Finite Group Databasebeta

← #11783878

Subgroups — #11783878

Order 1152.

805 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594954C211yesmaximal, characteristic
2C2×#63632C211yesmaximal, characteristic
3C3×C42×Dic3C211yesmaximal, characteristic, complemented
4C2×#63570C211yesmaximal, characteristic
5Dic3×#208C211yesmaximal, characteristic, complemented
6C3×#4523C211yesmaximal, characteristic, complemented
7#10589161C211yesmaximal, characteristic, complemented
8C4×#805—31nomaximal
9#68728—31nomaximal
10C2×#3828C2211yescharacteristic
11C2×C32×C42C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C3×#926C2211yescharacteristic
14C2×C3×C4×Dic3—22no—
15C2×C3×C4×Dic3C2211yescharacteristic
16C2×C3×C4×Dic3C2211yescharacteristic
17C2×C3×#208C2211yescharacteristic
18#63952—22no—
19#63894C412yescomplemented
20C4×#624—21no—
21#63874—21no—
22#63844C412yescomplemented
23#63632C414yescomplemented
24#63570C414yescomplemented
25#63554—21no—
26Dic3×C3⋊C8—21no—
27#5522—31no—
28C4×#235—31no—
29C3×C43—31no—
30C2×#825—31no—
31Dic3×M16—31no—
32C42×Dic3D311yescharacteristic, complemented
33C2×#805—31no—
34C2×#805—31no—
35C2×#805—31no—
36C2×#805—61no—
37C4×#208—31no—
38C3×#339—31no—
39#4532—31no—
40#4523—31no—
41#4523D311yescharacteristic, complemented
42C22×C32×C4—21no—
43C22×C32×C4C2311yescharacteristic
44C2×#638—21no—
45#3828—21no—
46#3828—21no—
47#3828C2×C412yes—
48#3828C2×C412yes—
49C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
50C2×C4×C3⋊D3—21no—
51C2×#634C2×C411yescharacteristic
52C22×C3×Dic3—21no—
53C22×C3×Dic3D412yes—
54C2×#624—22no—
55C32×C42—21no—
56C32×C42C2×C412yescomplemented
57#3748—21no—
58#3748C2×C412yescomplemented
59C2×C3⋊(C3⋊C8)—21no—
60C3×#217—21no—
61C3×C4⋊Dic3C2×C412yes—
62C3×C4×Dic3—28no—
63C3×C4×Dic3—21no—
64C3×C4×Dic3—21no—
65C3×C4×Dic3C2×C412yes—
66C3×C4×Dic3C2×C412yescomplemented
67C3×C4×Dic3D411yescharacteristic
68C3×C4×Dic3D411yescharacteristic
69C3×#208—21no—
70C3×#208C2×C412yescomplemented
71C2×C3×C3⋊C8—21no—
72#3724—22no—
73#3722—22no—
74Dic32—22no—
75C4×#104—91noSylow
76C2×#235—31no—
77C2×#235—31no—
78C2×#235—61no—
79C2×C3×M16—31no—
80C3×#117—31no—
81C2×C3×C42—21no—
82C2×C3×C42—31no—
83C2×C3×C42—31no—
84C2×C3×C42—62no—
85C2×C3×C42C2×D311yescharacteristic
86C2×C3×C42C2×D311yescharacteristic
87C4×#67—62no—
88#926C2×D311yescharacteristic
89C2×C4×Dic3—22no—
90C2×C4×Dic3C2×D311yescharacteristic
91C2×C4×Dic3C2×D311yescharacteristic
92C2×#208—31no—
93C2×#208—31no—
94C2×#208—61no—
95C2×#208C2×D311yescharacteristic
96#893—32no—
97#887—32no—
98#67⋊C4—62no—
99C4×D12—32no—
100#872—61no—
101#872—61no—
102C42×D3—61no—
103C42×D3—61no—
104C4×Dic6—32no—
105#825—34no—
106#815—61no—
107C8×Dic3—61no—
108#805—34no—
109#805—34no—
110#805—34no—
111#805—64no—
112#803—61no—
113C4×C3⋊C8—61no—
114C23×C32C2×D411yescharacteristic
115C22×C3⋊D3—21no—
116C2×C32×C4—24no—
