Finite Group Databasebeta

← C2×#10591268 #11801591

Subgroups — C2×#10591268 #11801591

Order 1152.

1809 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic
2C22×C3×Dic3⋊C4C211yesmaximal, characteristic
3C22×Dic3⋊Dic3C211yesmaximal, characteristic
4C22×Dic3⋊Dic3C211yesmaximal, characteristic
5C22×Dic32C211yesmaximal, characteristic
6C2×C3×C3⋊#95C211yesmaximal, characteristic
7C2×#63579C211yesmaximal, characteristic
8#10591268C218yesmaximal, direct product factor
9C2×#4984—31nomaximal
10C2×#4647—31nomaximal
11C23×C32×C4C2211yescharacteristic
12C23×C3⋊Dic3C2211yescharacteristic
13C23×C3⋊Dic3C2211yescharacteristic
14C23×C3×Dic3C2211yescharacteristic
15C23×C3×Dic3C2211yescharacteristic
16C23×C3×Dic3C2211yescharacteristic
17C23×C3×Dic3C2211yescharacteristic
18C2×C4⋊(C3⋊Dic3)—24no—
19C2×C4⋊(C3⋊Dic3)C2214yes—
20C2×C3×Dic3⋊C4C418yescomplemented
21C2×C3×Dic3⋊C4C2214yes—
22C2×Dic3⋊Dic3—24no—
23C2×Dic3⋊Dic3—24no—
24C2×Dic3⋊Dic3C2214yes—
25C2×Dic3⋊Dic3C2214yes—
26C2×Dic32—24no—
27C2×Dic32C2214yes—
28C3×C3⋊#95C2214yes—
29#63579C2214yes—
30C22×C3×C4⋊C4—31no—
31C22×C4⋊Dic3—31no—
32C22×C4⋊Dic3—31no—
33C22×C4⋊Dic3—31no—
34C22×C4⋊Dic3—31no—
35C22×C4⋊Dic3—61no—
36C22×Dic3⋊C4—31no—
37C22×Dic3⋊C4—31no—
38C22×Dic3⋊C4D311yescharacteristic
39C22×C4×Dic3—31no—
40C22×C4×Dic3—31no—
41C2×C3×#95—31no—
42C2×C3⋊#95—31no—
43C2×C3⋊#95—31no—
44C2×C3⋊#95D311yescharacteristic
45#4984—38no—
46#4647—38no—
47C24×C32C2311yescharacteristic
48C22×C32×C4—22no—
49C22×C32×C4—22no—
50C22×C32×C4C2×C414yes—
51C22×C32×C4C2312yes—
52C22×C3⋊Dic3—22no—
53C22×C3⋊Dic3—22no—
54C22×C3⋊Dic3—22no—
55C22×C3⋊Dic3—22no—
56C22×C3⋊Dic3—22no—
57C22×C3⋊Dic3D414yes—
58C22×C3⋊Dic3C2312yes—
59C22×C3⋊Dic3C2312yes—
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×Dic3D414yes—
70C22×C3×Dic3Q814yes—
71C22×C3×Dic3Q814yes—
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2312yes—
74C22×C3×Dic3C2312yes—
75C22×C3×Dic3C2312yes—
76C4⋊(C3⋊Dic3)—28no—
77C3×Dic3⋊C4C2×C4116yescomplemented
78Dic3⋊Dic3—28no—
79Dic3⋊Dic3—28no—
80Dic32—28no—
81C2×#389—91noSylow
82C23×C3×C4—21no—
83C23×C3×C4—31no—
84C23×C3×C4—31no—
85C23×C3×C4—31no—
86C23×C3×C4—31no—
87C23×C3×C4C2×D311yescharacteristic
88C23×C3×C4C2×D311yescharacteristic
89C23×Dic3—31no—
90C23×Dic3—31no—
91C23×Dic3—31no—
92C23×Dic3—31no—
93C23×Dic3—61no—
94C23×Dic3—61no—
95C23×Dic3C2×D311yescharacteristic
96C23×Dic3C2×D311yescharacteristic
97C23×Dic3C2×D311yescharacteristic
98C23×Dic3C2×D311yescharacteristic
99C2×C3×C4⋊C4—38no—
100C2×C3×C4⋊C4—34no—
101C2×C4⋊Dic3—34no—
102C2×C4⋊Dic3—34no—
103C2×C4⋊Dic3—34no—
104C2×C4⋊Dic3—34no—
105C2×C4⋊Dic3—64no—
106C2×C4⋊Dic3—64no—
107C2×C4⋊Dic3—64no—
108C2×C4⋊Dic3—64no—
109C2×C4⋊Dic3—64no—
110C2×C4⋊Dic3—68no—
