Finite Group Databasebeta

← C43×#25696 #24945713

Subgroups — C43×#25696 #24945713

Order 11008.

958 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3507C211yesmaximal, characteristic
2C43×#3165C211yesmaximal, characteristic, complemented
3C43×#3141C211yesmaximal, characteristic
4C43×#2568C211yesmaximal, characteristic, complemented
5C43×#2038C214yesmaximal, complemented
6C43×#1986C211yesmaximal, characteristic, complemented
7C43×#1980C211yesmaximal, characteristic
8C43×#1860C214yesmaximal, complemented
9C4×#101×C43C211yesmaximal, characteristic, complemented
10C43×#559—21no—
11C43×#557—21no—
12C43×#556—21no—
13C43×#556—22no—
14C43×#554—21no—
15C43×#552—22no—
16C43×#539—22no—
17C43×#536C2212yes—
18C43×#533C2211yescharacteristic
19C43×#532C2211yescharacteristic
20C2×C4⋊Q8×C43C2211yescharacteristic
21C43×#529—22no—
22C43×#520C2212yes—
23C2×C4×Q8×C43C2211yescharacteristic
24C43×#501—22no—
25C43×#500—21no—
26C43×#498—21no—
27C43×#489—22no—
28C43×#487—21no—
29C43×#486—21no—
30C43×#428C2214yes—
31C2×#104×C43C2214yes—
32C43×#417C2214yes—
33C2×#101×C43C2212yes—
34C4×M16×C43C2211yescharacteristic
35C4×M16×C43C2211yescharacteristic
36C43×#400—22no—
37C43×#391—22no—
38C43×#391C2212yes—
39C43×#382C2212yes—
40C4×C4⋊C4×C43C2211yescharacteristic
41C43×#343C2212yes—
42C43×#339C2214yes—
43C2×#41×C43C2312yes—
44C22×Q8×C43—21no—
45C22×Q8×C43C2311yescharacteristic
46C2×M16×C43C2312yes—
47C2×M16×C43C2312yes—
48C4⋊Q8×C43—22no—
49C4⋊Q8×C43—21no—
50C4⋊Q8×C43—21no—
51C4⋊Q8×C43—21no—
52C4⋊Q8×C43—21no—
53C4⋊Q8×C43D411yescharacteristic
54C4⋊Q8×C43D411yescharacteristic
55C4⋊Q8×C43D411yescharacteristic
56#127×C43D411yescharacteristic
57#126×C43—24no—
58#126×C43—24no—
59#125×C43—22no—
60#125×C43—24no—
61#125×C43D412yes—
62#124×C43—22no—
63#124×C43—22no—
64#124×C43D412yes—
65#123×C43—24no—
66#123×C43—24no—
67C22⋊Q8×C43—24no—
68C22⋊Q8×C43—21no—
69C22⋊Q8×C43—21no—
70C22⋊Q8×C43—22no—
71C22⋊Q8×C43—22no—
72#121×C43—21no—
73#121×C43—21no—
74C4×Q8×C43—22no—
75C4×Q8×C43—22no—
76C4×Q8×C43—21no—
77C4×Q8×C43—21no—
78C4×Q8×C43—21no—
79C4×Q8×C43—21no—
80C4×Q8×C43—21no—
81C4×Q8×C43—21no—
82C4×D4×C43—22no—
83C4×D4×C43—22no—
84C4×D4×C43—24no—
85C4×D4×C43—21no—
86C4×D4×C43—21no—
87#117×C43—24no—
88#117×C43—22no—
89#117×C43C2312yes—
90C2×C4⋊C4×C43—22no—
91C2×C4⋊C4×C43—21no—
92C2×C4⋊C4×C43—21no—
93C2×C4⋊C4×C43D412yes—
94C2×C4⋊C4×C43C2312yes—
95C2×C4⋊C4×C43C2311yescharacteristic
96C2×C42×C43D412yes—
97C2×C42×C43C2312yes—
98C2×C42×C43C2311yescharacteristic
99#107×C43—24no—
100#106×C43—24no—
101#104×C43—28no—
102#103×C43—24no—
103#102×C43—24no—
104#101×C43—24no—
105#97×C43—21no—
106#97×C43—21no—
107C4×C8×C43—21no—
108C4×C8×C43—21no—
109#95×C43—21no—
110#95×C43—24no—
111#95×C43—24no—
112#41×C43—24no—
113#41×C43—24no—
114C2×Q8×C43—21no—
115C2×Q8×C43—21no—
