Finite Group Databasebeta

← C3×#67694 #11772549

Subgroups — C3×#67694 #11772549

Order 1152.

573 conjugacy classes of subgroups.

The subgroup lattice has 485 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#99C211yesmaximal, characteristic
2C3×#5220C211yesmaximal, characteristic
3C2×C3×#833C211yesmaximal, characteristic
4C3×#1390—31nomaximal
5#67694C311yesmaximal, characteristic, direct product factor
6C22×C32×D4C2211yescharacteristic
7C23×C3×Dic3C411yescharacteristic, complemented
8C2×C32×C22⋊C4—21no—
9C2×C3×#217—21no—
10C2×C3×#217C411yescharacteristic, complemented
11C2×C3×#208—21no—
12C32×#99—21no—
13C32×#99C412yescomplemented
14C3×#833—21no—
15C3×#833C412yescomplemented
16C3×C3⋊#95—21no—
17C2×C3×#100—31no—
18C2×C3×#99—21no—
19C2×C3×#99D311yescharacteristic
20C2×C3×#99C2×C311yescharacteristic
21C3×#386—31no—
22#5220C2×C311yescharacteristic
23C2×#833C2×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×C4—41no—
33C22×C32×C4D411yescharacteristic
34C22×C3×Dic3—21no—
35C22×C3×Dic3—21no—
36C22×C3×Dic3—42no—
37C22×C3×Dic3—41no—
38C32×C22⋊C4—22no—
39C32×C22⋊C4—41no—
40C3×#217—42no—
41C3×#217—41no—
42C3×#208—22no—
43C3×#208—41no—
44C2×C3×C3⋊C8—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—61no—
52C2×C3×C22⋊C4—22no—
53C2×C3×C22⋊C4—21no—
54C2×C3×C22⋊C4—21no—
55C2×C3×C22⋊C4—31no—
56C2×C3×C22⋊C4—61no—
57C2×#217—21no—
58C2×#217C3×C411yescharacteristic, complemented
59C2×#208—21no—
60C3×#100—32no—
61C3×#100—61no—
62C3×#99—22no—
63C3×#99—21no—
64C3×#99—21no—
65C3×#99—22no—
66C3×#99Dic312yescomplemented
67C3×#99C3×C412yescomplemented
68C3×#95—61no—
69#833—21no—
70#833C3×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×C4—42no—
92C2×C32×C4—81no—
93C2×C32×C4—81no—
94C2×C32×C4C22⋊C411yescharacteristic
95C2×C32×C4C4⋊C411yescharacteristic
96C2×C3×Dic3—22no—
97C2×C3×Dic3—41no—
98C2×C3×Dic3—42no—
99C2×C3×Dic3—41no—
100C2×C3×Dic3—42no—
101C2×C3×Dic3—41no—
102C2×C3×Dic3—41no—
103C2×C3×Dic3—41no—
104C3×C3⋊C8—42no—
105C2×#100—31no—
106C2×#99C3×D311yescharacteristic
107#386—31no—
108C24×C3—21no—
109C24×C3—21no—
110C24×C3C4×D311yescharacteristic
111C24×C3#6711yescharacteristic
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—42no—
134C22×C3×C4—41no—
135C22×C3×C4—41no—
136C22×C3×C4—61no—
137C22×C3×C4—61no—
138C22×C3×C4—122no—
139C22×C3×C4—121no—
140C22×C3×C4D1211yescharacteristic
141C22×C3×C4C3×D411yescharacteristic
142C22×Dic3—21no—
143C22×Dic3—21no—
144C22×Dic3—42no—
145C22×Dic3—41no—
146C3×M16—62no—
147C3×M16—121no—
148C2×C3×C8—121no—
149C3×C22⋊C4—24no—
150C3×C22⋊C4—22no—
151C3×C22⋊C4—22no—
152C3×C22⋊C4—42no—
153C3×C22⋊C4—41no—
154C3×C22⋊C4—41no—
155C3×C22⋊C4—122no—
156C3×C22⋊C4—121no—
157#217—42no—
158#217—41no—
159#208—22no—
160#208—41no—
161C2×C3⋊C8—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—41no—
173C22×C32—41no—
174C22×C32—42no—
175C22×C32—41no—
176C22×C32—41no—
177C22×C32—81no—
178C22×C32#9511yescharacteristic
179C22×C32#9911yescharacteristic
