Finite Group Databasebeta

← #11887868

Subgroups — #11887868

Order 1152.

597 conjugacy classes of subgroups.

The subgroup lattice has 555 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10589667C211yesmaximal, characteristic, complemented
2#10589654C211yesmaximal, characteristic, complemented
3C8×D4×C9C211yesmaximal, characteristic, complemented
4#10588796C211yesmaximal, characteristic, complemented
5#10588795C211yesmaximal, characteristic, complemented
6#10588794C211yesmaximal, characteristic, complemented
7C2×#63376C211yesmaximal, characteristic, complemented
8#10588528C211yesmaximal, characteristic, complemented
9#10588511C211yesmaximal, characteristic, complemented
10#10588417C211yesmaximal, characteristic, complemented
11#10588416C211yesmaximal, characteristic, complemented
12#10588404C211yesmaximal, characteristic, complemented
13#10588403C211yesmaximal, characteristic, complemented
14#10588379C211yesmaximal, characteristic, complemented
15C4×#3664C211yesmaximal, characteristic, complemented
16#79450—31nomaximal
17C2×#3697C2211yescharacteristic
18C22×Dic18C2211yescharacteristic
19C22×C8×C9C2211yescharacteristic
20C22×C8×C9C2211yescharacteristic
21C4×D4×C9C2211yescharacteristic
22#63501—21no—
23#63501—21no—
24#63492C2211yescharacteristic
25#63492C2211yescharacteristic
26#63492C2211yescharacteristic
27#63488C2211yescharacteristic
28C2×C4⋊Dic9C2211yescharacteristic
29#63486C2211yescharacteristic
30C2×D72C2211yescharacteristic
31C2×#3664C2211yescharacteristic
32C2×#3664C2211yescharacteristic
33#63460—21no—
34#63458—21no—
35#63447—21no—
36#63445—21no—
37#611⋊C4—21no—
38#611⋊C4—21no—
39#63437C2211yescharacteristic
40C4×D36C2211yescharacteristic
41#63432C2211yescharacteristic
42C4×Dic18C2211yescharacteristic
43C9×C4⋊C8C2211yescharacteristic
44C9×C22⋊C8C2211yescharacteristic
45C9×C22⋊C8C2211yescharacteristic
46C4×C8×C9C2211yescharacteristic
47#63380C2211yescharacteristic
48#63380C2211yescharacteristic
49#63380C2211yescharacteristic
50#63380C2211yescharacteristic
51#63378C2211yescharacteristic
52#63377C2211yescharacteristic
53#63377C2211yescharacteristic
54#63376C2211yescharacteristic
55#63376C2211yescharacteristic
56#63376C2211yescharacteristic
57#63376C2211yescharacteristic
58#63376C2211yescharacteristic
59#63376C2211yescharacteristic
60#5565—31no—
61#5552—31no—
62C3×C8×D4D311yescharacteristic
63#5115—31no—
64#5114—31no—
65#5113—31no—
66C2×#816—31no—
67#4844—31no—
68#4829—31no—
69#4738—31no—
70#4735—31no—
71#4734—31no—
72#4723—31no—
73#4697—31no—
74C4×#204—31no—
75C2×D4×C9D411yescharacteristic
76C22×C4×C9C2311yescharacteristic
77C22×C4×C9C2311yescharacteristic
78C2×#611—21no—
79C2×#611—21no—
80C2×#611—21no—
81C2×#611—21no—
82C22×Dic9—21no—
83C22×Dic9—21no—
84#3697—22no—
85#3697—41no—
86C2×D36C2311yescharacteristic
87C2×D36C2311yescharacteristic
88C2×C4×D9—21no—
89C2×C4×D9—21no—
90C2×Dic18—22no—
91C2×Dic18—21no—
92C2×Dic18—41no—
93C2×Dic18C2311yescharacteristic
94C2×Dic18C2311yescharacteristic
95C2×C8×C9—41no—
96C2×C8×C9—41no—
97C2×C8×C9C2311yescharacteristic
98C2×C8×C9C2311yescharacteristic
99C2×C8×C9C2311yescharacteristic
100C2×C8×C9C2311yescharacteristic
101C9×C4⋊C4D411yescharacteristic
