Finite Group Databasebeta

← C3×#10261 #10628868

Subgroups — C3×#10261 #10628868

Order 768.

678 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#486C211yesmaximal, characteristic, complemented
2C2×C3×#461C211yesmaximal, characteristic, complemented
3C2×C3×#459C211yesmaximal, characteristic
4C3×#1954C211yesmaximal, characteristic, complemented
5C2×C3×#332C211yesmaximal, characteristic, complemented
6C2×C3×#331C211yesmaximal, characteristic, complemented
7C3×#1277C211yesmaximal, characteristic, complemented
8#10261C311yesmaximal, characteristic, direct product factor, Sylow
9C22×C3×SD16—21no—
10C22×C3×D8—21no—
11C2×C3×C4⋊Q8C2211yescharacteristic
12C2×C3×#127C2211yescharacteristic
13C2×C3×C4×D4C2211yescharacteristic
14C3×#486—22no—
15C3×#486—22no—
16C3×#461—22no—
17C3×#461—22no—
18C3×#459—22no—
19C3×#459—22no—
20C2×C3×C4⋊C8C2211yescharacteristic
21C2×C3×C4⋊C8C2211yescharacteristic
22C2×C3×C4⋊C8C2211yescharacteristic
23C2×C3×#103—21no—
24C2×C3×#102—22no—
25C2×C3×#102—21no—
26C2×C3×C22⋊C8—22no—
27C2×C3×C4×C8C2211yescharacteristic
28C3×#332—22no—
29C3×#331—22no—
30C2×#486C2×C311yescharacteristic, complemented
31C2×#461C2×C311yescharacteristic, complemented
32C2×#459C2×C311yescharacteristic
33#1954C2×C311yescharacteristic, complemented
34C2×#332C2×C311yescharacteristic, complemented
35C2×#331C2×C311yescharacteristic, complemented
36#1277C2×C311yescharacteristic, complemented
37C22×C3×Q8—21no—
38C22×C3×D4—21no—
39C22×C3×D4—21no—
40C22×C3×D4—21no—
41C22×C3×D4D411yescharacteristic
42C23×C3×C4—21no—
43C2×C3×SD16—24no—
44C2×C3×SD16—42no—
45C2×C3×SD16—42no—
46C2×C3×D8—24no—
47C2×C3×D8—42no—
48C2×C3×D8—42no—
49C22×C3×C8—21no—
50C22×C3×C8—21no—
51C22×C3×C8—21no—
52C22×C3×C8D412yes—
53C3×C4⋊Q8—21no—
54C3×C4⋊Q8—21no—
55C3×C4⋊Q8—21no—
56C3×C4⋊Q8D412yes—
57C3×#127—21no—
58C3×#127—21no—
59C3×#127—21no—
60C3×#127D412yes—
61C3×C4×D4—21no—
62C3×C4×D4—21no—
63C3×C4×D4—21no—
64C3×C4×D4—21no—
65C2×C3×C4⋊C4—21no—
66C2×C3×C4⋊C4—21no—
67C2×C3×C4⋊C4D411yescharacteristic
68C2×C3×C22⋊C4—21no—
69C2×C3×C42C2311yescharacteristic
70C3×C4⋊C8—21no—
71C3×C4⋊C8—21no—
72C3×C4⋊C8—21no—
73C3×C4⋊C8—21no—
74C3×C4⋊C8D412yes—
75C3×C4⋊C8D412yes—
76C3×#103—24no—
77C3×#102—24no—
78C3×#102—28no—
79C3×C22⋊C8—44no—
80C3×C4×C8—21no—
81C3×C4×C8—21no—
82C22×SD16—21no—
83C22×D8—21no—
84C2×C4⋊Q8C22×C311yescharacteristic
85C2×#127C22×C311yescharacteristic
86C2×C4×D4C22×C311yescharacteristic
87#486—22no—
88#486—22no—
89#461—22no—
90#461—22no—
91#459—22no—
92#459—22no—
93C2×C4⋊C8C22×C311yescharacteristic
94C2×C4⋊C8C22×C311yescharacteristic
