Finite Group Databasebeta

← C3×#2676 #84540

Subgroups — C3×#2676 #84540

Order 384.

676 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#124C211yesmaximal, characteristic, complemented
2C2×C3×C22⋊Q8C211yesmaximal, characteristic, complemented
3C2×C3×#121C211yesmaximal, characteristic, complemented
4C2×C3×#121C211yesmaximal, characteristic, complemented
5C3×#396C211yesmaximal, characteristic, complemented
6C3×#394C211yesmaximal, characteristic, complemented
7C3×#394C211yesmaximal, characteristic, complemented
8C3×#393C211yesmaximal, characteristic, complemented
9C3×#392C211yesmaximal, characteristic, complemented
10C3×#392C211yesmaximal, characteristic, complemented
11C3×#390C211yesmaximal, characteristic, complemented
12C3×#387C211yesmaximal, characteristic, complemented
13C3×#386C211yesmaximal, characteristic, complemented
14C3×#386C211yesmaximal, characteristic, complemented
15C3×#385C211yesmaximal, characteristic, complemented
16#2676C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×Q8C2211yescharacteristic
18C22×C3×D4C2211yescharacteristic
19C22×C3×D4C2211yescharacteristic
20C22×C3×D4C2211yescharacteristic
21C22×C3×D4C2211yescharacteristic
22C22×C3×D4C2211yescharacteristic
23C22×C3×D4C2211yescharacteristic
24C23×C3×C4C2211yescharacteristic
25C23×C3×C4C2211yescharacteristic
26C3×#124—24no—
27C3×C22⋊Q8—24no—
28C3×#121—24no—
29C3×#121—24no—
30C2×C3×C4⋊C4C2211yescharacteristic
31C2×C3×C4⋊C4C2211yescharacteristic
32C2×C3×C4⋊C4C2211yescharacteristic
33C2×C3×C4⋊C4C2211yescharacteristic
34C2×C3×C4⋊C4C2211yescharacteristic
35C2×C3×C22⋊C4C2211yescharacteristic
36C2×C3×C22⋊C4C2211yescharacteristic
37C2×C3×C22⋊C4C2211yescharacteristic
38C2×C3×C22⋊C4C2211yescharacteristic
39C2×C3×C22⋊C4C2211yescharacteristic
40C2×C3×C22⋊C4C2211yescharacteristic
41C2×C3×C22⋊C4C2211yescharacteristic
42C2×C3×C22⋊C4C2211yescharacteristic
43C2×C3×C22⋊C4C2211yescharacteristic
44C2×C3×C22⋊C4C2211yescharacteristic
45C2×C3×C22⋊C4C2211yescharacteristic
46C2×C3×C22⋊C4C2211yescharacteristic
47C2×C3×C22⋊C4C2211yescharacteristic
48C2×C3×C22⋊C4C2211yescharacteristic
49C2×C3×C42C2211yescharacteristic
50C3×#95C2211yescharacteristic
51C3×#95C2211yescharacteristic
52C3×#95C2211yescharacteristic
53C3×#95C2211yescharacteristic
54C3×#95C2211yescharacteristic
55C3×#95C2211yescharacteristic
56C2×#124C2×C311yescharacteristic, complemented
57C2×C22⋊Q8C2×C311yescharacteristic, complemented
58C2×#121C2×C311yescharacteristic, complemented
59C2×#121C2×C311yescharacteristic, complemented
60#396C2×C311yescharacteristic, complemented
61#394C2×C311yescharacteristic, complemented
62#394C2×C311yescharacteristic, complemented
63#393C2×C311yescharacteristic, complemented
64#392C2×C311yescharacteristic, complemented
65#392C2×C311yescharacteristic, complemented
66#390C2×C311yescharacteristic, complemented
67#387C2×C311yescharacteristic, complemented
68#386C2×C311yescharacteristic, complemented
69#386C2×C311yescharacteristic, complemented
70#385C2×C311yescharacteristic, complemented
71C24×C3C2311yescharacteristic
72C24×C3C2311yescharacteristic
