Finite Group Databasebeta

← C2×#10591093 #11869447

Subgroups — C2×#10591093 #11869447

Order 1152.

1101 conjugacy classes of subgroups.

The subgroup lattice has 521 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64135C211yesmaximal, characteristic, complemented
2C2×C3×#930C211yesmaximal, characteristic
3C2×C3×#830C211yesmaximal, characteristic, complemented
4C2×#63575C211yesmaximal, characteristic, complemented
5C2×#63573C211yesmaximal, characteristic, complemented
6#10591093C218yesmaximal, direct product factor
7C2×#63563C211yesmaximal, characteristic, complemented
8C2×#63563C211yesmaximal, characteristic, complemented
9C2×#5035—31nomaximal
10C2×#4737—31nomaximal
11C23×C32×C4C2211yescharacteristic
12C22×C3×#67—21no—
13C22×C3×D12C2211yescharacteristic
14C2×#3757—21no—
15#64135—22no—
16#64135C2214yescomplemented
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C2×C4×C3⋊Dic3—21no—
20C3×#930—22no—
21C3×#930C2214yes—
22C2×C3×(C2×D3)⋊C4—21no—
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25C22×C3×C3⋊C8C2211yescharacteristic
26C3×#830C2214yescomplemented
27#63575C2214yescomplemented
28#63573C2214yescomplemented
29#63563C2214yescomplemented
30#63563C2214yescomplemented
31C2×C3×#121—31no—
32C2×#930D311yescharacteristic
33C2×#926—31no—
34C2×#926—31no—
35C2×#926—61no—
36C2×C3×C22⋊C8—31no—
37C2×#832—31no—
38C2×#832—31no—
39C2×#830D311yescharacteristic, complemented
40C2×#821—31no—
41C2×#821—31no—
42C2×#818—31no—
43C2×#817—31no—
44#5035—38no—
45C2×#808—31no—
46C2×#807—31no—
47#4737—38no—
48C24×C32D411yescharacteristic
49C23×C3×D3—21no—
50C22×C32×C4—22no—
51C22×C32×C4—22no—
52C22×C32×C4D411yescharacteristic
53C22×C32×C4D412yes—
54C22×C32×C4C2312yes—
55C22×C32×C4C2311yescharacteristic
56C22×C3⋊Dic3—21no—
57C22×C3⋊Dic3—21no—
58C2×C3×#67—24no—
59C2×C3×#67—44no—
60C22×C3×Dic3—21no—
61C2×C3×D12—22no—
62C2×C3×D12—22no—
63C2×C3×D12—21no—
64C2×C3×D12C2312yes—
65#3757—24no—
66C4⋊(C3⋊Dic3)—21no—
67C4⋊(C3⋊Dic3)—21no—
68C4⋊(C3⋊Dic3)C2312yes—
69C4⋊(C3⋊Dic3)C2312yes—
70C4×C3⋊Dic3—24no—
71C3×(C2×D3)⋊C4—24no—
72C3×C4⋊Dic3—21no—
73C3×C4⋊Dic3C2312yes—
74C2×C3×C3⋊C8—22no—
75C2×C3×C3⋊C8—22no—
76C2×C3×C3⋊C8C2312yes—
77C2×C3×C3⋊C8C2312yes—
78C2×#482—91noSylow
79C22×C3×D4—31no—
80C22×C3×D4—61no—
81C23×C3×C4—21no—
82C23×C3×C4C2×D311yescharacteristic
83C23×C3×C4C2×D311yescharacteristic
84C22×#67—21no—
85C22×D12C2×D311yescharacteristic
86C22×C3×C8—31no—
87C22×C3×C8—31no—
88C3×#121—34no—
89C3×#121—62no—
90C2×C3×C4⋊C4—31no—
91C2×C3×C22⋊C4—61no—
92C2×#217—62no—
93C2×#217—61no—
94C2×#217—61no—
95#930—22no—
96#930C2×D314yes—
97C2×(C2×D3)⋊C4—21no—
98#926—34no—
99#926—34no—
100#926—64no—
101#926—64no—
102#926—62no—
103#926—62no—
104C2×C4⋊Dic3—31no—
105C2×C4⋊Dic3—31no—
106C2×C4⋊Dic3—31no—
107C2×C4⋊Dic3—31no—
108C2×C4⋊Dic3—61no—
109C2×C4⋊Dic3—61no—
110C2×C4⋊Dic3C2×D311yescharacteristic
111C2×C4×Dic3—62no—
112C2×C4×Dic3—61no—
113C2×C4×Dic3—61no—
114C22×C3⋊C8C2×D311yescharacteristic
115C22×C3⋊C8C2×D311yescharacteristic
