Finite Group Databasebeta

← C3×#68296 #11778507

Subgroups — C3×#68296 #11778507

Order 1152.

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

normal subgroups only

This group has 477 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
2C3×#5033C211yesmaximal, characteristic
3C3×#4721C211yesmaximal, characteristic, complemented
4C3×#4661C211yesmaximal, characteristic, complemented
5C32×#327C211yesmaximal, characteristic
6C3×#4469C211yesmaximal, characteristic, complemented
7C3×#4452C211yesmaximal, characteristic, complemented
8C3×#1609—31nomaximal
9#68296C311yesmaximal, characteristic, direct product factor
10C32×#121C2211yescharacteristic
11C3×#935—21no—
12C3×#935—21no—
13C3×D4×Dic3—21no—
14C2×C3×C4⋊Dic3—21no—
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C3×#924C2211yescharacteristic
17C2×C3×Dic3⋊C4C2211yescharacteristic
18C3×#889—21no—
19C3×#879—21no—
20C3×#878—21no—
21C32×C22⋊C8C2211yescharacteristic
22C32×#95C2211yescharacteristic
23C3×#832—21no—
24C3×C3⋊#95—21no—
25C3×#830C2211yescharacteristic
26C3×#817—21no—
27C3×#816—21no—
28C3×#807—21no—
29C3×#539—31no—
30#5602C2×C311yescharacteristic
31C3×#483—31no—
32C3×#480—31no—
33C3×#398—31no—
34#5033C2×C311yescharacteristic
35#4721C2×C311yescharacteristic, complemented
36#4661C2×C311yescharacteristic, complemented
37C3×#328—31no—
38C3×#327—21no—
39C3×#327D311yescharacteristic
40C3×#327C2×C311yescharacteristic
41C3×#324—31no—
42#4469C2×C311yescharacteristic, complemented
43#4452C2×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⋊C4D411yescharacteristic
55C32×C22⋊C4—21no—
56C3×#217—21no—
57C3×#217—21no—
58C3×#217—21no—
59C3×#217—21no—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3—21no—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3—42no—
64C3×C4⋊Dic3D411yescharacteristic
65C3×Dic3⋊C4—21no—
66C3×Dic3⋊C4—21no—
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—31no—
78C3×C22⋊Q8—61no—
79C3×#121—21no—
80C3×#121C2×D311yescharacteristic
81C3×#121C22×C311yescharacteristic
82C3×C4×D4—61no—
83C2×C3×C4⋊C4—31no—
84C2×C3×C4⋊C4—31no—
85C2×C3×C4⋊C4—61no—
86#935—21no—
87#935—21no—
88D4×Dic3—21no—
89C2×C4⋊Dic3—21no—
90C2×C4⋊Dic3C22×C311yescharacteristic
91#924C22×C311yescharacteristic
92C2×Dic3⋊C4C22×C311yescharacteristic
93#889—21no—
94#879—21no—
95#878—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#832—21no—
109C3⋊#95—21no—
110#830C22×C311yescharacteristic
111#817—21no—
112#816—21no—
113#807—21no—
114C23×C32—21no—
115C23×C32C2×D411yescharacteristic
116C32×D4—41no—
117C32×D4—41no—
118C32×D4—41no—
119C2×C32×C4—22no—
120C2×C32×C4—21no—
121C2×C32×C4—41no—
122C2×C32×C4—41no—
123C2×C32×C4—41no—
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C3×Dic3—21no—
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—
136C2×C3×Dic3—81no—
137C3×Dic6—41no—
138C32×C8—41no—
139C3×C3⋊C8—41no—
140#539—31no—
141#483—31no—
142#480—31no—
143#398—31no—
144#328—31no—
145#327C3×D311yescharacteristic
146#324—31no—
147C2×C3×Q8—31no—
148C2×C3×D4—21no—
149C2×C3×D4—21no—
150C2×C3×D4—21no—
151C2×C3×D4—41no—
152C2×C3×D4D1211yescharacteristic
