Finite Group Databasebeta

← C3×#69251 #11796843

Subgroups — C3×#69251 #11796843

Order 1152.

477 conjugacy classes of subgroups.

The subgroup lattice has 473 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×#135C211yesmaximal, characteristic
2C3×D3×M32C211yesmaximal, characteristic, complemented
3C3×#4860C211yesmaximal, characteristic, complemented
4C32×#360C211yesmaximal, characteristic, complemented
5C3×#4566C211yesmaximal, characteristic, complemented
6C3×#4518C211yesmaximal, characteristic, complemented
7C3×#4488C211yesmaximal, characteristic, complemented
8C3×#2145—31nomaximal
9#69251C311yesmaximal, characteristic, direct product factor
10C3×D3×#41—21no—
11C32×#135C2211yescharacteristic
12C3×#950—21no—
13C3×#919C411yescharacteristic, complemented
14C3×D3×Q16C411yescharacteristic, complemented
15C3×#916—21no—
16C3×D3×SD16—21no—
17C3×#912C411yescharacteristic, complemented
18C3×D3×D8C411yescharacteristic, complemented
19C3×#904C2211yescharacteristic
20C2×C3×D3×C8C2211yescharacteristic
21C3×#892—21no—
22C32×M32C2211yescharacteristic, complemented
23C32×#106C2211yescharacteristic, complemented
24C3×#817C2211yescharacteristic, complemented
25C3×#812C2211yescharacteristic, complemented
26C3×#807—21no—
27C3×#798—21no—
28C3×D3×C16—21no—
29C2×C3×#135—31no—
30D3×#135C2×C311yescharacteristic
31C2×C3×M32—31no—
32C3×#427—31no—
33D3×M32C2×C311yescharacteristic, complemented
34#4860C2×C311yescharacteristic, complemented
35C3×#360—21no—
36C3×#360—31no—
37C3×#360—31no—
38C3×#360—31no—
39C3×#360D311yescharacteristic, complemented
40C3×#360C2×C311yescharacteristic, complemented
41#4566C2×C311yescharacteristic, complemented
42#4518C2×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×C4×D3—41no—
54C2×C3×C4×D3D411yescharacteristic
55C32×Q16C2×C411yescharacteristic
56C32×SD16—21no—
57C32×D8C2×C411yescharacteristic
58C2×C32×C8C2311yescharacteristic
59C32×C4⋊C4—21no—
60C3×#216—21no—
61C3×#215—21no—
62C3×#214—21no—
63C3×#213—21no—
64C3×(C2×D3)⋊C4—41no—
65C3×C4⋊Dic3—21no—
66C3×C4×Dic3—41no—
67C2×C3×C3⋊C8D411yescharacteristic
68C3×Dic12C2×C411yescharacteristic
69C3×D24C2×C411yescharacteristic
70C3×#204—21no—
71C3×D3×C8C2×C411yescharacteristic
72C3×D3×C8C2×C411yescharacteristic
73C3×D3×C8D411yescharacteristic
74C3×D3×C8D411yescharacteristic
75C32×C16—21no—
76C3×C3⋊C16—21no—
77#2145—31noSylow
78C2×C3×#41—61no—
79D3×#41—21no—
80C3×#135—21no—
81C3×#135—31no—
82C3×#135—31no—
83C3×#135—31no—
84C3×#135—61no—
85C3×#135—61no—
86C3×#135C2×D311yescharacteristic
87C3×#135C22×C311yescharacteristic
88C2×C3×Q16—31no—
89C2×C3×SD16—61no—
90C2×C3×D8—31no—
91C22×C3×C8—31no—
92C3×#117—61no—
93#950—21no—
94#919C3×C411yescharacteristic, complemented
95D3×Q16C3×C411yescharacteristic, complemented
96#916—21no—
97D3×SD16—21no—
98#912C3×C411yescharacteristic, complemented
99D3×D8C3×C411yescharacteristic, complemented
100#904C22×C311yescharacteristic
101C2×D3×C8C22×C311yescharacteristic
102#892—21no—
