Finite Group Databasebeta

← C2×#10589797 #11903121

Subgroups — C2×#10589797 #11903121

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
1C2×C9×#125C211yesmaximal, characteristic, complemented
2#10589797C2116yesmaximal, direct product factor
3C2×#63460C212yesmaximal, complemented
4C2×#63457C212yesmaximal, complemented
5C2×#63457C211yesmaximal, characteristic, complemented
6C2×#63457C211yesmaximal, characteristic, complemented
7C2×#63456C212yesmaximal, complemented
8C2×#63455C212yesmaximal, complemented
9C2×#63454C211yesmaximal, characteristic, complemented
10C2×C4⋊C4×D9C211yesmaximal, characteristic, complemented
11C2×C4×D36C211yesmaximal, characteristic, complemented
12C2×C4×D36C211yesmaximal, characteristic, complemented
13C2×#5695—31nomaximal
14C22×D36C2211yescharacteristic
15C22×D36C2211yescharacteristic
16C22×D36C2212yes—
17C22×D36C2212yes—
18C22×C4×D9C2211yescharacteristic
19C22×C4×D9C2211yescharacteristic
20C22×C4×D9C2212yes—
21C22×C4×D9C2212yes—
22C9×#125C2218yescomplemented
23C2×C9×C4⋊C4C2211yescharacteristic
24C2×C9×C4⋊C4C2211yescharacteristic
25C2×C9×C4⋊C4C2212yes—
26C2×C9×C4⋊C4C2212yes—
27C2×C42×C9C2211yescharacteristic
28C2×(C2×D9)⋊C4C2211yescharacteristic
29C2×(C2×D9)⋊C4C2211yescharacteristic
30C2×(C2×D9)⋊C4C2212yes—
31C2×(C2×D9)⋊C4C2212yes—
32C2×(C2×D9)⋊C4C2212yes—
33C2×(C2×D9)⋊C4C2212yes—
34C2×C4⋊Dic9C2211yescharacteristic
35C2×C4⋊Dic9C2211yescharacteristic
36C2×Dic9⋊C4C2212yes—
37C2×C4×Dic9C2212yes—
38#63460C22116yescomplemented
39#63457C22116yescomplemented
40#63457C2218yescomplemented
41#63457C2218yescomplemented
42#63456C22116yescomplemented
43#63455C22116yescomplemented
44#63454C2218yescomplemented
45C4⋊C4×D9C2218yescomplemented
46C4×D36C2218yescomplemented
47C4×D36C2218yescomplemented
48C2×C3×#125D311yescharacteristic
49#5695—316no—
50C2×#898—32no—
51C2×#895—32no—
52C2×#895—31no—
53C2×#895—31no—
54C2×#894—32no—
55C2×#893—32no—
56C2×#892—31no—
57C2×D3×C4⋊C4—31no—
58C2×C4×D12—31no—
59C2×C4×D12—31no—
60C23×D9C2311yescharacteristic
61C23×D9C2312yes—
62C23×D9C2311yescharacteristic
63C22×C4×C9C2311yescharacteristic
64C22×C4×C9C2311yescharacteristic
65C22×C4×C9C2312yes—
66C22×C4×C9C2312yes—
67C22×C4×C9C2311yescharacteristic
68C22×Dic9C2311yescharacteristic
69C22×Dic9C2311yescharacteristic
70C22×Dic9C2312yes—
71C2×D36—24no—
72C2×D36—28no—
73C2×D36—24no—
74C2×D36—44no—
75C2×D36C2314yes—
76C2×D36C2314yes—
77C2×D36C2318yes—
78C2×D36C2318yes—
79C2×C4×D9—24no—
80C2×C4×D9—24no—
81C2×C4×D9—44no—
82C2×C4×D9—44no—
83C2×C4×D9C2314yes—
84C2×C4×D9C2314yes—
85C2×C4×D9C2318yes—
86C2×C4×D9C2318yes—
87C9×C4⋊C4C2314yes—
88C9×C4⋊C4C2314yes—
89C9×C4⋊C4C2318yes—
90C9×C4⋊C4C2318yes—
