Finite Group Databasebeta

← C4×#63480 #11860369

Subgroups — C4×#63480 #11860369

Order 1152.

726 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63480C211yesmaximal, characteristic
2C4×#3701C211yesmaximal, characteristic
3C4×Q8×D9C211yesmaximal, characteristic, complemented
4C4×C9×Q16C211yesmaximal, characteristic, complemented
5#10588864C211yesmaximal, characteristic, complemented
6C4×#3675C211yesmaximal, characteristic, complemented
7C4×#3674C211yesmaximal, characteristic, complemented
8#10588569C211yesmaximal, characteristic, complemented
9#10588561C211yesmaximal, characteristic, complemented
10#10588497C211yesmaximal, characteristic, complemented
11#10588483C211yesmaximal, characteristic
12#10588482C211yesmaximal, characteristic, complemented
13#10588469C211yesmaximal, characteristic, complemented
14C4×#3664C211yesmaximal, characteristic, complemented
15C4×#3663C211yesmaximal, characteristic, complemented
16C4×#918—31nomaximal
17C2×#3701C2211yescharacteristic
18C2×Q8×D9C2211yescharacteristic
19C2×C9×Q16C2211yescharacteristic
20C4×Q8×C9C2211yescharacteristic
21C4×Q8×C9C2211yescharacteristic
22Q8×Dic9C2211yescharacteristic
23Q8×Dic9C2211yescharacteristic
24C2×#3675C2211yescharacteristic
25C2×#3674C2211yescharacteristic
26#63480C418yesdirect product factor
27C2×#3664C2211yescharacteristic
28C2×#3663C2211yescharacteristic
29C2×#3663C2211yescharacteristic
30#63455—21no—
31#63455C2211yescharacteristic
32#63454—21no—
33#63454C2211yescharacteristic
34C4⋊C4×D9—21no—
35C4⋊C4×D9C2211yescharacteristic
36#63449—21no—
37#63449C2211yescharacteristic
38C4×D36—21no—
39C4×D36C2211yescharacteristic
40C42×D9—21no—
41C42×D9—21no—
42C42×D9C2211yescharacteristic
43C4×Dic18—21no—
44C4×Dic18C2211yescharacteristic
45C9×#107C2211yescharacteristic
46C9×#103C2211yescharacteristic
47C9×#103C2211yescharacteristic
48C4×C8×C9C2211yescharacteristic
49#63395C2211yescharacteristic
50#63395C2211yescharacteristic
51#63380C2211yescharacteristic
52#63377C2211yescharacteristic
53#63376C2211yescharacteristic
54#63375C2211yescharacteristic
55#63375C2211yescharacteristic
56#63369C2211yescharacteristic
57#63368C2211yescharacteristic
58#63367C2211yescharacteristic
59#63366C2211yescharacteristic
60C4×C9⋊C8C2211yescharacteristic
61C2×#918—31no—
62C4×#239—31no—
63C4×D3×Q8—31no—
64C3×C4×Q16D311yescharacteristic
65#5184—31no—
66C4×#216—31no—
67C4×#215—31no—
68#4889—31no—
69#4881—31no—
70#4817—31no—
71#4803—31no—
72#4802—31no—
73#4789—31no—
74C4×#204—31no—
75C4×ΓL(1,𝔽25)—31no—
