Finite Group Databasebeta

← C41×#9052 #23785253

Subgroups — C41×#9052 #23785253

Order 10496.

488 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3105C211yesmaximal, characteristic
2C41×#2992C211yesmaximal, characteristic, complemented
3C41×#1955C211yesmaximal, characteristic, complemented
4C41×#1524C211yesmaximal, characteristic, complemented
5C41×#1490C211yesmaximal, characteristic, complemented
6C41×#1302C211yesmaximal, characteristic, complemented
7C41×#1283C211yesmaximal, characteristic, complemented
8C41×#529C2211yescharacteristic
9C2×C4×D4×C41C2211yescharacteristic
10C41×#484C411yescharacteristic
11C41×#481C411yescharacteristic
12C41×#478—21no—
13C41×#463—21no—
14C41×#450C411yescharacteristic
15C41×#447C411yescharacteristic
16C41×#446—21no—
17C4×SD16×C41—21no—
18C4×D8×C41—21no—
19C41×#435—21no—
20C41×#435—21no—
21C8×D4×C41—21no—
22C41×#433—21no—
23C41×#432C2211yescharacteristic
24C41×#431C2211yescharacteristic
25C41×#424—21no—
26C2×C4⋊C8×C41C2211yescharacteristic
27C2×C22⋊C8×C41—21no—
28C2×C22⋊C8×C41—21no—
29C4×M16×C41C2211yescharacteristic
30C2×#97×C41C2211yescharacteristic
31C41×#330—21no—
32C41×#329—21no—
33C41×D4⋊C8—21no—
34C41×D4⋊C8—21no—
35C22×D4×C41C2×C411yescharacteristic
36C23×C4×C41—21no—
37C2×SD16×C41—21no—
38C2×D8×C41—21no—
39C2×M16×C41—21no—
40C2×M16×C41—21no—
41C22×C8×C41—21no—
42C22×C8×C41—21no—
43C22×C8×C41D411yescharacteristic
44C22×C8×C41D411yescharacteristic
45#126×C41—21no—
46#125×C41D411yescharacteristic
47#124×C41D411yescharacteristic
48#123×C41—21no—
49C22⋊Q8×C41C2×C411yescharacteristic
50#121×C41C2×C411yescharacteristic
51C4×Q8×C41D411yescharacteristic
52C4×D4×C41—21no—
53C4×D4×C41—21no—
54C4×D4×C41—21no—
55C4×D4×C41—21no—
56C4×D4×C41—21no—
57C4×D4×C41D411yescharacteristic
58#117×C41—21no—
59C2×C4⋊C4×C41C2×C411yescharacteristic
60C2×C22⋊C4×C41—21no—
61C2×C42×C41C2311yescharacteristic
62#107×C41—21no—
63#106×C41—21no—
64C4⋊C8×C41—21no—
65C4⋊C8×C41—21no—
66C4⋊C8×C41—21no—
67C4⋊C8×C41—21no—
68C4⋊C8×C41—21no—
69C4⋊C8×C41D411yescharacteristic
70C4⋊C8×C41D411yescharacteristic
71#103×C41—21no—
72#102×C41—21no—
73#102×C41—21no—
74#102×C41—21no—
75C22⋊C8×C41—21no—
76C22⋊C8×C41—21no—
77C22⋊C8×C41—21no—
78C22⋊C8×C41—42no—
79C22⋊C8×C41—42no—
80C22⋊C8×C41C2×C411yescharacteristic
81C22⋊C8×C41C2×C411yescharacteristic
82#97×C41—21no—
83#97×C41—21no—
84#97×C41—21no—
85#97×C41—21no—
86#97×C41—21no—
87C4×C8×C41—21no—
88C4×C8×C41—21no—
89C4×C8×C41—21no—
90C24×C41—21no—
91C2×Q8×C41C22⋊C411yescharacteristic
92C2×D4×C41—21no—
93C2×D4×C41—21no—
94C2×D4×C41—21no—
95C2×D4×C41—42no—
96C2×D4×C41C22⋊C411yescharacteristic
97C22×C4×C41—21no—
98C22×C4×C41—21no—
99C22×C4×C41—41no—
