Finite Group Databasebeta

← #11808811

Subgroups — #11808811

Order 1152.

1225 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×#627C211yesmaximal, characteristic, complemented
2C2×C4×#625C211yesmaximal, characteristic
3#10592631C211yesmaximal, characteristic, complemented
4C3×C4×(C2×D3)⋊C4C212yesmaximal, complemented
5#10591390C212yesmaximal
6#10591299C212yesmaximal, complemented
7#10591293C212yesmaximal, complemented
8C4×(C2×D3)⋊Dic3C212yesmaximal, complemented
9#10591211C212yesmaximal, complemented
10#73481—32nomaximal
11C22×C3×C4×D3C2212yes—
12C22×#627C2211yescharacteristic
13C22×#625C2211yescharacteristic
14C2×C32×C42C2211yescharacteristic
15C2×C4×C3⋊Dic3C2211yescharacteristic
16C2×C4×C3⋊Dic3C2211yescharacteristic
17C2×C3×(C2×D3)⋊C4C2212yes—
18C2×C3×(C2×D3)⋊C4C2212yes—
19C2×C3×C4×Dic3C2212yes—
20C2×#3724C2211yescharacteristic
21C2×#3724C2211yescharacteristic
22C2×Dic3⋊Dic3C2212yes—
23C2×(C2×D3)⋊Dic3C2212yes—
24C2×(C2×D3)⋊Dic3C2212yes—
25C2×(C2×D3)⋊Dic3C2212yes—
26C4×#627—24no—
27C4×#625—24no—
28#63658C2212yes—
29#63658C2212yes—
30C3×C3⋊#95C2212yes—
31C3×C3⋊#95C2212yes—
32#63579C2212yes—
33#63579C2212yes—
34C2×C4×#67—32no—
35C2×C4×Dic6—32no—
36C3×C4×C22⋊C4—32no—
37C4×#217—32no—
38#4961—32no—
39#4959—32no—
40#4952—32no—
41#4947—32no—
42C4×(C2×D3)⋊C4—32no—
43C4×(C2×D3)⋊C4D312yescomplemented
44#4932—32no—
45#4932—61no—
46#4675—32no—
47#4673—32no—
48#4660—32no—
49#4658—32no—
50C23×C3×D3C2312yes—
51C22×C32×C4C2312yes—
52C22×C32×C4C2311yescharacteristic
53C22×C3⋊Dic3C2312yes—
54C22×C3⋊Dic3C2311yescharacteristic
55C22×C3⋊Dic3C2311yescharacteristic
56C22×C3×Dic3C2312yes—
57C22×C3×Dic3C2312yes—
58C22×C3×Dic3C2312yes—
59C2×C3×C4×D3—24no—
60C2×C3×C4×D3—24no—
61C2×C3×C4×D3—24no—
62C2×#627—22no—
63C2×#627—24no—
64C2×#625—24no—
65C2×#625—22no—
66C32×C42—22no—
67C4×C3⋊Dic3—22no—
68C4×C3⋊Dic3D414yes—
69C3×(C2×D3)⋊C4—24no—
70C3×(C2×D3)⋊C4—24no—
71C3×C4×Dic3—24no—
72#3724—22no—
73#3724—22no—
74Dic3⋊Dic3—24no—
75(C2×D3)⋊Dic3—24no—
76(C2×D3)⋊Dic3—24no—
77(C2×D3)⋊Dic3—24no—
78#2398—91noSylow
79C23×C3×C4—32no—
80C22×#67—32no—
81C22×C4×D3C2×D312yes—
82C22×Dic6—32no—
83C2×C3×C22⋊C4—32no—
84C2×C3×C22⋊C4—32no—
85C2×C3×C42—21no—
86C2×C3×C42—32no—
87C2×C3×C42C2×D312yes—
88C2×#217—32no—
89C2×#217—32no—
90C2×#217—32no—
91C4×#67—68no—
92C2×(C2×D3)⋊C4—32no—
93C2×(C2×D3)⋊C4—32no—
94C2×(C2×D3)⋊C4—32no—
95C2×(C2×D3)⋊C4C2×D312yes—
96C2×(C2×D3)⋊C4C2×D312yes—
97C2×C4⋊Dic3—32no—
98C2×Dic3⋊C4—32no—
99C2×Dic3⋊C4—32no—
100C2×Dic3⋊C4—32no—
101C2×C4×Dic3—32no—
102C2×C4×Dic3—32no—
103C2×C4×Dic3—61no—
