Finite Group Databasebeta

← C31×#33798 #21490557

Subgroups — C31×#33798 #21490557

Order 7936.

468 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3168C211yesmaximal, characteristic
2C2×C31×#499C211yesmaximal, characteristic, complemented
3C31×#2253C212yesmaximal, complemented
4C31×#2242C212yesmaximal, complemented
5C31×#2236C211yesmaximal, characteristic, complemented
6C31×#2235C211yesmaximal, characteristic, complemented
7C31×#2233C211yesmaximal, characteristic
8C31×#2232C211yesmaximal, characteristic
9C31×#2229C212yesmaximal, complemented
10C31×#2228C212yesmaximal, complemented
11C31×#2162C211yesmaximal, characteristic, complemented
12C31×#529—21no—
13C2×C31×#125—21no—
14C31×#499—21no—
15C31×#499—21no—
16C31×#499C2212yes—
17C31×#499C2212yes—
18C31×#499C2211yescharacteristic
19C31×#495C2211yescharacteristic
20C31×#488—21no—
21C31×#467C2211yescharacteristic
22C31×#466C2211yescharacteristic
23C31×#465—21no—
24C4×Q16×C31C2211yescharacteristic
25C4×SD16×C31—21no—
26C4×D8×C31C2211yescharacteristic
27C2×C31×#107C2211yescharacteristic
28C2×C31×#107C2211yescharacteristic
29C2×C31×#106—21no—
30C2×C4×C8×C31C2211yescharacteristic
31C31×#367C2212yes—
32C31×#367C2212yes—
33C31×#366C2212yes—
34C31×#366C2212yes—
35C31×C4⋊C16C2212yes—
36C31×#358C2212yes—
37C31×#358C2212yes—
38C31×#357C2212yes—
39C31×#357C2212yes—
40C31×C22⋊C16C2211yescharacteristic
41C31×C22⋊C16C2211yescharacteristic
42C4×C16×C31C2212yes—
43C2×Q16×C31C2311yescharacteristic
44C2×SD16×C31—21no—
45C2×D8×C31C2311yescharacteristic
46C22×C8×C31D411yescharacteristic
47C22×C8×C31C2311yescharacteristic
48C31×#126—41no—
49C31×#125—21no—
50C31×#125—22no—
51C31×#125—22no—
52C31×#125—41no—
53C31×#125—41no—
54C31×#124—21no—
55C31×#123—41no—
56C31×C22⋊Q8—21no—
57C31×#121—21no—
58C4×Q8×C31—21no—
59C4×D4×C31—21no—
60C4×D4×C31—41no—
61C31×#117—41no—
62C2×C4⋊C4×C31—21no—
63C2×C4⋊C4×C31—21no—
64C2×C4⋊C4×C31—41no—
65C2×C4⋊C4×C31—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×D4×C31—21no—
88C2×D4×C31—41no—
89C22×C4×C31—41no—
90C22×C4×C31—41no—
91C22×C4×C31—41no—
92C22×C4×C31D811yescharacteristic
93C22×C4×C31D811yescharacteristic
94C22×C4×C31C2×D411yescharacteristic
95Q16×C31—22no—
96SD16×C31—42no—
97D8×C31—22no—
98C2×C8×C31—22no—
99C2×C8×C31—22no—
100C2×C8×C31C2×D411yescharacteristic
101C2×C8×C31C2×D411yescharacteristic
102C2×C8×C31C2×D411yescharacteristic
103C2×C8×C31C2411yescharacteristic
104C4⋊C4×C31—21no—
105C4⋊C4×C31—21no—
106C4⋊C4×C31—22no—
107C4⋊C4×C31—22no—
108C4⋊C4×C31—41no—
109C4⋊C4×C31—41no—
110C4⋊C4×C31—42no—
111C4⋊C4×C31—42no—
112C4⋊C4×C31—42no—
113C4⋊C4×C31—42no—
114C4⋊C4×C31—41no—
115C4⋊C4×C31—41no—
116C4⋊C4×C31—41no—
117C4⋊C4×C31—41no—
118C22⋊C4×C31—41no—
119C22⋊C4×C31—41no—
120C22⋊C4×C31—41no—
121C22⋊C4×C31—41no—
122C22⋊C4×C31—41no—
123C42×C31—41no—
124C42×C31D811yescharacteristic
125C42×C31D811yescharacteristic
126C42×C31C2×D411yescharacteristic
127C42×C31C2×D411yescharacteristic
128C16×C31—22no—
129C16×C31—22no—
