Finite Group Databasebeta

← C2×#10589721 #11901471

Subgroups — C2×#10589721 #11901471

Order 1152.

1890 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C9×#121C211yesmaximal, characteristic, complemented
2C2×#63502C211yesmaximal, characteristic, complemented
3C2×#63501C212yesmaximal, complemented
4C2×#63500C212yesmaximal, complemented
5C2×D4×Dic9C211yesmaximal, characteristic, complemented
6C2×#63492C211yesmaximal, characteristic, complemented
7C2×#63488C211yesmaximal, characteristic, complemented
8#10589721C2116yesmaximal, direct product factor
9C2×#63455C211yesmaximal, characteristic, complemented
10C2×#63452C211yesmaximal, characteristic, complemented
11C2×#63448C212yesmaximal, complemented
12C2×#63445C212yesmaximal, complemented
13C2×#5619—31nomaximal
14C22×D4×C9C2211yescharacteristic
15C22×D4×C9C2212yes—
16C23×C4×C9C2211yescharacteristic
17C22×#611C2212yes—
18C22×#611C2212yes—
19C22×#611C2212yes—
20C23×Dic9C2212yes—
21C22×D36C2211yescharacteristic
22C22×C4×D9C2212yes—
23C9×#121C2218yescomplemented
24C2×C9×C4⋊C4C2211yescharacteristic
25C2×C9×C22⋊C4C2212yes—
26C2×#3676C2212yes—
27C2×#3676C2211yescharacteristic
28C2×#3676C2211yescharacteristic
29#63502C2218yescomplemented
30#63501C22116yescomplemented
31#63500C22116yescomplemented
32D4×Dic9C2218yescomplemented
33#63492C2218yescomplemented
34C2×(C2×D9)⋊C4C2212yes—
35C2×(C2×D9)⋊C4C2212yes—
36#63488C2218yescomplemented
37C2×C4⋊Dic9C2211yescharacteristic
38C2×C4⋊Dic9C2211yescharacteristic
39C2×C4⋊Dic9C2212yes—
40C2×C4⋊Dic9C2211yescharacteristic
41C2×Dic9⋊C4C2212yes—
42C2×C4×Dic9C2211yescharacteristic
43C2×C4×Dic9C2211yescharacteristic
44#63455C2218yescomplemented
45#63452C2218yescomplemented
46#63448C22116yescomplemented
47#63445C22116yescomplemented
48C2×C3×#121D311yescharacteristic
49C2×#940—31no—
50C2×#939—32no—
51C2×#938—32no—
52C2×D4×Dic3—31no—
53C2×#930—31no—
54C2×#926—31no—
55#5619—316no—
56C2×#893—31no—
57C2×#890—31no—
58C2×#886—32no—
59C2×#883—32no—
60C24×C9C2311yescharacteristic
61C24×C9C2312yes—
62C23×D9C2312yes—
63C2×D4×C9—24no—
64C2×D4×C9—44no—
65C2×D4×C9C2314yes—
66C2×D4×C9C2318yes—
67C22×C4×C9—24no—
68C22×C4×C9C2314yes—
69C22×C4×C9C2311yescharacteristic
70C22×C4×C9C2312yes—
71C22×C4×C9C2311yescharacteristic
72C2×#611—44no—
73C2×#611—44no—
74C2×#611—44no—
75C2×#611C2318yes—
76C2×#611C2318yes—
77C2×#611C2318yes—
78C22×Dic9—44no—
79C22×Dic9C2311yescharacteristic
80C22×Dic9C2312yes—
81C22×Dic9C2311yescharacteristic
82C22×Dic9C2311yescharacteristic
83C22×Dic9C2311yescharacteristic
84C22×Dic9C2318yes—
85C2×D36—24no—
86C2×D36C2314yes—
87C2×C4×D9—44no—
88C2×C4×D9C2318yes—
89C9×C4⋊C4C2314yes—
90C9×C22⋊C4C2318yes—
91#3676C2314yes—
92#3676C2314yes—
93#3676C2318yes—
94(C2×D9)⋊C4C2318yes—
95(C2×D9)⋊C4C2318yes—
