Finite Group Databasebeta

← #11895677

Subgroups — #11895677

Order 1152.

755 conjugacy classes of subgroups.

The subgroup lattice has 513 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5721C211yesmaximal, characteristic, complemented
2#10593963C211yesmaximal, characteristic
3#10592787C211yesmaximal, characteristic
4C3×#5094C211yesmaximal, characteristic, complemented
5#10590537C212yesmaximal, complemented
6#10590536C212yesmaximal, complemented
7#10590470C212yesmaximal, complemented
8#10590458C212yesmaximal, complemented
9C4×#3718C211yesmaximal, characteristic, complemented
10#10590367C211yesmaximal, characteristic
11#10590250C211yesmaximal, characteristic, complemented
12#83697—31nomaximal
13#81041—31nomaximal
14C32×C4⋊Q8C2211yescharacteristic
15#64083C2211yescharacteristic
16C3×Q8×Dic3—21no—
17C3×#944—21no—
18C3×#890C2212yes—
19C3×#889—22no—
20C3×#887C2212yes—
21C3×C4×Dic6C2211yescharacteristic
22C3×C4×Dic6C2211yescharacteristic
23C3×C4×Dic6C2211yescharacteristic
24#63897—22no—
25#63894—21no—
26#63894C2212yes—
27#63864—21no—
28#63864C2212yes—
29C2×#3718C2211yescharacteristic
30C2×#3717C2212yes—
31#63636C2212yes—
32#63636C2212yes—
33C4×C3⋊(C3⋊C8)C2211yescharacteristic
34C3×#810C2212yes—
35C3×#808C2212yes—
36C3×C4⋊(C3⋊C8)C2211yescharacteristic
37#63576C2211yescharacteristic
38Dic3⋊(C3⋊C8)C2212yes—
39#63565C2211yescharacteristic
40#63565C2211yescharacteristic
41#63564C2212yes—
42Dic3×C3⋊C8C2212yes—
43C3×#557—31no—
44#5721D311yescharacteristic, complemented
45#5585—31no—
46#5585—31no—
47C3×#475—31no—
48#5094D311yescharacteristic, complemented
49#5088—31no—
50#5088—31no—
51#5088—61no—
52#5068—32no—
53#5066—32no—
54C4×#216—31no—
55C4×#216—31no—
56#5028—32no—
57#5027—31no—
58C4×#215—32no—
59Q8×C3⋊C8—31no—
60#4871—32no—
61#4852—32no—
62#4848—31no—
63#4830—31no—
64#4800—32no—
65#4798—32no—
66C2×C32×Q8—21no—
67C2×C4⋊(C3⋊D3)—21no—
68C2×C4⋊(C3⋊D3)—21no—
69C2×C4⋊(C3⋊D3)C2312yes—
70C2×C3×Dic6D411yescharacteristic
71C2×C3×Dic6C2311yescharacteristic
72C2×C3×Dic6C2311yescharacteristic
73C2×#624—22no—
74C32×C4⋊C4—21no—
75C32×C4⋊C4C2312yes—
76C32×C42C2311yescharacteristic
77C2×C3⋊(C3⋊C8)C2311yescharacteristic
78C2×C3⋊(C3⋊C8)C2311yescharacteristic
79C3×C4⋊Dic3—22no—
80C3×C4⋊Dic3D411yescharacteristic
81C3×C4⋊Dic3C2311yescharacteristic
82C3×C4⋊Dic3C2311yescharacteristic
83C3×Dic3⋊C4—21no—
84C3×Dic3⋊C4—21no—
85C3×Dic3⋊C4—22no—
86C3×Dic3⋊C4—22no—
87C3×Dic3⋊C4D412yes—
88C3×C4×Dic3—21no—
89C3×C4×Dic3—21no—
90C3×C4×Dic3—22no—
91C3×C4×Dic3C2312yes—
92C2×C3×C3⋊C8C2312yes—
93#3722—22no—
94#3722—22no—
95#3722—22no—
96#3718—22no—
97#3717—24no—
98#3365—91noSylow
99C3×C4⋊Q8—21no—
100C3×C4⋊Q8—61no—
101C3×C4⋊Q8C2×D311yescharacteristic
