Finite Group Databasebeta

← C41×#13385 #23789586

Subgroups — C41×#13385 #23789586

Order 10496.

408 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3061C211yesmaximal, characteristic
2C2×C41×#367C211yesmaximal, characteristic, complemented
3C2×C41×#359C211yesmaximal, characteristic, complemented
4C41×#2139C211yesmaximal, characteristic, complemented
5C2×C41×#350C211yesmaximal, characteristic, complemented
6C41×#1816C211yesmaximal, characteristic, complemented
7C41×#1387C211yesmaximal, characteristic, complemented
8C2×#135×C41C2211yescharacteristic
9C2×#131×C41C2211yescharacteristic
10C41×#537—21no—
11C2×M32×C41C2211yescharacteristic
12C22×C16×C41C2211yescharacteristic
13C41×#468—22no—
14C41×#467—21no—
15C41×#466—21no—
16C2×#108×C41C2211yescharacteristic
17C2×#107×C41C2211yescharacteristic
18C2×#107×C41C2211yescharacteristic
19C41×#417—21no—
20C41×#417—21no—
21C41×#367—22no—
22C41×#359—22no—
23C41×#358—21no—
24C41×#357—21no—
25C41×#350—22no—
26C41×#343—21no—
27C2×#41×C41—21no—
28C2×#41×C41D411yescharacteristic
29#135×C41—21no—
30#135×C41—21no—
31#135×C41—21no—
32#135×C41—21no—
33C2×Q16×C41D411yescharacteristic
34C2×SD16×C41—21no—
35C2×D8×C41D411yescharacteristic
36#131×C41—21no—
37#131×C41—21no—
38#131×C41—21no—
39#131×C41—21no—
40C2×M16×C41—21no—
41C2×M16×C41—21no—
42C2×M16×C41D411yescharacteristic
43C22×C8×C41—21no—
44C22×C8×C41C2311yescharacteristic
45C22⋊Q8×C41—22no—
46C22⋊Q8×C41—41no—
47#121×C41—22no—
48#121×C41—42no—
49#121×C41—41no—
50C2×C4⋊C4×C41—21no—
51C2×C4⋊C4×C41—21no—
52M32×C41—21no—
53M32×C41—21no—
54C2×C16×C41—21no—
55C2×C16×C41—21no—
56C2×C16×C41—21no—
57C2×C16×C41D412yescomplemented
58#108×C41—21no—
59#108×C41—21no—
60#107×C41—21no—
61#107×C41—21no—
62#107×C41—21no—
63#107×C41D412yes—
64#103×C41—22no—
65#103×C41—41no—
66#102×C41—22no—
67#102×C41—41no—
68#41×C41—21no—
69#41×C41—21no—
70#41×C41—21no—
71#41×C41—21no—
72#41×C41—41no—
73#41×C41—41no—
74#41×C41—41no—
75#41×C41—41no—
76C2×Q8×C41—21no—
77C2×Q8×C41D811yescharacteristic
78C2×D4×C41—21no—
79C2×D4×C41—21no—
80C2×D4×C41—41no—
81C2×D4×C41—42no—
82C2×D4×C41D811yescharacteristic
83C22×C4×C41—21no—
84C22×C4×C41—41no—
85C22×C4×C41—41no—
86C22×C4×C41—41no—
87C22×C4×C41C2×D411yescharacteristic
88Q16×C41—21no—
89Q16×C41—21no—
90SD16×C41—41no—
91SD16×C41—41no—
92D8×C41—21no—
93D8×C41—21no—
94M16×C41—21no—
95M16×C41—21no—
96M16×C41—41no—
97M16×C41—41no—
98M16×C41—41no—
99M16×C41—41no—
100C2×C8×C41—21no—
101C2×C8×C41—41no—
102C2×C8×C41—41no—
103C2×C8×C41—41no—
104C2×C8×C41C2×D411yescharacteristic
105C2×C8×C41C2×D411yescharacteristic
106C2×C8×C41C2×D411yescharacteristic
107C2×C8×C41#4111yescharacteristic
108C2×C8×C41#4111yescharacteristic
109C2×C8×C41#4111yescharacteristic
110C4⋊C4×C41—22no—
111C4⋊C4×C41—42no—
112C4⋊C4×C41—41no—
113C4⋊C4×C41—41no—
114C4⋊C4×C41—41no—
115C22⋊C4×C41—42no—
116C22⋊C4×C41—42no—
117C16×C41—22no—
118C16×C41—41no—
119C23×C41—21no—
120C23×C41—41no—
121C23×C41AGL(1,ℤ/8)11yescharacteristic
122Q8×C41—21no—
123Q8×C41—21no—
124Q8×C41—41no—
125Q8×C41—41no—
126D4×C41—21no—
