Finite Group Databasebeta

← C43×#10335 #24930352

Subgroups — C43×#10335 #24930352

Order 11008.

574 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 574 conjugacy classes of subgroups — too many to draw. Only its 106 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×#3195C211yesmaximal, characteristic
2C43×#2503C211yesmaximal, characteristic
3C43×#2502C211yesmaximal, characteristic
4C43×#1821C211yesmaximal, characteristic
5C43×#1508C211yesmaximal, characteristic
6C43×#1508C211yesmaximal, characteristic
7C43×#1297C211yesmaximal, characteristic
8C2×C22⋊Q8×C43C2211yescharacteristic
9C2×C22⋊Q8×C43C2211yescharacteristic
10C22×C4⋊C4×C43C2211yescharacteristic
11C43×#483—21no—
12C43×#483—21no—
13C43×#470—22no—
14C43×#451—21no—
15C43×#451—21no—
16C43×#407C2211yescharacteristic
17C43×#407C2211yescharacteristic
18C43×#400—22no—
19C43×#398—22no—
20C43×#391—21no—
21C43×#391—21no—
22C43×#385—22no—
23C43×#384—21no—
24C43×#382—21no—
25C43×#381—22no—
26C4×C22⋊C4×C43C2211yescharacteristic
27C4×C22⋊C4×C43C2211yescharacteristic
28C43×#343—22no—
29C43×#328—22no—
30C43×#328—22no—
31C22×Q8×C43D411yescharacteristic
32C22×Q8×C43D411yescharacteristic
33C23×C4×C43D412yes—
34C23×C4×C43C2311yescharacteristic
35C2×Q16×C43—22no—
36C2×M16×C43—21no—
37C2×M16×C43D412yes—
38C22⋊Q8×C43—21no—
39C22⋊Q8×C43—21no—
40C22⋊Q8×C43—21no—
41C22⋊Q8×C43—21no—
42C22⋊Q8×C43—21no—
43C22⋊Q8×C43—21no—
44C22⋊Q8×C43—21no—
45C22⋊Q8×C43—21no—
46C2×C4⋊C4×C43—21no—
47C2×C4⋊C4×C43—21no—
48C2×C4⋊C4×C43—21no—
49C2×C4⋊C4×C43—21no—
50C2×C4⋊C4×C43—21no—
51C2×C4⋊C4×C43—21no—
52C2×C4⋊C4×C43—21no—
53C2×C4⋊C4×C43—21no—
54C2×C4⋊C4×C43—24no—
55C2×C4⋊C4×C43D411yescharacteristic
56C2×C4⋊C4×C43D411yescharacteristic
57C2×C22⋊C4×C43—21no—
58C2×C22⋊C4×C43—21no—
59C2×C22⋊C4×C43—21no—
60C2×C22⋊C4×C43—21no—
61C2×C42×C43—21no—
62C2×C42×C43—21no—
63#106×C43—22no—
64#103×C43—22no—
65#103×C43—22no—
66C22⋊C8×C43—21no—
67C22⋊C8×C43—21no—
68C22⋊C8×C43—21no—
69C22⋊C8×C43—21no—
70#95×C43—24no—
71#95×C43—24no—
72#95×C43—24no—
73#95×C43D412yes—
74#95×C43D412yes—
75C24×C43C2×D411yescharacteristic
76C2×Q8×C43—21no—
77C2×Q8×C43—21no—
78C2×Q8×C43—21no—
79C2×Q8×C43—21no—
80C2×Q8×C43—42no—
81C2×Q8×C43—42no—
82C22×C4×C43—22no—
83C22×C4×C43—22no—
84C22×C4×C43—21no—
85C22×C4×C43—21no—
86C22×C4×C43—21no—
87C22×C4×C43—22no—
88C22×C4×C43—22no—
89C22×C4×C43—21no—
90C22×C4×C43—22no—
91C22×C4×C43—44no—
92C22×C4×C43—42no—
93C22×C4×C43C2×D411yescharacteristic
94C22×C4×C43C2×D411yescharacteristic
95C22×C4×C43C2×D411yescharacteristic
96C22×C4×C43C2×D411yescharacteristic
97C22×C4×C43C2×D411yescharacteristic
98C22×C4×C43#4111yescharacteristic
99Q16×C43—82no—
100M16×C43—42no—
101M16×C43—42no—
102C2×C8×C43—22no—
103C2×C8×C43—41no—
104C4⋊C4×C43—21no—
105C4⋊C4×C43—21no—
