Finite Group Databasebeta

← #11791851

Subgroups — #11791851

Order 1152.

777 conjugacy classes of subgroups.

The subgroup lattice has 479 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#924C211yesmaximal, characteristic
2C4×#3757C211yesmaximal, characteristic
3C3×#5212C211yesmaximal, characteristic
4#10589186C214yesmaximal
5#71701—31nomaximal
6#69529—31nomaximal
7C23×C32×C4C2211yescharacteristic
8C22×C3×Dic6C411yescharacteristic, complemented
9C2×#3757C2212yes—
10C2×C4×C3⋊Dic3—21no—
11C2×C3×#217C2212yes—
12C2×C3×#217C2212yes—
13C2×C3×C4⋊Dic3—21no—
14C2×C3×C4⋊Dic3C411yescharacteristic, complemented
15C3×#924—21no—
16C3×#924—21no—
17C3×#924—21no—
18C3×#924—21no—
19C2×C3×Dic3⋊C4C412yescomplemented
20#63658—21no—
21C3×C3⋊#95—21no—
22C2×C3×C22⋊Q8—31no—
23C2×#924D311yescharacteristic
24C3×#380—31no—
25#5212D311yescharacteristic
26C4×#217—31no—
27C4×#217—31no—
28C4×#217—61no—
29#4527—34no—
30#4526—34no—
31C24×C32C2311yescharacteristic
32C22×C32×C4—42no—
33C22×C32×C4C2×C411yescharacteristic
34C22×C32×C4C2×C411yescharacteristic
35C22×C32×C4D411yescharacteristic
36C22×C32×C4D411yescharacteristic
37C22×C32×C4D411yescharacteristic
38C22×C32×C4D411yescharacteristic
39C22×C3⋊Dic3—22no—
40C22×C3×Dic3—22no—
41C22×C3×Dic3C2×C412yes—
42C22×C3×Dic3C2×C412yes—
43C2×C3×Dic6—21no—
44C2×C3×Dic6—21no—
45C2×C3×Dic6—42no—
46#3757—22no—
47#3757Q814yescomplemented
48C4×C3⋊Dic3—42no—
49C3×#217—22no—
50C3×#217—22no—
51C3×#217—24no—
52C3×C4⋊Dic3—21no—
53C3×C4⋊Dic3—21no—
54C3×C4⋊Dic3—42no—
55C3×Dic3⋊C4—22no—
56C3×Dic3⋊C4—22no—
57#1996—91noSylow
58C22×C3×Q8—31no—
59C23×C3×C4—21no—
60C23×C3×C4C2×D311yescharacteristic
61C23×C3×C4C2×D311yescharacteristic
62C22×Dic6Dic311yescharacteristic, complemented
63C3×C22⋊Q8—61no—
64C3×C22⋊Q8—61no—
65C3×C22⋊Q8—61no—
66C3×C22⋊Q8—61no—
67C2×C3×C4⋊C4—32no—
68C2×C3×C4⋊C4—31no—
69C2×C3×C4⋊C4—61no—
70C2×C3×C22⋊C4—32no—
71C2×C3×C22⋊C4—32no—
72C2×#217—32no—
73C2×#217—32no—
74C2×#217—62no—
75C2×#217C2×D312yes—
76C2×#217C2×D312yes—
77C2×C4⋊Dic3—21no—
78C2×C4⋊Dic3Dic311yescharacteristic, complemented
79#924—21no—
80#924—21no—
81#924—21no—
82#924—21no—
83C2×Dic3⋊C4Dic312yescomplemented
84C2×C4×Dic3—62no—
85C2×C4×Dic3—61no—
86C2×C4×Dic3—61no—
87C3×#95—61no—
88C3⋊#95—21no—
89C3⋊#95—62no—
90C3⋊#95—61no—
91C3⋊#95—61no—
92C23×C32—41no—
93C23×C32—41no—
94C23×C32C22×C411yescharacteristic
95C23×C32C2×D411yescharacteristic
96C23×C32C2×D411yescharacteristic
97C23×C32C2×Q812yes—
98C23×C32#4112yes—
99C2×C32×C4—22no—
100C2×C32×C4—22no—
101C2×C32×C4—22no—
102C2×C32×C4—41no—
103C2×C32×C4—41no—
104C2×C32×C4—41no—
105C2×C32×C4C22⋊C411yescharacteristic
106C2×C32×C4C22⋊C411yescharacteristic
107C2×C32×C4C22⋊C411yescharacteristic
