Finite Group Databasebeta

← C43×#9955 #24929972

Subgroups — C43×#9955 #24929972

Order 11008.

888 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3189C211yesmaximal, characteristic, complemented
2C2×C43×#450C211yesmaximal, characteristic
3C43×#2435C211yesmaximal, characteristic
4C43×#1996C211yesmaximal, characteristic, complemented
5C43×#1786C211yesmaximal, characteristic
6C43×#1520C211yesmaximal, characteristic, complemented
7C43×#1282C211yesmaximal, characteristic, complemented
8C23×D4×C43C2211yescharacteristic
9C22×SD16×C43—21no—
10C2×#124×C43—21no—
11C2×C22⋊Q8×C43C2211yescharacteristic
12C2×C22⋊Q8×C43C2211yescharacteristic
13C43×#484—21no—
14C43×#484—21no—
15C43×#467—22no—
16C43×#451—21no—
17C43×#451—21no—
18C43×#450—22no—
19C43×#450—22no—
20C2×#102×C43—21no—
21C2×#102×C43—22no—
22C2×C22⋊C8×C43C2211yescharacteristic
23C2×C22⋊C8×C43C2211yescharacteristic
24C43×#394—22no—
25C43×#390—21no—
26C43×#380C2211yescharacteristic
27C43×#379—22no—
28C4×C22⋊C4×C43C2211yescharacteristic
29C43×#342—22no—
30C43×#328—22no—
31C25×C43—21no—
32C22×Q8×C43D411yescharacteristic
33C22×Q8×C43D411yescharacteristic
34C22×D4×C43—21no—
35C22×D4×C43—21no—
36C22×D4×C43—21no—
37C22×D4×C43—21no—
38C22×D4×C43—21no—
39C22×D4×C43—44no—
40C22×D4×C43D412yes—
41C23×C4×C43C2311yescharacteristic
42C2×Q16×C43—22no—
43C2×SD16×C43—24no—
44C2×SD16×C43—44no—
45C22×C8×C43—21no—
46C22×C8×C43D412yes—
47#124×C43—44no—
48C22⋊Q8×C43—21no—
49C22⋊Q8×C43—21no—
50C22⋊Q8×C43—21no—
51C22⋊Q8×C43—21no—
52C22⋊Q8×C43—21no—
53C22⋊Q8×C43—21no—
54C22⋊Q8×C43—21no—
55C22⋊Q8×C43—21no—
56C2×C4⋊C4×C43—21no—
57C2×C4⋊C4×C43—21no—
58C2×C4⋊C4×C43—21no—
59C2×C4⋊C4×C43D411yescharacteristic
60C2×C4⋊C4×C43D411yescharacteristic
61C2×C22⋊C4×C43—24no—
62C2×C22⋊C4×C43—21no—
63C2×C22⋊C4×C43—21no—
64C2×C22⋊C4×C43—21no—
65C2×C22⋊C4×C43—24no—
66C2×C22⋊C4×C43D412yes—
67C2×C42×C43—21no—
68#107×C43—22no—
69#103×C43—22no—
70#103×C43—22no—
71#102×C43—24no—
72#102×C43—44no—
73C22⋊C8×C43—21no—
74C22⋊C8×C43—21no—
75C22⋊C8×C43—21no—
76C22⋊C8×C43D412yes—
77#95×C43—21no—
78#95×C43—21no—
79C24×C43—22no—
80C24×C43—44no—
81C24×C43—41no—
82C24×C43—41no—
83C24×C43—42no—
84C24×C43—42no—
85C24×C43—82no—
86C24×C43C2×D411yescharacteristic
87C2×Q8×C43—21no—
88C2×Q8×C43—21no—
89C2×Q8×C43—21no—
90C2×Q8×C43—21no—
91C2×Q8×C43—42no—
92C2×Q8×C43—42no—
93C2×D4×C43—24no—
94C2×D4×C43—24no—
95C2×D4×C43—24no—
96C2×D4×C43—22no—
97C2×D4×C43—22no—
98C2×D4×C43—44no—
99C2×D4×C43—42no—
100C2×D4×C43—42no—
101C2×D4×C43—42no—
102C2×D4×C43—44no—
103C2×D4×C43—44no—
104C2×D4×C43—41no—
105C2×D4×C43—41no—
106C22×C4×C43—22no—
