Finite Group Databasebeta

← C4×#108×D43 #25094691

Subgroups — C4×#108×D43 #25094691

Order 11008.

1086 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×#108×D43C212yesmaximal
2C4×M16×D43C212yesmaximal
3C2×C4×C8×D43C211yesmaximal, characteristic
4#108×Dic43C212yesmaximal, complemented
5C4×#13063260C212yesmaximal, complemented
6C4×#13063261C211yesmaximal, characteristic, complemented
7#19134496C212yesmaximal, complemented
8#341×D43C212yesmaximal
9C4×#108×C43C211yesmaximal, characteristic, complemented
10C2×M16×D43C2214yes—
11C22×C8×D43C2211yescharacteristic
12C22×C8×D43C2211yescharacteristic
13C2×C42×D43C2211yescharacteristic
14C2×#13063261C2212yes—
15C2×#13063260C2214yes—
16#108×D43C4116yesdirect product factor
17C4×#10621877C2212yes—
18#14582851—22no—
19M16×Dic43C2214yes—
20C4×#10621872—22no—
21#97×D43—22no—
22C2×C4×C43⋊C8C2211yescharacteristic
23C2×C8×Dic43C2211yescharacteristic
24C2×C8×Dic43C2211yescharacteristic
25C4×C8×D43—22no—
26C4×C8×D43C414yes—
27C4×C8×D43C414yes—
28#14582664C2212yes—
29#14582663C2214yes—
30C2×#108×C43C2212yes—
31C4×M16×C43C2212yes—
32C2×C4×C8×C43C2211yescharacteristic
33C43×#341C2212yes—
34C22×C4×D43Q812yes—
35C22×C4×D43C2311yescharacteristic
36C2×#10621877C2314yes—
37C2×#10621872—24no—
38M16×D43—28no—
39M16×D43C2×C4116yes—
40C22×C43⋊C8C2311yescharacteristic
41C22×C43⋊C8C2311yescharacteristic
42C2×C8×D43—24no—
43C2×C8×D43—24no—
44C2×C8×D43C2×C412yes—
45C2×C8×D43C2×C412yes—
46C2×C8×D43C2×C412yes—
47C2×C8×D43C2×C412yes—
48C2×C8×D43C2×C418yes—
49C2×C4×Dic43Q812yes—
50C2×C4×Dic43C2311yescharacteristic
51C42×D43C2×C412yes—
52C42×D43C2×C412yes—
53C42×D43D411yescharacteristic
54C42×D43D411yescharacteristic
55C42×D43D411yescharacteristic
56C42×D43D411yescharacteristic
57#13063261C2×C418yescomplemented
58#13063260C2×C4116yescomplemented
59#13063236—22no—
60#13063235—24no—
61C4×C43⋊C8—22no—
62C4×C43⋊C8C2×C414yes—
63C8×Dic43—24no—
64C8×Dic43C2×C414yes—
65C8×Dic43C2×C414yes—
66C2×M16×C43C2314yes—
67C22×C8×C43C2311yescharacteristic
68C22×C8×C43C2311yescharacteristic
69C2×C42×C43C2311yescharacteristic
70#108×C43C2×C418yescomplemented
71#97×C43—22no—
72C4×C8×C43—22no—
73C4×C8×C43C2×C414yes—
74C23×D43C2×Q811yescharacteristic
75C22×C4×C43C2×Q812yes—
76C22×C4×C43C2411yescharacteristic
77C22×Dic43C2×Q812yes—
78C22×Dic43C2×Q811yescharacteristic
79C2×C4×D43—28no—
80C2×C4×D43C4⋊C412yes—
81C2×C4×D43C4⋊C412yes—
82C2×C4×D43C4⋊C412yes—
83C2×C4×D43C4⋊C412yes—
84C2×C4×D43C22×C411yescharacteristic
85C2×C4×D43C22×C411yescharacteristic
86C2×C4×D43C22×C414yes—
87C2×C4×D43C2×D411yescharacteristic
88C2×C4×D43C2×D411yescharacteristic
89C2×C4×D43#4114yes—
90M16×C43—24no—
91M16×C43C22×C418yes—
92C2×C8×C43—24no—
93C2×C8×C43—22no—
94C2×C8×C43C22×C412yes—
95C2×C8×C43C22×C412yes—
96C2×C8×C43C22×C414yes—
97C42×C43C22×C412yes—
98C42×C43C2×D411yescharacteristic
99C42×C43C2×D411yescharacteristic
100C4×Dic43C4⋊C412yes—
101C4×Dic43C4⋊C412yes—
102C4×Dic43C4⋊C412yes—
103C4×Dic43C4⋊C412yes—
104C4×Dic43C22×C412yes—
105C4×Dic43C2×D411yescharacteristic
106C4×Dic43C2×D411yescharacteristic
