Finite Group Databasebeta

← C31×#9179 #21465938

Subgroups — C31×#9179 #21465938

Order 7936.

620 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3036C211yesmaximal, characteristic
2C31×#2349C211yesmaximal, characteristic, complemented
3C31×#1517C211yesmaximal, characteristic, complemented
4C31×#1502C211yesmaximal, characteristic, complemented
5C31×#1478C211yesmaximal, characteristic, complemented
6C31×#1303C211yesmaximal, characteristic, complemented
7C31×#1286C211yesmaximal, characteristic, complemented
8C2×C31×AGL(1,ℤ/8)—21no—
9C31×#532C2211yescharacteristic
10C2×C4×D4×C31—21no—
11C2×C4×D4×C31C2211yescharacteristic
12C31×#463—22no—
13C31×#461C412yescomplemented
14C31×#459C412yescomplemented
15C31×#431C2211yescharacteristic
16C31×#431C2211yescharacteristic
17C31×#423C2211yescharacteristic
18C31×#417—21no—
19C31×#389—21no—
20C31×#385—22no—
21C31×#382C2211yescharacteristic
22C31×#380—21no—
23C4×C4⋊C4×C31C2211yescharacteristic
24C2×C31×#95—21no—
25C31×#327—21no—
26C31×#327—21no—
27C31×#327—22no—
28C31×D4⋊C8—22no—
29C2×#41×C31—21no—
30C22×D4×C31D411yescharacteristic
31C23×C4×C31—21no—
32C23×C4×C31—22no—
33C31×AGL(1,ℤ/8)—42no—
34C31×AGL(1,ℤ/8)—42no—
35C2×SD16×C31—22no—
36C2×D8×C31—22no—
37C2×M16×C31—21no—
38C31×C4⋊Q8C2×C411yescharacteristic, complemented
39C31×#127C2×C411yescharacteristic, complemented
40C31×#124—21no—
41C31×#121—21no—
42C31×#121—21no—
43C4×D4×C31—21no—
44C4×D4×C31—21no—
45C4×D4×C31—21no—
46C4×D4×C31—21no—
47C4×D4×C31—42no—
48C4×D4×C31—42no—
49C4×D4×C31C2×C412yes—
50C4×D4×C31D412yes—
51C2×C4⋊C4×C31—21no—
52C2×C4⋊C4×C31—21no—
53C2×C4⋊C4×C31—22no—
54C2×C4⋊C4×C31D411yescharacteristic
55C2×C22⋊C4×C31—21no—
56C2×C22⋊C4×C31—22no—
57C2×C42×C31—21no—
58C2×C42×C31C2311yescharacteristic
59C31×C4⋊C8—21no—
60C31×C4⋊C8—21no—
61C31×C4⋊C8—21no—
62C31×C4⋊C8C2×C412yescomplemented
63C31×#103—22no—
64C31×#102—22no—
65C31×C22⋊C8—21no—
66C31×C22⋊C8—21no—
67C4×C8×C31—21no—
68C4×C8×C31—21no—
69C31×#95—22no—
70C31×#95—21no—
71C31×#95D411yescharacteristic
72C31×#95D411yescharacteristic
73C31×#95D412yes—
74C24×C31—21no—
75#41×C31—41no—
76#41×C31—41no—
77#41×C31—41no—
78#41×C31—41no—
79C2×Q8×C31—21no—
80C2×D4×C31—21no—
81C2×D4×C31—21no—
82C2×D4×C31—21no—
83C2×D4×C31—21no—
84C2×D4×C31—21no—
85C2×D4×C31—21no—
86C2×D4×C31—41no—
87C2×D4×C31C22⋊C412yes—
88C2×D4×C31D812yes—
89C2×D4×C31SD1612yes—
90C22×C4×C31—21no—
91C22×C4×C31—21no—
92C22×C4×C31—22no—
93C22×C4×C31—22no—
94C22×C4×C31—22no—
95C22×C4×C31—21no—
96C22×C4×C31—44no—
97C22×C4×C31—44no—
98C22×C4×C31—41no—
99C22×C4×C31—82no—
100C22×C4×C31—82no—
101C22×C4×C31C2×D411yescharacteristic
102C22×C4×C31C2×D411yescharacteristic
