Finite Group Databasebeta

← C43×#60334 #24980351

Subgroups — C43×#60334 #24980351

Order 11008.

1710 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3461C211yesmaximal, characteristic
2C43×#2994C214yesmaximal, complemented
3C43×#2992C214yesmaximal, complemented
4C43×#2988C212yesmaximal, complemented
5C43×#2986C214yesmaximal, complemented
6C43×#2983C211yesmaximal, characteristic, complemented
7C43×#2969C214yesmaximal, complemented
8C43×#2966C214yesmaximal, complemented
9C43×#2965C212yesmaximal, complemented
10C43×#2962C214yesmaximal, complemented
11C2×C8×Q8×C43C211yesmaximal, characteristic, complemented
12C43×#544C411yescharacteristic
13C43×#542C414yes—
14C43×#541C414yes—
15C43×#539C414yes—
16C43×#537C411yescharacteristic
17C43×#536C412yes—
18C43×#533C2214yes—
19C43×#529C2214yes—
20C43×#529C2214yes—
21C4×#41×C43C2212yes—
22C2×C4×Q8×C43C2211yescharacteristic
23C43×#446C2212yes—
24C43×#446C2214yes—
25C43×#446C2214yes—
26C43×#446C2218yes—
27C43×#446C2212yes—
28C43×#446C2214yes—
29C8×Q8×C43C2214yes—
30C8×Q8×C43C2214yes—
31C8×Q8×C43C2214yes—
32C8×Q8×C43C2214yes—
33C43×#436C2212yes—
34C43×#436C2212yes—
35C43×#436C2214yes—
36C43×#435C2214yes—
37C43×#435C2214yes—
38C43×#435C2218yes—
39C8×D4×C43C2218yes—
40C8×D4×C43C2214yes—
41C8×D4×C43C2214yes—
42C43×#433C2218yes—
43C43×#433C2218yes—
44C43×#432C2214yes—
45C43×#431C2212yes—
46C43×#431C2214yes—
47C43×#431C2214yes—
48C43×#424C2218yes—
49C2×C4⋊C8×C43C2211yescharacteristic
50C2×C4⋊C8×C43C2212yes—
51C2×C4⋊C8×C43C2214yes—
52C43×#405C2218yes—
53C4×M16×C43C2214yes—
54C2×C4×C8×C43C2211yescharacteristic
55C2×C4×C8×C43C2212yes—
56C2×#41×C43C2×C412yes—
57C22×Q8×C43C2×C411yescharacteristic
58C2×M16×C43C2314yes—
59C2×M16×C43C2314yes—
60C22×C8×C43C2311yescharacteristic
61C22×C8×C43C2312yes—
62C22×C8×C43C2311yescharacteristic
63C22×C8×C43C2318yes—
64C4⋊Q8×C43C2×C414yes—
65C4⋊Q8×C43C2×C414yes—
66#126×C43C2×C418yes—
67#126×C43C2×C418yes—
68#125×C43C2×C414yes—
69#125×C43C2×C414yes—
70#125×C43C2×C418yes—
71#124×C43C2×C414yes—
72#124×C43C2×C414yes—
73#123×C43C2×C418yes—
74#123×C43C2×C418yes—
75C22⋊Q8×C43C2×C414yes—
76C22⋊Q8×C43C2×C414yes—
77C22⋊Q8×C43C2×C414yes—
78C22⋊Q8×C43C2×C414yes—
79C22⋊Q8×C43C2×C418yes—
80#121×C43C2×C414yes—
81#121×C43C2×C414yes—
82C4×Q8×C43C2×C414yes—
83C4×Q8×C43C2×C412yes—
84C4×Q8×C43C2314yes—
85C4×Q8×C43C2312yes—
86C4×Q8×C43C2314yes—
87C4×D4×C43C2×C414yes—
88C4×D4×C43C2×C412yes—
89C4×D4×C43C2314yes—
