Finite Group Databasebeta

← C3×#68330 #11778739

Subgroups — C3×#68330 #11778739

Order 1152.

456 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5645C211yesmaximal, characteristic
2C3×#5044C211yesmaximal, characteristic, complemented
3C3×#4735C211yesmaximal, characteristic
4C3×#4659C211yesmaximal, characteristic, complemented
5C32×#328C211yesmaximal, characteristic, complemented
6C3×#4469C211yesmaximal, characteristic, complemented
7C3×#4451C211yesmaximal, characteristic
8C3×#1615—31nomaximal
9#68330C311yesmaximal, characteristic, direct product factor
10C32×C22⋊Q8C2211yescharacteristic
11C3×#946—21no—
12C3×#930C2211yescharacteristic
13C2×C3×C4⋊Dic3C2211yescharacteristic
14C2×C3×Dic3⋊C4C2211yescharacteristic
15C3×#898—21no—
16C3×#894—21no—
17C3×#890—21no—
18C3×#886—21no—
19C3×#67⋊C4—21no—
20C32×C22⋊C8C2211yescharacteristic
21C32×#95C2211yescharacteristic
22C3×#835—21no—
23C3×C3⋊#95—21no—
24C3×C3⋊#95—21no—
25C3×#830C2211yescharacteristic
26C3×#821—21no—
27C3×#817—21no—
28C3×#807—21no—
29C3×#539—31no—
30#5645C2×C311yescharacteristic
31C3×#484—31no—
32C3×#481—31no—
33C3×#400—31no—
34#5044C2×C311yescharacteristic, complemented
35#4735C2×C311yescharacteristic
36#4659C2×C311yescharacteristic, complemented
37C3×#328—21no—
38C3×#328D311yescharacteristic, complemented
39C3×#328C2×C311yescharacteristic, complemented
40C3×#327—31no—
41C3×#324—31no—
42#4469C2×C311yescharacteristic, complemented
43#4451C2×C311yescharacteristic
44C2×C32×Q8D411yescharacteristic
45C22×C32×C4—21no—
46C22×C32×C4C2311yescharacteristic
47C2×C3×#67—21no—
48C22×C3×Dic3—21no—
49C22×C3×Dic3D411yescharacteristic
50C22×C3×Dic3D411yescharacteristic
51C2×C3×D12D411yescharacteristic
52C2×C3×C4×D3—21no—
53C2×C32×C8—21no—
54C32×C4⋊C4—21no—
55C32×C4⋊C4D411yescharacteristic
56C32×C22⋊C4—21no—
57C3×(C2×D3)⋊C4—21no—
58C3×(C2×D3)⋊C4—21no—
59C3×(C2×D3)⋊C4—21no—
60C3×(C2×D3)⋊C4—21no—
61C3×C4⋊Dic3—21no—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3—21no—
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3D411yescharacteristic
66C3×Dic3⋊C4—21no—
67C3×Dic3⋊C4—21no—
68C3×Dic3⋊C4—21no—
69C3×C4×Dic3—21no—
70C2×C3×C3⋊C8—21no—
71#1615—31noSylow
72C3×#126—61no—
73C3×#125—61no—
74C3×#123—61no—
75C3×#123—61no—
76C3×C22⋊Q8—21no—
77C3×C22⋊Q8—61no—
78C3×C22⋊Q8C2×D311yescharacteristic
79C3×C22⋊Q8C22×C311yescharacteristic
80C3×#121—31no—
81C3×C4×D4—61no—
82C2×C3×C4⋊C4—31no—
83C2×C3×C4⋊C4—31no—
84#946—21no—
85#930C22×C311yescharacteristic
86C2×C4⋊Dic3C22×C311yescharacteristic
87C2×Dic3⋊C4C22×C311yescharacteristic
88#898—21no—
89#894—21no—
90#890—21no—
91#886—21no—
92#67⋊C4—21no—
