Finite Group Databasebeta

← C2×#19139983 #25267830

Subgroups — C2×#19139983 #25267830

Order 11008.

2574 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063317C211yesmaximal, characteristic
2#19139983C2116yesmaximal, direct product factor
3C2×#14582830C212yesmaximal
4C2×#14582818C212yesmaximal
5C2×#14582797C212yesmaximal
6C2×#14582797C212yesmaximal
7C2×#14582794C214yesmaximal
8C2×C4×C4⋊Dic43C211yesmaximal, characteristic
9C22×C4×Q8×C43C211yesmaximal, characteristic
10C2×#13063317—28no—
11C2×#13063317C2218yes—
12C22×C4⋊Dic43C2211yescharacteristic
13C22×C4⋊Dic43C2211yescharacteristic
14C22×C4⋊Dic43C2212yes—
15C22×Dic43⋊C4C2214yes—
16C22×Dic43⋊C4C2212yes—
17C22×Dic43⋊C4C2212yes—
18C22×Dic43⋊C4C2214yes—
19C22×C4×Dic43C2212yes—
20#14582830C22116yes—
21#14582818C22116yes—
22#14582797C22116yes—
23#14582797C22116yes—
24#14582794C22132yes—
25C4×C4⋊Dic43C2218yes—
26C2×C43⋊#95C2214yes—
27C2×C43⋊#95C2212yes—
28C2×C43⋊#95C2214yes—
29C23×Q8×C43C2211yescharacteristic
30C2×C4×Q8×C43—28no—
31C2×C4×Q8×C43C2218yes—
32C22×C4⋊C4×C43C2212yes—
33C22×C4⋊C4×C43C2211yescharacteristic
34C22×C42×C43C2212yes—
35C22×C42×C43C2211yescharacteristic
36C23×Dic43C2312yes—
37C23×Dic43C2312yes—
38C23×Dic43C2314yes—
39#13063317—232no—
40C2×C4⋊Dic43—24no—
41C2×C4⋊Dic43—24no—
42C2×C4⋊Dic43Q8116yescomplemented
43C2×C4⋊Dic43C2314yes—
44C2×C4⋊Dic43C2314yes—
45C2×C4⋊Dic43C2318yes—
46C2×Dic43⋊C4—28no—
47C2×Dic43⋊C4—28no—
48C2×Dic43⋊C4—216no—
49C2×Dic43⋊C4—48no—
50C2×Dic43⋊C4C2318yes—
51C2×Dic43⋊C4C23116yes—
52C2×Dic43⋊C4C2318yes—
53C2×Dic43⋊C4C23116yes—
54C2×C4×Dic43—44no—
55C2×C4×Dic43C2318yes—
56C43⋊#95C23116yes—
57C43⋊#95C23116yes—
58C43⋊#95C2318yes—
59C22×Q8×C43—24no—
60C22×Q8×C43—28no—
61C22×Q8×C43C2314yes—
62C23×C4×C43C2312yes—
63C23×C4×C43C2311yescharacteristic
64C23×C4×C43C2311yescharacteristic
65C23×C4×C43C2312yes—
66C23×C4×C43C2311yescharacteristic
67C4×Q8×C43—232no—
68C2×C4⋊C4×C43—28no—
69C2×C4⋊C4×C43—24no—
70C2×C4⋊C4×C43C2318yes—
71C2×C4⋊C4×C43C2314yes—
72C2×C42×C43—28no—
73C2×C42×C43D418yes—
74C2×C42×C43C2318yes—
75C2×C42×C43C2314yes—
76C24×C43C2411yescharacteristic
77C2×Q8×C43—232no—
78C2×Q8×C43—28no—
79C2×Q8×C43—216no—
80C22×C4×C43—24no—
81C22×C4×C43—24no—
82C22×C4×C43—24no—
83C22×C4×C43—24no—
84C22×C4×C43—22no—
85C22×C4×C43—24no—
86C22×C4×C43—22no—
87C22×C4×C43—24no—
88C22×C4×C43C2×D414yes—
89C22×C4×C43C2×D414yes—
90C22×C4×C43C2×D414yes—
91C22×C4×C43C2×Q818yes—
92C22×C4×C43#4118yes—
93C22×C4×C43C2414yes—
94C22×C4×C43C2412yes—
95C22×C4×C43C2412yes—
96C22×C4×C43C2414yes—
97C22×C4×C43C2412yes—
98C22×Dic43—24no—
99C22×Dic43—24no—
100C22×Dic43—28no—
101C22×Dic43—28no—
102C22×Dic43—28no—
103C22×Dic43—24no—
104C22×Dic43—24no—
105C22×Dic43C2×Q8116yes—
106C22×Dic43C2414yes—
107C22×Dic43C2414yes—
108C22×Dic43C2418yes—
109C4⋊C4×C43—216no—
110C4⋊C4×C43—28no—
111C42×C43—216no—
112C42×C43C2×D4116yes—
113C4⋊Dic43—28no—
114C4⋊Dic43—28no—
115C4⋊Dic43C2×Q8132yescomplemented
116Dic43⋊C4—216no—
