Finite Group Databasebeta

← C2×#10591607 #11865702

Subgroups — C2×#10591607 #11865702

Order 1152.

1149 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3755C211yesmaximal, characteristic
2C2×C3×Q8×Dic3C211yesmaximal, characteristic, complemented
3C22×C3×#216C211yesmaximal, characteristic, complemented
4C2×#63864C211yesmaximal, characteristic
5#10591607C218yesmaximal, direct product factor
6C2×Dic3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
7C2×#63565C211yesmaximal, characteristic, complemented
8C2×#63564C211yesmaximal, characteristic
9C2×#5185—31nomaximal
10C2×#5028—31nomaximal
11C22×C32×Q8C2211yescharacteristic
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C2×#3755—24no—
15C2×#3755C2214yes—
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C3×Q8×Dic3—22no—
18C3×Q8×Dic3C2214yescomplemented
19C2×C3×#216—24no—
20C2×C3×#216C2214yescomplemented
21C2×C3×C4⋊Dic3—21no—
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×C4×Dic3—21no—
24C2×C3×C4×Dic3C2211yescharacteristic
25C22×C3×C3⋊C8C2211yescharacteristic
26C2×#3722—21no—
27C2×#3722—21no—
28#63864—22no—
29#63864C2214yes—
30Dic3⋊(C3⋊C8)C2214yescomplemented
31#63565C2214yescomplemented
32#63564C2214yes—
33C22×C3×Q16—31no—
34C2×C3×C4×Q8—31no—
35C2×#947—31no—
36C2×Q8×Dic3D311yescharacteristic, complemented
37C22×#216D311yescharacteristic, complemented
38C22×#215—31no—
39C22×#215—31no—
40C22×#215—61no—
41C2×#875—31no—
42C2×#835—31no—
43#5185—38no—
44C2×#821—31no—
45C2×Dic3⋊C8—31no—
46#5028—38no—
47C2×#810—31no—
48C2×#809—31no—
49C2×C4⋊(C3⋊C8)—31no—
50C23×C3⋊D3—21no—
51C2×C32×Q8—21no—
52C2×C32×Q8—22no—
53C2×C32×Q8D414yes—
54C2×C32×Q8C2312yes—
55C22×C32×C4—21no—
56C22×C32×C4C2311yescharacteristic
57C2×C4⋊(C3⋊D3)—22no—
58C2×C4⋊(C3⋊D3)—22no—
59C2×C4⋊(C3⋊D3)—21no—
60C2×C4⋊(C3⋊D3)C2312yes—
61C22×C3×Dic3—21no—
62C22×C3×Dic3—21no—
63C22×C3×Dic3D411yescharacteristic
64C22×C3×Dic3D411yescharacteristic
65C2×C3×Dic6—22no—
66C2×C3×Dic6—22no—
67C2×C3×Dic6—21no—
68C2×C3×Dic6C2312yes—
69#3755—28no—
70C2×C3⋊(C3⋊C8)—22no—
71C2×C3⋊(C3⋊C8)C2312yes—
72C3×#216—28no—
73C3×C4⋊Dic3—21no—
74C3×C4⋊Dic3—24no—
75C3×C4⋊Dic3C2312yes—
76C3×C4×Dic3—24no—
77C3×C4×Dic3D412yes—
78C3×C4×Dic3C2312yes—
79C2×C3×C3⋊C8—22no—
80C2×C3×C3⋊C8C2312yes—
81#3722—24no—
82#3722—24no—
83C2×#464—91noSylow
84C22×C3×Q8—21no—
85C22×C3×Q8—31no—
86C22×C3×Q8C2×D311yescharacteristic
87C22×C3×Q8C2×D311yescharacteristic
88C22×D12—31no—
89C22×D12—31no—
90C22×D12—61no—
91C22×Dic6C2×D311yescharacteristic
92C2×C3×Q16—34no—
93C2×C3×Q16—64no—
94C22×C3×C8—31no—
95C3×C4×Q8—34no—
96C3×C4×Q8—62no—
97C2×C3×C4⋊C4—31no—
98C2×C3×C4⋊C4—61no—
99C2×C3×C42—31no—
100C2×C3×C42—61no—
101#947—34no—
102#947—62no—
103Q8×Dic3—22no—
104Q8×Dic3C2×D314yescomplemented
105C2×#216—24no—
106C2×#216C2×D314yescomplemented
107C2×#215—34no—
108C2×#215—34no—
109C2×#215—64no—
110C2×#215—68no—
111C2×#215—64no—
112C2×#215—64no—
113C2×(C2×D3)⋊C4—61no—
