Finite Group Databasebeta

← C3×#67695 #11772597

Subgroups — C3×#67695 #11772597

Order 1152.

569 conjugacy classes of subgroups.

The subgroup lattice has 489 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#99C211yesmaximal, characteristic
2C3×#5221C211yesmaximal, characteristic
3C2×C3×#834C211yesmaximal, characteristic
4C3×#1393—31nomaximal
5#67695C311yesmaximal, characteristic, direct product factor
6C22×C32×D4C2211yescharacteristic
7C2×C32×C22⋊C4—21no—
8C2×C3×#217—21no—
9C2×C3×#217—21no—
10C2×C3×#217—21no—
11C2×C3×C4⋊Dic3C411yescharacteristic, complemented
12C2×C3×C4×Dic3C411yescharacteristic, complemented
13C32×#99—21no—
14C32×#99C412yescomplemented
15C3×#834—21no—
16C3×#834C412yescomplemented
17C2×C3×#99—21no—
18C2×C3×#99—31no—
19C2×C3×#99D311yescharacteristic
20C2×C3×#99C2×C311yescharacteristic
21C3×#390—31no—
22#5221C2×C311yescharacteristic
23C2×#834C2×C311yescharacteristic
24C24×C32D411yescharacteristic
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×C4C2×C411yescharacteristic
34C22×C3×Dic3—21no—
35C22×C3×Dic3—21no—
36C22×C3×Dic3—41no—
37C32×C22⋊C4—22no—
38C32×C22⋊C4—41no—
39C3×#217—22no—
40C3×#217—42no—
41C3×#217—42no—
42C3×#217—41no—
43C3×C4⋊Dic3—41no—
44C3×C4×Dic3—41no—
45#1393—31noSylow
46C22×C3×D4—21no—
47C22×C3×D4C2×D311yescharacteristic
48C22×C3×D4C22×C311yescharacteristic
49C2×C3×C4⋊C4—31no—
50C2×C3×C22⋊C4—22no—
51C2×C3×C22⋊C4—21no—
52C2×C3×C22⋊C4—21no—
53C2×C3×C22⋊C4—61no—
54C2×C3×C22⋊C4—61no—
55C2×C3×C22⋊C4—61no—
56C2×C3×C42—31no—
57C2×#217—21no—
58C2×#217—21no—
59C2×#217—21no—
60C2×C4⋊Dic3C3×C411yescharacteristic, complemented
61C2×C4×Dic3C3×C411yescharacteristic, complemented
62C3×#99—22no—
63C3×#99—21no—
64C3×#99—21no—
65C3×#99—22no—
66C3×#99—32no—
67C3×#99—61no—
68C3×#99Dic312yescomplemented
69C3×#99C3×C412yescomplemented
70#834—21no—
71#834C3×C412yescomplemented
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×C32C22⋊C411yescharacteristic
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×C4C4211yescharacteristic
95C2×C32×C4C4⋊C411yescharacteristic
96C2×C3×Dic3—22no—
97C2×C3×Dic3—41no—
98C2×C3×Dic3—41no—
99C2×C3×Dic3—42no—
100C2×C3×Dic3—41no—
101C2×C3×Dic3—41no—
102C2×C3×Dic3—41no—
103C2×C3×Dic3—81no—
104C2×C3×Dic3—81no—
105C2×#99—31no—
106C2×#99C3×D311yescharacteristic
107#390—31no—
108C24×C3—21no—
109C24×C3—21no—
110C24×C3D1211yescharacteristic
111C24×C3#6711yescharacteristic
112C24×C3C3×D411yescharacteristic
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—121no—
139C22×C3×C4C4×D311yescharacteristic
140C22×C3×C4C2×C3×C411yescharacteristic
141C22×Dic3—21no—
142C22×Dic3—21no—
143C22×Dic3—41no—
144C3×C4⋊C4—121no—
145C3×C22⋊C4—24no—
146C3×C22⋊C4—22no—
147C3×C22⋊C4—22no—
148C3×C22⋊C4—42no—
149C3×C22⋊C4—41no—
150C3×C22⋊C4—41no—
151C3×C22⋊C4—62no—
152C3×C22⋊C4—122no—
153C3×C22⋊C4—122no—
154C3×C22⋊C4—121no—
155C3×C42—121no—
156#217—22no—
157#217—42no—
158#217—42no—
159#217—41no—
160C4⋊Dic3—41no—
161C4×Dic3—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—41no—
175C22×C32—41no—
176C22×C32—81no—
