Finite Group Databasebeta

← C2×#10590848 #11866804

Subgroups — C2×#10590848 #11866804

Order 1152.

1105 conjugacy classes of subgroups.

The subgroup lattice has 507 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D3×C8C211yesmaximal, characteristic
2C2×#63857C211yesmaximal, characteristic
3C2×#63856C211yesmaximal, characteristic
4C22×#3719C211yesmaximal, characteristic, complemented
5C2×#63643C211yesmaximal, characteristic, complemented
6C2×C3×#816C211yesmaximal, characteristic, complemented
7C2×#63575C211yesmaximal, characteristic, complemented
8#10590848C218yesmaximal, direct product factor
9C2×#5116—31nomaximal
10C2×#4813—31nomaximal
11C22×#634C2211yescharacteristic
12C22×C3×C4×D3C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C22×C32×C8C2211yescharacteristic
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C2×C3×D3×C8—24no—
19C2×C3×D3×C8C2214yes—
20C2×#3724—21no—
21C2×Dic3⋊Dic3—21no—
22C2×(C2×D3)⋊Dic3—21no—
23C2×(C2×D3)⋊Dic3—21no—
24#63857—22no—
25#63857C2214yes—
26#63856—22no—
27#63856C2214yes—
28C2×#3719—24no—
29C2×#3719C2214yescomplemented
30#63643C2214yescomplemented
31C3×#816C2214yescomplemented
32#63575C2214yescomplemented
33C23×C3×C8—31no—
34C2×#946—31no—
35C22×#216—31no—
36C2×#924—31no—
37C2×#924—31no—
38C22×Dic12—31no—
39C22×D3×C8D311yescharacteristic
40C2×#897—31no—
41C2×C3×#103—31no—
42#5116—38no—
43C2×#818—31no—
44C2×#816—31no—
45C2×#816—31no—
46C2×#816—61no—
47C2×#816D311yescharacteristic, complemented
48C2×#807—31no—
49#4813—38no—
50C23×C3×D3D411yescharacteristic
51C22×C32×C4C2311yescharacteristic
52C22×C3⋊Dic3—21no—
53C22×C3⋊Dic3—21no—
54C2×#634—22no—
55C2×#634—22no—
56C2×#634—21no—
57C2×#634C2312yes—
58C22×C3×Dic3—21no—
59C22×C3×Dic3—21no—
60C22×C3×Dic3D411yescharacteristic
61C2×C3×C4×D3—22no—
62C2×C3×C4×D3—22no—
63C2×C3×C4×D3D412yes—
64C2×C3×C4×D3C2312yes—
65C2×C3×Dic6—22no—
66C2×C3×Dic6—22no—
67C2×C3×Dic6—21no—
68C2×C3×Dic6C2312yes—
69C2×C32×C8—22no—
70C2×C32×C8C2312yes—
71C4⋊(C3⋊Dic3)—21no—
72C4⋊(C3⋊Dic3)C2312yes—
73C3×C4⋊Dic3—21no—
74C3×C4⋊Dic3C2312yes—
75C2×C3×C3⋊C8D414yes—
76C2×C3×C3⋊C8C2312yes—
77C3×D3×C8—28no—
78#3724—24no—
79Dic3⋊Dic3—24no—
80(C2×D3)⋊Dic3—24no—
81(C2×D3)⋊Dic3—24no—
82#3719—28no—
83C2×#467—91noSylow
84C22×C3×Q8—31no—
85C23×C3×C4—31no—
86C22×C4×D3C2×D311yescharacteristic
87C22×Dic6—31no—
88C22×Dic6—31no—
89C22×Dic6—61no—
90C22×Dic6C2×D311yescharacteristic
91C22×C3×C8—21no—
92C22×C3×C8—31no—
93C22×C3×C8—34no—
94C22×C3×C8—64no—
95C22×C3×C8C2×D311yescharacteristic
96C22×C3×C8C2×D311yescharacteristic
97C2×C3×C4⋊C4—31no—
98C2×#217—61no—
99C2×#217—61no—
100#946—34no—
101#946—62no—
102C2×#216—34no—
103C2×#216—64no—
104C2×(C2×D3)⋊C4—61no—
105C2×(C2×D3)⋊C4—61no—
106C2×C4⋊Dic3—31no—
107C2×C4⋊Dic3—31no—
108C2×C4⋊Dic3—61no—
109C2×C4⋊Dic3—61no—
110C2×C4⋊Dic3C2×D311yescharacteristic
111#924—34no—
112#924—34no—
113#924—62no—
114#924—62no—
115C2×Dic3⋊C4—61no—