93C3×#107—61no—
94C3×#106—61no—
95C3×#103—61no—
96C3×#102—61no—
97C3×C22⋊C8—21no—
98C3×C22⋊C8—31no—
99C3×C22⋊C8C2×D311yescharacteristic
100C3×C22⋊C8C22×C311yescharacteristic
101C3×#95—21no—
102C3×#95—61no—
103C3×#95—61no—
104C3×#95C2×D311yescharacteristic
105C3×#95C22×C311yescharacteristic
106#835—21no—
107C3⋊#95—21no—
108C3⋊#95—21no—
109#830C22×C311yescharacteristic
110#821—21no—
111#817—21no—
112#807—21no—
113C23×C32C2×D411yescharacteristic
114C22×C3×D3—21no—
115C32×Q8—41no—
116C2×C32×C4—21no—
117C2×C32×C4—21no—
118C2×C32×C4—41no—
119C2×C32×C4—41no—
120C2×C32×C4—41no—
121C2×C32×C4—41no—
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C3×#67—41no—
125C3×#67—41no—
126C2×C3×Dic3—21no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—21no—
129C2×C3×Dic3—21no—
130C2×C3×Dic3—21no—
131C2×C3×Dic3—41no—
132C2×C3×Dic3—42no—
133C2×C3×Dic3—41no—
134C3×D12—41no—
135C3×C4×D3—81no—
136C32×C8—41no—
137C3×C3⋊C8—41no—
138#539—31no—
139#484—31no—
140#481—31no—
141#400—31no—
142#328C3×D311yescharacteristic, complemented
143#327—31no—
144#324—31no—
145C2×C3×Q8—21no—
146C2×C3×Q8D1211yescharacteristic
147C2×C3×Q8C3×D411yescharacteristic
148C2×C3×D4—31no—
149C2×C3×D4—61no—
150C22×C3×C4—21no—
151C22×C3×C4—21no—
152C22×C3×C4—21no—
153C22×C3×C4—31no—
154C22×C3×C4—31no—
155C22×C3×C4—41no—
156C22×C3×C4—61no—
157C22×C3×C4—61no—
158C22×C3×C4C22×D311yescharacteristic
159C22×C3×C4C23×C311yescharacteristic
160C2×#67—21no—
161C22×Dic3—21no—
162C22×Dic3C3×D411yescharacteristic
163C22×Dic3C3×D411yescharacteristic
164C2×D12C3×D411yescharacteristic
165C2×C4×D3—21no—
166C2×C3×C8—21no—
167C2×C3×C8—21no—
168C2×C3×C8—41no—
169C2×C3×C8—61no—
170C3×C4⋊C4—21no—
171C3×C4⋊C4—21no—
172C3×C4⋊C4—21no—
173C3×C4⋊C4—31no—
174C3×C4⋊C4—41no—
175C3×C4⋊C4—61no—
176C3×C4⋊C4—61no—
177C3×C4⋊C4—61no—
178C3×C4⋊C4—61no—
179C3×C4⋊C4—61no—
180C3×C4⋊C4—61no—
181C3×C4⋊C4—61no—
182C3×C4⋊C4D1211yescharacteristic
183C3×C4⋊C4C3×D411yescharacteristic
184C3×C22⋊C4—21no—
185C3×C22⋊C4—21no—
186C3×C22⋊C4—41no—
187C3×C22⋊C4—61no—
188C3×C22⋊C4—61no—
189C3×C22⋊C4—61no—
190C3×C22⋊C4—61no—
191C3×C42—61no—
192(C2×D3)⋊C4—21no—
193(C2×D3)⋊C4—21no—
194(C2×D3)⋊C4—21no—
195(C2×D3)⋊C4—21no—
196C4⋊Dic3—21no—
197C4⋊Dic3—21no—
198C4⋊Dic3—21no—
199C4⋊Dic3—21no—
200C4⋊Dic3C3×D411yescharacteristic
201Dic3⋊C4—21no—
202Dic3⋊C4—21no—
203Dic3⋊C4—21no—
204C4×Dic3—21no—
205C2×C3⋊C8—21no—
206C22×C32—21no—
207C22×C32—21no—
208C22×C32#12011yescharacteristic
209C22×C32#13511yescharacteristic
210C22×C32#13711yescharacteristic
211C2×C3×D3—41no—
212C2×C3×D3—41no—
213C2×C3×D3—41no—
214C32×C4—21no—
215C32×C4—21no—
