Finite Group Databasebeta

← C2×#10589615 #11902977

Subgroups — C2×#10589615 #11902977

Order 1152.

1686 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C9×C4⋊C4C211yesmaximal, characteristic, complemented
2C2×#63491C212yesmaximal
3C2×C4×#611C211yesmaximal, characteristic
4C2×#63488C212yesmaximal, complemented
5C2×#63486C211yesmaximal, characteristic, complemented
6#10589615C2116yesmaximal, direct product factor
7C2×#63460C212yesmaximal, complemented
8C2×#63459C211yesmaximal, characteristic, complemented
9C2×#63454C211yesmaximal, characteristic, complemented
10C2×#63452C211yesmaximal, characteristic, complemented
11C2×#63451C212yesmaximal, complemented
12C2×#63449C211yesmaximal, characteristic, complemented
13C2×#5513—31nomaximal
14C23×C4×C9C2211yescharacteristic
15C23×C4×C9C2212yes—
16C22×#611C2211yescharacteristic
17C22×C4×D9C2211yescharacteristic
18C22×Dic18C2211yescharacteristic
19C2×C9×C4⋊C4C2211yescharacteristic
20C2×C9×C4⋊C4C2212yes—
21C2×C9×C4⋊C4C2211yescharacteristic
22C2×C9×C4⋊C4C2218yescomplemented
23C2×#3676C2212yes—
24C2×#3676C2211yescharacteristic
25#63491C22116yes—
26C4×#611C2218yes—
27C2×(C2×D9)⋊C4C2212yes—
28C2×(C2×D9)⋊C4C2212yes—
29C2×(C2×D9)⋊C4C2211yescharacteristic
30#63488C22116yescomplemented
31C2×C4⋊Dic9C2212yes—
32C2×C4⋊Dic9C2211yescharacteristic
33C2×C4⋊Dic9C2212yes—
34#63486C2218yescomplemented
35C2×Dic9⋊C4C2212yes—
36C2×Dic9⋊C4C2211yescharacteristic
37C2×Dic9⋊C4C2212yes—
38C2×Dic9⋊C4C2212yes—
39C2×C4×Dic9C2211yescharacteristic
40C2×C4×Dic9C2212yes—
41C2×C4×Dic9C2212yes—
42#63460C22116yescomplemented
43#63459C2218yescomplemented
44#63454C2218yescomplemented
45#63452C2218yescomplemented
46#63451C22116yescomplemented
47#63449C2218yescomplemented
48C22×C3×C4⋊C4D311yescharacteristic
49C2×#929—32no—
50C2×C4×#67—31no—
51C2×#926—32no—
52C2×#924—31no—
53#5513—316no—
54C2×#898—32no—
55C2×#897—31no—
56C2×#892—31no—
57C2×#890—31no—
58C2×#889—32no—
59C2×#887—31no—
60C24×C9C2311yescharacteristic
61C23×D9C2311yescharacteristic
62C22×C4×C9—28no—
63C22×C4×C9—24no—
64C22×C4×C9C2318yes—
65C22×C4×C9C2312yes—
66C22×C4×C9C2311yescharacteristic
67C22×C4×C9C2312yes—
68C22×C4×C9C2314yes—
69C22×C4×C9C2311yescharacteristic
70C2×#611—24no—
71C2×#611C2314yes—
72C22×Dic9C2312yes—
73C22×Dic9C2311yescharacteristic
74C22×Dic9C2312yes—
75C22×Dic9C2311yescharacteristic
76C22×Dic9C2311yescharacteristic
77C2×C4×D9—24no—
78C2×C4×D9C2314yes—
79C2×Dic18—24no—
80C2×Dic18C2314yes—
81C9×C4⋊C4C2314yes—
82C9×C4⋊C4C2318yes—
83C9×C4⋊C4C2314yes—
84#3676C2314yes—
85#3676C2318yes—
86(C2×D9)⋊C4C2314yes—
87(C2×D9)⋊C4C2318yes—
