Finite Group Databasebeta

← C31×#10190 #21466949

Subgroups — C31×#10190 #21466949

Order 7936.

496 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3230C211yesmaximal, characteristic, complemented
2C31×#3077C211yesmaximal, characteristic
3C2×C31×#474C211yesmaximal, characteristic
4C31×#1548C211yesmaximal, characteristic, complemented
5C31×#1481C211yesmaximal, characteristic, complemented
6C31×#1460C211yesmaximal, characteristic
7C31×#1301C211yesmaximal, characteristic, complemented
8C31×#533C2211yescharacteristic
9C2×C31×C4⋊Q8C2211yescharacteristic
10C2×C4×D4×C31C2211yescharacteristic
11C31×#500—21no—
12C31×#487—21no—
13C31×#484—22no—
14C31×#478—22no—
15C31×#477—22no—
16C31×#476—21no—
17C31×#474—21no—
18C31×#474—22no—
19C31×#474—22no—
20C31×#431C2211yescharacteristic
21C31×#431C2211yescharacteristic
22C31×#428—21no—
23C2×C31×#107—21no—
24C31×#423C2211yescharacteristic
25C2×C31×C4⋊C8C2211yescharacteristic
26C31×#418—21no—
27C2×C31×#102—21no—
28C31×#333—22no—
29C31×Q8⋊C8—22no—
30C31×#323—22no—
31C22×Q8×C31—21no—
32C22×D4×C31D411yescharacteristic
33C23×C4×C31—21no—
34C2×M16×C31—21no—
35C22×C8×C31—21no—
36C31×C4⋊Q8—21no—
37C31×C4⋊Q8—21no—
38C31×C4⋊Q8—21no—
39C31×C4⋊Q8D412yes—
40C31×C4⋊Q8D411yescharacteristic
41C31×C4⋊Q8D411yescharacteristic
42C31×#125—21no—
43C31×C22⋊Q8—21no—
44C31×C22⋊Q8—21no—
45C4×Q8×C31—21no—
46C4×Q8×C31—21no—
47C4×D4×C31—21no—
48C4×D4×C31—21no—
49C4×D4×C31—21no—
50C4×D4×C31—21no—
51C31×#117—21no—
52C2×C4⋊C4×C31—21no—
53C2×C4⋊C4×C31—21no—
54C2×C4⋊C4×C31D411yescharacteristic
55C2×C22⋊C4×C31—21no—
56C2×C42×C31C2311yescharacteristic
57C31×#107—24no—
58C31×#107—22no—
59C31×#107—24no—
60C31×#106—22no—
61C31×C4⋊C8—21no—
62C31×C4⋊C8—21no—
63C31×C4⋊C8—21no—
64C31×C4⋊C8—21no—
65C31×C4⋊C8D412yes—
66C31×C4⋊C8D412yes—
67C31×#103—24no—
68C31×#102—24no—
69C31×#102—22no—
70C31×#102—22no—
71C31×C22⋊C8—21no—
72C31×C22⋊C8D412yes—
73C4×C8×C31—21no—
74C4×C8×C31—21no—
75C24×C31—21no—
76C2×Q8×C31—21no—
77C2×Q8×C31—21no—
78C2×Q8×C31—22no—
79C2×Q8×C31—41no—
80C2×Q8×C31—82no—
81C2×D4×C31—21no—
82C2×D4×C31—21no—
83C2×D4×C31—21no—
84C2×D4×C31—21no—
85C2×D4×C31—21no—
86C2×D4×C31Q1612yes—
87C22×C4×C31—21no—
88C22×C4×C31—41no—
89C22×C4×C31—41no—
90C22×C4×C31—41no—
91C22×C4×C31—82no—
92C22×C4×C31C2×D411yescharacteristic
93C22×C4×C31C2×D411yescharacteristic
94C22×C4×C31#4111yescharacteristic
95M16×C31—41no—
96M16×C31—41no—
97C2×C8×C31—22no—
98C2×C8×C31—22no—
99C2×C8×C31—22no—
100C2×C8×C31—41no—
101C2×C8×C31—41no—
102C2×C8×C31—41no—
103C4⋊C4×C31—21no—
104C4⋊C4×C31—22no—
105C4⋊C4×C31—21no—
106C4⋊C4×C31—22no—
107C4⋊C4×C31—21no—
108C4⋊C4×C31—21no—
109C4⋊C4×C31—21no—
110C4⋊C4×C31—21no—
111C4⋊C4×C31—41no—
112C4⋊C4×C31—41no—
113C4⋊C4×C31—41no—
114C4⋊C4×C31—41no—
115C22⋊C4×C31—41no—
116C22⋊C4×C31—41no—
117C22⋊C4×C31—41no—
118C42×C31—41no—
119C42×C31C2×D411yescharacteristic
120C42×C31C2×D411yescharacteristic
121C42×C31C2×D411yescharacteristic
