Finite Group Databasebeta

← C43×#19559 #24939576

Subgroups — C43×#19559 #24939576

Order 11008.

590 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3254C211yesmaximal, characteristic
2C43×#3229C211yesmaximal, characteristic, complemented
3C43×#3227C211yesmaximal, characteristic
4C43×#2979C211yesmaximal, characteristic
5C43×#1703C212yesmaximal, complemented
6C43×#1691C212yesmaximal, complemented
7C43×#1683C212yesmaximal, complemented
8C43×#1671C212yesmaximal, complemented
9C43×#1574C211yesmaximal, characteristic, complemented
10C43×#1548C211yesmaximal, characteristic, complemented
11C43×#1544C211yesmaximal, characteristic, complemented
12C43×#533C2211yescharacteristic
13C43×#532C2211yescharacteristic
14C2×C4⋊Q8×C43C2211yescharacteristic
15C43×#498—21no—
16C43×#498C2212yes—
17C43×#487C2212yes—
18C43×#486—21no—
19C43×#483—22no—
20C43×#481—22no—
21C43×#477—21no—
22C43×#476C2212yes—
23C43×#476C2212yes—
24C43×#475—21no—
25C43×#475—21no—
26C43×#474C2212yes—
27C43×#468—22no—
28C43×#461C2212yes—
29C43×#460—21no—
30C43×#436—21no—
31C43×#436C2212yes—
32C8×D4×C43—21no—
33C8×D4×C43C2212yes—
34C43×#431C2211yescharacteristic
35C43×#431C2211yescharacteristic
36C43×#431C2211yescharacteristic
37C43×#423C2211yescharacteristic
38C43×#408—22no—
39C43×#335C2212yes—
40C43×#334C2212yes—
41C43×#333C2212yes—
42C43×#333C2212yes—
43C43×#332C2211yescharacteristic
44C43×#332C2211yescharacteristic
45C43×#332C2211yescharacteristic
46C43×#332C2211yescharacteristic
47C2×#41×C43—21no—
48C22×Q8×C43—21no—
49C2×SD16×C43—22no—
50C2×M16×C43—21no—
51C2×M16×C43—22no—
52C22×C8×C43—22no—
53C4⋊Q8×C43—21no—
54C4⋊Q8×C43—21no—
55C4⋊Q8×C43—21no—
56C4⋊Q8×C43D411yescharacteristic
57C4⋊Q8×C43C2311yescharacteristic
58C4⋊Q8×C43C2312yes—
59C4⋊Q8×C43C2311yescharacteristic
60#127×C43D411yescharacteristic
61#125×C43—21no—
62#124×C43—21no—
63C22⋊Q8×C43—21no—
64C22⋊Q8×C43—21no—
65#121×C43—21no—
66#121×C43D412yes—
67C4×Q8×C43—21no—
68C4×Q8×C43—21no—
69C4×D4×C43—21no—
70C4×D4×C43C2312yes—
71#117×C43—21no—
72C2×C4⋊C4×C43—21no—
73C2×C4⋊C4×C43—21no—
74C2×C42×C43C2311yescharacteristic
75#107×C43—22no—
76#106×C43—22no—
77#106×C43—22no—
78#106×C43—22no—
79#106×C43—22no—
80C4⋊C8×C43—21no—
81C4⋊C8×C43D411yescharacteristic
82C4⋊C8×C43D411yescharacteristic
83C4⋊C8×C43C2311yescharacteristic
84C4⋊C8×C43C2311yescharacteristic
85C4⋊C8×C43C2311yescharacteristic
86C4⋊C8×C43C2311yescharacteristic
87C4⋊C8×C43C2312yes—
88#103×C43—22no—
89#103×C43—22no—
90#103×C43—22no—
91#102×C43—22no—
92#102×C43—22no—
93#102×C43—22no—
94C22⋊C8×C43—21no—
95C22⋊C8×C43—21no—
96C22⋊C8×C43—22no—
97C22⋊C8×C43—22no—