116C3×C22⋊C8—34no—
117#832—34no—
118#832—34no—
119#830C2×D314yescomplemented
120#821—34no—
121#821—34no—
122#818—34no—
123#817—34no—
124#808—34no—
125#807—34no—
126C23×C32—22no—
127C23×C32—22no—
128C23×C32—22no—
129C23×C32C2×D412yes—
130C23×C32C2×D411yescharacteristic
131C22×C3×D3—22no—
132C22×C3×D3—42no—
133C22×C3×D3—42no—
134C22×C3×D3—42no—
135C2×C32×C4—22no—
136C2×C32×C4—24no—
137C2×C32×C4—22no—
138C2×C32×C4—22no—
139C2×C32×C4C2×D412yes—
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4#4112yes—
142C2×C32×C4#4112yes—
143C2×C32×C4C2411yescharacteristic
144C2×C3⋊Dic3—22no—
145C2×C3⋊Dic3—22no—
146C2×C3⋊Dic3—42no—
147C2×C3⋊Dic3—42no—
148C3×#67—48no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—42no—
151C3×D12—22no—
152C3×D12—22no—
153C3×D12—42no—
154C3×C3⋊C8—22no—
155C3×C3⋊C8—22no—
156C2×#121—31no—
157C2×#117—91no—
158#482—98no—
159C2×#107—91no—
160C2×#106—91no—
161C2×#102—91no—
162C2×#102—91no—
163C2×C22⋊C8—31no—
164C24×C3—21no—
165C24×C3—61no—
166C24×C3D1211yescharacteristic
167C24×C3#6711yescharacteristic
168C23×D3—21no—
169C2×C3×D4—32no—
170C2×C3×D4—64no—
171C2×C3×D4—61no—
172C2×C3×D4—62no—
173C2×C3×D4—62no—
174C2×C3×D4—124no—
175C22×C3×C4—24no—
176C22×C3×C4—24no—
177C22×C3×C4—22no—
178C22×C3×C4—22no—
179C22×C3×C4—22no—
180C22×C3×C4—22no—
181C22×C3×C4—21no—
182C22×C3×C4—22no—
183C22×C3×C4—21no—
184C22×C3×C4—22no—
185C22×C3×C4—61no—
186C22×C3×C4D1211yescharacteristic
187C22×C3×C4D1212yes—
188C22×C3×C4#6711yescharacteristic
189C22×C3×C4#6712yes—
190C22×C3×C4C22×D312yes—
191C22×C3×C4C22×D312yes—
192C22×C3×C4C22×D311yescharacteristic
193C22×C3×C4C22×D311yescharacteristic
194C2×#67—24no—
195C2×#67—44no—
196C22×Dic3—21no—
197C22×Dic3—62no—
198C22×Dic3—62no—
199C22×Dic3—61no—
200C22×Dic3—61no—
201C22×Dic3—61no—
202C22×Dic3—61no—
203C2×D12—22no—
204C2×D12—22no—
205C2×D12—21no—
206C2×D12C22×D312yes—
207C2×C3×C8—32no—
208C2×C3×C8—32no—
209C2×C3×C8—62no—
210C2×C3×C8—62no—
211C3×C4⋊C4—32no—
212C3×C4⋊C4—61no—
213C3×C22⋊C4—64no—
214#217—68no—
215#217—64no—
216#217—64no—
217(C2×D3)⋊C4—24no—
218C4⋊Dic3—21no—
219C4⋊Dic3—32no—
220C4⋊Dic3—32no—
221C4⋊Dic3—32no—
222C4⋊Dic3—32no—
223C4⋊Dic3—62no—
224C4⋊Dic3—62no—
225C4⋊Dic3—62no—
226C4⋊Dic3—62no—
227C4⋊Dic3—61no—
228C4⋊Dic3—61no—
229C4⋊Dic3—61no—
230C4⋊Dic3—61no—
231C4⋊Dic3C22×D312yes—
232C4×Dic3—68no—
233C4×Dic3—64no—
234C4×Dic3—64no—
235C2×C3⋊C8—22no—
236C2×C3⋊C8—22no—
237C2×C3⋊C8C22×D312yes—
238C2×C3⋊C8C22×D312yes—
239C22×C32—22no—
240C22×C32—22no—
241C22×C32—22no—
242C22×C32—44no—
243C22×C32#12312yes—
244C22×C32#13512yes—
245C22×C32AGL(1,ℤ/8)12yes—
246C22×C32C22×D411yescharacteristic
247C2×C3×D3—42no—
248C2×C3×D3—42no—
249C2×C3×D3—42no—
250C2×C3×D3—84no—
251C32×C4—22no—
252C32×C4#12312yes—
253C32×C4C2×#4111yescharacteristic
254C32×C4C2×#4111yescharacteristic
255C3⋊Dic3—42no—
256C3⋊Dic3—42no—
257C3×Dic3—42no—
258C22×D4—31no—
259C22×D4—61no—
260C23×C4D3211yescharacteristic
261C22×C8—31no—
262C22×C8—31no—
263#121—34no—
264#121—62no—
