Finite Group Databasebeta

← C31×#9269 #21466028

Subgroups — C31×#9269 #21466028

Order 7936.

480 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×#3227C211yesmaximal, characteristic
2C31×#2935C211yesmaximal, characteristic
3C31×#1997C211yesmaximal, characteristic, complemented
4C31×#1547C211yesmaximal, characteristic
5C2×C31×#332C211yesmaximal, characteristic, complemented
6C31×#1301C211yesmaximal, characteristic, complemented
7C31×#1283C211yesmaximal, characteristic, complemented
8C2×C31×#131—21no—
9C31×#532C2211yescharacteristic
10C2×C31×C4⋊Q8C2211yescharacteristic
11C31×#498—21no—
12C31×#486—21no—
13C31×#481C414yes—
14C31×#476—22no—
15C31×#436—21no—
16C31×#435—22no—
17C8×D4×C31—21no—
18C31×#431C2211yescharacteristic
19C31×#423C2211yescharacteristic
20C2×C31×C4⋊C8C2211yescharacteristic
21C2×C31×C4⋊C8C2211yescharacteristic
22C31×#408—21no—
23C4×M16×C31C2211yescharacteristic
24C31×#343—21no—
25C31×#343—21no—
26C31×#332—21no—
27C31×#332—21no—
28C31×#332—21no—
29C31×#331—21no—
30C2×#41×C31—21no—
31C22×Q8×C31—21no—
32C31×#131—42no—
33C31×#131—42no—
34C2×M16×C31—22no—
35C2×M16×C31—21no—
36C2×M16×C31D411yescharacteristic
37C2×M16×C31D411yescharacteristic
38C22×C8×C31—22no—
39C22×C8×C31—21no—
40C22×C8×C31—21no—
41C31×C4⋊Q8—21no—
42C31×C4⋊Q8—21no—
43C31×C4⋊Q8—21no—
44C31×C4⋊Q8—21no—
45C31×C4⋊Q8D411yescharacteristic
46C31×#127D411yescharacteristic
47C31×#124—21no—
48C31×#121—21no—
49C31×#121C2×C412yes—
50C4×D4×C31—21no—
51C4×D4×C31D412yes—
52C2×C4⋊C4×C31—21no—
53C2×C4⋊C4×C31C2×C412yes—
54C2×C42×C31C2311yescharacteristic
55C31×#106—24no—
56C31×C4⋊C8—21no—
57C31×C4⋊C8—21no—
58C31×C4⋊C8—21no—
59C31×C4⋊C8—21no—
60C31×C4⋊C8—21no—
61C31×C4⋊C8—21no—
62C31×C4⋊C8D411yescharacteristic
63C31×C4⋊C8D411yescharacteristic
64C31×#102—24no—
65C31×C22⋊C8—22no—
66C31×C22⋊C8—22no—
67C31×C22⋊C8C2×C412yes—
68C31×#97—21no—
69C4×C8×C31—21no—
70C4×C8×C31—21no—
71#41×C31—41no—
72#41×C31—41no—
73#41×C31—41no—
74#41×C31—41no—
75C2×Q8×C31—21no—
76C2×Q8×C31—41no—
77C2×Q8×C31—41no—
78C2×Q8×C31—81no—
79C2×Q8×C31—81no—
80C2×D4×C31—22no—
81C2×D4×C31—21no—
82C2×D4×C31—21no—
83C2×D4×C31C22⋊C412yes—
84C22×C4×C31—22no—
85C22×C4×C31—22no—
86C22×C4×C31C22×C411yescharacteristic
87C22×C4×C31C2×D411yescharacteristic
88C22×C4×C31#4111yescharacteristic
89M16×C31—21no—
90M16×C31—21no—
91M16×C31—21no—
92M16×C31—44no—
93M16×C31—41no—
94M16×C31—41no—
95M16×C31SD1612yes—
96C2×C8×C31—21no—
97C2×C8×C31—22no—
98C2×C8×C31—21no—
99C2×C8×C31—21no—
100C2×C8×C31—21no—
101C2×C8×C31—44no—
102C2×C8×C31—41no—
103C2×C8×C31—41no—
104C2×C8×C31—41no—
105C2×C8×C31—41no—
106C2×C8×C31—81no—
107C4⋊C4×C31—21no—
108C4⋊C4×C31—22no—
109C4⋊C4×C31—22no—
110C4⋊C4×C31—41no—
111C4⋊C4×C31—41no—
112C4⋊C4×C31C22⋊C412yes—
113C22⋊C4×C31—22no—
114C22⋊C4×C31—22no—
115C42×C31C2×D411yescharacteristic
116C42×C31C2×D411yescharacteristic
117C42×C31C2×D411yescharacteristic
118C42×C31#4111yescharacteristic
119#9269C3111yesmaximal, characteristic, direct product factor, Sylow
120C23×C31—22no—
