Finite Group Databasebeta

← C31×#17397 #21474156

Subgroups — C31×#17397 #21474156

Order 7936.

1386 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×C22⋊Q8C211yesmaximal, characteristic
2C2×C31×#407C212yesmaximal
3C31×#1472C218yesmaximal, complemented
4C31×#1463C214yesmaximal, complemented
5C23×Q8×C31C411yescharacteristic
6C24×C4×C31C2211yescharacteristic
7C22×M16×C31—22no—
8C2×C31×C22⋊Q8—22no—
9C2×C31×C22⋊Q8—22no—
10C2×C31×C22⋊Q8—22no—
11C2×C31×C22⋊Q8—22no—
12C2×C31×C22⋊Q8C414yes—
13C2×C31×C22⋊Q8C2214yes—
14C22×C4⋊C4×C31C411yescharacteristic
15C22×C4⋊C4×C31C2212yes—
16C22×C22⋊C4×C31C412yes—
17C31×#407—22no—
18C31×#407—22no—
19C31×#407C2214yes—
20C31×#407C2214yes—
21C2×C31×C22⋊C8—22no—
22C2×C31×C22⋊C8C2214yes—
23C31×#324C22116yescomplemented
24C25×C31C2×C411yescharacteristic
25C22×Q8×C31—22no—
26C22×Q8×C31—21no—
27C22×Q8×C31—21no—
28C22×Q8×C31—44no—
29C22×Q8×C31C2×C414yes—
30C23×C4×C31—44no—
31C23×C4×C31C2×C411yescharacteristic
32C23×C4×C31C2×C412yes—
33C23×C4×C31C2×C412yes—
34C23×C4×C31C2×C412yes—
35C23×C4×C31D412yes—
36C23×C4×C31D412yes—
37C23×C4×C31D412yes—
38C23×C4×C31D412yes—
39C23×C4×C31C2312yes—
40C23×C4×C31C2311yescharacteristic
41C2×M16×C31—24no—
42C2×M16×C31—24no—
43C2×M16×C31—48no—
44C22×C8×C31—24no—
45C31×C22⋊Q8—24no—
46C31×C22⋊Q8—24no—
47C31×C22⋊Q8—24no—
48C31×C22⋊Q8—24no—
49C31×C22⋊Q8—24no—
50C31×C22⋊Q8—24no—
51C31×C22⋊Q8—24no—
52C31×C22⋊Q8—24no—
53C2×C4⋊C4×C31—21no—
54C2×C4⋊C4×C31—22no—
55C2×C4⋊C4×C31—21no—
56C2×C4⋊C4×C31—24no—
57C2×C4⋊C4×C31—24no—
58C2×C4⋊C4×C31C2×C414yes—
59C2×C4⋊C4×C31C2×C414yes—
60C2×C4⋊C4×C31C2314yes—
61C2×C22⋊C4×C31—24no—
62C2×C22⋊C4×C31—22no—
63C2×C22⋊C4×C31—22no—
64C2×C22⋊C4×C31C2×C418yes—
65C31×C22⋊C8—24no—
66C31×C22⋊C8—24no—
67C31×C22⋊C8—24no—
68C31×C22⋊C8C2318yes—
69C24×C31—24no—
70C24×C31—42no—
71C24×C31—42no—
72C24×C31C22⋊C412yes—
73C24×C31C22⋊C411yescharacteristic
74C24×C31C22⋊C411yescharacteristic
75C24×C31C22×C411yescharacteristic
76C24×C31C22×C412yes—
77C2×Q8×C31—24no—
78C2×Q8×C31—24no—
79C2×Q8×C31—44no—
80C2×Q8×C31—48no—
81C2×Q8×C31—48no—
82C2×Q8×C31—44no—
83C22×C4×C31—28no—
84C22×C4×C31—24no—
85C22×C4×C31—22no—
86C22×C4×C31—22no—
87C22×C4×C31—22no—
88C22×C4×C31—22no—
89C22×C4×C31—44no—
90C22×C4×C31—44no—
91C22×C4×C31—44no—
92C22×C4×C31—44no—
93C22×C4×C31—44no—
94C22×C4×C31—42no—
95C22×C4×C31—44no—
96C22×C4×C31—44no—
97C22×C4×C31C22⋊C411yescharacteristic
98C22×C4×C31C22⋊C412yes—
99C22×C4×C31C22⋊C412yes—
