Finite Group Databasebeta

← C2×#10590796 #11865708

Subgroups — C2×#10590796 #11865708

Order 1152.

1069 conjugacy classes of subgroups.

The subgroup lattice has 503 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#204C211yesmaximal, characteristic
2C2×#63863C211yesmaximal, characteristic
3C2×#63843C211yesmaximal, characteristic, complemented
4C22×#3718C211yesmaximal, characteristic, complemented
5C2×#63641C211yesmaximal, characteristic, complemented
6C2×C3×#816C211yesmaximal, characteristic, complemented
7C2×#63562C211yesmaximal, characteristic
8#10590796C218yesmaximal, direct product factor
9C2×#5166—31nomaximal
10C2×#4798—31nomaximal
11C22×C3×D12C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C22×C32×C8C2211yescharacteristic
15C2×C4×C3⋊Dic3C2211yescharacteristic
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×#204—24no—
19C2×C3×#204C2214yes—
20C2×Dic3⋊Dic3—21no—
21C2×(C2×D3)⋊Dic3—21no—
22C2×(C2×D3)⋊Dic3—21no—
23C2×Dic32—21no—
24#63863—22no—
25#63863C2214yes—
26#63843—22no—
27#63843C2214yescomplemented
28C2×#3718—24no—
29C2×#3718C2214yescomplemented
30#63641C2214yescomplemented
31C3×#816C2214yescomplemented
32#63562C2214yes—
33C22×C3×SD16—31no—
34C2×#947—31no—
35C2×Q8×Dic3—31no—
36C22×#216—31no—
37C22×#216—31no—
38C2×#936—31no—
39C22×#204D311yescharacteristic
40C2×#887—31no—
41C2×C3×#103—31no—
42C2×#832—31no—
43#5166—38no—
44C2×#816D311yescharacteristic, complemented
45C2×Dic3⋊C8—31no—
46C2×Dic3⋊C8—31no—
47C2×Dic3⋊C8—61no—
48C2×#809—31no—
49#4798—38no—
50C23×C3×D3—21no—
51C22×C32×C4C2311yescharacteristic
52C22×C3⋊Dic3D411yescharacteristic
53C22×C3⋊Dic3D411yescharacteristic
54C22×C3×Dic3—21no—
55C22×C3×Dic3—21no—
56C22×C3×Dic3—21no—
57C2×C3×D12—22no—
58C2×C3×D12—22no—
59C2×C3×D12—21no—
60C2×C3×D12C2312yes—
61C2×C3×Dic6—21no—
62C2×C3×Dic6—22no—
63C2×C3×Dic6—22no—
64C2×C3×Dic6—22no—
65C2×C3×Dic6—21no—
66C2×C3×Dic6D414yes—
67C2×C3×Dic6C2312yes—
68C2×C3×Dic6C2312yes—
69C2×C32×C8—22no—
70C2×C32×C8C2312yes—
71C4×C3⋊Dic3D412yes—
72C4×C3⋊Dic3C2312yes—
73C2×C3⋊(C3⋊C8)—22no—
74C2×C3⋊(C3⋊C8)C2312yes—
75C3×C4⋊Dic3—21no—
76C3×C4⋊Dic3C2312yes—
77C3×#204—28no—
78Dic3⋊Dic3—24no—
79(C2×D3)⋊Dic3—24no—
80(C2×D3)⋊Dic3—24no—
81Dic32—24no—
82#3718—28no—
83C2×#464—91noSylow
84C22×C3×Q8—31no—
85C22×C3×Q8—31no—
86C22×C3×D4—31no—
87C22×D12C2×D311yescharacteristic
88C22×Dic6C2×D311yescharacteristic
89C22×Dic6C2×D311yescharacteristic
90C2×C3×SD16—34no—
91C2×C3×SD16—64no—
92C22×C3×C8—21no—
93C22×C3×C8C2×D311yescharacteristic
94C22×C3×C8C2×D311yescharacteristic
95C2×C3×C4⋊C4—31no—
96C2×#217—61no—
97C2×#217—61no—
98#947—34no—
99#947—62no—
100Q8×Dic3—34no—
101Q8×Dic3—62no—
102C2×#216—34no—
103C2×#216—34no—
104C2×#216—64no—
105C2×#216—64no—
106#936—34no—
107#936—62no—
108C2×(C2×D3)⋊C4—61no—
