Finite Group Databasebeta

← C41×#13050 #23789251

Subgroups — C41×#13050 #23789251

Order 10496.

732 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 732 conjugacy classes of subgroups — too many to draw. Only its 118 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#455C211yesmaximal, characteristic
2C41×#2379C211yesmaximal, characteristic, complemented
3C2×C41×#354C211yesmaximal, characteristic, complemented
4C41×#1790C212yesmaximal
5C41×#1390C212yesmaximal, complemented
6C2×H(5,𝔽2)×C41C2211yescharacteristic
7C2×#137×C41—21no—
8C2×#124×C41C2211yescharacteristic
9C41×#455—22no—
10C41×#455C414yescomplemented
11C2×#104×C41—21no—
12C2×#100×C41C2211yescharacteristic
13C2×#99×C41—22no—
14C2×#99×C41C2212yes—
15C41×#391—21no—
16C41×#388—22no—
17C41×#386—22no—
18C41×#386C2212yes—
19C41×#385—22no—
20C41×#382—21no—
21C41×#354—22no—
22H(5,𝔽2)×C41—22no—
23H(5,𝔽2)×C41—21no—
24H(5,𝔽2)×C41—42no—
25H(5,𝔽2)×C41C2×C412yes—
26C2×#41×C41—21no—
27C2×#41×C41—41no—
28C22×Q8×C41D411yescharacteristic
29C22×D4×C41—22no—
30C22×D4×C41—41no—
31C22×D4×C41C2311yescharacteristic
32C23×C4×C41D412yes—
33#137×C41—24no—
34#137×C41—42no—
35C2×Q16×C41—41no—
36C2×SD16×C41—41no—
37C2×M16×C41—21no—
38#124×C41—22no—
39#124×C41C2×C412yes—
40#124×C41D412yes—
41C2×C4⋊C4×C41—21no—
42C2×C4⋊C4×C41—21no—
43C2×C4⋊C4×C41—21no—
44C2×C22⋊C4×C41—22no—
45C2×C22⋊C4×C41—22no—
46C2×C22⋊C4×C41—22no—
47C2×C22⋊C4×C41—42no—
48C2×C22⋊C4×C41D412yes—
49C2×C42×C41—21no—
50C2×C42×C41D411yescharacteristic
51#104×C41—24no—
52#100×C41—21no—
53#100×C41C2×C412yes—
54#99×C41—22no—
55#99×C41—22no—
56#99×C41—44no—
57#95×C41—22no—
58#95×C41—22no—
59#95×C41—22no—
60#95×C41—42no—
61C24×C41—22no—
62C24×C41C2×D412yes—
63#41×C41—22no—
64#41×C41—22no—
65#41×C41—42no—
66#41×C41—41no—
67#41×C41—44no—
68#41×C41—42no—
69#41×C41—41no—
70C2×Q8×C41—21no—
71C2×Q8×C41—21no—
72C2×Q8×C41—41no—
73C2×Q8×C41—41no—
74C2×Q8×C41C22⋊C412yescomplemented
75C2×D4×C41—21no—
76C2×D4×C41—24no—
77C2×D4×C41—24no—
78C2×D4×C41—41no—
79C2×D4×C41—41no—
80C2×D4×C41—42no—
81C2×D4×C41—42no—
82C2×D4×C41—42no—
83C2×D4×C41—42no—
84C2×D4×C41—44no—
85C2×D4×C41—41no—
86C2×D4×C41—42no—
87C2×D4×C41C22×C411yescharacteristic
88C2×D4×C41C2×D411yescharacteristic
89C2×D4×C41#4112yes—
90C22×C4×C41—22no—
91C22×C4×C41—21no—
92C22×C4×C41—21no—
93C22×C4×C41—22no—
94C22×C4×C41—22no—
95C22×C4×C41—41no—
96C22×C4×C41—42no—
97C22×C4×C41—42no—
98C22×C4×C41—82no—
99C22×C4×C41C2×D411yescharacteristic
100Q16×C41—44no—
101SD16×C41—44no—
102M16×C41—22no—
103M16×C41—41no—
104C2×C8×C41—41no—
105C4⋊C4×C41—81no—
106C4⋊C4×C41—81no—
107C4⋊C4×C41—81no—
108C22⋊C4×C41—24no—
109C22⋊C4×C41—24no—
110C22⋊C4×C41—42no—
111C22⋊C4×C41—42no—
112C22⋊C4×C41—42no—
113C22⋊C4×C41—82no—
114C22⋊C4×C41—84no—
115C42×C41—21no—
116C42×C41—81no—
117C42×C41C22⋊C412yescomplemented
118C23×C41—22no—
119C23×C41—22no—
120C23×C41—24no—
121C23×C41—42no—
122C23×C41—42no—
123C23×C41—42no—
124C23×C41—41no—
125C23×C41—82no—
126C23×C41—82no—
127C23×C41C4×D412yes—
128C23×C41#12011yescharacteristic
