Finite Group Databasebeta

← C3×#68173 #11774600

Subgroups — C3×#68173 #11774600

Order 1152.

533 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×C4×#237C211yesmaximal, characteristic
2C3×#4835C211yesmaximal, characteristic, complemented
3C3×#4685C211yesmaximal, characteristic, complemented
4C32×D4⋊C8C211yesmaximal, characteristic, complemented
5C3×D4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6C3×#4484C211yesmaximal, characteristic, complemented
7C3×#4456C211yesmaximal, characteristic, complemented
8C3×#1488—31nomaximal
9#68173C311yesmaximal, characteristic, direct product factor
10C2×C3×#237C411yescharacteristic
11C32×C4×D4C2211yescharacteristic
12C3×D4×Dic3C411yescharacteristic
13C3×C4×#67—21no—
14C2×C3×C4×Dic3—21no—
15C3×#892C411yescharacteristic
16C3×#887C411yescharacteristic
17C3×#67⋊C4—21no—
18C3×#877—21no—
19C3×C42×D3C2211yescharacteristic
20C3×C4×Dic6C2211yescharacteristic
21C32×C4⋊C8C2211yescharacteristic
22C32×C4×C8C2211yescharacteristic
23C3×(C2×D3)⋊C8—21no—
24C3×(C2×D3)⋊C8—21no—
25C3×#815—21no—
26C3×Dic3⋊C8—21no—
27C3×C4⋊(C3⋊C8)C2211yescharacteristic
28C3×C4×C3⋊C8C2211yescharacteristic
29C3×C4×#41—31no—
30C4×#237C2×C311yescharacteristic
31C3×#432—31no—
32C3×#431—31no—
33#4835C2×C311yescharacteristic, complemented
34#4685C2×C311yescharacteristic, complemented
35C3×Q8⋊C8—31no—
36C3×Q8⋊C8—31no—
37C3×D4⋊C8—21no—
38C3×D4⋊C8—31no—
39C3×D4⋊C8D311yescharacteristic, complemented
40C3×D4⋊C8C2×C311yescharacteristic, complemented
41D4⋊(C3⋊C8)C2×C311yescharacteristic, complemented
42#4484C2×C311yescharacteristic, complemented
43#4456C2×C311yescharacteristic, complemented
44C2×C32×D4C2×C411yescharacteristic
45C22×C32×C4—21no—
46C2×C3×#67—21no—
47C22×C3×Dic3—21no—
48C22×C3×Dic3—21no—
49C3×#237—22no—
50C3×#237—22no—
51C2×C3×C4×D3C2×C411yescharacteristic
52C2×C3×C4×D3D411yescharacteristic
53C2×C3×C4×D3D411yescharacteristic
54C2×C3×Dic6C2×C411yescharacteristic
55C2×C32×C8—21no—
56C2×C32×C8—21no—
57C32×C4⋊C4C2×C411yescharacteristic
58C32×C22⋊C4—21no—
59C32×C42C2311yescharacteristic
60C3×#217—21no—
61C3×(C2×D3)⋊C4—21no—
62C3×C4⋊Dic3C2×C411yescharacteristic
63C3×Dic3⋊C4—21no—
64C3×Dic3⋊C4—21no—
65C3×C4×Dic3—21no—
66C3×C4×Dic3—21no—
67C3×C4×Dic3—21no—
68C3×C4×Dic3C2×C411yescharacteristic
69C3×C4×Dic3D411yescharacteristic
70C3×C4×Dic3D411yescharacteristic
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8—21no—
73#1488—31noSylow
74C2×C3×#41—31no—
75C2×#237C3×C411yescharacteristic
76C3×C4×Q8—31no—
77C3×C4×Q8—31no—
78C3×C4×D4—21no—
79C3×C4×D4—31no—
80C3×C4×D4—61no—
81C3×C4×D4—61no—
82C3×C4×D4C2×D311yescharacteristic
83C3×C4×D4C22×C311yescharacteristic
84C3×#117—31no—
85C3×#117—61no—
86C2×C3×C42—31no—
87C2×C3×C42—61no—
88D4×Dic3C3×C411yescharacteristic
89C4×#67—21no—
90C2×C4×Dic3—21no—
91#892C3×C411yescharacteristic
92#887C3×C411yescharacteristic
93#67⋊C4—21no—
94#877—21no—
95C42×D3C22×C311yescharacteristic
96C4×Dic6C22×C311yescharacteristic
97C3×C4⋊C8—21no—
