Finite Group Databasebeta

← #11887643

Subgroups — #11887643

Order 1152.

831 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×Q8×D12C211yesmaximal, characteristic
2#10593956C211yesmaximal, characteristic
3C4×#3756C211yesmaximal, characteristic, complemented
4C3×#5021C211yesmaximal, characteristic, complemented
5#10591595C212yesmaximal, complemented
6D3×#835C212yesmaximal, complemented
7#10590579C212yesmaximal, complemented
8#10590440C212yesmaximal, complemented
9#10590388C211yesmaximal, characteristic, complemented
10#10590329C211yesmaximal, characteristic
11#10590290C211yesmaximal, characteristic, complemented
12#83551—31nomaximal
13#81119—31nomaximal
14C2×C3×D3×Q8C2212yes—
15C32×C4×Q8C2211yescharacteristic
16C2×#3756C2211yescharacteristic
17C4×#634C2211yescharacteristic
18C3×#897—22no—
19C3×#897C2212yes—
20C3×C4×D12—21no—
21C3×C4×D12C2211yescharacteristic
22C3×#869—21no—
23C3×#869C2211yescharacteristic
24C3×#869C2211yescharacteristic
25#63898—21no—
26D3×C4⋊Dic3C2212yes—
27#63887—22no—
28#63872—21no—
29#63857C2212yes—
30C2×#3719C2212yes—
31C2×D3×C3⋊C8C2212yes—
32#63662C2211yescharacteristic
33#63637C2211yescharacteristic
34#63634C2211yescharacteristic
35C4×C3⋊(C3⋊C8)C2211yescharacteristic
36C3×#835C2212yes—
37C3×#807C2212yes—
38C3×C4⋊(C3⋊C8)C2211yescharacteristic
39#63566C2212yes—
40#63565C2212yes—
41#63565C2212yes—
42(C2×D3)⋊(C3⋊C8)C2212yes—
43C3×D4×Q8—31no—
44#5730—31no—
45Q8×D12D311yescharacteristic
46#5543—31no—
47C3×#477—31no—
48#5228—32no—
49C2×#835—32no—
50#5093—31no—
51#5090—31no—
52#5079—31no—
53#5051—32no—
54#5044—32no—
55C4×#216—31no—
56C4×#216—31no—
57C4×#216—61no—
58#5021D311yescharacteristic, complemented
59D4×C3⋊C8—31no—
60#4887—32no—
61#4884—32no—
62#4849—31no—
63#4834—31no—
64#4809—32no—
65D3×#103—32no—
66C2×C32×Q8C2311yescharacteristic
67C2×#634C2311yescharacteristic
68C3×D3×Q8—24no—
69C3×D3×Q8—42no—
70C2×C3×D12D411yescharacteristic
71C2×C3×C4×D3—22no—
72C2×C3×C4×D3C2312yes—
73C2×C3×Dic6—22no—
74C2×C3×Dic6—21no—
75C2×C3×Dic6C2312yes—
76C2×D3×Dic3—22no—
77C32×C4⋊C4—21no—
78C32×C4⋊C4C2311yescharacteristic
79C32×C42—21no—
80C32×C42C2311yescharacteristic
81#3756—22no—
82C4⋊(C3⋊Dic3)C2311yescharacteristic
83#3750—21no—
84C4×C3⋊Dic3—21no—
85C2×C3⋊(C3⋊C8)C2311yescharacteristic
86C2×C3⋊(C3⋊C8)C2311yescharacteristic
87C3×(C2×D3)⋊C4—22no—
88C3×(C2×D3)⋊C4D412yes—
89C3×C4⋊Dic3—21no—
90C3×C4⋊Dic3—21no—
91C3×C4⋊Dic3—21no—
92C3×C4⋊Dic3—22no—
93C3×C4⋊Dic3D411yescharacteristic
94C3×C4⋊Dic3C2312yes—
95C2×C3×C3⋊C8C2312yes—
96Dic3⋊Dic3—22no—
97Dic3⋊Dic3—22no—
98(C2×D3)⋊Dic3—22no—
99#3719—42no—
100D3×C3⋊C8—42no—
101#3299—91noSylow
102C22×C3×Q8—32no—
103C2×D3×Q8C2×D312yes—
104C3×C4⋊Q8—31no—
105C3×C4⋊Q8—31no—
106C3×C4⋊Q8—61no—
107C3×C22⋊Q8—32no—
108C3×C22⋊Q8—62no—
109C3×C4×Q8—21no—
110C3×C4×Q8C2×D311yescharacteristic
111C3×C4×Q8C2×D311yescharacteristic
112C3×C4×D4—31no—
113C3×C4×D4—61no—
114#946—62no—
