Finite Group Databasebeta

← C31×#9447 #21466206

Subgroups — C31×#9447 #21466206

Order 7936.

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

normal subgroups only

This group has 568 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×#2544C211yesmaximal, characteristic
3C31×#1533C212yesmaximal, complemented
4C31×#1466C211yesmaximal, characteristic, complemented
5C31×#1285C212yesmaximal, complemented
6C2×C31×#127C411yescharacteristic
7C2×C31×#124C411yescharacteristic
8C2×C31×#124C2211yescharacteristic
9C2×C4×D4×C31C2211yescharacteristic
10C31×#435—24no—
11C31×#432C2212yes—
12C31×#432C2212yes—
13C31×#407—21no—
14C2×C31×C22⋊C8—21no—
15C31×#394—21no—
16C31×#394—21no—
17C31×#391C411yescharacteristic
18C31×#390C411yescharacteristic
19C31×#386—21no—
20C31×#386—21no—
21C4×C4⋊C4×C31C2211yescharacteristic
22C31×#329—24no—
23C31×#323—21no—
24C31×#323—21no—
25C22×Q8×C31C2×C411yescharacteristic
26C22×D4×C31—21no—
27C22×D4×C31—21no—
28C22×D4×C31C2×C411yescharacteristic
29C22×D4×C31C2×C411yescharacteristic
30C23×C4×C31D411yescharacteristic
31C23×C4×C31D411yescharacteristic
32C2×M16×C31—22no—
33C22×C8×C31—22no—
34C31×#127—42no—
35C31×#124—22no—
36C31×#124—22no—
37C31×#124—42no—
38C4×D4×C31—22no—
39C4×D4×C31—22no—
40C2×C4⋊C4×C31—21no—
41C2×C4⋊C4×C31C2×C411yescharacteristic
42C2×C22⋊C4×C31—21no—
43C2×C22⋊C4×C31—21no—
44C2×C22⋊C4×C31—21no—
45C2×C22⋊C4×C31—21no—
46C2×C22⋊C4×C31—21no—
47C2×C22⋊C4×C31—21no—
48C2×C22⋊C4×C31D411yescharacteristic
49C2×C22⋊C4×C31D411yescharacteristic
50C2×C42×C31C2×C411yescharacteristic
51C2×C42×C31C2×C411yescharacteristic
52C2×C42×C31C2311yescharacteristic
53C31×C4⋊C8—22no—
54C31×C4⋊C8—22no—
55C31×C22⋊C8—22no—
56C31×C22⋊C8—22no—
57C31×C22⋊C8—22no—
58C31×C22⋊C8—22no—
59C31×#97—22no—
60C31×#97D414yescomplemented
61C31×#95—21no—
62C31×#95—21no—
63C31×#95—21no—
64C24×C31—21no—
65C24×C31C22⋊C411yescharacteristic
66C24×C31C22⋊C411yescharacteristic
67C2×Q8×C31—22no—
68C2×Q8×C31—41no—
69C2×Q8×C31—41no—
70C2×D4×C31—22no—
71C2×D4×C31—22no—
72C2×D4×C31—22no—
73C2×D4×C31—41no—
74C2×D4×C31—42no—
75C2×D4×C31—42no—
76C2×D4×C31—41no—
77C2×D4×C31—41no—
78C2×D4×C31—42no—
79C2×D4×C31—42no—
80C2×D4×C31—81no—
81C2×D4×C31—81no—
82C22×C4×C31—21no—
83C22×C4×C31—21no—
84C22×C4×C31—21no—
85C22×C4×C31—21no—
86C22×C4×C31—21no—
87C22×C4×C31—21no—
88C22×C4×C31—21no—
89C22×C4×C31—81no—
90C22×C4×C31—81no—
91C22×C4×C31C22⋊C411yescharacteristic
92C22×C4×C31C22⋊C411yescharacteristic
93C22×C4×C31C22×C411yescharacteristic
94C22×C4×C31C2×D411yescharacteristic
95C22×C4×C31C2×D411yescharacteristic
96M16×C31—82no—
97C2×C8×C31—24no—
98C2×C8×C31—42no—
99C2×C8×C31—82no—
100C4⋊C4×C31—22no—
101C4⋊C4×C31—42no—
102C22⋊C4×C31—22no—
103C22⋊C4×C31—22no—
104C22⋊C4×C31—42no—
105C22⋊C4×C31—42no—
106C22⋊C4×C31—41no—
107C22⋊C4×C31—42no—
108C22⋊C4×C31—41no—
109C22⋊C4×C31—81no—
110C22⋊C4×C31—81no—
111C42×C31—41no—
112C42×C31—41no—
113C42×C31C2×D412yes—
114C42×C31#4112yes—