122C42×C31C2×D411yescharacteristic
123#10190C3111yesmaximal, characteristic, direct product factor, Sylow
124C23×C31—22no—
125C23×C31—41no—
126C23×C31—41no—
127C23×C31—81no—
128C23×C31—81no—
129C23×C31#12111yescharacteristic
130Q8×C31—42no—
131Q8×C31—42no—
132Q8×C31—82no—
133Q8×C31—82no—
134D4×C31—22no—
135D4×C31—22no—
136D4×C31—41no—
137D4×C31—41no—
138C2×C4×C31—22no—
139C2×C4×C31—41no—
140C2×C4×C31—41no—
141C2×C4×C31—41no—
142C2×C4×C31—41no—
143C2×C4×C31—42no—
144C2×C4×C31—82no—
145C2×C4×C31—82no—
146C2×C4×C31—82no—
147C2×C4×C31—81no—
148C2×C4×C31#12011yescharacteristic
149C2×C4×C31#12011yescharacteristic
150C2×C4×C31#12011yescharacteristic
151C2×C4×C31#12111yescharacteristic
152C2×C4×C31#12111yescharacteristic
153C2×C4×C31#12711yescharacteristic
154C2×C4×C31C2×Q1611yescharacteristic
155C2×C4×C31#13511yescharacteristic
156C2×C4×C31#13711yescharacteristic
157C2×C4×C31#13711yescharacteristic
158C8×C31—42no—
159C8×C31—42no—
160C8×C31—42no—
161C8×C31—81no—
162#3230C2×C3111yescharacteristic, complemented
163#3077C2×C3111yescharacteristic
164C2×#474C2×C3111yescharacteristic
165#1548C2×C3111yescharacteristic, complemented
166#1481C2×C3111yescharacteristic, complemented
167#1460C2×C3111yescharacteristic
168#1301C2×C3111yescharacteristic, complemented
169C22×C31—21no—
170C22×C31—21no—
171C22×C31—42no—
172C22×C31—82no—
173C22×C31—82no—
174C22×C31—81no—
175C22×C31—81no—
176C22×C31#39211yescharacteristic
177C22×C31#46711yescharacteristic
178C22×C31#47011yescharacteristic
179C4×C31—21no—
180C4×C31—21no—
181C4×C31—21no—
182C4×C31—81no—
183C4×C31—81no—
184C4×C31—82no—
185C4×C31—81no—
186C4×C31#45111yescharacteristic
187C4×C31#45111yescharacteristic
188C4×C31#45211yescharacteristic
189C4×C31#45211yescharacteristic
190C4×C31#47212yes—
191#533C22×C3111yescharacteristic
192C2×C4⋊Q8C22×C3111yescharacteristic
193C2×C4×D4C22×C3111yescharacteristic
194#500—21no—
195#487—21no—
196#484—22no—
197#478—22no—
198#477—22no—
199#476—21no—
200#474—21no—
201#474—22no—
202#474—22no—
203#431C22×C3111yescharacteristic
204#431C22×C3111yescharacteristic
205#428—21no—
206C2×#107—21no—
207#423C22×C3111yescharacteristic
208C2×C4⋊C8C22×C3111yescharacteristic
209#418—21no—
210C2×#102—21no—
211#333—22no—
212Q8⋊C8—22no—
213#323—22no—
214C2×C31—21no—
215C2×C31—21no—
216C2×C31—82no—
217C2×C31#200111yescharacteristic
218C2×C31#200911yescharacteristic
219C2×C31#201811yescharacteristic
220C22×Q8—21no—
221C22×D4D4×C3111yescharacteristic
222C23×C4—21no—
223C2×M16—21no—
224C22×C8—21no—
225C4⋊Q8—21no—
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8D4×C3112yes—
229C4⋊Q8D4×C3111yescharacteristic
230C4⋊Q8D4×C3111yescharacteristic
231#125—21no—
232C22⋊Q8—21no—
233C22⋊Q8—21no—
234C4×Q8—21no—
235C4×Q8—21no—
236C4×D4—21no—
237C4×D4—21no—
238C4×D4—21no—
239C4×D4—21no—
240#117—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4D4×C3111yescharacteristic
244C2×C22⋊C4—21no—
245C2×C42C23×C3111yescharacteristic
