Finite Group Databasebeta

← D3×#6452 #13058599

Subgroups — D3×#6452 #13058599

Order 1344.

452 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10621372C211yesmaximal, characteristic, complemented
2D3×C7×C4⋊C4C211yesmaximal, characteristic
3C3×#6452C211yesmaximal, characteristic, complemented
4D3×C4⋊Dic7C211yesmaximal, characteristic
5D3×Dic7⋊C4C211yesmaximal, characteristic
6D3×Dic7⋊C4C211yesmaximal, characteristic
7D3×Dic7⋊C4C211yesmaximal, characteristic
8D3×Dic7⋊C4C211yesmaximal, characteristic
9C4×D3×Dic7C211yesmaximal, characteristic
10#10620944C211yesmaximal, characteristic, complemented
11#10620940C211yesmaximal, characteristic, complemented
12#10620901C211yesmaximal, characteristic, complemented
13#10620898C211yesmaximal, characteristic, complemented
14#10620897C211yesmaximal, characteristic, complemented
15#10620896C211yesmaximal, characteristic, complemented
16C2×#6452—31nomaximal, Hall
17C2×C4×D3×C7C2211yescharacteristic
18C2×C4×D3×C7C2211yescharacteristic
19C2×C4×D3×C7C2211yescharacteristic
20C2×D3×Dic7C2211yescharacteristic
21C2×D3×Dic7C2211yescharacteristic
22C2×D3×Dic7C2211yescharacteristic
23C2×D3×Dic7C2211yescharacteristic
24C3×C7×C4⋊C4C2211yescharacteristic
25C4⋊Dic21C2211yescharacteristic
26#66629C2211yescharacteristic
27#66629C2211yescharacteristic
28#66629C2211yescharacteristic
29#66629C2211yescharacteristic
30C4×Dic21C2211yescharacteristic
31C7×C4⋊Dic3C2211yescharacteristic
32C7×Dic3⋊C4C2211yescharacteristic
33C7×Dic3⋊C4C2211yescharacteristic
34C3×C4⋊Dic7C2211yescharacteristic
35C3×Dic7⋊C4C2211yescharacteristic
36C3×Dic7⋊C4C2211yescharacteristic
37C3×Dic7⋊C4C2211yescharacteristic
38C3×Dic7⋊C4C2211yescharacteristic
39C3×C4×Dic7C2211yescharacteristic
40Dic3⋊Dic7C2211yescharacteristic
41Dic3⋊Dic7C2211yescharacteristic
42#66577C2211yescharacteristic
43#66577C2211yescharacteristic
44#66577C2211yescharacteristic
45#66577C2211yescharacteristic
46Dic7⋊Dic3C2211yescharacteristic
47Dic7⋊Dic3C2211yescharacteristic
48Dic7⋊Dic3C2211yescharacteristic
49Dic7⋊Dic3C2211yescharacteristic
50Dic3×Dic7C2211yescharacteristic
51Dic3×Dic7C2211yescharacteristic
52C2×C7×C4⋊C4—31no—
53C2×C4⋊Dic7—31no—
54C2×Dic7⋊C4—31no—
55C2×Dic7⋊C4—31no—
56C2×Dic7⋊C4—31no—
57C2×Dic7⋊C4—31no—
58C2×C4×Dic7—31no—
59#6452—31no—
60#6452—31no—
61#6452—31no—
62#6452—31no—
63#6452—31no—
64#6452—31no—
65#6452—31no—
66#6452D311yescharacteristic, direct product factor
67D3×#125—71nomaximal, Hall