115#9447C3111yesmaximal, characteristic, direct product factor, Sylow
116C23×C31—21no—
117C23×C31—21no—
118C23×C31—21no—
119C23×C31—21no—
120C23×C31—21no—
121C23×C31—41no—
122C23×C31—41no—
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#10012yes—
133C23×C31C2×C22⋊C411yescharacteristic
134Q8×C31—82no—
135D4×C31—44no—
136D4×C31—82no—
137D4×C31—84no—
138D4×C31—84no—
139C2×C4×C31—21no—
140C2×C4×C31—21no—
141C2×C4×C31—22no—
142C2×C4×C31—21no—
143C2×C4×C31—21no—
144C2×C4×C31—41no—
145C2×C4×C31—41no—
146C2×C4×C31—42no—
147C2×C4×C31—42no—
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—41no—
155C2×C4×C31—41no—
156C2×C4×C31—41no—
157C2×C4×C31—41no—
158C2×C4×C31—81no—
159C2×C4×C31—81no—
160C2×C4×C31C4×D412yes—
161C2×C4×C31#12011yescharacteristic
162C2×C4×C31#12112yes—
163C2×C4×C31#12311yescharacteristic
164C8×C31—44no—
165C8×C31—82no—
166#2973C2×C3111yescharacteristic, complemented
167#2544C2×C3111yescharacteristic
168#1533C2×C3112yescomplemented
169#1466C2×C3111yescharacteristic, complemented
170#1285C2×C3112yescomplemented
171C22×C31—21no—
172C22×C31—21no—
173C22×C31—22no—
174C22×C31—42no—
175C22×C31—42no—
176C22×C31—41no—
177C22×C31—41no—
178C22×C31—41no—
179C22×C31—41no—
180C22×C31—41no—
181C22×C31—81no—
182C22×C31—81no—
183C22×C31—81no—
184C22×C31—81no—
185C22×C31—81no—
186C22×C31—81no—
187C22×C31—81no—
188C22×C31—81no—
189C22×C31—81no—
190C22×C31#38611yescharacteristic
191C22×C31C2×#10011yescharacteristic
192C22×C31#41311yescharacteristic
193C4×C31—22no—
194C4×C31—22no—
195C4×C31—21no—
196C4×C31—21no—
197C4×C31—42no—
198C4×C31—41no—
199C4×C31—41no—
200C4×C31—81no—
201C4×C31—81no—
202C2×#127C4×C3111yescharacteristic
203C2×#124C4×C3111yescharacteristic
204C2×#124C22×C3111yescharacteristic
205C2×C4×D4C22×C3111yescharacteristic
206#435—24no—
207#432C22×C3112yes—
208#432C22×C3112yes—
209#407—21no—
210C2×C22⋊C8—21no—
211#394—21no—
212#394—21no—
213#391C4×C3111yescharacteristic
214#390C4×C3111yescharacteristic
215#386—21no—
216#386—21no—
217C4×C4⋊C4C22×C3111yescharacteristic
218#329—24no—
219#323—21no—
220#323—21no—
221C2×C31—21no—
222C2×C31—21no—
223C2×C31—42no—
224C2×C31—81no—
225C2×C31—161no—
226C2×C31#188411yescharacteristic
227C2×C31#190011yescharacteristic
228C2×C31#191111yescharacteristic
229C22×Q8C2×C4×C3111yescharacteristic
230C22×D4—21no—
231C22×D4—21no—
232C22×D4C2×C4×C3111yescharacteristic
233C22×D4C2×C4×C3111yescharacteristic
234C23×C4D4×C3111yescharacteristic
235C23×C4D4×C3111yescharacteristic
236C2×M16—22no—
237C22×C8—22no—
238#127—42no—
239#124—22no—
240#124—22no—
241#124—42no—
242C4×D4—22no—
243C4×D4—22no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4C2×C4×C3111yescharacteristic
246C2×C22⋊C4—21no—
247C2×C22⋊C4—21no—
248C2×C22⋊C4—21no—
249C2×C22⋊C4—21no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4D4×C3111yescharacteristic
253C2×C22⋊C4D4×C3111yescharacteristic
254C2×C42C2×C4×C3111yescharacteristic
255C2×C42C2×C4×C3111yescharacteristic
