Finite Group Databasebeta

← C2×#10591578 #11865707

Subgroups — C2×#10591578 #11865707

Order 1152.

1081 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
1C2×C3×#947C211yesmaximal, characteristic
2C22×C3×#216C211yesmaximal, characteristic, complemented
3C2×Dic3×Dic6C211yesmaximal, characteristic, complemented
4C22×#3715C211yesmaximal, characteristic
5C2×#63662C211yesmaximal, characteristic, complemented
6#10591578C218yesmaximal, direct product factor
7C2×Dic3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8C2×#63563C211yesmaximal, characteristic
9C2×#5185—31nomaximal
10C2×#5054—31nomaximal
11C22×C32×Q8C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C22×C3⋊(C3⋊C8)C2211yescharacteristic
16C3×#947—22no—
17C3×#947C2214yes—
18C2×C3×#216—24no—
19C2×C3×#216C2214yescomplemented
20C2×C3×(C2×D3)⋊C4—21no—
21C2×C3×(C2×D3)⋊C4—21no—
22C2×C3×C4×Dic3C2211yescharacteristic
23C22×C3×C3⋊C8C2211yescharacteristic
24C2×Dic3⋊Dic3—21no—
25C2×Dic32—21no—
26Dic3×Dic6—22no—
27Dic3×Dic6C2214yescomplemented
28C2×#3715—24no—
29C2×#3715C2214yes—
30#63662C2214yescomplemented
31Dic3⋊(C3⋊C8)C2214yescomplemented
32#63563C2214yes—
33C22×C3×Q16—31no—
34C2×C3×#124—31no—
35C2×#947D311yescharacteristic
36C2×Q8×Dic3—31no—
37C22×#216D311yescharacteristic, complemented
38C22×#215—31no—
39C22×#214—31no—
40C2×C4×Dic6—31no—
41C2×#835—31no—
42C2×#835—31no—
43C2×#835—61no—
44C2×#832—31no—
45#5185—38no—
46C2×#821—31no—
47C2×Dic3⋊C8—31no—
48#5054—38no—
49C2×C4⋊(C3⋊C8)—31no—
50C23×C3×D3—21no—
51C2×C32×Q8—21no—
52C2×C32×Q8—22no—
53C2×C32×Q8—22no—
54C2×C32×Q8C2312yes—
55C22×C32×C4—21no—
56C22×C32×C4C2311yescharacteristic
57C22×C3⋊Dic3—21no—
58C22×C3×Dic3—21no—
59C22×C3×Dic3D411yescharacteristic
60C22×C3×Dic3D411yescharacteristic
61C2×C3×D12—22no—
62C2×C3×D12—22no—
63C2×C3×D12—21no—
64C2×C3×D12C2312yes—
65C2×C3×Dic6—21no—
66C2×C3×Dic6—22no—
67C2×C3×Dic6D414yes—
68C2×C3×Dic6C2312yes—
69C4⋊(C3⋊Dic3)—21no—
70C4⋊(C3⋊Dic3)C2312yes—
71C2×C3⋊(C3⋊C8)—22no—
72C2×C3⋊(C3⋊C8)C2312yes—
73C3×#216—28no—
74C3×(C2×D3)⋊C4—24no—
75C3×(C2×D3)⋊C4—24no—
76C3×C4×Dic3D412yes—
77C3×C4×Dic3C2312yes—
78C2×C3×C3⋊C8—22no—
79C2×C3×C3⋊C8C2312yes—
80Dic3⋊Dic3—24no—
81Dic32—24no—
82#3715—28no—
83C2×#464—91noSylow
84C22×C3×Q8—21no—
85C22×C3×Q8—31no—
86C22×C3×Q8C2×D311yescharacteristic
87C22×C3×Q8C2×D311yescharacteristic
88C22×C3×D4—31no—
89C22×D12C2×D311yescharacteristic
90C22×Dic6C2×D311yescharacteristic
91C2×C3×Q16—34no—
92C2×C3×Q16—64no—
93C22×C3×C8—31no—
94C3×#124—34no—
95C3×#124—62no—
96C2×C3×C22⋊C4—61no—
97C2×C3×C22⋊C4—61no—
98C2×C3×C42—31no—
99#947—22no—
100#947C2×D314yes—
101Q8×Dic3—34no—
102Q8×Dic3—62no—
103C2×#216—24no—
104C2×#216C2×D314yescomplemented
105C2×#215—34no—
106C2×#215—64no—
107C2×#214—34no—
108C2×#214—64no—
109C2×(C2×D3)⋊C4—21no—
110C2×(C2×D3)⋊C4—21no—
111C2×C4⋊Dic3—31no—
