Finite Group Databasebeta

← C3×#70128 #11796519

Subgroups — C3×#70128 #11796519

Order 1152.

533 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5816C211yesmaximal, characteristic
2C2×C32×#101C211yesmaximal, characteristic, complemented
3C2×C3×#836C211yesmaximal, characteristic, complemented
4C3×#4478C212yesmaximal, complemented
5C3×#4477C212yesmaximal, complemented
6C3×#2133—31nomaximal
7#70128C311yesmaximal, characteristic, direct product factor
8C22×C32×Q8C2211yescharacteristic
9C2×C3×#235C411yescharacteristic
10C2×C32×M16—21no—
11C3×#947C411yescharacteristic
12C3×#947C2211yescharacteristic
13C3×#946—21no—
14C3×#946—21no—
15C3×#944C411yescharacteristic
16C3×#944C2211yescharacteristic
17C3×#929—21no—
18C3×#929—21no—
19C3×#926C411yescharacteristic
20C2×C3×#208—21no—
21C32×#101—21no—
22C32×#101C2212yes—
23C3×#836—21no—
24C3×#836C2212yes—
25C3×#536—31no—
26#5816C2×C311yescharacteristic
27C2×C3×#101—21no—
28C2×C3×#101—31no—
29C2×C3×#101D311yescharacteristic, complemented
30C2×C3×#101C2×C311yescharacteristic, complemented
31C2×#836C2×C311yescharacteristic, complemented
32C3×#356—32no—
33C3×#355—32no—
34#4478C2×C312yescomplemented
35#4477C2×C312yescomplemented
36C2×C32×Q8—41no—
37C2×C32×Q8—41no—
38C2×C32×Q8C2×C411yescharacteristic
39C2×C32×Q8D411yescharacteristic
40C2×C32×Q8D411yescharacteristic
41C2×C32×Q8C2311yescharacteristic
42C22×C32×C4C2×C411yescharacteristic
43C22×C32×C4D411yescharacteristic
44C22×C32×C4D411yescharacteristic
45C2×C3×#67—21no—
46C3×#235—41no—
47C3×#235—41no—
48C2×C3×D12C2×C411yescharacteristic
49C2×C3×C4×D3—21no—
50C2×C3×Dic6C2×C411yescharacteristic
51C32×M16—22no—
52C32×M16—41no—
53C2×C32×C8—41no—
54C3×#217—21no—
55C3×(C2×D3)⋊C4—21no—
56C3×(C2×D3)⋊C4—21no—
57C3×(C2×D3)⋊C4—21no—
58C3×(C2×D3)⋊C4—21no—
59C3×C4⋊Dic3—21no—
60C3×Dic3⋊C4—21no—
61C3×Dic3⋊C4—21no—
62C3×Dic3⋊C4—21no—
63C3×Dic3⋊C4—21no—
64C3×C4×Dic3C2×C411yescharacteristic
65C3×C4×Dic3C2×C411yescharacteristic
66C3×#208—22no—
67C3×#208—41no—
68C2×C3×C3⋊C8—41no—
69#2133—31noSylow
70C2×C3×#41—31no—
71C22×C3×Q8—21no—
72C22×C3×Q8C2×D311yescharacteristic
73C22×C3×Q8C22×C311yescharacteristic
74C2×#235C3×C411yescharacteristic
75C2×C3×M16—22no—
76C2×C3×M16—21no—
77C2×C3×M16—21no—
78C2×C3×M16—61no—
79C3×C4⋊Q8—31no—
80C3×C4⋊Q8—31no—
81C3×#124—31no—
82C3×#124—31no—
83C3×#123—61no—
84C3×#123—61no—
85C3×C22⋊Q8—61no—
86C3×C22⋊Q8—61no—
87C3×#117—31no—
88#947C3×C411yescharacteristic
89#947C22×C311yescharacteristic
90#946—21no—
91#946—21no—
92#944C3×C411yescharacteristic
93#944C22×C311yescharacteristic
94#929—21no—
95#929—21no—
96#926C3×C411yescharacteristic
97C2×#208—21no—
98C3×#101—22no—
99C3×#101—21no—
100C3×#101—21no—
101C3×#101—22no—
102C3×#101—32no—
103C3×#101—61no—
104C3×#101C2×D312yes—
105C3×#101C22×C312yes—
