Finite Group Databasebeta

← C3×#19081 #10637688

Subgroups — C3×#19081 #10637688

Order 768.

880 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3550C211yesmaximal, characteristic
2C3×#3165C211yesmaximal, characteristic, complemented
3C3×#3141C211yesmaximal, characteristic
4C3×#3139C211yesmaximal, characteristic, complemented
5C3×#1664C218yesmaximal, complemented
6C3×#1526C211yesmaximal, characteristic, complemented
7C3×#1526C211yesmaximal, characteristic, complemented
8C3×#1525C211yesmaximal, characteristic
9#19081C311yesmaximal, characteristic, direct product factor, Sylow
10C3×#563C2214yes—
11C3×#559—21no—
12C3×Q82—21no—
13C3×#556—21no—
14C3×#556—21no—
15C3×D4×Q8—21no—
16C3×D4×Q8—21no—
17C3×#542—22no—
18C3×#542—22no—
19C3×#536—22no—
20C3×#533C2211yescharacteristic
21C3×#533C2211yescharacteristic
22C3×#532C2211yescharacteristic
23C2×C3×C4⋊Q8C2211yescharacteristic
24C3×#501C2214yes—
25C3×#500—21no—
26C3×#498—21no—
27C3×#491C2214yes—
28C3×#489C2214yes—
29C3×#487—21no—
30C3×#487—21no—
31C3×#487—21no—
32C3×#486—21no—
33C3×#428—22no—
34C3×#419—22no—
35C3×#417—22no—
36C3×C4×M16C2211yescharacteristic
37C3×C4×M16C2211yescharacteristic
38C3×C4×M16C2211yescharacteristic
39C3×#330C2214yes—
40C3×#330C2214yes—
41C3×#329C2214yes—
42#3550C2×C311yescharacteristic
43#3165C2×C311yescharacteristic, complemented
44#3141C2×C311yescharacteristic
45#3139C2×C311yescharacteristic, complemented
46#1664C2×C318yescomplemented
47#1526C2×C311yescharacteristic, complemented
48#1526C2×C311yescharacteristic, complemented
49#1525C2×C311yescharacteristic
50C2×C3×#41D412yes—
51C22×C3×Q8—22no—
52C22×C3×Q8—21no—
53C2×C3×M16—21no—
54C2×C3×M16—21no—
55C2×C3×M16—21no—
56C3×C4⋊Q8—22no—
57C3×C4⋊Q8—22no—
58C3×C4⋊Q8—24no—
59C3×C4⋊Q8—21no—
60C3×C4⋊Q8—21no—
61C3×C4⋊Q8—21no—
62C3×C4⋊Q8D411yescharacteristic
63C3×C4⋊Q8D411yescharacteristic
64C3×C4⋊Q8D411yescharacteristic
65C3×C4⋊Q8D411yescharacteristic
66C3×C4⋊Q8D411yescharacteristic
67C3×C4⋊Q8C2312yes—
68C3×#127D411yescharacteristic
69C3×#126—24no—
70C3×#126—24no—
71C3×#125C2312yes—
72C3×#125C2312yes—
73C3×#124—22no—
74C3×#124—22no—
75C3×#124—24no—
76C3×#124C2312yes—
77C3×#123—24no—
78C3×#123—24no—
79C3×C22⋊Q8—22no—
80C3×C22⋊Q8—22no—
81C3×C22⋊Q8—21no—
82C3×C22⋊Q8—21no—
83C3×C22⋊Q8—21no—
84C3×C22⋊Q8—21no—
85C3×C22⋊Q8—24no—
86C3×C22⋊Q8—24no—
87C3×#121—21no—
88C3×#121—21no—
89C3×C4×Q8—22no—
90C3×C4×Q8—22no—
91C3×C4×Q8—21no—
92C3×C4×Q8—21no—
93C3×C4×Q8—21no—
94C3×C4×Q8—21no—
95C3×C4×D4—22no—
96C3×C4×D4—22no—
