Finite Group Databasebeta

← C4×#63505 #11860366

Subgroups — C4×#63505 #11860366

Order 1152.

726 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Q8×C9C211yesmaximal, characteristic, complemented
2C2×#63505C211yesmaximal, characteristic
3C4×#3697C211yesmaximal, characteristic
4#10588906C211yesmaximal, characteristic, complemented
5#10588709C212yesmaximal, complemented
6C4×#3675C212yesmaximal, complemented
7#10588706C212yesmaximal, complemented
8C4×#3674C212yesmaximal, complemented
9#10588649C211yesmaximal, characteristic
10#10588644C211yesmaximal, characteristic, complemented
11C4×#3667C211yesmaximal, characteristic, complemented
12C4×#942—31nomaximal
13C22×Q8×C9C2211yescharacteristic
14C2×#3697C2211yescharacteristic
15C4×Q8×C9—21no—
16C4×Q8×C9—21no—
17C4×Q8×C9C2212yes—
18C4×Q8×C9C2212yes—
19C2×C9×C4⋊C4—21no—
20C2×C9×C4⋊C4C2211yescharacteristic
21C2×C42×C9—21no—
22C2×C42×C9C2211yescharacteristic
23#63505C418yesdirect product factor
24C2×#3675C2212yes—
25C2×#3674C2212yes—
26C4×#611—21no—
27C4×#611—21no—
28#63488C2211yescharacteristic
29C2×#3667C2211yescharacteristic
30C2×#3667C2211yescharacteristic
31C4×D36C2211yescharacteristic
32C4×D36C2211yescharacteristic
33#63434—21no—
34C42×D9—21no—
35C4×Dic18C2211yescharacteristic
36C4×Dic18C2211yescharacteristic
37#63395C2212yes—
38#63395C2212yes—
39#63369C2212yes—
40#63368C2212yes—
41#63367C2212yes—
42#63366C2212yes—
43#63362C2212yes—
44C4×C9⋊C8C2212yes—
45C2×C3×C4×Q8D311yescharacteristic
46C2×#942—31no—
47C4×#235—31no—
48#5225—31no—
49#5030—32no—
50C4×#216—32no—
51#5026—32no—
52C4×#215—32no—
53#4966—31no—
54#4964—31no—
55C4×#208—31no—
56C2×Q8×C9—21no—
57C2×Q8×C9—22no—
58C2×Q8×C9C2×C414yescomplemented
59C2×Q8×C9C2312yes—
60C22×C4×C9—21no—
61C22×C4×C9—21no—
62C22×C4×C9D411yescharacteristic
63C22×C4×C9D411yescharacteristic
64C22×C4×C9C2311yescharacteristic
65C2×#611—21no—
66#3697—22no—
67#3697C2×C414yes—
68C2×D36C2311yescharacteristic
69C2×C4×D9—21no—
70C2×C4×D9—21no—
71C2×C4×D9—21no—
72C2×Dic18C2311yescharacteristic
73C9×C4⋊C4—22no—
74C9×C4⋊C4—22no—
75C9×C4⋊C4—21no—
76C9×C4⋊C4C2312yes—
77C42×C9—22no—
78C42×C9—22no—
79C42×C9D411yescharacteristic
80C42×C9D411yescharacteristic
81C42×C9C2311yescharacteristic
82C42×C9C2311yescharacteristic
83#3676—21no—
84#3675C2×C418yescomplemented
85#3674C2×C418yescomplemented
86(C2×D9)⋊C4—21no—
87(C2×D9)⋊C4—21no—
88C4⋊Dic9C2311yescharacteristic
89C4⋊Dic9C2311yescharacteristic
90Dic9⋊C4—21no—
91Dic9⋊C4—21no—
92C4×Dic9—21no—
93C4×Dic9—21no—
94C4×Dic9—21no—
95#3667—22no—
96#3667C2×C414yescomplemented
