41—81no—
166C22×C41—81no—
167C22×C41—81no—
168C22×C41—81no—
169C22×C41C22×D811yescharacteristic
170C4×C41—21no—
171C4×C41—22no—
172C4×C41—81no—
173C4×C41—81no—
174C4×C41—82no—
175C4×C41—82no—
176C4×C41#50912yes—
177C4×C41#54611yescharacteristic
178C4×C41#57711yescharacteristic
179#3334C2×C4111yescharacteristic, complemented
180#3283C2×C4111yescharacteristic, complemented
181#2241C2×C4111yescharacteristic, complemented
182#2236C2×C4112yescomplemented
183#2224C2×C4111yescharacteristic, complemented
184#2220C2×C4112yescomplemented
185#2208C2×C4111yescharacteristic, complemented
186#2186C2×C4112yescomplemented
187C4×D16C2×C4111yescharacteristic, complemented
188#2169C2×C4111yescharacteristic, complemented
189#2139C2×C4112yescomplemented
190C2×C41—42no—
191C2×C41—82no—
192C2×C41—161no—
193C2×C41#329411yescharacteristic
194C2×C41C2×#50911yescharacteristic
195C2×C41#341711yescharacteristic
196C2×#135C22×C4112yes—
197#547—21no—
198#547—21no—
199C2×SD32C22×C4112yes—
200C2×D16C22×C4111yescharacteristic
201C2×M32C22×C4112yes—
202#500C22×C4111yescharacteristic
203#494C22×C4111yescharacteristic
204#480—22no—
205#474—21no—
206#467C22×C4112yes—
207#466C22×C4112yes—
208#461—21no—
209#452—22no—
210C4×D8C22×C4111yescharacteristic
211C4×D8C22×C4111yescharacteristic
212C8×D4C22×C4111yescharacteristic
213C2×#107C22×C4112yes—
214#366C22×C4111yescharacteristic
215#366C22×C4112yes—
216C4⋊C16C22×C4111yescharacteristic
217#358C22×C4112yes—
218#358C22×C4112yes—
219#358C22×C4112yes—
220#357C22×C4111yescharacteristic
221#357C22×C4112yes—
222#357C22×C4111yescharacteristic
223C22⋊C16C22×C4112yes—
224C4×C16C22×C4111yescharacteristic
225C41#3389711yescharacteristic, direct product factor, Sylow
226C2×#41—22no—
227C2×#41—41no—
228#135—24no—
229#135—42no—
230C2×Q16—21no—
231C2×Q16C23×C4112yes—
232C2×SD16—22no—
233C2×D8C23×C4111yescharacteristic
234C2×D8C23×C4111yescharacteristic
235C22×C8C23×C4112yes—
236C4⋊Q8—21no—
237C4⋊Q8—21no—
238#123—42no—
239#123—42no—
240C22⋊Q8—22no—
241C22⋊Q8—41no—
242#121—22no—
243#121—41no—
244C4×D4—21no—
245C4×D4—21no—
246C4×D4D4×C4111yescharacteristic
247C2×C4⋊C4—22no—
248C2×C4⋊C4—41no—
249SD32—42no—
250D16—22no—
251M32—42no—
252C2×C16C23×C4111yescharacteristic
253C2×C16C23×C4111yescharacteristic
254C2×C16C23×C4112yes—
255#107—22no—
256#107—21no—
257#107C23×C4111yescharacteristic
258#107C23×C4112yes—
259#107C23×C4111yescharacteristic
260C4⋊C8D4×C4111yescharacteristic
261#103—22no—
262#102—21no—
263#102—21no—
264#102—22no—
265C22⋊C8D4×C4112yes—
266C4×C8C23×C4111yescharacteristic
267#41—44no—
268#41—82no—
269#41—84no—
270C2×Q8—22no—
271C2×Q8—41no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—42no—
275C2×D4—42no—
276C2×D4D8×C4111yescharacteristic
277C22×C4—42no—
