Finite Group Databasebeta

← C31×#8897 #21465656

Subgroups — C31×#8897 #21465656

Order 7936.

530 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2354C211yesmaximal, characteristic
2C31×#1947C211yesmaximal, characteristic, complemented
3C31×#1834C211yesmaximal, characteristic, complemented
4C31×#1802C211yesmaximal, characteristic
5C2×C31×D4⋊C8C211yesmaximal, characteristic
6C31×#1296C211yesmaximal, characteristic, complemented
7C31×#1279C211yesmaximal, characteristic, complemented
8C2×C4×D4×C31C2211yescharacteristic
9C2×C31×#117—21no—
10C2×C31×#107—21no—
11C2×C31×C4⋊C8C2211yescharacteristic
12C2×C31×C4⋊C8C2211yescharacteristic
13C2×C31×#102—21no—
14C2×C4×C8×C31C2211yescharacteristic
15C31×#390—21no—
16C31×#388—22no—
17C31×#384C2211yescharacteristic
18C31×#384C2211yescharacteristic
19C31×#380—21no—
20C4×C4⋊C4×C31—21no—
21C4×C4⋊C4×C31C2211yescharacteristic
22C31×#340—21no—
23C31×#340—22no—
24C31×#340—21no—
25C31×D4⋊C8C414yescomplemented
26C22×D4×C31D411yescharacteristic
27C23×C4×C31—21no—
28C22×C8×C31—21no—
29C22×C8×C31—21no—
30C22×C8×C31—21no—
31C4×D4×C31—21no—
32C4×D4×C31—21no—
33C4×D4×C31C2×C412yes—
34C4×D4×C31Q812yes—
35C31×#117—42no—
36C31×#117—42no—
37C2×C4⋊C4×C31—21no—
38C2×C4⋊C4×C31—21no—
39C2×C4⋊C4×C31—21no—
40C2×C4⋊C4×C31—21no—
41C2×C4⋊C4×C31—21no—
42C2×C4⋊C4×C31D411yescharacteristic
43C2×C4⋊C4×C31D411yescharacteristic
44C2×C4⋊C4×C31D411yescharacteristic
45C2×C4⋊C4×C31D412yes—
46C2×C22⋊C4×C31—21no—
47C2×C22⋊C4×C31—22no—
48C2×C22⋊C4×C31—22no—
49C2×C42×C31—22no—
50C2×C42×C31—21no—
51C2×C42×C31C2311yescharacteristic
52C31×#107—42no—
53C31×C4⋊C8—21no—
54C31×C4⋊C8—21no—
55C31×C4⋊C8—21no—
56C31×C4⋊C8C2×C412yes—
57C31×#102—42no—
58C4×C8×C31—21no—
59C4×C8×C31C2×C412yes—
60C31×#95—22no—
61C31×#95—21no—
62C24×C31—21no—
63C2×D4×C31—21no—
64C2×D4×C31—21no—
65C2×D4×C31—21no—
66C2×D4×C31—21no—
67C2×D4×C31—21no—
68C2×D4×C31C4⋊C412yes—
69C22×C4×C31—21no—
70C22×C4×C31—21no—
71C22×C4×C31—22no—
72C22×C4×C31—22no—
73C22×C4×C31—21no—
74C22×C4×C31—22no—
75C22×C4×C31—41no—
76C22×C4×C31—41no—
77C22×C4×C31—41no—
78C22×C4×C31—41no—
79C22×C4×C31—41no—
80C22×C4×C31C2×D411yescharacteristic
81C22×C4×C31C2×D411yescharacteristic
82C22×C4×C31C2×D411yescharacteristic
83C2×C8×C31—22no—
84C2×C8×C31—22no—
85C2×C8×C31—41no—
86C2×C8×C31—41no—
87C2×C8×C31—41no—
88C2×C8×C31—41no—
89C2×C8×C31—41no—
90C2×C8×C31—41no—
91C2×C8×C31—41no—
92C4⋊C4×C31—21no—
93C4⋊C4×C31—21no—
94C4⋊C4×C31—21no—
95C4⋊C4×C31—21no—
96C4⋊C4×C31—42no—
97C4⋊C4×C31—42no—
98C4⋊C4×C31—41no—
99C4⋊C4×C31—41no—
100C4⋊C4×C31—41no—
101C4⋊C4×C31—41no—
102C4⋊C4×C31—41no—
103C4⋊C4×C31—41no—
104C4⋊C4×C31—41no—
105C4⋊C4×C31—41no—
106C4⋊C4×C31C4⋊C412yes—
107C4⋊C4×C31D812yes—
108C22⋊C4×C31—22no—
109C22⋊C4×C31—22no—
110C22⋊C4×C31—44no—
111C22⋊C4×C31—82no—
112C42×C31—44no—
113C42×C31—41no—
114C42×C31—41no—
115C42×C31C22×C411yescharacteristic
116C42×C31C2×Q811yescharacteristic
117C42×C31#4111yescharacteristic
118C42×C31#4111yescharacteristic
119#8897C3111yesmaximal, characteristic, direct product factor, Sylow
120C23×C31—22no—
121C23×C31—41no—
122C23×C31—41no—
123C23×C31—41no—
124C23×C31—41no—
125C23×C31—41no—
126C23×C31—41no—
127C23×C31#12011yescharacteristic
128D4×C31—22no—
129D4×C31—22no—
130D4×C31—41no—
131D4×C31—41no—
132C2×C4×C31—21no—
133C2×C4×C31—21no—
134C2×C4×C31—22no—
135C2×C4×C31—22no—
136C2×C4×C31—41no—
137C2×C4×C31—41no—
