Finite Group Databasebeta

← C2×#10593865 #11903415

Subgroups — C2×#10593865 #11903415

Order 1152.

2437 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C4⋊(C3⋊D3)C211yesmaximal, characteristic
2C2×C3×#869C211yesmaximal, characteristic, complemented
3C2×C3×C4×Dic6C211yesmaximal, characteristic, complemented
4C2×#63871C212yesmaximal, complemented
5C2×#63864C212yesmaximal
6C2×#63849C212yesmaximal, complemented
7C2×#63848C214yesmaximal, complemented
8C2×Dic3×Dic6C212yesmaximal, complemented
9#10593865C2116yesmaximal, direct product factor
10C2×#5732—31nomaximal
11C2×#5584—31nomaximal
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C22×C4×C3⋊D3C2212yes—
14C22×C3×Dic6C2212yes—
15C22×C3×Dic6C2211yescharacteristic
16C2×C32×C42C2211yescharacteristic
17C2×#3752C2212yes—
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C4×C4⋊(C3⋊D3)C2218yes—
20C2×C3×C4⋊Dic3C2212yes—
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C2×C3×C4⋊Dic3C2212yes—
23C2×C3×Dic3⋊C4C2212yes—
24C2×C3×C4×Dic3C2212yes—
25C3×#869C2218yescomplemented
26C3×C4×Dic6C2218yescomplemented
27C2×Dic3⋊Dic3C2214yes—
28C2×#3722C2214yes—
29C2×#3722C2214yes—
30C2×Dic32C2214yes—
31#63871C22116yescomplemented
32#63864C22116yes—
33#63849C22116yescomplemented
34#63848C22132yescomplemented
35Dic3×Dic6C22116yescomplemented
36C2×C3×C4⋊Q8—31no—
37C2×C3×C4×Q8—31no—
38C2×#947—32no—
39C2×#946—32no—
40C2×Q8×Dic3—32no—
41#5732—316no—
42#5584—316no—
43C2×#898—34no—
44C2×#898—34no—
45C2×#897—32no—
46C2×#892—32no—
47C2×#892—32no—
48C2×#875—32no—
49C2×C4×D12—31no—
50C2×C4×D12—31no—
51C2×C4×D12—61no—
52C2×#869D311yescharacteristic, complemented
53C2×C4×Dic6—32no—
54C2×C4×Dic6D311yescharacteristic, complemented
55C23×C3⋊D3C2312yes—
56C22×C32×C4C2311yescharacteristic
57C22×C32×C4C2311yescharacteristic
58C22×C32×C4C2311yescharacteristic
59C22×C3⋊Dic3C2312yes—
60C2×C4⋊(C3⋊D3)—24no—
61C2×C4⋊(C3⋊D3)C2314yes—
62C2×C4×C3⋊D3—28no—
63C2×C4×C3⋊D3C2318yes—
64C22×C3×Dic3C2312yes—
65C22×C3×Dic3C2312yes—
66C22×C3×Dic3C2314yes—
67C2×C3×Dic6—24no—
68C2×C3×Dic6—28no—
69C2×C3×Dic6C2318yes—
70C2×C3×Dic6C2314yes—
71C32×C42C2314yes—
72#3752C2318yes—
73C4⋊(C3⋊Dic3)C2314yes—
74C3×C4⋊Dic3C2318yes—
75C3×C4⋊Dic3C2314yes—
76C3×C4⋊Dic3C2318yes—
77C3×Dic3⋊C4C2318yes—
78C3×C4×Dic3C2318yes—
79Dic3⋊Dic3C23116yes—
80#3722C23116yes—
81#3722C23116yes—
82Dic32C23116yes—
83C2×#556—91noSylow
84C22×C3×Q8—32no—
85C22×C3×Q8—31no—
86C22×D12—31no—
87C22×D12—31no—
88C22×D12—61no—
89C22×C4×D3—32no—
90C22×C4×D3—32no—
91C22×C4×D3—62no—
92C22×Dic6C2×D312yes—
93C22×Dic6C2×D311yescharacteristic
94C3×C4⋊Q8—38no—
95C3×C4×Q8—38no—
96C2×C3×C4⋊C4—32no—
97C2×C3×C4⋊C4—31no—
98C2×C3×C4⋊C4—32no—
99C2×C3×C4⋊C4—32no—
