Finite Group Databasebeta

← C3×#68178 #11774822

Subgroups — C3×#68178 #11774822

Order 1152.

473 conjugacy classes of subgroups.

The subgroup lattice has 461 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5557C211yesmaximal, characteristic
2C3×#4837C211yesmaximal, 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×#1495—31nomaximal
9#68178C311yesmaximal, characteristic, direct product factor
10C32×C4×D4C2211yescharacteristic
11C3×#938C411yescharacteristic
12C3×#936C411yescharacteristic
13C3×C4×#67—21no—
14C3×#926—21no—
15C2×C3×ΓL(1,𝔽25)—21no—
16C3×#897C411yescharacteristic
17C3×#890C411yescharacteristic
18C3×#883—21no—
19C3×#879—21no—
20C3×C42×D3C2211yescharacteristic
21C3×C4×Dic6C2211yescharacteristic
22C32×C4⋊C8C2211yescharacteristic
23C32×C4×C8C2211yescharacteristic
24C3×(C2×D3)⋊C8—21no—
25C3×Dic3⋊C8—21no—
26C3×Dic3⋊C8—21no—
27C3×C4⋊(C3⋊C8)C2211yescharacteristic
28C3×C4×C3⋊C8C2211yescharacteristic
29C3×#529—31no—
30#5557C2×C311yescharacteristic
31C3×#431—31no—
32C3×#423—31no—
33#4837C2×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—
47C2×C3×C4×D3C2×C411yescharacteristic
48C2×C3×C4×D3D411yescharacteristic
49C2×C3×C4×D3D411yescharacteristic
50C2×C3×Dic6C2×C411yescharacteristic
51C2×C32×C8—21no—
52C2×C32×C8—21no—
53C32×C4⋊C4C2×C411yescharacteristic
54C32×C22⋊C4—21no—
55C32×C42C2311yescharacteristic
56C3×#217—21no—
57C3×#217—21no—
58C3×#217—21no—
59C3×(C2×D3)⋊C4—21no—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3—21no—
62C3×C4⋊Dic3C2×C411yescharacteristic
63C3×Dic3⋊C4—21no—
64C3×Dic3⋊C4—21no—
65C3×C4×Dic3—21no—
66C3×C4×Dic3C2×C411yescharacteristic
67C3×C4×Dic3D411yescharacteristic
68C3×C4×Dic3D411yescharacteristic
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71C3×ΓL(1,𝔽25)—42no—
72#1495—31noSylow
73C2×C3×M16—61no—
74C3×#126—61no—
75C3×#125—31no—
76C3×#124—31no—
77C3×#123—61no—
78C3×C22⋊Q8—31no—
79C3×#121—31no—
80C3×C4×Q8—31no—
81C3×C4×D4—21no—
82C3×C4×D4—61no—
83C3×C4×D4C2×D311yescharacteristic
84C3×C4×D4C22×C311yescharacteristic
85C3×#117—61no—
86C2×C3×C42—31no—
87#938C3×C411yescharacteristic
88#936C3×C411yescharacteristic
89C4×#67—21no—
90#926—21no—
91C2×ΓL(1,𝔽25)—21no—
92#897C3×C411yescharacteristic
93#890C3×C411yescharacteristic
94#883—21no—
95#879—21no—
96C42×D3C22×C311yescharacteristic
97C4×Dic6C22×C311yescharacteristic
98C3×C4⋊C8—21no—
99C3×C4⋊C8—31no—
100C3×C4⋊C8—61no—
101C3×C4⋊C8—61no—
102C3×C4⋊C8C2×D311yescharacteristic
103C3×C4⋊C8C22×C311yescharacteristic
104C3×C22⋊C8—61no—
105C3×C4×C8—21no—
106C3×C4×C8—31no—
107C3×C4×C8C2×D311yescharacteristic
108C3×C4×C8C22×C311yescharacteristic
109(C2×D3)⋊C8—21no—
110Dic3⋊C8—21no—
111Dic3⋊C8—21no—
