Finite Group Databasebeta

← C43×#9300 #24929317

Subgroups — C43×#9300 #24929317

Order 11008.

508 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3226C211yesmaximal, characteristic
2C43×#2327C211yesmaximal, characteristic, complemented
3C43×#1963C211yesmaximal, characteristic
4C43×#1546C211yesmaximal, characteristic, complemented
5C43×#1517C211yesmaximal, characteristic
6C43×#1286C211yesmaximal, characteristic, complemented
7C43×#1274C211yesmaximal, characteristic, complemented
8C43×#532C2211yescharacteristic
9C2×C4⋊Q8×C43C2211yescharacteristic
10C2×C4×Q8×C43—21no—
11C43×#500C412yescomplemented
12C43×#486C412yescomplemented
13C43×#480—22no—
14C43×#474—22no—
15C43×#431C2211yescharacteristic
16C43×#431C2211yescharacteristic
17C43×#423C2211yescharacteristic
18C2×#104×C43—21no—
19C2×#104×C43—21no—
20C43×#391—21no—
21C43×#387—22no—
22C43×#387—22no—
23C43×#382C2211yescharacteristic
24C43×#376C2211yescharacteristic
25C43×#332—22no—
26C43×#327—22no—
27C2×#41×C43—21no—
28C22×Q8×C43—21no—
29C2×M16×C43—21no—
30C4⋊Q8×C43—21no—
31C4⋊Q8×C43—21no—
32C4⋊Q8×C43C2×C411yescharacteristic
33C4⋊Q8×C43C2×C412yes—
34C4⋊Q8×C43D412yes—
35#127×C43C2×C411yescharacteristic
36#124×C43—21no—
37#121×C43—21no—
38#121×C43—21no—
39C4×Q8×C43—42no—
40C4×Q8×C43—42no—
41C4×D4×C43—21no—
42C4×D4×C43—21no—
43C2×C4⋊C4×C43—21no—
44C2×C4⋊C4×C43—22no—
45C2×C4⋊C4×C43—21no—
46C2×C4⋊C4×C43D412yes—
47C2×C42×C43—22no—
48C2×C42×C43D411yescharacteristic
49C2×C42×C43D411yescharacteristic
50C2×C42×C43C2311yescharacteristic
51#107×C43—24no—
52C4⋊C8×C43—21no—
53C4⋊C8×C43—21no—
54C4⋊C8×C43—21no—
55C4⋊C8×C43—21no—
56#104×C43—42no—
57#104×C43—42no—
58#102×C43—24no—
59C22⋊C8×C43—21no—
60C22⋊C8×C43—21no—
61C4×C8×C43—21no—
62C4×C8×C43C2×C412yes—
63#95×C43—24no—
64#95×C43—21no—
65#95×C43—21no—
66#95×C43—21no—
67#95×C43D412yes—
68#41×C43—41no—
69#41×C43—41no—
70#41×C43—41no—
71#41×C43—41no—
72C2×Q8×C43—22no—
73C2×Q8×C43—22no—
74C2×Q8×C43—21no—
75C2×Q8×C43—41no—
76C2×Q8×C43—41no—
77C2×Q8×C43—41no—
78C2×Q8×C43—41no—
79C2×D4×C43—21no—
80C2×D4×C43—21no—
81C2×D4×C43—21no—
82C2×D4×C43—41no—
83C22×C4×C43—21no—
84C22×C4×C43—22no—
85C22×C4×C43—21no—
86C22×C4×C43—22no—
87C22×C4×C43—41no—
88C22×C4×C43C2×D411yescharacteristic
89C22×C4×C43C2×D411yescharacteristic
90C22×C4×C43C2×D411yescharacteristic
91M16×C43—41no—
92M16×C43—41no—
93C2×C8×C43—22no—
94C2×C8×C43—41no—
95C2×C8×C43—41no—
96C4⋊C4×C43—22no—
97C4⋊C4×C43—22no—
98C4⋊C4×C43—22no—
99C4⋊C4×C43—21no—
100C4⋊C4×C43—21no—
101C4⋊C4×C43—44no—
102C4⋊C4×C43—41no—
103C4⋊C4×C43—41no—
104C4⋊C4×C43C22⋊C414yes—
105C22⋊C4×C43—41no—
106C22⋊C4×C43—41no—
107C42×C43—21no—
108C42×C43—21no—
109C42×C43—21no—
110C42×C43—44no—
111C42×C43D812yes—
112C42×C43C22×C411yescharacteristic
113C42×C43C2×D411yescharacteristic
114C42×C43#4111yescharacteristic
115C42×C43#4111yescharacteristic
116C23×C43—41no—
117C23×C43#12011yescharacteristic
118Q8×C43—42no—
119Q8×C43—42no—
120Q8×C43—42no—
121Q8×C43—42no—
122Q8×C43—41no—
123Q8×C43—41no—
124D4×C43—42no—
125D4×C43—41no—
126D4×C43—41no—
127D4×C43—81no—
128D4×C43—81no—
