Finite Group Databasebeta

← C2×#10593954 #11901910

Subgroups — C2×#10593954 #11901910

Order 1152.

2273 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64079C211yesmaximal, characteristic, complemented
2C2×C3×#872C211yesmaximal, characteristic
3C2×C3×#869C211yesmaximal, characteristic, complemented
4C2×#63918C211yesmaximal, characteristic, complemented
5C2×#63899C212yesmaximal
6C2×D3×C4⋊Dic3C211yesmaximal, characteristic
7C2×#63887C212yesmaximal
8C2×#63869C211yesmaximal, characteristic, complemented
9C2×#63846C212yesmaximal, complemented
10C2×#63841C211yesmaximal, characteristic
11C2×#63839C212yesmaximal, complemented
12#10593954C2116yesmaximal, direct product factor
13C2×#5729—31nomaximal
14C2×#5519—31nomaximal
15C22×C3×C4×D3C2211yescharacteristic
16C22×C3×Dic6C2212yes—
17C22×#627C2212yes—
18C22×D3×Dic3C2212yes—
19C2×C32×C42C2211yescharacteristic
20C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C2×#3750C2212yes—
23C2×#3750C2212yes—
24#64079C2218yescomplemented
25C2×C3×(C2×D3)⋊C4C2211yescharacteristic
26C2×C3×(C2×D3)⋊C4C2211yescharacteristic
27C2×C3×C4⋊Dic3C2212yes—
28C2×C3×C4⋊Dic3C2211yescharacteristic
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C2×C3×Dic3⋊C4C2211yescharacteristic
31C2×C3×Dic3⋊C4C2211yescharacteristic
32C2×C3×C4×Dic3C2211yescharacteristic
33C3×#872C2218yes—
34C3×#869C2218yescomplemented
35C2×#3724C2212yes—
36C2×Dic3⋊Dic3C2212yes—
37C2×Dic3⋊Dic3C2212yes—
38C2×Dic3⋊Dic3C2212yes—
39C2×(C2×D3)⋊Dic3C2212yes—
40C2×Dic32C2212yes—
41#63918C2218yescomplemented
42#63899C22116yes—
43D3×C4⋊Dic3C2218yes—
44#63887C22116yes—
45#63869C2218yescomplemented
46#63846C22116yescomplemented
47#63841C2218yes—
48#63839C22116yescomplemented
49C2×C3×C4⋊Q8—31no—
50C2×C3×#117—31no—
51C2×#946—32no—
52C2×#944—32no—
53C2×#926—31no—
54C22×C4⋊Dic3—31no—
55#5729—316no—
56#5519—316no—
57C2×#896—32no—
58C2×#892—31no—
59C2×D3×C4⋊C4—31no—
60C2×#890—32no—
61C2×#890—31no—
62C2×#889—32no—
63C2×#888—32no—
64C2×#888—31no—
65C2×#878—32no—
66C2×#878—32no—
67C2×#872D311yescharacteristic
68C2×#870—31no—
69C2×#870—31no—
70C2×#870—31no—
71C2×#870—61no—
72C2×#869—31no—
73C2×#869D311yescharacteristic, complemented
74C23×C3×D3C2311yescharacteristic
75C22×C32×C4C2311yescharacteristic
76C22×C32×C4C2311yescharacteristic
77C22×C32×C4C2311yescharacteristic
