Finite Group Databasebeta

← C2×#10591251 #11801367

Subgroups — C2×#10591251 #11801367

Order 1152.

1633 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3750C211yesmaximal, characteristic
2C22×Dic3⋊Dic3C211yesmaximal, characteristic
3C22×Dic32C211yesmaximal, characteristic
4C2×C3×C3⋊#95C211yesmaximal, characteristic
5C2×C3×C3⋊#95C211yesmaximal, characteristic
6C2×#63579C211yesmaximal, characteristic
7C2×#63579C211yesmaximal, characteristic
8#10591251C218yesmaximal, direct product factor
9C2×#4654—31nomaximal
10C2×#4652—31nomaximal
11C23×C32×C4C2211yescharacteristic
12C23×C3⋊Dic3C2211yescharacteristic
13C23×C3⋊Dic3C2211yescharacteristic
14C23×C3×Dic3C2211yescharacteristic
15C23×C3×Dic3C2211yescharacteristic
16C23×C3×Dic3C2211yescharacteristic
17C23×C3×Dic3C2211yescharacteristic
18C2×#3750—24no—
19C2×#3750C2214yes—
20C2×Dic3⋊Dic3C418yescomplemented
21C2×Dic3⋊Dic3C2214yes—
22C2×Dic32—24no—
23C2×Dic32C2214yes—
24C3×C3⋊#95C2214yes—
25C3×C3⋊#95C2214yes—
26#63579C2214yes—
27#63579C2214yes—
28C22×C4⋊Dic3—31no—
29C22×Dic3⋊C4—31no—
30C22×Dic3⋊C4—31no—
31C22×Dic3⋊C4—31no—
32C22×Dic3⋊C4—61no—
33C22×C4×Dic3—31no—
34C22×C4×Dic3—31no—
35C2×C3×#95—31no—
36C2×C3×#95—31no—
37C2×C3⋊#95—31no—
38C2×C3⋊#95—31no—
39C2×C3⋊#95—31no—
40C2×C3⋊#95—31no—
41C2×C3⋊#95D311yescharacteristic
42C2×C3⋊#95D311yescharacteristic
43#4654—38no—
44#4652—38no—
45C24×C32C2311yescharacteristic
46C22×C32×C4—22no—
47C22×C32×C4—22no—
48C22×C32×C4—22no—
49C22×C32×C4C2312yes—
50C22×C3⋊Dic3—22no—
51C22×C3⋊Dic3—22no—
52C22×C3⋊Dic3—22no—
53C22×C3⋊Dic3—22no—
54C22×C3⋊Dic3C2×C414yes—
55C22×C3⋊Dic3D414yes—
56C22×C3⋊Dic3C2312yes—
57C22×C3⋊Dic3C2312yes—
58C22×C3×Dic3—22no—
59C22×C3×Dic3—22no—
60C22×C3×Dic3—22no—
61C22×C3×Dic3—22no—
62C22×C3×Dic3—22no—
63C22×C3×Dic3—22no—
64C22×C3×Dic3—22no—
65C22×C3×Dic3—22no—
66C22×C3×Dic3—22no—
67C22×C3×Dic3C2×C414yes—
68C22×C3×Dic3C2×C414yes—
69C22×C3×Dic3Q814yes—
70C22×C3×Dic3C2312yes—
71C22×C3×Dic3C2312yes—
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2312yes—
74#3750—28no—
75Dic3⋊Dic3C2×C4116yescomplemented
76Dic32—28no—
77C2×#387—91noSylow
78C23×C3×C4—21no—
79C23×C3×C4—31no—
80C23×C3×C4—31no—
81C23×C3×C4—31no—
82C23×C3×C4—31no—
83C23×C3×C4C2×D311yescharacteristic
84C23×C3×C4C2×D311yescharacteristic
85C23×Dic3—31no—
86C23×Dic3—31no—
87C23×Dic3—31no—
88C23×Dic3—31no—
89C23×Dic3—61no—
90C23×Dic3—61no—
91C23×Dic3C2×D311yescharacteristic
92C23×Dic3C2×D311yescharacteristic
93C23×Dic3C2×D311yescharacteristic
94C23×Dic3C2×D311yescharacteristic
95C2×C4⋊Dic3—38no—
96C2×C4⋊Dic3—34no—
97C2×Dic3⋊C4—38no—
