Finite Group Databasebeta

← C2×#10594445 #11900858

Subgroups — C2×#10594445 #11900858

Order 1152.

2449 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64099C211yesmaximal, characteristic, complemented
2C2×C3×#892C211yesmaximal, characteristic
3C2×C3×#888C211yesmaximal, characteristic, complemented
4C2×#63918C211yesmaximal, characteristic, complemented
5C2×#63893C212yesmaximal
6C2×#63887C212yesmaximal
7C2×C4×D3×Dic3C211yesmaximal, characteristic
8C2×#63872C211yesmaximal, characteristic, complemented
9C2×Dic3×Dic6C212yesmaximal, complemented
10C2×#63841C211yesmaximal, characteristic
11C2×#63837C212yesmaximal, complemented
12#10594445C2116yesmaximal, direct product factor
13C2×#5728—31nomaximal
14C2×#5517—31nomaximal
15C22×C3×C4×D3C2211yescharacteristic
16C22×C3×Dic6C2212yes—
17C22×#627C2212yes—
18C22×D3×Dic3C2211yescharacteristic
19C22×D3×Dic3C2211yescharacteristic
20C2×C32×C4⋊C4C2211yescharacteristic
21C2×C4⋊(C3⋊Dic3)C2212yes—
22C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C2×#3750C2212yes—
24C2×C4×C3⋊Dic3C2211yescharacteristic
25#64099C2218yescomplemented
26C2×C3×(C2×D3)⋊C4C2212yes—
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C2×C3×C4⋊Dic3C2211yescharacteristic
29C2×C3×Dic3⋊C4C2212yes—
30C2×C3×C4×Dic3C2212yes—
31C2×C3×C4×Dic3C2211yescharacteristic
32C3×#892C2218yes—
33C3×#888C2218yescomplemented
34C2×Dic3⋊Dic3C2212yes—
35C2×Dic3⋊Dic3C2212yes—
36C2×Dic3⋊Dic3C2212yes—
37C2×(C2×D3)⋊Dic3C2212yes—
38C2×Dic32C2211yescharacteristic
39C2×Dic32C2212yes—
40C2×Dic32C2211yescharacteristic
41#63918C2218yescomplemented
42#63893C22116yes—
43#63887C22116yes—
44C4×D3×Dic3C2218yes—
45#63872C2218yescomplemented
46Dic3×Dic6C22116yescomplemented
47#63841C2218yes—
48#63837C22116yescomplemented
49C2×C3×C4⋊Q8—31no—
50C2×C3×#117—31no—
51C2×#946—32no—
52C2×Q8×Dic3—32no—
53C2×#926—31no—
54C22×C4×Dic3—31no—
55#5728—316no—
56#5517—316no—
57C2×#897—32no—
58C2×#892—31no—
59C2×#892D311yescharacteristic
60C2×#890—31no—
61C2×#890—31no—
62C2×#890—31no—
63C2×#890—31no—
64C2×#890—61no—
65C2×#888—31no—
66C2×#888D311yescharacteristic, complemented
67C2×#887—32no—
68C2×#878—32no—
69C2×#878—32no—
70C2×C42×D3—31no—
71C2×#869—31no—
72C2×C4×Dic6—32no—
73C2×C4×Dic6—32no—
74C23×C3×D3C2311yescharacteristic
75C22×C32×C4C2312yes—
76C22×C32×C4C2311yescharacteristic