114C2×(C2×D3)⋊C4—61no—
115C2×(C2×D3)⋊C4—61no—
116C2×(C2×D3)⋊C4—61no—
117C2×C4⋊Dic3—21no—
118C2×C4⋊Dic3C2×D311yescharacteristic
119C2×C4×Dic3—21no—
120C2×C4×Dic3C2×D311yescharacteristic
121C22×C3⋊C8—31no—
122C22×C3⋊C8—31no—
123C22×C3⋊C8—61no—
124C22×C3⋊C8C2×D311yescharacteristic
125#875—34no—
126#875—62no—
127#835—34no—
128#821—34no—
129Dic3⋊C8—34no—
130#810—34no—
131#809—34no—
132C4⋊(C3⋊C8)—34no—
133C23×C32C2×D411yescharacteristic
134C22×C3⋊D3—22no—
135C22×C3⋊D3—42no—
136C22×C3⋊D3—42no—
137C22×C3⋊D3—42no—
138C32×Q8—24no—
139C32×Q8—22no—
140C32×Q8C2×D414yes—
141C2×C32×C4—24no—
142C2×C32×C4—22no—
143C2×C32×C4C2×D412yes—
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4#4112yes—
146C2×C32×C4C2411yescharacteristic
147C4⋊(C3⋊D3)—22no—
148C4⋊(C3⋊D3)—22no—
149C4⋊(C3⋊D3)—42no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3—22no—
154C2×C3×Dic3—42no—
155C2×C3×Dic3—42no—
156C2×C3×Dic3C2×D412yes—
157C2×C3×Dic3C2×D412yes—
158C3×Dic6—22no—
159C3×Dic6—22no—
160C3×Dic6—42no—
161C3⋊(C3⋊C8)—22no—
162C3×C3⋊C8—22no—
163C22×Q16—31no—
164C22×SD16—91no—
165C2×#124—91no—
166C2×C4×Q8—31no—
167#464—98no—
168C2×C4⋊C8—91no—
169C2×#103—91no—
170C2×#102—91no—
171C23×D3—61no—
172C23×D3—61no—
173C23×D3—121no—
174C2×C3×Q8—22no—
175C2×C3×Q8—21no—
176C2×C3×Q8—22no—
177C2×C3×Q8—21no—
178C2×C3×Q8—24no—
179C2×C3×Q8—22no—
180C2×C3×Q8—32no—
181C2×C3×Q8—42no—
182C2×C3×Q8—41no—
183C2×C3×Q8—61no—
184C2×C3×Q8—62no—
185C2×C3×Q8—62no—
186C2×C3×Q8D1214yes—
187C2×C3×Q8#6714yes—
188C2×C3×Q8C22×D312yes—
189C2×C3×Q8C22×D312yes—
190C22×C3×C4—21no—
191C22×C3×C4—21no—
192C22×C3×C4—21no—
193C22×C3×C4—31no—
194C22×C3×C4—31no—
195C22×C3×C4—41no—
196C22×C3×C4—61no—
197C22×C3×C4—61no—
198C22×C3×C4C22×D311yescharacteristic
199C22×C3×C4C22×D311yescharacteristic
200C22×Dic3—21no—
201C22×Dic3—21no—
202C22×Dic3#6711yescharacteristic
203C22×Dic3#6711yescharacteristic
204C2×D12—32no—
205C2×D12—32no—
206C2×D12—62no—
207C2×D12—64no—
208C2×D12—62no—
209C2×D12—62no—
210C2×D12—62no—
211C2×D12—62no—
212C2×D12—61no—
213C2×D12—61no—
214C2×D12—122no—
215C2×D12—121no—
216C2×Dic6—22no—
217C2×Dic6—22no—
218C2×Dic6—21no—
219C2×Dic6C22×D312yes—
220C3×Q16—68no—
221C2×C3×C8—32no—
222C2×C3×C8—62no—
223C3×C4⋊C4—32no—
224C3×C4⋊C4—64no—
225C3×C4⋊C4—61no—
226C3×C42—32no—
227C3×C42—32no—
228C3×C42—64no—
229#216—28no—
230#215—616no—
231#215—68no—
232#215—68no—
233(C2×D3)⋊C4—64no—
234(C2×D3)⋊C4—64no—
235(C2×D3)⋊C4—64no—
236(C2×D3)⋊C4—64no—
237C4⋊Dic3—21no—
238C4⋊Dic3—24no—
239C4⋊Dic3C22×D312yes—
240C4×Dic3—24no—
241C4×Dic3#6712yes—
242C4×Dic3C22×D312yes—
243C2×C3⋊C8—22no—
244C2×C3⋊C8—32no—
245C2×C3⋊C8—32no—
246C2×C3⋊C8—62no—
247C2×C3⋊C8—64no—
248C2×C3⋊C8—62no—
249C2×C3⋊C8—62no—
250C2×C3⋊C8C22×D312yes—
251C22×C32#12112yes—
252C22×C32#13512yes—
253C22×C32#13712yes—
254C22×C32C22×D411yescharacteristic
255C2×C3⋊D3—42no—
256C2×C3⋊D3—42no—
257C2×C3⋊D3—42no—
258C2×C3⋊D3—84no—
259C32×C4—24no—
260C32×C4#12112yes—
