Finite Group Databasebeta

← C31×#12995 #21469754

Subgroups — C31×#12995 #21469754

Order 7936.

476 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3067C211yesmaximal, characteristic
2C31×#2916C211yesmaximal, characteristic, complemented
3C31×#2143C211yesmaximal, characteristic, complemented
4C2×C31×#359C211yesmaximal, characteristic, complemented
5C2×C31×#350C211yesmaximal, characteristic, complemented
6C31×#1388C211yesmaximal, characteristic, complemented
7C31×#1381C211yesmaximal, characteristic, complemented
8C31×#575—21no—
9C2×C31×#135C2211yescharacteristic
10C31×#568—21no—
11C2×C31×#131C2211yescharacteristic
12C2×C31×M32C2211yescharacteristic
13C22×C16×C31C2211yescharacteristic
14C31×#473C412yes—
15C31×#472C412yes—
16C31×#471—22no—
17C31×#430—21no—
18C31×#430—22no—
19C2×C31×#108—22no—
20C2×C31×#108C2211yescharacteristic
21C2×C31×#108C2211yescharacteristic
22C2×C31×#108C2211yescharacteristic
23C31×#413—21no—
24C31×#359—22no—
25C31×#359—22no—
26C31×#350—22no—
27C2×#41×C31—21no—
28C2×#41×C31D411yescharacteristic
29C31×#137—22no—
30C31×#137—41no—
31C31×AGL(1,ℤ/8)—22no—
32C31×AGL(1,ℤ/8)—41no—
33C31×#135—21no—
34C31×#135—21no—
35C31×#135—21no—
36C31×#135—21no—
37C31×#135—42no—
38C2×Q16×C31C2×C411yescharacteristic
39C2×SD16×C31—21no—
40C2×D8×C31C2×C411yescharacteristic
41C31×#131—21no—
42C31×#131—21no—
43C31×#131—42no—
44C31×#131—42no—
45C31×#131C2×C412yes—
46C31×#131D412yes—
47C2×M16×C31—21no—
48C2×M16×C31—24no—
49C2×M16×C31—21no—
50C2×M16×C31—21no—
51C2×M16×C31—21no—
52C2×M16×C31D411yescharacteristic
53C22×C8×C31—21no—
54C22×C8×C31C2311yescharacteristic
55C31×M32—21no—
56C31×M32—21no—
57C2×C16×C31—21no—
58C2×C16×C31—21no—
59C2×C16×C31—21no—
60C2×C16×C31—21no—
61C31×#108—24no—
62C31×#108—21no—
63C31×#108—21no—
64C31×#108—21no—
65C31×#108C2×C412yes—
66C31×#108D412yes—
67C31×#108D412yes—
68C31×#101—22no—
69C31×#100—22no—
70#41×C31—21no—
71#41×C31—21no—
72#41×C31—41no—
73#41×C31—41no—
74#41×C31—41no—
75#41×C31—41no—
76#41×C31C22⋊C412yes—
77#41×C31D812yes—
78C2×Q8×C31—21no—
79C2×Q8×C31SD1611yescharacteristic
80C2×D4×C31—21no—
81C2×D4×C31—21no—
82C2×D4×C31—41no—
83C2×D4×C31SD1611yescharacteristic
84C22×C4×C31—21no—
85C22×C4×C31—41no—
86C22×C4×C31C2×D411yescharacteristic
87Q16×C31—21no—
88Q16×C31—21no—
89Q16×C31—42no—
90SD16×C31—42no—
91SD16×C31—42no—
92SD16×C31—41no—
93SD16×C31—41no—
94D8×C31—21no—
95D8×C31—21no—
96D8×C31—42no—
97M16×C31—21no—
98M16×C31—22no—
99M16×C31—22no—
100M16×C31—22no—
101M16×C31—22no—
102M16×C31—22no—
103M16×C31—44no—
104M16×C31—41no—
105M16×C31—41no—
106M16×C31—41no—
107M16×C31C22⋊C412yes—
108C2×C8×C31—21no—
109C2×C8×C31—22no—
110C2×C8×C31—22no—
111C2×C8×C31—44no—
112C2×C8×C31—41no—
113C2×C8×C31—41no—
114C2×C8×C31—41no—
115C2×C8×C31C22×C411yescharacteristic
116C2×C8×C31C2×D411yescharacteristic
117C2×C8×C31C2×D411yescharacteristic
118C2×C8×C31C2×D411yescharacteristic
119C2×C8×C31#4111yescharacteristic
120C2×C8×C31#4111yescharacteristic
121C16×C31—41no—
122C16×C31—41no—