102C3×C4⋊Q8C2×D311yescharacteristic
103C3×#125—32no—
104C3×#125—62no—
105C3×C4×Q8—31no—
106C3×C4×Q8—32no—
107C3×C4×Q8—31no—
108C3×C4×Q8—31no—
109C3×C4×Q8—61no—
110#947—32no—
111#947—61no—
112Q8×Dic3—21no—
113#944—21no—
114C2×#216—31no—
115C2×#216—31no—
116C2×#215—32no—
117C2×#204—32no—
118#894—62no—
119#894—62no—
120#893—32no—
121#893—61no—
122#890C2×D312yes—
123#889—22no—
124#887C2×D312yes—
125#875—32no—
126#875—61no—
127#874—31no—
128#874—31no—
129#874—61no—
130C4×D12—32no—
131C4×D12—61no—
132C4×Dic6C2×D311yescharacteristic
133C4×Dic6C2×D311yescharacteristic
134C4×Dic6C2×D311yescharacteristic
135C3×#106—32no—
136C3×C4⋊C8—31no—
137C3×#103—32no—
138#835—31no—
139#835—31no—
140#821—32no—
141Dic3⋊C8—32no—
142C8×Dic3—32no—
143#810—31no—
144#810—31no—
145#810C2×D312yes—
146#809—32no—
147#809—32no—
148#809—32no—
149#809—32no—
150#809—32no—
151#809—62no—
152#809—62no—
153#808C2×D312yes—
154#807—31no—
155#807—31no—
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—
163C32×Q8—42no—
164C2×C32×C4—22no—
165C2×C32×C4C2×D411yescharacteristic
166C2×C32×C4C2×D411yescharacteristic
167C2×C32×C4C2411yescharacteristic
168C4⋊(C3⋊D3)—22no—
169C4⋊(C3⋊D3)—22no—
170C4⋊(C3⋊D3)—42no—
171C4⋊(C3⋊D3)—81no—
172C2×C3×Dic3—21no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3C2×D412yes—
177C2×C3×Dic3C2×D412yes—
178C3×Dic6—22no—
179C3×Dic6—21no—
180C3×Dic6—21no—
181C3×Dic6—21no—
182C3×Dic6#4112yes—
183#624—82no—
184C3⋊(C3⋊C8)—21no—
185C3⋊(C3⋊C8)—21no—
186C3×C3⋊C8—22no—
187#559—91no—
188#557—31no—
189#488—92no—
190#486—91no—
191#478—92no—
192#475—31no—
193#464—92no—
194#460—91no—
195C8×Q8—91no—
196C4×Q16—91no—
197C4×SD16—92no—
198C2×C3×Q8—21no—
199C2×C3×Q8—21no—
200C2×C3×Q8—31no—
201C2×C3×Q8—31no—
202C2×C3×Q8—31no—
203C2×C3×Q8—41no—
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#6711yescharacteristic
216C2×Dic6C22×D311yescharacteristic
217C2×Dic6C22×D311yescharacteristic
218C2×C3×C8—32no—
219C3×C4⋊C4—21no—
220C3×C4⋊C4—21no—
221C3×C4⋊C4—22no—
222C3×C4⋊C4—31no—
223C3×C4⋊C4—32no—
224C3×C4⋊C4—31no—
225C3×C4⋊C4—31no—
226C3×C4⋊C4—41no—
227C3×C4⋊C4—62no—
228C3×C4⋊C4—62no—
229C3×C4⋊C4—62no—
230C3×C4⋊C4—61no—
231C3×C4⋊C4—61no—
232C3×C4⋊C4C22×D312yes—
233C3×C4⋊C4C22×D312yes—
234C3×C42—21no—
235C3×C42—32no—
236C3×C42—62no—
237C3×C42—61no—
238C3×C42—61no—
239C3×C42C22×D311yescharacteristic
240C3×C42C22×D311yescharacteristic
241#216—62no—
242#216—62no—
243#215—64no—
244(C2×D3)⋊C4—62no—
245(C2×D3)⋊C4—62no—
246(C2×D3)⋊C4—62no—
247(C2×D3)⋊C4—62no—
248(C2×D3)⋊C4—62no—
249(C2×D3)⋊C4—62no—
250C4⋊Dic3—22no—
251C4⋊Dic3#6711yescharacteristic
252C4⋊Dic3C22×D311yescharacteristic
253C4⋊Dic3C22×D311yescharacteristic
254Dic3⋊C4—21no—
