Finite Group Databasebeta

← C3×#70149 #11796546

Subgroups — C3×#70149 #11796546

Order 1152.

599 conjugacy classes of subgroups.

The subgroup lattice has 449 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5830C211yesmaximal, characteristic
2C32×#413C211yesmaximal, characteristic, complemented
3C3×#5237C211yesmaximal, characteristic, complemented
4C3×#4477C214yesmaximal, complemented
5C3×#2134—31nomaximal
6#70149C311yesmaximal, characteristic, direct product factor
7C2×C32×#41C2211yescharacteristic
8C22×C3×D12C411yescharacteristic
9C2×C32×M16—21no—
10C3×#947C2212yes—
11C3×#940C412yes—
12C3×#937—21no—
13C3×#937—21no—
14C3×#930—21no—
15C3×#930—21no—
16C3×#926C411yescharacteristic
17C2×C3×#208—21no—
18C32×#101C2212yescomplemented
19C32×#100—21no—
20C3×#836C2212yescomplemented
21C3×#833—21no—
22C3×#535—31no—
23#5830C2×C311yescharacteristic
24C3×#413—21no—
25C3×#413—31no—
26C3×#413D311yescharacteristic, complemented
27C3×#413C2×C311yescharacteristic, complemented
28#5237C2×C311yescharacteristic, complemented
29C3×#355—34no—
30#4477C2×C314yescomplemented
31C23×C3×D3—21no—
32C32×#41—41no—
33C32×#41—41no—
34C2×C32×Q8C2311yescharacteristic
35C2×C32×D4C2×C411yescharacteristic
36C2×C32×D4D411yescharacteristic
37C2×C32×D4D411yescharacteristic
38C22×C32×C4C2×C411yescharacteristic
39C22×C32×C4D411yescharacteristic
40C22×C32×C4D411yescharacteristic
41C2×C3×#67—22no—
42C2×C3×#67—22no—
43C2×C3×D12—21no—
44C2×C3×D12—41no—
45C2×C3×D12—41no—
46C2×C3×D12C2×C412yes—
47C32×M16—22no—
48C32×M16—41no—
49C2×C32×C8—41no—
50C3×#217—21no—
51C3×(C2×D3)⋊C4—22no—
52C3×(C2×D3)⋊C4—22no—
53C3×C4⋊Dic3—21no—
54C3×C4×Dic3C2×C412yes—
55C3×#208—22no—
56C3×#208—41no—
57C2×C3×C3⋊C8—41no—
58#2134—31noSylow
59C2×C3×#41—21no—
60C2×C3×#41C2×D311yescharacteristic
61C2×C3×#41C22×C311yescharacteristic
62C22×C3×D4—31no—
63C22×D12C3×C411yescharacteristic
64C2×C3×M16—22no—
65C2×C3×M16—21no—
66C2×C3×M16—21no—
67C2×C3×M16—61no—
68C3×#127—32no—
69C3×#124—32no—
70C3×#121—61no—
71C3×#121—61no—
72C3×#120—61no—
73C3×#120—61no—
74C3×#117—31no—
75#947C22×C312yes—
76#940C3×C412yes—
77#937—21no—
78#937—21no—
79#930—21no—
80#930—21no—
81#926C3×C411yescharacteristic
82C2×#208—21no—
83C3×#101—22no—
84C3×#101—32no—
85C3×#101C2×D312yescomplemented
86C3×#101C22×C312yescomplemented
87C3×#100—22no—
88C3×#100—21no—
89C3×#100—21no—
90C3×#100—61no—
91#836C22×C312yescomplemented
92#833—21no—
93C23×C32C22⋊C411yescharacteristic
94C23×C32C22⋊C411yescharacteristic
95C23×C32C22⋊C411yescharacteristic
96C22×C3×D3—22no—
97C22×C3×D3—42no—
98C22×C3×D3—82no—
99C32×Q8—41no—
100C32×D4—41no—
101C32×D4—41no—
102C32×D4—41no—
