Finite Group Databasebeta

← C41×#10076 #23786277

Subgroups — C41×#10076 #23786277

Order 10496.

654 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#500C211yesmaximal, characteristic, complemented
2C2×C41×#474C211yesmaximal, characteristic
3C41×#2542C211yesmaximal, characteristic
4C41×#1981C211yesmaximal, characteristic, complemented
5C2×C41×#332C211yesmaximal, characteristic, complemented
6C2×C41×D4⋊C8C211yesmaximal, characteristic
7C41×#1279C211yesmaximal, characteristic, complemented
8C2×C4⋊Q8×C41C2211yescharacteristic
9C2×C4⋊Q8×C41C2211yescharacteristic
10C2×C22⋊Q8×C41—22no—
11C2×C4×D4×C41C2211yescharacteristic
12C41×#500—22no—
13C41×#500—22no—
14C41×#474—22no—
15C41×#474—22no—
16C2×#107×C41—21no—
17C2×#107×C41—22no—
18C2×C4⋊C8×C41C2211yescharacteristic
19C2×C4⋊C8×C41C2211yescharacteristic
20C2×#103×C41—22no—
21C2×#102×C41—21no—
22C2×C4×C8×C41C2211yescharacteristic
23C41×#399—22no—
24C41×#390—21no—
25C41×#384—21no—
26C4×C4⋊C4×C41C2211yescharacteristic
27C41×#332—22no—
28C41×D4⋊C8—22no—
29C22×Q8×C41—21no—
30C22×Q8×C41—21no—
31C22×D4×C41D411yescharacteristic
32C23×C4×C41—21no—
33C22×C8×C41—21no—
34C22×C8×C41—21no—
35C22×C8×C41—21no—
36C4⋊Q8×C41—21no—
37C4⋊Q8×C41—21no—
38C4⋊Q8×C41—21no—
39C4⋊Q8×C41—21no—
40C4⋊Q8×C41—21no—
41C4⋊Q8×C41—21no—
42C4⋊Q8×C41—21no—
43C4⋊Q8×C41D412yes—
44C22⋊Q8×C41—44no—
45C22⋊Q8×C41—44no—
46C4×D4×C41—21no—
47C4×D4×C41—21no—
48C4×D4×C41—21no—
49C4×D4×C41—21no—
50C2×C4⋊C4×C41—21no—
51C2×C4⋊C4×C41—21no—
52C2×C4⋊C4×C41—24no—
53C2×C4⋊C4×C41—21no—
54C2×C4⋊C4×C41D411yescharacteristic
55C2×C4⋊C4×C41D412yes—
56C2×C4⋊C4×C41D412yes—
57C2×C22⋊C4×C41—24no—
58C2×C22⋊C4×C41—21no—
59C2×C42×C41—21no—
60C2×C42×C41C2311yescharacteristic
61#107×C41—28no—
62#107×C41—24no—
63C4⋊C8×C41—21no—
64C4⋊C8×C41—21no—
65C4⋊C8×C41—21no—
66C4⋊C8×C41D412yes—
67#103×C41—44no—
68#102×C41—24no—
69C4×C8×C41—21no—
70C4×C8×C41D412yes—
71#95×C41—21no—
72C24×C41—21no—
73C2×Q8×C41—22no—
74C2×Q8×C41—41no—
75C2×Q8×C41—41no—
76C2×Q8×C41—41no—
77C2×Q8×C41—42no—
78C2×Q8×C41—42no—
79C2×Q8×C41—42no—
80C2×Q8×C41—42no—
81C2×D4×C41—21no—
82C2×D4×C41—21no—
83C2×D4×C41—21no—
84C2×D4×C41—21no—
85C2×D4×C41—21no—
86C2×D4×C41Q1612yes—
87C22×C4×C41—22no—
88C22×C4×C41—22no—
89C22×C4×C41—21no—
90C22×C4×C41—41no—
91C22×C4×C41—41no—
92C22×C4×C41—41no—
93C22×C4×C41—42no—
94C22×C4×C41—42no—
95C22×C4×C41C2×D411yescharacteristic
96C22×C4×C41C2×D411yescharacteristic
97C22×C4×C41C2×D411yescharacteristic
98C2×C8×C41—24no—
99C2×C8×C41—22no—
100C2×C8×C41—22no—
101C2×C8×C41—41no—
102C2×C8×C41—41no—
103C2×C8×C41—41no—
104C2×C8×C41—42no—
105C4⋊C4×C41—22no—
106C4⋊C4×C41—22no—
107C4⋊C4×C41—22no—
108C4⋊C4×C41—21no—
109C4⋊C4×C41—22no—
110C4⋊C4×C41—21no—
111C4⋊C4×C41—22no—
112C4⋊C4×C41—48no—
113C4⋊C4×C41—41no—
114C4⋊C4×C41—41no—
115C4⋊C4×C41—41no—
116C4⋊C4×C41—41no—
117C4⋊C4×C41D814yes—
118C22⋊C4×C41—48no—
119C22⋊C4×C41—41no—
120C22⋊C4×C41—41no—
121C42×C41—41no—
122C42×C41—41no—
123C42×C41C2×D411yescharacteristic
124C42×C41C2×D411yescharacteristic
125C42×C41C2×D411yescharacteristic
126C42×C41#4111yescharacteristic
127C23×C41—22no—
128C23×C41—41no—
129C23×C41—42no—
130C23×C41—41no—
131C23×C41—42no—
132C23×C41#12011yescharacteristic
133Q8×C41—44no—
134Q8×C41—82no—
135Q8×C41—81no—
136Q8×C41—81no—