111C2×Dic3⋊C4—34no—
112C2×Dic3⋊C4—34no—
113C2×Dic3⋊C4—64no—
114C2×Dic3⋊C4—64no—
115C2×Dic3⋊C4Dic318yescomplemented
116C2×Dic3⋊C4C2×D314yes—
117C2×C4×Dic3—34no—
118C2×C4×Dic3—34no—
119C2×C4×Dic3—64no—
120C2×C4×Dic3—64no—
121C3×#95—34no—
122C3⋊#95—34no—
123C3⋊#95—34no—
124C3⋊#95C2×D314yes—
125C23×C32C22×C412yes—
126C23×C32C2×D412yes—
127C23×C32C2×D412yes—
128C23×C32C2×Q812yes—
129C23×C32C2×Q812yes—
130C23×C32#4112yes—
131C23×C32#4112yes—
132C23×C32C2411yescharacteristic
133C2×C32×C4—28no—
134C2×C32×C4—22no—
135C2×C32×C4—22no—
136C2×C32×C4C22×C414yes—
137C2×C3⋊Dic3—22no—
138C2×C3⋊Dic3—28no—
139C2×C3⋊Dic3—22no—
140C2×C3⋊Dic3—22no—
141C2×C3⋊Dic3—22no—
142C2×C3⋊Dic3—22no—
143C2×C3⋊Dic3—44no—
144C2×C3⋊Dic3C2×D414yes—
145C2×C3×Dic3—28no—
146C2×C3×Dic3—28no—
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—22no—
154C2×C3×Dic3—44no—
155C2×C3×Dic3C4⋊C4116yescomplemented
156C2×C3×Dic3C22×C414yes—
157C2×C3×Dic3C22×C414yes—
158C2×C3×Dic3C2×D414yes—
159C2×C3×Dic3C2×Q814yes—
160C2×C3×Dic3C2×Q814yes—
161C22×C4⋊C4—31no—
162C22×C4⋊C4—91no—
163C22×C4⋊C4—91no—
164C22×C4⋊C4—91no—
165C22×C42—91no—
166#389—98no—
167C2×#95—31no—
168C2×#95—91no—
169C24×C3—21no—
170C24×C3C22×D311yescharacteristic
171C24×C3C22×D311yescharacteristic
172C22×C3×C4—24no—
173C22×C3×C4—24no—
174C22×C3×C4—22no—
175C22×C3×C4—22no—
176C22×C3×C4—22no—
177C22×C3×C4—22no—
178C22×C3×C4—24no—
179C22×C3×C4—22no—
180C22×C3×C4—34no—
181C22×C3×C4—34no—
182C22×C3×C4—34no—
183C22×C3×C4—32no—
184C22×C3×C4—34no—
185C22×C3×C4—34no—
186C22×C3×C4—32no—
187C22×C3×C4—32no—
188C22×C3×C4—32no—
189C22×C3×C4—62no—
190C22×C3×C4—62no—
191C22×C3×C4—62no—
192C22×C3×C4—62no—
193C22×C3×C4—62no—
194C22×C3×C4—62no—
195C22×C3×C4—62no—
196C22×C3×C4C4×D314yes—
197C22×C3×C4C2×Dic314yes—
198C22×C3×C4C22×D312yes—
199C22×C3×C4C22×D312yes—
200C22×Dic3—22no—
201C22×Dic3—22no—
202C22×Dic3—22no—
203C22×Dic3—22no—
204C22×Dic3—22no—
205C22×Dic3—22no—
206C22×Dic3—22no—
207C22×Dic3—34no—
208C22×Dic3—34no—
209C22×Dic3—32no—
210C22×Dic3—32no—
211C22×Dic3—32no—
212C22×Dic3—32no—
213C22×Dic3—64no—
214C22×Dic3—62no—
215C22×Dic3—62no—
216C22×Dic3—62no—
217C22×Dic3—62no—
218C22×Dic3—62no—
219C22×Dic3—62no—
220C22×Dic3—64no—
221C22×Dic3—62no—
222C22×Dic3—62no—
223C22×Dic3—62no—
224C22×Dic3—62no—
225C22×Dic3—62no—
226C22×Dic3—62no—
227C22×Dic3—122no—
228C22×Dic3—122no—
229C22×Dic3—122no—
230C22×Dic3—122no—
231C22×Dic3Dic614yes—
232C22×Dic3Dic614yes—
233C22×Dic3D1214yes—
234C22×Dic3C2×Dic314yes—
235C22×Dic3C2×Dic314yes—
236C22×Dic3C22×D312yes—
237C22×Dic3C22×D312yes—
238C22×Dic3C22×D312yes—
239C22×Dic3C22×D312yes—
240C3×C4⋊C4—316no—
241C4⋊Dic3—68no—
242C4⋊Dic3—68no—
243C4⋊Dic3—68no—
244C4⋊Dic3—68no—
245C4⋊Dic3—616no—
