Finite Group Databasebeta

← C43×#60498 #24980515

Subgroups — C43×#60498 #24980515

Order 11008.

2006 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3503C211yesmaximal, characteristic, complemented
2C4×2−1+4×C43C211yesmaximal, characteristic
3C43×#3083C216yesmaximal, complemented
4C43×#3082C216yesmaximal, complemented
5C43×#3079C213yesmaximal, complemented
6C43×#3078C213yesmaximal, complemented
7C43×#3076C213yesmaximal, complemented
8C2×C43×#477C213yesmaximal, complemented
9C43×#2913C212yesmaximal, complemented
10C43×#2906C211yesmaximal, characteristic, complemented
11C43×#2898C212yesmaximal
12C2×2−1+4×C43C2211yescharacteristic
13C2×#131×C43C2212yes—
14Q82×C43—21no—
15C43×#557—21no—
16C43×#554—23no—
17D4×Q8×C43—23no—
18C43×#544C2216yes—
19C43×#533C2213yes—
20C2×C4⋊Q8×C43C2213yes—
21C43×#520—23no—
22C43×#520C2213yes—
23C43×#520C2212yes—
24C43×#520C2211yescharacteristic
25C43×#519—21no—
26C43×#519C2213yes—
27C4×#41×C43—23no—
28C4×#41×C43C2213yes—
29C4×#41×C43C2211yescharacteristic
30C2×C4×Q8×C43—21no—
31C2×C4×Q8×C43C2213yes—
32C43×#479C2216yes—
33C43×#479C22112yes—
34C43×#478C2216yes—
35C43×#477C2213yes—
36C43×#477C2216yes—
37C43×#477C22112yes—
38C43×#476C2213yes—
39C43×#475C2213yes—
40C43×#475C2216yes—
41C43×#474C2211yescharacteristic
42C43×#474C2216yes—
43C43×#428C2216yes—
44C43×#428C2216yes—
45C43×#427C2216yes—
46C2×#107×C43C2216yes—
47C43×#424C2216yes—
48C43×#423C2213yes—
49C2×C4⋊C8×C43C2213yes—
50C43×#419C2216yes—
51C43×#417C2216yes—
52C43×#416C2216yes—
53C2×#103×C43C2216yes—
542−1+4×C43—24no—
552−1+4×C43Q818yescomplemented
56C2×#41×C43—23no—
57C2×#41×C43C2313yes—
58C2×#41×C43C2311yescharacteristic
59C22×Q8×C43—21no—
60C22×Q8×C43—23no—
61C22×Q8×C43C2313yes—
62#131×C43—28no—
63C2×M16×C43C2316yes—
64C22×C8×C43C2316yes—
65C4⋊Q8×C43—26no—
66C4⋊Q8×C43—23no—
67C4⋊Q8×C43—23no—
68C4⋊Q8×C43C2313yes—
69C4⋊Q8×C43C2316yes—
70C4⋊Q8×C43C2311yescharacteristic
71#125×C43—26no—
72#125×C43C2316yes—
73C22⋊Q8×C43—23no—
74C22⋊Q8×C43—23no—
75C22⋊Q8×C43—212no—
76C4×Q8×C43—21no—
77C4×Q8×C43—22no—
78C4×Q8×C43—23no—
79C4×Q8×C43—23no—
80C4×Q8×C43—23no—
81C4×Q8×C43—23no—
82C4×Q8×C43—23no—
83C4×Q8×C43—23no—
84C4×Q8×C43D411yescharacteristic
85C4×Q8×C43D411yescharacteristic
86C4×Q8×C43C2313yes—
87C4×Q8×C43C2316yes—
88C4×Q8×C43C2313yes—
89C4×D4×C43—23no—
90C4×D4×C43—26no—
91C4×D4×C43—23no—
92C4×D4×C43—23no—
93C4×D4×C43—26no—
94C4×D4×C43D413yes—
95C4×D4×C43D413yes—