90C4×D4×C43C2312yes—
91C4×D4×C43C2314yes—
92#117×C43C2×C412yes—
93#117×C43C2×C414yes—
94#117×C43C2318yes—
95C2×C4⋊C4×C43C2×C411yescharacteristic
96C2×C4⋊C4×C43C2×C412yes—
97C2×C42×C43C2311yescharacteristic
98C2×C42×C43C2312yes—
99C2×C42×C43C2314yes—
100C4⋊C8×C43C2314yes—
101C4⋊C8×C43C2312yes—
102C4⋊C8×C43C2318yes—
103C4⋊C8×C43C2318yes—
104C4⋊C8×C43C2314yes—
105C4⋊C8×C43C2314yes—
106C4⋊C8×C43C2312yes—
107C4⋊C8×C43C2314yes—
108C4⋊C8×C43C2314yes—
109C22⋊C8×C43C2314yes—
110C22⋊C8×C43C2314yes—
111C22⋊C8×C43C2318yes—
112C22⋊C8×C43C2314yes—
113#97×C43C2314yes—
114#97×C43C2314yes—
115#97×C43C2318yes—
116C4×C8×C43C2312yes—
117C4×C8×C43C2314yes—
118C4×C8×C43C2312yes—
119C4×C8×C43C2314yes—
120C4×C8×C43C2314yes—
121C4×C8×C43C2318yes—
122#41×C43—28no—
123C2×Q8×C43—24no—
124C2×Q8×C43C22×C414yes—
125C2×Q8×C43C22×C412yes—
126C2×Q8×C43C22×C414yes—
127C2×D4×C43C22×C414yes—
128C2×D4×C43C22×C412yes—
129C2×D4×C43C22×C414yes—
130C22×C4×C43C22×C412yes—
131C22×C4×C43C22×C414yes—
132C22×C4×C43C22×C411yescharacteristic
133C22×C4×C43C22×C412yes—
134C22×C4×C43C22×C414yes—
135C22×C4×C43C22×C411yescharacteristic
136C22×C4×C43C2411yescharacteristic
137C22×C4×C43C2414yes—
138M16×C43—28no—
139M16×C43—44no—
140C2×C8×C43—22no—
141C2×C8×C43—42no—
142C2×C8×C43—48no—
143C2×C8×C43—41no—
144C2×C8×C43C2411yescharacteristic
145C2×C8×C43C2414yes—
146C2×C8×C43C2414yes—
147C2×C8×C43C2412yes—
148C2×C8×C43C2414yes—
149C2×C8×C43C2411yescharacteristic
150C4⋊C4×C43C22×C414yes—
151C4⋊C4×C43C22×C418yes—
152C4⋊C4×C43C22×C414yes—
153C4⋊C4×C43C22×C412yes—
154C4⋊C4×C43C22×C412yes—
155C4⋊C4×C43C22×C414yes—
156C4⋊C4×C43C22×C418yes—
157C4⋊C4×C43C22×C418yes—
158C4⋊C4×C43C22×C414yes—
159C4⋊C4×C43C22×C414yes—
160C4⋊C4×C43C22×C418yes—
161C22⋊C4×C43C22×C414yes—
162C22⋊C4×C43C22×C414yes—
163C22⋊C4×C43C22×C414yes—
164C22⋊C4×C43C22×C418yes—
165C22⋊C4×C43C22×C418yes—
166C22⋊C4×C43C22×C418yes—
167C42×C43C22×C412yes—
168C42×C43C22×C414yes—
169C42×C43C22×C414yes—
170C42×C43C22×C414yes—
171C42×C43C2412yes—
172C42×C43C2414yes—
173C42×C43C2414yes—
174C23×C43C23×C414yes—
175C23×C43C23×C411yescharacteristic
176Q8×C43—28no—
177Q8×C43—24no—
178Q8×C43—44no—
179D4×C43—28no—
180D4×C43—24no—
181D4×C43—44no—
182C2×C4×C43—24no—
183C2×C4×C43—28no—
184C2×C4×C43—21no—
185C2×C4×C43—24no—
186C2×C4×C43—21no—
187C2×C4×C43—24no—
188C2×C4×C43—41no—
189C2×C4×C43—44no—
190C2×C4×C43—42no—
191C2×C4×C43#13114yes—
192C2×C4×C43C23×C411yescharacteristic
