Finite Group Databasebeta

← C2×C43×#1584 #24937879

Subgroups — C2×C43×#1584 #24937879

Order 11008.

674 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#446C211yesmaximal, characteristic
2C2×C8×Q8×C43C211yesmaximal, characteristic
3C2×C4×Q16×C43C211yesmaximal, characteristic
4C43×#1584C218yesmaximal, direct product factor
5C2×C43×#335C211yesmaximal, characteristic
6C2×C43×Q8⋊C8C211yesmaximal, characteristic
7C2×C43×Q8⋊C8C211yesmaximal, characteristic
8C2×C43×#322C211yesmaximal, characteristic
9C22×Q16×C43C411yescharacteristic
10C2×C4×Q8×C43C2211yescharacteristic
11C2×C4×Q8×C43C2211yescharacteristic
12C43×#446—22no—
13C43×#446C2214yes—
14C8×Q8×C43—22no—
15C8×Q8×C43C2214yes—
16C4×Q16×C43C414yes—
17C4×Q16×C43C2214yes—
18C2×#107×C43C411yescharacteristic
19C2×C4⋊C8×C43—21no—
20C2×C4⋊C8×C43—21no—
21C2×C4⋊C8×C43C2211yescharacteristic
22C2×C4⋊C8×C43C2211yescharacteristic
23C2×#103×C43C411yescharacteristic
24C2×#103×C43C411yescharacteristic
25C2×#97×C43—21no—
26C2×C4×C8×C43—21no—
27C2×C4×C8×C43C2211yescharacteristic
28C2×C4×C8×C43C2211yescharacteristic
29C2×C4×C8×C43C2211yescharacteristic
30C43×#335C2214yes—
31C43×Q8⋊C8C2214yes—
32C43×Q8⋊C8C2214yes—
33C43×#322C2214yes—
34C22×Q8×C43C2×C411yescharacteristic
35C22×Q8×C43C2×C411yescharacteristic
36C2×Q16×C43—24no—
37C2×Q16×C43C2×C414yes—
38C22×C8×C43—21no—
39C22×C8×C43—21no—
40C22×C8×C43—21no—
41C22×C8×C43C2×C411yescharacteristic
42C22×C8×C43C2×C411yescharacteristic
43C22×C8×C43D411yescharacteristic
44C22×C8×C43D411yescharacteristic
45C4×Q8×C43—21no—
46C4×Q8×C43—21no—
47C4×Q8×C43—21no—
48C4×Q8×C43—21no—
49C4×Q8×C43C2×C412yes—
50C4×Q8×C43C2×C412yes—
51C4×Q8×C43C2312yes—
52C4×Q8×C43C2312yes—
53C2×C4⋊C4×C43—21no—
54C2×C4⋊C4×C43—21no—
55C2×C4⋊C4×C43C2×C411yescharacteristic
56C2×C4⋊C4×C43C2×C411yescharacteristic
57C2×C42×C43—21no—
58C2×C42×C43—21no—
59C2×C42×C43C2311yescharacteristic
60#107×C43C2×C414yes—
61C4⋊C8×C43—24no—
62C4⋊C8×C43—24no—
63C4⋊C8×C43—21no—
64C4⋊C8×C43—21no—
65C4⋊C8×C43C2312yes—
66C4⋊C8×C43C2312yes—
67#103×C43C2×C414yes—
68#103×C43C2×C414yes—
69#97×C43—24no—
70C4×C8×C43—24no—
71C4×C8×C43—21no—
72C4×C8×C43C2×C412yes—
73C4×C8×C43D412yes—
74C4×C8×C43C2312yes—
75C4×C8×C43C2312yes—
76C4×C8×C43C2312yes—
77C2×Q8×C43—21no—
78C2×Q8×C43—21no—
79C2×Q8×C43—22no—
80C2×Q8×C43—22no—
81C2×Q8×C43—22no—
82C2×Q8×C43M1614yes—
83C2×Q8×C43C22×C412yes—
84C2×Q8×C43C22×C412yes—
85C22×C4×C43—21no—
86C22×C4×C43—21no—
87C22×C4×C43—21no—
88C22×C4×C43—21no—
89C22×C4×C43C22×C411yescharacteristic
90C22×C4×C43C2×D411yescharacteristic
91C22×C4×C43#4111yescharacteristic
92Q16×C43—28no—
93C2×C8×C43—22no—
94C2×C8×C43—22no—
95C2×C8×C43—22no—
96C2×C8×C43—22no—
97C2×C8×C43—22no—
98C2×C8×C43—22no—
99C2×C8×C43—42no—
100C2×C8×C43—42no—
101C2×C8×C43—42no—
102C2×C8×C43Q1614yescomplemented
103C2×C8×C43C22×C412yes—
104C2×C8×C43C22×C412yes—
105C2×C8×C43C2×D412yes—
106C2×C8×C43C2×D412yes—
107C4⋊C4×C43—22no—
108C4⋊C4×C43—22no—
109C4⋊C4×C43—21no—
110C4⋊C4×C43—21no—
111C4⋊C4×C43—22no—
112C4⋊C4×C43—22no—
113C4⋊C4×C43C22×C412yes—
114C4⋊C4×C43C22×C412yes—
115C42×C43—22no—
116C42×C43—22no—
117C42×C43—22no—
118C42×C43—22no—
119C42×C43C22×C411yescharacteristic
