Finite Group Databasebeta

← C2×#10593956 #11903278

Subgroups — C2×#10593956 #11903278

Order 1152.

2549 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×#634C211yesmaximal, characteristic, complemented
2C2×C3×C4×D12C211yesmaximal, characteristic
3C2×C3×#869C211yesmaximal, characteristic, complemented
4C2×#63898C212yesmaximal
5C2×D3×C4⋊Dic3C212yesmaximal, complemented
6C2×#63887C214yesmaximal, complemented
7C2×#63872C212yesmaximal, complemented
8C2×#63857C212yesmaximal, complemented
9#10593956C2116yesmaximal, direct product factor
10C2×#5730—31nomaximal
11C2×#5543—31nomaximal
12C22×#634C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C22×C3×C4×D3C2212yes—
15C22×C3×Dic6C2212yes—
16C22×D3×Dic3C2214yes—
17C2×C32×C42C2211yescharacteristic
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C2×#3750C2212yes—
20C2×C4×C3⋊Dic3C2212yes—
21C4×#634C2218yescomplemented
22C2×C3×(C2×D3)⋊C4C2212yes—
23C2×C3×C4⋊Dic3C2212yes—
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C2×C3×C4⋊Dic3C2212yes—
26C3×C4×D12C2218yes—
27C3×#869C2218yescomplemented
28C2×Dic3⋊Dic3C2214yes—
29C2×Dic3⋊Dic3C2214yes—
30C2×(C2×D3)⋊Dic3C2214yes—
31#63898C22116yes—
32D3×C4⋊Dic3C22116yescomplemented
33#63887C22132yescomplemented
34#63872C22116yescomplemented
35#63857C22116yescomplemented
36C2×C3×C4⋊Q8—31no—
37C2×C3×C4×D4—31no—
38C2×#946—34no—
39C2×D4×Dic3—32no—
40C22×C4⋊Dic3—32no—
41C2×#924—32no—
42#5730—316no—
43#5543—316no—
44C2×#897—32no—
45C2×#893—32no—
46C2×D3×C4⋊C4—32no—
47C2×#890—32no—
48C2×#890—32no—
49C2×#878—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×D12Q818yescomplemented
66C2×C3×D12C2314yes—
67C2×C3×C4×D3—28no—
68C2×C3×C4×D3C2318yes—
69C2×C3×Dic6—44no—
70C2×C3×Dic6C2318yes—
71C2×D3×Dic3—48no—
72C2×D3×Dic3C23116yes—
73C32×C42C2314yes—
74C4⋊(C3⋊Dic3)C2314yes—
75#3750C2318yes—
76C4×C3⋊Dic3C2318yes—
77C3×(C2×D3)⋊C4C2318yes—
78C3×C4⋊Dic3C2318yes—
79C3×C4⋊Dic3C2314yes—
80C3×C4⋊Dic3C2318yes—
81Dic3⋊Dic3C23116yes—
82Dic3⋊Dic3C23116yes—
83(C2×D3)⋊Dic3C23116yes—
84C2×#554—91noSylow
85C22×C3×Q8—32no—
86C22×C3×D4—31no—
87C23×C3×C4—32no—
88C23×Dic3—34no—
89C22×D12C2×D311yescharacteristic
90C22×C4×D3—34no—
91C22×C4×D3C2×D312yes—
92C22×Dic6—31no—
93C22×Dic6—31no—
94C22×Dic6—61no—
95C22×Dic6C2×D312yes—
96C3×C4⋊Q8—38no—
97C3×C4×D4—38no—
98C2×C3×C4⋊C4—31no—
99C2×C3×C4⋊C4—32no—
100C2×C3×C4⋊C4—32no—
101C2×C3×C22⋊C4—32no—
102C2×C3×C42—21no—
103C2×C3×C42C2×D311yescharacteristic
104C2×C3×C42C2×D311yescharacteristic
105C2×#217—34no—
106#946—332no—
107D4×Dic3—316no—
108C2×(C2×D3)⋊C4—34no—
109C2×(C2×D3)⋊C4C2×D312yes—
110C2×C4⋊Dic3—31no—
111C2×C4⋊Dic3—31no—
112C2×C4⋊Dic3—34no—
113C2×C4⋊Dic3—34no—
114C2×C4⋊Dic3—316no—
115C2×C4⋊Dic3—61no—
116C2×C4⋊Dic3C2×D312yes—