73C24×C3C2311yescharacteristic
74C24×C3C2311yescharacteristic
75C2×C3×Q8—22no—
76C2×C3×Q8—22no—
77C2×C3×Q8—41no—
78C2×C3×D4—22no—
79C2×C3×D4—22no—
80C2×C3×D4—22no—
81C2×C3×D4—22no—
82C2×C3×D4—22no—
83C2×C3×D4—22no—
84C2×C3×D4—22no—
85C2×C3×D4—22no—
86C2×C3×D4—22no—
87C2×C3×D4—22no—
88C2×C3×D4—41no—
89C2×C3×D4—41no—
90C2×C3×D4—41no—
91C2×C3×D4—41no—
92C2×C3×D4—41no—
93C2×C3×D4—41no—
94C2×C3×D4—41no—
95C2×C3×D4—41no—
96C22×C3×C4—22no—
97C22×C3×C4—22no—
98C22×C3×C4—22no—
99C22×C3×C4—41no—
100C22×C3×C4—41no—
101C22×C3×C4—41no—
102C22×C3×C4C2311yescharacteristic
103C22×C3×C4C2311yescharacteristic
104C22×C3×C4C2311yescharacteristic
105C22×C3×C4C2311yescharacteristic
106C22×C3×C4C2311yescharacteristic
107C22×C3×C4C2311yescharacteristic
108C22×C3×C4C2311yescharacteristic
109C22×C3×C4C2311yescharacteristic
110C22×C3×C4C2311yescharacteristic
111C22×C3×C4C2311yescharacteristic
112C22×C3×C4C2311yescharacteristic
113C3×C4⋊C4—22no—
114C3×C4⋊C4—22no—
115C3×C4⋊C4—22no—
116C3×C4⋊C4—41no—
117C3×C4⋊C4D414yescomplemented
118C3×C22⋊C4—22no—
119C3×C22⋊C4—22no—
120C3×C22⋊C4—22no—
121C3×C22⋊C4—22no—
122C3×C22⋊C4—22no—
123C3×C22⋊C4—22no—
124C3×C22⋊C4—22no—
125C3×C22⋊C4—22no—
126C3×C22⋊C4—41no—
127C3×C22⋊C4—41no—
128C3×C22⋊C4—41no—
129C3×C22⋊C4—41no—
130C3×C22⋊C4—41no—
131C3×C22⋊C4D414yescomplemented
132C3×C42—22no—
133C22×Q8C22×C311yescharacteristic
134C22×D4C22×C311yescharacteristic
135C22×D4C22×C311yescharacteristic
136C22×D4C22×C311yescharacteristic
137C22×D4C22×C311yescharacteristic
138C22×D4C22×C311yescharacteristic
139C22×D4C22×C311yescharacteristic
140C23×C4C22×C311yescharacteristic
141C23×C4C22×C311yescharacteristic
142#124—24no—
143C22⋊Q8—24no—
144#121—24no—
145#121—24no—
146C2×C4⋊C4C22×C311yescharacteristic
147C2×C4⋊C4C22×C311yescharacteristic
148C2×C4⋊C4C22×C311yescharacteristic
149C2×C4⋊C4C22×C311yescharacteristic
150C2×C4⋊C4C22×C311yescharacteristic
151C2×C22⋊C4C22×C311yescharacteristic
152C2×C22⋊C4C22×C311yescharacteristic
153C2×C22⋊C4C22×C311yescharacteristic
154C2×C22⋊C4C22×C311yescharacteristic
155C2×C22⋊C4C22×C311yescharacteristic
156C2×C22⋊C4C22×C311yescharacteristic
157C2×C22⋊C4C22×C311yescharacteristic
158C2×C22⋊C4C22×C311yescharacteristic
159C2×C22⋊C4C22×C311yescharacteristic
160C2×C22⋊C4C22×C311yescharacteristic
161C2×C22⋊C4C22×C311yescharacteristic
162C2×C22⋊C4C22×C311yescharacteristic
163C2×C22⋊C4C22×C311yescharacteristic
164C2×C22⋊C4C22×C311yescharacteristic
165C2×C42C22×C311yescharacteristic
166#95C22×C311yescharacteristic
167#95C22×C311yescharacteristic
168#95C22×C311yescharacteristic
169#95C22×C311yescharacteristic
170#95C22×C311yescharacteristic
171#95C22×C311yescharacteristic
172C23×C3—21no—
173C23×C3—21no—
174C23×C3—21no—
175C23×C3—21no—
176C23×C3—21no—
177C23×C3—21no—
178C23×C3—21no—
179C23×C3—21no—
180C23×C3—21no—
181C23×C3—21no—
182C23×C3—21no—
183C23×C3—21no—
184C23×C3—21no—
185C23×C3—21no—
186C23×C3—21no—
187C23×C3—21no—
188C23×C3—21no—
189C23×C3—21no—
190C23×C3—21no—
191C23×C3—21no—
192C23×C3—21no—
193C23×C3—21no—
194C23×C3—21no—
195C23×C3—21no—
