Finite Group Databasebeta

← C31×#8155 #21464914

Subgroups — C31×#8155 #21464914

Order 7936.

710 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#388C211yesmaximal, characteristic
2C31×#1749C211yesmaximal, characteristic, complemented
3C4×C31×C22⋊C8C211yesmaximal, characteristic, complemented
4C2×C31×#323C212yesmaximal
5C31×#1280C212yesmaximal, complemented
6C22×C4⋊C4×C31C411yescharacteristic
7C22×C22⋊C4×C31C411yescharacteristic
8C22×C22⋊C4×C31C411yescharacteristic
9C22×C22⋊C4×C31C2211yescharacteristic
10C22×C42×C31C2211yescharacteristic
11C2×C31×C22⋊C8C2212yes—
12C2×C31×C22⋊C8C2212yes—
13C2×C31×#97—21no—
14C2×C4×C8×C31—21no—
15C31×#388—21no—
16C31×#388—21no—
17C31×#388—21no—
18C31×#388—21no—
19C2×C31×#95C411yescharacteristic
20C2×C31×#95C2211yescharacteristic
21C31×#336—21no—
22C31×#336—21no—
23C31×#323C418yescomplemented
24C25×C31C2×C411yescharacteristic
25C23×C4×C31C2×C411yescharacteristic
26C23×C4×C31C2×C411yescharacteristic
27C23×C4×C31C2×C411yescharacteristic
28C23×C4×C31C2×C411yescharacteristic
29C23×C4×C31C2×C411yescharacteristic
30C23×C4×C31C2311yescharacteristic
31C22×C8×C31—22no—
32C22×C8×C31—22no—
33C2×C4⋊C4×C31—21no—
34C2×C4⋊C4×C31—21no—
35C2×C4⋊C4×C31—42no—
36C2×C22⋊C4×C31—21no—
37C2×C22⋊C4×C31—21no—
38C2×C22⋊C4×C31—22no—
39C2×C22⋊C4×C31—21no—
40C2×C22⋊C4×C31—21no—
41C2×C22⋊C4×C31—21no—
42C2×C22⋊C4×C31—21no—
43C2×C22⋊C4×C31—42no—
44C2×C22⋊C4×C31—42no—
45C2×C22⋊C4×C31C2×C414yes—
46C2×C42×C31—42no—
47C2×C42×C31D411yescharacteristic
48C2×C42×C31D411yescharacteristic
49C2×C42×C31D411yescharacteristic
50C2×C42×C31D411yescharacteristic
51C31×C22⋊C8—22no—
52C31×C22⋊C8—22no—
53C31×C22⋊C8C2×C414yes—
54C31×C22⋊C8C2×C414yes—
55C31×#97—42no—
56C4×C8×C31—42no—
57C31×#95—21no—
58C31×#95—21no—
59C31×#95—21no—
60C31×#95—21no—
61C24×C31—21no—
62C24×C31—21no—
63C24×C31—22no—
64C24×C31—22no—
65C24×C31—41no—
66C24×C31—41no—
67C24×C31—41no—
68C24×C31—41no—
69C24×C31C4212yes—
70C24×C31C22×C411yescharacteristic
71C22×C4×C31—21no—
72C22×C4×C31—21no—
73C22×C4×C31—22no—
74C22×C4×C31—22no—
75C22×C4×C31—22no—
76C22×C4×C31—22no—
77C22×C4×C31—21no—
78C22×C4×C31—21no—
79C22×C4×C31—22no—
80C22×C4×C31—22no—
81C22×C4×C31—41no—
82C22×C4×C31—41no—
83C22×C4×C31—41no—
84C22×C4×C31—41no—
85C22×C4×C31—41no—
86C22×C4×C31—41no—
87C22×C4×C31—41no—
88C22×C4×C31—41no—
89C22×C4×C31—41no—
90C22×C4×C31—41no—
91C22×C4×C31C4212yes—
92C22×C4×C31C22⋊C411yescharacteristic
93C22×C4×C31C22⋊C411yescharacteristic
94C22×C4×C31C22⋊C411yescharacteristic
95C22×C4×C31C22⋊C411yescharacteristic
96C22×C4×C31C22×C412yes—
97C22×C4×C31C2×D411yescharacteristic
98C22×C4×C31C2×D411yescharacteristic
99C22×C4×C31#4112yes—
100C2×C8×C31—24no—
101C2×C8×C31—24no—
102C2×C8×C31—42no—
103C2×C8×C31—42no—
104C2×C8×C31—42no—
105C2×C8×C31—42no—
106C4⋊C4×C31—42no—
107C4⋊C4×C31—42no—
108C22⋊C4×C31—24no—
109C22⋊C4×C31—24no—
110C22⋊C4×C31—42no—
111C22⋊C4×C31—42no—
112C22⋊C4×C31—42no—
113C22⋊C4×C31—42no—
114C42×C31—22no—
115C42×C31—22no—
116C42×C31—41no—
117C42×C31—41no—
118#8155C3111yesmaximal, characteristic, direct product factor, Sylow
119C23×C31—21no—
120C23×C31—21no—
121C23×C31—21no—
122C23×C31—21no—
123C23×C31—22no—
124C23×C31—24no—
125C23×C31—42no—
126C23×C31—42no—
127C23×C31—42no—
128C23×C31—42no—
129C23×C31—41no—
130C23×C31—41no—
131C23×C31—41no—
132C23×C31—41no—
133C23×C31—41no—
134C23×C31—41no—
135C23×C31—42no—
136C23×C31—82no—
