Finite Group Databasebeta

← C2×#10591167 #11866977

Subgroups — C2×#10591167 #11866977

Order 1152.

1341 conjugacy classes of subgroups; only the 244 normal subgroups are shown.

normal subgroups only

This group has 1341 conjugacy classes of subgroups — too many to draw. Only its 244 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
1C22×#3748C211yesmaximal, characteristic, complemented
2C2×C3×#930C212yesmaximal, complemented
3C22×#3713C211yesmaximal, characteristic, complemented
4#10591167C218yesmaximal, direct product factor
5C2×#63574C211yesmaximal, characteristic, complemented
6C2×#63562C212yesmaximal, complemented
7C2×#5039—32nomaximal
8C23×C32×C4C2211yescharacteristic
9C22×C3×#67—22no—
10C22×C3×D12C2212yes—
11C2×#3748—24no—
12C2×#3748C2214yescomplemented
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C22×C3⋊(C3⋊C8)C2211yescharacteristic
15C3×#930—24no—
16C3×#930C2218yescomplemented
17C2×C3×(C2×D3)⋊C4—22no—
18C2×C3×C4⋊Dic3C2212yes—
19C2×#3713—24no—
20C2×#3713C2214yescomplemented
21#63574C2214yescomplemented
22#63562C2218yescomplemented
23C2×C3×#121—32no—
24C22×#213—32no—
25C2×#930D312yescomplemented
26C22×#208—32no—
27C22×#208—61no—
28C2×#832—32no—
29#5039—316no—
30C2×#809—32no—
31C2×#808—32no—
32C24×C32D411yescharacteristic
33C23×C3×D3—22no—
34C22×C32×C4—22no—
35C22×C32×C4—22no—
36C22×C32×C4D411yescharacteristic
37C22×C32×C4D412yes—
38C22×C32×C4C2312yes—
39C22×C32×C4C2311yescharacteristic
40C2×C3×#67—28no—
41C2×C3×#67—48no—
42C22×C3×Dic3—22no—
43C2×C3×D12—24no—
44C2×C3×D12—24no—
45C2×C3×D12—22no—
46C2×C3×D12C2314yes—
47#3748—28no—
48C2×C3⋊(C3⋊C8)—22no—
49C2×C3⋊(C3⋊C8)D414yescomplemented
50C2×C3⋊(C3⋊C8)C2312yes—
51C2×C3⋊(C3⋊C8)C2312yes—
52C3×(C2×D3)⋊C4—28no—
53C3×C4⋊Dic3—22no—
54C3×C4⋊Dic3C2314yes—
55#3713—28no—
56C2×#469—91noSylow
57C22×C3×D4—32no—
58C22×C3×D4—62no—
59C23×C3×C4—21no—
60C23×C3×C4C2×D312yes—
61C22×#67—22no—
62C22×D12C2×D312yes—
63C3×#121—38no—
64C3×#121—64no—
65C2×C3×C4⋊C4—32no—
66C2×C3×C22⋊C4—62no—
67C2×#213—38no—
68C2×#213—68no—
69#930—24no—
70#930C2×D318yescomplemented
71C2×(C2×D3)⋊C4—22no—
72C2×C4⋊Dic3C2×D312yes—
73C2×#208—38no—
74C2×#208—64no—
75C2×#208—68no—
76C2×#208—68no—
77C22×C3⋊C8—32no—
78C22×C3⋊C8—32no—
79C22×C3⋊C8—61no—
80C22×C3⋊C8—61no—
81#832—38no—
82#809—38no—
83#808—38no—
84C23×C32—22no—
85C23×C32—24no—
86C23×C32C2×D412yes—
87C23×C32C2×D411yescharacteristic
88C22×C3×D3—24no—
89C22×C3×D3—44no—
90C22×C3×D3—44no—
91C22×C3×D3—44no—
92C2×C32×C4—22no—
93C2×C32×C4—24no—
94C2×C32×C4—22no—
95C2×C32×C4—22no—
96C2×C32×C4C2×D412yes—
97C2×C32×C4C2×D412yes—
98C2×C32×C4C2×D411yescharacteristic
99C2×C32×C4#4112yes—
100C2×C32×C4C2411yescharacteristic
101C3×#67—416no—
102C2×C3×Dic3—24no—
103C2×C3×Dic3—44no—
104C3×D12—24no—
105C3×D12—24no—
106C3×D12—44no—
107C3⋊(C3⋊C8)—22no—