68C22×D3×C7C2311yescharacteristic
69C2×C3×C4×C7C2311yescharacteristic
70C2×C3×C4×C7C2311yescharacteristic
71C2×C3×C4×C7C2311yescharacteristic
72C2×Dic21C2311yescharacteristic
73C2×Dic21C2311yescharacteristic
74C2×Dic21C2311yescharacteristic
75C2×Dic21C2311yescharacteristic
76C2×C7×Dic3C2311yescharacteristic
77C2×C7×Dic3C2311yescharacteristic
78C2×C7×Dic3C2311yescharacteristic
79C4×D3×C7—22no—
80C4×D3×C7—22no—
81C4×D3×C7—22no—
82C2×C3×Dic7C2311yescharacteristic
83C2×C3×Dic7C2311yescharacteristic
84C2×C3×Dic7C2311yescharacteristic
85C2×C3×Dic7C2311yescharacteristic
86D3×Dic7—22no—
87D3×Dic7—22no—
88D3×Dic7—22no—
89D3×Dic7Q814yes—
90C22×C4×C7—31no—
91C22×C4×C7—31no—
92C22×C4×C7—31no—
93C22×Dic7—31no—
94C22×Dic7—31no—
95C22×Dic7—31no—
96C22×Dic7—31no—
97C7×C4⋊C4—31no—
98C7×C4⋊C4—31no—
99C7×C4⋊C4—31no—
100C7×C4⋊C4C2×D311yescharacteristic
101C4⋊Dic7—31no—
102C4⋊Dic7—31no—
103C4⋊Dic7—31no—
104C4⋊Dic7C2×D311yescharacteristic
105Dic7⋊C4—31no—
106Dic7⋊C4—31no—
107Dic7⋊C4—31no—
108Dic7⋊C4—31no—
109Dic7⋊C4—31no—
110Dic7⋊C4—31no—
111Dic7⋊C4—31no—
112Dic7⋊C4—31no—
113Dic7⋊C4—31no—
114Dic7⋊C4—31no—
115Dic7⋊C4—31no—
116Dic7⋊C4—31no—
117Dic7⋊C4C2×D311yescharacteristic
118Dic7⋊C4C2×D311yescharacteristic
119Dic7⋊C4C2×D311yescharacteristic
120Dic7⋊C4C2×D311yescharacteristic
121C4×Dic7—31no—
122C4×Dic7—31no—
123C4×Dic7—31no—
124C4×Dic7C2×D311yescharacteristic
125C3×#125—71no—
126D3×C4⋊C4—71no—
127D3×C4⋊C4—71no—
128D3×C4⋊C4—71no—
129D3×C4⋊C4—71no—
130D3×C4⋊C4—71no—
131D3×C4⋊C4D711yescharacteristic
132#890—71no—
133#890—71no—
134#889—71no—
135#889—71no—
136#889—71no—
137#889—71no—
138C42×D3—71no—
139#870—71no—
140C22×C3×C7C2411yescharacteristic
141C2×D3×C7C2×Q812yes—
142C2×D3×C7#4112yes—
143C2×D3×C7#4112yes—
144C3×C4×C7—21no—
145C3×C4×C7—21no—
146C3×C4×C7—21no—
147Dic21—21no—
148Dic21—21no—
149Dic21—21no—
150Dic21C2×Q812yes—
151C3×Dic7—21no—
152C3×Dic7—21no—
153C3×Dic7—21no—
154C3×Dic7C2×Q812yes—
155C7×Dic3—21no—
156C7×Dic3—21no—
157C7×Dic3—21no—
158C2×#125—211noSylow
159C23×C7—31no—
160C2×C4×C7—31no—
161C2×C4×C7—31no—
162C2×C4×C7—31no—
163C2×C4×C7—62no—
164C2×C4×C7—62no—
165C2×C4×C7—62no—
166C2×C4×C7C22×D311yescharacteristic
167C2×C4×C7C22×D311yescharacteristic
168C2×C4×C7C22×D311yescharacteristic
169C2×Dic7—31no—
170C2×Dic7—34no—
171C2×Dic7—31no—
172C2×Dic7—31no—
173C2×Dic7—31no—
174C2×Dic7—62no—
175C2×Dic7—62no—
176C2×Dic7—62no—
177C2×Dic7C22×D311yescharacteristic
178C2×Dic7C22×D311yescharacteristic
179C2×Dic7C22×D311yescharacteristic
