Finite Group Databasebeta

← C43×#13298 #24933315

Subgroups — C43×#13298 #24933315

Order 11008.

556 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 126 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
1C43×#2542C211yesmaximal, characteristic
2C43×#1799C211yesmaximal, characteristic
3C4×#99×C43C211yesmaximal, characteristic
4C43×#1393C214yesmaximal
5C2×C4⋊Q8×C43C411yescharacteristic, complemented
6C2×C22⋊Q8×C43—21no—
7C2×C22⋊Q8×C43—21no—
8C2×C4×D4×C43C2211yescharacteristic
9C2×#99×C43C2212yes—
10C2×#99×C43C2212yes—
11C43×#399—21no—
12C43×#399—21no—
13C43×#390C2212yes—
14C43×#384C412yescomplemented
15C43×#380—21no—
16C4×C4⋊C4×C43C411yescharacteristic, complemented
17C4×C22⋊C4×C43—21no—
18C43×#342—21no—
19C43×#342—21no—
20C22×Q8×C43—21no—
21C22×D4×C43C2311yescharacteristic
22C23×C4×C43D411yescharacteristic
23C23×C4×C43D411yescharacteristic
24C4⋊Q8×C43—41no—
25C4⋊Q8×C43—41no—
26C22⋊Q8×C43—44no—
27C22⋊Q8×C43—44no—
28C4×D4×C43—41no—
29C4×D4×C43—41no—
30C2×C4⋊C4×C43—21no—
31C2×C4⋊C4×C43—22no—
32C2×C4⋊C4×C43—22no—
33C2×C4⋊C4×C43—21no—
34C2×C4⋊C4×C43—41no—
35C2×C4⋊C4×C43C2×C412yes—
36C2×C4⋊C4×C43C2×C411yescharacteristic
37C2×C22⋊C4×C43—22no—
38C2×C22⋊C4×C43—22no—
39C2×C22⋊C4×C43—22no—
40C2×C22⋊C4×C43—22no—
41C2×C22⋊C4×C43D411yescharacteristic
42C2×C22⋊C4×C43D411yescharacteristic
43C2×C42×C43—41no—
44C2×C42×C43C2×C411yescharacteristic
45C2×C42×C43C2×C412yes—
46#99×C43—22no—
47#99×C43—24no—
48#99×C43Q814yescomplemented
49#95×C43—21no—
50#95×C43—41no—
51#95×C43—41no—
52C24×C43C2×D411yescharacteristic
53C24×C43C2×D411yescharacteristic
54C2×Q8×C43—42no—
55C2×Q8×C43—42no—
56C2×Q8×C43—41no—
57C2×Q8×C43—41no—
58C2×D4×C43—41no—
59C2×D4×C43—41no—
60C2×D4×C43C2×Q812yes—
61C2×D4×C43#4112yes—
62C22×C4×C43—21no—
63C22×C4×C43—21no—
64C22×C4×C43—21no—
65C22×C4×C43—21no—
66C22×C4×C43—22no—
67C22×C4×C43—22no—
68C22×C4×C43—42no—
69C22×C4×C43—42no—
70C22×C4×C43—42no—
71C22×C4×C43—42no—
72C22×C4×C43C22⋊C411yescharacteristic
73C22×C4×C43C22⋊C411yescharacteristic
74C22×C4×C43C22⋊C411yescharacteristic
75C22×C4×C43C22⋊C411yescharacteristic
76C22×C4×C43C22×C411yescharacteristic
77C4⋊C4×C43—24no—
78C4⋊C4×C43—41no—
79C4⋊C4×C43—42no—
80C4⋊C4×C43—44no—
81C4⋊C4×C43—44no—
82C4⋊C4×C43—42no—
83C4⋊C4×C43—82no—
84C22⋊C4×C43—24no—
85C22⋊C4×C43—41no—
86C22⋊C4×C43—41no—
87C22⋊C4×C43—42no—
88C22⋊C4×C43—42no—
89C22⋊C4×C43—44no—
90C22⋊C4×C43—44no—
91C22⋊C4×C43—42no—
92C42×C43—21no—
93C42×C43—21no—
94C42×C43—42no—
95C42×C43—82no—
96C23×C43—21no—
97C23×C43—21no—
98C23×C43—21no—
99C23×C43—21no—
100C23×C43—41no—
101C23×C43—41no—
102C23×C43—41no—
103C23×C43—41no—
104C23×C43C2×C22⋊C411yescharacteristic
105C23×C43C22⋊Q812yes—
106C23×C43#12411yescharacteristic