100C22×C4×C31C22⋊C412yes—
101C22×C4×C31C22⋊C412yes—
102C22×C4×C31C22⋊C412yes—
103C22×C4×C31C22⋊C411yescharacteristic
104C22×C4×C31C22×C414yes—
105C22×C4×C31C22×C412yes—
106C22×C4×C31C22×C414yes—
107C22×C4×C31C22×C411yescharacteristic
108C22×C4×C31C2×D412yes—
109C22×C4×C31C2×D412yes—
110C22×C4×C31C2×D412yes—
111C22×C4×C31C2×D412yes—
112C22×C4×C31C2×D412yes—
113C22×C4×C31C2×D412yes—
114C22×C4×C31C2411yescharacteristic
115M16×C31—48no—
116M16×C31—48no—
117C2×C8×C31—28no—
118C2×C8×C31—48no—
119C4⋊C4×C31—24no—
120C4⋊C4×C31—24no—
121C4⋊C4×C31—28no—
122C4⋊C4×C31—28no—
123C22⋊C4×C31—28no—
124C22⋊C4×C31—28no—
125#17397C3111yesmaximal, characteristic, direct product factor, Sylow
126C23×C31—22no—
127C23×C31—22no—
128C23×C31—22no—
129C23×C31—24no—
130C23×C31—24no—
131C23×C31—24no—
132C23×C31—22no—
133C23×C31—24no—
134C23×C31—41no—
135C23×C31—41no—
136C23×C31—42no—
137C23×C31—41no—
138C23×C31—42no—
139C23×C31—41no—
140C23×C31—416no—
141C23×C31#10114yes—
142C23×C31C2×C22⋊C412yes—
143C23×C31C2×C22⋊C411yescharacteristic
144C23×C31C2×C22⋊C412yes—
145C23×C31C2×C22⋊C411yescharacteristic
146C23×C31C23×C411yescharacteristic
147Q8×C31—48no—
148Q8×C31—48no—
149C2×C4×C31—24no—
150C2×C4×C31—22no—
151C2×C4×C31—24no—
152C2×C4×C31—24no—
153C2×C4×C31—24no—
154C2×C4×C31—24no—
155C2×C4×C31—24no—
156C2×C4×C31—24no—
157C2×C4×C31—24no—
158C2×C4×C31—24no—
159C2×C4×C31—28no—
160C2×C4×C31—42no—
161C2×C4×C31—42no—
162C2×C4×C31—41no—
163C2×C4×C31—42no—
164C2×C4×C31—42no—
165C2×C4×C31—42no—
166C2×C4×C31—41no—
167C2×C4×C31—44no—
168C2×C4×C31—44no—
169C2×C4×C31—44no—
170C2×C4×C31—44no—
171C2×C4×C31—44no—
172C2×C4×C31#9914yes—
173C2×C4×C31C2×C22⋊C412yes—
174C2×C4×C31C2×C22⋊C412yes—
175C2×C4×C31C2×C22⋊C412yes—
176C2×C4×C31C22×D412yes—
177C8×C31—48no—
178C22×C22⋊Q8C2×C3111yescharacteristic
179C2×#407C2×C3112yes—
180#1472C2×C3118yescomplemented
181#1463C2×C3114yescomplemented
182C22×C31—28no—
183C22×C31—21no—
184C22×C31—21no—
185C22×C31—22no—
186C22×C31—21no—
187C22×C31—21no—
188C22×C31—22no—
189C22×C31—21no—
190C22×C31—21no—
191C22×C31—22no—
192C22×C31—22no—
193C22×C31—22no—
194C22×C31—44no—
195C22×C31—48no—
196C22×C31—48no—
197C22×C31—44no—
198C22×C31C2×#9912yes—
199C22×C31C2×#10112yes—
200C22×C31C2×#10114yes—
201C22×C31C22×C22⋊C411yescharacteristic
202C22×C31#56812yes—
203C4×C31—22no—
204C4×C31—22no—
205C4×C31—22no—
206C4×C31—44no—
207C4×C31—44no—
208C4×C31C2×#9914yes—
209C23×Q8C4×C3111yescharacteristic
