Finite Group Databasebeta

← C31×#8911 #21465670

Subgroups — C31×#8911 #21465670

Order 7936.

484 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2379C211yesmaximal, characteristic
2C31×#1959C211yesmaximal, characteristic
3C31×#1847C211yesmaximal, characteristic, complemented
4C31×#1836C211yesmaximal, characteristic, complemented
5C2×C31×#329C211yesmaximal, characteristic
6C31×#1295C211yesmaximal, characteristic, complemented
7C31×#1295C211yesmaximal, characteristic, complemented
8C2×C31×#124C2211yescharacteristic
9C2×C31×#107—21no—
10C2×C31×#106—21no—
11C2×C31×#103—21no—
12C2×C31×#102—21no—
13C2×C31×#97C2211yescharacteristic
14C2×C31×#97C2211yescharacteristic
15C2×C31×#97C2211yescharacteristic
16C31×#391—21no—
17C31×#388—21no—
18C31×#388—21no—
19C31×#386—21no—
20C31×#385—21no—
21C31×#385—21no—
22C31×#384C2211yescharacteristic
23C31×#382C2211yescharacteristic
24C31×#382C2211yescharacteristic
25C31×#340—21no—
26C31×#340—21no—
27C31×#329C414yescomplemented
28C22×Q8×C31D411yescharacteristic
29C22×D4×C31D411yescharacteristic
30C23×C4×C31—21no—
31C22×C8×C31—21no—
32C22×C8×C31—21no—
33C22×C8×C31—21no—
34C31×#124—21no—
35C31×#124—21no—
36C31×#124C2×C412yes—
37C31×#124Q812yes—
38C2×C4⋊C4×C31—21no—
39C2×C4⋊C4×C31—21no—
40C2×C4⋊C4×C31—21no—
41C2×C4⋊C4×C31—21no—
42C2×C4⋊C4×C31D411yescharacteristic
43C2×C4⋊C4×C31D411yescharacteristic
44C2×C4⋊C4×C31D411yescharacteristic
45C2×C4⋊C4×C31D411yescharacteristic
46C2×C22⋊C4×C31—21no—
47C2×C22⋊C4×C31—21no—
48C2×C22⋊C4×C31—21no—
49C2×C22⋊C4×C31—21no—
50C2×C22⋊C4×C31—21no—
51C2×C42×C31—21no—
52C2×C42×C31C2311yescharacteristic
53C31×#107—42no—
54C31×#106—42no—
55C31×#103—42no—
56C31×#102—42no—
57C31×#97—21no—
58C31×#97—21no—
59C31×#97—21no—
60C31×#97—21no—
61C31×#97C2×C412yescomplemented
62C31×#97C2×C412yescomplemented
63C31×#95—21no—
64C31×#95—21no—
65C31×#95—21no—
66C31×#95—21no—
67C31×#95—21no—
68C31×#95—21no—
69C24×C31—21no—
70C2×Q8×C31—21no—
71C2×Q8×C31—41no—
72C2×Q8×C31—41no—
73C2×Q8×C31C4⋊C412yes—
74C2×D4×C31—21no—
75C2×D4×C31—41no—
76C2×D4×C31—41no—
77C2×D4×C31C4⋊C412yes—
78C22×C4×C31—21no—
79C22×C4×C31—21no—
80C22×C4×C31—21no—
81C22×C4×C31—21no—
82C22×C4×C31—21no—
83C22×C4×C31—41no—
84C22×C4×C31—81no—
85C22×C4×C31—81no—
86C22×C4×C31—81no—
87C22×C4×C31C2×D411yescharacteristic
88C22×C4×C31C2×D411yescharacteristic
89C22×C4×C31C2×D411yescharacteristic
90C2×C8×C31—22no—
91C2×C8×C31—22no—
92C2×C8×C31—22no—
93C2×C8×C31—22no—
94C2×C8×C31—22no—
95C2×C8×C31—41no—
96C2×C8×C31—41no—
97C2×C8×C31—41no—
98C2×C8×C31—41no—
99C4⋊C4×C31—41no—
100C4⋊C4×C31—41no—
101C4⋊C4×C31—41no—
102C4⋊C4×C31—41no—
103C4⋊C4×C31—41no—
104C4⋊C4×C31—41no—
105C4⋊C4×C31—41no—
106C4⋊C4×C31—41no—
107C4⋊C4×C31—42no—
108C4⋊C4×C31—81no—
109C22⋊C4×C31—22no—
110C22⋊C4×C31—22no—
111C22⋊C4×C31—22no—
112C22⋊C4×C31—22no—
113C22⋊C4×C31—81no—
114C22⋊C4×C31—81no—
115C22⋊C4×C31—81no—
116C42×C31—81no—
117C42×C31C22×C411yescharacteristic
118C42×C31C2×Q811yescharacteristic
119C42×C31#4111yescharacteristic
120C42×C31#4111yescharacteristic
121#8911C3111yesmaximal, characteristic, direct product factor, Sylow
122C23×C31—22no—
123C23×C31—41no—