78C22×C3⋊Dic3C2312yes—
79C22×C3⋊Dic3C2312yes—
80C22×C3×Dic3C2311yescharacteristic
81C22×C3×Dic3C2311yescharacteristic
82C22×C3×Dic3C2312yes—
83C22×C3×Dic3C2312yes—
84C22×C3×Dic3C2311yescharacteristic
85C2×C3×C4×D3Q818yescomplemented
86C2×C3×C4×D3C2314yes—
87C2×C3×Dic6—44no—
88C2×C3×Dic6C2318yes—
89C2×#627—44no—
90C2×#627C2318yes—
91C2×D3×Dic3—44no—
92C2×D3×Dic3C2318yes—
93C32×C42C2314yes—
94C4⋊(C3⋊Dic3)C2314yes—
95C4⋊(C3⋊Dic3)C2314yes—
96#3750C2318yes—
97#3750C2318yes—
98C3×(C2×D3)⋊C4C2314yes—
99C3×(C2×D3)⋊C4C2314yes—
100C3×C4⋊Dic3C2314yes—
101C3×C4⋊Dic3C2318yes—
102C3×C4⋊Dic3C2314yes—
103C3×Dic3⋊C4C2314yes—
104C3×Dic3⋊C4C2314yes—
105C3×C4×Dic3C2314yes—
106#3724C2318yes—
107Dic3⋊Dic3C2318yes—
108Dic3⋊Dic3C2318yes—
109Dic3⋊Dic3C2318yes—
110(C2×D3)⋊Dic3C2318yes—
111Dic32C2318yes—
112C2×#544—91noSylow
113C22×C3×Q8—32no—
114C23×C3×C4—31no—
115C23×Dic3—32no—
116C22×C4×D3—32no—
117C22×C4×D3C2×D311yescharacteristic
118C22×Dic6—32no—
119C22×Dic6—32no—
120C22×Dic6C2×D312yes—
121C3×C4⋊Q8—38no—
122C3×#117—38no—
123C2×C3×C4⋊C4—31no—
124C2×C3×C4⋊C4—31no—
125C2×C3×C4⋊C4—31no—
126C2×C3×C4⋊C4—32no—
127C2×C3×C4⋊C4—31no—
128C2×C3×C22⋊C4—31no—
129C2×C3×C22⋊C4—31no—
130C2×C3×C42—21no—
131C2×C3×C42—31no—
132C2×C3×C42C2×D311yescharacteristic
133C2×C3×C42C2×D311yescharacteristic
134C2×#217—32no—
135#946—316no—
136#944—316no—
137C2×(C2×D3)⋊C4—32no—
138C2×(C2×D3)⋊C4C2×D311yescharacteristic
139C2×(C2×D3)⋊C4C2×D311yescharacteristic
140#926—38no—
141C2×C4⋊Dic3—31no—
142C2×C4⋊Dic3—31no—
143C2×C4⋊Dic3—31no—
144C2×C4⋊Dic3—31no—
145C2×C4⋊Dic3—32no—
146C2×C4⋊Dic3—32no—
147C2×C4⋊Dic3—32no—
148C2×C4⋊Dic3—38no—
149C2×C4⋊Dic3—61no—
150C2×C4⋊Dic3—61no—
151C2×C4⋊Dic3C2×D311yescharacteristic
152C2×C4⋊Dic3C2×D311yescharacteristic
153C2×C4⋊Dic3C2×D312yes—
154C2×Dic3⋊C4—32no—
155C2×Dic3⋊C4—32no—
156C2×Dic3⋊C4—32no—
157C2×Dic3⋊C4—32no—
158C2×Dic3⋊C4—32no—
159C2×Dic3⋊C4—32no—
160C2×Dic3⋊C4—32no—
161C2×Dic3⋊C4—32no—
162C2×Dic3⋊C4—32no—
163C2×Dic3⋊C4—62no—
164C2×Dic3⋊C4—62no—
165C2×Dic3⋊C4C2×D311yescharacteristic
166C2×Dic3⋊C4C2×D311yescharacteristic
167C2×C4×Dic3—32no—
168C2×C4×Dic3—32no—
169C2×C4×Dic3C2×D311yescharacteristic
170#896—316no—
171#892—38no—
172D3×C4⋊C4—38no—
173#890—316no—
174#890—38no—
175#889—316no—
176#888—316no—
177#888—38no—
178#878—316no—
179#878—316no—
