Finite Group Databasebeta

← C2×#10591484 #11874191

Subgroups — C2×#10591484 #11874191

Order 1152.

1769 conjugacy classes of subgroups; only the 260 normal subgroups are shown.

normal subgroups only

This group has 1769 conjugacy classes of subgroups — too many to draw. Only its 260 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×#64149C211yesmaximal, characteristic, complemented
2C22×C3×#213C212yesmaximal, complemented
3C2×#63914C211yesmaximal, characteristic, complemented
4C22×#3714C212yesmaximal, complemented
5#10591484C218yesmaximal, direct product factor
6C2×#63553C211yesmaximal, characteristic, complemented
7C2×#5151—32nomaximal
8C22×C32×D4C2211yescharacteristic
9C22×#638—22no—
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×C3×D12C2212yes—
12C22×#625—22no—
13#64149—22no—
14#64149C2214yescomplemented
15C2×C4×C3⋊Dic3C2211yescharacteristic
16C2×C3×#213—28no—
17C2×C3×#213C2218yescomplemented
18C22×C3×C3⋊C8C2212yes—
19#63914—22no—
20#63914C2214yescomplemented
21C2×#3714—28no—
22C2×#3714C2218yescomplemented
23#63553C2214yescomplemented
24C22×C3×D8—32no—
25C2×#940—32no—
26C2×#940—32no—
27C2×#940—61no—
28C22×#213—32no—
29C22×#213D312yescomplemented
30C22×D24—32no—
31#5151—316no—
32C2×C8×Dic3—32no—
33C24×C32—21no—
34C23×C3⋊D3—21no—
35C23×C3×D3—22no—
36C2×C32×D4—24no—
37C2×C32×D4—21no—
38C2×C32×D4C2312yes—
39C22×C32×C4C2311yescharacteristic
40C2×#638—28no—
41C2×#638—48no—
42C22×C3⋊Dic3D412yes—
43C2×C4⋊(C3⋊D3)—24no—
44C2×C4⋊(C3⋊D3)—21no—
45C2×C4⋊(C3⋊D3)C2312yes—
46C2×C3×D12—24no—
47C2×C3×D12—24no—
48C2×C3×D12—22no—
49C2×C3×D12C2314yes—
50C2×#625—28no—
51C2×#625—48no—
52C4×C3⋊Dic3D412yes—
53C4×C3⋊Dic3C2312yes—
54C3×#213—216no—
55C2×C3×C3⋊C8D418yescomplemented
56C2×C3×C3⋊C8C2314yes—
57#3714—216no—
58C2×#493—91noSylow
59C22×C3×D4—21no—
60C22×C3×D4—32no—
61C22×C3×D4C2×D312yes—
62C22×#67—64no—
63C22×#67—64no—
64C22×#67—64no—
65C22×D12—32no—
66C22×D12—61no—
67C22×D12C2×D312yes—
68C2×C3×D8—38no—
69C2×C3×D8—68no—
70C22×C3×C8—32no—
71#940—38no—
72#940—38no—
73#940—64no—
74#940—64no—
75#940—64no—
76#940—64no—
77C2×#213—28no—
78C2×#213—38no—
79C2×#213—68no—
80C2×#213C2×D318yescomplemented
81C2×C4×Dic3—32no—
82C2×C4×Dic3—61no—
83C22×C3⋊C8C2×D312yes—
84C2×D24—38no—
85C2×D24—68no—
86C8×Dic3—38no—
87C23×C32—22no—
88C23×C32—42no—
89C23×C32—44no—
90C23×C32C2×D411yescharacteristic
91C22×C3⋊D3—22no—
92C22×C3⋊D3—42no—
93C22×C3⋊D3—44no—
94C22×C3×D3—24no—
95C22×C3×D3—44no—
96C22×C3×D3—48no—
97C32×D4—24no—
98C32×D4—42no—
99C2×C32×C4C2×D411yescharacteristic
100C2×C32×C4C2×D414yes—
101C2×C32×C4C2411yescharacteristic
102#638—416no—
103C2×C3⋊Dic3D818yescomplemented
104C2×C3⋊Dic3C2×D414yes—
105C4⋊(C3⋊D3)—24no—
106C4⋊(C3⋊D3)—42no—
107C3×D12—24no—
108C3×D12—24no—
109C3×D12—44no—
110#625—416no—