180C22×C32#9911yescharacteristic
181C32×C4—21no—
182C32×C4—21no—
183C32×C4—82no—
184C3×Dic3—42no—
185C3×Dic3—81no—
186C22×D4C2×C3×D311yescharacteristic
187C23×C4—31no—
188C2×M16—61no—
189C2×C22⋊C4—21no—
190C2×C22⋊C4—31no—
191C2×C22⋊C4—61no—
192#100—32no—
193#100—61no—
194#99—21no—
195#99C3×Dic312yescomplemented
196#95—61no—
197C23×C3—22no—
198C23×C3—22no—
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—21no—
211C23×C3—21no—
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×C3Dic3⋊C411yescharacteristic
229C23×C3(C2×D3)⋊C411yescharacteristic
230C23×C3#21711yescharacteristic
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—21no—
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—41no—
255C2×C3×C4—41no—
256C2×C3×C4—44no—
257C2×C3×C4—42no—
258C2×C3×C4—42no—
259C2×C3×C4—62no—
260C2×C3×C4—82no—
261C2×C3×C4—82no—
262C2×C3×C4—81no—
263C2×C3×C4—81no—
264C2×C3×C4—81no—
265C2×C3×C4—81no—
266C2×C3×C4—121no—
267C2×C3×C4—122no—
268C2×C3×C4—121no—
269C2×C3×C4—122no—
270C2×C3×C4—121no—
271C2×C3×C4—121no—
272C2×C3×C4—121no—
273C2×C3×C4C4⋊Dic311yescharacteristic
274C2×C3×C4(C2×D3)⋊C411yescharacteristic
275C2×C3×C4C3×C22⋊C411yescharacteristic
276C2×C3×C4C3×C4⋊C411yescharacteristic
277C2×Dic3—22no—
278C2×Dic3—41no—
279C2×Dic3—42no—
280C2×Dic3—41no—
281C2×Dic3—42no—
282C2×Dic3—41no—
283C2×Dic3—41no—
284C2×Dic3—41no—
285C3×C8—122no—
286C3⋊C8—42no—
287C2×C32—21no—
288C2×C32—21no—
289C2×C32—41no—
290C2×C32—41no—
291C2×C32—41no—
292C2×C32—41no—
293C2×C32#34211yescharacteristic
294C2×C32AΣL(1,𝔽16)11yescharacteristic
295C2×C32#35211yescharacteristic
296C24C3×C4×D311yescharacteristic
297C24C3×#6711yescharacteristic
298C2×D4—41no—
299C2×D4—41no—
300C2×D4C3×Dic611yescharacteristic
301C2×D4C3×C4×D311yescharacteristic
302C2×D4C2×C3×Dic311yescharacteristic
303C2×D4C3×#6711yescharacteristic
304C22×C4—41no—
305C22×C4—61no—
306C22×C4—61no—
307C22×C4—122no—
308C22×C4—121no—
309C22×C4C3×D1211yescharacteristic
310M16—62no—
311M16—121no—
312C2×C8—121no—
313C22⋊C4—22no—
314C22⋊C4—41no—
315C22⋊C4—122no—
316C22⋊C4—121no—
317C22×C3—21no—
318C22×C3—21no—
319C22×C3—21no—
320C22×C3—21no—
321C22×C3—22no—
322C22×C3—22no—
323C22×C3—21no—
324C22×C3—21no—
325C22×C3—21no—
326C22×C3—21no—
327C22×C3—21no—
328C22×C3—21no—
329C22×C3—21no—
330C22×C3—21no—
331C22×C3—21no—
332C22×C3—21no—
333C22×C3—21no—
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—41no—
345C22×C3—41no—
346C22×C3—42no—
347C22×C3—42no—
348C22×C3—42no—
349C22×C3—42no—
350C22×C3—41no—
351C22×C3—41no—
352C22×C3—41no—
353C22×C3—41no—
354C22×C3—41no—
355C22×C3—41no—
356C22×C3—41no—
357C22×C3—41no—
358C22×C3—81no—
359C22×C3—81no—
360C22×C3—81no—
361C22×C3—81no—
362C22×C3—81no—
363C22×C3—81no—
364C22×C3—82no—
365C22×C3—81no—
366C22×C3—81no—
367C22×C3—82no—
368C22×C3#80611yescharacteristic
369C22×C3#80611yescharacteristic
370C22×C3C3⋊#9511yescharacteristic
371C22×C3C3×#9511yescharacteristic
372C22×C3C3×#9911yescharacteristic
