Finite Group Databasebeta

← C43×#8312 #24928329

Subgroups — C43×#8312 #24928329

Order 11008.

1120 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#41×C43C211yesmaximal, characteristic
2C43×#1797C211yesmaximal, characteristic, complemented
3C4×C22⋊C8×C43C211yesmaximal, characteristic, complemented
4C2×C43×Q8⋊C8C212yesmaximal, complemented
5C2×C43×D4⋊C8C212yesmaximal, complemented
6C22×#41×C43C411yescharacteristic
7C4×#41×C43—24no—
8C4×#41×C43—24no—
9C2×C4×Q8×C43C411yescharacteristic
10C2×C4×Q8×C43C2211yescharacteristic
11C2×C4×D4×C43—21no—
12C2×C4×D4×C43—21no—
13C2×C4×D4×C43C411yescharacteristic
14C2×C4×D4×C43C2211yescharacteristic
15C2×#117×C43—21no—
16C2×#117×C43C411yescharacteristic
17C22×C42×C43—21no—
18C22×C42×C43C2211yescharacteristic
19C2×C4⋊C8×C43C2212yes—
20C2×C22⋊C8×C43—21no—
21C2×C22⋊C8×C43—21no—
22C2×C4×C8×C43C2212yes—
23C43×#336—21no—
24C43×#336—21no—
25C43×Q8⋊C8—24no—
26C43×D4⋊C8—24no—
27C2×#41×C43—22no—
28C2×#41×C43—22no—
29C2×#41×C43—22no—
30C2×#41×C43—22no—
31C2×#41×C43—22no—
32C2×#41×C43C814yescomplemented
33C22×Q8×C43C2×C411yescharacteristic
34C22×D4×C43—21no—
35C22×D4×C43C2×C411yescharacteristic
36C23×C4×C43—21no—
37C23×C4×C43—21no—
38C23×C4×C43—21no—
39C23×C4×C43C2×C411yescharacteristic
40C23×C4×C43D411yescharacteristic
41C23×C4×C43D411yescharacteristic
42C22×C8×C43—22no—
43C22×C8×C43—22no—
44C4×Q8×C43—22no—
45C4×Q8×C43—22no—
46C4×Q8×C43—22no—
47C4×Q8×C43D414yes—
48C4×D4×C43—28no—
49C4×D4×C43—28no—
50C4×D4×C43—22no—
51C4×D4×C43—22no—
52C4×D4×C43—22no—
53C4×D4×C43D414yes—
54#117×C43—28no—
55#117×C43—22no—
56#117×C43—22no—
57C2×C4⋊C4×C43—21no—
58C2×C4⋊C4×C43—21no—
59C2×C4⋊C4×C43C2×C411yescharacteristic
60C2×C4⋊C4×C43C2×C411yescharacteristic
61C2×C22⋊C4×C43—21no—
62C2×C22⋊C4×C43—21no—
63C2×C22⋊C4×C43—21no—
64C2×C42×C43—28no—
65C2×C42×C43—21no—
66C2×C42×C43—21no—
67C2×C42×C43—21no—
68C2×C42×C43—22no—
69C2×C42×C43—22no—
70C2×C42×C43C2×C411yescharacteristic
71C2×C42×C43D411yescharacteristic
72C2×C42×C43D411yescharacteristic
73C2×C42×C43C2311yescharacteristic
74C4⋊C8×C43—22no—
75C4⋊C8×C43—22no—
76C22⋊C8×C43—24no—
77C22⋊C8×C43—42no—
78C4×C8×C43—22no—
79C4×C8×C43—22no—
80C24×C43—21no—
81C24×C43C22⋊C411yescharacteristic
82#41×C43—28no—
83#41×C43—28no—
84#41×C43—28no—
85#41×C43—28no—
86C2×Q8×C43—21no—
87C2×Q8×C43—21no—
88C2×Q8×C43—21no—
89C2×Q8×C43C22⋊C412yes—
90C2×Q8×C43C2×C812yes—
91C2×Q8×C43M1612yes—
92C2×D4×C43—24no—
93C2×D4×C43—24no—
94C2×D4×C43—21no—
95C2×D4×C43—21no—
96C2×D4×C43—21no—
97C2×D4×C43—24no—
98C2×D4×C43C22⋊C412yes—
99C2×D4×C43C2×C812yes—
