Finite Group Databasebeta

← #11895175

Subgroups — #11895175

Order 1152.

801 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D4×Dic6C211yesmaximal, characteristic
2#10593861C211yesmaximal, characteristic, complemented
3C4×#3754C211yesmaximal, characteristic
4C3×#5019C211yesmaximal, characteristic
5#10591489C212yesmaximal
6Dic3×#214C212yesmaximal
7#10590560C212yesmaximal, complemented
8#10590486C212yesmaximal, complemented
9#10590307C211yesmaximal, characteristic, complemented
10#10590290C211yesmaximal, characteristic, complemented
11#10590250C211yesmaximal, characteristic, complemented
12#83568—31nomaximal
13#80414—31nomaximal
14C22×C3×Dic6—21no—
15C32×C4×D4C2211yescharacteristic
16C2×#3754C2211yescharacteristic
17C4×#634C2211yescharacteristic
18C3×D4×Dic3C2212yes—
19C2×C3×#214C2212yes—
20C3×#924—21no—
21C3×#888C2212yes—
22C3×#878—22no—
23C3×#869C2211yescharacteristic
24C3×#869C2211yescharacteristic
25C3×C4×Dic6C2211yescharacteristic
26#63872—21no—
27#63866C2212yes—
28#63846—22no—
29#63843—21no—
30Dic3×Dic6C2212yes—
31#63659C2211yescharacteristic
32#63637C2211yescharacteristic
33#63635C2211yescharacteristic
34C4×C3⋊(C3⋊C8)C2211yescharacteristic
35C3×#810C2212yes—
36C3×C4⋊(C3⋊C8)C2211yescharacteristic
37#63573C2212yes—
38Dic3⋊(C3⋊C8)C2212yes—
39#63567C2212yes—
40#63565C2212yes—
41#63565C2212yes—
42Dic3×C3⋊C8C2212yes—
43C3×D4×Q8—31no—
44#5721—31no—
45#5570—31no—
46D4×Dic6D311yescharacteristic
47C3×#461—31no—
48#5162—32no—
49Dic3×SD16—32no—
50#5094—32no—
51#5094—31no—
52#5093—31no—
53#5093—32no—
54#5079—31no—
55Q8×C3⋊C8—31no—
56#5019—32no—
57#5019D311yescharacteristic
58C4×#214—31no—
59C4×#214—31no—
60C4×#214—32no—
61C4×#214—61no—
62#4851—31no—
63#4830—31no—
64#4792—32no—
65#4791—32no—
66C2×C32×D4C2311yescharacteristic
67C22×C32×C4—21no—
68C2×#634C2311yescharacteristic
69C22×C3×Dic3—22no—
70C2×C3×Dic6—21no—
71C2×C3×Dic6—22no—
72C2×C3×Dic6—44no—
73C2×C3×Dic6D411yescharacteristic
74C2×C3×Dic6C2312yes—
75C32×C4⋊C4C2311yescharacteristic
76C32×C22⋊C4—21no—
77C32×C42C2311yescharacteristic
78#3754—22no—
79C4⋊(C3⋊Dic3)C2311yescharacteristic
80#3750—21no—
81C4×C3⋊Dic3—21no—
82C2×C3⋊(C3⋊C8)C2311yescharacteristic
83C2×C3⋊(C3⋊C8)C2311yescharacteristic
84C3×#217—22no—
85C3×#214—24no—
86C3×C4⋊Dic3—21no—
87C3×C4⋊Dic3—21no—
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3D411yescharacteristic
90C3×C4⋊Dic3C2312yes—
91C3×Dic3⋊C4—22no—
92C3×Dic3⋊C4D412yes—
93C3×C4×Dic3C2312yes—
94C2×C3×C3⋊C8C2312yes—
95Dic3⋊Dic3—22no—
96Dic3⋊Dic3—22no—
97Dic3⋊Dic3—22no—
98Dic32—22no—
99#3359—91noSylow
100C22×C3×Q8—61no—
101C22×Dic6—21no—
102C2×C3×SD16—32no—
103C3×C4⋊Q8—32no—
104C3×C4⋊Q8—31no—
105C3×C4⋊Q8—31no—
106C3×C22⋊Q8—62no—
107C3×C22⋊Q8—61no—
108C3×C4×Q8—31no—
109C3×C4×D4—21no—
110C3×C4×D4—32no—
111C3×C4×D4C2×D311yescharacteristic