106#836—21no—
107#836C22×C312yes—
108C23×C32C22⋊C411yescharacteristic
109C22×C3×D3—21no—
110C32×Q8—41no—
111C32×Q8—41no—
112C32×Q8—41no—
113C32×Q8—41no—
114C2×C32×C4—21no—
115C2×C32×C4—21no—
116C2×C32×C4—21no—
117C2×C32×C4—21no—
118C2×C32×C4—21no—
119C2×C32×C4—21no—
120C2×C32×C4C22⋊C411yescharacteristic
121C2×C32×C4C22⋊C411yescharacteristic
122C2×C32×C4C22⋊C411yescharacteristic
123C2×C32×C4C22×C411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C3×#67—41no—
127C3×#67—41no—
128C2×C3×Dic3—21no—
129C2×C3×Dic3—21no—
130C2×C3×Dic3—21no—
131C3×D12—41no—
132C3×C4×D3—42no—
133C3×Dic6—41no—
134C32×C8—42no—
135C3×C3⋊C8—42no—
136#536—31no—
137C2×#101—31no—
138C2×#101C3×D311yescharacteristic, complemented
139#356—32no—
140#355—32no—
141C3×#41—121no—
142C3×#41—121no—
143C2×C3×Q8—21no—
144C2×C3×Q8—21no—
145C2×C3×Q8—21no—
146C2×C3×Q8—21no—
147C2×C3×Q8—31no—
148C2×C3×Q8—41no—
149C2×C3×Q8—41no—
150C2×C3×Q8—41no—
151C2×C3×Q8—41no—
152C2×C3×Q8—42no—
153C2×C3×Q8—42no—
154C2×C3×Q8C4×D311yescharacteristic
155C2×C3×Q8D1211yescharacteristic
156C2×C3×Q8#6711yescharacteristic
157C2×C3×Q8C2×C3×C411yescharacteristic
158C2×C3×Q8C3×D411yescharacteristic
159C2×C3×Q8C3×D411yescharacteristic
160C2×C3×Q8C22×D311yescharacteristic
161C2×C3×Q8C23×C311yescharacteristic
162C2×C3×D4—31no—
163C2×C3×D4—61no—
164C22×C3×C4—21no—
165C22×C3×C4—21no—
166C22×C3×C4—21no—
167C22×C3×C4—61no—
168C22×C3×C4C4×D311yescharacteristic
169C22×C3×C4D1211yescharacteristic
170C22×C3×C4#6711yescharacteristic
171C22×C3×C4C2×C3×C411yescharacteristic
172C22×C3×C4C3×D411yescharacteristic
173C22×C3×C4C3×D411yescharacteristic
174C2×#67—21no—
175#235—41no—
176#235—41no—
177C2×D12C2×C3×C411yescharacteristic
178C2×C4×D3—21no—
179C2×Dic6C2×C3×C411yescharacteristic
180C3×M16—24no—
181C3×M16—22no—
182C3×M16—22no—
183C3×M16—42no—
184C3×M16—41no—
185C3×M16—41no—
186C3×M16—62no—
187C3×M16—121no—
188C2×C3×C8—42no—
189C2×C3×C8—41no—
190C2×C3×C8—41no—
191C2×C3×C8—121no—
192C3×C4⋊C4—61no—
193C3×C4⋊C4—61no—
194C3×C4⋊C4—61no—
195C3×C4⋊C4—61no—
196C3×C4⋊C4—61no—
197C3×C22⋊C4—61no—
198C3×C22⋊C4—61no—
199C3×C22⋊C4—61no—
200C3×C22⋊C4—61no—
201C3×C22⋊C4—61no—
202C3×C42—31no—
203C3×C42—31no—
204#217—21no—
205(C2×D3)⋊C4—21no—
206(C2×D3)⋊C4—21no—
207(C2×D3)⋊C4—21no—
208(C2×D3)⋊C4—21no—
209C4⋊Dic3—21no—
210Dic3⋊C4—21no—
211Dic3⋊C4—21no—
212Dic3⋊C4—21no—
213Dic3⋊C4—21no—
214C4×Dic3C2×C3×C411yescharacteristic
215C4×Dic3C2×C3×C411yescharacteristic
216#208—22no—
217#208—41no—
218C2×C3⋊C8—41no—
219C22×C32—41no—
220C22×C32#9911yescharacteristic
221C22×C32#9911yescharacteristic
222C22×C32C2×C22⋊C411yescharacteristic
223C2×C3×D3—42no—
224C2×C3×D3—41no—
225C32×C4—21no—
226C32×C4—21no—
227C32×C4—21no—
228C32×C4—21no—
229C32×C4—21no—
230C32×C4—21no—
