Finite Group Databasebeta

← C43×#34976 #24954993

Subgroups — C43×#34976 #24954993

Order 11008.

2810 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#41×C43C212yesmaximal, complemented
2C43×#2609C214yesmaximal, complemented
3C43×#2582C211yesmaximal, characteristic, complemented
4C43×#2538C212yesmaximal, complemented
5C43×#2537C211yesmaximal, characteristic, complemented
6C43×#2485C214yesmaximal, complemented
7C43×#2407C214yesmaximal, complemented
8C43×#2392C214yesmaximal, complemented
9C4×C22⋊Q8×C43C214yesmaximal, complemented
10C4×#121×C43C214yesmaximal, complemented
11C43×#2285C211yesmaximal, characteristic, complemented
12C22×#41×C43C2212yes—
13C2×C22⋊Q8×C43C2214yes—
14C2×#121×C43C2214yes—
15C4×#41×C43—216no—
16C2×C4×Q8×C43C2212yes—
17C2×C4×Q8×C43C2212yes—
18C2×C4×D4×C43C2214yes—
19C2×C4×D4×C43C2214yes—
20C2×C4×D4×C43C2212yes—
21C2×C4×D4×C43C2212yes—
22C2×C4×D4×C43C2214yes—
23C2×#117×C43C2214yes—
24C2×#117×C43C2212yes—
25C2×#117×C43C2212yes—
26C22×C42×C43C2214yes—
27C22×C42×C43C2211yescharacteristic
28C43×#398C2214yes—
29C43×#397C2214yes—
30C43×#396C2218yes—
31C43×#394C2214yes—
32C43×#394C2218yes—
33C43×#392C2214yes—
34C43×#391C2214yes—
35C43×#390C2214yes—
36C43×#389C2214yes—
37C43×#389C2214yes—
38C43×#388C2218yes—
39C43×#387C2218yes—
40C43×#386C2218yes—
41C43×#385C2218yes—
42C43×#384C2211yescharacteristic
43C43×#384C2211yescharacteristic
44C43×#382C2212yes—
45C43×#380C2214yes—
46C43×#380C2214yes—
47C43×#380C2214yes—
48C4×C4⋊C4×C43C2214yes—
49C4×C4⋊C4×C43C2214yes—
50C4×C22⋊C4×C43C2218yes—
51C2×#41×C43—28no—
52C2×#41×C43—28no—
53C2×#41×C43—28no—
54C22×Q8×C43C2312yes—
55C22×D4×C43C2314yes—
56C22×D4×C43C2314yes—
57C22×D4×C43C2312yes—
58C23×C4×C43C2314yes—
59C23×C4×C43C2314yes—
60C23×C4×C43C2314yes—
61C23×C4×C43C2312yes—
62C23×C4×C43C2311yescharacteristic
63C22⋊Q8×C43—216no—
64#121×C43—216no—
65C4×Q8×C43—28no—
66C4×Q8×C43—28no—
67C4×D4×C43—216no—
68C4×D4×C43—216no—
69C4×D4×C43—28no—
70C4×D4×C43—28no—
71C4×D4×C43—48no—
72#117×C43—28no—
73#117×C43—216no—
74#117×C43—44no—
75C2×C4⋊C4×C43C2312yes—
76C2×C4⋊C4×C43C2312yes—
77C2×C4⋊C4×C43C2314yes—
78C2×C4⋊C4×C43C2314yes—
79C2×C4⋊C4×C43C2314yes—
80C2×C4⋊C4×C43C2314yes—
81C2×C4⋊C4×C43C2318yes—
82C2×C4⋊C4×C43C2312yes—
83C2×C4⋊C4×C43C2312yes—
84C2×C4⋊C4×C43C2314yes—
85C2×C22⋊C4×C43C2314yes—
86C2×C22⋊C4×C43C2314yes—
87C2×C22⋊C4×C43C2314yes—
88C2×C22⋊C4×C43C2318yes—
89C2×C22⋊C4×C43C2318yes—
90C2×C22⋊C4×C43C2314yes—
91C2×C22⋊C4×C43C2318yes—
