Finite Group Databasebeta

← C3×#68101 #11773804

Subgroups — C3×#68101 #11773804

Order 1152.

673 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#67⋊C4C211yesmaximal, characteristic
2C3×#4718C212yesmaximal, complemented
3C32×#323C211yesmaximal, characteristic, complemented
4C3×#4525C211yesmaximal, characteristic, complemented
5C3×#4468C212yesmaximal, complemented
6C3×#1460—31nomaximal
7#68101C311yesmaximal, characteristic, direct product factor
8C22×C3×#67C411yescharacteristic
9C23×C3×Dic3C411yescharacteristic
10C22×C3×C4×D3C411yescharacteristic
11C2×C32×C22⋊C4C2211yescharacteristic
12C2×C3×(C2×D3)⋊C4C2211yescharacteristic
13C2×C3×Dic3⋊C4C411yescharacteristic
14C2×C3×C4×Dic3C2211yescharacteristic
15C3×#67⋊C4—22no—
16C3×#67⋊C4—22no—
17C32×C22⋊C8C2212yes—
18C3×#830C2212yes—
19C3×Dic3⋊C8—22no—
20C3×C8×Dic3—22no—
21C2×C3×C4×D4—31no—
22C2×#67⋊C4C2×C311yescharacteristic
23C3×#431—32no—
24#4718C2×C312yescomplemented
25C3×#323—21no—
26C3×#323—31no—
27C3×#323—32no—
28C3×#323D311yescharacteristic, complemented
29C3×#323C2×C311yescharacteristic, complemented
30#4525C2×C311yescharacteristic, complemented
31#4468C2×C312yescomplemented
32C24×C32C2×C411yescharacteristic
33C23×C3×D3C2×C411yescharacteristic
34C22×C32×C4C2×C411yescharacteristic
35C22×C32×C4C2311yescharacteristic
36C2×C3×#67—22no—
37C2×C3×#67—22no—
38C2×C3×#67C814yescomplemented
39C22×C3×Dic3—21no—
40C22×C3×Dic3—21no—
41C22×C3×Dic3—42no—
42C22×C3×Dic3C2×C411yescharacteristic
43C22×C3×Dic3C2×C411yescharacteristic
44C22×C3×Dic3C2×C411yescharacteristic
45C2×C3×C4×D3—21no—
46C2×C3×C4×D3—21no—
47C2×C3×C4×D3—42no—
48C2×C32×C8—22no—
49C32×C22⋊C4—22no—
50C3×(C2×D3)⋊C4—22no—
51C3×Dic3⋊C4—22no—
52C3×C4×Dic3D412yes—
53C3×C4×Dic3D412yes—
54C2×C3×C3⋊C8—22no—
55#1460—31noSylow
56C22×C3×D4—31no—
57C23×C3×C4—31no—
58C23×C3×C4—31no—
59C22×#67C3×C411yescharacteristic
60C23×Dic3C3×C411yescharacteristic
61C22×C4×D3C3×C411yescharacteristic
62C3×C4×D4—62no—
63C3×C4×D4—62no—
64C2×C3×C4⋊C4—31no—
65C2×C3×C22⋊C4—21no—
66C2×C3×C22⋊C4—31no—
67C2×C3×C22⋊C4C2×D311yescharacteristic
68C2×C3×C22⋊C4C22×C311yescharacteristic
69C2×C3×C42—31no—
70C2×(C2×D3)⋊C4C22×C311yescharacteristic
71C2×Dic3⋊C4C3×C411yescharacteristic
72C2×C4×Dic3C22×C311yescharacteristic
73#67⋊C4—22no—
74#67⋊C4—22no—
75C3×C4⋊C8—62no—
76C3×C22⋊C8—22no—
77C3×C22⋊C8—32no—
78C3×C22⋊C8C2×D312yes—
79C3×C22⋊C8C22×C312yes—
80C3×C4×C8—62no—
81#830C22×C312yes—
82Dic3⋊C8—22no—
83C8×Dic3—22no—
84C23×C32—21no—
85C23×C32—21no—
86C23×C32—41no—
87C23×C32—41no—
88C23×C32C2×C812yes—
89C23×C32C22×C411yescharacteristic
90C22×C3×D3—21no—
91C22×C3×D3—21no—
92C22×C3×D3—41no—
