Finite Group Databasebeta

← C31×#9203 #21465962

Subgroups — C31×#9203 #21465962

Order 7936.

762 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×#2617C211yesmaximal, characteristic
2C31×#2315C211yesmaximal, characteristic, complemented
3C31×#1519C212yesmaximal, complemented
4C2×C31×#323C211yesmaximal, characteristic, complemented
5C31×#1289C212yesmaximal, complemented
6C2×C31×#121C2211yescharacteristic
7C2×C31×#120—21no—
8C22×C22⋊C4×C31—21no—
9C22×C22⋊C4×C31C2211yescharacteristic
10C2×C31×C22⋊C8C2212yes—
11C31×#397C412yescomplemented
12C31×#394—22no—
13C31×#392C412yescomplemented
14C31×#386—21no—
15C31×#385—24no—
16C31×#380—21no—
17C31×#380C2211yescharacteristic
18C31×#380C2212yes—
19C31×#327—24no—
20C31×#323—22no—
21C25×C31D411yescharacteristic
22C22×D4×C31—21no—
23C22×D4×C31—22no—
24C22×D4×C31C2×C411yescharacteristic, complemented
25C23×C4×C31—22no—
26C23×C4×C31D411yescharacteristic
27C23×C4×C31C2311yescharacteristic
28C22×C8×C31—22no—
29C31×#121—22no—
30C31×#121—22no—
31C31×#120—42no—
32C31×#120—42no—
33C2×C4⋊C4×C31—22no—
34C2×C4⋊C4×C31—22no—
35C2×C4⋊C4×C31—21no—
36C2×C4⋊C4×C31C2×C411yescharacteristic, complemented
37C2×C22⋊C4×C31—22no—
38C2×C22⋊C4×C31—22no—
39C2×C22⋊C4×C31—22no—
40C2×C22⋊C4×C31—22no—
41C2×C22⋊C4×C31—22no—
42C2×C22⋊C4×C31—21no—
43C2×C22⋊C4×C31—21no—
44C2×C22⋊C4×C31—22no—
45C2×C22⋊C4×C31—42no—
46C2×C22⋊C4×C31—42no—
47C2×C22⋊C4×C31C2×C412yes—
48C2×C22⋊C4×C31D412yes—
49C31×C22⋊C8—22no—
50C31×C22⋊C8—22no—
51C31×#95—22no—
52C31×#95—22no—
53C31×#95C2×C412yescomplemented
54C31×#95D414yescomplemented
55C24×C31—21no—
56C24×C31—21no—
57C24×C31—21no—
58C24×C31—21no—
59C24×C31—21no—
60C24×C31—81no—
61C24×C31—81no—
62C24×C31C22⋊C412yes—
63C24×C31D812yes—
64C24×C31SD1612yes—
65C24×C31C2×D411yescharacteristic
66C2×D4×C31—22no—
67C2×D4×C31—44no—
68C2×D4×C31—41no—
69C2×D4×C31—41no—
70C2×D4×C31—41no—
71C2×D4×C31—41no—
72C2×D4×C31—41no—
73C2×D4×C31—41no—
74C2×D4×C31—82no—
75C2×D4×C31—82no—
76C2×D4×C31—81no—
77C22×C4×C31—21no—
78C22×C4×C31—21no—
79C22×C4×C31—21no—
80C22×C4×C31—22no—
81C22×C4×C31—24no—
82C22×C4×C31—44no—
83C22×C4×C31—81no—
84C22×C4×C31—81no—
85C22×C4×C31—82no—
86C22×C4×C31—82no—
87C22×C4×C31C22⋊C412yes—
88C22×C4×C31C22×C411yescharacteristic
89C22×C4×C31C2×D412yes—
90C22×C4×C31C2×D411yescharacteristic
91C22×C4×C31#4112yes—
92C2×C8×C31—42no—
93C2×C8×C31—82no—
94C4⋊C4×C31—22no—
95C4⋊C4×C31—82no—
96C4⋊C4×C31—81no—
97C4⋊C4×C31—82no—
98C22⋊C4×C31—24no—
99C22⋊C4×C31—24no—
100C22⋊C4×C31—44no—
101C22⋊C4×C31—44no—
102C22⋊C4×C31—42no—
103C22⋊C4×C31—41no—
104C22⋊C4×C31—41no—
105C22⋊C4×C31—42no—
106C22⋊C4×C31—42no—
107C22⋊C4×C31—82no—
108#9203C3111yesmaximal, characteristic, direct product factor, Sylow
109C23×C31—22no—
110C23×C31—22no—
111C23×C31—22no—
112C23×C31—22no—
113C23×C31—22no—
114C23×C31—22no—
115C23×C31—41no—
116C23×C31—41no—
117C23×C31—42no—
118C23×C31—42no—
119C23×C31—42no—
120C23×C31—42no—
121C23×C31—42no—
122C23×C31—42no—
123C23×C31—41no—
124C23×C31—41no—
125C23×C31—41no—
126C23×C31—81no—
127C23×C31—81no—
128C23×C31—82no—
129C23×C31—82no—
130C23×C31—82no—
131C23×C31—82no—
132C23×C31#10214yes—
133C23×C31C2×C22⋊C411yescharacteristic
134C23×C31#12011yescharacteristic
135C23×C31#12311yescharacteristic
136C23×C31C2×D811yescharacteristic
