Finite Group Databasebeta

← C2×#10589670 #11903365

Subgroups — C2×#10589670 #11903365

Order 1152.

1668 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Q8×C9C211yesmaximal, characteristic, complemented
2C2×#63509C211yesmaximal, characteristic
3C2×#63506C211yesmaximal, characteristic, complemented
4#10589670C2116yesmaximal, direct product factor
5C2×#63460C212yesmaximal, complemented
6C2×#63458C212yesmaximal, complemented
7C2×#63455C211yesmaximal, characteristic
8C2×#63449C211yesmaximal, characteristic, complemented
9C2×#63438C212yesmaximal, complemented
10C2×#63437C211yesmaximal, characteristic
11C2×#63434C212yesmaximal, complemented
12C2×C4×Dic18C211yesmaximal, characteristic, complemented
13C2×#5568—31nomaximal
14C22×Q8×C9C2211yescharacteristic
15C22×D36C2211yescharacteristic
16C22×C4×D9C2212yes—
17C22×Dic18C2211yescharacteristic
18C22×Dic18C2211yescharacteristic
19C4×Q8×C9C2218yescomplemented
20C2×C9×C4⋊C4C2211yescharacteristic
21C2×C9×C4⋊C4C2212yes—
22C2×C42×C9C2211yescharacteristic
23C2×C42×C9C2212yes—
24#63509C2218yes—
25#63506C2218yescomplemented
26C2×(C2×D9)⋊C4C2212yes—
27C2×(C2×D9)⋊C4C2212yes—
28C2×(C2×D9)⋊C4C2212yes—
29C2×(C2×D9)⋊C4C2212yes—
30C2×(C2×D9)⋊C4C2212yes—
31C2×C4⋊Dic9C2211yescharacteristic
32C2×Dic9⋊C4C2211yescharacteristic
33C2×Dic9⋊C4C2211yescharacteristic
34C2×Dic9⋊C4C2212yes—
35C2×Dic9⋊C4C2212yes—
36C2×Dic9⋊C4C2212yes—
37C2×C4×Dic9C2211yescharacteristic
38C2×C4×Dic9C2211yescharacteristic
39C2×C4×Dic9C2212yes—
40#63460C22116yescomplemented
41#63458C22116yescomplemented
42#63455C2218yes—
43#63449C2218yescomplemented
44#63438C22116yescomplemented
45#63437C2218yes—
46#63434C22116yescomplemented
47C4×Dic18C2218yescomplemented
48C2×C3×C4×Q8D311yescharacteristic
49C2×#947—31no—
50C2×#944—31no—
51#5568—316no—
52C2×#898—32no—
53C2×#896—32no—
54C2×#893—31no—
55C2×#887—31no—
56C2×#876—32no—
57C2×#875—31no—
58C2×#872—32no—
59C2×C4×Dic6—31no—
60C23×D9C2312yes—
61C2×Q8×C9—24no—
62C2×Q8×C9C2314yes—
63C22×C4×C9C2311yescharacteristic
64C22×C4×C9C2311yescharacteristic
65C22×C4×C9C2312yes—
66C22×C4×C9C2312yes—
67C22×C4×C9C2311yescharacteristic
68C22×Dic9C2312yes—
69C22×Dic9C2311yescharacteristic
70C22×Dic9C2311yescharacteristic
71C22×Dic9C2311yescharacteristic
72C22×Dic9C2311yescharacteristic
73C2×D36—24no—
74C2×D36C2314yes—
75C2×C4×D9—28no—
76C2×C4×D9C2318yes—
77C2×Dic18—24no—
78C2×Dic18—24no—
79C2×Dic18C2314yes—
80C2×Dic18C2314yes—
81C9×C4⋊C4C2314yes—
82C9×C4⋊C4C2318yes—
83C42×C9C2314yes—
84C42×C9C2318yes—
85(C2×D9)⋊C4C2318yes—