112C4⋊(C3⋊C8)C22×C311yescharacteristic
113C4×C3⋊C8C22×C311yescharacteristic
114C23×C32—21no—
115C22×C3×D3C22⋊C411yescharacteristic
116C32×D4—21no—
117C32×D4—21no—
118C2×C32×C4—21no—
119C2×C32×C4—41no—
120C2×C32×C4—41no—
121C2×C32×C4C22×C411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C3×#67—42no—
125C2×C3×Dic3—21no—
126C2×C3×Dic3—21no—
127C2×C3×Dic3C22⋊C411yescharacteristic
128C2×C3×Dic3C22⋊C411yescharacteristic
129C2×C3×Dic3C22⋊C411yescharacteristic
130C3×C4×D3—21no—
131C3×C4×D3—21no—
132C3×C4×D3—21no—
133C3×C4×D3—21no—
134C3×C4×D3—41no—
135C3×Dic6—21no—
136C3×Dic6—21no—
137C32×C8—41no—
138C32×C8—41no—
139C3×C3⋊C8—41no—
140C3×C3⋊C8—41no—
141#529—31no—
142#431—31no—
143#423—31no—
144Q8⋊C8—31no—
145Q8⋊C8—31no—
146D4⋊C8—31no—
147D4⋊C8C3×D311yescharacteristic, complemented
148C2×C3×Q8—31no—
149C2×C3×D4—21no—
150C2×C3×D4—61no—
151C2×C3×D4C4×D311yescharacteristic
152C2×C3×D4C2×C3×C411yescharacteristic
153C22×C3×C4—21no—
154C22×C3×C4—21no—
155C22×C3×C4—31no—
156C22×C3×C4—31no—
157C22×C3×C4—31no—
158C22×C3×C4—41no—
159C2×#67—21no—
160C2×C4×D3C2×C3×C411yescharacteristic
161C2×C4×D3C3×D411yescharacteristic
162C2×C4×D3C3×D411yescharacteristic
163C2×Dic6C2×C3×C411yescharacteristic
164C3×M16—122no—
165C2×C3×C8—21no—
166C2×C3×C8—21no—
167C2×C3×C8—21no—
168C2×C3×C8—21no—
169C2×C3×C8—41no—
170C2×C3×C8—41no—
171C2×C3×C8—61no—
172C2×C3×C8—61no—
173C3×C4⋊C4—21no—
174C3×C4⋊C4—31no—
175C3×C4⋊C4—61no—
176C3×C4⋊C4—61no—
177C3×C4⋊C4—61no—
178C3×C4⋊C4—61no—
179C3×C4⋊C4C4×D311yescharacteristic
180C3×C4⋊C4C2×C3×C411yescharacteristic
181C3×C22⋊C4—21no—
182C3×C22⋊C4—21no—
183C3×C22⋊C4—41no—
184C3×C22⋊C4—61no—
185C3×C22⋊C4—61no—
186C3×C22⋊C4—61no—
187C3×C22⋊C4—61no—
188C3×C42—21no—
189C3×C42—31no—
190C3×C42—31no—
191C3×C42—31no—
192C3×C42—61no—
193C3×C42C22×D311yescharacteristic
194C3×C42C23×C311yescharacteristic
195#217—21no—
196#217—21no—
197#217—21no—
198(C2×D3)⋊C4—21no—
199C4⋊Dic3—21no—
200C4⋊Dic3—21no—
201C4⋊Dic3C2×C3×C411yescharacteristic
202Dic3⋊C4—21no—
203Dic3⋊C4—21no—
204C4×Dic3—21no—
205C4×Dic3C2×C3×C411yescharacteristic
206C4×Dic3C3×D411yescharacteristic
207C4×Dic3C3×D411yescharacteristic
208C2×C3⋊C8—21no—
209C2×C3⋊C8—21no—
210ΓL(1,𝔽25)—42no—
211C22×C32—41no—
212C22×C32—41no—
213C22×C32—41no—
214C22×C32C2×C22⋊C411yescharacteristic
215C2×C3×D3—21no—
216C2×C3×D3—21no—
217C2×C3×D3—21no—
218C32×C4—21no—
219C32×C4—41no—
220C32×C4#13111yescharacteristic
221C32×C4#13111yescharacteristic
222C32×C4AGL(1,ℤ/8)11yescharacteristic
223C32×C4#13711yescharacteristic
224C3×Dic3—21no—
225C3×Dic3—21no—
226C3×Dic3—21no—
227C3×Dic3—41no—
228C3×Dic3—41no—
229C2×M16—61no—
230#126—61no—
231#125—31no—
232#124—31no—
233#123—61no—
