Finite Group Databasebeta

← C31×#10504 #21467263

Subgroups — C31×#10504 #21467263

Order 7936.

470 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×#3208C211yesmaximal, characteristic
2C31×#1986C211yesmaximal, characteristic, complemented
3C31×#1982C211yesmaximal, characteristic
4C31×#1965C211yesmaximal, characteristic
5C31×#1565C211yesmaximal, characteristic, complemented
6C31×#1550C211yesmaximal, characteristic, complemented
7C31×#1303C211yesmaximal, characteristic, complemented
8C31×#533C2211yescharacteristic
9C2×C31×#127C2211yescharacteristic
10C31×#492—21no—
11C31×#486—21no—
12C31×#460—21no—
13C31×#460—21no—
14C31×#450—22no—
15C31×#431C2211yescharacteristic
16C31×#423C2211yescharacteristic
17C2×C31×C4⋊C8C2211yescharacteristic
18C2×C31×#102—22no—
19C2×C31×#100—21no—
20C2×C31×#100—21no—
21C4×M16×C31C2211yescharacteristic
22C4×C4⋊C4×C31C2211yescharacteristic
23C31×#339—21no—
24C31×#339—21no—
25C31×#335—21no—
26C31×#334—21no—
27C31×#333—21no—
28C31×#332—21no—
29C22×D4×C31—21no—
30C22×D4×C31—21no—
31C22×D4×C31D412yes—
32C2×SD16×C31—22no—
33C2×SD16×C31—22no—
34C2×M16×C31—21no—
35C2×M16×C31D411yescharacteristic
36C2×M16×C31D411yescharacteristic
37C22×C8×C31—21no—
38C31×C4⋊Q8D411yescharacteristic
39C31×C4⋊Q8D411yescharacteristic
40C31×#127—21no—
41C31×#127—21no—
42C31×#127—21no—
43C31×#127—21no—
44C31×#125—21no—
45C31×C22⋊Q8—21no—
46C31×C22⋊Q8—21no—
47C4×Q8×C31—21no—
48C4×Q8×C31—21no—
49C31×#117—21no—
50C2×C4⋊C4×C31—21no—
51C2×C42×C31—21no—
52C2×C42×C31C2311yescharacteristic
53C31×C4⋊C8—21no—
54C31×C4⋊C8—21no—
55C31×C4⋊C8—21no—
56C31×C4⋊C8—21no—
57C31×C4⋊C8D411yescharacteristic
58C31×C4⋊C8D411yescharacteristic
59C31×#102—22no—
60C31×#102—22no—
61C31×#102—44no—
62C31×#100—42no—
63C31×#100—42no—
64C31×C22⋊C8—21no—
65C31×#97—21no—
66C4×C8×C31—21no—
67C4×C8×C31—21no—
68C31×#95—21no—
69C24×C31—22no—
70C2×Q8×C31—21no—
71C2×Q8×C31—21no—
72C2×D4×C31—22no—
73C2×D4×C31—22no—
74C2×D4×C31—42no—
75C2×D4×C31—42no—
76C2×D4×C31—41no—
77C2×D4×C31—41no—
78C2×D4×C31—41no—
79C2×D4×C31—41no—
80C2×D4×C31—41no—
81C2×D4×C31—41no—
82C2×D4×C31—41no—
83C2×D4×C31—41no—
84C2×D4×C31—82no—
85C22×C4×C31—41no—
86C22×C4×C31C2×D411yescharacteristic
87C22×C4×C31C2×D411yescharacteristic
88C22×C4×C31#4111yescharacteristic
89SD16×C31—82no—
90SD16×C31—82no—
91M16×C31—21no—
92M16×C31—21no—
93M16×C31—21no—
94M16×C31—41no—
95M16×C31—41no—
96M16×C31SD1612yescomplemented
97C2×C8×C31—21no—
98C2×C8×C31—21no—
99C2×C8×C31—21no—
100C2×C8×C31—21no—
101C2×C8×C31—42no—
102C2×C8×C31—41no—
103C2×C8×C31—41no—
104C4⋊C4×C31—22no—
105C4⋊C4×C31—21no—
106C4⋊C4×C31—21no—
107C4⋊C4×C31—21no—
108C4⋊C4×C31—21no—
109C4⋊C4×C31—41no—
110C4⋊C4×C31—41no—
111C4⋊C4×C31—41no—
112C22⋊C4×C31—41no—
113C42×C31—41no—
114C42×C31—41no—
115C42×C31—41no—
116C42×C31C2×D411yescharacteristic
117C42×C31C2×D411yescharacteristic
118C42×C31#4111yescharacteristic
119C42×C31#4111yescharacteristic
120#10504C3111yesmaximal, characteristic, direct product factor, Sylow
121C23×C31—42no—
122C23×C31—42no—
123C23×C31—42no—
124C23×C31—82no—
