Finite Group Databasebeta

← C2×#10589663 #11901611

Subgroups — C2×#10589663 #11901611

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×D4×C9C211yesmaximal, characteristic, complemented
2C2×#63500C211yesmaximal, characteristic
3C2×#63498C211yesmaximal, characteristic, complemented
4C2×#63491C212yesmaximal, complemented
5C2×#63486C212yesmaximal, complemented
6#10589663C2116yesmaximal, direct product factor
7C2×#63459C211yesmaximal, characteristic, complemented
8C2×#63450C211yesmaximal, characteristic, complemented
9C2×#63447C212yesmaximal, complemented
10C2×#63441C212yesmaximal, complemented
11C2×#63434C211yesmaximal, characteristic, complemented
12C2×C4×Dic18C211yesmaximal, characteristic, complemented
13C2×#5561—31nomaximal
14C22×D4×C9C2211yescharacteristic
15C23×C4×C9C2212yes—
16C22×#611C2212yes—
17C22×C4×D9C2211yescharacteristic
18C22×Dic18C2211yescharacteristic
19C22×Dic18C2212yes—
20C4×D4×C9C2218yescomplemented
21C2×C9×C4⋊C4C2211yescharacteristic
22C2×C9×C22⋊C4C2212yes—
23C2×C42×C9C2211yescharacteristic
24C2×#3676C2212yes—
25C2×#3676C2212yes—
26C2×#3676C2212yes—
27#63500C2218yes—
28#63498C2218yescomplemented
29#63491C22116yescomplemented
30C2×(C2×D9)⋊C4C2211yescharacteristic
31C2×(C2×D9)⋊C4C2211yescharacteristic
32C2×(C2×D9)⋊C4C2212yes—
33C2×C4⋊Dic9C2211yescharacteristic
34C2×C4⋊Dic9C2212yes—
35#63486C22116yescomplemented
36C2×Dic9⋊C4C2212yes—
37C2×Dic9⋊C4C2211yescharacteristic
38C2×Dic9⋊C4C2211yescharacteristic
39C2×Dic9⋊C4C2212yes—
40C2×C4×Dic9C2212yes—
41C2×C4×Dic9C2211yescharacteristic
42#63459C2218yescomplemented
43#63450C2218yescomplemented
44#63447C22116yescomplemented
45#63441C22116yescomplemented
46#63434C2218yescomplemented
47C4×Dic18C2218yescomplemented
48C2×C3×C4×D4D311yescharacteristic
49C2×#938—31no—
50C2×#936—31no—
51C2×#929—32no—
52C2×#924—32no—
53#5561—316no—
54C2×#897—31no—
55C2×#888—31no—
56C2×#885—32no—
57C2×#879—32no—
58C2×#872—31no—
59C2×C4×Dic6—31no—
60C24×C9C2312yes—
61C23×D9C2311yescharacteristic
62C2×D4×C9—24no—
63C2×D4×C9C2314yes—
64C22×C4×C9—44no—
65C22×C4×C9C2311yescharacteristic
66C22×C4×C9C2311yescharacteristic
67C22×C4×C9C2312yes—
68C22×C4×C9C2318yes—
69C22×C4×C9C2311yescharacteristic
70C2×#611—44no—
71C2×#611C2318yes—
72C22×Dic9C2311yescharacteristic
73C22×Dic9C2312yes—
74C22×Dic9C2311yescharacteristic
75C22×Dic9C2311yescharacteristic
76C22×Dic9C2312yes—
77C2×C4×D9—24no—
78C2×C4×D9C2314yes—
79C2×Dic18—24no—
80C2×Dic18—44no—
81C2×Dic18C2314yes—
82C2×Dic18C2318yes—
83C9×C4⋊C4C2314yes—
84C9×C22⋊C4C2318yes—
85C42×C9C2314yes—
86#3676C2318yes—
87#3676C2318yes—
88#3676C2318yes—
