Finite Group Databasebeta

← #11783917

Subgroups — #11783917

Order 1152.

711 conjugacy classes of subgroups.

The subgroup lattice has 472 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
4#10591222C211yesmaximal, characteristic, complemented
5C2×#63569C211yesmaximal, characteristic
6C3×#4555C211yesmaximal, characteristic, complemented
7#10589161C211yesmaximal, characteristic, complemented
8#70354—31nomaximal
9#68729—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—
18#63898C412yescomplemented
19C4×D3×Dic3—21no—
20#63855—21no—
21#63843C412yescomplemented
22#63642—21no—
23C8×C3⋊Dic3—21no—
24C3×#825C414yescomplemented
25#63579—22no—
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—
35#4932—31no—
36#4932—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—22no—
74#1759—91noSylow
75C2×C3×#41—31no—
76C2×#235C2×D311yescharacteristic
77C2×C3×M16—21no—
78C2×C3×M16C2×D311yescharacteristic
79C2×C3×M16C2×D311yescharacteristic
80C3×#117—31no—
81C2×C3×C42—31no—
82C2×C3×C42—31no—
83Q8×Dic3—32no—
84D4×Dic3—32no—
85D4×Dic3—62no—
86#926—61no—
87#926C2×D311yescharacteristic
88C2×C4×Dic3—31no—
89C2×C4×Dic3—31no—
90C2×C4×Dic3—61no—
91C2×C4×Dic3—61no—
92C2×C4×Dic3C2×D311yescharacteristic
93C2×C4×Dic3C2×D311yescharacteristic
94C2×#208—31no—
95C2×#208—31no—
96C2×#208—61no—
97#893—32no—
98#887—32no—
99#67⋊C4—62no—
100#872—61no—
101C42×D3—61no—
102C3×#104—34no—
103#837—34no—
104C3⋊#95—62no—
105C3⋊#95—62no—
106#825Dic314yescomplemented
107#815—61no—
108#815—61no—
109#815—62no—
110C8×Dic3—61no—
111C8×Dic3—61no—
112C8×Dic3—62no—
113#805—34no—
114C23×C32C2×D411yescharacteristic
115C22×C3×D3—21no—
116C2×C32×C4C22×C411yescharacteristic
117C2×C32×C4C22×C411yescharacteristic
118C2×C32×C4C22×C411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4#4111yescharacteristic
121C2×C32×C4#4111yescharacteristic
122C2×C3⋊Dic3—42no—
123C2×C3⋊Dic3C22⋊C412yes—
124C2×C3⋊Dic3C22⋊C412yes—
125C3×#67—22no—
126C3×#67—22no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—22no—
129C2×C3×Dic3—22no—
130C2×C3×Dic3—22no—
131C2×C3×Dic3—42no—
132C2×C3×Dic3—42no—
133C3×D12—21no—
134C3×D12C4212yes—
135C3×C4×D3—22no—
136C3×C4×D3—22no—
137C3×Dic6—21no—
138C3×Dic6C4212yes—
139D3×Dic3—44no—
140C32×C8—22no—
141C3⋊(C3⋊C8)—22no—
142C4×#41—91no—
143C2×#104—31no—
144C2×#104—91no—
145C4×M16—91no—
146#376—91no—
147#339—31no—
148#339—91no—
149C3×#41—32no—
150C3×#41—32no—
151C3×#41—61no—
152C3×#41—61no—
153C2×C3×Q8—31no—
154C2×C3×D4—31no—
155C2×C3×D4—61no—
156C22×C3×C4—21no—
157C22×C3×C4—61no—
158C22×C3×C4—61no—
159C22×C3×C4—61no—
160C22×C3×C4C22×D311yescharacteristic
161C22×C3×C4C22×D311yescharacteristic
162C2×#67—21no—
163C22×Dic3—21no—
164C22×Dic3—21no—
165C22×Dic3—32no—
166C22×Dic3—32no—
167C22×Dic3—62no—
168C22×Dic3—62no—
169#235—21no—
170#235—21no—
171#235C4×D312yes—
172#235C2×Dic312yes—
173C2×D12C4×D311yescharacteristic
174C2×C4×D3—21no—
175C2×C4×D3—62no—
176C2×Dic6C4×D311yescharacteristic
177C3×M16—22no—
178C3×M16—21no—
179C3×M16—21no—
180C3×M16—22no—
181C3×M16C4×D312yescomplemented
182C3×M16C2×Dic312yescomplemented
183C2×C3×C8—22no—
184C2×C3×C8—21no—
185C2×C3×C8—21no—
186C3×C4⋊C4—32no—
187C3×C22⋊C4—61no—
188C3×C42—32no—
189C3×C42—32no—
