Finite Group Databasebeta

← C2×#10591174 #11863624

Subgroups — C2×#10591174 #11863624

Order 1152.

1797 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×Dic6C211yesmaximal, characteristic, complemented
2C2×#64139C211yesmaximal, characteristic
3C22×#3717C212yesmaximal, complemented
4C2×C3×#830C211yesmaximal, characteristic, complemented
5#10591174C218yesmaximal, direct product factor
6C2×#63566C212yesmaximal, complemented
7C2×#5227—31nomaximal
8C2×#4738—31nomaximal
9C23×C32×C4C2211yescharacteristic
10C22×#638—21no—
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C23×C3×Dic3—21no—
13C22×C3×Dic6—22no—
14C22×C3×Dic6—21no—
15C22×C3×Dic6—28no—
16C22×C3×Dic6C2212yes—
17C22×C3×Dic6C2214yescomplemented
18#64139—22no—
19#64139C2214yes—
20C2×#3752—21no—
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C22×C3×C3⋊C8C2212yes—
23C2×#3717—28no—
24C2×#3717C2218yescomplemented
25C3×#830C2214yescomplemented
26#63566C2218yescomplemented
27C23×C3×Q8—31no—
28C23×Dic6D311yescharacteristic, complemented
29C22×#215—32no—
30C2×#930—31no—
31C2×#930—31no—
32C2×#930—61no—
33C22×#204—32no—
34C2×C3×C22⋊C8—31no—
35#5227—38no—
36C2×#835—32no—
37C2×#830D311yescharacteristic, complemented
38C2×#816—32no—
39#4738—38no—
40C24×C32D411yescharacteristic
41C23×C3⋊D3—21no—
42C22×C32×C4—24no—
43C22×C32×C4D411yescharacteristic
44C22×C32×C4D412yes—
45C22×C32×C4C2312yes—
46C22×C32×C4C2311yescharacteristic
47C2×#638—24no—
48C2×#638—44no—
49C22×C3⋊Dic3—21no—
50C2×C4⋊(C3⋊D3)—24no—
51C2×C4⋊(C3⋊D3)—21no—
52C2×C4⋊(C3⋊D3)C2312yes—
53C22×C3×Dic3—28no—
54C22×C3×Dic3—22no—
55C22×C3×Dic3—24no—
56C2×C3×Dic6—28no—
57C2×C3×Dic6—216no—
58C2×C3×Dic6—22no—
59C2×C3×Dic6—24no—
60C2×C3×Dic6—24no—
61C2×C3×Dic6—216no—
62C2×C3×Dic6D418yescomplemented
63C2×C3×Dic6C2314yes—
64#3752—24no—
65C4⋊(C3⋊Dic3)—21no—
66C4⋊(C3⋊Dic3)C2312yes—
67C2×C3×C3⋊C8—24no—
68C2×C3×C3⋊C8C2314yes—
69#3717—216no—
70C2×#448—91noSylow
71C22×C3×Q8—32no—
72C22×C3×Q8—34no—
73C22×C3×Q8—68no—
74C22×C3×Q8—61no—
75C22×C3×Q8—62no—
76C23×C3×C4—21no—
77C23×C3×C4—61no—
78C23×C3×C4C2×D311yescharacteristic
79C23×C3×C4C2×D311yescharacteristic
80C22×#67—62no—
81C22×#67—61no—
82C22×#67—61no—
83C23×Dic3—21no—
84C22×D12—31no—
85C22×D12—31no—
86C22×D12—61no—
87C22×Dic6—22no—
88C22×Dic6—21no—
89C22×Dic6—28no—
90C22×Dic6C2×D312yes—
91C22×Dic6C2×D314yescomplemented
92C22×C3×C8—32no—
93C2×#215—38no—
94C2×#215—68no—
95#930—34no—
96#930—34no—
97#930—64no—
98#930—64no—
99#930—62no—
100#930—62no—
101C2×(C2×D3)⋊C4—62no—
102C2×(C2×D3)⋊C4—61no—
103C2×(C2×D3)⋊C4—61no—
104C2×C4⋊Dic3—31no—
105C2×C4⋊Dic3—31no—
106C2×C4⋊Dic3—61no—
107C22×C3⋊C8C2×D312yes—
108C2×#204—38no—
109C2×#204—68no—
110C3×C22⋊C8—34no—
111#835—38no—
112#830C2×D314yescomplemented
113#816—38no—
114C23×C32—22no—
115C23×C32—22no—
116C23×C32SD1614yescomplemented
117C23×C32C2×D412yes—
118C23×C32C2×D411yescharacteristic
119C22×C3⋊D3—22no—
120C22×C3⋊D3—42no—
