Finite Group Databasebeta

← C2×#10589664 #11901465

Subgroups — C2×#10589664 #11901465

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×C4×D4×C9C211yesmaximal, characteristic, complemented
2C2×#63502C211yesmaximal, characteristic, complemented
3C2×#63500C211yesmaximal, characteristic, complemented
4C2×#63492C212yesmaximal, complemented
5C2×#63491C212yesmaximal, complemented
6#10589664C2116yesmaximal, direct product factor
7C2×#63457C211yesmaximal, characteristic, complemented
8C2×#63452C211yesmaximal, characteristic, complemented
9C2×#63446C212yesmaximal, complemented
10C2×#63445C212yesmaximal, complemented
11C2×C4×D36C211yesmaximal, characteristic, complemented
12C2×#63434C211yesmaximal, characteristic, complemented
13C2×#5562—31nomaximal
14C22×D4×C9C2211yescharacteristic
15C23×C4×C9C2212yes—
16C22×#611C2212yes—
17C22×#611C2212yes—
18C22×#611C2212yes—
19C22×D36C2211yescharacteristic
20C22×D36C2212yes—
21C22×C4×D9C2211yescharacteristic
22C22×C4×D9C2212yes—
23C4×D4×C9C2218yescomplemented
24C2×C9×C4⋊C4C2211yescharacteristic
25C2×C9×C22⋊C4C2212yes—
26C2×C42×C9C2211yescharacteristic
27C2×#3676C2212yes—
28#63502C2218yescomplemented
29#63500C2218yescomplemented
30#63492C22116yescomplemented
31#63491C22116yescomplemented
32C2×(C2×D9)⋊C4C2211yescharacteristic
33C2×(C2×D9)⋊C4C2211yescharacteristic
34C2×(C2×D9)⋊C4C2212yes—
35C2×(C2×D9)⋊C4C2212yes—
36C2×C4⋊Dic9C2211yescharacteristic
37C2×C4⋊Dic9C2212yes—
38C2×Dic9⋊C4C2211yescharacteristic
39C2×Dic9⋊C4C2211yescharacteristic
40C2×Dic9⋊C4C2212yes—
41C2×C4×Dic9C2211yescharacteristic
42#63457C2218yescomplemented
43#63452C2218yescomplemented
44#63446C22116yescomplemented
45#63445C22116yescomplemented
46C4×D36C2218yescomplemented
47#63434C2218yescomplemented
48C2×C3×C4×D4D311yescharacteristic
49C2×#940—31no—
50C2×#938—31no—
51C2×#930—32no—
52C2×#929—32no—
53#5562—316no—
54C2×#895—31no—
55C2×#890—31no—
56C2×#884—32no—
57C2×#883—32no—
58C2×C4×D12—31no—
59C2×#872—31no—
60C24×C9C2312yes—
61C23×D9C2311yescharacteristic
62C23×D9C2312yes—
63C2×D4×C9—24no—
64C2×D4×C9C2314yes—
65C22×C4×C9—44no—
66C22×C4×C9C2311yescharacteristic
67C22×C4×C9C2311yescharacteristic
68C22×C4×C9C2312yes—
69C22×C4×C9C2318yes—
70C22×C4×C9C2311yescharacteristic
71C2×#611—44no—
72C2×#611—44no—
73C2×#611—44no—
74C2×#611C2318yes—
75C2×#611C2318yes—
76C2×#611C2318yes—
77C22×Dic9C2311yescharacteristic
78C22×Dic9C2312yes—
79C22×Dic9C2311yescharacteristic
80C22×Dic9C2311yescharacteristic
81C2×D36—24no—
82C2×D36—44no—
83C2×D36C2314yes—
84C2×D36C2318yes—
85C2×C4×D9—24no—
86C2×C4×D9—44no—
87C2×C4×D9C2314yes—
88C2×C4×D9C2318yes—
89C9×C4⋊C4C2314yes—
90C9×C22⋊C4C2318yes—
91C42×C9C2314yes—
92#3676C2318yes—
93(C2×D9)⋊C4C2318yes—
94(C2×D9)⋊C4C2318yes—
