Finite Group Databasebeta

← C43×#60715 #24980732

Subgroups — C43×#60715 #24980732

Order 11008.

1830 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3509C212yesmaximal
2C43×#3185C214yesmaximal, complemented
3C43×#3177C218yesmaximal, complemented
4C43×#3170C214yesmaximal, complemented
5C43×#3160C211yesmaximal, characteristic, complemented
6C2×C43×#494C211yesmaximal, characteristic, complemented
7C43×#3139C212yesmaximal, complemented
8C43×#3059C214yesmaximal
9C43×#2950C214yesmaximal, complemented
10C4×#131×C43C211yesmaximal, characteristic
11C22×Q16×C43C2214yes—
12C2×#131×C43C2212yes—
13C43×#557—24no—
14C43×#556—24no—
15C43×#552—28no—
16C43×#541C2218yes—
17C43×#536C2214yes—
18C43×#533C2218yes—
19C43×#533C2212yes—
20C2×C4⋊Q8×C43C2212yes—
21C43×#519C2214yes—
22C4×#41×C43C2211yescharacteristic
23C43×#500C2212yes—
24C43×#499C2214yes—
25C43×#498C2212yes—
26C43×#494C2212yes—
27C43×#494C2214yes—
28C43×#494C2212yes—
29C43×#491C2218yes—
30C43×#487C2218yes—
31C43×#470C22116yes—
32C43×#467C22116yes—
33C43×#441C22116yes—
34C4×Q16×C43C22116yes—
35C43×#427C2214yes—
36C43×#419C2218yes—
37C43×#405C2214yes—
38C43×#405C2212yes—
39C4×M16×C43C2211yescharacteristic
40C4×M16×C43C2212yes—
41C2×C4×C8×C43C2211yescharacteristic
42C2×C4×C8×C43C2212yes—
43C2×#41×C43C2311yescharacteristic
44C22×Q8×C43C2314yes—
45C2×Q16×C43—216no—
46C2×Q16×C43C2318yes—
47C2×Q16×C43C2318yes—
48#131×C43—28no—
49C2×M16×C43C2312yes—
50C2×M16×C43C2314yes—
51C22×C8×C43C2314yes—
52C22×C8×C43C2312yes—
53C4⋊Q8×C43—24no—
54C4⋊Q8×C43—24no—
55C4⋊Q8×C43C2314yes—
56C4⋊Q8×C43C2314yes—
57C4⋊Q8×C43C2314yes—
58#126×C43—216no—
59#125×C43—216no—
60#125×C43—28no—
61#125×C43C2314yes—
62#124×C43—24no—
63#123×C43—28no—
64C22⋊Q8×C43—24no—
65C22⋊Q8×C43—28no—
66C22⋊Q8×C43C23116yes—
67C4×Q8×C43—28no—
68C4×Q8×C43—28no—
69C4×Q8×C43—24no—
70C4×Q8×C43D412yes—
71C4×Q8×C43C23116yes—
72C4×D4×C43D414yes—
73C4×D4×C43D412yes—
74#117×C43—28no—
75#117×C43—28no—
76#117×C43C2314yes—
77#117×C43C2311yescharacteristic
78#117×C43C2312yes—
79C2×C4⋊C4×C43—24no—
80C2×C42×C43C2311yescharacteristic
81C2×C42×C43C2312yes—
82#107×C43C2318yes—
83#106×C43C2318yes—
84#103×C43C23132yes—
85#97×C43C2314yes—
86#97×C43C2312yes—
87C4×C8×C43C2311yescharacteristic
88C4×C8×C43C2312yes—
89C4×C8×C43C2311yescharacteristic
90C4×C8×C43C2312yes—
91C4×C8×C43C2314yes—
92#41×C43—24no—
93C2×Q8×C43—24no—
94C2×Q8×C43—24no—
95C2×Q8×C43—216no—
96C2×Q8×C43C2×D411yescharacteristic
97C2×Q8×C43C2418yes—
98C2×D4×C43C2×D412yes—
99C2×D4×C43C2×D411yescharacteristic
100C22×C4×C43—24no—
101C22×C4×C43C2×D412yes—
102C22×C4×C43C2×D414yes—
103C22×C4×C43C2412yes—
104C22×C4×C43C2411yescharacteristic
105Q16×C43—216no—
106Q16×C43—216no—
107M16×C43—24no—
108M16×C43—28no—
109C2×C8×C43—28no—
110C2×C8×C43#4118yes—
111C2×C8×C43C2414yes—
112C2×C8×C43C2412yes—
113C2×C8×C43C2412yes—
114C4⋊C4×C43—28no—
115C4⋊C4×C43—28no—
116C4⋊C4×C43—24no—
117C4⋊C4×C43—216no—
118C4⋊C4×C43—28no—
119C4⋊C4×C43—216no—
120C4⋊C4×C43C2×D412yes—