180#872C2×D318yes—
181#870—38no—
182#870—38no—
183#870—38no—
184#870—68no—
185#869—38no—
186#869C2×D318yescomplemented
187C23×C32C2411yescharacteristic
188C22×C3×D3—22no—
189C22×C3×D3—22no—
190C22×C3×D3C2×Q814yes—
191C22×C3×D3C2412yes—
192C2×C32×C4—22no—
193C2×C32×C4—22no—
194C2×C32×C4C2×Q814yes—
195C2×C32×C4C2412yes—
196C2×C32×C4C2412yes—
197C2×C32×C4C2412yes—
198C2×C3⋊Dic3—24no—
199C2×C3⋊Dic3—24no—
200C2×C3⋊Dic3C2414yes—
201C2×C3⋊Dic3C2414yes—
202C2×C3×Dic3—24no—
203C2×C3×Dic3—22no—
204C2×C3×Dic3—24no—
205C2×C3×Dic3—22no—
206C2×C3×Dic3C2×Q814yes—
207C2×C3×Dic3C2414yes—
208C2×C3×Dic3C2412yes—
209C2×C3×Dic3C2414yes—
210C2×C3×Dic3C2412yes—
211C2×C3×Dic3C2412yes—
212C3×C4×D3C2×Q8116yescomplemented
213C3×Dic6—48no—
214#627—48no—
215D3×Dic3—48no—
216#544—916no—
217C2×C4⋊Q8—31no—
218C2×C4⋊Q8—91no—
219C2×C4⋊Q8—92no—
220C2×#125—91no—
221C2×#125—92no—
222C2×#125—91no—
223C2×C22⋊Q8—92no—
224C2×C22⋊Q8—92no—
225C2×#117—31no—
226C2×#117—91no—
227C22×C4⋊C4—91no—
228C24×C3—31no—
229C23×D3C22×D311yescharacteristic
230C2×C3×Q8—38no—
231C2×C3×Q8—124no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—31no—
236C22×C3×C4—38no—
237C22×C3×C4—34no—
238C22×C3×C4—32no—
239C22×C3×C4—31no—
240C22×C3×C4—32no—
241C22×C3×C4—31no—
242C22×C3×C4C22×D311yescharacteristic
243C22×C3×C4C22×D311yescharacteristic
244C22×C3×C4C22×D311yescharacteristic
245C22×C3×C4C22×D311yescharacteristic
246C22×C3×C4C22×D311yescharacteristic
247C22×C3×C4C22×D311yescharacteristic
248C22×Dic3—32no—
249C22×Dic3—32no—
250C22×Dic3—32no—
251C22×Dic3—32no—
252C22×Dic3—38no—
253C22×Dic3—62no—
254C22×Dic3—62no—
255C22×Dic3—124no—
256C22×Dic3C22×D312yes—
257C22×Dic3C22×D311yescharacteristic
258C22×Dic3C22×D311yescharacteristic
259C22×Dic3C22×D312yes—
260C22×Dic3C22×D311yescharacteristic
261C2×C4×D3—38no—
262C2×C4×D3—124no—
263C2×C4×D3Dic618yescomplemented
264C2×C4×D3C22×D314yes—
265C2×Dic6—38no—
266C2×Dic6—38no—
267C2×Dic6—44no—
268C2×Dic6—124no—
269C2×Dic6—124no—
270C2×Dic6C22×D318yes—
271C3×C4⋊C4—34no—
272C3×C4⋊C4—34no—
273C3×C4⋊C4—38no—
274C3×C4⋊C4—34no—
275C3×C4⋊C4—34no—
276C3×C22⋊C4—34no—
277C3×C22⋊C4—34no—
278C3×C42—24no—
279C3×C42—34no—
280C3×C42C22×D314yes—
281C3×C42C22×D314yes—
282#217—38no—
283(C2×D3)⋊C4—38no—
284(C2×D3)⋊C4C22×D314yes—
285(C2×D3)⋊C4C22×D314yes—
286C4⋊Dic3—34no—
287C4⋊Dic3—34no—
