Finite Group Databasebeta

← C2×#10593952 #11910316

Subgroups — C2×#10593952 #11910316

Order 1152.

2161 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64079C211yesmaximal, characteristic, complemented
2C2×C3×#875C211yesmaximal, characteristic
3C2×C3×#870C211yesmaximal, characteristic, complemented
4C2×#63899C212yesmaximal, complemented
5C2×#63893C212yesmaximal, complemented
6C2×#63884C212yesmaximal
7C2×#63861C212yesmaximal, complemented
8C2×#63858C212yesmaximal, complemented
9C2×#63839C212yesmaximal, complemented
10#10593952C2116yesmaximal, direct product factor
11C2×#5699—31nomaximal
12C2×#5672—31nomaximal
13C22×C3×D12C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15C22×#627C2212yes—
16C22×D3×Dic3C2212yes—
17C2×C32×C42C2211yescharacteristic
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
20C2×#3750C2212yes—
21C2×#3750C2212yes—
22#64079C2218yescomplemented
23C2×C3×(C2×D3)⋊C4C2212yes—
24C2×C3×(C2×D3)⋊C4C2212yes—
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C2×C3×Dic3⋊C4C2212yes—
28C2×C3×Dic3⋊C4C2212yes—
29C3×#875C2218yes—
30C3×#870C2218yescomplemented
31C2×#3724C2212yes—
32C2×Dic3⋊Dic3C2212yes—
33C2×(C2×D3)⋊Dic3C2212yes—
34C2×(C2×D3)⋊Dic3C2212yes—
35C2×(C2×D3)⋊Dic3C2212yes—
36C2×Dic32C2212yes—
37#63899C22116yescomplemented
38#63893C22116yescomplemented
39#63884C22116yes—
40#63861C22116yescomplemented
41#63858C22116yescomplemented
42#63839C22116yescomplemented
43C2×C3×#125—31no—
44C2×C3×#124—31no—
45C2×#944—32no—
46C2×#935—32no—
47#5699—316no—
48#5672—316no—
49C2×#898—32no—
50C2×#898—32no—
51C2×#897—32no—
52C2×#896—32no—
53C2×#894—32no—
54C2×#888—32no—
55C2×#879—32no—
56C2×#879—32no—
57C2×#878—32no—
58C2×#878—32no—
59C2×#875D311yescharacteristic
60C2×#870—31no—
61C2×#870—31no—
62C2×#870—61no—
63C2×#870D311yescharacteristic, complemented
64C23×C3×D3C2312yes—
65C22×C32×C4C2311yescharacteristic
66C22×C32×C4C2311yescharacteristic
67C22×C32×C4C2311yescharacteristic
68C22×C3⋊Dic3C2312yes—
69C22×C3⋊Dic3C2312yes—
70C22×C3×Dic3C2312yes—
71C22×C3×Dic3C2312yes—
72C22×C3×Dic3C2312yes—
73C2×C3×D12—42no—
74C2×C3×D12C2314yes—
75C2×C3×Dic6—42no—
76C2×C3×Dic6C2314yes—
77C2×#627—44no—
78C2×#627C2318yes—
79C2×D3×Dic3—44no—
80C2×D3×Dic3C2318yes—
81C32×C42C2314yes—
82C4⋊(C3⋊Dic3)C2314yes—
83C4⋊(C3⋊Dic3)C2314yes—
84#3750C2318yes—
85#3750C2318yes—
86C3×(C2×D3)⋊C4C2318yes—
87C3×(C2×D3)⋊C4C2318yes—
88C3×C4⋊Dic3C2314yes—
89C3×C4⋊Dic3C2314yes—
