Finite Group Databasebeta

← C3×#68106 #11777990

Subgroups — C3×#68106 #11777990

Order 1152.

785 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 785 conjugacy classes of subgroups — too many to draw. Only its 106 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
1C3×#5493C211yesmaximal, characteristic, complemented
2C3×#4960C211yesmaximal, characteristic, complemented
3C3×#4732C212yesmaximal, complemented
4C32×#323C211yesmaximal, characteristic, complemented
5C3×#4470C212yesmaximal, complemented
6C3×#1595—31nomaximal
7#68106C311yesmaximal, characteristic, direct product factor
8C22×C3×#67—21no—
9C22×C3×#67—21no—
10C22×C3×D12C2211yescharacteristic, complemented
11C2×C32×C22⋊C4C2211yescharacteristic
12C3×#930—21no—
13C3×#930C2212yes—
14C2×C3×(C2×D3)⋊C4—21no—
15C2×C3×D24—22no—
16C3×#886—22no—
17C3×#882—22no—
18C32×C22⋊C8C2212yescomplemented
19C3×C3⋊#95C2211yescharacteristic, complemented
20C3×#821—22no—
21C3×#534—31no—
22#5493C2×C311yescharacteristic, complemented
23C3×#447—32no—
24C3×#392—31no—
25#4960C2×C311yescharacteristic, complemented
26#4732C2×C312yescomplemented
27C3×#327—32no—
28C3×#323—21no—
29C3×#323D311yescharacteristic, complemented
30C3×#323C2×C311yescharacteristic, complemented
31#4470C2×C312yescomplemented
32C24×C32D411yescharacteristic
33C23×C3×D3—21no—
34C23×C3×D3—21no—
35C22×C32×C4D411yescharacteristic
36C22×C32×C4C2311yescharacteristic
37C2×C3×#67—22no—
38C2×C3×#67—22no—
39C2×C3×#67—42no—
40C2×C3×#67—42no—
41C2×C3×#67—42no—
42C2×C3×#67—42no—
43C2×C3×#67—42no—
44C22×C3×Dic3—21no—
45C22×C3×Dic3—21no—
46C2×C3×D12—22no—
47C2×C3×D12—21no—
48C2×C3×D12—42no—
49C2×C3×D12D412yescomplemented
50C2×C32×C8—22no—
51C32×C22⋊C4—22no—
52C3×(C2×D3)⋊C4—22no—
53C3×(C2×D3)⋊C4—22no—
54C3×(C2×D3)⋊C4—42no—
55C3×C4⋊Dic3—21no—
56C3×C4⋊Dic3D412yescomplemented
57C3×D24—44no—
58#1595—31noSylow
59C22×C3×D4—31no—
60C22×C3×D4—61no—
61C22×C3×D4—61no—
62C22×#67—21no—
63C22×#67—21no—
64C22×D12C22×C311yescharacteristic, complemented
65C2×C3×D8—62no—
66C3×#123—62no—
67C3×#121—32no—
68C3×#121—61no—
69C3×#120—62no—
70C2×C3×C22⋊C4—21no—
71C2×C3×C22⋊C4—61no—
72C2×C3×C22⋊C4C2×D311yescharacteristic
73C2×C3×C22⋊C4C22×C311yescharacteristic
74#930—21no—
75#930C22×C312yes—
76C2×(C2×D3)⋊C4—21no—
77C2×D24—22no—
78#886—22no—
79#882—22no—
80C3×#102—62no—
81C3×C22⋊C8—22no—
82C3×C22⋊C8C2×D312yescomplemented
83C3×C22⋊C8C22×C312yescomplemented
84C3×#95—31no—
85C3⋊#95C22×C311yescharacteristic, complemented
86#821—22no—
87C23×C32—21no—
88C23×C32—21no—
89C23×C32—41no—
90C23×C32—41no—
91C23×C32D812yescomplemented
92C23×C32C2×D411yescharacteristic
93C22×C3×D3—22no—
94C22×C3×D3—22no—
95C22×C3×D3—41no—
96C22×C3×D3—41no—
97C22×C3×D3—41no—
98C22×C3×D3—42no—
99C22×C3×D3—41no—
100C22×C3×D3—41no—
101C22×C3×D3—41no—
102C22×C3×D3—81no—
103C22×C3×D3—81no—
104C2×C32×C4—21no—
105C2×C32×C4—41no—
106C2×C32×C4—41no—
107C2×C32×C4C2×D412yes—
108C3×#67—44no—
109C3×#67—48no—
110C3×#67—42no—
111C3×#67—42no—
112C2×C3×Dic3—22no—
113C2×C3×Dic3—22no—
114C2×C3×Dic3—41no—
115C2×C3×Dic3—42no—
116C2×C3×Dic3—41no—
117C3×D12—24no—
118C3×D12—42no—
119C3×D12—42no—
120C3×D12—81no—
121C32×C8—42no—
122#534—31no—
123#447—32no—
124#392—31no—
125#327—32no—
126#323C3×D311yescharacteristic, complemented
127C24×C3—21no—
128C24×C3—61no—
129C24×C3—61no—
130C24×C3D1211yescharacteristic
131C24×C3C3×D411yescharacteristic
132C23×D3—21no—
133C23×D3—21no—
134C2×C3×D4—32no—
135C2×C3×D4—61no—