92C2×C42×C43—216no—
93C2×C42×C43D418yescomplemented
94C2×C42×C43C2314yes—
95C2×C42×C43C2314yes—
96C2×C42×C43C2314yes—
97C2×C42×C43C2314yes—
98C2×C42×C43C2311yescharacteristic
99C2×C42×C43C2311yescharacteristic
100C2×C42×C43C2312yes—
101#95×C43C2318yes—
102#95×C43C2318yes—
103#95×C43C2314yes—
104#95×C43C2318yes—
105#95×C43C2314yes—
106C24×C43C2411yescharacteristic
107C24×C43C2414yes—
108#41×C43—264no—
109C2×Q8×C43—24no—
110C2×Q8×C43—24no—
111C2×Q8×C43#4118yescomplemented
112C2×D4×C43—24no—
113C2×D4×C43—28no—
114C2×D4×C43—24no—
115C2×D4×C43—28no—
116C2×D4×C43—28no—
117C2×D4×C43—216no—
118C2×D4×C43—44no—
119C2×D4×C43#4118yescomplemented
120C22×C4×C43—28no—
121C22×C4×C43—28no—
122C22×C4×C43—24no—
123C22×C4×C43—24no—
124C22×C4×C43—22no—
125C22×C4×C43—22no—
126C22×C4×C43—28no—
127C22×C4×C43—28no—
128C22×C4×C43—28no—
129C22×C4×C43—28no—
130C22×C4×C43—28no—
131C22×C4×C43—28no—
132C22×C4×C43—28no—
133C22×C4×C43C2×D418yes—
134C22×C4×C43C2×D414yes—
135C22×C4×C43C2414yes—
136C22×C4×C43C2414yes—
137C22×C4×C43C2414yes—
138C22×C4×C43C2414yes—
139C22×C4×C43C2412yes—
140C22×C4×C43C2411yescharacteristic
141C22×C4×C43C2414yes—
142C22×C4×C43C2412yes—
143C22×C4×C43C2411yescharacteristic
144C4⋊C4×C43—28no—
145C4⋊C4×C43—28no—
146C4⋊C4×C43—24no—
147C4⋊C4×C43—24no—
148C4⋊C4×C43—28no—
149C4⋊C4×C43—28no—
150C4⋊C4×C43—216no—
151C4⋊C4×C43—42no—
152C4⋊C4×C43—42no—
153C4⋊C4×C43—44no—
154C22⋊C4×C43—28no—
155C22⋊C4×C43—28no—
156C22⋊C4×C43—216no—
157C22⋊C4×C43—28no—
158C22⋊C4×C43—216no—
159C22⋊C4×C43—44no—
160C22⋊C4×C43—48no—
161C42×C43—28no—
162C42×C43—28no—
163C42×C43—28no—
164C42×C43—28no—
165C42×C43C2×D418yes—
166C42×C43C2×D414yes—
167C42×C43C2×D414yes—
168C23×C43—24no—
169C23×C43—24no—
170C23×C43—22no—
171C23×C43—22no—
172C23×C43—24no—
173C23×C43—24no—
174C23×C43—21no—
175C23×C43—24no—
176C23×C43—21no—
177C23×C43—24no—
178C23×C43C22×D412yes—
179C23×C43C2×#4118yes—
180C23×C43C2511yescharacteristic
181Q8×C43—216no—
182D4×C43—232no—
183D4×C43—216no—
184D4×C43—416no—
185C2×C4×C43—232no—
186C2×C4×C43—24no—
187C2×C4×C43—22no—
188C2×C4×C43—22no—
189C2×C4×C43—24no—
190C2×C4×C43—21no—
191C2×C4×C43—21no—
192C2×C4×C43—216no—
193C2×C4×C43—28no—
194C2×C4×C43—24no—
195C2×C4×C43—24no—
196C2×C4×C43—24no—
197C2×C4×C43—28no—
198C2×C4×C43—28no—
199C2×C4×C43—24no—
200C2×C4×C43—24no—
201C2×C4×C43—24no—
202C2×C4×C43—24no—
203C2×C4×C43—24no—
204C2×C4×C43—416no—
205C2×C4×C43—416no—
206C2×C4×C43C22×D414yes—
207C2×C4×C43C22×D412yes—
