Finite Group Databasebeta

← C3×#68136 #11778736

Subgroups — C3×#68136 #11778736

Order 1152.

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

normal subgroups only

This group has 455 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×#5515C211yesmaximal, characteristic
2C3×#4986C211yesmaximal, characteristic, complemented
3C3×#4735C211yesmaximal, characteristic
4C3×#4722C211yesmaximal, characteristic, complemented
5C32×#324C211yesmaximal, characteristic, complemented
6C3×#4470C211yesmaximal, characteristic
7C3×#4467C211yesmaximal, characteristic, complemented
8C3×#1615—31nomaximal
9#68136C311yesmaximal, characteristic, direct product factor
10C2×C32×C4⋊C4C2211yescharacteristic
11C3×#930C2211yescharacteristic
12C3×#929—21no—
13C3×C4×#67—21no—
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C3×#924C2211yescharacteristic
16C3×#898—21no—
17C3×#896—21no—
18C3×#894—21no—
19C3×#889—21no—
20C32×C22⋊C8C2211yescharacteristic
21C32×C22⋊C8C2211yescharacteristic
22C3×C3⋊#95—21no—
23C3×C3⋊#95—21no—
24C3×C3⋊#95C2211yescharacteristic
25C3×#821—21no—
26C3×#818—21no—
27C3×#817—21no—
28C3×#816—21no—
29C3×#539—31no—
30#5515C2×C311yescharacteristic
31C3×#484—31no—
32C3×#481—31no—
33C3×#400—31no—
34#4986C2×C311yescharacteristic, complemented
35#4735C2×C311yescharacteristic
36#4722C2×C311yescharacteristic, complemented
37C3×#328—31no—
38C3×#327—31no—
39C3×#324—21no—
40C3×#324D311yescharacteristic, complemented
41C3×#324C2×C311yescharacteristic, complemented
42#4470C2×C311yescharacteristic
43#4467C2×C311yescharacteristic, complemented
44C22×C32×C4D411yescharacteristic
45C22×C32×C4D411yescharacteristic
46C22×C32×C4C2311yescharacteristic
47C2×C3×#67—21no—
48C22×C3×Dic3—21no—
49C22×C3×Dic3—21no—
50C2×C3×D12D411yescharacteristic
51C2×C3×C4×D3—21no—
52C2×C3×Dic6D411yescharacteristic
53C2×C32×C8—21no—
54C2×C32×C8—21no—
55C32×C4⋊C4—21no—
56C32×C4⋊C4—21no—
57C3×#217—21no—
58C3×(C2×D3)⋊C4—21no—
59C3×(C2×D3)⋊C4—21no—
60C3×(C2×D3)⋊C4—21no—
61C3×(C2×D3)⋊C4—21no—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3—21no—
64C3×C4⋊Dic3D411yescharacteristic
65C3×C4⋊Dic3D411yescharacteristic
66C3×Dic3⋊C4—21no—
67C3×Dic3⋊C4—21no—
68C3×Dic3⋊C4—21no—
69C3×Dic3⋊C4—21no—
70C3×C4×Dic3—21no—
71#1615—31noSylow
72C3×#126—61no—
73C3×#125—61no—
74C3×#123—61no—
75C3×#123—61no—
76C3×C22⋊Q8—31no—
77C3×C22⋊Q8—61no—
78C3×#121—31no—
79C3×C4×D4—61no—
80C2×C3×C4⋊C4—21no—
81C2×C3×C4⋊C4—31no—
82C2×C3×C4⋊C4C2×D311yescharacteristic
83C2×C3×C4⋊C4C22×C311yescharacteristic
84#930C22×C311yescharacteristic
85#929—21no—
86C4×#67—21no—
87C2×C4⋊Dic3C22×C311yescharacteristic
88#924C22×C311yescharacteristic
89#898—21no—
90#896—21no—
91#894—21no—
92#889—21no—
93C3×#107—61no—
94C3×#106—61no—
95C3×#103—61no—
96C3×#102—61no—
97C3×C22⋊C8—21no—
98C3×C22⋊C8—21no—
99C3×C22⋊C8C2×D311yescharacteristic
100C3×C22⋊C8C2×D311yescharacteristic
101C3×C22⋊C8C22×C311yescharacteristic
102C3×C22⋊C8C22×C311yescharacteristic
103C3×#95—31no—
104C3×#95—61no—
105C3×#95—61no—
106C3⋊#95—21no—
107C3⋊#95—21no—
108C3⋊#95C22×C311yescharacteristic
109#821—21no—
110#818—21no—
111#817—21no—
112#816—21no—
113C23×C32C2×D411yescharacteristic
114C22×C3×D3—21no—
115C2×C32×C4—21no—
116C2×C32×C4—21no—
117C2×C32×C4—21no—
118C2×C32×C4—21no—
119C2×C32×C4—41no—
