Finite Group Databasebeta

← C3×#69252 #11798271

Subgroups — C3×#69252 #11798271

Order 1152.

481 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 481 conjugacy classes of subgroups — too many to draw. Only its 94 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×#5768C211yesmaximal, characteristic, complemented
2C3×#5193C211yesmaximal, characteristic, complemented
3C3×#4908C211yesmaximal, characteristic, complemented
4C3×#4865C211yesmaximal, characteristic, complemented
5C32×#360C211yesmaximal, characteristic, complemented
6C3×#4514C211yesmaximal, characteristic, complemented
7C3×#4488C211yesmaximal, characteristic, complemented
8C3×#2190—31nomaximal
9#69252C311yesmaximal, characteristic, direct product factor
10C3×D3×#41—21no—
11C32×#135C2211yescharacteristic
12C3×#950—21no—
13C3×#918—21no—
14C3×#915—21no—
15C3×#914—21no—
16C3×#911—21no—
17C3×#904C2211yescharacteristic
18C2×C3×D24C2211yescharacteristic, complemented
19C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
20C3×#895—21no—
21C32×M32C2211yescharacteristic, complemented
22C32×#106C2211yescharacteristic, complemented
23C3×#828—21no—
24C3×#826—21no—
25C3×#812C2211yescharacteristic, complemented
26C3×#809—21no—
27C3×#800—21no—
28C3×D48—21no—
29C3×#575—31no—
30#5768C2×C311yescharacteristic, complemented
31C3×#509—31no—
32C3×#509—31no—
33C3×#469—31no—
34#5193C2×C311yescharacteristic, complemented
35#4908C2×C311yescharacteristic, complemented
36#4865C2×C311yescharacteristic, complemented
37C3×#360—21no—
38C3×#360—31no—
39C3×#360D311yescharacteristic, complemented
40C3×#360C2×C311yescharacteristic, complemented
41C3×#349—31no—
42#4514C2×C311yescharacteristic, complemented
43#4488C2×C311yescharacteristic, complemented
44C32×#41—21no—
45C3×#239—21no—
46C3×D3×Q8—21no—
47C3×#237—21no—
48C3×#237—41no—
49C3×D3×D4—21no—
50C3×D3×D4—41no—
51C3×#235—21no—
52C3×#235—41no—
53C2×C3×D12—21no—
54C2×C3×D12—41no—
55C2×C3×C4×D3—41no—
56C2×C3×C4×D3D411yescharacteristic
57C32×Q16D411yescharacteristic, complemented
58C32×SD16—21no—
59C32×D8D411yescharacteristic, complemented
60C2×C32×C8C2311yescharacteristic
61C32×C4⋊C4—21no—
62C3×#216—21no—
63C3×#215—21no—
64C3×#214—21no—
65C3×#213—21no—
66C3×(C2×D3)⋊C4—41no—
67C2×C3×C3⋊C8D411yescharacteristic
68C3×Dic12D411yescharacteristic, complemented
69C3×D24—21no—
70C3×D24—21no—
71C3×D24D411yescharacteristic, complemented
72C3×#204—21no—
73C3×ΓL(1,𝔽25)—21no—
74C3×ΓL(1,𝔽25)—21no—
75C32×C16—21no—
76C3×C3⋊C16—21no—
77#2190—31noSylow
78C2×C3×#41—61no—
79D3×#41—21no—
80C3×#137—61no—
81C3×#137—61no—
82C3×AGL(1,ℤ/8)—61no—
83C3×AGL(1,ℤ/8)—61no—
84C3×#135—21no—
85C3×#135—31no—
86C3×#135—61no—
87C3×#135C2×D311yescharacteristic
88C3×#135C22×C311yescharacteristic
89C2×C3×D8—31no—
90C2×C3×M16—31no—
91C3×#121—61no—
92#950—21no—
93#918—21no—
94#915—21no—
95#914—21no—
96#911—21no—
97#904C22×C311yescharacteristic
98C2×D24C22×C311yescharacteristic, complemented
99C2×ΓL(1,𝔽25)C22×C311yescharacteristic
100#895—21no—
101C3×SD32—61no—
102C3×SD32—61no—
103C3×D16—61no—
104C3×D16—61no—
105C3×M32—21no—
106C3×M32—31no—
107C3×M32C2×D311yescharacteristic, complemented
108C3×M32C22×C311yescharacteristic, complemented
109C3×#106—21no—
110C3×#106C2×D311yescharacteristic, complemented
111C3×#106C22×C311yescharacteristic, complemented
112C3×#102—61no—
113#828—21no—
114#826—21no—
115#812C22×C311yescharacteristic, complemented
116#809—21no—
117#800—21no—
118D48—21no—
119C22×C3×D3—41no—
120C22×C3×D3—41no—
