Finite Group Databasebeta

← C43×#8226 #24928243

Subgroups — C43×#8226 #24928243

Order 11008.

572 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#124×C43C211yesmaximal, characteristic
2C43×#1745C211yesmaximal, characteristic, complemented
3C4×#97×C43C211yesmaximal, characteristic, complemented
4C2×C43×#329C212yesmaximal
5C43×#1295C212yesmaximal, complemented
6C2×#124×C43C2211yescharacteristic
7C2×C4×Q8×C43C411yescharacteristic
8C2×C4×D4×C43C411yescharacteristic
9C2×#97×C43—21no—
10C2×#97×C43C2212yes—
11C2×#97×C43C2212yes—
12C2×C4×C8×C43—21no—
13C43×#391C411yescharacteristic
14C43×#390C411yescharacteristic
15C43×#388—21no—
16C43×#388—21no—
17C43×#382C2211yescharacteristic
18C4×C22⋊C4×C43—21no—
19C4×C22⋊C4×C43—21no—
20C43×C43C2211yescharacteristic
21C43×#336—21no—
22C43×#336—21no—
23C43×#329C418yescomplemented
24C22×Q8×C43C2×C411yescharacteristic
25C22×D4×C43C2×C411yescharacteristic
26C23×C4×C43—21no—
27C22×C8×C43—22no—
28C22×C8×C43—22no—
29#124×C43—22no—
30#124×C43C2×C414yes—
31C4×Q8×C43—42no—
32C4×D4×C43—42no—
33C2×C4⋊C4×C43—21no—
34C2×C4⋊C4×C43C2×C411yescharacteristic
35C2×C4⋊C4×C43C2×C411yescharacteristic
36C2×C22⋊C4×C43—21no—
37C2×C22⋊C4×C43—21no—
38C2×C22⋊C4×C43—21no—
39C2×C22⋊C4×C43—21no—
40C2×C22⋊C4×C43—21no—
41C2×C42×C43—21no—
42C2×C42×C43C2×C411yescharacteristic
43C2×C42×C43C2×C411yescharacteristic
44C2×C42×C43D411yescharacteristic
45C2×C42×C43D411yescharacteristic
46C2×C42×C43D411yescharacteristic
47C2×C42×C43D411yescharacteristic
48C2×C42×C43C2311yescharacteristic
49#97×C43—24no—
50#97×C43—22no—
51#97×C43—22no—
52#97×C43C2×C414yescomplemented
53#97×C43C2×C414yescomplemented
54C4×C8×C43—24no—
55#95×C43—21no—
56#95×C43—21no—
57#95×C43—21no—
58#95×C43—21no—
59C24×C43—21no—
60C2×Q8×C43—21no—
61C2×Q8×C43—41no—
62C2×Q8×C43—41no—
63C2×Q8×C43C4212yes—
64C2×D4×C43—21no—
65C2×D4×C43—41no—
66C2×D4×C43—41no—
67C2×D4×C43C4212yes—
68C22×C4×C43—21no—
69C22×C4×C43—21no—
70C22×C4×C43—21no—
71C22×C4×C43—42no—
72C22×C4×C43—42no—
73C22×C4×C43—42no—
74C22×C4×C43C22⋊C411yescharacteristic
75C22×C4×C43C22⋊C411yescharacteristic
76C22×C4×C43C22⋊C411yescharacteristic
77C22×C4×C43C22⋊C411yescharacteristic
78C22×C4×C43C22×C411yescharacteristic
79C22×C4×C43C2×D411yescharacteristic
80C22×C4×C43C2×D411yescharacteristic
81C2×C8×C43—24no—
82C2×C8×C43—24no—
83C2×C8×C43—24no—
84C2×C8×C43—24no—
85C2×C8×C43—42no—
86C2×C8×C43—42no—
87C4⋊C4×C43—41no—
88C4⋊C4×C43—41no—
89C4⋊C4×C43—42no—
90C22⋊C4×C43—24no—
91C22⋊C4×C43—24no—
92C22⋊C4×C43—42no—
93C22⋊C4×C43—42no—
94C22⋊C4×C43—42no—
95C42×C43—22no—
96C42×C43—22no—
97C42×C43—22no—
98C42×C43—41no—
99C42×C43—41no—
100C42×C43—41no—
101C42×C43—42no—
102C42×C43C22×C412yes—
103C42×C43#4112yes—
104C23×C43—22no—
105C23×C43—41no—
106C23×C43—41no—
107C23×C43—41no—
108C23×C43—41no—
109C23×C43—41no—
110C23×C43—41no—
111C23×C43C2×C22⋊C411yescharacteristic
112Q8×C43—42no—
113Q8×C43—42no—
114D4×C43—42no—
115D4×C43—42no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—22no—