86(C2×D9)⋊C4C2318yes—
87(C2×D9)⋊C4C2318yes—
88(C2×D9)⋊C4C2318yes—
89(C2×D9)⋊C4C2318yes—
90C4⋊Dic9C2314yes—
91Dic9⋊C4C2318yes—
92Dic9⋊C4C2318yes—
93Dic9⋊C4C2314yes—
94Dic9⋊C4C2314yes—
95Dic9⋊C4C2318yes—
96C4×Dic9C2314yes—
97C4×Dic9C2314yes—
98C4×Dic9C2318yes—
99C2×#556—91noSylow
100C22×C3×Q8C2×D311yescharacteristic
101C22×D12—31no—
102C22×C4×D3—32no—
103C22×Dic6—31no—
104C22×Dic6—31no—
105C3×C4×Q8C2×D318yes—
106C2×C3×C4⋊C4C2×D311yescharacteristic
107C2×C3×C4⋊C4C2×D312yes—
108C2×C3×C42C2×D311yescharacteristic
109C2×C3×C42C2×D312yes—
110#947—38no—
111#944—38no—
112C2×(C2×D3)⋊C4—32no—
113C2×(C2×D3)⋊C4—32no—
114C2×(C2×D3)⋊C4—32no—
115C2×(C2×D3)⋊C4—32no—
116C2×(C2×D3)⋊C4—32no—
117C2×C4⋊Dic3—31no—
118C2×Dic3⋊C4—31no—
119C2×Dic3⋊C4—31no—
120C2×Dic3⋊C4—32no—
121C2×Dic3⋊C4—32no—
122C2×Dic3⋊C4—32no—
123C2×C4×Dic3—31no—
124C2×C4×Dic3—31no—
125C2×C4×Dic3—32no—
126#898—316no—
127#896—316no—
128#893—38no—
129#887—38no—
130#876—316no—
131#875—38no—
132#872—316no—
133C4×Dic6—38no—
134C23×C9C2411yescharacteristic
135C22×D9—24no—
136C22×D9—24no—
137C22×D9—24no—
138C22×D9C2414yes—
139Q8×C9—28no—
140C2×C4×C9—22no—
141C2×C4×C9—24no—
142C2×C4×C9—24no—
143C2×C4×C9—22no—
144C2×C4×C9#4114yes—
145C2×C4×C9C2414yes—
146C2×C4×C9C2412yes—
147C2×C4×C9C2414yes—
148C2×C4×C9C2412yes—
149C2×C4×C9C2412yes—
150C2×Dic9—24no—
151C2×Dic9—22no—
152C2×Dic9—22no—
153C2×Dic9—22no—
154C2×Dic9#4114yes—
155C2×Dic9C2412yes—
156C2×Dic9C2412yes—
157C2×Dic9C2412yes—
158C2×Dic9C2414yes—
159C2×Dic9C2412yes—
160D36—28no—
161C4×D9—216no—
162Dic18—28no—
163Dic18—28no—
164#556—916no—
165C2×C4⋊Q8—91no—
166C2×#126—92no—
167C2×#126—92no—
168C2×#124—91no—
169C2×#124—91no—
170C2×C22⋊Q8—92no—
171C2×C4×Q8—91no—
172C2×C4×Q8—91no—
173C2×C4×Q8D911yescharacteristic, complemented
174C2×C4×D4—91no—
175C2×#117—92no—
176C23×D3—32no—
177C2×C3×Q8—24no—
178C2×C3×Q8C22×D314yes—
179C22×C3×C4C22×D312yes—
180C22×C3×C4C22×D311yescharacteristic
181C22×C3×C4C22×D312yes—
182C22×C3×C4C22×D311yescharacteristic
183C22×C3×C4C22×D311yescharacteristic
184C22×Dic3—31no—
185C22×Dic3—31no—
186C22×Dic3—31no—
187C22×Dic3—32no—
188C22×Dic3—31no—
189C2×D12—34no—
190C2×D12—64no—
191C2×C4×D3—38no—
192C2×C4×D3—68no—
193C2×Dic6—34no—
194C2×Dic6—34no—
195C2×Dic6—64no—
196C2×Dic6—64no—
197C3×C4⋊C4C22×D314yes—
198C3×C4⋊C4C22×D318yes—
199C3×C42C22×D314yes—
200C3×C42C22×D318yes—
201(C2×D3)⋊C4—38no—
202(C2×D3)⋊C4—38no—
203(C2×D3)⋊C4—38no—
204(C2×D3)⋊C4—38no—
205(C2×D3)⋊C4—38no—
206C4⋊Dic3—34no—
207Dic3⋊C4—34no—
208Dic3⋊C4—34no—
