Finite Group Databasebeta

← C41×#9352 #23785553

Subgroups — C41×#9352 #23785553

Order 10496.

414 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3080C211yesmaximal, characteristic
2C41×#2971C211yesmaximal, characteristic
3C41×#1528C211yesmaximal, characteristic, complemented
4C41×#1488C211yesmaximal, characteristic
5C41×#1470C211yesmaximal, characteristic, complemented
6C41×#1307C211yesmaximal, characteristic, complemented
7C41×#1299C211yesmaximal, characteristic, complemented
8C2×#125×C41C2211yescharacteristic
9C4×#41×C41C2211yescharacteristic
10C41×#479—21no—
11C41×#479—21no—
12C41×#478—21no—
13C41×#478—21no—
14C8×Q8×C41—21no—
15C41×#436—21no—
16C41×#436—22no—
17C41×#432—21no—
18C41×#432C2211yescharacteristic
19C41×#432C2211yescharacteristic
20C41×#431C2211yescharacteristic
21C41×#428C411yescharacteristic
22C41×#428C411yescharacteristic
23C41×#423C2211yescharacteristic
24C41×#417C411yescharacteristic
25C41×#417C411yescharacteristic
26C4×M16×C41—21no—
27C4×M16×C41C2211yescharacteristic
28C41×#330—21no—
29C41×#330—21no—
30C41×Q8⋊C8—21no—
31C41×D4⋊C8—21no—
32C41×#324—22no—
33C2×#41×C41C2×C411yescharacteristic
34C2×M16×C41—22no—
35C2×M16×C41—21no—
36C2×M16×C41C2×C411yescharacteristic
37C2×M16×C41C2×C411yescharacteristic
38#125×C41—21no—
39#125×C41—21no—
40#125×C41—21no—
41#125×C41—21no—
42C4×Q8×C41D411yescharacteristic
43C4×Q8×C41D411yescharacteristic
44C4×D4×C41—21no—
45C4×D4×C41—21no—
46C4×D4×C41D411yescharacteristic
47C4×D4×C41D411yescharacteristic
48#117×C41—21no—
49#117×C41C2×C411yescharacteristic
50C2×C4⋊C4×C41—21no—
51C2×C4⋊C4×C41—21no—
52C2×C4⋊C4×C41C2×C411yescharacteristic
53C2×C4⋊C4×C41C2×C411yescharacteristic
54C2×C42×C41—21no—
55C2×C42×C41C2311yescharacteristic
56#107×C41—21no—
57#107×C41—21no—
58#106×C41—21no—
59#106×C41—21no—
60C4⋊C8×C41—22no—
61C4⋊C8×C41—21no—
62C4⋊C8×C41—21no—
63C4⋊C8×C41—21no—
64C4⋊C8×C41—21no—
65C4⋊C8×C41—21no—
66#103×C41—21no—
67#103×C41—21no—
68#102×C41—21no—
69#102×C41—21no—
70C22⋊C8×C41—22no—
71C22⋊C8×C41—21no—
72C22⋊C8×C41—21no—
73C22⋊C8×C41D412yes—
74#97×C41—21no—
75#97×C41—21no—
76#97×C41D411yescharacteristic
77#97×C41D411yescharacteristic
78C4×C8×C41—22no—
79C4×C8×C41—21no—
80C4×C8×C41—21no—
81#41×C41—22no—
82#41×C41—41no—
83C2×Q8×C41C22⋊C411yescharacteristic
84C2×D4×C41—21no—
85C2×D4×C41C22⋊C411yescharacteristic
86C22×C4×C41—21no—
87C22×C4×C41—21no—
88C22×C4×C41—21no—
89C22×C4×C41—21no—
90C22×C4×C41—21no—
91C22×C4×C41C22×C411yescharacteristic
92C22×C4×C41C2×D411yescharacteristic
93C22×C4×C41#4111yescharacteristic
94M16×C41—42no—
95M16×C41—44no—
96M16×C41—41no—
97M16×C41—41no—
98C2×C8×C41—21no—
99C2×C8×C41—21no—
100C2×C8×C41—21no—
101C2×C8×C41—22no—
102C2×C8×C41—21no—
103C2×C8×C41—41no—
104C2×C8×C41—41no—
105C4⋊C4×C41—21no—
106C4⋊C4×C41—21no—
107C4⋊C4×C41—21no—
108C4⋊C4×C41—21no—
109C4⋊C4×C41—21no—
110C4⋊C4×C41—21no—
111C4⋊C4×C41—41no—
112C4⋊C4×C41—41no—
113C4⋊C4×C41—41no—
114C4⋊C4×C41—41no—
115C4⋊C4×C41C22⋊C411yescharacteristic
