Finite Group Databasebeta

← C3×#68428 #11776591

Subgroups — C3×#68428 #11776591

Order 1152.

488 conjugacy classes of subgroups.

The subgroup lattice has 393 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×C4⋊Q8C211yesmaximal, characteristic
2C3×#4835C211yesmaximal, characteristic
3C3×#4835C211yesmaximal, characteristic
4C32×#332C211yesmaximal, characteristic, complemented
5C3×#4547C211yesmaximal, characteristic, complemented
6C3×#4486C211yesmaximal, characteristic, complemented
7C3×#4482C211yesmaximal, characteristic, complemented
8C3×#1556—31nomaximal
9#68428C311yesmaximal, characteristic, direct product factor
10C2×C3×D3×Q8—21no—
11C32×C4⋊Q8C2211yescharacteristic
12C3×#944—21no—
13C3×D3×C4⋊C4—21no—
14C3×D3×C4⋊C4C412yes—
15C3×#888—21no—
16C3×#888C412yes—
17C3×C42×D3C2211yescharacteristic
18C3×#869C2211yescharacteristic
19C32×C4⋊C8C2211yescharacteristic
20C32×C4⋊C8C2211yescharacteristic
21C3×(C2×D3)⋊C8—21no—
22C3×(C2×D3)⋊C8—21no—
23C3×#815—21no—
24C3×#815—21no—
25C3×C4⋊(C3⋊C8)C2211yescharacteristic
26C3×C4⋊(C3⋊C8)C2211yescharacteristic
27C2×C3×C4⋊Q8—31no—
28D3×C4⋊Q8C2×C311yescharacteristic
29C3×#432—31no—
30C3×#432—31no—
31#4835C2×C311yescharacteristic
32#4835C2×C311yescharacteristic
33C3×#332—21no—
34C3×#332—31no—
35C3×#332—31no—
36C3×#332—31no—
37C3×#332D311yescharacteristic, complemented
38C3×#332C2×C311yescharacteristic, complemented
39#4547C2×C311yescharacteristic, complemented
40#4486C2×C311yescharacteristic, complemented
41#4482C2×C311yescharacteristic, complemented
42C2×C32×Q8—21no—
43C3×D3×Q8—42no—
44C3×D3×Q8—42no—
45C2×C3×C4×D3—22no—
46C2×C3×C4×D3C2×C411yescharacteristic
47C2×C3×C4×D3D411yescharacteristic
48C2×C3×C4×D3D411yescharacteristic
49C2×C3×Dic6—21no—
50C2×C3×Dic6—22no—
51C2×C32×C8—21no—
52C2×C32×C8—21no—
53C32×C4⋊C4—21no—
54C32×C4⋊C4C2×C412yes—
55C32×C42C2311yescharacteristic
56C3×C4⋊Dic3—21no—
57C3×C4⋊Dic3C2×C412yes—
58C3×Dic3⋊C4—22no—
59C3×Dic3⋊C4—22no—
60C3×C4×Dic3C2×C411yescharacteristic
61C3×C4×Dic3D411yescharacteristic
62C3×C4×Dic3D411yescharacteristic
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65#1556—31noSylow
66C22×C3×Q8—61no—
67C2×D3×Q8—21no—
68C3×C4⋊Q8—21no—
69C3×C4⋊Q8—32no—
70C3×C4⋊Q8—31no—
71C3×C4⋊Q8—61no—
72C3×C4⋊Q8—61no—
73C3×C4⋊Q8C2×D311yescharacteristic
74C3×C4⋊Q8C22×C311yescharacteristic
75C2×C3×C4⋊C4—32no—
76C2×C3×C4⋊C4—61no—
77C2×C3×C42—31no—
78#944—21no—
79D3×C4⋊C4—21no—
80D3×C4⋊C4C3×C412yes—
81#888—21no—
82#888C3×C412yes—
83C42×D3C22×C311yescharacteristic