130#33798C3111yesmaximal, characteristic, direct product factor, Sylow
131C23×C31—41no—
132C23×C31C2×D811yescharacteristic
133Q8×C31—41no—
134Q8×C31—41no—
135D4×C31—41no—
136D4×C31—41no—
137D4×C31—82no—
138C2×C4×C31—22no—
139C2×C4×C31—21no—
140C2×C4×C31—21no—
141C2×C4×C31—41no—
142C2×C4×C31—41no—
143C2×C4×C31—41no—
144C2×C4×C31—41no—
145C2×C4×C31—42no—
146C2×C4×C31—42no—
147C2×C4×C31—82no—
148C2×C4×C31—82no—
149C2×C4×C31—82no—
150C2×C4×C31C2×D811yescharacteristic
151C2×C4×C31C2×D811yescharacteristic
152C2×C4×C31C2×D811yescharacteristic
153C2×C4×C31C2×D811yescharacteristic
154C2×C4×C31C2×D811yescharacteristic
155C2×C4×C31C22×D411yescharacteristic
156C8×C31—21no—
157C8×C31—21no—
158C8×C31#13712yes—
159C8×C312−1+412yes—
160#3168C2×C3111yescharacteristic
161C2×#499C2×C3111yescharacteristic, complemented
162#2253C2×C3112yescomplemented
163#2242C2×C3112yescomplemented
164#2236C2×C3111yescharacteristic, complemented
165#2235C2×C3111yescharacteristic, complemented
166#2233C2×C3111yescharacteristic
167#2232C2×C3111yescharacteristic
168#2229C2×C3112yescomplemented
169#2228C2×C3112yescomplemented
170#2162C2×C3111yescharacteristic, complemented
171C22×C31—21no—
172C22×C31—21no—
173C22×C31—81no—
174C22×C31—81no—
175C22×C31—81no—
176C22×C31#50812yes—
177C22×C31C22×D811yescharacteristic
178C4×C31—21no—
179C4×C31—21no—
180C4×C31—21no—
181C4×C31—21no—
182C4×C31—21no—
183C4×C31—82no—
184C4×C31—81no—
185C4×C31—81no—
186C4×C31—82no—
187C4×C31—81no—
188C4×C31#53611yescharacteristic
189C4×C31C2×#13711yescharacteristic
190#529—21no—
191C2×#125—21no—
192#499—21no—
193#499—21no—
194#499C22×C3112yes—
195#499C22×C3112yes—
196#499C22×C3111yescharacteristic
197#495C22×C3111yescharacteristic
198#488—21no—
199#467C22×C3111yescharacteristic
200#466C22×C3111yescharacteristic
201#465—21no—
202C4×Q16C22×C3111yescharacteristic
203C4×SD16—21no—
204C4×D8C22×C3111yescharacteristic
205C2×#107C22×C3111yescharacteristic
206C2×#107C22×C3111yescharacteristic
207C2×#106—21no—
208C2×C4×C8C22×C3111yescharacteristic
209#367C22×C3112yes—
210#367C22×C3112yes—
211#366C22×C3112yes—
212#366C22×C3112yes—
213C4⋊C16C22×C3112yes—
214#358C22×C3112yes—
215#358C22×C3112yes—
216#357C22×C3112yes—
217#357C22×C3112yes—
218C22⋊C16C22×C3111yescharacteristic
219C22⋊C16C22×C3111yescharacteristic
220C4×C16C22×C3112yes—
221C2×C31—22no—
222C2×C31—161no—
223C2×C31#322611yescharacteristic
224C2×C31C2×#50811yescharacteristic
225C2×C31#341411yescharacteristic
226C2×Q16C23×C3111yescharacteristic
227C2×SD16—21no—
228C2×D8C23×C3111yescharacteristic
229C22×C8D4×C3111yescharacteristic
230C22×C8C23×C3111yescharacteristic
231#126—41no—
232#125—22no—
233#125—22no—
234#125—21no—
235#125—41no—
236#125—41no—
237#124—21no—
238#123—41no—
239C22⋊Q8—21no—
240#121—21no—
241C4×Q8—21no—
242C4×D4—21no—
243C4×D4—41no—
244#117—41no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—41no—
248C2×C4⋊C4—41no—
249C2×C42D4×C3111yescharacteristic
250C2×C16C23×C3112yes—