129D4×C43—81no—
130C2×C4×C43—24no—
131C2×C4×C43—22no—
132C2×C4×C43—41no—
133C2×C4×C43—41no—
134C2×C4×C43—41no—
135C2×C4×C43—41no—
136C2×C4×C43—42no—
137C2×C4×C43—42no—
138C2×C4×C43—41no—
139C2×C4×C43—42no—
140C2×C4×C43—41no—
141C2×C4×C43—42no—
142C2×C4×C43—41no—
143C2×C4×C43—42no—
144C2×C4×C43—41no—
145C2×C4×C43—81no—
146C2×C4×C43—81no—
147C2×C4×C43C2×C22⋊C411yescharacteristic
148C2×C4×C43C4×D411yescharacteristic
149C2×C4×C43C4×D411yescharacteristic
150C2×C4×C43#12111yescharacteristic
151C2×C4×C43#12111yescharacteristic
152C2×C4×C43#12311yescharacteristic
153C2×C4×C43C2×D811yescharacteristic
154C2×C4×C43#13511yescharacteristic
155C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
156C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
157C8×C43—42no—
158C8×C43—81no—
159C8×C43—81no—
160#9300C4311yesmaximal, characteristic, direct product factor, Sylow
161C22×C43—21no—
162C22×C43—21no—
163C22×C43—81no—
164C22×C43—81no—
165C22×C43—81no—
166C22×C43#38611yescharacteristic
167C22×C43#44711yescharacteristic
168C22×C43#44911yescharacteristic
169C4×C43—21no—
170C4×C43—21no—
171C4×C43—21no—
172C4×C43—21no—
173C4×C43—42no—
174C4×C43—44no—
175C4×C43—82no—
176C4×C43—81no—
177C4×C43—81no—
178C4×C43C4×D811yescharacteristic
179C4×C43#44211yescharacteristic
180C4×C43#45911yescharacteristic
181C4×C43#46311yescharacteristic
182#3226C2×C4311yescharacteristic
183#2327C2×C4311yescharacteristic, complemented
184#1963C2×C4311yescharacteristic
185#1546C2×C4311yescharacteristic, complemented
186#1517C2×C4311yescharacteristic
187#1286C2×C4311yescharacteristic, complemented
188#1274C2×C4311yescharacteristic, complemented
189C2×C43—21no—
190C2×C43—21no—
191C2×C43—161no—
192C2×C43#187911yescharacteristic
193C2×C43#190511yescharacteristic
194C2×C43#191211yescharacteristic
195#532C22×C4311yescharacteristic
196C2×C4⋊Q8C22×C4311yescharacteristic
197C2×C4×Q8—21no—
198#500C4×C4312yescomplemented
199#486C4×C4312yescomplemented
200#480—22no—
201#474—22no—
202#431C22×C4311yescharacteristic
203#431C22×C4311yescharacteristic
204#423C22×C4311yescharacteristic
205C2×#104—21no—
206C2×#104—21no—
207#391—21no—
208#387—22no—
209#387—22no—
210#382C22×C4311yescharacteristic
211#376C22×C4311yescharacteristic
212#332—22no—
213#327—22no—
214C43#930011yescharacteristic, direct product factor, Sylow
215C2×#41—21no—
216C22×Q8—21no—
217C2×M16—21no—
218C4⋊Q8—21no—
219C4⋊Q8—21no—
220C4⋊Q8C2×C4×C4311yescharacteristic
221C4⋊Q8C2×C4×C4312yes—
222C4⋊Q8D4×C4312yes—
223#127C2×C4×C4311yescharacteristic
224#124—21no—
225#121—21no—
226#121—21no—
227C4×Q8—42no—
228C4×Q8—42no—
229C4×D4—21no—
230C4×D4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—22no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4D4×C4312yes—
235C2×C42—22no—
236C2×C42D4×C4311yescharacteristic
237C2×C42D4×C4311yescharacteristic
238C2×C42C23×C4311yescharacteristic
239#107—24no—
240C4⋊C8—21no—
241C4⋊C8—21no—
242C4⋊C8—21no—
243C4⋊C8—21no—
244#104—42no—
245#104—42no—
246#102—24no—
247C22⋊C8—21no—
248C22⋊C8—21no—
249C4×C8—21no—
250C4×C8C2×C4×C4312yes—
251#95—24no—
