Finite Group Databasebeta

← D7×(C2×D3)⋊Dic3 #72246672

Subgroups — D7×(C2×D3)⋊Dic3 #72246672

Order 2016.

582 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 582 conjugacy classes of subgroups — too many to draw. Only its 130 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D3×D7C211yesmaximal, characteristic
2C2×D7×C3⋊Dic3C211yesmaximal, characteristic, complemented
3C2×C3×Dic3×D7C211yesmaximal, characteristic, complemented
4#11759225C211yesmaximal, characteristic, complemented
5(C2×D3)⋊Dic21C211yesmaximal, characteristic, complemented
6#11759207C211yesmaximal, characteristic, complemented
7C7×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
8D7×#217—31nomaximal
9D7×(C2×D3)⋊C4—31nomaximal
10C22×C3×D21C2211yescharacteristic
11C22×C3×D3×C7C2211yescharacteristic
12C22×C32×D7C2211yescharacteristic
13C2×C3×D3×D7—22no—
14C2×C3×D3×D7—22no—
15C2×C3×D3×D7C414yescomplemented
16C2×C3⋊Dic21C2211yescharacteristic, complemented
17C2×C7×C3⋊Dic3C2211yescharacteristic, complemented
18C2×C3×Dic21C2211yescharacteristic, complemented
19C2×C3×C7×Dic3C2211yescharacteristic, complemented
20D7×C3⋊Dic3—22no—
21C3×Dic3×D7—22no—
22C23×C3×D7—31no—
23C22×D3×D7D311yescharacteristic
24C2×C3×C4×D7—31no—
25C2×Dic3×D7—31no—
26C2×Dic3×D7—31no—
27C2×Dic3×D7—61no—
28C2×Dic3×D7D311yescharacteristic, complemented
29#66636—31no—
30#66631—31no—
31C7×#217—31no—
32C7×(C2×D3)⋊C4—31no—
33#66575—31no—
34(C2×D3)⋊Dic7—31no—
35(C2×D7)⋊Dic3—31no—
36(C2×D7)⋊Dic3—31no—
37C2×(C2×D3)⋊Dic3—71nomaximal, Hall
38C22×C32×C7C2311yescharacteristic
39C2×C3×D21—21no—
40C2×C3×D21—21no—
41C2×C3×D21C2×C412yescomplemented
42C2×C3×D3×C7—21no—
43C2×C3×D3×C7—21no—
44C2×C3×D3×C7C2×C412yescomplemented
45C2×C32×D7C2×C412yes—
46C2×C32×D7D412yes—
47C2×C32×D7D412yes—
48C3×D3×D7—28no—
49C3⋊Dic21—21no—
50C7×C3⋊Dic3—21no—
51C3×Dic21—21no—
52C3×C7×Dic3—21no—
53D7×C22⋊C4—91noHall
54C23×C3×C7—31no—
55C22×D21C2×D311yescharacteristic
56C22×D3×C7C2×D311yescharacteristic
57C22×C3×D7—21no—
58C22×C3×D7—31no—
59C22×C3×D7—34no—
60C22×C3×D7—62no—
61C22×C3×D7—62no—
62C22×C3×D7C2×D311yescharacteristic
63C22×C3×D7C2×D311yescharacteristic
64C2×D3×D7—22no—
65C2×D3×D7—22no—
66C2×D3×D7Dic314yescomplemented
67C2×C3×C4×C7—31no—
68C2×Dic21—31no—
69C2×Dic21—31no—
70C2×Dic21—61no—
71C2×Dic21C2×D311yescharacteristic, complemented
72C2×C7×Dic3—31no—
73C2×C7×Dic3—31no—
74C2×C7×Dic3—61no—
75C2×C7×Dic3C2×D311yescharacteristic, complemented
76C2×C3×Dic7—31no—
77C3×C4×D7—62no—
78Dic3×D7—22no—
79Dic3×D7—62no—
80Dic3×D7—62no—
81Dic3×D7—62no—
82Dic3×D7—62no—
