Finite Group Databasebeta

← C2×#10590607 #11857915

Subgroups — C2×#10590607 #11857915

Order 1152.

1713 conjugacy classes of subgroups.

The subgroup lattice has 567 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3795C211yesmaximal, characteristic
2C2×C3×D3×C4⋊C4C211yesmaximal, characteristic, complemented
3C22×#3711C211yesmaximal, characteristic, complemented
4C2×#63637C211yesmaximal, characteristic, complemented
5C2×C3×#809C211yesmaximal, characteristic, complemented
6C2×#63567C211yesmaximal, characteristic, complemented
7C2×#63562C211yesmaximal, characteristic, complemented
8#10590607C218yesmaximal, direct product factor
9C2×#4966—31nomaximal
10C2×#4771—31nomaximal
11C22×#634C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C22×C3×C4×D3—21no—
14C22×C3×C4×D3C2211yescharacteristic
15C22×#625—21no—
16C22×D3×Dic3—21no—
17C2×#3795—22no—
18C2×#3795—24no—
19C2×#3795C418yescomplemented
20C2×#3795C2214yes—
21C2×C32×C4⋊C4C2211yescharacteristic
22C22×C3⋊(C3⋊C8)C2211yescharacteristic
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×Dic3⋊C4—21no—
25C22×C3×C3⋊C8C2211yescharacteristic
26C3×D3×C4⋊C4—22no—
27C3×D3×C4⋊C4C2214yescomplemented
28C2×#3711—24no—
29C2×#3711C2214yescomplemented
30#63637C2214yescomplemented
31C3×#809C2214yescomplemented
32#63567C2214yescomplemented
33#63562C2214yescomplemented
34C22×#237—31no—
35C22×#235—31no—
36C22×C3×C4⋊C4—31no—
37C22×#208—31no—
38C22×ΓL(1,𝔽25)—31no—
39C2×D3×C4⋊C4D311yescharacteristic, complemented
40C2×C3×#102—31no—
41C2×#832—31no—
42C2×#816—31no—
43C2×#810—31no—
44C2×#810—31no—
45C2×#810—31no—
46C2×#810—61no—
47#4966—38no—
48C2×#809—31no—
49C2×#809D311yescharacteristic, complemented
50#4771—38no—
51C23×C3×D3—21no—
52C23×C3×D3D411yescharacteristic
53C22×C32×C4—21no—
54C22×C32×C4C2311yescharacteristic
55C22×C3⋊Dic3—21no—
56C2×#634—21no—
57C2×#634—22no—
58C2×#634C2×C414yescomplemented
59C2×#634C2312yes—
60C22×C3×Dic3—21no—
61C22×C3×Dic3D411yescharacteristic
62C2×C3×D12—21no—
63C2×C3×D12—22no—
64C2×C3×D12C2×C414yescomplemented
65C2×C3×D12C2312yes—
66C2×C3×C4×D3—24no—
67C2×C3×C4×D3—44no—
68C2×C3×C4×D3C2×C414yes—
69C2×C3×C4×D3D412yes—
70C2×C3×C4×D3D414yes—
71C2×C3×C4×D3C2312yes—
72C2×#625—28no—
73C2×#625—24no—
74C2×D3×Dic3—28no—
75C2×D3×Dic3—24no—
76#3795—216no—
77#3795—28no—
78#3795C2×C4116yescomplemented
79C32×C4⋊C4—21no—
80C32×C4⋊C4C2312yes—
81C2×C3⋊(C3⋊C8)—22no—
82C2×C3⋊(C3⋊C8)C2312yes—
83C3×C4⋊Dic3—21no—
84C3×C4⋊Dic3C2312yes—
85C3×Dic3⋊C4—24no—
86C2×C3×C3⋊C8—22no—
87C2×C3×C3⋊C8C2312yes—
88#3711—28no—
89C2×#417—91noSylow
90C22×C3×D4—31no—
91C23×C3×C4—31no—
92C23×C3×C4—61no—
93C22×#67—61no—
94C22×#67—61no—
95C23×Dic3—61no—