252#95—21no—
253#95—21no—
254#95—21no—
255#95D4×C4312yes—
256#41—41no—
257#41—41no—
258#41—41no—
259#41—41no—
260C2×Q8—22no—
261C2×Q8—22no—
262C2×Q8—21no—
263C2×Q8—41no—
264C2×Q8—41no—
265C2×Q8—41no—
266C2×Q8—41no—
267C2×D4—21no—
268C2×D4—21no—
269C2×D4—21no—
270C2×D4—41no—
271C22×C4—21no—
272C22×C4—22no—
273C22×C4—21no—
274C22×C4—22no—
275C22×C4—41no—
276C22×C4C2×D4×C4311yescharacteristic
277C22×C4C2×D4×C4311yescharacteristic
278C22×C4C2×D4×C4311yescharacteristic
279M16—41no—
280M16—41no—
281C2×C8—22no—
282C2×C8—41no—
283C2×C8—41no—
284C4⋊C4—22no—
285C4⋊C4—22no—
286C4⋊C4—22no—
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—44no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4C22⋊C4×C4314yes—
293C22⋊C4—41no—
294C22⋊C4—41no—
295C42—21no—
296C42—21no—
297C42—21no—
298C42—44no—
299C42D8×C4312yes—
300C42C22×C4×C4311yescharacteristic
301C42C2×D4×C4311yescharacteristic
302C42#41×C4311yescharacteristic
303C42#41×C4311yescharacteristic
304C23—41no—
305C23#120×C4311yescharacteristic
306Q8—42no—
307Q8—42no—
308Q8—42no—
309Q8—42no—
310Q8—41no—
311Q8—41no—
312D4—42no—
313D4—41no—
314D4—41no—
315D4—81no—
316D4—81no—
317D4—81no—
318C2×C4—24no—
319C2×C4—22no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—41no—
327C2×C4—42no—
328C2×C4—41no—
329C2×C4—42no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—41no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4C2×C22⋊C4×C4311yescharacteristic
336C2×C4C4×D4×C4311yescharacteristic
337C2×C4C4×D4×C4311yescharacteristic
338C2×C4#121×C4311yescharacteristic
339C2×C4#121×C4311yescharacteristic
340C2×C4#123×C4311yescharacteristic
341C2×C4C2×D8×C4311yescharacteristic
342C2×C4#135×C4311yescharacteristic
343C2×C4AGL(1,ℤ/8)×C4311yescharacteristic
344C2×C4AGL(1,ℤ/8)×C4311yescharacteristic
345C8—42no—
346C8—81no—
347C8—81no—
348C22—21no—
349C22—21no—
350C22—81no—
351C22—81no—
352C22—81no—
353C22C43×#38611yescharacteristic
354C22C43×#44711yescharacteristic
355C22C43×#44911yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—42no—
361C4—44no—
362C4—82no—
363C4—81no—
364C4—81no—
365C4C4×D8×C4311yescharacteristic
366C4C43×#44211yescharacteristic
367C4C43×#45911yescharacteristic
368C4C43×#46311yescharacteristic
369C2—21no—
370C2—21no—
371C2—161no—
372C2C43×#187911yescharacteristic
373C2C43×#190511yescharacteristic
374C2C43×#191211yescharacteristic
subgroupG/H
center, socleC22×C43#386
commutatorC42C22×C4×C43
Frattini, cosocleC2×C42C23×C43
prime radicalC43×#532C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C2×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#2327C2semidirect
4. C43×#1546C2semidirect
6. C43×#1286C2semidirect
7. C43×#1274C2semidirect
11. C43×#500C4semidirect
12. C43×#486C4semidirect
160. #9300C43direct (N × H)
183. #2327C2×C43semidirect
185. #1546C2×C43semidirect
187. #1286C2×C43semidirect
188. #1274C2×C43semidirect
198. #500C4×C43semidirect
199. #486C4×C43semidirect
214. C43#9300direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#32262
C43×#23272
C43×#19632
C43×#15462
C43×#15172
C43×#12862
C43×#12742
#930043