Finite Group Databasebeta

← C41×#9018 #23785219

Subgroups — C41×#9018 #23785219

Order 10496.

928 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 928 conjugacy classes of subgroups — too many to draw. Only its 150 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×#394C211yesmaximal, characteristic
2C41×#2313C211yesmaximal, characteristic, complemented
3C41×#1786C212yesmaximal
4C2×C41×#324C211yesmaximal, characteristic, complemented
5C41×#1294C212yesmaximal, complemented
6C23×D4×C41C2211yescharacteristic
7C22×C4⋊C4×C41C2211yescharacteristic
8C22×C22⋊C4×C41—21no—
9C22×C22⋊C4×C41—21no—
10C2×#102×C41—24no—
11C2×C22⋊C8×C41C2212yes—
12C41×#394—22no—
13C41×#394C414yescomplemented
14C41×#387—24no—
15C41×#381—21no—
16C41×#380C2212yes—
17C4×C22⋊C4×C41—21no—
18C2×#95×C41C2211yescharacteristic
19C41×#324—22no—
20C25×C41—21no—
21C22×D4×C41—22no—
22C22×D4×C41—21no—
23C22×D4×C41—22no—
24C22×D4×C41—44no—
25C22×D4×C41C2×C412yes—
26C23×C4×C41—21no—
27C23×C4×C41D411yescharacteristic
28C23×C4×C41D411yescharacteristic
29C23×C4×C41C2311yescharacteristic
30C22×C8×C41—22no—
31C2×C4⋊C4×C41—22no—
32C2×C4⋊C4×C41—22no—
33C2×C4⋊C4×C41C2×C412yes—
34C2×C4⋊C4×C41D412yes—
35C2×C4⋊C4×C41D414yes—
36C2×C22⋊C4×C41—22no—
37C2×C22⋊C4×C41—24no—
38C2×C22⋊C4×C41—24no—
39C2×C22⋊C4×C41—44no—
40C2×C22⋊C4×C41—44no—
41C2×C42×C41—22no—
42#102×C41—48no—
43C22⋊C8×C41—22no—
44C22⋊C8×C41—22no—
45#95×C41—22no—
46#95×C41—24no—
47#95×C41—21no—
48#95×C41—22no—
49#95×C41C2×C412yes—
50C24×C41—24no—
51C24×C41—22no—
52C24×C41—42no—
53C24×C41—42no—
54C24×C41—42no—
55C24×C41—41no—
56C24×C41—41no—
57C24×C41—42no—
58C24×C41—42no—
59C24×C41C2×D411yescharacteristic
60C2×D4×C41—28no—
61C2×D4×C41—24no—
62C2×D4×C41—44no—
63C2×D4×C41—44no—
64C2×D4×C41—48no—
65C2×D4×C41—44no—
66C2×D4×C41—42no—
67C22×C4×C41—21no—
68C22×C4×C41—21no—
69C22×C4×C41—21no—
70C22×C4×C41—22no—
71C22×C4×C41—22no—
72C22×C4×C41—21no—
73C22×C4×C41—22no—
74C22×C4×C41—24no—
75C22×C4×C41—42no—
76C22×C4×C41—42no—
77C22×C4×C41—42no—
78C22×C4×C41—42no—
79C22×C4×C41—42no—
80C22×C4×C41C22⋊C412yes—
81C22×C4×C41C22⋊C412yes—
82C22×C4×C41C22×C411yescharacteristic
83C22×C4×C41C2×D412yes—
84C22×C4×C41C2×D411yescharacteristic
85C22×C4×C41#4112yes—
86C2×C8×C41—44no—
87C2×C8×C41—42no—
88C4⋊C4×C41—24no—
89C4⋊C4×C41—24no—
90C4⋊C4×C41—44no—
91C22⋊C4×C41—48no—
92C22⋊C4×C41—48no—
93C22⋊C4×C41—42no—
94C22⋊C4×C41—42no—
95C42×C41—82no—
96C23×C41—22no—
97C23×C41—22no—
98C23×C41—24no—
99C23×C41—42no—
100C23×C41—44no—
101C23×C41—48no—
102C23×C41—48no—
103C23×C41—42no—
104C23×C41—42no—
105C23×C41—42no—
106C23×C41—42no—
107C23×C41—42no—
108C23×C41—44no—
109C23×C41—84no—
110C23×C41—84no—
111C23×C41—82no—
