Finite Group Databasebeta

← C31×#33023 #21489782

Subgroups — C31×#33023 #21489782

Order 7936.

1314 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3428C211yesmaximal, characteristic
2C31×#2484C212yesmaximal, complemented
3C31×#2406C211yesmaximal, characteristic
4C31×#1890C214yesmaximal, complemented
5C31×#1867C214yesmaximal, complemented
6C31×#1820C212yesmaximal, complemented
7C31×#1782C211yesmaximal, characteristic
8C22×#41×C31C2211yescharacteristic
9C2×C31×#123C2212yes—
10C31×#520—22no—
11C31×#520—22no—
12C31×#519—21no—
13C31×#518—21no—
14C31×#518C2214yes—
15C4×#41×C31—24no—
16C2×C31×#117—22no—
17C2×C31×#117C2212yes—
18C22×C4⋊C4×C31C2211yescharacteristic
19C2×C31×#99C2214yes—
20C31×#400—22no—
21C31×#398—22no—
22C31×#395—21no—
23C31×#394—21no—
24C31×#387—24no—
25C31×#386C2212yes—
26C31×#385—22no—
27C31×#385C2214yes—
28C31×#381C2214yes—
29C31×#381C2211yescharacteristic
30C31×#381C2212yes—
31C31×#342C2218yes—
32C2×#41×C31—28no—
33C2×#41×C31—22no—
34C2×#41×C31—22no—
35C22×Q8×C31D411yescharacteristic
36C22×D4×C31D411yescharacteristic
37C22×D4×C31C2312yes—
38C23×C4×C31D412yes—
39C23×C4×C31C2311yescharacteristic
40C23×C4×C31C2311yescharacteristic
41C23×C4×C31C2311yescharacteristic
42C31×#123—28no—
43C4×Q8×C31—24no—
44C4×Q8×C31—24no—
45C4×D4×C31—24no—
46C4×D4×C31—24no—
47C4×D4×C31—28no—
48C4×D4×C31—28no—
49C31×#117—24no—
50C31×#117—24no—
51C31×#117—22no—
52C31×#117—24no—
53C31×#117—22no—
54C31×#117—22no—
55C31×#117—22no—
56C2×C4⋊C4×C31—22no—
57C2×C4⋊C4×C31—22no—
58C2×C4⋊C4×C31—21no—
59C2×C4⋊C4×C31—22no—
60C2×C4⋊C4×C31—22no—
61C2×C4⋊C4×C31—24no—
62C2×C4⋊C4×C31—21no—
63C2×C4⋊C4×C31—22no—
64C2×C4⋊C4×C31D412yes—
65C2×C4⋊C4×C31D412yes—
66C2×C22⋊C4×C31—24no—
67C2×C22⋊C4×C31—22no—
68C2×C22⋊C4×C31—22no—
69C2×C22⋊C4×C31C2314yes—
70C2×C22⋊C4×C31C2312yes—
71C2×C22⋊C4×C31C2314yes—
72C2×C42×C31—24no—
73C2×C42×C31D414yes—
74C31×#99—28no—
75C31×#95—21no—
76C31×#95—22no—
77C31×#95—22no—
78C31×#95—24no—
79C31×#95—24no—
80C31×#95—24no—
81C31×#95—21no—
82C31×#95—22no—
83C24×C31C2×D412yes—
84C24×C31C2411yescharacteristic
85#41×C31—216no—
86#41×C31—216no—
87C2×Q8×C31—22no—
88C2×Q8×C31—24no—
89C2×D4×C31—24no—
90C2×D4×C31—24no—
91C2×D4×C31—24no—
92C2×D4×C31—22no—
93C2×D4×C31#4118yes—
94C22×C4×C31—24no—
95C22×C4×C31—24no—
96C22×C4×C31—22no—
97C22×C4×C31—22no—
98C22×C4×C31—24no—
99C22×C4×C31—21no—
100C22×C4×C31—22no—
101C22×C4×C31—24no—
102C22×C4×C31—24no—
103C22×C4×C31—24no—
104C22×C4×C31—22no—
105C22×C4×C31—22no—
106C22×C4×C31—21no—
107C22×C4×C31—24no—
108C22×C4×C31—42no—
109C22×C4×C31C2×D412yes—
110C22×C4×C31C2×D412yes—
111C22×C4×C31C2×D411yescharacteristic
112C22×C4×C31C2×D411yescharacteristic
113C22×C4×C31C2×D412yes—
114C22×C4×C31C2×D414yes—
115C22×C4×C31C2×D414yes—
116C4⋊C4×C31—24no—
117C4⋊C4×C31—24no—
118C4⋊C4×C31—22no—
119C4⋊C4×C31—22no—
120C4⋊C4×C31—22no—
121C4⋊C4×C31—22no—
122C4⋊C4×C31—48no—
123C4⋊C4×C31—41no—
124C4⋊C4×C31—42no—
125C4⋊C4×C31—41no—
126C4⋊C4×C31—44no—
127C22⋊C4×C31—28no—
128C22⋊C4×C31—24no—
129C22⋊C4×C31—24no—
130C22⋊C4×C31—28no—