190C3×C42—61no—
191C3×C42—61no—
192C3×C42—61no—
193#217—21no—
194#217—62no—
195(C2×D3)⋊C4—62no—
196C4⋊Dic3—62no—
197C4⋊Dic3C4×D312yes—
198Dic3⋊C4—62no—
199C4×Dic3—21no—
200C4×Dic3—21no—
201C4×Dic3—21no—
202C4×Dic3—32no—
203C4×Dic3—32no—
204C4×Dic3—31no—
205C4×Dic3—31no—
206C4×Dic3—31no—
207C4×Dic3—31no—
208C4×Dic3—61no—
209C4×Dic3—61no—
210C4×Dic3—62no—
211C4×Dic3—62no—
212C4×Dic3—62no—
213C4×Dic3C4×D312yescomplemented
214C4×Dic3C2×Dic312yescomplemented
215#208—32no—
216#208—32no—
217#208—62no—
218#208—62no—
219#208—61no—
220#208—61no—
221C2×C3⋊C8—62no—
222C2×C3⋊C8—61no—
223C2×C3⋊C8—61no—
224C22×C32—22no—
225C22×C32C2×C22⋊C411yescharacteristic
226C22×C32C4×D411yescharacteristic
227C22×C32C4×D411yescharacteristic
228C2×C3×D3—22no—
229C2×C3×D3—42no—
230C32×C4C2×C4211yescharacteristic
231C32×C4#11711yescharacteristic
232C32×C4C4×D411yescharacteristic
233C32×C4C4×D411yescharacteristic
234C3⋊Dic3—22no—
235C3⋊Dic3—22no—
236C3×Dic3—22no—
237C3×Dic3—42no—
238C3×Dic3—42no—
239C3×Dic3—42no—
240C2×#41—31no—
241C2×M16—91no—
242C2×M16D3211yescharacteristic
243C4×Q8—92no—
244C4×D4—92no—
245C4×D4—182no—
246#117—31no—
247#117—181no—
248C2×C42—31no—
249C2×C42—31no—
250C2×C42—91no—
251C2×C42—181no—
252#104—34no—
253#104—94no—
254#97—181no—
255C4×C8—181no—
256#95—182no—
257C23×C3—21no—
258C23×C3—61no—
259C23×C3D3×D411yescharacteristic
260C23×C3D3×D411yescharacteristic
261C22×D3—21no—
262C3×Q8—32no—
263C3×Q8—61no—
264C3×D4—32no—
265C3×D4—62no—
266C3×D4—62no—
267C3×D4—61no—
268C2×C3×C4—21no—
269C2×C3×C4—21no—
270C2×C3×C4—21no—
271C2×C3×C4—21no—
272C2×C3×C4—21no—
273C2×C3×C4—21no—
274C2×C3×C4—61no—
275C2×C3×C4—62no—
276C2×C3×C4—62no—
277C2×C3×C4—62no—
278C2×C3×C4—62no—
279C2×C3×C4—62no—
280C2×C3×C4—122no—
281C2×C3×C4—122no—
282C2×C3×C4C2×C4×D311yescharacteristic
283C2×C3×C4C2×C4×D311yescharacteristic
284C2×C3×C4C2×C4×D311yescharacteristic
285C2×C3×C4C2×C4×D311yescharacteristic
286C2×C3×C4C2×C4×D311yescharacteristic
287C2×C3×C4D3×D411yescharacteristic
288C2×C3×C4D3×D411yescharacteristic
289C2×C3×C4#23711yescharacteristic
290C2×C3×C4#23711yescharacteristic
291C2×C3×C4#23711yescharacteristic
292C2×C3×C4#23911yescharacteristic
293C2×C3×C4C22×Dic311yescharacteristic
294#67—22no—
295#67—22no—
296C2×Dic3—21no—
297C2×Dic3—22no—
298C2×Dic3—22no—
299C2×Dic3—22no—
300C2×Dic3—32no—
301C2×Dic3—32no—
302C2×Dic3—32no—
303C2×Dic3—32no—
304C2×Dic3—42no—
305C2×Dic3—42no—
306C2×Dic3—62no—
307C2×Dic3—62no—
308C2×Dic3—124no—
309C2×Dic3—122no—
310C2×Dic3—122no—
311C2×Dic3—124no—
312D12—21no—
313D12C4×Dic312yes—
314C4×D3—22no—
315C4×D3—22no—
316C4×D3—124no—
317Dic6—21no—
318Dic6C4×Dic312yes—
319C3×C8—24no—
320C3×C8—22no—
321C3×C8—22no—
322C3⋊C8—64no—
323C3⋊C8—62no—
324C3⋊C8—62no—
325C2×C32—21no—
326C2×C32—21no—
327C2×C32C4×C22⋊C411yescharacteristic
328C2×C32#42112yes—
329C3×D3—42no—
330#41—32no—
331#41—32no—
332#41—61no—
333#41—61no—
334C2×Q8—31no—
335C2×D4—31no—
336C2×D4—61no—
337C22×C4—61no—
338C22×C4—61no—
339C22×C4—61no—
340C22×C4—92no—
341C22×C4—182no—
342C22×C4C2×D3211yescharacteristic
343M16—21no—
344M16—92no—
345M16—181no—
346M16D3×Dic312yescomplemented
347C2×C8—21no—
348C2×C8—181no—
349C4⋊C4—32no—
350C4⋊C4—182no—
351C22⋊C4—61no—
352C22⋊C4—182no—
