Finite Group Databasebeta

← C31×#11688 #21468447

Subgroups — C31×#11688 #21468447

Order 7936.

432 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3054C211yesmaximal, characteristic
2C2×C31×#349C211yesmaximal, characteristic, complemented
3C2×C31×#338C211yesmaximal, characteristic, complemented
4C31×#1342C212yesmaximal, complemented
5C31×#1341C212yesmaximal, complemented
6C2×C31×#135C411yescharacteristic
7C22×M16×C31—21no—
8C22×M16×C31C2211yescharacteristic
9C31×#525—21no—
10C2×C31×M32—21no—
11C31×#470C411yescharacteristic
12C31×#470C2211yescharacteristic
13C31×#469C411yescharacteristic
14C31×#469C2211yescharacteristic
15C31×#468—21no—
16C31×#468—21no—
17C31×#427C411yescharacteristic
18C31×#416—21no—
19C31×#349—21no—
20C31×#349C2212yes—
21C31×#338—21no—
22C31×#338C2212yes—
23C2×#41×C31—21no—
24C23×C4×C31D411yescharacteristic
25C31×#135—41no—
26C31×#135—41no—
27C2×Q16×C31C2×C411yescharacteristic
28C2×SD16×C31—21no—
29C2×D8×C31C2×C411yescharacteristic
30C2×M16×C31—22no—
31C2×M16×C31—22no—
32C2×M16×C31—41no—
33C2×M16×C31—41no—
34C2×M16×C31—41no—
35C2×M16×C31—41no—
36C2×M16×C31—41no—
37C2×M16×C31—41no—
38C2×M16×C31C2×C411yescharacteristic
39C2×M16×C31D411yescharacteristic
40C2×M16×C31D411yescharacteristic
41C2×M16×C31C2311yescharacteristic
42C22×C8×C31—22no—
43C22×C8×C31C2×C411yescharacteristic
44C22×C8×C31D411yescharacteristic
45C31×#123—41no—
46C31×C22⋊Q8—21no—
47C31×C22⋊Q8—21no—
48C31×#121—21no—
49C31×#121—21no—
50C31×#120—41no—
51C4×D4×C31—41no—
52C4×D4×C31—41no—
53C31×#117—21no—
54C31×M32—22no—
55C31×M32—41no—
56C2×C16×C31—41no—
57C31×#107—21no—
58C31×#106C2×C411yescharacteristic
59C31×#106C2×C411yescharacteristic
60C31×#103—21no—
61C31×#103—21no—
62C31×#102—21no—
63C31×#102—21no—
64C24×C31SD1611yescharacteristic
65#41×C31—41no—
66#41×C31—41no—
67#41×C31—41no—
68#41×C31—41no—
69C2×Q8×C31—21no—
70C2×D4×C31—21no—
71C2×D4×C31—41no—
72C2×D4×C31—41no—
73C2×D4×C31—41no—
74C22×C4×C31—21no—
75C22×C4×C31—21no—
76C22×C4×C31—21no—
77C22×C4×C31—21no—
78C22×C4×C31—41no—
79C22×C4×C31C22⋊C411yescharacteristic
80C22×C4×C31C22⋊C411yescharacteristic
81C22×C4×C31D811yescharacteristic
82C22×C4×C31D811yescharacteristic
83C22×C4×C31SD1611yescharacteristic
84C22×C4×C31C2×D411yescharacteristic
85Q16×C31—41no—
86SD16×C31—42no—
87D8×C31—41no—
88M16×C31—41no—
89M16×C31—41no—
90M16×C31—41no—
91M16×C31—41no—
92M16×C31—42no—
93M16×C31—42no—
94M16×C31—42no—
95M16×C31—42no—
96C2×C8×C31—21no—
97C2×C8×C31—21no—
98C2×C8×C31—21no—
99C2×C8×C31—21no—
100C2×C8×C31—24no—
101C2×C8×C31—42no—
102C2×C8×C31—42no—
103C2×C8×C31C22⋊C411yescharacteristic
104C2×C8×C31C22⋊C411yescharacteristic
105C2×C8×C31C22×C411yescharacteristic
106C2×C8×C31C2×D411yescharacteristic
107C4⋊C4×C31—21no—
108C4⋊C4×C31—21no—
109C4⋊C4×C31—41no—
110C4⋊C4×C31—41no—
111C22⋊C4×C31—41no—
112C22⋊C4×C31—41no—
113C22⋊C4×C31—41no—
114C22⋊C4×C31—41no—
115C22⋊C4×C31—41no—
116C42×C31—41no—
117C16×C31—42no—
118#11688C3111yesmaximal, characteristic, direct product factor, Sylow