96C4×D4×C43C2311yescharacteristic
97C4×D4×C43C2313yes—
98#117×C43—23no—
99#117×C43—26no—
100#117×C43—23no—
101#117×C43C2313yes—
102#117×C43C2316yes—
103#117×C43C2313yes—
104C2×C4⋊C4×C43—23no—
105C2×C4⋊C4×C43—23no—
106C2×C4⋊C4×C43—23no—
107C2×C4⋊C4×C43C2313yes—
108C2×C4⋊C4×C43C2316yes—
109C2×C42×C43—23no—
110C2×C42×C43—23no—
111C2×C42×C43C2313yes—
112#107×C43C2316yes—
113#107×C43C23112yes—
114#107×C43C2312yes—
115#106×C43C2316yes—
116#106×C43C2316yes—
117C4⋊C8×C43C2311yescharacteristic
118C4⋊C8×C43C2313yes—
119C4⋊C8×C43C2316yes—
120C4⋊C8×C43C2316yes—
121#103×C43C2316yes—
122#103×C43C23112yes—
123#103×C43C2316yes—
124#102×C43C2312yes—
125#102×C43C2316yes—
126#41×C43—224no—
127#41×C43—26no—
128#41×C43C2×Q814yes—
129#41×C43C2×Q8112yescomplemented
130#41×C43#4114yes—
131C2×Q8×C43—28no—
132C2×Q8×C43—23no—
133C2×Q8×C43—21no—
134C2×Q8×C43—23no—
135C2×Q8×C43—26no—
136C2×Q8×C43—26no—
137C2×Q8×C43—86no—
138C2×Q8×C43C2×D411yescharacteristic
139C2×Q8×C43C2×Q8112yescomplemented
140C2×Q8×C43C2413yes—
141C2×D4×C43—23no—
142C2×D4×C43C2×D413yes—
143C2×D4×C43C2411yescharacteristic
144C22×C4×C43—23no—
145C22×C4×C43—21no—
146C22×C4×C43—23no—
147C22×C4×C43—23no—
148C22×C4×C43—23no—
149C22×C4×C43—26no—
150C22×C4×C43C2×D413yes—
151C22×C4×C43C2×D413yes—
152C22×C4×C43C2413yes—
153M16×C43—212no—
154C2×C8×C43—212no—
155C2×C8×C43C2416yes—
156C2×C8×C43C2412yes—
157C4⋊C4×C43—26no—
158C4⋊C4×C43—23no—
159C4⋊C4×C43—23no—
160C4⋊C4×C43—23no—
161C4⋊C4×C43—26no—
162C4⋊C4×C43—26no—
163C4⋊C4×C43—23no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—26no—
166C4⋊C4×C43—26no—
167C4⋊C4×C43C2×D413yes—
168C4⋊C4×C43C2×D413yes—
169C4⋊C4×C43C2412yes—
170C4⋊C4×C43C2416yes—
171C4⋊C4×C43C2411yescharacteristic
172C4⋊C4×C43C2413yes—
173C22⋊C4×C43—21no—
174C22⋊C4×C43—23no—
175C22⋊C4×C43—23no—
176C22⋊C4×C43—26no—
177C22⋊C4×C43C2×D416yes—
178C42×C43—23no—
179C42×C43—23no—
180C42×C43—26no—
181C42×C43—23no—
182C42×C43—26no—
183C42×C43C2×D413yes—
184C42×C43C2×D413yes—
185C42×C43C2411yescharacteristic
186C42×C43C2413yes—
187C23×C43—21no—
188C23×C43C22×D413yes—
189Q8×C43—212no—
190Q8×C43—23no—
191Q8×C43—46no—
192Q8×C43—42no—
193Q8×C43—86no—
194Q8×C43C22⋊Q814yes—
195Q8×C43C22×Q816yes—
196D4×C43—212no—
197D4×C43—21no—
198D4×C43C22⋊Q8112yes—
199D4×C43C22×Q812yes—
200C2×C4×C43—212no—
201C2×C4×C43—23no—
202C2×C4×C43—212no—
203C2×C4×C43—26no—
204C2×C4×C43—21no—
205C2×C4×C43—23no—
206C2×C4×C43—22no—
207C2×C4×C43—26no—
208C2×C4×C43—43no—
