Finite Group Databasebeta

← C43×#61393 #24981410

Subgroups — C43×#61393 #24981410

Order 11008.

1958 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3480C212yesmaximal, complemented
2C43×#3396C213yesmaximal, complemented
3C43×#3395C211yesmaximal, characteristic, complemented
4C43×#3394C216yesmaximal, complemented
5C43×#3393C213yesmaximal, complemented
6C43×#3392C212yesmaximal, complemented
7C43×#3391C211yesmaximal, characteristic, complemented
8C43×#3147C213yesmaximal, complemented
9C43×#3035C216yesmaximal, complemented
10C2×C8×Q8×C43C211yesmaximal, characteristic, complemented
11C4×#135×C43C213yesmaximal, complemented
12C2×#135×C43C2213yes—
13C2×#135×C43C2216yes—
14C43×#559C2216yes—
15C43×#557C2212yes—
16C43×#556C2216yes—
17C43×#553—26no—
18C43×#550C2212yes—
19C43×#548—22no—
20C43×#532C2216yes—
21C43×#529—26no—
22C4×#41×C43—22no—
23C4×#41×C43C2216yes—
24C2×C4×Q8×C43C2211yescharacteristic
25C43×#495C2216yes—
26C43×#495C2216yes—
27C43×#494C2213yes—
28C43×#493C2213yes—
29C43×#492C2216yes—
30C43×#464C22112yes—
31C43×#463C22112yes—
32C43×#462C2216yes—
33C43×#461C2216yes—
34C43×#460C2216yes—
35C43×#459C2216yes—
36C8×Q8×C43C2211yescharacteristic
37C8×Q8×C43C2211yescharacteristic
38C8×Q8×C43C2213yes—
39C8×Q8×C43C2213yes—
40C4×Q16×C43C2213yes—
41C4×Q16×C43C2213yes—
42C4×SD16×C43C2216yes—
43C4×SD16×C43C2216yes—
44C4×D8×C43C2213yes—
45C4×D8×C43C2213yes—
46C43×#427C2211yescharacteristic
47C2×C4⋊C8×C43C2213yes—
48C43×#416C2216yes—
49C2×C4×C8×C43C2213yes—
50C2×#41×C43—22no—
51C2×#41×C43C2316yes—
52C22×Q8×C43D411yescharacteristic
53#135×C43—212no—
54#135×C43—412no—
55C2×Q16×C43C2313yes—
56C2×Q16×C43C2316yes—
57C2×SD16×C43C2316yes—
58C2×SD16×C43C23112yes—
59C2×D8×C43C2313yes—
60C2×D8×C43C2316yes—
61C22×C8×C43C2313yes—
62C22×C8×C43C2311yescharacteristic
63C4⋊Q8×C43C2316yes—
64#127×C43C2316yes—
65#126×C43—212no—
66#125×C43—26no—
67#124×C43—26no—
68#124×C43C23112yes—
69#123×C43—212no—
70C22⋊Q8×C43—26no—
71#121×C43—26no—
72#121×C43—26no—
73#121×C43—26no—
74C4×Q8×C43—22no—
75C4×Q8×C43D411yescharacteristic
76C4×Q8×C43D413yes—
77C4×Q8×C43C2316yes—
78C4×Q8×C43C2316yes—
79C4×Q8×C43C2311yescharacteristic
80C4×Q8×C43C2313yes—
81C4×D4×C43—26no—
82C4×D4×C43—26no—
83C4×D4×C43—26no—
84C4×D4×C43—26no—
85C4×D4×C43—26no—
86C4×D4×C43C2316yes—
87C4×D4×C43C2316yes—
88#117×C43—26no—
89#117×C43—26no—
90#117×C43C2312yes—
91C2×C4⋊C4×C43D413yes—
92C2×C42×C43—26no—
93C2×C42×C43C2313yes—
94#107×C43C2311yescharacteristic
95#107×C43C2311yescharacteristic
96#106×C43C2312yes—
97C4⋊C8×C43C2313yes—
98C4⋊C8×C43C2313yes—
99C4⋊C8×C43C2316yes—
100#103×C43C2316yes—
101#103×C43C2316yes—
102#102×C43C2316yes—
103#102×C43C2316yes—
104C4×C8×C43C2313yes—
105C4×C8×C43C2313yes—
