Finite Group Databasebeta

← C2×#10590514 #11866704

Subgroups — C2×#10590514 #11866704

Order 1152.

1193 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#895C211yesmaximal, characteristic
2C2×#63856C211yesmaximal, characteristic, complemented
3C22×#3715C211yesmaximal, characteristic, complemented
4C22×D3×C3⋊C8C211yesmaximal, characteristic, complemented
5C2×#63635C211yesmaximal, characteristic, complemented
6C2×C3×#810C211yesmaximal, characteristic, complemented
7C2×#63563C211yesmaximal, characteristic, complemented
8#10590514C218yesmaximal, direct product factor
9C2×#5041—31nomaximal
10C2×#4807—31nomaximal
11C22×C3×D12—21no—
12C22×C3×D12C2211yescharacteristic
13C22×C3×C4×D3C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15C2×C32×C4⋊C4C2211yescharacteristic
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C2×C3×(C2×D3)⋊C4—21no—
19C22×C3×C3⋊C8C2211yescharacteristic
20C3×#895—22no—
21C3×#895C2214yes—
22C2×#3724—21no—
23C2×(C2×D3)⋊Dic3—21no—
24#63856—22no—
25#63856C2214yescomplemented
26C2×#3715—24no—
27C2×#3715C2214yescomplemented
28C2×D3×C3⋊C8—24no—
29C2×D3×C3⋊C8C2214yescomplemented
30#63635C2214yescomplemented
31C3×#810C2214yescomplemented
32#63563C2214yescomplemented
33C2×C3×#121—31no—
34C2×#946—31no—
35C22×#215—31no—
36C22×#214—31no—
37C2×#924—31no—
38C23×C3⋊C8—31no—
39C22×D3×C8—31no—
40C2×#895D311yescharacteristic
41C2×C3×#103—31no—
42C2×#832—31no—
43C2×#821—31no—
44#5041—38no—
45C2×#810D311yescharacteristic, complemented
46C2×#808—31no—
47C2×#808—31no—
48C2×#808—61no—
49#4807—38no—
50C23×C3×D3—21no—
51C23×C3×D3D411yescharacteristic
52C22×C32×C4—21no—
53C22×C32×C4C2311yescharacteristic
54C22×C3⋊Dic3—21no—
55C22×C3×Dic3—21no—
56C22×C3×Dic3D411yescharacteristic
57C2×C3×D12—22no—
58C2×C3×D12—22no—
59C2×C3×D12—24no—
60C2×C3×D12—21no—
61C2×C3×D12—44no—
62C2×C3×D12C2312yes—
63C2×C3×C4×D3—22no—
64C2×C3×C4×D3—22no—
65C2×C3×C4×D3D412yes—
66C2×C3×C4×D3C2312yes—
67C2×C3×Dic6—22no—
68C2×C3×Dic6—22no—
69C2×C3×Dic6—21no—
70C2×C3×Dic6C2312yes—
71C32×C4⋊C4—21no—
72C32×C4⋊C4C2312yes—
73C4⋊(C3⋊Dic3)—21no—
74C4⋊(C3⋊Dic3)C2312yes—
75C2×C3⋊(C3⋊C8)D414yescomplemented
76C2×C3⋊(C3⋊C8)C2312yes—
77C3×(C2×D3)⋊C4—24no—
78C2×C3×C3⋊C8—22no—
79C2×C3×C3⋊C8C2312yes—
80#3724—24no—
81(C2×D3)⋊Dic3—24no—
82#3715—28no—
83D3×C3⋊C8—28no—
84C2×#465—91noSylow
85C22×C3×Q8—31no—
86C22×C3×D4—31no—
87C22×C3×D4—61no—
88C23×C3×C4—31no—
89C22×D12—21no—
90C22×D12C2×D311yescharacteristic
