Finite Group Databasebeta

← C2×#10593881 #11901589

Subgroups — C2×#10593881 #11901589

Order 1152.

2153 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64078C211yesmaximal, characteristic, complemented
2C2×C3×#872C211yesmaximal, characteristic
3C2×C3×#870C211yesmaximal, characteristic, complemented
4C2×#63861C214yesmaximal
5C2×#63857C212yesmaximal
6C2×#63845C214yesmaximal, complemented
7C2×#63844C212yesmaximal, complemented
8#10593881C2116yesmaximal, direct product factor
9C2×#5698—31nomaximal
10C2×#5518—31nomaximal
11C22×#634C2212yes—
12C22×C3×C4×D3C2211yescharacteristic
13C2×C32×C42C2211yescharacteristic
14C2×C4⋊(C3⋊Dic3)C2214yes—
15#64078C2218yescomplemented
16C2×C3×(C2×D3)⋊C4C2212yes—
17C2×C3×C4⋊Dic3C2212yes—
18C2×C3×Dic3⋊C4C2212yes—
19C2×C3×Dic3⋊C4C2214yes—
20C2×C3×C4×Dic3C2211yescharacteristic
21C3×#872C2218yes—
22C3×#870C2218yescomplemented
23C2×#3724C2214yes—
24C2×Dic3⋊Dic3C2214yes—
25C2×(C2×D3)⋊Dic3C2214yes—
26C2×Dic32C2214yes—
27#63861C22132yes—
28#63857C22116yes—
29#63845C22132yescomplemented
30#63844C22116yescomplemented
31C2×C3×#125—31no—
32C2×C3×#117—31no—
33C2×#924—32no—
34#5698—316no—
35#5518—316no—
36C2×#898—34no—
37C2×#897—32no—
38C2×#890—34no—
39C2×#889—34no—
40C2×#887—32no—
41C2×#879—34no—
42C2×#872D311yescharacteristic
43C2×#870D311yescharacteristic, complemented
44C2×#869—31no—
45C2×#869—31no—
46C2×#869—61no—
47C2×C4×Dic6—32no—
48C23×C3×D3C2311yescharacteristic
49C22×C32×C4C2312yes—
50C22×C32×C4C2311yescharacteristic
51C22×C3⋊Dic3C2314yes—
52C2×#634—28no—
53C2×#634C2318yes—
54C22×C3×Dic3C2312yes—
55C22×C3×Dic3C2314yes—
56C22×C3×Dic3C2311yescharacteristic
57C2×C3×C4×D3—24no—
58C2×C3×C4×D3C2314yes—
59C32×C42C2314yes—
60C4⋊(C3⋊Dic3)C23116yes—
61C3×(C2×D3)⋊C4C2318yes—
62C3×C4⋊Dic3C2318yes—
63C3×Dic3⋊C4C2318yes—
64C3×Dic3⋊C4C23116yes—
65C3×C4×Dic3C2314yes—
66#3724C23116yes—
67Dic3⋊Dic3C23116yes—
68(C2×D3)⋊Dic3C23116yes—
69Dic32C23116yes—
70C2×#541—91noSylow
71C23×C3×C4—31no—
72C22×C4×D3C2×D311yescharacteristic
73C22×Dic6—32no—
74C22×Dic6—32no—
75C22×Dic6—62no—
76C3×#125—38no—
77C3×#117—38no—
78C2×C3×C4⋊C4—32no—
79C2×C3×C4⋊C4—34no—
80C2×C3×C4⋊C4—32no—
81C2×C3×C22⋊C4—32no—
82C2×C3×C42—21no—
83C2×C3×C42—31no—
84C2×C3×C42C2×D311yescharacteristic
85C2×C3×C42C2×D311yescharacteristic
86C2×#217—34no—
87C2×(C2×D3)⋊C4—34no—
88C2×(C2×D3)⋊C4C2×D312yes—
89C2×C4⋊Dic3—34no—
90C2×C4⋊Dic3—34no—
91C2×C4⋊Dic3—34no—
92C2×C4⋊Dic3—64no—
93C2×C4⋊Dic3C2×D312yes—
94#924—316no—
95C2×Dic3⋊C4—34no—
96C2×Dic3⋊C4—34no—
97C2×Dic3⋊C4—34no—
98C2×Dic3⋊C4C2×D314yes—
99C2×Dic3⋊C4C2×D312yes—
100C2×C4×Dic3—34no—
101C2×C4×Dic3—34no—
102C2×C4×Dic3C2×D311yescharacteristic
103#898—332no—
104#897—316no—
105#890—332no—
106#889—332no—
107#887—316no—
