Finite Group Databasebeta

← C2×C4×C31×#103 #21477166

Subgroups — C2×C4×C31×#103 #21477166

Order 7936.

1726 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Q8×C31C211yesmaximal, characteristic
2C22×C31×#103C212yesmaximal
3C22×C4×C8×C31C211yesmaximal, characteristic
4C2×C4×C4⋊C4×C31C211yesmaximal, characteristic
5C4×C31×#103C218yesmaximal, direct product factor
6C2×C31×#340C212yesmaximal
7C23×Q8×C31C2211yescharacteristic
8C23×C8×C31C2212yes—
9C2×C4×Q8×C31—24no—
10C2×C4×Q8×C31—22no—
11C2×C4×Q8×C31C418yescomplemented
12C2×C4×Q8×C31C2214yes—
13C22×C4⋊C4×C31—21no—
14C22×C4⋊C4×C31C2212yes—
15C22×C4⋊C4×C31C2211yescharacteristic
16C22×C42×C31—21no—
17C22×C42×C31—21no—
18C22×C42×C31C2211yescharacteristic
19C2×C31×#103C4116yesdirect product factor
20C2×C31×#103C2218yes—
21C2×C4×C8×C31—24no—
22C2×C4×C8×C31C2214yes—
23C4×C4⋊C4×C31—22no—
24C4×C4⋊C4×C31C2214yes—
25C2×C31×#95—21no—
26C31×#340C2218yes—
27C22×Q8×C31—22no—
28C22×Q8×C31—21no—
29C22×Q8×C31—24no—
30C22×Q8×C31C2×C418yes—
31C22×Q8×C31C2×C414yes—
32C22×Q8×C31C2312yes—
33C23×C4×C31—21no—
34C23×C4×C31—21no—
35C23×C4×C31—22no—
36C23×C4×C31D411yescharacteristic
37C23×C4×C31D411yescharacteristic
38C23×C4×C31C2311yescharacteristic
39C22×C8×C31—24no—
40C22×C8×C31—24no—
41C22×C8×C31C2×C418yes—
42C22×C8×C31C2314yes—
43C4×Q8×C31—216no—
44C4×Q8×C31—28no—
45C4×Q8×C31C2×C4116yescomplemented
46C2×C4⋊C4×C31—28no—
47C2×C4⋊C4×C31—24no—
48C2×C4⋊C4×C31—21no—
49C2×C4⋊C4×C31—22no—
50C2×C4⋊C4×C31—22no—
51C2×C4⋊C4×C31—24no—
52C2×C4⋊C4×C31C2×C418yes—
53C2×C4⋊C4×C31C2×C414yes—
54C2×C4⋊C4×C31C2314yes—
55C2×C4⋊C4×C31C2312yes—
56C2×C42×C31—28no—
57C2×C42×C31—24no—
58C2×C42×C31—24no—
59C2×C42×C31—44no—
60C2×C42×C31C2×C414yes—
61C2×C42×C31D412yes—
62C2×C42×C31D414yes—
63C2×C42×C31C2312yes—
64C31×#103C2×C4132yesdirect product factor
65C4×C8×C31—28no—
66C31×#95—24no—
67C24×C31C2×D411yescharacteristic
68C2×Q8×C31—24no—
69C2×Q8×C31—28no—
70C2×Q8×C31—28no—
71C2×Q8×C31—216no—
72C2×Q8×C31—22no—
73C2×Q8×C31—24no—
74C2×Q8×C31C42116yescomplemented
75C2×Q8×C31C22×C418yes—
76C2×Q8×C31C22×C414yes—
77C22×C4×C31—24no—
78C22×C4×C31—28no—
79C22×C4×C31—24no—
80C22×C4×C31—22no—
81C22×C4×C31—24no—
82C22×C4×C31—28no—
83C22×C4×C31—24no—
84C22×C4×C31—22no—
85C22×C4×C31—44no—
86C22×C4×C31—44no—
87C22×C4×C31—44no—
88C22×C4×C31C22⋊C414yes—
89C22×C4×C31C22⋊C414yes—
90C22×C4×C31SD1614yes—
91C22×C4×C31Q1614yes—
92C22×C4×C31C22×C412yes—
93C22×C4×C31C22×C414yes—
94C22×C4×C31C2×D412yes—
95C22×C4×C31C2×D411yescharacteristic