91C22×C4×D3C2×D311yescharacteristic
92C22×Dic6C2×D311yescharacteristic
93C22×C3×C8—31no—
94C3×#121—34no—
95C3×#121—62no—
96C2×C3×C4⋊C4—21no—
97C2×C3×C4⋊C4C2×D311yescharacteristic
98C2×C3×C4⋊C4C2×D311yescharacteristic
99C2×C3×C22⋊C4—61no—
100C2×#217—61no—
101#946—34no—
102#946—62no—
103C2×#215—34no—
104C2×#215—64no—
105C2×#214—34no—
106C2×#214—64no—
107C2×(C2×D3)⋊C4—21no—
108C2×(C2×D3)⋊C4—61no—
109C2×C4⋊Dic3—31no—
110C2×C4⋊Dic3—31no—
111C2×C4⋊Dic3—61no—
112#924—34no—
113#924—62no—
114C2×Dic3⋊C4—61no—
115C2×Dic3⋊C4—61no—
116C22×C3⋊C8—31no—
117C22×C3⋊C8—31no—
118C22×C3⋊C8—34no—
119C22×C3⋊C8—61no—
120C22×C3⋊C8—64no—
121C22×C3⋊C8C2×D311yescharacteristic
122C2×D3×C8—34no—
123C2×D3×C8—64no—
124#895—22no—
125#895C2×D314yes—
126C3×#103—34no—
127#832—34no—
128#821—34no—
129#810C2×D314yescomplemented
130#808—34no—
131#808—34no—
132#808—64no—
133C23×C32C2×D411yescharacteristic
134C22×C3×D3—22no—
135C22×C3×D3—22no—
136C22×C3×D3—22no—
137C22×C3×D3—42no—
138C22×C3×D3—42no—
139C22×C3×D3—42no—
140C22×C3×D3SD1614yescomplemented
141C22×C3×D3C2×D412yes—
142C2×C32×C4—22no—
143C2×C32×C4—42no—
144C2×C32×C4C2×D412yes—
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4#4112yes—
147C2×C32×C4C2411yescharacteristic
148C2×C3⋊Dic3—22no—
149C2×C3⋊Dic3—42no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—42no—
153C2×C3×Dic3C2×D412yes—
154C3×D12—22no—
155C3×D12—22no—
156C3×D12—48no—
157C3×D12—42no—
158C3×C4×D3—24no—
159C3×C4×D3—22no—
160C3×C4×D3—22no—
161C3×Dic6—22no—
162C3×Dic6—22no—
163C3×Dic6—42no—
164C3⋊(C3⋊C8)C2×D414yescomplemented
165C3×C3⋊C8—22no—
166C22×SD16—91no—
167C23×C8—91no—
168C2×C22⋊Q8—91no—
169C2×#121—31no—
170#465—98no—
171C2×#106—91no—
172C2×#103—31no—
173C2×#102—91no—
174C24×C3—31no—
175C24×C3—61no—
176C23×D3—21no—
177C23×D3#6711yescharacteristic
178C2×C3×Q8—32no—
179C2×C3×Q8—61no—
180C2×C3×Q8—62no—
181C2×C3×Q8—62no—
182C2×C3×D4—32no—
183C2×C3×D4—64no—
184C2×C3×D4—62no—
185C2×C3×D4—62no—
186C2×C3×D4—61no—
187C2×C3×D4—124no—
188C22×C3×C4—21no—
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4—31no—
192C22×C3×C4—32no—
193C22×C3×C4—32no—
194C22×C3×C4—41no—
195C22×C3×C4—62no—
196C22×C3×C4—62no—
197C22×C3×C4—61no—
198C22×C3×C4C22×D311yescharacteristic
199C22×C3×C4C22×D311yescharacteristic
200C22×Dic3—21no—
201C22×Dic3—61no—
202C22×Dic3—61no—
203C22×Dic3—121no—
204C22×Dic3#6711yescharacteristic
205C2×D12—22no—
206C2×D12—22no—
207C2×D12—24no—
