Finite Group Databasebeta

← C3×#68779 #11793091

Subgroups — C3×#68779 #11793091

Order 1152.

543 conjugacy classes of subgroups.

The subgroup lattice has 451 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5470C211yesmaximal, characteristic, complemented
2C3×#5139C211yesmaximal, characteristic
3C3×#5006C211yesmaximal, characteristic
4C2×C3×#805C211yesmaximal, characteristic
5C32×#339C211yesmaximal, characteristic, complemented
6C3×#4556C211yesmaximal, characteristic, complemented
7C3×#4531C211yesmaximal, characteristic, complemented
8C3×#2031—31nomaximal
9#68779C311yesmaximal, characteristic, direct product factor
10C2×C3×#235C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C32×#117C2211yescharacteristic
13C2×C32×C42C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C3×#926C2211yescharacteristic
16C3×#924—22no—
17C2×C3×#208C2211yescharacteristic
18C3×#870—21no—
19C3×#869—21no—
20C3×C4×Dic6—22no—
21C3×#825—22no—
22C3×#806—22no—
23C3×#805—21no—
24C3×#805—21no—
25C3×#533—31no—
26#5470C2×C311yescharacteristic, complemented
27C3×#421—31no—
28C2×C3×#104—31no—
29C3×#410—31no—
30#5139C2×C311yescharacteristic
31#5006C2×C311yescharacteristic
32C2×#805C2×C311yescharacteristic
33C3×#344—31no—
34C3×#339—21no—
35C3×#339D311yescharacteristic, complemented
36C3×#339C2×C311yescharacteristic, complemented
37C3×H(3,ℤ/4)—31no—
38#4556C2×C311yescharacteristic, complemented
39#4531C2×C311yescharacteristic, complemented
40C22×C32×C4—21no—
41C22×C32×C4C2311yescharacteristic
42C2×C3×#67—21no—
43C3×#235—21no—
44C3×#235—21no—
45C3×#235—21no—
46C3×#235—21no—
47C2×C3×D12Q811yescharacteristic, complemented
48C2×C3×C4×D3—21no—
49C2×C3×Dic6—22no—
50C2×C3×Dic6Q811yescharacteristic, complemented
51C32×M16—21no—
52C32×M16—21no—
53C2×C32×C8—21no—
54C32×C4⋊C4—21no—
55C32×C22⋊C4—21no—
56C32×C42—21no—
57C32×C42—21no—
58C32×C42D411yescharacteristic
59C32×C42D411yescharacteristic
60C3×#217—21no—
61C3×#217D412yes—
62C3×C4⋊Dic3—22no—
63C3×C4⋊Dic3—21no—
64C3×C4⋊Dic3—21no—
65C3×Dic3⋊C4—24no—
66C3×C4×Dic3—21no—
67C3×C4×Dic3D412yes—
68C3×#208—21no—
69C3×#208—21no—
70C2×C3×C3⋊C8—21no—
71#2031—31noSylow
72C2×C3×#41—31no—
73C2×#235C22×C311yescharacteristic
74C2×C3×M16—21no—
75C2×C3×M16—31no—
76C2×C3×M16C2×D311yescharacteristic
77C2×C3×M16C22×C311yescharacteristic
78C3×C4⋊Q8—61no—
79C3×#125—61no—
80C3×C22⋊Q8—62no—
81C3×C4×Q8—62no—
82C3×#117—21no—
83C3×#117—31no—
84C3×#117—31no—
85C3×#117C2×D311yescharacteristic
86C3×#117C22×C311yescharacteristic
87C2×C3×C42—21no—
88C2×C3×C42C2×D311yescharacteristic
89C2×C3×C42C22×C311yescharacteristic
90#926C22×C311yescharacteristic
91#926C22×C311yescharacteristic
92#924—22no—
93C2×#208C22×C311yescharacteristic
