Finite Group Databasebeta

← C43×#9364 #24929381

Subgroups — C43×#9364 #24929381

Order 11008.

732 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3007C211yesmaximal, characteristic
2C43×#2341C211yesmaximal, characteristic
3C43×#1996C211yesmaximal, characteristic, complemented
4C43×#1789C211yesmaximal, characteristic
5C43×#1508C211yesmaximal, characteristic, complemented
6C43×#1305C211yesmaximal, characteristic, complemented
7C43×#1297C211yesmaximal, characteristic, complemented
8C22×#41×C43C2211yescharacteristic
9C2×#137×C43C412yescomplemented
10C2×C22⋊Q8×C43C2211yescharacteristic
11C2×C4×Q8×C43—21no—
12C43×#452—22no—
13C43×#451—21no—
14C43×#450—21no—
15C2×#104×C43—22no—
16C43×#417C412yescomplemented
17C43×#407C2211yescharacteristic
18C43×#407C2211yescharacteristic
19C43×#390—21no—
20C43×#390—22no—
21C43×#380—21no—
22C43×#380C2211yescharacteristic
23C4×C22⋊C4×C43—21no—
24C4×C22⋊C4×C43C2211yescharacteristic
25C4×C22⋊C4×C43C2211yescharacteristic
26C43×#342—22no—
27C43×#328—21no—
28C43×#328—21no—
29C2×#41×C43—21no—
30C2×#41×C43—21no—
31C2×#41×C43—44no—
32C2×#41×C43C2×C412yes—
33C2×#41×C43D412yes—
34C22×Q8×C43C2×C411yescharacteristic
35C22×Q8×C43D411yescharacteristic
36C22×D4×C43—21no—
37C22×D4×C43D411yescharacteristic
38C23×C4×C43—21no—
39C23×C4×C43C2311yescharacteristic
40#137×C43—44no—
41C2×Q16×C43—22no—
42C2×SD16×C43—22no—
43C2×M16×C43—21no—
44C2×M16×C43C2×C412yes—
45C22⋊Q8×C43—21no—
46C22⋊Q8×C43—21no—
47C22⋊Q8×C43—21no—
48C22⋊Q8×C43—21no—
49C4×Q8×C43—44no—
50C2×C4⋊C4×C43—22no—
51C2×C4⋊C4×C43—21no—
52C2×C4⋊C4×C43—21no—
53C2×C4⋊C4×C43C2×C411yescharacteristic
54C2×C22⋊C4×C43—21no—
55C2×C22⋊C4×C43—22no—
56C2×C22⋊C4×C43—21no—
57C2×C22⋊C4×C43—21no—
58C2×C22⋊C4×C43—22no—
59C2×C22⋊C4×C43D412yes—
60C2×C42×C43—22no—
61C2×C42×C43—21no—
62C2×C42×C43—21no—
63#104×C43—44no—
64#103×C43—22no—
65#102×C43—22no—
66C22⋊C8×C43—21no—
67C22⋊C8×C43—21no—
68C22⋊C8×C43—21no—
69C22⋊C8×C43—21no—
70#95×C43—21no—
71#95×C43—21no—
72#95×C43D411yescharacteristic
73#95×C43D411yescharacteristic
74C24×C43—21no—
75C24×C43C2×D411yescharacteristic
76#41×C43—24no—
77#41×C43—24no—
78#41×C43—42no—
79#41×C43—42no—
80#41×C43—44no—
81#41×C43—44no—
82C2×Q8×C43—24no—
83C2×Q8×C43—21no—
84C2×Q8×C43—21no—
85C2×Q8×C43—21no—
86C2×Q8×C43—42no—
87C2×Q8×C43C22⋊C412yes—
88C2×D4×C43—21no—
89C2×D4×C43—22no—
90C2×D4×C43—22no—
91C2×D4×C43—42no—
92C2×D4×C43—44no—
93C2×D4×C43C22⋊C412yes—
94C22×C4×C43—22no—
95C22×C4×C43—22no—
96C22×C4×C43—21no—
97C22×C4×C43—21no—
98C22×C4×C43—21no—
99C22×C4×C43—21no—
100C22×C4×C43—22no—
101C22×C4×C43—21no—
102C22×C4×C43—42no—
103C22×C4×C43—44no—
104C22×C4×C43—41no—
105C22×C4×C43C22×C411yescharacteristic
106C22×C4×C43C2×D411yescharacteristic
107C22×C4×C43C2×D411yescharacteristic
108C22×C4×C43C2×D411yescharacteristic
109C22×C4×C43#4111yescharacteristic
110C22×C4×C43#4111yescharacteristic
111Q16×C43—44no—
112SD16×C43—44no—
113M16×C43—42no—
114M16×C43—42no—
115C2×C8×C43—22no—
116C2×C8×C43—41no—
117C4⋊C4×C43—21no—
118C4⋊C4×C43—21no—
119C4⋊C4×C43—44no—
120C4⋊C4×C43—42no—
121C4⋊C4×C43—41no—
122C4⋊C4×C43—41no—
123C22⋊C4×C43—22no—
124C22⋊C4×C43—42no—
125C22⋊C4×C43—41no—
126C22⋊C4×C43—42no—
127C22⋊C4×C43—44no—
128C22⋊C4×C43—41no—
129C22⋊C4×C43—41no—
130C22⋊C4×C43—82no—
131C42×C43—44no—
132C42×C43—42no—
133C42×C43—42no—
134C23×C43—21no—
135C23×C43—21no—
136C23×C43—22no—
137C23×C43—41no—
138C23×C43—41no—
139C23×C43—42no—
