Finite Group Databasebeta

← C3×#10247 #10628854

Subgroups — C3×#10247 #10628854

Order 768.

556 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3229C211yesmaximal, characteristic, complemented
2C3×#3077C211yesmaximal, characteristic
3C3×#2547C211yesmaximal, characteristic
4C3×#1546C211yesmaximal, characteristic, complemented
5C3×#1503C211yesmaximal, characteristic, complemented
6C3×#1478C211yesmaximal, characteristic
7C3×#1303C211yesmaximal, characteristic, complemented
8#10247C311yesmaximal, characteristic, direct product factor, Sylow
9C3×#533C2211yescharacteristic
10C2×C3×C4⋊Q8C2211yescharacteristic
11C2×C3×#124—21no—
12C2×C3×C4×D4C2211yescharacteristic
13C3×#498—21no—
14C3×#487—21no—
15C3×#483—22no—
16C3×#478—22no—
17C3×#476—21no—
18C3×#475—22no—
19C3×#474—21no—
20C3×#431C2211yescharacteristic
21C3×#431C2211yescharacteristic
22C3×#428—21no—
23C3×#423C2211yescharacteristic
24C3×#418—21no—
25C3×#397—22no—
26C3×#391—21no—
27C3×#380—22no—
28C3×C4×C4⋊C4C2211yescharacteristic
29C3×#332—22no—
30C3×#328—22no—
31C3×D4⋊C8—22no—
32#3229C2×C311yescharacteristic, complemented
33#3077C2×C311yescharacteristic
34#2547C2×C311yescharacteristic
35#1546C2×C311yescharacteristic, complemented
36#1503C2×C311yescharacteristic, complemented
37#1478C2×C311yescharacteristic
38#1303C2×C311yescharacteristic, complemented
39C22×C3×Q8—21no—
40C22×C3×D4D411yescharacteristic
41C23×C3×C4—21no—
42C2×C3×M16—21no—
43C3×C4⋊Q8—21no—
44C3×C4⋊Q8—21no—
45C3×C4⋊Q8—21no—
46C3×C4⋊Q8—21no—
47C3×C4⋊Q8D411yescharacteristic
48C3×C4⋊Q8D411yescharacteristic
49C3×#125—21no—
50C3×#124—42no—
51C3×#124—42no—
52C3×C22⋊Q8—21no—
53C3×C22⋊Q8—21no—
54C3×C4×Q8—21no—
55C3×C4×Q8—21no—
56C3×C4×D4—21no—
57C3×C4×D4—21no—
58C3×C4×D4—21no—
59C3×C4×D4—21no—
60C3×#117—21no—
61C2×C3×C4⋊C4—21no—
62C2×C3×C4⋊C4—21no—
63C2×C3×C4⋊C4D412yes—
64C2×C3×C4⋊C4D411yescharacteristic
65C2×C3×C22⋊C4—24no—
66C2×C3×C22⋊C4—21no—
67C2×C3×C42—21no—
68C2×C3×C42C2311yescharacteristic
69C3×#107—22no—
70C3×#106—22no—
71C3×#106—24no—
72C3×C4⋊C8—21no—
73C3×C4⋊C8—21no—
74C3×C4⋊C8D412yes—
75C3×C4⋊C8D412yes—
76C3×#103—24no—
77C3×#102—22no—
78C3×#102—22no—
79C3×C22⋊C8—21no—
80C3×C22⋊C8—21no—
81C3×C4×C8—21no—
82C3×C4×C8—21no—
83C3×#95—24no—
84C3×#95D412yes—
85#533C22×C311yescharacteristic
86C2×C4⋊Q8C22×C311yescharacteristic
87C2×#124—21no—
88C2×C4×D4C22×C311yescharacteristic
89#498—21no—
90#487—21no—
91#483—22no—
92#478—22no—
93#476—21no—
94#475—22no—
95#474—21no—
96#431C22×C311yescharacteristic
97#431C22×C311yescharacteristic
98#428—21no—
99#423C22×C311yescharacteristic
100#418—21no—
101#397—22no—
102#391—21no—
103#380—22no—
104C4×C4⋊C4C22×C311yescharacteristic
105#332—22no—
106#328—22no—
107D4⋊C8—22no—
108C24×C3—21no—
109C2×C3×Q8—21no—
110C2×C3×Q8—21no—
111C2×C3×Q8—41no—
112C2×C3×Q8—41no—
113C2×C3×Q8—41no—
114C2×C3×Q8—41no—
115C2×C3×Q8—41no—
116C2×C3×Q8—41no—
117C2×C3×D4—21no—
118C2×C3×D4—21no—
119C2×C3×D4—21no—
120C2×C3×D4—21no—
121C2×C3×D4—21no—
122C2×C3×D4SD1612yes—
123C22×C3×C4—21no—
124C22×C3×C4—22no—
125C22×C3×C4—22no—
