Finite Group Databasebeta

← C2×#10593862 #11901591

Subgroups — C2×#10593862 #11901591

Order 1152.

2121 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64079C211yesmaximal, characteristic, complemented
2C2×C3×#872C211yesmaximal, characteristic
3C2×C3×#869C211yesmaximal, characteristic, complemented
4C2×#63858C214yesmaximal
5C2×#63856C212yesmaximal
6C2×#63847C214yesmaximal, complemented
7C2×Dic3×Dic6C212yesmaximal, complemented
8#10593862C2116yesmaximal, direct product factor
9C2×#5731—31nomaximal
10C2×#5518—31nomaximal
11C22×C3×C4×D3C2211yescharacteristic
12C22×C3×Dic6C2212yes—
13C2×C32×C42C2211yescharacteristic
14C2×C4⋊(C3⋊Dic3)C2212yes—
15C2×#3750C2214yes—
16#64079C2218yescomplemented
17C2×C3×(C2×D3)⋊C4C2212yes—
18C2×C3×C4⋊Dic3C2214yes—
19C2×C3×Dic3⋊C4C2212yes—
20C2×C3×C4×Dic3C2211yescharacteristic
21C3×#872C2218yes—
22C3×#869C2218yescomplemented
23C2×#3724C2214yes—
24C2×Dic3⋊Dic3C2214yes—
25C2×(C2×D3)⋊Dic3C2214yes—
26C2×Dic32C2214yes—
27#63858C22132yes—
28#63856C22116yes—
29#63847C22132yescomplemented
30Dic3×Dic6C22116yescomplemented
31C2×C3×C4⋊Q8—31no—
32C2×C3×#117—31no—
33C2×#946—32no—
34C2×Q8×Dic3—32no—
35C2×#924—32no—
36#5731—316no—
37#5518—316no—
38C2×#898—34no—
39C2×#889—34no—
40C2×#889—34no—
41C2×#879—34no—
42C2×#872D311yescharacteristic
43C2×#870—31no—
44C2×#870—31no—
45C2×#870—61no—
46C2×#869D311yescharacteristic, complemented
47C2×C4×Dic6—32no—
48C23×C3×D3C2311yescharacteristic
49C22×C32×C4C2312yes—
50C22×C32×C4C2311yescharacteristic
51C22×C3⋊Dic3C2314yes—
52C22×C3×Dic3C2312yes—
53C22×C3×Dic3C2311yescharacteristic
54C22×C3×Dic3C2314yes—
55C2×C3×C4×D3—24no—
56C2×C3×C4×D3C2314yes—
57C2×C3×Dic6—28no—
58C2×C3×Dic6C2318yes—
59C32×C42C2314yes—
60C4⋊(C3⋊Dic3)C2318yes—
61#3750C23116yes—
62C3×(C2×D3)⋊C4C2318yes—
63C3×C4⋊Dic3C23116yes—
64C3×Dic3⋊C4C2318yes—
65C3×C4×Dic3C2314yes—
66#3724C23116yes—
67Dic3⋊Dic3C23116yes—
68(C2×D3)⋊Dic3C23116yes—
69Dic32C23116yes—
70C2×#541—91noSylow
71C22×C3×Q8—32no—
72C23×C3×C4—31no—
73C22×C4×D3C2×D311yescharacteristic
74C22×Dic6C2×D312yes—
75C3×C4⋊Q8—38no—
76C3×#117—38no—
77C2×C3×C4⋊C4—32no—
78C2×C3×C4⋊C4—34no—
79C2×C3×C22⋊C4—32no—
80C2×C3×C42—21no—
81C2×C3×C42—31no—
82C2×C3×C42C2×D311yescharacteristic
83C2×C3×C42C2×D311yescharacteristic
84C2×#217—34no—
85#946—316no—
86Q8×Dic3—316no—
87C2×(C2×D3)⋊C4—34no—
88C2×(C2×D3)⋊C4C2×D312yes—
89C2×C4⋊Dic3—32no—
90C2×C4⋊Dic3—32no—
91C2×C4⋊Dic3—34no—
92C2×C4⋊Dic3—62no—
93C2×C4⋊Dic3C2×D314yes—
94#924—316no—
95C2×Dic3⋊C4—34no—
96C2×Dic3⋊C4—34no—
97C2×Dic3⋊C4—34no—
98C2×Dic3⋊C4—34no—
99C2×Dic3⋊C4—34no—
100C2×Dic3⋊C4—64no—
101C2×Dic3⋊C4C2×D312yes—
102C2×C4×Dic3—34no—
103C2×C4×Dic3—34no—
104C2×C4×Dic3C2×D311yescharacteristic
105#898—332no—
106#889—332no—
107#889—332no—
108#879—332no—
109#872C2×D318yes—
110#870—38no—
111#870—38no—
112#870—68no—
113#869C2×D318yescomplemented
114C4×Dic6—316no—
115C23×C32C2411yescharacteristic
116C22×C3×D3—22no—