91C42×C9C2314yes—
92(C2×D9)⋊C4C2314yes—
93(C2×D9)⋊C4C2314yes—
94(C2×D9)⋊C4C2318yes—
95(C2×D9)⋊C4C2318yes—
96(C2×D9)⋊C4C2318yes—
97(C2×D9)⋊C4C2318yes—
98C4⋊Dic9C2314yes—
99C4⋊Dic9C2314yes—
100Dic9⋊C4C2318yes—
101C4×Dic9C2318yes—
102C2×#553—91noSylow
103C22×D12—31no—
104C22×D12—31no—
105C22×D12—32no—
106C22×D12—32no—
107C22×C4×D3—31no—
108C22×C4×D3—31no—
109C22×C4×D3—32no—
110C22×C4×D3—32no—
111C3×#125C2×D318yes—
112C2×C3×C4⋊C4C2×D311yescharacteristic
113C2×C3×C4⋊C4C2×D311yescharacteristic
114C2×C3×C4⋊C4C2×D312yes—
115C2×C3×C4⋊C4C2×D312yes—
116C2×C3×C42C2×D311yescharacteristic
117C2×(C2×D3)⋊C4—31no—
118C2×(C2×D3)⋊C4—31no—
119C2×(C2×D3)⋊C4—32no—
120C2×(C2×D3)⋊C4—32no—
121C2×(C2×D3)⋊C4—32no—
122C2×(C2×D3)⋊C4—32no—
123C2×C4⋊Dic3—31no—
124C2×C4⋊Dic3—31no—
125C2×Dic3⋊C4—32no—
126C2×C4×Dic3—32no—
127#898—316no—
128#895—316no—
129#895—38no—
130#895—38no—
131#894—316no—
132#893—316no—
133#892—38no—
134D3×C4⋊C4—38no—
135C4×D12—38no—
136C4×D12—38no—
137C23×C9C2411yescharacteristic
138C22×D9—22no—
139C22×D9—22no—
140C22×D9—22no—
141C22×D9—24no—
142C22×D9—22no—
143C22×D9—24no—
144C22×D9—24no—
145C22×D9—22no—
146C22×D9#4114yes—
147C22×D9C2412yes—
148C22×D9C2414yes—
149C22×D9C2412yes—
150C2×C4×C9—22no—
151C2×C4×C9—24no—
152C2×C4×C9—22no—
153C2×C4×C9—24no—
154C2×C4×C9#4114yes—
155C2×C4×C9C2414yes—
156C2×C4×C9C2414yes—
157C2×C4×C9C2412yes—
158C2×C4×C9C2412yes—
159C2×C4×C9C2412yes—
160C2×Dic9—22no—
161C2×Dic9—22no—
162C2×Dic9—24no—
163C2×Dic9C2412yes—
164C2×Dic9C2414yes—
165C2×Dic9C2412yes—
166D36—28no—
167D36—216no—
168D36—28no—
169D36—48no—
170C4×D9—28no—
171C4×D9—28no—
172C4×D9—48no—
173C4×D9—48no—
174#553—916no—
175C2×#126—92no—
176C2×#125D911yescharacteristic, complemented
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⋊C4—91no—
186C23×D3—31no—
187C23×D3—31no—
188C23×D3—32no—
189C22×C3×C4C22×D312yes—
190C22×C3×C4C22×D312yes—
191C22×C3×C4C22×D311yescharacteristic
192C22×C3×C4C22×D311yescharacteristic
193C22×C3×C4C22×D311yescharacteristic
194C22×Dic3—31no—
195C22×Dic3—32no—
196C22×Dic3—31no—
197C2×D12—34no—
198C2×D12—34no—
199C2×D12—38no—
200C2×D12—38no—
201C2×D12—64no—
202C2×D12—68no—
203C2×D12—64no—
204C2×D12—124no—
205C2×C4×D3—34no—
206C2×C4×D3—34no—
207C2×C4×D3—38no—
208C2×C4×D3—38no—
209C2×C4×D3—64no—
210C2×C4×D3—64no—
211C2×C4×D3—124no—
212C2×C4×D3—124no—
213C3×C4⋊C4C22×D314yes—
214C3×C4⋊C4C22×D314yes—
215C3×C4⋊C4C22×D318yes—
216C3×C4⋊C4C22×D318yes—
217C3×C42C22×D314yes—
218(C2×D3)⋊C4—34no—
219(C2×D3)⋊C4—34no—
220(C2×D3)⋊C4—38no—
221(C2×D3)⋊C4—38no—
222(C2×D3)⋊C4—38no—
223(C2×D3)⋊C4—38no—
224C4⋊Dic3—34no—
225C4⋊Dic3—34no—
226Dic3⋊C4—38no—
227C4×Dic3—38no—
228C22×C9C2×#4112yes—
229C22×C9C2×#4112yes—
