Finite Group Databasebeta

← #11783788

Subgroups — #11783788

Order 1152.

813 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
1C2×#63894C211yesmaximal, characteristic
2C2×#63650C211yesmaximal, characteristic
3C3×Dic3×M16C211yesmaximal, characteristic, complemented
4C2×#63559C211yesmaximal, characteristic
5Dic3×#208C211yesmaximal, characteristic, complemented
6C3×#4554C211yesmaximal, characteristic, complemented
7#10589167C211yesmaximal, characteristic, complemented
8C4×#823—31nomaximal
9#68972—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×#624C412yes—
12C2×C32×M16C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C2×C3×#208C2211yescharacteristic
18C2×#3722C412yes—
19#63894—21no—
20#63894—21no—
21#63894—21no—
22#63894—21no—
23#63650C414yescomplemented
24C3×#815—21no—
25C3×C8×Dic3—21no—
26#63559C414yescomplemented
27#63554—21no—
28Dic3×C3⋊C8—21no—
29C2×#893—31no—
30C2×C4×D12—31no—
31C3×C4×M16—31no—
32C2×#823—31no—
33C2×#823—31no—
34C2×#823—31no—
35C2×#823—31no—
36C2×#823—61no—
37Dic3×M16—31no—
38Dic3×M16D311yescharacteristic, complemented
39C4×#208—31no—
40C3×#343—31no—
41#4554—31no—
42#4554D311yescharacteristic, complemented
43#4530—31no—
44C23×C3⋊D3C2×C412yes—
45C22×C32×C4C2311yescharacteristic
46C2×C4⋊(C3⋊D3)—21no—
47C2×C4⋊(C3⋊D3)—21no—
48C2×C4⋊(C3⋊D3)—21no—
49C2×C4⋊(C3⋊D3)—21no—
50C2×C4⋊(C3⋊D3)C2×C412yes—
51C2×C4⋊(C3⋊D3)C2×C412yes—
52C22×C3×Dic3C2×C411yescharacteristic
53C22×C3×Dic3C2×C412yes—
54C22×C3×Dic3C2×C411yescharacteristic
55C2×#624—22no—
56C2×#624—22no—
57C2×#624—44no—
58C32×M16—21no—
59C32×M16C2×C412yescomplemented
60C2×C32×C8—21no—
61#3748—21no—
62#3748C2×C412yescomplemented
63C2×C3⋊(C3⋊C8)—21no—
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3—21no—
66C3×C4×Dic3D411yescharacteristic
67C3×C4×Dic3D411yescharacteristic
68C3×C4×Dic3D411yescharacteristic
69C3×C4×Dic3D411yescharacteristic
70C3×#208—21no—
71C3×#208—21no—
72C3×#208C2×C412yescomplemented
73C3×#208C2×C412yescomplemented
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8—21no—
76#3722—22no—
77#3722—22no—
78C4×#100—91noSylow
79C22×D12—31no—
80C22×D12—31no—
81C22×D12—61no—
82C22×C4×D3—32no—
83C22×C4×D3—32no—
84C2×C3×M16—21no—
85C2×C3×M16—31no—
86C2×C3×M16—31no—
87C2×C3×M16C2×D311yescharacteristic
88C2×C3×M16C2×D311yescharacteristic
89C2×C3×C4⋊C4—31no—
90C2×C3×C42—31no—
91C2×(C2×D3)⋊C4—32no—
92C2×(C2×D3)⋊C4—32no—
93C2×C4⋊Dic3C2×D311yescharacteristic
94C2×C4×Dic3C2×D311yescharacteristic
95C2×#208—31no—
96C2×#208—31no—
97C2×#208—61no—
98C2×#208C2×D311yescharacteristic
99C2×#208C2×D311yescharacteristic
100#893—61no—
101#893—61no—
102#893—61no—
103#893—61no—
104C4×D12—61no—
105C4×D12—61no—
106C4×D12—61no—
107C4×D12—61no—
108C3×#97—61no—
109C3×C4×C8—61no—
110#823—34no—
111#823—34no—
112#823—34no—
113#823—34no—
114#823—64no—
115#815—21no—
116#815—61no—
117C8×Dic3—21no—
118C8×Dic3—61no—
119#803—61no—
120C4×C3⋊C8—61no—
121C23×C32C22×C411yescharacteristic
122C22×C3⋊D3—22no—
123C22×C3⋊D3—22no—
124C22×C3⋊D3—42no—
125C22×C3⋊D3—42no—
126C22×C3⋊D3C4214yes—
127C2×C32×C4C22×C411yescharacteristic