96C4⋊Dic9C2314yes—
97C4⋊Dic9C2314yes—
98C4⋊Dic9C2314yes—
99C4⋊Dic9C2318yes—
100Dic9⋊C4C2318yes—
101C4×Dic9C2314yes—
102C4×Dic9C2314yes—
103C2×#540—91noSylow
104C22×C3×D4C2×D311yescharacteristic
105C22×C3×D4C2×D312yes—
106C23×C3×C4C2×D311yescharacteristic
107C22×#67—32no—
108C22×#67—32no—
109C22×#67—32no—
110C23×Dic3—32no—
111C22×D12—31no—
112C22×C4×D3—32no—
113C3×#121C2×D318yes—
114C2×C3×C4⋊C4C2×D311yescharacteristic
115C2×C3×C22⋊C4C2×D312yes—
116C2×#217—32no—
117C2×#217—31no—
118C2×#217—31no—
119#940—38no—
120#939—316no—
121#938—316no—
122D4×Dic3—38no—
123#930—38no—
124C2×(C2×D3)⋊C4—32no—
125C2×(C2×D3)⋊C4—32no—
126#926—38no—
127C2×C4⋊Dic3—31no—
128C2×C4⋊Dic3—31no—
129C2×C4⋊Dic3—32no—
130C2×C4⋊Dic3—31no—
131C2×Dic3⋊C4—32no—
132C2×C4×Dic3—31no—
133C2×C4×Dic3—31no—
134#893—38no—
135#890—38no—
136#886—316no—
137#883—316no—
138C23×C9—22no—
139C23×C9—24no—
140C23×C9—24no—
141C23×C9—22no—
142C23×C9—24no—
143C23×C9—22no—
144C23×C9C2412yes—
145C23×C9C2414yes—
146C23×C9C2411yescharacteristic
147C22×D9—24no—
148C22×D9—24no—
149C22×D9—24no—
150C22×D9C2414yes—
151D4×C9—28no—
152D4×C9—48no—
153C2×C4×C9—22no—
154C2×C4×C9—24no—
155C2×C4×C9—28no—
156C2×C4×C9#4114yes—
157C2×C4×C9C2414yes—
158C2×C4×C9C2412yes—
159C2×C4×C9C2412yes—
160#611—48no—
161#611—48no—
162#611—48no—
163C2×Dic9—22no—
164C2×Dic9—22no—
165C2×Dic9—24no—
166C2×Dic9—22no—
167C2×Dic9—22no—
168C2×Dic9—48no—
169C2×Dic9C2412yes—
170C2×Dic9C2412yes—
171C2×Dic9C2412yes—
172C2×Dic9C2412yes—
173C2×Dic9C2414yes—
174D36—28no—
175C4×D9—48no—
176#540—916no—
177C2×#127—91no—
178C2×#125—91no—
179C2×#123—92no—
180C2×#123—92no—
181C2×#121—92no—
182C2×#121—92no—
183C2×#121—91no—
184C2×#121D911yescharacteristic, complemented
185C2×C4×D4—91no—
186C2×C4×D4—91no—
187C2×#117—91no—
188C24×C3C22×D311yescharacteristic
189C24×C3C22×D312yes—
190C23×D3—32no—
191C2×C3×D4—24no—
192C2×C3×D4—44no—
193C2×C3×D4C22×D314yes—
194C2×C3×D4C22×D318yes—
195C22×C3×C4—24no—
196C22×C3×C4C22×D312yes—
197C22×C3×C4C22×D311yescharacteristic
198C22×C3×C4C22×D314yes—
199C22×C3×C4C22×D311yescharacteristic
200C2×#67—38no—
201C2×#67—38no—
202C2×#67—38no—
203C2×#67—124no—
204C2×#67—124no—
205C2×#67—124no—
206C22×Dic3—31no—
207C22×Dic3—31no—
208C22×Dic3—31no—
209C22×Dic3—31no—
210C22×Dic3—32no—
211C22×Dic3—38no—
212C22×Dic3—124no—
213C2×D12—34no—
214C2×D12—64no—
215C2×C4×D3—38no—
216C2×C4×D3—124no—
217C3×C4⋊C4C22×D314yes—
218C3×C22⋊C4C22×D318yes—
219#217—38no—
220#217—34no—
221#217—34no—
222(C2×D3)⋊C4—38no—
223(C2×D3)⋊C4—38no—
224C4⋊Dic3—34no—
225C4⋊Dic3—34no—
226C4⋊Dic3—38no—
227C4⋊Dic3—34no—
228Dic3⋊C4—38no—
229C4×Dic3—34no—
230C4×Dic3—34no—
231C22×C9—22no—
232C22×C9—24no—
233C22×C9—24no—
234C22×C9—22no—
235C22×C9—24no—
236C22×C9—22no—
237C22×C9—44no—
238C22×C9—48no—
