Finite Group Databasebeta

← C43×#7721 #24927738

Subgroups — C43×#7721 #24927738

Order 11008.

444 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#2855C211yesmaximal, characteristic
2C43×#1817C211yesmaximal, characteristic
3C43×#1817C211yesmaximal, characteristic
4C43×#1272C212yesmaximal, complemented
5C43×#1271C212yesmaximal, complemented
6C2×C22⋊Q8×C43C411yescharacteristic
7C22×C42×C43C2211yescharacteristic
8C2×C22⋊C8×C43—21no—
9C2×C22⋊C8×C43—21no—
10C43×#391C411yescharacteristic
11C43×#391C2211yescharacteristic
12C43×#389C411yescharacteristic
13C43×#389C2211yescharacteristic
14C43×#387—21no—
15C43×#387—21no—
16C43×#385—21no—
17C43×#381—21no—
18C43×#380C411yescharacteristic
19C43×#336—21no—
20C43×#336—21no—
21C43×#336C2212yes—
22C43×#336C2212yes—
23C22×Q8×C43C2×C411yescharacteristic
24C23×C4×C43C2×C411yescharacteristic
25C23×C4×C43D411yescharacteristic
26C23×C4×C43D411yescharacteristic
27C22×C8×C43—22no—
28C22×C8×C43—22no—
29C22⋊Q8×C43—42no—
30C2×C4⋊C4×C43—21no—
31C2×C4⋊C4×C43—21no—
32C2×C4⋊C4×C43—21no—
33C2×C4⋊C4×C43C2×C411yescharacteristic
34C2×C4⋊C4×C43C2×C411yescharacteristic
35C2×C4⋊C4×C43C2×C411yescharacteristic
36C2×C22⋊C4×C43—21no—
37C2×C22⋊C4×C43—21no—
38C2×C42×C43—42no—
39C2×C42×C43C2×C411yescharacteristic
40C2×C42×C43D411yescharacteristic
41C2×C42×C43D411yescharacteristic
42C2×C42×C43C2311yescharacteristic
43C22⋊C8×C43—42no—
44C22⋊C8×C43—42no—
45#95×C43—21no—
46#95×C43—21no—
47#95×C43—21no—
48#95×C43—21no—
49#95×C43—21no—
50#95×C43—21no—
51#95×C43—21no—
52C24×C43C22⋊C411yescharacteristic
53C2×Q8×C43—22no—
54C2×Q8×C43—41no—
55C2×Q8×C43—41no—
56C22×C4×C43—22no—
57C22×C4×C43—22no—
58C22×C4×C43—22no—
59C22×C4×C43—22no—
60C22×C4×C43—22no—
61C22×C4×C43—22no—
62C22×C4×C43—21no—
63C22×C4×C43—21no—
64C22×C4×C43—21no—
65C22×C4×C43—21no—
66C22×C4×C43—41no—
67C22×C4×C43—41no—
68C22×C4×C43—41no—
69C22×C4×C43C22⋊C411yescharacteristic
70C22×C4×C43C22⋊C411yescharacteristic
71C22×C4×C43C22⋊C411yescharacteristic
72C22×C4×C43C22×C411yescharacteristic
73C22×C4×C43C2×D411yescharacteristic
74C22×C4×C43C2×D411yescharacteristic
75C2×C8×C43—42no—
76C2×C8×C43—42no—
77C2×C8×C43—42no—
78C2×C8×C43—42no—
79C2×C8×C43—42no—
80C2×C8×C43—42no—
81C4⋊C4×C43—22no—
82C4⋊C4×C43—41no—
83C4⋊C4×C43—41no—
84C4⋊C4×C43—42no—
85C4⋊C4×C43—42no—
86C4⋊C4×C43—42no—
87C22⋊C4×C43—42no—
88C22⋊C4×C43—42no—
89C42×C43—41no—
90C42×C43—41no—
91C42×C43—41no—
92C42×C43—41no—
93C23×C43—21no—
94C23×C43—21no—
95C23×C43—21no—
96C23×C43—21no—
97C23×C43—21no—
98C23×C43—21no—
99C23×C43#9912yes—
100C23×C43C2×C22⋊C411yescharacteristic
101Q8×C43—82no—
102C2×C4×C43—21no—
103C2×C4×C43—21no—
104C2×C4×C43—21no—
105C2×C4×C43—21no—
106C2×C4×C43—21no—
107C2×C4×C43—21no—
108C2×C4×C43—21no—
109C2×C4×C43—21no—
110C2×C4×C43—21no—
111C2×C4×C43—21no—
112C2×C4×C43—21no—
113C2×C4×C43—21no—
114C2×C4×C43—21no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—44no—
118C2×C4×C43—44no—
119C2×C4×C43—44no—
120C2×C4×C43—41no—
121C2×C4×C43—41no—
122C2×C4×C43—41no—
123C2×C4×C43—41no—
124C2×C4×C43—41no—
125C2×C4×C43—41no—
126C2×C4×C43—41no—
127C2×C4×C43—41no—
128C2×C4×C43—41no—
129C2×C4×C43—41no—
130C2×C4×C43—41no—
131C2×C4×C43—41no—
132C2×C4×C43#13112yes—
133C2×C4×C43#13512yes—
134C2×C4×C43#13712yes—
135C8×C43—82no—
136C8×C43—82no—
137#7721C4311yesmaximal, characteristic, direct product factor, Sylow
138C22×C43—22no—
139C22×C43—22no—
140C22×C43—22no—
141C22×C43—41no—
142C22×C43—41no—
143C22×C43—41no—
144C22×C43—41no—
145C22×C43#40811yescharacteristic
146C22×C43C2×#9911yescharacteristic
147C22×C43#41311yescharacteristic
148C22×C43#41611yescharacteristic
149C22×C43#41911yescharacteristic
150C22×C43#42111yescharacteristic
151C22×C43#42111yescharacteristic
152C4×C43—22no—
153C4×C43—22no—
154C4×C43—22no—
155C4×C43—41no—
156C4×C43—41no—
157C4×C43—41no—
158C4×C43—81no—
159C4×C43—81no—
160C4×C43—81no—
161C4×C43—81no—
162#2855C2×C4311yescharacteristic
163#1817C2×C4311yescharacteristic
