Finite Group Databasebeta

← C2×#10589713 #11902492

Subgroups — C2×#10589713 #11902492

Order 1152.

2448 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3699C212yesmaximal, complemented
2C2×C9×#121C211yesmaximal, characteristic, complemented
3C2×#63500C211yesmaximal, characteristic, complemented
4C2×#63497C212yesmaximal, complemented
5C2×D4×Dic9C211yesmaximal, characteristic, complemented
6C2×C4×#611C211yesmaximal, characteristic, complemented
7C22×C4⋊Dic9C211yesmaximal, characteristic, complemented
8#10589713C2116yesmaximal, direct product factor
9C2×C4⋊C4×D9C211yesmaximal, characteristic, complemented
10C2×#63450C211yesmaximal, characteristic, complemented
11C2×#63445C212yesmaximal, complemented
12C2×#63440C212yesmaximal, complemented
13C2×#5611—31nomaximal
14C22×D4×C9C2212yes—
15C22×D4×C9C2211yescharacteristic
16C23×C4×C9C2211yescharacteristic
17C22×#611C2212yes—
18C22×#611C2211yescharacteristic
19C23×Dic9C2212yes—
20C23×Dic9C2212yes—
21C2×#3699—216no—
22C2×#3699C22116yescomplemented
23C22×C4×D9C2212yes—
24C22×C4×D9C2211yescharacteristic
25C22×Dic18C2212yes—
26C9×#121C2218yescomplemented
27C2×C9×C4⋊C4C2211yescharacteristic
28C2×C9×C22⋊C4C2212yes—
29C2×#3676C2212yes—
30C2×#3676C2212yes—
31C2×#3676C2211yescharacteristic
32#63500C2218yescomplemented
33#63497C22116yescomplemented
34D4×Dic9C2218yescomplemented
35C4×#611C2218yescomplemented
36C2×(C2×D9)⋊C4C2211yescharacteristic
37C2×C4⋊Dic9C2212yes—
38C2×C4⋊Dic9C2211yescharacteristic
39C2×C4⋊Dic9C2211yescharacteristic
40C2×C4⋊Dic9C2218yescomplemented
41C2×Dic9⋊C4C2211yescharacteristic
42C2×Dic9⋊C4C2212yes—
43C2×Dic9⋊C4C2212yes—
44C2×C4×Dic9C2211yescharacteristic
45C4⋊C4×D9C2218yescomplemented
46#63450C2218yescomplemented
47#63445C22116yescomplemented
48#63440C22116yescomplemented
49C22×#237—32no—
50C2×C3×#121D311yescharacteristic
51C2×#938—31no—
52C2×#935—32no—
53C2×D4×Dic3—31no—
54C2×C4×#67—31no—
55C22×C4⋊Dic3—31no—
56#5611—316no—
57C2×D3×C4⋊C4—31no—
58C2×#888—31no—
59C2×#883—32no—
60C2×#878—32no—
61C24×C9C2312yes—
62C24×C9C2311yescharacteristic
63C23×D9C2311yescharacteristic
64C2×D4×C9—28no—
65C2×D4×C9—24no—
66C2×D4×C9C2314yes—
67C2×D4×C9C2318yes—
68C22×C4×C9—24no—
69C22×C4×C9C2311yescharacteristic
70C22×C4×C9C2314yes—
71C22×C4×C9C2312yes—
72C22×C4×C9C2311yescharacteristic
73C2×#611—28no—
74C2×#611D418yescomplemented
75C2×#611C2318yes—
76C2×#611C2314yes—
77C22×Dic9—28no—
78C22×Dic9—28no—
79C22×Dic9C2311yescharacteristic
80C22×Dic9C2318yes—
81C22×Dic9C2318yes—
82C22×Dic9C2311yescharacteristic
83C22×Dic9C2312yes—
84C22×Dic9C2312yes—
85C22×Dic9C2311yescharacteristic
86#3699—264no—
87C2×C4×D9—28no—
88C2×C4×D9—24no—
89C2×C4×D9C2314yes—
90C2×C4×D9C2318yes—
91C2×Dic18—28no—
92C2×Dic18C2318yes—
93C9×C4⋊C4C2314yes—
94C9×C22⋊C4C2318yes—
95#3676C2314yes—
96#3676C2318yes—
97#3676C2318yes—
98(C2×D9)⋊C4C2314yes—
99C4⋊Dic9C2314yes—
100C4⋊Dic9C2314yes—
101C4⋊Dic9C2318yes—
