Finite Group Databasebeta

← #11895668

Subgroups — #11895668

Order 1152.

760 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5570C211yesmaximal, characteristic, complemented
2#10593963C211yesmaximal, characteristic
3#10592726C211yesmaximal, characteristic
4C3×C4×#216C211yesmaximal, characteristic, complemented
5#10591607C212yesmaximal, complemented
6#10591536C212yesmaximal, complemented
7#10590537C212yesmaximal, complemented
8#10590468C212yesmaximal, complemented
9#10590285C211yesmaximal, characteristic, complemented
10#10590281C211yesmaximal, characteristic
11C3⋊C8×Dic6C211yesmaximal, characteristic, complemented
12#83697—31nomaximal
13#79701—31nomaximal
14C32×C4×Q8C2211yescharacteristic
15C2×#3755C2212yes—
16#64083C2211yescharacteristic
17C3×Q8×Dic3C2212yes—
18C2×C3×#216C2211yescharacteristic
19C3×#890—22no—
20C3×#890C2212yes—
21C3×#869—21no—
22C3×#869C2211yescharacteristic
23C3×C4×Dic6—21no—
24C3×C4×Dic6C2211yescharacteristic
25C3×C4×Dic6C2211yescharacteristic
26#63897—22no—
27#63894—21no—
28#63894C2212yes—
29#63864—21no—
30#63864C2212yes—
31#63636C2212yes—
32C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
33C3×#835C2211yescharacteristic
34C3×#810C2211yescharacteristic
35C3×#807C2211yescharacteristic
36C3×C4×C3⋊C8C2211yescharacteristic
37#63574C2212yes—
38Dic3⋊(C3⋊C8)C2212yes—
39#63565C2212yes—
40#63564C2212yes—
41#63564C2212yes—
42Dic3×C3⋊C8C2212yes—
43C3×#557—31no—
44#5585—31no—
45#5585—31no—
46#5570D311yescharacteristic, complemented
47C3×C4×Q16—31no—
48#5185—32no—
49#5094—31no—
50#5088—31no—
51#5068—32no—
52#5066—32no—
53C4×#216D311yescharacteristic, complemented
54#5028—32no—
55#5027—31no—
56#5027—31no—
57#5027—61no—
58C4×#215—32no—
59Q8×C3⋊C8—31no—
60#5020—31no—
61#4891—32no—
62#4800—32no—
63#4788—32no—
64#4694—31no—
65C8×Dic6—31no—
66C2×C32×Q8C2311yescharacteristic
67C2×C4⋊(C3⋊D3)—21no—
68C2×C4⋊(C3⋊D3)—21no—
69C2×C4⋊(C3⋊D3)C2312yes—
70C2×C3×Dic6—21no—
71C2×C3×Dic6D411yescharacteristic
72C2×C3×Dic6C2311yescharacteristic
73C2×#624—22no—
74C32×C4⋊C4—21no—
75C32×C4⋊C4C2311yescharacteristic
76C32×C42—21no—
77C32×C42C2311yescharacteristic
78#3755—24no—
79C2×C3⋊(C3⋊C8)C2312yes—
80C3×#216—22no—
81C3×C4⋊Dic3—21no—
82C3×C4⋊Dic3—22no—
83C3×C4⋊Dic3—22no—
84C3×C4⋊Dic3D411yescharacteristic
85C3×C4⋊Dic3C2312yes—
86C3×C4⋊Dic3C2311yescharacteristic
87C3×Dic3⋊C4—21no—
88C3×Dic3⋊C4—22no—
89C3×Dic3⋊C4D412yes—
90C3×C4×Dic3—21no—
91C3×C4×Dic3—22no—
92C3×C4×Dic3C2312yes—
93C2×C3×C3⋊C8C2311yescharacteristic
94C2×C3×C3⋊C8C2311yescharacteristic
95#3722—22no—
96#3722—22no—
97#3722—22no—
98#3365—91noSylow
99C2×C3×Q16—31no—
100C3×C4⋊Q8—31no—
101C3×C4⋊Q8—61no—
102C3×#125—32no—
103C3×#125—62no—
104C3×C4×Q8—21no—
105C3×C4×Q8—31no—
106C3×C4×Q8—32no—
107C3×C4×Q8—31no—
108C3×C4×Q8—61no—
109C3×C4×Q8C2×D311yescharacteristic