140C23×C43—42no—
141C23×C43—41no—
142C23×C43—41no—
143C23×C43C4×D411yescharacteristic
144C23×C43#12011yescharacteristic
145C23×C43#12111yescharacteristic
146Q8×C43—24no—
147Q8×C43—22no—
148Q8×C43—42no—
149Q8×C43—81no—
150Q8×C43#9914yes—
151D4×C43—22no—
152D4×C43—22no—
153D4×C43—44no—
154D4×C43—44no—
155D4×C43—42no—
156C2×C4×C43—24no—
157C2×C4×C43—22no—
158C2×C4×C43—22no—
159C2×C4×C43—22no—
160C2×C4×C43—22no—
161C2×C4×C43—22no—
162C2×C4×C43—41no—
163C2×C4×C43—41no—
164C2×C4×C43—41no—
165C2×C4×C43—44no—
166C2×C4×C43—44no—
167C2×C4×C43—41no—
168C2×C4×C43—41no—
169C2×C4×C43—42no—
170C2×C4×C43—41no—
171C2×C4×C43—42no—
172C2×C4×C43—42no—
173C2×C4×C43—41no—
174C2×C4×C43—41no—
175C2×C4×C43—41no—
176C2×C4×C43—42no—
177C2×C4×C43—41no—
178C2×C4×C43—81no—
179C2×C4×C43—81no—
180C2×C4×C43—81no—
181C2×C4×C43—81no—
182C2×C4×C43C2×C22⋊C411yescharacteristic
183C2×C4×C43C4×D411yescharacteristic
184C2×C4×C43#12111yescharacteristic
185C2×C4×C43#12311yescharacteristic
186C8×C43—42no—
187C8×C43—81no—
188#9364C4311yesmaximal, characteristic, direct product factor, Sylow
189C22×C43—21no—
190C22×C43—21no—
191C22×C43—21no—
192C22×C43—21no—
193C22×C43—21no—
194C22×C43—21no—
195C22×C43—21no—
196C22×C43—21no—
197C22×C43—42no—
198C22×C43—42no—
199C22×C43—42no—
200C22×C43—81no—
201C22×C43—81no—
202C22×C43—82no—
203C22×C43—82no—
204C22×C43#38611yescharacteristic
205C22×C43#45511yescharacteristic
206C22×C43#45611yescharacteristic
207C4×C43—21no—
208C4×C43—24no—
209C4×C43—21no—
210C4×C43—21no—
211C4×C43—42no—
212C4×C43—82no—
213C4×C43—81no—
214C4×C43—82no—
215C4×C43—81no—
216C4×C43—81no—
217C4×C43C2×#9912yes—
218#3007C2×C4311yescharacteristic
219#2341C2×C4311yescharacteristic
220#1996C2×C4311yescharacteristic, complemented
221#1789C2×C4311yescharacteristic
222#1508C2×C4311yescharacteristic, complemented
223#1305C2×C4311yescharacteristic, complemented
224#1297C2×C4311yescharacteristic, complemented
225C2×C43—21no—
226C2×C43—21no—
227C2×C43—41no—
228C2×C43—41no—
229C2×C43—82no—
230C2×C43#188211yescharacteristic
231C2×C43#189811yescharacteristic
232C2×C43#190611yescharacteristic
233C22×#41C22×C4311yescharacteristic
234C2×#137C4×C4312yescomplemented
235C2×C22⋊Q8C22×C4311yescharacteristic
236C2×C4×Q8—21no—
237#452—22no—
238#451—21no—
239#450—21no—
240C2×#104—22no—
241#417C4×C4312yescomplemented
242#407C22×C4311yescharacteristic
243#407C22×C4311yescharacteristic
244#390—21no—
245#390—22no—
246#380—21no—
247#380C22×C4311yescharacteristic
248C4×C22⋊C4—21no—
249C4×C22⋊C4C22×C4311yescharacteristic
250C4×C22⋊C4C22×C4311yescharacteristic
251#342—22no—
252#328—21no—
253#328—21no—
254C43#936411yescharacteristic, direct product factor, Sylow
255C2×#41—21no—
256C2×#41—21no—
257C2×#41—44no—
258C2×#41C2×C4×C4312yes—
259C2×#41D4×C4312yes—
260C22×Q8C2×C4×C4311yescharacteristic
261C22×Q8D4×C4311yescharacteristic
262C22×D4—21no—
263C22×D4D4×C4311yescharacteristic
264C23×C4—21no—
265C23×C4C23×C4311yescharacteristic
266#137—44no—
267C2×Q16—22no—
268C2×SD16—22no—
269C2×M16—21no—
270C2×M16C2×C4×C4312yes—
271C22⋊Q8—21no—
272C22⋊Q8—21no—
273C22⋊Q8—21no—
274C22⋊Q8—21no—
275C4×Q8—44no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4C2×C4×C4311yescharacteristic
280C2×C22⋊C4—21no—
281C2×C22⋊C4—22no—
282C2×C22⋊C4—21no—
283C2×C22⋊C4—21no—
284C2×C22⋊C4—22no—
285C2×C22⋊C4D4×C4312yes—
286C2×C42—22no—
287C2×C42—21no—
288C2×C42—21no—
289#104—44no—