137C23×C31C2×SD1611yescharacteristic
138C23×C31AGL(1,ℤ/8)11yescharacteristic
139C23×C31#13711yescharacteristic
140D4×C31—82no—
141D4×C31—88no—
142D4×C31—81no—
143D4×C31—81no—
144D4×C31—81no—
145D4×C31—81no—
146C2×C4×C31—22no—
147C2×C4×C31—41no—
148C2×C4×C31—42no—
149C2×C4×C31—42no—
150C2×C4×C31—41no—
151C2×C4×C31—42no—
152C2×C4×C31—42no—
153C2×C4×C31—42no—
154C2×C4×C31—44no—
155C2×C4×C31—44no—
156C2×C4×C31—42no—
157C2×C4×C31—41no—
158C2×C4×C31—42no—
159C2×C4×C31—41no—
160C2×C4×C31—41no—
161C2×C4×C31—44no—
162C2×C4×C31—81no—
163C2×C4×C31—88no—
164C2×C4×C31C4×D412yes—
165C2×C4×C31#12112yes—
166C8×C31—82no—
167#2617C2×C3111yescharacteristic
168#2315C2×C3111yescharacteristic, complemented
169#1519C2×C3112yescomplemented
170C2×#323C2×C3111yescharacteristic, complemented
171#1289C2×C3112yescomplemented
172C22×C31—21no—
173C22×C31—21no—
174C22×C31—21no—
175C22×C31—21no—
176C22×C31—21no—
177C22×C31—21no—
178C22×C31—24no—
179C22×C31—41no—
180C22×C31—41no—
181C22×C31—41no—
182C22×C31—41no—
183C22×C31—44no—
184C22×C31—44no—
185C22×C31—44no—
186C22×C31—42no—
187C22×C31—42no—
188C22×C31—82no—
189C22×C31—82no—
190C22×C31—82no—
191C22×C31—82no—
192C22×C31—82no—
193C22×C31—81no—
194C22×C31—81no—
195C22×C31—81no—
196C22×C31#38611yescharacteristic
197C22×C31C2×#10211yescharacteristic
198C22×C31#41711yescharacteristic
199C22×C31#44711yescharacteristic
200C22×C31#44811yescharacteristic
201C22×C31#48011yescharacteristic
202C22×C31#48111yescharacteristic
203C4×C31—22no—
204C4×C31—22no—
205C4×C31—42no—
206C4×C31—84no—
207C4×C31—82no—
208C4×C31—81no—
209C2×#121C22×C3111yescharacteristic
210C2×#120—21no—
211C22×C22⋊C4—21no—
212C22×C22⋊C4C22×C3111yescharacteristic
213C2×C22⋊C8C22×C3112yes—
214#397C4×C3112yescomplemented
215#394—22no—
216#392C4×C3112yescomplemented
217#386—21no—
218#385—24no—
219#380—21no—
220#380C22×C3111yescharacteristic
221#380C22×C3112yes—
222#327—24no—
223#323—22no—
224C2×C31—21no—
225C2×C31—21no—
226C2×C31—21no—
227C2×C31—21no—
228C2×C31—21no—
229C2×C31—21no—
230C2×C31—44no—
231C2×C31—161no—
232C2×C31#187411yescharacteristic
233C2×C31#191111yescharacteristic
234C2×C31#191311yescharacteristic
235C25D4×C3111yescharacteristic
236C22×D4—21no—
237C22×D4—22no—
238C22×D4C2×C4×C3111yescharacteristic, complemented
239C23×C4—22no—
240C23×C4D4×C3111yescharacteristic
241C23×C4C23×C3111yescharacteristic
242C22×C8—22no—
243#121—22no—
244#121—22no—
245#120—42no—
246#120—42no—
247C2×C4⋊C4—22no—
248C2×C4⋊C4—22no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4C2×C4×C3111yescharacteristic, complemented
251C2×C22⋊C4—22no—
252C2×C22⋊C4—22no—
253C2×C22⋊C4—22no—
254C2×C22⋊C4—22no—
255C2×C22⋊C4—22no—
256C2×C22⋊C4—21no—
257C2×C22⋊C4—21no—
258C2×C22⋊C4—22no—
259C2×C22⋊C4—42no—
260C2×C22⋊C4—42no—
261C2×C22⋊C4C2×C4×C3112yes—
262C2×C22⋊C4D4×C3112yes—
263C22⋊C8—22no—
264C22⋊C8—22no—
265#95—22no—
266#95—22no—
267#95C2×C4×C3112yescomplemented
268#95D4×C3114yescomplemented
269C31#920311yescharacteristic, direct product factor, Sylow
270C24—21no—
271C24—21no—
272C24—21no—
273C24—21no—
274C24—21no—
275C24—81no—
276C24—81no—
277C24C22⋊C4×C3112yes—
278C24D8×C3112yes—
279C24SD16×C3112yes—
280C24C2×D4×C3111yescharacteristic
281C2×D4—22no—
282C2×D4—44no—
283C2×D4—41no—
284C2×D4—41no—
285C2×D4—41no—
286C2×D4—41no—
287C2×D4—41no—