110C3×C4×Q8C2×D311yescharacteristic
111#947—32no—
112#947—61no—
113Q8×Dic3C2×D312yes—
114C2×#216C2×D311yescharacteristic
115C2×#215—32no—
116C2×#215—32no—
117C2×#215—62no—
118#894—62no—
119#894—62no—
120#893—32no—
121#893—61no—
122#890—22no—
123#890C2×D312yes—
124#875—32no—
125#875—61no—
126#874—31no—
127#874—31no—
128#874—61no—
129C4×D12—32no—
130C4×D12—61no—
131#869—21no—
132#869C2×D311yescharacteristic
133C4×Dic6—21no—
134C4×Dic6C2×D311yescharacteristic
135C4×Dic6C2×D311yescharacteristic
136C3×#107—31no—
137C3×#103—31no—
138C3×#103—31no—
139C3×C4×C8—31no—
140#835—32no—
141#835C2×D311yescharacteristic
142#821—32no—
143#821—32no—
144Dic3⋊C8—32no—
145C8×Dic3—32no—
146#810—32no—
147#810C2×D311yescharacteristic
148#809—32no—
149#809—32no—
150#809—32no—
151#809—32no—
152#809—62no—
153#808—32no—
154#808—32no—
155#807C2×D311yescharacteristic
156C4⋊(C3⋊C8)—31no—
157C4⋊(C3⋊C8)—31no—
158C4⋊(C3⋊C8)—32no—
159C4⋊(C3⋊C8)—61no—
160C4×C3⋊C8—32no—
161C4×C3⋊C8C2×D311yescharacteristic
162C22×C3⋊D3—22no—
163C32×Q8—21no—
164C32×Q8#4112yes—
165C2×C32×C4—21no—
166C2×C32×C4—21no—
167C2×C32×C4C2×D411yescharacteristic
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2411yescharacteristic
170C4⋊(C3⋊D3)—22no—
171C4⋊(C3⋊D3)—22no—
172C4⋊(C3⋊D3)—42no—
173C4⋊(C3⋊D3)—81no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3C2×D412yes—
178C2×C3×Dic3C2×D412yes—
179C3×Dic6—22no—
180C3×Dic6—21no—
181C3×Dic6—21no—
182C3×Dic6—42no—
183#624—82no—
184C3⋊(C3⋊C8)—22no—
185C3×C3⋊C8—21no—
186C3×C3⋊C8—21no—
187#559—91no—
188#557—31no—
189#488—92no—
190#486—91no—
191#478—92no—
192#475—91no—
193#464—92no—
194#460—91no—
195C8×Q8—91no—
196C4×Q16—31no—
197C4×SD16—92no—
198C2×C3×Q8—21no—
199C2×C3×Q8—31no—
200C2×C3×Q8—31no—
201C2×C3×Q8—61no—
202C2×C3×Q8C22×D311yescharacteristic
203C2×C3×Q8C22×D311yescharacteristic
204C2×D12—32no—
205C2×D12—32no—
206C2×D12—62no—
207C2×D12—61no—
208C2×D12—61no—
209C2×D12—61no—
210C2×D12—61no—
211C2×D12—121no—
212C2×D12—121no—
213C2×C4×D3—62no—
214C2×C4×D3—62no—
215C2×Dic6—21no—
216C2×Dic6#6711yescharacteristic
217C2×Dic6C22×D311yescharacteristic
218C3×Q16—62no—
219C2×C3×C8—31no—
220C2×C3×C8—31no—
221C3×C4⋊C4—21no—
222C3×C4⋊C4—21no—
223C3×C4⋊C4—21no—
224C3×C4⋊C4—31no—
225C3×C4⋊C4—32no—
226C3×C4⋊C4—31no—
227C3×C4⋊C4—32no—
228C3×C4⋊C4—41no—
229C3×C4⋊C4—62no—
230C3×C4⋊C4—62no—
231C3×C4⋊C4—62no—
232C3×C4⋊C4—61no—
233C3×C4⋊C4—61no—
234C3×C4⋊C4C22×D311yescharacteristic
235C3×C4⋊C4C22×D311yescharacteristic
236C3×C42—21no—
237C3×C42—21no—
238C3×C42—21no—
239C3×C42—32no—
240C3×C42—41no—
241C3×C42—62no—
242C3×C42—61no—
243C3×C42C22×D311yescharacteristic
244C3×C42C22×D311yescharacteristic
245#216—22no—
246#215—64no—
247#215—64no—
248#215—124no—
249(C2×D3)⋊C4—62no—
250(C2×D3)⋊C4—62no—
251(C2×D3)⋊C4—62no—
252(C2×D3)⋊C4—62no—
253(C2×D3)⋊C4—62no—
