Finite Group Databasebeta

← C41×#11798 #23787999

Subgroups — C41×#11798 #23787999

Order 10496.

486 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#2392C211yesmaximal, characteristic
2C41×#1820C211yesmaximal, characteristic, complemented
3C41×#1464C211yesmaximal, characteristic, complemented
4C41×#1344C212yesmaximal, complemented
5C41×#1343C212yesmaximal
6C2×C4×D4×C41—21no—
7C2×C4×D4×C41C411yescharacteristic, complemented
8C2×#117×C41C2211yescharacteristic
9C41×#432—21no—
10C41×#398C411yescharacteristic, complemented
11C41×#397C2211yescharacteristic
12C41×#396—21no—
13C41×#394—21no—
14C41×#394C411yescharacteristic, complemented
15C41×#392C2211yescharacteristic
16C41×#381—21no—
17C4×C4⋊C4×C41C411yescharacteristic, complemented
18C4×C22⋊C4×C41—21no—
19C41×#342—21no—
20C41×#342C2212yes—
21C41×#324—21no—
22C41×#323C2212yes—
23C22×D4×C41—21no—
24C22×D4×C41C2×C411yescharacteristic
25C23×C4×C41—21no—
26C23×C4×C41D411yescharacteristic
27C4×D4×C41—41no—
28C4×D4×C41—41no—
29C4×D4×C41—44no—
30#117×C41—41no—
31#117×C41—41no—
32C2×C4⋊C4×C41—21no—
33C2×C4⋊C4×C41—21no—
34C2×C4⋊C4×C41C2×C411yescharacteristic
35C2×C4⋊C4×C41C2×C411yescharacteristic
36C2×C4⋊C4×C41D411yescharacteristic
37C2×C22⋊C4×C41—21no—
38C2×C22⋊C4×C41—21no—
39C2×C22⋊C4×C41—21no—
40C2×C22⋊C4×C41—21no—
41C2×C22⋊C4×C41—21no—
42C2×C22⋊C4×C41—22no—
43C2×C22⋊C4×C41D411yescharacteristic
44C2×C22⋊C4×C41C2311yescharacteristic
45C2×C42×C41—21no—
46C2×C42×C41C2×C411yescharacteristic
47C2×C42×C41D411yescharacteristic
48C4⋊C8×C41—41no—
49C22⋊C8×C41—22no—
50#97×C41—41no—
51#95×C41—21no—
52#95×C41—21no—
53#95×C41—41no—
54#95×C41—41no—
55#95×C41C2×C411yescharacteristic
56#95×C41C2×C411yescharacteristic
57C24×C41—21no—
58C24×C41C2×D411yescharacteristic
59C2×D4×C41—41no—
60C2×D4×C41—42no—
61C2×D4×C41—42no—
62C2×D4×C41—42no—
63C2×D4×C41—42no—
64C22×C4×C41—21no—
65C22×C4×C41—22no—
66C22×C4×C41—21no—
67C22×C4×C41—21no—
68C22×C4×C41—21no—
69C22×C4×C41—21no—
70C22×C4×C41—41no—
71C22×C4×C41—42no—
72C22×C4×C41—42no—
73C22×C4×C41—41no—
74C22×C4×C41—41no—
75C22×C4×C41—42no—
76C22×C4×C41C22⋊C411yescharacteristic
77C22×C4×C41C22⋊C411yescharacteristic
78C22×C4×C41C22⋊C411yescharacteristic
79C22×C4×C41C22⋊C411yescharacteristic
80C22×C4×C41C22×C411yescharacteristic
81C22×C4×C41C2×D411yescharacteristic
82C2×C8×C41—42no—
83C4⋊C4×C41—41no—
84C4⋊C4×C41—41no—
85C4⋊C4×C41—41no—
86C4⋊C4×C41—42no—
87C4⋊C4×C41—42no—
88C22⋊C4×C41—41no—
89C22⋊C4×C41—41no—
90C22⋊C4×C41—42no—
91C22⋊C4×C41—42no—
92C22⋊C4×C41—42no—
93C22⋊C4×C41—42no—
94C22⋊C4×C41—42no—
95C22⋊C4×C41—42no—
96C22⋊C4×C41—42no—
97C42×C41—21no—
98C42×C41—21no—
99C42×C41—21no—
100C42×C41—21no—
101C42×C41—42no—
102C23×C41—21no—
103C23×C41—21no—
104C23×C41—22no—
105C23×C41—41no—
106C23×C41—41no—
107C23×C41—41no—
108C23×C41—41no—
109C23×C41—41no—
110C23×C41—41no—
111C23×C41—41no—
112C23×C41—41no—
113C23×C41C2×C22⋊C411yescharacteristic