128C2×C32×C4C22×C411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4#4111yescharacteristic
132C2×C32×C4#4111yescharacteristic
133C4⋊(C3⋊D3)—22no—
134C4⋊(C3⋊D3)—22no—
135C4⋊(C3⋊D3)—22no—
136C4⋊(C3⋊D3)—22no—
137C2×C3×Dic3—22no—
138C2×C3×Dic3—22no—
139C2×C3×Dic3—41no—
140C2×C3×Dic3—42no—
141C2×C3×Dic3C22⋊C411yescharacteristic
142C2×C3×Dic3C22⋊C411yescharacteristic
143C2×C3×Dic3C22⋊C411yescharacteristic
144C2×C3×Dic3C22⋊C411yescharacteristic
145#624—44no—
146#624—44no—
147C32×C8—22no—
148C3⋊(C3⋊C8)—22no—
149C3×C3⋊C8—22no—
150C3×C3⋊C8—22no—
151C2×C4×D4—91no—
152C2×#100—91no—
153C2×#100—91no—
154C4×M16—31no—
155C4×M16—91no—
156#343—31no—
157#343—91no—
158C23×D3—32no—
159C23×D3—32no—
160C23×D3—62no—
161C22×C3×C4—21no—
162C22×C3×C4—31no—
163C22×C3×C4—31no—
164C22×C3×C4—32no—
165C22×C3×C4C22×D311yescharacteristic
166C22×C3×C4C22×D311yescharacteristic
167C22×Dic3C4×D311yescharacteristic
168C22×Dic3C4×D312yes—
169C22×Dic3C4×D311yescharacteristic
170C2×D12—32no—
171C2×D12—32no—
172C2×D12—32no—
173C2×D12—32no—
174C2×D12—62no—
175C2×D12—62no—
176C2×D12—61no—
177C2×D12—61no—
178C2×D12—61no—
179C2×D12—61no—
180C2×D12—61no—
181C2×D12—61no—
182C2×D12—61no—
183C2×D12—61no—
184C2×D12—121no—
185C2×D12—121no—
186C2×D12—121no—
187C2×D12—121no—
188C2×C4×D3—62no—
189C2×C4×D3—62no—
190C2×C4×D3—62no—
191C2×C4×D3—62no—
192C2×C4×D3—124no—
193C2×C4×D3—124no—
194C3×M16—21no—
195C3×M16—21no—
196C3×M16—22no—
197C3×M16—32no—
198C3×M16—32no—
199C3×M16—41no—
200C3×M16—61no—
201C3×M16—61no—
202C3×M16C4×D312yescomplemented
203C3×M16C4×D312yescomplemented
204C2×C3×C8—21no—
205C2×C3×C8—21no—
206C2×C3×C8—41no—
207C2×C3×C8—61no—
208C2×C3×C8—61no—
209C3×C4⋊C4—61no—
210C3×C4⋊C4—61no—
211C3×C42—31no—
212C3×C42—31no—
213C3×C42—31no—
214C3×C42—31no—
215(C2×D3)⋊C4—62no—
216(C2×D3)⋊C4—62no—
217(C2×D3)⋊C4—62no—
218(C2×D3)⋊C4—62no—
219C4⋊Dic3—21no—
220C4⋊Dic3—21no—
221C4×Dic3D1211yescharacteristic
222C4×Dic3D1211yescharacteristic
223C4×Dic3#6711yescharacteristic
224C4×Dic3#6711yescharacteristic
225#208—21no—
226#208—21no—
227#208—32no—
228#208—32no—
229#208—62no—
230#208—61no—
231#208—61no—
232#208—121no—
233#208C4×D312yescomplemented
234#208C4×D312yescomplemented
235C2×C3⋊C8—21no—
236C2×C3⋊C8—21no—
237C2×C3⋊C8—61no—
238C2×C3⋊C8—61no—
239C2×C3⋊C8—121no—
240C22×C32—21no—
241C22×C32—21no—
242C22×C32C2×C4211yescharacteristic
243C22×C32C2×C22⋊C411yescharacteristic
244C22×C32#11711yescharacteristic
245C2×C3⋊D3—24no—
246C2×C3⋊D3—44no—
247C2×C3⋊D3—42no—
248C2×C3⋊D3—42no—
249C2×C3⋊D3—44no—
250C32×C4C4×D411yescharacteristic
251C32×C4C4×D411yescharacteristic
252C32×C4C4×D411yescharacteristic
253C32×C4C4×D411yescharacteristic
254C3×Dic3—21no—
255C3×Dic3—21no—
256C3×Dic3—21no—
257C3×Dic3—42no—
258C3×Dic3#10012yescomplemented
259C22×D4—91no—
260C23×C4—92no—
261C2×M16—31no—
262C2×M16—31no—
263C2×M16—91no—
264C2×M16D3211yescharacteristic
265C4×D4—181no—
266C4×D4—181no—
267C4×D4—181no—
268C4×D4—181no—
269C2×C4⋊C4—31no—
270C2×C22⋊C4—92no—
271C2×C42—31no—
272#100—94no—
273#100—94no—
274#97—61no—
275#97—181no—
276C4×C8—61no—
277C4×C8—181no—