125C23×C31—82no—
126C23×C31#12111yescharacteristic
127Q8×C31—41no—
128Q8×C31—41no—
129Q8×C31—81no—
130D4×C31—44no—
131D4×C31—42no—
132D4×C31—42no—
133D4×C31—82no—
134D4×C31—82no—
135D4×C31—81no—
136D4×C31—81no—
137D4×C31—81no—
138D4×C31—81no—
139C2×C4×C31—21no—
140C2×C4×C31—21no—
141C2×C4×C31—41no—
142C2×C4×C31—42no—
143C2×C4×C31—41no—
144C2×C4×C31—41no—
145C2×C4×C31—81no—
146C2×C4×C31—81no—
147C2×C4×C31#12011yescharacteristic
148C2×C4×C31#12111yescharacteristic
149C2×C4×C31#12111yescharacteristic
150C2×C4×C31#12311yescharacteristic
151C2×C4×C31#12311yescharacteristic
152C2×C4×C31#12411yescharacteristic
153C2×C4×C31C2×SD1611yescharacteristic
154C2×C4×C31#13511yescharacteristic
155C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
156C2×C4×C31#13711yescharacteristic
157C8×C31—22no—
158C8×C31—41no—
159C8×C31—41no—
160C8×C31—41no—
161C8×C31—81no—
162C8×C31—81no—
163#3208C2×C3111yescharacteristic
164#1986C2×C3111yescharacteristic, complemented
165#1982C2×C3111yescharacteristic
166#1965C2×C3111yescharacteristic
167#1565C2×C3111yescharacteristic, complemented
168#1550C2×C3111yescharacteristic, complemented
169#1303C2×C3111yescharacteristic, complemented
170C22×C31—21no—
171C22×C31—21no—
172C22×C31—82no—
173C22×C31—82no—
174C22×C31—82no—
175C22×C31—162no—
176C22×C31—162no—
177C22×C31#39411yescharacteristic
178C22×C31#46111yescharacteristic
179C22×C31#46311yescharacteristic
180C4×C31—21no—
181C4×C31—21no—
182C4×C31—21no—
183C4×C31—82no—
184C4×C31—81no—
185C4×C31—81no—
186C4×C31#45311yescharacteristic
187C4×C31#45511yescharacteristic
188C4×C31#46011yescharacteristic
189C4×C31#46411yescharacteristic
190C4×C31#46511yescharacteristic
191C4×C31#46811yescharacteristic
192#533C22×C3111yescharacteristic
193C2×#127C22×C3111yescharacteristic
194#492—21no—
195#486—21no—
196#460—21no—
197#460—21no—
198#450—22no—
199#431C22×C3111yescharacteristic
200#423C22×C3111yescharacteristic
201C2×C4⋊C8C22×C3111yescharacteristic
202C2×#102—22no—
203C2×#100—21no—
204C2×#100—21no—
205C4×M16C22×C3111yescharacteristic
206C4×C4⋊C4C22×C3111yescharacteristic
207#339—21no—
208#339—21no—
209#335—21no—
210#334—21no—
211#333—21no—
212#332—21no—
213C2×C31—21no—
214C2×C31—21no—
215C2×C31—162no—
216C2×C31#203711yescharacteristic
217C2×C31#204811yescharacteristic
218C2×C31#205511yescharacteristic
219C22×D4—21no—
220C22×D4—21no—
221C22×D4D4×C3112yes—
222C2×SD16—22no—
223C2×SD16—22no—
224C2×M16—21no—
225C2×M16D4×C3111yescharacteristic
226C2×M16D4×C3111yescharacteristic
227C22×C8—21no—
228C4⋊Q8D4×C3111yescharacteristic
229C4⋊Q8D4×C3111yescharacteristic
230#127—21no—
231#127—21no—
232#127—21no—
233#127—21no—
234#125—21no—
235C22⋊Q8—21no—
236C22⋊Q8—21no—
237C4×Q8—21no—
238C4×Q8—21no—
239#117—21no—
240C2×C4⋊C4—21no—
241C2×C42—21no—
242C2×C42C23×C3111yescharacteristic
243C4⋊C8—21no—
244C4⋊C8—21no—
245C4⋊C8—21no—
246C4⋊C8—21no—
247C4⋊C8D4×C3111yescharacteristic
248C4⋊C8D4×C3111yescharacteristic
249#102—22no—
250#102—22no—
251#102—44no—
252#100—42no—
253#100—42no—
254C22⋊C8—21no—
255#97—21no—
256C4×C8—21no—
