Finite Group Databasebeta

← C31×#10186 #21466945

Subgroups — C31×#10186 #21466945

Order 7936.

528 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3229C211yesmaximal, characteristic, complemented
2C31×#3077C211yesmaximal, characteristic
3C2×C31×#461C211yesmaximal, characteristic
4C31×#1546C211yesmaximal, characteristic, complemented
5C31×#1481C211yesmaximal, characteristic, complemented
6C31×#1460C211yesmaximal, characteristic
7C31×#1301C211yesmaximal, characteristic, complemented
8C22×SD16×C31—21no—
9C31×#533C2211yescharacteristic
10C2×C31×C4⋊Q8C2211yescharacteristic
11C2×C4×D4×C31C2211yescharacteristic
12C31×#498—21no—
13C31×#487—21no—
14C31×#483—22no—
15C31×#478—22no—
16C31×#476—21no—
17C31×#475—22no—
18C31×#474—21no—
19C31×#461—22no—
20C31×#461—22no—
21C31×#431C2211yescharacteristic
22C31×#431C2211yescharacteristic
23C31×#428—21no—
24C31×#423C2211yescharacteristic
25C2×C31×C4⋊C8C2211yescharacteristic
26C31×#418—21no—
27C2×C31×#103—21no—
28C31×#332—22no—
29C31×Q8⋊C8—22no—
30C31×#323—22no—
31C22×Q8×C31—21no—
32C22×D4×C31D411yescharacteristic
33C23×C4×C31—21no—
34C2×SD16×C31—24no—
35C2×SD16×C31—42no—
36C2×SD16×C31—42no—
37C2×M16×C31—21no—
38C22×C8×C31—21no—
39C31×C4⋊Q8—21no—
40C31×C4⋊Q8—21no—
41C31×C4⋊Q8—21no—
42C31×C4⋊Q8D412yes—
43C31×C4⋊Q8D411yescharacteristic
44C31×C4⋊Q8D411yescharacteristic
45C31×#125—21no—
46C31×C22⋊Q8—21no—
47C31×C22⋊Q8—21no—
48C4×Q8×C31—21no—
49C4×Q8×C31—21no—
50C4×D4×C31—21no—
51C4×D4×C31—21no—
52C4×D4×C31—21no—
53C4×D4×C31—21no—
54C31×#117—21no—
55C2×C4⋊C4×C31—21no—
56C2×C4⋊C4×C31—21no—
57C2×C4⋊C4×C31D411yescharacteristic
58C2×C22⋊C4×C31—21no—
59C2×C42×C31C2311yescharacteristic
60C31×#107—22no—
61C31×#106—22no—
62C31×#106—24no—
63C31×C4⋊C8—21no—
64C31×C4⋊C8—21no—
65C31×C4⋊C8—21no—
66C31×C4⋊C8—21no—
67C31×C4⋊C8D412yes—
68C31×C4⋊C8D412yes—
69C31×#103—24no—
70C31×#103—24no—
71C31×#102—22no—
72C31×#102—22no—
73C31×C22⋊C8—21no—
74C31×C22⋊C8D412yes—
75C4×C8×C31—21no—
76C4×C8×C31—21no—
77C24×C31—21no—
78C2×Q8×C31—21no—
79C2×Q8×C31—22no—
80C2×Q8×C31—21no—
81C2×Q8×C31—41no—
82C2×Q8×C31—41no—
83C2×Q8×C31—41no—
84C2×Q8×C31—41no—
85C2×Q8×C31—41no—
86C2×D4×C31—21no—
87C2×D4×C31—21no—
88C2×D4×C31—21no—
89C2×D4×C31—21no—
90C2×D4×C31—21no—
91C2×D4×C31SD1612yes—
92C22×C4×C31—21no—
93C22×C4×C31—41no—
94C22×C4×C31—41no—
95C22×C4×C31—41no—
96C22×C4×C31—82no—
97C22×C4×C31C2×D411yescharacteristic
98C22×C4×C31C2×D411yescharacteristic
99C22×C4×C31#4111yescharacteristic
100SD16×C31—48no—
101M16×C31—41no—
102M16×C31—41no—
103C2×C8×C31—22no—
104C2×C8×C31—22no—
105C2×C8×C31—22no—
106C2×C8×C31—41no—
107C2×C8×C31—41no—
108C2×C8×C31—41no—
109C4⋊C4×C31—21no—
110C4⋊C4×C31—21no—
111C4⋊C4×C31—21no—
112C4⋊C4×C31—22no—
113C4⋊C4×C31—21no—
114C4⋊C4×C31—21no—
115C4⋊C4×C31—22no—
116C4⋊C4×C31—21no—
117C4⋊C4×C31—41no—
118C4⋊C4×C31—41no—
119C4⋊C4×C31—41no—
120C4⋊C4×C31—41no—
121C22⋊C4×C31—41no—
122C22⋊C4×C31—41no—
123C22⋊C4×C31—41no—
124C42×C31—41no—
125C42×C31C2×D411yescharacteristic
126C42×C31C2×D411yescharacteristic
127C42×C31C2×D411yescharacteristic
128C42×C31C2×D411yescharacteristic