137C23×C31—82no—
138C23×C31—82no—
139C23×C31—82no—
140C23×C31C2×C4211yescharacteristic
141C23×C31C2×C22⋊C411yescharacteristic
142C23×C31#11711yescharacteristic
143C23×C31#13112yes—
144C23×C31#13112yes—
145C2×C4×C31—21no—
146C2×C4×C31—21no—
147C2×C4×C31—21no—
148C2×C4×C31—21no—
149C2×C4×C31—21no—
150C2×C4×C31—21no—
151C2×C4×C31—21no—
152C2×C4×C31—21no—
153C2×C4×C31—22no—
154C2×C4×C31—21no—
155C2×C4×C31—21no—
156C2×C4×C31—21no—
157C2×C4×C31—21no—
158C2×C4×C31—21no—
159C2×C4×C31—21no—
160C2×C4×C31—42no—
161C2×C4×C31—42no—
162C2×C4×C31—44no—
163C2×C4×C31—44no—
164C2×C4×C31—42no—
165C2×C4×C31—41no—
166C2×C4×C31—41no—
167C2×C4×C31—42no—
168C2×C4×C31—41no—
169C2×C4×C31—41no—
170C2×C4×C31—41no—
171C2×C4×C31—41no—
172C2×C4×C31—41no—
173C2×C4×C31—41no—
174C2×C4×C31—82no—
175C2×C4×C31—82no—
176C2×C4×C31#9912yes—
177C2×C4×C31#10012yes—
178C2×C4×C31C4×D412yes—
179C2×C4×C31C4×D412yes—
180C8×C31—44no—
181C8×C31—44no—
182C2×#388C2×C3111yescharacteristic
183#1749C2×C3111yescharacteristic, complemented
184C4×C22⋊C8C2×C3111yescharacteristic, complemented
185C2×#323C2×C3112yes—
186#1280C2×C3112yescomplemented
187C22×C31—22no—
188C22×C31—22no—
189C22×C31—22no—
190C22×C31—22no—
191C22×C31—21no—
192C22×C31—21no—
193C22×C31—21no—
194C22×C31—21no—
195C22×C31—42no—
196C22×C31—42no—
197C22×C31—42no—
198C22×C31—84no—
199C22×C31—84no—
200C22×C31—81no—
201C22×C31—81no—
202C22×C31—81no—
203C22×C31—81no—
204C22×C31C4×C22⋊C411yescharacteristic
205C22×C31#40512yes—
206C22×C31#40811yescharacteristic
207C22×C31#40811yescharacteristic
208C22×C31C2×#9911yescharacteristic
209C22×C31#41011yescharacteristic
210C22×C31C2×#10011yescharacteristic
211C22×C31#41311yescharacteristic
212C22×C31#43312yes—
213C4×C31—22no—
214C4×C31—22no—
215C4×C31—22no—
216C4×C31—22no—
217C4×C31—41no—
218C4×C31—41no—
219C4×C31—42no—
220C4×C31—81no—
221C4×C31—81no—
222C22×C4⋊C4C4×C3111yescharacteristic
223C22×C22⋊C4C4×C3111yescharacteristic
224C22×C22⋊C4C4×C3111yescharacteristic
225C22×C22⋊C4C22×C3111yescharacteristic
226C22×C42C22×C3111yescharacteristic
227C2×C22⋊C8C22×C3112yes—
228C2×C22⋊C8C22×C3112yes—
229C2×#97—21no—
230C2×C4×C8—21no—
231#388—21no—
232#388—21no—
233#388—21no—
234#388—21no—
235C2×#95C4×C3111yescharacteristic
236C2×#95C22×C3111yescharacteristic
237#336—21no—
238#336—21no—
239#323C4×C3118yescomplemented
240C2×C31—22no—
241C2×C31—22no—
242C2×C31—82no—
243C2×C31#146811yescharacteristic
244C2×C31#146911yescharacteristic
245C2×C31#147111yescharacteristic
246C2×C31#147311yescharacteristic
247C2×C31#175011yescharacteristic
248C2×C31C4×#9911yescharacteristic
249C2×C31C4×#10011yescharacteristic
250C25C2×C4×C3111yescharacteristic
251C23×C4C2×C4×C3111yescharacteristic
252C23×C4C2×C4×C3111yescharacteristic
253C23×C4C2×C4×C3111yescharacteristic
254C23×C4C2×C4×C3111yescharacteristic
255C23×C4C2×C4×C3111yescharacteristic
256C23×C4C23×C3111yescharacteristic
257C22×C8—22no—
258C22×C8—22no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—42no—
262C2×C22⋊C4—21no—
263C2×C22⋊C4—21no—
264C2×C22⋊C4—22no—
265C2×C22⋊C4—21no—
266C2×C22⋊C4—21no—
267C2×C22⋊C4—21no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—42no—
270C2×C22⋊C4—42no—
271C2×C22⋊C4C2×C4×C3114yes—
272C2×C42—42no—
273C2×C42D4×C3111yescharacteristic
274C2×C42D4×C3111yescharacteristic
275C2×C42D4×C3111yescharacteristic
276C2×C42D4×C3111yescharacteristic
277C22⋊C8—22no—