116C2×Dic3⋊C4—61no—
117C2×Dic3⋊C4—61no—
118C22×C3⋊C8C2×D311yescharacteristic
119C2×Dic12—34no—
120C2×Dic12—64no—
121C2×D3×C8—24no—
122C2×D3×C8C2×D314yes—
123#897—34no—
124#897—62no—
125C3×#103—34no—
126#818—34no—
127#816—34no—
128#816—34no—
129#816—64no—
130#816C2×D314yescomplemented
131#807—34no—
132C23×C32C2×D411yescharacteristic
133C22×C3×D3—22no—
134C22×C3×D3—22no—
135C22×C3×D3Q1614yescomplemented
136C22×C3×D3C2×D412yes—
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2×D412yes—
139C2×C32×C4#4112yes—
140C2×C32×C4C2411yescharacteristic
141C2×C3⋊Dic3—22no—
142C2×C3⋊Dic3—22no—
143C2×C3⋊Dic3—42no—
144C2×C3⋊Dic3—42no—
145#634—22no—
146#634—22no—
147#634—42no—
148C2×C3×Dic3—22no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—42no—
152C2×C3×Dic3—42no—
153C2×C3×Dic3C2×D412yes—
154C3×C4×D3—24no—
155C3×C4×D3—22no—
156C3×C4×D3—22no—
157C3×Dic6—22no—
158C3×Dic6—22no—
159C3×Dic6—42no—
160C32×C8—22no—
161C3×C3⋊C8C2×D414yes—
162C22×Q16—91no—
163C23×C8—31no—
164C2×C22⋊Q8—91no—
165C2×C22⋊Q8—91no—
166#467—98no—
167C2×#107—91no—
168C2×#103—31no—
169C2×#103—91no—
170C24×C3—31no—
171C23×D3D1211yescharacteristic
172C2×C3×Q8—32no—
173C2×C3×Q8—61no—
174C2×C3×Q8—62no—
175C2×C3×Q8—62no—
176C22×C3×C4—21no—
177C22×C3×C4—31no—
178C22×C3×C4—32no—
179C22×C3×C4—32no—
180C22×C3×C4—62no—
181C22×C3×C4—62no—
182C22×C3×C4—61no—
183C22×C3×C4—61no—
184C22×C3×C4C22×D311yescharacteristic
185C22×C3×C4C22×D311yescharacteristic
186C22×Dic3—21no—
187C22×Dic3—21no—
188C22×Dic3—61no—
189C22×Dic3—61no—
190C22×Dic3—61no—
191C22×Dic3—61no—
192C22×Dic3—121no—
193C22×Dic3—121no—
194C22×Dic3D1211yescharacteristic
195C2×C4×D3—22no—
196C2×C4×D3—22no—
197C2×C4×D3D1212yes—
198C2×C4×D3C22×D312yes—
199C2×Dic6—22no—
200C2×Dic6—22no—
201C2×Dic6—21no—
202C2×Dic6—32no—
203C2×Dic6—32no—
204C2×Dic6—62no—
205C2×Dic6—64no—
206C2×Dic6—62no—
207C2×Dic6—62no—
208C2×Dic6—62no—
209C2×Dic6—62no—
210C2×Dic6—61no—
211C2×Dic6—61no—
212C2×Dic6—121no—
213C2×Dic6—122no—
214C2×Dic6C22×D312yes—
215C2×C3×C8—22no—
216C2×C3×C8—22no—
217C2×C3×C8—22no—
218C2×C3×C8—34no—
219C2×C3×C8—32no—
220C2×C3×C8—42no—
221C2×C3×C8—68no—
222C2×C3×C8C22×D312yes—
223C2×C3×C8C22×D312yes—
224C3×C4⋊C4—32no—
225C3×C4⋊C4—61no—
226#217—64no—
227#217—64no—
228#216—68no—
229(C2×D3)⋊C4—64no—
230(C2×D3)⋊C4—64no—
231C4⋊Dic3—21no—
232C4⋊Dic3—32no—
233C4⋊Dic3—32no—
234C4⋊Dic3—62no—
235C4⋊Dic3—61no—
236C4⋊Dic3—61no—
237C4⋊Dic3—64no—
238C4⋊Dic3—121no—
239C4⋊Dic3C22×D312yes—
240Dic3⋊C4—64no—
241Dic3⋊C4—64no—
242Dic3⋊C4—64no—
243C2×C3⋊C8#6714yes—
244C2×C3⋊C8C22×D312yes—
245Dic12—68no—
246D3×C8—28no—
247C22×C32#12112yes—
248C22×C32C2×Q1612yes—
249C22×C32#13512yes—
250C22×C32C22×D411yescharacteristic
251C2×C3×D3—22no—
252C2×C3×D3—22no—
253C2×C3×D3—28no—
254C2×C3×D3C2×Q1614yescomplemented
255C32×C4#12112yes—
256C32×C4C22×D411yescharacteristic
257C32×C4C2×#4111yescharacteristic
258C3⋊Dic3—42no—