290#103—22no—
291#102—22no—
292C22⋊C8—21no—
293C22⋊C8—21no—
294C22⋊C8—21no—
295C22⋊C8—21no—
296#95—21no—
297#95—21no—
298#95D4×C4311yescharacteristic
299#95D4×C4311yescharacteristic
300C24—21no—
301C24C2×D4×C4311yescharacteristic
302#41—24no—
303#41—24no—
304#41—42no—
305#41—42no—
306#41—44no—
307#41—44no—
308C2×Q8—24no—
309C2×Q8—21no—
310C2×Q8—21no—
311C2×Q8—21no—
312C2×Q8—42no—
313C2×Q8C22⋊C4×C4312yes—
314C2×D4—22no—
315C2×D4—22no—
316C2×D4—21no—
317C2×D4—42no—
318C2×D4—44no—
319C2×D4C22⋊C4×C4312yes—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—22no—
323C22×C4—22no—
324C22×C4—22no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—42no—
329C22×C4—44no—
330C22×C4—41no—
331C22×C4C22×C4×C4311yescharacteristic
332C22×C4C2×D4×C4311yescharacteristic
333C22×C4C2×D4×C4311yescharacteristic
334C22×C4C2×D4×C4311yescharacteristic
335C22×C4#41×C4311yescharacteristic
336C22×C4#41×C4311yescharacteristic
337Q16—44no—
338SD16—44no—
339M16—42no—
340M16—42no—
341C2×C8—22no—
342C2×C8—41no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—44no—
346C4⋊C4—42no—
347C4⋊C4—41no—
348C4⋊C4—41no—
349C22⋊C4—22no—
350C22⋊C4—42no—
351C22⋊C4—44no—
352C22⋊C4—41no—
353C22⋊C4—41no—
354C22⋊C4—41no—
355C22⋊C4—42no—
356C22⋊C4—82no—
357C42—44no—
358C42—42no—
359C42—42no—
360C23—21no—
361C23—21no—
362C23—22no—
363C23—41no—
364C23—41no—
365C23—42no—
366C23—42no—
367C23—41no—
368C23—41no—
369C23C4×D4×C4311yescharacteristic
370C23#120×C4311yescharacteristic
371C23#121×C4311yescharacteristic
372Q8—24no—
373Q8—22no—
374Q8—42no—
375Q8—81no—
376Q8#99×C4314yes—
377D4—22no—
378D4—22no—
379D4—44no—
380D4—44no—
381D4—42no—
382C2×C4—24no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—44no—
392C2×C4—44no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—42no—
396C2×C4—41no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—42no—
403C2×C4—41no—
404C2×C4—81no—
405C2×C4—81no—
406C2×C4—81no—
407C2×C4—81no—
408C2×C4C2×C22⋊C4×C4311yescharacteristic
409C2×C4C4×D4×C4311yescharacteristic
410C2×C4#121×C4311yescharacteristic
411C2×C4#123×C4311yescharacteristic
412C8—42no—
413C8—81no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—42no—
423C22—42no—
424C22—42no—
425C22—81no—
426C22—81no—
427C22—82no—
428C22—82no—
429C22C43×#38611yescharacteristic
430C22C43×#45511yescharacteristic
431C22C43×#45611yescharacteristic
432C4—21no—
433C4—24no—
434C4—21no—
435C4—21no—
436C4—42no—
437C4—82no—
438C4—81no—
439C4—82no—
440C4—81no—
441C4—81no—
442C4C2×#99×C4312yes—
443C2—21no—
444C2—21no—
445C2—41no—
446C2—41no—
447C2—82no—
448C2C43×#188211yescharacteristic
449C2C43×#189811yescharacteristic
450C2C43×#190611yescharacteristic
subgroupG/H
center, socleC22×C43#386
commutatorC22×C4C22×C4×C43
Frattini, cosocleC23×C4C23×C43
prime radicalC22×#41×C43C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C23×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
3. C43×#1996C2semidirect
5. C43×#1508C2semidirect
6. C43×#1305C2semidirect
7. C43×#1297C2semidirect
9. C2×#137×C43C4semidirect
16. C43×#417C4semidirect
188. #9364C43direct (N × H)
220. #1996C2×C43semidirect
222. #1508C2×C43semidirect
223. #1305C2×C43semidirect
224. #1297C2×C43semidirect
234. C2×#137C4×C43semidirect
241. #417C4×C43semidirect
254. C43#9364direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#30072
C43×#23412
C43×#19962
C43×#17892
C43×#15082
C43×#13052
C43×#12972
#936443