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43—41no—
133C2×C4×C43—41no—
134C2×C4×C43—41no—
135C2×C4×C43—41no—
136C2×C4×C43—41no—
137C2×C4×C43—41no—
138C2×C4×C43—41no—
139C2×C4×C43—41no—
140C2×C4×C43—84no—
141C2×C4×C43#10012yes—
142C2×C4×C43#10412yes—
143C2×C4×C43#10412yes—
144C2×C4×C43C2×C4211yescharacteristic
145C2×C4×C43#11711yescharacteristic
146C2×C4×C43C4×D412yes—
147C2×C4×C43C4×D412yes—
148C8×C43—28no—
149C8×C43—44no—
150#8226C4311yesmaximal, characteristic, direct product factor, Sylow
151C22×C43—42no—
152C22×C43—42no—
153C22×C43—42no—
154C22×C43—81no—
155C22×C43—81no—
156C22×C43—81no—
157C22×C43—81no—
158C22×C43C4×C22⋊C411yescharacteristic
159C22×C43C2×#10011yescharacteristic
160C22×C43#41311yescharacteristic
161C22×C43C2×#10411yescharacteristic
162C22×C43C2×#10411yescharacteristic
163C22×C43#42111yescharacteristic
164C22×C43#42111yescharacteristic
165C4×C43—21no—
166C4×C43—21no—
167C4×C43—22no—
168C4×C43—22no—
169C4×C43—22no—
170C4×C43—22no—
171C4×C43—22no—
172C4×C43—42no—
173C4×C43—41no—
174C4×C43—81no—
175C4×C43—81no—
176C4×#124C2×C4311yescharacteristic
177#1745C2×C4311yescharacteristic, complemented
178C4×#97C2×C4311yescharacteristic, complemented
179C2×#329C2×C4312yes—
180#1295C2×C4312yescomplemented
181C2×C43—82no—
182C2×C43#152711yescharacteristic
183C2×C43#152911yescharacteristic
184C2×C43#153011yescharacteristic
185C2×C43#153211yescharacteristic
186C2×C43C4×#10011yescharacteristic
187C2×C43C4×#10411yescharacteristic
188C2×C43#175911yescharacteristic
189C2×#124C22×C4311yescharacteristic
190C2×C4×Q8C4×C4311yescharacteristic
191C2×C4×D4C4×C4311yescharacteristic
192C2×#97—21no—
193C2×#97C22×C4312yes—
194C2×#97C22×C4312yes—
195C2×C4×C8—21no—
196#391C4×C4311yescharacteristic
197#390C4×C4311yescharacteristic
198#388—21no—
199#388—21no—
200#382C22×C4311yescharacteristic
201C4×C22⋊C4—21no—
202C4×C22⋊C4—21no—
203C43C22×C4311yescharacteristic
204#336—21no—
205#336—21no—
206#329C4×C4318yescomplemented
207C43#822611yescharacteristic, direct product factor, Sylow
208C22×Q8C2×C4×C4311yescharacteristic
209C22×D4C2×C4×C4311yescharacteristic
210C23×C4—21no—
211C22×C8—22no—
212C22×C8—22no—
213#124—22no—
214#124C2×C4×C4314yes—
215C4×Q8—42no—
216C4×D4—42no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4C2×C4×C4311yescharacteristic
219C2×C4⋊C4C2×C4×C4311yescharacteristic
220C2×C22⋊C4—21no—
221C2×C22⋊C4—21no—
222C2×C22⋊C4—21no—
223C2×C22⋊C4—21no—
224C2×C22⋊C4—21no—
225C2×C42—21no—
226C2×C42C2×C4×C4311yescharacteristic
227C2×C42C2×C4×C4311yescharacteristic
228C2×C42D4×C4311yescharacteristic
229C2×C42D4×C4311yescharacteristic
230C2×C42D4×C4311yescharacteristic
231C2×C42D4×C4311yescharacteristic
232C2×C42C23×C4311yescharacteristic
233#97—24no—
234#97—22no—
235#97—22no—
236#97C2×C4×C4314yescomplemented
237#97C2×C4×C4314yescomplemented
238C4×C8—24no—
239#95—21no—
240#95—21no—
241#95—21no—
242#95—21no—
243C24—21no—
244C2×Q8—21no—
