Finite Group Databasebeta

← C2×#10590306 #11875039

Subgroups — C2×#10590306 #11875039

Order 1152.

913 conjugacy classes of subgroups.

The subgroup lattice has 347 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64078C211yesmaximal, characteristic
2C2×C3×#870C211yesmaximal, characteristic
3C2×C3×#803C211yesmaximal, characteristic
4C2×#63575C212yesmaximal
5C2×#63573C212yesmaximal
6#10590306C218yesmaximal, direct product factor
7C2×#5064—31nomaximal
8C2×#4702—31nomaximal
9C22×#634—21no—
10C2×C32×C42C2211yescharacteristic
11C2×C4⋊(C3⋊Dic3)—21no—
12C2×C4⋊(C3⋊Dic3)C2212yes—
13#64078—22no—
14#64078C2214yes—
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×C3×Dic3⋊C4—21no—
18C2×C3×Dic3⋊C4—21no—
19C22×C3×C3⋊C8C2212yes—
20C3×#870—22no—
21C3×#870C2214yes—
22C3×#803C2214yes—
23#63575C2218yes—
24#63573C2218yes—
25C2×C3×#125—31no—
26C2×#870D311yescharacteristic
27C2×#869—31no—
28C2×#869—31no—
29C2×#869—61no—
30C2×C3×#97—31no—
31C2×#818—32no—
32C2×#817—32no—
33#5064—38no—
34C2×#808—32no—
35C2×#807—32no—
36C2×#803D311yescharacteristic
37#4702—38no—
38C22×C32×C4D411yescharacteristic
39C22×C32×C4D411yescharacteristic
40C22×C32×C4C2311yescharacteristic
41C22×C3⋊Dic3—22no—
42C2×#634—24no—
43C2×#634—44no—
44C22×C3×Dic3—21no—
45C22×C3×Dic3—21no—
46C32×C42D412yes—
47C32×C42C2312yes—
48C4⋊(C3⋊Dic3)—22no—
49C4⋊(C3⋊Dic3)—24no—
50C4⋊(C3⋊Dic3)C2314yes—
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3—21no—
53C3×C4⋊Dic3C2312yes—
54C3×C4⋊Dic3C2312yes—
55C3×Dic3⋊C4—24no—
56C3×Dic3⋊C4—24no—
57C2×C3×C3⋊C8Q818yescomplemented
58C2×C3×C3⋊C8C2314yes—
59C2×#501—91noSylow
60C22×Dic6—62no—
61C22×Dic6—61no—
62C22×Dic6—61no—
63C22×C3×C8—32no—
64C3×#125—34no—
65C3×#125—62no—
66C2×C3×C4⋊C4—31no—
67C2×C3×C4⋊C4—31no—
68C2×C3×C4⋊C4—61no—
69C2×C3×C4⋊C4—61no—
70C2×C3×C42—21no—
71C2×C3×C42C2×D311yescharacteristic
72C2×C3×C42C2×D311yescharacteristic
73C2×C4⋊Dic3—32no—
74C2×C4⋊Dic3—32no—
75C2×C4⋊Dic3—62no—
76C2×C4⋊Dic3—62no—
77C2×C4⋊Dic3—61no—
78C2×C4⋊Dic3—61no—
79C2×C4⋊Dic3C2×D311yescharacteristic
80C2×C4⋊Dic3C2×D311yescharacteristic
81C2×Dic3⋊C4—21no—
82C2×Dic3⋊C4—21no—
83C22×C3⋊C8C2×D312yes—
84#870—22no—
85#870C2×D314yes—
86#869—34no—
87#869—34no—
88#869—64no—
89#869—64no—
90#869—62no—
91#869—62no—
92C3×#97—34no—
93#818—38no—
94#817—38no—
95#808—38no—
96#807—38no—
97#803C2×D314yes—
98C23×C32C2×D411yescharacteristic
99C2×C32×C4—22no—
100C2×C32×C4—22no—
101C2×C32×C4C2×D412yes—
102C2×C32×C4C2×D412yes—
103C2×C32×C4C2×D411yescharacteristic
104C2×C32×C4C2×Q814yes—
105C2×C32×C4C2411yescharacteristic
106C2×C3⋊Dic3—24no—
107C2×C3⋊Dic3—44no—
108#634—48no—
109C2×C3×Dic3—22no—
110C2×C3×Dic3—22no—
111C2×C3×Dic3—42no—
112C2×C3×Dic3—42no—
113C3×C3⋊C8C2×Q818yescomplemented
114C2×C4⋊Q8—91no—
115C2×#125—31no—
116#501—98no—
117C2×#107—92no—
