Finite Group Databasebeta

← C31×#7690 #21464449

Subgroups — C31×#7690 #21464449

Order 7936.

600 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2850C211yesmaximal, characteristic
2C31×#1749C211yesmaximal, characteristic, complemented
3C2×C31×#336C211yesmaximal, characteristic, complemented
4C31×#1272C212yesmaximal, complemented
5C31×#1270C212yesmaximal, complemented
6C23×C8×C31—21no—
7C2×C31×#124C411yescharacteristic
8C2×C31×C22⋊Q8C411yescharacteristic
9C2×C31×#121C411yescharacteristic
10C22×C42×C31C2211yescharacteristic
11C2×C31×C22⋊C8—21no—
12C2×C31×#97—21no—
13C31×#391C2211yescharacteristic
14C31×#390C2211yescharacteristic
15C31×#388—21no—
16C31×#388—21no—
17C31×#386—21no—
18C31×#386—21no—
19C31×#382C411yescharacteristic
20C31×#336—21no—
21C31×#336C2212yes—
22C31×#336C2212yes—
23C22×Q8×C31C2×C411yescharacteristic
24C22×D4×C31—21no—
25C22×D4×C31C2×C411yescharacteristic
26C23×C4×C31C2×C411yescharacteristic
27C23×C4×C31D411yescharacteristic
28C23×C4×C31D411yescharacteristic
29C22×C8×C31—24no—
30C22×C8×C31—22no—
31C22×C8×C31—22no—
32C22×C8×C31—42no—
33C22×C8×C31—42no—
34C31×#124—42no—
35C31×C22⋊Q8—42no—
36C31×#121—42no—
37C2×C4⋊C4×C31—21no—
38C2×C4⋊C4×C31C2×C411yescharacteristic
39C2×C4⋊C4×C31C2×C411yescharacteristic
40C2×C22⋊C4×C31—21no—
41C2×C22⋊C4×C31—21no—
42C2×C22⋊C4×C31—21no—
43C2×C22⋊C4×C31—21no—
44C2×C22⋊C4×C31—21no—
45C2×C22⋊C4×C31—21no—
46C2×C42×C31—42no—
47C2×C42×C31C2×C411yescharacteristic
48C2×C42×C31D411yescharacteristic
49C2×C42×C31D411yescharacteristic
50C2×C42×C31C2311yescharacteristic
51C31×C22⋊C8—24no—
52C31×#97—42no—
53C31×#95—21no—
54C31×#95—21no—
55C31×#95—21no—
56C31×#95—21no—
57C24×C31—21no—
58C24×C31C22⋊C411yescharacteristic
59C2×Q8×C31—22no—
60C2×Q8×C31—41no—
61C2×Q8×C31—41no—
62C2×D4×C31—22no—
63C2×D4×C31—41no—
64C2×D4×C31—41no—
65C2×D4×C31—42no—
66C2×D4×C31—42no—
67C2×D4×C31—42no—
68C22×C4×C31—22no—
69C22×C4×C31—22no—
70C22×C4×C31—21no—
71C22×C4×C31—21no—
72C22×C4×C31—22no—
73C22×C4×C31—22no—
74C22×C4×C31—22no—
75C22×C4×C31—22no—
76C22×C4×C31—21no—
77C22×C4×C31—21no—
78C22×C4×C31—21no—
79C22×C4×C31—41no—
80C22×C4×C31—41no—
81C22×C4×C31C22⋊C411yescharacteristic
82C22×C4×C31C22⋊C411yescharacteristic
83C22×C4×C31C22⋊C411yescharacteristic
84C22×C4×C31C22×C411yescharacteristic
85C22×C4×C31C2×D411yescharacteristic
86C22×C4×C31C2×D411yescharacteristic
87C2×C8×C31—24no—
88C2×C8×C31—24no—
89C2×C8×C31—42no—
90C2×C8×C31—48no—
91C2×C8×C31—42no—
92C2×C8×C31—42no—
93C2×C8×C31—42no—
94C4⋊C4×C31—42no—
95C4⋊C4×C31—41no—
96C4⋊C4×C31—41no—
97C22⋊C4×C31—42no—
98C22⋊C4×C31—42no—
99C22⋊C4×C31—42no—
100C22⋊C4×C31—42no—
101C22⋊C4×C31—42no—
102C22⋊C4×C31—41no—
103C22⋊C4×C31—41no—
104C42×C31—22no—
105C42×C31—22no—
106C42×C31—41no—
107C42×C31—41no—
108#7690C3111yesmaximal, characteristic, direct product factor, Sylow
109C23×C31—21no—
110C23×C31—21no—
111C23×C31—21no—
112C23×C31—21no—
113C23×C31—41no—
114C23×C31—41no—
115C23×C31—41no—
116C23×C31—41no—
117C23×C31—41no—
118C23×C31—41no—
119C23×C31—41no—
120C23×C31#10012yes—