95C2×C4⋊C8C22×C311yescharacteristic
96C2×#103—21no—
97C2×#102—22no—
98C2×#102—21no—
99C2×C22⋊C8—22no—
100C2×C4×C8C22×C311yescharacteristic
101#332—22no—
102#331—22no—
103C24×C3—21no—
104C24×C3—41no—
105C2×C3×Q8—22no—
106C2×C3×Q8—41no—
107C2×C3×Q8—41no—
108C2×C3×Q8—41no—
109C2×C3×Q8—41no—
110C2×C3×Q8—41no—
111C2×C3×D4—21no—
112C2×C3×D4—21no—
113C2×C3×D4—22no—
114C2×C3×D4—22no—
115C2×C3×D4—22no—
116C2×C3×D4—21no—
117C2×C3×D4—21no—
118C2×C3×D4—21no—
119C2×C3×D4—41no—
120C2×C3×D4—41no—
121C2×C3×D4—41no—
122C2×C3×D4—41no—
123C2×C3×D4—41no—
124C2×C3×D4—42no—
125C2×C3×D4—41no—
126C2×C3×D4—41no—
127C2×C3×D4—42no—
128C2×C3×D4—82no—
129C2×C3×D4D812yes—
130C22×C3×C4—21no—
131C22×C3×C4—41no—
132C22×C3×C4—41no—
133C22×C3×C4—41no—
134C22×C3×C4—42no—
135C22×C3×C4—42no—
136C22×C3×C4C2×D411yescharacteristic
137C22×C3×C4C2×D411yescharacteristic
138C22×C3×C4#4111yescharacteristic
139C3×SD16—48no—
140C3×D8—48no—
141C2×C3×C8—22no—
142C2×C3×C8—22no—
143C2×C3×C8—22no—
144C2×C3×C8—22no—
145C2×C3×C8—22no—
146C2×C3×C8—41no—
147C2×C3×C8—41no—
148C2×C3×C8—41no—
149C2×C3×C8—41no—
150C2×C3×C8—41no—
151C2×C3×C8—42no—
152C3×C4⋊C4—22no—
153C3×C4⋊C4—21no—
154C3×C4⋊C4—21no—
155C3×C4⋊C4—22no—
156C3×C4⋊C4—41no—
157C3×C4⋊C4—41no—
158C3×C22⋊C4—41no—
159C3×C22⋊C4—41no—
160C3×C42C2×D411yescharacteristic
161C3×C42C2×D411yescharacteristic
162C3×C42C2×D411yescharacteristic
163C3×C42C2×D411yescharacteristic
164C22×Q8—21no—
165C22×D4—21no—
166C22×D4—21no—
167C22×D4—21no—
168C22×D4C3×D411yescharacteristic
169C23×C4—21no—
170C2×SD16—24no—
171C2×SD16—42no—
172C2×SD16—42no—
173C2×D8—24no—
174C2×D8—42no—
175C2×D8—42no—
176C22×C8—21no—
177C22×C8—21no—
178C22×C8—21no—
179C22×C8C3×D412yes—
180C4⋊Q8—21no—
181C4⋊Q8—21no—
182C4⋊Q8—21no—
183C4⋊Q8C3×D412yes—
184#127—21no—
185#127—21no—
186#127—21no—
187#127C3×D412yes—
188C4×D4—21no—
189C4×D4—21no—
190C4×D4—21no—
191C4×D4—21no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4C3×D411yescharacteristic
195C2×C22⋊C4—21no—
196C2×C42C23×C311yescharacteristic
197C4⋊C8—21no—
198C4⋊C8—21no—
199C4⋊C8—21no—
200C4⋊C8—21no—
201C4⋊C8C3×D412yes—
202C4⋊C8C3×D412yes—
203#103—24no—
204#102—24no—
205#102—28no—
206C22⋊C8—44no—
207C4×C8—21no—
208C4×C8—21no—
209C23×C3—22no—
210C23×C3—41no—
211C23×C3—42no—
212C23×C3—41no—
213C23×C3—42no—
214C23×C3—42no—
215C23×C3—82no—
216C23×C3—81no—
217C23×C3—81no—
218C23×C3—82no—
219C23×C3#12111yescharacteristic
220C3×Q8—42no—
221C3×Q8—42no—
222C3×Q8—81no—
223C3×Q8—81no—
224C3×D4—22no—
225C3×D4—22no—
226C3×D4—42no—
227C3×D4—41no—
228C3×D4—41no—
229C3×D4—42no—
