Finite Group Databasebeta

← C41×#19060 #23795261

Subgroups — C41×#19060 #23795261

Order 10496.

822 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×#3553C211yesmaximal, characteristic
2C41×#3238C212yesmaximal, complemented
3C2×C41×#491C211yesmaximal, characteristic, complemented
4C41×#1664C214yesmaximal, complemented
5C41×#1663C212yesmaximal, complemented
6C41×#1662C212yesmaximal, complemented
7C41×#1534C211yesmaximal, characteristic, complemented
8C41×#1532C212yesmaximal, complemented
9C41×#564C2211yescharacteristic
10C41×#563C2212yes—
11C41×#562C2211yescharacteristic
12C41×#554—22no—
13C41×#553—22no—
14C41×#552—22no—
15C41×#541—22no—
16C41×#539—22no—
17C41×#539—22no—
18C2×C4⋊Q8×C41C2211yescharacteristic
19C41×#529C2212yes—
20C2×#125×C41C2211yescharacteristic
21C41×#501C2214yes—
22C41×#491—22no—
23C41×#491C2212yes—
24C41×#491C2212yes—
25C41×#489C2214yes—
26C41×#483—22no—
27C41×#480—22no—
28C41×#477—22no—
29C41×#476—22no—
30C41×#432C2212yes—
31C2×#103×C41—22no—
32C2×#97×C41C2211yescharacteristic
33C41×#330C2214yes—
34C41×#330C2212yes—
35C41×#330C2212yes—
36C41×#329C2214yes—
37C22×Q8×C41—21no—
38C22×C8×C41—21no—
39C4⋊Q8×C41—22no—
40C4⋊Q8×C41—22no—
41C4⋊Q8×C41—21no—
42C4⋊Q8×C41C2312yes—
43#126×C41—22no—
44#126×C41—22no—
45#126×C41—22no—
46#126×C41—22no—
47#126×C41—22no—
48#125×C41—22no—
49#125×C41—22no—
50#125×C41—22no—
51#125×C41—22no—
52#125×C41—22no—
53#125×C41—22no—
54#125×C41D412yes—
55#125×C41C2312yes—
56#125×C41C2311yescharacteristic
57#125×C41C2311yescharacteristic
58#124×C41C2312yes—
59#123×C41—22no—
60#123×C41—22no—
61#123×C41—22no—
62#123×C41—22no—
63#123×C41—22no—
64C22⋊Q8×C41—22no—
65C22⋊Q8×C41—22no—
66C22⋊Q8×C41—22no—
67C22⋊Q8×C41—22no—
68C22⋊Q8×C41—22no—
69C22⋊Q8×C41—22no—
70C22⋊Q8×C41D412yes—
71#121×C41—22no—
72#121×C41—22no—
73#121×C41D412yes—
74C4×Q8×C41—22no—
75C4×Q8×C41D412yes—
76C4×D4×C41—22no—
77C4×D4×C41—22no—
78C4×D4×C41—22no—
79C4×D4×C41—22no—
80C4×D4×C41D412yes—
81#117×C41—22no—
82#117×C41—22no—
83C2×C4⋊C4×C41—22no—
84C2×C4⋊C4×C41—22no—
85C2×C4⋊C4×C41—22no—
86C2×C4⋊C4×C41D412yes—
87C2×C42×C41C2311yescharacteristic
88#107×C41—24no—
89#106×C41—24no—
90C4⋊C8×C41—22no—
91#103×C41—24no—
92#103×C41—24no—
93#103×C41—24no—
94#102×C41—24no—
95C22⋊C8×C41—22no—
96#97×C41—21no—
97#97×C41C2314yes—
98#97×C41C2312yes—
99C2×Q8×C41—22no—
100C2×Q8×C41—22no—
101C2×Q8×C41—44no—
102C2×Q8×C41—41no—
103C2×Q8×C41C2×D412yes—
104C2×D4×C41—22no—
105C2×D4×C41—22no—
106C2×D4×C41C2×D412yes—
107C22×C4×C41—22no—
108C22×C4×C41—22no—
109C22×C4×C41—22no—
110C22×C4×C41—22no—
111C22×C4×C41—41no—
112C22×C4×C41C2×D411yescharacteristic
113C22×C4×C41C2×D412yes—
114C2×C8×C41—22no—
115C2×C8×C41—24no—
116C2×C8×C41—42no—
117C4⋊C4×C41—22no—
118C4⋊C4×C41—22no—
119C4⋊C4×C41—22no—
120C4⋊C4×C41—22no—
121C4⋊C4×C41—22no—
122C4⋊C4×C41—22no—
123C4⋊C4×C41—22no—
124C4⋊C4×C41—22no—
125C4⋊C4×C41—22no—
126C4⋊C4×C41—22no—
127C4⋊C4×C41—22no—
128C4⋊C4×C41—22no—
129C4⋊C4×C41—22no—
130C4⋊C4×C41—22no—
