Finite Group Databasebeta

← C43×#61936 #24981953

Subgroups — C43×#61936 #24981953

Order 11008.

1634 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3556C211yesmaximal, characteristic, complemented
2C43×#3509C211yesmaximal, characteristic
3C43×#3398C214yesmaximal, complemented
4C43×#3395C214yesmaximal, complemented
5C43×#3374C214yesmaximal, complemented
6C43×#3364C214yesmaximal, complemented
7C43×#3223C214yesmaximal
8C43×#3209C212yesmaximal, complemented
9C43×#3127C214yesmaximal, complemented
10C43×#3107C212yesmaximal
11C43×#2986C211yesmaximal, characteristic, complemented
12C43×#564—22no—
13C43×#557—22no—
14C43×#557C2214yes—
15C43×#557C2214yes—
16C43×#557C2214yes—
17C43×#556C2214yes—
18C43×#552—24no—
19C43×#541—22no—
20C43×#541—24no—
21C43×#541C2214yes—
22C43×#536C2212yes—
23C43×#533—22no—
24C43×#533C2212yes—
25C43×#533C2211yescharacteristic
26C2×C4⋊Q8×C43C2211yescharacteristic
27C43×#519C2212yes—
28C4×#41×C43C2211yescharacteristic
29C43×#497C2214yes—
30C43×#494C2214yes—
31C43×#494C2214yes—
32C43×#491C2214yes—
33C43×#488C2214yes—
34C43×#487C2214yes—
35C43×#485C2214yes—
36C43×#479C2218yes—
37C43×#475C2212yes—
38C43×#474C2212yes—
39C43×#464C2218yes—
40C43×#462C2212yes—
41C43×#462C2214yes—
42C43×#462C2218yes—
43C43×#462C2214yes—
44C43×#462C2218yes—
45C43×#461C2212yes—
46C43×#452C2214yes—
47C43×#451C2218yes—
48C43×#446C2214yes—
49C8×Q8×C43C2214yes—
50C43×#441C2218yes—
51C4×Q16×C43C2214yes—
52C4×Q16×C43C2218yes—
53C4×SD16×C43C2214yes—
54C43×#433C2214yes—
55C43×#431C2212yes—
56C2×#41×C43C2311yescharacteristic
57C22×Q8×C43C2312yes—
58C2×Q16×C43C2318yes—
59C2×Q16×C43C2318yes—
60C2×Q16×C43C2314yes—
61C2×SD16×C43C2314yes—
62C4⋊Q8×C43—24no—
63C4⋊Q8×C43—21no—
64C4⋊Q8×C43—21no—
65C4⋊Q8×C43D412yes—
66C4⋊Q8×C43C2314yes—
67C4⋊Q8×C43C2314yes—
68C4⋊Q8×C43C2312yes—
69C4⋊Q8×C43C2314yes—
70C4⋊Q8×C43C2312yes—
71#126×C43—28no—
72#126×C43—28no—
73#125×C43—24no—
74#125×C43—28no—
75#125×C43—24no—
76#125×C43—28no—
77#125×C43—28no—
78#125×C43—28no—
79#125×C43—22no—
80#125×C43D412yes—
81#125×C43C2314yes—
82#124×C43C2314yes—
83#123×C43—24no—
84C22⋊Q8×C43—24no—
85C22⋊Q8×C43—22no—
86C22⋊Q8×C43—24no—
87C22⋊Q8×C43D414yes—
88C22⋊Q8×C43C2314yes—
89C4×Q8×C43—24no—
90C4×Q8×C43—24no—
91C4×Q8×C43—24no—
92C4×Q8×C43—24no—
93C4×Q8×C43—22no—
94C4×Q8×C43C2312yes—
95C4×Q8×C43C2318yes—
96C4×Q8×C43C2314yes—
97C4×Q8×C43C2318yes—
98C4×Q8×C43C2314yes—
99C4×D4×C43—22no—
100C4×D4×C43C2312yes—
101#117×C43—22no—
102#117×C43—24no—
103#117×C43—24no—
104#117×C43—21no—
105#117×C43C2311yescharacteristic
106#117×C43C2312yes—
107C2×C4⋊C4×C43—22no—
108C2×C42×C43—21no—
109C2×C42×C43C2311yescharacteristic