210C24×C4C22×C3111yescharacteristic
211C22×M16—22no—
212C2×C22⋊Q8—22no—
213C2×C22⋊Q8—22no—
214C2×C22⋊Q8—22no—
215C2×C22⋊Q8—22no—
216C2×C22⋊Q8C4×C3114yes—
217C2×C22⋊Q8C22×C3114yes—
218C22×C4⋊C4C4×C3111yescharacteristic
219C22×C4⋊C4C22×C3112yes—
220C22×C22⋊C4C4×C3112yes—
221#407—22no—
222#407—22no—
223#407C22×C3114yes—
224#407C22×C3114yes—
225C2×C22⋊C8—22no—
226C2×C22⋊C8C22×C3114yes—
227#324C22×C31116yescomplemented
228C2×C31—22no—
229C2×C31—22no—
230C2×C31—22no—
231C2×C31—24no—
232C2×C31—42no—
233C2×C31#287911yescharacteristic
234C2×C31C22×#9911yescharacteristic
235C2×C31C22×#10111yescharacteristic
236C25C2×C4×C3111yescharacteristic
237C22×Q8—22no—
238C22×Q8—21no—
239C22×Q8—21no—
240C22×Q8—44no—
241C22×Q8C2×C4×C3114yes—
242C23×C4—44no—
243C23×C4C2×C4×C3111yescharacteristic
244C23×C4C2×C4×C3112yes—
245C23×C4C2×C4×C3112yes—
246C23×C4C2×C4×C3112yes—
247C23×C4D4×C3112yes—
248C23×C4D4×C3112yes—
249C23×C4D4×C3112yes—
250C23×C4D4×C3112yes—
251C23×C4C23×C3111yescharacteristic
252C23×C4C23×C3112yes—
253C2×M16—24no—
254C2×M16—24no—
255C2×M16—48no—
256C22×C8—24no—
257C22⋊Q8—24no—
258C22⋊Q8—24no—
259C22⋊Q8—24no—
260C22⋊Q8—24no—
261C22⋊Q8—24no—
262C22⋊Q8—24no—
263C22⋊Q8—24no—
264C22⋊Q8—24no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—24no—
269C2×C4⋊C4—24no—
270C2×C4⋊C4C2×C4×C3114yes—
271C2×C4⋊C4C2×C4×C3114yes—
272C2×C4⋊C4C23×C3114yes—
273C2×C22⋊C4—24no—
274C2×C22⋊C4—22no—
275C2×C22⋊C4—22no—
276C2×C22⋊C4C2×C4×C3118yes—
277C22⋊C8—24no—
278C22⋊C8—24no—
279C22⋊C8—24no—
280C22⋊C8C23×C3118yes—
281C31#1739711yescharacteristic, direct product factor, Sylow
282C24—24no—
283C24—42no—
284C24—42no—
285C24C22⋊C4×C3112yes—
286C24C22⋊C4×C3111yescharacteristic
287C24C22⋊C4×C3111yescharacteristic
288C24C22×C4×C3111yescharacteristic
289C24C22×C4×C3112yes—
290C2×Q8—24no—
291C2×Q8—24no—
292C2×Q8—48no—
293C2×Q8—44no—
294C2×Q8—48no—
295C2×Q8—44no—
296C22×C4—28no—
297C22×C4—24no—
298C22×C4—22no—
299C22×C4—22no—
300C22×C4—22no—
301C22×C4—22no—
302C22×C4—44no—
303C22×C4—44no—
304C22×C4—44no—
305C22×C4—44no—
306C22×C4—44no—
307C22×C4—42no—
308C22×C4—44no—
309C22×C4—44no—
310C22×C4C22⋊C4×C3111yescharacteristic
311C22×C4C22⋊C4×C3112yes—
312C22×C4C22⋊C4×C3112yes—
313C22×C4C22⋊C4×C3112yes—
314C22×C4C22⋊C4×C3112yes—
315C22×C4C22⋊C4×C3112yes—
316C22×C4C22⋊C4×C3111yescharacteristic
317C22×C4C22×C4×C3114yes—
318C22×C4C22×C4×C3112yes—
319C22×C4C22×C4×C3114yes—
