Finite Group Databasebeta

← C31×#11697 #21468456

Subgroups — C31×#11697 #21468456

Order 7936.

536 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2392C211yesmaximal, characteristic
2C31×#1742C211yesmaximal, characteristic, complemented
3C31×#1458C211yesmaximal, characteristic, complemented
4C31×#1346C212yesmaximal, complemented
5C31×#1345C212yesmaximal, complemented
6C22×M16×C31—21no—
7C2×C4×D4×C31—21no—
8C2×C4×D4×C31C411yescharacteristic
9C2×C31×#117C2211yescharacteristic
10C31×#431—21no—
11C31×#398C2211yescharacteristic
12C31×#397C411yescharacteristic
13C31×#396—21no—
14C31×#394—21no—
15C31×#394C2211yescharacteristic
16C31×#392C411yescharacteristic
17C4×C4⋊C4×C31C411yescharacteristic
18C4×C22⋊C4×C31—21no—
19C31×#343—21no—
20C31×#343C2212yes—
21C31×#324C2212yes—
22C31×#323—21no—
23C22×D4×C31—21no—
24C22×D4×C31C2×C411yescharacteristic
25C23×C4×C31—21no—
26C23×C4×C31D411yescharacteristic
27C2×M16×C31—24no—
28C2×M16×C31—22no—
29C2×M16×C31—41no—
30C2×M16×C31—42no—
31C22×C8×C31—41no—
32C4×D4×C31—41no—
33C4×D4×C31—41no—
34C4×D4×C31—42no—
35C4×D4×C31—42no—
36C31×#117—41no—
37C31×#117—41no—
38C2×C4⋊C4×C31—21no—
39C2×C4⋊C4×C31—21no—
40C2×C4⋊C4×C31C2×C411yescharacteristic
41C2×C4⋊C4×C31D411yescharacteristic
42C2×C4⋊C4×C31C2311yescharacteristic
43C2×C22⋊C4×C31—21no—
44C2×C22⋊C4×C31—21no—
45C2×C22⋊C4×C31—21no—
46C2×C22⋊C4×C31—21no—
47C2×C22⋊C4×C31—21no—
48C2×C22⋊C4×C31C2×C411yescharacteristic
49C2×C22⋊C4×C31D411yescharacteristic
50C2×C42×C31—21no—
51C2×C42×C31C2×C411yescharacteristic
52C2×C42×C31D411yescharacteristic
53C31×C4⋊C8—41no—
54C31×C22⋊C8—22no—
55C4×C8×C31—41no—
56C31×#95—21no—
57C31×#95—21no—
58C31×#95C2×C411yescharacteristic
59C31×#95C2×C411yescharacteristic
60C24×C31—21no—
61C24×C31C22⋊C411yescharacteristic
62C2×D4×C31—42no—
63C2×D4×C31—41no—
64C2×D4×C31—42no—
65C2×D4×C31—42no—
66C2×D4×C31—42no—
67C22×C4×C31—21no—
68C22×C4×C31—21no—
69C22×C4×C31—22no—
70C22×C4×C31—21no—
71C22×C4×C31—21no—
72C22×C4×C31—21no—
73C22×C4×C31—41no—
74C22×C4×C31—41no—
75C22×C4×C31—42no—
76C22×C4×C31—42no—
77C22×C4×C31C22⋊C411yescharacteristic
78C22×C4×C31C22⋊C411yescharacteristic
79C22×C4×C31C22⋊C411yescharacteristic
80C22×C4×C31D812yes—
81C22×C4×C31SD1612yes—
82C22×C4×C31C22×C411yescharacteristic
83C22×C4×C31C2×D411yescharacteristic
84C22×C4×C31C2×D411yescharacteristic
85M16×C31—24no—
86M16×C31—44no—
87M16×C31—42no—
88C2×C8×C31—42no—
89C2×C8×C31—44no—
90C2×C8×C31—42no—
91C4⋊C4×C31—41no—
92C4⋊C4×C31—41no—
93C4⋊C4×C31—42no—
94C4⋊C4×C31—41no—
95C4⋊C4×C31—41no—
96C4⋊C4×C31—41no—
97C22⋊C4×C31—41no—
98C22⋊C4×C31—41no—
99C22⋊C4×C31—42no—
100C22⋊C4×C31—42no—
101C22⋊C4×C31—42no—
102C22⋊C4×C31—42no—
103C22⋊C4×C31—41no—
104C22⋊C4×C31—41no—
105C42×C31—21no—
106C42×C31—21no—
107C42×C31—21no—
108C42×C31—21no—
109C42×C31—42no—
110#11697C3111yesmaximal, characteristic, direct product factor, Sylow
111C23×C31—21no—
112C23×C31—21no—
113C23×C31—22no—
114C23×C31—41no—