117C2×C4⋊Dic3C2×D312yes—
118C2×C4⋊Dic3C2×D311yescharacteristic
119#924—316no—
120C2×Dic3⋊C4—32no—
121C2×Dic3⋊C4—32no—
122C2×Dic3⋊C4—34no—
123C2×Dic3⋊C4—34no—
124C2×Dic3⋊C4—62no—
125C2×C4×Dic3—32no—
126C2×C4×Dic3—32no—
127C2×C4×Dic3—62no—
128#897—316no—
129#893—316no—
130D3×C4⋊C4—316no—
131#890—316no—
132#890—316no—
133#878—332no—
134C4×D12C2×D318yes—
135#869C2×D318yescomplemented
136C4×Dic6—38no—
137C4×Dic6—38no—
138C4×Dic6—68no—
139C23×C32C2411yescharacteristic
140C22×C3×D3—24no—
141C22×C3×D3—24no—
142C22×C3×D3C2×Q818yes—
143C22×C3×D3C2414yes—
144C2×C32×C4—22no—
145C2×C32×C4C2×Q814yes—
146C2×C32×C4#4114yes—
147C2×C32×C4C2412yes—
148C2×C32×C4C2412yes—
149C2×C32×C4C2412yes—
150C2×C3⋊Dic3—24no—
151C2×C3⋊Dic3—24no—
152C2×C3⋊Dic3C2414yes—
153C2×C3⋊Dic3C2414yes—
154#634—28no—
155C2×C3×Dic3—24no—
156C2×C3×Dic3—28no—
157C2×C3×Dic3C2418yes—
158C2×C3×Dic3C2414yes—
159C3×D12C2×Q8116yescomplemented
160C3×C4×D3—216no—
161C3×Dic6—48no—
162D3×Dic3—416no—
163#554—916no—
164C2×C4⋊Q8—31no—
165C2×#125—92no—
166C2×C22⋊Q8—94no—
167C2×C22⋊Q8—92no—
168C2×C4×Q8—91no—
169C2×C4×D4—31no—
170C2×C4×D4—92no—
171C22×C4⋊C4—92no—
172C24×C3—32no—
173C23×D3C22×D312yes—
174C2×C3×Q8—38no—
175C2×C3×Q8—124no—
176C2×C3×D4—38no—
177C2×C3×D4—34no—
178C22×C3×C4—21no—
179C22×C3×C4—21no—
180C22×C3×C4—21no—
181C22×C3×C4—32no—
182C22×C3×C4—34no—
183C22×C3×C4—38no—
184C22×C3×C4—68no—
185C22×C3×C4C22×D311yescharacteristic
186C22×C3×C4C22×D311yescharacteristic
187C22×C3×C4C22×D311yescharacteristic
188C22×C3×C4C22×D311yescharacteristic
189C22×C3×C4C22×D311yescharacteristic
190C22×C3×C4C22×D311yescharacteristic
191C22×Dic3—32no—
192C22×Dic3—32no—
193C22×Dic3—32no—
194C22×Dic3—32no—
195C22×Dic3—316no—
196C22×Dic3—62no—
197C22×Dic3—62no—
198C22×Dic3—128no—
199C22×Dic3C22×D312yes—
200C22×Dic3C22×D314yes—
201C2×D12Dic618yescomplemented
202C2×D12C22×D314yes—
203C2×C4×D3—28no—
204C2×C4×D3—316no—
205C2×C4×D3—128no—
206C2×C4×D3C22×D318yes—
207C2×Dic6—34no—
208C2×Dic6—34no—
209C2×Dic6—44no—
210C2×Dic6—64no—
211C2×Dic6—68no—
212C2×Dic6—64no—
213C2×Dic6—64no—
214C2×Dic6C22×D318yes—
215C3×C4⋊C4—34no—
216C3×C4⋊C4—38no—
217C3×C4⋊C4—38no—
218C3×C22⋊C4—38no—
219C3×C42—24no—
220C3×C42C22×D314yes—
221C3×C42C22×D314yes—
222#217—316no—
223(C2×D3)⋊C4—316no—
224(C2×D3)⋊C4C22×D318yes—
225C4⋊Dic3—34no—
226C4⋊Dic3—34no—
227C4⋊Dic3—316no—
228C4⋊Dic3—316no—
229C4⋊Dic3—64no—
230C4⋊Dic3C22×D318yes—
231C4⋊Dic3C22×D318yes—
232C4⋊Dic3C22×D314yes—
233Dic3⋊C4—38no—
234Dic3⋊C4—38no—
235Dic3⋊C4—316no—
236Dic3⋊C4—316no—
237Dic3⋊C4—68no—
238C4×Dic3—38no—
239C4×Dic3—38no—
240C4×Dic3—68no—
241C22×C32C22×Q812yes—
242C22×C32C2×#4112yes—
243C22×C32H(5,𝔽2)12yes—
244C22×C32C2511yescharacteristic
245C2×C3×D3—216no—
246C2×C3×D3—24no—
247C2×C3×D3—24no—
