Finite Group Databasebeta

← C3×#71174 #11778501

Subgroups — C3×#71174 #11778501

Order 1152.

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

normal subgroups only

This group has 484 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
2C32×#483C211yesmaximal, characteristic, complemented
3C3×#4983C211yesmaximal, characteristic, complemented
4C3×#4967C211yesmaximal, characteristic
5C3×#4538C211yesmaximal, characteristic, complemented
6C3×#4470C211yesmaximal, characteristic
7C3×#4469C211yesmaximal, characteristic, complemented
8C3×#1609—31nomaximal
9#71174C311yesmaximal, characteristic, direct product factor
10C32×C22⋊Q8C2211yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
12C3×#946—21no—
13C3×#930C2211yescharacteristic
14C2×C3×Dic3⋊C4—21no—
15C2×C3×Dic3⋊C4C2211yescharacteristic
16C3×#898—21no—
17C3×#894—21no—
18C3×#890—21no—
19C3×#886—21no—
20C3×#67⋊C4—21no—
21C32×#106—21no—
22C32×#103—21no—
23C32×C22⋊C8C2211yescharacteristic
24C3×C3⋊#95—21no—
25C3×C3⋊#95C2211yescharacteristic
26C3×#830C2211yescharacteristic
27C3×#809—21no—
28C3×#807—21no—
29C3×#539—31no—
30#5645C2×C311yescharacteristic
31C3×#483—21no—
32C3×#483D311yescharacteristic, complemented
33C3×#483C2×C311yescharacteristic, complemented
34C3×#480—31no—
35C3×#398—31no—
36#4983C2×C311yescharacteristic, complemented
37#4967C2×C311yescharacteristic
38C3×#328—31no—
39C3×#327—31no—
40C3×#324—31no—
41#4538C2×C311yescharacteristic, complemented
42#4470C2×C311yescharacteristic
43#4469C2×C311yescharacteristic, complemented
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⋊C4—21no—
56C32×C4⋊C4—21no—
57C32×C4⋊C4D411yescharacteristic
58C32×C22⋊C4—21no—
59C3×(C2×D3)⋊C4—21no—
60C3×(C2×D3)⋊C4—21no—
61C3×(C2×D3)⋊C4—21no—
62C3×(C2×D3)⋊C4—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×Dic3⋊C4—42no—
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—21no—
84C2×C3×C4⋊C4—31no—
85C2×C3×C4⋊C4—61no—
86C2×C3×C4⋊C4C2×D311yescharacteristic
87C2×C3×C4⋊C4C22×C311yescharacteristic
88#946—21no—
89#930C22×C311yescharacteristic
90C2×Dic3⋊C4—21no—
91C2×Dic3⋊C4C22×C311yescharacteristic
92#898—21no—
93#894—21no—
94#890—21no—
95#886—21no—
96#67⋊C4—21no—
97C3×#107—61no—
98C3×#106—22no—
99C3×#106—21no—
100C3×#106—21no—
101C3×#103—22no—
102C3×#103—21no—
103C3×#103—21no—
104C3×#102—61no—
105C3×C22⋊C8—21no—
106C3×C22⋊C8—31no—
107C3×C22⋊C8C2×D311yescharacteristic
108C3×C22⋊C8C22×C311yescharacteristic
109C3×#95—31no—
110C3×#95—61no—
111C3⋊#95—21no—
112C3⋊#95C22×C311yescharacteristic
113#830C22×C311yescharacteristic
