Finite Group Databasebeta

← C31×#9076 #21465835

Subgroups — C31×#9076 #21465835

Order 7936.

690 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#431C211yesmaximal, characteristic, complemented
2C4×C31×#121C211yesmaximal, characteristic
3C31×#1797C211yesmaximal, characteristic, complemented
4C2×C31×D4⋊C8C212yesmaximal, complemented
5C31×#1279C212yesmaximal, complemented
6C2×C31×#121C411yescharacteristic
7C2×C4×D4×C31—21no—
8C2×C4×D4×C31C2211yescharacteristic
9C22×C42×C31C2211yescharacteristic
10C31×#431—24no—
11C2×C31×C4⋊C8—21no—
12C2×C31×C4⋊C8C2212yes—
13C2×C31×C22⋊C8—21no—
14C2×C31×C22⋊C8—21no—
15C2×C4×C8×C31C2212yes—
16C31×#390C411yescharacteristic
17C31×#389C411yescharacteristic
18C31×#388—21no—
19C31×#386—21no—
20C31×#380C411yescharacteristic
21C4×C4⋊C4×C31C2211yescharacteristic
22C4×C22⋊C4×C31—21no—
23C31×#336—21no—
24C31×D4⋊C8—24no—
25C22×D4×C31—21no—
26C22×D4×C31C2×C411yescharacteristic
27C23×C4×C31—21no—
28C23×C4×C31C2×C411yescharacteristic
29C23×C4×C31D411yescharacteristic
30C23×C4×C31D411yescharacteristic
31C22×C8×C31—22no—
32C22×C8×C31—22no—
33C31×#121—22no—
34C31×#121—22no—
35C4×D4×C31—22no—
36C4×D4×C31—22no—
37C4×D4×C31—42no—
38C4×D4×C31—42no—
39C2×C4⋊C4×C31—21no—
40C2×C4⋊C4×C31C2×C411yescharacteristic
41C2×C4⋊C4×C31C2×C411yescharacteristic
42C2×C4⋊C4×C31C2×C411yescharacteristic
43C2×C22⋊C4×C31—21no—
44C2×C22⋊C4×C31—21no—
45C2×C22⋊C4×C31—21no—
46C2×C22⋊C4×C31—21no—
47C2×C22⋊C4×C31—21no—
48C2×C42×C31—22no—
49C2×C42×C31—22no—
50C2×C42×C31—21no—
51C2×C42×C31C2×C411yescharacteristic
52C2×C42×C31D411yescharacteristic
53C2×C42×C31D411yescharacteristic
54C2×C42×C31C2311yescharacteristic
55C31×C4⋊C8—24no—
56C31×C4⋊C8—22no—
57C31×C4⋊C8—22no—
58C31×C22⋊C8—24no—
59C31×C22⋊C8—42no—
60C4×C8×C31—22no—
61C4×C8×C31D414yescomplemented
62C31×#95—21no—
63C31×#95—21no—
64C31×#95—21no—
65C24×C31—21no—
66C24×C31C22⋊C411yescharacteristic
67C2×D4×C31—24no—
68C2×D4×C31—22no—
69C2×D4×C31—21no—
70C2×D4×C31—22no—
71C2×D4×C31—42no—
72C2×D4×C31—42no—
73C2×D4×C31M1612yes—
74C22×C4×C31—22no—
75C22×C4×C31—22no—
76C22×C4×C31—21no—
77C22×C4×C31—22no—
78C22×C4×C31—21no—
79C22×C4×C31—21no—
80C22×C4×C31—21no—
81C22×C4×C31—21no—
82C22×C4×C31—22no—
83C22×C4×C31—21no—
84C22×C4×C31—21no—
85C22×C4×C31—41no—
86C22×C4×C31—41no—
87C22×C4×C31—42no—
88C22×C4×C31—41no—
89C22×C4×C31—41no—
90C22×C4×C31—42no—
91C22×C4×C31C22⋊C411yescharacteristic
92C22×C4×C31C22⋊C411yescharacteristic
93C22×C4×C31C22⋊C411yescharacteristic
94C22×C4×C31D812yes—
95C22×C4×C31SD1612yes—
96C22×C4×C31C22×C411yescharacteristic
97C22×C4×C31C2×D411yescharacteristic
98C22×C4×C31C2×D411yescharacteristic