97C3×C4×D4—21no—
98C3×C4×D4—21no—
99C3×#117—22no—
100C3×#117D412yes—
101C3×#117D412yes—
102C2×C3×C4⋊C4—21no—
103C2×C3×C4⋊C4—21no—
104C2×C3×C42C2311yescharacteristic
105C3×#107—24no—
106C3×#106—24no—
107C3×#103—24no—
108C3×#103—24no—
109C3×#103—24no—
110C3×#102—24no—
111C3×#97C2312yes—
112C3×#97C2312yes—
113C3×#97C2312yes—
114C3×C4×C8—21no—
115C3×C4×C8—21no—
116C3×C4×C8—21no—
117#563C22×C314yes—
118#559—21no—
119Q82—21no—
120#556—21no—
121#556—21no—
122D4×Q8—21no—
123D4×Q8—21no—
124#542—22no—
125#542—22no—
126#536—22no—
127#533C22×C311yescharacteristic
128#533C22×C311yescharacteristic
129#532C22×C311yescharacteristic
130C2×C4⋊Q8C22×C311yescharacteristic
131#501C22×C314yes—
132#500—21no—
133#498—21no—
134#491C22×C314yes—
135#489C22×C314yes—
136#487—21no—
137#487—21no—
138#487—21no—
139#486—21no—
140#428—22no—
141#419—22no—
142#417—22no—
143C4×M16C22×C311yescharacteristic
144C4×M16C22×C311yescharacteristic
145C4×M16C22×C311yescharacteristic
146#330C22×C314yes—
147#330C22×C314yes—
148#329C22×C314yes—
149C3×#41—44no—
150C2×C3×Q8—24no—
151C2×C3×Q8—21no—
152C2×C3×Q8—21no—
153C2×C3×Q8—21no—
154C2×C3×Q8—21no—
155C2×C3×Q8—22no—
156C2×C3×Q8—44no—
157C2×C3×Q8—41no—
158C2×C3×Q8—84no—
159C2×C3×Q8C2×D412yes—
160C2×C3×D4—22no—
161C2×C3×D4—21no—
162C2×C3×D4—21no—
163C2×C3×D4C2×D412yes—
164C22×C3×C4—24no—
165C22×C3×C4—22no—
166C22×C3×C4—41no—
167C22×C3×C4C2×D411yescharacteristic
168C22×C3×C4C2×D411yescharacteristic
169C22×C3×C4C2×D411yescharacteristic
170C3×M16—24no—
171C3×M16—42no—
172C3×M16—42no—
173C2×C3×C8—22no—
174C2×C3×C8—22no—
175C2×C3×C8—22no—
176C3×C4⋊C4—24no—
177C3×C4⋊C4—24no—
178C3×C4⋊C4—21no—
179C3×C4⋊C4—21no—
180C3×C4⋊C4—21no—
181C3×C4⋊C4—21no—
182C3×C4⋊C4—21no—
183C3×C4⋊C4—21no—
184C3×C4⋊C4—22no—
185C3×C4⋊C4—22no—
186C3×C4⋊C4—22no—
187C3×C4⋊C4—22no—
188C3×C4⋊C4—22no—
189C3×C4⋊C4—22no—
190C3×C4⋊C4—41no—
191C3×C4⋊C4—41no—
192C3×C4⋊C4C2×D412yes—
193C3×C4⋊C4C2×D412yes—
194C3×C4⋊C4C2×D412yes—
195C3×C4⋊C4C2×D412yes—
196C3×C22⋊C4—24no—
197C3×C22⋊C4—24no—
198C3×C22⋊C4—24no—
199C3×C22⋊C4—22no—
200C3×C22⋊C4—22no—
201C3×C22⋊C4—22no—
202C3×C22⋊C4—22no—
203C3×C42—24no—
204C3×C42—22no—
205C3×C42—22no—
206C3×C42C2×D411yescharacteristic
207C3×C42C2×D411yescharacteristic
208C3×C42C2×D411yescharacteristic
209C3×C42C2411yescharacteristic
210C2×#41C3×D412yes—
211C22×Q8—22no—
212C22×Q8—21no—
213C2×M16—21no—
214C2×M16—21no—
215C2×M16—21no—
216C4⋊Q8—22no—
217C4⋊Q8—22no—
218C4⋊Q8—24no—
219C4⋊Q8—21no—
220C4⋊Q8—21no—
221C4⋊Q8—21no—