106C4⋊C4×C43—21no—
107C4⋊C4×C43—21no—
108C4⋊C4×C43—41no—
109C4⋊C4×C43—41no—
110C4⋊C4×C43—41no—
111C4⋊C4×C43—41no—
112C4⋊C4×C43—41no—
113C4⋊C4×C43—41no—
114C4⋊C4×C43—41no—
115C4⋊C4×C43—41no—
116C4⋊C4×C43—84no—
117C22⋊C4×C43—24no—
118C22⋊C4×C43—42no—
119C22⋊C4×C43—41no—
120C22⋊C4×C43—41no—
121C22⋊C4×C43—41no—
122C22⋊C4×C43—41no—
123C42×C43—42no—
124C42×C43—42no—
125C23×C43—22no—
126C23×C43—22no—
127C23×C43—41no—
128C23×C43#12011yescharacteristic
129C23×C43#12011yescharacteristic
130C23×C43#12111yescharacteristic
131Q8×C43—42no—
132Q8×C43—42no—
133Q8×C43—81no—
134Q8×C43—81no—
135C2×C4×C43—22no—
136C2×C4×C43—22no—
137C2×C4×C43—22no—
138C2×C4×C43—24no—
139C2×C4×C43—41no—
140C2×C4×C43—41no—
141C2×C4×C43—41no—
142C2×C4×C43—42no—
143C2×C4×C43—42no—
144C2×C4×C43—42no—
145C2×C4×C43—42no—
146C2×C4×C43—44no—
147C2×C4×C43—42no—
148C2×C4×C43—42no—
149C2×C4×C43—41no—
150C2×C4×C43—41no—
151C2×C4×C43—41no—
152C2×C4×C43—41no—
153C2×C4×C43—42no—
154C2×C4×C43—42no—
155C2×C4×C43—44no—
156C2×C4×C43—42no—
157C2×C4×C43—42no—
158C2×C4×C43—82no—
159C2×C4×C43#12011yescharacteristic
160C2×C4×C43#12111yescharacteristic
161C2×C4×C43#12111yescharacteristic
162C2×C4×C43#12711yescharacteristic
163C8×C43—42no—
164C8×C43—81no—
165#10335C4311yesmaximal, characteristic, direct product factor, Sylow
166C22×C43—21no—
167C22×C43—21no—
168C22×C43—21no—
169C22×C43—21no—
170C22×C43—21no—
171C22×C43—21no—
172C22×C43—21no—
173C22×C43—44no—
174C22×C43#39211yescharacteristic
175C22×C43#45512yes—
176C22×C43#45612yes—
177C4×C43—21no—
178C4×C43—21no—
179C4×C43—21no—
180C4×C43—44no—
181C4×C43—82no—
182C4×C43—81no—
183C4×C43—82no—
184C4×C43—81no—
185C4×C43—81no—
186C4×C43—81no—
187C4×C43#45812yes—
188#3195C2×C4311yescharacteristic
189#2503C2×C4311yescharacteristic
190#2502C2×C4311yescharacteristic
191#1821C2×C4311yescharacteristic
192#1508C2×C4311yescharacteristic
193#1508C2×C4311yescharacteristic
194#1297C2×C4311yescharacteristic
195C2×C43—22no—
196C2×C43—22no—
197C2×C43—41no—
198C2×C43#200411yescharacteristic
199C2×C43#200511yescharacteristic
200C2×C43#202211yescharacteristic
201C2×C22⋊Q8C22×C4311yescharacteristic
202C2×C22⋊Q8C22×C4311yescharacteristic
203C22×C4⋊C4C22×C4311yescharacteristic
204#483—21no—
205#483—21no—
206#470—22no—
207#451—21no—
208#451—21no—
209#407C22×C4311yescharacteristic
210#407C22×C4311yescharacteristic
211#400—22no—
212#398—22no—
213#391—21no—
214#391—21no—
215#385—22no—
216#384—21no—
217#382—21no—
218#381—22no—
219C4×C22⋊C4C22×C4311yescharacteristic
220C4×C22⋊C4C22×C4311yescharacteristic
221#343—22no—
222#328—22no—
223#328—22no—
224C43#1033511yescharacteristic, direct product factor, Sylow
225C22×Q8D4×C4311yescharacteristic
226C22×Q8D4×C4311yescharacteristic
227C23×C4D4×C4312yes—
228C23×C4C23×C4311yescharacteristic
