Finite Group Databasebeta

← C2×#10589701 #11902691

Subgroups — C2×#10589701 #11902691

Order 1152.

2604 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×#63502C211yesmaximal, characteristic, complemented
5C2×#63502C212yesmaximal, complemented
6C2×#63501C212yesmaximal, complemented
7C2×C4×#611C211yesmaximal, characteristic, complemented
8#10589701C2116yesmaximal, direct product factor
9C2×#63457C211yesmaximal, characteristic, complemented
10C2×#63449C211yesmaximal, characteristic, complemented
11C2×#63446C212yesmaximal, complemented
12C2×#611⋊C4C212yesmaximal, complemented
13C2×#5599—31nomaximal
14C22×D4×C9C2211yescharacteristic
15C22×D4×C9C2212yes—
16C23×C4×C9C2211yescharacteristic
17C22×#611C2212yes—
18C22×#611C2212yes—
19C22×#611C2212yes—
20C22×#611C2211yescharacteristic
21C22×#611C2212yes—
22C23×Dic9C2212yes—
23C2×#3699—28no—
24C2×#3699C2218yescomplemented
25C2×#3697—28no—
26C2×#3697C2218yescomplemented
27C22×D36C2211yescharacteristic
28C22×D36C2212yes—
29C22×C4×D9C2212yes—
30C22×C4×D9C2211yescharacteristic
31C22×Dic18C2211yescharacteristic
32C9×#121C2218yescomplemented
33C2×C9×C4⋊C4C2211yescharacteristic
34C2×C9×C22⋊C4C2212yes—
35C2×#3676C2211yescharacteristic
36#63502C2218yescomplemented
37#63502C22116yescomplemented
38#63501C22116yescomplemented
39C4×#611C2218yescomplemented
40C2×(C2×D9)⋊C4C2212yes—
41C2×(C2×D9)⋊C4C2211yescharacteristic
42C2×Dic9⋊C4C2211yescharacteristic
43C2×Dic9⋊C4C2212yes—
44C2×C4×Dic9C2212yes—
45C2×C4×Dic9C2211yescharacteristic
46#63457C2218yescomplemented
47#63449C2218yescomplemented
48#63446C22116yescomplemented
49#611⋊C4C22116yescomplemented
50C22×#237—31no—
51C22×#235—31no—
52C2×C3×#121D311yescharacteristic
53C2×#940—32no—
54C2×#940—31no—
55C2×#939—32no—
56C2×C4×#67—31no—
57#5599—316no—
58C2×#895—31no—
59C2×#887—31no—
60C2×#884—32no—
61C2×#67⋊C4—32no—
62C24×C9C2311yescharacteristic
63C24×C9C2312yes—
64C23×D9C2312yes—
65C23×D9C2311yescharacteristic
66C2×D4×C9—24no—
67C2×D4×C9—44no—
68C2×D4×C9C2314yes—
69C2×D4×C9C2318yes—
70C22×C4×C9—24no—
71C22×C4×C9C2311yescharacteristic
72C22×C4×C9C2312yes—
73C22×C4×C9C2314yes—
74C22×C4×C9C2311yescharacteristic
75C2×#611—28no—
76C2×#611—28no—
77C2×#611—28no—
78C2×#611—24no—
79C2×#611—44no—
80C2×#611C2314yes—
81C2×#611C2318yes—
82C2×#611C2318yes—
83C2×#611C2318yes—
84C2×#611C2318yes—
85C22×Dic9—28no—
86C22×Dic9C2311yescharacteristic
87C22×Dic9C2311yescharacteristic
88C22×Dic9C2318yes—
89C22×Dic9C2312yes—
90C22×Dic9C2311yescharacteristic
91#3699—232no—
92#3697—232no—
93C2×D36—24no—
94C2×D36—44no—
95C2×D36C2314yes—
96C2×D36C2318yes—
97C2×C4×D9—24no—
98C2×C4×D9—28no—
99C2×C4×D9C2314yes—
100C2×C4×D9C2318yes—
101C2×Dic18D418yescomplemented
102C2×Dic18C2314yes—
103C9×C4⋊C4C2314yes—
104C9×C22⋊C4C2318yes—
105#3676C2314yes—
106(C2×D9)⋊C4C2314yes—
107(C2×D9)⋊C4C2318yes—
