Finite Group Databasebeta

← C31×#9107 #21465866

Subgroups — C31×#9107 #21465866

Order 7936.

674 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2972C211yesmaximal, characteristic, complemented
2C31×#2321C211yesmaximal, characteristic
3C31×#1459C211yesmaximal, characteristic, complemented
4C2×C31×#323C212yesmaximal, complemented
5C31×#1282C212yesmaximal, complemented
6C2×C31×#120C411yescharacteristic
7C2×C4×D4×C31C2211yescharacteristic
8C22×C22⋊C4×C31C2211yescharacteristic
9C8×D4×C31—24no—
10C31×#431—21no—
11C2×C31×C22⋊C8—21no—
12C2×C31×C22⋊C8C2212yes—
13C2×C31×C22⋊C8C2212yes—
14C31×#390—21no—
15C31×#388—21no—
16C31×#388—21no—
17C31×#386—21no—
18C31×#386C411yescharacteristic
19C31×#385C411yescharacteristic
20C31×#379C411yescharacteristic
21C4×C22⋊C4×C31C2211yescharacteristic
22C31×#324—21no—
23C31×#323—21no—
24C31×#323—24no—
25C25×C31C2×C411yescharacteristic
26C22×D4×C31—21no—
27C22×D4×C31C2×C411yescharacteristic
28C23×C4×C31C2×C411yescharacteristic
29C23×C4×C31D411yescharacteristic
30C23×C4×C31C2311yescharacteristic
31C22×C8×C31—22no—
32C22×C8×C31—22no—
33C22×C8×C31—22no—
34C31×#120—22no—
35C31×#120C814yescomplemented
36C4×D4×C31—22no—
37C4×D4×C31—22no—
38C2×C4⋊C4×C31—21no—
39C2×C4⋊C4×C31D411yescharacteristic
40C2×C22⋊C4×C31—21no—
41C2×C22⋊C4×C31—22no—
42C2×C22⋊C4×C31—21no—
43C2×C22⋊C4×C31—21no—
44C2×C22⋊C4×C31—22no—
45C2×C22⋊C4×C31—21no—
46C2×C22⋊C4×C31—21no—
47C2×C22⋊C4×C31—21no—
48C2×C22⋊C4×C31C2×C411yescharacteristic
49C2×C22⋊C4×C31C2×C411yescharacteristic
50C2×C22⋊C4×C31C2×C411yescharacteristic
51C2×C22⋊C4×C31D411yescharacteristic
52C2×C42×C31—21no—
53C2×C42×C31D411yescharacteristic
54C31×C4⋊C8—22no—
55C31×C22⋊C8—22no—
56C31×C22⋊C8—22no—
57C31×C22⋊C8—22no—
58C31×C22⋊C8—22no—
59C31×C22⋊C8D414yescomplemented
60C4×C8×C31—22no—
61C31×#95—21no—
62C31×#95—21no—
63C31×#95—21no—
64C24×C31—21no—
65C24×C31—22no—
66C24×C31—21no—
67C24×C31—22no—
68C24×C31—81no—
69C24×C31—81no—
70C24×C31C22⋊C411yescharacteristic
71C24×C31C2×C812yescomplemented
72C24×C31C22×C411yescharacteristic
73C2×D4×C31—22no—
74C2×D4×C31—22no—
75C2×D4×C31—24no—
76C2×D4×C31—81no—
77C2×D4×C31—81no—
78C2×D4×C31C2×C812yes—
79C2×D4×C31M1612yes—
80C22×C4×C31—21no—
81C22×C4×C31—21no—
82C22×C4×C31—21no—
83C22×C4×C31—21no—
84C22×C4×C31—21no—
85C22×C4×C31—22no—
86C22×C4×C31—81no—
87C22×C4×C31—81no—
88C22×C4×C31—81no—
89C22×C4×C31C22⋊C411yescharacteristic
90C22×C4×C31C22⋊C411yescharacteristic
91C22×C4×C31C22⋊C411yescharacteristic
92C22×C4×C31C2×D412yes—
93C22×C4×C31C2×D411yescharacteristic
94C22×C4×C31C2×D411yescharacteristic
95C22×C4×C31#4112yes—
96C2×C8×C31—24no—
97C2×C8×C31—42no—
98C2×C8×C31—82no—
99C2×C8×C31—82no—
100C2×C8×C31—82no—
101C4⋊C4×C31—22no—
102C4⋊C4×C31—81no—
103C22⋊C4×C31—22no—
104C22⋊C4×C31—21no—
105C22⋊C4×C31—24no—
106C22⋊C4×C31—22no—
107C22⋊C4×C31—22no—
108C22⋊C4×C31—41no—
109C22⋊C4×C31—42no—
110C22⋊C4×C31—41no—
111C22⋊C4×C31—81no—
112C22⋊C4×C31—81no—
113C22⋊C4×C31—81no—
114C22⋊C4×C31C2×C812yescomplemented
115C42×C31—21no—
116C42×C31—21no—
117C42×C31—81no—
118#9107C3111yesmaximal, characteristic, direct product factor, Sylow
119C23×C31—21no—
120C23×C31—21no—
121C23×C31—22no—
122C23×C31—24no—
123C23×C31—41no—
124C23×C31—41no—
125C23×C31—41no—
126C23×C31—41no—
127C23×C31—41no—
128C23×C31—41no—
129C23×C31—41no—
130C23×C31—41no—
131C23×C31—41no—
132C23×C31—41no—
133C23×C31—42no—
134C23×C31—82no—
