Finite Group Databasebeta

← C2×#10589684 #11901632

Subgroups — C2×#10589684 #11901632

Order 1152.

1698 conjugacy classes of subgroups.

The subgroup lattice has 444 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, complemented
3C2×#63508C211yesmaximal, characteristic, complemented
4#10589684C2116yesmaximal, direct product factor
5C2×#63458C212yesmaximal, complemented
6C2×#63457C211yesmaximal, characteristic
7C2×#63456C212yesmaximal, complemented
8C2×#63450C211yesmaximal, characteristic, complemented
9C2×#63438C212yesmaximal, complemented
10C2×#63437C212yesmaximal, complemented
11C2×C4×D36C211yesmaximal, characteristic, complemented
12C2×#63434C211yesmaximal, characteristic, complemented
13C2×#5582—31nomaximal
14C22×Q8×C9C2211yescharacteristic
15C22×D36C2211yescharacteristic
16C22×D36C2212yes—
17C22×C4×D9C2211yescharacteristic
18C22×C4×D9C2212yes—
19C22×Dic18C2212yes—
20C4×Q8×C9C2218yescomplemented
21C2×C9×C4⋊C4C2211yescharacteristic
22C2×C9×C4⋊C4C2212yes—
23C2×C42×C9C2211yescharacteristic
24C2×C42×C9C2212yes—
25#63509C2218yescomplemented
26#63508C2218yescomplemented
27C2×(C2×D9)⋊C4C2211yescharacteristic
28C2×(C2×D9)⋊C4C2211yescharacteristic
29C2×(C2×D9)⋊C4C2212yes—
30C2×(C2×D9)⋊C4C2212yes—
31C2×(C2×D9)⋊C4C2212yes—
32C2×(C2×D9)⋊C4C2212yes—
33C2×(C2×D9)⋊C4C2212yes—
34C2×C4⋊Dic9C2211yescharacteristic
35C2×Dic9⋊C4C2211yescharacteristic
36C2×Dic9⋊C4C2211yescharacteristic
37C2×Dic9⋊C4C2212yes—
38C2×Dic9⋊C4C2212yes—
39C2×C4×Dic9C2211yescharacteristic
40#63458C22116yescomplemented
41#63457C2218yes—
42#63456C22116yescomplemented
43#63450C2218yescomplemented
44#63438C22116yescomplemented
45#63437C22116yescomplemented
46C4×D36C2218yescomplemented
47#63434C2218yescomplemented
48C2×C3×C4×Q8D311yescharacteristic
49C2×#947—31no—
50C2×#946—31no—
51#5582—316no—
52C2×#896—32no—
53C2×#895—31no—
54C2×#894—32no—
55C2×#888—31no—
56C2×#876—32no—
57C2×#875—32no—
58C2×C4×D12—31no—
59C2×#872—31no—
60C23×D9C2311yescharacteristic
61C23×D9C2312yes—
62C2×Q8×C9—24no—
63C2×Q8×C9C2314yes—
64C22×C4×C9C2311yescharacteristic
65C22×C4×C9C2312yes—
66C22×C4×C9C2312yes—
67C22×C4×C9C2311yescharacteristic
68C22×C4×C9C2311yescharacteristic
69C22×Dic9C2311yescharacteristic
70C22×Dic9C2311yescharacteristic
71C22×Dic9C2312yes—
72C22×Dic9C2311yescharacteristic
73C2×D36—24no—
74C2×D36—44no—
75C2×D36C2314yes—
76C2×D36C2318yes—
77C2×C4×D9—24no—
78C2×C4×D9—44no—
79C2×C4×D9C2314yes—
80C2×C4×D9C2318yes—
81C2×Dic18—44no—
82C2×Dic18C2318yes—
83C9×C4⋊C4C2314yes—
84C9×C4⋊C4C2318yes—
85C42×C9C2314yes—
86C42×C9C2318yes—
87(C2×D9)⋊C4C2318yes—
88(C2×D9)⋊C4C2318yes—
89(C2×D9)⋊C4C2318yes—