76C2×Q8×C9C2311yescharacteristic
77C2×Q8×C9C2311yescharacteristic
78#3701—22no—
79#3701C2×C414yes—
80Q8×D9—22no—
81Q8×D9C2×C414yescomplemented
82C2×D36—21no—
83C2×D36C2311yescharacteristic
84C2×C4×D9—21no—
85C2×C4×D9—21no—
86C2×C4×D9—21no—
87C2×C4×D9—21no—
88C2×C4×D9—21no—
89C2×C4×D9D411yescharacteristic
90C2×C4×D9D411yescharacteristic
91C2×C4×D9C2311yescharacteristic
92C2×Dic18—21no—
93C2×Dic18C2311yescharacteristic
94C9×Q16C2×C414yescomplemented
95C2×C8×C9C2311yescharacteristic
96C2×C8×C9C2311yescharacteristic
97C9×C4⋊C4—21no—
98C9×C4⋊C4—21no—
99C9×C4⋊C4C2311yescharacteristic
100C9×C4⋊C4C2311yescharacteristic
101C42×C9—21no—
102C42×C9—21no—
103C42×C9C2311yescharacteristic
104#3675C2×C414yescomplemented
105#3674C2×C414yescomplemented
106(C2×D9)⋊C4—21no—
107(C2×D9)⋊C4—21no—
108(C2×D9)⋊C4—21no—
109C4⋊Dic9—21no—
110C4⋊Dic9—21no—
111C4⋊Dic9C2311yescharacteristic
112C4⋊Dic9C2311yescharacteristic
113Dic9⋊C4—21no—
114Dic9⋊C4—21no—
115Dic9⋊C4—21no—
116C4×Dic9—21no—
117C4×Dic9—21no—
118C4×Dic9—21no—
119C4×Dic9—21no—
120C4×Dic9—21no—
121C4×Dic9D411yescharacteristic
122C4×Dic9D411yescharacteristic
123C4×Dic9C2311yescharacteristic
124C2×C9⋊C8C2311yescharacteristic
125C2×C9⋊C8C2311yescharacteristic
126#3664C2×C414yescomplemented
127#3663—22no—
128#3663C2×C414yescomplemented
129C4×#137—91noSylow
130C2×#239—31no—
131C2×D3×Q8—31no—
132C2×C3×Q16C2×D311yescharacteristic
133C3×C4×Q8C2×D311yescharacteristic
134C3×C4×Q8C2×D311yescharacteristic
135Q8×Dic3—31no—
136Q8×Dic3—31no—
137C2×#216—31no—
138C2×#215—31no—
139#918—38no—
140C2×#204—31no—
141C2×ΓL(1,𝔽25)—31no—
142C2×ΓL(1,𝔽25)—31no—
143#893—31no—
144#893—61no—
145#892—31no—
146#892—61no—
147D3×C4⋊C4—31no—
148D3×C4⋊C4—61no—
149#887—31no—
150#887—61no—
151C4×D12—31no—
152C4×D12—61no—
153C42×D3—31no—
154C42×D3—61no—
155C42×D3—61no—
156C4×Dic6—31no—
157C4×Dic6—61no—
158C3×#107C2×D311yescharacteristic
159C3×#103C2×D311yescharacteristic
160C3×#103C2×D311yescharacteristic
161C3×C4×C8C2×D311yescharacteristic
162#835—31no—
163#835—31no—
164#821—31no—
165#817—31no—
166#816—31no—
167#815—31no—
168#815—31no—
169#810—31no—
170#809—31no—
171#808—31no—
172#807—31no—
173C4×C3⋊C8—31no—
174C22×D9—21no—
175C22×D9C2×D411yescharacteristic
176Q8×C9—21no—
177Q8×C9—21no—
178Q8×C9C22×C412yes—
179Q8×C9C22×C412yes—
180C2×C4×C9—21no—
181C2×C4×C9—21no—
182C2×C4×C9—21no—
183C2×C4×C9—21no—
184C2×C4×C9C2×D411yescharacteristic
185C2×C4×C9C2×D411yescharacteristic
186C2×C4×C9C2411yescharacteristic
187C2×Dic9—21no—
188C2×Dic9—21no—