129#10186C3111yesmaximal, characteristic, direct product factor, Sylow
130C23×C31—22no—
131C23×C31—41no—
132C23×C31—41no—
133C23×C31—81no—
134C23×C31—81no—
135C23×C31#12111yescharacteristic
136Q8×C31—42no—
137Q8×C31—42no—
138Q8×C31—42no—
139Q8×C31—42no—
140Q8×C31—81no—
141Q8×C31—81no—
142D4×C31—22no—
143D4×C31—22no—
144D4×C31—41no—
145D4×C31—41no—
146C2×C4×C31—22no—
147C2×C4×C31—41no—
148C2×C4×C31—41no—
149C2×C4×C31—41no—
150C2×C4×C31—41no—
151C2×C4×C31—42no—
152C2×C4×C31—82no—
153C2×C4×C31—81no—
154C2×C4×C31—81no—
155C2×C4×C31—82no—
156C2×C4×C31—81no—
157C2×C4×C31#12011yescharacteristic
158C2×C4×C31#12011yescharacteristic
159C2×C4×C31#12011yescharacteristic
160C2×C4×C31#12111yescharacteristic
161C2×C4×C31#12111yescharacteristic
162C2×C4×C31#12711yescharacteristic
163C2×C4×C31C2×SD1611yescharacteristic
164C2×C4×C31#13511yescharacteristic
165C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
166C2×C4×C31#13711yescharacteristic
167C8×C31—42no—
168C8×C31—42no—
169C8×C31—42no—
170C8×C31—81no—
171#3229C2×C3111yescharacteristic, complemented
172#3077C2×C3111yescharacteristic
173C2×#461C2×C3111yescharacteristic
174#1546C2×C3111yescharacteristic, complemented
175#1481C2×C3111yescharacteristic, complemented
176#1460C2×C3111yescharacteristic
177#1301C2×C3111yescharacteristic, complemented
178C22×C31—21no—
179C22×C31—21no—
180C22×C31—42no—
181C22×C31—82no—
182C22×C31—82no—
183C22×C31—81no—
184C22×C31—81no—
185C22×C31#39211yescharacteristic
186C22×C31#46511yescharacteristic
187C22×C31#46811yescharacteristic
188C4×C31—21no—
189C4×C31—21no—
190C4×C31—21no—
191C4×C31—82no—
192C4×C31—81no—
193C4×C31—81no—
194C4×C31—81no—
195C4×C31#44811yescharacteristic
196C4×C31#44911yescharacteristic
197C4×C31#45011yescharacteristic
198C4×C31#45211yescharacteristic
199C4×C31#47112yes—
200C22×SD16—21no—
201#533C22×C3111yescharacteristic
202C2×C4⋊Q8C22×C3111yescharacteristic
203C2×C4×D4C22×C3111yescharacteristic
204#498—21no—
205#487—21no—
206#483—22no—
207#478—22no—
208#476—21no—
209#475—22no—
210#474—21no—
211#461—22no—
212#461—22no—
213#431C22×C3111yescharacteristic
214#431C22×C3111yescharacteristic
215#428—21no—
216#423C22×C3111yescharacteristic
217C2×C4⋊C8C22×C3111yescharacteristic
218#418—21no—
219C2×#103—21no—
220#332—22no—
221Q8⋊C8—22no—
222#323—22no—
223C2×C31—21no—
224C2×C31—21no—
225C2×C31—82no—
226C2×C31#200011yescharacteristic
227C2×C31#200911yescharacteristic
228C2×C31#201911yescharacteristic
229C22×Q8—21no—
230C22×D4D4×C3111yescharacteristic
231C23×C4—21no—
232C2×SD16—24no—
233C2×SD16—42no—
234C2×SD16—42no—
235C2×M16—21no—
236C22×C8—21no—
237C4⋊Q8—21no—
238C4⋊Q8—21no—
239C4⋊Q8—21no—
240C4⋊Q8D4×C3112yes—
241C4⋊Q8D4×C3111yescharacteristic
242C4⋊Q8D4×C3111yescharacteristic
243#125—21no—
244C22⋊Q8—21no—
245C22⋊Q8—21no—
246C4×Q8—21no—
247C4×Q8—21no—
248C4×D4—21no—
249C4×D4—21no—
250C4×D4—21no—
251C4×D4—21no—
252#117—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4D4×C3111yescharacteristic
256C2×C22⋊C4—21no—
257C2×C42C23×C3111yescharacteristic
258#107—22no—
259#106—22no—
260#106—24no—
261C4⋊C8—21no—
262C4⋊C8—21no—
263C4⋊C8—21no—
264C4⋊C8—21no—