278C23×C3—21no—
279C23×C3C2×C4×D311yescharacteristic
280C23×C3C2×C4×D311yescharacteristic
281C22×D3—34no—
282C22×D3—34no—
283C22×D3—64no—
284C22×D3—62no—
285C22×D3—62no—
286C22×D3—62no—
287C22×D3—62no—
288C22×D3—122no—
289C22×D3—122no—
290C22×D3—122no—
291C22×D3—122no—
292C22×D3—122no—
293C22×D3—122no—
294C22×D3—242no—
295C22×D3—242no—
296C2×C3×C4—21no—
297C2×C3×C4—21no—
298C2×C3×C4—21no—
299C2×C3×C4—21no—
300C2×C3×C4—21no—
301C2×C3×C4—21no—
302C2×C3×C4—31no—
303C2×C3×C4—31no—
304C2×C3×C4—31no—
305C2×C3×C4—31no—
306C2×C3×C4—62no—
307C2×C3×C4—62no—
308C2×C3×C4—121no—
309C2×C3×C4—122no—
310C2×C3×C4C2×C4×D311yescharacteristic
311C2×C3×C4C2×C4×D311yescharacteristic
312C2×C3×C4C2×C4×D311yescharacteristic
313C2×C3×C4C2×C4×D311yescharacteristic
314C2×C3×C4C2×D1211yescharacteristic
315C2×C3×C4#23511yescharacteristic
316C2×C3×C4#23511yescharacteristic
317C2×C3×C4D3×D411yescharacteristic
318C2×C3×C4D3×D411yescharacteristic
319C2×C3×C4#23711yescharacteristic
320C2×C3×C4#23911yescharacteristic
321C2×C3×C4C2×#6711yescharacteristic
322C2×Dic3—22no—
323C2×Dic3—22no—
324C2×Dic3—41no—
325C2×Dic3—42no—
326C2×Dic3(C2×D3)⋊C411yescharacteristic
327C2×Dic3(C2×D3)⋊C411yescharacteristic
328C2×Dic3(C2×D3)⋊C411yescharacteristic
329C2×Dic3(C2×D3)⋊C411yescharacteristic
330D12—62no—
331D12—62no—
332D12—62no—
333D12—62no—
334D12—62no—
335D12—62no—
336D12—62no—
337D12—62no—
338D12—122no—
339D12—122no—
340D12—122no—
341D12—122no—
342C4×D3—124no—
343C4×D3—124no—
344C4×D3—124no—
345C4×D3—124no—
346C3×C8—22no—
347C3×C8—22no—
348C3×C8—42no—
349C3×C8—62no—
350C3×C8—62no—
351C3⋊C8—22no—
352C3⋊C8—22no—
353C3⋊C8—62no—
354C3⋊C8—62no—
355C3⋊C8—122no—
356C2×C32—21no—
357C2×C32—21no—
358C2×C32C4×C22⋊C411yescharacteristic
359C2×C32C2×#10011yescharacteristic
360C2×C32#41311yescharacteristic
361C3⋊D3—44no—
362C24—92no—
363C2×D4—92no—
364C2×D4—92no—
365C2×D4—181no—
366C2×D4—181no—
367C2×D4—181no—
368C2×D4—181no—
369C22×C4—31no—
370C22×C4—31no—
371C22×C4—32no—
372C22×C4—182no—
373C22×C4—182no—
374C22×C4—364no—
375C22×C4C2×D3211yescharacteristic
376M16—21no—
377M16—32no—
378M16—32no—
379M16—61no—
380M16—61no—
381M16—92no—
382M16—181no—
383M16#62412yescomplemented
384C2×C8—21no—
385C2×C8—61no—
386C2×C8—61no—
387C2×C8—181no—
388C4⋊C4—61no—
389C4⋊C4—61no—
390C22⋊C4—182no—
391C22⋊C4—182no—
392C42—31no—
393C42—31no—
394C42—31no—
395C42—31no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—21no—
399C22×C3—21no—
400C22×C3—21no—
401C22×C3—21no—
402C22×C3—21no—
403C22×C3—41no—
404C22×C3—41no—
405C22×C3C42×D311yescharacteristic
406C22×C3C42×D311yescharacteristic
407C22×C3#87211yescharacteristic
408C22×C3D3×C22⋊C411yescharacteristic
409C22×C3#89211yescharacteristic
410C22×C3C2×(C2×D3)⋊C411yescharacteristic
411C2×D3—64no—
412C2×D3—64no—
413C2×D3—124no—
414C2×D3—124no—
415C2×D3—124no—
416C2×D3—122no—
417C2×D3—122no—
418C2×D3—122no—
419C2×D3—122no—
420C2×D3—124no—
421C2×D3—124no—
422C2×D3—242no—
423C2×D3—242no—
424C2×D3—244no—
425C2×D3—244no—
426C3×C4—21no—
427C3×C4—21no—
428C3×C4—21no—
429C3×C4—21no—
430C3×C4—32no—
431C3×C4—61no—
432C3×C4—61no—
