Finite Group Databasebeta

← C31×#13316 #21470075

Subgroups — C31×#13316 #21470075

Order 7936.

604 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#509C211yesmaximal, characteristic, complemented
2C31×#3054C211yesmaximal, characteristic, complemented
3C2×C31×#469C211yesmaximal, characteristic, complemented
4C2×C31×#360C211yesmaximal, characteristic, complemented
5C31×#2140C211yesmaximal, characteristic, complemented
6C2×C31×#349C211yesmaximal, characteristic, complemented
7C31×#1386C211yesmaximal, characteristic, complemented
8C2×C31×#135C2211yescharacteristic
9C22×D8×C31C2211yescharacteristic
10C22×M16×C31C2211yescharacteristic
11C31×#525—21no—
12C2×C31×#121—21no—
13C31×#509—22no—
14C31×#509—22no—
15C2×C31×SD32—21no—
16C2×C31×D16—21no—
17C2×C31×M32C2211yescharacteristic
18C2×C31×M32C2211yescharacteristic
19C31×#470—21no—
20C31×#469—22no—
21C31×#469—21no—
22C31×#469—22no—
23C31×#468—22no—
24C31×#427C2211yescharacteristic
25C2×C31×#106C2211yescharacteristic
26C31×#416—21no—
27C2×C31×#102—21no—
28C31×#360—22no—
29C31×#357—22no—
30C31×#349—22no—
31C2×#41×C31—21no—
32C22×D4×C31—21no—
33C22×D4×C31—41no—
34C23×C4×C31D411yescharacteristic
35C31×#135—21no—
36C31×#135—21no—
37C31×#135—21no—
38C31×#135—21no—
39C2×Q16×C31D411yescharacteristic, complemented
40C2×SD16×C31—21no—
41C2×D8×C31—21no—
42C2×D8×C31—21no—
43C2×D8×C31—21no—
44C2×D8×C31—21no—
45C2×D8×C31—21no—
46C2×D8×C31D411yescharacteristic, complemented
47C2×D8×C31D412yescomplemented
48C2×M16×C31—21no—
49C2×M16×C31—21no—
50C2×M16×C31—21no—
51C2×M16×C31—21no—
52C2×M16×C31—21no—
53C2×M16×C31—21no—
54C22×C8×C31D411yescharacteristic
55C22×C8×C31C2311yescharacteristic
56C31×#123—41no—
57C31×C22⋊Q8—22no—
58C31×#121—22no—
59C31×#121—24no—
60C31×#121—42no—
61C31×#120—41no—
62C4×D4×C31—42no—
63C31×#117—21no—
64C2×C4⋊C4×C31—21no—
65C2×C22⋊C4×C31—41no—
66C31×SD32—24no—
67C31×D16—24no—
68C31×M32—21no—
69C31×M32—21no—
70C31×M32—21no—
71C31×M32D412yescomplemented
72C2×C16×C31—21no—
73C2×C16×C31—21no—
74C31×#107D412yescomplemented
75C31×#106—21no—
76C31×#106—21no—
77C31×#106D412yescomplemented
78C31×#103—22no—
79C31×#102—24no—
80C31×#102—22no—
81C24×C31—41no—
82C24×C31D811yescharacteristic
83#41×C31—41no—
84#41×C31—41no—
85#41×C31—41no—
86#41×C31—41no—
87C2×Q8×C31—21no—
88C2×D4×C31—22no—
89C2×D4×C31—21no—
90C2×D4×C31—42no—
91C2×D4×C31—44no—
92C2×D4×C31—41no—
93C2×D4×C31—41no—
94C2×D4×C31—41no—
95C2×D4×C31—41no—
96C2×D4×C31—41no—
97C2×D4×C31—41no—
98C2×D4×C31—84no—
99C22×C4×C31—21no—
100C22×C4×C31—21no—
101C22×C4×C31—21no—
102C22×C4×C31—21no—
103C22×C4×C31—21no—
104C22×C4×C31—21no—
105C22×C4×C31—41no—
106C22×C4×C31—41no—
107C22×C4×C31D811yescharacteristic
108C22×C4×C31C2×D411yescharacteristic
109Q16×C31—21no—
110Q16×C31—21no—
111SD16×C31—41no—
112SD16×C31—41no—
113D8×C31—21no—
114D8×C31—22no—
115D8×C31—22no—
116D8×C31—21no—
117D8×C31—41no—
118D8×C31—41no—
119M16×C31—41no—
120M16×C31—41no—
121M16×C31—41no—
122M16×C31—41no—
123C2×C8×C31—21no—
124C2×C8×C31—21no—
125C2×C8×C31—21no—
126C2×C8×C31C2×D411yescharacteristic
127C2×C8×C31C2×D411yescharacteristic
128C2×C8×C31C2×D411yescharacteristic
129C2×C8×C31C2×D411yescharacteristic
130C2×C8×C31C2×D411yescharacteristic
131C2×C8×C31#4111yescharacteristic
132C4⋊C4×C31—22no—
133C4⋊C4×C31—22no—
134C4⋊C4×C31—42no—
135C4⋊C4×C31—41no—
136C22⋊C4×C31—44no—
137C22⋊C4×C31—42no—
138C22⋊C4×C31—42no—
139C22⋊C4×C31—41no—
140C42×C31—41no—
141C16×C31—22no—
142C16×C31—41no—
143#13316C3111yesmaximal, characteristic, direct product factor, Sylow