93C22×C3×D3—41no—
94C22×C3×D3C2×C812yes—
95C2×C32×C4—21no—
96C2×C32×C4—41no—
97C2×C32×C4—41no—
98C2×C32×C4C2×D412yes—
99C3×#67—28no—
100C2×C3×Dic3—22no—
101C2×C3×Dic3—21no—
102C2×C3×Dic3—42no—
103C2×C3×Dic3—42no—
104C2×C3×Dic3—41no—
105C2×C3×Dic3C22⋊C411yescharacteristic
106C2×C3×Dic3C22⋊C412yes—
107C2×C3×Dic3C22⋊C411yescharacteristic
108C2×C3×Dic3C2×C812yes—
109C2×C3×Dic3M1612yes—
110C3×C4×D3—42no—
111C3×C4×D3—42no—
112C32×C8—42no—
113C3×C3⋊C8—42no—
114C2×C4×D4—31no—
115#431—32no—
116#323—31no—
117#323—32no—
118#323C3×D311yescharacteristic, complemented
119C24×C3—21no—
120C24×C3—31no—
121C24×C3C4×D311yescharacteristic
122C24×C3C2×C3×C411yescharacteristic
123C23×D3C2×C3×C411yescharacteristic
124C2×C3×D4—34no—
125C2×C3×D4—62no—
126C2×C3×D4—62no—
127C22×C3×C4—21no—
128C22×C3×C4—21no—
129C22×C3×C4—31no—
130C22×C3×C4—31no—
131C22×C3×C4—31no—
132C22×C3×C4—61no—
133C22×C3×C4—61no—
134C22×C3×C4—61no—
135C22×C3×C4—61no—
136C22×C3×C4—122no—
137C22×C3×C4—122no—
138C22×C3×C4C4×D311yescharacteristic
139C22×C3×C4C2×C3×C411yescharacteristic
140C22×C3×C4C22×D311yescharacteristic
141C22×C3×C4C23×C311yescharacteristic
142C2×#67—22no—
143C2×#67—22no—
144C2×#67C3×C814yescomplemented
145C22×Dic3—21no—
146C22×Dic3—21no—
147C22×Dic3—42no—
148C22×Dic3C2×C3×C411yescharacteristic
149C22×Dic3C2×C3×C411yescharacteristic
150C22×Dic3C2×C3×C411yescharacteristic
151C2×C4×D3—21no—
152C2×C4×D3—21no—
153C2×C4×D3—42no—
154C2×C3×C8—22no—
155C2×C3×C8—22no—
156C2×C3×C8—42no—
157C2×C3×C8—62no—
158C3×C4⋊C4—62no—
159C3×C22⋊C4—22no—
160C3×C22⋊C4—22no—
161C3×C22⋊C4—42no—
162C3×C22⋊C4—62no—
163C3×C42—32no—
164C3×C42—32no—
165(C2×D3)⋊C4—22no—
166Dic3⋊C4—22no—
167C4×Dic3C3×D412yes—
168C4×Dic3C3×D412yes—
169C2×C3⋊C8—22no—
170C22×C32—21no—
171C22×C32—21no—
172C22×C32—22no—
173C22×C32—42no—
174C22×C32—42no—
175C22×C32—41no—
176C22×C32—41no—
177C22×C32C2×C22⋊C411yescharacteristic
178C22×C32C22×C811yescharacteristic
179C22×C32C2×M1611yescharacteristic
180C2×C3×D3—22no—
181C2×C3×D3—42no—
182C2×C3×D3—41no—
183C2×C3×D3—41no—
184C2×C3×D3—42no—
185C32×C4—22no—
186C32×C4—41no—
187C3×Dic3—21no—
188C3×Dic3—41no—
189C3×Dic3C22⋊C814yes—
190C3×Dic3#10012yes—
191C22×D4—31no—
192C23×C4—31no—
193C23×C4—31no—
194C4×D4—62no—
195C4×D4—62no—
196C2×C4⋊C4—31no—
197C2×C22⋊C4—31no—
198C2×C22⋊C4C2×C3×D311yescharacteristic
199C2×C42—31no—
200C4⋊C8—62no—
201C22⋊C8—32no—
202C22⋊C8C2×C3×D312yes—
203C4×C8—62no—
204C23×C3—21no—
205C23×C3—21no—
206C23×C3—21no—
207C23×C3—21no—
208C23×C3—22no—
209C23×C3—21no—
210C23×C3—32no—
211C23×C3—41no—
212C23×C3—41no—
213C23×C3—41no—
214C23×C3—41no—
215C23×C3—41no—
