Finite Group Databasebeta

← C31×#9156 #21465915

Subgroups — C31×#9156 #21465915

Order 7936.

692 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2854C211yesmaximal, characteristic
2C2×C31×#382C211yesmaximal, characteristic, complemented
3C31×#1817C211yesmaximal, characteristic, complemented
4C2×C31×#327C212yesmaximal
5C31×#1294C212yesmaximal, complemented
6C2×C31×#123—21no—
7C2×C31×#121C2211yescharacteristic
8C22×C4⋊C4×C31—21no—
9C22×C42×C31C2211yescharacteristic
10C2×C31×C22⋊C8C2212yes—
11C31×#390C412yescomplemented
12C31×#389C412yescomplemented
13C31×#388—22no—
14C31×#386—21no—
15C31×#382—24no—
16C31×#380C2211yescharacteristic
17C2×C31×#95—21no—
18C2×C31×#95C2212yes—
19C31×#336—22no—
20C31×#327—24no—
21C22×D4×C31—21no—
22C22×D4×C31C2×C411yescharacteristic
23C23×C4×C31—22no—
24C23×C4×C31D411yescharacteristic
25C23×C4×C31D411yescharacteristic
26C23×C4×C31C2311yescharacteristic
27C22×C8×C31—22no—
28C31×#123—42no—
29C31×#123—42no—
30C31×#121—22no—
31C31×#121—22no—
32C2×C4⋊C4×C31—24no—
33C2×C4⋊C4×C31—22no—
34C2×C4⋊C4×C31—42no—
35C2×C4⋊C4×C31—42no—
36C2×C4⋊C4×C31C2×C411yescharacteristic
37C2×C4⋊C4×C31C2×C412yes—
38C2×C22⋊C4×C31—21no—
39C2×C22⋊C4×C31—22no—
40C2×C22⋊C4×C31—22no—
41C2×C22⋊C4×C31—21no—
42C2×C42×C31—22no—
43C2×C42×C31—22no—
44C2×C42×C31C2×C412yes—
45C2×C42×C31D412yes—
46C31×C22⋊C8—22no—
47C31×C22⋊C8—22no—
48C31×#95—24no—
49C31×#95—22no—
50C31×#95—22no—
51C31×#95—21no—
52C31×#95D414yes—
53C24×C31—21no—
54C24×C31C2×D411yescharacteristic
55C2×D4×C31—22no—
56C2×D4×C31—42no—
57C2×D4×C31—41no—
58C2×D4×C31—41no—
59C2×D4×C31—41no—
60C2×D4×C31—41no—
61C2×D4×C31—41no—
62C2×D4×C31—41no—
63C22×C4×C31—21no—
64C22×C4×C31—21no—
65C22×C4×C31—21no—
66C22×C4×C31—21no—
67C22×C4×C31—21no—
68C22×C4×C31—21no—
69C22×C4×C31—22no—
70C22×C4×C31—21no—
71C22×C4×C31—24no—
72C22×C4×C31—42no—
73C22×C4×C31—42no—
74C22×C4×C31—44no—
75C22×C4×C31—44no—
76C22×C4×C31—42no—
77C22×C4×C31—42no—
78C22×C4×C31C22⋊C412yes—
79C22×C4×C31C22⋊C412yes—
80C22×C4×C31D812yes—
81C22×C4×C31SD1612yes—
82C22×C4×C31C22×C411yescharacteristic
83C22×C4×C31C2×D411yescharacteristic
84C22×C4×C31C2×D412yes—
85C22×C4×C31#4112yes—
86C2×C8×C31—44no—
87C2×C8×C31—42no—
88C4⋊C4×C31—22no—
89C4⋊C4×C31—48no—
90C4⋊C4×C31—42no—
91C4⋊C4×C31—44no—
92C22⋊C4×C31—44no—
93C22⋊C4×C31—41no—
94C22⋊C4×C31—41no—
95C22⋊C4×C31—44no—
96C22⋊C4×C31—42no—
97C42×C31—24no—
98C42×C31—24no—
99#9156C3111yesmaximal, characteristic, direct product factor, Sylow
100C23×C31—22no—
101C23×C31—22no—
102C23×C31—41no—
103C23×C31—42no—
104C23×C31—41no—
105C23×C31—41no—
106C23×C31—42no—
107C23×C31C2×C22⋊C411yescharacteristic
108C23×C31#12011yescharacteristic
109C23×C31#12311yescharacteristic
110C23×C31C2×D811yescharacteristic
111C23×C31C2×SD1611yescharacteristic
112C23×C31AGL(1,ℤ/8)11yescharacteristic
113C23×C31#13711yescharacteristic