246Dic3⋊C4—68no—
247Dic3⋊C4—68no—
248Dic3⋊C4C2×Dic3116yescomplemented
249C4×Dic3—68no—
250C4×Dic3—68no—
251C22×C32C2×C4⋊C414yes—
252C22×C32C4×D414yes—
253C22×C32C4×Q814yes—
254C22×C32#12114yes—
255C22×C32C22⋊Q814yes—
256C22×C32#12514yes—
257C22×C32C4⋊Q814yes—
258C22×C32C23×C411yescharacteristic
259C22×C32C22×D411yescharacteristic
260C22×C32C22×D411yescharacteristic
261C22×C32C22×Q811yescharacteristic
262C22×C32C22×Q811yescharacteristic
263C22×C32C2×#4111yescharacteristic
264C22×C32C2×#4111yescharacteristic
265C32×C4—24no—
266C3⋊Dic3—24no—
267C3⋊Dic3—42no—
268C3×Dic3—24no—
269C3×Dic3—24no—
270C3×Dic3—42no—
271C3×Dic3C2×C4⋊C418yescomplemented
272C23×C4—31no—
273C23×C4—31no—
274C23×C4—31no—
275C23×C4—31no—
276C23×C4—91no—
277C23×C4—91no—
278C23×C4D3211yescharacteristic
279C2×C4⋊C4—38no—
280C2×C4⋊C4—34no—
281C2×C4⋊C4—94no—
282C2×C4⋊C4—94no—
283C2×C4⋊C4—94no—
284C2×C4⋊C4—184no—
285C2×C4⋊C4—184no—
286C2×C4⋊C4—184no—
287C2×C42—94no—
288C2×C42—184no—
289#95—34no—
290#95—94no—
291C23×C3—21no—
292C23×C3—22no—
293C23×C3—22no—
294C23×C3—22no—
295C23×C3—22no—
296C23×C3—22no—
297C23×C3—22no—
298C23×C3—22no—
299C23×C3C2×Dic612yes—
300C23×C3C2×Dic612yes—
301C23×C3C2×C4×D312yes—
302C23×C3C2×D1212yes—
303C23×C3#23512yes—
304C23×C3D3×D412yes—
305C23×C3D3×D412yes—
306C23×C3D3×D412yes—
307C23×C3#23712yes—
308C23×C3#23712yes—
309C23×C3D3×Q812yes—
310C23×C3D3×Q812yes—
311C23×C3#23912yes—
312C23×C3C22×Dic312yes—
313C23×C3C23×D311yescharacteristic
314C23×C3C23×D311yescharacteristic
315C2×C3×C4—24no—
316C2×C3×C4—24no—
317C2×C3×C4—216no—
318C2×C3×C4—28no—
319C2×C3×C4—28no—
320C2×C3×C4—22no—
321C2×C3×C4—22no—
322C2×C3×C4—22no—
323C2×C3×C4—22no—
324C2×C3×C4—24no—
325C2×C3×C4—316no—
326C2×C3×C4—34no—
327C2×C3×C4—34no—
328C2×C3×C4—34no—
329C2×C3×C4—34no—
330C2×C3×C4—34no—
331C2×C3×C4—68no—
332C2×C3×C4—68no—
333C2×C3×C4—62no—
334C2×C3×C4—62no—
335C2×C3×C4—62no—
336C2×C3×C4—62no—
337C2×C3×C4—62no—
338C2×C3×C4—62no—
339C2×C3×C4—62no—
340C2×C3×C4—124no—
341C2×C3×C4C2×C4×D314yes—
342C2×C3×C4C22×Dic314yes—
343C2×Dic3—28no—
344C2×Dic3—28no—
345C2×Dic3—22no—
346C2×Dic3—22no—
347C2×Dic3—22no—
348C2×Dic3—22no—
349C2×Dic3—22no—
350C2×Dic3—22no—
351C2×Dic3—22no—
352C2×Dic3—34no—
353C2×Dic3—34no—
354C2×Dic3—44no—
355C2×Dic3—64no—
356C2×Dic3—68no—
357C2×Dic3—68no—
358C2×Dic3—62no—
359C2×Dic3—62no—
360C2×Dic3—62no—
361C2×Dic3—62no—
362C2×Dic3—64no—
363C2×Dic3—62no—
364C2×Dic3—62no—
365C2×Dic3—62no—
366C2×Dic3—62no—
367C2×Dic3—62no—
368C2×Dic3—62no—
369C2×Dic3—122no—
370C2×Dic3—122no—
371C2×Dic3—128no—
372C2×Dic3—122no—
373C2×Dic3—122no—
374C2×Dic3—128no—
375C2×Dic3—124no—
376C2×Dic3—124no—
377C2×Dic3C4⋊Dic3116yescomplemented
378C2×Dic3C2×Dic614yes—
379C2×Dic3C2×Dic614yes—
