Finite Group Databasebeta

← #11889351

Subgroups — #11889351

Order 1152.

1128 conjugacy classes of subgroups.

The subgroup lattice has 525 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596012C211yesmaximal, characteristic
2D4×#634C211yesmaximal, characteristic
3C32×#435C211yesmaximal, characteristic
4#10592836C211yesmaximal, characteristic, complemented
5#10592819C211yesmaximal, characteristic, complemented
6#10592815C211yesmaximal, characteristic, complemented
7C2×#63643C211yesmaximal, characteristic, complemented
8#10592548C211yesmaximal, characteristic, complemented
9#10592528C211yesmaximal, characteristic, complemented
10#10592438C211yesmaximal, characteristic, complemented
11#10592438C211yesmaximal, characteristic, complemented
12#10592422C211yesmaximal, characteristic, complemented
13#10592420C211yesmaximal, characteristic, complemented
14#10592415C211yesmaximal, characteristic, complemented
15#10592402C211yesmaximal, characteristic, complemented
16#79511—34nomaximal
17C22×#634C2211yescharacteristic
18C22×#634C2211yescharacteristic
19C2×C32×M16C2211yescharacteristic
20C22×C32×C8C2211yescharacteristic
21C32×C4×D4C2211yescharacteristic
22#64144—21no—
23D4×C3⋊Dic3—21no—
24#64135C2211yescharacteristic
25C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
26#64133C2211yescharacteristic
27#64133C2211yescharacteristic
28#64133C2211yescharacteristic
29#64133C2211yescharacteristic
30C2×#3746C2211yescharacteristic
31C2×#3746C2211yescharacteristic
32C2×#3746C2211yescharacteristic
33#64098—21no—
34#64097—21no—
35#64088—21no—
36#64087—21no—
37#64087—21no—
38#64086—21no—
39#64079C2211yescharacteristic
40#64078C2211yescharacteristic
41C4×#634C2211yescharacteristic
42C4×#634C2211yescharacteristic
43C32×C4⋊C8C2211yescharacteristic
44C32×C22⋊C8C2211yescharacteristic
45C32×C22⋊C8C2211yescharacteristic
46C32×#97C2211yescharacteristic
47#63645C2211yescharacteristic
48#63644C2211yescharacteristic
49#63644C2211yescharacteristic
50#63643C2211yescharacteristic
51#63643C2211yescharacteristic
52#63643C2211yescharacteristic
53#63643C2211yescharacteristic
54#63643C2211yescharacteristic
55#63643C2211yescharacteristic
56#63643C2211yescharacteristic
57#63643C2211yescharacteristic
58#63643C2211yescharacteristic
59#63643C2211yescharacteristic
60#5541—34no—
61D4×Dic6—34no—
62C3×#435D314yes—
63#5137—34no—
64#5120—34no—
65#5116—34no—
66C2×#816—34no—
67#4849—34no—
68#4829—34no—
69#4739—34no—
70#4739—34no—
71#4723—34no—
72#4721—34no—
73#4716—34no—
74#4703—34no—
75C2×C32×D4D411yescharacteristic
76C22×C32×C4C2311yescharacteristic
77C22×C32×C4C2311yescharacteristic
78C22×C3⋊Dic3—21no—
79C22×C3⋊Dic3—21no—
80C22×C3⋊Dic3—21no—
81C2×#634—22no—
82C2×#634—22no—
83C2×#634—21no—
84C2×#634—21no—
85C2×#634—41no—
86C2×#634—41no—
87C2×#634C2311yescharacteristic
88C2×#634C2311yescharacteristic
89C2×#634C2311yescharacteristic
90C2×#634C2311yescharacteristic
91C32×M16—41no—
92C2×C32×C8—41no—
93C2×C32×C8C2311yescharacteristic
94C2×C32×C8C2311yescharacteristic
