Finite Group Databasebeta

← C2×#10589616 #11903106

Subgroups — C2×#10589616 #11903106

Order 1152.

1878 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C9×C4⋊C4C211yesmaximal, characteristic, complemented
2C2×#63492C212yesmaximal, complemented
3C2×#63492C211yesmaximal, characteristic, complemented
4C2×C4×#611C211yesmaximal, characteristic, complemented
5C2×C4×#611C212yesmaximal, complemented
6#10589616C2116yesmaximal, direct product factor
7C2×#63460C212yesmaximal, complemented
8C2×#63457C211yesmaximal, characteristic, complemented
9C2×#63456C212yesmaximal, complemented
10C2×#63455C211yesmaximal, characteristic, complemented
11C2×#63454C211yesmaximal, characteristic, complemented
12C2×#63452C211yesmaximal, characteristic, complemented
13C2×#5514—31nomaximal
14C23×C4×C9C2211yescharacteristic
15C23×C4×C9C2212yes—
16C22×#611C2212yes—
17C22×#611C2211yescharacteristic
18C22×D36C2211yescharacteristic
19C22×D36C2212yes—
20C22×C4×D9C2211yescharacteristic
21C22×C4×D9C2212yes—
22C2×C9×C4⋊C4C2211yescharacteristic
23C2×C9×C4⋊C4C2211yescharacteristic
24C2×C9×C4⋊C4C2212yes—
25C2×C9×C4⋊C4C2218yescomplemented
26C2×#3676C2211yescharacteristic
27#63492C2218yescomplemented
28#63492C22116yescomplemented
29C4×#611C2218yescomplemented
30C4×#611C22116yescomplemented
31C2×(C2×D9)⋊C4C2212yes—
32C2×(C2×D9)⋊C4C2212yes—
33C2×(C2×D9)⋊C4C2211yescharacteristic
34C2×(C2×D9)⋊C4C2212yes—
35C2×(C2×D9)⋊C4C2212yes—
36C2×C4⋊Dic9C2211yescharacteristic
37C2×C4⋊Dic9C2212yes—
38C2×Dic9⋊C4C2212yes—
39C2×Dic9⋊C4C2211yescharacteristic
40C2×C4×Dic9C2211yescharacteristic
41C2×C4×Dic9C2212yes—
42#63460C22116yescomplemented
43#63457C2218yescomplemented
44#63456C22116yescomplemented
45#63455C2218yescomplemented
46#63454C2218yescomplemented
47#63452C2218yescomplemented
48C22×C3×C4⋊C4D311yescharacteristic
49C2×#930—31no—
50C2×#930—32no—
51C2×C4×#67—31no—
52C2×C4×#67—32no—
53#5514—316no—
54C2×#898—32no—
55C2×#895—31no—
56C2×#894—32no—
57C2×#893—31no—
58C2×#892—31no—
59C2×#890—31no—
60C24×C9C2311yescharacteristic
61C23×D9C2311yescharacteristic
62C23×D9C2312yes—
63C22×C4×C9—24no—
64C22×C4×C9—44no—
65C22×C4×C9C2311yescharacteristic
66C22×C4×C9C2312yes—
67C22×C4×C9C2312yes—
68C22×C4×C9C2314yes—
69C22×C4×C9C2318yes—
70C22×C4×C9C2311yescharacteristic
71C2×#611—28no—
72C2×#611—24no—
73C2×#611C2314yes—
74C2×#611C2318yes—
75C22×Dic9C2311yescharacteristic
76C22×Dic9C2312yes—
77C22×Dic9C2311yescharacteristic
78C22×Dic9C2311yescharacteristic
79C2×D36—24no—
80C2×D36—44no—
81C2×D36C2314yes—
82C2×D36C2318yes—
83C2×C4×D9—24no—
84C2×C4×D9—44no—
85C2×C4×D9C2314yes—
86C2×C4×D9C2318yes—
87C9×C4⋊C4C2314yes—
88C9×C4⋊C4C2314yes—
89C9×C4⋊C4C2318yes—
90#3676C2314yes—
91(C2×D9)⋊C4C2314yes—
92(C2×D9)⋊C4C2318yes—
93(C2×D9)⋊C4C2318yes—
94(C2×D9)⋊C4C2318yes—