97C2×C9⋊C8C2312yes—
98C2×C9⋊C8C2312yes—
99C4×#137—91noSylow
100C22×C3×Q8C2×D311yescharacteristic
101C2×#235—31no—
102C3×C4×Q8—21no—
103C3×C4×Q8—21no—
104C3×C4×Q8C2×D312yes—
105C3×C4×Q8C2×D312yes—
106C2×C3×C4⋊C4—21no—
107C2×C3×C4⋊C4C2×D311yescharacteristic
108C2×C3×C42—21no—
109C2×C3×C42C2×D311yescharacteristic
110C2×#216—32no—
111#942—38no—
112C2×#215—32no—
113C4×#67—61no—
114C4×#67—61no—
115#926—31no—
116C2×#208—31no—
117C2×#208—31no—
118C4×D12—31no—
119C4×D12—31no—
120#872—61no—
121C42×D3—61no—
122C4×Dic6—31no—
123C4×Dic6—31no—
124#835—32no—
125#835—32no—
126#810—32no—
127#809—32no—
128#808—32no—
129#807—32no—
130#803—32no—
131C4×C3⋊C8—32no—
132C23×C9C2×D411yescharacteristic
133C22×D9—21no—
134Q8×C9—24no—
135Q8×C9—22no—
136Q8×C9C22×C414yes—
137C2×C4×C9—24no—
138C2×C4×C9—22no—
139C2×C4×C9—22no—
140C2×C4×C9—22no—
141C2×C4×C9—41no—
142C2×C4×C9—42no—
143C2×C4×C9C22×C412yes—
144C2×C4×C9C2×D411yescharacteristic
145C2×C4×C9C2×D411yescharacteristic
146C2×C4×C9C2×D411yescharacteristic
147C2×C4×C9C2×D411yescharacteristic
148C2×C4×C9C2×D411yescharacteristic
149C2×C4×C9#4112yes—
150C2×C4×C9C2411yescharacteristic
151#611—24no—
152C2×Dic9—21no—
153C2×Dic9—21no—
154C2×Dic9—21no—
155D36—21no—
156D36C22×C412yes—
157C4×D9—24no—
158C4×D9—42no—
159C4×D9—42no—
160Dic18—21no—
161Dic18C22×C412yes—
162C9⋊C8—22no—
163C9⋊C8C22×C414yes—
164C2×#137—91no—
165C4×#41—91no—
166C2×C4×Q8D911yescharacteristic, complemented
167#441—92no—
168#440—92no—
169C4×Q16—92no—
170C4×SD16—92no—
171#428—91no—
172#419—91no—
173#417—91no—
174C4×M16—91no—
175C2×C3×Q8—22no—
176C2×C3×Q8—21no—
177C2×C3×Q8C4×D314yes—
178C2×C3×Q8C22×D312yes—
179C22×C3×C4—21no—
180C22×C3×C4—21no—
181C22×C3×C4#6711yescharacteristic
182C22×C3×C4#6711yescharacteristic
183C22×C3×C4C22×D311yescharacteristic
184C2×#67—61no—
185#235—34no—
186#235—62no—
187C2×D12—31no—
188C2×C4×D3—61no—
189C2×C4×D3—61no—
190C2×C4×D3—61no—
191C2×Dic6—31no—
192C3×C4⋊C4—22no—
193C3×C4⋊C4—22no—
194C3×C4⋊C4—21no—
195C3×C4⋊C4C22×D312yes—
196C3×C42—22no—
197C3×C42—22no—
198C3×C42#6711yescharacteristic
199C3×C42#6711yescharacteristic
200C3×C42C22×D311yescharacteristic
201C3×C42C22×D311yescharacteristic
202#217—61no—
203#216—38no—
204#215—38no—
205(C2×D3)⋊C4—61no—
206(C2×D3)⋊C4—61no—
207C4⋊Dic3—31no—
208C4⋊Dic3—31no—
209Dic3⋊C4—61no—
210Dic3⋊C4—61no—
211C4×Dic3—61no—
212C4×Dic3—61no—
213C4×Dic3—61no—
214#208—34no—
215#208—62no—
216C2×C3⋊C8—32no—
217C2×C3⋊C8—32no—
218C22×C9—21no—
219C22×C9—21no—
220C22×C9C4×D412yes—
221C22×C9C22×D411yescharacteristic
