Finite Group Databasebeta

← C31×#12979 #21469738

Subgroups — C31×#12979 #21469738

Order 7936.

456 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3407C211yesmaximal, characteristic, complemented
2C31×#2955C211yesmaximal, characteristic
3C31×#2117C211yesmaximal, characteristic, complemented
4C2×C31×#350C211yesmaximal, characteristic, complemented
5C31×#2113C211yesmaximal, characteristic, complemented
6C31×#1379C211yesmaximal, characteristic, complemented
7C31×#1378C211yesmaximal, characteristic, complemented
8C31×#575C411yescharacteristic
9C2×C31×#131C2211yescharacteristic
10C2×C31×#131C2211yescharacteristic
11C31×#504—22no—
12C31×#504—22no—
13C2×C31×M32—22no—
14C2×C31×M32C2211yescharacteristic
15C2×C31×M32C2211yescharacteristic
16C2×C31×M32C2211yescharacteristic
17C22×C16×C31C2211yescharacteristic
18C31×#444—22no—
19C31×#443—22no—
20C31×#430C411yescharacteristic
21C31×#421C411yescharacteristic
22C31×#421C411yescharacteristic
23C31×#405C2211yescharacteristic
24C31×#350—22no—
25C31×#350—22no—
26C31×C22⋊C16—22no—
27C2×#41×C31C2×C411yescharacteristic
28C2×#41×C31C2×C411yescharacteristic
29C31×#137—21no—
30C31×#137C812yes—
31C31×AGL(1,ℤ/8)—21no—
32C31×AGL(1,ℤ/8)C812yes—
33C31×#135—22no—
34C31×#131—21no—
35C31×#131—21no—
36C31×#131—21no—
37C31×#131—21no—
38C31×#131—21no—
39C31×#131—21no—
40C31×#131D412yes—
41C31×#131D412yes—
42C2×M16×C31—21no—
43C2×M16×C31—21no—
44C2×M16×C31C2×C411yescharacteristic
45C2×M16×C31C2×C411yescharacteristic
46C2×M16×C31C2×C411yescharacteristic
47C22×C8×C31—21no—
48C22×C8×C31—21no—
49C22×C8×C31C2311yescharacteristic
50C31×#117C2×C411yescharacteristic
51C31×M32—24no—
52C31×M32—21no—
53C31×M32—21no—
54C31×M32—21no—
55C31×M32—21no—
56C31×M32—21no—
57C31×M32D412yes—
58C2×C16×C31—24no—
59C2×C16×C31—21no—
60C2×C16×C31—21no—
61C2×C16×C31—21no—
62C2×C16×C31—21no—
63C2×C16×C31—21no—
64C2×C16×C31D412yes—
65C31×#108—22no—
66C31×#104—22no—
67C31×#104—22no—
68C31×#97—21no—
69C4×C8×C31—21no—
70#41×C31—21no—
71#41×C31—21no—
72#41×C31—21no—
73#41×C31—21no—
74#41×C31—21no—
75#41×C31—21no—
76#41×C31C22⋊C412yes—
77#41×C31C2×C812yes—
78C2×Q8×C31C2×C811yescharacteristic
79C2×Q8×C31M1611yescharacteristic
80C2×D4×C31—21no—
81C2×D4×C31—21no—
82C2×D4×C31C2×C811yescharacteristic
83C2×D4×C31M1611yescharacteristic
84C22×C4×C31—21no—
85C22×C4×C31—21no—
86C22×C4×C31C22×C411yescharacteristic
87Q16×C31—22no—
88SD16×C31—22no—
89SD16×C31—22no—
90D8×C31—22no—
91M16×C31—21no—
92M16×C31—21no—
93M16×C31—22no—
94M16×C31—22no—
95M16×C31—21no—
96M16×C31—21no—
97M16×C31—41no—
98M16×C31—41no—
99M16×C31C22⋊C412yes—
100M16×C31C2×C812yes—
101C2×C8×C31—21no—
102C2×C8×C31—21no—
103C2×C8×C31—22no—
104C2×C8×C31—22no—
105C2×C8×C31—21no—
106C2×C8×C31—41no—
107C2×C8×C31—41no—
108C2×C8×C31C2×D411yescharacteristic
109C2×C8×C31C2×D411yescharacteristic
110C2×C8×C31C2×D411yescharacteristic
111C2×C8×C31C2×D411yescharacteristic
112C2×C8×C31#4111yescharacteristic
113C2×C8×C31#4111yescharacteristic
114C4⋊C4×C31—21no—
115C22⋊C4×C31—21no—
116C42×C31—21no—
117C16×C31—22no—
118C16×C31—22no—
119C16×C31—41no—