208C2×C4×C43C22×D414yes—
209C2×C4×C43C22×D412yes—
210C2×C4×C43C2×#4118yes—
211C2×C4×C43C2×#4114yes—
212C2×C4×C43C2×#4114yes—
213C2×C4×C43H(5,𝔽2)12yes—
214C2×C4×C432−1+412yes—
215#34976C4311yesmaximal, characteristic, direct product factor, Sylow
216C22×C43—24no—
217C22×C43—28no—
218C22×C43—22no—
219C22×C43—28no—
220C22×C43—28no—
221C22×C43—44no—
222C22×C43—44no—
223C22×C43—41no—
224C22×C43—42no—
225C22×C43—44no—
226C22×C43—44no—
227C22×C43—41no—
228C22×C43C23×D411yescharacteristic
229C22×C43C22×#4112yes—
230C22×C43C22×#4112yes—
231C22×C43C2×H(5,𝔽2)11yescharacteristic
232C22×C43C2×2−1+411yescharacteristic
233C4×C43—24no—
234C4×C43—28no—
235C4×C43—22no—
236C4×C43—44no—
237C4×C43—44no—
238C4×C43—44no—
239C4×C43—44no—
240C4×C43#52518yes—
241C4×C43#53714yes—
242C2×C4×#41C2×C4312yescomplemented
243#2609C2×C4314yescomplemented
244#2582C2×C4311yescharacteristic, complemented
245#2538C2×C4312yescomplemented
246#2537C2×C4311yescharacteristic, complemented
247#2485C2×C4314yescomplemented
248#2407C2×C4314yescomplemented
249#2392C2×C4314yescomplemented
250C4×C22⋊Q8C2×C4314yescomplemented
251C4×#121C2×C4314yescomplemented
252#2285C2×C4311yescharacteristic, complemented
253C2×C43—42no—
254C2×C43—48no—
255C2×C43C2×#52512yes—
256C2×C43C2×#53711yescharacteristic
257C2×C43#348111yescharacteristic
258C2×C43#348212yes—
259C2×C43#348311yescharacteristic
260C22×#41C22×C4312yes—
261C2×C22⋊Q8C22×C4314yes—
262C2×#121C22×C4314yes—
263C4×#41—216no—
264C2×C4×Q8C22×C4312yes—
265C2×C4×Q8C22×C4312yes—
266C2×C4×D4C22×C4314yes—
267C2×C4×D4C22×C4314yes—
268C2×C4×D4C22×C4312yes—
269C2×C4×D4C22×C4312yes—
270C2×C4×D4C22×C4314yes—
271C2×#117C22×C4314yes—
272C2×#117C22×C4312yes—
273C2×#117C22×C4312yes—
274C22×C42C22×C4314yes—
275C22×C42C22×C4311yescharacteristic
276#398C22×C4314yes—
277#397C22×C4314yes—
278#396C22×C4318yes—
279#394C22×C4314yes—
280#394C22×C4318yes—
281#392C22×C4314yes—
282#391C22×C4314yes—
283#390C22×C4314yes—
284#389C22×C4314yes—
285#389C22×C4314yes—
286#388C22×C4318yes—
287#387C22×C4318yes—
288#386C22×C4318yes—
289#385C22×C4318yes—
290#384C22×C4311yescharacteristic
291#384C22×C4311yescharacteristic
292#382C22×C4312yes—
293#380C22×C4314yes—
294#380C22×C4314yes—
295#380C22×C4314yes—
296C4×C4⋊C4C22×C4314yes—
297C4×C4⋊C4C22×C4314yes—
298C4×C22⋊C4C22×C4318yes—
299C43#3497611yescharacteristic, direct product factor, Sylow
300C2×#41—28no—
301C2×#41—28no—
302C2×#41—28no—
303C22×Q8C23×C4312yes—
304C22×D4C23×C4314yes—
