Finite Group Databasebeta

← C2×#10595176 #11902956

Subgroups — C2×#10595176 #11902956

Order 1152.

2827 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64144C211yesmaximal, characteristic, complemented
2C2×C3×#937C211yesmaximal, characteristic
3C2×C3×#936C211yesmaximal, characteristic, complemented
4C2×#67⋊Dic3C212yesmaximal, complemented
5C2×#63969C212yesmaximal, complemented
6C2×D3×#217C212yesmaximal, complemented
7C2×#63956C212yesmaximal, complemented
8#10595176C2116yesmaximal, direct product factor
9C2×#63887C212yesmaximal, complemented
10C2×#63877C212yesmaximal, complemented
11C2×#5679—31nomaximal
12C2×#5587—31nomaximal
13C24×C3×D3C2211yescharacteristic
14C22×C32×D4C2211yescharacteristic
15C23×C3⋊Dic3C2211yescharacteristic, complemented
16C22×C3×#67C2212yes—
17C22×C3×Dic6C2211yescharacteristic, complemented
18C22×D3×Dic3C2212yes—
19C22×D3×Dic3C2212yes—
20C2×#3757C2212yes—
21C2×#3757C2211yescharacteristic, complemented
22#64144C2218yescomplemented
23C2×#3750C2212yescomplemented
24C2×C3×#217C2212yes—
25C2×C3×#217C2211yescharacteristic
26C2×C3×#217C2212yescomplemented
27C3×#937C2218yes—
28C3×#936C2218yescomplemented
29C2×C3×(C2×D3)⋊C4C2212yes—
30C2×C3×C4×Dic3C2211yescharacteristic, complemented
31#67⋊Dic3C22116yescomplemented
32#63969C22116yescomplemented
33D3×#217C22116yescomplemented
34C2×#3724C2212yescomplemented
35C2×Dic3⋊Dic3C2212yescomplemented
36C2×Dic3⋊Dic3C2212yescomplemented
37C2×(C2×D3)⋊Dic3C2212yes—
38C2×(C2×D3)⋊Dic3C2212yes—
39#63956C22116yescomplemented
40C2×Dic32C2212yescomplemented
41#63887C22116yescomplemented
42#63877C22116yescomplemented
43C2×C3×#124—31no—
44C2×C3×#120—31no—
45C22×#217—32no—
46C2×#946—32no—
47C2×#937D311yescharacteristic
48C2×#936D311yescharacteristic, complemented
49C2×#935—31no—
50C2×#935—31no—
51C2×#935—32no—
52C2×#935—61no—
53C2×D4×Dic3—32no—
54#5679—316no—
55#5587—316no—
56C2×#883—32no—
57C2×#67⋊C4—32no—
58C2×D3×C22⋊C4—32no—
59C2×#879—32no—
60C2×#879—32no—
61C2×#878—32no—
62C2×#877—32no—
63C2×#872—32no—
64C24×C32C2311yescharacteristic
65C24×C32C2311yescharacteristic
66C23×C3×D3—28no—
67C23×C3×D3—42no—
68C23×C3×D3C2314yes—
69C23×C3×D3C2312yes—
70C2×C32×D4—42no—
71C2×C32×D4C2314yes—
72C22×C32×C4C2311yescharacteristic
73C22×C3⋊Dic3—42no—
74C22×C3⋊Dic3C2312yes—
75C22×C3⋊Dic3C2312yes—
76C22×C3⋊Dic3C2314yescomplemented
77C2×C3×#67—28no—
78C2×C3×#67C2318yes—
79C22×C3×Dic3C2312yes—
80C22×C3×Dic3C2312yes—
81C22×C3×Dic3C2312yes—
82C2×C3×Dic6—42no—
83C2×C3×Dic6C2314yescomplemented
84C2×D3×Dic3—28no—
85C2×D3×Dic3—44no—
86C2×D3×Dic3C2318yes—
87C2×D3×Dic3C2318yes—
88#3757C2318yes—
89#3757C2314yescomplemented
90#3750C2318yescomplemented
91C3×#217C2318yes—
92C3×#217C2314yes—
93C3×#217C2318yescomplemented
94C3×(C2×D3)⋊C4C2318yes—
95C3×C4×Dic3C2314yescomplemented
96#3724C2318yescomplemented