77C22×C3⋊Dic3C2311yescharacteristic
78C22×C3⋊Dic3C2311yescharacteristic
79C22×C3⋊Dic3C2312yes—
80C22×C3×Dic3C2312yes—
81C22×C3×Dic3C2312yes—
82C22×C3×Dic3C2311yescharacteristic
83C22×C3×Dic3C2311yescharacteristic
84C22×C3×Dic3C2311yescharacteristic
85C2×C3×C4×D3Q818yescomplemented
86C2×C3×C4×D3C2314yes—
87C2×C3×Dic6—28no—
88C2×C3×Dic6C2318yes—
89C2×#627—28no—
90C2×#627C2318yes—
91C2×D3×Dic3—24no—
92C2×D3×Dic3—24no—
93C2×D3×Dic3C2314yes—
94C2×D3×Dic3C2314yes—
95C32×C4⋊C4C2314yes—
96C4⋊(C3⋊Dic3)C2314yes—
97C4⋊(C3⋊Dic3)C2318yes—
98#3750C2318yes—
99C4×C3⋊Dic3C2314yes—
100C3×(C2×D3)⋊C4C2318yes—
101C3×C4⋊Dic3C2314yes—
102C3×C4⋊Dic3C2314yes—
103C3×Dic3⋊C4C2318yes—
104C3×C4×Dic3C2314yes—
105C3×C4×Dic3C2318yes—
106Dic3⋊Dic3C2318yes—
107Dic3⋊Dic3C2318yes—
108Dic3⋊Dic3C2318yes—
109(C2×D3)⋊Dic3C2318yes—
110Dic32C2314yes—
111Dic32C2318yes—
112Dic32C2314yes—
113C2×#533—91noSylow
114C22×C3×Q8—32no—
115C23×C3×C4—31no—
116C23×Dic3—31no—
117C23×Dic3—31no—
118C22×C4×D3—31no—
119C22×C4×D3—31no—
120C22×C4×D3C2×D311yescharacteristic
121C22×Dic6—32no—
122C22×Dic6—32no—
123C22×Dic6C2×D312yes—
124C3×C4⋊Q8—38no—
125C3×#117—38no—
126C2×C3×C4⋊C4—21no—
127C2×C3×C4⋊C4—32no—
128C2×C3×C4⋊C4—31no—
129C2×C3×C4⋊C4—31no—
130C2×C3×C4⋊C4C2×D311yescharacteristic
131C2×C3×C4⋊C4C2×D311yescharacteristic
132C2×C3×C22⋊C4—32no—
133C2×C3×C42—32no—
134C2×C3×C42—31no—
135C2×#217—32no—
136#946—316no—
137Q8×Dic3—316no—
138C2×(C2×D3)⋊C4—32no—
139C2×(C2×D3)⋊C4C2×D312yes—
140#926—38no—
141C2×C4⋊Dic3—32no—
142C2×C4⋊Dic3—31no—
143C2×C4⋊Dic3—31no—
144C2×C4⋊Dic3—32no—
145C2×C4⋊Dic3—32no—
146C2×C4⋊Dic3—32no—
147C2×C4⋊Dic3—32no—
148C2×C4⋊Dic3—61no—
149C2×C4⋊Dic3—62no—
150C2×C4⋊Dic3C2×D311yescharacteristic
151C2×C4⋊Dic3C2×D311yescharacteristic
152C2×Dic3⋊C4—32no—
153C2×Dic3⋊C4—32no—
154C2×Dic3⋊C4—32no—
155C2×Dic3⋊C4—32no—
156C2×Dic3⋊C4—32no—
157C2×Dic3⋊C4—62no—
158C2×Dic3⋊C4C2×D312yes—
159C2×C4×Dic3—31no—
160C2×C4×Dic3—31no—
161C2×C4×Dic3—31no—
162C2×C4×Dic3—31no—
163C2×C4×Dic3—32no—
164C2×C4×Dic3—31no—
165C2×C4×Dic3—31no—
166C2×C4×Dic3—32no—
167C2×C4×Dic3—38no—
168C2×C4×Dic3—61no—
169C2×C4×Dic3C2×D312yes—
170C2×C4×Dic3C2×D311yescharacteristic
171#897—316no—
172#892—38no—
173#892C2×D318yes—
174#890—38no—
175#890—38no—
176#890—38no—
177#890—38no—
178#890—68no—
179#888—38no—
180#888C2×D318yescomplemented