129C23×C41#12112yes—
130Q8×C41—22no—
131Q8×C41—42no—
132Q8×C41—41no—
133Q8×C41—81no—
134D4×C41—22no—
135D4×C41—41no—
136D4×C41—41no—
137D4×C41—42no—
138D4×C41—41no—
139D4×C41—44no—
140D4×C41—44no—
141D4×C41—42no—
142D4×C41—42no—
143C2×C4×C41—21no—
144C2×C4×C41—21no—
145C2×C4×C41—24no—
146C2×C4×C41—22no—
147C2×C4×C41—22no—
148C2×C4×C41—42no—
149C2×C4×C41—42no—
150C2×C4×C41—41no—
151C2×C4×C41—41no—
152C2×C4×C41—42no—
153C2×C4×C41—41no—
154C2×C4×C41—41no—
155C2×C4×C41—41no—
156C2×C4×C41—42no—
157C2×C4×C41—42no—
158C2×C4×C41—42no—
159C2×C4×C41—42no—
160C2×C4×C41—44no—
161C2×C4×C41—42no—
162C2×C4×C41—42no—
163C2×C4×C41—82no—
164C2×C4×C41—82no—
165C2×C4×C41—82no—
166C2×C4×C41—82no—
167C2×C4×C41C2×C22⋊C411yescharacteristic
168C2×C4×C41#12311yescharacteristic
169C8×C41—42no—
170#13050C4111yesmaximal, characteristic, direct product factor, Sylow
171C22×C41—21no—
172C22×C41—21no—
173C22×C41—22no—
174C22×C41—22no—
175C22×C41—42no—
176C22×C41—42no—
177C22×C41—42no—
178C22×C41—42no—
179C22×C41—42no—
180C22×C41—82no—
181C22×C41—84no—
182C22×C41—81no—
183C22×C41—81no—
184C22×C41—162no—
185C22×C41#38611yescharacteristic
186C22×C41B(4,𝔽2)11yescharacteristic
187C22×C41B(4,𝔽2)11yescharacteristic
188C4×C41—21no—
189C4×C41—21no—
190C4×C41—42no—
191C4×C41—42no—
192C4×C41—42no—
193C4×C41—82no—
194C4×C41—82no—
195C4×C41—162no—
196C2×#455C2×C4111yescharacteristic
197#2379C2×C4111yescharacteristic, complemented
198C2×#354C2×C4111yescharacteristic, complemented
199#1790C2×C4112yes—
200#1390C2×C4112yescomplemented
201C2×C41—21no—
202C2×C41—21no—
203C2×C41—42no—
204C2×C41—42no—
205C2×C41—82no—
206C2×C41#188911yescharacteristic
207C2×C41#219911yescharacteristic
208C2×C41#220111yescharacteristic
209C2×H(5,𝔽2)C22×C4111yescharacteristic
210C2×#137—21no—
211C2×#124C22×C4111yescharacteristic
212#455—22no—
213#455C4×C4114yescomplemented
214C2×#104—21no—
215C2×#100C22×C4111yescharacteristic
216C2×#99—22no—
217C2×#99C22×C4112yes—
218#391—21no—
219#388—22no—
220#386—22no—
221#386C22×C4112yes—
222#385—22no—
223#382—21no—
224#354—22no—
225C41#1305011yescharacteristic, direct product factor, Sylow
226H(5,𝔽2)—22no—
227H(5,𝔽2)—21no—
228H(5,𝔽2)—42no—
229H(5,𝔽2)C2×C4×C4112yes—
230C2×#41—21no—
231C2×#41—41no—
232C22×Q8D4×C4111yescharacteristic
233C22×D4—22no—
234C22×D4—41no—
235C22×D4C23×C4111yescharacteristic
236C23×C4D4×C4112yes—
237#137—24no—
238#137—42no—
239C2×Q16—41no—
240C2×SD16—41no—
241C2×M16—21no—
242#124—22no—
243#124C2×C4×C4112yes—
244#124D4×C4112yes—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C22⋊C4—22no—
249C2×C22⋊C4—22no—
250C2×C22⋊C4—22no—
251C2×C22⋊C4—42no—
252C2×C22⋊C4D4×C4112yes—
253C2×C42—21no—
254C2×C42D4×C4111yescharacteristic
255#104—24no—
256#100—21no—
257#100C2×C4×C4112yes—
258#99—22no—
259#99—22no—
260#99—44no—
261#95—22no—
262#95—22no—
263#95—22no—
264#95—42no—
265C24—22no—
266C24C2×D4×C4112yes—
267#41—22no—
268#41—22no—
269#41—42no—
270#41—41no—
271#41—44no—
272#41—42no—
273#41—41no—
274C2×Q8—21no—
275C2×Q8—21no—
276C2×Q8—41no—