116C4⋊C4×C41C22⋊C411yescharacteristic
117C22⋊C4×C41—21no—
118C22⋊C4×C41—21no—
119C22⋊C4×C41—21no—
120C42×C41—21no—
121C42×C41—21no—
122C42×C41—21no—
123C42×C41C2×D411yescharacteristic
124C42×C41C2×D411yescharacteristic
125C42×C41C2×D411yescharacteristic
126C42×C41#4111yescharacteristic
127C23×C41—21no—
128C23×C41C4×D411yescharacteristic
129Q8×C41—21no—
130Q8×C41#10112yes—
131D4×C41—21no—
132D4×C41—21no—
133D4×C41—42no—
134C2×C4×C41—21no—
135C2×C4×C41—21no—
136C2×C4×C41—21no—
137C2×C4×C41—21no—
138C2×C4×C41—21no—
139C2×C4×C41—41no—
140C2×C4×C41—41no—
141C2×C4×C41—42no—
142C2×C4×C41—42no—
143C2×C4×C41—42no—
144C2×C4×C41—41no—
145C2×C4×C41—41no—
146C2×C4×C41—81no—
147C2×C4×C41—81no—
148C2×C4×C41C2×C22⋊C411yescharacteristic
149C2×C4×C41C4×D411yescharacteristic
150C2×C4×C41#12011yescharacteristic
151C2×C4×C41#12111yescharacteristic
152C2×C4×C41#12111yescharacteristic
153C2×C4×C41#12311yescharacteristic
154C8×C41—22no—
155C8×C41—42no—
156C8×C41—41no—
157C8×C41—41no—
158C8×C41—41no—
159C8×C41—81no—
160C8×C41—81no—
161#9352C4111yesmaximal, characteristic, direct product factor, Sylow
162C22×C41—21no—
163C22×C41—21no—
164C22×C41—21no—
165C22×C41—41no—
166C22×C41—41no—
167C22×C41—41no—
168C22×C41#38611yescharacteristic
169C4×C41—21no—
170C4×C41—21no—
171C4×C41—21no—
172C4×C41—22no—
173C4×C41—21no—
174C4×C41—21no—
175C4×C41—41no—
176C4×C41—41no—
177C4×C41—81no—
178C4×C41—81no—
179C4×C41C2×#10111yescharacteristic
180C4×C41#41311yescharacteristic
181#3080C2×C4111yescharacteristic
182#2971C2×C4111yescharacteristic
183#1528C2×C4111yescharacteristic, complemented
184#1488C2×C4111yescharacteristic
185#1470C2×C4111yescharacteristic, complemented
186#1307C2×C4111yescharacteristic, complemented
187#1299C2×C4111yescharacteristic, complemented
188C2×C41—41no—
189C2×C41—81no—
190C2×C41#188111yescharacteristic
191C2×C41#190111yescharacteristic
192C2×C41#190611yescharacteristic
193C2×#125C22×C4111yescharacteristic
194C4×#41C22×C4111yescharacteristic
195#479—21no—
196#479—21no—
197#478—21no—
198#478—21no—
199C8×Q8—21no—
200#436—21no—
201#436—22no—
202#432—21no—
203#432C22×C4111yescharacteristic
204#432C22×C4111yescharacteristic
205#431C22×C4111yescharacteristic
206#428C4×C4111yescharacteristic
207#428C4×C4111yescharacteristic
208#423C22×C4111yescharacteristic
209#417C4×C4111yescharacteristic
210#417C4×C4111yescharacteristic
211C4×M16—21no—
212C4×M16C22×C4111yescharacteristic
213#330—21no—
214#330—21no—
215Q8⋊C8—21no—
216D4⋊C8—21no—
217#324—22no—
218C41#935211yescharacteristic, direct product factor, Sylow
219C2×#41C2×C4×C4111yescharacteristic
220C2×M16—22no—
221C2×M16—21no—
222C2×M16C2×C4×C4111yescharacteristic
223C2×M16C2×C4×C4111yescharacteristic
224#125—21no—
225#125—21no—
226#125—21no—
227#125—21no—
228C4×Q8D4×C4111yescharacteristic
229C4×Q8D4×C4111yescharacteristic
230C4×D4—21no—
231C4×D4—21no—
232C4×D4D4×C4111yescharacteristic
233C4×D4D4×C4111yescharacteristic
234#117—21no—