136C2×C3×D4—62no—
137C2×C3×D4—62no—
138C2×C3×D4—62no—
139C2×C3×D4—122no—
140C2×C3×D4—122no—
141C2×C3×D4—122no—
142C2×C3×D4—122no—
143C2×C3×D4—122no—
144C2×C3×D4—122no—
145C22×C3×C4—21no—
146C22×C3×C4—21no—
147C22×C3×C4—61no—
148C22×C3×C4—61no—
149C22×C3×C4D1211yescharacteristic
150C22×C3×C4C3×D411yescharacteristic
151C22×C3×C4C22×D311yescharacteristic
152C22×C3×C4C23×C311yescharacteristic
153C2×#67—22no—
154C2×#67—22no—
155C2×#67—42no—
156C2×#67—42no—
157C2×#67—42no—
158C2×#67—42no—
159C2×#67—42no—
160C22×Dic3—21no—
161C22×Dic3—21no—
162C2×D12—22no—
163C2×D12—21no—
164C2×D12—42no—
165C2×D12C3×D412yescomplemented
166C3×D8—124no—
167C2×C3×C8—22no—
168C2×C3×C8—22no—
169C2×C3×C8—42no—
170C3×C4⋊C4—32no—
171C3×C4⋊C4—61no—
172C3×C22⋊C4—22no—
173C3×C22⋊C4—22no—
174C3×C22⋊C4—42no—
175C3×C22⋊C4—62no—
176C3×C22⋊C4—62no—
177C3×C22⋊C4—122no—
178(C2×D3)⋊C4—22no—
179(C2×D3)⋊C4—22no—
180(C2×D3)⋊C4—42no—
181C4⋊Dic3—21no—
182C4⋊Dic3C3×D412yescomplemented
183D24—44no—
184C22×C32—21no—
185C22×C32—21no—
186C22×C32—22no—
187C22×C32—42no—
188C22×C32—41no—
189C22×C32—41no—
190C22×C32—81no—
191C22×C32#12011yescharacteristic
192C22×C32C2×D811yescharacteristic
193C22×C32AGL(1,ℤ/8)11yescharacteristic
194C2×C3×D3—42no—
195C2×C3×D3—42no—
196C2×C3×D3—42no—
197C2×C3×D3—42no—
198C2×C3×D3—42no—
199C2×C3×D3—42no—
200C2×C3×D3—81no—
201C2×C3×D3—81no—
202C2×C3×D3—84no—
203C2×C3×D3—81no—
204C2×C3×D3—81no—
205C32×C4—22no—
206C32×C4—41no—
207C3×Dic3—42no—
208C3×Dic3—42no—
209C22×D4—31no—
210C22×D4—61no—
211C22×D4—61no—
212C2×D8—62no—
213#123—62no—
214#121—32no—
215#121—61no—
216#120—62no—
217C2×C22⋊C4—61no—
218C2×C22⋊C4C2×C3×D311yescharacteristic
219#102—62no—
220C22⋊C8C2×C3×D312yescomplemented
221#95—31no—
222C23×C3—21no—
223C23×C3—21no—
224C23×C3—21no—
225C23×C3—21no—
226C23×C3—22no—
227C23×C3—21no—
228C23×C3—41no—
229C23×C3—41no—
230C23×C3—41no—
231C23×C3—41no—
232C23×C3—41no—
233C23×C3—41no—
234C23×C3—62no—
235C23×C3—62no—
236C23×C3—81no—
237C23×C3—81no—
238C23×C3—121no—
239C23×C3—121no—
240C23×C3—121no—
241C23×C3—122no—
242C23×C3—121no—
243C23×C3—121no—
244C23×C3—121no—
245C23×C3—241no—
246C23×C3—241no—
247C23×C3D2412yescomplemented
248C23×C3C3×D812yescomplemented
249C23×C3C2×D1211yescharacteristic
250C23×C3C2×C3×D411yescharacteristic
251C22×D3—22no—
252C22×D3—22no—
253C22×D3—41no—
254C22×D3—41no—
255C22×D3—41no—
256C22×D3—42no—
257C22×D3—41no—
258C22×D3—41no—
259C22×D3—41no—
260C22×D3—81no—
261C22×D3—81no—
262C3×D4—64no—
263C3×D4—122no—
264C3×D4—122no—
265C3×D4—124no—
266C3×D4—128no—
267C3×D4—122no—
268C3×D4—122no—
269C3×D4—241no—
270C2×C3×C4—21no—
271C2×C3×C4—21no—
272C2×C3×C4—22no—
273C2×C3×C4—41no—
274C2×C3×C4—41no—
275C2×C3×C4—41no—
276C2×C3×C4—41no—
277C2×C3×C4—41no—
278C2×C3×C4—62no—
279C2×C3×C4—62no—
280C2×C3×C4—81no—
281C2×C3×C4—81no—
282C2×C3×C4—121no—
283C2×C3×C4—122no—
284C2×C3×C4—121no—
285C2×C3×C4D3×D412yes—
286C2×C3×C4C2×C3×D412yes—
287#67—44no—
288#67—48no—
289#67—42no—
290#67—42no—
291C2×Dic3—22no—
292C2×Dic3—22no—
293C2×Dic3—41no—
294C2×Dic3—42no—
295C2×Dic3—41no—
296D12—24no—
297D12—42no—
298D12—42no—
299D12—81no—
300C3×C8—42no—
301C3×C8—42no—
302C3×C8—82no—
303C2×C32—21no—
304C2×C32—21no—
305C2×C32—42no—
306C2×C32#44711yescharacteristic
307C2×C32#45311yescharacteristic
308C2×C32B(4,𝔽2)11yescharacteristic
309C3×D3—82no—
310C3×D3—82no—
311C24—61no—
312C24—61no—
313C24C3×D1211yescharacteristic
314C2×D4—32no—
315C2×D4—61no—
316C2×D4—62no—
