Finite Group Databasebeta

← #11858806

Subgroups — #11858806

Order 1152.

893 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#10593992C211yesmaximal, characteristic
2C3⋊D3×C4⋊C8C211yesmaximal, characteristic, complemented
3C3×#4840C212yesmaximal, complemented
4#10590935C211yesmaximal, characteristic
5#10590935C211yesmaximal, characteristic
6#10590697C212yesmaximal, complemented
7#10590696C212yesmaximal, complemented
8#10590668C211yesmaximal, characteristic, complemented
9C8×#624C211yesmaximal, characteristic, complemented
10#10590331C211yesmaximal, characteristic, complemented
11#10590253C212yesmaximal, complemented
12D3×#433—32nomaximal
13C2×C4×D32C2211yescharacteristic
14C2×C8×C3⋊D3C2211yescharacteristic
15C2×C8×C3⋊D3C2211yescharacteristic
16C42×C3⋊D3C2211yescharacteristic
17C3×#872C2212yes—
18#63921C411yescharacteristic
19#63921C411yescharacteristic
20#63883C411yescharacteristic
21#63883C411yescharacteristic
22C4×#624C2211yescharacteristic
23#63878C412yes—
24#63878C412yes—
25#63855C2212yes—
26C2×#3710C2211yescharacteristic
27C2×#3710C2211yescharacteristic
28C32×C4⋊C8C2211yescharacteristic, complemented
29#63641C2211yescharacteristic, complemented
30#63641C2211yescharacteristic, complemented
31C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
32C3×(C2×D3)⋊C8C2212yes—
33C3×(C2×D3)⋊C8C2212yes—
34C3×#815C2212yescomplemented
35C3×C8×Dic3C2212yescomplemented
36C3×C4⋊(C3⋊C8)C2212yescomplemented
37#63572C2212yescomplemented
38(C2×D3)⋊(C3⋊C8)C2212yes—
39(C2×D3)⋊(C3⋊C8)C2212yes—
40#63554C2212yescomplemented
41Dic3×C3⋊C8C2212yescomplemented
42D3×#117—32no—
43C3×#433—32no—
44#5000—32no—
45#4840—32no—
46#4840D312yescomplemented
47D3×C4⋊C8—32no—
48D3×C4⋊C8—32no—
49D3×C4⋊C8—61no—
50D3×C22⋊C8—32no—
51D3×C22⋊C8—32no—
52#4720—32no—
53#4720—32no—
54#4709—32no—
55D3×#97—32no—
56#4690—32no—
57C4×D3×C8—32no—
58C22×D32C2×C411yescharacteristic
59C2×C4×C3⋊D3C2×C411yescharacteristic
60C2×C4×C3⋊D3C2×C411yescharacteristic
61C2×C4×C3⋊D3C2311yescharacteristic
62C2×C3×C4×D3C2312yes—
63C2×#624C2×C411yescharacteristic
64C2×#624C2×C411yescharacteristic
65C2×#624C2×C411yescharacteristic
66C2×D3×Dic3C2×C412yes—
67C4×D32—22no—
68C4×D32—22no—
69C2×C32×C8C2311yescharacteristic
70C2×C32×C8C2311yescharacteristic
71C32×C42C2311yescharacteristic
72C4×C3⋊Dic3C2×C411yescharacteristic
73C4×C3⋊Dic3C2×C411yescharacteristic
74C4×C3⋊Dic3C2311yescharacteristic
75C2×C3⋊(C3⋊C8)C2311yescharacteristic
76C2×C3⋊(C3⋊C8)C2311yescharacteristic
77C8×C3⋊D3—22no—
78C8×C3⋊D3—22no—
79C3×(C2×D3)⋊C4C2×C412yes—
80C3×(C2×D3)⋊C4C2×C412yes—
81C3×Dic3⋊C4C2×C412yes—
82C3×Dic3⋊C4C2×C412yes—
83C3×C4×Dic3C2312yes—
84C2×C3×C3⋊C8C2312yes—
85C2×C3×C3⋊C8C2312yes—
86Dic3⋊Dic3C2×C412yes—
87Dic3⋊Dic3C2×C412yes—
88(C2×D3)⋊Dic3C2×C412yes—
89(C2×D3)⋊Dic3C2×C412yes—
90Dic32C2×C412yes—
91#3710—22no—