117C2×C32×C4—22no—
118C2×C32×C4C22×C411yescharacteristic
119C2×C32×C4C22×C411yescharacteristic
120C2×C32×C4C22×C411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4#4111yescharacteristic
123C2×C32×C4#4111yescharacteristic
124#638—22no—
125#638—22no—
126C2×C3⋊Dic3—21no—
127C4⋊(C3⋊D3)—21no—
128C4⋊(C3⋊D3)C4212yescomplemented
129C4×C3⋊D3—22no—
130C4×C3⋊D3—22no—
131#634—21no—
132#634C4212yescomplemented
133C2×C3×Dic3—24no—
134C2×C3×Dic3—22no—
135C2×C3×Dic3—24no—
136C2×C3×Dic3—22no—
137C2×C3×Dic3C22⋊C412yes—
138C2×C3×Dic3C22⋊C412yes—
139#624—44no—
140C3⋊(C3⋊C8)—22no—
141C3×C3⋊C8—22no—
142C4×#41—91no—
143C2×#104—91no—
144C2×#104—91no—
145C4×M16—91no—
146C43—31no—
147#339—31no—
148#339—91no—
149C22×C3×C4—21no—
150C22×C3×C4—21no—
151C22×C3×C4—21no—
152C22×C3×C4—32no—
153C22×C3×C4—41no—
154C22×C3×C4—61no—
155C22×C3×C4C22×D311yescharacteristic
156C22×C3×C4C22×D311yescharacteristic
157C2×#67—61no—
158C2×#67—61no—
159C2×#67—121no—
160C22×Dic3—21no—
161C22×Dic3#6712yes—
162#235—32no—
163#235—32no—
164#235—32no—
165#235—32no—
166#235—62no—
167#235—62no—
168#235—61no—
169#235—61no—
170#235—61no—
171#235—61no—
172#235—121no—
173#235—121no—
174C2×D12—31no—
175C2×D12—31no—
176C2×D12—61no—
177C2×C4×D3—61no—
178C2×C4×D3—61no—
179C2×C4×D3—62no—
180C2×C4×D3—62no—
181C2×C4×D3—121no—
182C2×Dic6—31no—
183C2×Dic6—31no—
184C2×Dic6—61no—
185C3×M16—32no—
186C3×M16—61no—
187C2×C3×C8—61no—
188C3×C4⋊C4—32no—
189C3×C22⋊C4—61no—
190C3×C42—21no—
191C3×C42—21no—
192C3×C42—22no—
193C3×C42—32no—
194C3×C42—31no—
195C3×C42—31no—
196C3×C42—32no—
197C3×C42—41no—
198C3×C42—68no—
199C3×C42—61no—
200C3×C42—61no—
201C3×C42C4×D312yescomplemented
202C3×C42C4×D312yescomplemented
203#217—21no—
204(C2×D3)⋊C4—62no—
205(C2×D3)⋊C4—62no—
206C4⋊Dic3C4×D312yes—
207Dic3⋊C4—62no—
208Dic3⋊C4—62no—
209C4×Dic3—28no—
210C4×Dic3—21no—
211C4×Dic3—21no—
212C4×Dic3—62no—
213C4×Dic3—62no—
214C4×Dic3C4×D312yes—
215C4×Dic3C4×D312yescomplemented
216C4×Dic3D1211yescharacteristic
217C4×Dic3D1211yescharacteristic
218#208—21no—
219#208—32no—
220#208—32no—
221#208—62no—
222#208—61no—
223#208—61no—
224#208—121no—
225#208C4×D312yescomplemented
226C2×C3⋊C8—21no—
227C2×C3⋊C8—61no—
228C2×C3⋊C8—61no—
229C2×C3⋊C8—121no—
230C22×C32—22no—
231C22×C32C2×C22⋊C411yescharacteristic
232C22×C32C4×D411yescharacteristic
233C22×C32C4×D411yescharacteristic
234C2×C3⋊D3—22no—
235C2×C3⋊D3—42no—
236C32×C4—24no—
237C32×C4C2×C4211yescharacteristic
238C32×C4#11711yescharacteristic
239C32×C4C4×D411yescharacteristic
240C32×C4C4×D411yescharacteristic
241C3⋊Dic3—22no—
242C3×Dic3—24no—
243C3×Dic3—22no—
244C3×Dic3—42no—
245C3×Dic3#10414yescomplemented
246C2×#41—91no—
247C2×M16—31no—
248C2×M16—91no—
249C4×Q8—92no—
250C4×D4—92no—
251C4×D4—182no—
252#117—31no—
253#117—181no—
254C2×C42—31no—
255C2×C42—31no—
256C2×C42—62no—
257C2×C42—181no—
258C2×C42D3211yescharacteristic
259#104—94no—