120C42×C43C2×D411yescharacteristic
121C42×C43#4111yescharacteristic
122C42×C43C2411yescharacteristic
123C23×C43C4×D411yescharacteristic
124Q8×C43—22no—
125Q8×C43—24no—
126Q8×C43—22no—
127Q8×C43—22no—
128Q8×C43—42no—
129Q8×C43C2×M1614yes—
130C2×C4×C43—22no—
131C2×C4×C43—24no—
132C2×C4×C43—22no—
133C2×C4×C43—22no—
134C2×C4×C43—22no—
135C2×C4×C43—22no—
136C2×C4×C43—42no—
137C2×C4×C43—42no—
138C2×C4×C43—42no—
139C2×C4×C43C4×D411yescharacteristic
140C2×C4×C43C4×D411yescharacteristic
141C2×C4×C43C4×D411yescharacteristic
142C2×C4×C43C2×M1612yes—
143C2×C4×C43#13112yes—
144C2×C4×C43C2×Q1612yes—
145C2×C4×C43#13512yes—
146C2×C4×C43C23×C411yescharacteristic
147C2×C4×C43C22×D411yescharacteristic
148C2×C4×C43C2×#4111yescharacteristic
149C8×C43—22no—
150C8×C43—22no—
151C8×C43—22no—
152C8×C43—42no—
153C8×C43—42no—
154C8×C43—42no—
155C8×C43C2×Q1614yescomplemented
156C2×#1584C4311yesmaximal, characteristic, direct product factor, Sylow
157C22×C43#43512yes—
158C22×C43C4×Q1612yes—
159C22×C43#44412yes—
160C22×C43C2×C4×D411yescharacteristic
161C4×C43—24no—
162C4×C43—21no—
163C4×C43—21no—
164C4×C43—42no—
165C4×C43—42no—
166C4×C43—42no—
167C4×C43#43512yes—
168C4×C43C4×Q1612yes—
169C4×C43C22×M1611yescharacteristic
170C4×C43C2×#13111yescharacteristic
171C4×C43C22×Q1611yescharacteristic
172C4×C43C2×#13511yescharacteristic
173C2×#446C2×C4311yescharacteristic
174C2×C8×Q8C2×C4311yescharacteristic
175C2×C4×Q16C2×C4311yescharacteristic
176#1584C2×C4318yesdirect product factor
177C2×#335C2×C4311yescharacteristic
178C2×Q8⋊C8C2×C4311yescharacteristic
179C2×Q8⋊C8C2×C4311yescharacteristic
180C2×#322C2×C4311yescharacteristic
181C2×C43#158414yesdirect product factor
182C2×C43C2×#43511yescharacteristic
183C2×C43C2×C4×Q1611yescharacteristic
184C2×C43C2×#44411yescharacteristic
185C22×Q16C4×C4311yescharacteristic
186C2×C4×Q8C22×C4311yescharacteristic
187C2×C4×Q8C22×C4311yescharacteristic
188#446—22no—
189#446C22×C4314yes—
190C8×Q8—22no—
191C8×Q8C22×C4314yes—
192C4×Q16C4×C4314yes—
193C4×Q16C22×C4314yes—
194C2×#107C4×C4311yescharacteristic
195C2×C4⋊C8—21no—
196C2×C4⋊C8—21no—
197C2×C4⋊C8C22×C4311yescharacteristic
198C2×C4⋊C8C22×C4311yescharacteristic
199C2×#103C4×C4311yescharacteristic
200C2×#103C4×C4311yescharacteristic
201C2×#97—21no—
202C2×C4×C8—21no—
203C2×C4×C8C22×C4311yescharacteristic
204C2×C4×C8C22×C4311yescharacteristic
205C2×C4×C8C22×C4311yescharacteristic
206#335C22×C4314yes—
207Q8⋊C8C22×C4314yes—
208Q8⋊C8C22×C4314yes—
209#322C22×C4314yes—
210C43C2×#158411yescharacteristic, direct product factor, Sylow
211C22×Q8C2×C4×C4311yescharacteristic
212C22×Q8C2×C4×C4311yescharacteristic
213C2×Q16—24no—
214C2×Q16C2×C4×C4314yes—
215C22×C8—21no—
216C22×C8—21no—
217C22×C8—21no—
218C22×C8C2×C4×C4311yescharacteristic
219C22×C8C2×C4×C4311yescharacteristic
220C22×C8D4×C4311yescharacteristic
221C22×C8D4×C4311yescharacteristic
222C4×Q8—21no—
223C4×Q8—21no—
224C4×Q8—21no—
225C4×Q8—21no—
226C4×Q8C2×C4×C4312yes—
227C4×Q8C2×C4×C4312yes—
228C4×Q8C23×C4312yes—
229C4×Q8C23×C4312yes—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4C2×C4×C4311yescharacteristic
233C2×C4⋊C4C2×C4×C4311yescharacteristic
234C2×C42—21no—
235C2×C42—21no—