189C2×Dic9—21no—
190C2×Dic9C2×D411yescharacteristic
191C2×Dic9C2×D411yescharacteristic
192C2×Dic9C2×D411yescharacteristic
193D36—24no—
194D36—21no—
195D36C22×C412yes—
196C4×D9—24no—
197C4×D9—22no—
198C4×D9—24no—
199C4×D9—41no—
200C4×D9—42no—
201C4×D9—42no—
202C4×D9—42no—
203C4×D9C22×C412yes—
204C4×D9#4112yes—
205Dic18—21no—
206Dic18—24no—
207Dic18C22×C412yes—
208C8×C9—21no—
209C8×C9C22×C412yes—
210C9⋊C8—21no—
211C9⋊C8C22×C412yes—
212C2×#137—91no—
213C4×#41—91no—
214C2×C4×Q8—91no—
215#441—91no—
216#441—91no—
217#440—91no—
218#440—91no—
219C4×Q16—91no—
220C4×Q16D911yescharacteristic, complemented
221C4×SD16—91no—
222C4×SD16—91no—
223#428—91no—
224#419—91no—
225#417—91no—
226C4×M16—91no—
227C2×C3×Q8C22×D311yescharacteristic
228C2×C3×Q8C22×D311yescharacteristic
229#239—34no—
230#239—62no—
231D3×Q8—34no—
232D3×Q8—62no—
233C2×D12—31no—
234C2×D12—61no—
235C2×C4×D3—31no—
236C2×C4×D3—31no—
237C2×C4×D3—31no—
238C2×C4×D3—61no—
239C2×C4×D3—61no—
240C2×C4×D3—61no—
241C2×C4×D3—61no—
242C2×C4×D3—61no—
243C2×Dic6—31no—
244C2×Dic6—61no—
245C3×Q16C4×D314yes—
246C2×C3×C8C22×D311yescharacteristic
247C2×C3×C8C22×D311yescharacteristic
248C3×C4⋊C4—21no—
249C3×C4⋊C4—21no—
250C3×C4⋊C4C22×D311yescharacteristic
251C3×C4⋊C4C22×D311yescharacteristic
252C3×C42—21no—
253C3×C42—21no—
254C3×C42C22×D311yescharacteristic
255#216—34no—
256#215—34no—
257(C2×D3)⋊C4—61no—
258(C2×D3)⋊C4—61no—
259(C2×D3)⋊C4—61no—
260C4⋊Dic3—31no—
261C4⋊Dic3—31no—
262C4⋊Dic3—61no—
263C4⋊Dic3—61no—
264Dic3⋊C4—61no—
265Dic3⋊C4—61no—
266Dic3⋊C4—61no—
267C4×Dic3—31no—
268C4×Dic3—31no—
269C4×Dic3—31no—
270C4×Dic3—61no—
271C4×Dic3—61no—
272C4×Dic3—61no—
273C4×Dic3—61no—
274C4×Dic3—61no—
275C2×C3⋊C8—31no—
276C2×C3⋊C8—31no—
277#204—34no—
278ΓL(1,𝔽25)—34no—
279ΓL(1,𝔽25)—62no—
280C22×C9C22×D411yescharacteristic
281C2×D9—21no—
282C2×D9—21no—
283C2×D9—22no—
284C2×D9—41no—
285C2×D9—41no—
286C2×D9C4×D412yes—
287C4×C9—22no—
288C4×C9—22no—
289C4×C9—21no—
290C4×C9—41no—
291C4×C9—41no—
292C4×C9#13712yescomplemented
293C4×C9C23×C411yescharacteristic
294C4×C9C2×#4111yescharacteristic
295Dic9—22no—
296Dic9—21no—
297Dic9—21no—
298Dic9—41no—
299Dic9—41no—
300Dic9C4×D412yes—
301C2×#41—91no—
302C22×Q8—91no—
303#137—98no—
304C2×Q16—91no—
305C2×Q16C2×D911yescharacteristic
306C2×SD16—91no—
307C2×SD16—91no—
308C2×M16—91no—
309C2×M16—91no—
310C4×Q8—91no—
311C4×Q8—91no—
312C4×Q8—91no—
313C4×Q8—91no—
314C4×Q8—181no—
315C4×Q8—181no—
316C4×Q8C2×D911yescharacteristic
317C4×Q8C2×D911yescharacteristic
318C4×D4—91no—
319C4×D4—91no—