97Dic3⋊Dic3C2318yescomplemented
98Dic3⋊Dic3C2318yescomplemented
99(C2×D3)⋊Dic3C2318yes—
100(C2×D3)⋊Dic3C2318yes—
101Dic32C2318yescomplemented
102C2×#551—91noSylow
103C25×C3—31no—
104C24×D3C2×D311yescharacteristic
105C22×C3×Q8—31no—
106C22×C3×D4—21no—
107C22×C3×D4—32no—
108C22×C3×D4C2×D311yescharacteristic
109C22×C3×D4C2×D311yescharacteristic
110C22×#67C2×D312yes—
111C23×Dic3—31no—
112C23×Dic3—31no—
113C23×Dic3—32no—
114C23×Dic3—32no—
115C23×Dic3—61no—
116C22×C4×D3—32no—
117C22×C4×D3—32no—
118C22×Dic6C2×D311yescharacteristic, complemented
119C3×#124—38no—
120C3×#120—38no—
121C2×C3×C22⋊C4—31no—
122C2×C3×C22⋊C4—32no—
123C2×C3×C22⋊C4—32no—
124C2×C3×C22⋊C4—32no—
125C2×C3×C42—31no—
126C2×#217—32no—
127C2×#217—32no—
128C2×#217—31no—
129C2×#217—31no—
130C2×#217—32no—
131C2×#217—32no—
132C2×#217—316no—
133C2×#217—62no—
134C2×#217—61no—
135C2×#217C2×D311yescharacteristic
136C2×#217C2×D312yes—
137C2×#217C2×D312yescomplemented
138#946—316no—
139#937C2×D318yes—
140#936C2×D318yescomplemented
141#935—38no—
142#935—38no—
143#935—316no—
144#935—68no—
145D4×Dic3—316no—
146C2×(C2×D3)⋊C4—32no—
147C2×(C2×D3)⋊C4—32no—
148C2×(C2×D3)⋊C4C2×D312yes—
149C2×C4⋊Dic3—32no—
150C2×C4⋊Dic3—32no—
151C2×Dic3⋊C4—32no—
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×C4×Dic3—32no—
159C2×C4×Dic3—32no—
160C2×C4×Dic3C2×D311yescharacteristic, complemented
161#883—316no—
162#67⋊C4—316no—
163D3×C22⋊C4—316no—
164#879—316no—
165#879—316no—
166#878—316no—
167#877—316no—
168#872—316no—
169C23×C32—22no—
170C23×C32—24no—
171C23×C32—24no—
172C23×C32—22no—
173C23×C32C2412yes—
174C23×C32C2412yes—
175C23×C32C2411yescharacteristic
176C22×C3×D3—24no—
177C22×C3×D3—24no—
178C22×C3×D3—216no—
179C22×C3×D3—44no—
180C22×C3×D3—416no—
181C22×C3×D3#4118yes—
182C22×C3×D3C2414yes—
183C32×D4—44no—
184C2×C32×C4—22no—
185C2×C32×C4C2412yes—
186C2×C3⋊Dic3—24no—
187C2×C3⋊Dic3—24no—
188C2×C3⋊Dic3—44no—
189C2×C3⋊Dic3C2414yes—
190C2×C3⋊Dic3C2414yes—
191C3×#67—216no—
192C2×C3×Dic3—24no—
193C2×C3×Dic3—24no—
194C2×C3×Dic3—24no—
195C2×C3×Dic3C2414yes—
196C2×C3×Dic3C2414yes—
197C2×C3×Dic3C2414yes—
198C3×Dic6—44no—
199D3×Dic3—216no—
200D3×Dic3—48no—
201#551—916no—
202C2×#126—92no—
203C2×#124—31no—
204C2×#123—92no—
205C2×#123—91no—
206C2×C22⋊Q8—92no—
207C2×#120—31no—
208C2×C4×D4—92no—
209C2×#117—92no—
210C22×C22⋊C4—92no—
211C24×C3—21no—
212C24×C3—21no—
213C24×C3—32no—
214C24×C3—34no—
215C24×C3—68no—
216C24×C3—122no—
217C24×C3C22×D311yescharacteristic
218C24×C3C22×D311yescharacteristic
219C24×C3C22×D311yescharacteristic
220C24×C3C22×D311yescharacteristic
221C23×D3—28no—
222C23×D3—42no—
223C23×D3C22×D314yes—
224C23×D3C22×D312yes—
225C2×C3×Q8—34no—
226C2×C3×Q8—122no—
227C2×C3×D4—24no—
228C2×C3×D4—38no—
229C2×C3×D4—42no—
230C2×C3×D4—42no—
231C2×C3×D4—44no—
232C2×C3×D4—68no—
233C2×C3×D4C22×D314yes—
234C2×C3×D4C22×D314yes—
