Finite Group Databasebeta

← C2×#10593863 #11903414

Subgroups — C2×#10593863 #11903414

Order 1152.

2373 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#634C211yesmaximal, characteristic, complemented
2C2×C3×C4×D12C211yesmaximal, characteristic
3C2×C3×#869C211yesmaximal, characteristic, complemented
4C2×#63863C212yesmaximal
5C2×#63858C214yesmaximal, complemented
6C2×#63857C212yesmaximal, complemented
7C2×#63843C212yesmaximal, complemented
8C2×#63841C212yesmaximal, complemented
9#10593863C2116yesmaximal, direct product factor
10C2×#5732—31nomaximal
11C2×#5542—31nomaximal
12C22×#634C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C22×C3×C4×D3C2212yes—
15C22×C3×Dic6C2212yes—
16C2×C32×C42C2211yescharacteristic
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C2×#3750C2212yes—
19C2×C4×C3⋊Dic3C2212yes—
20C4×#634C2218yescomplemented
21C2×C3×(C2×D3)⋊C4C2212yes—
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×C4⋊Dic3C2212yes—
24C2×C3×C4⋊Dic3C2212yes—
25C3×C4×D12C2218yes—
26C3×#869C2218yescomplemented
27C2×Dic3⋊Dic3C2214yes—
28C2×(C2×D3)⋊Dic3C2214yes—
29C2×(C2×D3)⋊Dic3C2214yes—
30C2×Dic32C2214yes—
31#63863C22116yes—
32#63858C22132yescomplemented
33#63857C22116yescomplemented
34#63843C22116yescomplemented
35#63841C22116yescomplemented
36C2×C3×C4⋊Q8—31no—
37C2×C3×C4×D4—31no—
38C2×#947—32no—
39C2×Q8×Dic3—32no—
40C2×#936—32no—
41C2×#926—32no—
42C2×#924—32no—
43#5732—316no—
44#5542—316no—
45C2×#898—34no—
46C2×#897—32no—
47C2×#892—32no—
48C2×#887—32no—
49C2×#879—34no—
50C2×C4×D12D311yescharacteristic
51C2×#869D311yescharacteristic, complemented
52C2×C4×Dic6—31no—
53C2×C4×Dic6—31no—
54C2×C4×Dic6—61no—
55C23×C3×D3C2312yes—
56C22×C32×C4C2311yescharacteristic
57C22×C32×C4C2311yescharacteristic
58C22×C32×C4C2311yescharacteristic
59C22×C3⋊Dic3C2312yes—
60C22×C3⋊Dic3C2312yes—
61C2×#634—24no—
62C2×#634C2314yes—
63C22×C3×Dic3C2314yes—
64C22×C3×Dic3C2312yes—
65C2×C3×D12—24no—
66C2×C3×D12C2314yes—
67C2×C3×C4×D3—28no—
68C2×C3×C4×D3C2318yes—
69C2×C3×Dic6—28no—
70C2×C3×Dic6C2318yes—
71C32×C42C2314yes—
72C4⋊(C3⋊Dic3)C2314yes—
73#3750C2318yes—
74C4×C3⋊Dic3C2318yes—
75C3×(C2×D3)⋊C4C2318yes—
76C3×C4⋊Dic3C2318yes—
77C3×C4⋊Dic3C2314yes—
78C3×C4⋊Dic3C2318yes—
79Dic3⋊Dic3C23116yes—
80(C2×D3)⋊Dic3C23116yes—
81(C2×D3)⋊Dic3C23116yes—
82Dic32C23116yes—
83C2×#556—91noSylow
84C22×C3×Q8—32no—
85C22×C3×D4—31no—
86C23×C3×C4—32no—
87C22×D12C2×D311yescharacteristic
88C22×C4×D3C2×D312yes—
89C22×Dic6—31no—
90C22×Dic6—31no—
91C22×Dic6—61no—
92C22×Dic6C2×D312yes—
93C3×C4⋊Q8—38no—
94C3×C4×D4—38no—
95C2×C3×C4⋊C4—31no—
96C2×C3×C4⋊C4—32no—
97C2×C3×C4⋊C4—32no—
98C2×C3×C22⋊C4—32no—
99C2×C3×C42—21no—
100C2×C3×C42C2×D311yescharacteristic
101C2×C3×C42C2×D311yescharacteristic