83C23×C3×D3—71no—
84C22×C3⋊Dic3—71no—
85C22×C3×Dic3—71no—
86(C2×D3)⋊Dic3—71no—
87(C2×D3)⋊Dic3—71no—
88(C2×D3)⋊Dic3—71no—
89(C2×D3)⋊Dic3D711yescharacteristic, direct product factor
90C2×C32×C7C22×C411yescharacteristic
91C2×C32×C7C2×D411yescharacteristic
92C2×C32×C7C2×D411yescharacteristic
93C3×D21—22no—
94C3×D3×C7—22no—
95C32×D7C22⋊C414yescomplemented
96C23×D7—31no—
97C2×C4×D7—31no—
98C2×C4×D7—91no—
99C7×C22⋊C4—91no—
100C22⋊Dic7—91no—
101(C2×D7)⋊C4—91no—
102(C2×D7)⋊C4—91no—
103C2×#217—211no—
104C2×(C2×D3)⋊C4—211no—
105C22×C3×C7—21no—
106C22×C3×C7—32no—
107C22×C3×C7—61no—
108C22×C3×C7—61no—
109C22×C3×C7C22×D311yescharacteristic
110C22×C3×C7C22×D311yescharacteristic
111C2×D21—21no—
112C2×D21—21no—
113C2×D21C2×Dic312yescomplemented
114C2×D3×C7—21no—
115C2×D3×C7—21no—
116C2×D3×C7C2×Dic312yescomplemented
117C2×C3×D7—22no—
118C2×C3×D7—22no—
119C2×C3×D7—22no—
120C2×C3×D7—32no—
121C2×C3×D7—61no—
122C2×C3×D7—61no—
123C2×C3×D7—68no—
124C2×C3×D7C4×D312yes—
125C2×C3×D7D1212yes—
126C2×C3×D7C2×Dic312yes—
127C2×C3×D7#6712yes—
128C2×C3×D7#6712yes—
129C2×C3×D7#6712yes—
130D3×D7—28no—
131C3×C4×C7—61no—
132Dic21—21no—
133Dic21—61no—
134Dic21—61no—
135Dic21—61no—
136Dic21—61no—
137C3×Dic7—61no—
138C7×Dic3—21no—
139C7×Dic3—61no—
140C7×Dic3—61no—
141C7×Dic3—61no—
142C7×Dic3—61no—
143C23×C32—71no—
144C22×C3×D3—71no—
145C22×C3×D3—74no—
146C22×C3×D3—142no—
147C22×C3×D3—142no—
148C22×C3×D3C2×D711yescharacteristic
149C2×C3⋊Dic3—71no—
150C2×C3⋊Dic3—142no—
151C2×C3⋊Dic3C2×D711yescharacteristic, complemented
152C2×C3×Dic3—71no—
153C2×C3×Dic3—142no—
154C2×C3×Dic3C2×D711yescharacteristic, complemented
155C32×C7C2×C22⋊C411yescharacteristic, complemented, Hall
156C23×C7—31no—
157C22×D7—31no—
158C22×D7—34no—
159C22×D7—62no—
160C22×D7—62no—
161C22×D7D3211yescharacteristic
162C2×C4×C7—31no—
163C2×C4×C7—91no—
164C2×Dic7—31no—
165C2×Dic7—91no—
166C4×D7—62no—
167C4×D7—182no—
168C24×C3—211no—
169C23×D3—71no—
170C22×C3×C4—211no—
171C22×Dic3—71no—
172C22×Dic3—211no—
173C22×Dic3—211no—
174C22×Dic3—421no—
175#217—31no—
176#217—211no—
177#217—211no—
178#217—211no—
179(C2×D3)⋊C4—31no—
180(C2×D3)⋊C4—211no—
181(C2×D3)⋊C4—211no—
182(C2×D3)⋊C4—211no—
183C2×C3×C7—21no—
184C2×C3×C7—21no—
185C2×C3×C7—21no—
186C2×C3×C7—62no—
187C2×C3×C7C2×C4×D311yescharacteristic
188C2×C3×C7C2×D1211yescharacteristic
189C2×C3×C7C22×Dic311yescharacteristic
190C2×C3×C7C2×#6711yescharacteristic
191C2×C3×C7C2×#6711yescharacteristic
192C2×C3×C7C2×#6711yescharacteristic
193D21—22no—
194C3×D7—24no—
195C3×D7—62no—
196C3×D7(C2×D3)⋊C414yescomplemented
