Finite Group Databasebeta

← C2×#19133902 #25077718

Subgroups — C2×#19133902 #25077718

Order 11008.

1150 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 1150 conjugacy classes of subgroups — too many to draw. Only its 171 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583641C211yesmaximal, characteristic
2C2×#14583294C211yesmaximal, characteristic, complemented
3C2×#14583259C212yesmaximal, complemented
4#19133902C218yesmaximal, direct product factor
5C2×#14582638C212yesmaximal, complemented
6C2×C43×#329C211yesmaximal, characteristic, complemented
7C22×#10621885—21no—
8C22×#10621883—21no—
9#14583641—24no—
10#14583641—22no—
11#14583641C2214yes—
12C2×#13063325C2211yescharacteristic, complemented
13C2×#13063314—21no—
14C2×#13063313C2212yes—
15C2×#13063311—22no—
16C2×#13063295—22no—
17C2×#13063293—21no—
18#14583294—22no—
19#14583294C2214yescomplemented
20#14583259—24no—
21#14583259C2218yescomplemented
22C2×#13063250—22no—
23C2×#13063247—22no—
24C2×#13063236C2211yescharacteristic, complemented
25#14582638C2218yescomplemented
26C2×#124×C43C2211yescharacteristic
27C2×#97×C43C2212yescomplemented
28C43×#329C2214yescomplemented
29C24×D43—21no—
30C22×Dic86—21no—
31C22×Dic86D412yes—
32C22×D172—21no—
33C22×D172D412yes—
34C22×C22⋊D43—22no—
35C2×#10621885—24no—
36C2×#10621885—44no—
37C2×#10621883—24no—
38C2×#10621883—44no—
39C22×C43⋊C8—21no—
40#13063325—22no—
41#13063325—21no—
42#13063325C2312yescomplemented
43#13063314—24no—
44#13063314—24no—
45#13063313—22no—
46#13063313—22no—
47#13063313D414yes—
48#13063313C2314yes—
49#13063311—28no—
50#13063311—28no—
51#13063295—28no—
52#13063295—28no—
53#13063293—24no—
54#13063293—24no—
55C2×C4⋊Dic43—22no—
56C2×C22⋊Dic43—21no—
57C2×(C2×D43)⋊C4—22no—
58C2×(C2×D43)⋊C4—22no—
59C2×(C2×D43)⋊C4—22no—
60C2×C4×Dic43—21no—
61#13063250—28no—
62#13063247—28no—
63#13063236—21no—
64#13063236C2312yescomplemented
65C22×Q8×C43D411yescharacteristic
66C22×D4×C43D411yescharacteristic
67C22×C8×C43—22no—
68#124×C43—22no—
69#124×C43D412yes—
70#124×C43C2312yes—
71C2×C22⋊C4×C43—22no—
72C2×C42×C43C2311yescharacteristic
73#97×C43—22no—
74#97×C43C2314yescomplemented
75C24×C43—21no—
76C23×D43—22no—
77C23×D43—24no—
78C23×D43—82no—
79C23×D43—84no—
80C2×Q8×C43—21no—
81C2×Q8×C43—42no—
82C2×Q8×C43C2×D412yes—
83C2×D4×C43—21no—
84C2×D4×C43—42no—
85C2×D4×C43C2×D412yes—
86C22×C4×C43—21no—
87C22×C4×C43C2×D411yescharacteristic
88C22×C4×C43C2×D412yes—
89C2×C22⋊D43—28no—
90C2×C22⋊D43—84no—
91C22×Dic43—22no—
92C22×Dic43—41no—
93C2×D172—24no—
94C2×D172—22no—
95C2×D172—44no—
96C2×D172—82no—
97C2×D172C2×D414yes—
98C2×Dic86—22no—
99C2×Dic86—22no—
100C2×Dic86—44no—
101C2×Dic86—42no—
102C2×Dic86—42no—
103C2×Dic86—41no—
104C2×Dic86C2×D414yes—
105C2×C8×C43—24no—
106C2×C8×C43—44no—
107C22⋊C4×C43—24no—
108C22⋊C4×C43—24no—
109C42×C43C2×D411yescharacteristic
110C42×C43C2×D412yes—
111C42×C43C2411yescharacteristic
112C22⋊Dic43—24no—
113#10621885—48no—
114#10621883—48no—
