Finite Group Databasebeta

← #11895366

Subgroups — #11895366

Order 1152.

783 conjugacy classes of subgroups.

The subgroup lattice has 533 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5730C211yesmaximal, characteristic, complemented
2#10593963C211yesmaximal, characteristic, complemented
3#10592787C211yesmaximal, characteristic, complemented
4C3×#5091C211yesmaximal, characteristic, complemented
5#10590537C212yesmaximal, complemented
6#10590534C212yesmaximal, complemented
7#10590468C212yesmaximal, complemented
8#10590456C212yesmaximal, complemented
9C4×#3715C211yesmaximal, characteristic, complemented
10#10590349C211yesmaximal, characteristic
11#10590250C211yesmaximal, characteristic, complemented
12#83643—31nomaximal
13#81134—31nomaximal
14C32×C4⋊Q8C2211yescharacteristic
15#64083C2211yescharacteristic
16C3×#946—22no—
17C3×#897—21no—
18C3×#893C2212yes—
19C3×D3×C4⋊C4—21no—
20C3×#890C2212yes—
21C3×C4×D12C2211yescharacteristic
22C3×C4×Dic6C2211yescharacteristic
23C3×C4×Dic6C2211yescharacteristic
24#63897—22no—
25#63894—21no—
26#63894C2212yes—
27#63864—21no—
28#63864C2212yes—
29C2×#3715C2211yescharacteristic
30C2×#3714C2212yes—
31#63636C2212yes—
32#63636C2212yes—
33C4×C3⋊(C3⋊C8)C2211yescharacteristic
34C3×#810C2212yes—
35C3×#807C2212yes—
36C3×C4⋊(C3⋊C8)C2211yescharacteristic
37#63574C2211yescharacteristic
38Dic3⋊(C3⋊C8)C2212yes—
39#63565C2211yescharacteristic
40#63564C2212yes—
41#63562C2211yescharacteristic
42Dic3×C3⋊C8C2212yes—
43C3×#554—31no—
44#5730D311yescharacteristic, complemented
45#5585—31no—
46#5585—31no—
47C3×#477—31no—
48#5091D311yescharacteristic, complemented
49#5088—31no—
50#5088—31no—
51#5088—61no—
52#5068—32no—
53#5066—32no—
54C4×#215—31no—
55Q8×C3⋊C8—31no—
56C4×#214—31no—
57#5016—32no—
58#5015—31no—
59C4×#213—32no—
60#4891—32no—
61#4872—32no—
62#4843—31no—
63#4830—31no—
64#4819—32no—
65#4800—32no—
66C2×C32×Q8—21no—
67C2×C4⋊(C3⋊D3)—21no—
68C2×C4⋊(C3⋊D3)—21no—
69C2×C4⋊(C3⋊D3)C2312yes—
70C2×C3×D12C2311yescharacteristic
71C2×C3×C4×D3—21no—
72C2×C3×C4×D3—22no—
73C2×C3×Dic6D411yescharacteristic
74C2×C3×Dic6C2311yescharacteristic
75C2×#624—22no—
76C32×C4⋊C4—21no—
77C32×C4⋊C4C2312yes—
78C32×C42C2311yescharacteristic
79C2×C3⋊(C3⋊C8)C2311yescharacteristic
80C2×C3⋊(C3⋊C8)C2311yescharacteristic
81C3×(C2×D3)⋊C4—21no—
82C3×(C2×D3)⋊C4—22no—
83C3×C4⋊Dic3—22no—
84C3×C4⋊Dic3D411yescharacteristic
85C3×C4⋊Dic3C2311yescharacteristic
86C3×C4⋊Dic3C2311yescharacteristic
87C3×Dic3⋊C4—21no—
88C3×Dic3⋊C4—22no—
89C3×Dic3⋊C4D412yes—
90C3×C4×Dic3—21no—
91C3×C4×Dic3C2312yes—
92C2×C3×C3⋊C8C2312yes—
93#3722—22no—
94#3722—22no—
95#3722—22no—
96#3715—22no—
97#3714—24no—
98#3361—91noSylow
99C3×C4⋊Q8—21no—
100C3×C4⋊Q8C2×D311yescharacteristic
101C3×C4⋊Q8C2×D311yescharacteristic
102C3×#125—32no—
103C3×C22⋊Q8—61no—
104C3×C22⋊Q8—62no—
105C3×C4×Q8—31no—
106C3×C4×Q8—31no—
107C3×C4×D4—32no—
