Finite Group Databasebeta

← D3×#5082 #11873622

Subgroups — D3×#5082 #11873622

Order 1152.

813 conjugacy classes of subgroups.

The subgroup lattice has 377 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×C4⋊Q8C211yesmaximal, characteristic
2D3×#870C211yesmaximal, characteristic
3#10592781C211yesmaximal, characteristic, complemented
4C3×#5082C211yesmaximal, characteristic, complemented
5#10591613C214yesmaximal, complemented
6D3×#835C214yesmaximal
7D3×#803C211yesmaximal, characteristic
8#10590291C211yesmaximal, characteristic, complemented
9#10590289C211yesmaximal, characteristic, complemented
10C2×#5082—31nomaximal
11D3×#491—31nomaximal
12C2×C3×D3×Q8C2212yes—
13C32×C4⋊Q8C2211yescharacteristic
14#64079C2211yescharacteristic
15C3×#944C2212yes—
16C3×D3×C4⋊C4—22no—
17C3×#888—22no—
18C3×C42×D3C2211yescharacteristic
19C3×#870C2211yescharacteristic
20C3×#869C2211yescharacteristic
21D3×C4⋊Dic3C2212yes—
22D3×Dic3⋊C4—22no—
23#63869C2212yes—
24#63867—22no—
25C2×D3×C3⋊C8C2212yes—
26#63662C2214yes—
27#63630C2211yescharacteristic
28C3×#835C2214yes—
29C3×#803C2211yescharacteristic
30#63566C2214yes—
31#63565C2214yes—
32#63554C2212yes—
33C2×C3×C4⋊Q8—31no—
34D3×C4⋊Q8D311yescharacteristic
35D3×#125—31no—
36C2×#870—31no—
37C3×#491—31no—
38C2×#835—34no—
39#5082—31no—
40#5082—31no—
41#5082—31no—
42#5082—34no—
43#5082—31no—
44#5082—61no—
45#5082D311yescharacteristic, direct product factor
46#5069—31no—
47C2×#803—31no—
48D3×#103—34no—
49#4797—34no—
50D3×#97—31no—
51#4703—31no—
52C2×C32×Q8C2312yes—
53C3×D3×Q8—28no—
54C2×C3×C4×D3—22no—
55C2×C3×C4×D3D412yes—
56C2×C3×C4×D3C2311yescharacteristic
57C2×C3×Dic6—22no—
58C2×C3×Dic6C2312yes—
59C2×D3×Dic3—22no—
60C32×C4⋊C4—22no—
61C32×C42C2311yescharacteristic
62C4⋊(C3⋊Dic3)C2312yes—
63#3750—22no—
64C2×C3⋊(C3⋊C8)C2312yes—
65C3×C4⋊Dic3—22no—
66C3×C4⋊Dic3C2312yes—
67C3×Dic3⋊C4—22no—
68C3×Dic3⋊C4—24no—
69C3×C4×Dic3D412yes—
70C3×C4×Dic3C2311yescharacteristic
71C2×C3×C3⋊C8C2312yes—
72#3724—22no—
73Dic3⋊Dic3—22no—
74Dic3⋊Dic3—22no—
75D3×C3⋊C8—24no—
76C2×#491—91noSylow
77C22×C3×Q8—32no—
78C2×D3×Q8C2×D312yes—
79C3×C4⋊Q8—21no—
80C3×C4⋊Q8—32no—
81C3×C4⋊Q8—31no—
82C3×C4⋊Q8—62no—
83C3×C4⋊Q8C2×D311yescharacteristic
84C3×C4⋊Q8C2×D311yescharacteristic
85C3×#125—31no—
86C2×C3×C4⋊C4—62no—
87C2×C3×C42—31no—
88#944C2×D312yes—
89C2×C4⋊Dic3—32no—
90C2×Dic3⋊C4—62no—
91C22×C3⋊C8—32no—
92C2×D3×C8—32no—
93D3×C4⋊C4—22no—
94D3×C4⋊C4—32no—
95D3×C4⋊C4—62no—
96#890—32no—
97#889—62no—
98#888—22no—
99C42×D3C2×D311yescharacteristic
100#870—31no—
101#870—31no—
102#870—32no—
103#870—61no—
104#870—62no—
105#870C2×D311yescharacteristic
106#869C2×D311yescharacteristic
107C3×#103—34no—
108C3×#97—31no—
109#835—34no—
110#835—34no—
111#835—34no—
112#835—34no—
113#835—64no—
114#835C2×D314yes—
115#816—34no—
116#815—32no—
