Finite Group Databasebeta

← C3×#71693 #11787279

Subgroups — C3×#71693 #11787279

Order 1152.

881 conjugacy classes of subgroups.

The subgroup lattice has 445 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C22⋊Q8C211yesmaximal, characteristic
2C2×C3×#926C211yesmaximal, characteristic
3C2×C3×#835C212yesmaximal, complemented
4C2×C3×#830C211yesmaximal, characteristic
5C3×#4529C212yesmaximal, complemented
6C3×#1873—31nomaximal
7#71693C311yesmaximal, characteristic, direct product factor
8C22×C32×Q8C2211yescharacteristic
9C23×C32×C4C2211yescharacteristic
10C32×C22⋊Q8—22no—
11C32×C22⋊Q8C414yescomplemented
12C2×C32×C4⋊C4—21no—
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×C32×C22⋊C4—21no—
15C2×C3×#217—21no—
16C3×#926—24no—
17C2×C3×C4⋊Dic3C2212yes—
18C2×C3×C4×Dic3—21no—
19C22×C3×C3⋊C8C2212yes—
20C3×#835—24no—
21C3×#830—22no—
22C2×C3×C22⋊Q8—21no—
23C2×C3×C22⋊Q8D311yescharacteristic
24C2×C3×C22⋊Q8C2×C311yescharacteristic
25C2×C3×#117—31no—
26C2×#926C2×C311yescharacteristic
27C2×C3×#103—32no—
28C2×C3×C22⋊C8—31no—
29C2×#835C2×C312yescomplemented
30C2×#830C2×C311yescharacteristic
31C3×#340—32no—
32#4529C2×C312yescomplemented
33C24×C32D411yescharacteristic
34C2×C32×Q8—21no—
35C2×C32×Q8—22no—
36C2×C32×Q8—22no—
37C2×C32×Q8C2×C412yes—
38C22×C32×C4—22no—
39C22×C32×C4—22no—
40C22×C32×C4—21no—
41C22×C32×C4—21no—
42C22×C32×C4C2×C412yes—
43C22×C32×C4D411yescharacteristic
44C22×C32×C4D412yes—
45C22×C32×C4C2311yescharacteristic
46C22×C3×Dic3—22no—
47C32×C4⋊C4—24no—
48C32×C4⋊C4—21no—
49C32×C4⋊C4C2×C412yes—
50C32×C22⋊C4—24no—
51C3×#217—24no—
52C3×C4⋊Dic3—22no—
53C3×C4⋊Dic3D414yes—
54C3×C4×Dic3—24no—
55C2×C3×C3⋊C8—22no—
56C2×C3×C3⋊C8—22no—
57C2×C3×C3⋊C8—22no—
58#1873—31noSylow
59C22×C3×Q8—21no—
60C22×C3×Q8C2×D311yescharacteristic
61C22×C3×Q8C22×C311yescharacteristic
62C23×C3×C4—21no—
63C23×C3×C4C2×D311yescharacteristic
64C23×C3×C4C22×C311yescharacteristic
65C22×C3×C8—32no—
66C3×C22⋊Q8—24no—
67C3×C22⋊Q8—22no—
68C3×C22⋊Q8—22no—
69C3×C22⋊Q8—24no—
70C3×C22⋊Q8Dic314yescomplemented
71C3×C22⋊Q8C3×C414yescomplemented
72C3×#117—64no—
73C2×C3×C4⋊C4—22no—
74C2×C3×C4⋊C4—21no—
75C2×C3×C4⋊C4—21no—
76C2×C3×C4⋊C4—21no—
77C2×C3×C4⋊C4—32no—
78C2×C3×C4⋊C4C2×D311yescharacteristic
79C2×C3×C4⋊C4C22×C311yescharacteristic
80C2×C3×C22⋊C4—22no—
81C2×C3×C22⋊C4—21no—
82C2×C3×C22⋊C4—21no—
83C2×C3×C22⋊C4—61no—
84C2×C3×C42—61no—
85C2×#217—21no—
86#926—24no—
87C2×C4⋊Dic3C22×C312yes—
88C2×C4×Dic3—21no—
89C22×C3⋊C8C22×C312yes—
90C3×#103—64no—
91C3×C22⋊C8—62no—
92#835—24no—
93#830—22no—
94C23×C32—22no—
95C23×C32—21no—
96C23×C32—21no—
97C23×C32—22no—
98C23×C32C22⋊C412yes—
99C23×C32C2×D411yescharacteristic