98C2×Dic3⋊C4—34no—
99C2×Dic3⋊C4—34no—
100C2×Dic3⋊C4—34no—
101C2×Dic3⋊C4—64no—
102C2×Dic3⋊C4—64no—
103C2×Dic3⋊C4—64no—
104C2×Dic3⋊C4—68no—
105C2×C4×Dic3—34no—
106C2×C4×Dic3—34no—
107C2×C4×Dic3—64no—
108C2×C4×Dic3—64no—
109C3×#95—34no—
110C3×#95—34no—
111C3⋊#95—34no—
112C3⋊#95—34no—
113C3⋊#95—34no—
114C3⋊#95—34no—
115C3⋊#95C2×D314yes—
116C3⋊#95C2×D314yes—
117C23×C32C22×C412yes—
118C23×C32C2×D412yes—
119C23×C32C2×Q812yes—
120C23×C32#4112yes—
121C23×C32#4112yes—
122C23×C32#4112yes—
123C23×C32#4112yes—
124C23×C32C2411yescharacteristic
125C2×C32×C4—22no—
126C2×C32×C4—22no—
127C2×C32×C4—22no—
128C2×C32×C4—44no—
129C2×C3⋊Dic3—28no—
130C2×C3⋊Dic3—22no—
131C2×C3⋊Dic3—22no—
132C2×C3⋊Dic3—28no—
133C2×C3⋊Dic3—22no—
134C2×C3⋊Dic3—22no—
135C2×C3⋊Dic3C22×C414yes—
136C2×C3⋊Dic3C2×D414yes—
137C2×C3×Dic3—28no—
138C2×C3×Dic3—28no—
139C2×C3×Dic3—28no—
140C2×C3×Dic3—22no—
141C2×C3×Dic3—22no—
142C2×C3×Dic3—22no—
143C2×C3×Dic3—22no—
144C2×C3×Dic3—22no—
145C2×C3×Dic3—22no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—22no—
148C2×C3×Dic3—22no—
149C2×C3×Dic3—44no—
150C2×C3×Dic3C22×C414yes—
151C2×C3×Dic3C22×C414yes—
152C2×C3×Dic3C2×Q814yes—
153C22×C4⋊C4—91no—
154C22×C4⋊C4—91no—
155C22×C42—91no—
156#387—98no—
157C2×#95—31no—
158C2×#95—31no—
159C2×#95—91no—
160C2×#95—91no—
161C24×C3—21no—
162C24×C3C22×D311yescharacteristic
163C24×C3C22×D311yescharacteristic
164C22×C3×C4—24no—
165C22×C3×C4—22no—
166C22×C3×C4—22no—
167C22×C3×C4—22no—
168C22×C3×C4—22no—
169C22×C3×C4—22no—
170C22×C3×C4—22no—
171C22×C3×C4—22no—
172C22×C3×C4—34no—
173C22×C3×C4—34no—
174C22×C3×C4—34no—
175C22×C3×C4—32no—
176C22×C3×C4—32no—
177C22×C3×C4—32no—
178C22×C3×C4—32no—
179C22×C3×C4—42no—
180C22×C3×C4—42no—
181C22×C3×C4—62no—
182C22×C3×C4—62no—
183C22×C3×C4—62no—
184C22×C3×C4—62no—
185C22×C3×C4—62no—
186C22×C3×C4—62no—
187C22×C3×C4—62no—
188C22×C3×C4—62no—
189C22×C3×C4—62no—
190C22×C3×C4C22×D312yes—
191C22×C3×C4C22×D312yes—
192C22×Dic3—22no—
193C22×Dic3—22no—
194C22×Dic3—22no—
195C22×Dic3—22no—
196C22×Dic3—22no—
197C22×Dic3—22no—
198C22×Dic3—22no—
199C22×Dic3—22no—
200C22×Dic3—22no—
201C22×Dic3—34no—
202C22×Dic3—34no—
203C22×Dic3—34no—
204C22×Dic3—34no—
205C22×Dic3—32no—
206C22×Dic3—32no—
207C22×Dic3—32no—
208C22×Dic3—32no—
209C22×Dic3—62no—
210C22×Dic3—64no—
211C22×Dic3—64no—
212C22×Dic3—62no—
213C22×Dic3—64no—
214C22×Dic3—64no—
215C22×Dic3—62no—
216C22×Dic3—62no—
217C22×Dic3—62no—
218C22×Dic3—62no—
219C22×Dic3—62no—
220C22×Dic3—62no—
221C22×Dic3—62no—
222C22×Dic3—62no—
223C22×Dic3—122no—
224C22×Dic3—122no—
225C22×Dic3Dic614yes—
226C22×Dic3C4×D314yes—
227C22×Dic3C4×D314yes—
