Finite Group Databasebeta

← C2×#10594658 #11901346

Subgroups — C2×#10594658 #11901346

Order 1152.

2885 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×#64104C211yesmaximal, characteristic, complemented
2C2×C3×#898C212yesmaximal, complemented
3C2×#63923C212yesmaximal, complemented
4C2×#63921C211yesmaximal, characteristic, complemented
5C2×#63910C212yesmaximal, complemented
6C2×#63894C212yesmaximal, complemented
7C2×#63865C211yesmaximal, characteristic, complemented
8C2×#63854C212yesmaximal, complemented
9C2×#63852C212yesmaximal, complemented
10#10594658C2116yesmaximal, direct product factor
11C2×#5704—32nomaximal
12C23×D32C2211yescharacteristic
13C22×C4⋊(C3⋊D3)C2212yes—
14C22×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
15C22×C4×C3⋊D3C2211yescharacteristic
16C22×#627C2211yescharacteristic, complemented
17C22×#626C2212yes—
18C22×#626C2212yes—
19C22×#624C2211yescharacteristic
20C22×#624C2212yescomplemented
21C2×C32×C4⋊C4C2211yescharacteristic, complemented
22C2×#3752C2212yescomplemented
23#64104C2218yescomplemented
24C2×C3×(C2×D3)⋊C4C2212yes—
25C2×C3×(C2×D3)⋊C4C2212yes—
26C2×C3×(C2×D3)⋊C4C2212yes—
27C2×C3×C4⋊Dic3C2212yescomplemented
28C2×C3×Dic3⋊C4C2212yescomplemented
29C2×C3×C4×Dic3C2212yescomplemented
30C3×#898C22116yescomplemented
31C2×#3724C2211yescharacteristic, complemented
32C2×#3722C2212yes—
33C2×#3722C2212yescomplemented
34C2×(C2×D3)⋊Dic3C2212yes—
35#63923C22116yescomplemented
36#63921C2218yescomplemented
37#63910C22116yescomplemented
38#63894C22116yescomplemented
39#63865C2218yescomplemented
40#63854C22116yescomplemented
41#63852C22116yescomplemented
42C2×C3×#126—32no—
43#5704—332no—
44C2×#898D312yescomplemented
45C2×#896—32no—
46C2×#895—32no—
47C2×#895—32no—
48C2×#895—61no—
49C2×#894—32no—
50C2×#893—32no—
51C2×#885—32no—
52C2×#884—32no—
53C2×#883—32no—
54C2×#882—32no—
55C2×#882—32no—
56C2×D3×C22⋊C4—32no—
57C2×#875—32no—
58C2×C4×D12—32no—
59C23×C3⋊D3C2312yes—
60C23×C3⋊D3C2311yescharacteristic
61C23×C3×D3C2312yes—
62C22×D32—24no—
63C22×D32—42no—
64C22×D32—42no—
65C22×D32C2314yes—
66C22×C32×C4C2312yes—
67C22×C32×C4C2311yescharacteristic
68C22×C3⋊Dic3C2311yescharacteristic
69C2×C4⋊(C3⋊D3)—28no—
70C2×C4⋊(C3⋊D3)—42no—
71C2×C4⋊(C3⋊D3)C2318yes—
72C2×C4⋊(C3⋊D3)C2314yescomplemented
73C2×C4×C3⋊D3—42no—
74C2×C4×C3⋊D3C2314yes—
75C22×C3×Dic3C2312yes—
76C22×C3×Dic3C2312yes—
77C22×C3×Dic3C2312yes—
78C2×#627—42no—
79C2×#627C2314yescomplemented
80C2×#626—44no—
81C2×#626—44no—
82C2×#626C2318yes—
83C2×#626C2318yes—
84C2×#624—42no—
85C2×#624—44no—
86C2×#624C2314yes—
87C2×#624C2318yescomplemented
88C32×C4⋊C4C2314yescomplemented
89#3752C2318yescomplemented
90C3×(C2×D3)⋊C4C2318yes—
91C3×(C2×D3)⋊C4C2318yes—
92C3×(C2×D3)⋊C4C2318yes—
93C3×C4⋊Dic3C2318yescomplemented
