Finite Group Databasebeta

← C31×#10268 #21467027

Subgroups — C31×#10268 #21467027

Order 7936.

658 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#492C211yesmaximal, characteristic
2C2×C31×#475C211yesmaximal, characteristic, complemented
3C2×C31×#460C211yesmaximal, characteristic
4C31×#1984C211yesmaximal, characteristic, complemented
5C2×C31×#332C211yesmaximal, characteristic, complemented
6C2×C31×#331C211yesmaximal, characteristic
7C31×#1277C211yesmaximal, characteristic, complemented
8C22×SD16×C31—21no—
9C22×SD16×C31—22no—
10C2×C31×C4⋊Q8C2211yescharacteristic
11C2×C31×#127C2211yescharacteristic
12C2×C4×Q8×C31C2211yescharacteristic
13C31×#492—22no—
14C31×#492—22no—
15C31×#475—22no—
16C31×#475—22no—
17C31×#460—22no—
18C31×#460—22no—
19C2×C31×#106—21no—
20C2×C31×C4⋊C8C2211yescharacteristic
21C2×C31×C4⋊C8C2211yescharacteristic
22C2×C31×C4⋊C8C2211yescharacteristic
23C2×C31×#103—21no—
24C2×C31×#102—21no—
25C2×C4×C8×C31C2211yescharacteristic
26C31×#336—22no—
27C31×#332—22no—
28C31×#331—22no—
29C22×Q8×C31—21no—
30C22×Q8×C31D411yescharacteristic
31C22×D4×C31—21no—
32C22×D4×C31—21no—
33C22×D4×C31—21no—
34C2×SD16×C31—24no—
35C2×SD16×C31—28no—
36C2×SD16×C31—44no—
37C2×SD16×C31—42no—
38C2×SD16×C31—42no—
39C2×SD16×C31—44no—
40C22×C8×C31—21no—
41C22×C8×C31—21no—
42C22×C8×C31—21no—
43C22×C8×C31D412yes—
44C31×C4⋊Q8—21no—
45C31×C4⋊Q8—21no—
46C31×C4⋊Q8—21no—
47C31×C4⋊Q8D412yes—
48C31×#127—21no—
49C31×#127—21no—
50C31×#127—21no—
51C31×#127D412yes—
52C4×Q8×C31—21no—
53C4×Q8×C31—21no—
54C4×Q8×C31—21no—
55C4×Q8×C31—21no—
56C2×C4⋊C4×C31—21no—
57C2×C4⋊C4×C31—21no—
58C2×C4⋊C4×C31—21no—
59C2×C4⋊C4×C31D411yescharacteristic
60C2×C42×C31—21no—
61C2×C42×C31C2311yescharacteristic
62C31×#106—24no—
63C31×C4⋊C8—21no—
64C31×C4⋊C8—21no—
65C31×C4⋊C8—21no—
66C31×C4⋊C8—21no—
67C31×C4⋊C8D412yes—
68C31×C4⋊C8D412yes—
69C31×#103—24no—
70C31×#102—24no—
71C4×C8×C31—21no—
72C4×C8×C31—21no—
73C24×C31—41no—
74C2×Q8×C31—21no—
75C2×Q8×C31—21no—
76C2×Q8×C31—21no—
77C2×Q8×C31—22no—
78C2×Q8×C31—21no—
79C2×Q8×C31—21no—
80C2×Q8×C31—41no—
81C2×Q8×C31—42no—
82C2×Q8×C31—42no—
83C2×Q8×C31SD1612yescomplemented
84C2×D4×C31—22no—
85C2×D4×C31—22no—
86C2×D4×C31—22no—
87C2×D4×C31—41no—
88C2×D4×C31—41no—
89C2×D4×C31—41no—
90C2×D4×C31—41no—
91C2×D4×C31—42no—
92C2×D4×C31—41no—
93C2×D4×C31—41no—
94C2×D4×C31—42no—
95C2×D4×C31—41no—
96C2×D4×C31—82no—
97C22×C4×C31—21no—
98C22×C4×C31—21no—
99C22×C4×C31—41no—
100C22×C4×C31C2×D411yescharacteristic
101C22×C4×C31C2×D411yescharacteristic
102C22×C4×C31#4111yescharacteristic
103SD16×C31—416no—
104SD16×C31—48no—
105C2×C8×C31—22no—
106C2×C8×C31—22no—
107C2×C8×C31—22no—
108C2×C8×C31—22no—
109C2×C8×C31—41no—
110C2×C8×C31—41no—
111C2×C8×C31—41no—
112C2×C8×C31—41no—
113C2×C8×C31—41no—
114C2×C8×C31—42no—
115C2×C8×C31SD1614yescomplemented
116C4⋊C4×C31—21no—
117C4⋊C4×C31—22no—
118C4⋊C4×C31—21no—
119C4⋊C4×C31—22no—
120C4⋊C4×C31—41no—
121C4⋊C4×C31—41no—
122C4⋊C4×C31—41no—
123C4⋊C4×C31—41no—
124C42×C31—41no—
125C42×C31—41no—
126C42×C31C2×D411yescharacteristic
127C42×C31C2×D411yescharacteristic
128C42×C31C2×D411yescharacteristic
129C42×C31C2×D411yescharacteristic
130#10268C3111yesmaximal, characteristic, direct product factor, Sylow
131C23×C31—42no—
132C23×C31—82no—
133C23×C31—81no—
134C23×C31—81no—
135C23×C31—82no—