222C4⋊Q8C3×D411yescharacteristic
223C4⋊Q8C3×D411yescharacteristic
224C4⋊Q8C3×D411yescharacteristic
225C4⋊Q8C3×D411yescharacteristic
226C4⋊Q8C3×D411yescharacteristic
227C4⋊Q8C23×C312yes—
228#127C3×D411yescharacteristic
229#126—24no—
230#126—24no—
231#125C23×C312yes—
232#125C23×C312yes—
233#124—24no—
234#124—22no—
235#124—22no—
236#124C23×C312yes—
237#123—24no—
238#123—24no—
239C22⋊Q8—22no—
240C22⋊Q8—22no—
241C22⋊Q8—21no—
242C22⋊Q8—21no—
243C22⋊Q8—21no—
244C22⋊Q8—21no—
245C22⋊Q8—24no—
246C22⋊Q8—24no—
247#121—21no—
248#121—21no—
249C4×Q8—22no—
250C4×Q8—22no—
251C4×Q8—21no—
252C4×Q8—21no—
253C4×Q8—21no—
254C4×Q8—21no—
255C4×D4—22no—
256C4×D4—22no—
257C4×D4—21no—
258C4×D4—21no—
259#117—22no—
260#117C3×D412yes—
261#117C3×D412yes—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C42C23×C311yescharacteristic
265#107—24no—
266#106—24no—
267#103—24no—
268#103—24no—
269#103—24no—
270#102—24no—
271#97C23×C312yes—
272#97C23×C312yes—
273#97C23×C312yes—
274C4×C8—21no—
275C4×C8—21no—
276C4×C8—21no—
277C23×C3—22no—
278C23×C3#12011yescharacteristic
279C3×Q8—42no—
280C3×Q8—44no—
281C3×Q8—42no—
282C3×Q8—42no—
283C3×Q8—42no—
284C3×Q8—42no—
285C3×Q8—84no—
286C3×Q8—82no—
287C3×D4—42no—
288C3×D4—42no—
289C3×D4—42no—
290C3×D4—82no—
291C2×C3×C4—22no—
292C2×C3×C4—22no—
293C2×C3×C4—22no—
294C2×C3×C4—22no—
295C2×C3×C4—22no—
296C2×C3×C4—22no—
297C2×C3×C4—22no—
298C2×C3×C4—22no—
299C2×C3×C4—44no—
300C2×C3×C4—42no—
301C2×C3×C4—84no—
302C2×C3×C4—82no—
303C2×C3×C4#12011yescharacteristic
304C2×C3×C4#12011yescharacteristic
305C2×C3×C4#12011yescharacteristic
306C2×C3×C4C22×D411yescharacteristic
307C2×C3×C4C22×D411yescharacteristic
308C2×C3×C4C22×D411yescharacteristic
309C3×C8—24no—
310C3×C8—42no—
311C3×C8—42no—
312#41—44no—
313C2×Q8—24no—
314C2×Q8—21no—
315C2×Q8—21no—
316C2×Q8—21no—
317C2×Q8—21no—
318C2×Q8—22no—
319C2×Q8—44no—
320C2×Q8—41no—
321C2×Q8—84no—
322C2×Q8C2×C3×D412yes—
323C2×D4—22no—
324C2×D4—21no—
325C2×D4—21no—
326C2×D4C2×C3×D412yes—
327C22×C4—24no—
328C22×C4—22no—
329C22×C4—41no—
330C22×C4C2×C3×D411yescharacteristic
331C22×C4C2×C3×D411yescharacteristic
332C22×C4C2×C3×D411yescharacteristic
333M16—24no—
334M16—42no—
335M16—42no—
336C2×C8—22no—
337C2×C8—22no—
338C2×C8—22no—
339C4⋊C4—24no—
340C4⋊C4—24no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4—22no—
348C4⋊C4—22no—
349C4⋊C4—22no—
350C4⋊C4—22no—
351C4⋊C4—22no—
352C4⋊C4—22no—
353C4⋊C4—41no—
354C4⋊C4—41no—
355C4⋊C4C2×C3×D412yes—
356C4⋊C4C2×C3×D412yes—
357C4⋊C4C2×C3×D412yes—
