Finite Group Databasebeta

← C3×#72118 #11792394

Subgroups — C3×#72118 #11792394

Order 1152.

919 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 919 conjugacy classes of subgroups — too many to draw. Only its 142 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#575C211yesmaximal, characteristic, complemented
2C3×#5828C212yesmaximal, complemented
3C3×#5236C212yesmaximal, complemented
4C3×#5126C211yesmaximal, characteristic, complemented
5C3×#4557C211yesmaximal, characteristic, complemented
6C3×#2010—31nomaximal
7#72118C311yesmaximal, characteristic, direct product factor
8C2×C32×#41C2212yes—
9C22×C3×C4×D3C2211yescharacteristic
10C32×#137—22no—
11C32×AGL(1,ℤ/8)—22no—
12C32×#135—22no—
13C2×C32×M16C2211yescharacteristic
14C3×#946—22no—
15C3×#938—22no—
16C3×#937—22no—
17C3×#935—22no—
18C3×C4×#67—24no—
19C3×#926C2212yes—
20C2×C3×#208C2211yescharacteristic
21C3×#837—24no—
22C3×(C2×D3)⋊C8—22no—
23C3×#575—21no—
24C3×#575D311yescharacteristic, complemented
25C3×#575C2×C311yescharacteristic, complemented
26C3×#525—32no—
27#5828C2×C312yescomplemented
28C3×#421—32no—
29C3×#407—31no—
30#5236C2×C312yescomplemented
31#5126C2×C311yescharacteristic, complemented
32C3×H(3,ℤ/4)—31no—
33#4557C2×C311yescharacteristic, complemented
34C23×C3×D3D411yescharacteristic
35C32×#41—22no—
36C32×#41—22no—
37C32×#41—22no—
38C32×#41—22no—
39C2×C32×Q8D412yescomplemented
40C2×C32×D4—22no—
41C2×C32×D4D412yescomplemented
42C22×C32×C4—22no—
43C22×C32×C4C2311yescharacteristic
44C2×C3×#67—24no—
45C22×C3×Dic3D411yescharacteristic
46C2×C3×C4×D3—22no—
47C2×C3×C4×D3—22no—
48C2×C3×C4×D3—21no—
49C2×C3×C4×D3—21no—
50C32×Q16—22no—
51C32×SD16—24no—
52C32×D8—22no—
53C32×M16—22no—
54C2×C32×C8D412yescomplemented
55C3×#217—24no—
56C3×#217—22no—
57C3×(C2×D3)⋊C4—24no—
58C3×C4⋊Dic3—22no—
59C3×Dic3⋊C4—24no—
60C3×C4×Dic3D414yescomplemented
61C3×#208—22no—
62C2×C3×C3⋊C8—21no—
63#2010—31noSylow
64C2×C3×#41—22no—
65C2×C3×#41C2×D312yes—
66C2×C3×#41C22×C312yes—
67C23×C3×C4—31no—
68C22×C4×D3C22×C311yescharacteristic
69C3×#137—24no—
70C3×#137—22no—
71C3×#137—22no—
72C3×AGL(1,ℤ/8)—24no—
73C3×AGL(1,ℤ/8)—22no—
74C3×AGL(1,ℤ/8)—22no—
75C3×#135—24no—
76C3×#135—22no—
77C3×#135—22no—
78C2×C3×M16—21no—
79C2×C3×M16—31no—
80C2×C3×M16C2×D311yescharacteristic
81C2×C3×M16C22×C311yescharacteristic
82C3×#123—62no—
83C3×C22⋊Q8—62no—
84C3×#121—62no—
85C3×#120—62no—
86C3×C4×D4—64no—
87C3×#117—32no—
88#946—22no—
89#938—22no—
90#937—22no—
91#935—22no—
92C4×#67—24no—
93#926C22×C312yes—
94C2×#208C22×C311yescharacteristic
95C3×#104—64no—
96C3×C22⋊C8—62no—
97#837—24no—
98(C2×D3)⋊C8—22no—
99C23×C32—22no—
100C23×C32C2×D411yescharacteristic
101C22×C3×D3—22no—
102C22×C3×D3—21no—
103C22×C3×D3—42no—
104C32×Q8—22no—
105C32×Q8—22no—
106C32×D4—22no—
107C32×D4—22no—
108C32×D4—42no—
109C32×D4—42no—
110C2×C32×C4—22no—
111C2×C32×C4—42no—
112C2×C32×C4—42no—
113C2×C32×C4C2×D412yes—
114C2×C32×C4C2×D412yes—
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4#4111yescharacteristic
117C3×#67—48no—
118C2×C3×Dic3—24no—
119C2×C3×Dic3—22no—
120C2×C3×Dic3—21no—
121C3×C4×D3—41no—
122C3×C4×D3—42no—
123C3×C4×D3—41no—
124C32×C8—22no—
125C3×C3⋊C8—41no—
