Finite Group Databasebeta

← #11889342

Subgroups — #11889342

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#10596198C211yesmaximal, characteristic
2#10596165C211yesmaximal, characteristic
3C32×#491C211yesmaximal, characteristic, complemented
4#10592789C211yesmaximal, characteristic, complemented
5#10592762C211yesmaximal, characteristic, complemented
6#10592515C211yesmaximal, characteristic, complemented
7#10592514C211yesmaximal, characteristic, complemented
8#10592512C211yesmaximal, characteristic, complemented
9#10592508C211yesmaximal, characteristic, complemented
10#10592508C211yesmaximal, characteristic, complemented
11#10592504C211yesmaximal, characteristic, complemented
12#10592501C211yesmaximal, characteristic, complemented
13C3⋊D3×#103C211yesmaximal, characteristic, complemented
14#10592415C211yesmaximal, characteristic, complemented
15#10592405C211yesmaximal, characteristic
16#81749—34nomaximal
17C2×Q8×C3⋊D3C2211yescharacteristic
18C2×Q8×C3⋊D3C2211yescharacteristic
19C32×C4⋊Q8C2211yescharacteristic
20C32×#125C2211yescharacteristic
21#64155C2211yescharacteristic
22#64155C2211yescharacteristic
23C2×#3756C2211yescharacteristic
24C2×#3756C2211yescharacteristic
25C2×#3746C2211yescharacteristic
26C2×#3743C2211yescharacteristic
27C2×C8×C3⋊D3C2211yescharacteristic
28#64107—21no—
29#64106C2211yescharacteristic
30#64106C2211yescharacteristic
31#64105—21no—
32#64105—21no—
33#64103—21no—
34#64102—21no—
35#64101—21no—
36#64101C2211yescharacteristic
37C4⋊C4×C3⋊D3C2211yescharacteristic
38#64099—21no—
39#64097—21no—
40C4×C4⋊(C3⋊D3)C2211yescharacteristic
41C4×#634C2211yescharacteristic
42C4×#634C2211yescharacteristic
43C32×#103C2211yescharacteristic
44C32×#103C2211yescharacteristic
45C32×#103C2211yescharacteristic
46C32×#103C2211yescharacteristic
47C32×#97C2211yescharacteristic
48#63662C2211yescharacteristic
49#63662C2211yescharacteristic
50#63647C2211yescharacteristic
51#63647C2211yescharacteristic
52#63644C2211yescharacteristic
53#63643C2211yescharacteristic
54#63643C2211yescharacteristic
55#63637C2211yescharacteristic
56#63637C2211yescharacteristic
57#63635C2211yescharacteristic
58#63634C2211yescharacteristic
59C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
60#5727—34no—
61#5694—34no—
62C3×#491D314yescomplemented
63#5090—34no—
64#5063—34no—
65#4816—34no—
66#4815—34no—
67#4813—34no—
68#4809—34no—
69#4809—34no—
70#4805—34no—
71#4802—34no—
72D3×#103—34no—
73#4716—34no—
74#4706—34no—
75C2×C32×Q8C2311yescharacteristic
76C2×C32×Q8C2311yescharacteristic
77Q8×C3⋊D3—22no—
78Q8×C3⋊D3—22no—
79Q8×C3⋊D3—41no—
80Q8×C3⋊D3—41no—
81C2×C4⋊(C3⋊D3)D411yescharacteristic
82C2×C4×C3⋊D3—21no—
83C2×C4×C3⋊D3—21no—
84C2×C4×C3⋊D3—21no—
85C2×C4×C3⋊D3C2311yescharacteristic
86C2×C4×C3⋊D3C2311yescharacteristic
87C2×#634—21no—
88C2×#634—21no—
89C2×#634C2311yescharacteristic
90C2×#634C2311yescharacteristic
