Finite Group Databasebeta

← C2×#10593971 #11900800

Subgroups — C2×#10593971 #11900800

Order 1152.

3705 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3796C212yesmaximal, complemented
2C2×C42×C3⋊D3C211yesmaximal, characteristic, complemented
3C2×C3×#875C212yesmaximal, complemented
4C2×#63914C211yesmaximal, characteristic, complemented
5C2×#63912C214yesmaximal, complemented
6C2×#63902C214yesmaximal, complemented
7C2×#63873C211yesmaximal, characteristic, complemented
8#10593971C2116yesmaximal, direct product factor
9C2×#5668—32nomaximal
10C22×C4×C3⋊D3C2212yes—
11C22×C4×C3⋊D3C2211yescharacteristic
12C22×C3×D12C2212yes—
13C22×C3×Dic6C2212yes—
14C22×#626C2214yes—
15C22×#625C2214yes—
16C22×D3×Dic3C2214yes—
17C2×#3796—216no—
18C2×#3796C22116yescomplemented
19C2×C32×C42C2211yescharacteristic
20C2×C4×C3⋊Dic3C2211yescharacteristic
21C2×C4×C3⋊Dic3C2212yes—
22C42×C3⋊D3C2218yescomplemented
23C2×C3×(C2×D3)⋊C4C2218yes—
24C3×#875C22116yescomplemented
25C2×#3724C2214yes—
26#63914C2218yescomplemented
27#63912C22132yescomplemented
28#63902C22132yescomplemented
29#63873C2218yescomplemented
30C22×#239—32no—
31C22×#237—32no—
32C2×C3×#124—32no—
33C2×#944—32no—
34C2×#940—32no—
35#5668—332no—
36C2×#884—38no—
37C2×#67⋊C4—38no—
38C2×#875D312yescomplemented
39C2×C42×D3—32no—
40C2×C42×D3—61no—
41C23×C3⋊D3C2311yescharacteristic
42C23×C3×D3C2314yes—
43C22×C32×C4C2312yes—
44C22×C32×C4C2311yescharacteristic
45C22×C3⋊Dic3C2311yescharacteristic
46C22×C3⋊Dic3C2312yes—
47C2×C4×C3⋊D3—28no—
48C2×C4×C3⋊D3D418yescomplemented
49C2×C4×C3⋊D3C2318yes—
50C2×C4×C3⋊D3C2314yes—
51C22×C3×Dic3C2314yes—
52C2×C3×D12—28no—
53C2×C3×D12C2318yes—
54C2×C3×Dic6—28no—
55C2×C3×Dic6C2318yes—
56C2×#626—216no—
57C2×#626C23116yes—
58C2×#625—216no—
59C2×#625C23116yes—
60C2×D3×Dic3—216no—
61C2×D3×Dic3C23116yes—
62#3796—264no—
63C32×C42C2314yes—
64C4×C3⋊Dic3C2314yes—
65C4×C3⋊Dic3C2318yes—
66C3×(C2×D3)⋊C4C23132yes—
67#3724C23116yes—
68C2×#532—91noSylow
69C22×C3×Q8—32no—
70C22×C3×D4—32no—
71C22×#67—38no—
72C22×#67—34no—
73C23×Dic3—34no—
74C2×#239—316no—
75C2×#239—616no—
76C2×#237—316no—
77C2×#237—616no—
78C22×D12—34no—
79C22×D12C2×D312yes—
80C22×C4×D3—32no—
81C22×C4×D3—34no—
82C22×C4×D3—34no—
83C22×C4×D3—61no—
84C22×C4×D3—62no—
85C22×Dic6C2×D312yes—
86C3×#124—316no—
87C2×C3×C22⋊C4—38no—
88C2×C3×C42—21no—
89C2×C3×C42C2×D312yes—
90#944—316no—
91#940—316no—
92C2×(C2×D3)⋊C4C2×D318yes—
93C2×Dic3⋊C4—38no—
94C2×C4×Dic3—34no—
95C2×C4×Dic3—32no—
96C2×C4×Dic3—62no—
97C2×C4×Dic3—61no—
98#884—364no—
99#67⋊C4—364no—
100#875C2×D3116yescomplemented
101C42×D3—316no—
102C42×D3—68no—
103C23×C32C2411yescharacteristic
104C22×C3⋊D3—24no—
105C22×C3⋊D3C2×D414yes—
106C22×C3⋊D3C2412yes—
107C22×C3×D3—28no—
108C22×C3×D3—216no—
109C22×C3×D3C2418yes—
110C2×C32×C4—24no—
111C2×C32×C4C2×D414yes—
112C2×C32×C4C2414yes—
113C2×C32×C4C2412yes—
114C2×C3⋊Dic3C2×D414yes—
115C2×C3⋊Dic3#4118yescomplemented
116C2×C3⋊Dic3C2412yes—
