Finite Group Databasebeta

← C3×#68328 #11778513

Subgroups — C3×#68328 #11778513

Order 1152.

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

normal subgroups only

This group has 472 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×#5043C211yesmaximal, characteristic, complemented
3C3×#4736C211yesmaximal, characteristic
4C3×#4661C211yesmaximal, characteristic, complemented
5C32×#328C211yesmaximal, characteristic, complemented
6C3×#4469C211yesmaximal, characteristic, complemented
7C3×#4451C211yesmaximal, characteristic
8C3×#1609—31nomaximal
9#68328C311yesmaximal, characteristic, direct product factor
10C32×C22⋊Q8C2211yescharacteristic
11C3×#946—21no—
12C3×#930C2211yescharacteristic
13C2×C3×C4⋊Dic3—21no—
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×Dic3⋊C4C2211yescharacteristic
16C3×#898—21no—
17C3×#894—21no—
18C3×#890—21no—
19C3×#886—21no—
20C3×#67⋊C4—21no—
21C32×C22⋊C8C2211yescharacteristic
22C32×#95C2211yescharacteristic
23C3×#835—21no—
24C3×C3⋊#95—21no—
25C3×#830C2211yescharacteristic
26C3×#821—21no—
27C3×#818—21no—
28C3×#808—21no—
29C3×#539—31no—
30#5645C2×C311yescharacteristic
31C3×#483—31no—
32C3×#480—31no—
33C3×#398—31no—
34#5043C2×C311yescharacteristic, complemented
35#4736C2×C311yescharacteristic
36#4661C2×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⋊Dic3—42no—
66C3×C4⋊Dic3D411yescharacteristic
67C3×Dic3⋊C4—21no—
68C3×Dic3⋊C4—21no—
69C3×Dic3⋊C4—21no—
70C3×C4×Dic3—21no—
71C2×C3×C3⋊C8—21no—
72#1609—31noSylow
73C3×#126—61no—
74C3×#125—61no—
75C3×#123—61no—
76C3×#123—61no—
77C3×C22⋊Q8—21no—
78C3×C22⋊Q8—61no—
79C3×C22⋊Q8C2×D311yescharacteristic
80C3×C22⋊Q8C22×C311yescharacteristic
81C3×#121—31no—
82C3×C4×D4—61no—
83C2×C3×C4⋊C4—31no—
84C2×C3×C4⋊C4—31no—
85C2×C3×C4⋊C4—61no—
86#946—21no—
87#930C22×C311yescharacteristic
88C2×C4⋊Dic3—21no—
89C2×C4⋊Dic3C22×C311yescharacteristic
90C2×Dic3⋊C4C22×C311yescharacteristic
91#898—21no—
92#894—21no—
93#890—21no—
94#886—21no—
95#67⋊C4—21no—
96C3×#107—61no—
97C3×#106—61no—
98C3×#103—61no—
99C3×#102—61no—
100C3×C22⋊C8—21no—
101C3×C22⋊C8—31no—
102C3×C22⋊C8C2×D311yescharacteristic
103C3×C22⋊C8C22×C311yescharacteristic
104C3×#95—21no—
105C3×#95—61no—
106C3×#95C2×D311yescharacteristic
107C3×#95C22×C311yescharacteristic
108#835—21no—
109C3⋊#95—21no—
110#830C22×C311yescharacteristic
111#821—21no—
112#818—21no—
113#808—21no—
114C23×C32C2×D411yescharacteristic
115C22×C3×D3—21no—
116C32×Q8—41no—
117C2×C32×C4—22no—
118C2×C32×C4—21no—
119C2×C32×C4—21no—
120C2×C32×C4—41no—
121C2×C32×C4—41no—
122C2×C32×C4—41no—
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C3×#67—41no—
126C3×#67—41no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—21no—
129C2×C3×Dic3—21no—
130C2×C3×Dic3—21no—
131C2×C3×Dic3—21no—
132C2×C3×Dic3—41no—
133C2×C3×Dic3—41no—
134C2×C3×Dic3—41no—
135C2×C3×Dic3—41no—
136C3×D12—41no—
137C3×C4×D3—81no—
138C32×C8—41no—
139C3×C3⋊C8—41no—
140#539—31no—
141#483—31no—
142#480—31no—
143#398—31no—
144#328C3×D311yescharacteristic, complemented
145#327—31no—
146#324—31no—
147C2×C3×Q8—21no—
148C2×C3×Q8D1211yescharacteristic
149C2×C3×Q8C3×D411yescharacteristic
150C2×C3×D4—31no—
151C2×C3×D4—61no—
152C22×C3×C4—21no—
153C22×C3×C4—21no—
154C22×C3×C4—21no—
155C22×C3×C4—31no—