84#869C22×C311yescharacteristic
85C3×C4⋊C8—21no—
86C3×C4⋊C8—21no—
87C3×C4⋊C8—31no—
88C3×C4⋊C8—31no—
89C3×C4⋊C8C2×D311yescharacteristic
90C3×C4⋊C8C2×D311yescharacteristic
91C3×C4⋊C8C22×C311yescharacteristic
92C3×C4⋊C8C22×C311yescharacteristic
93C3×C22⋊C8—61no—
94C3×C22⋊C8—61no—
95C3×#97—61no—
96C3×#97—61no—
97(C2×D3)⋊C8—21no—
98(C2×D3)⋊C8—21no—
99#815—21no—
100#815—21no—
101C4⋊(C3⋊C8)C22×C311yescharacteristic
102C4⋊(C3⋊C8)C22×C311yescharacteristic
103C22×C3×D3C22⋊C411yescharacteristic
104C32×Q8—41no—
105C32×Q8—41no—
106C2×C32×C4—22no—
107C2×C32×C4C22×C411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C3×Dic3—22no—
111C2×C3×Dic3C22⋊C411yescharacteristic
112C2×C3×Dic3C22⋊C411yescharacteristic
113C2×C3×Dic3C22⋊C411yescharacteristic
114C3×C4×D3—22no—
115C3×C4×D3—21no—
116C3×C4×D3—21no—
117C3×C4×D3—21no—
118C3×C4×D3—21no—
119C3×C4×D3—44no—
120C3×Dic6—44no—
121C3×Dic6—41no—
122C3×Dic6—41no—
123C32×C8—41no—
124C32×C8—41no—
125C3×C3⋊C8—41no—
126C3×C3⋊C8—41no—
127C2×C4⋊Q8—31no—
128#432—31no—
129#432—31no—
130#332—31no—
131#332—31no—
132#332—31no—
133#332C3×D311yescharacteristic, complemented
134C2×C3×Q8—21no—
135C2×C3×Q8—21no—
136C2×C3×Q8—41no—
137C2×C3×Q8—62no—
138C2×C3×Q8—61no—
139C2×C3×Q8—122no—
140C2×C3×Q8—122no—
141C22×C3×C4—31no—
142C22×C3×C4—31no—
143C22×C3×C4—31no—
144C22×C3×C4—62no—
145D3×Q8—42no—
146D3×Q8—42no—
147C2×C4×D3—22no—
148C2×C4×D3C2×C3×C411yescharacteristic
149C2×C4×D3C3×D411yescharacteristic
150C2×C4×D3C3×D411yescharacteristic
151C2×Dic6—21no—
152C2×Dic6—22no—
153C2×C3×C8—21no—
154C2×C3×C8—21no—
155C2×C3×C8—21no—
156C2×C3×C8—21no—
157C2×C3×C8—41no—
158C2×C3×C8—41no—
159C2×C3×C8—61no—
160C2×C3×C8—61no—
161C3×C4⋊C4—21no—
162C3×C4⋊C4—21no—
163C3×C4⋊C4—22no—
164C3×C4⋊C4—32no—
165C3×C4⋊C4—41no—
166C3×C4⋊C4—62no—
167C3×C4⋊C4—62no—
168C3×C4⋊C4—61no—
169C3×C4⋊C4C4×D312yes—
170C3×C4⋊C4C2×C3×C412yes—
171C3×C42—21no—
172C3×C42—31no—
173C3×C42—31no—
174C3×C42—31no—
175C3×C42C22×D311yescharacteristic
176C3×C42C23×C311yescharacteristic
177C4⋊Dic3—21no—
178C4⋊Dic3C2×C3×C412yes—
179Dic3⋊C4—22no—
180Dic3⋊C4—22no—
181C4×Dic3C2×C3×C411yescharacteristic
182C4×Dic3C3×D411yescharacteristic
183C4×Dic3C3×D411yescharacteristic
184C2×C3⋊C8—21no—
185C2×C3⋊C8—21no—
186C22×C32C2×C22⋊C411yescharacteristic
187C2×C3×D3—21no—
188C2×C3×D3—21no—
189C2×C3×D3#10112yes—
190C32×C4—21no—
191C32×C4—42no—
192C32×C4AGL(1,ℤ/8)11yescharacteristic
193C32×C4AGL(1,ℤ/8)11yescharacteristic
194C32×C4#13711yescharacteristic