256C2×C42C23×C3111yescharacteristic
257C4⋊C8—22no—
258C4⋊C8—22no—
259C22⋊C8—22no—
260C22⋊C8—22no—
261C22⋊C8—22no—
262C22⋊C8—22no—
263#97—22no—
264#97D4×C3114yescomplemented
265#95—21no—
266#95—21no—
267#95—21no—
268C31#944711yescharacteristic, direct product factor, Sylow
269C24—21no—
270C24C22⋊C4×C3111yescharacteristic
271C24C22⋊C4×C3111yescharacteristic
272C2×Q8—22no—
273C2×Q8—41no—
274C2×Q8—41no—
275C2×D4—22no—
276C2×D4—22no—
277C2×D4—22no—
278C2×D4—41no—
279C2×D4—41no—
280C2×D4—41no—
281C2×D4—42no—
282C2×D4—42no—
283C2×D4—42no—
284C2×D4—42no—
285C2×D4—81no—
286C2×D4—81no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—81no—
295C22×C4—81no—
296C22×C4C22⋊C4×C3111yescharacteristic
297C22×C4C22⋊C4×C3111yescharacteristic
298C22×C4C22×C4×C3111yescharacteristic
299C22×C4C2×D4×C3111yescharacteristic
300C22×C4C2×D4×C3111yescharacteristic
301M16—82no—
302C2×C8—24no—
303C2×C8—42no—
304C2×C8—82no—
305C4⋊C4—22no—
306C4⋊C4—42no—
307C22⋊C4—22no—
308C22⋊C4—22no—
309C22⋊C4—42no—
310C22⋊C4—42no—
311C22⋊C4—41no—
312C22⋊C4—42no—
313C22⋊C4—41no—
314C22⋊C4—81no—
315C22⋊C4—81no—
316C42—41no—
317C42—41no—
318C42C2×D4×C3112yes—
319C42#41×C3112yes—
320C23—21no—
321C23—21no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23—41no—
326C23—41no—
327C23—41no—
328C23—41no—
329C23—41no—
330C23—41no—
331C23—41no—
332C23—41no—
333C23—41no—
334C23—41no—
335C23—41no—
336C23C31×#10012yes—
337C23C2×C22⋊C4×C3111yescharacteristic
338Q8—82no—
339D4—44no—
340D4—82no—
341D4—84no—
342D4—84no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—22no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—81no—
363C2×C4—81no—
364C2×C4C4×D4×C3112yes—
365C2×C4C31×#12011yescharacteristic
366C2×C4C31×#12112yes—
367C2×C4C31×#12311yescharacteristic
368C8—44no—
369C8—82no—
370C22—21no—
371C22—21no—
372C22—22no—
373C22—42no—
374C22—42no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—81no—
381C22—81no—
382C22—81no—
383C22—81no—
384C22—81no—
385C22—81no—
386C22—81no—
387C22—81no—
388C22—81no—
389C22C31×#38611yescharacteristic
390C22C2×C31×#10011yescharacteristic
391C22C31×#41311yescharacteristic
392C4—22no—
393C4—22no—
394C4—21no—
395C4—21no—
396C4—42no—
397C4—41no—
398C4—41no—
399C4—81no—
400C4—81no—
401C2—21no—
402C2—21no—
403C2—42no—
404C2—81no—
405C2—161no—
406C2C31×#188411yescharacteristic
407C2C31×#190011yescharacteristic
408C2C31×#191111yescharacteristic
subgroupG/H
center, socleC22×C31#386
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC2×C31×#127C4
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. C31×#1533C2semidirect
4. C31×#1466C2semidirect
5. C31×#1285C2semidirect
60. C31×#97D4semidirect
115. #9447C31direct (N × H)
166. #2973C2×C31semidirect
168. #1533C2×C31semidirect
169. #1466C2×C31semidirect
170. #1285C2×C31semidirect
264. #97D4×C31semidirect
268. C31#9447direct (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×#25442
C31×#15332
C31×#14662
C31×#12852
#944731