Finite Group Databasebeta

← C2×#10589659 #11900585

Subgroups — C2×#10589659 #11900585

Order 1152.

1848 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×C9C211yesmaximal, characteristic, complemented
2C2×#63500C211yesmaximal, characteristic
3C2×#63498C211yesmaximal, characteristic, complemented
4C2×C4×#611C212yesmaximal, complemented
5C2×#63488C212yesmaximal, complemented
6#10589659C2116yesmaximal, direct product factor
7C2×#63459C211yesmaximal, characteristic, complemented
8C2×#63452C211yesmaximal, characteristic, complemented
9C2×#63445C212yesmaximal, complemented
10C2×#63441C212yesmaximal, complemented
11C2×C42×D9C211yesmaximal, characteristic, complemented
12C2×C4×Dic18C211yesmaximal, characteristic, complemented
13C2×#5557—31nomaximal
14C22×D4×C9C2211yescharacteristic
15C23×C4×C9C2212yes—
16C22×#611C2212yes—
17C22×C4×D9C2211yescharacteristic
18C22×C4×D9C2211yescharacteristic
19C22×C4×D9C2211yescharacteristic
20C22×Dic18C2211yescharacteristic
21C4×D4×C9C2218yescomplemented
22C2×C9×C4⋊C4C2211yescharacteristic
23C2×C9×C22⋊C4C2212yes—
24C2×C42×C9C2211yescharacteristic
25C2×#3676C2212yes—
26C2×#3676C2212yes—
27C2×#3676C2212yes—
28#63500C2218yes—
29#63498C2218yescomplemented
30C4×#611C22116yescomplemented
31C2×(C2×D9)⋊C4C2212yes—
32#63488C22116yescomplemented
33C2×C4⋊Dic9C2211yescharacteristic
34C2×C4⋊Dic9C2212yes—
35C2×C4⋊Dic9C2212yes—
36C2×Dic9⋊C4C2212yes—
37C2×Dic9⋊C4C2212yes—
38C2×C4×Dic9C2212yes—
39C2×C4×Dic9C2211yescharacteristic
40C2×C4×Dic9C2211yescharacteristic
41C2×C4×Dic9C2211yescharacteristic
42#63459C2218yescomplemented
43#63452C2218yescomplemented
44#63445C22116yescomplemented
45#63441C22116yescomplemented
46C42×D9C2218yescomplemented
47C4×Dic18C2218yescomplemented
48C2×C3×C4×D4D311yescharacteristic
49C2×#938—31no—
50C2×#936—31no—
51C2×C4×#67—32no—
52C2×#926—32no—
53#5557—316no—
54C2×#897—31no—
55C2×#890—31no—
56C2×#883—32no—
57C2×#879—32no—
58C2×C42×D3—31no—
59C2×C4×Dic6—31no—
60C24×C9C2312yes—
61C23×D9C2311yescharacteristic
62C2×D4×C9—24no—
63C2×D4×C9C2314yes—
64C22×C4×C9—28no—
65C22×C4×C9C2318yes—
66C22×C4×C9C2312yes—
67C22×C4×C9C2311yescharacteristic
68C22×C4×C9C2311yescharacteristic
69C22×C4×C9C2311yescharacteristic
70C2×#611—28no—
71C2×#611C2318yes—
72C22×Dic9C2312yes—
73C22×Dic9C2311yescharacteristic
74C22×Dic9C2311yescharacteristic
75C22×Dic9C2311yescharacteristic
76C22×Dic9C2312yes—
77C2×C4×D9—24no—
78C2×C4×D9—24no—
79C2×C4×D9—24no—
80C2×C4×D9C2314yes—
81C2×C4×D9C2314yes—
82C2×C4×D9C2314yes—
83C2×Dic18—24no—
84C2×Dic18C2314yes—
85C9×C4⋊C4C2314yes—
86C9×C22⋊C4C2318yes—
87C42×C9C2314yes—
88#3676C2318yes—
89#3676C2318yes—
90#3676C2318yes—
91(C2×D9)⋊C4C2318yes—
