Finite Group Databasebeta

← C43×#8493 #24928510

Subgroups — C43×#8493 #24928510

Order 11008.

748 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3548C211yesmaximal, characteristic
2C43×#1963C211yesmaximal, characteristic, complemented
3C43×#1559C211yesmaximal, characteristic, complemented
4C43×#1557C211yesmaximal, characteristic, complemented
5C43×#1536C211yesmaximal, characteristic, complemented
6C43×#1506C211yesmaximal, characteristic, complemented
7C43×#1505C211yesmaximal, characteristic, complemented
8C43×#562—22no—
9C43×#554—21no—
10C43×#554C412yescomplemented
11C43×#550—21no—
12C43×#550C412yescomplemented
13C43×#547—21no—
14C43×#547—21no—
15C43×#540—22no—
16C43×#537—22no—
17C43×#537—22no—
18C43×#533C2211yescharacteristic
19C43×#532C2211yescharacteristic
20C43×#532C2211yescharacteristic
21C43×#432C2211yescharacteristic
22C43×#432C2211yescharacteristic
23C43×#423C2211yescharacteristic
24C2×#104×C43—22no—
25C43×#376C2211yescharacteristic
26C43×#333—21no—
27C43×#332—21no—
28C43×#332—21no—
29C43×#331—21no—
30C43×#329—22no—
31C43×#328—22no—
32C43×#327—22no—
33C2×#41×C43—22no—
34C2×#41×C43—22no—
35C2×#41×C43—21no—
36C2×#41×C43D412yes—
37C2×M16×C43—21no—
38C4⋊Q8×C43C2×C411yescharacteristic
39C4⋊Q8×C43D411yescharacteristic
40C4⋊Q8×C43D411yescharacteristic
41C4⋊Q8×C43D411yescharacteristic
42#127×C43—22no—
43#127×C43C2×C411yescharacteristic
44#127×C43D411yescharacteristic
45#125×C43—22no—
46#125×C43—21no—
47#124×C43—21no—
48#124×C43D412yes—
49#123×C43—24no—
50#123×C43—24no—
51C22⋊Q8×C43—22no—
52C22⋊Q8×C43—24no—
53C22⋊Q8×C43—22no—
54C22⋊Q8×C43—24no—
55C22⋊Q8×C43—21no—
56C22⋊Q8×C43D412yes—
57#121×C43—24no—
58#121×C43—24no—
59#121×C43—22no—
60#121×C43—24no—
61#121×C43—24no—
62#121×C43—21no—
63#121×C43—21no—
64#121×C43—21no—
65#121×C43—22no—
66#121×C43D412yes—
67C4×Q8×C43—21no—
68C4×Q8×C43C2×C412yes—
69C4×D4×C43—22no—
70C4×D4×C43—22no—
71C4×D4×C43—21no—
72C4×D4×C43—21no—
73C4×D4×C43—21no—
74C4×D4×C43C2×C412yes—
75#117×C43—21no—
76C2×C4⋊C4×C43—22no—
77C2×C4⋊C4×C43—22no—
78C2×C42×C43—21no—
79C2×C42×C43C2311yescharacteristic
80C4⋊C8×C43—21no—
81C4⋊C8×C43—21no—
82C4⋊C8×C43—21no—
83C4⋊C8×C43—21no—
84#104×C43—44no—
85C22⋊C8×C43—21no—
86C22⋊C8×C43—21no—
87#97×C43—21no—
88#97×C43—21no—
89#95×C43—21no—
90#95×C43—21no—
91#41×C43—42no—
92#41×C43—42no—
93#41×C43—82no—
94#41×C43—84no—
95#41×C43—82no—
96#41×C43—82no—
97C2×Q8×C43—21no—
98C2×Q8×C43—21no—
99C2×Q8×C43C22⋊C412yes—
100C2×Q8×C43C22⋊C412yes—
101C2×D4×C43—24no—
102C2×D4×C43—24no—
103C2×D4×C43—21no—
104C2×D4×C43—21no—