209Dic3⋊C4—38no—
210Dic3⋊C4—38no—
211Dic3⋊C4—38no—
212C4×Dic3—34no—
213C4×Dic3—34no—
214C4×Dic3—38no—
215C22×C9C2×#4112yes—
216C22×C9C2×#4112yes—
217C22×C92−1+412yes—
218C22×C9C2511yescharacteristic
219C2×D9—24no—
220C2×D9—24no—
221C2×D9—24no—
222C2×D9—48no—
223C4×C9—22no—
224C4×C9—24no—
225C4×C9—24no—
226C4×C9—22no—
227C4×C9C2×#4114yes—
228Dic9—24no—
229Dic9—22no—
230Dic9—22no—
231Dic9—22no—
232Dic9C2×#4114yes—
233C22×Q8—91no—
234C22×Q8—91no—
235C22×Q8C2×D911yescharacteristic
236C22×D4—91no—
237C23×C4—92no—
238C4⋊Q8—98no—
239#126—916no—
240#126—916no—
241#124—98no—
242#124—98no—
243C22⋊Q8—916no—
244C4×Q8—98no—
245C4×Q8—98no—
246C4×Q8C2×D918yescomplemented
247C4×D4—98no—
248#117—916no—
249C2×C4⋊C4—91no—
250C2×C4⋊C4—92no—
251C2×C4⋊C4—92no—
252C2×C4⋊C4—91no—
253C2×C4⋊C4—91no—
254C2×C4⋊C4—92no—
255C2×C4⋊C4C2×D911yescharacteristic
256C2×C4⋊C4C2×D912yes—
257C2×C22⋊C4—92no—
258C2×C22⋊C4—92no—
259C2×C22⋊C4—92no—
260C2×C22⋊C4—92no—
261C2×C22⋊C4—92no—
262C2×C42—92no—
263C2×C42—91no—
264C2×C42—91no—
265C2×C42C2×D912yes—
266C2×C42C2×D911yescharacteristic
267C23×C3C23×D311yescharacteristic
268C22×D3—34no—
269C22×D3—64no—
270C22×D3—64no—
271C22×D3—64no—
272C3×Q8—28no—
273C2×C3×C4—24no—
274C2×C3×C4—22no—
275C2×C3×C4—22no—
276C2×C3×C4—24no—
277C2×C3×C4#23514yes—
278C2×C3×C4C23×D314yes—
279C2×C3×C4C23×D312yes—
280C2×C3×C4C23×D314yes—
281C2×C3×C4C23×D312yes—
282C2×C3×C4C23×D312yes—
283C2×Dic3—34no—
284C2×Dic3—32no—
285C2×Dic3—32no—
286C2×Dic3—32no—
287C2×Dic3—34no—
288C2×Dic3—32no—
289C2×Dic3—64no—
290C2×Dic3—62no—
291C2×Dic3—62no—
292C2×Dic3—62no—
293D12—68no—
294C4×D3—616no—
295Dic6—68no—
296Dic6—68no—
297C2×C9#55614yescomplemented
298C2×C9C22×#4111yescharacteristic
299C2×C9C22×#4111yescharacteristic
300C2×C9C2×2−1+411yescharacteristic
301D9—44no—
302C24—92no—
303C2×Q8—24no—
304C2×Q8—94no—
305C2×Q8—94no—
306C2×Q8—184no—
307C2×Q8—184no—
308C2×Q8C22×D914yes—
309C2×D4—94no—
310C2×D4—184no—
311C22×C4—91no—
312C22×C4—91no—
313C22×C4—91no—
314C22×C4—92no—
315C22×C4—91no—
316C22×C4—98no—
317C22×C4—188no—
318C22×C4C22×D912yes—
319C22×C4C22×D911yescharacteristic
320C22×C4C22×D912yes—
321C22×C4C22×D911yescharacteristic
322C22×C4C22×D911yescharacteristic
323C4⋊C4—94no—
324C4⋊C4—98no—
325C4⋊C4—98no—
326C4⋊C4—94no—
327C4⋊C4—94no—
328C4⋊C4—98no—
329C4⋊C4C22×D914yes—
330C4⋊C4C22×D918yes—
331C22⋊C4—98no—
332C22⋊C4—98no—
333C22⋊C4—98no—
334C22⋊C4—98no—
335C22⋊C4—98no—
336C42—98no—
337C42—94no—
338C42—94no—
339C42C22×D918yes—
340C42C22×D914yes—
341C22×C3C2×#23512yes—