108C3×C4×D4—31no—
109C2×C3×C4⋊C4—61no—
110#947—32no—
111#947—61no—
112#946—22no—
113C2×#215—31no—
114C2×#214—31no—
115C2×#213—32no—
116C2×D24—32no—
117#897—21no—
118#894—62no—
119#894—62no—
120#893—32no—
121#893—61no—
122#893C2×D312yes—
123D3×C4⋊C4—21no—
124#890C2×D312yes—
125#875—32no—
126#875—61no—
127#874—31no—
128#874—31no—
129#874—61no—
130C4×D12—32no—
131C4×D12—61no—
132C4×D12C2×D311yescharacteristic
133C4×Dic6C2×D311yescharacteristic
134C4×Dic6C2×D311yescharacteristic
135C3×#107—32no—
136C3×C4⋊C8—31no—
137C3×#103—32no—
138#835—31no—
139#832—31no—
140#821—32no—
141Dic3⋊C8—32no—
142C8×Dic3—32no—
143#810—31no—
144#810C2×D312yes—
145#809—31no—
146#809—32no—
147#809—32no—
148#809—32no—
149#809—32no—
150#809—32no—
151#809—62no—
152#809—62no—
153#808—31no—
154#808—31no—
155#807C2×D312yes—
156C4⋊(C3⋊C8)—32no—
157C4⋊(C3⋊C8)C2×D311yescharacteristic
158C4×C3⋊C8—31no—
159C4×C3⋊C8—31no—
160C4×C3⋊C8—32no—
161C4×C3⋊C8—61no—
162C22×C3⋊D3—22no—
163C22×C3×D3—21no—
164C32×Q8—81no—
165C2×C32×C4—22no—
166C2×C32×C4C2×D411yescharacteristic
167C2×C32×C4C2×D411yescharacteristic
168C2×C32×C4C2411yescharacteristic
169C4⋊(C3⋊D3)—22no—
170C4⋊(C3⋊D3)—22no—
171C4⋊(C3⋊D3)—42no—
172C4⋊(C3⋊D3)—81no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3C2×D412yes—
177C2×C3×Dic3C2×D412yes—
178C3×D12—21no—
179C3×D12#4112yes—
180C3×C4×D3—42no—
181C3×C4×D3—82no—
182C3×Dic6—22no—
183C3×Dic6—21no—
184C3×Dic6—21no—
185#624—82no—
186C3⋊(C3⋊C8)—21no—
187C3⋊(C3⋊C8)—21no—
188C3×C3⋊C8—22no—
189#559—91no—
190#554—31no—
191#488—92no—
192#486—91no—
193#478—92no—
194#477—31no—
195#463—92no—
196#459—91no—
197C8×Q8—91no—
198C4×SD16—91no—
199C4×D8—92no—
200C2×C3×Q8—21no—
201C2×C3×Q8—21no—
202C2×C3×Q8—31no—
203C2×C3×Q8—31no—
204C2×C3×Q8—41no—
205C2×C3×D4—31no—
206C22×C3×C4—62no—
207C22×C3×C4—61no—
208C2×D12—32no—
209C2×D12—32no—
210C2×D12—62no—
211C2×D12—61no—
212C2×D12—61no—
213C2×D12—61no—
214C2×D12—61no—
215C2×D12—121no—
216C2×D12—121no—
217C2×D12C22×D311yescharacteristic
218C2×C4×D3—21no—
219C2×C4×D3—22no—
220C2×C4×D3—62no—
221C2×C4×D3—62no—
222C2×Dic6#6711yescharacteristic
223C2×Dic6C22×D311yescharacteristic
224C2×C3×C8—32no—
225C3×C4⋊C4—21no—
226C3×C4⋊C4—21no—
227C3×C4⋊C4—22no—
228C3×C4⋊C4—31no—
229C3×C4⋊C4—32no—
230C3×C4⋊C4—31no—
231C3×C4⋊C4—31no—
232C3×C4⋊C4—41no—
233C3×C4⋊C4—62no—
234C3×C4⋊C4—62no—
235C3×C4⋊C4—61no—
236C3×C4⋊C4C22×D312yes—
237C3×C4⋊C4C22×D312yes—
238C3×C22⋊C4—62no—
239C3×C22⋊C4—61no—
240C3×C42—21no—
241C3×C42—32no—
242C3×C42—61no—
243C3×C42C22×D311yescharacteristic
244C3×C42C22×D311yescharacteristic
245#215—62no—
246#214—62no—
247#213—64no—
248(C2×D3)⋊C4—21no—
249(C2×D3)⋊C4—22no—
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—
255(C2×D3)⋊C4—62no—
256C4⋊Dic3—22no—
257C4⋊Dic3#6711yescharacteristic
258C4⋊Dic3C22×D311yescharacteristic
259C4⋊Dic3C22×D311yescharacteristic
260Dic3⋊C4—21no—