208C2×D12—21no—
209C2×D12—44no—
210C2×D12C22×D312yes—
211C2×C4×D3—22no—
212C2×C4×D3—22no—
213C2×C4×D3#6712yes—
214C2×C4×D3C22×D312yes—
215C2×Dic6—22no—
216C2×Dic6—22no—
217C2×Dic6—21no—
218C2×Dic6C22×D312yes—
219C2×C3×C8—32no—
220C2×C3×C8—62no—
221C3×C4⋊C4—21no—
222C3×C4⋊C4—21no—
223C3×C4⋊C4—22no—
224C3×C4⋊C4—41no—
225C3×C4⋊C4C22×D312yes—
226C3×C4⋊C4C22×D312yes—
227C3×C22⋊C4—64no—
228#217—64no—
229#215—68no—
230#214—68no—
231(C2×D3)⋊C4—24no—
232(C2×D3)⋊C4—64no—
233C4⋊Dic3—32no—
234C4⋊Dic3—32no—
235C4⋊Dic3—62no—
236C4⋊Dic3—61no—
237C4⋊Dic3—61no—
238C4⋊Dic3—121no—
239Dic3⋊C4—64no—
240Dic3⋊C4—64no—
241C2×C3⋊C8—22no—
242C2×C3⋊C8—34no—
243C2×C3⋊C8—34no—
244C2×C3⋊C8—32no—
245C2×C3⋊C8—32no—
246C2×C3⋊C8—62no—
247C2×C3⋊C8—64no—
248C2×C3⋊C8—68no—
249C2×C3⋊C8C22×D312yes—
250D3×C8—68no—
251C22×C32#12112yes—
252C22×C32C2×SD1612yes—
253C22×C32#13512yes—
254C22×C32C22×D411yescharacteristic
255C2×C3×D3—22no—
256C2×C3×D3—22no—
257C2×C3×D3—28no—
258C2×C3×D3—42no—
259C2×C3×D3—42no—
260C2×C3×D3—42no—
261C2×C3×D3—84no—
262C2×C3×D3C2×SD1614yescomplemented
263C32×C4—42no—
264C32×C4#12112yes—
265C32×C4C22×D411yescharacteristic
266C32×C4C2×#4111yescharacteristic
267C3⋊Dic3—42no—
268C3×Dic3—22no—
269C3×Dic3—42no—
270C22×Q8—31no—
271C22×D4—31no—
272C22×D4—61no—
273C23×C4—31no—
274C2×SD16—94no—
275C2×SD16—184no—
276C22×C8—31no—
277C22×C8—94no—
278C22×C8—91no—
279C22×C8—184no—
280C22⋊Q8—94no—
281C22⋊Q8—182no—
282#121—34no—
283#121—62no—
284C2×C4⋊C4—91no—
285C2×C4⋊C4—181no—
286C2×C4⋊C4D3211yescharacteristic
287C2×C22⋊C4—61no—
288C2×C22⋊C4—181no—
289#106—94no—
290#103—34no—
291#102—94no—
292C23×C3—21no—
293C23×C3—34no—
294C23×C3—32no—
295C23×C3—62no—
296C23×C3—62no—
297C23×C3—62no—
298C23×C3—122no—
299C23×C3—122no—
300C23×C3—122no—
301C23×C3D3×D411yescharacteristic
302C23×C3C2×#6711yescharacteristic
303C22×D3—22no—
304C22×D3—22no—
305C22×D3—22no—
306C22×D3—42no—
307C22×D3—42no—
308C22×D3—42no—
309C22×D3#21414yescomplemented
310C22×D3C2×#6712yes—
311C3×Q8—62no—
312C3×Q8—62no—
313C3×Q8—122no—
314C3×D4—62no—
315C3×D4—62no—
316C3×D4—128no—
317C3×D4—122no—
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—42no—
326C2×C3×C4—42no—
327C2×C3×C4—42no—
328C2×C3×C4—62no—
329C2×C3×C4—64no—
330C2×C3×C4—62no—
331C2×C3×C4—62no—
332C2×C3×C4—62no—
333C2×C3×C4—82no—
334C2×C3×C4—122no—
335C2×C3×C4#23512yes—
336C2×C3×C4D3×D412yes—
337C2×C3×C4D3×D412yes—
338C2×C3×C4D3×D411yescharacteristic
339C2×C3×C4#23712yes—
