Finite Group Databasebeta

← C2×#10591198 #11808355

Subgroups — C2×#10591198 #11808355

Order 1152.

1593 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3750C211yesmaximal, characteristic
2C22×C3×Dic3⋊C4C211yesmaximal, characteristic
3C22×#3724C211yesmaximal, characteristic
4C22×Dic3⋊Dic3C211yesmaximal, characteristic
5C2×C3×C3⋊#95C211yesmaximal, characteristic
6C2×#63579C211yesmaximal, characteristic
7C2×#63579C211yesmaximal, characteristic
8#10591198C218yesmaximal, direct product factor
9C2×#4983—31nomaximal
10C2×#4657—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×C3×Dic3⋊C4—24no—
21C2×C3×Dic3⋊C4C2214yes—
22C2×#3724—24no—
23C2×#3724C2214yes—
24C2×Dic3⋊Dic3—24no—
25C2×Dic3⋊Dic3C2214yes—
26C3×C3⋊#95C2214yes—
27#63579C2214yes—
28#63579C2214yes—
29C22×C3×C4⋊C4—31no—
30C22×C4⋊Dic3—31no—
31C22×Dic3⋊C4—31no—
32C22×Dic3⋊C4—31no—
33C22×Dic3⋊C4—31no—
34C22×Dic3⋊C4—31no—
35C22×Dic3⋊C4—31no—
36C22×Dic3⋊C4—61no—
37C22×Dic3⋊C4D311yescharacteristic
38C2×C3×#95—31no—
39C2×C3⋊#95—31no—
40C2×C3⋊#95—31no—
41C2×C3⋊#95—31no—
42C2×C3⋊#95—31no—
43C2×C3⋊#95D311yescharacteristic
44#4983—38no—
45#4657—38no—
46C24×C32C2311yescharacteristic
47C22×C32×C4—22no—
48C22×C32×C4—22no—
49C22×C32×C4—22no—
50C22×C32×C4C2312yes—
51C22×C3⋊Dic3—22no—
52C22×C3⋊Dic3—22no—
53C22×C3⋊Dic3—22no—
54C22×C3⋊Dic3—22no—
55C22×C3⋊Dic3D414yes—
56C22×C3⋊Dic3Q814yes—
57C22×C3⋊Dic3C2312yes—
58C22×C3⋊Dic3C2312yes—
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×Dic3—22no—
68C22×C3×Dic3—22no—
69C22×C3×Dic3D414yes—
70C22×C3×Dic3Q814yes—
71C22×C3×Dic3C2312yes—
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2312yes—
74C22×C3×Dic3C2312yes—
75#3750—28no—
76C3×Dic3⋊C4—28no—
77#3724—28no—
78Dic3⋊Dic3—28no—
79C2×#398—91noSylow
80C23×C3×C4—21no—
81C23×C3×C4—31no—
82C23×C3×C4—31no—
83C23×C3×C4—31no—
84C23×C3×C4—31no—
85C23×C3×C4C2×D311yescharacteristic
86C23×C3×C4C2×D311yescharacteristic
87C23×Dic3—31no—
88C23×Dic3—31no—
89C23×Dic3—31no—
90C23×Dic3—31no—
91C23×Dic3—61no—
92C23×Dic3—61no—
93C23×Dic3C2×D311yescharacteristic
94C23×Dic3C2×D311yescharacteristic
95C23×Dic3C2×D311yescharacteristic
96C23×Dic3C2×D311yescharacteristic
97C2×C3×C4⋊C4—34no—
98C2×C3×C4⋊C4—64no—
99C2×C4⋊Dic3—34no—
100C2×C4⋊Dic3—64no—
101C2×Dic3⋊C4—24no—
102C2×Dic3⋊C4—34no—
103C2×Dic3⋊C4—34no—
104C2×Dic3⋊C4—34no—
105C2×Dic3⋊C4—34no—
106C2×Dic3⋊C4—34no—
107C2×Dic3⋊C4—64no—
108C2×Dic3⋊C4—64no—
109C2×Dic3⋊C4—64no—
110C2×Dic3⋊C4—64no—
111C2×Dic3⋊C4—64no—
112C2×Dic3⋊C4—68no—