138C2×C4×C31—41no—
139C2×C4×C31—41no—
140C2×C4×C31—42no—
141C2×C4×C31—42no—
142C2×C4×C31—42no—
143C2×C4×C31—42no—
144C2×C4×C31—42no—
145C2×C4×C31—41no—
146C2×C4×C31—41no—
147C2×C4×C31—42no—
148C2×C4×C31—41no—
149C2×C4×C31—42no—
150C2×C4×C31—81no—
151C2×C4×C31—81no—
152C2×C4×C31—81no—
153C2×C4×C31C2×C4⋊C411yescharacteristic
154C2×C4×C31C4×D411yescharacteristic
155C2×C4×C31C4×D411yescharacteristic
156C2×C4×C31C22⋊Q811yescharacteristic
157C2×C4×C31C22⋊Q811yescharacteristic
158C2×C4×C31#12311yescharacteristic
159C2×C4×C31C2×D811yescharacteristic
160C2×C4×C31#13511yescharacteristic
161C2×C4×C31#13511yescharacteristic
162C2×C4×C31#13511yescharacteristic
163C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
164C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
165C2×C4×C31#13711yescharacteristic
166C2×C4×C31#13711yescharacteristic
167C8×C31—42no—
168C8×C31—42no—
169C8×C31—81no—
170#2354C2×C3111yescharacteristic
171#1947C2×C3111yescharacteristic, complemented
172#1834C2×C3111yescharacteristic, complemented
173#1802C2×C3111yescharacteristic
174C2×D4⋊C8C2×C3111yescharacteristic
175#1296C2×C3111yescharacteristic, complemented
176#1279C2×C3111yescharacteristic, complemented
177C22×C31—42no—
178C22×C31—42no—
179C22×C31—42no—
180C22×C31—81no—
181C22×C31—81no—
182C22×C31—81no—
183C22×C31—81no—
184C22×C31#38511yescharacteristic
185C22×C31#44711yescharacteristic
186C22×C31#44911yescharacteristic
187C22×C31#45211yescharacteristic
188C22×C31#45211yescharacteristic
189C22×C31#45411yescharacteristic
190C22×C31#45511yescharacteristic
191C4×C31—21no—
192C4×C31—21no—
193C4×C31—42no—
194C4×C31—42no—
195C4×C31—82no—
196C4×C31—81no—
197C4×C31—161no—
198C4×C31#42711yescharacteristic
199C4×C31#42811yescharacteristic
200C4×C31C4×D811yescharacteristic
201C4×C31#44011yescharacteristic
202C4×C31#47411yescharacteristic
203C4×C31#47811yescharacteristic
204C4×C31#48211yescharacteristic
205C4×C31#48511yescharacteristic
206C2×C4×D4C22×C3111yescharacteristic
207C2×#117—21no—
208C2×#107—21no—
209C2×C4⋊C8C22×C3111yescharacteristic
210C2×C4⋊C8C22×C3111yescharacteristic
211C2×#102—21no—
212C2×C4×C8C22×C3111yescharacteristic
213#390—21no—
214#388—22no—
215#384C22×C3111yescharacteristic
216#384C22×C3111yescharacteristic
217#380—21no—
218C4×C4⋊C4—21no—
219C4×C4⋊C4C22×C3111yescharacteristic
220#340—21no—
221#340—22no—
222#340—21no—
223D4⋊C8C4×C3114yescomplemented
224C2×C31—82no—
225C2×C31#162511yescharacteristic
226C2×C31#163811yescharacteristic
227C2×C31#164111yescharacteristic
228C2×C31#164611yescharacteristic
229C2×C31#185411yescharacteristic
230C2×C31#186011yescharacteristic
231C2×C31#186211yescharacteristic
232C22×D4D4×C3111yescharacteristic
233C23×C4—21no—
234C22×C8—21no—
235C22×C8—21no—
236C22×C8—21no—
237C4×D4—21no—
238C4×D4—21no—
239C4×D4C2×C4×C3112yes—
240C4×D4Q8×C3112yes—
241#117—42no—
242#117—42no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4D4×C3111yescharacteristic
249C2×C4⋊C4D4×C3111yescharacteristic
250C2×C4⋊C4D4×C3111yescharacteristic
251C2×C4⋊C4D4×C3112yes—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—22no—
254C2×C22⋊C4—22no—
255C2×C42—22no—
256C2×C42—21no—
257C2×C42C23×C3111yescharacteristic
258#107—42no—
259C4⋊C8—21no—
260C4⋊C8—21no—
261C4⋊C8—21no—
262C4⋊C8C2×C4×C3112yes—
263#102—42no—
264C4×C8—21no—
265C4×C8C2×C4×C3112yes—
266#95—22no—
267#95—21no—
268C31#889711yescharacteristic, direct product factor, Sylow