126#575C3×D311yescharacteristic, complemented
127#525—32no—
128#421—32no—
129#407—31no—
130H(3,ℤ/4)—31no—
131C24×C3—31no—
132C23×D3C3×D411yescharacteristic
133C3×#41—24no—
134C3×#41—24no—
135C3×#41—22no—
136C3×#41—22no—
137C3×#41—22no—
138C3×#41—22no—
139C3×#41—22no—
140C3×#41—22no—
141C3×#41—22no—
142C3×#41—22no—
143C3×#41—42no—
144C3×#41—42no—
145C2×C3×Q8—22no—
146C2×C3×Q8#6712yescomplemented
147C2×C3×Q8C3×D412yescomplemented
148C2×C3×D4—22no—
149C2×C3×D4—22no—
150C2×C3×D4—22no—
151C2×C3×D4—42no—
152C2×C3×D4—64no—
153C2×C3×D4#6712yescomplemented
154C2×C3×D4C3×D412yescomplemented
155C22×C3×C4—22no—
156C22×C3×C4—22no—
157C22×C3×C4—21no—
158C22×C3×C4—31no—
159C22×C3×C4—42no—
160C22×C3×C4—62no—
161C22×C3×C4—61no—
162C22×C3×C4—61no—
163C22×C3×C4—62no—
164C22×C3×C4C22×D311yescharacteristic
165C22×C3×C4C23×C311yescharacteristic
166C2×#67—24no—
167C22×Dic3C3×D411yescharacteristic
168C2×C4×D3—21no—
169C2×C4×D3—22no—
170C2×C4×D3—22no—
171C2×C4×D3—21no—
172C3×Q16—24no—
173C3×Q16—22no—
174C3×Q16—22no—
175C3×SD16—28no—
176C3×SD16—24no—
177C3×SD16—24no—
178C3×D8—24no—
179C3×D8—22no—
180C3×D8—22no—
181C3×M16—24no—
182C3×M16—22no—
183C3×M16—22no—
184C3×M16—62no—
185C2×C3×C8—22no—
186C2×C3×C8—61no—
187C2×C3×C8#6712yescomplemented
188C2×C3×C8C3×D412yescomplemented
189C3×C4⋊C4—64no—
190C3×C4⋊C4—62no—
191C3×C22⋊C4—64no—
192C3×C22⋊C4—64no—
193C3×C22⋊C4—62no—
194C3×C42—34no—
195#217—24no—
196#217—22no—
197(C2×D3)⋊C4—24no—
198C4⋊Dic3—22no—
199Dic3⋊C4—24no—
200C4×Dic3C3×D414yescomplemented
201#208—22no—
202C2×C3⋊C8—21no—
203C22×C32—42no—
204C22×C32—41no—
205C22×C32—44no—
206C22×C32#12012yes—
207C22×C32#12111yescharacteristic
208C2×C3×D3—24no—
209C2×C3×D3—22no—
210C2×C3×D3—42no—
211C2×C3×D3—41no—
212C2×C3×D3—41no—
213C32×C4—42no—
214C32×C4#12011yescharacteristic
215C32×C4#12112yes—
216C32×C4#12711yescharacteristic
217C3×Dic3—44no—
218C3×Dic3—41no—
219C2×#41C2×C3×D312yes—
220C23×C4—31no—
221#137—22no—
222AGL(1,ℤ/8)—22no—
223#135—22no—
224C2×M16—31no—
225C2×M16C2×C3×D311yescharacteristic
226#123—62no—
227C22⋊Q8—62no—
228#121—62no—
229#120—62no—
230C4×D4—64no—
231#117—32no—
232#104—64no—
233C22⋊C8—62no—
234C23×C3—22no—
235C23×C3—22no—
236C23×C3—21no—
237C23×C3—42no—
238C23×C3—62no—
239C23×C3—61no—
240C23×C3—122no—
241C23×C3D3×D411yescharacteristic
242C23×C3C2×C3×D411yescharacteristic
243C22×D3—22no—
244C22×D3—21no—
245C22×D3—42no—
246C3×Q8—24no—
247C3×Q8—22no—
248C3×Q8—22no—
249C3×Q8—22no—
250C3×Q8—22no—
251C3×Q8—42no—
252C3×D4—24no—
253C3×D4—22no—
254C3×D4—22no—
255C3×D4—22no—
256C3×D4—22no—
257C3×D4—42no—
258C3×D4—44no—
259C3×D4—44no—
260C3×D4—42no—
261C3×D4—42no—
262C3×D4—42no—
263C3×D4—42no—
264C3×D4—128no—
265C2×C3×C4—22no—
266C2×C3×C4—22no—
267C2×C3×C4—22no—
268C2×C3×C4—21no—
269C2×C3×C4—21no—
270C2×C3×C4—22no—
271C2×C3×C4—42no—
272C2×C3×C4—44no—
273C2×C3×C4—44no—
274C2×C3×C4—42no—
275C2×C3×C4—42no—
276C2×C3×C4—42no—
277C2×C3×C4—42no—
278C2×C3×C4—64no—
279C2×C3×C4—62no—
280C2×C3×C4—61no—
281C2×C3×C4—122no—
282C2×C3×C4—121no—
283C2×C3×C4—121no—
284C2×C3×C4D3×D412yes—
285C2×C3×C4#23711yescharacteristic
286C2×C3×C4C2×#6712yes—
287C2×C3×C4C2×#6711yescharacteristic
288C2×C3×C4C2×C3×D412yes—