320C22×C4C22×C4×C3111yescharacteristic
321C22×C4C2×D4×C3112yes—
322C22×C4C2×D4×C3112yes—
323C22×C4C2×D4×C3112yes—
324C22×C4C2×D4×C3112yes—
325C22×C4C2×D4×C3112yes—
326C22×C4C2×D4×C3112yes—
327C22×C4C24×C3111yescharacteristic
328M16—48no—
329M16—48no—
330C2×C8—28no—
331C2×C8—48no—
332C4⋊C4—24no—
333C4⋊C4—24no—
334C4⋊C4—28no—
335C4⋊C4—28no—
336C22⋊C4—28no—
337C22⋊C4—28no—
338C23—22no—
339C23—22no—
340C23—22no—
341C23—24no—
342C23—24no—
343C23—22no—
344C23—24no—
345C23—24no—
346C23—41no—
347C23—41no—
348C23—42no—
349C23—41no—
350C23—42no—
351C23—41no—
352C23—416no—
353C23C31×#10114yes—
354C23C2×C22⋊C4×C3112yes—
355C23C2×C22⋊C4×C3111yescharacteristic
356C23C2×C22⋊C4×C3112yes—
357C23C2×C22⋊C4×C3111yescharacteristic
358C23C23×C4×C3111yescharacteristic
359Q8—48no—
360Q8—48no—
361C2×C4—24no—
362C2×C4—22no—
363C2×C4—24no—
364C2×C4—24no—
365C2×C4—24no—
366C2×C4—24no—
367C2×C4—24no—
368C2×C4—24no—
369C2×C4—24no—
370C2×C4—24no—
371C2×C4—28no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—41no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—41no—
379C2×C4—44no—
380C2×C4—44no—
381C2×C4—44no—
382C2×C4—44no—
383C2×C4—44no—
384C2×C4C31×#9914yes—
385C2×C4C2×C22⋊C4×C3112yes—
386C2×C4C2×C22⋊C4×C3112yes—
387C2×C4C2×C22⋊C4×C3112yes—
388C2×C4C22×D4×C3112yes—
389C8—48no—
390C22—28no—
391C22—21no—
392C22—21no—
393C22—22no—
394C22—21no—
395C22—21no—
396C22—22no—
397C22—21no—
398C22—21no—
399C22—22no—
400C22—22no—
401C22—22no—
402C22—44no—
403C22—48no—
404C22—48no—
405C22—44no—
406C22C2×C31×#9912yes—
407C22C2×C31×#10112yes—
408C22C2×C31×#10114yes—
409C22C22×C22⋊C4×C3111yescharacteristic
410C22C31×#56812yes—
411C4—22no—
412C4—22no—
413C4—22no—
414C4—44no—
415C4—44no—
416C4C2×C31×#9914yes—
417C2—22no—
418C2—22no—
419C2—22no—
420C2—24no—
421C2—42no—
422C2C31×#287911yescharacteristic
423C2C22×C31×#9911yescharacteristic
424C2C22×C31×#10111yescharacteristic
subgroupG/H
center, socleC22×C31C22×C22⋊C4
commutatorC23C23×C4×C31
Frattini, cosocleC22×C4C24×C31
prime radicalC25×C31C2×C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C24×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
3. C31×#1472C2semidirect
4. C31×#1463C2semidirect
23. C31×#324C22semidirect
125. #17397C31direct (N × H)
180. #1472C2×C31semidirect
181. #1463C2×C31semidirect
227. #324C22×C31semidirect
281. C31#17397direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C31×C22⋊Q82
C2×C31×#4072
C31×#14722
C31×#14632
#1739731