94C3×Dic3⋊C4C2318yescomplemented
95C3×C4×Dic3C2318yescomplemented
96#3724C2314yescomplemented
97#3722C2318yes—
98#3722C2318yescomplemented
99(C2×D3)⋊Dic3C2318yes—
100C2×#538—91noSylow
101C24×D3—32no—
102C22×#67—32no—
103C22×#67—32no—
104C22×D12—32no—
105C22×D12—32no—
106C22×D12—32no—
107C22×D12—32no—
108C22×D12—32no—
109C22×D12—62no—
110C22×D12—61no—
111C22×C4×D3—32no—
112C22×C4×D3—32no—
113C22×C4×D3—32no—
114C22×C4×D3—32no—
115C22×C4×D3—61no—
116C22×Dic6—32no—
117C3×#126—316no—
118C2×C3×C4⋊C4—21no—
119C2×C3×C4⋊C4—32no—
120C2×C3×C4⋊C4—32no—
121C2×C3×C4⋊C4C2×D312yescomplemented
122C2×C3×C22⋊C4—32no—
123C2×C3×C22⋊C4—32no—
124C2×C3×C22⋊C4—32no—
125C2×C3×C42—32no—
126C2×#217—32no—
127C2×(C2×D3)⋊C4—32no—
128C2×(C2×D3)⋊C4—32no—
129C2×(C2×D3)⋊C4—32no—
130C2×(C2×D3)⋊C4—32no—
131C2×(C2×D3)⋊C4—32no—
132C2×(C2×D3)⋊C4—32no—
133C2×(C2×D3)⋊C4—32no—
134C2×(C2×D3)⋊C4—62no—
135C2×(C2×D3)⋊C4C2×D312yes—
136C2×(C2×D3)⋊C4C2×D312yes—
137C2×(C2×D3)⋊C4C2×D312yes—
138C2×C4⋊Dic3C2×D312yescomplemented
139C2×Dic3⋊C4—32no—
140C2×Dic3⋊C4C2×D312yescomplemented
141C2×C4×Dic3C2×D312yescomplemented
142#898C2×D3116yescomplemented
143#896—316no—
144#895—316no—
145#895—316no—
146#895—68no—
147#894—316no—
148#893—316no—
149#885—316no—
150#884—316no—
151#883—316no—
152#882—316no—
153#882—316no—
154D3×C22⋊C4—316no—
155#875—316no—
156C4×D12—316no—
157C23×C32C2411yescharacteristic
158C22×C3⋊D3—22no—
159C22×C3⋊D3—22no—
160C22×C3⋊D3—24no—
161C22×C3⋊D3—24no—
162C22×C3⋊D3—24no—
163C22×C3⋊D3#4114yes—
164C22×C3⋊D3C2414yes—
165C22×C3⋊D3C2412yes—
166C22×C3×D3—24no—
167C22×C3×D3—24no—
168C22×C3×D3—24no—
169C22×C3×D3C2414yes—
170C2×D32—28no—
171C2×D32—44no—
172C2×D32—44no—
173C2×D32—416no—
174C2×C32×C4—22no—
175C2×C32×C4—24no—
176C2×C32×C4C2414yes—
177C2×C32×C4C2412yes—
178C2×C3⋊Dic3—22no—
179C2×C3⋊Dic3C2412yes—
180C4⋊(C3⋊D3)—216no—
181C4⋊(C3⋊D3)—44no—
182C4×C3⋊D3—44no—
183C2×C3×Dic3—24no—
184C2×C3×Dic3—24no—
185C2×C3×Dic3—24no—
186C2×C3×Dic3C2414yes—
187C2×C3×Dic3C2414yes—
188C2×C3×Dic3C2414yes—
189#627—44no—
190#626—48no—
191#626—48no—
192#624—44no—
193#624—48no—
194#538—916no—
195C2×#126—32no—
196C2×#124—92no—
197C2×#123—92no—
198C2×C22⋊Q8—91no—
199C2×#121—92no—
200C2×#121—91no—
201C2×#120—92no—
202C2×C4×D4—92no—
203C22×C22⋊C4—91no—
204C24×C3—32no—
205C23×D3—32no—
206C23×D3—32no—
207C23×D3—32no—
208C23×D3—38no—
209C23×D3—61no—
210C23×D3—62no—
211C23×D3—68no—
212C23×D3—124no—
213C23×D3—124no—
214C23×D3C22×D312yes—
215C22×C3×C4—21no—
216C22×C3×C4—22no—
217C22×C3×C4—32no—
218C22×C3×C4—32no—
219C22×C3×C4—32no—
220C22×C3×C4C22×D312yes—
221C22×C3×C4C22×D312yes—
222C22×C3×C4C22×D312yes—
223C2×#67—38no—
224C2×#67—38no—
225C2×#67—124no—
226C2×#67—124no—
227C22×Dic3—32no—
228C22×Dic3—61no—
229C22×Dic3C22×D312yes—