115C2×#216—31no—
116C2×#216—31no—
117C2×#216—32no—
118C2×#216—61no—
119D4×Dic3—61no—
120C2×C4⋊Dic3—32no—
121#924—32no—
122C22×C3⋊C8—32no—
123C2×Dic12—32no—
124C2×D3×C8—32no—
125#897—22no—
126#897—32no—
127#897C2×D312yes—
128#893—61no—
129D3×C4⋊C4—32no—
130#890—61no—
131#890—61no—
132#878—62no—
133C4×D12—21no—
134C4×D12C2×D311yescharacteristic
135#869—21no—
136#869C2×D311yescharacteristic
137#869C2×D311yescharacteristic
138C4×Dic6—31no—
139C4×Dic6—31no—
140C4×Dic6—61no—
141C3×#107—32no—
142C3×C4⋊C8—31no—
143C3×#103—32no—
144#835—31no—
145#835—31no—
146#835—32no—
147#835—32no—
148#835—32no—
149#835—61no—
150#835C2×D312yes—
151#830—32no—
152(C2×D3)⋊C8—32no—
153#816—32no—
154#810—32no—
155#810—32no—
156#810—31no—
157#810—31no—
158#810—61no—
159#807—31no—
160#807—31no—
161#807—61no—
162#807C2×D312yes—
163C4⋊(C3⋊C8)C2×D311yescharacteristic
164C4×C3⋊C8—31no—
165C4×C3⋊C8—31no—
166C4×C3⋊C8—61no—
167C22×C3×D3C2×D412yes—
168C32×Q8—21no—
169C32×Q8#4112yes—
170C2×C32×C4—21no—
171C2×C32×C4—21no—
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2×D411yescharacteristic
174C2×C32×C4C2411yescharacteristic
175C2×C3⋊Dic3—21no—
176C2×C3⋊Dic3—21no—
177#634—21no—
178#634—21no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3C2×D412yes—
182C3×D12Q1614yescomplemented
183C3×C4×D3—22no—
184C3×C4×D3—22no—
185C3×C4×D3—44no—
186C3×Dic6—22no—
187C3×Dic6—22no—
188C3×Dic6—44no—
189C3×Dic6—81no—
190D3×Dic3—82no—
191C3⋊(C3⋊C8)—21no—
192C3⋊(C3⋊C8)—21no—
193C3×C3⋊C8—22no—
194#554—91no—
195D4×Q8—31no—
196#487—91no—
197#484—92no—
198#477—31no—
199#467—92no—
200#462—91no—
201#451—92no—
202C4×Q16—91no—
203C8×D4—91no—
204C2×#103—92no—
205C2×C3×Q8—21no—
206C2×C3×Q8—32no—
207C2×C3×Q8—62no—
208C2×C3×Q8—61no—
209C2×C3×Q8—64no—
210C2×C3×Q8—122no—
211C2×C3×Q8C22×D311yescharacteristic
212C2×C3×Q8C22×D311yescharacteristic
213C2×C3×D4—31no—
214C22×C3×C4—32no—
215C22×C3×C4—62no—
216C22×Dic3—62no—
217D3×Q8—24no—
218D3×Q8—42no—
219C2×D12#6711yescharacteristic
220C2×C4×D3—22no—
221C2×C4×D3—62no—
222C2×C4×D3C22×D312yes—
223C2×Dic6—22no—
224C2×Dic6—21no—
225C2×Dic6—31no—
226C2×Dic6—31no—
227C2×Dic6—61no—
228C2×Dic6C22×D312yes—
229C2×C3×C8—32no—
230C3×C4⋊C4—21no—
231C3×C4⋊C4—21no—
232C3×C4⋊C4—21no—
233C3×C4⋊C4—31no—
234C3×C4⋊C4—32no—
235C3×C4⋊C4—41no—
236C3×C4⋊C4—62no—
237C3×C4⋊C4—61no—
238C3×C4⋊C4—61no—
239C3×C4⋊C4—61no—
240C3×C4⋊C4C22×D311yescharacteristic
241C3×C4⋊C4C22×D311yescharacteristic
242C3×C22⋊C4—32no—
243C3×C22⋊C4—62no—
244C3×C42—21no—
245C3×C42—21no—
246C3×C42—21no—
247C3×C42—41no—
248C3×C42C22×D311yescharacteristic
249C3×C42C22×D311yescharacteristic
250#217—62no—
251#216—64no—
252#216—62no—
253#216—62no—
254#216—122no—
255(C2×D3)⋊C4—22no—
256(C2×D3)⋊C4—62no—
257(C2×D3)⋊C4#6712yes—
258C4⋊Dic3—21no—
259C4⋊Dic3—21no—
260C4⋊Dic3—21no—
261C4⋊Dic3—22no—
262C4⋊Dic3—31no—
263C4⋊Dic3—31no—
264C4⋊Dic3—61no—
265C4⋊Dic3—62no—
266C4⋊Dic3—62no—