153C2×C3×D4C3×D411yescharacteristic
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
164C22×Dic3—21no—
165C22×Dic3—21no—
166C22×Dic3C3×D411yescharacteristic
167C22×Dic3C3×D411yescharacteristic
168C2×Dic6C3×D411yescharacteristic
169C2×C3×C8—21no—
170C2×C3×C8—21no—
171C2×C3×C8—41no—
172C2×C3×C8—61no—
173C3×C4⋊C4—21no—
174C3×C4⋊C4—31no—
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⋊C4—61no—
183C3×C4⋊C4—122no—
184C3×C4⋊C4D1211yescharacteristic
185C3×C4⋊C4C3×D411yescharacteristic
186C3×C22⋊C4—21no—
187C3×C22⋊C4—21no—
188C3×C22⋊C4—41no—
189C3×C22⋊C4—61no—
190C3×C22⋊C4—61no—
191C3×C22⋊C4—61no—
192C3×C22⋊C4—61no—
193C3×C42—61no—
194#217—21no—
195#217—21no—
196#217—21no—
197#217—21no—
198C4⋊Dic3—21no—
199C4⋊Dic3—21no—
200C4⋊Dic3—21no—
201C4⋊Dic3—42no—
202C4⋊Dic3C3×D411yescharacteristic
203Dic3⋊C4—21no—
204Dic3⋊C4—21no—
205Dic3⋊C4—21no—
206Dic3⋊C4—21no—
207Dic3⋊C4—21no—
208C4×Dic3—21no—
209C2×C3⋊C8—21no—
210C22×C32—21no—
211C22×C32—21no—
212C22×C32—41no—
213C22×C32—41no—
214C22×C32—41no—
215C22×C32#12011yescharacteristic
216C22×C32#13511yescharacteristic
217C22×C32AGL(1,ℤ/8)11yescharacteristic
218C32×C4—21no—
219C32×C4—21no—
220C32×C4—42no—
221C32×C4—41no—
222C3×Dic3—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—31no—
232C22⋊Q8—61no—
233#121C2×C3×D311yescharacteristic
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—21no—
248C23×C3—21no—
249C23×C3—41no—
250C23×C3D3×D411yescharacteristic
251C23×C3C2×C3×D411yescharacteristic
252C3×Q8—121no—
253C3×D4—41no—
254C3×D4—41no—
255C3×D4—41no—
256C3×D4—41no—
257C3×D4—41no—
258C3×D4—41no—
259C3×D4—81no—
260C3×D4—81no—
261C3×D4—81no—
262C2×C3×C4—22no—
263C2×C3×C4—22no—
264C2×C3×C4—21no—
265C2×C3×C4—21no—
266C2×C3×C4—21no—
267C2×C3×C4—21no—
268C2×C3×C4—41no—
269C2×C3×C4—42no—
270C2×C3×C4—41no—
271C2×C3×C4—41no—
272C2×C3×C4—41no—
273C2×C3×C4—41no—
274C2×C3×C4—41no—
275C2×C3×C4—41no—
276C2×C3×C4—61no—
277C2×C3×C4—61no—
278C2×C3×C4—61no—
279C2×C3×C4—61no—
280C2×C3×C4—61no—
281C2×C3×C4—61no—
282C2×C3×C4—81no—
283C2×C3×C4—81no—
284C2×C3×C4—81no—
285C2×C3×C4—121no—
286C2×C3×C4—121no—
287C2×C3×C4—121no—
288C2×C3×C4—121no—
289C2×C3×C4—241no—
290C2×C3×C4C2×D1211yescharacteristic
291C2×C3×C4D3×D411yescharacteristic
292C2×C3×C4C2×C3×D411yescharacteristic
293C2×C3×C4C2×C3×D411yescharacteristic
294C2×Dic3—21no—
295C2×Dic3—21no—
296C2×Dic3—21no—
297C2×Dic3—21no—
298C2×Dic3—21no—
299C2×Dic3—21no—
300C2×Dic3—41no—
301C2×Dic3—41no—
302C2×Dic3—41no—
303C2×Dic3—41no—
304C2×Dic3—81no—
305Dic6—41no—
306C3×C8—41no—
307C3×C8—41no—
308C3×C8—81no—
309C3×C8—121no—
310C3⋊C8—41no—
311C2×C32—21no—
312C2×C32—21no—
313C2×C32—81no—
314C2×C32#44911yescharacteristic
315C2×C32#45611yescharacteristic
316C2×C32#45811yescharacteristic
317C2×Q8—31no—
318C2×D4—21no—
319C2×D4C3×D1211yescharacteristic
320C22×C4—21no—
321C22×C4—31no—
322C22×C4—31no—
323C22×C4—61no—
324C22×C4—61no—
325C22×C4C22×C3×D311yescharacteristic
326C2×C8—21no—
327C2×C8—61no—
328C4⋊C4—31no—
329C4⋊C4—61no—
330C4⋊C4—61no—
331C4⋊C4—61no—
332C4⋊C4—61no—
333C4⋊C4—61no—
334C4⋊C4—61no—
335C4⋊C4—61no—
336C4⋊C4—61no—
337C4⋊C4—122no—
