Finite Group Databasebeta

← C31×#8570 #21465329

Subgroups — C31×#8570 #21465329

Order 7936.

472 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2295C211yesmaximal, characteristic
2C31×#1831C211yesmaximal, characteristic
3C4×C31×C4⋊C8C211yesmaximal, characteristic
4C2×C31×Q8⋊C8C212yesmaximal
5C31×#1279C212yesmaximal
6C2×C4×Q8×C31C2211yescharacteristic
7C2×C31×C4⋊C8—21no—
8C2×C31×C4⋊C8C2212yes—
9C2×C4×C8×C31C2212yes—
10C31×#391C411yescharacteristic
11C31×#391C411yescharacteristic
12C31×#389C411yescharacteristic
13C31×#389C411yescharacteristic
14C31×#387—21no—
15C31×#387—21no—
16C4×C4⋊C4×C31—21no—
17C4×C4⋊C4×C31C2211yescharacteristic
18C31×#376—21no—
19C43×C31C2211yescharacteristic
20C31×#336—21no—
21C31×#336—21no—
22C31×#336—21no—
23C31×Q8⋊C8—24no—
24C22×Q8×C31C2×C411yescharacteristic
25C22×C8×C31—22no—
26C22×C8×C31—22no—
27C4×Q8×C31—21no—
28C4×Q8×C31—21no—
29C4×Q8×C31D412yes—
30C4×Q8×C31Q812yes—
31C2×C4⋊C4×C31—21no—
32C2×C4⋊C4×C31—21no—
33C2×C4⋊C4×C31—21no—
34C2×C4⋊C4×C31C2×C411yescharacteristic
35C2×C4⋊C4×C31C2×C411yescharacteristic
36C2×C4⋊C4×C31C2×C411yescharacteristic
37C2×C42×C31—21no—
38C2×C42×C31—21no—
39C2×C42×C31C2×C411yescharacteristic
40C2×C42×C31C2×C411yescharacteristic
41C2×C42×C31D411yescharacteristic
42C2×C42×C31D411yescharacteristic
43C2×C42×C31D411yescharacteristic
44C2×C42×C31D411yescharacteristic
45C2×C42×C31C2311yescharacteristic
46C31×C4⋊C8—24no—
47C31×C4⋊C8—22no—
48C31×C4⋊C8—22no—
49C4×C8×C31—22no—
50C4×C8×C31—22no—
51C31×#95—21no—
52C31×#95—21no—
53C31×#95—21no—
54C31×#95—21no—
55C31×#95—21no—
56C31×#95—21no—
57C31×#95—21no—
58C2×Q8×C31—21no—
59C2×Q8×C31—22no—
60C2×Q8×C31—22no—
61C2×Q8×C31C4⋊C412yes—
62C22×C4×C31—21no—
63C22×C4×C31—21no—
64C22×C4×C31—21no—
65C22×C4×C31—21no—
66C22×C4×C31C22⋊C411yescharacteristic
67C22×C4×C31C22⋊C411yescharacteristic
68C22×C4×C31C22⋊C411yescharacteristic
69C22×C4×C31C22⋊C411yescharacteristic
70C22×C4×C31C22×C411yescharacteristic
71C22×C4×C31C2×D411yescharacteristic
72C22×C4×C31C2×D411yescharacteristic
73C2×C8×C31—24no—
74C2×C8×C31—42no—
75C2×C8×C31—42no—
76C2×C8×C31—42no—
77C2×C8×C31—42no—
78C2×C8×C31—42no—
79C4⋊C4×C31—21no—
80C4⋊C4×C31—22no—
81C4⋊C4×C31—22no—
82C4⋊C4×C31—22no—
83C4⋊C4×C31—22no—
84C4⋊C4×C31—42no—
85C4⋊C4×C31—42no—
86C4⋊C4×C31C4⋊C412yes—
87C42×C31—22no—
88C42×C31—22no—
89C42×C31—22no—
90C42×C31—22no—
91C42×C31—22no—
92C42×C31—22no—
93C42×C31—22no—
94C42×C31—41no—
95C42×C31—42no—
96C42×C31C2×D411yescharacteristic
97C42×C31C2×Q811yescharacteristic
98C42×C31#4111yescharacteristic
99C42×C31#4111yescharacteristic
100#8570C3111yesmaximal, characteristic, direct product factor, Sylow
101C23×C31C2×C22⋊C411yescharacteristic
102Q8×C31—24no—
103Q8×C31—42no—
104C2×C4×C31—21no—