113C2×Dic3⋊C4—64no—
114C2×Dic3⋊C4C2×D314yes—
115C3×#95—34no—
116C3⋊#95—34no—
117C3⋊#95—34no—
118C3⋊#95—34no—
119C3⋊#95—34no—
120C3⋊#95C2×D314yes—
121C23×C32C2×D412yes—
122C23×C32C2×D412yes—
123C23×C32C2×Q812yes—
124C23×C32C2×Q812yes—
125C23×C32#4112yes—
126C23×C32#4112yes—
127C23×C32#4112yes—
128C23×C32C2411yescharacteristic
129C2×C32×C4—22no—
130C2×C32×C4—22no—
131C2×C32×C4—22no—
132C2×C32×C4—44no—
133C2×C3⋊Dic3—28no—
134C2×C3⋊Dic3—22no—
135C2×C3⋊Dic3—22no—
136C2×C3⋊Dic3—28no—
137C2×C3⋊Dic3—22no—
138C2×C3⋊Dic3—22no—
139C2×C3⋊Dic3C2×D414yes—
140C2×C3⋊Dic3C2×Q814yes—
141C2×C3×Dic3—28no—
142C2×C3×Dic3—28no—
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—22no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3—44no—
154C2×C3×Dic3—44no—
155C2×C3×Dic3C2×D414yes—
156C2×C3×Dic3C2×Q814yes—
157C22×C4⋊C4—31no—
158C22×C4⋊C4—91no—
159C22×C4⋊C4—91no—
160C22×C4⋊C4—91no—
161#398—98no—
162C2×#95—31no—
163C2×#95—91no—
164C2×#95—91no—
165C24×C3—21no—
166C24×C3C22×D311yescharacteristic
167C24×C3C22×D311yescharacteristic
168C22×C3×C4—24no—
169C22×C3×C4—22no—
170C22×C3×C4—22no—
171C22×C3×C4—22no—
172C22×C3×C4—22no—
173C22×C3×C4—22no—
174C22×C3×C4—22no—
175C22×C3×C4—22no—
176C22×C3×C4—34no—
177C22×C3×C4—34no—
178C22×C3×C4—32no—
179C22×C3×C4—32no—
180C22×C3×C4—32no—
181C22×C3×C4—32no—
182C22×C3×C4—42no—
183C22×C3×C4—42no—
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×C4—62no—
191C22×C3×C4—62no—
192C22×C3×C4—62no—
193C22×C3×C4—62no—
194C22×C3×C4C22×D312yes—
195C22×C3×C4C22×D312yes—
196C22×Dic3—22no—
197C22×Dic3—22no—
198C22×Dic3—22no—
199C22×Dic3—22no—
200C22×Dic3—22no—
201C22×Dic3—22no—
202C22×Dic3—22no—
203C22×Dic3—22no—
204C22×Dic3—22no—
205C22×Dic3—22no—
206C22×Dic3—34no—
207C22×Dic3—34no—
208C22×Dic3—34no—
209C22×Dic3—34no—
210C22×Dic3—32no—
211C22×Dic3—32no—
212C22×Dic3—32no—
213C22×Dic3—32no—
214C22×Dic3—62no—
215C22×Dic3—64no—
216C22×Dic3—64no—
217C22×Dic3—62no—
218C22×Dic3—64no—
219C22×Dic3—64no—
220C22×Dic3—62no—
221C22×Dic3—62no—
222C22×Dic3—62no—
223C22×Dic3—62no—
224C22×Dic3—62no—
225C22×Dic3—62no—
226C22×Dic3—62no—
227C22×Dic3—62no—
228C22×Dic3—122no—
229C22×Dic3—122no—
230C22×Dic3Dic614yes—
231C22×Dic3#6714yes—
232C22×Dic3C22×D312yes—
233C22×Dic3C22×D312yes—
234C22×Dic3C22×D312yes—
235C22×Dic3C22×D312yes—
236C3×C4⋊C4—68no—
237C4⋊Dic3—68no—
238Dic3⋊C4—28no—
239Dic3⋊C4—68no—
240Dic3⋊C4—68no—
241Dic3⋊C4—68no—
242Dic3⋊C4—68no—
243Dic3⋊C4—616no—
244Dic3⋊C4—68no—
245C22×C32#12114yes—
246C22×C32C22⋊Q814yes—