102Dic9⋊C4C2314yes—
103Dic9⋊C4C2318yes—
104Dic9⋊C4C2318yes—
105C4×Dic9C2314yes—
106C2×#547—91noSylow
107C22×C3×D4C2×D312yes—
108C22×C3×D4C2×D311yescharacteristic
109C23×C3×C4C2×D311yescharacteristic
110C22×#67—31no—
111C22×#67—32no—
112C23×Dic3—32no—
113C23×Dic3—32no—
114C2×#237—316no—
115C2×#237—616no—
116C22×C4×D3—32no—
117C22×C4×D3—31no—
118C22×Dic6—32no—
119C3×#121C2×D318yes—
120C2×C3×C4⋊C4C2×D311yescharacteristic
121C2×C3×C22⋊C4C2×D312yes—
122C2×#217—32no—
123C2×#217—32no—
124C2×#217—31no—
125#938—38no—
126#935—316no—
127D4×Dic3—38no—
128C4×#67—38no—
129C2×(C2×D3)⋊C4—31no—
130C2×C4⋊Dic3—32no—
131C2×C4⋊Dic3—31no—
132C2×C4⋊Dic3—31no—
133C2×C4⋊Dic3—38no—
134C2×Dic3⋊C4—31no—
135C2×Dic3⋊C4—32no—
136C2×Dic3⋊C4—32no—
137C2×C4×Dic3—31no—
138D3×C4⋊C4—38no—
139#888—38no—
140#883—316no—
141#878—316no—
142C23×C9—22no—
143C23×C9—22no—
144C23×C9—24no—
145C23×C9—24no—
146C23×C9—24no—
147C23×C9C2×D414yes—
148C23×C9C2414yes—
149C23×C9C2412yes—
150C23×C9C2411yescharacteristic
151C22×D9—22no—
152C22×D9—22no—
153C22×D9C2×D414yes—
154C22×D9C2412yes—
155D4×C9—216no—
156D4×C9—28no—
157C2×C4×C9—24no—
158C2×C4×C9—22no—
159C2×C4×C9—28no—
160C2×C4×C9#4114yescomplemented
161C2×C4×C9C2414yes—
162C2×C4×C9C2412yes—
163C2×C4×C9C2412yes—
164#611—216no—
165#611C2×D4116yescomplemented
166C2×Dic9—24no—
167C2×Dic9—24no—
168C2×Dic9—216no—
169C2×Dic9—22no—
170C2×Dic9—22no—
171C2×Dic9—216no—
172C2×Dic9C2×D414yes—
173C2×Dic9C2412yes—
174C2×Dic9C2412yes—
175C2×Dic9C2414yes—
176C2×Dic9C2414yes—
177C2×Dic9C2412yes—
178C4×D9—216no—
179C4×D9—28no—
180Dic18—216no—
181C22×#41—92no—
182#547—916no—
183C2×C4⋊Q8—91no—
184C2×#123—92no—
185C2×#123—92no—
186C2×C22⋊Q8—92no—
187C2×#121—91no—
188C2×#121D911yescharacteristic, complemented
189C2×C4×D4—91no—
190C2×C4×D4—91no—
191C22×C4⋊C4—91no—
192C22×C4⋊C4—91no—
193C24×C3C22×D312yes—
194C24×C3C22×D311yescharacteristic
195C23×D3—31no—
196C2×C3×D4—28no—
197C2×C3×D4—24no—
198C2×C3×D4C22×D314yes—
199C2×C3×D4C22×D318yes—
200C22×C3×C4—24no—
201C22×C3×C4C22×D312yes—
202C22×C3×C4C22×D311yescharacteristic
203C22×C3×C4C22×D314yes—
204C22×C3×C4C22×D311yescharacteristic
205C2×#67—38no—
206C2×#67—34no—
207C2×#67—38no—
208C2×#67—68no—
209C22×Dic3—31no—
210C22×Dic3—38no—
211C22×Dic3—31no—
212C22×Dic3—31no—
213C22×Dic3—32no—
214C22×Dic3—32no—
215C22×Dic3—38no—
216C22×Dic3—68no—
217C22×Dic3—68no—
218#237—664no—
219C2×C4×D3—38no—
220C2×C4×D3—34no—
221C2×C4×D3—68no—
222C2×C4×D3—64no—
223C2×Dic6—38no—
224C2×Dic6—68no—
225C3×C4⋊C4C22×D314yes—
226C3×C22⋊C4C22×D318yes—
227#217—38no—
228#217—38no—
229#217—34no—
230(C2×D3)⋊C4—34no—
231C4⋊Dic3—38no—
232C4⋊Dic3—34no—
233C4⋊Dic3—34no—
234Dic3⋊C4—34no—
235Dic3⋊C4—38no—
236Dic3⋊C4—38no—
237C4×Dic3—34no—
238C22×C9—28no—
239C22×C9—22no—
240C22×C9—22no—
241C22×C9—24no—
242C22×C9—24no—
243C22×C9—24no—
244C22×C9—48no—
245C22×C9C22×D414yes—
246C22×C9C22×D412yes—
247C22×C9C2×#4112yes—