216C23×C3—41no—
217C23×C3—61no—
218C23×C3—61no—
219C23×C3—81no—
220C23×C3—81no—
221C23×C3—121no—
222C23×C3—121no—
223C23×C3D3×C812yes—
224C23×C3C2×C3×C812yes—
225C23×C3C2×C4×D311yescharacteristic
226C23×C3C22×C3×C411yescharacteristic
227C22×D3—21no—
228C22×D3—21no—
229C22×D3—41no—
230C22×D3—41no—
231C22×D3C2×C3×C812yes—
232C3×D4—68no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—22no—
236C2×C3×C4—32no—
237C2×C3×C4—31no—
238C2×C3×C4—32no—
239C2×C3×C4—32no—
240C2×C3×C4—31no—
241C2×C3×C4—41no—
242C2×C3×C4—41no—
243C2×C3×C4—41no—
244C2×C3×C4—41no—
245C2×C3×C4—41no—
246C2×C3×C4—62no—
247C2×C3×C4—61no—
248C2×C3×C4—81no—
249C2×C3×C4—81no—
250C2×C3×C4—122no—
251C2×C3×C4—122no—
252C2×C3×C4—122no—
253C2×C3×C4—122no—
254C2×C3×C4—121no—
255C2×C3×C4D3×D412yes—
256C2×C3×C4C2×C3×D412yes—
257#67—28no—
258C2×Dic3—22no—
259C2×Dic3—21no—
260C2×Dic3—42no—
261C2×Dic3—42no—
262C2×Dic3—41no—
263C2×Dic3C3×C22⋊C411yescharacteristic
264C2×Dic3C3×C22⋊C412yes—
265C2×Dic3C3×C22⋊C411yescharacteristic
266C2×Dic3C2×C3×C812yes—
267C2×Dic3C3×M1612yes—
268C4×D3—42no—
269C4×D3—42no—
270C3×C8—42no—
271C3×C8—42no—
272C3×C8—82no—
273C3×C8—122no—
274C3⋊C8—42no—
275C2×C32—21no—
276C2×C32—21no—
277C2×C32—42no—
278C2×C32C2×C22⋊C811yescharacteristic
279C2×C32#41011yescharacteristic
280C2×C32C2×#10011yescharacteristic
281C3×D3—42no—
282C24—31no—
283C24C3×C4×D311yescharacteristic
284C2×D4—34no—
285C2×D4—62no—
286C2×D4—62no—
287C22×C4—31no—
288C22×C4—31no—
289C22×C4—31no—
290C22×C4—61no—
291C22×C4—61no—
292C22×C4—61no—
293C22×C4—61no—
294C22×C4—122no—
295C22×C4—122no—
296C22×C4C3×C4×D311yescharacteristic
297C22×C4C22×C3×D311yescharacteristic
298C2×C8—22no—
299C2×C8—62no—
300C4⋊C4—62no—
301C22⋊C4—22no—
302C22⋊C4—62no—
303C42—32no—
304C42—32no—
305C22×C3—21no—
306C22×C3—21no—
307C22×C3—21no—
308C22×C3—21no—
309C22×C3—22no—
310C22×C3—22no—
311C22×C3—21no—
312C22×C3—21no—
313C22×C3—21no—
314C22×C3—41no—
315C22×C3—41no—
316C22×C3—42no—
317C22×C3—42no—
318C22×C3—42no—
319C22×C3—42no—
320C22×C3—42no—
321C22×C3—41no—
322C22×C3—41no—
323C22×C3—41no—
324C22×C3—41no—
325C22×C3—62no—
326C22×C3—81no—
327C22×C3—81no—
328C22×C3—82no—
329C22×C3—82no—
330C22×C3—122no—
331C22×C3—122no—
332C22×C3—121no—
333C22×C3—121no—
334C22×C3D3×C22⋊C411yescharacteristic
335C22×C3C2×D3×C811yescharacteristic
336C22×C3D3×M1611yescharacteristic
337C22×C3C2×C3×C22⋊C411yescharacteristic
338C22×C3C22×C3×C811yescharacteristic
339C22×C3C2×C3×M1611yescharacteristic
340C2×D3—22no—
341C2×D3—42no—
342C2×D3—41no—
343C2×D3—41no—
344C2×D3—42no—
345C3×C4—22no—
346C3×C4—22no—
347C3×C4—34no—
348C3×C4—32no—
349C3×C4—42no—
350C3×C4—41no—