235C22×C3×C4—21no—
236C22×C3×C4—32no—
237C22×C3×C4—32no—
238C22×C3×C4—32no—
239C22×C3×C4C22×D311yescharacteristic
240C22×C3×C4C22×D311yescharacteristic
241C2×#67—28no—
242C2×#67C22×D318yes—
243C22×Dic3—32no—
244C22×Dic3—32no—
245C22×Dic3—32no—
246C22×Dic3—32no—
247C22×Dic3—34no—
248C22×Dic3—34no—
249C22×Dic3—38no—
250C22×Dic3—38no—
251C22×Dic3—62no—
252C22×Dic3—62no—
253C22×Dic3—64no—
254C22×Dic3—68no—
255C22×Dic3—124no—
256C22×Dic3—122no—
257C22×Dic3—122no—
258C22×Dic3—124no—
259C22×Dic3C22×D312yes—
260C22×Dic3C22×D312yes—
261C22×Dic3C22×D312yes—
262C2×C4×D3—38no—
263C2×C4×D3—38no—
264C2×C4×D3—68no—
265C2×C4×D3—124no—
266C2×Dic6—42no—
267C2×Dic6C22×D314yescomplemented
268C3×C22⋊C4—34no—
269C3×C22⋊C4—38no—
270C3×C22⋊C4—38no—
271C3×C22⋊C4—38no—
272C3×C42—34no—
273#217—38no—
274#217—38no—
275#217—34no—
276#217—34no—
277#217—38no—
278#217—38no—
279#217—68no—
280#217—64no—
281#217C22×D314yes—
282#217C22×D318yes—
283#217C22×D318yescomplemented
284(C2×D3)⋊C4—38no—
285(C2×D3)⋊C4—38no—
286(C2×D3)⋊C4C22×D318yes—
287C4⋊Dic3—38no—
288C4⋊Dic3—38no—
289Dic3⋊C4—38no—
290Dic3⋊C4—38no—
291Dic3⋊C4—38no—
292Dic3⋊C4—38no—
293Dic3⋊C4—38no—
294Dic3⋊C4—38no—
295Dic3⋊C4—68no—
296C4×Dic3—38no—
297C4×Dic3—38no—
298C4×Dic3C22×D314yescomplemented
299C22×C32—22no—
300C22×C32—24no—
301C22×C32—24no—
302C22×C32—22no—
303C22×C32—44no—
304C22×C32—44no—
305C22×C32C2×#4114yes—
306C22×C32H(5,𝔽2)12yes—
307C22×C32C2511yescharacteristic
308C2×C3×D3—216no—
309C2×C3×D3—24no—
310C2×C3×D3—24no—
311C2×C3×D3—416no—
312C2×C3×D3C2×#4118yes—
313C32×C4—22no—
314C3⋊Dic3—24no—
315C3⋊Dic3—24no—
316C3×Dic3—24no—
317C3×Dic3—24no—
318C3×Dic3—24no—
319C25—31no—
320C22×Q8—31no—
321C22×D4—32no—
322C22×D4D3211yescharacteristic
323C23×C4—92no—
324C23×C4—92no—
325C23×C4—91no—
326#126—916no—
327#124—38no—
328#123—916no—
329#123—98no—
330C22⋊Q8—916no—
331#120—38no—
332C4×D4—916no—
333#117—916no—
334C2×C4⋊C4—92no—
335C2×C4⋊C4—92no—
336C2×C4⋊C4—92no—
337C2×C4⋊C4—92no—
338C2×C22⋊C4—32no—
339C2×C22⋊C4—32no—
340C2×C22⋊C4—31no—
341C2×C22⋊C4—32no—
342C2×C22⋊C4—916no—
343C2×C22⋊C4—92no—
344C2×C22⋊C4—92no—
345C2×C22⋊C4—92no—
346C2×C22⋊C4—91no—
347C2×C42—31no—
348C2×C42—92no—
349C23×C3—24no—
350C23×C3—24no—
351C23×C3—24no—
352C23×C3—22no—
353C23×C3—22no—
354C23×C3—22no—
355C23×C3—22no—
356C23×C3—24no—
357C23×C3—24no—
358C23×C3—22no—
359C23×C3—22no—
360C23×C3—21no—
361C23×C3—38no—
362C23×C3—34no—
363C23×C3—44no—
364C23×C3—42no—
365C23×C3—44no—
366C23×C3—616no—
367C23×C3—64no—
368C23×C3—64no—
369C23×C3—124no—
370C23×C3—1216no—
371C23×C3C23×D312yes—
372C23×C3C23×D312yes—
373C23×C3C23×D312yes—
374C23×C3C23×D312yes—
375C23×C3C23×D311yescharacteristic
376C23×C3C23×D311yescharacteristic
377C22×D3—24no—
378C22×D3—24no—
379C22×D3—216no—
380C22×D3—44no—
381C22×D3—416no—
382C22×D3#23718yes—
383C22×D3C23×D314yes—
384C3×Q8—124no—