100C22×C4×C41—41no—
101C22×C4×C41—41no—
102C22×C4×C41—41no—
103C22×C4×C41—41no—
104C22×C4×C41—41no—
105C22×C4×C41C22×C411yescharacteristic
106C22×C4×C41C2×D411yescharacteristic
107C22×C4×C41#4111yescharacteristic
108SD16×C41—42no—
109D8×C41—42no—
110M16×C41—22no—
111M16×C41—41no—
112M16×C41—81no—
113C2×C8×C41—22no—
114C2×C8×C41—21no—
115C2×C8×C41—21no—
116C2×C8×C41—21no—
117C2×C8×C41—21no—
118C2×C8×C41—21no—
119C2×C8×C41—21no—
120C2×C8×C41—41no—
121C2×C8×C41—41no—
122C2×C8×C41—41no—
123C2×C8×C41—41no—
124C2×C8×C41—41no—
125C2×C8×C41—81no—
126C4⋊C4×C41—21no—
127C4⋊C4×C41—21no—
128C4⋊C4×C41—21no—
129C4⋊C4×C41—21no—
130C4⋊C4×C41—21no—
131C4⋊C4×C41—21no—
132C4⋊C4×C41C22⋊C411yescharacteristic
133C4⋊C4×C41C22⋊C411yescharacteristic
134C22⋊C4×C41—21no—
135C22⋊C4×C41—21no—
136C22⋊C4×C41—21no—
137C22⋊C4×C41—21no—
138C22⋊C4×C41—21no—
139C22⋊C4×C41—41no—
140C22⋊C4×C41—41no—
141C42×C41—21no—
142C42×C41C2×D411yescharacteristic
143C42×C41C2×D411yescharacteristic
144C42×C41C2×D411yescharacteristic
145C42×C41#4111yescharacteristic
146C23×C41—22no—
147C23×C41—21no—
148C23×C41—41no—
149C23×C41—41no—
150C23×C41—41no—
151C23×C41—41no—
152C23×C41—41no—
153C23×C41—41no—
154C23×C41C4×D411yescharacteristic
155Q8×C41—41no—
156D4×C41—22no—
157D4×C41—22no—
158D4×C41—41no—
159D4×C41—41no—
160D4×C41—41no—
161D4×C41—41no—
162D4×C41—41no—
163C2×C4×C41—21no—
164C2×C4×C41—21no—
165C2×C4×C41—21no—
166C2×C4×C41—21no—
167C2×C4×C41—21no—
168C2×C4×C41—21no—
169C2×C4×C41—21no—
170C2×C4×C41—41no—
171C2×C4×C41—41no—
172C2×C4×C41—41no—
173C2×C4×C41—41no—
174C2×C4×C41—41no—
175C2×C4×C41—41no—
176C2×C4×C41—81no—
177C2×C4×C41—81no—
178C2×C4×C41—81no—
179C2×C4×C41—81no—
180C2×C4×C41C2×C22⋊C411yescharacteristic
181C2×C4×C41C4×D411yescharacteristic
182C2×C4×C41#12011yescharacteristic
183C2×C4×C41#12111yescharacteristic
184C2×C4×C41#12111yescharacteristic
185C2×C4×C41#12311yescharacteristic
186C8×C41—42no—
187C8×C41—41no—
188C8×C41—41no—
189C8×C41—42no—
190C8×C41—41no—
191C8×C41—41no—
192C8×C41—41no—
193C8×C41—41no—
194#9052C4111yesmaximal, characteristic, direct product factor, Sylow
195C22×C41—21no—
196C22×C41—21no—
197C22×C41—42no—
198C22×C41—42no—
199C22×C41—41no—
200C22×C41—41no—
201C22×C41—42no—
202C22×C41—41no—
203C22×C41—81no—
204C22×C41—81no—
205C22×C41—81no—
206C22×C41—81no—
207C22×C41#38611yescharacteristic
208C22×C41#44311yescharacteristic
209C22×C41#44411yescharacteristic
210C4×C41—21no—
211C4×C41—21no—
212C4×C41—21no—
213C4×C41—21no—
214C4×C41—21no—
215C4×C41—41no—
216C4×C41—41no—
217C4×C41—41no—
218C4×C41—81no—
219C4×C41#45311yescharacteristic
220C4×C41#45411yescharacteristic
221#3105C2×C4111yescharacteristic
