Finite Group Databasebeta

← C2×#10589710 #11901127

Subgroups — C2×#10589710 #11901127

Order 1152.

2460 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3699C211yesmaximal, characteristic, complemented
2C22×#3697C211yesmaximal, characteristic, complemented
3C2×C9×#121C211yesmaximal, characteristic, complemented
4C2×#63501C212yesmaximal, complemented
5C2×#63500C211yesmaximal, characteristic, complemented
6C2×#63500C212yesmaximal, complemented
7C2×#63486C211yesmaximal, characteristic, complemented
8#10589710C2116yesmaximal, direct product factor
9C2×#63459C211yesmaximal, characteristic, complemented
10C2×C4⋊C4×D9C211yesmaximal, characteristic, complemented
11C2×#63446C212yesmaximal, complemented
12C2×#63440C212yesmaximal, complemented
13C2×#5608—31nomaximal
14C22×D4×C9C2211yescharacteristic
15C22×D4×C9C2212yes—
16C23×C4×C9C2211yescharacteristic
17C22×#611C2211yescharacteristic
18C22×#611C2211yescharacteristic
19C22×#611C2212yes—
20C22×#611C2212yes—
21C23×Dic9C2212yes—
22C2×#3699—28no—
23C2×#3699C2218yescomplemented
24C2×#3697—28no—
25C2×#3697C2218yescomplemented
26C22×D36C2211yescharacteristic
27C22×C4×D9C2211yescharacteristic
28C22×C4×D9C2212yes—
29C22×C4×D9C2211yescharacteristic
30C22×Dic18C2211yescharacteristic
31C22×Dic18C2211yescharacteristic
32C9×#121C2218yescomplemented
33C2×C9×C4⋊C4C2211yescharacteristic
34C2×C9×C22⋊C4C2212yes—
35C2×#3676C2212yes—
36C2×#3676C2212yes—
37#63501C22116yescomplemented
38#63500C22116yescomplemented
39#63500C2218yescomplemented
40C2×(C2×D9)⋊C4C2212yes—
41C2×C4⋊Dic9C2212yes—
42C2×C4⋊Dic9C2211yescharacteristic
43#63486C2218yescomplemented
44C2×Dic9⋊C4C2212yes—
45C2×Dic9⋊C4C2212yes—
46#63459C2218yescomplemented
47C4⋊C4×D9C2218yescomplemented
48#63446C22116yescomplemented
49#63440C22116yescomplemented
50C22×#237—31no—
51C22×#235—31no—
52C2×C3×#121D311yescharacteristic
53C2×#939—32no—
54C2×#938—32no—
55C2×#938—31no—
56C2×#924—31no—
57#5608—316no—
58C2×#897—31no—
59C2×D3×C4⋊C4—31no—
60C2×#884—32no—
61C2×#878—32no—
62C24×C9C2311yescharacteristic
63C24×C9C2312yes—
64C23×D9C2311yescharacteristic
65C23×D9C2311yescharacteristic
66C2×D4×C9—24no—
67C2×D4×C9—44no—
68C2×D4×C9C2314yes—
69C2×D4×C9C2318yes—
70C22×C4×C9—24no—
71C22×C4×C9C2312yes—
72C22×C4×C9C2311yescharacteristic
73C22×C4×C9C2314yes—
74C22×C4×C9C2311yescharacteristic
75C2×#611—24no—
76C2×#611—28no—
77C2×#611—24no—
78C2×#611—44no—
79C2×#611C2314yes—
