Finite Group Databasebeta

← C2×#10589783 #11903801

Subgroups — C2×#10589783 #11903801

Order 1152.

1860 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C9×#124C211yesmaximal, characteristic, complemented
2C2×#63509C211yesmaximal, characteristic, complemented
3C2×Q8×Dic9C211yesmaximal, characteristic, complemented
4C2×#63502C211yesmaximal, characteristic
5C2×D4×Dic9C211yesmaximal, characteristic, complemented
6#10589783C2116yesmaximal, direct product factor
7C2×#63448C212yesmaximal, complemented
8C2×#63447C212yesmaximal, complemented
9C2×#63445C212yesmaximal, complemented
10C2×#611⋊C4C212yesmaximal, complemented
11C2×C4×D36C211yesmaximal, characteristic, complemented
12C2×C4×Dic18C211yesmaximal, characteristic, complemented
13C2×#5681—31nomaximal
14C22×Q8×C9C2211yescharacteristic
15C22×D4×C9C2211yescharacteristic
16C22×#611C2212yes—
17C22×#611C2212yes—
18C23×Dic9C2212yes—
19C22×D36C2211yescharacteristic
20C22×C4×D9C2212yes—
21C22×Dic18C2211yescharacteristic
22C9×#124C2218yescomplemented
23C2×C9×C22⋊C4C2212yes—
24C2×C9×C22⋊C4C2212yes—
25C2×C42×C9C2211yescharacteristic
26C2×#3676C2212yes—
27#63509C2218yescomplemented
28Q8×Dic9C2218yescomplemented
29#63502C2218yes—
30D4×Dic9C2218yescomplemented
31C2×(C2×D9)⋊C4C2212yes—
32C2×(C2×D9)⋊C4C2212yes—
33C2×(C2×D9)⋊C4C2212yes—
34C2×C4⋊Dic9C2211yescharacteristic
35C2×C4⋊Dic9C2211yescharacteristic
36C2×C4⋊Dic9C2212yes—
37C2×Dic9⋊C4C2211yescharacteristic
38C2×Dic9⋊C4C2211yescharacteristic
39C2×C4×Dic9C2211yescharacteristic
40C2×C4×Dic9C2211yescharacteristic
41C2×C4×Dic9C2212yes—
42#63448C22116yescomplemented
43#63447C22116yescomplemented
44#63445C22116yescomplemented
45#611⋊C4C22116yescomplemented
46C4×D36C2218yescomplemented
47C4×Dic18C2218yescomplemented
48C2×C3×#124D311yescharacteristic
49C2×#947—31no—
50C2×Q8×Dic3—31no—
51C2×#940—31no—
52C2×D4×Dic3—31no—
53#5681—316no—
54C2×#886—32no—
55C2×#885—32no—
56C2×#883—32no—
57C2×#67⋊C4—32no—
58C2×C4×D12—31no—
59C2×C4×Dic6—31no—
60C24×C9C2312yes—
61C23×D9C2312yes—
62C2×Q8×C9—24no—
63C2×Q8×C9C2314yes—
64C2×D4×C9—24no—
65C2×D4×C9C2314yes—
66C22×C4×C9C2311yescharacteristic
67C22×C4×C9C2312yes—
68C22×C4×C9C2311yescharacteristic
69C22×C4×C9C2311yescharacteristic
70C2×#611—28no—
71C2×#611—44no—
72C2×#611C2318yes—
73C2×#611C2318yes—
74C22×Dic9—44no—
75C22×Dic9C2311yescharacteristic
76C22×Dic9C2311yescharacteristic
77C22×Dic9C2312yes—
78C22×Dic9C2311yescharacteristic
79C22×Dic9C2318yes—
80C22×Dic9C2311yescharacteristic
81C2×D36—24no—
82C2×D36C2314yes—
83C2×C4×D9—44no—
84C2×C4×D9C2318yes—
85C2×Dic18—24no—
86C2×Dic18C2314yes—
87C9×C22⋊C4C2318yes—
88C9×C22⋊C4C2318yes—
89C42×C9C2314yes—
90#3676C2318yes—
91(C2×D9)⋊C4C2318yes—