115(C2×D43)⋊C4—28no—
116(C2×D43)⋊C4—24no—
117(C2×D43)⋊C4—24no—
118(C2×D43)⋊C4—24no—
119(C2×D43)⋊C4—24no—
120C4⋊Dic43—24no—
121C4⋊Dic43—42no—
122C4×Dic43—24no—
123C2×C43⋊C8—24no—
124C2×C43⋊C8—22no—
125C23×C43—22no—
126C23×C43—42no—
127C23×C43—44no—
128C23×C43#12011yescharacteristic
129C22×D43—24no—
130C22×D43—44no—
131C22×D43—44no—
132C22×D43—44no—
133C22×D43—84no—
134C22×D43—88no—
135C22×D43—816no—
136Q8×C43—42no—
137Q8×C43—81no—
138D4×C43—42no—
139D4×C43—81no—
140C2×C4×C43—22no—
141C2×C4×C43—24no—
142C2×C4×C43—22no—
143C2×C4×C43—42no—
144C2×C4×C43#12012yes—
145C2×C4×C43#12011yescharacteristic
146C2×C4×C43C22×D412yes—
147C2×C4×C43C22×D411yescharacteristic
148C22⋊D43—88no—
149C2×Dic43—24no—
150C2×Dic43—44no—
151C2×Dic43—42no—
152C2×Dic43—82no—
153D172—44no—
154D172—82no—
155D172—84no—
156Dic86—44no—
157Dic86—42no—
158Dic86—42no—
159Dic86—82no—
160Dic86—82no—
161C8×C43—44no—
162C43⋊C8—24no—
163C2×#1659—431nomaximal, Sylow
164C22×C43—42no—
165C22×C43—44no—
166C22×C43—84no—
167C22×C43#45312yes—
168C22×C43#45514yes—
169C22×C43C2×#12011yescharacteristic
170C2×D43—44no—
171C2×D43—44no—
172C2×D43—44no—
173C2×D43—816no—
174C2×D43—88no—
175C4×C43—21no—
176C4×C43—21no—
177C4×C43—22no—
178C4×C43—22no—
179C4×C43—42no—
180Dic43—44no—
181Dic43—82no—
182C2×H(3,𝔽4)—431no—
183C2×#497—431no—
184C2×#489—432no—
185#1659—438no—
186C2×#329—432no—
187C2×#329D4311yescharacteristic, complemented
188C2×C43—82no—
189C2×C43#165914yescomplemented
190C2×C43C2×#45311yescharacteristic
191C2×C43C2×#45512yes—
192D43—84no—
193C22×Q16—861no—
194C22×SD16—861no—
195H(3,𝔽4)—434no—
196H(3,𝔽4)—864no—
197H(3,𝔽4)—862no—
198C2×C4⋊Q8—431no—
199C2×#124—432no—
200C2×#124—862no—
201C2×#124—861no—
202C2×#124C2×D4311yescharacteristic
203C2×#120—862no—
204C2×#120—861no—
205#497—434no—
206#497—862no—
207#489—438no—
208#489—864no—
209C2×#103—862no—
210C2×#102—862no—
211C2×#97—431no—
212C2×#97C2×D4312yescomplemented
213#329—438no—
214#329C2×D4314yescomplemented
215C43C2×#165911yescharacteristic, complemented, Sylow
216C25—861no—
217C22×Q8—432no—
218C22×Q8—861no—
219C22×Q8D17211yescharacteristic
220C22×D4—432no—
221C22×D4—861no—
222C22×D4—862no—
223C22×D4D17211yescharacteristic
224C2×Q16—864no—
225C2×Q16—1724no—
226C2×SD16—864no—
227C2×SD16—1724no—
228C22×C8—22no—
229C22×C8—861no—
230C4⋊Q8—432no—
231C4⋊Q8—861no—
232C4⋊Q8—862no—
233#124—22no—
234#124—434no—
235#124—434no—
236#124—868no—
237#124—868no—
238#124—864no—
239#124—864no—
240#124—862no—
241#124—862no—
242#124D17212yes—
243#124C22×D4312yes—
244#120—868no—
245#120—868no—
246#120—864no—
247#120—864no—
248C2×C4⋊C4—862no—
249C2×C22⋊C4—22no—
250C2×C22⋊C4—862no—
251C2×C22⋊C4—861no—
252C2×C22⋊C4—862no—
253C2×C22⋊C4—862no—
254C2×C42—861no—
255C2×C42C22×D4311yescharacteristic
256#103—868no—
257#102—868no—
258#97—22no—
259#97—432no—
260#97—861no—
261#97C22×D4314yescomplemented
262C24—21no—
263C24—864no—
264C24—862no—
265C24—3442no—
266C24—3444no—
