Finite Group Databasebeta

← C3×#68322 #11778698

Subgroups — C3×#68322 #11778698

Order 1152.

512 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5634C211yesmaximal, characteristic
2C3×#5044C211yesmaximal, characteristic, complemented
3C3×#4722C211yesmaximal, characteristic, complemented
4C3×#4677C211yesmaximal, characteristic
5C32×#328C211yesmaximal, characteristic, complemented
6C3×#4468C211yesmaximal, characteristic
7C3×#4452C211yesmaximal, characteristic, complemented
8C3×#1614—31nomaximal
9#68322C311yesmaximal, characteristic, direct product factor
10C32×C22⋊Q8C2211yescharacteristic
11C3×#946—21no—
12C2×C3×(C2×D3)⋊C4—21no—
13C2×C3×(C2×D3)⋊C4C2211yescharacteristic
14C2×C3×C4⋊Dic3—21no—
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C3×#924C2211yescharacteristic
17C3×#897—21no—
18C3×#896—21no—
19C3×#896—21no—
20C3×D3×C22⋊C4—21no—
21C3×#878—21no—
22C32×C22⋊C8C2211yescharacteristic
23C32×#95C2211yescharacteristic
24C3×#835—21no—
25C3×#830C2211yescharacteristic
26C3×#818—21no—
27C3×#816—21no—
28C3×#807—21no—
29C3×#543—31no—
30#5634C2×C311yescharacteristic
31C3×#484—31no—
32C3×#484—31no—
33C3×#399—31no—
34#5044C2×C311yescharacteristic, complemented
35#4722C2×C311yescharacteristic, complemented
36#4677C2×C311yescharacteristic
37C3×#328—21no—
38C3×#328—31no—
39C3×#328D311yescharacteristic, complemented
40C3×#328C2×C311yescharacteristic, complemented
41C3×#323—31no—
42#4468C2×C311yescharacteristic
43#4452C2×C311yescharacteristic, complemented
44C23×C3×D3D411yescharacteristic
45C2×C32×Q8D411yescharacteristic
46C22×C32×C4—21no—
47C22×C32×C4C2311yescharacteristic
48C22×C3×Dic3—21no—
49C22×C3×Dic3D411yescharacteristic
50C2×C3×C4×D3—21no—
51C2×C3×C4×D3—21no—
52C2×C3×Dic6—21no—
53C2×C3×Dic6D411yescharacteristic
54C2×C32×C8—21no—
55C32×C4⋊C4—21no—
56C32×C4⋊C4D411yescharacteristic
57C32×C22⋊C4—21no—
58C3×#217—21no—
59C3×(C2×D3)⋊C4—21no—
60C3×(C2×D3)⋊C4—21no—
61C3×(C2×D3)⋊C4—21no—
62C3×(C2×D3)⋊C4—21no—
63C3×(C2×D3)⋊C4—42no—
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3—21no—
66C3×C4⋊Dic3—21no—
67C3×C4⋊Dic3—42no—
68C3×C4⋊Dic3D411yescharacteristic
69C3×Dic3⋊C4—21no—
70C3×Dic3⋊C4—21no—
71C3×Dic3⋊C4—21no—
72C2×C3×C3⋊C8—21no—
73#1614—31noSylow
74C3×C22⋊Q8—21no—
75C3×C22⋊Q8—31no—
76C3×C22⋊Q8—61no—
77C3×C22⋊Q8—61no—
78C3×C22⋊Q8—61no—
79C3×C22⋊Q8—61no—
80C3×C22⋊Q8—61no—
81C3×C22⋊Q8C2×D311yescharacteristic
82C3×C22⋊Q8C22×C311yescharacteristic
83C2×C3×C4⋊C4—31no—
84C2×C3×C4⋊C4—61no—
85C2×C3×C22⋊C4—31no—
86C2×C3×C22⋊C4—61no—
87C2×C3×C22⋊C4—61no—
88#946—21no—
89C2×(C2×D3)⋊C4—21no—
90C2×(C2×D3)⋊C4C22×C311yescharacteristic
91C2×C4⋊Dic3—21no—
92C2×C4⋊Dic3C22×C311yescharacteristic
93#924C22×C311yescharacteristic
94#897—21no—
95#896—21no—
96#896—21no—
97D3×C22⋊C4—21no—
