Finite Group Databasebeta

← C41×#33033 #23809234

Subgroups — C41×#33033 #23809234

Order 10496.

854 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#475C211yesmaximal, characteristic
2C2×C41×#462C211yesmaximal, characteristic
3C41×#2862C211yesmaximal, characteristic
4C42×Q8×C41C211yesmaximal, characteristic
5C41×#1988C211yesmaximal, characteristic
6C41×#1981C211yesmaximal, characteristic
7C41×#1927C214yesmaximal
8C41×#1878C214yesmaximal
9C41×#1831C211yesmaximal, characteristic
10C22×Q16×C41C2212yes—
11C2×C4⋊Q8×C41C2211yescharacteristic
12C2×C4⋊Q8×C41C2211yescharacteristic
13C2×C4×Q8×C41C2212yes—
14C2×C4×Q8×C41C2211yescharacteristic
15C41×#475—24no—
16C41×#462—24no—
17C2×#106×C41C2212yes—
18C2×C4⋊C8×C41C2211yescharacteristic
19C2×C4⋊C8×C41C2211yescharacteristic
20C2×#103×C41C2212yes—
21C2×#103×C41C2214yes—
22C2×#103×C41C2212yes—
23C41×#391—21no—
24C41×#391—21no—
25C41×#391C2214yes—
26C41×#382—22no—
27C4×C4⋊C4×C41—22no—
28C4×C4⋊C4×C41—21no—
29C4×C4⋊C4×C41C2212yes—
30C4×C4⋊C4×C41C2211yescharacteristic
31C43×C41—21no—
32C43×C41C2211yescharacteristic
33C41×#340C2214yes—
34C41×#336C2214yes—
35C22×Q8×C41—21no—
36C22×Q8×C41C2312yes—
37C22×Q8×C41C2311yescharacteristic
38C2×Q16×C41—24no—
39C2×Q16×C41—28no—
40C22×C8×C41C2312yes—
41C22×C8×C41C2312yes—
42C4⋊Q8×C41—22no—
43C4⋊Q8×C41—22no—
44C4⋊Q8×C41—22no—
45C4⋊Q8×C41—22no—
46C4×Q8×C41—24no—
47C4×Q8×C41—24no—
48C4×Q8×C41—22no—
49C4×Q8×C41D414yes—
50C2×C4⋊C4×C41—22no—
51C2×C4⋊C4×C41—21no—
52C2×C4⋊C4×C41—21no—
53C2×C4⋊C4×C41—21no—
54C2×C4⋊C4×C41—21no—
55C2×C4⋊C4×C41C2312yes—
56C2×C4⋊C4×C41C2311yescharacteristic
57C2×C4⋊C4×C41C2312yes—
58C2×C42×C41—22no—
59C2×C42×C41—21no—
60C2×C42×C41—21no—
61C2×C42×C41—22no—
62C2×C42×C41D411yescharacteristic
63C2×C42×C41D412yes—
64C2×C42×C41D411yescharacteristic
65C2×C42×C41C2312yes—
66C2×C42×C41C2311yescharacteristic
67#106×C41—24no—
68C4⋊C8×C41—22no—
69C4⋊C8×C41—22no—
70#103×C41—24no—
71#103×C41—24no—
72#103×C41—28no—
73#95×C41—22no—
74#95×C41—21no—
75#95×C41—24no—
76#95×C41—24no—
77C2×Q8×C41—21no—
78C2×Q8×C41—22no—
79C2×Q8×C41—22no—
80C2×Q8×C41—24no—
81C2×Q8×C41—22no—
82C2×Q8×C41—24no—
83C2×Q8×C41—42no—
84C2×Q8×C41—42no—
85C2×Q8×C41—42no—
86C2×Q8×C41C2×D412yes—
87C2×Q8×C41#4114yes—
88C22×C4×C41—21no—
89C22×C4×C41—21no—
90C22×C4×C41—22no—
91C22×C4×C41—22no—
92C22×C4×C41—22no—
93C22×C4×C41C2×D412yes—
94C22×C4×C41C2×D411yescharacteristic
95C22×C4×C41C2×D412yes—
96C22×C4×C41C2×D411yescharacteristic
97C22×C4×C41C2411yescharacteristic
98Q16×C41—48no—
99C2×C8×C41—22no—
100C2×C8×C41—22no—
101C2×C8×C41—24no—
102C2×C8×C41—24no—
103C4⋊C4×C41—28no—
104C4⋊C4×C41—24no—
105C4⋊C4×C41—21no—
106C4⋊C4×C41—22no—
107C4⋊C4×C41—22no—
108C4⋊C4×C41—22no—
109C4⋊C4×C41—42no—
110C4⋊C4×C41—42no—
111C4⋊C4×C41—42no—
112C4⋊C4×C41C2×D412yes—
113C4⋊C4×C41#4114yes—
114C42×C41—28no—
115C42×C41—24no—
116C42×C41—22no—
