Finite Group Databasebeta

← C4×#63477 #11860351

Subgroups — C4×#63477 #11860351

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×#63477C211yesmaximal, characteristic
2C4×Q8×D9C211yesmaximal, characteristic, complemented
3C4×#3699C211yesmaximal, characteristic
4C4×C9×SD16C211yesmaximal, characteristic, complemented
5#10588844C211yesmaximal, characteristic, complemented
6C4×#3674C211yesmaximal, characteristic, complemented
7C4×#3672C211yesmaximal, characteristic, complemented
8#10588541C211yesmaximal, characteristic, complemented
9#10588533C211yesmaximal, characteristic, complemented
10#10588482C211yesmaximal, characteristic, complemented
11#10588469C211yesmaximal, characteristic, complemented
12#10588451C211yesmaximal, characteristic
13#10588437C211yesmaximal, characteristic, complemented
14C4×#3663C211yesmaximal, characteristic, complemented
15C4×Dic36C211yesmaximal, characteristic, complemented
16C4×#915—31nomaximal
17C2×Q8×D9C2211yescharacteristic
18C2×#3699C2211yescharacteristic
19C2×C9×SD16C2211yescharacteristic
20C4×Q8×C9C2211yescharacteristic
21C4×D4×C9C2211yescharacteristic
22Q8×Dic9C2211yescharacteristic
23C2×#3674C2211yescharacteristic
24D4×Dic9C2211yescharacteristic
25C2×#3672C2211yescharacteristic
26C4×#611—21no—
27C2×C4×Dic9—21no—
28#63477C418yesdirect product factor
29C2×#3663C2211yescharacteristic
30C2×#3663C2211yescharacteristic
31C2×Dic36C2211yescharacteristic
32#63454C2211yescharacteristic
33C4⋊C4×D9—21no—
34C4⋊C4×D9C2211yescharacteristic
35#63449—21no—
36#63449C2211yescharacteristic
37#63449C2211yescharacteristic
38#611⋊C4—21no—
39#63439—21no—
40C42×D9—21no—
41C42×D9C2211yescharacteristic
42C4×Dic18—21no—
43C4×Dic18C2211yescharacteristic
44C4×Dic18C2211yescharacteristic
45C9×#106C2211yescharacteristic
46C9×#103C2211yescharacteristic
47C9×#102C2211yescharacteristic
48C4×C8×C9C2211yescharacteristic
49#63395C2211yescharacteristic
50#63392C2211yescharacteristic
51#63378C2211yescharacteristic
52#63376C2211yescharacteristic
53#63376C2211yescharacteristic
54#63375C2211yescharacteristic
55#63375C2211yescharacteristic
56#63368C2211yescharacteristic
57#63368C2211yescharacteristic
58#63367C2211yescharacteristic
59#63366C2211yescharacteristic
60C4×C9⋊C8C2211yescharacteristic
61C2×#915—31no—
62C4×D3×Q8—31no—
63C4×#237—31no—
64C3×C4×SD16D311yescharacteristic
65#5164—31no—
66C4×#216—31no—
67C4×#214—31no—
68#4861—31no—
69#4853—31no—
70#4802—31no—
71#4789—31no—
72#4771—31no—
73#4757—31no—
74C4×Dic12—31no—
75C4×ΓL(1,𝔽25)—31no—
76C2×Q8×C9C2311yescharacteristic
77C2×D4×C9C2311yescharacteristic
78C22×C4×C9—21no—
79C2×#611—21no—
80C22×Dic9—21no—
81C22×Dic9—21no—
82Q8×D9—22no—
83Q8×D9C2×C414yescomplemented
84#3699—22no—
85#3699C2×C414yes—
86C2×C4×D9—21no—
87C2×C4×D9—21no—
88C2×C4×D9D411yescharacteristic
89C2×C4×D9D411yescharacteristic
90C2×C4×D9C2311yescharacteristic
91C2×Dic18—21no—
92C2×Dic18C2311yescharacteristic
93C2×Dic18C2311yescharacteristic
