Finite Group Databasebeta

← C43×#29979 #24949996

Subgroups — C43×#29979 #24949996

Order 11008.

666 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#2629C211yesmaximal, characteristic
2C43×#2317C211yesmaximal, characteristic
3C43×#2100C211yesmaximal, characteristic, complemented
4C43×#2099C211yesmaximal, characteristic, complemented
5C43×#2088C211yesmaximal, characteristic, complemented
6C43×#2088C211yesmaximal, characteristic, complemented
7C43×#2087C211yesmaximal, characteristic, complemented
8C43×#2086C211yesmaximal, characteristic, complemented
9C43×#2059C211yesmaximal, characteristic, complemented
10C43×#2059C211yesmaximal, characteristic, complemented
11C43×#1853C211yesmaximal, characteristic
12C43×#1852C211yesmaximal, characteristic
13C43×#1825C211yesmaximal, characteristic
14C43×#1825C211yesmaximal, characteristic
15C43×#1798C211yesmaximal, characteristic
16C2×#125×C43C2211yescharacteristic
17C2×#117×C43C2211yescharacteristic
18C2×#117×C43C2211yescharacteristic
19C22×C4⋊C4×C43C2211yescharacteristic
20C2×#107×C43C2211yescharacteristic
21C2×#107×C43C2211yescharacteristic
22C2×#106×C43C2211yescharacteristic
23C2×#106×C43C2211yescharacteristic
24C2×C4⋊C8×C43C2211yescharacteristic
25C2×C4⋊C8×C43C2211yescharacteristic
26C2×C22⋊C8×C43C2211yescharacteristic
27C2×C22⋊C8×C43C2211yescharacteristic
28C43×#398—21no—
29C43×#398—21no—
30C43×#396—21no—
31C43×#396—21no—
32C43×#389C2211yescharacteristic
33C43×#389C2211yescharacteristic
34C43×#389C2211yescharacteristic
35C43×#389C2211yescharacteristic
36C43×#389C2211yescharacteristic
37C43×#389C2211yescharacteristic
38C43×#385—21no—
39C43×#385—21no—
40C43×#384—21no—
41C43×#384C2211yescharacteristic
42C43×#382—21no—
43C43×#380C2211yescharacteristic
44C43×#380C2211yescharacteristic
45C43×#340C2211yescharacteristic
46C43×#340C2211yescharacteristic
47C43×#340C2211yescharacteristic
48C43×#340C2211yescharacteristic
49C43×#340C2211yescharacteristic
50C43×#340C2211yescharacteristic
51C43×#340C2211yescharacteristic
52C43×#340C2211yescharacteristic
53C43×#340C2211yescharacteristic
54C43×#340C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#336C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C23×C4×C43—21no—
60C23×C4×C43C2311yescharacteristic
61C22×C8×C43C2311yescharacteristic
62C22×C8×C43C2311yescharacteristic
63C22×C8×C43C2311yescharacteristic
64C22×C8×C43C2311yescharacteristic
65#125×C43—41no—
66#125×C43—41no—
67#117×C43—22no—
68#117×C43—41no—
69#117×C43—41no—
70#117×C43Q814yes—
71C2×C4⋊C4×C43—21no—
72C2×C4⋊C4×C43—21no—
73C2×C4⋊C4×C43—21no—
74C2×C4⋊C4×C43—21no—
75C2×C4⋊C4×C43—21no—
76C2×C4⋊C4×C43—21no—
77C2×C4⋊C4×C43—21no—
78C2×C4⋊C4×C43—21no—
79C2×C4⋊C4×C43—21no—
80C2×C4⋊C4×C43—21no—
81C2×C4⋊C4×C43—21no—
82C2×C4⋊C4×C43—41no—
83C2×C4⋊C4×C43—41no—
84C2×C4⋊C4×C43D411yescharacteristic
85C2×C4⋊C4×C43D411yescharacteristic
86C2×C4⋊C4×C43C2311yescharacteristic
87C2×C4⋊C4×C43C2311yescharacteristic
88C2×C4⋊C4×C43C2311yescharacteristic
89C2×C4⋊C4×C43C2311yescharacteristic
90C2×C4⋊C4×C43C2311yescharacteristic
91C2×C4⋊C4×C43C2311yescharacteristic
92C2×C4⋊C4×C43C2311yescharacteristic
93C2×C4⋊C4×C43C2311yescharacteristic
94C2×C22⋊C4×C43—21no—
95C2×C22⋊C4×C43—21no—
96C2×C22⋊C4×C43—21no—
97C2×C22⋊C4×C43D411yescharacteristic