92(C2×D9)⋊C4C2318yes—
93(C2×D9)⋊C4C2318yes—
94C4⋊Dic9C2314yes—
95C4⋊Dic9C2318yes—
96C4⋊Dic9C2314yes—
97Dic9⋊C4C2314yes—
98Dic9⋊C4C2314yes—
99C4×Dic9C2314yes—
100C4×Dic9C2314yes—
101C4×Dic9C2318yes—
102C2×#559—91noSylow
103C22×C3×Q8C2×D311yescharacteristic
104C22×C3×D4C2×D311yescharacteristic
105C22×#67—32no—
106C22×#67—32no—
107C23×Dic3—32no—
108C22×D12—31no—
109C22×C4×D3—32no—
110C22×Dic6—31no—
111C3×#124C2×D318yes—
112C2×C3×C22⋊C4C2×D312yes—
113C2×C3×C22⋊C4C2×D312yes—
114C2×C3×C42C2×D311yescharacteristic
115C2×#217—32no—
116#947—38no—
117Q8×Dic3—38no—
118#940—38no—
119D4×Dic3—38no—
120C2×(C2×D3)⋊C4—32no—
121C2×(C2×D3)⋊C4—32no—
122C2×(C2×D3)⋊C4—32no—
123C2×C4⋊Dic3—31no—
124C2×C4⋊Dic3—31no—
125C2×C4⋊Dic3—32no—
126C2×Dic3⋊C4—31no—
127C2×Dic3⋊C4—31no—
128C2×C4×Dic3—31no—
129C2×C4×Dic3—31no—
130C2×C4×Dic3—32no—
131#886—316no—
132#885—316no—
133#883—316no—
134#67⋊C4—316no—
135C4×D12—38no—
136C4×Dic6—38no—
137C23×C9—24no—
138C23×C9—24no—
139C23×C9—24no—
140C23×C9C2414yes—
141C23×C9C2411yescharacteristic
142C22×D9—24no—
143C22×D9—24no—
144C22×D9—24no—
145C22×D9C2414yes—
146Q8×C9—28no—
147D4×C9—28no—
148C2×C4×C9—22no—
149C2×C4×C9—24no—
150C2×C4×C9—22no—
151C2×C4×C9#4114yes—
152C2×C4×C9C2414yes—
153C2×C4×C9C2412yes—
154C2×C4×C9C2412yes—
155C2×C4×C9C2412yes—
156#611—216no—
157#611—48no—
158C2×Dic9—22no—
159C2×Dic9—24no—
160C2×Dic9—22no—
161C2×Dic9—22no—
162C2×Dic9—48no—
163C2×Dic9#4114yes—
164C2×Dic9C2412yes—
165C2×Dic9C2412yes—
166C2×Dic9C2412yes—
167C2×Dic9C2414yes—
168C2×Dic9C2412yes—
169D36—28no—
170C4×D9—48no—
171Dic18—28no—
172#559—916no—
173C2×#127—91no—
174C2×#124—91no—
175C2×#124—92no—
176C2×#124D911yescharacteristic, complemented
177C2×#123—92no—
178C2×#123—92no—
179C2×C4×Q8—91no—
180C2×C4×Q8—91no—
181C2×C4×D4—91no—
182C2×C4×D4—92no—
183C2×C4×D4—91no—
184C24×C3C22×D312yes—
185C23×D3—32no—
186C2×C3×Q8—24no—
187C2×C3×Q8C22×D314yes—
188C2×C3×D4—24no—
189C2×C3×D4C22×D314yes—
190C22×C3×C4C22×D312yes—
191C22×C3×C4C22×D311yescharacteristic
192C22×C3×C4C22×D311yescharacteristic
193C22×C3×C4C22×D311yescharacteristic
194C2×#67—38no—
195C2×#67—38no—
196C2×#67—68no—
197C2×#67—124no—
198C22×Dic3—31no—
199C22×Dic3—31no—
200C22×Dic3—31no—
201C22×Dic3—31no—
202C22×Dic3—32no—
203C22×Dic3—38no—
204C22×Dic3—124no—
205C2×D12—34no—
206C2×D12—64no—
207C2×C4×D3—38no—
208C2×C4×D3—124no—
209C2×Dic6—34no—
210C2×Dic6—64no—
211C3×C22⋊C4C22×D318yes—
212C3×C22⋊C4C22×D318yes—
213C3×C42C22×D314yes—
214#217—38no—
215(C2×D3)⋊C4—38no—
216(C2×D3)⋊C4—38no—
217(C2×D3)⋊C4—38no—
218C4⋊Dic3—34no—
219C4⋊Dic3—34no—
220C4⋊Dic3—38no—
221Dic3⋊C4—34no—
222Dic3⋊C4—34no—
223C4×Dic3—34no—
224C4×Dic3—34no—
225C4×Dic3—38no—
226C22×C9—24no—
227C22×C9—24no—