114D4×C31—82no—
115D4×C31—81no—
116D4×C31—81no—
117D4×C31—81no—
118D4×C31—81no—
119C2×C4×C31—22no—
120C2×C4×C31—22no—
121C2×C4×C31—22no—
122C2×C4×C31—22no—
123C2×C4×C31—22no—
124C2×C4×C31—22no—
125C2×C4×C31—22no—
126C2×C4×C31—22no—
127C2×C4×C31—22no—
128C2×C4×C31—22no—
129C2×C4×C31—22no—
130C2×C4×C31—42no—
131C2×C4×C31—42no—
132C2×C4×C31—42no—
133C2×C4×C31—42no—
134C2×C4×C31—44no—
135C2×C4×C31—44no—
136C2×C4×C31—41no—
137C2×C4×C31—42no—
138C2×C4×C31—42no—
139C2×C4×C31—41no—
140C2×C4×C31—41no—
141C2×C4×C31—42no—
142C2×C4×C31—44no—
143C2×C4×C31—84no—
144C2×C4×C31—84no—
145C2×C4×C31#10214yes—
146C2×C4×C31C4×D412yes—
147C2×C4×C31#12112yes—
148C8×C31—82no—
149#2854C2×C3111yescharacteristic
150C2×#382C2×C3111yescharacteristic, complemented
151#1817C2×C3111yescharacteristic, complemented
152C2×#327C2×C3112yes—
153#1294C2×C3112yescomplemented
154C22×C31—21no—
155C22×C31—21no—
156C22×C31—21no—
157C22×C31—21no—
158C22×C31—22no—
159C22×C31—22no—
160C22×C31—22no—
161C22×C31—22no—
162C22×C31—81no—
163C22×C31—81no—
164C22×C31—81no—
165C22×C31—82no—
166C22×C31—82no—
167C22×C31#38611yescharacteristic
168C22×C31#41012yes—
169C22×C31C2×#10211yescharacteristic
170C22×C31#41711yescharacteristic
171C22×C31#42112yes—
172C22×C31#44711yescharacteristic
173C22×C31#44811yescharacteristic
174C22×C31#48011yescharacteristic
175C22×C31#48111yescharacteristic
176C4×C31—24no—
177C4×C31—22no—
178C4×C31—22no—
179C4×C31—42no—
180C4×C31—84no—
181C4×C31—81no—
182C4×C31—82no—
183C2×#123—21no—
184C2×#121C22×C3111yescharacteristic
185C22×C4⋊C4—21no—
186C22×C42C22×C3111yescharacteristic
187C2×C22⋊C8C22×C3112yes—
188#390C4×C3112yescomplemented
189#389C4×C3112yescomplemented
190#388—22no—
191#386—21no—
192#382—24no—
193#380C22×C3111yescharacteristic
194C2×#95—21no—
195C2×#95C22×C3112yes—
196#336—22no—
197#327—24no—
198C2×C31—21no—
199C2×C31—21no—
200C2×C31—21no—
201C2×C31—21no—
202C2×C31—161no—
203C2×C31#151212yes—
204C2×C31#151712yes—
205C2×C31#187411yescharacteristic
206C2×C31#189711yescharacteristic
207C2×C31#189911yescharacteristic
208C22×D4—21no—
209C22×D4C2×C4×C3111yescharacteristic
210C23×C4—22no—
211C23×C4D4×C3111yescharacteristic
212C23×C4D4×C3111yescharacteristic
213C23×C4C23×C3111yescharacteristic
214C22×C8—22no—
215#123—42no—
216#123—42no—
217#121—22no—
218#121—22no—
219C2×C4⋊C4—24no—
220C2×C4⋊C4—22no—
221C2×C4⋊C4—42no—
222C2×C4⋊C4—42no—
223C2×C4⋊C4C2×C4×C3111yescharacteristic
224C2×C4⋊C4C2×C4×C3112yes—
225C2×C22⋊C4—21no—
226C2×C22⋊C4—22no—
227C2×C22⋊C4—22no—
228C2×C22⋊C4—21no—
229C2×C42—22no—
230C2×C42—22no—
231C2×C42C2×C4×C3112yes—
232C2×C42D4×C3112yes—
233C22⋊C8—22no—
234C22⋊C8—22no—
235#95—24no—
236#95—22no—
237#95—22no—
238#95—21no—
239#95D4×C3114yes—
240C31#915611yescharacteristic, direct product factor, Sylow
241C24—21no—
242C24C2×D4×C3111yescharacteristic
