Finite Group Databasebeta

← C43×#12227 #24932244

Subgroups — C43×#12227 #24932244

Order 11008.

520 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#2463C211yesmaximal, characteristic
2C43×#2062C211yesmaximal, characteristic, complemented
3C43×#1602C211yesmaximal, characteristic, complemented
4C43×#1596C211yesmaximal, characteristic
5C43×#1351C211yesmaximal, characteristic, complemented
6C43×#1343C211yesmaximal, characteristic
7C43×#1326C211yesmaximal, characteristic, complemented
8C43×#543C2211yescharacteristic
9C2×C22⋊Q8×C43—21no—
10C2×C4×D4×C43—21no—
11C43×#451—21no—
12C43×#450—21no—
13C43×#394—21no—
14C43×#393C2211yescharacteristic
15C43×#392C2211yescharacteristic
16C43×#388—21no—
17C43×#387—21no—
18C43×#386—21no—
19C43×#385—21no—
20C43×#385C2211yescharacteristic
21C43×#342—21no—
22C43×#342C2211yescharacteristic
23C43×#328—21no—
24C43×#328—21no—
25C43×#323C2211yescharacteristic
26C43×#323C2211yescharacteristic
27C22×Q8×C43D411yescharacteristic
28C22×D4×C43—21no—
29C22×D4×C43D411yescharacteristic
30C23×C4×C43—21no—
31C23×C4×C43D411yescharacteristic
32C2×Q16×C43—41no—
33C2×SD16×C43—41no—
34C22⋊Q8×C43—21no—
35C22⋊Q8×C43—21no—
36C22⋊Q8×C43—41no—
37C22⋊Q8×C43—41no—
38C22⋊Q8×C43—44no—
39C4×D4×C43—44no—
40C2×C4⋊C4×C43—21no—
41C2×C4⋊C4×C43—21no—
42C2×C4⋊C4×C43—21no—
43C2×C4⋊C4×C43—41no—
44C2×C22⋊C4×C43—21no—
45C2×C22⋊C4×C43—21no—
46C2×C22⋊C4×C43—21no—
47C2×C22⋊C4×C43—21no—
48C2×C22⋊C4×C43—21no—
49C2×C22⋊C4×C43—21no—
50C2×C22⋊C4×C43—21no—
51C2×C22⋊C4×C43D411yescharacteristic
52C2×C22⋊C4×C43C2311yescharacteristic
53C2×C42×C43—21no—
54#103×C43—41no—
55#102×C43—41no—
56C22⋊C8×C43—21no—
57C22⋊C8×C43—21no—
58#95×C43—21no—
59#95×C43—21no—
60#95×C43—21no—
61#95×C43—41no—
62#95×C43D411yescharacteristic
63#95×C43D411yescharacteristic
64C24×C43—21no—
65C24×C43C2×D411yescharacteristic
66C2×Q8×C43—21no—
67C2×Q8×C43—21no—
68C2×Q8×C43—42no—
69C2×Q8×C43—41no—
70C2×D4×C43—42no—
71C2×D4×C43—42no—
72C2×D4×C43—42no—
73C2×D4×C43—41no—
74C2×D4×C43—41no—
75C2×D4×C43—41no—
76C22×C4×C43—21no—
77C22×C4×C43—21no—
78C22×C4×C43—21no—
79C22×C4×C43—21no—
80C22×C4×C43—21no—
81C22×C4×C43—21no—
82C22×C4×C43—21no—
83C22×C4×C43—41no—
84C22×C4×C43—41no—
85C22×C4×C43—42no—
86C22×C4×C43—42no—
87C22×C4×C43—42no—
88C22×C4×C43—81no—
89C22×C4×C43C2×D411yescharacteristic
90C22×C4×C43C2×D411yescharacteristic
91Q16×C43—82no—
92SD16×C43—82no—
93C2×C8×C43—41no—
94C2×C8×C43—41no—
95C4⋊C4×C43—24no—
96C4⋊C4×C43—21no—
97C4⋊C4×C43—21no—
98C4⋊C4×C43—42no—
99C4⋊C4×C43—42no—
100C4⋊C4×C43—41no—
101C4⋊C4×C43—41no—
102C4⋊C4×C43—82no—
103C22⋊C4×C43—22no—
104C22⋊C4×C43—21no—
105C22⋊C4×C43—21no—
106C22⋊C4×C43—41no—
107C22⋊C4×C43—42no—
108C22⋊C4×C43—41no—
109C22⋊C4×C43—42no—
110C22⋊C4×C43—42no—
111C22⋊C4×C43—42no—
112C22⋊C4×C43—42no—
113C22⋊C4×C43—41no—
114C22⋊C4×C43—41no—
115C42×C43—42no—
116C23×C43—21no—
117C23×C43—21no—
118C23×C43—22no—
119C23×C43—41no—
120C23×C43—41no—
121C23×C43—41no—
122C23×C43—41no—
