Finite Group Databasebeta

← C31×#8453 #21465212

Subgroups — C31×#8453 #21465212

Order 7936.

1330 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 1330 conjugacy classes of subgroups — too many to draw. Only its 158 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3484C211yesmaximal, characteristic
2C31×#1783C211yesmaximal, characteristic, complemented
3C31×#1504C214yesmaximal, complemented
4C31×#1438C211yesmaximal, characteristic, complemented
5C2×C31×H(5,𝔽2)C411yescharacteristic, complemented
6C23×D4×C31C2211yescharacteristic
7C31×#546—24no—
8D42×C31—24no—
9C31×#535C412yescomplemented
10C31×#534—22no—
11C31×#525C2212yes—
12C2×C31×#120—22no—
13C31×#518C411yescharacteristic, complemented
14C22×C22⋊C4×C31—22no—
15C2×C31×#100—22no—
16C31×#407C2212yescomplemented
17C2×C31×#95C2212yescomplemented
18C31×#328—24no—
19C31×#327—24no—
20C25×C31D412yes—
21C31×H(5,𝔽2)—44no—
22C2×#41×C31—22no—
23C2×#41×C31C2×C412yes—
24C22×D4×C31—22no—
25C22×D4×C31—24no—
26C22×D4×C31—22no—
27C22×D4×C31—24no—
28C22×D4×C31—44no—
29C22×D4×C31C2×C411yescharacteristic
30C22×D4×C31C2×C411yescharacteristic
31C22×D4×C31D412yes—
32C23×C4×C31—22no—
33C23×C4×C31C2311yescharacteristic
34C2×M16×C31—22no—
35C31×#127—22no—
36C31×#124—22no—
37C31×#123—24no—
38C31×#123—22no—
39C31×C22⋊Q8D414yes—
40C31×#121—28no—
41C31×#121—24no—
42C31×#121D414yes—
43C31×#120—28no—
44C31×#120—24no—
45C31×#120—24no—
46C31×#120—22no—
47C4×D4×C31—24no—
48C4×D4×C31—24no—
49C31×#117C2×C412yes—
50C2×C22⋊C4×C31—24no—
51C2×C22⋊C4×C31—22no—
52C2×C22⋊C4×C31—48no—
53C2×C22⋊C4×C31—44no—
54C31×#100—44no—
55C31×C22⋊C8—24no—
56C31×#95—24no—
57C24×C31—22no—
58C24×C31—24no—
59C24×C31—24no—
60C24×C31—42no—
61C24×C31—44no—
62C24×C31—44no—
63C24×C31C22⋊C412yes—
64C24×C31C22⋊C412yes—
65C24×C31C2×D411yescharacteristic
66#41×C31—44no—
67#41×C31—48no—
68C2×Q8×C31C22⋊C412yescomplemented
69C2×D4×C31—24no—
70C2×D4×C31—24no—
71C2×D4×C31—24no—
72C2×D4×C31—22no—
73C2×D4×C31—24no—
74C2×D4×C31—28no—
75C2×D4×C31—22no—
76C2×D4×C31—22no—
77C2×D4×C31—24no—
78C2×D4×C31—42no—
79C2×D4×C31—42no—
80C2×D4×C31—416no—
81C2×D4×C31—48no—
82C2×D4×C31—44no—
83C2×D4×C31—44no—
84C2×D4×C31—84no—
85C2×D4×C31—84no—
86C2×D4×C31C22⋊C412yescomplemented
87C22×C4×C31—22no—
88C22×C4×C31—24no—
89C22×C4×C31—22no—
90C22×C4×C31—24no—
91C22×C4×C31—42no—
92C22×C4×C31—44no—
93C22×C4×C31—44no—
94C22×C4×C31—42no—
95C22×C4×C31—42no—
96C22×C4×C31C22×C411yescharacteristic
97C22×C4×C31C2×D411yescharacteristic
98C22×C4×C31C2×D414yes—
99M16×C31—44no—
100C2×C8×C31—42no—
101C4⋊C4×C31—24no—
102C4⋊C4×C31C22⋊C414yescomplemented
103C22⋊C4×C31—24no—
104C22⋊C4×C31—28no—
105C22⋊C4×C31—22no—
106C22⋊C4×C31—24no—
107C22⋊C4×C31—24no—
108C22⋊C4×C31—416no—
109C42×C31—22no—
110#8453C3111yesmaximal, characteristic, direct product factor, Sylow
111C23×C31—22no—
112C23×C31—22no—
113C23×C31—22no—
114C23×C31—22no—
115C23×C31—22no—
116C23×C31—22no—
117C23×C31—22no—
118C23×C31—22no—
119C23×C31—22no—
120C23×C31—48no—
121C23×C31—44no—
