Finite Group Databasebeta

← #11783883

Subgroups — #11783883

Order 1152.

791 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594958C211yesmaximal, characteristic
2M16×C3⋊Dic3C211yesmaximal, characteristic, complemented
3C2×C3×#825C211yesmaximal, characteristic
4C4×Dic32C211yesmaximal, characteristic, complemented
5C2×#63569C211yesmaximal, characteristic
6C3×#4555C211yesmaximal, characteristic, complemented
7#10589161C211yesmaximal, characteristic, complemented
8Dic3×#104—31nomaximal
9#68728—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C2×C3×C4×Dic3C2211yescharacteristic
17#67⋊Dic3—22no—
18C2×Dic32—22no—
19#63898C412yescomplemented
20C4×D3×Dic3—21no—
21#63855—21no—
22#63843C412yescomplemented
23#63642—21no—
24C8×C3⋊Dic3—21no—
25C3×#825C414yescomplemented
26#63569C414yescomplemented
27Dic3×#41—31no—
28#5522—31no—
29C2×C3×#104—31no—
30C2×#837—31no—
31C2×#825D311yescharacteristic
32Dic3×M16—31no—
33Dic3×M16—31no—
34Dic3×M16—61no—
35C42×Dic3—31no—
36C42×Dic3—31no—
37C2×#805—31no—
38C3×#339—31no—
39#4555D311yescharacteristic, complemented
40#4532—31no—
41#4523—31no—
42C22×C32×C4C2311yescharacteristic
43C22×C3⋊Dic3D412yes—
44C2×C3×#67—21no—
45C22×C3×Dic3—21no—
46C22×C3×Dic3—21no—
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—
58C4×C3⋊Dic3C2×C412yes—
59C4×C3⋊Dic3D411yescharacteristic
60C4×C3⋊Dic3D411yescharacteristic
61#3748—21no—
62#3748C2×C412yescomplemented
63C2×C3⋊(C3⋊C8)—21no—
64C3×#217—21no—
65C3×C4⋊Dic3C2×C412yes—
66C3×C4×Dic3—21no—
67C3×C4×Dic3—21no—
68C3×C4×Dic3—21no—
69C3×C4×Dic3C2×C412yescomplemented
70C3×C4×Dic3C2×C412yescomplemented
71Dic3⋊Dic3—22no—
72(C2×D3)⋊Dic3—22no—
73Dic32—28no—
74Dic32—22no—
75C4×#104—91noSylow
76C2×C3×#41—31no—
77C2×#235C2×D311yescharacteristic
78C2×C3×M16—21no—
79C2×C3×M16C2×D311yescharacteristic
80C2×C3×M16C2×D311yescharacteristic
81C3×#117—31no—
82C2×C3×C42—31no—
83C2×C3×C42—31no—
84Q8×Dic3—32no—
85D4×Dic3—32no—
86D4×Dic3—62no—
87#926—61no—
88#926C2×D311yescharacteristic
89C2×C4×Dic3—31no—
90C2×C4×Dic3—31no—
91C2×C4×Dic3—61no—
92C2×C4×Dic3—61no—
93C2×C4×Dic3—62no—
94C2×C4×Dic3—62no—
95C2×C4×Dic3C2×D311yescharacteristic
96C2×C4×Dic3C2×D311yescharacteristic
97C2×#208—31no—
98C2×#208—31no—
99C2×#208—61no—
100#893—32no—
101#887—32no—
102#67⋊C4—62no—
103#872—61no—
104C42×D3—61no—
105C3×#104—34no—
106#837—34no—
107#825Dic314yescomplemented
108#815—61no—
109#815—61no—
110#815—62no—
111C8×Dic3—61no—
112C8×Dic3—61no—
113C8×Dic3—62no—
114#805—34no—
115C23×C32C2×D411yescharacteristic
116C22×C3×D3—21no—
117C2×C32×C4C22×C411yescharacteristic
118C2×C32×C4C22×C411yescharacteristic
119C2×C32×C4C22×C411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4#4111yescharacteristic
122C2×C32×C4#4111yescharacteristic