99C2×C8×C31—24no—
100C2×C8×C31—42no—
101C2×C8×C31—42no—
102C2×C8×C31—42no—
103C2×C8×C31—42no—
104C2×C8×C31—42no—
105C4⋊C4×C31—21no—
106C4⋊C4×C31—22no—
107C4⋊C4×C31—22no—
108C4⋊C4×C31—42no—
109C4⋊C4×C31M1612yes—
110C22⋊C4×C31—24no—
111C22⋊C4×C31—42no—
112C22⋊C4×C31—42no—
113C22⋊C4×C31—42no—
114C22⋊C4×C31—41no—
115C22⋊C4×C31—41no—
116C42×C31—22no—
117C42×C31—21no—
118C42×C31—22no—
119C42×C31—21no—
120C42×C31—41no—
121C42×C31—41no—
122C42×C31C2×D412yes—
123C42×C31#4112yes—
124#9076C3111yesmaximal, characteristic, direct product factor, Sylow
125C23×C31—21no—
126C23×C31—21no—
127C23×C31—21no—
128C23×C31—21no—
129C23×C31—21no—
130C23×C31—21no—
131C23×C31—22no—
132C23×C31—41no—
133C23×C31—41no—
134C23×C31—41no—
135C23×C31—41no—
136C23×C31—41no—
137C23×C31—41no—
138C23×C31#10212yes—
139C23×C31C2×C22⋊C411yescharacteristic
140D4×C31—24no—
141D4×C31—48no—
142D4×C31—42no—
143C2×C4×C31—21no—
144C2×C4×C31—21no—
145C2×C4×C31—21no—
146C2×C4×C31—21no—
147C2×C4×C31—24no—
148C2×C4×C31—24no—
149C2×C4×C31—21no—
150C2×C4×C31—21no—
151C2×C4×C31—21no—
152C2×C4×C31—22no—
153C2×C4×C31—21no—
154C2×C4×C31—21no—
155C2×C4×C31—21no—
156C2×C4×C31—42no—
157C2×C4×C31—42no—
158C2×C4×C31—41no—
159C2×C4×C31—41no—
160C2×C4×C31—42no—
161C2×C4×C31—42no—
162C2×C4×C31—41no—
163C2×C4×C31—41no—
164C2×C4×C31—41no—
165C2×C4×C31—41no—
166C2×C4×C31—41no—
167C2×C4×C31—41no—
168C2×C4×C31—82no—
169C2×C4×C31—82no—
170C2×C4×C31#10212yes—
171C2×C4×C31C4×D412yes—
172C2×C4×C31#12011yescharacteristic
173C2×C4×C31#12112yes—
174C2×C4×C31#12311yescharacteristic
175C2×C4×C31C2×M1611yescharacteristic
176C2×C4×C31C2×M1611yescharacteristic
177C2×C4×C31#13112yes—
178C2×C4×C31C2×D811yescharacteristic
179C2×C4×C31C2×SD1611yescharacteristic
180C2×C4×C31#13512yes—
181C8×C31—44no—
182C8×C31—82no—
183C2×#431C2×C3111yescharacteristic, complemented
184C4×#121C2×C3111yescharacteristic
185#1797C2×C3111yescharacteristic, complemented
186C2×D4⋊C8C2×C3112yescomplemented
187#1279C2×C3112yescomplemented
188C22×C31—22no—
189C22×C31—22no—
190C22×C31—22no—
191C22×C31—41no—
192C22×C31—41no—
193C22×C31—41no—
194C22×C31—41no—
195C22×C31—42no—
196C22×C31—42no—
197C22×C31—42no—
198C22×C31—81no—
199C22×C31—81no—
200C22×C31—81no—
201C22×C31—81no—
202C22×C31#38611yescharacteristic
203C22×C31#40711yescharacteristic
204C22×C31#40811yescharacteristic
205C22×C31C2×#10211yescharacteristic
206C22×C31#41611yescharacteristic
207C22×C31#42111yescharacteristic
208C22×C31#42111yescharacteristic
209C4×C31—22no—
210C4×C31—21no—
211C4×C31—21no—
212C4×C31—41no—
213C4×C31—41no—
214C4×C31—42no—
215C4×C31—81no—
216C4×C31—81no—
