Finite Group Databasebeta

← C2×#10593958 #11903279

Subgroups — C2×#10593958 #11903279

Order 1152.

2613 conjugacy classes of subgroups.

The subgroup lattice has 484 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×#63900C212yesmaximal, complemented
5C2×#63894C212yesmaximal
6C2×#63888C214yesmaximal, complemented
7C2×#63871C212yesmaximal, complemented
8C2×#63869C212yesmaximal, complemented
9#10593958C2116yesmaximal, direct product factor
10C2×#5730—31nomaximal
11C2×#5579—31nomaximal
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C22×C4×C3⋊D3C2212yes—
14C22×C3×Dic6C2211yescharacteristic
15C22×C3×Dic6C2212yes—
16C22×#624C2214yes—
17C2×C32×C42C2211yescharacteristic
18C2×#3752C2212yes—
19C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
20C4×C4⋊(C3⋊D3)C2218yes—
21C2×C3×C4⋊Dic3C2212yes—
22C2×C3×C4⋊Dic3C2212yes—
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×Dic3⋊C4C2212yes—
25C2×C3×C4×Dic3C2212yes—
26C3×#869C2218yescomplemented
27C3×C4×Dic6C2218yescomplemented
28C2×#3724C2214yes—
29C2×Dic3⋊Dic3C2214yes—
30C2×#3722C2214yes—
31#63900C22116yescomplemented
32#63894C22116yes—
33#63888C22132yescomplemented
34#63871C22116yescomplemented
35#63869C22116yescomplemented
36C2×C3×C4⋊Q8—31no—
37C2×C3×C4×Q8—31no—
38C2×#946—32no—
39C2×#946—34no—
40#5730—316no—
41#5579—316no—
42C2×#897—32no—
43C2×#896—34no—
44C2×#893—32no—
45C2×D3×C4⋊C4—32no—
46C2×D3×C4⋊C4—32no—
47C2×#890—32no—
48C2×C4×D12—31no—
49C2×C4×D12—31no—
50C2×C4×D12—32no—
51C2×C4×D12—61no—
52C2×#870—32no—
53C2×#869D311yescharacteristic, complemented
54C2×C4×Dic6D311yescharacteristic, complemented
55C23×C3⋊D3C2312yes—
56C22×C32×C4C2311yescharacteristic
57C22×C32×C4C2311yescharacteristic
58C22×C32×C4C2311yescharacteristic
59C22×C3⋊Dic3C2312yes—
60C2×C4⋊(C3⋊D3)Q818yescomplemented
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—44no—
69C2×C3×Dic6C2314yes—
70C2×C3×Dic6C2318yes—
71C2×#624—48no—
72C2×#624C23116yes—
73C32×C42C2314yes—
74#3752C2318yes—
75C4⋊(C3⋊Dic3)C2314yes—
76C3×C4⋊Dic3C2318yes—
77C3×C4⋊Dic3C2318yes—
78C3×C4⋊Dic3C2314yes—
79C3×Dic3⋊C4C2318yes—
80C3×C4×Dic3C2318yes—
81#3724C23116yes—
82Dic3⋊Dic3C23116yes—
83#3722C23116yes—
84C2×#554—91noSylow
85C22×C3×Q8—31no—
86C22×C3×Q8—32no—
87C22×D12—31no—
88C22×D12—31no—
89C22×D12—61no—
90C22×C4×D3—32no—
91C22×C4×D3—32no—
92C22×C4×D3—34no—
93C22×C4×D3—34no—
94C22×C4×D3—62no—
95C22×Dic6C2×D311yescharacteristic
96C22×Dic6C2×D312yes—
97C3×C4⋊Q8—38no—
98C3×C4×Q8—38no—
99C2×C3×C4⋊C4—32no—
100C2×C3×C4⋊C4—32no—
101C2×C3×C4⋊C4—31no—
102C2×C3×C4⋊C4—32no—
103C2×C3×C42—21no—
104C2×C3×C42—32no—
105C2×C3×C42C2×D311yescharacteristic