100C2×D4×C43M1612yes—
101C22×C4×C43—24no—
102C22×C4×C43—24no—
103C22×C4×C43—24no—
104C22×C4×C43—21no—
105C22×C4×C43—21no—
106C22×C4×C43—21no—
107C22×C4×C43—21no—
108C22×C4×C43—24no—
109C22×C4×C43—22no—
110C22×C4×C43—22no—
111C22×C4×C43—22no—
112C22×C4×C43—24no—
113C22×C4×C43—22no—
114C22×C4×C43—21no—
115C22×C4×C43—21no—
116C22×C4×C43—21no—
117C22×C4×C43—21no—
118C22×C4×C43—21no—
119C22×C4×C43—41no—
120C22×C4×C43—42no—
121C22×C4×C43—42no—
122C22×C4×C43—42no—
123C22×C4×C43—41no—
124C22×C4×C43—41no—
125C22×C4×C43C22⋊C411yescharacteristic
126C22×C4×C43C22⋊C411yescharacteristic
127C22×C4×C43C22⋊C411yescharacteristic
128C22×C4×C43C2×C812yes—
129C22×C4×C43M1612yes—
130C22×C4×C43C22×C411yescharacteristic
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C2×C8×C43—24no—
134C2×C8×C43—42no—
135C2×C8×C43—42no—
136C2×C8×C43—42no—
137C2×C8×C43—42no—
138C2×C8×C43—42no—
139C4⋊C4×C43—24no—
140C4⋊C4×C43—21no—
141C4⋊C4×C43—21no—
142C4⋊C4×C43—24no—
143C4⋊C4×C43C22⋊C412yes—
144C4⋊C4×C43C22⋊C412yes—
145C22⋊C4×C43—24no—
146C22⋊C4×C43—24no—
147C22⋊C4×C43—24no—
148C42×C43—24no—
149C42×C43—24no—
150C42×C43—21no—
151C42×C43—21no—
152C42×C43—22no—
153C42×C43—24no—
154C42×C43—22no—
155C42×C43C2×D412yes—
156C42×C43C2×D412yes—
157C23×C43—21no—
158C23×C43—22no—
159C23×C43—22no—
160C23×C43—21no—
161C23×C43—22no—
162C23×C43—21no—
163C23×C43—21no—
164C23×C43—21no—
165C23×C43—21no—
166C23×C43—41no—
167C23×C43—41no—
168C23×C43—41no—
169C23×C43—41no—
170C23×C43C22⋊C812yes—
171C23×C43C2×C22⋊C411yescharacteristic
172Q8×C43—22no—
173Q8×C43—22no—
174Q8×C43—22no—
175Q8×C43C22⋊C814yescomplemented
176D4×C43—216no—
177D4×C43—22no—
178D4×C43—22no—
179D4×C43—22no—
180D4×C43C22⋊C814yescomplemented
181C2×C4×C43—216no—
182C2×C4×C43—21no—
183C2×C4×C43—21no—
184C2×C4×C43—22no—
185C2×C4×C43—22no—
186C2×C4×C43—21no—
187C2×C4×C43—22no—
188C2×C4×C43—21no—
189C2×C4×C43—21no—
190C2×C4×C43—21no—
191C2×C4×C43—22no—
192C2×C4×C43—22no—
193C2×C4×C43—22no—
194C2×C4×C43—22no—
195C2×C4×C43—21no—
196C2×C4×C43—22no—
197C2×C4×C43—22no—
198C2×C4×C43—21no—
199C2×C4×C43—21no—
200C2×C4×C43—44no—
201C2×C4×C43—48no—
202C2×C4×C43—41no—
203C2×C4×C43—41no—
204C2×C4×C43—41no—
205C2×C4×C43—41no—
206C2×C4×C43—42no—
207C2×C4×C43—44no—
208C2×C4×C43—42no—
209C2×C4×C43—44no—
210C2×C4×C43C22⋊C812yes—
211C2×C4×C43#10412yes—
212C2×C4×C43C2×C22⋊C411yescharacteristic
213C2×C4×C43C2×C22⋊C411yescharacteristic
214C2×C4×C43#12012yes—
215C2×C4×C43#12012yes—
216C2×C4×C43C22×C811yescharacteristic
217C2×C4×C43C2×M1611yescharacteristic