259C3⋊Dic3—42no—
260C3×Dic3—22no—
261C3×Dic3—42no—
262C3×Dic3—42no—
263C22×Q8—31no—
264C22×Q8—91no—
265C23×C4—31no—
266C2×Q16—94no—
267C2×Q16—184no—
268C22×C8—31no—
269C22×C8—34no—
270C22×C8—64no—
271C22×C8D3211yescharacteristic
272C22⋊Q8—94no—
273C22⋊Q8—94no—
274C22⋊Q8—182no—
275C22⋊Q8—182no—
276C2×C4⋊C4—31no—
277C2×C4⋊C4—91no—
278C2×C4⋊C4—181no—
279C2×C4⋊C4—181no—
280C2×C22⋊C4—181no—
281C2×C22⋊C4—181no—
282#107—94no—
283#103—34no—
284#103—94no—
285C23×C3—21no—
286C23×C3—34no—
287C23×C3—32no—
288C23×C3—62no—
289C23×C3—62no—
290C23×C3C2×D1211yescharacteristic
291C23×C3D3×D411yescharacteristic
292C22×D3—22no—
293C22×D3—22no—
294C22×D3Dic1214yescomplemented
295C22×D3C2×D1212yes—
296C3×Q8—62no—
297C3×Q8—62no—
298C3×Q8—122no—
299C2×C3×C4—21no—
300C2×C3×C4—22no—
301C2×C3×C4—21no—
302C2×C3×C4—22no—
303C2×C3×C4—32no—
304C2×C3×C4—62no—
305C2×C3×C4—64no—
306C2×C3×C4—62no—
307C2×C3×C4—62no—
308C2×C3×C4—62no—
309C2×C3×C4—62no—
310C2×C3×C4—122no—
311C2×C3×C4—122no—
312C2×C3×C4C2×D1211yescharacteristic
313C2×C3×C4#23512yes—
314C2×C3×C4#23512yes—
315C2×C3×C4D3×D411yescharacteristic
316C2×C3×C4D3×D412yes—
317C2×C3×C4C2×#6712yes—
318C2×C3×C4C23×D311yescharacteristic
319C2×C3×C4C23×D311yescharacteristic
320C2×Dic3—22no—
321C2×Dic3—22no—
322C2×Dic3—22no—
323C2×Dic3—42no—
324C2×Dic3—42no—
325C2×Dic3—62no—
326C2×Dic3—62no—
327C2×Dic3—62no—
328C2×Dic3—62no—
329C2×Dic3—122no—
330C2×Dic3—122no—
331C2×Dic3—124no—
332C2×Dic3—122no—
333C2×Dic3—122no—
334C2×Dic3—122no—
335C2×Dic3—122no—
336C2×Dic3—242no—
337C2×Dic3C2×D1212yes—
338C4×D3—24no—
339C4×D3—22no—
340C4×D3—22no—
341Dic6—22no—
342Dic6—22no—
343Dic6—42no—
344Dic6—64no—
345Dic6—62no—
346Dic6—62no—
347Dic6—62no—
348Dic6—62no—
349Dic6—122no—
350Dic6—124no—
351Dic6—122no—
352Dic6—122no—
353C3×C8—22no—
354C3×C8—22no—
355C3×C8—34no—
356C3×C8—42no—
357C3⋊C8C2×#6714yes—
358C2×C32#46714yescomplemented
359C2×C32C2×#12111yescharacteristic
360C2×C32C22×Q1611yescharacteristic
361C2×C32C2×#13511yescharacteristic
362C3×D3—24no—
363C24—31no—
364C2×Q8—32no—
365C2×Q8—61no—
366C2×Q8—62no—
367C2×Q8—62no—
368C2×Q8—92no—
369C2×Q8—181no—
370C2×Q8—182no—
371C2×Q8—182no—
372C22×C4—31no—
373C22×C4—32no—
374C22×C4—32no—
375C22×C4—62no—
376C22×C4—62no—
377C22×C4—61no—
378C22×C4—61no—
379C22×C4—181no—
380C22×C4—181no—
381C22×C4C2×D3211yescharacteristic
382Q16—188no—
383C2×C8—22no—
384C2×C8—32no—
385C2×C8—34no—
386C2×C8—68no—
387C2×C8C2×D3212yes—
388C4⋊C4—32no—
389C4⋊C4—61no—
390C4⋊C4—92no—
391C4⋊C4—184no—
392C4⋊C4—184no—
393C4⋊C4—181no—
394C22⋊C4—184no—
395C22⋊C4—184no—
396C22×C3—21no—
397C22×C3—22no—
398C22×C3—22no—
399C22×C3—22no—
400C22×C3—34no—
401C22×C3—62no—
402C22×C3—62no—
403C22×C3—68no—
404C22×C3#88412yes—
405C22×C3#90412yes—
406C22×C3C2×Dic1212yes—
407C22×C3#91612yes—
408C22×C3D3×Q1612yes—
409C22×C3#93012yes—
410C22×C3C22×D1211yescharacteristic
411C22×C3C2×D3×D411yescharacteristic
412C2×D3—22no—