98C22⋊C8×C43D412yes—
99C4×C8×C43—21no—
100C4×C8×C43—21no—
101C4×C8×C43C2312yes—
102#41×C43—81no—
103#41×C43—81no—
104C2×Q8×C43—21no—
105C2×Q8×C43—21no—
106C2×Q8×C43—21no—
107C2×Q8×C43—22no—
108C2×Q8×C43—41no—
109C2×Q8×C43—82no—
110C2×D4×C43—21no—
111C2×D4×C43—21no—
112C2×D4×C43—22no—
113C2×D4×C43C2×D412yes—
114C22×C4×C43—22no—
115C22×C4×C43—41no—
116C22×C4×C43C2×D411yescharacteristic
117C22×C4×C43C2×D411yescharacteristic
118C22×C4×C43#4111yescharacteristic
119SD16×C43—82no—
120M16×C43—82no—
121M16×C43—81no—
122C2×C8×C43—21no—
123C2×C8×C43—21no—
124C2×C8×C43—21no—
125C2×C8×C43—21no—
126C2×C8×C43—22no—
127C2×C8×C43—82no—
128C2×C8×C43C2×D412yes—
129C2×C8×C43C2×D412yes—
130C4⋊C4×C43—21no—
131C4⋊C4×C43—22no—
132C4⋊C4×C43—21no—
133C4⋊C4×C43—22no—
134C4⋊C4×C43—21no—
135C4⋊C4×C43—21no—
136C4⋊C4×C43—21no—
137C4⋊C4×C43—41no—
138C4⋊C4×C43—41no—
139C4⋊C4×C43—41no—
140C4⋊C4×C43—41no—
141C4⋊C4×C43C2×D412yes—
142C22⋊C4×C43—22no—
143C22⋊C4×C43—22no—
144C22⋊C4×C43—41no—
145C42×C43—41no—
146C42×C43C2×D411yescharacteristic
147C42×C43C2×D411yescharacteristic
148C42×C43#4111yescharacteristic
149C42×C43C2411yescharacteristic
150C23×C43—22no—
151C23×C43#12111yescharacteristic
152Q8×C43—41no—
153Q8×C43—41no—
154Q8×C43—41no—
155Q8×C43—41no—
156Q8×C43—81no—
157Q8×C43—82no—
158Q8×C43—82no—
159D4×C43—22no—
160D4×C43—22no—
161D4×C43—42no—
162D4×C43—81no—
163D4×C43—82no—
164C2×C4×C43—21no—
165C2×C4×C43—21no—
166C2×C4×C43—21no—
167C2×C4×C43—21no—
168C2×C4×C43—22no—
169C2×C4×C43—22no—
170C2×C4×C43—42no—
171C2×C4×C43—42no—
172C2×C4×C43—41no—
173C2×C4×C43—41no—
174C2×C4×C43—42no—
175C2×C4×C43—82no—
176C2×C4×C43#12111yescharacteristic
177C2×C4×C43#12111yescharacteristic
178C2×C4×C43#12111yescharacteristic
179C2×C4×C43C22×D411yescharacteristic
180C2×C4×C43C22×D411yescharacteristic
181C2×C4×C43C2×#4111yescharacteristic
182C8×C43—22no—
183C8×C43—22no—
184C8×C43—41no—
185C8×C43—41no—
186C8×C43—41no—
187C8×C43—42no—
188C8×C43—41no—
189#19559C4311yesmaximal, characteristic, direct product factor, Sylow
190C22×C43—21no—
191C22×C43—21no—
192C22×C43—21no—
193C22×C43—42no—
194C22×C43—42no—
195C22×C43—42no—
196C22×C43C2×#12111yescharacteristic
197C4×C43—21no—
198C4×C43—21no—
199C4×C43—21no—
200C4×C43—42no—
201C4×C43—81no—
202C4×C43—81no—
203C4×C43—82no—
204C4×C43#47112yes—
205C4×C43#57711yescharacteristic
206C4×C43#57711yescharacteristic
207C4×C43#57711yescharacteristic
208C4×C43#57811yescharacteristic
209#3254C2×C4311yescharacteristic
210#3229C2×C4311yescharacteristic, complemented
211#3227C2×C4311yescharacteristic
212#2979C2×C4311yescharacteristic
213#1703C2×C4312yescomplemented