136C23×C31#12111yescharacteristic
137Q8×C31—22no—
138Q8×C31—22no—
139Q8×C31—41no—
140Q8×C31—41no—
141Q8×C31—44no—
142Q8×C31—81no—
143Q8×C31—81no—
144D4×C31—42no—
145D4×C31—44no—
146D4×C31—42no—
147D4×C31—82no—
148D4×C31—82no—
149D4×C31—81no—
150D4×C31—81no—
151D4×C31—81no—
152D4×C31—81no—
153C2×C4×C31—22no—
154C2×C4×C31—22no—
155C2×C4×C31—41no—
156C2×C4×C31—41no—
157C2×C4×C31—41no—
158C2×C4×C31—42no—
159C2×C4×C31—42no—
160C2×C4×C31—82no—
161C2×C4×C31#12011yescharacteristic
162C2×C4×C31#12011yescharacteristic
163C2×C4×C31#12011yescharacteristic
164C2×C4×C31#12111yescharacteristic
165C2×C4×C31#12111yescharacteristic
166C2×C4×C31#12711yescharacteristic
167C2×C4×C31C2×SD1611yescharacteristic
168C2×C4×C31C2×SD1612yes—
169C2×C4×C31#13511yescharacteristic
170C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
171C2×C4×C31AGL(1,ℤ/8)12yes—
172C2×C4×C31#13711yescharacteristic
173C8×C31—24no—
174C8×C31—42no—
175C8×C31—42no—
176C8×C31—81no—
177C2×#492C2×C3111yescharacteristic
178C2×#475C2×C3111yescharacteristic, complemented
179C2×#460C2×C3111yescharacteristic
180#1984C2×C3111yescharacteristic, complemented
181C2×#332C2×C3111yescharacteristic, complemented
182C2×#331C2×C3111yescharacteristic
183#1277C2×C3111yescharacteristic, complemented
184C22×C31—82no—
185C22×C31—82no—
186C22×C31—82no—
187C22×C31—162no—
188C22×C31—162no—
189C22×C31#39211yescharacteristic
190C22×C31#46012yes—
191C22×C31#46511yescharacteristic
192C22×C31#46811yescharacteristic
193C22×C31#47112yes—
194C4×C31—21no—
195C4×C31—21no—
196C4×C31—42no—
197C4×C31—82no—
198C4×C31—81no—
199C4×C31#44811yescharacteristic
200C4×C31#44911yescharacteristic
201C4×C31#45011yescharacteristic
202C4×C31#45012yes—
203C4×C31#45211yescharacteristic
204C4×C31#49211yescharacteristic
205C4×C31#49611yescharacteristic
206C22×SD16—21no—
207C22×SD16—22no—
208C2×C4⋊Q8C22×C3111yescharacteristic
209C2×#127C22×C3111yescharacteristic
210C2×C4×Q8C22×C3111yescharacteristic
211#492—22no—
212#492—22no—
213#475—22no—
214#475—22no—
215#460—22no—
216#460—22no—
217C2×#106—21no—
218C2×C4⋊C8C22×C3111yescharacteristic
219C2×C4⋊C8C22×C3111yescharacteristic
220C2×C4⋊C8C22×C3111yescharacteristic
221C2×#103—21no—
222C2×#102—21no—
223C2×C4×C8C22×C3111yescharacteristic
224#336—22no—
225#332—22no—
226#331—22no—
227C2×C31—162no—
228C2×C31#166612yes—
229C2×C31#168612yes—
230C2×C31#200011yescharacteristic
231C2×C31#201411yescharacteristic
232C2×C31#201911yescharacteristic
233C22×Q8—21no—
234C22×Q8D4×C3111yescharacteristic
235C22×D4—21no—
236C22×D4—21no—
237C22×D4—21no—
238C2×SD16—24no—
239C2×SD16—28no—
240C2×SD16—44no—
241C2×SD16—42no—
242C2×SD16—42no—
243C2×SD16—44no—
244C22×C8—21no—
245C22×C8—21no—
246C22×C8—21no—
247C22×C8D4×C3112yes—
248C4⋊Q8—21no—
249C4⋊Q8—21no—
250C4⋊Q8—21no—
251C4⋊Q8D4×C3112yes—
252#127—21no—
253#127—21no—
254#127—21no—
255#127D4×C3112yes—
256C4×Q8—21no—
257C4×Q8—21no—
258C4×Q8—21no—
259C4×Q8—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4D4×C3111yescharacteristic
264C2×C42—21no—
265C2×C42C23×C3111yescharacteristic
266#106—24no—
267C4⋊C8—21no—
268C4⋊C8—21no—
269C4⋊C8—21no—
270C4⋊C8—21no—
271C4⋊C8D4×C3112yes—
272C4⋊C8D4×C3112yes—
273#103—24no—
274#102—24no—
275C4×C8—21no—
276C4×C8—21no—
277C31#1026811yescharacteristic, direct product factor, Sylow
278C24—41no—