193C2×C4×C43C23×C412yes—
194C2×C4×C43C23×C414yes—
195C2×C4×C43C23×C414yes—
196C2×C4×C43C23×C414yes—
197C2×C4×C43C23×C414yes—
198C2×C4×C43C23×C414yes—
199C2×C4×C43C23×C412yes—
200C2×C4×C43C2511yescharacteristic
201C8×C43—21no—
202C8×C43—24no—
203C8×C43—24no—
204C8×C43—24no—
205C8×C43—22no—
206C8×C432−1+412yes—
207#60334C4311yesmaximal, characteristic, direct product factor, Sylow
208C22×C43—21no—
209C22×C43—21no—
210C22×C43—24no—
211C22×C43—24no—
212C22×C43—24no—
213C22×C43C2×#13112yes—
214C22×C43C24×C411yescharacteristic
215C4×C43—21no—
216C4×C43—24no—
217C4×C43—24no—
218C4×C43—24no—
219C4×C43—22no—
220C4×C43—24no—
221C4×C43—24no—
222C4×C43C2×#13114yes—
223C4×C43C2×2−1+411yescharacteristic
224C4×C43#58511yescharacteristic
225#3461C2×C4311yescharacteristic
226#2994C2×C4314yescomplemented
227#2992C2×C4314yescomplemented
228#2988C2×C4312yescomplemented
229#2986C2×C4314yescomplemented
230#2983C2×C4311yescharacteristic, complemented
231#2969C2×C4314yescomplemented
232#2966C2×C4314yescomplemented
233#2965C2×C4312yescomplemented
234#2962C2×C4314yescomplemented
235C2×C8×Q8C2×C4311yescharacteristic, complemented
236C2×C43—22no—
237C2×C43—44no—
238C2×C43C4×2−1+411yescharacteristic
239C2×C43C22×#13111yescharacteristic
240C2×C43#357311yescharacteristic
241#544C4×C4311yescharacteristic
242#542C4×C4314yes—
243#541C4×C4314yes—
244#539C4×C4314yes—
245#537C4×C4311yescharacteristic
246#536C4×C4312yes—
247#533C22×C4314yes—
248#529C22×C4314yes—
249#529C22×C4314yes—
250C4×#41C22×C4312yes—
251C2×C4×Q8C22×C4311yescharacteristic
252#446C22×C4312yes—
253#446C22×C4314yes—
254#446C22×C4314yes—
255#446C22×C4318yes—
256#446C22×C4312yes—
257#446C22×C4314yes—
258C8×Q8C22×C4314yes—
259C8×Q8C22×C4314yes—
260C8×Q8C22×C4314yes—
261C8×Q8C22×C4314yes—
262#436C22×C4312yes—
263#436C22×C4312yes—
264#436C22×C4314yes—
265#435C22×C4314yes—
266#435C22×C4314yes—
267#435C22×C4318yes—
268C8×D4C22×C4318yes—
269C8×D4C22×C4314yes—
270C8×D4C22×C4314yes—
271#433C22×C4318yes—
272#433C22×C4318yes—
273#432C22×C4314yes—
274#431C22×C4312yes—
275#431C22×C4314yes—
276#431C22×C4314yes—
277#424C22×C4318yes—
278C2×C4⋊C8C22×C4311yescharacteristic
279C2×C4⋊C8C22×C4312yes—
280C2×C4⋊C8C22×C4314yes—
281#405C22×C4318yes—
282C4×M16C22×C4314yes—
283C2×C4×C8C22×C4311yescharacteristic
284C2×C4×C8C22×C4312yes—
285C43#6033411yescharacteristic, direct product factor, Sylow
286C2×#41C2×C4×C4312yes—
