Finite Group Databasebeta

← C31×#10205 #21466964

Subgroups — C31×#10205 #21466964

Order 7936.

512 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3246C211yesmaximal, characteristic
2C31×#3226C211yesmaximal, characteristic
3C31×#3139C211yesmaximal, characteristic, complemented
4C31×#1988C211yesmaximal, characteristic, complemented
5C31×#1980C211yesmaximal, characteristic
6C31×#1503C211yesmaximal, characteristic, complemented
7C31×#1283C211yesmaximal, characteristic, complemented
8C31×#533C2211yescharacteristic
9C31×#532C2211yescharacteristic
10C2×C31×C4⋊Q8C2211yescharacteristic
11C31×#500—21no—
12C31×#491—22no—
13C31×#487—21no—
14C31×#487—21no—
15C31×#486—21no—
16C31×#480—22no—
17C31×#476—21no—
18C31×#475—21no—
19C31×#474—22no—
20C31×#465—22no—
21C31×#461—21no—
22C31×#460—21no—
23C31×#431C2211yescharacteristic
24C2×C31×C4⋊C8C2211yescharacteristic
25C2×C31×#104—22no—
26C31×#419—22no—
27C4×M16×C31C2211yescharacteristic
28C4×C4⋊C4×C31C2211yescharacteristic
29C31×#340—22no—
30C31×#328—22no—
31C2×#41×C31—21no—
32C22×Q8×C31—21no—
33C2×SD16×C31—22no—
34C2×M16×C31D412yes—
35C22×C8×C31D412yes—
36C31×C4⋊Q8—21no—
37C31×C4⋊Q8—21no—
38C31×C4⋊Q8—21no—
39C31×C4⋊Q8D411yescharacteristic
40C31×C4⋊Q8D412yes—
41C31×C4⋊Q8D411yescharacteristic
42C31×C4⋊Q8D411yescharacteristic
43C31×#127D411yescharacteristic
44C31×#125—21no—
45C31×#124—21no—
46C31×C22⋊Q8—21no—
47C31×C22⋊Q8—21no—
48C31×#121—21no—
49C31×#121—21no—
50C4×Q8×C31—21no—
51C4×Q8×C31—21no—
52C4×D4×C31—21no—
53C4×D4×C31—21no—
54C31×#117—21no—
55C2×C4⋊C4×C31—21no—
56C2×C4⋊C4×C31—21no—
57C2×C4⋊C4×C31—21no—
58C2×C42×C31—21no—
59C2×C42×C31C2311yescharacteristic
60C31×#107—24no—
61C31×#106—22no—
62C31×C4⋊C8—21no—
63C31×C4⋊C8—21no—
64C31×C4⋊C8—21no—
65C31×#104—44no—
66C31×#103—24no—
67C31×#103—24no—
68C31×#103—22no—
69C31×#102—22no—
70C31×#102—24no—
71C31×C22⋊C8D412yes—
72C31×#97—21no—
73C4×C8×C31—21no—
74C4×C8×C31—21no—
75C31×#95—21no—
76#41×C31—42no—
77#41×C31—42no—
78C2×Q8×C31—22no—
79C2×Q8×C31—21no—
80C2×Q8×C31—21no—
81C2×Q8×C31—21no—
82C2×Q8×C31—41no—
83C2×Q8×C31—42no—
84C2×Q8×C31—42no—
85C2×D4×C31—21no—
86C2×D4×C31—21no—
87C2×D4×C31—21no—
88C2×D4×C31—41no—
89C22×C4×C31—41no—
90C22×C4×C31—41no—
91C22×C4×C31—41no—
92C22×C4×C31C2×D411yescharacteristic
93C22×C4×C31C2×D411yescharacteristic
94C22×C4×C31C2×D411yescharacteristic
95SD16×C31—82no—
96M16×C31—22no—
97M16×C31—22no—
98C2×C8×C31—22no—
99C2×C8×C31—22no—
100C2×C8×C31—22no—
101C2×C8×C31—42no—
102C4⋊C4×C31—22no—
103C4⋊C4×C31—21no—
104C4⋊C4×C31—22no—
105C4⋊C4×C31—21no—
106C4⋊C4×C31—21no—
107C4⋊C4×C31—21no—
108C4⋊C4×C31—21no—
109C4⋊C4×C31—22no—
110C4⋊C4×C31—21no—
111C4⋊C4×C31—41no—
112C4⋊C4×C31—41no—
113C4⋊C4×C31—41no—
114C4⋊C4×C31—41no—
115C4⋊C4×C31—41no—
116C22⋊C4×C31—41no—
117C22⋊C4×C31—41no—
118C22⋊C4×C31—41no—
119C42×C31—41no—
120C42×C31—42no—
121C42×C31C2×D411yescharacteristic
122C42×C31C2×D411yescharacteristic