94C9×SD16C2×C414yescomplemented
95C2×C8×C9C2311yescharacteristic
96C2×C8×C9C2311yescharacteristic
97C9×C4⋊C4—21no—
98C9×C4⋊C4C2311yescharacteristic
99C9×C4⋊C4C2311yescharacteristic
100C9×C22⋊C4—21no—
101C42×C9—21no—
102C42×C9C2311yescharacteristic
103#3676—21no—
104#3674C2×C414yescomplemented
105#3672C2×C414yescomplemented
106(C2×D9)⋊C4—21no—
107C4⋊Dic9—21no—
108C4⋊Dic9C2311yescharacteristic
109C4⋊Dic9C2311yescharacteristic
110Dic9⋊C4—21no—
111Dic9⋊C4—21no—
112Dic9⋊C4—21no—
113Dic9⋊C4—21no—
114Dic9⋊C4—21no—
115C4×Dic9—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#3663—22no—
127#3663C2×C414yescomplemented
128Dic36C2×C414yescomplemented
129C4×#137—91noSylow
130C2×D3×Q8—31no—
131C2×#237—31no—
132C2×C3×SD16C2×D311yescharacteristic
133C3×C4×Q8C2×D311yescharacteristic
134C3×C4×D4C2×D311yescharacteristic
135Q8×Dic3—31no—
136C2×#216—31no—
137D4×Dic3—31no—
138C2×#214—31no—
139C4×#67—61no—
140C2×C4×Dic3—61no—
141#915—38no—
142C2×Dic12—31no—
143C2×ΓL(1,𝔽25)—31no—
144C2×ΓL(1,𝔽25)—31no—
145#892—31no—
146D3×C4⋊C4—31no—
147D3×C4⋊C4—61no—
148#887—31no—
149#887—31no—
150#887—61no—
151#67⋊C4—61no—
152#877—61no—
153C42×D3—31no—
154C42×D3—61no—
155C4×Dic6—31no—
156C4×Dic6—31no—
157C4×Dic6—61no—
158C3×#106C2×D311yescharacteristic
159C3×#103C2×D311yescharacteristic
160C3×#102C2×D311yescharacteristic
161C3×C4×C8C2×D311yescharacteristic
162#835—31no—
163#832—31no—
164#818—31no—
165#816—31no—
166#816—31no—
167#815—31no—
168#815—31no—
169#810—31no—
170#810—31no—
171#808—31no—
172#807—31no—
173C4×C3⋊C8—31no—
174C23×C9—21no—
175C22×D9C2×D411yescharacteristic
176Q8×C9—21no—
177Q8×C9C22×C412yes—
178D4×C9—21no—
179D4×C9C22×C412yes—
180C2×C4×C9—21no—
181C2×C4×C9—21no—
182C2×C4×C9—21no—
183C2×C4×C9—42no—
184C2×C4×C9C2×D411yescharacteristic
185C2×C4×C9C2×D411yescharacteristic
186C2×C4×C9C2411yescharacteristic
187#611—24no—
188C2×Dic9—21no—
189C2×Dic9—21no—
190C2×Dic9—24no—
191C2×Dic9—21no—
192C2×Dic9—21no—
193C2×Dic9—42no—
194C2×Dic9C2×D411yescharacteristic
195C2×Dic9C2×D411yescharacteristic
196C2×Dic9C2×D411yescharacteristic
197C4×D9—24no—
198C4×D9—22no—
199C4×D9—41no—
200C4×D9—42no—
201C4×D9C22×C412yes—
202C4×D9#4112yes—
203Dic18—21no—
204Dic18—21no—
205Dic18—24no—
206Dic18C22×C412yes—
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×Q16—91no—
221C4×SD16—91no—
222C4×SD16D911yescharacteristic, complemented
223#428—91no—
224#419—91no—
225#417—91no—
226C4×M16—91no—
227C2×C3×Q8C22×D311yescharacteristic
228C2×C3×D4C22×D311yescharacteristic
229C22×C3×C4—21no—
230C2×#67—61no—
231C22×Dic3—61no—
232C22×Dic3—61no—
233D3×Q8—34no—
234D3×Q8—62no—
235#237—34no—
236#237—62no—
237C2×C4×D3—31no—
238C2×C4×D3—31no—
239C2×C4×D3—31no—
240C2×C4×D3—61no—
241C2×C4×D3—61no—
242C2×Dic6—31no—
243C2×Dic6—31no—
244C2×Dic6—61no—
245C3×SD16C4×D314yes—
246C2×C3×C8C22×D311yescharacteristic
247C2×C3×C8C22×D311yescharacteristic
248C3×C4⋊C4—21no—
249C3×C4⋊C4C22×D311yescharacteristic
250C3×C4⋊C4C22×D311yescharacteristic