109C2×(C2×D3)⋊C4—61no—
110C2×C4⋊Dic3—61no—
111C2×C4⋊Dic3C2×D311yescharacteristic
112C2×Dic3⋊C4—61no—
113C2×C4×Dic3—31no—
114C2×C4×Dic3—31no—
115C2×C4×Dic3—61no—
116C2×C4×Dic3—61no—
117C2×C4×Dic3—61no—
118C22×C3⋊C8—31no—
119C22×C3⋊C8—31no—
120C22×C3⋊C8—61no—
121C2×#204—24no—
122C2×#204C2×D314yes—
123#887—34no—
124#887—62no—
125C3×#103—34no—
126#832—34no—
127#816C2×D314yescomplemented
128Dic3⋊C8—34no—
129Dic3⋊C8—34no—
130Dic3⋊C8—64no—
131#809—34no—
132C23×C32C2×D411yescharacteristic
133C22×C3×D3—22no—
134C22×C3×D3—42no—
135C22×C3×D3—42no—
136C22×C3×D3—42no—
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⋊Dic3C2×D412yes—
144C2×C3⋊Dic3C2×D412yes—
145C2×C3×Dic3—24no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—22no—
148C2×C3×Dic3—22no—
149C2×C3×Dic3—42no—
150C2×C3×Dic3—42no—
151C3×D12—22no—
152C3×D12—22no—
153C3×D12—42no—
154C3×Dic6—24no—
155C3×Dic6—22no—
156C3×Dic6—22no—
157C3×Dic6—22no—
158C3×Dic6—42no—
159C3×Dic6C2×D414yes—
160C32×C8—22no—
161C3⋊(C3⋊C8)—22no—
162C22×Q16—91no—
163C22×SD16—31no—
164C2×#124—91no—
165C2×C4×Q8—91no—
166#464—98no—
167C2×C4⋊C8—91no—
168C2×#103—31no—
169C2×#102—91no—
170C24×C3—61no—
171C23×D3—21no—
172C2×C3×Q8—34no—
173C2×C3×Q8—32no—
174C2×C3×Q8—32no—
175C2×C3×Q8—62no—
176C2×C3×Q8—61no—
177C2×C3×Q8—61no—
178C2×C3×Q8—62no—
179C2×C3×Q8—62no—
180C2×C3×D4—32no—
181C2×C3×D4—62no—
182C2×C3×D4—62no—
183C2×C3×D4—61no—
184C22×C3×C4—21no—
185C22×C3×C4—61no—
186C22×C3×C4—61no—
187C22×C3×C4—61no—
188C22×C3×C4C22×D311yescharacteristic
189C22×C3×C4C22×D311yescharacteristic
190C22×Dic3—21no—
191C22×Dic3—21no—
192C22×Dic3—21no—
193C22×Dic3—31no—
194C22×Dic3—31no—
195C22×Dic3—31no—
196C22×Dic3—31no—
197C22×Dic3—61no—
198C22×Dic3—61no—
199C2×D12—22no—
200C2×D12—22no—
201C2×D12—21no—
202C2×D12C22×D312yes—
203C2×Dic6—21no—
204C2×Dic6—22no—
205C2×Dic6—22no—
206C2×Dic6—22no—
207C2×Dic6—21no—
208C2×Dic6#6714yes—
209C2×Dic6C22×D312yes—
210C2×Dic6C22×D312yes—
211C3×SD16—68no—
212C2×C3×C8—22no—
213C2×C3×C8—22no—
214C2×C3×C8—22no—
215C2×C3×C8—42no—
216C2×C3×C8C22×D312yes—
217C2×C3×C8C22×D312yes—
218C3×C4⋊C4—32no—
219C3×C4⋊C4—61no—
220#217—64no—
221#217—64no—
222#216—68no—
223#216—68no—
224(C2×D3)⋊C4—64no—
225(C2×D3)⋊C4—64no—
226C4⋊Dic3—21no—
227C4⋊Dic3—64no—
228C4⋊Dic3C22×D312yes—
229Dic3⋊C4—64no—
230C4×Dic3—32no—
231C4×Dic3—32no—
232C4×Dic3—32no—
233C4×Dic3—32no—
234C4×Dic3—62no—
235C4×Dic3—62no—
236C4×Dic3—64no—
237C4×Dic3—64no—
238C2×C3⋊C8—32no—
239C2×C3⋊C8—32no—
240C2×C3⋊C8—62no—
241C2×C3⋊C8—62no—
242C2×C3⋊C8—62no—
243C2×C3⋊C8—122no—
244#204—28no—
245C22×C32#12112yes—
246C22×C32#13512yes—
247C22×C32#13712yes—
248C22×C32C22×D411yescharacteristic
249C2×C3×D3—42no—
250C2×C3×D3—42no—
251C2×C3×D3—42no—
252C2×C3×D3—84no—
253C32×C4#12112yes—
254C32×C4C22×D411yescharacteristic