288C2×D4—41no—
289C2×D4—82no—
290C2×D4—82no—
291C2×D4—81no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—22no—
296C22×C4—24no—
297C22×C4—44no—
298C22×C4—81no—
299C22×C4—81no—
300C22×C4—82no—
301C22×C4—82no—
302C22×C4C22⋊C4×C3112yes—
303C22×C4C22×C4×C3111yescharacteristic
304C22×C4C2×D4×C3112yes—
305C22×C4C2×D4×C3111yescharacteristic
306C22×C4#41×C3112yes—
307C2×C8—42no—
308C2×C8—82no—
309C4⋊C4—22no—
310C4⋊C4—82no—
311C4⋊C4—81no—
312C4⋊C4—82no—
313C22⋊C4—24no—
314C22⋊C4—24no—
315C22⋊C4—44no—
316C22⋊C4—44no—
317C22⋊C4—42no—
318C22⋊C4—41no—
319C22⋊C4—41no—
320C22⋊C4—42no—
321C22⋊C4—42no—
322C22⋊C4—82no—
323C23—22no—
324C23—22no—
325C23—22no—
326C23—22no—
327C23—22no—
328C23—22no—
329C23—41no—
330C23—41no—
331C23—42no—
332C23—42no—
333C23—42no—
334C23—42no—
335C23—42no—
336C23—42no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23—81no—
341C23—81no—
342C23—82no—
343C23—82no—
344C23—82no—
345C23—82no—
346C23C31×#10214yes—
347C23C2×C22⋊C4×C3111yescharacteristic
348C23C31×#12011yescharacteristic
349C23C31×#12311yescharacteristic
350C23C2×D8×C3111yescharacteristic
351C23C2×SD16×C3111yescharacteristic
352C23C31×AGL(1,ℤ/8)11yescharacteristic
353C23C31×#13711yescharacteristic
354D4—82no—
355D4—88no—
356D4—81no—
357D4—81no—
358D4—81no—
359D4—81no—
360C2×C4—22no—
361C2×C4—41no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—41no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—44no—
369C2×C4—44no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—44no—
375C2×C4—41no—
376C2×C4—81no—
377C2×C4—88no—
378C2×C4C4×D4×C3112yes—
379C2×C4C31×#12112yes—
380C8—82no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—24no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—44no—
393C22—44no—
394C22—44no—
395C22—42no—
396C22—42no—
397C22—82no—
398C22—82no—
399C22—82no—
400C22—82no—
401C22—82no—
402C22—81no—
403C22—81no—
404C22—81no—
405C22C31×#38611yescharacteristic
406C22C2×C31×#10211yescharacteristic
407C22C31×#41711yescharacteristic
408C22C31×#44711yescharacteristic
409C22C31×#44811yescharacteristic
410C22C31×#48011yescharacteristic
411C22C31×#48111yescharacteristic
412C4—22no—
413C4—22no—
414C4—42no—
415C4—84no—
416C4—82no—
417C4—81no—
418C2—21no—
419C2—21no—
420C2—21no—
421C2—21no—
422C2—21no—
423C2—21no—
424C2—44no—
425C2—161no—
426C2C31×#187411yescharacteristic
427C2C31×#191111yescharacteristic
428C2C31×#191311yescharacteristic
subgroupG/H
center, socleC22×C31#386
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC31×#2617C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#2315C2semidirect
3. C31×#1519C2semidirect
4. C2×C31×#323C2semidirect
5. C31×#1289C2semidirect
11. C31×#397C4semidirect
13. C31×#392C4semidirect
24. C22×D4×C31C2×C4semidirect
36. C2×C4⋊C4×C31C2×C4semidirect
53. C31×#95C2×C4semidirect
54. C31×#95D4semidirect
108. #9203C31direct (N × H)
168. #2315C2×C31semidirect
169. #1519C2×C31semidirect
170. C2×#323C2×C31semidirect
171. #1289C2×C31semidirect
214. #397C4×C31semidirect
216. #392C4×C31semidirect
238. C22×D4C2×C4×C31semidirect
250. C2×C4⋊C4C2×C4×C31semidirect
267. #95C2×C4×C31semidirect
268. #95D4×C31semidirect
269. C31#9203direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#26172
C31×#23152
C31×#15192
C2×C31×#3232
C31×#12892
#920331