90C3×Dic3⋊C4C2318yes—
91C3×Dic3⋊C4C2318yes—
92#3724C2318yes—
93Dic3⋊Dic3C2318yes—
94(C2×D3)⋊Dic3C2318yes—
95(C2×D3)⋊Dic3C2318yes—
96(C2×D3)⋊Dic3C2318yes—
97Dic32C2318yes—
98C2×#563—91noSylow
99C22×C3×Q8—31no—
100C22×C3×D4—31no—
101C23×Dic3—32no—
102C22×D12C2×D311yescharacteristic
103C22×C4×D3—32no—
104C22×Dic6—32no—
105C22×Dic6—32no—
106C22×Dic6C2×D311yescharacteristic
107C3×#125—38no—
108C3×#124—38no—
109C2×C3×C4⋊C4—32no—
110C2×C3×C4⋊C4—32no—
111C2×C3×C4⋊C4—31no—
112C2×C3×C4⋊C4—31no—
113C2×C3×C22⋊C4—32no—
114C2×C3×C22⋊C4—32no—
115C2×C3×C42—21no—
116C2×C3×C42C2×D311yescharacteristic
117C2×C3×C42C2×D311yescharacteristic
118C2×#217—32no—
119C2×#217—32no—
120C2×#217—32no—
121#944—316no—
122#935—316no—
123C2×(C2×D3)⋊C4—32no—
124C2×(C2×D3)⋊C4—32no—
125C2×(C2×D3)⋊C4—32no—
126C2×(C2×D3)⋊C4C2×D312yes—
127C2×(C2×D3)⋊C4C2×D312yes—
128C2×C4⋊Dic3—31no—
129C2×C4⋊Dic3—31no—
130C2×C4⋊Dic3—31no—
131C2×C4⋊Dic3—31no—
132C2×C4⋊Dic3—32no—
133C2×C4⋊Dic3—61no—
134C2×C4⋊Dic3—61no—
135C2×C4⋊Dic3C2×D311yescharacteristic
136C2×C4⋊Dic3C2×D311yescharacteristic
137C2×Dic3⋊C4—32no—
138C2×Dic3⋊C4—32no—
139C2×Dic3⋊C4—32no—
140C2×Dic3⋊C4—32no—
141C2×Dic3⋊C4—32no—
142C2×Dic3⋊C4—32no—
143C2×Dic3⋊C4—32no—
144C2×Dic3⋊C4—62no—
145C2×Dic3⋊C4—62no—
146C2×Dic3⋊C4C2×D312yes—
147C2×Dic3⋊C4C2×D312yes—
148C2×C4×Dic3—32no—
149C2×C4×Dic3—32no—
150#898—316no—
151#898—316no—
152#897—316no—
153#896—316no—
154#894—316no—
155#888—316no—
156#879—316no—
157#879—316no—
158#878—316no—
159#878—316no—
160#875C2×D318yes—
161#870—38no—
162#870—38no—
163#870—68no—
164#870C2×D318yescomplemented
165C23×C32C2411yescharacteristic
166C22×C3×D3—24no—
167C22×C3×D3—24no—
168C22×C3×D3—24no—
169C22×C3×D3C2414yes—
170C2×C32×C4—22no—
171C2×C32×C4—22no—
172C2×C32×C4—22no—
173C2×C32×C4C2412yes—
174C2×C32×C4C2412yes—
175C2×C32×C4C2412yes—
176C2×C3⋊Dic3—24no—
177C2×C3⋊Dic3—24no—
178C2×C3⋊Dic3C2414yes—
179C2×C3⋊Dic3C2414yes—
180C2×C3×Dic3—24no—
181C2×C3×Dic3—24no—
182C2×C3×Dic3—24no—
183C2×C3×Dic3C2414yes—
184C2×C3×Dic3C2414yes—
185C2×C3×Dic3C2414yes—
186C3×D12—44no—
187C3×Dic6—44no—
188#627—48no—
189D3×Dic3—48no—
190#563—916no—
191C2×C4⋊Q8—92no—
192C2×#126—92no—
193C2×#126—92no—
194C2×#125—31no—
195C2×#125—91no—
196C2×#124—31no—
197C2×#123—92no—
198C2×C22⋊Q8—92no—
199C2×C22⋊Q8—92no—
200C24×C3—32no—
201C23×D3C22×D312yes—
202C2×C3×Q8—34no—
203C2×C3×Q8—122no—
204C2×C3×D4—34no—
205C2×C3×D4—122no—
206C22×C3×C4—21no—
