Finite Group Databasebeta

← C2×#10594244 #11910186

Subgroups — C2×#10594244 #11910186

Order 1152.

3019 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64091C211yesmaximal, characteristic, complemented
2C2×C3×#883C212yesmaximal, complemented
3C2×#63981C212yesmaximal, complemented
4C2×#63979C211yesmaximal, characteristic, complemented
5C2×#63975C211yesmaximal, characteristic, complemented
6C2×#63910C212yesmaximal, complemented
7C2×#63909C212yesmaximal, complemented
8C2×#63906C212yesmaximal, complemented
9C2×#63848C212yesmaximal, complemented
10#10594244C2116yesmaximal, direct product factor
11C2×#5666—32nomaximal
12C24×C3⋊D3C2211yescharacteristic
13C22×#638C2211yescharacteristic
14C22×C4⋊(C3⋊D3)C2212yes—
15C22×C3×#67C2212yes—
16C22×C3×C4×D3C2212yescomplemented
17C22×#626C2212yes—
18C22×#626C2212yes—
19C22×#626C2212yescomplemented
20C22×#625C2211yescharacteristic, complemented
21C22×#624C2211yescharacteristic, complemented
22C2×C32×C22⋊C4C2211yescharacteristic
23C2×#3752C2212yes—
24#64091C2218yescomplemented
25C2×C3×#217C2212yes—
26C2×C3×(C2×D3)⋊C4C2212yescomplemented
27C2×C3×C4⋊Dic3C2212yescomplemented
28C2×C3×Dic3⋊C4C2212yescomplemented
29C3×#883C22116yescomplemented
30#63981C22116yescomplemented
31#63979C2218yescomplemented
32#63975C2218yescomplemented
33C2×Dic3⋊Dic3C2212yescomplemented
34C2×#3722C2212yes—
35C2×#3722C2212yes—
36C2×#3722C2211yescharacteristic, complemented
37C2×Dic32C2211yescharacteristic, complemented
38#63910C22116yescomplemented
39#63909C22116yescomplemented
40#63906C22116yescomplemented
41#63848C22116yescomplemented
42C2×C3×#123—32no—
43C2×#940—32no—
44C2×#937—32no—
45C2×#930—32no—
46C2×#930—32no—
47#5666—332no—
48C2×#898—32no—
49C2×#898—32no—
50C2×#895—32no—
51C2×#895—32no—
52C2×#884—32no—
53C2×#884—32no—
54C2×#883—32no—
55C2×#883D312yescomplemented
56C2×#882—32no—
57C2×#882—32no—
58C2×#882—61no—
59C24×C32C2311yescharacteristic
60C23×C3⋊D3—44no—
61C23×C3⋊D3—42no—
62C23×C3⋊D3C2311yescharacteristic
63C23×C3⋊D3C2312yes—
64C23×C3⋊D3C2314yes—
65C23×C3×D3C2312yes—
66C22×C32×C4C2312yes—
67C2×#638—42no—
68C2×#638C2314yes—
69C22×C3⋊Dic3C2311yescharacteristic
70C2×C4⋊(C3⋊D3)—44no—
71C2×C4⋊(C3⋊D3)C2318yes—
72C2×C3×#67—44no—
73C2×C3×#67C2318yes—
74C22×C3×Dic3C2312yes—
75C22×C3×Dic3C2312yes—
76C22×C3×Dic3C2312yes—
77C2×C3×C4×D3—44no—
78C2×C3×C4×D3C2318yescomplemented
79C2×#626—44no—
80C2×#626—44no—
81C2×#626—44no—
82C2×#626C2318yes—
83C2×#626C2318yes—
84C2×#626C2318yescomplemented
85C2×#625—42no—
86C2×#625C2314yescomplemented
87C2×#624—42no—
88C2×#624C2314yescomplemented
89C32×C22⋊C4C2314yes—
90#3752C2318yes—
91C3×#217C2318yes—
92C3×(C2×D3)⋊C4C2318yescomplemented
93C3×C4⋊Dic3C2318yescomplemented
94C3×Dic3⋊C4C2318yescomplemented