243C2×D4—22no—
244C2×D4—42no—
245C2×D4—41no—
246C2×D4—41no—
247C2×D4—41no—
248C2×D4—41no—
249C2×D4—41no—
250C2×D4—41no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—22no—
258C22×C4—21no—
259C22×C4—24no—
260C22×C4—42no—
261C22×C4—42no—
262C22×C4—44no—
263C22×C4—44no—
264C22×C4—42no—
265C22×C4—42no—
266C22×C4C22⋊C4×C3112yes—
267C22×C4C22⋊C4×C3112yes—
268C22×C4D8×C3112yes—
269C22×C4SD16×C3112yes—
270C22×C4C22×C4×C3111yescharacteristic
271C22×C4C2×D4×C3111yescharacteristic
272C22×C4C2×D4×C3112yes—
273C22×C4#41×C3112yes—
274C2×C8—44no—
275C2×C8—42no—
276C4⋊C4—22no—
277C4⋊C4—42no—
278C4⋊C4—48no—
279C4⋊C4—44no—
280C22⋊C4—44no—
281C22⋊C4—41no—
282C22⋊C4—41no—
283C22⋊C4—44no—
284C22⋊C4—42no—
285C42—24no—
286C42—24no—
287C23—22no—
288C23—22no—
289C23—42no—
290C23—41no—
291C23—41no—
292C23—42no—
293C23—41no—
294C23C2×C22⋊C4×C3111yescharacteristic
295C23C31×#12011yescharacteristic
296C23C31×#12311yescharacteristic
297C23C2×D8×C3111yescharacteristic
298C23C2×SD16×C3111yescharacteristic
299C23C31×AGL(1,ℤ/8)11yescharacteristic
300C23C31×#13711yescharacteristic
301D4—82no—
302D4—81no—
303D4—81no—
304D4—81no—
305D4—81no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—44no—
322C2×C4—44no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—42no—
328C2×C4—44no—
329C2×C4—41no—
330C2×C4—84no—
331C2×C4—84no—
332C2×C4C31×#10214yes—
333C2×C4C4×D4×C3112yes—
334C2×C4C31×#12112yes—
335C8—82no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—22no—
341C22—22no—
342C22—22no—
343C22—22no—
344C22—81no—
345C22—81no—
346C22—81no—
347C22—82no—
348C22—82no—
349C22C31×#38611yescharacteristic
350C22C31×#41012yes—
351C22C2×C31×#10211yescharacteristic
352C22C31×#41711yescharacteristic
353C22C31×#42112yes—
354C22C31×#44711yescharacteristic
355C22C31×#44811yescharacteristic
356C22C31×#48011yescharacteristic
357C22C31×#48111yescharacteristic
358C4—24no—
359C4—22no—
360C4—22no—
361C4—42no—
362C4—84no—
363C4—81no—
364C4—82no—
365C2—21no—
366C2—21no—
367C2—21no—
368C2—21no—
369C2—161no—
370C2C31×#151212yes—
371C2C31×#151712yes—
372C2C31×#187411yescharacteristic
373C2C31×#189711yescharacteristic
374C2C31×#189911yescharacteristic
subgroupG/H
center, socleC23×C31C2×C22⋊C4
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC2×C31×#121C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C22×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#382C2semidirect
3. C31×#1817C2semidirect
5. C31×#1294C2semidirect
11. C31×#390C4semidirect
12. C31×#389C4semidirect
99. #9156C31direct (N × H)
150. C2×#382C2×C31semidirect
151. #1817C2×C31semidirect
153. #1294C2×C31semidirect
188. #390C4×C31semidirect
189. #389C4×C31semidirect
240. C31#9156direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#28542
C2×C31×#3822
C31×#18172
C2×C31×#3272
C31×#12942
#915631