Finite Group Databasebeta

← C43×#19522 #24939539

Subgroups — C43×#19522 #24939539

Order 11008.

646 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3216C211yesmaximal, characteristic, complemented
2C43×#3208C211yesmaximal, characteristic, complemented
3C43×#3205C211yesmaximal, characteristic
4C43×#2985C211yesmaximal, characteristic, complemented
5C43×#1702C212yesmaximal, complemented
6C43×#1688C212yesmaximal, complemented
7C43×#1682C212yesmaximal, complemented
8C43×#1668C212yesmaximal, complemented
9C43×#1572C211yesmaximal, characteristic, complemented
10C43×#1555C211yesmaximal, characteristic, complemented
11C43×#1553C211yesmaximal, characteristic, complemented
12C43×#533C2211yescharacteristic
13C43×#532C2211yescharacteristic
14C2×#127×C43C2211yescharacteristic
15C43×#497—21no—
16C43×#493C2211yescharacteristic
17C43×#493C2211yescharacteristic
18C43×#492—21no—
19C43×#489—21no—
20C43×#486—21no—
21C43×#486C2211yescharacteristic
22C43×#486C2211yescharacteristic
23C43×#462C2212yescomplemented
24C43×#460C2212yes—
25C43×#460C2212yes—
26C43×#460C2212yescomplemented
27C43×#459—22no—
28C43×#452—22no—
29C43×#450—22no—
30C43×#447—22no—
31C43×#446—22no—
32C43×#446C2212yescomplemented
33C8×Q8×C43C2212yescomplemented
34C43×#433—22no—
35C43×#432C2211yescharacteristic
36C43×#432C2211yescharacteristic
37C43×#431C2211yescharacteristic
38C43×#431C2211yescharacteristic
39C43×#335C2212yescomplemented
40C43×#334C2212yescomplemented
41C43×#332C2212yescomplemented
42C43×#331C2212yes—
43C43×#331C2212yes—
44C43×#331C2212yescomplemented
45C2×#41×C43—21no—
46C22×D4×C43—21no—
47C22×D4×C43—21no—
48C22×D4×C43—21no—
49C2×Q16×C43—22no—
50C2×SD16×C43—22no—
51C2×SD16×C43—22no—
52C2×SD16×C43—22no—
53C2×D8×C43—22no—
54C2×D8×C43—22no—
55C4⋊Q8×C43D411yescharacteristic
56C4⋊Q8×C43D411yescharacteristic
57C4⋊Q8×C43C2311yescharacteristic
58#127×C43—21no—
59#127×C43—21no—
60#127×C43—21no—
61#127×C43C2311yescharacteristic
62#127×C43C2311yescharacteristic
63#127×C43C2311yescharacteristic
64#125×C43—21no—
65#124×C43—21no—
66C22⋊Q8×C43—21no—
67C22⋊Q8×C43D412yes—
68#121×C43—21no—
69#121×C43—21no—
70C4×Q8×C43—21no—
71C4×Q8×C43C2312yes—
72C4×D4×C43—21no—
73C4×D4×C43—21no—
74#117×C43—21no—
75C2×C42×C43C2311yescharacteristic
76C4⋊C8×C43—22no—
77C4⋊C8×C43—22no—
78C4⋊C8×C43D412yes—
79C4⋊C8×C43C2312yes—
80C4⋊C8×C43C2312yes—
81C4⋊C8×C43C2312yes—
82#103×C43—22no—
83#102×C43—22no—
84#102×C43—22no—
85#102×C43—22no—
86#102×C43—22no—
87#102×C43—22no—
88C22⋊C8×C43—21no—
89C22⋊C8×C43—21no—
90C22⋊C8×C43—21no—
91C22⋊C8×C43D412yes—
92#97×C43—22no—
93#97×C43—21no—
94#97×C43—21no—
95C4×C8×C43—22no—
96C4×C8×C43—21no—
97C4×C8×C43C2311yescharacteristic
98C4×C8×C43C2311yescharacteristic
99C24×C43—41no—
100#41×C43—82no—
101C2×Q8×C43—21no—
102C2×Q8×C43—21no—
103C2×Q8×C43C2×D412yes—
104C2×D4×C43—21no—