106C4×C8×C43C2313yes—
107C4×C8×C43C2313yes—
108#41×C43—212no—
109#41×C43—212no—
110#41×C43—48no—
111C2×Q8×C43—24no—
112C2×Q8×C43C2×D413yes—
113C2×Q8×C43C2×D411yescharacteristic
114C2×Q8×C43C2416yes—
115C2×D4×C43—26no—
116C2×D4×C43—26no—
117C2×D4×C43—26no—
118C2×D4×C43C2416yes—
119C22×C4×C43—26no—
120C22×C4×C43—26no—
121C22×C4×C43—26no—
122C22×C4×C43C2×D413yes—
123C22×C4×C43C2×D413yes—
124C22×C4×C43C2411yescharacteristic
125Q16×C43—26no—
126Q16×C43—46no—
127SD16×C43—212no—
128SD16×C43—412no—
129D8×C43—26no—
130D8×C43—46no—
131C2×C8×C43—26no—
132C2×C8×C43#4114yescomplemented
133C2×C8×C43C2413yes—
134C2×C8×C43C2413yes—
135C2×C8×C43C2411yescharacteristic
136C2×C8×C43C2411yescharacteristic
137C4⋊C4×C43—26no—
138C4⋊C4×C43—26no—
139C4⋊C4×C43—26no—
140C4⋊C4×C43—26no—
141C4⋊C4×C43C2×D413yes—
142C4⋊C4×C43C2×D413yes—
143C4⋊C4×C43C2×D416yes—
144C4⋊C4×C43C2412yes—
145C4⋊C4×C43C2412yes—
146C22⋊C4×C43—212no—
147C22⋊C4×C43—26no—
148C22⋊C4×C43—26no—
149C22⋊C4×C43—212no—
150C22⋊C4×C43—22no—
151C42×C43—26no—
152C42×C43—26no—
153C42×C43—22no—
154C42×C43C2×D413yes—
155C42×C43C2×D413yes—
156C42×C43C2413yes—
157C42×C43C2413yes—
158C23×C43—26no—
159C23×C43C22×D411yescharacteristic
160Q8×C43—26no—
161Q8×C43—26no—
162Q8×C43—26no—
163Q8×C43#13514yescomplemented
164D4×C43—26no—
165D4×C43—26no—
166D4×C43—412no—
167D4×C43—412no—
168D4×C43—86no—
169C2×C4×C43—26no—
170C2×C4×C43—22no—
171C2×C4×C43—22no—
172C2×C4×C43—26no—
173C2×C4×C43—43no—
174C2×C4×C43—412no—
175C2×C4×C43—412no—
176C2×C4×C43—86no—
177C2×C4×C43C22×D413yes—
178C2×C4×C43C22×D413yes—
179C2×C4×C43C22×D413yes—
180C2×C4×C43C22×D413yes—
181C2×C4×C43C22×D411yescharacteristic
182C2×C4×C43C2×#4112yes—
183C2×C4×C43H(5,𝔽2)12yes—
184C2×C4×C43C2511yescharacteristic
185C8×C43—23no—
186C8×C43—23no—
187C8×C43C2×#4112yes—
188C8×C43C2×#4112yes—
189#61393C4311yesmaximal, characteristic, direct product factor, Sylow
190C22×C43—21no—
191C22×C43—21no—
192C22×C43—46no—
193C22×C43—46no—
194C22×C43—46no—
195C22×C43#55012yes—
196C22×C43C23×D411yescharacteristic
197C4×C43—23no—
198C4×C43—23no—
199C4×C43—23no—
200C4×C43—42no—
201C4×C43—46no—
202C4×C43—42no—
203C4×C43#55012yes—
204C4×C43C2×#13516yes—
205C4×C43C22×#4111yescharacteristic
206C4×C43C2×H(5,𝔽2)11yescharacteristic
207#3480C2×C4312yescomplemented
208#3396C2×C4313yescomplemented
209#3395C2×C4311yescharacteristic, complemented
210#3394C2×C4316yescomplemented
211#3393C2×C4313yescomplemented
212#3392C2×C4312yescomplemented
213#3391C2×C4311yescharacteristic, complemented
214#3147C2×C4313yescomplemented
215#3035C2×C4316yescomplemented
216C2×C8×Q8C2×C4311yescharacteristic, complemented
217C4×#135C2×C4313yescomplemented
218C2×C43—22no—
219C2×C43—86no—
220C2×C43C2×#55011yescharacteristic