96C2×#237—38no—
97C2×#237—34no—
98C2×#237—64no—
99C2×#237—62no—
100C2×#235—38no—
101C2×#235—34no—
102C2×#235—64no—
103C2×#235—62no—
104C22×D12C2×D311yescharacteristic
105C22×C4×D3—21no—
106C22×C4×D3—61no—
107C22×C4×D3C2×D311yescharacteristic
108C22×Dic6—31no—
109C22×Dic6—31no—
110C22×Dic6—61no—
111C22×C3×C8—31no—
112C2×C3×C4⋊C4—21no—
113C2×C3×C4⋊C4—31no—
114C2×C3×C4⋊C4—34no—
115C2×C3×C4⋊C4—62no—
116C2×C3×C4⋊C4—61no—
117C2×C3×C4⋊C4C2×D311yescharacteristic
118C2×C3×C4⋊C4C2×D311yescharacteristic
119C2×C4⋊Dic3C2×D311yescharacteristic
120C2×Dic3⋊C4—21no—
121C2×#208—34no—
122C2×#208—64no—
123C22×C3⋊C8—31no—
124C22×C3⋊C8—31no—
125C22×C3⋊C8—61no—
126C22×C3⋊C8C2×D311yescharacteristic
127C2×ΓL(1,𝔽25)—34no—
128C2×ΓL(1,𝔽25)—64no—
129D3×C4⋊C4—22no—
130D3×C4⋊C4C2×D314yescomplemented
131C3×#102—34no—
132#832—34no—
133#816—34no—
134#810—34no—
135#810—34no—
136#810—34no—
137#810—64no—
138#809—34no—
139#809C2×D314yescomplemented
140C23×C32C2×D411yescharacteristic
141C22×C3×D3—22no—
142C22×C3×D3—22no—
143C22×C3×D3—24no—
144C22×C3×D3—22no—
145C22×C3×D3—42no—
146C22×C3×D3—42no—
147C22×C3×D3C22⋊C414yes—
148C22×C3×D3C2×D412yes—
149C2×C32×C4—22no—
150C2×C32×C4—42no—
151C2×C32×C4C22×C412yes—
152C2×C32×C4C2×D412yes—
153C2×C32×C4C2×D411yescharacteristic
154C2×C32×C4C2411yescharacteristic
155C2×C3⋊Dic3—24no—
156C2×C3⋊Dic3—22no—
157#634—24no—
158#634—22no—
159#634C22×C414yescomplemented
160C2×C3×Dic3—22no—
161C2×C3×Dic3—42no—
162C2×C3×Dic3C22⋊C414yes—
163C2×C3×Dic3C2×D412yes—
164C3×D12—24no—
165C3×D12—22no—
166C3×D12C22×C414yescomplemented
167C3×C4×D3—48no—
168C3×C4×D3C22⋊C418yes—
169C3×C4×D3C22×C414yes—
170C3×C4×D3C2×D414yes—
171#625—216no—
172D3×Dic3—216no—
173C3⋊(C3⋊C8)—22no—
174C3×C3⋊C8—22no—
175C22×#41—91no—
176C22×M16—91no—
177C22×C4⋊C4—31no—
178#417—98no—
179C2×#103—91no—
180C2×#103—91no—
181C2×#102—31no—
182C2×#102—91no—
183C24×C3—31no—
184C24×C3—61no—
185C23×D3—21no—
186C23×D3#6711yescharacteristic
187C2×C3×D4—34no—
188C2×C3×D4—32no—
189C2×C3×D4—62no—
190C2×C3×D4—61no—
191C22×C3×C4—21no—
192C22×C3×C4—21no—
193C22×C3×C4—21no—
194C22×C3×C4—31no—
195C22×C3×C4—34no—
196C22×C3×C4—34no—
197C22×C3×C4—32no—
198C22×C3×C4—32no—
199C22×C3×C4—41no—
200C22×C3×C4—64no—
201C22×C3×C4—61no—
202C22×C3×C4—124no—
203C22×C3×C4C22×D311yescharacteristic
204C22×C3×C4C22×D311yescharacteristic
205C2×#67—68no—
206C2×#67—64no—
207C2×#67—68no—
208C2×#67—64no—
209C22×Dic3—21no—
210C22×Dic3—61no—
211C22×Dic3—61no—
212C22×Dic3—68no—
213C22×Dic3—64no—
214C22×Dic3—121no—
215C22×Dic3#6711yescharacteristic
216#237—316no—
217#237—616no—
218#237—68no—
219#235—316no—
220#235—616no—
221#235—68no—
222C2×D12—22no—
223C2×D12—21no—