235#117C2×C4×C4111yescharacteristic
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4C2×C4×C4111yescharacteristic
239C2×C4⋊C4C2×C4×C4111yescharacteristic
240C2×C42—21no—
241C2×C42C23×C4111yescharacteristic
242#107—21no—
243#107—21no—
244#106—21no—
245#106—21no—
246C4⋊C8—22no—
247C4⋊C8—21no—
248C4⋊C8—21no—
249C4⋊C8—21no—
250C4⋊C8—21no—
251C4⋊C8—21no—
252#103—21no—
253#103—21no—
254#102—21no—
255#102—21no—
256C22⋊C8—22no—
257C22⋊C8—21no—
258C22⋊C8—21no—
259C22⋊C8D4×C4112yes—
260#97—21no—
261#97—21no—
262#97D4×C4111yescharacteristic
263#97D4×C4111yescharacteristic
264C4×C8—22no—
265C4×C8—21no—
266C4×C8—21no—
267#41—22no—
268#41—41no—
269C2×Q8C22⋊C4×C4111yescharacteristic
270C2×D4—21no—
271C2×D4C22⋊C4×C4111yescharacteristic
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4C22×C4×C4111yescharacteristic
278C22×C4C2×D4×C4111yescharacteristic
279C22×C4#41×C4111yescharacteristic
280M16—42no—
281M16—44no—
282M16—41no—
283M16—41no—
284C2×C8—21no—
285C2×C8—21no—
286C2×C8—21no—
287C2×C8—22no—
288C2×C8—21no—
289C2×C8—41no—
290C2×C8—41no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4C22⋊C4×C4111yescharacteristic
302C4⋊C4C22⋊C4×C4111yescharacteristic
303C22⋊C4—21no—
304C22⋊C4—21no—
305C22⋊C4—21no—
306C42—21no—
307C42—21no—
308C42—21no—
309C42C2×D4×C4111yescharacteristic
310C42C2×D4×C4111yescharacteristic
311C42C2×D4×C4111yescharacteristic
312C42#41×C4111yescharacteristic
313C23—21no—
314C23C4×D4×C4111yescharacteristic
315Q8—21no—
316Q8#101×C4112yes—
317D4—21no—
318D4—21no—
319D4—42no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4C2×C22⋊C4×C4111yescharacteristic
335C2×C4C4×D4×C4111yescharacteristic
336C2×C4#120×C4111yescharacteristic
337C2×C4#121×C4111yescharacteristic
338C2×C4#121×C4111yescharacteristic
339C2×C4#123×C4111yescharacteristic
340C8—22no—
341C8—42no—
342C8—41no—
343C8—41no—
344C8—41no—
345C8—81no—
346C8—81no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22C41×#38611yescharacteristic
354C4—21no—
355C4—21no—
356C4—21no—
357C4—22no—
358C4—21no—
359C4—21no—
360C4—41no—
361C4—41no—
362C4—81no—
363C4—81no—
364C4C2×#101×C4111yescharacteristic
365C4C41×#41311yescharacteristic
366C2—41no—
367C2—81no—
368C2C41×#188111yescharacteristic
369C2C41×#190111yescharacteristic
370C2C41×#190611yescharacteristic
subgroupG/H
center, socleC22×C41#386
commutatorC22×C4C22×C4×C41
Frattini, cosocleC2×C42C23×C41
prime radicalC2×#41×C41C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C41 ◁ C2×C42×C41 ◁ G

Complements

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

NH ≅ G/Ntype
3. C41×#1528C2semidirect
5. C41×#1470C2semidirect
6. C41×#1307C2semidirect
7. C41×#1299C2semidirect
161. #9352C41direct (N × H)
183. #1528C2×C41semidirect
185. #1470C2×C41semidirect
186. #1307C2×C41semidirect
187. #1299C2×C41semidirect
218. C41#9352direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#30802
C41×#29712
C41×#15282
C41×#14882
C41×#14702
C41×#13072
C41×#12992
#935241