Finite Group Databasebeta

← #11788349

Subgroups — #11788349

Order 1152.

825 conjugacy classes of subgroups.

The subgroup lattice has 483 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3748C211yesmaximal, characteristic
2C2×C3×#924C211yesmaximal, characteristic
3C3×#5207C211yesmaximal, characteristic
4C2×#63560C212yesmaximal, complemented
5#10589167C212yesmaximal, complemented
6#71698—31nomaximal
7#69986—31nomaximal
8C23×C32×C4C2211yescharacteristic
9C22×C3×Dic6C2211yescharacteristic
10C2×#3748—21no—
11C2×#3748—24no—
12C2×#3748C2212yes—
13C22×C3⋊(C3⋊C8)—21no—
14C2×C3×#217C412yes—
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C3×#924—21no—
17C3×#924—21no—
18C3×#924—21no—
19C3×#924—21no—
20C2×C3×Dic3⋊C4C412yes—
21C2×C3×#208C2212yes—
22C3×#830—21no—
23C3×#830—21no—
24#63560—24no—
25C2×C3×C22⋊Q8—31no—
26C2×#924D311yescharacteristic
27C22×#208—31no—
28C22×#208—31no—
29C22×#208—61no—
30C3×#407—31no—
31C2×#836—32no—
32#5207D311yescharacteristic
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—24no—
52#3748—22no—
53#3748D414yes—
54C2×C3⋊(C3⋊C8)—24no—
55C2×C3⋊(C3⋊C8)—22no—
56C3×#217—22no—
57C3×#217—22no—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3—21no—
60C3×Dic3⋊C4—22no—
61C3×Dic3⋊C4—22no—
62C3×#208—22no—
63C3×#208—22no—
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—
72C3×C22⋊Q8—61no—
73C3×C22⋊Q8—61no—
74C3×C22⋊Q8—61no—
75C3×C22⋊Q8—61no—
76C2×C3×C4⋊C4—32no—
77C2×C3×C4⋊C4—31no—
78C2×C3×C22⋊C4—32no—
79C2×#217Dic312yes—
80C2×C4⋊Dic3C2×D311yescharacteristic
81#924—21no—
82#924—21no—
83#924—21no—
84#924—21no—
85C2×Dic3⋊C4Dic312yes—
86C2×#208—32no—
87C2×#208—32no—
88C2×#208—62no—
89C2×#208—64no—
90C2×#208—64no—
91C2×#208—68no—
92C2×#208—62no—
93C2×#208—61no—
94C2×#208—61no—
95C2×#208C2×D312yes—
96C22×C3⋊C8—62no—
97C22×C3⋊C8—61no—
98C22×C3⋊C8—61no—
99C3×C22⋊C8—61no—
100C3×C22⋊C8—61no—
101#836—64no—
102#830—21no—
103#830—21no—
104#824—64no—
105C23×C32—22no—
106C23×C32—22no—
107C23×C32—41no—
108C23×C32C22⋊C411yescharacteristic
109C23×C32C22⋊C411yescharacteristic
110C23×C32C22×C411yescharacteristic
111C2×C32×C4—22no—
112C2×C32×C4—21no—
113C2×C32×C4—21no—
114C2×C32×C4—22no—
115C2×C32×C4—22no—
116C2×C32×C4—21no—
117C2×C32×C4—21no—
118C2×C32×C4C22⋊C411yescharacteristic
119C2×C32×C4C22⋊C411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×D412yes—
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4#4112yes—
124C2×C3×Dic3—22no—
125C2×C3×Dic3—22no—
126C2×C3×Dic3—24no—
127C2×C3×Dic3—42no—
128C3×Dic6—41no—
129C3×Dic6—42no—
130C3×Dic6—41no—
131C3⋊(C3⋊C8)—24no—
132C3×C3⋊C8—42no—
133C22×M16—91no—
134C2×C22⋊Q8—31no—
135C2×#101—92no—
136#407—31no—
137#343—92no—
138C24×C3—21no—
139C24×C3C4×D311yescharacteristic
140C24×C3C2×Dic311yescharacteristic
141C2×C3×Q8—61no—
142C2×C3×Q8—62no—
143C2×C3×Q8—62no—
144C2×C3×Q8—61no—
145C22×C3×C4—24no—
146C22×C3×C4—24no—
147C22×C3×C4—22no—
148C22×C3×C4—22no—
149C22×C3×C4—22no—
150C22×C3×C4—22no—
151C22×C3×C4—21no—
152C22×C3×C4—21no—
153C22×C3×C4—21no—
154C22×C3×C4—21no—
155C22×C3×C4—21no—
156C22×C3×C4—21no—
157C22×C3×C4—32no—
158C22×C3×C4—32no—
159C22×C3×C4C4×D311yescharacteristic
160C22×C3×C4D1211yescharacteristic
161C22×C3×C4D1211yescharacteristic
162C22×C3×C4C2×Dic311yescharacteristic
163C22×C3×C4#6711yescharacteristic
164C22×C3×C4#6711yescharacteristic
165C22×C3×C4#6711yescharacteristic
