Finite Group Databasebeta

← C31×#9379 #21466138

Subgroups — C31×#9379 #21466138

Order 7936.

492 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3215C211yesmaximal, characteristic
2C31×#2337C211yesmaximal, characteristic
3C31×#1986C211yesmaximal, characteristic, complemented
4C31×#1527C211yesmaximal, characteristic
5C31×#1515C211yesmaximal, characteristic, complemented
6C31×#1288C211yesmaximal, characteristic, complemented
7C31×#1285C211yesmaximal, characteristic, complemented
8C31×#533C2211yescharacteristic
9C2×C31×#124C2211yescharacteristic
10C31×#497C412yescomplemented
11C31×#489C412yescomplemented
12C31×#464—22no—
13C31×#451—21no—
14C31×#450—21no—
15C31×#432C2211yescharacteristic
16C31×#432C2211yescharacteristic
17C4×M16×C31C2211yescharacteristic
18C31×#391—21no—
19C31×#388—21no—
20C31×#388—21no—
21C31×#386—21no—
22C31×#385—21no—
23C31×#383C2211yescharacteristic
24C4×C4⋊C4×C31C2211yescharacteristic
25C4×C22⋊C4×C31—21no—
26C31×#339—21no—
27C31×#339—21no—
28C31×#329—22no—
29C31×#328—21no—
30C31×#328—21no—
31C22×Q8×C31D411yescharacteristic
32C22×D4×C31D411yescharacteristic
33C23×C4×C31—21no—
34C2×Q16×C31—22no—
35C2×SD16×C31—22no—
36C2×M16×C31—21no—
37C31×C4⋊Q8C2×C411yescharacteristic, complemented
38C31×C4⋊Q8C2×C411yescharacteristic, complemented
39C31×#125—21no—
40C31×#124—21no—
41C31×#124—21no—
42C31×#124C2×C412yes—
43C31×#124D412yes—
44C31×C22⋊Q8—21no—
45C31×C22⋊Q8—21no—
46C4×Q8×C31—21no—
47C4×Q8×C31—21no—
48C31×#117—21no—
49C2×C4⋊C4×C31—21no—
50C2×C4⋊C4×C31—21no—
51C2×C22⋊C4×C31—21no—
52C2×C22⋊C4×C31—21no—
53C2×C22⋊C4×C31—21no—
54C2×C22⋊C4×C31—21no—
55C2×C22⋊C4×C31—21no—
56C2×C42×C31—21no—
57C2×C42×C31D411yescharacteristic
58C2×C42×C31D411yescharacteristic
59C2×C42×C31C2311yescharacteristic
60C31×C4⋊C8—21no—
61C31×C4⋊C8—21no—
62C31×#103—22no—
63C31×#102—22no—
64C31×C22⋊C8—21no—
65C31×C22⋊C8—21no—
66C31×#97—21no—
67C31×#97—21no—
68C31×#97C2×C412yescomplemented
69C4×C8×C31—21no—
70C31×#95—21no—
71C31×#95—21no—
72C31×#95—21no—
73C31×#95—21no—
74C31×#95—21no—
75C31×#95D411yescharacteristic
76C31×#95D411yescharacteristic
77C24×C31—21no—
78C2×Q8×C31—21no—
79C2×Q8×C31—21no—
80C2×Q8×C31—21no—
81C2×Q8×C31—81no—
82C2×Q8×C31C22⋊C412yes—
83C2×D4×C31—21no—
84C2×D4×C31—81no—
85C2×D4×C31C22⋊C412yes—
86C22×C4×C31—21no—
87C22×C4×C31—21no—
88C22×C4×C31—21no—
89C22×C4×C31—21no—
90C22×C4×C31—21no—
91C22×C4×C31—42no—
92C22×C4×C31—81no—
93C22×C4×C31—81no—
94C22×C4×C31C2×D411yescharacteristic
95C22×C4×C31C2×D411yescharacteristic
96C22×C4×C31C2×D411yescharacteristic
97Q16×C31—82no—
98SD16×C31—82no—
99M16×C31—22no—
100M16×C31—41no—
101C2×C8×C31—22no—
102C2×C8×C31—41no—
103C2×C8×C31—41no—
104C4⋊C4×C31—21no—
105C4⋊C4×C31—21no—
106C4⋊C4×C31—21no—
107C4⋊C4×C31—21no—
108C4⋊C4×C31—42no—
109C4⋊C4×C31—41no—
110C4⋊C4×C31—41no—
111C4⋊C4×C31—81no—
112C22⋊C4×C31—22no—
113C22⋊C4×C31—22no—
114C22⋊C4×C31—22no—
115C22⋊C4×C31—22no—
116C22⋊C4×C31—42no—
117C22⋊C4×C31—41no—
118C22⋊C4×C31—81no—
119C22⋊C4×C31—81no—
120C42×C31—41no—
121C42×C31—41no—
122C42×C31—41no—
123C42×C31—81no—
124C42×C31C22×C411yescharacteristic
125C42×C31C2×D411yescharacteristic
126C42×C31#4111yescharacteristic
