Finite Group Databasebeta

← C41×#13026 #23789227

Subgroups — C41×#13026 #23789227

Order 10496.

486 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#510C211yesmaximal, characteristic
2C41×#2943C211yesmaximal, characteristic
3C2×C41×#360C211yesmaximal, characteristic
4C41×#2141C211yesmaximal, characteristic, complemented
5C41×#1971C211yesmaximal, characteristic, complemented
6C41×#1386C211yesmaximal, characteristic, complemented
7C41×#1377C211yesmaximal, characteristic, complemented
8C2×#135×C41C2211yescharacteristic
9C22×Q16×C41C2211yescharacteristic
10C4×#41×C41—21no—
11C41×#510—22no—
12C41×#510C414yescomplemented
13C2×Q32×C41—21no—
14C2×SD32×C41—21no—
15C2×M32×C41C2211yescharacteristic
16C2×M32×C41C2211yescharacteristic
17C41×#442—21no—
18C41×#441—21no—
19C41×#440—22no—
20C41×#427C2211yescharacteristic
21C2×#106×C41C2211yescharacteristic
22C41×#416—21no—
23C2×#103×C41—21no—
24C2×#97×C41C2211yescharacteristic
25C41×#391—21no—
26C41×#360—22no—
27C41×#358—22no—
28C2×#41×C41—21no—
29C22×Q8×C41—21no—
30#135×C41—21no—
31#135×C41—21no—
32#135×C41C2×C412yes—
33#135×C41D412yes—
34C2×Q16×C41—21no—
35C2×Q16×C41—21no—
36C2×Q16×C41—21no—
37C2×Q16×C41—21no—
38C2×Q16×C41—21no—
39C2×Q16×C41C2×C412yescomplemented
40C2×Q16×C41D411yescharacteristic
41C2×SD16×C41—21no—
42C2×D8×C41D411yescharacteristic
43C22×C8×C41D411yescharacteristic
44C22×C8×C41C2311yescharacteristic
45C4×Q8×C41—22no—
46C4×D4×C41—22no—
47C4×D4×C41—42no—
48#117×C41—21no—
49#117×C41—41no—
50C2×C4⋊C4×C41—21no—
51C2×C42×C41—41no—
52C2×C42×C41D411yescharacteristic
53Q32×C41—24no—
54SD32×C41—24no—
55M32×C41—21no—
56M32×C41—21no—
57M32×C41—21no—
58M32×C41C2×C412yescomplemented
59C2×C16×C41—21no—
60C2×C16×C41—21no—
61#107×C41D412yes—
62#106×C41—21no—
63#106×C41—21no—
64#106×C41—21no—
65#103×C41—22no—
66#103×C41—42no—
67#102×C41—22no—
68#97×C41—21no—
69#97×C41—21no—
70#95×C41—42no—
71#41×C41—22no—
72#41×C41—22no—
73#41×C41—41no—
74#41×C41—41no—
75C2×Q8×C41—22no—
76C2×Q8×C41—21no—
77C2×Q8×C41—41no—
78C2×Q8×C41—41no—
79C2×Q8×C41—41no—
80C2×Q8×C41—41no—
81C2×Q8×C41—41no—
82C2×D4×C41—21no—
83C2×D4×C41—41no—
84C22×C4×C41—42no—
85C22×C4×C41—41no—
86C22×C4×C41—41no—
87C22×C4×C41—41no—
88C22×C4×C41D812yes—
89C22×C4×C41C2×D411yescharacteristic
90Q16×C41—22no—
91Q16×C41—22no—
92Q16×C41—21no—
93Q16×C41—41no—
94Q16×C41—41no—
95Q16×C41C22⋊C412yes—
96SD16×C41—22no—
97SD16×C41—22no—
98D8×C41—21no—
99D8×C41C22⋊C412yes—
100C2×C8×C41—21no—
101C2×C8×C41—21no—
102C2×C8×C41—21no—
103C2×C8×C41C22×C411yescharacteristic
104C2×C8×C41C2×D411yescharacteristic
105C2×C8×C41C2×D411yescharacteristic
106C2×C8×C41C2×D411yescharacteristic
107C2×C8×C41#4111yescharacteristic
108C2×C8×C41#4111yescharacteristic
109C4⋊C4×C41—22no—
110C4⋊C4×C41—42no—
111C4⋊C4×C41—41no—
112C4⋊C4×C41—41no—
113C22⋊C4×C41—42no—
114C22⋊C4×C41—41no—
115C42×C41—21no—
116C42×C41—21no—
117C42×C41—42no—
118C42×C41—41no—
119C16×C41—22no—
120C16×C41—41no—
121C23×C41—41no—
122C23×C41C2×D811yescharacteristic
