Finite Group Databasebeta

← D4×A4×D7 #13062165

Subgroups — D4×A4×D7 #13062165

Order 1344.

634 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 634 conjugacy classes of subgroups — too many to draw. Only its 75 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×A4×D7C212yesmaximal, complemented
2C7×D4×A4C211yesmaximal, characteristic, complemented
3A4×C22⋊D7C212yesmaximal, complemented
4A4×D28C211yesmaximal, characteristic, complemented
5C4×A4×D7C211yesmaximal, characteristic, complemented
6C22×D4×D7C311yesmaximal, characteristic, complemented, Hall
7C22×C7×A4C2212yescomplemented
8C2×A4×D7—24no—
9C2×A4×D7C2211yescharacteristic
10C2×A4×D7C2212yescomplemented
11C3×D4×D7—41nomaximal
12C4×C7×A4C2211yescharacteristic, complemented
13A4×Dic7C2211yescharacteristic, complemented
14C24×D7C2×C312yescomplemented
15C22×C7×D4C2×C311yescharacteristic, complemented
16C22×C22⋊D7C2×C312yescomplemented
17C2×D4×D7—31no—
18C2×D4×D7—31no—
19C2×D4×D7—31no—
20C2×D4×D7—32no—
21C2×D4×D7—31no—
22C2×D4×D7—32no—
23C22×D28C2×C311yescharacteristic, complemented
24C22×C4×D7C2×C311yescharacteristic, complemented
25C2×D4×A4—71nomaximal, Hall
26C22×C3×D7—42no—
27C2×C7×A4—22no—
28C2×C7×A4C2311yescharacteristic
29A4×D7—22no—
30A4×D7D412yesdirect product factor
31C3×C7×D4—41no—
32C3×C22⋊D7—42no—
33C3×D28—41no—
34C3×C4×D7—41no—
35C24×C7C22×C312yescomplemented
36C23×D7—24no—
37C23×D7—32no—
38C23×D7—32no—
39C23×D7—32no—
40C23×D7—32no—
41C23×D7—64no—
42C23×D7C22×C311yescharacteristic
43C23×D7C22×C312yescomplemented
44C2×C7×D4—31no—
45C2×C7×D4—31no—
46C2×C7×D4—32no—
47C22×C4×C7C22×C311yescharacteristic, complemented
48C2×C22⋊D7—32no—
49C2×C22⋊D7—32no—
50C2×C22⋊D7—32no—
51C2×C22⋊D7—32no—
52C22×Dic7C22×C311yescharacteristic, complemented
53D4×D7—34no—
54D4×D7—34no—
55D4×D7—32no—
56D4×D7—32no—
57D4×D7—32no—
58D4×D7—32no—
59D4×D7—31no—
60D4×D7—32no—
61D4×D7—31no—
62D4×D7—31no—
63D4×D7A411yescharacteristic, direct product factor
64C2×D28—31no—
65C2×D28—32no—
66C2×D28—31no—
67C2×C4×D7—31no—
68C2×C4×D7—31no—
69C2×C4×D7—31no—
70C2×C4×D7—31no—
71C23×A4—72no—
72D4×A4—72no—
73D4×A4—71no—
74D4×A4D711yescharacteristic, direct product factor
75C2×C4×A4—71no—
76C22×C3×C7—42no—
77C2×C3×D7—41no—
78C2×C3×D7—42no—
79C2×C3×D7—84no—
80C7×A4C2×D411yescharacteristic, complemented
81C3×C4×C7—41no—
82C3×Dic7—41no—
83C23×D4—71noSylow
84C23×C7—22no—
85C23×C7—32no—
86C23×C7—32no—
87C23×C7—62no—
88C23×C7C23×C311yescharacteristic
89C22×D7—22no—
90C22×D7—31no—
91C22×D7—31no—
92C22×D7—32no—
93C22×D7—34no—
94C22×D7—32no—
95C22×D7—32no—
96C22×D7—32no—
97C22×D7—32no—
98C22×D7—32no—
99C22×D7—64no—
100C22×D7—64no—
101C22×D7—64no—
102C22×D7—64no—
103C22×D7—64no—
104C22×D7—64no—
105C22×D7—64no—
106C22×D7—64no—
107C22×D7—62no—
108C22×D7C3×D412yescomplemented
109C22×D7C2×A412yescomplemented
110C7×D4—32no—
111C7×D4—32no—
112C7×D4—31no—
113C7×D4C2×A411yescharacteristic, complemented
114C2×C4×C7—31no—
115C2×C4×C7—31no—
116C22⋊D7—34no—
117C22⋊D7—32no—
118C22⋊D7—32no—
119C22⋊D7—32no—
120C22⋊D7C2×A412yescomplemented
121C2×Dic7—31no—
122C2×Dic7—31no—
123D28—32no—
124D28—32no—
125D28—31no—
126D28C2×A411yescharacteristic, complemented
127C4×D7—32no—
128C4×D7—31no—
129C4×D7—31no—
130C4×D7—31no—
131C4×D7C2×A411yescharacteristic, complemented
132C22×A4—71no—
133C22×A4—72no—
134C22×A4—144no—
135C22×A4C2×D712yescomplemented
136C2×C3×D4—281no—
137C4×A4—71no—
138C4×A4C2×D711yescharacteristic, complemented
139C2×C3×C7—41no—
140C2×C3×C7—82no—
141C3×D7—42no—
142C3×D7—82no—
143C25—72no—
144C22×D4—72no—
145C22×D4—71no—
146C22×D4—211no—
147C22×D4—211no—
