Finite Group Databasebeta

← #11788348

Subgroups — #11788348

Order 1152.

771 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#924C211yesmaximal, characteristic
2C22×C3×#208C211yesmaximal, characteristic
3#10592906C211yesmaximal, characteristic
4C2×#63560C212yesmaximal, complemented
5#10589167C212yesmaximal, complemented
6#72003—31nomaximal
7#71698—31nomaximal
8C23×C32×C4C2211yescharacteristic
9C22×C3×Dic6C2211yescharacteristic
10C2×#3748C2212yes—
11C2×C3×#217C412yes—
12C2×C3×C4⋊Dic3C2211yescharacteristic
13C3×#924—21no—
14C3×#924—21no—
15C3×#924—21no—
16C3×#924—21no—
17C2×C3×Dic3⋊C4C412yes—
18C2×C3×#208—21no—
19C2×C3×#208—24no—
20C2×C3×#208C2212yes—
21C22×C3×C3⋊C8—21no—
22#63657—21no—
23#63657—21no—
24#63560—24no—
25C22×C3×M16—31no—
26C2×C3×C22⋊Q8—31no—
27C2×#924D311yescharacteristic
28C22×#208D311yescharacteristic
29C2×#836—32no—
30#5207—31no—
31#5207—31no—
32#5207—61no—
33C2×#824—32no—
34#4554—32no—
35#4530—32no—
36C24×C32C2×C411yescharacteristic
37C22×C32×C4—22no—
38C22×C32×C4—22no—
39C22×C32×C4C2×C411yescharacteristic
40C22×C32×C4D411yescharacteristic
41C22×C32×C4D411yescharacteristic
42C22×C32×C4D411yescharacteristic
43C22×C32×C4D411yescharacteristic
44C22×C32×C4C2311yescharacteristic
45C22×C3×Dic3C2×C412yes—
46C22×C3×Dic3C2×C412yes—
47C2×C3×Dic6—21no—
48C2×C3×Dic6—21no—
49C2×C3×Dic6—22no—
50C2×C3×Dic6—22no—
51#3748—22no—
52#3748—22no—
53C2×C3⋊(C3⋊C8)—22no—
54C3×#217—22no—
55C3×#217—22no—
56C3×C4⋊Dic3—21no—
57C3×C4⋊Dic3—21no—
58C3×Dic3⋊C4—22no—
59C3×Dic3⋊C4—22no—
60C3×#208—24no—
61C3×#208—22no—
62C3×#208D414yes—
63C2×C3×C3⋊C8—24no—
64C2×C3×C3⋊C8—22no—
65#1901—91noSylow
66C22×C3×Q8—31no—
67C23×C3×C4—21no—
68C23×C3×C4C2×D311yescharacteristic
69C23×C3×C4C2×D311yescharacteristic
70C22×Dic6C2×D311yescharacteristic
71C2×C3×M16—32no—
72C2×C3×M16—64no—
73C2×C3×M16—61no—
74C22×C3×C8—61no—
75C3×C22⋊Q8—61no—
76C3×C22⋊Q8—61no—
77C3×C22⋊Q8—61no—
78C3×C22⋊Q8—61no—
79C2×C3×C4⋊C4—32no—
80C2×C3×C4⋊C4—31no—
81C2×C3×C22⋊C4—32no—
82C2×#217Dic312yes—
83C2×C4⋊Dic3C2×D311yescharacteristic
84#924—21no—
85#924—21no—
86#924—21no—
87#924—21no—
88C2×Dic3⋊C4Dic312yes—
89C2×#208—21no—
90C2×#208—24no—
91C2×#208—32no—
92C2×#208—32no—
93C2×#208—62no—
94C2×#208C2×D312yes—
95C22×C3⋊C8—21no—
96#836—64no—
97#830—62no—
98#830—62no—
99#830—61no—
100#830—61no—
101#830—61no—
102#830—61no—
103#824—64no—
104C23×C32—22no—
105C23×C32—22no—
106C23×C32—41no—
107C23×C32C22⋊C411yescharacteristic
108C23×C32C22⋊C411yescharacteristic
109C23×C32C22×C411yescharacteristic
110C2×C32×C4—22no—
111C2×C32×C4—21no—
112C2×C32×C4—21no—
113C2×C32×C4—22no—
114C2×C32×C4—22no—
115C2×C32×C4—21no—
116C2×C32×C4—21no—
117C2×C32×C4C22⋊C411yescharacteristic
