Finite Group Databasebeta

← C31×#10913 #21467672

Subgroups — C31×#10913 #21467672

Order 7936.

826 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×M16×C31C211yesmaximal, characteristic
2C2×C31×#389C211yesmaximal, characteristic
3C2×C31×#343C212yesmaximal
4C2×C31×#343C212yesmaximal
5C31×#1728C211yesmaximal, characteristic
6C22×M16×C31C2212yes—
7C22×M16×C31C2212yes—
8C22×C4⋊C4×C31C412yes—
9C22×C4⋊C4×C31C2211yescharacteristic
10C22×C4⋊C4×C31C2211yescharacteristic
11C22×C42×C31C2211yescharacteristic
12C4×M16×C31—24no—
13C2×C31×#97—21no—
14C2×C4×C8×C31—21no—
15C31×#389—21no—
16C31×#389—21no—
17C31×#389—21no—
18C31×#389—21no—
19C2×C31×#95C412yes—
20C31×#343—24no—
21C31×#343C418yescomplemented
22C31×#336—21no—
23C31×#336—21no—
24C23×C4×C31C2×C411yescharacteristic
25C23×C4×C31C2×C411yescharacteristic
26C23×C4×C31C2×C412yes—
27C23×C4×C31C2×C412yes—
28C23×C4×C31C2311yescharacteristic
29C2×M16×C31—22no—
30C2×M16×C31—22no—
31C2×M16×C31—22no—
32C2×M16×C31—22no—
33C2×M16×C31—22no—
34C2×M16×C31—22no—
35C2×M16×C31—22no—
36C2×M16×C31—22no—
37C2×M16×C31C2×C414yes—
38C2×M16×C31C2×C414yes—
39C2×M16×C31D414yes—
40C2×M16×C31Q814yes—
41C22×C8×C31—22no—
42C22×C8×C31—22no—
43C2×C4⋊C4×C31—21no—
44C2×C4⋊C4×C31—21no—
45C2×C4⋊C4×C31—22no—
46C2×C4⋊C4×C31—22no—
47C2×C4⋊C4×C31—22no—
48C2×C4⋊C4×C31—22no—
49C2×C4⋊C4×C31—21no—
50C2×C4⋊C4×C31—21no—
51C2×C4⋊C4×C31—22no—
52C2×C4⋊C4×C31—44no—
53C2×C4⋊C4×C31C2×C414yes—
54C2×C42×C31—22no—
55C2×C42×C31—22no—
56C2×C42×C31D411yescharacteristic
57C2×C42×C31D411yescharacteristic
58C2×C42×C31D411yescharacteristic
59C2×C42×C31D411yescharacteristic
60C31×#97—24no—
61C4×C8×C31—24no—
62C31×#95—22no—
63C31×#95—22no—
64C24×C31C22×C411yescharacteristic
65C22×C4×C31—22no—
66C22×C4×C31—22no—
67C22×C4×C31—22no—
68C22×C4×C31—22no—
69C22×C4×C31—22no—
70C22×C4×C31—22no—
71C22×C4×C31—22no—
72C22×C4×C31—24no—
73C22×C4×C31—41no—
74C22×C4×C31—41no—
75C22×C4×C31—42no—
76C22×C4×C31—42no—
77C22×C4×C31—42no—
78C22×C4×C31—42no—
79C22×C4×C31C4214yes—
80C22×C4×C31C22⋊C411yescharacteristic
81C22×C4×C31C22⋊C411yescharacteristic
82C22×C4×C31C22⋊C411yescharacteristic
83C22×C4×C31C22⋊C411yescharacteristic
84C22×C4×C31C22×C412yes—
85C22×C4×C31C2×D412yes—
86C22×C4×C31C2×D411yescharacteristic
87C22×C4×C31C2×D411yescharacteristic
88C22×C4×C31C2×Q812yes—
89C22×C4×C31#4112yes—
90C22×C4×C31#4112yes—
91C22×C4×C31#4112yes—
92M16×C31—24no—
93M16×C31—24no—
94M16×C31—24no—
95M16×C31—24no—
96M16×C31—24no—
97M16×C31—42no—
98M16×C31—42no—
99M16×C31C4⋊C418yescomplemented
100C2×C8×C31—24no—
101C2×C8×C31—24no—
102C2×C8×C31—24no—
103C2×C8×C31—24no—
104C2×C8×C31—42no—
105C2×C8×C31—42no—
106C4⋊C4×C31—24no—
107C4⋊C4×C31—24no—
108C4⋊C4×C31—44no—
109C4⋊C4×C31—44no—
110C4⋊C4×C31—41no—
111C4⋊C4×C31—42no—
112C4⋊C4×C31—41no—
113C42×C31—21no—
114C42×C31—21no—
115C42×C31—22no—
116C42×C31—22no—
117C42×C31—21no—
118C42×C31—21no—
119#10913C3111yesmaximal, characteristic, direct product factor, Sylow
120C23×C31—21no—
121C23×C31—21no—
122C23×C31—21no—
123C23×C31—21no—
124C23×C31C2×C4211yescharacteristic
125C23×C31C2×C22⋊C411yescharacteristic
126C23×C31#11711yescharacteristic
127C23×C31C4×D412yes—
128C23×C31C4×Q812yes—
129C2×C4×C31—21no—
130C2×C4×C31—21no—
131C2×C4×C31—21no—
132C2×C4×C31—21no—
133C2×C4×C31—24no—