107#10621877—24no—
108#10621877C22×C418yes—
109C2×C43⋊C8—24no—
110C2×C43⋊C8—22no—
111C2×C43⋊C8C22×C412yes—
112C2×C43⋊C8C22×C412yes—
113C2×C43⋊C8C22×C414yes—
114#10621872—216no—
115C8×D43—24no—
116C8×D43—24no—
117C8×D43—216no—
118C8×D43C4218yes—
119C8×D43C4218yes—
120C23×C43C22×Q811yescharacteristic
121C22×D43—24no—
122C22×D43C2×C4⋊C411yescharacteristic
123C22×D43C2×C4⋊C411yescharacteristic
124C22×D43C4×Q814yes—
125C2×C4×C43—24no—
126C2×C4×C43C2×C4⋊C412yes—
127C2×C4×C43C2×C4⋊C412yes—
128C2×C4×C43C23×C411yescharacteristic
129C2×C4×C43C23×C412yes—
130C2×C4×C43C22×D411yescharacteristic
131C2×C4×C43C2×#4112yes—
132C2×Dic43—24no—
133C2×Dic43C2×C4⋊C412yes—
134C2×Dic43C2×C4⋊C411yescharacteristic
135C2×Dic43C2×C4⋊C411yescharacteristic
136C2×Dic43C2×C4⋊C412yes—
137C2×Dic43C4×Q814yes—
138C4×D43—24no—
139C4×D43—24no—
140C4×D43—24no—
141C4×D43#10818yesdirect product factor
142C4×D43C2×C4212yes—
143C4×D43C2×C4212yes—
144C4×D43#11712yes—
145C4×D43#11712yes—
146C4×D43C4×D414yes—
147C4×D43C4×D414yes—
148C8×C43—22no—
149C8×C43—28no—
150C8×C43C2×C4214yes—
151C43⋊C8—22no—
152C43⋊C8—28no—
153C43⋊C8C2×C4214yes—
154C2×C4×#108—431nomaximal, Sylow
155C22×C43—22no—
156C22×C43C22×C4⋊C411yescharacteristic
157C22×C43C2×C4×Q812yes—
158C2×D43—22no—
159C2×D43—28no—
160C2×D43C4×C4⋊C412yes—
161C2×D43C4×C4⋊C412yes—
162C2×D43C2×#10814yes—
163C4×C43—22no—
164C4×C43C2×#10814yescomplemented
165C4×C43C22×C4211yescharacteristic
166C4×C43C2×#11711yescharacteristic
167C4×C43C2×C4×D412yes—
168Dic43—22no—
169Dic43C4×C4⋊C412yes—
170Dic43C4×C4⋊C412yes—
171Dic43C2×#10814yescomplemented
172C22×#108—432no—
173C2×C4×M16—432no—
174C22×C4×C8—431no—
175C4×#108—432no—
176C4×#108—432no—
177C4×#108—431no—
178C4×#108—432no—
179C4×#108D4311yescharacteristic, direct product factor
180C2×#341—432no—
181C2×C43—22no—
182C2×C43C2×C4×C4⋊C411yescharacteristic
183C2×C43C22×#10812yes—
184D43—22no—
185D43C4×#10814yesdirect product factor
186C22×M16—434no—
187C23×C8—431no—
188C23×C8—431no—
189C22×C42—431no—
190C2×#108—434no—
191C2×#108—432no—
192C2×#108—4316no—
193C2×#108C2×D4312yes—
194C4×M16—434no—
195C4×M16—432no—
196C4×M16—862no—
197C4×M16—862no—
198C4×M16C2×D4312yes—
199C2×#97—862no—
200C2×C4×C8—431no—
201C2×C4×C8—431no—
202C2×C4×C8—431no—
203C2×C4×C8—434no—
204C2×C4×C8—434no—
205C2×C4×C8—862no—
206C2×C4×C8C2×D4311yescharacteristic
207#341—434no—
208#341—432no—
209#341C2×D4312yes—
210C43C2×C4×#10811yescharacteristic, complemented, Sylow
211C23×C4—431no—
212C23×C4—432no—
213C2×M16—434no—
214C2×M16—4316no—
215C2×M16—864no—
216C2×M16—868no—
217C2×M16C22×D4314yes—
218C22×C8—431no—
219C22×C8—432no—
220C22×C8—432no—
221C22×C8—438no—
222C22×C8—431no—
223C22×C8—432no—
224C22×C8—432no—
225C22×C8—864no—
226C22×C8—864no—
227C22×C8C22×D4311yescharacteristic
228C22×C8C22×D4311yescharacteristic
229C2×C42—432no—
230C2×C42—431no—
231C2×C42—432no—
232C2×C42—432no—
233C2×C42—431no—
234C2×C42—431no—
235C2×C42—431no—
236C2×C42—431no—
237C2×C42C22×D4311yescharacteristic
238#108—4316no—
239#108—438no—
240#108C4×D4318yesdirect product factor
241#97—22no—
