Finite Group Databasebeta

← #11895673

Subgroups — #11895673

Order 1152.

751 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593951C211yesmaximal, characteristic
2#10593864C211yesmaximal, characteristic, complemented
3C4×#3746C211yesmaximal, characteristic, complemented
4C3×#4694C211yesmaximal, characteristic
5C3×C8×Dic6C211yesmaximal, characteristic, complemented
6#10590863C212yesmaximal, complemented
7#10590861C212yesmaximal, complemented
8#10590767C212yesmaximal, complemented
9#10590744C212yesmaximal, complemented
10#10590377C211yesmaximal, characteristic
11#10590307C211yesmaximal, characteristic, complemented
12#81589—31nomaximal
13#79935—31nomaximal
14C2×#3746C2211yescharacteristic
15C4×#634C2211yescharacteristic
16C4×#634C2211yescharacteristic
17C3×#874C2211yescharacteristic
18C3×#869C2211yescharacteristic
19C3×C4×Dic6C2211yescharacteristic
20#63898—21no—
21Dic3×D12C2212yes—
22#63884—22no—
23#63873—21no—
24#63869C2212yes—
25#63863—21no—
26#63860C2212yes—
27#63847—22no—
28#63844C2212yes—
29#63843—21no—
30C2×#3716C2212yes—
31C32×C4×C8C2211yescharacteristic
32#63645C2211yescharacteristic
33#63643C2211yescharacteristic
34#63643C2211yescharacteristic
35C3×#821C2212yes—
36C3×#821C2212yes—
37C3×Dic3⋊C8C2212yes—
38C3×C8×Dic3C2212yes—
39C3×C4⋊(C3⋊C8)C2211yescharacteristic
40#63573C2212yes—
41#63567C2212yes—
42#63563C2212yes—
43#5721—31no—
44#5713—31no—
45#5585—31no—
46#5567—31no—
47C3×#486—31no—
48C3×C8×Q8—31no—
49#5094—31no—
50#5075—31no—
51#4851—31no—
52#4848—31no—
53#4847—32no—
54#4845—32no—
55#4768—32no—
56#4767—32no—
57#4766—32no—
58#4758—32no—
59C4×Dic12—31no—
60C4×Dic12—31no—
61C4×Dic12—61no—
62#4697—32no—
63#4694D311yescharacteristic
64C4×#204—32no—
65C8×Dic6D311yescharacteristic, complemented
66C2×#634C2311yescharacteristic
67C2×#634C2311yescharacteristic
68C2×C3×D12—21no—
69C2×C3×D12—21no—
70C2×C3×D12C2312yes—
71C2×C3×Dic6—21no—
72C2×C3×Dic6D411yescharacteristic
73C2×D3×Dic3—22no—
74C2×C32×C8C2311yescharacteristic
75C2×C32×C8C2311yescharacteristic
76C32×C42C2311yescharacteristic
77C4⋊(C3⋊Dic3)C2311yescharacteristic
78C4⋊(C3⋊Dic3)C2311yescharacteristic
79#3750—21no—
80#3750—21no—
81C4×C3⋊Dic3—21no—
82C4×C3⋊Dic3—21no—
83#3746—22no—
84C3×C4⋊Dic3—21no—
85C3×C4⋊Dic3D411yescharacteristic
86C3×C4⋊Dic3C2312yes—
87C3×Dic3⋊C4D412yes—
88C3×C4×Dic3C2312yes—
89C2×C3×C3⋊C8C2312yes—
90#3724—22no—
91#3724—22no—
92Dic3⋊Dic3—22no—
93(C2×D3)⋊Dic3—22no—
94(C2×D3)⋊Dic3—22no—
95(C2×D3)⋊Dic3—22no—
96Dic32—22no—
97#3716—24no—
98#3365—91noSylow
99C3×C4⋊Q8—31no—
100C3×#127—31no—
101C3×C4×Q8—31no—
102#947—61no—
103Q8×Dic3—61no—
104#944—61no—
105#944—61no—
106#936—32no—
107#936—61no—
108#935—62no—
109D4×Dic3—32no—
110D4×Dic3—61no—
111C2×#214—32no—
112C2×Dic12—31no—
113C2×Dic12—31no—