137Q8×C41—81no—
138Q8×C41—81no—
139D4×C41—22no—
140D4×C41—22no—
141D4×C41—41no—
142D4×C41—41no—
143C2×C4×C41—22no—
144C2×C4×C41—24no—
145C2×C4×C41—42no—
146C2×C4×C41—42no—
147C2×C4×C41—41no—
148C2×C4×C41—42no—
149C2×C4×C41—42no—
150C2×C4×C41—44no—
151C2×C4×C41—42no—
152C2×C4×C41—82no—
153C2×C4×C41—82no—
154C2×C4×C41—81no—
155C2×C4×C41—81no—
156C2×C4×C41#12011yescharacteristic
157C2×C4×C41#12011yescharacteristic
158C2×C4×C41#12111yescharacteristic
159C2×C4×C41#12111yescharacteristic
160C2×C4×C41#12111yescharacteristic
161C2×C4×C41#12711yescharacteristic
162C2×C4×C41C2×D812yes—
163C2×C4×C41C2×Q1611yescharacteristic
164C2×C4×C41#13511yescharacteristic
165C2×C4×C41AGL(1,ℤ/8)12yes—
166C2×C4×C41#13711yescharacteristic
167C2×C4×C41#13711yescharacteristic
168C8×C41—24no—
169C8×C41—42no—
170C8×C41—81no—
171#10076C4111yesmaximal, characteristic, direct product factor, Sylow
172C22×C41—44no—
173C22×C41—42no—
174C22×C41—82no—
175C22×C41—81no—
176C22×C41—81no—
177C22×C41#39211yescharacteristic
178C22×C41#44712yes—
179C22×C41#45111yescharacteristic
180C22×C41#45211yescharacteristic
181C22×C41#45612yes—
182C4×C41—21no—
183C4×C41—21no—
184C4×C41—44no—
185C4×C41—81no—
186C4×C41—82no—
187C4×C41—82no—
188C4×C41#45111yescharacteristic
189C4×C41#45211yescharacteristic
190C4×C41#45912yes—
191C4×C41#46711yescharacteristic
192C4×C41#47011yescharacteristic
193C4×C41#49311yescharacteristic
194C4×C41#49611yescharacteristic
195C2×#500C2×C4111yescharacteristic, complemented
196C2×#474C2×C4111yescharacteristic
197#2542C2×C4111yescharacteristic
198#1981C2×C4111yescharacteristic, complemented
199C2×#332C2×C4111yescharacteristic, complemented
200C2×D4⋊C8C2×C4111yescharacteristic
201#1279C2×C4111yescharacteristic, complemented
202C2×C41—82no—
203C2×C41#164712yes—
204C2×C41#164912yes—
205C2×C41#200111yescharacteristic
206C2×C41#200511yescharacteristic
207C2×C41#201111yescharacteristic
208C2×C4⋊Q8C22×C4111yescharacteristic
209C2×C4⋊Q8C22×C4111yescharacteristic
210C2×C22⋊Q8—22no—
211C2×C4×D4C22×C4111yescharacteristic
212#500—22no—
213#500—22no—
214#474—22no—
215#474—22no—
216C2×#107—22no—
217C2×#107—21no—
218C2×C4⋊C8C22×C4111yescharacteristic
219C2×C4⋊C8C22×C4111yescharacteristic
220C2×#103—22no—
221C2×#102—21no—
222C2×C4×C8C22×C4111yescharacteristic
223#399—22no—
224#390—21no—
225#384—21no—
226C4×C4⋊C4C22×C4111yescharacteristic
227#332—22no—
228D4⋊C8—22no—
229C41#1007611yescharacteristic, direct product factor, Sylow
230C22×Q8—21no—
231C22×Q8—21no—
232C22×D4D4×C4111yescharacteristic
233C23×C4—21no—
234C22×C8—21no—
235C22×C8—21no—
236C22×C8—21no—
237C4⋊Q8—21no—
238C4⋊Q8—21no—
239C4⋊Q8—21no—
240C4⋊Q8—21no—
241C4⋊Q8—21no—
242C4⋊Q8—21no—
243C4⋊Q8—21no—
244C4⋊Q8D4×C4112yes—
245C22⋊Q8—44no—
246C22⋊Q8—44no—
247C4×D4—21no—
248C4×D4—21no—
249C4×D4—21no—
250C4×D4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—24no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4D4×C4111yescharacteristic
256C2×C4⋊C4D4×C4112yes—
257C2×C4⋊C4D4×C4112yes—
258C2×C22⋊C4—24no—
259C2×C22⋊C4—21no—
260C2×C42—21no—
261C2×C42C23×C4111yescharacteristic
262#107—24no—
263#107—28no—
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8—21no—
267C4⋊C8D4×C4112yes—
268#103—44no—
269#102—24no—
270C4×C8—21no—