320C4×D4—181no—
321C4×D4—181no—
322#117—91no—
323#117—181no—
324C2×C4⋊C4—91no—
325C2×C4⋊C4—181no—
326C2×C42—91no—
327C2×C42—181no—
328C2×C42—181no—
329#107—91no—
330#107C2×D911yescharacteristic
331#106—91no—
332#106—91no—
333#103—91no—
334#103—91no—
335#103—91no—
336#103—91no—
337#103C2×D911yescharacteristic
338#103C2×D911yescharacteristic
339#102—91no—
340#102—91no—
341#97—91no—
342#97—91no—
343C4×C8—91no—
344C4×C8C2×D911yescharacteristic
345C22×D3—31no—
346C22×D3—61no—
347C3×Q8—21no—
348C3×Q8—21no—
349C3×Q8C2×C4×D312yes—
350C3×Q8C2×C4×D312yes—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4—21no—
354C2×C3×C4—21no—
355C2×C3×C4D3×D411yescharacteristic
356C2×C3×C4D3×D411yescharacteristic
357C2×C3×C4C23×D311yescharacteristic
358C2×Dic3—31no—
359C2×Dic3—31no—
360C2×Dic3—31no—
361C2×Dic3—61no—
362C2×Dic3—61no—
363C2×Dic3—61no—
364D12—32no—
365D12—64no—
366D12—61no—
367C4×D3—32no—
368C4×D3—32no—
369C4×D3—64no—
370C4×D3—64no—
371C4×D3—62no—
372C4×D3—121no—
373C4×D3—122no—
374C4×D3—122no—
375C4×D3—122no—
376Dic6—32no—
377Dic6—64no—
378Dic6—61no—
379C3×C8—21no—
380C3×C8C2×C4×D312yes—
381C3⋊C8—32no—
382C3⋊C8—61no—
383C2×C9C2×C4×D411yescharacteristic
384C2×C9C2×#13711yescharacteristic
385C2×C9#57511yescharacteristic
386D9—22no—
387D9—42no—
388#41—94no—
389#41—182no—
390C2×Q8—94no—
391C2×Q8—91no—
392C2×Q8—181no—
393C2×Q8—182no—
394C2×Q8C22×D911yescharacteristic
395C2×Q8C22×D911yescharacteristic
396C2×D4—91no—
397C2×D4—181no—
398C22×C4—91no—
399C22×C4—91no—
400C22×C4—91no—
401C22×C4—181no—
402C22×C4—181no—
403C22×C4—181no—
404C22×C4—181no—
405C22×C4—181no—
406Q16—94no—
407Q16C4×D914yescomplemented
408SD16—94no—
409SD16—94no—
410M16—94no—
411M16—182no—
412C2×C8—91no—
413C2×C8—91no—
414C2×C8C22×D911yescharacteristic
415C2×C8C22×D911yescharacteristic
416C4⋊C4—21no—
417C4⋊C4—21no—
418C4⋊C4—91no—
419C4⋊C4—91no—
420C4⋊C4—181no—
421C4⋊C4—181no—
422C4⋊C4—181no—
423C4⋊C4—181no—
424C4⋊C4—181no—
425C4⋊C4C22×D911yescharacteristic
426C4⋊C4C22×D911yescharacteristic
427C22⋊C4—181no—
428C22⋊C4—181no—
429C22⋊C4—181no—
430C42—21no—
431C42—21no—
432C42—91no—
433C42—91no—
434C42—91no—
435C42—181no—
436C42—181no—
437C42—181no—
438C42—181no—
439C42—181no—
440C42C22×D911yescharacteristic
441C22×C3C2×D3×D411yescharacteristic
442C2×D3—32no—
443C2×D3—61no—
444C2×D3—61no—
445C2×D3—62no—
446C2×D3—121no—
447C2×D3—121no—
448C3×C4—21no—
449C3×C4—22no—
450C3×C4—22no—
451C3×C4—41no—
452C3×C4—41no—
453C3×C4#91812yes—
454C3×C4C22×C4×D311yescharacteristic