112C2×C4⋊Dic3—31no—
113C2×C4⋊Dic3—61no—
114C2×C4⋊Dic3—61no—
115C2×Dic3⋊C4—61no—
116C2×C4×Dic3—61no—
117C2×C4×Dic3—61no—
118C2×C4×Dic3C2×D311yescharacteristic
119C22×C3⋊C8—31no—
120C22×C3⋊C8—31no—
121C22×C3⋊C8—61no—
122C22×C3⋊C8C2×D311yescharacteristic
123C4×Dic6—34no—
124C4×Dic6—62no—
125#835—34no—
126#835—34no—
127#835—64no—
128#832—34no—
129#821—34no—
130Dic3⋊C8—34no—
131C4⋊(C3⋊C8)—34no—
132C23×C32C2×D411yescharacteristic
133C22×C3×D3—22no—
134C22×C3×D3—42no—
135C22×C3×D3—42no—
136C22×C3×D3—42no—
137C32×Q8—22no—
138C32×Q8—22no—
139C32×Q8—42no—
140C2×C32×C4—22no—
141C2×C32×C4—42no—
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4C2×D412yes—
144C2×C32×C4#4112yes—
145C2×C32×C4C2411yescharacteristic
146C2×C3⋊Dic3—22no—
147C2×C3⋊Dic3—42no—
148C2×C3×Dic3—24no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3C2×D412yes—
153C2×C3×Dic3C2×D412yes—
154C3×D12—22no—
155C3×D12—22no—
156C3×D12—42no—
157C3×Dic6—24no—
158C3×Dic6—22no—
159C3×Dic6C2×D414yes—
160C3⋊(C3⋊C8)—22no—
161C3×C3⋊C8—22no—
162C22×Q16—31no—
163C22×SD16—91no—
164C2×#124—31no—
165C2×C4×Q8—91no—
166#464—98no—
167C2×C4⋊C8—91no—
168C2×#103—91no—
169C2×#102—91no—
170C24×C3—61no—
171C23×D3—21no—
172C2×C3×Q8—21no—
173C2×C3×Q8—21no—
174C2×C3×Q8—24no—
175C2×C3×Q8—22no—
176C2×C3×Q8—22no—
177C2×C3×Q8—22no—
178C2×C3×Q8—22no—
179C2×C3×Q8—22no—
180C2×C3×Q8—34no—
181C2×C3×Q8—32no—
182C2×C3×Q8—41no—
183C2×C3×Q8—42no—
184C2×C3×Q8—62no—
185C2×C3×Q8—61no—
186C2×C3×Q8C22×D312yes—
187C2×C3×Q8C22×D312yes—
188C2×C3×D4—32no—
189C2×C3×D4—61no—
190C2×C3×D4—62no—
191C2×C3×D4—62no—
192C22×C3×C4—21no—
193C22×C3×C4—21no—
194C22×C3×C4—21no—
195C22×C3×C4—31no—
196C22×C3×C4—31no—
197C22×C3×C4—41no—
198C22×C3×C4—61no—
199C22×C3×C4C22×D311yescharacteristic
200C22×C3×C4C22×D311yescharacteristic
201C22×Dic3—21no—
202C22×Dic3—61no—
203C22×Dic3—61no—
204C22×Dic3—121no—
205C22×Dic3#6711yescharacteristic
206C22×Dic3#6711yescharacteristic
207C2×D12—22no—
208C2×D12—22no—
209C2×D12—21no—
210C2×D12C22×D312yes—
211C2×Dic6—21no—
212C2×Dic6—22no—
213C2×Dic6#6714yes—
214C2×Dic6C22×D312yes—
215C3×Q16—68no—
216C2×C3×C8—32no—
217C2×C3×C8—62no—
218C3×C22⋊C4—64no—
219C3×C22⋊C4—64no—
220C3×C42—32no—
221C3×C42—32no—
222#216—28no—
223#215—68no—
224#214—68no—
225(C2×D3)⋊C4—24no—
226(C2×D3)⋊C4—24no—
227C4⋊Dic3—32no—
228C4⋊Dic3—32no—
229C4⋊Dic3—62no—
230C4⋊Dic3—61no—
231C4⋊Dic3—61no—
232C4⋊Dic3—64no—
233C4⋊Dic3—121no—
234Dic3⋊C4—64no—
235C4×Dic3—64no—
236C4×Dic3—64no—
237C4×Dic3#6712yes—
238C4×Dic3C22×D312yes—
239C2×C3⋊C8—22no—
240C2×C3⋊C8—32no—
241C2×C3⋊C8—32no—
242C2×C3⋊C8—62no—
243C2×C3⋊C8—62no—
244C2×C3⋊C8—62no—
245C2×C3⋊C8—122no—
246C2×C3⋊C8C22×D312yes—
247C22×C32#12112yes—
248C22×C32#13512yes—
249C22×C32#13712yes—
250C22×C32C22×D411yescharacteristic
251C2×C3×D3—42no—
252C2×C3×D3—42no—
253C2×C3×D3—42no—
254C2×C3×D3—84no—