269C24—21no—
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4C4⋊C4×C3112yes—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—21no—
281C22×C4—22no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4C2×D4×C3111yescharacteristic
288C22×C4C2×D4×C3111yescharacteristic
289C22×C4C2×D4×C3111yescharacteristic
290C2×C8—22no—
291C2×C8—22no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8—41no—
295C2×C8—41no—
296C2×C8—41no—
297C2×C8—41no—
298C2×C8—41no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—42no—
304C4⋊C4—42no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4C4⋊C4×C3112yes—
314C4⋊C4D8×C3112yes—
315C22⋊C4—22no—
316C22⋊C4—22no—
317C22⋊C4—44no—
318C22⋊C4—82no—
319C42—44no—
320C42—41no—
321C42—41no—
322C42C22×C4×C3111yescharacteristic
323C42C2×Q8×C3111yescharacteristic
324C42#41×C3111yescharacteristic
325C42#41×C3111yescharacteristic
326C23—22no—
327C23—41no—
328C23—41no—
329C23—41no—
330C23—41no—
331C23—41no—
332C23—41no—
333C23C31×#12011yescharacteristic
334D4—22no—
335D4—22no—
336D4—41no—
337D4—41no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—42no—
354C2×C4—41no—
355C2×C4—42no—
356C2×C4—81no—
357C2×C4—81no—
358C2×C4—81no—
359C2×C4C2×C4⋊C4×C3111yescharacteristic
360C2×C4C4×D4×C3111yescharacteristic
361C2×C4C4×D4×C3111yescharacteristic
362C2×C4C31×C22⋊Q811yescharacteristic
363C2×C4C31×C22⋊Q811yescharacteristic
364C2×C4C31×#12311yescharacteristic
365C2×C4C2×D8×C3111yescharacteristic
366C2×C4C31×#13511yescharacteristic
367C2×C4C31×#13511yescharacteristic
368C2×C4C31×#13511yescharacteristic
369C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
370C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
371C2×C4C31×#13711yescharacteristic
372C2×C4C31×#13711yescharacteristic
373C8—42no—
374C8—42no—
375C8—81no—
376C22—42no—
377C22—42no—
378C22—42no—
379C22—81no—
380C22—81no—
381C22—81no—
382C22—81no—
383C22C31×#38511yescharacteristic
384C22C31×#44711yescharacteristic
385C22C31×#44911yescharacteristic
386C22C31×#45211yescharacteristic
387C22C31×#45211yescharacteristic
388C22C31×#45411yescharacteristic
389C22C31×#45511yescharacteristic
390C4—21no—
391C4—21no—
392C4—42no—
393C4—42no—
394C4—82no—
395C4—81no—
396C4—161no—
397C4C31×#42711yescharacteristic
398C4C31×#42811yescharacteristic
399C4C4×D8×C3111yescharacteristic
400C4C31×#44011yescharacteristic
401C4C31×#47411yescharacteristic
402C4C31×#47811yescharacteristic
403C4C31×#48211yescharacteristic
404C4C31×#48511yescharacteristic
405C2—82no—
406C2C31×#162511yescharacteristic
407C2C31×#163811yescharacteristic
408C2C31×#164111yescharacteristic
409C2C31×#164611yescharacteristic
410C2C31×#185411yescharacteristic
411C2C31×#186011yescharacteristic
412C2C31×#186211yescharacteristic
subgroupG/H
center, socleC23×C31#120
commutatorC42C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC22×D4×C31D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#1947C2semidirect
3. C31×#1834C2semidirect
6. C31×#1296C2semidirect
7. C31×#1279C2semidirect
25. C31×D4⋊C8C4semidirect
119. #8897C31direct (N × H)
171. #1947C2×C31semidirect
172. #1834C2×C31semidirect
175. #1296C2×C31semidirect
176. #1279C2×C31semidirect
223. D4⋊C8C4×C31semidirect
268. C31#8897direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#23542
C31×#19472
C31×#18342
C31×#18022
C2×C31×D4⋊C82
C31×#12962
C31×#12792
#889731