Finite Group Databasebeta

← C43×#8990 #24929007

Subgroups — C43×#8990 #24929007

Order 11008.

462 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3104C211yesmaximal, characteristic
2Q8×M16×C43C211yesmaximal, characteristic
3C43×#1986C211yesmaximal, characteristic
4C4×#103×C43C211yesmaximal, characteristic
5C43×#1493C211yesmaximal, characteristic
6C43×#1303C211yesmaximal, characteristic
7C43×#1278C211yesmaximal, characteristic
8C43×#533C2211yescharacteristic
9C2×C4×Q8×C43C2211yescharacteristic
10C43×#484—21no—
11C43×#477C411yescharacteristic, complemented
12C43×#477C411yescharacteristic, complemented
13C43×#462C411yescharacteristic, complemented
14C43×#462C411yescharacteristic, complemented
15C43×#451—21no—
16C43×#446—21no—
17C43×#446—22no—
18C8×Q8×C43—21no—
19C4×Q16×C43—21no—
20C4×Q16×C43—21no—
21C43×#431C2211yescharacteristic
22C43×#423—21no—
23C43×#423C2211yescharacteristic
24C2×#103×C43—21no—
25C4×M16×C43—21no—
26C4×M16×C43C2211yescharacteristic
27C2×C4×C8×C43C2211yescharacteristic
28C4×C4⋊C4×C43C2211yescharacteristic
29C43×#340—21no—
30C43×#339—21no—
31C43×#339—21no—
32C43×Q8⋊C8—22no—
33C22×Q8×C43D411yescharacteristic
34C2×Q16×C43—21no—
35C2×Q16×C43—21no—
36C2×M16×C43—21no—
37C2×M16×C43D411yescharacteristic
38C2×M16×C43D411yescharacteristic
39C22×C8×C43—21no—
40C4⋊Q8×C43C2×C411yescharacteristic
41C4⋊Q8×C43C2×C411yescharacteristic
42#125×C43—21no—
43C22⋊Q8×C43—21no—
44C22⋊Q8×C43—21no—
45C4×Q8×C43—21no—
46C4×Q8×C43—21no—
47C4×Q8×C43—21no—
48C4×Q8×C43—21no—
49C4×Q8×C43C2×C411yescharacteristic
50C4×Q8×C43C2×C411yescharacteristic
51C4×Q8×C43D411yescharacteristic
52C4×Q8×C43D411yescharacteristic
53#117×C43—21no—
54C2×C4⋊C4×C43—21no—
55C2×C4⋊C4×C43—21no—
56C2×C4⋊C4×C43D411yescharacteristic
57C2×C42×C43—21no—
58C2×C42×C43—21no—
59C2×C42×C43C2311yescharacteristic
60#107×C43—21no—
61#107×C43—21no—
62C4⋊C8×C43—22no—
63C4⋊C8×C43—22no—
64C4⋊C8×C43—21no—
65C4⋊C8×C43C2×C411yescharacteristic
66C4⋊C8×C43C2×C411yescharacteristic
67C4⋊C8×C43D412yes—
68#103×C43—24no—
69#103×C43—21no—
70#103×C43—21no—
71#103×C43—21no—
72#103×C43—21no—
73C22⋊C8×C43—21no—
74#97×C43—22no—
75#97×C43—21no—
76C4×C8×C43—22no—
77C4×C8×C43—21no—
78C4×C8×C43—21no—
79C4×C8×C43—21no—
80C4×C8×C43—21no—
81#95×C43—21no—
82C2×Q8×C43—21no—
83C2×Q8×C43—22no—
84C2×Q8×C43—21no—
85C2×Q8×C43—21no—
86C2×Q8×C43—41no—
87C2×Q8×C43C22⋊C411yescharacteristic
88C2×Q8×C43C22⋊C411yescharacteristic
89C22×C4×C43—21no—
90C22×C4×C43—21no—
91C22×C4×C43—41no—
92C22×C4×C43C2×D411yescharacteristic
93C22×C4×C43C2×D411yescharacteristic
94C22×C4×C43#4111yescharacteristic
95Q16×C43—42no—
96Q16×C43—42no—
97M16×C43—21no—
98M16×C43—21no—
99M16×C43—21no—
100M16×C43—41no—
101M16×C43—41no—
102M16×C43Q1612yescomplemented
103C2×C8×C43—21no—
104C2×C8×C43—22no—
105C2×C8×C43—21no—
106C2×C8×C43—21no—
107C2×C8×C43—21no—
108C2×C8×C43—22no—
109C2×C8×C43—41no—
110C2×C8×C43—41no—
111C4⋊C4×C43—21no—
112C4⋊C4×C43—21no—
113C4⋊C4×C43—21no—
114C4⋊C4×C43—21no—
115C4⋊C4×C43—21no—
116C4⋊C4×C43—22no—
117C4⋊C4×C43—21no—
118C4⋊C4×C43—21no—
119C4⋊C4×C43—21no—
120C4⋊C4×C43—21no—
121C4⋊C4×C43—41no—
122C4⋊C4×C43—41no—
123C4⋊C4×C43—41no—
124C4⋊C4×C43C22⋊C411yescharacteristic
125C4⋊C4×C43C22⋊C411yescharacteristic
126C22⋊C4×C43—41no—
127C42×C43—21no—
128C42×C43—21no—
129C42×C43—21no—
130C42×C43—21no—
131C42×C43—41no—
132C42×C43—41no—
133C42×C43—41no—
134C42×C43C22×C411yescharacteristic
