Finite Group Databasebeta

← #11887671

Subgroups — #11887671

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
1#10593956C211yesmaximal, characteristic
2#10593904C211yesmaximal, characteristic
3C4×#3746C211yesmaximal, characteristic, complemented
4C3×C8×D12C211yesmaximal, characteristic
5C3×#4681C211yesmaximal, characteristic, complemented
6#10590952C212yesmaximal, complemented
7#10590848C212yesmaximal, complemented
8#10590682C212yesmaximal, complemented
9D3×#816C212yesmaximal, complemented
10#10590388C211yesmaximal, characteristic, complemented
11#10590284C211yesmaximal, characteristic, complemented
12#81613—31nomaximal
13#79448—31nomaximal
14C2×D3×Dic6C2212yes—
15C2×#3746C2211yescharacteristic
16C4×#634C2211yescharacteristic
17C4×#634C2211yescharacteristic
18C2×C3×D3×C8C2212yes—
19C3×C4×D12C2211yescharacteristic
20C3×#869C2211yescharacteristic
21C3×#869C2211yescharacteristic
22#63919—21no—
23#63899—22no—
24#63898—21no—
25#63898—21no—
26D3×C4⋊Dic3C2212yes—
27#63887—22no—
28#63872—21no—
29#63857C2212yes—
30#63856C2212yes—
31C2×#3719C2212yes—
32C32×C4×C8C2211yescharacteristic
33#63645C2211yescharacteristic
34#63643C2211yescharacteristic
35#63643C2211yescharacteristic
36C3×(C2×D3)⋊C8C2212yes—
37C3×#816C2212yes—
38C3×#816C2212yes—
39C3×C4⋊(C3⋊C8)C2211yescharacteristic
40#63575C2212yes—
41#63567C2212yes—
42#63566C2212yes—
43#5730—31no—
44#5727—31no—
45#5543—31no—
46D4×Dic6—31no—
47C3×#487—31no—
48C3×C8×D4—31no—
49#5116—32no—
50C2×#816—32no—
51#5091—31no—
52#5090—31no—
53#4850—31no—
54#4849—31no—
55#4813—32no—
56#4811—32no—
57#4809—32no—
58D3×#103—32no—
59#4739—32no—
60#4722—32no—
61C4×Dic12—31no—
62C4×Dic12—31no—
63C4×Dic12—61no—
64C8×D12D311yescharacteristic
65#4681D311yescharacteristic, complemented
66C2×#634C2311yescharacteristic
67C2×#634C2311yescharacteristic
68C2×C3×D12D411yescharacteristic
69C2×C3×C4×D3C2312yes—
70C2×C3×Dic6—21no—
71C2×C3×Dic6C2312yes—
72C2×#627—22no—
73C2×D3×Dic3—22no—
74C2×D3×Dic3—22no—
75D3×Dic6—24no—
76D3×Dic6—42no—
77C2×C32×C8C2311yescharacteristic
78C2×C32×C8C2311yescharacteristic
79C32×C42C2311yescharacteristic
80C4⋊(C3⋊Dic3)C2311yescharacteristic
81C4⋊(C3⋊Dic3)C2311yescharacteristic
82#3750—21no—
83#3750—21no—
84C4×C3⋊Dic3—21no—
85C4×C3⋊Dic3—21no—
86#3746—22no—
87C3×(C2×D3)⋊C4D412yes—
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3—21no—
90C3×C4⋊Dic3—21no—
91C3×C4⋊Dic3D411yescharacteristic
92C3×C4⋊Dic3C2312yes—
93C2×C3×C3⋊C8C2312yes—
94C3×D3×C8—42no—
95#3724—22no—
96Dic3⋊Dic3—22no—
97Dic3⋊Dic3—22no—
98(C2×D3)⋊Dic3—22no—
99(C2×D3)⋊Dic3—22no—
100#3719—42no—
101#3299—91noSylow
102C2×D3×Q8—32no—
103C22×Dic6—32no—
104C22×C3×C8—32no—
105C3×C4⋊Q8—31no—
106C3×C4⋊Q8—31no—
107C3×C4×D4—31no—
108#946—32no—
109#946—62no—
110C2×#216—32no—
111D4×Dic3—61no—
112D4×Dic3—61no—
113C2×C4⋊Dic3—32no—
114#924—32no—
115#924—32no—
116C2×Dic12—31no—
117C2×Dic12—31no—
118C2×Dic12—32no—