278C22×C4—41no—
279C22×C4—42no—
280C22×C4—41no—
281C22×C4C2×D4×C4112yes—
282Q16—22no—
283Q16—22no—
284Q16—81no—
285SD16—44no—
286D8—21no—
287D8—21no—
288D8—21no—
289D8#41×C4112yescomplemented
290C2×C8—22no—
291C2×C8—22no—
292C2×C8C2×D4×C4111yescharacteristic
293C2×C8C2×D4×C4112yes—
294C2×C8C24×C4111yescharacteristic
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—22no—
298C4⋊C4—42no—
299C4⋊C4—41no—
300C4⋊C4—42no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4D8×C4111yescharacteristic
304C22⋊C4—42no—
305C22⋊C4—41no—
306C22⋊C4—41no—
307C22⋊C4—42no—
308C22⋊C4D8×C4112yes—
309C42C2×D4×C4111yescharacteristic
310C16—21no—
311C16—21no—
312C16—22no—
313C23—41no—
314C23—41no—
315C23C2×D8×C4112yes—
316Q8—42no—
317Q8—42no—
318Q8—82no—
319D4—22no—
320D4—22no—
321D4—41no—
322D4—41no—
323D4—41no—
324D4—84no—
325D4—84no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—84no—
333C2×C4—84no—
334C2×C4—82no—
335C2×C4—82no—
336C2×C4C2×D8×C4111yescharacteristic
337C2×C4C2×D8×C4112yes—
338C2×C4C2×D8×C4111yescharacteristic
339C2×C4C22×D4×C4111yescharacteristic
340C8—22no—
341C8—21no—
342C8C2×#41×C4111yescharacteristic
343C8H(5,𝔽2)×C4111yescharacteristic
344C22—22no—
345C22—22no—
346C22—22no—
347C22—42no—
348C22—81no—
349C22—81no—
350C22—81no—
351C22—81no—
352C22—81no—
353C22C22×D8×C4111yescharacteristic
354C4—22no—
355C4—21no—
356C4—82no—
357C4—81no—
358C4—82no—
359C4—81no—
360C4C41×#50912yes—
361C4C41×#54611yescharacteristic
362C4C41×#57711yescharacteristic
363C2—42no—
364C2—82no—
365C2—161no—
366C2C41×#329411yescharacteristic
367C2C2×C41×#50911yescharacteristic
368C2C41×#341711yescharacteristic
subgroupG/H
center, socleC22×C41C22×D8
commutator, Frattini, cosocleC2×C8C24×C41
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C41 ◁ C4×D4×C41 ◁ C8×D4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C41×#3334C2semidirect
2. C41×#3283C2semidirect
3. C41×#2241C2semidirect
4. C41×#2236C2semidirect
5. C41×#2224C2semidirect
6. C41×#2220C2semidirect
7. C41×#2208C2semidirect
8. C41×#2186C2semidirect
9. C4×D16×C41C2semidirect
10. C41×#2169C2semidirect
11. C41×#2139C2semidirect
104. D8×C41#41semidirect
159. #33897C41direct (N × H)
179. #3334C2×C41semidirect
180. #3283C2×C41semidirect
181. #2241C2×C41semidirect
182. #2236C2×C41semidirect
183. #2224C2×C41semidirect
184. #2220C2×C41semidirect
185. #2208C2×C41semidirect
186. #2186C2×C41semidirect
187. C4×D16C2×C41semidirect
188. #2169C2×C41semidirect
189. #2139C2×C41semidirect
225. C41#33897direct (N × H)
289. D8#41×C41semidirect

Maximal subgroups

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

subgroupindex
C41×#33342
C41×#32832
C41×#22412
C41×#22362
C41×#22242
C41×#22202
C41×#22082
C41×#21862
C4×D16×C412
C41×#21692
C41×#21392
#3389741