118C2×C32×C4C22⋊C411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D412yes—
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4#4112yes—
123C2×C3×Dic3—22no—
124C2×C3×Dic3—22no—
125C2×C3×Dic3—24no—
126C2×C3×Dic3—42no—
127C3×Dic6—41no—
128C3×Dic6—42no—
129C3×Dic6—41no—
130C3⋊(C3⋊C8)—42no—
131C3×C3⋊C8—24no—
132C22×M16—31no—
133C2×C22⋊Q8—31no—
134C2×#101—92no—
135#407—91no—
136#343—92no—
137C24×C3—21no—
138C24×C3C4×D311yescharacteristic
139C24×C3C2×Dic311yescharacteristic
140C2×C3×Q8—61no—
141C2×C3×Q8—62no—
142C2×C3×Q8—62no—
143C2×C3×Q8—61no—
144C22×C3×C4—22no—
145C22×C3×C4—22no—
146C22×C3×C4—22no—
147C22×C3×C4—22no—
148C22×C3×C4—21no—
149C22×C3×C4—21no—
150C22×C3×C4—21no—
151C22×C3×C4—21no—
152C22×C3×C4—21no—
153C22×C3×C4—21no—
154C22×C3×C4—32no—
155C22×C3×C4—32no—
156C22×C3×C4—42no—
157C22×C3×C4—42no—
158C22×C3×C4C4×D311yescharacteristic
159C22×C3×C4D1211yescharacteristic
160C22×C3×C4D1211yescharacteristic
161C22×C3×C4C2×Dic311yescharacteristic
162C22×C3×C4#6711yescharacteristic
163C22×C3×C4#6711yescharacteristic
164C22×C3×C4#6711yescharacteristic
165C22×C3×C4#6711yescharacteristic
166C22×C3×C4#6711yescharacteristic
167C22×C3×C4#6711yescharacteristic
168C22×C3×C4C22×D311yescharacteristic
169C22×C3×C4C22×D311yescharacteristic
170C22×Dic3C2×Dic312yes—
171C22×Dic3C2×Dic312yes—
172C2×Dic6—22no—
173C2×Dic6—22no—
174C2×Dic6—21no—
175C2×Dic6—21no—
176C3×M16—34no—
177C3×M16—64no—
178C3×M16—62no—
179C2×C3×C8—64no—
180C2×C3×C8—62no—
181C3×C4⋊C4—62no—
182C3×C4⋊C4—62no—
183C3×C4⋊C4—61no—
184C3×C4⋊C4—61no—
185C3×C22⋊C4—62no—
186C3×C22⋊C4—62no—
187#217—22no—
188#217—22no—
189C4⋊Dic3—21no—
190C4⋊Dic3—21no—
191Dic3⋊C4—22no—
192Dic3⋊C4—22no—
193#208—24no—
194#208—22no—
195#208—62no—
196#208—62no—
197#208—62no—
198#208—62no—
199#208—122no—
200#208—122no—
201#208#6714yes—
202C2×C3⋊C8—24no—
203C2×C3⋊C8—22no—
204C2×C3⋊C8—64no—
205C2×C3⋊C8—62no—
206C2×C3⋊C8—62no—
207C22×C32—21no—
208C22×C32—21no—
209C22×C32—21no—
210C22×C32—21no—
211C22×C32—21no—
212C22×C32—21no—
213C22×C32—21no—
214C22×C32—44no—
215C22×C32#10112yescomplemented
216C22×C32C2×C22⋊C411yescharacteristic
217C22×C32C4×D412yes—
218C32×C4—21no—
219C32×C4—21no—
220C32×C4#12011yescharacteristic
221C32×C4#12112yes—
222C32×C4#12311yescharacteristic
223C3×Dic3—42no—
224C3×Dic3—42no—
225C22×Q8—31no—
226C23×C4D3211yescharacteristic
227C2×M16—32no—
228C2×M16—64no—
229C2×M16—61no—
230C2×M16—92no—
231C22×C8—61no—
232C22⋊Q8—61no—
233C22⋊Q8—61no—
234C22⋊Q8—61no—
235C22⋊Q8—61no—
236C2×C4⋊C4—32no—
237C2×C4⋊C4—31no—
238C2×C22⋊C4—32no—
239#101—184no—
240C22⋊C8—181no—
241C22⋊C8—181no—
242C23×C3—22no—
243C23×C3—22no—
244C23×C3—22no—
245C23×C3—22no—
246C23×C3—21no—
247C23×C3—21no—
248C23×C3—21no—
