Finite Group Databasebeta

← C3×#71166 #11778495

Subgroups — C3×#71166 #11778495

Order 1152.

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

normal subgroups only

This group has 489 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×#5602C211yesmaximal, characteristic
2C32×#480C211yesmaximal, characteristic
3C3×#4983C211yesmaximal, characteristic, complemented
4C3×#4971C211yesmaximal, characteristic, complemented
5C3×#4537C211yesmaximal, characteristic
6C3×#4469C211yesmaximal, characteristic, complemented
7C3×#4467C211yesmaximal, characteristic, complemented
8C3×#1609—31nomaximal
9#71166C311yesmaximal, characteristic, direct product factor
10C32×#121C2211yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
12C3×#935—21no—
13C3×#935—21no—
14C3×D4×Dic3—21no—
15C3×#924C2211yescharacteristic
16C2×C3×Dic3⋊C4—21no—
17C2×C3×Dic3⋊C4C2211yescharacteristic
18C3×#889—21no—
19C3×#879—21no—
20C3×#878—21no—
21C32×#107—21no—
22C32×#102—21no—
23C32×C22⋊C8C2211yescharacteristic
24C3×C3⋊#95—21no—
25C3×C3⋊#95C2211yescharacteristic
26C3×#830C2211yescharacteristic
27C3×#810—21no—
28C3×#808—21no—
29C3×#539—31no—
30#5602C2×C311yescharacteristic
31C3×#483—31no—
32C3×#480—21no—
33C3×#480D311yescharacteristic
34C3×#480C2×C311yescharacteristic
35C3×#398—31no—
36#4983C2×C311yescharacteristic, complemented
37#4971C2×C311yescharacteristic, complemented
38C3×#328—31no—
39C3×#327—31no—
40C3×#324—31no—
41#4537C2×C311yescharacteristic
42#4469C2×C311yescharacteristic, complemented
43#4467C2×C311yescharacteristic, complemented
44C2×C32×D4—21no—
45C2×C32×D4D411yescharacteristic
46C22×C32×C4—21no—
47C22×C32×C4C2311yescharacteristic
48C22×C3×Dic3—21no—
49C22×C3×Dic3—21no—
50C22×C3×Dic3D411yescharacteristic
51C22×C3×Dic3D411yescharacteristic
52C2×C3×Dic6D411yescharacteristic
53C2×C32×C8—21no—
54C32×C4⋊C4—21no—
55C32×C4⋊C4—21no—
56C32×C4⋊C4D411yescharacteristic
57C32×C22⋊C4—21no—
58C3×#217—21no—
59C3×#217—21no—
60C3×#217—21no—
61C3×#217—21no—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3D411yescharacteristic
64C3×Dic3⋊C4—21no—
65C3×Dic3⋊C4—21no—
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—31no—
78C3×C22⋊Q8—61no—
79C3×#121—21no—
80C3×#121C2×D311yescharacteristic
81C3×#121C22×C311yescharacteristic
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#935—21no—
89#935—21no—
90D4×Dic3—21no—
91#924C22×C311yescharacteristic
92C2×Dic3⋊C4—21no—
93C2×Dic3⋊C4C22×C311yescharacteristic
94#889—21no—
95#879—21no—
96#878—21no—
97C3×#107—22no—
98C3×#107—21no—
99C3×#107—21no—
100C3×#106—61no—
101C3×#103—61no—
102C3×#102—22no—
103C3×#102—21no—
104C3×#102—21no—
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#810—21no—
115#808—21no—
116C23×C32—21no—
117C23×C32C2×D411yescharacteristic
118C32×D4—41no—
119C32×D4—41no—
120C32×D4—41no—
121C2×C32×C4—21no—
122C2×C32×C4—41no—
123C2×C32×C4—41no—
124C2×C32×C4—41no—
125C2×C32×C4—41no—
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C3×Dic3—22no—
129C2×C3×Dic3—21no—
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—
138C2×C3×Dic3—81no—
139C3×Dic6—41no—
140C32×C8—41no—
141C3×C3⋊C8—41no—
142#539—31no—
143#483—31no—
144#480C3×D311yescharacteristic
145#398—31no—
146#328—31no—
147#327—31no—
148#324—31no—
149C2×C3×Q8—31no—
150C2×C3×D4—21no—
151C2×C3×D4—21no—
152C2×C3×D4—21no—
153C2×C3×D4—41no—
154C2×C3×D4#6711yescharacteristic
155C2×C3×D4C3×D411yescharacteristic
