Finite Group Databasebeta

← #11887714

Subgroups — #11887714

Order 1152.

579 conjugacy classes of subgroups.

The subgroup lattice has 537 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10589654C211yesmaximal, characteristic
2#10589643C211yesmaximal, characteristic, complemented
3C8×D4×C9C211yesmaximal, characteristic, complemented
4#10588795C211yesmaximal, characteristic, complemented
5#10588794C211yesmaximal, characteristic, complemented
6#10588788C211yesmaximal, characteristic, complemented
7C2×#63376C211yesmaximal, characteristic, complemented
8#10588529C211yesmaximal, characteristic, complemented
9#10588511C211yesmaximal, characteristic, complemented
10#10588418C211yesmaximal, characteristic, complemented
11#10588415C211yesmaximal, characteristic, complemented
12#10588405C211yesmaximal, characteristic, complemented
13#10588403C211yesmaximal, characteristic, complemented
14#10588379C211yesmaximal, characteristic, complemented
15C4×Dic36C211yesmaximal, characteristic, complemented
16#79449—31nomaximal
17C2×#3697C2211yescharacteristic
18C22×Dic18C2211yescharacteristic
19C22×C8×C9C2211yescharacteristic
20C22×C8×C9C2211yescharacteristic
21C4×D4×C9C2211yescharacteristic
22#63501—21no—
23#63497—21no—
24#63492C2211yescharacteristic
25#63488C2211yescharacteristic
26C2×C4⋊Dic9C2211yescharacteristic
27#63486C2211yescharacteristic
28#63486C2211yescharacteristic
29#63486C2211yescharacteristic
30C2×#3664C2211yescharacteristic
31C2×Dic36C2211yescharacteristic
32C2×Dic36C2211yescharacteristic
33#63458—21no—
34#63451—21no—
35#63447—21no—
36#611⋊C4—21no—
37#63441—21no—
38#63439—21no—
39#63437C2211yescharacteristic
40#63432C2211yescharacteristic
41C4×Dic18C2211yescharacteristic
42C4×Dic18C2211yescharacteristic
43C9×C4⋊C8C2211yescharacteristic
44C9×C22⋊C8C2211yescharacteristic
45C9×C22⋊C8C2211yescharacteristic
46C4×C8×C9C2211yescharacteristic
47#63380C2211yescharacteristic
48#63380C2211yescharacteristic
49#63380C2211yescharacteristic
50#63378C2211yescharacteristic
51#63378C2211yescharacteristic
52#63377C2211yescharacteristic
53#63376C2211yescharacteristic
54#63376C2211yescharacteristic
55#63376C2211yescharacteristic
56#63376C2211yescharacteristic
57#63376C2211yescharacteristic
58#63376C2211yescharacteristic
59#63376C2211yescharacteristic
60#5552—31no—
61#5541—31no—
62C3×C8×D4D311yescharacteristic
63#5116—31no—
64#5114—31no—
65#5113—31no—
66C2×#816—31no—
67#4845—31no—
68#4829—31no—
69#4739—31no—
70#4736—31no—
71#4733—31no—
72#4723—31no—
73C4×Dic12—31no—
74#4697—31no—
75C2×D4×C9D411yescharacteristic
76C22×C4×C9C2311yescharacteristic
77C22×C4×C9C2311yescharacteristic
78C2×#611—21no—
79C2×#611—21no—
80C22×Dic9—21no—
81C22×Dic9—21no—
82#3697—22no—
83#3697—41no—
84C2×D36C2311yescharacteristic
85C2×C4×D9—21no—
86C2×Dic18—22no—
87C2×Dic18—21no—
88C2×Dic18—41no—
89C2×Dic18C2311yescharacteristic
90C2×Dic18C2311yescharacteristic
91C2×Dic18C2311yescharacteristic
92C2×C8×C9—41no—
93C2×C8×C9—41no—
94C2×C8×C9C2311yescharacteristic
95C2×C8×C9C2311yescharacteristic
