Finite Group Databasebeta

← C43×#7658 #24927675

Subgroups — C43×#7658 #24927675

Order 11008.

544 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#2854C211yesmaximal, characteristic
2C43×#1797C211yesmaximal, characteristic, complemented
3C4×C22⋊C8×C43C211yesmaximal, characteristic, complemented
4C43×#1271C212yesmaximal, complemented
5C43×#1270C212yesmaximal, complemented
6C2×#123×C43—21no—
7C2×#121×C43C411yescharacteristic
8C22×C42×C43C2211yescharacteristic
9C2×C4⋊C8×C43—21no—
10C2×C22⋊C8×C43—21no—
11C2×C22⋊C8×C43—21no—
12C2×C4×C8×C43—21no—
13C43×#390C411yescharacteristic
14C43×#390C2211yescharacteristic
15C43×#389C411yescharacteristic
16C43×#389C2211yescharacteristic
17C43×#388—21no—
18C43×#388—21no—
19C43×#386—21no—
20C43×#380C411yescharacteristic
21C43×#336C2212yes—
22C43×#336C2212yes—
23C22×D4×C43—21no—
24C22×D4×C43C2×C411yescharacteristic
25C23×C4×C43C2×C411yescharacteristic
26C23×C4×C43D411yescharacteristic
27C23×C4×C43D411yescharacteristic
28C22×C8×C43—22no—
29C22×C8×C43—22no—
30#123×C43—42no—
31#123×C43—42no—
32#121×C43—42no—
33C2×C4⋊C4×C43—21no—
34C2×C4⋊C4×C43—21no—
35C2×C4⋊C4×C43C2×C411yescharacteristic
36C2×C4⋊C4×C43C2×C411yescharacteristic
37C2×C4⋊C4×C43C2×C411yescharacteristic
38C2×C22⋊C4×C43—21no—
39C2×C22⋊C4×C43—21no—
40C2×C22⋊C4×C43—21no—
41C2×C22⋊C4×C43—21no—
42C2×C22⋊C4×C43—21no—
43C2×C22⋊C4×C43—21no—
44C2×C42×C43—42no—
45C2×C42×C43C2×C411yescharacteristic
46C2×C42×C43D411yescharacteristic
47C2×C42×C43D411yescharacteristic
48C2×C42×C43C2311yescharacteristic
49C4⋊C8×C43—42no—
50C22⋊C8×C43—24no—
51C22⋊C8×C43—42no—
52C4×C8×C43—42no—
53#95×C43—21no—
54#95×C43—21no—
55#95×C43—21no—
56C24×C43—21no—
57C24×C43C22⋊C411yescharacteristic
58C2×D4×C43—22no—
59C2×D4×C43—42no—
60C2×D4×C43—42no—
61C2×D4×C43—42no—
62C2×D4×C43—41no—
63C2×D4×C43—41no—
64C22×C4×C43—22no—
65C22×C4×C43—22no—
66C22×C4×C43—22no—
67C22×C4×C43—22no—
68C22×C4×C43—21no—
69C22×C4×C43—21no—
70C22×C4×C43—21no—
71C22×C4×C43—41no—
72C22×C4×C43—41no—
73C22×C4×C43—41no—
74C22×C4×C43—41no—
75C22×C4×C43C22⋊C411yescharacteristic
76C22×C4×C43C22⋊C411yescharacteristic
77C22×C4×C43C22⋊C411yescharacteristic
78C22×C4×C43D812yes—
79C22×C4×C43SD1612yes—
80C22×C4×C43C22×C411yescharacteristic
81C22×C4×C43C2×D411yescharacteristic
82C22×C4×C43C2×D411yescharacteristic
83C2×C8×C43—24no—
84C2×C8×C43—42no—
85C2×C8×C43—42no—
86C2×C8×C43—42no—
87C2×C8×C43—42no—
88C2×C8×C43—42no—
89C4⋊C4×C43—22no—
90C4⋊C4×C43—41no—
91C4⋊C4×C43—41no—
92C4⋊C4×C43—42no—
93C4⋊C4×C43—41no—
94C4⋊C4×C43—41no—
95C22⋊C4×C43—42no—
96C22⋊C4×C43—42no—
97C22⋊C4×C43—42no—
98C22⋊C4×C43—41no—
99C22⋊C4×C43—41no—
100C22⋊C4×C43—42no—
101C22⋊C4×C43—42no—
102C42×C43—22no—
103C42×C43—22no—
104C42×C43—41no—
105C42×C43—41no—
106C23×C43—21no—
107C23×C43—21no—
108C23×C43—21no—
109C23×C43—21no—
110C23×C43—21no—
111C23×C43—21no—
112C23×C43—41no—
113C23×C43—41no—
114C23×C43—41no—
115C23×C43—41no—
116C23×C43—41no—
117C23×C43—41no—
118C23×C43—41no—
119C23×C43#10212yes—