255Dic3⋊C4—21no—
256Dic3⋊C4—22no—
257Dic3⋊C4—22no—
258Dic3⋊C4#6712yes—
259C4×Dic3—21no—
260C4×Dic3—21no—
261C4×Dic3—22no—
262C4×Dic3C22×D312yes—
263C2×C3⋊C8—31no—
264C2×C3⋊C8—31no—
265C2×C3⋊C8—31no—
266C2×C3⋊C8—31no—
267C2×C3⋊C8—61no—
268C2×C3⋊C8—61no—
269C2×C3⋊C8C22×D312yes—
270#204—64no—
271C22×C32C22×D411yescharacteristic
272C2×C3⋊D3—42no—
273C2×C3⋊D3—42no—
274C2×C3⋊D3—42no—
275C32×C4—21no—
276C32×C4—42no—
277C32×C4#13512yes—
278C32×C4C2×#4111yescharacteristic
279C32×C42−1+411yescharacteristic
280C3×Dic3—22no—
281C3×Dic3—22no—
282C3×Dic3—22no—
283C3×Dic3—41no—
284C3×Dic3—41no—
285C3×Dic3—41no—
286C2×Q16—91no—
287C2×SD16—92no—
288C4⋊Q8—61no—
289C4⋊Q8D3211yescharacteristic
290#127—91no—
291#125—32no—
292#125—62no—
293#124—92no—
294#124—181no—
295#123—182no—
296C4×Q8—31no—
297C4×Q8—32no—
298C4×Q8—31no—
299C4×Q8—31no—
300C4×Q8—61no—
301C4×D4—92no—
302C4×D4—181no—
303#107—91no—
304#106—32no—
305C4⋊C8—31no—
306C4⋊C8—92no—
307#103—32no—
308#103—91no—
309#103—91no—
310#102—92no—
311#102—92no—
312#102—92no—
313C4×C8—92no—
314C4×C8—91no—
315C22×D3—62no—
316C22×D3—62no—
317C22×D3—122no—
318C3×Q8—32no—
319C3×Q8—42no—
320C3×Q8—42no—
321C3×Q8—62no—
322C3×Q8—61no—
323C3×Q8—61no—
324C3×Q8—61no—
325C3×Q8—82no—
326C2×C3×C4—22no—
327C2×C3×C4—22no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—32no—
332C2×C3×C4—32no—
333C2×C3×C4—42no—
334C2×C3×C4—61no—
335C2×C3×C4—61no—
336C2×C3×C4—61no—
337C2×C3×C4—61no—
338C2×C3×C4D3×D411yescharacteristic
339C2×C3×C4D3×D411yescharacteristic
340C2×C3×C4C2×#6711yescharacteristic
341C2×C3×C4C2×#6711yescharacteristic
342C2×C3×C4C23×D311yescharacteristic
343C2×C3×C4C23×D311yescharacteristic
344C2×Dic3—21no—
345C2×Dic3—21no—
346C2×Dic3—21no—
347C2×Dic3—21no—
348C2×Dic3C2×#6712yes—
349C2×Dic3C2×#6712yes—
350D12—62no—
351D12—62no—
352D12—62no—
353D12—62no—
354D12—122no—
355D12—122no—
356D12—122no—
357D12—122no—
358D12—242no—
359D12—241no—
360D12—241no—
361D12—242no—
362C4×D3—242no—
363C4×D3—242no—
364Dic6—22no—
365Dic6—21no—
366Dic6—21no—
367Dic6—21no—
368Dic6#23912yes—
369C3×C8—62no—
370C3⋊C8—22no—
371C3⋊C8—61no—
372C3⋊C8—61no—
373C3⋊C8—61no—
374C3⋊C8—61no—
375C3⋊C8—121no—
376C3⋊C8—121no—
377C2×C32#54811yescharacteristic
378C2×C32C2×#13511yescharacteristic
379C2×C32#57711yescharacteristic
380C3⋊D3—82no—
381C2×Q8—21no—
382C2×Q8—31no—
383C2×Q8—31no—
384C2×Q8—31no—
385C2×D4—92no—
386C2×D4—181no—
387C2×D4—181no—
388C22×C4—182no—
389Q16—182no—
390SD16—184no—
391C2×C8—32no—
392C2×C8—91no—
393C2×C8—91no—
394C4⋊C4—21no—
395C4⋊C4—31no—
396C4⋊C4—32no—
397C4⋊C4—31no—
398C4⋊C4—31no—
399C4⋊C4—62no—
400C4⋊C4—62no—
401C4⋊C4—62no—
402C4⋊C4—61no—
403C4⋊C4—61no—
404C4⋊C4C2×D3212yes—
