Finite Group Databasebeta

← D3×#4855 #11874886

Subgroups — D3×#4855 #11874886

Order 1152.

897 conjugacy classes of subgroups.

The subgroup lattice has 449 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#888C212yesmaximal
2#10592554C211yesmaximal, characteristic, complemented
3C3×D3×#106C211yesmaximal, characteristic
4C3×#4855C211yesmaximal, characteristic, complemented
5#10590900C211yesmaximal, characteristic, complemented
6#10590889C211yesmaximal, characteristic, complemented
7D3×#817C211yesmaximal, characteristic
8D3×C8×Dic3C211yesmaximal, characteristic
9D3×#808C212yesmaximal
10#10590416C212yesmaximal, complemented
11#10590412C212yesmaximal, complemented
12D3×#498—31nomaximal
13C2×#4855—31nomaximal
14C2×D3×Dic6—22no—
15#64097C2212yes—
16C2×C3×D3×C8C2211yescharacteristic
17C3×D3×C4⋊C4C2212yes—
18C3×#888C2212yes—
19#63919C2212yes—
20#63918C2212yes—
21D3×C4⋊Dic3C2212yes—
22D3×Dic3⋊C4—22no—
23C4×D3×Dic3C2211yescharacteristic
24#63840—22no—
25#63839—22no—
26C2×D3×C3⋊C8C2211yescharacteristic
27C32×#106C2211yescharacteristic
28#63644C2211yescharacteristic
29C8×C3⋊Dic3C2211yescharacteristic
30#63635C2212yes—
31C3×#817C2211yescharacteristic
32C3×#817C2211yescharacteristic
33C3×C8×Dic3C2211yescharacteristic
34C3×#808C2212yes—
35C3×#808C2212yes—
36#63574C2212yes—
37#63573C2212yes—
38#63573C2212yes—
39#63553C2211yescharacteristic
40Dic3×C3⋊C8C2211yescharacteristic
41D3×C4⋊Q8—32no—
42C2×#888—32no—
43C3×#498—31no—
44C2×C3×#106—31no—
45C2×#817—31no—
46C2×C8×Dic3—31no—
47#5080—32no—
48C2×#808—32no—
49D3×#106—31no—
50D3×#106—32no—
51D3×#106D311yescharacteristic
52#4855—32no—
53#4855—31no—
54#4855—31no—
55#4855—31no—
56#4855—31no—
57#4855—31no—
58#4855—32no—
59#4855—32no—
60#4855—61no—
61#4855D311yescharacteristic, direct product factor
62C4×D3×C8—31no—
63#4680—31no—
64C2×#634—22no—
65C2×C3×C4×D3—22no—
66C2×C3×C4×D3C2311yescharacteristic
67C2×C3×Dic6—22no—
68C2×#627—22no—
69C2×#627—22no—
70C2×D3×Dic3—22no—
71C2×D3×Dic3D412yes—
72D3×Dic6—48no—
73C2×C32×C8C2311yescharacteristic
74C32×C4⋊C4C2312yes—
75C4⋊(C3⋊Dic3)C2312yes—
76#3750—22no—
77C4×C3⋊Dic3C2311yescharacteristic
78C2×C3⋊(C3⋊C8)C2311yescharacteristic
79C3×C4⋊Dic3C2312yes—
80C3×C4⋊Dic3C2312yes—
81C3×Dic3⋊C4—22no—
82C3×Dic3⋊C4—22no—
83C3×C4×Dic3C2311yescharacteristic
84C2×C3×C3⋊C8C2311yescharacteristic
85C2×C3×C3⋊C8C2311yescharacteristic
86C3×D3×C8Q814yescomplemented
87#3724—22no—
88Dic3⋊Dic3—22no—
89Dic3⋊Dic3—22no—
90Dic32D412yes—
91D3×C3⋊C8Q814yescomplemented
92C2×#498—91noSylow
93C2×D3×Q8—62no—
94C22×Dic6—62no—
95C22×C3×C8—31no—
96C3×C4⋊Q8—32no—
97C2×C3×C4⋊C4—32no—
98#944—62no—