180C2×Dic7C22×D311yescharacteristic
181C2×C4×D3—71no—
182C2×C4×D3—71no—
183C2×C4×D3—71no—
184C2×C4×D3—71no—
185C2×C4×D3C2×D711yescharacteristic
186C2×C4×D3C2×D711yescharacteristic
187C2×C4×D3C2×D711yescharacteristic
188C3×C4⋊C4—71no—
189C3×C4⋊C4—71no—
190C3×C4⋊C4—71no—
191C3×C4⋊C4—71no—
192C3×C4⋊C4—71no—
193C3×C4⋊C4C2×D711yescharacteristic
194C3×C42—71no—
195C4⋊Dic3—71no—
196C4⋊Dic3—71no—
197C4⋊Dic3—71no—
198C4⋊Dic3—71no—
199C4⋊Dic3—71no—
200C4⋊Dic3C2×D711yescharacteristic
201Dic3⋊C4—71no—
202Dic3⋊C4—71no—
203Dic3⋊C4—71no—
204Dic3⋊C4—71no—
205Dic3⋊C4—71no—
206Dic3⋊C4—71no—
207Dic3⋊C4—71no—
208Dic3⋊C4—71no—
209Dic3⋊C4—71no—
210Dic3⋊C4—71no—
211Dic3⋊C4C2×D711yescharacteristic
212Dic3⋊C4C2×D711yescharacteristic
213C4×Dic3—71no—
214C4×Dic3—71no—
215C4×Dic3—71no—
216C2×C3×C7C22×Q811yescharacteristic
217C2×C3×C7C2×#4111yescharacteristic
218C2×C3×C7C2×#4111yescharacteristic
219D3×C7#12514yescomplemented
220#125—71no—
221#125—211no—
222#125—211no—
223#125—211no—
224#125—211no—
225#125—211no—
226#125—211no—
227#125—211no—
228C2×C4⋊C4—31no—
229C2×C4⋊C4—211no—
230C2×C4⋊C4—211no—
231C2×C4⋊C4—211no—
232C2×C4⋊C4—211no—
233C2×C4⋊C4—211no—
234C2×C42—211no—
235C22×C7—32no—
236C22×C7—32no—
237C22×C7—32no—
238C22×C7C23×D311yescharacteristic
239C4×C7—21no—
240C4×C7—21no—
241C4×C7—21no—
242C4×C7—61no—
243C4×C7—61no—
244C4×C7—61no—
245Dic7—21no—
246Dic7—21no—
247Dic7—21no—
248Dic7—32no—
249Dic7—61no—
250Dic7—61no—
251Dic7—61no—
252Dic7D3×Q812yes—
253C22×D3C22×D711yescharacteristic
254C2×C3×C4—71no—
255C2×C3×C4—71no—
256C2×C3×C4—71no—
257C2×C3×C4—71no—
258C2×C3×C4C22×D711yescharacteristic
259C2×C3×C4C22×D711yescharacteristic
260C2×C3×C4C22×D711yescharacteristic
261C2×Dic3—71no—
262C2×Dic3—71no—
263C2×Dic3—71no—
264C2×Dic3—71no—
265C2×Dic3C22×D711yescharacteristic
266C2×Dic3C22×D711yescharacteristic
267C2×Dic3C22×D711yescharacteristic
268C4×D3—22no—
269C4×D3—22no—
270C4×D3—22no—
271C4×D3—74no—
272C4×D3—142no—
273C4×D3—142no—
274C4×D3—142no—
275C3×C7C2×#12511yescharacteristic, complemented, Hall
276C22×C4—31no—
277C22×C4—31no—
278C22×C4—31no—
279C22×C4—211no—
280C22×C4—211no—
281C22×C4—211no—
282C22×C4—211no—
283C4⋊C4—31no—
284C4⋊C4—31no—
285C4⋊C4—31no—
286C4⋊C4—71no—
287C4⋊C4—71no—
288C4⋊C4—71no—
289C4⋊C4—71no—
290C4⋊C4—71no—
291C4⋊C4—211no—
292C4⋊C4—211no—
293C4⋊C4—211no—
294C4⋊C4—211no—
295C4⋊C4—211no—
296C4⋊C4—211no—
297C4⋊C4—211no—
298C4⋊C4—211no—
299C4⋊C4—211no—
300C4⋊C4—211no—
301C4⋊C4—211no—