181#887—316no—
182#878—316no—
183#878—316no—
184C42×D3—38no—
185#869—38no—
186C4×Dic6—316no—
187C4×Dic6—316no—
188C23×C32C2411yescharacteristic
189C22×C3×D3—22no—
190C22×C3×D3—22no—
191C22×C3×D3C2×Q814yes—
192C22×C3×D3C2412yes—
193C2×C32×C4—24no—
194C2×C32×C4C2×Q814yes—
195C2×C32×C4C2414yes—
196C2×C32×C4C2412yes—
197C2×C3⋊Dic3—22no—
198C2×C3⋊Dic3—22no—
199C2×C3⋊Dic3—24no—
200C2×C3⋊Dic3C2414yes—
201C2×C3⋊Dic3C2412yes—
202C2×C3⋊Dic3C2412yes—
203C2×C3×Dic3—24no—
204C2×C3×Dic3—24no—
205C2×C3×Dic3C2×Q814yes—
206C2×C3×Dic3#4114yes—
207C2×C3×Dic3#4114yes—
208C2×C3×Dic3C2414yes—
209C2×C3×Dic3C2414yes—
210C2×C3×Dic3C2412yes—
211C2×C3×Dic3C2412yes—
212C2×C3×Dic3C2412yes—
213C3×C4×D3C2×Q8116yescomplemented
214C3×Dic6—216no—
215#627—216no—
216D3×Dic3—28no—
217D3×Dic3—28no—
218#533—916no—
219C2×C4⋊Q8—31no—
220C2×C4⋊Q8—91no—
221C2×#125—91no—
222C2×#125—91no—
223C2×C22⋊Q8—92no—
224C2×C22⋊Q8—92no—
225C2×C4×Q8—92no—
226C2×C4×Q8—92no—
227C2×#117—31no—
228C2×#117—91no—
229C22×C42—91no—
230C24×C3—31no—
231C23×D3C22×D311yescharacteristic
232C2×C3×Q8—38no—
233C2×C3×Q8—68no—
234C22×C3×C4—21no—
235C22×C3×C4—22no—
236C22×C3×C4—31no—
237C22×C3×C4—31no—
238C22×C3×C4—31no—
239C22×C3×C4—38no—
240C22×C3×C4—34no—
241C22×C3×C4—32no—
242C22×C3×C4—32no—
243C22×C3×C4C22×D312yes—
244C22×C3×C4C22×D312yes—
245C22×C3×C4C22×D311yescharacteristic
246C22×C3×C4C22×D311yescharacteristic
247C22×Dic3—31no—
248C22×Dic3—31no—
249C22×Dic3—31no—
250C22×Dic3—31no—
251C22×Dic3—32no—
252C22×Dic3—32no—
253C22×Dic3—34no—
254C22×Dic3—34no—
255C22×Dic3—61no—
256C22×Dic3—61no—
257C22×Dic3—62no—
258C22×Dic3—64no—
259C22×Dic3—64no—
260C22×Dic3C22×D312yes—
261C22×Dic3C22×D312yes—
262C22×Dic3C22×D311yescharacteristic
263C22×Dic3C22×D311yescharacteristic
264C22×Dic3C22×D311yescharacteristic
265C2×C4×D3—34no—
266C2×C4×D3—34no—
267C2×C4×D3—64no—
268C2×C4×D3—64no—
269C2×C4×D3Dic618yescomplemented
270C2×C4×D3C22×D314yes—
271C2×Dic6—28no—
272C2×Dic6—38no—
273C2×Dic6—38no—
274C2×Dic6—68no—
275C2×Dic6—68no—
276C2×Dic6C22×D318yes—
277C3×C4⋊C4—24no—
278C3×C4⋊C4—38no—
279C3×C4⋊C4—34no—
280C3×C4⋊C4—34no—
281C3×C4⋊C4C22×D314yes—
282C3×C4⋊C4C22×D314yes—
283C3×C22⋊C4—38no—
284C3×C42—38no—
285C3×C42—34no—
286#217—38no—
287(C2×D3)⋊C4—38no—
288(C2×D3)⋊C4C22×D318yes—
289C4⋊Dic3—38no—
290C4⋊Dic3—34no—
291C4⋊Dic3—34no—
292C4⋊Dic3—38no—