222C2×D9—22no—
223C2×D9—41no—
224C2×D9—41no—
225C4×C9—24no—
226C4×C9—21no—
227C4×C9—21no—
228C4×C9—21no—
229C4×C9—42no—
230C4×C9C4×D412yes—
231C4×C9#13712yescomplemented
232C4×C9C23×C411yescharacteristic
233C4×C9C2×#4111yescharacteristic
234Dic9—22no—
235Dic9—41no—
236Dic9—41no—
237C2×#41—91no—
238C22×Q8C2×D911yescharacteristic
239#137—98no—
240C2×Q16—92no—
241C2×SD16—92no—
242C2×M16—91no—
243C2×M16—91no—
244C4×Q8—21no—
245C4×Q8—21no—
246C4×Q8—91no—
247C4×Q8—91no—
248C4×Q8C2×D912yes—
249C4×Q8C2×D912yes—
250C4×D4—91no—
251C4×D4—91no—
252C4×D4—181no—
253C4×D4—181no—
254#117—91no—
255#117—181no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4C2×D911yescharacteristic
258C2×C42—21no—
259C2×C42—181no—
260C2×C42C2×D911yescharacteristic
261#107—92no—
262#106—92no—
263#103—92no—
264#103—92no—
265#103—92no—
266#102—92no—
267#97—92no—
268C4×C8—92no—
269C23×C3C2×#6711yescharacteristic
270C22×D3—61no—
271C3×Q8—24no—
272C3×Q8—22no—
273C3×Q8C2×C4×D314yes—
274C2×C3×C4—24no—
275C2×C3×C4—22no—
276C2×C3×C4—22no—
277C2×C3×C4—22no—
278C2×C3×C4—41no—
279C2×C3×C4—42no—
280C2×C3×C4C2×C4×D312yes—
281C2×C3×C4#23512yes—
282C2×C3×C4C2×#6711yescharacteristic
283C2×C3×C4C2×#6711yescharacteristic
284C2×C3×C4C2×#6711yescharacteristic
285C2×C3×C4C2×#6711yescharacteristic
286C2×C3×C4C2×#6711yescharacteristic
287C2×C3×C4C23×D311yescharacteristic
288#67—64no—
289C2×Dic3—61no—
290C2×Dic3—61no—
291C2×Dic3—61no—
292D12—32no—
293D12—61no—
294C4×D3—64no—
295C4×D3—122no—
296C4×D3—122no—
297Dic6—32no—
298Dic6—61no—
299C3⋊C8—34no—
300C3⋊C8—62no—
301C2×C9—22no—
302C2×C9C2×C4×D411yescharacteristic
303C2×C9C2×#13711yescharacteristic
304C2×C9#57511yescharacteristic
305D9—42no—
306#41—94no—
307#41—182no—
308C2×Q8—22no—
309C2×Q8—21no—
310C2×Q8—91no—
311C2×Q8C4×D914yescomplemented
312C2×Q8C22×D912yes—
313C2×D4—91no—
314C2×D4—181no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—181no—
318C22×C4—181no—
319C22×C4—181no—
320C22×C4#61111yescharacteristic
321C22×C4#61111yescharacteristic
322C22×C4C22×D911yescharacteristic
323Q16—98no—
324SD16—98no—
325M16—94no—
326M16—182no—
327C2×C8—92no—
328C2×C8—92no—
329C4⋊C4—22no—
330C4⋊C4—22no—
331C4⋊C4—21no—
332C4⋊C4—91no—
333C4⋊C4—91no—
334C4⋊C4—181no—
335C4⋊C4—181no—
336C4⋊C4C22×D912yes—
337C22⋊C4—181no—
338C22⋊C4—181no—
339C22⋊C4—181no—
340C42—22no—
341C42—22no—
342C42—181no—
343C42—181no—
344C42—181no—
345C42#61111yescharacteristic
346C42#61111yescharacteristic
347C42C22×D911yescharacteristic
348C42C22×D911yescharacteristic
349C22×C3—21no—
350C22×C3—21no—