123C23×C43—41no—
124C23×C43—41no—
125C23×C43—41no—
126C23×C43—41no—
127C23×C43#12011yescharacteristic
128C23×C43#13511yescharacteristic
129C23×C43#13711yescharacteristic
130Q8×C43—42no—
131Q8×C43—81no—
132Q8×C43—81no—
133Q8×C43—81no—
134D4×C43—42no—
135D4×C43—44no—
136D4×C43—44no—
137D4×C43—81no—
138C2×C4×C43—22no—
139C2×C4×C43—22no—
140C2×C4×C43—22no—
141C2×C4×C43—21no—
142C2×C4×C43—21no—
143C2×C4×C43—41no—
144C2×C4×C43—41no—
145C2×C4×C43—41no—
146C2×C4×C43—41no—
147C2×C4×C43—41no—
148C2×C4×C43—41no—
149C2×C4×C43—41no—
150C2×C4×C43—41no—
151C2×C4×C43—42no—
152C2×C4×C43—41no—
153C2×C4×C43—42no—
154C2×C4×C43—41no—
155C2×C4×C43—41no—
156C2×C4×C43—41no—
157C2×C4×C43—41no—
158C2×C4×C43—41no—
159C2×C4×C43—41no—
160C2×C4×C43—41no—
161C2×C4×C43—81no—
162C2×C4×C43—84no—
163C2×C4×C43—81no—
164C2×C4×C43—81no—
165C2×C4×C43—81no—
166C2×C4×C43—81no—
167C8×C43—81no—
168C8×C43—81no—
169#12227C4311yesmaximal, characteristic, direct product factor, Sylow
170C22×C43—21no—
171C22×C43—21no—
172C22×C43—21no—
173C22×C43—21no—
174C22×C43—41no—
175C22×C43—41no—
176C22×C43—42no—
177C22×C43—42no—
178C22×C43—41no—
179C22×C43—41no—
180C22×C43—42no—
181C22×C43—81no—
182C22×C43—81no—
183C22×C43—81no—
184C22×C43—81no—
185C22×C43—81no—
186C22×C43#45211yescharacteristic
187C22×C43#45611yescharacteristic
188C22×C43B(4,𝔽2)11yescharacteristic
189C4×C43—42no—
190C4×C43—41no—
191C4×C43—42no—
192C4×C43—42no—
193C4×C43—41no—
194C4×C43—81no—
195C4×C43—81no—
196C4×C43—82no—
197C4×C43—81no—
198C4×C43—81no—
199#2463C2×C4311yescharacteristic
200#2062C2×C4311yescharacteristic, complemented
201#1602C2×C4311yescharacteristic, complemented
202#1596C2×C4311yescharacteristic
203#1351C2×C4311yescharacteristic, complemented
204#1343C2×C4311yescharacteristic
205#1326C2×C4311yescharacteristic, complemented
206C2×C43—21no—
207C2×C43—21no—
208C2×C43—41no—
209C2×C43—41no—
210C2×C43—82no—
211C2×C43#160311yescharacteristic
212C2×C43#219611yescharacteristic
213C2×C43#219711yescharacteristic
214#543C22×C4311yescharacteristic
215C2×C22⋊Q8—21no—
216C2×C4×D4—21no—
217#451—21no—
218#450—21no—
219#394—21no—
220#393C22×C4311yescharacteristic
221#392C22×C4311yescharacteristic
222#388—21no—
223#387—21no—
224#386—21no—
225#385—21no—
226#385C22×C4311yescharacteristic
227#342—21no—
228#342C22×C4311yescharacteristic
229#328—21no—
230#328—21no—
231#323C22×C4311yescharacteristic
232#323C22×C4311yescharacteristic
233C43#1222711yescharacteristic, direct product factor, Sylow
234C22×Q8D4×C4311yescharacteristic
235C22×D4—21no—
236C22×D4D4×C4311yescharacteristic
237C23×C4—21no—
238C23×C4D4×C4311yescharacteristic
239C2×Q16—41no—
240C2×SD16—41no—
241C22⋊Q8—21no—
242C22⋊Q8—21no—
243C22⋊Q8—41no—
244C22⋊Q8—41no—
245C22⋊Q8—44no—
246C4×D4—44no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—41no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—21no—
254C2×C22⋊C4—21no—
255C2×C22⋊C4—21no—
256C2×C22⋊C4—21no—