102C2×#217—34no—
103C2×#217—34no—
104#947—316no—
105Q8×Dic3—316no—
106#936—316no—
107C2×(C2×D3)⋊C4—34no—
108C2×(C2×D3)⋊C4—34no—
109C2×(C2×D3)⋊C4C2×D312yes—
110#926—316no—
111C2×C4⋊Dic3—31no—
112C2×C4⋊Dic3—31no—
113C2×C4⋊Dic3—34no—
114C2×C4⋊Dic3—61no—
115C2×C4⋊Dic3C2×D312yes—
116C2×C4⋊Dic3C2×D312yes—
117C2×C4⋊Dic3C2×D311yescharacteristic
118#924—316no—
119C2×Dic3⋊C4—32no—
120C2×Dic3⋊C4—32no—
121C2×Dic3⋊C4—34no—
122C2×Dic3⋊C4—62no—
123C2×C4×Dic3—32no—
124C2×C4×Dic3—32no—
125C2×C4×Dic3—34no—
126C2×C4×Dic3—34no—
127C2×C4×Dic3—62no—
128#898—332no—
129#897—316no—
130#892—316no—
131#887—316no—
132#879—332no—
133C4×D12C2×D318yes—
134#869C2×D318yescomplemented
135C4×Dic6—38no—
136C4×Dic6—38no—
137C4×Dic6—68no—
138C23×C32C2411yescharacteristic
139C22×C3×D3—24no—
140C22×C3×D3—24no—
141C22×C3×D3—24no—
142C22×C3×D3C2414yes—
143C2×C32×C4—22no—
144C2×C32×C4#4114yes—
145C2×C32×C4#4114yes—
146C2×C32×C4C2412yes—
147C2×C32×C4C2412yes—
148C2×C32×C4C2412yes—
149C2×C3⋊Dic3—24no—
150C2×C3⋊Dic3—24no—
151C2×C3⋊Dic3C2414yes—
152C2×C3⋊Dic3C2414yes—
153#634—28no—
154C2×C3×Dic3—28no—
155C2×C3×Dic3—24no—
156C2×C3×Dic3C2414yes—
157C2×C3×Dic3C2418yes—
158C3×D12—28no—
159C3×C4×D3—216no—
160C3×Dic6—216no—
161#556—916no—
162C2×C4⋊Q8—31no—
163C2×#126—94no—
164C2×#124—92no—
165C2×C22⋊Q8—92no—
166C2×C4×Q8—92no—
167C2×C4×Q8—91no—
168C2×C4×D4—31no—
169C2×#117—92no—
170C24×C3—32no—
171C23×D3C22×D312yes—
172C2×C3×Q8—38no—
173C2×C3×Q8—68no—
174C2×C3×D4—34no—
175C2×C3×D4—64no—
176C22×C3×C4—21no—
177C22×C3×C4—21no—
178C22×C3×C4—21no—
179C22×C3×C4—32no—
180C22×C3×C4—34no—
181C22×C3×C4—38no—
182C22×C3×C4—68no—
183C22×C3×C4C22×D311yescharacteristic
184C22×C3×C4C22×D311yescharacteristic
185C22×C3×C4C22×D311yescharacteristic
186C22×C3×C4C22×D311yescharacteristic
187C22×C3×C4C22×D311yescharacteristic
188C22×C3×C4C22×D311yescharacteristic
189C22×Dic3—32no—
190C22×Dic3—32no—
191C22×Dic3—32no—
192C22×Dic3—32no—
193C22×Dic3—62no—
194C22×Dic3—62no—
195C22×Dic3C22×D312yes—
196C22×Dic3C22×D314yes—
197C2×D12—24no—
198C2×D12C22×D314yes—
199C2×C4×D3—28no—
200C2×C4×D3C22×D318yes—
201C2×Dic6—28no—
202C2×Dic6—34no—
203C2×Dic6—34no—
204C2×Dic6—64no—
205C2×Dic6—68no—
206C2×Dic6—64no—
207C2×Dic6—64no—
208C2×Dic6C22×D318yes—
209C3×C4⋊C4—34no—
210C3×C4⋊C4—38no—
211C3×C4⋊C4—38no—
212C3×C22⋊C4—38no—
213C3×C42—24no—
214C3×C42C22×D314yes—
215C3×C42C22×D314yes—
216#217—316no—
217#217—316no—
218(C2×D3)⋊C4—316no—
219(C2×D3)⋊C4—316no—
220(C2×D3)⋊C4C22×D318yes—
221C4⋊Dic3—34no—
222C4⋊Dic3—34no—
223C4⋊Dic3—316no—
224C4⋊Dic3—64no—
225C4⋊Dic3C22×D318yes—
226C4⋊Dic3C22×D318yes—
227C4⋊Dic3C22×D314yes—
228Dic3⋊C4—38no—
229Dic3⋊C4—38no—
230Dic3⋊C4—316no—
231Dic3⋊C4—68no—
232C4×Dic3—38no—
233C4×Dic3—38no—
234C4×Dic3—316no—
235C4×Dic3—316no—