92#3710—22no—
93C2×#433—91noSylow
94C22×C4×D3—32no—
95C3×#117—32no—
96#926—32no—
97C2×D3×C8—32no—
98C2×D3×C8—32no—
99C2×D3×C8—32no—
100C2×D3×C8—32no—
101C2×D3×C8—61no—
102C2×D3×C8—61no—
103#892—32no—
104#892—32no—
105D3×C4⋊C4—32no—
106D3×C4⋊C4—32no—
107D3×C22⋊C4—32no—
108D3×C22⋊C4—32no—
109#877—32no—
110#877—32no—
111#872—32no—
112#872C2×D312yes—
113C42×D3—32no—
114C42×D3—32no—
115C42×D3—61no—
116C3×C4⋊C8—21no—
117C3×C4⋊C8—32no—
118C3×C4⋊C8C2×D312yescomplemented
119C3×C22⋊C8—32no—
120C3×C22⋊C8—32no—
121C3×#97—32no—
122C3×C4×C8—32no—
123#830—32no—
124#830—32no—
125(C2×D3)⋊C8—32no—
126(C2×D3)⋊C8—32no—
127(C2×D3)⋊C8C2×D312yes—
128(C2×D3)⋊C8C2×D312yes—
129#815—32no—
130#815C2×D312yescomplemented
131Dic3⋊C8—32no—
132Dic3⋊C8—32no—
133Dic3⋊C8—32no—
134Dic3⋊C8—32no—
135Dic3⋊C8—61no—
136Dic3⋊C8—61no—
137C8×Dic3—32no—
138C8×Dic3C2×D312yescomplemented
139C4⋊(C3⋊C8)—32no—
140C4⋊(C3⋊C8)—61no—
141C4⋊(C3⋊C8)C2×D312yescomplemented
142#803—32no—
143C4×C3⋊C8—32no—
144C22×C3⋊D3C22×C411yescharacteristic
145C22×C3×D3C22×C412yes—
146C2×D32—22no—
147C2×D32—22no—
148C2×D32—22no—
149C2×C32×C4C22×C411yescharacteristic
150C2×C32×C4C22×C411yescharacteristic
151C2×C32×C4C2411yescharacteristic
152C2×C3⋊Dic3C22×C411yescharacteristic
153C2×C3⋊Dic3C22×C411yescharacteristic
154C2×C3⋊Dic3C22×C411yescharacteristic
155C4×C3⋊D3—22no—
156C4×C3⋊D3—22no—
157C4×C3⋊D3#4112yes—
158C4×C3⋊D3#4112yes—
159C2×C3×Dic3C22×C412yes—
160C2×C3×Dic3C22×C412yes—
161C2×C3×Dic3C22×C412yes—
162C3×C4×D3—22no—
163C3×C4×D3—22no—
164#624—22no—
165#624—22no—
166#624—22no—
167D3×Dic3—24no—
168C32×C8—21no—
169C32×C8—21no—
170C3⋊(C3⋊C8)—21no—
171C3⋊(C3⋊C8)—21no—
172C3×C3⋊C8—22no—
173C3×C3⋊C8—22no—
174C2×#117—91no—
175#433—32no—
176#433—92no—
177#433—92no—
178#433—92no—
179C2×C4⋊C8—91no—
180C2×C4⋊C8—91no—
181C2×C22⋊C8—91no—
182C2×C22⋊C8—91no—
183C2×#97—91no—
184C2×C4×C8—91no—
185C23×D3—32no—
186C22×C3×C4—32no—
187C22×Dic3—32no—
188C2×C4×D3—32no—
189C2×C4×D3—32no—
190C2×C4×D3—32no—
191C2×C4×D3—32no—
192C2×C4×D3—32no—
193C2×C4×D3—32no—
194C2×C4×D3—32no—
195C2×C4×D3—61no—
196C2×C4×D3—61no—
197C2×C4×D3—61no—
198C2×C4×D3—64no—
199C2×C4×D3—64no—
200C2×C4×D3C22×D312yes—
201C2×C3×C8—21no—
202C2×C3×C8—21no—
203C2×C3×C8—32no—
204C2×C3×C8—32no—
205C2×C3×C8C22×D312yes—
206C2×C3×C8C22×D312yes—
207C3×C4⋊C4—32no—
208C3×C4⋊C4—32no—
209C3×C22⋊C4—32no—
210C3×C22⋊C4—32no—
211C3×C42—21no—
212C3×C42—32no—
213C3×C42C22×D312yes—
214#217—32no—
215#217—32no—
216(C2×D3)⋊C4—32no—
217(C2×D3)⋊C4—32no—
218(C2×D3)⋊C4C4×D312yes—
219(C2×D3)⋊C4C4×D312yes—
220C4⋊Dic3—32no—
221C4⋊Dic3—32no—
222Dic3⋊C4—32no—
223Dic3⋊C4—32no—
224Dic3⋊C4C4×D312yes—
225Dic3⋊C4C4×D312yes—
226C4×Dic3—32no—
227C4×Dic3—32no—
228C4×Dic3—32no—
229C4×Dic3—32no—
230C4×Dic3—32no—
231C4×Dic3—61no—
232C4×Dic3—61no—
233C4×Dic3—61no—
234C4×Dic3C22×D312yes—