90(C2×D9)⋊C4C2314yes—
91(C2×D9)⋊C4C2314yes—
92(C2×D9)⋊C4C2318yes—
93(C2×D9)⋊C4C2318yes—
94C4⋊Dic9C2314yes—
95Dic9⋊C4C2318yes—
96Dic9⋊C4C2314yes—
97Dic9⋊C4C2314yes—
98Dic9⋊C4C2318yes—
99C4×Dic9C2314yes—
100C2×#542—91noSylow
101C22×C3×Q8C2×D311yescharacteristic
102C22×D12—31no—
103C22×D12—32no—
104C22×C4×D3—31no—
105C22×C4×D3—32no—
106C22×Dic6—32no—
107C3×C4×Q8C2×D318yes—
108C2×C3×C4⋊C4C2×D311yescharacteristic
109C2×C3×C4⋊C4C2×D312yes—
110C2×C3×C42C2×D311yescharacteristic
111C2×C3×C42C2×D312yes—
112#947—38no—
113#946—38no—
114C2×(C2×D3)⋊C4—31no—
115C2×(C2×D3)⋊C4—31no—
116C2×(C2×D3)⋊C4—32no—
117C2×(C2×D3)⋊C4—32no—
118C2×(C2×D3)⋊C4—32no—
119C2×(C2×D3)⋊C4—32no—
120C2×(C2×D3)⋊C4—32no—
121C2×C4⋊Dic3—31no—
122C2×Dic3⋊C4—31no—
123C2×Dic3⋊C4—31no—
124C2×Dic3⋊C4—32no—
125C2×Dic3⋊C4—32no—
126C2×C4×Dic3—31no—
127#896—316no—
128#895—38no—
129#894—316no—
130#888—38no—
131#876—316no—
132#875—316no—
133C4×D12—38no—
134#872—38no—
135C23×C9C2411yescharacteristic
136C22×D9—22no—
137C22×D9—24no—
138C22×D9—24no—
139C22×D9—22no—
140C22×D9—22no—
141C22×D9—24no—
142C22×D9C2412yes—
143C22×D9C2414yes—
144Q8×C9—28no—
145C2×C4×C9—24no—
146C2×C4×C9—24no—
147C2×C4×C9—22no—
148C2×C4×C9—22no—
149C2×C4×C9#4114yes—
150C2×C4×C9C2412yes—
151C2×C4×C9C2414yes—
152C2×C4×C9C2414yes—
153C2×C4×C9C2412yes—
154C2×C4×C9C2412yes—
155C2×Dic9—22no—
156C2×Dic9—22no—
157C2×Dic9—24no—
158C2×Dic9—22no—
159C2×Dic9C2412yes—
160C2×Dic9C2412yes—
161C2×Dic9C2412yes—
162C2×Dic9C2414yes—
163D36—28no—
164D36—48no—
165C4×D9—28no—
166C4×D9—48no—
167Dic18—48no—
168#542—916no—
169C2×C4⋊Q8—91no—
170C2×#126—92no—
171C2×#124—91no—
172C2×#124—92no—
173C2×#123—92no—
174C2×C22⋊Q8—91no—
175C2×C22⋊Q8—92no—
176C2×#121—91no—
177C2×C4×Q8D911yescharacteristic, complemented
178C2×C4×D4—91no—
179C2×#117—91no—
180C23×D3—31no—
181C23×D3—32no—
182C2×C3×Q8—24no—
183C2×C3×Q8C22×D314yes—
184C22×C3×C4C22×D311yescharacteristic
185C22×C3×C4C22×D312yes—
186C22×C3×C4C22×D312yes—
187C22×C3×C4C22×D311yescharacteristic
188C22×C3×C4C22×D311yescharacteristic
189C22×Dic3—31no—
190C22×Dic3—31no—
191C22×Dic3—31no—
192C22×Dic3—32no—
193C2×D12—34no—
194C2×D12—38no—
195C2×D12—64no—
196C2×D12—124no—
197C2×C4×D3—34no—
198C2×C4×D3—38no—
199C2×C4×D3—64no—
200C2×C4×D3—124no—
201C2×Dic6—38no—
202C2×Dic6—124no—
203C3×C4⋊C4C22×D314yes—
204C3×C4⋊C4C22×D318yes—
205C3×C42C22×D314yes—
206C3×C42C22×D318yes—
207(C2×D3)⋊C4—34no—
208(C2×D3)⋊C4—34no—
209(C2×D3)⋊C4—38no—
210(C2×D3)⋊C4—38no—
211(C2×D3)⋊C4—38no—
212(C2×D3)⋊C4—38no—
213(C2×D3)⋊C4—38no—
214C4⋊Dic3—34no—
215Dic3⋊C4—34no—
216Dic3⋊C4—34no—
217Dic3⋊C4—38no—
218Dic3⋊C4—38no—
219C4×Dic3—34no—
