Finite Group Databasebeta

← C31×#9161 #21465920

Subgroups — C31×#9161 #21465920

Order 7936.

474 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3115C211yesmaximal, characteristic
2C31×#2970C211yesmaximal, characteristic, complemented
3C31×#1759C211yesmaximal, characteristic, complemented
4C31×#1525C211yesmaximal, characteristic, complemented
5C31×#1505C211yesmaximal, characteristic, complemented
6C31×#1300C211yesmaximal, characteristic, complemented
7C31×#1291C211yesmaximal, characteristic, complemented
8C31×#532C2211yescharacteristic
9C4×#41×C31C2211yescharacteristic
10C31×#482—21no—
11C31×#475C411yescharacteristic, complemented
12C31×#474C411yescharacteristic, complemented
13C31×#460C411yescharacteristic, complemented
14C31×#459C411yescharacteristic, complemented
15C31×#449—21no—
16C31×#446—21no—
17C31×#442—21no—
18C31×#440—21no—
19C31×#435—22no—
20C8×D4×C31—21no—
21C31×#432—21no—
22C31×#432C2211yescharacteristic
23C31×#432C2211yescharacteristic
24C2×C31×#104—21no—
25C4×M16×C31C2211yescharacteristic
26C4×M16×C31C2211yescharacteristic
27C2×C31×#97—21no—
28C31×#376C2211yescharacteristic
29C31×#339—21no—
30C31×#329—21no—
31C31×#329—21no—
32C31×#327—22no—
33C2×#41×C31—21no—
34C2×#41×C31D411yescharacteristic
35C2×SD16×C31—21no—
36C2×D8×C31—21no—
37C2×M16×C31—21no—
38C2×M16×C31—21no—
39C22×C8×C31—22no—
40C31×C4⋊Q8C2×C411yescharacteristic
41C31×#127C2×C411yescharacteristic
42C31×#124—21no—
43C31×#121—21no—
44C31×#121—21no—
45C4×Q8×C31C2×C411yescharacteristic
46C4×Q8×C31D411yescharacteristic
47C4×D4×C31—21no—
48C4×D4×C31—21no—
49C4×D4×C31—21no—
50C4×D4×C31—21no—
51C4×D4×C31C2×C411yescharacteristic
52C4×D4×C31D411yescharacteristic
53C31×#117—21no—
54C31×#117D411yescharacteristic
55C2×C42×C31—21no—
56C2×C42×C31—21no—
57C2×C42×C31C2311yescharacteristic
58C31×#107—21no—
59C31×#106—21no—
60C31×C4⋊C8—22no—
61C31×C4⋊C8—21no—
62C31×C4⋊C8C2×C411yescharacteristic
63C31×C4⋊C8C2×C411yescharacteristic
64C31×#104—24no—
65C31×#103—21no—
66C31×#102—21no—
67C31×#102—21no—
68C31×#102—21no—
69C31×C22⋊C8—22no—
70C31×C22⋊C8—21no—
71C31×C22⋊C8D412yes—
72C31×#97—22no—
73C31×#97—21no—
74C31×#97—21no—
75C31×#97—21no—
76C31×#97D411yescharacteristic
77C31×#97D411yescharacteristic
78C4×C8×C31—21no—
79C4×C8×C31—21no—
80C31×#95—21no—
81C31×#95—21no—
82#41×C31—22no—
83#41×C31—41no—
84#41×C31—82no—
85C2×Q8×C31—21no—
86C2×Q8×C31C22⋊C411yescharacteristic
87C2×D4×C31—21no—
88C2×D4×C31—21no—
89C2×D4×C31—21no—
90C2×D4×C31—21no—
91C2×D4×C31—41no—
92C2×D4×C31C22⋊C411yescharacteristic
93C22×C4×C31—21no—
94C22×C4×C31—21no—
95C22×C4×C31—21no—
96C22×C4×C31—41no—
97C22×C4×C31—41no—
98C22×C4×C31C2×D411yescharacteristic
99C22×C4×C31C2×D411yescharacteristic
100C22×C4×C31#4111yescharacteristic
101SD16×C31—42no—
102D8×C31—42no—
103M16×C31—22no—
104M16×C31—42no—
105M16×C31—41no—
106C2×C8×C31—21no—
107C2×C8×C31—21no—
108C2×C8×C31—21no—
109C2×C8×C31—21no—
110C2×C8×C31—22no—
111C2×C8×C31—44no—
112C2×C8×C31—41no—
113C4⋊C4×C31—21no—
114C4⋊C4×C31—21no—
115C4⋊C4×C31—21no—
116C4⋊C4×C31—21no—
117C4⋊C4×C31C22⋊C411yescharacteristic
118C4⋊C4×C31C22⋊C411yescharacteristic
119C22⋊C4×C31—21no—
120C22⋊C4×C31—21no—
121C22⋊C4×C31—21no—
122C22⋊C4×C31—41no—
123C22⋊C4×C31—41no—
124C42×C31—21no—
125C42×C31—21no—
126C42×C31—21no—
127C42×C31—22no—
128C42×C31—41no—