96C22×C4×C31C2×D412yes—
97C22×C4×C31C2×D412yes—
98C22×C4×C31#4114yes—
99C22×C4×C31C2411yescharacteristic
100C2×C8×C31—216no—
101C2×C8×C31—24no—
102C2×C8×C31—24no—
103C2×C8×C31C22×C418yes—
104C4⋊C4×C31—216no—
105C4⋊C4×C31—24no—
106C4⋊C4×C31—28no—
107C4⋊C4×C31—22no—
108C4⋊C4×C31—24no—
109C4⋊C4×C31C22×C418yes—
110C4⋊C4×C31C22×C414yes—
111C42×C31—216no—
112C42×C31—48no—
113C42×C31C22⋊C418yes—
114C42×C31C22×C414yes—
115C42×C31C2×D414yes—
116C2×C4×#103C3111yesmaximal, characteristic, direct product factor, Sylow
117C23×C31C2×C22⋊C412yes—
118C23×C31C4×D414yes—
119C23×C31C2×SD1612yes—
120C23×C31C2×Q1612yes—
121C23×C31#13514yes—
122C23×C31C22×D411yescharacteristic
123Q8×C31—24no—
124Q8×C31—28no—
125Q8×C31—216no—
126Q8×C31C2×C4218yescomplemented
127C2×C4×C31—24no—
128C2×C4×C31—28no—
129C2×C4×C31—24no—
130C2×C4×C31—216no—
131C2×C4×C31—28no—
132C2×C4×C31—24no—
133C2×C4×C31—28no—
134C2×C4×C31—44no—
135C2×C4×C31—44no—
136C2×C4×C31—44no—
137C2×C4×C31—48no—
138C2×C4×C31—416no—
139C2×C4×C31#103116yesdirect product factor
140C2×C4×C31C2×C4214yes—
141C2×C4×C31C2×C22⋊C414yes—
142C2×C4×C31C2×C22⋊C412yes—
143C2×C4×C31C2×C22⋊C414yes—
144C2×C4×C31#11714yes—
145C2×C4×C31C4×D418yes—
146C2×C4×C31C4×D414yes—
147C2×C4×C31C2×SD1614yes—
148C2×C4×C31C2×Q1614yes—
149C2×C4×C31C23×C411yescharacteristic
150C2×C4×C31C23×C412yes—
151C2×C4×C31C22×D411yescharacteristic
152C2×C4×C31C2×#4112yes—
153C8×C31—28no—
154C22×C4×Q8C2×C3111yescharacteristic
155C22×#103C2×C3112yes—
156C22×C4×C8C2×C3111yescharacteristic
157C2×C4×C4⋊C4C2×C3111yescharacteristic
158C4×#103C2×C3118yesdirect product factor
159C2×#340C2×C3112yes—
160C22×C31C4×C22⋊C414yes—
161C22×C31C2×#10314yes—
162C22×C31#41614yes—
163C22×C31C4×SD1618yes—
164C22×C31C4×Q1618yes—
165C22×C31C22×C22⋊C411yescharacteristic
166C22×C31C2×C4×D412yes—
167C22×C31C22×SD1611yescharacteristic
168C22×C31C22×Q1611yescharacteristic
169C22×C31C2×#13512yes—
170C4×C31—24no—
171C4×C31—28no—
172C4×C31—44no—
173C4×C31—48no—
174C4×C31C4×C22⋊C414yes—
175C4×C31C2×#10318yesdirect product factor
176C4×C31C22×C4211yescharacteristic
177C4×C31C2×#11711yescharacteristic
178C4×C31C2×C4×D412yes—
179C23×Q8C22×C3111yescharacteristic
180C23×C8C22×C3112yes—
181C2×C4×Q8—24no—
182C2×C4×Q8—22no—
183C2×C4×Q8C4×C3118yescomplemented
184C2×C4×Q8C22×C3114yes—
185C22×C4⋊C4—21no—
186C22×C4⋊C4C22×C3112yes—
187C22×C4⋊C4C22×C3111yescharacteristic
188C22×C42—21no—
189C22×C42—21no—
190C22×C42C22×C3111yescharacteristic
191C2×#103C4×C31116yesdirect product factor