255C32×C4C2×#4111yescharacteristic
256C3⋊Dic3—22no—
257C3⋊Dic3—22no—
258C3×Dic3—24no—
259C3×Dic3—42no—
260C3×Dic3—42no—
261C22×Q8—31no—
262C22×Q8—31no—
263C22×D4—31no—
264C2×Q16—94no—
265C2×Q16—184no—
266C2×SD16—34no—
267C2×SD16—64no—
268C22×C8—91no—
269C22×C8D3211yescharacteristic
270#124—94no—
271#124—182no—
272C4×Q8—94no—
273C4×Q8—182no—
274C2×C4⋊C4—31no—
275C2×C4⋊C4—181no—
276C2×C22⋊C4—181no—
277C2×C22⋊C4—181no—
278C2×C42—91no—
279C2×C42—181no—
280C4⋊C8—94no—
281#103—34no—
282#102—94no—
283C23×C3—21no—
284C23×C3—62no—
285C23×C3—122no—
286C23×C3—122no—
287C23×C3—122no—
288C23×C3D3×D411yescharacteristic
289C23×C3D3×D411yescharacteristic
290C22×D3—22no—
291C22×D3—42no—
292C22×D3—42no—
293C22×D3—42no—
294C3×Q8—34no—
295C3×Q8—64no—
296C3×Q8—62no—
297C3×Q8—62no—
298C3×Q8—62no—
299C3×Q8—122no—
300C3×D4—62no—
301C3×D4—62no—
302C3×D4—122no—
303C2×C3×C4—21no—
304C2×C3×C4—22no—
305C2×C3×C4—21no—
306C2×C3×C4—22no—
307C2×C3×C4—64no—
308C2×C3×C4—62no—
309C2×C3×C4—62no—
310C2×C3×C4—62no—
311C2×C3×C4—122no—
312C2×C3×C4—122no—
313C2×C3×C4#23512yes—
314C2×C3×C4D3×D411yescharacteristic
315C2×C3×C4D3×D411yescharacteristic
316C2×C3×C4D3×D412yes—
317C2×C3×C4#23712yes—
318C2×C3×C4C2×#6712yes—
319C2×C3×C4C23×D311yescharacteristic
320C2×C3×C4C23×D311yescharacteristic
321C2×Dic3—24no—
322C2×Dic3—22no—
323C2×Dic3—22no—
324C2×Dic3—22no—
325C2×Dic3—32no—
326C2×Dic3—32no—
327C2×Dic3—32no—
328C2×Dic3—32no—
329C2×Dic3—42no—
330C2×Dic3—42no—
331C2×Dic3—62no—
332C2×Dic3—62no—
333C2×Dic3—64no—
334C2×Dic3—62no—
335C2×Dic3—62no—
336C2×Dic3—62no—
337C2×Dic3—62no—
338C2×Dic3—122no—
339D12—22no—
340D12—22no—
341D12—42no—
342Dic6—24no—
343Dic6—22no—
344Dic6—22no—
345Dic6—22no—
346Dic6—42no—
347Dic6C2×#6714yes—
348C3×C8—22no—
349C3×C8—22no—
350C3×C8—42no—
351C3⋊C8—62no—
352C3⋊C8—62no—
353C3⋊C8—122no—
354C2×C32#46414yescomplemented
355C2×C32C2×#12111yescharacteristic
356C2×C32C2×#13511yescharacteristic
357C2×C32C2×#13711yescharacteristic
358C3×D3—82no—
359C24—61no—
360C2×Q8—32no—
361C2×Q8—32no—
362C2×Q8—34no—
363C2×Q8—62no—
364C2×Q8—61no—
365C2×Q8—61no—
366C2×Q8—62no—
367C2×Q8—62no—
368C2×D4—32no—
369C2×D4—62no—
370C2×D4—61no—
371C2×D4—62no—
372C22×C4—61no—
373C22×C4—61no—
374C22×C4—61no—
375C22×C4—91no—
376C22×C4—91no—
377C22×C4C2×D3211yescharacteristic
378Q16—188no—
379SD16—68no—
380C2×C8—22no—
381C2×C8—92no—
382C2×C8—182no—
383C2×C8C2×D3212yes—
384C4⋊C4—32no—
385C4⋊C4—61no—
386C4⋊C4—184no—
387C22⋊C4—184no—
388C22⋊C4—184no—
389C42—92no—
390C42—92no—
391C42—184no—
392C22×C3—21no—
393C22×C3—22no—
394C22×C3—22no—
395C22×C3—22no—
396C22×C3—122no—
397C22×C3—122no—
398C22×C3—122no—
399C22×C3—244no—
400C22×C3#88412yes—
401C22×C3#91512yes—
402C22×C3#91612yes—
403C22×C3#91612yes—
404C22×C3#91812yes—
405C22×C3#93912yes—
406C22×C3C2×D3×D411yescharacteristic