224C2×D12C4×D314yescomplemented
225C2×D12C22×D312yes—
226C2×C4×D3—24no—
227C2×C4×D3—44no—
228C2×C4×D3—68no—
229C2×C4×D3—64no—
230C2×C4×D3C4×D314yes—
231C2×C4×D3D1214yes—
232C2×C4×D3#6712yes—
233C2×C4×D3C22×D312yes—
234C2×Dic6—34no—
235C2×Dic6—34no—
236C2×Dic6—32no—
237C2×Dic6—32no—
238C2×Dic6—62no—
239C2×Dic6—64no—
240C2×Dic6—62no—
241C2×Dic6—62no—
242C2×Dic6—61no—
243C2×Dic6—61no—
244C2×Dic6—122no—
245C2×Dic6—121no—
246C2×C3×C8—32no—
247C2×C3×C8—62no—
248C3×C4⋊C4—21no—
249C3×C4⋊C4—21no—
250C3×C4⋊C4—22no—
251C3×C4⋊C4—32no—
252C3×C4⋊C4—41no—
253C3×C4⋊C4—64no—
254C3×C4⋊C4—61no—
255C3×C4⋊C4C22×D312yes—
256C3×C4⋊C4C22×D312yes—
257C4⋊Dic3—21no—
258C4⋊Dic3C22×D312yes—
259Dic3⋊C4—24no—
260#208—68no—
261C2×C3⋊C8—22no—
262C2×C3⋊C8—32no—
263C2×C3⋊C8—32no—
264C2×C3⋊C8—62no—
265C2×C3⋊C8—62no—
266C2×C3⋊C8—62no—
267C2×C3⋊C8—122no—
268C2×C3⋊C8C22×D312yes—
269ΓL(1,𝔽25)—68no—
270C22×C32C2×C22⋊C412yes—
271C22×C32AGL(1,ℤ/8)12yes—
272C22×C32#13712yes—
273C22×C32C22×D411yescharacteristic
274C2×C3×D3—22no—
275C2×C3×D3—22no—
276C2×C3×D3—28no—
277C2×C3×D3—24no—
278C2×C3×D3—42no—
279C2×C3×D3—42no—
280C2×C3×D3—48no—
281C2×C3×D3C2×C22⋊C414yes—
282C32×C4—42no—
283C32×C4C2×C22⋊C412yes—
284C32×C4C23×C411yescharacteristic
285C32×C4C22×D411yescharacteristic
286C3⋊Dic3—24no—
287C3×Dic3—42no—
288C3×Dic3C2×C22⋊C414yes—
289C2×#41—94no—
290C2×#41—98no—
291C2×#41—184no—
292C2×#41—182no—
293C22×Q8—91no—
294C22×D4—31no—
295C22×D4—181no—
296C23×C4—31no—
297C23×C4—61no—
298C23×C4—181no—
299C2×M16—94no—
300C2×M16—184no—
301C22×C8—31no—
302C22×C8—91no—
303C2×C4⋊C4—31no—
304C2×C4⋊C4—34no—
305C2×C4⋊C4—62no—
306C2×C4⋊C4—61no—
307C2×C4⋊C4D3211yescharacteristic
308#103—94no—
309#103—94no—
310#102—34no—
311#102—94no—
312C23×C3—21no—
313C23×C3—34no—
314C23×C3—32no—
315C23×C3—62no—
316C23×C3—62no—
317C23×C3—64no—
318C23×C3—62no—
319C23×C3—122no—
320C23×C3—122no—
321C23×C3D3×D411yescharacteristic
322C23×C3C2×#6711yescharacteristic
323C22×D3—22no—
324C22×D3—22no—
325C22×D3—24no—
326C22×D3—22no—
327C22×D3—42no—
328C22×D3—42no—
329C22×D3(C2×D3)⋊C414yes—
330C22×D3C2×#6712yes—
331C3×D4—34no—
332C3×D4—64no—
333C3×D4—62no—
334C2×C3×C4—22no—
335C2×C3×C4—22no—
336C2×C3×C4—21no—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4—21no—
340C2×C3×C4—34no—
341C2×C3×C4—32no—
342C2×C3×C4—38no—
343C2×C3×C4—34no—
344C2×C3×C4—34no—
345C2×C3×C4—42no—
346C2×C3×C4—42no—
347C2×C3×C4—42no—
348C2×C3×C4—62no—
349C2×C3×C4—82no—
350C2×C3×C4—128no—
351C2×C3×C4—122no—
352C2×C3×C4C2×C4×D312yes—
353C2×C3×C4C2×C4×D312yes—
354C2×C3×C4C2×D1212yes—
355C2×C3×C4D3×D412yes—
356C2×C3×C4D3×D411yescharacteristic
357C2×C3×C4C2×#6711yescharacteristic
358C2×C3×C4C23×D311yescharacteristic
