Finite Group Databasebeta

← C3×#67698 #11772555

Subgroups — C3×#67698 #11772555

Order 1152.

561 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#100C211yesmaximal, characteristic
2C3×#5220C211yesmaximal, characteristic
3C2×C3×#834C211yesmaximal, characteristic
4C3×#1390—31nomaximal
5#67698C311yesmaximal, characteristic, direct product factor
6C22×C32×D4C2211yescharacteristic
7C23×C3×Dic3C411yescharacteristic, complemented
8C2×C32×M16—21no—
9C2×C3×#217—21no—
10C2×C3×#217—21no—
11C2×C3×#217C411yescharacteristic, complemented
12C32×#100—21no—
13C32×#100C412yescomplemented
14C3×#834—21no—
15C3×#834C412yescomplemented
16C3×C3⋊#95—21no—
17C2×C3×#100—21no—
18C2×C3×#100D311yescharacteristic
19C2×C3×#100C2×C311yescharacteristic
20C2×C3×#99—31no—
21C3×#386—31no—
22#5220C2×C311yescharacteristic
23C2×#834C2×C311yescharacteristic
24C24×C32C2×C411yescharacteristic
25C24×C32D411yescharacteristic
26C2×C32×D4—41no—
27C2×C32×D4—41no—
28C2×C32×D4C2×C411yescharacteristic
29C2×C32×D4C2×C411yescharacteristic
30C2×C32×D4D411yescharacteristic
31C2×C32×D4Q811yescharacteristic
32C22×C32×C4D411yescharacteristic
33C22×C3×Dic3—21no—
34C22×C3×Dic3—21no—
35C22×C3×Dic3—42no—
36C22×C3×Dic3—41no—
37C22×C3×Dic3—41no—
38C32×M16—22no—
39C32×M16—41no—
40C2×C32×C8—41no—
41C3×#217—22no—
42C3×#217—42no—
43C3×#217—41no—
44C3×#217—41no—
45#1390—31noSylow
46C22×C3×D4—21no—
47C22×C3×D4C2×D311yescharacteristic
48C22×C3×D4C22×C311yescharacteristic
49C23×C3×C4—31no—
50C23×Dic3C3×C411yescharacteristic, complemented
51C2×C3×M16—22no—
52C2×C3×M16—21no—
53C2×C3×M16—21no—
54C2×C3×C22⋊C4—31no—
55C2×C3×C22⋊C4—61no—
56C2×C3×C22⋊C4—61no—
57C2×#217—21no—
58C2×#217—21no—
59C2×#217C3×C411yescharacteristic, complemented
60C3×#100—22no—
61C3×#100—21no—
62C3×#100—21no—
63C3×#100—22no—
64C3×#100Dic312yescomplemented
65C3×#100C3×C412yescomplemented
66C3×#99—32no—
67C3×#99—61no—
68C3×#95—61no—
69#834—21no—
70#834C3×C412yescomplemented
71C3⋊#95—21no—
72C23×C32—21no—
73C23×C32—21no—
74C23×C32—21no—
75C23×C32—21no—
76C23×C32—41no—
77C23×C32—41no—
78C23×C32—41no—
79C23×C32—41no—
80C23×C32C4211yescharacteristic
81C23×C32C22⋊C411yescharacteristic
82C23×C32C22⋊C411yescharacteristic
83C23×C32C4⋊C411yescharacteristic
84C23×C32C4⋊C411yescharacteristic
85C32×D4—41no—
86C32×D4—41no—
87C32×D4—41no—
88C32×D4—41no—
89C2×C32×C4—21no—
90C2×C32×C4—21no—
91C2×C32×C4C22⋊C411yescharacteristic
92C2×C32×C4C4⋊C411yescharacteristic
93C2×C3×Dic3—22no—
94C2×C3×Dic3—41no—
95C2×C3×Dic3—42no—
96C2×C3×Dic3—41no—
97C2×C3×Dic3—42no—
98C2×C3×Dic3—42no—
99C2×C3×Dic3—41no—
100C2×C3×Dic3—41no—
101C2×C3×Dic3—41no—
102C2×C3×Dic3—81no—
103C2×C3×Dic3—81no—
104C32×C8—42no—
105C2×#100C3×D311yescharacteristic
106C2×#99—31no—
107#386—31no—
108C24×C3—21no—