106C2×C3×C42C2×D311yescharacteristic
107#946—316no—
108#946—332no—
109C2×(C2×D3)⋊C4—32no—
110C2×(C2×D3)⋊C4—32no—
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⋊C4—34no—
123C2×Dic3⋊C4—34no—
124C2×Dic3⋊C4C2×D312yes—
125C2×C4×Dic3C2×D312yes—
126#897—316no—
127#896—332no—
128#893—316no—
129D3×C4⋊C4—316no—
130D3×C4⋊C4—316no—
131#890—316no—
132C4×D12—38no—
133C4×D12—38no—
134C4×D12—316no—
135C4×D12—68no—
136#870—316no—
137#869C2×D318yescomplemented
138C4×Dic6C2×D318yescomplemented
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⋊Dic3C2414yes—
152C4⋊(C3⋊D3)C2×Q8116yescomplemented
153C4×C3⋊D3—216no—
154C2×C3×Dic3—24no—
155C2×C3×Dic3—24no—
156C2×C3×Dic3—28no—
157C2×C3×Dic3C2414yes—
158C2×C3×Dic3C2418yes—
159C2×C3×Dic3C2414yes—
160C3×Dic6—28no—
161C3×Dic6—48no—
162#624—416no—
163#554—916no—
164C2×C4⋊Q8—31no—
165C2×#125—92no—
166C2×C22⋊Q8—94no—
167C2×C22⋊Q8—92no—
168C2×C4×Q8—31no—
169C2×C4×D4—92no—
170C2×C4×D4—91no—
171C22×C4⋊C4—92no—
172C23×D3—32no—
173C23×D3—32no—
174C23×D3—62no—
175C2×C3×Q8—34no—
176C2×C3×Q8—38no—
177C2×C3×Q8—64no—
178C2×C3×Q8—124no—
179C22×C3×C4—21no—
180C22×C3×C4—21no—
181C22×C3×C4—21no—
182C22×C3×C4—32no—
183C22×C3×C4—32no—
184C22×C3×C4—34no—
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—62no—
194C22×Dic3C22×D312yes—
195C22×Dic3C22×D312yes—
196C22×Dic3C22×D314yes—
197C2×D12—38no—
198C2×D12—38no—
199C2×D12—34no—
200C2×D12—34no—
201C2×D12—64no—
202C2×D12—68no—
203C2×C4×D3—38no—
204C2×C4×D3—38no—
205C2×C4×D3—316no—
206C2×C4×D3—316no—
207C2×C4×D3—68no—
208C2×C4×D3—68no—
209C2×C4×D3—68no—
210C2×C4×D3—128no—
211C2×C4×D3—128no—
212C2×C4×D3—128no—
213C2×Dic6—24no—
214C2×Dic6—44no—
215C2×Dic6C22×D314yes—
216C2×Dic6C22×D318yes—
217C3×C4⋊C4—38no—
218C3×C4⋊C4—34no—
219C3×C4⋊C4—38no—
220C3×C4⋊C4—38no—
221C3×C42—24no—
222C3×C42—38no—
223C3×C42C22×D314yes—
224C3×C42C22×D314yes—
225(C2×D3)⋊C4—38no—
226(C2×D3)⋊C4—38no—
227(C2×D3)⋊C4—316no—
228(C2×D3)⋊C4—316no—
229(C2×D3)⋊C4—68no—
230C4⋊Dic3—34no—
231C4⋊Dic3—34no—
232C4⋊Dic3—316no—
233C4⋊Dic3—64no—
234C4⋊Dic3C22×D314yes—
235C4⋊Dic3C22×D318yes—
236C4⋊Dic3C22×D318yes—
237Dic3⋊C4—316no—
238Dic3⋊C4—316no—
239Dic3⋊C4—316no—
240Dic3⋊C4C22×D318yes—
241C4×Dic3C22×D318yes—
242C22×C32C22×Q812yes—
243C22×C32C2×#4112yes—
244C22×C32H(5,𝔽2)12yes—
245C22×C32C2511yescharacteristic
246C2×C3⋊D3—216no—
247C2×C3⋊D3—24no—
248C2×C3⋊D3—24no—
249C2×C3⋊D3C22×Q818yes—
250C32×C4—22no—
251C32×C4C22×Q814yes—
252C32×C4C2×#4114yes—
253C3⋊Dic3—24no—
254C3×Dic3—24no—
255C3×Dic3—24no—
256C3×Dic3—28no—
257C22×Q8—31no—
258C22×Q8—32no—
259C22×D4—91no—
260C23×C4—94no—
261C23×C4—92no—
262C4⋊Q8—38no—
263#125—916no—
264C22⋊Q8—932no—