373C22×C3C3×#9911yescharacteristic
374C3×C4—21no—
375C3×C4—21no—
376C3×C4—21no—
377C3×C4—21no—
378C3×C4—41no—
379C3×C4—41no—
380C3×C4—84no—
381C3×C4—82no—
382C3×C4—82no—
383C3×C4—122no—
384C3×C4—241no—
385Dic3—42no—
386Dic3—81no—
387C32#139011yescharacteristic, complemented, Sylow
388C23—21no—
389C23—21no—
390C23—21no—
391C23—21no—
392C23—41no—
393C23—41no—
394C23—41no—
395C23—41no—
396C23C3×C4×Dic311yescharacteristic
397C23C3×Dic3⋊C411yescharacteristic
398C23C3×Dic3⋊C411yescharacteristic
399C23C3×(C2×D3)⋊C411yescharacteristic
400C23C3×#21711yescharacteristic
401D4—41no—
402D4—41no—
403D4—41no—
404D4—41no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—42no—
408C2×C4—62no—
409C2×C4—81no—
410C2×C4—81no—
411C2×C4—121no—
412C2×C4—122no—
413C2×C4—121no—
414C2×C4—122no—
415C2×C4—121no—
416C2×C4—121no—
417C2×C4—121no—
418C2×C4C3×C4⋊Dic311yescharacteristic
419C2×C4C3×(C2×D3)⋊C411yescharacteristic
420C8—122no—
421C2×C3—21no—
422C2×C3—21no—
423C2×C3—21no—
424C2×C3—21no—
425C2×C3—21no—
426C2×C3—21no—
427C2×C3—21no—
428C2×C3—41no—
429C2×C3—41no—
430C2×C3—42no—
431C2×C3—42no—
432C2×C3—41no—
433C2×C3—41no—
434C2×C3—41no—
435C2×C3—41no—
436C2×C3—41no—
437C2×C3—41no—
438C2×C3—41no—
439C2×C3—41no—
440C2×C3—81no—
441C2×C3—81no—
442C2×C3#447111yescharacteristic
443C2×C3#447211yescharacteristic
444C2×C3#452711yescharacteristic
445C2×C3C3×#34211yescharacteristic
446C2×C3C3×AΣL(1,𝔽16)11yescharacteristic
447C2×C3C3×#35211yescharacteristic
448C22—21no—
449C22—21no—
450C22—21no—
451C22—21no—
452C22—21no—
453C22—21no—
454C22—41no—
455C22—41no—
456C22—41no—
457C22—41no—
458C22—42no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—81no—
464C22C3×#80611yescharacteristic
465C22C3×#80611yescharacteristic
466C22C3×C3⋊#9511yescharacteristic
467C4—21no—
468C4—21no—
469C4—82no—
470C4—122no—
471C4—241no—
472C3—21no—
473C3#6769411yescharacteristic, direct product factor
474C3C3×#139011yescharacteristic, complemented
475C2—21no—
476C2—21no—
477C2—41no—
478C2—41no—
479C2—41no—
480C2—41no—
481C2C3×#447111yescharacteristic
482C2C3×#447211yescharacteristic
483C2C3×#452711yescharacteristic
subgroupG/H
centerC22×C3#806
commutatorC23×C3C3×C42
FrattiniC22×D4C2×C3×D3
FittingC2×C32×#99C2
socleC22×C32#99
prime radicalC22×C32×D4C22
cosocleC22×C3×D4C22×C3
hypercenterC2×C3×#99D3
hypocenterC3C3×#1390
LCSG ▷ C23×C3 ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C23×C3 ◁ C22×C3×D4 ◁ C2×C3×#99

Complements

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

NH ≅ G/Ntype
5. #67694C3direct (N × H)
7. C23×C3×Dic3C4semidirect
10. C2×C3×#217C4semidirect
13. C32×#99C4semidirect
15. C3×#833C4semidirect
50. C23×Dic3C3×C4semidirect
58. C2×#217C3×C4semidirect
66. C3×#99Dic3semidirect
67. C3×#99C3×C4semidirect
70. #833C3×C4semidirect
195. #99C3×Dic3semidirect
387. C32#1390semidirect
473. C3#67694direct (N × H)
474. C3C3×#1390semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#992
C3×#52202
C2×C3×#8332
C3×#13903
#676943