95(C2×D9)⋊C4C2314yes—
96(C2×D9)⋊C4C2314yes—
97C4⋊Dic9C2318yes—
98C4⋊Dic9C2314yes—
99Dic9⋊C4C2314yes—
100Dic9⋊C4C2318yes—
101Dic9⋊C4C2314yes—
102C4×Dic9C2314yes—
103C2×#540—91noSylow
104C22×C3×D4C2×D311yescharacteristic
105C23×C3×C4C2×D312yes—
106C22×#67—32no—
107C22×#67—32no—
108C22×#67—32no—
109C22×D12—31no—
110C22×D12—32no—
111C22×C4×D3—31no—
112C22×C4×D3—32no—
113C3×C4×D4C2×D318yes—
114C2×C3×C4⋊C4C2×D311yescharacteristic
115C2×C3×C22⋊C4C2×D312yes—
116C2×C3×C42C2×D311yescharacteristic
117C2×#217—32no—
118#940—38no—
119#938—38no—
120#930—316no—
121#929—316no—
122C2×(C2×D3)⋊C4—31no—
123C2×(C2×D3)⋊C4—31no—
124C2×(C2×D3)⋊C4—32no—
125C2×(C2×D3)⋊C4—32no—
126C2×C4⋊Dic3—31no—
127C2×C4⋊Dic3—32no—
128C2×Dic3⋊C4—31no—
129C2×Dic3⋊C4—31no—
130C2×Dic3⋊C4—32no—
131C2×C4×Dic3—31no—
132#895—38no—
133#890—38no—
134#884—316no—
135#883—316no—
136C4×D12—38no—
137#872—38no—
138C23×C9—24no—
139C23×C9—24no—
140C23×C9—24no—
141C23×C9C2414yes—
142C23×C9C2411yescharacteristic
143C22×D9—22no—
144C22×D9—24no—
145C22×D9—24no—
146C22×D9—22no—
147C22×D9—24no—
148C22×D9—22no—
149C22×D9C2412yes—
150C22×D9C2414yes—
151D4×C9—28no—
152C2×C4×C9—22no—
153C2×C4×C9—24no—
154C2×C4×C9—22no—
155C2×C4×C9—48no—
156C2×C4×C9#4114yes—
157C2×C4×C9C2414yes—
158C2×C4×C9C2412yes—
159C2×C4×C9C2412yes—
160C2×C4×C9C2412yes—
161#611—48no—
162#611—48no—
163#611—48no—
164C2×Dic9—22no—
165C2×Dic9—24no—
166C2×Dic9—22no—
167C2×Dic9—22no—
168C2×Dic9C2412yes—
169C2×Dic9C2412yes—
170C2×Dic9C2412yes—
171C2×Dic9C2414yes—
172D36—28no—
173D36—48no—
174C4×D9—28no—
175C4×D9—48no—
176#540—916no—
177C2×#127—91no—
178C2×#125—91no—
179C2×#123—92no—
180C2×#123—92no—
181C2×#121—91no—
182C2×#121—92no—
183C2×#121—91no—
184C2×#121—92no—
185C2×C4×D4—91no—
186C2×C4×D4D911yescharacteristic, complemented
187C2×#117—91no—
188C24×C3C22×D312yes—
189C23×D3—31no—
190C23×D3—32no—
191C2×C3×D4—24no—
192C2×C3×D4C22×D314yes—
193C22×C3×C4—44no—
194C22×C3×C4C22×D312yes—
195C22×C3×C4C22×D311yescharacteristic
196C22×C3×C4C22×D311yescharacteristic
197C22×C3×C4C22×D318yes—
198C22×C3×C4C22×D311yescharacteristic
199C2×#67—38no—
200C2×#67—38no—
201C2×#67—38no—
202C2×#67—124no—
203C2×#67—124no—
204C2×#67—124no—
205C22×Dic3—31no—
206C22×Dic3—31no—
207C22×Dic3—31no—
208C22×Dic3—32no—
209C2×D12—34no—
210C2×D12—38no—
211C2×D12—64no—
212C2×D12—124no—
213C2×C4×D3—34no—
214C2×C4×D3—38no—
215C2×C4×D3—64no—
216C2×C4×D3—124no—
217C3×C4⋊C4C22×D314yes—
218C3×C22⋊C4C22×D318yes—
219C3×C42C22×D314yes—
220#217—38no—
221(C2×D3)⋊C4—34no—
222(C2×D3)⋊C4—34no—
223(C2×D3)⋊C4—38no—
224(C2×D3)⋊C4—38no—
225C4⋊Dic3—34no—
226C4⋊Dic3—38no—
227Dic3⋊C4—34no—
228Dic3⋊C4—34no—
229Dic3⋊C4—38no—
230C4×Dic3—34no—
231C22×C9—24no—
232C22×C9—24no—
233C22×C9—24no—
234C22×C9—48no—
