Finite Group Databasebeta

← C31×#7654 #21464413

Subgroups — C31×#7654 #21464413

Order 7936.

580 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2854C211yesmaximal, characteristic
2C31×#1817C211yesmaximal, characteristic, complemented
3C2×C31×#336C211yesmaximal, characteristic, complemented
4C31×#1271C212yesmaximal, complemented
5C31×#1270C212yesmaximal, complemented
6C23×C8×C31—21no—
7C2×C31×#123—21no—
8C2×C31×#121C411yescharacteristic
9C22×C42×C31C2211yescharacteristic
10C2×C31×C22⋊C8—21no—
11C31×#390C411yescharacteristic
12C31×#390C2211yescharacteristic
13C31×#389C411yescharacteristic
14C31×#389C2211yescharacteristic
15C31×#388—21no—
16C31×#388—21no—
17C31×#386—21no—
18C31×#380C411yescharacteristic
19C31×#336—21no—
20C31×#336—21no—
21C31×#336C2212yes—
22C31×#336C2212yes—
23C22×D4×C31—21no—
24C22×D4×C31C2×C411yescharacteristic
25C23×C4×C31C2×C411yescharacteristic
26C23×C4×C31D411yescharacteristic
27C23×C4×C31D411yescharacteristic
28C22×C8×C31—24no—
29C22×C8×C31—22no—
30C22×C8×C31—22no—
31C22×C8×C31—42no—
32C22×C8×C31—42no—
33C31×#123—42no—
34C31×#123—42no—
35C31×#121—42no—
36C2×C4⋊C4×C31—21no—
37C2×C4⋊C4×C31—21no—
38C2×C4⋊C4×C31C2×C411yescharacteristic
39C2×C4⋊C4×C31C2×C411yescharacteristic
40C2×C4⋊C4×C31C2×C411yescharacteristic
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×C22⋊C4×C31—21no—
47C2×C42×C31—42no—
48C2×C42×C31C2×C411yescharacteristic
49C2×C42×C31D411yescharacteristic
50C2×C42×C31D411yescharacteristic
51C2×C42×C31C2311yescharacteristic
52C31×C22⋊C8—42no—
53C31×#95—21no—
54C31×#95—21no—
55C31×#95—21no—
56C24×C31—21no—
57C24×C31C22⋊C411yescharacteristic
58C2×D4×C31—22no—
59C2×D4×C31—41no—
60C2×D4×C31—41no—
61C2×D4×C31—42no—
62C2×D4×C31—42no—
63C2×D4×C31—42no—
64C22×C4×C31—22no—
65C22×C4×C31—22no—
66C22×C4×C31—22no—
67C22×C4×C31—22no—
68C22×C4×C31—22no—
69C22×C4×C31—22no—
70C22×C4×C31—21no—
71C22×C4×C31—21no—
72C22×C4×C31—21no—
73C22×C4×C31—41no—
74C22×C4×C31—41no—
75C22×C4×C31C22⋊C411yescharacteristic
76C22×C4×C31C22⋊C411yescharacteristic
77C22×C4×C31C22⋊C411yescharacteristic
78C22×C4×C31D812yes—
79C22×C4×C31SD1612yes—
80C22×C4×C31C22×C411yescharacteristic
81C22×C4×C31C2×D411yescharacteristic
82C22×C4×C31C2×D411yescharacteristic
83C2×C8×C31—24no—
84C2×C8×C31—48no—
85C2×C8×C31—42no—
86C2×C8×C31—42no—
87C2×C8×C31—42no—
88C2×C8×C31—42no—
89C2×C8×C31—42no—
90C4⋊C4×C31—22no—
91C4⋊C4×C31—41no—
92C4⋊C4×C31—41no—
93C4⋊C4×C31—42no—
94C4⋊C4×C31—41no—
95C4⋊C4×C31—41no—
96C22⋊C4×C31—42no—
97C22⋊C4×C31—42no—
98C22⋊C4×C31—42no—
99C22⋊C4×C31—42no—
100C22⋊C4×C31—41no—
101C22⋊C4×C31—41no—
102C22⋊C4×C31—42no—
103C42×C31—41no—
104C42×C31—41no—
105C42×C31—41no—
106C42×C31—41no—
107#7654C3111yesmaximal, characteristic, direct product factor, Sylow
108C23×C31—21no—
109C23×C31—21no—
110C23×C31—21no—
111C23×C31—21no—
112C23×C31—41no—
113C23×C31—41no—
114C23×C31—41no—