118C2×#106—92no—
119C2×#97—31no—
120C22×C3×C4—21no—
121C22×C3×C4—21no—
122C22×C3×C4—21no—
123C22×C3×C4—61no—
124C22×C3×C4—61no—
125C22×C3×C4D1211yescharacteristic
126C22×C3×C4D1211yescharacteristic
127C22×C3×C4#6711yescharacteristic
128C22×C3×C4#6711yescharacteristic
129C22×C3×C4C22×D311yescharacteristic
130C22×C3×C4C22×D311yescharacteristic
131C22×Dic3—21no—
132C22×Dic3—21no—
133C22×Dic3—64no—
134C22×Dic3—62no—
135C22×Dic3—62no—
136C2×Dic6—68no—
137C2×Dic6—64no—
138C2×Dic6—64no—
139C2×Dic6—128no—
140C2×Dic6—124no—
141C2×Dic6—124no—
142C2×C3×C8—38no—
143C2×C3×C8—34no—
144C3×C4⋊C4—32no—
145C3×C4⋊C4—32no—
146C3×C4⋊C4—64no—
147C3×C4⋊C4—64no—
148C3×C4⋊C4—61no—
149C3×C4⋊C4—61no—
150C3×C42—22no—
151C3×C42—22no—
152C3×C42D1212yes—
153C3×C42#6712yes—
154C3×C42C22×D312yes—
155C3×C42C22×D312yes—
156C4⋊Dic3—21no—
157C4⋊Dic3—21no—
158C4⋊Dic3—34no—
159C4⋊Dic3—34no—
160C4⋊Dic3—64no—
161C4⋊Dic3—64no—
162C4⋊Dic3—68no—
163C4⋊Dic3—64no—
164C4⋊Dic3—62no—
165C4⋊Dic3—64no—
166C4⋊Dic3—62no—
167C4⋊Dic3C22×D312yes—
168C4⋊Dic3C22×D312yes—
169Dic3⋊C4—24no—
170Dic3⋊C4—24no—
171C2×C3⋊C8Dic618yescomplemented
172C2×C3⋊C8C22×D314yes—
173C22×C32C4⋊Q812yes—
174C22×C32AGL(1,ℤ/8)12yes—
175C22×C32#13712yes—
176C22×C32C22×D411yescharacteristic
177C32×C4—22no—
178C32×C4—22no—
179C32×C4C4⋊Q812yes—
180C32×C4C22×Q812yes—
181C3⋊Dic3—44no—
182C3×Dic3—42no—
183C3×Dic3—42no—
184C22×Q8—181no—
185C22×C8—32no—
186C4⋊Q8—94no—
187C4⋊Q8—182no—
188#125—34no—
189#125—62no—
190C2×C4⋊C4—31no—
191C2×C4⋊C4—31no—
192C2×C4⋊C4—61no—
193C2×C4⋊C4—61no—
194C2×C4⋊C4—92no—
195C2×C4⋊C4—181no—
196C2×C42D3211yescharacteristic
197#107—98no—
198#106—98no—
199#97—34no—
200C23×C3—21no—
201C23×C3C2×D1211yescharacteristic
202C23×C3C2×#6711yescharacteristic
203C2×C3×C4—24no—
204C2×C3×C4—24no—
205C2×C3×C4—22no—
206C2×C3×C4—22no—
207C2×C3×C4—22no—
208C2×C3×C4—22no—
209C2×C3×C4—21no—
210C2×C3×C4—24no—
211C2×C3×C4—22no—
212C2×C3×C4—21no—
213C2×C3×C4—22no—
214C2×C3×C4—62no—
215C2×C3×C4—62no—
216C2×C3×C4—122no—
217C2×C3×C4—122no—
218C2×C3×C4C2×Dic614yes—
219C2×C3×C4C2×D1212yes—
220C2×C3×C4C2×D1212yes—
221C2×C3×C4C2×D1211yescharacteristic
222C2×C3×C4D3×Q814yes—
223C2×C3×C4C2×#6712yes—
224C2×C3×C4C2×#6712yes—
225C2×C3×C4C2×#6711yescharacteristic
226C2×C3×C4C23×D311yescharacteristic
227C2×C3×C4C23×D311yescharacteristic
228C2×Dic3—22no—
229C2×Dic3—22no—
230C2×Dic3—42no—
231C2×Dic3—42no—
232C2×Dic3—68no—
233C2×Dic3—64no—
234C2×Dic3—64no—
235C2×Dic3—128no—
236C2×Dic3—124no—
237C2×Dic3—124no—
238Dic6—1216no—
239Dic6—128no—
240Dic6—128no—
241C3×C8—38no—
242C3⋊C8C2×Dic618yescomplemented
243C2×C32#50114yescomplemented
244C2×C32C2×C4⋊Q811yescharacteristic
245C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
246C2×C32C2×#13711yescharacteristic
247C2×Q8—184no—
248C2×Q8—364no—