117C2×C3⋊Dic3C2414yes—
118C4×C3⋊D3—216no—
119C4×C3⋊D3C2×D4116yescomplemented
120C2×C3×Dic3—28no—
121C2×C3×Dic3C2418yes—
122C3×D12—216no—
123C3×Dic6—216no—
124#626—232no—
125#625—232no—
126D3×Dic3—232no—
127C22×#41—92no—
128#532—916no—
129C2×C4⋊Q8—91no—
130C2×#127—91no—
131C2×#124—32no—
132C2×#121—94no—
133C2×C4×D4—94no—
134C22×C42—91no—
135C24×C3—34no—
136C23×D3—32no—
137C23×D3—61no—
138C23×D3C22×D314yes—
139C2×C3×Q8—38no—
140C2×C3×Q8—68no—
141C2×C3×D4—38no—
142C2×C3×D4—68no—
143C22×C3×C4—22no—
144C22×C3×C4—21no—
145C22×C3×C4—34no—
146C22×C3×C4C22×D314yes—
147C22×C3×C4C22×D312yes—
148C2×#67—332no—
149C2×#67—316no—
150C2×#67—616no—
151C2×#67—632no—
152C22×Dic3—34no—
153C22×Dic3—32no—
154C22×Dic3—316no—
155C22×Dic3—62no—
156C22×Dic3—61no—
157C22×Dic3—616no—
158C22×Dic3C22×D314yes—
159#239—664no—
160#237—664no—
161C2×D12—28no—
162C2×D12—316no—
163C2×D12—616no—
164C2×D12C22×D318yes—
165C2×C4×D3—316no—
166C2×C4×D3—38no—
167C2×C4×D3—316no—
168C2×C4×D3—316no—
169C2×C4×D3—64no—
170C2×C4×D3—68no—
171C2×C4×D3—68no—
172C2×C4×D3—616no—
173C2×C4×D3—616no—
174C2×C4×D3—616no—
175C2×Dic6—28no—
176C2×Dic6C22×D318yes—
177C3×C22⋊C4—332no—
178C3×C42—24no—
179C3×C42C22×D318yes—
180(C2×D3)⋊C4C22×D3132yes—
181Dic3⋊C4—332no—
182C4×Dic3—316no—
183C4×Dic3—38no—
184C4×Dic3—68no—
185C4×Dic3—64no—
186C22×C32C22×D412yes—
187C22×C32C2×#4114yes—
188C22×C32C2511yescharacteristic
189C2×C3⋊D3—28no—
190C2×C3⋊D3—24no—
191C2×C3⋊D3C22×D414yes—
192C2×C3×D3—28no—
193C2×C3×D3—216no—
194C2×C3×D3—416no—
195C32×C4—24no—
196C32×C4C22×D414yes—
197C3⋊Dic3C22×D414yes—
198C3⋊Dic3C2×#4118yescomplemented
199C3×Dic3—28no—
200C2×#41—916no—
201C2×#41—1816no—
202C22×Q8—32no—
203C22×D4—32no—
204C22×D4—94no—
205C22×D4—94no—
206C23×C4—94no—
207C23×C4—91no—
208C23×C4—92no—
209C4⋊Q8—98no—
210#127—98no—
211#124—316no—
212#121—932no—
213C4×D4—932no—
214C2×C4⋊C4—94no—
215C2×C22⋊C4—38no—
216C2×C42—92no—
217C2×C42—91no—
218C2×C42—98no—
219C2×C42D3211yescharacteristic
220C23×C3—21no—
221C23×C3—38no—
222C23×C3—68no—
223C23×C3—616no—
224C23×C3C23×D312yes—
225C22×D3—28no—
226C22×D3—216no—
227C22×D3—38no—
228C22×D3—34no—
229C22×D3—64no—
230C22×D3—62no—
231C22×D3—68no—
232C22×D3—68no—
233C22×D3C23×D318yes—
234C3×Q8—616no—
235C3×D4—616no—
236C2×C3×C4—28no—
237C2×C3×C4—28no—
238C2×C3×C4—24no—
239C2×C3×C4—22no—
240C2×C3×C4—24no—
241C2×C3×C4—38no—
242C2×C3×C4—68no—
243C2×C3×C4D3×D418yes—
244C2×C3×C4C23×D318yes—
245C2×C3×C4C23×D314yes—
246#67—632no—
247#67—664no—
248C2×Dic3—28no—
249C2×Dic3—38no—
250C2×Dic3—316no—
251C2×Dic3—38no—
252C2×Dic3—34no—
253C2×Dic3—64no—
254C2×Dic3—68no—
255C2×Dic3—64no—
256C2×Dic3—62no—
257C2×Dic3—632no—
258C2×Dic3C23×D318yes—
259D12—216no—
260D12—632no—
261C4×D3—332no—
262C4×D3—616no—
263C4×D3—632no—
264C4×D3—632no—
265C4×D3—632no—
266Dic6—216no—
267C2×C32#53214yescomplemented
268C2×C32C23×D411yescharacteristic
269C2×C32C22×#4112yes—
270C3⋊D3—24no—
271C3×D3—48no—
272C24—34no—