121C23×C31C4×D411yescharacteristic
122Q8×C31—41no—
123Q8×C31—41no—
124Q8×C31—82no—
125Q8×C31—81no—
126Q8×C31—81no—
127D4×C31—42no—
128D4×C31—42no—
129D4×C31—42no—
130D4×C31—41no—
131D4×C31—41no—
132D4×C31—41no—
133D4×C31—41no—
134C2×C4×C31—21no—
135C2×C4×C31—21no—
136C2×C4×C31—22no—
137C2×C4×C31—41no—
138C2×C4×C31—42no—
139C2×C4×C31—42no—
140C2×C4×C31—42no—
141C2×C4×C31—82no—
142C2×C4×C31C2×C22⋊C411yescharacteristic
143C2×C4×C31C4×D411yescharacteristic
144C2×C4×C31#12011yescharacteristic
145C2×C4×C31#12111yescharacteristic
146C2×C4×C31#12111yescharacteristic
147C2×C4×C31#12311yescharacteristic
148C2×C4×C31C2×SD1611yescharacteristic
149C2×C4×C31#13511yescharacteristic
150C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C31#13711yescharacteristic
152C8×C31—22no—
153C8×C31—42no—
154C8×C31—41no—
155C8×C31—41no—
156C8×C31—41no—
157C8×C31—81no—
158C8×C31—81no—
159#3227C2×C3111yescharacteristic
160#2935C2×C3111yescharacteristic
161#1997C2×C3111yescharacteristic, complemented
162#1547C2×C3111yescharacteristic
163C2×#332C2×C3111yescharacteristic, complemented
164#1301C2×C3111yescharacteristic, complemented
165#1283C2×C3111yescharacteristic, complemented
166C22×C31—21no—
167C22×C31—21no—
168C22×C31—42no—
169C22×C31—42no—
170C22×C31—42no—
171C22×C31#38611yescharacteristic
172C22×C31C4×SD1611yescharacteristic
173C22×C31#44011yescharacteristic
174C4×C31—21no—
175C4×C31—21no—
176C4×C31—21no—
177C4×C31—42no—
178C4×C31—82no—
179C4×C31#45011yescharacteristic
180C4×C31#45211yescharacteristic
181C4×C31#46111yescharacteristic
182C4×C31#46311yescharacteristic
183C4×C31#47111yescharacteristic
184C4×C31#47211yescharacteristic
185C2×#131—21no—
186#532C22×C3111yescharacteristic
187C2×C4⋊Q8C22×C3111yescharacteristic
188#498—21no—
189#486—21no—
190#481C4×C3114yes—
191#476—22no—
192#436—21no—
193#435—22no—
194C8×D4—21no—
195#431C22×C3111yescharacteristic
196#423C22×C3111yescharacteristic
197C2×C4⋊C8C22×C3111yescharacteristic
198C2×C4⋊C8C22×C3111yescharacteristic
199#408—21no—
200C4×M16C22×C3111yescharacteristic
201#343—21no—
202#343—21no—
203#332—21no—
204#332—21no—
205#332—21no—
206#331—21no—
207C2×C31—21no—
208C2×C31—21no—
209C2×C31—82no—
210C2×C31#187711yescharacteristic
211C2×C31#190711yescharacteristic
212C2×C31#191511yescharacteristic
213C2×#41—21no—
214C22×Q8—21no—
215#131—42no—
216#131—42no—
217C2×M16—22no—
218C2×M16—21no—
219C2×M16D4×C3111yescharacteristic
220C2×M16D4×C3111yescharacteristic
221C22×C8—22no—
222C22×C8—21no—
223C22×C8—21no—
224C4⋊Q8—21no—
225C4⋊Q8—21no—
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8D4×C3111yescharacteristic
229#127D4×C3111yescharacteristic
230#124—21no—
231#121—21no—
232#121C2×C4×C3112yes—
233C4×D4—21no—
234C4×D4D4×C3112yes—
235C2×C4⋊C4—21no—
236C2×C4⋊C4C2×C4×C3112yes—
237C2×C42C23×C3111yescharacteristic
238#106—24no—
239C4⋊C8—21no—
240C4⋊C8—21no—
241C4⋊C8—21no—
242C4⋊C8—21no—
243C4⋊C8—21no—
244C4⋊C8—21no—
245C4⋊C8D4×C3111yescharacteristic
246C4⋊C8D4×C3111yescharacteristic
247#102—24no—
248C22⋊C8—22no—