242#97—864no—
243#97—862no—
244C4×C8—22no—
245C4×C8—434no—
246C4×C8—434no—
247C4×C8—434no—
248C4×C8—864no—
249C4×C8—862no—
250C4×C8C4×D4314yes—
251C24—431no—
252C22×C4—431no—
253C22×C4—432no—
254C22×C4—431no—
255C22×C4—431no—
256C22×C4—434no—
257C22×C4—431no—
258C22×C4—431no—
259C22×C4—434no—
260C22×C4—432no—
261C22×C4—432no—
262C22×C4—432no—
263C22×C4—432no—
264C22×C4—868no—
265C22×C4Q8×D4312yes—
266C22×C4C23×D4311yescharacteristic
267M16—24no—
268M16—438no—
269M16—8616no—
270M16—864no—
271M16C2×C4×D4318yes—
272C2×C8—24no—
273C2×C8—22no—
274C2×C8—432no—
275C2×C8—434no—
276C2×C8—438no—
277C2×C8—438no—
278C2×C8—432no—
279C2×C8—864no—
280C2×C8—864no—
281C2×C8—8616no—
282C2×C8—864no—
283C2×C8—862no—
284C2×C8C2×C4×D4312yes—
285C2×C8C2×C4×D4312yes—
286C2×C8C2×C4×D4314yes—
287C42—432no—
288C42—432no—
289C42—432no—
290C42—432no—
291C42—432no—
292C42—431no—
293C42—431no—
294C42C2×C4×D4312yes—
295C42D4×D4311yescharacteristic
296C42D4×D4311yescharacteristic
297C23—431no—
298C23—431no—
299C23—434no—
300C23—864no—
301C23C2×Q8×D4311yescharacteristic
302C2×C4—24no—
303C2×C4—432no—
304C2×C4—431no—
305C2×C4—431no—
306C2×C4—434no—
307C2×C4—432no—
308C2×C4—432no—
309C2×C4—432no—
310C2×C4—432no—
311C2×C4—434no—
312C2×C4—434no—
313C2×C4—438no—
314C2×C4—432no—
315C2×C4—864no—
316C2×C4—864no—
317C2×C4—864no—
318C2×C4—864no—
319C2×C4C4⋊C4×D4312yes—
320C2×C4C4⋊C4×D4312yes—
321C2×C4C22×C4×D4311yescharacteristic
322C2×C4C22×C4×D4312yes—
323C2×C4C2×D4×D4311yescharacteristic
324C2×C4#41×D4312yes—
325C8—22no—
326C8—28no—
327C8—434no—
328C8—862no—
329C8—868no—
330C8C42×D4314yes—
331C22—22no—
332C22—434no—
333C22—432no—
334C22—432no—
335C22—868no—
336C22—862no—
337C22C2×C4⋊C4×D4311yescharacteristic
338C22C4×Q8×D4312yes—
339C4—22no—
340C4—434no—
341C4—432no—
342C4—432no—
343C4—862no—
344C4#108×D4314yesdirect product factor
345C4C2×C42×D4311yescharacteristic
346C4#117×D4311yescharacteristic
347C4C4×D4×D4312yes—
348C2—22no—
349C2—434no—
350C2—862no—
351C2C4×C4⋊C4×D4311yescharacteristic
352C2C2×#108×D4312yes—
subgroupG/H
centerC42D4×D43
commutatorC4×C43C22×C42
FrattiniC22×C4C23×D43
FittingC4×#108×C43C2
socleC22×C43C22×C4⋊C4
prime radicalC23×D43C2×Q8
cosocleC22×C4×C43C24
hypercenterC4×#108D43
hypocenterC43C2×C4×#108
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C42 ◁ C2×C42 ◁ C4×#108

Complements

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

NH ≅ G/Ntype
4. #108×Dic43C2semidirect
5. C4×#13063260C2semidirect
6. C4×#13063261C2semidirect
7. #19134496C2semidirect
9. C4×#108×C43C2semidirect
16. #108×D43C4direct (N × H)
57. #13063261C2×C4semidirect
58. #13063260C2×C4semidirect
70. #108×C43C2×C4semidirect
141. C4×D43#108direct (N × H)
164. C4×C43C2×#108semidirect
171. Dic43C2×#108semidirect
179. C4×#108D43direct (N × H)
185. D43C4×#108direct (N × H)
210. C43C2×C4×#108semidirect
240. #108C4×D43direct (N × H)
344. C4#108×D43direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#108×D432
C4×M16×D432
C2×C4×C8×D432
#108×Dic432
C4×#130632602
C4×#130632612
#191344962
#341×D432
C4×#108×C432
C2×C4×#10843