Finite Group Databasebeta

← C31×#7614 #21464373

Subgroups — C31×#7614 #21464373

Order 7936.

504 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2293C211yesmaximal, characteristic
2C31×#1831C211yesmaximal, characteristic, complemented
3C31×#1767C211yesmaximal, characteristic, complemented
4C31×#1271C212yesmaximal, complemented
5C31×#1270C212yesmaximal
6C2×C4×D4×C31C411yescharacteristic
7C2×C31×#117—21no—
8C2×C31×C4⋊C8—21no—
9C2×C31×C4⋊C8—21no—
10C2×C31×#97—21no—
11C31×#390C411yescharacteristic
12C31×#390C2211yescharacteristic
13C31×#389C411yescharacteristic
14C31×#389C2211yescharacteristic
15C31×#388—21no—
16C31×#388—21no—
17C4×C4⋊C4×C31C411yescharacteristic
18C4×C22⋊C4×C31—21no—
19C43×C31C2211yescharacteristic
20C31×#336—21no—
21C31×#336C2212yes—
22C31×#336C2212yes—
23C22×D4×C31C2×C411yescharacteristic
24C23×C4×C31—21no—
25C22×C8×C31—22no—
26C22×C8×C31—22no—
27C4×D4×C31—22no—
28C4×D4×C31—22no—
29C31×#117—42no—
30C31×#117—42no—
31C2×C4⋊C4×C31—21no—
32C2×C4⋊C4×C31—21no—
33C2×C4⋊C4×C31C2×C411yescharacteristic
34C2×C4⋊C4×C31C2×C411yescharacteristic
35C2×C4⋊C4×C31C2×C411yescharacteristic
36C2×C22⋊C4×C31—21no—
37C2×C22⋊C4×C31—21no—
38C2×C22⋊C4×C31—21no—
39C2×C22⋊C4×C31—21no—
40C2×C22⋊C4×C31—21no—
41C2×C42×C31—21no—
42C2×C42×C31C2×C411yescharacteristic
43C2×C42×C31C2×C411yescharacteristic
44C2×C42×C31D411yescharacteristic
45C2×C42×C31D411yescharacteristic
46C2×C42×C31D411yescharacteristic
47C2×C42×C31D411yescharacteristic
48C2×C42×C31C2311yescharacteristic
49C31×C4⋊C8—24no—
50C31×C4⋊C8—42no—
51C31×#97—42no—
52C31×#95—21no—
53C31×#95—21no—
54C31×#95—21no—
55C24×C31—21no—
56C2×D4×C31—21no—
57C2×D4×C31—41no—
58C2×D4×C31—41no—
59C2×D4×C31M1612yes—
60C22×C4×C31—24no—
61C22×C4×C31—21no—
62C22×C4×C31—21no—
63C22×C4×C31—21no—
64C22×C4×C31—42no—
65C22×C4×C31—42no—
66C22×C4×C31C22⋊C411yescharacteristic
67C22×C4×C31C22⋊C411yescharacteristic
68C22×C4×C31C22⋊C411yescharacteristic
69C22×C4×C31C22⋊C411yescharacteristic
70C22×C4×C31C22×C411yescharacteristic
71C22×C4×C31C2×D411yescharacteristic
72C22×C4×C31C2×D411yescharacteristic
73C2×C8×C31—24no—
74C2×C8×C31—42no—
75C2×C8×C31—42no—
76C2×C8×C31—42no—
77C2×C8×C31—42no—
78C2×C8×C31—42no—
79C4⋊C4×C31—21no—
80C4⋊C4×C31—41no—
81C4⋊C4×C31—41no—
82C4⋊C4×C31—42no—
83C4⋊C4×C31—41no—
84C4⋊C4×C31—41no—
85C4⋊C4×C31M1612yes—
86C22⋊C4×C31—24no—
87C22⋊C4×C31—42no—
88C22⋊C4×C31—42no—
89C22⋊C4×C31—41no—
90C22⋊C4×C31—41no—
91C22⋊C4×C31—41no—
92C22⋊C4×C31—41no—
93C42×C31—22no—
94C42×C31—21no—
95C42×C31—21no—
96C42×C31—21no—
97C42×C31—21no—
98C42×C31—41no—
99C42×C31—41no—
100C42×C31—41no—
101C42×C31—42no—
102C42×C31D812yes—
103C42×C31SD1612yes—
104#7614C3111yesmaximal, characteristic, direct product factor, Sylow
105C23×C31—22no—
106C23×C31—41no—
107C23×C31—41no—
108C23×C31—41no—
109C23×C31—41no—
110C23×C31—41no—
111C23×C31—41no—
112C23×C31C2×C22⋊C411yescharacteristic
113D4×C31—42no—
114D4×C31—42no—
115C2×C4×C31—21no—
116C2×C4×C31—21no—
117C2×C4×C31—21no—