109C24×C3—21no—
110C24×C3C4×D311yescharacteristic
111C24×C3D1211yescharacteristic
112C24×C3C2×C3×C411yescharacteristic
113C24×C3C3×D411yescharacteristic
114C2×C3×D4—21no—
115C2×C3×D4—21no—
116C2×C3×D4—21no—
117C2×C3×D4—21no—
118C2×C3×D4—41no—
119C2×C3×D4—41no—
120C2×C3×D4—41no—
121C2×C3×D4—41no—
122C2×C3×D4—42no—
123C2×C3×D4—42no—
124C2×C3×D4Dic611yescharacteristic
125C2×C3×D4C4×D311yescharacteristic
126C2×C3×D4C2×Dic311yescharacteristic
127C2×C3×D4#6711yescharacteristic
128C2×C3×D4C2×C3×C411yescharacteristic
129C2×C3×D4C2×C3×C411yescharacteristic
130C2×C3×D4C3×D411yescharacteristic
131C2×C3×D4C3×Q811yescharacteristic
132C22×C3×C4—21no—
133C22×C3×C4—61no—
134C22×C3×C4—61no—
135C22×C3×C4—122no—
136C22×C3×C4—121no—
137C22×C3×C4—121no—
138C22×C3×C4#6711yescharacteristic
139C22×C3×C4C3×D411yescharacteristic
140C22×Dic3—21no—
141C22×Dic3—21no—
142C22×Dic3—42no—
143C22×Dic3—41no—
144C22×Dic3—41no—
145C3×M16—24no—
146C3×M16—22no—
147C3×M16—22no—
148C3×M16—42no—
149C3×M16—41no—
150C3×M16—41no—
151C2×C3×C8—42no—
152C2×C3×C8—41no—
153C2×C3×C8—41no—
154C3×C22⋊C4—62no—
155C3×C22⋊C4—122no—
156C3×C22⋊C4—121no—
157C3×C22⋊C4—121no—
158#217—22no—
159#217—42no—
160#217—41no—
161#217—41no—
162C22×C32—21no—
163C22×C32—21no—
164C22×C32—21no—
165C22×C32—21no—
166C22×C32—21no—
167C22×C32—21no—
168C22×C32—41no—
169C22×C32—41no—
170C22×C32—41no—
171C22×C32—41no—
172C22×C32—42no—
173C22×C32—41no—
174C22×C32—41no—
175C22×C32—41no—
176C22×C32—41no—
177C22×C32—81no—
178C22×C32#9511yescharacteristic
179C22×C32#9911yescharacteristic
180C22×C32#9911yescharacteristic
181C32×C4—21no—
182C32×C4—21no—
183C3×Dic3—42no—
184C3×Dic3—81no—
185C3×Dic3—82no—
186C22×D4C2×C3×D311yescharacteristic
187C23×C4—31no—
188C2×M16—21no—
189C2×C22⋊C4—31no—
190C2×C22⋊C4—61no—
191C2×C22⋊C4—61no—
192#100—21no—
193#100C3×Dic312yescomplemented
194#99—32no—
195#99—61no—
196#95—61no—
197C23×C3—21no—
198C23×C3—21no—
199C23×C3—21no—
200C23×C3—21no—
201C23×C3—21no—
202C23×C3—21no—
203C23×C3—21no—
204C23×C3—21no—
205C23×C3—21no—
206C23×C3—21no—
207C23×C3—21no—
208C23×C3—21no—
209C23×C3—21no—
210C23×C3—41no—
211C23×C3—41no—
212C23×C3—41no—
213C23×C3—41no—
214C23×C3—41no—
215C23×C3—41no—
216C23×C3—41no—
217C23×C3—41no—
218C23×C3—41no—
219C23×C3—41no—
220C23×C3—41no—
221C23×C3—41no—
222C23×C3—81no—
223C23×C3—81no—
224C23×C3—81no—
225C23×C3—81no—
226C23×C3C4×Dic311yescharacteristic
227C23×C3Dic3⋊C411yescharacteristic
228C23×C3C4⋊Dic311yescharacteristic
229C23×C3(C2×D3)⋊C411yescharacteristic
230C23×C3(C2×D3)⋊C411yescharacteristic
231C23×C3C3×C4211yescharacteristic
232C23×C3C3×C22⋊C411yescharacteristic
233C23×C3C3×C22⋊C411yescharacteristic
234C23×C3C3×C4⋊C411yescharacteristic
235C23×C3C3×C4⋊C411yescharacteristic
236C3×D4—41no—