261Dic3⋊C4—22no—
262Dic3⋊C4#6712yes—
263C4×Dic3—21no—
264C4×Dic3C22×D312yes—
265C2×C3⋊C8—31no—
266C2×C3⋊C8—31no—
267C2×C3⋊C8—31no—
268C2×C3⋊C8—31no—
269C2×C3⋊C8—61no—
270C2×C3⋊C8—61no—
271C2×C3⋊C8C22×D312yes—
272D24—64no—
273C22×C32C22×D411yescharacteristic
274C2×C3⋊D3—42no—
275C2×C3⋊D3—42no—
276C2×C3⋊D3—42no—
277C2×C3×D3—22no—
278C2×C3×D3—41no—
279C2×C3×D3—41no—
280C32×C4—21no—
281C32×C4—42no—
282C32×C4#13512yes—
283C32×C4C2×#4111yescharacteristic
284C32×C42−1+411yescharacteristic
285C3×Dic3—22no—
286C3×Dic3—22no—
287C3×Dic3—41no—
288C3×Dic3—41no—
289C3×Dic3—41no—
290C2×SD16—91no—
291C2×D8—92no—
292C4⋊Q8D3211yescharacteristic
293#127—91no—
294#125—32no—
295#124—92no—
296#124—181no—
297#123—182no—
298C22⋊Q8—61no—
299C22⋊Q8—62no—
300C4×Q8—31no—
301C4×Q8—31no—
302C4×D4—32no—
303C4×D4—31no—
304C4×D4—92no—
305C4×D4—181no—
306C2×C4⋊C4—61no—
307#107—32no—
308#106—91no—
309C4⋊C8—31no—
310C4⋊C8—92no—
311#103—32no—
312#103—91no—
313#102—92no—
314#102—91no—
315#102—92no—
316#102—92no—
317C4×C8—92no—
318C4×C8—91no—
319C23×C3—61no—
320C22×D3—21no—
321C22×D3—62no—
322C22×D3—62no—
323C22×D3—122no—
324C3×Q8—62no—
325C3×Q8—61no—
326C3×Q8—61no—
327C3×Q8—81no—
328C3×Q8—81no—
329C3×Q8—82no—
330C3×D4—32no—
331C3×D4—61no—
332C2×C3×C4—22no—
333C2×C3×C4—22no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—32no—
338C2×C3×C4—32no—
339C2×C3×C4—42no—
340C2×C3×C4—61no—
341C2×C3×C4—61no—
342C2×C3×C4—61no—
343C2×C3×C4—122no—
344C2×C3×C4—242no—
345C2×C3×C4D3×D411yescharacteristic
346C2×C3×C4D3×D411yescharacteristic
347C2×C3×C4C2×#6711yescharacteristic
348C2×C3×C4C2×#6711yescharacteristic
349C2×C3×C4C23×D311yescharacteristic
350C2×C3×C4C23×D311yescharacteristic
351C2×Dic3—21no—
352C2×Dic3—21no—
353C2×Dic3—21no—
354C2×Dic3C2×#6712yes—
355C2×Dic3C2×#6712yes—
356D12—21no—
357D12—62no—
358D12—62no—
359D12—62no—
360D12—62no—
361D12—122no—
362D12—122no—
363D12—122no—
364D12—122no—
365D12—242no—
366D12—241no—
367D12—241no—
368D12—242no—
369D12#23912yes—
370C4×D3—42no—
371C4×D3—82no—
372C4×D3—242no—
373C4×D3—242no—
374Dic6—22no—
375Dic6—21no—
376Dic6—21no—
377C3×C8—62no—
378C3⋊C8—22no—
379C3⋊C8—61no—
380C3⋊C8—61no—
381C3⋊C8—61no—
382C3⋊C8—61no—
383C3⋊C8—121no—
384C3⋊C8—121no—
385C2×C32#54811yescharacteristic
386C2×C32C2×#13511yescharacteristic
387C2×C32#57611yescharacteristic
388C3⋊D3—82no—
389C3×D3—42no—
390C2×Q8—21no—
391C2×Q8—31no—
392C2×Q8—31no—
393C2×D4—31no—
394C2×D4—92no—
395C2×D4—181no—
396C2×D4—181no—
397C22×C4—62no—
398C22×C4—61no—
399C22×C4—182no—
400SD16—182no—
401D8—184no—
402C2×C8—32no—
403C2×C8—91no—
404C2×C8—91no—
405C4⋊C4—21no—
406C4⋊C4—31no—
407C4⋊C4—32no—
408C4⋊C4—31no—
409C4⋊C4—31no—
410C4⋊C4—62no—
411C4⋊C4—62no—
412C4⋊C4—61no—
413C4⋊C4C2×D3212yes—
414C22⋊C4—62no—
415C22⋊C4—61no—
416C22⋊C4—182no—
417C22⋊C4—182no—
418C22⋊C4—182no—
419C42—32no—
420C42—61no—
421C42C2×D3211yescharacteristic