98#878—21no—
99C3×#107—61no—
100C3×#107—61no—
101C3×#103—61no—
102C3×#103—61no—
103C3×C22⋊C8—21no—
104C3×C22⋊C8—31no—
105C3×C22⋊C8C2×D311yescharacteristic
106C3×C22⋊C8C22×C311yescharacteristic
107C3×#95—21no—
108C3×#95C2×D311yescharacteristic
109C3×#95C22×C311yescharacteristic
110#835—21no—
111#830C22×C311yescharacteristic
112#818—21no—
113#816—21no—
114#807—21no—
115C23×C32C2×D411yescharacteristic
116C22×C3×D3—21no—
117C22×C3×D3—21no—
118C22×C3×D3—41no—
119C22×C3×D3—41no—
120C22×C3×D3Q1612yes—
121C32×Q8—41no—
122C2×C32×C4—22no—
123C2×C32×C4—21no—
124C2×C32×C4—21no—
125C2×C32×C4—41no—
126C2×C32×C4—41no—
127C2×C32×C4—41no—
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C3×Dic3—21no—
131C2×C3×Dic3—21no—
132C2×C3×Dic3—21no—
133C2×C3×Dic3—41no—
134C2×C3×Dic3—41no—
135C2×C3×Dic3—41no—
136C2×C3×Dic3—41no—
137C3×C4×D3—81no—
138C3×C4×D3—81no—
139C3×Dic6—41no—
140C3×Dic6—81no—
141C32×C8—41no—
142C3×C3⋊C8—41no—
143#543—31no—
144#484—31no—
145#484—31no—
146#399—31no—
147#328—31no—
148#328C3×D311yescharacteristic, complemented
149#323—31no—
150C24×C3—31no—
151C23×D3C3×D411yescharacteristic
152C2×C3×Q8—21no—
153C2×C3×Q8—31no—
154C2×C3×Q8—61no—
155C2×C3×Q8D1211yescharacteristic
156C2×C3×Q8C3×D411yescharacteristic
157C22×C3×C4—21no—
158C22×C3×C4—21no—
159C22×C3×C4—21no—
160C22×C3×C4—31no—
161C22×C3×C4—41no—
162C22×C3×C4—61no—
163C22×C3×C4—61no—
164C22×C3×C4—61no—
165C22×C3×C4C22×D311yescharacteristic
166C22×C3×C4C23×C311yescharacteristic
167C22×Dic3—21no—
168C22×Dic3C3×D411yescharacteristic
169C2×C4×D3—21no—
170C2×C4×D3—21no—
171C2×Dic6—21no—
172C2×Dic6C3×D411yescharacteristic
173C2×C3×C8—21no—
174C2×C3×C8—21no—
175C2×C3×C8—41no—
176C2×C3×C8—61no—
177C3×C4⋊C4—21no—
178C3×C4⋊C4—21no—
179C3×C4⋊C4—21no—
180C3×C4⋊C4—31no—
181C3×C4⋊C4—41no—
182C3×C4⋊C4—61no—
183C3×C4⋊C4—61no—
184C3×C4⋊C4—61no—
185C3×C4⋊C4—61no—
186C3×C4⋊C4—61no—
187C3×C4⋊C4—61no—
188C3×C4⋊C4—122no—
189C3×C4⋊C4D1211yescharacteristic
190C3×C4⋊C4C3×D411yescharacteristic
191C3×C22⋊C4—21no—
192C3×C22⋊C4—21no—
193C3×C22⋊C4—41no—
194C3×C22⋊C4—61no—
195C3×C22⋊C4—61no—
196C3×C22⋊C4—61no—
197C3×C22⋊C4—61no—
198C3×C22⋊C4—61no—
199C3×C22⋊C4—122no—
200#217—21no—
201(C2×D3)⋊C4—21no—
202(C2×D3)⋊C4—21no—
203(C2×D3)⋊C4—21no—
204(C2×D3)⋊C4—21no—
205(C2×D3)⋊C4—42no—
206C4⋊Dic3—21no—
207C4⋊Dic3—21no—
208C4⋊Dic3—21no—
209C4⋊Dic3—42no—
210C4⋊Dic3C3×D411yescharacteristic
211Dic3⋊C4—21no—
212Dic3⋊C4—21no—
213Dic3⋊C4—21no—
214C2×C3⋊C8—21no—
215C22×C32—21no—
216C22×C32—21no—
217C22×C32#12011yescharacteristic
218C22×C32C2×Q1611yescharacteristic
219C22×C32#13711yescharacteristic
220C2×C3×D3—22no—
221C2×C3×D3—41no—
222C2×C3×D3—41no—
223C2×C3×D3—42no—
224C2×C3×D3—81no—
225C32×C4—21no—
226C32×C4—21no—
227C32×C4—42no—