99C2×C4⋊Dic3—32no—
100C2×Dic3⋊C4—62no—
101C2×C4×Dic3—31no—
102C22×C3⋊C8—31no—
103C2×D3×C8—31no—
104C2×D3×C8C2×D311yescharacteristic
105D3×C4⋊C4—32no—
106D3×C4⋊C4—62no—
107D3×C4⋊C4C2×D312yes—
108#888—32no—
109#888—32no—
110#888—32no—
111#888—32no—
112#888—32no—
113#888—62no—
114#888—62no—
115#888—62no—
116#888—62no—
117#888C2×D312yes—
118C42×D3—31no—
119#869—32no—
120C3×#106—21no—
121C3×#106—31no—
122C3×#106—31no—
123C3×#106—32no—
124C3×#106—32no—
125C3×#106C2×D311yescharacteristic
126C3×#106C2×D311yescharacteristic
127C3×C4×C8—31no—
128#817—31no—
129#817—31no—
130#817—32no—
131#817—32no—
132#817—61no—
133#817C2×D311yescharacteristic
134#817C2×D311yescharacteristic
135C8×Dic3—31no—
136C8×Dic3—31no—
137C8×Dic3—31no—
138C8×Dic3—31no—
139C8×Dic3—31no—
140C8×Dic3—61no—
141C8×Dic3C2×D311yescharacteristic
142#808—32no—
143#808—32no—
144#808—32no—
145#808—32no—
146#808—32no—
147#808—32no—
148#808—62no—
149#808C2×D312yes—
150#808C2×D312yes—
151C4×C3⋊C8—31no—
152C22×C3×D3C2×D411yescharacteristic
153C2×C32×C4—22no—
154C2×C32×C4C2411yescharacteristic
155C2×C3⋊Dic3—22no—
156C2×C3⋊Dic3C2×D412yes—
157#634—44no—
158C2×C3×Dic3—22no—
159C2×C3×Dic3—22no—
160C2×C3×Dic3C2×D411yescharacteristic
161C2×C3×Dic3C2×D412yes—
162C3×C4×D3—44no—
163C3×C4×D3C2×Q812yes—
164C3×C4×D3C2×Q812yes—
165C3×Dic6—44no—
166#627—44no—
167#627—44no—
168D3×Dic3—44no—
169D3×Dic3SD1618yes—
170C32×C8C2×Q812yescomplemented
171C3⋊(C3⋊C8)C2×Q812yescomplemented
172C3×C3⋊C8C2×Q812yescomplemented
173C3×C3⋊C8C2×Q812yescomplemented
174C2×C4⋊Q8—92no—
175#498—31no—
176#498—91no—
177#498—92no—
178#498—91no—
179#498—92no—
180#498—91no—
181C2×#106—31no—
182C2×#106—92no—
183C2×#106—91no—
184C2×C4×C8—91no—
185C2×C3×Q8—62no—
186C22×C3×C4—31no—
187C22×C3×C4—62no—
188C22×Dic3—32no—
189C22×Dic3—62no—
190D3×Q8—128no—
191C2×C4×D3—22no—
192C2×C4×D3—32no—
193C2×C4×D3—62no—
194C2×C4×D3C22×D311yescharacteristic
195C2×Dic6—22no—
196C2×Dic6—62no—
197C2×Dic6—62no—
198C2×Dic6—62no—
199C2×Dic6—62no—
200C2×Dic6—62no—
201C2×Dic6—62no—
202C2×Dic6—122no—
203C2×Dic6—128no—
204C2×C3×C8—21no—
205C2×C3×C8—31no—
206C2×C3×C8—31no—
207C2×C3×C8—34no—
208C2×C3×C8C22×D311yescharacteristic
209C2×C3×C8C22×D311yescharacteristic
210C3×C4⋊C4—22no—
211C3×C4⋊C4—32no—
212C3×C4⋊C4—32no—
213C3×C4⋊C4—62no—
214C3×C4⋊C4—62no—
215C3×C4⋊C4C22×D312yes—
216C3×C4⋊C4C22×D312yes—
217C3×C42—31no—
218C4⋊Dic3—32no—
219C4⋊Dic3—32no—
220C4⋊Dic3—62no—
221C4⋊Dic3—62no—
222C4⋊Dic3—62no—
223C4⋊Dic3C22×D312yes—
224C4⋊Dic3C22×D312yes—
225Dic3⋊C4—22no—
226Dic3⋊C4—22no—
227Dic3⋊C4—62no—
228Dic3⋊C4—62no—
229Dic3⋊C4—62no—
230Dic3⋊C4—62no—
231Dic3⋊C4—62no—
232Dic3⋊C4—62no—