117C22×C3×D3—24no—
118C22×C3×D3C2412yes—
119C2×C32×C4—24no—
120C2×C32×C4#4114yes—
121C2×C32×C4C2414yes—
122C2×C32×C4C2412yes—
123C2×C3⋊Dic3—28no—
124C2×C3⋊Dic3C2418yes—
125C2×C3×Dic3—28no—
126C2×C3×Dic3—22no—
127C2×C3×Dic3—24no—
128C2×C3×Dic3C2414yes—
129C2×C3×Dic3C2418yes—
130C2×C3×Dic3C2412yes—
131C3×C4×D3—28no—
132C3×Dic6—216no—
133#541—916no—
134C2×C4⋊Q8—31no—
135C2×#126—94no—
136C2×#125—94no—
137C2×#125—91no—
138C2×C22⋊Q8—92no—
139C2×C4×Q8—92no—
140C2×#117—31no—
141C24×C3—31no—
142C23×D3C22×D311yescharacteristic
143C2×C3×Q8—38no—
144C2×C3×Q8—68no—
145C22×C3×C4—21no—
146C22×C3×C4—22no—
147C22×C3×C4—32no—
148C22×C3×C4—34no—
149C22×C3×C4—31no—
150C22×C3×C4—34no—
151C22×C3×C4—64no—
152C22×C3×C4C22×D312yes—
153C22×C3×C4C22×D312yes—
154C22×C3×C4C22×D311yescharacteristic
155C22×C3×C4C22×D311yescharacteristic
156C22×Dic3—34no—
157C22×Dic3—34no—
158C22×Dic3—64no—
159C22×Dic3C22×D312yes—
160C22×Dic3C22×D314yes—
161C22×Dic3C22×D311yescharacteristic
162C2×C4×D3—24no—
163C2×C4×D3C22×D314yes—
164C2×Dic6—28no—
165C2×Dic6C22×D318yes—
166C3×C4⋊C4—38no—
167C3×C4⋊C4—316no—
168C3×C22⋊C4—38no—
169C3×C42—24no—
170C3×C42—34no—
171C3×C42C22×D314yes—
172C3×C42C22×D314yes—
173#217—316no—
174(C2×D3)⋊C4—316no—
175(C2×D3)⋊C4C22×D318yes—
176C4⋊Dic3—38no—
177C4⋊Dic3—38no—
178C4⋊Dic3—316no—
179C4⋊Dic3—68no—
180C4⋊Dic3C22×D3116yes—
181Dic3⋊C4—316no—
182Dic3⋊C4—316no—
183Dic3⋊C4—316no—
184Dic3⋊C4—316no—
185Dic3⋊C4—316no—
186Dic3⋊C4—616no—
187Dic3⋊C4C22×D318yes—
188C4×Dic3—316no—
189C4×Dic3—316no—
190C4×Dic3C22×D314yes—
191C22×C32C2×#4112yes—
192C22×C322−1+414yes—
193C22×C32C2511yescharacteristic
194C2×C3×D3—22no—
195C2×C3×D3—24no—
196C2×C3×D3—44no—
197C32×C4—24no—
198C32×C4C2×#4114yes—
199C3⋊Dic3—28no—
200C3×Dic3—28no—
201C3×Dic3—22no—
202C3×Dic3—24no—
203C22×Q8—32no—
204C23×C4—31no—
205C4⋊Q8—38no—
206#126—932no—
207#125—932no—
208#125—98no—
209C22⋊Q8—916no—
210C4×Q8—916no—
211#117—38no—
212C2×C4⋊C4—32no—
213C2×C4⋊C4—34no—
214C2×C4⋊C4—94no—
215C2×C4⋊C4—94no—
216C2×C4⋊C4—92no—
217C2×C4⋊C4—94no—
218C2×C22⋊C4—32no—
219C2×C22⋊C4—94no—
220C2×C42—31no—
221C2×C42—94no—
222C2×C42D3211yescharacteristic
223C23×C3—21no—
224C23×C3—32no—
225C23×C3—62no—
226C23×C3—64no—
227C23×C3C23×D311yescharacteristic
228C23×C3C23×D311yescharacteristic
229C22×D3—22no—
230C22×D3—24no—
231C22×D3C23×D312yes—
232C3×Q8—616no—
233C2×C3×C4—24no—
234C2×C3×C4—24no—
235C2×C3×C4—22no—
236C2×C3×C4—24no—
237C2×C3×C4—24no—
238C2×C3×C4—34no—
239C2×C3×C4—38no—
240C2×C3×C4—32no—
241C2×C3×C4—44no—
242C2×C3×C4—68no—
243C2×C3×C4—62no—
244C2×C3×C4—64no—
245C2×C3×C4—68no—
246C2×C3×C4#23514yes—
247C2×C3×C4#23714yes—
248C2×C3×C4C23×D314yes—
249C2×C3×C4C23×D314yes—
250C2×C3×C4C23×D312yes—
251C2×C3×C4C23×D312yes—
252C2×Dic3—22no—
253C2×Dic3—28no—
254C2×Dic3—24no—
255C2×Dic3—38no—
256C2×Dic3—38no—
257C2×Dic3—68no—
258C2×Dic3—68no—
259C2×Dic3—68no—
260C2×Dic3—128no—
261C2×Dic3C23×D314yes—
262C2×Dic3C23×D318yes—