123Q8×C41—22no—
124Q8×C41—41no—
125Q8×C41—42no—
126Q8×C41—42no—
127Q8×C41—81no—
128Q8×C41—81no—
129D4×C41—22no—
130D4×C41—42no—
131D4×C41—42no—
132D4×C41—41no—
133C2×C4×C41—22no—
134C2×C4×C41—41no—
135C2×C4×C41—42no—
136C2×C4×C41—42no—
137C2×C4×C41—42no—
138C2×C4×C41—42no—
139C2×C4×C41—42no—
140C2×C4×C41—84no—
141C2×C4×C41—81no—
142C2×C4×C41—81no—
143C2×C4×C41—82no—
144C2×C4×C41—81no—
145C2×C4×C41C4×D411yescharacteristic
146C2×C4×C41#12011yescharacteristic
147C2×C4×C41#12111yescharacteristic
148C2×C4×C41#13511yescharacteristic
149C2×C4×C41AGL(1,ℤ/8)11yescharacteristic
150C2×C4×C41AGL(1,ℤ/8)11yescharacteristic
151C8×C41—41no—
152C8×C41C2×C22⋊C411yescharacteristic
153C8×C41C4×D411yescharacteristic
154C8×C41#12111yescharacteristic
155C8×C41#12311yescharacteristic
156#13026C4111yesmaximal, characteristic, direct product factor, Sylow
157C22×C41—22no—
158C22×C41—42no—
159C22×C41—82no—
160C22×C41C4×D811yescharacteristic
161C22×C41#44711yescharacteristic
162C22×C41#45911yescharacteristic
163C4×C41—42no—
164C4×C41—42no—
165C4×C41—82no—
166C4×C41—82no—
167C4×C41—161no—
168C4×C41#38611yescharacteristic
169C4×C41#44211yescharacteristic
170C4×C41#44911yescharacteristic
171C4×C41#46311yescharacteristic
172C2×#510C2×C4111yescharacteristic
173#2943C2×C4111yescharacteristic
174C2×#360C2×C4111yescharacteristic
175#2141C2×C4111yescharacteristic, complemented
176#1971C2×C4111yescharacteristic, complemented
177#1386C2×C4111yescharacteristic, complemented
178#1377C2×C4111yescharacteristic, complemented
179C2×C41—21no—
180C2×C41—21no—
181C2×C41—82no—
182C2×C41#187911yescharacteristic
183C2×C41#219112yes—
184C2×#135C22×C4111yescharacteristic
185C22×Q16C22×C4111yescharacteristic
186C4×#41—21no—
187#510—22no—
188#510C4×C4114yescomplemented
189C2×Q32—21no—
190C2×SD32—21no—
191C2×M32C22×C4111yescharacteristic
192C2×M32C22×C4111yescharacteristic
193#442—21no—
194#441—21no—
195#440—22no—
196#427C22×C4111yescharacteristic
197C2×#106C22×C4111yescharacteristic
198#416—21no—
199C2×#103—21no—
200C2×#97C22×C4111yescharacteristic
201#391—21no—
202#360—22no—
203#358—22no—
204C41#1302611yescharacteristic, direct product factor, Sylow
205C2×#41—21no—
206C22×Q8—21no—
207#135—21no—
208#135—21no—
209#135C2×C4×C4112yes—
210#135D4×C4112yes—
211C2×Q16—21no—
212C2×Q16—21no—
213C2×Q16—21no—
214C2×Q16—21no—
215C2×Q16—21no—
216C2×Q16C2×C4×C4112yescomplemented
217C2×Q16D4×C4111yescharacteristic
218C2×SD16—21no—
219C2×D8D4×C4111yescharacteristic
220C22×C8D4×C4111yescharacteristic
221C22×C8C23×C4111yescharacteristic
222C4×Q8—22no—
223C4×D4—22no—
224C4×D4—42no—
225#117—21no—
226#117—41no—
227C2×C4⋊C4—21no—
228C2×C42—41no—
229C2×C42D4×C4111yescharacteristic
230Q32—24no—
231SD32—24no—
232M32—21no—
233M32—21no—
234M32—21no—
235M32C2×C4×C4112yescomplemented
236C2×C16—21no—
237C2×C16—21no—
238#107D4×C4112yes—
239#106—21no—
240#106—21no—
241#106—21no—
242#103—22no—
243#103—42no—
244#102—22no—
245#97—21no—
246#97—21no—
247#95—42no—