112C3×C4×D4C2×D311yescharacteristic
113Q8×Dic3—32no—
114Q8×Dic3—61no—
115#944—32no—
116D4×Dic3C2×D312yes—
117C2×#214—31no—
118C2×#214—31no—
119C2×#214—61no—
120C2×#214C2×D312yes—
121#924—21no—
122#890—62no—
123#890—61no—
124#890—61no—
125#889—62no—
126#888C2×D312yes—
127#887—61no—
128#878—22no—
129#869—32no—
130#869C2×D311yescharacteristic
131#869C2×D311yescharacteristic
132C4×Dic6—32no—
133C4×Dic6—31no—
134C4×Dic6—31no—
135C4×Dic6—61no—
136C4×Dic6C2×D311yescharacteristic
137C3×C4⋊C8—31no—
138C3×#103—32no—
139#835—32no—
140#835—32no—
141#832—31no—
142#832—31no—
143#832—61no—
144#817—32no—
145#816—32no—
146Dic3⋊C8—32no—
147C8×Dic3—32no—
148#810—32no—
149#810—32no—
150#810—31no—
151#810—31no—
152#810—32no—
153#810—61no—
154#810C2×D312yes—
155#808—31no—
156#808—31no—
157#808—32no—
158#808—61no—
159C4⋊(C3⋊C8)—32no—
160C4⋊(C3⋊C8)C2×D311yescharacteristic
161C4×C3⋊C8—31no—
162C4×C3⋊C8—31no—
163C4×C3⋊C8—32no—
164C4×C3⋊C8—61no—
165C23×C32—21no—
166C32×D4—21no—
167C32×D4#4112yes—
168C2×C32×C4—21no—
169C2×C32×C4—42no—
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2411yescharacteristic
173C2×C3⋊Dic3—21no—
174C2×C3⋊Dic3—21no—
175#634—21no—
176#634—21no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—44no—
180C2×C3×Dic3C2×D412yes—
181C2×C3×Dic3C2×D412yes—
182C3×Dic6—22no—
183C3×Dic6—22no—
184C3×Dic6—42no—
185C3×Dic6—44no—
186C3×Dic6SD1614yescomplemented
187C3⋊(C3⋊C8)—21no—
188C3⋊(C3⋊C8)—21no—
189C3×C3⋊C8—22no—
190#557—91no—
191D4×Q8—31no—
192#487—92no—
193#487—91no—
194#475—92no—
195#475—91no—
196#461—31no—
197#461—92no—
198C8×Q8—91no—
199C4×SD16—92no—
200C4×SD16—91no—
201C2×C3×Q8—31no—
202C2×C3×Q8—32no—
203C2×C3×Q8—62no—
204C2×C3×Q8—61no—
205C2×C3×Q8—124no—
206C2×C3×D4—21no—
207C2×C3×D4C22×D311yescharacteristic
208C2×C3×D4C22×D311yescharacteristic
209C22×C3×C4—21no—
210C22×C3×C4—21no—
211C22×C3×C4—41no—
212C22×C3×C4—62no—
213C22×Dic3—22no—
214C2×Dic6—21no—
215C2×Dic6—22no—
216C2×Dic6—31no—
217C2×Dic6—31no—
218C2×Dic6—44no—
219C2×Dic6—61no—
220C2×Dic6#6711yescharacteristic
221C2×Dic6C22×D312yes—
222C3×SD16—64no—
223C2×C3×C8—32no—
224C3×C4⋊C4—21no—
225C3×C4⋊C4—32no—
226C3×C4⋊C4—31no—
227C3×C4⋊C4—32no—
228C3×C4⋊C4—62no—
229C3×C4⋊C4—61no—
230C3×C4⋊C4—61no—
231C3×C4⋊C4—61no—
232C3×C4⋊C4C22×D311yescharacteristic
233C3×C4⋊C4C22×D311yescharacteristic
234C3×C22⋊C4—21no—
235C3×C22⋊C4—21no—
236C3×C22⋊C4—41no—
237C3×C22⋊C4—62no—
238C3×C42—21no—
239C3×C42—32no—
240C3×C42C22×D311yescharacteristic
241C3×C42C22×D311yescharacteristic
242#217—22no—
243#214—24no—
244#214—64no—
245#214—62no—
246#214—62no—
247C4⋊Dic3—21no—
248C4⋊Dic3—21no—
249C4⋊Dic3—21no—
250C4⋊Dic3—31no—
251C4⋊Dic3—31no—
252C4⋊Dic3—61no—
253C4⋊Dic3—62no—
254C4⋊Dic3—62no—
255C4⋊Dic3—62no—
256C4⋊Dic3#6711yescharacteristic
257C4⋊Dic3C22×D312yes—
258Dic3⋊C4—22no—
259Dic3⋊C4—62no—
260Dic3⋊C4—61no—