257C2×C22⋊C4—21no—
258C2×C22⋊C4D4×C4311yescharacteristic
259C2×C22⋊C4C23×C4311yescharacteristic
260C2×C42—21no—
261#103—41no—
262#102—41no—
263C22⋊C8—21no—
264C22⋊C8—21no—
265#95—21no—
266#95—21no—
267#95—21no—
268#95—41no—
269#95D4×C4311yescharacteristic
270#95D4×C4311yescharacteristic
271C24—21no—
272C24C2×D4×C4311yescharacteristic
273C2×Q8—21no—
274C2×Q8—21no—
275C2×Q8—42no—
276C2×Q8—41no—
277C2×D4—42no—
278C2×D4—41no—
279C2×D4—42no—
280C2×D4—41no—
281C2×D4—41no—
282C2×D4—42no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—42no—
291C22×C4—42no—
292C22×C4—42no—
293C22×C4—41no—
294C22×C4—41no—
295C22×C4—81no—
296C22×C4C2×D4×C4311yescharacteristic
297C22×C4C2×D4×C4311yescharacteristic
298Q16—82no—
299SD16—82no—
300C2×C8—41no—
301C2×C8—41no—
302C4⋊C4—24no—
303C4⋊C4—21no—
304C4⋊C4—21no—
305C4⋊C4—42no—
306C4⋊C4—42no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4—82no—
310C22⋊C4—22no—
311C22⋊C4—21no—
312C22⋊C4—21no—
313C22⋊C4—41no—
314C22⋊C4—42no—
315C22⋊C4—42no—
316C22⋊C4—42no—
317C22⋊C4—42no—
318C22⋊C4—41no—
319C22⋊C4—42no—
320C22⋊C4—41no—
321C22⋊C4—41no—
322C42—42no—
323C23—21no—
324C23—21no—
325C23—22no—
326C23—41no—
327C23—41no—
328C23—41no—
329C23—41no—
330C23—41no—
331C23—41no—
332C23—41no—
333C23—41no—
334C23#120×C4311yescharacteristic
335C23#135×C4311yescharacteristic
336C23#137×C4311yescharacteristic
337Q8—42no—
338Q8—81no—
339Q8—81no—
340Q8—81no—
341D4—42no—
342D4—44no—
343D4—44no—
344D4—81no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—42no—
359C2×C4—41no—
360C2×C4—42no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—81no—
369C2×C4—84no—
370C2×C4—81no—
371C2×C4—81no—
372C2×C4—81no—
373C2×C4—81no—
374C8—81no—
375C8—81no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—41no—
381C22—41no—
382C22—42no—
383C22—42no—
384C22—41no—
385C22—41no—
386C22—42no—
387C22—81no—
388C22—81no—
389C22—81no—
390C22—81no—
391C22—81no—
392C22C43×#45211yescharacteristic
393C22C43×#45611yescharacteristic
394C22C43×B(4,𝔽2)11yescharacteristic
395C4—42no—
396C4—41no—
397C4—42no—
398C4—42no—
399C4—41no—
400C4—81no—
401C4—81no—
402C4—82no—
403C4—81no—
404C4—81no—
405C2—21no—
406C2—21no—
407C2—41no—
408C2—41no—
409C2—82no—
410C2C43×#160311yescharacteristic
411C2C43×#219611yescharacteristic
412C2C43×#219711yescharacteristic
subgroupG/H
center, socleC22×C43B(4,𝔽2)
commutator, Frattini, cosocleC2×C22⋊C4C23×C43
prime radicalC43×#392C22
LCSG ▷ C2×C22⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C23×C43 ◁ C2×C22⋊C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#2062C2semidirect
3. C43×#1602C2semidirect
5. C43×#1351C2semidirect
7. C43×#1326C2semidirect
169. #12227C43direct (N × H)
200. #2062C2×C43semidirect
201. #1602C2×C43semidirect
203. #1351C2×C43semidirect
205. #1326C2×C43semidirect
233. C43#12227direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#24632
C43×#20622
C43×#16022
C43×#15962
C43×#13512
C43×#13432
C43×#13262
#1222743