Finite Group Databasebeta

← C43×#60274 #24980291

Subgroups — C43×#60274 #24980291

Order 11008.

1862 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3480C211yesmaximal, characteristic
2C43×#2994C216yesmaximal, complemented
3C43×#2993C216yesmaximal, complemented
4C43×#2991C212yesmaximal, complemented
5C43×#2988C212yesmaximal, complemented
6Q8×M16×C43C211yesmaximal, characteristic, complemented
7C2×C8×Q8×C43C211yesmaximal, characteristic, complemented
8C43×#2935C213yesmaximal, complemented
9C43×#2931C213yesmaximal, complemented
10C43×#2922C213yesmaximal, complemented
11C43×#2906C213yesmaximal, complemented
12C2×#131×C43C2216yes—
13C43×#559C413yes—
14C43×#557C411yescharacteristic
15C43×#556C413yes—
16C43×#553C416yes—
17C43×#550C411yescharacteristic
18C43×#548C412yes—
19C43×#532C2213yes—
20C43×#529C2216yes—
21C4×#41×C43C2212yes—
22C4×#41×C43C2213yes—
23C2×C4×Q8×C43C2211yescharacteristic
24C43×#446C2216yes—
25C8×Q8×C43C2211yescharacteristic
26C8×Q8×C43C2211yescharacteristic
27C8×Q8×C43C2213yes—
28C8×Q8×C43C2213yes—
29C8×Q8×C43C2212yes—
30C43×#436C2216yes—
31C43×#436C2216yes—
32C43×#436C2216yes—
33C43×#435C22112yes—
34C8×D4×C43C2216yes—
35C8×D4×C43C2216yes—
36C8×D4×C43C2216yes—
37C43×#433C2216yes—
38C43×#433C2216yes—
39C43×#431C2216yes—
40C43×#431C2216yes—
41C43×#424C2213yes—
42C43×#424C22112yes—
43C43×#424C2211yescharacteristic
44C43×#423C2213yes—
45C43×#423C2216yes—
46C2×C4⋊C8×C43C2213yes—
47C2×C4⋊C8×C43C2216yes—
48C43×#408C2213yes—
49C43×#408C2213yes—
50C4×M16×C43C2213yes—
51C2×C4×C8×C43C2213yes—
52C2×#41×C43C2×C412yes—
53C2×#41×C43C2313yes—
54C22×Q8×C43C2×C411yescharacteristic
55#131×C43—412no—
56C2×M16×C43C2313yes—
57C2×M16×C43C2311yescharacteristic
58C2×M16×C43C23112yes—
59C22×C8×C43C2313yes—
60C22×C8×C43C2311yescharacteristic
61C22×C8×C43C23112yes—
62C4⋊Q8×C43C2×C413yes—
63#127×C43C2×C413yes—
64#126×C43C2×C4112yes—
65#125×C43C2×C416yes—
66#124×C43C2×C416yes—
67#124×C43C2×C416yes—
68#123×C43C2×C4112yes—
69C22⋊Q8×C43C2×C416yes—
70#121×C43C2×C416yes—
71#121×C43C2×C416yes—
72#121×C43C2×C416yes—
73C4×Q8×C43C2×C411yescharacteristic
74C4×Q8×C43C2×C413yes—
75C4×Q8×C43C2×C412yes—
76C4×Q8×C43C2×C413yes—
77C4×Q8×C43C2×C413yes—
78C4×Q8×C43C2311yescharacteristic
79C4×Q8×C43C2313yes—
80C4×D4×C43C2×C416yes—
81C4×D4×C43C2×C413yes—
82C4×D4×C43C2×C416yes—
83C4×D4×C43C2×C416yes—
84C4×D4×C43C2×C413yes—
85C4×D4×C43C2316yes—
86C4×D4×C43C2316yes—
87#117×C43C2×C416yes—
88#117×C43C2311yescharacteristic
89#117×C43C2316yes—
90C2×C4⋊C4×C43C2×C413yes—
91C2×C42×C43C2313yes—
92C2×C42×C43C2316yes—
93C4⋊C8×C43C2313yes—
94C4⋊C8×C43C2316yes—
95C4⋊C8×C43C2316yes—
96C4⋊C8×C43C2313yes—
97C4⋊C8×C43C2316yes—
98C4⋊C8×C43C2316yes—
99C4⋊C8×C43C2316yes—
100C4⋊C8×C43C2312yes—
101C4⋊C8×C43C2312yes—
102C22⋊C8×C43C2316yes—
103C22⋊C8×C43C2316yes—
104C22⋊C8×C43C2316yes—
105C22⋊C8×C43C2316yes—
106#97×C43C2316yes—
107C4×C8×C43C2313yes—
108C4×C8×C43C2313yes—