119C2×Dic12—61no—
120C2×D3×C8C2×D312yes—
121#897—32no—
122#896—62no—
123#893—61no—
124#893—61no—
125D3×C4⋊C4—32no—
126#890—61no—
127#890—61no—
128#888—61no—
129#888—61no—
130#878—62no—
131#878—62no—
132C4×D12C2×D311yescharacteristic
133#869C2×D311yescharacteristic
134#869C2×D311yescharacteristic
135C4×Dic6—31no—
136C4×Dic6—31no—
137C4×Dic6—31no—
138C4×Dic6—31no—
139C4×Dic6—61no—
140C4×Dic6—61no—
141C3×C4⋊C8—31no—
142C3×#103—32no—
143C3×#103—32no—
144C3×C22⋊C8—32no—
145C3×C4×C8—21no—
146C3×C4×C8C2×D311yescharacteristic
147C3×C4×C8C2×D311yescharacteristic
148#835—32no—
149(C2×D3)⋊C8C2×D312yes—
150#818—31no—
151#818—31no—
152#818—32no—
153#818—61no—
154#816—32no—
155#816—31no—
156#816—31no—
157#816—31no—
158#816—31no—
159#816—32no—
160#816—61no—
161#816—61no—
162#816C2×D312yes—
163#816C2×D312yes—
164#810—32no—
165#807—32no—
166C4⋊(C3⋊C8)C2×D311yescharacteristic
167C22×C3×D3C2×D412yes—
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2411yescharacteristic
171C2×C3⋊Dic3—21no—
172C2×C3⋊Dic3—21no—
173C2×C3⋊Dic3—21no—
174C2×C3⋊Dic3—21no—
175#634—21no—
176#634—21no—
177#634—21no—
178#634#4112yes—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3C2×D412yes—
182C3×D12Q1614yescomplemented
183C3×C4×D3—22no—
184C3×C4×D3—22no—
185C3×Dic6—22no—
186C3×Dic6—22no—
187C3×Dic6—81no—
188#627—44no—
189D3×Dic3—44no—
190D3×Dic3—82no—
191C32×C8—21no—
192C32×C8—21no—
193C3×C3⋊C8—22no—
194#554—91no—
195D4×Q8—91no—
196#487—31no—
197#484—92no—
198#477—91no—
199#467—92no—
200#462—91no—
201#451—92no—
202C4×Q16—91no—
203C8×D4—31no—
204C2×#103—92no—
205C2×C3×Q8—32no—
206C2×C3×Q8—61no—
207C2×C3×D4—31no—
208C22×C3×C4—32no—
209C22×Dic3—62no—
210C22×Dic3—62no—
211D3×Q8—64no—
212D3×Q8—122no—
213C2×D12D1211yescharacteristic
214C2×C4×D3—62no—
215C2×C4×D3—62no—
216C2×C4×D3C22×D312yes—
217C2×Dic6—21no—
218C2×Dic6—31no—
219C2×Dic6—31no—
220C2×Dic6—31no—
221C2×Dic6—31no—
222C2×Dic6—61no—
223C2×Dic6—61no—
224C2×Dic6—64no—
225C2×Dic6—62no—
226C2×Dic6—62no—
227C2×Dic6—122no—
228C2×Dic6C22×D312yes—
229C2×C3×C8—21no—
230C2×C3×C8—21no—
231C2×C3×C8—32no—
232C2×C3×C8—122no—
233C2×C3×C8C22×D311yescharacteristic
234C2×C3×C8C22×D311yescharacteristic
235C2×C3×C8C22×D311yescharacteristic
236C2×C3×C8C22×D311yescharacteristic
237C3×C4⋊C4—31no—
238C3×C4⋊C4—32no—
239C3×C4⋊C4—61no—
240C3×C4⋊C4—61no—
241C3×C4⋊C4—61no—
242C3×C22⋊C4—32no—
243C3×C42—21no—
244C3×C42C22×D311yescharacteristic
245C3×C42C22×D311yescharacteristic
246#217—62no—
247#217—62no—
248#216—122no—
249(C2×D3)⋊C4—62no—
250(C2×D3)⋊C4—62no—
251(C2×D3)⋊C4D1212yes—
252C4⋊Dic3—21no—
253C4⋊Dic3—21no—
254C4⋊Dic3—21no—
255C4⋊Dic3—31no—
256C4⋊Dic3—31no—
257C4⋊Dic3—31no—
258C4⋊Dic3—31no—
259C4⋊Dic3—61no—
260C4⋊Dic3—61no—
261C4⋊Dic3—62no—
262C4⋊Dic3—62no—
263C4⋊Dic3D1211yescharacteristic
264C4⋊Dic3C22×D312yes—
265Dic3⋊C4—62no—
266Dic3⋊C4—62no—
267Dic3⋊C4—61no—
268Dic3⋊C4—61no—
269Dic3⋊C4—61no—