108C2×C32×C4C22⋊C411yescharacteristic
109C2×C3⋊Dic3—24no—
110C2×C3⋊Dic3—42no—
111C2×C3⋊Dic3—42no—
112C2×C3×Dic3—22no—
113C2×C3×Dic3—22no—
114C2×C3×Dic3—42no—
115C2×C3×Dic3—42no—
116C2×C3×Dic3—42no—
117C2×C3×Dic3—42no—
118C2×C3×Dic3—42no—
119C3×Dic6—42no—
120C3×Dic6—42no—
121C2×C22⋊Q8—31no—
122#380—31no—
123C4×C22⋊C4—91no—
124#342—94no—
125C24×C3—21no—
126C24×C3C22×D311yescharacteristic
127C24×C3C22×D311yescharacteristic
128C2×C3×Q8—61no—
129C2×C3×Q8—61no—
130C2×C3×Q8—122no—
131C22×C3×C4—21no—
132C22×C3×C4—21no—
133C22×C3×C4—21no—
134C22×C3×C4—21no—
135C22×C3×C4—21no—
136C22×C3×C4—21no—
137C22×C3×C4—32no—
138C22×C3×C4—32no—
139C22×C3×C4—42no—
140C22×C3×C4—42no—
141C22×C3×C4—44no—
142C22×C3×C4—62no—
143C22×C3×C4C4×D311yescharacteristic
144C22×C3×C4C4×D311yescharacteristic
145C22×C3×C4D1211yescharacteristic
146C22×C3×C4D1211yescharacteristic
147C22×C3×C4C2×Dic311yescharacteristic
148C22×C3×C4C2×Dic311yescharacteristic
149C22×C3×C4#6711yescharacteristic
150C22×C3×C4#6711yescharacteristic
151C22×C3×C4#6711yescharacteristic
152C22×C3×C4#6711yescharacteristic
153C22×C3×C4#6711yescharacteristic
154C22×C3×C4#6711yescharacteristic
155C22×Dic3—22no—
156C22×Dic3—64no—
157C22×Dic3—62no—
158C22×Dic3—62no—
159C22×Dic3C2×Dic312yes—
160C22×Dic3C2×Dic312yes—
161C2×Dic6—21no—
162C2×Dic6—21no—
163C2×Dic6—42no—
164C3×C4⋊C4—62no—
165C3×C4⋊C4—62no—
166C3×C4⋊C4—61no—
167C3×C4⋊C4—61no—
168C3×C4⋊C4—122no—
169C3×C22⋊C4—62no—
170C3×C22⋊C4—62no—
171C3×C22⋊C4—64no—
172#217—22no—
173#217—22no—
174#217—24no—
175#217—34no—
176#217—34no—
177#217—64no—
178#217—64no—
179#217—62no—
180#217—62no—
181C4⋊Dic3—21no—
182C4⋊Dic3—21no—
183C4⋊Dic3—42no—
184Dic3⋊C4—22no—
185Dic3⋊C4—22no—
186C4×Dic3—124no—
187C4×Dic3—122no—
188C4×Dic3—122no—
189C22×C32—21no—
190C22×C32—21no—
191C22×C32—21no—
192C22×C32—21no—
193C22×C32—21no—
194C22×C32—21no—
195C22×C32—42no—
196C22×C32—42no—
197C22×C32C2×C22⋊C411yescharacteristic
198C22×C32C4×Q812yes—
199C22×C32C22⋊Q812yes—
200C22×C32#12411yescharacteristic
201C22×C32C4⋊Q811yescharacteristic
202C32×C4—21no—
203C32×C4—21no—
204C32×C4—21no—
205C32×C4#9912yes—
206C3⋊Dic3—44no—
207C3×Dic3—42no—
208C3×Dic3—42no—
209C3×Dic3—82no—
210C22×Q8—31no—
211C23×C4D3211yescharacteristic
212C22⋊Q8—61no—
213C22⋊Q8—61no—
214C22⋊Q8—61no—
215C22⋊Q8—61no—
216C2×C4⋊C4—32no—
217C2×C4⋊C4—31no—
218C2×C4⋊C4—61no—
219C2×C22⋊C4—32no—
220C2×C22⋊C4—32no—
221C2×C22⋊C4—92no—
222C2×C42—181no—
223#95—61no—
224#95—181no—
225C23×C3—22no—
226C23×C3—22no—
227C23×C3—21no—
228C23×C3—21no—
229C23×C3—21no—
230C23×C3—41no—
231C23×C3—41no—
232C23×C3—41no—
233C23×C3—41no—
234C23×C3—42no—
235C23×C3—42no—
236C23×C3C2×C4×D311yescharacteristic
237C23×C3C2×D1211yescharacteristic
238C23×C3#23712yes—
239C23×C3D3×Q812yes—