108C3⋊(C3⋊C8)C2×D414yescomplemented
109C22×D8—91no—
110C22×M16—91no—
111C2×#121—32no—
112#469—98no—
113C2×#106—91no—
114C2×#102—92no—
115C24×C3—21no—
116C24×C3—62no—
117C24×C3#6712yes—
118C23×D3—22no—
119C2×C3×D4—34no—
120C2×C3×D4—68no—
121C2×C3×D4—64no—
122C2×C3×D4—64no—
123C2×C3×D4—62no—
124C2×C3×D4—128no—
125C22×C3×C4—24no—
126C22×C3×C4—24no—
127C22×C3×C4—24no—
128C22×C3×C4—24no—
129C22×C3×C4—22no—
130C22×C3×C4—21no—
131C22×C3×C4—21no—
132C22×C3×C4—22no—
133C22×C3×C4—62no—
134C22×C3×C4#6712yes—
135C22×C3×C4#6714yes—
136C22×C3×C4C22×D314yes—
137C22×C3×C4C22×D312yes—
138C2×#67—28no—
139C2×#67—48no—
140C22×Dic3—22no—
141C2×D12—24no—
142C2×D12—24no—
143C2×D12—22no—
144C2×D12C22×D314yes—
145C3×C4⋊C4—34no—
146C3×C4⋊C4—62no—
147C3×C22⋊C4—68no—
148#213—616no—
149(C2×D3)⋊C4—28no—
150C4⋊Dic3—22no—
151C4⋊Dic3C22×D314yes—
152#208—616no—
153#208—616no—
154C2×C3⋊C8—38no—
155C2×C3⋊C8—34no—
156C2×C3⋊C8—34no—
157C2×C3⋊C8—64no—
158C2×C3⋊C8—62no—
159C2×C3⋊C8—62no—
160C2×C3⋊C8—64no—
161C2×C3⋊C8—64no—
162C22×C32—22no—
163C22×C32—24no—
164C22×C32—44no—
165C22×C32#12112yes—
166C22×C32AGL(1,ℤ/8)14yes—
167C22×C32C22×D411yescharacteristic
168C2×C3×D3—44no—
169C2×C3×D3—44no—
170C2×C3×D3—44no—
171C2×C3×D3—88no—
172C32×C4—22no—
173C32×C4#12112yes—
174C32×C4C22×D411yescharacteristic
175C32×C4C2×#4111yescharacteristic
176C3×Dic3—44no—
177C22×D4—32no—
178C22×D4—62no—
179C23×C4D3211yescharacteristic
180C2×D8—94no—
181C2×D8—184no—
182C2×M16—94no—
183C2×M16—184no—
184C22×C8—91no—
185C22×C8—91no—
186#121—38no—
187#121—64no—
188C2×C4⋊C4—32no—
189C2×C22⋊C4—62no—
190#106—94no—
191#102—98no—
192C23×C3—24no—
193C23×C3—24no—
194C23×C3—24no—
195C23×C3—24no—
196C23×C3—22no—
197C23×C3—21no—
198C23×C3—44no—
199C23×C3—64no—
200C23×C3—124no—
201C23×C3—124no—
202C23×C3—124no—
203C23×C3C2×#6714yes—
204C23×C3C2×#6712yes—
205C22×D3—24no—
206C22×D3—44no—
207C22×D3—44no—
208C22×D3—44no—
209C3×D4—64no—
210C3×D4—64no—
211C3×D4—1216no—
212C3×D4—124no—
213C2×C3×C4—24no—
214C2×C3×C4—24no—
215C2×C3×C4—24no—
216C2×C3×C4—28no—
217C2×C3×C4—24no—
218C2×C3×C4—28no—
219C2×C3×C4—24no—
220C2×C3×C4—24no—
221C2×C3×C4—21no—
222C2×C3×C4—22no—
223C2×C3×C4—22no—
224C2×C3×C4—21no—
225C2×C3×C4—22no—
226C2×C3×C4—64no—
227C2×C3×C4—124no—
228C2×C3×C4D3×D414yes—
229C2×C3×C4#23714yes—
230C2×C3×C4C2×#6714yes—
231C2×C3×C4C2×#6712yes—
232C2×C3×C4C23×D312yes—
233#67—416no—
234C2×Dic3—24no—
235C2×Dic3—44no—
236D12—24no—
237D12—24no—
238D12—44no—
239C3⋊C8—38no—
240C3⋊C8—64no—
241C3⋊C8—64no—
242C3⋊C8—64no—
243C2×C32—42no—
244C2×C32#46914yescomplemented
245C2×C32C2×#12111yescharacteristic
246C2×C32C2×AGL(1,ℤ/8)12yes—
247C3×D3—84no—
248C24—62no—
249C24#62511yescharacteristic
250C2×D4—34no—
251C2×D4—68no—
252C2×D4—64no—
253C2×D4—62no—
254C2×D4—64no—
255C2×D4—128no—
256C22×C4—22no—
257C22×C4—22no—