302C4⋊C4—211no—
303C4⋊C4—211no—
304C4⋊C4—211no—
305C4⋊C4—211no—
306C4⋊C4D3×D711yescharacteristic
307C42—71no—
308C42—211no—
309C42—211no—
310C42—211no—
311C2×C7—34no—
312C2×C7C2×D3×Q811yescharacteristic
313C2×C7D3×#4111yescharacteristic
314C2×C7D3×#4111yescharacteristic
315C22×C3C23×D711yescharacteristic
316C2×D3#115712yes—
317C2×D3#115912yes—
318C2×D3Q8×D712yes—
319C3×C4—21no—
320C3×C4—21no—
321C3×C4—21no—
322C3×C4—72no—
323C3×C4—141no—
324C3×C4—141no—
325C3×C4—141no—
326Dic3—21no—
327Dic3—21no—
328Dic3—21no—
329Dic3—72no—
330Dic3—141no—
331Dic3—141no—
332Dic3—141no—
333C23—31no—
334C2×C4—31no—
335C2×C4—31no—
336C2×C4—31no—
337C2×C4—62no—
338C2×C4—62no—
339C2×C4—62no—
340C2×C4—71no—
341C2×C4—71no—
342C2×C4—71no—
343C2×C4—71no—
344C2×C4—214no—
345C2×C4—211no—
346C2×C4—211no—
347C2×C4—211no—
348C2×C4—211no—
349C2×C4—422no—
350C2×C4—422no—
351C2×C4—422no—
352C2×C4C2×D3×D711yescharacteristic
353C2×C4C2×D3×D711yescharacteristic
354C2×C4C2×D3×D711yescharacteristic
355C7D3×#12511yescharacteristic, complemented, Sylow
356C2×C3C2×#115711yescharacteristic
357C2×C3C2×#115911yescharacteristic
358C2×C3C2×Q8×D711yescharacteristic
359D3#645214yesdirect product factor
360C22—32no—
361C22—32no—
362C22—32no—
363C22C22×D3×D711yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—61no—
368C4—61no—
369C4—61no—
370C4—72no—
371C4—141no—
372C4—141no—
373C4—141no—
374C4—212no—
375C4—421no—
376C4—421no—
377C4—421no—
378C3C2×#645211yescharacteristic, complemented, Sylow
379C2—34no—
380C2D3×#115711yescharacteristic
381C2D3×#115911yescharacteristic
382C2D3×Q8×D711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D7
commutator, socle, cosocleC22×C3×C7C24
FittingC3×C7×C4⋊C4C22
prime radicalC22×D3×C7C23
hypercenterC4⋊C4D3×D7
hypocenterC3×C7C2×#125
LCSG ▷ C22×C3×C7 ▷ C3×C7
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #10621372C2semidirect
3. C3×#6452C2semidirect
10. #10620944C2semidirect
11. #10620940C2semidirect
12. #10620901C2semidirect
13. #10620898C2semidirect
14. #10620897C2semidirect
15. #10620896C2semidirect
66. #6452D3direct (N × H)
219. D3×C7#125semidirect
275. C3×C7C2×#125semidirect
355. C7D3×#125semidirect
359. D3#6452direct (N × H)
378. C3C2×#6452semidirect

Maximal subgroups

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

subgroupindex
#106213722
D3×C7×C4⋊C42
C3×#64522
D3×C4⋊Dic72
D3×Dic7⋊C42
C4×D3×Dic72
#106209442
#106209402
#106209012
#106208982
#106208972
#106208962
C2×#64523
D3×#1257