98C2×C22⋊C4×C43D411yescharacteristic
99C2×C42×C43—21no—
100C2×C42×C43C2311yescharacteristic
101C2×C42×C43C2311yescharacteristic
102#107×C43—41no—
103#107×C43—41no—
104#106×C43—41no—
105#106×C43—41no—
106C4⋊C8×C43—41no—
107C4⋊C8×C43—41no—
108C22⋊C8×C43—22no—
109C22⋊C8×C43—22no—
110#95×C43—21no—
111#95×C43—21no—
112#95×C43—21no—
113#95×C43—21no—
114#95×C43—21no—
115#95×C43—21no—
116#95×C43—21no—
117#95×C43—21no—
118C24×C43C2×D411yescharacteristic
119C22×C4×C43—21no—
120C22×C4×C43—21no—
121C22×C4×C43—21no—
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43—21no—
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—42no—
132C22×C4×C43—81no—
133C22×C4×C43—81no—
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×Q812yes—
140C22×C4×C43#4112yes—
141C22×C4×C43C2411yescharacteristic
142C2×C8×C43—21no—
143C2×C8×C43—21no—
144C2×C8×C43—21no—
145C2×C8×C43—21no—
146C2×C8×C43—21no—
147C2×C8×C43—21no—
148C2×C8×C43—21no—
149C2×C8×C43—21no—
150C2×C8×C43—21no—
151C2×C8×C43—21no—
152C2×C8×C43—21no—
153C2×C8×C43—21no—
154C4⋊C4×C43—21no—
155C4⋊C4×C43—21no—
156C4⋊C4×C43—21no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—41no—
169C4⋊C4×C43—41no—
170C4⋊C4×C43—42no—
171C4⋊C4×C43—42no—
172C4⋊C4×C43—42no—
173C4⋊C4×C43—81no—
174C4⋊C4×C43—81no—
175C4⋊C4×C43—81no—
176C4⋊C4×C43—81no—
177C4⋊C4×C43—81no—
178C4⋊C4×C43—81no—
179C4⋊C4×C43—81no—
180C4⋊C4×C43—81no—
181C4⋊C4×C43C2×Q812yes—
182C4⋊C4×C43C2×Q812yes—
183C22⋊C4×C43—24no—
184C22⋊C4×C43—41no—
185C22⋊C4×C43—41no—
186C22⋊C4×C43—81no—
187C22⋊C4×C43—81no—
188C42×C43—24no—
189C42×C43—21no—
190C42×C43—21no—
191C42×C43—21no—
192C42×C43—21no—
193C23×C43—21no—
194C23×C43—21no—
195C23×C43—21no—
196C23×C43—21no—
197C23×C43—21no—
198C23×C43—21no—
199C23×C43C22⋊Q812yes—
200C23×C43C22×D411yescharacteristic
201C2×C4×C43—21no—
202C2×C4×C43—21no—
203C2×C4×C43—22no—
204C2×C4×C43—22no—
205C2×C4×C43—22no—
206C2×C4×C43—22no—
207C2×C4×C43—22no—
208C2×C4×C43—22no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—84no—
244C2×C4×C43C22⋊Q812yes—
245C2×C4×C43C22×Q811yescharacteristic
246C2×C4×C43C2×#4111yescharacteristic
247C2×C4×C43H(5,𝔽2)11yescharacteristic
248C2×C4×C43H(5,𝔽2)11yescharacteristic
249C2×C4×C432−1+411yescharacteristic
250C2×C4×C432−1+411yescharacteristic
251C8×C43—41no—
252C8×C43—41no—
253C8×C43—41no—
254C8×C43—41no—
255#29979C4311yesmaximal, characteristic, direct product factor, Sylow
256C22×C43—22no—
257C22×C43—22no—
258C22×C43—22no—
259C22×C43—41no—
260C22×C43—41no—
261C22×C43—41no—
262C22×C43—41no—
263C22×C43C2×C22⋊Q811yescharacteristic
264C22×C43#53411yescharacteristic
265C22×C43#53611yescharacteristic
266C22×C43#57611yescharacteristic
267C22×C43#57711yescharacteristic
268C22×C43#57711yescharacteristic
269C22×C43#57811yescharacteristic
270C4×C43—22no—
271C4×C43—42no—
272C4×C43—42no—
273C4×C43—41no—
274C4×C43—41no—
275C4×C43—41no—
276C4×C43—41no—
277C4×C43—81no—
278C4×C43—81no—
279C4×C43—81no—
280C4×C43—81no—
281C4×C43—81no—
282C4×C43—81no—
283C4×C43#53911yescharacteristic
284C4×C43#53911yescharacteristic
285C4×C43#54411yescharacteristic
286C4×C43#54411yescharacteristic
287#2629C2×C4311yescharacteristic
288#2317C2×C4311yescharacteristic
289#2100C2×C4311yescharacteristic, complemented