246#107—24no—
247#107—22no—
248#107—24no—
249#106—22no—
250C4⋊C8—21no—
251C4⋊C8—21no—
252C4⋊C8—21no—
253C4⋊C8—21no—
254C4⋊C8D4×C3112yes—
255C4⋊C8D4×C3112yes—
256#103—24no—
257#102—24no—
258#102—22no—
259#102—22no—
260C22⋊C8—21no—
261C22⋊C8D4×C3112yes—
262C4×C8—21no—
263C4×C8—21no—
264C31#1019011yescharacteristic, direct product factor, Sylow
265C24—21no—
266C2×Q8—21no—
267C2×Q8—21no—
268C2×Q8—22no—
269C2×Q8—41no—
270C2×Q8—82no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4—21no—
276C2×D4Q16×C3112yes—
277C22×C4—21no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4—82no—
282C22×C4C2×D4×C3111yescharacteristic
283C22×C4C2×D4×C3111yescharacteristic
284C22×C4#41×C3111yescharacteristic
285M16—41no—
286M16—41no—
287C2×C8—22no—
288C2×C8—22no—
289C2×C8—22no—
290C2×C8—41no—
291C2×C8—41no—
292C2×C8—41no—
293C4⋊C4—21no—
294C4⋊C4—22no—
295C4⋊C4—21no—
296C4⋊C4—22no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C22⋊C4—41no—
306C22⋊C4—41no—
307C22⋊C4—41no—
308C42—41no—
309C42C2×D4×C3111yescharacteristic
310C42C2×D4×C3111yescharacteristic
311C42C2×D4×C3111yescharacteristic
312C42C2×D4×C3111yescharacteristic
313C23—22no—
314C23—41no—
315C23—41no—
316C23—81no—
317C23—81no—
318C23C31×#12111yescharacteristic
319Q8—42no—
320Q8—42no—
321Q8—82no—
322Q8—82no—
323D4—22no—
324D4—22no—
325D4—41no—
326D4—41no—
327C2×C4—22no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—42no—
333C2×C4—82no—
334C2×C4—82no—
335C2×C4—82no—
336C2×C4—81no—
337C2×C4C31×#12011yescharacteristic
338C2×C4C31×#12011yescharacteristic
339C2×C4C31×#12011yescharacteristic
340C2×C4C31×#12111yescharacteristic
341C2×C4C31×#12111yescharacteristic
342C2×C4C31×#12711yescharacteristic
343C2×C4C2×Q16×C3111yescharacteristic
344C2×C4C31×#13511yescharacteristic
345C2×C4C31×#13711yescharacteristic
346C2×C4C31×#13711yescharacteristic
347C8—42no—
348C8—42no—
349C8—42no—
350C8—81no—
351C22—21no—
352C22—21no—
353C22—42no—
354C22—82no—
355C22—82no—
356C22—81no—
357C22—81no—
358C22C31×#39211yescharacteristic
359C22C31×#46711yescharacteristic
360C22C31×#47011yescharacteristic
361C4—21no—
362C4—21no—
363C4—21no—
364C4—81no—
365C4—81no—
366C4—82no—
367C4—81no—
368C4C31×#45111yescharacteristic
369C4C31×#45111yescharacteristic
370C4C31×#45211yescharacteristic
371C4C31×#45211yescharacteristic
372C4C31×#47212yes—
373C2—21no—
374C2—21no—
375C2—82no—
376C2C31×#200111yescharacteristic
377C2C31×#200911yescharacteristic
378C2C31×#201811yescharacteristic
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×#3230C2semidirect
4. C31×#1548C2semidirect
5. C31×#1481C2semidirect
7. C31×#1301C2semidirect
123. #10190C31direct (N × H)
162. #3230C2×C31semidirect
165. #1548C2×C31semidirect
166. #1481C2×C31semidirect
168. #1301C2×C31semidirect
264. C31#10190direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#32302
C31×#30772
C2×C31×#4742
C31×#15482
C31×#14812
C31×#14602
C31×#13012
#1019031