209C2×C4×C43—42no—
210C2×C4×C43—83no—
211C2×C4×C43—83no—
212C2×C4×C43—86no—
213C2×C4×C43C22×D413yes—
214C2×C4×C43C22×D413yes—
215C2×C4×C43C22×D411yescharacteristic
216C2×C4×C43C22×D413yes—
217C2×C4×C43C22×D411yescharacteristic
218C2×C4×C43C22×Q816yes—
219C2×C4×C43C2×#4116yes—
220C2×C4×C43C2511yescharacteristic
221C8×C43—22no—
222C8×C43—26no—
223#60498C4311yesmaximal, characteristic, direct product factor, Sylow
224C22×C43—23no—
225C22×C43—23no—
226C22×C43—22no—
227C22×C43—41no—
228C22×C43—41no—
229C22×C43C2×C22⋊Q816yes—
230C22×C43C23×D411yescharacteristic
231C4×C43—21no—
232C4×C43—23no—
233C4×C43—26no—
234C4×C43—23no—
235C4×C43—43no—
236C4×C43—46no—
237C4×C43—41no—
238C4×C43—42no—
239C4×C43C2×C22⋊Q816yes—
240C4×C43#57812yes—
241C4×C43C23×Q811yescharacteristic
242C4×C43C22×#4111yescharacteristic
243#3503C2×C4311yescharacteristic, complemented
244C4×2−1+4C2×C4311yescharacteristic
245#3083C2×C4316yescomplemented
246#3082C2×C4316yescomplemented
247#3079C2×C4313yescomplemented
248#3078C2×C4313yescomplemented
249#3076C2×C4313yescomplemented
250C2×#477C2×C4313yescomplemented
251#2913C2×C4312yescomplemented
252#2906C2×C4311yescharacteristic, complemented
253#2898C2×C4312yes—
254C2×C43—26no—
255C2×C43—42no—
256C2×C43C22×C22⋊Q811yescharacteristic
257C2×C43C2×#57811yescharacteristic
258C2×C43#358511yescharacteristic
259C2×2−1+4C22×C4311yescharacteristic
260C2×#131C22×C4312yes—
261Q82—21no—
262#557—21no—
263#554—23no—
264D4×Q8—23no—
265#544C22×C4316yes—
266#533C22×C4313yes—
267C2×C4⋊Q8C22×C4313yes—
268#520—23no—
269#520C22×C4313yes—
270#520C22×C4312yes—
271#520C22×C4311yescharacteristic
272#519—21no—
273#519C22×C4313yes—
274C4×#41—23no—
275C4×#41C22×C4313yes—
276C4×#41C22×C4311yescharacteristic
277C2×C4×Q8—21no—
278C2×C4×Q8C22×C4313yes—
279#479C22×C4316yes—
280#479C22×C43112yes—
281#478C22×C4316yes—
282#477C22×C4313yes—
283#477C22×C4316yes—
284#477C22×C43112yes—
285#476C22×C4313yes—
286#475C22×C4313yes—
287#475C22×C4316yes—
288#474C22×C4311yescharacteristic
289#474C22×C4316yes—
290#428C22×C4316yes—
291#428C22×C4316yes—
292#427C22×C4316yes—
293C2×#107C22×C4316yes—
294#424C22×C4316yes—
295#423C22×C4313yes—
296C2×C4⋊C8C22×C4313yes—
297#419C22×C4316yes—
298#417C22×C4316yes—
299#416C22×C4316yes—
300C2×#103C22×C4316yes—
301C43#6049811yescharacteristic, direct product factor, Sylow
3022−1+4—24no—
3032−1+4Q8×C4318yescomplemented
304C2×#41—23no—
305C2×#41C23×C4313yes—