288C4⋊Dic3—34no—
289C4⋊Dic3—34no—
290C4⋊Dic3—38no—
291C4⋊Dic3—38no—
292C4⋊Dic3—38no—
293C4⋊Dic3—64no—
294C4⋊Dic3—64no—
295C4⋊Dic3C22×D314yes—
296C4⋊Dic3C22×D314yes—
297C4⋊Dic3C22×D318yes—
298Dic3⋊C4—38no—
299Dic3⋊C4—38no—
300Dic3⋊C4—38no—
301Dic3⋊C4—38no—
302Dic3⋊C4—38no—
303Dic3⋊C4—38no—
304Dic3⋊C4—38no—
305Dic3⋊C4—38no—
306Dic3⋊C4—38no—
307Dic3⋊C4—68no—
308Dic3⋊C4—68no—
309Dic3⋊C4C22×D314yes—
310Dic3⋊C4C22×D314yes—
311C4×Dic3—38no—
312C4×Dic3—38no—
313C4×Dic3C22×D314yes—
314C22×C32C22×Q812yes—
315C22×C32H(5,𝔽2)12yes—
316C22×C322−1+412yes—
317C22×C32C2511yescharacteristic
318C2×C3×D3—28no—
319C2×C3×D3—22no—
320C2×C3×D3—22no—
321C2×C3×D3C22×Q814yes—
322C32×C4—22no—
323C32×C4—22no—
324C32×C4C22×Q814yes—
325C3⋊Dic3—24no—
326C3⋊Dic3—24no—
327C3×Dic3—24no—
328C3×Dic3—22no—
329C3×Dic3—24no—
330C3×Dic3—22no—
331C3×Dic3C22×Q814yes—
332C22×Q8—32no—
333C22×Q8—92no—
334C23×C4—31no—
335C23×C4—92no—
336C4⋊Q8—38no—
337C4⋊Q8—98no—
338C4⋊Q8—916no—
339#125—98no—
340#125—916no—
341#125—98no—
342C22⋊Q8—916no—
343C22⋊Q8—916no—
344#117—38no—
345#117—98no—
346C2×C4⋊C4—31no—
347C2×C4⋊C4—31no—
348C2×C4⋊C4—31no—
349C2×C4⋊C4—31no—
350C2×C4⋊C4—32no—
351C2×C4⋊C4—98no—
352C2×C4⋊C4—92no—
353C2×C4⋊C4—92no—
354C2×C4⋊C4—92no—
355C2×C4⋊C4—92no—
356C2×C4⋊C4—91no—
357C2×C4⋊C4—91no—
358C2×C4⋊C4—92no—
359C2×C4⋊C4—92no—
360C2×C22⋊C4—31no—
361C2×C22⋊C4—31no—
362C2×C22⋊C4—92no—
363C2×C42—31no—
364C2×C42—92no—
365C2×C42D3211yescharacteristic
366C23×C3—21no—
367C23×C3—34no—
368C23×C3—32no—
369C23×C3—62no—
370C23×C3—62no—
371C23×C3C23×D311yescharacteristic
372C23×C3C23×D311yescharacteristic
373C22×D3—22no—
374C22×D3—22no—
375C22×D3C2×Dic614yes—
376C22×D3C23×D312yes—
377C3×Q8—128no—
378C2×C3×C4—22no—
379C2×C3×C4—22no—
380C2×C3×C4—22no—
381C2×C3×C4—22no—
382C2×C3×C4—22no—
383C2×C3×C4—22no—
384C2×C3×C4—22no—
385C2×C3×C4—24no—
386C2×C3×C4—34no—
387C2×C3×C4—32no—
388C2×C3×C4—316no—
389C2×C3×C4—34no—
390C2×C3×C4—32no—
391C2×C3×C4—34no—
392C2×C3×C4—32no—
393C2×C3×C4—42no—
394C2×C3×C4—42no—
395C2×C3×C4—62no—
396C2×C3×C4—62no—
397C2×C3×C4—64no—
398C2×C3×C4—64no—
399C2×C3×C4C2×Dic614yes—
400C2×C3×C4D3×Q814yes—
401C2×C3×C4C23×D312yes—
402C2×C3×C4C23×D312yes—
403C2×C3×C4C23×D312yes—
404C2×C3×C4C23×D312yes—
405C2×C3×C4C23×D312yes—
406C2×C3×C4C23×D312yes—
407C2×Dic3—24no—
408C2×Dic3—24no—
409C2×Dic3—22no—
