Finite Group Databasebeta

← C2×#10591127 #11869509

Subgroups — C2×#10591127 #11869509

Order 1152.

997 conjugacy classes of subgroups.

The subgroup lattice has 489 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64135C211yesmaximal, characteristic
2C2×C3×#924C211yesmaximal, characteristic
3C2×C3×#830C211yesmaximal, characteristic
4C2×#63575C211yesmaximal, characteristic, complemented
5#10591127C218yesmaximal, direct product factor
6C2×#63573C211yesmaximal, characteristic, complemented
7C2×#63566C211yesmaximal, characteristic, complemented
8C2×#63566C211yesmaximal, characteristic, complemented
9C2×#5045—31nomaximal
10C2×#4723—31nomaximal
11C23×C32×C4C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C2×#3757—21no—
14#64135—22no—
15#64135C2214yes—
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C2×C4×C3⋊Dic3—21no—
19C2×C3×#217—21no—
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C3×#924—22no—
22C3×#924C2214yes—
23C2×C3×Dic3⋊C4—21no—
24C22×C3×C3⋊C8C2211yescharacteristic
25C22×C3×C3⋊C8C2211yescharacteristic
26C3×#830C2214yes—
27#63575C2214yescomplemented
28#63573C2214yescomplemented
29#63566C2214yescomplemented
30#63566C2214yescomplemented
31C2×C3×C22⋊Q8—31no—
32C2×#926—31no—
33C2×#926—31no—
34C2×#926—61no—
35C2×#924D311yescharacteristic
36C2×C3×C22⋊C8—31no—
37C2×#835—31no—
38C2×#835—31no—
39C2×#830D311yescharacteristic
40C2×#818—31no—
41C2×#817—31no—
42C2×#816—31no—
43C2×#816—31no—
44#5045—38no—
45C2×#808—31no—
46C2×#807—31no—
47#4723—38no—
48C24×C32D411yescharacteristic
49C22×C32×C4—22no—
50C22×C32×C4—22no—
51C22×C32×C4D411yescharacteristic
52C22×C32×C4D412yes—
53C22×C32×C4C2312yes—
54C22×C32×C4C2311yescharacteristic
55C22×C3⋊Dic3—21no—
56C22×C3⋊Dic3—21no—
57C22×C3×Dic3—21no—
58C22×C3×Dic3—21no—
59C2×C3×Dic6—22no—
60C2×C3×Dic6—22no—
61C2×C3×Dic6—21no—
62C2×C3×Dic6C2312yes—
63#3757—24no—
64C4⋊(C3⋊Dic3)—21no—
65C4⋊(C3⋊Dic3)—21no—
66C4⋊(C3⋊Dic3)C2312yes—
67C4⋊(C3⋊Dic3)C2312yes—
68C4×C3⋊Dic3—24no—
69C3×#217—24no—
70C3×C4⋊Dic3—21no—
71C3×C4⋊Dic3C2312yes—
72C3×Dic3⋊C4—24no—
73C2×C3×C3⋊C8—22no—
74C2×C3×C3⋊C8—22no—
75C2×C3×C3⋊C8C2312yes—
76C2×C3×C3⋊C8C2312yes—
77C2×#485—91noSylow
78C22×C3×Q8—31no—
79C23×C3×C4—21no—
80C23×C3×C4C2×D311yescharacteristic
81C23×C3×C4C2×D311yescharacteristic
82C22×Dic6C2×D311yescharacteristic
83C22×C3×C8—31no—
84C22×C3×C8—31no—
85C3×C22⋊Q8—34no—
86C3×C22⋊Q8—62no—
87C2×C3×C4⋊C4—31no—
88C2×C3×C4⋊C4—61no—
89C2×C3×C22⋊C4—61no—
90C2×#217—21no—
91C2×#217—62no—
92C2×#217—61no—
93C2×#217—61no—
94#926—34no—
95#926—34no—
96#926—64no—
97#926—64no—
98#926—62no—
99#926—62no—
100C2×C4⋊Dic3—31no—
101C2×C4⋊Dic3—31no—
102C2×C4⋊Dic3—31no—
103C2×C4⋊Dic3—31no—
104C2×C4⋊Dic3—61no—
105C2×C4⋊Dic3—61no—
106C2×C4⋊Dic3C2×D311yescharacteristic
107#924—22no—
108#924C2×D314yes—
109C2×Dic3⋊C4—21no—