271C4×C8D4×C4112yes—
272#95—21no—
273C24—21no—
274C2×Q8—22no—
275C2×Q8—41no—
276C2×Q8—41no—
277C2×Q8—41no—
278C2×Q8—42no—
279C2×Q8—42no—
280C2×Q8—42no—
281C2×Q8—42no—
282C2×D4—21no—
283C2×D4—21no—
284C2×D4—21no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4Q16×C4112yes—
288C22×C4—22no—
289C22×C4—22no—
290C22×C4—21no—
291C22×C4—41no—
292C22×C4—41no—
293C22×C4—41no—
294C22×C4—42no—
295C22×C4—42no—
296C22×C4C2×D4×C4111yescharacteristic
297C22×C4C2×D4×C4111yescharacteristic
298C22×C4C2×D4×C4111yescharacteristic
299C2×C8—24no—
300C2×C8—22no—
301C2×C8—22no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—42no—
306C4⋊C4—22no—
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—21no—
310C4⋊C4—22no—
311C4⋊C4—21no—
312C4⋊C4—22no—
313C4⋊C4—48no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4D8×C4114yes—
319C22⋊C4—48no—
320C22⋊C4—41no—
321C22⋊C4—41no—
322C42—41no—
323C42—41no—
324C42C2×D4×C4111yescharacteristic
325C42C2×D4×C4111yescharacteristic
326C42C2×D4×C4111yescharacteristic
327C42#41×C4111yescharacteristic
328C23—22no—
329C23—41no—
330C23—42no—
331C23—41no—
332C23—42no—
333C23#120×C4111yescharacteristic
334Q8—44no—
335Q8—82no—
336Q8—81no—
337Q8—81no—
338Q8—81no—
339Q8—81no—
340D4—22no—
341D4—22no—
342D4—41no—
343D4—41no—
344C2×C4—22no—
345C2×C4—24no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—41no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—44no—
352C2×C4—42no—
353C2×C4—82no—
354C2×C4—82no—
355C2×C4—81no—
356C2×C4—81no—
357C2×C4#120×C4111yescharacteristic
358C2×C4#120×C4111yescharacteristic
359C2×C4#121×C4111yescharacteristic
360C2×C4#121×C4111yescharacteristic
361C2×C4#121×C4111yescharacteristic
362C2×C4#127×C4111yescharacteristic
363C2×C4C2×D8×C4112yes—
364C2×C4C2×Q16×C4111yescharacteristic
365C2×C4#135×C4111yescharacteristic
366C2×C4AGL(1,ℤ/8)×C4112yes—
367C2×C4#137×C4111yescharacteristic
368C2×C4#137×C4111yescharacteristic
369C8—24no—
370C8—42no—
371C8—81no—
372C22—44no—
373C22—42no—
374C22—82no—
375C22—81no—
376C22—81no—
377C22C41×#39211yescharacteristic
378C22C41×#44712yes—
379C22C41×#45111yescharacteristic
380C22C41×#45211yescharacteristic
381C22C41×#45612yes—
382C4—21no—
383C4—21no—
384C4—44no—
385C4—81no—
386C4—82no—
387C4—82no—
388C4C41×#45111yescharacteristic
389C4C41×#45211yescharacteristic
390C4C41×#45912yes—
391C4C41×#46711yescharacteristic
392C4C41×#47011yescharacteristic
393C4C41×#49311yescharacteristic
394C4C41×#49611yescharacteristic
395C2—82no—
396C2C41×#164712yes—
397C2C41×#164912yes—
398C2C41×#200111yescharacteristic
399C2C41×#200511yescharacteristic
400C2C41×#201111yescharacteristic
subgroupG/H
center, socleC23×C41#120
commutator, Frattini, cosocleC2×C42C23×C41
prime radicalC22×D4×C41D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C41 ◁ C2×C42×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C41×#500C2semidirect
4. C41×#1981C2semidirect
5. C2×C41×#332C2semidirect
7. C41×#1279C2semidirect
171. #10076C41direct (N × H)
195. C2×#500C2×C41semidirect
198. #1981C2×C41semidirect
199. C2×#332C2×C41semidirect
201. #1279C2×C41semidirect
229. C41#10076direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C41×#5002
C2×C41×#4742
C41×#25422
C41×#19812
C2×C41×#3322
C2×C41×D4⋊C82
C41×#12792
#1007641