Finite Group Databasebeta

← #11787977

Subgroups — #11787977

Order 1152.

943 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64144C211yesmaximal, characteristic
2C3×#5798C211yesmaximal, characteristic
3C2×C3×#834C211yesmaximal, characteristic
4#10591697C212yesmaximal, complemented
5#10589186C212yesmaximal, complemented
6#71655—31nomaximal
7#70023—31nomaximal
8C22×C32×D4C2211yescharacteristic
9C23×C3⋊Dic3C2211yescharacteristic
10C2×#3757—21no—
11C2×#3757C2211yescharacteristic
12#64144—22no—
13#64144C414yescomplemented
14C2×#3750—21no—
15C2×C3×#217—21no—
16C2×C3×#217C2212yes—
17C2×C3×#217C2212yes—
18C3×D4×Dic3—24no—
19C3×#926—21no—
20C3×#834—22no—
21#63579—24no—
22C3×#518—31no—
23#5798D311yescharacteristic
24C2×#935—31no—
25C2×#935—31no—
26C2×#935—61no—
27C2×C3×#99—31no—
28C2×#834D311yescharacteristic
29#4943—32no—
30#4943—32no—
31#4527—32no—
32#4526—32no—
33C24×C32D411yescharacteristic
34C24×C32C2311yescharacteristic
35C2×C32×D4—22no—
36C2×C32×D4—22no—
37C2×C32×D4C2×C412yes—
38C2×C32×D4D412yes—
39C22×C32×C4D411yescharacteristic
40C22×C3⋊Dic3—21no—
41C22×C3⋊Dic3—21no—
42C22×C3⋊Dic3—21no—
43C22×C3⋊Dic3—22no—
44C22×C3⋊Dic3—22no—
45C22×C3⋊Dic3C2×C412yescomplemented
46C22×C3×Dic3—22no—
47C22×C3×Dic3—22no—
48C22×C3×Dic3D414yes—
49#3757—24no—
50#3757—21no—
51#3757C2×C412yescomplemented
52#3750—24no—
53C3×#217—22no—
54C3×#217—22no—
55C3×#217—22no—
56C3×#217—22no—
57C3×#217—22no—
58C3×C4⋊Dic3—22no—
59C3×C4×Dic3—22no—
60#1890—91noSylow
61C22×C3×D4—21no—
62C22×C3×D4C2×D311yescharacteristic
63C22×C3×D4C2×D311yescharacteristic
64C23×Dic3—31no—
65C23×Dic3—31no—
66C23×Dic3—61no—
67C3×C4×D4—64no—
68C3×#117—61no—
69C2×C3×C22⋊C4—32no—
70C2×C3×C22⋊C4—32no—
71C2×C3×C22⋊C4—61no—
72C2×#217—21no—
73C2×#217—31no—
74C2×#217—31no—
75C2×#217—61no—
76C2×#217—62no—
77C2×#217—61no—
78C2×#217—61no—
79C2×#217C2×D312yes—
80C2×#217C2×D312yes—
81#935—34no—
82#935—34no—
83#935—64no—
84#935—64no—
85#935—62no—
86#935—62no—
87D4×Dic3—24no—
88#926—21no—
89C2×Dic3⋊C4—62no—
90C2×Dic3⋊C4—61no—
91C2×Dic3⋊C4—61no—
92C3×#99—62no—
93#834—22no—
94C3⋊#95—64no—
95C3⋊#95—64no—
96C23×C32—21no—
97C23×C32—21no—
98C23×C32—42no—
99C23×C32—42no—
100C23×C32C22⋊C412yes—
101C23×C32C22×C411yescharacteristic
102C23×C32C2×D411yescharacteristic
103C23×C32C2×D411yescharacteristic
104C23×C32C2×D412yes—
105C23×C32#4112yes—
106C32×D4—24no—
107C32×D4—24no—
108C2×C32×C4—21no—
109C2×C32×C4—21no—
110C2×C32×C4C22⋊C412yes—
111C2×C3⋊Dic3—22no—
112C2×C3⋊Dic3—22no—
