Finite Group Databasebeta

← C31×#9687 #21466446

Subgroups — C31×#9687 #21466446

Order 7936.

526 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2861C211yesmaximal, characteristic
2C31×#1767C211yesmaximal, characteristic, complemented
3C4×C31×#97C211yesmaximal, characteristic, complemented
4C2×C31×#330C212yesmaximal, complemented
5C2×C31×#329C212yesmaximal
6C2×C31×#125C2211yescharacteristic
7C2×C31×#124C2211yescharacteristic
8C2×C31×C4⋊C8—21no—
9C2×C31×#97—21no—
10C2×C31×#97C2212yes—
11C2×C31×#97C2212yes—
12C2×C4×C8×C31—21no—
13C31×#391C411yescharacteristic
14C31×#391C411yescharacteristic
15C31×#390C411yescharacteristic
16C31×#390C411yescharacteristic
17C31×#388—21no—
18C31×#388—21no—
19C31×#388—21no—
20C31×#388—21no—
21C43×C31C2211yescharacteristic
22C31×#336—21no—
23C31×#330—24no—
24C31×#329—24no—
25C22×Q8×C31C2×C411yescharacteristic
26C22×D4×C31C2×C411yescharacteristic
27C22×C8×C31—22no—
28C22×C8×C31—22no—
29C31×#125—22no—
30C31×#125—22no—
31C31×#124—22no—
32C31×#124—22no—
33C2×C4⋊C4×C31—21no—
34C2×C4⋊C4×C31—21no—
35C2×C4⋊C4×C31C2×C411yescharacteristic
36C2×C4⋊C4×C31C2×C411yescharacteristic
37C2×C22⋊C4×C31—21no—
38C2×C22⋊C4×C31—21no—
39C2×C22⋊C4×C31—21no—
40C2×C22⋊C4×C31—21no—
41C2×C22⋊C4×C31—21no—
42C2×C22⋊C4×C31—21no—
43C2×C42×C31C2×C411yescharacteristic
44C2×C42×C31C2×C411yescharacteristic
45C2×C42×C31D411yescharacteristic
46C2×C42×C31D411yescharacteristic
47C2×C42×C31D411yescharacteristic
48C2×C42×C31D411yescharacteristic
49C2×C42×C31C2311yescharacteristic
50C31×C4⋊C8—24no—
51C31×#97—24no—
52C31×#97—22no—
53C31×#97—22no—
54C31×#97—22no—
55C31×#97D414yes—
56C4×C8×C31—24no—
57C31×#95—21no—
58C31×#95—21no—
59C31×#95—21no—
60C31×#95—21no—
61C24×C31—21no—
62C2×Q8×C31—22no—
63C2×Q8×C31—41no—
64C2×Q8×C31—41no—
65C2×D4×C31—22no—
66C2×D4×C31—41no—
67C2×D4×C31—41no—
68C22×C4×C31—21no—
69C22×C4×C31—21no—
70C22×C4×C31—21no—
71C22×C4×C31C22⋊C411yescharacteristic
72C22×C4×C31C22⋊C411yescharacteristic
73C22×C4×C31C22⋊C411yescharacteristic
74C22×C4×C31C22⋊C411yescharacteristic
75C22×C4×C31C22×C411yescharacteristic
76C22×C4×C31C2×D411yescharacteristic
77C22×C4×C31C2×D411yescharacteristic
78C2×C8×C31—24no—
79C2×C8×C31—24no—
80C2×C8×C31—24no—
81C2×C8×C31—24no—
82C2×C8×C31—42no—
83C2×C8×C31—42no—
84C4⋊C4×C31—22no—
85C4⋊C4×C31—22no—
86C4⋊C4×C31—42no—
87C4⋊C4×C31—41no—
88C4⋊C4×C31—41no—
89C22⋊C4×C31—42no—
90C22⋊C4×C31—42no—
91C22⋊C4×C31—42no—
92C22⋊C4×C31—42no—
93C22⋊C4×C31—42no—
94C22⋊C4×C31—41no—
95C22⋊C4×C31—41no—
96C42×C31—22no—
97C42×C31—22no—
98C42×C31—22no—
99C42×C31—41no—
100C42×C31—41no—
101C42×C31—41no—
102C42×C31C2×D412yes—
103C42×C31#4112yes—
104#9687C3111yesmaximal, characteristic, direct product factor, Sylow
105C23×C31—41no—
106C23×C31—41no—
107C23×C31—41no—
108C23×C31—41no—
109C23×C31—41no—
110C23×C31—41no—
111C23×C31—41no—
112C23×C31C2×C22⋊C411yescharacteristic
113Q8×C31—82no—
114D4×C31—82no—
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—21no—
129C2×C4×C31—21no—
130C2×C4×C31—41no—
131C2×C4×C31—41no—
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#10412yes—
140C2×C4×C31#10412yes—
141C2×C4×C31#10412yes—
142C2×C4×C31C4×D412yes—
143C2×C4×C31#12112yes—
144C2×C4×C31#12411yescharacteristic
145C2×C4×C31#12711yescharacteristic
146C8×C31—28no—
147C8×C31—44no—
148#2861C2×C3111yescharacteristic
149#1767C2×C3111yescharacteristic, complemented
150C4×#97C2×C3111yescharacteristic, complemented
151C2×#330C2×C3112yescomplemented
152C2×#329C2×C3112yes—
153C22×C31—81no—
154C22×C31—81no—
155C22×C31—81no—
156C22×C31—81no—
157C22×C31—81no—
158C22×C31—81no—
159C22×C31—81no—
160C22×C31#39011yescharacteristic
161C22×C31#41311yescharacteristic
162C22×C31#41311yescharacteristic
163C22×C31C2×#10411yescharacteristic
164C22×C31C2×#10411yescharacteristic
165C22×C31C2×#10411yescharacteristic
166C22×C31#42111yescharacteristic
167C4×C31—22no—
168C4×C31—22no—
169C4×C31—21no—
170C4×C31—21no—
171C4×C31—22no—