156C22×C3×C4—21no—
157C22×C3×C4—21no—
158C22×C3×C4—21no—
159C22×C3×C4—31no—
160C22×C3×C4—31no—
161C22×C3×C4—41no—
162C22×C3×C4—61no—
163C22×C3×C4—61no—
164C22×C3×C4C22×D311yescharacteristic
165C22×C3×C4C23×C311yescharacteristic
166C22×Dic3—21no—
167C22×Dic3—21no—
168C22×Dic3C3×D411yescharacteristic
169C22×Dic3C3×D411yescharacteristic
170C2×Dic6C3×D411yescharacteristic
171C2×C3×C8—22no—
172C2×C3×C8—21no—
173C2×C3×C8—21no—
174C2×C3×C8—61no—
175C3×C4⋊C4—22no—
176C3×C4⋊C4—21no—
177C3×C4⋊C4—21no—
178C3×C4⋊C4—21no—
179C3×C4⋊C4—21no—
180C3×C4⋊C4—21no—
181C3×C4⋊C4—31no—
182C3×C4⋊C4—41no—
183C3×C4⋊C4—61no—
184C3×C4⋊C4—61no—
185C3×C4⋊C4—61no—
186C3×C4⋊C4—61no—
187C3×C4⋊C4—61no—
188C3×C4⋊C4—61no—
189C3×C4⋊C4—122no—
190C3×C4⋊C4#6711yescharacteristic
191C3×C4⋊C4C3×D411yescharacteristic
192C3×C22⋊C4—21no—
193C3×C22⋊C4—21no—
194C3×C22⋊C4—41no—
195C3×C22⋊C4—61no—
196C3×C22⋊C4—61no—
197C3×C22⋊C4—61no—
198C3×C22⋊C4—61no—
199C3×C42—61no—
200#217—21no—
201#217—21no—
202#217—21no—
203#217—21no—
204C4⋊Dic3—21no—
205C4⋊Dic3C3×D411yescharacteristic
206Dic3⋊C4—21no—
207Dic3⋊C4—21no—
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—41no—
217C22×C32—41no—
218C22×C32—41no—
219C22×C32#12011yescharacteristic
220C22×C32#13511yescharacteristic
221C22×C32AGL(1,ℤ/8)11yescharacteristic
222C32×C4—21no—
223C32×C4—21no—
224C32×C4—41no—
225C32×C4—81no—
226C3×Dic3—42no—
227C3×Dic3—41no—
228C3×Dic3—41no—
229C3×Dic3—41no—
230C3×Dic3—41no—
231#126—61no—
232#125—61no—
233#123—61no—
234#123—61no—
235C22⋊Q8—31no—
236C22⋊Q8—61no—
237#121C2×C3×D311yescharacteristic
238C4×D4—61no—
239C2×C4⋊C4—31no—
240C2×C4⋊C4—61no—
241C2×C4⋊C4C2×C3×D311yescharacteristic
242#107—21no—
243#106—61no—
244#103—61no—
245#102—21no—
246C22⋊C8—31no—
247C22⋊C8C2×C3×D311yescharacteristic
248#95—31no—
249#95—61no—
250C23×C3—21no—
251C23×C3—21no—
252C23×C3—21no—
253C23×C3—41no—
254C23×C3D3×D411yescharacteristic
255C23×C3C2×C3×D411yescharacteristic
256C3×Q8—121no—
257C3×D4—41no—
258C3×D4—41no—
259C3×D4—42no—
260C3×D4—41no—
261C3×D4—41no—
262C3×D4—41no—
263C3×D4—41no—
264C3×D4—81no—
265C3×D4—81no—
266C2×C3×C4—21no—
267C2×C3×C4—21no—
268C2×C3×C4—21no—
269C2×C3×C4—21no—
270C2×C3×C4—41no—
271C2×C3×C4—41no—
272C2×C3×C4—41no—
273C2×C3×C4—42no—
274C2×C3×C4—42no—
275C2×C3×C4—41no—
276C2×C3×C4—41no—
277C2×C3×C4—41no—
278C2×C3×C4—41no—
279C2×C3×C4—41no—
280C2×C3×C4—41no—
281C2×C3×C4—62no—
282C2×C3×C4—61no—
283C2×C3×C4—61no—
284C2×C3×C4—61no—
285C2×C3×C4—61no—
286C2×C3×C4—61no—
287C2×C3×C4—61no—
288C2×C3×C4—81no—
289C2×C3×C4—81no—
290C2×C3×C4—121no—
291C2×C3×C4—121no—
292C2×C3×C4—121no—
293C2×C3×C4—241no—
294C2×C3×C4D3×D411yescharacteristic
295C2×C3×C4C2×#6711yescharacteristic
296C2×C3×C4C2×C3×D411yescharacteristic
297C2×C3×C4C2×C3×D411yescharacteristic
298C2×Dic3—22no—
299C2×Dic3—21no—
300C2×Dic3—21no—
301C2×Dic3—21no—
302C2×Dic3—21no—
303C2×Dic3—21no—
304C2×Dic3—21no—
305C2×Dic3—41no—
306C2×Dic3—41no—
307C2×Dic3—41no—
308C2×Dic3—81no—
309Dic6—41no—
310C3×C8—42no—
311C3×C8—41no—
312C3×C8—41no—
313C3×C8—121no—
314C3⋊C8—41no—
315C2×C32—21no—
316C2×C32—21no—
317C2×C32—81no—
318C2×C32#44911yescharacteristic
319C2×C32#45611yescharacteristic
320C2×C32#45811yescharacteristic
321C2×Q8—31no—
322C2×D4—21no—
323C2×D4C3×#6711yescharacteristic
324C22×C4—21no—
325C22×C4—31no—
326C22×C4—31no—
327C22×C4—61no—
328C22×C4—61no—
329C22×C4C22×C3×D311yescharacteristic