121C23×C31#10412yes—
122C23×C31#10412yes—
123C23×C31C2×C22⋊C411yescharacteristic
124Q8×C31—82no—
125D4×C31—82no—
126D4×C31—84no—
127C2×C4×C31—24no—
128C2×C4×C31—24no—
129C2×C4×C31—21no—
130C2×C4×C31—21no—
131C2×C4×C31—21no—
132C2×C4×C31—21no—
133C2×C4×C31—21no—
134C2×C4×C31—21no—
135C2×C4×C31—21no—
136C2×C4×C31—21no—
137C2×C4×C31—21no—
138C2×C4×C31—21no—
139C2×C4×C31—21no—
140C2×C4×C31—21no—
141C2×C4×C31—21no—
142C2×C4×C31—21no—
143C2×C4×C31—44no—
144C2×C4×C31—44no—
145C2×C4×C31—41no—
146C2×C4×C31—41no—
147C2×C4×C31—41no—
148C2×C4×C31—41no—
149C2×C4×C31—41no—
150C2×C4×C31—41no—
151C2×C4×C31—41no—
152C2×C4×C31—41no—
153C2×C4×C31—41no—
154C2×C4×C31#9912yes—
155C2×C4×C31#13112yes—
156C2×C4×C31#13512yes—
157C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C31#13711yescharacteristic
159C8×C31—44no—
160C8×C31—44no—
161#2850C2×C3111yescharacteristic
162#1749C2×C3111yescharacteristic, complemented
163C2×#336C2×C3111yescharacteristic, complemented
164#1272C2×C3112yescomplemented
165#1270C2×C3112yescomplemented
166C22×C31—22no—
167C22×C31—22no—
168C22×C31—22no—
169C22×C31—22no—
170C22×C31—22no—
171C22×C31—22no—
172C22×C31—81no—
173C22×C31—81no—
174C22×C31—81no—
175C22×C31—81no—
176C22×C31—81no—
177C22×C31—81no—
178C22×C31—81no—
179C22×C31#32914yes—
180C22×C31#40811yescharacteristic
181C22×C31C2×#9911yescharacteristic
182C22×C31C2×#10011yescharacteristic
183C22×C31#41611yescharacteristic
184C22×C31#41711yescharacteristic
185C22×C31C2×#10411yescharacteristic
186C22×C31C2×#10411yescharacteristic
187C4×C31—22no—
188C4×C31—22no—
189C4×C31—21no—
190C4×C31—22no—
191C4×C31—21no—
192C4×C31—41no—
193C4×C31—41no—
194C4×C31—81no—
195C4×C31—81no—
196C4×C31—81no—
197C23×C8—21no—
198C2×#124C4×C3111yescharacteristic
199C2×C22⋊Q8C4×C3111yescharacteristic
200C2×#121C4×C3111yescharacteristic
201C22×C42C22×C3111yescharacteristic
202C2×C22⋊C8—21no—
203C2×#97—21no—
204#391C22×C3111yescharacteristic
205#390C22×C3111yescharacteristic
206#388—21no—
207#388—21no—
208#386—21no—
209#386—21no—
210#382C4×C3111yescharacteristic
211#336—21no—
212#336C22×C3112yes—
213#336C22×C3112yes—
214C2×C31—24no—
215C2×C31—161no—
216C2×C31#147111yescharacteristic
217C2×C31#148311yescharacteristic
218C2×C31#149411yescharacteristic
219C2×C31#150111yescharacteristic
220C2×C31#150411yescharacteristic
221C2×C31C2×#32911yescharacteristic
222C2×C31#155111yescharacteristic
223C22×Q8C2×C4×C3111yescharacteristic
224C22×D4—21no—
225C22×D4C2×C4×C3111yescharacteristic
226C23×C4C2×C4×C3111yescharacteristic
227C23×C4D4×C3111yescharacteristic
228C23×C4D4×C3111yescharacteristic
229C22×C8—24no—
230C22×C8—22no—
231C22×C8—22no—
232C22×C8—42no—
233C22×C8—42no—
234#124—42no—
235C22⋊Q8—42no—
236#121—42no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4C2×C4×C3111yescharacteristic
239C2×C4⋊C4C2×C4×C3111yescharacteristic
240C2×C22⋊C4—21no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—21no—
244C2×C22⋊C4—21no—
245C2×C22⋊C4—21no—
246C2×C42—42no—
247C2×C42C2×C4×C3111yescharacteristic
