Finite Group Databasebeta

← C31×#13449 #21470208

Subgroups — C31×#13449 #21470208

Order 7936.

446 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×SD32C211yesmaximal, characteristic
2C2×C31×C4⋊C16C211yesmaximal, characteristic, complemented
3C2×C31×#358C211yesmaximal, characteristic, complemented
4C2×C31×#357C211yesmaximal, characteristic
5C31×#1970C211yesmaximal, characteristic
6C31×#1969C211yesmaximal, characteristic, complemented
7C31×#1380C211yesmaximal, characteristic, complemented
8C22×Q16×C31C2211yescharacteristic
9C22×D8×C31C2211yescharacteristic
10C2×C31×SD32—22no—
11C2×C31×SD32—22no—
12C2×C31×SD32—22no—
13C22×C16×C31C2211yescharacteristic
14C22×C16×C31C2211yescharacteristic
15C2×C31×#107C2211yescharacteristic
16C2×C31×#107C2211yescharacteristic
17C2×C31×#103—21no—
18C2×C31×#102—21no—
19C2×C4×C8×C31C2211yescharacteristic
20C31×#391—21no—
21C31×#390—21no—
22C31×C4⋊C16—22no—
23C31×#358—22no—
24C31×#357—22no—
25C22×Q8×C31—21no—
26C22×D4×C31—21no—
27C2×Q16×C31—21no—
28C2×Q16×C31—21no—
29C2×Q16×C31—21no—
30C2×Q16×C31—21no—
31C2×Q16×C31—21no—
32C2×Q16×C31D412yes—
33C2×D8×C31—21no—
34C2×D8×C31—21no—
35C2×D8×C31—21no—
36C2×D8×C31—21no—
37C2×D8×C31—21no—
38C2×D8×C31D412yes—
39C22×C8×C31D411yescharacteristic
40C22×C8×C31C2311yescharacteristic
41C2×C4⋊C4×C31—21no—
42C2×C4⋊C4×C31—21no—
43C2×C22⋊C4×C31—41no—
44C2×C22⋊C4×C31—41no—
45C2×C42×C31D411yescharacteristic
46C31×SD32—28no—
47C2×C16×C31—21no—
48C2×C16×C31—21no—
49C2×C16×C31—21no—
50C2×C16×C31—21no—
51C2×C16×C31—21no—
52C2×C16×C31D412yes—
53C31×#107—21no—
54C31×#107—21no—
55C31×#107—21no—
56C31×#107—21no—
57C31×#103—42no—
58C31×#102—42no—
59C4×C8×C31—21no—
60C4×C8×C31—21no—
61C31×#95—41no—
62C31×#95—41no—
63C24×C31—41no—
64C2×Q8×C31—22no—
65C2×Q8×C31—41no—
66C2×Q8×C31—41no—
67C2×Q8×C31—41no—
68C2×Q8×C31—41no—
69C2×Q8×C31—41no—
70C2×D4×C31—22no—
71C2×D4×C31—41no—
72C2×D4×C31—41no—
73C2×D4×C31—41no—
74C2×D4×C31—41no—
75C2×D4×C31—41no—
76C22×C4×C31—41no—
77C22×C4×C31—41no—
78C22×C4×C31—41no—
79C22×C4×C31D811yescharacteristic
80C22×C4×C31D811yescharacteristic
81C22×C4×C31C2×D411yescharacteristic
82Q16×C31—22no—
83Q16×C31—22no—
84Q16×C31—41no—
85Q16×C31—41no—
86D8×C31—22no—
87D8×C31—22no—
88D8×C31—41no—
89D8×C31—41no—
90C2×C8×C31—21no—
91C2×C8×C31—21no—
92C2×C8×C31—21no—
93C2×C8×C31C2×D411yescharacteristic
94C2×C8×C31C2×D411yescharacteristic
95C2×C8×C31C2×D411yescharacteristic
96C2×C8×C31#4111yescharacteristic
97C2×C8×C31#4111yescharacteristic
98C2×C8×C31#4111yescharacteristic
99C4⋊C4×C31—41no—
100C4⋊C4×C31—41no—
101C4⋊C4×C31—41no—
102C4⋊C4×C31—41no—
103C22⋊C4×C31—82no—
104C22⋊C4×C31—82no—
105C42×C31—21no—
106C42×C31—21no—
107C16×C31—22no—
108C16×C31—41no—
109#13449C3111yesmaximal, characteristic, direct product factor, Sylow
110C23×C31—42no—
111C23×C31—81no—
112C23×C31—81no—
113C23×C31—81no—
114C23×C31—81no—
115C23×C31—81no—
116C23×C31—81no—
117C23×C31C2×D811yescharacteristic
118Q8×C31—42no—
119Q8×C31—42no—
120Q8×C31—81no—
121Q8×C31—81no—
122D4×C31—42no—
123D4×C31—42no—
124D4×C31—81no—
125D4×C31—81no—