95Dic3⋊Dic3C2318yescomplemented
96#3722C2318yes—
97#3722C2318yes—
98#3722C2314yescomplemented
99Dic32C2314yescomplemented
100C2×#560—91noSylow
101C24×D3—32no—
102C24×D3—61no—
103C22×C3×D4—32no—
104C23×C3×C4—32no—
105C22×#67—32no—
106C22×#67—32no—
107C22×#67—32no—
108C22×#67—32no—
109C22×#67—32no—
110C22×#67—61no—
111C22×#67C2×D312yes—
112C22×D12—32no—
113C22×D12—32no—
114C22×D12—32no—
115C22×D12—32no—
116C22×D12—32no—
117C22×D12—62no—
118C22×C4×D3—32no—
119C22×C4×D3C2×D312yescomplemented
120C3×#123—316no—
121C2×C3×C4⋊C4—32no—
122C2×C3×C4⋊C4—32no—
123C2×C3×C22⋊C4—21no—
124C2×C3×C22⋊C4—32no—
125C2×C3×C22⋊C4—32no—
126C2×C3×C22⋊C4C2×D312yes—
127C2×#217C2×D312yes—
128#940—316no—
129#937—316no—
130#930—316no—
131#930—316no—
132C2×(C2×D3)⋊C4—32no—
133C2×(C2×D3)⋊C4—32no—
134C2×(C2×D3)⋊C4—32no—
135C2×(C2×D3)⋊C4—32no—
136C2×(C2×D3)⋊C4—32no—
137C2×(C2×D3)⋊C4—32no—
138C2×(C2×D3)⋊C4—32no—
139C2×(C2×D3)⋊C4—62no—
140C2×(C2×D3)⋊C4C2×D312yescomplemented
141C2×C4⋊Dic3—32no—
142C2×C4⋊Dic3C2×D312yescomplemented
143C2×Dic3⋊C4—32no—
144C2×Dic3⋊C4C2×D312yescomplemented
145C2×C4×Dic3—32no—
146#898—316no—
147#898—316no—
148#895—316no—
149#895—316no—
150#884—316no—
151#884—316no—
152#883—316no—
153#883C2×D3116yescomplemented
154#882—316no—
155#882—316no—
156#882—68no—
157C23×C32—22no—
158C23×C32—24no—
159C23×C32C2412yes—
160C23×C32C2411yescharacteristic
161C22×C3⋊D3—24no—
162C22×C3⋊D3—24no—
163C22×C3⋊D3—24no—
164C22×C3⋊D3—22no—
165C22×C3⋊D3—24no—
166C22×C3⋊D3—48no—
167C22×C3⋊D3—44no—
168C22×C3⋊D3—416no—
169C22×C3⋊D3C2414yes—
170C22×C3⋊D3C2412yes—
171C22×C3×D3—24no—
172C22×C3×D3—24no—
173C22×C3×D3—24no—
174C22×C3×D3C2414yes—
175C2×C32×C4—24no—
176C2×C32×C4C2414yes—
177#638—44no—
178C2×C3⋊Dic3—22no—
179C2×C3⋊Dic3C2412yes—
180C4⋊(C3⋊D3)—48no—
181C3×#67—48no—
182C2×C3×Dic3—24no—
183C2×C3×Dic3—24no—
184C2×C3×Dic3—24no—
185C2×C3×Dic3C2414yes—
186C2×C3×Dic3C2414yes—
187C2×C3×Dic3C2414yes—
188C3×C4×D3—48no—
189#626—48no—
190#626—48no—
191#626—48no—
192#625—44no—
193#624—44no—
194#560—916no—
195C2×#127—91no—
196C2×#126—92no—
197C2×#123—32no—
198C2×#123—91no—
199C2×#121—92no—
200C2×#121—92no—
201C2×#121—92no—
202C2×#120—92no—
203C2×#120—91no—
204C24×C3—21no—
205C24×C3—32no—
206C24×C3C22×D312yes—
207C23×D3—32no—
208C23×D3—32no—
209C23×D3—32no—
210C23×D3—38no—
211C23×D3—62no—
212C23×D3—64no—
213C23×D3—61no—
214C23×D3—124no—
215C23×D3—124no—
216C23×D3—124no—
217C23×D3—128no—
218C23×D3—124no—
219C23×D3C22×D312yes—
220C2×C3×D4—38no—
221C2×C3×D4—124no—
222C22×C3×C4—22no—
223C22×C3×C4—32no—
224C22×C3×C4—32no—
225C22×C3×C4—32no—
226C22×C3×C4—38no—
227C22×C3×C4—124no—
228C22×C3×C4C22×D312yes—
229C22×C3×C4C22×D312yes—
230C2×#67—38no—
231C2×#67—38no—
232C2×#67—38no—
233C2×#67—38no—
234C2×#67—38no—
235C2×#67—44no—
