Finite Group Databasebeta

← C41×#10192 #23786393

Subgroups — C41×#10192 #23786393

Order 10496.

678 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3245C211yesmaximal, characteristic, complemented
2C41×#3205C211yesmaximal, characteristic, complemented
3C41×#3151C211yesmaximal, characteristic, complemented
4C41×#1982C211yesmaximal, characteristic, complemented
5C41×#1980C211yesmaximal, characteristic, complemented
6C41×#1502C211yesmaximal, characteristic, complemented
7C41×#1283C211yesmaximal, characteristic, complemented
8C2×AGL(1,ℤ/8)×C41—22no—
9C41×#532C2211yescharacteristic
10C41×#532C2211yescharacteristic
11C2×#127×C41C2211yescharacteristic
12C41×#496—22no—
13C41×#493—21no—
14C41×#493—21no—
15C41×#492—21no—
16C41×#486—21no—
17C41×#474—21no—
18C41×#474—21no—
19C41×#466—22no—
20C41×#459—22no—
21C41×#459—21no—
22C41×#459—21no—
23C41×#447—22no—
24C41×#431C2211yescharacteristic
25C2×C4⋊C8×C41C2211yescharacteristic
26C2×#104×C41—22no—
27C2×#102×C41—22no—
28C4×M16×C41C2211yescharacteristic
29C4×C4⋊C4×C41C2211yescharacteristic
30C41×#327—22no—
31C2×#41×C41—21no—
32C2×#41×C41—21no—
33C22×D4×C41—21no—
34C22×D4×C41—21no—
35C22×D4×C41—21no—
36AGL(1,ℤ/8)×C41—44no—
37AGL(1,ℤ/8)×C41—44no—
38C2×SD16×C41—24no—
39C2×D8×C41—24no—
40C2×D8×C41—24no—
41C2×D8×C41—22no—
42C2×M16×C41D412yes—
43C22×C8×C41D412yes—
44C4⋊Q8×C41D411yescharacteristic
45C4⋊Q8×C41D411yescharacteristic
46#127×C41—21no—
47#127×C41—21no—
48#127×C41—21no—
49#127×C41D412yes—
50#127×C41D411yescharacteristic
51#127×C41D411yescharacteristic
52#124×C41—21no—
53#124×C41—21no—
54#121×C41—21no—
55#121×C41—21no—
56#121×C41—21no—
57#121×C41—21no—
58C4×D4×C41—21no—
59C4×D4×C41—21no—
60C4×D4×C41—21no—
61C4×D4×C41—21no—
62C2×C4⋊C4×C41—21no—
63C2×C42×C41—21no—
64C2×C42×C41C2311yescharacteristic
65#107×C41—22no—
66C4⋊C8×C41—21no—
67C4⋊C8×C41—21no—
68C4⋊C8×C41—21no—
69#104×C41—44no—
70#102×C41—24no—
71#102×C41—22no—
72#102×C41—22no—
73#102×C41—44no—
74C22⋊C8×C41D412yes—
75#97×C41—21no—
76C4×C8×C41—21no—
77C4×C8×C41—21no—
78#95×C41—21no—
79C24×C41—41no—
80#41×C41—42no—
81#41×C41—42no—
82#41×C41—42no—
83#41×C41—42no—
84C2×Q8×C41—21no—
85C2×Q8×C41—21no—
86C2×D4×C41—21no—
87C2×D4×C41—21no—
88C2×D4×C41—22no—
89C2×D4×C41—21no—
90C2×D4×C41—21no—
91C2×D4×C41—22no—
92C2×D4×C41—21no—
93C2×D4×C41—22no—
94C2×D4×C41—21no—
95C2×D4×C41—42no—
96C2×D4×C41—42no—
97C2×D4×C41—41no—
98C2×D4×C41—41no—
99C2×D4×C41—41no—
100C2×D4×C41—41no—
101C2×D4×C41—41no—
102C2×D4×C41—42no—
103C2×D4×C41—42no—
104C2×D4×C41—82no—
105C22×C4×C41—41no—
106C22×C4×C41—41no—
107C22×C4×C41—41no—
108C22×C4×C41C2×D411yescharacteristic
109C22×C4×C41C2×D411yescharacteristic
110C22×C4×C41C2×D411yescharacteristic
111SD16×C41—48no—
112D8×C41—48no—
113D8×C41—84no—
114D8×C41—82no—
115M16×C41—22no—
116M16×C41D814yescomplemented
117C2×C8×C41—22no—
118C2×C8×C41—22no—
119C2×C8×C41—22no—
120C2×C8×C41—42no—
121C4⋊C4×C41—22no—
122C4⋊C4×C41—21no—
123C4⋊C4×C41—21no—
124C4⋊C4×C41—21no—
125C4⋊C4×C41—21no—
126C4⋊C4×C41—41no—
127C22⋊C4×C41—41no—
128C22⋊C4×C41—41no—
129C22⋊C4×C41—41no—
130C22⋊C4×C41—41no—
131C42×C41—42no—
132C42×C41C2×D411yescharacteristic
133C42×C41C2×D411yescharacteristic
134C42×C41C2×D411yescharacteristic
135C42×C41#4111yescharacteristic
136C23×C41—41no—
137C23×C41—41no—
138C23×C41—42no—
139C23×C41—82no—
140C23×C41—82no—
141C23×C41—81no—
142C23×C41—81no—
143C23×C41#12711yescharacteristic