237C3×D4—41no—
238C3×D4—41no—
239C3×D4—41no—
240C3×D4—41no—
241C3×D4—41no—
242C3×D4—41no—
243C3×D4—41no—
244C3×D4—42no—
245C3×D4—42no—
246C3×D4—42no—
247C3×D4—42no—
248C2×C3×C4—22no—
249C2×C3×C4—22no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—62no—
257C2×C3×C4—121no—
258C2×C3×C4—122no—
259C2×C3×C4—121no—
260C2×C3×C4—122no—
261C2×C3×C4—122no—
262C2×C3×C4—121no—
263C2×C3×C4—121no—
264C2×C3×C4—121no—
265C2×C3×C4—241no—
266C2×C3×C4—241no—
267C2×C3×C4Dic3⋊C411yescharacteristic
268C2×C3×C4#21711yescharacteristic
269C2×C3×C4C3×C22⋊C411yescharacteristic
270C2×C3×C4C3×C4⋊C411yescharacteristic
271C2×Dic3—22no—
272C2×Dic3—41no—
273C2×Dic3—42no—
274C2×Dic3—41no—
275C2×Dic3—42no—
276C2×Dic3—42no—
277C2×Dic3—41no—
278C2×Dic3—41no—
279C2×Dic3—41no—
280C2×Dic3—81no—
281C2×Dic3—81no—
282C3×C8—44no—
283C3×C8—42no—
284C3×C8—42no—
285C2×C32—21no—
286C2×C32—21no—
287C2×C32—41no—
288C2×C32—41no—
289C2×C32—41no—
290C2×C32—41no—
291C2×C32#34211yescharacteristic
292C2×C32AΣL(1,𝔽16)11yescharacteristic
293C2×C32#35211yescharacteristic
294C24C3×C4×D311yescharacteristic
295C24C3×D1211yescharacteristic
296C2×D4—41no—
297C2×D4—41no—
298C2×D4C3×Dic611yescharacteristic
299C2×D4C3×C4×D311yescharacteristic
300C2×D4C2×C3×Dic311yescharacteristic
301C2×D4C3×#6711yescharacteristic
302C22×C4—61no—
303C22×C4—61no—
304C22×C4—122no—
305C22×C4—121no—
306C22×C4—121no—
307C22×C4C3×#6711yescharacteristic
308M16—22no—
309M16—41no—
310C2×C8—41no—
311C22⋊C4—62no—
312C22⋊C4—122no—
313C22⋊C4—121no—
314C22⋊C4—121no—
315C22×C3—21no—
316C22×C3—21no—
317C22×C3—21no—
318C22×C3—21no—
319C22×C3—21no—
320C22×C3—21no—
321C22×C3—21no—
322C22×C3—21no—
323C22×C3—21no—
324C22×C3—21no—
325C22×C3—21no—
326C22×C3—21no—
327C22×C3—21no—
328C22×C3—21no—
329C22×C3—21no—
330C22×C3—41no—
331C22×C3—41no—
332C22×C3—41no—
333C22×C3—41no—
334C22×C3—41no—
335C22×C3—41no—
336C22×C3—41no—
337C22×C3—41no—
338C22×C3—41no—
339C22×C3—41no—
340C22×C3—41no—
341C22×C3—41no—
342C22×C3—41no—
343C22×C3—41no—
344C22×C3—42no—
345C22×C3—42no—
346C22×C3—41no—
347C22×C3—41no—
348C22×C3—41no—
349C22×C3—41no—
350C22×C3—41no—
351C22×C3—41no—
352C22×C3—41no—
353C22×C3—41no—
354C22×C3—81no—
355C22×C3—81no—
356C22×C3—81no—
357C22×C3—81no—
358C22×C3—81no—
359C22×C3—81no—
360C22×C3—81no—
361C22×C3—81no—
362C22×C3—82no—
363C22×C3—81no—
364C22×C3—81no—
365C22×C3—82no—
366C22×C3#80611yescharacteristic
367C22×C3#80611yescharacteristic
368C22×C3C3⋊#9511yescharacteristic
369C22×C3C3×#9511yescharacteristic
370C22×C3C3×#9911yescharacteristic
371C22×C3C3×#9911yescharacteristic
372C3×C4—22no—
373C3×C4—22no—
374C3×C4—21no—
375C3×C4—21no—
376C3×C4—21no—
377C3×C4—21no—
378C3×C4—122no—
379C3×C4—241no—
380C3×C4—242no—
381Dic3—42no—
382Dic3—81no—
383Dic3—82no—