289C2×C3×C4C2×C3×D412yes—
290C2×C3×C4C2×C3×D411yescharacteristic
291C2×C3×C4C3×#4111yescharacteristic
292#67—48no—
293C2×Dic3—24no—
294C2×Dic3—22no—
295C2×Dic3—21no—
296C4×D3—41no—
297C4×D3—42no—
298C4×D3—41no—
299C3×C8—24no—
300C3×C8—22no—
301C3×C8—22no—
302C3×C8—121no—
303C3⋊C8—41no—
304C2×C32—22no—
305C2×C32—21no—
306C2×C32—82no—
307C2×C32#39211yescharacteristic
308C3×D3—42no—
309C24—31no—
310#41—22no—
311#41—22no—
312#41—22no—
313#41—22no—
314C2×Q8C3×#6712yescomplemented
315C2×D4—22no—
316C2×D4—64no—
317C2×D4C3×#6712yescomplemented
318C22×C4—22no—
319C22×C4—31no—
320C22×C4—62no—
321C22×C4—61no—
322C22×C4—61no—
323C22×C4—62no—
324C22×C4C22×C3×D311yescharacteristic
325Q16—22no—
326SD16—24no—
327D8—22no—
328M16—22no—
329M16—62no—
330C2×C8—61no—
331C2×C8C3×#6712yescomplemented
332C4⋊C4—64no—
333C4⋊C4—62no—
334C22⋊C4—64no—
335C22⋊C4—64no—
336C22⋊C4—62no—
337C42—34no—
338C22×C3—22no—
339C22×C3—21no—
340C22×C3—41no—
341C22×C3—41no—
342C22×C3—44no—
343C22×C3—44no—
344C22×C3—44no—
345C22×C3—42no—
346C22×C3—42no—
347C22×C3—64no—
348C22×C3—62no—
349C22×C3—81no—
350C22×C3—84no—
351C22×C3—122no—
352C22×C3—121no—
353C22×C3—121no—
354C22×C3#93712yes—
355C22×C3#93811yescharacteristic
356C22×C3C3×#12012yes—
357C22×C3C3×#12111yescharacteristic
358C2×D3—24no—
359C2×D3—22no—
360C2×D3—42no—
361C2×D3—41no—
362C2×D3—41no—
363C3×C4—22no—
364C3×C4—21no—
365C3×C4—21no—
366C3×C4—44no—
367C3×C4—42no—
368C3×C4—42no—
369C3×C4—124no—
370C3×C4—121no—
371C3×C4#93912yes—
372C3×C4#94011yescharacteristic
373C3×C4#95311yescharacteristic
374C3×C4C3×#12011yescharacteristic
375C3×C4C3×#12112yes—
376C3×C4C3×#12711yescharacteristic
377Dic3—44no—
378Dic3—41no—
379C32#201011yescharacteristic, complemented, Sylow
380C23—22no—
381C23—62no—
382C23—61no—
383C23—122no—
384C23C3×D3×D411yescharacteristic
385Q8—22no—
386Q8—22no—
387D4—22no—
388D4—22no—
389D4—42no—
390D4—42no—
391D4—128no—
392C2×C4—22no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—64no—
396C2×C4—62no—
397C2×C4—61no—
398C2×C4—122no—
399C2×C4—121no—
400C2×C4—121no—
401C2×C4C3×D3×D412yes—
402C2×C4C3×#23711yescharacteristic
403C2×C4C2×C3×#6712yes—
404C2×C4C2×C3×#6711yescharacteristic
405C8—22no—
406C8—121no—
407C2×C3—22no—
408C2×C3—21no—
409C2×C3—22no—
410C2×C3—21no—
411C2×C3—21no—
412C2×C3—42no—
413C2×C3—41no—
414C2×C3—84no—
415C2×C3—82no—
416C2×C3—82no—
417C2×C3—122no—
418C2×C3#522311yescharacteristic
419C2×C3C3×#39211yescharacteristic
420D3—42no—
421C22—41no—
422C22—44no—
423C22—42no—
424C22—64no—
425C22—62no—
426C22—122no—
427C22—121no—
428C22—121no—
429C22C3×#93712yes—
430C22C3×#93811yescharacteristic
431C4—42no—
432C4—124no—
433C4—121no—
434C4C3×#93912yes—
435C4C3×#94011yescharacteristic
436C4C3×#95311yescharacteristic
437C3—21no—
438C3#7211811yescharacteristic, direct product factor
439C3C3×#201011yescharacteristic, complemented
440C2—22no—
441C2—21no—
442C2—82no—
443C2—122no—
444C2C3×#522311yescharacteristic
subgroupG/H
centerC3×C4#940
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC32×#575C2
socleC2×C32#392
hypercenterC3×#575D3
hypocenterC3C3×#2010
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C3×C4 ◁ C22×C3×C4 ◁ C3×#575

