Finite Group Databasebeta

← C31×#19404 #21476163

Subgroups — C31×#19404 #21476163

Order 7936.

676 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3226C211yesmaximal, characteristic
2C31×#3037C211yesmaximal, characteristic
3C2×C31×#462C211yesmaximal, characteristic, complemented
4C31×#2982C211yesmaximal, characteristic, complemented
5C31×#1682C214yesmaximal, complemented
6C31×#1674C214yesmaximal, complemented
7C31×#1571C211yesmaximal, characteristic, complemented
8C31×#1546C211yesmaximal, characteristic, complemented
9C31×#1540C211yesmaximal, characteristic
10C2×C31×#137—21no—
11C22×Q16×C31—21no—
12C31×#532C2211yescharacteristic
13C2×C31×C4⋊Q8C2211yescharacteristic
14C2×C4×Q8×C31C2211yescharacteristic
15C31×#500C2212yes—
16C31×#486C2212yes—
17C31×#480—22no—
18C31×#474—22no—
19C31×#464—22no—
20C31×#462—22no—
21C31×#462C2212yes—
22C31×#462C2214yes—
23C31×#460C2212yes—
24C8×Q8×C31—22no—
25C8×Q8×C31C2214yes—
26C31×#431—22no—
27C31×#431C2211yescharacteristic
28C31×#431C2211yescharacteristic
29C31×#423C2211yescharacteristic
30C2×C31×C4⋊C8C2211yescharacteristic
31C31×#417—21no—
32C2×C31×#103—21no—
33C31×#335C2214yes—
34C31×#332C2212yes—
35C31×#332C2214yes—
36C31×#331C2212yes—
37C2×#41×C31—21no—
38C22×Q8×C31—21no—
39C22×Q8×C31D411yescharacteristic
40C31×#137—44no—
41C2×Q16×C31—24no—
42C2×Q16×C31—22no—
43C2×Q16×C31—44no—
44C2×SD16×C31—22no—
45C2×M16×C31—21no—
46C22×C8×C31—21no—
47C31×C4⋊Q8—21no—
48C31×C4⋊Q8—21no—
49C31×C4⋊Q8—21no—
50C31×C4⋊Q8C2312yes—
51C31×C4⋊Q8C2311yescharacteristic
52C31×#127C2311yescharacteristic
53C31×#124—21no—
54C31×#121—21no—
55C31×#121—21no—
56C4×Q8×C31—21no—
57C4×Q8×C31—21no—
58C4×Q8×C31D412yes—
59C4×Q8×C31C2312yes—
60C4×D4×C31—21no—
61C4×D4×C31—21no—
62C2×C4⋊C4×C31—21no—
63C2×C4⋊C4×C31—21no—
64C2×C4⋊C4×C31—21no—
65C2×C4⋊C4×C31D411yescharacteristic
66C2×C42×C31—21no—
67C2×C42×C31C2311yescharacteristic
68C31×#107—24no—
69C31×C4⋊C8—24no—
70C31×C4⋊C8—21no—
71C31×C4⋊C8—21no—
72C31×C4⋊C8D412yes—
73C31×C4⋊C8C2312yes—
74C31×C4⋊C8C2312yes—
75C31×C4⋊C8C2312yes—
76C31×#103—24no—
77C31×#103—22no—
78C31×#102—24no—
79C31×#102—22no—
80C31×C22⋊C8—21no—
81C31×C22⋊C8D412yes—
82C4×C8×C31—24no—
83C4×C8×C31—21no—
84C4×C8×C31C2312yes—
85#41×C31—42no—
86#41×C31—42no—
87C2×Q8×C31—21no—
88C2×Q8×C31—22no—
89C2×Q8×C31—21no—
90C2×Q8×C31—22no—
91C2×Q8×C31—41no—
92C2×Q8×C31—42no—
93C2×Q8×C31—42no—
94C2×Q8×C31D814yes—
95C2×Q8×C31C2×D412yes—
96C2×D4×C31—21no—
97C2×D4×C31—21no—
98C2×D4×C31—21no—
99C2×D4×C31—41no—
100C22×C4×C31—21no—
101C22×C4×C31—21no—
102C22×C4×C31—41no—
103C22×C4×C31—41no—
104C22×C4×C31C2×D411yescharacteristic
105C22×C4×C31C2×D411yescharacteristic
106C22×C4×C31#4111yescharacteristic
107Q16×C31—48no—
108Q16×C31—44no—
109SD16×C31—44no—
110M16×C31—42no—
111C2×C8×C31—22no—
112C2×C8×C31—22no—
113C2×C8×C31—22no—
114C2×C8×C31—42no—
115C2×C8×C31C2×D414yes—
116C4⋊C4×C31—22no—
117C4⋊C4×C31—21no—
118C4⋊C4×C31—22no—
119C4⋊C4×C31—22no—
120C4⋊C4×C31—21no—
121C4⋊C4×C31—22no—
122C4⋊C4×C31—21no—
123C4⋊C4×C31—41no—
124C4⋊C4×C31—41no—
125C4⋊C4×C31C2×D412yes—
126C22⋊C4×C31—41no—
127C22⋊C4×C31—41no—
128C42×C31—22no—