195C32×C4#13711yescharacteristic
196C3×Dic3—21no—
197C3×Dic3—21no—
198C3×Dic3—21no—
199C3×Dic3—42no—
200C22×Q8—61no—
201C4⋊Q8—32no—
202C4⋊Q8—31no—
203C4⋊Q8—61no—
204C4⋊Q8—61no—
205C4⋊Q8C2×C3×D311yescharacteristic
206C2×C4⋊C4—32no—
207C2×C4⋊C4—61no—
208C2×C42—31no—
209C4⋊C8—31no—
210C4⋊C8—31no—
211C4⋊C8C2×C3×D311yescharacteristic
212C4⋊C8C2×C3×D311yescharacteristic
213C22⋊C8—61no—
214C22⋊C8—61no—
215#97—61no—
216#97—61no—
217C23×C3—31no—
218C22×D3C3×C22⋊C411yescharacteristic
219C3×Q8—41no—
220C3×Q8—41no—
221C3×Q8—41no—
222C3×Q8—41no—
223C3×Q8—81no—
224C3×Q8—81no—
225C3×Q8—124no—
226C3×Q8—121no—
227C3×Q8—121no—
228C2×C3×C4—22no—
229C2×C3×C4—22no—
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—31no—
234C2×C3×C4—31no—
235C2×C3×C4—31no—
236C2×C3×C4—42no—
237C2×C3×C4—62no—
238C2×C3×C4—61no—
239C2×C3×C4—61no—
240C2×C3×C4—61no—
241C2×C3×C4—61no—
242C2×C3×C4—62no—
243C2×C3×C4—124no—
244C2×C3×C4C2×C4×D311yescharacteristic
245C2×C3×C4D3×D411yescharacteristic
246C2×C3×C4D3×D411yescharacteristic
247C2×C3×C4C22×C3×C411yescharacteristic
248C2×C3×C4C2×C3×D411yescharacteristic
249C2×C3×C4C2×C3×D411yescharacteristic
250C2×Dic3—22no—
251C2×Dic3C3×C22⋊C411yescharacteristic
252C2×Dic3C3×C22⋊C411yescharacteristic
253C2×Dic3C3×C22⋊C411yescharacteristic
254C4×D3—22no—
255C4×D3—21no—
256C4×D3—21no—
257C4×D3—21no—
258C4×D3—21no—
259C4×D3—44no—
260Dic6—44no—
261Dic6—41no—
262Dic6—41no—
263C3×C8—41no—
264C3×C8—41no—
265C3×C8—41no—
266C3×C8—41no—
267C3×C8—81no—
268C3×C8—81no—
269C3×C8—121no—
270C3×C8—121no—
271C3⋊C8—41no—
272C3⋊C8—41no—
273C2×C32C2×#10111yescharacteristic
274C2×C32#41811yescharacteristic
275C2×C32#41911yescharacteristic
276C3×D3—22no—
277C2×Q8—21no—
278C2×Q8—62no—
279C2×Q8—61no—
280C2×Q8—122no—
281C2×Q8—122no—
282C22×C4—31no—
283C22×C4—31no—
284C22×C4—31no—
285C22×C4—62no—
286C2×C8—21no—
287C2×C8—21no—
288C2×C8—61no—
289C2×C8—61no—
290C4⋊C4—21no—
291C4⋊C4—32no—
292C4⋊C4—62no—
293C4⋊C4—62no—
294C4⋊C4—61no—
295C4⋊C4C3×C4×D312yes—
296C42—31no—
297C42—31no—
298C42—31no—
299C42C22×C3×D311yescharacteristic
300C22×C3—21no—
301C22×C3—32no—
302C22×C3—61no—
303C22×C3—61no—
304C22×C3D3×C22⋊C411yescharacteristic
305C22×C3C2×C3×C22⋊C411yescharacteristic
306C2×D3—21no—
307C2×D3—21no—
308C2×D3C3×#10112yes—
309C3×C4—21no—
310C3×C4—21no—
311C3×C4—21no—
312C3×C4—21no—
313C3×C4—21no—
314C3×C4—21no—
315C3×C4—41no—
316C3×C4—42no—
317C3×C4—42no—
318C3×C4—61no—
319C3×C4—61no—
320C3×C4—61no—
321C3×C4—82no—
322C3×C4—122no—
323C3×C4#91111yescharacteristic