257C4×C8—21no—
258#95—21no—
259C31#1050411yescharacteristic, direct product factor, Sylow
260C24—22no—
261C2×Q8—21no—
262C2×Q8—21no—
263C2×D4—22no—
264C2×D4—22no—
265C2×D4—42no—
266C2×D4—42no—
267C2×D4—41no—
268C2×D4—41no—
269C2×D4—41no—
270C2×D4—41no—
271C2×D4—41no—
272C2×D4—41no—
273C2×D4—41no—
274C2×D4—41no—
275C2×D4—82no—
276C22×C4—41no—
277C22×C4C2×D4×C3111yescharacteristic
278C22×C4C2×D4×C3111yescharacteristic
279C22×C4#41×C3111yescharacteristic
280SD16—82no—
281SD16—82no—
282M16—21no—
283M16—21no—
284M16—21no—
285M16—41no—
286M16—41no—
287M16SD16×C3112yescomplemented
288C2×C8—21no—
289C2×C8—21no—
290C2×C8—21no—
291C2×C8—21no—
292C2×C8—42no—
293C2×C8—41no—
294C2×C8—41no—
295C4⋊C4—22no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C22⋊C4—41no—
304C42—41no—
305C42—41no—
306C42—41no—
307C42C2×D4×C3111yescharacteristic
308C42C2×D4×C3111yescharacteristic
309C42#41×C3111yescharacteristic
310C42#41×C3111yescharacteristic
311C23—42no—
312C23—42no—
313C23—42no—
314C23—82no—
315C23—82no—
316C23C31×#12111yescharacteristic
317Q8—41no—
318Q8—41no—
319Q8—81no—
320D4—44no—
321D4—42no—
322D4—42no—
323D4—82no—
324D4—82no—
325D4—81no—
326D4—81no—
327D4—81no—
328D4—81no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—41no—
332C2×C4—42no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4C31×#12011yescharacteristic
338C2×C4C31×#12111yescharacteristic
339C2×C4C31×#12111yescharacteristic
340C2×C4C31×#12311yescharacteristic
341C2×C4C31×#12311yescharacteristic
342C2×C4C31×#12411yescharacteristic
343C2×C4C2×SD16×C3111yescharacteristic
344C2×C4C31×#13511yescharacteristic
345C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
346C2×C4C31×#13711yescharacteristic
347C8—22no—
348C8—41no—
349C8—41no—
350C8—41no—
351C8—81no—
352C8—81no—
353C22—21no—
354C22—21no—
355C22—82no—
356C22—82no—
357C22—82no—
358C22—162no—
359C22—162no—
360C22C31×#39411yescharacteristic
361C22C31×#46111yescharacteristic
362C22C31×#46311yescharacteristic
363C4—21no—
364C4—21no—
365C4—21no—
366C4—82no—
367C4—81no—
368C4—81no—
369C4C31×#45311yescharacteristic
370C4C31×#45511yescharacteristic
371C4C31×#46011yescharacteristic
372C4C31×#46411yescharacteristic
373C4C31×#46511yescharacteristic
374C4C31×#46811yescharacteristic
375C2—21no—
376C2—21no—
377C2—162no—
378C2C31×#203711yescharacteristic
379C2C31×#204811yescharacteristic
380C2C31×#205511yescharacteristic
subgroupG/H
center, socleC22×C31#394
commutator, Frattini, cosocleC2×C42C23×C31
prime radicalC2×C31×#127C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#1986C2semidirect
5. C31×#1565C2semidirect
6. C31×#1550C2semidirect
7. C31×#1303C2semidirect
96. M16×C31SD16semidirect
120. #10504C31direct (N × H)
164. #1986C2×C31semidirect
167. #1565C2×C31semidirect
168. #1550C2×C31semidirect
169. #1303C2×C31semidirect
259. C31#10504direct (N × H)
287. M16SD16×C31semidirect

Maximal subgroups

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

subgroupindex
C31×#32082
C31×#19862
C31×#19822
C31×#19652
C31×#15652
C31×#15502
C31×#13032
#1050431