131C22⋊C4×C31—24no—
132C22⋊C4×C31—44no—
133C22⋊C4×C31—44no—
134C42×C31—28no—
135C42×C31—24no—
136C42×C31—24no—
137#33023C3111yesmaximal, characteristic, direct product factor, Sylow
138C23×C31—22no—
139C23×C31—22no—
140C23×C31—41no—
141C23×C31—41no—
142C23×C31—42no—
143C23×C31—42no—
144C23×C31#12314yes—
145C23×C31C22×D411yescharacteristic
146C23×C31C22×D412yes—
147C23×C31C2×#4114yes—
148Q8×C31—28no—
149D4×C31—28no—
150D4×C31—216no—
151C2×C4×C31—28no—
152C2×C4×C31—28no—
153C2×C4×C31—22no—
154C2×C4×C31—22no—
155C2×C4×C31—22no—
156C2×C4×C31—22no—
157C2×C4×C31—24no—
158C2×C4×C31—24no—
159C2×C4×C31—22no—
160C2×C4×C31—24no—
161C2×C4×C31—24no—
162C2×C4×C31—24no—
163C2×C4×C31—42no—
164C2×C4×C31—41no—
165C2×C4×C31—41no—
166C2×C4×C31—44no—
167C2×C4×C31—44no—
168C2×C4×C31—42no—
169C2×C4×C31—44no—
170C2×C4×C31—44no—
171C2×C4×C31—42no—
172C2×C4×C31—41no—
173C2×C4×C31—42no—
174C2×C4×C31—42no—
175C2×C4×C31—44no—
176C2×C4×C31—44no—
177C2×C4×C31—84no—
178C2×C4×C31—84no—
179C2×C4×C31#12011yescharacteristic
180C2×C4×C31#12012yes—
181C2×C4×C31#12011yescharacteristic
182C2×C4×C31#12314yes—
183#3428C2×C3111yescharacteristic
184#2484C2×C3112yescomplemented
185#2406C2×C3111yescharacteristic
186#1890C2×C3114yescomplemented
187#1867C2×C3114yescomplemented
188#1820C2×C3112yescomplemented
189#1782C2×C3111yescharacteristic
190C22×C31—22no—
191C22×C31—21no—
192C22×C31—22no—
193C22×C31—21no—
194C22×C31—24no—
195C22×C31—44no—
196C22×C31—44no—
197C22×C31—42no—
198C22×C31—42no—
199C22×C31—82no—
200C22×C31C2×#12011yescharacteristic
201C22×C31C2×#12312yes—
202C22×C31#52514yes—
203C4×C31—21no—
204C4×C31—21no—
205C4×C31—22no—
206C4×C31—24no—
207C4×C31—42no—
208C4×C31—44no—
209C4×C31—44no—
210C4×C31—82no—
211C4×C31—84no—
212C4×C31—81no—
213C22×#41C22×C3111yescharacteristic
214C2×#123C22×C3112yes—
215#520—22no—
216#520—22no—
217#519—21no—
218#518—21no—
219#518C22×C3114yes—
220C4×#41—24no—
221C2×#117—22no—
222C2×#117C22×C3112yes—
223C22×C4⋊C4C22×C3111yescharacteristic
224C2×#99C22×C3114yes—
225#400—22no—
226#398—22no—
227#395—21no—
228#394—21no—
229#387—24no—
230#386C22×C3112yes—
231#385—22no—
232#385C22×C3114yes—
233#381C22×C3111yescharacteristic
234#381C22×C3112yes—
235#381C22×C3114yes—
236#342C22×C3118yes—
237C2×C31—22no—
238C2×C31—24no—
239C2×C31—44no—
240C2×C31#284911yescharacteristic
241C2×C31#302511yescharacteristic
242C2×C31#302811yescharacteristic
243C2×#41—28no—
244C2×#41—22no—
245C2×#41—22no—
246C22×Q8D4×C3111yescharacteristic
247C22×D4D4×C3111yescharacteristic
248C22×D4C23×C3112yes—
249C23×C4D4×C3112yes—
250C23×C4C23×C3111yescharacteristic
251C23×C4C23×C3111yescharacteristic
252C23×C4C23×C3111yescharacteristic
253#123—28no—
254C4×Q8—24no—
255C4×Q8—24no—
256C4×D4—24no—
257C4×D4—24no—
258C4×D4—28no—
259C4×D4—28no—
260#117—24no—
261#117—24no—
262#117—22no—
263#117—24no—
264#117—22no—
265#117—22no—
266#117—22no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4D4×C3112yes—
276C2×C4⋊C4D4×C3112yes—
277C2×C22⋊C4—24no—
278C2×C22⋊C4—22no—
279C2×C22⋊C4—22no—