247C22×C32C22⋊Q814yes—
248C22×C32#12314yes—
249C22×C32#12514yes—
250C22×C32#12514yes—
251C22×C32C4⋊Q814yes—
252C22×C32C22×D411yescharacteristic
253C22×C32C22×D411yescharacteristic
254C22×C32C22×Q811yescharacteristic
255C22×C32C22×Q811yescharacteristic
256C22×C32C2×#4111yescharacteristic
257C22×C32C2×#4111yescharacteristic
258C22×C32C2×#4111yescharacteristic
259C32×C4—42no—
260C3⋊Dic3—24no—
261C3⋊Dic3—24no—
262C3×Dic3—24no—
263C3×Dic3—24no—
264C3×Dic3—42no—
265C3×Dic3—42no—
266C23×C4—31no—
267C23×C4—31no—
268C23×C4—31no—
269C23×C4—31no—
270C23×C4—91no—
271C23×C4—91no—
272C23×C4D3211yescharacteristic
273C2×C4⋊C4—34no—
274C2×C4⋊C4—64no—
275C2×C4⋊C4—94no—
276C2×C4⋊C4—94no—
277C2×C4⋊C4—94no—
278C2×C4⋊C4—184no—
279C2×C4⋊C4—184no—
280C2×C4⋊C4—184no—
281#95—34no—
282#95—94no—
283#95—94no—
284C23×C3—21no—
285C23×C3—22no—
286C23×C3—22no—
287C23×C3—22no—
288C23×C3—22no—
289C23×C3—22no—
290C23×C3—22no—
291C23×C3—22no—
292C23×C3C2×Dic612yes—
293C23×C3#23512yes—
294C23×C3#23512yes—
295C23×C3#23512yes—
296C23×C3#23512yes—
297C23×C3D3×D412yes—
298C23×C3D3×D412yes—
299C23×C3D3×D412yes—
300C23×C3#23712yes—
301C23×C3#23712yes—
302C23×C3D3×Q812yes—
303C23×C3D3×Q812yes—
304C23×C3D3×Q812yes—
305C23×C3C2×#6712yes—
306C23×C3C23×D311yescharacteristic
307C23×C3C23×D311yescharacteristic
308C2×C3×C4—24no—
309C2×C3×C4—22no—
310C2×C3×C4—22no—
311C2×C3×C4—22no—
312C2×C3×C4—22no—
313C2×C3×C4—22no—
314C2×C3×C4—22no—
315C2×C3×C4—34no—
316C2×C3×C4—34no—
317C2×C3×C4—42no—
318C2×C3×C4—42no—
319C2×C3×C4—48no—
320C2×C3×C4—44no—
321C2×C3×C4—44no—
322C2×C3×C4—68no—
323C2×C3×C4—68no—
324C2×C3×C4—62no—
325C2×C3×C4—62no—
326C2×C3×C4—62no—
327C2×C3×C4—62no—
328C2×C3×C4—62no—
329C2×C3×C4—62no—
330C2×C3×C4—62no—
331C2×C3×C4—62no—
332C2×C3×C4—62no—
333C2×C3×C4—62no—
334C2×C3×C4—124no—
335C2×C3×C4—124no—
336C2×Dic3—28no—
337C2×Dic3—28no—
338C2×Dic3—22no—
339C2×Dic3—22no—
340C2×Dic3—22no—
341C2×Dic3—22no—
342C2×Dic3—22no—
343C2×Dic3—22no—
344C2×Dic3—22no—
345C2×Dic3—22no—
346C2×Dic3—22no—
347C2×Dic3—22no—
348C2×Dic3—34no—
349C2×Dic3—34no—
350C2×Dic3—34no—
351C2×Dic3—34no—
352C2×Dic3—44no—
353C2×Dic3—44no—
354C2×Dic3—64no—
355C2×Dic3—64no—
356C2×Dic3—64no—
357C2×Dic3—64no—
358C2×Dic3—616no—
359C2×Dic3—68no—
360C2×Dic3—68no—
361C2×Dic3—68no—
362C2×Dic3—68no—
363C2×Dic3—62no—
364C2×Dic3—62no—
365C2×Dic3—62no—
366C2×Dic3—62no—
367C2×Dic3—62no—
368C2×Dic3—62no—
369C2×Dic3—62no—
370C2×Dic3—62no—
371C2×Dic3—122no—
372C2×Dic3—122no—
373C2×Dic3—128no—