108Dic9⋊C4C2314yes—
109Dic9⋊C4C2318yes—
110C4×Dic9C2314yes—
111C4×Dic9C2318yes—
112C2×#550—91noSylow
113C22×C3×D4C2×D311yescharacteristic
114C22×C3×D4C2×D312yes—
115C23×C3×C4C2×D311yescharacteristic
116C22×#67—32no—
117C22×#67—32no—
118C22×#67—32no—
119C22×#67—31no—
120C22×#67—32no—
121C23×Dic3—32no—
122C2×#237—38no—
123C2×#237—68no—
124C2×#235—38no—
125C2×#235—68no—
126C22×D12—31no—
127C22×D12—32no—
128C22×C4×D3—32no—
129C22×C4×D3—31no—
130C22×Dic6—31no—
131C3×#121C2×D318yes—
132C2×C3×C4⋊C4C2×D311yescharacteristic
133C2×C3×C22⋊C4C2×D312yes—
134C2×#217—31no—
135#940—316no—
136#940—38no—
137#939—316no—
138C4×#67—38no—
139C2×(C2×D3)⋊C4—32no—
140C2×(C2×D3)⋊C4—31no—
141C2×Dic3⋊C4—31no—
142C2×Dic3⋊C4—32no—
143C2×C4×Dic3—32no—
144C2×C4×Dic3—31no—
145#895—38no—
146#887—38no—
147#884—316no—
148#67⋊C4—316no—
149C23×C9—24no—
150C23×C9—22no—
151C23×C9—22no—
152C23×C9—24no—
153C23×C9—24no—
154C23×C9—22no—
155C23×C9C2412yes—
156C23×C9C2414yes—
157C23×C9C2411yescharacteristic
158C22×D9—24no—
159C22×D9—22no—
160C22×D9—24no—
161C22×D9—22no—
162C22×D9—22no—
163C22×D9—24no—
164C22×D9C2414yes—
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×C9C2414yes—
173C2×C4×C9C2412yes—
174C2×C4×C9C2412yes—
175#611—216no—
176#611—216no—
177#611—28no—
178#611—216no—
179#611—48no—
180C2×Dic9—22no—
181C2×Dic9—22no—
182C2×Dic9—216no—
183C2×Dic9C2×D418yes—
184C2×Dic9#4114yescomplemented
185C2×Dic9C2412yes—
186C2×Dic9C2412yes—
187C2×Dic9C2414yes—
188C2×Dic9C2412yes—
189D36—28no—
190D36—48no—
191C4×D9—28no—
192C4×D9—216no—
193Dic18C2×D4116yescomplemented
194C22×#41—91no—
195C22×#41—91no—
196#550—916no—
197C2×#127—92no—
198C2×#127—91no—
199C2×#121—92no—
200C2×#121—91no—
201C2×#121—92no—
202C2×#121D911yescharacteristic, complemented
203C2×C4×Q8—91no—
204C2×C4×D4—91no—
205C2×C4×D4—92no—
206C24×C3C22×D311yescharacteristic
207C24×C3C22×D312yes—
208C23×D3—32no—
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×D312yes—
216C22×C3×C4C22×D311yescharacteristic
217C22×C3×C4C22×D314yes—
218C22×C3×C4C22×D311yescharacteristic
219C2×#67—38no—
220C2×#67—38no—
221C2×#67—34no—
222C2×#67—38no—
223C2×#67—38no—
224C2×#67—68no—
225C2×#67—68no—
226C2×#67—68no—
227C2×#67—64no—
228C2×#67—124no—
229C22×Dic3—31no—
230C22×Dic3—32no—
231C22×Dic3—38no—
232C22×Dic3—31no—
233C22×Dic3—31no—
234C22×Dic3—68no—
235#237—632no—
236#235—632no—
237C2×D12—34no—
238C2×D12—38no—
239C2×D12—64no—
240C2×D12—124no—
241C2×C4×D3—38no—
242C2×C4×D3—34no—
243C2×C4×D3—68no—
244C2×C4×D3—64no—
245C2×Dic6—38no—
246C2×Dic6—34no—
247C3×C4⋊C4C22×D314yes—
248C3×C22⋊C4C22×D318yes—
249#217—34no—
250(C2×D3)⋊C4—38no—
251(C2×D3)⋊C4—34no—
252Dic3⋊C4—34no—
253Dic3⋊C4—38no—
254C4×Dic3—38no—
255C4×Dic3—34no—
256C22×C9—24no—
257C22×C9—22no—
258C22×C9—22no—
259C22×C9—24no—
260C22×C9—24no—
261C22×C9—22no—
262C22×C9—48no—
263C22×C9—44no—