217C4×C31#43512yes—
218C4×C31#43612yes—
219C4×C31#46512yes—
220C4×C31#46612yes—
221C2×#121C4×C3111yescharacteristic
222C2×C4×D4—21no—
223C2×C4×D4C22×C3111yescharacteristic
224C22×C42C22×C3111yescharacteristic
225#431—24no—
226C2×C4⋊C8—21no—
227C2×C4⋊C8C22×C3112yes—
228C2×C22⋊C8—21no—
229C2×C22⋊C8—21no—
230C2×C4×C8C22×C3112yes—
231#390C4×C3111yescharacteristic
232#389C4×C3111yescharacteristic
233#388—21no—
234#386—21no—
235#380C4×C3111yescharacteristic
236C4×C4⋊C4C22×C3111yescharacteristic
237C4×C22⋊C4—21no—
238#336—21no—
239D4⋊C8—24no—
240C2×C31—42no—
241C2×C31—82no—
242C2×C31#148011yescharacteristic
243C2×C31#148211yescharacteristic
244C2×C31#148611yescharacteristic
245C2×C31#148811yescharacteristic
246C2×C31#187011yescharacteristic
247C2×C31#189311yescharacteristic
248C2×C31#189711yescharacteristic
249C22×D4—21no—
250C22×D4C2×C4×C3111yescharacteristic
251C23×C4—21no—
252C23×C4C2×C4×C3111yescharacteristic
253C23×C4D4×C3111yescharacteristic
254C23×C4D4×C3111yescharacteristic
255C22×C8—22no—
256C22×C8—22no—
257#121—22no—
258#121—22no—
259C4×D4—22no—
260C4×D4—22no—
261C4×D4—42no—
262C4×D4—42no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4C2×C4×C3111yescharacteristic
265C2×C4⋊C4C2×C4×C3111yescharacteristic
266C2×C4⋊C4C2×C4×C3111yescharacteristic
267C2×C22⋊C4—21no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—21no—
271C2×C22⋊C4—21no—
272C2×C42—22no—
273C2×C42—22no—
274C2×C42—21no—
275C2×C42C2×C4×C3111yescharacteristic
276C2×C42D4×C3111yescharacteristic
277C2×C42D4×C3111yescharacteristic
278C2×C42C23×C3111yescharacteristic
279C4⋊C8—24no—
280C4⋊C8—22no—
281C4⋊C8—22no—
282C22⋊C8—24no—
283C22⋊C8—42no—
284C4×C8—22no—
285C4×C8D4×C3114yescomplemented
286#95—21no—
287#95—21no—
288#95—21no—
289C31#907611yescharacteristic, direct product factor, Sylow
290C24—21no—
291C24C22⋊C4×C3111yescharacteristic
292C2×D4—24no—
293C2×D4—22no—
294C2×D4—21no—
295C2×D4—22no—
296C2×D4—42no—
297C2×D4—42no—
298C2×D4M16×C3112yes—
299C22×C4—22no—
300C22×C4—22no—
301C22×C4—21no—
302C22×C4—22no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—22no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—42no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—42no—
316C22×C4C22⋊C4×C3111yescharacteristic
317C22×C4C22⋊C4×C3111yescharacteristic
318C22×C4C22⋊C4×C3111yescharacteristic
319C22×C4D8×C3112yes—
320C22×C4SD16×C3112yes—
321C22×C4C22×C4×C3111yescharacteristic
322C22×C4C2×D4×C3111yescharacteristic
323C22×C4C2×D4×C3111yescharacteristic
324C2×C8—24no—
325C2×C8—42no—
326C2×C8—42no—
327C2×C8—42no—
328C2×C8—42no—
329C2×C8—42no—
330C4⋊C4—21no—
331C4⋊C4—22no—
332C4⋊C4—22no—