359C2×C3×C4C23×D311yescharacteristic
360#67—616no—
361#67—616no—
362C2×Dic3—22no—
363C2×Dic3—42no—
364C2×Dic3—64no—
365C2×Dic3—64no—
366C2×Dic3—62no—
367C2×Dic3—62no—
368C2×Dic3—616no—
369C2×Dic3—122no—
370C2×Dic3—124no—
371C2×Dic3(C2×D3)⋊C414yes—
372C2×Dic3C2×#6712yes—
373D12—24no—
374D12—22no—
375D12C2×C4×D314yescomplemented
376C4×D3—48no—
377C4×D3—616no—
378C4×D3(C2×D3)⋊C418yes—
379C4×D3C2×C4×D314yes—
380C4×D3C2×D1214yes—
381Dic6—34no—
382Dic6—34no—
383Dic6—64no—
384Dic6—64no—
385Dic6—64no—
386Dic6—62no—
387Dic6—62no—
388Dic6—122no—
389Dic6—124no—
390C3×C8—62no—
391C3⋊C8—22no—
392C3⋊C8—62no—
393C3⋊C8—62no—
394C3⋊C8—122no—
395C2×C32#41714yescomplemented
396C2×C32C22×C22⋊C411yescharacteristic
397C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
398C2×C32C2×#13711yescharacteristic
399C3×D3—24no—
400C3×D3—44no—
401C24—31no—
402C24—61no—
403#41—916no—
404#41—188no—
405#41—1816no—
406C2×Q8—92no—
407C2×Q8—94no—
408C2×Q8—182no—
409C2×Q8—181no—
410C2×D4—32no—
411C2×D4—34no—
412C2×D4—62no—
413C2×D4—61no—
414C2×D4—184no—
415C2×D4—188no—
416C22×C4—21no—
417C22×C4—31no—
418C22×C4—32no—
419C22×C4—34no—
420C22×C4—34no—
421C22×C4—32no—
422C22×C4—64no—
423C22×C4—61no—
424C22×C4—124no—
425C22×C4—184no—
426C22×C4—188no—
427C22×C4—181no—
428C22×C4C2×D3211yescharacteristic
429M16—188no—
430C2×C8—32no—
431C2×C8—62no—
432C2×C8—92no—
433C2×C8—182no—
434C4⋊C4—21no—
435C4⋊C4—32no—
436C4⋊C4—64no—
437C4⋊C4—61no—
438C4⋊C4C2×D3212yes—
439C22×C3—21no—
440C22×C3—22no—
441C22×C3—22no—
442C22×C3—22no—
443C22×C3—34no—
444C22×C3—62no—
445C22×C3—62no—
446C22×C3—68no—
447C22×C3—64no—
448C22×C3—128no—
449C22×C3—122no—
450C22×C3—122no—
451C22×C3D3×C22⋊C412yes—
452C22×C3#91112yes—
453C22×C3#91512yes—
454C22×C3C2×(C2×D3)⋊C412yes—
455C22×C3#93212yes—
456C22×C3#94212yes—
457C22×C3C2×D3×D411yescharacteristic
458C22×C3C22×#6711yescharacteristic
459C2×D3—28no—
460C2×D3—22no—
461C2×D3—22no—
462C2×D3—24no—
463C2×D3—42no—
464C2×D3—42no—
465C2×D3—48no—
466C2×D3C2×(C2×D3)⋊C414yes—
467C3×C4—21no—
468C3×C4—21no—
469C3×C4—22no—
470C3×C4—34no—
471C3×C4—42no—
472C3×C4—42no—
473C3×C4—82no—
474C3×C4—122no—
475C3×C4D3×C22⋊C412yes—
476C3×C4C2×(C2×D3)⋊C412yes—
477C3×C4C22×C4×D311yescharacteristic
478C3×C4C22×C4×D311yescharacteristic
479C3×C4C22×D1211yescharacteristic
480C3×C4C2×D3×D411yescharacteristic
481Dic3—42no—
482Dic3—64no—
483Dic3—64no—
484Dic3—124no—
485Dic3C2×(C2×D3)⋊C414yes—
486C32C2×#41711yescharacteristic, complemented, Sylow
487C23—32no—
488C23—34no—
489C23—62no—
490C23—62no—
491C23—62no—
492C23—64no—
493C23—122no—
494C23—122no—
495C23D3×#6711yescharacteristic
496Q8—94no—
497Q8—182no—
498Q8—184no—