407C22×C3C2×D3×D411yescharacteristic
408C2×D3—42no—
409C2×D3—42no—
410C2×D3—42no—
411C2×D3—84no—
412C3×C4—21no—
413C3×C4—21no—
414C3×C4—22no—
415C3×C4—64no—
416C3×C4—122no—
417C3×C4—122no—
418C3×C4#88412yes—
419C3×C4#93912yes—
420C3×C4C2×#23511yescharacteristic
421C3×C4C2×D3×D411yescharacteristic
422C3×C4C2×#23711yescharacteristic
423C3×C4C22×#6711yescharacteristic
424Dic3—24no—
425Dic3—42no—
426Dic3—42no—
427Dic3—64no—
428Dic3—62no—
429Dic3—62no—
430Dic3—62no—
431Dic3—62no—
432Dic3—122no—
433C32C2×#46411yescharacteristic, complemented, Sylow
434C23—62no—
435C23—122no—
436C23—122no—
437C23—122no—
438C23#380211yescharacteristic
439Q8—34no—
440Q8—62no—
441Q8—64no—
442Q8—62no—
443Q8—62no—
444Q8—122no—
445D4—62no—
446D4—62no—
447D4—122no—
448C2×C4—62no—
449C2×C4—64no—
450C2×C4—62no—
451C2×C4—62no—
452C2×C4—92no—
453C2×C4—92no—
454C2×C4—122no—
455C2×C4—122no—
456C2×C4—182no—
457C2×C4—182no—
458C2×C4#379512yes—
459C2×C4#380211yescharacteristic
460C2×C4D3×#6712yes—
461C2×C4C22×D3211yescharacteristic
462C8—22no—
463C8—182no—
464C2×C3—21no—
465C2×C3—24no—
466C2×C3—21no—
467C2×C3—21no—
468C2×C3—242no—
469C2×C3#479814yescomplemented
470C2×C3#516614yescomplemented
471C2×C3C2×#88411yescharacteristic
472C2×C3C2×#91511yescharacteristic
473C2×C3C2×#91611yescharacteristic
474C2×C3C2×#91611yescharacteristic
475C2×C3C2×#91811yescharacteristic
476C2×C3C2×#93911yescharacteristic
477D3—82no—
478C22—122no—
479C22—122no—
480C22—122no—
481C22—244no—
482C22#6380912yes—
483C22#6381112yes—
484C22#6388512yes—
485C22C2×#380211yescharacteristic
486C4—64no—
487C4—122no—
488C4—122no—
489C4—182no—
490C4—182no—
491C4#6388512yes—
492C4C2×#379511yescharacteristic
493C4C2×D3×#6711yescharacteristic
494C3—21no—
495C3C2×#479811yescharacteristic, complemented
496C3C2×#516611yescharacteristic, complemented
497C2—242no—
498C2#1059079614yesdirect product factor
499C2C2×#6380911yescharacteristic
500C2C2×#6381111yescharacteristic
501C2C2×#6388511yescharacteristic
subgroupG/H
centerC23#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
hypercenterC22×C8D32
hypocenterC32C2×#464
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
3. C2×#63843C2semidirect
4. C22×#3718C2semidirect
5. C2×#63641C2semidirect
6. C2×C3×#816C2semidirect
8. #10590796C2direct (N × H)
27. #63843C22semidirect
29. C2×#3718C22semidirect
30. #63641C22semidirect
31. C3×#816C22semidirect
44. C2×#816D3semidirect
127. #816C2×D3semidirect
354. C2×C32#464semidirect
433. C32C2×#464semidirect
469. C2×C3#4798semidirect
470. C2×C3#5166semidirect
495. C3C2×#4798semidirect
496. C3C2×#5166semidirect
498. C2#10590796direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2042
C2×#638632
C2×#638432
C22×#37182
C2×#636412
C2×C3×#8162
C2×#635622
#105907962
C2×#51663
C2×#47983