117#810—34no—
118#803—31no—
119#803—31no—
120#803—32no—
121#803—61no—
122#803C2×D311yescharacteristic
123C22×C3×D3C2×D411yescharacteristic
124C32×Q8—24no—
125C2×C32×C4—22no—
126C2×C32×C4C2×D412yes—
127C2×C32×C4C2411yescharacteristic
128C2×C3⋊Dic3—22no—
129C2×C3×Dic3—22no—
130C2×C3×Dic3—22no—
131C2×C3×Dic3C2×D412yes—
132C2×C3×Dic3C2×D411yescharacteristic
133C3×C4×D3—24no—
134C3×C4×D3—44no—
135C3×C4×D3#4114yes—
136C3×Dic6—24no—
137C3×Dic6—44no—
138D3×Dic3—44no—
139C3⋊(C3⋊C8)—22no—
140C3×C3⋊C8—22no—
141C2×C4⋊Q8—31no—
142C2×#125—91no—
143#491—31no—
144#491—91no—
145#491—94no—
146#491—91no—
147#491—91no—
148C2×#103—94no—
149C2×#97—91no—
150C2×C3×Q8—22no—
151C2×C3×Q8—32no—
152C2×C3×Q8—62no—
153C2×C3×Q8—68no—
154C2×C3×Q8C22×D312yes—
155C2×C3×Q8C22×D312yes—
156C22×C3×C4—31no—
157C22×C3×C4—32no—
158C22×C3×C4—62no—
159C22×Dic3—62no—
160D3×Q8—28no—
161C2×C4×D3—22no—
162C2×C4×D3—62no—
163C2×C4×D3#6712yes—
164C2×C4×D3C22×D311yescharacteristic
165C2×Dic6—22no—
166C2×Dic6C22×D312yes—
167C2×C3×C8—32no—
168C3×C4⋊C4—22no—
169C3×C4⋊C4—22no—
170C3×C4⋊C4—32no—
171C3×C4⋊C4—42no—
172C3×C4⋊C4—64no—
173C3×C4⋊C4—62no—
174C3×C4⋊C4—62no—
175C3×C42—21no—
176C3×C42—32no—
177C3×C42—31no—
178C3×C42C22×D311yescharacteristic
179C3×C42C22×D311yescharacteristic
180C4⋊Dic3—22no—
181C4⋊Dic3—32no—
182C4⋊Dic3—32no—
183C4⋊Dic3—62no—
184C4⋊Dic3—62no—
185C4⋊Dic3—62no—
186C4⋊Dic3C22×D312yes—
187Dic3⋊C4—22no—
188Dic3⋊C4—24no—
189Dic3⋊C4—62no—
190Dic3⋊C4—62no—
191Dic3⋊C4—62no—
192Dic3⋊C4—62no—
193Dic3⋊C4—62no—
194Dic3⋊C4—62no—
195Dic3⋊C4—122no—
196C4×Dic3#6712yes—
197C4×Dic3C22×D311yescharacteristic
198C2×C3⋊C8—32no—
199C2×C3⋊C8—32no—
200C2×C3⋊C8—62no—
201C2×C3⋊C8—64no—
202C2×C3⋊C8C22×D312yes—
203D3×C8—64no—
204C22×C32C22×D411yescharacteristic
205C2×C3×D3#12412yes—
206C2×C3×D3#13714yes—
207C32×C4—22no—
208C32×C4—42no—
209C32×C4C2×#4112yes—
210C3⋊Dic3—42no—
211C3×Dic3—22no—
212C3×Dic3—42no—
213C3×Dic3—42no—
214C3×Dic3#12412yes—
215C22×Q8—32no—
216C22×C8—92no—
217C4⋊Q8—32no—
218C4⋊Q8—31no—
219C4⋊Q8—62no—
220C4⋊Q8D3211yescharacteristic
221#125—31no—
222#125—92no—
223#125—91no—
224#125—182no—
225C2×C4⋊C4—62no—
226C2×C4⋊C4—92no—
227C2×C4⋊C4—182no—
228C2×C42—31no—
229#103—34no—
230#103—94no—
231#103—94no—
232#103—94no—
233#97—31no—
234#97—92no—
235#97—91no—
236C23×C3—31no—
237C22×D3C2×#6711yescharacteristic
238C3×Q8—24no—
239C3×Q8—24no—
240C3×Q8—44no—
241C3×Q8—64no—
242C3×Q8—124no—
243C2×C3×C4—22no—
244C2×C3×C4—22no—
245C2×C3×C4—21no—
246C2×C3×C4—22no—
247C2×C3×C4—31no—
248C2×C3×C4—34no—
249C2×C3×C4—32no—
250C2×C3×C4—42no—
251C2×C3×C4—64no—
252C2×C3×C4—62no—
253C2×C3×C4—62no—
254C2×C3×C4—124no—
255C2×C3×C4D3×D412yes—
256C2×C3×C4C2×#6712yes—
257C2×C3×C4C23×D311yescharacteristic
258C2×C3×C4C23×D311yescharacteristic
259C2×Dic3—22no—
260C2×Dic3—22no—