374C2×Dic3C2×Dic614yes—
375C2×Dic3C2×#6714yes—
376C2×C32#39818yescomplemented
377C2×C32C2×#12111yescharacteristic
378C2×C32C2×C22⋊Q811yescharacteristic
379C2×C32C2×C22⋊Q811yescharacteristic
380C2×C32C2×#12311yescharacteristic
381C2×C32C2×#12511yescharacteristic
382C2×C32C2×#12511yescharacteristic
383C2×C32C2×C4⋊Q811yescharacteristic
384C24C2×D3211yescharacteristic
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—32no—
389C22×C4—32no—
390C22×C4—34no—
391C22×C4—34no—
392C22×C4—32no—
393C22×C4—32no—
394C22×C4—62no—
395C22×C4—62no—
396C22×C4—62no—
397C22×C4—62no—
398C22×C4—62no—
399C22×C4—62no—
400C22×C4—62no—
401C22×C4—62no—
402C22×C4—62no—
403C22×C4—62no—
404C22×C4—92no—
405C22×C4—92no—
406C22×C4—94no—
407C22×C4—94no—
408C22×C4—182no—
409C22×C4—182no—
410C22×C4—182no—
411C22×C4—182no—
412C22×C4C2×D3212yes—
413C4⋊C4—68no—
414C4⋊C4—188no—
415C4⋊C4—188no—
416C4⋊C4—188no—
417C22×C3—21no—
418C22×C3—21no—
419C22×C3—21no—
420C22×C3—21no—
421C22×C3—21no—
422C22×C3—21no—
423C22×C3—21no—
424C22×C3—24no—
425C22×C3—24no—
426C22×C3—24no—
427C22×C3—24no—
428C22×C3—24no—
429C22×C3—24no—
430C22×C3—24no—
431C22×C3#87014yes—
432C22×C3#87814yes—
433C22×C3#88314yes—
434C22×C3#88414yes—
435C22×C3#88814yes—
436C22×C3#88914yes—
437C22×C3#88914yes—
438C22×C3#88914yes—
439C22×C3#89614yes—
440C22×C3#89614yes—
441C22×C3#89614yes—
442C22×C3#92914yes—
443C22×C3#93814yes—
444C22×C3#94414yes—
445C22×C3C22×Dic611yescharacteristic
446C22×C3C2×#23511yescharacteristic
447C22×C3C2×#23511yescharacteristic
448C22×C3C2×#23511yescharacteristic
449C22×C3C2×#23511yescharacteristic
450C22×C3C2×D3×D411yescharacteristic
451C22×C3C2×D3×D411yescharacteristic
452C22×C3C2×D3×D411yescharacteristic
453C22×C3C2×#23711yescharacteristic
454C22×C3C2×#23711yescharacteristic
455C22×C3C2×D3×Q811yescharacteristic
456C22×C3C2×D3×Q811yescharacteristic
457C22×C3C2×D3×Q811yescharacteristic
458C22×C3C22×#6711yescharacteristic
459C3×C4—44no—
460C3×C4—42no—
461C3×C4—42no—
462C3×C4—64no—
463C3×C4—64no—
464C3×C4—122no—
465C3×C4—122no—
466Dic3—24no—
467Dic3—24no—
468Dic3—42no—
469Dic3—42no—
470Dic3—68no—
471Dic3—64no—
472Dic3—64no—
473Dic3—64no—
474Dic3—64no—
475Dic3—124no—
476C32C2×#39811yescharacteristic, complemented, Sylow
477C23D3×Dic612yes—
478C23#379512yes—
479C23#379712yes—
480C23#379812yes—
481C23#380412yes—
482C23D3×#6712yes—
483C23#381112yes—
484C23C22×D3211yescharacteristic
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—34no—
489C2×C4—34no—
