Finite Group Databasebeta

← C31×#9961 #21466720

Subgroups — C31×#9961 #21466720

Order 7936.

552 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3189C211yesmaximal, characteristic
2C2×C31×#483C211yesmaximal, characteristic
3C31×#2503C211yesmaximal, characteristic
4C31×#1996C211yesmaximal, characteristic
5C31×#1823C211yesmaximal, characteristic
6C31×#1520C211yesmaximal, characteristic
7C31×#1282C211yesmaximal, characteristic
8C2×C31×C22⋊Q8C2211yescharacteristic
9C2×C31×C22⋊Q8C2211yescharacteristic
10C22×C4⋊C4×C31C2211yescharacteristic
11C31×#484—21no—
12C31×#484—21no—
13C31×#483—22no—
14C31×#483—22no—
15C31×#467—22no—
16C31×#451—21no—
17C31×#451—21no—
18C2×C31×#106—21no—
19C2×C31×#103—21no—
20C2×C31×C22⋊C8C2211yescharacteristic
21C2×C31×C22⋊C8C2211yescharacteristic
22C31×#400—22no—
23C31×#391—21no—
24C31×#382—21no—
25C31×#381—22no—
26C31×#380C2211yescharacteristic
27C4×C22⋊C4×C31C2211yescharacteristic
28C31×#342—22no—
29C31×#340—22no—
30C31×#328—22no—
31C22×Q8×C31D411yescharacteristic
32C22×Q8×C31D411yescharacteristic
33C23×C4×C31—21no—
34C23×C4×C31C2311yescharacteristic
35C2×Q16×C31—22no—
36C22×C8×C31—21no—
37C22×C8×C31D412yes—
38C31×C22⋊Q8—21no—
39C31×C22⋊Q8—21no—
40C31×C22⋊Q8—21no—
41C31×C22⋊Q8—21no—
42C31×C22⋊Q8—21no—
43C31×C22⋊Q8—21no—
44C31×C22⋊Q8—21no—
45C31×C22⋊Q8—21no—
46C2×C4⋊C4×C31—21no—
47C2×C4⋊C4×C31—21no—
48C2×C4⋊C4×C31—21no—
49C2×C4⋊C4×C31—21no—
50C2×C4⋊C4×C31—21no—
51C2×C4⋊C4×C31—21no—
52C2×C4⋊C4×C31—21no—
53C2×C4⋊C4×C31—21no—
54C2×C4⋊C4×C31D412yes—
55C2×C4⋊C4×C31D411yescharacteristic
56C2×C4⋊C4×C31D411yescharacteristic
57C2×C22⋊C4×C31—21no—
58C2×C22⋊C4×C31—21no—
59C2×C22⋊C4×C31—21no—
60C2×C22⋊C4×C31D412yes—
61C2×C42×C31—21no—
62C31×#107—22no—
63C31×#106—24no—
64C31×#103—24no—
65C31×#103—22no—
66C31×#103—22no—
67C31×C22⋊C8—21no—
68C31×C22⋊C8—21no—
69C31×C22⋊C8—21no—
70C31×C22⋊C8D412yes—
71C31×#95—24no—
72C31×#95—24no—
73C31×#95—21no—
74C31×#95—21no—
75C24×C31C2×D411yescharacteristic
76C2×Q8×C31—21no—
77C2×Q8×C31—21no—
78C2×Q8×C31—21no—
79C2×Q8×C31—21no—
80C2×Q8×C31—42no—
81C2×Q8×C31—42no—
82C22×C4×C31—22no—
83C22×C4×C31—21no—
84C22×C4×C31—21no—
85C22×C4×C31—22no—
86C22×C4×C31—21no—
87C22×C4×C31—21no—
88C22×C4×C31—42no—
89C22×C4×C31—41no—
90C22×C4×C31—41no—
91C22×C4×C31—42no—
92C22×C4×C31—42no—
93C22×C4×C31—41no—
94C22×C4×C31C2×D411yescharacteristic
95C22×C4×C31C2×D411yescharacteristic
96C22×C4×C31C2×D411yescharacteristic
97C22×C4×C31C2×D411yescharacteristic
98C22×C4×C31C2×D411yescharacteristic
99C22×C4×C31#4111yescharacteristic
100Q16×C31—82no—
101C2×C8×C31—22no—
102C2×C8×C31—22no—
103C2×C8×C31—42no—
104C2×C8×C31—42no—
105C4⋊C4×C31—22no—
106C4⋊C4×C31—21no—
107C4⋊C4×C31—21no—
108C4⋊C4×C31—21no—
109C4⋊C4×C31—22no—
110C4⋊C4×C31—21no—
111C4⋊C4×C31—42no—
112C4⋊C4×C31—41no—
113C4⋊C4×C31—41no—
114C4⋊C4×C31—41no—
115C4⋊C4×C31—41no—
116C4⋊C4×C31—41no—