103C3×M32—21no—
104C3×M32—31no—
105C3×M32—61no—
106C3×M32C2×D311yescharacteristic, complemented
107C3×M32C22×C311yescharacteristic, complemented
108C2×C3×C16—61no—
109C3×#107—61no—
110C3×#106—21no—
111C3×#106—31no—
112C3×#106C2×D311yescharacteristic, complemented
113C3×#106C22×C311yescharacteristic, complemented
114#817C22×C311yescharacteristic, complemented
115#812C22×C311yescharacteristic, complemented
116#807—21no—
117#798—21no—
118D3×C16—21no—
119C22×C3×D3—41no—
120C22×C3×D3D811yescharacteristic
121C32×Q8—21no—
122C32×D4—21no—
123C32×D4—41no—
124C2×C32×C4—41no—
125C2×C32×C4—41no—
126C2×C32×C4C2×D411yescharacteristic
127C3×#67—41no—
128C3×#67—41no—
129C3×#67—41no—
130C2×C3×Dic3—41no—
131C2×C3×Dic3—41no—
132C2×C3×Dic3D811yescharacteristic
133C3×D12—21no—
134C3×D12—41no—
135C3×C4×D3—41no—
136C3×C4×D3—41no—
137C3×C4×D3—41no—
138C3×C4×D3C22⋊C411yescharacteristic
139C3×C4×D3C22⋊C411yescharacteristic
140C3×C4×D3SD1611yescharacteristic
141C3×C4×D3SD1611yescharacteristic
142C3×Dic6—21no—
143C3×Dic6—41no—
144C32×C8C22×C411yescharacteristic
145C32×C8C2×D411yescharacteristic
146C3×C3⋊C8C22⋊C411yescharacteristic
147C3×C3⋊C8C22⋊C411yescharacteristic
148C2×#135—31no—
149C2×M32—31no—
150#427—31no—
151#360—31no—
152#360—31no—
153#360—31no—
154#360C3×D311yescharacteristic, complemented
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—121no—
166C22×C3×C4—31no—
167C22×C3×C4—121no—
168#239—21no—
169D3×Q8—21no—
170#237—21no—
171#237—41no—
172D3×D4—21no—
173D3×D4—41no—
174#235—21no—
175#235—41no—
176C2×C4×D3—41no—
177C2×C4×D3C3×D411yescharacteristic
178C3×Q16—21no—
179C3×Q16—31no—
180C3×Q16—61no—
181C3×Q16C4×D311yescharacteristic
182C3×Q16C2×C3×C411yescharacteristic
183C3×SD16—21no—
184C3×SD16—21no—
185C3×SD16—41no—
186C3×SD16—61no—
187C3×SD16—61no—
188C3×SD16—61no—
189C3×D8—21no—
190C3×D8—31no—
191C3×D8—61no—
192C3×D8C4×D311yescharacteristic
193C3×D8C2×C3×C411yescharacteristic
194C2×C3×C8—21no—
195C2×C3×C8—31no—
196C2×C3×C8—31no—
197C2×C3×C8—31no—
198C2×C3×C8—31no—
199C2×C3×C8—31no—
200C2×C3×C8C22×D311yescharacteristic
201C2×C3×C8C23×C311yescharacteristic
202C3×C4⋊C4—21no—
203C3×C4⋊C4—21no—
204C3×C4⋊C4—41no—
205C3×C4⋊C4—61no—
206C3×C22⋊C4—121no—
207C3×C42—121no—
208#216—21no—
209#215—21no—
210#214—21no—
211#213—21no—
212(C2×D3)⋊C4—41no—
213C4⋊Dic3—21no—
214C4×Dic3—41no—
215C2×C3⋊C8C3×D411yescharacteristic
216Dic12C2×C3×C411yescharacteristic
217D24C2×C3×C411yescharacteristic
218#204—21no—
219D3×C8C2×C3×C411yescharacteristic
220D3×C8C2×C3×C411yescharacteristic
221D3×C8C3×D411yescharacteristic
222D3×C8C3×D411yescharacteristic
223C3×C16—21no—
224C3×C16—21no—
225C3×C16—41no—
226C3×C16—61no—
227C3⋊C16—21no—
228C22×C32—41no—
229C22×C32C2×D811yescharacteristic
230C2×C3×D3—41no—
231C2×C3×D3—41no—
232C2×C3×D3—82no—
233C2×C3×D3#10211yescharacteristic
234C2×C3×D3#10211yescharacteristic
235C32×C4—41no—
236C32×C4—81no—
237C32×C4C2×C22⋊C411yescharacteristic
238C32×C4C2×SD1611yescharacteristic