156C22×C3×C4—31no—
157C22×C3×C4—41no—
158C22×C3×C4—61no—
159C22×C3×C4—61no—
160C22×C3×C4C22×D311yescharacteristic
161C22×C3×C4C23×C311yescharacteristic
162C2×#67—21no—
163C22×Dic3—21no—
164C22×Dic3C3×D411yescharacteristic
165C22×Dic3C3×D411yescharacteristic
166C2×D12C3×D411yescharacteristic
167C2×C4×D3—21no—
168C2×C3×C8—21no—
169C2×C3×C8—21no—
170C2×C3×C8—41no—
171C2×C3×C8—61no—
172C3×C4⋊C4—21no—
173C3×C4⋊C4—21no—
174C3×C4⋊C4—21no—
175C3×C4⋊C4—31no—
176C3×C4⋊C4—41no—
177C3×C4⋊C4—61no—
178C3×C4⋊C4—61no—
179C3×C4⋊C4—61no—
180C3×C4⋊C4—61no—
181C3×C4⋊C4—61no—
182C3×C4⋊C4—61no—
183C3×C4⋊C4—61no—
184C3×C4⋊C4—122no—
185C3×C4⋊C4D1211yescharacteristic
186C3×C4⋊C4C3×D411yescharacteristic
187C3×C22⋊C4—21no—
188C3×C22⋊C4—21no—
189C3×C22⋊C4—41no—
190C3×C22⋊C4—61no—
191C3×C22⋊C4—61no—
192C3×C22⋊C4—61no—
193C3×C22⋊C4—61no—
194C3×C42—61no—
195(C2×D3)⋊C4—21no—
196(C2×D3)⋊C4—21no—
197(C2×D3)⋊C4—21no—
198(C2×D3)⋊C4—21no—
199C4⋊Dic3—21no—
200C4⋊Dic3—21no—
201C4⋊Dic3—21no—
202C4⋊Dic3—21no—
203C4⋊Dic3—42no—
204C4⋊Dic3C3×D411yescharacteristic
205Dic3⋊C4—21no—
206Dic3⋊C4—21no—
207Dic3⋊C4—21no—
208C4×Dic3—21no—
209C2×C3⋊C8—21no—
210C22×C32—21no—
211C22×C32—21no—
212C22×C32#12011yescharacteristic
213C22×C32#13511yescharacteristic
214C22×C32AGL(1,ℤ/8)11yescharacteristic
215C2×C3×D3—41no—
216C2×C3×D3—41no—
217C2×C3×D3—41no—
218C32×C4—21no—
219C32×C4—21no—
220C32×C4—42no—
221C32×C4—41no—
222C32×C4—41no—
223C3×Dic3—41no—
224C3×Dic3—41no—
225C3×Dic3—41no—
226C3×Dic3—81no—
227#126—61no—
228#125—61no—
229#123—61no—
230#123—61no—
231C22⋊Q8—61no—
232C22⋊Q8C2×C3×D311yescharacteristic
233#121—31no—
234C4×D4—61no—
235C2×C4⋊C4—31no—
236C2×C4⋊C4—31no—
237C2×C4⋊C4—61no—
238#107—61no—
239#106—61no—
240#103—61no—
241#102—61no—
242C22⋊C8—31no—
243C22⋊C8C2×C3×D311yescharacteristic
244#95—61no—
245#95C2×C3×D311yescharacteristic
246C23×C3—21no—
247C23×C3—61no—
248C23×C3D3×D411yescharacteristic
249C23×C3C2×C3×D411yescharacteristic
250C22×D3—21no—
251C3×Q8—41no—
252C3×Q8—41no—
253C3×Q8—81no—
254C3×D4—121no—
255C3×D4—121no—
256C3×D4—121no—
257C2×C3×C4—22no—
258C2×C3×C4—22no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—41no—
266C2×C3×C4—41no—
267C2×C3×C4—42no—
268C2×C3×C4—41no—
269C2×C3×C4—41no—
270C2×C3×C4—41no—
271C2×C3×C4—41no—
272C2×C3×C4—41no—
273C2×C3×C4—41no—
274C2×C3×C4—61no—
275C2×C3×C4—61no—
276C2×C3×C4—61no—
277C2×C3×C4—61no—
278C2×C3×C4—61no—
279C2×C3×C4—81no—
280C2×C3×C4—81no—
281C2×C3×C4—81no—
282C2×C3×C4—121no—
283C2×C3×C4—121no—
284C2×C3×C4—121no—
285C2×C3×C4—121no—
286C2×C3×C4—241no—
287C2×C3×C4C2×D1211yescharacteristic
288C2×C3×C4D3×D411yescharacteristic
289C2×C3×C4C2×C3×D411yescharacteristic
290C2×C3×C4C2×C3×D411yescharacteristic
291#67—41no—
292#67—41no—
293C2×Dic3—21no—
294C2×Dic3—21no—
295C2×Dic3—21no—
296C2×Dic3—21no—
297C2×Dic3—21no—
298C2×Dic3—41no—
299C2×Dic3—41no—
300C2×Dic3—41no—
301C2×Dic3—41no—
302D12—41no—
303C4×D3—81no—
304C3×C8—41no—
305C3×C8—41no—
306C3×C8—81no—
307C3×C8—121no—
308C3⋊C8—41no—
309C2×C32—21no—
310C2×C32—21no—
311C2×C32#44911yescharacteristic
312C2×C32#45611yescharacteristic
313C2×C32#45811yescharacteristic
314C3×D3—81no—
315C2×Q8C3×D1211yescharacteristic
316C2×D4—31no—
317C2×D4—61no—
318C22×C4—21no—
319C22×C4—31no—