105C2×D4×C43—21no—
106C2×D4×C43—21no—
107C2×D4×C43—22no—
108C2×D4×C43—22no—
109C2×D4×C43C22⋊C412yes—
110C2×D4×C43C22⋊C412yes—
111C22×C4×C43—24no—
112C22×C4×C43—24no—
113C22×C4×C43—22no—
114C22×C4×C43—22no—
115C22×C4×C43—41no—
116C22×C4×C43C2×D411yescharacteristic
117C22×C4×C43C2×D411yescharacteristic
118C22×C4×C43C2×D411yescharacteristic
119M16×C43—42no—
120C2×C8×C43—41no—
121C2×C8×C43—41no—
122C2×C8×C43—41no—
123C4⋊C4×C43—24no—
124C4⋊C4×C43—24no—
125C4⋊C4×C43—21no—
126C4⋊C4×C43—21no—
127C4⋊C4×C43—22no—
128C4⋊C4×C43—21no—
129C4⋊C4×C43—21no—
130C4⋊C4×C43—21no—
131C4⋊C4×C43—21no—
132C4⋊C4×C43—22no—
133C4⋊C4×C43C22⋊C412yes—
134C4⋊C4×C43C22⋊C412yes—
135C22⋊C4×C43—24no—
136C22⋊C4×C43—24no—
137C22⋊C4×C43—22no—
138C22⋊C4×C43—22no—
139C22⋊C4×C43—22no—
140C22⋊C4×C43—22no—
141C22⋊C4×C43—22no—
142C42×C43—22no—
143C42×C43—22no—
144C42×C43—41no—
145C42×C43C22×C411yescharacteristic
146C42×C43C2×D411yescharacteristic
147C42×C43C2×D411yescharacteristic
148C42×C43C2×D411yescharacteristic
149C23×C43—22no—
150C23×C43—22no—
151C23×C43#12011yescharacteristic
152Q8×C43—42no—
153Q8×C43—42no—
154Q8×C43—41no—
155Q8×C43—41no—
156Q8×C43—81no—
157D4×C43—42no—
158D4×C43—42no—
159D4×C43—42no—
160D4×C43—42no—
161D4×C43—41no—
162D4×C43—41no—
163D4×C43—81no—
164D4×C43—82no—
165D4×C43—82no—
166D4×C43—84no—
167D4×C43—84no—
168C2×C4×C43—21no—
169C2×C4×C43—21no—
170C2×C4×C43—22no—
171C2×C4×C43—22no—
172C2×C4×C43—22no—
173C2×C4×C43—22no—
174C2×C4×C43—41no—
175C2×C4×C43—41no—
176C2×C4×C43—44no—
177C2×C4×C43—42no—
178C2×C4×C43—42no—
179C2×C4×C43—42no—
180C2×C4×C43—84no—
181C2×C4×C43—84no—
182C2×C4×C43—81no—
183C2×C4×C43—81no—
184C2×C4×C43C2×C22⋊C411yescharacteristic
185C2×C4×C43C2×C22⋊C411yescharacteristic
186C2×C4×C43C2×C22⋊C411yescharacteristic
187C2×C4×C43#12011yescharacteristic
188C2×C4×C43#12011yescharacteristic
189C2×C4×C43#12011yescharacteristic
190C8×C43—81no—
191C8×C43—81no—
192C8×C43—81no—
193#8493C4311yesmaximal, characteristic, direct product factor, Sylow
194C22×C43—21no—
195C22×C43—21no—
196C22×C43—21no—
197C22×C43—42no—
198C22×C43—42no—
199C22×C43—42no—
200C22×C43—42no—
201C22×C43—42no—
202C22×C43—42no—
203C22×C43#37911yescharacteristic
204C4×C43—21no—
205C4×C43—21no—
206C4×C43—21no—
207C4×C43—21no—
208C4×C43—21no—
209C4×C43—42no—
210C4×C43—42no—
211C4×C43—42no—
212C4×C43—42no—
213C4×C43—82no—
214C4×C43#45311yescharacteristic
215C4×C43#45511yescharacteristic
216#3548C2×C4311yescharacteristic
217#1963C2×C4311yescharacteristic, complemented
218#1559C2×C4311yescharacteristic, complemented