105C2×C4×C31—21no—
106C2×C4×C31—21no—
107C2×C4×C31—21no—
108C2×C4×C31—22no—
109C2×C4×C31—22no—
110C2×C4×C31—21no—
111C2×C4×C31—21no—
112C2×C4×C31—21no—
113C2×C4×C31—21no—
114C2×C4×C31—21no—
115C2×C4×C31—21no—
116C2×C4×C31—21no—
117C2×C4×C31—21no—
118C2×C4×C31—21no—
119C2×C4×C31—41no—
120C2×C4×C31—41no—
121C2×C4×C31—41no—
122C2×C4×C31—41no—
123C2×C4×C31—41no—
124C2×C4×C31—41no—
125C2×C4×C31—41no—
126C2×C4×C31—41no—
127C2×C4×C31—41no—
128C2×C4×C31—41no—
129C2×C4×C31#10412yes—
130C2×C4×C31C2×C4⋊C411yescharacteristic
131C2×C4×C31#11711yescharacteristic
132C2×C4×C31#12111yescharacteristic
133C2×C4×C31#12111yescharacteristic
134C2×C4×C31C22⋊Q811yescharacteristic
135C2×C4×C31C22⋊Q811yescharacteristic
136C2×C4×C31#13112yes—
137C2×C4×C31#13112yes—
138C2×C4×C31#13512yes—
139C2×C4×C31#13712yes—
140C8×C31—44no—
141C8×C31—82no—
142#2295C2×C3111yescharacteristic
143#1831C2×C3111yescharacteristic
144C4×C4⋊C8C2×C3111yescharacteristic
145C2×Q8⋊C8C2×C3112yes—
146#1279C2×C3112yes—
147C22×C31#38011yescharacteristic
148C22×C31#40811yescharacteristic
149C22×C31#40811yescharacteristic
150C22×C31#41611yescharacteristic
151C22×C31#41911yescharacteristic
152C22×C31C2×#10411yescharacteristic
153C22×C31#42111yescharacteristic
154C4×C31—21no—
155C4×C31—21no—
156C4×C31—22no—
157C4×C31—42no—
158C4×C31—42no—
159C4×C31—41no—
160C4×C31—41no—
161C4×C31—41no—
162C4×C31—81no—
163C4×C31—81no—
164C4×C31#42412yes—
165C4×C31#43312yes—
166C4×C31#46412yes—
167C4×C31#47912yes—
168C2×C4×Q8C22×C3111yescharacteristic
169C2×C4⋊C8—21no—
170C2×C4⋊C8C22×C3112yes—
171C2×C4×C8C22×C3112yes—
172#391C4×C3111yescharacteristic
173#391C4×C3111yescharacteristic
174#389C4×C3111yescharacteristic
175#389C4×C3111yescharacteristic
176#387—21no—
177#387—21no—
178C4×C4⋊C4—21no—
179C4×C4⋊C4C22×C3111yescharacteristic
180#376—21no—
181C43C22×C3111yescharacteristic
182#336—21no—
183#336—21no—
184#336—21no—
185Q8⋊C8—24no—
186C2×C31#148211yescharacteristic
187C2×C31#148511yescharacteristic
188C2×C31#149411yescharacteristic
189C2×C31#149711yescharacteristic
190C2×C31#179811yescharacteristic
191C2×C31#180511yescharacteristic
192C2×C31#180611yescharacteristic
193C22×Q8C2×C4×C3111yescharacteristic
194C22×C8—22no—
195C22×C8—22no—
196C4×Q8—21no—
197C4×Q8—21no—
198C4×Q8D4×C3112yes—
199C4×Q8Q8×C3112yes—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4C2×C4×C3111yescharacteristic
204C2×C4⋊C4C2×C4×C3111yescharacteristic
205C2×C4⋊C4C2×C4×C3111yescharacteristic
206C2×C42—21no—
207C2×C42—21no—
208C2×C42C2×C4×C3111yescharacteristic
209C2×C42C2×C4×C3111yescharacteristic
210C2×C42D4×C3111yescharacteristic
211C2×C42D4×C3111yescharacteristic
212C2×C42D4×C3111yescharacteristic
213C2×C42D4×C3111yescharacteristic