110#107×C43C2314yes—
111#106×C43C2314yes—
112C4⋊C8×C43C2312yes—
113C4⋊C8×C43C2312yes—
114C4⋊C8×C43C2318yes—
115#103×C43C2314yes—
116#103×C43C2314yes—
117#103×C43C2318yes—
118#103×C43C2314yes—
119#103×C43C2318yes—
120#102×C43C2314yes—
121C22⋊C8×C43C2314yes—
122#97×C43C2314yes—
123C4×C8×C43C2314yes—
124C4×C8×C43C2314yes—
125#41×C43—42no—
126C2×Q8×C43—22no—
127C2×Q8×C43—22no—
128C2×Q8×C43—44no—
129C2×Q8×C43C2×D414yes—
130C2×Q8×C43C2414yes—
131C2×Q8×C43C2411yescharacteristic
132C2×Q8×C43C2414yes—
133C2×D4×C43—21no—
134C2×D4×C43C2411yescharacteristic
135C22×C4×C43—22no—
136C22×C4×C43—21no—
137C22×C4×C43—22no—
138C22×C4×C43C2×D412yes—
139C22×C4×C43C2411yescharacteristic
140Q16×C43—48no—
141Q16×C43—48no—
142Q16×C43—44no—
143SD16×C43—44no—
144C2×C8×C43C2414yes—
145C2×C8×C43C2414yes—
146C4⋊C4×C43—24no—
147C4⋊C4×C43—24no—
148C4⋊C4×C43—22no—
149C4⋊C4×C43—28no—
150C4⋊C4×C43—22no—
151C4⋊C4×C43—22no—
152C4⋊C4×C43—22no—
153C4⋊C4×C43—28no—
154C4⋊C4×C43—24no—
155C4⋊C4×C43—28no—
156C4⋊C4×C43—28no—
157C4⋊C4×C43—24no—
158C4⋊C4×C43—28no—
159C4⋊C4×C43C2×D414yes—
160C4⋊C4×C43C2×D414yes—
161C4⋊C4×C43C2×D418yes—
162C4⋊C4×C43C2414yes—
163C4⋊C4×C43C2412yes—
164C22⋊C4×C43—22no—
165C22⋊C4×C43—28no—
166C22⋊C4×C43—21no—
167C22⋊C4×C43—24no—
168C22⋊C4×C43C2×D414yes—
169C42×C43—21no—
170C42×C43—22no—
171C42×C43—28no—
172C42×C43—24no—
173C42×C43—28no—
174C42×C43C2×D411yescharacteristic
175C42×C43C2×D411yescharacteristic
176C42×C43C2412yes—
177C42×C43C2414yes—
178C23×C43—21no—
179C23×C43C22×D411yescharacteristic
180Q8×C43—28no—
181Q8×C43—24no—
182Q8×C43—24no—
183Q8×C43—28no—
184Q8×C43—22no—
185Q8×C43—44no—
186Q8×C43—44no—
187D4×C43—22no—
188D4×C43—42no—
189C2×C4×C43—24no—
190C2×C4×C43—22no—
191C2×C4×C43—22no—
192C2×C4×C43—24no—
193C2×C4×C43—24no—
194C2×C4×C43—24no—
195C2×C4×C43—21no—
196C2×C4×C43—42no—
197C2×C4×C43—44no—
198C2×C4×C43—44no—
199C2×C4×C43C22×D418yes—
200C2×C4×C43C22×D411yescharacteristic
201C2×C4×C43C22×D412yes—
202C2×C4×C43C22×D412yes—
203C2×C4×C43C2511yescharacteristic
204C8×C43—24no—
205C8×C43—24no—
206#61936C4311yesmaximal, characteristic, direct product factor, Sylow
207C22×C43—21no—
208C22×C43—22no—
209C22×C43—41no—
210C22×C43—42no—
211C22×C43C23×D411yescharacteristic
212C4×C43—21no—
213C4×C43—22no—
214C4×C43—28no—
215C4×C43—41no—
216C4×C43—44no—
217C4×C43—44no—
218C4×C43—42no—
219C4×C43—44no—
220C4×C43#57814yes—
221C4×C43#58512yes—
222#3556C2×C4311yescharacteristic, complemented
223#3509C2×C4311yescharacteristic
224#3398C2×C4314yescomplemented
225#3395C2×C4314yescomplemented
226#3374C2×C4314yescomplemented
227#3364C2×C4314yescomplemented
228#3223C2×C4314yes—
229#3209C2×C4312yescomplemented