117C42×C41—22no—
118C42×C41—24no—
119C42×C41—22no—
120C42×C41—22no—
121C42×C41—42no—
122C42×C41—44no—
123C42×C41C2×D412yes—
124C42×C41#4112yes—
125C23×C41C22×D411yescharacteristic
126Q8×C41—24no—
127Q8×C41—22no—
128Q8×C41—42no—
129Q8×C41—44no—
130Q8×C41—42no—
131Q8×C41—84no—
132Q8×C41#12414yes—
133C2×C4×C41—22no—
134C2×C4×C41—22no—
135C2×C4×C41—24no—
136C2×C4×C41—22no—
137C2×C4×C41—22no—
138C2×C4×C41—22no—
139C2×C4×C41—22no—
140C2×C4×C41—24no—
141C2×C4×C41—22no—
142C2×C4×C41—22no—
143C2×C4×C41—42no—
144C2×C4×C41—42no—
145C2×C4×C41—42no—
146C2×C4×C41—42no—
147C2×C4×C41—42no—
148C2×C4×C41—44no—
149C2×C4×C41—42no—
150C2×C4×C41—42no—
151C2×C4×C41#12112yes—
152C2×C4×C41#12112yes—
153C2×C4×C41#13512yes—
154C2×C4×C41#13714yes—
155C2×C4×C41#13712yes—
156C2×C4×C41C22×D411yescharacteristic
157C2×C4×C41C2×#4112yes—
158C2×C4×C41C2×#4111yescharacteristic
159C2×C4×C41C2×#4112yes—
160C8×C41—42no—
161C8×C41—42no—
162#33033C4111yesmaximal, characteristic, direct product factor, Sylow
163C22×C41C2×#12111yescharacteristic
164C22×C41#52512yes—
165C22×C41C2×#13511yescharacteristic
166C22×C41C2×#13712yes—
167C22×C41C2×#13711yescharacteristic
168C4×C41—24no—
169C4×C41—24no—
170C4×C41—22no—
171C4×C41—42no—
172C4×C41—44no—
173C4×C41—42no—
174C4×C41—82no—
175C4×C41—82no—
176C4×C41#46414yes—
177C4×C41C2×#12411yescharacteristic
178C4×C41#52912yes—
179C4×C41#53211yescharacteristic
180C2×#475C2×C4111yescharacteristic
181C2×#462C2×C4111yescharacteristic
182#2862C2×C4111yescharacteristic
183C42×Q8C2×C4111yescharacteristic
184#1988C2×C4111yescharacteristic
185#1981C2×C4111yescharacteristic
186#1927C2×C4114yes—
187#1878C2×C4114yes—
188#1831C2×C4111yescharacteristic
189C2×C41#285011yescharacteristic
190C2×C41C2×#46411yescharacteristic
191C2×C41#303911yescharacteristic
192C2×C41#310712yes—
193C2×C41#311312yes—
194C22×Q16C22×C4112yes—
195C2×C4⋊Q8C22×C4111yescharacteristic
196C2×C4⋊Q8C22×C4111yescharacteristic
197C2×C4×Q8C22×C4112yes—
198C2×C4×Q8C22×C4111yescharacteristic
199#475—24no—
200#462—24no—
201C2×#106C22×C4112yes—
202C2×C4⋊C8C22×C4111yescharacteristic
203C2×C4⋊C8C22×C4111yescharacteristic
204C2×#103C22×C4112yes—
205C2×#103C22×C4114yes—
206C2×#103C22×C4112yes—
207#391—21no—
208#391—21no—
209#391C22×C4114yes—
210#382—22no—
211C4×C4⋊C4—22no—
212C4×C4⋊C4—21no—
213C4×C4⋊C4C22×C4112yes—
214C4×C4⋊C4C22×C4111yescharacteristic
215C43—21no—
216C43C22×C4111yescharacteristic
217#340C22×C4114yes—
218#336C22×C4114yes—
219C41#3303311yescharacteristic, direct product factor, Sylow
220C22×Q8—21no—
221C22×Q8C23×C4112yes—
222C22×Q8C23×C4111yescharacteristic
223C2×Q16—24no—
224C2×Q16—28no—
225C22×C8C23×C4112yes—
226C22×C8C23×C4112yes—
227C4⋊Q8—22no—
228C4⋊Q8—22no—
229C4⋊Q8—22no—
230C4⋊Q8—22no—
231C4×Q8—24no—
232C4×Q8—24no—
233C4×Q8—22no—
234C4×Q8D4×C4114yes—
235C2×C4⋊C4—22no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4C23×C4112yes—