279C2×Q8—21no—
280C2×Q8—21no—
281C2×Q8—21no—
282C2×Q8—22no—
283C2×Q8—21no—
284C2×Q8—21no—
285C2×Q8—41no—
286C2×Q8—42no—
287C2×Q8—42no—
288C2×Q8SD16×C3112yescomplemented
289C2×D4—22no—
290C2×D4—22no—
291C2×D4—22no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4—42no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—42no—
300C2×D4—41no—
301C2×D4—82no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—41no—
305C22×C4C2×D4×C3111yescharacteristic
306C22×C4C2×D4×C3111yescharacteristic
307C22×C4#41×C3111yescharacteristic
308SD16—416no—
309SD16—48no—
310C2×C8—22no—
311C2×C8—22no—
312C2×C8—22no—
313C2×C8—22no—
314C2×C8—41no—
315C2×C8—41no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—41no—
319C2×C8—42no—
320C2×C8SD16×C3114yescomplemented
321C4⋊C4—21no—
322C4⋊C4—22no—
323C4⋊C4—21no—
324C4⋊C4—22no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C42—41no—
330C42—41no—
331C42C2×D4×C3111yescharacteristic
332C42C2×D4×C3111yescharacteristic
333C42C2×D4×C3111yescharacteristic
334C42C2×D4×C3111yescharacteristic
335C23—42no—
336C23—82no—
337C23—81no—
338C23—81no—
339C23—82no—
340C23C31×#12111yescharacteristic
341Q8—22no—
342Q8—22no—
343Q8—41no—
344Q8—41no—
345Q8—44no—
346Q8—81no—
347Q8—81no—
348D4—42no—
349D4—44no—
350D4—42no—
351D4—82no—
352D4—82no—
353D4—81no—
354D4—81no—
355D4—81no—
356D4—81no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—42no—
362C2×C4—41no—
363C2×C4—42no—
364C2×C4—82no—
365C2×C4C31×#12011yescharacteristic
366C2×C4C31×#12011yescharacteristic
367C2×C4C31×#12011yescharacteristic
368C2×C4C31×#12111yescharacteristic
369C2×C4C31×#12111yescharacteristic
370C2×C4C31×#12711yescharacteristic
371C2×C4C2×SD16×C3111yescharacteristic
372C2×C4C2×SD16×C3112yes—
373C2×C4C31×#13511yescharacteristic
374C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
375C2×C4C31×AGL(1,ℤ/8)12yes—
376C2×C4C31×#13711yescharacteristic
377C8—24no—
378C8—42no—
379C8—42no—
380C8—81no—
381C22—82no—
382C22—82no—
383C22—82no—
384C22—162no—
385C22—162no—
386C22C31×#39211yescharacteristic
387C22C31×#46012yes—
388C22C31×#46511yescharacteristic
389C22C31×#46811yescharacteristic
390C22C31×#47112yes—
391C4—21no—
392C4—21no—
393C4—42no—
394C4—82no—
395C4—81no—
396C4C31×#44811yescharacteristic
397C4C31×#44911yescharacteristic
398C4C31×#45011yescharacteristic
399C4C31×#45012yes—
400C4C31×#45211yescharacteristic
401C4C31×#49211yescharacteristic
402C4C31×#49611yescharacteristic
403C2—162no—
404C2C31×#166612yes—
405C2C31×#168612yes—
406C2C31×#200011yescharacteristic
407C2C31×#201411yescharacteristic
408C2C31×#201911yescharacteristic
subgroupG/H
center, socleC23×C31#121
commutator, Frattini, cosocleC2×C42C23×C31
prime radicalC2×C31×#127C22
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
2. C2×C31×#475C2semidirect
4. C31×#1984C2semidirect
5. C2×C31×#332C2semidirect
7. C31×#1277C2semidirect
83. C2×Q8×C31SD16semidirect
115. C2×C8×C31SD16semidirect
130. #10268C31direct (N × H)
178. C2×#475C2×C31semidirect
180. #1984C2×C31semidirect
181. C2×#332C2×C31semidirect
183. #1277C2×C31semidirect
277. C31#10268direct (N × H)
288. C2×Q8SD16×C31semidirect
320. C2×C8SD16×C31semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#4922
C2×C31×#4752
C2×C31×#4602
C31×#19842
C2×C31×#3322
C2×C31×#3312
C31×#12772
#1026831