118C2×C4×C31—21no—
119C2×C4×C31—21no—
120C2×C4×C31—21no—
121C2×C4×C31—21no—
122C2×C4×C31—21no—
123C2×C4×C31—21no—
124C2×C4×C31—21no—
125C2×C4×C31—21no—
126C2×C4×C31—21no—
127C2×C4×C31—21no—
128C2×C4×C31—22no—
129C2×C4×C31—21no—
130C2×C4×C31—21no—
131C2×C4×C31—48no—
132C2×C4×C31—41no—
133C2×C4×C31—41no—
134C2×C4×C31—41no—
135C2×C4×C31—41no—
136C2×C4×C31—41no—
137C2×C4×C31—41no—
138C2×C4×C31—41no—
139C2×C4×C31—41no—
140C2×C4×C31#10212yes—
141C2×C4×C31#10212yes—
142C2×C4×C31#10412yes—
143C2×C4×C31C2×M1611yescharacteristic
144C2×C4×C31C2×M1611yescharacteristic
145C2×C4×C31C2×D811yescharacteristic
146C2×C4×C31C2×SD1611yescharacteristic
147C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
148C2×C4×C31#13711yescharacteristic
149C8×C31—44no—
150C8×C31—82no—
151#2293C2×C3111yescharacteristic
152#1831C2×C3111yescharacteristic, complemented
153#1767C2×C3111yescharacteristic, complemented
154#1271C2×C3112yescomplemented
155#1270C2×C3112yes—
156C22×C31—42no—
157C22×C31—42no—
158C22×C31—42no—
159C22×C31—81no—
160C22×C31—81no—
161C22×C31—81no—
162C22×C31—81no—
163C22×C31#40711yescharacteristic
164C22×C31#41011yescharacteristic
165C22×C31#41311yescharacteristic
166C22×C31C2×#10211yescharacteristic
167C22×C31#41711yescharacteristic
168C22×C31C2×#10411yescharacteristic
169C22×C31#42111yescharacteristic
170C4×C31—22no—
171C4×C31—21no—
172C4×C31—21no—
173C4×C31—22no—
174C4×C31—21no—
175C4×C31—21no—
176C4×C31—21no—
177C4×C31—21no—
178C4×C31—22no—
179C4×C31—42no—
180C4×C31—41no—
181C4×C31—81no—
182C4×C31—81no—
183C2×C4×D4C4×C3111yescharacteristic
184C2×#117—21no—
185C2×C4⋊C8—21no—
186C2×C4⋊C8—21no—
187C2×#97—21no—
188#390C4×C3111yescharacteristic
189#390C22×C3111yescharacteristic
190#389C4×C3111yescharacteristic
191#389C22×C3111yescharacteristic
192#388—21no—
193#388—21no—
194C4×C4⋊C4C4×C3111yescharacteristic
195C4×C22⋊C4—21no—
196C43C22×C3111yescharacteristic
197#336—21no—
198#336C22×C3112yes—
199#336C22×C3112yes—
200C2×C31—82no—
201C2×C31#146411yescharacteristic
202C2×C31#148611yescharacteristic
203C2×C31#148911yescharacteristic
204C2×C31#150211yescharacteristic
205C2×C31#151211yescharacteristic
206C2×C31#153211yescharacteristic
207C2×C31#154711yescharacteristic
208C22×D4C2×C4×C3111yescharacteristic
209C23×C4—21no—
210C22×C8—22no—
211C22×C8—22no—
212C4×D4—22no—
213C4×D4—22no—
214#117—42no—
215#117—42no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4C2×C4×C3111yescharacteristic
219C2×C4⋊C4C2×C4×C3111yescharacteristic
220C2×C4⋊C4C2×C4×C3111yescharacteristic
221C2×C22⋊C4—21no—
222C2×C22⋊C4—21no—
223C2×C22⋊C4—21no—
224C2×C22⋊C4—21no—
225C2×C22⋊C4—21no—
226C2×C42—21no—
227C2×C42C2×C4×C3111yescharacteristic
228C2×C42C2×C4×C3111yescharacteristic
229C2×C42D4×C3111yescharacteristic
230C2×C42D4×C3111yescharacteristic
231C2×C42D4×C3111yescharacteristic
232C2×C42D4×C3111yescharacteristic
233C2×C42C23×C3111yescharacteristic
234C4⋊C8—24no—
235C4⋊C8—42no—
236#97—42no—
237#95—21no—
238#95—21no—
