Finite Group Databasebeta

← C43×#9051 #24929068

Subgroups — C43×#9051 #24929068

Order 11008.

436 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3108C211yesmaximal, characteristic
2C43×#2992C211yesmaximal, characteristic
3C43×#1985C211yesmaximal, characteristic, complemented
4C43×#1524C211yesmaximal, characteristic
5C43×#1491C211yesmaximal, characteristic, complemented
6C43×#1302C211yesmaximal, characteristic, complemented
7C43×#1283C211yesmaximal, characteristic, complemented
8C43×#529C2211yescharacteristic
9C2×C4×Q8×C43C2211yescharacteristic
10C43×#483C411yescharacteristic
11C43×#480C411yescharacteristic
12C43×#479—21no—
13C43×#464—21no—
14C43×#451C411yescharacteristic
15C43×#448C411yescharacteristic
16C43×#446—21no—
17C4×Q16×C43—21no—
18C4×SD16×C43—21no—
19C43×#435—21no—
20C43×#435—21no—
21C8×D4×C43—21no—
22C43×#433—21no—
23C43×#432C2211yescharacteristic
24C43×#431C2211yescharacteristic
25C43×#424—21no—
26C2×C4⋊C8×C43C2211yescharacteristic
27C4×M16×C43C2211yescharacteristic
28C2×#97×C43C2211yescharacteristic
29C43×#336—21no—
30C43×#336—21no—
31C43×#330—21no—
32C43×#329—21no—
33C43×Q8⋊C8—21no—
34C43×Q8⋊C8—21no—
35C22×Q8×C43C2×C411yescharacteristic
36C2×Q16×C43—21no—
37C2×SD16×C43—21no—
38C2×M16×C43—21no—
39C2×M16×C43—21no—
40C22×C8×C43—21no—
41C22×C8×C43—21no—
42C22×C8×C43D411yescharacteristic
43C22×C8×C43D411yescharacteristic
44#126×C43—21no—
45#125×C43D411yescharacteristic
46#124×C43D411yescharacteristic
47#123×C43—21no—
48C22⋊Q8×C43C2×C411yescharacteristic
49#121×C43C2×C411yescharacteristic
50C4×Q8×C43—21no—
51C4×Q8×C43—21no—
52C4×Q8×C43—21no—
53C4×Q8×C43—21no—
54C4×Q8×C43D411yescharacteristic
55C4×D4×C43—21no—
56C4×D4×C43D411yescharacteristic
57#117×C43—21no—
58C2×C4⋊C4×C43—21no—
59C2×C4⋊C4×C43C2×C411yescharacteristic
60C2×C42×C43—21no—
61C2×C42×C43C2311yescharacteristic
62#107×C43—21no—
63#106×C43—21no—
64C4⋊C8×C43—21no—
65C4⋊C8×C43—21no—
66C4⋊C8×C43—21no—
67C4⋊C8×C43—21no—
68C4⋊C8×C43—21no—
69C4⋊C8×C43D411yescharacteristic
70C4⋊C8×C43D411yescharacteristic
71#103×C43—21no—
72#103×C43—21no—
73#103×C43—21no—
74#102×C43—21no—
75C22⋊C8×C43—21no—
76C22⋊C8×C43—21no—
77C22⋊C8×C43—21no—
78C22⋊C8×C43C2×C411yescharacteristic
79C22⋊C8×C43C2×C411yescharacteristic
80#97×C43—21no—
81#97×C43—21no—
82#97×C43—21no—
83#97×C43—21no—
84#97×C43—21no—
85C4×C8×C43—21no—
86C4×C8×C43—21no—
87C4×C8×C43—21no—
88C2×Q8×C43—21no—
89C2×Q8×C43—21no—
90C2×Q8×C43—42no—
91C2×Q8×C43C22⋊C411yescharacteristic
92C2×D4×C43—21no—
93C2×D4×C43C22⋊C411yescharacteristic
94C22×C4×C43—21no—
95C22×C4×C43—21no—
96C22×C4×C43—21no—
97C22×C4×C43C22×C411yescharacteristic
98C22×C4×C43C2×D411yescharacteristic
99C22×C4×C43#4111yescharacteristic
100Q16×C43—42no—
101SD16×C43—42no—
102M16×C43—22no—
103M16×C43—41no—
104M16×C43—81no—
105C2×C8×C43—22no—
106C2×C8×C43—21no—
107C2×C8×C43—21no—
108C2×C8×C43—21no—
109C2×C8×C43—21no—
110C2×C8×C43—21no—
111C2×C8×C43—21no—
112C2×C8×C43—41no—
113C2×C8×C43—41no—
114C2×C8×C43—41no—
115C2×C8×C43—41no—
116C2×C8×C43—41no—
117C2×C8×C43—81no—
118C4⋊C4×C43—21no—
119C4⋊C4×C43—21no—
120C4⋊C4×C43—21no—
121C4⋊C4×C43—21no—
122C4⋊C4×C43—21no—
123C4⋊C4×C43—21no—
124C4⋊C4×C43—41no—
125C4⋊C4×C43—41no—
126C4⋊C4×C43C22⋊C411yescharacteristic
127C4⋊C4×C43C22⋊C411yescharacteristic
128C22⋊C4×C43—21no—