121C4⋊C4×C43C2×D414yes—
122C4⋊C4×C43C2418yes—
123C22⋊C4×C43—24no—
124C22⋊C4×C43—216no—
125C22⋊C4×C43C2×D412yes—
126C22⋊C4×C43C2×D414yes—
127C42×C43—216no—
128C42×C43—24no—
129C42×C43C2×D414yes—
130C42×C43C2×D412yes—
131C42×C43C2411yescharacteristic
132C42×C43C2412yes—
133C42×C43C2411yescharacteristic
134C23×C43C22×D412yes—
135C23×C43C22×D411yescharacteristic
136Q8×C43—22no—
137Q8×C43—216no—
138Q8×C43—48no—
139Q8×C43—48no—
140D4×C43—24no—
141D4×C43—22no—
142C2×C4×C43—24no—
143C2×C4×C43—28no—
144C2×C4×C43—24no—
145C2×C4×C43—28no—
146C2×C4×C43—28no—
147C2×C4×C43—48no—
148C2×C4×C43C22×D414yes—
149C2×C4×C43C22×D412yes—
150C2×C4×C43C22×D412yes—
151C2×C4×C43C22×D411yescharacteristic
152C2×C4×C43C22×D412yes—
153C2×C4×C43C2×#4114yes—
154C2×C4×C43C2511yescharacteristic
155C8×C43—24no—
156C8×C43C2×#4114yes—
157C8×C43C2×#4114yes—
158#60715C4311yesmaximal, characteristic, direct product factor, Sylow
159C22×C43—22no—
160C22×C43—22no—
161C22×C43—24no—
162C22×C43#53212yes—
163C22×C43C23×D411yescharacteristic
164C4×C43—22no—
165C4×C43—24no—
166C4×C43—22no—
167C4×C43—48no—
168C4×C43—48no—
169C4×C43#53212yes—
170C4×C43#57814yes—
171C4×C43C22×#4112yes—
172#3509C2×C4312yes—
173#3185C2×C4314yescomplemented
174#3177C2×C4318yescomplemented
175#3170C2×C4314yescomplemented
176#3160C2×C4311yescharacteristic, complemented
177C2×#494C2×C4311yescharacteristic, complemented
178#3139C2×C4312yescomplemented
179#3059C2×C4314yes—
180#2950C2×C4314yescomplemented
181C4×#131C2×C4311yescharacteristic
182C2×C43—22no—
183C2×C43—42no—
184C2×C43C2×#53211yescharacteristic
185C2×C43C2×#57812yes—
186C22×Q16C22×C4314yes—
187C2×#131C22×C4312yes—
188#557—24no—
189#556—24no—
190#552—28no—
191#541C22×C4318yes—
192#536C22×C4314yes—
193#533C22×C4318yes—
194#533C22×C4312yes—
195C2×C4⋊Q8C22×C4312yes—
196#519C22×C4314yes—
197C4×#41C22×C4311yescharacteristic
198#500C22×C4312yes—
199#499C22×C4314yes—
200#498C22×C4312yes—
201#494C22×C4312yes—
202#494C22×C4314yes—
203#494C22×C4312yes—
204#491C22×C4318yes—
205#487C22×C4318yes—
206#470C22×C43116yes—
207#467C22×C43116yes—
208#441C22×C43116yes—
209C4×Q16C22×C43116yes—
210#427C22×C4314yes—
211#419C22×C4318yes—
212#405C22×C4314yes—
213#405C22×C4312yes—
214C4×M16C22×C4311yescharacteristic
215C4×M16C22×C4312yes—
216C2×C4×C8C22×C4311yescharacteristic
217C2×C4×C8C22×C4312yes—
218C43#6071511yescharacteristic, direct product factor, Sylow
219C2×#41C23×C4311yescharacteristic
220C22×Q8C23×C4314yes—
221C2×Q16—216no—
222C2×Q16C23×C4318yes—
223C2×Q16C23×C4318yes—
224#131—28no—
225C2×M16C23×C4312yes—
226C2×M16C23×C4314yes—
227C22×C8C23×C4314yes—
228C22×C8C23×C4312yes—
229C4⋊Q8—24no—
230C4⋊Q8—24no—
231C4⋊Q8C23×C4314yes—
232C4⋊Q8C23×C4314yes—
233C4⋊Q8C23×C4314yes—
234#126—216no—
235#125—216no—
236#125—28no—
237#125C23×C4314yes—
238#124—24no—
239#123—28no—
240C22⋊Q8—24no—
241C22⋊Q8—28no—
242C22⋊Q8C23×C43116yes—
243C4×Q8—28no—
244C4×Q8—28no—
245C4×Q8—24no—
246C4×Q8D4×C4312yes—