131C4⋊C4×C41—22no—
132C4⋊C4×C41—24no—
133C4⋊C4×C41—42no—
134C4⋊C4×C41C2×D412yes—
135C4⋊C4×C41C2×D412yes—
136C4⋊C4×C41C2×D412yes—
137C4⋊C4×C41C2×D412yes—
138C22⋊C4×C41—22no—
139C22⋊C4×C41—22no—
140C22⋊C4×C41—22no—
141C22⋊C4×C41—22no—
142C22⋊C4×C41—22no—
143C22⋊C4×C41—22no—
144C22⋊C4×C41—22no—
145C22⋊C4×C41—22no—
146C22⋊C4×C41—22no—
147C42×C41—22no—
148C42×C41—22no—
149C42×C41—22no—
150C42×C41C2×D411yescharacteristic
151C42×C41C2×D412yes—
152C42×C41C2411yescharacteristic
153C23×C41—22no—
154C23×C41#12011yescharacteristic
155Q8×C41—42no—
156Q8×C41—44no—
157Q8×C41—82no—
158Q8×C41—82no—
159D4×C41—42no—
160D4×C41—44no—
161D4×C41—82no—
162C2×C4×C41—22no—
163C2×C4×C41—22no—
164C2×C4×C41—22no—
165C2×C4×C41—22no—
166C2×C4×C41—22no—
167C2×C4×C41—22no—
168C2×C4×C41—42no—
169C2×C4×C41—42no—
170C2×C4×C41—82no—
171C2×C4×C41—82no—
172C2×C4×C41—82no—
173C2×C4×C41—82no—
174C2×C4×C41—82no—
175C2×C4×C41#12012yes—
176C2×C4×C41#12011yescharacteristic
177C2×C4×C41C22×D411yescharacteristic
178C2×C4×C41C22×D412yes—
179C8×C41—44no—
180C8×C41—42no—
181#19060C4111yesmaximal, characteristic, direct product factor, Sylow
182C22×C41—22no—
183C22×C41—42no—
184C22×C41—42no—
185C22×C41—42no—
186C22×C41#45412yes—
187C22×C41C2×#12011yescharacteristic
188C4×C41—21no—
189C4×C41—21no—
190C4×C41—22no—
191C4×C41—22no—
192C4×C41—42no—
193C4×C41—42no—
194C4×C41—42no—
195C4×C41—42no—
196C4×C41—42no—
197C4×C41—82no—
198#3553C2×C4111yescharacteristic
199#3238C2×C4112yescomplemented
200C2×#491C2×C4111yescharacteristic, complemented
201#1664C2×C4114yescomplemented
202#1663C2×C4112yescomplemented
203#1662C2×C4112yescomplemented
204#1534C2×C4111yescharacteristic, complemented
205#1532C2×C4112yescomplemented
206C2×C41—22no—
207C2×C41—82no—
208C2×C41C2×#45411yescharacteristic
209C2×C41#302212yes—
210#564C22×C4111yescharacteristic
211#563C22×C4112yes—
212#562C22×C4111yescharacteristic
213#554—22no—
214#553—22no—
215#552—22no—
216#541—22no—
217#539—22no—
218#539—22no—
219C2×C4⋊Q8C22×C4111yescharacteristic
220#529C22×C4112yes—
221C2×#125C22×C4111yescharacteristic
222#501C22×C4114yes—
223#491—22no—
224#491C22×C4112yes—
225#491C22×C4112yes—
226#489C22×C4114yes—
227#483—22no—
228#480—22no—
229#477—22no—
230#476—22no—
231#432C22×C4112yes—
232C2×#103—22no—
233C2×#97C22×C4111yescharacteristic
234#330C22×C4112yes—
235#330C22×C4114yes—
236#330C22×C4112yes—
237#329C22×C4114yes—
238C41#1906011yescharacteristic, direct product factor, Sylow
239C22×Q8—21no—
240C22×C8—21no—
241C4⋊Q8—22no—
242C4⋊Q8—22no—
243C4⋊Q8—21no—
244C4⋊Q8C23×C4112yes—
245#126—22no—
246#126—22no—
247#126—22no—
248#126—22no—
249#126—22no—
250#125—22no—
251#125—22no—
252#125—22no—
253#125—22no—
254#125—22no—
255#125—22no—
256#125D4×C4112yes—
257#125C23×C4111yescharacteristic
258#125C23×C4111yescharacteristic
259#125C23×C4112yes—
260#124C23×C4112yes—
261#123—22no—
262#123—22no—
263#123—22no—
264#123—22no—
265#123—22no—
266C22⋊Q8—22no—
267C22⋊Q8—22no—
