Finite Group Databasebeta

← C43×#9348 #24929365

Subgroups — C43×#9348 #24929365

Order 11008.

470 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3094C211yesmaximal, characteristic
2C43×#2924C211yesmaximal, characteristic, complemented
3C43×#1825C211yesmaximal, characteristic, complemented
4C43×#1519C211yesmaximal, characteristic
5C43×#1471C211yesmaximal, characteristic
6C43×#1305C211yesmaximal, characteristic, complemented
7C43×#1298C211yesmaximal, characteristic, complemented
8C2×#121×C43C2211yescharacteristic
9C2×#117×C43C2211yescharacteristic
10C43×#482—21no—
11C43×#482—21no—
12C43×#481—21no—
13C43×#480—21no—
14C43×#433—22no—
15C43×#432—21no—
16C43×#431—21no—
17C43×#428C411yescharacteristic, complemented
18C43×#428C411yescharacteristic, complemented
19C43×#424—21no—
20C43×#418C411yescharacteristic, complemented
21C43×#418C411yescharacteristic, complemented
22C43×#407C2211yescharacteristic
23C43×#407C2211yescharacteristic
24C2×C22⋊C8×C43C2211yescharacteristic
25C2×C22⋊C8×C43C2211yescharacteristic
26C43×#405—21no—
27C43×#380C2211yescharacteristic
28C43×#340—21no—
29C43×#340—21no—
30C43×#327—21no—
31C43×#327—21no—
32C43×#323—22no—
33C22×D4×C43—21no—
34C22×D4×C43C2×C411yescharacteristic
35C23×C4×C43C2311yescharacteristic
36C2×M16×C43—21no—
37C2×M16×C43C2×C411yescharacteristic
38C2×M16×C43C2×C411yescharacteristic
39C22×C8×C43—21no—
40C22×C8×C43—21no—
41#121×C43—21no—
42#121×C43—21no—
43#121×C43—21no—
44#121×C43—21no—
45#117×C43—21no—
46#117×C43—21no—
47#117×C43C2×C411yescharacteristic
48#117×C43C2×C411yescharacteristic
49#117×C43D411yescharacteristic
50#117×C43D411yescharacteristic
51C2×C4⋊C4×C43—21no—
52C2×C4⋊C4×C43C2×C411yescharacteristic
53C2×C4⋊C4×C43D411yescharacteristic
54C2×C4⋊C4×C43D411yescharacteristic
55C2×C22⋊C4×C43—21no—
56C2×C22⋊C4×C43—21no—
57C2×C22⋊C4×C43—21no—
58C2×C42×C43—21no—
59#107×C43—21no—
60#107×C43—21no—
61#106×C43—21no—
62#106×C43—21no—
63C4⋊C8×C43—22no—
64C4⋊C8×C43—22no—
65#102×C43—21no—
66#102×C43—21no—
67#102×C43—21no—
68#102×C43—21no—
69C22⋊C8×C43—21no—
70C22⋊C8×C43—21no—
71C22⋊C8×C43—21no—
72C22⋊C8×C43—21no—
73C22⋊C8×C43—21no—
74C22⋊C8×C43—21no—
75C22⋊C8×C43D412yes—
76C22⋊C8×C43D411yescharacteristic
77C22⋊C8×C43D411yescharacteristic
78#97×C43—22no—
79C4×C8×C43—22no—
80#95×C43—21no—
81C24×C43—21no—
82C24×C43#4111yescharacteristic
83C2×D4×C43—21no—
84C2×D4×C43—21no—
85C2×D4×C43—41no—
86C2×D4×C43—41no—
87C2×D4×C43—41no—
88C2×D4×C43—41no—
89C2×D4×C43—81no—
90C2×D4×C43—81no—
91C22×C4×C43—21no—
92C22×C4×C43—21no—
93C22×C4×C43—21no—
94C22×C4×C43—41no—
95C22×C4×C43—41no—
96C22×C4×C43—41no—
97C22×C4×C43C22×C411yescharacteristic