95C2×C32×C8C2311yescharacteristic
96C2×C32×C8C2311yescharacteristic
97C32×C4⋊C4D411yescharacteristic
98C32×C22⋊C4D411yescharacteristic
99C32×C22⋊C4D411yescharacteristic
100C32×C42C2311yescharacteristic
101#3757—21no—
102#3757—21no—
103#3757—21no—
104#3757—21no—
105#3757—21no—
106C4⋊(C3⋊Dic3)—21no—
107C4⋊(C3⋊Dic3)—21no—
108C4⋊(C3⋊Dic3)—21no—
109C4⋊(C3⋊Dic3)C2311yescharacteristic
110C4⋊(C3⋊Dic3)C2311yescharacteristic
111C4⋊(C3⋊Dic3)C2311yescharacteristic
112C4⋊(C3⋊Dic3)C2311yescharacteristic
113#3750—21no—
114#3750—21no—
115#3750—21no—
116#3750—21no—
117#3750—21no—
118#3750—21no—
119#3750—21no—
120#3750—21no—
121C4×C3⋊Dic3—21no—
122C4×C3⋊Dic3—21no—
123C4×C3⋊Dic3—21no—
124#3746—22no—
125#3746—41no—
126#3746—41no—
127#3312—91noSylow
128C22×Dic6—34no—
129C22×Dic6—34no—
130C2×C3×M16C2×D314yes—
131C22×C3×C8C2×D314yes—
132C3×C4×D4C2×D314yes—
133#935—64no—
134D4×Dic3—64no—
135#926—34no—
136C2×C4⋊Dic3—34no—
137#924—34no—
138#924—34no—
139#924—34no—
140#924—34no—
141C2×Dic12—34no—
142C2×Dic12—34no—
143C2×Dic12—34no—
144#889—64no—
145#888—64no—
146#879—64no—
147#878—64no—
148#878—64no—
149#877—64no—
150#870—34no—
151#869—34no—
152C4×Dic6—34no—
153C4×Dic6—34no—
154C3×C4⋊C8C2×D314yes—
155C3×C22⋊C8C2×D314yes—
156C3×C22⋊C8C2×D314yes—
157C3×#97C2×D314yes—
158#818—34no—
159#817—34no—
160#817—34no—
161#816—34no—
162#816—34no—
163#816—34no—
164#816—34no—
165#816—34no—
166#816—34no—
167#816—34no—
168#816—34no—
169#816—34no—
170#816—34no—
171C23×C32C2×D411yescharacteristic
172C23×C32C2×D411yescharacteristic
173C32×D4—22no—
174C2×C32×C4—21no—
175C2×C32×C4—21no—
176C2×C32×C4—21no—
177C2×C32×C4—21no—
178C2×C32×C4C2×D411yescharacteristic
179C2×C32×C4C2×D411yescharacteristic
180C2×C32×C4C2×D411yescharacteristic
181C2×C32×C4C2×D411yescharacteristic
182C2×C32×C4C2411yescharacteristic
183C2×C3⋊Dic3—21no—
184C2×C3⋊Dic3—21no—
185C2×C3⋊Dic3—21no—
186C2×C3⋊Dic3—21no—
187C2×C3⋊Dic3—21no—
188C2×C3⋊Dic3—21no—
189C2×C3⋊Dic3—21no—
190C2×C3⋊Dic3—21no—
191C2×C3⋊Dic3—42no—
192C2×C3⋊Dic3—42no—
193C2×C3⋊Dic3—42no—
194#634—21no—
195#634—21no—
196#634—21no—
197#634—21no—
198#634—21no—
199#634—21no—
200#634—21no—
201#634—42no—
202#634—42no—
203#634#4112yes—
204C32×C8—21no—
205C32×C8—21no—
206C32×C8—21no—
207C32×C8—21no—
208#552—91no—
209D4×Q8—91no—
210#491—91no—
211#485—91no—
212#483—91no—
213#479—91no—
214#470—91no—
215#467—91no—
216#462—91no—
217#451—91no—
218#451—91no—
219#441—91no—
220#435C3⋊D311yescharacteristic
221#419—91no—
222C2×#103—91no—
223C2×C3×D4D1214yes—
224C22×C3×C4C22×D314yes—
225C22×C3×C4C22×D314yes—
226C22×Dic3—64no—
227C22×Dic3—64no—
228C22×Dic3—64no—
229C2×Dic6—34no—
230C2×Dic6—34no—
231C2×Dic6—34no—
232C2×Dic6—34no—
233C2×Dic6—68no—
234C2×Dic6—68no—
235C2×Dic6—64no—
236C2×Dic6—64no—
237C2×Dic6—124no—
238C2×Dic6—124no—
239C3×M16—44no—
240C2×C3×C8—44no—
241C2×C3×C8C22×D314yes—
242C2×C3×C8C22×D314yes—
243C2×C3×C8C22×D314yes—
244C2×C3×C8C22×D314yes—
245C3×C4⋊C4D1214yes—
246C3×C22⋊C4D1214yes—
247C3×C22⋊C4D1214yes—
248C3×C42C22×D314yes—
249#217—64no—
250#217—64no—
251#217—64no—