290#2099C2×C4311yescharacteristic, complemented
291#2088C2×C4311yescharacteristic, complemented
292#2088C2×C4311yescharacteristic, complemented
293#2087C2×C4311yescharacteristic, complemented
294#2086C2×C4311yescharacteristic, complemented
295#2059C2×C4311yescharacteristic, complemented
296#2059C2×C4311yescharacteristic, complemented
297#1853C2×C4311yescharacteristic
298#1852C2×C4311yescharacteristic
299#1825C2×C4311yescharacteristic
300#1825C2×C4311yescharacteristic
301#1798C2×C4311yescharacteristic
302C2×C43—42no—
303C2×C43#262711yescharacteristic
304C2×C43#308311yescharacteristic
305C2×C43#308411yescharacteristic
306C2×C43#319811yescharacteristic
307C2×C43#320111yescharacteristic
308C2×C43#324111yescharacteristic
309C2×C43#324211yescharacteristic
310C2×#125C22×C4311yescharacteristic
311C2×#117C22×C4311yescharacteristic
312C2×#117C22×C4311yescharacteristic
313C22×C4⋊C4C22×C4311yescharacteristic
314C2×#107C22×C4311yescharacteristic
315C2×#107C22×C4311yescharacteristic
316C2×#106C22×C4311yescharacteristic
317C2×#106C22×C4311yescharacteristic
318C2×C4⋊C8C22×C4311yescharacteristic
319C2×C4⋊C8C22×C4311yescharacteristic
320C2×C22⋊C8C22×C4311yescharacteristic
321C2×C22⋊C8C22×C4311yescharacteristic
322#398—21no—
323#398—21no—
324#396—21no—
325#396—21no—
326#389C22×C4311yescharacteristic
327#389C22×C4311yescharacteristic
328#389C22×C4311yescharacteristic
329#389C22×C4311yescharacteristic
330#389C22×C4311yescharacteristic
331#389C22×C4311yescharacteristic
332#385—21no—
333#385—21no—
334#384—21no—
335#384C22×C4311yescharacteristic
336#382—21no—
337#380C22×C4311yescharacteristic
338#380C22×C4311yescharacteristic
339#340C22×C4311yescharacteristic
340#340C22×C4311yescharacteristic
341#340C22×C4311yescharacteristic
342#340C22×C4311yescharacteristic
343#340C22×C4311yescharacteristic
344#340C22×C4311yescharacteristic
345#340C22×C4311yescharacteristic
346#340C22×C4311yescharacteristic
347#340C22×C4311yescharacteristic
348#340C22×C4311yescharacteristic
349#340C22×C4311yescharacteristic
350#340C22×C4311yescharacteristic
351#336C22×C4311yescharacteristic
352#336C22×C4311yescharacteristic
353C43#2997911yescharacteristic, direct product factor, Sylow
354C23×C4—21no—
355C23×C4C23×C4311yescharacteristic
356C22×C8C23×C4311yescharacteristic
357C22×C8C23×C4311yescharacteristic
358C22×C8C23×C4311yescharacteristic
359C22×C8C23×C4311yescharacteristic
360#125—41no—
361#125—41no—
362#117—22no—
363#117—41no—
364#117—41no—
365#117Q8×C4314yes—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—41no—
378C2×C4⋊C4—41no—
379C2×C4⋊C4D4×C4311yescharacteristic
380C2×C4⋊C4D4×C4311yescharacteristic
381C2×C4⋊C4C23×C4311yescharacteristic
382C2×C4⋊C4C23×C4311yescharacteristic
383C2×C4⋊C4C23×C4311yescharacteristic
384C2×C4⋊C4C23×C4311yescharacteristic
385C2×C4⋊C4C23×C4311yescharacteristic
386C2×C4⋊C4C23×C4311yescharacteristic
387C2×C4⋊C4C23×C4311yescharacteristic
388C2×C4⋊C4C23×C4311yescharacteristic
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4D4×C4311yescharacteristic
393C2×C22⋊C4D4×C4311yescharacteristic
394C2×C42—21no—
395C2×C42C23×C4311yescharacteristic
396C2×C42C23×C4311yescharacteristic
397#107—41no—
398#107—41no—
399#106—41no—
400#106—41no—
401C4⋊C8—41no—
402C4⋊C8—41no—