353C42—32no—
354C42—32no—
355C42—61no—
356C42—61no—
357C42—61no—
358C42—92no—
359C42—91no—
360C42—91no—
361C42—182no—
362C22×C3—22no—
363C22×C3—22no—
364C22×C3—21no—
365C22×C3—21no—
366C22×C3—21no—
367C22×C3—42no—
368C22×C3—62no—
369C22×C3—122no—
370C22×C3D3×C22⋊C411yescharacteristic
371C22×C3D3×C22⋊C411yescharacteristic
372C22×C3#67⋊C411yescharacteristic
373C22×C3#67⋊C411yescharacteristic
374C22×C3#89311yescharacteristic
375C22×C3D4×Dic311yescharacteristic
376C2×D3—22no—
377C2×D3—42no—
378C3×C4—21no—
379C3×C4—21no—
380C3×C4—21no—
381C3×C4—21no—
382C3×C4—62no—
383C3×C4—122no—
384C3×C4—122no—
385C3×C4—122no—
386C3×C4C42×D311yescharacteristic
387C3×C4#87711yescharacteristic
388C3×C4#67⋊C411yescharacteristic
389C3×C4#67⋊C411yescharacteristic
390C3×C4#89211yescharacteristic
391C3×C4#89311yescharacteristic
392C3×C4C2×C4×Dic311yescharacteristic
393C3×C4D4×Dic311yescharacteristic
394Dic3—22no—
395Dic3—42no—
396Dic3—42no—
397Dic3—42no—
398Dic3—64no—
399Dic3—62no—
400Dic3—62no—
401Dic3—62no—
402Dic3—62no—
403Dic3—122no—
404C32#175911yescharacteristic, complemented, Sylow
405C23—61no—
406C23#380211yescharacteristic
407Q8—32no—
408Q8—61no—
409D4—32no—
410D4—62no—
411D4—62no—
412D4—61no—
413C2×C4—61no—
414C2×C4—62no—
415C2×C4—62no—
416C2×C4—62no—
417C2×C4—62no—
418C2×C4—62no—
419C2×C4—92no—
420C2×C4—92no—
421C2×C4—122no—
422C2×C4—122no—
423C2×C4—364no—
424C2×C4—362no—
425C2×C4#379611yescharacteristic
426C2×C4C4×D3211yescharacteristic
427C2×C4C4×D3211yescharacteristic
428C2×C4C2×D3×Dic311yescharacteristic
429C2×C4#380511yescharacteristic
430C2×C4#381111yescharacteristic
431C8—22no—
432C8—182no—
433C2×C3—21no—
434C2×C3—21no—
435C2×C3—21no—
436C2×C3—21no—
437C2×C3—22no—
438C2×C3—21no—
439C2×C3—41no—
440C2×C3—41no—
441C2×C3—122no—
442C2×C3#466611yescharacteristic
443C2×C3#482112yes—
444C2×C3#482112yes—
445C2×C3Dic3×C22⋊C411yescharacteristic
446D3—42no—
447C22—22no—
448C22—62no—
449C22—122no—
450C22#6389811yescharacteristic
451C22#6390211yescharacteristic
452C22#6392111yescharacteristic
453C4—62no—
454C4—122no—
455C4—122no—
456C4—122no—
457C4—182no—
458C4—182no—
459C4C4×D3×Dic311yescharacteristic
460C4#6387811yescharacteristic
461C4#6388111yescharacteristic
462C4#67⋊Dic311yescharacteristic
463C3—21no—
464C3#6872911yescharacteristic, complemented
465C3#7035411yescharacteristic, complemented
466C2—21no—
467C2—21no—
468C2—122no—
469C2#1059100912yes—
470C2#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
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
2. M16×C3⋊Dic3C2semidirect
4. #10591222C2semidirect
6. C3×#4555C2semidirect
7. #10589161C2semidirect
18. #63898C4semidirect
21. #63843C4semidirect
24. C3×#825C4semidirect
26. #63569C4semidirect
39. #4555D3semidirect
56. C32×M16C2×C4semidirect
62. #3748C2×C4semidirect
69. C3×C4×Dic3C2×C4semidirect
70. C3×C4×Dic3C2×C4semidirect
106. #825Dic3semidirect
181. C3×M16C4×D3semidirect
182. C3×M16C2×Dic3semidirect
213. C4×Dic3C4×D3semidirect
214. C4×Dic3C2×Dic3semidirect
346. M16D3×Dic3semidirect
404. C32#1759semidirect
464. C3#68729semidirect
465. C3#70354semidirect

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
#105912222
C2×#635692
C3×#45552
#105891612
#703543
#687293