Finite Group Databasebeta

← C31×#10064 #21466823

Subgroups — C31×#10064 #21466823

Order 7936.

614 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#487C211yesmaximal, characteristic, complemented
2C2×C31×#461C211yesmaximal, characteristic
3C31×#2563C211yesmaximal, characteristic
4C31×#1988C211yesmaximal, characteristic, complemented
5C2×C31×#333C211yesmaximal, characteristic, complemented
6C2×C31×D4⋊C8C211yesmaximal, characteristic
7C31×#1279C211yesmaximal, characteristic, complemented
8C22×SD16×C31—21no—
9C2×C31×C4⋊Q8C2211yescharacteristic
10C2×C31×C4⋊Q8C2211yescharacteristic
11C2×C4×D4×C31C2211yescharacteristic
12C31×#487—22no—
13C31×#487—22no—
14C31×#461—22no—
15C31×#461—22no—
16C2×C31×C4⋊C8C2211yescharacteristic
17C2×C31×C4⋊C8C2211yescharacteristic
18C2×C31×#103—22no—
19C2×C31×#103—21no—
20C2×C4×C8×C31C2211yescharacteristic
21C31×#393—22no—
22C31×#390—21no—
23C31×#382—21no—
24C31×#380—22no—
25C4×C4⋊C4×C31C2211yescharacteristic
26C31×#340—22no—
27C31×#333—22no—
28C31×D4⋊C8—22no—
29C22×Q8×C31—21no—
30C22×Q8×C31D412yes—
31C22×D4×C31D411yescharacteristic
32C23×C4×C31—21no—
33C2×SD16×C31—24no—
34C2×SD16×C31—42no—
35C2×SD16×C31—42no—
36C22×C8×C31—21no—
37C22×C8×C31—21no—
38C22×C8×C31—21no—
39C31×C4⋊Q8—21no—
40C31×C4⋊Q8—21no—
41C31×C4⋊Q8—21no—
42C31×C4⋊Q8—21no—
43C31×C4⋊Q8—21no—
44C31×C4⋊Q8—21no—
45C31×C4⋊Q8—21no—
46C31×C4⋊Q8D412yes—
47C4×D4×C31—21no—
48C4×D4×C31—21no—
49C4×D4×C31—21no—
50C4×D4×C31—21no—
51C2×C4⋊C4×C31—21no—
52C2×C4⋊C4×C31—21no—
53C2×C4⋊C4×C31—21no—
54C2×C4⋊C4×C31—21no—
55C2×C4⋊C4×C31D411yescharacteristic
56C2×C4⋊C4×C31D412yes—
57C2×C22⋊C4×C31—21no—
58C2×C22⋊C4×C31—24no—
59C2×C42×C31—21no—
60C2×C42×C31C2311yescharacteristic
61C31×C4⋊C8—21no—
62C31×C4⋊C8—21no—
63C31×C4⋊C8—21no—
64C31×C4⋊C8D412yes—
65C31×#103—24no—
66C31×#103—28no—
67C4×C8×C31—21no—
68C4×C8×C31D412yes—
69C31×#95—24no—
70C31×#95—21no—
71C24×C31—21no—
72C2×Q8×C31—22no—
73C2×Q8×C31—22no—
74C2×Q8×C31—22no—
75C2×Q8×C31—44no—
76C2×Q8×C31—41no—
77C2×Q8×C31—41no—
78C2×Q8×C31—41no—
79C2×Q8×C31—41no—
80C2×Q8×C31—41no—
81C2×D4×C31—21no—
82C2×D4×C31—21no—
83C2×D4×C31—21no—
84C2×D4×C31—21no—
85C2×D4×C31—21no—
86C2×D4×C31SD1612yes—
87C22×C4×C31—21no—
88C22×C4×C31—22no—
89C22×C4×C31—22no—
90C22×C4×C31—41no—
91C22×C4×C31—41no—
92C22×C4×C31—41no—
93C22×C4×C31—42no—
94C22×C4×C31—42no—
95C22×C4×C31C2×D411yescharacteristic
96C22×C4×C31C2×D411yescharacteristic
97C22×C4×C31C2×D411yescharacteristic
98SD16×C31—48no—
99C2×C8×C31—22no—
100C2×C8×C31—22no—
101C2×C8×C31—42no—
102C2×C8×C31—41no—
103C2×C8×C31—41no—
104C2×C8×C31—41no—
105C2×C8×C31—42no—
106C4⋊C4×C31—22no—
107C4⋊C4×C31—21no—
108C4⋊C4×C31—22no—
109C4⋊C4×C31—21no—
110C4⋊C4×C31—22no—
111C4⋊C4×C31—22no—
112C4⋊C4×C31—41no—
113C4⋊C4×C31—41no—
114C4⋊C4×C31—41no—
115C4⋊C4×C31—41no—
116C4⋊C4×C31—41no—
117C4⋊C4×C31—41no—
118C22⋊C4×C31—41no—
119C22⋊C4×C31—41no—
120C22⋊C4×C31—84no—
121C42×C31—41no—
122C42×C31—41no—
123C42×C31C2×D411yescharacteristic
124C42×C31C2×D411yescharacteristic
125C42×C31C2×D411yescharacteristic
126C42×C31#4111yescharacteristic
127#10064C3111yesmaximal, characteristic, direct product factor, Sylow
128C23×C31—22no—
129C23×C31—41no—
130C23×C31—41no—
