Finite Group Databasebeta

← #11783916

Subgroups — #11783916

Order 1152.

695 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Dic3×#235C211yesmaximal, characteristic
2C2×C3×#825C211yesmaximal, characteristic
3C3×Dic3×M16C211yesmaximal, characteristic, complemented
4#10591222C211yesmaximal, characteristic, complemented
5C2×#63568C211yesmaximal, characteristic
6#10589421C211yesmaximal, characteristic, complemented
7#10589162C211yesmaximal, characteristic, complemented
8#70354—31nomaximal
9#69866—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12#64135C2211yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C2×C3×C4×Dic3C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17Dic3×#67—22no—
18Dic3×D12C412yescomplemented
19C4×D3×Dic3—21no—
20#63855—21no—
21Dic3×Dic6C412yescomplemented
22C3×#825C414yescomplemented
23C3×#815—21no—
24C3×C8×Dic3—21no—
25#63579—22no—
26#63568C414yescomplemented
27Dic3×#41—31no—
28C4×#235—31no—
29C2×C3×#104—31no—
30C3×C4×M16—31no—
31C2×#837—31no—
32C2×#825—31no—
33C2×#825D311yescharacteristic
34Dic3×M16D311yescharacteristic, complemented
35#4932—31no—
36#4932—31no—
37#4555—31no—
38#4555—31no—
39#4555—31no—
40#4555—61no—
41#4523—31no—
42C22×C32×C4C2311yescharacteristic
43C22×C3⋊Dic3—21no—
44C2×C3×#67—21no—
45C22×C3×Dic3—21no—
46C22×C3×Dic3D412yes—
47C3×#235—21no—
48C3×#235—21no—
49C3×#235C2×C412yes—
50C3×#235C2×C412yes—
51C2×C3×D12C2×C411yescharacteristic
52C2×C3×C4×D3—21no—
53C2×C3×Dic6C2×C411yescharacteristic
54C2×D3×Dic3—22no—
55C32×M16—21no—
56C32×M16C2×C412yescomplemented
57C2×C32×C8—21no—
58#3757—21no—
59C4⋊(C3⋊Dic3)C2×C412yes—
60C4×C3⋊Dic3—21no—
61C4×C3⋊Dic3—21no—
62C4×C3⋊Dic3C2×C412yescomplemented
63C3×C4×Dic3—21no—
64C3×C4×Dic3C2×C412yes—
65C3×C4×Dic3C2×C412yescomplemented
66C3×C4×Dic3D411yescharacteristic
67C3×C4×Dic3D411yescharacteristic
68C3×#208—21no—
69C3×#208C2×C412yescomplemented
70C2×C3×C3⋊C8—21no—
71Dic3⋊Dic3—22no—
72(C2×D3)⋊Dic3—22no—
73Dic32—22no—
74#1759—91noSylow
75C2×C3×#41—31no—
76C2×#235C2×D311yescharacteristic
77C2×C3×M16—21no—
78C2×C3×M16—31no—
79C2×C3×M16C2×D311yescharacteristic
80C2×C3×M16C2×D311yescharacteristic
81C2×C3×C42—31no—
82C2×C3×C42—31no—
83Q8×Dic3—32no—
84D4×Dic3—32no—
85D4×Dic3—62no—
86C4×#67—62no—
87#926—31no—
88#926—31no—
89#926—61no—
90#926—61no—
91C2×C4×Dic3—31no—
92C2×C4×Dic3—31no—
93C2×C4×Dic3—61no—
94C2×C4×Dic3—61no—
95C2×C4×Dic3C2×D311yescharacteristic
96C2×C4×Dic3C2×D311yescharacteristic
97C2×#208C2×D311yescharacteristic
98C4×D12—32no—
99#872—61no—
100C42×D3—61no—
101C4×Dic6—32no—
102C3×#104—34no—
103C3×#97—61no—
104C3×C4×C8—61no—
105#837—34no—
106C3⋊#95—62no—
107C3⋊#95—62no—
108#825—34no—
109#825Dic314yescomplemented
110#815—21no—
111C8×Dic3—21no—
112C23×C32C2×D411yescharacteristic