248C22×C92−1+412yes—
249C22×C9C2511yescharacteristic
250C2×D9—28no—
251C2×D9—22no—
252C2×D9—22no—
253C2×D9C22×D414yes—
254C4×C9—24no—
255C4×C9—22no—
256C4×C9C2×#4114yescomplemented
257Dic9—24no—
258Dic9—24no—
259Dic9—22no—
260Dic9—22no—
261Dic9C22×D414yes—
262C2×#41—916no—
263C2×#41—1816no—
264C22×Q8—92no—
265C22×D4—91no—
266C22×D4—92no—
267C22×D4C2×D911yescharacteristic
268C22×D4C2×D912yes—
269C23×C4—92no—
270C23×C4—92no—
271C23×C4—91no—
272C23×C4—92no—
273C23×C4C2×D911yescharacteristic
274C4⋊Q8—98no—
275#123—916no—
276#123—916no—
277C22⋊Q8—916no—
278#121—98no—
279#121C2×D918yescomplemented
280C4×D4—98no—
281C4×D4—98no—
282C2×C4⋊C4—91no—
283C2×C4⋊C4—91no—
284C2×C4⋊C4—92no—
285C2×C4⋊C4—92no—
286C2×C4⋊C4—98no—
287C2×C4⋊C4—91no—
288C2×C4⋊C4—92no—
289C2×C4⋊C4—98no—
290C2×C4⋊C4C2×D911yescharacteristic
291C2×C22⋊C4—91no—
292C2×C22⋊C4—92no—
293C2×C22⋊C4—92no—
294C2×C22⋊C4—91no—
295C2×C22⋊C4C2×D912yes—
296C2×C42—91no—
297C23×C3—22no—
298C23×C3—22no—
299C23×C3—24no—
300C23×C3—24no—
301C23×C3—24no—
302C23×C3D3×D414yes—
303C23×C3C23×D314yes—
304C23×C3C23×D312yes—
305C23×C3C23×D311yescharacteristic
306C22×D3—34no—
307C22×D3—32no—
308C22×D3—62no—
309C22×D3—62no—
310C3×D4—216no—
311C3×D4—28no—
312C2×C3×C4—24no—
313C2×C3×C4—22no—
314C2×C3×C4—28no—
315C2×C3×C4#23714yes—
316C2×C3×C4C23×D314yes—
317C2×C3×C4C23×D312yes—
318C2×C3×C4C23×D312yes—
319#67—316no—
320#67—616no—
321C2×Dic3—34no—
322C2×Dic3—32no—
323C2×Dic3—32no—
324C2×Dic3—32no—
325C2×Dic3—34no—
326C2×Dic3—34no—
327C2×Dic3—616no—
328C2×Dic3—64no—
329C2×Dic3—64no—
330C2×Dic3—616no—
331C2×Dic3—62no—
332C2×Dic3—62no—
333C4×D3—616no—
334C4×D3—68no—
335Dic6—616no—
336C2×C9—24no—
337C2×C9—44no—
338C2×C9#54714yescomplemented
339C2×C9C23×D411yescharacteristic
340C2×C9C22×#4111yescharacteristic
341C2×C9C2×2−1+411yescharacteristic
342D9—24no—
343C24—91no—
344C24C22×D912yes—
345C24C22×D911yescharacteristic
346#41—1864no—
347C2×Q8—98no—
348C2×Q8—188no—
349C2×D4—28no—
350C2×D4—24no—
351C2×D4—98no—
352C2×D4—94no—
353C2×D4—98no—
354C2×D4—188no—
355C2×D4C22×D914yes—
356C2×D4C22×D918yes—
357C22×C4—24no—
358C22×C4—91no—
359C22×C4—98no—
360C22×C4—98no—
361C22×C4—91no—
362C22×C4—91no—
363C22×C4—92no—
364C22×C4—92no—
365C22×C4—94no—
366C22×C4—98no—
367C22×C4—188no—
368C22×C4—188no—
369C22×C4—188no—
370C22×C4—184no—
371C22×C4C22×D914yes—
372C22×C4C22×D911yescharacteristic
373C22×C4C22×D912yes—
374C22×C4C22×D911yescharacteristic
375C4⋊C4—94no—
376C4⋊C4—94no—
377C4⋊C4—98no—
378C4⋊C4—98no—
379C4⋊C4—94no—
380C4⋊C4—98no—
381C4⋊C4C22×D914yes—
382C22⋊C4—94no—
383C22⋊C4—98no—
384C22⋊C4—98no—
385C22⋊C4—94no—
386C22⋊C4C22×D918yes—
387C42—94no—
388C22×C3—22no—
389C22×C3—22no—
390C22×C3—28no—
391C22×C3—24no—
392C22×C3—24no—
393C22×C3—24no—
394C22×C3—48no—
395C22×C3C2×D3×D414yes—
396C22×C3C2×D3×D412yes—
397C22×C3C2×#23712yes—
398C22×C3#101012yes—
399C22×C3C24×D311yescharacteristic
400C2×D3—34no—