192C2×#103C22×C3118yes—
193C2×C4×C8—24no—
194C2×C4×C8C22×C3114yes—
195C4×C4⋊C4—22no—
196C4×C4⋊C4C22×C3114yes—
197C2×#95—21no—
198#340C22×C3118yes—
199C2×C31C4×#10318yesdirect product factor
200C2×C31C2×C4×C22⋊C411yescharacteristic
201C2×C31C22×#10311yescharacteristic
202C2×C31C2×#41611yescharacteristic
203C2×C31C2×C4×SD1612yes—
204C2×C31C2×C4×Q1612yes—
205C22×Q8—22no—
206C22×Q8—21no—
207C22×Q8—24no—
208C22×Q8C2×C4×C3114yes—
209C22×Q8C2×C4×C3118yes—
210C22×Q8C23×C3112yes—
211C23×C4—21no—
212C23×C4—21no—
213C23×C4—22no—
214C23×C4D4×C3111yescharacteristic
215C23×C4D4×C3111yescharacteristic
216C23×C4C23×C3111yescharacteristic
217C22×C8—24no—
218C22×C8—24no—
219C22×C8C2×C4×C3118yes—
220C22×C8C23×C3114yes—
221C4×Q8—216no—
222C4×Q8—28no—
223C4×Q8C2×C4×C31116yescomplemented
224C2×C4⋊C4—28no—
225C2×C4⋊C4—24no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—22no—
228C2×C4⋊C4—22no—
229C2×C4⋊C4—24no—
230C2×C4⋊C4C2×C4×C3114yes—
231C2×C4⋊C4C2×C4×C3118yes—
232C2×C4⋊C4C23×C3112yes—
233C2×C4⋊C4C23×C3114yes—
234C2×C42—28no—
235C2×C42—24no—
236C2×C42—24no—
237C2×C42—44no—
238C2×C42C2×C4×C3114yes—
239C2×C42D4×C3112yes—
240C2×C42D4×C3114yes—
241C2×C42C23×C3112yes—
242#103C2×C4×C31132yesdirect product factor
243C4×C8—28no—
244#95—24no—
245C31C2×C4×#10311yescharacteristic, direct product factor, Sylow
246C24C2×D4×C3111yescharacteristic
247C2×Q8—24no—
248C2×Q8—28no—
249C2×Q8—28no—
250C2×Q8—216no—
251C2×Q8—22no—
252C2×Q8—24no—
253C2×Q8C42×C31116yescomplemented
254C2×Q8C22×C4×C3118yes—
255C2×Q8C22×C4×C3114yes—
256C22×C4—24no—
257C22×C4—28no—
258C22×C4—24no—
259C22×C4—22no—
260C22×C4—24no—
261C22×C4—28no—
262C22×C4—24no—
263C22×C4—22no—
264C22×C4—44no—
265C22×C4—44no—
266C22×C4—44no—
267C22×C4C22⋊C4×C3114yes—
268C22×C4C22⋊C4×C3114yes—
269C22×C4SD16×C3114yes—
270C22×C4Q16×C3114yes—
271C22×C4C22×C4×C3112yes—
272C22×C4C22×C4×C3114yes—
273C22×C4C2×D4×C3112yes—
274C22×C4C2×D4×C3111yescharacteristic
275C22×C4C2×D4×C3112yes—
276C22×C4C2×D4×C3112yes—
277C22×C4#41×C3114yes—
278C22×C4C24×C3111yescharacteristic
279C2×C8—216no—
280C2×C8—24no—
281C2×C8—24no—
282C2×C8C22×C4×C3118yes—
283C4⋊C4—216no—
284C4⋊C4—24no—
285C4⋊C4—28no—
286C4⋊C4—22no—
287C4⋊C4—24no—
288C4⋊C4C22×C4×C3118yes—
289C4⋊C4C22×C4×C3114yes—
290C42—216no—
291C42—48no—
292C42C22⋊C4×C3118yes—
293C42C22×C4×C3114yes—
294C42C2×D4×C3114yes—
295C23C2×C22⋊C4×C3112yes—
296C23C4×D4×C3114yes—
297C23C2×SD16×C3112yes—
298C23C2×Q16×C3112yes—
299C23C31×#13514yes—
