Finite Group Databasebeta

← C31×#9459 #21466218

Subgroups — C31×#9459 #21466218

Order 7936.

904 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 904 conjugacy classes of subgroups — too many to draw. Only its 130 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×#2435C211yesmaximal, characteristic
2C31×#2308C211yesmaximal, characteristic
3C31×#1783C211yesmaximal, characteristic
4C31×#1511C212yesmaximal, complemented
5C31×#1284C212yesmaximal, complemented
6C23×D4×C31C2211yescharacteristic
7C2×C31×#124C412yescomplemented
8C2×C31×C22⋊Q8C2211yescharacteristic
9C22×C22⋊C4×C31—21no—
10C2×C31×#100—22no—
11C31×#407C2212yes—
12C31×#394—22no—
13C31×#390C412yescomplemented
14C31×#386—24no—
15C31×#381C2212yes—
16C31×#379—21no—
17C31×#379—21no—
18C31×#379—21no—
19C4×C22⋊C4×C31C2211yescharacteristic
20C31×#328—24no—
21C25×C31D411yescharacteristic
22C25×C31D411yescharacteristic
23C22×Q8×C31C2×C411yescharacteristic, complemented
24C22×D4×C31—22no—
25C22×D4×C31—22no—
26C22×D4×C31—44no—
27C22×D4×C31C2×C412yes—
28C22×D4×C31D412yes—
29C23×C4×C31—22no—
30C23×C4×C31C2311yescharacteristic
31C2×M16×C31—22no—
32C31×#124—44no—
33C31×C22⋊Q8—22no—
34C31×C22⋊Q8—22no—
35C2×C4⋊C4×C31—21no—
36C2×C4⋊C4×C31C2×C411yescharacteristic, complemented
37C2×C22⋊C4×C31—22no—
38C2×C22⋊C4×C31—22no—
39C2×C22⋊C4×C31—22no—
40C2×C22⋊C4×C31—22no—
41C2×C22⋊C4×C31—21no—
42C2×C22⋊C4×C31—21no—
43C2×C22⋊C4×C31—22no—
44C2×C22⋊C4×C31—22no—
45C2×C22⋊C4×C31—22no—
46C2×C22⋊C4×C31—22no—
47C2×C22⋊C4×C31—44no—
48C2×C42×C31C2×C412yescomplemented
49C31×#100—44no—
50C31×C22⋊C8—22no—
51C31×C22⋊C8—22no—
52C31×#95—21no—
53C31×#95—22no—
54C31×#95D414yes—
55C24×C31—21no—
56C24×C31—24no—
57C24×C31—21no—
58C24×C31—21no—
59C24×C31—21no—
60C24×C31—42no—
61C24×C31—42no—
62C24×C31—42no—
63C24×C31—81no—
64C24×C31—81no—
65C24×C31C22⋊C412yes—
66C24×C31C22⋊C412yes—
67C24×C31C2×D411yescharacteristic
68C2×Q8×C31—22no—
69C2×Q8×C31—42no—
70C2×D4×C31—24no—
71C2×D4×C31—24no—
72C2×D4×C31—24no—
73C2×D4×C31—24no—
74C2×D4×C31—42no—
75C2×D4×C31—42no—
76C2×D4×C31—44no—
77C2×D4×C31—44no—
78C2×D4×C31—48no—
79C22×C4×C31—22no—
80C22×C4×C31—21no—
81C22×C4×C31—21no—
82C22×C4×C31—24no—
83C22×C4×C31—42no—
84C22×C4×C31—44no—
85C22×C4×C31—82no—
86C22×C4×C31—82no—
87C22×C4×C31C22×C411yescharacteristic
88C22×C4×C31C2×D411yescharacteristic
89C22×C4×C31C2×D412yes—
90C22×C4×C31#4112yes—
91M16×C31—44no—
92C2×C8×C31—42no—
93C4⋊C4×C31—22no—
94C4⋊C4×C31—42no—
95C22⋊C4×C31—42no—
96C22⋊C4×C31—44no—
97C22⋊C4×C31—44no—
98C22⋊C4×C31—44no—
99C22⋊C4×C31—44no—
100C22⋊C4×C31—41no—
101C22⋊C4×C31—41no—
102C22⋊C4×C31—82no—
103C22⋊C4×C31—82no—
104C22⋊C4×C31—82no—
105C22⋊C4×C31—82no—
106C42×C31—42no—
107#9459C3111yesmaximal, characteristic, direct product factor, Sylow
108C23×C31—22no—
109C23×C31—22no—
110C23×C31—24no—
111C23×C31—22no—
112C23×C31—22no—
113C23×C31—22no—
114C23×C31—22no—
115C23×C31—22no—
116C23×C31—22no—
117C23×C31—22no—
118C23×C31—41no—
119C23×C31—42no—
120C23×C31—42no—