117C4⋊C4×C31—41no—
118C22⋊C4×C31—22no—
119C22⋊C4×C31—22no—
120C22⋊C4×C31—41no—
121C22⋊C4×C31—41no—
122C22⋊C4×C31—41no—
123C22⋊C4×C31—41no—
124C22⋊C4×C31—42no—
125C42×C31—42no—
126#9961C3111yesmaximal, characteristic, direct product factor, Sylow
127C23×C31—41no—
128C23×C31—41no—
129C23×C31#12011yescharacteristic
130C23×C31#12111yescharacteristic
131C23×C31#12711yescharacteristic
132C23×C31#13512yes—
133C23×C31#13712yes—
134Q8×C31—42no—
135Q8×C31—42no—
136Q8×C31—42no—
137Q8×C31—81no—
138C2×C4×C31—22no—
139C2×C4×C31—22no—
140C2×C4×C31—22no—
141C2×C4×C31—41no—
142C2×C4×C31—41no—
143C2×C4×C31—41no—
144C2×C4×C31—42no—
145C2×C4×C31—42no—
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—42no—
153C2×C4×C31—42no—
154C2×C4×C31—44no—
155C2×C4×C31—82no—
156C2×C4×C31—81no—
157C2×C4×C31—81no—
158C2×C4×C31—81no—
159C2×C4×C31—81no—
160C2×C4×C31—81no—
161C2×C4×C31—81no—
162C2×C4×C31—81no—
163C2×C4×C31#12011yescharacteristic
164C2×C4×C31#12011yescharacteristic
165C2×C4×C31#12111yescharacteristic
166C2×C4×C31#12111yescharacteristic
167C8×C31—42no—
168C8×C31—42no—
169#3189C2×C3111yescharacteristic
170C2×#483C2×C3111yescharacteristic
171#2503C2×C3111yescharacteristic
172#1996C2×C3111yescharacteristic
173#1823C2×C3111yescharacteristic
174#1520C2×C3111yescharacteristic
175#1282C2×C3111yescharacteristic
176C22×C31—21no—
177C22×C31—21no—
178C22×C31—21no—
179C22×C31—21no—
180C22×C31—21no—
181C22×C31—21no—
182C22×C31—42no—
183C22×C31—42no—
184C22×C31#39211yescharacteristic
185C22×C31#45212yes—
186C22×C31#46412yes—
187C22×C31#49511yescharacteristic
188C22×C31#49711yescharacteristic
189C4×C31—21no—
190C4×C31—21no—
191C4×C31—21no—
192C4×C31—82no—
193C4×C31—81no—
194C4×C31—81no—
195C4×C31—82no—
196C4×C31—81no—
197C4×C31—81no—
198C4×C31—161no—
199C4×C31#45812yes—
200C2×C22⋊Q8C22×C3111yescharacteristic
201C2×C22⋊Q8C22×C3111yescharacteristic
202C22×C4⋊C4C22×C3111yescharacteristic
203#484—21no—
204#484—21no—
205#483—22no—
206#483—22no—
207#467—22no—
208#451—21no—
209#451—21no—
210C2×#106—21no—
211C2×#103—21no—
212C2×C22⋊C8C22×C3111yescharacteristic
213C2×C22⋊C8C22×C3111yescharacteristic
214#400—22no—
215#391—21no—
216#382—21no—
217#381—22no—
218#380C22×C3111yescharacteristic
219C4×C22⋊C4C22×C3111yescharacteristic
220#342—22no—
221#340—22no—
222#328—22no—
223C2×C31—22no—
224C2×C31—21no—
225C2×C31—22no—
226C2×C31—21no—
227C2×C31#200911yescharacteristic
228C2×C31#201511yescharacteristic
229C2×C31#202211yescharacteristic
230C22×Q8D4×C3111yescharacteristic
231C22×Q8D4×C3111yescharacteristic
232C23×C4—21no—
233C23×C4C23×C3111yescharacteristic
234C2×Q16—22no—
235C22×C8—21no—
236C22×C8D4×C3112yes—
237C22⋊Q8—21no—
238C22⋊Q8—21no—
239C22⋊Q8—21no—
240C22⋊Q8—21no—
241C22⋊Q8—21no—
242C22⋊Q8—21no—
243C22⋊Q8—21no—
244C22⋊Q8—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4D4×C3112yes—
254C2×C4⋊C4D4×C3111yescharacteristic
