Finite Group Databasebeta

← C43×#9352 #24929369

Subgroups — C43×#9352 #24929369

Order 11008.

414 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3080C211yesmaximal, characteristic
2C43×#2971C211yesmaximal, characteristic
3C43×#1528C211yesmaximal, characteristic, complemented
4C43×#1488C211yesmaximal, characteristic
5C43×#1470C211yesmaximal, characteristic, complemented
6C43×#1307C211yesmaximal, characteristic, complemented
7C43×#1299C211yesmaximal, characteristic, complemented
8C2×#125×C43C2211yescharacteristic
9C4×#41×C43C2211yescharacteristic
10C43×#479—21no—
11C43×#479—21no—
12C43×#478—21no—
13C43×#478—21no—
14C8×Q8×C43—21no—
15C43×#436—21no—
16C43×#436—22no—
17C43×#432—21no—
18C43×#432C2211yescharacteristic
19C43×#432C2211yescharacteristic
20C43×#431C2211yescharacteristic
21C43×#428C411yescharacteristic
22C43×#428C411yescharacteristic
23C43×#423C2211yescharacteristic
24C43×#417C411yescharacteristic
25C43×#417C411yescharacteristic
26C4×M16×C43—21no—
27C4×M16×C43C2211yescharacteristic
28C43×#330—21no—
29C43×#330—21no—
30C43×Q8⋊C8—21no—
31C43×D4⋊C8—21no—
32C43×#324—22no—
33C2×#41×C43C2×C411yescharacteristic
34C2×M16×C43—22no—
35C2×M16×C43—21no—
36C2×M16×C43C2×C411yescharacteristic
37C2×M16×C43C2×C411yescharacteristic
38#125×C43—21no—
39#125×C43—21no—
40#125×C43—21no—
41#125×C43—21no—
42C4×Q8×C43D411yescharacteristic
43C4×Q8×C43D411yescharacteristic
44C4×D4×C43—21no—
45C4×D4×C43—21no—
46C4×D4×C43D411yescharacteristic
47C4×D4×C43D411yescharacteristic
48#117×C43—21no—
49#117×C43C2×C411yescharacteristic
50C2×C4⋊C4×C43—21no—
51C2×C4⋊C4×C43—21no—
52C2×C4⋊C4×C43C2×C411yescharacteristic
53C2×C4⋊C4×C43C2×C411yescharacteristic
54C2×C42×C43—21no—
55C2×C42×C43C2311yescharacteristic
56#107×C43—21no—
57#107×C43—21no—
58#106×C43—21no—
59#106×C43—21no—
60C4⋊C8×C43—22no—
61C4⋊C8×C43—21no—
62C4⋊C8×C43—21no—
63C4⋊C8×C43—21no—
64C4⋊C8×C43—21no—
65C4⋊C8×C43—21no—
66#103×C43—21no—
67#103×C43—21no—
68#102×C43—21no—
69#102×C43—21no—
70C22⋊C8×C43—22no—
71C22⋊C8×C43—21no—
72C22⋊C8×C43—21no—
73C22⋊C8×C43D412yes—
74#97×C43—21no—
75#97×C43—21no—
76#97×C43D411yescharacteristic
77#97×C43D411yescharacteristic
78C4×C8×C43—22no—
79C4×C8×C43—21no—
80C4×C8×C43—21no—
81#41×C43—22no—
82#41×C43—41no—
83C2×Q8×C43C22⋊C411yescharacteristic
84C2×D4×C43—21no—
85C2×D4×C43C22⋊C411yescharacteristic
86C22×C4×C43—21no—
87C22×C4×C43—21no—
88C22×C4×C43—21no—
89C22×C4×C43—21no—
90C22×C4×C43—21no—
91C22×C4×C43C22×C411yescharacteristic
92C22×C4×C43C2×D411yescharacteristic
93C22×C4×C43#4111yescharacteristic
94M16×C43—42no—
95M16×C43—44no—
96M16×C43—41no—
97M16×C43—41no—
98C2×C8×C43—21no—
99C2×C8×C43—21no—
100C2×C8×C43—21no—
101C2×C8×C43—22no—
102C2×C8×C43—21no—
103C2×C8×C43—41no—
104C2×C8×C43—41no—
105C4⋊C4×C43—21no—
106C4⋊C4×C43—21no—
107C4⋊C4×C43—21no—
108C4⋊C4×C43—21no—
109C4⋊C4×C43—21no—
110C4⋊C4×C43—21no—
111C4⋊C4×C43—41no—
112C4⋊C4×C43—41no—
113C4⋊C4×C43—41no—
114C4⋊C4×C43—41no—