120C23×C43C2×C22⋊C411yescharacteristic
121D4×C43—82no—
122D4×C43—84no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43—21no—
133C2×C4×C43—21no—
134C2×C4×C43—21no—
135C2×C4×C43—42no—
136C2×C4×C43—42no—
137C2×C4×C43—44no—
138C2×C4×C43—44no—
139C2×C4×C43—41no—
140C2×C4×C43—41no—
141C2×C4×C43—41no—
142C2×C4×C43—41no—
143C2×C4×C43—41no—
144C2×C4×C43—41no—
145C2×C4×C43—41no—
146C2×C4×C43—41no—
147C2×C4×C43—41no—
148C2×C4×C43#9912yes—
149C2×C4×C43#10212yes—
150C2×C4×C43#10412yes—
151C2×C4×C43#13112yes—
152C2×C4×C43C2×D811yescharacteristic
153C2×C4×C43C2×SD1611yescharacteristic
154C2×C4×C43#13512yes—
155C8×C43—44no—
156C8×C43—82no—
157#7658C4311yesmaximal, characteristic, direct product factor, Sylow
158C22×C43—22no—
159C22×C43—22no—
160C22×C43—22no—
161C22×C43—41no—
162C22×C43—41no—
163C22×C43—41no—
164C22×C43—41no—
165C22×C43—81no—
166C22×C43—81no—
167C22×C43—81no—
168C22×C43—81no—
169C22×C43—81no—
170C22×C43—81no—
171C22×C43—81no—
172C22×C43#40811yescharacteristic
173C22×C43C2×#9911yescharacteristic
174C22×C43#41311yescharacteristic
175C22×C43C2×#10211yescharacteristic
176C22×C43#41611yescharacteristic
177C22×C43C2×#10411yescharacteristic
178C22×C43#42111yescharacteristic
179C4×C43—22no—
180C4×C43—22no—
181C4×C43—22no—
182C4×C43—22no—
183C4×C43—21no—
184C4×C43—22no—
185C4×C43—21no—
186C4×C43—81no—
187C4×C43—81no—
188C4×C43—81no—
189#2854C2×C4311yescharacteristic
190#1797C2×C4311yescharacteristic, complemented
191C4×C22⋊C8C2×C4311yescharacteristic, complemented
192#1271C2×C4312yescomplemented
193#1270C2×C4312yescomplemented
194C2×C43—42no—
195C2×C43—161no—
196C2×C43#146811yescharacteristic
197C2×C43#148211yescharacteristic
198C2×C43#149211yescharacteristic
199C2×C43#150111yescharacteristic
200C2×C43#151911yescharacteristic
201C2×C43#152911yescharacteristic
202C2×C43#154011yescharacteristic
203C2×#123—21no—
204C2×#121C4×C4311yescharacteristic
205C22×C42C22×C4311yescharacteristic
206C2×C4⋊C8—21no—
207C2×C22⋊C8—21no—
208C2×C22⋊C8—21no—
209C2×C4×C8—21no—
210#390C4×C4311yescharacteristic
211#390C22×C4311yescharacteristic
212#389C4×C4311yescharacteristic
213#389C22×C4311yescharacteristic
214#388—21no—
215#388—21no—
216#386—21no—
217#380C4×C4311yescharacteristic
218#336C22×C4312yes—
219#336C22×C4312yes—
220C43#765811yescharacteristic, direct product factor, Sylow
221C22×D4—21no—
222C22×D4C2×C4×C4311yescharacteristic
223C23×C4C2×C4×C4311yescharacteristic
224C23×C4D4×C4311yescharacteristic
225C23×C4D4×C4311yescharacteristic
226C22×C8—22no—
227C22×C8—22no—
228#123—42no—
229#123—42no—
230#121—42no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4C2×C4×C4311yescharacteristic
234C2×C4⋊C4C2×C4×C4311yescharacteristic
235C2×C4⋊C4C2×C4×C4311yescharacteristic
236C2×C22⋊C4—21no—
237C2×C22⋊C4—21no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—21no—
240C2×C22⋊C4—21no—
241C2×C22⋊C4—21no—
242C2×C42—42no—
243C2×C42C2×C4×C4311yescharacteristic
244C2×C42D4×C4311yescharacteristic
245C2×C42D4×C4311yescharacteristic