103C22×C4×C31C2×D411yescharacteristic
104SD16×C31—44no—
105D8×C31—44no—
106M16×C31—41no—
107M16×C31—41no—
108C2×C8×C31—22no—
109C2×C8×C31—41no—
110C2×C8×C31—41no—
111C4⋊C4×C31—21no—
112C4⋊C4×C31—21no—
113C4⋊C4×C31—21no—
114C4⋊C4×C31—42no—
115C4⋊C4×C31—41no—
116C4⋊C4×C31—41no—
117C4⋊C4×C31—82no—
118C4⋊C4×C31C22⋊C412yes—
119C22⋊C4×C31—22no—
120C22⋊C4×C31—22no—
121C22⋊C4×C31—44no—
122C22⋊C4×C31—41no—
123C22⋊C4×C31—41no—
124C42×C31—41no—
125C42×C31—41no—
126C42×C31C22×C411yescharacteristic
127C42×C31C2×D411yescharacteristic
128C42×C31#4111yescharacteristic
129C42×C31#4111yescharacteristic
130#9179C3111yesmaximal, characteristic, direct product factor, Sylow
131C23×C31—22no—
132C23×C31—22no—
133C23×C31—22no—
134C23×C31—42no—
135C23×C31—42no—
136C23×C31—41no—
137C23×C31#12011yescharacteristic
138Q8×C31—41no—
139Q8×C31—41no—
140D4×C31—22no—
141D4×C31—22no—
142D4×C31—22no—
143D4×C31—41no—
144D4×C31—41no—
145D4×C31—81no—
146D4×C31—81no—
147D4×C31—81no—
148D4×C31—81no—
149D4×C31#10214yes—
150C2×C4×C31—22no—
151C2×C4×C31—22no—
152C2×C4×C31—41no—
153C2×C4×C31—41no—
154C2×C4×C31—42no—
155C2×C4×C31—41no—
156C2×C4×C31—41no—
157C2×C4×C31—41no—
158C2×C4×C31—41no—
159C2×C4×C31—42no—
160C2×C4×C31—42no—
161C2×C4×C31—41no—
162C2×C4×C31—41no—
163C2×C4×C31—42no—
164C2×C4×C31—82no—
165C2×C4×C31—82no—
166C2×C4×C31—88no—
167C2×C4×C31—81no—
168C2×C4×C31—81no—
169C2×C4×C31C2×C22⋊C411yescharacteristic
170C2×C4×C31C4×D411yescharacteristic
171C2×C4×C31C4×D411yescharacteristic
172C2×C4×C31#12111yescharacteristic
173C2×C4×C31#12111yescharacteristic
174C2×C4×C31#12311yescharacteristic
175C2×C4×C31C2×D811yescharacteristic
176C2×C4×C31C2×SD1611yescharacteristic
177C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
178C2×C4×C31#13711yescharacteristic
179C8×C31—42no—
180C8×C31—81no—
181C8×C31—81no—
182#3036C2×C3111yescharacteristic
183#2349C2×C3111yescharacteristic, complemented
184#1517C2×C3111yescharacteristic, complemented
185#1502C2×C3111yescharacteristic, complemented
186#1478C2×C3111yescharacteristic, complemented
187#1303C2×C3111yescharacteristic, complemented
188#1286C2×C3111yescharacteristic, complemented
189C22×C31—21no—
190C22×C31—21no—
191C22×C31—24no—
192C22×C31—44no—
193C22×C31—44no—
194C22×C31—42no—
195C22×C31—42no—
196C22×C31—81no—
197C22×C31—81no—
198C22×C31—81no—
199C22×C31#38611yescharacteristic
200C22×C31#44711yescharacteristic
201C22×C31#44811yescharacteristic
202C4×C31—21no—
203C4×C31—21no—
204C4×C31—21no—
205C4×C31—21no—
206C4×C31—42no—
207C4×C31—42no—
208C4×C31—81no—
209C4×C31—82no—
210C4×C31—81no—
211C4×C31C2×#10211yescharacteristic
212C4×C31#41711yescharacteristic