305C22×D4C23×C4314yes—
306C22×D4C23×C4312yes—
307C23×C4C23×C4314yes—
308C23×C4C23×C4314yes—
309C23×C4C23×C4314yes—
310C23×C4C23×C4311yescharacteristic
311C23×C4C23×C4312yes—
312C22⋊Q8—216no—
313#121—216no—
314C4×Q8—28no—
315C4×Q8—28no—
316C4×D4—216no—
317C4×D4—216no—
318C4×D4—28no—
319C4×D4—28no—
320C4×D4—48no—
321#117—28no—
322#117—216no—
323#117—44no—
324C2×C4⋊C4C23×C4312yes—
325C2×C4⋊C4C23×C4312yes—
326C2×C4⋊C4C23×C4314yes—
327C2×C4⋊C4C23×C4314yes—
328C2×C4⋊C4C23×C4314yes—
329C2×C4⋊C4C23×C4314yes—
330C2×C4⋊C4C23×C4318yes—
331C2×C4⋊C4C23×C4312yes—
332C2×C4⋊C4C23×C4312yes—
333C2×C4⋊C4C23×C4314yes—
334C2×C22⋊C4C23×C4314yes—
335C2×C22⋊C4C23×C4314yes—
336C2×C22⋊C4C23×C4314yes—
337C2×C22⋊C4C23×C4318yes—
338C2×C22⋊C4C23×C4318yes—
339C2×C22⋊C4C23×C4314yes—
340C2×C22⋊C4C23×C4318yes—
341C2×C42—216no—
342C2×C42D4×C4318yescomplemented
343C2×C42C23×C4314yes—
344C2×C42C23×C4314yes—
345C2×C42C23×C4314yes—
346C2×C42C23×C4314yes—
347C2×C42C23×C4311yescharacteristic
348C2×C42C23×C4311yescharacteristic
349C2×C42C23×C4312yes—
350#95C23×C4318yes—
351#95C23×C4318yes—
352#95C23×C4314yes—
353#95C23×C4318yes—
354#95C23×C4314yes—
355C24C24×C4311yescharacteristic
356C24C24×C4314yes—
357#41—264no—
358C2×Q8—24no—
359C2×Q8—24no—
360C2×Q8#41×C4318yescomplemented
361C2×D4—28no—
362C2×D4—28no—
363C2×D4—216no—
364C2×D4—24no—
365C2×D4—28no—
366C2×D4—24no—
367C2×D4—44no—
368C2×D4#41×C4318yescomplemented
369C22×C4—28no—
370C22×C4—28no—
371C22×C4—28no—
372C22×C4—24no—
373C22×C4—24no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—28no—
377C22×C4—28no—
378C22×C4—28no—
379C22×C4—28no—
380C22×C4—28no—
381C22×C4—28no—
382C22×C4C2×D4×C4318yes—
383C22×C4C2×D4×C4314yes—
384C22×C4C24×C4314yes—
385C22×C4C24×C4314yes—
386C22×C4C24×C4314yes—
387C22×C4C24×C4314yes—
388C22×C4C24×C4312yes—
389C22×C4C24×C4311yescharacteristic
390C22×C4C24×C4314yes—
391C22×C4C24×C4312yes—
392C22×C4C24×C4311yescharacteristic
393C4⋊C4—28no—
394C4⋊C4—28no—
395C4⋊C4—24no—
396C4⋊C4—24no—
397C4⋊C4—28no—
398C4⋊C4—28no—
399C4⋊C4—216no—
400C4⋊C4—42no—
401C4⋊C4—42no—
402C4⋊C4—44no—
403C22⋊C4—28no—
404C22⋊C4—216no—
405C22⋊C4—28no—
406C22⋊C4—28no—
407C22⋊C4—216no—
408C22⋊C4—44no—
409C22⋊C4—48no—
410C42—28no—
411C42—28no—
412C42—28no—
413C42—28no—
414C42C2×D4×C4318yes—
415C42C2×D4×C4314yes—
416C42C2×D4×C4314yes—
417C23—24no—
418C23—24no—
419C23—22no—
420C23—22no—
421C23—24no—
422C23—24no—
423C23—21no—
424C23—24no—
425C23—21no—
426C23—24no—
427C23C22×D4×C4312yes—