88(C2×D9)⋊C4C2318yes—
89C4⋊Dic9C2318yes—
90C4⋊Dic9C2318yes—
91C4⋊Dic9C2314yes—
92Dic9⋊C4C2314yes—
93Dic9⋊C4C2318yes—
94Dic9⋊C4C2318yes—
95Dic9⋊C4C2318yes—
96C4×Dic9C2318yes—
97C4×Dic9C2318yes—
98C4×Dic9C2314yes—
99C2×#552—91noSylow
100C23×C3×C4C2×D311yescharacteristic
101C23×C3×C4C2×D312yes—
102C22×#67—31no—
103C22×C4×D3—31no—
104C22×Dic6—31no—
105C2×C3×C4⋊C4C2×D311yescharacteristic
106C2×C3×C4⋊C4C2×D312yes—
107C2×C3×C4⋊C4C2×D311yescharacteristic
108C2×C3×C4⋊C4C2×D318yes—
109C2×#217—32no—
110C2×#217—31no—
111#929—316no—
112C4×#67—38no—
113C2×(C2×D3)⋊C4—32no—
114C2×(C2×D3)⋊C4—32no—
115C2×(C2×D3)⋊C4—31no—
116#926—316no—
117C2×C4⋊Dic3—32no—
118C2×C4⋊Dic3—31no—
119C2×C4⋊Dic3—32no—
120#924—38no—
121C2×Dic3⋊C4—32no—
122C2×Dic3⋊C4—31no—
123C2×Dic3⋊C4—32no—
124C2×Dic3⋊C4—32no—
125C2×C4×Dic3—31no—
126C2×C4×Dic3—32no—
127C2×C4×Dic3—32no—
128#898—316no—
129#897—38no—
130#892—38no—
131#890—38no—
132#889—316no—
133#887—38no—
134C23×C9—22no—
135C23×C9—22no—
136C23×C9#4114yes—
137C23×C9C2412yes—
138C23×C9C2411yescharacteristic
139C22×D9—22no—
140C22×D9—22no—
141C22×D9—22no—
142C22×D9C2412yes—
143C2×C4×C9—22no—
144C2×C4×C9—216no—
145C2×C4×C9—24no—
146C2×C4×C9—24no—
147C2×C4×C9—28no—
148C2×C4×C9#4114yes—
149C2×C4×C9C2414yes—
150C2×C4×C9C2412yes—
151C2×C4×C9C2414yes—
152C2×C4×C9C2412yes—
153#611—28no—
154C2×Dic9—24no—
155C2×Dic9—22no—
156C2×Dic9—22no—
157C2×Dic9—22no—
158C2×Dic9—24no—
159C2×Dic9C2412yes—
160C2×Dic9C2412yes—
161C2×Dic9C2412yes—
162C2×Dic9C2414yes—
163C2×Dic9C2414yes—
164C4×D9—28no—
165Dic18—28no—
166#552—916no—
167C2×#126—92no—
168C2×#125—92no—
169C2×#125—91no—
170C2×#123—92no—
171C2×C22⋊Q8—91no—
172C2×C22⋊Q8—91no—
173C2×C4×Q8—91no—
174C2×C4×D4—91no—
175C2×#117—92no—
176C2×#117—91no—
177C22×C4⋊C4D911yescharacteristic, complemented
178C24×C3C22×D311yescharacteristic
179C23×D3—31no—
180C22×C3×C4—28no—
181C22×C3×C4—24no—
182C22×C3×C4C22×D312yes—
183C22×C3×C4C22×D311yescharacteristic
184C22×C3×C4C22×D312yes—
185C22×C3×C4C22×D314yes—
186C22×C3×C4C22×D318yes—
187C22×C3×C4C22×D311yescharacteristic
188C2×#67—34no—
189C2×#67—64no—
190C22×Dic3—31no—
191C22×Dic3—31no—
192C22×Dic3—31no—
193C22×Dic3—32no—
194C22×Dic3—32no—
195C2×C4×D3—34no—
196C2×C4×D3—64no—
197C2×Dic6—34no—
198C2×Dic6—64no—
199C3×C4⋊C4C22×D314yes—
200C3×C4⋊C4C22×D318yes—
201C3×C4⋊C4C22×D314yes—
202#217—38no—
203#217—34no—
204(C2×D3)⋊C4—38no—
205(C2×D3)⋊C4—38no—
206(C2×D3)⋊C4—34no—
207C4⋊Dic3—38no—
208C4⋊Dic3—34no—
209C4⋊Dic3—38no—
210Dic3⋊C4—38no—
211Dic3⋊C4—34no—
212Dic3⋊C4—38no—
213Dic3⋊C4—38no—
214C4×Dic3—34no—
215C4×Dic3—38no—
216C4×Dic3—38no—