94#870—21no—
95#869—21no—
96C4×Dic6—22no—
97C3×#104—62no—
98C3×#104—61no—
99C3×#104—61no—
100C3×#99—62no—
101#825—22no—
102#806—22no—
103#805—21no—
104#805—21no—
105C23×C32C2×D411yescharacteristic
106C22×C3×D3—21no—
107C2×C32×C4—21no—
108C2×C32×C4—21no—
109C2×C32×C4—42no—
110C2×C32×C4—41no—
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4C2×Q811yescharacteristic
114C2×C32×C4#4111yescharacteristic
115C2×C32×C4#4111yescharacteristic
116C2×C32×C4#4111yescharacteristic
117C3×#67—41no—
118C3×#67—41no—
119C2×C3×Dic3—22no—
120C2×C3×Dic3—22no—
121C2×C3×Dic3—21no—
122C3×D12—21no—
123C3×D12—21no—
124C3×C4×D3—41no—
125C3×C4×D3—41no—
126C3×Dic6—21no—
127C3×Dic6—21no—
128C3×Dic6—44no—
129C32×C8—41no—
130C3×C3⋊C8—41no—
131#533—31no—
132#421—31no—
133C2×#104—31no—
134#410—31no—
135#344—31no—
136#339C3×D311yescharacteristic, complemented
137H(3,ℤ/4)—31no—
138C3×#41—61no—
139C3×#41—61no—
140C3×#41—61no—
141C3×#41—61no—
142C2×C3×Q8—31no—
143C2×C3×Q8—62no—
144C2×C3×D4—31no—
145C2×C3×D4—61no—
146C22×C3×C4—21no—
147C22×C3×C4—21no—
148C22×C3×C4—21no—
149C22×C3×C4—41no—
150C22×C3×C4—61no—
151C22×C3×C4C22×D311yescharacteristic
152C22×C3×C4C23×C311yescharacteristic
153C2×#67—21no—
154#235—21no—
155#235—21no—
156#235—21no—
157#235—21no—
158C2×D12C3×Q811yescharacteristic, complemented
159C2×C4×D3—21no—
160C2×Dic6—22no—
161C2×Dic6C3×Q811yescharacteristic, complemented
162C3×M16—22no—
163C3×M16—21no—
164C3×M16—21no—
165C3×M16—21no—
166C3×M16—21no—
167C3×M16—41no—
168C3×M16—61no—
169C3×M16—61no—
170C2×C3×C8—21no—
171C2×C3×C8—21no—
172C2×C3×C8—41no—
173C2×C3×C8—61no—
174C3×C4⋊C4—22no—
175C3×C4⋊C4—21no—
176C3×C4⋊C4—21no—
177C3×C4⋊C4—64no—
178C3×C4⋊C4—62no—
179C3×C4⋊C4—61no—
180C3×C4⋊C4—61no—
181C3×C22⋊C4—21no—
182C3×C22⋊C4—21no—
183C3×C22⋊C4—32no—
184C3×C22⋊C4—41no—
185C3×C22⋊C4—61no—
186C3×C42—21no—
187C3×C42—21no—
188C3×C42—21no—
189C3×C42—21no—
190C3×C42—21no—
191C3×C42—21no—
192C3×C42—32no—
193C3×C42—41no—
194C3×C42—41no—
195C3×C42—61no—
196C3×C42D1211yescharacteristic
197C3×C42D1211yescharacteristic
198C3×C42C3×D411yescharacteristic
199C3×C42C3×D411yescharacteristic
200#217—21no—
201#217C3×D412yes—
202C4⋊Dic3—22no—
203C4⋊Dic3—21no—
204C4⋊Dic3—21no—
205Dic3⋊C4—24no—
206C4×Dic3—21no—
207C4×Dic3C3×D412yes—
208#208—21no—
209#208—21no—
210C2×C3⋊C8—21no—
211C22×C32—41no—
212C22×C32#12011yescharacteristic
213C22×C32C22⋊Q811yescharacteristic
214C22×C32#12411yescharacteristic
215C2×C3×D3—41no—
216C2×C3×D3—81no—
217C32×C4—22no—
218C32×C4—41no—
219C32×C4—81no—
220C32×C4C22⋊Q811yescharacteristic
221C32×C4C22⋊Q811yescharacteristic
222C32×C4#12411yescharacteristic
223C32×C4#12411yescharacteristic
224C3×Dic3—42no—
225C3×Dic3—42no—
226C3×Dic3—41no—
227C2×#41—31no—