119C23×C31—21no—
120C23×C31—21no—
121C23×C31—41no—
122C23×C31—81no—
123C23×C31#10211yescharacteristic
124C23×C31#10211yescharacteristic
125C23×C31C2×SD1611yescharacteristic
126Q8×C31—41no—
127Q8×C31—41no—
128D4×C31—41no—
129D4×C31—41no—
130D4×C31—82no—
131D4×C31—82no—
132D4×C31—81no—
133D4×C31—81no—
134C2×C4×C31—21no—
135C2×C4×C31—21no—
136C2×C4×C31—21no—
137C2×C4×C31—21no—
138C2×C4×C31—21no—
139C2×C4×C31—21no—
140C2×C4×C31—21no—
141C2×C4×C31—21no—
142C2×C4×C31—21no—
143C2×C4×C31—21no—
144C2×C4×C31—41no—
145C2×C4×C31—41no—
146C2×C4×C31—41no—
147C2×C4×C31—81no—
148C2×C4×C31—81no—
149C2×C4×C31#9911yescharacteristic
150C2×C4×C31#9911yescharacteristic
151C2×C4×C31#10211yescharacteristic
152C2×C4×C31#10211yescharacteristic
153C2×C4×C31#10411yescharacteristic
154C2×C4×C31#10411yescharacteristic
155C2×C4×C31C2×C22⋊C411yescharacteristic
156C2×C4×C31C2×D811yescharacteristic
157C8×C31—21no—
158C8×C31—21no—
159C8×C31—21no—
160C8×C31—21no—
161C8×C31—44no—
162#3054C2×C3111yescharacteristic
163C2×#349C2×C3111yescharacteristic, complemented
164C2×#338C2×C3111yescharacteristic, complemented
165#1342C2×C3112yescomplemented
166#1341C2×C3112yescomplemented
167C22×C31—21no—
168C22×C31—21no—
169C22×C31—41no—
170C22×C31—41no—
171C22×C31—41no—
172C22×C31—42no—
173C22×C31—81no—
174C22×C31—81no—
175C22×C31—81no—
176C22×C31—81no—
177C22×C31#32711yescharacteristic
178C22×C31#32711yescharacteristic
179C22×C31C2×#10211yescharacteristic
180C4×C31—21no—
181C4×C31—21no—
182C4×C31—81no—
183C4×C31—81no—
184C4×C31—81no—
185C4×C31#32711yescharacteristic
186C4×C31#32711yescharacteristic
187C4×C31C2×#9911yescharacteristic
188C4×C31C2×#10411yescharacteristic
189C2×#135C4×C3111yescharacteristic
190C22×M16—21no—
191C22×M16C22×C3111yescharacteristic
192#525—21no—
193C2×M32—21no—
194#470C4×C3111yescharacteristic
195#470C22×C3111yescharacteristic
196#469C4×C3111yescharacteristic
197#469C22×C3111yescharacteristic
198#468—21no—
199#468—21no—
200#427C4×C3111yescharacteristic
201#416—21no—
202#349—21no—
203#349C22×C3112yes—
204#338—21no—
205#338C22×C3112yes—
206C2×C31—21no—
207C2×C31—21no—
208C2×C31—21no—
209C2×C31—41no—
210C2×C31—41no—
211C2×C31—161no—
212C2×C31C2×#32711yescharacteristic
213C2×#41—21no—
214C23×C4D4×C3111yescharacteristic
215#135—41no—
216#135—41no—
217C2×Q16C2×C4×C3111yescharacteristic
218C2×SD16—21no—
219C2×D8C2×C4×C3111yescharacteristic
220C2×M16—22no—
221C2×M16—22no—
222C2×M16—41no—
223C2×M16—41no—
224C2×M16—41no—
225C2×M16—41no—
226C2×M16—41no—
227C2×M16—41no—
228C2×M16C2×C4×C3111yescharacteristic
229C2×M16D4×C3111yescharacteristic
230C2×M16D4×C3111yescharacteristic
231C2×M16C23×C3111yescharacteristic
232C22×C8—22no—
233C22×C8C2×C4×C3111yescharacteristic
234C22×C8D4×C3111yescharacteristic
235#123—41no—
236C22⋊Q8—21no—
237C22⋊Q8—21no—
238#121—21no—
239#121—21no—
240#120—41no—
241C4×D4—41no—
242C4×D4—41no—
243#117—21no—
244M32—22no—
245M32—41no—
246C2×C16—41no—
247#107—21no—
248#106C2×C4×C3111yescharacteristic
249#106C2×C4×C3111yescharacteristic