236C2×#67—64no—
237C2×#67—124no—
238C2×#67—124no—
239C2×#67—124no—
240C2×#67—124no—
241C2×#67—124no—
242C2×#67—124no—
243C2×#67C22×D318yes—
244C22×Dic3—32no—
245C22×Dic3—61no—
246C22×Dic3C22×D312yes—
247C22×Dic3C22×D312yes—
248C22×Dic3C22×D312yes—
249C2×D12—38no—
250C2×D12—38no—
251C2×D12—38no—
252C2×D12—38no—
253C2×D12—38no—
254C2×D12—68no—
255C2×D12—124no—
256C2×D12—124no—
257C2×D12—128no—
258C2×D12—124no—
259C2×D12—124no—
260C2×D12—124no—
261C2×C4×D3—38no—
262C2×C4×D3—44no—
263C2×C4×D3—124no—
264C2×C4×D3C22×D318yescomplemented
265C3×C4⋊C4—38no—
266C3×C4⋊C4—38no—
267C3×C22⋊C4—24no—
268C3×C22⋊C4—38no—
269C3×C22⋊C4—38no—
270C3×C22⋊C4C22×D318yes—
271#217C22×D318yes—
272(C2×D3)⋊C4—38no—
273(C2×D3)⋊C4—38no—
274(C2×D3)⋊C4—38no—
275(C2×D3)⋊C4—38no—
276(C2×D3)⋊C4—38no—
277(C2×D3)⋊C4—38no—
278(C2×D3)⋊C4—38no—
279(C2×D3)⋊C4—68no—
280(C2×D3)⋊C4C22×D318yescomplemented
281C4⋊Dic3—38no—
282C4⋊Dic3C22×D318yescomplemented
283Dic3⋊C4—38no—
284Dic3⋊C4C22×D318yescomplemented
285C4×Dic3—38no—
286C22×C32—22no—
287C22×C32—24no—
288C22×C32—44no—
289C22×C32H(5,𝔽2)14yes—
290C22×C32H(5,𝔽2)12yes—
291C22×C32C2511yescharacteristic
292C2×C3⋊D3—24no—
293C2×C3⋊D3—22no—
294C2×C3⋊D3—24no—
295C2×C3⋊D3—24no—
296C2×C3⋊D3—24no—
297C2×C3⋊D3—416no—
298C2×C3⋊D3—48no—
299C2×C3⋊D3—44no—
300C2×C3×D3—24no—
301C2×C3×D3—24no—
302C2×C3×D3—24no—
303C2×C3×D3—48no—
304C32×C4—24no—
305C3⋊Dic3—22no—
306C3×Dic3—24no—
307C3×Dic3—24no—
308C3×Dic3—24no—
309C25—91no—
310C22×D4—32no—
311C22×D4—92no—
312C22×D4—92no—
313C22×D4—92no—
314C22×D4—91no—
315C22×D4—91no—
316C22×D4—92no—
317C23×C4—32no—
318C23×C4—91no—
319#127—98no—
320#126—916no—
321#123—316no—
322#123—98no—
323#121—916no—
324#121—916no—
325#121—916no—
326#120—916no—
327#120—98no—
328C2×C4⋊C4—32no—
329C2×C4⋊C4—32no—
330C2×C4⋊C4—92no—
331C2×C22⋊C4—32no—
332C2×C22⋊C4—32no—
333C2×C22⋊C4—92no—
334C2×C22⋊C4—92no—
335C2×C22⋊C4—91no—
336C2×C22⋊C4—92no—
337C2×C22⋊C4D3211yescharacteristic
338C2×C42—91no—
339C23×C3—24no—
340C23×C3—24no—
341C23×C3—24no—
342C23×C3—24no—
343C23×C3—22no—
344C23×C3—21no—
345C23×C3—34no—
346C23×C3—44no—
347C23×C3—64no—
348C23×C3—64no—
349C23×C3—64no—
350C23×C3C23×D314yes—
351C23×C3C23×D312yes—
352C22×D3—24no—
353C22×D3—24no—
354C22×D3—24no—
355C22×D3—34no—
356C22×D3—34no—
357C22×D3—34no—
358C22×D3—64no—
359C22×D3—62no—
360C22×D3—68no—
361C22×D3—64no—
362C22×D3—64no—
363C22×D3—64no—
364C22×D3—64no—
365C22×D3—64no—
366C22×D3—64no—
367C22×D3—64no—
368C22×D3—64no—
369C22×D3—64no—
370C22×D3—124no—
371C22×D3—124no—
372C22×D3—124no—
373C22×D3—122no—
374C22×D3—128no—
375C22×D3—128no—
376C22×D3—128no—
377C22×D3—1216no—
378C22×D3—128no—
379C22×D3—1232no—
380C22×D3—1232no—
381C22×D3C23×D314yes—
382C3×D4—128no—
383C2×C3×C4—24no—
384C2×C3×C4—24no—