235C2×C3⋊C8—32no—
236C2×C3⋊C8—32no—
237C2×C3⋊C8—61no—
238C2×C3⋊C8—61no—
239C2×C3⋊C8C22×D312yes—
240C2×C3⋊C8C22×D312yes—
241D3×C8—64no—
242D3×C8—64no—
243D3×C8—64no—
244D3×C8—64no—
245D3×C8—122no—
246D3×C8—122no—
247C22×C32C23×C411yescharacteristic
248C2×C3⋊D3#11712yes—
249C2×C3⋊D3#13112yes—
250C2×C3⋊D3#13112yes—
251C2×C3×D3—22no—
252C2×C3×D3—22no—
253C2×C3×D3—22no—
254D32—44no—
255C32×C4—21no—
256C32×C4—21no—
257C32×C4C2×#4111yescharacteristic
258C32×C4C2×#4111yescharacteristic
259C3⋊Dic3—21no—
260C3⋊Dic3—21no—
261C3⋊Dic3#11712yes—
262C3×Dic3—22no—
263C3×Dic3—22no—
264C3×Dic3—22no—
265C23×C4—91no—
266C22×C8—91no—
267C22×C8—91no—
268C22×C8—91no—
269C22×C8—91no—
270#117—32no—
271#117—92no—
272#117—92no—
273#117—92no—
274C2×C4⋊C4—91no—
275C2×C4⋊C4—91no—
276C2×C22⋊C4—91no—
277C2×C22⋊C4—91no—
278C2×C42—91no—
279C2×C42—91no—
280C4⋊C8—32no—
281C4⋊C8—92no—
282C4⋊C8—91no—
283C4⋊C8—91no—
284C4⋊C8—91no—
285C4⋊C8D3211yescharacteristic, complemented
286C22⋊C8—32no—
287C22⋊C8—32no—
288C22⋊C8—92no—
289C22⋊C8—92no—
290#97—32no—
291#97—92no—
292C4×C8—32no—
293C4×C8—92no—
294C23×C3—32no—
295C22×D3—32no—
296C22×D3—61no—
297C22×D3—64no—
298C22×D3—64no—
299C22×D3—64no—
300C22×D3C2×C4×D312yes—
301C2×C3×C4—21no—
302C2×C3×C4—21no—
303C2×C3×C4—21no—
304C2×C3×C4—32no—
305C2×C3×C4—32no—
306C2×C3×C4—32no—
307C2×C3×C4—62no—
308C2×C3×C4—62no—
309C2×C3×C4C2×C4×D312yes—
310C2×C3×C4C2×C4×D312yes—
311C2×C3×C4C23×D312yes—
312C2×Dic3—32no—
313C2×Dic3—32no—
314C2×Dic3—32no—
315C2×Dic3—61no—
316C2×Dic3—61no—
317C2×Dic3—61no—
318C2×Dic3—64no—
319C2×Dic3C2×C4×D312yes—
320C2×Dic3C2×C4×D312yes—
321C2×Dic3C2×C4×D312yes—
322C4×D3—22no—
323C4×D3—22no—
324C4×D3—34no—
325C4×D3—34no—
326C4×D3—62no—
327C4×D3—62no—
328C4×D3—64no—
329C4×D3—64no—
330C4×D3—64no—
331C4×D3—64no—
332C4×D3—64no—
333C4×D3—64no—
334C4×D3—64no—
335C4×D3—122no—
336C3×C8—22no—
337C3×C8—22no—
338C3×C8—41no—
339C3×C8—41no—
340C3×C8—62no—
341C3×C8—62no—
342C3⋊C8—22no—
343C3⋊C8—22no—
344C3⋊C8—62no—
345C3⋊C8—62no—
346C3⋊C8—121no—
347C3⋊C8—121no—
348C2×C32C2×#11711yescharacteristic
349C2×C32C2×#13111yescharacteristic
350C2×C32C2×#13111yescharacteristic
351C3⋊D3#43314yescomplemented
352C3×D3—42no—
353C24—91no—
354C22×C4—32no—
355C22×C4—91no—
356C22×C4—91no—
357C22×C4—91no—
358C22×C4—92no—
359C22×C4—91no—
360C22×C4—91no—
361C22×C4—91no—
362C22×C4—182no—
363C22×C4—182no—
364C2×C8—32no—
365C2×C8—32no—
366C2×C8—91no—
367C2×C8—91no—
368C2×C8—182no—
369C2×C8—182no—
370C2×C8—182no—
371C2×C8—182no—
372C2×C8C2×D3211yescharacteristic
373C2×C8C2×D3211yescharacteristic
374C4⋊C4—32no—
375C4⋊C4—32no—
376C4⋊C4—92no—
377C4⋊C4—92no—
378C22⋊C4—32no—
379C22⋊C4—32no—
380C22⋊C4—92no—
381C22⋊C4—92no—
382C42—32no—
383C42—92no—
384C42—91no—
385C42—91no—
386C42—91no—
387C42C2×D3211yescharacteristic
388C22×C3—21no—
389C22×C3—62no—