490C2×C4—44no—
491C2×C4—62no—
492C2×C4—62no—
493C2×C4—62no—
494C2×C4—62no—
495C2×C4—68no—
496C2×C4—68no—
497C2×C4—62no—
498C2×C4—62no—
499C2×C4—62no—
500C2×C4—62no—
501C2×C4—62no—
502C2×C4—62no—
503C2×C4—94no—
504C2×C4—94no—
505C2×C4—124no—
506C2×C4—124no—
507C2×C4—182no—
508C2×C4—182no—
509C2×C4—182no—
510C2×C4—182no—
511C2×C4—188no—
512C2×C4—188no—
513C2×C3—21no—
514C2×C3—21no—
515C2×C3—21no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—28no—
520C2×C3—21no—
521C2×C3#465718yescomplemented
522C2×C3#498318yescomplemented
523C2×C3C2×#87011yescharacteristic
524C2×C3C2×#87811yescharacteristic
525C2×C3C2×#88311yescharacteristic
526C2×C3C2×#88411yescharacteristic
527C2×C3C2×#88811yescharacteristic
528C2×C3C2×#88911yescharacteristic
529C2×C3C2×#88911yescharacteristic
530C2×C3C2×#88911yescharacteristic
531C2×C3C2×#89611yescharacteristic
532C2×C3C2×#89611yescharacteristic
533C2×C3C2×#89611yescharacteristic
534C2×C3C2×#92911yescharacteristic
535C2×C3C2×#93811yescharacteristic
536C2×C3C2×#94411yescharacteristic
537C22#6383914yes—
538C22#6384714yes—
539C22#6386514yes—
540C22#6386714yes—
541C22#6389614yes—
542C22#6390514yes—
543C22#6395814yes—
544C22C2×D3×Dic611yescharacteristic
545C22C2×#379511yescharacteristic
546C22C2×#379711yescharacteristic
547C22C2×#379811yescharacteristic
548C22C2×#380411yescharacteristic
549C22C2×D3×#6711yescharacteristic
550C22C2×#381111yescharacteristic
551C4—42no—
552C4—64no—
553C4—64no—
554C4—122no—
555C4—122no—
556C4—184no—
557C4—184no—
558C3—21no—
559C3C2×#465711yescharacteristic, complemented
560C3C2×#498311yescharacteristic, complemented
561C2#1059119818yesdirect product factor
562C2C2×#6383911yescharacteristic
563C2C2×#6384711yescharacteristic
564C2C2×#6386511yescharacteristic
565C2C2×#6386711yescharacteristic
566C2C2×#6389611yescharacteristic
567C2C2×#6390511yescharacteristic
568C2C2×#6395811yescharacteristic
subgroupG/H
centerC24C2×D32
commutator, cosocleC23×C32C24
FrattiniC23C22×D32
FittingC23×C32×C4C22
socle, prime radicalC24×C32C23
hypercenterC23×C4D32
hypocenterC32C2×#398
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
8. #10591198C2direct (N × H)
376. C2×C32#398semidirect
476. C32C2×#398semidirect
521. C2×C3#4657semidirect
522. C2×C3#4983semidirect
559. C3C2×#4657semidirect
560. C3C2×#4983semidirect
561. C2#10591198direct (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×C3×Dic3⋊C42
C22×#37242
C22×Dic3⋊Dic32
C2×C3×C3⋊#952
C2×#635792
#105911982
C2×#49833
C2×#46573