129C42×C31—22no—
130C42×C31C2×D411yescharacteristic
131C42×C31C2×D411yescharacteristic
132C42×C31#4111yescharacteristic
133C42×C31C2411yescharacteristic
134#19404C3111yesmaximal, characteristic, direct product factor, Sylow
135C23×C31—41no—
136C23×C31#12111yescharacteristic
137Q8×C31—22no—
138Q8×C31—24no—
139Q8×C31—42no—
140Q8×C31—41no—
141Q8×C31—42no—
142Q8×C31—41no—
143Q8×C31—82no—
144Q8×C31C2×D814yes—
145D4×C31—41no—
146D4×C31—41no—
147D4×C31—42no—
148D4×C31—81no—
149D4×C31—82no—
150C2×C4×C31—22no—
151C2×C4×C31—24no—
152C2×C4×C31—22no—
153C2×C4×C31—22no—
154C2×C4×C31—41no—
155C2×C4×C31—41no—
156C2×C4×C31—42no—
157C2×C4×C31—81no—
158C2×C4×C31—82no—
159C2×C4×C31—82no—
160C2×C4×C31#12111yescharacteristic
161C2×C4×C31#12111yescharacteristic
162C2×C4×C31#12111yescharacteristic
163C2×C4×C31C2×D812yes—
164C2×C4×C31#13512yes—
165C2×C4×C31C22×D411yescharacteristic
166C2×C4×C31C22×D411yescharacteristic
167C2×C4×C31C2×#4111yescharacteristic
168C8×C31—24no—
169C8×C31—42no—
170C8×C31—42no—
171C8×C31—42no—
172#3226C2×C3111yescharacteristic
173#3037C2×C3111yescharacteristic
174C2×#462C2×C3111yescharacteristic, complemented
175#2982C2×C3111yescharacteristic, complemented
176#1682C2×C3114yescomplemented
177#1674C2×C3114yescomplemented
178#1571C2×C3111yescharacteristic, complemented
179#1546C2×C3111yescharacteristic, complemented
180#1540C2×C3111yescharacteristic
181C22×C31—21no—
182C22×C31—21no—
183C22×C31—81no—
184C22×C31—81no—
185C22×C31—81no—
186C22×C31#46612yes—
187C22×C31C2×#12111yescharacteristic
188C4×C31—21no—
189C4×C31—24no—
190C4×C31—21no—
191C4×C31—21no—
192C4×C31—42no—
193C4×C31—81no—
194C4×C31—82no—
195C4×C31#46612yes—
196C4×C31C22×D811yescharacteristic
197C4×C31C2×#13511yescharacteristic
198C4×C31#57812yes—
199C2×#137—21no—
200C22×Q16—21no—
201#532C22×C3111yescharacteristic
202C2×C4⋊Q8C22×C3111yescharacteristic
203C2×C4×Q8C22×C3111yescharacteristic
204#500C22×C3112yes—
205#486C22×C3112yes—
206#480—22no—
207#474—22no—
208#464—22no—
209#462—22no—
210#462C22×C3112yes—
211#462C22×C3114yes—
212#460C22×C3112yes—
213C8×Q8—22no—
214C8×Q8C22×C3114yes—
215#431—22no—
216#431C22×C3111yescharacteristic
217#431C22×C3111yescharacteristic
218#423C22×C3111yescharacteristic
219C2×C4⋊C8C22×C3111yescharacteristic
220#417—21no—
221C2×#103—21no—
222#335C22×C3114yes—
223#332C22×C3112yes—
224#332C22×C3114yes—
225#331C22×C3112yes—
226C2×C31—22no—
227C2×C31—161no—
228C2×C31#304411yescharacteristic
229C2×C31C2×#46611yescharacteristic
230C2×C31#306911yescharacteristic
231C2×#41—21no—
232C22×Q8—21no—
233C22×Q8D4×C3111yescharacteristic
234#137—44no—
235C2×Q16—24no—
236C2×Q16—22no—
237C2×Q16—44no—
238C2×SD16—22no—
239C2×M16—21no—
240C22×C8—21no—
241C4⋊Q8—21no—
242C4⋊Q8—21no—
243C4⋊Q8—21no—
244C4⋊Q8C23×C3112yes—
245C4⋊Q8C23×C3111yescharacteristic
246#127C23×C3111yescharacteristic
247#124—21no—
248#121—21no—
249#121—21no—
250C4×Q8—21no—
251C4×Q8—21no—
252C4×Q8D4×C3112yes—
253C4×Q8C23×C3112yes—
254C4×D4—21no—
255C4×D4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4D4×C3111yescharacteristic
260C2×C42—21no—
261C2×C42C23×C3111yescharacteristic