129C42×C31C22×C411yescharacteristic
130C42×C31C2×D411yescharacteristic
131C42×C31C2×D411yescharacteristic
132C42×C31#4111yescharacteristic
133#9161C3111yesmaximal, characteristic, direct product factor, Sylow
134C23×C31—21no—
135C23×C31—41no—
136C23×C31#12111yescharacteristic
137Q8×C31—21no—
138Q8×C31—21no—
139Q8×C31—81no—
140D4×C31—21no—
141D4×C31—42no—
142D4×C31—41no—
143D4×C31—41no—
144D4×C31—81no—
145D4×C31—81no—
146D4×C31—82no—
147D4×C31#10412yes—
148C2×C4×C31—21no—
149C2×C4×C31—21no—
150C2×C4×C31—21no—
151C2×C4×C31—21no—
152C2×C4×C31—21no—
153C2×C4×C31—41no—
154C2×C4×C31—41no—
155C2×C4×C31—42no—
156C2×C4×C31—42no—
157C2×C4×C31—42no—
158C2×C4×C31—41no—
159C2×C4×C31—81no—
160C2×C4×C31—82no—
161C2×C4×C31—81no—
162C2×C4×C31—81no—
163C2×C4×C31C2×C22⋊C411yescharacteristic
164C2×C4×C31C4×D411yescharacteristic
165C2×C4×C31C4×D411yescharacteristic
166C2×C4×C31#12011yescharacteristic
167C2×C4×C31#12111yescharacteristic
168C2×C4×C31#12311yescharacteristic
169C8×C31—22no—
170C8×C31—42no—
171C8×C31—41no—
172C8×C31—42no—
173C8×C31—41no—
174C8×C31—41no—
175#3115C2×C3111yescharacteristic
176#2970C2×C3111yescharacteristic, complemented
177#1759C2×C3111yescharacteristic, complemented
178#1525C2×C3111yescharacteristic, complemented
179#1505C2×C3111yescharacteristic, complemented
180#1300C2×C3111yescharacteristic, complemented
181#1291C2×C3111yescharacteristic, complemented
182C22×C31—21no—
183C22×C31—22no—
184C22×C31—21no—
185C22×C31—21no—
186C22×C31—41no—
187C22×C31—41no—
188C22×C31—81no—
189C22×C31—81no—
190C22×C31—81no—
191C22×C31#38611yescharacteristic
192C4×C31—21no—
193C4×C31—21no—
194C4×C31—21no—
195C4×C31—21no—
196C4×C31—21no—
197C4×C31—41no—
198C4×C31—41no—
199C4×C31—41no—
200C4×C31—82no—
201C4×C31—81no—
202C4×C31C2×#10411yescharacteristic
203C4×C31#42111yescharacteristic
204#532C22×C3111yescharacteristic
205C4×#41C22×C3111yescharacteristic
206#482—21no—
207#475C4×C3111yescharacteristic, complemented
208#474C4×C3111yescharacteristic, complemented
209#460C4×C3111yescharacteristic, complemented
210#459C4×C3111yescharacteristic, complemented
211#449—21no—
212#446—21no—
213#442—21no—
214#440—21no—
215#435—22no—
216C8×D4—21no—
217#432—21no—
218#432C22×C3111yescharacteristic
219#432C22×C3111yescharacteristic
220C2×#104—21no—
221C4×M16C22×C3111yescharacteristic
222C4×M16C22×C3111yescharacteristic
223C2×#97—21no—
224#376C22×C3111yescharacteristic
225#339—21no—
226#329—21no—
227#329—21no—
228#327—22no—
229C2×C31—41no—
230C2×C31—42no—
231C2×C31—161no—
232C2×C31#187111yescharacteristic
233C2×C31#190311yescharacteristic
234C2×C31#190611yescharacteristic
235C2×#41—21no—
236C2×#41D4×C3111yescharacteristic
237C2×SD16—21no—
238C2×D8—21no—
239C2×M16—21no—
240C2×M16—21no—
241C22×C8—22no—
242C4⋊Q8C2×C4×C3111yescharacteristic
243#127C2×C4×C3111yescharacteristic
244#124—21no—
245#121—21no—
246#121—21no—
247C4×Q8C2×C4×C3111yescharacteristic
248C4×Q8D4×C3111yescharacteristic
249C4×D4—21no—
250C4×D4—21no—
251C4×D4—21no—
252C4×D4—21no—
253C4×D4C2×C4×C3111yescharacteristic
254C4×D4D4×C3111yescharacteristic
255#117—21no—
256#117D4×C3111yescharacteristic
257C2×C42—21no—
258C2×C42—21no—
259C2×C42C23×C3111yescharacteristic
260#107—21no—
261#106—21no—
262C4⋊C8—22no—
263C4⋊C8—21no—
264C4⋊C8C2×C4×C3111yescharacteristic
265C4⋊C8C2×C4×C3111yescharacteristic