92C4⋊Dic9C2318yes—
93C4⋊Dic9C2318yes—
94C4⋊Dic9C2314yes—
95Dic9⋊C4C2318yes—
96Dic9⋊C4C2318yes—
97C4×Dic9C2314yes—
98C4×Dic9C2318yes—
99C4×Dic9C2314yes—
100C4×Dic9C2314yes—
101C2×#529—91noSylow
102C22×C3×D4C2×D311yescharacteristic
103C23×C3×C4C2×D312yes—
104C22×#67—32no—
105C22×C4×D3—31no—
106C22×C4×D3—31no—
107C22×C4×D3—31no—
108C22×Dic6—31no—
109C3×C4×D4C2×D318yes—
110C2×C3×C4⋊C4C2×D311yescharacteristic
111C2×C3×C22⋊C4C2×D312yes—
112C2×C3×C42C2×D311yescharacteristic
113C2×#217—32no—
114C2×#217—32no—
115C2×#217—32no—
116#938—38no—
117#936—38no—
118C4×#67—316no—
119C2×(C2×D3)⋊C4—32no—
120#926—316no—
121C2×C4⋊Dic3—31no—
122C2×C4⋊Dic3—32no—
123C2×C4⋊Dic3—32no—
124C2×Dic3⋊C4—32no—
125C2×Dic3⋊C4—32no—
126C2×C4×Dic3—32no—
127C2×C4×Dic3—31no—
128C2×C4×Dic3—31no—
129C2×C4×Dic3—31no—
130#897—38no—
131#890—38no—
132#883—316no—
133#879—316no—
134C42×D3—38no—
135C4×Dic6—38no—
136C23×C9—24no—
137C23×C9—24no—
138C23×C9—24no—
139C23×C9C2414yes—
140C23×C9C2411yescharacteristic
141C22×D9—22no—
142C22×D9—22no—
143C22×D9#4114yes—
144C22×D9C2412yes—
145D4×C9—28no—
146C2×C4×C9—22no—
147C2×C4×C9—24no—
148C2×C4×C9—216no—
149C2×C4×C9#4114yes—
150C2×C4×C9#4114yes—
151C2×C4×C9C2412yes—
152C2×C4×C9C2414yes—
153C2×C4×C9C2412yes—
154C2×C4×C9C2412yes—
155#611—216no—
156C2×Dic9—24no—
157C2×Dic9—22no—
158C2×Dic9—22no—
159C2×Dic9—22no—
160C2×Dic9—24no—
161C2×Dic9C2412yes—
162C2×Dic9C2412yes—
163C2×Dic9C2412yes—
164C2×Dic9C2414yes—
165C2×Dic9C2414yes—
166C4×D9—28no—
167C4×D9—28no—
168C4×D9—28no—
169Dic18—28no—
170#529—916no—
171C2×#126—92no—
172C2×#125—91no—
173C2×#124—91no—
174C2×#123—92no—
175C2×C22⋊Q8—91no—
176C2×#121—91no—
177C2×C4×Q8—91no—
178C2×C4×D4—92no—
179C2×C4×D4D911yescharacteristic, complemented
180C2×#117—92no—
181C22×C42—91no—
182C24×C3C22×D312yes—
183C23×D3—31no—
184C2×C3×D4—24no—
185C2×C3×D4C22×D314yes—
186C22×C3×C4—28no—
187C22×C3×C4C22×D311yescharacteristic
188C22×C3×C4C22×D312yes—
189C22×C3×C4C22×D318yes—
190C22×C3×C4C22×D311yescharacteristic
191C22×C3×C4C22×D311yescharacteristic
192C2×#67—38no—
193C2×#67—68no—
194C22×Dic3—31no—
195C22×Dic3—31no—
196C22×Dic3—31no—
197C22×Dic3—32no—
198C22×Dic3—32no—
199C2×C4×D3—34no—
200C2×C4×D3—34no—
201C2×C4×D3—34no—
202C2×C4×D3—64no—
203C2×C4×D3—64no—
204C2×C4×D3—64no—
205C2×Dic6—34no—
206C2×Dic6—64no—
207C3×C4⋊C4C22×D314yes—
208C3×C22⋊C4C22×D318yes—
209C3×C42C22×D314yes—
210#217—38no—
211#217—38no—
212#217—38no—
213(C2×D3)⋊C4—38no—
214C4⋊Dic3—34no—
215C4⋊Dic3—38no—
216C4⋊Dic3—38no—
217Dic3⋊C4—38no—
218Dic3⋊C4—38no—
219C4×Dic3—38no—
220C4×Dic3—34no—
221C4×Dic3—34no—
222C4×Dic3—34no—
223C22×C9—24no—
224C22×C9—24no—
225C22×C9—24no—
226C22×C9—48no—