124C23×C31—41no—
125C23×C31—41no—
126C23×C31—41no—
127C23×C31—41no—
128C23×C31—41no—
129C23×C31#12011yescharacteristic
130Q8×C31—42no—
131Q8×C31—81no—
132D4×C31—42no—
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—22no—
141C2×C4×C31—41no—
142C2×C4×C31—41no—
143C2×C4×C31—41no—
144C2×C4×C31—41no—
145C2×C4×C31—41no—
146C2×C4×C31—41no—
147C2×C4×C31—41no—
148C2×C4×C31—41no—
149C2×C4×C31—41no—
150C2×C4×C31—41no—
151C2×C4×C31—41no—
152C2×C4×C31—41no—
153C2×C4×C31—41no—
154C2×C4×C31—41no—
155C2×C4×C31—84no—
156C2×C4×C31—81no—
157C2×C4×C31—81no—
158C2×C4×C31—81no—
159C2×C4×C31C2×C4⋊C411yescharacteristic
160C2×C4×C31C4×D411yescharacteristic
161C2×C4×C31C4×D411yescharacteristic
162C2×C4×C31C22⋊Q811yescharacteristic
163C2×C4×C31C22⋊Q811yescharacteristic
164C2×C4×C31#12311yescharacteristic
165C8×C31—24no—
166C8×C31—42no—
167C8×C31—42no—
168#2379C2×C3111yescharacteristic
169#1959C2×C3111yescharacteristic
170#1847C2×C3111yescharacteristic, complemented
171#1836C2×C3111yescharacteristic, complemented
172C2×#329C2×C3111yescharacteristic
173#1295C2×C3111yescharacteristic, complemented
174#1295C2×C3111yescharacteristic, complemented
175C22×C31—42no—
176C22×C31—42no—
177C22×C31—42no—
178C22×C31—81no—
179C22×C31—81no—
180C22×C31—81no—
181C22×C31—81no—
182C22×C31#38511yescharacteristic
183C22×C31#45311yescharacteristic
184C22×C31#45311yescharacteristic
185C22×C31#45411yescharacteristic
186C22×C31#45511yescharacteristic
187C22×C31#45511yescharacteristic
188C22×C31#45611yescharacteristic
189C4×C31—21no—
190C4×C31—21no—
191C4×C31—21no—
192C4×C31—21no—
193C4×C31—21no—
194C4×C31—21no—
195C4×C31—42no—
196C4×C31—81no—
197C4×C31—81no—
198C4×C31—81no—
199C4×C31—81no—
200C4×C31—161no—
201C2×#124C22×C3111yescharacteristic
202C2×#107—21no—
203C2×#106—21no—
204C2×#103—21no—
205C2×#102—21no—
206C2×#97C22×C3111yescharacteristic
207C2×#97C22×C3111yescharacteristic
208C2×#97C22×C3111yescharacteristic
209#391—21no—
210#388—21no—
211#388—21no—
212#386—21no—
213#385—21no—
214#385—21no—
215#384C22×C3111yescharacteristic
216#382C22×C3111yescharacteristic
217#382C22×C3111yescharacteristic
218#340—21no—
219#340—21no—
220#329C4×C3114yescomplemented
221C2×C31—82no—
222C2×C31#165611yescharacteristic
223C2×C31#165911yescharacteristic
224C2×C31#166111yescharacteristic
225C2×C31#166411yescharacteristic
226C2×C31#185611yescharacteristic
227C2×C31#185911yescharacteristic
228C2×C31#186011yescharacteristic
229C22×Q8D4×C3111yescharacteristic
230C22×D4D4×C3111yescharacteristic
231C23×C4—21no—
232C22×C8—21no—
233C22×C8—21no—
234C22×C8—21no—
235#124—21no—
236#124—21no—
237#124C2×C4×C3112yes—
238#124Q8×C3112yes—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4D4×C3111yescharacteristic
244C2×C4⋊C4D4×C3111yescharacteristic
245C2×C4⋊C4D4×C3111yescharacteristic
246C2×C4⋊C4D4×C3111yescharacteristic
247C2×C22⋊C4—21no—
248C2×C22⋊C4—21no—
249C2×C22⋊C4—21no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—21no—
252C2×C42—21no—
253C2×C42C23×C3111yescharacteristic
254#107—42no—
255#106—42no—
256#103—42no—
257#102—42no—
258#97—21no—
259#97—21no—
260#97—21no—
261#97—21no—