135C23×C31—82no—
136C23×C31—82no—
137C23×C31—82no—
138C23×C31—84no—
139C23×C31C22⋊C812yes—
140C23×C31C2×C22⋊C411yescharacteristic
141C23×C31C4×D412yes—
142C23×C31C22×C811yescharacteristic
143C23×C31C2×M1611yescharacteristic
144C23×C31#13112yes—
145D4×C31—24no—
146D4×C31—24no—
147D4×C31—84no—
148C2×C4×C31—21no—
149C2×C4×C31—21no—
150C2×C4×C31—21no—
151C2×C4×C31—21no—
152C2×C4×C31—22no—
153C2×C4×C31—41no—
154C2×C4×C31—42no—
155C2×C4×C31—42no—
156C2×C4×C31—41no—
157C2×C4×C31—42no—
158C2×C4×C31—41no—
159C2×C4×C31—41no—
160C2×C4×C31—41no—
161C2×C4×C31—41no—
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—81no—
169C2×C4×C31—82no—
170C2×C4×C31C22⋊C812yes—
171C2×C4×C31#12011yescharacteristic
172C2×C4×C31#12112yes—
173C2×C4×C31#12311yescharacteristic
174C8×C31—44no—
175C8×C31—82no—
176#2972C2×C3111yescharacteristic, complemented
177#2321C2×C3111yescharacteristic
178#1459C2×C3111yescharacteristic, complemented
179C2×#323C2×C3112yescomplemented
180#1282C2×C3112yescomplemented
181C22×C31—21no—
182C22×C31—22no—
183C22×C31—21no—
184C22×C31—22no—
185C22×C31—22no—
186C22×C31—41no—
187C22×C31—41no—
188C22×C31—42no—
189C22×C31—42no—
190C22×C31—42no—
191C22×C31—42no—
192C22×C31—41no—
193C22×C31—41no—
194C22×C31—42no—
195C22×C31—81no—
196C22×C31—84no—
197C22×C31—81no—
198C22×C31—81no—
199C22×C31—84no—
200C22×C31—81no—
201C22×C31—81no—
202C22×C31#38611yescharacteristic
203C22×C31C2×C22⋊C811yescharacteristic
204C22×C31#40811yescharacteristic
205C22×C31C8×D412yes—
206C22×C31#43512yes—
207C4×C31—22no—
208C4×C31—21no—
209C4×C31—22no—
210C4×C31—21no—
211C4×C31—42no—
212C4×C31—41no—
213C4×C31—41no—
214C4×C31—81no—
215C4×C31—81no—
216C2×#120C4×C3111yescharacteristic
217C2×C4×D4C22×C3111yescharacteristic
218C22×C22⋊C4C22×C3111yescharacteristic
219C8×D4—24no—
220#431—21no—
221C2×C22⋊C8—21no—
222C2×C22⋊C8C22×C3112yes—
223C2×C22⋊C8C22×C3112yes—
224#390—21no—
225#388—21no—
226#388—21no—
227#386—21no—
228#386C4×C3111yescharacteristic
229#385C4×C3111yescharacteristic
230#379C4×C3111yescharacteristic
231C4×C22⋊C4C22×C3111yescharacteristic
232#324—21no—
233#323—21no—
234#323—24no—
235C2×C31—21no—
236C2×C31—21no—
237C2×C31—22no—
238C2×C31—22no—
239C2×C31—42no—
240C2×C31—82no—
241C2×C31#186911yescharacteristic
242C2×C31#191311yescharacteristic
243C2×C31#191411yescharacteristic
244C25C2×C4×C3111yescharacteristic
245C22×D4—21no—
246C22×D4C2×C4×C3111yescharacteristic
247C23×C4C2×C4×C3111yescharacteristic
248C23×C4D4×C3111yescharacteristic
249C23×C4C23×C3111yescharacteristic
250C22×C8—22no—
251C22×C8—22no—
252C22×C8—22no—
253#120—22no—
254#120C8×C3114yescomplemented
255C4×D4—22no—
256C4×D4—22no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4D4×C3111yescharacteristic
259C2×C22⋊C4—21no—
260C2×C22⋊C4—22no—
261C2×C22⋊C4—21no—
262C2×C22⋊C4—21no—
263C2×C22⋊C4—22no—
264C2×C22⋊C4—21no—
265C2×C22⋊C4—21no—
266C2×C22⋊C4—21no—
267C2×C22⋊C4C2×C4×C3111yescharacteristic
268C2×C22⋊C4C2×C4×C3111yescharacteristic
269C2×C22⋊C4C2×C4×C3111yescharacteristic
270C2×C22⋊C4D4×C3111yescharacteristic
271C2×C42—21no—
272C2×C42D4×C3111yescharacteristic
273C4⋊C8—22no—
274C22⋊C8—22no—
275C22⋊C8—22no—
276C22⋊C8—22no—
277C22⋊C8—22no—
278C22⋊C8D4×C3114yescomplemented
279C4×C8—22no—
280#95—21no—
281#95—21no—
282#95—21no—
283C31#910711yescharacteristic, direct product factor, Sylow
284C24—21no—
285C24—22no—
286C24—21no—
287C24—22no—
288C24—81no—