104C2×C4×Dic3—61no—
105C2×C4×Dic3C2×D312yes—
106C4×Dic6—68no—
107C3×#95—32no—
108C3×#95—32no—
109C3⋊#95—32no—
110C3⋊#95—32no—
111C3⋊#95—32no—
112C3⋊#95—32no—
113C3⋊#95—32no—
114C3⋊#95—32no—
115C3⋊#95—32no—
116C3⋊#95—32no—
117C3⋊#95—62no—
118C3⋊#95—62no—
119C3⋊#95C2×D312yes—
120C3⋊#95C2×D312yes—
121C23×C32C2411yescharacteristic
122C22×C3×D3—22no—
123C22×C3×D3—22no—
124C22×C3×D3—22no—
125C22×C3×D3—22no—
126C22×C3×D3—22no—
127C22×C3×D3—22no—
128C22×C3×D3#4114yes—
129C2×C32×C4—22no—
130C2×C32×C4—22no—
131C2×C32×C4—22no—
132C2×C32×C4C2×D412yes—
133C2×C32×C4#4112yes—
134C2×C32×C4#4112yes—
135C2×C3⋊Dic3—22no—
136C2×C3⋊Dic3—22no—
137C2×C3⋊Dic3—22no—
138C2×C3⋊Dic3—22no—
139C2×C3⋊Dic3—22no—
140C2×C3⋊Dic3C2×D412yes—
141C2×C3⋊Dic3C2×D412yes—
142C2×C3×Dic3—22no—
143C2×C3×Dic3—22no—
144C2×C3×Dic3—22no—
145C2×C3×Dic3—22no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—22no—
148C2×C3×Dic3—22no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3#4114yes—
151C3×C4×D3—48no—
152#627—28no—
153#625—28no—
154C2×C4×Q8—91no—
155C2×C4×D4—91no—
156#400—92no—
157#397—92no—
158#394—92no—
159#393—92no—
160C4×C22⋊C4—32no—
161C4×C22⋊C4—92no—
162#376—91no—
163C24×C3—32no—
164C23×D3C22×D312yes—
165C22×C3×C4—22no—
166C22×C3×C4—21no—
167C22×C3×C4—32no—
168C22×C3×C4—32no—
169C22×C3×C4—32no—
170C22×C3×C4—64no—
171C22×C3×C4—64no—
172C22×C3×C4—64no—
173C22×C3×C4C22×D312yes—
174C22×C3×C4C22×D312yes—
175C22×C3×C4C22×D312yes—
176C2×#67—64no—
177C2×#67—64no—
178C2×#67—64no—
179C22×Dic3—32no—
180C22×Dic3—32no—
181C22×Dic3—32no—
182C22×Dic3—32no—
183C22×Dic3—61no—
184C22×Dic3—61no—
185C22×Dic3—62no—
186C22×Dic3C22×D312yes—
187C22×Dic3C22×D312yes—
188C22×Dic3C22×D312yes—
189C2×C4×D3—24no—
190C2×C4×D3—24no—
191C2×C4×D3—24no—
192C2×Dic6—64no—
193C2×Dic6—64no—
194C2×Dic6—64no—
195C3×C22⋊C4—64no—
196C3×C22⋊C4—64no—
197C3×C42—24no—
198C3×C42—24no—
199C3×C42—64no—
200#217—64no—
201#217—64no—
202#217—64no—
203(C2×D3)⋊C4—24no—
204(C2×D3)⋊C4—24no—
205(C2×D3)⋊C4—64no—
206(C2×D3)⋊C4—64no—
207(C2×D3)⋊C4—64no—
208C4⋊Dic3—64no—
209Dic3⋊C4—64no—
210Dic3⋊C4—64no—
211Dic3⋊C4—64no—
212C4×Dic3—24no—
213C4×Dic3—38no—
214C4×Dic3—64no—
215C4×Dic3—64no—
216C4×Dic3—64no—
217C22×C32C22×D411yescharacteristic
218C22×C32C2×#4111yescharacteristic
219C22×C32C2×#4112yes—
220C22×C32C2×#4112yes—
221C22×C32C2×#4111yescharacteristic
222C2×C3×D3—24no—
223C2×C3×D3—24no—
224C2×C3×D3—24no—
225C2×C3×D3—42no—
226C2×C3×D3—42no—
227C2×C3×D3—42no—
228C2×C3×D3—42no—
229C32×C4—42no—
230C32×C4#12414yes—
231C3⋊Dic3—22no—
232C3⋊Dic3—22no—
233C3⋊Dic3—42no—
234C3×Dic3—24no—
