Finite Group Databasebeta

← #11858836

Subgroups — #11858836

Order 1152.

1063 conjugacy classes of subgroups.

The subgroup lattice has 487 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#624C211yesmaximal, characteristic
2#10592825C211yesmaximal, characteristic
3C3×#5118C211yesmaximal, characteristic, complemented
4C3×Dic3×M16C211yesmaximal, characteristic, complemented
5#10591115C211yesmaximal, characteristic, complemented
6#10591074C211yesmaximal, characteristic
7Dic3×#208C211yesmaximal, characteristic, complemented
8#10590665C214yesmaximal, complemented
9#10590643C214yesmaximal, complemented
10#79038—31nomaximal
11#78517—31nomaximal
12C22×C4×C3⋊D3C2211yescharacteristic
13C22×#624C412yes—
14C2×C32×M16C2211yescharacteristic
15C2×#3748C2211yescharacteristic
16C2×C3×C4×Dic3C2211yescharacteristic
17C2×C3×C4×Dic3C2211yescharacteristic
18C2×C3×#208C2211yescharacteristic
19C2×C3×#208C2211yescharacteristic
20C2×Dic32C412yes—
21C4×#624C412yes—
22C4×#624C412yes—
23C4×#624C2212yes—
24C4×#624C2212yes—
25#63647C2214yes—
26C3×#815C2212yescomplemented
27C3×Dic3⋊C8C2214yescomplemented
28C3×C8×Dic3C2212yescomplemented
29Dic3⋊(C3⋊C8)C2214yescomplemented
30#63557C2214yes—
31#63554C2212yescomplemented
32Dic3×C3⋊C8C2212yescomplemented
33C2×C42×D3—31no—
34C2×C42×D3—31no—
35C3×#423—31no—
36C3×C4×M16—31no—
37#5126—31no—
38#5126—31no—
39#5126—31no—
40#5126—31no—
41#5126—61no—
42#5118—31no—
43#5118D311yescharacteristic, complemented
44Dic3×M16—31no—
45Dic3×M16D311yescharacteristic, complemented
46#4924—31no—
47C4×#208—31no—
48#4835—34no—
49#4833—34no—
50#4705—34no—
51#4685—34no—
52C23×C3⋊D3C2×C411yescharacteristic
53C22×C32×C4C2311yescharacteristic
54C22×C3⋊Dic3C2×C411yescharacteristic
55C2×C4×C3⋊D3—22no—
56C2×C4×C3⋊D3—22no—
57C2×C4×C3⋊D3C2×C412yes—
58C2×C4×C3⋊D3C2312yes—
59C22×C3×Dic3C2×C412yes—
60C22×C3×Dic3C2×C412yes—
61C2×#624—28no—
62C2×#624C2×C412yes—
63C2×#624C2×C412yes—
64C2×#624C2×C412yes—
65C2×#624C2×C412yes—
66C32×M16—22no—
67C2×C32×C8C2312yes—
68#3748—22no—
69C2×C3⋊(C3⋊C8)C2312yes—
70C3×C4×Dic3C2×C411yescharacteristic
71C3×C4×Dic3C2×C412yes—
72C3×C4×Dic3C2×C411yescharacteristic
73C3×C4×Dic3C2311yescharacteristic
74C3×C4×Dic3C2311yescharacteristic
75C3×C4×Dic3C2312yes—
76C3×#208—22no—
77C3×#208—22no—
78C2×C3×C3⋊C8C2312yes—
79C2×C3×C3⋊C8C2312yes—
80Dic32C2×C412yes—
81Dic32C2×C412yes—
82Dic32C2×C412yes—
83Dic32C2×C412yes—
84#2920—91noSylow
85C22×C4×D3—31no—
86C22×C4×D3—31no—
87C22×C4×D3—32no—
88C22×C4×D3—32no—
89C22×C4×D3—61no—
90C2×C3×M16—21no—
91C2×C3×M16—31no—
92C2×C3×M16—31no—
93C2×C3×M16C2×D311yescharacteristic
94C2×C3×M16C2×D311yescharacteristic
95C2×C3×C42—31no—
96C2×C3×C42—31no—
97C2×C4×Dic3—32no—
98C2×C4×Dic3—32no—
99C2×C4×Dic3C2×D311yescharacteristic
100C2×C4×Dic3C2×D311yescharacteristic
