Finite Group Databasebeta

← C31×#11848 #21468607

Subgroups — C31×#11848 #21468607

Order 7936.

572 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 102 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×#2406C211yesmaximal, characteristic
2C31×#1821C211yesmaximal, characteristic, complemented
3C2×C31×#324C211yesmaximal, characteristic, complemented
4C31×#1354C212yesmaximal, complemented
5C31×#1345C212yesmaximal, complemented
6C22×#41×C31C411yescharacteristic
7C2×C31×#123—21no—
8C22×C4⋊C4×C31C2211yescharacteristic
9C31×#407—21no—
10C2×C31×C22⋊C8—21no—
11C31×#395C411yescharacteristic
12C31×#395C2211yescharacteristic
13C31×#394C411yescharacteristic
14C31×#394C2211yescharacteristic
15C31×#386—21no—
16C31×#385—21no—
17C31×#385—21no—
18C31×#381C411yescharacteristic
19C31×#343—21no—
20C31×#343C2212yes—
21C31×#324—21no—
22C31×#324C2212yes—
23C2×#41×C31—41no—
24C2×#41×C31—41no—
25C2×#41×C31—44no—
26C22×Q8×C31C2×C411yescharacteristic
27C22×D4×C31—21no—
28C22×D4×C31C2×C411yescharacteristic
29C23×C4×C31—21no—
30C23×C4×C31C2×C411yescharacteristic
31C23×C4×C31D411yescharacteristic
32C23×C4×C31D411yescharacteristic
33C2×M16×C31—22no—
34C22×C8×C31—41no—
35C31×#123—44no—
36C2×C4⋊C4×C31—21no—
37C2×C4⋊C4×C31—21no—
38C2×C4⋊C4×C31—41no—
39C2×C4⋊C4×C31—41no—
40C2×C4⋊C4×C31C2×C411yescharacteristic
41C2×C4⋊C4×C31D411yescharacteristic
42C2×C4⋊C4×C31D411yescharacteristic
43C2×C4⋊C4×C31C2311yescharacteristic
44C2×C22⋊C4×C31—21no—
45C2×C22⋊C4×C31—21no—
46C2×C22⋊C4×C31—21no—
47C2×C22⋊C4×C31—21no—
48C2×C22⋊C4×C31—21no—
49C31×C22⋊C8—22no—
50C31×C22⋊C8—41no—
51C31×C22⋊C8—41no—
52C31×C22⋊C8—41no—
53C31×#95—21no—
54C31×#95—21no—
55C31×#95—21no—
56C31×#95C2×C411yescharacteristic
57C31×#95C2×C411yescharacteristic
58C24×C31—21no—
59C24×C31C22⋊C411yescharacteristic
60#41×C31—44no—
61#41×C31—44no—
62#41×C31—44no—
63#41×C31—44no—
64C2×Q8×C31—42no—
65C2×Q8×C31—41no—
66C2×D4×C31—24no—
67C2×D4×C31—41no—
68C2×D4×C31—42no—
69C2×D4×C31—41no—
70C2×D4×C31—41no—
71C2×D4×C31—42no—
72C22×C4×C31—21no—
73C22×C4×C31—21no—
74C22×C4×C31—21no—
75C22×C4×C31—21no—
76C22×C4×C31—21no—
77C22×C4×C31—21no—
78C22×C4×C31—21no—
79C22×C4×C31—22no—
80C22×C4×C31—21no—
81C22×C4×C31—21no—
82C22×C4×C31—41no—
83C22×C4×C31—42no—
84C22×C4×C31—42no—
85C22×C4×C31—42no—
86C22×C4×C31—42no—
87C22×C4×C31—42no—
88C22×C4×C31C22⋊C411yescharacteristic
89C22×C4×C31C22⋊C411yescharacteristic
90C22×C4×C31C22⋊C411yescharacteristic
91C22×C4×C31C22×C411yescharacteristic
92C22×C4×C31C2×D411yescharacteristic
93C22×C4×C31C2×D411yescharacteristic
94M16×C31—42no—
95M16×C31—42no—
96C2×C8×C31—42no—
97C2×C8×C31—42no—
98C2×C8×C31—82no—
99C4⋊C4×C31—41no—
100C4⋊C4×C31—41no—
101C4⋊C4×C31—41no—
102C4⋊C4×C31—41no—
103C4⋊C4×C31—42no—
104C4⋊C4×C31—42no—
105C22⋊C4×C31—42no—
106C22⋊C4×C31—42no—
107C22⋊C4×C31—42no—
108C22⋊C4×C31—42no—
109C22⋊C4×C31—42no—