112C23×C41—82no—
113C23×C41—82no—
114C23×C41—82no—
115C23×C41C2×C22⋊C411yescharacteristic
116C23×C41#12011yescharacteristic
117C23×C41#12311yescharacteristic
118C23×C41#13512yes—
119C23×C41AGL(1,ℤ/8)12yes—
120D4×C41—28no—
121D4×C41—48no—
122D4×C41—44no—
123C2×C4×C41—24no—
124C2×C4×C41—22no—
125C2×C4×C41—22no—
126C2×C4×C41—22no—
127C2×C4×C41—22no—
128C2×C4×C41—41no—
129C2×C4×C41—41no—
130C2×C4×C41—42no—
131C2×C4×C41—42no—
132C2×C4×C41—42no—
133C2×C4×C41—42no—
134C2×C4×C41—42no—
135C2×C4×C41—42no—
136C2×C4×C41—42no—
137C2×C4×C41—42no—
138C2×C4×C41—44no—
139C2×C4×C41—44no—
140C2×C4×C41—44no—
141C2×C4×C41—81no—
142C2×C4×C41—84no—
143C2×C4×C41C4×D412yes—
144C2×C4×C41#12112yes—
145C8×C41—82no—
146#9018C4111yesmaximal, characteristic, direct product factor, Sylow
147C22×C41—24no—
148C22×C41—24no—
149C22×C41—21no—
150C22×C41—21no—
151C22×C41—21no—
152C22×C41—21no—
153C22×C41—44no—
154C22×C41—44no—
155C22×C41—44no—
156C22×C41—82no—
157C22×C41—82no—
158C22×C41—88no—
159C22×C41—88no—
160C22×C41—82no—
161C22×C41—82no—
162C22×C41#38611yescharacteristic
163C22×C41#41611yescharacteristic
164C22×C41#41811yescharacteristic
165C22×C41#44912yes—
166C22×C41#45412yes—
167C22×C41B(4,𝔽2)12yes—
168C22×C41#48212yes—
169C4×C41—22no—
170C4×C41—22no—
171C4×C41—42no—
172C4×C41—42no—
173C4×C41—82no—
174C4×C41—84no—
175C2×#394C2×C4111yescharacteristic
176#2313C2×C4111yescharacteristic, complemented
177#1786C2×C4112yes—
178C2×#324C2×C4111yescharacteristic, complemented
179#1294C2×C4112yescomplemented
180C2×C41—21no—
181C2×C41—21no—
182C2×C41—22no—
183C2×C41—84no—
184C2×C41#159714yes—
185C2×C41#187511yescharacteristic
186C2×C41#188811yescharacteristic
187C2×C41#188911yescharacteristic
188C23×D4C22×C4111yescharacteristic
189C22×C4⋊C4C22×C4111yescharacteristic
190C22×C22⋊C4—21no—
191C22×C22⋊C4—21no—
192C2×#102—24no—
193C2×C22⋊C8C22×C4112yes—
194#394—22no—
195#394C4×C4114yescomplemented
196#387—24no—
197#381—21no—
198#380C22×C4112yes—
199C4×C22⋊C4—21no—
200C2×#95C22×C4111yescharacteristic
201#324—22no—
202C41#901811yescharacteristic, direct product factor, Sylow
203C25—21no—
204C22×D4—22no—
205C22×D4—21no—
206C22×D4—22no—
207C22×D4—44no—
208C22×D4C2×C4×C4112yes—
209C23×C4—21no—
210C23×C4D4×C4111yescharacteristic
211C23×C4D4×C4111yescharacteristic
212C23×C4C23×C4111yescharacteristic
213C22×C8—22no—
214C2×C4⋊C4—22no—
215C2×C4⋊C4—22no—
216C2×C4⋊C4C2×C4×C4112yes—
217C2×C4⋊C4D4×C4112yes—
218C2×C4⋊C4D4×C4114yes—
219C2×C22⋊C4—22no—
220C2×C22⋊C4—24no—
221C2×C22⋊C4—24no—
222C2×C22⋊C4—44no—
223C2×C22⋊C4—44no—
224C2×C42—22no—
225#102—48no—
226C22⋊C8—22no—
227C22⋊C8—22no—
228#95—22no—
229#95—24no—
230#95—21no—
231#95—22no—