333C4⋊C4—42no—
334C4⋊C4M16×C3112yes—
335C22⋊C4—24no—
336C22⋊C4—42no—
337C22⋊C4—42no—
338C22⋊C4—42no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C42—22no—
342C42—21no—
343C42—22no—
344C42—21no—
345C42—41no—
346C42—41no—
347C42C2×D4×C3112yes—
348C42#41×C3112yes—
349C23—21no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—22no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—41no—
361C23—41no—
362C23C31×#10212yes—
363C23C2×C22⋊C4×C3111yescharacteristic
364D4—24no—
365D4—48no—
366D4—42no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—24no—
372C2×C4—24no—
373C2×C4—21no—
374C2×C4—22no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—82no—
393C2×C4—82no—
394C2×C4C31×#10212yes—
395C2×C4C4×D4×C3112yes—
396C2×C4C31×#12011yescharacteristic
397C2×C4C31×#12112yes—
398C2×C4C31×#12311yescharacteristic
399C2×C4C2×M16×C3111yescharacteristic
400C2×C4C2×M16×C3111yescharacteristic
401C2×C4C31×#13112yes—
402C2×C4C2×D8×C3111yescharacteristic
403C2×C4C2×SD16×C3111yescharacteristic
404C2×C4C31×#13512yes—
405C8—44no—
406C8—82no—
407C22—22no—
408C22—22no—
409C22—22no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—42no—
415C22—42no—
416C22—42no—
417C22—81no—
418C22—81no—
419C22—81no—
420C22—81no—
421C22C31×#38611yescharacteristic
422C22C31×#40711yescharacteristic
423C22C31×#40811yescharacteristic
424C22C2×C31×#10211yescharacteristic
425C22C31×#41611yescharacteristic
426C22C31×#42111yescharacteristic
427C22C31×#42111yescharacteristic
428C4—22no—
429C4—21no—
430C4—21no—
431C4—41no—
432C4—41no—
433C4—42no—
434C4—81no—
435C4—81no—
436C4C31×#43512yes—
437C4C31×#43612yes—
438C4C31×#46512yes—
439C4C31×#46612yes—
440C2—42no—
441C2—82no—
442C2C31×#148011yescharacteristic
443C2C31×#148211yescharacteristic
444C2C31×#148611yescharacteristic
445C2C31×#148811yescharacteristic
446C2C31×#187011yescharacteristic
447C2C31×#189311yescharacteristic
448C2C31×#189711yescharacteristic
subgroupG/H
centerC22×C4×C31C2×D4
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C42C23×C31
socleC23×C31C2×C22⋊C4
prime radicalC2×C31×#121C4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C31 ◁ C22×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#431C2semidirect
3. C31×#1797C2semidirect
4. C2×C31×D4⋊C8C2semidirect
5. C31×#1279C2semidirect
61. C4×C8×C31D4semidirect
124. #9076C31direct (N × H)
183. C2×#431C2×C31semidirect
185. #1797C2×C31semidirect
186. C2×D4⋊C8C2×C31semidirect
187. #1279C2×C31semidirect
285. C4×C8D4×C31semidirect
289. C31#9076direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4312
C4×C31×#1212
C31×#17972
C2×C31×D4⋊C82
C31×#12792
#907631