268C22⋊Q8—22no—
269C22⋊Q8—22no—
270C22⋊Q8—22no—
271C22⋊Q8—22no—
272C22⋊Q8D4×C4112yes—
273#121—22no—
274#121—22no—
275#121D4×C4112yes—
276C4×Q8—22no—
277C4×Q8D4×C4112yes—
278C4×D4—22no—
279C4×D4—22no—
280C4×D4—22no—
281C4×D4—22no—
282C4×D4D4×C4112yes—
283#117—22no—
284#117—22no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4D4×C4112yes—
289C2×C42C23×C4111yescharacteristic
290#107—24no—
291#106—24no—
292C4⋊C8—22no—
293#103—24no—
294#103—24no—
295#103—24no—
296#102—24no—
297C22⋊C8—22no—
298#97—21no—
299#97C23×C4112yes—
300#97C23×C4114yes—
301C2×Q8—22no—
302C2×Q8—22no—
303C2×Q8—44no—
304C2×Q8—41no—
305C2×Q8C2×D4×C4112yes—
306C2×D4—22no—
307C2×D4—22no—
308C2×D4C2×D4×C4112yes—
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—22no—
313C22×C4—41no—
314C22×C4C2×D4×C4111yescharacteristic
315C22×C4C2×D4×C4112yes—
316C2×C8—22no—
317C2×C8—24no—
318C2×C8—42no—
319C4⋊C4—22no—
320C4⋊C4—22no—
321C4⋊C4—22no—
322C4⋊C4—22no—
323C4⋊C4—22no—
324C4⋊C4—22no—
325C4⋊C4—22no—
326C4⋊C4—22no—
327C4⋊C4—22no—
328C4⋊C4—22no—
329C4⋊C4—22no—
330C4⋊C4—22no—
331C4⋊C4—22no—
332C4⋊C4—22no—
333C4⋊C4—22no—
334C4⋊C4—24no—
335C4⋊C4—42no—
336C4⋊C4C2×D4×C4112yes—
337C4⋊C4C2×D4×C4112yes—
338C4⋊C4C2×D4×C4112yes—
339C4⋊C4C2×D4×C4112yes—
340C22⋊C4—22no—
341C22⋊C4—22no—
342C22⋊C4—22no—
343C22⋊C4—22no—
344C22⋊C4—22no—
345C22⋊C4—22no—
346C22⋊C4—22no—
347C22⋊C4—22no—
348C22⋊C4—22no—
349C42—22no—
350C42—22no—
351C42—22no—
352C42C2×D4×C4111yescharacteristic
353C42C2×D4×C4112yes—
354C42C24×C4111yescharacteristic
355C23—22no—
356C23#120×C4111yescharacteristic
357Q8—42no—
358Q8—44no—
359Q8—82no—
360Q8—82no—
361D4—42no—
362D4—44no—
363D4—82no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—82no—
373C2×C4—82no—
374C2×C4—82no—
375C2×C4—82no—
376C2×C4—82no—
377C2×C4#120×C4112yes—
378C2×C4#120×C4111yescharacteristic
379C2×C4C22×D4×C4111yescharacteristic
380C2×C4C22×D4×C4112yes—
381C8—42no—
382C8—44no—
383C22—22no—
384C22—42no—
385C22—42no—
386C22—42no—
387C22C41×#45412yes—
388C22C2×#120×C4111yescharacteristic
389C4—21no—
390C4—21no—
391C4—22no—
392C4—22no—
393C4—42no—
394C4—42no—
395C4—42no—
396C4—42no—
397C4—42no—
398C4—82no—
399C2—22no—
400C2—82no—
401C2C2×C41×#45411yescharacteristic
402C2C41×#302212yes—
subgroupG/H
center, socleC22×C41C2×#120
commutator, Frattini, cosocleC42C24×C41
prime radicalC41×#3553C2
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
2. C41×#3238C2semidirect
3. C2×C41×#491C2semidirect
4. C41×#1664C2semidirect
5. C41×#1663C2semidirect
6. C41×#1662C2semidirect
7. C41×#1534C2semidirect
8. C41×#1532C2semidirect
181. #19060C41direct (N × H)
199. #3238C2×C41semidirect
200. C2×#491C2×C41semidirect
201. #1664C2×C41semidirect
202. #1663C2×C41semidirect
203. #1662C2×C41semidirect
204. #1534C2×C41semidirect
205. #1532C2×C41semidirect
238. C41#19060direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#35532
C41×#32382
C2×C41×#4912
C41×#16642
C41×#16632
C41×#16622
C41×#15342
C41×#15322
#1906041