Finite Group Databasebeta

← C41×#9244 #23785445

Subgroups — C41×#9244 #23785445

Order 10496.

464 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#464C211yesmaximal, characteristic
2C41×#2984C211yesmaximal, characteristic, complemented
3C41×#1527C211yesmaximal, characteristic
4C41×#1491C211yesmaximal, characteristic, complemented
5C41×#1469C211yesmaximal, characteristic
6C41×#1290C211yesmaximal, characteristic, complemented
7C41×#1283C211yesmaximal, characteristic, complemented
8C22×Q16×C41C411yescharacteristic
9C22×SD16×C41C411yescharacteristic
10C2×#124×C41C2211yescharacteristic
11C2×C4×Q8×C41C2211yescharacteristic
12C41×#464—21no—
13C41×#464—21no—
14C41×#464—21no—
15C41×#464—21no—
16C41×#446—21no—
17C41×#446—22no—
18C8×Q8×C41—21no—
19C41×#432—21no—
20C41×#432C2211yescharacteristic
21C41×#432C2211yescharacteristic
22C41×#431—21no—
23C41×#431C2211yescharacteristic
24C2×C4⋊C8×C41C2211yescharacteristic
25C2×#103×C41C411yescharacteristic
26C2×#102×C41C411yescharacteristic
27C4×M16×C41C2211yescharacteristic
28C41×#329—22no—
29C41×Q8⋊C8—21no—
30C41×Q8⋊C8—21no—
31C41×#323—21no—
32C41×#323—21no—
33C22×Q8×C41C2×C411yescharacteristic
34C22×Q8×C41C2×C411yescharacteristic
35C22×D4×C41C2×C411yescharacteristic
36C2×Q16×C41—21no—
37C2×Q16×C41—21no—
38C2×Q16×C41—42no—
39C2×SD16×C41—21no—
40C2×SD16×C41—21no—
41C2×SD16×C41—42no—
42C2×M16×C41—21no—
43C22×C8×C41C2×C411yescharacteristic
44C22×C8×C41C2×C411yescharacteristic
45#124×C41—21no—
46#124×C41—21no—
47#124×C41—21no—
48#124×C41—21no—
49C4×Q8×C41—21no—
50C4×Q8×C41—21no—
51C4×Q8×C41D411yescharacteristic
52C4×Q8×C41D411yescharacteristic
53C4×Q8×C41D411yescharacteristic
54C4×Q8×C41D411yescharacteristic
55C2×C4⋊C4×C41—21no—
56C2×C4⋊C4×C41C2×C411yescharacteristic
57C2×C22⋊C4×C41—21no—
58C2×C22⋊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—
68#103×C41—21no—
69#103×C41—21no—
70#102×C41—21no—
71#102×C41—21no—
72C22⋊C8×C41—21no—
73C22⋊C8×C41—21no—
74C22⋊C8×C41D411yescharacteristic
75C22⋊C8×C41D411yescharacteristic
76#97×C41—22no—
77#97×C41—21no—
78#97×C41—21no—
79#97×C41D412yes—
80C4×C8×C41—22no—
81C4×C8×C41—21no—
82C4×C8×C41—21no—
83C24×C41—21no—
84C2×Q8×C41—21no—
85C2×Q8×C41—22no—
86C2×Q8×C41—21no—
87C2×Q8×C41—21no—
88C2×Q8×C41—41no—
89C2×Q8×C41—41no—
90C2×Q8×C41—41no—
91C2×Q8×C41C22⋊C411yescharacteristic
92C2×Q8×C41C22⋊C411yescharacteristic
93C2×D4×C41—21no—
94C2×D4×C41—21no—
95C2×D4×C41—41no—
96C2×D4×C41—41no—
97C22×C4×C41—21no—
98C22×C4×C41—21no—
99C22×C4×C41—21no—
100C22×C4×C41C22×C411yescharacteristic
101C22×C4×C41C2×D411yescharacteristic
102C22×C4×C41#4111yescharacteristic
103Q16×C41—42no—
104Q16×C41—42no—
105SD16×C41—42no—
106SD16×C41—42no—
107M16×C41—22no—
108M16×C41—41no—
109C2×C8×C41—21no—
110C2×C8×C41—21no—
111C2×C8×C41—21no—
112C2×C8×C41—21no—
113C2×C8×C41—22no—
114C2×C8×C41—41no—
115C2×C8×C41—41no—
116C2×C8×C41—41no—
117C2×C8×C41—41no—
118C4⋊C4×C41—21no—
119C4⋊C4×C41—21no—
120C4⋊C4×C41—21no—
121C4⋊C4×C41—21no—
122C4⋊C4×C41—21no—
123C4⋊C4×C41C22⋊C411yescharacteristic
124C4⋊C4×C41C22⋊C411yescharacteristic
125C22⋊C4×C41—41no—
126C22⋊C4×C41—41no—
127C22⋊C4×C41—41no—
128C22⋊C4×C41—41no—
129C42×C41—21no—
130C42×C41—21no—
131C42×C41—21no—
132C42×C41—21no—
133C42×C41C2×D411yescharacteristic
134C42×C41C2×D411yescharacteristic
