Finite Group Databasebeta

← C3×#10263 #10628870

Subgroups — C3×#10263 #10628870

Order 768.

626 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#486C211yesmaximal, characteristic
2C2×C3×#462C211yesmaximal, characteristic, complemented
3C2×C3×#460C211yesmaximal, characteristic
4C3×#1984C211yesmaximal, characteristic, complemented
5C2×C3×#332C211yesmaximal, characteristic, complemented
6C2×C3×#331C211yesmaximal, characteristic
7C3×#1277C211yesmaximal, characteristic, complemented
8#10263C311yesmaximal, characteristic, direct product factor, Sylow
9C22×C3×Q16—21no—
10C22×C3×SD16—21no—
11C2×C3×C4⋊Q8C2211yescharacteristic
12C2×C3×#127C2211yescharacteristic
13C2×C3×C4×Q8C2211yescharacteristic
14C3×#486—22no—
15C3×#486—22no—
16C3×#462—22no—
17C3×#462—22no—
18C3×#460—22no—
19C3×#460—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×C4×C8C2211yescharacteristic
27C3×#336—22no—
28C3×#332—22no—
29C3×#331—22no—
30C2×#486C2×C311yescharacteristic
31C2×#462C2×C311yescharacteristic, complemented
32C2×#460C2×C311yescharacteristic
33#1984C2×C311yescharacteristic, complemented
34C2×#332C2×C311yescharacteristic, complemented
35C2×#331C2×C311yescharacteristic
36#1277C2×C311yescharacteristic, complemented
37C22×C3×Q8—21no—
38C22×C3×Q8D411yescharacteristic
39C22×C3×D4—21no—
40C22×C3×D4—21no—
41C22×C3×D4—21no—
42C2×C3×Q16—24no—
43C2×C3×Q16—42no—
44C2×C3×Q16—42no—
45C2×C3×SD16—24no—
46C2×C3×SD16—42no—
47C2×C3×SD16—42no—
48C22×C3×C8—21no—
49C22×C3×C8—21no—
50C22×C3×C8—21no—
51C22×C3×C8D412yes—
52C3×C4⋊Q8—21no—
53C3×C4⋊Q8—21no—
54C3×C4⋊Q8—21no—
55C3×C4⋊Q8D412yes—
56C3×#127—21no—
57C3×#127—21no—
58C3×#127—21no—
59C3×#127D412yes—
60C3×C4×Q8—21no—
61C3×C4×Q8—21no—
62C3×C4×Q8—21no—
63C3×C4×Q8—21no—
64C2×C3×C4⋊C4—21no—
65C2×C3×C4⋊C4—21no—
66C2×C3×C4⋊C4—21no—
67C2×C3×C4⋊C4D411yescharacteristic
68C2×C3×C42—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×C4×C8—21no—
80C3×C4×C8—21no—
81C22×Q16—21no—
82C22×SD16—21no—
83C2×C4⋊Q8C22×C311yescharacteristic
84C2×#127C22×C311yescharacteristic
85C2×C4×Q8C22×C311yescharacteristic
86#486—22no—
87#486—22no—
88#462—22no—
89#462—22no—
90#460—22no—
91#460—22no—
92C2×C4⋊C8C22×C311yescharacteristic
93C2×C4⋊C8C22×C311yescharacteristic
94C2×C4⋊C8C22×C311yescharacteristic
95C2×#103—21no—
96C2×#102—22no—
97C2×#102—21no—
98C2×C4×C8C22×C311yescharacteristic
99#336—22no—
100#332—22no—
101#331—22no—
102C24×C3—41no—
103C2×C3×Q8—21no—
104C2×C3×Q8—21no—
105C2×C3×Q8—21no—
106C2×C3×Q8—22no—
107C2×C3×Q8—21no—
108C2×C3×Q8—21no—
109C2×C3×Q8—41no—
110C2×C3×Q8—41no—
111C2×C3×Q8—41no—
112C2×C3×Q8—41no—
113C2×C3×Q8—41no—
114C2×C3×Q8D812yes—
115C2×C3×D4—22no—
116C2×C3×D4—22no—
117C2×C3×D4—22no—
118C2×C3×D4—41no—
119C2×C3×D4—41no—
120C2×C3×D4—41no—
121C2×C3×D4—41no—
122C2×C3×D4—41no—
123C2×C3×D4—42no—
124C2×C3×D4—41no—
125C2×C3×D4—41no—
126C2×C3×D4—42no—
127C2×C3×D4—82no—
128C22×C3×C4—21no—
129C22×C3×C4—21no—
130C22×C3×C4—41no—
131C22×C3×C4C2×D411yescharacteristic
132C22×C3×C4C2×D411yescharacteristic
133C22×C3×C4#4111yescharacteristic
134C3×Q16—48no—
135C3×SD16—48no—