231C3×Dic3—41no—
232C3×Dic3—41no—
233C3×Dic3—41no—
234C2×#41—31no—
235C22×Q8C2×C3×D311yescharacteristic
236C2×M16—21no—
237C2×M16—61no—
238C4⋊Q8—31no—
239C4⋊Q8—31no—
240#124—31no—
241#124—31no—
242#123—61no—
243#123—61no—
244C22⋊Q8—61no—
245C22⋊Q8—61no—
246#117—31no—
247#101—21no—
248#101—32no—
249#101—61no—
250#101C2×C3×D312yes—
251C23×C3—21no—
252C23×C3—61no—
253C23×C3(C2×D3)⋊C411yescharacteristic
254C23×C3C3×C22⋊C411yescharacteristic
255C22×D3—21no—
256C3×Q8—41no—
257C3×Q8—41no—
258C3×Q8—41no—
259C3×Q8—41no—
260C3×Q8—41no—
261C3×Q8—41no—
262C3×Q8—41no—
263C3×Q8—41no—
264C3×Q8—42no—
265C3×Q8—42no—
266C3×Q8—42no—
267C3×Q8—42no—
268C3×Q8—121no—
269C3×D4—121no—
270C3×D4—121no—
271C3×D4—121no—
272C2×C3×C4—22no—
273C2×C3×C4—22no—
274C2×C3×C4—21no—
275C2×C3×C4—21no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—21no—
284C2×C3×C4—21no—
285C2×C3×C4—21no—
286C2×C3×C4—21no—
287C2×C3×C4—21no—
288C2×C3×C4—21no—
289C2×C3×C4—21no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—41no—
293C2×C3×C4—41no—
294C2×C3×C4—41no—
295C2×C3×C4—41no—
296C2×C3×C4—61no—
297C2×C3×C4—61no—
298C2×C3×C4—61no—
299C2×C3×C4—122no—
300C2×C3×C4(C2×D3)⋊C411yescharacteristic
301C2×C3×C4(C2×D3)⋊C411yescharacteristic
302C2×C3×C4(C2×D3)⋊C411yescharacteristic
303C2×C3×C4C3×C22⋊C411yescharacteristic
304C2×C3×C4C3×C22⋊C411yescharacteristic
305C2×C3×C4C3×C22⋊C411yescharacteristic
306C2×C3×C4C2×C4×D311yescharacteristic
307C2×C3×C4C2×D1211yescharacteristic
308C2×C3×C4C2×#6711yescharacteristic
309C2×C3×C4C22×C3×C411yescharacteristic
310C2×C3×C4C2×C3×D411yescharacteristic
311C2×C3×C4C2×C3×D411yescharacteristic
312#67—41no—
313#67—41no—
314C2×Dic3—21no—
315C2×Dic3—21no—
316C2×Dic3—21no—
317D12—41no—
318C4×D3—42no—
319Dic6—41no—
320C3×C8—44no—
321C3×C8—42no—
322C3×C8—42no—
323C3×C8—122no—
324C3⋊C8—42no—
325C2×C32—21no—
326C2×C32—21no—
327C2×C32—21no—
328C2×C32C2×#9911yescharacteristic
329C3×D3—81no—
330#41—121no—
331#41—121no—
332C2×Q8—31no—
333C2×Q8—41no—
334C2×Q8—41no—
335C2×Q8C3×C4×D311yescharacteristic
336C2×Q8C3×D1211yescharacteristic
337C2×Q8C3×#6711yescharacteristic
338C2×Q8C22×C3×D311yescharacteristic
339C2×D4—31no—
340C2×D4—61no—
341C22×C4—61no—
342C22×C4C3×C4×D311yescharacteristic
343C22×C4C3×D1211yescharacteristic
344C22×C4C3×#6711yescharacteristic
345M16—22no—
346M16—41no—
347M16—62no—
348M16—121no—
349C2×C8—41no—
350C2×C8—121no—
351C4⋊C4—61no—
352C4⋊C4—61no—
353C4⋊C4—61no—
354C4⋊C4—61no—
355C4⋊C4—61no—
356C22⋊C4—61no—
357C22⋊C4—61no—
358C22⋊C4—61no—
359C22⋊C4—61no—
360C22⋊C4—61no—
361C42—31no—
362C42—31no—
363C22×C3—21no—
364C22×C3—21no—
365C22×C3—21no—
366C22×C3—41no—
367C22×C3—41no—
368C22×C3—42no—
369C22×C3—122no—
370C22×C3—121no—
371C22×C3#80611yescharacteristic
372C22×C3#80611yescharacteristic