120C16×C31—41no—
121#12979C3111yesmaximal, characteristic, direct product factor, Sylow
122C23×C31—21no—
123C23×C31—21no—
124C23×C31#13111yescharacteristic
125Q8×C31—21no—
126Q8×C31—21no—
127Q8×C31—21no—
128Q8×C31C22⋊C812yes—
129D4×C31—22no—
130D4×C31—22no—
131D4×C31—21no—
132D4×C31—21no—
133D4×C31—21no—
134D4×C31—41no—
135D4×C31—41no—
136D4×C31C22⋊C812yes—
137C2×C4×C31—21no—
138C2×C4×C31—22no—
139C2×C4×C31—22no—
140C2×C4×C31—21no—
141C2×C4×C31—41no—
142C2×C4×C31—41no—
143C2×C4×C31—41no—
144C2×C4×C31C2×C22⋊C411yescharacteristic
145C2×C4×C31C4×D411yescharacteristic
146C2×C4×C31C4×D411yescharacteristic
147C2×C4×C31C22×C811yescharacteristic
148C2×C4×C31C2×M1611yescharacteristic
149C2×C4×C31#13111yescharacteristic
150C8×C31—22no—
151C8×C31—22no—
152C8×C31—41no—
153C8×C31#12011yescharacteristic
154C8×C31#12111yescharacteristic
155C8×C31#12111yescharacteristic
156C8×C31#12311yescharacteristic
157#3407C2×C3111yescharacteristic, complemented
158#2955C2×C3111yescharacteristic
159#2117C2×C3111yescharacteristic, complemented
160C2×#350C2×C3111yescharacteristic, complemented
161#2113C2×C3111yescharacteristic, complemented
162#1379C2×C3111yescharacteristic, complemented
163#1378C2×C3111yescharacteristic, complemented
164C22×C31—22no—
165C22×C31—41no—
166C22×C31—42no—
167C22×C31—41no—
168C22×C31—81no—
169C22×C31#40811yescharacteristic
170C22×C31C8×D411yescharacteristic
171C22×C31#43511yescharacteristic
172C4×C31—22no—
173C4×C31—41no—
174C4×C31—81no—
175C4×C31#38611yescharacteristic
176C4×C31C2×C22⋊C811yescharacteristic
177C4×C31C8×D411yescharacteristic
178C4×C31#43511yescharacteristic
179#575C4×C3111yescharacteristic
180C2×#131C22×C3111yescharacteristic
181C2×#131C22×C3111yescharacteristic
182#504—22no—
183#504—22no—
184C2×M32—22no—
185C2×M32C22×C3111yescharacteristic
186C2×M32C22×C3111yescharacteristic
187C2×M32C22×C3111yescharacteristic
188C22×C16C22×C3111yescharacteristic
189#444—22no—
190#443—22no—
191#430C4×C3111yescharacteristic
192#421C4×C3111yescharacteristic
193#421C4×C3111yescharacteristic
194#405C22×C3111yescharacteristic
195#350—22no—
196#350—22no—
197C22⋊C16—22no—
198C2×C31—21no—
199C2×C31—21no—
200C2×C31—21no—
201C2×C31—42no—
202C2×C31—81no—
203C2×C31#186911yescharacteristic
204C2×#41C2×C4×C3111yescharacteristic
205C2×#41C2×C4×C3111yescharacteristic
206#137—21no—
207#137C8×C3112yes—
208AGL(1,ℤ/8)—21no—
209AGL(1,ℤ/8)C8×C3112yes—
210#135—22no—
211#131—21no—
212#131—21no—
213#131—21no—
214#131—21no—
215#131—21no—
216#131—21no—
217#131D4×C3112yes—
218#131D4×C3112yes—
219C2×M16—21no—
220C2×M16—21no—
221C2×M16C2×C4×C3111yescharacteristic
222C2×M16C2×C4×C3111yescharacteristic
223C2×M16C2×C4×C3111yescharacteristic
224C22×C8—21no—
225C22×C8—21no—
226C22×C8C23×C3111yescharacteristic
227#117C2×C4×C3111yescharacteristic
228M32—24no—
229M32—21no—
230M32—21no—
231M32—21no—
232M32—21no—
233M32—21no—
234M32D4×C3112yes—
235C2×C16—24no—
236C2×C16—21no—
237C2×C16—21no—
238C2×C16—21no—
239C2×C16—21no—
240C2×C16—21no—
241C2×C16D4×C3112yes—
242#108—22no—
243#104—22no—
244#104—22no—