110C2×C4×Dic3—62no—
111C2×C4×Dic3—61no—
112C2×C4×Dic3—61no—
113C22×C3⋊C8C2×D311yescharacteristic
114C22×C3⋊C8C2×D311yescharacteristic
115C3×C22⋊C8—34no—
116#835—34no—
117#835—34no—
118#830C2×D314yes—
119#818—34no—
120#817—34no—
121#816—34no—
122#816—34no—
123#808—34no—
124#807—34no—
125C23×C32—22no—
126C23×C32—22no—
127C23×C32—22no—
128C23×C32C2×D412yes—
129C23×C32C2×D411yescharacteristic
130C2×C32×C4—22no—
131C2×C32×C4—24no—
132C2×C32×C4—22no—
133C2×C32×C4—22no—
134C2×C32×C4C2×D412yes—
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4#4112yes—
137C2×C32×C4#4112yes—
138C2×C32×C4C2411yescharacteristic
139C2×C3⋊Dic3—22no—
140C2×C3⋊Dic3—22no—
141C2×C3⋊Dic3—42no—
142C2×C3⋊Dic3—42no—
143C2×C3×Dic3—22no—
144C2×C3×Dic3—22no—
145C2×C3×Dic3—42no—
146C2×C3×Dic3—42no—
147C3×Dic6—22no—
148C3×Dic6—22no—
149C3×Dic6—42no—
150C3×C3⋊C8—22no—
151C3×C3⋊C8—22no—
152C2×C22⋊Q8—31no—
153C2×#117—91no—
154#485—98no—
155C2×#107—91no—
156C2×#106—91no—
157C2×#103—91no—
158C2×#103—91no—
159C2×C22⋊C8—31no—
160C24×C3—21no—
161C24×C3D1211yescharacteristic
162C24×C3#6711yescharacteristic
163C2×C3×Q8—32no—
164C2×C3×Q8—61no—
165C2×C3×Q8—62no—
166C2×C3×Q8—62no—
167C22×C3×C4—24no—
168C22×C3×C4—24no—
169C22×C3×C4—22no—
170C22×C3×C4—22no—
171C22×C3×C4—22no—
172C22×C3×C4—22no—
173C22×C3×C4—21no—
174C22×C3×C4—22no—
175C22×C3×C4—21no—
176C22×C3×C4—22no—
177C22×C3×C4—61no—
178C22×C3×C4—61no—
179C22×C3×C4D1211yescharacteristic
180C22×C3×C4D1212yes—
181C22×C3×C4#6711yescharacteristic
182C22×C3×C4#6712yes—
183C22×C3×C4C22×D312yes—
184C22×C3×C4C22×D312yes—
185C22×C3×C4C22×D311yescharacteristic
186C22×C3×C4C22×D311yescharacteristic
187C22×Dic3—21no—
188C22×Dic3—21no—
189C22×Dic3—62no—
190C22×Dic3—62no—
191C22×Dic3—61no—
192C22×Dic3—61no—
193C22×Dic3—61no—
194C22×Dic3—61no—
195C2×Dic6—22no—
196C2×Dic6—22no—
197C2×Dic6—21no—
198C2×Dic6C22×D312yes—
199C2×C3×C8—32no—
200C2×C3×C8—32no—
201C2×C3×C8—62no—
202C2×C3×C8—62no—
203C3×C4⋊C4—32no—
204C3×C4⋊C4—64no—
205C3×C4⋊C4—61no—
206C3×C22⋊C4—64no—
207#217—24no—
208#217—68no—
209#217—64no—
210#217—64no—
211C4⋊Dic3—21no—
212C4⋊Dic3—32no—
213C4⋊Dic3—32no—
214C4⋊Dic3—32no—
215C4⋊Dic3—32no—
216C4⋊Dic3—62no—
217C4⋊Dic3—62no—
218C4⋊Dic3—62no—
219C4⋊Dic3—62no—
220C4⋊Dic3—61no—
221C4⋊Dic3—61no—
222C4⋊Dic3—61no—
223C4⋊Dic3—61no—
224C4⋊Dic3C22×D312yes—
225Dic3⋊C4—24no—
226C4×Dic3—68no—
227C4×Dic3—64no—
228C4×Dic3—64no—
229C2×C3⋊C8—22no—
230C2×C3⋊C8—22no—
231C2×C3⋊C8C22×D312yes—
232C2×C3⋊C8C22×D312yes—
233C22×C32—22no—
234C22×C32—22no—
235C22×C32—22no—
236C22×C32—44no—
237C22×C32#12312yes—
238C22×C32#13512yes—
239C22×C32#13712yes—
240C22×C32C22×D411yescharacteristic
241C32×C4—22no—
242C32×C4#12312yes—
243C32×C4C2×#4111yescharacteristic
244C32×C4C2×#4111yescharacteristic
245C3⋊Dic3—42no—
246C3⋊Dic3—42no—
247C3×Dic3—42no—