239C3×Dic3—41no—
240C3×Dic3—81no—
241C3×Dic3#10211yescharacteristic
242C3×Dic3#10211yescharacteristic
243C2×#41—61no—
244#135—31no—
245#135—31no—
246#135—31no—
247#135—61no—
248#135—61no—
249#135C2×C3×D311yescharacteristic
250C2×Q16—31no—
251C2×SD16—61no—
252C2×D8—31no—
253C22×C8—31no—
254#117—61no—
255M32—31no—
256M32—61no—
257M32C2×C3×D311yescharacteristic, complemented
258C2×C16—61no—
259#107—61no—
260#106—31no—
261#106C2×C3×D311yescharacteristic, complemented
262C23×C3—31no—
263C23×C3—121no—
264C22×D3—41no—
265C22×D3C3×D811yescharacteristic
266C3×Q8—21no—
267C3×Q8—21no—
268C3×Q8—41no—
269C3×Q8—61no—
270C3×Q8—121no—
271C3×D4—21no—
272C3×D4—21no—
273C3×D4—41no—
274C3×D4—41no—
275C3×D4—41no—
276C3×D4—61no—
277C3×D4—81no—
278C3×D4—121no—
279C3×D4—121no—
280C3×D4—121no—
281C3×D4—121no—
282C2×C3×C4—21no—
283C2×C3×C4—31no—
284C2×C3×C4—31no—
285C2×C3×C4—31no—
286C2×C3×C4—31no—
287C2×C3×C4—31no—
288C2×C3×C4—41no—
289C2×C3×C4—41no—
290C2×C3×C4—41no—
291C2×C3×C4—41no—
292C2×C3×C4—81no—
293C2×C3×C4—81no—
294C2×C3×C4—121no—
295C2×C3×C4—121no—
296C2×C3×C4—121no—
297C2×C3×C4—121no—
298C2×C3×C4—121no—
299C2×C3×C4D3×D411yescharacteristic
300C2×C3×C4C2×C3×D411yescharacteristic
301#67—41no—
302#67—41no—
303#67—41no—
304C2×Dic3—41no—
305C2×Dic3—41no—
306C2×Dic3C3×D811yescharacteristic
307D12—21no—
308D12—41no—
309C4×D3—41no—
310C4×D3—41no—
311C4×D3—41no—
312C4×D3C3×C22⋊C411yescharacteristic
313C4×D3C3×C22⋊C411yescharacteristic
314C4×D3C3×SD1611yescharacteristic
315C4×D3C3×SD1611yescharacteristic
316Dic6—21no—
317Dic6—41no—
318C3×C8—21no—
319C3×C8—21no—
320C3×C8—31no—
321C3×C8—31no—
322C3×C8C2×C4×D311yescharacteristic
323C3×C8D3×D411yescharacteristic
324C3×C8C22×C3×C411yescharacteristic
325C3×C8C2×C3×D411yescharacteristic
326C3⋊C8C3×C22⋊C411yescharacteristic
327C3⋊C8C3×C22⋊C411yescharacteristic
328C2×C32—21no—
329C2×C32—81no—
330C2×C32C2×#10211yescharacteristic
331C3×D3—21no—
332C3×D3—21no—
333C3×D3—81no—
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—121no—
343C22×C4—31no—
344C22×C4—121no—
345Q16—31no—
346Q16—61no—
347Q16C3×C4×D311yescharacteristic
348SD16—21no—
349SD16—61no—
350SD16—61no—
351SD16—61no—
352D8—31no—
353D8—61no—
354D8C3×C4×D311yescharacteristic
355C2×C8—31no—
356C2×C8—31no—
357C2×C8—31no—
358C2×C8—31no—
359C2×C8—31no—
360C2×C8C22×C3×D311yescharacteristic
361C4⋊C4—21no—
362C4⋊C4—61no—
363C22⋊C4—121no—
364C42—121no—
365C16—21no—
366C16—61no—
367C22×C3—21no—
368C22×C3—31no—
369C22×C3—31no—
370C22×C3—41no—
371C22×C3—41no—
372C22×C3—81no—
373C22×C3—121no—
374C22×C3—121no—
375C22×C3—242no—
376C22×C3D3×D811yescharacteristic
377C22×C3C2×C3×D811yescharacteristic
378C2×D3—41no—
379C2×D3—41no—
380C2×D3—82no—
381C2×D3C3×#10211yescharacteristic
382C2×D3C3×#10211yescharacteristic
383C3×C4—21no—
384C3×C4—21no—
385C3×C4—31no—
386C3×C4—31no—
387C3×C4—41no—
388C3×C4—41no—
389C3×C4—81no—
390C3×C4—81no—
391C3×C4—81no—
392C3×C4—121no—
393C3×C4—161no—
394C3×C4—241no—