261C32×C4C22×D411yescharacteristic
262C32×C4C2×#4111yescharacteristic
263C3×Dic3—22no—
264C3×Dic3—22no—
265C3×Dic3—42no—
266C3×Dic3—42no—
267C22×Q8—31no—
268C22×Q8D3211yescharacteristic
269C22×D4—91no—
270C2×Q16—34no—
271C2×Q16—64no—
272C2×SD16—94no—
273C2×SD16—184no—
274C22×C8—31no—
275C22×C8—91no—
276#124—94no—
277#124—182no—
278C4×Q8—34no—
279C4×Q8—62no—
280C2×C4⋊C4—31no—
281C2×C4⋊C4—61no—
282C2×C22⋊C4—181no—
283C2×C22⋊C4—181no—
284C2×C42—31no—
285C2×C42—61no—
286C4⋊C8—94no—
287#103—94no—
288#102—94no—
289C23×C3—21no—
290C23×C3D3×D411yescharacteristic
291C23×C3C2×#6711yescharacteristic
292C22×D3—62no—
293C22×D3—62no—
294C22×D3—122no—
295C22×D3—124no—
296C22×D3—122no—
297C22×D3—122no—
298C22×D3—122no—
299C22×D3—122no—
300C22×D3—122no—
301C22×D3—122no—
302C22×D3—242no—
303C22×D3—242no—
304C3×Q8—24no—
305C3×Q8—24no—
306C3×Q8—22no—
307C3×Q8—22no—
308C3×Q8—24no—
309C3×Q8—42no—
310C3×Q8—44no—
311C3×Q8—62no—
312C3×Q8—62no—
313C3×Q8—122no—
314C3×Q8C2×D1214yes—
315C3×Q8C2×#6714yes—
316C2×C3×C4—24no—
317C2×C3×C4—24no—
318C2×C3×C4—22no—
319C2×C3×C4—22no—
320C2×C3×C4—21no—
321C2×C3×C4—22no—
322C2×C3×C4—22no—
323C2×C3×C4—21no—
324C2×C3×C4—32no—
325C2×C3×C4—32no—
326C2×C3×C4—42no—
327C2×C3×C4—44no—
328C2×C3×C4—62no—
329C2×C3×C4—62no—
330C2×C3×C4—62no—
331C2×C3×C4—62no—
332C2×C3×C4—122no—
333C2×C3×C4—122no—
334C2×C3×C4C2×D1212yes—
335C2×C3×C4#23512yes—
336C2×C3×C4D3×D411yescharacteristic
337C2×C3×C4#23712yes—
338C2×C3×C4C2×#6712yes—
339C2×C3×C4C2×#6711yescharacteristic
340C2×C3×C4C23×D311yescharacteristic
341C2×C3×C4C23×D311yescharacteristic
342C2×Dic3—22no—
343C2×Dic3—22no—
344C2×Dic3—22no—
345C2×Dic3—22no—
346C2×Dic3—42no—
347C2×Dic3—42no—
348C2×Dic3C2×#6712yes—
349C2×Dic3C2×#6712yes—
350D12—64no—
351D12—62no—
352D12—62no—
353D12—62no—
354D12—62no—
355D12—122no—
356D12—124no—
357D12—122no—
358D12—122no—
359Dic6—22no—
360Dic6—22no—
361Dic6—42no—
362C3×C8—62no—
363C3⋊C8—22no—
364C3⋊C8—64no—
365C3⋊C8—62no—
366C3⋊C8—62no—
367C2×C32#46414yescomplemented
368C2×C32C2×#12111yescharacteristic
369C2×C32C2×#13511yescharacteristic
370C2×C32C2×#13711yescharacteristic
371C3⋊D3—82no—
372C24—181no—
373C2×Q8—22no—
374C2×Q8—21no—
375C2×Q8—32no—
376C2×Q8—61no—
377C2×Q8—62no—
378C2×Q8—62no—
379C2×Q8#62614yes—
380C2×Q8C2×D3212yes—
381C2×D4—92no—
382C2×D4—182no—
383C2×D4—182no—
384C2×D4—181no—
385C22×C4—21no—
386C22×C4—31no—
387C22×C4—31no—
388C22×C4—61no—
389C22×C4—61no—
390C22×C4C2×D3211yescharacteristic
391Q16—68no—
392SD16—188no—
393C2×C8—32no—
394C2×C8—62no—
395C2×C8—92no—
396C2×C8—182no—
397C4⋊C4—32no—
398C4⋊C4—64no—
399C4⋊C4—61no—
400C22⋊C4—184no—
401C22⋊C4—184no—
402C42—32no—
403C42—32no—
404C42—64no—
405C22×C3—21no—
406C22×C3—22no—
407C22×C3—22no—
408C22×C3—22no—
409C22×C3#91812yes—
410C22×C3#91912yes—
411C22×C3#93012yes—
412C22×C3#93912yes—
413C22×C3#94212yes—
414C22×C3#95012yes—
415C22×C3C2×D3×D411yescharacteristic
416C22×C3C22×#6711yescharacteristic