123C2×C3⋊Dic3—24no—
124C2×C3⋊Dic3C22⋊C412yes—
125C2×C3⋊Dic3C22⋊C412yes—
126C3×#67—22no—
127C3×#67—22no—
128C2×C3×Dic3—24no—
129C2×C3×Dic3—24no—
130C2×C3×Dic3—21no—
131C2×C3×Dic3—22no—
132C2×C3×Dic3—22no—
133C2×C3×Dic3—22no—
134C3×D12—21no—
135C3×D12C4212yescomplemented
136C3×C4×D3—22no—
137C3×C4×D3—22no—
138C3×Dic6—21no—
139C3×Dic6C4212yescomplemented
140D3×Dic3—44no—
141C32×C8—22no—
142C3⋊(C3⋊C8)—22no—
143C4×#41—91no—
144C2×#104—31no—
145C2×#104—91no—
146C4×M16—91no—
147C43—91no—
148#339—31no—
149#339—91no—
150C3×#41—32no—
151C3×#41—32no—
152C3×#41—61no—
153C3×#41—61no—
154C2×C3×Q8—31no—
155C2×C3×D4—31no—
156C2×C3×D4—61no—
157C22×C3×C4—21no—
158C22×C3×C4—61no—
159C22×C3×C4—61no—
160C22×C3×C4—61no—
161C22×C3×C4C22×D311yescharacteristic
162C22×C3×C4C22×D311yescharacteristic
163C2×#67—21no—
164C22×Dic3—21no—
165C22×Dic3—21no—
166C22×Dic3—32no—
167C22×Dic3—32no—
168C22×Dic3—62no—
169C22×Dic3—62no—
170#235—21no—
171#235—21no—
172#235C4×D312yes—
173#235C2×Dic312yes—
174C2×D12C4×D311yescharacteristic
175C2×C4×D3—21no—
176C2×C4×D3—62no—
177C2×Dic6C4×D311yescharacteristic
178C3×M16—22no—
179C3×M16—21no—
180C3×M16—21no—
181C3×M16—22no—
182C3×M16C4×D312yescomplemented
183C3×M16C2×Dic312yescomplemented
184C2×C3×C8—22no—
185C2×C3×C8—21no—
186C2×C3×C8—21no—
187C3×C4⋊C4—32no—
188C3×C22⋊C4—61no—
189C3×C42—32no—
190C3×C42—32no—
191C3×C42—61no—
192C3×C42—61no—
193C3×C42—61no—
194#217—21no—
195#217—62no—
196(C2×D3)⋊C4—62no—
197C4⋊Dic3—62no—
198C4⋊Dic3C4×D312yes—
199Dic3⋊C4—62no—
200C4×Dic3—21no—
201C4×Dic3—21no—
202C4×Dic3—21no—
203C4×Dic3—32no—
204C4×Dic3—32no—
205C4×Dic3—31no—
206C4×Dic3—31no—
207C4×Dic3—31no—
208C4×Dic3—31no—
209C4×Dic3—61no—
210C4×Dic3—61no—
211C4×Dic3—62no—
212C4×Dic3—62no—
213C4×Dic3—62no—
214C4×Dic3—68no—
215C4×Dic3—68no—
216C4×Dic3C4×D312yescomplemented
217C4×Dic3C2×Dic312yescomplemented
218#208—32no—
219#208—32no—
220#208—62no—
221#208—62no—
222#208—61no—
223#208—61no—
224C2×C3⋊C8—62no—
225C2×C3⋊C8—61no—
226C2×C3⋊C8—61no—
227C22×C32—22no—
228C22×C32C2×C22⋊C411yescharacteristic
229C22×C32C4×D411yescharacteristic
230C22×C32C4×D411yescharacteristic
231C2×C3×D3—22no—
232C2×C3×D3—42no—
233C32×C4C2×C4211yescharacteristic
234C32×C4#11711yescharacteristic
235C32×C4C4×D411yescharacteristic
236C32×C4C4×D411yescharacteristic
237C3⋊Dic3—22no—
238C3⋊Dic3#10414yescomplemented
239C3×Dic3—24no—
240C3×Dic3—24no—
241C3×Dic3—22no—
242C3×Dic3—42no—
243C2×#41—31no—
244C2×M16—91no—
245C2×M16D3211yescharacteristic
246C4×Q8—92no—
247C4×D4—92no—
248C4×D4—182no—
249#117—31no—
250#117—181no—
251C2×C42—31no—
252C2×C42—31no—
253C2×C42—91no—
254C2×C42—181no—
255C2×C42—182no—
256#104—34no—
257#104—94no—
258#97—181no—
259C4×C8—181no—
260C23×C3—21no—
261C23×C3—61no—
262C23×C3D3×D411yescharacteristic