234C22⋊Q8—31no—
235#121—31no—
236C4×Q8—31no—
237C4×D4—61no—
238C4×D4C2×C3×D311yescharacteristic
239#117—61no—
240C2×C42—31no—
241C4⋊C8—31no—
242C4⋊C8—61no—
243C4⋊C8—61no—
244C4⋊C8C2×C3×D311yescharacteristic
245C22⋊C8—61no—
246C4×C8—31no—
247C4×C8C2×C3×D311yescharacteristic
248C23×C3—21no—
249C23×C3—21no—
250C23×C3—31no—
251C23×C3—41no—
252C22×D3C3×C22⋊C411yescharacteristic
253C3×Q8—61no—
254C3×Q8—61no—
255C3×D4—22no—
256C3×D4—21no—
257C3×D4—21no—
258C3×D4—21no—
259C3×D4—21no—
260C3×D4—41no—
261C3×D4—122no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—21no—
266C2×C3×C4—21no—
267C2×C3×C4—31no—
268C2×C3×C4—31no—
269C2×C3×C4—31no—
270C2×C3×C4—41no—
271C2×C3×C4—41no—
272C2×C3×C4—41no—
273C2×C3×C4—41no—
274C2×C3×C4—41no—
275C2×C3×C4—61no—
276C2×C3×C4—61no—
277C2×C3×C4—61no—
278C2×C3×C4—61no—
279C2×C3×C4—61no—
280C2×C3×C4—61no—
281C2×C3×C4—81no—
282C2×C3×C4—81no—
283C2×C3×C4—121no—
284C2×C3×C4C2×C4×D311yescharacteristic
285C2×C3×C4D3×D411yescharacteristic
286C2×C3×C4D3×D411yescharacteristic
287C2×C3×C4C22×C3×C411yescharacteristic
288C2×C3×C4C2×C3×D411yescharacteristic
289C2×C3×C4C2×C3×D411yescharacteristic
290#67—42no—
291C2×Dic3—21no—
292C2×Dic3—21no—
293C2×Dic3C3×C22⋊C411yescharacteristic
294C2×Dic3C3×C22⋊C411yescharacteristic
295C2×Dic3C3×C22⋊C411yescharacteristic
296C4×D3—21no—
297C4×D3—21no—
298C4×D3—21no—
299C4×D3—21no—
300C4×D3—41no—
301Dic6—21no—
302Dic6—21no—
303C3×C8—41no—
304C3×C8—41no—
305C3×C8—42no—
306C3×C8—41no—
307C3×C8—41no—
308C3×C8—81no—
309C3×C8—121no—
310C3×C8—121no—
311C3⋊C8—41no—
312C3⋊C8—41no—
313C2×C32—81no—
314C2×C32#40811yescharacteristic
315C2×C32#41711yescharacteristic
316C2×C32#42111yescharacteristic
317C3×D3—41no—
318C2×Q8—31no—
319C2×D4—61no—
320C2×D4C3×C4×D311yescharacteristic
321C22×C4—21no—
322C22×C4—31no—
323C22×C4—31no—
324C22×C4—31no—
325M16—122no—
326C2×C8—21no—
327C2×C8—21no—
328C2×C8—61no—
329C2×C8—61no—
330C4⋊C4—31no—
331C4⋊C4—61no—
332C4⋊C4—61no—
333C4⋊C4—61no—
334C4⋊C4—61no—
335C4⋊C4C3×C4×D311yescharacteristic
336C22⋊C4—21no—
337C22⋊C4—61no—
338C22⋊C4—61no—
339C22⋊C4—61no—
340C22⋊C4—61no—
341C42—31no—
342C42—31no—
343C42—31no—
344C42—61no—
345C42C22×C3×D311yescharacteristic
346C22×C3—21no—
347C22×C3—42no—
348C22×C3—41no—
349C22×C3—41no—
350C22×C3—41no—
351C22×C3—41no—
352C22×C3—41no—
353C22×C3—41no—
354C22×C3—61no—
355C22×C3—61no—
356C22×C3—61no—
357C22×C3—81no—
358C22×C3—81no—
359C22×C3D3×C22⋊C411yescharacteristic
360C22×C3C2×C3×C22⋊C411yescharacteristic
361C2×D3—21no—
362C2×D3—21no—
363C2×D3—21no—
364C3×C4—21no—
365C3×C4—21no—
366C3×C4—21no—
367C3×C4—21no—
368C3×C4—21no—
369C3×C4—21no—
370C3×C4—41no—
371C3×C4—41no—
372C3×C4—41no—