103C2×C32×C4—21no—
104C2×C32×C4—21no—
105C2×C32×C4—21no—
106C2×C32×C4—21no—
107C2×C32×C4—21no—
108C2×C32×C4—21no—
109C2×C32×C4C22⋊C411yescharacteristic
110C2×C32×C4C22×C411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4C2×D411yescharacteristic
113C3×#67—82no—
114C3×#67—82no—
115C2×C3×Dic3—22no—
116C3×D12—42no—
117C3×D12—41no—
118C3×D12—41no—
119C32×C8—42no—
120C3×C3⋊C8—42no—
121#535—31no—
122#413—31no—
123#413C3×D311yescharacteristic, complemented
124#355—34no—
125C24×C3—61no—
126C23×D3—21no—
127C3×#41—41no—
128C3×#41—41no—
129C3×#41—41no—
130C3×#41—41no—
131C3×#41—42no—
132C3×#41—42no—
133C2×C3×Q8—21no—
134C2×C3×Q8C22×D311yescharacteristic
135C2×C3×Q8C23×C311yescharacteristic
136C2×C3×D4—21no—
137C2×C3×D4—21no—
138C2×C3×D4—21no—
139C2×C3×D4—32no—
140C2×C3×D4—62no—
141C2×C3×D4—62no—
142C2×C3×D4—61no—
143C2×C3×D4—121no—
144C2×C3×D4—121no—
145C2×C3×D4C4×D311yescharacteristic
146C2×C3×D4D1211yescharacteristic
147C2×C3×D4#6711yescharacteristic
148C2×C3×D4C2×C3×C411yescharacteristic
149C2×C3×D4C3×D411yescharacteristic
150C2×C3×D4C3×D411yescharacteristic
151C22×C3×C4—21no—
152C22×C3×C4—21no—
153C22×C3×C4—21no—
154C22×C3×C4C4×D311yescharacteristic
155C22×C3×C4D1211yescharacteristic
156C22×C3×C4#6711yescharacteristic
157C22×C3×C4C2×C3×C411yescharacteristic
158C22×C3×C4C3×D411yescharacteristic
159C22×C3×C4C3×D411yescharacteristic
160C2×#67—22no—
161C2×#67—22no—
162C2×D12—21no—
163C2×D12—41no—
164C2×D12—41no—
165C2×D12C2×C3×C412yes—
166C3×M16—24no—
167C3×M16—22no—
168C3×M16—22no—
169C3×M16—42no—
170C3×M16—41no—
171C3×M16—41no—
172C3×M16—62no—
173C3×M16—121no—
174C2×C3×C8—42no—
175C2×C3×C8—41no—
176C2×C3×C8—41no—
177C2×C3×C8—121no—
178C3×C4⋊C4—61no—
179C3×C22⋊C4—61no—
180C3×C22⋊C4—62no—
181C3×C22⋊C4—62no—
182C3×C42—32no—
183#217—21no—
184(C2×D3)⋊C4—22no—
185(C2×D3)⋊C4—22no—
186C4⋊Dic3—21no—
187C4×Dic3C2×C3×C412yes—
188#208—22no—
189#208—41no—
190C2×C3⋊C8—41no—
191C22×C32—21no—
192C22×C32—21no—
193C22×C32—21no—
194C22×C32—41no—
195C22×C32—41no—
196C22×C32—41no—
197C22×C32C2×C22⋊C411yescharacteristic
198C2×C3×D3—42no—
199C2×C3×D3—42no—
200C2×C3×D3—42no—
201C2×C3×D3—84no—
202C32×C4—21no—
203C32×C4—21no—
204C32×C4—21no—
205C32×C4#9911yescharacteristic
206C32×C4#9911yescharacteristic
207C3×Dic3—42no—
208C2×#41C2×C3×D311yescharacteristic
209C22×D4—31no—
210C2×M16—21no—
211C2×M16—61no—
212#127—32no—
213#124—32no—
214#121—61no—
215#121—61no—
216#120—61no—
217#120—61no—
218#117—31no—
219#101—32no—
220#101C2×C3×D312yescomplemented
221#100—21no—
222#100—61no—
223C23×C3—21no—
224C23×C3—21no—
225C23×C3—21no—
226C23×C3—62no—
227C23×C3—122no—
228C23×C3—242no—