351C3×C4—41no—
352C3×C4—61no—
353C3×C4—81no—
354C3×C4—121no—
355Dic3—21no—
356Dic3—41no—
357Dic3C3×C22⋊C814yes—
358Dic3C3×#10012yes—
359C32#146011yescharacteristic, complemented, Sylow
360C23—21no—
361C23—21no—
362C23—32no—
363C23—41no—
364C23—41no—
365C23—61no—
366C23—61no—
367C23—121no—
368C23—121no—
369C23C3×D3×C812yes—
370C23C2×C3×C4×D311yescharacteristic
371D4—68no—
372C2×C4—21no—
373C2×C4—32no—
374C2×C4—31no—
375C2×C4—32no—
376C2×C4—32no—
377C2×C4—31no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—62no—
381C2×C4—61no—
382C2×C4—122no—
383C2×C4—122no—
384C2×C4—122no—
385C2×C4—122no—
386C2×C4—121no—
387C2×C4C3×D3×D412yes—
388C8—42no—
389C8—122no—
390C2×C3—21no—
391C2×C3—21no—
392C2×C3—21no—
393C2×C3—21no—
394C2×C3—21no—
395C2×C3—21no—
396C2×C3—21no—
397C2×C3—41no—
398C2×C3—41no—
399C2×C3—42no—
400C2×C3—42no—
401C2×C3—82no—
402C2×C3—122no—
403C2×C3D3×C22⋊C811yescharacteristic
404C2×C3#474011yescharacteristic
405C2×C3D3×#10011yescharacteristic
406C2×C3C2×C3×C22⋊C811yescharacteristic
407C2×C3C3×#41011yescharacteristic
408C2×C3C2×C3×#10011yescharacteristic
409D3—42no—
410C22—21no—
411C22—21no—
412C22—22no—
413C22—42no—
414C22—42no—
415C22—41no—
416C22—41no—
417C22—62no—
418C22—122no—
419C22—122no—
420C22—121no—
421C22—121no—
422C22C3×D3×C22⋊C411yescharacteristic
423C22C2×C3×D3×C811yescharacteristic
424C22C3×D3×M1611yescharacteristic
425C4—22no—
426C4—34no—
427C4—32no—
428C4—41no—
429C4—61no—
430C4—121no—
431C3—21no—
432C3#6810111yescharacteristic, direct product factor
433C3C3×#146011yescharacteristic, complemented
434C2—21no—
435C2—21no—
436C2—42no—
437C2—122no—
438C2C3×D3×C22⋊C811yescharacteristic
439C2C3×#474011yescharacteristic
440C2C3×D3×#10011yescharacteristic
subgroupG/H
centerC22×C3D3×C22⋊C4
commutatorC22×C3C22×C3×C8
FrattiniC22×C4C22×C3×D3
FittingC32×#323C2
socleC22×C32C2×C22⋊C4
prime radicalC22×C3×#67C4
cosocleC22×C3×C4C23×C3
hypercenterC3×#323D3
hypocenterC3C3×#1460
LCSG ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#323

Complements

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

NH ≅ G/Ntype
2. C3×#4718C2semidirect
3. C32×#323C2semidirect
4. C3×#4525C2semidirect
5. C3×#4468C2semidirect
7. #68101C3direct (N × H)
24. #4718C2×C3semidirect
28. C3×#323D3semidirect
29. C3×#323C2×C3semidirect
30. #4525C2×C3semidirect
31. #4468C2×C3semidirect
38. C2×C3×#67C8semidirect
118. #323C3×D3semidirect
144. C2×#67C3×C8semidirect
359. C32#1460semidirect
432. C3#68101direct (N × H)
433. C3C3×#1460semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#67⋊C42
C3×#47182
C32×#3232
C3×#45252
C3×#44682
C3×#14603
#681013