148C22×D4—211no—
149C22×D4—211no—
150C22×D4—212no—
151C22×D4—212no—
152C22×D4C3×D711yescharacteristic, complemented
153C23×C4—71no—
154C22×C7—31no—
155C22×C7—31no—
156C22×C7—32no—
157C22×C7—62no—
158C22×C7—62no—
159C22×C7—62no—
160C22×C7—62no—
161C22×C7C2×C3×D411yescharacteristic, complemented
162C22×C7C22×A412yescomplemented
163C2×D7—24no—
164C2×D7—32no—
165C2×D7—31no—
166C2×D7—32no—
167C2×D7—32no—
168C2×D7—32no—
169C2×D7—32no—
170C2×D7—64no—
171C2×D7—62no—
172C2×D7—62no—
173C2×D7—64no—
174C2×D7—68no—
175C2×D7—64no—
176C2×D7—62no—
177C2×D7—62no—
178C2×D7C22×A411yescharacteristic
179C2×D7C22×A412yescomplemented
180C4×C7—31no—
181C4×C7C22×A411yescharacteristic, complemented
182Dic7—31no—
183Dic7C22×A411yescharacteristic, complemented
184C23×C3—282no—
185C2×A4—22no—
186C2×A4—72no—
187C2×A4—142no—
188C2×A4C22×D711yescharacteristic
189C3×D4—41no—
190C3×D4—281no—
191C3×D4—282no—
192C2×C3×C4—281no—
193C3×C7—41noHall
194C24—71no—
195C24—72no—
196C24—144no—
197C24—212no—
198C24—212no—
199C24—212no—
200C24—212no—
201C24—424no—
202C24C2×C3×D712yescomplemented
203C2×D4—31no—
204C2×D4—31no—
205C2×D4—32no—
206C2×D4—71no—
207C2×D4—211no—
208C2×D4—211no—
209C2×D4—212no—
210C2×D4—211no—
211C2×D4—212no—
212C2×D4—211no—
213C2×D4—212no—
214C2×D4—212no—
215C2×D4—212no—
216C2×D4—214no—
217C2×D4—214no—
218C2×D4—212no—
219C2×D4—212no—
220C2×D4—211no—
221C2×D4—212no—
222C2×D4—212no—
223C2×D4—212no—
224C22×C4—71no—
225C22×C4—211no—
226C22×C4—211no—
227C22×C4—211no—
228C22×C4—211no—
229C22×C4C2×C3×D711yescharacteristic, complemented
230C2×C7—22no—
231C2×C7—31no—
232C2×C7—31no—
233C2×C7—62no—
234C2×C7C23×A411yescharacteristic
235D7—22no—
236D7—32no—
237D7—62no—
238D7D4×A412yesdirect product factor
239C22×C3—42no—
240C22×C3—281no—
241C22×C3—282no—
242C22×C3—564no—
243A4D4×D711yescharacteristic, direct product factor
244C3×C4—41no—
245C3×C4—281no—
246C23—22no—
247C23—32no—
248C23—32no—
249C23—62no—
250C23—72no—
251C23—72no—
252C23—142no—
253C23—211no—
254C23—212no—
255C23—212no—
256C23—212no—
257C23—211no—
258C23—212no—
259C23—214no—
260C23—212no—
261C23—212no—
262C23—422no—
263C23—424no—
264C23—424no—
265C23—424no—
266C23—424no—
267C23—424no—
268C23—424no—
269C23—424no—
270C23—424no—
271C23C22×C3×D711yescharacteristic
272D4—32no—
273D4—32no—
274D4—31no—
275D4—72no—
276D4—71no—
277D4—212no—
278D4—212no—
279D4—212no—
280D4—212no—
281D4—214no—
282D4—212no—
283D4—211no—
284D4A4×D711yescharacteristic, direct product factor
285C2×C4—31no—
286C2×C4—31no—
287C2×C4—71no—
288C2×C4—211no—
289C2×C4—211no—
290C2×C4—212no—
291C2×C4—211no—
292C2×C4—211no—
293C2×C4—211no—
294C7C2×D4×A411yescharacteristic, complemented, Sylow
295C2×C3—41no—
296C2×C3—82no—
297C2×C3—282no—
298C2×C3—562no—
299C22—31no—
300C22—31no—
301C22—32no—
302C22—62no—
303C22—62no—
304C22—62no—
305C22—62no—
306C22—71no—
307C22—72no—
308C22—144no—
309C22—212no—
310C22—212no—
311C22—212no—
312C22—212no—
313C22—211no—
314C22—212no—
315C22—424no—
316C22—422no—
317C22—422no—
318C22—422no—
319C22—422no—
320C22—424no—
321C22—424no—
322C22—428no—
323C22C3×D4×D711yescharacteristic, complemented
324C22C2×A4×D712yescomplemented
325C4—31no—
326C4—71no—
327C4—211no—
328C4C2×A4×D711yescharacteristic, complemented
329C3—41noSylow
330C2—22no—
331C2—31no—
332C2—31no—
333C2—62no—
334C2—72no—
335C2—142no—
336C2—212no—
337C2—422no—
338C2C22×A4×D711yescharacteristic
subgroupG/H
center, FrattiniC2C22×A4×D7
commutator, socle, cosocleC23×C7C23×C3
FittingC22×C7×D4C2×C3
hypercenterD4A4×D7
hypocenterC22×C7C2×C3×D4
LCSG ▷ C23×C7 ▷ C22×C7
UCSC1 ◁ C2 ◁ D4