164#1817C2×C4311yescharacteristic
165#1272C2×C4312yescomplemented
166#1271C2×C4312yescomplemented
167C2×C43—42no—
168C2×C43#146811yescharacteristic
169C2×C43#148211yescharacteristic
170C2×C43#149711yescharacteristic
171C2×C43#151111yescharacteristic
172C2×C43#151611yescharacteristic
173C2×C43#153511yescharacteristic
174C2×C43#155411yescharacteristic
175C2×C22⋊Q8C4×C4311yescharacteristic
176C22×C42C22×C4311yescharacteristic
177C2×C22⋊C8—21no—
178C2×C22⋊C8—21no—
179#391C4×C4311yescharacteristic
180#391C22×C4311yescharacteristic
181#389C4×C4311yescharacteristic
182#389C22×C4311yescharacteristic
183#387—21no—
184#387—21no—
185#385—21no—
186#381—21no—
187#380C4×C4311yescharacteristic
188#336—21no—
189#336—21no—
190#336C22×C4312yes—
191#336C22×C4312yes—
192C43#772111yescharacteristic, direct product factor, Sylow
193C22×Q8C2×C4×C4311yescharacteristic
194C23×C4C2×C4×C4311yescharacteristic
195C23×C4D4×C4311yescharacteristic
196C23×C4D4×C4311yescharacteristic
197C22×C8—22no—
198C22×C8—22no—
199C22⋊Q8—42no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4C2×C4×C4311yescharacteristic
204C2×C4⋊C4C2×C4×C4311yescharacteristic
205C2×C4⋊C4C2×C4×C4311yescharacteristic
206C2×C22⋊C4—21no—
207C2×C22⋊C4—21no—
208C2×C42—42no—
209C2×C42C2×C4×C4311yescharacteristic
210C2×C42D4×C4311yescharacteristic
211C2×C42D4×C4311yescharacteristic
212C2×C42C23×C4311yescharacteristic
213C22⋊C8—42no—
214C22⋊C8—42no—
215#95—21no—
216#95—21no—
217#95—21no—
218#95—21no—
219#95—21no—
220#95—21no—
221#95—21no—
222C24C22⋊C4×C4311yescharacteristic
223C2×Q8—22no—
224C2×Q8—41no—
225C2×Q8—41no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—22no—
230C22×C4—22no—
231C22×C4—22no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—41no—
237C22×C4—41no—
238C22×C4—41no—
239C22×C4C22⋊C4×C4311yescharacteristic
240C22×C4C22⋊C4×C4311yescharacteristic
241C22×C4C22⋊C4×C4311yescharacteristic
242C22×C4C22×C4×C4311yescharacteristic
243C22×C4C2×D4×C4311yescharacteristic
244C22×C4C2×D4×C4311yescharacteristic
245C2×C8—42no—
246C2×C8—42no—
247C2×C8—42no—
248C2×C8—42no—
249C2×C8—42no—
250C2×C8—42no—
251C4⋊C4—22no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—42no—
255C4⋊C4—42no—
256C4⋊C4—42no—
257C22⋊C4—42no—
258C22⋊C4—42no—
259C42—41no—
260C42—41no—
261C42—41no—
262C42—41no—
263C23—21no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23—21no—
268C23—21no—
269C23#99×C4312yes—
270C23C2×C22⋊C4×C4311yescharacteristic
271Q8—82no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—44no—
288C2×C4—44no—
289C2×C4—44no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4#131×C4312yes—
303C2×C4#135×C4312yes—
304C2×C4#137×C4312yes—
305C8—82no—
306C8—82no—
307C22—22no—
308C22—22no—
309C22—22no—
310C22—41no—
311C22—41no—
312C22—41no—
313C22—41no—
314C22C43×#40811yescharacteristic
315C22C2×#99×C4311yescharacteristic
316C22C43×#41311yescharacteristic
317C22C43×#41611yescharacteristic
318C22C43×#41911yescharacteristic
319C22C43×#42111yescharacteristic
320C22C43×#42111yescharacteristic
321C4—22no—
322C4—22no—
323C4—22no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—81no—
328C4—81no—
329C4—81no—
330C4—81no—
331C2—42no—
332C2C43×#146811yescharacteristic
333C2C43×#148211yescharacteristic
334C2C43×#149711yescharacteristic
335C2C43×#151111yescharacteristic
336C2C43×#151611yescharacteristic
337C2C43×#153511yescharacteristic
338C2C43×#155411yescharacteristic
subgroupG/H
center, socleC23×C43C2×C22⋊C4
commutatorC22×C4C22×C4×C43
Frattini, cosocleC2×C42C23×C43
prime radicalC24×C43C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C43 ◁ C22×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
4. C43×#1272C2semidirect
5. C43×#1271C2semidirect
137. #7721C43direct (N × H)
165. #1272C2×C43semidirect
166. #1271C2×C43semidirect
192. C43#7721direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#28552
C43×#18172
C43×#12722
C43×#12712
#772143