123C42×C31C2×D411yescharacteristic
124C42×C31#4111yescharacteristic
125#10205C3111yesmaximal, characteristic, direct product factor, Sylow
126C23×C31—41no—
127C23×C31#12711yescharacteristic
128Q8×C31—44no—
129Q8×C31—41no—
130Q8×C31—41no—
131Q8×C31—42no—
132Q8×C31—81no—
133Q8×C31—82no—
134D4×C31—42no—
135D4×C31—41no—
136D4×C31—41no—
137D4×C31—42no—
138D4×C31—81no—
139D4×C31—81no—
140C2×C4×C31—21no—
141C2×C4×C31—21no—
142C2×C4×C31—41no—
143C2×C4×C31—42no—
144C2×C4×C31—41no—
145C2×C4×C31—41no—
146C2×C4×C31—41no—
147C2×C4×C31—42no—
148C2×C4×C31—81no—
149C2×C4×C31—81no—
150C2×C4×C31—81no—
151C2×C4×C31—81no—
152C2×C4×C31—82no—
153C2×C4×C31#12011yescharacteristic
154C2×C4×C31#12011yescharacteristic
155C2×C4×C31#12011yescharacteristic
156C2×C4×C31#12111yescharacteristic
157C2×C4×C31#12111yescharacteristic
158C2×C4×C31#12111yescharacteristic
159C2×C4×C31#13512yes—
160C2×C4×C31AGL(1,ℤ/8)12yes—
161C8×C31—42no—
162C8×C31—42no—
163C8×C31—42no—
164#3246C2×C3111yescharacteristic
165#3226C2×C3111yescharacteristic
166#3139C2×C3111yescharacteristic, complemented
167#1988C2×C3111yescharacteristic, complemented
168#1980C2×C3111yescharacteristic
169#1503C2×C3111yescharacteristic, complemented
170#1283C2×C3111yescharacteristic, complemented
171C22×C31—21no—
172C22×C31—21no—
173C22×C31—81no—
174C22×C31—81no—
175C22×C31—81no—
176C22×C31#39211yescharacteristic
177C22×C31#49511yescharacteristic
178C22×C31#49611yescharacteristic
179C4×C31—21no—
180C4×C31—21no—
181C4×C31—21no—
182C4×C31—82no—
183C4×C31—81no—
184C4×C31—81no—
185C4×C31—81no—
186C4×C31—82no—
187C4×C31#44912yes—
188C4×C31#45511yescharacteristic
189C4×C31#45611yescharacteristic
190C4×C31#46312yes—
191#533C22×C3111yescharacteristic
192#532C22×C3111yescharacteristic
193C2×C4⋊Q8C22×C3111yescharacteristic
194#500—21no—
195#491—22no—
196#487—21no—
197#487—21no—
198#486—21no—
199#480—22no—
200#476—21no—
201#475—21no—
202#474—22no—
203#465—22no—
204#461—21no—
205#460—21no—
206#431C22×C3111yescharacteristic
207C2×C4⋊C8C22×C3111yescharacteristic
208C2×#104—22no—
209#419—22no—
210C4×M16C22×C3111yescharacteristic
211C4×C4⋊C4C22×C3111yescharacteristic
212#340—22no—
213#328—22no—
214C2×C31—21no—
215C2×C31—21no—
216C2×C31—161no—
217C2×C31#200711yescharacteristic
218C2×C31#200911yescharacteristic
219C2×C31#201211yescharacteristic
220C2×#41—21no—
221C22×Q8—21no—
222C2×SD16—22no—
223C2×M16D4×C3112yes—
224C22×C8D4×C3112yes—
225C4⋊Q8—21no—
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8D4×C3112yes—
229C4⋊Q8D4×C3111yescharacteristic
230C4⋊Q8D4×C3111yescharacteristic
231C4⋊Q8D4×C3111yescharacteristic
232#127D4×C3111yescharacteristic
233#125—21no—
234#124—21no—
235C22⋊Q8—21no—
236C22⋊Q8—21no—
237#121—21no—
238#121—21no—
239C4×Q8—21no—
240C4×Q8—21no—
241C4×D4—21no—
242C4×D4—21no—
243#117—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C42—21no—
248C2×C42C23×C3111yescharacteristic
249#107—24no—
250#106—22no—