89(C2×D9)⋊C4C2314yes—
90(C2×D9)⋊C4C2318yes—
91(C2×D9)⋊C4C2314yes—
92C4⋊Dic9C2314yes—
93C4⋊Dic9C2318yes—
94Dic9⋊C4C2318yes—
95Dic9⋊C4C2318yes—
96Dic9⋊C4C2314yes—
97Dic9⋊C4C2314yes—
98C4×Dic9C2314yes—
99C4×Dic9C2318yes—
100C2×#542—91noSylow
101C22×C3×D4C2×D311yescharacteristic
102C23×C3×C4C2×D312yes—
103C22×#67—32no—
104C22×C4×D3—31no—
105C22×Dic6—31no—
106C22×Dic6—32no—
107C3×C4×D4C2×D318yes—
108C2×C3×C4⋊C4C2×D311yescharacteristic
109C2×C3×C22⋊C4C2×D312yes—
110C2×C3×C42C2×D311yescharacteristic
111C2×#217—32no—
112C2×#217—32no—
113C2×#217—32no—
114#938—38no—
115#936—38no—
116#929—316no—
117C2×(C2×D3)⋊C4—31no—
118C2×(C2×D3)⋊C4—31no—
119C2×(C2×D3)⋊C4—32no—
120C2×C4⋊Dic3—31no—
121C2×C4⋊Dic3—32no—
122#924—316no—
123C2×Dic3⋊C4—32no—
124C2×Dic3⋊C4—31no—
125C2×Dic3⋊C4—31no—
126C2×Dic3⋊C4—32no—
127C2×C4×Dic3—32no—
128C2×C4×Dic3—31no—
129#897—38no—
130#888—38no—
131#885—316no—
132#879—316no—
133#872—38no—
134C4×Dic6—38no—
135C23×C9—24no—
136C23×C9—24no—
137C23×C9—24no—
138C23×C9C2414yes—
139C23×C9C2411yescharacteristic
140C22×D9—22no—
141C22×D9—22no—
142C22×D9—22no—
143C22×D9C2412yes—
144D4×C9—28no—
145C2×C4×C9—24no—
146C2×C4×C9—22no—
147C2×C4×C9—22no—
148C2×C4×C9—48no—
149C2×C4×C9#4114yes—
150C2×C4×C9C2412yes—
151C2×C4×C9C2412yes—
152C2×C4×C9C2414yes—
153C2×C4×C9C2412yes—
154#611—48no—
155C2×Dic9—24no—
156C2×Dic9—22no—
157C2×Dic9—22no—
158C2×Dic9—24no—
159C2×Dic9—22no—
160C2×Dic9C2412yes—
161C2×Dic9C2414yes—
162C2×Dic9C2414yes—
163C2×Dic9C2412yes—
164C2×Dic9C2412yes—
165C4×D9—28no—
166Dic18—28no—
167Dic18—48no—
168#542—916no—
169C2×C4⋊Q8—91no—
170C2×#126—92no—
171C2×#124—91no—
172C2×#124—92no—
173C2×#123—92no—
174C2×C22⋊Q8—92no—
175C2×C22⋊Q8—91no—
176C2×#121—91no—
177C2×C4×Q8—91no—
178C2×C4×D4D911yescharacteristic, complemented
179C2×#117—91no—
180C24×C3C22×D312yes—
181C23×D3—31no—
182C2×C3×D4—24no—
183C2×C3×D4C22×D314yes—
184C22×C3×C4—44no—
185C22×C3×C4C22×D311yescharacteristic
186C22×C3×C4C22×D311yescharacteristic
187C22×C3×C4C22×D312yes—
188C22×C3×C4C22×D318yes—
189C22×C3×C4C22×D311yescharacteristic
190C2×#67—38no—
191C2×#67—124no—
192C22×Dic3—31no—
193C22×Dic3—32no—
194C22×Dic3—32no—
195C22×Dic3—31no—
196C22×Dic3—31no—
197C2×C4×D3—34no—
198C2×C4×D3—64no—
199C2×Dic6—34no—
200C2×Dic6—38no—
201C2×Dic6—64no—
202C2×Dic6—124no—
203C3×C4⋊C4C22×D314yes—
204C3×C22⋊C4C22×D318yes—
205C3×C42C22×D314yes—
206#217—38no—
207#217—38no—
208#217—38no—
209(C2×D3)⋊C4—34no—
210(C2×D3)⋊C4—34no—
211(C2×D3)⋊C4—38no—
212C4⋊Dic3—34no—
213C4⋊Dic3—38no—
214Dic3⋊C4—38no—
215Dic3⋊C4—34no—
216Dic3⋊C4—34no—
217Dic3⋊C4—38no—
218C4×Dic3—38no—
