Finite Group Databasebeta

← C31×#9187 #21465946

Subgroups — C31×#9187 #21465946

Order 7936.

560 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 122 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2973C211yesmaximal, characteristic, complemented
2C31×#2631C211yesmaximal, characteristic
3C4×C31×#100C211yesmaximal, characteristic, complemented
4C31×#1527C212yesmaximal, complemented
5C31×#1288C212yesmaximal, complemented
6C2×C31×#124C2211yescharacteristic
7C2×C4×D4×C31C2211yescharacteristic
8C31×#435—24no—
9C31×#432C2212yes—
10C2×C31×#100—21no—
11C31×#407—21no—
12C2×C31×C22⋊C8—21no—
13C4×M16×C31C2212yes—
14C31×#397—21no—
15C31×#393C411yescharacteristic
16C31×#393C411yescharacteristic
17C31×#392—21no—
18C31×#392C411yescharacteristic
19C31×#392C411yescharacteristic
20C31×#386—21no—
21C31×#386—21no—
22C31×#383C2211yescharacteristic
23C31×#343—21no—
24C31×#329—24no—
25C22×Q8×C31C2×C411yescharacteristic
26C22×D4×C31—21no—
27C22×D4×C31—21no—
28C22×D4×C31C2×C411yescharacteristic
29C22×D4×C31D411yescharacteristic
30C23×C4×C31D411yescharacteristic
31C23×C4×C31D411yescharacteristic
32C2×M16×C31—22no—
33C2×M16×C31—22no—
34C22×C8×C31—22no—
35C31×#124—22no—
36C31×#124—22no—
37C4×D4×C31—22no—
38C4×D4×C31—22no—
39C2×C4⋊C4×C31D411yescharacteristic
40C2×C22⋊C4×C31—21no—
41C2×C22⋊C4×C31—21no—
42C2×C22⋊C4×C31—21no—
43C2×C22⋊C4×C31—21no—
44C2×C22⋊C4×C31—21no—
45C2×C22⋊C4×C31—21no—
46C2×C22⋊C4×C31C2×C411yescharacteristic
47C2×C22⋊C4×C31C2×C411yescharacteristic
48C2×C42×C31C2311yescharacteristic
49C31×C4⋊C8—22no—
50C31×#100—24no—
51C31×C22⋊C8—22no—
52C31×C22⋊C8—22no—
53C31×C22⋊C8—22no—
54C31×#97—22no—
55C31×#97D414yescomplemented
56C4×C8×C31—22no—
57C31×#95—21no—
58C31×#95—21no—
59C31×#95—21no—
60C31×#95—21no—
61C31×#95C2×C411yescharacteristic
62C31×#95C2×C411yescharacteristic
63C24×C31—21no—
64C24×C31C22⋊C411yescharacteristic
65C24×C31C22⋊C411yescharacteristic
66C2×Q8×C31—22no—
67C2×Q8×C31—81no—
68C2×D4×C31—22no—
69C2×D4×C31—22no—
70C2×D4×C31—22no—
71C2×D4×C31—41no—
72C2×D4×C31—42no—
73C2×D4×C31—42no—
74C2×D4×C31—81no—
75C2×D4×C31—81no—
76C2×D4×C31—81no—
77C2×D4×C31—81no—
78C2×D4×C31—81no—
79C22×C4×C31—21no—
80C22×C4×C31—21no—
81C22×C4×C31—21no—
82C22×C4×C31—21no—
83C22×C4×C31—21no—
84C22×C4×C31—21no—
85C22×C4×C31—21no—
86C22×C4×C31—81no—
87C22×C4×C31—81no—
88C22×C4×C31C22⋊C411yescharacteristic
89C22×C4×C31C22⋊C411yescharacteristic
90C22×C4×C31C22×C411yescharacteristic
91C22×C4×C31C2×D411yescharacteristic
92C22×C4×C31C2×D411yescharacteristic
93M16×C31—24no—
94M16×C31—42no—
95M16×C31—82no—
96C2×C8×C31—24no—
97C2×C8×C31—42no—
98C2×C8×C31—82no—
99C4⋊C4×C31—22no—
100C22⋊C4×C31—22no—
101C22⋊C4×C31—22no—
102C22⋊C4×C31—41no—
103C22⋊C4×C31—42no—
104C22⋊C4×C31—41no—
105C22⋊C4×C31—81no—
106C22⋊C4×C31—81no—
107C22⋊C4×C31—81no—
108C22⋊C4×C31—81no—
109C42×C31C2×D412yes—
110C42×C31#4112yes—
111#9187C3111yesmaximal, characteristic, direct product factor, Sylow
