Finite Group Databasebeta

← C2×#10595393 #11910311

Subgroups — C2×#10595393 #11910311

Order 1152.

2193 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64153C211yesmaximal, characteristic, complemented
2C2×C3×#947C211yesmaximal, characteristic
3C2×C3×#944C211yesmaximal, characteristic, complemented
4#10595393C2116yesmaximal, direct product factor
5C2×#63896C212yesmaximal, complemented
6C2×#63887C212yesmaximal, complemented
7C2×#63884C212yesmaximal
8C2×#63867C212yesmaximal, complemented
9C2×#63862C212yesmaximal, complemented
10C2×#63859C212yesmaximal, complemented
11C2×#5735—31nomaximal
12C2×#5672—31nomaximal
13C22×C32×Q8C2211yescharacteristic
14C22×#634C2211yescharacteristic
15C22×C3×D12C2211yescharacteristic
16C22×C3×Dic6C2211yescharacteristic
17C22×D3×Dic3C2212yes—
18#64153C2218yescomplemented
19C2×#3750C2212yes—
20C2×#3750C2212yes—
21C2×C4×C3⋊Dic3C2211yescharacteristic
22C3×#947C2218yes—
23C3×#944C2218yescomplemented
24C2×C3×(C2×D3)⋊C4C2212yes—
25C2×C3×(C2×D3)⋊C4C2212yes—
26C2×C3×Dic3⋊C4C2212yes—
27C2×C3×Dic3⋊C4C2212yes—
28C2×C3×C4×Dic3C2211yescharacteristic
29C2×C3×C4×Dic3C2211yescharacteristic
30C2×#3724C2212yes—
31C2×Dic3⋊Dic3C2212yes—
32C2×Dic3⋊Dic3C2212yes—
33C2×Dic3⋊Dic3C2212yes—
34C2×(C2×D3)⋊Dic3C2212yes—
35C2×(C2×D3)⋊Dic3C2212yes—
36C2×(C2×D3)⋊Dic3C2212yes—
37#63896C22116yescomplemented
38#63887C22116yescomplemented
39#63884C22116yes—
40#63867C22116yescomplemented
41#63862C22116yescomplemented
42#63859C22116yescomplemented
43C2×C3×C4⋊Q8—31no—
44C2×C3×#124—31no—
45C2×#947D311yescharacteristic
46C2×#946—32no—
47C2×#944—31no—
48C2×#944—31no—
49C2×#944—61no—
50C2×#944D311yescharacteristic, complemented
51C2×#935—32no—
52#5735—316no—
53#5672—316no—
54C2×#898—32no—
55C2×#896—32no—
56C2×#894—32no—
57C2×#889—32no—
58C2×#879—32no—
59C2×#879—32no—
60C2×#878—32no—
61C2×#878—32no—
62C2×#876—32no—
63C2×#870—32no—
64C23×C3×D3C2312yes—
65C2×C32×Q8—42no—
66C2×C32×Q8C2314yes—
67C22×C32×C4C2311yescharacteristic
68C22×C32×C4C2311yescharacteristic
69C22×C32×C4C2311yescharacteristic
70C22×C3⋊Dic3C2312yes—
71C22×C3⋊Dic3C2312yes—
72C2×#634—42no—
73C2×#634C2314yes—
74C22×C3×Dic3C2312yes—
75C22×C3×Dic3C2312yes—
76C22×C3×Dic3C2312yes—
77C2×C3×D12—42no—
78C2×C3×D12C2314yes—
79C2×C3×Dic6—42no—
80C2×C3×Dic6C2314yes—
81C2×D3×Dic3—44no—
82C2×D3×Dic3C2318yes—
83#3750C2318yes—
84#3750C2318yes—
85C4×C3⋊Dic3C2314yes—
86C3×(C2×D3)⋊C4C2318yes—
87C3×(C2×D3)⋊C4C2318yes—
88C3×Dic3⋊C4C2318yes—
89C3×Dic3⋊C4C2318yes—
90C3×C4×Dic3C2314yes—
91C3×C4×Dic3C2314yes—
92#3724C2318yes—
93Dic3⋊Dic3C2318yes—
94Dic3⋊Dic3C2318yes—
95Dic3⋊Dic3C2318yes—
96(C2×D3)⋊Dic3C2318yes—
97(C2×D3)⋊Dic3C2318yes—
98(C2×D3)⋊Dic3C2318yes—
99C2×#563—91noSylow
100C22×C3×Q8—21no—
101C22×C3×Q8—31no—
102C22×C3×Q8C2×D311yescharacteristic
103C22×C3×Q8C2×D311yescharacteristic
104C22×C3×D4—31no—
105C23×Dic3—32no—