80C2×#611C2318yes—
81C2×#611C2314yes—
82C2×#611C2318yes—
83C22×Dic9—28no—
84C22×Dic9C2312yes—
85C22×Dic9C2318yes—
86C22×Dic9C2311yescharacteristic
87C22×Dic9C2312yes—
88C22×Dic9C2311yescharacteristic
89#3699—232no—
90#3697—232no—
91C2×D36—24no—
92C2×D36C2314yes—
93C2×C4×D9—24no—
94C2×C4×D9—44no—
95C2×C4×D9D418yescomplemented
96C2×C4×D9C2314yes—
97C2×C4×D9C2318yes—
98C2×C4×D9C2314yes—
99C2×Dic18—24no—
100C2×Dic18—24no—
101C2×Dic18C2314yes—
102C2×Dic18C2314yes—
103C9×C4⋊C4C2314yes—
104C9×C22⋊C4C2318yes—
105#3676C2318yes—
106#3676C2318yes—
107(C2×D9)⋊C4C2318yes—
108C4⋊Dic9C2318yes—
109C4⋊Dic9C2314yes—
110Dic9⋊C4C2318yes—
111Dic9⋊C4C2318yes—
112C2×#537—91noSylow
113C22×C3×D4C2×D311yescharacteristic
114C22×C3×D4C2×D312yes—
115C23×C3×C4C2×D311yescharacteristic
116C22×#67—31no—
117C22×#67—31no—
118C22×#67—32no—
119C22×#67—32no—
120C23×Dic3—32no—
121C2×#237—38no—
122C2×#237—68no—
123C2×#235—38no—
124C2×#235—68no—
125C22×D12—31no—
126C22×C4×D3—31no—
127C22×C4×D3—31no—
128C22×C4×D3—32no—
129C22×Dic6—31no—
130C22×Dic6—31no—
131C3×#121C2×D318yes—
132C2×C3×C4⋊C4C2×D311yescharacteristic
133C2×C3×C22⋊C4C2×D312yes—
134C2×#217—32no—
135C2×#217—32no—
136#939—316no—
137#938—316no—
138#938—38no—
139C2×(C2×D3)⋊C4—32no—
140C2×C4⋊Dic3—32no—
141C2×C4⋊Dic3—31no—
142#924—38no—
143C2×Dic3⋊C4—32no—
144C2×Dic3⋊C4—32no—
145#897—38no—
146D3×C4⋊C4—38no—
147#884—316no—
148#878—316no—
149C23×C9—24no—
150C23×C9—22no—
151C23×C9—24no—
152C23×C9—22no—
153C23×C9—22no—
154C23×C9—24no—
155C23×C9C2412yes—
156C23×C9C2414yes—
157C23×C9C2411yescharacteristic
158C22×D9—22no—
159C22×D9—22no—
160C22×D9—22no—
161C22×D9—22no—
162C22×D9—22no—
163C22×D9C2×D414yes—
164C22×D9C2412yes—
165C22×D9C2412yes—
166D4×C9—28no—
167D4×C9—48no—
168C2×C4×C9—22no—
169C2×C4×C9—24no—
170C2×C4×C9—28no—
171C2×C4×C9C2×D414yes—
172C2×C4×C9C2412yes—
173C2×C4×C9C2414yes—
174C2×C4×C9C2412yes—
175#611—28no—
176#611—216no—
177#611—28no—
178#611—48no—
179C2×Dic9—22no—
180C2×Dic9—24no—
181C2×Dic9—24no—
182C2×Dic9—216no—
183C2×Dic9C2×D414yes—
184C2×Dic9C2414yes—
185C2×Dic9C2414yes—
186C2×Dic9C2412yes—
187C2×Dic9C2412yes—
188D36—28no—
189C4×D9—28no—
190C4×D9—48no—
191C4×D9C2×D4116yescomplemented
192Dic18—28no—
193Dic18—28no—
194C22×#41—91no—
195C22×#41—91no—
196#537—916no—
197C2×C22⋊Q8—91no—
198C2×C22⋊Q8—91no—
199C2×C22⋊Q8—92no—
200C2×#121—91no—
201C2×#121—92no—
202C2×#121—92no—
203C2×#121—92no—
204C2×#121D911yescharacteristic, complemented