384C32#139011yescharacteristic, complemented, Sylow
385C23—21no—
386C23—21no—
387C23—21no—
388C23—21no—
389C23—41no—
390C23—41no—
391C23—41no—
392C23—41no—
393C23C3×C4×Dic311yescharacteristic
394C23C3×Dic3⋊C411yescharacteristic
395C23C3×C4⋊Dic311yescharacteristic
396C23C3×(C2×D3)⋊C411yescharacteristic
397C23C3×(C2×D3)⋊C411yescharacteristic
398D4—41no—
399D4—41no—
400D4—41no—
401D4—41no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—62no—
405C2×C4—121no—
406C2×C4—122no—
407C2×C4—121no—
408C2×C4—122no—
409C2×C4—122no—
410C2×C4—121no—
411C2×C4—121no—
412C2×C4—121no—
413C2×C4—241no—
414C2×C4—241no—
415C2×C4C3×Dic3⋊C411yescharacteristic
416C2×C4C3×#21711yescharacteristic
417C8—42no—
418C2×C3—21no—
419C2×C3—21no—
420C2×C3—21no—
421C2×C3—21no—
422C2×C3—21no—
423C2×C3—21no—
424C2×C3—21no—
425C2×C3—41no—
426C2×C3—41no—
427C2×C3—41no—
428C2×C3—41no—
429C2×C3—41no—
430C2×C3—41no—
431C2×C3—41no—
432C2×C3—41no—
433C2×C3—41no—
434C2×C3—41no—
435C2×C3—81no—
436C2×C3—81no—
437C2×C3—81no—
438C2×C3—81no—
439C2×C3#447511yescharacteristic
440C2×C3#447611yescharacteristic
441C2×C3#452711yescharacteristic
442C2×C3C3×#34211yescharacteristic
443C2×C3C3×AΣL(1,𝔽16)11yescharacteristic
444C2×C3C3×#35211yescharacteristic
445C22—21no—
446C22—21no—
447C22—21no—
448C22—21no—
449C22—21no—
450C22—21no—
451C22—41no—
452C22—41no—
453C22—41no—
454C22—41no—
455C22—42no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—81no—
461C22C3×#80611yescharacteristic
462C22C3×#80611yescharacteristic
463C22C3×C3⋊#9511yescharacteristic
464C4—21no—
465C4—21no—
466C4—122no—
467C4—241no—
468C4—242no—
469C3—21no—
470C3#6769811yescharacteristic, direct product factor
471C3C3×#139011yescharacteristic, complemented
472C2—21no—
473C2—21no—
474C2—41no—
475C2—41no—
476C2—41no—
477C2—41no—
478C2C3×#447511yescharacteristic
479C2C3×#447611yescharacteristic
480C2C3×#452711yescharacteristic
subgroupG/H
centerC22×C3#806
commutatorC23×C3C3×C42
FrattiniC22×D4C2×C3×D3
FittingC2×C32×#100C2
socleC22×C32#99
prime radicalC22×C32×D4C22
cosocleC22×C3×D4C22×C3
hypercenterC2×C3×#100D3
hypocenterC3C3×#1390
LCSG ▷ C23×C3 ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C23×C3 ◁ C22×C3×D4 ◁ C2×C3×#100

Complements

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

NH ≅ G/Ntype
5. #67698C3direct (N × H)
7. C23×C3×Dic3C4semidirect
11. C2×C3×#217C4semidirect
13. C32×#100C4semidirect
15. C3×#834C4semidirect
50. C23×Dic3C3×C4semidirect
59. C2×#217C3×C4semidirect
64. C3×#100Dic3semidirect
65. C3×#100C3×C4semidirect
70. #834C3×C4semidirect
193. #100C3×Dic3semidirect
384. C32#1390semidirect
470. C3#67698direct (N × H)
471. C3C3×#1390semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1002
C3×#52202
C2×C3×#8342
C3×#13903
#676983