228C22×Dic3C22×D312yes—
229C22×Dic3C22×D312yes—
230C22×Dic3C22×D312yes—
231C22×Dic3C22×D312yes—
232C4⋊Dic3—316no—
233Dic3⋊C4—316no—
234Dic3⋊C4—68no—
235Dic3⋊C4—68no—
236Dic3⋊C4—616no—
237C4×Dic3—68no—
238C4×Dic3—68no—
239C22×C32#11714yes—
240C22×C32C4×D414yes—
241C22×C32C4×Q814yes—
242C22×C32C22⋊Q814yes—
243C22×C32#12314yes—
244C22×C32#12514yes—
245C22×C32#12614yes—
246C22×C32C23×C411yescharacteristic
247C22×C32C22×D411yescharacteristic
248C22×C32C22×Q811yescharacteristic
249C22×C32C2×#4111yescharacteristic
250C22×C32C2×#4111yescharacteristic
251C22×C32C2×#4111yescharacteristic
252C22×C32C2×#4111yescharacteristic
253C32×C4—42no—
254C3⋊Dic3—24no—
255C3⋊Dic3—24no—
256C3×Dic3—24no—
257C3×Dic3—24no—
258C3×Dic3—24no—
259C3×Dic3—42no—
260C23×C4—31no—
261C23×C4—31no—
262C23×C4—31no—
263C23×C4—31no—
264C23×C4—91no—
265C23×C4—91no—
266C23×C4D3211yescharacteristic
267C2×C4⋊C4—94no—
268C2×C4⋊C4—98no—
269C2×C4⋊C4—94no—
270C2×C4⋊C4—184no—
271C2×C42—94no—
272C2×C42—184no—
273#95—34no—
274#95—34no—
275#95—94no—
276#95—94no—
277C23×C3—21no—
278C23×C3—22no—
279C23×C3—22no—
280C23×C3—22no—
281C23×C3—22no—
282C23×C3—22no—
283C23×C3—22no—
284C23×C3—22no—
285C23×C3C2×Dic612yes—
286C23×C3C2×C4×D312yes—
287C23×C3C2×C4×D312yes—
288C23×C3#23512yes—
289C23×C3#23512yes—
290C23×C3#23512yes—
291C23×C3D3×D412yes—
292C23×C3D3×D412yes—
293C23×C3#23712yes—
294C23×C3#23712yes—
295C23×C3#23712yes—
296C23×C3#23712yes—
297C23×C3D3×Q812yes—
298C23×C3#23912yes—
299C23×C3C23×D311yescharacteristic
300C23×C3C23×D311yescharacteristic
301C2×C3×C4—24no—
302C2×C3×C4—22no—
303C2×C3×C4—22no—
304C2×C3×C4—22no—
305C2×C3×C4—22no—
306C2×C3×C4—22no—
307C2×C3×C4—22no—
308C2×C3×C4—34no—
309C2×C3×C4—34no—
310C2×C3×C4—34no—
311C2×C3×C4—42no—
312C2×C3×C4—42no—
313C2×C3×C4—48no—
314C2×C3×C4—44no—
315C2×C3×C4—44no—
316C2×C3×C4—68no—
317C2×C3×C4—68no—
318C2×C3×C4—68no—
319C2×C3×C4—62no—
320C2×C3×C4—62no—
321C2×C3×C4—62no—
322C2×C3×C4—62no—
323C2×C3×C4—62no—
324C2×C3×C4—62no—
325C2×C3×C4—62no—
326C2×C3×C4—62no—
327C2×C3×C4—62no—
328C2×C3×C4—124no—
329C2×Dic3—28no—
330C2×Dic3—28no—
331C2×Dic3—28no—
332C2×Dic3—22no—
333C2×Dic3—22no—
334C2×Dic3—22no—
335C2×Dic3—22no—
336C2×Dic3—22no—
337C2×Dic3—22no—
338C2×Dic3—22no—
339C2×Dic3—22no—
340C2×Dic3—22no—
341C2×Dic3—34no—
342C2×Dic3—34no—
343C2×Dic3—34no—
344C2×Dic3—34no—
345C2×Dic3—44no—
346C2×Dic3—64no—
347C2×Dic3—64no—
348C2×Dic3—64no—
349C2×Dic3—64no—
350C2×Dic3—616no—
351C2×Dic3—68no—
352C2×Dic3—68no—
353C2×Dic3—68no—
354C2×Dic3—68no—
355C2×Dic3—62no—
356C2×Dic3—62no—
357C2×Dic3—62no—
358C2×Dic3—62no—