113C22×C3×D3—21no—
114C2×C32×C4C22×C411yescharacteristic
115C2×C32×C4C22×C411yescharacteristic
116C2×C32×C4C22×C411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4#4111yescharacteristic
119C2×C32×C4#4111yescharacteristic
120C2×C3⋊Dic3—22no—
121C2×C3⋊Dic3—22no—
122C2×C3⋊Dic3—42no—
123C3×#67—22no—
124C3×#67—22no—
125C2×C3×Dic3—21no—
126C2×C3×Dic3—22no—
127C2×C3×Dic3—42no—
128C2×C3×Dic3—42no—
129C2×C3×Dic3C22⋊C412yes—
130C2×C3×Dic3C22⋊C412yes—
131C3×D12—21no—
132C3×D12C4212yes—
133C3×C4×D3—22no—
134C3×C4×D3—22no—
135C3×Dic6—21no—
136C3×Dic6C4212yes—
137D3×Dic3—44no—
138C32×C8—22no—
139C3×C3⋊C8—22no—
140C4×#41—91no—
141C2×#104—31no—
142C2×#104—91no—
143C4×M16—31no—
144#376—91no—
145#339—91no—
146#339—91no—
147C3×#41—32no—
148C3×#41—32no—
149C3×#41—61no—
150C3×#41—61no—
151C2×C3×Q8—31no—
152C2×C3×D4—31no—
153C2×C3×D4—61no—
154C22×C3×C4—21no—
155C22×C3×C4—32no—
156C22×C3×C4—61no—
157C22×C3×C4—61no—
158C22×C3×C4C22×D311yescharacteristic
159C22×C3×C4C22×D311yescharacteristic
160C2×#67—21no—
161C22×Dic3—21no—
162C22×Dic3—61no—
163C22×Dic3—61no—
164C22×Dic3—62no—
165C22×Dic3—121no—
166C22×Dic3D1212yes—
167#235—21no—
168#235—21no—
169#235C4×D312yes—
170#235C2×Dic312yes—
171C2×D12C4×D311yescharacteristic
172C2×C4×D3—21no—
173C2×C4×D3—62no—
174C2×Dic6C4×D311yescharacteristic
175C3×M16—21no—
176C3×M16—21no—
177C3×M16—22no—
178C3×M16—32no—
179C3×M16—41no—
180C3×M16—61no—
181C3×M16C4×D312yescomplemented
182C3×M16C2×Dic312yescomplemented
183C2×C3×C8—21no—
184C2×C3×C8—21no—
185C2×C3×C8—41no—
186C2×C3×C8—61no—
187C3×C42—32no—
188C3×C42—31no—
189C3×C42—31no—
190C3×C42—32no—
191C3×C42—61no—
192#217—61no—
193#217—61no—
194#217—62no—
195#217—121no—
196(C2×D3)⋊C4—62no—
197C4⋊Dic3—32no—
198C4⋊Dic3—32no—
199C4⋊Dic3—62no—
200C4⋊Dic3—62no—
201Dic3⋊C4—62no—
202C4×Dic3—21no—
203C4×Dic3—32no—
204C4×Dic3—32no—
205C4×Dic3—62no—
206C4×Dic3—62no—
207C4×Dic3—61no—
208C4×Dic3—61no—
209C4×Dic3—61no—
210C4×Dic3—61no—
211C4×Dic3—62no—
212C4×Dic3—121no—
213C4×Dic3—121no—
214C4×Dic3C4×D312yes—
215C4×Dic3C2×Dic312yescomplemented
216C4×Dic3#6711yescharacteristic
217C4×Dic3#6711yescharacteristic
218#208—21no—
219#208C4×D312yescomplemented
220C2×C3⋊C8—21no—
221C22×C32—22no—
222C22×C32C2×C22⋊C411yescharacteristic
223C22×C32C4×D411yescharacteristic
224C22×C32C4×D411yescharacteristic
225C2×C3×D3—22no—
226C2×C3×D3—42no—
227C32×C4C2×C4211yescharacteristic
228C32×C4#11711yescharacteristic
229C32×C4C4×D411yescharacteristic
230C32×C4C4×D411yescharacteristic
231C3⋊Dic3—42no—
232C3⋊Dic3—42no—
233C3×Dic3—22no—
234C3×Dic3—22no—
235C3×Dic3—22no—
236C3×Dic3—42no—
237C2×#41—31no—
238C2×M16—31no—
239C2×M16D3211yescharacteristic
240C4×Q8—92no—
241C4×D4—92no—
242C4×D4—182no—
243#117—91no—
244#117—181no—
245C2×C42—31no—
246C2×C42—31no—
