Finite Group Databasebeta

← C2×#10591338 #11808196

Subgroups — C2×#10591338 #11808196

Order 1152.

1981 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#627C211yesmaximal, characteristic
2C22×C3×C4⋊Dic3C211yesmaximal, characteristic
3C22×#3724C211yesmaximal, characteristic
4C22×Dic3⋊Dic3C211yesmaximal, characteristic
5C2×#63658C211yesmaximal, characteristic
6C2×C3×C3⋊#95C211yesmaximal, characteristic
7C2×#63579C211yesmaximal, characteristic
8#10591338C218yesmaximal, direct product factor
9C2×#4979—31nomaximal
10C2×#4656—31nomaximal
11C23×C32×C4C2211yescharacteristic
12C23×C3⋊Dic3C2211yescharacteristic
13C23×C3⋊Dic3C2211yescharacteristic
14C23×C3×Dic3C2211yescharacteristic
15C23×C3×Dic3C2211yescharacteristic
16C23×C3×Dic3C2211yescharacteristic
17C23×C3×Dic3C2211yescharacteristic
18C22×#627—24no—
19C22×#627—24no—
20C22×#627—24no—
21C22×#627C2214yes—
22C2×C3×C4⋊Dic3—24no—
23C2×C3×C4⋊Dic3C2214yes—
24C2×#3724—24no—
25C2×#3724C2214yes—
26C2×Dic3⋊Dic3—24no—
27C2×Dic3⋊Dic3C2214yes—
28#63658C2214yes—
29C3×C3⋊#95C2214yes—
30#63579C2214yes—
31C23×Dic6—31no—
32C23×Dic6—31no—
33C22×C3×C4⋊C4—31no—
34C22×C4⋊Dic3—31no—
35C22×C4⋊Dic3D311yescharacteristic
36C22×Dic3⋊C4—31no—
37C22×Dic3⋊C4—31no—
38C22×Dic3⋊C4—31no—
39C2×C3×#95—31no—
40C2×C3⋊#95—31no—
41C2×C3⋊#95—31no—
42C2×C3⋊#95—31no—
43C2×C3⋊#95—31no—
44C2×C3⋊#95—61no—
45C2×C3⋊#95D311yescharacteristic
46#4979—38no—
47#4656—38no—
48C24×C32C2311yescharacteristic
49C22×C32×C4—22no—
50C22×C32×C4—22no—
51C22×C32×C4Q814yescomplemented
52C22×C32×C4C2312yes—
53C22×C3⋊Dic3—22no—
54C22×C3⋊Dic3—22no—
55C22×C3⋊Dic3—22no—
56C22×C3⋊Dic3—22no—
57C22×C3⋊Dic3D414yes—
58C22×C3⋊Dic3Q814yescomplemented
59C22×C3⋊Dic3C2312yes—
60C22×C3⋊Dic3C2312yes—
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×Dic3—22no—
70C22×C3×Dic3D414yes—
71C22×C3×Dic3D414yes—
72C22×C3×Dic3Q814yescomplemented
73C22×C3×Dic3C2312yes—
74C22×C3×Dic3C2312yes—
75C22×C3×Dic3C2312yes—
76C22×C3×Dic3C2312yes—
77C2×#627—232no—
78C2×#627—28no—
79C2×#627—28no—
80C2×#627—28no—
81C3×C4⋊Dic3—28no—
82#3724—28no—
83Dic3⋊Dic3—28no—
84C2×#395—91noSylow
85C23×C3×C4—21no—
86C23×C3×C4—31no—
87C23×C3×C4—31no—
88C23×C3×C4—31no—
89C23×C3×C4—31no—
90C23×C3×C4C2×D311yescharacteristic
91C23×C3×C4C2×D311yescharacteristic
92C23×Dic3—31no—
93C23×Dic3—31no—
94C23×Dic3—31no—
95C23×Dic3—31no—
96C23×Dic3—61no—
97C23×Dic3—61no—
98C23×Dic3C2×D311yescharacteristic
99C23×Dic3C2×D311yescharacteristic
100C23×Dic3C2×D311yescharacteristic
101C23×Dic3C2×D311yescharacteristic
102C22×Dic6—34no—
103C22×Dic6—34no—
104C22×Dic6—64no—
105C22×Dic6—64no—
106C22×Dic6—64no—
107C22×Dic6—64no—
108C22×Dic6—64no—
109C22×Dic6—64no—
110C2×C3×C4⋊C4—34no—
111C2×C3×C4⋊C4—64no—
112C2×C4⋊Dic3—24no—
113C2×C4⋊Dic3—34no—
114C2×C4⋊Dic3—64no—