123#12995C3111yesmaximal, characteristic, direct product factor, Sylow
124C23×C31—21no—
125C23×C31—41no—
126C23×C31#13711yescharacteristic
127Q8×C31—21no—
128Q8×C31—41no—
129Q8×C31—41no—
130Q8×C31#10212yes—
131D4×C31—22no—
132D4×C31—22no—
133D4×C31—21no—
134D4×C31—41no—
135D4×C31—41no—
136D4×C31—81no—
137D4×C31—81no—
138D4×C31#10212yes—
139C2×C4×C31—21no—
140C2×C4×C31—22no—
141C2×C4×C31—22no—
142C2×C4×C31—41no—
143C2×C4×C31—81no—
144C2×C4×C31—81no—
145C2×C4×C31C2×C22⋊C411yescharacteristic
146C2×C4×C31#12011yescharacteristic
147C2×C4×C31#12311yescharacteristic
148C2×C4×C31C2×D811yescharacteristic
149C2×C4×C31C2×SD1611yescharacteristic
150C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
151C8×C31—22no—
152C8×C31—42no—
153C8×C31—42no—
154C8×C31—42no—
155C8×C31C4×D411yescharacteristic
156C8×C31C4×D411yescharacteristic
157C8×C31#12111yescharacteristic
158C8×C31#12111yescharacteristic
159#3067C2×C3111yescharacteristic
160#2916C2×C3111yescharacteristic, complemented
161#2143C2×C3111yescharacteristic, complemented
162C2×#359C2×C3111yescharacteristic, complemented
163C2×#350C2×C3111yescharacteristic, complemented
164#1388C2×C3111yescharacteristic, complemented
165#1381C2×C3111yescharacteristic, complemented
166C22×C31—22no—
167C22×C31—41no—
168C22×C31—81no—
169C22×C31—81no—
170C22×C31—161no—
171C22×C31#41711yescharacteristic
172C22×C31#44811yescharacteristic
173C22×C31#48011yescharacteristic
174C4×C31—22no—
175C4×C31—81no—
176C4×C31#38611yescharacteristic
177C4×C31C2×#10211yescharacteristic
178C4×C31#44711yescharacteristic
179C4×C31#48111yescharacteristic
180#575—21no—
181C2×#135C22×C3111yescharacteristic
182#568—21no—
183C2×#131C22×C3111yescharacteristic
184C2×M32C22×C3111yescharacteristic
185C22×C16C22×C3111yescharacteristic
186#473C4×C3112yes—
187#472C4×C3112yes—
188#471—22no—
189#430—21no—
190#430—22no—
191C2×#108—22no—
192C2×#108C22×C3111yescharacteristic
193C2×#108C22×C3111yescharacteristic
194C2×#108C22×C3111yescharacteristic
195#413—21no—
196#359—22no—
197#359—22no—
198#350—22no—
199C2×C31—21no—
200C2×C31—21no—
201C2×C31—21no—
202C2×C31—42no—
203C2×C31—161no—
204C2×C31#187411yescharacteristic
205C2×#41—21no—
206C2×#41D4×C3111yescharacteristic
207#137—22no—
208#137—41no—
209AGL(1,ℤ/8)—22no—
210AGL(1,ℤ/8)—41no—
211#135—21no—
212#135—21no—
213#135—21no—
214#135—21no—
215#135—42no—
216C2×Q16C2×C4×C3111yescharacteristic
217C2×SD16—21no—
218C2×D8C2×C4×C3111yescharacteristic
219#131—21no—
220#131—21no—
221#131—42no—
222#131—42no—
223#131C2×C4×C3112yes—
224#131D4×C3112yes—
225C2×M16—21no—
226C2×M16—24no—
227C2×M16—21no—
228C2×M16—21no—
229C2×M16—21no—
230C2×M16D4×C3111yescharacteristic
231C22×C8—21no—
232C22×C8C23×C3111yescharacteristic
233M32—21no—
234M32—21no—
235C2×C16—21no—
236C2×C16—21no—
237C2×C16—21no—
238C2×C16—21no—
239#108—24no—
240#108—21no—
241#108—21no—
242#108—21no—
243#108C2×C4×C3112yes—
244#108D4×C3112yes—
245#108D4×C3112yes—
246#101—22no—
247#100—22no—
248C31#1299511yescharacteristic, direct product factor, Sylow