385C3×D4—44no—
386C3×D4—44no—
387C3×D4—48no—
388C3×D4—616no—
389C2×C3×C4—22no—
390C2×C3×C4—22no—
391C2×C3×C4—22no—
392C2×C3×C4—34no—
393C2×C3×C4—34no—
394C2×C3×C4—34no—
395C2×C3×C4—42no—
396C2×C3×C4—64no—
397C2×C3×C4—64no—
398C2×C3×C4—64no—
399C2×C3×C4C23×D312yes—
400C2×C3×C4C23×D312yes—
401#67—216no—
402C2×Dic3—24no—
403C2×Dic3—24no—
404C2×Dic3—24no—
405C2×Dic3—34no—
406C2×Dic3—34no—
407C2×Dic3—34no—
408C2×Dic3—34no—
409C2×Dic3—64no—
410C2×Dic3—64no—
411C2×Dic3—616no—
412C2×Dic3—64no—
413C2×Dic3—64no—
414C2×Dic3—64no—
415C2×Dic3—64no—
416C2×Dic3—124no—
417C2×Dic3—124no—
418C2×Dic3—128no—
419C2×Dic3—124no—
420C2×Dic3—124no—
421C2×Dic3—128no—
422C2×Dic3C23×D314yes—
423C2×Dic3C23×D314yes—
424C2×Dic3C23×D314yes—
425C4×D3—616no—
426C4×D3—128no—
427Dic6—44no—
428C2×C32—42no—
429C2×C32—42no—
430C2×C32#55114yescomplemented
431C2×C32C22×#4112yes—
432C2×C32C2×H(5,𝔽2)11yescharacteristic
433C3×D3—28no—
434C24—32no—
435C24—34no—
436C24—68no—
437C24—122no—
438C24C2×D3211yescharacteristic
439C24C2×D3211yescharacteristic
440C2×Q8—34no—
441C2×Q8—122no—
442C2×D4—38no—
443C2×D4—42no—
444C2×D4—68no—
445C2×D4C2×D3214yes—
446C22×C4—32no—
447C22×C4—32no—
448C22×C4—32no—
449C22×C4—98no—
450C22×C4—98no—
451C22×C4—92no—
452C22×C4—92no—
453C22×C4—94no—
454C22×C4—188no—
455C22×C4—364no—
456C22×C4—362no—
457C22×C4C2×D3211yescharacteristic
458C4⋊C4—98no—
459C4⋊C4—98no—
460C4⋊C4—98no—
461C4⋊C4—98no—
462C22⋊C4—38no—
463C22⋊C4—38no—
464C22⋊C4—34no—
465C22⋊C4—38no—
466C22⋊C4—98no—
467C22⋊C4—98no—
468C22⋊C4—98no—
469C22⋊C4—94no—
470C42—34no—
471C42—98no—
472C22×C3—24no—
473C22×C3—24no—
474C22×C3—24no—
475C22×C3—22no—
476C22×C3—22no—
477C22×C3—22no—
478C22×C3—22no—
479C22×C3—24no—
480C22×C3—24no—
481C22×C3—24no—
482C22×C3—22no—
483C22×C3—21no—
484C22×C3—38no—
485C22×C3—44no—
486C22×C3—42no—
487C22×C3—44no—
488C22×C3—48no—
489C22×C3—44no—
490C22×C3—44no—
491C22×C3—44no—
492C22×C3—44no—
493C22×C3—616no—
494C22×C3—64no—
495C22×C3—64no—
496C22×C3—84no—
497C22×C3—1216no—
498C22×C3C2×#23714yes—
499C22×C3#100412yes—
500C22×C3#100412yes—
501C22×C3D3×#4114yes—
502C22×C3C24×D311yescharacteristic
503C22×C3C24×D311yescharacteristic
504C2×D3—24no—
505C2×D3—24no—
506C2×D3—216no—
507C2×D3—416no—
508C2×D3C2×#23718yes—
509C3×C4—22no—
510C3×C4—22no—
511C3×C4—42no—
512C3×C4—64no—
513C3×C4—64no—
514C3×C4—64no—
515Dic3—24no—
516Dic3—24no—
517Dic3—24no—
518Dic3—64no—
519Dic3—64no—
520Dic3—64no—
521Dic3—64no—
522Dic3—124no—
523Dic3—124no—
524C32C2×#55111yescharacteristic, complemented, Sylow
525C23—24no—
526C23—24no—
527C23—22no—
528C23—22no—
529C23—38no—
530C23—34no—
531C23—616no—
532C23—64no—
533C23—64no—
534C23—124no—
535C23—1216no—
536C23C22×D3212yes—
537C23C22×D3212yes—
538C23C22×D3211yescharacteristic
539Q8—124no—
540D4—44no—
541D4—616no—
542C2×C4—22no—
543C2×C4—34no—
544C2×C4—34no—