205C22×C4⋊C4—91no—
206C24×C3C22×D311yescharacteristic
207C24×C3C22×D312yes—
208C23×D3—31no—
209C23×D3—31no—
210C2×C3×D4—24no—
211C2×C3×D4—44no—
212C2×C3×D4C22×D314yes—
213C2×C3×D4C22×D318yes—
214C22×C3×C4—24no—
215C22×C3×C4C22×D311yescharacteristic
216C22×C3×C4C22×D312yes—
217C22×C3×C4C22×D314yes—
218C22×C3×C4C22×D311yescharacteristic
219C2×#67—38no—
220C2×#67—34no—
221C2×#67—34no—
222C2×#67—38no—
223C2×#67—64no—
224C2×#67—64no—
225C2×#67—68no—
226C2×#67—124no—
227C22×Dic3—31no—
228C22×Dic3—38no—
229C22×Dic3—32no—
230C22×Dic3—32no—
231C22×Dic3—31no—
232C22×Dic3—68no—
233#237—632no—
234#235—632no—
235C2×D12—34no—
236C2×D12—64no—
237C2×C4×D3—38no—
238C2×C4×D3—34no—
239C2×C4×D3—34no—
240C2×C4×D3—38no—
241C2×C4×D3—64no—
242C2×C4×D3—124no—
243C2×Dic6—34no—
244C2×Dic6—34no—
245C2×Dic6—64no—
246C2×Dic6—64no—
247C3×C4⋊C4C22×D314yes—
248C3×C22⋊C4C22×D318yes—
249#217—38no—
250#217—38no—
251(C2×D3)⋊C4—38no—
252C4⋊Dic3—38no—
253C4⋊Dic3—34no—
254Dic3⋊C4—38no—
255Dic3⋊C4—38no—
256C22×C9—24no—
257C22×C9—22no—
258C22×C9—24no—
259C22×C9—22no—
260C22×C9—22no—
261C22×C9—24no—
262C22×C9—48no—
263C22×C9—44no—
264C22×C9C22×D412yes—
265C22×C9H(5,𝔽2)12yes—
266C22×C92−1+412yes—
267C22×C9C2511yescharacteristic
268C2×D9—28no—
269C2×D9—22no—
270C2×D9—22no—
271C2×D9—22no—
272C2×D9—22no—
273C2×D9—22no—
274C2×D9—44no—
275C2×D9C22×D414yes—
276C4×C9—22no—
277C4×C9—24no—
278C4×C9C22×D414yes—
279Dic9—22no—
280Dic9—24no—
281Dic9—24no—
282Dic9C22×D414yes—
283C2×#41—98no—
284C2×#41—98no—
285C2×#41—188no—
286C2×#41—188no—
287C22×Q8—91no—
288C22×Q8—91no—
289C22×D4—91no—
290C22×D4—91no—
291C22×D4—92no—
292C22×D4—92no—
293C22×D4—91no—
294C22×D4C2×D911yescharacteristic
295C22×D4C2×D912yes—
296C23×C4—91no—
297C23×C4—92no—
298C23×C4—91no—
299C23×C4—92no—
300C23×C4C2×D911yescharacteristic
301C22⋊Q8—98no—
302C22⋊Q8—98no—
303C22⋊Q8—916no—
304#121—98no—
305#121—916no—
306#121—916no—
307#121—916no—
308#121C2×D918yescomplemented
309C2×C4⋊C4—92no—
310C2×C4⋊C4—91no—
311C2×C4⋊C4—92no—
312C2×C4⋊C4—92no—
313C2×C4⋊C4—98no—
314C2×C4⋊C4C2×D911yescharacteristic
315C2×C22⋊C4—92no—
316C2×C22⋊C4—92no—
317C2×C22⋊C4—92no—
318C2×C22⋊C4C2×D912yes—
319C23×C3—24no—
320C23×C3—22no—
321C23×C3—24no—
322C23×C3—22no—
323C23×C3—22no—
324C23×C3—24no—
325C23×C3C23×D312yes—
326C23×C3C23×D314yes—
327C23×C3C23×D311yescharacteristic
328C22×D3—34no—
329C22×D3—32no—
330C22×D3—32no—
331C22×D3—62no—