91C2×C32×C8C2311yescharacteristic
92C2×C32×C8C2311yescharacteristic
93C32×C4⋊C4—21no—
94C32×C4⋊C4—21no—
95C32×C4⋊C4—21no—
96C32×C4⋊C4—21no—
97C32×C4⋊C4C2311yescharacteristic
98C32×C4⋊C4C2311yescharacteristic
99C32×C42C2311yescharacteristic
100#3756—41no—
101#3756—41no—
102#3752—21no—
103#3752—21no—
104#3752—21no—
105#3752—21no—
106#3752—21no—
107#3752D411yescharacteristic
108#3752D411yescharacteristic
109C4⋊(C3⋊Dic3)—21no—
110C4⋊(C3⋊Dic3)—21no—
111C4⋊(C3⋊Dic3)D411yescharacteristic
112C4⋊(C3⋊Dic3)C2311yescharacteristic
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114#3750—21no—
115#3750—21no—
116#3750—21no—
117#3750—21no—
118#3750—21no—
119C4×C3⋊Dic3—21no—
120C4×C3⋊Dic3—21no—
121C4×C3⋊Dic3—21no—
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124#3746—22no—
125#3743—41no—
126C8×C3⋊D3—41no—
127#3312—91noSylow
128C2×D3×Q8—34no—
129C2×D3×Q8—34no—
130C3×C4⋊Q8C2×D314yes—
131C3×#125C2×D314yes—
132#946—34no—
133#946—34no—
134C2×#216—34no—
135C2×#216—34no—
136C2×Dic12—34no—
137C2×ΓL(1,𝔽25)—34no—
138C2×D3×C8—34no—
139#898—64no—
140#897—34no—
141#897—34no—
142#896—64no—
143#896—64no—
144#894—64no—
145#893—64no—
146#892—34no—
147#892—64no—
148D3×C4⋊C4—34no—
149#890—64no—
150#888—64no—
151C4×D12—34no—
152C4×Dic6—34no—
153C4×Dic6—34no—
154C3×#103C2×D314yes—
155C3×#103C2×D314yes—
156C3×#103C2×D314yes—
157C3×#103C2×D314yes—
158C3×#97C2×D314yes—
159#835—34no—
160#835—34no—
161(C2×D3)⋊C8—34no—
162(C2×D3)⋊C8—34no—
163#817—34no—
164#816—34no—
165#816—34no—
166#810—34no—
167#810—34no—
168#808—34no—
169#807—34no—
170C4⋊(C3⋊C8)—34no—
171C22×C3⋊D3C2×D411yescharacteristic
172C22×C3⋊D3C2×D411yescharacteristic
173C32×Q8—21no—
174C32×Q8—21no—
175C32×Q8—21no—
176C32×Q8—21no—
177C2×C32×C4—21no—
178C2×C32×C4—21no—
179C2×C32×C4—21no—
180C2×C32×C4—21no—
181C2×C32×C4C2×D411yescharacteristic
182C2×C32×C4C2×D411yescharacteristic
183C2×C32×C4C2411yescharacteristic
184C2×C3⋊Dic3—21no—
185C2×C3⋊Dic3—21no—
186C2×C3⋊Dic3—21no—
187C2×C3⋊Dic3—21no—
188C2×C3⋊Dic3C2×D411yescharacteristic
189C2×C3⋊Dic3C2×D411yescharacteristic
190C4⋊(C3⋊D3)—22no—
191C4×C3⋊D3—21no—
192C4×C3⋊D3—21no—
193C4×C3⋊D3—21no—
194C4×C3⋊D3—21no—
195C4×C3⋊D3—42no—
196C4×C3⋊D3—42no—
197C4×C3⋊D3—42no—
198#634—21no—
199#634—21no—
200#634—21no—
201#634—42no—
202#634—42no—
203#634#4112yes—
204C32×C8—21no—
205C32×C8—21no—
206C3⋊(C3⋊C8)—21no—
207C3⋊(C3⋊C8)—21no—
208#552—91no—
209D4×Q8—91no—
210#491C3⋊D311yescharacteristic, complemented
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#435—91no—
221#419—91no—
222C2×#103—91no—
223C2×C3×Q8C22×D314yes—
224C2×C3×Q8C22×D314yes—
225D3×Q8—68no—
226D3×Q8—68no—
227D3×Q8—124no—
228D3×Q8—124no—
229C2×D12—34no—
230C2×C4×D3—34no—
231C2×C4×D3—34no—
232C2×C4×D3—64no—
233C2×C4×D3—64no—
234C2×C4×D3—64no—
235C2×Dic6—34no—
236C2×Dic6—34no—
237C2×Dic6—64no—
238C2×Dic6—64no—
239C2×C3×C8C22×D314yes—
240C2×C3×C8C22×D314yes—
241C3×C4⋊C4—24no—
