Finite Group Databasebeta

← C31×#11841 #21468600

Subgroups — C31×#11841 #21468600

Order 7936.

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

normal subgroups only

This group has 506 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×#2482C211yesmaximal, characteristic
2C31×#1819C211yesmaximal, characteristic
3C2×C31×#323C211yesmaximal, characteristic
4C31×#1352C212yesmaximal, complemented
5C31×#1344C212yesmaximal, complemented
6C2×C31×#117C411yescharacteristic, complemented
7C22×C22⋊C4×C31C2211yescharacteristic
8C2×C31×C22⋊C8—21no—
9C31×#399C411yescharacteristic, complemented
10C31×#399C2211yescharacteristic
11C31×#397C411yescharacteristic, complemented
12C31×#397C2211yescharacteristic
13C31×#388—21no—
14C31×#388—21no—
15C31×#385—21no—
16C31×#381C411yescharacteristic, complemented
17C31×#379—21no—
18C31×#379—21no—
19C31×#342—21no—
20C31×#342C2212yes—
21C31×#323—21no—
22C31×#323C2212yes—
23C25×C31D411yescharacteristic
24C23×C4×C31C2×C411yescharacteristic
25C23×C4×C31D411yescharacteristic
26C22×C8×C31—41no—
27C31×#117—41no—
28C31×#117—41no—
29C2×C4⋊C4×C31—21no—
30C2×C4⋊C4×C31—21no—
31C2×C4⋊C4×C31C2×C411yescharacteristic
32C2×C4⋊C4×C31C2×C411yescharacteristic
33C2×C22⋊C4×C31—21no—
34C2×C22⋊C4×C31—21no—
35C2×C22⋊C4×C31—21no—
36C2×C22⋊C4×C31—21no—
37C2×C22⋊C4×C31—22no—
38C2×C22⋊C4×C31—21no—
39C2×C22⋊C4×C31—21no—
40C2×C22⋊C4×C31—41no—
41C2×C22⋊C4×C31—41no—
42C2×C22⋊C4×C31—41no—
43C2×C22⋊C4×C31—41no—
44C2×C22⋊C4×C31C2×C411yescharacteristic
45C2×C22⋊C4×C31D411yescharacteristic
46C2×C22⋊C4×C31D411yescharacteristic
47C2×C22⋊C4×C31C2311yescharacteristic
48C2×C42×C31—21no—
49C31×C22⋊C8—22no—
50C31×C22⋊C8—41no—
51C31×#95—21no—
52C31×#95—21no—
53C31×#95—21no—
54C31×#95C2×C411yescharacteristic
55C31×#95C2×C411yescharacteristic
56C24×C31—21no—
57C24×C31—21no—
58C24×C31—22no—
59C24×C31—41no—
60C24×C31—42no—
61C24×C31—81no—
62C24×C31C22⋊C411yescharacteristic
63C24×C31C22⋊C411yescharacteristic
64C24×C31C2×D411yescharacteristic
65C22×C4×C31—21no—
66C22×C4×C31—21no—
67C22×C4×C31—21no—
68C22×C4×C31—21no—
69C22×C4×C31—21no—
70C22×C4×C31—21no—
71C22×C4×C31—21no—
72C22×C4×C31—21no—
73C22×C4×C31—42no—
74C22×C4×C31—42no—
75C22×C4×C31—81no—
76C22×C4×C31C22⋊C411yescharacteristic
77C22×C4×C31C22⋊C411yescharacteristic
78C22×C4×C31C22×C411yescharacteristic
79C22×C4×C31C2×D411yescharacteristic
80C2×C8×C31—42no—
81C2×C8×C31—82no—
82C4⋊C4×C31—41no—
83C4⋊C4×C31—41no—
84C4⋊C4×C31—81no—
85C4⋊C4×C31—81no—
86C22⋊C4×C31—41no—
87C22⋊C4×C31—41no—
88C22⋊C4×C31—41no—
89C22⋊C4×C31—41no—
90C22⋊C4×C31—42no—
91C22⋊C4×C31—42no—
92C22⋊C4×C31—41no—
93C22⋊C4×C31—41no—
94C22⋊C4×C31—42no—
95C22⋊C4×C31—42no—
96C22⋊C4×C31—42no—
97C22⋊C4×C31—81no—
98C22⋊C4×C31—81no—
99C22⋊C4×C31—82no—
100C22⋊C4×C31—82no—
101C42×C31—42no—
102#11841C3111yesmaximal, characteristic, direct product factor, Sylow
103C23×C31—22no—
104C23×C31—21no—
105C23×C31—21no—
106C23×C31—21no—
107C23×C31—21no—
108C23×C31—21no—
109C23×C31—21no—
110C23×C31—21no—