373C3×C4—61no—
374C3×C4—61no—
375C3×C4—61no—
376C3×C4—81no—
377C3×C4—121no—
378C3×C4—121no—
379C3×C4#90111yescharacteristic
380C3×C4#90711yescharacteristic
381C3×C4#91111yescharacteristic
382C3×C4#91511yescharacteristic
383C3×C4C3×#13111yescharacteristic
384C3×C4C3×#13111yescharacteristic
385C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
386C3×C4C3×#13711yescharacteristic
387Dic3—21no—
388Dic3—21no—
389Dic3—21no—
390Dic3—41no—
391Dic3—41no—
392C32#149511yescharacteristic, complemented, Sylow
393C23—21no—
394C23—31no—
395Q8—61no—
396Q8—61no—
397D4—21no—
398D4—21no—
399D4—122no—
400C2×C4—21no—
401C2×C4—31no—
402C2×C4—31no—
403C2×C4—31no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—61no—
407C2×C4—61no—
408C2×C4—61no—
409C2×C4—61no—
410C2×C4—61no—
411C2×C4—61no—
412C2×C4—121no—
413C2×C4C2×C3×C4×D311yescharacteristic
414C2×C4C3×D3×D411yescharacteristic
415C2×C4C3×D3×D411yescharacteristic
416C8—41no—
417C8—41no—
418C8—121no—
419C8—121no—
420C2×C3—21no—
421C2×C3—21no—
422C2×C3—21no—
423C2×C3—82no—
424C2×C3—81no—
425C2×C3—81no—
426C2×C3—121no—
427C2×C3#472711yescharacteristic
428C2×C3#477111yescharacteristic
429C2×C3#482111yescharacteristic
430C2×C3C3×#40811yescharacteristic
431C2×C3C3×#41711yescharacteristic
432C2×C3C3×#42111yescharacteristic
433D3—41no—
434C22—41no—
435C22—41no—
436C22—41no—
437C22—61no—
438C22—61no—
439C22—61no—
440C22C3×D3×C22⋊C411yescharacteristic
441C4—21no—
442C4—41no—
443C4—61no—
444C4—61no—
445C4—61no—
446C4—121no—
447C4—121no—
448C4C3×#90111yescharacteristic
449C4C3×#90711yescharacteristic
450C4C3×#91111yescharacteristic
451C4C3×#91511yescharacteristic
452C3—21no—
453C3#6817811yescharacteristic, direct product factor
454C3C3×#149511yescharacteristic, complemented
455C2—81no—
456C2—121no—
457C2C3×#472711yescharacteristic
458C2C3×#477111yescharacteristic
459C2C3×#482111yescharacteristic
subgroupG/H
centerC2×C3×C4D3×D4
commutatorC2×C3×C4C22×C3×C4
FrattiniC42C22×C3×D3
FittingC32×D4⋊C8C2
socleC22×C32C2×C22⋊C4
prime radicalC3×#938C4
cosocleC3×C42C23×C3
hypercenterC3×D4⋊C8D3
hypocenterC3C3×#1495
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×#4837C2semidirect
3. C3×#4685C2semidirect
4. C32×D4⋊C8C2semidirect
5. C3×D4⋊(C3⋊C8)C2semidirect
6. C3×#4484C2semidirect
7. C3×#4456C2semidirect
9. #68178C3direct (N × H)
33. #4837C2×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
147. D4⋊C8C3×D3semidirect
392. C32#1495semidirect
453. C3#68178direct (N × H)
454. C3C3×#1495semidirect

Maximal subgroups

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

subgroupindex
C3×#55572
C3×#48372
C3×#46852
C32×D4⋊C82
C3×D4⋊(C3⋊C8)2
C3×#44842
C3×#44562
C3×#14953
#681783