Complements

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

NH ≅ G/Ntype
1. C32×#575C2semidirect
2. C3×#5828C2semidirect
3. C3×#5236C2semidirect
4. C3×#5126C2semidirect
5. C3×#4557C2semidirect
7. #72118C3direct (N × H)
24. C3×#575D3semidirect
25. C3×#575C2×C3semidirect
27. #5828C2×C3semidirect
30. #5236C2×C3semidirect
31. #5126C2×C3semidirect
33. #4557C2×C3semidirect
39. C2×C32×Q8D4semidirect
41. C2×C32×D4D4semidirect
54. C2×C32×C8D4semidirect
60. C3×C4×Dic3D4semidirect
126. #575C3×D3semidirect
146. C2×C3×Q8#67semidirect
147. C2×C3×Q8C3×D4semidirect
153. C2×C3×D4#67semidirect
154. C2×C3×D4C3×D4semidirect
187. C2×C3×C8#67semidirect
188. C2×C3×C8C3×D4semidirect
200. C4×Dic3C3×D4semidirect
314. C2×Q8C3×#67semidirect
317. C2×D4C3×#67semidirect
331. C2×C8C3×#67semidirect
379. C32#2010semidirect
438. C3#72118direct (N × H)
439. C3C3×#2010semidirect

Maximal subgroups

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

subgroupindex
C32×#5752
C3×#58282
C3×#52362
C3×#51262
C3×#45572
C3×#20103
#721183