Finite Group Databasebeta

← C43×#19199 #24939216

Subgroups — C43×#19199 #24939216

Order 11008.

650 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3227C211yesmaximal, characteristic
2C43×#3226C211yesmaximal, characteristic
3C2×C43×#487C211yesmaximal, characteristic, complemented
4C43×#2931C211yesmaximal, characteristic
5C43×#1703C214yesmaximal, complemented
6C43×#1683C214yesmaximal, complemented
7C43×#1564C211yesmaximal, characteristic, complemented
8C43×#1548C211yesmaximal, characteristic, complemented
9C43×#1546C211yesmaximal, characteristic, complemented
10C2×#131×C43—21no—
11C43×#532C2211yescharacteristic
12C2×C4⋊Q8×C43C2211yescharacteristic
13C2×C4⋊Q8×C43C2211yescharacteristic
14C43×#500—21no—
15C43×#498—21no—
16C43×#487—21no—
17C43×#487—21no—
18C43×#487C2212yes—
19C43×#487C2212yes—
20C43×#486—21no—
21C43×#486—21no—
22C43×#481—22no—
23C43×#480—22no—
24C43×#476C2214yes—
25C43×#474C2214yes—
26C43×#436—21no—
27C43×#436C2212yes—
28C8×D4×C43—21no—
29C8×D4×C43C2212yes—
30C43×#431C2211yescharacteristic
31C43×#431C2211yescharacteristic
32C43×#423C2211yescharacteristic
33C2×#103×C43—21no—
34C2×#103×C43—21no—
35C43×#408—21no—
36C2×C4×C8×C43C2211yescharacteristic
37C43×#335C2212yes—
38C43×#334C2212yes—
39C43×#333C2214yes—
40C43×#332C2214yes—
41C2×#41×C43—21no—
42C22×Q8×C43—21no—
43C22×Q8×C43—21no—
44#131×C43—44no—
45C2×M16×C43—21no—
46C2×M16×C43—22no—
47C22×C8×C43—22no—
48C22×C8×C43D411yescharacteristic
49C22×C8×C43D411yescharacteristic
50C4⋊Q8×C43—21no—
51C4⋊Q8×C43—21no—
52C4⋊Q8×C43—21no—
53C4⋊Q8×C43—21no—
54C4⋊Q8×C43—21no—
55C4⋊Q8×C43—21no—
56C4⋊Q8×C43D411yescharacteristic
57C4⋊Q8×C43C2312yes—
58C4⋊Q8×C43C2312yes—
59#127×C43D411yescharacteristic
60#124×C43—21no—
61#121×C43—21no—
62#121×C43D412yes—
63C4×D4×C43—21no—
64C4×D4×C43C2312yes—
65C2×C4⋊C4×C43—21no—
66C2×C4⋊C4×C43—21no—
67C2×C4⋊C4×C43—21no—
68C2×C4⋊C4×C43—21no—
69C2×C42×C43C2311yescharacteristic
70#107×C43—24no—
71#106×C43—24no—
72C4⋊C8×C43—21no—
73C4⋊C8×C43C2312yes—
74C4⋊C8×C43C2312yes—
75C4⋊C8×C43C2312yes—
76#103×C43—22no—
77#103×C43—22no—
78#103×C43—22no—
79#103×C43—22no—
80#102×C43—24no—
81#102×C43—24no—
82C22⋊C8×C43—21no—
83C22⋊C8×C43—21no—
84C22⋊C8×C43—22no—
85C22⋊C8×C43—22no—
86C4×C8×C43—21no—
87C4×C8×C43—21no—
88C4×C8×C43D411yescharacteristic
89C4×C8×C43D411yescharacteristic
90C4×C8×C43C2311yescharacteristic
91C4×C8×C43C2311yescharacteristic
92#41×C43—42no—
93#41×C43—42no—
94C2×Q8×C43—21no—
95C2×Q8×C43—22no—
96C2×Q8×C43—22no—
97C2×Q8×C43—41no—
98C2×Q8×C43—41no—
99C2×Q8×C43—42no—
100C2×Q8×C43—42no—
101C2×Q8×C43—82no—
102C2×D4×C43—21no—
103C2×D4×C43—21no—
104C2×D4×C43—22no—
105C2×D4×C43C2×D412yes—
106C22×C4×C43—22no—
107C22×C4×C43—41no—
108C22×C4×C43—41no—
109C22×C4×C43C2×D411yescharacteristic
110C22×C4×C43C2×D411yescharacteristic
111C22×C4×C43#4111yescharacteristic
112M16×C43—44no—
113M16×C43—42no—
114C2×C8×C43—22no—
115C2×C8×C43—22no—
116C2×C8×C43—22no—
117C2×C8×C43—22no—
118C2×C8×C43—22no—
119C2×C8×C43—44no—
120C2×C8×C43C2×D411yescharacteristic
121C2×C8×C43C2×D411yescharacteristic
122C2×C8×C43C2×D411yescharacteristic
123C2×C8×C43C2×D411yescharacteristic
124C4⋊C4×C43—21no—
125C4⋊C4×C43—22no—
126C4⋊C4×C43—22no—