263C23×C3D3×D411yescharacteristic
264C22×D3—21no—
265C3×Q8—32no—
266C3×Q8—61no—
267C3×D4—32no—
268C3×D4—62no—
269C3×D4—62no—
270C3×D4—61no—
271C2×C3×C4—21no—
272C2×C3×C4—21no—
273C2×C3×C4—21no—
274C2×C3×C4—21no—
275C2×C3×C4—21no—
276C2×C3×C4—21no—
277C2×C3×C4—64no—
278C2×C3×C4—64no—
279C2×C3×C4—61no—
280C2×C3×C4—62no—
281C2×C3×C4—62no—
282C2×C3×C4—62no—
283C2×C3×C4—62no—
284C2×C3×C4—62no—
285C2×C3×C4C2×C4×D311yescharacteristic
286C2×C3×C4C2×C4×D311yescharacteristic
287C2×C3×C4C2×C4×D311yescharacteristic
288C2×C3×C4C2×C4×D311yescharacteristic
289C2×C3×C4C2×C4×D311yescharacteristic
290C2×C3×C4D3×D411yescharacteristic
291C2×C3×C4D3×D411yescharacteristic
292C2×C3×C4#23711yescharacteristic
293C2×C3×C4#23711yescharacteristic
294C2×C3×C4#23711yescharacteristic
295C2×C3×C4#23911yescharacteristic
296C2×C3×C4C22×Dic311yescharacteristic
297#67—22no—
298#67—22no—
299C2×Dic3—24no—
300C2×Dic3—24no—
301C2×Dic3—21no—
302C2×Dic3—22no—
303C2×Dic3—22no—
304C2×Dic3—22no—
305C2×Dic3—32no—
306C2×Dic3—32no—
307C2×Dic3—32no—
308C2×Dic3—32no—
309C2×Dic3—62no—
310C2×Dic3—62no—
311C2×Dic3—64no—
312C2×Dic3—64no—
313C2×Dic3—124no—
314C2×Dic3—124no—
315D12—21no—
316D12C4×Dic312yescomplemented
317C4×D3—22no—
318C4×D3—22no—
319C4×D3—124no—
320Dic6—21no—
321Dic6C4×Dic312yescomplemented
322C3×C8—24no—
323C3×C8—22no—
324C3×C8—22no—
325C3⋊C8—64no—
326C3⋊C8—62no—
327C3⋊C8—62no—
328C2×C32—21no—
329C2×C32—21no—
330C2×C32C4×C22⋊C411yescharacteristic
331C2×C32C2×#10412yes—
332C3×D3—42no—
333#41—32no—
334#41—32no—
335#41—61no—
336#41—61no—
337C2×Q8—31no—
338C2×D4—31no—
339C2×D4—61no—
340C22×C4—61no—
341C22×C4—61no—
342C22×C4—61no—
343C22×C4—92no—
344C22×C4—182no—
345C22×C4C2×D3211yescharacteristic
346M16—21no—
347M16—92no—
348M16—181no—
349M16D3×Dic312yescomplemented
350C2×C8—21no—
351C2×C8—181no—
352C4⋊C4—32no—
353C4⋊C4—182no—
354C22⋊C4—61no—
355C22⋊C4—182no—
356C42—32no—
357C42—32no—
358C42—61no—
359C42—61no—
360C42—61no—
361C42—92no—
362C42—91no—
363C42—91no—
364C42—182no—
365C42—188no—
366C22×C3—22no—
367C22×C3—22no—
368C22×C3—21no—
369C22×C3—21no—
370C22×C3—21no—
371C22×C3—42no—
372C22×C3—62no—
373C22×C3—122no—
374C22×C3D3×C22⋊C411yescharacteristic
375C22×C3D3×C22⋊C411yescharacteristic
376C22×C3#67⋊C411yescharacteristic
377C22×C3#67⋊C411yescharacteristic
378C22×C3#89311yescharacteristic
379C22×C3D4×Dic311yescharacteristic
380C2×D3—22no—
381C2×D3—42no—
382C3×C4—21no—
383C3×C4—21no—
384C3×C4—21no—
385C3×C4—21no—
386C3×C4—64no—
387C3×C4—64no—
388C3×C4—62no—
389C3×C4—122no—
390C3×C4C42×D311yescharacteristic
391C3×C4#87711yescharacteristic
392C3×C4#67⋊C411yescharacteristic
393C3×C4#67⋊C411yescharacteristic
394C3×C4#89211yescharacteristic
395C3×C4#89311yescharacteristic
