Finite Group Databasebeta

← C2×#10592446 #11864770

Subgroups — C2×#10592446 #11864770

Order 1152.

2532 conjugacy classes of subgroups; only the 313 normal subgroups are shown.

normal subgroups only

This group has 2532 conjugacy classes of subgroups — too many to draw. Only its 313 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×#64361C211yesmaximal, characteristic, complemented
2C2×#64149C211yesmaximal, characteristic, complemented
3C2×#64117C212yesmaximal, complemented
4C2×C32×#100C211yesmaximal, characteristic, complemented
5C2×#63652C212yesmaximal, complemented
6#10592446C218yesmaximal, direct product factor
7C2×#4747—34nomaximal
8C22×C32×D4C2211yescharacteristic
9C22×#638—22no—
10C22×#638—22no—
11#64361—22no—
12#64361—24no—
13#64361C2214yescomplemented
14C2×#3830—22no—
15C2×D4×C3⋊D3—22no—
16C2×#3828C2212yes—
17C22×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
18C2×C32×M16C2212yescomplemented
19#64149—22no—
20#64149C2214yescomplemented
21C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
22#64117—24no—
23#64117C2218yescomplemented
24C2×#3745—22no—
25C2×#3744—22no—
26C32×#100C2214yescomplemented
27#63652C2218yescomplemented
28C2×#1004—34no—
29C2×#940—34no—
30C2×#908—38no—
31C2×C3×#100D314yescomplemented
32C2×#825—38no—
33#4747—332no—
34C24×C32D412yes—
35C23×C3⋊D3—22no—
36C23×C3⋊D3—21no—
37C2×C32×D4—22no—
38C2×C32×D4—22no—
39C2×C32×D4D412yes—
40C2×C32×D4C2312yes—
41C22×C32×C4C2311yescharacteristic
42C2×#638—24no—
43C2×#638—28no—
44C2×#638—22no—
45C2×#638—28no—
46C2×#638—28no—
47C2×#638—48no—
48C22×C3⋊Dic3—22no—
49C22×C3⋊Dic3—21no—
50#3830—28no—
51#3830—28no—
52D4×C3⋊D3—28no—
53D4×C3⋊D3—28no—
54#3828—22no—
55#3828—22no—
56#3828D414yescomplemented
57#3828C2314yes—
58C2×C4⋊(C3⋊D3)—22no—
59C2×C4⋊(C3⋊D3)—22no—
60C2×C4⋊(C3⋊D3)—21no—
61C2×C4⋊(C3⋊D3)D412yescomplemented
62C2×C4⋊(C3⋊D3)C2312yescomplemented
63C2×C4×C3⋊D3—22no—
64C2×#634D412yescomplemented
65C32×M16—22no—
66C32×M16C2314yescomplemented
67C2×C32×C8—22no—
68C4×C3⋊Dic3—21no—
69C4×C3⋊Dic3C2312yescomplemented
70#3745—28no—
71#3744—28no—
72C2×#453—91noSylow
73C22×C3×D4C2×D314yes—
74C22×#67—68no—
75C22×#67—68no—
76#1004—316no—
77#1004—616no—
78#1004—68no—
79C2×#237—68no—
80C2×D3×D4—68no—
81C2×#235—38no—
82C22×D12—34no—
83C2×C3×M16C2×D318yescomplemented
84#940—316no—
85#940—68no—
86C2×C4×Dic3—34no—
87#908—332no—
88#908—616no—
89C2×D24—68no—
90C2×#204—68no—
91C3×#100C2×D3116yescomplemented
92#825—332no—
93C23×C32—22no—
94C23×C32—22no—
95C23×C32—44no—
96C23×C32C2×D411yescharacteristic
97C23×C32C2×D414yes—
98C22×C3⋊D3—22no—
99C22×C3⋊D3—28no—
100C22×C3⋊D3—22no—
101C22×C3⋊D3—44no—
102C22×C3⋊D3—41no—
103C22×C3⋊D3—41no—
104C22×C3⋊D3—84no—
105C32×D4—24no—
106C32×D4—24no—
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2×D412yes—
109C2×C32×C4C2×D412yes—
110C2×C32×C4C2411yescharacteristic
111#638—216no—
112#638—24no—
113#638—24no—
114#638—416no—
115C2×C3⋊Dic3—28no—
116C2×C3⋊Dic3—24no—
117C2×C3⋊Dic3—22no—
118C2×C3⋊Dic3—22no—
119C4⋊(C3⋊D3)—22no—
120C4⋊(C3⋊D3)—24no—
121C4⋊(C3⋊D3)—42no—