122C23×C31—44no—
123C23×C31—44no—
124C23×C31—48no—
125C23×C31—44no—
126C23×C31—44no—
127C23×C31—44no—
128C23×C31—44no—
129C23×C31—84no—
130C23×C31—82no—
131C23×C31—84no—
132C23×C31—82no—
133C23×C31—84no—
134C23×C31#9914yes—
135C23×C31C2×C22⋊C411yescharacteristic
136C23×C31#12012yes—
137Q8×C31—42no—
138D4×C31—28no—
139D4×C31—48no—
140D4×C31—42no—
141D4×C31—44no—
142D4×C31—48no—
143D4×C31—44no—
144D4×C31—44no—
145D4×C31—44no—
146D4×C31—88no—
147C2×C4×C31—22no—
148C2×C4×C31—22no—
149C2×C4×C31—24no—
150C2×C4×C31—22no—
151C2×C4×C31—44no—
152C2×C4×C31—44no—
153C2×C4×C31—44no—
154C2×C4×C31—48no—
155C2×C4×C31—44no—
156C2×C4×C31—84no—
157C2×C4×C31—84no—
158C2×C4×C31—82no—
159C2×C4×C31—82no—
160C2×C4×C31C2×C22⋊C412yes—
161C2×C4×C31#12012yes—
162C8×C31—82no—
163#3484C2×C3111yescharacteristic
164#1783C2×C3111yescharacteristic, complemented
165#1504C2×C3114yescomplemented
166#1438C2×C3111yescharacteristic, complemented
167C22×C31—22no—
168C22×C31—24no—
169C22×C31—22no—
170C22×C31—22no—
171C22×C31—22no—
172C22×C31—22no—
173C22×C31—24no—
174C22×C31—44no—
175C22×C31—44no—
176C22×C31—44no—
177C22×C31—44no—
178C22×C31—44no—
179C22×C31—42no—
180C22×C31—42no—
181C22×C31—82no—
182C22×C31—88no—
183C22×C31—88no—
184C22×C31—82no—
185C22×C31—164no—
186C22×C31#37911yescharacteristic
187C22×C31C2×#9912yes—
188C22×C31#45312yes—
189C22×C31#45512yes—
190C4×C31—22no—
191C4×C31—22no—
192C4×C31—44no—
193C4×C31—42no—
194C4×C31—84no—
195C2×H(5,𝔽2)C4×C3111yescharacteristic, complemented
196C23×D4C22×C3111yescharacteristic
197#546—24no—
198D42—24no—
199#535C4×C3112yescomplemented
200#534—22no—
201#525C22×C3112yes—
202C2×#120—22no—
203#518C4×C3111yescharacteristic, complemented
204C22×C22⋊C4—22no—
205C2×#100—22no—
206#407C22×C3112yescomplemented
207C2×#95C22×C3112yescomplemented
208#328—24no—
209#327—24no—
210C2×C31—22no—
211C2×C31—22no—
212C2×C31—22no—
213C2×C31—44no—
214C2×C31—82no—
215C2×C31—82no—
216C2×C31#178111yescharacteristic
217C2×C31#179212yes—
218C25D4×C3112yes—
219H(5,𝔽2)—44no—
220C2×#41—22no—
221C2×#41C2×C4×C3112yes—
222C22×D4—22no—
223C22×D4—24no—
224C22×D4—22no—
225C22×D4—24no—
226C22×D4—44no—
227C22×D4C2×C4×C3111yescharacteristic
228C22×D4C2×C4×C3111yescharacteristic
229C22×D4D4×C3112yes—
230C23×C4—22no—
231C23×C4C23×C3111yescharacteristic
232C2×M16—22no—
233#127—22no—
234#124—22no—
235#123—24no—
236#123—22no—
237C22⋊Q8D4×C3114yes—
238#121—28no—
239#121—24no—
240#121D4×C3114yes—
241#120—28no—
242#120—24no—
243#120—24no—
244#120—22no—
245C4×D4—24no—
246C4×D4—24no—
247#117C2×C4×C3112yes—
248C2×C22⋊C4—24no—
249C2×C22⋊C4—22no—
250C2×C22⋊C4—48no—
251C2×C22⋊C4—44no—
252#100—44no—
253C22⋊C8—24no—
254#95—24no—
255C31#845311yescharacteristic, direct product factor, Sylow
256C24—22no—
257C24—24no—
258C24—24no—
259C24—42no—
260C24—44no—
261C24—44no—
262C24C22⋊C4×C3112yes—
263C24C22⋊C4×C3112yes—
264C24C2×D4×C3111yescharacteristic
265#41—44no—
266#41—48no—
267C2×Q8C22⋊C4×C3112yescomplemented
268C2×D4—24no—
269C2×D4—24no—
270C2×D4—24no—