232#95C2×C4×C4112yes—
233C24—24no—
234C24—22no—
235C24—42no—
236C24—42no—
237C24—42no—
238C24—41no—
239C24—41no—
240C24—42no—
241C24—42no—
242C24C2×D4×C4111yescharacteristic
243C2×D4—28no—
244C2×D4—24no—
245C2×D4—44no—
246C2×D4—44no—
247C2×D4—48no—
248C2×D4—44no—
249C2×D4—42no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—21no—
256C22×C4—22no—
257C22×C4—24no—
258C22×C4—42no—
259C22×C4—42no—
260C22×C4—42no—
261C22×C4—42no—
262C22×C4—42no—
263C22×C4C22⋊C4×C4112yes—
264C22×C4C22⋊C4×C4112yes—
265C22×C4C22×C4×C4111yescharacteristic
266C22×C4C2×D4×C4112yes—
267C22×C4C2×D4×C4111yescharacteristic
268C22×C4#41×C4112yes—
269C2×C8—44no—
270C2×C8—42no—
271C4⋊C4—24no—
272C4⋊C4—24no—
273C4⋊C4—44no—
274C22⋊C4—48no—
275C22⋊C4—48no—
276C22⋊C4—42no—
277C22⋊C4—42no—
278C42—82no—
279C23—22no—
280C23—22no—
281C23—24no—
282C23—42no—
283C23—44no—
284C23—48no—
285C23—48no—
286C23—42no—
287C23—42no—
288C23—42no—
289C23—42no—
290C23—42no—
291C23—44no—
292C23—84no—
293C23—84no—
294C23—82no—
295C23—82no—
296C23—82no—
297C23—82no—
298C23C2×C22⋊C4×C4111yescharacteristic
299C23#120×C4111yescharacteristic
300C23#123×C4111yescharacteristic
301C23#135×C4112yes—
302C23AGL(1,ℤ/8)×C4112yes—
303D4—28no—
304D4—48no—
305D4—44no—
306C2×C4—24no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—44no—
322C2×C4—44no—
323C2×C4—44no—
324C2×C4—81no—
325C2×C4—84no—
326C2×C4C4×D4×C4112yes—
327C2×C4#121×C4112yes—
328C8—82no—
329C22—24no—
330C22—24no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—44no—
336C22—44no—
337C22—44no—
338C22—82no—
339C22—82no—
340C22—88no—
341C22—88no—
342C22—82no—
343C22—82no—
344C22C41×#38611yescharacteristic
345C22C41×#41611yescharacteristic
346C22C41×#41811yescharacteristic
347C22C41×#44912yes—
348C22C41×#45412yes—
349C22C41×B(4,𝔽2)12yes—
350C22C41×#48212yes—
351C4—22no—
352C4—22no—
353C4—42no—
354C4—42no—
355C4—82no—
356C4—84no—
357C2—21no—
358C2—21no—
359C2—22no—
360C2—84no—
361C2C41×#159714yes—
362C2C41×#187511yescharacteristic
363C2C41×#188811yescharacteristic
364C2C41×#188911yescharacteristic
subgroupG/H
center, socleC23×C41#120
commutatorC22×C4C22×C4×C41
Frattini, cosocleC23×C4C23×C41
prime radicalC23×D4×C41C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C41 ◁ C23×C4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C41×#2313C2semidirect
4. C2×C41×#324C2semidirect
5. C41×#1294C2semidirect
13. C41×#394C4semidirect
146. #9018C41direct (N × H)
176. #2313C2×C41semidirect
178. C2×#324C2×C41semidirect
179. #1294C2×C41semidirect
195. #394C4×C41semidirect
202. C41#9018direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C41×#3942
C41×#23132
C41×#17862
C2×C41×#3242
C41×#12942
#901841