116C2×Q8×C43—21no—
117C2×Q8×C43—21no—
118C2×Q8×C43—22no—
119C2×Q8×C43—22no—
120C2×Q8×C43—44no—
121C2×Q8×C43—41no—
122C2×Q8×C43—41no—
123C2×Q8×C43C2×D412yes—
124C2×D4×C43—21no—
125C2×D4×C43—21no—
126C2×D4×C43—22no—
127C2×D4×C43C2×D412yes—
128C22×C4×C43—24no—
129C22×C4×C43—22no—
130C22×C4×C43—22no—
131C22×C4×C43—22no—
132C22×C4×C43C2×D412yes—
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2×D412yes—
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2411yescharacteristic
137M16×C43—22no—
138M16×C43—22no—
139M16×C43—22no—
140M16×C43#4114yes—
141C2×C8×C43—22no—
142C2×C8×C43—22no—
143C4⋊C4×C43—24no—
144C4⋊C4×C43—24no—
145C4⋊C4×C43—24no—
146C4⋊C4×C43—22no—
147C4⋊C4×C43—22no—
148C4⋊C4×C43—22no—
149C4⋊C4×C43—21no—
150C4⋊C4×C43—21no—
151C4⋊C4×C43—21no—
152C4⋊C4×C43—22no—
153C4⋊C4×C43—21no—
154C4⋊C4×C43—21no—
155C4⋊C4×C43—21no—
156C4⋊C4×C43—22no—
157C4⋊C4×C43—22no—
158C4⋊C4×C43—42no—
159C4⋊C4×C43—41no—
160C4⋊C4×C43—41no—
161C4⋊C4×C43C2×D412yes—
162C4⋊C4×C43C2×D412yes—
163C22⋊C4×C43—24no—
164C22⋊C4×C43—24no—
165C22⋊C4×C43—24no—
166C22⋊C4×C43—22no—
167C22⋊C4×C43—22no—
168C22⋊C4×C43—22no—
169C42×C43—24no—
170C42×C43—22no—
171C42×C43—22no—
172C42×C43—22no—
173C42×C43—24no—
174C42×C43C2×D411yescharacteristic
175C42×C43C2×D411yescharacteristic
176C42×C43C2×D411yescharacteristic
177C42×C43C2×D411yescharacteristic
178C23×C43—22no—
179C23×C43C22×D411yescharacteristic
180Q8×C43—24no—
181Q8×C43—42no—
182Q8×C43—42no—
183Q8×C43—42no—
184Q8×C43—81no—
185Q8×C43—82no—
186Q8×C43—82no—
187D4×C43—24no—
188D4×C43—42no—
189D4×C43—42no—
190D4×C43—42no—
191D4×C43—81no—
192C2×C4×C43—22no—
193C2×C4×C43—22no—
194C2×C4×C43—22no—
195C2×C4×C43—22no—
196C2×C4×C43—22no—
197C2×C4×C43—22no—
198C2×C4×C43—22no—
199C2×C4×C43—22no—
200C2×C4×C43—41no—
201C2×C4×C43—44no—
202C2×C4×C43—42no—
203C2×C4×C43—42no—
204C2×C4×C43—42no—
205C2×C4×C43—44no—
206C2×C4×C43—42no—
207C2×C4×C43—42no—
208C2×C4×C43—84no—
209C2×C4×C43#12011yescharacteristic
210C2×C4×C43#12011yescharacteristic
211C2×C4×C43#12011yescharacteristic
212C2×C4×C43#12011yescharacteristic
213C2×C4×C43C22×D411yescharacteristic
214C2×C4×C43C22×D411yescharacteristic
215C2×C4×C43C2×#4112yes—
216C2×C4×C432−1+412yes—
217C8×C43—24no—
218C8×C43—42no—
219#25696C4311yesmaximal, characteristic, direct product factor, Sylow
220C22×C43—21no—
221C22×C43—21no—
222C22×C43—42no—
223C22×C43—42no—
224C22×C43—42no—
225C22×C43C2×#12011yescharacteristic
226C22×C43#53211yescharacteristic
227C22×C43#53611yescharacteristic
228C4×C43—21no—
229C4×C43—21no—
230C4×C43—21no—
231C4×C43—42no—
232C4×C43—42no—
233C4×C43—42no—
234C4×C43—42no—
235C4×C43—42no—
236C4×C43—82no—
237C4×C43—82no—
238C4×C43#45412yes—
239C4×C43#54712yes—
240C4×C43#54812yes—
241#3507C2×C4311yescharacteristic
242#3165C2×C4311yescharacteristic, complemented