230C22×Dic3C22×D312yes—
231C22×Dic3C22×D312yes—
232C2×D12—38no—
233C2×D12—38no—
234C2×D12—38no—
235C2×D12—38no—
236C2×D12—38no—
237C2×D12—68no—
238C2×D12—64no—
239C2×D12—68no—
240C2×D12—68no—
241C2×D12—128no—
242C2×D12—124no—
243C2×D12—124no—
244C2×D12—124no—
245C2×D12—124no—
246C2×C4×D3—38no—
247C2×C4×D3—38no—
248C2×C4×D3—38no—
249C2×C4×D3—38no—
250C2×C4×D3—64no—
251C2×C4×D3—124no—
252C2×C4×D3—124no—
253C2×C4×D3—124no—
254C2×C4×D3—124no—
255C2×C4×D3—124no—
256C2×Dic6—38no—
257C2×Dic6—124no—
258C3×C4⋊C4—24no—
259C3×C4⋊C4—38no—
260C3×C4⋊C4—38no—
261C3×C4⋊C4C22×D318yescomplemented
262C3×C22⋊C4—38no—
263C3×C22⋊C4—38no—
264C3×C22⋊C4—38no—
265C3×C42—38no—
266#217—38no—
267(C2×D3)⋊C4—38no—
268(C2×D3)⋊C4—38no—
269(C2×D3)⋊C4—38no—
270(C2×D3)⋊C4—38no—
271(C2×D3)⋊C4—38no—
272(C2×D3)⋊C4—38no—
273(C2×D3)⋊C4—38no—
274(C2×D3)⋊C4—68no—
275(C2×D3)⋊C4C22×D318yes—
276(C2×D3)⋊C4C22×D318yes—
277(C2×D3)⋊C4C22×D318yes—
278C4⋊Dic3C22×D318yescomplemented
279Dic3⋊C4—38no—
280Dic3⋊C4C22×D318yescomplemented
281C4×Dic3C22×D318yescomplemented
282C22×C32C2×#4112yes—
283C22×C32H(5,𝔽2)12yes—
284C22×C32H(5,𝔽2)12yes—
285C22×C32C2511yescharacteristic
286C2×C3⋊D3—28no—
287C2×C3⋊D3—22no—
288C2×C3⋊D3—22no—
289C2×C3⋊D3—24no—
290C2×C3⋊D3—24no—
291C2×C3⋊D3—24no—
292C2×C3⋊D3—48no—
293C2×C3⋊D3C2×#4114yes—
294C2×C3×D3—24no—
295C2×C3×D3—24no—
296C2×C3×D3—24no—
297C2×C3×D3—48no—
298D32—416no—
299C32×C4—22no—
300C32×C4—24no—
301C3⋊Dic3—22no—
302C3×Dic3—24no—
303C3×Dic3—24no—
304C3×Dic3—24no—
305C25—91no—
306C22×Q8—91no—
307C22×D4—92no—
308C22×D4—92no—
309C22×D4—92no—
310C22×D4—91no—
311C23×C4—91no—
312C23×C4—92no—
313C23×C4—91no—
314#126—316no—
315#124—916no—
316#123—916no—
317C22⋊Q8—98no—
318#121—916no—
319#121—98no—
320#120—916no—
321C4×D4—916no—
322C2×C4⋊C4—32no—
323C2×C4⋊C4—32no—
324C2×C4⋊C4—91no—
325C2×C4⋊C4D3211yescharacteristic, complemented
326C2×C22⋊C4—32no—
327C2×C22⋊C4—32no—
328C2×C22⋊C4—32no—
329C2×C22⋊C4—98no—
330C2×C22⋊C4—92no—
331C2×C22⋊C4—92no—
332C2×C22⋊C4—92no—
333C2×C22⋊C4—92no—
334C2×C42—32no—
335C23×C3—21no—
336C23×C3—34no—
337C23×C3—64no—
338C23×C3—64no—
339C23×C3—64no—
340C23×C3C23×D312yes—
341C22×D3—24no—
342C22×D3—24no—
343C22×D3—24no—
344C22×D3—38no—
345C22×D3—34no—
346C22×D3—34no—
347C22×D3—34no—
348C22×D3—64no—
349C22×D3—62no—
350C22×D3—64no—
351C22×D3—616no—
352C22×D3—64no—
353C22×D3—64no—
354C22×D3—64no—
355C22×D3—64no—
356C22×D3—64no—
357C22×D3—64no—
358C22×D3—64no—
359C22×D3—64no—
360C22×D3—122no—
361C22×D3—122no—
362C22×D3—124no—
363C22×D3—124no—
364C22×D3—124no—
365C22×D3—128no—
366C22×D3—128no—
367C22×D3—1232no—
368C22×D3C23×D314yes—
369C2×C3×C4—24no—
370C2×C3×C4—24no—
371C2×C3×C4—24no—
372C2×C3×C4—24no—
373C2×C3×C4—22no—
374C2×C3×C4—24no—
375C2×C3×C4—34no—
376C2×C3×C4—34no—