112C23×C31—21no—
113C23×C31—21no—
114C23×C31—21no—
115C23×C31—21no—
116C23×C31—21no—
117C23×C31—41no—
118C23×C31—41no—
119C23×C31—41no—
120C23×C31—41no—
121C23×C31—41no—
122C23×C31—41no—
123C23×C31—41no—
124C23×C31—41no—
125C23×C31—41no—
126C23×C31—41no—
127C23×C31—41no—
128C23×C31#10412yes—
129C23×C31C2×C22⋊C411yescharacteristic
130Q8×C31—82no—
131D4×C31—44no—
132D4×C31—82no—
133D4×C31—84no—
134D4×C31—84no—
135C2×C4×C31—21no—
136C2×C4×C31—21no—
137C2×C4×C31—21no—
138C2×C4×C31—21no—
139C2×C4×C31—41no—
140C2×C4×C31—41no—
141C2×C4×C31—42no—
142C2×C4×C31—42no—
143C2×C4×C31—41no—
144C2×C4×C31—41no—
145C2×C4×C31—41no—
146C2×C4×C31—41no—
147C2×C4×C31—41no—
148C2×C4×C31—41no—
149C2×C4×C31—41no—
150C2×C4×C31—41no—
151C2×C4×C31—41no—
152C2×C4×C31—41no—
153C2×C4×C31—41no—
154C2×C4×C31—81no—
155C2×C4×C31—81no—
156C2×C4×C31C4×D412yes—
157C2×C4×C31#12011yescharacteristic
158C2×C4×C31#12112yes—
159C2×C4×C31#12311yescharacteristic
160C8×C31—44no—
161C8×C31—44no—
162#2973C2×C3111yescharacteristic, complemented
163#2631C2×C3111yescharacteristic
164C4×#100C2×C3111yescharacteristic, complemented
165#1527C2×C3112yescomplemented
166#1288C2×C3112yescomplemented
167C22×C31—21no—
168C22×C31—21no—
169C22×C31—22no—
170C22×C31—42no—
171C22×C31—42no—
172C22×C31—41no—
173C22×C31—41no—
174C22×C31—41no—
175C22×C31—41no—
176C22×C31—41no—
177C22×C31—81no—
178C22×C31—81no—
179C22×C31—81no—
180C22×C31—81no—
181C22×C31—81no—
182C22×C31—81no—
183C22×C31—81no—
184C22×C31—81no—
185C22×C31—81no—
186C22×C31#38611yescharacteristic
187C22×C31C2×#10411yescharacteristic
188C22×C31#42111yescharacteristic
189C4×C31—22no—
190C4×C31—21no—
191C4×C31—21no—
192C4×C31—22no—
193C4×C31—41no—
194C4×C31—41no—
195C4×C31—81no—
196C4×C31—81no—
197C4×C31—81no—
198C2×#124C22×C3111yescharacteristic
199C2×C4×D4C22×C3111yescharacteristic
200#435—24no—
201#432C22×C3112yes—
202C2×#100—21no—
203#407—21no—
204C2×C22⋊C8—21no—
205C4×M16C22×C3112yes—
206#397—21no—
207#393C4×C3111yescharacteristic
208#393C4×C3111yescharacteristic
209#392—21no—
210#392C4×C3111yescharacteristic
211#392C4×C3111yescharacteristic
212#386—21no—
213#386—21no—
214#383C22×C3111yescharacteristic
215#343—21no—
216#329—24no—
217C2×C31—21no—
218C2×C31—21no—
219C2×C31—42no—
220C2×C31—81no—
221C2×C31—161no—
222C2×C31#187111yescharacteristic
223C2×C31#191111yescharacteristic
224C2×C31#191411yescharacteristic
225C22×Q8C2×C4×C3111yescharacteristic
226C22×D4—21no—
227C22×D4—21no—
228C22×D4C2×C4×C3111yescharacteristic
229C22×D4D4×C3111yescharacteristic
230C23×C4D4×C3111yescharacteristic
231C23×C4D4×C3111yescharacteristic
232C2×M16—22no—
233C2×M16—22no—
234C22×C8—22no—
235#124—22no—
236#124—22no—
237C4×D4—22no—
238C4×D4—22no—
239C2×C4⋊C4D4×C3111yescharacteristic
240C2×C22⋊C4—21no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—21no—
244C2×C22⋊C4—21no—
245C2×C22⋊C4—21no—
246C2×C22⋊C4C2×C4×C3111yescharacteristic