499D4—34no—
500D4—62no—
501D4—64no—
502D4—1816no—
503C2×C4—22no—
504C2×C4—32no—
505C2×C4—34no—
506C2×C4—34no—
507C2×C4—34no—
508C2×C4—38no—
509C2×C4—42no—
510C2×C4—62no—
511C2×C4—128no—
512C2×C4—122no—
513C2×C4—1816no—
514C2×C4—182no—
515C2×C4—184no—
516C2×C4C4×D3212yes—
517C2×C4D3×D1212yes—
518C2×C4D3×#6711yescharacteristic
519C2×C4C22×D3211yescharacteristic
520C8—62no—
521C8—182no—
522C2×C3—21no—
523C2×C3—21no—
524C2×C3—24no—
525C2×C3—21no—
526C2×C3—64no—
527C2×C3—124no—
528C2×C3#477114yescomplemented
529C2×C3#496614yescomplemented
530C2×C3C2×D3×C22⋊C411yescharacteristic
531C2×C3C2×#91111yescharacteristic
532C2×C3C2×#91511yescharacteristic
533C2×C3C22×(C2×D3)⋊C411yescharacteristic
534C2×C3C2×#93211yescharacteristic
535C2×C3C2×#94211yescharacteristic
536D3—24no—
537D3—44no—
538C22—34no—
539C22—62no—
540C22—62no—
541C22—68no—
542C22—64no—
543C22—122no—
544C22—122no—
545C22—128no—
546C22D3×(C2×D3)⋊C412yes—
547C22#6393212yes—
548C22#6394612yes—
549C22C2×D3×#6711yescharacteristic
550C4—34no—
551C4—42no—
552C4—122no—
553C4—184no—
554C4D3×(C2×D3)⋊C412yes—
555C4C2×C4×D3211yescharacteristic
556C4C2×D3×D1211yescharacteristic
557C3—21no—
558C3C2×#477111yescharacteristic, complemented
559C3C2×#496611yescharacteristic, complemented
560C2—64no—
561C2—124no—
562C2#1059060714yesdirect product factor
563C2C2×D3×(C2×D3)⋊C411yescharacteristic
564C2C2×#6393211yescharacteristic
565C2C2×#6394611yescharacteristic
subgroupG/H
centerC23D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×#3795C2
cosocleC2×C32×C4C24
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#417
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×D3×C4⋊C4C2semidirect
3. C22×#3711C2semidirect
4. C2×#63637C2semidirect
5. C2×C3×#809C2semidirect
6. C2×#63567C2semidirect
7. C2×#63562C2semidirect
8. #10590607C2direct (N × H)
19. C2×#3795C4semidirect
27. C3×D3×C4⋊C4C22semidirect
29. C2×#3711C22semidirect
30. #63637C22semidirect
31. C3×#809C22semidirect
32. #63567C22semidirect
33. #63562C22semidirect
39. C2×D3×C4⋊C4D3semidirect
49. C2×#809D3semidirect
58. C2×#634C2×C4semidirect
64. C2×C3×D12C2×C4semidirect
78. #3795C2×C4semidirect
130. D3×C4⋊C4C2×D3semidirect
139. #809C2×D3semidirect
159. #634C22×C4semidirect
166. C3×D12C22×C4semidirect
224. C2×D12C4×D3semidirect
375. D12C2×C4×D3semidirect
395. C2×C32#417semidirect
486. C32C2×#417semidirect
528. C2×C3#4771semidirect
529. C2×C3#4966semidirect
558. C3C2×#4771semidirect
559. C3C2×#4966semidirect
562. C2#10590607direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37952
C2×C3×D3×C4⋊C42
C22×#37112
C2×#636372
C2×C3×#8092
C2×#635672
C2×#635622
#105906072
C2×#49663
C2×#47713