114C2×Dic12—61no—
115C2×#204—32no—
116#894—62no—
117#893—61no—
118#890—32no—
119#889—62no—
120#889—62no—
121#887—32no—
122#887—61no—
123#875—32no—
124#874C2×D311yescharacteristic
125C4×D12—32no—
126#870—32no—
127#869C2×D311yescharacteristic
128C4×Dic6—31no—
129C4×Dic6—31no—
130C4×Dic6—31no—
131C4×Dic6—31no—
132C4×Dic6—32no—
133C4×Dic6—61no—
134C4×Dic6—61no—
135C4×Dic6C2×D311yescharacteristic
136C3×C4⋊C8—32no—
137C3×C4⋊C8—31no—
138C3×#102—32no—
139C3×#102—32no—
140C3×C4×C8—21no—
141C3×C4×C8—32no—
142C3×C4×C8C2×D311yescharacteristic
143C3×C4×C8C2×D311yescharacteristic
144#832—32no—
145#821—32no—
146#821C2×D312yes—
147#821C2×D312yes—
148#818—31no—
149#818—31no—
150#818—61no—
151#817—32no—
152#816—31no—
153#816—31no—
154#816—31no—
155#816—31no—
156#816—32no—
157#816—61no—
158#816—61no—
159Dic3⋊C8C2×D312yes—
160C8×Dic3C2×D312yes—
161#810—32no—
162#808—32no—
163C4⋊(C3⋊C8)C2×D311yescharacteristic
164C22×C3×D3—22no—
165C2×C32×C4C2×D411yescharacteristic
166C2×C32×C4C2×D411yescharacteristic
167C2×C32×C4C2411yescharacteristic
168C2×C3⋊Dic3—21no—
169C2×C3⋊Dic3—21no—
170C2×C3⋊Dic3—21no—
171C2×C3⋊Dic3—21no—
172#634—21no—
173#634—21no—
174#634—21no—
175#634#4112yes—
176C2×C3×Dic3—22no—
177C2×C3×Dic3C2×D412yes—
178C2×C3×Dic3C2×D412yes—
179C3×D12—22no—
180C3×D12—22no—
181C3×D12—42no—
182C3×D12—81no—
183C3×Dic6—22no—
184C3×Dic6—42no—
185D3×Dic3—82no—
186C32×C8—21no—
187C32×C8—21no—
188C3×C3⋊C8—22no—
189#559—91no—
190#557—91no—
191#488—92no—
192#486—31no—
193#478—92no—
194#475—91no—
195#464—92no—
196#460—91no—
197C8×Q8—31no—
198C4×Q16—91no—
199C4×SD16—92no—
200C2×C3×Q8—31no—
201C2×C3×Q8—61no—
202C2×C3×D4—32no—
203C2×C3×D4—61no—
204C2×C3×D4—61no—
205C22×Dic3—62no—
206C2×D12—21no—
207C2×D12—21no—
208C2×D12C22×D312yes—
209C2×C4×D3—62no—
210C2×Dic6—21no—
211C2×Dic6—31no—
212C2×Dic6—31no—
213C2×Dic6—31no—
214C2×Dic6—31no—
215C2×Dic6—61no—
216C2×Dic6—61no—
217C2×Dic6D1211yescharacteristic
218C2×C3×C8—21no—
219C2×C3×C8—21no—
220C2×C3×C8—32no—
221C2×C3×C8C22×D311yescharacteristic
222C2×C3×C8C22×D311yescharacteristic
223C2×C3×C8C22×D311yescharacteristic
224C2×C3×C8C22×D311yescharacteristic
225C3×C4⋊C4—31no—
226C3×C4⋊C4—32no—
227C3×C4⋊C4—32no—
228C3×C4⋊C4—61no—
229C3×C42—21no—
230C3×C42—32no—
231C3×C42C22×D311yescharacteristic
232C3×C42C22×D311yescharacteristic
233#217—62no—
234#217—62no—
235#217—62no—
236#214—64no—
237(C2×D3)⋊C4—62no—
238(C2×D3)⋊C4—62no—
239(C2×D3)⋊C4—62no—
240C4⋊Dic3—21no—
241C4⋊Dic3—31no—
242C4⋊Dic3—31no—
243C4⋊Dic3—31no—
244C4⋊Dic3—31no—
245C4⋊Dic3—61no—
246C4⋊Dic3—61no—
247C4⋊Dic3—62no—
248C4⋊Dic3D1211yescharacteristic
249C4⋊Dic3C22×D312yes—
250Dic3⋊C4—62no—
251Dic3⋊C4—62no—
252Dic3⋊C4—62no—
253Dic3⋊C4—61no—
254Dic3⋊C4—61no—
255Dic3⋊C4—61no—
256Dic3⋊C4—61no—
257Dic3⋊C4—62no—