433C3×C4—61no—
434C3×C4—122no—
435C3×C4C4×D1211yescharacteristic
436C3×C4C4×D1211yescharacteristic
437C3×C4#67⋊C411yescharacteristic
438C3×C4#67⋊C411yescharacteristic
439C3×C4#89311yescharacteristic
440C3×C4#89311yescharacteristic
441C3×C4C4×#6711yescharacteristic
442C3×C4C4×#6711yescharacteristic
443Dic3—21no—
444Dic3—21no—
445Dic3—21no—
446Dic3—42no—
447Dic3#82312yescomplemented
448C32C4×#10011yescharacteristic, complemented, Sylow
449C23—94no—
450C23—182no—
451C23—182no—
452C23—362no—
453C23—362no—
454C23C4×D3211yescharacteristic
455D4—182no—
456D4—182no—
457D4—182no—
458D4—182no—
459C2×C4—31no—
460C2×C4—31no—
461C2×C4—31no—
462C2×C4—31no—
463C2×C4—62no—
464C2×C4—62no—
465C2×C4—121no—
466C2×C4—122no—
467C2×C4—364no—
468C2×C4—364no—
469C2×C4#379911yescharacteristic
470C2×C4C4×D3211yescharacteristic
471C2×C4D3×D1211yescharacteristic
472C2×C4#380411yescharacteristic
473C2×C4C2×#62411yescharacteristic
474C2×C4D3×#6711yescharacteristic
475C8—22no—
476C8—62no—
477C8—62no—
478C8—182no—
479C2×C3—21no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—21no—
483C2×C3—21no—
484C2×C3—21no—
485C2×C3—21no—
486C2×C3—41no—
487C2×C3—41no—
488C2×C3#466611yescharacteristic
489C2×C3D3×#10011yescharacteristic
490C2×C3#475111yescharacteristic
491C2×C3C4×(C2×D3)⋊C411yescharacteristic
492C2×C3C2×#82311yescharacteristic
493C2×C3#513211yescharacteristic
494D3—124no—
495D3—124no—
496D3—244no—
497C22—21no—
498C22—21no—
499C22—184no—
500C22—364no—
501C22—364no—
502C22—362no—
503C22—362no—
504C22#6383611yescharacteristic
505C22C4×#62411yescharacteristic
506C22D3×(C2×D3)⋊C411yescharacteristic
507C4—32no—
508C4—61no—
509C4—61no—
510C4—61no—
511C4—122no—
512C4#6388011yescharacteristic
513C4#6389411yescharacteristic
514C4#6390411yescharacteristic
515C4#6395211yescharacteristic
516C3—21no—
517C3#6897211yescharacteristic, complemented
518C3C4×#82311yescharacteristic, complemented
519C2—21no—
520C2—21no—
521C2—364no—
522C2D3×#82311yescharacteristic
523C2#1059100711yescharacteristic
524C2#1059123311yescharacteristic
subgroupG/H
centerC22D3×(C2×D3)⋊C4
commutatorC22×C32C2×C42
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32C2×C22⋊C4
prime radicalC22×C4⋊(C3⋊D3)C22
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32C4×#100
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
3. C3×Dic3×M16C2semidirect
5. Dic3×#208C2semidirect
6. C3×#4554C2semidirect
7. #10589167C2semidirect
23. #63650C4semidirect
26. #63559C4semidirect
38. Dic3×M16D3semidirect
42. #4554D3semidirect
59. C32×M16C2×C4semidirect
62. #3748C2×C4semidirect
72. C3×#208C2×C4semidirect
73. C3×#208C2×C4semidirect
202. C3×M16C4×D3semidirect
203. C3×M16C4×D3semidirect
233. #208C4×D3semidirect
234. #208C4×D3semidirect
258. C3×Dic3#100semidirect
383. M16#624semidirect
447. Dic3#823semidirect
448. C32C4×#100semidirect
517. C3#68972semidirect
518. C3C4×#823semidirect

Maximal subgroups

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

subgroupindex
C2×#638942
C2×#636502
C3×Dic3×M162
C2×#635592
Dic3×#2082
C3×#45542
#105891672
C4×#8233
#689723