127C4⋊C4×C43—22no—
128C4⋊C4×C43—22no—
129C4⋊C4×C43—41no—
130C4⋊C4×C43—41no—
131C4⋊C4×C43—41no—
132C4⋊C4×C43—41no—
133C4⋊C4×C43C2×D412yes—
134C22⋊C4×C43—22no—
135C22⋊C4×C43—22no—
136C42×C43C2×D411yescharacteristic
137C42×C43C2×D411yescharacteristic
138C42×C43#4111yescharacteristic
139C42×C43C2411yescharacteristic
140C23×C43—22no—
141C23×C43#12111yescharacteristic
142Q8×C43—42no—
143Q8×C43—42no—
144Q8×C43—42no—
145Q8×C43—82no—
146Q8×C43—82no—
147Q8×C43—82no—
148D4×C43—24no—
149D4×C43—44no—
150D4×C43—42no—
151D4×C43—42no—
152C2×C4×C43—22no—
153C2×C4×C43—22no—
154C2×C4×C43—22no—
155C2×C4×C43—42no—
156C2×C4×C43—42no—
157C2×C4×C43—42no—
158C2×C4×C43—42no—
159C2×C4×C43—82no—
160C2×C4×C43—82no—
161C2×C4×C43#12111yescharacteristic
162C2×C4×C43#12111yescharacteristic
163C2×C4×C43#12111yescharacteristic
164C2×C4×C43#13512yes—
165C2×C4×C43AGL(1,ℤ/8)12yes—
166C2×C4×C43C22×D411yescharacteristic
167C2×C4×C43C22×D411yescharacteristic
168C2×C4×C43C2×#4111yescharacteristic
169C8×C43—21no—
170C8×C43—21no—
171C8×C43—21no—
172C8×C43—21no—
173C8×C43—42no—
174C8×C43—42no—
175C8×C43—42no—
176#19199C4311yesmaximal, characteristic, direct product factor, Sylow
177C22×C43—21no—
178C22×C43—21no—
179C22×C43—42no—
180C22×C43—42no—
181C22×C43—42no—
182C22×C43#46312yes—
183C22×C43C2×#12111yescharacteristic
184C4×C43—21no—
185C4×C43—21no—
186C4×C43—42no—
187C4×C43—82no—
188C4×C43—82no—
189C4×C43#46312yes—
190C4×C43#47112yes—
191C4×C43C2×#13511yescharacteristic
192C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
193C4×C43#57812yes—
194#3227C2×C4311yescharacteristic
195#3226C2×C4311yescharacteristic
196C2×#487C2×C4311yescharacteristic, complemented
197#2931C2×C4311yescharacteristic
198#1703C2×C4314yescomplemented
199#1683C2×C4314yescomplemented
200#1564C2×C4311yescharacteristic, complemented
201#1548C2×C4311yescharacteristic, complemented
202#1546C2×C4311yescharacteristic, complemented
203C2×C43—22no—
204C2×C43—82no—
205C2×C43C2×#46311yescharacteristic
206C2×C43#305911yescharacteristic
207C2×C43C2×#47111yescharacteristic
208C2×#131—21no—
209#532C22×C4311yescharacteristic
210C2×C4⋊Q8C22×C4311yescharacteristic
211C2×C4⋊Q8C22×C4311yescharacteristic
212#500—21no—
213#498—21no—
214#487—21no—
215#487—21no—
216#487C22×C4312yes—
217#487C22×C4312yes—
218#486—21no—
219#486—21no—
220#481—22no—
221#480—22no—
222#476C22×C4314yes—
223#474C22×C4314yes—
224#436—21no—
225#436C22×C4312yes—
226C8×D4—21no—
227C8×D4C22×C4312yes—
228#431C22×C4311yescharacteristic
229#431C22×C4311yescharacteristic
230#423C22×C4311yescharacteristic
231C2×#103—21no—
232C2×#103—21no—
233#408—21no—
234C2×C4×C8C22×C4311yescharacteristic
235#335C22×C4312yes—
236#334C22×C4312yes—
237#333C22×C4314yes—
238#332C22×C4314yes—
239C43#1919911yescharacteristic, direct product factor, Sylow
240C2×#41—21no—
241C22×Q8—21no—
242C22×Q8—21no—
243#131—44no—
244C2×M16—21no—
245C2×M16—22no—
246C22×C8—22no—
247C22×C8D4×C4311yescharacteristic
248C22×C8D4×C4311yescharacteristic
249C4⋊Q8—21no—
250C4⋊Q8—21no—
251C4⋊Q8—21no—
252C4⋊Q8—21no—
253C4⋊Q8—21no—
254C4⋊Q8—21no—
255C4⋊Q8D4×C4311yescharacteristic
256C4⋊Q8C23×C4312yes—
257C4⋊Q8C23×C4312yes—
258#127D4×C4311yescharacteristic
259#124—21no—