220C22×C9C2×#4112yes—
221C22×C9H(5,𝔽2)12yes—
222C22×C92−1+412yes—
223C22×C9C2511yescharacteristic
224C2×D9—22no—
225C2×D9—24no—
226C2×D9—24no—
227C2×D9—22no—
228C2×D9—22no—
229C2×D9—24no—
230C2×D9—44no—
231C2×D9—48no—
232C4×C9—24no—
233C4×C9—24no—
234C4×C9—22no—
235C4×C9—22no—
236C4×C9C2×#4114yes—
237Dic9—22no—
238Dic9—22no—
239Dic9—24no—
240Dic9—22no—
241C22×Q8—92no—
242C22×Q8C2×D911yescharacteristic
243C22×D4—91no—
244C22×D4—92no—
245C23×C4—91no—
246C23×C4—92no—
247C4⋊Q8—98no—
248#126—916no—
249#124—98no—
250#124—916no—
251#123—916no—
252C22⋊Q8—98no—
253C22⋊Q8—916no—
254#121—98no—
255C4×Q8C2×D918yescomplemented
256C4×D4—98no—
257#117—98no—
258C2×C4⋊C4—91no—
259C2×C4⋊C4—91no—
260C2×C4⋊C4—91no—
261C2×C4⋊C4—92no—
262C2×C4⋊C4—92no—
263C2×C4⋊C4C2×D911yescharacteristic
264C2×C4⋊C4C2×D912yes—
265C2×C22⋊C4—91no—
266C2×C22⋊C4—91no—
267C2×C22⋊C4—92no—
268C2×C22⋊C4—92no—
269C2×C22⋊C4—92no—
270C2×C22⋊C4—92no—
271C2×C22⋊C4—92no—
272C2×C42—91no—
273C2×C42C2×D911yescharacteristic
274C2×C42C2×D912yes—
275C23×C3C23×D311yescharacteristic
276C22×D3—32no—
277C22×D3—34no—
278C22×D3—62no—
279C22×D3—64no—
280C22×D3—62no—
281C22×D3—64no—
282C22×D3—64no—
283C22×D3—62no—
284C3×Q8—28no—
285C2×C3×C4—24no—
286C2×C3×C4—22no—
287C2×C3×C4—24no—
288C2×C3×C4—22no—
289C2×C3×C4#23514yes—
290C2×C3×C4C23×D312yes—
291C2×C3×C4C23×D314yes—
292C2×C3×C4C23×D314yes—
293C2×C3×C4C23×D312yes—
294C2×C3×C4C23×D312yes—
295C2×Dic3—32no—
296C2×Dic3—32no—
297C2×Dic3—32no—
298C2×Dic3—34no—
299C2×Dic3—62no—
300C2×Dic3—62no—
301C2×Dic3—62no—
302C2×Dic3—64no—
303D12—68no—
304D12—128no—
305C4×D3—68no—
306C4×D3—128no—
307Dic6—128no—
308C2×C9#54214yescomplemented
309C2×C9C22×#4111yescharacteristic
310C2×C9C2×H(5,𝔽2)11yescharacteristic
311C2×C9C2×2−1+411yescharacteristic
312D9—42no—
313D9—44no—
314C24—91no—
315C24—92no—
316C2×Q8—24no—
317C2×Q8—98no—
318C2×Q8—364no—
319C2×Q8C22×D914yes—
320C2×D4—94no—
321C2×D4—98no—
322C2×D4—184no—
323C2×D4—364no—
324C22×C4—91no—
325C22×C4—91no—
326C22×C4—91no—
327C22×C4—92no—
328C22×C4—94no—
329C22×C4—98no—
330C22×C4—184no—
331C22×C4—364no—
332C22×C4C22×D911yescharacteristic
333C22×C4C22×D912yes—
334C22×C4C22×D911yescharacteristic
335C22×C4C22×D912yes—
336C22×C4C22×D911yescharacteristic
337C4⋊C4—94no—
338C4⋊C4—94no—
339C4⋊C4—94no—
340C4⋊C4—98no—
341C4⋊C4—98no—
342C4⋊C4C22×D914yes—
343C4⋊C4C22×D918yes—
344C22⋊C4—94no—
345C22⋊C4—94no—
346C22⋊C4—98no—
347C22⋊C4—98no—
348C22⋊C4—98no—
349C22⋊C4—98no—
350C22⋊C4—98no—
351C42—94no—
352C42C22×D914yes—
353C42C22×D918yes—
354C22×C3C2×#23512yes—
355C22×C3#100712yes—
356C22×C3#100912yes—
357C22×C3C24×D311yescharacteristic