235C3×Dic3—42no—
236C3×Dic3—42no—
237C22×Q8—91no—
238C22×D4—91no—
239C23×C4—32no—
240C4×Q8—184no—
241C4×D4—184no—
242C2×C4⋊C4—91no—
243C2×C4⋊C4—92no—
244C2×C4⋊C4—91no—
245C2×C22⋊C4—32no—
246C2×C22⋊C4—32no—
247C2×C22⋊C4—92no—
248C2×C22⋊C4—92no—
249C2×C22⋊C4—92no—
250C2×C42—32no—
251C2×C42—91no—
252C2×C42—91no—
253C2×C42D3211yescharacteristic
254#95—32no—
255#95—32no—
256#95—92no—
257#95—92no—
258#95—92no—
259#95—92no—
260C23×C3—21no—
261C23×C3—34no—
262C23×C3—62no—
263C23×C3—62no—
264C23×C3—62no—
265C23×C3—62no—
266C23×C3—62no—
267C23×C3—62no—
268C23×C3C23×D312yes—
269C22×D3—22no—
270C22×D3—22no—
271C22×D3—22no—
272C22×D3—22no—
273C22×D3—22no—
274C22×D3—22no—
275C22×D3#23514yes—
276C2×C3×C4—24no—
277C2×C3×C4—22no—
278C2×C3×C4—22no—
279C2×C3×C4—22no—
280C2×C3×C4—22no—
281C2×C3×C4—22no—
282C2×C3×C4—22no—
283C2×C3×C4—22no—
284C2×C3×C4—22no—
285C2×C3×C4—22no—
286C2×C3×C4—34no—
287C2×C3×C4—42no—
288C2×C3×C4—42no—
289C2×C3×C4—62no—
290C2×C3×C4—62no—
291C2×C3×C4—62no—
292C2×C3×C4—62no—
293C2×C3×C4—62no—
294C2×C3×C4—62no—
295C2×C3×C4—62no—
296C2×C3×C4—62no—
297C2×C3×C4—128no—
298C2×C3×C4#23514yes—
299C2×C3×C4D3×D414yes—
300C2×C3×C4#23714yes—
301#67—616no—
302C2×Dic3—22no—
303C2×Dic3—22no—
304C2×Dic3—22no—
305C2×Dic3—22no—
306C2×Dic3—22no—
307C2×Dic3—22no—
308C2×Dic3—22no—
309C2×Dic3—22no—
310C2×Dic3—34no—
311C2×Dic3—34no—
312C2×Dic3—62no—
313C2×Dic3—62no—
314C2×Dic3—62no—
315C2×Dic3—62no—
316C2×Dic3—62no—
317C2×Dic3—62no—
318C2×Dic3—64no—
319C2×Dic3—62no—
320C2×Dic3—62no—
321C2×Dic3—62no—
322C2×Dic3—62no—
323C2×Dic3—62no—
324C2×Dic3—62no—
325C2×Dic3—122no—
326C2×Dic3—122no—
327C2×Dic3—122no—
328C2×Dic3—122no—
329C2×Dic3#23514yes—
330C4×D3—48no—
331Dic6—616no—
332C2×C32#52511yescharacteristic
333C2×C32#52511yescharacteristic
334C2×C32C2×#12411yescharacteristic
335C2×C32#52912yes—
336C2×C32#52912yes—
337C3×D3—44no—
338C24—32no—
339C2×Q8—184no—
340C2×Q8—182no—
341C2×D4—182no—
342C2×D4—184no—
343C22×C4—32no—
344C22×C4—32no—
345C22×C4—32no—
346C22×C4—64no—
347C22×C4—64no—
348C22×C4—64no—
349C22×C4—91no—
350C22×C4—91no—
351C22×C4—92no—
352C22×C4C2×D3212yes—
353C22×C4C2×D3211yescharacteristic
354C4⋊C4—182no—
355C4⋊C4—182no—
356C4⋊C4—184no—
357C22⋊C4—64no—
358C22⋊C4—64no—
359C22⋊C4—184no—
360C22⋊C4—184no—
361C22⋊C4—184no—
362C42—22no—
363C42—64no—
364C42—94no—
365C42—182no—
366C22×C3—21no—
367C22×C3—21no—
368C22×C3—22no—
369C22×C3—22no—
370C22×C3—21no—
371C22×C3—64no—
372C22×C3—64no—
373C22×C3—64no—
374C22×C3—122no—
375C22×C3—122no—
376C22×C3—122no—
377C22×C3—122no—
378C22×C3C2×#23512yes—