114#809—21no—
115#807—21no—
116C23×C32C2×D411yescharacteristic
117C22×C3×D3—21no—
118C32×Q8—41no—
119C2×C32×C4—21no—
120C2×C32×C4—21no—
121C2×C32×C4—41no—
122C2×C32×C4—41no—
123C2×C32×C4—41no—
124C2×C32×C4—41no—
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C3×#67—41no—
128C3×#67—41no—
129C2×C3×Dic3—22no—
130C2×C3×Dic3—21no—
131C2×C3×Dic3—21no—
132C2×C3×Dic3—21no—
133C2×C3×Dic3—21no—
134C2×C3×Dic3—21no—
135C2×C3×Dic3—41no—
136C2×C3×Dic3—41no—
137C2×C3×Dic3—41no—
138C3×D12—41no—
139C3×C4×D3—81no—
140C32×C8—41no—
141C3×C3⋊C8—41no—
142#539—31no—
143#483C3×D311yescharacteristic, complemented
144#480—31no—
145#398—31no—
146#328—31no—
147#327—31no—
148#324—31no—
149C2×C3×Q8—21no—
150C2×C3×Q8#6711yescharacteristic
151C2×C3×Q8C3×D411yescharacteristic
152C2×C3×D4—31no—
153C2×C3×D4—61no—
154C22×C3×C4—21no—
155C22×C3×C4—21no—
156C22×C3×C4—21no—
157C22×C3×C4—31no—
158C22×C3×C4—31no—
159C22×C3×C4—41no—
160C22×C3×C4—61no—
161C22×C3×C4—61no—
162C22×C3×C4C22×D311yescharacteristic
163C22×C3×C4C23×C311yescharacteristic
164C2×#67—21no—
165C22×Dic3—21no—
166C22×Dic3C3×D411yescharacteristic
167C22×Dic3C3×D411yescharacteristic
168C2×D12C3×D411yescharacteristic
169C2×C4×D3—21no—
170C2×C3×C8—22no—
171C2×C3×C8—21no—
172C2×C3×C8—21no—
173C2×C3×C8—61no—
174C3×C4⋊C4—21no—
175C3×C4⋊C4—21no—
176C3×C4⋊C4—22no—
177C3×C4⋊C4—21no—
178C3×C4⋊C4—21no—
179C3×C4⋊C4—21no—
180C3×C4⋊C4—21no—
181C3×C4⋊C4—21no—
182C3×C4⋊C4—31no—
183C3×C4⋊C4—41no—
184C3×C4⋊C4—41no—
185C3×C4⋊C4—61no—
186C3×C4⋊C4—61no—
187C3×C4⋊C4—61no—
188C3×C4⋊C4—61no—
189C3×C4⋊C4—61no—
190C3×C4⋊C4—122no—
191C3×C4⋊C4#6711yescharacteristic
192C3×C4⋊C4C3×D411yescharacteristic
193C3×C22⋊C4—21no—
194C3×C22⋊C4—21no—
195C3×C22⋊C4—41no—
196C3×C22⋊C4—61no—
197C3×C22⋊C4—61no—
198C3×C22⋊C4—61no—
199C3×C22⋊C4—61no—
200C3×C42—61no—
201(C2×D3)⋊C4—21no—
202(C2×D3)⋊C4—21no—
203(C2×D3)⋊C4—21no—
204(C2×D3)⋊C4—21no—
205C4⋊Dic3—21no—
206C4⋊Dic3—21no—
207C4⋊Dic3C3×D411yescharacteristic
208Dic3⋊C4—21no—
209Dic3⋊C4—21no—
210Dic3⋊C4—21no—
211Dic3⋊C4—42no—
212C4×Dic3—21no—
213C2×C3⋊C8—21no—
214C22×C32—21no—
215C22×C32—21no—
216C22×C32#12011yescharacteristic
217C22×C32#13511yescharacteristic
218C22×C32AGL(1,ℤ/8)11yescharacteristic
219C2×C3×D3—41no—
220C2×C3×D3—41no—
221C2×C3×D3—41no—
222C32×C4—21no—
223C32×C4—21no—
224C32×C4—41no—
225C32×C4—41no—
226C32×C4—81no—
227C3×Dic3—42no—
228C3×Dic3—41no—
229C3×Dic3—41no—
230C3×Dic3—41no—
231#126—61no—
232#125—61no—
233#123—61no—
234#123—61no—
235C22⋊Q8—61no—
236C22⋊Q8C2×C3×D311yescharacteristic
237#121—31no—