255C2×C4⋊C4D4×C3111yescharacteristic
256C2×C22⋊C4—21no—
257C2×C22⋊C4—21no—
258C2×C22⋊C4—21no—
259C2×C22⋊C4D4×C3112yes—
260C2×C42—21no—
261#107—22no—
262#106—24no—
263#103—24no—
264#103—22no—
265#103—22no—
266C22⋊C8—21no—
267C22⋊C8—21no—
268C22⋊C8—21no—
269C22⋊C8D4×C3112yes—
270#95—24no—
271#95—24no—
272#95—21no—
273#95—21no—
274C31#996111yescharacteristic, direct product factor, Sylow
275C24C2×D4×C3111yescharacteristic
276C2×Q8—21no—
277C2×Q8—21no—
278C2×Q8—21no—
279C2×Q8—21no—
280C2×Q8—42no—
281C2×Q8—42no—
282C22×C4—22no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—22no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—42no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4—42no—
292C22×C4—42no—
293C22×C4—41no—
294C22×C4C2×D4×C3111yescharacteristic
295C22×C4C2×D4×C3111yescharacteristic
296C22×C4C2×D4×C3111yescharacteristic
297C22×C4C2×D4×C3111yescharacteristic
298C22×C4C2×D4×C3111yescharacteristic
299C22×C4#41×C3111yescharacteristic
300Q16—82no—
301C2×C8—22no—
302C2×C8—22no—
303C2×C8—42no—
304C2×C8—42no—
305C4⋊C4—22no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—21no—
309C4⋊C4—22no—
310C4⋊C4—21no—
311C4⋊C4—42no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C22⋊C4—22no—
319C22⋊C4—22no—
320C22⋊C4—41no—
321C22⋊C4—41no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C22⋊C4—42no—
325C42—42no—
326C23—41no—
327C23—41no—
328C23C31×#12011yescharacteristic
329C23C31×#12111yescharacteristic
330C23C31×#12711yescharacteristic
331C23C31×#13512yes—
332C23C31×#13712yes—
333Q8—42no—
334Q8—42no—
335Q8—42no—
336Q8—81no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—44no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—42no—
354C2×C4—82no—
355C2×C4—81no—
356C2×C4—81no—
357C2×C4—81no—
358C2×C4—81no—
359C2×C4—81no—
360C2×C4—81no—
361C2×C4—81no—
362C2×C4C31×#12011yescharacteristic
363C2×C4C31×#12011yescharacteristic
364C2×C4C31×#12111yescharacteristic
365C2×C4C31×#12111yescharacteristic
366C8—42no—
367C8—42no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—42no—
375C22—42no—
376C22C31×#39211yescharacteristic
377C22C31×#45212yes—
378C22C31×#46412yes—
379C22C31×#49511yescharacteristic
380C22C31×#49711yescharacteristic
381C4—21no—
382C4—21no—
383C4—21no—
384C4—82no—
385C4—81no—
386C4—81no—
387C4—82no—
388C4—81no—
389C4—81no—
390C4—161no—
391C4C31×#45812yes—
392C2—22no—
393C2—21no—
394C2—22no—
395C2—21no—
396C2C31×#200911yescharacteristic
397C2C31×#201511yescharacteristic
398C2C31×#202211yescharacteristic
subgroupG/H
center, socleC22×C31#392
commutator, Frattini, cosocleC23×C4C23×C31
prime radicalC24×C31C2×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
126. #9961C31direct (N × H)
274. C31#9961direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#31892
C2×C31×#4832
C31×#25032
C31×#19962
C31×#18232
C31×#15202
C31×#12822
#996131