101C2×#208—31no—
102C2×#208—31no—
103C2×#208—61no—
104C2×#208C2×D311yescharacteristic
105C2×#208C2×D311yescharacteristic
106C42×D3—32no—
107C42×D3—32no—
108C42×D3—32no—
109C42×D3—32no—
110C42×D3—32no—
111C42×D3—32no—
112C42×D3—32no—
113C42×D3—32no—
114C3×C4⋊C8—34no—
115C3×#97—32no—
116C3×C4×C8—32no—
117(C2×D3)⋊C8—34no—
118(C2×D3)⋊C8—34no—
119(C2×D3)⋊C8—34no—
120(C2×D3)⋊C8—34no—
121(C2×D3)⋊C8—64no—
122#815—32no—
123#815C2×D312yescomplemented
124Dic3⋊C8—34no—
125Dic3⋊C8C2×D314yescomplemented
126C8×Dic3—32no—
127C8×Dic3C2×D312yescomplemented
128C4⋊(C3⋊C8)—34no—
129#803—32no—
130C4×C3⋊C8—32no—
131C23×C32C22×C411yescharacteristic
132C22×C3⋊D3—22no—
133C22×C3⋊D3—24no—
134C22×C3⋊D3C22×C412yes—
135C2×C32×C4C22×C411yescharacteristic
136C2×C32×C4#4112yes—
137C2×C32×C4#4112yes—
138C2×C32×C4C2411yescharacteristic
139C2×C3⋊Dic3—22no—
140C2×C3⋊Dic3C22×C412yes—
141C4×C3⋊D3—24no—
142C4×C3⋊D3—22no—
143C4×C3⋊D3—22no—
144C2×C3×Dic3—24no—
145C2×C3×Dic3—24no—
146C2×C3×Dic3C22×C412yes—
147C2×C3×Dic3C22×C412yes—
148C2×C3×Dic3C22×C412yes—
149C2×C3×Dic3C22×C412yes—
150#624—24no—
151#624—24no—
152#624—24no—
153#624M1618yescomplemented
154C32×C8—22no—
155C3⋊(C3⋊C8)—22no—
156C3×C3⋊C8—22no—
157C3×C3⋊C8—22no—
158C22×C42—91no—
159#432—94no—
160#431—94no—
161#423—31no—
162#423—91no—
163#407—91no—
164#407—91no—
165C4×M16—31no—
166C4×M16—91no—
167C23×D3—31no—
168C23×D3—31no—
169C23×D3—61no—
170C22×C3×C4—21no—
171C22×C3×C4—32no—
172C22×C3×C4—32no—
173C22×C3×C4C22×D311yescharacteristic
174C22×C3×C4C22×D311yescharacteristic
175C22×Dic3—31no—
176C22×Dic3—31no—
177C22×Dic3—61no—
178C22×Dic3C4×D312yes—
179C22×Dic3C4×D312yes—
180C2×C4×D3—32no—
181C2×C4×D3—32no—
182C2×C4×D3—32no—
183C2×C4×D3—32no—
184C2×C4×D3—32no—
185C2×C4×D3—32no—
186C2×C4×D3—32no—
187C2×C4×D3—32no—
188C2×C4×D3—32no—
189C2×C4×D3—32no—
190C2×C4×D3—32no—
191C2×C4×D3—32no—
192C2×C4×D3—62no—
193C2×C4×D3—62no—
194C2×C4×D3—68no—
195C2×C4×D3—68no—
196C2×C4×D3—62no—
197C2×C4×D3—62no—
198C2×C4×D3—62no—
199C2×C4×D3—62no—
200C2×C4×D3—122no—
201C2×C4×D3—122no—
202C3×M16—22no—
203C3×M16—22no—
204C3×M16—42no—
205C3×M16—62no—
206C3×M16—62no—
207C2×C3×C8—22no—
208C2×C3×C8—32no—
209C2×C3×C8—32no—
210C2×C3×C8C22×D312yes—
211C2×C3×C8C22×D312yes—
212C3×C42—31no—
213C3×C42—32no—
214C3×C42—31no—
215C3×C42—31no—
216C3×C42—31no—
217C3×C42—32no—
218C4×Dic3—32no—
219C4×Dic3—32no—
220C4×Dic3—32no—
221C4×Dic3—32no—
222C4×Dic3—32no—
223C4×Dic3—32no—
224C4×Dic3—32no—
225C4×Dic3—32no—
226C4×Dic3C4×D311yescharacteristic
227C4×Dic3C4×D312yes—
228C4×Dic3C4×D311yescharacteristic
229C4×Dic3C22×D311yescharacteristic
230C4×Dic3C22×D312yes—
231C4×Dic3C22×D311yescharacteristic
232#208—22no—
233#208—22no—
234#208—62no—
235#208—62no—
236#208—122no—
237C2×C3⋊C8—32no—
238C2×C3⋊C8—32no—