108#879—332no—
109#872C2×D318yes—
110#870C2×D318yescomplemented
111#869—38no—
112#869—38no—
113#869—68no—
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—
125#634—216no—
126C2×C3×Dic3—22no—
127C2×C3×Dic3—24no—
128C2×C3×Dic3—28no—
129C2×C3×Dic3C2414yes—
130C2×C3×Dic3C2418yes—
131C2×C3×Dic3C2412yes—
132C3×C4×D3—28no—
133#541—916no—
134C2×C4⋊Q8—91no—
135C2×#126—94no—
136C2×#125—31no—
137C2×#125—94no—
138C2×C22⋊Q8—92no—
139C2×C4×Q8—92no—
140C2×#117—31no—
141C24×C3—31no—
142C23×D3C22×D311yescharacteristic
143C22×C3×C4—22no—
144C22×C3×C4—21no—
145C22×C3×C4—32no—
146C22×C3×C4—34no—
147C22×C3×C4—31no—
148C22×C3×C4—34no—
149C22×C3×C4—64no—
150C22×C3×C4C22×D312yes—
151C22×C3×C4C22×D312yes—
152C22×C3×C4C22×D311yescharacteristic
153C22×C3×C4C22×D311yescharacteristic
154C22×Dic3—34no—
155C22×Dic3—34no—
156C22×Dic3—64no—
157C22×Dic3C22×D312yes—
158C22×Dic3C22×D314yes—
159C22×Dic3C22×D311yescharacteristic
160C2×C4×D3—24no—
161C2×C4×D3C22×D314yes—
162C2×Dic6—38no—
163C2×Dic6—38no—
164C2×Dic6—68no—
165C2×Dic6—68no—
166C2×Dic6—68no—
167C2×Dic6—128no—
168C3×C4⋊C4—38no—
169C3×C4⋊C4—38no—
170C3×C4⋊C4—316no—
171C3×C22⋊C4—38no—
172C3×C42—24no—
173C3×C42—34no—
174C3×C42C22×D314yes—
175C3×C42C22×D314yes—
176#217—316no—
177(C2×D3)⋊C4—316no—
178(C2×D3)⋊C4C22×D318yes—
179C4⋊Dic3—316no—
180C4⋊Dic3—316no—
181C4⋊Dic3—316no—
182C4⋊Dic3—616no—
183C4⋊Dic3C22×D318yes—
184Dic3⋊C4—316no—
185Dic3⋊C4—316no—
186Dic3⋊C4—316no—
187Dic3⋊C4C22×D3116yes—
188Dic3⋊C4C22×D318yes—
189C4×Dic3—316no—
190C4×Dic3—316no—
191C4×Dic3C22×D314yes—
192C22×C32C2×#4112yes—
193C22×C322−1+414yes—
194C22×C32C2511yescharacteristic
195C2×C3×D3—22no—
196C2×C3×D3—24no—
197C2×C3×D3—44no—
198C32×C4—24no—
199C32×C4C2×#4114yes—
200C3⋊Dic3—28no—
201C3×Dic3—22no—
202C3×Dic3—24no—
203C3×Dic3—28no—
204C22×Q8—92no—
205C23×C4—31no—
206C4⋊Q8—98no—
207#126—932no—
208#125—38no—
209#125—932no—
210C22⋊Q8—916no—
211C4×Q8—916no—
212#117—38no—
213C2×C4⋊C4—32no—
214C2×C4⋊C4—32no—
215C2×C4⋊C4—34no—
216C2×C4⋊C4—94no—
217C2×C4⋊C4—94no—
218C2×C4⋊C4—94no—
219C2×C22⋊C4—32no—
220C2×C22⋊C4—94no—
221C2×C42—31no—
222C2×C42—94no—
223C2×C42D3211yescharacteristic
224C23×C3—21no—
225C23×C3—32no—
226C23×C3—62no—
227C23×C3—64no—
228C23×C3C23×D311yescharacteristic
229C23×C3C23×D311yescharacteristic
230C22×D3—22no—
231C22×D3—24no—
232C22×D3C23×D312yes—
233C2×C3×C4—28no—
234C2×C3×C4—24no—
235C2×C3×C4—24no—
236C2×C3×C4—24no—
237C2×C3×C4—22no—
238C2×C3×C4—24no—
239C2×C3×C4—34no—
240C2×C3×C4—38no—
241C2×C3×C4—32no—
242C2×C3×C4—62no—
243C2×C3×C4—64no—
244C2×C3×C4—68no—
245C2×C3×C4—68no—
246C2×C3×C4#23514yes—
247C2×C3×C4#23914yes—
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—616no—
266Dic6—616no—
267Dic6—1216no—