413C2×D3—22no—
414C2×D3—28no—
415C2×D3C2×Dic1214yescomplemented
416C3×C4—21no—
417C3×C4—21no—
418C3×C4—22no—
419C3×C4—62no—
420C3×C4—122no—
421C3×C4—122no—
422C3×C4#88412yes—
423C3×C4#93012yes—
424C3×C4C2×#23511yescharacteristic
425C3×C4C2×#23511yescharacteristic
426C3×C4C2×D3×D411yescharacteristic
427C3×C4C22×#6711yescharacteristic
428Dic3—22no—
429Dic3—42no—
430Dic3—42no—
431Dic3—124no—
432Dic3—122no—
433Dic3—122no—
434Dic3—122no—
435Dic3—122no—
436Dic3—242no—
437C32C2×#46711yescharacteristic, complemented, Sylow
438C23—32no—
439C23—34no—
440C23—62no—
441C23—62no—
442C23D3×D1211yescharacteristic
443Q8—62no—
444Q8—62no—
445Q8—122no—
446Q8—182no—
447Q8—182no—
448Q8—362no—
449C2×C4—32no—
450C2×C4—62no—
451C2×C4—62no—
452C2×C4—62no—
453C2×C4—64no—
454C2×C4—62no—
455C2×C4—62no—
456C2×C4—122no—
457C2×C4—122no—
458C2×C4—182no—
459C2×C4—182no—
460C2×C4—362no—
461C2×C4—362no—
462C2×C4#379812yes—
463C2×C4D3×D1211yescharacteristic
464C2×C4D3×#6712yes—
465C2×C4C22×D3211yescharacteristic
466C8—22no—
467C8—34no—
468C2×C3—24no—
469C2×C3—21no—
470C2×C3—21no—
471C2×C3—21no—
472C2×C3—64no—
473C2×C3#481314yescomplemented
474C2×C3#511614yescomplemented
475C2×C3C2×#88411yescharacteristic
476C2×C3C2×#90411yescharacteristic
477C2×C3C22×Dic1211yescharacteristic
478C2×C3C2×#91611yescharacteristic
479C2×C3C2×D3×Q1611yescharacteristic
480C2×C3C2×#93011yescharacteristic
481D3—24no—
482C22—34no—
483C22—68no—
484C22—62no—
485C22—62no—
486C22D3×Dic1212yes—
487C22#6380612yes—
488C22#6390612yes—
489C22C2×D3×D1211yescharacteristic
490C4—62no—
491C4—122no—
492C4—122no—
493C4—362no—
494C4—362no—
495C4#6390612yes—
496C4C2×#379811yescharacteristic
497C4C2×D3×#6711yescharacteristic
498C3—21no—
499C3C2×#481311yescharacteristic, complemented
500C3C2×#511611yescharacteristic, complemented
501C2—64no—
502C2#1059084814yesdirect product factor
503C2C2×D3×Dic1211yescharacteristic
504C2C2×#6380611yescharacteristic
505C2C2×#6390611yescharacteristic
subgroupG/H
centerC23D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC23×C3×D3D4
hypercenterC22×C8D32
hypocenterC32C2×#467
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
4. C22×#3719C2semidirect
5. C2×#63643C2semidirect
6. C2×C3×#816C2semidirect
7. C2×#63575C2semidirect
8. #10590848C2direct (N × H)
29. C2×#3719C22semidirect
30. #63643C22semidirect
31. C3×#816C22semidirect
32. #63575C22semidirect
47. C2×#816D3semidirect
130. #816C2×D3semidirect
135. C22×C3×D3Q16semidirect
254. C2×C3×D3C2×Q16semidirect
294. C22×D3Dic12semidirect
358. C2×C32#467semidirect
415. C2×D3C2×Dic12semidirect
437. C32C2×#467semidirect
473. C2×C3#4813semidirect
474. C2×C3#5116semidirect
499. C3C2×#4813semidirect
500. C3C2×#5116semidirect
502. C2#10590848direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×D3×C82
C2×#638572
C2×#638562
C22×#37192
C2×#636432
C2×C3×#8162
C2×#635752
#105908482
C2×#51163
C2×#48133