100C2×C3×C42—21no—
101C2×C3×C42—32no—
102C2×C3×C42C2×D311yescharacteristic
103C2×C3×C42C2×D311yescharacteristic
104#947—316no—
105#946—316no—
106Q8×Dic3—316no—
107C2×(C2×D3)⋊C4—32no—
108C2×(C2×D3)⋊C4—32no—
109C2×(C2×D3)⋊C4—34no—
110C2×(C2×D3)⋊C4—34no—
111C2×(C2×D3)⋊C4—34no—
112C2×(C2×D3)⋊C4—34no—
113C2×(C2×D3)⋊C4—62no—
114C2×C4⋊Dic3—31no—
115C2×C4⋊Dic3—31no—
116C2×C4⋊Dic3—34no—
117C2×C4⋊Dic3—61no—
118C2×C4⋊Dic3C2×D311yescharacteristic
119C2×C4⋊Dic3C2×D312yes—
120C2×C4⋊Dic3C2×D312yes—
121C2×Dic3⋊C4—34no—
122C2×Dic3⋊C4C2×D312yes—
123C2×C4×Dic3—34no—
124C2×C4×Dic3—34no—
125C2×C4×Dic3C2×D312yes—
126#898—332no—
127#898—332no—
128#897—316no—
129#892—316no—
130#892—316no—
131#875—316no—
132C4×D12—38no—
133C4×D12—38no—
134C4×D12—68no—
135#869C2×D318yescomplemented
136C4×Dic6—316no—
137C4×Dic6C2×D318yescomplemented
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⋊Dic3C2414yes—
151C4⋊(C3⋊D3)—28no—
152C4×C3⋊D3—216no—
153C2×C3×Dic3—24no—
154C2×C3×Dic3—28no—
155C2×C3×Dic3—24no—
156C2×C3×Dic3C2414yes—
157C2×C3×Dic3C2418yes—
158C2×C3×Dic3C2414yes—
159C3×Dic6—28no—
160C3×Dic6—216no—
161#556—916no—
162C2×C4⋊Q8—31no—
163C2×#126—94no—
164C2×#124—92no—
165C2×C22⋊Q8—92no—
166C2×C4×Q8—31no—
167C2×C4×Q8—92no—
168C2×C4×D4—91no—
169C2×#117—92no—
170C23×D3—32no—
171C23×D3—32no—
172C23×D3—62no—
173C2×C3×Q8—38no—
174C2×C3×Q8—34no—
175C2×C3×Q8—68no—
176C2×C3×Q8—64no—
177C22×C3×C4—21no—
178C22×C3×C4—21no—
179C22×C3×C4—21no—
180C22×C3×C4—32no—
181C22×C3×C4—34no—
182C22×C3×C4—32no—
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—62no—
192C22×Dic3C22×D312yes—
193C22×Dic3C22×D314yes—
194C22×Dic3C22×D312yes—
195C2×D12—34no—
196C2×D12—34no—
197C2×D12—64no—
198C2×D12—68no—
199C2×D12—64no—
200C2×D12—64no—
201C2×C4×D3—38no—
202C2×C4×D3—38no—
203C2×C4×D3—68no—
204C2×C4×D3—68no—
205C2×C4×D3—68no—
206C2×C4×D3—128no—
207C2×Dic6—24no—
208C2×Dic6—28no—
209C2×Dic6C22×D318yes—
210C2×Dic6C22×D314yes—
211C3×C4⋊C4—34no—
212C3×C4⋊C4—38no—
213C3×C4⋊C4—38no—
214C3×C4⋊C4—38no—
215C3×C42—24no—
216C3×C42—38no—
217C3×C42C22×D314yes—
218C3×C42C22×D314yes—
219(C2×D3)⋊C4—38no—
220(C2×D3)⋊C4—38no—
221(C2×D3)⋊C4—316no—
222(C2×D3)⋊C4—316no—
223(C2×D3)⋊C4—316no—
224(C2×D3)⋊C4—316no—
225(C2×D3)⋊C4—68no—
226C4⋊Dic3—34no—
227C4⋊Dic3—34no—
228C4⋊Dic3—316no—
229C4⋊Dic3—64no—
230C4⋊Dic3C22×D314yes—
231C4⋊Dic3C22×D318yes—
232C4⋊Dic3C22×D318yes—
233Dic3⋊C4—316no—
234Dic3⋊C4C22×D318yes—
235C4×Dic3—316no—
236C4×Dic3—316no—
237C4×Dic3C22×D318yes—
238C22×C32C2×#4112yes—
239C22×C32C2×#4112yes—
240C22×C322−1+412yes—
241C22×C32C2511yescharacteristic
242C2×C3⋊D3—24no—
243C2×C3⋊D3—24no—
244C2×C3⋊D3—24no—
245C2×C3⋊D3—48no—
246C32×C4—22no—
247C32×C4C2×#4114yes—