135C42×C43C2×D411yescharacteristic
136C42×C43C2×D411yescharacteristic
137C42×C43#4111yescharacteristic
138C23×C43#12111yescharacteristic
139Q8×C43—21no—
140Q8×C43—21no—
141Q8×C43—21no—
142Q8×C43—42no—
143Q8×C43—42no—
144Q8×C43—41no—
145Q8×C43—41no—
146Q8×C43#10412yes—
147C2×C4×C43—21no—
148C2×C4×C43—21no—
149C2×C4×C43—21no—
150C2×C4×C43—21no—
151C2×C4×C43—21no—
152C2×C4×C43—21no—
153C2×C4×C43—41no—
154C2×C4×C43—42no—
155C2×C4×C43—42no—
156C2×C4×C43—41no—
157C2×C4×C43—41no—
158C2×C4×C43—81no—
159C2×C4×C43—81no—
160C2×C4×C43—81no—
161C2×C4×C43C2×C22⋊C411yescharacteristic
162C2×C4×C43C4×D411yescharacteristic
163C2×C4×C43C4×D411yescharacteristic
164C2×C4×C43#12011yescharacteristic
165C2×C4×C43#12111yescharacteristic
166C2×C4×C43#12311yescharacteristic
167C2×C4×C43C2×Q1611yescharacteristic
168C2×C4×C43#13511yescharacteristic
169C2×C4×C43#13711yescharacteristic
170C2×C4×C43#13711yescharacteristic
171C8×C43—22no—
172C8×C43—42no—
173C8×C43—41no—
174C8×C43—41no—
175C8×C43—41no—
176C8×C43—42no—
177#8990C4311yesmaximal, characteristic, direct product factor, Sylow
178C22×C43—21no—
179C22×C43—21no—
180C22×C43#38611yescharacteristic
181C22×C43#46211yescharacteristic
182C22×C43#46411yescharacteristic
183C4×C43—21no—
184C4×C43—22no—
185C4×C43—21no—
186C4×C43—21no—
187C4×C43—41no—
188C4×C43—41no—
189C4×C43—41no—
190C4×C43—82no—
191C4×C43—81no—
192C4×C43—81no—
193C4×C43C2×#10411yescharacteristic
194C4×C43#42111yescharacteristic
195C4×C43C4×Q1611yescharacteristic
196C4×C43#44111yescharacteristic
197C4×C43#45111yescharacteristic
198C4×C43#45211yescharacteristic
199#3104C2×C4311yescharacteristic
200Q8×M16C2×C4311yescharacteristic
201#1986C2×C4311yescharacteristic
202C4×#103C2×C4311yescharacteristic
203#1493C2×C4311yescharacteristic
204#1303C2×C4311yescharacteristic
205#1278C2×C4311yescharacteristic
206C2×C43—21no—
207C2×C43—21no—
208C2×C43#187111yescharacteristic
209C2×C43#187811yescharacteristic
210C2×C43#188111yescharacteristic
211#533C22×C4311yescharacteristic
212C2×C4×Q8C22×C4311yescharacteristic
213#484—21no—
214#477C4×C4311yescharacteristic, complemented
215#477C4×C4311yescharacteristic, complemented
216#462C4×C4311yescharacteristic, complemented
217#462C4×C4311yescharacteristic, complemented
218#451—21no—
219#446—21no—
220#446—22no—
221C8×Q8—21no—
222C4×Q16—21no—
223C4×Q16—21no—
224#431C22×C4311yescharacteristic
225#423—21no—
226#423C22×C4311yescharacteristic
227C2×#103—21no—
228C4×M16—21no—
229C4×M16C22×C4311yescharacteristic
230C2×C4×C8C22×C4311yescharacteristic
231C4×C4⋊C4C22×C4311yescharacteristic
232#340—21no—
233#339—21no—
234#339—21no—
235Q8⋊C8—22no—
236C43#899011yescharacteristic, direct product factor, Sylow
237C22×Q8D4×C4311yescharacteristic
238C2×Q16—21no—
239C2×Q16—21no—
240C2×M16—21no—
241C2×M16D4×C4311yescharacteristic
242C2×M16D4×C4311yescharacteristic
243C22×C8—21no—
244C4⋊Q8C2×C4×C4311yescharacteristic
245C4⋊Q8C2×C4×C4311yescharacteristic
246#125—21no—
247C22⋊Q8—21no—
248C22⋊Q8—21no—
249C4×Q8—21no—
250C4×Q8—21no—
251C4×Q8—21no—
252C4×Q8—21no—
253C4×Q8C2×C4×C4311yescharacteristic
254C4×Q8C2×C4×C4311yescharacteristic
255C4×Q8D4×C4311yescharacteristic
256C4×Q8D4×C4311yescharacteristic
257#117—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4D4×C4311yescharacteristic
261C2×C42—21no—
262C2×C42—21no—
263C2×C42C23×C4311yescharacteristic
264#107—21no—