455C3×C4D3×#4111yescharacteristic
456Dic3—32no—
457Dic3—61no—
458Dic3—61no—
459Dic3—62no—
460Dic3—121no—
461Dic3—121no—
462C9C4×#13711yescharacteristic, complemented, Sylow
463C23—91no—
464C23—181no—
465Q8—21no—
466Q8—21no—
467Q8—92no—
468Q8—184no—
469Q8—181no—
470Q8C2×C4×D912yes—
471Q8C2×C4×D912yes—
472D4—92no—
473D4—184no—
474D4—181no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—91no—
480C2×C4—92no—
481C2×C4—92no—
482C2×C4—91no—
483C2×C4—91no—
484C2×C4—184no—
485C2×C4—184no—
486C2×C4—181no—
487C2×C4—182no—
488C2×C4—181no—
489C2×C4—181no—
490C2×C4—361no—
491C2×C4—362no—
492C2×C4—362no—
493C2×C4—362no—
494C2×C4D4×D911yescharacteristic
495C2×C4D4×D911yescharacteristic
496C2×C4C23×D911yescharacteristic
497C8—21no—
498C8—92no—
499C8—181no—
500C8C2×C4×D912yes—
501C2×C3C4×D3×D411yescharacteristic
502C2×C3C2×#91811yescharacteristic
503C2×C3#576811yescharacteristic
504D3—62no—
505D3—122no—
506C22—92no—
507C22—181no—
508C22—181no—
509C22—182no—
510C22—361no—
511C22—361no—
512C22C2×D4×D911yescharacteristic
513C4—21no—
514C4—22no—
515C4—22no—
516C4—41no—
517C4—41no—
518C4—92no—
519C4—181no—
520C4—181no—
521C4—182no—
522C4—361no—
523C4—361no—
524C4#6348012yesdirect product factor
525C4C22×C4×D911yescharacteristic
526C4#41×D911yescharacteristic
527C3C4×#91811yescharacteristic
528C2—182no—
529C2—362no—
530C2C4×D4×D911yescharacteristic
531C2C2×#6348011yescharacteristic
532C2#1058987011yescharacteristic
subgroupG/H
centerC2×C4D4×D9
commutatorC4×C9C23×C4
FrattiniC2×C3×C4C23×D3
FittingC4×C9×Q16C2
socleC22×C3C2×D3×D4
prime radicalC2×#3701C22
cosocleC2×C4×C9C24
hypercenterC4×Q16D9
hypocenterC9C4×#137
LCSG ▷ C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
3. C4×Q8×D9C2semidirect
4. C4×C9×Q16C2semidirect
5. #10588864C2semidirect
6. C4×#3675C2semidirect
7. C4×#3674C2semidirect
8. #10588569C2semidirect
9. #10588561C2semidirect
10. #10588497C2semidirect
12. #10588482C2semidirect
13. #10588469C2semidirect
14. C4×#3664C2semidirect
15. C4×#3663C2semidirect
26. #63480C4direct (N × H)
81. Q8×D9C2×C4semidirect
94. C9×Q16C2×C4semidirect
104. #3675C2×C4semidirect
105. #3674C2×C4semidirect
126. #3664C2×C4semidirect
128. #3663C2×C4semidirect
220. C4×Q16D9semidirect
292. C4×C9#137semidirect
407. Q16C4×D9semidirect
462. C9C4×#137semidirect
524. C4#63480direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#634802
C4×#37012
C4×Q8×D92
C4×C9×Q162
#105888642
C4×#36752
C4×#36742
#105885692
#105885612
#105884972
#105884832
#105884822
#105884692
C4×#36642
C4×#36632
C4×#9183