Finite Group Databasebeta

← C2×#10590301 #11868407

Subgroups — C2×#10590301 #11868407

Order 1152.

977 conjugacy classes of subgroups.

The subgroup lattice has 377 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64078C211yesmaximal, characteristic
2C2×C3×C4×Dic6C211yesmaximal, characteristic
3C2×C3×C4⋊(C3⋊C8)C211yesmaximal, characteristic
4C2×#63573C212yesmaximal
5C2×#63566C212yesmaximal
6#10590301C218yesmaximal, direct product factor
7C2×#5020—31nomaximal
8C2×#4851—31nomaximal
9C22×#634—21no—
10C22×C3×Dic6C2211yescharacteristic
11C2×C32×C42C2211yescharacteristic
12C2×C4⋊(C3⋊Dic3)—21no—
13C2×C4⋊(C3⋊Dic3)C2212yes—
14#64078—22no—
15#64078C2214yes—
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×C3×Dic3⋊C4—21no—
18C2×C3×C4×Dic3—21no—
19C22×C3×C3⋊C8C2212yes—
20C3×C4×Dic6—22no—
21C3×C4×Dic6C2214yes—
22C3×C4⋊(C3⋊C8)C2214yes—
23#63573C2218yes—
24#63566C2218yes—
25C2×C3×C4×Q8—31no—
26C2×#869—31no—
27C2×#869—31no—
28C2×#869—61no—
29C2×C4×Dic6D311yescharacteristic
30C2×C3×C4⋊C8—31no—
31C2×#835—32no—
32C2×#817—32no—
33C2×#816—32no—
34#5020—38no—
35C2×#808—32no—
36C2×C4⋊(C3⋊C8)D311yescharacteristic
37#4851—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—
46C2×C3×Dic6—21no—
47C2×C3×Dic6—22no—
48C2×C3×Dic6Q814yescomplemented
49C2×C3×Dic6C2312yes—
50C32×C42D412yes—
51C32×C42C2312yes—
52C4⋊(C3⋊Dic3)—22no—
53C4⋊(C3⋊Dic3)—24no—
54C4⋊(C3⋊Dic3)C2314yes—
55C3×C4⋊Dic3—21no—
56C3×C4⋊Dic3C2312yes—
57C3×Dic3⋊C4—24no—
58C3×C4×Dic3—24no—
59C2×C3×C3⋊C8—24no—
60C2×C3×C3⋊C8C2314yes—
61C2×#475—91noSylow
62C22×C3×Q8—31no—
63C22×Dic6—62no—
64C22×Dic6—61no—
65C22×Dic6—61no—
66C22×Dic6C2×D311yescharacteristic
67C22×C3×C8—32no—
68C3×C4×Q8—34no—
69C3×C4×Q8—62no—
70C2×C3×C4⋊C4—31no—
71C2×C3×C4⋊C4—61no—
72C2×C3×C42—21no—
73C2×C3×C42—61no—
74C2×C3×C42C2×D311yescharacteristic
75C2×C3×C42C2×D311yescharacteristic
76C2×C4⋊Dic3—32no—
77C2×C4⋊Dic3—32no—
78C2×C4⋊Dic3—62no—
79C2×C4⋊Dic3—62no—
80C2×C4⋊Dic3—61no—
81C2×C4⋊Dic3—61no—
82C2×C4⋊Dic3C2×D311yescharacteristic
83C2×Dic3⋊C4—21no—
84C2×C4×Dic3—21no—
85C22×C3⋊C8C2×D312yes—
86#869—34no—
87#869—34no—
88#869—64no—
89#869—64no—
90#869—62no—
91#869—62no—
92C4×Dic6—22no—
93C4×Dic6C2×D314yes—
94C3×C4⋊C8—34no—
95#835—38no—
96#817—38no—
97#816—38no—
98#808—38no—
99C4⋊(C3⋊C8)C2×D314yes—
100C23×C32C2×D411yescharacteristic
101C2×C32×C4—22no—
102C2×C32×C4SD1614yes—
103C2×C32×C4C2×D412yes—
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4C2×D412yes—
106C2×C32×C4C2×Q812yes—
107C2×C32×C4#4112yes—
108C2×C32×C4C2411yescharacteristic
109C2×C3⋊Dic3—24no—
110C2×C3⋊Dic3—44no—
111#634—48no—
112C2×C3×Dic3—24no—
113C2×C3×Dic3—22no—
114C2×C3×Dic3—22no—
115C2×C3×Dic3—42no—
116C3×Dic6—24no—
117C3×Dic6—22no—
118C3×Dic6C2×Q814yescomplemented
119C3×C3⋊C8—24no—
120C2×C4⋊Q8—91no—
121C2×C4×Q8—31no—
122#475—98no—
123C2×#106—92no—
124C2×C4⋊C8—31no—
125C2×#103—92no—
126C2×C3×Q8—34no—
127C2×C3×Q8—32no—
128C2×C3×Q8—61no—
129C2×C3×Q8—62no—
130C22×C3×C4—21no—
131C22×C3×C4—21no—