228C32×C4—41no—
229C32×C4—41no—
230C3×Dic3—41no—
231C3×Dic3—41no—
232C3×Dic3—41no—
233C3×Dic3—81no—
234C22⋊Q8—31no—
235C22⋊Q8—61no—
236C22⋊Q8—61no—
237C22⋊Q8—61no—
238C22⋊Q8—61no—
239C22⋊Q8—61no—
240C22⋊Q8C2×C3×D311yescharacteristic
241C2×C4⋊C4—31no—
242C2×C4⋊C4—61no—
243C2×C22⋊C4—31no—
244C2×C22⋊C4—61no—
245C2×C22⋊C4—61no—
246#107—61no—
247#107—61no—
248#103—61no—
249#103—61no—
250C22⋊C8—31no—
251C22⋊C8C2×C3×D311yescharacteristic
252#95C2×C3×D311yescharacteristic
253C23×C3—21no—
254C23×C3—32no—
255C23×C3—61no—
256C23×C3—61no—
257C23×C3—121no—
258C23×C3—121no—
259C23×C3D3×D411yescharacteristic
260C23×C3C2×C3×D411yescharacteristic
261C22×D3—21no—
262C22×D3—21no—
263C22×D3—41no—
264C22×D3—41no—
265C22×D3C3×Q1612yes—
266C3×Q8—41no—
267C3×Q8—41no—
268C3×Q8—81no—
269C3×Q8—121no—
270C3×Q8—241no—
271C2×C3×C4—22no—
272C2×C3×C4—22no—
273C2×C3×C4—21no—
274C2×C3×C4—21no—
275C2×C3×C4—21no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—41no—
280C2×C3×C4—41no—
281C2×C3×C4—42no—
282C2×C3×C4—41no—
283C2×C3×C4—41no—
284C2×C3×C4—41no—
285C2×C3×C4—41no—
286C2×C3×C4—41no—
287C2×C3×C4—41no—
288C2×C3×C4—61no—
289C2×C3×C4—61no—
290C2×C3×C4—61no—
291C2×C3×C4—81no—
292C2×C3×C4—81no—
293C2×C3×C4—81no—
294C2×C3×C4—121no—
295C2×C3×C4—121no—
296C2×C3×C4—121no—
297C2×C3×C4—121no—
298C2×C3×C4—241no—
299C2×C3×C4—241no—
300C2×C3×C4C2×D1211yescharacteristic
301C2×C3×C4D3×D411yescharacteristic
302C2×C3×C4C2×C3×D411yescharacteristic
303C2×C3×C4C2×C3×D411yescharacteristic
304C2×Dic3—21no—
305C2×Dic3—21no—
306C2×Dic3—21no—
307C2×Dic3—41no—
308C2×Dic3—41no—
309C2×Dic3—41no—
310C2×Dic3—41no—
311C4×D3—81no—
312C4×D3—81no—
313Dic6—41no—
314Dic6—81no—
315C3×C8—41no—
316C3×C8—41no—
317C3×C8—81no—
318C3×C8—121no—
319C3⋊C8—41no—
320C2×C32—21no—
321C2×C32—21no—
322C2×C32#45111yescharacteristic
323C2×C32#45311yescharacteristic
324C2×C32#45811yescharacteristic
325C3×D3—42no—
326C24—31no—
327C2×Q8—31no—
328C2×Q8—61no—
329C2×Q8C3×D1211yescharacteristic
330C22×C4—21no—
331C22×C4—31no—
332C22×C4—61no—
333C22×C4—61no—
334C22×C4—61no—
335C22×C4C22×C3×D311yescharacteristic
336C2×C8—21no—
337C2×C8—61no—
338C4⋊C4—21no—
339C4⋊C4—31no—
340C4⋊C4—61no—
341C4⋊C4—61no—
342C4⋊C4—61no—
343C4⋊C4—61no—
344C4⋊C4—61no—
345C4⋊C4—61no—
346C4⋊C4—122no—
347C4⋊C4C3×D1211yescharacteristic
348C22⋊C4—21no—
349C22⋊C4—61no—
350C22⋊C4—61no—
351C22⋊C4—61no—
352C22⋊C4—61no—
353C22⋊C4—61no—
354C22⋊C4—122no—
355C22×C3—21no—
356C22×C3—21no—
357C22×C3—21no—
358C22×C3—21no—
359C22×C3—21no—
360C22×C3—21no—
361C22×C3—21no—
362C22×C3—41no—
363C22×C3—41no—
364C22×C3—62no—
365C22×C3—122no—
366C22×C3—121no—
367C22×C3—121no—
368C22×C3—241no—
369C22×C3#88211yescharacteristic
370C22×C3#91511yescharacteristic
371C22×C3D3×Q1611yescharacteristic