95(C2×D9)⋊C4C2318yes—
96C4⋊Dic9C2314yes—
97C4⋊Dic9C2318yes—
98Dic9⋊C4C2318yes—
99Dic9⋊C4C2314yes—
100C4×Dic9C2314yes—
101C4×Dic9C2318yes—
102C2×#553—91noSylow
103C23×C3×C4C2×D311yescharacteristic
104C23×C3×C4C2×D312yes—
105C22×#67—31no—
106C22×#67—32no—
107C22×D12—31no—
108C22×D12—32no—
109C22×C4×D3—31no—
110C22×C4×D3—32no—
111C2×C3×C4⋊C4C2×D311yescharacteristic
112C2×C3×C4⋊C4C2×D311yescharacteristic
113C2×C3×C4⋊C4C2×D312yes—
114C2×C3×C4⋊C4C2×D318yes—
115C2×#217—31no—
116#930—38no—
117#930—316no—
118C4×#67—38no—
119C4×#67—316no—
120C2×(C2×D3)⋊C4—32no—
121C2×(C2×D3)⋊C4—32no—
122C2×(C2×D3)⋊C4—31no—
123C2×(C2×D3)⋊C4—32no—
124C2×(C2×D3)⋊C4—32no—
125C2×C4⋊Dic3—31no—
126C2×C4⋊Dic3—32no—
127C2×Dic3⋊C4—32no—
128C2×Dic3⋊C4—31no—
129C2×C4×Dic3—31no—
130C2×C4×Dic3—32no—
131#898—316no—
132#895—38no—
133#894—316no—
134#893—38no—
135#892—38no—
136#890—38no—
137C23×C9—22no—
138C23×C9—22no—
139C23×C9#4114yes—
140C23×C9C2412yes—
141C23×C9C2411yescharacteristic
142C22×D9—22no—
143C22×D9—24no—
144C22×D9—22no—
145C22×D9—24no—
146C22×D9—24no—
147C22×D9—22no—
148C22×D9C2412yes—
149C22×D9C2414yes—
150C2×C4×C9—22no—
151C2×C4×C9—24no—
152C2×C4×C9—24no—
153C2×C4×C9—28no—
154C2×C4×C9—48no—
155C2×C4×C9#4114yes—
156C2×C4×C9C2414yes—
157C2×C4×C9C2414yes—
158C2×C4×C9C2412yes—
159C2×C4×C9C2412yes—
160#611—28no—
161#611—216no—
162C2×Dic9—22no—
163C2×Dic9—24no—
164C2×Dic9—22no—
165C2×Dic9—22no—
166C2×Dic9C2412yes—
167C2×Dic9C2412yes—
168C2×Dic9C2412yes—
169C2×Dic9C2414yes—
170D36—28no—
171D36—48no—
172C4×D9—28no—
173C4×D9—48no—
174#553—916no—
175C2×#126—92no—
176C2×#125—91no—
177C2×#123—92no—
178C2×#121—92no—
179C2×#121—91no—
180C2×#121—91no—
181C2×C4×D4—92no—
182C2×C4×D4—91no—
183C2×C4×D4—91no—
184C2×#117—91no—
185C22×C4⋊C4D911yescharacteristic, complemented
186C24×C3C22×D311yescharacteristic
187C23×D3—31no—
188C23×D3—32no—
189C22×C3×C4—24no—
190C22×C3×C4—44no—
191C22×C3×C4C22×D312yes—
192C22×C3×C4C22×D312yes—
193C22×C3×C4C22×D311yescharacteristic
194C22×C3×C4C22×D314yes—
195C22×C3×C4C22×D318yes—
196C22×C3×C4C22×D311yescharacteristic
197C2×#67—34no—
198C2×#67—38no—
199C2×#67—64no—
200C2×#67—68no—
201C22×Dic3—31no—
202C22×Dic3—31no—
203C22×Dic3—31no—
204C22×Dic3—32no—
205C2×D12—34no—
206C2×D12—38no—
207C2×D12—64no—
208C2×D12—124no—
209C2×C4×D3—34no—
210C2×C4×D3—38no—
211C2×C4×D3—64no—
212C2×C4×D3—124no—
213C3×C4⋊C4C22×D314yes—
214C3×C4⋊C4C22×D314yes—
215C3×C4⋊C4C22×D318yes—
216#217—34no—
217(C2×D3)⋊C4—38no—
218(C2×D3)⋊C4—38no—
219(C2×D3)⋊C4—34no—
220(C2×D3)⋊C4—38no—
221(C2×D3)⋊C4—38no—
222C4⋊Dic3—34no—
223C4⋊Dic3—38no—
224Dic3⋊C4—38no—
225Dic3⋊C4—34no—
226C4×Dic3—34no—
227C4×Dic3—38no—
228C22×C9—28no—
229C22×C9—22no—
230C22×C9—22no—
231C22×C9C2×#4112yes—
232C22×C9C2×#4114yes—
233C22×C9C2×#4112yes—
234C22×C9H(5,𝔽2)12yes—