197C3×D7#21714yescomplemented
198D3×C7—22no—
199C22×C32—72no—
200C22×C32—72no—
201C22×C32—72no—
202C22×C32C22×D711yescharacteristic
203C2×C3×D3—21no—
204C2×C3×D3—21no—
205C2×C3×D3—72no—
206C2×C3×D3—148no—
207C2×C3×D3—141no—
208C2×C3×D3—141no—
209C2×C3×D3C4×D712yescomplemented
210C3⋊Dic3—21no—
211C3⋊Dic3—141no—
212C3×Dic3—21no—
213C3×Dic3—141no—
214C2×C22⋊C4—631noSylow
215C22×C7—32no—
216C22×C7—61no—
217C22×C7—61no—
218C22×C7C2×D3211yescharacteristic
219C2×D7—32no—
220C2×D7—61no—
221C2×D7—61no—
222C2×D7—68no—
223C2×D7D3×Dic312yes—
224C2×D7#62512yes—
225C2×D7#62612yes—
226C4×C7—61no—
227C4×C7—181no—
228Dic7—61no—
229Dic7—181no—
230C23×C3—31no—
231C23×C3—71no—
232C23×C3—71no—
233C23×C3—141no—
234C23×C3—214no—
235C23×C3—211no—
236C23×C3—422no—
237C23×C3—422no—
238C22×D3—71no—
239C22×D3—74no—
240C22×D3—142no—
241C22×D3—142no—
242C22×D3D3×D711yescharacteristic
243C2×C3×C4—31no—
244C2×C3×C4—211no—
245C2×C3×C4—422no—
246C2×Dic3—31no—
247C2×Dic3—31no—
248C2×Dic3—61no—
249C2×Dic3—71no—
250C2×Dic3—142no—
251C2×Dic3—211no—
252C2×Dic3—211no—
253C2×Dic3—421no—
254C2×Dic3—422no—
255C2×Dic3—422no—
256C2×Dic3—422no—
257C2×Dic3—422no—
258C2×Dic3D3×D711yescharacteristic, complemented
259C3×C7—21no—
260C3×C7C2×(C2×D3)⋊C411yescharacteristic, complemented
261C3×C7C2×#21711yescharacteristic, complemented
262C2×C32—74no—
263C2×C32C2×C4×D711yescharacteristic
264C2×C32D4×D711yescharacteristic
265C2×C32D4×D711yescharacteristic
266C3×D3—22no—
267C3×D3—142no—
268C24—211no—
269C22×C4—211no—
270C22×C4—631no—
271C22⋊C4—91no—
272C22⋊C4—631no—
273C22⋊C4—631no—
274C22⋊C4—631no—
275C2×C7—62no—
276C2×C7C2×D3×Dic311yescharacteristic
277C2×C7C2×#62511yescharacteristic
278C2×C7C2×#62611yescharacteristic
279D7—62no—
280D7(C2×D3)⋊Dic314yesdirect product factor
281C22×C3—21no—
282C22×C3—32no—
283C22×C3—61no—
284C22×C3—61no—
285C22×C3—72no—
286C22×C3—72no—
287C22×C3—72no—
288C22×C3—72no—
289C22×C3—72no—
290C22×C3—72no—
291C22×C3—142no—
292C22×C3—142no—
293C22×C3—142no—
294C22×C3—212no—
295C22×C3—428no—
296C22×C3—421no—
297C22×C3—421no—
298C22×C3C2×D3×D711yescharacteristic
299C22×C3C2×D3×D711yescharacteristic
300C2×D3—21no—
301C2×D3—21no—
302C2×D3—72no—
303C2×D3—148no—
304C2×D3—141no—
305C2×D3—141no—
306C2×D3Dic3×D712yescomplemented
307C3×C4—61no—
308C3×C4—421no—
309Dic3—21no—
310Dic3—61no—
311Dic3—61no—
312Dic3—61no—
313Dic3—61no—
314Dic3—141no—
315Dic3—421no—
316Dic3—421no—
317Dic3—421no—
318Dic3—421no—
319C32D7×C22⋊C411yescharacteristic, complemented, Sylow
320C23—31no—
321C23—71no—
322C23—214no—
323C23—211no—
324C23—422no—