110#11848C3111yesmaximal, characteristic, direct product factor, Sylow
111C23×C31—22no—
112C23×C31—21no—
113C23×C31—21no—
114C23×C31—22no—
115C23×C31—41no—
116C23×C31—41no—
117C23×C31—41no—
118C23×C31—41no—
119C23×C31—41no—
120C23×C31—41no—
121C23×C31—41no—
122C23×C31#9911yescharacteristic
123C23×C31#9911yescharacteristic
124C23×C31C2×C22⋊C411yescharacteristic
125Q8×C31—42no—
126Q8×C31—42no—
127D4×C31—44no—
128D4×C31—42no—
129D4×C31—42no—
130D4×C31—44no—
131C2×C4×C31—21no—
132C2×C4×C31—21no—
133C2×C4×C31—22no—
134C2×C4×C31—21no—
135C2×C4×C31—21no—
136C2×C4×C31—21no—
137C2×C4×C31—21no—
138C2×C4×C31—21no—
139C2×C4×C31—21no—
140C2×C4×C31—21no—
141C2×C4×C31—42no—
142C2×C4×C31—42no—
143C2×C4×C31—41no—
144C2×C4×C31—42no—
145C2×C4×C31—48no—
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—41no—
159C2×C4×C31—81no—
160C2×C4×C31#13512yes—
161C8×C31—82no—
162C8×C31—82no—
163#2406C2×C3111yescharacteristic
164#1821C2×C3111yescharacteristic, complemented
165C2×#324C2×C3111yescharacteristic, complemented
166#1354C2×C3112yescomplemented
167#1345C2×C3112yescomplemented
168C22×C31—21no—
169C22×C31—21no—
170C22×C31—21no—
171C22×C31—21no—
172C22×C31—21no—
173C22×C31—21no—
174C22×C31—21no—
175C22×C31—42no—
176C22×C31—42no—
177C22×C31—42no—
178C22×C31—42no—
179C22×C31—42no—
180C22×C31—81no—
181C22×C31—81no—
182C22×C31—81no—
183C22×C31—81no—
184C22×C31AΣL(1,𝔽16)12yes—
185C22×C31C2×#9911yescharacteristic
186C22×C31#41611yescharacteristic
187C22×C31#42111yescharacteristic
188C4×C31—22no—
189C4×C31—41no—
190C4×C31—41no—
191C4×C31—42no—
192C4×C31—41no—
193C4×C31—41no—
194C4×C31—41no—
195C4×C31—81no—
196C4×C31—81no—
197C22×#41C4×C3111yescharacteristic
198C2×#123—21no—
199C22×C4⋊C4C22×C3111yescharacteristic
200#407—21no—
201C2×C22⋊C8—21no—
202#395C4×C3111yescharacteristic
203#395C22×C3111yescharacteristic
204#394C4×C3111yescharacteristic
205#394C22×C3111yescharacteristic
206#386—21no—
207#385—21no—
208#385—21no—
209#381C4×C3111yescharacteristic
210#343—21no—
211#343C22×C3112yes—
212#324—21no—
213#324C22×C3112yes—
214C2×C31—21no—
215C2×C31—21no—
216C2×C31—22no—
217C2×C31—41no—
218C2×C31—82no—
219C2×C31#151611yescharacteristic
220C2×C31C2×AΣL(1,𝔽16)11yescharacteristic
221C2×C31#213311yescharacteristic
222C2×#41—41no—
223C2×#41—41no—
224C2×#41—44no—
225C22×Q8C2×C4×C3111yescharacteristic
226C22×D4—21no—
227C22×D4C2×C4×C3111yescharacteristic
228C23×C4—21no—
229C23×C4C2×C4×C3111yescharacteristic
230C23×C4D4×C3111yescharacteristic
231C23×C4D4×C3111yescharacteristic
232C2×M16—22no—
233C22×C8—41no—
234#123—44no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—41no—
238C2×C4⋊C4—41no—
239C2×C4⋊C4C2×C4×C3111yescharacteristic
240C2×C4⋊C4D4×C3111yescharacteristic
241C2×C4⋊C4D4×C3111yescharacteristic
242C2×C4⋊C4C23×C3111yescharacteristic
243C2×C22⋊C4—21no—
244C2×C22⋊C4—21no—
245C2×C22⋊C4—21no—
246C2×C22⋊C4—21no—
247C2×C22⋊C4—21no—