249C23×C3—42no—
250C23×C3—42no—
251C23×C3—41no—
252C23×C3—41no—
253C23×C3—42no—
254C23×C3(C2×D3)⋊C411yescharacteristic
255C23×C3(C2×D3)⋊C411yescharacteristic
256C23×C3#21711yescharacteristic
257C23×C3#21711yescharacteristic
258C23×C3C2×C4×D311yescharacteristic
259C23×C3C22×Dic311yescharacteristic
260C3×Q8—121no—
261C3×Q8—122no—
262C3×Q8—121no—
263C2×C3×C4—22no—
264C2×C3×C4—22no—
265C2×C3×C4—21no—
266C2×C3×C4—21no—
267C2×C3×C4—22no—
268C2×C3×C4—22no—
269C2×C3×C4—21no—
270C2×C3×C4—21no—
271C2×C3×C4—21no—
272C2×C3×C4—21no—
273C2×C3×C4—22no—
274C2×C3×C4—22no—
275C2×C3×C4—21no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—22no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—22no—
283C2×C3×C4—41no—
284C2×C3×C4—41no—
285C2×C3×C4—41no—
286C2×C3×C4—41no—
287C2×C3×C4—42no—
288C2×C3×C4—42no—
289C2×C3×C4—42no—
290C2×C3×C4—62no—
291C2×C3×C4—62no—
292C2×C3×C4—64no—
293C2×C3×C4—122no—
294C2×C3×C4(C2×D3)⋊C411yescharacteristic
295C2×C3×C4(C2×D3)⋊C411yescharacteristic
296C2×C3×C4#21711yescharacteristic
297C2×C3×C4#21711yescharacteristic
298C2×C3×C4C2×D1211yescharacteristic
299C2×C3×C4#23512yes—
300C2×C3×C4D3×D412yes—
301C2×C3×C4#23712yes—
302C2×C3×C4C2×#6711yescharacteristic
303C2×C3×C4C2×#6711yescharacteristic
304C2×C3×C4C2×#6711yescharacteristic
305C2×C3×C4C2×#6712yes—
306C2×Dic3—24no—
307C2×Dic3—22no—
308C2×Dic3—22no—
309C2×Dic3—42no—
310Dic6—41no—
311Dic6—41no—
312Dic6—42no—
313C3×C8—64no—
314C3⋊C8—24no—
315C3⋊C8—124no—
316C3⋊C8—122no—
317C3⋊C8—122no—
318C2×C32—22no—
319C2×C32—22no—
320C2×C32—41no—
321C2×C32#38611yescharacteristic
322C2×C32C2×#10111yescharacteristic
323C2×C32#41311yescharacteristic
324C24D3×Dic311yescharacteristic
325C2×Q8—62no—
326C2×Q8—61no—
327C2×Q8—61no—
328C2×Q8—62no—
329C22×C4—22no—
330C22×C4—22no—
331C22×C4—32no—
332C22×C4—32no—
333C22×C4D3×Dic311yescharacteristic
334C22×C4#62511yescharacteristic
335C22×C4#62511yescharacteristic
336C22×C4#62611yescharacteristic
337C22×C4#62611yescharacteristic
338C22×C4C2×D3211yescharacteristic
339M16—34no—
340M16—64no—
341M16—62no—
342M16—182no—
343M16—182no—
344C2×C8—64no—
345C2×C8—62no—
346C2×C8—182no—
347C4⋊C4—62no—
348C4⋊C4—62no—
349C4⋊C4—61no—
350C4⋊C4—61no—
351C22⋊C4—62no—
352C22⋊C4—62no—
353C22×C3—21no—
354C22×C3—21no—
355C22×C3—21no—
356C22×C3—21no—
357C22×C3—21no—
358C22×C3—21no—
359C22×C3—21no—
360C22×C3—21no—
361C22×C3—22no—
362C22×C3—21no—
363C22×C3—21no—
364C22×C3—21no—
365C22×C3—21no—
366C22×C3—21no—
367C22×C3—21no—
368C22×C3—22no—
369C22×C3—21no—
370C22×C3—22no—
371C22×C3—41no—
372C22×C3—41no—
373C22×C3—41no—
374C22×C3—41no—
375C22×C3—41no—
376C22×C3—41no—
377C22×C3—44no—
378C22×C3—44no—
379C22×C3—48no—
380C22×C3#82412yescomplemented