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—82no—
186C3×Dic3—81no—
187C22×D4C2×C3×D311yescharacteristic
188C2×C4⋊C4—31no—
189C2×C22⋊C4—21no—
190C2×C22⋊C4—61no—
191C2×C22⋊C4—61no—
192C2×C22⋊C4—61no—
193C2×C42—31no—
194#99—21no—
195#99—32no—
196#99—61no—
197#99C3×Dic312yescomplemented
198C23×C3—22no—
199C23×C3—22no—
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—21no—
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—41no—
223C23×C3—81no—
224C23×C3—81no—
225C23×C3—81no—
226C23×C3—81no—
227C23×C3Dic3⋊C411yescharacteristic
228C23×C3C4⋊Dic311yescharacteristic
229C23×C3(C2×D3)⋊C411yescharacteristic
230C23×C3(C2×D3)⋊C411yescharacteristic
231C23×C3#21711yescharacteristic
232C23×C3C3×C22⋊C411yescharacteristic
233C23×C3C3×C22⋊C411yescharacteristic
234C23×C3C3×C22⋊C411yescharacteristic
235C23×C3C3×C4⋊C411yescharacteristic
236C23×C3C3×C4⋊C411yescharacteristic
237C3×D4—41no—
238C3×D4—41no—
239C3×D4—41no—
240C3×D4—41no—
241C3×D4—41no—
242C3×D4—41no—
243C3×D4—41no—
244C3×D4—41no—
245C3×D4—42no—
246C3×D4—42no—
247C3×D4—42no—
248C3×D4—42no—
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—41no—
256C2×C3×C4—41no—
257C2×C3×C4—44no—
258C2×C3×C4—42no—
259C2×C3×C4—42no—
260C2×C3×C4—62no—
261C2×C3×C4—82no—
262C2×C3×C4—82no—
263C2×C3×C4—81no—
264C2×C3×C4—81no—
265C2×C3×C4—81no—
266C2×C3×C4—81no—
267C2×C3×C4—121no—
268C2×C3×C4—121no—
269C2×C3×C4—122no—
270C2×C3×C4—121no—
271C2×C3×C4—121no—
272C2×C3×C4—121no—
273C2×C3×C4—241no—
274C2×C3×C4—241no—
275C2×C3×C4C4×Dic311yescharacteristic
276C2×C3×C4Dic3⋊C411yescharacteristic
277C2×C3×C4C3×C4211yescharacteristic
278C2×C3×C4C3×C4⋊C411yescharacteristic
279C2×Dic3—22no—
280C2×Dic3—41no—
281C2×Dic3—41no—
282C2×Dic3—42no—
283C2×Dic3—41no—
284C2×Dic3—41no—
285C2×Dic3—41no—
286C2×Dic3—81no—
287C2×Dic3—81no—
288C2×C32—21no—
289C2×C32—21no—
290C2×C32—41no—
291C2×C32—41no—
292C2×C32—41no—
293C2×C32—41no—
294C2×C32#34211yescharacteristic
295C2×C32#35311yescharacteristic
296C2×C32#35411yescharacteristic
297C24C3×D1211yescharacteristic
298C24C3×#6711yescharacteristic
299C2×D4—41no—
300C2×D4—41no—
301C2×D4C3×Dic611yescharacteristic
302C2×D4C3×C4×D311yescharacteristic
303C2×D4C2×C3×Dic311yescharacteristic
304C2×D4C3×#6711yescharacteristic
305C22×C4—41no—
306C22×C4—61no—
307C22×C4—61no—
308C22×C4—121no—
309C22×C4C3×C4×D311yescharacteristic
310C4⋊C4—121no—
311C22⋊C4—22no—
312C22⋊C4—41no—
313C22⋊C4—62no—
314C22⋊C4—122no—
315C22⋊C4—122no—
316C22⋊C4—121no—
317C42—121no—
318C22×C3—21no—
319C22×C3—21no—
320C22×C3—21no—
321C22×C3—21no—
322C22×C3—22no—
323C22×C3—22no—
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—21no—
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—41no—
347C22×C3—42no—
348C22×C3—42no—
349C22×C3—41no—
350C22×C3—41no—
351C22×C3—41no—
352C22×C3—41no—
353C22×C3—41no—
354C22×C3—41no—
355C22×C3—41no—
356C22×C3—41no—
357C22×C3—81no—
358C22×C3—81no—
359C22×C3—81no—
360C22×C3—81no—
361C22×C3—81no—
362C22×C3—81no—
363C22×C3—81no—
364C22×C3—81no—
365C22×C3—81no—
366C22×C3—81no—
367C22×C3—82no—
368C22×C3—82no—