246C2×C42C23×C4311yescharacteristic
247C4⋊C8—42no—
248C22⋊C8—24no—
249C22⋊C8—42no—
250C4×C8—42no—
251#95—21no—
252#95—21no—
253#95—21no—
254C24—21no—
255C24C22⋊C4×C4311yescharacteristic
256C2×D4—22no—
257C2×D4—41no—
258C2×D4—41no—
259C2×D4—42no—
260C2×D4—42no—
261C2×D4—42no—
262C22×C4—22no—
263C22×C4—22no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—41no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4C22⋊C4×C4311yescharacteristic
274C22×C4C22⋊C4×C4311yescharacteristic
275C22×C4C22⋊C4×C4311yescharacteristic
276C22×C4D8×C4312yes—
277C22×C4SD16×C4312yes—
278C22×C4C22×C4×C4311yescharacteristic
279C22×C4C2×D4×C4311yescharacteristic
280C22×C4C2×D4×C4311yescharacteristic
281C2×C8—24no—
282C2×C8—42no—
283C2×C8—42no—
284C2×C8—42no—
285C2×C8—42no—
286C2×C8—42no—
287C4⋊C4—22no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—42no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C22⋊C4—42no—
294C22⋊C4—42no—
295C22⋊C4—42no—
296C22⋊C4—42no—
297C22⋊C4—41no—
298C22⋊C4—41no—
299C22⋊C4—42no—
300C42—22no—
301C42—22no—
302C42—41no—
303C42—41no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—21no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23#102×C4312yes—
318C23C2×C22⋊C4×C4311yescharacteristic
319D4—82no—
320D4—84no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—44no—
336C2×C4—44no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4#99×C4312yes—
347C2×C4#102×C4312yes—
348C2×C4#104×C4312yes—
349C2×C4#131×C4312yes—
350C2×C4C2×D8×C4311yescharacteristic
351C2×C4C2×SD16×C4311yescharacteristic
352C2×C4#135×C4312yes—
353C8—44no—
354C8—82no—
355C22—22no—
356C22—22no—
357C22—22no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—81no—
363C22—81no—
364C22—81no—
365C22—81no—
366C22—81no—
367C22—81no—
368C22—81no—
369C22C43×#40811yescharacteristic
370C22C2×#99×C4311yescharacteristic
371C22C43×#41311yescharacteristic
372C22C2×#102×C4311yescharacteristic
373C22C43×#41611yescharacteristic
374C22C2×#104×C4311yescharacteristic
375C22C43×#42111yescharacteristic
376C4—22no—
377C4—22no—
378C4—22no—
379C4—22no—
380C4—21no—
381C4—22no—
382C4—21no—
383C4—81no—
384C4—81no—
385C4—81no—
386C2—42no—
387C2—161no—
388C2C43×#146811yescharacteristic
389C2C43×#148211yescharacteristic
390C2C43×#149211yescharacteristic
391C2C43×#150111yescharacteristic
392C2C43×#151911yescharacteristic
393C2C43×#152911yescharacteristic
394C2C43×#154011yescharacteristic
subgroupG/H
center, socleC23×C43C2×C22⋊C4
commutatorC22×C4C22×C4×C43
Frattini, cosocleC2×C42C23×C43
prime radicalC2×#121×C43C4
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
2. C43×#1797C2semidirect
3. C4×C22⋊C8×C43C2semidirect
4. C43×#1271C2semidirect
5. C43×#1270C2semidirect
157. #7658C43direct (N × H)
190. #1797C2×C43semidirect
191. C4×C22⋊C8C2×C43semidirect
192. #1271C2×C43semidirect
193. #1270C2×C43semidirect
220. C43#7658direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#28542
C43×#17972
C4×C22⋊C8×C432
C43×#12712
C43×#12702
#765843