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—44no—
141C2×C4×C31—44no—
142C2×C4×C31—44no—
143C2×C4×C31—42no—
144C2×C4×C31—42no—
145C2×C4×C31—44no—
146C2×C4×C31—42no—
147C2×C4×C31—42no—
148C2×C4×C31—42no—
149C2×C4×C31—84no—
150C2×C4×C31#10012yes—
151C2×C4×C31#10112yes—
152C2×C4×C31C2×C4⋊C412yes—
153C2×C4×C31#11712yes—
154C2×C4×C31C4×D412yes—
155C2×C4×C31C4×D412yes—
156C2×C4×C31C4×D412yes—
157C2×C4×C31C4×Q812yes—
158C2×C4×C31#12011yescharacteristic
159C2×C4×C31#12112yes—
160C2×C4×C31C22⋊Q812yes—
161C2×C4×C31C22⋊Q812yes—
162C2×C4×C31#12312yes—
163C2×C4×C31#12311yescharacteristic
164C2×C4×C31#12411yescharacteristic
165C2×C4×C31#12512yes—
166C2×C4×C31#12612yes—
167C2×C4×C31C4⋊Q811yescharacteristic
168C8×C31—28no—
169C8×C31—44no—
170C2×C4×M16C2×C3111yescharacteristic
171C2×#389C2×C3111yescharacteristic
172C2×#343C2×C3112yes—
173C2×#343C2×C3112yes—
174#1728C2×C3111yescharacteristic
175C22×C31—22no—
176C22×C31—22no—
177C22×C31—22no—
178C22×C31—22no—
179C22×C31—21no—
180C22×C31—21no—
181C22×C31—21no—
182C22×C31—21no—
183C22×C31C4×C22⋊C411yescharacteristic
184C22×C31C4×C4⋊C412yes—
185C22×C31#38611yescharacteristic
186C22×C31#38712yes—
187C22×C31#39111yescharacteristic
188C22×C31C2×#10011yescharacteristic
189C22×C31C2×#10111yescharacteristic
190C22×C31#41311yescharacteristic
191C22×C31#41311yescharacteristic
192C4×C31—22no—
193C4×C31—22no—
194C4×C31—41no—
195C4×C31—41no—
196C4×C31—44no—
197C4×C31—82no—
198C4×C31#38512yes—
199C4×C31#38712yes—
200C4×C31#38812yes—
201C4×C31#38912yes—
202C22×M16C22×C3112yes—
203C22×M16C22×C3112yes—
204C22×C4⋊C4C4×C3112yes—
205C22×C4⋊C4C22×C3111yescharacteristic
206C22×C4⋊C4C22×C3111yescharacteristic
207C22×C42C22×C3111yescharacteristic
208C4×M16—24no—
209C2×#97—21no—
210C2×C4×C8—21no—
211#389—21no—
212#389—21no—
213#389—21no—
214#389—21no—
215C2×#95C4×C3112yes—
216#343—24no—
217#343C4×C3118yescomplemented
218#336—21no—
219#336—21no—
220C2×C31—22no—
221C2×C31—22no—
222C2×C31#143611yescharacteristic
223C2×C31C4×#10011yescharacteristic
224C2×C31C4×#10111yescharacteristic
225C2×C31#190011yescharacteristic
226C2×C31#190111yescharacteristic
227C2×C31#199711yescharacteristic
228C2×C31#199811yescharacteristic
229C23×C4C2×C4×C3111yescharacteristic
230C23×C4C2×C4×C3111yescharacteristic
231C23×C4C2×C4×C3112yes—
232C23×C4C2×C4×C3112yes—
233C23×C4C23×C3111yescharacteristic
234C2×M16—22no—
235C2×M16—22no—
236C2×M16—22no—
237C2×M16—22no—
238C2×M16—22no—
239C2×M16—22no—
240C2×M16—22no—
241C2×M16—22no—
242C2×M16C2×C4×C3114yes—
243C2×M16C2×C4×C3114yes—
244C2×M16D4×C3114yes—
245C2×M16Q8×C3114yes—
246C22×C8—22no—
247C22×C8—22no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—22no—
251C2×C4⋊C4—22no—
252C2×C4⋊C4—22no—
253C2×C4⋊C4—22no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—22no—
257C2×C4⋊C4—44no—
258C2×C4⋊C4C2×C4×C3114yes—
259C2×C42—22no—
260C2×C42—22no—
261C2×C42D4×C3111yescharacteristic
262C2×C42D4×C3111yescharacteristic
263C2×C42D4×C3111yescharacteristic
264C2×C42D4×C3111yescharacteristic
265#97—24no—
266C4×C8—24no—
267#95—22no—
268#95—22no—
269C31#1091311yescharacteristic, direct product factor, Sylow
270C24C22×C4×C3111yescharacteristic
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—24no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4—42no—