113C2×C3⋊Dic3—24no—
114C2×C3⋊Dic3—42no—
115C2×C3⋊Dic3—41no—
116C2×C3⋊Dic3—42no—
117C2×C3⋊Dic3—41no—
118C2×C3×Dic3—24no—
119C2×C3×Dic3—44no—
120C2×C3×Dic3—44no—
121C2×C3×Dic3—42no—
122C2×C3×Dic3—82no—
123C2×#123—91no—
124#518—31no—
125C2×#99—31no—
126#381—92no—
127#342—92no—
128C24×C3—21no—
129C24×C3—21no—
130C24×C3D1211yescharacteristic
131C24×C3#6711yescharacteristic
132C24×C3C22×D311yescharacteristic
133C24×C3C22×D311yescharacteristic
134C2×C3×D4—22no—
135C2×C3×D4—22no—
136C2×C3×D4—22no—
137C2×C3×D4—22no—
138C2×C3×D4—22no—
139C2×C3×D4—22no—
140C2×C3×D4—42no—
141C2×C3×D4—42no—
142C2×C3×D4C4×D312yes—
143C2×C3×D4C4×D312yes—
144C2×C3×D4D1212yes—
145C2×C3×D4#6712yes—
146C22×C3×C4—21no—
147C22×C3×C4—34no—
148C22×C3×C4—62no—
149C22×C3×C4—62no—
150C22×C3×C4D1211yescharacteristic
151C22×C3×C4#6711yescharacteristic
152C22×Dic3—22no—
153C22×Dic3—22no—
154C22×Dic3—32no—
155C22×Dic3—32no—
156C22×Dic3—62no—
157C22×Dic3—62no—
158C22×Dic3—62no—
159C22×Dic3—62no—
160C22×Dic3—61no—
161C22×Dic3—61no—
162C22×Dic3—61no—
163C22×Dic3—62no—
164C22×Dic3—62no—
165C22×Dic3—62no—
166C22×Dic3—62no—
167C22×Dic3—61no—
168C22×Dic3—61no—
169C22×Dic3—61no—
170C22×Dic3—122no—
171C22×Dic3—122no—
172C22×Dic3#6714yes—
173C3×C4⋊C4—62no—
174C3×C22⋊C4—62no—
175C3×C22⋊C4—62no—
176C3×C22⋊C4—62no—
177C3×C22⋊C4—62no—
178C3×C22⋊C4—62no—
179C3×C42—62no—
180#217—22no—
181#217—22no—
182#217—22no—
183#217—22no—
184#217—22no—
185#217—32no—
186#217—32no—
187#217—62no—
188#217—68no—
189#217—62no—
190#217—64no—
191#217—64no—
192#217—61no—
193#217—61no—
194C4⋊Dic3—22no—
195Dic3⋊C4—68no—
196Dic3⋊C4—64no—
197Dic3⋊C4—64no—
198C4×Dic3—22no—
199C22×C32—22no—
200C22×C32—24no—
201C22×C32—22no—
202C22×C32—41no—
203C22×C32—41no—
204C22×C32—42no—
205C22×C32—42no—
206C22×C32—42no—
207C22×C32—81no—
208C22×C32C2×C22⋊C411yescharacteristic
209C22×C32C4×D412yes—
210C22×C32#12011yescharacteristic
211C22×C32#12112yes—
212C22×C32#12311yescharacteristic
213C32×C4—22no—
214C3⋊Dic3—42no—
215C3⋊Dic3—42no—
216C3×Dic3—44no—
217C3×Dic3—82no—
218C22×D4D3211yescharacteristic
219C23×C4—91no—
220#123—94no—
221#123—182no—
222C4×D4—64no—
223#117—61no—
224C2×C4⋊C4—181no—
225C2×C22⋊C4—32no—
226C2×C22⋊C4—32no—
227C2×C22⋊C4—61no—
228C2×C22⋊C4—91no—
229C2×C22⋊C4—181no—
230#99—62no—
231#95—184no—
232C23×C3—21no—
233C23×C3—21no—
234C23×C3—21no—
235C23×C3—21no—
236C23×C3—22no—
237C23×C3—22no—
238C23×C3—21no—
239C23×C3—21no—
240C23×C3—21no—
241C23×C3—22no—
242C23×C3—41no—
243C23×C3—41no—
244C23×C3—42no—