166C22×C3×C4#6711yescharacteristic
167C22×C3×C4#6711yescharacteristic
168C22×C3×C4#6711yescharacteristic
169C22×C3×C4C22×D311yescharacteristic
170C22×C3×C4C22×D311yescharacteristic
171C22×Dic3C2×Dic312yes—
172C22×Dic3C2×Dic312yes—
173C2×Dic6—22no—
174C2×Dic6—22no—
175C2×Dic6—21no—
176C2×Dic6—21no—
177C3×M16—62no—
178C3×M16—62no—
179C2×C3×C8—62no—
180C3×C4⋊C4—62no—
181C3×C4⋊C4—62no—
182C3×C4⋊C4—61no—
183C3×C4⋊C4—61no—
184C3×C22⋊C4—62no—
185C3×C22⋊C4—62no—
186#217—22no—
187#217—22no—
188C4⋊Dic3—21no—
189C4⋊Dic3—21no—
190Dic3⋊C4—22no—
191Dic3⋊C4—22no—
192#208—22no—
193#208—22no—
194#208—34no—
195#208—34no—
196#208—64no—
197#208—68no—
198#208—64no—
199#208—64no—
200#208—64no—
201#208—62no—
202#208—62no—
203C2×C3⋊C8—22no—
204C2×C3⋊C8—68no—
205C2×C3⋊C8—64no—
206C2×C3⋊C8—64no—
207C2×C3⋊C8—64no—
208C2×C3⋊C8—62no—
209C2×C3⋊C8—62no—
210C22×C32—21no—
211C22×C32—21no—
212C22×C32—21no—
213C22×C32—21no—
214C22×C32—21no—
215C22×C32—21no—
216C22×C32—21no—
217C22×C32—44no—
218C22×C32#10112yescomplemented
219C22×C32C2×C22⋊C411yescharacteristic
220C22×C32C4×D412yes—
221C32×C4—21no—
222C32×C4—21no—
223C32×C4#12011yescharacteristic
224C32×C4#12112yes—
225C32×C4#12311yescharacteristic
226C3×Dic3—42no—
227C3×Dic3—42no—
228C22×Q8—31no—
229C23×C4D3211yescharacteristic
230C2×M16—32no—
231C2×M16—92no—
232C2×M16—184no—
233C2×M16—181no—
234C22×C8—181no—
235C22⋊Q8—61no—
236C22⋊Q8—61no—
237C22⋊Q8—61no—
238C22⋊Q8—61no—
239C2×C4⋊C4—32no—
240C2×C4⋊C4—31no—
241C2×C22⋊C4—32no—
242#101—184no—
243C22⋊C8—61no—
244C22⋊C8—61no—
245C23×C3—24no—
246C23×C3—22no—
247C23×C3—22no—
248C23×C3—22no—
249C23×C3—22no—
250C23×C3—21no—
251C23×C3—21no—
252C23×C3—21no—
253C23×C3—42no—
254C23×C3—41no—
255C23×C3—41no—
256C23×C3—42no—
257C23×C3(C2×D3)⋊C411yescharacteristic
258C23×C3(C2×D3)⋊C411yescharacteristic
259C23×C3#21711yescharacteristic
260C23×C3#21711yescharacteristic
261C23×C3C2×C4×D311yescharacteristic
262C23×C3C22×Dic311yescharacteristic
263C3×Q8—121no—
264C3×Q8—121no—
265C3×Q8—122no—
266C2×C3×C4—22no—
267C2×C3×C4—22no—
268C2×C3×C4—24no—
269C2×C3×C4—22no—
270C2×C3×C4—22no—
271C2×C3×C4—24no—
272C2×C3×C4—24no—
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—21no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—22no—
284C2×C3×C4—22no—
285C2×C3×C4—22no—
286C2×C3×C4—22no—
287C2×C3×C4—21no—
288C2×C3×C4—21no—
289C2×C3×C4—22no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—22no—
293C2×C3×C4—64no—
294C2×C3×C4—62no—
295C2×C3×C4—62no—
296C2×C3×C4—122no—
297C2×C3×C4(C2×D3)⋊C411yescharacteristic
298C2×C3×C4(C2×D3)⋊C411yescharacteristic
299C2×C3×C4#21711yescharacteristic
300C2×C3×C4#21711yescharacteristic
301C2×C3×C4C2×D1211yescharacteristic
302C2×C3×C4D3×D412yes—
303C2×C3×C4D3×D412yes—
304C2×C3×C4#23712yes—
305C2×C3×C4#23712yes—
306C2×C3×C4C2×#6711yescharacteristic
307C2×C3×C4C2×#6711yescharacteristic
308C2×C3×C4C2×#6711yescharacteristic
309C2×Dic3—24no—
310C2×Dic3—22no—
311C2×Dic3—22no—
312C2×Dic3—42no—
313Dic6—41no—
314Dic6—41no—
315Dic6—42no—
316C3×C8—122no—
317C3⋊C8—42no—
318C3⋊C8—68no—
319C3⋊C8—64no—
320C3⋊C8—64no—
321C2×C32—22no—
322C2×C32—22no—
323C2×C32—41no—
324C2×C32#38611yescharacteristic
325C2×C32C2×#10111yescharacteristic
326C2×C32#41311yescharacteristic
327C24D3×Dic311yescharacteristic
328C2×Q8—62no—
329C2×Q8—61no—
330C2×Q8—61no—
331C2×Q8—62no—
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—32no—