377C2×C3×C4—34no—
378C2×C3×C4—44no—
379C2×C3×C4—64no—
380C2×C3×C4—64no—
381C2×C3×C4—64no—
382C2×C3×C4C23×D314yes—
383C2×C3×C4C23×D314yes—
384C2×C3×C4C23×D314yes—
385#67—128no—
386#67—128no—
387C2×Dic3—24no—
388C2×Dic3—24no—
389C2×Dic3—24no—
390C2×Dic3—34no—
391C2×Dic3—62no—
392C2×Dic3—64no—
393C2×Dic3—122no—
394C2×Dic3C23×D314yes—
395C2×Dic3C23×D314yes—
396C2×Dic3C23×D314yes—
397D12—616no—
398D12—616no—
399D12—1216no—
400D12—128no—
401D12—128no—
402D12—128no—
403D12—128no—
404C4×D3—128no—
405C4×D3—128no—
406C4×D3—128no—
407C4×D3—128no—
408C4×D3—128no—
409Dic6—128no—
410C2×C32#53814yescomplemented
411C2×C32C22×#4111yescharacteristic
412C2×C32C2×H(5,𝔽2)11yescharacteristic
413C2×C32C2×H(5,𝔽2)11yescharacteristic
414C3⋊D3—24no—
415C3⋊D3—44no—
416C3×D3—44no—
417C24—32no—
418C24—94no—
419C24—91no—
420C24—92no—
421C24—184no—
422C24—362no—
423C24—362no—
424C2×Q8—94no—
425C2×Q8—362no—
426C2×D4—98no—
427C2×D4—98no—
428C2×D4—98no—
429C2×D4—94no—
430C2×D4—188no—
431C2×D4—362no—
432C2×D4—364no—
433C2×D4—364no—
434C22×C4—32no—
435C22×C4—32no—
436C22×C4—32no—
437C22×C4—94no—
438C22×C4—98no—
439C22×C4—91no—
440C22×C4—94no—
441C22×C4—362no—
442C22×C4—362no—
443C22×C4—364no—
444C22×C4C2×D3212yes—
445C22×C4C2×D3211yescharacteristic
446C4⋊C4—38no—
447C4⋊C4—38no—
448C4⋊C4—94no—
449C4⋊C4C2×D3214yescomplemented
450C22⋊C4—38no—
451C22⋊C4—38no—
452C22⋊C4—38no—
453C22⋊C4—98no—
454C22⋊C4—98no—
455C22⋊C4—98no—
456C22⋊C4—98no—
457C42—38no—
458C22×C3—22no—
459C22×C3—22no—
460C22×C3—22no—
461C22×C3—21no—
462C22×C3—64no—
463C22×C3—64no—
464C22×C3—64no—
465C22×C3—128no—
466C22×C3D3×#4114yes—
467C22×C3#100914yes—
468C22×C3#100914yes—
469C22×C3C24×D312yes—
470C2×D3—24no—
471C2×D3—24no—
472C2×D3—24no—
473C2×D3—38no—
474C2×D3—48no—
475C2×D3—64no—
476C2×D3—616no—
477C2×D3—64no—
478C2×D3—64no—
479C2×D3—64no—
480C2×D3—64no—
481C2×D3—64no—
482C2×D3—64no—
483C2×D3—64no—
484C2×D3—64no—
485C2×D3—122no—
486C2×D3—122no—
487C2×D3—128no—
488C2×D3—124no—
489C2×D3—124no—
490C2×D3—124no—
491C2×D3—1232no—
492C2×D3—128no—
493C2×D3—128no—
494C2×D3—248no—
495C3×C4—24no—
496C3×C4—24no—
497C3×C4—24no—
498C3×C4—24no—
499C3×C4—44no—
500C3×C4—64no—
501C3×C4—64no—
502C3×C4—64no—
503Dic3—24no—
504Dic3—24no—
505Dic3—24no—
506Dic3—64no—
507Dic3—122no—
508C32C2×#53811yescharacteristic, complemented, Sylow
509C23—34no—
510C23—64no—
511C23—64no—
512C23—64no—
513C23—94no—
514C23—92no—
515C23—94no—
516C23—188no—
517C23—182no—
518C23—182no—
519C23—184no—
520C23—184no—
521C23—184no—
522C23—364no—
523C23—364no—
524C23—3616no—
525C23C22×D3211yescharacteristic
526Q8—364no—
527D4—1816no—
528D4—364no—
529D4—368no—
530D4—368no—
531C2×C4—22no—
532C2×C4—24no—
533C2×C4—34no—
534C2×C4—34no—
535C2×C4—34no—
536C2×C4—64no—
537C2×C4—64no—