245C23×C3—42no—
246C23×C3—44no—
247C23×C3—42no—
248C23×C3—42no—
249C23×C3—44no—
250C23×C3(C2×D3)⋊C412yes—
251C23×C3(C2×D3)⋊C412yes—
252C23×C3C2×C4×D311yescharacteristic
253C23×C3C2×C4×D311yescharacteristic
254C23×C3C2×D1211yescharacteristic
255C23×C3C2×D1211yescharacteristic
256C23×C3#23512yes—
257C23×C3D3×D412yes—
258C23×C3#23712yes—
259C23×C3C2×#6711yescharacteristic
260C23×C3C2×#6711yescharacteristic
261C23×C3C2×#6712yes—
262C3×D4—24no—
263C3×D4—24no—
264C3×D4—24no—
265C3×D4—24no—
266C3×D4—44no—
267C3×D4—44no—
268C2×C3×C4—21no—
269C2×C3×C4—21no—
270C2×C3×C4—21no—
271C2×C3×C4—21no—
272C2×C3×C4—22no—
273C2×C3×C4—41no—
274C2×C3×C4—41no—
275C2×C3×C4—64no—
276C2×C3×C4—124no—
277C2×C3×C4—124no—
278C2×C3×C4—122no—
279C2×C3×C4—242no—
280C2×C3×C4(C2×D3)⋊C412yes—
281C2×C3×C4(C2×D3)⋊C412yes—
282C2×Dic3—24no—
283C2×Dic3—44no—
284C2×Dic3—44no—
285C2×Dic3—42no—
286C2×Dic3—64no—
287C2×Dic3—64no—
288C2×Dic3—64no—
289C2×Dic3—62no—
290C2×Dic3—62no—
291C2×Dic3—62no—
292C2×Dic3—62no—
293C2×Dic3—64no—
294C2×Dic3—82no—
295C2×Dic3—124no—
296C2×Dic3—124no—
297C2×Dic3—122no—
298C2×Dic3—122no—
299C2×Dic3—122no—
300C2×Dic3—122no—
301C2×Dic3—124no—
302C2×Dic3—121no—
303C2×Dic3—121no—
304C2×Dic3—121no—
305C2×Dic3—122no—
306C2×Dic3—122no—
307C2×Dic3—121no—
308C2×C32—21no—
309C2×C32—21no—
310C2×C32—22no—
311C2×C32—22no—
312C2×C32—42no—
313C2×C32#38611yescharacteristic
314C2×C32#45812yes—
315C24#62611yescharacteristic
316C24C2×D3211yescharacteristic
317C2×D4—22no—
318C2×D4—22no—
319C2×D4#62412yes—
320C2×D4#62612yes—
321C22×C4—34no—
322C22×C4—62no—
323C22×C4—62no—
324C22×C4—92no—
325C22×C4—182no—
326C22×C4—181no—
327C22×C4—181no—
328C22×C4—181no—
329C22×C4—182no—
330C22×C4#62611yescharacteristic
331C4⋊C4—62no—
332C4⋊C4—184no—
333C22⋊C4—62no—
334C22⋊C4—62no—
335C22⋊C4—62no—
336C22⋊C4—62no—
337C22⋊C4—62no—
338C22⋊C4—92no—
339C22⋊C4—184no—
340C22⋊C4—181no—
341C42—62no—
342C22×C3—24no—
343C22×C3—24no—
344C22×C3—22no—
345C22×C3—24no—
346C22×C3—22no—
347C22×C3—22no—
348C22×C3—22no—
349C22×C3—22no—
350C22×C3—21no—
351C22×C3—21no—
352C22×C3—21no—
353C22×C3—22no—
354C22×C3—44no—
355C22×C3—42no—
356C22×C3—41no—
357C22×C3—41no—
358C22×C3—41no—
359C22×C3—42no—
360C22×C3—42no—
361C22×C3—41no—
362C22×C3—42no—
363C22×C3—42no—
364C22×C3—44no—
365C22×C3—42no—
366C22×C3—42no—
367C22×C3—44no—
368C22×C3—42no—
369C22×C3—42no—
370C22×C3—82no—
371C22×C3—81no—
372C22×C3—81no—
373C22×C3—82no—
374C22×C3#67⋊C412yes—
375C22×C3#88211yescharacteristic
376C22×C3#88611yescharacteristic
