Finite Group Databasebeta

← C41×#9171 #23785372

Subgroups — C41×#9171 #23785372

Order 10496.

510 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3039C211yesmaximal, characteristic
2C41×#2906C211yesmaximal, characteristic
3C41×#1546C211yesmaximal, characteristic, complemented
4C2×C41×#332C211yesmaximal, characteristic, complemented
5C41×#1477C211yesmaximal, characteristic
6C41×#1301C211yesmaximal, characteristic, complemented
7C41×#1292C211yesmaximal, characteristic, complemented
8C2×#137×C41—21no—
9C2×#131×C41—21no—
10C2×C4⋊Q8×C41C2211yescharacteristic
11C4×#41×C41C2211yescharacteristic
12C41×#462—21no—
13C41×#462C412yes—
14C41×#461—21no—
15C41×#461C412yes—
16C41×#431C2211yescharacteristic
17C41×#424—21no—
18C41×#424—22no—
19C41×#423—21no—
20C41×#423C2211yescharacteristic
21C41×#423C2211yescharacteristic
22C2×C4⋊C8×C41—21no—
23C2×C4⋊C8×C41C2211yescharacteristic
24C2×C4⋊C8×C41C2211yescharacteristic
25C41×#419—21no—
26C41×#332—21no—
27C41×#332—21no—
28C41×#332—22no—
29C41×Q8⋊C8—21no—
30C41×D4⋊C8—21no—
31C2×#41×C41D411yescharacteristic
32C22×Q8×C41—21no—
33#137×C41—42no—
34#137×C41—42no—
35C2×Q16×C41—22no—
36C2×SD16×C41—22no—
37#131×C41—42no—
38#131×C41—42no—
39C2×M16×C41—22no—
40C2×M16×C41—21no—
41C2×M16×C41—21no—
42C22×C8×C41—22no—
43C22×C8×C41—21no—
44C22×C8×C41—21no—
45C4⋊Q8×C41—21no—
46C4⋊Q8×C41—21no—
47C4⋊Q8×C41—21no—
48C4⋊Q8×C41C2×C412yes—
49C4×Q8×C41C2×C411yescharacteristic
50C4×Q8×C41D411yescharacteristic
51C4×D4×C41—21no—
52C4×D4×C41—21no—
53C4×D4×C41C2×C411yescharacteristic
54C4×D4×C41D411yescharacteristic
55#117×C41—21no—
56#117×C41D411yescharacteristic
57C2×C4⋊C4×C41—21no—
58C2×C4⋊C4×C41—21no—
59C2×C42×C41—21no—
60C2×C42×C41C2311yescharacteristic
61C4⋊C8×C41—22no—
62C4⋊C8×C41—22no—
63C4⋊C8×C41—21no—
64C4⋊C8×C41—21no—
65C4⋊C8×C41—21no—
66C4⋊C8×C41—21no—
67C4⋊C8×C41—21no—
68C4⋊C8×C41—21no—
69C4⋊C8×C41C2×C412yes—
70C4⋊C8×C41D411yescharacteristic
71C4⋊C8×C41D411yescharacteristic
72C4⋊C8×C41D412yes—
73#103×C41—22no—
74#103×C41—22no—
75C22⋊C8×C41—21no—
76C4×C8×C41—21no—
77#41×C41—21no—
78#41×C41—21no—
79#41×C41D812yes—
80#41×C41SD1612yes—
81C2×Q8×C41—22no—
82C2×Q8×C41—41no—
83C2×Q8×C41—41no—
84C2×Q8×C41—41no—
85C2×Q8×C41—41no—
86C2×Q8×C41—41no—
87C2×Q8×C41C22⋊C411yescharacteristic
88C2×D4×C41—21no—
89C2×D4×C41C22⋊C411yescharacteristic
90C22×C4×C41—21no—
91C22×C4×C41—21no—
92C22×C4×C41—21no—
93C22×C4×C41—41no—
94C22×C4×C41C2×D411yescharacteristic
95C22×C4×C41#4111yescharacteristic
96C22×C4×C41#4111yescharacteristic
97Q16×C41—44no—
98SD16×C41—44no—
99M16×C41—44no—
100M16×C41—41no—
101M16×C41—41no—
102M16×C41—41no—
103M16×C41—41no—
104C2×C8×C41—22no—
105C2×C8×C41—21no—
106C2×C8×C41—22no—
107C2×C8×C41—21no—
108C2×C8×C41—44no—
109C2×C8×C41—41no—
110C2×C8×C41—41no—
111C2×C8×C41—41no—
112C2×C8×C41—41no—
113C2×C8×C41—81no—
114C4⋊C4×C41—21no—
115C4⋊C4×C41—21no—
116C4⋊C4×C41—22no—
117C4⋊C4×C41—22no—
118C4⋊C4×C41—41no—
119C4⋊C4×C41—41no—
120C4⋊C4×C41C22⋊C411yescharacteristic
121C4⋊C4×C41C22⋊C411yescharacteristic
122C22⋊C4×C41—21no—
123C22⋊C4×C41—21no—
124C22⋊C4×C41—21no—
125C42×C41—21no—
126C42×C41—21no—
127C42×C41—21no—
128C42×C41C22×C411yescharacteristic
129C42×C41C2×D411yescharacteristic
130C42×C41C2×D411yescharacteristic
131C42×C41C2×D411yescharacteristic