538C2×C4—64no—
539C2×C4—92no—
540C2×C4—182no—
541C2×C4—364no—
542C2×C4—364no—
543C2×C4—368no—
544C2×C4C22×D3214yes—
545C2×C4C22×D3212yes—
546C2×C3—21no—
547C2×C3—21no—
548C2×C3—21no—
549C2×C3—24no—
550C2×C3—124no—
551C2×C3#570418yescomplemented
552C2×C3C2×D3×#4112yes—
553C2×C3C2×#100912yes—
554C2×C3C2×#100912yes—
555D3—44no—
556D3—68no—
557D3—124no—
558D3—124no—
559D3—124no—
560D3—244no—
561C22—64no—
562C22—64no—
563C22—64no—
564C22—94no—
565C22—128no—
566C22—182no—
567C22—182no—
568C22—188no—
569C22—184no—
570C22—184no—
571C22—184no—
572C22—3616no—
573C22—368no—
574C22#6430812yes—
575C22#6431212yes—
576C22#6432012yes—
577C22C23×D3211yescharacteristic
578C4—22no—
579C4—24no—
580C4—64no—
581C4—64no—
582C4—64no—
583C4—182no—
584C3—21no—
585C3C2×#570412yescomplemented
586C2—124no—
587C2—184no—
588C2—364no—
589C2#1059465814yesdirect product factor
590C2C2×#6430811yescharacteristic
591C2C2×#6431211yescharacteristic
592C2C2×#6432011yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#538
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×#64104C2semidirect
2. C2×C3×#898C2semidirect
3. C2×#63923C2semidirect
4. C2×#63921C2semidirect
5. C2×#63910C2semidirect
6. C2×#63894C2semidirect
7. C2×#63865C2semidirect
8. C2×#63854C2semidirect
9. C2×#63852C2semidirect
10. #10594658C2direct (N × H)
14. C22×C4⋊(C3⋊D3)C22semidirect
16. C22×#627C22semidirect
20. C22×#624C22semidirect
21. C2×C32×C4⋊C4C22semidirect
22. C2×#3752C22semidirect
23. #64104C22semidirect
27. C2×C3×C4⋊Dic3C22semidirect
28. C2×C3×Dic3⋊C4C22semidirect
29. C2×C3×C4×Dic3C22semidirect
30. C3×#898C22semidirect
31. C2×#3724C22semidirect
33. C2×#3722C22semidirect
35. #63923C22semidirect
36. #63921C22semidirect
37. #63910C22semidirect
38. #63894C22semidirect
39. #63865C22semidirect
40. #63854C22semidirect
41. #63852C22semidirect
44. C2×#898D3semidirect
72. C2×C4⋊(C3⋊D3)C23semidirect
79. C2×#627C23semidirect
87. C2×#624C23semidirect
88. C32×C4⋊C4C23semidirect
89. #3752C23semidirect
93. C3×C4⋊Dic3C23semidirect
94. C3×Dic3⋊C4C23semidirect
95. C3×C4×Dic3C23semidirect
96. #3724C23semidirect
98. #3722C23semidirect
121. C2×C3×C4⋊C4C2×D3semidirect
138. C2×C4⋊Dic3C2×D3semidirect
140. C2×Dic3⋊C4C2×D3semidirect
141. C2×C4×Dic3C2×D3semidirect
142. #898C2×D3semidirect
261. C3×C4⋊C4C22×D3semidirect
278. C4⋊Dic3C22×D3semidirect
280. Dic3⋊C4C22×D3semidirect
281. C4×Dic3C22×D3semidirect
325. C2×C4⋊C4D32semidirect
410. C2×C32#538semidirect
449. C4⋊C4C2×D32semidirect
508. C32C2×#538semidirect
551. C2×C3#5704semidirect
585. C3C2×#5704semidirect
589. C2#10594658direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641042
C2×C3×#8982
C2×#639232
C2×#639212
C2×#639102
C2×#638942
C2×#638652
C2×#638542
C2×#638522
#105946582
C2×#57043