260#104—94no—
261#97—181no—
262C4×C8—181no—
263C23×C3—21no—
264C23×C3D3×D411yescharacteristic
265C23×C3C2×#6711yescharacteristic
266C22×D3—61no—
267C22×D3—61no—
268C22×D3—121no—
269C2×C3×C4—24no—
270C2×C3×C4—24no—
271C2×C3×C4—22no—
272C2×C3×C4—22no—
273C2×C3×C4—21no—
274C2×C3×C4—21no—
275C2×C3×C4—21no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—32no—
280C2×C3×C4—32no—
281C2×C3×C4—42no—
282C2×C3×C4—44no—
283C2×C3×C4—64no—
284C2×C3×C4—64no—
285C2×C3×C4—62no—
286C2×C3×C4—62no—
287C2×C3×C4C2×C4×D311yescharacteristic
288C2×C3×C4C2×C4×D311yescharacteristic
289C2×C3×C4C2×C4×D311yescharacteristic
290C2×C3×C4C2×C4×D311yescharacteristic
291C2×C3×C4C2×C4×D311yescharacteristic
292C2×C3×C4C2×C4×D311yescharacteristic
293C2×C3×C4C2×D1211yescharacteristic
294C2×C3×C4#23511yescharacteristic
295C2×C3×C4#23511yescharacteristic
296C2×C3×C4D3×D411yescharacteristic
297C2×C3×C4#23711yescharacteristic
298C2×C3×C4#23911yescharacteristic
299#67—62no—
300#67—62no—
301#67—62no—
302#67—62no—
303#67—122no—
304#67—122no—
305C2×Dic3—24no—
306C2×Dic3—22no—
307C2×Dic3—24no—
308C2×Dic3—22no—
309C2×Dic3—61no—
310C2×Dic3—61no—
311C2×Dic3—121no—
312C2×Dic3(C2×D3)⋊C412yes—
313C2×Dic3(C2×D3)⋊C412yes—
314D12—32no—
315D12—32no—
316D12—62no—
317D12—61no—
318D12—61no—
319D12—121no—
320C4×D3—62no—
321C4×D3—62no—
322C4×D3—62no—
323C4×D3—62no—
324C4×D3—122no—
325C4×D3—122no—
326C4×D3—124no—
327C4×D3—124no—
328Dic6—32no—
329Dic6—32no—
330Dic6—62no—
331Dic6—61no—
332Dic6—61no—
333Dic6—121no—
334C3×C8—62no—
335C3⋊C8—22no—
336C3⋊C8—62no—
337C3⋊C8—62no—
338C3⋊C8—122no—
339C2×C32—21no—
340C2×C32—21no—
341C2×C32C4×C22⋊C411yescharacteristic
342C2×C32C2×#10412yes—
343C3⋊D3—42no—
344#41—92no—
345#41—92no—
346#41—181no—
347#41—181no—
348C2×Q8—91no—
349C2×D4—91no—
350C2×D4—181no—
351C22×C4—21no—
352C22×C4—32no—
353C22×C4—61no—
354C22×C4—182no—
355C22×C4—181no—
356C22×C4C2×D3211yescharacteristic
357M16—32no—
358M16—61no—
359M16—92no—
360M16—181no—
361C2×C8—61no—
362C2×C8—181no—
363C4⋊C4—32no—
364C4⋊C4—182no—
365C22⋊C4—61no—
366C22⋊C4—182no—
367C42—21no—
368C42—32no—
369C42—31no—
370C42—31no—
371C42—32no—
372C42—68no—
373C42—61no—
374C42—61no—
375C42—182no—
376C42#62412yescomplemented
377C22×C3—22no—
378C22×C3—22no—
379C22×C3—21no—
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—42no—
383C22×C3D3×C22⋊C411yescharacteristic
384C22×C3#67⋊C411yescharacteristic
385C22×C3#89311yescharacteristic
386C22×C3C2×(C2×D3)⋊C411yescharacteristic
387C22×C3C4×#6711yescharacteristic
388C22×C3C4×#6711yescharacteristic
389C2×D3—62no—
390C2×D3—62no—
391C2×D3—122no—
392C2×D3—122no—
393C2×D3—122no—
394C2×D3—242no—
395C3×C4—24no—
396C3×C4—24no—
397C3×C4—21no—
398C3×C4—21no—
399C3×C4—21no—
400C3×C4—21no—
401C3×C4—34no—
402C3×C4—44no—
403C3×C4—64no—
404C3×C4—62no—
405C3×C4—122no—
406C3×C4C42×D311yescharacteristic
407C3×C4C42×D311yescharacteristic
