Finite Group Databasebeta

← C2×#10590554 #11873584

Subgroups — C2×#10590554 #11873584

Order 1152.

1089 conjugacy classes of subgroups; only the 212 normal subgroups are shown.

normal subgroups only

This group has 1089 conjugacy classes of subgroups — too many to draw. Only its 212 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×#64099C211yesmaximal, characteristic, complemented
2C2×#63914C211yesmaximal, characteristic
3C2×C3×#809C212yesmaximal, complemented
4C2×#63563C212yesmaximal, complemented
5C2×#63555C211yesmaximal, characteristic, complemented
6#10590554C218yesmaximal, direct product factor
7C2×#4764—32nomaximal
8C22×C3×D12C2212yes—
9C22×#625—21no—
10C22×#625—21no—
11C2×C32×C4⋊C4C2211yescharacteristic
12C2×C4⋊(C3⋊Dic3)—21no—
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×#3750—21no—
15C2×C4×C3⋊Dic3C2211yescharacteristic
16#64099—22no—
17#64099C2214yescomplemented
18C22×C3×C3⋊C8C2212yes—
19#63914—22no—
20#63914C2214yes—
21C3×#809C2218yescomplemented
22#63563C2218yescomplemented
23#63555C2214yescomplemented
24C2×#940—32no—
25C2×#890—32no—
26C2×#890—61no—
27C2×C3×#102—32no—
28C2×#832—32no—
29C2×#821—32no—
30C2×#815—32no—
31C2×#809D312yescomplemented
32#4764—316no—
33C23×C3×D3—22no—
34C22×C32×C4—21no—
35C22×C32×C4C2311yescharacteristic
36C22×C3⋊Dic3—21no—
37C22×C3⋊Dic3D411yescharacteristic
38C22×C3⋊Dic3D411yescharacteristic
39C2×C3×D12—24no—
40C2×C3×D12—24no—
41C2×C3×D12—22no—
42C2×C3×D12C2314yes—
43C2×#625—24no—
44C2×#625—24no—
45C2×#625—44no—
46C2×#625—44no—
47C32×C4⋊C4—21no—
48C32×C4⋊C4C2312yes—
49C4⋊(C3⋊Dic3)—21no—
50C4⋊(C3⋊Dic3)—24no—
51C4⋊(C3⋊Dic3)C2312yes—
52#3750—24no—
53C4×C3⋊Dic3D412yes—
54C4×C3⋊Dic3C2312yes—
55C2×C3×C3⋊C8—24no—
56C2×C3×C3⋊C8C2314yes—
57C2×#490—91noSylow
58C22×C3×D4—32no—
59C22×#67—62no—
60C22×#67—62no—
61C22×D12C2×D312yes—
62C22×C3×C8—32no—
63C2×C3×C4⋊C4—21no—
64C2×C3×C4⋊C4C2×D312yes—
65#940—38no—
66#940—64no—
67C2×C4⋊Dic3—32no—
68C2×C4⋊Dic3—61no—
69C2×C4⋊Dic3—62no—
70C2×C4⋊Dic3—62no—
71C2×Dic3⋊C4—62no—
72C2×Dic3⋊C4—62no—
73C2×C4×Dic3—32no—
74C2×C4×Dic3—61no—
75C22×C3⋊C8C2×D312yes—
76#890—38no—
77#890—64no—
78#890—64no—
79#890—64no—
80C3×#102—38no—
81#832—38no—
82#821—38no—
83#815—38no—
84#809C2×D318yescomplemented
85C23×C32C2×D411yescharacteristic
86C22×C3×D3—24no—
87C22×C3×D3—44no—
88C22×C3×D3—44no—
89C22×C3×D3—44no—
90C2×C32×C4—22no—
91C2×C32×C4—42no—
92C2×C32×C4C2×D411yescharacteristic
93C2×C32×C4#4114yes—
94C2×C32×C4C2411yescharacteristic
95C2×C3⋊Dic3—22no—
96C2×C3⋊Dic3—22no—
97C2×C3⋊Dic3—22no—
98C2×C3⋊Dic3—42no—
99C2×C3⋊Dic3C2×D412yes—
100C2×C3⋊Dic3C2×D412yes—