227C22×C9C2×#4112yes—
228C22×C9C2×#4112yes—
229C22×C9C2×#4112yes—
230C22×C9C2511yescharacteristic
231C2×D9—28no—
232C2×D9—22no—
233C2×D9—22no—
234C2×D9C2×#4114yes—
235C4×C9—22no—
236C4×C9—24no—
237C4×C9C2×#4114yes—
238C4×C9C2×#4114yes—
239Dic9—24no—
240Dic9—22no—
241Dic9—22no—
242Dic9—22no—
243Dic9—24no—
244C22×Q8—91no—
245C22×D4—92no—
246C22×D4C2×D911yescharacteristic
247C23×C4—91no—
248C23×C4—91no—
249C23×C4—91no—
250C23×C4C2×D912yes—
251#126—916no—
252#125—98no—
253#124—98no—
254#123—916no—
255C22⋊Q8—98no—
256#121—98no—
257C4×Q8—98no—
258C4×D4—916no—
259C4×D4C2×D918yescomplemented
260#117—916no—
261C2×C4⋊C4—92no—
262C2×C4⋊C4—92no—
263C2×C4⋊C4—92no—
264C2×C4⋊C4—91no—
265C2×C4⋊C4—92no—
266C2×C4⋊C4C2×D911yescharacteristic
267C2×C22⋊C4—92no—
268C2×C22⋊C4—92no—
269C2×C22⋊C4—92no—
270C2×C22⋊C4—92no—
271C2×C22⋊C4C2×D912yes—
272C2×C42—91no—
273C2×C42—91no—
274C2×C42—91no—
275C2×C42—92no—
276C2×C42—98no—
277C2×C42C2×D911yescharacteristic
278C23×C3—24no—
279C23×C3—24no—
280C23×C3—24no—
281C23×C3C23×D314yes—
282C23×C3C23×D311yescharacteristic
283C22×D3—34no—
284C22×D3—32no—
285C22×D3—62no—
286C22×D3—62no—
287C3×D4—28no—
288C2×C3×C4—24no—
289C2×C3×C4—22no—
290C2×C3×C4—216no—
291C2×C3×C4#23514yes—
292C2×C3×C4#23714yes—
293C2×C3×C4C23×D312yes—
294C2×C3×C4C23×D314yes—
295C2×C3×C4C23×D312yes—
296C2×C3×C4C23×D312yes—
297#67—616no—
298C2×Dic3—32no—
299C2×Dic3—32no—
300C2×Dic3—32no—
301C2×Dic3—34no—
302C2×Dic3—34no—
303C2×Dic3—64no—
304C2×Dic3—62no—
305C2×Dic3—62no—
306C2×Dic3—62no—
307C2×Dic3—64no—
308C4×D3—68no—
309C4×D3—68no—
310C4×D3—68no—
311Dic6—68no—
312C2×C9—44no—
313C2×C9#52914yescomplemented
314C2×C9C22×#4111yescharacteristic
315C2×C9C22×#4111yescharacteristic
316C2×C9C22×#4111yescharacteristic
317D9—24no—
318C24—91no—
319C24C22×D912yes—
320C2×Q8—94no—
321C2×Q8—184no—
322C2×D4—24no—
323C2×D4—98no—
324C2×D4—188no—
325C2×D4C22×D914yes—
326C22×C4—28no—
327C22×C4—91no—
328C22×C4—91no—
329C22×C4—91no—
330C22×C4—92no—
331C22×C4—92no—
332C22×C4—94no—
333C22×C4—94no—
334C22×C4—94no—
335C22×C4—184no—
336C22×C4—184no—
337C22×C4—184no—
338C22×C4C22×D911yescharacteristic
339C22×C4C22×D912yes—
340C22×C4C22×D918yes—
341C22×C4C22×D911yescharacteristic
342C22×C4C22×D911yescharacteristic
343C4⋊C4—98no—
344C4⋊C4—98no—
345C4⋊C4—98no—
346C4⋊C4—94no—
347C4⋊C4—98no—
348C4⋊C4C22×D914yes—
349C22⋊C4—98no—
350C22⋊C4—98no—
351C22⋊C4—98no—
352C22⋊C4—98no—
353C22⋊C4C22×D918yes—
354C42—94no—
355C42—94no—
356C42—94no—
357C42—98no—
358C42C22×D914yes—
359C22×C3—24no—
360C22×C3—24no—
361C22×C3—24no—
362C22×C3—48no—
363C22×C3C2×#23512yes—
364C22×C3C2×#23712yes—
365C22×C3D3×#4112yes—
366C22×C3C24×D311yescharacteristic
367C2×D3—34no—