265C22⋊Q8—916no—
266C4×Q8—38no—
267C4×D4—916no—
268C4×D4—98no—
269C2×C4⋊C4—31no—
270C2×C4⋊C4—32no—
271C2×C4⋊C4—32no—
272C2×C4⋊C4—32no—
273C2×C4⋊C4—916no—
274C2×C4⋊C4—94no—
275C2×C4⋊C4—94no—
276C2×C4⋊C4—91no—
277C2×C22⋊C4—94no—
278C2×C22⋊C4—92no—
279C2×C42—32no—
280C2×C42D3211yescharacteristic
281C23×C3—21no—
282C23×C3C23×D311yescharacteristic
283C23×C3C23×D311yescharacteristic
284C22×D3—38no—
285C22×D3—38no—
286C22×D3—34no—
287C22×D3—34no—
288C22×D3—68no—
289C22×D3—64no—
290C22×D3—64no—
291C22×D3—64no—
292C22×D3—64no—
293C22×D3—64no—
294C22×D3—124no—
295C22×D3—124no—
296C3×Q8—68no—
297C3×Q8—128no—
298C2×C3×C4—22no—
299C2×C3×C4—22no—
300C2×C3×C4—22no—
301C2×C3×C4—22no—
302C2×C3×C4—22no—
303C2×C3×C4—24no—
304C2×C3×C4—24no—
305C2×C3×C4—34no—
306C2×C3×C4—34no—
307C2×C3×C4—38no—
308C2×C3×C4—42no—
309C2×C3×C4—64no—
310C2×C3×C4—64no—
311C2×C3×C4—68no—
312C2×C3×C4#23514yes—
313C2×C3×C4D3×Q814yes—
314C2×C3×C4D3×Q814yes—
315C2×C3×C4#23914yes—
316C2×C3×C4C23×D312yes—
317C2×C3×C4C23×D312yes—
318C2×C3×C4C23×D312yes—
319C2×C3×C4C23×D312yes—
320C2×C3×C4C23×D312yes—
321C2×C3×C4C23×D312yes—
322C2×Dic3—24no—
323C2×Dic3—28no—
324C2×Dic3—24no—
325C2×Dic3—34no—
326C2×Dic3—34no—
327C2×Dic3—64no—
328C2×Dic3—64no—
329C2×Dic3—64no—
330C2×Dic3—124no—
331C2×Dic3C23×D314yes—
332C2×Dic3C23×D314yes—
333C2×Dic3C23×D318yes—
334D12—316no—
335D12—316no—
336D12—616no—
337C4×D3—616no—
338C4×D3—616no—
339C4×D3—1216no—
340C4×D3—1216no—
341C4×D3—1216no—
342Dic6—28no—
343Dic6—48no—
344C2×C32#55414yescomplemented
345C2×C32C23×Q811yescharacteristic
346C2×C32C22×#4111yescharacteristic
347C2×C32C2×H(5,𝔽2)11yescharacteristic
348C3⋊D3—28no—
349C24—92no—
350C2×Q8—34no—
351C2×Q8—38no—
352C2×Q8—64no—
353C2×Q8—124no—
354C2×D4—94no—
355C2×D4—98no—
356C22×C4—32no—
357C22×C4—32no—
358C22×C4—34no—
359C22×C4—916no—
360C22×C4—92no—
361C22×C4—98no—
362C22×C4—188no—
363C22×C4—368no—
364C22×C4C2×D3211yescharacteristic
365C22×C4C2×D3211yescharacteristic
366C22×C4C2×D3211yescharacteristic
367C4⋊C4—34no—
368C4⋊C4—38no—
369C4⋊C4—38no—
370C4⋊C4—38no—
371C4⋊C4—916no—
372C4⋊C4—916no—
373C4⋊C4—94no—
374C22⋊C4—916no—
375C22⋊C4—98no—
376C42—38no—
377C42C2×D3214yes—
378C22×C3—22no—
379C22×C3—22no—
380C22×C3—22no—
381C22×C3—21no—
382C22×C3C2×#23512yes—
383C22×C3#100412yes—
384C22×C3C2×D3×Q812yes—
385C22×C3C2×D3×Q812yes—
386C22×C3C2×#23912yes—
387C22×C3#100912yes—
388C22×C3C24×D311yescharacteristic
389C22×C3C24×D311yescharacteristic
390C2×D3—38no—
391C2×D3—38no—
392C2×D3—68no—
393C2×D3—64no—
394C2×D3—64no—
395C2×D3—64no—
396C2×D3—64no—
397C2×D3—616no—
398C2×D3—616no—
399C2×D3—124no—
400C2×D3—124no—
401C2×D3—1216no—
402C3×C4—22no—