293C4⋊Dic3—38no—
294C4⋊Dic3—38no—
295C4⋊Dic3—38no—
296C4⋊Dic3—64no—
297C4⋊Dic3—68no—
298C4⋊Dic3C22×D314yes—
299C4⋊Dic3C22×D314yes—
300Dic3⋊C4—38no—
301Dic3⋊C4—38no—
302Dic3⋊C4—38no—
303Dic3⋊C4—38no—
304Dic3⋊C4—38no—
305Dic3⋊C4—68no—
306Dic3⋊C4C22×D318yes—
307C4×Dic3—34no—
308C4×Dic3—34no—
309C4×Dic3—34no—
310C4×Dic3—34no—
311C4×Dic3—38no—
312C4×Dic3—34no—
313C4×Dic3—34no—
314C4×Dic3—38no—
315C4×Dic3—64no—
316C4×Dic3C22×D318yes—
317C4×Dic3C22×D314yes—
318C22×C32C22×Q812yes—
319C22×C32C2×#4112yes—
320C22×C32C2×#4112yes—
321C22×C32C2511yescharacteristic
322C2×C3×D3—28no—
323C2×C3×D3—22no—
324C2×C3×D3—22no—
325C2×C3×D3C22×Q814yes—
326C32×C4—24no—
327C32×C4C22×Q814yes—
328C3⋊Dic3—22no—
329C3⋊Dic3—22no—
330C3⋊Dic3—24no—
331C3×Dic3—24no—
332C3×Dic3—24no—
333C3×Dic3C22×Q814yes—
334C3×Dic3C2×#4114yes—
335C3×Dic3C2×#4114yes—
336C22×Q8—32no—
337C22×Q8—92no—
338C23×C4—31no—
339C23×C4—91no—
340C23×C4—91no—
341C4⋊Q8—38no—
342C4⋊Q8—98no—
343#125—98no—
344#125—98no—
345C22⋊Q8—916no—
346C22⋊Q8—916no—
347C4×Q8—916no—
348C4×Q8—916no—
349#117—38no—
350#117—98no—
351C2×C4⋊C4—31no—
352C2×C4⋊C4—31no—
353C2×C4⋊C4—32no—
354C2×C4⋊C4—92no—
355C2×C4⋊C4—92no—
356C2×C4⋊C4—92no—
357C2×C4⋊C4—91no—
358C2×C4⋊C4—92no—
359C2×C4⋊C4—92no—
360C2×C4⋊C4D3211yescharacteristic
361C2×C22⋊C4—32no—
362C2×C22⋊C4—92no—
363C2×C42—32no—
364C2×C42—31no—
365C2×C42—98no—
366C2×C42—92no—
367C2×C42—91no—
368C2×C42—91no—
369C2×C42—91no—
370C23×C3—21no—
371C23×C3—34no—
372C23×C3—32no—
373C23×C3—62no—
374C23×C3—62no—
375C23×C3C23×D311yescharacteristic
376C23×C3C23×D311yescharacteristic
377C22×D3—22no—
378C22×D3—22no—
379C22×D3C2×Dic614yes—
380C22×D3C23×D312yes—
381C3×Q8—616no—
382C2×C3×C4—24no—
383C2×C3×C4—24no—
384C2×C3×C4—22no—
385C2×C3×C4—24no—
386C2×C3×C4—24no—
387C2×C3×C4—34no—
388C2×C3×C4—34no—
389C2×C3×C4—34no—
390C2×C3×C4—32no—
391C2×C3×C4—32no—
392C2×C3×C4—32no—
393C2×C3×C4—316no—
394C2×C3×C4—34no—
395C2×C3×C4—34no—
396C2×C3×C4—44no—
397C2×C3×C4—64no—
398C2×C3×C4—64no—
399C2×C3×C4C2×Dic614yes—
400C2×C3×C4D3×Q814yes—
401C2×C3×C4C23×D314yes—
402C2×C3×C4C23×D314yes—
403C2×C3×C4C23×D312yes—
404C2×C3×C4C23×D312yes—
405C2×Dic3—24no—
406C2×Dic3—24no—
407C2×Dic3—32no—
408C2×Dic3—32no—
409C2×Dic3—32no—
410C2×Dic3—32no—
411C2×Dic3—34no—
412C2×Dic3—34no—
413C2×Dic3—62no—
414C2×Dic3—62no—