249C22×C4—61no—
250C22×C4—61no—
251C22×C4—182no—
252C22×C4#62611yescharacteristic
253C22×C4#62611yescharacteristic
254C22×C4C2×D3211yescharacteristic
255C2×C8—34no—
256C2×C8—38no—
257C4⋊C4—32no—
258C4⋊C4—32no—
259C4⋊C4—61no—
260C4⋊C4—61no—
261C4⋊C4—64no—
262C4⋊C4—64no—
263C4⋊C4—94no—
264C4⋊C4—182no—
265C4⋊C4—184no—
266C42#62612yes—
267C42C2×D3212yes—
268C22×C3—21no—
269C22×C3—22no—
270C22×C3—22no—
271C22×C3—22no—
272C22×C3#86912yes—
273C22×C3#90812yes—
274C22×C3#90912yes—
275C22×C3#94412yes—
276C22×C3#94912yes—
277C22×C3#95112yes—
278C22×C3C22×D1211yescharacteristic
279C22×C3C22×#6711yescharacteristic
280C3×C4—24no—
281C3×C4—24no—
282C3×C4—22no—
283C3×C4—22no—
284C3×C4—22no—
285C3×C4—22no—
286C3×C4—22no—
287C3×C4—22no—
288C3×C4—122no—
289C3×C4—122no—
290C3×C4#86912yes—
291C3×C4#94412yes—
292C3×C4C22×Dic612yes—
293C3×C4C2×D3×Q812yes—
294Dic3—42no—
295Dic3—42no—
296Dic3—128no—
297Dic3—124no—
298Dic3—124no—
299C32C2×#50111yescharacteristic, complemented, Sylow
300C23C2×#62611yescharacteristic
301Q8—368no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—62no—
305C2×C4—62no—
306C2×C4—122no—
307C2×C4—122no—
308C2×C4—184no—
309C2×C4—364no—
310C2×C4D3×Dic614yes—
311C2×C4C2×#62612yes—
312C2×C4C2×#62612yes—
313C2×C4C2×#62611yescharacteristic
314C2×C4C22×D3211yescharacteristic
315C8—38no—
316C2×C3—21no—
317C2×C3—24no—
318C2×C3—21no—
319C2×C3—21no—
320C2×C3#470214yescomplemented
321C2×C3#506414yescomplemented
322C2×C3C2×#86911yescharacteristic
323C2×C3C2×#90811yescharacteristic
324C2×C3C2×#90911yescharacteristic
325C2×C3C2×#94411yescharacteristic
326C2×C3C2×#94911yescharacteristic
327C2×C3C2×#95111yescharacteristic
328C22#6382512yes—
329C22#6383112yes—
330C22#6386612yes—
331C22C22×#62611yescharacteristic
332C4—22no—
333C4—22no—
334C4—122no—
335C4—122no—
336C4—364no—
337C4#6386612yes—
338C4C2×D3×Dic612yes—
339C3—21no—
340C3C2×#470211yescharacteristic, complemented
341C3C2×#506411yescharacteristic, complemented
342C2#1059030614yesdirect product factor
343C2C2×#6382511yescharacteristic
344C2C2×#6383111yescharacteristic
345C2C2×#6386611yescharacteristic
subgroupG/H
centerC23C2×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C42C22
socle, prime radicalC23×C32C2×D4
hypercenterC2×C42D32
hypocenterC32C2×#501
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
6. #10590306C2direct (N × H)
57. C2×C3×C3⋊C8Q8semidirect
113. C3×C3⋊C8C2×Q8semidirect
171. C2×C3⋊C8Dic6semidirect
242. C3⋊C8C2×Dic6semidirect
243. C2×C32#501semidirect
299. C32C2×#501semidirect
320. C2×C3#4702semidirect
321. C2×C3#5064semidirect
340. C3C2×#4702semidirect
341. C3C2×#5064semidirect
342. C2#10590306direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640782
C2×C3×#8702
C2×C3×#8032
C2×#635752
C2×#635732
#105903062
C2×#50643
C2×#47023