395C3×C4D3×C22⋊C411yescharacteristic
396C3×C4D3×SD1611yescharacteristic
397C3×C4C2×C3×C22⋊C411yescharacteristic
398C3×C4C2×C3×SD1611yescharacteristic
399Dic3—41no—
400Dic3—81no—
401Dic3C3×#10211yescharacteristic
402Dic3C3×#10211yescharacteristic
403C32#214511yescharacteristic, complemented, Sylow
404C23—31no—
405C23—121no—
406Q8—21no—
407Q8—61no—
408Q8—121no—
409D4—21no—
410D4—41no—
411D4—61no—
412D4—121no—
413D4—121no—
414D4—121no—
415D4—121no—
416C2×C4—31no—
417C2×C4—31no—
418C2×C4—31no—
419C2×C4—31no—
420C2×C4—31no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—121no—
424C2×C4—121no—
425C2×C4—121no—
426C2×C4—121no—
427C2×C4—121no—
428C2×C4C3×D3×D411yescharacteristic
429C8—31no—
430C8—31no—
431C8C2×C3×C4×D311yescharacteristic
432C8C3×D3×D411yescharacteristic
433C2×C3—21no—
434C2×C3—21no—
435C2×C3—21no—
436C2×C3—41no—
437C2×C3—61no—
438C2×C3—61no—
439C2×C3—81no—
440C2×C3—81no—
441C2×C3—161no—
442C2×C3—241no—
443C2×C3D3×#10211yescharacteristic
444C2×C3C2×C3×#10211yescharacteristic
445D3—21no—
446D3—21no—
447D3—81no—
448C22—31no—
449C22—31no—
450C22—41no—
451C22—121no—
452C22—121no—
453C22—242no—
454C22C3×D3×D811yescharacteristic
455C4—31no—
456C4—31no—
457C4—41no—
458C4—81no—
459C4—121no—
460C4—241no—
461C4C3×D3×C22⋊C411yescharacteristic
462C4C3×D3×SD1611yescharacteristic
463C3—21no—
464C3#6925111yescharacteristic, direct product factor
465C3C3×#214511yescharacteristic, complemented
466C2—21no—
467C2—61no—
468C2—61no—
469C2—81no—
470C2—241no—
471C2C3×D3×#10211yescharacteristic
subgroupG/H
centerC2×C3D3×#102
commutatorC3×C8C22×C3×C4
FrattiniC2×C8C22×C3×D3
FittingC32×#360C2
socleC2×C32C2×#102
prime radicalC3×D3×#135C2
cosocleC2×C3×C8C23×C3
hypercenterC3×#360D3
hypocenterC3C3×#2145
LCSG ▷ 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
2. C3×D3×M32C2semidirect
3. C3×#4860C2semidirect
4. C32×#360C2semidirect
5. C3×#4566C2semidirect
6. C3×#4518C2semidirect
7. C3×#4488C2semidirect
9. #69251C3direct (N × H)
13. C3×#919C4semidirect
14. C3×D3×Q16C4semidirect
17. C3×#912C4semidirect
18. C3×D3×D8C4semidirect
22. C32×M32C22semidirect
23. C32×#106C22semidirect
24. C3×#817C22semidirect
25. C3×#812C22semidirect
33. D3×M32C2×C3semidirect
34. #4860C2×C3semidirect
39. C3×#360D3semidirect
40. C3×#360C2×C3semidirect
41. #4566C2×C3semidirect
42. #4518C2×C3semidirect
43. #4488C2×C3semidirect
94. #919C3×C4semidirect
95. D3×Q16C3×C4semidirect
98. #912C3×C4semidirect
99. D3×D8C3×C4semidirect
106. C3×M32C2×D3semidirect
107. C3×M32C22×C3semidirect
112. C3×#106C2×D3semidirect
113. C3×#106C22×C3semidirect
114. #817C22×C3semidirect
115. #812C22×C3semidirect
154. #360C3×D3semidirect
257. M32C2×C3×D3semidirect
261. #106C2×C3×D3semidirect
403. C32#2145semidirect
464. C3#69251direct (N × H)
465. C3C3×#2145semidirect

Maximal subgroups

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

subgroupindex
C3×D3×#1352
C3×D3×M322
C3×#48602
C32×#3602
C3×#45662
C3×#45182
C3×#44882
C3×#21453
#692513