248#41—22no—
249#41—22no—
250#41—41no—
251#41—41no—
252C2×Q8—22no—
253C2×Q8—21no—
254C2×Q8—41no—
255C2×Q8—41no—
256C2×Q8—41no—
257C2×Q8—41no—
258C2×Q8—41no—
259C2×D4—21no—
260C2×D4—41no—
261C22×C4—42no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4D8×C4112yes—
266C22×C4C2×D4×C4111yescharacteristic
267Q16—22no—
268Q16—22no—
269Q16—21no—
270Q16—41no—
271Q16—41no—
272Q16C22⋊C4×C4112yes—
273SD16—22no—
274SD16—22no—
275D8—21no—
276D8C22⋊C4×C4112yes—
277C2×C8—21no—
278C2×C8—21no—
279C2×C8—21no—
280C2×C8C22×C4×C4111yescharacteristic
281C2×C8C2×D4×C4111yescharacteristic
282C2×C8C2×D4×C4111yescharacteristic
283C2×C8C2×D4×C4111yescharacteristic
284C2×C8#41×C4111yescharacteristic
285C2×C8#41×C4111yescharacteristic
286C4⋊C4—22no—
287C4⋊C4—42no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C22⋊C4—42no—
291C22⋊C4—41no—
292C42—21no—
293C42—21no—
294C42—42no—
295C42—41no—
296C16—22no—
297C16—41no—
298C23—41no—
299C23C2×D8×C4111yescharacteristic
300Q8—22no—
301Q8—41no—
302Q8—42no—
303Q8—42no—
304Q8—81no—
305Q8—81no—
306D4—22no—
307D4—42no—
308D4—42no—
309D4—41no—
310C2×C4—22no—
311C2×C4—41no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—84no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—82no—
321C2×C4—81no—
322C2×C4C4×D4×C4111yescharacteristic
323C2×C4#120×C4111yescharacteristic
324C2×C4#121×C4111yescharacteristic
325C2×C4#135×C4111yescharacteristic
326C2×C4AGL(1,ℤ/8)×C4111yescharacteristic
327C2×C4AGL(1,ℤ/8)×C4111yescharacteristic
328C8—41no—
329C8C2×C22⋊C4×C4111yescharacteristic
330C8C4×D4×C4111yescharacteristic
331C8#121×C4111yescharacteristic
332C8#123×C4111yescharacteristic
333C22—22no—
334C22—42no—
335C22—82no—
336C22C4×D8×C4111yescharacteristic
337C22C41×#44711yescharacteristic
338C22C41×#45911yescharacteristic
339C4—42no—
340C4—42no—
341C4—82no—
342C4—82no—
343C4—161no—
344C4C41×#38611yescharacteristic
345C4C41×#44211yescharacteristic
346C4C41×#44911yescharacteristic
347C4C41×#46311yescharacteristic
348C2—21no—
349C2—21no—
350C2—82no—
351C2C41×#187911yescharacteristic
352C2C41×#219112yes—
subgroupG/H
center, socleC22×C41#447
commutatorC2×C8C22×C4×C41
Frattini, cosocleC22×C8C23×C41
prime radicalC2×#135×C41C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C41 ◁ C22×C4×C41 ◁ C2×#97×C41 ◁ G

Complements

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

NH ≅ G/Ntype
4. C41×#2141C2semidirect
5. C41×#1971C2semidirect
6. C41×#1386C2semidirect
7. C41×#1377C2semidirect
12. C41×#510C4semidirect
39. C2×Q16×C41C2×C4semidirect
58. M32×C41C2×C4semidirect
156. #13026C41direct (N × H)
175. #2141C2×C41semidirect
176. #1971C2×C41semidirect
177. #1386C2×C41semidirect
178. #1377C2×C41semidirect
188. #510C4×C41semidirect
204. C41#13026direct (N × H)
216. C2×Q16C2×C4×C41semidirect
235. M32C2×C4×C41semidirect

Maximal subgroups

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

subgroupindex
C2×C41×#5102
C41×#29432
C2×C41×#3602
C41×#21412
C41×#19712
C41×#13862
C41×#13772
#1302641