236C4×Dic3—68no—
237C22×C32C2×#4112yes—
238C22×C32C2×#4112yes—
239C22×C322−1+412yes—
240C22×C32C2511yescharacteristic
241C2×C3×D3—24no—
242C2×C3×D3—24no—
243C2×C3×D3—24no—
244C2×C3×D3—48no—
245C32×C4—22no—
246C32×C4C2×#4114yes—
247C32×C4C2×#4114yes—
248C3⋊Dic3—24no—
249C3⋊Dic3—24no—
250C3×Dic3—28no—
251C3×Dic3—24no—
252C22×Q8—32no—
253C22×Q8—91no—
254C22×D4—31no—
255C23×C4—32no—
256C4⋊Q8—38no—
257#126—932no—
258#124—916no—
259C22⋊Q8—916no—
260C4×Q8—916no—
261C4×Q8—98no—
262C4×D4—38no—
263#117—916no—
264C2×C4⋊C4—32no—
265C2×C4⋊C4—31no—
266C2×C4⋊C4—32no—
267C2×C4⋊C4—94no—
268C2×C4⋊C4—91no—
269C2×C4⋊C4—92no—
270C2×C22⋊C4—32no—
271C2×C22⋊C4—94no—
272C2×C22⋊C4—94no—
273C2×C42—94no—
274C2×C42—92no—
275C2×C42D3211yescharacteristic
276C23×C3—21no—
277C23×C3—34no—
278C23×C3—64no—
279C23×C3—64no—
280C23×C3—64no—
281C23×C3C23×D311yescharacteristic
282C23×C3C23×D311yescharacteristic
283C22×D3—24no—
284C22×D3—24no—
285C22×D3—24no—
286C22×D3C23×D314yes—
287C3×Q8—616no—
288C3×D4—68no—
289C2×C3×C4—22no—
290C2×C3×C4—22no—
291C2×C3×C4—22no—
292C2×C3×C4—22no—
293C2×C3×C4—22no—
294C2×C3×C4—24no—
295C2×C3×C4—24no—
296C2×C3×C4—34no—
297C2×C3×C4—38no—
298C2×C3×C4—42no—
299C2×C3×C4—68no—
300C2×C3×C4—64no—
301C2×C3×C4—616no—
302C2×C3×C4#23514yes—
303C2×C3×C4#23714yes—
304C2×C3×C4#23714yes—
305C2×C3×C4#23914yes—
306C2×C3×C4C23×D312yes—
307C2×C3×C4C23×D312yes—
308C2×C3×C4C23×D312yes—
309C2×C3×C4C23×D312yes—
310C2×C3×C4C23×D312yes—
311C2×C3×C4C23×D312yes—
312C2×Dic3—28no—
313C2×Dic3—24no—
314C2×Dic3—34no—
315C2×Dic3—34no—
316C2×Dic3—34no—
317C2×Dic3—34no—
318C2×Dic3—64no—
319C2×Dic3—64no—
320C2×Dic3—68no—
321C2×Dic3—64no—
322C2×Dic3—64no—
323C2×Dic3—64no—
324C2×Dic3—64no—
325C2×Dic3—124no—
326C2×Dic3C23×D314yes—
327C2×Dic3C23×D318yes—
328D12—28no—
329C4×D3—216no—
330Dic6—216no—
331Dic6—616no—
332Dic6—68no—
333Dic6—68no—
334C2×C32#55614yescomplemented
335C2×C32C22×#4111yescharacteristic
336C2×C32C22×#4111yescharacteristic
337C2×C32C2×2−1+411yescharacteristic
338C3×D3—44no—
339C24—32no—
340C2×Q8—38no—
341C2×Q8—68no—
342C2×Q8—94no—
343C2×Q8—184no—
344C2×D4—34no—
345C2×D4—64no—
346C22×C4—32no—
347C22×C4—34no—
348C22×C4—38no—
349C22×C4—68no—
350C22×C4—92no—
351C22×C4—92no—
352C22×C4C2×D3211yescharacteristic
353C22×C4C2×D3211yescharacteristic
354C22×C4C2×D3211yescharacteristic
355C4⋊C4—38no—
356C4⋊C4—34no—
357C4⋊C4—38no—
358C4⋊C4—916no—
359C4⋊C4—94no—
360C4⋊C4—98no—
361C22⋊C4—38no—
362C22⋊C4—916no—
363C22⋊C4—916no—
364C42—916no—
365C42—98no—
366C42C2×D3214yes—
367C22×C3—22no—
368C22×C3—22no—
369C22×C3—22no—
370C22×C3—21no—
371C22×C3—64no—
372C22×C3—64no—
373C22×C3—64no—
374C22×C3—128no—
375C22×C3C2×#23512yes—
376C22×C3C2×#23712yes—
377C22×C3C2×#23712yes—
378C22×C3C2×#23912yes—