229C2×Q16—22no—
230C2×M16—21no—
231C2×M16D4×C4312yes—
232C22⋊Q8—21no—
233C22⋊Q8—21no—
234C22⋊Q8—21no—
235C22⋊Q8—21no—
236C22⋊Q8—21no—
237C22⋊Q8—21no—
238C22⋊Q8—21no—
239C22⋊Q8—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—24no—
249C2×C4⋊C4D4×C4311yescharacteristic
250C2×C4⋊C4D4×C4311yescharacteristic
251C2×C22⋊C4—21no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—21no—
254C2×C22⋊C4—21no—
255C2×C42—21no—
256C2×C42—21no—
257#106—22no—
258#103—22no—
259#103—22no—
260C22⋊C8—21no—
261C22⋊C8—21no—
262C22⋊C8—21no—
263C22⋊C8—21no—
264#95—24no—
265#95—24no—
266#95—24no—
267#95D4×C4312yes—
268#95D4×C4312yes—
269C24C2×D4×C4311yescharacteristic
270C2×Q8—21no—
271C2×Q8—21no—
272C2×Q8—21no—
273C2×Q8—21no—
274C2×Q8—42no—
275C2×Q8—42no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—21no—
284C22×C4—22no—
285C22×C4—42no—
286C22×C4—44no—
287C22×C4C2×D4×C4311yescharacteristic
288C22×C4C2×D4×C4311yescharacteristic
289C22×C4C2×D4×C4311yescharacteristic
290C22×C4C2×D4×C4311yescharacteristic
291C22×C4C2×D4×C4311yescharacteristic
292C22×C4#41×C4311yescharacteristic
293Q16—82no—
294M16—42no—
295M16—42no—
296C2×C8—22no—
297C2×C8—41no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C4⋊C4—84no—
311C22⋊C4—24no—
312C22⋊C4—42no—
313C22⋊C4—41no—
314C22⋊C4—41no—
315C22⋊C4—41no—
316C22⋊C4—41no—
317C42—42no—
318C42—42no—
319C23—22no—
320C23—22no—
321C23—41no—
322C23#120×C4311yescharacteristic
323C23#120×C4311yescharacteristic
324C23#121×C4311yescharacteristic
325Q8—42no—
326Q8—42no—
327Q8—81no—
328Q8—81no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—24no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—44no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—44no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—82no—
353C2×C4#120×C4311yescharacteristic
354C2×C4#121×C4311yescharacteristic
355C2×C4#121×C4311yescharacteristic
356C2×C4#127×C4311yescharacteristic
357C8—42no—
358C8—81no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—44no—
367C22C43×#39211yescharacteristic
368C22C43×#45512yes—
369C22C43×#45612yes—
370C4—21no—
371C4—21no—
372C4—21no—
373C4—44no—
374C4—82no—
375C4—82no—
376C4—81no—
377C4—81no—
378C4—81no—
379C4—81no—
380C4C43×#45812yes—
381C2—22no—
382C2—22no—
383C2—41no—
384C2C43×#200411yescharacteristic
385C2C43×#200511yescharacteristic
386C2C43×#202211yescharacteristic
subgroupG/H
center, socleC22×C43#392
commutator, Frattini, cosocleC23×C4C23×C43
prime radicalC24×C43C2×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C23×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
165. #10335C43direct (N × H)
224. C43#10335direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#31952
C43×#25032
C43×#25022
C43×#18212
C43×#15082
C43×#12972
#1033543