Complements

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

NH ≅ G/Ntype
1. C22×A4×D7C2semidirect
2. C7×D4×A4C2semidirect
3. A4×C22⋊D7C2semidirect
4. A4×D28C2semidirect
5. C4×A4×D7C2semidirect
6. C22×D4×D7C3semidirect
7. C22×C7×A4C22semidirect
10. C2×A4×D7C22semidirect
12. C4×C7×A4C22semidirect
13. A4×Dic7C22semidirect
14. C24×D7C2×C3semidirect
15. C22×C7×D4C2×C3semidirect
16. C22×C22⋊D7C2×C3semidirect
23. C22×D28C2×C3semidirect
24. C22×C4×D7C2×C3semidirect
30. A4×D7D4direct (N × H)
35. C24×C7C22×C3semidirect
43. C23×D7C22×C3semidirect
47. C22×C4×C7C22×C3semidirect
52. C22×Dic7C22×C3semidirect
63. D4×D7A4direct (N × H)
74. D4×A4D7direct (N × H)
80. C7×A4C2×D4semidirect
108. C22×D7C3×D4semidirect
109. C22×D7C2×A4semidirect
113. C7×D4C2×A4semidirect
120. C22⋊D7C2×A4semidirect
126. D28C2×A4semidirect
131. C4×D7C2×A4semidirect
135. C22×A4C2×D7semidirect
138. C4×A4C2×D7semidirect
152. C22×D4C3×D7semidirect
161. C22×C7C2×C3×D4semidirect
162. C22×C7C22×A4semidirect
179. C2×D7C22×A4semidirect
181. C4×C7C22×A4semidirect
183. Dic7C22×A4semidirect
202. C24C2×C3×D7semidirect
229. C22×C4C2×C3×D7semidirect
238. D7D4×A4direct (N × H)
243. A4D4×D7direct (N × H)
284. D4A4×D7direct (N × H)
294. C7C2×D4×A4semidirect
323. C22C3×D4×D7semidirect
324. C22C2×A4×D7semidirect
328. C4C2×A4×D7semidirect

Maximal subgroups

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

subgroupindex
C22×A4×D72
C7×D4×A42
A4×C22⋊D72
A4×D282
C4×A4×D72
C22×D4×D73
C3×D4×D74
C2×D4×A47