222#2992C2×C4111yescharacteristic, complemented
223#1955C2×C4111yescharacteristic, complemented
224#1524C2×C4111yescharacteristic, complemented
225#1490C2×C4111yescharacteristic, complemented
226#1302C2×C4111yescharacteristic, complemented
227#1283C2×C4111yescharacteristic, complemented
228C2×C41—21no—
229C2×C41—21no—
230C2×C41—81no—
231C2×C41—82no—
232C2×C41#187611yescharacteristic
233C2×C41#188311yescharacteristic
234C2×C41#189111yescharacteristic
235#529C22×C4111yescharacteristic
236C2×C4×D4C22×C4111yescharacteristic
237#484C4×C4111yescharacteristic
238#481C4×C4111yescharacteristic
239#478—21no—
240#463—21no—
241#450C4×C4111yescharacteristic
242#447C4×C4111yescharacteristic
243#446—21no—
244C4×SD16—21no—
245C4×D8—21no—
246#435—21no—
247#435—21no—
248C8×D4—21no—
249#433—21no—
250#432C22×C4111yescharacteristic
251#431C22×C4111yescharacteristic
252#424—21no—
253C2×C4⋊C8C22×C4111yescharacteristic
254C2×C22⋊C8—21no—
255C2×C22⋊C8—21no—
256C4×M16C22×C4111yescharacteristic
257C2×#97C22×C4111yescharacteristic
258#330—21no—
259#329—21no—
260D4⋊C8—21no—
261D4⋊C8—21no—
262C41#905211yescharacteristic, direct product factor, Sylow
263C22×D4C2×C4×C4111yescharacteristic
264C23×C4—21no—
265C2×SD16—21no—
266C2×D8—21no—
267C2×M16—21no—
268C2×M16—21no—
269C22×C8—21no—
270C22×C8—21no—
271C22×C8D4×C4111yescharacteristic
272C22×C8D4×C4111yescharacteristic
273#126—21no—
274#125D4×C4111yescharacteristic
275#124D4×C4111yescharacteristic
276#123—21no—
277C22⋊Q8C2×C4×C4111yescharacteristic
278#121C2×C4×C4111yescharacteristic
279C4×Q8D4×C4111yescharacteristic
280C4×D4—21no—
281C4×D4—21no—
282C4×D4—21no—
283C4×D4—21no—
284C4×D4—21no—
285C4×D4D4×C4111yescharacteristic
286#117—21no—
287C2×C4⋊C4C2×C4×C4111yescharacteristic
288C2×C22⋊C4—21no—
289C2×C42C23×C4111yescharacteristic
290#107—21no—
291#106—21no—
292C4⋊C8—21no—
293C4⋊C8—21no—
294C4⋊C8—21no—
295C4⋊C8—21no—
296C4⋊C8—21no—
297C4⋊C8D4×C4111yescharacteristic
298C4⋊C8D4×C4111yescharacteristic
299#103—21no—
300#102—21no—
301#102—21no—
302#102—21no—
303C22⋊C8—21no—
304C22⋊C8—21no—
305C22⋊C8—21no—
306C22⋊C8—42no—
307C22⋊C8—42no—
308C22⋊C8C2×C4×C4111yescharacteristic
309C22⋊C8C2×C4×C4111yescharacteristic
310#97—21no—
311#97—21no—
312#97—21no—
313#97—21no—
314#97—21no—
315C4×C8—21no—
316C4×C8—21no—
317C4×C8—21no—
318C24—21no—
319C2×Q8C22⋊C4×C4111yescharacteristic
320C2×D4—21no—
321C2×D4—21no—
322C2×D4—21no—
323C2×D4—42no—
324C2×D4C22⋊C4×C4111yescharacteristic
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—41no—
333C22×C4C22×C4×C4111yescharacteristic
334C22×C4C2×D4×C4111yescharacteristic
335C22×C4#41×C4111yescharacteristic
336SD16—42no—
337D8—42no—
338M16—22no—