260#121—21no—
261#121D4×C4312yes—
262C4×D4—21no—
263C4×D4C23×C4312yes—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C42C23×C4311yescharacteristic
269#107—24no—
270#106—24no—
271C4⋊C8—21no—
272C4⋊C8C23×C4312yes—
273C4⋊C8C23×C4312yes—
274C4⋊C8C23×C4312yes—
275#103—22no—
276#103—22no—
277#103—22no—
278#103—22no—
279#102—24no—
280#102—24no—
281C22⋊C8—21no—
282C22⋊C8—21no—
283C22⋊C8—22no—
284C22⋊C8—22no—
285C4×C8—21no—
286C4×C8—21no—
287C4×C8D4×C4311yescharacteristic
288C4×C8D4×C4311yescharacteristic
289C4×C8C23×C4311yescharacteristic
290C4×C8C23×C4311yescharacteristic
291#41—42no—
292#41—42no—
293C2×Q8—21no—
294C2×Q8—22no—
295C2×Q8—22no—
296C2×Q8—41no—
297C2×Q8—41no—
298C2×Q8—42no—
299C2×Q8—42no—
300C2×Q8—82no—
301C2×D4—22no—
302C2×D4—21no—
303C2×D4—21no—
304C2×D4C2×D4×C4312yes—
305C22×C4—22no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4C2×D4×C4311yescharacteristic
309C22×C4C2×D4×C4311yescharacteristic
310C22×C4#41×C4311yescharacteristic
311M16—44no—
312M16—42no—
313C2×C8—22no—
314C2×C8—22no—
315C2×C8—22no—
316C2×C8—22no—
317C2×C8—22no—
318C2×C8—44no—
319C2×C8C2×D4×C4311yescharacteristic
320C2×C8C2×D4×C4311yescharacteristic
321C2×C8C2×D4×C4311yescharacteristic
322C2×C8C2×D4×C4311yescharacteristic
323C4⋊C4—21no—
324C4⋊C4—22no—
325C4⋊C4—22no—
326C4⋊C4—22no—
327C4⋊C4—22no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4C2×D4×C4312yes—
333C22⋊C4—22no—
334C22⋊C4—22no—
335C42C2×D4×C4311yescharacteristic
336C42C2×D4×C4311yescharacteristic
337C42#41×C4311yescharacteristic
338C42C24×C4311yescharacteristic
339C23—22no—
340C23#121×C4311yescharacteristic
341Q8—42no—
342Q8—42no—
343Q8—42no—
344Q8—82no—
345Q8—82no—
346Q8—82no—
347D4—24no—
348D4—44no—
349D4—42no—
350D4—42no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—82no—
359C2×C4—82no—
360C2×C4#121×C4311yescharacteristic
361C2×C4#121×C4311yescharacteristic
362C2×C4#121×C4311yescharacteristic
363C2×C4#135×C4312yes—
364C2×C4AGL(1,ℤ/8)×C4312yes—
365C2×C4C22×D4×C4311yescharacteristic
366C2×C4C22×D4×C4311yescharacteristic
367C2×C4C2×#41×C4311yescharacteristic
368C8—21no—
369C8—21no—
370C8—21no—
371C8—21no—
372C8—42no—
373C8—42no—
374C8—42no—
375C22—21no—
376C22—21no—
377C22—42no—
378C22—42no—
379C22—42no—
380C22C43×#46312yes—
381C22C2×#121×C4311yescharacteristic
382C4—21no—
383C4—21no—
384C4—42no—
385C4—82no—
386C4—82no—
387C4C43×#46312yes—
388C4C43×#47112yes—
389C4C2×#135×C4311yescharacteristic
390C4C2×AGL(1,ℤ/8)×C4311yescharacteristic
391C4C43×#57812yes—
392C2—22no—
393C2—82no—
394C2C2×C43×#46311yescharacteristic
395C2C43×#305911yescharacteristic
396C2C2×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
3. C2×C43×#487C2semidirect
5. C43×#1703C2semidirect
6. C43×#1683C2semidirect
7. C43×#1564C2semidirect
8. C43×#1548C2semidirect
9. C43×#1546C2semidirect
176. #19199C43direct (N × H)
196. C2×#487C2×C43semidirect
198. #1703C2×C43semidirect
199. #1683C2×C43semidirect
200. #1564C2×C43semidirect
201. #1548C2×C43semidirect
202. #1546C2×C43semidirect
239. C43#19199direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#32272
C43×#32262
C2×C43×#4872
C43×#29312
C43×#17032
C43×#16832
C43×#15642
C43×#15482
C43×#15462
#1919943