102C9×C22⋊C4D411yescharacteristic
103C9×C22⋊C4D411yescharacteristic
104C42×C9C2311yescharacteristic
105#3676—21no—
106#3676—21no—
107(C2×D9)⋊C4—21no—
108(C2×D9)⋊C4—21no—
109(C2×D9)⋊C4—21no—
110(C2×D9)⋊C4—21no—
111(C2×D9)⋊C4—21no—
112(C2×D9)⋊C4—21no—
113C4⋊Dic9—21no—
114C4⋊Dic9C2311yescharacteristic
115C4⋊Dic9C2311yescharacteristic
116C4⋊Dic9C2311yescharacteristic
117C4⋊Dic9C2311yescharacteristic
118Dic9⋊C4—21no—
119Dic9⋊C4—21no—
120Dic9⋊C4—21no—
121Dic9⋊C4—21no—
122C4×Dic9—21no—
123C4×Dic9—21no—
124D72—41no—
125#3664—22no—
126#3664—41no—
127#3301—91noSylow
128C2×#235—31no—
129C22×Dic6—31no—
130C22×C3×C8C2×D311yescharacteristic
131C22×C3×C8C2×D311yescharacteristic
132C3×C4×D4C2×D311yescharacteristic
133#939—61no—
134#939—61no—
135#930—31no—
136#930—31no—
137#930—31no—
138#926—31no—
139C2×C4⋊Dic3—31no—
140#924—31no—
141C2×D24—31no—
142C2×#204—31no—
143C2×#204—31no—
144#898—61no—
145#896—61no—
146#885—61no—
147#883—61no—
148#67⋊C4—61no—
149#67⋊C4—61no—
150#875—31no—
151C4×D12—31no—
152#870—31no—
153C4×Dic6—31no—
154C3×C4⋊C8C2×D311yescharacteristic
155C3×C22⋊C8C2×D311yescharacteristic
156C3×C22⋊C8C2×D311yescharacteristic
157C3×C4×C8C2×D311yescharacteristic
158#821—31no—
159#821—31no—
160#821—31no—
161#821—31no—
162#818—31no—
163#817—31no—
164#817—31no—
165#816—31no—
166#816—31no—
167#816—31no—
168#816—31no—
169#816—31no—
170#816—31no—
171C23×C9C2×D411yescharacteristic
172C23×C9C2×D411yescharacteristic
173C22×D9—21no—
174C22×D9—21no—
175D4×C9—22no—
176C2×C4×C9—21no—
177C2×C4×C9—21no—
178C2×C4×C9—21no—
179C2×C4×C9—21no—
180C2×C4×C9C2×D411yescharacteristic
181C2×C4×C9C2×D411yescharacteristic
182C2×C4×C9C2×D411yescharacteristic
183C2×C4×C9C2×D411yescharacteristic
184C2×C4×C9C2411yescharacteristic
185#611—42no—
186#611—42no—
187#611—42no—
188#611—81no—
189C2×Dic9—21no—
190C2×Dic9—21no—
191C2×Dic9—21no—
192C2×Dic9—21no—
193C2×Dic9—21no—
194C2×Dic9—21no—
195C2×Dic9—42no—
196C2×Dic9—81no—
197D36—21no—
198D36—21no—
199D36—21no—
200D36—21no—
201C4×D9—42no—
202C4×D9—81no—
203Dic18—21no—
204Dic18—21no—
205Dic18—21no—
206Dic18—42no—
207Dic18#4112yes—
208C8×C9—21no—
209C8×C9—21no—
210C8×C9—21no—
211C8×C9—21no—
212#553—91no—
213#548—91no—
214#488—91no—
215#485—91no—
216#481—91no—
217#479—91no—
218#466—91no—
219#465—91no—
220#463—91no—
221#449—91no—
222#448—91no—
223C4×SD16—91no—
224C8×D4D911yescharacteristic, complemented
225#416—91no—
226C2×#103—91no—
227C2×C3×D4D1211yescharacteristic
228C22×C3×C4C22×D311yescharacteristic
229C22×C3×C4C22×D311yescharacteristic
230C2×#67—61no—
231C2×#67—61no—
232C2×#67—61no—
233C2×#67—61no—
234C22×Dic3—61no—
235C22×Dic3—61no—
236#235—62no—
237#235—121no—
238C2×D12—31no—
239C2×D12—31no—
240C2×C4×D3—61no—
241C2×C4×D3—61no—
242C2×Dic6—31no—
243C2×Dic6—31no—
244C2×Dic6—62no—
245C2×Dic6—61no—
246C2×Dic6—121no—
247C2×C3×C8—41no—
248C2×C3×C8—41no—
249C2×C3×C8C22×D311yescharacteristic
250C2×C3×C8C22×D311yescharacteristic
251C2×C3×C8C22×D311yescharacteristic
252C2×C3×C8C22×D311yescharacteristic
253C3×C4⋊C4D1211yescharacteristic
254C3×C22⋊C4D1211yescharacteristic
255C3×C22⋊C4D1211yescharacteristic
256C3×C42C22×D311yescharacteristic
257#217—61no—
258#217—61no—
259(C2×D3)⋊C4—61no—