338C4⋊C4C3×D1211yescharacteristic
339C22⋊C4—21no—
340C22⋊C4—61no—
341C22⋊C4—61no—
342C22⋊C4—61no—
343C22⋊C4—61no—
344C42—61no—
345C22×C3—21no—
346C22×C3—21no—
347C22×C3—21no—
348C22×C3—21no—
349C22×C3—21no—
350C22×C3—21no—
351C22×C3—21no—
352C22×C3—41no—
353C22×C3—41no—
354C22×C3—41no—
355C22×C3—41no—
356C22×C3—41no—
357C22×C3—41no—
358C22×C3—41no—
359C22×C3—41no—
360C22×C3—81no—
361C22×C3—81no—
362C22×C3—81no—
363C22×C3#88211yescharacteristic
364C22×C3#91111yescharacteristic
365C22×C3#91611yescharacteristic
366C22×C3C3×#12011yescharacteristic
367C22×C3C3×#13511yescharacteristic
368C22×C3C3×AGL(1,ℤ/8)11yescharacteristic
369C3×C4—21no—
370C3×C4—21no—
371C3×C4—21no—
372C3×C4—21no—
373C3×C4—41no—
374C3×C4—41no—
375C3×C4—42no—
376C3×C4—42no—
377C3×C4—41no—
378C3×C4—41no—
379C3×C4—81no—
380C3×C4—82no—
381C3×C4—121no—
382C3×C4—121no—
383C3×C4—121no—
384C3×C4—121no—
385C3×C4—241no—
386Dic3—41no—
387Dic3—41no—
388Dic3—41no—
389Dic3—41no—
390Dic3—81no—
391C32#160911yescharacteristic, complemented, Sylow
392C23—21no—
393C23C3×D3×D411yescharacteristic
394Q8—121no—
395D4—41no—
396D4—41no—
397D4—41no—
398C2×C4—22no—
399C2×C4—21no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—61no—
404C2×C4—61no—
405C2×C4—61no—
406C2×C4—61no—
407C2×C4—61no—
408C2×C4—61no—
409C2×C4—121no—
410C2×C4—121no—
411C2×C4—121no—
412C2×C4—121no—
413C2×C4—241no—
414C2×C4C2×C3×D1211yescharacteristic
415C2×C4C3×D3×D411yescharacteristic
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—81no—
428C2×C3—81no—
429C2×C3—161no—
430C2×C3#474211yescharacteristic
431C2×C3#478111yescharacteristic
432C2×C3#482611yescharacteristic
433C2×C3C3×#44911yescharacteristic
434C2×C3C3×#45611yescharacteristic
435C2×C3C3×#45811yescharacteristic
436C22—21no—
437C22—21no—
438C22—41no—
439C22—41no—
440C22—41no—
441C22C3×#88211yescharacteristic
442C22C3×#91111yescharacteristic
443C22C3×#91611yescharacteristic
444C4—21no—
445C4—21no—
446C4—42no—
447C4—41no—
448C4—121no—
449C4—121no—
450C4—121no—
451C4—121no—
452C4—241no—
453C3—21no—
454C3#6829611yescharacteristic, direct product factor
455C3C3×#160911yescharacteristic, complemented
456C2—21no—
457C2—21no—
458C2—81no—
459C2C3×#474211yescharacteristic
460C2C3×#478111yescharacteristic
461C2C3×#482611yescharacteristic
subgroupG/H
centerC22×C3#882
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC32×#327C2
socleC22×C32#120
prime radicalC32×#121C22
hypercenterC3×#327D3
hypocenterC3C3×#1609
LCSG ▷ C22×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#327

Complements

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

NH ≅ G/Ntype
3. C3×#4721C2semidirect
4. C3×#4661C2semidirect
6. C3×#4469C2semidirect
7. C3×#4452C2semidirect
9. #68296C3direct (N × H)
35. #4721C2×C3semidirect
36. #4661C2×C3semidirect
42. #4469C2×C3semidirect
43. #4452C2×C3semidirect
391. C32#1609semidirect
454. C3#68296direct (N × H)
455. C3C3×#1609semidirect

Maximal subgroups

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

subgroupindex
C3×#56022
C3×#50332
C3×#47212
C3×#46612
C32×#3272
C3×#44692
C3×#44522
C3×#16093
#682963