105C2×D4×C43—21no—
106C2×D4×C43—21no—
107C2×D4×C43—21no—
108C2×D4×C43—21no—
109C2×D4×C43—21no—
110C2×D4×C43—21no—
111C2×D4×C43—21no—
112C2×D4×C43—21no—
113C2×D4×C43—41no—
114C2×D4×C43—41no—
115C2×D4×C43—41no—
116C2×D4×C43—41no—
117C2×D4×C43—82no—
118C2×D4×C43—82no—
119C2×D4×C43—82no—
120C22×C4×C43—41no—
121C22×C4×C43C2×D411yescharacteristic
122C22×C4×C43C2×D411yescharacteristic
123C22×C4×C43#4111yescharacteristic
124Q16×C43—82no—
125SD16×C43—82no—
126SD16×C43—82no—
127SD16×C43—82no—
128D8×C43—82no—
129D8×C43—82no—
130C2×C8×C43—22no—
131C2×C8×C43—22no—
132C2×C8×C43—22no—
133C2×C8×C43C2×D412yes—
134C2×C8×C43C2×D412yes—
135C4⋊C4×C43—21no—
136C4⋊C4×C43—21no—
137C4⋊C4×C43—21no—
138C4⋊C4×C43—22no—
139C4⋊C4×C43—22no—
140C4⋊C4×C43—21no—
141C4⋊C4×C43—21no—
142C4⋊C4×C43C2×D412yes—
143C22⋊C4×C43—22no—
144C22⋊C4×C43—41no—
145C22⋊C4×C43—41no—
146C42×C43—22no—
147C42×C43C2×D411yescharacteristic
148C42×C43C2×D411yescharacteristic
149C42×C43#4111yescharacteristic
150C42×C43C2411yescharacteristic
151C23×C43—41no—
152C23×C43—41no—
153C23×C43—41no—
154C23×C43—82no—
155C23×C43—82no—
156C23×C43—82no—
157C23×C43#12111yescharacteristic
158Q8×C43—22no—
159Q8×C43—22no—
160Q8×C43—42no—
161Q8×C43—81no—
162D4×C43—42no—
163D4×C43—42no—
164D4×C43—42no—
165D4×C43—42no—
166D4×C43—42no—
167D4×C43—42no—
168D4×C43—81no—
169D4×C43—81no—
170D4×C43—81no—
171D4×C43—82no—
172D4×C43—82no—
173D4×C43—82no—
174D4×C43—82no—
175C2×C4×C43—22no—
176C2×C4×C43—22no—
177C2×C4×C43—22no—
178C2×C4×C43—22no—
179C2×C4×C43—41no—
180C2×C4×C43—41no—
181C2×C4×C43—82no—
182C2×C4×C43#12111yescharacteristic
183C2×C4×C43#12111yescharacteristic
184C2×C4×C43#12111yescharacteristic
185C2×C4×C43C22×D411yescharacteristic
186C2×C4×C43C22×D411yescharacteristic
187C2×C4×C43C2×#4111yescharacteristic
188C8×C43—22no—
189C8×C43—22no—
190C8×C43—42no—
191C8×C43—42no—
192C8×C43—42no—
193#19522C4311yesmaximal, characteristic, direct product factor, Sylow
194C22×C43—21no—
195C22×C43—21no—
196C22×C43—21no—
197C22×C43—81no—
198C22×C43—81no—
199C22×C43—81no—
200C22×C43—81no—
201C22×C43—81no—
202C22×C43—81no—
203C22×C43—81no—
204C22×C43—81no—
205C22×C43—81no—
206C22×C43—164no—
207C22×C43C2×#12111yescharacteristic
208C4×C43—21no—
209C4×C43—21no—
210C4×C43—21no—
211C4×C43—21no—
212C4×C43—42no—
213C4×C43—42no—
214C4×C43—81no—
215C4×C43#57612yes—
216C4×C43#57712yes—
217#3216C2×C4311yescharacteristic, complemented
218#3208C2×C4311yescharacteristic, complemented
219#3205C2×C4311yescharacteristic
220#2985C2×C4311yescharacteristic, complemented
221#1702C2×C4312yescomplemented
222#1688C2×C4312yescomplemented
223#1682C2×C4312yescomplemented
224#1668C2×C4312yescomplemented
225#1572C2×C4311yescharacteristic, complemented
226#1555C2×C4311yescharacteristic, complemented
227#1553C2×C4311yescharacteristic, complemented