207C22×C3×C4—21no—
208C22×C3×C4—21no—
209C22×C3×C4—32no—
210C22×C3×C4—32no—
211C22×C3×C4—32no—
212C22×C3×C4C22×D311yescharacteristic
213C22×C3×C4C22×D311yescharacteristic
214C22×C3×C4C22×D311yescharacteristic
215C22×C3×C4C22×D311yescharacteristic
216C22×C3×C4C22×D311yescharacteristic
217C22×C3×C4C22×D311yescharacteristic
218C22×Dic3—32no—
219C22×Dic3—32no—
220C22×Dic3—32no—
221C22×Dic3—32no—
222C22×Dic3—38no—
223C22×Dic3—62no—
224C22×Dic3—62no—
225C22×Dic3—124no—
226C22×Dic3C22×D312yes—
227C22×Dic3C22×D312yes—
228C22×Dic3C22×D312yes—
229C2×D12—42no—
230C2×D12C22×D314yes—
231C2×C4×D3—38no—
232C2×C4×D3—124no—
233C2×Dic6—38no—
234C2×Dic6—38no—
235C2×Dic6—42no—
236C2×Dic6—124no—
237C2×Dic6—124no—
238C2×Dic6C22×D314yes—
239C3×C4⋊C4—38no—
240C3×C4⋊C4—34no—
241C3×C4⋊C4—38no—
242C3×C4⋊C4—34no—
243C3×C22⋊C4—38no—
244C3×C22⋊C4—38no—
245C3×C42—24no—
246C3×C42C22×D314yes—
247C3×C42C22×D314yes—
248#217—38no—
249#217—38no—
250#217—38no—
251(C2×D3)⋊C4—38no—
252(C2×D3)⋊C4—38no—
253(C2×D3)⋊C4—38no—
254(C2×D3)⋊C4C22×D318yes—
255(C2×D3)⋊C4C22×D318yes—
256C4⋊Dic3—34no—
257C4⋊Dic3—34no—
258C4⋊Dic3—34no—
259C4⋊Dic3—34no—
260C4⋊Dic3—38no—
261C4⋊Dic3—64no—
262C4⋊Dic3—64no—
263C4⋊Dic3C22×D314yes—
264C4⋊Dic3C22×D314yes—
265Dic3⋊C4—38no—
266Dic3⋊C4—38no—
267Dic3⋊C4—38no—
268Dic3⋊C4—38no—
269Dic3⋊C4—38no—
270Dic3⋊C4—38no—
271Dic3⋊C4—38no—
272Dic3⋊C4—68no—
273Dic3⋊C4—68no—
274Dic3⋊C4C22×D318yes—
275Dic3⋊C4C22×D318yes—
276C4×Dic3—38no—
277C4×Dic3—38no—
278C22×C32H(5,𝔽2)12yes—
279C22×C322−1+412yes—
280C22×C322−1+412yes—
281C22×C32C2511yescharacteristic
282C2×C3×D3—24no—
283C2×C3×D3—24no—
284C2×C3×D3—24no—
285C2×C3×D3—48no—
286C32×C4—22no—
287C32×C4—22no—
288C32×C4—22no—
289C3⋊Dic3—24no—
290C3⋊Dic3—24no—
291C3×Dic3—24no—
292C3×Dic3—24no—
293C3×Dic3—24no—
294C22×Q8—31no—
295C22×Q8—92no—
296C22×D4—31no—
297C23×C4—92no—
298C4⋊Q8—916no—
299#126—916no—
300#126—916no—
301#125—38no—
302#125—98no—
303#124—38no—
304#123—916no—
305C22⋊Q8—916no—
306C22⋊Q8—916no—
307C2×C4⋊C4—31no—
308C2×C4⋊C4—32no—
309C2×C4⋊C4—32no—
310C2×C4⋊C4—31no—
311C2×C4⋊C4—92no—
312C2×C4⋊C4—92no—
313C2×C4⋊C4—91no—
314C2×C4⋊C4—92no—
315C2×C4⋊C4—92no—
316C2×C4⋊C4—91no—
317C2×C22⋊C4—32no—
318C2×C22⋊C4—32no—
319C2×C22⋊C4—92no—
320C2×C22⋊C4—92no—
321C2×C22⋊C4—92no—
322C2×C42—92no—
323C2×C42D3211yescharacteristic
324C23×C3—21no—
325C23×C3—34no—
326C23×C3—64no—
327C23×C3—64no—
328C23×C3—64no—
329C23×C3C23×D311yescharacteristic