228C2×M16—31no—
229C2×M16C2×C3×D311yescharacteristic
230C4⋊Q8—61no—
231#125—61no—
232C22⋊Q8—62no—
233C4×Q8—62no—
234#117—31no—
235#117—31no—
236#117C2×C3×D311yescharacteristic
237C2×C42C2×C3×D311yescharacteristic
238#104—62no—
239#104—61no—
240#104—61no—
241#99—62no—
242C23×C3—21no—
243C23×C3—61no—
244C23×C3D3×D411yescharacteristic
245C23×C3C2×C3×D411yescharacteristic
246C22×D3—21no—
247C3×Q8—61no—
248C3×Q8—61no—
249C3×Q8—124no—
250C3×D4—61no—
251C3×D4—61no—
252C3×D4—121no—
253C3×D4—121no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—41no—
265C2×C3×C4—41no—
266C2×C3×C4—42no—
267C2×C3×C4—42no—
268C2×C3×C4—44no—
269C2×C3×C4—42no—
270C2×C3×C4—41no—
271C2×C3×C4—41no—
272C2×C3×C4—62no—
273C2×C3×C4—62no—
274C2×C3×C4—61no—
275C2×C3×C4—121no—
276C2×C3×C4—121no—
277C2×C3×C4C2×D1211yescharacteristic
278C2×C3×C4#23511yescharacteristic
279C2×C3×C4#23511yescharacteristic
280C2×C3×C4D3×D411yescharacteristic
281C2×C3×C4#23711yescharacteristic
282C2×C3×C4D3×Q811yescharacteristic
283C2×C3×C4C2×C3×D411yescharacteristic
284C2×C3×C4C2×C3×D411yescharacteristic
285C2×C3×C4C2×C3×Q811yescharacteristic
286C2×C3×C4C3×#4111yescharacteristic
287C2×C3×C4C3×#4111yescharacteristic
288C2×C3×C4C3×#4111yescharacteristic
289#67—41no—
290#67—41no—
291C2×Dic3—22no—
292C2×Dic3—22no—
293C2×Dic3—21no—
294D12—21no—
295D12—21no—
296C4×D3—41no—
297C4×D3—41no—
298Dic6—21no—
299Dic6—21no—
300Dic6—44no—
301C3×C8—42no—
302C3×C8—41no—
303C3×C8—41no—
304C3×C8—121no—
305C3⋊C8—41no—
306C2×C32—21no—
307C2×C32—21no—
308C2×C32—21no—
309C2×C32#39311yescharacteristic
310C3×D3—81no—
311#41—61no—
312#41—61no—
313#41—61no—
314#41—61no—
315C2×Q8—31no—
316C2×Q8—62no—
317C2×D4—31no—
318C2×D4—61no—
319C22×C4—21no—
320C22×C4—61no—
321C22×C4C22×C3×D311yescharacteristic
322M16—21no—
323M16—21no—
324M16—61no—
325M16—61no—
326C2×C8—21no—
327C2×C8—61no—
328C4⋊C4—21no—
329C4⋊C4—64no—
330C4⋊C4—62no—
331C4⋊C4—61no—
332C4⋊C4—61no—
333C22⋊C4—21no—
334C22⋊C4—32no—
335C22⋊C4—61no—
336C42—21no—
337C42—21no—
338C42—32no—
339C42—61no—
340C42C3×D1211yescharacteristic
341C42C3×D1211yescharacteristic
342C22×C3—21no—
343C22×C3—21no—
344C22×C3—21no—
345C22×C3—41no—
346C22×C3—41no—
347C22×C3—42no—
348C22×C3—121no—
349C22×C3—241no—
350C22×C3#88211yescharacteristic
351C22×C3#88511yescharacteristic
352C22×C3#89611yescharacteristic
353C22×C3C3×#12011yescharacteristic
354C22×C3C3×C22⋊Q811yescharacteristic
355C22×C3C3×#12411yescharacteristic
356C2×D3—41no—
357C2×D3—81no—
358C3×C4—22no—
359C3×C4—22no—
360C3×C4—21no—
361C3×C4—21no—
362C3×C4—21no—
363C3×C4—21no—
364C3×C4—42no—
365C3×C4—41no—
366C3×C4—41no—
367C3×C4—42no—
368C3×C4—82no—
369C3×C4—81no—
370C3×C4—81no—
371C3×C4—122no—
372C3×C4—122no—