121C22×C3×D3D811yescharacteristic
122C32×Q8—21no—
123C32×D4—21no—
124C32×D4—41no—
125C2×C32×C4—41no—
126C2×C32×C4—41no—
127C2×C32×C4C2×D411yescharacteristic
128C3×#67—41no—
129C3×#67—41no—
130C3×#67—41no—
131C2×C3×Dic3—41no—
132C2×C3×Dic3D811yescharacteristic
133C3×D12—21no—
134C3×D12—41no—
135C3×D12—41no—
136C3×D12—41no—
137C3×D12—82no—
138C3×C4×D3—21no—
139C3×C4×D3—21no—
140C3×C4×D3—41no—
141C3×C4×D3—41no—
142C3×C4×D3—41no—
143C3×Dic6—21no—
144C3×Dic6—41no—
145C32×C8C2×D411yescharacteristic
146C32×C8C2×D411yescharacteristic
147C3×C3⋊C8—21no—
148#575—31no—
149#509—31no—
150#509—31no—
151#469—31no—
152#360—31no—
153#360C3×D311yescharacteristic, complemented
154#349—31no—
155C3×#41—21no—
156C3×#41—21no—
157C3×#41—41no—
158C3×#41—61no—
159C3×#41—61no—
160C3×#41—61no—
161C3×#41—121no—
162C3×#41—121no—
163C2×C3×Q8—61no—
164C2×C3×D4—61no—
165C2×C3×D4—61no—
166C2×C3×D4—121no—
167C2×C3×D4—121no—
168C22×C3×C4—31no—
169C22×C3×C4—121no—
170#239—21no—
171D3×Q8—21no—
172#237—21no—
173#237—41no—
174D3×D4—21no—
175D3×D4—41no—
176#235—21no—
177#235—41no—
178C2×D12—21no—
179C2×D12—41no—
180C2×C4×D3—41no—
181C2×C4×D3C3×D411yescharacteristic
182C3×Q16—21no—
183C3×Q16—31no—
184C3×Q16—61no—
185C3×Q16D1211yescharacteristic, complemented
186C3×Q16C3×D411yescharacteristic, complemented
187C3×SD16—21no—
188C3×SD16—21no—
189C3×SD16—41no—
190C3×SD16—61no—
191C3×SD16—61no—
192C3×SD16—61no—
193C3×D8—21no—
194C3×D8—31no—
195C3×D8—61no—
196C3×D8—61no—
197C3×D8—61no—
198C3×D8D1211yescharacteristic, complemented
199C3×D8C3×D411yescharacteristic, complemented
200C3×M16—61no—
201C3×M16—61no—
202C2×C3×C8—21no—
203C2×C3×C8—31no—
204C2×C3×C8C22×D311yescharacteristic
205C2×C3×C8C23×C311yescharacteristic
206C3×C4⋊C4—21no—
207C3×C4⋊C4—21no—
208C3×C4⋊C4—41no—
209C3×C22⋊C4—121no—
210#216—21no—
211#215—21no—
212#214—21no—
213#213—21no—
214(C2×D3)⋊C4—41no—
215C2×C3⋊C8C3×D411yescharacteristic
216Dic12C3×D411yescharacteristic, complemented
217D24—21no—
218D24—21no—
219D24C3×D411yescharacteristic, complemented
220#204—21no—
221ΓL(1,𝔽25)—21no—
222ΓL(1,𝔽25)—21no—
223C3×C16—21no—
224C3×C16—21no—
225C3×C16—41no—
226C3×C16—61no—
227C3⋊C16—21no—
228C22×C32—41no—
229C22×C32C2×D811yescharacteristic
230C2×C3×D3—21no—
231C2×C3×D3—41no—
232C2×C3×D3—41no—
233C2×C3×D3—82no—
234C2×C3×D3—81no—
235C2×C3×D3—81no—
236C2×C3×D3—81no—
237C32×C4—41no—
238C32×C4—81no—
239C32×C4#12011yescharacteristic
240C32×C4AGL(1,ℤ/8)11yescharacteristic
241C3×Dic3—21no—
242C3×Dic3—41no—
243C2×#41—61no—
244#137—61no—
245#137—61no—
246AGL(1,ℤ/8)—61no—
247AGL(1,ℤ/8)—61no—
248#135—31no—
249#135—61no—
250#135C2×C3×D311yescharacteristic
251C2×D8—31no—
252C2×M16—31no—
253#121—61no—
254SD32—61no—
255SD32—61no—
256D16—61no—
257D16—61no—
258M32—31no—
259M32C2×C3×D311yescharacteristic, complemented
260#106C2×C3×D311yescharacteristic, complemented
261#102—61no—
262C23×C3—31no—
263C23×C3—121no—
264C23×C3—121no—
265C22×D3—41no—
266C22×D3—41no—
267C22×D3C3×D811yescharacteristic
268C3×Q8—21no—
269C3×Q8—21no—
270C3×Q8—41no—
271C3×Q8—61no—
272C3×Q8—121no—
273C3×D4—21no—
274C3×D4—21no—
275C3×D4—41no—
276C3×D4—41no—
277C3×D4—41no—
278C3×D4—61no—
279C3×D4—81no—
280C3×D4—121no—
281C3×D4—121no—
282C3×D4—121no—
283C3×D4—121no—
284C3×D4—121no—
285C3×D4—121no—
286C3×D4—242no—
287C2×C3×C4—21no—
288C2×C3×C4—31no—
289C2×C3×C4—41no—
290C2×C3×C4—41no—
291C2×C3×C4—41no—
292C2×C3×C4—41no—
293C2×C3×C4—61no—
294C2×C3×C4—61no—
295C2×C3×C4—81no—
296C2×C3×C4—81no—
297C2×C3×C4—121no—
298C2×C3×C4—121no—