320C22×C4—31no—
321C22×C4—61no—
322C22×C4—61no—
323C22×C4C22×C3×D311yescharacteristic
324C2×C8—21no—
325C2×C8—61no—
326C4⋊C4—21no—
327C4⋊C4—31no—
328C4⋊C4—61no—
329C4⋊C4—61no—
330C4⋊C4—61no—
331C4⋊C4—61no—
332C4⋊C4—61no—
333C4⋊C4—61no—
334C4⋊C4—61no—
335C4⋊C4—122no—
336C4⋊C4C3×D1211yescharacteristic
337C22⋊C4—21no—
338C22⋊C4—61no—
339C22⋊C4—61no—
340C22⋊C4—61no—
341C22⋊C4—61no—
342C42—61no—
343C22×C3—21no—
344C22×C3—21no—
345C22×C3—21no—
346C22×C3—21no—
347C22×C3—21no—
348C22×C3—21no—
349C22×C3—21no—
350C22×C3—41no—
351C22×C3—41no—
352C22×C3—121no—
353C22×C3—121no—
354C22×C3—121no—
355C22×C3#88211yescharacteristic
356C22×C3#91411yescharacteristic
357C22×C3#91911yescharacteristic
358C22×C3C3×#12011yescharacteristic
359C22×C3C3×#13511yescharacteristic
360C22×C3C3×AGL(1,ℤ/8)11yescharacteristic
361C2×D3—41no—
362C2×D3—41no—
363C2×D3—41no—
364C3×C4—21no—
365C3×C4—21no—
366C3×C4—21no—
367C3×C4—21no—
368C3×C4—41no—
369C3×C4—41no—
370C3×C4—42no—
371C3×C4—42no—
372C3×C4—41no—
373C3×C4—41no—
374C3×C4—41no—
375C3×C4—41no—
376C3×C4—81no—
377C3×C4—81no—
378C3×C4—82no—
379C3×C4—121no—
380C3×C4—121no—
381C3×C4—121no—
382C3×C4—241no—
383Dic3—41no—
384Dic3—41no—
385Dic3—41no—
386Dic3—81no—
387C32#160911yescharacteristic, complemented, Sylow
388C23—61no—
389C23C3×D3×D411yescharacteristic
390Q8—41no—
391D4—121no—
392D4—121no—
393D4—121no—
394C2×C4—22no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—61no—
401C2×C4—61no—
402C2×C4—61no—
403C2×C4—61no—
404C2×C4—61no—
405C2×C4—121no—
406C2×C4—121no—
407C2×C4—121no—
408C2×C4—121no—
409C2×C4—241no—
410C2×C4C2×C3×D1211yescharacteristic
411C2×C4C3×D3×D411yescharacteristic
412C8—41no—
413C8—121no—
414C2×C3—21no—
415C2×C3—21no—
416C2×C3—21no—
417C2×C3—21no—
418C2×C3—21no—
419C2×C3—21no—
420C2×C3—21no—
421C2×C3—41no—
422C2×C3—41no—
423C2×C3—241no—
424C2×C3#474211yescharacteristic
425C2×C3#481011yescharacteristic
426C2×C3#482611yescharacteristic
427C2×C3C3×#44911yescharacteristic
428C2×C3C3×#45611yescharacteristic
429C2×C3C3×#45811yescharacteristic
430D3—81no—
431C22—21no—
432C22—21no—
433C22—121no—
434C22—121no—
435C22—121no—
436C22C3×#88211yescharacteristic
437C22C3×#91411yescharacteristic
438C22C3×#91911yescharacteristic
439C4—21no—
440C4—21no—
441C4—42no—
442C4—41no—
443C4—41no—
444C4—121no—
445C4—121no—
446C4—121no—
447C4—241no—
448C3—21no—
449C3#6832811yescharacteristic, direct product factor
450C3C3×#160911yescharacteristic, complemented
451C2—21no—
452C2—21no—
453C2—241no—
454C2C3×#474211yescharacteristic
455C2C3×#481011yescharacteristic
456C2C3×#482611yescharacteristic
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×#1609
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×#5043C2semidirect
4. C3×#4661C2semidirect
5. C32×#328C2semidirect
6. C3×#4469C2semidirect
9. #68328C3direct (N × H)
34. #5043C2×C3semidirect
36. #4661C2×C3semidirect
38. C3×#328D3semidirect
39. C3×#328C2×C3semidirect
42. #4469C2×C3semidirect
144. #328C3×D3semidirect
387. C32#1609semidirect
449. C3#68328direct (N × H)
450. C3C3×#1609semidirect

Maximal subgroups

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

subgroupindex
C3×#56452
C3×#50432
C3×#47362
C3×#46612
C32×#3282
C3×#44692
C3×#44512
C3×#16093
#683283