115C2×C4⋊Dic3C2×D314yes—
116C2×Dic3⋊C4—34no—
117C2×Dic3⋊C4—34no—
118C2×Dic3⋊C4—34no—
119C2×Dic3⋊C4—64no—
120C2×Dic3⋊C4—64no—
121C2×Dic3⋊C4—64no—
122C3×#95—34no—
123C3⋊#95—34no—
124C3⋊#95—34no—
125C3⋊#95—34no—
126C3⋊#95—34no—
127C3⋊#95—64no—
128C3⋊#95C2×D314yes—
129C23×C32C2×D412yes—
130C23×C32C2×D412yes—
131C23×C32C2×D412yes—
132C23×C32C2×Q812yes—
133C23×C32C2×Q812yes—
134C23×C32C2×Q812yes—
135C23×C32#4112yes—
136C23×C32C2411yescharacteristic
137C2×C32×C4—28no—
138C2×C32×C4—22no—
139C2×C32×C4—22no—
140C2×C32×C4C2×Q814yescomplemented
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⋊Dic3C2×D414yes—
148C2×C3⋊Dic3C2×Q814yescomplemented
149C2×C3×Dic3—28no—
150C2×C3×Dic3—28no—
151C2×C3×Dic3—28no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3—22no—
154C2×C3×Dic3—22no—
155C2×C3×Dic3—22no—
156C2×C3×Dic3—22no—
157C2×C3×Dic3—22no—
158C2×C3×Dic3—22no—
159C2×C3×Dic3—22no—
160C2×C3×Dic3—22no—
161C2×C3×Dic3—44no—
162C2×C3×Dic3C2×D414yes—
163C2×C3×Dic3C2×D414yes—
164C2×C3×Dic3C2×Q814yescomplemented
165#627—232no—
166C23×Q8—91no—
167C22×C4⋊C4—31no—
168C22×C4⋊C4—91no—
169C22×C4⋊C4—91no—
170#395—98no—
171C2×#95—31no—
172C2×#95—91no—
173C2×#95—91no—
174C24×C3—21no—
175C24×C3C22×D311yescharacteristic
176C24×C3C22×D311yescharacteristic
177C22×C3×C4—22no—
178C22×C3×C4—22no—
179C22×C3×C4—22no—
180C22×C3×C4—22no—
181C22×C3×C4—24no—
182C22×C3×C4—22no—
183C22×C3×C4—34no—
184C22×C3×C4—34no—
185C22×C3×C4—34no—
186C22×C3×C4—32no—
187C22×C3×C4—32no—
188C22×C3×C4—32no—
189C22×C3×C4—32no—
190C22×C3×C4—42no—
191C22×C3×C4—42no—
192C22×C3×C4—62no—
193C22×C3×C4—62no—
194C22×C3×C4—62no—
195C22×C3×C4—62no—
196C22×C3×C4—62no—
197C22×C3×C4—62no—
198C22×C3×C4—62no—
199C22×C3×C4—62no—
200C22×C3×C4—62no—
201C22×C3×C4Dic614yescomplemented
202C22×C3×C4Dic614yescomplemented
203C22×C3×C4C22×D312yes—
204C22×C3×C4C22×D312yes—
205C22×Dic3—22no—
206C22×Dic3—22no—
207C22×Dic3—22no—
208C22×Dic3—22no—
209C22×Dic3—22no—
210C22×Dic3—22no—
211C22×Dic3—22no—
212C22×Dic3—22no—
213C22×Dic3—22no—
214C22×Dic3—34no—
215C22×Dic3—34no—
216C22×Dic3—34no—
217C22×Dic3—34no—
218C22×Dic3—32no—
219C22×Dic3—32no—
220C22×Dic3—32no—
221C22×Dic3—32no—
222C22×Dic3—62no—
223C22×Dic3—62no—
224C22×Dic3—64no—
225C22×Dic3—64no—
226C22×Dic3—62no—
227C22×Dic3—62no—
228C22×Dic3—62no—
229C22×Dic3—62no—
230C22×Dic3—62no—
231C22×Dic3—62no—
232C22×Dic3—62no—
233C22×Dic3—62no—
234C22×Dic3—122no—
235C22×Dic3—122no—
236C22×Dic3—122no—
237C22×Dic3—122no—
238C22×Dic3Dic614yescomplemented
239C22×Dic3D1214yes—
240C22×Dic3#6714yes—
241C22×Dic3C22×D312yes—
242C22×Dic3C22×D312yes—
243C22×Dic3C22×D312yes—
244C22×Dic3C22×D312yes—
245C2×Dic6—68no—
246C2×Dic6—68no—
247C2×Dic6—68no—
248C2×Dic6—68no—
249C2×Dic6—632no—
250C2×Dic6—632no—
251C2×Dic6—68no—
252C2×Dic6—68no—