230C3×D4—44no—
231C3×D4—82no—
232C3×D4—82no—
233C3×D4—81no—
234C3×D4—81no—
235C3×D4—81no—
236C3×D4—81no—
237C2×C3×C4—22no—
238C2×C3×C4—41no—
239C2×C3×C4—42no—
240C2×C3×C4—42no—
241C2×C3×C4—81no—
242C2×C3×C4—81no—
243C2×C3×C4—82no—
244C2×C3×C4—81no—
245C2×C3×C4—81no—
246C2×C3×C4#12011yescharacteristic
247C2×C3×C4#12011yescharacteristic
248C2×C3×C4#12011yescharacteristic
249C2×C3×C4#12111yescharacteristic
250C2×C3×C4#12111yescharacteristic
251C2×C3×C4#12711yescharacteristic
252C2×C3×C4C2×D811yescharacteristic
253C2×C3×C4#13511yescharacteristic
254C2×C3×C4#13512yes—
255C2×C3×C4AGL(1,ℤ/8)11yescharacteristic
256C2×C3×C4AGL(1,ℤ/8)11yescharacteristic
257C2×C3×C4AGL(1,ℤ/8)12yes—
258C3×C8—42no—
259C3×C8—42no—
260C3×C8—42no—
261C3×C8—81no—
262C24—21no—
263C24—41no—
264C2×Q8—22no—
265C2×Q8—41no—
266C2×Q8—41no—
267C2×Q8—41no—
268C2×Q8—41no—
269C2×Q8—41no—
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—22no—
273C2×D4—22no—
274C2×D4—22no—
275C2×D4—21no—
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—41no—
279C2×D4—41no—
280C2×D4—41no—
281C2×D4—41no—
282C2×D4—41no—
283C2×D4—42no—
284C2×D4—41no—
285C2×D4—41no—
286C2×D4—42no—
287C2×D4—82no—
288C2×D4C3×D812yes—
289C22×C4—21no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4—41no—
293C22×C4—42no—
294C22×C4—42no—
295C22×C4C2×C3×D411yescharacteristic
296C22×C4C2×C3×D411yescharacteristic
297C22×C4C3×#4111yescharacteristic
298SD16—48no—
299D8—48no—
300C2×C8—22no—
301C2×C8—22no—
302C2×C8—22no—
303C2×C8—22no—
304C2×C8—22no—
305C2×C8—41no—
306C2×C8—41no—
307C2×C8—41no—
308C2×C8—41no—
309C2×C8—41no—
310C2×C8—42no—
311C4⋊C4—22no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—22no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C22⋊C4—41no—
318C22⋊C4—41no—
319C42C2×C3×D411yescharacteristic
320C42C2×C3×D411yescharacteristic
321C42C2×C3×D411yescharacteristic
322C42C2×C3×D411yescharacteristic
323C22×C3—44no—
324C22×C3—42no—
325C22×C3—82no—
326C22×C3—81no—
327C22×C3—81no—
328C22×C3—82no—
329C22×C3—82no—
330C22×C3—82no—
331C22×C3—162no—
332C22×C3—162no—
333C22×C3#39211yescharacteristic
334C22×C3#46312yes—
335C22×C3#46611yescharacteristic
336C22×C3#46911yescharacteristic
337C22×C3#47112yes—
338C3×C4—21no—
339C3×C4—21no—
340C3×C4—82no—
341C3×C4—81no—
342C3×C4#44711yescharacteristic
343C3×C4#44711yescharacteristic
344C3×C4#44911yescharacteristic
345C3×C4#44911yescharacteristic
346C3×C4#44912yes—
347C3×C4#49511yescharacteristic
348C3×C4#49611yescharacteristic
349C23—22no—
350C23—41no—
351C23—42no—
352C23—41no—
353C23—42no—
354C23—42no—