221C2×C43C22×#13511yescharacteristic
222C2×C43#358411yescharacteristic
223C2×#135C22×C4313yes—
224C2×#135C22×C4316yes—
225#559C22×C4316yes—
226#557C22×C4312yes—
227#556C22×C4316yes—
228#553—26no—
229#550C22×C4312yes—
230#548—22no—
231#532C22×C4316yes—
232#529—26no—
233C4×#41—22no—
234C4×#41C22×C4316yes—
235C2×C4×Q8C22×C4311yescharacteristic
236#495C22×C4316yes—
237#495C22×C4316yes—
238#494C22×C4313yes—
239#493C22×C4313yes—
240#492C22×C4316yes—
241#464C22×C43112yes—
242#463C22×C43112yes—
243#462C22×C4316yes—
244#461C22×C4316yes—
245#460C22×C4316yes—
246#459C22×C4316yes—
247C8×Q8C22×C4311yescharacteristic
248C8×Q8C22×C4311yescharacteristic
249C8×Q8C22×C4313yes—
250C8×Q8C22×C4313yes—
251C4×Q16C22×C4313yes—
252C4×Q16C22×C4313yes—
253C4×SD16C22×C4316yes—
254C4×SD16C22×C4316yes—
255C4×D8C22×C4313yes—
256C4×D8C22×C4313yes—
257#427C22×C4311yescharacteristic
258C2×C4⋊C8C22×C4313yes—
259#416C22×C4316yes—
260C2×C4×C8C22×C4313yes—
261C43#6139311yescharacteristic, direct product factor, Sylow
262C2×#41—22no—
263C2×#41C23×C4316yes—
264C22×Q8D4×C4311yescharacteristic
265#135—212no—
266#135—412no—
267C2×Q16C23×C4313yes—
268C2×Q16C23×C4316yes—
269C2×SD16C23×C4316yes—
270C2×SD16C23×C43112yes—
271C2×D8C23×C4313yes—
272C2×D8C23×C4316yes—
273C22×C8C23×C4313yes—
274C22×C8C23×C4311yescharacteristic
275C4⋊Q8C23×C4316yes—
276#127C23×C4316yes—
277#126—212no—
278#125—26no—
279#124—26no—
280#124C23×C43112yes—
281#123—212no—
282C22⋊Q8—26no—
283#121—26no—
284#121—26no—
285#121—26no—
286C4×Q8—22no—
287C4×Q8D4×C4311yescharacteristic
288C4×Q8D4×C4313yes—
289C4×Q8C23×C4316yes—
290C4×Q8C23×C4316yes—
291C4×Q8C23×C4311yescharacteristic
292C4×Q8C23×C4313yes—
293C4×D4—26no—
294C4×D4—26no—
295C4×D4—26no—
296C4×D4—26no—
297C4×D4—26no—
298C4×D4C23×C4316yes—
299C4×D4C23×C4316yes—
300#117—26no—
301#117—26no—
302#117C23×C4312yes—
303C2×C4⋊C4D4×C4313yes—
304C2×C42—26no—
305C2×C42C23×C4313yes—
306#107C23×C4311yescharacteristic
307#107C23×C4311yescharacteristic
308#106C23×C4312yes—
309C4⋊C8C23×C4313yes—
310C4⋊C8C23×C4313yes—
311C4⋊C8C23×C4316yes—
312#103C23×C4316yes—
313#103C23×C4316yes—
314#102C23×C4316yes—
315#102C23×C4316yes—
316C4×C8C23×C4313yes—
317C4×C8C23×C4313yes—
318C4×C8C23×C4313yes—
319C4×C8C23×C4313yes—
320#41—212no—
321#41—212no—
322#41—48no—
323C2×Q8—24no—
324C2×Q8C2×D4×C4313yes—
325C2×Q8C2×D4×C4311yescharacteristic
326C2×Q8C24×C4316yes—
327C2×D4—26no—
328C2×D4—26no—
329C2×D4—26no—
330C2×D4C24×C4316yes—
331C22×C4—26no—
332C22×C4—26no—
333C22×C4—26no—
334C22×C4C2×D4×C4313yes—
335C22×C4C2×D4×C4313yes—
336C22×C4C24×C4311yescharacteristic
337Q16—26no—
338Q16—46no—
339SD16—212no—
340SD16—412no—
341D8—26no—
342D8—46no—
343C2×C8—26no—
344C2×C8#41×C4314yescomplemented