358C4⋊C4C2×C3×D412yes—
359C22⋊C4—24no—
360C22⋊C4—24no—
361C22⋊C4—24no—
362C22⋊C4—22no—
363C22⋊C4—22no—
364C22⋊C4—22no—
365C22⋊C4—22no—
366C42—24no—
367C42—22no—
368C42—22no—
369C42C2×C3×D411yescharacteristic
370C42C2×C3×D411yescharacteristic
371C42C2×C3×D411yescharacteristic
372C42C24×C311yescharacteristic
373C22×C3—21no—
374C22×C3—21no—
375C22×C3—21no—
376C22×C3—42no—
377C22×C3—42no—
378C22×C3—42no—
379C22×C3C2×#12011yescharacteristic
380C3×C4—21no—
381C3×C4—21no—
382C3×C4—21no—
383C3×C4—42no—
384C3×C4—42no—
385C3×C4—42no—
386C3×C4—42no—
387C3×C4—42no—
388C3×C4—82no—
389C3×C4#45412yes—
390C3×C4#45512yes—
391C3×C4#45612yes—
392C23—22no—
393C23C3×#12011yescharacteristic
394Q8—42no—
395Q8—44no—
396Q8—42no—
397Q8—42no—
398Q8—42no—
399Q8—42no—
400Q8—84no—
401Q8—82no—
402D4—42no—
403D4—42no—
404D4—42no—
405D4—82no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—44no—
415C2×C4—42no—
416C2×C4—84no—
417C2×C4—82no—
418C2×C4C3×#12011yescharacteristic
419C2×C4C3×#12011yescharacteristic
420C2×C4C3×#12011yescharacteristic
421C2×C4C22×C3×D411yescharacteristic
422C2×C4C22×C3×D411yescharacteristic
423C2×C4C22×C3×D411yescharacteristic
424C8—24no—
425C8—42no—
426C8—42no—
427C2×C3—41no—
428C2×C3—82no—
429C2×C3C2×#45511yescharacteristic
430C2×C3C2×#45411yescharacteristic
431C2×C3C2×#45611yescharacteristic
432C22—21no—
433C22—21no—
434C22—21no—
435C22—42no—
436C22—42no—
437C22—42no—
438C22C2×C3×#12011yescharacteristic
439C4—21no—
440C4—21no—
441C4—21no—
442C4—42no—
443C4—42no—
444C4—42no—
445C4—42no—
446C4—42no—
447C4—82no—
448C4C3×#45412yes—
449C4C3×#45512yes—
450C4C3×#45612yes—
451C3#1908111yescharacteristic, direct product factor, Sylow
452C2—41no—
453C2—82no—
454C2C2×C3×#45511yescharacteristic
455C2C2×C3×#45411yescharacteristic
456C2C2×C3×#45611yescharacteristic
subgroupG/H
center, socleC22×C3C2×#120
commutator, Frattini, cosocleC42C24×C3
prime radicalC3×#532C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C3 ◁ C2×C3×C42 ◁ G

Complements

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

NH ≅ G/Ntype
2. C3×#3165C2semidirect
4. C3×#3139C2semidirect
5. C3×#1664C2semidirect
6. C3×#1526C2semidirect
7. C3×#1526C2semidirect
9. #19081C3direct (N × H)
43. #3165C2×C3semidirect
45. #3139C2×C3semidirect
46. #1664C2×C3semidirect
47. #1526C2×C3semidirect
48. #1526C2×C3semidirect
451. C3#19081direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#35502
C3×#31652
C3×#31412
C3×#31392
C3×#16642
C3×#15262
C3×#15252
#190813