120C2×C32×C4—41no—
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C3×#67—41no—
124C3×#67—41no—
125C2×C3×Dic3—21no—
126C2×C3×Dic3—21no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—41no—
129C2×C3×Dic3—41no—
130C2×C3×Dic3—42no—
131C2×C3×Dic3—41no—
132C2×C3×Dic3—41no—
133C3×D12—41no—
134C3×C4×D3—81no—
135C3×Dic6—41no—
136C32×C8—41no—
137C32×C8—41no—
138#539—31no—
139#484—31no—
140#481—31no—
141#400—31no—
142#328—31no—
143#327—31no—
144#324C3×D311yescharacteristic, complemented
145C2×C3×Q8—31no—
146C2×C3×D4—31no—
147C2×C3×D4—61no—
148C22×C3×C4—21no—
149C22×C3×C4—21no—
150C22×C3×C4—21no—
151C22×C3×C4—61no—
152C22×C3×C4—61no—
153C22×C3×C4—61no—
154C22×C3×C4D1211yescharacteristic
155C22×C3×C4D1211yescharacteristic
156C22×C3×C4C3×D411yescharacteristic
157C22×C3×C4C3×D411yescharacteristic
158C22×C3×C4C22×D311yescharacteristic
159C22×C3×C4C23×C311yescharacteristic
160C2×#67—21no—
161C22×Dic3—21no—
162C22×Dic3—21no—
163C2×D12C3×D411yescharacteristic
164C2×C4×D3—21no—
165C2×Dic6C3×D411yescharacteristic
166C2×C3×C8—21no—
167C2×C3×C8—21no—
168C2×C3×C8—21no—
169C2×C3×C8—21no—
170C2×C3×C8—41no—
171C2×C3×C8—41no—
172C3×C4⋊C4—21no—
173C3×C4⋊C4—21no—
174C3×C4⋊C4—21no—
175C3×C4⋊C4—21no—
176C3×C4⋊C4—31no—
177C3×C4⋊C4—31no—
178C3×C4⋊C4—41no—
179C3×C4⋊C4—41no—
180C3×C4⋊C4—61no—
181C3×C4⋊C4—61no—
182C3×C4⋊C4—61no—
183C3×C4⋊C4—61no—
184C3×C4⋊C4—61no—
185C3×C4⋊C4—61no—
186C3×C22⋊C4—61no—
187C3×C22⋊C4—61no—
188C3×C22⋊C4—61no—
189C3×C22⋊C4—61no—
190C3×C22⋊C4—61no—
191C3×C42—61no—
192#217—21no—
193(C2×D3)⋊C4—21no—
194(C2×D3)⋊C4—21no—
195(C2×D3)⋊C4—21no—
196(C2×D3)⋊C4—21no—
197C4⋊Dic3—21no—
198C4⋊Dic3—21no—
199C4⋊Dic3C3×D411yescharacteristic
200C4⋊Dic3C3×D411yescharacteristic
201Dic3⋊C4—21no—
202Dic3⋊C4—21no—
203Dic3⋊C4—21no—
204Dic3⋊C4—21no—
205C4×Dic3—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—
218C3×Dic3—41no—
219C3×Dic3—41no—
220C3×Dic3—41no—
221C3×Dic3—81no—
222C3×Dic3—81no—
223#126—61no—
224#125—61no—
225#123—61no—
226#123—61no—
227C22⋊Q8—31no—
228C22⋊Q8—61no—
229#121—31no—
230C4×D4—61no—
231C2×C4⋊C4—31no—
232C2×C4⋊C4C2×C3×D311yescharacteristic
233#107—61no—
234#106—61no—
235#103—61no—
236#102—61no—
237C22⋊C8C2×C3×D311yescharacteristic
238C22⋊C8C2×C3×D311yescharacteristic
239#95—31no—
240#95—61no—
241#95—61no—
242C23×C3—21no—
243C23×C3—61no—
244C23×C3C2×D1211yescharacteristic
245C23×C3C2×C3×D411yescharacteristic
246C22×D3—21no—
247C3×Q8—121no—
248C3×D4—121no—
249C3×D4—121no—
250C3×D4—121no—
251C2×C3×C4—22no—
252C2×C3×C4—21no—
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—21no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—41no—
263C2×C3×C4—41no—
264C2×C3×C4—41no—
265C2×C3×C4—41no—
266C2×C3×C4—41no—
267C2×C3×C4—41no—
268C2×C3×C4—41no—
269C2×C3×C4—61no—
270C2×C3×C4—61no—
271C2×C3×C4—61no—
272C2×C3×C4—81no—
273C2×C3×C4—81no—
274C2×C3×C4—121no—
275C2×C3×C4—121no—
276C2×C3×C4—122no—
277C2×C3×C4—121no—
278C2×C3×C4—121no—
279C2×C3×C4—241no—
280C2×C3×C4D3×D411yescharacteristic
281C2×C3×C4D3×D411yescharacteristic
282C2×C3×C4C2×C3×D411yescharacteristic
283C2×C3×C4C2×C3×D411yescharacteristic
284#67—41no—
285#67—41no—
286C2×Dic3—21no—
287C2×Dic3—21no—
288C2×Dic3—21no—
289C2×Dic3—41no—
290C2×Dic3—41no—
291C2×Dic3—42no—
292C2×Dic3—41no—
293C2×Dic3—41no—
294D12—41no—
295C4×D3—81no—