127C42×C31#4111yescharacteristic
128#9379C3111yesmaximal, characteristic, direct product factor, Sylow
129C23×C31—22no—
130C23×C31—41no—
131C23×C31—41no—
132C23×C31—41no—
133C23×C31—41no—
134C23×C31—41no—
135C23×C31—41no—
136C23×C31#12011yescharacteristic
137Q8×C31—42no—
138Q8×C31—42no—
139Q8×C31—81no—
140Q8×C31—81no—
141D4×C31—42no—
142D4×C31—81no—
143C2×C4×C31—21no—
144C2×C4×C31—21no—
145C2×C4×C31—22no—
146C2×C4×C31—22no—
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—41no—
156C2×C4×C31—41no—
157C2×C4×C31—41no—
158C2×C4×C31—41no—
159C2×C4×C31—41no—
160C2×C4×C31—41no—
161C2×C4×C31—41no—
162C2×C4×C31—41no—
163C2×C4×C31—41no—
164C2×C4×C31—84no—
165C2×C4×C31C2×C22⋊C411yescharacteristic
166C2×C4×C31C4×D411yescharacteristic
167C2×C4×C31C4×D411yescharacteristic
168C2×C4×C31#12111yescharacteristic
169C2×C4×C31#12111yescharacteristic
170C2×C4×C31#12311yescharacteristic
171C8×C31—42no—
172C8×C31—42no—
173C8×C31—81no—
174#3215C2×C3111yescharacteristic
175#2337C2×C3111yescharacteristic
176#1986C2×C3111yescharacteristic, complemented
177#1527C2×C3111yescharacteristic
178#1515C2×C3111yescharacteristic, complemented
179#1288C2×C3111yescharacteristic, complemented
180#1285C2×C3111yescharacteristic, complemented
181C22×C31—21no—
182C22×C31—21no—
183C22×C31—42no—
184C22×C31—42no—
185C22×C31—42no—
186C22×C31—81no—
187C22×C31—81no—
188C22×C31—81no—
189C22×C31—81no—
190C22×C31#38611yescharacteristic
191C22×C31#45511yescharacteristic
192C22×C31#45611yescharacteristic
193C4×C31—21no—
194C4×C31—21no—
195C4×C31—21no—
196C4×C31—21no—
197C4×C31—21no—
198C4×C31—21no—
199C4×C31—42no—
200C4×C31—42no—
201C4×C31—81no—
202C4×C31—81no—
203C4×C31—81no—
204C4×C31—81no—
205C4×C31—81no—
206#533C22×C3111yescharacteristic
207C2×#124C22×C3111yescharacteristic
208#497C4×C3112yescomplemented
209#489C4×C3112yescomplemented
210#464—22no—
211#451—21no—
212#450—21no—
213#432C22×C3111yescharacteristic
214#432C22×C3111yescharacteristic
215C4×M16C22×C3111yescharacteristic
216#391—21no—
217#388—21no—
218#388—21no—
219#386—21no—
220#385—21no—
221#383C22×C3111yescharacteristic
222C4×C4⋊C4C22×C3111yescharacteristic
223C4×C22⋊C4—21no—
224#339—21no—
225#339—21no—
226#329—22no—
227#328—21no—
228#328—21no—
229C2×C31—21no—
230C2×C31—21no—
231C2×C31—82no—
232C2×C31#188211yescharacteristic
233C2×C31#190611yescharacteristic
234C2×C31#191111yescharacteristic
235C22×Q8D4×C3111yescharacteristic
236C22×D4D4×C3111yescharacteristic
237C23×C4—21no—
238C2×Q16—22no—
239C2×SD16—22no—
240C2×M16—21no—
241C4⋊Q8C2×C4×C3111yescharacteristic, complemented
242C4⋊Q8C2×C4×C3111yescharacteristic, complemented
243#125—21no—
244#124—21no—
245#124—21no—
246#124C2×C4×C3112yes—
247#124D4×C3112yes—
248C22⋊Q8—21no—
249C22⋊Q8—21no—
250C4×Q8—21no—
251C4×Q8—21no—
252#117—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C22⋊C4—21no—
256C2×C22⋊C4—21no—
257C2×C22⋊C4—21no—
258C2×C22⋊C4—21no—
259C2×C22⋊C4—21no—
260C2×C42—21no—
261C2×C42D4×C3111yescharacteristic
262C2×C42D4×C3111yescharacteristic
263C2×C42C23×C3111yescharacteristic
264C4⋊C8—21no—
265C4⋊C8—21no—
266#103—22no—
267#102—22no—
268C22⋊C8—21no—