248C3×Dic3—42no—
249C22×Q8—31no—
250C23×C4D3211yescharacteristic
251C22×C8—31no—
252C22×C8—31no—
253C22⋊Q8—34no—
254C22⋊Q8—62no—
255#117—94no—
256#117—182no—
257C2×C4⋊C4—31no—
258C2×C4⋊C4—61no—
259C2×C4⋊C4—91no—
260C2×C4⋊C4—91no—
261C2×C22⋊C4—61no—
262C2×C22⋊C4—181no—
263C2×C42—181no—
264#107—94no—
265#106—94no—
266#103—94no—
267#103—94no—
268C22⋊C8—34no—
269C23×C3—24no—
270C23×C3—22no—
271C23×C3—22no—
272C23×C3—22no—
273C23×C3—22no—
274C23×C3—22no—
275C23×C3—22no—
276C23×C3—22no—
277C23×C3—21no—
278C23×C3—42no—
279C23×C3—42no—
280C23×C3C2×D1212yes—
281C23×C3C2×D1211yescharacteristic
282C23×C3C2×#6712yes—
283C23×C3C2×#6711yescharacteristic
284C3×Q8—62no—
285C3×Q8—62no—
286C3×Q8—122no—
287C2×C3×C4—24no—
288C2×C3×C4—24no—
289C2×C3×C4—24no—
290C2×C3×C4—28no—
291C2×C3×C4—22no—
292C2×C3×C4—22no—
293C2×C3×C4—24no—
294C2×C3×C4—24no—
295C2×C3×C4—22no—
296C2×C3×C4—22no—
297C2×C3×C4—22no—
298C2×C3×C4—22no—
299C2×C3×C4—21no—
300C2×C3×C4—22no—
301C2×C3×C4—22no—
302C2×C3×C4—22no—
303C2×C3×C4—21no—
304C2×C3×C4—62no—
305C2×C3×C4—62no—
306C2×C3×C4—122no—
307C2×C3×C4—122no—
308C2×C3×C4C2×D1212yes—
309C2×C3×C4C2×D1211yescharacteristic
310C2×C3×C4#23712yes—
311C2×C3×C4#23712yes—
312C2×C3×C4#23712yes—
313C2×C3×C4#23712yes—
314C2×C3×C4C2×#6712yes—
315C2×C3×C4C2×#6711yescharacteristic
316C2×C3×C4C23×D311yescharacteristic
317C2×C3×C4C23×D311yescharacteristic
318C2×Dic3—22no—
319C2×Dic3—22no—
320C2×Dic3—42no—
321C2×Dic3—42no—
322C2×Dic3—64no—
323C2×Dic3—64no—
324C2×Dic3—62no—
325C2×Dic3—62no—
326C2×Dic3—62no—
327C2×Dic3—62no—
328C2×Dic3—124no—
329C2×Dic3—124no—
330C2×Dic3—122no—
331C2×Dic3—122no—
332C2×Dic3—122no—
333C2×Dic3—122no—
334Dic6—22no—
335Dic6—22no—
336Dic6—42no—
337C3×C8—62no—
338C3×C8—62no—
339C3⋊C8—22no—
340C3⋊C8—22no—
341C2×C32—42no—
342C2×C32#48514yescomplemented
343C2×C32C2×#12311yescharacteristic
344C2×C32C2×#13511yescharacteristic
345C2×C32C2×#13711yescharacteristic
346C24#62611yescharacteristic
347C2×Q8—32no—
348C2×Q8—61no—
349C2×Q8—62no—
350C2×Q8—62no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—61no—
354C22×C4—61no—
355C22×C4—181no—
356C22×C4—181no—
357C22×C4#62612yes—
358C22×C4#62611yescharacteristic
359C22×C4C2×D3212yes—
360C22×C4C2×D3211yescharacteristic
361C2×C8—32no—
362C2×C8—32no—
363C2×C8—62no—
364C2×C8—62no—
365C4⋊C4—32no—
366C4⋊C4—61no—
367C4⋊C4—64no—
368C4⋊C4—92no—
369C4⋊C4—92no—
370C4⋊C4—181no—
371C4⋊C4—181no—
372C22⋊C4—64no—
373C22⋊C4—184no—
374C42—184no—
375C22×C3—24no—
376C22×C3—22no—
377C22×C3—22no—
378C22×C3—22no—
379C22×C3—22no—
380C22×C3—22no—
381C22×C3—22no—
382C22×C3—21no—
383C22×C3—22no—
384C22×C3—22no—
385C22×C3—22no—
386C22×C3—42no—
387C22×C3—42no—
388C22×C3—48no—
389C22×C3—44no—
390C22×C3—44no—
391C22×C3#88612yes—
392C22×C3#90412yes—
393C22×C3#90912yes—
394C22×C3#93512yes—