247C2×C42—91no—
248C2×C42—181no—
249#104—34no—
250#104—94no—
251#97—61no—
252C4×C8—61no—
253#95—182no—
254C23×C3—21no—
255C23×C3—61no—
256C23×C3C2×D1211yescharacteristic
257C23×C3D3×D411yescharacteristic
258C22×D3—21no—
259C3×Q8—32no—
260C3×Q8—61no—
261C3×D4—32no—
262C3×D4—62no—
263C3×D4—62no—
264C3×D4—61no—
265C2×C3×C4—21no—
266C2×C3×C4—21no—
267C2×C3×C4—21no—
268C2×C3×C4—21no—
269C2×C3×C4—21no—
270C2×C3×C4—21no—
271C2×C3×C4—32no—
272C2×C3×C4—32no—
273C2×C3×C4—61no—
274C2×C3×C4—62no—
275C2×C3×C4—62no—
276C2×C3×C4—62no—
277C2×C3×C4—122no—
278C2×C3×C4—122no—
279C2×C3×C4C2×C4×D311yescharacteristic
280C2×C3×C4C2×C4×D311yescharacteristic
281C2×C3×C4C2×C4×D311yescharacteristic
282C2×C3×C4C2×C4×D311yescharacteristic
283C2×C3×C4C2×C4×D311yescharacteristic
284C2×C3×C4#23511yescharacteristic
285C2×C3×C4#23511yescharacteristic
286C2×C3×C4D3×D411yescharacteristic
287C2×C3×C4#23711yescharacteristic
288C2×C3×C4#23711yescharacteristic
289C2×C3×C4C22×Dic311yescharacteristic
290C2×C3×C4C2×#6711yescharacteristic
291#67—22no—
292#67—22no—
293C2×Dic3—21no—
294C2×Dic3—22no—
295C2×Dic3—42no—
296C2×Dic3—42no—
297C2×Dic3—62no—
298C2×Dic3—62no—
299C2×Dic3—62no—
300C2×Dic3—62no—
301C2×Dic3—122no—
302C2×Dic3—122no—
303C2×Dic3—124no—
304C2×Dic3—122no—
305C2×Dic3—122no—
306C2×Dic3—124no—
307C2×Dic3(C2×D3)⋊C412yes—
308C2×Dic3(C2×D3)⋊C412yes—
309D12—21no—
310D12C4×Dic312yes—
311C4×D3—22no—
312C4×D3—22no—
313C4×D3—124no—
314Dic6—21no—
315Dic6C4×Dic312yes—
316C3×C8—22no—
317C3×C8—22no—
318C3×C8—42no—
319C3×C8—62no—
320C3⋊C8—22no—
321C2×C32—21no—
322C2×C32—21no—
323C2×C32C4×C22⋊C411yescharacteristic
324C2×C32#42112yes—
325C3×D3—42no—
326#41—32no—
327#41—32no—
328#41—61no—
329#41—61no—
330C2×Q8—31no—
331C2×D4—31no—
332C2×D4—61no—
333C22×C4—32no—
334C22×C4—61no—
335C22×C4—61no—
336C22×C4—182no—
337C22×C4—181no—
338C22×C4C2×D3211yescharacteristic
339M16—21no—
340M16—32no—
341M16—61no—
342M16D3×Dic312yescomplemented
343C2×C8—21no—
344C2×C8—61no—
345C4⋊C4—92no—
346C4⋊C4—182no—
347C22⋊C4—182no—
348C22⋊C4—181no—
349C42—32no—
350C42—31no—
351C42—31no—
352C42—32no—
353C42—61no—
354C42—92no—
355C42—182no—
356C42—181no—
357C42—181no—
358C22×C3—22no—
359C22×C3—22no—
360C22×C3—21no—
361C22×C3—21no—
362C22×C3—21no—
363C22×C3—42no—
364C22×C3—62no—
365C22×C3—122no—
366C22×C3C4×D1211yescharacteristic
367C22×C3C4×D1211yescharacteristic
368C22×C3D3×C22⋊C411yescharacteristic
369C22×C3#67⋊C411yescharacteristic
370C22×C3C2×(C2×D3)⋊C411yescharacteristic
371C22×C3D4×Dic311yescharacteristic
372C2×D3—22no—
373C2×D3—42no—
374C3×C4—21no—
375C3×C4—21no—
376C3×C4—21no—
377C3×C4—21no—
378C3×C4—62no—
379C3×C4—62no—
380C3×C4—62no—
381C3×C4—122no—
382C3×C4C42×D311yescharacteristic
383C3×C4#87211yescharacteristic
384C3×C4#87711yescharacteristic