260(C2×D3)⋊C4—61no—
261(C2×D3)⋊C4—61no—
262(C2×D3)⋊C4—61no—
263(C2×D3)⋊C4—61no—
264(C2×D3)⋊C4—61no—
265C4⋊Dic3—31no—
266C4⋊Dic3—31no—
267C4⋊Dic3—31no—
268C4⋊Dic3—31no—
269C4⋊Dic3—61no—
270Dic3⋊C4—61no—
271Dic3⋊C4—61no—
272Dic3⋊C4—61no—
273Dic3⋊C4—61no—
274C4×Dic3—61no—
275C4×Dic3—61no—
276D24—121no—
277#204—62no—
278#204—121no—
279C22×C9—21no—
280C22×C9—21no—
281C22×C9—21no—
282C22×C9—21no—
283C22×C9—21no—
284C22×C9#13512yes—
285C22×C9C22×D411yescharacteristic
286C2×D9—41no—
287C2×D9—41no—
288C2×D9—41no—
289C2×D9—41no—
290C2×D9—41no—
291C2×D9—41no—
292C4×C9—21no—
293C4×C9—21no—
294C4×C9—21no—
295C4×C9—21no—
296C4×C9C2×#4111yescharacteristic
297C4×C9H(5,𝔽2)11yescharacteristic
298Dic9—22no—
299Dic9—41no—
300Dic9—41no—
301Dic9—41no—
302Dic9—41no—
303Dic9—41no—
304C2×#41—91no—
305C22×Q8—91no—
306C2×SD16—91no—
307C2×SD16—91no—
308C2×D8—91no—
309C22×C8C2×D911yescharacteristic
310C22×C8C2×D911yescharacteristic
311#126—181no—
312#125—91no—
313#124—91no—
314#124—181no—
315#123—181no—
316C22⋊Q8—91no—
317C22⋊Q8—181no—
318#121—91no—
319#121—91no—
320#121—91no—
321#121—181no—
322#121—181no—
323C4×Q8—91no—
324C4×D4—91no—
325C4×D4—181no—
326C4×D4—181no—
327C4×D4C2×D911yescharacteristic
328#117—91no—
329C2×C4⋊C4—91no—
330#107—91no—
331#106—91no—
332#106—91no—
333C4⋊C8C2×D911yescharacteristic
334#103—91no—
335#103—91no—
336#103—91no—
337#103—91no—
338#103—91no—
339#103—91no—
340#102—91no—
341#102—91no—
342#102—91no—
343#102—91no—
344C22⋊C8C2×D911yescharacteristic
345C22⋊C8C2×D911yescharacteristic
346C4×C8C2×D911yescharacteristic
347C23×C3C2×D1211yescharacteristic
348C23×C3C2×D1211yescharacteristic
349C22×D3—61no—
350C22×D3—61no—
351C3×D4—22no—
352C2×C3×C4—21no—
353C2×C3×C4—21no—
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4C2×D1211yescharacteristic
357C2×C3×C4C2×D1211yescharacteristic
358C2×C3×C4C2×D1211yescharacteristic
359C2×C3×C4C2×D1211yescharacteristic
360C2×C3×C4C23×D311yescharacteristic
361#67—122no—
362#67—122no—
363#67—122no—
364#67—241no—
365C2×Dic3—61no—
366C2×Dic3—61no—
367C2×Dic3—61no—
368C2×Dic3—61no—
369C2×Dic3—61no—
370C2×Dic3—61no—
371C2×Dic3—122no—
372C2×Dic3—241no—
373D12—61no—
374D12—61no—
375D12—61no—
376D12—61no—
377C4×D3—122no—
378C4×D3—241no—
379Dic6—32no—
380Dic6—61no—
381Dic6—61no—
382Dic6—61no—
383Dic6—122no—
384C3×C8—21no—
385C3×C8—21no—
386C3×C8—21no—
387C3×C8—21no—
388C2×C9—22no—
389C2×C9—41no—
390C2×C9#54611yescharacteristic
391C2×C9C2×#13511yescharacteristic
392C2×C9#57711yescharacteristic
393D9—81no—
394D9—81no—
395#41—182no—
396#41—361no—
397C2×Q8—91no—
398C2×Q8—91no—
399C2×Q8—182no—
400C2×Q8—181no—
401C2×Q8—361no—
402C2×D4—91no—
403C2×D4—91no—
404C2×D4—181no—
405C2×D4—181no—
406C2×D4—181no—
407C2×D4—181no—
408C2×D4D3611yescharacteristic
409C22×C4—181no—
410C22×C4—181no—
411C22×C4—181no—
412C22×C4—181no—
413C22×C4C22×D911yescharacteristic
414C22×C4C22×D911yescharacteristic
415SD16—182no—
416SD16—361no—
417D8—361no—
418C2×C8—41no—
419C2×C8—41no—
420C2×C8C22×D911yescharacteristic
421C2×C8C22×D911yescharacteristic
422C2×C8C22×D911yescharacteristic
423C2×C8C22×D911yescharacteristic
424C4⋊C4—91no—
425C4⋊C4—91no—
426C4⋊C4—91no—
427C4⋊C4—91no—
428C4⋊C4—181no—
429C4⋊C4—181no—