385C2×C3×C4—24no—
386C2×C3×C4—34no—
387C2×C3×C4—34no—
388C2×C3×C4—34no—
389C2×C3×C4—44no—
390C2×C3×C4—64no—
391C2×C3×C4—64no—
392C2×C3×C4—64no—
393C2×C3×C4—128no—
394C2×C3×C4C23×D314yes—
395C2×C3×C4C23×D314yes—
396#67—48no—
397#67—128no—
398#67—128no—
399#67—128no—
400#67—128no—
401#67—128no—
402#67—128no—
403C2×Dic3—24no—
404C2×Dic3—24no—
405C2×Dic3—24no—
406C2×Dic3—34no—
407C2×Dic3—62no—
408C2×Dic3—64no—
409C2×Dic3—122no—
410C2×Dic3C23×D314yes—
411C2×Dic3C23×D314yes—
412C2×Dic3C23×D314yes—
413D12—128no—
414D12—128no—
415D12—1216no—
416D12—128no—
417D12—128no—
418D12—128no—
419C4×D3—48no—
420C4×D3—128no—
421C2×C32—42no—
422C2×C32#56014yescomplemented
423C2×C32C2×H(5,𝔽2)12yes—
424C2×C32C2×H(5,𝔽2)11yescharacteristic
425C3⋊D3—44no—
426C3⋊D3—42no—
427C3×D3—44no—
428C24—32no—
429C24—92no—
430C24—91no—
431C24—94no—
432C24—362no—
433C24—364no—
434C24C2×D3211yescharacteristic
435C2×D4—38no—
436C2×D4—98no—
437C2×D4—98no—
438C2×D4—98no—
439C2×D4—94no—
440C2×D4—94no—
441C2×D4—98no—
442C2×D4—124no—
443C2×D4—364no—
444C2×D4—364no—
445C2×D4—364no—
446C2×D4—364no—
447C2×D4—362no—
448C2×D4—362no—
449C22×C4—32no—
450C22×C4—32no—
451C22×C4—32no—
452C22×C4—38no—
453C22×C4—94no—
454C22×C4—91no—
455C22×C4—124no—
456C22×C4—362no—
457C22×C4C2×D3212yes—
458C4⋊C4—38no—
459C4⋊C4—38no—
460C4⋊C4—98no—
461C22⋊C4—38no—
462C22⋊C4—38no—
463C22⋊C4—98no—
464C22⋊C4—98no—
465C22⋊C4—94no—
466C22⋊C4—98no—
467C22⋊C4C2×D3214yes—
468C42—94no—
469C22×C3—24no—
470C22×C3—24no—
471C22×C3—24no—
472C22×C3—24no—
473C22×C3—22no—
474C22×C3—24no—
475C22×C3—21no—
476C22×C3—44no—
477C22×C3—48no—
478C22×C3—48no—
479C22×C3—64no—
480C22×C3—64no—
481C22×C3—64no—
482C22×C3—128no—
483C22×C3#100414yes—
484C22×C3#100914yes—
485C22×C3#100914yes—
486C22×C3C24×D312yes—
487C2×D3—24no—
488C2×D3—24no—
489C2×D3—24no—
490C2×D3—48no—
491C2×D3—68no—
492C2×D3—64no—
493C2×D3—64no—
494C2×D3—64no—
495C2×D3—64no—
496C2×D3—64no—
497C2×D3—64no—
498C2×D3—64no—
499C2×D3—64no—
500C2×D3—64no—
501C2×D3—124no—
502C2×D3—124no—
503C2×D3—124no—
504C2×D3—122no—
505C2×D3—1216no—
506C2×D3—1232no—
507C2×D3—1232no—
508C2×D3—128no—
509C2×D3—128no—
510C2×D3—128no—
511C2×D3—244no—
512C3×C4—24no—
513C3×C4—24no—
514C3×C4—44no—
515C3×C4—64no—
516C3×C4—64no—
517C3×C4—64no—
518Dic3—24no—
519Dic3—24no—
520Dic3—24no—
521Dic3—64no—
522Dic3—122no—
523C32C2×#56011yescharacteristic, complemented, Sylow
524C23—22no—
525C23—24no—
526C23—34no—
527C23—64no—
528C23—64no—
529C23—64no—
530C23—94no—
531C23—92no—
532C23—182no—
533C23—184no—
534C23—184no—
535C23—184no—
536C23—184no—
537C23—364no—
538C23—368no—
539C23—3616no—
540C23C22×D3212yes—
541C23C22×D3211yescharacteristic
542D4—128no—
543D4—368no—
544D4—368no—
545D4—368no—
546D4—368no—
547D4—364no—
548D4—364no—