415C2×Dic3—64no—
416C2×Dic3—62no—
417C2×Dic3—64no—
418C2×Dic3—62no—
419C2×Dic3—64no—
420C2×Dic3—62no—
421C2×Dic3—62no—
422C2×Dic3—68no—
423C2×Dic3—68no—
424C2×Dic3—122no—
425C2×Dic3—122no—
426C2×Dic3—124no—
427C2×Dic3C2×Dic614yes—
428C2×Dic3#23714yes—
429C2×Dic3#23914yes—
430C2×Dic3C23×D314yes—
431C2×Dic3C23×D314yes—
432C2×Dic3C23×D312yes—
433C2×Dic3C23×D312yes—
434C2×Dic3C23×D312yes—
435C4×D3—68no—
436C4×D3—68no—
437C4×D3C2×Dic6116yescomplemented
438Dic6—216no—
439Dic6—616no—
440Dic6—616no—
441C2×C32#53314yescomplemented
442C2×C32C23×Q811yescharacteristic
443C2×C32C22×#4111yescharacteristic
444C2×C32C22×#4111yescharacteristic
445C3×D3—24no—
446C24—31no—
447C2×Q8—38no—
448C2×Q8—68no—
449C2×Q8—98no—
450C2×Q8—188no—
451C22×C4—31no—
452C22×C4—31no—
453C22×C4—31no—
454C22×C4—34no—
455C22×C4—38no—
456C22×C4—32no—
457C22×C4—32no—
458C22×C4—94no—
459C22×C4—94no—
460C22×C4—91no—
461C22×C4—91no—
462C22×C4—92no—
463C22×C4—184no—
464C22×C4—184no—
465C22×C4C2×D3212yes—
466C22×C4C2×D3211yescharacteristic
467C4⋊C4—34no—
468C4⋊C4—34no—
469C4⋊C4—38no—
470C4⋊C4—98no—
471C4⋊C4—98no—
472C4⋊C4—98no—
473C4⋊C4—94no—
474C4⋊C4—98no—
475C4⋊C4—98no—
476C4⋊C4C2×D3214yes—
477C22⋊C4—38no—
478C22⋊C4—98no—
479C42—34no—
480C42—38no—
481C42—94no—
482C42—94no—
483C42—98no—
484C42—94no—
485C22×C3—22no—
486C22×C3—22no—
487C22×C3—22no—
488C22×C3—21no—
489C22×C3—34no—
490C22×C3—62no—
491C22×C3—62no—
492C22×C3—68no—
493C22×C3C22×Dic612yes—
494C22×C3C2×#23712yes—
495C22×C3C2×D3×Q812yes—
496C22×C3C2×#23912yes—
497C22×C3D3×#4112yes—
498C22×C3D3×#4112yes—
499C22×C3C24×D311yescharacteristic
500C22×C3C24×D311yescharacteristic
501C2×D3—22no—
502C2×D3—22no—
503C2×D3—28no—
504C2×D3C22×Dic614yes—
505C3×C4—24no—
506C3×C4—24no—
507C3×C4—24no—
508C3×C4—34no—
509C3×C4—34no—
510C3×C4—34no—
511C3×C4—44no—
512C3×C4—64no—
513C3×C4—64no—
514C3×C4C22×Dic614yes—
515C3×C4C2×D3×Q814yes—
516Dic3—24no—
517Dic3—24no—
518Dic3—62no—
519Dic3—64no—
520Dic3—62no—
521Dic3—64no—
522Dic3—62no—
523Dic3—62no—
524Dic3—122no—
525Dic3—122no—
526Dic3—124no—
527Dic3C22×Dic614yes—
528Dic3C2×#23714yes—
529Dic3C2×#23914yes—
530C32C2×#53311yescharacteristic, complemented, Sylow
531C23—34no—
532C23—32no—
533C23—62no—
534C23—62no—
535C23C22×D3211yescharacteristic
536Q8—616no—
537Q8—1816no—
538C2×C4—24no—
539C2×C4—34no—
540C2×C4—34no—