98C3×C4⋊C8—31no—
99C3×C4⋊C8—61no—
100C3×C4⋊C8C2×D311yescharacteristic
101C3×C4⋊C8C22×C311yescharacteristic
102C3×C22⋊C8—61no—
103C3×C22⋊C8—61no—
104C3×#97—61no—
105C3×C4×C8—21no—
106C3×C4×C8—31no—
107C3×C4×C8C2×D311yescharacteristic
108C3×C4×C8C22×C311yescharacteristic
109(C2×D3)⋊C8—21no—
110(C2×D3)⋊C8—21no—
111#815—21no—
112Dic3⋊C8—21no—
113C4⋊(C3⋊C8)C22×C311yescharacteristic
114C4×C3⋊C8C22×C311yescharacteristic
115C23×C32—21no—
116C22×C3×D3C22⋊C411yescharacteristic
117C32×D4—21no—
118C32×D4M1612yes—
119C2×C32×C4—21no—
120C2×C32×C4—41no—
121C2×C32×C4—41no—
122C2×C32×C4C22×C411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C3×#67—24no—
126C2×C3×Dic3—24no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—21no—
129C2×C3×Dic3—42no—
130C2×C3×Dic3C22⋊C411yescharacteristic
131C2×C3×Dic3C22⋊C411yescharacteristic
132C2×C3×Dic3C22⋊C411yescharacteristic
133C3×C4×D3—21no—
134C3×C4×D3—21no—
135C3×C4×D3—21no—
136C3×C4×D3—21no—
137C3×C4×D3—41no—
138C3×Dic6—21no—
139C3×Dic6M1612yes—
140C32×C8—41no—
141C32×C8—41no—
142C3×C3⋊C8—41no—
143C3×C3⋊C8—41no—
144C4×#41—31no—
145#432—31no—
146#431—31no—
147Q8⋊C8—31no—
148Q8⋊C8—31no—
149D4⋊C8—31no—
150D4⋊C8C3×D311yescharacteristic, complemented
151C3×#41—62no—
152C3×#41—62no—
153C2×C3×Q8—31no—
154C2×C3×D4—21no—
155C2×C3×D4—61no—
156C2×C3×D4C4×D311yescharacteristic
157C2×C3×D4C2×C3×C411yescharacteristic
158C22×C3×C4—21no—
159C22×C3×C4—21no—
160C22×C3×C4—31no—
161C22×C3×C4—31no—
162C22×C3×C4—31no—
163C22×C3×C4—41no—
164C22×C3×C4—61no—
165C22×C3×C4—61no—
166C2×#67—21no—
167C22×Dic3—21no—
168C22×Dic3—21no—
169#237—22no—
170#237—22no—
171C2×C4×D3C2×C3×C411yescharacteristic
172C2×C4×D3C3×D411yescharacteristic
173C2×C4×D3C3×D411yescharacteristic
174C2×Dic6C2×C3×C411yescharacteristic
175C2×C3×C8—21no—
176C2×C3×C8—21no—
177C2×C3×C8—21no—
178C2×C3×C8—21no—
179C2×C3×C8—41no—
180C2×C3×C8—41no—
181C2×C3×C8—61no—
182C2×C3×C8—61no—
183C3×C4⋊C4—21no—
184C3×C4⋊C4—31no—
185C3×C4⋊C4—61no—
186C3×C4⋊C4—61no—
187C3×C4⋊C4C4×D311yescharacteristic
188C3×C4⋊C4C2×C3×C411yescharacteristic
189C3×C22⋊C4—21no—
190C3×C22⋊C4—21no—
191C3×C22⋊C4—41no—
192C3×C22⋊C4—61no—
193C3×C22⋊C4—61no—
194C3×C42—21no—
195C3×C42—31no—
196C3×C42—31no—
197C3×C42—31no—
198C3×C42—61no—
199C3×C42—61no—
200C3×C42—61no—
201C3×C42C22×D311yescharacteristic
202C3×C42C23×C311yescharacteristic
203#217—21no—
204(C2×D3)⋊C4—21no—
205C4⋊Dic3C2×C3×C411yescharacteristic
206Dic3⋊C4—21no—
207Dic3⋊C4—21no—
208C4×Dic3—21no—
209C4×Dic3—21no—
210C4×Dic3—21no—
211C4×Dic3C2×C3×C411yescharacteristic
212C4×Dic3C3×D411yescharacteristic
213C4×Dic3C3×D411yescharacteristic
214C2×C3⋊C8—21no—
215C2×C3⋊C8—21no—
216C22×C32—22no—
217C22×C32—41no—
218C22×C32—41no—
219C22×C32C2×C22⋊C411yescharacteristic
220C2×C3×D3—21no—
221C2×C3×D3—21no—
222C2×C3×D3—21no—
223C32×C4—21no—
224C32×C4—41no—
225C32×C4C2×M1611yescharacteristic
226C32×C4C2×M1611yescharacteristic
227C32×C4#13511yescharacteristic
228C32×C4#13511yescharacteristic