258Dic3⋊C4—62no—
259Dic3⋊C4—121no—
260Dic3⋊C4—121no—
261Dic3⋊C4D1212yes—
262C4×Dic3—62no—
263C4×Dic3—61no—
264C4×Dic3—61no—
265C4×Dic3—61no—
266C4×Dic3—61no—
267C4×Dic3—62no—
268C4×Dic3—121no—
269C4×Dic3—121no—
270C4×Dic3C22×D312yes—
271C2×C3⋊C8C22×D312yes—
272Dic12—62no—
273Dic12—62no—
274Dic12—64no—
275#204—64no—
276C22×C32C22×D411yescharacteristic
277C2×C3×D3—42no—
278C2×C3×D3—42no—
279C2×C3×D3—42no—
280C32×C4—21no—
281C32×C4#13512yes—
282C32×C4C2×#4111yescharacteristic
283C32×C42−1+411yescharacteristic
284C3⋊Dic3—22no—
285C3⋊Dic3—41no—
286C3⋊Dic3—41no—
287C3⋊Dic3—41no—
288C3×Dic3—22no—
289C3×Dic3—22no—
290C3×Dic3—42no—
291C2×Q16—91no—
292C2×SD16—92no—
293C4⋊Q8—31no—
294C4⋊Q8—181no—
295#127—31no—
296#125—92no—
297#125—182no—
298#124—92no—
299#124—181no—
300#123—182no—
301C4×Q8—31no—
302C4×Q8—92no—
303C4×Q8—91no—
304C4×Q8—91no—
305C4×Q8—181no—
306C4×D4—92no—
307C4×D4—181no—
308#107—91no—
309#106—92no—
310C4⋊C8—32no—
311C4⋊C8—31no—
312#103—92no—
313#103—91no—
314#103—91no—
315#102—32no—
316#102—32no—
317#102—92no—
318C4×C8—32no—
319C4×C8D3211yescharacteristic
320C23×C3—62no—
321C22×D3—22no—
322C3×Q8—62no—
323C3×Q8—122no—
324C3×D4—62no—
325C3×D4—62no—
326C3×D4—122no—
327C3×D4—241no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—32no—
332C2×C3×C4—32no—
333C2×C3×C4—62no—
334C2×C3×C4C2×D1211yescharacteristic
335C2×C3×C4C2×D1211yescharacteristic
336C2×C3×C4D3×D411yescharacteristic
337C2×C3×C4D3×D411yescharacteristic
338C2×C3×C4C23×D311yescharacteristic
339C2×C3×C4C23×D311yescharacteristic
340C2×Dic3—22no—
341C2×Dic3—61no—
342C2×Dic3—61no—
343C2×Dic3—61no—
344C2×Dic3—61no—
345C2×Dic3—61no—
346C2×Dic3—61no—
347C2×Dic3—61no—
348C2×Dic3—61no—
349C2×Dic3—121no—
350C2×Dic3—121no—
351C2×Dic3—121no—
352C2×Dic3—121no—
353C2×Dic3—242no—
354C2×Dic3C2×D1212yes—
355C2×Dic3C2×D1212yes—
356D12—22no—
357D12—22no—
358D12—42no—
359D12—81no—
360C4×D3—242no—
361Dic6—22no—
362Dic6—32no—
363Dic6—32no—
364Dic6—42no—
365Dic6—62no—
366Dic6—61no—
367Dic6—61no—
368Dic6—62no—
369Dic6—61no—
370Dic6—61no—
371Dic6—61no—
372Dic6—61no—
373Dic6—121no—
374Dic6—121no—
375C3×C8—22no—
376C3×C8—21no—
377C3×C8—21no—
378C3×C8—21no—
379C3×C8—21no—
380C3×C8—41no—
381C3×C8—62no—
382C3⋊C8—22no—
383C2×C32#54811yescharacteristic
384C2×C32C2×#13511yescharacteristic
385C2×C32#57711yescharacteristic
386C3×D3—82no—
387C2×Q8—31no—
388C2×Q8—61no—
389C2×Q8—91no—
390C2×Q8—91no—
391C2×D4—32no—
392C2×D4—61no—
393C2×D4—61no—
394C22×C4—182no—
395Q16—182no—
396SD16—184no—
397C2×C8—32no—
398C2×C8C2×D3211yescharacteristic
399C2×C8C2×D3211yescharacteristic
400C4⋊C4—31no—
401C4⋊C4—32no—
402C4⋊C4—32no—
403C4⋊C4—61no—
404C4⋊C4—91no—
405C4⋊C4—91no—
406C4⋊C4—182no—
407C4⋊C4—182no—
408C4⋊C4—182no—
409C4⋊C4—181no—
410C4⋊C4—181no—