109C4×C8×C43C2313yes—
110C4×C8×C43C2313yes—
111C4×C8×C43C2316yes—
112#41×C43—28no—
113#41×C43—26no—
114#41×C43—26no—
115C2×Q8×C43—24no—
116C2×Q8×C43C22×C413yes—
117C2×Q8×C43C22×C413yes—
118C2×Q8×C43C22×C411yescharacteristic
119C2×D4×C43C22×C416yes—
120C2×D4×C43C22×C413yes—
121C2×D4×C43C22×C416yes—
122C2×D4×C43C22×C416yes—
123C22×C4×C43C22×C413yes—
124C22×C4×C43C22×C416yes—
125C22×C4×C43C22×C413yes—
126C22×C4×C43C22×C416yes—
127C22×C4×C43C2416yes—
128C22×C4×C43C2411yescharacteristic
129M16×C43—26no—
130M16×C43—22no—
131M16×C43—412no—
132C2×C8×C43—26no—
133C2×C8×C43—22no—
134C2×C8×C43—412no—
135C2×C8×C43C2411yescharacteristic
136C2×C8×C43C2411yescharacteristic
137C2×C8×C43C2412yes—
138C2×C8×C43C2413yes—
139C2×C8×C43C2413yes—
140C2×C8×C43C2416yes—
141C4⋊C4×C43C22×C413yes—
142C4⋊C4×C43C22×C413yes—
143C4⋊C4×C43C22×C416yes—
144C4⋊C4×C43C22×C416yes—
145C4⋊C4×C43C22×C411yescharacteristic
146C4⋊C4×C43C22×C411yescharacteristic
147C4⋊C4×C43C22×C416yes—
148C4⋊C4×C43C22×C416yes—
149C4⋊C4×C43C22×C416yes—
150C22⋊C4×C43C22×C4112yes—
151C22⋊C4×C43C22×C412yes—
152C22⋊C4×C43C22×C416yes—
153C22⋊C4×C43C22×C416yes—
154C22⋊C4×C43C22×C4112yes—
155C42×C43C22×C416yes—
156C42×C43C22×C416yes—
157C42×C43C22×C413yes—
158C42×C43C22×C413yes—
159C42×C43C2413yes—
160C42×C43C2413yes—
161C42×C43C2412yes—
162C23×C43C23×C416yes—
163C23×C43C23×C411yescharacteristic
164Q8×C43—26no—
165Q8×C43—26no—
166Q8×C43#13114yescomplemented
167D4×C43—212no—
168D4×C43—26no—
169D4×C43—212no—
170D4×C43—46no—
171C2×C4×C43—26no—
172C2×C4×C43—212no—
173C2×C4×C43—26no—
174C2×C4×C43—26no—
175C2×C4×C43—46no—
176C2×C4×C43—43no—
177C2×C4×C43C23×C412yes—
178C2×C4×C43C23×C413yes—
179C2×C4×C43C23×C412yes—
180C2×C4×C43C23×C416yes—
181C2×C4×C43C23×C413yes—
182C2×C4×C43C23×C413yes—
183C2×C4×C43C23×C411yescharacteristic
184C2×C4×C43C23×C413yes—
185C2×C4×C43H(5,𝔽2)12yes—
186C2×C4×C432−1+412yes—
187C2×C4×C43C2511yescharacteristic
188C8×C43—23no—
189C8×C43—23no—
190C8×C43—26no—
191C8×C43—21no—
192C8×C43—21no—
193C8×C43—22no—
194#60274C4311yesmaximal, characteristic, direct product factor, Sylow
195C22×C43—21no—
196C22×C43—21no—
197C22×C43—26no—
198C22×C43—26no—
199C22×C43—26no—
200C22×C43#52012yes—
201C22×C43C24×C411yescharacteristic
202C4×C43—26no—
203C4×C43—22no—
204C4×C43—23no—
205C4×C43—22no—
206C4×C43—23no—
207C4×C43—23no—
208C4×C43#52012yes—
209C4×C43C2×#13116yes—
210C4×C43C2×H(5,𝔽2)11yescharacteristic
211C4×C43C2×2−1+411yescharacteristic
212#3480C2×C4311yescharacteristic
213#2994C2×C4316yescomplemented
214#2993C2×C4316yescomplemented
215#2991C2×C4312yescomplemented
216#2988C2×C4312yescomplemented
217Q8×M16C2×C4311yescharacteristic, complemented
218C2×C8×Q8C2×C4311yescharacteristic, complemented
219#2935C2×C4313yescomplemented
220#2931C2×C4313yescomplemented
221#2922C2×C4313yescomplemented
222#2906C2×C4313yescomplemented
223C2×C43—22no—
224C2×C43—46no—
225C2×C43C2×#52011yescharacteristic