106C22×D12C2×D311yescharacteristic
107C22×C4×D3—32no—
108C22×Dic6—31no—
109C22×Dic6—31no—
110C22×Dic6—61no—
111C22×Dic6C2×D311yescharacteristic
112C3×C4⋊Q8—38no—
113C3×#124—38no—
114C2×C3×C4⋊C4—32no—
115C2×C3×C4⋊C4—32no—
116C2×C3×C22⋊C4—32no—
117C2×C3×C22⋊C4—32no—
118C2×C3×C42—31no—
119C2×C3×C42—31no—
120C2×#217—32no—
121C2×#217—32no—
122C2×#217—32no—
123#947C2×D318yes—
124#946—316no—
125#944—38no—
126#944—38no—
127#944—68no—
128#944C2×D318yescomplemented
129#935—316no—
130C2×(C2×D3)⋊C4—32no—
131C2×(C2×D3)⋊C4—32no—
132C2×(C2×D3)⋊C4—32no—
133C2×(C2×D3)⋊C4C2×D312yes—
134C2×(C2×D3)⋊C4C2×D312yes—
135C2×C4⋊Dic3—32no—
136C2×C4⋊Dic3—32no—
137C2×C4⋊Dic3—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—32no—
145C2×Dic3⋊C4—32no—
146C2×Dic3⋊C4—32no—
147C2×Dic3⋊C4—62no—
148C2×Dic3⋊C4—62no—
149C2×Dic3⋊C4C2×D312yes—
150C2×Dic3⋊C4C2×D312yes—
151C2×C4×Dic3—31no—
152C2×C4×Dic3—31no—
153C2×C4×Dic3—61no—
154C2×C4×Dic3C2×D311yescharacteristic
155C2×C4×Dic3C2×D311yescharacteristic
156#898—316no—
157#896—316no—
158#894—316no—
159#889—316no—
160#879—316no—
161#879—316no—
162#878—316no—
163#878—316no—
164#876—316no—
165#870—316no—
166C23×C32C2411yescharacteristic
167C22×C3×D3—24no—
168C22×C3×D3—28no—
169C22×C3×D3C2414yes—
170C32×Q8—44no—
171C2×C32×C4—22no—
172C2×C32×C4—22no—
173C2×C32×C4—22no—
174C2×C32×C4C2412yes—
175C2×C32×C4C2412yes—
176C2×C32×C4C2412yes—
177C2×C3⋊Dic3—24no—
178C2×C3⋊Dic3—24no—
179C2×C3⋊Dic3C2414yes—
180C2×C3⋊Dic3C2414yes—
181#634—44no—
182C2×C3×Dic3—24no—
183C2×C3×Dic3—24no—
184C2×C3×Dic3—24no—
185C2×C3×Dic3C2414yes—
186C2×C3×Dic3C2414yes—
187C2×C3×Dic3C2414yes—
188C3×D12—44no—
189C3×Dic6—44no—
190D3×Dic3—48no—
191#563—916no—
192C2×C4⋊Q8—31no—
193C2×C4⋊Q8—91no—
194C2×#126—92no—
195C2×#126—92no—
196C2×#125—92no—
197C2×#124—31no—
198C2×#123—92no—
199C2×C22⋊Q8—92no—
200C2×C22⋊Q8—92no—
201C24×C3—32no—
202C23×D3C22×D312yes—
203C2×C3×Q8—24no—
204C2×C3×Q8—34no—
205C2×C3×Q8—42no—
206C2×C3×Q8—42no—
207C2×C3×Q8—44no—
208C2×C3×Q8—122no—
209C2×C3×Q8C22×D314yes—
210C2×C3×Q8C22×D314yes—
211C2×C3×D4—34no—
212C2×C3×D4—122no—
213C22×C3×C4—21no—
214C22×C3×C4—21no—
215C22×C3×C4—21no—
216C22×C3×C4—32no—
217C22×C3×C4—32no—
218C22×C3×C4—32no—
219C22×C3×C4C22×D311yescharacteristic
220C22×C3×C4C22×D311yescharacteristic
221C22×C3×C4C22×D311yescharacteristic
222C22×C3×C4C22×D311yescharacteristic
223C22×C3×C4C22×D311yescharacteristic
224C22×C3×C4C22×D311yescharacteristic
225C22×Dic3—32no—
226C22×Dic3—32no—
227C22×Dic3—32no—
228C22×Dic3—32no—
229C22×Dic3—38no—
230C22×Dic3—62no—
231C22×Dic3—62no—
232C22×Dic3—124no—
233C22×Dic3C22×D312yes—
234C22×Dic3C22×D312yes—
235C22×Dic3C22×D312yes—
236C2×D12—42no—
237C2×D12C22×D314yes—
238C2×C4×D3—38no—
239C2×C4×D3—124no—
240C2×Dic6—34no—
241C2×Dic6—34no—
242C2×Dic6—42no—
243C2×Dic6—64no—
244C2×Dic6—122no—
245C2×Dic6—122no—