261Dic3⋊C4—61no—
262Dic3⋊C4—62no—
263Dic3⋊C4—62no—
264Dic3⋊C4—121no—
265Dic3⋊C4#6712yes—
266C4×Dic3—62no—
267C4×Dic3—61no—
268C4×Dic3—61no—
269C4×Dic3—62no—
270C4×Dic3—121no—
271C4×Dic3C22×D312yes—
272C2×C3⋊C8—31no—
273C2×C3⋊C8—31no—
274C2×C3⋊C8—31no—
275C2×C3⋊C8—31no—
276C2×C3⋊C8—61no—
277C2×C3⋊C8—61no—
278C2×C3⋊C8C22×D312yes—
279C22×C32—22no—
280C22×C32—41no—
281C22×C32—41no—
282C22×C32C22×D411yescharacteristic
283C32×C4—21no—
284C32×C4—41no—
285C32×C4C2×SD1612yes—
286C32×C4C2×#4111yescharacteristic
287C32×C42−1+411yescharacteristic
288C3⋊Dic3—41no—
289C3⋊Dic3—41no—
290C3×Dic3—22no—
291C3×Dic3—42no—
292C3×Dic3—42no—
293C3×Dic3C2×SD1614yes—
294C22×Q8—61no—
295C2×SD16—32no—
296C2×SD16—91no—
297C4⋊Q8—32no—
298C4⋊Q8—31no—
299C4⋊Q8—31no—
300C4⋊Q8—92no—
301#125—182no—
302#125—181no—
303C22⋊Q8—62no—
304C22⋊Q8—61no—
305C4×Q8—31no—
306C4×Q8—92no—
307C4×Q8—91no—
308C4×Q8—181no—
309C4×D4—32no—
310C4×D4D3211yescharacteristic
311#106—92no—
312#106—91no—
313C4⋊C8—31no—
314C4⋊C8—92no—
315#103—32no—
316#103—92no—
317#103—92no—
318#103—92no—
319#103—91no—
320#102—91no—
321C4×C8—92no—
322C4×C8—91no—
323C23×C3—21no—
324C23×C3—21no—
325C23×C3—41no—
326C3×Q8—34no—
327C3×Q8—62no—
328C3×Q8—62no—
329C3×Q8—124no—
330C3×Q8—122no—
331C3×D4—21no—
332C3×D4—21no—
333C3×D4—22no—
334C3×D4—41no—
335C3×D4#23712yes—
336C3×D4#23912yes—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—32no—
343C2×C3×C4—32no—
344C2×C3×C4—41no—
345C2×C3×C4—42no—
346C2×C3×C4—42no—
347C2×C3×C4—62no—
348C2×C3×C4—62no—
349C2×C3×C4—82no—
350C2×C3×C4—124no—
351C2×C3×C4D3×D411yescharacteristic
352C2×C3×C4D3×D411yescharacteristic
353C2×C3×C4C2×#6711yescharacteristic
354C2×C3×C4C2×#6711yescharacteristic
355C2×C3×C4C23×D311yescharacteristic
356C2×C3×C4C23×D311yescharacteristic
357C2×Dic3—22no—
358C2×Dic3—22no—
359C2×Dic3—44no—
360C2×Dic3—61no—
361C2×Dic3—61no—
362C2×Dic3—61no—
363C2×Dic3—61no—
364C2×Dic3—121no—
365C2×Dic3—121no—
366C2×Dic3C2×#6712yes—
367C2×Dic3C2×#6712yes—
368Dic6—22no—
369Dic6—22no—
370Dic6—42no—
371Dic6—44no—
372Dic6—62no—
373Dic6—61no—
374Dic6—61no—
375Dic6—61no—
376Dic6—61no—
377Dic6—121no—
378Dic6#21414yescomplemented
379C3×C8—62no—
380C3⋊C8—22no—
381C3⋊C8—62no—
382C3⋊C8—61no—
383C3⋊C8—61no—
384C3⋊C8—61no—
385C3⋊C8—61no—
386C3⋊C8—121no—
387C2×C32—42no—
388C2×C32#54811yescharacteristic
389C2×C32C22×SD1611yescharacteristic
390C2×C32#57811yescharacteristic
391C2×Q8—31no—
392C2×Q8—32no—
393C2×Q8—62no—
394C2×Q8—61no—
395C2×Q8—91no—
396C2×Q8—124no—
397C2×D4C2×D3211yescharacteristic
398C22×C4—21no—
399C22×C4—62no—
400SD16—64no—
401SD16—182no—
402C2×C8—32no—
403C2×C8—91no—
404C2×C8—91no—
405C4⋊C4—32no—
406C4⋊C4—31no—
407C4⋊C4—32no—
408C4⋊C4—62no—
409C4⋊C4—61no—
410C4⋊C4—61no—
411C4⋊C4—61no—
412C4⋊C4—91no—
413C4⋊C4—182no—
414C4⋊C4—182no—
415C4⋊C4—182no—
416C4⋊C4—181no—