264C22×C9C22×D412yes—
265C22×C9C2×#4112yes—
266C22×C9H(5,𝔽2)12yes—
267C22×C9C2511yescharacteristic
268C2×D9—24no—
269C2×D9—22no—
270C2×D9—24no—
271C2×D9—22no—
272C2×D9—22no—
273C2×D9—24no—
274C2×D9—48no—
275C2×D9—44no—
276C4×C9—22no—
277C4×C9—24no—
278C4×C9C22×D414yes—
279Dic9—22no—
280Dic9—22no—
281Dic9C22×D418yes—
282Dic9C2×#4114yescomplemented
283C2×#41—98no—
284C2×#41—98no—
285C2×#41—188no—
286C2×#41—188no—
287C22×Q8—91no—
288C22×D4—91no—
289C22×D4—92no—
290C22×D4—92no—
291C22×D4—92no—
292C22×D4—92no—
293C22×D4—91no—
294C22×D4—92no—
295C22×D4C2×D911yescharacteristic
296C22×D4C2×D912yes—
297C23×C4—92no—
298C23×C4—92no—
299C23×C4—91no—
300C23×C4C2×D911yescharacteristic
301#127—916no—
302#127—98no—
303#121—916no—
304#121—98no—
305#121—916no—
306#121C2×D918yescomplemented
307C4×Q8—98no—
308C4×D4—98no—
309C4×D4—916no—
310C2×C4⋊C4—91no—
311C2×C4⋊C4—92no—
312C2×C4⋊C4C2×D911yescharacteristic
313C2×C22⋊C4—91no—
314C2×C22⋊C4—91no—
315C2×C22⋊C4—92no—
316C2×C22⋊C4C2×D912yes—
317C2×C42—92no—
318C2×C42—91no—
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—64no—
331C22×D3—62no—
332C22×D3—62no—
333C22×D3—64no—
334C22×D3—64no—
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×D314yes—
343C2×C3×C4C23×D312yes—
344C2×C3×C4C23×D312yes—
345#67—616no—
346#67—616no—
347#67—616no—
348#67—68no—
349#67—128no—
350C2×Dic3—38no—
351C2×Dic3—34no—
352C2×Dic3—32no—
353C2×Dic3—34no—
354C2×Dic3—32no—
355C2×Dic3—32no—
356C2×Dic3—616no—
357C2×Dic3—62no—
358C2×Dic3—62no—
359D12—68no—
360D12—128no—
361C4×D3—616no—
362C4×D3—68no—
363Dic6—316no—
364C2×C9—44no—
365C2×C9—42no—
366C2×C9#55014yescomplemented
367C2×C9C23×D411yescharacteristic
368C2×C9C22×#4111yescharacteristic
369C2×C9C2×H(5,𝔽2)11yescharacteristic
370D9—44no—
371D9—42no—
372C24—91no—
373C24—92no—
374C24C22×D911yescharacteristic
375C24C22×D912yes—
376#41—1832no—
377#41—1832no—
378C2×Q8—98no—
379C2×Q8—94no—
380C2×D4—24no—
381C2×D4—44no—
382C2×D4—94no—
383C2×D4—98no—
384C2×D4—98no—
385C2×D4—98no—
386C2×D4—98no—
387C2×D4—94no—
388C2×D4—98no—
389C2×D4—188no—
390C2×D4—188no—
391C2×D4—184no—
392C2×D4—188no—
393C2×D4—184no—
394C2×D4—364no—
395C2×D4—364no—
396C2×D4C22×D914yes—
397C2×D4C22×D918yes—
398C22×C4—24no—
399C22×C4—91no—
400C22×C4—92no—
401C22×C4—98no—
402C22×C4—91no—
403C22×C4—91no—
404C22×C4—98no—
405C22×C4—94no—
406C22×C4—188no—
407C22×C4—188no—
408C22×C4—184no—
409C22×C4C22×D914yes—
410C22×C4C22×D912yes—
411C22×C4C22×D911yescharacteristic
412C22×C4C22×D911yescharacteristic
413C4⋊C4—94no—
414C4⋊C4—98no—
415C4⋊C4C22×D914yes—
416C22⋊C4—94no—
417C22⋊C4—94no—
418C22⋊C4—98no—
419C22⋊C4C22×D918yes—
420C42—98no—
421C42—94no—
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×C3D3×#4112yes—
433C22×C3C24×D311yescharacteristic
434C2×D3—64no—
435C2×D3—62no—
436C2×D3—62no—
437C2×D3—64no—
438C2×D3—64no—
439C2×D3—62no—