248C32×C4C2×#4114yes—
249C3⋊Dic3—24no—
250C3×Dic3—24no—
251C3×Dic3—28no—
252C3×Dic3—24no—
253C22×Q8—31no—
254C22×Q8—32no—
255C22×D4—91no—
256C23×C4—92no—
257C4⋊Q8—38no—
258#126—932no—
259#124—916no—
260C22⋊Q8—916no—
261C4×Q8—38no—
262C4×Q8—916no—
263C4×D4—98no—
264#117—916no—
265C2×C4⋊C4—31no—
266C2×C4⋊C4—32no—
267C2×C4⋊C4—32no—
268C2×C4⋊C4—32no—
269C2×C4⋊C4—94no—
270C2×C4⋊C4—91no—
271C2×C22⋊C4—94no—
272C2×C22⋊C4—94no—
273C2×C22⋊C4—92no—
274C2×C42—32no—
275C2×C42—94no—
276C2×C42D3211yescharacteristic
277C23×C3—21no—
278C23×C3C23×D311yescharacteristic
279C23×C3C23×D311yescharacteristic
280C22×D3—34no—
281C22×D3—34no—
282C22×D3—64no—
283C22×D3—68no—
284C22×D3—64no—
285C22×D3—64no—
286C22×D3—64no—
287C22×D3—64no—
288C22×D3—64no—
289C22×D3—64no—
290C22×D3—124no—
291C22×D3—124no—
292C3×Q8—616no—
293C3×Q8—68no—
294C2×C3×C4—22no—
295C2×C3×C4—22no—
296C2×C3×C4—22no—
297C2×C3×C4—22no—
298C2×C3×C4—22no—
299C2×C3×C4—24no—
300C2×C3×C4—24no—
301C2×C3×C4—34no—
302C2×C3×C4—38no—
303C2×C3×C4—34no—
304C2×C3×C4—42no—
305C2×C3×C4—68no—
306C2×C3×C4—64no—
307C2×C3×C4—64no—
308C2×C3×C4#23514yes—
309C2×C3×C4#23714yes—
310C2×C3×C4#23914yes—
311C2×C3×C4#23914yes—
312C2×C3×C4C23×D312yes—
313C2×C3×C4C23×D312yes—
314C2×C3×C4C23×D312yes—
315C2×C3×C4C23×D312yes—
316C2×C3×C4C23×D312yes—
317C2×C3×C4C23×D312yes—
318C2×Dic3—24no—
319C2×Dic3—28no—
320C2×Dic3—24no—
321C2×Dic3—34no—
322C2×Dic3—34no—
323C2×Dic3—64no—
324C2×Dic3—64no—
325C2×Dic3—64no—
326C2×Dic3—124no—
327C2×Dic3C23×D314yes—
328C2×Dic3C23×D318yes—
329C2×Dic3C23×D314yes—
330D12—616no—
331D12—68no—
332D12—68no—
333C4×D3—616no—
334C4×D3—616no—
335C4×D3—1216no—
336Dic6—28no—
337Dic6—216no—
338C2×C32#55614yescomplemented
339C2×C32C22×#4111yescharacteristic
340C2×C32C22×#4111yescharacteristic
341C2×C32C2×2−1+411yescharacteristic
342C3⋊D3—44no—
343C24—92no—
344C2×Q8—34no—
345C2×Q8—38no—
346C2×Q8—68no—
347C2×Q8—64no—
348C2×D4—94no—
349C2×D4—184no—
350C22×C4—32no—
351C22×C4—32no—
352C22×C4—34no—
353C22×C4—92no—
354C22×C4—98no—
355C22×C4—188no—
356C22×C4C2×D3211yescharacteristic
357C22×C4C2×D3211yescharacteristic
358C22×C4C2×D3211yescharacteristic
359C4⋊C4—34no—
360C4⋊C4—38no—
361C4⋊C4—38no—
362C4⋊C4—38no—
363C4⋊C4—916no—
364C4⋊C4—94no—
365C22⋊C4—916no—
366C22⋊C4—916no—
367C22⋊C4—98no—
368C42—38no—
369C42—916no—
370C42C2×D3214yes—
371C22×C3—22no—
372C22×C3—22no—
373C22×C3—22no—
374C22×C3—21no—
375C22×C3C2×#23512yes—
376C22×C3C2×#23712yes—
377C22×C3C2×#23912yes—
378C22×C3C2×#23912yes—
379C22×C3#100712yes—
380C22×C3#101012yes—
381C22×C3C24×D311yescharacteristic
382C22×C3C24×D311yescharacteristic
383C2×D3—68no—
384C2×D3—64no—
385C2×D3—64no—
386C2×D3—64no—
387C2×D3—64no—
388C2×D3—64no—
389C2×D3—64no—