107C22×C4×C43—21no—
108C22×C4×C43—21no—
109C22×C4×C43—21no—
110C22×C4×C43—21no—
111C22×C4×C43—42no—
112C22×C4×C43—41no—
113C22×C4×C43C2×D411yescharacteristic
114C22×C4×C43C2×D411yescharacteristic
115C22×C4×C43C2×D411yescharacteristic
116C22×C4×C43C2×D411yescharacteristic
117C22×C4×C43C2×D411yescharacteristic
118C22×C4×C43#4111yescharacteristic
119Q16×C43—82no—
120SD16×C43—48no—
121C2×C8×C43—22no—
122C2×C8×C43—22no—
123C2×C8×C43—42no—
124C2×C8×C43—42no—
125C4⋊C4×C43—21no—
126C4⋊C4×C43—21no—
127C4⋊C4×C43—21no—
128C4⋊C4×C43—21no—
129C4⋊C4×C43—42no—
130C4⋊C4×C43—41no—
131C4⋊C4×C43—41no—
132C4⋊C4×C43—41no—
133C4⋊C4×C43—41no—
134C22⋊C4×C43—22no—
135C22⋊C4×C43—22no—
136C22⋊C4×C43—48no—
137C22⋊C4×C43—41no—
138C22⋊C4×C43—41no—
139C22⋊C4×C43—41no—
140C22⋊C4×C43—41no—
141C22⋊C4×C43—42no—
142C22⋊C4×C43—84no—
143C42×C43—42no—
144C23×C43—24no—
145C23×C43—41no—
146C23×C43—41no—
147C23×C43—44no—
148C23×C43—44no—
149C23×C43—44no—
150C23×C43—42no—
151C23×C43—42no—
152C23×C43—44no—
153C23×C43—82no—
154C23×C43—82no—
155C23×C43—88no—
156C23×C43—88no—
157C23×C43—82no—
158C23×C43—81no—
159C23×C43—81no—
160C23×C43#12011yescharacteristic
161C23×C43#12111yescharacteristic
162C23×C43#12711yescharacteristic
163C23×C43#13512yes—
164C23×C43#13712yes—
165Q8×C43—42no—
166Q8×C43—42no—
167Q8×C43—42no—
168Q8×C43—81no—
169D4×C43—24no—
170D4×C43—24no—
171D4×C43—42no—
172D4×C43—42no—
173D4×C43—44no—
174D4×C43—44no—
175C2×C4×C43—22no—
176C2×C4×C43—22no—
177C2×C4×C43—22no—
178C2×C4×C43—41no—
179C2×C4×C43—41no—
180C2×C4×C43—41no—
181C2×C4×C43—42no—
182C2×C4×C43—42no—
183C2×C4×C43—42no—
184C2×C4×C43—42no—
185C2×C4×C43—41no—
186C2×C4×C43—41no—
187C2×C4×C43—41no—
188C2×C4×C43—41no—
189C2×C4×C43—42no—
190C2×C4×C43—81no—
191C2×C4×C43—81no—
192C2×C4×C43—81no—
193C2×C4×C43—81no—
194C2×C4×C43—81no—
195C2×C4×C43#12011yescharacteristic
196C2×C4×C43#12011yescharacteristic
197C2×C4×C43#12111yescharacteristic
198C2×C4×C43#12111yescharacteristic
199C8×C43—42no—
200C8×C43—42no—
201#9955C4311yesmaximal, characteristic, direct product factor, Sylow
202C22×C43—21no—
203C22×C43—21no—
204C22×C43—21no—
205C22×C43—21no—
206C22×C43—21no—
207C22×C43—21no—
208C22×C43—42no—
209C22×C43—42no—
210C22×C43—48no—
211C22×C43—44no—
212C22×C43—84no—
213C22×C43—84no—
214C22×C43—88no—
215C22×C43—84no—
216C22×C43—82no—
217C22×C43—82no—
218C22×C43#39211yescharacteristic
219C22×C43#45212yes—
220C22×C43#46412yes—
221C22×C43#49511yescharacteristic
222C22×C43#49711yescharacteristic
223C4×C43—21no—
224C4×C43—21no—
225C4×C43—21no—
226C4×C43—82no—
227C4×C43—81no—
228C4×C43—81no—