233Dic3⋊C4—122no—
234C4×Dic3—31no—
235C4×Dic3—31no—
236C4×Dic3—32no—
237C4×Dic3—32no—
238C4×Dic3—61no—
239C4×Dic3C22×D311yescharacteristic
240C2×C3⋊C8—31no—
241C2×C3⋊C8—31no—
242C2×C3⋊C8—34no—
243C2×C3⋊C8—61no—
244C2×C3⋊C8C22×D311yescharacteristic
245C2×C3⋊C8C22×D311yescharacteristic
246D3×C8—34no—
247D3×C8Dic614yescomplemented
248C22×C32C22×D411yescharacteristic
249C2×C3×D3C4⋊Q812yes—
250C2×C3×D3C2×SD1614yes—
251C32×C4—42no—
252C32×C4C22×Q811yescharacteristic
253C32×C4C22×Q811yescharacteristic
254C3⋊Dic3—42no—
255C3⋊Dic3C2×SD1614yes—
256C3×Dic3—42no—
257C3×Dic3—42no—
258C3×Dic3C4⋊Q812yes—
259C3×Dic3C2×SD1614yes—
260C22×Q8—182no—
261C22×C8—31no—
262C22×C8—91no—
263C4⋊Q8—32no—
264C4⋊Q8—92no—
265C4⋊Q8—92no—
266C4⋊Q8—92no—
267C4⋊Q8—182no—
268C4⋊Q8—182no—
269C2×C4⋊C4—32no—
270C2×C4⋊C4—92no—
271C2×C4⋊C4—182no—
272C2×C42—91no—
273#106—31no—
274#106—31no—
275#106—32no—
276#106—32no—
277#106—92no—
278#106—92no—
279#106—92no—
280#106—91no—
281#106—92no—
282#106D3211yescharacteristic
283C4×C8—31no—
284C4×C8—91no—
285C4×C8—91no—
286C4×C8—91no—
287C23×C3—31no—
288C22×D3D3×D411yescharacteristic
289C3×Q8—124no—
290C2×C3×C4—22no—
291C2×C3×C4—22no—
292C2×C3×C4—21no—
293C2×C3×C4—31no—
294C2×C3×C4—32no—
295C2×C3×C4—32no—
296C2×C3×C4—32no—
297C2×C3×C4—42no—
298C2×C3×C4—62no—
299C2×C3×C4—62no—
300C2×C3×C4—124no—
301C2×C3×C4C23×D311yescharacteristic
302C2×C3×C4C23×D311yescharacteristic
303C2×Dic3—22no—
304C2×Dic3—22no—
305C2×Dic3—32no—
306C2×Dic3—32no—
307C2×Dic3—38no—
308C2×Dic3—62no—
309C2×Dic3—62no—
310C2×Dic3—62no—
311C2×Dic3—122no—
312C2×Dic3—124no—
313C2×Dic3D3×D411yescharacteristic
314C2×Dic3D3×D412yes—
315C4×D3—38no—
316C4×D3—44no—
317C4×D3—124no—
318C4×D3C2×Dic612yes—
319C4×D3D3×Q812yes—
320Dic6—44no—
321Dic6—124no—
322Dic6—124no—
323Dic6—124no—
324Dic6—124no—
325Dic6—124no—
326Dic6—124no—
327Dic6—244no—
328C3×C8—22no—
329C3×C8—32no—
330C3×C8—32no—
331C3×C8C2×Dic612yescomplemented
332C3×C8D3×Q812yescomplemented
333C3⋊C8—32no—
334C3⋊C8—32no—
335C3⋊C8—62no—
336C3⋊C8C2×Dic612yescomplemented
337C3⋊C8D3×Q812yescomplemented
338C2×C32C2×C4⋊Q811yescharacteristic
339C2×C32C22×SD1612yes—
340C3×D3#49814yescomplemented
341C2×Q8—62no—
342C2×Q8—182no—
343C2×Q8—182no—
344C2×Q8—182no—
345C2×Q8—368no—
346C22×C4—31no—
347C22×C4—62no—
348C22×C4—92no—
349C22×C4—182no—
350C2×C8—31no—
351C2×C8—31no—
352C2×C8—34no—
353C2×C8—94no—
354C2×C8—91no—
355C2×C8C2×D3211yescharacteristic
356C4⋊C4—32no—
357C4⋊C4—32no—
358C4⋊C4—62no—
359C4⋊C4—62no—
360C4⋊C4—92no—
361C4⋊C4—182no—
362C4⋊C4—182no—
363C4⋊C4—182no—
364C4⋊C4—182no—
365C4⋊C4C2×D3212yes—
366C42—31no—
367C42—92no—
368C42—91no—