226C2×C43C22×#13111yescharacteristic
227C2×C43#357311yescharacteristic
228C2×#131C22×C4316yes—
229#559C4×C4313yes—
230#557C4×C4311yescharacteristic
231#556C4×C4313yes—
232#553C4×C4316yes—
233#550C4×C4311yescharacteristic
234#548C4×C4312yes—
235#532C22×C4313yes—
236#529C22×C4316yes—
237C4×#41C22×C4313yes—
238C4×#41C22×C4312yes—
239C2×C4×Q8C22×C4311yescharacteristic
240#446C22×C4316yes—
241C8×Q8C22×C4311yescharacteristic
242C8×Q8C22×C4311yescharacteristic
243C8×Q8C22×C4313yes—
244C8×Q8C22×C4313yes—
245C8×Q8C22×C4312yes—
246#436C22×C4316yes—
247#436C22×C4316yes—
248#436C22×C4316yes—
249#435C22×C43112yes—
250C8×D4C22×C4316yes—
251C8×D4C22×C4316yes—
252C8×D4C22×C4316yes—
253#433C22×C4316yes—
254#433C22×C4316yes—
255#431C22×C4316yes—
256#431C22×C4316yes—
257#424C22×C4313yes—
258#424C22×C43112yes—
259#424C22×C4311yescharacteristic
260#423C22×C4313yes—
261#423C22×C4316yes—
262C2×C4⋊C8C22×C4313yes—
263C2×C4⋊C8C22×C4316yes—
264#408C22×C4313yes—
265#408C22×C4313yes—
266C4×M16C22×C4313yes—
267C2×C4×C8C22×C4313yes—
268C43#6027411yescharacteristic, direct product factor, Sylow
269C2×#41C2×C4×C4312yes—
270C2×#41C23×C4313yes—
271C22×Q8C2×C4×C4311yescharacteristic
272#131—412no—
273C2×M16C23×C4313yes—
274C2×M16C23×C4311yescharacteristic
275C2×M16C23×C43112yes—
276C22×C8C23×C4313yes—
277C22×C8C23×C4311yescharacteristic
278C22×C8C23×C43112yes—
279C4⋊Q8C2×C4×C4313yes—
280#127C2×C4×C4313yes—
281#126C2×C4×C43112yes—
282#125C2×C4×C4316yes—
283#124C2×C4×C4316yes—
284#124C2×C4×C4316yes—
285#123C2×C4×C43112yes—
286C22⋊Q8C2×C4×C4316yes—
287#121C2×C4×C4316yes—
288#121C2×C4×C4316yes—
289#121C2×C4×C4316yes—
290C4×Q8C2×C4×C4311yescharacteristic
291C4×Q8C2×C4×C4313yes—
292C4×Q8C2×C4×C4312yes—
293C4×Q8C2×C4×C4313yes—
294C4×Q8C2×C4×C4313yes—
295C4×Q8C23×C4311yescharacteristic
296C4×Q8C23×C4313yes—
297C4×D4C2×C4×C4316yes—
298C4×D4C2×C4×C4313yes—
299C4×D4C2×C4×C4316yes—
300C4×D4C2×C4×C4316yes—
301C4×D4C2×C4×C4313yes—
302C4×D4C23×C4316yes—
303C4×D4C23×C4316yes—
304#117C2×C4×C4316yes—
305#117C23×C4311yescharacteristic
306#117C23×C4316yes—
307C2×C4⋊C4C2×C4×C4313yes—
308C2×C42C23×C4313yes—
309C2×C42C23×C4316yes—
310C4⋊C8C23×C4313yes—
311C4⋊C8C23×C4316yes—
312C4⋊C8C23×C4316yes—
313C4⋊C8C23×C4313yes—
314C4⋊C8C23×C4316yes—
315C4⋊C8C23×C4316yes—
316C4⋊C8C23×C4316yes—
317C4⋊C8C23×C4312yes—
318C4⋊C8C23×C4312yes—
319C22⋊C8C23×C4316yes—
320C22⋊C8C23×C4316yes—
321C22⋊C8C23×C4316yes—
322C22⋊C8C23×C4316yes—
323#97C23×C4316yes—
324C4×C8C23×C4313yes—
325C4×C8C23×C4313yes—
326C4×C8C23×C4313yes—
327C4×C8C23×C4313yes—
328C4×C8C23×C4316yes—
329#41—28no—
330#41—26no—
331#41—26no—
332C2×Q8—24no—
333C2×Q8C22×C4×C4313yes—
334C2×Q8C22×C4×C4313yes—
335C2×Q8C22×C4×C4311yescharacteristic
336C2×D4C22×C4×C4316yes—
337C2×D4C22×C4×C4316yes—
338C2×D4C22×C4×C4313yes—
339C2×D4C22×C4×C4316yes—
340C22×C4C22×C4×C4313yes—
341C22×C4C22×C4×C4316yes—
342C22×C4C22×C4×C4313yes—
343C22×C4C22×C4×C4316yes—
344C22×C4C24×C4316yes—