111C3×C3⋊C8C2×D418yescomplemented
112C22×D8—32no—
113C22×D8—92no—
114C2×#127—91no—
115C2×#127—91no—
116#493—98no—
117C2×C4×C8—91no—
118C24×C3—22no—
119C24×C3—22no—
120C24×C3—62no—
121C23×D3—22no—
122C23×D3—62no—
123C23×D3—62no—
124C2×C3×D4—22no—
125C2×C3×D4—24no—
126C2×C3×D4—22no—
127C2×C3×D4—24no—
128C2×C3×D4—22no—
129C2×C3×D4—34no—
130C2×C3×D4—44no—
131C2×C3×D4—64no—
132C2×C3×D4—62no—
133C2×C3×D4—64no—
134C2×C3×D4C22×D314yes—
135C22×C3×C4—21no—
136C22×C3×C4C22×D312yes—
137C2×#67—616no—
138C2×#67—616no—
139C2×#67—616no—
140C2×#67—1216no—
141C2×#67—1216no—
142C2×#67—1216no—
143C22×Dic3—34no—
144C22×Dic3—62no—
145C2×D12—24no—
146C2×D12—24no—
147C2×D12—22no—
148C2×D12—34no—
149C2×D12—62no—
150C2×D12—64no—
151C2×D12—64no—
152C2×D12—62no—
153C2×D12—62no—
154C2×D12—124no—
155C2×D12C22×D314yes—
156C3×D8—616no—
157C2×C3×C8—38no—
158C2×C3×C8—34no—
159#213—216no—
160#213—616no—
161C4×Dic3—34no—
162C4×Dic3—34no—
163C4×Dic3—62no—
164C4×Dic3—62no—
165C2×C3⋊C8#6718yescomplemented
166C2×C3⋊C8C22×D314yes—
167D24—616no—
168C22×C32—42no—
169C22×C32—44no—
170C22×C32—84no—
171C22×C32#12712yes—
172C22×C32C2×D814yes—
173C22×C32C22×D411yescharacteristic
174C2×C3⋊D3—42no—
175C2×C3⋊D3—44no—
176C2×C3⋊D3—84no—
177C2×C3×D3—44no—
178C2×C3×D3—48no—
179C2×C3×D3—88no—
180C32×C4#12712yes—
181C32×C4C22×D412yes—
182C3⋊Dic3C2×D818yescomplemented
183C22×D4—32no—
184C22×D4—91no—
185C22×D4—182no—
186C22×D4—182no—
187C22×D4D3211yescharacteristic
188C2×D8—38no—
189C2×D8—68no—
190C2×D8—98no—
191C2×D8—188no—
192C22×C8—32no—
193#127—94no—
194#127—94no—
195#127—182no—
196#127—182no—
197C2×C42—91no—
198C4×C8—94no—
199C23×C3—24no—
200C23×C3—24no—
201C23×C3—21no—
202C23×C3—48no—
203C23×C3—44no—
204C23×C3—48no—
205C23×C3—44no—
206C23×C3—64no—
207C23×C3—128no—
208C23×C3—124no—
209C23×C3D3×D412yes—
210C22×D3—24no—
211C22×D3—48no—
212C22×D3—44no—
213C22×D3—64no—
214C22×D3—64no—
215C22×D3—124no—
216C22×D3—128no—
217C22×D3—128no—
218C22×D3—124no—
219C3×D4—24no—
220C3×D4—24no—
221C3×D4—44no—
222C3×D4—44no—
223C3×D4—44no—
224C3×D4—64no—
225C3×D4—64no—
226C3×D4—124no—
227C2×C3×C4—21no—
228C2×C3×C4—24no—
229C2×C3×C4—21no—
230C2×C3×C4D3×D414yes—
231C2×C3×C4D3×D412yes—
232C2×C3×C4C2×#6714yes—
233C2×C3×C4C23×D312yes—
234#67—1232no—
235#67—1232no—
236#67—1232no—
237C2×Dic3—316no—
238C2×Dic3—38no—
239C2×Dic3—68no—
240C2×Dic3—64no—
241D12—24no—
242D12—24no—
243D12—44no—
244D12—64no—
245D12—64no—
246D12—124no—
247D12—124no—
248D12—124no—
249C3×C8—38no—
250C3⋊C8C2×#6718yescomplemented
251C2×C32—82no—
252C2×C32#49314yescomplemented
253C2×C32C2×#12711yescharacteristic
254C2×C32C22×D812yes—
255C3⋊D3—82no—
256C3×D3—84no—
257C24—21no—
258C24—62no—
259C24—181no—
260C2×D4—24no—
261C2×D4—21no—
262C2×D4—34no—
263C2×D4—64no—
264C2×D4—64no—
265C2×D4—62no—
266C2×D4—92no—