261C2×Dic3—62no—
262C2×Dic3—62no—
263C2×Dic3—122no—
264C2×Dic3—124no—
265C2×Dic3C2×#6712yes—
266C2×Dic3C2×#6711yescharacteristic
267C4×D3—24no—
268C4×D3—44no—
269C4×D3—124no—
270C4×D3#23714yes—
271Dic6—24no—
272Dic6—44no—
273C3×C8—62no—
274C3⋊C8—22no—
275C3⋊C8—62no—
276C3⋊C8—62no—
277C3⋊C8—122no—
278C2×C32C2×#12411yescharacteristic
279C2×C32C2×#13712yes—
280C3×D3#49114yescomplemented
281C2×Q8—32no—
282C2×Q8—62no—
283C2×Q8—68no—
284C2×Q8C2×D3212yes—
285C22×C4—31no—
286C22×C4—32no—
287C22×C4—62no—
288C22×C4—182no—
289C2×C8—32no—
290C2×C8—92no—
291C2×C8—184no—
292C4⋊C4—22no—
293C4⋊C4—32no—
294C4⋊C4—64no—
295C4⋊C4—62no—
296C4⋊C4—62no—
297C4⋊C4—92no—
298C4⋊C4—182no—
299C4⋊C4—182no—
300C4⋊C4—182no—
301C4⋊C4—182no—
302C42—31no—
303C42—32no—
304C42C2×D3211yescharacteristic
305C22×C3—21no—
306C22×C3—32no—
307C22×C3—34no—
308C22×C3C2×D3×D411yescharacteristic
309C22×C3C22×#6711yescharacteristic
310C2×D3#93612yes—
311C2×D3#94214yes—
312C3×C4—22no—
313C3×C4—22no—
314C3×C4—22no—
315C3×C4—32no—
316C3×C4—42no—
317C3×C4—42no—
318C3×C4—42no—
319C3×C4—62no—
320C3×C4—82no—
321C3×C4—122no—
322C3×C4—122no—
323C3×C4C2×#23712yes—
324C3×C4D3×#4112yes—
325Dic3—22no—
326Dic3—42no—
327Dic3—42no—
328Dic3—122no—
329Dic3—122no—
330Dic3—242no—
331Dic3#93612yes—
332C32C2×#49111yescharacteristic, complemented, Sylow
333C23—31no—
334Q8—24no—
335Q8—64no—
336Q8—124no—
337C2×C4—22no—
338C2×C4—31no—
339C2×C4—34no—
340C2×C4—32no—
341C2×C4—64no—
342C2×C4—62no—
343C2×C4—62no—
344C2×C4—124no—
345C2×C4—182no—
346C2×C4—364no—
347C2×C4D3×#6712yes—
348C2×C4C22×D3211yescharacteristic
349C8—62no—
350C8—182no—
351C2×C3—21no—
352C2×C3—22no—
353C2×C3—34no—
354C2×C3D3×#12411yescharacteristic
355C2×C3D3×#13712yes—
356C2×C3C2×#93611yescharacteristic
357C2×C3C2×#94212yes—
358D3#508214yesdirect product factor
359C22—32no—
360C22—34no—
361C22C2×D3×#6711yescharacteristic
362C4—22no—
363C4—32no—
364C4—42no—
365C4—62no—
366C4—122no—
367C4—122no—
368C4—362no—
369C4D3×#23712yes—
370C3—21no—
371C3D3×#49111yescharacteristic, complemented
372C3C2×#508211yescharacteristic, complemented
373C2—34no—
374C2D3×#93611yescharacteristic
375C2D3×#94212yes—
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
hypercenterC4⋊Q8D32
hypocenterC32C2×#491
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. #10592781C2semidirect
4. C3×#5082C2semidirect
5. #10591613C2semidirect
8. #10590291C2semidirect
9. #10590289C2semidirect
45. #5082D3direct (N × H)
280. C3×D3#491semidirect
332. C32C2×#491semidirect
358. D3#5082direct (N × H)
371. C3D3×#491semidirect
372. C3C2×#5082semidirect

Maximal subgroups

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

subgroupindex
C3×D3×C4⋊Q82
D3×#8702
#105927812
C3×#50822
#105916132
D3×#8352
D3×#8032
#105902912
#105902892
C2×#50823
D3×#4913