299C2×C3×C4—121no—
300C2×C3×C4—121no—
301C2×C3×C4D3×D411yescharacteristic
302C2×C3×C4C2×C3×D411yescharacteristic
303#67—41no—
304#67—41no—
305#67—41no—
306C2×Dic3—41no—
307C2×Dic3C3×D811yescharacteristic
308D12—21no—
309D12—41no—
310D12—41no—
311D12—41no—
312D12—82no—
313C4×D3—21no—
314C4×D3—21no—
315C4×D3—41no—
316C4×D3—41no—
317C4×D3—41no—
318Dic6—21no—
319Dic6—41no—
320C3×C8—21no—
321C3×C8—21no—
322C3×C8—61no—
323C3×C8C2×D1211yescharacteristic
324C3×C8D3×D411yescharacteristic
325C3×C8C2×C3×D411yescharacteristic
326C3×C8C2×C3×D411yescharacteristic
327C3⋊C8—21no—
328C2×C32—21no—
329C2×C32—81no—
330C2×C32#44711yescharacteristic
331C3×D3—41no—
332C3×D3—81no—
333C3×D3—161no—
334#41—21no—
335#41—61no—
336#41—61no—
337#41—61no—
338#41—121no—
339#41—121no—
340C2×Q8—61no—
341C2×D4—61no—
342C2×D4—61no—
343C2×D4—121no—
344C2×D4—121no—
345C22×C4—31no—
346C22×C4—121no—
347Q16—31no—
348Q16—61no—
349Q16C3×D1211yescharacteristic, complemented
350SD16—21no—
351SD16—61no—
352SD16—61no—
353SD16—61no—
354D8—31no—
355D8—61no—
356D8—61no—
357D8—61no—
358D8C3×D1211yescharacteristic, complemented
359M16—61no—
360M16—61no—
361C2×C8—31no—
362C2×C8C22×C3×D311yescharacteristic
363C4⋊C4—21no—
364C22⋊C4—121no—
365C16—21no—
366C16—61no—
367C22×C3—21no—
368C22×C3—41no—
369C22×C3—41no—
370C22×C3—61no—
371C22×C3—81no—
372C22×C3—121no—
373C22×C3—121no—
374C22×C3—241no—
375C22×C3—241no—
376C22×C3—242no—
377C22×C3—241no—
378C22×C3D3×D811yescharacteristic
379C22×C3C2×C3×D811yescharacteristic
380C2×D3—21no—
381C2×D3—41no—
382C2×D3—41no—
383C2×D3—82no—
384C2×D3—81no—
385C2×D3—81no—
386C2×D3—81no—
387C3×C4—21no—
388C3×C4—21no—
389C3×C4—41no—
390C3×C4—41no—
391C3×C4—61no—
392C3×C4—81no—
393C3×C4—81no—
394C3×C4—81no—
395C3×C4—121no—
396C3×C4—161no—
397C3×C4#88211yescharacteristic
398C3×C4#91411yescharacteristic
399C3×C4C3×#12011yescharacteristic
400C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
401Dic3—21no—
402Dic3—41no—
403C32#219011yescharacteristic, complemented, Sylow
404C23—31no—
405C23—121no—
406C23—121no—
407Q8—21no—
408Q8—61no—
409Q8—121no—
410D4—21no—
411D4—41no—
412D4—61no—
413D4—121no—
414D4—121no—
415D4—121no—
416D4—121no—
417D4—121no—
418D4—121no—
419D4—242no—
420C2×C4—31no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—61no—
424C2×C4—61no—
425C2×C4—121no—
426C2×C4—121no—
427C2×C4—121no—
428C2×C4—121no—
429C2×C4C3×D3×D411yescharacteristic
430C8—61no—
431C8C2×C3×D1211yescharacteristic
432C8C3×D3×D411yescharacteristic
433C2×C3—21no—
434C2×C3—21no—
435C2×C3—21no—
436C2×C3—41no—
437C2×C3—81no—
438C2×C3—81no—
439C2×C3—121no—
440C2×C3—161no—
441C2×C3—241no—
442C2×C3—481no—
443C2×C3#477311yescharacteristic
444C2×C3C3×#44711yescharacteristic
445D3—41no—
446D3—81no—
447D3—161no—
448C22—41no—
449C22—61no—
450C22—121no—
451C22—121no—
452C22—241no—
453C22—241no—
454C22—242no—
455C22—241no—
456C22C3×D3×D811yescharacteristic
457C4—41no—
458C4—61no—
459C4—81no—
460C4—121no—
461C4C3×#88211yescharacteristic
462C4C3×#91411yescharacteristic
463C3—21no—
464C3#6925211yescharacteristic, direct product factor
465C3C3×#219011yescharacteristic, complemented
466C2—21no—
467C2—81no—
468C2—121no—
469C2—241no—
470C2—481no—
471C2C3×#477311yescharacteristic
subgroupG/H
centerC2×C3#4773
commutator, cosocleC2×C3×C8C23×C3
FrattiniC2×C8C22×C3×D3
FittingC32×#360C2
socleC2×C32#447
hypercenterC3×#360D3
hypocenterC3C3×#2190
LCSG ▷ C2×C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C2×C3×C8 ◁ C3×#360