428C23C2×#41×C4318yes—
429C23C25×C4311yescharacteristic
430Q8—216no—
431D4—232no—
432D4—216no—
433D4—416no—
434C2×C4—232no—
435C2×C4—24no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—24no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—216no—
442C2×C4—28no—
443C2×C4—24no—
444C2×C4—24no—
445C2×C4—24no—
446C2×C4—28no—
447C2×C4—28no—
448C2×C4—24no—
449C2×C4—24no—
450C2×C4—24no—
451C2×C4—24no—
452C2×C4—24no—
453C2×C4—416no—
454C2×C4—416no—
455C2×C4C22×D4×C4314yes—
456C2×C4C22×D4×C4312yes—
457C2×C4C22×D4×C4314yes—
458C2×C4C22×D4×C4312yes—
459C2×C4C2×#41×C4318yes—
460C2×C4C2×#41×C4314yes—
461C2×C4C2×#41×C4314yes—
462C2×C4H(5,𝔽2)×C4312yes—
463C2×C42−1+4×C4312yes—
464C22—24no—
465C22—28no—
466C22—22no—
467C22—28no—
468C22—28no—
469C22—44no—
470C22—44no—
471C22—41no—
472C22—42no—
473C22—44no—
474C22—44no—
475C22—41no—
476C22C23×D4×C4311yescharacteristic
477C22C22×#41×C4312yes—
478C22C22×#41×C4312yes—
479C22C2×H(5,𝔽2)×C4311yescharacteristic
480C22C2×2−1+4×C4311yescharacteristic
481C4—24no—
482C4—28no—
483C4—22no—
484C4—44no—
485C4—44no—
486C4—44no—
487C4—44no—
488C4C43×#52518yes—
489C4C43×#53714yes—
490C2—42no—
491C2—48no—
492C2C2×C43×#52512yes—
493C2C2×C43×#53711yescharacteristic
494C2C43×#348111yescharacteristic
495C2C43×#348212yes—
496C2C43×#348311yescharacteristic
subgroupG/H
centerC22×C4×C43C24
commutator, Frattini, cosocleC23C25×C43
socleC23×C43C25
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C4×#41×C43C2semidirect
2. C43×#2609C2semidirect
3. C43×#2582C2semidirect
4. C43×#2538C2semidirect
5. C43×#2537C2semidirect
6. C43×#2485C2semidirect
7. C43×#2407C2semidirect
8. C43×#2392C2semidirect
9. C4×C22⋊Q8×C43C2semidirect
10. C4×#121×C43C2semidirect
11. C43×#2285C2semidirect
93. C2×C42×C43D4semidirect
111. C2×Q8×C43#41semidirect
119. C2×D4×C43#41semidirect
215. #34976C43direct (N × H)
242. C2×C4×#41C2×C43semidirect
243. #2609C2×C43semidirect
244. #2582C2×C43semidirect
245. #2538C2×C43semidirect
246. #2537C2×C43semidirect
247. #2485C2×C43semidirect
248. #2407C2×C43semidirect
249. #2392C2×C43semidirect
250. C4×C22⋊Q8C2×C43semidirect
251. C4×#121C2×C43semidirect
252. #2285C2×C43semidirect
299. C43#34976direct (N × H)
342. C2×C42D4×C43semidirect
360. C2×Q8#41×C43semidirect
368. C2×D4#41×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#41×C432
C43×#26092
C43×#25822
C43×#25382
C43×#25372
C43×#24852
C43×#24072
C43×#23922
C4×C22⋊Q8×C432
C4×#121×C432
C43×#22852
#3497643