247C4×Q8C23×C43116yes—
248C4×D4D4×C4314yes—
249C4×D4D4×C4312yes—
250#117—28no—
251#117—28no—
252#117C23×C4314yes—
253#117C23×C4311yescharacteristic
254#117C23×C4312yes—
255C2×C4⋊C4—24no—
256C2×C42C23×C4311yescharacteristic
257C2×C42C23×C4312yes—
258#107C23×C4318yes—
259#106C23×C4318yes—
260#103C23×C43132yes—
261#97C23×C4314yes—
262#97C23×C4312yes—
263C4×C8C23×C4311yescharacteristic
264C4×C8C23×C4312yes—
265C4×C8C23×C4311yescharacteristic
266C4×C8C23×C4314yes—
267C4×C8C23×C4312yes—
268#41—24no—
269C2×Q8—24no—
270C2×Q8—24no—
271C2×Q8—216no—
272C2×Q8C2×D4×C4311yescharacteristic
273C2×Q8C24×C4318yes—
274C2×D4C2×D4×C4312yes—
275C2×D4C2×D4×C4311yescharacteristic
276C22×C4—24no—
277C22×C4C2×D4×C4312yes—
278C22×C4C2×D4×C4314yes—
279C22×C4C24×C4312yes—
280C22×C4C24×C4311yescharacteristic
281Q16—216no—
282Q16—216no—
283M16—24no—
284M16—28no—
285C2×C8—28no—
286C2×C8#41×C4318yes—
287C2×C8C24×C4314yes—
288C2×C8C24×C4312yes—
289C2×C8C24×C4312yes—
290C4⋊C4—28no—
291C4⋊C4—28no—
292C4⋊C4—24no—
293C4⋊C4—216no—
294C4⋊C4—28no—
295C4⋊C4—216no—
296C4⋊C4C2×D4×C4312yes—
297C4⋊C4C2×D4×C4314yes—
298C4⋊C4C24×C4318yes—
299C22⋊C4—24no—
300C22⋊C4—216no—
301C22⋊C4C2×D4×C4312yes—
302C22⋊C4C2×D4×C4314yes—
303C42—216no—
304C42—24no—
305C42C2×D4×C4314yes—
306C42C2×D4×C4312yes—
307C42C24×C4311yescharacteristic
308C42C24×C4312yes—
309C42C24×C4311yescharacteristic
310C23C22×D4×C4312yes—
311C23C22×D4×C4311yescharacteristic
312Q8—22no—
313Q8—216no—
314Q8—48no—
315Q8—48no—
316D4—24no—
317D4—22no—
318C2×C4—24no—
319C2×C4—28no—
320C2×C4—24no—
321C2×C4—28no—
322C2×C4—28no—
323C2×C4—48no—
324C2×C4C22×D4×C4314yes—
325C2×C4C22×D4×C4312yes—
326C2×C4C22×D4×C4312yes—
327C2×C4C22×D4×C4311yescharacteristic
328C2×C4C22×D4×C4312yes—
329C2×C4C2×#41×C4314yes—
330C2×C4C25×C4311yescharacteristic
331C8—24no—
332C8C2×#41×C4314yes—
333C8C2×#41×C4314yes—
334C22—22no—
335C22—22no—
336C22—24no—
337C22C43×#53212yes—
338C22C23×D4×C4311yescharacteristic
339C4—22no—
340C4—24no—
341C4—22no—
342C4—48no—
343C4—48no—
344C4C43×#53212yes—
345C4C43×#57814yes—
346C4C22×#41×C4312yes—
347C2—22no—
348C2—42no—
349C2C2×C43×#53211yescharacteristic
350C2C2×C43×#57812yes—
subgroupG/H
center, socleC22×C43C23×D4
commutator, Frattini, cosocleC2×C4C25×C43
prime radicalC2×#41×C43C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C4×#41×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#3185C2semidirect
3. C43×#3177C2semidirect
4. C43×#3170C2semidirect
5. C43×#3160C2semidirect
6. C2×C43×#494C2semidirect
7. C43×#3139C2semidirect
9. C43×#2950C2semidirect
158. #60715C43direct (N × H)
173. #3185C2×C43semidirect
174. #3177C2×C43semidirect
175. #3170C2×C43semidirect
176. #3160C2×C43semidirect
177. C2×#494C2×C43semidirect
178. #3139C2×C43semidirect
180. #2950C2×C43semidirect
218. C43#60715direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#35092
C43×#31852
C43×#31772
C43×#31702
C43×#31602
C2×C43×#4942
C43×#31392
C43×#30592
C43×#29502
C4×#131×C432
#6071543