144C23×C31—21no—
145C23×C31—21no—
146C23×C31—21no—
147C23×C31—42no—
148C23×C31—42no—
149C23×C31—41no—
150C23×C31—82no—
151C23×C31—82no—
152C23×C31—81no—
153C23×C31—81no—
154C23×C31C2×D811yescharacteristic
155Q8×C31—41no—
156Q8×C31—41no—
157D4×C31—42no—
158D4×C31—41no—
159D4×C31—42no—
160D4×C31—41no—
161D4×C31—84no—
162D4×C31—88no—
163D4×C31—81no—
164D4×C31—81no—
165D4×C31—81no—
166D4×C31—81no—
167C2×C4×C31—21no—
168C2×C4×C31—21no—
169C2×C4×C31—21no—
170C2×C4×C31—41no—
171C2×C4×C31—41no—
172C2×C4×C31—41no—
173C2×C4×C31—41no—
174C2×C4×C31—42no—
175C2×C4×C31—42no—
176C2×C4×C31—41no—
177C2×C4×C31—82no—
178C2×C4×C31—81no—
179C2×C4×C31—81no—
180C2×C4×C31#12011yescharacteristic
181C2×C4×C31#12011yescharacteristic
182C2×C4×C31#12111yescharacteristic
183C2×C4×C31#13511yescharacteristic
184C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
185C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
186C8×C31—41no—
187C8×C31#12011yescharacteristic
188C8×C31#12111yescharacteristic
189C8×C31#12111yescharacteristic
190C8×C31#12711yescharacteristic
191C2×#509C2×C3111yescharacteristic, complemented
192#3054C2×C3111yescharacteristic, complemented
193C2×#469C2×C3111yescharacteristic, complemented
194C2×#360C2×C3111yescharacteristic, complemented
195#2140C2×C3111yescharacteristic, complemented
196C2×#349C2×C3111yescharacteristic, complemented
197#1386C2×C3111yescharacteristic, complemented
198C22×C31—22no—
199C22×C31—42no—
200C22×C31—42no—
201C22×C31—41no—
202C22×C31—81no—
203C22×C31—82no—
204C22×C31—82no—
205C22×C31—82no—
206C22×C31—81no—
207C22×C31—82no—
208C22×C31—162no—
209C22×C31—162no—
210C22×C31#44711yescharacteristic
211C22×C31#44711yescharacteristic
212C22×C31#46611yescharacteristic
213C4×C31—41no—
214C4×C31—82no—
215C4×C31—82no—
216C4×C31—81no—
217C4×C31#39211yescharacteristic
218C4×C31#44911yescharacteristic
219C4×C31#44911yescharacteristic
220C4×C31#46911yescharacteristic
221C2×#135C22×C3111yescharacteristic
222C22×D8C22×C3111yescharacteristic
223C22×M16C22×C3111yescharacteristic
224#525—21no—
225C2×#121—21no—
226#509—22no—
227#509—22no—
228C2×SD32—21no—
229C2×D16—21no—
230C2×M32C22×C3111yescharacteristic
231C2×M32C22×C3111yescharacteristic
232#470—21no—
233#469—22no—
234#469—21no—
235#469—22no—
236#468—22no—
237#427C22×C3111yescharacteristic
238C2×#106C22×C3111yescharacteristic
239#416—21no—
240C2×#102—21no—
241#360—22no—
242#357—22no—
243#349—22no—
244C2×C31—21no—
245C2×C31—21no—
246C2×C31—81no—
247C2×C31—161no—
248C2×C31—162no—
249C2×C31#199911yescharacteristic
250C2×C31#219012yes—
251C2×#41—21no—
252C22×D4—21no—
253C22×D4—41no—
254C23×C4D4×C3111yescharacteristic
255#135—21no—
256#135—21no—
257#135—21no—
258#135—21no—
259C2×Q16D4×C3111yescharacteristic, complemented
260C2×SD16—21no—
261C2×D8—21no—
262C2×D8—21no—
263C2×D8—21no—
264C2×D8—21no—
265C2×D8—21no—
266C2×D8D4×C3112yescomplemented
267C2×D8D4×C3111yescharacteristic, complemented
268C2×M16—21no—
269C2×M16—21no—
270C2×M16—21no—
271C2×M16—21no—
272C2×M16—21no—
273C2×M16—21no—
274C22×C8D4×C3111yescharacteristic
275C22×C8C23×C3111yescharacteristic
276#123—41no—
277C22⋊Q8—22no—
278#121—24no—
279#121—22no—
280#121—42no—
281#120—41no—
282C4×D4—42no—
283#117—21no—
284C2×C4⋊C4—21no—
285C2×C22⋊C4—41no—
286SD32—24no—
287D16—24no—
288M32—21no—
289M32—21no—
290M32—21no—
291M32D4×C3112yescomplemented
292C2×C16—21no—
293C2×C16—21no—
294#107D4×C3112yescomplemented
295#106—21no—
296#106—21no—
297#106D4×C3112yescomplemented
298#103—22no—
299#102—24no—
300#102—22no—