277C2×Q8—41no—
278C2×Q8C22⋊C4×C4112yescomplemented
279C2×D4—21no—
280C2×D4—24no—
281C2×D4—24no—
282C2×D4—41no—
283C2×D4—41no—
284C2×D4—42no—
285C2×D4—42no—
286C2×D4—42no—
287C2×D4—42no—
288C2×D4—44no—
289C2×D4—41no—
290C2×D4—42no—
291C2×D4C22×C4×C4111yescharacteristic
292C2×D4C2×D4×C4111yescharacteristic
293C2×D4#41×C4112yes—
294C22×C4—22no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—22no—
298C22×C4—22no—
299C22×C4—41no—
300C22×C4—42no—
301C22×C4—42no—
302C22×C4—82no—
303C22×C4C2×D4×C4111yescharacteristic
304Q16—44no—
305SD16—44no—
306M16—22no—
307M16—41no—
308C2×C8—41no—
309C4⋊C4—81no—
310C4⋊C4—81no—
311C4⋊C4—81no—
312C22⋊C4—24no—
313C22⋊C4—24no—
314C22⋊C4—42no—
315C22⋊C4—42no—
316C22⋊C4—42no—
317C22⋊C4—82no—
318C22⋊C4—84no—
319C42—21no—
320C42—81no—
321C42C22⋊C4×C4112yescomplemented
322C23—22no—
323C23—22no—
324C23—24no—
325C23—42no—
326C23—42no—
327C23—42no—
328C23—41no—
329C23—82no—
330C23—82no—
331C23C4×D4×C4112yes—
332C23#120×C4111yescharacteristic
333C23#121×C4112yes—
334Q8—22no—
335Q8—42no—
336Q8—41no—
337Q8—81no—
338D4—22no—
339D4—41no—
340D4—41no—
341D4—42no—
342D4—41no—
343D4—44no—
344D4—44no—
345D4—42no—
346D4—42no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—24no—
350C2×C4—22no—
351C2×C4—22no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—41no—
355C2×C4—42no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—42no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—44no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—82no—
368C2×C4—82no—
369C2×C4—82no—
370C2×C4—82no—
371C2×C4C2×C22⋊C4×C4111yescharacteristic
372C2×C4#123×C4111yescharacteristic
373C8—42no—
374C22—21no—
375C22—21no—
376C22—22no—
377C22—22no—
378C22—42no—
379C22—42no—
380C22—42no—
381C22—42no—
382C22—42no—
383C22—82no—
384C22—84no—
385C22—81no—
386C22—81no—
387C22—162no—
388C22C41×#38611yescharacteristic
389C22C41×B(4,𝔽2)11yescharacteristic
390C22C41×B(4,𝔽2)11yescharacteristic
391C4—21no—
392C4—21no—
393C4—42no—
394C4—42no—
395C4—42no—
396C4—82no—
397C4—82no—
398C4—162no—
399C2—21no—
400C2—21no—
401C2—42no—
402C2—42no—
403C2—82no—
404C2C41×#188911yescharacteristic
405C2C41×#219911yescharacteristic
406C2C41×#220111yescharacteristic
subgroupG/H
center, socleC22×C41B(4,𝔽2)
commutatorC2×D4C22×C4×C41
Frattini, cosocleC22×D4C23×C41
prime radicalC2×H(5,𝔽2)×C41C22
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C41 ◁ C23×C41 ◁ C22×D4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C41×#2379C2semidirect
3. C2×C41×#354C2semidirect
5. C41×#1390C2semidirect
10. C41×#455C4semidirect
74. C2×Q8×C41C22⋊C4semidirect
117. C42×C41C22⋊C4semidirect
170. #13050C41direct (N × H)
197. #2379C2×C41semidirect
198. C2×#354C2×C41semidirect
200. #1390C2×C41semidirect
213. #455C4×C41semidirect
225. C41#13050direct (N × H)
278. C2×Q8C22⋊C4×C41semidirect
321. C42C22⋊C4×C41semidirect

Maximal subgroups

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

subgroupindex
C2×C41×#4552
C41×#23792
C2×C41×#3542
C41×#17902
C41×#13902
#1305041