247C2×C22⋊C4C2×C4×C3111yescharacteristic
248C2×C42C23×C3111yescharacteristic
249C4⋊C8—22no—
250#100—24no—
251C22⋊C8—22no—
252C22⋊C8—22no—
253C22⋊C8—22no—
254#97—22no—
255#97D4×C3114yescomplemented
256C4×C8—22no—
257#95—21no—
258#95—21no—
259#95—21no—
260#95—21no—
261#95C2×C4×C3111yescharacteristic
262#95C2×C4×C3111yescharacteristic
263C31#918711yescharacteristic, direct product factor, Sylow
264C24—21no—
265C24C22⋊C4×C3111yescharacteristic
266C24C22⋊C4×C3111yescharacteristic
267C2×Q8—22no—
268C2×Q8—81no—
269C2×D4—22no—
270C2×D4—22no—
271C2×D4—22no—
272C2×D4—41no—
273C2×D4—42no—
274C2×D4—42no—
275C2×D4—81no—
276C2×D4—81no—
277C2×D4—81no—
278C2×D4—81no—
279C2×D4—81no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—81no—
288C22×C4—81no—
289C22×C4C22⋊C4×C3111yescharacteristic
290C22×C4C22⋊C4×C3111yescharacteristic
291C22×C4C22×C4×C3111yescharacteristic
292C22×C4C2×D4×C3111yescharacteristic
293C22×C4C2×D4×C3111yescharacteristic
294M16—24no—
295M16—42no—
296M16—82no—
297C2×C8—24no—
298C2×C8—42no—
299C2×C8—82no—
300C4⋊C4—22no—
301C22⋊C4—22no—
302C22⋊C4—22no—
303C22⋊C4—41no—
304C22⋊C4—42no—
305C22⋊C4—41no—
306C22⋊C4—81no—
307C22⋊C4—81no—
308C22⋊C4—81no—
309C22⋊C4—81no—
310C42C2×D4×C3112yes—
311C42#41×C3112yes—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23—41no—
324C23—41no—
325C23—41no—
326C23—41no—
327C23—41no—
328C23C31×#10412yes—
329C23C2×C22⋊C4×C3111yescharacteristic
330Q8—82no—
331D4—44no—
332D4—82no—
333D4—84no—
334D4—84no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—81no—
355C2×C4—81no—
356C2×C4C4×D4×C3112yes—
357C2×C4C31×#12011yescharacteristic
358C2×C4C31×#12112yes—
359C2×C4C31×#12311yescharacteristic
360C8—44no—
361C8—44no—
362C22—21no—
363C22—21no—
364C22—22no—
365C22—42no—
366C22—42no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—81no—
373C22—81no—
374C22—81no—
375C22—81no—
376C22—81no—
377C22—81no—
378C22—81no—
379C22—81no—
380C22—81no—
381C22C31×#38611yescharacteristic
382C22C2×C31×#10411yescharacteristic
383C22C31×#42111yescharacteristic
384C4—22no—
385C4—21no—
386C4—21no—
387C4—22no—
388C4—41no—
389C4—41no—
390C4—81no—
391C4—81no—
392C4—81no—
393C2—21no—
394C2—21no—
395C2—42no—
396C2—81no—
397C2—161no—
398C2C31×#187111yescharacteristic
399C2C31×#191111yescharacteristic
400C2C31×#191411yescharacteristic
subgroupG/H
center, socleC22×C31#386
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC31×#2631C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#2973C2semidirect
3. C4×C31×#100C2semidirect
4. C31×#1527C2semidirect
5. C31×#1288C2semidirect
55. C31×#97D4semidirect
111. #9187C31direct (N × H)
162. #2973C2×C31semidirect
164. C4×#100C2×C31semidirect
165. #1527C2×C31semidirect
166. #1288C2×C31semidirect
255. #97D4×C31semidirect
263. C31#9187direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#29732
C31×#26312
C4×C31×#1002
C31×#15272
C31×#12882
#918731