96C2×C8×C9C2311yescharacteristic
97C2×C8×C9C2311yescharacteristic
98C9×C4⋊C4D411yescharacteristic
99C9×C22⋊C4D411yescharacteristic
100C9×C22⋊C4D411yescharacteristic
101C42×C9C2311yescharacteristic
102#3676—21no—
103#3676—21no—
104#3676—21no—
105#3676—21no—
106(C2×D9)⋊C4—21no—
107(C2×D9)⋊C4—21no—
108(C2×D9)⋊C4—21no—
109C4⋊Dic9—21no—
110C4⋊Dic9C2311yescharacteristic
111C4⋊Dic9C2311yescharacteristic
112C4⋊Dic9C2311yescharacteristic
113C4⋊Dic9C2311yescharacteristic
114Dic9⋊C4—21no—
115Dic9⋊C4—21no—
116Dic9⋊C4—21no—
117Dic9⋊C4—21no—
118Dic9⋊C4—21no—
119Dic9⋊C4—21no—
120Dic9⋊C4—21no—
121C4×Dic9—21no—
122C4×Dic9—21no—
123C4×Dic9—21no—
124#3664—41no—
125Dic36—22no—
126Dic36—41no—
127#3300—91noSylow
128C2×#235—31no—
129C22×Dic6—31no—
130C22×C3×C8C2×D311yescharacteristic
131C22×C3×C8C2×D311yescharacteristic
132C3×C4×D4C2×D311yescharacteristic
133#939—61no—
134#935—61no—
135#930—31no—
136#926—31no—
137C2×C4⋊Dic3—31no—
138#924—31no—
139#924—31no—
140#924—31no—
141C2×Dic12—31no—
142C2×Dic12—31no—
143C2×#204—31no—
144#896—61no—
145#889—61no—
146#885—61no—
147#67⋊C4—61no—
148#879—61no—
149#877—61no—
150#875—31no—
151#870—31no—
152C4×Dic6—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#818—31no—
162#818—31no—
163#817—31no—
164#816—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—
174D4×C9—22no—
175C2×C4×C9—21no—
176C2×C4×C9—21no—
177C2×C4×C9—21no—
178C2×C4×C9—21no—
179C2×C4×C9C2×D411yescharacteristic
180C2×C4×C9C2×D411yescharacteristic
181C2×C4×C9C2×D411yescharacteristic
182C2×C4×C9C2×D411yescharacteristic
183C2×C4×C9C2411yescharacteristic
184#611—42no—
185#611—42no—
186C2×Dic9—21no—
187C2×Dic9—21no—
188C2×Dic9—21no—
189C2×Dic9—21no—
190C2×Dic9—21no—
191C2×Dic9—21no—
192C2×Dic9—21no—
193C2×Dic9—42no—
194C2×Dic9—42no—
195D36—21no—
196D36—21no—
197C4×D9—42no—
198Dic18—21no—
199Dic18—21no—
200Dic18—21no—
201Dic18—21no—
202Dic18—21no—
203Dic18—42no—
204Dic18#4112yes—
205C8×C9—21no—
206C8×C9—21no—
207C8×C9—21no—
208C8×C9—21no—
209#552—91no—
210#548—91no—
211#488—91no—
212#485—91no—
213#480—91no—
214#479—91no—
215#467—91no—
216#465—91no—
217#464—91no—
218#452—91no—
219#451—91no—
220C4×Q16—91no—
221C8×D4D911yescharacteristic, complemented
222#416—91no—
223C2×#103—91no—
224C2×C3×D4D1211yescharacteristic
225C22×C3×C4C22×D311yescharacteristic
226C22×C3×C4C22×D311yescharacteristic
227C2×#67—61no—
228C2×#67—61no—
229C22×Dic3—61no—
230C22×Dic3—61no—
231#235—62no—
232#235—121no—
233C2×D12—31no—
234C2×C4×D3—61no—
235C2×Dic6—31no—
236C2×Dic6—31no—
237C2×Dic6—31no—
238C2×Dic6—62no—
239C2×Dic6—61no—
240C2×Dic6—121no—
241C2×C3×C8—41no—
242C2×C3×C8—41no—
243C2×C3×C8C22×D311yescharacteristic
244C2×C3×C8C22×D311yescharacteristic
245C2×C3×C8C22×D311yescharacteristic
246C2×C3×C8C22×D311yescharacteristic
247C3×C4⋊C4D1211yescharacteristic
248C3×C22⋊C4D1211yescharacteristic
249C3×C22⋊C4D1211yescharacteristic
250C3×C42C22×D311yescharacteristic
251#217—61no—
252#217—61no—
253#217—61no—
254#217—61no—
255(C2×D3)⋊C4—61no—
256(C2×D3)⋊C4—61no—
257(C2×D3)⋊C4—61no—
258C4⋊Dic3—31no—