239C2×C3⋊C8—62no—
240C2×C3⋊C8C22×D312yes—
241C2×C3⋊C8C22×D312yes—
242C22×C32—22no—
243C22×C32#11712yes—
244C22×C32C23×C411yescharacteristic
245C2×C3⋊D3—28no—
246C2×C3⋊D3—22no—
247C2×C3⋊D3—22no—
248C2×C3⋊D3C2×M1614yes—
249C32×C4#11712yes—
250C32×C4C2×#4111yescharacteristic
251C32×C4C2×#4111yescharacteristic
252C3⋊Dic3—22no—
253C3×Dic3—22no—
254C3×Dic3—22no—
255C3×Dic3C2×M1614yes—
256C3×Dic3C2×M1614yes—
257C23×C4—92no—
258C23×C4—91no—
259C2×M16—31no—
260C2×M16—31no—
261C2×M16—91no—
262C2×M16D3211yescharacteristic
263C2×C42—31no—
264C2×C42—31no—
265C2×C42—92no—
266C2×C42—92no—
267C2×C42—92no—
268C2×C42—92no—
269C2×C42—92no—
270C4⋊C8—34no—
271C4⋊C8—94no—
272C22⋊C8—94no—
273C22⋊C8—94no—
274#97—32no—
275#97—92no—
276C4×C8—32no—
277C4×C8—92no—
278C23×C3—21no—
279C23×C3C2×C4×D311yescharacteristic
280C23×C3C2×C4×D311yescharacteristic
281C22×D3—32no—
282C22×D3—32no—
283C22×D3—62no—
284C22×D3—64no—
285C22×D3—64no—
286C22×D3—62no—
287C22×D3—62no—
288C22×D3—124no—
289C22×D3—122no—
290C2×C3×C4—21no—
291C2×C3×C4—22no—
292C2×C3×C4—21no—
293C2×C3×C4—22no—
294C2×C3×C4—32no—
295C2×C3×C4—32no—
296C2×C3×C4—32no—
297C2×C3×C4—32no—
298C2×C3×C4—64no—
299C2×C3×C4—64no—
300C2×C3×C4C2×C4×D311yescharacteristic
301C2×C3×C4C2×C4×D311yescharacteristic
302C2×C3×C4#23512yes—
303C2×C3×C4#23512yes—
304C2×C3×C4#23712yes—
305C2×C3×C4#23912yes—
306C2×C3×C4C23×D311yescharacteristic
307C2×C3×C4C23×D311yescharacteristic
308C2×Dic3—24no—
309C2×Dic3—24no—
310C2×Dic3—32no—
311C2×Dic3—32no—
312C2×Dic3—62no—
313C2×Dic3—62no—
314C2×Dic3—62no—
315C2×Dic3—122no—
316C2×Dic3C2×C4×D312yes—
317C2×Dic3C2×C4×D312yes—
318C2×Dic3C2×C4×D312yes—
319C2×Dic3C2×C4×D312yes—
320C4×D3—38no—
321C4×D3—38no—
322C4×D3—64no—
323C4×D3—64no—
324C4×D3—64no—
325C4×D3—64no—
326C4×D3—64no—
327C4×D3—64no—
328C4×D3—62no—
329C4×D3—62no—
330C4×D3—62no—
331C4×D3—62no—
332C4×D3—64no—
333C4×D3—64no—
334C4×D3—122no—
335C4×D3—122no—
336C4×D3—124no—
337C3×C8—22no—
338C3×C8—22no—
339C3×C8—42no—
340C3×C8—62no—
341C3×C8—62no—
342C3⋊C8—22no—
343C3⋊C8—22no—
344C3⋊C8—62no—
345C3⋊C8—62no—
346C3⋊C8—122no—
347C2×C32—22no—
348C2×C32C2×#11711yescharacteristic
349C2×C32C22×M1612yes—
350C3⋊D3—24no—
351C24—91no—
352C22×C4—32no—
353C22×C4—32no—
354C22×C4—92no—
355C22×C4—92no—
356C22×C4—92no—
357C22×C4—92no—
358C22×C4—91no—
359C22×C4—92no—
360C22×C4—92no—
361C22×C4—188no—
362C22×C4—182no—
363C22×C4—182no—
364C22×C4C2×D3211yescharacteristic
365M16—22no—
366M16—62no—
367M16—62no—
368M16—182no—
369C2×C8—32no—
370C2×C8—32no—
371C2×C8—92no—
372C2×C8C2×D3212yes—
373C42—31no—
374C42—31no—
375C42—32no—
376C42—31no—
377C42—32no—
378C42—31no—
379C42—92no—
380C42—92no—
381C42—92no—
382C42—92no—
383C22×C3—22no—
384C22×C3—22no—
385C22×C3—21no—
386C22×C3—22no—
387C22×C3—42no—
388C22×C3#87212yes—
389C22×C3#89212yes—