121C23×C31—42no—
122C23×C31—42no—
123C23×C31—42no—
124C23×C31—42no—
125C23×C31—42no—
126C23×C31—42no—
127C23×C31—42no—
128C23×C31—42no—
129C23×C31—81no—
130C23×C31—81no—
131C23×C31—81no—
132C23×C31—81no—
133C23×C31—88no—
134C23×C31—88no—
135C23×C31#9914yes—
136C23×C31C2×C22⋊C411yescharacteristic
137C23×C31#12011yescharacteristic
138C23×C31#12311yescharacteristic
139Q8×C31—82no—
140D4×C31—48no—
141D4×C31—48no—
142C2×C4×C31—22no—
143C2×C4×C31—22no—
144C2×C4×C31—42no—
145C2×C4×C31—42no—
146C2×C4×C31—44no—
147C2×C4×C31—42no—
148C2×C4×C31—42no—
149C2×C4×C31—42no—
150C2×C4×C31—44no—
151C2×C4×C31—41no—
152C2×C4×C31—41no—
153C2×C4×C31—42no—
154C2×C4×C31—42no—
155C2×C4×C31—44no—
156C2×C4×C31—88no—
157C2×C4×C31C4×D412yes—
158C2×C4×C31#12112yes—
159C8×C31—82no—
160#2435C2×C3111yescharacteristic
161#2308C2×C3111yescharacteristic
162#1783C2×C3111yescharacteristic
163#1511C2×C3112yescomplemented
164#1284C2×C3112yescomplemented
165C22×C31—21no—
166C22×C31—21no—
167C22×C31—21no—
168C22×C31—21no—
169C22×C31—21no—
170C22×C31—21no—
171C22×C31—24no—
172C22×C31—21no—
173C22×C31—44no—
174C22×C31—44no—
175C22×C31—44no—
176C22×C31—44no—
177C22×C31—44no—
178C22×C31—42no—
179C22×C31—42no—
180C22×C31—42no—
181C22×C31—42no—
182C22×C31—42no—
183C22×C31—82no—
184C22×C31—82no—
185C22×C31—84no—
186C22×C31—84no—
187C22×C31—84no—
188C22×C31#38611yescharacteristic
189C22×C31C2×#9912yes—
190C22×C31#45512yes—
191C4×C31—22no—
192C4×C31—22no—
193C4×C31—82no—
194C4×C31—84no—
195C4×C31—81no—
196C4×C31—81no—
197C23×D4C22×C3111yescharacteristic
198C2×#124C4×C3112yescomplemented
199C2×C22⋊Q8C22×C3111yescharacteristic
200C22×C22⋊C4—21no—
201C2×#100—22no—
202#407C22×C3112yes—
203#394—22no—
204#390C4×C3112yescomplemented
205#386—24no—
206#381C22×C3112yes—
207#379—21no—
208#379—21no—
209#379—21no—
210C4×C22⋊C4C22×C3111yescharacteristic
211#328—24no—
212C2×C31—22no—
213C2×C31—22no—
214C2×C31—41no—
215C2×C31—44no—
216C2×C31—82no—
217C2×C31#188511yescharacteristic
218C2×C31#189811yescharacteristic
219C2×C31#191111yescharacteristic
220C25D4×C3111yescharacteristic
221C25D4×C3111yescharacteristic
222C22×Q8C2×C4×C3111yescharacteristic, complemented
223C22×D4—22no—
224C22×D4—22no—
225C22×D4—44no—
226C22×D4C2×C4×C3112yes—
227C22×D4D4×C3112yes—
228C23×C4—22no—
229C23×C4C23×C3111yescharacteristic
230C2×M16—22no—
231#124—44no—
232C22⋊Q8—22no—
233C22⋊Q8—22no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4C2×C4×C3111yescharacteristic, complemented
236C2×C22⋊C4—22no—
237C2×C22⋊C4—22no—
238C2×C22⋊C4—22no—
239C2×C22⋊C4—22no—
240C2×C22⋊C4—21no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—22no—
243C2×C22⋊C4—22no—
244C2×C22⋊C4—22no—
245C2×C22⋊C4—22no—
246C2×C22⋊C4—44no—
247C2×C42C2×C4×C3112yescomplemented
248#100—44no—
249C22⋊C8—22no—
250C22⋊C8—22no—
251#95—21no—
252#95—22no—
253#95D4×C3114yes—
254C31#945911yescharacteristic, direct product factor, Sylow
255C24—21no—
256C24—24no—
257C24—21no—
258C24—21no—