111C23×C31—41no—
112C23×C31—42no—
113C23×C31—42no—
114C23×C31—41no—
115C23×C31—41no—
116C23×C31—41no—
117C23×C31—41no—
118C23×C31—42no—
119C23×C31—42no—
120C23×C31—81no—
121C23×C31—81no—
122C23×C31—84no—
123C23×C31—84no—
124C23×C31#9911yescharacteristic
125C23×C31#9911yescharacteristic
126C23×C31C2×C22⋊C411yescharacteristic
127C23×C31#13512yes—
128C2×C4×C31—21no—
129C2×C4×C31—21no—
130C2×C4×C31—21no—
131C2×C4×C31—21no—
132C2×C4×C31—42no—
133C2×C4×C31—42no—
134C2×C4×C31—42no—
135C2×C4×C31—41no—
136C2×C4×C31—41no—
137C2×C4×C31—41no—
138C2×C4×C31—41no—
139C2×C4×C31—41no—
140C2×C4×C31—41no—
141C2×C4×C31—41no—
142C2×C4×C31—41no—
143C2×C4×C31—41no—
144C2×C4×C31—41no—
145C2×C4×C31—41no—
146C2×C4×C31—41no—
147C2×C4×C31—41no—
148C2×C4×C31—41no—
149C2×C4×C31—41no—
150C2×C4×C31—41no—
151C2×C4×C31—81no—
152C2×C4×C31—82no—
153C2×C4×C31—82no—
154C2×C4×C31—82no—
155C8×C31—82no—
156#2482C2×C3111yescharacteristic
157#1819C2×C3111yescharacteristic
158C2×#323C2×C3111yescharacteristic
159#1352C2×C3112yescomplemented
160#1344C2×C3112yescomplemented
161C22×C31—21no—
162C22×C31—21no—
163C22×C31—21no—
164C22×C31—21no—
165C22×C31—21no—
166C22×C31—21no—
167C22×C31—22no—
168C22×C31—21no—
169C22×C31—42no—
170C22×C31—42no—
171C22×C31—42no—
172C22×C31—42no—
173C22×C31—41no—
174C22×C31—41no—
175C22×C31—41no—
176C22×C31—41no—
177C22×C31—41no—
178C22×C31—81no—
179C22×C31—84no—
180C22×C31—81no—
181C22×C31—84no—
182C22×C31#35212yes—
183C22×C31C2×#9911yescharacteristic
184C22×C31#41611yescharacteristic
185C22×C31#42111yescharacteristic
186C4×C31—41no—
187C4×C31—41no—
188C4×C31—41no—
189C4×C31—41no—
190C4×C31—81no—
191C4×C31—81no—
192C4×C31—81no—
193C4×C31—81no—
194C4×C31—162no—
195C2×#117C4×C3111yescharacteristic, complemented
196C22×C22⋊C4C22×C3111yescharacteristic
197C2×C22⋊C8—21no—
198#399C4×C3111yescharacteristic, complemented
199#399C22×C3111yescharacteristic
200#397C4×C3111yescharacteristic, complemented
201#397C22×C3111yescharacteristic
202#388—21no—
203#388—21no—
204#385—21no—
205#381C4×C3111yescharacteristic, complemented
206#379—21no—
207#379—21no—
208#342—21no—
209#342C22×C3112yes—
210#323—21no—
211#323C22×C3112yes—
212C2×C31—21no—
213C2×C31—21no—
214C2×C31—22no—
215C2×C31—42no—
216C2×C31—41no—
217C2×C31—81no—
218C2×C31#151611yescharacteristic
219C2×C31C2×#35211yescharacteristic
220C2×C31#212711yescharacteristic
221C25D4×C3111yescharacteristic
222C23×C4C2×C4×C3111yescharacteristic
223C23×C4D4×C3111yescharacteristic
224C22×C8—41no—
225#117—41no—
226#117—41no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4C2×C4×C3111yescharacteristic
230C2×C4⋊C4C2×C4×C3111yescharacteristic
231C2×C22⋊C4—21no—
232C2×C22⋊C4—21no—
233C2×C22⋊C4—21no—
234C2×C22⋊C4—21no—
235C2×C22⋊C4—22no—
236C2×C22⋊C4—21no—
237C2×C22⋊C4—21no—
238C2×C22⋊C4—41no—
239C2×C22⋊C4—41no—
240C2×C22⋊C4—41no—
241C2×C22⋊C4—41no—
242C2×C22⋊C4C2×C4×C3111yescharacteristic
243C2×C22⋊C4D4×C3111yescharacteristic
244C2×C22⋊C4D4×C3111yescharacteristic