259C4⋊Dic3—31no—
260C4⋊Dic3—31no—
261C4⋊Dic3—31no—
262C4⋊Dic3—61no—
263Dic3⋊C4—61no—
264Dic3⋊C4—61no—
265Dic3⋊C4—61no—
266Dic3⋊C4—61no—
267Dic3⋊C4—61no—
268Dic3⋊C4—61no—
269Dic3⋊C4—61no—
270C4×Dic3—61no—
271C4×Dic3—61no—
272C4×Dic3—61no—
273Dic12—62no—
274Dic12—121no—
275#204—121no—
276C22×C9—21no—
277C22×C9—21no—
278C22×C9—21no—
279C22×C9—21no—
280C22×C9—21no—
281C22×C9#13512yes—
282C22×C9C22×D411yescharacteristic
283C2×D9—41no—
284C2×D9—41no—
285C2×D9—41no—
286C4×C9—21no—
287C4×C9—21no—
288C4×C9—21no—
289C4×C9—21no—
290C4×C9C2×#4111yescharacteristic
291C4×C9H(5,𝔽2)11yescharacteristic
292Dic9—22no—
293Dic9—41no—
294Dic9—41no—
295Dic9—41no—
296Dic9—41no—
297Dic9—41no—
298Dic9—41no—
299C2×#41—91no—
300C22×Q8—91no—
301C2×Q16—91no—
302C2×Q16—91no—
303C2×SD16—91no—
304C22×C8C2×D911yescharacteristic
305C22×C8C2×D911yescharacteristic
306#126—181no—
307#125—91no—
308#125—181no—
309#124—91no—
310#124—181no—
311#123—181no—
312C22⋊Q8—91no—
313C22⋊Q8—91no—
314C22⋊Q8—91no—
315C22⋊Q8—181no—
316#121—91no—
317#121—181no—
318C4×Q8—91no—
319C4×Q8—91no—
320C4×D4—181no—
321C4×D4C2×D911yescharacteristic
322#117—91no—
323#117—181no—
324C2×C4⋊C4—91no—
325#107—91no—
326#107—91no—
327#106—91no—
328C4⋊C8C2×D911yescharacteristic
329#103—91no—
330#103—91no—
331#103—91no—
332#103—91no—
333#103—91no—
334#103—91no—
335#103—91no—
336#102—91no—
337#102—91no—
338#102—91no—
339C22⋊C8C2×D911yescharacteristic
340C22⋊C8C2×D911yescharacteristic
341C4×C8C2×D911yescharacteristic
342C23×C3C2×D1211yescharacteristic
343C23×C3C2×D1211yescharacteristic
344C22×D3—61no—
345C3×D4—22no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4C2×D1211yescharacteristic
351C2×C3×C4C2×D1211yescharacteristic
352C2×C3×C4C2×D1211yescharacteristic
353C2×C3×C4C2×D1211yescharacteristic
354C2×C3×C4C23×D311yescharacteristic
355#67—122no—
356#67—122no—
357C2×Dic3—61no—
358C2×Dic3—61no—
359C2×Dic3—61no—
360C2×Dic3—61no—
361C2×Dic3—61no—
362C2×Dic3—61no—
363C2×Dic3—61no—
364C2×Dic3—122no—
365C2×Dic3—122no—
366D12—61no—
367D12—61no—
368C4×D3—122no—
369Dic6—32no—
370Dic6—61no—
371Dic6—61no—
372Dic6—61no—
373Dic6—61no—
374Dic6—61no—
375Dic6—122no—
376C3×C8—21no—
377C3×C8—21no—
378C3×C8—21no—
379C3×C8—21no—
380C2×C9—22no—
381C2×C9—41no—
382C2×C9#54611yescharacteristic
383C2×C9C2×#13511yescharacteristic
384C2×C9#57811yescharacteristic
385D9—81no—
386#41—182no—
387#41—361no—
388C2×Q8—91no—
389C2×Q8—91no—
390C2×Q8—91no—
391C2×Q8—182no—
392C2×Q8—181no—
393C2×Q8—361no—
394C2×D4—91no—
395C2×D4—181no—
396C2×D4—181no—
397C2×D4D3611yescharacteristic
398C22×C4—181no—
399C22×C4—181no—
400C22×C4—181no—
401C22×C4C22×D911yescharacteristic
402C22×C4C22×D911yescharacteristic
403Q16—182no—
404Q16—361no—
405SD16—361no—
406C2×C8—41no—
407C2×C8—41no—
408C2×C8C22×D911yescharacteristic
409C2×C8C22×D911yescharacteristic
410C2×C8C22×D911yescharacteristic
411C2×C8C22×D911yescharacteristic
412C4⋊C4—91no—
413C4⋊C4—91no—
414C4⋊C4—91no—
415C4⋊C4—91no—
416C4⋊C4—181no—
417C4⋊C4—181no—
418C4⋊C4—181no—
419C4⋊C4—181no—
420C4⋊C4—181no—