Complements

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

NH ≅ G/Ntype
1. C3×#5768C2semidirect
2. C3×#5193C2semidirect
3. C3×#4908C2semidirect
4. C3×#4865C2semidirect
5. C32×#360C2semidirect
6. C3×#4514C2semidirect
7. C3×#4488C2semidirect
9. #69252C3direct (N × H)
18. C2×C3×D24C22semidirect
21. C32×M32C22semidirect
22. C32×#106C22semidirect
25. C3×#812C22semidirect
30. #5768C2×C3semidirect
34. #5193C2×C3semidirect
35. #4908C2×C3semidirect
36. #4865C2×C3semidirect
39. C3×#360D3semidirect
40. C3×#360C2×C3semidirect
42. #4514C2×C3semidirect
43. #4488C2×C3semidirect
57. C32×Q16D4semidirect
59. C32×D8D4semidirect
68. C3×Dic12D4semidirect
71. C3×D24D4semidirect
98. C2×D24C22×C3semidirect
107. C3×M32C2×D3semidirect
108. C3×M32C22×C3semidirect
110. C3×#106C2×D3semidirect
111. C3×#106C22×C3semidirect
115. #812C22×C3semidirect
153. #360C3×D3semidirect
185. C3×Q16D12semidirect
186. C3×Q16C3×D4semidirect
198. C3×D8D12semidirect
199. C3×D8C3×D4semidirect
216. Dic12C3×D4semidirect
219. D24C3×D4semidirect
259. M32C2×C3×D3semidirect
260. #106C2×C3×D3semidirect
349. Q16C3×D12semidirect
358. D8C3×D12semidirect
403. C32#2190semidirect
464. C3#69252direct (N × H)
465. C3C3×#2190semidirect

Maximal subgroups

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

subgroupindex
C3×#57682
C3×#51932
C3×#49082
C3×#48652
C32×#3602
C3×#45142
C3×#44882
C3×#21903
#692523