545C2×C4—34no—
546C2×C4—64no—
547C2×C4—64no—
548C2×C4—64no—
549C2×C4—94no—
550C2×C4—94no—
551C2×C4—1816no—
552C2×C4—184no—
553C2×C4—184no—
554C2×C4—368no—
555C2×C4—364no—
556C2×C4C22×D3212yes—
557C2×C3—22no—
558C2×C3—21no—
559C2×C3—24no—
560C2×C3—44no—
561C2×C3—42no—
562C2×C3—42no—
563C2×C3—42no—
564C2×C3—42no—
565C2×C3—68no—
566C2×C3—82no—
567C2×C3#558714yescomplemented
568C2×C3#567914yescomplemented
569C2×C3C22×#23712yes—
570C2×C3C2×#100411yescharacteristic
571C2×C3C2×#100411yescharacteristic
572C2×C3C2×D3×#4112yes—
573D3—28no—
574C22—24no—
575C22—24no—
576C22—22no—
577C22—22no—
578C22—38no—
579C22—44no—
580C22—44no—
581C22—64no—
582C22—64no—
583C22—616no—
584C22—1216no—
585C22D3×#23714yes—
586C22#6433012yes—
587C22C23×D3211yescharacteristic
588C4—22no—
589C4—64no—
590C4—64no—
591C4—64no—
592C4—184no—
593C4—184no—
594C3—21no—
595C3C2×#558711yescharacteristic, complemented
596C3C2×#567911yescharacteristic, complemented
597C2—42no—
598C2—42no—
599C2—68no—
600C2#1059517614yesdirect product factor
601C2C2×D3×#23712yes—
602C2C2×#6433011yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×D4C22
socleC23×C32C24
prime radicalC2×C3×#937C2
hypercenterC22×D4D32
hypocenterC32C2×#551
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×#64144C2semidirect
3. C2×C3×#936C2semidirect
4. C2×#67⋊Dic3C2semidirect
5. C2×#63969C2semidirect
6. C2×D3×#217C2semidirect
7. C2×#63956C2semidirect
8. #10595176C2direct (N × H)
9. C2×#63887C2semidirect
10. C2×#63877C2semidirect
15. C23×C3⋊Dic3C22semidirect
17. C22×C3×Dic6C22semidirect
21. C2×#3757C22semidirect
22. #64144C22semidirect
23. C2×#3750C22semidirect
26. C2×C3×#217C22semidirect
28. C3×#936C22semidirect
30. C2×C3×C4×Dic3C22semidirect
31. #67⋊Dic3C22semidirect
32. #63969C22semidirect
33. D3×#217C22semidirect
34. C2×#3724C22semidirect
35. C2×Dic3⋊Dic3C22semidirect
36. C2×Dic3⋊Dic3C22semidirect
39. #63956C22semidirect
40. C2×Dic32C22semidirect
41. #63887C22semidirect
42. #63877C22semidirect
48. C2×#936D3semidirect
76. C22×C3⋊Dic3C23semidirect
83. C2×C3×Dic6C23semidirect
89. #3757C23semidirect
90. #3750C23semidirect
93. C3×#217C23semidirect
95. C3×C4×Dic3C23semidirect
96. #3724C23semidirect
97. Dic3⋊Dic3C23semidirect
98. Dic3⋊Dic3C23semidirect
101. Dic32C23semidirect
118. C22×Dic6C2×D3semidirect
137. C2×#217C2×D3semidirect
140. #936C2×D3semidirect
160. C2×C4×Dic3C2×D3semidirect
267. C2×Dic6C22×D3semidirect
283. #217C22×D3semidirect
298. C4×Dic3C22×D3semidirect
430. C2×C32#551semidirect
524. C32C2×#551semidirect
567. C2×C3#5587semidirect
568. C2×C3#5679semidirect
595. C3C2×#5587semidirect
596. C3C2×#5679semidirect
600. C2#10595176direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641442
C2×C3×#9372
C2×C3×#9362
C2×#67⋊Dic32
C2×#639692
C2×D3×#2172
C2×#639562
#105951762
C2×#638872
C2×#638772
C2×#56793
C2×#55873