144Q8×C41—42no—
145Q8×C41—42no—
146D4×C41—42no—
147D4×C41—44no—
148D4×C41—44no—
149D4×C41—42no—
150D4×C41—44no—
151D4×C41—41no—
152D4×C41—41no—
153D4×C41—41no—
154D4×C41—41no—
155D4×C41—42no—
156D4×C41—81no—
157D4×C41—82no—
158D4×C41—81no—
159D4×C41—81no—
160D4×C41—81no—
161D4×C41—81no—
162D4×C41—81no—
163D4×C41—81no—
164D4×C41—82no—
165C2×C4×C41—21no—
166C2×C4×C41—21no—
167C2×C4×C41—41no—
168C2×C4×C41—42no—
169C2×C4×C41—41no—
170C2×C4×C41—41no—
171C2×C4×C41—81no—
172C2×C4×C41—81no—
173C2×C4×C41—82no—
174C2×C4×C41—82no—
175C2×C4×C41#12011yescharacteristic
176C2×C4×C41#12011yescharacteristic
177C2×C4×C41#12011yescharacteristic
178C2×C4×C41#12111yescharacteristic
179C2×C4×C41#12111yescharacteristic
180C2×C4×C41#12111yescharacteristic
181C2×C4×C41C2×D812yes—
182C2×C4×C41AGL(1,ℤ/8)12yes—
183C8×C41—24no—
184C8×C41—42no—
185C8×C41—42no—
186#10192C4111yesmaximal, characteristic, direct product factor, Sylow
187C22×C41—21no—
188C22×C41—21no—
189C22×C41—82no—
190C22×C41—81no—
191C22×C41—81no—
192C22×C41—82no—
193C22×C41—81no—
194C22×C41—81no—
195C22×C41—81no—
196C22×C41—81no—
197C22×C41—82no—
198C22×C41—162no—
199C22×C41—162no—
200C22×C41#39211yescharacteristic
201C22×C41#49311yescharacteristic
202C22×C41#49611yescharacteristic
203C4×C41—21no—
204C4×C41—21no—
205C4×C41—21no—
206C4×C41—82no—
207C4×C41—81no—
208C4×C41—81no—
209C4×C41#44712yes—
210C4×C41#45311yescharacteristic
211C4×C41#45411yescharacteristic
212C4×C41#45912yes—
213#3245C2×C4111yescharacteristic, complemented
214#3205C2×C4111yescharacteristic, complemented
215#3151C2×C4111yescharacteristic, complemented
216#1982C2×C4111yescharacteristic, complemented
217#1980C2×C4111yescharacteristic, complemented
218#1502C2×C4111yescharacteristic, complemented
219#1283C2×C4111yescharacteristic, complemented
220C2×C41—21no—
221C2×C41—21no—
222C2×C41—161no—
223C2×C41—161no—
224C2×C41—162no—
225C2×C41#200611yescharacteristic
226C2×C41#200811yescharacteristic
227C2×C41#201111yescharacteristic
228C2×AGL(1,ℤ/8)—22no—
229#532C22×C4111yescharacteristic
230#532C22×C4111yescharacteristic
231C2×#127C22×C4111yescharacteristic
232#496—22no—
233#493—21no—
234#493—21no—
235#492—21no—
236#486—21no—
237#474—21no—
238#474—21no—
239#466—22no—
240#459—22no—
241#459—21no—
242#459—21no—
243#447—22no—
244#431C22×C4111yescharacteristic
245C2×C4⋊C8C22×C4111yescharacteristic
246C2×#104—22no—
247C2×#102—22no—
248C4×M16C22×C4111yescharacteristic
249C4×C4⋊C4C22×C4111yescharacteristic
250#327—22no—
251C41#1019211yescharacteristic, direct product factor, Sylow
252C2×#41—21no—
253C2×#41—21no—
254C22×D4—21no—
255C22×D4—21no—
256C22×D4—21no—
257AGL(1,ℤ/8)—44no—
258AGL(1,ℤ/8)—44no—
259C2×SD16—24no—
260C2×D8—24no—
261C2×D8—24no—
262C2×D8—22no—
263C2×M16D4×C4112yes—
264C22×C8D4×C4112yes—
265C4⋊Q8D4×C4111yescharacteristic
266C4⋊Q8D4×C4111yescharacteristic
267#127—21no—
268#127—21no—
269#127—21no—
270#127D4×C4112yes—
271#127D4×C4111yescharacteristic
272#127D4×C4111yescharacteristic
273#124—21no—
274#124—21no—
275#121—21no—
276#121—21no—
277#121—21no—
278#121—21no—
279C4×D4—21no—
280C4×D4—21no—
281C4×D4—21no—
282C4×D4—21no—
283C2×C4⋊C4—21no—
284C2×C42—21no—
285C2×C42C23×C4111yescharacteristic
286#107—22no—
287C4⋊C8—21no—
288C4⋊C8—21no—
289C4⋊C8—21no—
290#104—44no—
291#102—24no—
292#102—22no—
293#102—22no—
294#102—44no—
295C22⋊C8D4×C4112yes—
296#97—21no—