262#97C2×C4×C3112yescomplemented
263#97C2×C4×C3112yescomplemented
264#95—21no—
265#95—21no—
266#95—21no—
267#95—21no—
268#95—21no—
269#95—21no—
270C31#891111yescharacteristic, direct product factor, Sylow
271C24—21no—
272C2×Q8—21no—
273C2×Q8—41no—
274C2×Q8—41no—
275C2×Q8C4⋊C4×C3112yes—
276C2×D4—21no—
277C2×D4—41no—
278C2×D4—41no—
279C2×D4C4⋊C4×C3112yes—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—41no—
286C22×C4—81no—
287C22×C4—81no—
288C22×C4—81no—
289C22×C4C2×D4×C3111yescharacteristic
290C22×C4C2×D4×C3111yescharacteristic
291C22×C4C2×D4×C3111yescharacteristic
292C2×C8—22no—
293C2×C8—22no—
294C2×C8—22no—
295C2×C8—22no—
296C2×C8—22no—
297C2×C8—41no—
298C2×C8—41no—
299C2×C8—41no—
300C2×C8—41no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4—42no—
310C4⋊C4—81no—
311C22⋊C4—22no—
312C22⋊C4—22no—
313C22⋊C4—22no—
314C22⋊C4—22no—
315C22⋊C4—81no—
316C22⋊C4—81no—
317C22⋊C4—81no—
318C42—81no—
319C42C22×C4×C3111yescharacteristic
320C42C2×Q8×C3111yescharacteristic
321C42#41×C3111yescharacteristic
322C42#41×C3111yescharacteristic
323C23—22no—
324C23—41no—
325C23—41no—
326C23—41no—
327C23—41no—
328C23—41no—
329C23—41no—
330C23C31×#12011yescharacteristic
331Q8—42no—
332Q8—81no—
333D4—42no—
334D4—81no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—22no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—84no—
357C2×C4—81no—
358C2×C4—81no—
359C2×C4—81no—
360C2×C4C2×C4⋊C4×C3111yescharacteristic
361C2×C4C4×D4×C3111yescharacteristic
362C2×C4C4×D4×C3111yescharacteristic
363C2×C4C31×C22⋊Q811yescharacteristic
364C2×C4C31×C22⋊Q811yescharacteristic
365C2×C4C31×#12311yescharacteristic
366C8—24no—
367C8—42no—
368C8—42no—
369C22—42no—
370C22—42no—
371C22—42no—
372C22—81no—
373C22—81no—
374C22—81no—
375C22—81no—
376C22C31×#38511yescharacteristic
377C22C31×#45311yescharacteristic
378C22C31×#45311yescharacteristic
379C22C31×#45411yescharacteristic
380C22C31×#45511yescharacteristic
381C22C31×#45511yescharacteristic
382C22C31×#45611yescharacteristic
383C4—21no—
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—21no—
389C4—42no—
390C4—81no—
391C4—81no—
392C4—81no—
393C4—81no—
394C4—161no—
395C2—82no—
396C2C31×#165611yescharacteristic
397C2C31×#165911yescharacteristic
398C2C31×#166111yescharacteristic
399C2C31×#166411yescharacteristic
400C2C31×#185611yescharacteristic
401C2C31×#185911yescharacteristic
402C2C31×#186011yescharacteristic
subgroupG/H
center, socleC23×C31#120
commutatorC42C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC22×D4×C31D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
3. C31×#1847C2semidirect
4. C31×#1836C2semidirect
6. C31×#1295C2semidirect
7. C31×#1295C2semidirect
27. C31×#329C4semidirect
61. C31×#97C2×C4semidirect
62. C31×#97C2×C4semidirect
121. #8911C31direct (N × H)
170. #1847C2×C31semidirect
171. #1836C2×C31semidirect
173. #1295C2×C31semidirect
174. #1295C2×C31semidirect
220. #329C4×C31semidirect
262. #97C2×C4×C31semidirect
263. #97C2×C4×C31semidirect
270. C31#8911direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#23792
C31×#19592
C31×#18472
C31×#18362
C2×C31×#3292
C31×#12952
#891131