217C22×C9—28no—
218C22×C9—22no—
219C22×C9—22no—
220C22×C9C2×#4112yes—
221C22×C9C2×#4114yes—
222C22×C9C2×#4112yes—
223C22×C92−1+412yes—
224C22×C9C2511yescharacteristic
225C2×D9—22no—
226C2×D9—22no—
227C2×D9—22no—
228C2×D9—44no—
229C4×C9—22no—
230C4×C9—24no—
231C4×C9—24no—
232C4×C9C2×#4114yes—
233Dic9—24no—
234Dic9—22no—
235Dic9—22no—
236Dic9—22no—
237Dic9—24no—
238C22×Q8—91no—
239C22×D4—91no—
240C23×C4—91no—
241C23×C4C2×D912yes—
242C23×C4C2×D911yescharacteristic
243#126—916no—
244#125—916no—
245#125—98no—
246#123—916no—
247C22⋊Q8—98no—
248C22⋊Q8—98no—
249C4×Q8—98no—
250C4×D4—98no—
251#117—916no—
252#117—98no—
253C2×C4⋊C4—92no—
254C2×C4⋊C4—91no—
255C2×C4⋊C4—92no—
256C2×C4⋊C4—91no—
257C2×C4⋊C4—92no—
258C2×C4⋊C4—92no—
259C2×C4⋊C4—92no—
260C2×C4⋊C4C2×D911yescharacteristic
261C2×C4⋊C4C2×D911yescharacteristic
262C2×C4⋊C4C2×D912yes—
263C2×C4⋊C4C2×D918yescomplemented
264C2×C22⋊C4—91no—
265C2×C22⋊C4—92no—
266C2×C22⋊C4—92no—
267C2×C22⋊C4—91no—
268C2×C22⋊C4—92no—
269C2×C42—92no—
270C2×C42—92no—
271C2×C42—91no—
272C23×C3—22no—
273C23×C3—22no—
274C23×C3#23714yes—
275C23×C3C23×D312yes—
276C23×C3C23×D311yescharacteristic
277C22×D3—32no—
278C22×D3—62no—
279C22×D3—62no—
280C22×D3—62no—
281C2×C3×C4—22no—
282C2×C3×C4—216no—
283C2×C3×C4—24no—
284C2×C3×C4—24no—
285C2×C3×C4—28no—
286C2×C3×C4#23514yes—
287C2×C3×C4C23×D314yes—
288C2×C3×C4C23×D312yes—
289C2×C3×C4C23×D314yes—
290C2×C3×C4C23×D312yes—
291#67—68no—
292C2×Dic3—32no—
293C2×Dic3—32no—
294C2×Dic3—32no—
295C2×Dic3—34no—
296C2×Dic3—34no—
297C2×Dic3—64no—
298C2×Dic3—62no—
299C2×Dic3—62no—
300C2×Dic3—62no—
301C2×Dic3—64no—
302C4×D3—68no—
303Dic6—68no—
304C2×C9—24no—
305C2×C9#55214yescomplemented
306C2×C9C22×#4111yescharacteristic
307C2×C9C22×#4111yescharacteristic
308C2×C9C2×2−1+411yescharacteristic
309D9—42no—
310C24—91no—
311C24C22×D911yescharacteristic
312C2×Q8—94no—
313C2×Q8—184no—
314C2×D4—94no—
315C2×D4—184no—
316C22×C4—28no—
317C22×C4—24no—
318C22×C4—91no—
319C22×C4—91no—
320C22×C4—92no—
321C22×C4—92no—
322C22×C4—91no—
323C22×C4—94no—
324C22×C4—184no—
325C22×C4C22×D918yes—
326C22×C4C22×D914yes—
327C22×C4C22×D912yes—
328C22×C4C22×D911yescharacteristic
329C22×C4C22×D912yes—
330C22×C4C22×D911yescharacteristic
331C4⋊C4—98no—
332C4⋊C4—94no—
333C4⋊C4—98no—
334C4⋊C4—94no—
335C4⋊C4—98no—
336C4⋊C4—98no—
337C4⋊C4—98no—
338C4⋊C4C22×D914yes—
339C4⋊C4C22×D914yes—
340C4⋊C4C22×D918yes—
341C22⋊C4—94no—
342C22⋊C4—98no—
343C22⋊C4—98no—
344C22⋊C4—94no—
345C22⋊C4—98no—
346C42—98no—
347C42—98no—
348C42—94no—
349C22×C3—22no—
350C22×C3—22no—
351C22×C3—28no—
352C22×C3C2×#23512yes—
353C22×C3C2×#23714yes—