107C23×C43C4⋊Q811yescharacteristic
108Q8×C43—82no—
109Q8×C43—82no—
110D4×C43—42no—
111D4×C43—42no—
112C2×C4×C43—21no—
113C2×C4×C43—21no—
114C2×C4×C43—22no—
115C2×C4×C43—24no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—42no—
120C2×C4×C43—42no—
121C2×C4×C43—42no—
122C2×C4×C43—42no—
123C2×C4×C43—41no—
124C2×C4×C43—41no—
125C2×C4×C43—41no—
126C2×C4×C43—44no—
127C2×C4×C43—42no—
128C2×C4×C43—42no—
129C2×C4×C43—42no—
130C2×C4×C43—81no—
131C2×C4×C43—81no—
132C2×C4×C43—82no—
133C2×C4×C43—82no—
134C2×C4×C43—82no—
135C2×C4×C43—82no—
136C2×C4×C43—82no—
137C2×C4×C43#9911yescharacteristic
138C2×C4×C43#9911yescharacteristic
139C2×C4×C43C4×Q812yes—
140#13298C4311yesmaximal, characteristic, direct product factor, Sylow
141C22×C43—21no—
142C22×C43—21no—
143C22×C43—22no—
144C22×C43—21no—
145C22×C43—21no—
146C22×C43—42no—
147C22×C43—41no—
148C22×C43—41no—
149C22×C43—41no—
150C22×C43—41no—
151C22×C43—41no—
152C22×C43—41no—
153C22×C43—81no—
154C22×C43—81no—
155C22×C43#39111yescharacteristic
156C22×C43C2×#9911yescharacteristic
157C22×C43#41011yescharacteristic
158C4×C43—21no—
159C4×C43—22no—
160C4×C43—44no—
161C4×C43—41no—
162C4×C43—41no—
163C4×C43—41no—
164C4×C43—84no—
165C4×C43—82no—
166C4×C43—162no—
167C4×C43#35312yes—
168#2542C2×C4311yescharacteristic
169#1799C2×C4311yescharacteristic
170C4×#99C2×C4311yescharacteristic
171#1393C2×C4314yes—
172C2×C43—21no—
173C2×C43—21no—
174C2×C43—42no—
175C2×C43—41no—
176C2×C43—41no—
177C2×C43#199611yescharacteristic
178C2×C43C2×#35311yescharacteristic
179C2×C43#212911yescharacteristic
180C2×C4⋊Q8C4×C4311yescharacteristic, complemented
181C2×C22⋊Q8—21no—
182C2×C22⋊Q8—21no—
183C2×C4×D4C22×C4311yescharacteristic
184C2×#99C22×C4312yes—
185C2×#99C22×C4312yes—
186#399—21no—
187#399—21no—
188#390C22×C4312yes—
189#384C4×C4312yescomplemented
190#380—21no—
191C4×C4⋊C4C4×C4311yescharacteristic, complemented
192C4×C22⋊C4—21no—
193#342—21no—
194#342—21no—
195C43#1329811yescharacteristic, direct product factor, Sylow
196C22×Q8—21no—
197C22×D4C23×C4311yescharacteristic
198C23×C4D4×C4311yescharacteristic
199C23×C4D4×C4311yescharacteristic
200C4⋊Q8—41no—
201C4⋊Q8—41no—
202C22⋊Q8—44no—
203C22⋊Q8—44no—
204C4×D4—41no—
205C4×D4—41no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—22no—
208C2×C4⋊C4—22no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—41no—
211C2×C4⋊C4C2×C4×C4312yes—
212C2×C4⋊C4C2×C4×C4311yescharacteristic
213C2×C22⋊C4—22no—
214C2×C22⋊C4—22no—
215C2×C22⋊C4—22no—
216C2×C22⋊C4—22no—
217C2×C22⋊C4D4×C4311yescharacteristic
218C2×C22⋊C4D4×C4311yescharacteristic
219C2×C42—41no—
220C2×C42C2×C4×C4311yescharacteristic
221C2×C42C2×C4×C4312yes—
222#99—22no—
223#99—24no—
224#99Q8×C4314yescomplemented