339M16—41no—
340M16—81no—
341C2×C8—22no—
342C2×C8—21no—
343C2×C8—21no—
344C2×C8—21no—
345C2×C8—21no—
346C2×C8—21no—
347C2×C8—21no—
348C2×C8—41no—
349C2×C8—41no—
350C2×C8—41no—
351C2×C8—41no—
352C2×C8—41no—
353C2×C8—81no—
354C4⋊C4—21no—
355C4⋊C4—21no—
356C4⋊C4—21no—
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—21no—
360C4⋊C4C22⋊C4×C4111yescharacteristic
361C4⋊C4C22⋊C4×C4111yescharacteristic
362C22⋊C4—21no—
363C22⋊C4—21no—
364C22⋊C4—21no—
365C22⋊C4—21no—
366C22⋊C4—21no—
367C22⋊C4—41no—
368C22⋊C4—41no—
369C42—21no—
370C42C2×D4×C4111yescharacteristic
371C42C2×D4×C4111yescharacteristic
372C42C2×D4×C4111yescharacteristic
373C42#41×C4111yescharacteristic
374C23—22no—
375C23—21no—
376C23—41no—
377C23—41no—
378C23—41no—
379C23—41no—
380C23—41no—
381C23—41no—
382C23C4×D4×C4111yescharacteristic
383Q8—41no—
384D4—22no—
385D4—22no—
386D4—41no—
387D4—41no—
388D4—41no—
389D4—41no—
390D4—41no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—81no—
405C2×C4—81no—
406C2×C4—81no—
407C2×C4—81no—
408C2×C4C2×C22⋊C4×C4111yescharacteristic
409C2×C4C4×D4×C4111yescharacteristic
410C2×C4#120×C4111yescharacteristic
411C2×C4#121×C4111yescharacteristic
412C2×C4#121×C4111yescharacteristic
413C2×C4#123×C4111yescharacteristic
414C8—42no—
415C8—41no—
416C8—41no—
417C8—42no—
418C8—41no—
419C8—41no—
420C8—41no—
421C8—41no—
422C22—21no—
423C22—21no—
424C22—42no—
425C22—42no—
426C22—41no—
427C22—41no—
428C22—42no—
429C22—41no—
430C22—81no—
431C22—81no—
432C22—81no—
433C22—81no—
434C22C41×#38611yescharacteristic
435C22C41×#44311yescharacteristic
436C22C41×#44411yescharacteristic
437C4—21no—
438C4—21no—
439C4—21no—
440C4—21no—
441C4—21no—
442C4—41no—
443C4—41no—
444C4—41no—
445C4—81no—
446C4C41×#45311yescharacteristic
447C4C41×#45411yescharacteristic
448C2—21no—
449C2—21no—
450C2—82no—
451C2—81no—
452C2C41×#187611yescharacteristic
453C2C41×#188311yescharacteristic
454C2C41×#189111yescharacteristic
subgroupG/H
centerC2×C4×C41#120
commutatorC22×C4C22×C4×C41
Frattini, cosocleC2×C42C23×C41
socleC22×C41#386
prime radicalC41×#447C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C41 ◁ C2×C42×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C41×#2992C2semidirect
3. C41×#1955C2semidirect
4. C41×#1524C2semidirect
5. C41×#1490C2semidirect
6. C41×#1302C2semidirect
7. C41×#1283C2semidirect
194. #9052C41direct (N × H)
222. #2992C2×C41semidirect
223. #1955C2×C41semidirect
224. #1524C2×C41semidirect
225. #1490C2×C41semidirect
226. #1302C2×C41semidirect
227. #1283C2×C41semidirect
262. C41#9052direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#31052
C41×#29922
C41×#19552
C41×#15242
C41×#14902
C41×#13022
C41×#12832
#905241