430C4⋊C4—181no—
431C4⋊C4—181no—
432C4⋊C4—181no—
433C4⋊C4D3611yescharacteristic
434C22⋊C4—181no—
435C22⋊C4—181no—
436C22⋊C4—181no—
437C22⋊C4—181no—
438C22⋊C4—181no—
439C22⋊C4—181no—
440C22⋊C4—181no—
441C22⋊C4—181no—
442C22⋊C4D3611yescharacteristic
443C22⋊C4D3611yescharacteristic
444C42—181no—
445C42—181no—
446C42C22×D911yescharacteristic
447C22×C3—21no—
448C22×C3—21no—
449C22×C3—21no—
450C22×C3—21no—
451C22×C3—21no—
452C22×C3#90412yes—
453C22×C3C22×D1211yescharacteristic
454C2×D3—121no—
455C2×D3—121no—
456C2×D3—121no—
457C2×D3—121no—
458C2×D3—121no—
459C2×D3—121no—
460C3×C4—21no—
461C3×C4—21no—
462C3×C4—21no—
463C3×C4—21no—
464C3×C4#100411yescharacteristic
465C3×C4D3×#4111yescharacteristic
466Dic3—62no—
467Dic3—121no—
468Dic3—121no—
469Dic3—121no—
470Dic3—121no—
471Dic3—121no—
472C9#330111yescharacteristic, complemented, Sylow
473C23—181no—
474C23—181no—
475C23C2×D3611yescharacteristic
476C23C2×D3611yescharacteristic
477Q8—92no—
478Q8—181no—
479Q8—181no—
480Q8—181no—
481Q8—362no—
482D4—22no—
483D4—181no—
484D4—181no—
485D4—181no—
486D4—181no—
487D4—362no—
488D4—362no—
489D4—362no—
490D4—721no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—181no—
496C2×C4—181no—
497C2×C4—181no—
498C2×C4—181no—
499C2×C4—181no—
500C2×C4—181no—
501C2×C4—362no—
502C2×C4—362no—
503C2×C4—721no—
504C2×C4—721no—
505C2×C4C2×D3611yescharacteristic
506C2×C4C2×D3611yescharacteristic
507C2×C4C2×D3611yescharacteristic
508C2×C4C2×D3611yescharacteristic
509C2×C4C23×D911yescharacteristic
510C8—21no—
511C8—21no—
512C8—21no—
513C8—21no—
514C2×C3—22no—
515C2×C3—41no—
516C2×C3#555411yescharacteristic
517C2×C3C2×#90411yescharacteristic
518C2×C3#575111yescharacteristic
519D3—241no—
520D3—241no—
521C22—21no—
522C22—21no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22—361no—
527C22—361no—
528C22—361no—
529C22—361no—
530C22—361no—
531C22—361no—
532C22#6346712yes—
533C22C22×D3611yescharacteristic
534C4—21no—
535C4—21no—
536C4—21no—
537C4—21no—
538C4—182no—
539C4—361no—
540C4—361no—
541C4—361no—
542C4—361no—
543C4—361no—
544C4#6371011yescharacteristic
545C4#41×D911yescharacteristic
546C3#7945011yescharacteristic
547C2—22no—
548C2—41no—
549C2—721no—
550C2—721no—
551C2#1058965611yescharacteristic
552C2C2×#6346711yescharacteristic
553C2#1058985311yescharacteristic
subgroupG/H
centerC22C22×D36
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC8×D4×C9C2
socleC22×C3C22×D12
hypercenterC8×D4D9
hypocenterC9#3301
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. #10589667C2semidirect
2. #10589654C2semidirect
3. C8×D4×C9C2semidirect
4. #10588796C2semidirect
5. #10588795C2semidirect
6. #10588794C2semidirect
7. C2×#63376C2semidirect
8. #10588528C2semidirect
9. #10588511C2semidirect
10. #10588417C2semidirect
11. #10588416C2semidirect
12. #10588404C2semidirect
13. #10588403C2semidirect
14. #10588379C2semidirect
15. C4×#3664C2semidirect
224. C8×D4D9semidirect
472. C9#3301semidirect

Maximal subgroups

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

subgroupindex
#105896672
#105896542
C8×D4×C92
#105887962
#105887952
#105887942
C2×#633762
#105885282
#105885112
#105884172
#105884162
#105884042
#105884032
#105883792
C4×#36642
#794503