Finite Group Databasebeta

← C2×#10594485 #11903289

Subgroups — C2×#10594485 #11903289

Order 1152.

2545 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64097C211yesmaximal, characteristic, complemented
2C2×C3×#893C211yesmaximal, characteristic
3C2×C3×#890C211yesmaximal, characteristic, complemented
4C2×C4×#627C211yesmaximal, characteristic, complemented
5C2×#63899C212yesmaximal, complemented
6C2×#63898C211yesmaximal, characteristic
7C2×#63896C212yesmaximal, complemented
8C2×Dic3×D12C211yesmaximal, characteristic
9C2×D3×Dic3⋊C4C212yesmaximal, complemented
10C2×#63869C211yesmaximal, characteristic, complemented
11C2×#63857C212yesmaximal, complemented
12#10594485C2116yesmaximal, direct product factor
13C2×#5690—31nomaximal
14C2×#5539—31nomaximal
15C22×#634C2212yes—
16C22×C3×D12C2211yescharacteristic
17C22×C3×C4×D3C2212yes—
18C22×#627C2211yescharacteristic
19C22×D3×Dic3C2212yes—
20C22×D3×Dic3C2212yes—
21C2×C32×C4⋊C4C2211yescharacteristic
22C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C2×#3750C2212yes—
24C2×C4×C3⋊Dic3C2211yescharacteristic
25#64097C2218yescomplemented
26C2×C3×(C2×D3)⋊C4C2212yes—
27C2×C3×C4⋊Dic3C2212yes—
28C2×C3×C4⋊Dic3C2211yescharacteristic
29C2×C3×Dic3⋊C4C2212yes—
30C2×C3×C4×Dic3C2211yescharacteristic
31C2×C3×C4×Dic3C2211yescharacteristic
32C3×#893C2218yes—
33C3×#890C2218yescomplemented
34C2×#3724C2212yes—
35C2×#3724C2211yescharacteristic
36C2×Dic3⋊Dic3C2211yescharacteristic
37C2×Dic3⋊Dic3C2212yes—
38C2×Dic3⋊Dic3C2211yescharacteristic
39C2×(C2×D3)⋊Dic3C2212yes—
40C2×(C2×D3)⋊Dic3C2212yes—
41C4×#627C2218yescomplemented
42#63899C22116yescomplemented
43#63898C2218yes—
44#63896C22116yescomplemented
45Dic3×D12C2218yes—
46D3×Dic3⋊C4C22116yescomplemented
47#63869C2218yescomplemented
48#63857C22116yescomplemented
49C2×C3×#125—31no—
50C2×C3×C4×D4—31no—
51C2×D4×Dic3—31no—
52C2×D4×Dic3—31no—
53C2×#924—32no—
54C22×Dic3⋊C4—32no—
55#5690—316no—
56#5539—316no—
57C2×#897—32no—
58C2×#896—32no—
59C2×#896—32no—
60C2×#893—31no—
61C2×#893D311yescharacteristic
62C2×D3×C4⋊C4—32no—
63C2×#890—31no—
64C2×#890D311yescharacteristic, complemented
65C2×#888—31no—
66C2×#888—31no—
67C2×#888—61no—
68C2×#878—32no—
69C2×#878—32no—
70C2×C4×D12—31no—
71C2×#870—31no—
72C2×C4×Dic6—31no—
73C2×C4×Dic6—31no—
74C23×C3×D3C2312yes—
75C22×C32×C4C2312yes—
76C22×C32×C4C2311yescharacteristic
77C22×C3⋊Dic3C2312yes—