230#3127C2×C4314yescomplemented
231#3107C2×C4312yes—
232#2986C2×C4311yescharacteristic, complemented
233C2×C43—41no—
234C2×C43—81no—
235C2×C43#348711yescharacteristic
236C2×C43C2×#57812yes—
237#564—22no—
238#557—22no—
239#557C22×C4314yes—
240#557C22×C4314yes—
241#557C22×C4314yes—
242#556C22×C4314yes—
243#552—24no—
244#541—22no—
245#541—24no—
246#541C22×C4314yes—
247#536C22×C4312yes—
248#533—22no—
249#533C22×C4312yes—
250#533C22×C4311yescharacteristic
251C2×C4⋊Q8C22×C4311yescharacteristic
252#519C22×C4312yes—
253C4×#41C22×C4311yescharacteristic
254#497C22×C4314yes—
255#494C22×C4314yes—
256#494C22×C4314yes—
257#491C22×C4314yes—
258#488C22×C4314yes—
259#487C22×C4314yes—
260#485C22×C4314yes—
261#479C22×C4318yes—
262#475C22×C4312yes—
263#474C22×C4312yes—
264#464C22×C4318yes—
265#462C22×C4312yes—
266#462C22×C4314yes—
267#462C22×C4318yes—
268#462C22×C4314yes—
269#462C22×C4318yes—
270#461C22×C4312yes—
271#452C22×C4314yes—
272#451C22×C4318yes—
273#446C22×C4314yes—
274C8×Q8C22×C4314yes—
275#441C22×C4318yes—
276C4×Q16C22×C4314yes—
277C4×Q16C22×C4318yes—
278C4×SD16C22×C4314yes—
279#433C22×C4314yes—
280#431C22×C4312yes—
281C43#6193611yescharacteristic, direct product factor, Sylow
282C2×#41C23×C4311yescharacteristic
283C22×Q8C23×C4312yes—
284C2×Q16C23×C4318yes—
285C2×Q16C23×C4314yes—
286C2×Q16C23×C4318yes—
287C2×SD16C23×C4314yes—
288C4⋊Q8—24no—
289C4⋊Q8—21no—
290C4⋊Q8—21no—
291C4⋊Q8D4×C4312yes—
292C4⋊Q8C23×C4314yes—
293C4⋊Q8C23×C4312yes—
294C4⋊Q8C23×C4314yes—
295C4⋊Q8C23×C4314yes—
296C4⋊Q8C23×C4312yes—
297#126—28no—
298#126—28no—
299#125—24no—
300#125—28no—
301#125—24no—
302#125—28no—
303#125—28no—
304#125—28no—
305#125—22no—
306#125D4×C4312yes—
307#125C23×C4314yes—
308#124C23×C4314yes—
309#123—24no—
310C22⋊Q8—24no—
311C22⋊Q8—22no—
312C22⋊Q8—24no—
313C22⋊Q8D4×C4314yes—
314C22⋊Q8C23×C4314yes—
315C4×Q8—24no—
316C4×Q8—24no—
317C4×Q8—24no—
318C4×Q8—24no—
319C4×Q8—22no—
320C4×Q8C23×C4312yes—
321C4×Q8C23×C4318yes—
322C4×Q8C23×C4314yes—
323C4×Q8C23×C4318yes—
324C4×Q8C23×C4314yes—
325C4×D4—22no—
326C4×D4C23×C4312yes—
327#117—22no—
328#117—24no—
329#117—24no—
330#117—21no—
331#117C23×C4311yescharacteristic
332#117C23×C4312yes—
333C2×C4⋊C4—22no—
334C2×C42—21no—
335C2×C42C23×C4311yescharacteristic
336#107C23×C4314yes—
337#106C23×C4314yes—
338C4⋊C8C23×C4312yes—
339C4⋊C8C23×C4312yes—
340C4⋊C8C23×C4318yes—
341#103C23×C4314yes—
342#103C23×C4314yes—
343#103C23×C4318yes—
344#103C23×C4314yes—
345#103C23×C4318yes—
346#102C23×C4314yes—
347C22⋊C8C23×C4314yes—
348#97C23×C4314yes—
349C4×C8C23×C4314yes—
350C4×C8C23×C4314yes—
351#41—42no—
352C2×Q8—22no—
353C2×Q8—22no—
354C2×Q8—44no—