235C22×C9C2511yescharacteristic
236C2×D9—22no—
237C2×D9—24no—
238C2×D9—22no—
239C2×D9—24no—
240C2×D9—24no—
241C2×D9—22no—
242C2×D9—44no—
243C2×D9—48no—
244C4×C9—22no—
245C4×C9—24no—
246C4×C9—24no—
247C4×C9C2×#4114yes—
248Dic9—22no—
249Dic9—22no—
250Dic9—24no—
251Dic9—22no—
252C22×D4—92no—
253C22×D4—91no—
254C22×D4—91no—
255C22×D4—92no—
256C23×C4—91no—
257C23×C4—92no—
258C23×C4C2×D911yescharacteristic
259C23×C4C2×D912yes—
260#126—916no—
261#125—98no—
262#123—916no—
263#121—916no—
264#121—98no—
265#121—98no—
266C4×D4—916no—
267C4×D4—98no—
268C4×D4—98no—
269#117—98no—
270C2×C4⋊C4—91no—
271C2×C4⋊C4—92no—
272C2×C4⋊C4—91no—
273C2×C4⋊C4—92no—
274C2×C4⋊C4C2×D911yescharacteristic
275C2×C4⋊C4C2×D911yescharacteristic
276C2×C4⋊C4C2×D912yes—
277C2×C4⋊C4C2×D918yescomplemented
278C2×C22⋊C4—91no—
279C2×C22⋊C4—92no—
280C2×C22⋊C4—92no—
281C2×C22⋊C4—92no—
282C2×C22⋊C4—91no—
283C2×C22⋊C4—92no—
284C2×C42—92no—
285C2×C42—91no—
286C23×C3—22no—
287C23×C3—22no—
288C23×C3#23914yes—
289C23×C3C23×D312yes—
290C23×C3C23×D311yescharacteristic
291C22×D3—32no—
292C22×D3—34no—
293C22×D3—62no—
294C22×D3—64no—
295C22×D3—64no—
296C22×D3—62no—
297C22×D3—62no—
298C22×D3—64no—
299C2×C3×C4—22no—
300C2×C3×C4—24no—
301C2×C3×C4—24no—
302C2×C3×C4—28no—
303C2×C3×C4—48no—
304C2×C3×C4#23514yes—
305C2×C3×C4C23×D314yes—
306C2×C3×C4C23×D314yes—
307C2×C3×C4C23×D312yes—
308C2×C3×C4C23×D312yes—
309#67—68no—
310#67—616no—
311C2×Dic3—32no—
312C2×Dic3—32no—
313C2×Dic3—32no—
314C2×Dic3—34no—
315C2×Dic3—62no—
316C2×Dic3—62no—
317C2×Dic3—62no—
318C2×Dic3—64no—
319D12—68no—
320D12—128no—
321C4×D3—68no—
322C4×D3—128no—
323C2×C9—24no—
324C2×C9#55314yescomplemented
325C2×C9C22×#4111yescharacteristic
326C2×C9C22×#4111yescharacteristic
327C2×C9C2×H(5,𝔽2)11yescharacteristic
328D9—42no—
329D9—44no—
330C24—91no—
331C24—92no—
332C24C22×D911yescharacteristic
333C2×D4—98no—
334C2×D4—94no—
335C2×D4—94no—
336C2×D4—98no—
337C2×D4—188no—
338C2×D4—184no—
339C2×D4—184no—
340C2×D4—364no—
341C22×C4—24no—
342C22×C4—44no—
343C22×C4—91no—
344C22×C4—92no—
345C22×C4—91no—
346C22×C4—91no—
347C22×C4—94no—
348C22×C4—98no—
349C22×C4—184no—
350C22×C4—364no—
351C22×C4C22×D914yes—
352C22×C4C22×D912yes—
353C22×C4C22×D911yescharacteristic
354C22×C4C22×D912yes—
355C22×C4C22×D918yes—
356C22×C4C22×D911yescharacteristic
357C4⋊C4—94no—
358C4⋊C4—98no—
359C4⋊C4—94no—
360C4⋊C4—98no—
361C4⋊C4C22×D914yes—
362C4⋊C4C22×D914yes—
363C4⋊C4C22×D918yes—
364C22⋊C4—94no—
365C22⋊C4—98no—
366C22⋊C4—98no—
367C22⋊C4—98no—
368C22⋊C4—94no—
369C22⋊C4—98no—
370C42—98no—
371C42—94no—
372C22×C3—22no—
373C22×C3—22no—
374C22×C3—28no—
375C22×C3C2×#23512yes—
376C22×C3#100412yes—
377C22×C3C2×#23914yes—
378C22×C3C2×#23912yes—
379C22×C3C24×D311yescharacteristic
380C2×D3—62no—
381C2×D3—64no—
382C2×D3—64no—
383C2×D3—62no—
