Finite Group Databasebeta

← C43×#10207 #24930224

Subgroups — C43×#10207 #24930224

Order 11008.

474 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3249C211yesmaximal, characteristic
2C43×#3229C211yesmaximal, characteristic
3C43×#3139C211yesmaximal, characteristic
4C43×#1988C211yesmaximal, characteristic
5C43×#1986C211yesmaximal, characteristic
6C43×#1503C211yesmaximal, characteristic
7C43×#1283C211yesmaximal, characteristic
8C43×#533C2211yescharacteristic
9C43×#533C2211yescharacteristic
10C2×C4⋊Q8×C43C2211yescharacteristic
11C43×#498—21no—
12C43×#491—22no—
13C43×#487—21no—
14C43×#487—21no—
15C43×#487—21no—
16C43×#483—22no—
17C43×#477—21no—
18C43×#477—21no—
19C43×#475—22no—
20C43×#467—22no—
21C43×#462—21no—
22C43×#462—21no—
23C43×#431C2211yescharacteristic
24C2×C4⋊C8×C43C2211yescharacteristic
25C43×#419—22no—
26C4×M16×C43C2211yescharacteristic
27C4×C4⋊C4×C43C2211yescharacteristic
28C43×#340—22no—
29C43×#339—22no—
30C43×#328—22no—
31C22×Q8×C43—21no—
32C2×Q16×C43—22no—
33C2×M16×C43D412yes—
34C22×C8×C43D412yes—
35C4⋊Q8×C43—21no—
36C4⋊Q8×C43—21no—
37C4⋊Q8×C43—21no—
38C4⋊Q8×C43D411yescharacteristic
39C4⋊Q8×C43D412yes—
40C4⋊Q8×C43D411yescharacteristic
41C4⋊Q8×C43D411yescharacteristic
42C4⋊Q8×C43D411yescharacteristic
43#125×C43—21no—
44#125×C43—21no—
45C22⋊Q8×C43—21no—
46C22⋊Q8×C43—21no—
47C22⋊Q8×C43—21no—
48C22⋊Q8×C43—21no—
49C4×Q8×C43—21no—
50C4×Q8×C43—21no—
51C4×Q8×C43—21no—
52C4×Q8×C43—21no—
53#117×C43—21no—
54#117×C43—21no—
55C2×C4⋊C4×C43—21no—
56C2×C4⋊C4×C43—21no—
57C2×C4⋊C4×C43—21no—
58C2×C42×C43—21no—
59C2×C42×C43C2311yescharacteristic
60#107×C43—22no—
61#106×C43—24no—
62C4⋊C8×C43—21no—
63C4⋊C8×C43—21no—
64C4⋊C8×C43—21no—
65#103×C43—24no—
66#103×C43—24no—
67#103×C43—22no—
68#103×C43—22no—
69#103×C43—24no—
70C22⋊C8×C43D412yes—
71#97×C43—21no—
72C4×C8×C43—21no—
73C4×C8×C43—21no—
74#95×C43—21no—
75C2×Q8×C43—21no—
76C2×Q8×C43—22no—
77C2×Q8×C43—21no—
78C2×Q8×C43—21no—
79C2×Q8×C43—21no—
80C2×Q8×C43—41no—
81C2×Q8×C43—42no—
82C2×Q8×C43—42no—
83C22×C4×C43—41no—
84C22×C4×C43—41no—
85C22×C4×C43C2×D411yescharacteristic
86C22×C4×C43C2×D411yescharacteristic
87C22×C4×C43C2×D411yescharacteristic
88Q16×C43—82no—
89M16×C43—22no—
90M16×C43—22no—
91C2×C8×C43—22no—
92C2×C8×C43—22no—
93C2×C8×C43—22no—
94C2×C8×C43—42no—
95C4⋊C4×C43—22no—
96C4⋊C4×C43—21no—
97C4⋊C4×C43—21no—
98C4⋊C4×C43—22no—
99C4⋊C4×C43—21no—
100C4⋊C4×C43—21no—
101C4⋊C4×C43—21no—
102C4⋊C4×C43—22no—
103C4⋊C4×C43—21no—
104C4⋊C4×C43—21no—
105C4⋊C4×C43—21no—
106C4⋊C4×C43—41no—
107C4⋊C4×C43—41no—
108C4⋊C4×C43—41no—
109C4⋊C4×C43—41no—
110C4⋊C4×C43—41no—
111C4⋊C4×C43—41no—
112C4⋊C4×C43—41no—
113C22⋊C4×C43—41no—
114C22⋊C4×C43—41no—
115C42×C43—41no—