245C2×C22⋊C4C23×C3111yescharacteristic
246C2×C42—21no—
247C22⋊C8—22no—
248C22⋊C8—41no—
249#95—21no—
250#95—21no—
251#95—21no—
252#95C2×C4×C3111yescharacteristic
253#95C2×C4×C3111yescharacteristic
254C31#1184111yescharacteristic, direct product factor, Sylow
255C24—21no—
256C24—21no—
257C24—22no—
258C24—41no—
259C24—42no—
260C24—81no—
261C24C22⋊C4×C3111yescharacteristic
262C24C22⋊C4×C3111yescharacteristic
263C24C2×D4×C3111yescharacteristic
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—42no—
273C22×C4—42no—
274C22×C4—81no—
275C22×C4C22⋊C4×C3111yescharacteristic
276C22×C4C22⋊C4×C3111yescharacteristic
277C22×C4C22×C4×C3111yescharacteristic
278C22×C4C2×D4×C3111yescharacteristic
279C2×C8—42no—
280C2×C8—82no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—81no—
284C4⋊C4—81no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C22⋊C4—41no—
288C22⋊C4—41no—
289C22⋊C4—42no—
290C22⋊C4—42no—
291C22⋊C4—41no—
292C22⋊C4—41no—
293C22⋊C4—42no—
294C22⋊C4—42no—
295C22⋊C4—42no—
296C22⋊C4—81no—
297C22⋊C4—81no—
298C22⋊C4—82no—
299C22⋊C4—82no—
300C42—42no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—22no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—41no—
310C23—42no—
311C23—42no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—42no—
317C23—42no—
318C23—81no—
319C23—81no—
320C23—84no—
321C23—84no—
322C23C31×#9911yescharacteristic
323C23C31×#9911yescharacteristic
324C23C2×C22⋊C4×C3111yescharacteristic
325C23C31×#13512yes—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—81no—
350C2×C4—82no—
351C2×C4—82no—
352C2×C4—82no—
353C8—82no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—22no—
361C22—21no—
362C22—42no—
363C22—42no—
364C22—42no—
365C22—42no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—81no—
372C22—84no—
373C22—81no—
374C22—84no—
375C22C31×#35212yes—
376C22C2×C31×#9911yescharacteristic
377C22C31×#41611yescharacteristic
378C22C31×#42111yescharacteristic
379C4—41no—
380C4—41no—
381C4—41no—
382C4—41no—
383C4—81no—
384C4—81no—
385C4—81no—
386C4—81no—
387C4—162no—
388C2—21no—
389C2—21no—
390C2—22no—
391C2—42no—
392C2—41no—
393C2—81no—
394C2C31×#151611yescharacteristic
395C2C2×C31×#35211yescharacteristic
396C2C31×#212711yescharacteristic
subgroupG/H
center, socleC22×C31C2×#99
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C22⋊C4C23×C31
prime radicalC25×C31D4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C24×C31 ◁ C22×C22⋊C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
4. C31×#1352C2semidirect
5. C31×#1344C2semidirect
6. C2×C31×#117C4semidirect
9. C31×#399C4semidirect
11. C31×#397C4semidirect
16. C31×#381C4semidirect
102. #11841C31direct (N × H)
159. #1352C2×C31semidirect
160. #1344C2×C31semidirect
195. C2×#117C4×C31semidirect
198. #399C4×C31semidirect
200. #397C4×C31semidirect
205. #381C4×C31semidirect
254. C31#11841direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#24822
C31×#18192
C2×C31×#3232
C31×#13522
C31×#13442
#1184131