Finite Group Databasebeta

← C31×#10335 #21467094

Subgroups — C31×#10335 #21467094

Order 7936.

574 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 574 conjugacy classes of subgroups — too many to draw. Only its 106 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×#3195C211yesmaximal, characteristic
2C31×#2503C211yesmaximal, characteristic
3C31×#2502C211yesmaximal, characteristic
4C31×#1821C211yesmaximal, characteristic
5C31×#1508C211yesmaximal, characteristic
6C31×#1508C211yesmaximal, characteristic
7C31×#1297C211yesmaximal, characteristic
8C2×C31×C22⋊Q8C2211yescharacteristic
9C2×C31×C22⋊Q8C2211yescharacteristic
10C22×C4⋊C4×C31C2211yescharacteristic
11C31×#483—21no—
12C31×#483—21no—
13C31×#470—22no—
14C31×#451—21no—
15C31×#451—21no—
16C31×#407C2211yescharacteristic
17C31×#407C2211yescharacteristic
18C31×#400—22no—
19C31×#398—22no—
20C31×#391—21no—
21C31×#391—21no—
22C31×#385—22no—
23C31×#384—21no—
24C31×#382—21no—
25C31×#381—22no—
26C4×C22⋊C4×C31C2211yescharacteristic
27C4×C22⋊C4×C31C2211yescharacteristic
28C31×#343—22no—
29C31×#328—22no—
30C31×#328—22no—
31C22×Q8×C31D411yescharacteristic
32C22×Q8×C31D411yescharacteristic
33C23×C4×C31D412yes—
34C23×C4×C31C2311yescharacteristic
35C2×Q16×C31—22no—
36C2×M16×C31—21no—
37C2×M16×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×C31—24no—
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×C31—21no—
61C2×C42×C31—21no—
62C2×C42×C31—21no—
63C31×#106—22no—
64C31×#103—22no—
65C31×#103—22no—
66C31×C22⋊C8—21no—
67C31×C22⋊C8—21no—
68C31×C22⋊C8—21no—
69C31×C22⋊C8—21no—
70C31×#95—24no—
71C31×#95—24no—
72C31×#95—24no—
73C31×#95D412yes—
74C31×#95D412yes—
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—22no—
84C22×C4×C31—21no—
85C22×C4×C31—21no—
86C22×C4×C31—21no—
87C22×C4×C31—22no—
88C22×C4×C31—22no—
89C22×C4×C31—21no—
90C22×C4×C31—22no—
91C22×C4×C31—42no—
92C22×C4×C31—44no—
93C22×C4×C31C2×D411yescharacteristic
94C22×C4×C31C2×D411yescharacteristic
95C22×C4×C31C2×D411yescharacteristic
96C22×C4×C31C2×D411yescharacteristic
97C22×C4×C31C2×D411yescharacteristic
98C22×C4×C31#4111yescharacteristic
99Q16×C31—82no—
100M16×C31—42no—
101M16×C31—42no—
102C2×C8×C31—22no—
103C2×C8×C31—41no—
104C4⋊C4×C31—21no—
105C4⋊C4×C31—21no—
106C4⋊C4×C31—21no—
107C4⋊C4×C31—21no—
108C4⋊C4×C31—41no—
109C4⋊C4×C31—41no—
110C4⋊C4×C31—41no—
111C4⋊C4×C31—41no—
112C4⋊C4×C31—41no—
113C4⋊C4×C31—41no—
114C4⋊C4×C31—41no—
115C4⋊C4×C31—41no—
116C4⋊C4×C31—84no—
117C22⋊C4×C31—24no—
118C22⋊C4×C31—42no—
119C22⋊C4×C31—41no—
120C22⋊C4×C31—41no—
121C22⋊C4×C31—41no—
122C22⋊C4×C31—41no—
123C42×C31—42no—
124C42×C31—42no—
125#10335C3111yesmaximal, characteristic, direct product factor, Sylow
126C23×C31—22no—
127C23×C31—22no—
128C23×C31—41no—
129C23×C31#12011yescharacteristic
130C23×C31#12011yescharacteristic
131C23×C31#12111yescharacteristic
132Q8×C31—42no—
133Q8×C31—42no—
134Q8×C31—81no—
135Q8×C31—81no—
136C2×C4×C31—22no—
137C2×C4×C31—22no—
138C2×C4×C31—22no—
139C2×C4×C31—24no—
140C2×C4×C31—41no—
141C2×C4×C31—41no—
142C2×C4×C31—41no—
143C2×C4×C31—42no—
144C2×C4×C31—42no—
145C2×C4×C31—42no—
146C2×C4×C31—42no—
147C2×C4×C31—44no—
148C2×C4×C31—42no—
149C2×C4×C31—42no—
150C2×C4×C31—41no—
151C2×C4×C31—41no—
152C2×C4×C31—41no—
153C2×C4×C31—41no—
154C2×C4×C31—42no—
155C2×C4×C31—42no—
156C2×C4×C31—44no—
157C2×C4×C31—42no—
158C2×C4×C31—42no—
159C2×C4×C31—82no—
160C2×C4×C31#12011yescharacteristic
161C2×C4×C31#12111yescharacteristic
162C2×C4×C31#12111yescharacteristic
163C2×C4×C31#12711yescharacteristic
164C8×C31—42no—
165C8×C31—81no—
166#3195C2×C3111yescharacteristic
167#2503C2×C3111yescharacteristic
168#2502C2×C3111yescharacteristic
169#1821C2×C3111yescharacteristic
170#1508C2×C3111yescharacteristic
171#1508C2×C3111yescharacteristic
172#1297C2×C3111yescharacteristic