126C2×C4×C31—21no—
127C2×C4×C31—21no—
128C2×C4×C31—21no—
129C2×C4×C31—21no—
130C2×C4×C31—21no—
131C2×C4×C31—42no—
132C2×C4×C31—81no—
133C2×C4×C31—81no—
134C2×C4×C31—81no—
135C2×C4×C31—81no—
136C2×C4×C31—81no—
137C2×C4×C31—81no—
138C2×C4×C31—81no—
139C2×C4×C31—81no—
140C2×C4×C31SD3212yescomplemented
141C2×C4×C31#12111yescharacteristic
142C2×C4×C31#12111yescharacteristic
143C2×C4×C31#12111yescharacteristic
144C2×C4×C31#13511yescharacteristic
145C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
147C8×C31—41no—
148C8×C31#12011yescharacteristic
149C8×C31#12311yescharacteristic
150C8×C31#12311yescharacteristic
151C8×C31#12411yescharacteristic
152C22×SD32C2×C3111yescharacteristic
153C2×C4⋊C16C2×C3111yescharacteristic, complemented
154C2×#358C2×C3111yescharacteristic, complemented
155C2×#357C2×C3111yescharacteristic
156#1970C2×C3111yescharacteristic
157#1969C2×C3111yescharacteristic, complemented
158#1380C2×C3111yescharacteristic, complemented
159C22×C31—82no—
160C22×C31—82no—
161C22×C31—82no—
162C22×C31—161no—
163C22×C31—161no—
164C22×C31—161no—
165C22×C31—161no—
166C22×C31#45911yescharacteristic
167C22×C31#45911yescharacteristic
168C22×C31#46611yescharacteristic
169C22×C31C2×SD3211yescharacteristic
170C22×C31#50811yescharacteristic
171C22×C31#50911yescharacteristic
172C22×C31#51011yescharacteristic
173C4×C31—22no—
174C4×C31—41no—
175C4×C31—82no—
176C4×C31—161no—
177C4×C31—161no—
178C4×C31#39411yescharacteristic
179C4×C31#46311yescharacteristic
180C4×C31#46311yescharacteristic
181C4×C31#46911yescharacteristic
182C22×Q16C22×C3111yescharacteristic
183C22×D8C22×C3111yescharacteristic
184C2×SD32—22no—
185C2×SD32—22no—
186C2×SD32—22no—
187C22×C16C22×C3111yescharacteristic
188C22×C16C22×C3111yescharacteristic
189C2×#107C22×C3111yescharacteristic
190C2×#107C22×C3111yescharacteristic
191C2×#103—21no—
192C2×#102—21no—
193C2×C4×C8C22×C3111yescharacteristic
194#391—21no—
195#390—21no—
196C4⋊C16—22no—
197#358—22no—
198#357—22no—
199C2×C31—162no—
200C2×C31#205411yescharacteristic
201C2×C31#220711yescharacteristic
202C2×C31#220811yescharacteristic
203C2×C31#221011yescharacteristic
204C2×C31#221111yescharacteristic
205C2×C31#221711yescharacteristic
206C2×C31#222011yescharacteristic
207C22×Q8—21no—
208C22×D4—21no—
209C2×Q16—21no—
210C2×Q16—21no—
211C2×Q16—21no—
212C2×Q16—21no—
213C2×Q16—21no—
214C2×Q16D4×C3112yes—
215C2×D8—21no—
216C2×D8—21no—
217C2×D8—21no—
218C2×D8—21no—
219C2×D8—21no—
220C2×D8D4×C3112yes—
221C22×C8D4×C3111yescharacteristic
222C22×C8C23×C3111yescharacteristic
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C22⋊C4—41no—
226C2×C22⋊C4—41no—
227C2×C42D4×C3111yescharacteristic
228SD32—28no—
229C2×C16—21no—
230C2×C16—21no—
231C2×C16—21no—
232C2×C16—21no—
233C2×C16—21no—
234C2×C16D4×C3112yes—
235#107—21no—
236#107—21no—
237#107—21no—
238#107—21no—
239#103—42no—
240#102—42no—
241C4×C8—21no—
242C4×C8—21no—
243#95—41no—
244#95—41no—
245C31#1344911yescharacteristic, direct product factor, Sylow
246C24—41no—
247C2×Q8—22no—
248C2×Q8—41no—
249C2×Q8—41no—
250C2×Q8—41no—
251C2×Q8—41no—