422C22×C3—21no—
423C22×C3—62no—
424C22×C3—121no—
425C22×C3—121no—
426C22×C3C2×D3×D411yescharacteristic
427C22×C3C22×#6711yescharacteristic
428C2×D3—22no—
429C2×D3—41no—
430C2×D3—41no—
431C2×D3—122no—
432C2×D3—122no—
433C2×D3—122no—
434C2×D3—122no—
435C2×D3—122no—
436C2×D3—122no—
437C2×D3—242no—
438C2×D3—242no—
439C2×D3—242no—
440C3×C4—22no—
441C3×C4—21no—
442C3×C4—21no—
443C3×C4—21no—
444C3×C4—21no—
445C3×C4—22no—
446C3×C4—42no—
447C3×C4—42no—
448C3×C4—62no—
449C3×C4—62no—
450C3×C4—82no—
451C3×C4—121no—
452C3×C4—121no—
453C3×C4—121no—
454C3×C4#91912yes—
455C3×C4#95012yes—
456C3×C4C2×#23911yescharacteristic
457C3×C4#100711yescharacteristic
458C3×C4#100711yescharacteristic
459C3×C4D3×#4111yescharacteristic
460Dic3—22no—
461Dic3—22no—
462Dic3—41no—
463Dic3—41no—
464Dic3—41no—
465C32#336111yescharacteristic, complemented, Sylow
466C23—61no—
467C23—182no—
468Q8—62no—
469Q8—61no—
470Q8—61no—
471Q8—81no—
472D4—32no—
473D4—61no—
474D4—182no—
475D4—182no—
476D4—362no—
477D4—721no—
478C2×C4—22no—
479C2×C4—32no—
480C2×C4—32no—
481C2×C4—61no—
482C2×C4—61no—
483C2×C4—61no—
484C2×C4—122no—
485C2×C4—242no—
486C2×C4—722no—
487C2×C4D3×#6711yescharacteristic
488C2×C4D3×#6711yescharacteristic
489C2×C4C22×D3211yescharacteristic
490C8—62no—
491C8—181no—
492C8—181no—
493C2×C3—21no—
494C2×C3—21no—
495C2×C3—21no—
496C2×C3—122no—
497C2×C3#563311yescharacteristic
498C2×C3C2×#91911yescharacteristic
499C2×C3#577411yescharacteristic
500C2×C3#581711yescharacteristic
501C2×C3C2×#95011yescharacteristic
502C2×C3#583511yescharacteristic
503D3—42no—
504D3—242no—
505D3—242no—
506D3—482no—
507C22—62no—
508C22—121no—
509C22—121no—
510C22—362no—
511C22—362no—
512C22—362no—
513C22C2×D3×#6711yescharacteristic
514C4—21no—
515C4—42no—
516C4—62no—
517C4—62no—
518C4—121no—
519C4—121no—
520C4—121no—
521C4#6394912yes—
522C4#6431611yescharacteristic
523C4D3×#23911yescharacteristic
524C3—21no—
525C3#8113411yescharacteristic, complemented
526C3#8364311yescharacteristic, complemented
527C2—122no—
528C2—722no—
529C2#1059509711yescharacteristic
530C2C2×#6394911yescharacteristic
531C2#1059540211yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radical#10590349C2
hypercenterC4⋊Q8D32
hypocenterC32#3361
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×#5730C2semidirect
2. #10593963C2semidirect
3. #10592787C2semidirect
4. C3×#5091C2semidirect
5. #10590537C2semidirect
6. #10590534C2semidirect
7. #10590468C2semidirect
8. #10590456C2semidirect
9. C4×#3715C2semidirect
11. #10590250C2semidirect
44. #5730D3semidirect
48. #5091D3semidirect
465. C32#3361semidirect
525. C3#81134semidirect
526. C3#83643semidirect

Maximal subgroups

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

subgroupindex
C3×#57302
#105939632
#105927872
C3×#50912
#105905372
#105905342
#105904682
#105904562
C4×#37152
#105903492
#105902502
#836433
#811343