265#117—94no—
266#117—182no—
267C2×C4⋊C4—31no—
268C2×C4⋊C4—91no—
269C2×C4⋊C4—91no—
270C2×C22⋊C4—61no—
271C2×C22⋊C4—181no—
272C2×C42—181no—
273#107—94no—
274#106—94no—
275#102—94no—
276#102—94no—
277C22⋊C8—34no—
278C23×C3—24no—
279C23×C3—22no—
280C23×C3—22no—
281C23×C3—22no—
282C23×C3—22no—
283C23×C3—22no—
284C23×C3—22no—
285C23×C3—22no—
286C23×C3—21no—
287C23×C3—42no—
288C23×C3—42no—
289C23×C3—62no—
290C23×C3—122no—
291C23×C3—122no—
292C23×C3—122no—
293C23×C3C2×D1212yes—
294C23×C3C2×D1211yescharacteristic
295C23×C3C2×#6712yes—
296C23×C3C2×#6711yescharacteristic
297C22×D3—22no—
298C22×D3—42no—
299C22×D3—42no—
300C22×D3—42no—
301C3×D4—62no—
302C3×D4—62no—
303C3×D4—128no—
304C3×D4—122no—
305C2×C3×C4—24no—
306C2×C3×C4—24no—
307C2×C3×C4—24no—
308C2×C3×C4—28no—
309C2×C3×C4—22no—
310C2×C3×C4—22no—
311C2×C3×C4—24no—
312C2×C3×C4—24no—
313C2×C3×C4—22no—
314C2×C3×C4—22no—
315C2×C3×C4—22no—
316C2×C3×C4—22no—
317C2×C3×C4—21no—
318C2×C3×C4—22no—
319C2×C3×C4—22no—
320C2×C3×C4—22no—
321C2×C3×C4—21no—
322C2×C3×C4—62no—
323C2×C3×C4—122no—
324C2×C3×C4C2×D1212yes—
325C2×C3×C4C2×D1211yescharacteristic
326C2×C3×C4#23712yes—
327C2×C3×C4#23712yes—
328C2×C3×C4#23712yes—
329C2×C3×C4#23712yes—
330C2×C3×C4C2×#6712yes—
331C2×C3×C4C2×#6711yescharacteristic
332C2×C3×C4C23×D311yescharacteristic
333C2×C3×C4C23×D311yescharacteristic
334#67—48no—
335C2×Dic3—22no—
336C2×Dic3—42no—
337C2×Dic3—64no—
338C2×Dic3—64no—
339C2×Dic3—62no—
340C2×Dic3—62no—
341C2×Dic3—62no—
342C2×Dic3—62no—
343C2×Dic3—124no—
344C2×Dic3—124no—
345C2×Dic3—122no—
346C2×Dic3—122no—
347C2×Dic3—122no—
348C2×Dic3—122no—
349D12—22no—
350D12—22no—
351D12—42no—
352C3×C8—62no—
353C3×C8—62no—
354C3⋊C8—22no—
355C3⋊C8—22no—
356C2×C32—42no—
357C2×C32#48214yescomplemented
358C2×C32C2×#12311yescharacteristic
359C2×C32C2×#13511yescharacteristic
360C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
361C3×D3—82no—
362C24—61no—
363C24#62611yescharacteristic
364C2×D4—32no—
365C2×D4—64no—
366C2×D4—62no—
367C2×D4—62no—
368C2×D4—61no—
369C2×D4—124no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—61no—
373C22×C4—181no—
374C22×C4—181no—
375C22×C4#62612yes—
376C22×C4#62611yescharacteristic
377C22×C4C2×D3212yes—
378C22×C4C2×D3211yescharacteristic
379C2×C8—32no—
380C2×C8—32no—
381C2×C8—62no—
382C2×C8—62no—
383C4⋊C4—32no—
384C4⋊C4—61no—
385C4⋊C4—92no—
386C4⋊C4—92no—
387C4⋊C4—181no—
388C4⋊C4—181no—
389C22⋊C4—64no—
390C22⋊C4—184no—
391C42—184no—
392C22×C3—24no—
393C22×C3—22no—
394C22×C3—22no—
395C22×C3—22no—
396C22×C3—22no—
397C22×C3—22no—
398C22×C3—22no—
399C22×C3—21no—
400C22×C3—22no—
401C22×C3—22no—
402C22×C3—22no—
403C22×C3—42no—
404C22×C3—42no—
405C22×C3—48no—
406C22×C3—44no—
407C22×C3—44no—
408C22×C3—122no—
409C22×C3—122no—
410C22×C3—122no—
411C22×C3—244no—
412C22×C3#88612yes—
413C22×C3#90412yes—
414C22×C3#90812yes—
415C22×C3#93212yes—
416C22×C3#93512yes—
417C22×C3#95012yes—
418C22×C3C22×D1211yescharacteristic
419C22×C3C22×#6711yescharacteristic
420C2×D3—42no—