117Dic43⋊C4—216no—
118Dic43⋊C4—232no—
119Dic43⋊C4—416no—
120C4×Dic43—48no—
121C23×C43C22×D412yes—
122C23×C43C22×Q814yes—
123C23×C43C2×#4114yes—
124C23×C43H(5,𝔽2)12yes—
125C23×C432−1+412yes—
126C23×C43C2511yescharacteristic
127Q8×C43—232no—
128C2×C4×C43—28no—
129C2×C4×C43—216no—
130C2×C4×C43—28no—
131C2×C4×C43—24no—
132C2×C4×C43—24no—
133C2×C4×C43—24no—
134C2×C4×C43—22no—
135C2×C4×C43—22no—
136C2×C4×C43—24no—
137C2×C4×C43—24no—
138C2×C4×C43—24no—
139C2×C4×C43—48no—
140C2×C4×C43C4⋊Q8116yes—
141C2×C4×C43C22×D414yes—
142C2×C4×C43C22×D414yes—
143C2×C4×C43C22×D414yes—
144C2×C4×C43C22×Q818yes—
145C2×C4×C43C2×#4118yes—
146C2×Dic43—232no—
147C2×Dic43—28no—
148C2×Dic43—28no—
149C2×Dic43—24no—
150C2×Dic43—24no—
151C2×Dic43—28no—
152C2×Dic43—24no—
153C2×Dic43—24no—
154C2×Dic43—48no—
155C2×Dic43—48no—
156C2×Dic43C22×Q8116yes—
157C2×#2584—431nomaximal, Sylow
158C22×C43#52514yes—
159C22×C43C2×C4⋊Q814yes—
160C22×C43#53714yes—
161C22×C43#55418yes—
162C22×C43#55718yes—
163C22×C43C23×D411yescharacteristic
164C22×C43C23×Q812yes—
165C22×C43C22×#4112yes—
166C22×C43C2×H(5,𝔽2)11yescharacteristic
167C22×C43C2×2−1+411yescharacteristic
168C4×C43—24no—
169C4×C43—28no—
170C4×C43—24no—
171C4×C43—44no—
172C4×C43C2×C4⋊Q818yes—
173Dic43—216no—
174Dic43—44no—
175Dic43—44no—
176C22×#125—431no—
177C22×C4×Q8D4311yescharacteristic
178#2584—4316no—
179C2×#398—432no—
180C2×#395—432no—
181C2×#389—432no—
182C2×#389—432no—
183C2×#389—434no—
184C2×C4×C4⋊C4—431no—
185C2×C43#258418yescomplemented
186C2×C43C2×#52511yescharacteristic
187C2×C43C22×C4⋊Q811yescharacteristic
188C2×C43C2×#53711yescharacteristic
189C2×C43C2×#55412yes—
190C2×C43C2×#55712yes—
191C23×Q8C2×D4311yescharacteristic
192C2×#125—438no—
193C2×#125—868no—
194C2×C4×Q8—28no—
195C2×C4×Q8C2×D4318yes—
196C22×C4⋊C4—432no—
197C22×C4⋊C4—432no—
198C22×C4⋊C4—434no—
199C22×C4⋊C4—432no—
200C22×C4⋊C4—431no—
201C22×C4⋊C4—431no—
202C22×C4⋊C4—434no—
203C22×C4⋊C4C2×D4311yescharacteristic
204C22×C4⋊C4C2×D4312yes—
205C22×C42—432no—
206C22×C42C2×D4312yes—
207C22×C42C2×D4311yescharacteristic
208#398—4316no—
209#395—4316no—
210#389—4332no—
211#389—4316no—
212#389—4316no—
213C4×C4⋊C4—438no—
214C2×#95—432no—
215C2×#95—434no—
216C2×#95—434no—
217C43C2×#258411yescharacteristic, complemented, Sylow
218C22×Q8—28no—
219C22×Q8—24no—
220C22×Q8C22×D4314yes—
221C23×C4—434no—
222C23×C4—432no—
223C23×C4—432no—
224C23×C4C22×D4312yes—
225C23×C4C22×D4312yes—
226C23×C4C22×D4311yescharacteristic
227C23×C4C22×D4311yescharacteristic
228C23×C4C22×D4311yescharacteristic
229#125—8632no—
230C4×Q8—232no—
231C2×C4⋊C4—28no—
232C2×C4⋊C4—24no—
233C2×C4⋊C4—4316no—
234C2×C4⋊C4—438no—
235C2×C4⋊C4—438no—
236C2×C4⋊C4—438no—
237C2×C4⋊C4—434no—
238C2×C4⋊C4—434no—
239C2×C4⋊C4—4316no—
240C2×C4⋊C4—4316no—
241C2×C4⋊C4—8616no—
242C2×C4⋊C4—868no—
243C2×C4⋊C4—868no—
244C2×C4⋊C4—864no—
245C2×C4⋊C4—864no—
246C2×C4⋊C4—1728no—
247C2×C4⋊C4C22×D4318yes—
248C2×C4⋊C4C22×D4314yes—
249C2×C42—28no—
250C2×C42—438no—