115C23×C31—41no—
116C23×C31—41no—
117C23×C31—41no—
118C23×C31—41no—
119C23×C31#9912yes—
120C23×C31#10212yes—
121C23×C31#10412yes—
122C23×C31C2×C22⋊C411yescharacteristic
123D4×C31—82no—
124D4×C31—84no—
125C2×C4×C31—24no—
126C2×C4×C31—24no—
127C2×C4×C31—21no—
128C2×C4×C31—21no—
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—44no—
142C2×C4×C31—44no—
143C2×C4×C31—41no—
144C2×C4×C31—41no—
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#10212yes—
153C2×C4×C31#13112yes—
154C2×C4×C31C2×D811yescharacteristic
155C2×C4×C31C2×SD1611yescharacteristic
156C2×C4×C31#13512yes—
157C8×C31—44no—
158C8×C31—82no—
159#2854C2×C3111yescharacteristic
160#1817C2×C3111yescharacteristic, complemented
161C2×#336C2×C3111yescharacteristic, complemented
162#1271C2×C3112yescomplemented
163#1270C2×C3112yescomplemented
164C22×C31—22no—
165C22×C31—22no—
166C22×C31—22no—
167C22×C31—22no—
168C22×C31—22no—
169C22×C31—22no—
170C22×C31—81no—
171C22×C31—81no—
172C22×C31—81no—
173C22×C31—81no—
174C22×C31—81no—
175C22×C31—81no—
176C22×C31—81no—
177C22×C31#32714yes—
178C22×C31#40811yescharacteristic
179C22×C31C2×#9911yescharacteristic
180C22×C31#41311yescharacteristic
181C22×C31C2×#10211yescharacteristic
182C22×C31#41611yescharacteristic
183C22×C31C2×#10411yescharacteristic
184C22×C31#42111yescharacteristic
185C4×C31—22no—
186C4×C31—21no—
187C4×C31—22no—
188C4×C31—21no—
189C4×C31—22no—
190C4×C31—41no—
191C4×C31—41no—
192C4×C31—81no—
193C4×C31—81no—
194C4×C31—81no—
195C23×C8—21no—
196C2×#123—21no—
197C2×#121C4×C3111yescharacteristic
198C22×C42C22×C3111yescharacteristic
199C2×C22⋊C8—21no—
200#390C4×C3111yescharacteristic
201#390C22×C3111yescharacteristic
202#389C4×C3111yescharacteristic
203#389C22×C3111yescharacteristic
204#388—21no—
205#388—21no—
206#386—21no—
207#380C4×C3111yescharacteristic
208#336—21no—
209#336—21no—
210#336C22×C3112yes—
211#336C22×C3112yes—
212C2×C31—24no—
213C2×C31—161no—
214C2×C31#146811yescharacteristic
215C2×C31#148011yescharacteristic
216C2×C31#149411yescharacteristic
217C2×C31C2×#32711yescharacteristic
218C2×C31#151611yescharacteristic
219C2×C31#153211yescharacteristic
220C2×C31#154011yescharacteristic
221C22×D4—21no—
222C22×D4C2×C4×C3111yescharacteristic
223C23×C4C2×C4×C3111yescharacteristic
224C23×C4D4×C3111yescharacteristic
225C23×C4D4×C3111yescharacteristic
226C22×C8—24no—
227C22×C8—22no—
228C22×C8—22no—
229C22×C8—42no—
230C22×C8—42no—
231#123—42no—
232#123—42no—
233#121—42no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4C2×C4×C3111yescharacteristic
237C2×C4⋊C4C2×C4×C3111yescharacteristic
238C2×C4⋊C4C2×C4×C3111yescharacteristic
239C2×C22⋊C4—21no—
240C2×C22⋊C4—21no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—21no—
244C2×C22⋊C4—21no—
245C2×C42—42no—
246C2×C42C2×C4×C3111yescharacteristic
247C2×C42D4×C3111yescharacteristic
248C2×C42D4×C3111yescharacteristic