127D4×C41—21no—
128D4×C41—41no—
129D4×C41—41no—
130D4×C41—41no—
131D4×C41—41no—
132D4×C41—81no—
133D4×C41—81no—
134D4×C41—162no—
135C2×C4×C41—21no—
136C2×C4×C41—41no—
137C2×C4×C41—41no—
138C2×C4×C41—42no—
139C2×C4×C41—41no—
140C2×C4×C41—81no—
141C2×C4×C41—81no—
142C2×C4×C41—81no—
143C2×C4×C41—161no—
144C2×C4×C41—161no—
145C2×C4×C41#12011yescharacteristic
146C2×C4×C41#12111yescharacteristic
147C2×C4×C41#12311yescharacteristic
148C2×C4×C41C2×D811yescharacteristic
149C2×C4×C41#13511yescharacteristic
150C2×C4×C41#13711yescharacteristic
151C8×C41—41no—
152C8×C41—81no—
153C8×C41#12111yescharacteristic
154C8×C41#12111yescharacteristic
155C8×C41#12311yescharacteristic
156C8×C41#12411yescharacteristic
157#13385C4111yesmaximal, characteristic, direct product factor, Sylow
158C22×C41—21no—
159C22×C41—21no—
160C22×C41—41no—
161C22×C41—41no—
162C22×C41—41no—
163C22×C41—81no—
164C22×C41—81no—
165C22×C41—81no—
166C22×C41#44711yescharacteristic
167C22×C41#46811yescharacteristic
168C22×C41#48211yescharacteristic
169C4×C41—41no—
170C4×C41—82no—
171C4×C41—81no—
172C4×C41—161no—
173C4×C41#39411yescharacteristic
174C4×C41#45211yescharacteristic
175C4×C41#46611yescharacteristic
176C4×C41#48011yescharacteristic
177#3061C2×C4111yescharacteristic
178C2×#367C2×C4111yescharacteristic, complemented
179C2×#359C2×C4111yescharacteristic, complemented
180#2139C2×C4111yescharacteristic, complemented
181C2×#350C2×C4111yescharacteristic, complemented
182#1816C2×C4111yescharacteristic, complemented
183#1387C2×C4111yescharacteristic, complemented
184C2×C41—21no—
185C2×C41—21no—
186C2×C41—81no—
187C2×C41—161no—
188C2×C41#203311yescharacteristic
189C2×C41#219311yescharacteristic
190C2×C41#219411yescharacteristic
191C2×#135C22×C4111yescharacteristic
192C2×#131C22×C4111yescharacteristic
193#537—21no—
194C2×M32C22×C4111yescharacteristic
195C22×C16C22×C4111yescharacteristic
196#468—22no—
197#467—21no—
198#466—21no—
199C2×#108C22×C4111yescharacteristic
200C2×#107C22×C4111yescharacteristic
201C2×#107C22×C4111yescharacteristic
202#417—21no—
203#417—21no—
204#367—22no—
205#359—22no—
206#358—21no—
207#357—21no—
208#350—22no—
209#343—21no—
210C41#1338511yescharacteristic, direct product factor, Sylow
211C2×#41—21no—
212C2×#41D4×C4111yescharacteristic
213#135—21no—
214#135—21no—
215#135—21no—
216#135—21no—
217C2×Q16D4×C4111yescharacteristic
218C2×SD16—21no—
219C2×D8D4×C4111yescharacteristic
220#131—21no—
221#131—21no—
222#131—21no—
223#131—21no—
224C2×M16—21no—
225C2×M16—21no—
226C2×M16D4×C4111yescharacteristic
227C22×C8—21no—
228C22×C8C23×C4111yescharacteristic
229C22⋊Q8—22no—
230C22⋊Q8—41no—
231#121—22no—
232#121—42no—
233#121—41no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236M32—21no—
237M32—21no—
238C2×C16—21no—
239C2×C16—21no—
240C2×C16—21no—
241C2×C16D4×C4112yescomplemented
242#108—21no—
243#108—21no—
244#107—21no—
245#107—21no—
246#107—21no—
247#107D4×C4112yes—
248#103—22no—
249#103—41no—
250#102—22no—
251#102—41no—
252#41—21no—
253#41—21no—
254#41—21no—
255#41—21no—
256#41—41no—
257#41—41no—