252#217—64no—
253#217—64no—
254C4⋊Dic3—34no—
255C4⋊Dic3—34no—
256C4⋊Dic3—34no—
257C4⋊Dic3—34no—
258C4⋊Dic3—64no—
259C4⋊Dic3—64no—
260C4⋊Dic3—64no—
261Dic3⋊C4—64no—
262Dic3⋊C4—64no—
263Dic3⋊C4—64no—
264Dic3⋊C4—64no—
265Dic3⋊C4—64no—
266Dic3⋊C4—64no—
267Dic3⋊C4—64no—
268Dic3⋊C4—64no—
269C4×Dic3—64no—
270C4×Dic3—64no—
271C4×Dic3—64no—
272Dic12—68no—
273Dic12—124no—
274Dic12—124no—
275C22×C32—21no—
276C22×C32—21no—
277C22×C32—21no—
278C22×C32—21no—
279C22×C32—21no—
280C22×C32#13712yes—
281C22×C32C22×D411yescharacteristic
282C32×C4—21no—
283C32×C4—21no—
284C32×C4—21no—
285C32×C4—21no—
286C32×C4C2×#4111yescharacteristic
287C32×C4H(5,𝔽2)11yescharacteristic
288C3⋊Dic3—22no—
289C3⋊Dic3—41no—
290C3⋊Dic3—41no—
291C3⋊Dic3—41no—
292C3⋊Dic3—41no—
293C3⋊Dic3—41no—
294C3⋊Dic3—41no—
295C3⋊Dic3—41no—
296C22×Q8—91no—
297C22×Q8—91no—
298C2×Q16—91no—
299C2×Q16—91no—
300C2×Q16—91no—
301C2×M16C2×C3⋊D311yescharacteristic
302C22×C8C2×C3⋊D311yescharacteristic
303C4⋊Q8—91no—
304C4⋊Q8—181no—
305#126—181no—
306#125—91no—
307#125—181no—
308#123—181no—
309C22⋊Q8—91no—
310C22⋊Q8—91no—
311C22⋊Q8—91no—
312C22⋊Q8—91no—
313C22⋊Q8—181no—
314C22⋊Q8—181no—
315C4×Q8—91no—
316C4×Q8—91no—
317C4×D4—181no—
318C4×D4C2×C3⋊D311yescharacteristic
319#117—91no—
320#117—181no—
321C2×C4⋊C4—91no—
322#107—91no—
323#106—91no—
324#106—91no—
325C4⋊C8C2×C3⋊D311yescharacteristic
326#103—91no—
327#103—91no—
328#103—91no—
329#103—91no—
330#103—91no—
331#103—91no—
332#103—91no—
333#103—91no—
334#103—91no—
335#103—91no—
336C22⋊C8C2×C3⋊D311yescharacteristic
337C22⋊C8C2×C3⋊D311yescharacteristic
338#97C2×C3⋊D311yescharacteristic
339C23×C3C2×D1214yes—
340C23×C3C2×D1214yes—
341C3×D4—28no—
342C2×C3×C4—24no—
343C2×C3×C4—24no—
344C2×C3×C4—24no—
345C2×C3×C4—24no—
346C2×C3×C4C2×D1214yes—
347C2×C3×C4C2×D1214yes—
348C2×C3×C4C2×D1214yes—
349C2×C3×C4C2×D1214yes—
350C2×C3×C4C23×D314yes—
351C2×Dic3—64no—
352C2×Dic3—64no—
353C2×Dic3—64no—
354C2×Dic3—64no—
355C2×Dic3—64no—
356C2×Dic3—64no—
357C2×Dic3—64no—
358C2×Dic3—64no—
359C2×Dic3—128no—
360C2×Dic3—128no—
361C2×Dic3—128no—
362Dic6—38no—
363Dic6—64no—
364Dic6—64no—
365Dic6—64no—
366Dic6—64no—
367Dic6—64no—
368Dic6—64no—
369Dic6—64no—
370Dic6—128no—
371Dic6—128no—
372C3×C8—24no—
373C3×C8—24no—
374C3×C8—24no—
375C3×C8—24no—
376C2×C32—22no—
377C2×C32—41no—
378C2×C32#54611yescharacteristic
379C2×C32C2×#13711yescharacteristic
380C2×C32#57811yescharacteristic
381C2×Q8—91no—
382C2×Q8—91no—
383C2×Q8—91no—
384C2×Q8—91no—
385C2×Q8—182no—
386C2×Q8—182no—
387C2×Q8—181no—
388C2×Q8—181no—
389C2×Q8—361no—
390C2×Q8—361no—
391C2×D4C4⋊(C3⋊D3)11yescharacteristic
392C22×C4—181no—
393C22×C4—181no—
394C22×C4—181no—
395C22×C4C22×C3⋊D311yescharacteristic
396C22×C4C22×C3⋊D311yescharacteristic
397Q16—182no—
398Q16—361no—
399Q16—361no—
400M16—41no—
401C2×C8—41no—
402C2×C8C22×C3⋊D311yescharacteristic
403C2×C8C22×C3⋊D311yescharacteristic
404C2×C8C22×C3⋊D311yescharacteristic
405C2×C8C22×C3⋊D311yescharacteristic
406C4⋊C4—91no—
407C4⋊C4—91no—
408C4⋊C4—91no—
409C4⋊C4—91no—
410C4⋊C4—181no—
411C4⋊C4—181no—