340C2×C3×C4C2×#6711yescharacteristic
341C2×C3×C4C23×D311yescharacteristic
342C2×C3×C4C23×D311yescharacteristic
343C2×Dic3—22no—
344C2×Dic3—22no—
345C2×Dic3—42no—
346C2×Dic3—62no—
347C2×Dic3—62no—
348C2×Dic3—122no—
349C2×Dic3—122no—
350C2×Dic3—122no—
351C2×Dic3—242no—
352C2×Dic3C2×#6712yes—
353D12—22no—
354D12—22no—
355D12—48no—
356D12—42no—
357C4×D3—24no—
358C4×D3—22no—
359C4×D3—22no—
360Dic6—22no—
361Dic6—22no—
362Dic6—42no—
363C3×C8—62no—
364C3⋊C8—22no—
365C3⋊C8—34no—
366C3⋊C8—34no—
367C3⋊C8—64no—
368C2×C32#46514yescomplemented
369C2×C32C2×#12111yescharacteristic
370C2×C32C22×SD1611yescharacteristic
371C2×C32C2×#13511yescharacteristic
372C3×D3—24no—
373C3×D3—82no—
374C24—31no—
375C24—61no—
376C2×Q8—32no—
377C2×Q8—61no—
378C2×Q8—62no—
379C2×Q8—62no—
380C2×D4—32no—
381C2×D4—64no—
382C2×D4—62no—
383C2×D4—62no—
384C2×D4—61no—
385C2×D4—124no—
386C22×C4—21no—
387C22×C4—31no—
388C22×C4—32no—
389C22×C4—32no—
390C22×C4—62no—
391C22×C4—62no—
392C22×C4—61no—
393C22×C4—181no—
394C22×C4C2×D3211yescharacteristic
395SD16—188no—
396C2×C8—32no—
397C2×C8—62no—
398C2×C8—92no—
399C2×C8—94no—
400C2×C8—188no—
401C4⋊C4—21no—
402C4⋊C4—92no—
403C4⋊C4—184no—
404C4⋊C4—181no—
405C4⋊C4C2×D3212yes—
406C22⋊C4—64no—
407C22⋊C4—184no—
408C22×C3—21no—
409C22×C3—22no—
410C22×C3—22no—
411C22×C3—22no—
412C22×C3—34no—
413C22×C3—62no—
414C22×C3—62no—
415C22×C3—68no—
416C22×C3—122no—
417C22×C3—122no—
418C22×C3—122no—
419C22×C3—244no—
420C22×C3#88412yes—
421C22×C3D3×SD1612yes—
422C22×C3#91912yes—
423C22×C3C2×#21412yes—
424C22×C3#93912yes—
425C22×C3#95012yes—
426C22×C3C2×D3×D411yescharacteristic
427C22×C3C22×#6711yescharacteristic
428C2×D3—22no—
429C2×D3—28no—
430C2×D3—22no—
431C2×D3—42no—
432C2×D3—42no—
433C2×D3—42no—
434C2×D3—84no—
435C2×D3C2×#21414yescomplemented
436C3×C4—21no—
437C3×C4—21no—
438C3×C4—22no—
439C3×C4—42no—
440C3×C4—42no—
441C3×C4—62no—
442C3×C4—82no—
443C3×C4—122no—
444C3×C4#88412yes—
445C3×C4#93912yes—
446C3×C4C2×#23511yescharacteristic
447C3×C4C2×D3×D411yescharacteristic
448C3×C4C2×D3×D411yescharacteristic
449C3×C4C2×#23711yescharacteristic
450Dic3—22no—
451Dic3—42no—
452Dic3—122no—
453Dic3—122no—
454Dic3—242no—
455C32C2×#46511yescharacteristic, complemented, Sylow
456C23—32no—
457C23—34no—
458C23—62no—
459C23—62no—
460C23—62no—
461C23—122no—
462C23—122no—
463C23—122no—
464C23D3×#6711yescharacteristic
465Q8—62no—
466Q8—62no—
467Q8—122no—
468D4—62no—
469D4—62no—