115C23×C31—41no—
116C23×C31—41no—
117C23×C31—41no—
118C23×C31—41no—
119C23×C31—41no—
120C23×C31—41no—
121C23×C31—41no—
122C23×C31#10212yes—
123C23×C31C2×C22⋊C411yescharacteristic
124D4×C31—42no—
125D4×C31—48no—
126D4×C31—42no—
127C2×C4×C31—21no—
128C2×C4×C31—21no—
129C2×C4×C31—22no—
130C2×C4×C31—22no—
131C2×C4×C31—22no—
132C2×C4×C31—22no—
133C2×C4×C31—22no—
134C2×C4×C31—21no—
135C2×C4×C31—21no—
136C2×C4×C31—21no—
137C2×C4×C31—21no—
138C2×C4×C31—41no—
139C2×C4×C31—41no—
140C2×C4×C31—41no—
141C2×C4×C31—41no—
142C2×C4×C31—41no—
143C2×C4×C31—41no—
144C2×C4×C31—41no—
145C2×C4×C31—41no—
146C2×C4×C31—41no—
147C2×C4×C31—41no—
148C2×C4×C31—41no—
149C2×C4×C31—41no—
150C2×C4×C31—82no—
151C2×C4×C31—82no—
152C2×C4×C31#9911yescharacteristic
153C2×C4×C31#9911yescharacteristic
154C2×C4×C31#10212yes—
155C2×C4×C31#10412yes—
156C2×C4×C31C2×D811yescharacteristic
157C2×C4×C31C2×SD1611yescharacteristic
158C8×C31—44no—
159C8×C31—82no—
160#2392C2×C3111yescharacteristic
161#1742C2×C3111yescharacteristic, complemented
162#1458C2×C3111yescharacteristic, complemented
163#1346C2×C3112yescomplemented
164#1345C2×C3112yescomplemented
165C22×C31—21no—
166C22×C31—21no—
167C22×C31—22no—
168C22×C31—42no—
169C22×C31—42no—
170C22×C31—42no—
171C22×C31—41no—
172C22×C31—41no—
173C22×C31—42no—
174C22×C31—81no—
175C22×C31—81no—
176C22×C31—81no—
177C22×C31—81no—
178C22×C31—81no—
179C22×C31C2×#9911yescharacteristic
180C22×C31C2×#10211yescharacteristic
181C22×C31C2×#10411yescharacteristic
182C4×C31—21no—
183C4×C31—21no—
184C4×C31—42no—
185C4×C31—41no—
186C4×C31—41no—
187C4×C31—41no—
188C4×C31—41no—
189C4×C31—81no—
190C4×C31—81no—
191C4×C31#32712yes—
192C4×C31#32712yes—
193C22×M16—21no—
194C2×C4×D4—21no—
195C2×C4×D4C4×C3111yescharacteristic
196C2×#117C22×C3111yescharacteristic
197#431—21no—
198#398C22×C3111yescharacteristic
199#397C4×C3111yescharacteristic
200#396—21no—
201#394—21no—
202#394C22×C3111yescharacteristic
203#392C4×C3111yescharacteristic
204C4×C4⋊C4C4×C3111yescharacteristic
205C4×C22⋊C4—21no—
206#343—21no—
207#343C22×C3112yes—
208#324C22×C3112yes—
209#323—21no—
210C2×C31—21no—
211C2×C31—21no—
212C2×C31—42no—
213C2×C31—82no—
214C2×C31C2×#32711yescharacteristic
215C2×C31#212011yescharacteristic
216C2×C31#213211yescharacteristic
217C22×D4—21no—
218C22×D4C2×C4×C3111yescharacteristic
219C23×C4—21no—
220C23×C4D4×C3111yescharacteristic
221C2×M16—24no—
222C2×M16—22no—
223C2×M16—41no—
224C2×M16—42no—
225C22×C8—41no—
226C4×D4—41no—
227C4×D4—41no—
228C4×D4—42no—
229C4×D4—42no—
230#117—41no—
231#117—41no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4C2×C4×C3111yescharacteristic
235C2×C4⋊C4D4×C3111yescharacteristic
236C2×C4⋊C4C23×C3111yescharacteristic
237C2×C22⋊C4—21no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—21no—
240C2×C22⋊C4—21no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4C2×C4×C3111yescharacteristic
243C2×C22⋊C4D4×C3111yescharacteristic
244C2×C42—21no—