408C3×C4#87211yescharacteristic
409C3×C4C4×D1211yescharacteristic
410C3×C4C4×D1211yescharacteristic
411C3×C4#67⋊C411yescharacteristic
412C3×C4#89211yescharacteristic
413C3×C4#89311yescharacteristic
414Dic3—24no—
415Dic3—22no—
416Dic3—42no—
417Dic3—62no—
418Dic3—62no—
419Dic3—122no—
420Dic3#80514yescomplemented
421C32C4×#10411yescharacteristic, complemented, Sylow
422C23—181no—
423C23D3×#6711yescharacteristic
424Q8—92no—
425Q8—181no—
426D4—92no—
427D4—182no—
428D4—182no—
429D4—181no—
430C2×C4—24no—
431C2×C4—22no—
432C2×C4—32no—
433C2×C4—32no—
434C2×C4—64no—
435C2×C4—64no—
436C2×C4—62no—
437C2×C4—62no—
438C2×C4—181no—
439C2×C4—182no—
440C2×C4—182no—
441C2×C4—364no—
442C2×C4#379911yescharacteristic
443C2×C4C4×D3211yescharacteristic
444C2×C4C4×D3211yescharacteristic
445C2×C4D3×D1211yescharacteristic
446C2×C4#380411yescharacteristic
447C2×C4C2×#62411yescharacteristic
448C8—62no—
449C8—182no—
450C2×C3—21no—
451C2×C3—21no—
452C2×C3—21no—
453C2×C3—21no—
454C2×C3—21no—
455C2×C3—22no—
456C2×C3—41no—
457C2×C3—41no—
458C2×C3#466611yescharacteristic
459C2×C3D3×#10412yes—
460C2×C3C2×#80512yes—
461C2×C3C4×(C2×D3)⋊C411yescharacteristic
462D3—122no—
463D3—122no—
464D3—242no—
465C22—22no—
466C22—182no—
467C22—362no—
468C22#6390411yescharacteristic
469C22D3×(C2×D3)⋊C411yescharacteristic
470C22#6395211yescharacteristic
471C4—24no—
472C4—34no—
473C4—64no—
474C4—62no—
475C4—122no—
476C4—182no—
477C4#6383611yescharacteristic
478C4#6388011yescharacteristic
479C4C4×#62411yescharacteristic
480C4#6389411yescharacteristic
481C3—21no—
482C3#6872811yescharacteristic, complemented
483C3C4×#80511yescharacteristic, complemented
484C2—21no—
485C2—21no—
486C2—362no—
487C2D3×#80512yes—
488C2#1059123311yescharacteristic
subgroupG/H
centerC2×C4D3×D12
commutatorC32×C4C2×C42
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC22×C32C2×C22⋊C4
prime radicalC2×#3828C22
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32C4×#104
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
3. C3×C42×Dic3C2semidirect
5. Dic3×#208C2semidirect
6. C3×#4523C2semidirect
7. #10589161C2semidirect
19. #63894C4semidirect
22. #63844C4semidirect
23. #63632C4semidirect
24. #63570C4semidirect
32. C42×Dic3D3semidirect
41. #4523D3semidirect
56. C32×C42C2×C4semidirect
58. #3748C2×C4semidirect
66. C3×C4×Dic3C2×C4semidirect
70. C3×#208C2×C4semidirect
128. C4⋊(C3⋊D3)C42semidirect
132. #634C42semidirect
201. C3×C42C4×D3semidirect
202. C3×C42C4×D3semidirect
215. C4×Dic3C4×D3semidirect
225. #208C4×D3semidirect
245. C3×Dic3#104semidirect
376. C42#624semidirect
420. Dic3#805semidirect
421. C32C4×#104semidirect
482. C3#68728semidirect
483. C3C4×#805semidirect

Maximal subgroups

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

subgroupindex
#105949542
C2×#636322
C3×C42×Dic32
C2×#635702
Dic3×#2082
C3×#45232
#105891612
C4×#8053
#687283