116C42×C43—41no—
117C42×C43—42no—
118C42×C43C2×D411yescharacteristic
119C42×C43C2×D411yescharacteristic
120C42×C43C2×D411yescharacteristic
121C42×C43#4111yescharacteristic
122C23×C43#12711yescharacteristic
123Q8×C43—42no—
124Q8×C43—44no—
125Q8×C43—41no—
126Q8×C43—41no—
127Q8×C43—41no—
128Q8×C43—41no—
129Q8×C43—81no—
130Q8×C43—82no—
131C2×C4×C43—21no—
132C2×C4×C43—21no—
133C2×C4×C43—41no—
134C2×C4×C43—42no—
135C2×C4×C43—41no—
136C2×C4×C43—41no—
137C2×C4×C43—41no—
138C2×C4×C43—41no—
139C2×C4×C43—42no—
140C2×C4×C43—81no—
141C2×C4×C43—81no—
142C2×C4×C43—81no—
143C2×C4×C43—81no—
144C2×C4×C43#12011yescharacteristic
145C2×C4×C43#12011yescharacteristic
146C2×C4×C43#12011yescharacteristic
147C2×C4×C43#12111yescharacteristic
148C2×C4×C43#12111yescharacteristic
149C2×C4×C43#12111yescharacteristic
150C2×C4×C43#13512yes—
151C2×C4×C43#13712yes—
152C8×C43—42no—
153C8×C43—42no—
154C8×C43—42no—
155#10207C4311yesmaximal, characteristic, direct product factor, Sylow
156C22×C43—21no—
157C22×C43—21no—
158C22×C43#39211yescharacteristic
159C22×C43#49511yescharacteristic
160C22×C43#49711yescharacteristic
161C4×C43—21no—
162C4×C43—21no—
163C4×C43—21no—
164C4×C43—82no—
165C4×C43—81no—
166C4×C43—81no—
167C4×C43—81no—
168C4×C43—81no—
169C4×C43—82no—
170C4×C43#45212yes—
171C4×C43#45511yescharacteristic
172C4×C43#45611yescharacteristic
173C4×C43#46412yes—
174#3249C2×C4311yescharacteristic
175#3229C2×C4311yescharacteristic
176#3139C2×C4311yescharacteristic
177#1988C2×C4311yescharacteristic
178#1986C2×C4311yescharacteristic
179#1503C2×C4311yescharacteristic
180#1283C2×C4311yescharacteristic
181C2×C43—21no—
182C2×C43—21no—
183C2×C43#200711yescharacteristic
184C2×C43#200911yescharacteristic
185C2×C43#201511yescharacteristic
186#533C22×C4311yescharacteristic
187#533C22×C4311yescharacteristic
188C2×C4⋊Q8C22×C4311yescharacteristic
189#498—21no—
190#491—22no—
191#487—21no—
192#487—21no—
193#487—21no—
194#483—22no—
195#477—21no—
196#477—21no—
197#475—22no—
198#467—22no—
199#462—21no—
200#462—21no—
201#431C22×C4311yescharacteristic
202C2×C4⋊C8C22×C4311yescharacteristic
203#419—22no—
204C4×M16C22×C4311yescharacteristic
205C4×C4⋊C4C22×C4311yescharacteristic
206#340—22no—
207#339—22no—
208#328—22no—
209C43#1020711yescharacteristic, direct product factor, Sylow
210C22×Q8—21no—
211C2×Q16—22no—
212C2×M16D4×C4312yes—
213C22×C8D4×C4312yes—
214C4⋊Q8—21no—
215C4⋊Q8—21no—
216C4⋊Q8—21no—
217C4⋊Q8D4×C4312yes—
218C4⋊Q8D4×C4311yescharacteristic
219C4⋊Q8D4×C4311yescharacteristic
220C4⋊Q8D4×C4311yescharacteristic
221C4⋊Q8D4×C4311yescharacteristic
222#125—21no—
223#125—21no—
224C22⋊Q8—21no—
225C22⋊Q8—21no—
226C22⋊Q8—21no—
227C22⋊Q8—21no—