132C23×C41—21no—
133C23×C41#12311yescharacteristic
134Q8×C41—21no—
135Q8×C41—42no—
136Q8×C41—42no—
137Q8×C41—81no—
138Q8×C41—81no—
139Q8×C41#10212yes—
140D4×C41—22no—
141D4×C41—22no—
142D4×C41—21no—
143D4×C41#10212yes—
144C2×C4×C41—21no—
145C2×C4×C41—22no—
146C2×C4×C41—22no—
147C2×C4×C41—21no—
148C2×C4×C41—21no—
149C2×C4×C41—21no—
150C2×C4×C41—21no—
151C2×C4×C41—41no—
152C2×C4×C41—41no—
153C2×C4×C41—41no—
154C2×C4×C41—42no—
155C2×C4×C41—81no—
156C2×C4×C41—81no—
157C2×C4×C41—81no—
158C2×C4×C41C2×C22⋊C411yescharacteristic
159C2×C4×C41C4×D411yescharacteristic
160C2×C4×C41C4×D411yescharacteristic
161C2×C4×C41#12011yescharacteristic
162C2×C4×C41#12111yescharacteristic
163C2×C4×C41#12111yescharacteristic
164C2×C4×C41C2×D811yescharacteristic
165C2×C4×C41C2×SD1611yescharacteristic
166C2×C4×C41AGL(1,ℤ/8)11yescharacteristic
167C2×C4×C41#13711yescharacteristic
168C8×C41—42no—
169C8×C41—41no—
170C8×C41—42no—
171C8×C41—41no—
172C8×C41—81no—
173C8×C41—81no—
174#9171C4111yesmaximal, characteristic, direct product factor, Sylow
175C22×C41—21no—
176C22×C41—21no—
177C22×C41—22no—
178C22×C41—41no—
179C22×C41—41no—
180C22×C41#38611yescharacteristic
181C22×C41#48011yescharacteristic
182C22×C41#48111yescharacteristic
183C4×C41—22no—
184C4×C41—21no—
185C4×C41—21no—
186C4×C41—21no—
187C4×C41—41no—
188C4×C41—41no—
189C4×C41—82no—
190C4×C41C2×#10211yescharacteristic
191C4×C41#41711yescharacteristic
192C4×C41#44711yescharacteristic
193C4×C41#44811yescharacteristic
194C4×C41#47111yescharacteristic
195C4×C41#47311yescharacteristic
196#3039C2×C4111yescharacteristic
197#2906C2×C4111yescharacteristic
198#1546C2×C4111yescharacteristic, complemented
199C2×#332C2×C4111yescharacteristic, complemented
200#1477C2×C4111yescharacteristic
201#1301C2×C4111yescharacteristic, complemented
202#1292C2×C4111yescharacteristic, complemented
203C2×C41—21no—
204C2×C41—21no—
205C2×C41—42no—
206C2×C41#187411yescharacteristic
207C2×C41#190211yescharacteristic
208C2×C41#190811yescharacteristic
209C2×#137—21no—
210C2×#131—21no—
211C2×C4⋊Q8C22×C4111yescharacteristic
212C4×#41C22×C4111yescharacteristic
213#462—21no—
214#462C4×C4112yes—
215#461—21no—
216#461C4×C4112yes—
217#431C22×C4111yescharacteristic
218#424—21no—
219#424—22no—
220#423—21no—
221#423C22×C4111yescharacteristic
222#423C22×C4111yescharacteristic
223C2×C4⋊C8—21no—
224C2×C4⋊C8C22×C4111yescharacteristic
225C2×C4⋊C8C22×C4111yescharacteristic
226#419—21no—
227#332—21no—
228#332—21no—
229#332—22no—
230Q8⋊C8—21no—
231D4⋊C8—21no—
232C41#917111yescharacteristic, direct product factor, Sylow
233C2×#41D4×C4111yescharacteristic
234C22×Q8—21no—
235#137—42no—
236#137—42no—
237C2×Q16—22no—
238C2×SD16—22no—
239#131—42no—
240#131—42no—
241C2×M16—22no—
242C2×M16—21no—
243C2×M16—21no—
244C22×C8—22no—
245C22×C8—21no—
246C22×C8—21no—
247C4⋊Q8—21no—
248C4⋊Q8—21no—
249C4⋊Q8—21no—
250C4⋊Q8C2×C4×C4112yes—
251C4×Q8C2×C4×C4111yescharacteristic
252C4×Q8D4×C4111yescharacteristic
253C4×D4—21no—
254C4×D4—21no—
255C4×D4C2×C4×C4111yescharacteristic
256C4×D4D4×C4111yescharacteristic
257#117—21no—
258#117D4×C4111yescharacteristic
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C42—21no—
262C2×C42C23×C4111yescharacteristic
263C4⋊C8—22no—
264C4⋊C8—22no—
265C4⋊C8—21no—
266C4⋊C8—21no—
267C4⋊C8—21no—
