Finite Group Databasebeta

← C31×#9311 #21466070

Subgroups — C31×#9311 #21466070

Order 7936.

514 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3115C211yesmaximal, characteristic
2C31×#2875C211yesmaximal, characteristic, complemented
3C31×#1530C211yesmaximal, characteristic, complemented
4C31×#1488C211yesmaximal, characteristic, complemented
5C31×#1484C211yesmaximal, characteristic, complemented
6C31×#1302C211yesmaximal, characteristic, complemented
7C31×#1291C211yesmaximal, characteristic, complemented
8C2×C31×#131—21no—
9C31×#532C2211yescharacteristic
10C4×#41×C31C2211yescharacteristic
11C31×#482—21no—
12C31×#475C411yescharacteristic
13C31×#474C411yescharacteristic
14C31×#460C411yescharacteristic
15C31×#459C411yescharacteristic
16C31×#449—21no—
17C31×#442—21no—
18C31×#440—21no—
19C31×#432C2211yescharacteristic
20C31×#432C2211yescharacteristic
21C31×#431C2211yescharacteristic
22C31×#405—21no—
23C31×#405—22no—
24C4×M16×C31—21no—
25C4×M16×C31C2211yescharacteristic
26C2×C31×#97—21no—
27C2×C31×#97C2211yescharacteristic
28C31×#329—21no—
29C31×#329—21no—
30C31×Q8⋊C8—21no—
31C31×D4⋊C8—21no—
32C31×D4⋊C8—22no—
33C2×#41×C31—21no—
34C2×#41×C31D411yescharacteristic
35C2×SD16×C31—21no—
36C2×D8×C31—21no—
37C31×#131—24no—
38C31×#131—24no—
39C2×M16×C31—22no—
40C2×M16×C31—21no—
41C22×C8×C31—22no—
42C22×C8×C31—21no—
43C31×C4⋊Q8C2×C411yescharacteristic
44C31×#127C2×C411yescharacteristic
45C31×#124—21no—
46C31×#121—21no—
47C31×#121—21no—
48C4×Q8×C31C2×C411yescharacteristic
49C4×Q8×C31D411yescharacteristic
50C4×D4×C31—21no—
51C4×D4×C31—21no—
52C4×D4×C31—21no—
53C4×D4×C31—21no—
54C4×D4×C31C2×C411yescharacteristic
55C4×D4×C31D411yescharacteristic
56C31×#117—21no—
57C31×#117D411yescharacteristic
58C2×C42×C31—21no—
59C2×C42×C31C2311yescharacteristic
60C31×#107—21no—
61C31×#106—21no—
62C31×C4⋊C8—21no—
63C31×C4⋊C8—21no—
64C31×C4⋊C8C2×C411yescharacteristic
65C31×C4⋊C8C2×C411yescharacteristic
66C31×#103—21no—
67C31×#102—21no—
68C31×#102—21no—
69C31×#102—21no—
70C31×C22⋊C8—21no—
71C31×C22⋊C8—21no—
72C31×C22⋊C8—21no—
73C31×#97—22no—
74C31×#97—21no—
75C31×#97—21no—
76C31×#97—21no—
77C31×#97—21no—
78C31×#97D411yescharacteristic
79C31×#97D411yescharacteristic
80C4×C8×C31—22no—
81C4×C8×C31—21no—
82C4×C8×C31D412yes—
83#41×C31—22no—
84#41×C31—22no—
85#41×C31—82no—
86C2×Q8×C31—21no—
87C2×Q8×C31C22⋊C411yescharacteristic
88C2×D4×C31—21no—
89C2×D4×C31—21no—
90C2×D4×C31—21no—
91C2×D4×C31—21no—
92C2×D4×C31—41no—
93C2×D4×C31C22⋊C411yescharacteristic
94C22×C4×C31—21no—
95C22×C4×C31—21no—
96C22×C4×C31—21no—
97C22×C4×C31—41no—
98C22×C4×C31C2×D411yescharacteristic
99C22×C4×C31#4111yescharacteristic
100C22×C4×C31#4111yescharacteristic
101SD16×C31—42no—
102D8×C31—42no—
103M16×C31—28no—
104M16×C31—22no—
105M16×C31—22no—
106C2×C8×C31—28no—
107C2×C8×C31—22no—
108C2×C8×C31—22no—
109C2×C8×C31—21no—
110C2×C8×C31—22no—
111C2×C8×C31—21no—
112C2×C8×C31—21no—
113C2×C8×C31—21no—
114C2×C8×C31—41no—
115C2×C8×C31—41no—
116C4⋊C4×C31—21no—
117C4⋊C4×C31—21no—
118C4⋊C4×C31—21no—
119C4⋊C4×C31—21no—
120C4⋊C4×C31C22⋊C411yescharacteristic
121C4⋊C4×C31C22⋊C411yescharacteristic
122C22⋊C4×C31—21no—
123C22⋊C4×C31—21no—
124C22⋊C4×C31—21no—
125C22⋊C4×C31—41no—
126C22⋊C4×C31—41no—