242C3×C4⋊C4—24no—
243C3×C4⋊C4—24no—
244C3×C4⋊C4—24no—
245C3×C4⋊C4C22×D314yes—
246C3×C4⋊C4C22×D314yes—
247C3×C42C22×D314yes—
248#216—124no—
249#216—124no—
250(C2×D3)⋊C4—34no—
251(C2×D3)⋊C4—34no—
252(C2×D3)⋊C4—64no—
253(C2×D3)⋊C4—64no—
254(C2×D3)⋊C4—64no—
255(C2×D3)⋊C4—64no—
256(C2×D3)⋊C4—64no—
257C4⋊Dic3—34no—
258C4⋊Dic3—34no—
259C4⋊Dic3—34no—
260C4⋊Dic3—64no—
261C4⋊Dic3—64no—
262Dic3⋊C4—64no—
263Dic3⋊C4—64no—
264Dic3⋊C4—64no—
265Dic3⋊C4—64no—
266Dic3⋊C4—64no—
267C4×Dic3—64no—
268C4×Dic3—64no—
269C4×Dic3—64no—
270C2×C3⋊C8—34no—
271C2×C3⋊C8—34no—
272Dic12—68no—
273ΓL(1,𝔽25)—124no—
274D3×C8—124no—
275C22×C32C22×D411yescharacteristic
276C2×C3⋊D3—21no—
277C2×C3⋊D3—21no—
278C2×C3⋊D3—21no—
279C2×C3⋊D3—21no—
280C2×C3⋊D3—21no—
281C2×C3⋊D3#13712yes—
282C32×C4—21no—
283C32×C4—21no—
284C32×C4—41no—
285C32×C4—41no—
286C32×C4—41no—
287C32×C4—41no—
288C32×C4C2×#4111yescharacteristic
289C32×C4H(5,𝔽2)11yescharacteristic
290C3⋊Dic3—22no—
291C3⋊Dic3—21no—
292C3⋊Dic3—21no—
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×M16—91no—
302C22×C8—91no—
303C4⋊Q8—181no—
304C4⋊Q8C2×C3⋊D311yescharacteristic
305#126—181no—
306#125—181no—
307#125C2×C3⋊D311yescharacteristic
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—91no—
318C4×D4—181no—
319#117—91no—
320#117—181no—
321C2×C4⋊C4—91no—
322#107—91no—
323#106—91no—
324#106—91no—
325C4⋊C8—91no—
326#103—91no—
327#103—91no—
328#103—91no—
329#103—91no—
330#103—91no—
331#103—91no—
332#103C2×C3⋊D311yescharacteristic
333#103C2×C3⋊D311yescharacteristic
334#103C2×C3⋊D311yescharacteristic
335#103C2×C3⋊D311yescharacteristic
336C22⋊C8—91no—
337C22⋊C8—91no—
338#97C2×C3⋊D311yescharacteristic
339C22×D3—34no—
340C22×D3—34no—
341C3×Q8—24no—
342C3×Q8—24no—
343C3×Q8—24no—
344C3×Q8—24no—
345C2×C3×C4—24no—
346C2×C3×C4—24no—
347C2×C3×C4—24no—
348C2×C3×C4—24no—
349C2×C3×C4D3×D414yes—
350C2×C3×C4D3×D414yes—
351C2×C3×C4C23×D314yes—
352C2×Dic3—34no—
353C2×Dic3—34no—
354C2×Dic3—64no—
355C2×Dic3—64no—
356C2×Dic3—64no—
357C2×Dic3—64no—
358D12—68no—
359C4×D3—64no—
360C4×D3—64no—
361C4×D3—64no—
362C4×D3—64no—
363C4×D3—128no—
364C4×D3—128no—
365C4×D3—128no—
366Dic6—38no—
367Dic6—64no—
368Dic6—64no—
369Dic6—64no—
370Dic6—128no—
371Dic6—128no—
372C3×C8—24no—
373C3×C8—24no—
374C3⋊C8—64no—
375C3⋊C8—64no—
376C2×C32#54611yescharacteristic
377C2×C32C2×#13711yescharacteristic
378C2×C32#57811yescharacteristic
379C3⋊D3—22no—
380C3⋊D3—41no—
381C2×Q8—91no—
382C2×Q8—91no—
383C2×Q8—181no—
384C2×Q8—181no—
385C2×Q8—182no—
386C2×Q8—182no—
387C2×Q8—361no—
388C2×Q8—361no—
389C2×Q8C22×C3⋊D311yescharacteristic
390C2×Q8C22×C3⋊D311yescharacteristic
391C2×D4—91no—
392C22×C4—91no—
393C22×C4—91no—
394C22×C4—181no—
395C22×C4—181no—
396C22×C4—181no—
397Q16—182no—
398Q16—361no—
399Q16—361no—
400M16—361no—
401C2×C8—91no—
402C2×C8—91no—
403C2×C8—361no—
404C2×C8C22×C3⋊D311yescharacteristic
405C2×C8C22×C3⋊D311yescharacteristic
406C4⋊C4—21no—