403C22⋊C8—22no—
404C22⋊C8—22no—
405#95—21no—
406#95—21no—
407#95—21no—
408#95—21no—
409#95—21no—
410#95—21no—
411#95—21no—
412#95—21no—
413C24C2×D4×C4311yescharacteristic
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—42no—
427C22×C4—81no—
428C22×C4—81no—
429C22×C4C2×D4×C4311yescharacteristic
430C22×C4C2×D4×C4311yescharacteristic
431C22×C4C2×D4×C4311yescharacteristic
432C22×C4C2×D4×C4311yescharacteristic
433C22×C4C2×D4×C4311yescharacteristic
434C22×C4C2×Q8×C4312yes—
435C22×C4#41×C4312yes—
436C22×C4C24×C4311yescharacteristic
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—41no—
464C4⋊C4—41no—
465C4⋊C4—42no—
466C4⋊C4—42no—
467C4⋊C4—42no—
468C4⋊C4—81no—
469C4⋊C4—81no—
470C4⋊C4—81no—
471C4⋊C4—81no—
472C4⋊C4—81no—
473C4⋊C4—81no—
474C4⋊C4—81no—
475C4⋊C4—81no—
476C4⋊C4C2×Q8×C4312yes—
477C4⋊C4C2×Q8×C4312yes—
478C22⋊C4—24no—
479C22⋊C4—41no—
480C22⋊C4—41no—
481C22⋊C4—81no—
482C22⋊C4—81no—
483C42—24no—
484C42—21no—
485C42—21no—
486C42—21no—
487C42—21no—
488C23—21no—
489C23—21no—
490C23—21no—
491C23—21no—
492C23—21no—
493C23—21no—
494C23C22⋊Q8×C4312yes—
495C23C22×D4×C4311yescharacteristic
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—84no—
539C2×C4C22⋊Q8×C4312yes—
540C2×C4C22×Q8×C4311yescharacteristic
541C2×C4C2×#41×C4311yescharacteristic
542C2×C4H(5,𝔽2)×C4311yescharacteristic
543C2×C4H(5,𝔽2)×C4311yescharacteristic
544C2×C42−1+4×C4311yescharacteristic
545C2×C42−1+4×C4311yescharacteristic
546C8—41no—
547C8—41no—
548C8—41no—
549C8—41no—
550C22—22no—
551C22—22no—
552C22—22no—
553C22—41no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22C2×C22⋊Q8×C4311yescharacteristic
558C22C43×#53411yescharacteristic
559C22C43×#53611yescharacteristic
560C22C43×#57611yescharacteristic
561C22C43×#57711yescharacteristic
562C22C43×#57711yescharacteristic
563C22C43×#57811yescharacteristic
564C4—22no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—41no—
569C4—42no—
570C4—42no—
571C4—81no—
572C4—81no—
573C4—81no—
574C4—81no—
575C4—81no—
576C4—81no—
577C4C43×#53911yescharacteristic
578C4C43×#53911yescharacteristic
579C4C43×#54411yescharacteristic
580C4C43×#54411yescharacteristic
581C2—42no—
582C2C43×#262711yescharacteristic
583C2C43×#308311yescharacteristic
584C2C43×#308411yescharacteristic
585C2C43×#319811yescharacteristic
586C2C43×#320111yescharacteristic
587C2C43×#324111yescharacteristic
588C2C43×#324211yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC24×C43C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C2×#117×C43 ◁ G

Complements

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

NH ≅ G/Ntype
3. C43×#2100C2semidirect
4. C43×#2099C2semidirect
5. C43×#2088C2semidirect
6. C43×#2088C2semidirect
7. C43×#2087C2semidirect
8. C43×#2086C2semidirect
9. C43×#2059C2semidirect
10. C43×#2059C2semidirect
255. #29979C43direct (N × H)
289. #2100C2×C43semidirect
290. #2099C2×C43semidirect
291. #2088C2×C43semidirect
292. #2088C2×C43semidirect
293. #2087C2×C43semidirect
294. #2086C2×C43semidirect
295. #2059C2×C43semidirect
296. #2059C2×C43semidirect
353. C43#29979direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#26292
C43×#23172
C43×#21002
C43×#20992
C43×#20882
C43×#20872
C43×#20862
C43×#20592
C43×#18532
C43×#18522
C43×#18252
C43×#17982
#2997943