417C4⋊C4C2×D3211yescharacteristic
418C22⋊C4—21no—
419C22⋊C4—62no—
420C42—32no—
421C42—182no—
422C42—181no—
423C42C2×D3211yescharacteristic
424C22×C3—22no—
425C22×C3—22no—
426C22×C3—21no—
427C22×C3—42no—
428C22×C3—41no—
429C22×C3—41no—
430C22×C3—41no—
431C22×C3—41no—
432C22×C3—81no—
433C22×C3—81no—
434C22×C3C2×D3×D411yescharacteristic
435C22×C3C22×#6711yescharacteristic
436C3×C4—21no—
437C3×C4—21no—
438C3×C4—21no—
439C3×C4—21no—
440C3×C4—22no—
441C3×C4—34no—
442C3×C4—41no—
443C3×C4—41no—
444C3×C4—41no—
445C3×C4—62no—
446C3×C4—81no—
447C3×C4—122no—
448C3×C4—122no—
449C3×C4D3×SD1612yes—
450C3×C4C2×#21412yes—
451C3×C4C2×#23711yescharacteristic
452C3×C4C2×#23911yescharacteristic
453C3×C4#100711yescharacteristic
454C3×C4#101011yescharacteristic
455Dic3—22no—
456Dic3—42no—
457Dic3—42no—
458Dic3—122no—
459Dic3—121no—
460Dic3—121no—
461Dic3—121no—
462Dic3—121no—
463Dic3—241no—
464Dic3C2×#21414yes—
465C32#335911yescharacteristic, complemented, Sylow
466C23—21no—
467Q8—34no—
468Q8—62no—
469Q8—62no—
470Q8—124no—
471Q8—122no—
472Q8—181no—
473Q8—181no—
474D4—21no—
475D4#379612yes—
476C2×C4—21no—
477C2×C4—32no—
478C2×C4—32no—
479C2×C4—42no—
480C2×C4—62no—
481C2×C4—62no—
482C2×C4—124no—
483C2×C4—181no—
484C2×C4—181no—
485C2×C4D3×#6711yescharacteristic
486C2×C4D3×#6711yescharacteristic
487C2×C4C22×D3211yescharacteristic
488C8—62no—
489C8—181no—
490C8—181no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—21no—
494C2×C3—42no—
495C2×C3—42no—
496C2×C3—82no—
497C2×C3#559811yescharacteristic
498C2×C3C2×D3×SD1611yescharacteristic
499C2×C3#577911yescharacteristic
500C2×C3C22×#21411yescharacteristic
501C2×C3#581711yescharacteristic
502C2×C3#583811yescharacteristic
503C22—22no—
504C22—41no—
505C22—41no—
506C22C2×D3×#6711yescharacteristic
507C4—21no—
508C4—34no—
509C4—41no—
510C4—62no—
511C4—122no—
512C4—122no—
513C4—361no—
514C4—361no—
515C4D3×#21412yes—
516C4C2×#379611yescharacteristic
517C4#6429711yescharacteristic
518C3—21no—
519C3#8041411yescharacteristic, complemented
520C3#8356811yescharacteristic, complemented
521C2—42no—
522C2#1059490011yescharacteristic
523C2C2×D3×#21411yescharacteristic
524C2#1059546511yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC2×C32×D4C23
hypercenterC4×D4D32
hypocenterC32#3359
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. #10593861C2semidirect
7. #10590560C2semidirect
8. #10590486C2semidirect
9. #10590307C2semidirect
10. #10590290C2semidirect
11. #10590250C2semidirect
186. C3×Dic6SD16semidirect
378. Dic6#214semidirect
465. C32#3359semidirect
519. C3#80414semidirect
520. C3#83568semidirect

Maximal subgroups

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

subgroupindex
C3×D4×Dic62
#105938612
C4×#37542
C3×#50192
#105914892
Dic3×#2142
#105905602
#105904862
#105903072
#105902902
#105902502
#835683
#804143