78C22×C3⋊Dic3C2311yescharacteristic
79C22×C3⋊Dic3C2311yescharacteristic
80C2×#634—44no—
81C2×#634C2318yes—
82C22×C3×Dic3C2311yescharacteristic
83C22×C3×Dic3C2311yescharacteristic
84C22×C3×Dic3C2311yescharacteristic
85C22×C3×Dic3C2311yescharacteristic
86C22×C3×Dic3C2312yes—
87C2×C3×D12Q818yescomplemented
88C2×C3×D12C2314yes—
89C2×C3×C4×D3—44no—
90C2×C3×C4×D3C2318yes—
91C2×#627—24no—
92C2×#627C2314yes—
93C2×D3×Dic3—28no—
94C2×D3×Dic3—44no—
95C2×D3×Dic3C2318yes—
96C2×D3×Dic3C2318yes—
97C32×C4⋊C4C2314yes—
98C4⋊(C3⋊Dic3)C2314yes—
99#3750C2318yes—
100C4×C3⋊Dic3C2314yes—
101C3×(C2×D3)⋊C4C2318yes—
102C3×C4⋊Dic3C2318yes—
103C3×C4⋊Dic3C2314yes—
104C3×Dic3⋊C4C2318yes—
105C3×C4×Dic3C2314yes—
106C3×C4×Dic3C2314yes—
107#3724C2318yes—
108#3724C2314yes—
109Dic3⋊Dic3C2314yes—
110Dic3⋊Dic3C2318yes—
111Dic3⋊Dic3C2314yes—
112(C2×D3)⋊Dic3C2318yes—
113(C2×D3)⋊Dic3C2318yes—
114C2×#554—91noSylow
115C22×C3×D4—31no—
116C23×C3×C4—32no—
117C23×Dic3—32no—
118C23×Dic3—32no—
119C22×D12C2×D311yescharacteristic
120C22×C4×D3—32no—
121C22×C4×D3—32no—
122C22×C4×D3C2×D312yes—
123C22×Dic6—31no—
124C22×Dic6—31no—
125C22×Dic6—32no—
126C22×Dic6—32no—
127C22×Dic6—62no—
128C3×#125—38no—
129C3×C4×D4—38no—
130C2×C3×C4⋊C4—21no—
131C2×C3×C4⋊C4—32no—
132C2×C3×C4⋊C4—31no—
133C2×C3×C4⋊C4—32no—
134C2×C3×C4⋊C4C2×D311yescharacteristic
135C2×C3×C4⋊C4C2×D311yescharacteristic
136C2×C3×C22⋊C4—32no—
137C2×C3×C42—31no—
138C2×C3×C42—31no—
139C2×#217—32no—
140C2×#217—32no—
141D4×Dic3—38no—
142D4×Dic3—38no—
143C2×(C2×D3)⋊C4—32no—
144C2×(C2×D3)⋊C4—32no—
145C2×(C2×D3)⋊C4C2×D312yes—
146C2×C4⋊Dic3—31no—
147C2×C4⋊Dic3—31no—
148C2×C4⋊Dic3—31no—
149C2×C4⋊Dic3—31no—
150C2×C4⋊Dic3—32no—
151C2×C4⋊Dic3—61no—
152C2×C4⋊Dic3C2×D311yescharacteristic
153C2×C4⋊Dic3C2×D312yes—
154#924—316no—
155C2×Dic3⋊C4—32no—
156C2×Dic3⋊C4—32no—
157C2×Dic3⋊C4—31no—
158C2×Dic3⋊C4—31no—
159C2×Dic3⋊C4—31no—
160C2×Dic3⋊C4—31no—
161C2×Dic3⋊C4—32no—
162C2×Dic3⋊C4—32no—
163C2×Dic3⋊C4—32no—
164C2×Dic3⋊C4—316no—
165C2×Dic3⋊C4—62no—
166C2×Dic3⋊C4C2×D312yes—
167C2×C4×Dic3—31no—
168C2×C4×Dic3—31no—
169C2×C4×Dic3—61no—
170C2×C4×Dic3C2×D311yescharacteristic
171C2×C4×Dic3C2×D311yescharacteristic
172#897—316no—
173#896—316no—
174#896—316no—
175#893—38no—
176#893C2×D318yes—
177D3×C4⋊C4—316no—
178#890—38no—
179#890C2×D318yescomplemented
180#888—38no—
181#888—38no—
182#888—68no—
183#878—316no—