267C4⋊Dic3#6711yescharacteristic
268C4⋊Dic3C22×D312yes—
269Dic3⋊C4—62no—
270Dic3⋊C4—61no—
271Dic3⋊C4—61no—
272Dic3⋊C4—62no—
273Dic3⋊C4—121no—
274C4×Dic3—61no—
275C4×Dic3—61no—
276C4×Dic3—121no—
277C2×C3⋊C8—31no—
278C2×C3⋊C8—31no—
279C2×C3⋊C8—31no—
280C2×C3⋊C8—31no—
281C2×C3⋊C8—61no—
282C2×C3⋊C8—61no—
283C2×C3⋊C8—122no—
284C2×C3⋊C8C22×D312yes—
285Dic12—122no—
286D3×C8—122no—
287C22×C32C22×D411yescharacteristic
288C2×C3×D3—22no—
289C2×C3×D3—22no—
290C2×C3×D3C2×Q1614yes—
291C32×C4—22no—
292C32×C4—21no—
293C32×C4—41no—
294C32×C4C2×Q1612yes—
295C32×C4C2×#4111yescharacteristic
296C32×C4H(5,𝔽2)11yescharacteristic
297C3⋊Dic3—41no—
298C3⋊Dic3—41no—
299C3×Dic3—22no—
300C3×Dic3—42no—
301C3×Dic3—42no—
302C22×Q8—32no—
303C2×Q16—92no—
304C2×Q16—91no—
305C22×C8—92no—
306C4⋊Q8—31no—
307C4⋊Q8—31no—
308C4⋊Q8—61no—
309#125—181no—
310C22⋊Q8—32no—
311C22⋊Q8—62no—
312C22⋊Q8—92no—
313C22⋊Q8—182no—
314C4×Q8—91no—
315C4×Q8D3211yescharacteristic
316C4×D4—31no—
317C4×D4—61no—
318C4×D4—181no—
319C2×C4⋊C4—92no—
320#107—32no—
321#107—91no—
322C4⋊C8—31no—
323#103—32no—
324#103—92no—
325#103—92no—
326#103—92no—
327#103—91no—
328#103—91no—
329C22⋊C8—92no—
330C4×C8—91no—
331C23×C3—32no—
332C22×D3C2×#6712yes—
333C3×Q8—21no—
334C3×Q8—21no—
335C3×Q8—22no—
336C3×Q8—41no—
337C3×Q8—62no—
338C3×Q8—62no—
339C3×Q8—124no—
340C3×Q8—241no—
341C3×Q8#23712yes—
342C3×Q8#23912yes—
343C3×D4—34no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—32no—
352C2×C3×C4—41no—
353C2×C3×C4—41no—
354C2×C3×C4—62no—
355C2×C3×C4—62no—
356C2×C3×C4—62no—
357C2×C3×C4—62no—
358C2×C3×C4—124no—
359C2×C3×C4D3×D411yescharacteristic
360C2×C3×C4D3×D411yescharacteristic
361C2×C3×C4C2×#6711yescharacteristic
362C2×C3×C4C2×#6711yescharacteristic
363C2×C3×C4C23×D311yescharacteristic
364C2×C3×C4C23×D311yescharacteristic
365C2×Dic3—22no—
366C2×Dic3—22no—
367C2×Dic3—61no—
368C2×Dic3—61no—
369C2×Dic3—61no—
370C2×Dic3—61no—
371C2×Dic3—121no—
372C2×Dic3—121no—
373C2×Dic3—242no—
374C2×Dic3C2×#6712yes—
375D12#21614yescomplemented
376C4×D3—22no—
377C4×D3—22no—
378C4×D3—44no—
379C4×D3—242no—
380Dic6—22no—
381Dic6—22no—
382Dic6—44no—
383Dic6—62no—
384Dic6—61no—
385Dic6—61no—
386Dic6—61no—
387Dic6—61no—
388Dic6—81no—
389Dic6—121no—
390C3×C8—62no—
391C3⋊C8—22no—
392C3⋊C8—62no—
393C3⋊C8—61no—
394C3⋊C8—61no—
395C3⋊C8—61no—
396C3⋊C8—61no—
397C3⋊C8—121no—
398C2×C32#54611yescharacteristic
399C2×C32C22×Q1611yescharacteristic
400C2×C32#57711yescharacteristic
401C3×D3—24no—
402C2×Q8—32no—
403C2×Q8—62no—
404C2×Q8—61no—
405C2×Q8—64no—
406C2×Q8—91no—
407C2×Q8—122no—
408C2×Q8C2×D3211yescharacteristic
409C2×D4—31no—
410C22×C4—32no—
411C22×C4—62no—
412C22×C4—182no—
413Q16—182no—
414Q16—362no—
415C2×C8—32no—
416C2×C8—91no—
417C2×C8—91no—
418C2×C8—362no—
419C4⋊C4—21no—
420C4⋊C4—31no—
421C4⋊C4—32no—
422C4⋊C4—62no—
423C4⋊C4—61no—
424C4⋊C4—61no—
425C4⋊C4—61no—
426C4⋊C4—91no—
427C4⋊C4—182no—
428C4⋊C4—182no—