417C2×D3—124no—
418C2×D3—122no—
419C2×D3—122no—
420C2×D3—122no—
421C2×D3—122no—
422C2×D3—122no—
423C2×D3—122no—
424C2×D3—242no—
425C2×D3—242no—
426C2×D3—248no—
427C2×D3—244no—
428C2×D3—244no—
429C3×C4—24no—
430C3×C4—24no—
431C3×C4—21no—
432C3×C4—21no—
433C3×C4—22no—
434C3×C4—44no—
435C3×C4—62no—
436C3×C4—62no—
437C3×C4—122no—
438C3×C4—122no—
439C3×C4#93012yes—
440C3×C4#93912yes—
441C3×C4C22×D1211yescharacteristic
442C3×C4C2×#23511yescharacteristic
443C3×C4C2×#23711yescharacteristic
444C3×C4C22×#6711yescharacteristic
445Dic3—22no—
446Dic3—22no—
447Dic3—42no—
448Dic3—42no—
449C32C2×#46411yescharacteristic, complemented, Sylow
450C23—182no—
451C23—362no—
452C23—362no—
453C23—362no—
454C23D3×#6711yescharacteristic
455Q8—22no—
456Q8—24no—
457Q8—62no—
458Q8—62no—
459Q8—122no—
460Q8C2×#62614yes—
461D4—182no—
462D4—182no—
463D4—362no—
464C2×C4—22no—
465C2×C4—24no—
466C2×C4—32no—
467C2×C4—32no—
468C2×C4—62no—
469C2×C4—62no—
470C2×C4—62no—
471C2×C4—62no—
472C2×C4—122no—
473C2×C4—122no—
474C2×C4#380412yes—
475C2×C4C2×#62612yes—
476C2×C4D3×#6711yescharacteristic
477C2×C4C22×D3211yescharacteristic
478C8—62no—
479C8—182no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—24no—
483C2×C3—21no—
484C2×C3#502814yescomplemented
485C2×C3#518514yescomplemented
486C2×C3C2×#91811yescharacteristic
487C2×C3C2×#91911yescharacteristic
488C2×C3C2×#93011yescharacteristic
489C2×C3C2×#93911yescharacteristic
490C2×C3C2×#94211yescharacteristic
491C2×C3C2×#95011yescharacteristic
492D3—244no—
493D3—242no—
494D3—242no—
495C22—362no—
496C22—362no—
497C22—362no—
498C22—724no—
499C22#6394812yes—
500C22#6394912yes—
501C22#6397812yes—
502C22C2×D3×#6711yescharacteristic
503C4—24no—
504C4—62no—
505C4—62no—
506C4—122no—
507C4—122no—
508C4#6397812yes—
509C4C2×#380411yescharacteristic
510C4C22×#62611yescharacteristic
511C3—21no—
512C3C2×#502811yescharacteristic, complemented
513C3C2×#518511yescharacteristic, complemented
514C2—722no—
515C2#1059160714yesdirect product factor
516C2C2×#6394811yescharacteristic
517C2C2×#6394911yescharacteristic
518C2C2×#6397811yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC22×Q8D32
hypocenterC32C2×#464
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C2×C3×Q8×Dic3C2semidirect
3. C22×C3×#216C2semidirect
5. #10591607C2direct (N × H)
6. C2×Dic3⋊(C3⋊C8)C2semidirect
7. C2×#63565C2semidirect
18. C3×Q8×Dic3C22semidirect
20. C2×C3×#216C22semidirect
30. Dic3⋊(C3⋊C8)C22semidirect
31. #63565C22semidirect
36. C2×Q8×Dic3D3semidirect
37. C22×#216D3semidirect
104. Q8×Dic3C2×D3semidirect
106. C2×#216C2×D3semidirect
367. C2×C32#464semidirect
449. C32C2×#464semidirect
484. C2×C3#5028semidirect
485. C2×C3#5185semidirect
512. C3C2×#5028semidirect
513. C3C2×#5185semidirect
515. C2#10591607direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37552
C2×C3×Q8×Dic32
C22×C3×#2162
C2×#638642
#105916072
C2×Dic3⋊(C3⋊C8)2
C2×#635652
C2×#635642
C2×#51853
C2×#50283