270Dic3⋊C4—61no—
271Dic3⋊C4—62no—
272Dic3⋊C4—62no—
273Dic3⋊C4—121no—
274Dic3⋊C4—121no—
275C4×Dic3—61no—
276C4×Dic3—61no—
277C4×Dic3—61no—
278C4×Dic3—61no—
279C4×Dic3—121no—
280C4×Dic3—121no—
281C2×C3⋊C8C22×D312yes—
282Dic12—62no—
283Dic12—62no—
284Dic12—64no—
285Dic12—122no—
286D3×C8—42no—
287C22×C32C22×D411yescharacteristic
288C2×C3×D3—22no—
289C2×C3×D3—22no—
290C2×C3×D3C2×Q1614yes—
291C32×C4—21no—
292C32×C4C2×Q1612yes—
293C32×C4C2×#4111yescharacteristic
294C32×C4H(5,𝔽2)11yescharacteristic
295C3⋊Dic3—22no—
296C3⋊Dic3—41no—
297C3⋊Dic3—41no—
298C3⋊Dic3—41no—
299C3×Dic3—22no—
300C3×Dic3—42no—
301C3×Dic3—42no—
302C22×Q8—92no—
303C2×Q16—92no—
304C2×Q16—91no—
305C22×C8—32no—
306C4⋊Q8—31no—
307C4⋊Q8—31no—
308C4⋊Q8—181no—
309#125—181no—
310C22⋊Q8—92no—
311C22⋊Q8—92no—
312C22⋊Q8—182no—
313C22⋊Q8—182no—
314C4×Q8—91no—
315C4×Q8—91no—
316C4×D4—31no—
317C4×D4—181no—
318C4×D4—181no—
319C2×C4⋊C4—92no—
320#107—92no—
321#107—91no—
322C4⋊C8—31no—
323#103—32no—
324#103—32no—
325#103—92no—
326#103—92no—
327#103—91no—
328#103—91no—
329C22⋊C8—32no—
330C4×C8D3211yescharacteristic
331C23×C3—32no—
332C22×D3C2×D1212yes—
333C3×Q8—62no—
334C3×Q8—62no—
335C3×Q8—241no—
336C3×D4—34no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—32no—
341C2×C3×C4—62no—
342C2×C3×C4—62no—
343C2×C3×C4—62no—
344C2×C3×C4—62no—
345C2×C3×C4C2×D1211yescharacteristic
346C2×C3×C4C2×D1211yescharacteristic
347C2×C3×C4D3×D411yescharacteristic
348C2×C3×C4D3×D411yescharacteristic
349C2×C3×C4C23×D311yescharacteristic
350C2×C3×C4C23×D311yescharacteristic
351C2×Dic3—22no—
352C2×Dic3—22no—
353C2×Dic3—61no—
354C2×Dic3—61no—
355C2×Dic3—61no—
356C2×Dic3—61no—
357C2×Dic3—61no—
358C2×Dic3—61no—
359C2×Dic3—61no—
360C2×Dic3—61no—
361C2×Dic3—121no—
362C2×Dic3—121no—
363C2×Dic3—121no—
364C2×Dic3—121no—
365C2×Dic3—124no—
366C2×Dic3—242no—
367C2×Dic3C2×D1212yes—
368D12Dic1214yescomplemented
369C4×D3—22no—
370C4×D3—22no—
371C4×D3—124no—
372C4×D3—242no—
373Dic6—22no—
374Dic6—22no—
375Dic6—32no—
376Dic6—32no—
377Dic6—62no—
378Dic6—61no—
379Dic6—61no—
380Dic6—62no—
381Dic6—61no—
382Dic6—61no—
383Dic6—61no—
384Dic6—61no—
385Dic6—81no—
386Dic6—121no—
387Dic6—121no—
388Dic6—124no—
389Dic6—124no—
390C3×C8—22no—
391C3×C8—21no—
392C3×C8—21no—
393C3×C8—21no—
394C3×C8—21no—
395C3×C8—41no—
396C3×C8—62no—
397C3⋊C8—22no—
398C2×C32#54611yescharacteristic
399C2×C32C22×Q1611yescharacteristic
400C2×C32#57711yescharacteristic
401C3×D3—24no—
402C2×Q8—32no—
403C2×Q8—61no—
404C2×Q8—91no—
405C2×Q8—91no—
406C2×Q8—182no—
407C2×Q8—184no—
408C2×Q8—362no—
409C2×D4—31no—
410C22×C4—32no—
411C22×C4—182no—
412C22×C4—182no—
413Q16—182no—
414Q16—362no—
415C2×C8—32no—
416C2×C8—122no—
417C2×C8C2×D3211yescharacteristic
418C2×C8C2×D3211yescharacteristic
419C4⋊C4—31no—
420C4⋊C4—32no—
421C4⋊C4—61no—
422C4⋊C4—61no—
423C4⋊C4—61no—
424C4⋊C4—91no—
425C4⋊C4—91no—
426C4⋊C4—182no—
427C4⋊C4—182no—