213C4×C31#48011yescharacteristic
214C4×C31#48111yescharacteristic
215C2×AGL(1,ℤ/8)—21no—
216#532C22×C3111yescharacteristic
217C2×C4×D4—21no—
218C2×C4×D4C22×C3111yescharacteristic
219#463—22no—
220#461C4×C3112yescomplemented
221#459C4×C3112yescomplemented
222#431C22×C3111yescharacteristic
223#431C22×C3111yescharacteristic
224#423C22×C3111yescharacteristic
225#417—21no—
226#389—21no—
227#385—22no—
228#382C22×C3111yescharacteristic
229#380—21no—
230C4×C4⋊C4C22×C3111yescharacteristic
231C2×#95—21no—
232#327—21no—
233#327—21no—
234#327—22no—
235D4⋊C8—22no—
236C2×C31—21no—
237C2×C31—21no—
238C2×C31—44no—
239C2×C31—161no—
240C2×C31#187411yescharacteristic
241C2×C31#190411yescharacteristic
242C2×C31#190611yescharacteristic
243C2×#41—21no—
244C22×D4D4×C3111yescharacteristic
245C23×C4—21no—
246C23×C4—22no—
247AGL(1,ℤ/8)—42no—
248AGL(1,ℤ/8)—42no—
249C2×SD16—22no—
250C2×D8—22no—
251C2×M16—21no—
252C4⋊Q8C2×C4×C3111yescharacteristic, complemented
253#127C2×C4×C3111yescharacteristic, complemented
254#124—21no—
255#121—21no—
256#121—21no—
257C4×D4—21no—
258C4×D4—21no—
259C4×D4—21no—
260C4×D4—21no—
261C4×D4—42no—
262C4×D4—42no—
263C4×D4C2×C4×C3112yes—
264C4×D4D4×C3112yes—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4D4×C3111yescharacteristic
269C2×C22⋊C4—21no—
270C2×C22⋊C4—22no—
271C2×C42—21no—
272C2×C42C23×C3111yescharacteristic
273C4⋊C8—21no—
274C4⋊C8—21no—
275C4⋊C8—21no—
276C4⋊C8C2×C4×C3112yescomplemented
277#103—22no—
278#102—22no—
279C22⋊C8—21no—
280C22⋊C8—21no—
281C4×C8—21no—
282C4×C8—21no—
283#95—22no—
284#95—21no—
285#95D4×C3111yescharacteristic
286#95D4×C3111yescharacteristic
287#95D4×C3112yes—
288C31#917911yescharacteristic, direct product factor, Sylow
289C24—21no—
290#41—41no—
291#41—41no—
292#41—41no—
293#41—41no—
294C2×Q8—21no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—21no—
298C2×D4—21no—
299C2×D4—21no—
300C2×D4—21no—
301C2×D4—41no—
302C2×D4C22⋊C4×C3112yes—
303C2×D4D8×C3112yes—
304C2×D4SD16×C3112yes—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—22no—
308C22×C4—22no—
309C22×C4—22no—
310C22×C4—21no—
311C22×C4—44no—
312C22×C4—44no—
313C22×C4—41no—
314C22×C4—82no—
315C22×C4—82no—
316C22×C4C2×D4×C3111yescharacteristic
317C22×C4C2×D4×C3111yescharacteristic
318C22×C4C2×D4×C3111yescharacteristic
319SD16—44no—
320D8—44no—
321M16—41no—
322M16—41no—
323C2×C8—22no—
324C2×C8—41no—
325C2×C8—41no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—42no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—82no—
333C4⋊C4C22⋊C4×C3112yes—
334C22⋊C4—22no—
335C22⋊C4—22no—
336C22⋊C4—44no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C42—41no—
340C42—41no—