280C2×C22⋊C4C23×C3112yes—
281C2×C22⋊C4C23×C3114yes—
282C2×C22⋊C4C23×C3114yes—
283C2×C42—24no—
284C2×C42D4×C3114yes—
285#99—28no—
286#95—21no—
287#95—22no—
288#95—24no—
289#95—24no—
290#95—21no—
291#95—22no—
292#95—22no—
293#95—24no—
294C31#3302311yescharacteristic, direct product factor, Sylow
295C24C2×D4×C3112yes—
296C24C24×C3111yescharacteristic
297#41—216no—
298#41—216no—
299C2×Q8—22no—
300C2×Q8—24no—
301C2×D4—24no—
302C2×D4—24no—
303C2×D4—24no—
304C2×D4—22no—
305C2×D4#41×C3118yes—
306C22×C4—24no—
307C22×C4—24no—
308C22×C4—22no—
309C22×C4—22no—
310C22×C4—24no—
311C22×C4—21no—
312C22×C4—22no—
313C22×C4—24no—
314C22×C4—24no—
315C22×C4—24no—
316C22×C4—22no—
317C22×C4—22no—
318C22×C4—21no—
319C22×C4—24no—
320C22×C4—42no—
321C22×C4C2×D4×C3112yes—
322C22×C4C2×D4×C3112yes—
323C22×C4C2×D4×C3111yescharacteristic
324C22×C4C2×D4×C3111yescharacteristic
325C22×C4C2×D4×C3112yes—
326C22×C4C2×D4×C3114yes—
327C22×C4C2×D4×C3114yes—
328C4⋊C4—24no—
329C4⋊C4—24no—
330C4⋊C4—22no—
331C4⋊C4—22no—
332C4⋊C4—22no—
333C4⋊C4—22no—
334C4⋊C4—48no—
335C4⋊C4—41no—
336C4⋊C4—42no—
337C4⋊C4—41no—
338C4⋊C4—44no—
339C22⋊C4—28no—
340C22⋊C4—24no—
341C22⋊C4—24no—
342C22⋊C4—28no—
343C22⋊C4—24no—
344C22⋊C4—44no—
345C22⋊C4—44no—
346C42—28no—
347C42—24no—
348C42—24no—
349C23—22no—
350C23—22no—
351C23—41no—
352C23—41no—
353C23—42no—
354C23—42no—
355C23C31×#12314yes—
356C23C22×D4×C3111yescharacteristic
357C23C22×D4×C3112yes—
358C23C2×#41×C3114yes—
359Q8—28no—
360D4—28no—
361D4—216no—
362C2×C4—28no—
363C2×C4—28no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—24no—
369C2×C4—24no—
370C2×C4—22no—
371C2×C4—24no—
372C2×C4—24no—
373C2×C4—24no—
374C2×C4—42no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—44no—
378C2×C4—44no—
379C2×C4—42no—
380C2×C4—44no—
381C2×C4—44no—
382C2×C4—42no—
383C2×C4—41no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—44no—
387C2×C4—44no—
388C2×C4—84no—
389C2×C4—84no—
390C2×C4C31×#12011yescharacteristic
391C2×C4C31×#12012yes—
392C2×C4C31×#12011yescharacteristic
393C2×C4C31×#12314yes—
394C22—22no—
395C22—21no—
396C22—22no—
397C22—21no—
398C22—24no—
399C22—44no—
400C22—44no—
401C22—42no—
402C22—42no—
403C22—82no—
404C22C2×C31×#12011yescharacteristic
405C22C2×C31×#12312yes—
406C22C31×#52514yes—
407C4—21no—
408C4—21no—
409C4—22no—
410C4—24no—
411C4—42no—
412C4—44no—
413C4—44no—
414C4—82no—
415C4—84no—
416C4—81no—
417C2—22no—
418C2—24no—
419C2—44no—
420C2C31×#284911yescharacteristic
421C2C31×#302511yescharacteristic
422C2C31×#302811yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC24C24×C31
prime radicalC22×#41×C31C22
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#2484C2semidirect
4. C31×#1890C2semidirect
5. C31×#1867C2semidirect
6. C31×#1820C2semidirect
137. #33023C31direct (N × H)
184. #2484C2×C31semidirect
186. #1890C2×C31semidirect
187. #1867C2×C31semidirect
188. #1820C2×C31semidirect
294. C31#33023direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#34282
C31×#24842
C31×#24062
C31×#18902
C31×#18672
C31×#18202
C31×#17822
#3302331