306C2×#41C23×C4311yescharacteristic
307C22×Q8—21no—
308C22×Q8—23no—
309C22×Q8C23×C4313yes—
310#131—28no—
311C2×M16C23×C4316yes—
312C22×C8C23×C4316yes—
313C4⋊Q8—26no—
314C4⋊Q8—23no—
315C4⋊Q8—23no—
316C4⋊Q8C23×C4313yes—
317C4⋊Q8C23×C4316yes—
318C4⋊Q8C23×C4311yescharacteristic
319#125—26no—
320#125C23×C4316yes—
321C22⋊Q8—23no—
322C22⋊Q8—23no—
323C22⋊Q8—212no—
324C4×Q8—21no—
325C4×Q8—22no—
326C4×Q8—23no—
327C4×Q8—23no—
328C4×Q8—23no—
329C4×Q8—23no—
330C4×Q8—23no—
331C4×Q8—23no—
332C4×Q8D4×C4311yescharacteristic
333C4×Q8D4×C4311yescharacteristic
334C4×Q8C23×C4313yes—
335C4×Q8C23×C4316yes—
336C4×Q8C23×C4313yes—
337C4×D4—23no—
338C4×D4—26no—
339C4×D4—23no—
340C4×D4—23no—
341C4×D4—26no—
342C4×D4D4×C4313yes—
343C4×D4D4×C4313yes—
344C4×D4C23×C4311yescharacteristic
345C4×D4C23×C4313yes—
346#117—23no—
347#117—26no—
348#117—23no—
349#117C23×C4313yes—
350#117C23×C4316yes—
351#117C23×C4313yes—
352C2×C4⋊C4—23no—
353C2×C4⋊C4—23no—
354C2×C4⋊C4—23no—
355C2×C4⋊C4C23×C4313yes—
356C2×C4⋊C4C23×C4316yes—
357C2×C42—23no—
358C2×C42—23no—
359C2×C42C23×C4313yes—
360#107C23×C4316yes—
361#107C23×C43112yes—
362#107C23×C4312yes—
363#106C23×C4316yes—
364#106C23×C4316yes—
365C4⋊C8C23×C4311yescharacteristic
366C4⋊C8C23×C4313yes—
367C4⋊C8C23×C4316yes—
368C4⋊C8C23×C4316yes—
369#103C23×C4316yes—
370#103C23×C43112yes—
371#103C23×C4316yes—
372#102C23×C4312yes—
373#102C23×C4316yes—
374#41—224no—
375#41—26no—
376#41C2×Q8×C4314yes—
377#41C2×Q8×C43112yescomplemented
378#41#41×C4314yes—
379C2×Q8—28no—
380C2×Q8—23no—
381C2×Q8—21no—
382C2×Q8—23no—
383C2×Q8—26no—
384C2×Q8—26no—
385C2×Q8—86no—
386C2×Q8C2×D4×C4311yescharacteristic
387C2×Q8C2×Q8×C43112yescomplemented
388C2×Q8C24×C4313yes—
389C2×D4—23no—
390C2×D4C2×D4×C4313yes—
391C2×D4C24×C4311yescharacteristic
392C22×C4—23no—
393C22×C4—23no—
394C22×C4—23no—
395C22×C4—26no—
396C22×C4—21no—
397C22×C4—23no—
398C22×C4C2×D4×C4313yes—
399C22×C4C2×D4×C4313yes—
400C22×C4C24×C4313yes—
401M16—212no—
402C2×C8—212no—
403C2×C8C24×C4316yes—
404C2×C8C24×C4312yes—
405C4⋊C4—26no—
406C4⋊C4—23no—
407C4⋊C4—23no—
408C4⋊C4—23no—
409C4⋊C4—26no—
410C4⋊C4—26no—
411C4⋊C4—23no—
412C4⋊C4—21no—
413C4⋊C4—26no—
414C4⋊C4—26no—
415C4⋊C4C2×D4×C4313yes—
416C4⋊C4C2×D4×C4313yes—
417C4⋊C4C24×C4312yes—
418C4⋊C4C24×C4316yes—
419C4⋊C4C24×C4311yescharacteristic
420C4⋊C4C24×C4313yes—
421C22⋊C4—23no—
422C22⋊C4—26no—
423C22⋊C4—21no—
424C22⋊C4—23no—
425C22⋊C4C2×D4×C4316yes—
426C42—23no—
427C42—23no—
428C42—26no—