229C3×Dic3—22no—
230C3×Dic3—21no—
231C3×Dic3—21no—
232C3×Dic3—21no—
233C3×Dic3—41no—
234C2×#41—31no—
235C4×Q8—31no—
236C4×Q8—31no—
237C4×D4—31no—
238C4×D4—61no—
239C4×D4—61no—
240C4×D4C2×C3×D311yescharacteristic
241#117—31no—
242#117—61no—
243C2×C42—31no—
244C2×C42—61no—
245C4⋊C8—31no—
246C4⋊C8—61no—
247C4⋊C8C2×C3×D311yescharacteristic
248C22⋊C8—61no—
249C22⋊C8—61no—
250#97—61no—
251C4×C8—31no—
252C4×C8C2×C3×D311yescharacteristic
253C23×C3—21no—
254C23×C3—21no—
255C23×C3—31no—
256C23×C3—41no—
257C22×D3C3×C22⋊C411yescharacteristic
258C3×Q8—32no—
259C3×Q8—61no—
260C3×D4—21no—
261C3×D4—21no—
262C3×D4—22no—
263C3×D4—41no—
264C3×D4—64no—
265C3×D4ΓL(1,𝔽25)12yes—
266C3×D4C3×M1612yes—
267C2×C3×C4—21no—
268C2×C3×C4—21no—
269C2×C3×C4—21no—
270C2×C3×C4—21no—
271C2×C3×C4—21no—
272C2×C3×C4—31no—
273C2×C3×C4—31no—
274C2×C3×C4—31no—
275C2×C3×C4—41no—
276C2×C3×C4—41no—
277C2×C3×C4—41no—
278C2×C3×C4—41no—
279C2×C3×C4—41no—
280C2×C3×C4—64no—
281C2×C3×C4—61no—
282C2×C3×C4—61no—
283C2×C3×C4—61no—
284C2×C3×C4—61no—
285C2×C3×C4—61no—
286C2×C3×C4—61no—
287C2×C3×C4—81no—
288C2×C3×C4—81no—
289C2×C3×C4—121no—
290C2×C3×C4—122no—
291C2×C3×C4C2×C4×D311yescharacteristic
292C2×C3×C4D3×D411yescharacteristic
293C2×C3×C4D3×D411yescharacteristic
294C2×C3×C4C22×C3×C411yescharacteristic
295C2×C3×C4C2×C3×D411yescharacteristic
296C2×C3×C4C2×C3×D411yescharacteristic
297#67—24no—
298C2×Dic3—24no—
299C2×Dic3—21no—
300C2×Dic3—21no—
301C2×Dic3—42no—
302C2×Dic3C3×C22⋊C411yescharacteristic
303C2×Dic3C3×C22⋊C411yescharacteristic
304C2×Dic3C3×C22⋊C411yescharacteristic
305C4×D3—21no—
306C4×D3—21no—
307C4×D3—21no—
308C4×D3—21no—
309C4×D3—41no—
310Dic6—21no—
311Dic6C3×M1612yes—
312C3×C8—41no—
313C3×C8—41no—
314C3×C8—42no—
315C3×C8—41no—
316C3×C8—41no—
317C3×C8—81no—
318C3×C8—121no—
319C3×C8—121no—
320C3⋊C8—41no—
321C3⋊C8—41no—
322C2×C32—42no—
323C2×C32#40711yescharacteristic
324C2×C32#41611yescharacteristic
325C2×C32#42111yescharacteristic
326C3×D3—41no—
327#41—62no—
328#41—62no—
329C2×Q8—31no—
330C2×D4—61no—
331C2×D4C3×C4×D311yescharacteristic
332C22×C4—21no—
333C22×C4—31no—
334C22×C4—31no—
335C22×C4—31no—
336C22×C4—61no—
337C22×C4—61no—
338C2×C8—21no—
339C2×C8—21no—
340C2×C8—61no—
341C2×C8—61no—
342C4⋊C4—31no—
343C4⋊C4—61no—
344C4⋊C4—61no—
345C4⋊C4C3×C4×D311yescharacteristic
346C22⋊C4—21no—
347C22⋊C4—61no—
348C22⋊C4—61no—
349C42—31no—
350C42—31no—
351C42—31no—
352C42—61no—
353C42—61no—
354C42—61no—
355C42C22×C3×D311yescharacteristic
356C22×C3—22no—
357C22×C3—22no—
358C22×C3—21no—
359C22×C3—42no—
360C22×C3—41no—
361C22×C3—41no—
362C22×C3—41no—
363C22×C3—41no—
364C22×C3—61no—
365C22×C3—61no—
366C22×C3—61no—
367C22×C3—81no—
368C22×C3—81no—
369C22×C3D3×C22⋊C411yescharacteristic
370C22×C3C2×C3×C22⋊C411yescharacteristic
371C2×D3—21no—
372C2×D3—21no—
373C2×D3—21no—
374C3×C4—21no—
375C3×C4—21no—
376C3×C4—21no—
377C3×C4—21no—
378C3×C4—21no—
379C3×C4—21no—
380C3×C4—41no—
381C3×C4—41no—
382C3×C4—41no—