254(C2×D3)⋊C4—62no—
255C4⋊Dic3—21no—
256C4⋊Dic3—22no—
257C4⋊Dic3—22no—
258C4⋊Dic3#6711yescharacteristic
259C4⋊Dic3C22×D311yescharacteristic
260C4⋊Dic3C22×D312yes—
261Dic3⋊C4—21no—
262Dic3⋊C4—22no—
263Dic3⋊C4#6712yes—
264C4×Dic3—21no—
265C4×Dic3—22no—
266C4×Dic3C22×D312yes—
267C2×C3⋊C8—32no—
268C2×C3⋊C8—32no—
269C2×C3⋊C8—62no—
270C2×C3⋊C8C22×D311yescharacteristic
271C2×C3⋊C8C22×D311yescharacteristic
272C22×C32C22×D411yescharacteristic
273C2×C3⋊D3—42no—
274C2×C3⋊D3—42no—
275C2×C3⋊D3—42no—
276C32×C4—22no—
277C32×C4—21no—
278C32×C4—41no—
279C32×C4#13512yes—
280C32×C4C2×#4111yescharacteristic
281C32×C42−1+411yescharacteristic
282C3×Dic3—22no—
283C3×Dic3—22no—
284C3×Dic3—41no—
285C3×Dic3—42no—
286C3×Dic3—41no—
287C2×Q16—31no—
288C2×SD16—92no—
289C4⋊Q8—31no—
290C4⋊Q8—61no—
291#127—91no—
292#125—32no—
293#125—62no—
294#124—92no—
295#124—181no—
296#123—182no—
297C4×Q8—31no—
298C4×Q8—32no—
299C4×Q8—31no—
300C4×Q8—61no—
301C4×Q8D3211yescharacteristic
302C4×D4—92no—
303C4×D4—181no—
304#107—31no—
305#106—92no—
306C4⋊C8—92no—
307C4⋊C8—91no—
308#103—31no—
309#103—31no—
310#103—92no—
311#102—92no—
312#102—92no—
313#102—92no—
314C4×C8—31no—
315C4×C8—92no—
316C22×D3—62no—
317C22×D3—62no—
318C22×D3—122no—
319C3×Q8—21no—
320C3×Q8—21no—
321C3×Q8—22no—
322C3×Q8—41no—
323C3×Q8—62no—
324C3×Q8—61no—
325C3×Q8—61no—
326C3×Q8—122no—
327C3×Q8#23512yes—
328C3×Q8#23912yes—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—32no—
337C2×C3×C4—32no—
338C2×C3×C4—41no—
339C2×C3×C4—41no—
340C2×C3×C4—62no—
341C2×C3×C4—61no—
342C2×C3×C4—61no—
343C2×C3×C4D3×D411yescharacteristic
344C2×C3×C4D3×D411yescharacteristic
345C2×C3×C4C2×#6711yescharacteristic
346C2×C3×C4C2×#6711yescharacteristic
347C2×C3×C4C23×D311yescharacteristic
348C2×C3×C4C23×D311yescharacteristic
349C2×Dic3—21no—
350C2×Dic3—21no—
351C2×Dic3—22no—
352C2×Dic3C2×#6712yes—
353C2×Dic3C2×#6712yes—
354D12—62no—
355D12—62no—
356D12—62no—
357D12—62no—
358D12—122no—
359D12—122no—
360D12—122no—
361D12—122no—
362D12—242no—
363D12—241no—
364D12—241no—
365D12—242no—
366C4×D3—242no—
367C4×D3—242no—
368Dic6—22no—
369Dic6—21no—
370Dic6—21no—
371Dic6—42no—
372C3×C8—61no—
373C3×C8—61no—
374C3⋊C8—21no—
375C3⋊C8—21no—
376C3⋊C8—62no—
377C3⋊C8—62no—
378C3⋊C8—122no—
379C2×C32#54811yescharacteristic
380C2×C32C2×#13511yescharacteristic
381C2×C32#57711yescharacteristic
382C3⋊D3—82no—
383C2×Q8—31no—
384C2×Q8—31no—
385C2×Q8—61no—
386C2×Q8C2×D3211yescharacteristic
387C2×D4—92no—
388C2×D4—181no—
389C2×D4—181no—
390C22×C4—182no—
391Q16—62no—
392SD16—184no—
393C2×C8—31no—
394C2×C8—31no—
395C2×C8—92no—
396C4⋊C4—21no—
397C4⋊C4—31no—
398C4⋊C4—32no—
399C4⋊C4—32no—
400C4⋊C4—31no—
401C4⋊C4—62no—
402C4⋊C4—62no—
403C4⋊C4—62no—
404C4⋊C4—61no—
405C4⋊C4—61no—
406C4⋊C4C2×D3211yescharacteristic
407C22⋊C4—182no—
408C22⋊C4—182no—