214#1691C2×C4312yescomplemented
215#1683C2×C4312yescomplemented
216#1671C2×C4312yescomplemented
217#1574C2×C4311yescharacteristic, complemented
218#1548C2×C4311yescharacteristic, complemented
219#1544C2×C4311yescharacteristic, complemented
220C2×C43—41no—
221C2×C43—82no—
222C2×C43#304211yescharacteristic
223C2×C43#306311yescharacteristic
224C2×C43C2×#47111yescharacteristic
225#533C22×C4311yescharacteristic
226#532C22×C4311yescharacteristic
227C2×C4⋊Q8C22×C4311yescharacteristic
228#498—21no—
229#498C22×C4312yes—
230#487C22×C4312yes—
231#486—21no—
232#483—22no—
233#481—22no—
234#477—21no—
235#476C22×C4312yes—
236#476C22×C4312yes—
237#475—21no—
238#475—21no—
239#474C22×C4312yes—
240#468—22no—
241#461C22×C4312yes—
242#460—21no—
243#436—21no—
244#436C22×C4312yes—
245C8×D4—21no—
246C8×D4C22×C4312yes—
247#431C22×C4311yescharacteristic
248#431C22×C4311yescharacteristic
249#431C22×C4311yescharacteristic
250#423C22×C4311yescharacteristic
251#408—22no—
252#335C22×C4312yes—
253#334C22×C4312yes—
254#333C22×C4312yes—
255#333C22×C4312yes—
256#332C22×C4311yescharacteristic
257#332C22×C4311yescharacteristic
258#332C22×C4311yescharacteristic
259#332C22×C4311yescharacteristic
260C43#1955911yescharacteristic, direct product factor, Sylow
261C2×#41—21no—
262C22×Q8—21no—
263C2×SD16—22no—
264C2×M16—21no—
265C2×M16—22no—
266C22×C8—22no—
267C4⋊Q8—21no—
268C4⋊Q8—21no—
269C4⋊Q8—21no—
270C4⋊Q8D4×C4311yescharacteristic
271C4⋊Q8C23×C4312yes—
272C4⋊Q8C23×C4311yescharacteristic
273C4⋊Q8C23×C4311yescharacteristic
274#127D4×C4311yescharacteristic
275#125—21no—
276#124—21no—
277C22⋊Q8—21no—
278C22⋊Q8—21no—
279#121—21no—
280#121D4×C4312yes—
281C4×Q8—21no—
282C4×Q8—21no—
283C4×D4—21no—
284C4×D4C23×C4312yes—
285#117—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C42C23×C4311yescharacteristic
289#107—22no—
290#106—22no—
291#106—22no—
292#106—22no—
293#106—22no—
294C4⋊C8—21no—
295C4⋊C8D4×C4311yescharacteristic
296C4⋊C8D4×C4311yescharacteristic
297C4⋊C8C23×C4311yescharacteristic
298C4⋊C8C23×C4311yescharacteristic
299C4⋊C8C23×C4311yescharacteristic
300C4⋊C8C23×C4311yescharacteristic
301C4⋊C8C23×C4312yes—
302#103—22no—
303#103—22no—
304#103—22no—
305#102—22no—
306#102—22no—
307#102—22no—
308C22⋊C8—21no—
309C22⋊C8—21no—
310C22⋊C8—22no—
311C22⋊C8—22no—
312C22⋊C8D4×C4312yes—
313C4×C8—21no—
314C4×C8—21no—
315C4×C8C23×C4312yes—
316#41—81no—
317#41—81no—
318C2×Q8—21no—
319C2×Q8—21no—
320C2×Q8—21no—
321C2×Q8—22no—
322C2×Q8—41no—
323C2×Q8—82no—
324C2×D4—22no—
325C2×D4—21no—
326C2×D4—21no—
327C2×D4C2×D4×C4312yes—
328C22×C4—22no—
329C22×C4—41no—
