Finite Group Databasebeta

← C3×#71600 #11773785

Subgroups — C3×#71600 #11773785

Order 1152.

877 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×C32×C4×D4C211yesmaximal, characteristic
2C2×C3×#830C212yesmaximal, complemented
3C3×#4528C212yesmaximal, complemented
4C3×#4525C212yesmaximal, complemented
5C3×#1459—31nomaximal
6#71600C311yesmaximal, characteristic, direct product factor
7C22×C32×D4C411yescharacteristic
8C23×C32×C4C411yescharacteristic
9C23×C32×C4C2211yescharacteristic
10C32×C4×D4—22no—
11C32×C4×D4—22no—
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×C32×C22⋊C4C411yescharacteristic
14C2×C32×C22⋊C4C2211yescharacteristic
15C2×C32×C42C411yescharacteristic
16C22×C3×C3⋊C8—22no—
17C3×#830—22no—
18C3×#830C2214yes—
19C2×C3×C4×D4—21no—
20C2×C3×C4×D4D311yescharacteristic
21C2×C3×C4×D4C2×C311yescharacteristic
22C2×C3×C22⋊C8—32no—
23C2×#830C2×C312yescomplemented
24C3×#324—32no—
25C3×#323—32no—
26#4528C2×C312yescomplemented
27#4525C2×C312yescomplemented
28C24×C32C2×C411yescharacteristic
29C24×C32C2×C411yescharacteristic
30C2×C32×D4—22no—
31C2×C32×D4—22no—
32C2×C32×D4C814yescomplemented
33C22×C32×C4—21no—
34C22×C32×C4—21no—
35C22×C32×C4—42no—
36C22×C32×C4—42no—
37C22×C32×C4C2×C411yescharacteristic
38C22×C32×C4C2×C411yescharacteristic
39C22×C32×C4C2×C411yescharacteristic
40C22×C32×C4C2×C411yescharacteristic
41C22×C32×C4D412yes—
42C22×C32×C4D412yes—
43C22×C32×C4C2311yescharacteristic
44C32×C4⋊C4—22no—
45C32×C22⋊C4—22no—
46C32×C22⋊C4—22no—
47C32×C42—21no—
48C32×C42—21no—
49C2×C3×C3⋊C8—24no—
50C2×C3×C3⋊C8—44no—
51#1459—31noSylow
52C22×C3×D4—21no—
53C22×C3×D4Dic311yescharacteristic
54C22×C3×D4C3×C411yescharacteristic
55C23×C3×C4—21no—
56C23×C3×C4—21no—
57C23×C3×C4Dic311yescharacteristic
58C23×C3×C4C3×C411yescharacteristic
59C23×C3×C4C2×D311yescharacteristic
60C23×C3×C4C22×C311yescharacteristic
61C22×C3×C8—62no—
62C3×C4×D4—24no—
63C3×C4×D4—24no—
64C3×C4×D4—22no—
65C3×C4×D4—22no—
66C3×C4×D4—22no—
67C3×C4×D4—22no—
68C2×C3×C4⋊C4—21no—
69C2×C3×C4⋊C4C2×D311yescharacteristic
70C2×C3×C4⋊C4C22×C311yescharacteristic
71C2×C3×C22⋊C4—21no—
72C2×C3×C22⋊C4—21no—
73C2×C3×C22⋊C4Dic311yescharacteristic
74C2×C3×C22⋊C4C3×C411yescharacteristic
75C2×C3×C22⋊C4C2×D311yescharacteristic
76C2×C3×C22⋊C4C22×C311yescharacteristic
77C2×C3×C42—21no—
78C2×C3×C42Dic311yescharacteristic
79C2×C3×C42C3×C411yescharacteristic
80C22×C3⋊C8—22no—
81C3×C22⋊C8—34no—
82C3×C22⋊C8—62no—
83#830—22no—
84#830C22×C314yes—
85C23×C32—21no—
86C23×C32—21no—
87C23×C32—41no—
88C23×C32—41no—
89C23×C32—41no—
90C23×C32—41no—
91C23×C32C22⋊C412yes—
92C23×C32C2×C812yes—
93C23×C32C2×C812yescomplemented
94C23×C32M1612yes—
95C23×C32C22×C411yescharacteristic
96C32×D4—28no—
97C2×C32×C4—21no—
98C2×C32×C4—21no—
99C2×C32×C4—22no—
100C2×C32×C4—21no—
101C2×C32×C4—21no—
102C2×C32×C4—24no—
103C2×C32×C4—42no—
104C2×C32×C4—41no—
105C2×C32×C4—42no—
106C2×C32×C4—42no—
107C2×C32×C4—41no—
108C2×C32×C4—41no—
109C2×C32×C4C22⋊C411yescharacteristic