289C24—81no—
290C24C22⋊C4×C3111yescharacteristic
291C24C2×C8×C3112yescomplemented
292C24C22×C4×C3111yescharacteristic
293C2×D4—22no—
294C2×D4—22no—
295C2×D4—24no—
296C2×D4—81no—
297C2×D4—81no—
298C2×D4C2×C8×C3112yes—
299C2×D4M16×C3112yes—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—22no—
306C22×C4—81no—
307C22×C4—81no—
308C22×C4—81no—
309C22×C4C22⋊C4×C3111yescharacteristic
310C22×C4C22⋊C4×C3111yescharacteristic
311C22×C4C22⋊C4×C3111yescharacteristic
312C22×C4C2×D4×C3112yes—
313C22×C4C2×D4×C3111yescharacteristic
314C22×C4C2×D4×C3111yescharacteristic
315C22×C4#41×C3112yes—
316C2×C8—24no—
317C2×C8—42no—
318C2×C8—82no—
319C2×C8—82no—
320C2×C8—82no—
321C4⋊C4—22no—
322C4⋊C4—81no—
323C22⋊C4—22no—
324C22⋊C4—21no—
325C22⋊C4—24no—
326C22⋊C4—22no—
327C22⋊C4—22no—
328C22⋊C4—41no—
329C22⋊C4—42no—
330C22⋊C4—41no—
331C22⋊C4—81no—
332C22⋊C4—81no—
333C22⋊C4—81no—
334C22⋊C4C2×C8×C3112yescomplemented
335C42—21no—
336C42—21no—
337C42—81no—
338C23—21no—
339C23—21no—
340C23—22no—
341C23—24no—
342C23—41no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23—41no—
348C23—41no—
349C23—41no—
350C23—41no—
351C23—42no—
352C23—41no—
353C23—82no—
354C23—82no—
355C23—82no—
356C23—82no—
357C23—84no—
358C23C31×C22⋊C812yes—
359C23C2×C22⋊C4×C3111yescharacteristic
360C23C4×D4×C3112yes—
361C23C22×C8×C3111yescharacteristic
362C23C2×M16×C3111yescharacteristic
363C23C31×#13112yes—
364D4—24no—
365D4—24no—
366D4—84no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—22no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—41no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—41no—
376C2×C4—42no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—81no—
388C2×C4—82no—
389C2×C4C31×C22⋊C812yes—
390C2×C4C31×#12011yescharacteristic
391C2×C4C31×#12112yes—
392C2×C4C31×#12311yescharacteristic
393C8—44no—
394C8—82no—
395C22—21no—
396C22—22no—
397C22—21no—
398C22—22no—
399C22—22no—
400C22—41no—
401C22—41no—
402C22—42no—
403C22—42no—
404C22—42no—
405C22—42no—
406C22—41no—
407C22—41no—
408C22—42no—
409C22—81no—
410C22—84no—
411C22—81no—
412C22—81no—
413C22—84no—
414C22—81no—
415C22—81no—
416C22C31×#38611yescharacteristic
417C22C2×C31×C22⋊C811yescharacteristic
418C22C31×#40811yescharacteristic
419C22C8×D4×C3112yes—
420C22C31×#43512yes—
421C4—22no—
422C4—21no—
423C4—22no—
424C4—21no—
425C4—42no—
426C4—41no—
427C4—41no—
428C4—81no—
429C4—81no—
430C2—21no—
431C2—21no—
432C2—22no—
433C2—22no—
434C2—42no—
435C2—82no—
436C2C31×#186911yescharacteristic
437C2C31×#191311yescharacteristic
438C2C31×#191411yescharacteristic
subgroupG/H
center, socleC22×C31#386
commutatorC23C22×C8×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC2×C31×#120C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#2972C2semidirect
3. C31×#1459C2semidirect
4. C2×C31×#323C2semidirect
5. C31×#1282C2semidirect
35. C31×#120C8semidirect
59. C31×C22⋊C8D4semidirect
71. C24×C31C2×C8semidirect
114. C22⋊C4×C31C2×C8semidirect
118. #9107C31direct (N × H)
176. #2972C2×C31semidirect
178. #1459C2×C31semidirect
179. C2×#323C2×C31semidirect
180. #1282C2×C31semidirect
254. #120C8×C31semidirect
278. C22⋊C8D4×C31semidirect
283. C31#9107direct (N × H)
291. C24C2×C8×C31semidirect
334. C22⋊C4C2×C8×C31semidirect

Maximal subgroups

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

subgroupindex
C31×#29722
C31×#23212
C31×#14592
C2×C31×#3232
C31×#12822
#910731