300C23C22×D4×C3111yescharacteristic
301Q8—24no—
302Q8—28no—
303Q8—216no—
304Q8C2×C42×C3118yescomplemented
305C2×C4—28no—
306C2×C4—24no—
307C2×C4—28no—
308C2×C4—24no—
309C2×C4—216no—
310C2×C4—24no—
311C2×C4—28no—
312C2×C4—48no—
313C2×C4—416no—
314C2×C4—44no—
315C2×C4—44no—
316C2×C4—44no—
317C2×C4C31×#103116yesdirect product factor
318C2×C4C2×C42×C3114yes—
319C2×C4C2×C22⋊C4×C3114yes—
320C2×C4C2×C22⋊C4×C3114yes—
321C2×C4C2×C22⋊C4×C3112yes—
322C2×C4C31×#11714yes—
323C2×C4C4×D4×C3118yes—
324C2×C4C4×D4×C3114yes—
325C2×C4C2×SD16×C3114yes—
326C2×C4C2×Q16×C3114yes—
327C2×C4C23×C4×C3111yescharacteristic
328C2×C4C23×C4×C3112yes—
329C2×C4C22×D4×C3111yescharacteristic
330C2×C4C2×#41×C3112yes—
331C8—28no—
332C22C4×C22⋊C4×C3114yes—
333C22C2×C31×#10314yes—
334C22C31×#41614yes—
335C22C4×SD16×C3118yes—
336C22C4×Q16×C3118yes—
337C22C22×C22⋊C4×C3111yescharacteristic
338C22C2×C4×D4×C3112yes—
339C22C22×SD16×C3111yescharacteristic
340C22C22×Q16×C3111yescharacteristic
341C22C2×C31×#13512yes—
342C4—24no—
343C4—28no—
344C4—44no—
345C4—48no—
346C4C4×C22⋊C4×C3114yes—
347C4C2×C31×#10318yesdirect product factor
348C4C22×C42×C3111yescharacteristic
349C4C2×C31×#11711yescharacteristic
350C4C2×C4×D4×C3112yes—
351C2C4×C31×#10318yesdirect product factor
352C2C2×C4×C22⋊C4×C3111yescharacteristic
353C2C22×C31×#10311yescharacteristic
354C2C2×C31×#41611yescharacteristic
355C2C2×C4×SD16×C3112yes—
356C2C2×C4×Q16×C3112yes—
subgroupG/H
centerC23×C4×C31D4
commutatorC4C22×C42×C31
Frattini, cosocleC22×C4C24×C31
socle, prime radicalC24×C31C2×D4
LCSG ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C4×C31 ◁ C22×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
5. C4×C31×#103C2direct (N × H)
11. C2×C4×Q8×C31C4semidirect
19. C2×C31×#103C4direct (N × H)
45. C4×Q8×C31C2×C4semidirect
64. C31×#103C2×C4direct (N × H)
74. C2×Q8×C31C42semidirect
116. C2×C4×#103C31direct (N × H)
126. Q8×C31C2×C42semidirect
139. C2×C4×C31#103direct (N × H)
158. C4×#103C2×C31direct (N × H)
175. C4×C31C2×#103direct (N × H)
183. C2×C4×Q8C4×C31semidirect
191. C2×#103C4×C31direct (N × H)
199. C2×C31C4×#103direct (N × H)
223. C4×Q8C2×C4×C31semidirect
242. #103C2×C4×C31direct (N × H)
245. C31C2×C4×#103direct (N × H)
253. C2×Q8C42×C31semidirect
304. Q8C2×C42×C31semidirect
317. C2×C4C31×#103direct (N × H)
347. C4C2×C31×#103direct (N × H)
351. C2C4×C31×#103direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×Q8×C312
C22×C31×#1032
C22×C4×C8×C312
C2×C4×C4⋊C4×C312
C4×C31×#1032
C2×C31×#3402
C2×C4×#10331