249C2×C42C23×C3111yescharacteristic
250C22⋊C8—42no—
251#95—21no—
252#95—21no—
253#95—21no—
254C31#765411yescharacteristic, direct product factor, Sylow
255C24—21no—
256C24C22⋊C4×C3111yescharacteristic
257C2×D4—22no—
258C2×D4—41no—
259C2×D4—41no—
260C2×D4—42no—
261C2×D4—42no—
262C2×D4—42no—
263C22×C4—22no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4C22⋊C4×C3111yescharacteristic
275C22×C4C22⋊C4×C3111yescharacteristic
276C22×C4C22⋊C4×C3111yescharacteristic
277C22×C4D8×C3112yes—
278C22×C4SD16×C3112yes—
279C22×C4C22×C4×C3111yescharacteristic
280C22×C4C2×D4×C3111yescharacteristic
281C22×C4C2×D4×C3111yescharacteristic
282C2×C8—24no—
283C2×C8—42no—
284C2×C8—48no—
285C2×C8—42no—
286C2×C8—42no—
287C2×C8—42no—
288C2×C8—42no—
289C4⋊C4—22no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—42no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C22⋊C4—42no—
296C22⋊C4—42no—
297C22⋊C4—42no—
298C22⋊C4—42no—
299C22⋊C4—41no—
300C22⋊C4—41no—
301C22⋊C4—42no—
302C42—41no—
303C42—41no—
304C42—41no—
305C42—41no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—21no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23C31×#9912yes—
318C23C31×#10212yes—
319C23C31×#10412yes—
320C23C2×C22⋊C4×C3111yescharacteristic
321D4—82no—
322D4—84no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—24no—
332C2×C4—24no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—44no—
340C2×C4—44no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4C31×#10212yes—
351C2×C4C31×#13112yes—
352C2×C4C2×D8×C3111yescharacteristic
353C2×C4C2×SD16×C3111yescharacteristic
354C2×C4C31×#13512yes—
355C8—44no—
356C8—82no—
357C22—22no—
358C22—22no—
359C22—22no—
360C22—22no—
361C22—22no—
362C22—22no—
363C22—81no—
364C22—81no—
365C22—81no—
366C22—81no—
367C22—81no—
368C22—81no—
369C22—81no—
370C22C31×#32714yes—
371C22C31×#40811yescharacteristic
372C22C2×C31×#9911yescharacteristic
373C22C31×#41311yescharacteristic
374C22C2×C31×#10211yescharacteristic
375C22C31×#41611yescharacteristic
376C22C2×C31×#10411yescharacteristic
377C22C31×#42111yescharacteristic
378C4—22no—
379C4—21no—
380C4—22no—
381C4—21no—
382C4—22no—
383C4—41no—
384C4—41no—
385C4—81no—
386C4—81no—
387C4—81no—
388C2—24no—
389C2—161no—
390C2C31×#146811yescharacteristic
391C2C31×#148011yescharacteristic
392C2C31×#149411yescharacteristic
393C2C2×C31×#32711yescharacteristic
394C2C31×#151611yescharacteristic
395C2C31×#153211yescharacteristic
396C2C31×#154011yescharacteristic
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×#1817C2semidirect
3. C2×C31×#336C2semidirect
4. C31×#1271C2semidirect
5. C31×#1270C2semidirect
107. #7654C31direct (N × H)
160. #1817C2×C31semidirect
161. C2×#336C2×C31semidirect
162. #1271C2×C31semidirect
163. #1270C2×C31semidirect
254. C31#7654direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#28542
C31×#18172
C2×C31×#3362
C31×#12712
C31×#12702
#765431