135C42×C41C2×D411yescharacteristic
136C42×C41#4111yescharacteristic
137C23×C41—41no—
138C23×C41—41no—
139C23×C41—41no—
140C23×C41—81no—
141C23×C41—81no—
142C23×C41C4×D411yescharacteristic
143Q8×C41—21no—
144Q8×C41—21no—
145Q8×C41—21no—
146Q8×C41—42no—
147Q8×C41—41no—
148Q8×C41—41no—
149Q8×C41—81no—
150Q8×C41#10012yes—
151D4×C41—41no—
152D4×C41—41no—
153D4×C41—81no—
154C2×C4×C41—21no—
155C2×C4×C41—21no—
156C2×C4×C41—21no—
157C2×C4×C41—21no—
158C2×C4×C41—21no—
159C2×C4×C41—21no—
160C2×C4×C41—21no—
161C2×C4×C41—21no—
162C2×C4×C41—41no—
163C2×C4×C41—42no—
164C2×C4×C41—41no—
165C2×C4×C41—41no—
166C2×C4×C41—41no—
167C2×C4×C41—81no—
168C2×C4×C41C2×C22⋊C411yescharacteristic
169C2×C4×C41C4×D411yescharacteristic
170C2×C4×C41#12011yescharacteristic
171C2×C4×C41#12111yescharacteristic
172C2×C4×C41#12111yescharacteristic
173C2×C4×C41#12311yescharacteristic
174C8×C41—41no—
175C8×C41—41no—
176C8×C41—42no—
177C8×C41—42no—
178C8×C41—41no—
179C8×C41—41no—
180C8×C41—81no—
181#9244C4111yesmaximal, characteristic, direct product factor, Sylow
182C22×C41—21no—
183C22×C41—21no—
184C22×C41—81no—
185C22×C41—81no—
186C22×C41—81no—
187C22×C41—161no—
188C22×C41—161no—
189C22×C41#38611yescharacteristic
190C22×C41#44311yescharacteristic
191C22×C41#44411yescharacteristic
192C4×C41—21no—
193C4×C41—21no—
194C4×C41—21no—
195C4×C41—22no—
196C4×C41—21no—
197C4×C41—21no—
198C4×C41—41no—
199C4×C41—41no—
200C4×C41—41no—
201C4×C41—81no—
202C4×C41C2×#10011yescharacteristic
203C4×C41#41311yescharacteristic
204C2×#464C2×C4111yescharacteristic
205#2984C2×C4111yescharacteristic, complemented
206#1527C2×C4111yescharacteristic
207#1491C2×C4111yescharacteristic, complemented
208#1469C2×C4111yescharacteristic
209#1290C2×C4111yescharacteristic, complemented
210#1283C2×C4111yescharacteristic, complemented
211C2×C41—21no—
212C2×C41—21no—
213C2×C41—161no—
214C2×C41#187611yescharacteristic
215C2×C41#190011yescharacteristic
216C2×C41#190511yescharacteristic
217C22×Q16C4×C4111yescharacteristic
218C22×SD16C4×C4111yescharacteristic
219C2×#124C22×C4111yescharacteristic
220C2×C4×Q8C22×C4111yescharacteristic
221#464—21no—
222#464—21no—
223#464—21no—
224#464—21no—
225#446—21no—
226#446—22no—
227C8×Q8—21no—
228#432—21no—
229#432C22×C4111yescharacteristic
230#432C22×C4111yescharacteristic
231#431—21no—
232#431C22×C4111yescharacteristic
233C2×C4⋊C8C22×C4111yescharacteristic
234C2×#103C4×C4111yescharacteristic
235C2×#102C4×C4111yescharacteristic
236C4×M16C22×C4111yescharacteristic
237#329—22no—
238Q8⋊C8—21no—
239Q8⋊C8—21no—
240#323—21no—
241#323—21no—
242C41#924411yescharacteristic, direct product factor, Sylow
243C22×Q8C2×C4×C4111yescharacteristic
244C22×Q8C2×C4×C4111yescharacteristic
245C22×D4C2×C4×C4111yescharacteristic
246C2×Q16—21no—
247C2×Q16—21no—
248C2×Q16—42no—
249C2×SD16—21no—
250C2×SD16—21no—
251C2×SD16—42no—
252C2×M16—21no—
253C22×C8C2×C4×C4111yescharacteristic
254C22×C8C2×C4×C4111yescharacteristic
255#124—21no—
256#124—21no—
257#124—21no—
258#124—21no—
259C4×Q8—21no—
260C4×Q8—21no—
261C4×Q8D4×C4111yescharacteristic
262C4×Q8D4×C4111yescharacteristic
263C4×Q8D4×C4111yescharacteristic
264C4×Q8D4×C4111yescharacteristic
265C2×C4⋊C4—21no—
266C2×C4⋊C4C2×C4×C4111yescharacteristic
267C2×C22⋊C4—21no—
268C2×C22⋊C4—21no—