259C24—21no—
260C24—42no—
261C24—42no—
262C24—42no—
263C24—81no—
264C24—81no—
265C24C22⋊C4×C3112yes—
266C24C22⋊C4×C3112yes—
267C24C2×D4×C3111yescharacteristic
268C2×Q8—22no—
269C2×Q8—42no—
270C2×D4—24no—
271C2×D4—24no—
272C2×D4—24no—
273C2×D4—24no—
274C2×D4—42no—
275C2×D4—42no—
276C2×D4—44no—
277C2×D4—44no—
278C2×D4—48no—
279C22×C4—22no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—24no—
283C22×C4—42no—
284C22×C4—44no—
285C22×C4—82no—
286C22×C4—82no—
287C22×C4C22×C4×C3111yescharacteristic
288C22×C4C2×D4×C3111yescharacteristic
289C22×C4C2×D4×C3112yes—
290C22×C4#41×C3112yes—
291M16—44no—
292C2×C8—42no—
293C4⋊C4—22no—
294C4⋊C4—42no—
295C22⋊C4—42no—
296C22⋊C4—44no—
297C22⋊C4—44no—
298C22⋊C4—44no—
299C22⋊C4—44no—
300C22⋊C4—41no—
301C22⋊C4—41no—
302C22⋊C4—82no—
303C22⋊C4—82no—
304C22⋊C4—82no—
305C22⋊C4—82no—
306C42—42no—
307C23—22no—
308C23—22no—
309C23—24no—
310C23—22no—
311C23—22no—
312C23—22no—
313C23—22no—
314C23—22no—
315C23—22no—
316C23—22no—
317C23—41no—
318C23—42no—
319C23—42no—
320C23—42no—
321C23—42no—
322C23—42no—
323C23—42no—
324C23—42no—
325C23—42no—
326C23—42no—
327C23—42no—
328C23—81no—
329C23—81no—
330C23—81no—
331C23—81no—
332C23—88no—
333C23—88no—
334C23C31×#9914yes—
335C23C2×C22⋊C4×C3111yescharacteristic
336C23C31×#12011yescharacteristic
337C23C31×#12311yescharacteristic
338Q8—82no—
339D4—48no—
340D4—48no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—44no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—44no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—44no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—88no—
356C2×C4C4×D4×C3112yes—
357C2×C4C31×#12112yes—
358C8—82no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—24no—
366C22—21no—
367C22—44no—
368C22—44no—
369C22—44no—
370C22—44no—
371C22—44no—
372C22—42no—
373C22—42no—
374C22—42no—
375C22—42no—
376C22—42no—
377C22—82no—
378C22—82no—
379C22—84no—
380C22—84no—
381C22—84no—
382C22C31×#38611yescharacteristic
383C22C2×C31×#9912yes—
384C22C31×#45512yes—
385C4—22no—
386C4—22no—
387C4—84no—
388C4—82no—
389C4—81no—
390C4—81no—
391C2—22no—
392C2—22no—
393C2—41no—
394C2—44no—
395C2—82no—
396C2C31×#188511yescharacteristic
397C2C31×#189811yescharacteristic
398C2C31×#191111yescharacteristic
subgroupG/H
center, socleC22×C31#386
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC23×D4×C31C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
4. C31×#1511C2semidirect
5. C31×#1284C2semidirect
7. C2×C31×#124C4semidirect
13. C31×#390C4semidirect
23. C22×Q8×C31C2×C4semidirect
36. C2×C4⋊C4×C31C2×C4semidirect
48. C2×C42×C31C2×C4semidirect
107. #9459C31direct (N × H)
163. #1511C2×C31semidirect
164. #1284C2×C31semidirect
198. C2×#124C4×C31semidirect
204. #390C4×C31semidirect
222. C22×Q8C2×C4×C31semidirect
235. C2×C4⋊C4C2×C4×C31semidirect
247. C2×C42C2×C4×C31semidirect
254. C31#9459direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#24352
C31×#23082
C31×#17832
C31×#15112
C31×#12842
#945931