100C32×Q8—24no—
101C32×Q8—42no—
102C2×C32×C4—22no—
103C2×C32×C4—22no—
104C2×C32×C4—21no—
105C2×C32×C4—21no—
106C2×C32×C4—24no—
107C2×C32×C4—24no—
108C2×C32×C4—41no—
109C2×C32×C4—41no—
110C2×C32×C4—42no—
111C2×C32×C4C22⋊C412yes—
112C2×C32×C4C22×C411yescharacteristic
113C2×C32×C4C2×D412yes—
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4#4112yes—
116C2×C3×Dic3—24no—
117C2×C3×Dic3—42no—
118C2×C3×Dic3—42no—
119C3×C3⋊C8—42no—
120C2×C22⋊Q8C3×D311yescharacteristic
121C2×#117—31no—
122C2×#103—32no—
123C2×C22⋊C8—31no—
124#340—32no—
125C24×C3—21no—
126C24×C3#6711yescharacteristic
127C24×C3C3×D411yescharacteristic
128C2×C3×Q8—22no—
129C2×C3×Q8—21no—
130C2×C3×Q8—21no—
131C2×C3×Q8—22no—
132C2×C3×Q8—22no—
133C2×C3×Q8—22no—
134C2×C3×Q8—22no—
135C2×C3×Q8—22no—
136C2×C3×Q8—42no—
137C2×C3×Q8—42no—
138C2×C3×Q8C2×Dic312yes—
139C2×C3×Q8C2×C3×C412yes—
140C22×C3×C4—22no—
141C22×C3×C4—22no—
142C22×C3×C4—22no—
143C22×C3×C4—22no—
144C22×C3×C4—22no—
145C22×C3×C4—22no—
146C22×C3×C4—21no—
147C22×C3×C4—21no—
148C22×C3×C4—21no—
149C22×C3×C4—21no—
150C22×C3×C4—22no—
151C22×C3×C4—21no—
152C22×C3×C4—22no—
153C22×C3×C4—21no—
154C22×C3×C4—42no—
155C22×C3×C4—42no—
156C22×C3×C4—62no—
157C22×C3×C4C2×Dic312yes—
158C22×C3×C4#6711yescharacteristic
159C22×C3×C4#6712yes—
160C22×C3×C4C2×C3×C412yes—
161C22×C3×C4C3×D411yescharacteristic
162C22×C3×C4C3×D412yes—
163C22×C3×C4C22×D311yescharacteristic
164C22×C3×C4C23×C311yescharacteristic
165C22×Dic3—22no—
166C2×C3×C8—62no—
167C2×C3×C8—62no—
168C2×C3×C8—62no—
169C3×C4⋊C4—28no—
170C3×C4⋊C4—22no—
171C3×C4⋊C4—24no—
172C3×C4⋊C4—24no—
173C3×C4⋊C4—21no—
174C3×C4⋊C4—21no—
175C3×C4⋊C4—22no—
176C3×C4⋊C4—34no—
177C3×C4⋊C4—62no—
178C3×C4⋊C4C2×Dic312yes—
179C3×C4⋊C4C2×C3×C412yes—
180C3×C22⋊C4—28no—
181C3×C22⋊C4—24no—
182C3×C22⋊C4—24no—
183C3×C22⋊C4—64no—
184C3×C42—64no—
185#217—24no—
186C4⋊Dic3—22no—
187C4⋊Dic3C3×D414yes—
188C4×Dic3—24no—
189C2×C3⋊C8—22no—
190C2×C3⋊C8—22no—
191C2×C3⋊C8—22no—
192C22×C32—22no—
193C22×C32—22no—
194C22×C32—22no—
195C22×C32—42no—
196C22×C32—42no—
197C22×C32C2×C22⋊C411yescharacteristic
198C22×C32#12011yescharacteristic
199C22×C32#12311yescharacteristic
200C22×C32#13512yes—
201C22×C32#13712yes—
202C32×C4—22no—
203C32×C4—42no—
204C32×C4—42no—
205C32×C4C4×D412yes—
206C32×C4#12112yes—
207C3×Dic3—44no—
208C22×Q8C2×C3×D311yescharacteristic
209C23×C4C2×C3×D311yescharacteristic
210C22×C8—32no—
211C22⋊Q8—22no—
212C22⋊Q8C3×Dic314yescomplemented
213#117—64no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—32no—
216C2×C4⋊C4C2×C3×D311yescharacteristic
217C2×C22⋊C4—21no—
218C2×C22⋊C4—61no—
219C2×C42—61no—
220#103—64no—
221C22⋊C8—62no—