101C3×D12—24no—
102C3×D12—24no—
103C3×D12—44no—
104#625—48no—
105#625—48no—
106C3×C3⋊C8—24no—
107C2×#127—91no—
108C2×#125—91no—
109#490—98no—
110C2×#102—32no—
111C2×#102—92no—
112C2×#97—91no—
113C24×C3—62no—
114C23×D3—22no—
115C2×C3×D4—34no—
116C2×C3×D4—64no—
117C2×C3×D4—62no—
118C2×C3×D4—64no—
119C22×C3×C4—22no—
120C22×C3×C4—22no—
121C22×C3×C4—21no—
122C22×C3×C4C22×D312yes—
123C2×#67—68no—
124C2×#67—68no—
125C2×#67—128no—
126C2×#67—128no—
127C22×Dic3—32no—
128C22×Dic3—32no—
129C22×Dic3—61no—
130C22×Dic3—61no—
131C22×Dic3—62no—
132C22×Dic3—62no—
133C2×D12—24no—
134C2×D12—24no—
135C2×D12—22no—
136C2×D12C22×D314yes—
137C2×C3×C8—34no—
138C2×C3×C8—64no—
139C3×C4⋊C4—22no—
140C3×C4⋊C4—22no—
141C3×C4⋊C4—22no—
142C3×C4⋊C4C22×D314yes—
143C4⋊Dic3—34no—
144C4⋊Dic3—62no—
145C4⋊Dic3—68no—
146C4⋊Dic3—68no—
147C4⋊Dic3—62no—
148C4⋊Dic3—62no—
149Dic3⋊C4—68no—
150Dic3⋊C4—68no—
151C4×Dic3—34no—
152C4×Dic3—34no—
153C4×Dic3—62no—
154C4×Dic3—62no—
155C2×C3⋊C8—24no—
156C2×C3⋊C8C22×D314yes—
157C22×C32#12412yes—
158C22×C32AGL(1,ℤ/8)12yes—
159C22×C32AGL(1,ℤ/8)12yes—
160C22×C32C22×D411yescharacteristic
161C2×C3×D3—44no—
162C2×C3×D3—44no—
163C2×C3×D3—44no—
164C2×C3×D3—88no—
165C32×C4—42no—
166C32×C4#12412yes—
167C32×C4C2×#4112yes—
168C3⋊Dic3—22no—
169C3⋊Dic3—22no—
170C3⋊Dic3—42no—
171C22×D4—32no—
172C22×D4—181no—
173C22×D4—181no—
174C22×C8—32no—
175#127—94no—
176#127—182no—
177#125—94no—
178#125—182no—
179C2×C4⋊C4—91no—
180C2×C4⋊C4—181no—
181C2×C4⋊C4—181no—
182C2×C4⋊C4D3211yescharacteristic
183C2×C42—91no—
184#102—38no—
185#102—98no—
186#97—94no—
187C23×C3—21no—
188C23×C3—64no—
189C23×C3—124no—
190C23×C3—124no—
191C23×C3—124no—
192C23×C3D3×D412yes—
193C22×D3—24no—
194C22×D3—44no—
195C22×D3—44no—
196C22×D3—44no—
197C3×D4—64no—
198C3×D4—64no—
199C3×D4—124no—
200C2×C3×C4—24no—
201C2×C3×C4—24no—
202C2×C3×C4—21no—
203C2×C3×C4—24no—
204C2×C3×C4—21no—
205C2×C3×C4—44no—
206C2×C3×C4—44no—
207C2×C3×C4#23514yes—
208C2×C3×C4D3×D412yes—
209C2×C3×C4#23714yes—
210C2×C3×C4C23×D312yes—
211#67—1216no—
212#67—1216no—
213C2×Dic3—34no—
214C2×Dic3—34no—
215C2×Dic3—62no—
216C2×Dic3—62no—
217C2×Dic3—64no—
218C2×Dic3—64no—
219C2×Dic3—64no—
220C2×Dic3—64no—
221C2×Dic3—122no—
222C2×Dic3—122no—
223C2×Dic3—124no—
224C2×Dic3—124no—
225D12—24no—
226D12—24no—
227D12—44no—
228C3×C8—64no—
229C3⋊C8—24no—
230C2×C32#49014yescomplemented
231C2×C32C2×#12411yescharacteristic
232C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
233C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
234C3×D3—84no—
235C24—62no—
236C2×D4—34no—
237C2×D4—64no—
238C2×D4—64no—
