Finite Group Databasebeta

← C31×#33799 #21490558

Subgroups — C31×#33799 #21490558

Order 7936.

466 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3168C211yesmaximal, characteristic
2C31×#3160C211yesmaximal, characteristic, complemented
3C31×#2253C212yesmaximal, complemented
4C31×#2242C212yesmaximal, complemented
5C31×#2237C212yesmaximal, complemented
6C31×#2234C212yesmaximal
7C31×#2227C211yesmaximal, characteristic, complemented
8C31×#2226C211yesmaximal, characteristic, complemented
9C31×#2225C211yesmaximal, characteristic, complemented
10C31×#2224C211yesmaximal, characteristic, complemented
11C31×#2162C211yesmaximal, characteristic, complemented
12C31×#533—21no—
13C31×#529—21no—
14C31×#500C2211yescharacteristic
15C31×#500C2211yescharacteristic
16C31×#499—21no—
17C31×#499C2212yes—
18C31×#499C2211yescharacteristic
19C31×#498—21no—
20C31×#495C2211yescharacteristic
21C31×#488—21no—
22C31×#467C2211yescharacteristic
23C31×#466C2211yescharacteristic
24C31×#465—21no—
25C4×Q16×C31C2211yescharacteristic
26C4×SD16×C31—21no—
27C4×D8×C31C2211yescharacteristic
28C31×#427—21no—
29C31×#427C2212yes—
30C2×C4×C8×C31C2211yescharacteristic
31C31×#367C2212yes—
32C31×#367C2212yes—
33C31×#366C2212yes—
34C31×#366C2212yes—
35C31×C4⋊C16C2211yescharacteristic
36C31×C4⋊C16C2211yescharacteristic
37C31×#358C2212yes—
38C31×#358C2212yes—
39C31×#357C2212yes—
40C31×#357C2212yes—
41C31×C22⋊C16C2212yes—
42C4×C16×C31C2212yes—
43C2×Q16×C31C2311yescharacteristic
44C2×SD16×C31—21no—
45C2×D8×C31C2311yescharacteristic
46C22×C8×C31D411yescharacteristic
47C22×C8×C31C2311yescharacteristic
48C31×C4⋊Q8—21no—
49C31×C4⋊Q8—21no—
50C31×#126—41no—
51C31×#125—21no—
52C31×#125—22no—
53C31×#124—21no—
54C31×#123—41no—
55C31×C22⋊Q8—21no—
56C31×C22⋊Q8—41no—
57C31×C22⋊Q8—41no—
58C31×#121—21no—
59C4×Q8×C31—21no—
60C4×Q8×C31—41no—
61C4×Q8×C31—41no—
62C4×D4×C31—21no—
63C4×D4×C31—41no—
64C31×#117—22no—
65C31×#117—41no—
66C2×C42×C31D411yescharacteristic
67C2×C16×C31C2312yes—
68C2×C16×C31C2312yes—
69C31×#107—21no—
70C31×#107—21no—
71C31×#107C2312yes—
72C31×#107C2312yes—
73C31×#107C2311yescharacteristic
74C31×#107C2311yescharacteristic
75C31×#106—22no—
76C31×#106—22no—
77C31×#106—21no—
78C31×#103—21no—
79C31×#103—21no—
80C31×#102—21no—
81C31×#102—21no—
82C4×C8×C31D411yescharacteristic
83C4×C8×C31D411yescharacteristic
84C4×C8×C31C2311yescharacteristic
85C4×C8×C31C2311yescharacteristic
86C2×Q8×C31—21no—
87C2×Q8×C31—41no—
88C2×Q8×C31—41no—
89C2×D4×C31—21no—
90C2×D4×C31—41no—
91C22×C4×C31—41no—
92C22×C4×C31D811yescharacteristic
93C22×C4×C31D811yescharacteristic
94C22×C4×C31C2×D411yescharacteristic
95Q16×C31—21no—
96Q16×C31—21no—
97SD16×C31—42no—
98D8×C31—21no—
99D8×C31—21no—
100C2×C8×C31—22no—
101C2×C8×C31—21no—
102C2×C8×C31—21no—
103C2×C8×C31C2×D411yescharacteristic
104C2×C8×C31C2×D411yescharacteristic
105C2×C8×C31C2×D411yescharacteristic
106C2×C8×C31C2411yescharacteristic
107C4⋊C4×C31—21no—
108C4⋊C4×C31—21no—
109C4⋊C4×C31—22no—
110C4⋊C4×C31—22no—
111C4⋊C4×C31—41no—
112C4⋊C4×C31—41no—
113C4⋊C4×C31—41no—
114C4⋊C4×C31—41no—
115C4⋊C4×C31—42no—
116C4⋊C4×C31—42no—
117C4⋊C4×C31—41no—
118C4⋊C4×C31—41no—
119C22⋊C4×C31—42no—
120C22⋊C4×C31—41no—
121C22⋊C4×C31—41no—
122C22⋊C4×C31—41no—
123C22⋊C4×C31—41no—
124C22⋊C4×C31—41no—