114C23×C41AGL(1,ℤ/8)12yes—
115D4×C41—42no—
116D4×C41—48no—
117D4×C41—42no—
118C2×C4×C41—21no—
119C2×C4×C41—21no—
120C2×C4×C41—22no—
121C2×C4×C41—21no—
122C2×C4×C41—21no—
123C2×C4×C41—21no—
124C2×C4×C41—21no—
125C2×C4×C41—21no—
126C2×C4×C41—21no—
127C2×C4×C41—21no—
128C2×C4×C41—42no—
129C2×C4×C41—42no—
130C2×C4×C41—41no—
131C2×C4×C41—41no—
132C2×C4×C41—41no—
133C2×C4×C41—41no—
134C2×C4×C41—41no—
135C2×C4×C41—41no—
136C2×C4×C41—41no—
137C2×C4×C41—41no—
138C2×C4×C41—41no—
139C2×C4×C41—41no—
140C2×C4×C41—41no—
141C2×C4×C41—41no—
142C2×C4×C41—82no—
143C2×C4×C41—82no—
144C2×C4×C41—82no—
145C2×C4×C41—82no—
146C2×C4×C41—82no—
147C2×C4×C41#9911yescharacteristic
148C2×C4×C41#9911yescharacteristic
149C8×C41—82no—
150#11798C4111yesmaximal, characteristic, direct product factor, Sylow
151C22×C41—21no—
152C22×C41—21no—
153C22×C41—22no—
154C22×C41—42no—
155C22×C41—42no—
156C22×C41—42no—
157C22×C41—41no—
158C22×C41—41no—
159C22×C41—42no—
160C22×C41—81no—
161C22×C41—81no—
162C22×C41—81no—
163C22×C41—81no—
164C22×C41—81no—
165C22×C41C2×#9911yescharacteristic
166C22×C41#41811yescharacteristic
167C22×C41#42111yescharacteristic
168C4×C41—21no—
169C4×C41—21no—
170C4×C41—42no—
171C4×C41—41no—
172C4×C41—41no—
173C4×C41—41no—
174C4×C41—41no—
175C4×C41—41no—
176C4×C41—81no—
177C4×C41—81no—
178C4×C41—162no—
179#2392C2×C4111yescharacteristic
180#1820C2×C4111yescharacteristic, complemented
181#1464C2×C4111yescharacteristic, complemented
182#1344C2×C4112yescomplemented
183#1343C2×C4112yes—
184C2×C41—21no—
185C2×C41—21no—
186C2×C41—42no—
187C2×C41—82no—
188C2×C41#151011yescharacteristic
189C2×C41#212011yescharacteristic
190C2×C41#212611yescharacteristic
191C2×C4×D4—21no—
192C2×C4×D4C4×C4111yescharacteristic, complemented
193C2×#117C22×C4111yescharacteristic
194#432—21no—
195#398C4×C4111yescharacteristic, complemented
196#397C22×C4111yescharacteristic
197#396—21no—
198#394—21no—
199#394C4×C4111yescharacteristic, complemented
200#392C22×C4111yescharacteristic
201#381—21no—
202C4×C4⋊C4C4×C4111yescharacteristic, complemented
203C4×C22⋊C4—21no—
204#342—21no—
205#342C22×C4112yes—
206#324—21no—
207#323C22×C4112yes—
208C41#1179811yescharacteristic, direct product factor, Sylow
209C22×D4—21no—
210C22×D4C2×C4×C4111yescharacteristic
211C23×C4—21no—
212C23×C4D4×C4111yescharacteristic
213C4×D4—41no—
214C4×D4—41no—
215C4×D4—44no—
216#117—41no—
217#117—41no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4C2×C4×C4111yescharacteristic
221C2×C4⋊C4C2×C4×C4111yescharacteristic
222C2×C4⋊C4D4×C4111yescharacteristic
223C2×C22⋊C4—21no—
224C2×C22⋊C4—21no—
225C2×C22⋊C4—21no—
226C2×C22⋊C4—21no—
227C2×C22⋊C4—21no—
228C2×C22⋊C4—22no—
229C2×C22⋊C4D4×C4111yescharacteristic
230C2×C22⋊C4C23×C4111yescharacteristic
231C2×C42—21no—
232C2×C42C2×C4×C4111yescharacteristic
233C2×C42D4×C4111yescharacteristic
234C4⋊C8—41no—
235C22⋊C8—22no—