136C2×C3×C8—22no—
137C2×C3×C8—22no—
138C2×C3×C8—22no—
139C2×C3×C8—22no—
140C2×C3×C8—22no—
141C2×C3×C8—41no—
142C2×C3×C8—41no—
143C2×C3×C8—41no—
144C2×C3×C8—41no—
145C2×C3×C8—41no—
146C2×C3×C8—42no—
147C3×C4⋊C4—22no—
148C3×C4⋊C4—21no—
149C3×C4⋊C4—21no—
150C3×C4⋊C4—22no—
151C3×C4⋊C4—41no—
152C3×C4⋊C4—41no—
153C3×C4⋊C4—41no—
154C3×C4⋊C4—41no—
155C3×C42—41no—
156C3×C42—41no—
157C3×C42C2×D411yescharacteristic
158C3×C42C2×D411yescharacteristic
159C3×C42C2×D411yescharacteristic
160C3×C42C2×D411yescharacteristic
161C22×Q8—21no—
162C22×Q8C3×D411yescharacteristic
163C22×D4—21no—
164C22×D4—21no—
165C22×D4—21no—
166C2×Q16—24no—
167C2×Q16—42no—
168C2×Q16—42no—
169C2×SD16—24no—
170C2×SD16—42no—
171C2×SD16—42no—
172C22×C8—21no—
173C22×C8—21no—
174C22×C8—21no—
175C22×C8C3×D412yes—
176C4⋊Q8—21no—
177C4⋊Q8—21no—
178C4⋊Q8—21no—
179C4⋊Q8C3×D412yes—
180#127—21no—
181#127—21no—
182#127—21no—
183#127C3×D412yes—
184C4×Q8—21no—
185C4×Q8—21no—
186C4×Q8—21no—
187C4×Q8—21no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4C3×D411yescharacteristic
192C2×C42—21no—
193C2×C42C23×C311yescharacteristic
194C4⋊C8—21no—
195C4⋊C8—21no—
196C4⋊C8—21no—
197C4⋊C8—21no—
198C4⋊C8C3×D412yes—
199C4⋊C8C3×D412yes—
200#103—24no—
201#102—24no—
202#102—28no—
203C4×C8—21no—
204C4×C8—21no—
205C23×C3—42no—
206C23×C3—82no—
207C23×C3—81no—
208C23×C3—81no—
209C23×C3—82no—
210C23×C3#12111yescharacteristic
211C3×Q8—22no—
212C3×Q8—22no—
213C3×Q8—41no—
214C3×Q8—41no—
215C3×Q8—42no—
216C3×Q8—42no—
217C3×Q8—81no—
218C3×Q8—81no—
219C3×D4—42no—
220C3×D4—42no—
221C3×D4—44no—
222C3×D4—82no—
223C3×D4—82no—
224C3×D4—81no—
225C3×D4—81no—
226C3×D4—81no—
227C3×D4—81no—
228C2×C3×C4—22no—
229C2×C3×C4—22no—
230C2×C3×C4—41no—
231C2×C3×C4—41no—
232C2×C3×C4—41no—
233C2×C3×C4—42no—
234C2×C3×C4—42no—
235C2×C3×C4—81no—
236C2×C3×C4—81no—
237C2×C3×C4#12011yescharacteristic
238C2×C3×C4#12011yescharacteristic
239C2×C3×C4#12011yescharacteristic
240C2×C3×C4#12111yescharacteristic
241C2×C3×C4#12111yescharacteristic
242C2×C3×C4#12711yescharacteristic
243C2×C3×C4C2×D811yescharacteristic
244C2×C3×C4#13511yescharacteristic
245C2×C3×C4#13512yes—
246C2×C3×C4AGL(1,ℤ/8)11yescharacteristic
247C2×C3×C4AGL(1,ℤ/8)11yescharacteristic
248C2×C3×C4#13712yes—
249C3×C8—42no—
250C3×C8—42no—
251C3×C8—42no—
252C3×C8—81no—
253C24—41no—
254C2×Q8—21no—
255C2×Q8—21no—
256C2×Q8—21no—
257C2×Q8—22no—
258C2×Q8—21no—
259C2×Q8—21no—
260C2×Q8—41no—
261C2×Q8—41no—
262C2×Q8—41no—
263C2×Q8—41no—
264C2×Q8—41no—
265C2×Q8C3×D812yes—
266C2×D4—22no—
267C2×D4—22no—
268C2×D4—22no—
269C2×D4—41no—
270C2×D4—41no—
271C2×D4—41no—
272C2×D4—41no—
273C2×D4—41no—
274C2×D4—42no—
275C2×D4—41no—
276C2×D4—41no—
277C2×D4—42no—
278C2×D4—82no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—41no—
282C22×C4C2×C3×D411yescharacteristic
283C22×C4C2×C3×D411yescharacteristic
284C22×C4C3×#4111yescharacteristic
285Q16—48no—
286SD16—48no—
287C2×C8—22no—
288C2×C8—22no—
289C2×C8—22no—
290C2×C8—22no—
291C2×C8—22no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8—41no—
295C2×C8—41no—
296C2×C8—41no—