258#41—41no—
259#41—41no—
260C2×Q8—21no—
261C2×Q8D8×C4111yescharacteristic
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—41no—
265C2×D4—42no—
266C2×D4D8×C4111yescharacteristic
267C22×C4—21no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—41no—
271C22×C4C2×D4×C4111yescharacteristic
272Q16—21no—
273Q16—21no—
274SD16—41no—
275SD16—41no—
276D8—21no—
277D8—21no—
278M16—21no—
279M16—21no—
280M16—41no—
281M16—41no—
282M16—41no—
283M16—41no—
284C2×C8—21no—
285C2×C8—41no—
286C2×C8—41no—
287C2×C8—41no—
288C2×C8C2×D4×C4111yescharacteristic
289C2×C8C2×D4×C4111yescharacteristic
290C2×C8C2×D4×C4111yescharacteristic
291C2×C8#41×C4111yescharacteristic
292C2×C8#41×C4111yescharacteristic
293C2×C8#41×C4111yescharacteristic
294C4⋊C4—22no—
295C4⋊C4—42no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C22⋊C4—42no—
300C22⋊C4—42no—
301C16—22no—
302C16—41no—
303C23—21no—
304C23—41no—
305C23AGL(1,ℤ/8)×C4111yescharacteristic
306Q8—21no—
307Q8—21no—
308Q8—41no—
309Q8—41no—
310D4—21no—
311D4—21no—
312D4—41no—
313D4—41no—
314D4—41no—
315D4—41no—
316D4—81no—
317D4—81no—
318D4—162no—
319C2×C4—21no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—42no—
323C2×C4—41no—
324C2×C4—81no—
325C2×C4—81no—
326C2×C4—81no—
327C2×C4—161no—
328C2×C4—161no—
329C2×C4#120×C4111yescharacteristic
330C2×C4#121×C4111yescharacteristic
331C2×C4#123×C4111yescharacteristic
332C2×C4C2×D8×C4111yescharacteristic
333C2×C4#135×C4111yescharacteristic
334C2×C4#137×C4111yescharacteristic
335C8—41no—
336C8—81no—
337C8#121×C4111yescharacteristic
338C8#121×C4111yescharacteristic
339C8#123×C4111yescharacteristic
340C8#124×C4111yescharacteristic
341C22—21no—
342C22—21no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—81no—
347C22—81no—
348C22—81no—
349C22C41×#44711yescharacteristic
350C22C41×#46811yescharacteristic
351C22C41×#48211yescharacteristic
352C4—41no—
353C4—81no—
354C4—82no—
355C4—161no—
356C4C41×#39411yescharacteristic
357C4C41×#45211yescharacteristic
358C4C41×#46611yescharacteristic
359C4C41×#48011yescharacteristic
360C2—21no—
361C2—21no—
362C2—81no—
363C2—161no—
364C2C41×#203311yescharacteristic
365C2C41×#219311yescharacteristic
366C2C41×#219411yescharacteristic
subgroupG/H
center, socleC22×C41#447
commutator, Frattini, cosocleC22×C8C23×C41
prime radicalC41×#3061C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C41 ◁ C22×C4×C41 ◁ C2×#131×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C41×#367C2semidirect
3. C2×C41×#359C2semidirect
4. C41×#2139C2semidirect
5. C2×C41×#350C2semidirect
6. C41×#1816C2semidirect
7. C41×#1387C2semidirect
57. C2×C16×C41D4semidirect
157. #13385C41direct (N × H)
178. C2×#367C2×C41semidirect
179. C2×#359C2×C41semidirect
180. #2139C2×C41semidirect
181. C2×#350C2×C41semidirect
182. #1816C2×C41semidirect
183. #1387C2×C41semidirect
210. C41#13385direct (N × H)
241. C2×C16D4×C41semidirect

Maximal subgroups

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

subgroupindex
C41×#30612
C2×C41×#3672
C2×C41×#3592
C41×#21392
C2×C41×#3502
C41×#18162
C41×#13872
#1338541