253C3×C4⋊C4—68no—
254C4⋊Dic3—28no—
255C4⋊Dic3—68no—
256Dic3⋊C4—68no—
257Dic3⋊C4—68no—
258Dic3⋊C4—68no—
259C22×C32#12014yes—
260C22×C32C22⋊Q814yes—
261C22×C32C22⋊Q814yes—
262C22×C32C22⋊Q814yes—
263C22×C32C4⋊Q814yes—
264C22×C32C4⋊Q814yes—
265C22×C32C4⋊Q814yes—
266C22×C32C22×D411yescharacteristic
267C22×C32C22×D411yescharacteristic
268C22×C32C22×D411yescharacteristic
269C22×C32C22×Q811yescharacteristic
270C22×C32C22×Q811yescharacteristic
271C22×C32C22×Q811yescharacteristic
272C22×C32C2×#4111yescharacteristic
273C32×C4—24no—
274C3⋊Dic3—24no—
275C3⋊Dic3—24no—
276C3×Dic3—24no—
277C3×Dic3—24no—
278C3×Dic3—24no—
279C3×Dic3—42no—
280C22×Q8—94no—
281C22×Q8—184no—
282C22×Q8—184no—
283C22×Q8—184no—
284C23×C4—31no—
285C23×C4—31no—
286C23×C4—31no—
287C23×C4—31no—
288C23×C4—91no—
289C23×C4—91no—
290C23×C4D3211yescharacteristic
291C2×C4⋊C4—34no—
292C2×C4⋊C4—64no—
293C2×C4⋊C4—94no—
294C2×C4⋊C4—94no—
295C2×C4⋊C4—184no—
296C2×C4⋊C4—184no—
297#95—34no—
298#95—94no—
299#95—94no—
300C23×C3—21no—
301C23×C3—22no—
302C23×C3—22no—
303C23×C3—22no—
304C23×C3—22no—
305C23×C3—22no—
306C23×C3—22no—
307C23×C3—22no—
308C23×C3C2×Dic612yes—
309C23×C3C2×Dic612yes—
310C23×C3C2×Dic612yes—
311C23×C3C2×D1212yes—
312C23×C3#23512yes—
313C23×C3D3×D412yes—
314C23×C3D3×D412yes—
315C23×C3D3×D412yes—
316C23×C3D3×D412yes—
317C23×C3#23712yes—
318C23×C3D3×Q812yes—
319C23×C3D3×Q812yes—
320C23×C3D3×Q812yes—
321C23×C3C2×#6712yes—
322C23×C3C23×D311yescharacteristic
323C23×C3C23×D311yescharacteristic
324C2×C3×C4—28no—
325C2×C3×C4—28no—
326C2×C3×C4—22no—
327C2×C3×C4—22no—
328C2×C3×C4—22no—
329C2×C3×C4—22no—
330C2×C3×C4—24no—
331C2×C3×C4—34no—
332C2×C3×C4—34no—
333C2×C3×C4—34no—
334C2×C3×C4—42no—
335C2×C3×C4—42no—
336C2×C3×C4—48no—
337C2×C3×C4—68no—
338C2×C3×C4—68no—
339C2×C3×C4—68no—
340C2×C3×C4—62no—
341C2×C3×C4—62no—
342C2×C3×C4—62no—
343C2×C3×C4—62no—
344C2×C3×C4—62no—
345C2×C3×C4—62no—
346C2×C3×C4—62no—
347C2×C3×C4—62no—
348C2×C3×C4—62no—
349C2×C3×C4—124no—
350C2×C3×C4C2×Dic614yescomplemented
351C2×C3×C4C2×Dic614yescomplemented
352C2×Dic3—28no—
353C2×Dic3—28no—
354C2×Dic3—28no—
355C2×Dic3—22no—
356C2×Dic3—22no—
357C2×Dic3—22no—
358C2×Dic3—22no—
359C2×Dic3—22no—
360C2×Dic3—22no—
361C2×Dic3—22no—
362C2×Dic3—22no—
363C2×Dic3—22no—
364C2×Dic3—34no—
365C2×Dic3—34no—
366C2×Dic3—34no—
367C2×Dic3—34no—
368C2×Dic3—44no—
369C2×Dic3—64no—
370C2×Dic3—64no—
371C2×Dic3—68no—
372C2×Dic3—68no—
373C2×Dic3—68no—
374C2×Dic3—68no—
375C2×Dic3—62no—
376C2×Dic3—62no—
377C2×Dic3—62no—
378C2×Dic3—62no—
379C2×Dic3—62no—
380C2×Dic3—62no—
381C2×Dic3—62no—
382C2×Dic3—62no—
383C2×Dic3—122no—
384C2×Dic3—122no—
385C2×Dic3—122no—
386C2×Dic3—122no—
387C2×Dic3—128no—
388C2×Dic3—128no—
389C2×Dic3C2×Dic614yescomplemented
390C2×Dic3C2×D1214yes—