229C4×C43—81no—
230C4×C43—81no—
231C4×C43—161no—
232C4×C43B(4,𝔽2)12yes—
233#3189C2×C4311yescharacteristic, complemented
234C2×#450C2×C4311yescharacteristic
235#2435C2×C4311yescharacteristic
236#1996C2×C4311yescharacteristic, complemented
237#1786C2×C4311yescharacteristic
238#1520C2×C4311yescharacteristic, complemented
239#1282C2×C4311yescharacteristic, complemented
240C2×C43—22no—
241C2×C43—21no—
242C2×C43—22no—
243C2×C43—21no—
244C2×C43—84no—
245C2×C43#200811yescharacteristic
246C2×C43#201511yescharacteristic
247C2×C43#202111yescharacteristic
248C23×D4C22×C4311yescharacteristic
249C22×SD16—21no—
250C2×#124—21no—
251C2×C22⋊Q8C22×C4311yescharacteristic
252C2×C22⋊Q8C22×C4311yescharacteristic
253#484—21no—
254#484—21no—
255#467—22no—
256#451—21no—
257#451—21no—
258#450—22no—
259#450—22no—
260C2×#102—21no—
261C2×#102—22no—
262C2×C22⋊C8C22×C4311yescharacteristic
263C2×C22⋊C8C22×C4311yescharacteristic
264#394—22no—
265#390—21no—
266#380C22×C4311yescharacteristic
267#379—22no—
268C4×C22⋊C4C22×C4311yescharacteristic
269#342—22no—
270#328—22no—
271C43#995511yescharacteristic, direct product factor, Sylow
272C25—21no—
273C22×Q8D4×C4311yescharacteristic
274C22×Q8D4×C4311yescharacteristic
275C22×D4—21no—
276C22×D4—21no—
277C22×D4—21no—
278C22×D4—21no—
279C22×D4—21no—
280C22×D4—44no—
281C22×D4D4×C4312yes—
282C23×C4C23×C4311yescharacteristic
283C2×Q16—22no—
284C2×SD16—24no—
285C2×SD16—44no—
286C22×C8—21no—
287C22×C8D4×C4312yes—
288#124—44no—
289C22⋊Q8—21no—
290C22⋊Q8—21no—
291C22⋊Q8—21no—
292C22⋊Q8—21no—
293C22⋊Q8—21no—
294C22⋊Q8—21no—
295C22⋊Q8—21no—
296C22⋊Q8—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4D4×C4311yescharacteristic
301C2×C4⋊C4D4×C4311yescharacteristic
302C2×C22⋊C4—24no—
303C2×C22⋊C4—21no—
304C2×C22⋊C4—21no—
305C2×C22⋊C4—21no—
306C2×C22⋊C4—24no—
307C2×C22⋊C4D4×C4312yes—
308C2×C42—21no—
309#107—22no—
310#103—22no—
311#103—22no—
312#102—24no—
313#102—44no—
314C22⋊C8—21no—
315C22⋊C8—21no—
316C22⋊C8—21no—
317C22⋊C8D4×C4312yes—
318#95—21no—
319#95—21no—
320C24—22no—
321C24—44no—
322C24—41no—
323C24—41no—
324C24—42no—
325C24—42no—
326C24—82no—
327C24C2×D4×C4311yescharacteristic
328C2×Q8—21no—
329C2×Q8—21no—
330C2×Q8—21no—
331C2×Q8—21no—
332C2×Q8—42no—
333C2×Q8—42no—
334C2×D4—24no—
335C2×D4—24no—
336C2×D4—24no—
337C2×D4—22no—
338C2×D4—22no—
339C2×D4—42no—
340C2×D4—42no—
341C2×D4—42no—
342C2×D4—44no—
343C2×D4—44no—
344C2×D4—44no—
345C2×D4—41no—
346C2×D4—41no—
347C22×C4—22no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—42no—
353C22×C4—41no—
354C22×C4C2×D4×C4311yescharacteristic
355C22×C4C2×D4×C4311yescharacteristic