269C2×C42—21no—
270C2×C42C23×C4111yescharacteristic
271C4⋊C8—22no—
272C4⋊C8—22no—
273C4⋊C8—21no—
274C4⋊C8—21no—
275C4⋊C8—21no—
276C4⋊C8—21no—
277C4⋊C8—21no—
278#103—21no—
279#103—21no—
280#102—21no—
281#102—21no—
282C22⋊C8—21no—
283C22⋊C8—21no—
284C22⋊C8D4×C4111yescharacteristic
285C22⋊C8D4×C4111yescharacteristic
286#97—22no—
287#97—21no—
288#97—21no—
289#97D4×C4112yes—
290C4×C8—22no—
291C4×C8—21no—
292C4×C8—21no—
293C24—21no—
294C2×Q8—21no—
295C2×Q8—22no—
296C2×Q8—21no—
297C2×Q8—21no—
298C2×Q8—41no—
299C2×Q8—41no—
300C2×Q8—41no—
301C2×Q8C22⋊C4×C4111yescharacteristic
302C2×Q8C22⋊C4×C4111yescharacteristic
303C2×D4—21no—
304C2×D4—21no—
305C2×D4—41no—
306C2×D4—41no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4C22×C4×C4111yescharacteristic
311C22×C4C2×D4×C4111yescharacteristic
312C22×C4#41×C4111yescharacteristic
313Q16—42no—
314Q16—42no—
315SD16—42no—
316SD16—42no—
317M16—22no—
318M16—41no—
319C2×C8—21no—
320C2×C8—21no—
321C2×C8—21no—
322C2×C8—21no—
323C2×C8—22no—
324C2×C8—41no—
325C2×C8—41no—
326C2×C8—41no—
327C2×C8—41no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—21no—
332C4⋊C4—21no—
333C4⋊C4C22⋊C4×C4111yescharacteristic
334C4⋊C4C22⋊C4×C4111yescharacteristic
335C22⋊C4—41no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C42—21no—
340C42—21no—
341C42—21no—
342C42—21no—
343C42C2×D4×C4111yescharacteristic
344C42C2×D4×C4111yescharacteristic
345C42C2×D4×C4111yescharacteristic
346C42#41×C4111yescharacteristic
347C23—41no—
348C23—41no—
349C23—41no—
350C23—81no—
351C23—81no—
352C23C4×D4×C4111yescharacteristic
353Q8—21no—
354Q8—21no—
355Q8—21no—
356Q8—42no—
357Q8—41no—
358Q8—41no—
359Q8—81no—
360Q8#100×C4112yes—
361D4—41no—
362D4—41no—
363D4—81no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—41no—
373C2×C4—42no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—81no—
378C2×C4C2×C22⋊C4×C4111yescharacteristic
379C2×C4C4×D4×C4111yescharacteristic
380C2×C4#120×C4111yescharacteristic
381C2×C4#121×C4111yescharacteristic
382C2×C4#121×C4111yescharacteristic
383C2×C4#123×C4111yescharacteristic
384C8—41no—
385C8—41no—
386C8—42no—
387C8—42no—
388C8—41no—
389C8—41no—
390C8—81no—
391C22—21no—
392C22—21no—
393C22—81no—
394C22—81no—
395C22—81no—
396C22—161no—
397C22—161no—
398C22C41×#38611yescharacteristic
399C22C41×#44311yescharacteristic
400C22C41×#44411yescharacteristic
401C4—21no—
402C4—21no—
403C4—21no—
404C4—22no—
405C4—21no—
406C4—21no—
407C4—41no—
408C4—41no—
409C4—41no—
410C4—81no—
411C4C2×#100×C4111yescharacteristic
412C4C41×#41311yescharacteristic
413C2—21no—
414C2—21no—
415C2—161no—
416C2C41×#187611yescharacteristic
417C2C41×#190011yescharacteristic
418C2C41×#190511yescharacteristic
subgroupG/H
center, socleC22×C41#386
commutatorC22×C4C22×C4×C41
Frattini, cosocleC2×C42C23×C41
prime radicalC22×D4×C41C2×C4
LCSG ▷ C22×C4 ▷ 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×#2984C2semidirect
4. C41×#1491C2semidirect
6. C41×#1290C2semidirect
7. C41×#1283C2semidirect
181. #9244C41direct (N × H)
205. #2984C2×C41semidirect
207. #1491C2×C41semidirect
209. #1290C2×C41semidirect
210. #1283C2×C41semidirect
242. C41#9244direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C41×#4642
C41×#29842
C41×#15272
C41×#14912
C41×#14692
C41×#12902
C41×#12832
#924441