248C2×C3×D3C22×Q818yes—
249C32×C4—22no—
250C32×C4C22×Q814yes—
251C32×C4C2×#4114yes—
252C3⋊Dic3—24no—
253C3⋊Dic3—24no—
254C3×Dic3—24no—
255C3×Dic3—28no—
256C22×Q8—32no—
257C22×Q8—91no—
258C22×D4—31no—
259C23×C4—32no—
260C23×C4—94no—
261C4⋊Q8—38no—
262#125—916no—
263C22⋊Q8—932no—
264C22⋊Q8—916no—
265C4×Q8—98no—
266C4×D4—38no—
267C4×D4—916no—
268C2×C4⋊C4—32no—
269C2×C4⋊C4—31no—
270C2×C4⋊C4—32no—
271C2×C4⋊C4—916no—
272C2×C4⋊C4—94no—
273C2×C4⋊C4—94no—
274C2×C4⋊C4—91no—
275C2×C4⋊C4—92no—
276C2×C22⋊C4—32no—
277C2×C22⋊C4—94no—
278C2×C42—92no—
279C2×C42D3211yescharacteristic
280C23×C3—21no—
281C23×C3—38no—
282C23×C3—34no—
283C23×C3—64no—
284C23×C3—64no—
285C23×C3C23×D311yescharacteristic
286C23×C3C23×D311yescharacteristic
287C22×D3—24no—
288C22×D3—24no—
289C22×D3C2×Dic618yes—
290C22×D3C23×D314yes—
291C3×Q8—128no—
292C3×D4—316no—
293C2×C3×C4—22no—
294C2×C3×C4—22no—
295C2×C3×C4—22no—
296C2×C3×C4—22no—
297C2×C3×C4—22no—
298C2×C3×C4—24no—
299C2×C3×C4—24no—
300C2×C3×C4—34no—
301C2×C3×C4—38no—
302C2×C3×C4—42no—
303C2×C3×C4—64no—
304C2×C3×C4—68no—
305C2×C3×C4—616no—
306C2×C3×C4C2×Dic614yes—
307C2×C3×C4#23714yes—
308C2×C3×C4D3×Q814yes—
309C2×C3×C4#23914yes—
310C2×C3×C4C23×D312yes—
311C2×C3×C4C23×D312yes—
312C2×C3×C4C23×D312yes—
313C2×C3×C4C23×D312yes—
314C2×C3×C4C23×D312yes—
315C2×C3×C4C23×D312yes—
316C2×Dic3—24no—
317C2×Dic3—28no—
318C2×Dic3—34no—
319C2×Dic3—34no—
320C2×Dic3—34no—
321C2×Dic3—34no—
322C2×Dic3—64no—
323C2×Dic3—64no—
324C2×Dic3—68no—
325C2×Dic3—64no—
326C2×Dic3—64no—
327C2×Dic3—64no—
328C2×Dic3—64no—
329C2×Dic3—124no—
330C2×Dic3—1216no—
331C2×Dic3C23×D314yes—
332C2×Dic3C23×D318yes—
333D12C2×Dic6116yescomplemented
334C4×D3—216no—
335C4×D3—1216no—
336Dic6—48no—
337Dic6—616no—
338Dic6—68no—
339Dic6—68no—
340C2×C32#55414yescomplemented
341C2×C32C23×Q811yescharacteristic
342C2×C32C22×#4111yescharacteristic
343C2×C32C2×H(5,𝔽2)11yescharacteristic
344C3×D3—28no—
345C24—32no—
346C2×Q8—38no—
347C2×Q8—94no—
348C2×Q8—124no—
349C2×Q8—184no—
350C2×D4—34no—
351C2×D4—38no—
352C22×C4—32no—
353C22×C4—34no—
354C22×C4—38no—
355C22×C4—68no—
356C22×C4—916no—
357C22×C4—92no—
358C22×C4—92no—
359C22×C4—368no—
360C22×C4C2×D3211yescharacteristic
361C22×C4C2×D3211yescharacteristic
362C22×C4C2×D3211yescharacteristic
363C4⋊C4—38no—
364C4⋊C4—34no—
365C4⋊C4—38no—
366C4⋊C4—916no—
367C4⋊C4—916no—
368C4⋊C4—94no—
369C4⋊C4—98no—
370C22⋊C4—38no—
371C22⋊C4—916no—
372C42—98no—
373C42C2×D3214yes—
374C22×C3—22no—
375C22×C3—22no—
376C22×C3—22no—
377C22×C3—21no—
378C22×C3—38no—
379C22×C3—64no—
380C22×C3—64no—
381C22×C3—616no—
382C22×C3C22×Dic612yes—
383C22×C3C2×#23712yes—
384C22×C3#100412yes—
385C22×C3C2×D3×Q812yes—
386C22×C3C2×#23912yes—
387C22×C3#100912yes—
388C22×C3C24×D311yescharacteristic