330C23×C3C23×D311yescharacteristic
331C22×D3—24no—
332C22×D3—24no—
333C22×D3—24no—
334C22×D3C23×D314yes—
335C3×Q8—124no—
336C3×D4—124no—
337C2×C3×C4—24no—
338C2×C3×C4—22no—
339C2×C3×C4—22no—
340C2×C3×C4—22no—
341C2×C3×C4—22no—
342C2×C3×C4—22no—
343C2×C3×C4—22no—
344C2×C3×C4—22no—
345C2×C3×C4—22no—
346C2×C3×C4—22no—
347C2×C3×C4—34no—
348C2×C3×C4—34no—
349C2×C3×C4—34no—
350C2×C3×C4—42no—
351C2×C3×C4—42no—
352C2×C3×C4—64no—
353C2×C3×C4—64no—
354C2×C3×C4—64no—
355C2×C3×C4C23×D312yes—
356C2×C3×C4C23×D312yes—
357C2×C3×C4C23×D312yes—
358C2×C3×C4C23×D312yes—
359C2×C3×C4C23×D312yes—
360C2×C3×C4C23×D312yes—
361C2×Dic3—24no—
362C2×Dic3—24no—
363C2×Dic3—24no—
364C2×Dic3—34no—
365C2×Dic3—34no—
366C2×Dic3—34no—
367C2×Dic3—34no—
368C2×Dic3—64no—
369C2×Dic3—64no—
370C2×Dic3—64no—
371C2×Dic3—64no—
372C2×Dic3—64no—
373C2×Dic3—64no—
374C2×Dic3—124no—
375C2×Dic3—124no—
376C2×Dic3—128no—
377C2×Dic3C23×D314yes—
378C2×Dic3C23×D314yes—
379C2×Dic3C23×D314yes—
380D12—44no—
381C4×D3—128no—
382Dic6—44no—
383Dic6—128no—
384Dic6—128no—
385C2×C32#56314yescomplemented
386C2×C32C2×H(5,𝔽2)11yescharacteristic
387C2×C32C2×2−1+411yescharacteristic
388C2×C32C2×2−1+411yescharacteristic
389C3×D3—44no—
390C24—32no—
391C2×Q8—34no—
392C2×Q8—98no—
393C2×Q8—122no—
394C2×Q8—364no—
395C2×D4—34no—
396C2×D4—122no—
397C22×C4—32no—
398C22×C4—32no—
399C22×C4—32no—
400C22×C4—98no—
401C22×C4—92no—
402C22×C4—92no—
403C22×C4—364no—
404C22×C4C2×D3211yescharacteristic
405C22×C4C2×D3211yescharacteristic
406C22×C4C2×D3211yescharacteristic
407C4⋊C4—34no—
408C4⋊C4—38no—
409C4⋊C4—38no—
410C4⋊C4—34no—
411C4⋊C4—98no—
412C4⋊C4—98no—
413C4⋊C4—94no—
414C4⋊C4—98no—
415C4⋊C4—98no—
416C4⋊C4—94no—
417C22⋊C4—38no—
418C22⋊C4—38no—
419C22⋊C4—98no—
420C22⋊C4—98no—
421C22⋊C4—98no—
422C42—98no—
423C42C2×D3214yes—
424C22×C3—22no—
425C22×C3—22no—
426C22×C3—22no—
427C22×C3—21no—
428C22×C3—64no—
429C22×C3—64no—
430C22×C3—64no—
431C22×C3—128no—
432C22×C3#100412yes—
433C22×C3#100712yes—
434C22×C3#100912yes—
435C22×C3#101012yes—
436C22×C3#101012yes—
437C22×C3#101012yes—
438C22×C3C24×D311yescharacteristic
439C22×C3C24×D311yescharacteristic
440C2×D3—24no—
441C2×D3—24no—
442C2×D3—24no—
443C2×D3—48no—
444C3×C4—24no—
445C3×C4—22no—
446C3×C4—22no—
447C3×C4—22no—
448C3×C4—22no—
449C3×C4—22no—
450C3×C4—22no—
451C3×C4—42no—
452C3×C4—42no—
453C3×C4—64no—
454C3×C4—64no—
455C3×C4—64no—
456Dic3—24no—
457Dic3—24no—