238C4×D4—61no—
239C2×C4⋊C4—31no—
240C2×C4⋊C4—61no—
241C2×C4⋊C4C2×C3×D311yescharacteristic
242#107—61no—
243#106—21no—
244#103—21no—
245#102—61no—
246C22⋊C8—31no—
247C22⋊C8C2×C3×D311yescharacteristic
248#95—31no—
249#95—61no—
250C23×C3—21no—
251C23×C3—61no—
252C23×C3D3×D411yescharacteristic
253C23×C3C2×C3×D411yescharacteristic
254C22×D3—21no—
255C3×Q8—41no—
256C3×Q8—41no—
257C3×Q8—42no—
258C3×D4—121no—
259C3×D4—121no—
260C3×D4—121no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—21no—
266C2×C3×C4—21no—
267C2×C3×C4—41no—
268C2×C3×C4—41no—
269C2×C3×C4—41no—
270C2×C3×C4—41no—
271C2×C3×C4—42no—
272C2×C3×C4—42no—
273C2×C3×C4—41no—
274C2×C3×C4—41no—
275C2×C3×C4—41no—
276C2×C3×C4—41no—
277C2×C3×C4—41no—
278C2×C3×C4—41no—
279C2×C3×C4—62no—
280C2×C3×C4—61no—
281C2×C3×C4—61no—
282C2×C3×C4—61no—
283C2×C3×C4—61no—
284C2×C3×C4—61no—
285C2×C3×C4—81no—
286C2×C3×C4—81no—
287C2×C3×C4—121no—
288C2×C3×C4—121no—
289C2×C3×C4—121no—
290C2×C3×C4—241no—
291C2×C3×C4D3×D411yescharacteristic
292C2×C3×C4C2×#6711yescharacteristic
293C2×C3×C4C2×C3×D411yescharacteristic
294C2×C3×C4C2×C3×D411yescharacteristic
295#67—41no—
296#67—41no—
297C2×Dic3—22no—
298C2×Dic3—21no—
299C2×Dic3—21no—
300C2×Dic3—21no—
301C2×Dic3—21no—
302C2×Dic3—21no—
303C2×Dic3—41no—
304C2×Dic3—41no—
305C2×Dic3—41no—
306D12—41no—
307C4×D3—81no—
308C3×C8—42no—
309C3×C8—41no—
310C3×C8—41no—
311C3×C8—121no—
312C3⋊C8—41no—
313C2×C32—21no—
314C2×C32—21no—
315C2×C32#44911yescharacteristic
316C2×C32#45611yescharacteristic
317C2×C32#45811yescharacteristic
318C3×D3—81no—
319C2×Q8C3×#6711yescharacteristic
320C2×D4—31no—
321C2×D4—61no—
322C22×C4—21no—
323C22×C4—31no—
324C22×C4—31no—
325C22×C4—61no—
326C22×C4—61no—
327C22×C4C22×C3×D311yescharacteristic
328C2×C8—21no—
329C2×C8—61no—
330C4⋊C4—21no—
331C4⋊C4—21no—
332C4⋊C4—21no—
333C4⋊C4—31no—
334C4⋊C4—61no—
335C4⋊C4—61no—
336C4⋊C4—61no—
337C4⋊C4—61no—
338C4⋊C4—61no—
339C4⋊C4—122no—
340C4⋊C4C3×#6711yescharacteristic
341C22⋊C4—21no—
342C22⋊C4—61no—
343C22⋊C4—61no—
344C22⋊C4—61no—
345C22⋊C4—61no—
346C42—61no—
347C22×C3—21no—
348C22×C3—21no—
349C22×C3—21no—
350C22×C3—21no—
351C22×C3—21no—
352C22×C3—21no—
353C22×C3—21no—
354C22×C3—41no—
355C22×C3—41no—
356C22×C3—121no—
357C22×C3—121no—
358C22×C3—121no—
359C22×C3#91411yescharacteristic
360C22×C3#91611yescharacteristic
361C22×C3#93711yescharacteristic
362C22×C3C3×#12011yescharacteristic
363C22×C3C3×#13511yescharacteristic
364C22×C3C3×AGL(1,ℤ/8)11yescharacteristic
365C2×D3—41no—
366C2×D3—41no—
367C2×D3—41no—
368C3×C4—22no—
369C3×C4—21no—