126C22×C3×C4—44no—
127C22×C3×C4—41no—
128C22×C3×C4—41no—
129C22×C3×C4C2×D411yescharacteristic
130C22×C3×C4C2×D411yescharacteristic
131C22×C3×C4C2×D411yescharacteristic
132C3×M16—41no—
133C3×M16—41no—
134C2×C3×C8—22no—
135C2×C3×C8—22no—
136C2×C3×C8—41no—
137C3×C4⋊C4—21no—
138C3×C4⋊C4—21no—
139C3×C4⋊C4—22no—
140C3×C4⋊C4—21no—
141C3×C4⋊C4—21no—
142C3×C4⋊C4—21no—
143C3×C4⋊C4—22no—
144C3×C4⋊C4—21no—
145C3×C4⋊C4—42no—
146C3×C4⋊C4—41no—
147C3×C4⋊C4—41no—
148C3×C4⋊C4—41no—
149C3×C4⋊C4—41no—
150C3×C22⋊C4—48no—
151C3×C22⋊C4—41no—
152C3×C22⋊C4—41no—
153C3×C22⋊C4—41no—
154C3×C42—41no—
155C3×C42—41no—
156C3×C42—41no—
157C3×C42C2×D411yescharacteristic
158C3×C42C2×D411yescharacteristic
159C3×C42C2×D411yescharacteristic
160C3×C42#4111yescharacteristic
161C22×Q8—21no—
162C22×D4C3×D411yescharacteristic
163C23×C4—21no—
164C2×M16—21no—
165C4⋊Q8—21no—
166C4⋊Q8—21no—
167C4⋊Q8—21no—
168C4⋊Q8—21no—
169C4⋊Q8C3×D411yescharacteristic
170C4⋊Q8C3×D411yescharacteristic
171#125—21no—
172#124—42no—
173#124—42no—
174C22⋊Q8—21no—
175C22⋊Q8—21no—
176C4×Q8—21no—
177C4×Q8—21no—
178C4×D4—21no—
179C4×D4—21no—
180C4×D4—21no—
181C4×D4—21no—
182#117—21no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4C3×D411yescharacteristic
186C2×C4⋊C4C3×D412yes—
187C2×C22⋊C4—24no—
188C2×C22⋊C4—21no—
189C2×C42—21no—
190C2×C42C23×C311yescharacteristic
191#107—22no—
192#106—22no—
193#106—24no—
194C4⋊C8—21no—
195C4⋊C8—21no—
196C4⋊C8C3×D412yes—
197C4⋊C8C3×D412yes—
198#103—24no—
199#102—22no—
200#102—22no—
201C22⋊C8—21no—
202C22⋊C8—21no—
203C4×C8—21no—
204C4×C8—21no—
205#95—24no—
206#95C3×D412yes—
207C23×C3—22no—
208C23×C3—42no—
209C23×C3—42no—
210C23×C3—41no—
211C23×C3—41no—
212C23×C3#12011yescharacteristic
213C3×Q8—42no—
214C3×Q8—81no—
215C3×Q8—81no—
216C3×Q8—81no—
217C3×Q8—81no—
218C3×Q8—81no—
219C3×D4—22no—
220C3×D4—22no—
221C3×D4—41no—
222C3×D4—41no—
223C2×C3×C4—22no—
224C2×C3×C4—41no—
225C2×C3×C4—42no—
226C2×C3×C4—42no—
227C2×C3×C4—42no—
228C2×C3×C4—41no—
229C2×C3×C4—41no—
230C2×C3×C4—41no—
231C2×C3×C4—42no—
232C2×C3×C4—42no—
233C2×C3×C4—42no—
234C2×C3×C4—42no—
235C2×C3×C4—82no—
236C2×C3×C4—82no—
237C2×C3×C4#12011yescharacteristic
238C2×C3×C4#12011yescharacteristic
239C2×C3×C4#12111yescharacteristic
240C2×C3×C4#12111yescharacteristic
241C2×C3×C4#12111yescharacteristic
242C2×C3×C4#12711yescharacteristic
243C2×C3×C4C2×SD1611yescharacteristic
244C2×C3×C4#13511yescharacteristic
245C2×C3×C4AGL(1,ℤ/8)11yescharacteristic
246C2×C3×C4#13711yescharacteristic
247C3×C8—42no—
248C3×C8—42no—
249C3×C8—81no—
250C24—21no—
251C2×Q8—21no—
252C2×Q8—21no—
253C2×Q8—41no—
254C2×Q8—41no—
255C2×Q8—41no—
256C2×Q8—41no—
257C2×Q8—41no—
258C2×Q8—41no—
259C2×D4—21no—
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4C3×SD1612yes—
265C22×C4—21no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—44no—
269C22×C4—41no—
270C22×C4—41no—
271C22×C4C2×C3×D411yescharacteristic
272C22×C4C2×C3×D411yescharacteristic
273C22×C4C2×C3×D411yescharacteristic
274M16—41no—
275M16—41no—
276C2×C8—22no—
277C2×C8—22no—