541C2×C4—34no—
542C2×C4—32no—
543C2×C4—32no—
544C2×C4—32no—
545C2×C4—316no—
546C2×C4—34no—
547C2×C4—34no—
548C2×C4—64no—
549C2×C4—64no—
550C2×C4—92no—
551C2×C4—92no—
552C2×C4—94no—
553C2×C4—188no—
554C2×C4—188no—
555C2×C4—182no—
556C2×C4—182no—
557C2×C4—184no—
558C2×C4D3×Dic614yes—
559C2×C4C22×D3214yes—
560C2×C4C22×D3212yes—
561C2×C3—21no—
562C2×C3—21no—
563C2×C3—21no—
564C2×C3—24no—
565C2×C3—64no—
566C2×C3#551714yescomplemented
567C2×C3#572814yescomplemented
568C2×C3C23×Dic611yescharacteristic
569C2×C3C22×#23711yescharacteristic
570C2×C3C22×D3×Q811yescharacteristic
571C2×C3C22×#23911yescharacteristic
572C2×C3C2×D3×#4111yescharacteristic
573C2×C3C2×D3×#4111yescharacteristic
574D3—24no—
575C22—34no—
576C22—62no—
577C22—62no—
578C22—68no—
579C22C2×D3×Dic612yes—
580C22D3×#23712yes—
581C22D3×#23912yes—
582C22C23×D3211yescharacteristic
583C4—24no—
584C4—34no—
585C4—34no—
586C4—34no—
587C4—64no—
588C4—64no—
589C4—182no—
590C4—182no—
591C4—184no—
592C4C2×D3×Dic614yes—
593C3—21no—
594C3C2×#551711yescharacteristic, complemented
595C3C2×#572811yescharacteristic, complemented
596C2—64no—
597C2#1059444514yesdirect product factor
598C2C22×D3×Dic611yescharacteristic
599C2C2×D3×#23711yescharacteristic
600C2C2×D3×#23911yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
prime radicalC23×C3×D3C23
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#533
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64099C2semidirect
3. C2×C3×#888C2semidirect
4. C2×#63918C2semidirect
8. C2×#63872C2semidirect
9. C2×Dic3×Dic6C2semidirect
11. C2×#63837C2semidirect
12. #10594445C2direct (N × H)
25. #64099C22semidirect
33. C3×#888C22semidirect
41. #63918C22semidirect
45. #63872C22semidirect
46. Dic3×Dic6C22semidirect
48. #63837C22semidirect
66. C2×#888D3semidirect
85. C2×C3×C4×D3Q8semidirect
180. #888C2×D3semidirect
213. C3×C4×D3C2×Q8semidirect
269. C2×C4×D3Dic6semidirect
437. C4×D3C2×Dic6semidirect
441. C2×C32#533semidirect
530. C32C2×#533semidirect
566. C2×C3#5517semidirect
567. C2×C3#5728semidirect
594. C3C2×#5517semidirect
595. C3C2×#5728semidirect
597. C2#10594445direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640992
C2×C3×#8922
C2×C3×#8882
C2×#639182
C2×#638932
C2×#638872
C2×C4×D3×Dic32
C2×#638722
C2×Dic3×Dic62
C2×#638412
C2×#638372
#105944452
C2×#57283
C2×#55173