381C22×C3#83612yescomplemented
382C22×C3C2×(C2×D3)⋊C411yescharacteristic
383C22×C3C4×#6712yes—
384C22×C3D4×Dic312yes—
385C22×C3C2×#21711yescharacteristic
386C3×C4—21no—
387C3×C4—21no—
388C3×C4—21no—
389C3×C4—21no—
390C3×C4—21no—
391C3×C4—21no—
392C3×C4—22no—
393C3×C4—41no—
394C3×C4—41no—
395C3×C4—122no—
396C3×C4—122no—
397C3×C4#92911yescharacteristic
398C3×C4#93012yes—
399C3×C4#93511yescharacteristic
400C3×C4#93711yescharacteristic
401C3×C4#93912yes—
402C3×C4#95311yescharacteristic
403Dic3—42no—
404Dic3—42no—
405C32#190111yescharacteristic, complemented, Sylow
406C23—22no—
407C23—22no—
408C23—41no—
409C23(C2×D3)⋊Dic311yescharacteristic
410C23(C2×D3)⋊Dic311yescharacteristic
411C23C2×D3×Dic311yescharacteristic
412Q8—121no—
413Q8—121no—
414Q8—122no—
415C2×C4—22no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—62no—
423C2×C4—62no—
424C2×C4—64no—
425C2×C4—122no—
426C2×C4(C2×D3)⋊Dic311yescharacteristic
427C2×C4(C2×D3)⋊Dic311yescharacteristic
428C2×C4#380412yes—
429C2×C4C2×#62511yescharacteristic
430C2×C4C2×#62611yescharacteristic
431C2×C4D3×#6712yes—
432C8—64no—
433C8—362no—
434C2×C3—22no—
435C2×C3—22no—
436C2×C3—22no—
437C2×C3—22no—
438C2×C3—21no—
439C2×C3—21no—
440C2×C3—21no—
441C2×C3—42no—
442C2×C3—42no—
443C2×C3—42no—
444C2×C3—41no—
445C2×C3—41no—
446C2×C3#513211yescharacteristic
447C2×C3C2×#82411yescharacteristic
448C2×C3#521311yescharacteristic
449C2×C3#522011yescharacteristic
450C2×C3C2×#83611yescharacteristic
451C2×C3#523711yescharacteristic
452C22—21no—
453C22—21no—
454C22—21no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22—44no—
460C22#6356012yescomplemented
461C22C2×(C2×D3)⋊Dic311yescharacteristic
462C22Dic3×#6712yes—
463C4—21no—
464C4—21no—
465C4—122no—
466C4—122no—
467C4#6396111yescharacteristic
468C4#6397611yescharacteristic
469C4#6397812yes—
470C3—21no—
471C3#7169811yescharacteristic, complemented
472C3#7200311yescharacteristic, complemented
473C2—22no—
474C2—22no—
475C2—41no—
476C2#1059107611yescharacteristic
477C2C2×#6356011yescharacteristic
478C2#1059171011yescharacteristic
subgroupG/H
centerC22C2×(C2×D3)⋊Dic3
commutatorC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC23×C32×C4C22
socleC22×C32C2×C22⋊C4
prime radicalC24×C32C2×C4
cosocleC22×C32×C4C23
hypercenterC23×C4D32
hypocenterC32#1901
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
4. C2×#63560C2semidirect
5. #10589167C2semidirect
215. C22×C32#101semidirect
380. C22×C3#824semidirect
381. C22×C3#836semidirect
405. C32#1901semidirect
460. C22#63560semidirect
471. C3#71698semidirect
472. C3#72003semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9242
C22×C3×#2082
#105929062
C2×#635602
#105891672
#720033
#716983