383C3×C4—61no—
384C3×C4—62no—
385C3×C4—61no—
386C3×C4—61no—
387C3×C4—81no—
388C3×C4—121no—
389C3×C4C2×ΓL(1,𝔽25)11yescharacteristic
390C3×C4D3×M1611yescharacteristic
391C3×C4#91211yescharacteristic
392C3×C4#91611yescharacteristic
393C3×C4C2×C3×M1611yescharacteristic
394C3×C4C2×C3×M1611yescharacteristic
395C3×C4C3×#13511yescharacteristic
396C3×C4C3×#13511yescharacteristic
397Dic3—22no—
398Dic3—21no—
399Dic3—21no—
400Dic3—21no—
401Dic3—41no—
402C32#148811yescharacteristic, complemented, Sylow
403C23—21no—
404C23—31no—
405Q8—32no—
406Q8—61no—
407D4—21no—
408D4—64no—
409D4C3×ΓL(1,𝔽25)12yes—
410C2×C4—21no—
411C2×C4—31no—
412C2×C4—31no—
413C2×C4—31no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—64no—
417C2×C4—61no—
418C2×C4—61no—
419C2×C4—61no—
420C2×C4—61no—
421C2×C4—61no—
422C2×C4—61no—
423C2×C4—121no—
424C2×C4—122no—
425C2×C4C2×C3×C4×D311yescharacteristic
426C2×C4C3×D3×D411yescharacteristic
427C2×C4C3×D3×D411yescharacteristic
428C8—41no—
429C8—41no—
430C8—121no—
431C8—121no—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3—21no—
435C2×C3—42no—
436C2×C3—42no—
437C2×C3—82no—
438C2×C3—121no—
439C2×C3#472611yescharacteristic
440C2×C3#477211yescharacteristic
441C2×C3#482111yescharacteristic
442C2×C3C3×#40711yescharacteristic
443C2×C3C3×#41611yescharacteristic
444C2×C3C3×#42111yescharacteristic
445D3—41no—
446C22—22no—
447C22—41no—
448C22—41no—
449C22—61no—
450C22—61no—
451C22—61no—
452C22C3×D3×C22⋊C411yescharacteristic
453C4—21no—
454C4—41no—
455C4—61no—
456C4—62no—
457C4—61no—
458C4—61no—
459C4—121no—
460C4C2×C3×ΓL(1,𝔽25)11yescharacteristic
461C4C3×D3×M1611yescharacteristic
462C4C3×#91211yescharacteristic
463C4C3×#91611yescharacteristic
464C3—21no—
465C3#6817311yescharacteristic, direct product factor
466C3C3×#148811yescharacteristic, complemented
467C2—42no—
468C2—121no—
469C2C3×#472611yescharacteristic
470C2C3×#477211yescharacteristic
471C2C3×#482111yescharacteristic
subgroupG/H
centerC2×C3×C4D3×D4
commutatorC2×C3×C4C22×C3×C4
FrattiniC42C22×C3×D3
FittingC32×D4⋊C8C2
socleC22×C32C2×C22⋊C4
prime radicalC2×C3×#237C4
cosocleC3×C42C23×C3
hypercenterC3×D4⋊C8D3
hypocenterC3C3×#1488
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C3×C42 ◁ C3×D4⋊C8

Complements

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

NH ≅ G/Ntype
2. C3×#4835C2semidirect
3. C3×#4685C2semidirect
4. C32×D4⋊C8C2semidirect
5. C3×D4⋊(C3⋊C8)C2semidirect
6. C3×#4484C2semidirect
7. C3×#4456C2semidirect
9. #68173C3direct (N × H)
33. #4835C2×C3semidirect
34. #4685C2×C3semidirect
39. C3×D4⋊C8D3semidirect
40. C3×D4⋊C8C2×C3semidirect
41. D4⋊(C3⋊C8)C2×C3semidirect
42. #4484C2×C3semidirect
43. #4456C2×C3semidirect
150. D4⋊C8C3×D3semidirect
402. C32#1488semidirect
465. C3#68173direct (N × H)
466. C3C3×#1488semidirect

Maximal subgroups

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

subgroupindex
C3×C4×#2372
C3×#48352
C3×#46852
C32×D4⋊C82
C3×D4⋊(C3⋊C8)2
C3×#44842
C3×#44562
C3×#14883
#681733