358C2×D3—62no—
359C2×D3—64no—
360C2×D3—62no—
361C2×D3—64no—
362C2×D3—64no—
363C2×D3—62no—
364C2×D3—124no—
365C2×D3—128no—
366C3×C4—24no—
367C3×C4—22no—
368C3×C4—24no—
369C3×C4—22no—
370C3×C4C2×#23514yes—
371Dic3—62no—
372Dic3—62no—
373Dic3—62no—
374Dic3—64no—
375C9C2×#54211yescharacteristic, complemented, Sylow
376C23—92no—
377C23—94no—
378C23—182no—
379C23—184no—
380C23—182no—
381C23—184no—
382C23—184no—
383C23—182no—
384C23C23×D911yescharacteristic
385Q8—28no—
386Q8—368no—
387D4—188no—
388D4—368no—
389C2×C4—24no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—24no—
393C2×C4—92no—
394C2×C4—92no—
395C2×C4—92no—
396C2×C4—94no—
397C2×C4—182no—
398C2×C4—182no—
399C2×C4—184no—
400C2×C4—182no—
401C2×C4—188no—
402C2×C4—368no—
403C2×C4#369714yes—
404C2×C4C23×D912yes—
405C2×C4C23×D914yes—
406C2×C4C23×D912yes—
407C2×C4C23×D914yes—
408C2×C4C23×D912yes—
409C2×C3#558214yes—
410C2×C3C22×#23511yescharacteristic
411C2×C3C2×#100711yescharacteristic
412C2×C3C2×#100911yescharacteristic
413D3—122no—
414D3—124no—
415C22—182no—
416C22—184no—
417C22—182no—
418C22—184no—
419C22—184no—
420C22—182no—
421C22—364no—
422C22—368no—
423C22C2×#369712yes—
424C22#6371312yes—
425C22#6371512yes—
426C22C24×D911yescharacteristic
427C4—24no—
428C4—22no—
429C4—22no—
430C4—24no—
431C4—182no—
432C4—182no—
433C4—184no—
434C4—182no—
435C4C2×#369714yes—
436C3C2×#558211yescharacteristic
437C2—362no—
438C2—364no—
439C2#1058968414yesdirect product factor
440C2C22×#369711yescharacteristic
441C2C2×#6371311yescharacteristic
442C2C2×#6371511yescharacteristic
subgroupG/H
centerC23C23×D9
commutator, cosocleC22×C9C25
FrattiniC22×C3C24×D3
FittingC2×C4×Q8×C9C2
socleC23×C3C23×D3
prime radicalC2×#63457C2
hypercenterC2×C4×Q8D9
hypocenterC9C2×#542
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
2. C2×#63509C2semidirect
3. C2×#63508C2semidirect
4. #10589684C2direct (N × H)
5. C2×#63458C2semidirect
7. C2×#63456C2semidirect
8. C2×#63450C2semidirect
9. C2×#63438C2semidirect
10. C2×#63437C2semidirect
11. C2×C4×D36C2semidirect
12. C2×#63434C2semidirect
20. C4×Q8×C9C22semidirect
25. #63509C22semidirect
26. #63508C22semidirect
40. #63458C22semidirect
42. #63456C22semidirect
43. #63450C22semidirect
44. #63438C22semidirect
45. #63437C22semidirect
46. C4×D36C22semidirect
47. #63434C22semidirect
177. C2×C4×Q8D9semidirect
255. C4×Q8C2×D9semidirect
308. C2×C9#542semidirect
375. C9C2×#542semidirect
439. C2#10589684direct (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×#635082
#105896842
C2×#634582
C2×#634572
C2×#634562
C2×#634502
C2×#634382
C2×#634372
C2×C4×D362
C2×#634342
C2×#55823