278C2×C8—41no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—22no—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—22no—
286C4⋊C4—21no—
287C4⋊C4—42no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C22⋊C4—48no—
293C22⋊C4—41no—
294C22⋊C4—41no—
295C22⋊C4—41no—
296C42—41no—
297C42—41no—
298C42—41no—
299C42C2×C3×D411yescharacteristic
300C42C2×C3×D411yescharacteristic
301C42C2×C3×D411yescharacteristic
302C42C3×#4111yescharacteristic
303C22×C3—21no—
304C22×C3—21no—
305C22×C3—44no—
306C22×C3—42no—
307C22×C3—82no—
308C22×C3—81no—
309C22×C3—81no—
310C22×C3#39211yescharacteristic
311C22×C3#45011yescharacteristic
312C22×C3#45211yescharacteristic
313C3×C4—21no—
314C3×C4—21no—
315C3×C4—21no—
316C3×C4—82no—
317C3×C4—82no—
318C3×C4—81no—
319C3×C4—81no—
320C3×C4—81no—
321C3×C4#44811yescharacteristic
322C3×C4#44911yescharacteristic
323C3×C4#45412yes—
324C3×C4#46511yescharacteristic
325C3×C4#46811yescharacteristic
326C23—22no—
327C23—42no—
328C23—42no—
329C23—41no—
330C23—41no—
331C23C3×#12011yescharacteristic
332Q8—42no—
333Q8—81no—
334Q8—81no—
335Q8—81no—
336Q8—81no—
337Q8—81no—
338D4—22no—
339D4—22no—
340D4—41no—
341D4—41no—
342C2×C4—22no—
343C2×C4—41no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—82no—
355C2×C4—82no—
356C2×C4C3×#12011yescharacteristic
357C2×C4C3×#12011yescharacteristic
358C2×C4C3×#12111yescharacteristic
359C2×C4C3×#12111yescharacteristic
360C2×C4C3×#12111yescharacteristic
361C2×C4C3×#12711yescharacteristic
362C2×C4C2×C3×SD1611yescharacteristic
363C2×C4C3×#13511yescharacteristic
364C2×C4C3×AGL(1,ℤ/8)11yescharacteristic
365C2×C4C3×#13711yescharacteristic
366C8—42no—
367C8—42no—
368C8—81no—
369C2×C3—21no—
370C2×C3—21no—
371C2×C3—82no—
372C2×C3#200011yescharacteristic
373C2×C3#200311yescharacteristic
374C2×C3#200911yescharacteristic
375C22—21no—
376C22—21no—
377C22—44no—
378C22—42no—
379C22—82no—
380C22—81no—
381C22—81no—
382C22C3×#39211yescharacteristic
383C22C3×#45011yescharacteristic
384C22C3×#45211yescharacteristic
385C4—21no—
386C4—21no—
387C4—21no—
388C4—82no—
389C4—82no—
390C4—81no—
391C4—81no—
392C4—81no—
393C4C3×#44811yescharacteristic
394C4C3×#44911yescharacteristic
395C4C3×#45412yes—
396C4C3×#46511yescharacteristic
397C4C3×#46811yescharacteristic
398C3#1024711yescharacteristic, direct product factor, Sylow
399C2—21no—
400C2—21no—
401C2—82no—
402C2C3×#200011yescharacteristic
403C2C3×#200311yescharacteristic
404C2C3×#200911yescharacteristic
subgroupG/H
center, socleC22×C3#392
commutator, Frattini, cosocleC2×C42C23×C3
prime radicalC22×C3×D4D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C3 ◁ C2×C3×C42 ◁ G

Complements

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

NH ≅ G/Ntype
1. C3×#3229C2semidirect
4. C3×#1546C2semidirect
5. C3×#1503C2semidirect
7. C3×#1303C2semidirect
8. #10247C3direct (N × H)
32. #3229C2×C3semidirect
35. #1546C2×C3semidirect
36. #1503C2×C3semidirect
38. #1303C2×C3semidirect
398. C3#10247direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#32292
C3×#30772
C3×#25472
C3×#15462
C3×#15032
C3×#14782
C3×#13032
#102473