407C4⋊C4—21no—
408C4⋊C4—21no—
409C4⋊C4—21no—
410C4⋊C4—91no—
411C4⋊C4—91no—
412C4⋊C4—91no—
413C4⋊C4—181no—
414C4⋊C4—181no—
415C4⋊C4—181no—
416C4⋊C4—181no—
417C4⋊C4—181no—
418C4⋊C4—181no—
419C4⋊C4—181no—
420C4⋊C4C22×C3⋊D311yescharacteristic
421C4⋊C4C22×C3⋊D311yescharacteristic
422C22⋊C4—91no—
423C22⋊C4—91no—
424C22⋊C4—181no—
425C22⋊C4—181no—
426C22⋊C4—181no—
427C22⋊C4—181no—
428C22⋊C4—181no—
429C42—181no—
430C42—181no—
431C42—181no—
432C42C22×C3⋊D311yescharacteristic
433C22×C3C2×D3×D414yes—
434C2×D3—38no—
435C2×D3—64no—
436C2×D3—64no—
437C2×D3—64no—
438C2×D3—64no—
439C2×D3—64no—
440C3×C4—24no—
441C3×C4—24no—
442C3×C4—44no—
443C3×C4—44no—
444C3×C4—44no—
445C3×C4—44no—
446C3×C4D3×#4114yes—
447C3×C4#100914yes—
448Dic3—68no—
449Dic3—64no—
450Dic3—64no—
451Dic3—124no—
452Dic3—124no—
453Dic3—124no—
454C32#331211yescharacteristic, complemented, Sylow
455C23—91no—
456C23—91no—
457Q8—21no—
458Q8—21no—
459Q8—21no—
460Q8—21no—
461Q8—92no—
462Q8—181no—
463Q8—181no—
464Q8—181no—
465Q8—362no—
466Q8—362no—
467D4—182no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—91no—
473C2×C4—91no—
474C2×C4—181no—
475C2×C4—181no—
476C2×C4—181no—
477C2×C4—181no—
478C2×C4—181no—
479C2×C4—181no—
480C2×C4—181no—
481C2×C4—181no—
482C2×C4—362no—
483C2×C4—362no—
484C2×C4—362no—
485C2×C4D4×C3⋊D311yescharacteristic
486C2×C4D4×C3⋊D311yescharacteristic
487C2×C4C23×C3⋊D311yescharacteristic
488C8—21no—
489C8—21no—
490C8—181no—
491C8—181no—
492C2×C3#567614yes—
493C2×C3D3×#13714yes—
494C2×C3#577914yes—
495D3—68no—
496D3—124no—
497C22—92no—
498C22—181no—
499C22—181no—
500C22—181no—
501C22—181no—
502C22—181no—
503C22C2×D4×C3⋊D311yescharacteristic
504C4—21no—
505C4—21no—
506C4—41no—
507C4—41no—
508C4—41no—
509C4—41no—
510C4—181no—
511C4—181no—
512C4—182no—
513C4—361no—
514C4—361no—
515C4—361no—
516C4#41×C3⋊D311yescharacteristic
517C4#6436611yescharacteristic
518C3#8174914yescomplemented
519C2—182no—
520C2—361no—
521C2#1059614711yescharacteristic
522C2C3⋊D3×#13711yescharacteristic
523C2#1059625011yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#491C2
socleC22×C32C22×D4
prime radicalC2×C4⋊(C3⋊D3)D4
hypercenter#491C3⋊D3
hypocenterC32#3312
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
3. C32×#491C2semidirect
4. #10592789C2semidirect
5. #10592762C2semidirect
6. #10592515C2semidirect
7. #10592514C2semidirect
8. #10592512C2semidirect
9. #10592508C2semidirect
10. #10592508C2semidirect
11. #10592504C2semidirect
12. #10592501C2semidirect
13. C3⋊D3×#103C2semidirect
14. #10592415C2semidirect
62. C3×#491D3semidirect
210. #491C3⋊D3semidirect
454. C32#3312semidirect
518. C3#81749semidirect

Maximal subgroups

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

subgroupindex
#105961982
#105961652
C32×#4912
#105927892
#105927622
#105925152
#105925142
#105925122
#105925082
#105925042
#105925012
C3⋊D3×#1032
#105924152
#105924052
#817493