236#97—41no—
237#95—21no—
238#95—21no—
239#95—41no—
240#95—41no—
241#95C2×C4×C4111yescharacteristic
242#95C2×C4×C4111yescharacteristic
243C24—21no—
244C24C2×D4×C4111yescharacteristic
245C2×D4—41no—
246C2×D4—42no—
247C2×D4—42no—
248C2×D4—42no—
249C2×D4—42no—
250C22×C4—21no—
251C22×C4—22no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—41no—
257C22×C4—42no—
258C22×C4—42no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—42no—
262C22×C4C22⋊C4×C4111yescharacteristic
263C22×C4C22⋊C4×C4111yescharacteristic
264C22×C4C22⋊C4×C4111yescharacteristic
265C22×C4C22⋊C4×C4111yescharacteristic
266C22×C4C22×C4×C4111yescharacteristic
267C22×C4C2×D4×C4111yescharacteristic
268C2×C8—42no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—42no—
273C4⋊C4—42no—
274C22⋊C4—41no—
275C22⋊C4—41no—
276C22⋊C4—42no—
277C22⋊C4—42no—
278C22⋊C4—42no—
279C22⋊C4—42no—
280C22⋊C4—42no—
281C22⋊C4—42no—
282C22⋊C4—42no—
283C42—21no—
284C42—21no—
285C42—21no—
286C42—21no—
287C42—42no—
288C23—21no—
289C23—21no—
290C23—22no—
291C23—41no—
292C23—41no—
293C23—41no—
294C23—41no—
295C23—41no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23C2×C22⋊C4×C4111yescharacteristic
300C23AGL(1,ℤ/8)×C4112yes—
301D4—42no—
302D4—48no—
303D4—42no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—22no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—82no—
329C2×C4—82no—
330C2×C4—82no—
331C2×C4—82no—
332C2×C4—82no—
333C2×C4#99×C4111yescharacteristic
334C2×C4#99×C4111yescharacteristic
335C8—82no—
336C22—21no—
337C22—21no—
338C22—22no—
339C22—42no—
340C22—42no—
341C22—42no—
342C22—41no—
343C22—41no—
344C22—42no—
345C22—81no—
346C22—81no—
347C22—81no—
348C22—81no—
349C22—81no—
350C22C2×#99×C4111yescharacteristic
351C22C41×#41811yescharacteristic
352C22C41×#42111yescharacteristic
353C4—21no—
354C4—21no—
355C4—42no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—41no—
361C4—81no—
362C4—81no—
363C4—162no—
364C2—21no—
365C2—21no—
366C2—42no—
367C2—82no—
368C2C41×#151011yescharacteristic
369C2C41×#212011yescharacteristic
370C2C41×#212611yescharacteristic
subgroupG/H
center, socleC22×C41C2×#99
commutatorC22×C4C22×C4×C41
Frattini, cosocleC2×C22⋊C4C23×C41
prime radicalC41×#392C22
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C41 ◁ C22×C4×C41 ◁ C2×#117×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C41×#1820C2semidirect
3. C41×#1464C2semidirect
4. C41×#1344C2semidirect
7. C2×C4×D4×C41C4semidirect
10. C41×#398C4semidirect
14. C41×#394C4semidirect
17. C4×C4⋊C4×C41C4semidirect
150. #11798C41direct (N × H)
180. #1820C2×C41semidirect
181. #1464C2×C41semidirect
182. #1344C2×C41semidirect
192. C2×C4×D4C4×C41semidirect
195. #398C4×C41semidirect
199. #394C4×C41semidirect
202. C4×C4⋊C4C4×C41semidirect
208. C41#11798direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#23922
C41×#18202
C41×#14642
C41×#13442
C41×#13432
#1179841