251C3×C22⋊C4—21no—
252C3×C42—21no—
253C3×C42C22×D311yescharacteristic
254#217—61no—
255#216—34no—
256#214—34no—
257(C2×D3)⋊C4—61no—
258C4⋊Dic3—31no—
259C4⋊Dic3—31no—
260C4⋊Dic3—61no—
261Dic3⋊C4—61no—
262Dic3⋊C4—61no—
263Dic3⋊C4—61no—
264Dic3⋊C4—61no—
265Dic3⋊C4—61no—
266C4×Dic3—31no—
267C4×Dic3—31no—
268C4×Dic3—31no—
269C4×Dic3—61no—
270C4×Dic3—61no—
271C4×Dic3—61no—
272C4×Dic3—61no—
273C4×Dic3—61no—
274C4×Dic3—61no—
275C2×C3⋊C8—31no—
276C2×C3⋊C8—31no—
277Dic12—34no—
278ΓL(1,𝔽25)—34no—
279ΓL(1,𝔽25)—62no—
280C22×C9—22no—
281C22×C9—41no—
282C22×C9—41no—
283C22×C9C22×D411yescharacteristic
284C2×D9—21no—
285C2×D9—21no—
286C2×D9C4×D412yes—
287C4×C9—22no—
288C4×C9—21no—
289C4×C9—41no—
290C4×C9—41no—
291C4×C9#13712yescomplemented
292C4×C9C23×C411yescharacteristic
293C4×C9C2×#4111yescharacteristic
294Dic9—22no—
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×Q16—91no—
306C2×SD16—91no—
307C2×SD16C2×D911yescharacteristic
308C2×M16—91no—
309C2×M16—91no—
310C4×Q8—91no—
311C4×Q8—91no—
312C4×Q8—91no—
313C4×Q8—91no—
314C4×Q8—91no—
315C4×Q8—181no—
316C4×Q8—181no—
317C4×Q8C2×D911yescharacteristic
318C4×D4—91no—
319C4×D4—181no—
320C4×D4—181no—
321C4×D4C2×D911yescharacteristic
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#107—91no—
331#106—91no—
332#106C2×D911yescharacteristic
333#103—91no—
334#103—91no—
335#103—91no—
336#103—91no—
337#103—91no—
338#103C2×D911yescharacteristic
339#102—91no—
340#102C2×D911yescharacteristic
341#97—91no—
342#97—91no—
343C4×C8—91no—
344C4×C8C2×D911yescharacteristic
345C23×C3—21no—
346C22×D3—31no—
347C3×Q8—21no—
348C3×Q8C2×C4×D312yes—
349C3×D4—21no—
350C3×D4C2×C4×D312yes—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4—21no—
354C2×C3×C4—42no—
355C2×C3×C4D3×D411yescharacteristic
356C2×C3×C4D3×D411yescharacteristic
357C2×C3×C4C23×D311yescharacteristic
358#67—64no—
359C2×Dic3—31no—
360C2×Dic3—31no—
361C2×Dic3—31no—
362C2×Dic3—64no—
363C2×Dic3—61no—
364C2×Dic3—61no—
365C2×Dic3—61no—
366C2×Dic3—61no—
367C2×Dic3—122no—
368C4×D3—32no—
369C4×D3—32no—
370C4×D3—64no—
371C4×D3—62no—
372C4×D3—121no—
373C4×D3—122no—
374Dic6—32no—
375Dic6—32no—
376Dic6—64no—
377Dic6—61no—
378Dic6—61no—
379C3×C8—21no—
380C3×C8C2×C4×D312yes—
381C3⋊C8—32no—
382C3⋊C8—61no—
383C2×C9—42no—
384C2×C9C2×C4×D411yescharacteristic
385C2×C9C2×#13711yescharacteristic
386C2×C9#57511yescharacteristic
387D9—22no—
388#41—94no—
389#41—182no—
390C2×Q8—94no—
391C2×Q8—91no—
392C2×Q8—91no—
393C2×Q8—181no—
394C2×Q8—182no—
395C2×Q8C22×D911yescharacteristic
396C2×D4—181no—
397C2×D4C22×D911yescharacteristic
398C22×C4—21no—
399C22×C4—91no—
400C22×C4—91no—
401C22×C4—91no—
402C22×C4—181no—
403C22×C4—181no—
404C22×C4—181no—
405C22×C4—181no—
406Q16—94no—
407Q16—94no—
408SD16—94no—
409SD16C4×D914yescomplemented
410M16—94no—
411M16—182no—
412C2×C8—91no—
413C2×C8—91no—
414C2×C8C22×D911yescharacteristic
415C2×C8C22×D911yescharacteristic
416C4⋊C4—21no—
417C4⋊C4—91no—
418C4⋊C4—91no—
419C4⋊C4—181no—