262#107—24no—
263C4⋊C8—24no—
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8D4×C3112yes—
267C4⋊C8C23×C3112yes—
268C4⋊C8C23×C3112yes—
269C4⋊C8C23×C3112yes—
270#103—24no—
271#103—22no—
272#102—24no—
273#102—22no—
274C22⋊C8—21no—
275C22⋊C8D4×C3112yes—
276C4×C8—24no—
277C4×C8—21no—
278C4×C8C23×C3112yes—
279C31#1940411yescharacteristic, direct product factor, Sylow
280#41—42no—
281#41—42no—
282C2×Q8—21no—
283C2×Q8—22no—
284C2×Q8—21no—
285C2×Q8—22no—
286C2×Q8—41no—
287C2×Q8—42no—
288C2×Q8—42no—
289C2×Q8D8×C3114yes—
290C2×Q8C2×D4×C3112yes—
291C2×D4—21no—
292C2×D4—21no—
293C2×D4—21no—
294C2×D4—41no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—41no—
298C22×C4—41no—
299C22×C4C2×D4×C3111yescharacteristic
300C22×C4C2×D4×C3111yescharacteristic
301C22×C4#41×C3111yescharacteristic
302Q16—48no—
303Q16—44no—
304SD16—44no—
305M16—42no—
306C2×C8—22no—
307C2×C8—22no—
308C2×C8—22no—
309C2×C8—42no—
310C2×C8C2×D4×C3114yes—
311C4⋊C4—22no—
312C4⋊C4—21no—
313C4⋊C4—22no—
314C4⋊C4—22no—
315C4⋊C4—21no—
316C4⋊C4—22no—
317C4⋊C4—21no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4C2×D4×C3112yes—
321C22⋊C4—41no—
322C22⋊C4—41no—
323C42—22no—
324C42—22no—
325C42C2×D4×C3111yescharacteristic
326C42C2×D4×C3111yescharacteristic
327C42#41×C3111yescharacteristic
328C42C24×C3111yescharacteristic
329C23—41no—
330C23C31×#12111yescharacteristic
331Q8—24no—
332Q8—22no—
333Q8—42no—
334Q8—41no—
335Q8—42no—
336Q8—41no—
337Q8—82no—
338Q8C2×D8×C3114yes—
339D4—41no—
340D4—41no—
341D4—42no—
342D4—81no—
343D4—82no—
344C2×C4—24no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—42no—
351C2×C4—81no—
352C2×C4—82no—
353C2×C4—82no—
354C2×C4C31×#12111yescharacteristic
355C2×C4C31×#12111yescharacteristic
356C2×C4C31×#12111yescharacteristic
357C2×C4C2×D8×C3112yes—
358C2×C4C31×#13512yes—
359C2×C4C22×D4×C3111yescharacteristic
360C2×C4C22×D4×C3111yescharacteristic
361C2×C4C2×#41×C3111yescharacteristic
362C8—24no—
363C8—42no—
364C8—42no—
365C8—42no—
366C22—21no—
367C22—21no—
368C22—81no—
369C22—81no—
370C22—81no—
371C22C31×#46612yes—
372C22C2×C31×#12111yescharacteristic
373C4—21no—
374C4—24no—
375C4—21no—
376C4—21no—
377C4—42no—
378C4—81no—
379C4—82no—
380C4C31×#46612yes—
381C4C22×D8×C3111yescharacteristic
382C4C2×C31×#13511yescharacteristic
383C4C31×#57812yes—
384C2—22no—
385C2—161no—
386C2C31×#304411yescharacteristic
387C2C2×C31×#46611yescharacteristic
388C2C31×#306911yescharacteristic
subgroupG/H
center, socleC22×C31C2×#121
commutator, Frattini, cosocleC42C24×C31
prime radicalC31×#532C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C31×#462C2semidirect
4. C31×#2982C2semidirect
5. C31×#1682C2semidirect
6. C31×#1674C2semidirect
7. C31×#1571C2semidirect
8. C31×#1546C2semidirect
134. #19404C31direct (N × H)
174. C2×#462C2×C31semidirect
175. #2982C2×C31semidirect
176. #1682C2×C31semidirect
177. #1674C2×C31semidirect
178. #1571C2×C31semidirect
179. #1546C2×C31semidirect
279. C31#19404direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#32262
C31×#30372
C2×C31×#4622
C31×#29822
C31×#16822
C31×#16742
C31×#15712
C31×#15462
C31×#15402
#1940431