458Dic3—24no—
459Dic3—64no—
460Dic3—64no—
461Dic3—64no—
462Dic3—64no—
463Dic3—124no—
464Dic3—124no—
465C32C2×#56311yescharacteristic, complemented, Sylow
466C23—34no—
467C23—64no—
468C23—64no—
469C23—64no—
470C23C22×D3211yescharacteristic
471Q8—124no—
472Q8—368no—
473D4—124no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—34no—
478C2×C4—34no—
479C2×C4—34no—
480C2×C4—64no—
481C2×C4—64no—
482C2×C4—64no—
483C2×C4—94no—
484C2×C4—94no—
485C2×C4—184no—
486C2×C4—184no—
487C2×C4—368no—
488C2×C4C22×D3212yes—
489C2×C4C22×D3212yes—
490C2×C4C22×D3212yes—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—21no—
494C2×C3—24no—
495C2×C3—124no—
496C2×C3#567214yescomplemented
497C2×C3#569914yescomplemented
498C2×C3C2×#100411yescharacteristic
499C2×C3C2×#100711yescharacteristic
500C2×C3C2×#100911yescharacteristic
501C2×C3C2×#101011yescharacteristic
502C2×C3C2×#101011yescharacteristic
503C2×C3C2×#101011yescharacteristic
504D3—44no—
505C22—64no—
506C22—64no—
507C22—64no—
508C22—128no—
509C22#6429712yes—
510C22#6429812yes—
511C22#6430712yes—
512C22C23×D3211yescharacteristic
513C4—22no—
514C4—22no—
515C4—22no—
516C4—64no—
517C4—64no—
518C4—64no—
519C4—184no—
520C4—184no—
521C3—21no—
522C3C2×#567211yescharacteristic, complemented
523C3C2×#569911yescharacteristic, complemented
524C2—124no—
525C2#1059395214yesdirect product factor
526C2C2×#6429711yescharacteristic
527C2C2×#6429811yescharacteristic
528C2C2×#6430711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
socleC23×C32C24
prime radicalC22×C3×D12C22
hypercenterC2×C42D32
hypocenterC32C2×#563
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×#64079C2semidirect
3. C2×C3×#870C2semidirect
4. C2×#63899C2semidirect
5. C2×#63893C2semidirect
7. C2×#63861C2semidirect
8. C2×#63858C2semidirect
9. C2×#63839C2semidirect
10. #10593952C2direct (N × H)
22. #64079C22semidirect
30. C3×#870C22semidirect
37. #63899C22semidirect
38. #63893C22semidirect
40. #63861C22semidirect
41. #63858C22semidirect
42. #63839C22semidirect
63. C2×#870D3semidirect
164. #870C2×D3semidirect
385. C2×C32#563semidirect
465. C32C2×#563semidirect
496. C2×C3#5672semidirect
497. C2×C3#5699semidirect
522. C3C2×#5672semidirect
523. C3C2×#5699semidirect
525. C2#10593952direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640792
C2×C3×#8752
C2×C3×#8702
C2×#638992
C2×#638932
C2×#638842
C2×#638612
C2×#638582
C2×#638392
#105939522
C2×#56993
C2×#56723