250#103—21no—
251#103—21no—
252#102—21no—
253#102—21no—
254C31#1168811yescharacteristic, direct product factor, Sylow
255C24SD16×C3111yescharacteristic
256#41—41no—
257#41—41no—
258#41—41no—
259#41—41no—
260C2×Q8—21no—
261C2×D4—21no—
262C2×D4—41no—
263C2×D4—41no—
264C2×D4—41no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—41no—
270C22×C4C22⋊C4×C3111yescharacteristic
271C22×C4C22⋊C4×C3111yescharacteristic
272C22×C4D8×C3111yescharacteristic
273C22×C4D8×C3111yescharacteristic
274C22×C4SD16×C3111yescharacteristic
275C22×C4C2×D4×C3111yescharacteristic
276Q16—41no—
277SD16—42no—
278D8—41no—
279M16—41no—
280M16—41no—
281M16—41no—
282M16—41no—
283M16—42no—
284M16—42no—
285M16—42no—
286M16—42no—
287C2×C8—21no—
288C2×C8—21no—
289C2×C8—21no—
290C2×C8—21no—
291C2×C8—24no—
292C2×C8—42no—
293C2×C8—42no—
294C2×C8C22⋊C4×C3111yescharacteristic
295C2×C8C22⋊C4×C3111yescharacteristic
296C2×C8C22×C4×C3111yescharacteristic
297C2×C8C2×D4×C3111yescharacteristic
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C22⋊C4—41no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C22⋊C4—41no—
307C42—41no—
308C16—42no—
309C23—21no—
310C23—21no—
311C23—41no—
312C23—81no—
313C23C31×#10211yescharacteristic
314C23C31×#10211yescharacteristic
315C23C2×SD16×C3111yescharacteristic
316Q8—41no—
317Q8—41no—
318D4—41no—
319D4—41no—
320D4—82no—
321D4—82no—
322D4—81no—
323D4—81no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4C31×#9911yescharacteristic
340C2×C4C31×#9911yescharacteristic
341C2×C4C31×#10211yescharacteristic
342C2×C4C31×#10211yescharacteristic
343C2×C4C31×#10411yescharacteristic
344C2×C4C31×#10411yescharacteristic
345C2×C4C2×C22⋊C4×C3111yescharacteristic
346C2×C4C2×D8×C3111yescharacteristic
347C8—21no—
348C8—21no—
349C8—21no—
350C8—21no—
351C8—44no—
352C22—21no—
353C22—21no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—42no—
358C22—81no—
359C22—81no—
360C22—81no—
361C22—81no—
362C22C31×#32711yescharacteristic
363C22C31×#32711yescharacteristic
364C22C2×C31×#10211yescharacteristic
365C4—21no—
366C4—21no—
367C4—81no—
368C4—81no—
369C4—81no—
370C4C31×#32711yescharacteristic
371C4C31×#32711yescharacteristic
372C4C2×C31×#9911yescharacteristic
373C4C2×C31×#10411yescharacteristic
374C2—21no—
375C2—21no—
376C2—21no—
377C2—41no—
378C2—41no—
379C2—161no—
380C2C2×C31×#32711yescharacteristic
subgroupG/H
centerC4×C31#327
commutatorC2×C8C22×C4×C31
Frattini, cosocleC2×M16C23×C31
socleC2×C31C2×#327
prime radicalC31×#3054C2
LCSG ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C31 ◁ C22×C4×C31 ◁ C22×M16×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#349C2semidirect
3. C2×C31×#338C2semidirect
4. C31×#1342C2semidirect
5. C31×#1341C2semidirect
118. #11688C31direct (N × H)
163. C2×#349C2×C31semidirect
164. C2×#338C2×C31semidirect
165. #1342C2×C31semidirect
166. #1341C2×C31semidirect
254. C31#11688direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#30542
C2×C31×#3492
C2×C31×#3382
C31×#13422
C31×#13412
#1168831