246C2×Dic6—124no—
247C2×Dic6C22×D314yes—
248C3×C4⋊C4—38no—
249C3×C4⋊C4—38no—
250C3×C22⋊C4—38no—
251C3×C22⋊C4—38no—
252C3×C42—34no—
253C3×C42—34no—
254#217—38no—
255#217—38no—
256#217—38no—
257(C2×D3)⋊C4—38no—
258(C2×D3)⋊C4—38no—
259(C2×D3)⋊C4—38no—
260(C2×D3)⋊C4C22×D318yes—
261(C2×D3)⋊C4C22×D318yes—
262C4⋊Dic3—38no—
263C4⋊Dic3—38no—
264C4⋊Dic3—38no—
265Dic3⋊C4—38no—
266Dic3⋊C4—38no—
267Dic3⋊C4—38no—
268Dic3⋊C4—38no—
269Dic3⋊C4—38no—
270Dic3⋊C4—38no—
271Dic3⋊C4—38no—
272Dic3⋊C4—38no—
273Dic3⋊C4—38no—
274Dic3⋊C4—68no—
275Dic3⋊C4—68no—
276Dic3⋊C4C22×D318yes—
277Dic3⋊C4C22×D318yes—
278C4×Dic3—34no—
279C4×Dic3—34no—
280C4×Dic3—64no—
281C4×Dic3C22×D314yes—
282C4×Dic3C22×D314yes—
283C22×C32H(5,𝔽2)12yes—
284C22×C322−1+414yes—
285C22×C32C2511yescharacteristic
286C2×C3×D3—24no—
287C2×C3×D3—28no—
288C2×C3×D3—48no—
289C32×C4—22no—
290C32×C4—22no—
291C32×C4—22no—
292C3⋊Dic3—24no—
293C3⋊Dic3—24no—
294C3×Dic3—24no—
295C3×Dic3—24no—
296C3×Dic3—24no—
297C22×Q8—31no—
298C22×Q8—91no—
299C22×Q8D3211yescharacteristic
300C22×D4—31no—
301C23×C4—92no—
302C4⋊Q8—38no—
303C4⋊Q8—98no—
304#126—916no—
305#126—916no—
306#125—916no—
307#124—38no—
308#123—916no—
309C22⋊Q8—916no—
310C22⋊Q8—916no—
311C2×C4⋊C4—32no—
312C2×C4⋊C4—32no—
313C2×C4⋊C4—92no—
314C2×C4⋊C4—92no—
315C2×C4⋊C4—92no—
316C2×C4⋊C4—92no—
317C2×C4⋊C4—92no—
318C2×C4⋊C4—92no—
319C2×C22⋊C4—32no—
320C2×C22⋊C4—32no—
321C2×C22⋊C4—92no—
322C2×C22⋊C4—92no—
323C2×C22⋊C4—92no—
324C2×C42—31no—
325C2×C42—31no—
326C2×C42—91no—
327C23×C3—21no—
328C23×C3—34no—
329C23×C3—64no—
330C23×C3—68no—
331C23×C3C23×D311yescharacteristic
332C23×C3C23×D311yescharacteristic
333C22×D3—24no—
334C22×D3—28no—
335C22×D3C23×D314yes—
336C3×Q8—44no—
337C3×Q8—44no—
338C3×Q8—48no—
339C3×Q8—124no—
340C3×D4—124no—
341C2×C3×C4—24no—
342C2×C3×C4—22no—
343C2×C3×C4—22no—
344C2×C3×C4—22no—
345C2×C3×C4—22no—
346C2×C3×C4—22no—
347C2×C3×C4—22no—
348C2×C3×C4—22no—
349C2×C3×C4—22no—
350C2×C3×C4—22no—
351C2×C3×C4—34no—
352C2×C3×C4—34no—
353C2×C3×C4—34no—
354C2×C3×C4—42no—
355C2×C3×C4—42no—
356C2×C3×C4—64no—
357C2×C3×C4—64no—
358C2×C3×C4—64no—
359C2×C3×C4C23×D312yes—
360C2×C3×C4C23×D312yes—
361C2×C3×C4C23×D312yes—
362C2×C3×C4C23×D312yes—
363C2×C3×C4C23×D312yes—
364C2×C3×C4C23×D312yes—
365C2×Dic3—24no—
366C2×Dic3—24no—
367C2×Dic3—24no—
368C2×Dic3—34no—
369C2×Dic3—34no—
370C2×Dic3—34no—
371C2×Dic3—34no—
372C2×Dic3—64no—
373C2×Dic3—64no—
374C2×Dic3—68no—
375C2×Dic3—64no—
376C2×Dic3—64no—
377C2×Dic3—64no—
378C2×Dic3—64no—
379C2×Dic3—124no—
380C2×Dic3—128no—
381C2×Dic3C23×D314yes—
382C2×Dic3C23×D314yes—
383C2×Dic3C23×D314yes—
384D12—44no—
385C4×D3—128no—
386Dic6—44no—
387Dic6—124no—
388Dic6—124no—
389Dic6—128no—
390C2×C32#56314yescomplemented
391C2×C32C2×H(5,𝔽2)11yescharacteristic
392C2×C32C2×2−1+412yes—
393C3×D3—44no—
394C24—32no—
395C2×Q8—34no—
396C2×Q8—42no—
397C2×Q8—94no—