330C22×C4C2×D4×C4311yescharacteristic
331C22×C4C2×D4×C4311yescharacteristic
332C22×C4#41×C4311yescharacteristic
333SD16—82no—
334M16—82no—
335M16—81no—
336C2×C8—21no—
337C2×C8—21no—
338C2×C8—21no—
339C2×C8—21no—
340C2×C8—22no—
341C2×C8—82no—
342C2×C8C2×D4×C4312yes—
343C2×C8C2×D4×C4312yes—
344C4⋊C4—21no—
345C4⋊C4—22no—
346C4⋊C4—21no—
347C4⋊C4—22no—
348C4⋊C4—21no—
349C4⋊C4—21no—
350C4⋊C4—21no—
351C4⋊C4—41no—
352C4⋊C4—41no—
353C4⋊C4—41no—
354C4⋊C4—41no—
355C4⋊C4C2×D4×C4312yes—
356C22⋊C4—22no—
357C22⋊C4—22no—
358C22⋊C4—41no—
359C42—41no—
360C42C2×D4×C4311yescharacteristic
361C42C2×D4×C4311yescharacteristic
362C42#41×C4311yescharacteristic
363C42C24×C4311yescharacteristic
364C23—22no—
365C23#121×C4311yescharacteristic
366Q8—41no—
367Q8—41no—
368Q8—41no—
369Q8—41no—
370Q8—81no—
371Q8—82no—
372Q8—82no—
373D4—22no—
374D4—22no—
375D4—42no—
376D4—81no—
377D4—82no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—42no—
389C2×C4—82no—
390C2×C4#121×C4311yescharacteristic
391C2×C4#121×C4311yescharacteristic
392C2×C4#121×C4311yescharacteristic
393C2×C4C22×D4×C4311yescharacteristic
394C2×C4C22×D4×C4311yescharacteristic
395C2×C4C2×#41×C4311yescharacteristic
396C8—22no—
397C8—22no—
398C8—41no—
399C8—41no—
400C8—42no—
401C8—41no—
402C8—41no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—42no—
407C22—42no—
408C22—42no—
409C22C2×#121×C4311yescharacteristic
410C4—21no—
411C4—21no—
412C4—21no—
413C4—42no—
414C4—81no—
415C4—81no—
416C4—82no—
417C4C43×#47112yes—
418C4C43×#57711yescharacteristic
419C4C43×#57711yescharacteristic
420C4C43×#57711yescharacteristic
421C4C43×#57811yescharacteristic
422C2—41no—
423C2—82no—
424C2C43×#304211yescharacteristic
425C2C43×#306311yescharacteristic
426C2C2×C43×#47111yescharacteristic
subgroupG/H
center, socleC22×C43C2×#121
commutator, Frattini, cosocleC42C24×C43
prime radicalC43×#532C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C2×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#3229C2semidirect
5. C43×#1703C2semidirect
6. C43×#1691C2semidirect
7. C43×#1683C2semidirect
8. C43×#1671C2semidirect
9. C43×#1574C2semidirect
10. C43×#1548C2semidirect
11. C43×#1544C2semidirect
189. #19559C43direct (N × H)
210. #3229C2×C43semidirect
213. #1703C2×C43semidirect
214. #1691C2×C43semidirect
215. #1683C2×C43semidirect
216. #1671C2×C43semidirect
217. #1574C2×C43semidirect
218. #1548C2×C43semidirect
219. #1544C2×C43semidirect
260. C43#19559direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#32542
C43×#32292
C43×#32272
C43×#29792
C43×#17032
C43×#16912
C43×#16832
C43×#16712
C43×#15742
C43×#15482
C43×#15442
#1955943