380C2×Dic3C2×D1214yes—
381C2×Dic3C22×Dic314yes—
382C2×Dic3C22×Dic314yes—
383C2×C32#38918yescomplemented
384C2×C32C22×C4⋊C411yescharacteristic
385C2×C32C2×C4×D411yescharacteristic
386C2×C32C2×C4×Q811yescharacteristic
387C2×C32C2×#12111yescharacteristic
388C2×C32C2×C22⋊Q811yescharacteristic
389C2×C32C2×#12511yescharacteristic
390C2×C32C2×C4⋊Q811yescharacteristic
391C24C2×D3211yescharacteristic
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—32no—
395C22×C4—34no—
396C22×C4—34no—
397C22×C4—34no—
398C22×C4—32no—
399C22×C4—32no—
400C22×C4—34no—
401C22×C4—34no—
402C22×C4—32no—
403C22×C4—62no—
404C22×C4—62no—
405C22×C4—62no—
406C22×C4—62no—
407C22×C4—62no—
408C22×C4—62no—
409C22×C4—62no—
410C22×C4—92no—
411C22×C4—94no—
412C22×C4—92no—
413C22×C4—182no—
414C22×C4—182no—
415C22×C4—182no—
416C22×C4—182no—
417C22×C4—182no—
418C22×C4D3×Dic314yes—
419C22×C4C2×D3212yes—
420C4⋊C4—316no—
421C4⋊C4—188no—
422C4⋊C4—188no—
423C4⋊C4—188no—
424C42—188no—
425C22×C3—21no—
426C22×C3—21no—
427C22×C3—21no—
428C22×C3—21no—
429C22×C3—21no—
430C22×C3—21no—
431C22×C3—21no—
432C22×C3—24no—
433C22×C3—24no—
434C22×C3—24no—
435C22×C3—24no—
436C22×C3—24no—
437C22×C3—24no—
438C22×C3—24no—
439C22×C3C4×Dic614yes—
440C22×C3#87814yes—
441C22×C3#67⋊C414yes—
442C22×C3#88414yes—
443C22×C3#88814yes—
444C22×C3#88814yes—
445C22×C3#88914yes—
446C22×C3#89014yes—
447C22×C3D3×C4⋊C414yes—
448C22×C3#89514yes—
449C22×C3#89714yes—
450C22×C3C2×C4⋊Dic314yes—
451C22×C3D4×Dic314yes—
452C22×C3Q8×Dic314yes—
453C22×C3C22×Dic611yescharacteristic
454C22×C3C22×Dic611yescharacteristic
455C22×C3C22×C4×D311yescharacteristic
456C22×C3C22×D1211yescharacteristic
457C22×C3C2×#23511yescharacteristic
458C22×C3C2×D3×D411yescharacteristic
459C22×C3C2×D3×D411yescharacteristic
460C22×C3C2×D3×D411yescharacteristic
461C22×C3C2×#23711yescharacteristic
462C22×C3C2×#23711yescharacteristic
463C22×C3C2×D3×Q811yescharacteristic
464C22×C3C2×D3×Q811yescharacteristic
465C22×C3C2×#23911yescharacteristic
466C22×C3C23×Dic311yescharacteristic
467C3×C4—28no—
468C3×C4—24no—
469C3×C4—24no—
470C3×C4—38no—
471C3×C4—64no—
472C3×C4—64no—
473C3×C4—122no—
474Dic3—24no—
475Dic3—24no—
476Dic3—42no—
477Dic3—64no—
478Dic3—64no—
479Dic3—124no—
480Dic3—124no—
481Dic3—122no—
482Dic3—122no—
483Dic3C2×C4⋊Dic318yescomplemented
484C32C2×#38911yescharacteristic, complemented, Sylow
485C23D3×Dic612yes—
486C23D3×Dic612yes—
487C23#379912yes—
488C23D3×D1212yes—
489C23C2×D3×Dic312yes—
490C23#380512yes—
491C23#381112yes—
492C23C22×D3211yescharacteristic
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—28no—
496C2×C4—34no—
497C2×C4—34no—
498C2×C4—34no—
499C2×C4—316no—
500C2×C4—34no—
501C2×C4—34no—
502C2×C4—62no—
503C2×C4—62no—
504C2×C4—62no—