379C22×C3C2×#23512yes—
380C22×C3C2×#23512yes—
381C22×C3C2×D3×D412yes—
382C22×C3C2×#23712yes—
383C22×C3D3×#4112yes—
384C22×C3D3×#4112yes—
385C2×D3—24no—
386C2×D3—24no—
387C2×D3—24no—
388C2×D3—42no—
389C2×D3—42no—
390C2×D3—42no—
391C2×D3—42no—
392C3×C4—24no—
393C3×C4—44no—
394C3×C4—42no—
395C3×C4—42no—
396C3×C4—64no—
397C3×C4—122no—
398C3×C4—122no—
399C3×C4#88518yes—
400Dic3—24no—
401Dic3—42no—
402Dic3—42no—
403Dic3—64no—
404Dic3—64no—
405Dic3—122no—
406Dic3—122no—
407Dic3—124no—
408Dic3—122no—
409Dic3—122no—
410C32#239811yescharacteristic, complemented, Sylow
411C23—34no—
412C23—62no—
413C23—62no—
414C23—62no—
415C23—62no—
416C23—62no—
417C23—62no—
418C23C22×D3211yescharacteristic
419Q8—188no—
420D4—188no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—34no—
425C2×C4—62no—
426C2×C4—62no—
427C2×C4—62no—
428C2×C4—62no—
429C2×C4—62no—
430C2×C4—62no—
431C2×C4—62no—
432C2×C4—62no—
433C2×C4—92no—
434C2×C4—92no—
435C2×C4—128no—
436C2×C4—182no—
437C2×C4—182no—
438C2×C4—182no—
439C2×C4—182no—
440C2×C4—182no—
441C2×C4#379812yes—
442C2×C4#380212yes—
443C2×C4#380512yes—
444C2×C3—22no—
445C2×C3—22no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—21no—
449C2×C3—124no—
450C2×C3#547912yes—
451C2×C3C2×#88512yes—
452C2×C3#552812yes—
453C2×C3#553812yes—
454C2×C3#554712yes—
455C2×C3#554712yes—
456C2×C3#555712yes—
457D3—44no—
458C22—64no—
459C22—64no—
460C22—64no—
461C22—122no—
462C22—122no—
463C22—122no—
464C22—122no—
465C22C2×#379811yescharacteristic
466C22C2×#380211yescharacteristic
467C22D3×#23512yes—
468C22D3×#23512yes—
469C22C2×#380511yescharacteristic
470C4—42no—
471C4—64no—
472C4—122no—
473C4—122no—
474C4—182no—
475C4—182no—
476C4—362no—
477C4#6391514yes—
478C3—21no—
479C3#7348112yescomplemented
480C2—124no—
481C2#1059397312yes—
482C2#1059400611yescharacteristic
483C2#1059400611yescharacteristic
484C2#1059493412yes—
485C2C2×#6391511yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutator, socle, cosocleC23×C32C24
FrattiniC23C22×D32
FittingC2×C32×C42C22
prime radicalC22×#625C22
hypercenterC2×C42D32
hypocenterC32#2398
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×C4×#627C2semidirect
3. #10592631C2semidirect
4. C3×C4×(C2×D3)⋊C4C2semidirect
6. #10591299C2semidirect
7. #10591293C2semidirect
8. C4×(C2×D3)⋊Dic3C2semidirect
9. #10591211C2semidirect
43. C4×(C2×D3)⋊C4D3semidirect
410. C32#2398semidirect
479. C3#73481semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6272
C2×C4×#6252
#105926312
C3×C4×(C2×D3)⋊C42
#105913902
#105912992
#105912932
C4×(C2×D3)⋊Dic32
#105912112
#734813