115C4⋊C4×C43C22⋊C411yescharacteristic
116C4⋊C4×C43C22⋊C411yescharacteristic
117C22⋊C4×C43—21no—
118C22⋊C4×C43—21no—
119C22⋊C4×C43—21no—
120C42×C43—21no—
121C42×C43—21no—
122C42×C43—21no—
123C42×C43C2×D411yescharacteristic
124C42×C43C2×D411yescharacteristic
125C42×C43C2×D411yescharacteristic
126C42×C43#4111yescharacteristic
127C23×C43—21no—
128C23×C43C4×D411yescharacteristic
129Q8×C43—21no—
130Q8×C43#10112yes—
131D4×C43—21no—
132D4×C43—21no—
133D4×C43—42no—
134C2×C4×C43—21no—
135C2×C4×C43—21no—
136C2×C4×C43—21no—
137C2×C4×C43—21no—
138C2×C4×C43—21no—
139C2×C4×C43—41no—
140C2×C4×C43—41no—
141C2×C4×C43—42no—
142C2×C4×C43—42no—
143C2×C4×C43—42no—
144C2×C4×C43—41no—
145C2×C4×C43—41no—
146C2×C4×C43—81no—
147C2×C4×C43—81no—
148C2×C4×C43C2×C22⋊C411yescharacteristic
149C2×C4×C43C4×D411yescharacteristic
150C2×C4×C43#12011yescharacteristic
151C2×C4×C43#12111yescharacteristic
152C2×C4×C43#12111yescharacteristic
153C2×C4×C43#12311yescharacteristic
154C8×C43—22no—
155C8×C43—42no—
156C8×C43—41no—
157C8×C43—41no—
158C8×C43—41no—
159C8×C43—81no—
160C8×C43—81no—
161#9352C4311yesmaximal, characteristic, direct product factor, Sylow
162C22×C43—21no—
163C22×C43—21no—
164C22×C43—21no—
165C22×C43—41no—
166C22×C43—41no—
167C22×C43—41no—
168C22×C43#38611yescharacteristic
169C4×C43—21no—
170C4×C43—21no—
171C4×C43—21no—
172C4×C43—22no—
173C4×C43—21no—
174C4×C43—21no—
175C4×C43—41no—
176C4×C43—41no—
177C4×C43—81no—
178C4×C43—81no—
179C4×C43C2×#10111yescharacteristic
180C4×C43#41311yescharacteristic
181#3080C2×C4311yescharacteristic
182#2971C2×C4311yescharacteristic
183#1528C2×C4311yescharacteristic, complemented
184#1488C2×C4311yescharacteristic
185#1470C2×C4311yescharacteristic, complemented
186#1307C2×C4311yescharacteristic, complemented
187#1299C2×C4311yescharacteristic, complemented
188C2×C43—41no—
189C2×C43—81no—
190C2×C43#188111yescharacteristic
191C2×C43#190111yescharacteristic
192C2×C43#190611yescharacteristic
193C2×#125C22×C4311yescharacteristic
194C4×#41C22×C4311yescharacteristic
195#479—21no—
196#479—21no—
197#478—21no—
198#478—21no—
199C8×Q8—21no—
200#436—21no—
201#436—22no—
202#432—21no—
203#432C22×C4311yescharacteristic
204#432C22×C4311yescharacteristic
205#431C22×C4311yescharacteristic
206#428C4×C4311yescharacteristic
207#428C4×C4311yescharacteristic
208#423C22×C4311yescharacteristic
209#417C4×C4311yescharacteristic
210#417C4×C4311yescharacteristic
211C4×M16—21no—
212C4×M16C22×C4311yescharacteristic
213#330—21no—
214#330—21no—
215Q8⋊C8—21no—
216D4⋊C8—21no—
217#324—22no—
218C43#935211yescharacteristic, direct product factor, Sylow
219C2×#41C2×C4×C4311yescharacteristic
220C2×M16—22no—
221C2×M16—21no—
222C2×M16C2×C4×C4311yescharacteristic
223C2×M16C2×C4×C4311yescharacteristic
224#125—21no—
225#125—21no—
226#125—21no—
227#125—21no—
228C4×Q8D4×C4311yescharacteristic
229C4×Q8D4×C4311yescharacteristic
230C4×D4—21no—
231C4×D4—21no—
232C4×D4D4×C4311yescharacteristic