505C2×C4—62no—
506C2×C4—68no—
507C2×C4—68no—
508C2×C4—62no—
509C2×C4—62no—
510C2×C4—62no—
511C2×C4—94no—
512C2×C4—124no—
513C2×C4—182no—
514C2×C4—182no—
515C2×C4—188no—
516C2×C4—182no—
517C2×C4—182no—
518C2×C4—182no—
519C2×C4—364no—
520C2×C4C2×D3×Dic314yes—
521C2×C3—21no—
522C2×C3—21no—
523C2×C3—28no—
524C2×C3—21no—
525C2×C3—21no—
526C2×C3—21no—
527C2×C3—21no—
528C2×C3—21no—
529C2×C3#464718yescomplemented
530C2×C3#498418yescomplemented
531C2×C3C2×C4×Dic611yescharacteristic
532C2×C3C2×#87811yescharacteristic
533C2×C3C2×#67⋊C411yescharacteristic
534C2×C3C2×#88411yescharacteristic
535C2×C3C2×#88811yescharacteristic
536C2×C3C2×#88811yescharacteristic
537C2×C3C2×#88911yescharacteristic
538C2×C3C2×#89011yescharacteristic
539C2×C3C2×D3×C4⋊C411yescharacteristic
540C2×C3C2×#89511yescharacteristic
541C2×C3C2×#89711yescharacteristic
542C2×C3C22×C4⋊Dic311yescharacteristic
543C2×C3C2×D4×Dic311yescharacteristic
544C2×C3C2×Q8×Dic311yescharacteristic
545C22#6384014yes—
546C22Dic3×Dic614yes—
547C22#6384514yes—
548C22D3×C4⋊Dic314yes—
549C22#6389314yes—
550C22#6391014yes—
551C22#67⋊Dic314yes—
552C22C2×D3×Dic611yescharacteristic
553C22C2×D3×Dic611yescharacteristic
554C22C2×#379911yescharacteristic
555C22C2×D3×D1211yescharacteristic
556C22C22×D3×Dic311yescharacteristic
557C22C2×#380511yescharacteristic
558C22C2×#381111yescharacteristic
559C4—24no—
560C4—38no—
561C4—64no—
562C4—64no—
563C4—122no—
564C4—184no—
565C4—362no—
566C3—21no—
567C3C2×#464711yescharacteristic, complemented
568C3C2×#498411yescharacteristic, complemented
569C2#1059126818yesdirect product factor
570C2C2×#6384011yescharacteristic
571C2C2×Dic3×Dic611yescharacteristic
572C2C2×#6384511yescharacteristic
573C2C2×D3×C4⋊Dic311yescharacteristic
574C2C2×#6389311yescharacteristic
575C2C2×#6391011yescharacteristic
576C2C2×#67⋊Dic311yescharacteristic
subgroupG/H
centerC24C2×D32
commutatorC22×C32C23×C4
FrattiniC23C22×D32
FittingC23×C32×C4C22
socle, prime radicalC24×C32C23
cosocleC23×C32C24
hypercenterC23×C4D32
hypocenterC32C2×#389
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
8. #10591268C2direct (N × H)
20. C2×C3×Dic3⋊C4C4semidirect
77. C3×Dic3⋊C4C2×C4semidirect
115. C2×Dic3⋊C4Dic3semidirect
155. C2×C3×Dic3C4⋊C4semidirect
248. Dic3⋊C4C2×Dic3semidirect
271. C3×Dic3C2×C4⋊C4semidirect
377. C2×Dic3C4⋊Dic3semidirect
383. C2×C32#389semidirect
483. Dic3C2×C4⋊Dic3semidirect
484. C32C2×#389semidirect
529. C2×C3#4647semidirect
530. C2×C3#4984semidirect
567. C3C2×#4647semidirect
568. C3C2×#4984semidirect
569. C2#10591268direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4⋊(C3⋊Dic3)2
C22×C3×Dic3⋊C42
C22×Dic3⋊Dic32
C22×Dic322
C2×C3×C3⋊#952
C2×#635792
#105912682
C2×#49843
C2×#46473