429C42—23no—
430C42—26no—
431C42C2×D4×C4313yes—
432C42C2×D4×C4313yes—
433C42C24×C4311yescharacteristic
434C42C24×C4313yes—
435C23—21no—
436C23C22×D4×C4313yes—
437Q8—212no—
438Q8—23no—
439Q8—46no—
440Q8—42no—
441Q8—86no—
442Q8C22⋊Q8×C4314yes—
443Q8C22×Q8×C4316yes—
444D4—212no—
445D4—21no—
446D4C22⋊Q8×C43112yes—
447D4C22×Q8×C4312yes—
448C2×C4—212no—
449C2×C4—23no—
450C2×C4—212no—
451C2×C4—26no—
452C2×C4—21no—
453C2×C4—23no—
454C2×C4—22no—
455C2×C4—26no—
456C2×C4—43no—
457C2×C4—42no—
458C2×C4—83no—
459C2×C4—86no—
460C2×C4—83no—
461C2×C4C22×D4×C4313yes—
462C2×C4C22×D4×C4313yes—
463C2×C4C22×D4×C4311yescharacteristic
464C2×C4C22×D4×C4313yes—
465C2×C4C22×D4×C4311yescharacteristic
466C2×C4C22×Q8×C4316yes—
467C2×C4C2×#41×C4316yes—
468C2×C4C25×C4311yescharacteristic
469C8—22no—
470C8—26no—
471C22—23no—
472C22—23no—
473C22—22no—
474C22—41no—
475C22—41no—
476C22C2×C22⋊Q8×C4316yes—
477C22C23×D4×C4311yescharacteristic
478C4—26no—
479C4—23no—
480C4—21no—
481C4—23no—
482C4—41no—
483C4—42no—
484C4—43no—
485C4—46no—
486C4C2×C22⋊Q8×C4316yes—
487C4C43×#57812yes—
488C4C23×Q8×C4311yescharacteristic
489C4C22×#41×C4311yescharacteristic
490C2—26no—
491C2—42no—
492C2C22×C22⋊Q8×C4311yescharacteristic
493C2C2×C43×#57811yescharacteristic
494C2C43×#358511yescharacteristic
subgroupG/H
center, socleC22×C43C23×D4
commutator, Frattini, cosocleC2×C4C25×C43
prime radicalC2×2−1+4×C43C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C4×#41×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#3503C2semidirect
3. C43×#3083C2semidirect
4. C43×#3082C2semidirect
5. C43×#3079C2semidirect
6. C43×#3078C2semidirect
7. C43×#3076C2semidirect
8. C2×C43×#477C2semidirect
9. C43×#2913C2semidirect
10. C43×#2906C2semidirect
55. 2−1+4×C43Q8semidirect
129. #41×C43C2×Q8semidirect
139. C2×Q8×C43C2×Q8semidirect
223. #60498C43direct (N × H)
243. #3503C2×C43semidirect
245. #3083C2×C43semidirect
246. #3082C2×C43semidirect
247. #3079C2×C43semidirect
248. #3078C2×C43semidirect
249. #3076C2×C43semidirect
250. C2×#477C2×C43semidirect
251. #2913C2×C43semidirect
252. #2906C2×C43semidirect
301. C43#60498direct (N × H)
303. 2−1+4Q8×C43semidirect
377. #41C2×Q8×C43semidirect
387. C2×Q8C2×Q8×C43semidirect

Maximal subgroups

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

subgroupindex
C43×#35032
C4×2−1+4×C432
C43×#30832
C43×#30822
C43×#30792
C43×#30782
C43×#30762
C2×C43×#4772
C43×#29132
C43×#29062
C43×#28982
#6049843