273C24—91no—
274#41—1864no—
275C2×Q8—38no—
276C2×Q8—68no—
277C2×D4—38no—
278C2×D4—68no—
279C2×D4—916no—
280C2×D4—916no—
281C2×D4—1816no—
282C2×D4—1816no—
283C22×C4—34no—
284C22×C4—916no—
285C22×C4—92no—
286C22×C4—91no—
287C22×C4—94no—
288C22×C4—98no—
289C22×C4—98no—
290C22×C4—188no—
291C22×C4—1816no—
292C22×C4C2×D3212yes—
293C22×C4C2×D3211yescharacteristic
294C4⋊C4—916no—
295C22⋊C4—332no—
296C42—98no—
297C42—94no—
298C42C2×D3214yes—
299C22×C3—22no—
300C22×C3—24no—
301C22×C3—21no—
302C22×C3—68no—
303C22×C3—616no—
304C22×C3—1216no—
305C22×C3C2×D3×D414yes—
306C22×C3D3×#4118yes—
307C22×C3C24×D312yes—
308C2×D3—28no—
309C2×D3—216no—
310C2×D3—38no—
311C2×D3—416no—
312C2×D3—64no—
313C2×D3—68no—
314C2×D3—616no—
315C2×D3—616no—
316C2×D3—68no—
317C3×C4—28no—
318C3×C4—28no—
319C3×C4—24no—
320C3×C4—68no—
321C3×C4C2×D3×D418yes—
322Dic3—28no—
323Dic3—38no—
324Dic3—316no—
325Dic3—64no—
326Dic3—68no—
327C32C2×#53211yescharacteristic, complemented, Sylow
328C23—38no—
329C23—68no—
330C23—616no—
331C23—94no—
332C23—92no—
333C23—184no—
334C23C22×D3211yescharacteristic
335Q8—616no—
336D4—616no—
337D4—1832no—
338D4—1832no—
339C2×C4—24no—
340C2×C4—38no—
341C2×C4—68no—
342C2×C4—94no—
343C2×C4—98no—
344C2×C4—94no—
345C2×C4—92no—
346C2×C4—916no—
347C2×C4—1816no—
348C2×C4—1832no—
349C2×C4#380214yes—
350C2×C4C22×D3214yes—
351C2×C4C22×D3212yes—
352C2×C3—21no—
353C2×C3—22no—
354C2×C3—24no—
355C2×C3—128no—
356C2×C3#566818yescomplemented
357C2×C3C22×D3×D412yes—
358C2×C3C2×D3×#4114yes—
359D3—48no—
360D3—68no—
361D3—68no—
362C22—68no—
363C22—616no—
364C22—94no—
365C22—1216no—
366C22—184no—
367C22—188no—
368C22C2×#380212yes—
369C22#6430614yes—
370C22C23×D3211yescharacteristic
371C4—24no—
372C4—68no—
373C4—94no—
374C4—98no—
375C4C2×#380214yes—
376C3—21no—
377C3C2×#566812yescomplemented
378C2—128no—
379C2—184no—
380C2#1059397114yesdirect product factor
381C2C22×#380211yescharacteristic
382C2C2×#6430612yes—
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
socleC23×C32C24
hypercenterC2×C42D32
hypocenterC32C2×#532
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C22×#3796C2semidirect
2. C2×C42×C3⋊D3C2semidirect
3. C2×C3×#875C2semidirect
4. C2×#63914C2semidirect
5. C2×#63912C2semidirect
6. C2×#63902C2semidirect
7. C2×#63873C2semidirect
8. #10593971C2direct (N × H)
18. C2×#3796C22semidirect
22. C42×C3⋊D3C22semidirect
24. C3×#875C22semidirect
26. #63914C22semidirect
27. #63912C22semidirect
28. #63902C22semidirect
29. #63873C22semidirect
38. C2×#875D3semidirect
48. C2×C4×C3⋊D3D4semidirect
100. #875C2×D3semidirect
115. C2×C3⋊Dic3#41semidirect
119. C4×C3⋊D3C2×D4semidirect
198. C3⋊Dic3C2×#41semidirect
267. C2×C32#532semidirect
327. C32C2×#532semidirect
356. C2×C3#5668semidirect
377. C3C2×#5668semidirect
380. C2#10593971direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37962
C2×C42×C3⋊D32
C2×C3×#8752
C2×#639142
C2×#639122
C2×#639022
C2×#638732
#105939712
C2×#56683