214C2×C42C23×C3111yescharacteristic
215C4⋊C8—24no—
216C4⋊C8—22no—
217C4⋊C8—22no—
218C4×C8—22no—
219C4×C8—22no—
220#95—21no—
221#95—21no—
222#95—21no—
223#95—21no—
224#95—21no—
225#95—21no—
226#95—21no—
227C31#857011yescharacteristic, direct product factor, Sylow
228C2×Q8—21no—
229C2×Q8—22no—
230C2×Q8—22no—
231C2×Q8C4⋊C4×C3112yes—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4C22⋊C4×C3111yescharacteristic
237C22×C4C22⋊C4×C3111yescharacteristic
238C22×C4C22⋊C4×C3111yescharacteristic
239C22×C4C22⋊C4×C3111yescharacteristic
240C22×C4C22×C4×C3111yescharacteristic
241C22×C4C2×D4×C3111yescharacteristic
242C22×C4C2×D4×C3111yescharacteristic
243C2×C8—24no—
244C2×C8—42no—
245C2×C8—42no—
246C2×C8—42no—
247C2×C8—42no—
248C2×C8—42no—
249C4⋊C4—21no—
250C4⋊C4—22no—
251C4⋊C4—22no—
252C4⋊C4—22no—
253C4⋊C4—22no—
254C4⋊C4—42no—
255C4⋊C4—42no—
256C4⋊C4C4⋊C4×C3112yes—
257C42—22no—
258C42—22no—
259C42—22no—
260C42—22no—
261C42—22no—
262C42—22no—
263C42—22no—
264C42—41no—
265C42—42no—
266C42C2×D4×C3111yescharacteristic
267C42C2×Q8×C3111yescharacteristic
268C42#41×C3111yescharacteristic
269C42#41×C3111yescharacteristic
270C23C2×C22⋊C4×C3111yescharacteristic
271Q8—24no—
272Q8—42no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4C31×#10412yes—
299C2×C4C2×C4⋊C4×C3111yescharacteristic
300C2×C4C31×#11711yescharacteristic
301C2×C4C31×#12111yescharacteristic
302C2×C4C31×#12111yescharacteristic
303C2×C4C31×C22⋊Q811yescharacteristic
304C2×C4C31×C22⋊Q811yescharacteristic
305C2×C4C31×#13112yes—
306C2×C4C31×#13112yes—
307C2×C4C31×#13512yes—
308C2×C4C31×#13712yes—
309C8—44no—
310C8—82no—
311C22C31×#38011yescharacteristic
312C22C31×#40811yescharacteristic
313C22C31×#40811yescharacteristic
314C22C31×#41611yescharacteristic
315C22C31×#41911yescharacteristic
316C22C2×C31×#10411yescharacteristic
317C22C31×#42111yescharacteristic
318C4—21no—
319C4—21no—
320C4—22no—
321C4—42no—
322C4—42no—
323C4—41no—
324C4—41no—
325C4—41no—
326C4—81no—
327C4—81no—
328C4C31×#42412yes—
329C4C31×#43312yes—
330C4C31×#46412yes—
331C4C31×#47912yes—
332C2C31×#148211yescharacteristic
333C2C31×#148511yescharacteristic
334C2C31×#149411yescharacteristic
335C2C31×#149711yescharacteristic
336C2C31×#179811yescharacteristic
337C2C31×#180511yescharacteristic
338C2C31×#180611yescharacteristic
subgroupG/H
centerC22×C4×C31C2×D4
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C42C23×C31
socle, prime radicalC23×C31C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C31 ◁ C43×C31 ◁ G

Complements

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

NH ≅ G/Ntype
100. #8570C31direct (N × H)
227. C31#8570direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#22952
C31×#18312
C4×C31×C4⋊C82
C2×C31×Q8⋊C82
C31×#12792
#857031