345C22×C4C24×C4311yescharacteristic
346M16—26no—
347M16—22no—
348M16—412no—
349C2×C8—26no—
350C2×C8—22no—
351C2×C8—412no—
352C2×C8C24×C4311yescharacteristic
353C2×C8C24×C4311yescharacteristic
354C2×C8C24×C4312yes—
355C2×C8C24×C4313yes—
356C2×C8C24×C4313yes—
357C2×C8C24×C4316yes—
358C4⋊C4C22×C4×C4313yes—
359C4⋊C4C22×C4×C4313yes—
360C4⋊C4C22×C4×C4316yes—
361C4⋊C4C22×C4×C4311yescharacteristic
362C4⋊C4C22×C4×C4311yescharacteristic
363C4⋊C4C22×C4×C4316yes—
364C4⋊C4C22×C4×C4316yes—
365C4⋊C4C22×C4×C4316yes—
366C4⋊C4C22×C4×C4316yes—
367C22⋊C4C22×C4×C4312yes—
368C22⋊C4C22×C4×C4316yes—
369C22⋊C4C22×C4×C4316yes—
370C22⋊C4C22×C4×C43112yes—
371C22⋊C4C22×C4×C43112yes—
372C42C22×C4×C4316yes—
373C42C22×C4×C4316yes—
374C42C22×C4×C4313yes—
375C42C22×C4×C4313yes—
376C42C24×C4313yes—
377C42C24×C4313yes—
378C42C24×C4312yes—
379C23C23×C4×C4316yes—
380C23C23×C4×C4311yescharacteristic
381Q8—26no—
382Q8—26no—
383Q8#131×C4314yescomplemented
384D4—212no—
385D4—26no—
386D4—212no—
387D4—46no—
388C2×C4—26no—
389C2×C4—212no—
390C2×C4—26no—
391C2×C4—26no—
392C2×C4—46no—
393C2×C4—43no—
394C2×C4C23×C4×C4312yes—
395C2×C4C23×C4×C4313yes—
396C2×C4C23×C4×C4312yes—
397C2×C4C23×C4×C4316yes—
398C2×C4C23×C4×C4313yes—
399C2×C4C23×C4×C4313yes—
400C2×C4C23×C4×C4311yescharacteristic
401C2×C4C23×C4×C4313yes—
402C2×C4H(5,𝔽2)×C4312yes—
403C2×C42−1+4×C4312yes—
404C2×C4C25×C4311yescharacteristic
405C8—23no—
406C8—23no—
407C8—26no—
408C8—21no—
409C8—21no—
410C8—22no—
411C22—21no—
412C22—21no—
413C22—26no—
414C22—26no—
415C22—26no—
416C22C43×#52012yes—
417C22C24×C4×C4311yescharacteristic
418C4—26no—
419C4—22no—
420C4—23no—
421C4—22no—
422C4—23no—
423C4—23no—
424C4C43×#52012yes—
425C4C2×#131×C4316yes—
426C4C2×H(5,𝔽2)×C4311yescharacteristic
427C4C2×2−1+4×C4311yescharacteristic
428C2—22no—
429C2—46no—
430C2C2×C43×#52011yescharacteristic
431C2C22×#131×C4311yescharacteristic
432C2C43×#357311yescharacteristic
subgroupG/H
centerC2×C4×C43C25
commutatorC22C24×C4×C43
Frattini, cosocleC2×C4C25×C43
socleC22×C43C24×C4
prime radicalC43×#3480C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#2994C2semidirect
3. C43×#2993C2semidirect
4. C43×#2991C2semidirect
5. C43×#2988C2semidirect
6. Q8×M16×C43C2semidirect
7. C2×C8×Q8×C43C2semidirect
8. C43×#2935C2semidirect
9. C43×#2931C2semidirect
10. C43×#2922C2semidirect
11. C43×#2906C2semidirect
166. Q8×C43#131semidirect
194. #60274C43direct (N × H)
213. #2994C2×C43semidirect
214. #2993C2×C43semidirect
215. #2991C2×C43semidirect
216. #2988C2×C43semidirect
217. Q8×M16C2×C43semidirect
218. C2×C8×Q8C2×C43semidirect
219. #2935C2×C43semidirect
220. #2931C2×C43semidirect
221. #2922C2×C43semidirect
222. #2906C2×C43semidirect
268. C43#60274direct (N × H)
383. Q8#131×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#34802
C43×#29942
C43×#29932
C43×#29912
C43×#29882
Q8×M16×C432
C2×C8×Q8×C432
C43×#29352
C43×#29312
C43×#29222
C43×#29062
#6027443