410C2×Dic3—22no—
411C2×Dic3—34no—
412C2×Dic3—34no—
413C2×Dic3—34no—
414C2×Dic3—34no—
415C2×Dic3—64no—
416C2×Dic3—64no—
417C2×Dic3—64no—
418C2×Dic3—64no—
419C2×Dic3—64no—
420C2×Dic3—64no—
421C2×Dic3—124no—
422C2×Dic3—124no—
423C2×Dic3—128no—
424C2×Dic3C2×Dic614yes—
425C2×Dic3C23×D314yes—
426C2×Dic3C23×D312yes—
427C2×Dic3C23×D312yes—
428C2×Dic3C23×D314yes—
429C2×Dic3C23×D312yes—
430C4×D3—128no—
431C4×D3C2×Dic6116yescomplemented
432Dic6—48no—
433Dic6—128no—
434Dic6—128no—
435C2×C32#54414yescomplemented
436C2×C32C23×Q811yescharacteristic
437C2×C32C2×H(5,𝔽2)11yescharacteristic
438C2×C32C2×2−1+411yescharacteristic
439C3×D3—24no—
440C24—31no—
441C2×Q8—38no—
442C2×Q8—98no—
443C2×Q8—124no—
444C2×Q8—364no—
445C22×C4—31no—
446C22×C4—34no—
447C22×C4—38no—
448C22×C4—31no—
449C22×C4—31no—
450C22×C4—32no—
451C22×C4—32no—
452C22×C4—98no—
453C22×C4—92no—
454C22×C4—92no—
455C22×C4—364no—
456C22×C4C2×D3211yescharacteristic
457C22×C4C2×D3211yescharacteristic
458C22×C4C2×D3211yescharacteristic
459C4⋊C4—34no—
460C4⋊C4—34no—
461C4⋊C4—34no—
462C4⋊C4—34no—
463C4⋊C4—38no—
464C4⋊C4—98no—
465C4⋊C4—98no—
466C4⋊C4—98no—
467C4⋊C4—98no—
468C4⋊C4—94no—
469C4⋊C4—94no—
470C4⋊C4—98no—
471C4⋊C4—98no—
472C22⋊C4—34no—
473C22⋊C4—34no—
474C22⋊C4—98no—
475C42—34no—
476C42—98no—
477C42C2×D3214yes—
478C22×C3—22no—
479C22×C3—22no—
480C22×C3—22no—
481C22×C3—21no—
482C22×C3—34no—
483C22×C3—62no—
484C22×C3—62no—
485C22×C3—68no—
486C22×C3C22×Dic612yes—
487C22×C3#100412yes—
488C22×C3C2×D3×Q812yes—
489C22×C3#100712yes—
490C22×C3#100912yes—
491C22×C3#101012yes—
492C22×C3C24×D311yescharacteristic
493C22×C3C24×D311yescharacteristic
494C2×D3—22no—
495C2×D3—22no—
496C2×D3—28no—
497C2×D3C22×Dic614yes—
498C3×C4—22no—
499C3×C4—22no—
500C3×C4—22no—
501C3×C4—22no—
502C3×C4—24no—
503C3×C4—34no—
504C3×C4—42no—
505C3×C4—42no—
506C3×C4—62no—
507C3×C4—62no—
508C3×C4—64no—
509C3×C4—64no—
510C3×C4C22×Dic614yes—
511C3×C4C2×D3×Q814yes—
512Dic3—24no—
513Dic3—24no—
514Dic3—22no—
515Dic3—22no—
516Dic3—64no—
517Dic3—64no—
518Dic3—64no—
519Dic3—64no—
520Dic3—124no—
521Dic3—124no—
522Dic3C22×Dic614yes—
523C32C2×#54411yescharacteristic, complemented, Sylow
524C23—34no—
525C23—32no—
526C23—62no—
527C23—62no—
528C23C22×D3211yescharacteristic
529Q8—128no—
530Q8—368no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—34no—