239C2×D4—62no—
240C2×D4—184no—
241C2×D4—184no—
242C2×D4—364no—
243C2×D4—364no—
244C22×C4—21no—
245C22×C4—91no—
246C22×C4—91no—
247C22×C4—181no—
248C22×C4C2×D3211yescharacteristic
249C2×C8—34no—
250C2×C8—64no—
251C4⋊C4—21no—
252C4⋊C4—92no—
253C4⋊C4—184no—
254C4⋊C4—184no—
255C4⋊C4—181no—
256C4⋊C4C2×D3212yes—
257C42—92no—
258C42—92no—
259C22×C3—21no—
260C22×C3—22no—
261C22×C3—22no—
262C22×C3—22no—
263C22×C3—124no—
264C22×C3—124no—
265C22×C3—124no—
266C22×C3—248no—
267C22×C3#88514yes—
268C22×C3#91114yes—
269C22×C3#91414yes—
270C22×C3C2×D3×D412yes—
271C2×D3—44no—
272C2×D3—44no—
273C2×D3—44no—
274C2×D3—88no—
275C3×C4—22no—
276C3×C4—22no—
277C3×C4—44no—
278C3×C4—44no—
279C3×C4#88514yes—
280C3×C4C2×#23512yes—
281C3×C4C2×#23712yes—
282Dic3—64no—
283Dic3—64no—
284Dic3—122no—
285Dic3—122no—
286Dic3—124no—
287Dic3—124no—
288C32C2×#49011yescharacteristic, complemented, Sylow
289C23—64no—
290C23—124no—
291C23—124no—
292C23—124no—
293C23#381111yescharacteristic
294D4—64no—
295D4—64no—
296D4—124no—
297D4—368no—
298D4—368no—
299C2×C4—22no—
300C2×C4—42no—
301C2×C4—92no—
302C2×C4—92no—
303C2×C4—182no—
304C2×C4—182no—
305C2×C4—182no—
306C2×C4—362no—
307C2×C4#379514yes—
308C2×C4#381111yescharacteristic
309C2×C4C22×D3211yescharacteristic
310C8—64no—
311C2×C3—21no—
312C2×C3—24no—
313C2×C3—21no—
314C2×C3—21no—
315C2×C3—244no—
316C2×C3#476418yescomplemented
317C2×C3C2×#88512yes—
318C2×C3C2×#91112yes—
319C2×C3C2×#91412yes—
320D3—84no—
321C22—124no—
322C22—124no—
323C22—124no—
324C22—248no—
325C22#6391312yes—
326C22#6392712yes—
327C22#6394112yes—
328C22C2×#381111yescharacteristic
329C4—42no—
330C4—182no—
331C4—182no—
332C4—362no—
333C4#6391312yes—
334C4C2×#379512yes—
335C3—21no—
336C3C2×#476412yescomplemented
337C2—244no—
338C2#1059055414yesdirect product factor
339C2C2×#6391311yescharacteristic
340C2C2×#6392711yescharacteristic
341C2C2×#6394111yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC2×#63914C2
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#490
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64099C2semidirect
3. C2×C3×#809C2semidirect
4. C2×#63563C2semidirect
5. C2×#63555C2semidirect
6. #10590554C2direct (N × H)
17. #64099C22semidirect
21. C3×#809C22semidirect
22. #63563C22semidirect
23. #63555C22semidirect
31. C2×#809D3semidirect
84. #809C2×D3semidirect
230. C2×C32#490semidirect
288. C32C2×#490semidirect
316. C2×C3#4764semidirect
336. C3C2×#4764semidirect
338. C2#10590554direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640992
C2×#639142
C2×C3×#8092
C2×#635632
C2×#635552
#105905542
C2×#47643