355C23—82no—
356C23—81no—
357C23—81no—
358C23—82no—
359C23C3×#12111yescharacteristic
360Q8—42no—
361Q8—42no—
362Q8—81no—
363Q8—81no—
364D4—22no—
365D4—22no—
366D4—42no—
367D4—41no—
368D4—41no—
369D4—42no—
370D4—44no—
371D4—82no—
372D4—82no—
373D4—81no—
374D4—81no—
375D4—81no—
376D4—81no—
377C2×C4—22no—
378C2×C4—41no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—81no—
382C2×C4—81no—
383C2×C4—82no—
384C2×C4—81no—
385C2×C4—81no—
386C2×C4C3×#12011yescharacteristic
387C2×C4C3×#12011yescharacteristic
388C2×C4C3×#12011yescharacteristic
389C2×C4C3×#12111yescharacteristic
390C2×C4C3×#12111yescharacteristic
391C2×C4C3×#12711yescharacteristic
392C2×C4C2×C3×D811yescharacteristic
393C2×C4C3×#13511yescharacteristic
394C2×C4C3×#13512yes—
395C2×C4C3×AGL(1,ℤ/8)11yescharacteristic
396C2×C4C3×AGL(1,ℤ/8)11yescharacteristic
397C2×C4C3×AGL(1,ℤ/8)12yes—
398C8—42no—
399C8—42no—
400C8—42no—
401C8—81no—
402C2×C3—82no—
403C2×C3—162no—
404C2×C3#168112yes—
405C2×C3#170112yes—
406C2×C3#199911yescharacteristic
407C2×C3#201211yescharacteristic
408C2×C3#201911yescharacteristic
409C22—42no—
410C22—44no—
411C22—81no—
412C22—81no—
413C22—82no—
414C22—82no—
415C22—82no—
416C22—82no—
417C22—162no—
418C22—162no—
419C22C3×#39211yescharacteristic
420C22C3×#46312yes—
421C22C3×#46611yescharacteristic
422C22C3×#46911yescharacteristic
423C22C3×#47112yes—
424C4—21no—
425C4—21no—
426C4—82no—
427C4—81no—
428C4C3×#44711yescharacteristic
429C4C3×#44711yescharacteristic
430C4C3×#44911yescharacteristic
431C4C3×#44911yescharacteristic
432C4C3×#44912yes—
433C4C3×#49511yescharacteristic
434C4C3×#49611yescharacteristic
435C3#1026111yescharacteristic, direct product factor, Sylow
436C2—82no—
437C2—162no—
438C2C3×#168112yes—
439C2C3×#170112yes—
440C2C3×#199911yescharacteristic
441C2C3×#201211yescharacteristic
442C2C3×#201911yescharacteristic
subgroupG/H
center, socleC23×C3#121
commutator, Frattini, cosocleC2×C42C23×C3
prime radicalC2×C3×#459C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C3 ◁ C2×C3×C42 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#486C2semidirect
2. C2×C3×#461C2semidirect
4. C3×#1954C2semidirect
5. C2×C3×#332C2semidirect
6. C2×C3×#331C2semidirect
7. C3×#1277C2semidirect
8. #10261C3direct (N × H)
30. C2×#486C2×C3semidirect
31. C2×#461C2×C3semidirect
33. #1954C2×C3semidirect
34. C2×#332C2×C3semidirect
35. C2×#331C2×C3semidirect
36. #1277C2×C3semidirect
435. C3#10261direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#4862
C2×C3×#4612
C2×C3×#4592
C3×#19542
C2×C3×#3322
C2×C3×#3312
C3×#12772
#102613