184#878—316no—
185C4×D12—38no—
186#870—38no—
187C4×Dic6—38no—
188C4×Dic6—38no—
189C23×C32C2411yescharacteristic
190C22×C3×D3—24no—
191C22×C3×D3—24no—
192C22×C3×D3C2×Q818yes—
193C22×C3×D3C2414yes—
194C2×C32×C4—24no—
195C2×C32×C4C2×Q814yes—
196C2×C32×C4C2414yes—
197C2×C32×C4C2412yes—
198C2×C3⋊Dic3—22no—
199C2×C3⋊Dic3—24no—
200C2×C3⋊Dic3#4114yes—
201C2×C3⋊Dic3C2412yes—
202C2×C3⋊Dic3C2414yes—
203C2×C3⋊Dic3C2412yes—
204#634—48no—
205C2×C3×Dic3—24no—
206C2×C3×Dic3—22no—
207C2×C3×Dic3—22no—
208C2×C3×Dic3—22no—
209C2×C3×Dic3—22no—
210C2×C3×Dic3C2412yes—
211C2×C3×Dic3C2414yes—
212C2×C3×Dic3C2412yes—
213C2×C3×Dic3C2412yes—
214C2×C3×Dic3C2412yes—
215C3×D12C2×Q8116yescomplemented
216C3×C4×D3—48no—
217#627—28no—
218D3×Dic3—216no—
219D3×Dic3—48no—
220#554—916no—
221C2×C4⋊Q8—91no—
222C2×#125—31no—
223C2×#125—91no—
224C2×C22⋊Q8—92no—
225C2×C22⋊Q8—92no—
226C2×C22⋊Q8—92no—
227C2×C4×Q8—91no—
228C2×C4×D4—31no—
229C2×C4×D4—91no—
230C2×C4×D4—91no—
231C22×C4⋊C4—92no—
232C24×C3—32no—
233C23×D3C22×D312yes—
234C2×C3×D4—38no—
235C2×C3×D4—34no—
236C22×C3×C4—21no—
237C22×C3×C4—22no—
238C22×C3×C4—31no—
239C22×C3×C4—31no—
240C22×C3×C4—31no—
241C22×C3×C4—32no—
242C22×C3×C4—31no—
243C22×C3×C4—38no—
244C22×C3×C4—124no—
245C22×C3×C4C22×D312yes—
246C22×C3×C4C22×D312yes—
247C22×C3×C4C22×D311yescharacteristic
248C22×C3×C4C22×D311yescharacteristic
249C22×Dic3—31no—
250C22×Dic3—31no—
251C22×Dic3—31no—
252C22×Dic3—31no—
253C22×Dic3—32no—
254C22×Dic3—32no—
255C22×Dic3—38no—
256C22×Dic3—38no—
257C22×Dic3—61no—
258C22×Dic3—61no—
259C22×Dic3—62no—
260C22×Dic3—68no—
261C22×Dic3—124no—
262C22×Dic3C22×D311yescharacteristic
263C22×Dic3C22×D311yescharacteristic
264C22×Dic3C22×D311yescharacteristic
265C22×Dic3C22×D311yescharacteristic
266C22×Dic3C22×D312yes—
267C2×D12Dic618yescomplemented
268C2×D12C22×D314yes—
269C2×C4×D3—38no—
270C2×C4×D3—38no—
271C2×C4×D3—44no—
272C2×C4×D3—68no—
273C2×C4×D3—124no—
274C2×C4×D3C22×D318yes—
275C2×Dic6—34no—
276C2×Dic6—34no—
277C2×Dic6—38no—
278C2×Dic6—38no—
279C2×Dic6—68no—
280C2×Dic6—64no—
281C2×Dic6—64no—
282C2×Dic6—124no—
283C2×Dic6—124no—
284C2×Dic6—128no—
285C3×C4⋊C4—24no—
286C3×C4⋊C4—34no—
287C3×C4⋊C4—38no—
288C3×C4⋊C4—38no—
289C3×C4⋊C4C22×D314yes—
290C3×C4⋊C4C22×D314yes—
291C3×C22⋊C4—38no—
292C3×C42—34no—
293C3×C42—34no—
294#217—38no—
295#217—38no—
296(C2×D3)⋊C4—38no—
297(C2×D3)⋊C4—38no—