216C32×C4—41no—
217C32×C4—41no—
218C32×C4—81no—
219C3×Dic3—41no—
220C3×Dic3—41no—
221C3×Dic3—41no—
222C3×Dic3—81no—
223#126—61no—
224#125—61no—
225#123—61no—
226#123—61no—
227C22⋊Q8—61no—
228C22⋊Q8C2×C3×D311yescharacteristic
229#121—31no—
230C4×D4—61no—
231C2×C4⋊C4—31no—
232C2×C4⋊C4—31no—
233#107—61no—
234#106—61no—
235#103—61no—
236#102—61no—
237C22⋊C8—31no—
238C22⋊C8C2×C3×D311yescharacteristic
239#95—61no—
240#95—61no—
241#95C2×C3×D311yescharacteristic
242C23×C3—21no—
243C23×C3—61no—
244C23×C3D3×D411yescharacteristic
245C23×C3C2×C3×D411yescharacteristic
246C22×D3—21no—
247C3×Q8—41no—
248C3×Q8—41no—
249C3×Q8—81no—
250C3×D4—121no—
251C3×D4—121no—
252C3×D4—121no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—41no—
260C2×C3×C4—41no—
261C2×C3×C4—41no—
262C2×C3×C4—41no—
263C2×C3×C4—41no—
264C2×C3×C4—41no—
265C2×C3×C4—41no—
266C2×C3×C4—41no—
267C2×C3×C4—42no—
268C2×C3×C4—41no—
269C2×C3×C4—41no—
270C2×C3×C4—61no—
271C2×C3×C4—61no—
272C2×C3×C4—61no—
273C2×C3×C4—61no—
274C2×C3×C4—61no—
275C2×C3×C4—81no—
276C2×C3×C4—81no—
277C2×C3×C4—81no—
278C2×C3×C4—121no—
279C2×C3×C4—122no—
280C2×C3×C4—121no—
281C2×C3×C4—241no—
282C2×C3×C4C2×D1211yescharacteristic
283C2×C3×C4D3×D411yescharacteristic
284C2×C3×C4C2×C3×D411yescharacteristic
285C2×C3×C4C2×C3×D411yescharacteristic
286#67—41no—
287#67—41no—
288C2×Dic3—21no—
289C2×Dic3—21no—
290C2×Dic3—21no—
291C2×Dic3—21no—
292C2×Dic3—21no—
293C2×Dic3—41no—
294C2×Dic3—42no—
295C2×Dic3—41no—
296D12—41no—
297C4×D3—81no—
298C3×C8—41no—
299C3×C8—41no—
300C3×C8—81no—
301C3×C8—121no—
302C3⋊C8—41no—
303C2×C32—21no—
304C2×C32—21no—
305C2×C32#45211yescharacteristic
306C2×C32#45411yescharacteristic
307C2×C32#45811yescharacteristic
308C3×D3—81no—
309C2×Q8C3×D1211yescharacteristic
310C2×D4—31no—
311C2×D4—61no—
312C22×C4—21no—
313C22×C4—31no—
314C22×C4—31no—
315C22×C4—61no—
316C22×C4—61no—
317C22×C4C22×C3×D311yescharacteristic
318C2×C8—21no—
319C2×C8—61no—
320C4⋊C4—21no—
321C4⋊C4—31no—
322C4⋊C4—61no—
323C4⋊C4—61no—
324C4⋊C4—61no—
325C4⋊C4—61no—
326C4⋊C4—61no—
327C4⋊C4—61no—
328C4⋊C4—61no—
329C4⋊C4C3×D1211yescharacteristic
330C22⋊C4—21no—
331C22⋊C4—61no—
332C22⋊C4—61no—
333C22⋊C4—61no—
334C22⋊C4—61no—
335C42—61no—
336C22×C3—21no—
337C22×C3—21no—
338C22×C3—21no—
339C22×C3—21no—
340C22×C3—21no—
341C22×C3—21no—
342C22×C3—21no—
343C22×C3—41no—
344C22×C3—41no—
345C22×C3—121no—
346C22×C3—121no—
347C22×C3—121no—
348C22×C3#88211yescharacteristic
349C22×C3#91611yescharacteristic
350C22×C3#91811yescharacteristic
351C22×C3C3×#12011yescharacteristic
352C22×C3C3×#13511yescharacteristic
353C22×C3C3×#13711yescharacteristic