268C4⋊C8—21no—
269C4⋊C8—21no—
270C4⋊C8—21no—
271C4⋊C8C2×C4×C4112yes—
272C4⋊C8D4×C4111yescharacteristic
273C4⋊C8D4×C4111yescharacteristic
274C4⋊C8D4×C4112yes—
275#103—22no—
276#103—22no—
277C22⋊C8—21no—
278C4×C8—21no—
279#41—21no—
280#41—21no—
281#41D8×C4112yes—
282#41SD16×C4112yes—
283C2×Q8—22no—
284C2×Q8—41no—
285C2×Q8—41no—
286C2×Q8—41no—
287C2×Q8—41no—
288C2×Q8—41no—
289C2×Q8C22⋊C4×C4111yescharacteristic
290C2×D4—21no—
291C2×D4C22⋊C4×C4111yescharacteristic
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—41no—
296C22×C4C2×D4×C4111yescharacteristic
297C22×C4#41×C4111yescharacteristic
298C22×C4#41×C4111yescharacteristic
299Q16—44no—
300SD16—44no—
301M16—44no—
302M16—41no—
303M16—41no—
304M16—41no—
305M16—41no—
306C2×C8—22no—
307C2×C8—21no—
308C2×C8—22no—
309C2×C8—21no—
310C2×C8—44no—
311C2×C8—41no—
312C2×C8—41no—
313C2×C8—41no—
314C2×C8—41no—
315C2×C8—81no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—22no—
319C4⋊C4—22no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4C22⋊C4×C4111yescharacteristic
323C4⋊C4C22⋊C4×C4111yescharacteristic
324C22⋊C4—21no—
325C22⋊C4—21no—
326C22⋊C4—21no—
327C42—21no—
328C42—21no—
329C42—21no—
330C42C22×C4×C4111yescharacteristic
331C42C2×D4×C4111yescharacteristic
332C42C2×D4×C4111yescharacteristic
333C42C2×D4×C4111yescharacteristic
334C23—21no—
335C23#123×C4111yescharacteristic
336Q8—21no—
337Q8—42no—
338Q8—42no—
339Q8—81no—
340Q8—81no—
341Q8#102×C4112yes—
342D4—22no—
343D4—22no—
344D4—21no—
345D4#102×C4112yes—
346C2×C4—21no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—42no—
357C2×C4—81no—
358C2×C4—81no—
359C2×C4—81no—
360C2×C4C2×C22⋊C4×C4111yescharacteristic
361C2×C4C4×D4×C4111yescharacteristic
362C2×C4C4×D4×C4111yescharacteristic
363C2×C4#120×C4111yescharacteristic
364C2×C4#121×C4111yescharacteristic
365C2×C4#121×C4111yescharacteristic
366C2×C4C2×D8×C4111yescharacteristic
367C2×C4C2×SD16×C4111yescharacteristic
368C2×C4AGL(1,ℤ/8)×C4111yescharacteristic
369C2×C4#137×C4111yescharacteristic
370C8—42no—
371C8—41no—
372C8—42no—
373C8—41no—
374C8—81no—
375C8—81no—
376C22—21no—
377C22—21no—
378C22—22no—
379C22—41no—
380C22—41no—
381C22C41×#38611yescharacteristic
382C22C41×#48011yescharacteristic
383C22C41×#48111yescharacteristic
384C4—22no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—41no—
389C4—41no—
390C4—82no—
391C4C2×#102×C4111yescharacteristic
392C4C41×#41711yescharacteristic
393C4C41×#44711yescharacteristic
394C4C41×#44811yescharacteristic
395C4C41×#47111yescharacteristic
396C4C41×#47311yescharacteristic
397C2—21no—
398C2—21no—
399C2—42no—
400C2C41×#187411yescharacteristic
401C2C41×#190211yescharacteristic
402C2C41×#190811yescharacteristic
subgroupG/H
center, socleC22×C41#386
commutatorC42C22×C4×C41
Frattini, cosocleC2×C42C23×C41
prime radicalC2×#41×C41D4
LCSG ▷ C42 ▷ 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×#1546C2semidirect
4. C2×C41×#332C2semidirect
6. C41×#1301C2semidirect
7. C41×#1292C2semidirect
174. #9171C41direct (N × H)
198. #1546C2×C41semidirect
199. C2×#332C2×C41semidirect
201. #1301C2×C41semidirect
202. #1292C2×C41semidirect
232. C41#9171direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#30392
C41×#29062
C41×#15462
C2×C41×#3322
C41×#14772
C41×#13012
C41×#12922
#917141