125C42×C31—42no—
126C42×C31—41no—
127C42×C31D811yescharacteristic
128C42×C31D811yescharacteristic
129C42×C31C2×D411yescharacteristic
130C42×C31C2×D411yescharacteristic
131C16×C31—22no—
132C16×C31—22no—
133#33799C3111yesmaximal, characteristic, direct product factor, Sylow
134C23×C31—41no—
135C23×C31C2×D811yescharacteristic
136Q8×C31—41no—
137Q8×C31—41no—
138Q8×C31—82no—
139Q8×C31—82no—
140D4×C31—41no—
141D4×C31—41no—
142D4×C31—82no—
143C2×C4×C31—21no—
144C2×C4×C31—21no—
145C2×C4×C31—22no—
146C2×C4×C31—41no—
147C2×C4×C31—41no—
148C2×C4×C31—41no—
149C2×C4×C31—42no—
150C2×C4×C31—42no—
151C2×C4×C31—41no—
152C2×C4×C31—82no—
153C2×C4×C31C2×D811yescharacteristic
154C2×C4×C31C2×D811yescharacteristic
155C2×C4×C31C2×D811yescharacteristic
156C2×C4×C31C2×D811yescharacteristic
157C2×C4×C31C2×D811yescharacteristic
158C2×C4×C31C22×D411yescharacteristic
159C8×C31—21no—
160C8×C31—21no—
161C8×C31#13712yes—
162C8×C312−1+411yescharacteristic
163C8×C312−1+411yescharacteristic
164#3168C2×C3111yescharacteristic
165#3160C2×C3111yescharacteristic, complemented
166#2253C2×C3112yescomplemented
167#2242C2×C3112yescomplemented
168#2237C2×C3112yescomplemented
169#2234C2×C3112yes—
170#2227C2×C3111yescharacteristic, complemented
171#2226C2×C3111yescharacteristic, complemented
172#2225C2×C3111yescharacteristic, complemented
173#2224C2×C3111yescharacteristic, complemented
174#2162C2×C3111yescharacteristic, complemented
175C22×C31—21no—
176C22×C31—21no—
177C22×C31—21no—
178C22×C31—81no—
179C22×C31—81no—
180C22×C31—81no—
181C22×C31C22×D811yescharacteristic
182C4×C31—21no—
183C4×C31—21no—
184C4×C31—21no—
185C4×C31—21no—
186C4×C31—81no—
187C4×C31—82no—
188C4×C31—81no—
189C4×C31—82no—
190C4×C31—81no—
191C4×C31#50812yes—
192C4×C31#53611yescharacteristic
193C4×C31C2×#13711yescharacteristic
194#533—21no—
195#529—21no—
196#500C22×C3111yescharacteristic
197#500C22×C3111yescharacteristic
198#499—21no—
199#499C22×C3112yes—
200#499C22×C3111yescharacteristic
201#498—21no—
202#495C22×C3111yescharacteristic
203#488—21no—
204#467C22×C3111yescharacteristic
205#466C22×C3111yescharacteristic
206#465—21no—
207C4×Q16C22×C3111yescharacteristic
208C4×SD16—21no—
209C4×D8C22×C3111yescharacteristic
210#427—21no—
211#427C22×C3112yes—
212C2×C4×C8C22×C3111yescharacteristic
213#367C22×C3112yes—
214#367C22×C3112yes—
215#366C22×C3112yes—
216#366C22×C3112yes—
217C4⋊C16C22×C3111yescharacteristic
218C4⋊C16C22×C3111yescharacteristic
219#358C22×C3112yes—
220#358C22×C3112yes—
221#357C22×C3112yes—
222#357C22×C3112yes—
223C22⋊C16C22×C3112yes—
224C4×C16C22×C3112yes—
225C2×C31—41no—
226C2×C31—161no—
227C2×C31#322611yescharacteristic
228C2×C31C2×#50811yescharacteristic
229C2×C31#341411yescharacteristic
230C2×Q16C23×C3111yescharacteristic
231C2×SD16—21no—
232C2×D8C23×C3111yescharacteristic
233C22×C8D4×C3111yescharacteristic
234C22×C8C23×C3111yescharacteristic
235C4⋊Q8—21no—
236C4⋊Q8—21no—
237#126—41no—
238#125—21no—
239#125—22no—
240#124—21no—
241#123—41no—
242C22⋊Q8—21no—
243C22⋊Q8—41no—
244C22⋊Q8—41no—
245#121—21no—
246C4×Q8—21no—
247C4×Q8—41no—
248C4×Q8—41no—
249C4×D4—21no—
250C4×D4—41no—
251#117—22no—
252#117—41no—
253C2×C42D4×C3111yescharacteristic
254C2×C16C23×C3112yes—
255C2×C16C23×C3112yes—
256#107—21no—
257#107—21no—
258#107C23×C3112yes—