269C22⋊C8—21no—
270#97—21no—
271#97—21no—
272#97C2×C4×C3112yescomplemented
273C4×C8—21no—
274#95—21no—
275#95—21no—
276#95—21no—
277#95—21no—
278#95—21no—
279#95D4×C3111yescharacteristic
280#95D4×C3111yescharacteristic
281C31#937911yescharacteristic, direct product factor, Sylow
282C24—21no—
283C2×Q8—21no—
284C2×Q8—21no—
285C2×Q8—21no—
286C2×Q8—81no—
287C2×Q8C22⋊C4×C3112yes—
288C2×D4—21no—
289C2×D4—81no—
290C2×D4C22⋊C4×C3112yes—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—42no—
297C22×C4—81no—
298C22×C4—81no—
299C22×C4C2×D4×C3111yescharacteristic
300C22×C4C2×D4×C3111yescharacteristic
301C22×C4C2×D4×C3111yescharacteristic
302Q16—82no—
303SD16—82no—
304M16—22no—
305M16—41no—
306C2×C8—22no—
307C2×C8—41no—
308C2×C8—41no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—42no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—81no—
317C22⋊C4—22no—
318C22⋊C4—22no—
319C22⋊C4—22no—
320C22⋊C4—22no—
321C22⋊C4—42no—
322C22⋊C4—41no—
323C22⋊C4—81no—
324C22⋊C4—81no—
325C42—41no—
326C42—41no—
327C42—41no—
328C42—81no—
329C42C22×C4×C3111yescharacteristic
330C42C2×D4×C3111yescharacteristic
331C42#41×C3111yescharacteristic
332C42#41×C3111yescharacteristic
333C23—22no—
334C23—41no—
335C23—41no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23C31×#12011yescharacteristic
341Q8—42no—
342Q8—42no—
343Q8—81no—
344Q8—81no—
345D4—42no—
346D4—81no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—22no—
350C2×C4—22no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—84no—
369C2×C4C2×C22⋊C4×C3111yescharacteristic
370C2×C4C4×D4×C3111yescharacteristic
371C2×C4C4×D4×C3111yescharacteristic
372C2×C4C31×#12111yescharacteristic
373C2×C4C31×#12111yescharacteristic
374C2×C4C31×#12311yescharacteristic
375C8—42no—
376C8—42no—
377C8—81no—
378C22—21no—
379C22—21no—
380C22—42no—
381C22—42no—
382C22—42no—
383C22—81no—
384C22—81no—
385C22—81no—
386C22—81no—
387C22C31×#38611yescharacteristic
388C22C31×#45511yescharacteristic
389C22C31×#45611yescharacteristic
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—21no—
395C4—21no—
396C4—42no—
397C4—42no—
398C4—81no—
399C4—81no—
400C4—81no—
401C4—81no—
402C4—81no—
403C2—21no—
404C2—21no—
405C2—82no—
406C2C31×#188211yescharacteristic
407C2C31×#190611yescharacteristic
408C2C31×#191111yescharacteristic
subgroupG/H
center, socleC22×C31#386
commutatorC42C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC22×D4×C31D4
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
3. C31×#1986C2semidirect
5. C31×#1515C2semidirect
6. C31×#1288C2semidirect
7. C31×#1285C2semidirect
10. C31×#497C4semidirect
11. C31×#489C4semidirect
37. C31×C4⋊Q8C2×C4semidirect
38. C31×C4⋊Q8C2×C4semidirect
68. C31×#97C2×C4semidirect
128. #9379C31direct (N × H)
176. #1986C2×C31semidirect
178. #1515C2×C31semidirect
179. #1288C2×C31semidirect
180. #1285C2×C31semidirect
208. #497C4×C31semidirect
209. #489C4×C31semidirect
241. C4⋊Q8C2×C4×C31semidirect
242. C4⋊Q8C2×C4×C31semidirect
272. #97C2×C4×C31semidirect
281. C31#9379direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#32152
C31×#23372
C31×#19862
C31×#15272
C31×#15152
C31×#12882
C31×#12852
#937931