377C22×C3C2×(C2×D3)⋊C411yescharacteristic
378C22×C3C2×(C2×D3)⋊C411yescharacteristic
379C22×C3C4×#6712yes—
380C22×C3#92911yescharacteristic
381C22×C3#93012yes—
382C22×C3#93912yes—
383C22×C3#95311yescharacteristic
384C3×C4—22no—
385C3×C4—22no—
386C3×C4—42no—
387C3×C4—124no—
388C3×C4—242no—
389Dic3—44no—
390Dic3—82no—
391Dic3—124no—
392Dic3—124no—
393Dic3—122no—
394Dic3—122no—
395Dic3—122no—
396Dic3—122no—
397C32#189011yescharacteristic, complemented, Sylow
398C23—21no—
399C23—21no—
400C23—42no—
401C23—42no—
402C23#372212yes—
403C23#380412yes—
404C23C2×#62411yescharacteristic
405C23C2×#62611yescharacteristic
406C23C2×#62611yescharacteristic
407C23D3×#6712yes—
408D4—24no—
409D4—24no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—64no—
413C2×C4—124no—
414C2×C4—124no—
415C2×C4—122no—
416C2×C4—184no—
417C2×C4—182no—
418C2×C4—182no—
419C2×C4—242no—
420C2×C4—362no—
421C2×C4—361no—
422C2×C4—361no—
423C2×C4—362no—
424C2×C4#372212yes—
425C2×C3—22no—
426C2×C3—22no—
427C2×C3—22no—
428C2×C3—21no—
429C2×C3—21no—
430C2×C3—22no—
431C2×C3—21no—
432C2×C3—22no—
433C2×C3—21no—
434C2×C3—22no—
435C2×C3—22no—
436C2×C3—21no—
437C2×C3—42no—
438C2×C3—42no—
439C2×C3—42no—
440C2×C3—42no—
441C2×C3—82no—
442C2×C3#474212yes—
443C2×C3#495811yescharacteristic
444C2×C3#521311yescharacteristic
445C2×C3#524312yes—
446C22—24no—
447C22—22no—
448C22—22no—
449C22—42no—
450C22—41no—
451C22—41no—
452C22—42no—
453C22—42no—
454C22—81no—
455C22#6395212yes—
456C22C2×#372211yescharacteristic
457C22#6396611yescharacteristic
458C22#6397711yescharacteristic
459C22#6397812yes—
460C4—22no—
461C4—124no—
462C4—242no—
463C4—362no—
464C4—362no—
465C3—21no—
466C3#7002311yescharacteristic, complemented
467C3#7165511yescharacteristic, complemented
468C2—22no—
469C2—21no—
470C2—21no—
471C2—22no—
472C2—42no—
473C2#1059153412yes—
474C2#1059171111yescharacteristic
subgroupG/H
centerC22#63977
commutatorC23×C32C22×C4
FrattiniC24C2×D32
Fitting, prime radicalC22×C32×D4C22
socleC22×C32#120
cosocleC24×C32C23
hypercenterC22×D4D32
hypocenterC32#1890
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
4. #10591697C2semidirect
5. #10589186C2semidirect
13. #64144C4semidirect
45. C22×C3⋊Dic3C2×C4semidirect
51. #3757C2×C4semidirect
397. C32#1890semidirect
466. C3#70023semidirect
467. C3#71655semidirect

Maximal subgroups

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

subgroupindex
C2×#641442
C3×#57982
C2×C3×#8342
#105916972
#105891862
#716553
#700233