251C2×C42—1724no—
252C2×C42C22⋊D4318yes—
253C2×C42C22×D4318yes—
254C2×C42C22×D4314yes—
255#95—438no—
256#95—4316no—
257#95—4316no—
258C24C23×D4311yescharacteristic
259C2×Q8—232no—
260C2×Q8—28no—
261C2×Q8—216no—
262C22×C4—24no—
263C22×C4—24no—
264C22×C4—24no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—24no—
268C22×C4—24no—
269C22×C4—24no—
270C22×C4—4316no—
271C22×C4—438no—
272C22×C4—434no—
273C22×C4—434no—
274C22×C4—868no—
275C22×C4—868no—
276C22×C4—864no—
277C22×C4—864no—
278C22×C4—868no—
279C22×C4—864no—
280C22×C4—864no—
281C22×C4#1062189818yes—
282C22×C4Q8×D4318yes—
283C22×C4C2×C22⋊D4314yes—
284C22×C4C2×C22⋊D4314yes—
285C22×C4C2×C22⋊D4314yes—
286C22×C4C23×D4314yes—
287C22×C4C23×D4312yes—
288C22×C4C23×D4312yes—
289C22×C4C23×D4314yes—
290C22×C4C23×D4312yes—
291C4⋊C4—216no—
292C4⋊C4—28no—
293C4⋊C4—4332no—
294C4⋊C4—8616no—
295C4⋊C4—8616no—
296C4⋊C4—868no—
297C4⋊C4—868no—
298C4⋊C4—8632no—
299C4⋊C4—17216no—
300C42—216no—
301C42—1728no—
302C42C2×C22⋊D43116yes—
303C23C22×C22⋊D4312yes—
304C23C2×Q8×D4314yes—
305C23C2×#1062189814yes—
306C23#1306337112yes—
307C23#1306337212yes—
308C23C24×D4311yescharacteristic
309Q8—232no—
310C2×C4—216no—
311C2×C4—28no—
312C2×C4—24no—
313C2×C4—24no—
314C2×C4—24no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—28no—
318C2×C4—24no—
319C2×C4—24no—
320C2×C4—24no—
321C2×C4—48no—
322C2×C4—4316no—
323C2×C4—8632no—
324C2×C4—868no—
325C2×C4—868no—
326C2×C4—864no—
327C2×C4—864no—
328C2×C4—868no—
329C2×C4—864no—
330C2×C4—864no—
331C2×C4—1728no—
332C2×C4—1728no—
333C2×C4#13063323116yes—
334C2×C4C22×C22⋊D4314yes—
335C2×C4C22×C22⋊D4314yes—
336C2×C4C22×C22⋊D4314yes—
337C2×C4C2×Q8×D4318yes—
338C2×C4C2×#1062189818yes—
339C22#1458341014yes—
340C22C2×#1306332314yes—
341C22#1458347714yes—
342C22#1458360918yes—
343C22#1458362718yes—
344C22C23×C22⋊D4311yescharacteristic
345C22C22×Q8×D4312yes—
346C22C22×#1062189812yes—
347C22C2×#1306337111yescharacteristic
348C22C2×#1306337211yescharacteristic
349C4—24no—
350C4—28no—
351C4—24no—
352C4—44no—
353C4—8616no—
354C4—1724no—
355C4—1724no—
356C4C2×#1306332318yes—
357C2#1913998318yesdirect product factor
358C2C2×#1458341011yescharacteristic
359C2C22×#1306332311yescharacteristic
360C2C2×#1458347711yescharacteristic
361C2C2×#1458360912yes—
362C2C2×#1458362712yes—
subgroupG/H
centerC24C23×D43
commutator, cosocleC23×C43C25
FrattiniC23C24×D43
FittingC22×C4×Q8×C43C2
socle, prime radicalC24×C43C24
hypercenterC22×C4×Q8D43
hypocenterC43C2×#2584
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22×C4×Q8

Complements

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

NH ≅ G/Ntype
2. #19139983C2direct (N × H)
42. C2×C4⋊Dic43Q8semidirect
115. C4⋊Dic43C2×Q8semidirect
185. C2×C43#2584semidirect
217. C43C2×#2584semidirect
357. C2#19139983direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633172
#191399832
C2×#145828302
C2×#145828182
C2×#145827972
C2×#145827942
C2×C4×C4⋊Dic432
C22×C4×Q8×C432
C2×#258443