129C22⋊C4×C43—21no—
130C22⋊C4×C43—21no—
131C22⋊C4×C43—21no—
132C22⋊C4×C43—21no—
133C42×C43—21no—
134C42×C43—41no—
135C42×C43—41no—
136C42×C43C2×D411yescharacteristic
137C42×C43C2×D411yescharacteristic
138C42×C43C2×D411yescharacteristic
139C42×C43#4111yescharacteristic
140C23×C43—21no—
141C23×C43C4×D411yescharacteristic
142Q8×C43—22no—
143Q8×C43—22no—
144Q8×C43—41no—
145Q8×C43—41no—
146Q8×C43—41no—
147D4×C43—41no—
148D4×C43—41no—
149D4×C43—41no—
150C2×C4×C43—21no—
151C2×C4×C43—21no—
152C2×C4×C43—21no—
153C2×C4×C43—21no—
154C2×C4×C43—22no—
155C2×C4×C43—21no—
156C2×C4×C43—21no—
157C2×C4×C43—21no—
158C2×C4×C43—41no—
159C2×C4×C43—41no—
160C2×C4×C43—41no—
161C2×C4×C43—41no—
162C2×C4×C43—41no—
163C2×C4×C43—41no—
164C2×C4×C43—41no—
165C2×C4×C43—41no—
166C2×C4×C43C2×C22⋊C411yescharacteristic
167C2×C4×C43C4×D411yescharacteristic
168C2×C4×C43#12011yescharacteristic
169C2×C4×C43#12111yescharacteristic
170C2×C4×C43#12111yescharacteristic
171C2×C4×C43#12311yescharacteristic
172C8×C43—42no—
173C8×C43—41no—
174C8×C43—41no—
175C8×C43—42no—
176C8×C43—41no—
177C8×C43—41no—
178C8×C43—41no—
179C8×C43—41no—
180#9051C4311yesmaximal, characteristic, direct product factor, Sylow
181C22×C43—21no—
182C22×C43—21no—
183C22×C43—41no—
184C22×C43—41no—
185C22×C43—41no—
186C22×C43#38611yescharacteristic
187C22×C43#44311yescharacteristic
188C22×C43#44411yescharacteristic
189C4×C43—21no—
190C4×C43—21no—
191C4×C43—21no—
192C4×C43—21no—
193C4×C43—21no—
194C4×C43—41no—
195C4×C43—41no—
196C4×C43—42no—
197C4×C43—41no—
198C4×C43—81no—
199C4×C43#45511yescharacteristic
200C4×C43#45611yescharacteristic
201#3108C2×C4311yescharacteristic
202#2992C2×C4311yescharacteristic
203#1985C2×C4311yescharacteristic, complemented
204#1524C2×C4311yescharacteristic
205#1491C2×C4311yescharacteristic, complemented
206#1302C2×C4311yescharacteristic, complemented
207#1283C2×C4311yescharacteristic, complemented
208C2×C43—21no—
209C2×C43—21no—
210C2×C43—81no—
211C2×C43#187611yescharacteristic
212C2×C43#188211yescharacteristic
213C2×C43#189111yescharacteristic
214#529C22×C4311yescharacteristic
215C2×C4×Q8C22×C4311yescharacteristic
216#483C4×C4311yescharacteristic
217#480C4×C4311yescharacteristic
218#479—21no—
219#464—21no—
220#451C4×C4311yescharacteristic
221#448C4×C4311yescharacteristic
222#446—21no—
223C4×Q16—21no—
224C4×SD16—21no—
225#435—21no—
226#435—21no—
227C8×D4—21no—
228#433—21no—
229#432C22×C4311yescharacteristic
230#431C22×C4311yescharacteristic
231#424—21no—
232C2×C4⋊C8C22×C4311yescharacteristic
233C4×M16C22×C4311yescharacteristic
234C2×#97C22×C4311yescharacteristic
235#336—21no—
236#336—21no—
237#330—21no—
238#329—21no—
239Q8⋊C8—21no—
240Q8⋊C8—21no—
241C43#905111yescharacteristic, direct product factor, Sylow
242C22×Q8C2×C4×C4311yescharacteristic
243C2×Q16—21no—
244C2×SD16—21no—
245C2×M16—21no—
246C2×M16—21no—
247C22×C8—21no—
248C22×C8—21no—
249C22×C8D4×C4311yescharacteristic
250C22×C8D4×C4311yescharacteristic
251#126—21no—
252#125D4×C4311yescharacteristic
253#124D4×C4311yescharacteristic
254#123—21no—
255C22⋊Q8C2×C4×C4311yescharacteristic
256#121C2×C4×C4311yescharacteristic
257C4×Q8—21no—
258C4×Q8—21no—
259C4×Q8—21no—
260C4×Q8—21no—
261C4×Q8D4×C4311yescharacteristic
262C4×D4—21no—
263C4×D4D4×C4311yescharacteristic