368C2×D3—62no—
369C2×D3—62no—
370C2×D3—68no—
371C3×C4—24no—
372C3×C4—22no—
373C3×C4C2×#23514yes—
374C3×C4C2×#23714yes—
375Dic3—64no—
376Dic3—62no—
377Dic3—62no—
378Dic3—62no—
379Dic3—64no—
380C9C2×#52911yescharacteristic, complemented, Sylow
381C23—24no—
382C23—24no—
383C23—24no—
384C23—92no—
385C23—94no—
386C23—182no—
387C23—182no—
388C23C23×D914yes—
389C23C23×D911yescharacteristic
390Q8—188no—
391D4—28no—
392D4—1816no—
393C2×C4—24no—
394C2×C4—22no—
395C2×C4—216no—
396C2×C4—92no—
397C2×C4—92no—
398C2×C4—92no—
399C2×C4—94no—
400C2×C4—94no—
401C2×C4—188no—
402C2×C4—182no—
403C2×C4—184no—
404C2×C4—182no—
405C2×C4—182no—
406C2×C4—184no—
407C2×C4—188no—
408C2×C4—188no—
409C2×C4#369714yes—
410C2×C4#369914yes—
411C2×C4C23×D912yes—
412C2×C4C23×D914yes—
413C2×C4C23×D912yes—
414C2×C4C23×D912yes—
415C2×C3—44no—
416C2×C3#555714yes—
417C2×C3C22×#23511yescharacteristic
418C2×C3C22×#23711yescharacteristic
419C2×C3C2×D3×#4111yescharacteristic
420D3—64no—
421C22—24no—
422C22—24no—
423C22—24no—
424C22—48no—
425C22—94no—
426C22—182no—
427C22—182no—
428C22—188no—
429C22C2×#369712yes—
430C22C2×#369912yes—
431C22#41×D912yes—
432C22C24×D911yescharacteristic
433C4—24no—
434C4—22no—
435C4—182no—
436C4—184no—
437C4—182no—
438C4—182no—
439C4—184no—
440C4C2×#369714yes—
441C4C2×#369914yes—
442C3C2×#555711yescharacteristic
443C2—44no—
444C2—184no—
445C2#1058965914yesdirect product factor
446C2C22×#369711yescharacteristic
447C2C22×#369911yescharacteristic
448C2C2×#41×D911yescharacteristic
subgroupG/H
centerC22×C4C22×D9
commutator, cosocleC22×C9C25
FrattiniC22×C3C24×D3
FittingC2×C4×D4×C9C2
socleC23×C3C23×D3
prime radicalC2×#63500C2
hypercenterC2×C4×D4D9
hypocenterC9C2×#529
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22×C4 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×C4×D4×C9C2semidirect
3. C2×#63498C2semidirect
4. C2×C4×#611C2semidirect
5. C2×#63488C2semidirect
6. #10589659C2direct (N × H)
7. C2×#63459C2semidirect
8. C2×#63452C2semidirect
9. C2×#63445C2semidirect
10. C2×#63441C2semidirect
11. C2×C42×D9C2semidirect
12. C2×C4×Dic18C2semidirect
21. C4×D4×C9C22semidirect
29. #63498C22semidirect
30. C4×#611C22semidirect
32. #63488C22semidirect
42. #63459C22semidirect
43. #63452C22semidirect
44. #63445C22semidirect
45. #63441C22semidirect
46. C42×D9C22semidirect
47. C4×Dic18C22semidirect
179. C2×C4×D4D9semidirect
259. C4×D4C2×D9semidirect
313. C2×C9#529semidirect
380. C9C2×#529semidirect
445. C2#10589659direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×D4×C92
C2×#635002
C2×#634982
C2×C4×#6112
C2×#634882
#105896592
C2×#634592
C2×#634522
C2×#634452
C2×#634412
C2×C42×D92
C2×C4×Dic182
C2×#55573