245C2×C42C2×C4×C3111yescharacteristic
246C2×C42D4×C3111yescharacteristic
247C4⋊C8—41no—
248C22⋊C8—22no—
249C4×C8—41no—
250#95—21no—
251#95—21no—
252#95C2×C4×C3111yescharacteristic
253#95C2×C4×C3111yescharacteristic
254C31#1169711yescharacteristic, direct product factor, Sylow
255C24—21no—
256C24C22⋊C4×C3111yescharacteristic
257C2×D4—41no—
258C2×D4—42no—
259C2×D4—42no—
260C2×D4—42no—
261C2×D4—42no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—22no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—42no—
271C22×C4—42no—
272C22×C4C22⋊C4×C3111yescharacteristic
273C22×C4C22⋊C4×C3111yescharacteristic
274C22×C4C22⋊C4×C3111yescharacteristic
275C22×C4D8×C3112yes—
276C22×C4SD16×C3112yes—
277C22×C4C22×C4×C3111yescharacteristic
278C22×C4C2×D4×C3111yescharacteristic
279C22×C4C2×D4×C3111yescharacteristic
280M16—24no—
281M16—44no—
282M16—42no—
283C2×C8—42no—
284C2×C8—44no—
285C2×C8—42no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—42no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C22⋊C4—41no—
293C22⋊C4—41no—
294C22⋊C4—42no—
295C22⋊C4—42no—
296C22⋊C4—42no—
297C22⋊C4—42no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C42—21no—
301C42—21no—
302C42—21no—
303C42—21no—
304C42—42no—
305C23—21no—
306C23—21no—
307C23—22no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23C31×#10212yes—
317C23C2×C22⋊C4×C3111yescharacteristic
318D4—42no—
319D4—48no—
320D4—42no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—82no—
345C2×C4—82no—
346C2×C4C31×#9911yescharacteristic
347C2×C4C31×#9911yescharacteristic
348C2×C4C31×#10212yes—
349C2×C4C31×#10412yes—
350C2×C4C2×D8×C3111yescharacteristic
351C2×C4C2×SD16×C3111yescharacteristic
352C8—44no—
353C8—82no—
354C22—21no—
355C22—21no—
356C22—22no—
357C22—42no—
358C22—42no—
359C22—42no—
360C22—41no—
361C22—41no—
362C22—42no—
363C22—81no—
364C22—81no—
365C22—81no—
366C22—81no—
367C22—81no—
368C22C2×C31×#9911yescharacteristic
369C22C2×C31×#10211yescharacteristic
370C22C2×C31×#10411yescharacteristic
371C4—21no—
372C4—21no—
373C4—42no—
374C4—41no—
375C4—41no—
376C4—41no—
377C4—41no—
378C4—81no—
379C4—81no—
380C4C31×#32712yes—
381C4C31×#32712yes—
382C2—21no—
383C2—21no—
384C2—42no—
385C2—82no—
386C2C2×C31×#32711yescharacteristic
387C2C31×#212011yescharacteristic
388C2C31×#213211yescharacteristic
subgroupG/H
centerC2×C4×C31#99
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C4⋊C4C23×C31
socleC22×C31C2×#99
prime radicalC31×#392C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C31 ◁ C22×C4×C31 ◁ C2×C31×#117 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#1742C2semidirect
3. C31×#1458C2semidirect
4. C31×#1346C2semidirect
5. C31×#1345C2semidirect
110. #11697C31direct (N × H)
161. #1742C2×C31semidirect
162. #1458C2×C31semidirect
163. #1346C2×C31semidirect
164. #1345C2×C31semidirect
254. C31#11697direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#23922
C31×#17422
C31×#14582
C31×#13462
C31×#13452
#1169731