222C23×C3—24no—
223C23×C3—21no—
224C23×C3—21no—
225C23×C3—22no—
226C23×C3—22no—
227C23×C3—21no—
228C23×C3—21no—
229C23×C3—22no—
230C23×C3—22no—
231C23×C3—22no—
232C23×C3—21no—
233C23×C3—41no—
234C23×C3—41no—
235C23×C3—42no—
236C23×C3#21712yes—
237C23×C3C3×C22⋊C412yes—
238C23×C3C2×#6711yescharacteristic
239C23×C3C2×C3×D411yescharacteristic
240C3×Q8—24no—
241C3×Q8—24no—
242C3×Q8—44no—
243C3×Q8—44no—
244C3×Q8—42no—
245C3×Q8—42no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—24no—
251C2×C3×C4—24no—
252C2×C3×C4—24no—
253C2×C3×C4—24no—
254C2×C3×C4—24no—
255C2×C3×C4—24no—
256C2×C3×C4—22no—
257C2×C3×C4—22no—
258C2×C3×C4—22no—
259C2×C3×C4—22no—
260C2×C3×C4—22no—
261C2×C3×C4—22no—
262C2×C3×C4—22no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—44no—
266C2×C3×C4—44no—
267C2×C3×C4—41no—
268C2×C3×C4—41no—
269C2×C3×C4—44no—
270C2×C3×C4—42no—
271C2×C3×C4—42no—
272C2×C3×C4—41no—
273C2×C3×C4—41no—
274C2×C3×C4—42no—
275C2×C3×C4—41no—
276C2×C3×C4—41no—
277C2×C3×C4—42no—
278C2×C3×C4—64no—
279C2×C3×C4—122no—
280C2×C3×C4—122no—
281C2×C3×C4#21712yes—
282C2×C3×C4C3×C22⋊C412yes—
283C2×C3×C4D3×D412yes—
284C2×C3×C4#23712yes—
285C2×C3×C4C22×Dic311yescharacteristic
286C2×C3×C4C2×#6711yescharacteristic
287C2×C3×C4C22×C3×C411yescharacteristic
288C2×C3×C4C2×C3×D412yes—
289C2×C3×C4C2×C3×D411yescharacteristic
290C2×C3×C4C3×#4112yes—
291C2×Dic3—24no—
292C2×Dic3—42no—
293C2×Dic3—42no—
294C3×C8—122no—
295C3⋊C8—42no—
296C2×C32—42no—
297C2×C32#38611yescharacteristic
298C2×C32#41611yescharacteristic
299C2×C32#41911yescharacteristic
300C2×C32#45212yes—
301C2×C32#48512yes—
302C24C3×#6711yescharacteristic
303C2×Q8—21no—
304C2×Q8—22no—
305C2×Q8—22no—
306C2×Q8C2×C3×Dic312yes—
307C22×C4—22no—
308C22×C4—22no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—62no—
312C22×C4C2×C3×Dic312yes—
313C22×C4C3×#6711yescharacteristic
314C22×C4C3×#6712yes—
315C22×C4C22×C3×D311yescharacteristic
316C2×C8—62no—
317C2×C8—62no—
318C2×C8—62no—
319C4⋊C4—24no—
320C4⋊C4—21no—
321C4⋊C4—34no—
322C4⋊C4—62no—
323C4⋊C4C2×C3×Dic312yes—
324C22⋊C4—24no—
325C22⋊C4—64no—
326C42—64no—
327C22×C3—24no—
328C22×C3—22no—
329C22×C3—22no—
330C22×C3—22no—
331C22×C3—22no—
332C22×C3—22no—
333C22×C3—22no—
334C22×C3—21no—
335C22×C3—21no—
336C22×C3—22no—
337C22×C3—22no—
338C22×C3—21no—
339C22×C3—42no—
340C22×C3—42no—
341C22×C3—44no—
342C22×C3—44no—
343C22×C3—42no—
344C22×C3—42no—
345C22×C3—42no—
346C22×C3—42no—
347C22×C3#93511yescharacteristic
348C22×C3#93711yescharacteristic
349C22×C3#94212yes—
350C22×C3#95012yes—
351C22×C3C2×#21711yescharacteristic
352C22×C3C2×C3×C22⋊C411yescharacteristic
353C22×C3C3×#12011yescharacteristic