271C2×D4—22no—
272C2×D4—24no—
273C2×D4—28no—
274C2×D4—22no—
275C2×D4—22no—
276C2×D4—24no—
277C2×D4—42no—
278C2×D4—42no—
279C2×D4—416no—
280C2×D4—48no—
281C2×D4—44no—
282C2×D4—44no—
283C2×D4—84no—
284C2×D4—84no—
285C2×D4C22⋊C4×C3112yescomplemented
286C22×C4—22no—
287C22×C4—24no—
288C22×C4—22no—
289C22×C4—24no—
290C22×C4—42no—
291C22×C4—44no—
292C22×C4—44no—
293C22×C4—42no—
294C22×C4—42no—
295C22×C4C22×C4×C3111yescharacteristic
296C22×C4C2×D4×C3111yescharacteristic
297C22×C4C2×D4×C3114yes—
298M16—44no—
299C2×C8—42no—
300C4⋊C4—24no—
301C4⋊C4C22⋊C4×C3114yescomplemented
302C22⋊C4—24no—
303C22⋊C4—28no—
304C22⋊C4—22no—
305C22⋊C4—24no—
306C22⋊C4—24no—
307C22⋊C4—416no—
308C42—22no—
309C23—22no—
310C23—22no—
311C23—22no—
312C23—22no—
313C23—22no—
314C23—22no—
315C23—22no—
316C23—22no—
317C23—22no—
318C23—48no—
319C23—44no—
320C23—44no—
321C23—44no—
322C23—48no—
323C23—44no—
324C23—44no—
325C23—44no—
326C23—44no—
327C23—84no—
328C23—82no—
329C23—84no—
330C23—82no—
331C23—84no—
332C23C31×#9914yes—
333C23C2×C22⋊C4×C3111yescharacteristic
334C23C31×#12012yes—
335Q8—42no—
336D4—28no—
337D4—48no—
338D4—42no—
339D4—44no—
340D4—48no—
341D4—44no—
342D4—44no—
343D4—44no—
344D4—88no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—24no—
348C2×C4—22no—
349C2×C4—44no—
350C2×C4—44no—
351C2×C4—44no—
352C2×C4—48no—
353C2×C4—44no—
354C2×C4—84no—
355C2×C4—84no—
356C2×C4—82no—
357C2×C4—82no—
358C2×C4C2×C22⋊C4×C3112yes—
359C2×C4C31×#12012yes—
360C8—82no—
361C22—22no—
362C22—24no—
363C22—22no—
364C22—22no—
365C22—22no—
366C22—22no—
367C22—24no—
368C22—44no—
369C22—44no—
370C22—44no—
371C22—42no—
372C22—42no—
373C22—44no—
374C22—44no—
375C22—82no—
376C22—88no—
377C22—88no—
378C22—82no—
379C22—164no—
380C22C31×#37911yescharacteristic
381C22C2×C31×#9912yes—
382C22C31×#45312yes—
383C22C31×#45512yes—
384C4—22no—
385C4—22no—
386C4—42no—
387C4—44no—
388C4—84no—
389C2—22no—
390C2—22no—
391C2—22no—
392C2—44no—
393C2—82no—
394C2—82no—
395C2C31×#178111yescharacteristic
396C2C31×#179212yes—
subgroupG/H
center, socleC22×C31#379
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC31×#3484C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#1783C2semidirect
3. C31×#1504C2semidirect
4. C31×#1438C2semidirect
5. C2×C31×H(5,𝔽2)C4semidirect
9. C31×#535C4semidirect
13. C31×#518C4semidirect
16. C31×#407C22semidirect
17. C2×C31×#95C22semidirect
68. C2×Q8×C31C22⋊C4semidirect
86. C2×D4×C31C22⋊C4semidirect
102. C4⋊C4×C31C22⋊C4semidirect
110. #8453C31direct (N × H)
164. #1783C2×C31semidirect
165. #1504C2×C31semidirect
166. #1438C2×C31semidirect
195. C2×H(5,𝔽2)C4×C31semidirect
199. #535C4×C31semidirect
203. #518C4×C31semidirect
206. #407C22×C31semidirect
207. C2×#95C22×C31semidirect
255. C31#8453direct (N × H)
267. C2×Q8C22⋊C4×C31semidirect
285. C2×D4C22⋊C4×C31semidirect
301. C4⋊C4C22⋊C4×C31semidirect

Maximal subgroups

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

subgroupindex
C31×#34842
C31×#17832
C31×#15042
C31×#14382
#845331