98C22×C4×C43C2×D411yescharacteristic
99C22×C4×C43C2×D411yescharacteristic
100C22×C4×C43C2×D411yescharacteristic
101C22×C4×C43C2×D411yescharacteristic
102C22×C4×C43#4111yescharacteristic
103M16×C43—41no—
104M16×C43—41no—
105M16×C43—41no—
106M16×C43—41no—
107C2×C8×C43—21no—
108C2×C8×C43—21no—
109C2×C8×C43—21no—
110C2×C8×C43—22no—
111C2×C8×C43—21no—
112C2×C8×C43—41no—
113C2×C8×C43—41no—
114C2×C8×C43—41no—
115C2×C8×C43—41no—
116C2×C8×C43—41no—
117C4⋊C4×C43—21no—
118C4⋊C4×C43—21no—
119C4⋊C4×C43—21no—
120C4⋊C4×C43—21no—
121C4⋊C4×C43—41no—
122C4⋊C4×C43—41no—
123C4⋊C4×C43C22⋊C411yescharacteristic
124C4⋊C4×C43C22⋊C411yescharacteristic
125C4⋊C4×C43C22⋊C411yescharacteristic
126C4⋊C4×C43C22⋊C411yescharacteristic
127C22⋊C4×C43—21no—
128C22⋊C4×C43—21no—
129C22⋊C4×C43—21no—
130C22⋊C4×C43—21no—
131C22⋊C4×C43—41no—
132C22⋊C4×C43—41no—
133C22⋊C4×C43—81no—
134C42×C43—21no—
135C42×C43—21no—
136C42×C43—21no—
137C42×C43—21no—
138C23×C43—21no—
139C23×C43—21no—
140C23×C43—41no—
141C23×C43—41no—
142C23×C43—42no—
143C23×C43—41no—
144C23×C43—81no—
145C23×C43—81no—
146C23×C43C4×D411yescharacteristic
147C23×C43#12111yescharacteristic
148C23×C43#12311yescharacteristic
149D4×C43—41no—
150D4×C43—41no—
151D4×C43—81no—
152D4×C43—82no—
153D4×C43—81no—
154D4×C43—81no—
155C2×C4×C43—21no—
156C2×C4×C43—21no—
157C2×C4×C43—21no—
158C2×C4×C43—21no—
159C2×C4×C43—21no—
160C2×C4×C43—21no—
161C2×C4×C43—21no—
162C2×C4×C43—21no—
163C2×C4×C43—21no—
164C2×C4×C43—21no—
165C2×C4×C43—41no—
166C2×C4×C43—41no—
167C2×C4×C43—41no—
168C2×C4×C43—41no—
169C2×C4×C43—41no—
170C2×C4×C43—41no—
171C2×C4×C43—81no—
172C2×C4×C43—81no—
173C2×C4×C43—81no—
174C2×C4×C43—81no—
175C2×C4×C43—81no—
176C2×C4×C43C2×C22⋊C411yescharacteristic
177C2×C4×C43C4×D411yescharacteristic
178C2×C4×C43#12011yescharacteristic
179C2×C4×C43#12111yescharacteristic
180C8×C43—41no—
181C8×C43—41no—
182C8×C43—42no—
183C8×C43—41no—
184C8×C43—41no—
185C8×C43—81no—
186#9348C4311yesmaximal, characteristic, direct product factor, Sylow
187C22×C43—21no—
188C22×C43—21no—
189C22×C43—21no—
190C22×C43—21no—
191C22×C43—21no—
192C22×C43—21no—
193C22×C43—21no—
194C22×C43—21no—
195C22×C43—81no—
196C22×C43—81no—
197C22×C43—81no—
198C22×C43—81no—
199C22×C43—81no—
200C22×C43—162no—
201C22×C43#38611yescharacteristic
202C22×C43#47111yescharacteristic
203C22×C43#47211yescharacteristic
204C4×C43—21no—
205C4×C43—21no—
206C4×C43—21no—
207C4×C43—41no—
208C4×C43—41no—
209C4×C43—41no—
210C4×C43—41no—
211C4×C43—81no—
212C4×C43—161no—
213C4×C43#41011yescharacteristic
214C4×C43#41011yescharacteristic
215#3094C2×C4311yescharacteristic
216#2924C2×C4311yescharacteristic, complemented