218C2×C4×C43C2×M1611yescharacteristic
219C2×C4×C43C2×M1611yescharacteristic
220C2×C4×C43#13512yes—
221C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
222C2×C4×C43#13711yescharacteristic
223C8×C43—44no—
224C8×C43—82no—
225#8312C4311yesmaximal, characteristic, direct product factor, Sylow
226C22×C43—22no—
227C22×C43—22no—
228C22×C43—24no—
229C22×C43—22no—
230C22×C43—42no—
231C22×C43—42no—
232C22×C43—41no—
233C22×C43—42no—
234C22×C43—41no—
235C22×C43—42no—
236C22×C43—41no—
237C22×C43—42no—
238C22×C43—41no—
239C22×C43—42no—
240C22×C43#37911yescharacteristic
241C22×C43C2×C22⋊C811yescharacteristic
242C22×C43#40711yescharacteristic
243C22×C43#41611yescharacteristic
244C22×C43#41711yescharacteristic
245C22×C43C2×#10411yescharacteristic
246C22×C43#42111yescharacteristic
247C4×C43—22no—
248C4×C43—24no—
249C4×C43—22no—
250C4×C43—22no—
251C4×C43—41no—
252C4×C43—42no—
253C4×C43—42no—
254C4×C43C2×C22⋊C811yescharacteristic
255C4×C43C2×C22⋊C811yescharacteristic
256C4×C43#40711yescharacteristic
257C4×C43#40711yescharacteristic
258C4×C43#44912yes—
259C4×C43#45212yes—
260C2×C4×#41C2×C4311yescharacteristic
261#1797C2×C4311yescharacteristic, complemented
262C4×C22⋊C8C2×C4311yescharacteristic, complemented
263C2×Q8⋊C8C2×C4312yescomplemented
264C2×D4⋊C8C2×C4312yescomplemented
265C2×C43—42no—
266C2×C43—44no—
267C2×C43#147611yescharacteristic
268C2×C43#147711yescharacteristic
269C2×C43#148811yescharacteristic
270C2×C43#148911yescharacteristic
271C2×C43#177911yescharacteristic
272C2×C43#178811yescharacteristic
273C2×C43#178911yescharacteristic
274C22×#41C4×C4311yescharacteristic
275C4×#41—24no—
276C4×#41—24no—
277C2×C4×Q8C4×C4311yescharacteristic
278C2×C4×Q8C22×C4311yescharacteristic
279C2×C4×D4—21no—
280C2×C4×D4—21no—
281C2×C4×D4C4×C4311yescharacteristic
282C2×C4×D4C22×C4311yescharacteristic
283C2×#117—21no—
284C2×#117C4×C4311yescharacteristic
285C22×C42—21no—
286C22×C42C22×C4311yescharacteristic
287C2×C4⋊C8C22×C4312yes—
288C2×C22⋊C8—21no—
289C2×C22⋊C8—21no—
290C2×C4×C8C22×C4312yes—
291#336—21no—
292#336—21no—
293Q8⋊C8—24no—
294D4⋊C8—24no—
295C43#831211yescharacteristic, direct product factor, Sylow
296C2×#41—22no—
297C2×#41—22no—
298C2×#41—22no—
299C2×#41—22no—
300C2×#41—22no—
301C2×#41C8×C4314yescomplemented
302C22×Q8C2×C4×C4311yescharacteristic
303C22×D4—21no—
304C22×D4C2×C4×C4311yescharacteristic
305C23×C4—21no—
306C23×C4—21no—
307C23×C4—21no—
308C23×C4C2×C4×C4311yescharacteristic
309C23×C4D4×C4311yescharacteristic
310C23×C4D4×C4311yescharacteristic
311C22×C8—22no—
312C22×C8—22no—
313C4×Q8—22no—