398C2×Q8—122no—
399C2×Q8—362no—
400C2×Q8C2×D3214yes—
401C2×D4—34no—
402C2×D4—122no—
403C22×C4—32no—
404C22×C4—32no—
405C22×C4—32no—
406C22×C4—98no—
407C22×C4—92no—
408C22×C4—92no—
409C22×C4—364no—
410C22×C4C2×D3211yescharacteristic
411C22×C4C2×D3211yescharacteristic
412C22×C4C2×D3211yescharacteristic
413C4⋊C4—38no—
414C4⋊C4—38no—
415C4⋊C4—98no—
416C4⋊C4—98no—
417C4⋊C4—98no—
418C4⋊C4—98no—
419C4⋊C4—98no—
420C4⋊C4—98no—
421C22⋊C4—38no—
422C22⋊C4—38no—
423C22⋊C4—98no—
424C22⋊C4—98no—
425C22⋊C4—98no—
426C42—34no—
427C42—34no—
428C42—94no—
429C22×C3—24no—
430C22×C3—22no—
431C22×C3—21no—
432C22×C3—64no—
433C22×C3—68no—
434C22×C3—128no—
435C22×C3#100412yes—
436C22×C3#100412yes—
437C22×C3#100714yes—
438C22×C3#101014yes—
439C22×C3C24×D311yescharacteristic
440C22×C3C24×D311yescharacteristic
441C2×D3—24no—
442C2×D3—28no—
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—68no—
460Dic3—64no—
461Dic3—64no—
462Dic3—64no—
463Dic3—64no—
464Dic3—124no—
465C32C2×#56311yescharacteristic, complemented, Sylow
466C23—34no—
467C23—68no—
468C23—64no—
469C23C22×D3211yescharacteristic
470Q8—44no—
471Q8—124no—
472Q8—364no—
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—24no—
492C2×C3—22no—
493C2×C3—21no—
494C2×C3—124no—
495C2×C3#567214yescomplemented
496C2×C3#573514yescomplemented
497C2×C3C2×#100411yescharacteristic
498C2×C3C2×#100411yescharacteristic
499C2×C3C2×#100712yes—
500C2×C3C2×#101012yes—
501D3—44no—
502C22—68no—
503C22—64no—
504C22—128no—
505C22#6431514yes—
506C22#6433012yes—
507C22C23×D3211yescharacteristic
508C4—22no—
509C4—22no—
510C4—22no—
511C4—64no—
512C4—64no—
513C4—64no—
514C4—184no—
515C4—184no—
516C3—21no—
517C3C2×#567211yescharacteristic, complemented
518C3C2×#573511yescharacteristic, complemented
519C2—124no—
520C2#1059539314yesdirect product factor
521C2C2×#6431512yes—
522C2C2×#6433011yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×Q8C22
socleC23×C32C24
prime radicalC22×C3×D12C22
hypercenterC22×Q8D32
hypocenterC32C2×#563
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#64153C2semidirect
3. C2×C3×#944C2semidirect
4. #10595393C2direct (N × H)
5. C2×#63896C2semidirect
6. C2×#63887C2semidirect
8. C2×#63867C2semidirect
9. C2×#63862C2semidirect
10. C2×#63859C2semidirect
18. #64153C22semidirect
23. C3×#944C22semidirect
37. #63896C22semidirect
38. #63887C22semidirect
40. #63867C22semidirect
41. #63862C22semidirect
42. #63859C22semidirect
50. C2×#944D3semidirect
128. #944C2×D3semidirect
390. C2×C32#563semidirect
465. C32C2×#563semidirect
495. C2×C3#5672semidirect
496. C2×C3#5735semidirect
517. C3C2×#5672semidirect
518. C3C2×#5735semidirect
520. C2#10595393direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641532
C2×C3×#9472
C2×C3×#9442
#105953932
C2×#638962
C2×#638872
C2×#638842
C2×#638672
C2×#638622
C2×#638592
C2×#57353
C2×#56723