265#107—21no—
266C4⋊C8—22no—
267C4⋊C8—22no—
268C4⋊C8—21no—
269C4⋊C8C2×C4×C4311yescharacteristic
270C4⋊C8C2×C4×C4311yescharacteristic
271C4⋊C8D4×C4312yes—
272#103—24no—
273#103—21no—
274#103—21no—
275#103—21no—
276#103—21no—
277C22⋊C8—21no—
278#97—22no—
279#97—21no—
280C4×C8—22no—
281C4×C8—21no—
282C4×C8—21no—
283C4×C8—21no—
284C4×C8—21no—
285#95—21no—
286C2×Q8—21no—
287C2×Q8—22no—
288C2×Q8—21no—
289C2×Q8—21no—
290C2×Q8—41no—
291C2×Q8C22⋊C4×C4311yescharacteristic
292C2×Q8C22⋊C4×C4311yescharacteristic
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—41no—
296C22×C4C2×D4×C4311yescharacteristic
297C22×C4C2×D4×C4311yescharacteristic
298C22×C4#41×C4311yescharacteristic
299Q16—42no—
300Q16—42no—
301M16—21no—
302M16—21no—
303M16—21no—
304M16—41no—
305M16—41no—
306M16Q16×C4312yescomplemented
307C2×C8—21no—
308C2×C8—22no—
309C2×C8—21no—
310C2×C8—21no—
311C2×C8—21no—
312C2×C8—22no—
313C2×C8—41no—
314C2×C8—41no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—22no—
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4C22⋊C4×C4311yescharacteristic
329C4⋊C4C22⋊C4×C4311yescharacteristic
330C22⋊C4—41no—
331C42—21no—
332C42—21no—
333C42—21no—
334C42—21no—
335C42—41no—
336C42—41no—
337C42—41no—
338C42C22×C4×C4311yescharacteristic
339C42C2×D4×C4311yescharacteristic
340C42C2×D4×C4311yescharacteristic
341C42#41×C4311yescharacteristic
342C23#121×C4311yescharacteristic
343Q8—21no—
344Q8—21no—
345Q8—21no—
346Q8—42no—
347Q8—42no—
348Q8—41no—
349Q8—41no—
350Q8#104×C4312yes—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—41no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—81no—
363C2×C4—81no—
364C2×C4—81no—
365C2×C4C2×C22⋊C4×C4311yescharacteristic
366C2×C4C4×D4×C4311yescharacteristic
367C2×C4C4×D4×C4311yescharacteristic
368C2×C4#120×C4311yescharacteristic
369C2×C4#121×C4311yescharacteristic
370C2×C4#123×C4311yescharacteristic
371C2×C4C2×Q16×C4311yescharacteristic
372C2×C4#135×C4311yescharacteristic
373C2×C4#137×C4311yescharacteristic
374C2×C4#137×C4311yescharacteristic
375C8—22no—
376C8—42no—
377C8—41no—
378C8—41no—
379C8—41no—
380C8—42no—
381C22—21no—
382C22—21no—
383C22C43×#38611yescharacteristic
384C22C43×#46211yescharacteristic
385C22C43×#46411yescharacteristic
386C4—21no—
387C4—22no—
388C4—21no—
389C4—21no—
390C4—41no—
391C4—41no—
392C4—41no—
393C4—82no—
394C4—81no—
395C4—81no—
396C4C2×#104×C4311yescharacteristic
397C4C43×#42111yescharacteristic
398C4C4×Q16×C4311yescharacteristic
399C4C43×#44111yescharacteristic
400C4C43×#45111yescharacteristic
401C4C43×#45211yescharacteristic
402C2—21no—
403C2—21no—
404C2C43×#187111yescharacteristic
405C2C43×#187811yescharacteristic
406C2C43×#188111yescharacteristic
subgroupG/H
centerC2×C4×C43#120
commutatorC42C22×C4×C43
Frattini, cosocleC2×C42C23×C43
socleC22×C43#386
prime radicalC23×C43#121
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C43 ◁ C2×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
11. C43×#477C4semidirect
12. C43×#477C4semidirect
13. C43×#462C4semidirect
14. C43×#462C4semidirect
102. M16×C43Q16semidirect
177. #8990C43direct (N × H)
214. #477C4×C43semidirect
215. #477C4×C43semidirect
216. #462C4×C43semidirect
217. #462C4×C43semidirect
236. C43#8990direct (N × H)
306. M16Q16×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#31042
Q8×M16×C432
C43×#19862
C4×#103×C432
C43×#14932
C43×#13032
C43×#12782
#899043