287C22×Q8C2×C4×C4311yescharacteristic
288C2×M16C23×C4314yes—
289C2×M16C23×C4314yes—
290C22×C8C23×C4311yescharacteristic
291C22×C8C23×C4312yes—
292C22×C8C23×C4311yescharacteristic
293C22×C8C23×C4318yes—
294C4⋊Q8C2×C4×C4314yes—
295C4⋊Q8C2×C4×C4314yes—
296#126C2×C4×C4318yes—
297#126C2×C4×C4318yes—
298#125C2×C4×C4314yes—
299#125C2×C4×C4314yes—
300#125C2×C4×C4318yes—
301#124C2×C4×C4314yes—
302#124C2×C4×C4314yes—
303#123C2×C4×C4318yes—
304#123C2×C4×C4318yes—
305C22⋊Q8C2×C4×C4314yes—
306C22⋊Q8C2×C4×C4314yes—
307C22⋊Q8C2×C4×C4314yes—
308C22⋊Q8C2×C4×C4314yes—
309C22⋊Q8C2×C4×C4318yes—
310#121C2×C4×C4314yes—
311#121C2×C4×C4314yes—
312C4×Q8C2×C4×C4314yes—
313C4×Q8C2×C4×C4312yes—
314C4×Q8C23×C4314yes—
315C4×Q8C23×C4312yes—
316C4×Q8C23×C4314yes—
317C4×D4C2×C4×C4314yes—
318C4×D4C2×C4×C4312yes—
319C4×D4C23×C4314yes—
320C4×D4C23×C4312yes—
321C4×D4C23×C4314yes—
322#117C2×C4×C4312yes—
323#117C2×C4×C4314yes—
324#117C23×C4318yes—
325C2×C4⋊C4C2×C4×C4311yescharacteristic
326C2×C4⋊C4C2×C4×C4312yes—
327C2×C42C23×C4311yescharacteristic
328C2×C42C23×C4312yes—
329C2×C42C23×C4314yes—
330C4⋊C8C23×C4314yes—
331C4⋊C8C23×C4312yes—
332C4⋊C8C23×C4318yes—
333C4⋊C8C23×C4318yes—
334C4⋊C8C23×C4314yes—
335C4⋊C8C23×C4314yes—
336C4⋊C8C23×C4312yes—
337C4⋊C8C23×C4314yes—
338C4⋊C8C23×C4314yes—
339C22⋊C8C23×C4314yes—
340C22⋊C8C23×C4314yes—
341C22⋊C8C23×C4318yes—
342C22⋊C8C23×C4314yes—
343#97C23×C4314yes—
344#97C23×C4314yes—
345#97C23×C4318yes—
346C4×C8C23×C4312yes—
347C4×C8C23×C4314yes—
348C4×C8C23×C4312yes—
349C4×C8C23×C4314yes—
350C4×C8C23×C4314yes—
351C4×C8C23×C4318yes—
352#41—28no—
353C2×Q8—24no—
354C2×Q8C22×C4×C4314yes—
355C2×Q8C22×C4×C4312yes—
356C2×Q8C22×C4×C4314yes—
357C2×D4C22×C4×C4314yes—
358C2×D4C22×C4×C4312yes—
359C2×D4C22×C4×C4314yes—
360C22×C4C22×C4×C4312yes—
361C22×C4C22×C4×C4314yes—
362C22×C4C22×C4×C4311yescharacteristic
363C22×C4C22×C4×C4312yes—
364C22×C4C22×C4×C4314yes—
365C22×C4C22×C4×C4311yescharacteristic
366C22×C4C24×C4311yescharacteristic
367C22×C4C24×C4314yes—
368M16—28no—
369M16—44no—
370C2×C8—22no—
371C2×C8—42no—
372C2×C8—48no—
373C2×C8—41no—
374C2×C8C24×C4311yescharacteristic
375C2×C8C24×C4314yes—
376C2×C8C24×C4314yes—
377C2×C8C24×C4312yes—
378C2×C8C24×C4314yes—
379C2×C8C24×C4311yescharacteristic
380C4⋊C4C22×C4×C4314yes—
381C4⋊C4C22×C4×C4318yes—
382C4⋊C4C22×C4×C4318yes—
383C4⋊C4C22×C4×C4318yes—
384C4⋊C4C22×C4×C4312yes—
385C4⋊C4C22×C4×C4314yes—
386C4⋊C4C22×C4×C4314yes—