127C42×C31—21no—
128C42×C31—21no—
129C42×C31—21no—
130C42×C31C22×C411yescharacteristic
131C42×C31C2×D411yescharacteristic
132C42×C31C2×D411yescharacteristic
133C42×C31C2×D411yescharacteristic
134#9311C3111yesmaximal, characteristic, direct product factor, Sylow
135C23×C31—21no—
136C23×C31—41no—
137C23×C31#12311yescharacteristic
138Q8×C31—21no—
139Q8×C31—81no—
140Q8×C31#10412yes—
141D4×C31—24no—
142D4×C31—21no—
143D4×C31—42no—
144D4×C31—41no—
145D4×C31—41no—
146D4×C31—81no—
147D4×C31—82no—
148D4×C31#10412yes—
149C2×C4×C31—24no—
150C2×C4×C31—21no—
151C2×C4×C31—21no—
152C2×C4×C31—21no—
153C2×C4×C31—21no—
154C2×C4×C31—21no—
155C2×C4×C31—41no—
156C2×C4×C31—41no—
157C2×C4×C31—41no—
158C2×C4×C31—81no—
159C2×C4×C31—81no—
160C2×C4×C31—82no—
161C2×C4×C31C2×C22⋊C411yescharacteristic
162C2×C4×C31C4×D411yescharacteristic
163C2×C4×C31C4×D411yescharacteristic
164C2×C4×C31#12011yescharacteristic
165C2×C4×C31#12111yescharacteristic
166C2×C4×C31#12111yescharacteristic
167C8×C31—22no—
168C8×C31—22no—
169C8×C31—24no—
170C8×C31—41no—
171C8×C31—41no—
172C8×C31—81no—
173C8×C31—81no—
174#3115C2×C3111yescharacteristic
175#2875C2×C3111yescharacteristic, complemented
176#1530C2×C3111yescharacteristic, complemented
177#1488C2×C3111yescharacteristic, complemented
178#1484C2×C3111yescharacteristic, complemented
179#1302C2×C3111yescharacteristic, complemented
180#1291C2×C3111yescharacteristic, complemented
181C22×C31—21no—
182C22×C31—21no—
183C22×C31—22no—
184C22×C31—21no—
185C22×C31—41no—
186C22×C31—41no—
187C22×C31—81no—
188C22×C31—81no—
189C22×C31—81no—
190C22×C31#38611yescharacteristic
191C4×C31—21no—
192C4×C31—21no—
193C4×C31—21no—
194C4×C31—22no—
195C4×C31—21no—
196C4×C31—21no—
197C4×C31—41no—
198C4×C31—41no—
199C4×C31—81no—
200C4×C31C2×#10411yescharacteristic
201C4×C31C2×#10411yescharacteristic
202C2×#131—21no—
203#532C22×C3111yescharacteristic
204C4×#41C22×C3111yescharacteristic
205#482—21no—
206#475C4×C3111yescharacteristic
207#474C4×C3111yescharacteristic
208#460C4×C3111yescharacteristic
209#459C4×C3111yescharacteristic
210#449—21no—
211#442—21no—
212#440—21no—
213#432C22×C3111yescharacteristic
214#432C22×C3111yescharacteristic
215#431C22×C3111yescharacteristic
216#405—21no—
217#405—22no—
218C4×M16—21no—
219C4×M16C22×C3111yescharacteristic
220C2×#97—21no—
221C2×#97C22×C3111yescharacteristic
222#329—21no—
223#329—21no—
224Q8⋊C8—21no—
225D4⋊C8—21no—
226D4⋊C8—22no—
227C2×C31—41no—
228C2×C31—42no—
229C2×C31—161no—
230C2×C31#188111yescharacteristic
231C2×C31#189611yescharacteristic
232C2×C31#190311yescharacteristic
233C2×#41—21no—
234C2×#41D4×C3111yescharacteristic
235C2×SD16—21no—
236C2×D8—21no—
237#131—24no—
238#131—24no—
239C2×M16—22no—
240C2×M16—21no—
241C22×C8—22no—
242C22×C8—21no—
243C4⋊Q8C2×C4×C3111yescharacteristic
244#127C2×C4×C3111yescharacteristic
245#124—21no—
246#121—21no—
247#121—21no—
248C4×Q8C2×C4×C3111yescharacteristic
249C4×Q8D4×C3111yescharacteristic
250C4×D4—21no—
251C4×D4—21no—
252C4×D4—21no—
253C4×D4—21no—
254C4×D4C2×C4×C3111yescharacteristic
255C4×D4D4×C3111yescharacteristic
256#117—21no—
257#117D4×C3111yescharacteristic
258C2×C42—21no—
259C2×C42C23×C3111yescharacteristic
260#107—21no—
261#106—21no—