429C4⋊C4—181no—
430C4⋊C4C2×D3211yescharacteristic
431C22⋊C4—32no—
432C22⋊C4—62no—
433C22⋊C4—182no—
434C42—21no—
435C42—181no—
436C42C2×D3211yescharacteristic
437C22×C3—21no—
438C22×C3—34no—
439C22×C3—62no—
440C22×C3—62no—
441C22×C3C2×D3×D411yescharacteristic
442C22×C3C22×#6711yescharacteristic
443C2×D3—22no—
444C2×D3—22no—
445C2×D3C2×#21614yes—
446C3×C4—21no—
447C3×C4—22no—
448C3×C4—21no—
449C3×C4—22no—
450C3×C4—21no—
451C3×C4—21no—
452C3×C4—22no—
453C3×C4—41no—
454C3×C4—42no—
455C3×C4—41no—
456C3×C4—41no—
457C3×C4—62no—
458C3×C4—81no—
459C3×C4—122no—
460C3×C4—122no—
461C3×C4D3×Q1612yes—
462C3×C4C2×#21612yes—
463C3×C4C2×#23711yescharacteristic
464C3×C4#100411yescharacteristic
465C3×C4C2×#23911yescharacteristic
466C3×C4#100911yescharacteristic
467Dic3—22no—
468Dic3—42no—
469Dic3—42no—
470Dic3—122no—
471Dic3—121no—
472Dic3—121no—
473Dic3—121no—
474Dic3—121no—
475Dic3—241no—
476C32#329911yescharacteristic, complemented, Sylow
477C23—32no—
478Q8—21no—
479Q8—62no—
480Q8—62no—
481Q8—124no—
482Q8—181no—
483Q8—181no—
484Q8—241no—
485Q8#379612yes—
486D4—34no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—32no—
490C2×C4—62no—
491C2×C4—62no—
492C2×C4—62no—
493C2×C4—62no—
494C2×C4—124no—
495C2×C4—181no—
496C2×C4—181no—
497C2×C4—722no—
498C2×C4D3×#6711yescharacteristic
499C2×C4D3×#6711yescharacteristic
500C2×C4C22×D3211yescharacteristic
501C8—62no—
502C8—181no—
503C8—181no—
504C2×C3—21no—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—64no—
508C2×C3#563011yescharacteristic
509C2×C3C2×D3×Q1611yescharacteristic
510C2×C3#577511yescharacteristic
511C2×C3#580611yescharacteristic
512C2×C3C22×#21611yescharacteristic
513C2×C3#583711yescharacteristic
514D3—24no—
515C22—34no—
516C22—62no—
517C22—62no—
518C22C2×D3×#6711yescharacteristic
519C4—22no—
520C4—21no—
521C4—41no—
522C4—62no—
523C4—122no—
524C4—122no—
525C4—361no—
526C4—361no—
527C4D3×#21612yes—
528C4C2×#379611yescharacteristic
529C4#6430711yescharacteristic
530C3—21no—
531C3#8111911yescharacteristic, complemented
532C3#8355111yescharacteristic, complemented
533C2—64no—
534C2#1059488911yescharacteristic
535C2C2×D3×#21611yescharacteristic
536C2#1059545511yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalC2×C3×D12D4
hypercenterC4×Q8D32
hypocenterC32#3299
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
3. C4×#3756C2semidirect
4. C3×#5021C2semidirect
5. #10591595C2semidirect
6. D3×#835C2semidirect
7. #10590579C2semidirect
8. #10590440C2semidirect
9. #10590388C2semidirect
11. #10590290C2semidirect
58. #5021D3semidirect
182. C3×D12Q16semidirect
375. D12#216semidirect
476. C32#3299semidirect
531. C3#81119semidirect
532. C3#83551semidirect

Maximal subgroups

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

subgroupindex
C3×Q8×D122
#105939562
C4×#37562
C3×#50212
#105915952
D3×#8352
#105905792
#105904402
#105903882
#105903292
#105902902
#835513
#811193