412C4⋊C4—181no—
413C4⋊C4—181no—
414C4⋊C4—181no—
415C4⋊C4—181no—
416C4⋊C4—181no—
417C4⋊C4—181no—
418C4⋊C4—181no—
419C4⋊C4—181no—
420C4⋊C4—181no—
421C4⋊C4C4⋊(C3⋊D3)11yescharacteristic
422C22⋊C4—181no—
423C22⋊C4—181no—
424C22⋊C4—181no—
425C22⋊C4—181no—
426C22⋊C4—181no—
427C22⋊C4C4⋊(C3⋊D3)11yescharacteristic
428C22⋊C4C4⋊(C3⋊D3)11yescharacteristic
429C42—181no—
430C42—181no—
431C42—181no—
432C42C22×C3⋊D311yescharacteristic
433C22×C3—24no—
434C22×C3—24no—
435C22×C3—24no—
436C22×C3—24no—
437C22×C3—24no—
438C22×C3#90918yes—
439C22×C3C22×D1214yes—
440C3×C4—24no—
441C3×C4—24no—
442C3×C4—24no—
443C3×C4—24no—
444C3×C4#100414yes—
445C3×C4D3×#4114yes—
446Dic3—68no—
447Dic3—124no—
448Dic3—124no—
449Dic3—124no—
450Dic3—124no—
451Dic3—124no—
452Dic3—124no—
453Dic3—124no—
454C32#331211yescharacteristic, complemented, Sylow
455C23C2×C4⋊(C3⋊D3)11yescharacteristic
456C23C2×C4⋊(C3⋊D3)11yescharacteristic
457Q8—92no—
458Q8—181no—
459Q8—181no—
460Q8—181no—
461Q8—181no—
462Q8—181no—
463Q8—181no—
464Q8—181no—
465Q8—362no—
466Q8—362no—
467D4—22no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—181no—
473C2×C4—181no—
474C2×C4—181no—
475C2×C4—181no—
476C2×C4—181no—
477C2×C4—181no—
478C2×C4—181no—
479C2×C4—181no—
480C2×C4—362no—
481C2×C4—362no—
482C2×C4—362no—
483C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
484C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
485C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
486C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
487C2×C4C23×C3⋊D311yescharacteristic
488C8—21no—
489C8—21no—
490C8—21no—
491C8—21no—
492C2×C3—28no—
493C2×C3—44no—
494C2×C3#555414yes—
495C2×C3C2×#90914yes—
496C2×C3#575314yes—
497C22—21no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22#6411812yes—
503C22C22×C4⋊(C3⋊D3)11yescharacteristic
504C4—21no—
505C4—21no—
506C4—21no—
507C4—21no—
508C4—182no—
509C4—361no—
510C4—361no—
511C4—361no—
512C4—361no—
513C4—361no—
514C4—361no—
515C4—361no—
516C4#6436111yescharacteristic
517C4#41×C3⋊D311yescharacteristic
518C3#7951114yescomplemented
519C2—22no—
520C2—41no—
521C2#1059602511yescharacteristic
522C2C2×#6411811yescharacteristic
523C2#1059622411yescharacteristic
subgroupG/H
centerC22C22×C4⋊(C3⋊D3)
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#435C2
socleC22×C32C22×D4
prime radicalC2×C32×D4D4
hypercenter#435C3⋊D3
hypocenterC32#3312
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
4. #10592836C2semidirect
5. #10592819C2semidirect
6. #10592815C2semidirect
7. C2×#63643C2semidirect
8. #10592548C2semidirect
9. #10592528C2semidirect
10. #10592438C2semidirect
11. #10592438C2semidirect
12. #10592422C2semidirect
13. #10592420C2semidirect
14. #10592415C2semidirect
15. #10592402C2semidirect
454. C32#3312semidirect
518. C3#79511semidirect

Maximal subgroups

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

subgroupindex
#105960122
D4×#6342
C32×#4352
#105928362
#105928192
#105928152
C2×#636432
#105925482
#105925282
#105924382
#105924222
#105924202
#105924152
#105924022
#795113