405C22⋊C4—182no—
406C22⋊C4—182no—
407C22⋊C4—182no—
408C42—32no—
409C42—62no—
410C42—61no—
411C42—61no—
412C42C2×D3211yescharacteristic
413C22×C3—21no—
414C22×C3C2×D3×D411yescharacteristic
415C22×C3C22×#6711yescharacteristic
416C2×D3—122no—
417C2×D3—122no—
418C2×D3—122no—
419C2×D3—122no—
420C2×D3—122no—
421C2×D3—122no—
422C2×D3—242no—
423C2×D3—242no—
424C2×D3—242no—
425C3×C4—22no—
426C3×C4—21no—
427C3×C4—21no—
428C3×C4—21no—
429C3×C4—21no—
430C3×C4—22no—
431C3×C4—42no—
432C3×C4—42no—
433C3×C4—62no—
434C3×C4—62no—
435C3×C4—62no—
436C3×C4—82no—
437C3×C4—121no—
438C3×C4—121no—
439C3×C4—121no—
440C3×C4#91612yes—
441C3×C4#95012yes—
442C3×C4C2×#23911yescharacteristic
443C3×C4#100711yescharacteristic
444C3×C4#100711yescharacteristic
445C3×C4D3×#4111yescharacteristic
446Dic3—22no—
447Dic3—22no—
448Dic3—22no—
449Dic3—41no—
450Dic3—41no—
451Dic3—41no—
452C32#336511yescharacteristic, complemented, Sylow
453C23—182no—
454Q8—32no—
455Q8—42no—
456Q8—61no—
457Q8—62no—
458Q8—61no—
459Q8—61no—
460D4—182no—
461D4—182no—
462D4—362no—
463D4—721no—
464C2×C4—22no—
465C2×C4—32no—
466C2×C4—32no—
467C2×C4—61no—
468C2×C4—61no—
469C2×C4—61no—
470C2×C4—61no—
471C2×C4—722no—
472C2×C4D3×#6711yescharacteristic
473C2×C4D3×#6711yescharacteristic
474C2×C4C22×D3211yescharacteristic
475C8—62no—
476C8—181no—
477C8—181no—
478C2×C3—21no—
479C2×C3—21no—
480C2×C3—21no—
481C2×C3#563311yescharacteristic
482C2×C3C2×#91611yescharacteristic
483C2×C3#577811yescharacteristic
484C2×C3#581711yescharacteristic
485C2×C3C2×#95011yescharacteristic
486C2×C3#583711yescharacteristic
487D3—242no—
488D3—242no—
489D3—482no—
490C22—362no—
491C22—362no—
492C22—362no—
493C22C2×D3×#6711yescharacteristic
494C4—21no—
495C4—42no—
496C4—62no—
497C4—62no—
498C4—62no—
499C4—121no—
500C4—121no—
501C4—121no—
502C4#6393512yes—
503C4#6431611yescharacteristic
504C4D3×#23911yescharacteristic
505C3—21no—
506C3#8104111yescharacteristic, complemented
507C3#8369711yescharacteristic, complemented
508C2—722no—
509C2C2×#6393511yescharacteristic
510C2#1059531911yescharacteristic
511C2#1059540211yescharacteristic
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×#5721C2semidirect
4. C3×#5094C2semidirect
5. #10590537C2semidirect
6. #10590536C2semidirect
7. #10590470C2semidirect
8. #10590458C2semidirect
9. C4×#3718C2semidirect
11. #10590250C2semidirect
44. #5721D3semidirect
48. #5094D3semidirect
452. C32#3365semidirect
506. C3#81041semidirect
507. C3#83697semidirect

Maximal subgroups

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

subgroupindex
C3×#57212
#105939632
#105927872
C3×#50942
#105905372
#105905362
#105904702
#105904582
C4×#37182
#105903672
#105902502
#836973
#810413