230C22×C9H(5,𝔽2)12yes—
231C22×C9C2511yescharacteristic
232C2×D9—28no—
233C2×D9—22no—
234C2×D9—22no—
235C2×D9—22no—
236C2×D9—24no—
237C2×D9—22no—
238C2×D9—24no—
239C2×D9—24no—
240C2×D9—22no—
241C2×D9—44no—
242C2×D9—48no—
243C2×D9C2×#4114yes—
244C4×C9—24no—
245C4×C9—22no—
246C4×C9—22no—
247C4×C9—24no—
248C4×C9C2×#4114yes—
249Dic9—22no—
250Dic9—22no—
251Dic9—24no—
252C22×D4—92no—
253C22×D4—91no—
254C22×D4—91no—
255C22×D4—92no—
256C23×C4—91no—
257C23×C4—91no—
258C23×C4—92no—
259C23×C4—92no—
260#126—916no—
261#125C2×D918yescomplemented
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—98no—
274C2×C4⋊C4C2×D911yescharacteristic
275C2×C4⋊C4C2×D911yescharacteristic
276C2×C4⋊C4C2×D912yes—
277C2×C4⋊C4C2×D912yes—
278C2×C22⋊C4—92no—
279C2×C22⋊C4—91no—
280C2×C22⋊C4—92no—
281C2×C22⋊C4—92no—
282C2×C22⋊C4—91no—
283C2×C22⋊C4—92no—
284C2×C42—92no—
285C2×C42C2×D911yescharacteristic
286C23×C3C23×D311yescharacteristic
287C22×D3—34no—
288C22×D3—32no—
289C22×D3—32no—
290C22×D3—34no—
291C22×D3—62no—
292C22×D3—62no—
293C22×D3—62no—
294C22×D3—64no—
295C22×D3—62no—
296C22×D3—64no—
297C22×D3—64no—
298C22×D3—62no—
299C2×C3×C4—24no—
300C2×C3×C4—22no—
301C2×C3×C4—22no—
302C2×C3×C4—24no—
303C2×C3×C4#23914yes—
304C2×C3×C4C23×D314yes—
305C2×C3×C4C23×D314yes—
306C2×C3×C4C23×D312yes—
307C2×C3×C4C23×D312yes—
308C2×C3×C4C23×D312yes—
309C2×Dic3—32no—
310C2×Dic3—34no—
311C2×Dic3—32no—
312C2×Dic3—62no—
313C2×Dic3—62no—
314C2×Dic3—64no—
315D12—68no—
316D12—616no—
317D12—68no—
318D12—128no—
319C4×D3—68no—
320C4×D3—68no—
321C4×D3—128no—
322C4×D3—128no—
323C2×C9#55314yescomplemented
324C2×C9C22×#4111yescharacteristic
325C2×C9C22×#4111yescharacteristic
326C2×C9C2×H(5,𝔽2)11yescharacteristic
327D9—24no—
328D9—42no—
329D9—44no—
330C24—91no—
331C24—91no—
332C24—92no—
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—91no—
342C22×C4—92no—
343C22×C4—91no—
344C22×C4—94no—
345C22×C4—94no—
346C22×C4—98no—
347C22×C4—98no—
348C22×C4—184no—
349C22×C4—184no—
350C22×C4—364no—
351C22×C4—364no—
352C22×C4C22×D912yes—
353C22×C4C22×D911yescharacteristic
354C22×C4C22×D911yescharacteristic
355C22×C4C22×D912yes—
356C22×C4C22×D911yescharacteristic
357C4⋊C4—94no—
358C4⋊C4—98no—
359C4⋊C4—94no—
360C4⋊C4C22×D914yes—
361C4⋊C4C22×D914yes—
362C4⋊C4C22×D918yes—
363C4⋊C4C22×D918yes—
364C22⋊C4—98no—
365C22⋊C4—94no—
366C22⋊C4—98no—
367C22⋊C4—98no—
368C22⋊C4—94no—
369C22⋊C4—98no—
370C42—98no—
371C42C22×D914yes—
372C22×C3C2×#23912yes—
373C22×C3D3×#4112yes—
374C22×C3#100912yes—
375C22×C3C24×D311yescharacteristic
376C2×D3—34no—
377C2×D3—68no—
378C2×D3—62no—
379C2×D3—62no—
380C2×D3—62no—
381C2×D3—64no—
382C2×D3—62no—
383C2×D3—64no—
384C2×D3—64no—
385C2×D3—62no—