259#107C23×C3112yes—
260#107C23×C3111yescharacteristic
261#107C23×C3111yescharacteristic
262#106—22no—
263#106—22no—
264#106—21no—
265#103—21no—
266#103—21no—
267#102—21no—
268#102—21no—
269C4×C8D4×C3111yescharacteristic
270C4×C8D4×C3111yescharacteristic
271C4×C8C23×C3111yescharacteristic
272C4×C8C23×C3111yescharacteristic
273C31#3379911yescharacteristic, direct product factor, Sylow
274C2×Q8—21no—
275C2×Q8—41no—
276C2×Q8—41no—
277C2×D4—21no—
278C2×D4—41no—
279C22×C4—41no—
280C22×C4D8×C3111yescharacteristic
281C22×C4D8×C3111yescharacteristic
282C22×C4C2×D4×C3111yescharacteristic
283Q16—21no—
284Q16—21no—
285SD16—42no—
286D8—21no—
287D8—21no—
288C2×C8—22no—
289C2×C8—21no—
290C2×C8—21no—
291C2×C8C2×D4×C3111yescharacteristic
292C2×C8C2×D4×C3111yescharacteristic
293C2×C8C2×D4×C3111yescharacteristic
294C2×C8C24×C3111yescharacteristic
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—22no—
298C4⋊C4—22no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—42no—
304C4⋊C4—42no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C22⋊C4—42no—
308C22⋊C4—41no—
309C22⋊C4—41no—
310C22⋊C4—41no—
311C22⋊C4—41no—
312C22⋊C4—41no—
313C42—42no—
314C42—41no—
315C42D8×C3111yescharacteristic
316C42D8×C3111yescharacteristic
317C42C2×D4×C3111yescharacteristic
318C42C2×D4×C3111yescharacteristic
319C16—22no—
320C16—22no—
321C23—41no—
322C23C2×D8×C3111yescharacteristic
323Q8—41no—
324Q8—41no—
325Q8—82no—
326Q8—82no—
327D4—41no—
328D4—41no—
329D4—82no—
330C2×C4—22no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—41no—
339C2×C4—82no—
340C2×C4C2×D8×C3111yescharacteristic
341C2×C4C2×D8×C3111yescharacteristic
342C2×C4C2×D8×C3111yescharacteristic
343C2×C4C2×D8×C3111yescharacteristic
344C2×C4C2×D8×C3111yescharacteristic
345C2×C4C22×D4×C3111yescharacteristic
346C8—21no—
347C8—21no—
348C8C31×#13712yes—
349C8C31×2−1+411yescharacteristic
350C8C31×2−1+411yescharacteristic
351C22—21no—
352C22—21no—
353C22—21no—
354C22—81no—
355C22—81no—
356C22—81no—
357C22C22×D8×C3111yescharacteristic
358C4—21no—
359C4—21no—
360C4—21no—
361C4—21no—
362C4—81no—
363C4—82no—
364C4—81no—
365C4—82no—
366C4—81no—
367C4C31×#50812yes—
368C4C31×#53611yescharacteristic
369C4C2×C31×#13711yescharacteristic
370C2—41no—
371C2—161no—
372C2C31×#322611yescharacteristic
373C2C2×C31×#50811yescharacteristic
374C2C31×#341411yescharacteristic
subgroupG/H
center, socleC22×C31C22×D8
commutator, Frattini, cosocleC2×C8C24×C31
prime radicalC31×#466C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ C2×C4×C8×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#3160C2semidirect
3. C31×#2253C2semidirect
4. C31×#2242C2semidirect
5. C31×#2237C2semidirect
7. C31×#2227C2semidirect
8. C31×#2226C2semidirect
9. C31×#2225C2semidirect
10. C31×#2224C2semidirect
11. C31×#2162C2semidirect
133. #33799C31direct (N × H)
165. #3160C2×C31semidirect
166. #2253C2×C31semidirect
167. #2242C2×C31semidirect
168. #2237C2×C31semidirect
170. #2227C2×C31semidirect
171. #2226C2×C31semidirect
172. #2225C2×C31semidirect
173. #2224C2×C31semidirect
174. #2162C2×C31semidirect
273. C31#33799direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#31682
C31×#31602
C31×#22532
C31×#22422
C31×#22372
C31×#22342
C31×#22272
C31×#22262
C31×#22252
C31×#22242
C31×#21622
#3379931