236C2×C42C23×C4311yescharacteristic
237#107C2×C4×C4314yes—
238C4⋊C8—24no—
239C4⋊C8—24no—
240C4⋊C8—21no—
241C4⋊C8—21no—
242C4⋊C8C23×C4312yes—
243C4⋊C8C23×C4312yes—
244#103C2×C4×C4314yes—
245#103C2×C4×C4314yes—
246#97—24no—
247C4×C8—24no—
248C4×C8—21no—
249C4×C8C2×C4×C4312yes—
250C4×C8D4×C4312yes—
251C4×C8C23×C4312yes—
252C4×C8C23×C4312yes—
253C4×C8C23×C4312yes—
254C2×Q8—21no—
255C2×Q8—21no—
256C2×Q8—22no—
257C2×Q8—22no—
258C2×Q8—22no—
259C2×Q8M16×C4314yes—
260C2×Q8C22×C4×C4312yes—
261C2×Q8C22×C4×C4312yes—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4C22×C4×C4311yescharacteristic
267C22×C4C2×D4×C4311yescharacteristic
268C22×C4#41×C4311yescharacteristic
269Q16—28no—
270C2×C8—22no—
271C2×C8—22no—
272C2×C8—22no—
273C2×C8—22no—
274C2×C8—22no—
275C2×C8—22no—
276C2×C8—42no—
277C2×C8—42no—
278C2×C8—42no—
279C2×C8Q16×C4314yescomplemented
280C2×C8C22×C4×C4312yes—
281C2×C8C22×C4×C4312yes—
282C2×C8C2×D4×C4312yes—
283C2×C8C2×D4×C4312yes—
284C4⋊C4—22no—
285C4⋊C4—22no—
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—22no—
289C4⋊C4—22no—
290C4⋊C4C22×C4×C4312yes—
291C4⋊C4C22×C4×C4312yes—
292C42—22no—
293C42—22no—
294C42—22no—
295C42—22no—
296C42C22×C4×C4311yescharacteristic
297C42C2×D4×C4311yescharacteristic
298C42#41×C4311yescharacteristic
299C42C24×C4311yescharacteristic
300C23C4×D4×C4311yescharacteristic
301Q8—22no—
302Q8—24no—
303Q8—22no—
304Q8—22no—
305Q8—42no—
306Q8C2×M16×C4314yes—
307C2×C4—22no—
308C2×C4—24no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4C4×D4×C4311yescharacteristic
317C2×C4C4×D4×C4311yescharacteristic
318C2×C4C4×D4×C4311yescharacteristic
319C2×C4C2×M16×C4312yes—
320C2×C4#131×C4312yes—
321C2×C4C2×Q16×C4312yes—
322C2×C4#135×C4312yes—
323C2×C4C23×C4×C4311yescharacteristic
324C2×C4C22×D4×C4311yescharacteristic
325C2×C4C2×#41×C4311yescharacteristic
326C8—22no—
327C8—22no—
328C8—22no—
329C8—42no—
330C8—42no—
331C8—42no—
332C8C2×Q16×C4314yescomplemented
333C22C43×#43512yes—
334C22C4×Q16×C4312yes—
335C22C43×#44412yes—
336C22C2×C4×D4×C4311yescharacteristic
337C4—24no—
338C4—21no—
339C4—21no—
340C4—42no—
341C4—42no—
342C4—42no—
343C4C43×#43512yes—
344C4C4×Q16×C4312yes—
345C4C22×M16×C4311yescharacteristic
346C4C2×#131×C4311yescharacteristic
347C4C22×Q16×C4311yescharacteristic
348C4C2×#135×C4311yescharacteristic
349C2C43×#158414yesdirect product factor
350C2C2×C43×#43511yescharacteristic
351C2C2×C4×Q16×C4311yescharacteristic
352C2C2×C43×#44411yescharacteristic
subgroupG/H
centerC22×C4×C43C2×D4
commutatorC2×C4C23×C4×C43
Frattini, cosocleC42C24×C43
socle, prime radicalC23×C43C4×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C43 ◁ C2×C4×C8×C43 ◁ G

Complements

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

NH ≅ G/Ntype
4. C43×#1584C2direct (N × H)
102. C2×C8×C43Q16semidirect
155. C8×C43C2×Q16semidirect
156. C2×#1584C43direct (N × H)
176. #1584C2×C43direct (N × H)
181. C2×C43#1584direct (N × H)
210. C43C2×#1584direct (N × H)
279. C2×C8Q16×C43semidirect
332. C8C2×Q16×C43semidirect
349. C2C43×#1584direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C43×#4462
C2×C8×Q8×C432
C2×C4×Q16×C432
C43×#15842
C2×C43×#3352
C2×C43×Q8⋊C82
C2×C43×#3222
C2×#158443