359C2×Dic3—62no—
360C2×Dic3—62no—
361C2×Dic3—62no—
362C2×Dic3—62no—
363C2×Dic3—122no—
364C2×Dic3—122no—
365C2×Dic3—128no—
366C2×Dic3C2×Dic614yes—
367C2×Dic3C2×C4×D314yes—
368C2×Dic3C2×C4×D314yes—
369C2×C32#38718yescomplemented
370C2×C32C2×#11711yescharacteristic
371C2×C32C2×C4×D411yescharacteristic
372C2×C32C2×C4×Q811yescharacteristic
373C2×C32C2×C22⋊Q811yescharacteristic
374C2×C32C2×#12311yescharacteristic
375C2×C32C2×#12511yescharacteristic
376C2×C32C2×#12611yescharacteristic
377C24C2×D3211yescharacteristic
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—32no—
382C22×C4—32no—
383C22×C4—32no—
384C22×C4—34no—
385C22×C4—34no—
386C22×C4—34no—
387C22×C4—32no—
388C22×C4—62no—
389C22×C4—62no—
390C22×C4—62no—
391C22×C4—62no—
392C22×C4—62no—
393C22×C4—62no—
394C22×C4—62no—
395C22×C4—62no—
396C22×C4—62no—
397C22×C4—92no—
398C22×C4—92no—
399C22×C4—94no—
400C22×C4—94no—
401C22×C4—182no—
402C22×C4—182no—
403C22×C4—182no—
404C22×C4—182no—
405C22×C4C2×D3212yes—
406C4⋊C4—916no—
407C4⋊C4—188no—
408C42—188no—
409C22×C3—21no—
410C22×C3—21no—
411C22×C3—21no—
412C22×C3—21no—
413C22×C3—21no—
414C22×C3—21no—
415C22×C3—21no—
416C22×C3—24no—
417C22×C3—24no—
418C22×C3—24no—
419C22×C3—24no—
420C22×C3—24no—
421C22×C3—24no—
422C22×C3—24no—
423C22×C3C4×Dic614yes—
424C22×C3#87214yes—
425C22×C3#87714yes—
426C22×C3#87814yes—
427C22×C3#87914yes—
428C22×C3#67⋊C414yes—
429C22×C3#88314yes—
430C22×C3#88314yes—
431C22×C3#88714yes—
432C22×C3#88914yes—
433C22×C3#89014yes—
434C22×C3#89314yes—
435C22×C3#89614yes—
436C22×C3#89814yes—
437C22×C3C22×Dic611yescharacteristic
438C22×C3C22×C4×D311yescharacteristic
439C22×C3C22×C4×D311yescharacteristic
440C22×C3C2×#23511yescharacteristic
441C22×C3C2×#23511yescharacteristic
442C22×C3C2×#23511yescharacteristic
443C22×C3C2×D3×D411yescharacteristic
444C22×C3C2×D3×D411yescharacteristic
445C22×C3C2×#23711yescharacteristic
446C22×C3C2×#23711yescharacteristic
447C22×C3C2×#23711yescharacteristic
448C22×C3C2×#23711yescharacteristic
449C22×C3C2×D3×Q811yescharacteristic
450C22×C3C2×#23911yescharacteristic
451C3×C4—44no—
452C3×C4—42no—
453C3×C4—42no—
454C3×C4—64no—
455C3×C4—64no—
456C3×C4—64no—
457C3×C4—122no—
458Dic3—24no—
459Dic3—24no—
460Dic3—24no—
461Dic3—42no—
462Dic3—68no—
463Dic3—64no—
464Dic3—64no—
465Dic3—64no—
466Dic3—64no—
467Dic3—124no—
468C32C2×#38711yescharacteristic, complemented, Sylow
469C23D3×Dic612yes—
470C23#379512yes—
471C23#379612yes—
472C23C4×D3212yes—
473C23#380412yes—
474C23#380412yes—
475C23#381112yes—
476C23C22×D3211yescharacteristic
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—34no—