372C22×C3C3×#12011yescharacteristic
373C22×C3C2×C3×Q1611yescharacteristic
374C22×C3C3×#13711yescharacteristic
375C2×D3—22no—
376C2×D3—41no—
377C2×D3—41no—
378C2×D3—42no—
379C2×D3—81no—
380C3×C4—21no—
381C3×C4—21no—
382C3×C4—21no—
383C3×C4—21no—
384C3×C4—41no—
385C3×C4—41no—
386C3×C4—42no—
387C3×C4—42no—
388C3×C4—41no—
389C3×C4—41no—
390C3×C4—41no—
391C3×C4—41no—
392C3×C4—81no—
393C3×C4—81no—
394C3×C4—82no—
395C3×C4—121no—
396C3×C4—121no—
397C3×C4—121no—
398C3×C4—241no—
399Dic3—41no—
400Dic3—41no—
401Dic3—41no—
402Dic3—81no—
403C32#161411yescharacteristic, complemented, Sylow
404C23—32no—
405C23—61no—
406C23—61no—
407C23—121no—
408C23—121no—
409C23C3×D3×D411yescharacteristic
410Q8—41no—
411Q8—121no—
412Q8—241no—
413C2×C4—22no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—61no—
420C2×C4—61no—
421C2×C4—61no—
422C2×C4—121no—
423C2×C4—121no—
424C2×C4—121no—
425C2×C4—121no—
426C2×C4—241no—
427C2×C4—241no—
428C2×C4C2×C3×D1211yescharacteristic
429C2×C4C3×D3×D411yescharacteristic
430C8—41no—
431C8—121no—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3—21no—
435C2×C3—21no—
436C2×C3—21no—
437C2×C3—21no—
438C2×C3—21no—
439C2×C3—41no—
440C2×C3—41no—
441C2×C3—122no—
442C2×C3#474211yescharacteristic
443C2×C3#480911yescharacteristic
444C2×C3#482211yescharacteristic
445C2×C3C3×#45111yescharacteristic
446C2×C3C3×#45311yescharacteristic
447C2×C3C3×#45811yescharacteristic
448D3—42no—
449C22—21no—
450C22—21no—
451C22—62no—
452C22—122no—
453C22—121no—
454C22—121no—
455C22—241no—
456C22C3×#88211yescharacteristic
457C22C3×#91511yescharacteristic
458C22C3×D3×Q1611yescharacteristic
459C4—21no—
460C4—21no—
461C4—42no—
462C4—41no—
463C4—41no—
464C4—121no—
465C4—121no—
466C4—121no—
467C4—241no—
468C3—21no—
469C3#6832211yescharacteristic, direct product factor
470C3C3×#161411yescharacteristic, complemented
471C2—21no—
472C2—21no—
473C2—122no—
474C2C3×#474211yescharacteristic
475C2C3×#480911yescharacteristic
476C2C3×#482211yescharacteristic
subgroupG/H
centerC22×C3#882
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC32×#328C2
socleC22×C32#120
prime radicalC23×C3×D3D4
hypercenterC3×#328D3
hypocenterC3C3×#1614
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×#5044C2semidirect
3. C3×#4722C2semidirect
5. C32×#328C2semidirect
7. C3×#4452C2semidirect
9. #68322C3direct (N × H)
34. #5044C2×C3semidirect
35. #4722C2×C3semidirect
39. C3×#328D3semidirect
40. C3×#328C2×C3semidirect
43. #4452C2×C3semidirect
148. #328C3×D3semidirect
403. C32#1614semidirect
469. C3#68322direct (N × H)
470. C3C3×#1614semidirect

Maximal subgroups

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

subgroupindex
C3×#56342
C3×#50442
C3×#47222
C3×#46772
C32×#3282
C3×#44682
C3×#44522
C3×#16143
#683223