267C2×Q8—21no—
268C2×Q8—42no—
269C2×Q8—434no—
270C2×Q8—862no—
271C2×Q8—862no—
272C2×Q8—1722no—
273C2×Q8—1722no—
274C2×Q8—1724no—
275C2×Q8—1721no—
276C2×Q8C2×D17212yes—
277C2×D4—21no—
278C2×D4—42no—
279C2×D4—434no—
280C2×D4—864no—
281C2×D4—868no—
282C2×D4—862no—
283C2×D4—3442no—
284C2×D4—3444no—
285C2×D4—1724no—
286C2×D4C2×D17212yes—
287C22×C4—21no—
288C22×C4—862no—
289C22×C4—1721no—
290C22×C4C2×D17211yescharacteristic
291C22×C4D4×D4312yes—
292Q16—1728no—
293SD16—1728no—
294C2×C8—24no—
295C2×C8—44no—
296C2×C8—864no—
297C2×C8—862no—
298C4⋊C4—864no—
299C4⋊C4—1722no—
300C22⋊C4—24no—
301C22⋊C4—24no—
302C22⋊C4—868no—
303C22⋊C4—864no—
304C22⋊C4—864no—
305C22⋊C4—864no—
306C22⋊C4—864no—
307C22⋊C4—864no—
308C42—864no—
309C42C2×D17211yescharacteristic
310C42D4×D4312yes—
311C42C23×D4311yescharacteristic
312C23—22no—
313C23—42no—
314C23—44no—
315C23—864no—
316C23—3444no—
317C23—3448no—
318C23—34416no—
319C23—1724no—
320C23—1724no—
321C23—1724no—
322C23#1306329511yescharacteristic
323Q8—42no—
324Q8—81no—
325Q8—3442no—
326Q8—3442no—
327Q8—1722no—
328Q8—1722no—
329Q8—1724no—
330D4—42no—
331D4—81no—
332D4—3442no—
333D4—3444no—
334D4—3448no—
335D4—1724no—
336C2×C4—22no—
337C2×C4—24no—
338C2×C4—22no—
339C2×C4—42no—
340C2×C4—864no—
341C2×C4—3442no—
342C2×C4—1722no—
343C2×C4—1724no—
344C2×C4#1306329512yes—
345C2×C4#1306329511yescharacteristic
346C2×C4C2×D4×D4312yes—
347C2×C4C22×D17211yescharacteristic
348C8—44no—
349C8—864no—
350C22—42no—
351C22—44no—
352C22—84no—
353C22—34416no—
354C22—3448no—
355C22—1724no—
356C22—1724no—
357C22—1724no—
358C22#1458306912yes—
359C22#1458307814yes—
360C22C2×#1306329511yescharacteristic
361C4—21no—
362C4—21no—
363C4—22no—
364C4—22no—
365C4—42no—
366C4—3442no—
367C4—1724no—
368C2—82no—
369C2—3444no—
370C2#1913390214yesdirect product factor
371C2C2×#1458306911yescharacteristic
372C2C2×#1458307812yes—
subgroupG/H
centerC23#13063295
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC2×C43×#329C2
socleC23×C43#120
prime radicalC2×#14583641C2
hypercenterC2×#329D43
hypocenterC43C2×#1659
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#329

Complements

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

NH ≅ G/Ntype
2. C2×#14583294C2semidirect
3. C2×#14583259C2semidirect
4. #19133902C2direct (N × H)
5. C2×#14582638C2semidirect
6. C2×C43×#329C2semidirect
12. C2×#13063325C22semidirect
19. #14583294C22semidirect
21. #14583259C22semidirect
24. C2×#13063236C22semidirect
25. #14582638C22semidirect
27. C2×#97×C43C22semidirect
28. C43×#329C22semidirect
42. #13063325C23semidirect
64. #13063236C23semidirect
74. #97×C43C23semidirect
187. C2×#329D43semidirect
189. C2×C43#1659semidirect
212. C2×#97C2×D43semidirect
214. #329C2×D43semidirect
215. C43C2×#1659semidirect
261. #97C22×D43semidirect
370. C2#19133902direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836412
C2×#145832942
C2×#145832592
#191339022
C2×#145826382
C2×C43×#3292
C2×#165943