385C3×C4#67⋊C411yescharacteristic
386C3×C4C2×C4×Dic311yescharacteristic
387C3×C4C4×#6711yescharacteristic
388C3×C4C4×#6711yescharacteristic
389C3×C4D4×Dic311yescharacteristic
390Dic3—22no—
391Dic3—22no—
392Dic3—22no—
393Dic3—42no—
394Dic3—122no—
395Dic3—122no—
396Dic3—124no—
397Dic3—122no—
398Dic3—122no—
399Dic3—242no—
400C32#175911yescharacteristic, complemented, Sylow
401C23—61no—
402C23D3×D1211yescharacteristic
403Q8—32no—
404Q8—61no—
405D4—32no—
406D4—62no—
407D4—62no—
408D4—61no—
409C2×C4—32no—
410C2×C4—32no—
411C2×C4—61no—
412C2×C4—62no—
413C2×C4—62no—
414C2×C4—62no—
415C2×C4—122no—
416C2×C4—122no—
417C2×C4—182no—
418C2×C4—182no—
419C2×C4—364no—
420C2×C4—362no—
421C2×C4#379511yescharacteristic
422C2×C4C4×D3211yescharacteristic
423C2×C4C4×D3211yescharacteristic
424C2×C4C2×D3×Dic311yescharacteristic
425C2×C4#380411yescharacteristic
426C2×C4D3×#6711yescharacteristic
427C8—22no—
428C8—62no—
429C2×C3—21no—
430C2×C3—21no—
431C2×C3—21no—
432C2×C3—21no—
433C2×C3—22no—
434C2×C3—21no—
435C2×C3—41no—
436C2×C3—41no—
437C2×C3—122no—
438C2×C3#482112yes—
439C2×C3C4×(C2×D3)⋊C411yescharacteristic
440C2×C3Dic3×C22⋊C411yescharacteristic
441C2×C3#513912yes—
442D3—42no—
443C22—22no—
444C22—62no—
445C22—122no—
446C22#6388011yescharacteristic
447C22Dic3×D1211yescharacteristic
448C22D3×(C2×D3)⋊C411yescharacteristic
449C4—62no—
450C4—62no—
451C4—62no—
452C4—122no—
453C4—362no—
454C4—362no—
455C4C4×D3×Dic311yescharacteristic
456C4#6387711yescharacteristic
457C4#6387911yescharacteristic
458C4Dic3×#6711yescharacteristic
459C3—21no—
460C3#6986611yescharacteristic, complemented
461C3#7035411yescharacteristic, complemented
462C2—21no—
463C2—21no—
464C2—122no—
465C2#1059100512yes—
466C2Dic3×(C2×D3)⋊C411yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC32×C4C2×C42
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32C2×C22⋊C4
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1759
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
3. C3×Dic3×M16C2semidirect
4. #10591222C2semidirect
6. #10589421C2semidirect
7. #10589162C2semidirect
18. Dic3×D12C4semidirect
21. Dic3×Dic6C4semidirect
22. C3×#825C4semidirect
26. #63568C4semidirect
34. Dic3×M16D3semidirect
56. C32×M16C2×C4semidirect
62. C4×C3⋊Dic3C2×C4semidirect
65. C3×C4×Dic3C2×C4semidirect
69. C3×#208C2×C4semidirect
109. #825Dic3semidirect
181. C3×M16C4×D3semidirect
182. C3×M16C2×Dic3semidirect
215. C4×Dic3C2×Dic3semidirect
219. #208C4×D3semidirect
342. M16D3×Dic3semidirect
400. C32#1759semidirect
460. C3#69866semidirect
461. C3#70354semidirect

Maximal subgroups

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

subgroupindex
Dic3×#2352
C2×C3×#8252
C3×Dic3×M162
#105912222
C2×#635682
#105894212
#105891622
#703543
#698663