314C4×Q8—22no—
315C4×Q8—22no—
316C4×Q8D4×C4314yes—
317C4×D4—28no—
318C4×D4—28no—
319C4×D4—22no—
320C4×D4—22no—
321C4×D4—22no—
322C4×D4D4×C4314yes—
323#117—28no—
324#117—22no—
325#117—22no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4C2×C4×C4311yescharacteristic
329C2×C4⋊C4C2×C4×C4311yescharacteristic
330C2×C22⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—21no—
333C2×C42—28no—
334C2×C42—21no—
335C2×C42—21no—
336C2×C42—21no—
337C2×C42—22no—
338C2×C42—22no—
339C2×C42C2×C4×C4311yescharacteristic
340C2×C42D4×C4311yescharacteristic
341C2×C42D4×C4311yescharacteristic
342C2×C42C23×C4311yescharacteristic
343C4⋊C8—22no—
344C4⋊C8—22no—
345C22⋊C8—24no—
346C22⋊C8—42no—
347C4×C8—22no—
348C4×C8—22no—
349C24—21no—
350C24C22⋊C4×C4311yescharacteristic
351#41—28no—
352#41—28no—
353#41—28no—
354#41—28no—
355C2×Q8—21no—
356C2×Q8—21no—
357C2×Q8—21no—
358C2×Q8C22⋊C4×C4312yes—
359C2×Q8C2×C8×C4312yes—
360C2×Q8M16×C4312yes—
361C2×D4—24no—
362C2×D4—24no—
363C2×D4—24no—
364C2×D4—21no—
365C2×D4—21no—
366C2×D4—21no—
367C2×D4C22⋊C4×C4312yes—
368C2×D4C2×C8×C4312yes—
369C2×D4M16×C4312yes—
370C22×C4—24no—
371C22×C4—24no—
372C22×C4—21no—
373C22×C4—24no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—24no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—24no—
385C22×C4—22no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—41no—
389C22×C4—42no—
390C22×C4—42no—
391C22×C4—42no—
392C22×C4—41no—
393C22×C4—41no—
394C22×C4C22⋊C4×C4311yescharacteristic
395C22×C4C22⋊C4×C4311yescharacteristic
396C22×C4C22⋊C4×C4311yescharacteristic
397C22×C4C2×C8×C4312yes—
398C22×C4M16×C4312yes—
399C22×C4C22×C4×C4311yescharacteristic
400C22×C4C2×D4×C4311yescharacteristic
401C22×C4C2×D4×C4311yescharacteristic
402C2×C8—24no—
403C2×C8—42no—
404C2×C8—42no—
405C2×C8—42no—
406C2×C8—42no—
407C2×C8—42no—
408C4⋊C4—24no—
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—24no—
412C4⋊C4C22⋊C4×C4312yes—
413C4⋊C4C22⋊C4×C4312yes—
414C22⋊C4—24no—
415C22⋊C4—24no—
416C22⋊C4—24no—
417C42—24no—
418C42—24no—
419C42—21no—
420C42—21no—
421C42—22no—
422C42—24no—
423C42—22no—
424C42C2×D4×C4312yes—
425C42C2×D4×C4312yes—
426C23—21no—
427C23—22no—
428C23—22no—
429C23—21no—
430C23—22no—
431C23—21no—
432C23—21no—
433C23—21no—
434C23—21no—
435C23—41no—
436C23—41no—
437C23—41no—
438C23—41no—
439C23C22⋊C8×C4312yes—
440C23C2×C22⋊C4×C4311yescharacteristic
441Q8—22no—
442Q8—22no—
443Q8—22no—
444Q8C22⋊C8×C4314yescomplemented
445D4—216no—
446D4—22no—
447D4—22no—
448D4—22no—
449D4C22⋊C8×C4314yescomplemented