219C4×Dic3—34no—
220C22×C9—24no—
221C22×C9—24no—
222C22×C9—24no—
223C22×C9—48no—
224C22×C9C2×#4112yes—
225C22×C9H(5,𝔽2)12yes—
226C22×C92−1+412yes—
227C22×C9C2511yescharacteristic
228C2×D9—22no—
229C2×D9—22no—
230C2×D9—22no—
231C2×D9—44no—
232C4×C9—24no—
233C4×C9—22no—
234C4×C9—22no—
235C4×C9C2×#4114yes—
236Dic9—24no—
237Dic9—22no—
238Dic9—22no—
239Dic9—24no—
240Dic9—22no—
241C22×Q8—91no—
242C22×Q8—92no—
243C22×D4—92no—
244C22×D4C2×D911yescharacteristic
245C23×C4—91no—
246C23×C4C2×D912yes—
247C4⋊Q8—98no—
248#126—916no—
249#124—98no—
250#124—916no—
251#123—916no—
252C22⋊Q8—916no—
253C22⋊Q8—98no—
254#121—98no—
255C4×Q8—98no—
256C4×D4C2×D918yescomplemented
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⋊C4—92no—
264C2×C4⋊C4C2×D911yescharacteristic
265C2×C22⋊C4—92no—
266C2×C22⋊C4—92no—
267C2×C22⋊C4—92no—
268C2×C22⋊C4—91no—
269C2×C22⋊C4—91no—
270C2×C22⋊C4—92no—
271C2×C22⋊C4C2×D912yes—
272C2×C42—91no—
273C2×C42—92no—
274C2×C42C2×D911yescharacteristic
275C23×C3—24no—
276C23×C3—24no—
277C23×C3—24no—
278C23×C3C23×D314yes—
279C23×C3C23×D311yescharacteristic
280C22×D3—32no—
281C22×D3—62no—
282C22×D3—62no—
283C22×D3—62no—
284C3×D4—28no—
285C2×C3×C4—24no—
286C2×C3×C4—22no—
287C2×C3×C4—22no—
288C2×C3×C4—48no—
289C2×C3×C4#23514yes—
290C2×C3×C4C23×D312yes—
291C2×C3×C4C23×D312yes—
292C2×C3×C4C23×D314yes—
293C2×C3×C4C23×D312yes—
294#67—128no—
295C2×Dic3—32no—
296C2×Dic3—34no—
297C2×Dic3—34no—
298C2×Dic3—32no—
299C2×Dic3—32no—
300C2×Dic3—64no—
301C2×Dic3—62no—
302C2×Dic3—62no—
303C2×Dic3—64no—
304C2×Dic3—62no—
305C4×D3—68no—
306Dic6—68no—
307Dic6—128no—
308C2×C9—44no—
309C2×C9#54214yescomplemented
310C2×C9C22×#4111yescharacteristic
311C2×C9C2×H(5,𝔽2)11yescharacteristic
312C2×C9C2×2−1+411yescharacteristic
313D9—42no—
314C24—91no—
315C24C22×D912yes—
316C2×Q8—94no—
317C2×Q8—98no—
318C2×Q8—184no—
319C2×Q8—364no—
320C2×D4—24no—
321C2×D4—98no—
322C2×D4—364no—
323C2×D4C22×D914yes—
324C22×C4—44no—
325C22×C4—91no—
326C22×C4—92no—
327C22×C4—91no—
328C22×C4—92no—
329C22×C4—91no—
330C22×C4—94no—
331C22×C4—184no—
332C22×C4C22×D911yescharacteristic
333C22×C4C22×D911yescharacteristic
334C22×C4C22×D912yes—
335C22×C4C22×D918yes—
336C22×C4C22×D911yescharacteristic
337C4⋊C4—94no—
338C4⋊C4—94no—
339C4⋊C4—94no—
340C4⋊C4—98no—
341C4⋊C4—98no—
342C4⋊C4—98no—
343C4⋊C4C22×D914yes—
344C22⋊C4—98no—
345C22⋊C4—98no—
346C22⋊C4—98no—
347C22⋊C4—94no—
348C22⋊C4—94no—
349C22⋊C4—98no—
350C22⋊C4C22×D918yes—
351C42—94no—
352C42—98no—
353C42C22×D914yes—
354C22×C3—24no—
355C22×C3—24no—
356C22×C3—24no—
357C22×C3—48no—
358C22×C3C2×#23512yes—
359C22×C3#100412yes—
360C22×C3#101012yes—