335C22×C4—32no—
336C22×C4D3×Dic311yescharacteristic
337C22×C4#62511yescharacteristic
338C22×C4#62511yescharacteristic
339C22×C4#62611yescharacteristic
340C22×C4#62611yescharacteristic
341C22×C4C2×D3211yescharacteristic
342M16—62no—
343M16—62no—
344M16—94no—
345M16—184no—
346M16—182no—
347C2×C8—62no—
348C2×C8—184no—
349C2×C8—182no—
350C4⋊C4—62no—
351C4⋊C4—62no—
352C4⋊C4—61no—
353C4⋊C4—61no—
354C22⋊C4—62no—
355C22⋊C4—62no—
356C22×C3—22no—
357C22×C3—22no—
358C22×C3—21no—
359C22×C3—21no—
360C22×C3—21no—
361C22×C3—21no—
362C22×C3—21no—
363C22×C3—21no—
364C22×C3—21no—
365C22×C3—21no—
366C22×C3—22no—
367C22×C3—21no—
368C22×C3—21no—
369C22×C3—21no—
370C22×C3—21no—
371C22×C3—21no—
372C22×C3—21no—
373C22×C3—22no—
374C22×C3—21no—
375C22×C3—22no—
376C22×C3—41no—
377C22×C3—41no—
378C22×C3—41no—
379C22×C3—41no—
380C22×C3—44no—
381C22×C3—44no—
382C22×C3—48no—
383C22×C3#82412yescomplemented
384C22×C3#83612yescomplemented
385C22×C3#67⋊C412yes—
386C22×C3C2×(C2×D3)⋊C411yescharacteristic
387C22×C3D4×Dic312yes—
388C22×C3C2×#21711yescharacteristic
389C3×C4—22no—
390C3×C4—22no—
391C3×C4—21no—
392C3×C4—21no—
393C3×C4—21no—
394C3×C4—21no—
395C3×C4—21no—
396C3×C4—22no—
397C3×C4—21no—
398C3×C4—122no—
399C3×C4—122no—
400C3×C4#88211yescharacteristic
401C3×C4#88611yescharacteristic
402C3×C4#93511yescharacteristic
403C3×C4#93711yescharacteristic
404C3×C4#93912yes—
405C3×C4#93912yes—
406Dic3—42no—
407Dic3—42no—
408C32#190111yescharacteristic, complemented, Sylow
409C23—22no—
410C23—22no—
411C23—41no—
412C23(C2×D3)⋊Dic311yescharacteristic
413C23(C2×D3)⋊Dic311yescharacteristic
414C23C2×D3×Dic311yescharacteristic
415Q8—121no—
416Q8—122no—
417Q8—121no—
418C2×C4—22no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—62no—
426C2×C4—62no—
427C2×C4—64no—
428C2×C4—122no—
429C2×C4(C2×D3)⋊Dic311yescharacteristic
430C2×C4(C2×D3)⋊Dic311yescharacteristic
431C2×C4#380512yes—
432C2×C4C2×#62511yescharacteristic
433C2×C4C2×#62611yescharacteristic
434C2×C4#381112yes—
435C8—122no—
436C8—184no—
437C2×C3—24no—
438C2×C3—22no—
439C2×C3—22no—
440C2×C3—22no—
441C2×C3—22no—
442C2×C3—21no—
443C2×C3—21no—
444C2×C3—21no—
445C2×C3—42no—
446C2×C3—42no—
447C2×C3—41no—
448C2×C3—41no—
449C2×C3#495811yescharacteristic
450C2×C3#513211yescharacteristic
451C2×C3C2×#82411yescharacteristic
452C2×C3#522011yescharacteristic
453C2×C3C2×#83611yescharacteristic
454C2×C3#523711yescharacteristic
455C22—21no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—21no—
462C22—44no—
463C22#6356012yescomplemented
464C22C2×(C2×D3)⋊Dic311yescharacteristic
465C22#67⋊Dic312yes—
466C4—21no—
467C4—21no—
468C4—122no—
469C4—122no—
470C4#6396211yescharacteristic
471C4#6398012yes—
472C4#6398111yescharacteristic
473C3—21no—
474C3#6998611yescharacteristic, complemented
475C3#7169811yescharacteristic, complemented
476C2—22no—
477C2—22no—
478C2—41no—
479C2#1059107611yescharacteristic
480C2C2×#6356011yescharacteristic
481C2#1059171311yescharacteristic
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
218. C22×C32#101semidirect
383. C22×C3#824semidirect
384. C22×C3#836semidirect
408. C32#1901semidirect
463. C22#63560semidirect
474. C3#69986semidirect
475. C3#71698semidirect

Maximal subgroups

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

subgroupindex
C22×#37482
C2×C3×#9242
C3×#52072
C2×#635602
#105891672
#716983
#699863