228C22×C9—24no—
229C22×C9—48no—
230C22×C9C2×#4112yes—
231C22×C9C2×#4112yes—
232C22×C9H(5,𝔽2)12yes—
233C22×C9C2511yescharacteristic
234C2×D9—24no—
235C2×D9—24no—
236C2×D9—24no—
237C2×D9—48no—
238C4×C9—22no—
239C4×C9—24no—
240C4×C9—22no—
241C4×C9C2×#4114yes—
242Dic9—22no—
243Dic9—24no—
244Dic9—22no—
245Dic9—22no—
246Dic9C2×#4114yes—
247C22×Q8—91no—
248C22×Q8C2×D911yescharacteristic
249C22×D4—92no—
250C22×D4—92no—
251C22×D4—91no—
252C22×D4C2×D911yescharacteristic
253C23×C4—92no—
254C23×C4—92no—
255#127—98no—
256#124—98no—
257#124—916no—
258#124C2×D918yescomplemented
259#123—916no—
260#123—916no—
261C4×Q8—98no—
262C4×Q8—98no—
263C4×D4—98no—
264C4×D4—916no—
265C4×D4—98no—
266C2×C4⋊C4—91no—
267C2×C4⋊C4—91no—
268C2×C4⋊C4—91no—
269C2×C4⋊C4—92no—
270C2×C4⋊C4—91no—
271C2×C22⋊C4—92no—
272C2×C22⋊C4—92no—
273C2×C22⋊C4—92no—
274C2×C22⋊C4—92no—
275C2×C22⋊C4C2×D912yes—
276C2×C22⋊C4C2×D912yes—
277C2×C42—92no—
278C2×C42—91no—
279C2×C42—91no—
280C2×C42C2×D911yescharacteristic
281C23×C3—24no—
282C23×C3—24no—
283C23×C3—24no—
284C23×C3C23×D314yes—
285C23×C3C23×D311yescharacteristic
286C22×D3—34no—
287C22×D3—64no—
288C22×D3—64no—
289C22×D3—64no—
290C3×Q8—28no—
291C3×D4—28no—
292C2×C3×C4—24no—
293C2×C3×C4—22no—
294C2×C3×C4—22no—
295C2×C3×C4#23714yes—
296C2×C3×C4C23×D314yes—
297C2×C3×C4C23×D312yes—
298C2×C3×C4C23×D312yes—
299C2×C3×C4C23×D312yes—
300#67—616no—
301#67—128no—
302C2×Dic3—34no—
303C2×Dic3—32no—
304C2×Dic3—32no—
305C2×Dic3—32no—
306C2×Dic3—32no—
307C2×Dic3—34no—
308C2×Dic3—62no—
309C2×Dic3—64no—
310C2×Dic3—62no—
311C2×Dic3—62no—
312C2×Dic3—128no—
313D12—68no—
314C4×D3—128no—
315Dic6—68no—
316C2×C9—44no—
317C2×C9#55914yescomplemented
318C2×C9C22×#4111yescharacteristic
319C2×C9C22×#4111yescharacteristic
320C2×C9C2×H(5,𝔽2)11yescharacteristic
321D9—44no—
322C24—92no—
323C24C22×D912yes—
324C2×Q8—24no—
325C2×Q8—94no—
326C2×Q8—184no—
327C2×Q8C22×D914yes—
328C2×D4—24no—
329C2×D4—98no—
330C2×D4—98no—
331C2×D4—94no—
332C2×D4—188no—
333C2×D4—184no—
334C2×D4—364no—
335C2×D4C22×D914yes—
336C22×C4—91no—
337C22×C4—91no—
338C22×C4—92no—
339C22×C4—91no—
340C22×C4—91no—
341C22×C4—98no—
342C22×C4—98no—
343C22×C4—364no—
344C22×C4—364no—
345C22×C4C22×D912yes—
346C22×C4C22×D911yescharacteristic
347C22×C4C22×D911yescharacteristic
348C22×C4C22×D911yescharacteristic
349C4⋊C4—94no—
350C4⋊C4—94no—
351C4⋊C4—94no—
352C4⋊C4—98no—
353C4⋊C4—94no—
354C22⋊C4—98no—
355C22⋊C4—98no—
356C22⋊C4—98no—
357C22⋊C4—98no—
358C22⋊C4C22×D918yes—
359C22⋊C4C22×D918yes—
360C42—98no—
361C42—94no—
362C42—94no—
363C42C22×D914yes—
364C22×C3—24no—
365C22×C3—24no—
366C22×C3—24no—
367C22×C3—48no—
368C22×C3C2×#23712yes—
369C22×C3D3×#4112yes—
370C22×C3#100912yes—
371C22×C3C24×D311yescharacteristic