421C4⋊C4—181no—
422C4⋊C4—181no—
423C4⋊C4—181no—
424C4⋊C4D3611yescharacteristic
425C22⋊C4—181no—
426C22⋊C4—181no—
427C22⋊C4—181no—
428C22⋊C4—181no—
429C22⋊C4—181no—
430C22⋊C4—181no—
431C22⋊C4—181no—
432C22⋊C4D3611yescharacteristic
433C22⋊C4D3611yescharacteristic
434C42—181no—
435C42—181no—
436C42—181no—
437C42C22×D911yescharacteristic
438C22×C3—21no—
439C22×C3—21no—
440C22×C3—21no—
441C22×C3—21no—
442C22×C3—21no—
443C22×C3#90412yes—
444C22×C3C22×D1211yescharacteristic
445C2×D3—121no—
446C2×D3—121no—
447C2×D3—121no—
448C3×C4—21no—
449C3×C4—21no—
450C3×C4—21no—
451C3×C4—21no—
452C3×C4#100411yescharacteristic
453C3×C4D3×#4111yescharacteristic
454Dic3—62no—
455Dic3—121no—
456Dic3—121no—
457Dic3—121no—
458Dic3—121no—
459Dic3—121no—
460Dic3—121no—
461C9#330011yescharacteristic, complemented, Sylow
462C23—181no—
463C23C2×D3611yescharacteristic
464C23C2×D3611yescharacteristic
465Q8—92no—
466Q8—181no—
467Q8—181no—
468Q8—181no—
469Q8—181no—
470Q8—181no—
471Q8—362no—
472D4—22no—
473D4—181no—
474D4—181no—
475D4—362no—
476D4—362no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—181no—
482C2×C4—181no—
483C2×C4—181no—
484C2×C4—181no—
485C2×C4—181no—
486C2×C4—181no—
487C2×C4—181no—
488C2×C4—362no—
489C2×C4—362no—
490C2×C4—362no—
491C2×C4C2×D3611yescharacteristic
492C2×C4C2×D3611yescharacteristic
493C2×C4C2×D3611yescharacteristic
494C2×C4C2×D3611yescharacteristic
495C2×C4C23×D911yescharacteristic
496C8—21no—
497C8—21no—
498C8—21no—
499C8—21no—
500C2×C3—22no—
501C2×C3—41no—
502C2×C3#555411yescharacteristic
503C2×C3C2×#90411yescharacteristic
504C2×C3#575311yescharacteristic
505D3—241no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—361no—
512C22—361no—
513C22—361no—
514C22#6346712yes—
515C22C22×D3611yescharacteristic
516C4—21no—
517C4—21no—
518C4—21no—
519C4—21no—
520C4—182no—
521C4—361no—
522C4—361no—
523C4—361no—
524C4—361no—
525C4—361no—
526C4—361no—
527C4#6371011yescharacteristic
528C4#41×D911yescharacteristic
529C3#7944911yescharacteristic
530C2—22no—
531C2—41no—
532C2—721no—
533C2#1058965611yescharacteristic
534C2C2×#6346711yescharacteristic
535C2#1058985511yescharacteristic
subgroupG/H
centerC22C22×D36
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC8×D4×C9C2
socleC22×C3C22×D12
prime radical#10589654C2
hypercenterC8×D4D9
hypocenterC9#3300
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
2. #10589643C2semidirect
3. C8×D4×C9C2semidirect
4. #10588795C2semidirect
5. #10588794C2semidirect
6. #10588788C2semidirect
7. C2×#63376C2semidirect
8. #10588529C2semidirect
9. #10588511C2semidirect
10. #10588418C2semidirect
11. #10588415C2semidirect
12. #10588405C2semidirect
13. #10588403C2semidirect
14. #10588379C2semidirect
15. C4×Dic36C2semidirect
221. C8×D4D9semidirect
461. C9#3300semidirect

Maximal subgroups

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

subgroupindex
#105896542
#105896432
C8×D4×C92
#105887952
#105887942
#105887882
C2×#633762
#105885292
#105885112
#105884182
#105884152
#105884052
#105884032
#105883792
C4×Dic362
#794493