255C32×C4—42no—
256C32×C4#12112yes—
257C32×C4C22×D411yescharacteristic
258C32×C4C2×#4111yescharacteristic
259C3⋊Dic3—42no—
260C3×Dic3—24no—
261C3×Dic3—22no—
262C3×Dic3—22no—
263C22×Q8—31no—
264C22×Q8D3211yescharacteristic
265C22×D4—31no—
266C2×Q16—34no—
267C2×Q16—64no—
268C2×SD16—94no—
269C2×SD16—184no—
270C22×C8—31no—
271C22×C8—91no—
272#124—34no—
273#124—62no—
274C4×Q8—94no—
275C4×Q8—182no—
276C2×C4⋊C4—91no—
277C2×C4⋊C4—181no—
278C2×C22⋊C4—61no—
279C2×C22⋊C4—61no—
280C2×C42—31no—
281C2×C42—181no—
282C4⋊C8—94no—
283#103—94no—
284#102—94no—
285C23×C3—21no—
286C23×C3—62no—
287C23×C3—122no—
288C23×C3—122no—
289C23×C3—122no—
290C23×C3D3×D411yescharacteristic
291C23×C3C2×#6711yescharacteristic
292C22×D3—22no—
293C22×D3—42no—
294C22×D3—42no—
295C22×D3—42no—
296C3×Q8—24no—
297C3×Q8—22no—
298C3×Q8—22no—
299C3×Q8—22no—
300C3×Q8—22no—
301C3×Q8—34no—
302C3×Q8—42no—
303C3×Q8—44no—
304C3×Q8—42no—
305C3×Q8—42no—
306C3×Q8—64no—
307C3×Q8—62no—
308C3×D4—62no—
309C3×D4—62no—
310C3×D4—122no—
311C2×C3×C4—22no—
312C2×C3×C4—22no—
313C2×C3×C4—21no—
314C2×C3×C4—22no—
315C2×C3×C4—22no—
316C2×C3×C4—21no—
317C2×C3×C4—32no—
318C2×C3×C4—32no—
319C2×C3×C4—42no—
320C2×C3×C4—44no—
321C2×C3×C4—42no—
322C2×C3×C4—42no—
323C2×C3×C4—62no—
324C2×C3×C4—62no—
325C2×C3×C4—64no—
326C2×C3×C4—62no—
327C2×C3×C4D3×D412yes—
328C2×C3×C4D3×D411yescharacteristic
329C2×C3×C4#23712yes—
330C2×C3×C4#23712yes—
331C2×C3×C4C2×#6711yescharacteristic
332C2×C3×C4C2×#6712yes—
333C2×C3×C4C23×D311yescharacteristic
334C2×C3×C4C23×D311yescharacteristic
335C2×Dic3—24no—
336C2×Dic3—22no—
337C2×Dic3—22no—
338C2×Dic3—22no—
339C2×Dic3—62no—
340C2×Dic3—62no—
341C2×Dic3—122no—
342C2×Dic3—122no—
343C2×Dic3—122no—
344C2×Dic3—242no—
345C2×Dic3C2×#6712yes—
346C2×Dic3C2×#6712yes—
347D12—22no—
348D12—22no—
349D12—42no—
350Dic6—24no—
351Dic6—22no—
352Dic6C2×#6714yes—
353C3×C8—62no—
354C3⋊C8—22no—
355C3⋊C8—62no—
356C3⋊C8—62no—
357C3⋊C8—122no—
358C2×C32#46414yescomplemented
359C2×C32C2×#12111yescharacteristic
360C2×C32C2×#13511yescharacteristic
361C2×C32C2×#13711yescharacteristic
362C3×D3—82no—
363C24—61no—
364C2×Q8—21no—
365C2×Q8—22no—
366C2×Q8—22no—
367C2×Q8—32no—
368C2×Q8—34no—
369C2×Q8—62no—
370C2×Q8—61no—
371C2×Q8C2×D3212yes—
372C2×D4—32no—
373C2×D4—62no—
374C2×D4—62no—
375C2×D4—61no—
376C22×C4—21no—
377C22×C4—31no—
378C22×C4—31no—
379C22×C4—61no—
380C22×C4—181no—
381C22×C4C2×D3211yescharacteristic
382Q16—68no—
383SD16—188no—
384C2×C8—32no—
385C2×C8—62no—
386C2×C8—92no—
387C2×C8—182no—
388C4⋊C4—92no—
389C4⋊C4—184no—
390C4⋊C4—181no—
391C22⋊C4—64no—
392C22⋊C4—64no—
393C42—32no—
394C42—32no—
395C42—184no—
396C22×C3—21no—
397C22×C3—22no—
398C22×C3—22no—
399C22×C3—22no—
400C22×C3—122no—
401C22×C3—122no—
402C22×C3—122no—
403C22×C3—244no—
404C22×C3#91812yes—
405C22×C3#91912yes—
406C22×C3#93812yes—