252C2×Q8—41no—
253C2×D4—22no—
254C2×D4—41no—
255C2×D4—41no—
256C2×D4—41no—
257C2×D4—41no—
258C2×D4—41no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4D8×C3111yescharacteristic
263C22×C4D8×C3111yescharacteristic
264C22×C4C2×D4×C3111yescharacteristic
265Q16—22no—
266Q16—22no—
267Q16—41no—
268Q16—41no—
269D8—22no—
270D8—22no—
271D8—41no—
272D8—41no—
273C2×C8—21no—
274C2×C8—21no—
275C2×C8—21no—
276C2×C8C2×D4×C3111yescharacteristic
277C2×C8C2×D4×C3111yescharacteristic
278C2×C8C2×D4×C3111yescharacteristic
279C2×C8#41×C3111yescharacteristic
280C2×C8#41×C3111yescharacteristic
281C2×C8#41×C3111yescharacteristic
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C22⋊C4—82no—
287C22⋊C4—82no—
288C42—21no—
289C42—21no—
290C16—22no—
291C16—41no—
292C23—42no—
293C23—81no—
294C23—81no—
295C23—81no—
296C23—81no—
297C23—81no—
298C23—81no—
299C23C2×D8×C3111yescharacteristic
300Q8—42no—
301Q8—42no—
302Q8—81no—
303Q8—81no—
304D4—42no—
305D4—42no—
306D4—81no—
307D4—81no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—42no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4C31×SD3212yescomplemented
323C2×C4C31×#12111yescharacteristic
324C2×C4C31×#12111yescharacteristic
325C2×C4C31×#12111yescharacteristic
326C2×C4C31×#13511yescharacteristic
327C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
328C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
329C8—41no—
330C8C31×#12011yescharacteristic
331C8C31×#12311yescharacteristic
332C8C31×#12311yescharacteristic
333C8C31×#12411yescharacteristic
334C22—82no—
335C22—82no—
336C22—82no—
337C22—161no—
338C22—161no—
339C22—161no—
340C22—161no—
341C22C31×#45911yescharacteristic
342C22C31×#45911yescharacteristic
343C22C31×#46611yescharacteristic
344C22C2×C31×SD3211yescharacteristic
345C22C31×#50811yescharacteristic
346C22C31×#50911yescharacteristic
347C22C31×#51011yescharacteristic
348C4—22no—
349C4—41no—
350C4—82no—
351C4—161no—
352C4—161no—
353C4C31×#39411yescharacteristic
354C4C31×#46311yescharacteristic
355C4C31×#46311yescharacteristic
356C4C31×#46911yescharacteristic
357C2—162no—
358C2C31×#205411yescharacteristic
359C2C31×#220711yescharacteristic
360C2C31×#220811yescharacteristic
361C2C31×#221011yescharacteristic
362C2C31×#221111yescharacteristic
363C2C31×#221711yescharacteristic
364C2C31×#222011yescharacteristic
subgroupG/H
center, socleC23×C31C2×D8
commutator, Frattini, cosocleC22×C8C23×C31
prime radicalC22×D8×C31C22
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×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×C4⋊C16C2semidirect
3. C2×C31×#358C2semidirect
6. C31×#1969C2semidirect
7. C31×#1380C2semidirect
109. #13449C31direct (N × H)
140. C2×C4×C31SD32semidirect
153. C2×C4⋊C16C2×C31semidirect
154. C2×#358C2×C31semidirect
157. #1969C2×C31semidirect
158. #1380C2×C31semidirect
245. C31#13449direct (N × H)
322. C2×C4C31×SD32semidirect

Maximal subgroups

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

subgroupindex
C22×C31×SD322
C2×C31×C4⋊C162
C2×C31×#3582
C2×C31×#3572
C31×#19702
C31×#19692
C31×#13802
#1344931