297C4×C8—21no—
298C4×C8—21no—
299#95—21no—
300C24—41no—
301#41—42no—
302#41—42no—
303#41—42no—
304#41—42no—
305C2×Q8—21no—
306C2×Q8—21no—
307C2×D4—21no—
308C2×D4—21no—
309C2×D4—22no—
310C2×D4—21no—
311C2×D4—21no—
312C2×D4—22no—
313C2×D4—21no—
314C2×D4—22no—
315C2×D4—21no—
316C2×D4—42no—
317C2×D4—42no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—41no—
322C2×D4—41no—
323C2×D4—42no—
324C2×D4—42no—
325C2×D4—82no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4C2×D4×C4111yescharacteristic
330C22×C4C2×D4×C4111yescharacteristic
331C22×C4C2×D4×C4111yescharacteristic
332SD16—48no—
333D8—48no—
334D8—84no—
335D8—82no—
336M16—22no—
337M16D8×C4114yescomplemented
338C2×C8—22no—
339C2×C8—22no—
340C2×C8—22no—
341C2×C8—42no—
342C4⋊C4—22no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4—41no—
348C22⋊C4—41no—
349C22⋊C4—41no—
350C22⋊C4—41no—
351C22⋊C4—41no—
352C42—42no—
353C42C2×D4×C4111yescharacteristic
354C42C2×D4×C4111yescharacteristic
355C42C2×D4×C4111yescharacteristic
356C42#41×C4111yescharacteristic
357C23—41no—
358C23—41no—
359C23—42no—
360C23—82no—
361C23—82no—
362C23—81no—
363C23—81no—
364C23#127×C4111yescharacteristic
365Q8—42no—
366Q8—42no—
367D4—42no—
368D4—44no—
369D4—44no—
370D4—42no—
371D4—44no—
372D4—41no—
373D4—41no—
374D4—41no—
375D4—41no—
376D4—42no—
377D4—81no—
378D4—82no—
379D4—81no—
380D4—81no—
381D4—81no—
382D4—81no—
383D4—81no—
384D4—81no—
385D4—82no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—41no—
389C2×C4—42no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—81no—
393C2×C4—81no—
394C2×C4—82no—
395C2×C4—82no—
396C2×C4#120×C4111yescharacteristic
397C2×C4#120×C4111yescharacteristic
398C2×C4#120×C4111yescharacteristic
399C2×C4#121×C4111yescharacteristic
400C2×C4#121×C4111yescharacteristic
401C2×C4#121×C4111yescharacteristic
402C2×C4C2×D8×C4112yes—
403C2×C4AGL(1,ℤ/8)×C4112yes—
404C8—24no—
405C8—42no—
406C8—42no—
407C22—21no—
408C22—21no—
409C22—82no—
410C22—81no—
411C22—81no—
412C22—82no—
413C22—81no—
414C22—81no—
415C22—81no—
416C22—81no—
417C22—82no—
418C22—162no—
419C22—162no—
420C22C41×#39211yescharacteristic
421C22C41×#49311yescharacteristic
422C22C41×#49611yescharacteristic
423C4—21no—
424C4—21no—
425C4—21no—
426C4—82no—
427C4—81no—
428C4—81no—
429C4C41×#44712yes—
430C4C41×#45311yescharacteristic
431C4C41×#45411yescharacteristic
432C4C41×#45912yes—
433C2—21no—
434C2—21no—
435C2—162no—
436C2—161no—
437C2—161no—
438C2C41×#200611yescharacteristic
439C2C41×#200811yescharacteristic
440C2C41×#201111yescharacteristic
subgroupG/H
center, socleC22×C41#392
commutator, Frattini, cosocleC2×C42C23×C41
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C41 ◁ C2×C42×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C41×#3245C2semidirect
2. C41×#3205C2semidirect
3. C41×#3151C2semidirect
4. C41×#1982C2semidirect
5. C41×#1980C2semidirect
6. C41×#1502C2semidirect
7. C41×#1283C2semidirect
116. M16×C41D8semidirect
186. #10192C41direct (N × H)
213. #3245C2×C41semidirect
214. #3205C2×C41semidirect
215. #3151C2×C41semidirect
216. #1982C2×C41semidirect
217. #1980C2×C41semidirect
218. #1502C2×C41semidirect
219. #1283C2×C41semidirect
251. C41#10192direct (N × H)
337. M16D8×C41semidirect

Maximal subgroups

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

subgroupindex
C41×#32452
C41×#32052
C41×#31512
C41×#19822
C41×#19802
C41×#15022
C41×#12832
#1019241