132C22×C3×C4—21no—
133C22×C3×C4—61no—
134C22×C3×C4—61no—
135C22×C3×C4D1211yescharacteristic
136C22×C3×C4D1211yescharacteristic
137C22×C3×C4#6711yescharacteristic
138C22×C3×C4#6711yescharacteristic
139C22×C3×C4C22×D311yescharacteristic
140C22×C3×C4C22×D311yescharacteristic
141C22×Dic3—21no—
142C22×Dic3—21no—
143C22×Dic3—64no—
144C22×Dic3—62no—
145C22×Dic3—62no—
146C2×Dic6—22no—
147C2×Dic6—21no—
148C2×Dic6—68no—
149C2×Dic6—64no—
150C2×Dic6—64no—
151C2×Dic6—128no—
152C2×Dic6—124no—
153C2×Dic6—124no—
154C2×Dic6Dic614yescomplemented
155C2×Dic6C22×D312yes—
156C2×C3×C8—34no—
157C2×C3×C8—64no—
158C3×C4⋊C4—32no—
159C3×C4⋊C4—64no—
160C3×C4⋊C4—61no—
161C3×C42—22no—
162C3×C42—22no—
163C3×C42—64no—
164C3×C42D1212yes—
165C3×C42#6712yes—
166C3×C42C22×D312yes—
167C3×C42C22×D312yes—
168C4⋊Dic3—21no—
169C4⋊Dic3—34no—
170C4⋊Dic3—34no—
171C4⋊Dic3—64no—
172C4⋊Dic3—64no—
173C4⋊Dic3—68no—
174C4⋊Dic3—64no—
175C4⋊Dic3—62no—
176C4⋊Dic3—64no—
177C4⋊Dic3—62no—
178C4⋊Dic3C22×D312yes—
179Dic3⋊C4—24no—
180C4×Dic3—24no—
181C2×C3⋊C8—24no—
182C2×C3⋊C8C22×D314yes—
183C22×C32C22⋊Q812yes—
184C22×C32C2×SD1612yes—
185C22×C32#13712yes—
186C22×C32C22×D411yescharacteristic
187C32×C4—22no—
188C32×C4C22⋊Q812yes—
189C32×C4C2×SD1614yes—
190C32×C4C22×Q811yescharacteristic
191C32×C4C2×#4111yescharacteristic
192C3⋊Dic3—44no—
193C3×Dic3—24no—
194C3×Dic3—42no—
195C22×Q8—31no—
196C22×Q8—181no—
197C22×C8—32no—
198C4⋊Q8—94no—
199C4⋊Q8—182no—
200C4×Q8—34no—
201C4×Q8—62no—
202C2×C4⋊C4—31no—
203C2×C4⋊C4—61no—
204C2×C4⋊C4—92no—
205C2×C4⋊C4—181no—
206C2×C42—61no—
207C2×C42D3211yescharacteristic
208#106—98no—
209C4⋊C8—34no—
210#103—98no—
211C23×C3—21no—
212C23×C3C2×D1211yescharacteristic
213C23×C3C2×#6711yescharacteristic
214C3×Q8—34no—
215C3×Q8—64no—
216C3×Q8—62no—
217C2×C3×C4—24no—
218C2×C3×C4—22no—
219C2×C3×C4—22no—
220C2×C3×C4—21no—
221C2×C3×C4—24no—
222C2×C3×C4—22no—
223C2×C3×C4—22no—
224C2×C3×C4—22no—
225C2×C3×C4—21no—
226C2×C3×C4—22no—
227C2×C3×C4—64no—
228C2×C3×C4—62no—
229C2×C3×C4—62no—
230C2×C3×C4—122no—
231C2×C3×C4#20414yes—
232C2×C3×C4#21514yes—
233C2×C3×C4C2×Dic612yes—
234C2×C3×C4C2×D1212yes—
235C2×C3×C4C2×D1211yescharacteristic
236C2×C3×C4C2×D1212yes—
237C2×C3×C4#23512yes—
238C2×C3×C4#23712yes—
239C2×C3×C4D3×Q812yes—
240C2×C3×C4C2×#6712yes—
241C2×C3×C4C2×#6711yescharacteristic
242C2×C3×C4C2×#6712yes—
243C2×C3×C4C23×D311yescharacteristic
244C2×C3×C4C23×D311yescharacteristic
245C2×Dic3—24no—
246C2×Dic3—22no—
247C2×Dic3—22no—
248C2×Dic3—42no—
249C2×Dic3—68no—
250C2×Dic3—64no—
251C2×Dic3—64no—
252C2×Dic3—128no—
253C2×Dic3—124no—
254C2×Dic3—124no—
255Dic6—24no—
256Dic6—22no—
257Dic6—1216no—
258Dic6—128no—
259Dic6—128no—
260Dic6C2×Dic614yescomplemented
261C3×C8—64no—
262C3⋊C8—24no—
263C2×C32#47514yescomplemented
264C2×C32C2×C22⋊Q811yescharacteristic
265C2×C32C22×SD1611yescharacteristic
266C2×C32C2×#13711yescharacteristic
267C2×Q8—32no—
268C2×Q8—34no—
269C2×Q8—62no—
270C2×Q8—61no—
271C2×Q8—184no—
272C2×Q8—364no—
273C22×C4—61no—