450C2×C4—216no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—21no—
456C2×C4—22no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—21no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—44no—
470C2×C4—48no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—42no—
476C2×C4—44no—
477C2×C4—42no—
478C2×C4—44no—
479C2×C4C22⋊C8×C4312yes—
480C2×C4#104×C4312yes—
481C2×C4C2×C22⋊C4×C4311yescharacteristic
482C2×C4C2×C22⋊C4×C4311yescharacteristic
483C2×C4#120×C4312yes—
484C2×C4#120×C4312yes—
485C2×C4C22×C8×C4311yescharacteristic
486C2×C4C2×M16×C4311yescharacteristic
487C2×C4C2×M16×C4311yescharacteristic
488C2×C4C2×M16×C4311yescharacteristic
489C2×C4#135×C4312yes—
490C2×C4AGL(1,ℤ/8)×C4311yescharacteristic
491C2×C4#137×C4311yescharacteristic
492C8—44no—
493C8—82no—
494C22—22no—
495C22—22no—
496C22—22no—
497C22—24no—
498C22—42no—
499C22—42no—
500C22—41no—
501C22—42no—
502C22—41no—
503C22—42no—
504C22—41no—
505C22—42no—
506C22—41no—
507C22—42no—
508C22C43×#37911yescharacteristic
509C22C2×C22⋊C8×C4311yescharacteristic
510C22C43×#40711yescharacteristic
511C22C43×#41611yescharacteristic
512C22C43×#41711yescharacteristic
513C22C2×#104×C4311yescharacteristic
514C22C43×#42111yescharacteristic
515C4—22no—
516C4—24no—
517C4—22no—
518C4—22no—
519C4—41no—
520C4—42no—
521C4—42no—
522C4C2×C22⋊C8×C4311yescharacteristic
523C4C2×C22⋊C8×C4311yescharacteristic
524C4C43×#40711yescharacteristic
525C4C43×#40711yescharacteristic
526C4C43×#44912yes—
527C4C43×#45212yes—
528C2—42no—
529C2—44no—
530C2C43×#147611yescharacteristic
531C2C43×#147711yescharacteristic
532C2C43×#148811yescharacteristic
533C2C43×#148911yescharacteristic
534C2C43×#177911yescharacteristic
535C2C43×#178811yescharacteristic
536C2C43×#178911yescharacteristic
subgroupG/H
centerC22×C4×C43C2×D4
commutatorC2×C4C22×C8×C43
Frattini, cosocleC2×C42C23×C43
socleC23×C43C2×C22⋊C4
prime radicalC22×#41×C43C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C43 ◁ C22×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#1797C2semidirect
3. C4×C22⋊C8×C43C2semidirect
4. C2×C43×Q8⋊C8C2semidirect
5. C2×C43×D4⋊C8C2semidirect
32. C2×#41×C43C8semidirect
175. Q8×C43C22⋊C8semidirect
180. D4×C43C22⋊C8semidirect
225. #8312C43direct (N × H)
261. #1797C2×C43semidirect
262. C4×C22⋊C8C2×C43semidirect
263. C2×Q8⋊C8C2×C43semidirect
264. C2×D4⋊C8C2×C43semidirect
295. C43#8312direct (N × H)
301. C2×#41C8×C43semidirect
444. Q8C22⋊C8×C43semidirect
449. D4C22⋊C8×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#41×C432
C43×#17972
C4×C22⋊C8×C432
C2×C43×Q8⋊C82
C2×C43×D4⋊C82
#831243