390C22×C3C22×C4×D311yescharacteristic
391C22×C3C22×C4×D311yescharacteristic
392C2×D3—34no—
393C2×D3—34no—
394C2×D3—64no—
395C2×D3—68no—
396C2×D3—68no—
397C2×D3—62no—
398C2×D3—62no—
399C2×D3—62no—
400C2×D3—62no—
401C2×D3—122no—
402C2×D3—122no—
403C2×D3—128no—
404C3×C4—21no—
405C3×C4—21no—
406C3×C4—22no—
407C3×C4—34no—
408C3×C4—34no—
409C3×C4—62no—
410C3×C4—62no—
411C3×C4#87212yes—
412C3×C4#89212yes—
413C3×C4C2×#23511yescharacteristic
414C3×C4C2×#23511yescharacteristic
415C3×C4C2×#23711yescharacteristic
416C3×C4C2×#23911yescharacteristic
417Dic3—22no—
418Dic3—22no—
419Dic3—62no—
420Dic3—62no—
421Dic3—122no—
422Dic3D3×M1614yes—
423Dic3D3×M1614yes—
424C32#292011yescharacteristic, complemented, Sylow
425C23—92no—
426C23—184no—
427C23—182no—
428C23C4×D3211yescharacteristic
429C2×C4—32no—
430C2×C4—32no—
431C2×C4—32no—
432C2×C4—32no—
433C2×C4—64no—
434C2×C4—64no—
435C2×C4—98no—
436C2×C4—92no—
437C2×C4—184no—
438C2×C4—184no—
439C2×C4—184no—
440C2×C4—182no—
441C2×C4—182no—
442C2×C4—182no—
443C2×C4—184no—
444C2×C4#379912yes—
445C2×C4C4×D3211yescharacteristic
446C2×C4#380412yes—
447C2×C4C22×D3211yescharacteristic
448C8—22no—
449C8—62no—
450C8—62no—
451C8—182no—
452C2×C3—22no—
453C2×C3—22no—
454C2×C3—22no—
455C2×C3—21no—
456C2×C3—42no—
457C2×C3C2×#87211yescharacteristic
458C2×C3C2×#89211yescharacteristic
459C2×C3C2×D3×M1612yes—
460C2×C3C2×D3×M1612yes—
461D3—64no—
462D3—64no—
463D3—124no—
464C22—22no—
465C22—94no—
466C22—188no—
467C22—182no—
468C22—182no—
469C22#6383612yes—
470C22C2×C4×D3211yescharacteristic
471C4—34no—
472C4—34no—
473C4—62no—
474C4—62no—
475C4—182no—
476C4#6383612yes—
477C4C2×#379911yescharacteristic
478C4C2×#380411yescharacteristic
479C3—21no—
480C3#7851711yescharacteristic, complemented
481C3#7903811yescharacteristic, complemented
482C2—22no—
483C2—184no—
484C2D32×M1612yes—
485C2C2×#6383611yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC2×C32×M16C22
prime radicalC23×C3⋊D3C2×C4
cosocleC2×C32×C4C24
hypercenterC2×M16D32
hypocenterC32#2920
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
3. C3×#5118C2semidirect
4. C3×Dic3×M16C2semidirect
5. #10591115C2semidirect
7. Dic3×#208C2semidirect
8. #10590665C2semidirect
9. #10590643C2semidirect
26. C3×#815C22semidirect
27. C3×Dic3⋊C8C22semidirect
28. C3×C8×Dic3C22semidirect
29. Dic3⋊(C3⋊C8)C22semidirect
31. #63554C22semidirect
32. Dic3×C3⋊C8C22semidirect
43. #5118D3semidirect
45. Dic3×M16D3semidirect
123. #815C2×D3semidirect
125. Dic3⋊C8C2×D3semidirect
127. C8×Dic3C2×D3semidirect
153. #624M16semidirect
424. C32#2920semidirect
480. C3#78517semidirect
481. C3#79038semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6242
#105928252
C3×#51182
C3×Dic3×M162
#105911152
#105910742
Dic3×#2082
#105906652
#105906432
#790383
#785173