386C2×D3—124no—
387C2×D3—128no—
388C3×C4—24no—
389C3×C4—22no—
390C3×C4—22no—
391C3×C4—24no—
392C3×C4C2×#23914yes—
393Dic3—62no—
394Dic3—62no—
395Dic3—64no—
396C9C2×#55311yescharacteristic, complemented, Sylow
397C23—92no—
398C23—94no—
399C23—92no—
400C23—94no—
401C23—182no—
402C23—182no—
403C23—182no—
404C23—184no—
405C23—182no—
406C23—184no—
407C23—184no—
408C23—182no—
409C23C23×D911yescharacteristic
410D4—1816no—
411D4—188no—
412D4—188no—
413D4—368no—
414C2×C4—24no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—24no—
418C2×C4—92no—
419C2×C4—94no—
420C2×C4—92no—
421C2×C4—182no—
422C2×C4—182no—
423C2×C4—184no—
424C2×C4—188no—
425C2×C4—188no—
426C2×C4—368no—
427C2×C4—368no—
428C2×C4#370114yes—
429C2×C4C23×D914yes—
430C2×C4C23×D912yes—
431C2×C4C23×D912yes—
432C2×C4C23×D914yes—
433C2×C4C23×D912yes—
434C2×C3#569514yes—
435C2×C3C22×#23911yescharacteristic
436C2×C3C2×D3×#4111yescharacteristic
437C2×C3C2×#100911yescharacteristic
438D3—64no—
439D3—122no—
440D3—124no—
441C22—94no—
442C22—188no—
443C22—182no—
444C22—182no—
445C22—182no—
446C22—184no—
447C22—182no—
448C22—184no—
449C22—184no—
450C22—182no—
451C22—364no—
452C22—368no—
453C22C2×#370112yes—
454C22#41×D912yes—
455C22#6371512yes—
456C22C24×D911yescharacteristic
457C4—24no—
458C4—22no—
459C4—22no—
460C4—24no—
461C4—182no—
462C4—182no—
463C4—184no—
464C4C2×#370114yes—
465C3C2×#569511yescharacteristic
466C2—184no—
467C2—362no—
468C2—364no—
469C2#1058979714yesdirect product factor
470C2C22×#370111yescharacteristic
471C2C2×#41×D911yescharacteristic
472C2C2×#6371511yescharacteristic
subgroupG/H
centerC23C23×D9
commutator, cosocleC22×C9C25
FrattiniC22×C3C24×D3
FittingC2×C9×#125C2
socleC23×C3C23×D3
hypercenterC2×#125D9
hypocenterC9C2×#553
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
1. C2×C9×#125C2semidirect
2. #10589797C2direct (N × H)
3. C2×#63460C2semidirect
4. C2×#63457C2semidirect
5. C2×#63457C2semidirect
6. C2×#63457C2semidirect
7. C2×#63456C2semidirect
8. C2×#63455C2semidirect
9. C2×#63454C2semidirect
10. C2×C4⋊C4×D9C2semidirect
11. C2×C4×D36C2semidirect
12. C2×C4×D36C2semidirect
22. C9×#125C22semidirect
38. #63460C22semidirect
39. #63457C22semidirect
40. #63457C22semidirect
41. #63457C22semidirect
42. #63456C22semidirect
43. #63455C22semidirect
44. #63454C22semidirect
45. C4⋊C4×D9C22semidirect
46. C4×D36C22semidirect
47. C4×D36C22semidirect
176. C2×#125D9semidirect
261. #125C2×D9semidirect
323. C2×C9#553semidirect
396. C9C2×#553semidirect
469. C2#10589797direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C9×#1252
#105897972
C2×#634602
C2×#634572
C2×#634562
C2×#634552
C2×#634542
C2×C4⋊C4×D92
C2×C4×D362
C2×#56953