549C2×C4—24no—
550C2×C4—34no—
551C2×C4—34no—
552C2×C4—34no—
553C2×C4—64no—
554C2×C4—64no—
555C2×C4—64no—
556C2×C4—92no—
557C2×C4—128no—
558C2×C4—182no—
559C2×C4—364no—
560C2×C4C22×D3214yes—
561C2×C3—21no—
562C2×C3—22no—
563C2×C3—24no—
564C2×C3—44no—
565C2×C3—44no—
566C2×C3—124no—
567C2×C3#566618yescomplemented
568C2×C3C2×#100412yes—
569C2×C3C2×#100912yes—
570C2×C3C2×#100912yes—
571D3—44no—
572D3—128no—
573D3—124no—
574D3—124no—
575D3—124no—
576D3—242no—
577C22—22no—
578C22—24no—
579C22—44no—
580C22—64no—
581C22—64no—
582C22—64no—
583C22—128no—
584C22—182no—
585C22—184no—
586C22—184no—
587C22—184no—
588C22—184no—
589C22—3616no—
590C22—368no—
591C22—364no—
592C22#6430812yes—
593C22#6431414yes—
594C22C23×D3211yescharacteristic
595C4—24no—
596C4—64no—
597C4—64no—
598C4—64no—
599C4—182no—
600C3—21no—
601C3C2×#566612yescomplemented
602C2—42no—
603C2—124no—
604C2—364no—
605C2—362no—
606C2#1059424414yesdirect product factor
607C2C2×#6430811yescharacteristic
608C2C2×#6431412yes—
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#560
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64091C2semidirect
2. C2×C3×#883C2semidirect
3. C2×#63981C2semidirect
4. C2×#63979C2semidirect
5. C2×#63975C2semidirect
6. C2×#63910C2semidirect
7. C2×#63909C2semidirect
8. C2×#63906C2semidirect
9. C2×#63848C2semidirect
10. #10594244C2direct (N × H)
16. C22×C3×C4×D3C22semidirect
19. C22×#626C22semidirect
20. C22×#625C22semidirect
21. C22×#624C22semidirect
24. #64091C22semidirect
26. C2×C3×(C2×D3)⋊C4C22semidirect
27. C2×C3×C4⋊Dic3C22semidirect
28. C2×C3×Dic3⋊C4C22semidirect
29. C3×#883C22semidirect
30. #63981C22semidirect
31. #63979C22semidirect
32. #63975C22semidirect
33. C2×Dic3⋊Dic3C22semidirect
36. C2×#3722C22semidirect
37. C2×Dic32C22semidirect
38. #63910C22semidirect
39. #63909C22semidirect
40. #63906C22semidirect
41. #63848C22semidirect
55. C2×#883D3semidirect
78. C2×C3×C4×D3C23semidirect
84. C2×#626C23semidirect
86. C2×#625C23semidirect
88. C2×#624C23semidirect
92. C3×(C2×D3)⋊C4C23semidirect
93. C3×C4⋊Dic3C23semidirect
94. C3×Dic3⋊C4C23semidirect
95. Dic3⋊Dic3C23semidirect
98. #3722C23semidirect
99. Dic32C23semidirect
119. C22×C4×D3C2×D3semidirect
140. C2×(C2×D3)⋊C4C2×D3semidirect
142. C2×C4⋊Dic3C2×D3semidirect
144. C2×Dic3⋊C4C2×D3semidirect
153. #883C2×D3semidirect
264. C2×C4×D3C22×D3semidirect
280. (C2×D3)⋊C4C22×D3semidirect
282. C4⋊Dic3C22×D3semidirect
284. Dic3⋊C4C22×D3semidirect
422. C2×C32#560semidirect
523. C32C2×#560semidirect
567. C2×C3#5666semidirect
601. C3C2×#5666semidirect
606. C2#10594244direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640912
C2×C3×#8832
C2×#639812
C2×#639792
C2×#639752
C2×#639102
C2×#639092
C2×#639062
C2×#638482
#105942442
C2×#56663