342C22×C3#100712yes—
343C22×C3D3×#4112yes—
344C22×C3C24×D311yescharacteristic
345C2×D3—64no—
346C2×D3—64no—
347C2×D3—64no—
348C2×D3—128no—
349C3×C4—24no—
350C3×C4—22no—
351C3×C4—22no—
352C3×C4—24no—
353C3×C4C2×#23514yes—
354Dic3—34no—
355Dic3—64no—
356Dic3—62no—
357Dic3—62no—
358Dic3—62no—
359C9C2×#55611yescharacteristic, complemented, Sylow
360C23—94no—
361C23—184no—
362C23—184no—
363C23—184no—
364C23C23×D911yescharacteristic
365Q8—28no—
366Q8—188no—
367Q8—188no—
368D4—188no—
369C2×C4—24no—
370C2×C4—22no—
371C2×C4—24no—
372C2×C4—22no—
373C2×C4—92no—
374C2×C4—94no—
375C2×C4—92no—
376C2×C4—92no—
377C2×C4—94no—
378C2×C4—92no—
379C2×C4—1816no—
380C2×C4—184no—
381C2×C4—182no—
382C2×C4—182no—
383C2×C4—182no—
384C2×C4#369714yes—
385C2×C4C23×D914yes—
386C2×C4C23×D912yes—
387C2×C4C23×D914yes—
388C2×C4C23×D912yes—
389C2×C4C23×D912yes—
390C2×C3#556814yes—
391C2×C3C22×#23511yescharacteristic
392C2×C3C2×#100711yescharacteristic
393C2×C3C2×D3×#4111yescharacteristic
394D3—124no—
395C22—184no—
396C22—184no—
397C22—184no—
398C22—368no—
399C22C2×#369712yes—
400C22#6371312yes—
401C22#41×D912yes—
402C22C24×D911yescharacteristic
403C4—24no—
404C4—22no—
405C4—24no—
406C4—22no—
407C4—94no—
408C4—184no—
409C4—182no—
410C4—182no—
411C4—182no—
412C4C2×#369714yes—
413C3C2×#556811yescharacteristic
414C2—364no—
415C2#1058967014yesdirect product factor
416C2C22×#369711yescharacteristic
417C2C2×#6371311yescharacteristic
418C2C2×#41×D911yescharacteristic
subgroupG/H
centerC23C23×D9
commutator, cosocleC22×C9C25
FrattiniC22×C3C24×D3
FittingC2×C4×Q8×C9C2
socleC23×C3C23×D3
prime radicalC22×D36C22
hypercenterC2×C4×Q8D9
hypocenterC9C2×#556
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C23 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C4×Q8×C9C2semidirect
3. C2×#63506C2semidirect
4. #10589670C2direct (N × H)
5. C2×#63460C2semidirect
6. C2×#63458C2semidirect
8. C2×#63449C2semidirect
9. C2×#63438C2semidirect
11. C2×#63434C2semidirect
12. C2×C4×Dic18C2semidirect
19. C4×Q8×C9C22semidirect
25. #63506C22semidirect
40. #63460C22semidirect
41. #63458C22semidirect
43. #63449C22semidirect
44. #63438C22semidirect
46. #63434C22semidirect
47. C4×Dic18C22semidirect
173. C2×C4×Q8D9semidirect
246. C4×Q8C2×D9semidirect
297. C2×C9#556semidirect
359. C9C2×#556semidirect
415. C2#10589670direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×Q8×C92
C2×#635092
C2×#635062
#105896702
C2×#634602
C2×#634582
C2×#634552
C2×#634492
C2×#634382
C2×#634372
C2×#634342
C2×C4×Dic182
C2×#55683