Finite Group Databasebeta

← C2×C31×#1407 #21470335

Subgroups — C2×C31×#1407 #21470335

Order 7936.

416 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 94 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
1C2×C31×#497C211yesmaximal, characteristic
2C2×C31×#355C211yesmaximal, characteristic
3C2×C31×#354C211yesmaximal, characteristic
4C31×#1407C214yesmaximal, direct product factor
5C22×Q16×C31—21no—
6C22×SD16×C31—21no—
7C2×C31×C4⋊Q8C411yescharacteristic, complemented
8C2×C31×#124C2211yescharacteristic
9C31×#497—21no—
10C31×#497—21no—
11C31×#497C412yescomplemented
12C31×#497C2212yes—
13C2×C31×#101—21no—
14C2×C31×#99—21no—
15C2×C31×#97C411yescharacteristic, complemented
16C31×#355—21no—
17C31×#355C2212yes—
18C31×#354—21no—
19C31×#354C2212yes—
20C22×Q8×C31—21no—
21C22×Q8×C31D411yescharacteristic
22C22×D4×C31D411yescharacteristic
23C2×Q16×C31—22no—
24C2×Q16×C31—22no—
25C2×Q16×C31—42no—
26C2×Q16×C31—42no—
27C2×SD16×C31—22no—
28C2×SD16×C31—22no—
29C2×SD16×C31—42no—
30C2×SD16×C31—42no—
31C2×M16×C31—41no—
32C22×C8×C31—21no—
33C31×C4⋊Q8—21no—
34C31×C4⋊Q8—41no—
35C31×C4⋊Q8C2×C412yescomplemented
36C31×#124—41no—
37C31×#124C2×C411yescharacteristic
38C31×#124D411yescharacteristic
39C31×#124D411yescharacteristic
40C31×#124C2311yescharacteristic
41C2×C4⋊C4×C31—41no—
42C2×C22⋊C4×C31—41no—
43C2×C22⋊C4×C31—41no—
44C2×C42×C31C2×C411yescharacteristic
45C31×#101—22no—
46C31×#101—41no—
47C31×#99—22no—
48C31×#99—41no—
49C31×#97—21no—
50C31×#97C2×C412yescomplemented
51C24×C31—21no—
52C2×Q8×C31—21no—
53C2×Q8×C31—22no—
54C2×Q8×C31—41no—
55C2×Q8×C31—41no—
56C2×Q8×C31—41no—
57C2×Q8×C31—41no—
58C2×Q8×C31—41no—
59C2×Q8×C31—41no—
60C2×Q8×C31—41no—
61C2×Q8×C31C22⋊C411yescharacteristic
62C2×Q8×C31C2×D411yescharacteristic
63C2×D4×C31—21no—
64C2×D4×C31—41no—
65C2×D4×C31—41no—
66C2×D4×C31C22⋊C411yescharacteristic
67C2×D4×C31C2×D411yescharacteristic
68C22×C4×C31—21no—
69C22×C4×C31—21no—
70C22×C4×C31—41no—
71C22×C4×C31—81no—
72C22×C4×C31C22⋊C411yescharacteristic
73Q16×C31—44no—
74Q16×C31—44no—
75SD16×C31—44no—
76SD16×C31—44no—
77M16×C31—42no—
78M16×C31—81no—
79C2×C8×C31—22no—
80C2×C8×C31—22no—
81C2×C8×C31—22no—
82C2×C8×C31—81no—
83C4⋊C4×C31—42no—
84C4⋊C4×C31—42no—
85C22⋊C4×C31—41no—
86C22⋊C4×C31—41no—
87C22⋊C4×C31—41no—
88C22⋊C4×C31—41no—
89C22⋊C4×C31—42no—
90C22⋊C4×C31—81no—
91C42×C31—21no—
92C42×C31C22⋊C411yescharacteristic
93C42×C31C22×C411yescharacteristic
94C2×#1407C3111yesmaximal, characteristic, direct product factor, Sylow
95C23×C31—21no—
96C23×C31—21no—
97C23×C31—41no—
98C23×C31—41no—
99C23×C31—82no—
100C23×C31#9911yescharacteristic
101Q8×C31—41no—
102Q8×C31—41no—
103Q8×C31—42no—
104Q8×C31—42no—
105Q8×C31—81no—
106Q8×C31—81no—
107Q8×C31—81no—
108D4×C31—41no—
109D4×C31—41no—
110D4×C31—81no—
111C2×C4×C31—21no—
112C2×C4×C31—21no—
113C2×C4×C31—21no—
114C2×C4×C31—21no—
115C2×C4×C31—21no—
116C2×C4×C31—21no—
117C2×C4×C31—42no—
118C2×C4×C31—41no—
119C2×C4×C31—41no—
120C2×C4×C31—42no—
121C2×C4×C31—81no—
122C2×C4×C31—81no—
123C2×C4×C31—82no—
124C2×C4×C31—162no—
125C2×C4×C31#9911yescharacteristic
126C2×C4×C31C2×C22⋊C411yescharacteristic
127C8×C31—24no—
128C8×C31—82no—
129C2×#497C2×C3111yescharacteristic
130C2×#355C2×C3111yescharacteristic
131C2×#354C2×C3111yescharacteristic
132#1407C2×C3114yesdirect product factor
133C22×C31—22no—
134C22×C31—41no—
135C22×C31—41no—
136C22×C31—81no—
137C22×C31—81no—
138C22×C31—82no—
139C22×C31—161no—
140C22×C31#35311yescharacteristic
141C22×C31#35311yescharacteristic
142C22×C31C2×#9911yescharacteristic
143C4×C31—21no—
144C4×C31—21no—
145C4×C31—41no—
146C4×C31—41no—
147C4×C31—41no—
148C4×C31—41no—
149C4×C31—82no—
150C4×C31—162no—
151C22×Q16—21no—
152C22×SD16—21no—
153C2×C4⋊Q8C4×C3111yescharacteristic, complemented