258C22×C4—62no—
259C22×C4#62512yes—
260C22×C4#62511yescharacteristic
261C22×C4C2×D3212yes—
262C22×C4C2×D3211yescharacteristic
263D8—188no—
264M16—188no—
265C2×C8—92no—
266C2×C8—94no—
267C2×C8—92no—
268C2×C8—182no—
269C4⋊C4—34no—
270C4⋊C4—62no—
271C22⋊C4—68no—
272C22×C3—24no—
273C22×C3—24no—
274C22×C3—24no—
275C22×C3—24no—
276C22×C3—21no—
277C22×C3—24no—
278C22×C3—22no—
279C22×C3—44no—
280C22×C3—48no—
281C22×C3—48no—
282C22×C3—124no—
283C22×C3—124no—
284C22×C3—124no—
285C22×C3—248no—
286C22×C3#93214yes—
287C22×C3#93914yes—
288C22×C3#94914yes—
289C22×C3C22×#6712yes—
290C2×D3—44no—
291C2×D3—44no—
292C2×D3—44no—
293C2×D3—88no—
294C3×C4—24no—
295C3×C4—24no—
296C3×C4—21no—
297C3×C4—21no—
298C3×C4—22no—
299C3×C4—124no—
300C3×C4#93914yes—
301C3×C4C2×D3×D412yes—
302C3×C4C2×#23712yes—
303Dic3—44no—
304C32C2×#46911yescharacteristic, complemented, Sylow
305C23—24no—
306C23—22no—
307C23—64no—
308C23—124no—
309C23—124no—
310C23—124no—
311C23C2×#62512yes—
312C23C2×#62511yescharacteristic
313D4—64no—
314D4—64no—
315D4—1216no—
316D4—124no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—24no—
321C2×C4—64no—
322C2×C4—124no—
323C2×C4#380512yes—
324C2×C4C2×#62512yes—
325C2×C4C2×#62511yescharacteristic
326C2×C4#381112yes—
327C2×C4C22×D3211yescharacteristic
328C8—94no—
329C8—182no—
330C2×C3—21no—
331C2×C3—24no—
332C2×C3—22no—
333C2×C3—44no—
334C2×C3—44no—
335C2×C3—244no—
336C2×C3#503918yescomplemented
337C2×C3C2×#93212yes—
338C2×C3C2×#93912yes—
339C2×C3C2×#94912yes—
340D3—84no—
341C22—22no—
342C22—24no—
343C22—44no—
344C22—124no—
345C22—124no—
346C22—124no—
347C22—248no—
348C22#6382314yes—
349C22#6398012yes—
350C22C22×#62511yescharacteristic
351C4—22no—
352C4—124no—
353C4#6398012yes—
354C4C2×#380511yescharacteristic
355C4C2×#381111yescharacteristic
356C3—21no—
357C3C2×#503912yescomplemented
358C2—42no—
359C2—244no—
360C2#1059116714yesdirect product factor
361C2C2×#6382312yes—
362C2C2×#6398011yescharacteristic
subgroupG/H
centerC23C2×#625
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC23×C32×C4C22
socleC23×C32C2×D4
hypercenterC23×C4D32
hypocenterC32C2×#469
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×#3748C2semidirect
2. C2×C3×#930C2semidirect
3. C22×#3713C2semidirect
4. #10591167C2direct (N × H)
5. C2×#63574C2semidirect
6. C2×#63562C2semidirect
12. C2×#3748C22semidirect
16. C3×#930C22semidirect
20. C2×#3713C22semidirect
21. #63574C22semidirect
22. #63562C22semidirect
25. C2×#930D3semidirect
49. C2×C3⋊(C3⋊C8)D4semidirect
70. #930C2×D3semidirect
108. C3⋊(C3⋊C8)C2×D4semidirect
244. C2×C32#469semidirect
304. C32C2×#469semidirect
336. C2×C3#5039semidirect
357. C3C2×#5039semidirect
360. C2#10591167direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37482
C2×C3×#9302
C22×#37132
#105911672
C2×#635742
C2×#635622
C2×#50393