332C22×D3—62no—
333C22×D3—62no—
334C22×D3—62no—
335C22×D3—62no—
336C3×D4—28no—
337C3×D4—48no—
338C2×C3×C4—22no—
339C2×C3×C4—24no—
340C2×C3×C4—28no—
341C2×C3×C4D3×D414yes—
342C2×C3×C4C23×D312yes—
343C2×C3×C4C23×D314yes—
344C2×C3×C4C23×D312yes—
345#67—68no—
346#67—68no—
347#67—616no—
348#67—128no—
349C2×Dic3—34no—
350C2×Dic3—32no—
351C2×Dic3—34no—
352C2×Dic3—34no—
353C2×Dic3—32no—
354C2×Dic3—616no—
355C2×Dic3—62no—
356C2×Dic3—64no—
357C2×Dic3—64no—
358D12—68no—
359C4×D3—316no—
360C4×D3—68no—
361C4×D3—128no—
362Dic6—68no—
363Dic6—68no—
364C2×C9—44no—
365C2×C9—42no—
366C2×C9#53714yescomplemented
367C2×C9C23×D411yescharacteristic
368C2×C9C2×H(5,𝔽2)11yescharacteristic
369C2×C9C2×2−1+411yescharacteristic
370D9—24no—
371D9—42no—
372C24—91no—
373C24—91no—
374C24C22×D911yescharacteristic
375C24C22×D912yes—
376#41—1832no—
377#41—1832no—
378C2×Q8—94no—
379C2×Q8—94no—
380C2×Q8—184no—
381C2×Q8—184no—
382C2×D4—24no—
383C2×D4—44no—
384C2×D4—94no—
385C2×D4—94no—
386C2×D4—98no—
387C2×D4—98no—
388C2×D4—94no—
389C2×D4—184no—
390C2×D4—184no—
391C2×D4—184no—
392C2×D4—188no—
393C2×D4—364no—
394C2×D4C22×D914yes—
395C2×D4C22×D918yes—
396C22×C4—24no—
397C22×C4—91no—
398C22×C4—98no—
399C22×C4—94no—
400C22×C4—98no—
401C22×C4—92no—
402C22×C4—91no—
403C22×C4—92no—
404C22×C4—94no—
405C22×C4—98no—
406C22×C4—188no—
407C22×C4—184no—
408C22×C4—364no—
409C22×C4C22×D914yes—
410C22×C4C22×D912yes—
411C22×C4C22×D911yescharacteristic
412C22×C4C22×D911yescharacteristic
413C4⋊C4—98no—
414C4⋊C4—94no—
415C4⋊C4—98no—
416C4⋊C4—98no—
417C4⋊C4C22×D914yes—
418C22⋊C4—98no—
419C22⋊C4—98no—
420C22⋊C4—98no—
421C22⋊C4C22×D918yes—
422C22×C3—24no—
423C22×C3—22no—
424C22×C3—24no—
425C22×C3—22no—
426C22×C3—22no—
427C22×C3—24no—
428C22×C3—48no—
429C22×C3—44no—
430C22×C3C2×D3×D412yes—
431C22×C3#100412yes—
432C22×C3#101012yes—
433C22×C3C24×D311yescharacteristic
434C2×D3—34no—
435C2×D3—62no—
436C2×D3—62no—
437C2×D3—68no—
438C2×D3—62no—
439C2×D3—62no—
440C2×D3—62no—
441C2×D3—124no—
442C3×C4—22no—
443C3×C4—24no—
444C3×C4C2×D3×D414yes—
445Dic3—34no—
446Dic3—62no—
447Dic3—64no—
448Dic3—64no—
449C9C2×#53711yescharacteristic, complemented, Sylow
450C23—22no—
451C23—24no—
452C23—22no—
453C23—24no—
454C23—22no—
455C23—24no—
456C23—92no—
457C23—94no—
458C23—92no—
459C23—182no—
460C23—182no—
461C23—182no—
462C23—182no—
463C23—182no—
464C23C23×D912yes—
465C23C23×D914yes—
466C23C23×D911yescharacteristic