428C4⋊C4—182no—
429C4⋊C4—181no—
430C4⋊C4—181no—
431C22⋊C4—32no—
432C22⋊C4—182no—
433C22⋊C4—182no—
434C42—181no—
435C42—181no—
436C42C2×D3211yescharacteristic
437C22×C3—21no—
438C22×C3—34no—
439C22×C3—62no—
440C22×C3—62no—
441C22×C3C22×D1211yescharacteristic
442C22×C3C2×D3×D411yescharacteristic
443C2×D3—22no—
444C2×D3—22no—
445C2×D3C2×Dic1214yes—
446C3×C4—21no—
447C3×C4—21no—
448C3×C4—21no—
449C3×C4—21no—
450C3×C4—22no—
451C3×C4—41no—
452C3×C4—62no—
453C3×C4—122no—
454C3×C4—122no—
455C3×C4C2×Dic1212yes—
456C3×C4D3×Q1612yes—
457C3×C4#100411yescharacteristic
458C3×C4D3×#4111yescharacteristic
459C3×C4D3×#4111yescharacteristic
460C3×C4#100911yescharacteristic
461Dic3—22no—
462Dic3—42no—
463Dic3—42no—
464Dic3—62no—
465Dic3—62no—
466Dic3—122no—
467Dic3—122no—
468Dic3—121no—
469Dic3—121no—
470Dic3—121no—
471Dic3—121no—
472Dic3—121no—
473Dic3—121no—
474Dic3—241no—
475Dic3—241no—
476C32#329911yescharacteristic, complemented, Sylow
477C23—32no—
478Q8—62no—
479Q8—62no—
480Q8—92no—
481Q8—181no—
482Q8—181no—
483Q8—181no—
484Q8—241no—
485Q8—364no—
486D4—34no—
487C2×C4—32no—
488C2×C4—62no—
489C2×C4—62no—
490C2×C4—62no—
491C2×C4—62no—
492C2×C4—181no—
493C2×C4—181no—
494C2×C4—181no—
495C2×C4—181no—
496C2×C4—364no—
497C2×C4—722no—
498C2×C4D3×D1211yescharacteristic
499C2×C4D3×D1211yescharacteristic
500C2×C4C22×D3211yescharacteristic
501C8—21no—
502C8—21no—
503C8—62no—
504C2×C3—21no—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—64no—
508C2×C3#555411yescharacteristic
509C2×C3#567611yescharacteristic
510C2×C3C22×Dic1211yescharacteristic
511C2×C3#575111yescharacteristic
512C2×C3#576211yescharacteristic
513C2×C3C2×D3×Q1611yescharacteristic
514D3—24no—
515C22—34no—
516C22—62no—
517C22—62no—
518C22C2×D3×D1211yescharacteristic
519C4—21no—
520C4—62no—
521C4—122no—
522C4—122no—
523C4—182no—
524C4—361no—
525C4—361no—
526C4—361no—
527C4D3×Dic1212yes—
528C4#6430611yescharacteristic
529C4#6430711yescharacteristic
530C3—21no—
531C3#7944811yescharacteristic, complemented
532C3#8161311yescharacteristic, complemented
533C2—64no—
534C2#1059400511yescharacteristic
535C2#1059467711yescharacteristic
536C2C2×D3×Dic1211yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radicalC2×C3×D12D4
hypercenterC4×C8D32
hypocenterC32#3299
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
3. C4×#3746C2semidirect
5. C3×#4681C2semidirect
6. #10590952C2semidirect
7. #10590848C2semidirect
8. #10590682C2semidirect
9. D3×#816C2semidirect
10. #10590388C2semidirect
11. #10590284C2semidirect
65. #4681D3semidirect
182. C3×D12Q16semidirect
368. D12Dic12semidirect
476. C32#3299semidirect
531. C3#79448semidirect
532. C3#81613semidirect

Maximal subgroups

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

subgroupindex
#105939562
#105939042
C4×#37462
C3×C8×D122
C3×#46812
#105909522
#105908482
#105906822
D3×#8162
#105903882
#105902842
#816133
#794483