297C2×C8—42no—
298C4⋊C4—22no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—22no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C42—41no—
307C42—41no—
308C42C2×C3×D411yescharacteristic
309C42C2×C3×D411yescharacteristic
310C42C2×C3×D411yescharacteristic
311C42C2×C3×D411yescharacteristic
312C22×C3—82no—
313C22×C3—82no—
314C22×C3—82no—
315C22×C3—162no—
316C22×C3—162no—
317C22×C3#39211yescharacteristic
318C22×C3#46412yes—
319C22×C3#46611yescharacteristic
320C22×C3#46911yescharacteristic
321C22×C3#47112yes—
322C3×C4—21no—
323C3×C4—21no—
324C3×C4—42no—
325C3×C4—82no—
326C3×C4—81no—
327C3×C4#44711yescharacteristic
328C3×C4#44711yescharacteristic
329C3×C4#44911yescharacteristic
330C3×C4#44911yescharacteristic
331C3×C4#45212yes—
332C3×C4#49511yescharacteristic
333C3×C4#49711yescharacteristic
334C23—42no—
335C23—82no—
336C23—81no—
337C23—81no—
338C23—82no—
339C23C3×#12111yescharacteristic
340Q8—22no—
341Q8—22no—
342Q8—41no—
343Q8—41no—
344Q8—42no—
345Q8—42no—
346Q8—81no—
347Q8—81no—
348D4—42no—
349D4—42no—
350D4—44no—
351D4—82no—
352D4—82no—
353D4—81no—
354D4—81no—
355D4—81no—
356D4—81no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—81no—
365C2×C4—81no—
366C2×C4C3×#12011yescharacteristic
367C2×C4C3×#12011yescharacteristic
368C2×C4C3×#12011yescharacteristic
369C2×C4C3×#12111yescharacteristic
370C2×C4C3×#12111yescharacteristic
371C2×C4C3×#12711yescharacteristic
372C2×C4C2×C3×D811yescharacteristic
373C2×C4C3×#13511yescharacteristic
374C2×C4C3×#13512yes—
375C2×C4C3×AGL(1,ℤ/8)11yescharacteristic
376C2×C4C3×AGL(1,ℤ/8)11yescharacteristic
377C2×C4C3×#13712yes—
378C8—42no—
379C8—42no—
380C8—42no—
381C8—81no—
382C2×C3—162no—
383C2×C3#168212yes—
384C2×C3#170212yes—
385C2×C3#199911yescharacteristic
386C2×C3#201511yescharacteristic
387C2×C3#201911yescharacteristic
388C22—82no—
389C22—82no—
390C22—82no—
391C22—162no—
392C22—162no—
393C22C3×#39211yescharacteristic
394C22C3×#46412yes—
395C22C3×#46611yescharacteristic
396C22C3×#46911yescharacteristic
397C22C3×#47112yes—
398C4—21no—
399C4—21no—
400C4—42no—
401C4—82no—
402C4—81no—
403C4C3×#44711yescharacteristic
404C4C3×#44711yescharacteristic
405C4C3×#44911yescharacteristic
406C4C3×#44911yescharacteristic
407C4C3×#45212yes—
408C4C3×#49511yescharacteristic
409C4C3×#49711yescharacteristic
410C3#1026311yescharacteristic, direct product factor, Sylow
411C2—162no—
412C2C3×#168212yes—
413C2C3×#170212yes—
414C2C3×#199911yescharacteristic
415C2C3×#201511yescharacteristic
416C2C3×#201911yescharacteristic
subgroupG/H
center, socleC23×C3#121
commutator, Frattini, cosocleC2×C42C23×C3
prime radicalC2×C3×#127C22
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
2. C2×C3×#462C2semidirect
4. C3×#1984C2semidirect
5. C2×C3×#332C2semidirect
7. C3×#1277C2semidirect
8. #10263C3direct (N × H)
31. C2×#462C2×C3semidirect
33. #1984C2×C3semidirect
34. C2×#332C2×C3semidirect
36. #1277C2×C3semidirect
410. C3#10263direct (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×#4622
C2×C3×#4602
C3×#19842
C2×C3×#3322
C2×C3×#3312
C3×#12772
#102633