225#95—21no—
226#95—41no—
227#95—41no—
228C24C2×D4×C4311yescharacteristic
229C24C2×D4×C4311yescharacteristic
230C2×Q8—42no—
231C2×Q8—42no—
232C2×Q8—41no—
233C2×Q8—41no—
234C2×D4—41no—
235C2×D4—41no—
236C2×D4C2×Q8×C4312yes—
237C2×D4#41×C4312yes—
238C22×C4—22no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—22no—
244C22×C4—42no—
245C22×C4—42no—
246C22×C4—42no—
247C22×C4—42no—
248C22×C4C22⋊C4×C4311yescharacteristic
249C22×C4C22⋊C4×C4311yescharacteristic
250C22×C4C22⋊C4×C4311yescharacteristic
251C22×C4C22⋊C4×C4311yescharacteristic
252C22×C4C22×C4×C4311yescharacteristic
253C4⋊C4—24no—
254C4⋊C4—41no—
255C4⋊C4—42no—
256C4⋊C4—44no—
257C4⋊C4—44no—
258C4⋊C4—42no—
259C4⋊C4—82no—
260C22⋊C4—24no—
261C22⋊C4—41no—
262C22⋊C4—41no—
263C22⋊C4—44no—
264C22⋊C4—44no—
265C22⋊C4—42no—
266C22⋊C4—42no—
267C22⋊C4—42no—
268C42—21no—
269C42—21no—
270C42—42no—
271C42—82no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—41no—
277C23—41no—
278C23—41no—
279C23—41no—
280C23C2×C22⋊C4×C4311yescharacteristic
281C23C22⋊Q8×C4312yes—
282C23#124×C4311yescharacteristic
283C23C4⋊Q8×C4311yescharacteristic
284Q8—82no—
285Q8—82no—
286D4—42no—
287D4—42no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—22no—
291C2×C4—24no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—44no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4—82no—
309C2×C4—82no—
310C2×C4—82no—
311C2×C4—82no—
312C2×C4—82no—
313C2×C4#99×C4311yescharacteristic
314C2×C4#99×C4311yescharacteristic
315C2×C4C4×Q8×C4312yes—
316C22—21no—
317C22—21no—
318C22—22no—
319C22—21no—
320C22—21no—
321C22—42no—
322C22—41no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—81no—
329C22—81no—
330C22C43×#39111yescharacteristic
331C22C2×#99×C4311yescharacteristic
332C22C43×#41011yescharacteristic
333C4—21no—
334C4—22no—
335C4—44no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—84no—
340C4—82no—
341C4—162no—
342C4C43×#35312yes—
343C2—21no—
344C2—21no—
345C2—42no—
346C2—41no—
347C2—41no—
348C2C43×#199611yescharacteristic
349C2C2×C43×#35311yescharacteristic
350C2C43×#212911yescharacteristic
subgroupG/H
center, socleC22×C43C2×#99
commutatorC22×C4C22×C4×C43
Frattini, cosocleC22×D4C23×C43
prime radicalC22×D4×C43C23
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C22×C4×C43 ◁ C2×C4×D4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
5. C2×C4⋊Q8×C43C4semidirect
14. C43×#384C4semidirect
16. C4×C4⋊C4×C43C4semidirect
48. #99×C43Q8semidirect
140. #13298C43direct (N × H)
180. C2×C4⋊Q8C4×C43semidirect
189. #384C4×C43semidirect
191. C4×C4⋊C4C4×C43semidirect
195. C43#13298direct (N × H)
224. #99Q8×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#25422
C43×#17992
C4×#99×C432
C43×#13932
#1329843