301C31#1331611yescharacteristic, direct product factor, Sylow
302C24—41no—
303C24D8×C3111yescharacteristic
304#41—41no—
305#41—41no—
306#41—41no—
307#41—41no—
308C2×Q8—21no—
309C2×D4—22no—
310C2×D4—21no—
311C2×D4—42no—
312C2×D4—44no—
313C2×D4—41no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—84no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4D8×C3111yescharacteristic
329C22×C4C2×D4×C3111yescharacteristic
330Q16—21no—
331Q16—21no—
332SD16—41no—
333SD16—41no—
334D8—21no—
335D8—22no—
336D8—22no—
337D8—21no—
338D8—41no—
339D8—41no—
340M16—41no—
341M16—41no—
342M16—41no—
343M16—41no—
344C2×C8—21no—
345C2×C8—21no—
346C2×C8—21no—
347C2×C8C2×D4×C3111yescharacteristic
348C2×C8C2×D4×C3111yescharacteristic
349C2×C8C2×D4×C3111yescharacteristic
350C2×C8C2×D4×C3111yescharacteristic
351C2×C8C2×D4×C3111yescharacteristic
352C2×C8#41×C3111yescharacteristic
353C4⋊C4—22no—
354C4⋊C4—22no—
355C4⋊C4—42no—
356C4⋊C4—41no—
357C22⋊C4—44no—
358C22⋊C4—42no—
359C22⋊C4—42no—
360C22⋊C4—41no—
361C42—41no—
362C16—22no—
363C16—41no—
364C23—21no—
365C23—21no—
366C23—21no—
367C23—42no—
368C23—41no—
369C23—42no—
370C23—82no—
371C23—82no—
372C23—81no—
373C23—81no—
374C23C2×D8×C3111yescharacteristic
375Q8—41no—
376Q8—41no—
377D4—42no—
378D4—41no—
379D4—42no—
380D4—41no—
381D4—84no—
382D4—88no—
383D4—81no—
384D4—81no—
385D4—81no—
386D4—81no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—41no—
397C2×C4—82no—
398C2×C4—81no—
399C2×C4—81no—
400C2×C4C31×#12011yescharacteristic
401C2×C4C31×#12011yescharacteristic
402C2×C4C31×#12111yescharacteristic
403C2×C4C31×#13511yescharacteristic
404C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
405C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
406C8—41no—
407C8C31×#12011yescharacteristic
408C8C31×#12111yescharacteristic
409C8C31×#12111yescharacteristic
410C8C31×#12711yescharacteristic
411C22—22no—
412C22—42no—
413C22—42no—
414C22—41no—
415C22—81no—
416C22—82no—
417C22—82no—
418C22—82no—
419C22—81no—
420C22—82no—
421C22—162no—
422C22—162no—
423C22C31×#44711yescharacteristic
424C22C31×#44711yescharacteristic
425C22C31×#46611yescharacteristic
426C4—41no—
427C4—82no—
428C4—82no—
429C4—81no—
430C4C31×#39211yescharacteristic
431C4C31×#44911yescharacteristic
432C4C31×#44911yescharacteristic
433C4C31×#46911yescharacteristic
434C2—21no—
435C2—21no—
436C2—81no—
437C2—162no—
438C2—161no—
439C2C31×#199911yescharacteristic
440C2C31×#219012yes—
subgroupG/H
center, socleC22×C31#447
commutator, Frattini, cosocleC22×C8C23×C31
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C22×C4×C31 ◁ C22×M16×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#509C2semidirect
2. C31×#3054C2semidirect
3. C2×C31×#469C2semidirect
4. C2×C31×#360C2semidirect
5. C31×#2140C2semidirect
6. C2×C31×#349C2semidirect
7. C31×#1386C2semidirect
39. C2×Q16×C31D4semidirect
46. C2×D8×C31D4semidirect
47. C2×D8×C31D4semidirect
71. C31×M32D4semidirect
74. C31×#107D4semidirect
77. C31×#106D4semidirect
143. #13316C31direct (N × H)
191. C2×#509C2×C31semidirect
192. #3054C2×C31semidirect
193. C2×#469C2×C31semidirect
194. C2×#360C2×C31semidirect
195. #2140C2×C31semidirect
196. C2×#349C2×C31semidirect
197. #1386C2×C31semidirect
259. C2×Q16D4×C31semidirect
266. C2×D8D4×C31semidirect
267. C2×D8D4×C31semidirect
291. M32D4×C31semidirect
294. #107D4×C31semidirect
297. #106D4×C31semidirect
301. C31#13316direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5092
C31×#30542
C2×C31×#4692
C2×C31×#3602
C31×#21402
C2×C31×#3492
C31×#13862
#1331631