239C22×C9C2×#4112yes—
240C22×C9H(5,𝔽2)12yes—
241C22×C9H(5,𝔽2)12yes—
242C22×C9C2511yescharacteristic
243C2×D9—24no—
244C2×D9—24no—
245C2×D9—24no—
246C2×D9—48no—
247C4×C9—22no—
248C4×C9—24no—
249C4×C9C2×#4114yes—
250Dic9—22no—
251Dic9—22no—
252Dic9—24no—
253Dic9—22no—
254Dic9—22no—
255C22×D4—92no—
256C22×D4—92no—
257C22×D4—92no—
258C22×D4—91no—
259C22×D4C2×D911yescharacteristic
260C22×D4C2×D912yes—
261C23×C4—92no—
262C23×C4—92no—
263C23×C4C2×D911yescharacteristic
264#127—98no—
265#125—98no—
266#123—916no—
267#123—916no—
268#121—916no—
269#121—916no—
270#121—98no—
271#121C2×D918yescomplemented
272C4×D4—98no—
273C4×D4—98no—
274#117—98no—
275C2×C4⋊C4—91no—
276C2×C4⋊C4—91no—
277C2×C4⋊C4—91no—
278C2×C4⋊C4—92no—
279C2×C4⋊C4—92no—
280C2×C4⋊C4C2×D911yescharacteristic
281C2×C22⋊C4—91no—
282C2×C22⋊C4—91no—
283C2×C22⋊C4—92no—
284C2×C22⋊C4—92no—
285C2×C22⋊C4—92no—
286C2×C22⋊C4C2×D912yes—
287C2×C42—91no—
288C2×C42—91no—
289C23×C3—22no—
290C23×C3—24no—
291C23×C3—24no—
292C23×C3—22no—
293C23×C3—24no—
294C23×C3—22no—
295C23×C3C23×D312yes—
296C23×C3C23×D314yes—
297C23×C3C23×D311yescharacteristic
298C22×D3—34no—
299C22×D3—64no—
300C22×D3—64no—
301C22×D3—64no—
302C3×D4—28no—
303C3×D4—48no—
304C2×C3×C4—22no—
305C2×C3×C4—24no—
306C2×C3×C4—28no—
307C2×C3×C4#23714yes—
308C2×C3×C4C23×D314yes—
309C2×C3×C4C23×D312yes—
310C2×C3×C4C23×D312yes—
311#67—128no—
312#67—128no—
313#67—128no—
314C2×Dic3—32no—
315C2×Dic3—32no—
316C2×Dic3—32no—
317C2×Dic3—32no—
318C2×Dic3—34no—
319C2×Dic3—62no—
320C2×Dic3—62no—
321C2×Dic3—62no—
322C2×Dic3—64no—
323C2×Dic3—62no—
324C2×Dic3—128no—
325D12—68no—
326C4×D3—128no—
327C2×C9—42no—
328C2×C9—44no—
329C2×C9#54014yescomplemented
330C2×C9C22×#4111yescharacteristic
331C2×C9C2×H(5,𝔽2)11yescharacteristic
332C2×C9C2×H(5,𝔽2)11yescharacteristic
333D9—44no—
334C24—92no—
335C24C22×D911yescharacteristic
336C24C22×D912yes—
337C2×D4—24no—
338C2×D4—44no—
339C2×D4—98no—
340C2×D4—98no—
341C2×D4—98no—
342C2×D4—94no—
343C2×D4—184no—
344C2×D4—364no—
345C2×D4—364no—
346C2×D4—364no—
347C2×D4C22×D914yes—
348C2×D4C22×D918yes—
349C22×C4—24no—
350C22×C4—91no—
351C22×C4—91no—
352C22×C4—91no—
353C22×C4—91no—
354C22×C4—92no—
355C22×C4—98no—
356C22×C4—98no—
357C22×C4—364no—
358C22×C4—364no—
359C22×C4C22×D914yes—
360C22×C4C22×D911yescharacteristic
361C22×C4C22×D912yes—
362C22×C4C22×D911yescharacteristic
363C4⋊C4—94no—
364C4⋊C4—94no—
365C4⋊C4—94no—
366C4⋊C4—98no—
367C4⋊C4—98no—
368C4⋊C4C22×D914yes—
369C22⋊C4—94no—
370C22⋊C4—94no—
371C22⋊C4—98no—
372C22⋊C4—98no—
373C22⋊C4—98no—
374C22⋊C4C22×D918yes—
375C42—94no—
376C42—94no—
377C22×C3—22no—
378C22×C3—24no—
379C22×C3—24no—
380C22×C3—22no—
381C22×C3—24no—
382C22×C3—22no—
383C22×C3—44no—
384C22×C3—48no—
385C22×C3C2×#23712yes—
386C22×C3#100412yes—