154C2×#124C22×C3111yescharacteristic
155#497—21no—
156#497—21no—
157#497C4×C3112yescomplemented
158#497C22×C3112yes—
159C2×#101—21no—
160C2×#99—21no—
161C2×#97C4×C3111yescharacteristic, complemented
162#355—21no—
163#355C22×C3112yes—
164#354—21no—
165#354C22×C3112yes—
166C2×C31—21no—
167C2×C31—21no—
168C2×C31—81no—
169C2×C31—81no—
170C2×C31#140712yesdirect product factor
171C2×C31C2×#35311yescharacteristic
172C22×Q8—21no—
173C22×Q8D4×C3111yescharacteristic
174C22×D4D4×C3111yescharacteristic
175C2×Q16—22no—
176C2×Q16—22no—
177C2×Q16—42no—
178C2×Q16—42no—
179C2×SD16—22no—
180C2×SD16—22no—
181C2×SD16—42no—
182C2×SD16—42no—
183C2×M16—41no—
184C22×C8—21no—
185C4⋊Q8—21no—
186C4⋊Q8—41no—
187C4⋊Q8C2×C4×C3112yescomplemented
188#124—41no—
189#124C2×C4×C3111yescharacteristic
190#124D4×C3111yescharacteristic
191#124D4×C3111yescharacteristic
192#124C23×C3111yescharacteristic
193C2×C4⋊C4—41no—
194C2×C22⋊C4—41no—
195C2×C22⋊C4—41no—
196C2×C42C2×C4×C3111yescharacteristic
197#101—22no—
198#101—41no—
199#99—22no—
200#99—41no—
201#97—21no—
202#97C2×C4×C3112yescomplemented
203C31C2×#140711yescharacteristic, direct product factor, Sylow
204C24—21no—
205C2×Q8—21no—
206C2×Q8—22no—
207C2×Q8—41no—
208C2×Q8—41no—
209C2×Q8—41no—
210C2×Q8—41no—
211C2×Q8—41no—
212C2×Q8—41no—
213C2×Q8—41no—
214C2×Q8C22⋊C4×C3111yescharacteristic
215C2×Q8C2×D4×C3111yescharacteristic
216C2×D4—21no—
217C2×D4—41no—
218C2×D4—41no—
219C2×D4C22⋊C4×C3111yescharacteristic
220C2×D4C2×D4×C3111yescharacteristic
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—41no—
224C22×C4—81no—
225C22×C4C22⋊C4×C3111yescharacteristic
226Q16—44no—
227Q16—44no—
228SD16—44no—
229SD16—44no—
230M16—42no—
231M16—81no—
232C2×C8—22no—
233C2×C8—22no—
234C2×C8—22no—
235C2×C8—81no—
236C4⋊C4—42no—
237C4⋊C4—42no—
238C22⋊C4—41no—
239C22⋊C4—41no—
240C22⋊C4—41no—
241C22⋊C4—41no—
242C22⋊C4—42no—
243C22⋊C4—81no—
244C42—21no—
245C42C22⋊C4×C3111yescharacteristic
246C42C22×C4×C3111yescharacteristic
247C23—21no—
248C23—21no—
249C23—41no—
250C23—41no—
251C23—82no—
252C23C31×#9911yescharacteristic
253Q8—41no—
254Q8—41no—
255Q8—42no—
256Q8—42no—
257Q8—81no—
258Q8—81no—
259Q8—81no—
260D4—41no—
261D4—41no—
262D4—81no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—42no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—42no—
273C2×C4—81no—
274C2×C4—81no—
275C2×C4—82no—
276C2×C4—162no—
277C2×C4C31×#9911yescharacteristic
278C2×C4C2×C22⋊C4×C3111yescharacteristic
279C8—24no—
280C8—82no—
281C22—22no—
282C22—41no—
283C22—41no—
284C22—81no—
285C22—81no—
286C22—82no—
287C22—161no—
288C22C31×#35311yescharacteristic
289C22C31×#35311yescharacteristic
290C22C2×C31×#9911yescharacteristic
291C4—21no—
292C4—21no—
293C4—41no—
294C4—41no—
295C4—41no—
296C4—41no—
297C4—82no—
298C4—162no—
299C2—21no—
300C2—21no—
301C2—81no—
302C2—81no—
303C2C31×#140712yesdirect product factor
304C2C2×C31×#35311yescharacteristic
subgroupG/H
center, socleC22×C31#353
commutatorC42C22×C4×C31
Frattini, cosocle#124C23×C31
prime radicalC22×D4×C31D4
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C31 ◁ C22×C4×C31 ◁ C2×C31×#124 ◁ G

Complements

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

NH ≅ G/Ntype
4. C31×#1407C2direct (N × H)
7. C2×C31×C4⋊Q8C4semidirect
11. C31×#497C4semidirect
15. C2×C31×#97C4semidirect
35. C31×C4⋊Q8C2×C4semidirect
50. C31×#97C2×C4semidirect
94. C2×#1407C31direct (N × H)
132. #1407C2×C31direct (N × H)
153. C2×C4⋊Q8C4×C31semidirect
157. #497C4×C31semidirect
161. C2×#97C4×C31semidirect
170. C2×C31#1407direct (N × H)
187. C4⋊Q8C2×C4×C31semidirect
202. #97C2×C4×C31semidirect
203. C31C2×#1407direct (N × H)
303. C2C31×#1407direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4972
C2×C31×#3552
C2×C31×#3542
C31×#14072
C2×#140731