373C3×C4—121no—
374C3×C4#87511yescharacteristic
375C3×C4#88511yescharacteristic
376C3×C4#89611yescharacteristic
377C3×C4#89711yescharacteristic
378C3×C4C3×C22⋊Q811yescharacteristic
379C3×C4C3×C22⋊Q811yescharacteristic
380C3×C4C3×#12411yescharacteristic
381C3×C4C3×#12411yescharacteristic
382Dic3—42no—
383Dic3—42no—
384Dic3—41no—
385C32#203111yescharacteristic, complemented, Sylow
386C23—61no—
387C23C3×D3×D411yescharacteristic
388Q8—61no—
389Q8—61no—
390Q8—124no—
391D4—61no—
392D4—61no—
393D4—121no—
394D4—121no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—42no—
398C2×C4—41no—
399C2×C4—62no—
400C2×C4—62no—
401C2×C4—61no—
402C2×C4—121no—
403C2×C4—121no—
404C2×C4C2×C3×D1211yescharacteristic
405C2×C4C3×#23511yescharacteristic
406C2×C4C3×#23511yescharacteristic
407C2×C4C3×D3×D411yescharacteristic
408C2×C4C3×#23711yescharacteristic
409C2×C4C3×D3×Q811yescharacteristic
410C8—41no—
411C8—121no—
412C2×C3—22no—
413C2×C3—21no—
414C2×C3—21no—
415C2×C3—21no—
416C2×C3—21no—
417C2×C3—21no—
418C2×C3—21no—
419C2×C3—21no—
420C2×C3—41no—
421C2×C3—41no—
422C2×C3—241no—
423C2×C3#467311yescharacteristic
424C2×C3C3×#39311yescharacteristic
425D3—81no—
426C22—41no—
427C22—121no—
428C22—241no—
429C22C3×#88211yescharacteristic
430C22C3×#88511yescharacteristic
431C22C3×#89611yescharacteristic
432C4—22no—
433C4—41no—
434C4—81no—
435C4—122no—
436C4—122no—
437C4—121no—
438C4C3×#87511yescharacteristic
439C4C3×#88511yescharacteristic
440C4C3×#89611yescharacteristic
441C4C3×#89711yescharacteristic
442C3—21no—
443C3#6877911yescharacteristic, direct product factor
444C3C3×#203111yescharacteristic, complemented
445C2—21no—
446C2—21no—
447C2—21no—
448C2—241no—
449C2C3×#467311yescharacteristic
subgroupG/H
centerC3×C4#885
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC32×#339C2
socleC2×C32#393
prime radicalC2×C3×#235C22
hypercenterC3×#339D3
hypocenterC3C3×#2031
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C3×C4 ◁ C22×C3×C4 ◁ C3×#339

Complements

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

NH ≅ G/Ntype
1. C3×#5470C2semidirect
5. C32×#339C2semidirect
6. C3×#4556C2semidirect
7. C3×#4531C2semidirect
9. #68779C3direct (N × H)
26. #5470C2×C3semidirect
35. C3×#339D3semidirect
36. C3×#339C2×C3semidirect
38. #4556C2×C3semidirect
39. #4531C2×C3semidirect
47. C2×C3×D12Q8semidirect
50. C2×C3×Dic6Q8semidirect
136. #339C3×D3semidirect
158. C2×D12C3×Q8semidirect
161. C2×Dic6C3×Q8semidirect
385. C32#2031semidirect
443. C3#68779direct (N × H)
444. C3C3×#2031semidirect

Maximal subgroups

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

subgroupindex
C3×#54702
C3×#51392
C3×#50062
C2×C3×#8052
C32×#3392
C3×#45562
C3×#45312
C3×#20313
#687793