370C3×C4—21no—
371C3×C4—21no—
372C3×C4—21no—
373C3×C4—41no—
374C3×C4—41no—
375C3×C4—41no—
376C3×C4—41no—
377C3×C4—41no—
378C3×C4—81no—
379C3×C4—81no—
380C3×C4—82no—
381C3×C4—81no—
382C3×C4—81no—
383C3×C4—122no—
384C3×C4—121no—
385C3×C4—121no—
386C3×C4—121no—
387Dic3—42no—
388Dic3—41no—
389Dic3—41no—
390Dic3—41no—
391C32#160911yescharacteristic, complemented, Sylow
392C23—61no—
393C23C3×D3×D411yescharacteristic
394Q8—41no—
395D4—121no—
396D4—121no—
397D4—121no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—62no—
405C2×C4—61no—
406C2×C4—61no—
407C2×C4—61no—
408C2×C4—61no—
409C2×C4—61no—
410C2×C4—121no—
411C2×C4—121no—
412C2×C4—121no—
413C2×C4—241no—
414C2×C4C3×D3×D411yescharacteristic
415C2×C4C2×C3×#6711yescharacteristic
416C8—41no—
417C8—121no—
418C2×C3—21no—
419C2×C3—21no—
420C2×C3—21no—
421C2×C3—21no—
422C2×C3—21no—
423C2×C3—21no—
424C2×C3—21no—
425C2×C3—41no—
426C2×C3—41no—
427C2×C3—241no—
428C2×C3#505311yescharacteristic
429C2×C3#517211yescharacteristic
430C2×C3#520511yescharacteristic
431C2×C3C3×#44911yescharacteristic
432C2×C3C3×#45611yescharacteristic
433C2×C3C3×#45811yescharacteristic
434D3—81no—
435C22—21no—
436C22—21no—
437C22—121no—
438C22—121no—
439C22—121no—
440C22C3×#91411yescharacteristic
441C22C3×#91611yescharacteristic
442C22C3×#93711yescharacteristic
443C4—21no—
444C4—21no—
445C4—41no—
446C4—41no—
447C4—81no—
448C4—122no—
449C4—121no—
450C4—121no—
451C4—121no—
452C3—21no—
453C3#7117411yescharacteristic, direct product factor
454C3C3×#160911yescharacteristic, complemented
455C2—21no—
456C2—21no—
457C2—241no—
458C2C3×#505311yescharacteristic
459C2C3×#517211yescharacteristic
460C2C3×#520511yescharacteristic
subgroupG/H
centerC22×C3#937
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC32×#483C2
socleC22×C32#120
prime radicalC3×#930C22
hypercenterC3×#483D3
hypocenterC3C3×#1609
LCSG ▷ C22×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#483

Complements

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

NH ≅ G/Ntype
2. C32×#483C2semidirect
3. C3×#4983C2semidirect
5. C3×#4538C2semidirect
7. C3×#4469C2semidirect
9. #71174C3direct (N × H)
32. C3×#483D3semidirect
33. C3×#483C2×C3semidirect
36. #4983C2×C3semidirect
41. #4538C2×C3semidirect
43. #4469C2×C3semidirect
143. #483C3×D3semidirect
391. C32#1609semidirect
453. C3#71174direct (N × H)
454. C3C3×#1609semidirect

Maximal subgroups

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

subgroupindex
C3×#56452
C32×#4832
C3×#49832
C3×#49672
C3×#45382
C3×#44702
C3×#44692
C3×#16093
#711743