341C42C22×C4×C3111yescharacteristic
342C42C2×D4×C3111yescharacteristic
343C42#41×C3111yescharacteristic
344C42#41×C3111yescharacteristic
345C23—22no—
346C23—22no—
347C23—22no—
348C23—42no—
349C23—42no—
350C23—41no—
351C23C31×#12011yescharacteristic
352Q8—41no—
353Q8—41no—
354D4—22no—
355D4—22no—
356D4—22no—
357D4—41no—
358D4—41no—
359D4—81no—
360D4—81no—
361D4—81no—
362D4—81no—
363D4C31×#10214yes—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—42no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—41no—
376C2×C4—42no—
377C2×C4—41no—
378C2×C4—82no—
379C2×C4—82no—
380C2×C4—88no—
381C2×C4—81no—
382C2×C4—81no—
383C2×C4C2×C22⋊C4×C3111yescharacteristic
384C2×C4C4×D4×C3111yescharacteristic
385C2×C4C4×D4×C3111yescharacteristic
386C2×C4C31×#12111yescharacteristic
387C2×C4C31×#12111yescharacteristic
388C2×C4C31×#12311yescharacteristic
389C2×C4C2×D8×C3111yescharacteristic
390C2×C4C2×SD16×C3111yescharacteristic
391C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
392C2×C4C31×#13711yescharacteristic
393C8—42no—
394C8—81no—
395C8—81no—
396C22—21no—
397C22—21no—
398C22—24no—
399C22—44no—
400C22—44no—
401C22—42no—
402C22—42no—
403C22—81no—
404C22—81no—
405C22—81no—
406C22C31×#38611yescharacteristic
407C22C31×#44711yescharacteristic
408C22C31×#44811yescharacteristic
409C4—21no—
410C4—21no—
411C4—21no—
412C4—21no—
413C4—42no—
414C4—42no—
415C4—82no—
416C4—81no—
417C4—81no—
418C4C2×C31×#10211yescharacteristic
419C4C31×#41711yescharacteristic
420C4C31×#48011yescharacteristic
421C4C31×#48111yescharacteristic
422C2—21no—
423C2—21no—
424C2—44no—
425C2—161no—
426C2C31×#187411yescharacteristic
427C2C31×#190411yescharacteristic
428C2C31×#190611yescharacteristic
subgroupG/H
center, socleC22×C31#386
commutatorC42C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC31×#3036C2
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×#2349C2semidirect
3. C31×#1517C2semidirect
4. C31×#1502C2semidirect
5. C31×#1478C2semidirect
6. C31×#1303C2semidirect
7. C31×#1286C2semidirect
13. C31×#461C4semidirect
14. C31×#459C4semidirect
38. C31×C4⋊Q8C2×C4semidirect
39. C31×#127C2×C4semidirect
62. C31×C4⋊C8C2×C4semidirect
130. #9179C31direct (N × H)
183. #2349C2×C31semidirect
184. #1517C2×C31semidirect
185. #1502C2×C31semidirect
186. #1478C2×C31semidirect
187. #1303C2×C31semidirect
188. #1286C2×C31semidirect
220. #461C4×C31semidirect
221. #459C4×C31semidirect
252. C4⋊Q8C2×C4×C31semidirect
253. #127C2×C4×C31semidirect
276. C4⋊C8C2×C4×C31semidirect
288. C31#9179direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#30362
C31×#23492
C31×#15172
C31×#15022
C31×#14782
C31×#13032
C31×#12862
#917931