228C4×Q8—21no—
229C4×Q8—21no—
230C4×Q8—21no—
231C4×Q8—21no—
232#117—21no—
233#117—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C42—21no—
238C2×C42C23×C4311yescharacteristic
239#107—22no—
240#106—24no—
241C4⋊C8—21no—
242C4⋊C8—21no—
243C4⋊C8—21no—
244#103—24no—
245#103—24no—
246#103—22no—
247#103—22no—
248#103—24no—
249C22⋊C8D4×C4312yes—
250#97—21no—
251C4×C8—21no—
252C4×C8—21no—
253#95—21no—
254C2×Q8—21no—
255C2×Q8—22no—
256C2×Q8—21no—
257C2×Q8—21no—
258C2×Q8—21no—
259C2×Q8—41no—
260C2×Q8—42no—
261C2×Q8—42no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4C2×D4×C4311yescharacteristic
265C22×C4C2×D4×C4311yescharacteristic
266C22×C4C2×D4×C4311yescharacteristic
267Q16—82no—
268M16—22no—
269M16—22no—
270C2×C8—22no—
271C2×C8—22no—
272C2×C8—22no—
273C2×C8—42no—
274C4⋊C4—22no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—22no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—22no—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C22⋊C4—41no—
293C22⋊C4—41no—
294C42—41no—
295C42—41no—
296C42—42no—
297C42C2×D4×C4311yescharacteristic
298C42C2×D4×C4311yescharacteristic
299C42C2×D4×C4311yescharacteristic
300C42#41×C4311yescharacteristic
301C23#127×C4311yescharacteristic
302Q8—42no—
303Q8—44no—
304Q8—41no—
305Q8—41no—
306Q8—41no—
307Q8—41no—
308Q8—81no—
309Q8—82no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—41no—
313C2×C4—42no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—42no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4#120×C4311yescharacteristic
324C2×C4#120×C4311yescharacteristic
325C2×C4#120×C4311yescharacteristic
326C2×C4#121×C4311yescharacteristic
327C2×C4#121×C4311yescharacteristic
328C2×C4#121×C4311yescharacteristic
329C2×C4#135×C4312yes—
330C2×C4#137×C4312yes—
331C8—42no—
332C8—42no—
333C8—42no—
334C22—21no—
335C22—21no—
336C22C43×#39211yescharacteristic
337C22C43×#49511yescharacteristic
338C22C43×#49711yescharacteristic
339C4—21no—
340C4—21no—
341C4—21no—
342C4—82no—
343C4—81no—
344C4—81no—
345C4—81no—
346C4—81no—
347C4—82no—
348C4C43×#45212yes—
349C4C43×#45511yescharacteristic
350C4C43×#45611yescharacteristic
351C4C43×#46412yes—
352C2—21no—
353C2—21no—
354C2C43×#200711yescharacteristic
355C2C43×#200911yescharacteristic
356C2C43×#201511yescharacteristic
subgroupG/H
center, socleC22×C43#392
commutator, Frattini, cosocleC2×C42C23×C43
prime radicalC23×C43#127
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C2×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
155. #10207C43direct (N × H)
209. C43#10207direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#32492
C43×#32292
C43×#31392
C43×#19882
C43×#19862
C43×#15032
C43×#12832
#1020743