235C22×C9C2×#4112yes—
236C22×C9H(5,𝔽2)12yes—
237C22×C9H(5,𝔽2)12yes—
238C22×C9C2511yescharacteristic
239C2×D9—22no—
240C2×D9—24no—
241C2×D9—24no—
242C2×D9—22no—
243C2×D9—24no—
244C2×D9—22no—
245C2×D9—44no—
246C2×D9—48no—
247C4×C9—22no—
248C4×C9—24no—
249C4×C9—22no—
250C4×C9C2×#4114yes—
251Dic9—22no—
252Dic9—24no—
253Dic9—22no—
254Dic9—22no—
255C22×D4—92no—
256C22×D4—92no—
257C22×D4—92no—
258C22×D4—91no—
259C22×D4—92no—
260C22×D4C2×D911yescharacteristic
261C23×C4—91no—
262C23×C4—92no—
263C23×C4C2×D912yes—
264#127—98no—
265#125—98no—
266#123—916no—
267#123—916no—
268#121—98no—
269#121—916no—
270#121—98no—
271#121—916no—
272C4×D4—98no—
273C4×D4C2×D918yescomplemented
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—92no—
282C2×C22⋊C4—91no—
283C2×C22⋊C4—91no—
284C2×C22⋊C4—92no—
285C2×C22⋊C4—92no—
286C2×C22⋊C4C2×D912yes—
287C2×C42—91no—
288C2×C42C2×D911yescharacteristic
289C23×C3—24no—
290C23×C3—24no—
291C23×C3—24no—
292C23×C3C23×D314yes—
293C23×C3C23×D311yescharacteristic
294C22×D3—32no—
295C22×D3—34no—
296C22×D3—62no—
297C22×D3—64no—
298C22×D3—62no—
299C22×D3—64no—
300C22×D3—64no—
301C22×D3—62no—
302C3×D4—28no—
303C2×C3×C4—24no—
304C2×C3×C4—22no—
305C2×C3×C4—22no—
306C2×C3×C4—48no—
307C2×C3×C4#23514yes—
308C2×C3×C4C23×D314yes—
309C2×C3×C4C23×D312yes—
310C2×C3×C4C23×D312yes—
311C2×C3×C4C23×D312yes—
312#67—128no—
313#67—128no—
314#67—128no—
315C2×Dic3—32no—
316C2×Dic3—32no—
317C2×Dic3—32no—
318C2×Dic3—34no—
319C2×Dic3—62no—
320C2×Dic3—62no—
321C2×Dic3—64no—
322C2×Dic3—62no—
323D12—68no—
324D12—128no—
325C4×D3—68no—
326C4×D3—128no—
327C2×C9—44no—
328C2×C9#54014yescomplemented
329C2×C9C22×#4111yescharacteristic
330C2×C9C2×H(5,𝔽2)11yescharacteristic
331C2×C9C2×H(5,𝔽2)11yescharacteristic
332D9—42no—
333D9—44no—
334C24—91no—
335C24—92no—
336C24C22×D912yes—
337C2×D4—24no—
338C2×D4—98no—
339C2×D4—98no—
340C2×D4—98no—
341C2×D4—94no—
342C2×D4—98no—
343C2×D4—184no—
344C2×D4—364no—
345C2×D4—364no—
346C2×D4—364no—
347C2×D4—364no—
348C2×D4C22×D914yes—
349C22×C4—44no—
350C22×C4—91no—
351C22×C4—91no—
352C22×C4—91no—
353C22×C4—92no—
354C22×C4—94no—
355C22×C4—98no—
356C22×C4—184no—
357C22×C4—364no—
358C22×C4C22×D911yescharacteristic
359C22×C4C22×D911yescharacteristic
360C22×C4C22×D912yes—
361C22×C4C22×D918yes—
362C22×C4C22×D911yescharacteristic
363C4⋊C4—94no—
364C4⋊C4—94no—
365C4⋊C4—94no—
366C4⋊C4—98no—
367C4⋊C4—98no—
368C4⋊C4C22×D914yes—
369C22⋊C4—98no—
370C22⋊C4—94no—
371C22⋊C4—94no—
372C22⋊C4—98no—
373C22⋊C4—98no—
374C22⋊C4C22×D918yes—
375C42—94no—
376C42C22×D914yes—
377C22×C3—24no—
378C22×C3—24no—
379C22×C3—24no—
380C22×C3—48no—
381C22×C3C2×#23512yes—
382C22×C3#100412yes—
383C22×C3#100912yes—
384C22×C3C24×D311yescharacteristic
385C2×D3—62no—
386C2×D3—64no—
387C2×D3—62no—