131C23×C31—42no—
132C23×C31—42no—
133C23×C31#12011yescharacteristic
134Q8×C31—44no—
135Q8×C31—42no—
136Q8×C31—42no—
137Q8×C31—82no—
138Q8×C31—81no—
139Q8×C31—81no—
140D4×C31—22no—
141D4×C31—22no—
142D4×C31—41no—
143D4×C31—41no—
144C2×C4×C31—22no—
145C2×C4×C31—41no—
146C2×C4×C31—42no—
147C2×C4×C31—42no—
148C2×C4×C31—42no—
149C2×C4×C31—42no—
150C2×C4×C31—42no—
151C2×C4×C31—42no—
152C2×C4×C31—44no—
153C2×C4×C31—81no—
154C2×C4×C31—81no—
155C2×C4×C31—82no—
156C2×C4×C31—81no—
157C2×C4×C31—81no—
158C2×C4×C31#12011yescharacteristic
159C2×C4×C31#12011yescharacteristic
160C2×C4×C31#12111yescharacteristic
161C2×C4×C31#12111yescharacteristic
162C2×C4×C31#12111yescharacteristic
163C2×C4×C31#12711yescharacteristic
164C2×C4×C31C2×SD1611yescharacteristic
165C2×C4×C31#13511yescharacteristic
166C2×C4×C31#13512yes—
167C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
168C2×C4×C31#13711yescharacteristic
169C2×C4×C31#13712yes—
170C8×C31—42no—
171C8×C31—42no—
172C8×C31—81no—
173C2×#487C2×C3111yescharacteristic, complemented
174C2×#461C2×C3111yescharacteristic
175#2563C2×C3111yescharacteristic
176#1988C2×C3111yescharacteristic, complemented
177C2×#333C2×C3111yescharacteristic, complemented
178C2×D4⋊C8C2×C3111yescharacteristic
179#1279C2×C3111yescharacteristic, complemented
180C22×C31—44no—
181C22×C31—42no—
182C22×C31—82no—
183C22×C31—81no—
184C22×C31—81no—
185C22×C31#39211yescharacteristic
186C22×C31#44811yescharacteristic
187C22×C31#44911yescharacteristic
188C22×C31#45212yes—
189C22×C31#45512yes—
190C4×C31—21no—
191C4×C31—21no—
192C4×C31—82no—
193C4×C31—82no—
194C4×C31—82no—
195C4×C31—81no—
196C4×C31#45011yescharacteristic
197C4×C31#45211yescharacteristic
198C4×C31#46412yes—
199C4×C31#46511yescharacteristic
200C4×C31#46811yescharacteristic
201C4×C31#49511yescharacteristic
202C4×C31#49711yescharacteristic
203C22×SD16—21no—
204C2×C4⋊Q8C22×C3111yescharacteristic
205C2×C4⋊Q8C22×C3111yescharacteristic
206C2×C4×D4C22×C3111yescharacteristic
207#487—22no—
208#487—22no—
209#461—22no—
210#461—22no—
211C2×C4⋊C8C22×C3111yescharacteristic
212C2×C4⋊C8C22×C3111yescharacteristic
213C2×#103—22no—
214C2×#103—21no—
215C2×C4×C8C22×C3111yescharacteristic
216#393—22no—
217#390—21no—
218#382—21no—
219#380—22no—
220C4×C4⋊C4C22×C3111yescharacteristic
221#340—22no—
222#333—22no—
223D4⋊C8—22no—
224C2×C31—82no—
225C2×C31#164312yes—
226C2×C31#164612yes—
227C2×C31#200011yescharacteristic
228C2×C31#200411yescharacteristic
229C2×C31#201511yescharacteristic
230C22×Q8—21no—
231C22×Q8D4×C3112yes—
232C22×D4D4×C3111yescharacteristic
233C23×C4—21no—
234C2×SD16—24no—
235C2×SD16—42no—
236C2×SD16—42no—
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—21no—
240C4⋊Q8—21no—
241C4⋊Q8—21no—
242C4⋊Q8—21no—
243C4⋊Q8—21no—
244C4⋊Q8—21no—
245C4⋊Q8—21no—
246C4⋊Q8—21no—
247C4⋊Q8D4×C3112yes—
248C4×D4—21no—
249C4×D4—21no—
250C4×D4—21no—
251C4×D4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4D4×C3111yescharacteristic
257C2×C4⋊C4D4×C3112yes—
258C2×C22⋊C4—21no—
259C2×C22⋊C4—24no—
260C2×C42—21no—
261C2×C42C23×C3111yescharacteristic
262C4⋊C8—21no—
263C4⋊C8—21no—
264C4⋊C8—21no—
265C4⋊C8D4×C3112yes—
266#103—24no—
267#103—28no—
268C4×C8—21no—
269C4×C8D4×C3112yes—