440C2×D3—128no—
441C2×D3—124no—
442C3×C4—22no—
443C3×C4—24no—
444C3×C4C2×D3×D414yes—
445Dic3—38no—
446Dic3—34no—
447Dic3—62no—
448Dic3—62no—
449C9C2×#55011yescharacteristic, complemented, Sylow
450C23—22no—
451C23—24no—
452C23—22no—
453C23—24no—
454C23—22no—
455C23—24no—
456C23—92no—
457C23—94no—
458C23—184no—
459C23—182no—
460C23—182no—
461C23—184no—
462C23—182no—
463C23—184no—
464C23C23×D912yes—
465C23C23×D914yes—
466C23C23×D911yescharacteristic
467Q8—916no—
468D4—28no—
469D4—48no—
470D4—1816no—
471D4—1816no—
472D4—188no—
473D4—1816no—
474D4—188no—
475D4—368no—
476D4—368no—
477C2×C4—22no—
478C2×C4—24no—
479C2×C4—28no—
480C2×C4—92no—
481C2×C4—94no—
482C2×C4—98no—
483C2×C4—94no—
484C2×C4—92no—
485C2×C4—92no—
486C2×C4—1816no—
487C2×C4—1816no—
488C2×C4—182no—
489C2×C4—182no—
490C2×C4—188no—
491C2×C4D4×D914yes—
492C2×C4C23×D914yes—
493C2×C4C23×D912yes—
494C2×C4C23×D912yes—
495C2×C3—44no—
496C2×C3—42no—
497C2×C3#559914yes—
498C2×C3C22×D3×D411yescharacteristic
499C2×C3C2×#100411yescharacteristic
500C2×C3C2×D3×#4111yescharacteristic
501D3—124no—
502D3—122no—
503C22—22no—
504C22—24no—
505C22—22no—
506C22—24no—
507C22—22no—
508C22—24no—
509C22—44no—
510C22—48no—
511C22—184no—
512C22—182no—
513C22—182no—
514C22—184no—
515C22—182no—
516C22—184no—
517C22—368no—
518C22—364no—
519C22C2×D4×D912yes—
520C22#6371012yes—
521C22#41×D912yes—
522C22C24×D911yescharacteristic
523C4—22no—
524C4—24no—
525C4—98no—
526C4—94no—
527C4—182no—
528C4—182no—
529C4C2×D4×D914yes—
530C3C2×#559911yescharacteristic
531C2—42no—
532C2—44no—
533C2—364no—
534C2—362no—
535C2#1058970114yesdirect product factor
536C2C22×D4×D911yescharacteristic
537C2C2×#6371011yescharacteristic
538C2C2×#41×D911yescharacteristic
subgroupG/H
centerC23C23×D9
commutator, cosocleC22×C9C25
FrattiniC22×C3C24×D3
FittingC2×C9×#121C2
socleC23×C3C23×D3
hypercenterC2×#121D9
hypocenterC9C2×#550
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×#63502C2semidirect
5. C2×#63502C2semidirect
6. C2×#63501C2semidirect
7. C2×C4×#611C2semidirect
8. #10589701C2direct (N × H)
9. C2×#63457C2semidirect
10. C2×#63449C2semidirect
11. C2×#63446C2semidirect
12. C2×#611⋊C4C2semidirect
24. C2×#3699C22semidirect
26. C2×#3697C22semidirect
32. C9×#121C22semidirect
36. #63502C22semidirect
37. #63502C22semidirect
38. #63501C22semidirect
39. C4×#611C22semidirect
46. #63457C22semidirect
47. #63449C22semidirect
48. #63446C22semidirect
49. #611⋊C4C22semidirect
101. C2×Dic18D4semidirect
184. C2×Dic9#41semidirect
193. Dic18C2×D4semidirect
202. C2×#121D9semidirect
282. Dic9C2×#41semidirect
306. #121C2×D9semidirect
366. C2×C9#550semidirect
449. C9C2×#550semidirect
535. C2#10589701direct (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×#635022
C2×#635012
C2×C4×#6112
#105897012
C2×#634572
C2×#634492
C2×#634462
C2×#611⋊C42
C2×#55993