325C23—422no—
326C2×C4—31no—
327C2×C4—91no—
328C2×C4—211no—
329C2×C4—422no—
330C2×C4—631no—
331C2×C4—1262no—
332C7C2×(C2×D3)⋊Dic311yescharacteristic, complemented, Sylow
333C2×C3—21no—
334C2×C3—21no—
335C2×C3—21no—
336C2×C3—62no—
337C2×C3—74no—
338C2×C3—74no—
339C2×C3—144no—
340C2×C3—422no—
341C2×C3C4×D3×D711yescharacteristic
342C2×C3D7×D1211yescharacteristic
343C2×C3C2×Dic3×D711yescharacteristic
344C2×C3D7×#6711yescharacteristic
345C2×C3D7×#6711yescharacteristic
346C2×C3D7×#6711yescharacteristic
347D3—22no—
348D3—142no—
349C22—32no—
350C22—61no—
351C22—61no—
352C22—72no—
353C22—72no—
354C22—72no—
355C22—212no—
356C22—428no—
357C22—421no—
358C22—421no—
359C22D32×D711yescharacteristic
360C4—61no—
361C4—181no—
362C4—421no—
363C4—1261no—
364C3—21no—
365C3D7×(C2×D3)⋊C411yescharacteristic, complemented
366C3D7×#21711yescharacteristic, complemented
367C2—62no—
368C2—74no—
369C2—422no—
370C2D3×Dic3×D711yescharacteristic
371C2D7×#62511yescharacteristic
372C2D7×#62611yescharacteristic
subgroupG/H
center, Frattini, hypercenterC22D32×D7
commutatorC2×C32×C7C22×C4
Fitting, socle, cosocleC22×C32×C7C23
prime radicalC22×C3×D3×D7C2
hypocenterC32×C7C2×C22⋊C4
LCSG ▷ C2×C32×C7 ▷ C32×C7
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
2. C2×D7×C3⋊Dic3C2semidirect
3. C2×C3×Dic3×D7C2semidirect
4. #11759225C2semidirect
5. (C2×D3)⋊Dic21C2semidirect
6. #11759207C2semidirect
7. C7×(C2×D3)⋊Dic3C2semidirect
15. C2×C3×D3×D7C4semidirect
16. C2×C3⋊Dic21C22semidirect
17. C2×C7×C3⋊Dic3C22semidirect
18. C2×C3×Dic21C22semidirect
19. C2×C3×C7×Dic3C22semidirect
28. C2×Dic3×D7D3semidirect
41. C2×C3×D21C2×C4semidirect
44. C2×C3×D3×C7C2×C4semidirect
66. C2×D3×D7Dic3semidirect
71. C2×Dic21C2×D3semidirect
75. C2×C7×Dic3C2×D3semidirect
89. (C2×D3)⋊Dic3D7direct (N × H)
95. C32×D7C22⋊C4semidirect
113. C2×D21C2×Dic3semidirect
116. C2×D3×C7C2×Dic3semidirect
151. C2×C3⋊Dic3C2×D7semidirect
154. C2×C3×Dic3C2×D7semidirect
155. C32×C7C2×C22⋊C4semidirect
196. C3×D7(C2×D3)⋊C4semidirect
197. C3×D7#217semidirect
209. C2×C3×D3C4×D7semidirect
258. C2×Dic3D3×D7semidirect
260. C3×C7C2×(C2×D3)⋊C4semidirect
261. C3×C7C2×#217semidirect
280. D7(C2×D3)⋊Dic3direct (N × H)
306. C2×D3Dic3×D7semidirect
319. C32D7×C22⋊C4semidirect
332. C7C2×(C2×D3)⋊Dic3semidirect
365. C3D7×(C2×D3)⋊C4semidirect
366. C3D7×#217semidirect

Maximal subgroups

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

subgroupindex
C22×C3×D3×D72
C2×D7×C3⋊Dic32
C2×C3×Dic3×D72
#117592252
(C2×D3)⋊Dic212
#117592072
C7×(C2×D3)⋊Dic32
D7×#2173
D7×(C2×D3)⋊C43
C2×(C2×D3)⋊Dic37