389C22×C3C24×D311yescharacteristic
390C2×D3—24no—
391C2×D3—24no—
392C2×D3—216no—
393C2×D3C22×Dic618yes—
394C3×C4—22no—
395C3×C4—22no—
396C3×C4—24no—
397C3×C4—24no—
398C3×C4—42no—
399C3×C4—64no—
400C3×C4—68no—
401C3×C4C22×Dic614yes—
402C3×C4C2×#23714yes—
403C3×C4C2×D3×Q814yes—
404C3×C4C2×#23914yes—
405Dic3—24no—
406Dic3—28no—
407Dic3—68no—
408Dic3—64no—
409Dic3—64no—
410Dic3—64no—
411Dic3—64no—
412Dic3—124no—
413C32C2×#55411yescharacteristic, complemented, Sylow
414C23—38no—
415C23—34no—
416C23—64no—
417C23—64no—
418C23C22×D3211yescharacteristic
419Q8—128no—
420Q8—188no—
421D4—316no—
422C2×C4—22no—
423C2×C4—34no—
424C2×C4—38no—
425C2×C4—64no—
426C2×C4—68no—
427C2×C4—616no—
428C2×C4—94no—
429C2×C4—94no—
430C2×C4—184no—
431C2×C4—184no—
432C2×C4—3616no—
433C2×C4D3×Dic614yes—
434C2×C4#379614yes—
435C2×C4C22×D3212yes—
436C2×C4C22×D3212yes—
437C2×C4C22×D3212yes—
438C2×C3—21no—
439C2×C3—21no—
440C2×C3—21no—
441C2×C3—24no—
442C2×C3—68no—
443C2×C3#554314yescomplemented
444C2×C3#573014yescomplemented
445C2×C3C23×Dic611yescharacteristic
446C2×C3C22×#23711yescharacteristic
447C2×C3C2×#100411yescharacteristic
448C2×C3C22×D3×Q811yescharacteristic
449C2×C3C22×#23911yescharacteristic
450C2×C3C2×#100911yescharacteristic
451D3—28no—
452C22—38no—
453C22—64no—
454C22—64no—
455C22—616no—
456C22C2×D3×Dic612yes—
457C22C2×#379612yes—
458C22#6430712yes—
459C22C23×D3211yescharacteristic
460C4—22no—
461C4—64no—
462C4—68no—
463C4—184no—
464C4—184no—
465C4C2×D3×Dic614yes—
466C4C2×#379614yes—
467C3—21no—
468C3C2×#554311yescharacteristic, complemented
469C3C2×#573011yescharacteristic, complemented
470C2—68no—
471C2#1059395614yesdirect product factor
472C2C22×D3×Dic611yescharacteristic
473C2C22×#379611yescharacteristic
474C2C2×#6430711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
socleC23×C32C24
prime radicalC22×C3×D12C22
hypercenterC2×C42D32
hypocenterC32C2×#554
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×D3×C4⋊Dic3C2semidirect
6. C2×#63887C2semidirect
7. C2×#63872C2semidirect
8. C2×#63857C2semidirect
9. #10593956C2direct (N × H)
21. C4×#634C22semidirect
27. C3×#869C22semidirect
32. D3×C4⋊Dic3C22semidirect
33. #63887C22semidirect
34. #63872C22semidirect
35. #63857C22semidirect
51. C2×#869D3semidirect
65. C2×C3×D12Q8semidirect
135. #869C2×D3semidirect
159. C3×D12C2×Q8semidirect
201. C2×D12Dic6semidirect
333. D12C2×Dic6semidirect
340. C2×C32#554semidirect
413. C32C2×#554semidirect
443. C2×C3#5543semidirect
444. C2×C3#5730semidirect
468. C3C2×#5543semidirect
469. C3C2×#5730semidirect
471. C2#10593956direct (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×#638982
C2×D3×C4⋊Dic32
C2×#638872
C2×#638722
C2×#638572
#105939562
C2×#57303
C2×#55433