121C22×C3⋊D3—42no—
122C22×C3⋊D3—42no—
123C2×C32×C4—22no—
124C2×C32×C4—24no—
125C2×C32×C4—24no—
126C2×C32×C4C2×D412yes—
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×D414yes—
129C2×C32×C4C2411yescharacteristic
130#638—48no—
131C2×C3⋊Dic3—22no—
132C2×C3⋊Dic3—42no—
133C4⋊(C3⋊D3)—24no—
134C4⋊(C3⋊D3)—42no—
135C2×C3×Dic3—216no—
136C2×C3×Dic3—28no—
137C2×C3×Dic3—24no—
138C3×Dic6—216no—
139C3×Dic6—28no—
140C3×Dic6—24no—
141C3×Dic6C2×D418yescomplemented
142C3×C3⋊C8—24no—
143C23×Q8—31no—
144C22×SD16—92no—
145C2×#121—91no—
146#448—98no—
147C2×#103—92no—
148C2×C22⋊C8—31no—
149C24×C3—21no—
150C24×C3D1211yescharacteristic
151C24×C3#6711yescharacteristic
152C23×D3—62no—
153C23×D3—61no—
154C23×D3—61no—
155C2×C3×Q8—38no—
156C2×C3×Q8—34no—
157C2×C3×Q8—616no—
158C2×C3×Q8—68no—
159C2×C3×Q8—616no—
160C2×C3×Q8—64no—
161C2×C3×Q8—62no—
162C2×C3×Q8—64no—
163C22×C3×C4—24no—
164C22×C3×C4—24no—
165C22×C3×C4—21no—
166C22×C3×C4—22no—
167C22×C3×C4—21no—
168C22×C3×C4—22no—
169C22×C3×C4—44no—
170C22×C3×C4—68no—
171C22×C3×C4—64no—
172C22×C3×C4—62no—
173C22×C3×C4D1211yescharacteristic
174C22×C3×C4D1212yes—
175C22×C3×C4#6711yescharacteristic
176C22×C3×C4#6712yes—
177C22×C3×C4C22×D312yes—
178C22×C3×C4C22×D312yes—
179C22×C3×C4C22×D311yescharacteristic
180C22×C3×C4C22×D311yescharacteristic
181C2×#67—68no—
182C2×#67—64no—
183C2×#67—64no—
184C2×#67—128no—
185C2×#67—124no—
186C2×#67—124no—
187C22×Dic3—28no—
188C22×Dic3—22no—
189C22×Dic3—24no—
190C22×Dic3—62no—
191C22×Dic3—61no—
192C22×Dic3—61no—
193C2×D12—32no—
194C2×D12—32no—
195C2×D12—62no—
196C2×D12—64no—
197C2×D12—64no—
198C2×D12—62no—
199C2×D12—61no—
200C2×D12—61no—
201C2×D12—124no—
202C2×Dic6—28no—
203C2×Dic6—216no—
204C2×Dic6—22no—
205C2×Dic6—24no—
206C2×Dic6—24no—
207C2×Dic6—216no—
208C2×Dic6#6718yescomplemented
209C2×Dic6C22×D314yes—
210C2×C3×C8—34no—
211C2×C3×C8—64no—
212#215—616no—
213(C2×D3)⋊C4—68no—
214(C2×D3)⋊C4—64no—
215(C2×D3)⋊C4—64no—
216C4⋊Dic3—32no—
217C4⋊Dic3—32no—
218C4⋊Dic3—62no—
219C4⋊Dic3—62no—
220C4⋊Dic3—61no—
221C4⋊Dic3—61no—
222C2×C3⋊C8—24no—
223C2×C3⋊C8C22×D314yes—
224#204—616no—
225C22×C32—22no—
226C22×C32—22no—
227C22×C32—28no—
228C22×C32#12012yes—
229C22×C32C2×SD1612yes—
230C22×C32C2×SD1614yescomplemented
231C22×C32#13712yes—
232C22×C32C22×D411yescharacteristic
233C2×C3⋊D3—42no—
234C2×C3⋊D3—42no—
235C2×C3⋊D3—42no—
236C2×C3⋊D3—84no—
237C32×C4—22no—
238C32×C4#12012yes—
239C32×C4C22×D412yes—
240C3⋊Dic3—42no—
241C3×Dic3—28no—
242C22×Q8—32no—
243C22×Q8—34no—
244C22×Q8—68no—
245C22×Q8—62no—
246C22×Q8—61no—
247C22×D4—91no—
248C22×D4—181no—
249C23×C4—61no—
250C23×C4D3211yescharacteristic
251C2×SD16—98no—
252C2×SD16—188no—
253C22×C8—32no—
254#121—94no—
255#121—182no—
256C2×C4⋊C4—91no—
257C2×C22⋊C4—181no—
258#103—98no—
259C22⋊C8—34no—
260C23×C3—22no—
261C23×C3—22no—
262C23×C3—22no—
263C23×C3—22no—
264C23×C3—24no—
265C23×C3—22no—
266C23×C3—21no—
267C23×C3—42no—
268C23×C3—42no—