251C4⋊C8—21no—
252C4⋊C8—21no—
253C4⋊C8—21no—
254#104—44no—
255#103—24no—
256#103—24no—
257#103—22no—
258#102—22no—
259#102—24no—
260C22⋊C8D4×C3112yes—
261#97—21no—
262C4×C8—21no—
263C4×C8—21no—
264#95—21no—
265C31#1020511yescharacteristic, direct product factor, Sylow
266#41—42no—
267#41—42no—
268C2×Q8—22no—
269C2×Q8—21no—
270C2×Q8—21no—
271C2×Q8—21no—
272C2×Q8—41no—
273C2×Q8—42no—
274C2×Q8—42no—
275C2×D4—21no—
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—41no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4C2×D4×C3111yescharacteristic
283C22×C4C2×D4×C3111yescharacteristic
284C22×C4C2×D4×C3111yescharacteristic
285SD16—82no—
286M16—22no—
287M16—22no—
288C2×C8—22no—
289C2×C8—22no—
290C2×C8—22no—
291C2×C8—42no—
292C4⋊C4—22no—
293C4⋊C4—21no—
294C4⋊C4—22no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—22no—
300C4⋊C4—21no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C22⋊C4—41no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C42—41no—
310C42—42no—
311C42C2×D4×C3111yescharacteristic
312C42C2×D4×C3111yescharacteristic
313C42C2×D4×C3111yescharacteristic
314C42#41×C3111yescharacteristic
315C23—41no—
316C23C31×#12711yescharacteristic
317Q8—44no—
318Q8—41no—
319Q8—41no—
320Q8—42no—
321Q8—81no—
322Q8—82no—
323D4—42no—
324D4—41no—
325D4—41no—
326D4—42no—
327D4—81no—
328D4—81no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—41no—
332C2×C4—42no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—42no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4—82no—
342C2×C4C31×#12011yescharacteristic
343C2×C4C31×#12011yescharacteristic
344C2×C4C31×#12011yescharacteristic
345C2×C4C31×#12111yescharacteristic
346C2×C4C31×#12111yescharacteristic
347C2×C4C31×#12111yescharacteristic
348C2×C4C31×#13512yes—
349C2×C4C31×AGL(1,ℤ/8)12yes—
350C8—42no—
351C8—42no—
352C8—42no—
353C22—21no—
354C22—21no—
355C22—81no—
356C22—81no—
357C22—81no—
358C22C31×#39211yescharacteristic
359C22C31×#49511yescharacteristic
360C22C31×#49611yescharacteristic
361C4—21no—
362C4—21no—
363C4—21no—
364C4—82no—
365C4—81no—
366C4—81no—
367C4—81no—
368C4—82no—
369C4C31×#44912yes—
370C4C31×#45511yescharacteristic
371C4C31×#45611yescharacteristic
372C4C31×#46312yes—
373C2—21no—
374C2—21no—
375C2—161no—
376C2C31×#200711yescharacteristic
377C2C31×#200911yescharacteristic
378C2C31×#201211yescharacteristic
subgroupG/H
center, socleC22×C31#392
commutator, Frattini, cosocleC2×C42C23×C31
prime radicalC31×#532C22
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
3. C31×#3139C2semidirect
4. C31×#1988C2semidirect
6. C31×#1503C2semidirect
7. C31×#1283C2semidirect
125. #10205C31direct (N × H)
166. #3139C2×C31semidirect
167. #1988C2×C31semidirect
169. #1503C2×C31semidirect
170. #1283C2×C31semidirect
265. C31#10205direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#32462
C31×#32262
C31×#31392
C31×#19882
C31×#19802
C31×#15032
C31×#12832
#1020531