249#41—21no—
250#41—21no—
251#41—41no—
252#41—41no—
253#41—41no—
254#41—41no—
255#41C22⋊C4×C3112yes—
256#41D8×C3112yes—
257C2×Q8—21no—
258C2×Q8SD16×C3111yescharacteristic
259C2×D4—21no—
260C2×D4—21no—
261C2×D4—41no—
262C2×D4SD16×C3111yescharacteristic
263C22×C4—21no—
264C22×C4—41no—
265C22×C4C2×D4×C3111yescharacteristic
266Q16—21no—
267Q16—21no—
268Q16—42no—
269SD16—42no—
270SD16—42no—
271SD16—41no—
272SD16—41no—
273D8—21no—
274D8—21no—
275D8—42no—
276M16—21no—
277M16—22no—
278M16—22no—
279M16—22no—
280M16—22no—
281M16—22no—
282M16—44no—
283M16—41no—
284M16—41no—
285M16—41no—
286M16C22⋊C4×C3112yes—
287C2×C8—21no—
288C2×C8—22no—
289C2×C8—22no—
290C2×C8—44no—
291C2×C8—41no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8C22×C4×C3111yescharacteristic
295C2×C8C2×D4×C3111yescharacteristic
296C2×C8C2×D4×C3111yescharacteristic
297C2×C8C2×D4×C3111yescharacteristic
298C2×C8#41×C3111yescharacteristic
299C2×C8#41×C3111yescharacteristic
300C16—41no—
301C16—41no—
302C23—21no—
303C23—41no—
304C23C31×#13711yescharacteristic
305Q8—21no—
306Q8—41no—
307Q8—41no—
308Q8C31×#10212yes—
309D4—22no—
310D4—22no—
311D4—21no—
312D4—41no—
313D4—41no—
314D4—81no—
315D4—81no—
316D4C31×#10212yes—
317C2×C4—21no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—41no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4C2×C22⋊C4×C3111yescharacteristic
324C2×C4C31×#12011yescharacteristic
325C2×C4C31×#12311yescharacteristic
326C2×C4C2×D8×C3111yescharacteristic
327C2×C4C2×SD16×C3111yescharacteristic
328C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
329C8—22no—
330C8—42no—
331C8—42no—
332C8—42no—
333C8C4×D4×C3111yescharacteristic
334C8C4×D4×C3111yescharacteristic
335C8C31×#12111yescharacteristic
336C8C31×#12111yescharacteristic
337C22—22no—
338C22—41no—
339C22—81no—
340C22—81no—
341C22—161no—
342C22C31×#41711yescharacteristic
343C22C31×#44811yescharacteristic
344C22C31×#48011yescharacteristic
345C4—22no—
346C4—81no—
347C4C31×#38611yescharacteristic
348C4C2×C31×#10211yescharacteristic
349C4C31×#44711yescharacteristic
350C4C31×#48111yescharacteristic
351C2—21no—
352C2—21no—
353C2—21no—
354C2—42no—
355C2—161no—
356C2C31×#187411yescharacteristic
subgroupG/H
centerC4×C31#447
commutatorC2×C8C22×C4×C31
Frattini, cosocleC22×C8C23×C31
socleC2×C31#1874
prime radicalC31×#3067C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C31 ◁ C22×C4×C31 ◁ C2×C31×#131 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#2916C2semidirect
3. C31×#2143C2semidirect
4. C2×C31×#359C2semidirect
5. C2×C31×#350C2semidirect
6. C31×#1388C2semidirect
7. C31×#1381C2semidirect
123. #12995C31direct (N × H)
160. #2916C2×C31semidirect
161. #2143C2×C31semidirect
162. C2×#359C2×C31semidirect
163. C2×#350C2×C31semidirect
164. #1388C2×C31semidirect
165. #1381C2×C31semidirect
248. C31#12995direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#30672
C31×#29162
C31×#21432
C2×C31×#3592
C2×C31×#3502
C31×#13882
C31×#13812
#1299531