264#117—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4C2×C4×C4311yescharacteristic
267C2×C42—21no—
268C2×C42C23×C4311yescharacteristic
269#107—21no—
270#106—21no—
271C4⋊C8—21no—
272C4⋊C8—21no—
273C4⋊C8—21no—
274C4⋊C8—21no—
275C4⋊C8—21no—
276C4⋊C8D4×C4311yescharacteristic
277C4⋊C8D4×C4311yescharacteristic
278#103—21no—
279#103—21no—
280#103—21no—
281#102—21no—
282C22⋊C8—21no—
283C22⋊C8—21no—
284C22⋊C8—21no—
285C22⋊C8C2×C4×C4311yescharacteristic
286C22⋊C8C2×C4×C4311yescharacteristic
287#97—21no—
288#97—21no—
289#97—21no—
290#97—21no—
291#97—21no—
292C4×C8—21no—
293C4×C8—21no—
294C4×C8—21no—
295C2×Q8—21no—
296C2×Q8—21no—
297C2×Q8—42no—
298C2×Q8C22⋊C4×C4311yescharacteristic
299C2×D4—21no—
300C2×D4C22⋊C4×C4311yescharacteristic
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4C22×C4×C4311yescharacteristic
305C22×C4C2×D4×C4311yescharacteristic
306C22×C4#41×C4311yescharacteristic
307Q16—42no—
308SD16—42no—
309M16—22no—
310M16—41no—
311M16—81no—
312C2×C8—22no—
313C2×C8—21no—
314C2×C8—21no—
315C2×C8—21no—
316C2×C8—21no—
317C2×C8—21no—
318C2×C8—21no—
319C2×C8—41no—
320C2×C8—41no—
321C2×C8—41no—
322C2×C8—41no—
323C2×C8—41no—
324C2×C8—81no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4C22⋊C4×C4311yescharacteristic
334C4⋊C4C22⋊C4×C4311yescharacteristic
335C22⋊C4—21no—
336C22⋊C4—21no—
337C22⋊C4—21no—
338C22⋊C4—21no—
339C22⋊C4—21no—
340C42—21no—
341C42—41no—
342C42—41no—
343C42C2×D4×C4311yescharacteristic
344C42C2×D4×C4311yescharacteristic
345C42C2×D4×C4311yescharacteristic
346C42#41×C4311yescharacteristic
347C23—21no—
348C23C4×D4×C4311yescharacteristic
349Q8—22no—
350Q8—22no—
351Q8—41no—
352Q8—41no—
353Q8—41no—
354D4—41no—
355D4—41no—
356D4—41no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—22no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4C2×C22⋊C4×C4311yescharacteristic
374C2×C4C4×D4×C4311yescharacteristic
375C2×C4#120×C4311yescharacteristic
376C2×C4#121×C4311yescharacteristic
377C2×C4#121×C4311yescharacteristic
378C2×C4#123×C4311yescharacteristic
379C8—42no—
380C8—41no—
381C8—41no—
382C8—42no—
383C8—41no—
384C8—41no—
385C8—41no—
386C8—41no—
387C22—21no—
388C22—21no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22C43×#38611yescharacteristic
393C22C43×#44311yescharacteristic
394C22C43×#44411yescharacteristic
395C4—21no—
396C4—21no—
397C4—21no—
398C4—21no—
399C4—21no—
400C4—41no—
401C4—41no—
402C4—42no—
403C4—41no—
404C4—81no—
405C4C43×#45511yescharacteristic
406C4C43×#45611yescharacteristic
407C2—21no—
408C2—21no—
409C2—81no—
410C2C43×#187611yescharacteristic
411C2C43×#188211yescharacteristic
412C2C43×#189111yescharacteristic
subgroupG/H
centerC2×C4×C43#120
commutatorC22×C4C22×C4×C43
Frattini, cosocleC2×C42C23×C43
socleC22×C43#386
prime radical#121×C43C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C43 ◁ C2×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
3. C43×#1985C2semidirect
5. C43×#1491C2semidirect
6. C43×#1302C2semidirect
7. C43×#1283C2semidirect
180. #9051C43direct (N × H)
203. #1985C2×C43semidirect
205. #1491C2×C43semidirect
206. #1302C2×C43semidirect
207. #1283C2×C43semidirect
241. C43#9051direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#31082
C43×#29922
C43×#19852
C43×#15242
C43×#14912
C43×#13022
C43×#12832
#905143