298(C2×D3)⋊C4C22×D318yes—
299C4⋊Dic3—34no—
300C4⋊Dic3—34no—
301C4⋊Dic3—34no—
302C4⋊Dic3—34no—
303C4⋊Dic3—38no—
304C4⋊Dic3—64no—
305C4⋊Dic3C22×D314yes—
306C4⋊Dic3C22×D318yes—
307Dic3⋊C4—38no—
308Dic3⋊C4—38no—
309Dic3⋊C4—34no—
310Dic3⋊C4—34no—
311Dic3⋊C4—34no—
312Dic3⋊C4—34no—
313Dic3⋊C4—38no—
314Dic3⋊C4—38no—
315Dic3⋊C4—38no—
316Dic3⋊C4—68no—
317Dic3⋊C4C22×D318yes—
318C4×Dic3—34no—
319C4×Dic3—34no—
320C4×Dic3—64no—
321C4×Dic3C22×D314yes—
322C4×Dic3C22×D314yes—
323C22×C32C22×Q812yes—
324C22×C32C2×#4112yes—
325C22×C32H(5,𝔽2)12yes—
326C22×C32C2511yescharacteristic
327C2×C3×D3—216no—
328C2×C3×D3—24no—
329C2×C3×D3—24no—
330C2×C3×D3C22×Q818yes—
331C32×C4—24no—
332C32×C4C22×Q814yes—
333C3⋊Dic3—22no—
334C3⋊Dic3—24no—
335C3⋊Dic3C2×#4114yes—
336C3×Dic3—24no—
337C3×Dic3—22no—
338C3×Dic3—22no—
339C3×Dic3—22no—
340C3×Dic3—22no—
341C22×Q8—91no—
342C22×Q8—92no—
343C22×D4—31no—
344C23×C4—32no—
345C23×C4—92no—
346C23×C4—92no—
347C4⋊Q8—98no—
348#125—38no—
349#125—98no—
350C22⋊Q8—916no—
351C22⋊Q8—916no—
352C22⋊Q8—916no—
353C4×Q8—98no—
354C4×D4—38no—
355C4×D4—98no—
356C4×D4—98no—
357C2×C4⋊C4—32no—
358C2×C4⋊C4—31no—
359C2×C4⋊C4—32no—
360C2×C4⋊C4—916no—
361C2×C4⋊C4—91no—
362C2×C4⋊C4—92no—
363C2×C4⋊C4—91no—
364C2×C4⋊C4—91no—
365C2×C4⋊C4—92no—
366C2×C4⋊C4—92no—
367C2×C4⋊C4—91no—
368C2×C4⋊C4D3211yescharacteristic
369C2×C22⋊C4—32no—
370C2×C22⋊C4—92no—
371C2×C22⋊C4—92no—
372C2×C42—31no—
373C2×C42—31no—
374C2×C42—91no—
375C23×C3—21no—
376C23×C3—38no—
377C23×C3—34no—
378C23×C3—64no—
379C23×C3—64no—
380C23×C3C23×D311yescharacteristic
381C23×C3C23×D311yescharacteristic
382C22×D3—24no—
383C22×D3—24no—
384C22×D3C2×Dic618yes—
385C22×D3C23×D314yes—
386C3×D4—316no—
387C2×C3×C4—24no—
388C2×C3×C4—24no—
389C2×C3×C4—22no—
390C2×C3×C4—24no—
391C2×C3×C4—24no—
392C2×C3×C4—32no—
393C2×C3×C4—32no—
394C2×C3×C4—32no—
395C2×C3×C4—34no—
396C2×C3×C4—32no—
397C2×C3×C4—44no—
398C2×C3×C4—62no—
399C2×C3×C4—62no—
400C2×C3×C4—62no—
401C2×C3×C4—64no—
402C2×C3×C4—62no—
403C2×C3×C4—128no—
404C2×C3×C4C2×Dic614yes—
405C2×C3×C4D3×Q814yes—
406C2×C3×C4C23×D314yes—
407C2×C3×C4C23×D314yes—
408C2×C3×C4C23×D312yes—
409C2×C3×C4C23×D312yes—
410C2×Dic3—22no—
411C2×Dic3—22no—
412C2×Dic3—22no—
413C2×Dic3—24no—
414C2×Dic3—22no—
415C2×Dic3—34no—
416C2×Dic3—34no—
417C2×Dic3—32no—
418C2×Dic3—32no—
419C2×Dic3—32no—
420C2×Dic3—32no—
421C2×Dic3—34no—
422C2×Dic3—34no—