411C22⋊C4—182no—
412C22⋊C4—182no—
413C22⋊C4—182no—
414C42—32no—
415C42—182no—
416C42—181no—
417C42—181no—
418C42C2×D3211yescharacteristic
419C22×C3—21no—
420C22×C3—122no—
421C22×C3—122no—
422C22×C3—122no—
423C22×C3C22×D1211yescharacteristic
424C22×C3C2×D3×D411yescharacteristic
425C2×D3—42no—
426C2×D3—42no—
427C2×D3—42no—
428C3×C4—21no—
429C3×C4—21no—
430C3×C4—21no—
431C3×C4—21no—
432C3×C4—22no—
433C3×C4—41no—
434C3×C4—62no—
435C3×C4—62no—
436C3×C4—122no—
437C3×C4#90412yes—
438C3×C4#91212yes—
439C3×C4#100711yescharacteristic
440C3×C4D3×#4111yescharacteristic
441C3×C4D3×#4111yescharacteristic
442C3×C4#101011yescharacteristic
443Dic3—22no—
444Dic3—22no—
445Dic3—42no—
446Dic3—62no—
447Dic3—62no—
448Dic3—122no—
449Dic3—122no—
450Dic3—121no—
451Dic3—121no—
452Dic3—121no—
453Dic3—121no—
454Dic3—121no—
455Dic3—121no—
456Dic3—241no—
457Dic3—241no—
458C32#336511yescharacteristic, complemented, Sylow
459C23—62no—
460Q8—62no—
461Q8—92no—
462Q8—122no—
463Q8—181no—
464Q8—181no—
465Q8—181no—
466D4—62no—
467D4—62no—
468D4—122no—
469D4—241no—
470C2×C4—32no—
471C2×C4—32no—
472C2×C4—62no—
473C2×C4—181no—
474C2×C4—181no—
475C2×C4—181no—
476C2×C4—181no—
477C2×C4—722no—
478C2×C4D3×D1211yescharacteristic
479C2×C4D3×D1211yescharacteristic
480C2×C4C22×D3211yescharacteristic
481C8—21no—
482C8—21no—
483C8—62no—
484C2×C3—21no—
485C2×C3—21no—
486C2×C3—21no—
487C2×C3—242no—
488C2×C3#557611yescharacteristic
489C2×C3#567711yescharacteristic
490C2×C3C2×#90411yescharacteristic
491C2×C3#575111yescharacteristic
492C2×C3C2×#91211yescharacteristic
493C2×C3#576211yescharacteristic
494D3—82no—
495C22—122no—
496C22—122no—
497C22—122no—
498C22C2×D3×D1211yescharacteristic
499C4—21no—
500C4—62no—
501C4—62no—
502C4—122no—
503C4—182no—
504C4—361no—
505C4—361no—
506C4—361no—
507C4#6380712yes—
508C4#6429711yescharacteristic
509C4#6430611yescharacteristic
510C3—21no—
511C3#7993511yescharacteristic, complemented
512C3#8158911yescharacteristic, complemented
513C2—242no—
514C2#1059390111yescharacteristic
515C2#1059467711yescharacteristic
516C2C2×#6380711yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radicalC3×#874C22
hypercenterC4×C8D32
hypocenterC32#3365
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. #10593864C2semidirect
3. C4×#3746C2semidirect
5. C3×C8×Dic6C2semidirect
6. #10590863C2semidirect
7. #10590861C2semidirect
8. #10590767C2semidirect
9. #10590744C2semidirect
11. #10590307C2semidirect
65. C8×Dic6D3semidirect
458. C32#3365semidirect
511. C3#79935semidirect
512. C3#81589semidirect

Maximal subgroups

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

subgroupindex
#105939512
#105938642
C4×#37462
C3×#46942
C3×C8×Dic62
#105908632
#105908612
#105907672
#105907442
#105903772
#105903072
#815893
#799353