534C2×C4—32no—
535C2×C4—316no—
536C2×C4—32no—
537C2×C4—32no—
538C2×C4—34no—
539C2×C4—34no—
540C2×C4—62no—
541C2×C4—64no—
542C2×C4—64no—
543C2×C4—62no—
544C2×C4—94no—
545C2×C4—94no—
546C2×C4—184no—
547C2×C4—184no—
548C2×C4—368no—
549C2×C4D3×Dic614yes—
550C2×C4C22×D3212yes—
551C2×C4C22×D3212yes—
552C2×C4C22×D3212yes—
553C2×C3—21no—
554C2×C3—21no—
555C2×C3—21no—
556C2×C3—24no—
557C2×C3—64no—
558C2×C3#551914yescomplemented
559C2×C3#572914yescomplemented
560C2×C3C23×Dic611yescharacteristic
561C2×C3C2×#100411yescharacteristic
562C2×C3C22×D3×Q811yescharacteristic
563C2×C3C2×#100711yescharacteristic
564C2×C3C2×#100911yescharacteristic
565C2×C3C2×#101011yescharacteristic
566D3—24no—
567C22—34no—
568C22—62no—
569C22—62no—
570C22—68no—
571C22C2×D3×Dic612yes—
572C22#6429712yes—
573C22#6430712yes—
574C22C23×D3211yescharacteristic
575C4—22no—
576C4—22no—
577C4—34no—
578C4—62no—
579C4—64no—
580C4—64no—
581C4—62no—
582C4—184no—
583C4—184no—
584C4C2×D3×Dic614yes—
585C3—21no—
586C3C2×#551911yescharacteristic, complemented
587C3C2×#572911yescharacteristic, complemented
588C2—64no—
589C2#1059395414yesdirect product factor
590C2C22×D3×Dic611yescharacteristic
591C2C2×#6429711yescharacteristic
592C2C2×#6430711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
socleC23×C32C24
prime radicalC23×C3×D3C23
hypercenterC2×C42D32
hypocenterC32C2×#544
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×#64079C2semidirect
3. C2×C3×#869C2semidirect
4. C2×#63918C2semidirect
8. C2×#63869C2semidirect
9. C2×#63846C2semidirect
11. C2×#63839C2semidirect
12. #10593954C2direct (N × H)
24. #64079C22semidirect
34. C3×#869C22semidirect
41. #63918C22semidirect
45. #63869C22semidirect
46. #63846C22semidirect
48. #63839C22semidirect
73. C2×#869D3semidirect
85. C2×C3×C4×D3Q8semidirect
186. #869C2×D3semidirect
212. C3×C4×D3C2×Q8semidirect
263. C2×C4×D3Dic6semidirect
431. C4×D3C2×Dic6semidirect
435. C2×C32#544semidirect
523. C32C2×#544semidirect
558. C2×C3#5519semidirect
559. C2×C3#5729semidirect
586. C3C2×#5519semidirect
587. C3C2×#5729semidirect
589. C2#10593954direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640792
C2×C3×#8722
C2×C3×#8692
C2×#639182
C2×#638992
C2×D3×C4⋊Dic32
C2×#638872
C2×#638692
C2×#638462
C2×#638412
C2×#638392
#105939542
C2×#57293
C2×#55193