423C2×Dic3—64no—
424C2×Dic3—62no—
425C2×Dic3—62no—
426C2×Dic3—64no—
427C2×Dic3—616no—
428C2×Dic3—64no—
429C2×Dic3—62no—
430C2×Dic3—64no—
431C2×Dic3—62no—
432C2×Dic3—64no—
433C2×Dic3—124no—
434C2×Dic3—128no—
435C2×Dic3C23×D312yes—
436C2×Dic3C23×D312yes—
437C2×Dic3C23×D312yes—
438C2×Dic3C23×D312yes—
439C2×Dic3C23×D314yes—
440D12C2×Dic6116yescomplemented
441C4×D3—48no—
442C4×D3—616no—
443C4×D3—128no—
444Dic6—68no—
445Dic6—68no—
446Dic6—128no—
447Dic6—128no—
448Dic6—1216no—
449C2×C32#55414yescomplemented
450C2×C32C23×Q811yescharacteristic
451C2×C32C22×#4111yescharacteristic
452C2×C32C2×H(5,𝔽2)11yescharacteristic
453C3×D3—28no—
454C24—32no—
455C2×Q8—94no—
456C2×Q8—98no—
457C2×Q8—184no—
458C2×Q8—364no—
459C2×D4—34no—
460C2×D4—38no—
461C22×C4—31no—
462C22×C4—31no—
463C22×C4—31no—
464C22×C4—31no—
465C22×C4—32no—
466C22×C4—38no—
467C22×C4—98no—
468C22×C4—98no—
469C22×C4—91no—
470C22×C4—91no—
471C22×C4—92no—
472C22×C4—124no—
473C22×C4—188no—
474C22×C4—364no—
475C22×C4C2×D3212yes—
476C22×C4C2×D3211yescharacteristic
477C4⋊C4—38no—
478C4⋊C4—34no—
479C4⋊C4—38no—
480C4⋊C4—94no—
481C4⋊C4—98no—
482C4⋊C4—94no—
483C4⋊C4—94no—
484C4⋊C4—98no—
485C4⋊C4—98no—
486C4⋊C4—94no—
487C4⋊C4C2×D3214yes—
488C22⋊C4—38no—
489C22⋊C4—98no—
490C22⋊C4—98no—
491C42—34no—
492C42—34no—
493C42—94no—
494C22×C3—22no—
495C22×C3—22no—
496C22×C3—22no—
497C22×C3—21no—
498C22×C3—38no—
499C22×C3—616no—
500C22×C3—64no—
501C22×C3—64no—
502C22×C3C22×Dic612yes—
503C22×C3#100412yes—
504C22×C3C2×D3×Q812yes—
505C22×C3D3×#4112yes—
506C22×C3D3×#4112yes—
507C22×C3#100912yes—
508C22×C3C24×D311yescharacteristic
509C22×C3C24×D311yescharacteristic
510C2×D3—24no—
511C2×D3—24no—
512C2×D3—216no—
513C2×D3C22×Dic618yes—
514C3×C4—24no—
515C3×C4—24no—
516C3×C4—24no—
517C3×C4—44no—
518C3×C4—62no—
519C3×C4—62no—
520C3×C4—62no—
521C3×C4—64no—
522C3×C4—62no—
523C3×C4C22×Dic614yes—
524C3×C4C2×D3×Q814yes—
525Dic3—22no—
526Dic3—22no—
527Dic3—22no—
528Dic3—24no—
529Dic3—22no—
530Dic3—34no—
531Dic3—34no—
532Dic3—64no—
533Dic3—64no—
534Dic3—62no—
535Dic3—64no—
536Dic3—62no—
537Dic3—64no—
538Dic3—124no—
539C32C2×#55411yescharacteristic, complemented, Sylow
540C23—38no—
541C23—34no—
542C23—64no—
543C23—64no—
544C23C22×D3211yescharacteristic
545Q8—188no—
546Q8—368no—
547D4—316no—
548C2×C4—24no—
549C2×C4—32no—
550C2×C4—32no—
551C2×C4—32no—
552C2×C4—32no—
553C2×C4—34no—
554C2×C4—62no—