282C22×C4—42no—
283C22×C4—42no—
284C22×C4—42no—
285C22×C4C42×C3114yes—
286C22×C4C22⋊C4×C3111yescharacteristic
287C22×C4C22⋊C4×C3111yescharacteristic
288C22×C4C22⋊C4×C3111yescharacteristic
289C22×C4C22⋊C4×C3111yescharacteristic
290C22×C4C22×C4×C3112yes—
291C22×C4C2×D4×C3112yes—
292C22×C4C2×D4×C3111yescharacteristic
293C22×C4C2×D4×C3111yescharacteristic
294C22×C4C2×Q8×C3112yes—
295C22×C4#41×C3112yes—
296C22×C4#41×C3112yes—
297C22×C4#41×C3112yes—
298M16—24no—
299M16—24no—
300M16—24no—
301M16—24no—
302M16—24no—
303M16—42no—
304M16—42no—
305M16C4⋊C4×C3118yescomplemented
306C2×C8—24no—
307C2×C8—24no—
308C2×C8—24no—
309C2×C8—24no—
310C2×C8—42no—
311C2×C8—42no—
312C4⋊C4—24no—
313C4⋊C4—24no—
314C4⋊C4—44no—
315C4⋊C4—44no—
316C4⋊C4—41no—
317C4⋊C4—42no—
318C4⋊C4—41no—
319C42—21no—
320C42—21no—
321C42—22no—
322C42—22no—
323C42—21no—
324C42—21no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23C2×C42×C3111yescharacteristic
330C23C2×C22⋊C4×C3111yescharacteristic
331C23C31×#11711yescharacteristic
332C23C4×D4×C3112yes—
333C23C4×Q8×C3112yes—
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—24no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—44no—
346C2×C4—44no—
347C2×C4—44no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—44no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—84no—
355C2×C4C31×#10012yes—
356C2×C4C31×#10112yes—
357C2×C4C2×C4⋊C4×C3112yes—
358C2×C4C31×#11712yes—
359C2×C4C4×D4×C3112yes—
360C2×C4C4×D4×C3112yes—
361C2×C4C4×D4×C3112yes—
362C2×C4C4×Q8×C3112yes—
363C2×C4C31×#12011yescharacteristic
364C2×C4C31×#12112yes—
365C2×C4C31×C22⋊Q812yes—
366C2×C4C31×C22⋊Q812yes—
367C2×C4C31×#12312yes—
368C2×C4C31×#12311yescharacteristic
369C2×C4C31×#12411yescharacteristic
370C2×C4C31×#12512yes—
371C2×C4C31×#12612yes—
372C2×C4C31×C4⋊Q811yescharacteristic
373C8—28no—
374C8—44no—
375C22—22no—
376C22—22no—
377C22—22no—
378C22—22no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22C4×C22⋊C4×C3111yescharacteristic
384C22C4×C4⋊C4×C3112yes—
385C22C31×#38611yescharacteristic
386C22C31×#38712yes—
387C22C31×#39111yescharacteristic
388C22C2×C31×#10011yescharacteristic
389C22C2×C31×#10111yescharacteristic
390C22C31×#41311yescharacteristic
391C22C31×#41311yescharacteristic
392C4—22no—
393C4—22no—
394C4—41no—
395C4—41no—
396C4—44no—
397C4—82no—
398C4C31×#38512yes—
399C4C31×#38712yes—
400C4C31×#38812yes—
401C4C31×#38912yes—
402C2—22no—
403C2—22no—
404C2C31×#143611yescharacteristic
405C2C4×C31×#10011yescharacteristic
406C2C4×C31×#10111yescharacteristic
407C2C31×#190011yescharacteristic
408C2C31×#190111yescharacteristic
409C2C31×#199711yescharacteristic
410C2C31×#199811yescharacteristic
subgroupG/H
center, socleC23×C31C2×C22⋊C4
commutatorC23C2×C42×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC24×C31C22×C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C22×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
21. C31×#343C4semidirect
99. M16×C31C4⋊C4semidirect
119. #10913C31direct (N × H)
217. #343C4×C31semidirect
269. C31#10913direct (N × H)
305. M16C4⋊C4×C31semidirect

Maximal subgroups

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

subgroupindex
C2×C4×M16×C312
C2×C31×#3892
C2×C31×#3432
C31×#17282
#1091331