409C22⋊C4—182no—
410C42—21no—
411C42—32no—
412C42—62no—
413C42—61no—
414C42C2×D3211yescharacteristic
415C22×C3—21no—
416C22×C3C2×D3×D411yescharacteristic
417C22×C3C22×#6711yescharacteristic
418C2×D3—122no—
419C2×D3—122no—
420C2×D3—122no—
421C2×D3—122no—
422C2×D3—122no—
423C2×D3—122no—
424C2×D3—242no—
425C2×D3—242no—
426C2×D3—242no—
427C3×C4—21no—
428C3×C4—22no—
429C3×C4—22no—
430C3×C4—21no—
431C3×C4—21no—
432C3×C4—21no—
433C3×C4—22no—
434C3×C4—41no—
435C3×C4—42no—
436C3×C4—41no—
437C3×C4—41no—
438C3×C4—62no—
439C3×C4—62no—
440C3×C4—81no—
441C3×C4—122no—
442C3×C4—121no—
443C3×C4—121no—
444C3×C4#91912yes—
445C3×C4#95012yes—
446C3×C4C2×#23511yescharacteristic
447C3×C4C2×#23911yescharacteristic
448C3×C4#100711yescharacteristic
449C3×C4#101011yescharacteristic
450Dic3—22no—
451Dic3—22no—
452Dic3—41no—
453Dic3—41no—
454Dic3—42no—
455C32#336511yescharacteristic, complemented, Sylow
456C23—182no—
457Q8—21no—
458Q8—62no—
459Q8—61no—
460Q8—61no—
461Q8—122no—
462Q8#379912yes—
463D4—182no—
464D4—182no—
465D4—362no—
466D4—721no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—32no—
470C2×C4—32no—
471C2×C4—61no—
472C2×C4—61no—
473C2×C4—62no—
474C2×C4—722no—
475C2×C4D3×#6711yescharacteristic
476C2×C4D3×#6711yescharacteristic
477C2×C4C22×D3211yescharacteristic
478C8—61no—
479C8—61no—
480C8—182no—
481C2×C3—21no—
482C2×C3—21no—
483C2×C3—21no—
484C2×C3#555211yescharacteristic
485C2×C3C2×#91911yescharacteristic
486C2×C3#577011yescharacteristic
487C2×C3#581711yescharacteristic
488C2×C3C2×#95011yescharacteristic
489C2×C3#583711yescharacteristic
490D3—242no—
491D3—242no—
492D3—482no—
493C22—362no—
494C22—362no—
495C22—362no—
496C22C2×D3×#6711yescharacteristic
497C4—22no—
498C4—21no—
499C4—41no—
500C4—62no—
501C4—62no—
502C4—122no—
503C4—121no—
504C4—121no—
505C4#6394912yes—
506C4#6429711yescharacteristic
507C4C2×#379911yescharacteristic
508C3—21no—
509C3#7970111yescharacteristic, complemented
510C3#8369711yescharacteristic, complemented
511C2—722no—
512C2#1059490211yescharacteristic
513C2C2×#6394911yescharacteristic
514C2#1059545711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radical#64083C22
hypercenterC4×Q8D32
hypocenterC32#3365
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
1. C3×#5570C2semidirect
4. C3×C4×#216C2semidirect
5. #10591607C2semidirect
6. #10591536C2semidirect
7. #10590537C2semidirect
8. #10590468C2semidirect
9. #10590285C2semidirect
11. C3⋊C8×Dic6C2semidirect
46. #5570D3semidirect
53. C4×#216D3semidirect
455. C32#3365semidirect
509. C3#79701semidirect
510. C3#83697semidirect

Maximal subgroups

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

subgroupindex
C3×#55702
#105939632
#105927262
C3×C4×#2162
#105916072
#105915362
#105905372
#105904682
#105902852
#105902812
C3⋊C8×Dic62
#836973
#797013