233C4×D4D4×C4311yescharacteristic
234#117—21no—
235#117C2×C4×C4311yescharacteristic
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4C2×C4×C4311yescharacteristic
239C2×C4⋊C4C2×C4×C4311yescharacteristic
240C2×C42—21no—
241C2×C42C23×C4311yescharacteristic
242#107—21no—
243#107—21no—
244#106—21no—
245#106—21no—
246C4⋊C8—22no—
247C4⋊C8—21no—
248C4⋊C8—21no—
249C4⋊C8—21no—
250C4⋊C8—21no—
251C4⋊C8—21no—
252#103—21no—
253#103—21no—
254#102—21no—
255#102—21no—
256C22⋊C8—22no—
257C22⋊C8—21no—
258C22⋊C8—21no—
259C22⋊C8D4×C4312yes—
260#97—21no—
261#97—21no—
262#97D4×C4311yescharacteristic
263#97D4×C4311yescharacteristic
264C4×C8—22no—
265C4×C8—21no—
266C4×C8—21no—
267#41—22no—
268#41—41no—
269C2×Q8C22⋊C4×C4311yescharacteristic
270C2×D4—21no—
271C2×D4C22⋊C4×C4311yescharacteristic
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4C22×C4×C4311yescharacteristic
278C22×C4C2×D4×C4311yescharacteristic
279C22×C4#41×C4311yescharacteristic
280M16—42no—
281M16—44no—
282M16—41no—
283M16—41no—
284C2×C8—21no—
285C2×C8—21no—
286C2×C8—21no—
287C2×C8—22no—
288C2×C8—21no—
289C2×C8—41no—
290C2×C8—41no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4C22⋊C4×C4311yescharacteristic
302C4⋊C4C22⋊C4×C4311yescharacteristic
303C22⋊C4—21no—
304C22⋊C4—21no—
305C22⋊C4—21no—
306C42—21no—
307C42—21no—
308C42—21no—
309C42C2×D4×C4311yescharacteristic
310C42C2×D4×C4311yescharacteristic
311C42C2×D4×C4311yescharacteristic
312C42#41×C4311yescharacteristic
313C23—21no—
314C23C4×D4×C4311yescharacteristic
315Q8—21no—
316Q8#101×C4312yes—
317D4—21no—
318D4—21no—
319D4—42no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4C2×C22⋊C4×C4311yescharacteristic
335C2×C4C4×D4×C4311yescharacteristic
336C2×C4#120×C4311yescharacteristic
337C2×C4#121×C4311yescharacteristic
338C2×C4#121×C4311yescharacteristic
339C2×C4#123×C4311yescharacteristic
340C8—22no—
341C8—42no—
342C8—41no—
343C8—41no—
344C8—41no—
345C8—81no—
346C8—81no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22C43×#38611yescharacteristic
354C4—21no—
355C4—21no—
356C4—21no—
357C4—22no—
358C4—21no—
359C4—21no—
360C4—41no—
361C4—41no—
362C4—81no—
363C4—81no—
364C4C2×#101×C4311yescharacteristic
365C4C43×#41311yescharacteristic
366C2—41no—
367C2—81no—
368C2C43×#188111yescharacteristic
369C2C43×#190111yescharacteristic
370C2C43×#190611yescharacteristic
subgroupG/H
center, socleC22×C43#386
commutatorC22×C4C22×C4×C43
Frattini, cosocleC2×C42C23×C43
prime radicalC2×#41×C43C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C2×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
3. C43×#1528C2semidirect
5. C43×#1470C2semidirect
6. C43×#1307C2semidirect
7. C43×#1299C2semidirect
161. #9352C43direct (N × H)
183. #1528C2×C43semidirect
185. #1470C2×C43semidirect
186. #1307C2×C43semidirect
187. #1299C2×C43semidirect
218. C43#9352direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#30802
C43×#29712
C43×#15282
C43×#14882
C43×#14702
C43×#13072
C43×#12992
#935243