470D4—128no—
471D4—122no—
472C2×C4—22no—
473C2×C4—32no—
474C2×C4—42no—
475C2×C4—62no—
476C2×C4—62no—
477C2×C4—62no—
478C2×C4—64no—
479C2×C4—62no—
480C2×C4—122no—
481C2×C4—182no—
482C2×C4—362no—
483C2×C4#379512yes—
484C2×C4#380212yes—
485C2×C4D3×#6711yescharacteristic
486C2×C4C22×D3211yescharacteristic
487C8—62no—
488C8—94no—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—24no—
492C2×C3—21no—
493C2×C3—64no—
494C2×C3—242no—
495C2×C3#480714yescomplemented
496C2×C3#504114yescomplemented
497C2×C3C2×#88411yescharacteristic
498C2×C3C2×D3×SD1611yescharacteristic
499C2×C3C2×#91911yescharacteristic
500C2×C3C22×#21411yescharacteristic
501C2×C3C2×#93911yescharacteristic
502C2×C3C2×#95011yescharacteristic
503D3—24no—
504D3—82no—
505C22—34no—
506C22—62no—
507C22—68no—
508C22—62no—
509C22—122no—
510C22—122no—
511C22—122no—
512C22—244no—
513C22#6388512yes—
514C22D3×#21412yes—
515C22#6394912yes—
516C22C2×D3×#6711yescharacteristic
517C4—42no—
518C4—62no—
519C4—122no—
520C4—362no—
521C4#6388512yes—
522C4C2×#379511yescharacteristic
523C4C2×#380211yescharacteristic
524C3—21no—
525C3C2×#480711yescharacteristic, complemented
526C3C2×#504111yescharacteristic, complemented
527C2—64no—
528C2—242no—
529C2#1059051414yesdirect product factor
530C2C2×#6388511yescharacteristic
531C2C2×D3×#21411yescharacteristic
532C2C2×#6394911yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC2×C3×#895C2
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#465
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#63856C2semidirect
3. C22×#3715C2semidirect
4. C22×D3×C3⋊C8C2semidirect
5. C2×#63635C2semidirect
6. C2×C3×#810C2semidirect
7. C2×#63563C2semidirect
8. #10590514C2direct (N × H)
25. #63856C22semidirect
27. C2×#3715C22semidirect
29. C2×D3×C3⋊C8C22semidirect
30. #63635C22semidirect
31. C3×#810C22semidirect
32. #63563C22semidirect
45. C2×#810D3semidirect
75. C2×C3⋊(C3⋊C8)D4semidirect
129. #810C2×D3semidirect
140. C22×C3×D3SD16semidirect
164. C3⋊(C3⋊C8)C2×D4semidirect
262. C2×C3×D3C2×SD16semidirect
309. C22×D3#214semidirect
368. C2×C32#465semidirect
435. C2×D3C2×#214semidirect
455. C32C2×#465semidirect
495. C2×C3#4807semidirect
496. C2×C3#5041semidirect
525. C3C2×#4807semidirect
526. C3C2×#5041semidirect
529. C2#10590514direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#8952
C2×#638562
C22×#37152
C22×D3×C3⋊C82
C2×#636352
C2×C3×#8102
C2×#635632
#105905142
C2×#50413
C2×#48073