265C4⋊C8D4×C3112yes—
266C4⋊C8D4×C3112yes—
267#103—24no—
268#103—24no—
269#102—22no—
270#102—22no—
271C22⋊C8—21no—
272C22⋊C8D4×C3112yes—
273C4×C8—21no—
274C4×C8—21no—
275C31#1018611yescharacteristic, direct product factor, Sylow
276C24—21no—
277C2×Q8—21no—
278C2×Q8—22no—
279C2×Q8—21no—
280C2×Q8—41no—
281C2×Q8—41no—
282C2×Q8—41no—
283C2×Q8—41no—
284C2×Q8—41no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—21no—
289C2×D4—21no—
290C2×D4SD16×C3112yes—
291C22×C4—21no—
292C22×C4—41no—
293C22×C4—41no—
294C22×C4—41no—
295C22×C4—82no—
296C22×C4C2×D4×C3111yescharacteristic
297C22×C4C2×D4×C3111yescharacteristic
298C22×C4#41×C3111yescharacteristic
299SD16—48no—
300M16—41no—
301M16—41no—
302C2×C8—22no—
303C2×C8—22no—
304C2×C8—22no—
305C2×C8—41no—
306C2×C8—41no—
307C2×C8—41no—
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—22no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—22no—
315C4⋊C4—21no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C22⋊C4—41no—
321C22⋊C4—41no—
322C22⋊C4—41no—
323C42—41no—
324C42C2×D4×C3111yescharacteristic
325C42C2×D4×C3111yescharacteristic
326C42C2×D4×C3111yescharacteristic
327C42C2×D4×C3111yescharacteristic
328C23—22no—
329C23—41no—
330C23—41no—
331C23—81no—
332C23—81no—
333C23C31×#12111yescharacteristic
334Q8—42no—
335Q8—42no—
336Q8—42no—
337Q8—42no—
338Q8—81no—
339Q8—81no—
340D4—22no—
341D4—22no—
342D4—41no—
343D4—41no—
344C2×C4—22no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—42no—
350C2×C4—82no—
351C2×C4—81no—
352C2×C4—81no—
353C2×C4—82no—
354C2×C4—81no—
355C2×C4C31×#12011yescharacteristic
356C2×C4C31×#12011yescharacteristic
357C2×C4C31×#12011yescharacteristic
358C2×C4C31×#12111yescharacteristic
359C2×C4C31×#12111yescharacteristic
360C2×C4C31×#12711yescharacteristic
361C2×C4C2×SD16×C3111yescharacteristic
362C2×C4C31×#13511yescharacteristic
363C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
364C2×C4C31×#13711yescharacteristic
365C8—42no—
366C8—42no—
367C8—42no—
368C8—81no—
369C22—21no—
370C22—21no—
371C22—42no—
372C22—82no—
373C22—82no—
374C22—81no—
375C22—81no—
376C22C31×#39211yescharacteristic
377C22C31×#46511yescharacteristic
378C22C31×#46811yescharacteristic
379C4—21no—
380C4—21no—
381C4—21no—
382C4—82no—
383C4—81no—
384C4—81no—
385C4—81no—
386C4C31×#44811yescharacteristic
387C4C31×#44911yescharacteristic
388C4C31×#45011yescharacteristic
389C4C31×#45211yescharacteristic
390C4C31×#47112yes—
391C2—21no—
392C2—21no—
393C2—82no—
394C2C31×#200011yescharacteristic
395C2C31×#200911yescharacteristic
396C2C31×#201911yescharacteristic
subgroupG/H
center, socleC22×C31#392
commutator, Frattini, cosocleC2×C42C23×C31
prime radicalC22×D4×C31D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#3229C2semidirect
4. C31×#1546C2semidirect
5. C31×#1481C2semidirect
7. C31×#1301C2semidirect
129. #10186C31direct (N × H)
171. #3229C2×C31semidirect
174. #1546C2×C31semidirect
175. #1481C2×C31semidirect
177. #1301C2×C31semidirect
275. C31#10186direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#32292
C31×#30772
C2×C31×#4612
C31×#15462
C31×#14812
C31×#14602
C31×#13012
#1018631