228C2×C43—41no—
229C2×C43—161no—
230C2×C43—161no—
231C2×C43—161no—
232C2×C43#304311yescharacteristic
233C2×C43#305811yescharacteristic
234C2×C43#306811yescharacteristic
235#533C22×C4311yescharacteristic
236#532C22×C4311yescharacteristic
237C2×#127C22×C4311yescharacteristic
238#497—21no—
239#493C22×C4311yescharacteristic
240#493C22×C4311yescharacteristic
241#492—21no—
242#489—21no—
243#486—21no—
244#486C22×C4311yescharacteristic
245#486C22×C4311yescharacteristic
246#462C22×C4312yescomplemented
247#460C22×C4312yes—
248#460C22×C4312yes—
249#460C22×C4312yescomplemented
250#459—22no—
251#452—22no—
252#450—22no—
253#447—22no—
254#446—22no—
255#446C22×C4312yescomplemented
256C8×Q8C22×C4312yescomplemented
257#433—22no—
258#432C22×C4311yescharacteristic
259#432C22×C4311yescharacteristic
260#431C22×C4311yescharacteristic
261#431C22×C4311yescharacteristic
262#335C22×C4312yescomplemented
263#334C22×C4312yescomplemented
264#332C22×C4312yescomplemented
265#331C22×C4312yes—
266#331C22×C4312yes—
267#331C22×C4312yescomplemented
268C43#1952211yescharacteristic, direct product factor, Sylow
269C2×#41—21no—
270C22×D4—21no—
271C22×D4—21no—
272C22×D4—21no—
273C2×Q16—22no—
274C2×SD16—22no—
275C2×SD16—22no—
276C2×SD16—22no—
277C2×D8—22no—
278C2×D8—22no—
279C4⋊Q8D4×C4311yescharacteristic
280C4⋊Q8D4×C4311yescharacteristic
281C4⋊Q8C23×C4311yescharacteristic
282#127—21no—
283#127—21no—
284#127—21no—
285#127C23×C4311yescharacteristic
286#127C23×C4311yescharacteristic
287#127C23×C4311yescharacteristic
288#125—21no—
289#124—21no—
290C22⋊Q8—21no—
291C22⋊Q8D4×C4312yes—
292#121—21no—
293#121—21no—
294C4×Q8—21no—
295C4×Q8C23×C4312yes—
296C4×D4—21no—
297C4×D4—21no—
298#117—21no—
299C2×C42C23×C4311yescharacteristic
300C4⋊C8—22no—
301C4⋊C8—22no—
302C4⋊C8D4×C4312yes—
303C4⋊C8C23×C4312yes—
304C4⋊C8C23×C4312yes—
305C4⋊C8C23×C4312yes—
306#103—22no—
307#102—22no—
308#102—22no—
309#102—22no—
310#102—22no—
311#102—22no—
312C22⋊C8—21no—
313C22⋊C8—21no—
314C22⋊C8—21no—
315C22⋊C8D4×C4312yes—
316#97—22no—
317#97—21no—
318#97—21no—
319C4×C8—22no—
320C4×C8—21no—
321C4×C8C23×C4311yescharacteristic
322C4×C8C23×C4311yescharacteristic
323C24—41no—
324#41—82no—
325C2×Q8—21no—
326C2×Q8—21no—
327C2×Q8C2×D4×C4312yes—
328C2×D4—21no—
329C2×D4—21no—
330C2×D4—21no—
331C2×D4—21no—
332C2×D4—21no—
333C2×D4—21no—
334C2×D4—21no—
335C2×D4—21no—
336C2×D4—21no—
337C2×D4—41no—
338C2×D4—41no—
339C2×D4—41no—
340C2×D4—41no—
341C2×D4—82no—
342C2×D4—82no—
343C2×D4—82no—
344C22×C4—41no—
345C22×C4C2×D4×C4311yescharacteristic
346C22×C4C2×D4×C4311yescharacteristic
347C22×C4#41×C4311yescharacteristic
348Q16—82no—
349SD16—82no—
350SD16—82no—
351SD16—82no—
352D8—82no—
353D8—82no—
354C2×C8—22no—
355C2×C8—22no—
356C2×C8—22no—
357C2×C8C2×D4×C4312yes—
358C2×C8C2×D4×C4312yes—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4—21no—