263C2×Dic3C23×D312yes—
264C4×D3—28no—
265Dic6—216no—
266C2×C32#54114yescomplemented
267C2×C32C22×#4111yescharacteristic
268C2×C32C2×2−1+412yes—
269C3×D3—42no—
270C24—31no—
271C2×Q8—38no—
272C2×Q8—68no—
273C22×C4—32no—
274C22×C4—34no—
275C22×C4—31no—
276C22×C4—34no—
277C22×C4—64no—
278C22×C4—94no—
279C22×C4C2×D3212yes—
280C22×C4C2×D3211yescharacteristic
281C4⋊C4—38no—
282C4⋊C4—316no—
283C4⋊C4—916no—
284C4⋊C4—916no—
285C4⋊C4—98no—
286C4⋊C4—916no—
287C22⋊C4—38no—
288C22⋊C4—916no—
289C42—34no—
290C42—916no—
291C42C2×D3214yes—
292C22×C3—22no—
293C22×C3—24no—
294C22×C3—21no—
295C22×C3—62no—
296C22×C3—64no—
297C22×C3—124no—
298C22×C3C2×#23512yes—
299C22×C3C2×#23712yes—
300C22×C3#100714yes—
301C22×C3#101014yes—
302C22×C3C24×D311yescharacteristic
303C22×C3C24×D311yescharacteristic
304C2×D3—22no—
305C2×D3—24no—
306C2×D3—44no—
307C3×C4—24no—
308C3×C4—24no—
309C3×C4—24no—
310C3×C4—44no—
311C3×C4—68no—
312C3×C4—62no—
313C3×C4—64no—
314C3×C4C2×#23514yes—
315C3×C4C2×#23714yes—
316Dic3—22no—
317Dic3—28no—
318Dic3—24no—
319Dic3—68no—
320Dic3—68no—
321Dic3—128no—
322C32C2×#54111yescharacteristic, complemented, Sylow
323C23—32no—
324C23—62no—
325C23—64no—
326C23C22×D3211yescharacteristic
327Q8—616no—
328C2×C4—24no—
329C2×C4—34no—
330C2×C4—38no—
331C2×C4—32no—
332C2×C4—62no—
333C2×C4—68no—
334C2×C4—64no—
335C2×C4—68no—
336C2×C4—98no—
337C2×C4—188no—
338C2×C4#379514yes—
339C2×C4C22×D3214yes—
340C2×C4C22×D3212yes—
341C2×C3—21no—
342C2×C3—22no—
343C2×C3—24no—
344C2×C3—122no—
345C2×C3#551814yescomplemented
346C2×C3#573114yescomplemented
347C2×C3C22×#23511yescharacteristic
348C2×C3C22×#23711yescharacteristic
349C2×C3C2×#100712yes—
350C2×C3C2×#101012yes—
351D3—42no—
352C22—62no—
353C22—64no—
354C22—124no—
355C22C2×#379512yes—
356C22#6429714yes—
357C22C23×D3211yescharacteristic
358C4—24no—
359C4—62no—
360C4—68no—
361C4—64no—
362C4—188no—
363C4C2×#379514yes—
364C3—21no—
365C3C2×#551811yescharacteristic, complemented
366C3C2×#573111yescharacteristic, complemented
367C2—122no—
368C2#1059386214yesdirect product factor
369C2C22×#379511yescharacteristic
370C2C2×#6429712yes—
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
socleC23×C32C24
prime radicalC23×C3×D3C23
hypercenterC2×C42D32
hypocenterC32C2×#541
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×#64079C2semidirect
3. C2×C3×#869C2semidirect
6. C2×#63847C2semidirect
7. C2×Dic3×Dic6C2semidirect
8. #10593862C2direct (N × H)
16. #64079C22semidirect
22. C3×#869C22semidirect
29. #63847C22semidirect
30. Dic3×Dic6C22semidirect
46. C2×#869D3semidirect
113. #869C2×D3semidirect
266. C2×C32#541semidirect
322. C32C2×#541semidirect
345. C2×C3#5518semidirect
346. C2×C3#5731semidirect
365. C3C2×#5518semidirect
366. C3C2×#5731semidirect
368. C2#10593862direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640792
C2×C3×#8722
C2×C3×#8692
C2×#638582
C2×#638562
C2×#638472
C2×Dic3×Dic62
#105938622
C2×#57313
C2×#55183