196C23×C3—21no—
197C23×C3—21no—
198C23×C3C2×D412yes—
199C23×C3#4112yes—
200C23×C3C2411yescharacteristic
201C3×Q8—44no—
202C3×D4—44no—
203C3×D4—44no—
204C3×D4—44no—
205C3×D4—44no—
206C3×D4—44no—
207C3×D4—44no—
208C2×C3×C4—21no—
209C2×C3×C4—21no—
210C2×C3×C4—21no—
211C2×C3×C4—21no—
212C2×C3×C4—21no—
213C2×C3×C4—21no—
214C2×C3×C4—21no—
215C2×C3×C4—21no—
216C2×C3×C4—21no—
217C2×C3×C4—21no—
218C2×C3×C4—21no—
219C2×C3×C4—21no—
220C2×C3×C4—21no—
221C2×C3×C4—21no—
222C2×C3×C4—21no—
223C2×C3×C4—21no—
224C2×C3×C4—21no—
225C2×C3×C4—21no—
226C2×C3×C4—21no—
227C2×C3×C4—21no—
228C2×C3×C4—21no—
229C2×C3×C4—21no—
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—21no—
236C2×C3×C4—44no—
237C2×C3×C4—44no—
238C2×C3×C4C2×D412yes—
239C2×C3×C4C2×D412yes—
240C2×C3×C4C2×D412yes—
241C2×C3×C4C2×D412yes—
242C2×C3×C4C2×D412yes—
243C24C23×C311yescharacteristic
244C24C23×C311yescharacteristic
245C24C23×C311yescharacteristic
246C24C23×C311yescharacteristic
247C2×Q8—22no—
248C2×Q8—22no—
249C2×Q8—41no—
250C2×D4—22no—
251C2×D4—22no—
252C2×D4—22no—
253C2×D4—22no—
254C2×D4—22no—
255C2×D4—22no—
256C2×D4—22no—
257C2×D4—22no—
258C2×D4—22no—
259C2×D4—22no—
260C2×D4—41no—
261C2×D4—41no—
262C2×D4—41no—
263C2×D4—41no—
264C2×D4—41no—
265C2×D4—41no—
266C2×D4—41no—
267C2×D4—41no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4C23×C311yescharacteristic
275C22×C4C23×C311yescharacteristic
276C22×C4C23×C311yescharacteristic
277C22×C4C23×C311yescharacteristic
278C22×C4C23×C311yescharacteristic
279C22×C4C23×C311yescharacteristic
280C22×C4C23×C311yescharacteristic
281C22×C4C23×C311yescharacteristic
282C22×C4C23×C311yescharacteristic
283C22×C4C23×C311yescharacteristic
284C22×C4C23×C311yescharacteristic
285C4⋊C4—22no—
286C4⋊C4—22no—
287C4⋊C4—22no—
288C4⋊C4—41no—
289C4⋊C4C3×D414yescomplemented
290C22⋊C4—22no—
291C22⋊C4—22no—
292C22⋊C4—22no—
293C22⋊C4—22no—
294C22⋊C4—22no—
295C22⋊C4—22no—
296C22⋊C4—22no—
297C22⋊C4—22no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C22⋊C4—41no—
301C22⋊C4—41no—
302C22⋊C4—41no—
303C22⋊C4C3×D414yescomplemented
304C42—22no—
305C22×C3—22no—
306C22×C3—22no—
307C22×C3—22no—
308C22×C3—22no—
309C22×C3—22no—
310C22×C3—22no—
311C22×C3—41no—
312C22×C3—41no—
313C22×C3—41no—
314C22×C3—41no—
315C22×C3—41no—
316C22×C3—41no—
317C22×C3—41no—
318C22×C3—41no—
319C22×C3—41no—
320C22×C3—41no—
321C22×C3—41no—
322C22×C3—41no—
323C22×C3—41no—
324C22×C3—41no—
325C22×C3—41no—
326C22×C3—41no—
327C22×C3—41no—
328C22×C3—41no—
329C22×C3—41no—
330C22×C3—41no—
331C22×C3—41no—
332C22×C3—41no—
333C22×C3C22×D411yescharacteristic
334C22×C3C22×D411yescharacteristic
335C22×C3C2×#4111yescharacteristic
336C22×C3H(5,𝔽2)11yescharacteristic
337C22×C3H(5,𝔽2)11yescharacteristic
338C22×C3H(5,𝔽2)11yescharacteristic
339C22×C32−1+411yescharacteristic
340C3×C4—22no—
341C3×C4—22no—
342C3×C4—22no—
343C3×C4—22no—
344C3×C4—22no—
345C3×C4—41no—
346C3×C4—41no—
347C3×C4—41no—
348C3×C4—41no—
349C3×C4—41no—
350C3×C4—41no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—21no—
362C23—21no—
363C23—21no—
364C23—21no—
365C23—21no—
366C23—21no—