387C22×C3#100912yes—
388C22×C3C24×D311yescharacteristic
389C2×D3—64no—
390C2×D3—64no—
391C2×D3—64no—
392C2×D3—128no—
393C3×C4—22no—
394C3×C4—24no—
395C3×C4C2×#23714yes—
396Dic3—62no—
397Dic3—62no—
398Dic3—62no—
399Dic3—64no—
400Dic3—62no—
401C9C2×#54011yescharacteristic, complemented, Sylow
402C23—22no—
403C23—24no—
404C23—22no—
405C23—24no—
406C23—24no—
407C23—22no—
408C23—94no—
409C23—184no—
410C23—184no—
411C23—184no—
412C23C23×D912yes—
413C23C23×D914yes—
414C23C23×D911yescharacteristic
415D4—28no—
416D4—48no—
417D4—188no—
418D4—368no—
419D4—368no—
420D4—368no—
421C2×C4—22no—
422C2×C4—24no—
423C2×C4—28no—
424C2×C4—92no—
425C2×C4—92no—
426C2×C4—92no—
427C2×C4—92no—
428C2×C4—94no—
429C2×C4—182no—
430C2×C4—182no—
431C2×C4—182no—
432C2×C4—184no—
433C2×C4—182no—
434C2×C4—368no—
435C2×C4—368no—
436C2×C4#369914yes—
437C2×C4C23×D912yes—
438C2×C4C23×D914yes—
439C2×C4C23×D912yes—
440C2×C3—42no—
441C2×C3—44no—
442C2×C3#561914yes—
443C2×C3C22×#23711yescharacteristic
444C2×C3C2×#100411yescharacteristic
445C2×C3C2×#100911yescharacteristic
446D3—124no—
447C22—22no—
448C22—24no—
449C22—22no—
450C22—24no—
451C22—24no—
452C22—22no—
453C22—44no—
454C22—48no—
455C22—184no—
456C22—184no—
457C22—184no—
458C22—368no—
459C22C2×#369912yes—
460C22#6371012yes—
461C22#6371512yes—
462C22C24×D911yescharacteristic
463C4—22no—
464C4—24no—
465C4—182no—
466C4—182no—
467C4—182no—
468C4—184no—
469C4—182no—
470C4C2×#369914yes—
471C3C2×#561911yescharacteristic
472C2—42no—
473C2—44no—
474C2—364no—
475C2#1058972114yesdirect product factor
476C2C22×#369911yescharacteristic
477C2C2×#6371011yescharacteristic
478C2C2×#6371511yescharacteristic
subgroupG/H
centerC23C23×D9
commutator, cosocleC22×C9C25
FrattiniC22×C3C24×D3
FittingC2×C9×#121C2
socleC23×C3C23×D3
hypercenterC2×#121D9
hypocenterC9C2×#540
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×C9×#121C2semidirect
2. C2×#63502C2semidirect
3. C2×#63501C2semidirect
4. C2×#63500C2semidirect
5. C2×D4×Dic9C2semidirect
6. C2×#63492C2semidirect
7. C2×#63488C2semidirect
8. #10589721C2direct (N × H)
9. C2×#63455C2semidirect
10. C2×#63452C2semidirect
11. C2×#63448C2semidirect
12. C2×#63445C2semidirect
23. C9×#121C22semidirect
29. #63502C22semidirect
30. #63501C22semidirect
31. #63500C22semidirect
32. D4×Dic9C22semidirect
33. #63492C22semidirect
36. #63488C22semidirect
44. #63455C22semidirect
45. #63452C22semidirect
46. #63448C22semidirect
47. #63445C22semidirect
184. C2×#121D9semidirect
271. #121C2×D9semidirect
329. C2×C9#540semidirect
401. C9C2×#540semidirect
475. C2#10589721direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C9×#1212
C2×#635022
C2×#635012
C2×#635002
C2×D4×Dic92
C2×#634922
C2×#634882
#105897212
C2×#634552
C2×#634522
C2×#634482
C2×#634452
C2×#56193