240C23×C3D3×Q812yes—
241C23×C3#23912yes—
242C23×C3C22×Dic311yescharacteristic
243C23×C3C2×#6711yescharacteristic
244C23×C3C2×#6711yescharacteristic
245C23×C3C2×#6711yescharacteristic
246C3×Q8—122no—
247C3×Q8—122no—
248C2×C3×C4—24no—
249C2×C3×C4—22no—
250C2×C3×C4—22no—
251C2×C3×C4—22no—
252C2×C3×C4—22no—
253C2×C3×C4—22no—
254C2×C3×C4—22no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—42no—
260C2×C3×C4—42no—
261C2×C3×C4—41no—
262C2×C3×C4—41no—
263C2×C3×C4—41no—
264C2×C3×C4—41no—
265C2×C3×C4—41no—
266C2×C3×C4—41no—
267C2×C3×C4—42no—
268C2×C3×C4—42no—
269C2×C3×C4—42no—
270C2×C3×C4—62no—
271C2×C3×C4—62no—
272C2×C3×C4—122no—
273C2×C3×C4—122no—
274C2×C3×C4—122no—
275C2×C3×C4—122no—
276C2×C3×C4—122no—
277C2×C3×C4(C2×D3)⋊C411yescharacteristic
278C2×C3×C4(C2×D3)⋊C411yescharacteristic
279C2×C3×C4(C2×D3)⋊C411yescharacteristic
280C2×C3×C4(C2×D3)⋊C411yescharacteristic
281C2×C3×C4#21711yescharacteristic
282C2×C3×C4#21711yescharacteristic
283C2×C3×C4#21711yescharacteristic
284C2×C3×C4#21711yescharacteristic
285C2×Dic3—22no—
286C2×Dic3—22no—
287C2×Dic3—42no—
288C2×Dic3—42no—
289C2×Dic3—42no—
290C2×Dic3—42no—
291C2×Dic3—42no—
292C2×Dic3—68no—
293C2×Dic3—64no—
294C2×Dic3—64no—
295C2×Dic3—124no—
296C2×Dic3—122no—
297C2×Dic3—122no—
298C2×Dic3—124no—
299C2×Dic3—122no—
300C2×Dic3—122no—
301Dic6—42no—
302Dic6—42no—
303C2×C32—22no—
304C2×C32—21no—
305C2×C32—22no—
306C2×C32—21no—
307C2×C32#39111yescharacteristic
308C2×C32C2×#9911yescharacteristic
309C2×C32#41011yescharacteristic
310C24C2×D3211yescharacteristic
311C2×Q8—61no—
312C2×Q8—61no—
313C2×Q8—122no—
314C22×C4—32no—
315C22×C4—32no—
316C22×C4—42no—
317C22×C4—62no—
318C22×C4—182no—
319C22×C4D3×Dic311yescharacteristic
320C22×C4D3×Dic311yescharacteristic
321C22×C4#62511yescharacteristic
322C22×C4#62511yescharacteristic
323C22×C4#62611yescharacteristic
324C22×C4#62611yescharacteristic
325C4⋊C4—62no—
326C4⋊C4—62no—
327C4⋊C4—61no—
328C4⋊C4—61no—
329C4⋊C4—122no—
330C22⋊C4—62no—
331C22⋊C4—62no—
332C22⋊C4—64no—
333C22⋊C4—94no—
334C22⋊C4—182no—
335C42—362no—
336C22×C3—22no—
337C22×C3—22no—
338C22×C3—21no—
339C22×C3—21no—
340C22×C3—21no—
341C22×C3—21no—
342C22×C3—21no—
343C22×C3—21no—
344C22×C3—21no—
345C22×C3—21no—
346C22×C3—21no—
347C22×C3—21no—
348C22×C3—21no—
349C22×C3—21no—
350C22×C3—22no—
351C22×C3—21no—
352C22×C3—22no—
353C22×C3—21no—
354C22×C3—21no—
355C22×C3—41no—
356C22×C3—41no—
357C22×C3—41no—
358C22×C3—41no—
359C22×C3—42no—
360C22×C3—42no—
361C22×C3—42no—
362C22×C3—42no—
363C22×C3—44no—
364C22×C3—44no—
365C22×C3#88712yes—
366C22×C3#89712yes—
367C22×C3C2×(C2×D3)⋊C411yescharacteristic
368C22×C3#93611yescharacteristic
369C22×C3#94411yescharacteristic
370C22×C3#94411yescharacteristic