241C2×C4⋊C4C23×C4111yescharacteristic
242C2×C4⋊C4C23×C4112yes—
243C2×C42—22no—
244C2×C42—21no—
245C2×C42—21no—
246C2×C42—22no—
247C2×C42D4×C4111yescharacteristic
248C2×C42D4×C4112yes—
249C2×C42D4×C4111yescharacteristic
250C2×C42C23×C4112yes—
251C2×C42C23×C4111yescharacteristic
252#106—24no—
253C4⋊C8—22no—
254C4⋊C8—22no—
255#103—24no—
256#103—24no—
257#103—28no—
258#95—22no—
259#95—21no—
260#95—24no—
261#95—24no—
262C2×Q8—21no—
263C2×Q8—22no—
264C2×Q8—22no—
265C2×Q8—24no—
266C2×Q8—22no—
267C2×Q8—24no—
268C2×Q8—42no—
269C2×Q8—42no—
270C2×Q8—42no—
271C2×Q8C2×D4×C4112yes—
272C2×Q8#41×C4114yes—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4C2×D4×C4112yes—
279C22×C4C2×D4×C4111yescharacteristic
280C22×C4C2×D4×C4112yes—
281C22×C4C2×D4×C4111yescharacteristic
282C22×C4C24×C4111yescharacteristic
283Q16—48no—
284C2×C8—22no—
285C2×C8—22no—
286C2×C8—24no—
287C2×C8—24no—
288C4⋊C4—28no—
289C4⋊C4—24no—
290C4⋊C4—21no—
291C4⋊C4—22no—
292C4⋊C4—22no—
293C4⋊C4—22no—
294C4⋊C4—42no—
295C4⋊C4—42no—
296C4⋊C4—42no—
297C4⋊C4C2×D4×C4112yes—
298C4⋊C4#41×C4114yes—
299C42—28no—
300C42—24no—
301C42—22no—
302C42—22no—
303C42—24no—
304C42—22no—
305C42—22no—
306C42—42no—
307C42—44no—
308C42C2×D4×C4112yes—
309C42#41×C4112yes—
310C23C22×D4×C4111yescharacteristic
311Q8—24no—
312Q8—22no—
313Q8—42no—
314Q8—44no—
315Q8—42no—
316Q8—84no—
317Q8#124×C4114yes—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—24no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—24no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—44no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4#121×C4112yes—
337C2×C4#121×C4112yes—
338C2×C4#135×C4112yes—
339C2×C4#137×C4114yes—
340C2×C4#137×C4112yes—
341C2×C4C22×D4×C4111yescharacteristic
342C2×C4C2×#41×C4112yes—
343C2×C4C2×#41×C4111yescharacteristic
344C2×C4C2×#41×C4112yes—
345C8—42no—
346C8—42no—
347C22C2×#121×C4111yescharacteristic
348C22C41×#52512yes—
349C22C2×#135×C4111yescharacteristic
350C22C2×#137×C4112yes—
351C22C2×#137×C4111yescharacteristic
352C4—22no—
353C4—24no—
354C4—24no—
355C4—42no—
356C4—42no—
357C4—44no—
358C4—82no—
359C4—82no—
360C4C41×#46414yes—
361C4C2×#124×C4111yescharacteristic
362C4C41×#52912yes—
363C4C41×#53211yescharacteristic
364C2C41×#285011yescharacteristic
365C2C2×C41×#46411yescharacteristic
366C2C41×#303911yescharacteristic
367C2C41×#310712yes—
368C2C41×#311312yes—
subgroupG/H
center, socle, prime radicalC23×C41C22×D4
commutator, Frattini, cosocleC22×C4C24×C41
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C41 ◁ C43×C41 ◁ G

Complements

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

NH ≅ G/Ntype
162. #33033C41direct (N × H)
219. C41#33033direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C41×#4752
C2×C41×#4622
C41×#28622
C42×Q8×C412
C41×#19882
C41×#19812
C41×#19272
C41×#18782
C41×#18312
#3303341