384C2×D3—62no—
385C2×D3—64no—
386C2×D3—124no—
387C2×D3—128no—
388C3×C4—22no—
389C3×C4—24no—
390C3×C4—24no—
391C3×C4C2×#23514yes—
392Dic3—62no—
393Dic3—62no—
394Dic3—62no—
395Dic3—64no—
396C9C2×#55311yescharacteristic, complemented, Sylow
397C23—22no—
398C23—22no—
399C23—92no—
400C23—94no—
401C23—182no—
402C23—184no—
403C23—184no—
404C23—182no—
405C23—182no—
406C23—184no—
407C23#370114yes—
408C23C23×D912yes—
409C23C23×D911yescharacteristic
410D4—1816no—
411D4—188no—
412D4—188no—
413D4—368no—
414C2×C4—22no—
415C2×C4—24no—
416C2×C4—24no—
417C2×C4—28no—
418C2×C4—48no—
419C2×C4—92no—
420C2×C4—94no—
421C2×C4—92no—
422C2×C4—92no—
423C2×C4—182no—
424C2×C4—182no—
425C2×C4—184no—
426C2×C4—182no—
427C2×C4—188no—
428C2×C4—368no—
429C2×C4#369714yes—
430C2×C4C23×D914yes—
431C2×C4C23×D912yes—
432C2×C4C23×D914yes—
433C2×C4C23×D912yes—
434C2×C3—24no—
435C2×C3#551414yes—
436C2×C3C22×#23511yescharacteristic
437C2×C3C2×#100411yescharacteristic
438C2×C3C22×#23911yescharacteristic
439D3—122no—
440D3—124no—
441C22—22no—
442C22—22no—
443C22—28no—
444C22—182no—
445C22—184no—
446C22—184no—
447C22—182no—
448C22—182no—
449C22—184no—
450C22—364no—
451C22—368no—
452C22C2×#369712yes—
453C22#6371012yes—
454C22C2×#370114yes—
455C22C2×#370112yes—
456C22C24×D911yescharacteristic
457C4—22no—
458C4—24no—
459C4—24no—
460C4—182no—
461C4—182no—
462C4—184no—
463C4—182no—
464C4C2×#369714yes—
465C3C2×#551411yescharacteristic
466C2—24no—
467C2—362no—
468C2—364no—
469C2#1058961614yesdirect product factor
470C2C22×#369711yescharacteristic
471C2C2×#6371011yescharacteristic
472C2C22×#370111yescharacteristic
subgroupG/H
centerC23C23×D9
commutator, cosocleC22×C9C25
FrattiniC22×C3C24×D3
FittingC22×C9×C4⋊C4C2
socleC23×C3C23×D3
hypercenterC22×C4⋊C4D9
hypocenterC9C2×#553
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C23 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×C9×C4⋊C4C2semidirect
2. C2×#63492C2semidirect
3. C2×#63492C2semidirect
4. C2×C4×#611C2semidirect
5. C2×C4×#611C2semidirect
6. #10589616C2direct (N × H)
7. C2×#63460C2semidirect
8. C2×#63457C2semidirect
9. C2×#63456C2semidirect
10. C2×#63455C2semidirect
11. C2×#63454C2semidirect
12. C2×#63452C2semidirect
25. C2×C9×C4⋊C4C22semidirect
27. #63492C22semidirect
28. #63492C22semidirect
29. C4×#611C22semidirect
30. C4×#611C22semidirect
42. #63460C22semidirect
43. #63457C22semidirect
44. #63456C22semidirect
45. #63455C22semidirect
46. #63454C22semidirect
47. #63452C22semidirect
185. C22×C4⋊C4D9semidirect
277. C2×C4⋊C4C2×D9semidirect
324. C2×C9#553semidirect
396. C9C2×#553semidirect
469. C2#10589616direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C9×C4⋊C42
C2×#634922
C2×C4×#6112
#105896162
C2×#634602
C2×#634572
C2×#634562
C2×#634552
C2×#634542
C2×#634522
C2×#55143