229C23×C3(C2×D3)⋊C411yescharacteristic
230C23×C3(C2×D3)⋊C411yescharacteristic
231C23×C3(C2×D3)⋊C411yescharacteristic
232C23×C3C3×C22⋊C411yescharacteristic
233C23×C3C3×C22⋊C411yescharacteristic
234C23×C3C3×C22⋊C411yescharacteristic
235C22×D3—22no—
236C22×D3—42no—
237C22×D3—82no—
238C3×Q8—41no—
239C3×Q8—41no—
240C3×Q8—42no—
241C3×D4—41no—
242C3×D4—41no—
243C3×D4—41no—
244C3×D4—41no—
245C3×D4—41no—
246C3×D4—41no—
247C3×D4—42no—
248C3×D4—42no—
249C3×D4—42no—
250C3×D4—122no—
251C3×D4—121no—
252C3×D4—121no—
253C3×D4—242no—
254C3×D4—242no—
255C2×C3×C4—22no—
256C2×C3×C4—22no—
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—21no—
265C2×C3×C4—21no—
266C2×C3×C4—21no—
267C2×C3×C4—21no—
268C2×C3×C4—21no—
269C2×C3×C4—21no—
270C2×C3×C4—21no—
271C2×C3×C4—21no—
272C2×C3×C4—21no—
273C2×C3×C4—41no—
274C2×C3×C4—41no—
275C2×C3×C4—41no—
276C2×C3×C4—41no—
277C2×C3×C4—62no—
278C2×C3×C4(C2×D3)⋊C411yescharacteristic
279C2×C3×C4C3×C22⋊C411yescharacteristic
280C2×C3×C4C2×C4×D311yescharacteristic
281C2×C3×C4C2×D1211yescharacteristic
282C2×C3×C4C2×#6711yescharacteristic
283C2×C3×C4C22×C3×C411yescharacteristic
284C2×C3×C4C2×C3×D411yescharacteristic
285C2×C3×C4C2×C3×D411yescharacteristic
286#67—82no—
287#67—82no—
288C2×Dic3—22no—
289D12—42no—
290D12—41no—
291D12—41no—
292C3×C8—44no—
293C3×C8—42no—
294C3×C8—42no—
295C3×C8—122no—
296C3⋊C8—42no—
297C2×C32—21no—
298C2×C32—41no—
299C2×C32—41no—
300C2×C32—41no—
301C2×C32C2×#9911yescharacteristic
302C3×D3—82no—
303C24—61no—
304#41—41no—
305#41—41no—
306C2×Q8C22×C3×D311yescharacteristic
307C2×D4—32no—
308C2×D4—62no—
309C2×D4—62no—
310C2×D4—61no—
311C2×D4—121no—
312C2×D4—121no—
313C2×D4C3×C4×D311yescharacteristic
314C2×D4C3×D1211yescharacteristic
315C2×D4C3×#6711yescharacteristic
316C22×C4C3×C4×D311yescharacteristic
317C22×C4C3×D1211yescharacteristic
318C22×C4C3×#6711yescharacteristic
319M16—22no—
320M16—41no—
321M16—62no—
322M16—121no—
323C2×C8—41no—
324C2×C8—121no—
325C4⋊C4—61no—
326C22⋊C4—61no—
327C22⋊C4—62no—
328C22⋊C4—62no—
329C42—32no—
330C22×C3—22no—
331C22×C3—21no—
332C22×C3—21no—
333C22×C3—21no—
334C22×C3—21no—
335C22×C3—21no—
336C22×C3—21no—
337C22×C3—21no—
338C22×C3—41no—
339C22×C3—41no—
340C22×C3—41no—
341C22×C3—41no—
342C22×C3—41no—
343C22×C3—41no—
344C22×C3—41no—
345C22×C3—41no—
346C22×C3—81no—
347C22×C3—81no—
348C22×C3—81no—
349C22×C3—122no—
350C22×C3—122no—
351C22×C3—122no—
352C22×C3—244no—
353C22×C3C2×(C2×D3)⋊C411yescharacteristic
354C22×C3C2×C3×C22⋊C411yescharacteristic
355C2×D3—42no—
356C2×D3—42no—
357C2×D3—42no—
358C2×D3—84no—
359C3×C4—22no—
360C3×C4—21no—
361C3×C4—21no—
362C3×C4—21no—
363C3×C4—21no—