249C22⋊C8—22no—
250C22⋊C8C2×C4×C3112yes—
251#97—21no—
252C4×C8—21no—
253C4×C8—21no—
254C31#926911yescharacteristic, direct product factor, Sylow
255#41—41no—
256#41—41no—
257#41—41no—
258#41—41no—
259C2×Q8—21no—
260C2×Q8—41no—
261C2×Q8—41no—
262C2×Q8—81no—
263C2×Q8—81no—
264C2×D4—22no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4C22⋊C4×C3112yes—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4C22×C4×C3111yescharacteristic
271C22×C4C2×D4×C3111yescharacteristic
272C22×C4#41×C3111yescharacteristic
273M16—21no—
274M16—21no—
275M16—21no—
276M16—44no—
277M16—41no—
278M16—41no—
279M16SD16×C3112yes—
280C2×C8—21no—
281C2×C8—22no—
282C2×C8—21no—
283C2×C8—21no—
284C2×C8—21no—
285C2×C8—44no—
286C2×C8—41no—
287C2×C8—41no—
288C2×C8—41no—
289C2×C8—41no—
290C2×C8—81no—
291C4⋊C4—21no—
292C4⋊C4—22no—
293C4⋊C4—22no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4C22⋊C4×C3112yes—
297C22⋊C4—22no—
298C22⋊C4—22no—
299C42C2×D4×C3111yescharacteristic
300C42C2×D4×C3111yescharacteristic
301C42C2×D4×C3111yescharacteristic
302C42#41×C3111yescharacteristic
303C23—22no—
304C23C4×D4×C3111yescharacteristic
305Q8—41no—
306Q8—41no—
307Q8—82no—
308Q8—81no—
309Q8—81no—
310D4—42no—
311D4—42no—
312D4—42no—
313D4—41no—
314D4—41no—
315D4—41no—
316D4—41no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—22no—
320C2×C4—41no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—82no—
325C2×C4C2×C22⋊C4×C3111yescharacteristic
326C2×C4C4×D4×C3111yescharacteristic
327C2×C4C31×#12011yescharacteristic
328C2×C4C31×#12111yescharacteristic
329C2×C4C31×#12111yescharacteristic
330C2×C4C31×#12311yescharacteristic
331C2×C4C2×SD16×C3111yescharacteristic
332C2×C4C31×#13511yescharacteristic
333C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
334C2×C4C31×#13711yescharacteristic
335C8—22no—
336C8—42no—
337C8—41no—
338C8—41no—
339C8—41no—
340C8—81no—
341C8—81no—
342C22—21no—
343C22—21no—
344C22—42no—
345C22—42no—
346C22—42no—
347C22C31×#38611yescharacteristic
348C22C4×SD16×C3111yescharacteristic
349C22C31×#44011yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—42no—
354C4—82no—
355C4C31×#45011yescharacteristic
356C4C31×#45211yescharacteristic
357C4C31×#46111yescharacteristic
358C4C31×#46311yescharacteristic
359C4C31×#47111yescharacteristic
360C4C31×#47211yescharacteristic
361C2—21no—
362C2—21no—
363C2—82no—
364C2C31×#187711yescharacteristic
365C2C31×#190711yescharacteristic
366C2C31×#191511yescharacteristic
subgroupG/H
center, socleC22×C31#386
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC31×#532C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
3. C31×#1997C2semidirect
5. C2×C31×#332C2semidirect
6. C31×#1301C2semidirect
7. C31×#1283C2semidirect
119. #9269C31direct (N × H)
161. #1997C2×C31semidirect
163. C2×#332C2×C31semidirect
164. #1301C2×C31semidirect
165. #1283C2×C31semidirect
254. C31#9269direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#32272
C31×#29352
C31×#19972
C31×#15472
C2×C31×#3322
C31×#13012
C31×#12832
#926931