388C2×D3—64no—
389C2×D3—64no—
390C2×D3—62no—
391C2×D3—124no—
392C2×D3—128no—
393C3×C4—24no—
394C3×C4—22no—
395C3×C4—22no—
396C3×C4C2×#23514yes—
397Dic3—62no—
398Dic3—62no—
399Dic3—64no—
400Dic3—62no—
401C9C2×#54011yescharacteristic, complemented, Sylow
402C23—24no—
403C23—24no—
404C23—24no—
405C23—92no—
406C23—94no—
407C23—182no—
408C23—184no—
409C23—182no—
410C23—184no—
411C23—184no—
412C23—182no—
413C23C23×D914yes—
414C23C23×D911yescharacteristic
415D4—28no—
416D4—188no—
417D4—368no—
418D4—368no—
419D4—368no—
420D4—368no—
421C2×C4—22no—
422C2×C4—24no—
423C2×C4—22no—
424C2×C4—48no—
425C2×C4—92no—
426C2×C4—92no—
427C2×C4—92no—
428C2×C4—94no—
429C2×C4—182no—
430C2×C4—182no—
431C2×C4—184no—
432C2×C4—182no—
433C2×C4—188no—
434C2×C4—368no—
435C2×C4#369714yes—
436C2×C4C23×D912yes—
437C2×C4C23×D912yes—
438C2×C4C23×D914yes—
439C2×C4C23×D912yes—
440C2×C3—44no—
441C2×C3#556214yes—
442C2×C3C22×#23511yescharacteristic
443C2×C3C2×#100411yescharacteristic
444C2×C3C2×#100911yescharacteristic
445D3—122no—
446D3—124no—
447C22—24no—
448C22—24no—
449C22—24no—
450C22—48no—
451C22—182no—
452C22—184no—
453C22—182no—
454C22—184no—
455C22—184no—
456C22—182no—
457C22—364no—
458C22—368no—
459C22C2×#369712yes—
460C22#6371012yes—
461C22#6371512yes—
462C22C24×D911yescharacteristic
463C4—22no—
464C4—24no—
465C4—22no—
466C4—182no—
467C4—182no—
468C4—184no—
469C4—182no—
470C4C2×#369714yes—
471C3C2×#556211yescharacteristic
472C2—44no—
473C2—362no—
474C2—364no—
475C2#1058966414yesdirect product factor
476C2C22×#369711yescharacteristic
477C2C2×#6371011yescharacteristic
478C2C2×#6371511yescharacteristic
subgroupG/H
centerC23C23×D9
commutator, cosocleC22×C9C25
FrattiniC22×C3C24×D3
FittingC2×C4×D4×C9C2
socleC23×C3C23×D3
hypercenterC2×C4×D4D9
hypocenterC9C2×#540
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×C4×D4×C9C2semidirect
2. C2×#63502C2semidirect
3. C2×#63500C2semidirect
4. C2×#63492C2semidirect
5. C2×#63491C2semidirect
6. #10589664C2direct (N × H)
7. C2×#63457C2semidirect
8. C2×#63452C2semidirect
9. C2×#63446C2semidirect
10. C2×#63445C2semidirect
11. C2×C4×D36C2semidirect
12. C2×#63434C2semidirect
23. C4×D4×C9C22semidirect
28. #63502C22semidirect
29. #63500C22semidirect
30. #63492C22semidirect
31. #63491C22semidirect
42. #63457C22semidirect
43. #63452C22semidirect
44. #63446C22semidirect
45. #63445C22semidirect
46. C4×D36C22semidirect
47. #63434C22semidirect
186. C2×C4×D4D9semidirect
273. C4×D4C2×D9semidirect
328. C2×C9#540semidirect
401. C9C2×#540semidirect
475. C2#10589664direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×D4×C92
C2×#635022
C2×#635002
C2×#634922
C2×#634912
#105896642
C2×#634572
C2×#634522
C2×#634462
C2×#634452
C2×C4×D362
C2×#634342
C2×#55623