239#95—21no—
240C31#761411yescharacteristic, direct product factor, Sylow
241C24—21no—
242C2×D4—21no—
243C2×D4—41no—
244C2×D4—41no—
245C2×D4M16×C3112yes—
246C22×C4—24no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—42no—
251C22×C4—42no—
252C22×C4C22⋊C4×C3111yescharacteristic
253C22×C4C22⋊C4×C3111yescharacteristic
254C22×C4C22⋊C4×C3111yescharacteristic
255C22×C4C22⋊C4×C3111yescharacteristic
256C22×C4C22×C4×C3111yescharacteristic
257C22×C4C2×D4×C3111yescharacteristic
258C22×C4C2×D4×C3111yescharacteristic
259C2×C8—24no—
260C2×C8—42no—
261C2×C8—42no—
262C2×C8—42no—
263C2×C8—42no—
264C2×C8—42no—
265C4⋊C4—21no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—42no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4M16×C3112yes—
272C22⋊C4—24no—
273C22⋊C4—42no—
274C22⋊C4—42no—
275C22⋊C4—41no—
276C22⋊C4—41no—
277C22⋊C4—41no—
278C22⋊C4—41no—
279C42—22no—
280C42—21no—
281C42—21no—
282C42—21no—
283C42—21no—
284C42—41no—
285C42—41no—
286C42—41no—
287C42—42no—
288C42D8×C3112yes—
289C42SD16×C3112yes—
290C23—22no—
291C23—41no—
292C23—41no—
293C23—41no—
294C23—41no—
295C23—41no—
296C23—41no—
297C23C2×C22⋊C4×C3111yescharacteristic
298D4—42no—
299D4—42no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—22no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—48no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4C31×#10212yes—
326C2×C4C31×#10212yes—
327C2×C4C31×#10412yes—
328C2×C4C2×M16×C3111yescharacteristic
329C2×C4C2×M16×C3111yescharacteristic
330C2×C4C2×D8×C3111yescharacteristic
331C2×C4C2×SD16×C3111yescharacteristic
332C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
333C2×C4C31×#13711yescharacteristic
334C8—44no—
335C8—82no—
336C22—42no—
337C22—42no—
338C22—42no—
339C22—81no—
340C22—81no—
341C22—81no—
342C22—81no—
343C22C31×#40711yescharacteristic
344C22C31×#41011yescharacteristic
345C22C31×#41311yescharacteristic
346C22C2×C31×#10211yescharacteristic
347C22C31×#41711yescharacteristic
348C22C2×C31×#10411yescharacteristic
349C22C31×#42111yescharacteristic
350C4—22no—
351C4—21no—
352C4—21no—
353C4—22no—
354C4—21no—
355C4—21no—
356C4—21no—
357C4—21no—
358C4—22no—
359C4—42no—
360C4—41no—
361C4—81no—
362C4—81no—
363C2—82no—
364C2C31×#146411yescharacteristic
365C2C31×#148611yescharacteristic
366C2C31×#148911yescharacteristic
367C2C31×#150211yescharacteristic
368C2C31×#151211yescharacteristic
369C2C31×#153211yescharacteristic
370C2C31×#154711yescharacteristic
subgroupG/H
center, socleC23×C31C2×C22⋊C4
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC22×D4×C31C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C43×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#1831C2semidirect
3. C31×#1767C2semidirect
4. C31×#1271C2semidirect
104. #7614C31direct (N × H)
152. #1831C2×C31semidirect
153. #1767C2×C31semidirect
154. #1271C2×C31semidirect
240. C31#7614direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#22932
C31×#18312
C31×#17672
C31×#12712
C31×#12702
#761431