217#1825C2×C4311yescharacteristic, complemented
218#1519C2×C4311yescharacteristic
219#1471C2×C4311yescharacteristic
220#1305C2×C4311yescharacteristic, complemented
221#1298C2×C4311yescharacteristic, complemented
222C2×C43—21no—
223C2×C43—21no—
224C2×C43—41no—
225C2×C43—41no—
226C2×C43—161no—
227C2×C43#188111yescharacteristic
228C2×C43#189911yescharacteristic
229C2×C43#190711yescharacteristic
230C2×#121C22×C4311yescharacteristic
231C2×#117C22×C4311yescharacteristic
232#482—21no—
233#482—21no—
234#481—21no—
235#480—21no—
236#433—22no—
237#432—21no—
238#431—21no—
239#428C4×C4311yescharacteristic, complemented
240#428C4×C4311yescharacteristic, complemented
241#424—21no—
242#418C4×C4311yescharacteristic, complemented
243#418C4×C4311yescharacteristic, complemented
244#407C22×C4311yescharacteristic
245#407C22×C4311yescharacteristic
246C2×C22⋊C8C22×C4311yescharacteristic
247C2×C22⋊C8C22×C4311yescharacteristic
248#405—21no—
249#380C22×C4311yescharacteristic
250#340—21no—
251#340—21no—
252#327—21no—
253#327—21no—
254#323—22no—
255C43#934811yescharacteristic, direct product factor, Sylow
256C22×D4—21no—
257C22×D4C2×C4×C4311yescharacteristic
258C23×C4C23×C4311yescharacteristic
259C2×M16—21no—
260C2×M16C2×C4×C4311yescharacteristic
261C2×M16C2×C4×C4311yescharacteristic
262C22×C8—21no—
263C22×C8—21no—
264#121—21no—
265#121—21no—
266#121—21no—
267#121—21no—
268#117—21no—
269#117—21no—
270#117C2×C4×C4311yescharacteristic
271#117C2×C4×C4311yescharacteristic
272#117D4×C4311yescharacteristic
273#117D4×C4311yescharacteristic
274C2×C4⋊C4—21no—
275C2×C4⋊C4C2×C4×C4311yescharacteristic
276C2×C4⋊C4D4×C4311yescharacteristic
277C2×C4⋊C4D4×C4311yescharacteristic
278C2×C22⋊C4—21no—
279C2×C22⋊C4—21no—
280C2×C22⋊C4—21no—
281C2×C42—21no—
282#107—21no—
283#107—21no—
284#106—21no—
285#106—21no—
286C4⋊C8—22no—
287C4⋊C8—22no—
288#102—21no—
289#102—21no—
290#102—21no—
291#102—21no—
292C22⋊C8—21no—
293C22⋊C8—21no—
294C22⋊C8—21no—
295C22⋊C8—21no—
296C22⋊C8—21no—
297C22⋊C8—21no—
298C22⋊C8D4×C4312yes—
299C22⋊C8D4×C4311yescharacteristic
300C22⋊C8D4×C4311yescharacteristic
301#97—22no—
302C4×C8—22no—
303#95—21no—
304C24—21no—
305C24#41×C4311yescharacteristic
306C2×D4—21no—
307C2×D4—21no—
308C2×D4—41no—
309C2×D4—41no—
310C2×D4—41no—
311C2×D4—41no—
312C2×D4—81no—
313C2×D4—81no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—41no—
318C22×C4—41no—
319C22×C4—41no—
320C22×C4C22×C4×C4311yescharacteristic
321C22×C4C2×D4×C4311yescharacteristic
322C22×C4C2×D4×C4311yescharacteristic
323C22×C4C2×D4×C4311yescharacteristic
324C22×C4C2×D4×C4311yescharacteristic
325C22×C4#41×C4311yescharacteristic