372C2×D3—64no—
373C2×D3—64no—
374C2×D3—64no—
375C2×D3—128no—
376C3×C4—24no—
377C3×C4—22no—
378C3×C4—22no—
379C3×C4C2×#23714yes—
380Dic3—34no—
381Dic3—62no—
382Dic3—64no—
383Dic3—62no—
384Dic3—62no—
385C9C2×#55911yescharacteristic, complemented, Sylow
386C23—24no—
387C23—24no—
388C23—24no—
389C23—94no—
390C23—184no—
391C23—184no—
392C23—184no—
393C23C23×D914yes—
394C23C23×D911yescharacteristic
395Q8—28no—
396Q8—188no—
397D4—28no—
398D4—1816no—
399D4—188no—
400D4—368no—
401C2×C4—24no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—92no—
405C2×C4—94no—
406C2×C4—92no—
407C2×C4—94no—
408C2×C4—92no—
409C2×C4—92no—
410C2×C4—182no—
411C2×C4—184no—
412C2×C4—182no—
413C2×C4—182no—
414C2×C4—368no—
415C2×C4—368no—
416C2×C4#369914yes—
417C2×C4C23×D914yes—
418C2×C4C23×D912yes—
419C2×C4C23×D912yes—
420C2×C4C23×D912yes—
421C2×C3—44no—
422C2×C3#568114yes—
423C2×C3C22×#23711yescharacteristic
424C2×C3C2×D3×#4111yescharacteristic
425C2×C3C2×#100911yescharacteristic
426D3—124no—
427C22—24no—
428C22—24no—
429C22—24no—
430C22—48no—
431C22—184no—
432C22—184no—
433C22—184no—
434C22—368no—
435C22C2×#369912yes—
436C22#41×D912yes—
437C22#6371512yes—
438C22C24×D911yescharacteristic
439C4—24no—
440C4—22no—
441C4—22no—
442C4—94no—
443C4—182no—
444C4—184no—
445C4—182no—
446C4—182no—
447C4C2×#369914yes—
448C3C2×#568111yescharacteristic
449C2—44no—
450C2—364no—
451C2#1058978314yesdirect product factor
452C2C22×#369911yescharacteristic
453C2C2×#41×D911yescharacteristic
454C2C2×#6371511yescharacteristic
subgroupG/H
centerC23C23×D9
commutator, cosocleC22×C9C25
FrattiniC22×C3C24×D3
FittingC2×C9×#124C2
socleC23×C3C23×D3
prime radicalC2×#63502C2
hypercenterC2×#124D9
hypocenterC9C2×#559
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C23 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×C9×#124C2semidirect
2. C2×#63509C2semidirect
3. C2×Q8×Dic9C2semidirect
5. C2×D4×Dic9C2semidirect
6. #10589783C2direct (N × H)
7. C2×#63448C2semidirect
8. C2×#63447C2semidirect
9. C2×#63445C2semidirect
10. C2×#611⋊C4C2semidirect
11. C2×C4×D36C2semidirect
12. C2×C4×Dic18C2semidirect
22. C9×#124C22semidirect
27. #63509C22semidirect
28. Q8×Dic9C22semidirect
30. D4×Dic9C22semidirect
42. #63448C22semidirect
43. #63447C22semidirect
44. #63445C22semidirect
45. #611⋊C4C22semidirect
46. C4×D36C22semidirect
47. C4×Dic18C22semidirect
176. C2×#124D9semidirect
258. #124C2×D9semidirect
317. C2×C9#559semidirect
385. C9C2×#559semidirect
451. C2#10589783direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C9×#1242
C2×#635092
C2×Q8×Dic92
C2×#635022
C2×D4×Dic92
#105897832
C2×#634482
C2×#634472
C2×#634452
C2×#611⋊C42
C2×C4×D362
C2×C4×Dic182
C2×#56813