274C22×C4—61no—
275C22×C4—182no—
276C22×C4#62611yescharacteristic
277C22×C4#62611yescharacteristic
278C22×C4C2×D3211yescharacteristic
279C2×C8—34no—
280C2×C8—64no—
281C4⋊C4—32no—
282C4⋊C4—61no—
283C4⋊C4—64no—
284C4⋊C4—94no—
285C4⋊C4—182no—
286C4⋊C4—184no—
287C42—64no—
288C42#62612yes—
289C42C2×D3212yes—
290C22×C3—21no—
291C22×C3—22no—
292C22×C3—22no—
293C22×C3—22no—
294C22×C3#89712yes—
295C22×C3C2×#20412yes—
296C22×C3#90912yes—
297C22×C3#92412yes—
298C22×C3C2×#21512yes—
299C22×C3#95112yes—
300C22×C3C22×D1211yescharacteristic
301C22×C3C22×#6711yescharacteristic
302C3×C4—24no—
303C3×C4—22no—
304C3×C4—22no—
305C3×C4—21no—
306C3×C4—21no—
307C3×C4—24no—
308C3×C4—22no—
309C3×C4—64no—
310C3×C4—122no—
311C3×C4#89712yes—
312C3×C4C2×#20414yes—
313C3×C4#92412yes—
314C3×C4C2×#21514yes—
315C3×C4C22×Dic611yescharacteristic
316C3×C4C2×#23511yescharacteristic
317C3×C4C2×#23711yescharacteristic
318C3×C4C2×D3×Q811yescharacteristic
319Dic3—24no—
320Dic3—42no—
321Dic3—128no—
322Dic3—124no—
323Dic3—124no—
324C32C2×#47511yescharacteristic, complemented, Sylow
325C23C2×#62611yescharacteristic
326Q8—34no—
327Q8—62no—
328Q8—64no—
329Q8—368no—
330C2×C4—22no—
331C2×C4—62no—
332C2×C4—64no—
333C2×C4—62no—
334C2×C4—122no—
335C2×C4—184no—
336C2×C4—364no—
337C2×C4#371714yes—
338C2×C4D3×Dic612yes—
339C2×C4#379512yes—
340C2×C4C2×#62612yes—
341C2×C4C2×#62612yes—
342C2×C4C2×#62611yescharacteristic
343C2×C4C22×D3211yescharacteristic
344C8—64no—
345C2×C3—21no—
346C2×C3—24no—
347C2×C3—21no—
348C2×C3—21no—
349C2×C3#485114yescomplemented
350C2×C3#502014yescomplemented
351C2×C3C2×#89711yescharacteristic
352C2×C3C22×#20411yescharacteristic
353C2×C3C2×#90911yescharacteristic
354C2×C3C2×#92411yescharacteristic
355C2×C3C22×#21511yescharacteristic
356C2×C3C2×#95111yescharacteristic
357C22#6383112yes—
358C22C2×#371712yes—
359C22#6385712yes—
360C22C22×#62611yescharacteristic
361C4—22no—
362C4—64no—
363C4—122no—
364C4—364no—
365C4C2×#371714yes—
366C4#6385712yes—
367C4C2×D3×Dic611yescharacteristic
368C4C2×#379511yescharacteristic
369C3—21no—
370C3C2×#485111yescharacteristic, complemented
371C3C2×#502011yescharacteristic, complemented
372C2#1059030114yesdirect product factor
373C2C2×#6383111yescharacteristic
374C2C22×#371711yescharacteristic
375C2C2×#6385711yescharacteristic
subgroupG/H
centerC23C2×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C42C22
socle, prime radicalC23×C32C2×D4
hypercenterC2×C42D32
hypocenterC32C2×#475
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. #10590301C2direct (N × H)
48. C2×C3×Dic6Q8semidirect
118. C3×Dic6C2×Q8semidirect
154. C2×Dic6Dic6semidirect
260. Dic6C2×Dic6semidirect
263. C2×C32#475semidirect
324. C32C2×#475semidirect
349. C2×C3#4851semidirect
350. C2×C3#5020semidirect
370. C3C2×#4851semidirect
371. C3C2×#5020semidirect
372. C2#10590301direct (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×C4×Dic62
C2×C3×C4⋊(C3⋊C8)2
C2×#635732
C2×#635662
#105903012
C2×#50203
C2×#48513