330C2×C8—21no—
331C2×C8—61no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—31no—
335C4⋊C4—61no—
336C4⋊C4—61no—
337C4⋊C4—61no—
338C4⋊C4—61no—
339C4⋊C4—61no—
340C4⋊C4—61no—
341C4⋊C4—122no—
342C4⋊C4C3×#6711yescharacteristic
343C22⋊C4—21no—
344C22⋊C4—61no—
345C22⋊C4—61no—
346C22⋊C4—61no—
347C22⋊C4—61no—
348C42—61no—
349C22×C3—21no—
350C22×C3—21no—
351C22×C3—21no—
352C22×C3—21no—
353C22×C3—21no—
354C22×C3—21no—
355C22×C3—21no—
356C22×C3—41no—
357C22×C3—41no—
358C22×C3—41no—
359C22×C3—41no—
360C22×C3—41no—
361C22×C3—41no—
362C22×C3—41no—
363C22×C3—41no—
364C22×C3—81no—
365C22×C3—81no—
366C22×C3—81no—
367C22×C3#91111yescharacteristic
368C22×C3#91211yescharacteristic
369C22×C3#93711yescharacteristic
370C22×C3C3×#12011yescharacteristic
371C22×C3C3×#13511yescharacteristic
372C22×C3C3×AGL(1,ℤ/8)11yescharacteristic
373C3×C4—22no—
374C3×C4—21no—
375C3×C4—21no—
376C3×C4—21no—
377C3×C4—21no—
378C3×C4—41no—
379C3×C4—41no—
380C3×C4—41no—
381C3×C4—81no—
382C3×C4—82no—
383C3×C4—81no—
384C3×C4—81no—
385C3×C4—122no—
386C3×C4—121no—
387C3×C4—121no—
388C3×C4—121no—
389C3×C4—121no—
390Dic3—42no—
391Dic3—41no—
392Dic3—41no—
393Dic3—41no—
394Dic3—41no—
395C32#160911yescharacteristic, complemented, Sylow
396C23—21no—
397C23C3×D3×D411yescharacteristic
398Q8—121no—
399D4—41no—
400D4—41no—
401D4—41no—
402C2×C4—21no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—62no—
408C2×C4—61no—
409C2×C4—61no—
410C2×C4—61no—
411C2×C4—61no—
412C2×C4—61no—
413C2×C4—61no—
414C2×C4—121no—
415C2×C4—121no—
416C2×C4—121no—
417C2×C4—241no—
418C2×C4C3×D3×D411yescharacteristic
419C2×C4C2×C3×#6711yescharacteristic
420C8—41no—
421C8—121no—
422C2×C3—21no—
423C2×C3—21no—
424C2×C3—21no—
425C2×C3—21no—
426C2×C3—21no—
427C2×C3—21no—
428C2×C3—21no—
429C2×C3—41no—
430C2×C3—41no—
431C2×C3—81no—
432C2×C3—81no—
433C2×C3—161no—
434C2×C3#505311yescharacteristic
435C2×C3#515811yescharacteristic
436C2×C3#520511yescharacteristic
437C2×C3C3×#44911yescharacteristic
438C2×C3C3×#45611yescharacteristic
439C2×C3C3×#45811yescharacteristic
440C22—21no—
441C22—21no—
442C22—41no—
443C22—41no—
444C22—41no—
445C22C3×#91111yescharacteristic
446C22C3×#91211yescharacteristic
447C22C3×#93711yescharacteristic
448C4—21no—
449C4—21no—
450C4—41no—
451C4—81no—
452C4—122no—
453C4—121no—
454C4—121no—
455C4—121no—
456C4—121no—
457C3—21no—
458C3#7116611yescharacteristic, direct product factor
459C3C3×#160911yescharacteristic, complemented
460C2—21no—
461C2—21no—
462C2—81no—
463C2C3×#505311yescharacteristic
464C2C3×#515811yescharacteristic
465C2C3×#520511yescharacteristic
subgroupG/H
centerC22×C3#937
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC32×#480C2
socleC22×C32#120
prime radicalC32×#121C22
hypercenterC3×#480D3
hypocenterC3C3×#1609
LCSG ▷ C22×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#480

Complements

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

NH ≅ G/Ntype
3. C3×#4983C2semidirect
4. C3×#4971C2semidirect
6. C3×#4469C2semidirect
7. C3×#4467C2semidirect
9. #71166C3direct (N × H)
36. #4983C2×C3semidirect
37. #4971C2×C3semidirect
42. #4469C2×C3semidirect
43. #4467C2×C3semidirect
395. C32#1609semidirect
458. C3#71166direct (N × H)
459. C3C3×#1609semidirect

Maximal subgroups

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

subgroupindex
C3×#56022
C32×#4802
C3×#49832
C3×#49712
C3×#45372
C3×#44692
C3×#44672
C3×#16093
#711663