373C22×C3C3×#9911yescharacteristic
374C22×C3C3×#9911yescharacteristic
375C22×C3C2×(C2×D3)⋊C411yescharacteristic
376C22×C3C2×C3×C22⋊C411yescharacteristic
377C2×D3—42no—
378C2×D3—41no—
379C3×C4—22no—
380C3×C4—22no—
381C3×C4—21no—
382C3×C4—21no—
383C3×C4—21no—
384C3×C4—21no—
385C3×C4—21no—
386C3×C4—21no—
387C3×C4—21no—
388C3×C4—21no—
389C3×C4—21no—
390C3×C4—21no—
391C3×C4—21no—
392C3×C4—21no—
393C3×C4—41no—
394C3×C4—41no—
395C3×C4—41no—
396C3×C4—41no—
397C3×C4—121no—
398C3×C4—121no—
399C3×C4—121no—
400Dic3—41no—
401Dic3—41no—
402Dic3—41no—
403C32#213311yescharacteristic, complemented, Sylow
404C23—61no—
405C23C3×(C2×D3)⋊C411yescharacteristic
406Q8—41no—
407Q8—41no—
408Q8—41no—
409Q8—41no—
410Q8—121no—
411D4—121no—
412D4—121no—
413D4—121no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—61no—
421C2×C4—61no—
422C2×C4—61no—
423C2×C4—122no—
424C2×C4C3×(C2×D3)⋊C411yescharacteristic
425C2×C4C3×(C2×D3)⋊C411yescharacteristic
426C2×C4C3×(C2×D3)⋊C411yescharacteristic
427C2×C4C2×C3×C4×D311yescharacteristic
428C2×C4C2×C3×D1211yescharacteristic
429C2×C4C2×C3×#6711yescharacteristic
430C8—42no—
431C8—122no—
432C2×C3—22no—
433C2×C3—21no—
434C2×C3—21no—
435C2×C3—21no—
436C2×C3—21no—
437C2×C3—21no—
438C2×C3—21no—
439C2×C3—21no—
440C2×C3—41no—
441C2×C3—41no—
442C2×C3—241no—
443C2×C3C2×#80611yescharacteristic
444C2×C3C2×C3×#9911yescharacteristic
445D3—81no—
446C22—41no—
447C22—122no—
448C22—121no—
449C22C3×#80611yescharacteristic
450C22C3×#80611yescharacteristic
451C22C2×C3×(C2×D3)⋊C411yescharacteristic
452C4—21no—
453C4—21no—
454C4—21no—
455C4—21no—
456C4—21no—
457C4—21no—
458C4—121no—
459C4—121no—
460C4—121no—
461C3—21no—
462C3#7012811yescharacteristic, direct product factor
463C3C3×#213311yescharacteristic, complemented
464C2—21no—
465C2—21no—
466C2—21no—
467C2—241no—
468C2C2×C3×#80611yescharacteristic
subgroupG/H
centerC2×C3C2×#806
commutatorC2×C3×C4C22×C3×C4
FrattiniC2×Q8C22×C3×D3
FittingC2×C32×#101C2
socleC2×C32C2×#99
prime radicalC2×C3×#235C4
cosocleC2×C3×Q8C23×C3
hypercenterC2×C3×#101D3
hypocenterC3C3×#2133
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C23×C3 ◁ C22×C3×Q8 ◁ C2×C3×#101

Complements

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

NH ≅ G/Ntype
2. C2×C32×#101C2semidirect
3. C2×C3×#836C2semidirect
4. C3×#4478C2semidirect
5. C3×#4477C2semidirect
7. #70128C3direct (N × H)
29. C2×C3×#101D3semidirect
30. C2×C3×#101C2×C3semidirect
31. C2×#836C2×C3semidirect
34. #4478C2×C3semidirect
35. #4477C2×C3semidirect
138. C2×#101C3×D3semidirect
403. C32#2133semidirect
462. C3#70128direct (N × H)
463. C3C3×#2133semidirect

Maximal subgroups

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

subgroupindex
C3×#58162
C2×C32×#1012
C2×C3×#8362
C3×#44782
C3×#44772
C3×#21333
#701283