266#104—24no—
267#103—21no—
268#102—21no—
269#102—21no—
270#102—21no—
271C22⋊C8—22no—
272C22⋊C8—21no—
273C22⋊C8D4×C3112yes—
274#97—22no—
275#97—21no—
276#97—21no—
277#97—21no—
278#97D4×C3111yescharacteristic
279#97D4×C3111yescharacteristic
280C4×C8—21no—
281C4×C8—21no—
282#95—21no—
283#95—21no—
284C31#916111yescharacteristic, direct product factor, Sylow
285#41—22no—
286#41—41no—
287#41—82no—
288C2×Q8—21no—
289C2×Q8C22⋊C4×C3111yescharacteristic
290C2×D4—21no—
291C2×D4—21no—
292C2×D4—21no—
293C2×D4—21no—
294C2×D4—41no—
295C2×D4C22⋊C4×C3111yescharacteristic
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4C2×D4×C3111yescharacteristic
302C22×C4C2×D4×C3111yescharacteristic
303C22×C4#41×C3111yescharacteristic
304SD16—42no—
305D8—42no—
306M16—22no—
307M16—42no—
308M16—41no—
309C2×C8—21no—
310C2×C8—21no—
311C2×C8—21no—
312C2×C8—21no—
313C2×C8—22no—
314C2×C8—44no—
315C2×C8—41no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4C22⋊C4×C3111yescharacteristic
321C4⋊C4C22⋊C4×C3111yescharacteristic
322C22⋊C4—21no—
323C22⋊C4—21no—
324C22⋊C4—21no—
325C22⋊C4—41no—
326C22⋊C4—41no—
327C42—21no—
328C42—21no—
329C42—21no—
330C42—22no—
331C42—41no—
332C42C22×C4×C3111yescharacteristic
333C42C2×D4×C3111yescharacteristic
334C42C2×D4×C3111yescharacteristic
335C42#41×C3111yescharacteristic
336C23—21no—
337C23—41no—
338C23C31×#12111yescharacteristic
339Q8—21no—
340Q8—21no—
341Q8—81no—
342D4—21no—
343D4—42no—
344D4—41no—
345D4—41no—
346D4—81no—
347D4—81no—
348D4—82no—
349D4C31×#10412yes—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—41no—
361C2×C4—81no—
362C2×C4—82no—
363C2×C4—81no—
364C2×C4—81no—
365C2×C4C2×C22⋊C4×C3111yescharacteristic
366C2×C4C4×D4×C3111yescharacteristic
367C2×C4C4×D4×C3111yescharacteristic
368C2×C4C31×#12011yescharacteristic
369C2×C4C31×#12111yescharacteristic
370C2×C4C31×#12311yescharacteristic
371C8—22no—
372C8—42no—
373C8—41no—
374C8—42no—
375C8—41no—
376C8—41no—
377C22—21no—
378C22—22no—
379C22—21no—
380C22—21no—
381C22—41no—
382C22—41no—
383C22—81no—
384C22—81no—
385C22—81no—
386C22C31×#38611yescharacteristic
387C4—21no—
388C4—21no—
389C4—21no—
390C4—21no—
391C4—21no—
392C4—41no—
393C4—41no—
394C4—41no—
395C4—82no—
396C4—81no—
397C4C2×C31×#10411yescharacteristic
398C4C31×#42111yescharacteristic
399C2—41no—
400C2—42no—
401C2—161no—
402C2C31×#187111yescharacteristic
403C2C31×#190311yescharacteristic
404C2C31×#190611yescharacteristic
subgroupG/H
center, socleC22×C31#386
commutatorC42C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC31×#3115C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#2970C2semidirect
3. C31×#1759C2semidirect
4. C31×#1525C2semidirect
5. C31×#1505C2semidirect
6. C31×#1300C2semidirect
7. C31×#1291C2semidirect
11. C31×#475C4semidirect
12. C31×#474C4semidirect
13. C31×#460C4semidirect
14. C31×#459C4semidirect
133. #9161C31direct (N × H)
176. #2970C2×C31semidirect
177. #1759C2×C31semidirect
178. #1525C2×C31semidirect
179. #1505C2×C31semidirect
180. #1300C2×C31semidirect
181. #1291C2×C31semidirect
207. #475C4×C31semidirect
208. #474C4×C31semidirect
209. #460C4×C31semidirect
210. #459C4×C31semidirect
284. C31#9161direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#31152
C31×#29702
C31×#17592
C31×#15252
C31×#15052
C31×#13002
C31×#12912
#916131