324C3×C4#91411yescharacteristic
325C3×C4#91511yescharacteristic
326C3×C4#91811yescharacteristic
327C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
328C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
329C3×C4C3×#13711yescharacteristic
330C3×C4C3×#13711yescharacteristic
331Dic3—21no—
332Dic3—21no—
333Dic3—21no—
334Dic3—42no—
335C32#155611yescharacteristic, complemented, Sylow
336C23—31no—
337Q8—41no—
338Q8—41no—
339Q8—124no—
340Q8—121no—
341Q8—121no—
342C2×C4—22no—
343C2×C4—31no—
344C2×C4—31no—
345C2×C4—31no—
346C2×C4—62no—
347C2×C4—61no—
348C2×C4—61no—
349C2×C4—61no—
350C2×C4—61no—
351C2×C4—62no—
352C2×C4—124no—
353C2×C4C2×C3×C4×D311yescharacteristic
354C2×C4C3×D3×D411yescharacteristic
355C2×C4C3×D3×D411yescharacteristic
356C8—41no—
357C8—41no—
358C8—121no—
359C8—121no—
360C2×C3—21no—
361C2×C3—21no—
362C2×C3—21no—
363C2×C3—62no—
364C2×C3D3×#10111yescharacteristic
365C2×C3#477011yescharacteristic
366C2×C3#480211yescharacteristic
367C2×C3C2×C3×#10111yescharacteristic
368C2×C3C3×#41811yescharacteristic
369C2×C3C3×#41911yescharacteristic
370D3—22no—
371C22—32no—
372C22—61no—
373C22—61no—
374C22C3×D3×C22⋊C411yescharacteristic
375C4—21no—
376C4—42no—
377C4—61no—
378C4—61no—
379C4—61no—
380C4—122no—
381C4C3×#91111yescharacteristic
382C4C3×#91411yescharacteristic
383C4C3×#91511yescharacteristic
384C4C3×#91811yescharacteristic
385C3—21no—
386C3#6842811yescharacteristic, direct product factor
387C3C3×#155611yescharacteristic, complemented
388C2—62no—
389C2C3×D3×#10111yescharacteristic
390C2C3×#477011yescharacteristic
391C2C3×#480211yescharacteristic
subgroupG/H
centerC22×C3D3×C22⋊C4
commutatorC2×C3×C4C22×C3×C4
FrattiniC42C22×C3×D3
FittingC32×#332C2
socleC22×C32C2×C22⋊C4
prime radicalC22×C3×D3C22⋊C4
cosocleC3×C42C23×C3
hypercenterC3×#332D3
hypocenterC3C3×#1556
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#332

Complements

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

NH ≅ G/Ntype
4. C32×#332C2semidirect
5. C3×#4547C2semidirect
6. C3×#4486C2semidirect
7. C3×#4482C2semidirect
9. #68428C3direct (N × H)
37. C3×#332D3semidirect
38. C3×#332C2×C3semidirect
39. #4547C2×C3semidirect
40. #4486C2×C3semidirect
41. #4482C2×C3semidirect
133. #332C3×D3semidirect
335. C32#1556semidirect
386. C3#68428direct (N × H)
387. C3C3×#1556semidirect

Maximal subgroups

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

subgroupindex
C3×D3×C4⋊Q82
C3×#48352
C32×#3322
C3×#45472
C3×#44862
C3×#44822
C3×#15563
#684283