401C2×D3—62no—
402C2×D3—62no—
403C2×D3—68no—
404C3×C4—24no—
405C3×C4—22no—
406C3×C4C2×#23714yes—
407Dic3—34no—
408Dic3—64no—
409Dic3—64no—
410Dic3—62no—
411Dic3—62no—
412C9C2×#54711yescharacteristic, complemented, Sylow
413C23—22no—
414C23—22no—
415C23—24no—
416C23—24no—
417C23—24no—
418C23—92no—
419C23—94no—
420C23—182no—
421C23—182no—
422C23D4×D914yes—
423C23C23×D914yes—
424C23C23×D912yes—
425C23C23×D911yescharacteristic
426Q8—1816no—
427D4—216no—
428D4—28no—
429D4—916no—
430D4—1816no—
431C2×C4—24no—
432C2×C4—22no—
433C2×C4—28no—
434C2×C4—92no—
435C2×C4—94no—
436C2×C4—92no—
437C2×C4—92no—
438C2×C4—94no—
439C2×C4—94no—
440C2×C4—1816no—
441C2×C4—1816no—
442C2×C4—184no—
443C2×C4—184no—
444C2×C4—1816no—
445C2×C4—182no—
446C2×C4—182no—
447C2×C4—188no—
448C2×C4#369914yescomplemented
449C2×C4C23×D912yes—
450C2×C4C23×D914yes—
451C2×C4C23×D912yes—
452C2×C3—24no—
453C2×C3—44no—
454C2×C3#561114yes—
455C2×C3C22×D3×D411yescharacteristic
456C2×C3C22×#23711yescharacteristic
457C2×C3C2×#101011yescharacteristic
458D3—64no—
459C22—28no—
460C22—22no—
461C22—22no—
462C22—24no—
463C22—24no—
464C22—24no—
465C22—48no—
466C22—94no—
467C22—188no—
468C22—182no—
469C22—182no—
470C22C2×D4×D914yes—
471C22C2×D4×D912yes—
472C22C2×#369912yes—
473C22#6371612yes—
474C22C24×D911yescharacteristic
475C4—24no—
476C4—22no—
477C4—94no—
478C4—184no—
479C4—184no—
480C4—182no—
481C4—182no—
482C4C2×#369914yescomplemented
483C3C2×#561111yescharacteristic
484C2—24no—
485C2—44no—
486C2—184no—
487C2#1058971314yesdirect product factor
488C2C22×D4×D911yescharacteristic
489C2C22×#369911yescharacteristic
490C2C2×#6371611yescharacteristic
subgroupG/H
centerC23C23×D9
commutator, cosocleC22×C9C25
FrattiniC22×C3C24×D3
FittingC2×C9×#121C2
socleC23×C3C23×D3
hypercenterC2×#121D9
hypocenterC9C2×#547
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. C2×C9×#121C2semidirect
3. C2×#63500C2semidirect
4. C2×#63497C2semidirect
5. C2×D4×Dic9C2semidirect
6. C2×C4×#611C2semidirect
7. C22×C4⋊Dic9C2semidirect
8. #10589713C2direct (N × H)
9. C2×C4⋊C4×D9C2semidirect
10. C2×#63450C2semidirect
11. C2×#63445C2semidirect
12. C2×#63440C2semidirect
22. C2×#3699C22semidirect
26. C9×#121C22semidirect
32. #63500C22semidirect
33. #63497C22semidirect
34. D4×Dic9C22semidirect
35. C4×#611C22semidirect
40. C2×C4⋊Dic9C22semidirect
45. C4⋊C4×D9C22semidirect
46. #63450C22semidirect
47. #63445C22semidirect
48. #63440C22semidirect
74. C2×#611D4semidirect
160. C2×C4×C9#41semidirect
165. #611C2×D4semidirect
188. C2×#121D9semidirect
256. C4×C9C2×#41semidirect
279. #121C2×D9semidirect
338. C2×C9#547semidirect
412. C9C2×#547semidirect
448. C2×C4#3699semidirect
482. C4C2×#3699semidirect
487. C2#10589713direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#36992
C2×C9×#1212
C2×#635002
C2×#634972
C2×D4×Dic92
C2×C4×#6112
C22×C4⋊Dic92
#105897132
C2×C4⋊C4×D92
C2×#634502
C2×#634452
C2×#634402
C2×#56113