407C22×C3#93912yes—
408C22×C3#95012yes—
409C22×C3#95112yes—
410C22×C3C2×D3×D411yescharacteristic
411C22×C3C22×#6711yescharacteristic
412C2×D3—42no—
413C2×D3—42no—
414C2×D3—42no—
415C2×D3—84no—
416C3×C4—21no—
417C3×C4—21no—
418C3×C4—22no—
419C3×C4—44no—
420C3×C4—42no—
421C3×C4—42no—
422C3×C4—62no—
423C3×C4—62no—
424C3×C4—64no—
425C3×C4#93812yes—
426C3×C4#93912yes—
427C3×C4C2×D3×D411yescharacteristic
428C3×C4C2×#23711yescharacteristic
429C3×C4C2×#23711yescharacteristic
430C3×C4C22×#6711yescharacteristic
431Dic3—24no—
432Dic3—22no—
433Dic3—22no—
434Dic3—122no—
435Dic3—122no—
436Dic3—242no—
437C32C2×#46411yescharacteristic, complemented, Sylow
438C23—62no—
439C23—122no—
440C23—122no—
441C23—122no—
442C23D3×#6711yescharacteristic
443Q8—22no—
444Q8—22no—
445Q8—34no—
446Q8—42no—
447Q8—62no—
448Q8—64no—
449D4—62no—
450D4—62no—
451D4—122no—
452C2×C4—22no—
453C2×C4—32no—
454C2×C4—32no—
455C2×C4—42no—
456C2×C4—62no—
457C2×C4—62no—
458C2×C4—62no—
459C2×C4—64no—
460C2×C4—182no—
461C2×C4—362no—
462C2×C4#380512yes—
463C2×C4D3×#6712yes—
464C2×C4D3×#6711yescharacteristic
465C2×C4C22×D3211yescharacteristic
466C8—62no—
467C8—182no—
468C2×C3—21no—
469C2×C3—24no—
470C2×C3—21no—
471C2×C3—21no—
472C2×C3—242no—
473C2×C3#505414yescomplemented
474C2×C3#518514yescomplemented
475C2×C3C2×#91811yescharacteristic
476C2×C3C2×#91911yescharacteristic
477C2×C3C2×#93811yescharacteristic
478C2×C3C2×#93911yescharacteristic
479C2×C3C2×#95011yescharacteristic
480C2×C3C2×#95111yescharacteristic
481D3—82no—
482C22—122no—
483C22—122no—
484C22—122no—
485C22—244no—
486C22#6394312yes—
487C22#6394912yes—
488C22#6397012yes—
489C22C2×D3×#6711yescharacteristic
490C4—42no—
491C4—62no—
492C4—64no—
493C4—62no—
494C4—362no—
495C4#6397012yes—
496C4C2×#380511yescharacteristic
497C4C2×D3×#6711yescharacteristic
498C3—21no—
499C3C2×#505411yescharacteristic, complemented
500C3C2×#518511yescharacteristic, complemented
501C2—242no—
502C2#1059157814yesdirect product factor
503C2C2×#6394311yescharacteristic
504C2C2×#6394911yescharacteristic
505C2C2×#6397011yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
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. C22×C3×#216C2semidirect
3. C2×Dic3×Dic6C2semidirect
5. C2×#63662C2semidirect
6. #10591578C2direct (N × H)
7. C2×Dic3⋊(C3⋊C8)C2semidirect
19. C2×C3×#216C22semidirect
27. Dic3×Dic6C22semidirect
30. #63662C22semidirect
31. Dic3⋊(C3⋊C8)C22semidirect
37. C22×#216D3semidirect
104. C2×#216C2×D3semidirect
358. C2×C32#464semidirect
437. C32C2×#464semidirect
473. C2×C3#5054semidirect
474. C2×C3#5185semidirect
499. C3C2×#5054semidirect
500. C3C2×#5185semidirect
502. C2#10591578direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#9472
C22×C3×#2162
C2×Dic3×Dic62
C22×#37152
C2×#636622
#105915782
C2×Dic3⋊(C3⋊C8)2
C2×#635632
C2×#51853
C2×#50543