351C22×C3C4×#6712yes—
352C22×C3C22×#6711yescharacteristic
353C2×D3—62no—
354C2×D3—121no—
355C2×D3—121no—
356C3×C4—24no—
357C3×C4—21no—
358C3×C4—21no—
359C3×C4—21no—
360C3×C4—42no—
361C3×C4C4×#6712yes—
362C3×C4#94212yes—
363C3×C4C22×C4×D311yescharacteristic
364C3×C4C2×#23511yescharacteristic
365Dic3—62no—
366Dic3—121no—
367Dic3—121no—
368C9C4×#13711yescharacteristic, complemented, Sylow
369C23—181no—
370C23C2×#61111yescharacteristic
371Q8—24no—
372Q8—22no—
373Q8—92no—
374Q8—181no—
375Q8C2×C4×D914yes—
376D4—92no—
377D4—184no—
378D4—181no—
379C2×C4—24no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—41no—
384C2×C4—42no—
385C2×C4—181no—
386C2×C4—184no—
387C2×C4—181no—
388C2×C4—181no—
389C2×C4—362no—
390C2×C4—362no—
391C2×C4C2×C4×D912yes—
392C2×C4#369712yes—
393C2×C4C2×#61111yescharacteristic
394C2×C4C2×#61111yescharacteristic
395C2×C4C2×#61111yescharacteristic
396C2×C4C2×#61111yescharacteristic
397C2×C4C2×#61111yescharacteristic
398C2×C4C23×D911yescharacteristic
399C8—94no—
400C8—182no—
401C2×C3—22no—
402C2×C3C2×C4×#6711yescharacteristic
403C2×C3C2×#94211yescharacteristic
404C2×C3#582211yescharacteristic
405D3—122no—
406C22—21no—
407C22—21no—
408C22—182no—
409C22—361no—
410C22—361no—
411C22C4×#61112yes—
412C22C22×#61111yescharacteristic
413C4—24no—
414C4—21no—
415C4—21no—
416C4—21no—
417C4—42no—
418C4—182no—
419C4—361no—
420C4—361no—
421C4C4×#61112yes—
422C4#6350512yesdirect product factor
423C4C22×C4×D911yescharacteristic
424C4C2×#369711yescharacteristic
425C3C4×#94211yescharacteristic
426C2—22no—
427C2—362no—
428C2C2×C4×#61111yescharacteristic
429C2C2×#6350511yescharacteristic
430C2#1058992511yescharacteristic
subgroupG/H
centerC2×C4C2×#611
commutatorC4×C9C23×C4
FrattiniC2×C3×C4C23×D3
FittingC2×C4×Q8×C9C2
socleC22×C3C22×#67
prime radicalC2×#3697C22
cosocleC2×C4×C9C24
hypercenterC2×C4×Q8D9
hypocenterC9C4×#137
LCSG ▷ C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C4×Q8×C9C2semidirect
4. #10588906C2semidirect
5. #10588709C2semidirect
6. C4×#3675C2semidirect
7. #10588706C2semidirect
8. C4×#3674C2semidirect
10. #10588644C2semidirect
11. C4×#3667C2semidirect
23. #63505C4direct (N × H)
58. C2×Q8×C9C2×C4semidirect
84. #3675C2×C4semidirect
85. #3674C2×C4semidirect
96. #3667C2×C4semidirect
166. C2×C4×Q8D9semidirect
231. C4×C9#137semidirect
311. C2×Q8C4×D9semidirect
368. C9C4×#137semidirect
422. C4#63505direct (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×#635052
C4×#36972
#105889062
#105887092
C4×#36752
#105887062
C4×#36742
#105886492
#105886442
C4×#36672
C4×#9423