390C2×D3—124no—
391C2×D3—124no—
392C2×D3—1216no—
393C2×D3—128no—
394C2×D3—128no—
395C3×C4—22no—
396C3×C4—22no—
397C3×C4—24no—
398C3×C4—24no—
399C3×C4—42no—
400C3×C4—68no—
401C3×C4—64no—
402C3×C4—64no—
403C3×C4C2×#23514yes—
404C3×C4C2×#23714yes—
405C3×C4C2×#23914yes—
406C3×C4C2×#23914yes—
407Dic3—24no—
408Dic3—28no—
409Dic3—24no—
410Dic3—64no—
411Dic3—64no—
412Dic3—124no—
413C32C2×#55611yescharacteristic, complemented, Sylow
414C23—94no—
415C23—184no—
416C23—184no—
417C23—184no—
418C23C22×D3211yescharacteristic
419Q8—616no—
420Q8—68no—
421D4—188no—
422C2×C4—22no—
423C2×C4—34no—
424C2×C4—34no—
425C2×C4—38no—
426C2×C4—68no—
427C2×C4—64no—
428C2×C4—64no—
429C2×C4—94no—
430C2×C4—184no—
431C2×C4—1816no—
432C2×C4#379614yes—
433C2×C4#379914yes—
434C2×C4C22×D3212yes—
435C2×C4C22×D3212yes—
436C2×C4C22×D3212yes—
437C2×C3—21no—
438C2×C3—21no—
439C2×C3—21no—
440C2×C3—24no—
441C2×C3#558414yescomplemented
442C2×C3#573214yescomplemented
443C2×C3C22×#23511yescharacteristic
444C2×C3C22×#23711yescharacteristic
445C2×C3C22×#23911yescharacteristic
446C2×C3C22×#23911yescharacteristic
447C2×C3C2×#100711yescharacteristic
448C2×C3C2×#101011yescharacteristic
449D3—128no—
450D3—124no—
451D3—124no—
452C22—184no—
453C22—184no—
454C22—184no—
455C22—368no—
456C22C2×#379612yes—
457C22#6429712yes—
458C22C2×#379912yes—
459C22C23×D3211yescharacteristic
460C4—22no—
461C4—68no—
462C4—64no—
463C4—64no—
464C4—184no—
465C4C2×#379614yes—
466C4C2×#379914yes—
467C3—21no—
468C3C2×#558411yescharacteristic, complemented
469C3C2×#573211yescharacteristic, complemented
470C2—364no—
471C2#1059386514yesdirect product factor
472C2C22×#379611yescharacteristic
473C2C2×#6429711yescharacteristic
474C2C22×#379911yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
socleC23×C32C24
prime radicalC22×C4⋊(C3⋊D3)C22
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
2. C2×C3×#869C2semidirect
3. C2×C3×C4×Dic6C2semidirect
4. C2×#63871C2semidirect
6. C2×#63849C2semidirect
7. C2×#63848C2semidirect
8. C2×Dic3×Dic6C2semidirect
9. #10593865C2direct (N × H)
25. C3×#869C22semidirect
26. C3×C4×Dic6C22semidirect
31. #63871C22semidirect
33. #63849C22semidirect
34. #63848C22semidirect
35. Dic3×Dic6C22semidirect
52. C2×#869D3semidirect
54. C2×C4×Dic6D3semidirect
135. #869C2×D3semidirect
137. C4×Dic6C2×D3semidirect
338. C2×C32#556semidirect
413. C32C2×#556semidirect
441. C2×C3#5584semidirect
442. C2×C3#5732semidirect
468. C3C2×#5584semidirect
469. C3C2×#5732semidirect
471. C2#10593865direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×C4⋊(C3⋊D3)2
C2×C3×#8692
C2×C3×C4×Dic62
C2×#638712
C2×#638642
C2×#638492
C2×#638482
C2×Dic3×Dic62
#105938652
C2×#57323
C2×#55843