467Q8—188no—
468Q8—188no—
469D4—28no—
470D4—48no—
471D4—188no—
472D4—188no—
473D4—188no—
474D4—1816no—
475D4—368no—
476C2×C4—22no—
477C2×C4—24no—
478C2×C4—28no—
479C2×C4—92no—
480C2×C4—94no—
481C2×C4—916no—
482C2×C4—94no—
483C2×C4—92no—
484C2×C4—94no—
485C2×C4—1816no—
486C2×C4—184no—
487C2×C4—182no—
488C2×C4—184no—
489C2×C4—188no—
490C2×C4—368no—
491C2×C4D4×D914yes—
492C2×C4C23×D914yes—
493C2×C4C23×D912yes—
494C2×C4C23×D912yes—
495C2×C3—44no—
496C2×C3—42no—
497C2×C3#560814yes—
498C2×C3C22×D3×D411yescharacteristic
499C2×C3C2×#100411yescharacteristic
500C2×C3C2×#101011yescharacteristic
501D3—64no—
502D3—122no—
503C22—22no—
504C22—24no—
505C22—22no—
506C22—24no—
507C22—22no—
508C22—24no—
509C22—44no—
510C22—48no—
511C22—94no—
512C22—188no—
513C22—182no—
514C22—182no—
515C22—182no—
516C22—182no—
517C22—182no—
518C22—364no—
519C22C2×D4×D912yes—
520C22#6371012yes—
521C22#6371612yes—
522C22C24×D911yescharacteristic
523C4—22no—
524C4—24no—
525C4—94no—
526C4—184no—
527C4—182no—
528C4—184no—
529C4C2×D4×D914yes—
530C3C2×#560811yescharacteristic
531C2—42no—
532C2—44no—
533C2—184no—
534C2—362no—
535C2#1058971014yesdirect product factor
536C2C22×D4×D911yescharacteristic
537C2C2×#6371011yescharacteristic
538C2C2×#6371611yescharacteristic
subgroupG/H
centerC23C23×D9
commutator, cosocleC22×C9C25
FrattiniC22×C3C24×D3
FittingC2×C9×#121C2
socleC23×C3C23×D3
hypercenterC2×#121D9
hypocenterC9C2×#537
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C22×#3699C2semidirect
2. C22×#3697C2semidirect
3. C2×C9×#121C2semidirect
4. C2×#63501C2semidirect
5. C2×#63500C2semidirect
6. C2×#63500C2semidirect
7. C2×#63486C2semidirect
8. #10589710C2direct (N × H)
9. C2×#63459C2semidirect
10. C2×C4⋊C4×D9C2semidirect
11. C2×#63446C2semidirect
12. C2×#63440C2semidirect
23. C2×#3699C22semidirect
25. C2×#3697C22semidirect
32. C9×#121C22semidirect
37. #63501C22semidirect
38. #63500C22semidirect
39. #63500C22semidirect
43. #63486C22semidirect
46. #63459C22semidirect
47. C4⋊C4×D9C22semidirect
48. #63446C22semidirect
49. #63440C22semidirect
95. C2×C4×D9D4semidirect
191. C4×D9C2×D4semidirect
204. C2×#121D9semidirect
308. #121C2×D9semidirect
366. C2×C9#537semidirect
449. C9C2×#537semidirect
535. C2#10589710direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#36992
C22×#36972
C2×C9×#1212
C2×#635012
C2×#635002
C2×#634862
#105897102
C2×#634592
C2×C4⋊C4×D92
C2×#634462
C2×#634402
C2×#56083