354C22×C3C2×#23712yes—
355C22×C3#100712yes—
356C22×C3C24×D311yescharacteristic
357C2×D3—62no—
358C2×D3—62no—
359C2×D3—62no—
360C2×D3—124no—
361C3×C4—22no—
362C3×C4—24no—
363C3×C4—24no—
364C3×C4C2×#23514yes—
365Dic3—64no—
366Dic3—62no—
367Dic3—62no—
368Dic3—62no—
369Dic3—64no—
370C9C2×#55211yescharacteristic, complemented, Sylow
371C23—22no—
372C23—22no—
373C23—92no—
374C23—182no—
375C23—182no—
376C23—182no—
377C23#369914yes—
378C23C23×D912yes—
379C23C23×D911yescharacteristic
380Q8—188no—
381D4—188no—
382C2×C4—22no—
383C2×C4—216no—
384C2×C4—24no—
385C2×C4—24no—
386C2×C4—28no—
387C2×C4—92no—
388C2×C4—92no—
389C2×C4—94no—
390C2×C4—94no—
391C2×C4—92no—
392C2×C4—182no—
393C2×C4—184no—
394C2×C4—182no—
395C2×C4—182no—
396C2×C4—184no—
397C2×C4—188no—
398C2×C4#369714yes—
399C2×C4C23×D914yes—
400C2×C4C23×D912yes—
401C2×C4C23×D914yes—
402C2×C4C23×D912yes—
403C2×C3—24no—
404C2×C3#551314yes—
405C2×C3C22×#23511yescharacteristic
406C2×C3C22×#23711yescharacteristic
407C2×C3C2×#100711yescharacteristic
408D3—122no—
409C22—22no—
410C22—22no—
411C22—28no—
412C22—182no—
413C22—182no—
414C22—182no—
415C22—364no—
416C22C2×#369712yes—
417C22C2×#369914yes—
418C22C2×#369912yes—
419C22#6371312yes—
420C22C24×D911yescharacteristic
421C4—22no—
422C4—24no—
423C4—24no—
424C4—182no—
425C4—184no—
426C4—182no—
427C4—182no—
428C4—184no—
429C4C2×#369714yes—
430C3C2×#551311yescharacteristic
431C2—24no—
432C2—362no—
433C2#1058961514yesdirect product factor
434C2C22×#369711yescharacteristic
435C2C22×#369911yescharacteristic
436C2C2×#6371311yescharacteristic
subgroupG/H
centerC23C23×D9
commutator, cosocleC22×C9C25
FrattiniC22×C3C24×D3
FittingC22×C9×C4⋊C4C2
socleC23×C3C23×D3
prime radicalC22×#611C22
hypercenterC22×C4⋊C4D9
hypocenterC9C2×#552
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
4. C2×#63488C2semidirect
5. C2×#63486C2semidirect
6. #10589615C2direct (N × H)
7. C2×#63460C2semidirect
8. C2×#63459C2semidirect
9. C2×#63454C2semidirect
10. C2×#63452C2semidirect
11. C2×#63451C2semidirect
12. C2×#63449C2semidirect
22. C2×C9×C4⋊C4C22semidirect
30. #63488C22semidirect
34. #63486C22semidirect
42. #63460C22semidirect
43. #63459C22semidirect
44. #63454C22semidirect
45. #63452C22semidirect
46. #63451C22semidirect
47. #63449C22semidirect
177. C22×C4⋊C4D9semidirect
263. C2×C4⋊C4C2×D9semidirect
305. C2×C9#552semidirect
370. C9C2×#552semidirect
433. C2#10589615direct (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×#634912
C2×C4×#6112
C2×#634882
C2×#634862
#105896152
C2×#634602
C2×#634592
C2×#634542
C2×#634522
C2×#634512
C2×#634492
C2×#55133