361C22×C3C24×D311yescharacteristic
362C2×D3—62no—
363C2×D3—62no—
364C2×D3—62no—
365C2×D3—124no—
366C3×C4—24no—
367C3×C4—22no—
368C3×C4—22no—
369C3×C4C2×#23514yes—
370Dic3—64no—
371Dic3—62no—
372Dic3—62no—
373Dic3—64no—
374Dic3—62no—
375C9C2×#54211yescharacteristic, complemented, Sylow
376C23—24no—
377C23—24no—
378C23—24no—
379C23—92no—
380C23—182no—
381C23—182no—
382C23—182no—
383C23C23×D914yes—
384C23C23×D911yescharacteristic
385Q8—188no—
386Q8—368no—
387D4—28no—
388D4—368no—
389C2×C4—22no—
390C2×C4—24no—
391C2×C4—22no—
392C2×C4—48no—
393C2×C4—92no—
394C2×C4—94no—
395C2×C4—92no—
396C2×C4—94no—
397C2×C4—92no—
398C2×C4—182no—
399C2×C4—184no—
400C2×C4—184no—
401C2×C4—182no—
402C2×C4—182no—
403C2×C4—188no—
404C2×C4#369714yes—
405C2×C4C23×D912yes—
406C2×C4C23×D912yes—
407C2×C4C23×D914yes—
408C2×C4C23×D912yes—
409C2×C3—44no—
410C2×C3#556114yes—
411C2×C3C22×#23511yescharacteristic
412C2×C3C2×#100411yescharacteristic
413C2×C3C2×#101011yescharacteristic
414D3—122no—
415C22—24no—
416C22—24no—
417C22—24no—
418C22—48no—
419C22—182no—
420C22—182no—
421C22—182no—
422C22—364no—
423C22C2×#369712yes—
424C22#6371012yes—
425C22#6371612yes—
426C22C24×D911yescharacteristic
427C4—22no—
428C4—24no—
429C4—22no—
430C4—182no—
431C4—184no—
432C4—184no—
433C4—182no—
434C4—182no—
435C4C2×#369714yes—
436C3C2×#556111yescharacteristic
437C2—44no—
438C2—362no—
439C2#1058966314yesdirect product factor
440C2C22×#369711yescharacteristic
441C2C2×#6371011yescharacteristic
442C2C2×#6371611yescharacteristic
subgroupG/H
centerC23C23×D9
commutator, cosocleC22×C9C25
FrattiniC22×C3C24×D3
FittingC2×C4×D4×C9C2
socleC23×C3C23×D3
prime radicalC2×#63500C2
hypercenterC2×C4×D4D9
hypocenterC9C2×#542
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C23 ◁ 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×#63491C2semidirect
5. C2×#63486C2semidirect
6. #10589663C2direct (N × H)
7. C2×#63459C2semidirect
8. C2×#63450C2semidirect
9. C2×#63447C2semidirect
10. C2×#63441C2semidirect
11. C2×#63434C2semidirect
12. C2×C4×Dic18C2semidirect
20. C4×D4×C9C22semidirect
28. #63498C22semidirect
29. #63491C22semidirect
35. #63486C22semidirect
42. #63459C22semidirect
43. #63450C22semidirect
44. #63447C22semidirect
45. #63441C22semidirect
46. #63434C22semidirect
47. C4×Dic18C22semidirect
178. C2×C4×D4D9semidirect
256. C4×D4C2×D9semidirect
309. C2×C9#542semidirect
375. C9C2×#542semidirect
439. C2#10589663direct (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×#634912
C2×#634862
#105896632
C2×#634592
C2×#634502
C2×#634472
C2×#634412
C2×#634342
C2×C4×Dic182
C2×#55613