122C4⋊(C3⋊D3)C2×D414yescomplemented
123C4×C3⋊D3—24no—
124C4×C3⋊D3—24no—
125#634—22no—
126#634C2×D414yescomplemented
127C32×C8—24no—
128C2×H(5,𝔽2)—91no—
129C2×AGL(1,ℤ/8)—92no—
130C2×#127—91no—
131#453—98no—
132C2×#104—92no—
133C2×#100C3⋊D311yescharacteristic, complemented
134C24×C3D1218yes—
135C23×D3—68no—
136C23×D3—64no—
137C2×C3×D4—28no—
138C2×C3×D4—28no—
139C2×C3×D4D1218yes—
140C2×C3×D4C22×D318yes—
141C22×C3×C4C22×D314yes—
142C2×#67—616no—
143C2×#67—632no—
144C2×#67—68no—
145C2×#67—632no—
146C2×#67—632no—
147C2×#67—1232no—
148C22×Dic3—68no—
149C22×Dic3—64no—
150#237—632no—
151#237—632no—
152D3×D4—632no—
153D3×D4—632no—
154#235—316no—
155#235—316no—
156#235—68no—
157#235—68no—
158C2×D12—38no—
159C2×D12—38no—
160C2×D12—68no—
161C2×D12—68no—
162C2×D12—64no—
163C2×C4×D3—68no—
164C2×Dic6—38no—
165C3×M16—28no—
166C3×M16C22×D3116yescomplemented
167C2×C3×C8—28no—
168C4×Dic3—38no—
169C4×Dic3—64no—
170D24—632no—
171#204—632no—
172C22×C32—22no—
173C22×C32—24no—
174C22×C32—44no—
175C22×C32—44no—
176C22×C32—82no—
177C22×C32#12011yescharacteristic
178C22×C32#12011yescharacteristic
179C22×C32C22×D411yescharacteristic
180C2×C3⋊D3—24no—
181C2×C3⋊D3—44no—
182C2×C3⋊D3—44no—
183C2×C3⋊D3—42no—
184C2×C3⋊D3—88no—
185C2×C3⋊D3—82no—
186C2×C3⋊D3—82no—
187C32×C4#12012yes—
188C32×C4C22×D412yes—
189C3⋊Dic3—24no—
190C3⋊Dic3—24no—
191H(5,𝔽2)—94no—
192H(5,𝔽2)—184no—
193H(5,𝔽2)—182no—
194C2×#41—92no—
195C2×#41—182no—
196C22×D4—91no—
197C22×D4—182no—
198C22×D4—182no—
199C22×D4—182no—
200C22×D4C2×C3⋊D311yescharacteristic
201AGL(1,ℤ/8)—98no—
202AGL(1,ℤ/8)—184no—
203C2×SD16—182no—
204C2×D8—182no—
205C2×M16C2×C3⋊D312yescomplemented
206#127—94no—
207#127—182no—
208C2×C42—91no—
209#104—98no—
210#100C2×C3⋊D314yescomplemented
211C23×C3—28no—
212C23×C3—28no—
213C23×C3—416no—
214C23×C3C2×D1214yes—
215C23×C3C2×D12116yes—
216C22×D3—68no—
217C22×D3—632no—
218C22×D3—68no—
219C22×D3—1216no—
220C22×D3—124no—
221C22×D3—124no—
222C22×D3—2416no—
223C3×D4—216no—
224C3×D4—216no—
225C2×C3×C4C2×D1214yes—
226C2×C3×C4D3×D418yes—
227C2×C3×C4D3×D418yes—
228C2×C3×C4C23×D314yes—
229#67—664no—
230#67—616no—
231#67—616no—
232#67—1264no—
233C2×Dic3—632no—
234C2×Dic3—616no—
235C2×Dic3—68no—
236C2×Dic3—68no—
237D12—316no—
238D12—68no—
239D12—616no—
240D12—128no—
241C4×D3—616no—
242C4×D3—616no—
243Dic6—316no—
244Dic6—68no—
245C3×C8—216no—
246C2×C32—21no—
247C2×C32—21no—
248C2×C32—44no—
249C2×C32#45312yescomplemented
250C2×C32C2×#12011yescharacteristic
251C3⋊D3—44no—
252C3⋊D3—82no—
253C24—182no—
254C24—181no—
255C24C4⋊(C3⋊D3)12yes—
256#41—94no—
257#41—94no—
258#41—188no—
259#41—188no—
260#41—182no—
261#41—182no—
262C2×Q8—92no—
263C2×D4—22no—
264C2×D4—22no—
265C2×D4—92no—
266C2×D4—92no—
267C2×D4—188no—
268C2×D4—188no—
269C2×D4—184no—
270C2×D4—188no—
271C2×D4—182no—
272C2×D4—188no—
273C2×D4—188no—
274C2×D4—181no—
275C2×D4—182no—
276C2×D4—182no—
277C2×D4—368no—
278C2×D4C4⋊(C3⋊D3)12yes—
279C2×D4C22×C3⋊D312yes—
280C22×C4—182no—
281C22×C4—181no—
282C22×C4—182no—
283C22×C4C22×C3⋊D311yescharacteristic
284SD16—188no—