262C4⋊C8—21no—
263C4⋊C8—21no—
264C4⋊C8C2×C4×C3111yescharacteristic
265C4⋊C8C2×C4×C3111yescharacteristic
266#103—21no—
267#102—21no—
268#102—21no—
269#102—21no—
270C22⋊C8—21no—
271C22⋊C8—21no—
272C22⋊C8—21no—
273#97—22no—
274#97—21no—
275#97—21no—
276#97—21no—
277#97—21no—
278#97D4×C3111yescharacteristic
279#97D4×C3111yescharacteristic
280C4×C8—22no—
281C4×C8—21no—
282C4×C8D4×C3112yes—
283C31#931111yescharacteristic, direct product factor, Sylow
284#41—22no—
285#41—22no—
286#41—82no—
287C2×Q8—21no—
288C2×Q8C22⋊C4×C3111yescharacteristic
289C2×D4—21no—
290C2×D4—21no—
291C2×D4—21no—
292C2×D4—21no—
293C2×D4—41no—
294C2×D4C22⋊C4×C3111yescharacteristic
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—41no—
299C22×C4C2×D4×C3111yescharacteristic
300C22×C4#41×C3111yescharacteristic
301C22×C4#41×C3111yescharacteristic
302SD16—42no—
303D8—42no—
304M16—28no—
305M16—22no—
306M16—22no—
307C2×C8—28no—
308C2×C8—22no—
309C2×C8—22no—
310C2×C8—21no—
311C2×C8—22no—
312C2×C8—21no—
313C2×C8—21no—
314C2×C8—21no—
315C2×C8—41no—
316C2×C8—41no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4C22⋊C4×C3111yescharacteristic
322C4⋊C4C22⋊C4×C3111yescharacteristic
323C22⋊C4—21no—
324C22⋊C4—21no—
325C22⋊C4—21no—
326C22⋊C4—41no—
327C22⋊C4—41no—
328C42—21no—
329C42—21no—
330C42—21no—
331C42C22×C4×C3111yescharacteristic
332C42C2×D4×C3111yescharacteristic
333C42C2×D4×C3111yescharacteristic
334C42C2×D4×C3111yescharacteristic
335C23—21no—
336C23—41no—
337C23C31×#12311yescharacteristic
338Q8—21no—
339Q8—81no—
340Q8C31×#10412yes—
341D4—24no—
342D4—21no—
343D4—42no—
344D4—41no—
345D4—41no—
346D4—81no—
347D4—82no—
348D4C31×#10412yes—
349C2×C4—24no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—81no—
359C2×C4—81no—
360C2×C4—82no—
361C2×C4C2×C22⋊C4×C3111yescharacteristic
362C2×C4C4×D4×C3111yescharacteristic
363C2×C4C4×D4×C3111yescharacteristic
364C2×C4C31×#12011yescharacteristic
365C2×C4C31×#12111yescharacteristic
366C2×C4C31×#12111yescharacteristic
367C8—22no—
368C8—22no—
369C8—24no—
370C8—41no—
371C8—41no—
372C8—81no—
373C8—81no—
374C22—21no—
375C22—21no—
376C22—22no—
377C22—21no—
378C22—41no—
379C22—41no—
380C22—81no—
381C22—81no—
382C22—81no—
383C22C31×#38611yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—22no—
388C4—21no—
389C4—21no—
390C4—41no—
391C4—41no—
392C4—81no—
393C4C2×C31×#10411yescharacteristic
394C4C2×C31×#10411yescharacteristic
395C2—41no—
396C2—42no—
397C2—161no—
398C2C31×#188111yescharacteristic
399C2C31×#189611yescharacteristic
400C2C31×#190311yescharacteristic
subgroupG/H
center, socleC22×C31#386
commutatorC42C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC31×#3115C2
LCSG ▷ 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×#2875C2semidirect
3. C31×#1530C2semidirect
4. C31×#1488C2semidirect
5. C31×#1484C2semidirect
6. C31×#1302C2semidirect
7. C31×#1291C2semidirect
134. #9311C31direct (N × H)
175. #2875C2×C31semidirect
176. #1530C2×C31semidirect
177. #1488C2×C31semidirect
178. #1484C2×C31semidirect
179. #1302C2×C31semidirect
180. #1291C2×C31semidirect
283. C31#9311direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#31152
C31×#28752
C31×#15302
C31×#14882
C31×#14842
C31×#13022
C31×#12912
#931131