420C4⋊C4—181no—
421C4⋊C4—181no—
422C4⋊C4—181no—
423C4⋊C4—181no—
424C4⋊C4—181no—
425C4⋊C4C22×D911yescharacteristic
426C4⋊C4C22×D911yescharacteristic
427C22⋊C4—21no—
428C22⋊C4—181no—
429C22⋊C4—181no—
430C42—21no—
431C42—91no—
432C42—91no—
433C42—91no—
434C42—181no—
435C42—181no—
436C42—181no—
437C42—181no—
438C42—181no—
439C42—181no—
440C42C22×D911yescharacteristic
441C22×C3—22no—
442C22×C3—41no—
443C22×C3—41no—
444C22×C3C2×D3×D411yescharacteristic
445C2×D3—32no—
446C2×D3—61no—
447C2×D3—61no—
448C3×C4—21no—
449C3×C4—22no—
450C3×C4—41no—
451C3×C4—41no—
452C3×C4#91512yes—
453C3×C4C22×C4×D311yescharacteristic
454C3×C4D3×#4111yescharacteristic
455Dic3—32no—
456Dic3—61no—
457Dic3—61no—
458Dic3—62no—
459Dic3—62no—
460Dic3—121no—
461Dic3—121no—
462C9C4×#13711yescharacteristic, complemented, Sylow
463C23—21no—
464C23—91no—
465Q8—21no—
466Q8—92no—
467Q8—92no—
468Q8—184no—
469Q8—181no—
470Q8—181no—
471Q8C2×C4×D912yes—
472D4—21no—
473D4—184no—
474D4C2×C4×D912yes—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—42no—
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—181no—
488C2×C4—182no—
489C2×C4—181no—
490C2×C4—181no—
491C2×C4—361no—
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×C3—42no—
502C2×C3C4×D3×D411yescharacteristic
503C2×C3C2×#91511yescharacteristic
504C2×C3#576811yescharacteristic
505D3—62no—
506C22—22no—
507C22—41no—
508C22—41no—
509C22—92no—
510C22—181no—
511C22—181no—
512C22C2×D4×D911yescharacteristic
513C4—21no—
514C4—22no—
515C4—41no—
516C4—41no—
517C4—92no—
518C4—181no—
519C4—181no—
520C4—182no—
521C4—182no—
522C4—361no—
523C4—361no—
524C4#6347712yesdirect product factor
525C4C22×C4×D911yescharacteristic
526C4#41×D911yescharacteristic
527C3C4×#91511yescharacteristic
528C2—42no—
529C2—182no—
530C2C4×D4×D911yescharacteristic
531C2C2×#6347711yescharacteristic
532C2#1058987011yescharacteristic
subgroupG/H
centerC2×C4D4×D9
commutatorC4×C9C23×C4
FrattiniC2×C3×C4C23×D3
FittingC4×C9×SD16C2
socleC22×C3C2×D3×D4
prime radicalC2×#3699C22
cosocleC2×C4×C9C24
hypercenterC4×SD16D9
hypocenterC9C4×#137
LCSG ▷ C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
2. C4×Q8×D9C2semidirect
4. C4×C9×SD16C2semidirect
5. #10588844C2semidirect
6. C4×#3674C2semidirect
7. C4×#3672C2semidirect
8. #10588541C2semidirect
9. #10588533C2semidirect
10. #10588482C2semidirect
11. #10588469C2semidirect
13. #10588437C2semidirect
14. C4×#3663C2semidirect
15. C4×Dic36C2semidirect
28. #63477C4direct (N × H)
83. Q8×D9C2×C4semidirect
94. C9×SD16C2×C4semidirect
104. #3674C2×C4semidirect
105. #3672C2×C4semidirect
127. #3663C2×C4semidirect
128. Dic36C2×C4semidirect
222. C4×SD16D9semidirect
291. C4×C9#137semidirect
409. SD16C4×D9semidirect
462. C9C4×#137semidirect
524. C4#63477direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#634772
C4×Q8×D92
C4×#36992
C4×C9×SD162
#105888442
C4×#36742
C4×#36722
#105885412
#105885332
#105884822
#105884692
#105884512
#105884372
C4×#36632
C4×Dic362
C4×#9153