345C2×C8C24×C4313yes—
346C2×C8C24×C4313yes—
347C2×C8C24×C4311yescharacteristic
348C2×C8C24×C4311yescharacteristic
349C4⋊C4—26no—
350C4⋊C4—26no—
351C4⋊C4—26no—
352C4⋊C4—26no—
353C4⋊C4C2×D4×C4313yes—
354C4⋊C4C2×D4×C4313yes—
355C4⋊C4C2×D4×C4316yes—
356C4⋊C4C24×C4312yes—
357C4⋊C4C24×C4312yes—
358C22⋊C4—22no—
359C22⋊C4—212no—
360C22⋊C4—26no—
361C22⋊C4—26no—
362C22⋊C4—212no—
363C42—22no—
364C42—26no—
365C42—26no—
366C42C2×D4×C4313yes—
367C42C2×D4×C4313yes—
368C42C24×C4313yes—
369C42C24×C4313yes—
370C23—26no—
371C23C22×D4×C4311yescharacteristic
372Q8—26no—
373Q8—26no—
374Q8—26no—
375Q8#135×C4314yescomplemented
376D4—26no—
377D4—26no—
378D4—412no—
379D4—412no—
380D4—86no—
381C2×C4—26no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—26no—
385C2×C4—43no—
386C2×C4—412no—
387C2×C4—412no—
388C2×C4—86no—
389C2×C4C22×D4×C4313yes—
390C2×C4C22×D4×C4313yes—
391C2×C4C22×D4×C4313yes—
392C2×C4C22×D4×C4311yescharacteristic
393C2×C4C22×D4×C4313yes—
394C2×C4C2×#41×C4312yes—
395C2×C4H(5,𝔽2)×C4312yes—
396C2×C4C25×C4311yescharacteristic
397C8—23no—
398C8—23no—
399C8C2×#41×C4312yes—
400C8C2×#41×C4312yes—
401C22—21no—
402C22—21no—
403C22—46no—
404C22—46no—
405C22—46no—
406C22C43×#55012yes—
407C22C23×D4×C4311yescharacteristic
408C4—23no—
409C4—23no—
410C4—23no—
411C4—46no—
412C4—42no—
413C4—42no—
414C4C43×#55012yes—
415C4C2×#135×C4316yes—
416C4C22×#41×C4311yescharacteristic
417C4C2×H(5,𝔽2)×C4311yescharacteristic
418C2—22no—
419C2—86no—
420C2C2×C43×#55011yescharacteristic
421C2C22×#135×C4311yescharacteristic
422C2C43×#358411yescharacteristic
subgroupG/H
centerC2×C4×C43C22×D4
commutator, Frattini, cosocleC2×C4C25×C43
socleC22×C43C23×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C43 ◁ C2×C4×Q8×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#3480C2semidirect
2. C43×#3396C2semidirect
3. C43×#3395C2semidirect
4. C43×#3394C2semidirect
5. C43×#3393C2semidirect
6. C43×#3392C2semidirect
7. C43×#3391C2semidirect
8. C43×#3147C2semidirect
9. C43×#3035C2semidirect
10. C2×C8×Q8×C43C2semidirect
11. C4×#135×C43C2semidirect
132. C2×C8×C43#41semidirect
163. Q8×C43#135semidirect
189. #61393C43direct (N × H)
207. #3480C2×C43semidirect
208. #3396C2×C43semidirect
209. #3395C2×C43semidirect
210. #3394C2×C43semidirect
211. #3393C2×C43semidirect
212. #3392C2×C43semidirect
213. #3391C2×C43semidirect
214. #3147C2×C43semidirect
215. #3035C2×C43semidirect
216. C2×C8×Q8C2×C43semidirect
217. C4×#135C2×C43semidirect
261. C43#61393direct (N × H)
344. C2×C8#41×C43semidirect
375. Q8#135×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#34802
C43×#33962
C43×#33952
C43×#33942
C43×#33932
C43×#33922
C43×#33912
C43×#31472
C43×#30352
C2×C8×Q8×C432
C4×#135×C432
#6139343