110C2×C32×C4C22⋊C411yescharacteristic
111C2×C32×C4C2×C812yescomplemented
112C2×C32×C4C2×D412yes—
113C3×C3⋊C8—44no—
114C2×C4×D4C3×D311yescharacteristic
115C2×C22⋊C8—32no—
116#324—32no—
117#323—32no—
118C24×C3—21no—
119C24×C3—21no—
120C24×C3C2×Dic311yescharacteristic
121C24×C3C2×Dic311yescharacteristic
122C24×C3C2×C3×C411yescharacteristic
123C24×C3C2×C3×C411yescharacteristic
124C2×C3×D4—24no—
125C2×C3×D4—24no—
126C2×C3×D4—22no—
127C2×C3×D4—22no—
128C2×C3×D4—22no—
129C2×C3×D4—22no—
130C2×C3×D4—24no—
131C2×C3×D4C3⋊C814yescomplemented
132C2×C3×D4C3×C814yescomplemented
133C22×C3×C4—22no—
134C22×C3×C4—22no—
135C22×C3×C4—21no—
136C22×C3×C4—21no—
137C22×C3×C4—21no—
138C22×C3×C4—21no—
139C22×C3×C4—21no—
140C22×C3×C4—21no—
141C22×C3×C4—21no—
142C22×C3×C4—21no—
143C22×C3×C4—22no—
144C22×C3×C4—22no—
145C22×C3×C4—21no—
146C22×C3×C4—42no—
147C22×C3×C4—42no—
148C22×C3×C4—44no—
149C22×C3×C4—44no—
150C22×C3×C4—42no—
151C22×C3×C4—42no—
152C22×C3×C4C2×Dic311yescharacteristic
153C22×C3×C4C2×Dic311yescharacteristic
154C22×C3×C4C2×Dic311yescharacteristic
155C22×C3×C4C2×Dic311yescharacteristic
156C22×C3×C4#6712yes—
157C22×C3×C4#6712yes—
158C22×C3×C4C2×C3×C411yescharacteristic
159C22×C3×C4C2×C3×C411yescharacteristic
160C22×C3×C4C2×C3×C411yescharacteristic
161C22×C3×C4C2×C3×C411yescharacteristic
162C22×C3×C4C3×D412yes—
163C22×C3×C4C3×D412yes—
164C22×C3×C4C22×D311yescharacteristic
165C22×C3×C4C23×C311yescharacteristic
166C2×C3×C8—64no—
167C2×C3×C8—124no—
168C3×C4⋊C4—24no—
169C3×C4⋊C4—22no—
170C3×C4⋊C4—22no—
171C3×C22⋊C4—24no—
172C3×C22⋊C4—24no—
173C3×C22⋊C4—22no—
174C3×C22⋊C4—22no—
175C3×C22⋊C4—22no—
176C3×C22⋊C4—22no—
177C3×C42—22no—
178C3×C42—22no—
179C3×C42—21no—
180C3×C42—21no—
181C3×C42—21no—
182C3×C42—21no—
183C2×C3⋊C8—24no—
184C2×C3⋊C8—44no—
185C22×C32—21no—
186C22×C32—21no—
187C22×C32—22no—
188C22×C32—22no—
189C22×C32—22no—
190C22×C32—42no—
191C22×C32—42no—
192C22×C32—42no—
193C22×C32—42no—
194C22×C32—41no—
195C22×C32—41no—
196C22×C32C22⋊C814yes—
197C22×C32C2×C22⋊C411yescharacteristic
198C22×C32C22×C811yescharacteristic
199C22×C32C2×M1611yescharacteristic
200C32×C4—22no—
201C32×C4—21no—
202C32×C4—22no—
203C32×C4—41no—
204C32×C4—41no—
205C32×C4#9912yes—
206C22×D4C3×Dic311yescharacteristic
207C23×C4C3×Dic311yescharacteristic
208C23×C4C2×C3×D311yescharacteristic
209C22×C8—62no—
210C4×D4—22no—
211C4×D4—22no—
212C2×C4⋊C4C2×C3×D311yescharacteristic
213C2×C22⋊C4C3×Dic311yescharacteristic
214C2×C22⋊C4C2×C3×D311yescharacteristic
215C2×C42C3×Dic311yescharacteristic
216C22⋊C8—34no—
217C22⋊C8—62no—
218C23×C3—22no—
219C23×C3—22no—
220C23×C3—21no—
221C23×C3—21no—
222C23×C3—21no—
223C23×C3—21no—
224C23×C3—22no—
225C23×C3—22no—
226C23×C3—22no—
227C23×C3—22no—
228C23×C3—21no—
229C23×C3—41no—
230C23×C3—41no—
231C23×C3—41no—
232C23×C3—41no—
233C23×C3—41no—
234C23×C3—41no—
235C23×C3—41no—
236C23×C3—41no—
237C23×C3—42no—
238C23×C3—42no—
239C23×C3—42no—
240C23×C3—42no—
241C23×C3C2×C3⋊C812yes—
242C23×C3C2×C3⋊C812yescomplemented