396C3×C4C2×C4×Dic311yescharacteristic
397C3×C4D4×Dic311yescharacteristic
398Dic3—24no—
399Dic3—24no—
400Dic3—22no—
401Dic3—34no—
402Dic3—34no—
403Dic3—42no—
404Dic3—64no—
405Dic3—62no—
406Dic3—62no—
407Dic3—122no—
408C32C4×#10411yescharacteristic, complemented, Sylow
409C23—61no—
410C23#380211yescharacteristic
411Q8—32no—
412Q8—61no—
413D4—32no—
414D4—62no—
415D4—62no—
416D4—61no—
417C2×C4—64no—
418C2×C4—64no—
419C2×C4—62no—
420C2×C4—62no—
421C2×C4—61no—
422C2×C4—62no—
423C2×C4—62no—
424C2×C4—62no—
425C2×C4—92no—
426C2×C4—92no—
427C2×C4—184no—
428C2×C4—364no—
429C2×C4#379611yescharacteristic
430C2×C4C4×D3211yescharacteristic
431C2×C4C4×D3211yescharacteristic
432C2×C4C2×D3×Dic311yescharacteristic
433C2×C4#380511yescharacteristic
434C2×C4#381111yescharacteristic
435C8—22no—
436C8—182no—
437C2×C3—21no—
438C2×C3—21no—
439C2×C3—21no—
440C2×C3—21no—
441C2×C3—22no—
442C2×C3—21no—
443C2×C3—41no—
444C2×C3—41no—
445C2×C3—122no—
446C2×C3#466611yescharacteristic
447C2×C3D3×#10412yes—
448C2×C3D3×#10412yes—
449C2×C3Dic3×C22⋊C411yescharacteristic
450D3—42no—
451C22—22no—
452C22—62no—
453C22—122no—
454C22#6389811yescharacteristic
455C22#6390211yescharacteristic
456C22#6392111yescharacteristic
457C4—64no—
458C4—64no—
459C4—62no—
460C4—94no—
461C4—122no—
462C4—182no—
463C4C4×D3×Dic311yescharacteristic
464C4#6387811yescharacteristic
465C4#6388111yescharacteristic
466C4#67⋊Dic311yescharacteristic
467C3—21no—
468C3#6872811yescharacteristic, complemented
469C3Dic3×#10411yescharacteristic, complemented
470C2—21no—
471C2—21no—
472C2—122no—
473C2#1059100812yes—
474C2#1059136811yescharacteristic
subgroupG/H
centerC2×C4#3811
commutatorC32×C4C2×C42
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32C2×C22⋊C4
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32C4×#104
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
2. M16×C3⋊Dic3C2semidirect
4. C4×Dic32C2semidirect
6. C3×#4555C2semidirect
7. #10589161C2semidirect
19. #63898C4semidirect
22. #63843C4semidirect
25. C3×#825C4semidirect
26. #63569C4semidirect
39. #4555D3semidirect
56. C32×M16C2×C4semidirect
62. #3748C2×C4semidirect
69. C3×C4×Dic3C2×C4semidirect
70. C3×C4×Dic3C2×C4semidirect
107. #825Dic3semidirect
135. C3×D12C42semidirect
139. C3×Dic6C42semidirect
182. C3×M16C4×D3semidirect
183. C3×M16C2×Dic3semidirect
216. C4×Dic3C4×D3semidirect
217. C4×Dic3C2×Dic3semidirect
238. C3⋊Dic3#104semidirect
316. D12C4×Dic3semidirect
321. Dic6C4×Dic3semidirect
349. M16D3×Dic3semidirect
408. C32C4×#104semidirect
468. C3#68728semidirect
469. C3Dic3×#104semidirect

Maximal subgroups

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

subgroupindex
#105949582
M16×C3⋊Dic32
C2×C3×#8252
C4×Dic322
C2×#635692
C3×#45552
#105891612
Dic3×#1043
#687283