364C3×C4—21no—
365C3×C4—21no—
366C3×C4—21no—
367C3×C4—21no—
368C3×C4—41no—
369C3×C4—41no—
370C3×C4—122no—
371C3×C4#80611yescharacteristic
372C3×C4#80611yescharacteristic
373C3×C4C3×#9911yescharacteristic
374C3×C4C3×#9911yescharacteristic
375Dic3—42no—
376C32#213411yescharacteristic, complemented, Sylow
377C23—62no—
378C23—122no—
379C23—242no—
380C23C3×(C2×D3)⋊C411yescharacteristic
381C23C3×(C2×D3)⋊C411yescharacteristic
382C23C3×(C2×D3)⋊C411yescharacteristic
383Q8—41no—
384D4—41no—
385D4—41no—
386D4—41no—
387D4—122no—
388D4—121no—
389D4—121no—
390D4—242no—
391D4—242no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—62no—
399C2×C4C3×(C2×D3)⋊C411yescharacteristic
400C2×C4C2×C3×C4×D311yescharacteristic
401C2×C4C2×C3×D1211yescharacteristic
402C2×C4C2×C3×#6711yescharacteristic
403C8—42no—
404C8—122no—
405C2×C3—21no—
406C2×C3—21no—
407C2×C3—21no—
408C2×C3—41no—
409C2×C3—42no—
410C2×C3—41no—
411C2×C3—41no—
412C2×C3—41no—
413C2×C3—41no—
414C2×C3—41no—
415C2×C3—41no—
416C2×C3—81no—
417C2×C3—81no—
418C2×C3—242no—
419C2×C3C2×#80611yescharacteristic
420C2×C3C2×C3×#9911yescharacteristic
421D3—82no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—41no—
426C22—41no—
427C22—41no—
428C22—122no—
429C22—122no—
430C22—122no—
431C22—244no—
432C22C2×C3×(C2×D3)⋊C411yescharacteristic
433C4—21no—
434C4—21no—
435C4—21no—
436C4—122no—
437C4C3×#80611yescharacteristic
438C4C3×#80611yescharacteristic
439C3—21no—
440C3#7014911yescharacteristic, direct product factor
441C3C3×#213411yescharacteristic, complemented
442C2—21no—
443C2—41no—
444C2—41no—
445C2—41no—
446C2—242no—
447C2C2×C3×#80611yescharacteristic
subgroupG/H
centerC2×C3C2×#806
commutatorC2×C3×C4C22×C3×C4
FrattiniC2×Q8C22×C3×D3
FittingC32×#413C2
socleC2×C32C2×#99
prime radicalC3×#5830C2
cosocleC2×C3×Q8C23×C3
hypercenterC3×#413D3
hypocenterC3C3×#2134
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C2×C3×#41 ◁ C3×#413

Complements

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

NH ≅ G/Ntype
2. C32×#413C2semidirect
3. C3×#5237C2semidirect
4. C3×#4477C2semidirect
6. #70149C3direct (N × H)
18. C32×#101C22semidirect
20. C3×#836C22semidirect
26. C3×#413D3semidirect
27. C3×#413C2×C3semidirect
28. #5237C2×C3semidirect
30. #4477C2×C3semidirect
85. C3×#101C2×D3semidirect
86. C3×#101C22×C3semidirect
91. #836C22×C3semidirect
123. #413C3×D3semidirect
220. #101C2×C3×D3semidirect
376. C32#2134semidirect
440. C3#70149direct (N × H)
441. C3C3×#2134semidirect

Maximal subgroups

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

subgroupindex
C3×#58302
C32×#4132
C3×#52372
C3×#44772
C3×#21343
#701493