317C2×D4—62no—
318C2×D4—62no—
319C2×D4—122no—
320C2×D4—122no—
321C2×D4—122no—
322C2×D4—122no—
323C2×D4—122no—
324C2×D4—122no—
325C22×C4—61no—
326C22×C4—61no—
327C22×C4C3×D1211yescharacteristic
328C22×C4C22×C3×D311yescharacteristic
329D8—124no—
330C2×C8—22no—
331C4⋊C4—32no—
332C4⋊C4—61no—
333C22⋊C4—22no—
334C22⋊C4—62no—
335C22⋊C4—62no—
336C22⋊C4—122no—
337C22×C3—21no—
338C22×C3—21no—
339C22×C3—21no—
340C22×C3—21no—
341C22×C3—22no—
342C22×C3—22no—
343C22×C3—21no—
344C22×C3—21no—
345C22×C3—21no—
346C22×C3—41no—
347C22×C3—41no—
348C22×C3—42no—
349C22×C3—42no—
350C22×C3—42no—
351C22×C3—41no—
352C22×C3—41no—
353C22×C3—41no—
354C22×C3—41no—
355C22×C3—81no—
356C22×C3—81no—
357C22×C3—82no—
358C22×C3—81no—
359C22×C3—81no—
360C22×C3—82no—
361C22×C3—122no—
362C22×C3—122no—
363C22×C3—122no—
364C22×C3—122no—
365C22×C3—122no—
366C22×C3—122no—
367C22×C3—241no—
368C22×C3—241no—
369C22×C3—244no—
370C22×C3—241no—
371C22×C3—241no—
372C22×C3#88211yescharacteristic
373C22×C3C2×D2411yescharacteristic
374C22×C3#90811yescharacteristic
375C22×C3C3×#12011yescharacteristic
376C22×C3C2×C3×D811yescharacteristic
377C22×C3C3×AGL(1,ℤ/8)11yescharacteristic
378C2×D3—42no—
379C2×D3—42no—
380C2×D3—42no—
381C2×D3—42no—
382C2×D3—42no—
383C2×D3—42no—
384C2×D3—81no—
385C2×D3—81no—
386C2×D3—84no—
387C2×D3—81no—
388C2×D3—81no—
389C3×C4—22no—
390C3×C4—22no—
391C3×C4—42no—
392C3×C4—41no—
393C3×C4—41no—
394C3×C4—81no—
395C3×C4—122no—
396C3×C4—122no—
397Dic3—42no—
398Dic3—42no—
399C32#159511yescharacteristic, complemented, Sylow
400C23—21no—
401C23—21no—
402C23—41no—
403C23—41no—
404C23—62no—
405C23—62no—
406C23—121no—
407C23—121no—
408C23—121no—
409C23—122no—
410C23—121no—
411C23—121no—
412C23—121no—
413C23—241no—
414C23—241no—
415C23C3×D2412yescomplemented
416C23C2×C3×D1211yescharacteristic
417D4—64no—
418D4—122no—
419D4—122no—
420D4—124no—
421D4—128no—
422D4—122no—
423D4—122no—
424D4—241no—
425C2×C4—21no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—62no—
429C2×C4—62no—
430C2×C4—121no—
431C2×C4—122no—
432C2×C4—121no—
433C2×C4C3×D3×D412yes—
434C8—42no—
435C2×C3—21no—
436C2×C3—21no—
437C2×C3—21no—
438C2×C3—21no—
439C2×C3—21no—
440C2×C3—21no—
441C2×C3—21no—
442C2×C3—41no—
443C2×C3—41no—
444C2×C3—42no—
445C2×C3—42no—
446C2×C3—82no—
447C2×C3—242no—
448C2×C3—242no—
449C2×C3#473211yescharacteristic
450C2×C3#474111yescharacteristic
451C2×C3#474711yescharacteristic
452C2×C3C3×#44711yescharacteristic
453C2×C3C3×#45311yescharacteristic
454C2×C3C3×B(4,𝔽2)11yescharacteristic
455D3—82no—
456D3—82no—
457C22—21no—
458C22—21no—
459C22—22no—
460C22—42no—
461C22—41no—
462C22—41no—
463C22—81no—
464C22—122no—
465C22—122no—
466C22—122no—
467C22—122no—
468C22—122no—
469C22—122no—
470C22—241no—
471C22—241no—
472C22—244no—
473C22—241no—
474C22—241no—
475C22C3×#88211yescharacteristic
476C22C2×C3×D2411yescharacteristic
477C22C3×#90811yescharacteristic
478C4—22no—
479C4—41no—
480C4—122no—
481C4—122no—
482C3—21no—
483C3#6810611yescharacteristic, direct product factor
484C3C3×#159511yescharacteristic, complemented
485C2—21no—
486C2—21no—
487C2—42no—
488C2—242no—
489C2—242no—
490C2C3×#473211yescharacteristic
491C2C3×#474111yescharacteristic
492C2C3×#474711yescharacteristic
subgroupG/H
centerC22×C3#882
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC32×#323C2
socleC22×C32#120
hypercenterC3×#323D3
hypocenterC3C3×#1595
LCSG ▷ C22×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#323