390C22×C3—62no—
391C22×C3—62no—
392C22×C3C22×C4×D312yes—
393C2×D3—22no—
394C2×D3—22no—
395C2×D3—22no—
396C2×D3—34no—
397C2×D3—34no—
398C2×D3—34no—
399C2×D3—62no—
400C2×D3—62no—
401C2×D3—62no—
402C2×D3—128no—
403C3×C4—22no—
404C3×C4—22no—
405C3×C4—22no—
406C3×C4—21no—
407C3×C4—21no—
408C3×C4—41no—
409C3×C4—62no—
410C3×C4—62no—
411C3×C4—62no—
412C3×C4D3×#4112yes—
413C3×C4D3×#4112yes—
414Dic3—22no—
415Dic3—22no—
416Dic3—22no—
417Dic3—34no—
418Dic3—62no—
419Dic3—62no—
420Dic3—62no—
421Dic3—62no—
422Dic3—121no—
423C32C2×#43311yescharacteristic, complemented, Sylow
424C23—32no—
425C23—91no—
426C23—182no—
427C23—182no—
428C23—182no—
429C2×C4—32no—
430C2×C4—32no—
431C2×C4—32no—
432C2×C4—62no—
433C2×C4—62no—
434C2×C4—91no—
435C2×C4—92no—
436C2×C4—92no—
437C2×C4—91no—
438C2×C4—91no—
439C2×C4—182no—
440C2×C4—182no—
441C2×C4—182no—
442C2×C4—182no—
443C2×C4—182no—
444C2×C4—184no—
445C2×C4C4×D3211yescharacteristic
446C2×C4C4×D3211yescharacteristic
447C2×C4C22×D3211yescharacteristic
448C8—21no—
449C8—21no—
450C8—62no—
451C8—62no—
452C8—181no—
453C8—181no—
454C2×C3—21no—
455C2×C3—21no—
456C2×C3—21no—
457C2×C3—122no—
458C2×C3D3×#11712yes—
459C2×C3D3×#13112yes—
460C2×C3D3×#13112yes—
461D3—38no—
462D3—42no—
463D3—64no—
464C22—62no—
465C22—62no—
466C22—62no—
467C22—92no—
468C22—92no—
469C22—92no—
470C22—364no—
471C22C2×C4×D3211yescharacteristic
472C4—21no—
473C4—21no—
474C4—62no—
475C4—62no—
476C4—62no—
477C4—92no—
478C4—181no—
479C4—181no—
480C4#6431211yescharacteristic
481C4#6431911yescharacteristic
482C3—21no—
483C3D3×#43312yescomplemented
484C2—94no—
485C2—122no—
486C2#1059460211yescharacteristic
487C2#1059466911yescharacteristic
488C2#1059470711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC32×C4⋊C8C22
prime radicalC22×D32C2×C4
cosocleC2×C32×C4C24
hypercenterC4⋊C8D32
hypocenterC32C2×#433
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. C3⋊D3×C4⋊C8C2semidirect
3. C3×#4840C2semidirect
6. #10590697C2semidirect
7. #10590696C2semidirect
8. #10590668C2semidirect
9. C8×#624C2semidirect
10. #10590331C2semidirect
11. #10590253C2semidirect
28. C32×C4⋊C8C22semidirect
29. #63641C22semidirect
30. #63641C22semidirect
31. C4⋊(C3⋊(C3⋊C8))C22semidirect
34. C3×#815C22semidirect
35. C3×C8×Dic3C22semidirect
36. C3×C4⋊(C3⋊C8)C22semidirect
37. #63572C22semidirect
40. #63554C22semidirect
41. Dic3×C3⋊C8C22semidirect
46. #4840D3semidirect
118. C3×C4⋊C8C2×D3semidirect
130. #815C2×D3semidirect
138. C8×Dic3C2×D3semidirect
141. C4⋊(C3⋊C8)C2×D3semidirect
285. C4⋊C8D32semidirect
351. C3⋊D3#433semidirect
423. C32C2×#433semidirect
483. C3D3×#433semidirect

Maximal subgroups

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

subgroupindex
#105939922
C3⋊D3×C4⋊C82
C3×#48402
#105909352
#105906972
#105906962
#105906682
C8×#6242
#105903312
#105902532
D3×#4333