379C22×C3#100712yes—
380C22×C3#101012yes—
381C22×C3C24×D311yescharacteristic
382C22×C3C24×D311yescharacteristic
383C2×D3—24no—
384C2×D3—24no—
385C2×D3—24no—
386C2×D3—48no—
387C3×C4—22no—
388C3×C4—22no—
389C3×C4—24no—
390C3×C4—24no—
391C3×C4—42no—
392C3×C4—68no—
393C3×C4—64no—
394C3×C4C2×#23514yes—
395C3×C4C2×#23714yes—
396C3×C4C2×#23714yes—
397C3×C4C2×#23914yes—
398Dic3—28no—
399Dic3—24no—
400Dic3—68no—
401Dic3—64no—
402Dic3—64no—
403Dic3—64no—
404Dic3—64no—
405Dic3—124no—
406C32C2×#55611yescharacteristic, complemented, Sylow
407C23—34no—
408C23—64no—
409C23—64no—
410C23—64no—
411C23C22×D3211yescharacteristic
412Q8—616no—
413Q8—188no—
414D4—68no—
415C2×C4—22no—
416C2×C4—34no—
417C2×C4—38no—
418C2×C4—68no—
419C2×C4—64no—
420C2×C4—616no—
421C2×C4—94no—
422C2×C4—94no—
423C2×C4—184no—
424C2×C4—184no—
425C2×C4#379514yes—
426C2×C4#379614yes—
427C2×C4C22×D3212yes—
428C2×C4C22×D3212yes—
429C2×C4C22×D3212yes—
430C2×C3—21no—
431C2×C3—21no—
432C2×C3—21no—
433C2×C3—24no—
434C2×C3—124no—
435C2×C3#554214yescomplemented
436C2×C3#573214yescomplemented
437C2×C3C22×#23511yescharacteristic
438C2×C3C22×#23711yescharacteristic
439C2×C3C22×#23711yescharacteristic
440C2×C3C22×#23911yescharacteristic
441C2×C3C2×#100711yescharacteristic
442C2×C3C2×#101011yescharacteristic
443D3—44no—
444C22—64no—
445C22—64no—
446C22—64no—
447C22—128no—
448C22C2×#379512yes—
449C22C2×#379612yes—
450C22#6429712yes—
451C22C23×D3211yescharacteristic
452C4—22no—
453C4—68no—
454C4—64no—
455C4—184no—
456C4—184no—
457C4C2×#379514yes—
458C4C2×#379614yes—
459C3—21no—
460C3C2×#554211yescharacteristic, complemented
461C3C2×#573211yescharacteristic, complemented
462C2—124no—
463C2#1059386314yesdirect product factor
464C2C22×#379511yescharacteristic
465C2C22×#379611yescharacteristic
466C2C2×#6429711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
socleC23×C32C24
prime radicalC22×C3×D12C22
hypercenterC2×C42D32
hypocenterC32C2×#556
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×C4×#634C2semidirect
3. C2×C3×#869C2semidirect
5. C2×#63858C2semidirect
6. C2×#63857C2semidirect
7. C2×#63843C2semidirect
8. C2×#63841C2semidirect
9. #10593863C2direct (N × H)
20. C4×#634C22semidirect
26. C3×#869C22semidirect
32. #63858C22semidirect
33. #63857C22semidirect
34. #63843C22semidirect
35. #63841C22semidirect
51. C2×#869D3semidirect
134. #869C2×D3semidirect
334. C2×C32#556semidirect
406. C32C2×#556semidirect
435. C2×C3#5542semidirect
436. C2×C3#5732semidirect
460. C3C2×#5542semidirect
461. C3C2×#5732semidirect
463. C2#10593863direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#6342
C2×C3×C4×D122
C2×C3×#8692
C2×#638632
C2×#638582
C2×#638572
C2×#638432
C2×#638412
#105938632
C2×#57323
C2×#55423