267C2×D4—188no—
268C2×D4—188no—
269C2×D4—184no—
270C2×D4—181no—
271C2×D4—368no—
272C2×D4—368no—
273C2×D4C2×D3212yes—
274C22×C4—92no—
275C22×C4C2×D3211yescharacteristic
276D8—616no—
277D8—1816no—
278C2×C8—34no—
279C2×C8—38no—
280C42—92no—
281C42—92no—
282C22×C3—21no—
283C22×C3—24no—
284C22×C3—22no—
285C22×C3—48no—
286C22×C3—44no—
287C22×C3—48no—
288C22×C3—44no—
289C22×C3—88no—
290C22×C3—88no—
291C22×C3—128no—
292C22×C3—124no—
293C22×C3—248no—
294C22×C3D3×D818yes—
295C22×C3#94014yes—
296C22×C3C2×D3×D412yes—
297C2×D3—48no—
298C2×D3—44no—
299C2×D3—88no—
300C2×D3—124no—
301C2×D3—128no—
302C2×D3—128no—
303C2×D3—124no—
304C2×D3—248no—
305C2×D3—248no—
306C3×C4—22no—
307C3×C4—22no—
308C3×C4#94014yes—
309C3×C4C2×D3×D412yes—
310C3×C4C22×#6712yes—
311Dic3—316no—
312Dic3—68no—
313C32C2×#49311yescharacteristic, complemented, Sylow
314C23—22no—
315C23—44no—
316C23—42no—
317C23—64no—
318C23—128no—
319C23—124no—
320C23—182no—
321C23—364no—
322C23—362no—
323C23#381111yescharacteristic
324D4—24no—
325D4—42no—
326D4—64no—
327D4—64no—
328D4—124no—
329D4—184no—
330D4—3616no—
331D4—3616no—
332D4—362no—
333C2×C4—94no—
334C2×C4—98no—
335C2×C4D3×#6714yes—
336C2×C4#381111yescharacteristic
337C2×C4C22×D3211yescharacteristic
338C8—38no—
339C2×C3—22no—
340C2×C3—21no—
341C2×C3—24no—
342C2×C3—84no—
343C2×C3—84no—
344C2×C3—244no—
345C2×C3#515118yescomplemented
346C2×C3C2×D3×D814yes—
347C2×C3C2×#94012yes—
348D3—84no—
349D3—244no—
350D3—244no—
351C22—44no—
352C22—42no—
353C22—84no—
354C22—128no—
355C22—124no—
356C22—248no—
357C22—364no—
358C22—362no—
359C22—724no—
360C22#6392614yes—
361C22#6397912yes—
362C22C2×#381111yescharacteristic
363C4—98no—
364C4#6397912yes—
365C4C2×D3×#6712yes—
366C3—21no—
367C3C2×#515112yescomplemented
368C2—82no—
369C2—244no—
370C2—722no—
371C2#1059148414yesdirect product factor
372C2C2×#6392612yes—
373C2C2×#6397911yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC23×C32C2×D4
hypercenterC22×D4D32
hypocenterC32C2×#493
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×#64149C2semidirect
2. C22×C3×#213C2semidirect
3. C2×#63914C2semidirect
4. C22×#3714C2semidirect
5. #10591484C2direct (N × H)
6. C2×#63553C2semidirect
14. #64149C22semidirect
17. C2×C3×#213C22semidirect
20. #63914C22semidirect
22. C2×#3714C22semidirect
23. #63553C22semidirect
29. C22×#213D3semidirect
55. C2×C3×C3⋊C8D4semidirect
80. C2×#213C2×D3semidirect
103. C2×C3⋊Dic3D8semidirect
111. C3×C3⋊C8C2×D4semidirect
165. C2×C3⋊C8#67semidirect
182. C3⋊Dic3C2×D8semidirect
250. C3⋊C8C2×#67semidirect
252. C2×C32#493semidirect
313. C32C2×#493semidirect
345. C2×C3#5151semidirect
367. C3C2×#5151semidirect
371. C2#10591484direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641492
C22×C3×#2132
C2×#639142
C22×#37142
#105914842
C2×#635532
C2×#51513