555C2×C4—62no—
556C2×C4—64no—
557C2×C4—62no—
558C2×C4—62no—
559C2×C4—94no—
560C2×C4—92no—
561C2×C4—92no—
562C2×C4—94no—
563C2×C4—128no—
564C2×C4—1816no—
565C2×C4—184no—
566C2×C4—182no—
567C2×C4—368no—
568C2×C4D3×Dic614yes—
569C2×C4C22×D3214yes—
570C2×C4C22×D3212yes—
571C2×C3—21no—
572C2×C3—21no—
573C2×C3—21no—
574C2×C3—24no—
575C2×C3—68no—
576C2×C3#553914yescomplemented
577C2×C3#569014yescomplemented
578C2×C3C23×Dic611yescharacteristic
579C2×C3C2×#100411yescharacteristic
580C2×C3C22×D3×Q811yescharacteristic
581C2×C3C2×D3×#4111yescharacteristic
582C2×C3C2×D3×#4111yescharacteristic
583C2×C3C2×#100911yescharacteristic
584D3—28no—
585C22—38no—
586C22—64no—
587C22—64no—
588C22—616no—
589C22C2×D3×Dic612yes—
590C22#6431412yes—
591C22#6431912yes—
592C22C23×D3211yescharacteristic
593C4—24no—
594C4—62no—
595C4—62no—
596C4—64no—
597C4—62no—
598C4—62no—
599C4—94no—
600C4—184no—
601C4—182no—
602C4C2×D3×Dic614yes—
603C3—21no—
604C3C2×#553911yescharacteristic, complemented
605C3C2×#569011yescharacteristic, complemented
606C2—68no—
607C2#1059448514yesdirect product factor
608C2C22×D3×Dic611yescharacteristic
609C2C2×#6431411yescharacteristic
610C2C2×#6431911yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
prime radicalC22×C3×D12C22
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#554
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×#64097C2semidirect
3. C2×C3×#890C2semidirect
4. C2×C4×#627C2semidirect
5. C2×#63899C2semidirect
7. C2×#63896C2semidirect
9. C2×D3×Dic3⋊C4C2semidirect
10. C2×#63869C2semidirect
11. C2×#63857C2semidirect
12. #10594485C2direct (N × H)
25. #64097C22semidirect
33. C3×#890C22semidirect
41. C4×#627C22semidirect
42. #63899C22semidirect
44. #63896C22semidirect
46. D3×Dic3⋊C4C22semidirect
47. #63869C22semidirect
48. #63857C22semidirect
64. C2×#890D3semidirect
87. C2×C3×D12Q8semidirect
179. #890C2×D3semidirect
215. C3×D12C2×Q8semidirect
267. C2×D12Dic6semidirect
440. D12C2×Dic6semidirect
449. C2×C32#554semidirect
539. C32C2×#554semidirect
576. C2×C3#5539semidirect
577. C2×C3#5690semidirect
604. C3C2×#5539semidirect
605. C3C2×#5690semidirect
607. C2#10594485direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640972
C2×C3×#8932
C2×C3×#8902
C2×C4×#6272
C2×#638992
C2×#638982
C2×#638962
C2×Dic3×D122
C2×D3×Dic3⋊C42
C2×#638692
C2×#638572
#105944852
C2×#56903
C2×#55393