278C22⋊C8—22no—
279C22⋊C8C2×C4×C3114yes—
280C22⋊C8C2×C4×C3114yes—
281#97—42no—
282C4×C8—42no—
283#95—21no—
284#95—21no—
285#95—21no—
286#95—21no—
287C31#815511yescharacteristic, direct product factor, Sylow
288C24—21no—
289C24—21no—
290C24—22no—
291C24—22no—
292C24—41no—
293C24—41no—
294C24—41no—
295C24—41no—
296C24C42×C3112yes—
297C24C22×C4×C3111yescharacteristic
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—22no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—22no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4C42×C3112yes—
319C22×C4C22⋊C4×C3111yescharacteristic
320C22×C4C22⋊C4×C3111yescharacteristic
321C22×C4C22⋊C4×C3111yescharacteristic
322C22×C4C22⋊C4×C3111yescharacteristic
323C22×C4C22×C4×C3112yes—
324C22×C4C2×D4×C3111yescharacteristic
325C22×C4C2×D4×C3111yescharacteristic
326C22×C4#41×C3112yes—
327C2×C8—24no—
328C2×C8—24no—
329C2×C8—42no—
330C2×C8—42no—
331C2×C8—42no—
332C2×C8—42no—
333C4⋊C4—42no—
334C4⋊C4—42no—
335C22⋊C4—24no—
336C22⋊C4—24no—
337C22⋊C4—42no—
338C22⋊C4—42no—
339C22⋊C4—42no—
340C22⋊C4—42no—
341C42—22no—
342C42—22no—
343C42—41no—
344C42—41no—
345C23—21no—
346C23—21no—
347C23—21no—
348C23—21no—
349C23—22no—
350C23—24no—
351C23—42no—
352C23—42no—
353C23—42no—
354C23—42no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—41no—
361C23—42no—
362C23—82no—
363C23—82no—
364C23—82no—
365C23—82no—
366C23C2×C42×C3111yescharacteristic
367C23C2×C22⋊C4×C3111yescharacteristic
368C23C31×#11711yescharacteristic
369C23C31×#13112yes—
370C23C31×#13112yes—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—22no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—44no—
389C2×C4—44no—
390C2×C4—42no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—42no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—82no—
401C2×C4—82no—
402C2×C4C31×#9912yes—
403C2×C4C31×#10012yes—
404C2×C4C4×D4×C3112yes—
405C2×C4C4×D4×C3112yes—
406C8—44no—
407C8—44no—
408C22—22no—
409C22—22no—
410C22—22no—
411C22—22no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—42no—
417C22—42no—
418C22—42no—
419C22—84no—
420C22—84no—
421C22—81no—
422C22—81no—
423C22—81no—
424C22—81no—
425C22C4×C22⋊C4×C3111yescharacteristic
426C22C31×#40512yes—
427C22C31×#40811yescharacteristic
428C22C31×#40811yescharacteristic
429C22C2×C31×#9911yescharacteristic
430C22C31×#41011yescharacteristic
431C22C2×C31×#10011yescharacteristic
432C22C31×#41311yescharacteristic
433C22C31×#43312yes—
434C4—22no—
435C4—22no—
436C4—22no—
437C4—22no—
438C4—41no—
439C4—41no—
440C4—42no—
441C4—81no—
442C4—81no—
443C2—22no—
444C2—22no—
445C2—82no—
446C2C31×#146811yescharacteristic
447C2C31×#146911yescharacteristic
448C2C31×#147111yescharacteristic
449C2C31×#147311yescharacteristic
450C2C31×#175011yescharacteristic
451C2C4×C31×#9911yescharacteristic
452C2C4×C31×#10011yescharacteristic
subgroupG/H
center, socleC23×C31C2×C22⋊C4
commutatorC23C2×C42×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC25×C31C2×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
2. C31×#1749C2semidirect
3. C4×C31×C22⋊C8C2semidirect
5. C31×#1280C2semidirect
23. C31×#323C4semidirect
118. #8155C31direct (N × H)
183. #1749C2×C31semidirect
184. C4×C22⋊C8C2×C31semidirect
186. #1280C2×C31semidirect
239. #323C4×C31semidirect
287. C31#8155direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3882
C31×#17492
C4×C31×C22⋊C82
C2×C31×#3232
C31×#12802
#815531