391C2×Dic3C2×#6714yes—
392Dic6—632no—
393Dic6—632no—
394C2×C32#39518yescomplemented
395C2×C32C2×#12011yescharacteristic
396C2×C32C2×C22⋊Q811yescharacteristic
397C2×C32C2×C22⋊Q811yescharacteristic
398C2×C32C2×C22⋊Q811yescharacteristic
399C2×C32C2×C4⋊Q811yescharacteristic
400C2×C32C2×C4⋊Q811yescharacteristic
401C2×C32C2×C4⋊Q811yescharacteristic
402C24C2×D3211yescharacteristic
403C2×Q8—188no—
404C2×Q8—188no—
405C2×Q8—188no—
406C2×Q8—1832no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—32no—
410C22×C4—32no—
411C22×C4—32no—
412C22×C4—34no—
413C22×C4—34no—
414C22×C4—34no—
415C22×C4—32no—
416C22×C4—62no—
417C22×C4—62no—
418C22×C4—62no—
419C22×C4—62no—
420C22×C4—62no—
421C22×C4—62no—
422C22×C4—62no—
423C22×C4—62no—
424C22×C4—62no—
425C22×C4—92no—
426C22×C4—92no—
427C22×C4—94no—
428C22×C4—94no—
429C22×C4—182no—
430C22×C4—182no—
431C22×C4—182no—
432C22×C4—182no—
433C22×C4#62714yescomplemented
434C22×C4C2×D3212yes—
435C4⋊C4—68no—
436C4⋊C4—188no—
437C4⋊C4—188no—
438C22×C3—21no—
439C22×C3—21no—
440C22×C3—21no—
441C22×C3—21no—
442C22×C3—21no—
443C22×C3—21no—
444C22×C3—21no—
445C22×C3—24no—
446C22×C3—24no—
447C22×C3—24no—
448C22×C3—24no—
449C22×C3—24no—
450C22×C3—24no—
451C22×C3—24no—
452C22×C3#86914yes—
453C22×C3#87814yes—
454C22×C3#87814yes—
455C22×C3#88214yes—
456C22×C3#88814yes—
457C22×C3#88814yes—
458C22×C3#88814yes—
459C22×C3#88814yes—
460C22×C3#89614yes—
461C22×C3#89614yes—
462C22×C3#89714yes—
463C22×C3#92414yes—
464C22×C3#93714yes—
465C22×C3#94414yes—
466C22×C3C22×Dic611yescharacteristic
467C22×C3C22×Dic611yescharacteristic
468C22×C3C22×Dic611yescharacteristic
469C22×C3C22×D1211yescharacteristic
470C22×C3C2×#23511yescharacteristic
471C22×C3C2×D3×D411yescharacteristic
472C22×C3C2×D3×D411yescharacteristic
473C22×C3C2×D3×D411yescharacteristic
474C22×C3C2×D3×D411yescharacteristic
475C22×C3C2×#23711yescharacteristic
476C22×C3C2×D3×Q811yescharacteristic
477C22×C3C2×D3×Q811yescharacteristic
478C22×C3C2×D3×Q811yescharacteristic
479C22×C3C22×#6711yescharacteristic
480C3×C4—24no—
481C3×C4—24no—
482C3×C4—44no—
483C3×C4—64no—
484C3×C4—64no—
485C3×C4—64no—
486C3×C4—122no—
487Dic3—24no—
488Dic3—24no—
489Dic3—24no—
490Dic3—42no—
491Dic3—64no—
492Dic3—64no—
493Dic3—64no—
494Dic3—64no—
495Dic3—124no—
496Dic3—124no—
497C32C2×#39511yescharacteristic, complemented, Sylow
498C23D3×Dic612yes—
499C23#379712yes—
500C23D3×D1212yes—
501C23#380212yes—
502C23#380412yes—
503C23C2×#62712yes—
504C23D3×#6712yes—
505C23C22×D3211yescharacteristic
506Q8—1832no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—28no—
510C2×C4—34no—
511C2×C4—34no—
512C2×C4—34no—
513C2×C4—62no—
514C2×C4—62no—
515C2×C4—62no—
516C2×C4—62no—
517C2×C4—62no—
518C2×C4—62no—
519C2×C4—68no—
520C2×C4—68no—
521C2×C4—68no—
522C2×C4—62no—