Complements

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

NH ≅ G/Ntype
1. C3×#5493C2semidirect
2. C3×#4960C2semidirect
3. C3×#4732C2semidirect
4. C32×#323C2semidirect
5. C3×#4470C2semidirect
7. #68106C3direct (N × H)
10. C22×C3×D12C22semidirect
18. C32×C22⋊C8C22semidirect
19. C3×C3⋊#95C22semidirect
22. #5493C2×C3semidirect
25. #4960C2×C3semidirect
26. #4732C2×C3semidirect
29. C3×#323D3semidirect
30. C3×#323C2×C3semidirect
31. #4470C2×C3semidirect
49. C2×C3×D12D4semidirect
56. C3×C4⋊Dic3D4semidirect
64. C22×D12C22×C3semidirect
82. C3×C22⋊C8C2×D3semidirect
83. C3×C22⋊C8C22×C3semidirect
85. C3⋊#95C22×C3semidirect
91. C23×C32D8semidirect
126. #323C3×D3semidirect
165. C2×D12C3×D4semidirect
182. C4⋊Dic3C3×D4semidirect
220. C22⋊C8C2×C3×D3semidirect
247. C23×C3D24semidirect
248. C23×C3C3×D8semidirect
399. C32#1595semidirect
415. C23C3×D24semidirect
483. C3#68106direct (N × H)
484. C3C3×#1595semidirect

Maximal subgroups

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

subgroupindex
C3×#54932
C3×#49602
C3×#47322
C32×#3232
C3×#44702
C3×#15953
#681063