251C2×C16C23×C3112yes—
252#107—21no—
253#107—21no—
254#107C23×C3112yes—
255#107C23×C3112yes—
256#107C23×C3111yescharacteristic
257#107C23×C3111yescharacteristic
258#106—22no—
259#106—22no—
260#106—21no—
261#103—21no—
262#103—21no—
263#102—21no—
264#102—21no—
265C4×C8D4×C3111yescharacteristic
266C4×C8D4×C3111yescharacteristic
267C4×C8C23×C3111yescharacteristic
268C4×C8C23×C3111yescharacteristic
269C31#3379811yescharacteristic, direct product factor, Sylow
270C2×Q8—21no—
271C2×D4—21no—
272C2×D4—41no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4D8×C3111yescharacteristic
277C22×C4D8×C3111yescharacteristic
278C22×C4C2×D4×C3111yescharacteristic
279Q16—22no—
280SD16—42no—
281D8—22no—
282C2×C8—22no—
283C2×C8—22no—
284C2×C8C2×D4×C3111yescharacteristic
285C2×C8C2×D4×C3111yescharacteristic
286C2×C8C2×D4×C3111yescharacteristic
287C2×C8C24×C3111yescharacteristic
288C4⋊C4—21no—
289C4⋊C4—21no—
290C4⋊C4—22no—
291C4⋊C4—22no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—42no—
295C4⋊C4—42no—
296C4⋊C4—42no—
297C4⋊C4—42no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C22⋊C4—41no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C22⋊C4—41no—
307C42—41no—
308C42D8×C3111yescharacteristic
309C42D8×C3111yescharacteristic
310C42C2×D4×C3111yescharacteristic
311C42C2×D4×C3111yescharacteristic
312C16—22no—
313C16—22no—
314C23—41no—
315C23C2×D8×C3111yescharacteristic
316Q8—41no—
317Q8—41no—
318D4—41no—
319D4—41no—
320D4—82no—
321C2×C4—22no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—82no—
331C2×C4—82no—
332C2×C4—82no—
333C2×C4C2×D8×C3111yescharacteristic
334C2×C4C2×D8×C3111yescharacteristic
335C2×C4C2×D8×C3111yescharacteristic
336C2×C4C2×D8×C3111yescharacteristic
337C2×C4C2×D8×C3111yescharacteristic
338C2×C4C22×D4×C3111yescharacteristic
339C8—21no—
340C8—21no—
341C8C31×#13712yes—
342C8C31×2−1+412yes—
343C22—21no—
344C22—21no—
345C22—81no—
346C22—81no—
347C22—81no—
348C22C31×#50812yes—
349C22C22×D8×C3111yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—21no—
355C4—82no—
356C4—81no—
357C4—81no—
358C4—82no—
359C4—81no—
360C4C31×#53611yescharacteristic
361C4C2×C31×#13711yescharacteristic
362C2—22no—
363C2—161no—
364C2C31×#322611yescharacteristic
365C2C2×C31×#50811yescharacteristic
366C2C31×#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. C2×C31×#499C2semidirect
3. C31×#2253C2semidirect
4. C31×#2242C2semidirect
5. C31×#2236C2semidirect
6. C31×#2235C2semidirect
9. C31×#2229C2semidirect
10. C31×#2228C2semidirect
11. C31×#2162C2semidirect
130. #33798C31direct (N × H)
161. C2×#499C2×C31semidirect
162. #2253C2×C31semidirect
163. #2242C2×C31semidirect
164. #2236C2×C31semidirect
165. #2235C2×C31semidirect
168. #2229C2×C31semidirect
169. #2228C2×C31semidirect
170. #2162C2×C31semidirect
269. C31#33798direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#31682
C2×C31×#4992
C31×#22532
C31×#22422
C31×#22362
C31×#22352
C31×#22332
C31×#22322
C31×#22292
C31×#22282
C31×#21622
#3379831