219#1557C2×C4311yescharacteristic, complemented
220#1536C2×C4311yescharacteristic, complemented
221#1506C2×C4311yescharacteristic, complemented
222#1505C2×C4311yescharacteristic, complemented
223C2×C43—41no—
224C2×C43—82no—
225C2×C43—82no—
226C2×C43#179211yescharacteristic
227C2×C43#179511yescharacteristic
228C2×C43#179611yescharacteristic
229#562—22no—
230#554—21no—
231#554C4×C4312yescomplemented
232#550—21no—
233#550C4×C4312yescomplemented
234#547—21no—
235#547—21no—
236#540—22no—
237#537—22no—
238#537—22no—
239#533C22×C4311yescharacteristic
240#532C22×C4311yescharacteristic
241#532C22×C4311yescharacteristic
242#432C22×C4311yescharacteristic
243#432C22×C4311yescharacteristic
244#423C22×C4311yescharacteristic
245C2×#104—22no—
246#376C22×C4311yescharacteristic
247#333—21no—
248#332—21no—
249#332—21no—
250#331—21no—
251#329—22no—
252#328—22no—
253#327—22no—
254C43#849311yescharacteristic, direct product factor, Sylow
255C2×#41—22no—
256C2×#41—22no—
257C2×#41—21no—
258C2×#41D4×C4312yes—
259C2×M16—21no—
260C4⋊Q8C2×C4×C4311yescharacteristic
261C4⋊Q8D4×C4311yescharacteristic
262C4⋊Q8D4×C4311yescharacteristic
263C4⋊Q8D4×C4311yescharacteristic
264#127—22no—
265#127C2×C4×C4311yescharacteristic
266#127D4×C4311yescharacteristic
267#125—22no—
268#125—21no—
269#124—21no—
270#124D4×C4312yes—
271#123—24no—
272#123—24no—
273C22⋊Q8—22no—
274C22⋊Q8—24no—
275C22⋊Q8—22no—
276C22⋊Q8—24no—
277C22⋊Q8—21no—
278C22⋊Q8D4×C4312yes—
279#121—24no—
280#121—24no—
281#121—22no—
282#121—24no—
283#121—24no—
284#121—21no—
285#121—21no—
286#121—21no—
287#121—22no—
288#121D4×C4312yes—
289C4×Q8—21no—
290C4×Q8C2×C4×C4312yes—
291C4×D4—22no—
292C4×D4—22no—
293C4×D4—21no—
294C4×D4—21no—
295C4×D4—21no—
296C4×D4C2×C4×C4312yes—
297#117—21no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C42—21no—
301C2×C42C23×C4311yescharacteristic
302C4⋊C8—21no—
303C4⋊C8—21no—
304C4⋊C8—21no—
305C4⋊C8—21no—
306#104—44no—
307C22⋊C8—21no—
308C22⋊C8—21no—
309#97—21no—
310#97—21no—
311#95—21no—
312#95—21no—
313#41—42no—
314#41—42no—
315#41—82no—
316#41—84no—
317#41—82no—
318#41—82no—
319C2×Q8—21no—
320C2×Q8—21no—
321C2×Q8C22⋊C4×C4312yes—
322C2×Q8C22⋊C4×C4312yes—
323C2×D4—24no—
324C2×D4—24no—
325C2×D4—22no—
326C2×D4—22no—
327C2×D4—21no—
328C2×D4—21no—
329C2×D4—21no—
330C2×D4—21no—
331C2×D4C22⋊C4×C4312yes—
332C2×D4C22⋊C4×C4312yes—
333C22×C4—24no—
334C22×C4—24no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—41no—
338C22×C4C2×D4×C4311yescharacteristic
339C22×C4C2×D4×C4311yescharacteristic