245C2×Q8—41no—
246C2×Q8—41no—
247C2×Q8C42×C4312yes—
248C2×D4—21no—
249C2×D4—41no—
250C2×D4—41no—
251C2×D4C42×C4312yes—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—42no—
256C22×C4—42no—
257C22×C4—42no—
258C22×C4C22⋊C4×C4311yescharacteristic
259C22×C4C22⋊C4×C4311yescharacteristic
260C22×C4C22⋊C4×C4311yescharacteristic
261C22×C4C22⋊C4×C4311yescharacteristic
262C22×C4C22×C4×C4311yescharacteristic
263C22×C4C2×D4×C4311yescharacteristic
264C22×C4C2×D4×C4311yescharacteristic
265C2×C8—24no—
266C2×C8—24no—
267C2×C8—24no—
268C2×C8—24no—
269C2×C8—42no—
270C2×C8—42no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—42no—
274C22⋊C4—24no—
275C22⋊C4—24no—
276C22⋊C4—42no—
277C22⋊C4—42no—
278C22⋊C4—42no—
279C42—22no—
280C42—22no—
281C42—22no—
282C42—41no—
283C42—41no—
284C42—41no—
285C42—42no—
286C42C22×C4×C4312yes—
287C42#41×C4312yes—
288C23—22no—
289C23—41no—
290C23—41no—
291C23—41no—
292C23—41no—
293C23—41no—
294C23—41no—
295C23C2×C22⋊C4×C4311yescharacteristic
296Q8—42no—
297Q8—42no—
298D4—42no—
299D4—42no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—22no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
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—84no—
325C2×C4#100×C4312yes—
326C2×C4#104×C4312yes—
327C2×C4#104×C4312yes—
328C2×C4C2×C42×C4311yescharacteristic
329C2×C4#117×C4311yescharacteristic
330C2×C4C4×D4×C4312yes—
331C2×C4C4×D4×C4312yes—
332C8—28no—
333C8—44no—
334C22—42no—
335C22—42no—
336C22—42no—
337C22—81no—
338C22—81no—
339C22—81no—
340C22—81no—
341C22C4×C22⋊C4×C4311yescharacteristic
342C22C2×#100×C4311yescharacteristic
343C22C43×#41311yescharacteristic
344C22C2×#104×C4311yescharacteristic
345C22C2×#104×C4311yescharacteristic
346C22C43×#42111yescharacteristic
347C22C43×#42111yescharacteristic
348C4—21no—
349C4—21no—
350C4—22no—
351C4—22no—
352C4—22no—
353C4—22no—
354C4—22no—
355C4—42no—
356C4—41no—
357C4—81no—
358C4—81no—
359C2—82no—
360C2C43×#152711yescharacteristic
361C2C43×#152911yescharacteristic
362C2C43×#153011yescharacteristic
363C2C43×#153211yescharacteristic
364C2C4×#100×C4311yescharacteristic
365C2C4×#104×C4311yescharacteristic
366C2C43×#175911yescharacteristic
subgroupG/H
center, socleC23×C43C2×C22⋊C4
commutatorC2×C4C2×C42×C43
Frattini, cosocleC2×C42C23×C43
prime radicalC22×D4×C43C2×C4
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C43 ◁ C43×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#1745C2semidirect
3. C4×#97×C43C2semidirect
5. C43×#1295C2semidirect
23. C43×#329C4semidirect
52. #97×C43C2×C4semidirect
53. #97×C43C2×C4semidirect
150. #8226C43direct (N × H)
177. #1745C2×C43semidirect
178. C4×#97C2×C43semidirect
180. #1295C2×C43semidirect
206. #329C4×C43semidirect
207. C43#8226direct (N × H)
236. #97C2×C4×C43semidirect
237. #97C2×C4×C43semidirect

Maximal subgroups

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

subgroupindex
C4×#124×C432
C43×#17452
C4×#97×C432
C2×C43×#3292
C43×#12952
#822643