326M16—41no—
327M16—41no—
328M16—41no—
329M16—41no—
330C2×C8—21no—
331C2×C8—21no—
332C2×C8—21no—
333C2×C8—22no—
334C2×C8—21no—
335C2×C8—41no—
336C2×C8—41no—
337C2×C8—41no—
338C2×C8—41no—
339C2×C8—41no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—41no—
345C4⋊C4—41no—
346C4⋊C4C22⋊C4×C4311yescharacteristic
347C4⋊C4C22⋊C4×C4311yescharacteristic
348C4⋊C4C22⋊C4×C4311yescharacteristic
349C4⋊C4C22⋊C4×C4311yescharacteristic
350C22⋊C4—21no—
351C22⋊C4—21no—
352C22⋊C4—21no—
353C22⋊C4—21no—
354C22⋊C4—41no—
355C22⋊C4—41no—
356C22⋊C4—81no—
357C42—21no—
358C42—21no—
359C42—21no—
360C42—21no—
361C23—21no—
362C23—21no—
363C23—41no—
364C23—41no—
365C23—42no—
366C23—41no—
367C23—81no—
368C23—81no—
369C23C4×D4×C4311yescharacteristic
370C23#121×C4311yescharacteristic
371C23#123×C4311yescharacteristic
372D4—41no—
373D4—41no—
374D4—81no—
375D4—82no—
376D4—81no—
377D4—81no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—81no—
395C2×C4—81no—
396C2×C4—81no—
397C2×C4—81no—
398C2×C4—81no—
399C2×C4C2×C22⋊C4×C4311yescharacteristic
400C2×C4C4×D4×C4311yescharacteristic
401C2×C4#120×C4311yescharacteristic
402C2×C4#121×C4311yescharacteristic
403C8—41no—
404C8—41no—
405C8—42no—
406C8—41no—
407C8—41no—
408C8—81no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—81no—
418C22—81no—
419C22—81no—
420C22—81no—
421C22—81no—
422C22—162no—
423C22C43×#38611yescharacteristic
424C22C43×#47111yescharacteristic
425C22C43×#47211yescharacteristic
426C4—21no—
427C4—21no—
428C4—21no—
429C4—41no—
430C4—41no—
431C4—41no—
432C4—41no—
433C4—81no—
434C4—161no—
435C4C43×#41011yescharacteristic
436C4C43×#41011yescharacteristic
437C2—21no—
438C2—21no—
439C2—41no—
440C2—41no—
441C2—161no—
442C2C43×#188111yescharacteristic
443C2C43×#189911yescharacteristic
444C2C43×#190711yescharacteristic
subgroupG/H
center, socleC22×C43#386
commutatorC22×C4C22×C4×C43
Frattini, cosocleC23×C4C23×C43
prime radicalC2×#121×C43C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C23×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#2924C2semidirect
3. C43×#1825C2semidirect
6. C43×#1305C2semidirect
7. C43×#1298C2semidirect
17. C43×#428C4semidirect
18. C43×#428C4semidirect
20. C43×#418C4semidirect
21. C43×#418C4semidirect
186. #9348C43direct (N × H)
216. #2924C2×C43semidirect
217. #1825C2×C43semidirect
220. #1305C2×C43semidirect
221. #1298C2×C43semidirect
239. #428C4×C43semidirect
240. #428C4×C43semidirect
242. #418C4×C43semidirect
243. #418C4×C43semidirect
255. C43#9348direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#30942
C43×#29242
C43×#18252
C43×#15192
C43×#14712
C43×#13052
C43×#12982
#934843