355C2×Q8C2×D4×C4314yes—
356C2×Q8C24×C4314yes—
357C2×Q8C24×C4311yescharacteristic
358C2×Q8C24×C4314yes—
359C2×D4—21no—
360C2×D4C24×C4311yescharacteristic
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—21no—
364C22×C4C2×D4×C4312yes—
365C22×C4C24×C4311yescharacteristic
366Q16—48no—
367Q16—48no—
368Q16—44no—
369SD16—44no—
370C2×C8C24×C4314yes—
371C2×C8C24×C4314yes—
372C4⋊C4—24no—
373C4⋊C4—24no—
374C4⋊C4—22no—
375C4⋊C4—28no—
376C4⋊C4—22no—
377C4⋊C4—22no—
378C4⋊C4—22no—
379C4⋊C4—28no—
380C4⋊C4—24no—
381C4⋊C4—28no—
382C4⋊C4—28no—
383C4⋊C4—24no—
384C4⋊C4—28no—
385C4⋊C4C2×D4×C4314yes—
386C4⋊C4C2×D4×C4314yes—
387C4⋊C4C2×D4×C4318yes—
388C4⋊C4C24×C4314yes—
389C4⋊C4C24×C4312yes—
390C22⋊C4—21no—
391C22⋊C4—24no—
392C22⋊C4—22no—
393C22⋊C4—28no—
394C22⋊C4C2×D4×C4314yes—
395C42—21no—
396C42—22no—
397C42—28no—
398C42—24no—
399C42—28no—
400C42C2×D4×C4311yescharacteristic
401C42C2×D4×C4311yescharacteristic
402C42C24×C4312yes—
403C42C24×C4314yes—
404C23—21no—
405C23C22×D4×C4311yescharacteristic
406Q8—28no—
407Q8—24no—
408Q8—24no—
409Q8—28no—
410Q8—22no—
411Q8—44no—
412Q8—44no—
413D4—22no—
414D4—42no—
415C2×C4—24no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—24no—
419C2×C4—24no—
420C2×C4—24no—
421C2×C4—21no—
422C2×C4—42no—
423C2×C4—44no—
424C2×C4—44no—
425C2×C4C22×D4×C4318yes—
426C2×C4C22×D4×C4311yescharacteristic
427C2×C4C22×D4×C4312yes—
428C2×C4C22×D4×C4312yes—
429C2×C4C25×C4311yescharacteristic
430C8—24no—
431C8—24no—
432C22—21no—
433C22—22no—
434C22—41no—
435C22—42no—
436C22C23×D4×C4311yescharacteristic
437C4—21no—
438C4—22no—
439C4—28no—
440C4—41no—
441C4—44no—
442C4—44no—
443C4—42no—
444C4—44no—
445C4C43×#57814yes—
446C4C43×#58512yes—
447C2—41no—
448C2—81no—
449C2C43×#348711yescharacteristic
450C2C2×C43×#57812yes—
subgroupG/H
center, socleC22×C43C23×D4
commutator, Frattini, cosocleC2×C4C25×C43
prime radicalC2×#41×C43C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C43×#533 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#3556C2semidirect
3. C43×#3398C2semidirect
4. C43×#3395C2semidirect
5. C43×#3374C2semidirect
6. C43×#3364C2semidirect
8. C43×#3209C2semidirect
9. C43×#3127C2semidirect
11. C43×#2986C2semidirect
206. #61936C43direct (N × H)
222. #3556C2×C43semidirect
224. #3398C2×C43semidirect
225. #3395C2×C43semidirect
226. #3374C2×C43semidirect
227. #3364C2×C43semidirect
229. #3209C2×C43semidirect
230. #3127C2×C43semidirect
232. #2986C2×C43semidirect
281. C43#61936direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#35562
C43×#35092
C43×#33982
C43×#33952
C43×#33742
C43×#33642
C43×#32232
C43×#32092
C43×#31272
C43×#31072
C43×#29862
#6193643