354C22×C3C3×#12311yescharacteristic
355C22×C3C3×#13512yes—
356C22×C3C3×#13712yes—
357C3×C4—22no—
358C3×C4—22no—
359C3×C4—22no—
360C3×C4—22no—
361C3×C4—42no—
362C3×C4—44no—
363C3×C4—44no—
364C3×C4—42no—
365C3×C4—42no—
366C3×C4—42no—
367C3×C4—42no—
368C3×C4—124no—
369C3×C4D4×Dic312yes—
370C3×C4#93912yes—
371C3×C4C3×C4×D412yes—
372C3×C4C3×#12112yes—
373Dic3—44no—
374C32#187311yescharacteristic, complemented, Sylow
375C23—21no—
376C23—21no—
377C23—22no—
378C23—22no—
379C23C3×#21712yes—
380C23C2×C3×#6711yescharacteristic
381Q8—24no—
382Q8—42no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—24no—
386C2×C4—24no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—42no—
392C2×C4—64no—
393C2×C4—122no—
394C2×C4—122no—
395C2×C4C3×#21712yes—
396C2×C4C3×D3×D412yes—
397C2×C4C3×#23712yes—
398C2×C4C22×C3×Dic311yescharacteristic
399C2×C4C2×C3×#6711yescharacteristic
400C8—122no—
401C2×C3—21no—
402C2×C3—21no—
403C2×C3—21no—
404C2×C3—22no—
405C2×C3—22no—
406C2×C3—44no—
407C2×C3—42no—
408C2×C3—42no—
409C2×C3#504512yes—
410C2×C3#504712yes—
411C2×C3#522011yescharacteristic
412C2×C3#522511yescharacteristic
413C2×C3#523311yescharacteristic
414C2×C3C3×#38611yescharacteristic
415C2×C3C3×#41611yescharacteristic
416C2×C3C3×#41911yescharacteristic
417C2×C3C3×#45212yes—
418C2×C3C3×#48512yes—
419C22—22no—
420C22—22no—
421C22—22no—
422C22—42no—
423C22—42no—
424C22C3×#93511yescharacteristic
425C22C3×#93711yescharacteristic
426C22C3×#94212yes—
427C22C3×#95012yes—
428C22C2×C3×#21711yescharacteristic
429C4—22no—
430C4—42no—
431C4—42no—
432C4—124no—
433C4C3×D4×Dic312yes—
434C4C3×#93912yes—
435C3—21no—
436C3#7169311yescharacteristic, direct product factor
437C3C3×#187311yescharacteristic, complemented
438C2—42no—
439C2C3×#504512yes—
440C2C3×#504712yes—
441C2C3×#522011yescharacteristic
442C2C3×#522511yescharacteristic
443C2C3×#523311yescharacteristic
subgroupG/H
centerC23×C3C2×#67
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC2×C32×C22⋊Q8C2
socleC23×C32C2×D4
prime radicalC24×C32D4
cosocleC22×C3×C4C23×C3
hypercenterC2×C3×C22⋊Q8D3
hypocenterC3C3×#1873
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C23×C3×C4 ◁ C2×C3×C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. C2×C3×#835C2semidirect
5. C3×#4529C2semidirect
7. #71693C3direct (N × H)
11. C32×C22⋊Q8C4semidirect
29. C2×#835C2×C3semidirect
32. #4529C2×C3semidirect
70. C3×C22⋊Q8Dic3semidirect
71. C3×C22⋊Q8C3×C4semidirect
212. C22⋊Q8C3×Dic3semidirect
374. C32#1873semidirect
436. C3#71693direct (N × H)
437. C3C3×#1873semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C22⋊Q82
C2×C3×#9262
C2×C3×#8352
C2×C3×#8302
C3×#45292
C3×#18733
#716933