340C22×C4C2×D4×C4311yescharacteristic
341M16—42no—
342C2×C8—41no—
343C2×C8—41no—
344C2×C8—41no—
345C4⋊C4—24no—
346C4⋊C4—24no—
347C4⋊C4—21no—
348C4⋊C4—21no—
349C4⋊C4—22no—
350C4⋊C4—21no—
351C4⋊C4—21no—
352C4⋊C4—21no—
353C4⋊C4—21no—
354C4⋊C4—22no—
355C4⋊C4C22⋊C4×C4312yes—
356C4⋊C4C22⋊C4×C4312yes—
357C22⋊C4—24no—
358C22⋊C4—24no—
359C22⋊C4—22no—
360C22⋊C4—22no—
361C22⋊C4—22no—
362C22⋊C4—22no—
363C22⋊C4—22no—
364C42—22no—
365C42—22no—
366C42—41no—
367C42C22×C4×C4311yescharacteristic
368C42C2×D4×C4311yescharacteristic
369C42C2×D4×C4311yescharacteristic
370C42C2×D4×C4311yescharacteristic
371C23—22no—
372C23—22no—
373C23#120×C4311yescharacteristic
374Q8—42no—
375Q8—42no—
376Q8—41no—
377Q8—41no—
378Q8—81no—
379D4—42no—
380D4—42no—
381D4—42no—
382D4—42no—
383D4—41no—
384D4—41no—
385D4—81no—
386D4—82no—
387D4—82no—
388D4—84no—
389D4—84no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—44no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—84no—
403C2×C4—84no—
404C2×C4—81no—
405C2×C4—81no—
406C2×C4C2×C22⋊C4×C4311yescharacteristic
407C2×C4C2×C22⋊C4×C4311yescharacteristic
408C2×C4C2×C22⋊C4×C4311yescharacteristic
409C2×C4#120×C4311yescharacteristic
410C2×C4#120×C4311yescharacteristic
411C2×C4#120×C4311yescharacteristic
412C8—81no—
413C8—81no—
414C8—81no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—42no—
419C22—42no—
420C22—42no—
421C22—42no—
422C22—42no—
423C22—42no—
424C22C43×#37911yescharacteristic
425C4—21no—
426C4—21no—
427C4—21no—
428C4—21no—
429C4—21no—
430C4—42no—
431C4—42no—
432C4—42no—
433C4—42no—
434C4—82no—
435C4C43×#45311yescharacteristic
436C4C43×#45511yescharacteristic
437C2—41no—
438C2—82no—
439C2—82no—
440C2C43×#179211yescharacteristic
441C2C43×#179511yescharacteristic
442C2C43×#179611yescharacteristic
subgroupG/H
center, socleC22×C43#379
commutatorC42C22×C4×C43
Frattini, cosocleC2×C42C23×C43
prime radicalC43×#3548C2
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
2. C43×#1963C2semidirect
3. C43×#1559C2semidirect
4. C43×#1557C2semidirect
5. C43×#1536C2semidirect
6. C43×#1506C2semidirect
7. C43×#1505C2semidirect
10. C43×#554C4semidirect
12. C43×#550C4semidirect
193. #8493C43direct (N × H)
217. #1963C2×C43semidirect
218. #1559C2×C43semidirect
219. #1557C2×C43semidirect
220. #1536C2×C43semidirect
221. #1506C2×C43semidirect
222. #1505C2×C43semidirect
231. #554C4×C43semidirect
233. #550C4×C43semidirect
254. C43#8493direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#35482
C43×#19632
C43×#15592
C43×#15572
C43×#15362
C43×#15062
C43×#15052
#849343