269C23×C3#20414yescomplemented
270C23×C3#21514yescomplemented
271C23×C3C2×D1212yes—
272C23×C3C2×D1211yescharacteristic
273C23×C3C2×#6712yes—
274C23×C3C2×#6711yescharacteristic
275C22×D3—64no—
276C22×D3—62no—
277C22×D3—62no—
278C22×D3—124no—
279C22×D3—124no—
280C22×D3—124no—
281C22×D3—122no—
282C22×D3—122no—
283C22×D3—122no—
284C22×D3—122no—
285C22×D3—122no—
286C22×D3—122no—
287C3×Q8—38no—
288C3×Q8—616no—
289C3×Q8—68no—
290C3×Q8—64no—
291C2×C3×C4—22no—
292C2×C3×C4—22no—
293C2×C3×C4—24no—
294C2×C3×C4—24no—
295C2×C3×C4—24no—
296C2×C3×C4—24no—
297C2×C3×C4—21no—
298C2×C3×C4—21no—
299C2×C3×C4—22no—
300C2×C3×C4—24no—
301C2×C3×C4—44no—
302C2×C3×C4—44no—
303C2×C3×C4—42no—
304C2×C3×C4—616no—
305C2×C3×C4—68no—
306C2×C3×C4—64no—
307C2×C3×C4C2×D1212yes—
308C2×C3×C4C2×D1211yescharacteristic
309C2×C3×C4D3×D414yes—
310C2×C3×C4C2×#6712yes—
311C2×C3×C4C2×#6711yescharacteristic
312C2×C3×C4C2×#6714yes—
313C2×C3×C4C23×D311yescharacteristic
314C2×C3×C4C23×D311yescharacteristic
315#67—1216no—
316#67—128no—
317#67—128no—
318C2×Dic3—216no—
319C2×Dic3—28no—
320C2×Dic3—24no—
321C2×Dic3—64no—
322C2×Dic3—62no—
323C2×Dic3—62no—
324C2×Dic3—124no—
325C2×Dic3—122no—
326C2×Dic3—122no—
327D12—64no—
328D12—64no—
329D12—124no—
330D12—124no—
331D12—122no—
332D12—122no—
333Dic6—216no—
334Dic6—28no—
335Dic6—24no—
336Dic6C2×#6718yescomplemented
337C3×C8—64no—
338C3⋊C8—24no—
339C2×C32—24no—
340C2×C32#44814yescomplemented
341C2×C32C2×#12011yescharacteristic
342C2×C32C22×SD1611yescharacteristic
343C2×C32C2×#13711yescharacteristic
344C3⋊D3—82no—
345C24—181no—
346C24#62611yescharacteristic
347C2×Q8—34no—
348C2×Q8—38no—
349C2×Q8—616no—
350C2×Q8—68no—
351C2×Q8—616no—
352C2×Q8—64no—
353C2×Q8—62no—
354C2×Q8—64no—
355C2×D4—92no—
356C2×D4—184no—
357C2×D4—181no—
358C2×D4—184no—
359C2×D4—364no—
360C22×C4—24no—
361C22×C4—68no—
362C22×C4—64no—
363C22×C4—62no—
364C22×C4—181no—
365C22×C4#62612yes—
366C22×C4#62611yescharacteristic
367C22×C4C2×D3212yes—
368C22×C4C2×D3211yescharacteristic
369SD16—1816no—
370C2×C8—34no—
371C2×C8—64no—
372C4⋊C4—92no—
373C4⋊C4—181no—
374C22⋊C4—184no—
375C22×C3—28no—
376C22×C3—22no—
377C22×C3—22no—
378C22×C3—28no—
379C22×C3—22no—
380C22×C3—22no—
381C22×C3—21no—
382C22×C3—22no—
383C22×C3—24no—
384C22×C3—22no—
385C22×C3—22no—
386C22×C3—42no—
387C22×C3—48no—
388C22×C3—42no—
389C22×C3#88212yes—
390C22×C3C2×#20412yes—
391C22×C3C2×#20414yescomplemented
392C22×C3#90912yes—
393C22×C3C2×#21512yes—
394C22×C3C2×#21514yescomplemented
395C22×C3#94212yes—
396C22×C3#95312yes—
397C22×C3C22×D1211yescharacteristic
398C22×C3C22×#6711yescharacteristic
399C2×D3—124no—
400C2×D3—124no—
401C2×D3—124no—
402C2×D3—122no—
403C2×D3—122no—
404C2×D3—122no—
405C2×D3—122no—
406C2×D3—122no—
407C2×D3—122no—
408C2×D3—248no—
409C2×D3—244no—
410C2×D3—244no—
411C3×C4—22no—
412C3×C4—22no—
413C3×C4—22no—
414C3×C4—22no—
415C3×C4—42no—
416C3×C4—68no—
417C3×C4#88212yes—