248C22⋊C8—22no—
249C22⋊C8—41no—
250C22⋊C8—41no—
251C22⋊C8—41no—
252#95—21no—
253#95—21no—
254#95—21no—
255#95C2×C4×C3111yescharacteristic
256#95C2×C4×C3111yescharacteristic
257C31#1184811yescharacteristic, direct product factor, Sylow
258C24—21no—
259C24C22⋊C4×C3111yescharacteristic
260#41—44no—
261#41—44no—
262#41—44no—
263#41—44no—
264C2×Q8—42no—
265C2×Q8—41no—
266C2×D4—24no—
267C2×D4—41no—
268C2×D4—42no—
269C2×D4—41no—
270C2×D4—41no—
271C2×D4—42no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—22no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—41no—
283C22×C4—42no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4C22⋊C4×C3111yescharacteristic
289C22×C4C22⋊C4×C3111yescharacteristic
290C22×C4C22⋊C4×C3111yescharacteristic
291C22×C4C22×C4×C3111yescharacteristic
292C22×C4C2×D4×C3111yescharacteristic
293C22×C4C2×D4×C3111yescharacteristic
294M16—42no—
295M16—42no—
296C2×C8—42no—
297C2×C8—42no—
298C2×C8—82no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—42no—
304C4⋊C4—42no—
305C22⋊C4—42no—
306C22⋊C4—42no—
307C22⋊C4—42no—
308C22⋊C4—42no—
309C22⋊C4—42no—
310C23—21no—
311C23—21no—
312C23—22no—
313C23—22no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23C31×#9911yescharacteristic
322C23C31×#9911yescharacteristic
323C23C2×C22⋊C4×C3111yescharacteristic
324Q8—42no—
325Q8—42no—
326D4—44no—
327D4—42no—
328D4—42no—
329D4—44no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—22no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—41no—
343C2×C4—42no—
344C2×C4—48no—
345C2×C4—41no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—81no—
359C2×C4C31×#13512yes—
360C8—82no—
361C8—82no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—42no—
370C22—42no—
371C22—42no—
372C22—42no—
373C22—42no—
374C22—81no—
375C22—81no—
376C22—81no—
377C22—81no—
378C22C31×AΣL(1,𝔽16)12yes—
379C22C2×C31×#9911yescharacteristic
380C22C31×#41611yescharacteristic
381C22C31×#42111yescharacteristic
382C4—22no—
383C4—41no—
384C4—41no—
385C4—42no—
386C4—41no—
387C4—41no—
388C4—41no—
389C4—81no—
390C4—81no—
391C2—21no—
392C2—21no—
393C2—22no—
394C2—41no—
395C2—82no—
396C2C31×#151611yescharacteristic
397C2C2×C31×AΣL(1,𝔽16)11yescharacteristic
398C2C31×#213311yescharacteristic
subgroupG/H
center, socleC22×C31C2×#99
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C4⋊C4C23×C31
prime radicalC22×#41×C31C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C24×C31 ◁ C22×C4⋊C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#1821C2semidirect
3. C2×C31×#324C2semidirect
4. C31×#1354C2semidirect
5. C31×#1345C2semidirect
110. #11848C31direct (N × H)
164. #1821C2×C31semidirect
165. C2×#324C2×C31semidirect
166. #1354C2×C31semidirect
167. #1345C2×C31semidirect
257. C31#11848direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#24062
C31×#18212
C2×C31×#3242
C31×#13542
C31×#13452
#1184831