421C2×D3—42no—
422C2×D3—42no—
423C2×D3—84no—
424C3×C4—24no—
425C3×C4—22no—
426C3×C4—22no—
427C3×C4—21no—
428C3×C4—21no—
429C3×C4—22no—
430C3×C4—122no—
431C3×C4#88612yes—
432C3×C4#93512yes—
433C3×C4C2×#23711yescharacteristic
434C3×C4C2×#23711yescharacteristic
435C3×C4C2×#23711yescharacteristic
436C3×C4C2×#23711yescharacteristic
437Dic3—42no—
438Dic3—124no—
439Dic3—124no—
440Dic3—122no—
441Dic3—122no—
442Dic3—122no—
443Dic3—122no—
444C32C2×#48211yescharacteristic, complemented, Sylow
445C23—22no—
446C23—22no—
447C23—22no—
448C23—62no—
449C23—122no—
450C23—122no—
451C23—122no—
452C23C2×#62612yes—
453C23C2×#62611yescharacteristic
454D4—62no—
455D4—62no—
456D4—128no—
457D4—122no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—24no—
462C2×C4—62no—
463C2×C4—122no—
464C2×C4—182no—
465C2×C4—182no—
466C2×C4—362no—
467C2×C4—362no—
468C2×C4#380512yes—
469C2×C4#380512yes—
470C2×C4C2×#62612yes—
471C2×C4C2×#62611yescharacteristic
472C2×C4C22×D3211yescharacteristic
473C8—62no—
474C8—62no—
475C2×C3—24no—
476C2×C3—21no—
477C2×C3—21no—
478C2×C3—21no—
479C2×C3—44no—
480C2×C3—42no—
481C2×C3—42no—
482C2×C3—242no—
483C2×C3#473714yescomplemented
484C2×C3#503514yescomplemented
485C2×C3C2×#88611yescharacteristic
486C2×C3C2×#90411yescharacteristic
487C2×C3C2×#90811yescharacteristic
488C2×C3C2×#93211yescharacteristic
489C2×C3C2×#93511yescharacteristic
490C2×C3C2×#95011yescharacteristic
491D3—82no—
492C22—22no—
493C22—22no—
494C22—22no—
495C22—44no—
496C22—122no—
497C22—122no—
498C22—122no—
499C22—244no—
500C22#6382912yes—
501C22#6383012yes—
502C22#6396212yes—
503C22C22×#62611yescharacteristic
504C4—22no—
505C4—122no—
506C4—362no—
507C4—362no—
508C4#6396212yes—
509C4C2×#380511yescharacteristic
510C4C2×#380511yescharacteristic
511C3—21no—
512C3C2×#473711yescharacteristic, complemented
513C3C2×#503511yescharacteristic, complemented
514C2—42no—
515C2—242no—
516C2#1059109314yesdirect product factor
517C2C2×#6382911yescharacteristic
518C2C2×#6383011yescharacteristic
519C2C2×#6396211yescharacteristic
subgroupG/H
centerC23C2×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC23×C32×C4C22
socleC23×C32C2×D4
prime radicalC2×C3×#930C2
hypercenterC23×C4D32
hypocenterC32C2×#482
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C2×#64135C2semidirect
3. C2×C3×#830C2semidirect
4. C2×#63575C2semidirect
5. C2×#63573C2semidirect
6. #10591093C2direct (N × H)
7. C2×#63563C2semidirect
8. C2×#63563C2semidirect
16. #64135C22semidirect
26. C3×#830C22semidirect
27. #63575C22semidirect
28. #63573C22semidirect
29. #63563C22semidirect
30. #63563C22semidirect
39. C2×#830D3semidirect
119. #830C2×D3semidirect
357. C2×C32#482semidirect
444. C32C2×#482semidirect
483. C2×C3#4737semidirect
484. C2×C3#5035semidirect
512. C3C2×#4737semidirect
513. C3C2×#5035semidirect
516. C2#10591093direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641352
C2×C3×#9302
C2×C3×#8302
C2×#635752
C2×#635732
#105910932
C2×#635632
C2×#50353
C2×#47373