354C2×D3—41no—
355C2×D3—41no—
356C2×D3—41no—
357C3×C4—21no—
358C3×C4—21no—
359C3×C4—21no—
360C3×C4—21no—
361C3×C4—41no—
362C3×C4—41no—
363C3×C4—41no—
364C3×C4—41no—
365C3×C4—41no—
366C3×C4—41no—
367C3×C4—81no—
368C3×C4—81no—
369C3×C4—81no—
370C3×C4—81no—
371C3×C4—82no—
372C3×C4—121no—
373C3×C4—121no—
374C3×C4—121no—
375C3×C4—241no—
376Dic3—41no—
377Dic3—41no—
378Dic3—41no—
379Dic3—81no—
380C32#161511yescharacteristic, complemented, Sylow
381C23—61no—
382C23C3×D3×D411yescharacteristic
383Q8—41no—
384D4—121no—
385D4—121no—
386D4—121no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—61no—
394C2×C4—61no—
395C2×C4—61no—
396C2×C4—61no—
397C2×C4—61no—
398C2×C4—121no—
399C2×C4—122no—
400C2×C4—121no—
401C2×C4—241no—
402C2×C4C2×C3×D1211yescharacteristic
403C2×C4C3×D3×D411yescharacteristic
404C8—41no—
405C8—121no—
406C2×C3—21no—
407C2×C3—21no—
408C2×C3—21no—
409C2×C3—21no—
410C2×C3—21no—
411C2×C3—21no—
412C2×C3—21no—
413C2×C3—41no—
414C2×C3—41no—
415C2×C3—241no—
416C2×C3#474211yescharacteristic
417C2×C3#480811yescharacteristic
418C2×C3#482711yescharacteristic
419C2×C3C3×#45211yescharacteristic
420C2×C3C3×#45411yescharacteristic
421C2×C3C3×#45811yescharacteristic
422D3—81no—
423C22—21no—
424C22—21no—
425C22—121no—
426C22—121no—
427C22—121no—
428C22C3×#88211yescharacteristic
429C22C3×#91611yescharacteristic
430C22C3×#91811yescharacteristic
431C4—21no—
432C4—21no—
433C4—41no—
434C4—41no—
435C4—81no—
436C4—121no—
437C4—121no—
438C4—121no—
439C4—241no—
440C3—21no—
441C3#6833011yescharacteristic, direct product factor
442C3C3×#161511yescharacteristic, complemented
443C2—21no—
444C2—21no—
445C2—241no—
446C2C3×#474211yescharacteristic
447C2C3×#480811yescharacteristic
448C2C3×#482711yescharacteristic
subgroupG/H
centerC22×C3#882
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC32×#328C2
socleC22×C32#120
prime radicalC3×#930C22
hypercenterC3×#328D3
hypocenterC3C3×#1615
LCSG ▷ C22×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#328

Complements

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

NH ≅ G/Ntype
2. C3×#5044C2semidirect
4. C3×#4659C2semidirect
5. C32×#328C2semidirect
6. C3×#4469C2semidirect
9. #68330C3direct (N × H)
34. #5044C2×C3semidirect
36. #4659C2×C3semidirect
38. C3×#328D3semidirect
39. C3×#328C2×C3semidirect
42. #4469C2×C3semidirect
142. #328C3×D3semidirect
380. C32#1615semidirect
441. C3#68330direct (N × H)
442. C3C3×#1615semidirect

Maximal subgroups

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

subgroupindex
C3×#56452
C3×#50442
C3×#47352
C3×#46592
C32×#3282
C3×#44692
C3×#44512
C3×#16153
#683303