285D8—188no—
286M16—22no—
287M16C22×C3⋊D314yescomplemented
288C2×C8—22no—
289C42—92no—
290C42—181no—
291C22×C3—28no—
292C22×C3—216no—
293C22×C3—416no—
294C22×C3—416no—
295C22×C3—88no—
296C22×C3#88214yes—
297C22×C3#88214yes—
298C22×C3C22×D1214yes—
299C2×D3—616no—
300C2×D3—1216no—
301C2×D3—1216no—
302C2×D3—128no—
303C2×D3—2432no—
304C2×D3—248no—
305C2×D3—248no—
306C3×C4#88218yes—
307C3×C4C2×D3×D418yes—
308Dic3—616no—
309Dic3—616no—
310C32C2×#45311yescharacteristic, complemented, Sylow
311C23—22no—
312C23—22no—
313C23—44no—
314C23—188no—
315C23—182no—
316C23—182no—
317C23—364no—
318C23—361no—
319C23—361no—
320C23—724no—
321C23C2×C4⋊(C3⋊D3)11yescharacteristic
322C23C2×C4⋊(C3⋊D3)14yes—
323Q8—94no—
324Q8—182no—
325D4—24no—
326D4—24no—
327D4—94no—
328D4—1816no—
329D4—184no—
330D4—184no—
331D4—182no—
332D4—184no—
333D4—3616no—
334D4—362no—
335C2×C4—188no—
336C2×C4—184no—
337C2×C4—182no—
338C2×C4—182no—
339C2×C4—184no—
340C2×C4—184no—
341C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
342C2×C4D4×C3⋊D312yes—
343C2×C4D4×C3⋊D312yes—
344C2×C4C23×C3⋊D311yescharacteristic
345C8—24no—
346C2×C3—24no—
347C2×C3—24no—
348C2×C3—416no—
349C2×C3#474718yescomplemented
350C2×C3C2×#88214yes—
351D3—1216no—
352D3—248no—
353C22—22no—
354C22—24no—
355C22—44no—
356C22—44no—
357C22—82no—
358C22—184no—
359C22—364no—
360C22—364no—
361C22—362no—
362C22—722no—
363C22—728no—
364C22—722no—
365C22#6409111yescharacteristic
366C22#6409111yescharacteristic
367C22C22×C4⋊(C3⋊D3)11yescharacteristic
368C4—184no—
369C4—184no—
370C4#6409112yes—
371C4C2×D4×C3⋊D312yes—
372C3C2×#474714yescomplemented
373C2—21no—
374C2—21no—
375C2—44no—
376C2—364no—
377C2—722no—
378C2#1059244612yesdirect product factor
379C2C2×#6409111yescharacteristic
subgroupG/H
centerC22#64091
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC2×C32×#100C2
socleC22×C32#120
hypercenterC2×#100C3⋊D3
hypocenterC32C2×#453
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
1. C2×#64361C2semidirect
2. C2×#64149C2semidirect
3. C2×#64117C2semidirect
4. C2×C32×#100C2semidirect
5. C2×#63652C2semidirect
6. #10592446C2direct (N × H)
13. #64361C22semidirect
17. C22×C4⋊(C3⋊D3)C22semidirect
18. C2×C32×M16C22semidirect
20. #64149C22semidirect
21. C2×C4×C3⋊Dic3C22semidirect
23. #64117C22semidirect
26. C32×#100C22semidirect
27. #63652C22semidirect
31. C2×C3×#100D3semidirect
56. #3828D4semidirect
61. C2×C4⋊(C3⋊D3)D4semidirect
62. C2×C4⋊(C3⋊D3)C23semidirect
64. C2×#634D4semidirect
66. C32×M16C23semidirect
69. C4×C3⋊Dic3C23semidirect
83. C2×C3×M16C2×D3semidirect
91. C3×#100C2×D3semidirect
122. C4⋊(C3⋊D3)C2×D4semidirect
126. #634C2×D4semidirect
133. C2×#100C3⋊D3semidirect
166. C3×M16C22×D3semidirect
205. C2×M16C2×C3⋊D3semidirect
210. #100C2×C3⋊D3semidirect
249. C2×C32#453semidirect
287. M16C22×C3⋊D3semidirect
310. C32C2×#453semidirect
349. C2×C3#4747semidirect
372. C3C2×#4747semidirect
378. C2#10592446direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#643612
C2×#641492
C2×#641172
C2×C32×#1002
C2×#636522
#105924462
C2×#47473