523C2×C4—62no—
524C2×C4—62no—
525C2×C4—94no—
526C2×C4—94no—
527C2×C4—124no—
528C2×C4—182no—
529C2×C4—182no—
530C2×C4—182no—
531C2×C4—182no—
532C2×C4—188no—
533C2×C4—188no—
534C2×C4C2×#62714yescomplemented
535C2×C3—21no—
536C2×C3—28no—
537C2×C3—21no—
538C2×C3—21no—
539C2×C3—21no—
540C2×C3—21no—
541C2×C3—21no—
542C2×C3—21no—
543C2×C3#465618yescomplemented
544C2×C3#497918yescomplemented
545C2×C3C2×#86911yescharacteristic
546C2×C3C2×#87811yescharacteristic
547C2×C3C2×#87811yescharacteristic
548C2×C3C2×#88211yescharacteristic
549C2×C3C2×#88811yescharacteristic
550C2×C3C2×#88811yescharacteristic
551C2×C3C2×#88811yescharacteristic
552C2×C3C2×#88811yescharacteristic
553C2×C3C2×#89611yescharacteristic
554C2×C3C2×#89611yescharacteristic
555C2×C3C2×#89711yescharacteristic
556C2×C3C2×#92411yescharacteristic
557C2×C3C2×#93711yescharacteristic
558C2×C3C2×#94411yescharacteristic
559C22#6383914yes—
560C22#6389514yes—
561C22#6389914yes—
562C22#6391814yes—
563C22#6391914yes—
564C22#6392214yes—
565C22#6396414yes—
566C22C2×D3×Dic611yescharacteristic
567C22C2×#379711yescharacteristic
568C22C2×D3×D1211yescharacteristic
569C22C2×#380211yescharacteristic
570C22C2×#380411yescharacteristic
571C22C22×#62711yescharacteristic
572C22C2×D3×#6711yescharacteristic
573C4—24no—
574C4—64no—
575C4—64no—
576C4—64no—
577C4—122no—
578C4—184no—
579C4—184no—
580C3—21no—
581C3C2×#465611yescharacteristic, complemented
582C3C2×#497911yescharacteristic, complemented
583C2#1059133818yesdirect product factor
584C2C2×#6383911yescharacteristic
585C2C2×#6389511yescharacteristic
586C2C2×#6389911yescharacteristic
587C2C2×#6391811yescharacteristic
588C2C2×#6391911yescharacteristic
589C2C2×#6392211yescharacteristic
590C2C2×#6396411yescharacteristic
subgroupG/H
centerC24C2×D32
commutator, cosocleC23×C32C24
FrattiniC23C22×D32
FittingC23×C32×C4C22
socle, prime radicalC24×C32C23
hypercenterC23×C4D32
hypocenterC32C2×#395
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
8. #10591338C2direct (N × H)
51. C22×C32×C4Q8semidirect
58. C22×C3⋊Dic3Q8semidirect
72. C22×C3×Dic3Q8semidirect
140. C2×C32×C4C2×Q8semidirect
148. C2×C3⋊Dic3C2×Q8semidirect
164. C2×C3×Dic3C2×Q8semidirect
201. C22×C3×C4Dic6semidirect
202. C22×C3×C4Dic6semidirect
238. C22×Dic3Dic6semidirect
350. C2×C3×C4C2×Dic6semidirect
351. C2×C3×C4C2×Dic6semidirect
389. C2×Dic3C2×Dic6semidirect
394. C2×C32#395semidirect
433. C22×C4#627semidirect
497. C32C2×#395semidirect
534. C2×C4C2×#627semidirect
543. C2×C3#4656semidirect
544. C2×C3#4979semidirect
581. C3C2×#4656semidirect
582. C3C2×#4979semidirect
583. C2#10591338direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#6272
C22×C3×C4⋊Dic32
C22×#37242
C22×Dic3⋊Dic32
C2×#636582
C2×C3×C3⋊#952
C2×#635792
#105913382
C2×#49793
C2×#46563