481C2×C4—34no—
482C2×C4—34no—
483C2×C4—44no—
484C2×C4—62no—
485C2×C4—62no—
486C2×C4—62no—
487C2×C4—62no—
488C2×C4—62no—
489C2×C4—62no—
490C2×C4—68no—
491C2×C4—68no—
492C2×C4—68no—
493C2×C4—62no—
494C2×C4—62no—
495C2×C4—62no—
496C2×C4—94no—
497C2×C4—94no—
498C2×C4—124no—
499C2×C4—182no—
500C2×C4—182no—
501C2×C4—182no—
502C2×C4—182no—
503C2×C4—188no—
504C2×C4—188no—
505C2×C3—21no—
506C2×C3—28no—
507C2×C3—21no—
508C2×C3—21no—
509C2×C3—21no—
510C2×C3—21no—
511C2×C3—21no—
512C2×C3—21no—
513C2×C3#465218yescomplemented
514C2×C3#465418yescomplemented
515C2×C3C2×C4×Dic611yescharacteristic
516C2×C3C2×#87211yescharacteristic
517C2×C3C2×#87711yescharacteristic
518C2×C3C2×#87811yescharacteristic
519C2×C3C2×#87911yescharacteristic
520C2×C3C2×#67⋊C411yescharacteristic
521C2×C3C2×#88311yescharacteristic
522C2×C3C2×#88311yescharacteristic
523C2×C3C2×#88711yescharacteristic
524C2×C3C2×#88911yescharacteristic
525C2×C3C2×#89011yescharacteristic
526C2×C3C2×#89311yescharacteristic
527C2×C3C2×#89611yescharacteristic
528C2×C3C2×#89811yescharacteristic
529C22#6383714yes—
530C22#6384614yes—
531C22#6385814yes—
532C22#6387714yes—
533C22#6388114yes—
534C22#6389614yes—
535C22#6397514yes—
536C22C2×D3×Dic611yescharacteristic
537C22C2×#379511yescharacteristic
538C22C2×#379611yescharacteristic
539C22C2×C4×D3211yescharacteristic
540C22C2×#380411yescharacteristic
541C22C2×#380411yescharacteristic
542C22C2×#381111yescharacteristic
543C4—42no—
544C4—64no—
545C4—64no—
546C4—64no—
547C4—122no—
548C4—184no—
549C4—184no—
550C3—21no—
551C3C2×#465211yescharacteristic, complemented
552C3C2×#465411yescharacteristic, complemented
553C2#1059125118yesdirect product factor
554C2C2×#6383711yescharacteristic
555C2C2×#6384611yescharacteristic
556C2C2×#6385811yescharacteristic
557C2C2×#6387711yescharacteristic
558C2C2×#6388111yescharacteristic
559C2C2×#6389611yescharacteristic
560C2C2×#6397511yescharacteristic
subgroupG/H
centerC24C2×D32
commutatorC22×C32C23×C4
FrattiniC23C22×D32
FittingC23×C32×C4C22
socle, prime radicalC24×C32C23
cosocleC23×C32C24
hypercenterC23×C4D32
hypocenterC32C2×#387
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
8. #10591251C2direct (N × H)
20. C2×Dic3⋊Dic3C4semidirect
75. Dic3⋊Dic3C2×C4semidirect
369. C2×C32#387semidirect
468. C32C2×#387semidirect
513. C2×C3#4652semidirect
514. C2×C3#4654semidirect
551. C3C2×#4652semidirect
552. C3C2×#4654semidirect
553. C2#10591251direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37502
C22×Dic3⋊Dic32
C22×Dic322
C2×C3×C3⋊#952
C2×#635792
#105912512
C2×#46543
C2×#46523