243C23×C3#20812yes—
244C23×C3#21712yes—
245C23×C3C3×C22⋊C412yes—
246C23×C3C2×C3×C812yes—
247C23×C3C2×C3×C812yescomplemented
248C23×C3C3×M1612yes—
249C23×C3C22×Dic311yescharacteristic
250C23×C3C22×C3×C411yescharacteristic
251C3×D4—216no—
252C3×D4—28no—
253C3×D4—28no—
254C2×C3×C4—22no—
255C2×C3×C4—24no—
256C2×C3×C4—22no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—24no—
262C2×C3×C4—22no—
263C2×C3×C4—24no—
264C2×C3×C4—22no—
265C2×C3×C4—22no—
266C2×C3×C4—22no—
267C2×C3×C4—21no—
268C2×C3×C4—21no—
269C2×C3×C4—21no—
270C2×C3×C4—21no—
271C2×C3×C4—22no—
272C2×C3×C4—21no—
273C2×C3×C4—21no—
274C2×C3×C4—22no—
275C2×C3×C4—44no—
276C2×C3×C4—42no—
277C2×C3×C4—42no—
278C2×C3×C4—41no—
279C2×C3×C4—41no—
280C2×C3×C4—44no—
281C2×C3×C4—44no—
282C2×C3×C4—42no—
283C2×C3×C4—42no—
284C2×C3×C4—44no—
285C2×C3×C4—42no—
286C2×C3×C4—42no—
287C2×C3×C4—42no—
288C2×C3×C4—42no—
289C2×C3×C4—42no—
290C2×C3×C4—41no—
291C2×C3×C4—41no—
292C2×C3×C4—41no—
293C2×C3×C4—41no—
294C2×C3×C4C2×C3⋊C812yescomplemented
295C2×C3×C4#21711yescharacteristic
296C2×C3×C4#21711yescharacteristic
297C2×C3×C4C3×C22⋊C411yescharacteristic
298C2×C3×C4C3×C22⋊C411yescharacteristic
299C2×C3×C4C2×C3×C812yescomplemented
300C2×C3×C4C2×#6712yes—
301C2×C3×C4C2×C3×D412yes—
302C3×C8—124no—
303C3⋊C8—44no—
304C2×C32—21no—
305C2×C32—21no—
306C2×C32—24no—
307C2×C32—42no—
308C2×C32C2×C22⋊C811yescharacteristic
309C2×C32C2×#9911yescharacteristic
310C2×C32#41311yescharacteristic
311C24C2×C3×Dic311yescharacteristic
312C24C2×C3×Dic311yescharacteristic
313C2×D4—22no—
314C2×D4—22no—
315C2×D4C3×C3⋊C814yescomplemented
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—42no—
319C22×C4—42no—
320C22×C4C2×C3×Dic311yescharacteristic
321C22×C4C2×C3×Dic311yescharacteristic
322C22×C4C2×C3×Dic311yescharacteristic
323C22×C4C2×C3×Dic311yescharacteristic
324C22×C4C3×#6712yes—
325C22×C4C3×#6712yes—
326C22×C4C22×C3×D311yescharacteristic
327C2×C8—64no—
328C2×C8—124no—
329C4⋊C4—22no—
330C22⋊C4—22no—
331C22⋊C4—22no—
332C42—21no—
333C42—21no—
334C22×C3—22no—
335C22×C3—22no—
336C22×C3—21no—
337C22×C3—22no—
338C22×C3—21no—
339C22×C3—22no—
340C22×C3—21no—
341C22×C3—22no—
342C22×C3—21no—
343C22×C3—22no—
344C22×C3—24no—
345C22×C3—22no—
346C22×C3—22no—
347C22×C3—21no—
348C22×C3—21no—
349C22×C3—21no—
350C22×C3—24no—
351C22×C3—42no—
352C22×C3—42no—
353C22×C3—42no—
354C22×C3—42no—
355C22×C3—42no—
356C22×C3—42no—
357C22×C3—42no—
358C22×C3—42no—
359C22×C3—42no—
360C22×C3—44no—
361C22×C3—44no—
362C22×C3—44no—
363C22×C3—44no—
364C22×C3—42no—
365C22×C3—42no—
366C22×C3—42no—
367C22×C3—41no—
368C22×C3—41no—
369C22×C3—41no—
370C22×C3—41no—
371C22×C3#83014yes—
372C22×C3C3×C22⋊C814yes—
373C22×C3C22×C3⋊C811yescharacteristic
374C22×C3C2×#20811yescharacteristic
375C22×C3C2×#21711yescharacteristic
376C22×C3C2×C3×C22⋊C411yescharacteristic
377C22×C3C22×C3×C811yescharacteristic
378C22×C3C2×C3×M1611yescharacteristic
379C3×C4—22no—
380C3×C4—24no—
381C3×C4—22no—
382C3×C4—22no—
383C3×C4—21no—
384C3×C4—22no—