387C4⋊C4C22×C4×C4312yes—
388C4⋊C4C22×C4×C4314yes—
389C4⋊C4C22×C4×C4314yes—
390C4⋊C4C22×C4×C4318yes—
391C22⋊C4C22×C4×C4318yes—
392C22⋊C4C22×C4×C4318yes—
393C22⋊C4C22×C4×C4314yes—
394C22⋊C4C22×C4×C4314yes—
395C22⋊C4C22×C4×C4314yes—
396C22⋊C4C22×C4×C4318yes—
397C42C22×C4×C4312yes—
398C42C22×C4×C4314yes—
399C42C22×C4×C4314yes—
400C42C22×C4×C4314yes—
401C42C24×C4312yes—
402C42C24×C4314yes—
403C42C24×C4314yes—
404C23C23×C4×C4314yes—
405C23C23×C4×C4311yescharacteristic
406Q8—28no—
407Q8—24no—
408Q8—44no—
409D4—28no—
410D4—24no—
411D4—44no—
412C2×C4—24no—
413C2×C4—28no—
414C2×C4—21no—
415C2×C4—24no—
416C2×C4—21no—
417C2×C4—24no—
418C2×C4—41no—
419C2×C4—44no—
420C2×C4—42no—
421C2×C4#131×C4314yes—
422C2×C4C23×C4×C4311yescharacteristic
423C2×C4C23×C4×C4312yes—
424C2×C4C23×C4×C4314yes—
425C2×C4C23×C4×C4314yes—
426C2×C4C23×C4×C4314yes—
427C2×C4C23×C4×C4314yes—
428C2×C4C23×C4×C4314yes—
429C2×C4C23×C4×C4312yes—
430C2×C4C25×C4311yescharacteristic
431C8—21no—
432C8—24no—
433C8—24no—
434C8—24no—
435C8—22no—
436C82−1+4×C4312yes—
437C22—21no—
438C22—21no—
439C22—24no—
440C22—24no—
441C22—24no—
442C22C2×#131×C4312yes—
443C22C24×C4×C4311yescharacteristic
444C4—21no—
445C4—24no—
446C4—24no—
447C4—24no—
448C4—22no—
449C4—24no—
450C4—24no—
451C4C2×#131×C4314yes—
452C4C2×2−1+4×C4311yescharacteristic
453C4C43×#58511yescharacteristic
454C2—22no—
455C2—44no—
456C2C4×2−1+4×C4311yescharacteristic
457C2C22×#131×C4311yescharacteristic
458C2C43×#357311yescharacteristic
subgroupG/H
centerC2×C4×C43C25
commutatorC22C24×C4×C43
Frattini, cosocleC2×C4C25×C43
socleC22×C43C24×C4
prime radicalC43×#537C4
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#2994C2semidirect
3. C43×#2992C2semidirect
4. C43×#2988C2semidirect
5. C43×#2986C2semidirect
6. C43×#2983C2semidirect
7. C43×#2969C2semidirect
8. C43×#2966C2semidirect
9. C43×#2965C2semidirect
10. C43×#2962C2semidirect
11. C2×C8×Q8×C43C2semidirect
207. #60334C43direct (N × H)
226. #2994C2×C43semidirect
227. #2992C2×C43semidirect
228. #2988C2×C43semidirect
229. #2986C2×C43semidirect
230. #2983C2×C43semidirect
231. #2969C2×C43semidirect
232. #2966C2×C43semidirect
233. #2965C2×C43semidirect
234. #2962C2×C43semidirect
235. C2×C8×Q8C2×C43semidirect
285. C43#60334direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#34612
C43×#29942
C43×#29922
C43×#29882
C43×#29862
C43×#29832
C43×#29692
C43×#29662
C43×#29652
C43×#29622
C2×C8×Q8×C432
#6033443