172C4×C31—22no—
173C4×C31—22no—
174C4×C31—41no—
175C4×C31—81no—
176C4×C31—81no—
177C4×C31—81no—
178C2×#125C22×C3111yescharacteristic
179C2×#124C22×C3111yescharacteristic
180C2×C4⋊C8—21no—
181C2×#97—21no—
182C2×#97C22×C3112yes—
183C2×#97C22×C3112yes—
184C2×C4×C8—21no—
185#391C4×C3111yescharacteristic
186#391C4×C3111yescharacteristic
187#390C4×C3111yescharacteristic
188#390C4×C3111yescharacteristic
189#388—21no—
190#388—21no—
191#388—21no—
192#388—21no—
193C43C22×C3111yescharacteristic
194#336—21no—
195#330—24no—
196#329—24no—
197C2×C31—161no—
198C2×C31#152411yescharacteristic
199C2×C31#152411yescharacteristic
200C2×C31#152911yescharacteristic
201C2×C31#153211yescharacteristic
202C2×C31#196211yescharacteristic
203C2×C31#196711yescharacteristic
204C2×C31#198011yescharacteristic
205C22×Q8C2×C4×C3111yescharacteristic
206C22×D4C2×C4×C3111yescharacteristic
207C22×C8—22no—
208C22×C8—22no—
209#125—22no—
210#125—22no—
211#124—22no—
212#124—22no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4C2×C4×C3111yescharacteristic
216C2×C4⋊C4C2×C4×C3111yescharacteristic
217C2×C22⋊C4—21no—
218C2×C22⋊C4—21no—
219C2×C22⋊C4—21no—
220C2×C22⋊C4—21no—
221C2×C22⋊C4—21no—
222C2×C22⋊C4—21no—
223C2×C42C2×C4×C3111yescharacteristic
224C2×C42C2×C4×C3111yescharacteristic
225C2×C42D4×C3111yescharacteristic
226C2×C42D4×C3111yescharacteristic
227C2×C42D4×C3111yescharacteristic
228C2×C42D4×C3111yescharacteristic
229C2×C42C23×C3111yescharacteristic
230C4⋊C8—24no—
231#97—24no—
232#97—22no—
233#97—22no—
234#97—22no—
235#97D4×C3114yes—
236C4×C8—24no—
237#95—21no—
238#95—21no—
239#95—21no—
240#95—21no—
241C31#968711yescharacteristic, direct product factor, Sylow
242C24—21no—
243C2×Q8—22no—
244C2×Q8—41no—
245C2×Q8—41no—
246C2×D4—22no—
247C2×D4—41no—
248C2×D4—41no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
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—24no—
261C2×C8—24no—
262C2×C8—24no—
263C2×C8—42no—
264C2×C8—42no—
265C4⋊C4—22no—
266C4⋊C4—22no—
267C4⋊C4—42no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C22⋊C4—42no—
271C22⋊C4—42no—
272C22⋊C4—42no—
273C22⋊C4—42no—
274C22⋊C4—42no—
275C22⋊C4—41no—
276C22⋊C4—41no—
277C42—22no—
278C42—22no—
279C42—22no—
280C42—41no—
281C42—41no—
282C42—41no—
283C42C2×D4×C3112yes—
284C42#41×C3112yes—
285C23—41no—
286C23—41no—
287C23—41no—
288C23—41no—
289C23—41no—
290C23—41no—
291C23—41no—
292C23C2×C22⋊C4×C3111yescharacteristic
293Q8—82no—
294D4—82no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
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—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4C31×#10412yes—
320C2×C4C31×#10412yes—
321C2×C4C31×#10412yes—
322C2×C4C4×D4×C3112yes—
323C2×C4C31×#12112yes—
324C2×C4C31×#12411yescharacteristic
325C2×C4C31×#12711yescharacteristic
326C8—28no—
327C8—44no—
328C22—81no—
329C22—81no—
330C22—81no—
331C22—81no—
332C22—81no—
333C22—81no—
334C22—81no—
335C22C31×#39011yescharacteristic
336C22C31×#41311yescharacteristic
337C22C31×#41311yescharacteristic
338C22C2×C31×#10411yescharacteristic
339C22C2×C31×#10411yescharacteristic
340C22C2×C31×#10411yescharacteristic
341C22C31×#42111yescharacteristic
342C4—22no—
343C4—22no—
344C4—21no—
345C4—21no—
346C4—22no—
347C4—22no—
348C4—22no—
349C4—41no—
350C4—81no—
351C4—81no—
352C4—81no—
353C2—161no—
354C2C31×#152411yescharacteristic
355C2C31×#152411yescharacteristic
356C2C31×#152911yescharacteristic
357C2C31×#153211yescharacteristic
358C2C31×#196211yescharacteristic
359C2C31×#196711yescharacteristic
360C2C31×#198011yescharacteristic
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×#1767C2semidirect
3. C4×C31×#97C2semidirect
4. C2×C31×#330C2semidirect
104. #9687C31direct (N × H)
149. #1767C2×C31semidirect
150. C4×#97C2×C31semidirect
151. C2×#330C2×C31semidirect
241. C31#9687direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#28612
C31×#17672
C4×C31×#972
C2×C31×#3302
C2×C31×#3292
#968731