369C22×C3#80611yescharacteristic
370C22×C3#80611yescharacteristic
371C22×C3C3⋊#9511yescharacteristic
372C22×C3C3×#9511yescharacteristic
373C22×C3C3×#9911yescharacteristic
374C22×C3C3×#9911yescharacteristic
375C3×C4—21no—
376C3×C4—21no—
377C3×C4—21no—
378C3×C4—21no—
379C3×C4—41no—
380C3×C4—41no—
381C3×C4—84no—
382C3×C4—82no—
383C3×C4—82no—
384C3×C4—122no—
385C3×C4—242no—
386C3×C4—241no—
387Dic3—42no—
388Dic3—82no—
389Dic3—81no—
390C32#139311yescharacteristic, complemented, Sylow
391C23—21no—
392C23—21no—
393C23—21no—
394C23—21no—
395C23—41no—
396C23—41no—
397C23—41no—
398C23—41no—
399C23C3×Dic3⋊C411yescharacteristic
400C23C3×C4⋊Dic311yescharacteristic
401C23C3×(C2×D3)⋊C411yescharacteristic
402C23C3×(C2×D3)⋊C411yescharacteristic
403C23C3×#21711yescharacteristic
404D4—41no—
405D4—41no—
406D4—41no—
407D4—41no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—42no—
411C2×C4—62no—
412C2×C4—81no—
413C2×C4—81no—
414C2×C4—121no—
415C2×C4—121no—
416C2×C4—122no—
417C2×C4—121no—
418C2×C4—121no—
419C2×C4—121no—
420C2×C4—241no—
421C2×C4—241no—
422C2×C4C3×C4×Dic311yescharacteristic
423C2×C4C3×Dic3⋊C411yescharacteristic
424C2×C3—21no—
425C2×C3—21no—
426C2×C3—21no—
427C2×C3—21no—
428C2×C3—21no—
429C2×C3—21no—
430C2×C3—21no—
431C2×C3—41no—
432C2×C3—41no—
433C2×C3—42no—
434C2×C3—42no—
435C2×C3—41no—
436C2×C3—41no—
437C2×C3—41no—
438C2×C3—41no—
439C2×C3—41no—
440C2×C3—41no—
441C2×C3—41no—
442C2×C3—41no—
443C2×C3—81no—
444C2×C3—81no—
445C2×C3#447311yescharacteristic
446C2×C3#447411yescharacteristic
447C2×C3#452711yescharacteristic
448C2×C3C3×#34211yescharacteristic
449C2×C3C3×#35311yescharacteristic
450C2×C3C3×#35411yescharacteristic
451C22—21no—
452C22—21no—
453C22—21no—
454C22—21no—
455C22—21no—
456C22—21no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—41no—
465C22—81no—
466C22—81no—
467C22C3×#80611yescharacteristic
468C22C3×#80611yescharacteristic
469C22C3×C3⋊#9511yescharacteristic
470C4—21no—
471C4—21no—
472C4—82no—
473C4—122no—
474C4—242no—
475C4—241no—
476C3—21no—
477C3#6769511yescharacteristic, direct product factor
478C3C3×#139311yescharacteristic, complemented
479C2—21no—
480C2—21no—
481C2—41no—
482C2—41no—
483C2—41no—
484C2—41no—
485C2C3×#447311yescharacteristic
486C2C3×#447411yescharacteristic
487C2C3×#452711yescharacteristic
subgroupG/H
centerC22×C3#806
commutatorC2×C3×C4C3×C42
FrattiniC22×D4C2×C3×D3
FittingC2×C32×#99C2
socleC22×C32#99
prime radicalC22×C32×D4C22
cosocleC22×C3×D4C22×C3
hypercenterC2×C3×#99D3
hypocenterC3C3×#1393
LCSG ▷ C2×C3×C4 ▷ 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. #67695C3direct (N × H)
11. C2×C3×C4⋊Dic3C4semidirect
12. C2×C3×C4×Dic3C4semidirect
14. C32×#99C4semidirect
16. C3×#834C4semidirect
60. C2×C4⋊Dic3C3×C4semidirect
61. C2×C4×Dic3C3×C4semidirect
68. C3×#99Dic3semidirect
69. C3×#99C3×C4semidirect
71. #834C3×C4semidirect
197. #99C3×Dic3semidirect
390. C32#1393semidirect
477. C3#67695direct (N × H)
478. C3C3×#1393semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#992
C3×#52212
C2×C3×#8342
C3×#13933
#676953