245#97—21no—
246C4×C8—21no—
247C31#1297911yescharacteristic, direct product factor, Sylow
248#41—21no—
249#41—21no—
250#41—21no—
251#41—21no—
252#41—21no—
253#41—21no—
254#41C22⋊C4×C3112yes—
255#41C2×C8×C3112yes—
256C2×Q8C2×C8×C3111yescharacteristic
257C2×Q8M16×C3111yescharacteristic
258C2×D4—21no—
259C2×D4—21no—
260C2×D4C2×C8×C3111yescharacteristic
261C2×D4M16×C3111yescharacteristic
262C22×C4—21no—
263C22×C4—21no—
264C22×C4C22×C4×C3111yescharacteristic
265Q16—22no—
266SD16—22no—
267SD16—22no—
268D8—22no—
269M16—21no—
270M16—21no—
271M16—22no—
272M16—22no—
273M16—21no—
274M16—21no—
275M16—41no—
276M16—41no—
277M16C22⋊C4×C3112yes—
278M16C2×C8×C3112yes—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8—22no—
282C2×C8—22no—
283C2×C8—21no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8C2×D4×C3111yescharacteristic
287C2×C8C2×D4×C3111yescharacteristic
288C2×C8C2×D4×C3111yescharacteristic
289C2×C8C2×D4×C3111yescharacteristic
290C2×C8#41×C3111yescharacteristic
291C2×C8#41×C3111yescharacteristic
292C4⋊C4—21no—
293C22⋊C4—21no—
294C42—21no—
295C16—22no—
296C16—22no—
297C16—41no—
298C16—41no—
299C23—21no—
300C23—21no—
301C23C31×#13111yescharacteristic
302Q8—21no—
303Q8—21no—
304Q8—21no—
305Q8C31×C22⋊C812yes—
306D4—22no—
307D4—22no—
308D4—21no—
309D4—21no—
310D4—21no—
311D4—41no—
312D4—41no—
313D4C31×C22⋊C812yes—
314C2×C4—21no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—21no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4C2×C22⋊C4×C3111yescharacteristic
322C2×C4C4×D4×C3111yescharacteristic
323C2×C4C4×D4×C3111yescharacteristic
324C2×C4C22×C8×C3111yescharacteristic
325C2×C4C2×M16×C3111yescharacteristic
326C2×C4C31×#13111yescharacteristic
327C8—22no—
328C8—22no—
329C8—41no—
330C8C31×#12011yescharacteristic
331C8C31×#12111yescharacteristic
332C8C31×#12111yescharacteristic
333C8C31×#12311yescharacteristic
334C22—22no—
335C22—41no—
336C22—42no—
337C22—41no—
338C22—81no—
339C22C31×#40811yescharacteristic
340C22C8×D4×C3111yescharacteristic
341C22C31×#43511yescharacteristic
342C4—22no—
343C4—41no—
344C4—81no—
345C4C31×#38611yescharacteristic
346C4C2×C31×C22⋊C811yescharacteristic
347C4C8×D4×C3111yescharacteristic
348C4C31×#43511yescharacteristic
349C2—21no—
350C2—21no—
351C2—21no—
352C2—42no—
353C2—81no—
354C2C31×#186911yescharacteristic
subgroupG/H
centerC8×C31#120
commutatorC2×C4C22×C8×C31
Frattini, cosocleC22×C8C23×C31
socleC2×C31#1869
prime radicalC31×#575C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C8×C31 ◁ C22×C8×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#3407C2semidirect
3. C31×#2117C2semidirect
4. C2×C31×#350C2semidirect
5. C31×#2113C2semidirect
6. C31×#1379C2semidirect
7. C31×#1378C2semidirect
121. #12979C31direct (N × H)
157. #3407C2×C31semidirect
159. #2117C2×C31semidirect
160. C2×#350C2×C31semidirect
161. #2113C2×C31semidirect
162. #1379C2×C31semidirect
163. #1378C2×C31semidirect
247. C31#12979direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#34072
C31×#29552
C31×#21172
C2×C31×#3502
C31×#21132
C31×#13792
C31×#13782
#1297931