243#3141C2×C4311yescharacteristic
244#2568C2×C4311yescharacteristic, complemented
245#2038C2×C4314yescomplemented
246#1986C2×C4311yescharacteristic, complemented
247#1980C2×C4311yescharacteristic
248#1860C2×C4314yescomplemented
249C4×#101C2×C4311yescharacteristic, complemented
250C2×C43—21no—
251C2×C43—21no—
252C2×C43—82no—
253C2×C43#243211yescharacteristic
254C2×C43C2×#45411yescharacteristic
255C2×C43#302211yescharacteristic
256#559—21no—
257#557—21no—
258#556—21no—
259#556—22no—
260#554—21no—
261#552—22no—
262#539—22no—
263#536C22×C4312yes—
264#533C22×C4311yescharacteristic
265#532C22×C4311yescharacteristic
266C2×C4⋊Q8C22×C4311yescharacteristic
267#529—22no—
268#520C22×C4312yes—
269C2×C4×Q8C22×C4311yescharacteristic
270#501—22no—
271#500—21no—
272#498—21no—
273#489—22no—
274#487—21no—
275#486—21no—
276#428C22×C4314yes—
277C2×#104C22×C4314yes—
278#417C22×C4314yes—
279C2×#101C22×C4312yes—
280C4×M16C22×C4311yescharacteristic
281C4×M16C22×C4311yescharacteristic
282#400—22no—
283#391—22no—
284#391C22×C4312yes—
285#382C22×C4312yes—
286C4×C4⋊C4C22×C4311yescharacteristic
287#343C22×C4312yes—
288#339C22×C4314yes—
289C43#2569611yescharacteristic, direct product factor, Sylow
290C2×#41C23×C4312yes—
291C22×Q8—21no—
292C22×Q8C23×C4311yescharacteristic
293C2×M16C23×C4312yes—
294C2×M16C23×C4312yes—
295C4⋊Q8—22no—
296C4⋊Q8—21no—
297C4⋊Q8—21no—
298C4⋊Q8—21no—
299C4⋊Q8—21no—
300C4⋊Q8D4×C4311yescharacteristic
301C4⋊Q8D4×C4311yescharacteristic
302C4⋊Q8D4×C4311yescharacteristic
303#127D4×C4311yescharacteristic
304#126—24no—
305#126—24no—
306#125—22no—
307#125—24no—
308#125D4×C4312yes—
309#124—22no—
310#124—22no—
311#124D4×C4312yes—
312#123—24no—
313#123—24no—
314C22⋊Q8—24no—
315C22⋊Q8—21no—
316C22⋊Q8—21no—
317C22⋊Q8—22no—
318C22⋊Q8—22no—
319#121—21no—
320#121—21no—
321C4×Q8—22no—
322C4×Q8—22no—
323C4×Q8—21no—
324C4×Q8—21no—
325C4×Q8—21no—
326C4×Q8—21no—
327C4×Q8—21no—
328C4×Q8—21no—
329C4×D4—22no—
330C4×D4—22no—
331C4×D4—24no—
332C4×D4—21no—
333C4×D4—21no—
334#117—24no—
335#117—22no—
336#117C23×C4312yes—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4D4×C4312yes—
341C2×C4⋊C4C23×C4312yes—
342C2×C4⋊C4C23×C4311yescharacteristic
343C2×C42D4×C4312yes—
344C2×C42C23×C4312yes—
345C2×C42C23×C4311yescharacteristic
346#107—24no—
347#106—24no—
348#104—28no—
349#103—24no—
350#102—24no—
351#101—24no—
352#97—21no—
353#97—21no—
354C4×C8—21no—
355C4×C8—21no—
356#95—21no—
357#95—24no—
358#95—24no—
359#41—24no—
360#41—24no—
361C2×Q8—21no—
362C2×Q8—21no—
363C2×Q8—21no—
364C2×Q8—21no—
365C2×Q8—22no—
366C2×Q8—22no—
367C2×Q8—44no—
368C2×Q8—41no—
369C2×Q8—41no—
370C2×Q8C2×D4×C4312yes—
371C2×D4—22no—
372C2×D4—21no—
373C2×D4—21no—
374C2×D4C2×D4×C4312yes—
375C22×C4—24no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4C2×D4×C4312yes—