173C22×C31—21no—
174C22×C31—21no—
175C22×C31—21no—
176C22×C31—21no—
177C22×C31—21no—
178C22×C31—21no—
179C22×C31—21no—
180C22×C31—44no—
181C22×C31#39211yescharacteristic
182C22×C31#45512yes—
183C22×C31#45612yes—
184C4×C31—21no—
185C4×C31—21no—
186C4×C31—21no—
187C4×C31—44no—
188C4×C31—82no—
189C4×C31—81no—
190C4×C31—82no—
191C4×C31—81no—
192C4×C31—81no—
193C4×C31—81no—
194C4×C31#45812yes—
195C2×C22⋊Q8C22×C3111yescharacteristic
196C2×C22⋊Q8C22×C3111yescharacteristic
197C22×C4⋊C4C22×C3111yescharacteristic
198#483—21no—
199#483—21no—
200#470—22no—
201#451—21no—
202#451—21no—
203#407C22×C3111yescharacteristic
204#407C22×C3111yescharacteristic
205#400—22no—
206#398—22no—
207#391—21no—
208#391—21no—
209#385—22no—
210#384—21no—
211#382—21no—
212#381—22no—
213C4×C22⋊C4C22×C3111yescharacteristic
214C4×C22⋊C4C22×C3111yescharacteristic
215#343—22no—
216#328—22no—
217#328—22no—
218C2×C31—22no—
219C2×C31—22no—
220C2×C31—41no—
221C2×C31#200411yescharacteristic
222C2×C31#200511yescharacteristic
223C2×C31#202211yescharacteristic
224C22×Q8D4×C3111yescharacteristic
225C22×Q8D4×C3111yescharacteristic
226C23×C4D4×C3112yes—
227C23×C4C23×C3111yescharacteristic
228C2×Q16—22no—
229C2×M16—21no—
230C2×M16D4×C3112yes—
231C22⋊Q8—21no—
232C22⋊Q8—21no—
233C22⋊Q8—21no—
234C22⋊Q8—21no—
235C22⋊Q8—21no—
236C22⋊Q8—21no—
237C22⋊Q8—21no—
238C22⋊Q8—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—24no—
248C2×C4⋊C4D4×C3111yescharacteristic
249C2×C4⋊C4D4×C3111yescharacteristic
250C2×C22⋊C4—21no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—21no—
254C2×C42—21no—
255C2×C42—21no—
256#106—22no—
257#103—22no—
258#103—22no—
259C22⋊C8—21no—
260C22⋊C8—21no—
261C22⋊C8—21no—
262C22⋊C8—21no—
263#95—24no—
264#95—24no—
265#95—24no—
266#95D4×C3112yes—
267#95D4×C3112yes—
268C31#1033511yescharacteristic, direct product factor, Sylow
269C24C2×D4×C3111yescharacteristic
270C2×Q8—21no—
271C2×Q8—21no—
272C2×Q8—21no—
273C2×Q8—21no—
274C2×Q8—42no—
275C2×Q8—42no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—21no—
284C22×C4—22no—
285C22×C4—42no—
286C22×C4—44no—
287C22×C4C2×D4×C3111yescharacteristic
288C22×C4C2×D4×C3111yescharacteristic
289C22×C4C2×D4×C3111yescharacteristic
290C22×C4C2×D4×C3111yescharacteristic
291C22×C4C2×D4×C3111yescharacteristic
292C22×C4#41×C3111yescharacteristic
293Q16—82no—
294M16—42no—
295M16—42no—
296C2×C8—22no—
297C2×C8—41no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C4⋊C4—84no—
311C22⋊C4—24no—
312C22⋊C4—42no—
313C22⋊C4—41no—
314C22⋊C4—41no—
315C22⋊C4—41no—
316C22⋊C4—41no—
317C42—42no—
318C42—42no—
319C23—22no—
320C23—22no—
321C23—41no—
322C23C31×#12011yescharacteristic
323C23C31×#12011yescharacteristic
324C23C31×#12111yescharacteristic
325Q8—42no—
326Q8—42no—
327Q8—81no—
328Q8—81no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—24no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—44no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—44no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—42no—
352C2×C4—82no—
353C2×C4C31×#12011yescharacteristic
354C2×C4C31×#12111yescharacteristic
355C2×C4C31×#12111yescharacteristic
356C2×C4C31×#12711yescharacteristic
357C8—42no—
358C8—81no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—44no—
367C22C31×#39211yescharacteristic
368C22C31×#45512yes—
369C22C31×#45612yes—
370C4—21no—
371C4—21no—
372C4—21no—
373C4—44no—
374C4—82no—
375C4—82no—
376C4—81no—
377C4—81no—
378C4—81no—
379C4—81no—
380C4C31×#45812yes—
381C2—22no—
382C2—22no—
383C2—41no—
384C2C31×#200411yescharacteristic
385C2C31×#200511yescharacteristic
386C2C31×#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
125. #10335C31direct (N × H)
268. C31#10335direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#31952
C31×#25032
C31×#25022
C31×#18212
C31×#15082
C31×#12972
#1033531