296Dic6—41no—
297C3×C8—41no—
298C3×C8—41no—
299C3×C8—41no—
300C3×C8—41no—
301C3×C8—81no—
302C3×C8—81no—
303C2×C32—21no—
304C2×C32—21no—
305C2×C32#45211yescharacteristic
306C2×C32#45411yescharacteristic
307C2×C32#45811yescharacteristic
308C3×D3—81no—
309C2×Q8—31no—
310C2×D4—31no—
311C2×D4—61no—
312C22×C4—61no—
313C22×C4—61no—
314C22×C4—61no—
315C22×C4C3×D1211yescharacteristic
316C22×C4C3×D1211yescharacteristic
317C22×C4C22×C3×D311yescharacteristic
318C2×C8—21no—
319C2×C8—21no—
320C4⋊C4—21no—
321C4⋊C4—21no—
322C4⋊C4—31no—
323C4⋊C4—31no—
324C4⋊C4—61no—
325C4⋊C4—61no—
326C4⋊C4—61no—
327C4⋊C4—61no—
328C4⋊C4—61no—
329C4⋊C4—61no—
330C22⋊C4—61no—
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#90411yescharacteristic
350C22×C3#90911yescharacteristic
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—42no—
364C3×C4—41no—
365C3×C4—41no—
366C3×C4—41no—
367C3×C4—41no—
368C3×C4—81no—
369C3×C4—121no—
370C3×C4—121no—
371C3×C4—121no—
372C3×C4—241no—
373C3×C4—241no—
374Dic3—41no—
375Dic3—41no—
376Dic3—41no—
377Dic3—81no—
378Dic3—81no—
379C32#161511yescharacteristic, complemented, Sylow
380C23—61no—
381C23C2×C3×D1211yescharacteristic
382Q8—121no—
383D4—121no—
384D4—121no—
385D4—121no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—61no—
393C2×C4—61no—
394C2×C4—61no—
395C2×C4—121no—
396C2×C4—121no—
397C2×C4—122no—
398C2×C4—121no—
399C2×C4—121no—
400C2×C4—241no—
401C2×C4C3×D3×D411yescharacteristic
402C2×C4C3×D3×D411yescharacteristic
403C8—41no—
404C8—41no—
405C2×C3—21no—
406C2×C3—21no—
407C2×C3—21no—
408C2×C3—21no—
409C2×C3—21no—
410C2×C3—21no—
411C2×C3—21no—
412C2×C3—41no—
413C2×C3—41no—
414C2×C3—241no—
415C2×C3#473311yescharacteristic
416C2×C3#474211yescharacteristic
417C2×C3#475311yescharacteristic
418C2×C3C3×#45211yescharacteristic
419C2×C3C3×#45411yescharacteristic
420C2×C3C3×#45811yescharacteristic
421D3—81no—
422C22—21no—
423C22—21no—
424C22—121no—
425C22—121no—
426C22—121no—
427C22C3×#88211yescharacteristic
428C22C3×#90411yescharacteristic
429C22C3×#90911yescharacteristic
430C4—21no—
431C4—21no—
432C4—41no—
433C4—41no—
434C4—121no—
435C4—121no—
436C4—121no—
437C4—241no—
438C4—241no—
439C3—21no—
440C3#6813611yescharacteristic, direct product factor
441C3C3×#161511yescharacteristic, complemented
442C2—21no—
443C2—21no—
444C2—241no—
445C2C3×#473311yescharacteristic
446C2C3×#474211yescharacteristic
447C2C3×#475311yescharacteristic
subgroupG/H
centerC22×C3#882
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC32×#324C2
socleC22×C32#120
prime radicalC3×#930C22
hypercenterC3×#324D3
hypocenterC3C3×#1615
LCSG ▷ C22×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#324

Complements

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

NH ≅ G/Ntype
2. C3×#4986C2semidirect
4. C3×#4722C2semidirect
5. C32×#324C2semidirect
7. C3×#4467C2semidirect
9. #68136C3direct (N × H)
34. #4986C2×C3semidirect
36. #4722C2×C3semidirect
40. C3×#324D3semidirect
41. C3×#324C2×C3semidirect
43. #4467C2×C3semidirect
144. #324C3×D3semidirect
379. C32#1615semidirect
440. C3#68136direct (N × H)
441. C3C3×#1615semidirect

Maximal subgroups

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

subgroupindex
C3×#55152
C3×#49862
C3×#47352
C3×#47222
C32×#3242
C3×#44702
C3×#44672
C3×#16153
#681363