369C22×C3—21no—
370C22×C3—32no—
371C22×C3—34no—
372C22×C3C2×D3×D411yescharacteristic
373C22×C3C2×D3×D411yescharacteristic
374C2×D3#88812yes—
375C2×D3D3×SD1614yes—
376C3×C4—21no—
377C3×C4—21no—
378C3×C4—32no—
379C3×C4—34no—
380C3×C4—42no—
381C3×C4—42no—
382C3×C4—82no—
383C3×C4—122no—
384C3×C4—122no—
385C3×C4C22×Dic611yescharacteristic
386C3×C4C2×D3×Q811yescharacteristic
387C3×C4C2×D3×Q811yescharacteristic
388C3×C4C2×D3×Q811yescharacteristic
389Dic3—34no—
390Dic3—34no—
391Dic3—42no—
392Dic3—42no—
393Dic3—64no—
394Dic3—122no—
395Dic3—122no—
396Dic3—242no—
397Dic3#88812yes—
398Dic3D3×SD1614yes—
399C32C2×#49811yescharacteristic, complemented, Sylow
400C23—31no—
401Q8—124no—
402Q8—364no—
403Q8—364no—
404Q8—364no—
405C2×C4—22no—
406C2×C4—32no—
407C2×C4—31no—
408C2×C4—32no—
409C2×C4—32no—
410C2×C4—62no—
411C2×C4—62no—
412C2×C4—98no—
413C2×C4—92no—
414C2×C4—124no—
415C2×C4—182no—
416C2×C4—364no—
417C2×C4C22×D3211yescharacteristic
418C8—32no—
419C8—32no—
420C8—92no—
421C8D3×Dic612yescomplemented
422C2×C3—21no—
423C2×C3—22no—
424C2×C3—34no—
425C2×C3C2×#88811yescharacteristic
426C2×C3D3×C4⋊Q811yescharacteristic
427C2×C3C2×D3×SD1612yes—
428C2×C3C2×D3×SD1612yes—
429D3#485514yesdirect product factor
430C22—32no—
431C22—34no—
432C22D32×D411yescharacteristic
433C4—32no—
434C4—34no—
435C4—42no—
436C4—94no—
437C4—122no—
438C4—122no—
439C4—362no—
440C4C2×D3×Dic611yescharacteristic
441C4D32×Q811yescharacteristic
442C3—21no—
443C3C2×#485511yescharacteristic, complemented
444C3D3×#49811yescharacteristic, complemented
445C2—34no—
446C2D3×#88811yescharacteristic
447C2D32×SD1612yes—
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
hypercenter#106D32
hypocenterC32C2×#498
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
2. #10592554C2semidirect
4. C3×#4855C2semidirect
5. #10590900C2semidirect
6. #10590889C2semidirect
10. #10590416C2semidirect
11. #10590412C2semidirect
61. #4855D3direct (N × H)
86. C3×D3×C8Q8semidirect
91. D3×C3⋊C8Q8semidirect
170. C32×C8C2×Q8semidirect
171. C3⋊(C3⋊C8)C2×Q8semidirect
172. C3×C3⋊C8C2×Q8semidirect
173. C3×C3⋊C8C2×Q8semidirect
247. D3×C8Dic6semidirect
331. C3×C8C2×Dic6semidirect
332. C3×C8D3×Q8semidirect
336. C3⋊C8C2×Dic6semidirect
337. C3⋊C8D3×Q8semidirect
340. C3×D3#498semidirect
399. C32C2×#498semidirect
421. C8D3×Dic6semidirect
429. D3#4855direct (N × H)
443. C3C2×#4855semidirect
444. C3D3×#498semidirect

Maximal subgroups

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

subgroupindex
D3×#8882
#105925542
C3×D3×#1062
C3×#48552
#105909002
#105908892
D3×#8172
D3×C8×Dic32
D3×#8082
#105904162
#105904122
D3×#4983
C2×#48553