268C2×C32#54114yescomplemented
269C2×C32C22×#4111yescharacteristic
270C2×C32C2×2−1+412yes—
271C3×D3—42no—
272C24—31no—
273C2×Q8—98no—
274C2×Q8—188no—
275C22×C4—32no—
276C22×C4—34no—
277C22×C4—31no—
278C22×C4—34no—
279C22×C4—64no—
280C22×C4—94no—
281C22×C4C2×D3212yes—
282C22×C4C2×D3211yescharacteristic
283C4⋊C4—38no—
284C4⋊C4—38no—
285C4⋊C4—316no—
286C4⋊C4—916no—
287C4⋊C4—916no—
288C4⋊C4—916no—
289C22⋊C4—38no—
290C22⋊C4—916no—
291C42—34no—
292C42—916no—
293C42C2×D3214yes—
294C22×C3—24no—
295C22×C3—22no—
296C22×C3—21no—
297C22×C3—62no—
298C22×C3—64no—
299C22×C3—124no—
300C22×C3C2×#23512yes—
301C22×C3C2×#23912yes—
302C22×C3#101014yes—
303C22×C3#101014yes—
304C22×C3C24×D311yescharacteristic
305C22×C3C24×D311yescharacteristic
306C2×D3—22no—
307C2×D3—24no—
308C2×D3—44no—
309C3×C4—28no—
310C3×C4—24no—
311C3×C4—24no—
312C3×C4—24no—
313C3×C4—62no—
314C3×C4—64no—
315C3×C4—68no—
316C3×C4C2×#23514yes—
317C3×C4C2×#23914yes—
318Dic3—22no—
319Dic3—28no—
320Dic3—24no—
321Dic3—68no—
322Dic3—68no—
323Dic3—128no—
324C32C2×#54111yescharacteristic, complemented, Sylow
325C23—32no—
326C23—64no—
327C23—62no—
328C23C22×D3211yescharacteristic
329Q8—1816no—
330C2×C4—24no—
331C2×C4—34no—
332C2×C4—38no—
333C2×C4—32no—
334C2×C4—64no—
335C2×C4—68no—
336C2×C4—62no—
337C2×C4—68no—
338C2×C4—98no—
339C2×C4—188no—
340C2×C4#379914yes—
341C2×C4C22×D3214yes—
342C2×C4C22×D3212yes—
343C2×C3—22no—
344C2×C3—21no—
345C2×C3—24no—
346C2×C3—122no—
347C2×C3#551814yescomplemented
348C2×C3#569814yescomplemented
349C2×C3C22×#23511yescharacteristic
350C2×C3C22×#23911yescharacteristic
351C2×C3C2×#101012yes—
352C2×C3C2×#101012yes—
353D3—42no—
354C22—64no—
355C22—62no—
356C22—124no—
357C22#6429814yes—
358C22C2×#379912yes—
359C22C23×D3211yescharacteristic
360C4—24no—
361C4—64no—
362C4—68no—
363C4—62no—
364C4—188no—
365C4C2×#379914yes—
366C3—21no—
367C3C2×#551811yescharacteristic, complemented
368C3C2×#569811yescharacteristic, complemented
369C2—122no—
370C2#1059388114yesdirect product factor
371C2C2×#6429812yes—
372C2C22×#379911yescharacteristic
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×#64078C2semidirect
3. C2×C3×#870C2semidirect
6. C2×#63845C2semidirect
7. C2×#63844C2semidirect
8. #10593881C2direct (N × H)
15. #64078C22semidirect
22. C3×#870C22semidirect
29. #63845C22semidirect
30. #63844C22semidirect
43. C2×#870D3semidirect
110. #870C2×D3semidirect
268. C2×C32#541semidirect
324. C32C2×#541semidirect
347. C2×C3#5518semidirect
348. C2×C3#5698semidirect
367. C3C2×#5518semidirect
368. C3C2×#5698semidirect
370. C2#10593881direct (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×#8722
C2×C3×#8702
C2×#638612
C2×#638572
C2×#638452
C2×#638442
#105938812
C2×#56983
C2×#55183