362C4⋊C4—22no—
363C4⋊C4—22no—
364C4⋊C4—21no—
365C4⋊C4—21no—
366C4⋊C4C2×D4×C4312yes—
367C22⋊C4—22no—
368C22⋊C4—41no—
369C22⋊C4—41no—
370C42—22no—
371C42C2×D4×C4311yescharacteristic
372C42C2×D4×C4311yescharacteristic
373C42#41×C4311yescharacteristic
374C42C24×C4311yescharacteristic
375C23—41no—
376C23—41no—
377C23—41no—
378C23—82no—
379C23—82no—
380C23—82no—
381C23#121×C4311yescharacteristic
382Q8—22no—
383Q8—22no—
384Q8—42no—
385Q8—81no—
386D4—42no—
387D4—42no—
388D4—42no—
389D4—42no—
390D4—42no—
391D4—42no—
392D4—81no—
393D4—81no—
394D4—81no—
395D4—82no—
396D4—82no—
397D4—82no—
398D4—82no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—82no—
406C2×C4#121×C4311yescharacteristic
407C2×C4#121×C4311yescharacteristic
408C2×C4#121×C4311yescharacteristic
409C2×C4C22×D4×C4311yescharacteristic
410C2×C4C22×D4×C4311yescharacteristic
411C2×C4C2×#41×C4311yescharacteristic
412C8—22no—
413C8—22no—
414C8—42no—
415C8—42no—
416C8—42no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—81no—
421C22—81no—
422C22—81no—
423C22—81no—
424C22—81no—
425C22—81no—
426C22—81no—
427C22—81no—
428C22—81no—
429C22—164no—
430C22C2×#121×C4311yescharacteristic
431C4—21no—
432C4—21no—
433C4—21no—
434C4—21no—
435C4—42no—
436C4—42no—
437C4—81no—
438C4C43×#57612yes—
439C4C43×#57712yes—
440C2—41no—
441C2—161no—
442C2—161no—
443C2—161no—
444C2C43×#304311yescharacteristic
445C2C43×#305811yescharacteristic
446C2C43×#306811yescharacteristic
subgroupG/H
center, socleC22×C43C2×#121
commutator, Frattini, cosocleC42C24×C43
prime radicalC43×#3205C2
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
1. C43×#3216C2semidirect
2. C43×#3208C2semidirect
4. C43×#2985C2semidirect
5. C43×#1702C2semidirect
6. C43×#1688C2semidirect
7. C43×#1682C2semidirect
8. C43×#1668C2semidirect
9. C43×#1572C2semidirect
10. C43×#1555C2semidirect
11. C43×#1553C2semidirect
23. C43×#462C22semidirect
26. C43×#460C22semidirect
32. C43×#446C22semidirect
33. C8×Q8×C43C22semidirect
39. C43×#335C22semidirect
40. C43×#334C22semidirect
41. C43×#332C22semidirect
44. C43×#331C22semidirect
193. #19522C43direct (N × H)
217. #3216C2×C43semidirect
218. #3208C2×C43semidirect
220. #2985C2×C43semidirect
221. #1702C2×C43semidirect
222. #1688C2×C43semidirect
223. #1682C2×C43semidirect
224. #1668C2×C43semidirect
225. #1572C2×C43semidirect
226. #1555C2×C43semidirect
227. #1553C2×C43semidirect
246. #462C22×C43semidirect
249. #460C22×C43semidirect
255. #446C22×C43semidirect
256. C8×Q8C22×C43semidirect
262. #335C22×C43semidirect
263. #334C22×C43semidirect
264. #332C22×C43semidirect
267. #331C22×C43semidirect
268. C43#19522direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#32162
C43×#32082
C43×#32052
C43×#29852
C43×#17022
C43×#16882
C43×#16822
C43×#16682
C43×#15722
C43×#15552
C43×#15532
#1952243