371C22×C3Q8×Dic312yes—
372C22×C3#94612yes—
373C22×C3#94711yescharacteristic
374C22×C3C2×#21711yescharacteristic
375C3×C4—22no—
376C3×C4—21no—
377C3×C4—21no—
378C3×C4—21no—
379C3×C4—21no—
380C3×C4—21no—
381C3×C4—21no—
382C3×C4—22no—
383C3×C4—41no—
384C3×C4—41no—
385C3×C4—122no—
386C3×C4—122no—
387C3×C4—242no—
388C3×C4#80612yes—
389C3×C4#83412yes—
390Dic3—42no—
391Dic3—42no—
392Dic3—82no—
393Dic3—128no—
394Dic3—124no—
395Dic3—124no—
396C32#199611yescharacteristic, complemented, Sylow
397C23—41no—
398C23—41no—
399C23#379612yes—
400C23#379712yes—
401C23C2×D3×Dic311yescharacteristic
402C23C2×#62511yescharacteristic
403C23C2×#62611yescharacteristic
404Q8—122no—
405Q8—122no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—62no—
413C2×C4—62no—
414C2×C4—122no—
415C2×C4—122no—
416C2×C4—122no—
417C2×C4—122no—
418C2×C4—122no—
419C2×C4—184no—
420C2×C4—362no—
421C2×C4—362no—
422C2×C4(C2×D3)⋊Dic311yescharacteristic
423C2×C4(C2×D3)⋊Dic311yescharacteristic
424C2×C4(C2×D3)⋊Dic311yescharacteristic
425C2×C4(C2×D3)⋊Dic311yescharacteristic
426C2×C3—24no—
427C2×C3—22no—
428C2×C3—21no—
429C2×C3—21no—
430C2×C3—22no—
431C2×C3—21no—
432C2×C3—22no—
433C2×C3—22no—
434C2×C3—21no—
435C2×C3—21no—
436C2×C3—21no—
437C2×C3—21no—
438C2×C3—41no—
439C2×C3—42no—
440C2×C3—41no—
441C2×C3C2×#80611yescharacteristic
442C2×C3#497311yescharacteristic
443C2×C3#500611yescharacteristic
444C2×C3C2×#83411yescharacteristic
445C2×C3#522911yescharacteristic
446C2×C3#524011yescharacteristic
447C22—21no—
448C22—21no—
449C22—21no—
450C22—21no—
451C22—21no—
452C22—21no—
453C22—42no—
454C22—42no—
455C22#6384312yes—
456C22#6386311yescharacteristic
457C22#6387112yes—
458C22#6387311yescharacteristic
459C22C2×(C2×D3)⋊Dic311yescharacteristic
460C4—21no—
461C4—21no—
462C4—21no—
463C4—122no—
464C4—122no—
465C4—242no—
466C4—364no—
467C4#6358012yes—
468C3—21no—
469C3#6952911yescharacteristic, complemented
470C3#7170111yescharacteristic, complemented
471C2—21no—
472C2—22no—
473C2—22no—
474C2—21no—
475C2#1059122111yescharacteristic
476C2#1059123111yescharacteristic
477C2C2×#6358011yescharacteristic
subgroupG/H
centerC22C2×(C2×D3)⋊Dic3
commutatorC23×C32C22×C4
FrattiniC24C2×D32
FittingC23×C32×C4C22
socleC22×C32C2×C22⋊C4
prime radical, cosocleC24×C32C23
hypercenterC23×C4D32
hypocenterC32#1996
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
8. C22×C3×Dic6C4semidirect
14. C2×C3×C4⋊Dic3C4semidirect
19. C2×C3×Dic3⋊C4C4semidirect
47. #3757Q8semidirect
62. C22×Dic6Dic3semidirect
78. C2×C4⋊Dic3Dic3semidirect
83. C2×Dic3⋊C4Dic3semidirect
396. C32#1996semidirect
469. C3#69529semidirect
470. C3#71701semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9242
C4×#37572
C3×#52122
#105891862
#717013
#695293