367C23—21no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—21no—
373C23—21no—
374C23—21no—
375C23—21no—
376C23—21no—
377C23C2×C3×D412yes—
378C23C3×#4112yes—
379C23C24×C311yescharacteristic
380Q8—44no—
381D4—44no—
382D4—44no—
383D4—44no—
384D4—44no—
385D4—44no—
386D4—44no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—44no—
416C2×C4—44no—
417C2×C4C2×C3×D412yes—
418C2×C4C2×C3×D412yes—
419C2×C4C2×C3×D412yes—
420C2×C4C2×C3×D412yes—
421C2×C4C2×C3×D412yes—
422C2×C3—42no—
423C2×C3—42no—
424C2×C3—81no—
425C2×C3—81no—
426C2×C3#53511yescharacteristic
427C2×C3#53711yescharacteristic
428C2×C3#53811yescharacteristic
429C2×C3D4211yescharacteristic
430C2×C3#54611yescharacteristic
431C2×C3#54811yescharacteristic
432C2×C3#56211yescharacteristic
433C22—22no—
434C22—22no—
435C22—22no—
436C22—22no—
437C22—22no—
438C22—22no—
439C22—41no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22—41no—
444C22—41no—
445C22—41no—
446C22—41no—
447C22—41no—
448C22—41no—
449C22—41no—
450C22—41no—
451C22—41no—
452C22—41no—
453C22—41no—
454C22—41no—
455C22—41no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22C22×C3×D411yescharacteristic
462C22C22×C3×D411yescharacteristic
463C22C2×C3×#4111yescharacteristic
464C22C3×H(5,𝔽2)11yescharacteristic
465C22C3×H(5,𝔽2)11yescharacteristic
466C22C3×H(5,𝔽2)11yescharacteristic
467C22C3×2−1+411yescharacteristic
468C4—22no—
469C4—22no—
470C4—22no—
471C4—22no—
472C4—22no—
473C4—41no—
474C4—41no—
475C4—41no—
476C4—41no—
477C4—41no—
478C4—41no—
479C3#267611yescharacteristic, direct product factor, Sylow
480C2—42no—
481C2—42no—
482C2—81no—
483C2—81no—
484C2C3×#53511yescharacteristic
485C2C3×#53711yescharacteristic
486C2C3×#53811yescharacteristic
487C2C3×D4211yescharacteristic
488C2C3×#54611yescharacteristic
489C2C3×#54811yescharacteristic
490C2C3×#56211yescharacteristic
subgroupG/H
center, socleC23×C3C24
commutator, Frattini, cosocleC23C24×C3
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C3 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#124C2semidirect
2. C2×C3×C22⋊Q8C2semidirect
3. C2×C3×#121C2semidirect
4. C2×C3×#121C2semidirect
5. C3×#396C2semidirect
6. C3×#394C2semidirect
7. C3×#394C2semidirect
8. C3×#393C2semidirect
9. C3×#392C2semidirect
10. C3×#392C2semidirect
11. C3×#390C2semidirect
12. C3×#387C2semidirect
13. C3×#386C2semidirect
14. C3×#386C2semidirect
15. C3×#385C2semidirect
16. #2676C3direct (N × H)
56. C2×#124C2×C3semidirect
57. C2×C22⋊Q8C2×C3semidirect
58. C2×#121C2×C3semidirect
59. C2×#121C2×C3semidirect
60. #396C2×C3semidirect
61. #394C2×C3semidirect
62. #394C2×C3semidirect
63. #393C2×C3semidirect
64. #392C2×C3semidirect
65. #392C2×C3semidirect
66. #390C2×C3semidirect
67. #387C2×C3semidirect
68. #386C2×C3semidirect
69. #386C2×C3semidirect
70. #385C2×C3semidirect
117. C3×C4⋊C4D4semidirect
131. C3×C22⋊C4D4semidirect
289. C4⋊C4C3×D4semidirect
303. C22⋊C4C3×D4semidirect
479. C3#2676direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#1242
C2×C3×C22⋊Q82
C2×C3×#1212
C3×#3962
C3×#3942
C3×#3932
C3×#3922
C3×#3902
C3×#3872
C3×#3862
C3×#3852
#26763