356C22×C4C2×D4×C4311yescharacteristic
357C22×C4C2×D4×C4311yescharacteristic
358C22×C4C2×D4×C4311yescharacteristic
359C22×C4#41×C4311yescharacteristic
360Q16—82no—
361SD16—48no—
362C2×C8—22no—
363C2×C8—22no—
364C2×C8—42no—
365C2×C8—42no—
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—42no—
371C4⋊C4—41no—
372C4⋊C4—41no—
373C4⋊C4—41no—
374C4⋊C4—41no—
375C22⋊C4—22no—
376C22⋊C4—22no—
377C22⋊C4—48no—
378C22⋊C4—41no—
379C22⋊C4—41no—
380C22⋊C4—41no—
381C22⋊C4—41no—
382C22⋊C4—42no—
383C22⋊C4—84no—
384C42—42no—
385C23—24no—
386C23—41no—
387C23—41no—
388C23—44no—
389C23—44no—
390C23—44no—
391C23—42no—
392C23—42no—
393C23—44no—
394C23—82no—
395C23—82no—
396C23—88no—
397C23—88no—
398C23—81no—
399C23—82no—
400C23—81no—
401C23#120×C4311yescharacteristic
402C23#121×C4311yescharacteristic
403C23#127×C4311yescharacteristic
404C23#135×C4312yes—
405C23#137×C4312yes—
406Q8—42no—
407Q8—42no—
408Q8—42no—
409Q8—81no—
410D4—24no—
411D4—24no—
412D4—42no—
413D4—42no—
414D4—44no—
415D4—44no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—42no—
431C2×C4—81no—
432C2×C4—81no—
433C2×C4—81no—
434C2×C4—81no—
435C2×C4—81no—
436C2×C4#120×C4311yescharacteristic
437C2×C4#120×C4311yescharacteristic
438C2×C4#121×C4311yescharacteristic
439C2×C4#121×C4311yescharacteristic
440C8—42no—
441C8—42no—
442C22—21no—
443C22—21no—
444C22—21no—
445C22—21no—
446C22—21no—
447C22—21no—
448C22—42no—
449C22—42no—
450C22—48no—
451C22—44no—
452C22—84no—
453C22—84no—
454C22—84no—
455C22—88no—
456C22—82no—
457C22—82no—
458C22C43×#39211yescharacteristic
459C22C43×#45212yes—
460C22C43×#46412yes—
461C22C43×#49511yescharacteristic
462C22C43×#49711yescharacteristic
463C4—21no—
464C4—21no—
465C4—21no—
466C4—82no—
467C4—81no—
468C4—81no—
469C4—81no—
470C4—81no—
471C4—161no—
472C4C43×B(4,𝔽2)12yes—
473C2—22no—
474C2—21no—
475C2—21no—
476C2—22no—
477C2—84no—
478C2C43×#200811yescharacteristic
479C2C43×#201511yescharacteristic
480C2C43×#202111yescharacteristic
subgroupG/H
center, socleC22×C43#392
commutator, Frattini, cosocleC23×C4C23×C43
prime radicalC23×D4×C43C22
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C23×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#3189C2semidirect
4. C43×#1996C2semidirect
6. C43×#1520C2semidirect
7. C43×#1282C2semidirect
201. #9955C43direct (N × H)
233. #3189C2×C43semidirect
236. #1996C2×C43semidirect
238. #1520C2×C43semidirect
239. #1282C2×C43semidirect
271. C43#9955direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#31892
C2×C43×#4502
C43×#24352
C43×#19962
C43×#17862
C43×#15202
C43×#12822
#995543