403C3×C4—22no—
404C3×C4—24no—
405C3×C4—24no—
406C3×C4—42no—
407C3×C4—64no—
408C3×C4—64no—
409C3×C4—68no—
410C3×C4C2×#23514yes—
411C3×C4C2×D3×Q814yes—
412C3×C4C2×D3×Q814yes—
413C3×C4C2×#23914yes—
414Dic3—24no—
415Dic3—28no—
416Dic3—24no—
417Dic3—64no—
418Dic3—64no—
419Dic3—124no—
420C32C2×#55411yescharacteristic, complemented, Sylow
421C23—98no—
422C23—94no—
423C23—184no—
424C23—184no—
425C23C22×D3211yescharacteristic
426Q8—68no—
427Q8—128no—
428D4—916no—
429C2×C4—22no—
430C2×C4—34no—
431C2×C4—34no—
432C2×C4—38no—
433C2×C4—64no—
434C2×C4—64no—
435C2×C4—68no—
436C2×C4—94no—
437C2×C4—184no—
438C2×C4—1816no—
439C2×C4—3616no—
440C2×C4#379714yes—
441C2×C4#379914yes—
442C2×C4C22×D3212yes—
443C2×C4C22×D3212yes—
444C2×C4C22×D3212yes—
445C2×C3—21no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—24no—
449C2×C3#557914yescomplemented
450C2×C3#573014yescomplemented
451C2×C3C22×#23511yescharacteristic
452C2×C3C2×#100411yescharacteristic
453C2×C3C22×D3×Q811yescharacteristic
454C2×C3C22×D3×Q811yescharacteristic
455C2×C3C22×#23911yescharacteristic
456C2×C3C2×#100911yescharacteristic
457D3—68no—
458D3—68no—
459D3—128no—
460C22—98no—
461C22—184no—
462C22—184no—
463C22—1816no—
464C22C2×#379712yes—
465C22C2×#379912yes—
466C22#6430712yes—
467C22C23×D3211yescharacteristic
468C4—22no—
469C4—64no—
470C4—64no—
471C4—68no—
472C4—184no—
473C4C2×#379714yes—
474C4C2×#379914yes—
475C3—21no—
476C3C2×#557911yescharacteristic, complemented
477C3C2×#573011yescharacteristic, complemented
478C2—188no—
479C2#1059395814yesdirect product factor
480C2C22×#379711yescharacteristic
481C2C22×#379911yescharacteristic
482C2C2×#6430711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
socleC23×C32C24
prime radicalC22×C4⋊(C3⋊D3)C22
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
2. C2×C3×#869C2semidirect
3. C2×C3×C4×Dic6C2semidirect
4. C2×#63900C2semidirect
6. C2×#63888C2semidirect
7. C2×#63871C2semidirect
8. C2×#63869C2semidirect
9. #10593958C2direct (N × H)
26. C3×#869C22semidirect
27. C3×C4×Dic6C22semidirect
31. #63900C22semidirect
33. #63888C22semidirect
34. #63871C22semidirect
35. #63869C22semidirect
53. C2×#869D3semidirect
54. C2×C4×Dic6D3semidirect
60. C2×C4⋊(C3⋊D3)Q8semidirect
137. #869C2×D3semidirect
138. C4×Dic6C2×D3semidirect
152. C4⋊(C3⋊D3)C2×Q8semidirect
344. C2×C32#554semidirect
420. C32C2×#554semidirect
449. C2×C3#5579semidirect
450. C2×C3#5730semidirect
476. C3C2×#5579semidirect
477. C3C2×#5730semidirect
479. C2#10593958direct (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×#639002
C2×#638942
C2×#638882
C2×#638712
C2×#638692
#105939582
C2×#57303
C2×#55793