270#95—24no—
271#95—21no—
272C31#1006411yescharacteristic, direct product factor, Sylow
273C24—21no—
274C2×Q8—22no—
275C2×Q8—22no—
276C2×Q8—22no—
277C2×Q8—44no—
278C2×Q8—41no—
279C2×Q8—41no—
280C2×Q8—41no—
281C2×Q8—41no—
282C2×Q8—41no—
283C2×D4—21no—
284C2×D4—21no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4SD16×C3112yes—
289C22×C4—21no—
290C22×C4—22no—
291C22×C4—22no—
292C22×C4—41no—
293C22×C4—41no—
294C22×C4—41no—
295C22×C4—42no—
296C22×C4—42no—
297C22×C4C2×D4×C3111yescharacteristic
298C22×C4C2×D4×C3111yescharacteristic
299C22×C4C2×D4×C3111yescharacteristic
300SD16—48no—
301C2×C8—22no—
302C2×C8—22no—
303C2×C8—42no—
304C2×C8—41no—
305C2×C8—41no—
306C2×C8—41no—
307C2×C8—42no—
308C4⋊C4—22no—
309C4⋊C4—21no—
310C4⋊C4—22no—
311C4⋊C4—21no—
312C4⋊C4—22no—
313C4⋊C4—22no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C22⋊C4—41no—
321C22⋊C4—41no—
322C22⋊C4—84no—
323C42—41no—
324C42—41no—
325C42C2×D4×C3111yescharacteristic
326C42C2×D4×C3111yescharacteristic
327C42C2×D4×C3111yescharacteristic
328C42#41×C3111yescharacteristic
329C23—22no—
330C23—41no—
331C23—42no—
332C23—42no—
333C23—41no—
334C23C31×#12011yescharacteristic
335Q8—44no—
336Q8—42no—
337Q8—42no—
338Q8—82no—
339Q8—81no—
340Q8—81no—
341D4—22no—
342D4—22no—
343D4—41no—
344D4—41no—
345C2×C4—22no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—44no—
351C2×C4—41no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—81no—
355C2×C4—81no—
356C2×C4—82no—
357C2×C4—81no—
358C2×C4—81no—
359C2×C4C31×#12011yescharacteristic
360C2×C4C31×#12011yescharacteristic
361C2×C4C31×#12111yescharacteristic
362C2×C4C31×#12111yescharacteristic
363C2×C4C31×#12111yescharacteristic
364C2×C4C31×#12711yescharacteristic
365C2×C4C2×SD16×C3111yescharacteristic
366C2×C4C31×#13511yescharacteristic
367C2×C4C31×#13512yes—
368C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
369C2×C4C31×#13711yescharacteristic
370C2×C4C31×#13712yes—
371C8—42no—
372C8—42no—
373C8—81no—
374C22—44no—
375C22—42no—
376C22—82no—
377C22—81no—
378C22—81no—
379C22C31×#39211yescharacteristic
380C22C31×#44811yescharacteristic
381C22C31×#44911yescharacteristic
382C22C31×#45212yes—
383C22C31×#45512yes—
384C4—21no—
385C4—21no—
386C4—82no—
387C4—82no—
388C4—82no—
389C4—81no—
390C4C31×#45011yescharacteristic
391C4C31×#45211yescharacteristic
392C4C31×#46412yes—
393C4C31×#46511yescharacteristic
394C4C31×#46811yescharacteristic
395C4C31×#49511yescharacteristic
396C4C31×#49711yescharacteristic
397C2—82no—
398C2C31×#164312yes—
399C2C31×#164612yes—
400C2C31×#200011yescharacteristic
401C2C31×#200411yescharacteristic
402C2C31×#201511yescharacteristic
subgroupG/H
center, socleC23×C31#120
commutator, Frattini, cosocleC2×C42C23×C31
prime radicalC22×D4×C31D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#487C2semidirect
4. C31×#1988C2semidirect
5. C2×C31×#333C2semidirect
7. C31×#1279C2semidirect
127. #10064C31direct (N × H)
173. C2×#487C2×C31semidirect
176. #1988C2×C31semidirect
177. C2×#333C2×C31semidirect
179. #1279C2×C31semidirect
272. C31#10064direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4872
C2×C31×#4612
C31×#25632
C31×#19882
C2×C31×#3332
C2×C31×D4⋊C82
C31×#12792
#1006431