248C2×C42D4×C3111yescharacteristic
249C2×C42D4×C3111yescharacteristic
250C2×C42C23×C3111yescharacteristic
251C22⋊C8—24no—
252#97—42no—
253#95—21no—
254#95—21no—
255#95—21no—
256#95—21no—
257C31#769011yescharacteristic, direct product factor, Sylow
258C24—21no—
259C24C22⋊C4×C3111yescharacteristic
260C2×Q8—22no—
261C2×Q8—41no—
262C2×Q8—41no—
263C2×D4—22no—
264C2×D4—41no—
265C2×D4—41no—
266C2×D4—42no—
267C2×D4—42no—
268C2×D4—42no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4C22⋊C4×C3111yescharacteristic
283C22×C4C22⋊C4×C3111yescharacteristic
284C22×C4C22⋊C4×C3111yescharacteristic
285C22×C4C22×C4×C3111yescharacteristic
286C22×C4C2×D4×C3111yescharacteristic
287C22×C4C2×D4×C3111yescharacteristic
288C2×C8—24no—
289C2×C8—24no—
290C2×C8—42no—
291C2×C8—48no—
292C2×C8—42no—
293C2×C8—42no—
294C2×C8—42no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—42no—
298C22⋊C4—42no—
299C22⋊C4—42no—
300C22⋊C4—42no—
301C22⋊C4—42no—
302C22⋊C4—42no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C42—22no—
306C42—22no—
307C42—41no—
308C42—41no—
309C23—21no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23C31×#10012yes—
321C23C31×#10412yes—
322C23C31×#10412yes—
323C23C2×C22⋊C4×C3111yescharacteristic
324Q8—82no—
325D4—82no—
326D4—84no—
327C2×C4—24no—
328C2×C4—24no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—44no—
344C2×C4—44no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4C31×#9912yes—
355C2×C4C31×#13112yes—
356C2×C4C31×#13512yes—
357C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
358C2×C4C31×#13711yescharacteristic
359C8—44no—
360C8—44no—
361C22—22no—
362C22—22no—
363C22—22no—
364C22—22no—
365C22—22no—
366C22—22no—
367C22—81no—
368C22—81no—
369C22—81no—
370C22—81no—
371C22—81no—
372C22—81no—
373C22—81no—
374C22C31×#32914yes—
375C22C31×#40811yescharacteristic
376C22C2×C31×#9911yescharacteristic
377C22C2×C31×#10011yescharacteristic
378C22C31×#41611yescharacteristic
379C22C31×#41711yescharacteristic
380C22C2×C31×#10411yescharacteristic
381C22C2×C31×#10411yescharacteristic
382C4—22no—
383C4—22no—
384C4—21no—
385C4—22no—
386C4—21no—
387C4—41no—
388C4—41no—
389C4—81no—
390C4—81no—
391C4—81no—
392C2—24no—
393C2—161no—
394C2C31×#147111yescharacteristic
395C2C31×#148311yescharacteristic
396C2C31×#149411yescharacteristic
397C2C31×#150111yescharacteristic
398C2C31×#150411yescharacteristic
399C2C2×C31×#32911yescharacteristic
400C2C31×#155111yescharacteristic
subgroupG/H
center, socleC23×C31C2×C22⋊C4
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC2×C31×#121C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C22×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#1749C2semidirect
3. C2×C31×#336C2semidirect
4. C31×#1272C2semidirect
5. C31×#1270C2semidirect
108. #7690C31direct (N × H)
162. #1749C2×C31semidirect
163. C2×#336C2×C31semidirect
164. #1272C2×C31semidirect
165. #1270C2×C31semidirect
257. C31#7690direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#28502
C31×#17492
C2×C31×#3362
C31×#12722
C31×#12702
#769031