385C3×C4—22no—
386C3×C4—21no—
387C3×C4—22no—
388C3×C4—42no—
389C3×C4—42no—
390C3×C4—42no—
391C3×C4—41no—
392C3×C4—41no—
393C3×C4—41no—
394C3×C4—41no—
395C3×C4#83412yes—
396C3×C4C3×#9912yes—
397C32#145911yescharacteristic, complemented, Sylow
398C23—21no—
399C23—21no—
400C23—41no—
401C23—41no—
402C23—41no—
403C23—41no—
404C23C2×C3×C3⋊C812yes—
405C23C2×C3×C3⋊C812yescomplemented
406C23C3×#20812yes—
407C23C3×#21712yes—
408C23C22×C3×Dic311yescharacteristic
409D4—28no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—24no—
413C2×C4—22no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—42no—
417C2×C4—41no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4C2×C3×C3⋊C812yescomplemented
423C2×C4C3×#21711yescharacteristic
424C2×C4C3×#21711yescharacteristic
425C2×C4C2×C3×#6712yes—
426C8—124no—
427C2×C3—22no—
428C2×C3—22no—
429C2×C3—21no—
430C2×C3—21no—
431C2×C3—24no—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3—24no—
435C2×C3—21no—
436C2×C3—21no—
437C2×C3—21no—
438C2×C3—44no—
439C2×C3—44no—
440C2×C3—42no—
441C2×C3—42no—
442C2×C3C2×#83011yescharacteristic
443C2×C3C2×#83411yescharacteristic
444C2×C3#523711yescharacteristic
445C2×C3C2×C3×C22⋊C811yescharacteristic
446C2×C3C2×C3×#9911yescharacteristic
447C2×C3C3×#41311yescharacteristic
448C22—21no—
449C22—22no—
450C22—21no—
451C22—22no—
452C22—22no—
453C22—42no—
454C22—42no—
455C22—42no—
456C22—42no—
457C22—41no—
458C22—41no—
459C22C3×#83014yes—
460C22C22×C3×C3⋊C811yescharacteristic
461C22C2×C3×#20811yescharacteristic
462C22C2×C3×#21711yescharacteristic
463C4—22no—
464C4—22no—
465C4—21no—
466C4—41no—
467C4—41no—
468C4C3×#83412yes—
469C3—21no—
470C3#7160011yescharacteristic, direct product factor
471C3C3×#145911yescharacteristic, complemented
472C2—21no—
473C2—21no—
474C2—24no—
475C2—42no—
476C2C2×C3×#83011yescharacteristic
477C2C2×C3×#83411yescharacteristic
478C2C3×#523711yescharacteristic
subgroupG/H
centerC2×C3×C4#217
commutatorC22×C3C22×C3×C8
FrattiniC22×C4C22×C3×D3
FittingC2×C32×C4×D4C2
socleC22×C32C2×C22⋊C4
prime radicalC22×C32×D4C4
cosocleC22×C3×C4C23×C3
hypercenterC2×C3×C4×D4D3
hypocenterC3C3×#1459
LCSG ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C23×C3×C4 ◁ C2×C3×C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#830C2semidirect
3. C3×#4528C2semidirect
4. C3×#4525C2semidirect
6. #71600C3direct (N × H)
23. C2×#830C2×C3semidirect
26. #4528C2×C3semidirect
27. #4525C2×C3semidirect
32. C2×C32×D4C8semidirect
93. C23×C32C2×C8semidirect
111. C2×C32×C4C2×C8semidirect
131. C2×C3×D4C3⋊C8semidirect
132. C2×C3×D4C3×C8semidirect
242. C23×C3C2×C3⋊C8semidirect
247. C23×C3C2×C3×C8semidirect
294. C2×C3×C4C2×C3⋊C8semidirect
299. C2×C3×C4C2×C3×C8semidirect
315. C2×D4C3×C3⋊C8semidirect
397. C32#1459semidirect
405. C23C2×C3×C3⋊C8semidirect
422. C2×C4C2×C3×C3⋊C8semidirect
470. C3#71600direct (N × H)
471. C3C3×#1459semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4×D42
C2×C3×#8302
C3×#45282
C3×#45252
C3×#14593
#716003