380C22×C4C2×D4×C4311yescharacteristic
381C22×C4C2×D4×C4312yes—
382C22×C4C2×D4×C4311yescharacteristic
383C22×C4C24×C4311yescharacteristic
384M16—22no—
385M16—22no—
386M16—22no—
387M16#41×C4314yes—
388C2×C8—22no—
389C2×C8—22no—
390C4⋊C4—24no—
391C4⋊C4—24no—
392C4⋊C4—24no—
393C4⋊C4—22no—
394C4⋊C4—22no—
395C4⋊C4—22no—
396C4⋊C4—21no—
397C4⋊C4—21no—
398C4⋊C4—21no—
399C4⋊C4—22no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—22no—
404C4⋊C4—22no—
405C4⋊C4—42no—
406C4⋊C4—41no—
407C4⋊C4—41no—
408C4⋊C4C2×D4×C4312yes—
409C4⋊C4C2×D4×C4312yes—
410C22⋊C4—24no—
411C22⋊C4—24no—
412C22⋊C4—24no—
413C22⋊C4—22no—
414C22⋊C4—22no—
415C22⋊C4—22no—
416C42—24no—
417C42—22no—
418C42—22no—
419C42—22no—
420C42—24no—
421C42C2×D4×C4311yescharacteristic
422C42C2×D4×C4311yescharacteristic
423C42C2×D4×C4311yescharacteristic
424C42C2×D4×C4311yescharacteristic
425C23—22no—
426C23C22×D4×C4311yescharacteristic
427Q8—24no—
428Q8—42no—
429Q8—42no—
430Q8—42no—
431Q8—81no—
432Q8—82no—
433Q8—82no—
434D4—24no—
435D4—42no—
436D4—42no—
437D4—42no—
438D4—81no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—41no—
448C2×C4—44no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—44no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—84no—
456C2×C4#120×C4311yescharacteristic
457C2×C4#120×C4311yescharacteristic
458C2×C4#120×C4311yescharacteristic
459C2×C4#120×C4311yescharacteristic
460C2×C4C22×D4×C4311yescharacteristic
461C2×C4C22×D4×C4311yescharacteristic
462C2×C4C2×#41×C4312yes—
463C2×C42−1+4×C4312yes—
464C8—24no—
465C8—42no—
466C22—21no—
467C22—21no—
468C22—42no—
469C22—42no—
470C22—42no—
471C22C2×#120×C4311yescharacteristic
472C22C43×#53211yescharacteristic
473C22C43×#53611yescharacteristic
474C4—21no—
475C4—21no—
476C4—21no—
477C4—42no—
478C4—42no—
479C4—42no—
480C4—42no—
481C4—42no—
482C4—82no—
483C4—82no—
484C4C43×#45412yes—
485C4C43×#54712yes—
486C4C43×#54812yes—
487C2—21no—
488C2—21no—
489C2—82no—
490C2C43×#243211yescharacteristic
491C2C2×C43×#45411yescharacteristic
492C2C43×#302211yescharacteristic
subgroupG/H
center, socleC22×C43C2×#120
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC43×#532C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C2×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#3165C2semidirect
4. C43×#2568C2semidirect
5. C43×#2038C2semidirect
6. C43×#1986C2semidirect
8. C43×#1860C2semidirect
9. C4×#101×C43C2semidirect
219. #25696C43direct (N × H)
242. #3165C2×C43semidirect
244. #2568C2×C43semidirect
245. #2038C2×C43semidirect
246. #1986C2×C43semidirect
248. #1860C2×C43semidirect
249. C4×#101C2×C43semidirect
289. C43#25696direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#35072
C43×#31652
C43×#31412
C43×#25682
C43×#20382
C43×#19862
C43×#19802
C43×#18602
C4×#101×C432
#2569643