418C3×C4#95312yes—
419C3×C4C2×D3×D412yes—
420C3×C4C22×#6712yes—
421Dic3—28no—
422Dic3—124no—
423Dic3—122no—
424Dic3—122no—
425C32C2×#44811yescharacteristic, complemented, Sylow
426C23—22no—
427C23—22no—
428C23—182no—
429C23—362no—
430C23—362no—
431C23—362no—
432C23#371714yescomplemented
433C23C2×#62612yes—
434C23C2×#62611yescharacteristic
435Q8—38no—
436Q8—616no—
437Q8—64no—
438Q8—68no—
439D4—184no—
440D4—368no—
441D4—362no—
442C2×C4—22no—
443C2×C4—24no—
444C2×C4—24no—
445C2×C4—616no—
446C2×C4—64no—
447C2×C4—68no—
448C2×C4—182no—
449C2×C4—362no—
450C2×C4C2×#62612yes—
451C2×C4C2×#62611yescharacteristic
452C2×C4D3×#6714yes—
453C2×C4C22×D3211yescharacteristic
454C8—64no—
455C2×C3—24no—
456C2×C3—24no—
457C2×C3—21no—
458C2×C3—24no—
459C2×C3—21no—
460C2×C3—21no—
461C2×C3—44no—
462C2×C3#473814yescomplemented
463C2×C3#522714yescomplemented
464C2×C3C2×#88211yescharacteristic
465C2×C3C22×#20411yescharacteristic
466C2×C3C2×#90911yescharacteristic
467C2×C3C22×#21511yescharacteristic
468C2×C3C2×#94211yescharacteristic
469C2×C3C2×#95311yescharacteristic
470D3—244no—
471D3—242no—
472D3—242no—
473C22—22no—
474C22—28no—
475C22—22no—
476C22—362no—
477C22—362no—
478C22—362no—
479C22—724no—
480C22C2×#371712yes—
481C22C2×#371714yescomplemented
482C22#6383312yes—
483C22#6397712yes—
484C22C22×#62611yescharacteristic
485C4—22no—
486C4—68no—
487C4—362no—
488C4#6397712yes—
489C4C2×D3×#6712yes—
490C3—21no—
491C3C2×#473811yescharacteristic, complemented
492C3C2×#522711yescharacteristic, complemented
493C2—24no—
494C2—722no—
495C2#1059117414yesdirect product factor
496C2C22×#371711yescharacteristic
497C2C2×#6383311yescharacteristic
498C2C2×#6397711yescharacteristic
subgroupG/H
centerC23C2×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC23×C32×C4C22
socleC23×C32C2×D4
prime radicalC2×#64139C2
hypercenterC23×C4D32
hypocenterC32C2×#448
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C23×C3×Dic6C2semidirect
3. C22×#3717C2semidirect
4. C2×C3×#830C2semidirect
5. #10591174C2direct (N × H)
6. C2×#63566C2semidirect
17. C22×C3×Dic6C22semidirect
24. C2×#3717C22semidirect
25. C3×#830C22semidirect
26. #63566C22semidirect
28. C23×Dic6D3semidirect
37. C2×#830D3semidirect
62. C2×C3×Dic6D4semidirect
91. C22×Dic6C2×D3semidirect
112. #830C2×D3semidirect
116. C23×C32SD16semidirect
141. C3×Dic6C2×D4semidirect
208. C2×Dic6#67semidirect
230. C22×C32C2×SD16semidirect
269. C23×C3#204semidirect
270. C23×C3#215semidirect
336. Dic6C2×#67semidirect
340. C2×C32#448semidirect
391. C22×C3C2×#204semidirect
394. C22×C3C2×#215semidirect
425. C32C2×#448semidirect
432. C23#3717semidirect
462. C2×C3#4738semidirect
463. C2×C3#5227semidirect
481. C22C2×#3717semidirect
491. C3C2×#4738semidirect
492. C3C2×#5227semidirect
495. C2#10591174direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×Dic62
C2×#641392
C22×#37172
C2×C3×#8302
#105911742
C2×#635662
C2×#52273
C2×#47383