395C22×C3#94212yes—
396C22×C3#95012yes—
397C22×C3C22×D1211yescharacteristic
398C22×C3C22×#6711yescharacteristic
399C3×C4—24no—
400C3×C4—22no—
401C3×C4—22no—
402C3×C4—21no—
403C3×C4—21no—
404C3×C4—22no—
405C3×C4—122no—
406C3×C4—122no—
407C3×C4#88612yes—
408C3×C4#93512yes—
409C3×C4C2×#23711yescharacteristic
410C3×C4C2×#23711yescharacteristic
411C3×C4C2×#23711yescharacteristic
412C3×C4C2×#23711yescharacteristic
413Dic3—42no—
414Dic3—42no—
415Dic3—124no—
416Dic3—124no—
417Dic3—122no—
418Dic3—122no—
419Dic3—122no—
420Dic3—122no—
421C32C2×#48511yescharacteristic, complemented, Sylow
422C23—22no—
423C23—22no—
424C23—22no—
425C23C2×#62612yes—
426C23C2×#62611yescharacteristic
427Q8—62no—
428Q8—62no—
429Q8—122no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—24no—
434C2×C4—62no—
435C2×C4—62no—
436C2×C4—122no—
437C2×C4—122no—
438C2×C4—182no—
439C2×C4—182no—
440C2×C4—362no—
441C2×C4—362no—
442C2×C4#380512yes—
443C2×C4#380512yes—
444C2×C4C2×#62612yes—
445C2×C4C2×#62611yescharacteristic
446C2×C4C22×D3211yescharacteristic
447C8—62no—
448C8—62no—
449C2×C3—24no—
450C2×C3—21no—
451C2×C3—21no—
452C2×C3—21no—
453C2×C3—44no—
454C2×C3—42no—
455C2×C3—42no—
456C2×C3#472314yescomplemented
457C2×C3#504514yescomplemented
458C2×C3C2×#88611yescharacteristic
459C2×C3C2×#90411yescharacteristic
460C2×C3C2×#90911yescharacteristic
461C2×C3C2×#93511yescharacteristic
462C2×C3C2×#94211yescharacteristic
463C2×C3C2×#95011yescharacteristic
464C22—22no—
465C22—22no—
466C22—22no—
467C22—44no—
468C22#6382912yes—
469C22#6383312yes—
470C22#6396212yes—
471C22C22×#62611yescharacteristic
472C4—22no—
473C4—122no—
474C4—122no—
475C4—362no—
476C4—362no—
477C4#6396212yes—
478C4C2×#380511yescharacteristic
479C4C2×#380511yescharacteristic
480C3—21no—
481C3C2×#472311yescharacteristic, complemented
482C3C2×#504511yescharacteristic, complemented
483C2—42no—
484C2#1059112714yesdirect product factor
485C2C2×#6382911yescharacteristic
486C2C2×#6383311yescharacteristic
487C2C2×#6396211yescharacteristic
subgroupG/H
centerC23C2×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC23×C32×C4C22
socleC23×C32C2×D4
prime radicalC24×C32D4
hypercenterC23×C4D32
hypocenterC32C2×#485
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
4. C2×#63575C2semidirect
5. #10591127C2direct (N × H)
6. C2×#63573C2semidirect
7. C2×#63566C2semidirect
8. C2×#63566C2semidirect
27. #63575C22semidirect
28. #63573C22semidirect
29. #63566C22semidirect
30. #63566C22semidirect
342. C2×C32#485semidirect
421. C32C2×#485semidirect
456. C2×C3#4723semidirect
457. C2×C3#5045semidirect
481. C3C2×#4723semidirect
482. C3C2×#5045semidirect
484. C2#10591127direct (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×#9242
C2×C3×#8302
C2×#635752
#105911272
C2×#635732
C2×#635662
C2×#50453
C2×#47233