Finite Group Databasebeta

← C31×#13421 #21470180

Subgroups — C31×#13421 #21470180

Order 7936.

496 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2724C211yesmaximal, characteristic
2C2×C31×#352C212yesmaximal
3C31×#1890C212yesmaximal
4C31×#1856C211yesmaximal, characteristic
5C31×#1393C211yesmaximal, characteristic
6C2×C31×#123C2212yes—
7C31×#518C2211yescharacteristic
8C31×#428—21no—
9C2×C31×#100C2211yescharacteristic
10C2×C31×#99C2212yes—
11C31×#398—21no—
12C31×#397—22no—
13C31×#390C2211yescharacteristic
14C31×#389—21no—
15C31×#385—22no—
16C31×#381—22no—
17C31×#352—24no—
18C31×#342—22no—
19C31×#339—21no—
20C22×D4×C31C2311yescharacteristic
21C23×C4×C31D412yes—
22C2×M16×C31—21no—
23C31×#123—22no—
24C31×#123—22no—
25C31×#123—22no—
26C31×#123—22no—
27C4×D4×C31—41no—
28C4×D4×C31—41no—
29C31×#117—21no—
30C2×C4⋊C4×C31—21no—
31C2×C4⋊C4×C31—22no—
32C2×C4⋊C4×C31—21no—
33C2×C4⋊C4×C31—21no—
34C2×C4⋊C4×C31D411yescharacteristic
35C2×C22⋊C4×C31—22no—
36C2×C22⋊C4×C31—22no—
37C2×C22⋊C4×C31—22no—
38C2×C22⋊C4×C31—22no—
39C2×C22⋊C4×C31D412yes—
40C2×C42×C31D411yescharacteristic
41C31×#107—41no—
42C31×#106—41no—
43C31×#100—21no—
44C31×#100D412yes—
45C31×#99—22no—
46C31×#99—22no—
47C31×#95—21no—
48C31×#95—22no—
49C31×#95—22no—
50C31×#95—42no—
51C31×#95—42no—
52C24×C31C2×D412yes—
53C2×D4×C31—41no—
54C2×D4×C31—41no—
55C2×D4×C31C2×D411yescharacteristic
56C2×D4×C31#4111yescharacteristic
57C2×D4×C31#4112yes—
58C22×C4×C31—21no—
59C22×C4×C31—21no—
60C22×C4×C31—22no—
61C22×C4×C31—22no—
62C22×C4×C31—22no—
63C22×C4×C31—22no—
64C22×C4×C31—22no—
65C22×C4×C31—22no—
66C22×C4×C31—42no—
67C22×C4×C31—42no—
68C22×C4×C31—42no—
69C22×C4×C31C2×D411yescharacteristic
70M16×C31—22no—
71M16×C31—41no—
72C2×C8×C31—41no—
73C4⋊C4×C31—21no—
74C4⋊C4×C31—21no—
75C4⋊C4×C31—42no—
76C4⋊C4×C31—41no—
77C4⋊C4×C31—42no—
78C4⋊C4×C31—42no—
79C4⋊C4×C31—81no—
80C4⋊C4×C31—81no—
81C22⋊C4×C31—22no—
82C22⋊C4×C31—22no—
83C22⋊C4×C31—44no—
84C22⋊C4×C31—42no—
85C22⋊C4×C31—41no—
86C22⋊C4×C31—42no—
87C22⋊C4×C31—42no—
88C22⋊C4×C31—42no—
89C22⋊C4×C31—42no—
90C42×C31—41no—
91C42×C31—41no—
92#13421C3111yesmaximal, characteristic, direct product factor, Sylow
93C23×C31—22no—
94C23×C31—22no—
95C23×C31—42no—
96C23×C31—42no—
97C23×C31#12011yescharacteristic
98C23×C31#12112yes—
99C23×C31#12312yes—
100D4×C31—41no—
101D4×C31—41no—
102D4×C31—42no—
103C2×C4×C31—21no—
104C2×C4×C31—21no—
105C2×C4×C31—22no—
106C2×C4×C31—41no—
107C2×C4×C31—41no—
108C2×C4×C31—42no—
109C2×C4×C31—42no—
110C2×C4×C31—42no—
111C2×C4×C31—44no—
112C2×C4×C31—42no—
113C2×C4×C31—42no—
114C2×C4×C31—41no—
115C2×C4×C31—41no—
116C2×C4×C31—41no—
117C2×C4×C31—42no—
118C2×C4×C31—42no—
119C2×C4×C31—82no—
120C2×C4×C31—82no—
121C2×C4×C31—82no—
122C2×C4×C31—82no—
123C2×C4×C31—82no—
124C2×C4×C31—82no—
125C2×C4×C31#12111yescharacteristic
126C2×C4×C31#12411yescharacteristic
127C8×C31—42no—
128#2724C2×C3111yescharacteristic
129C2×#352C2×C3112yes—
130#1890C2×C3112yes—
131#1856C2×C3111yescharacteristic
132#1393C2×C3111yescharacteristic
133C22×C31—21no—
134C22×C31—21no—
135C22×C31—22no—
136C22×C31—22no—
137C22×C31—42no—
138C22×C31—42no—
139C22×C31—42no—
140C22×C31—42no—
141C22×C31—82no—
142C22×C31#39411yescharacteristic
143C22×C31B(4,𝔽2)11yescharacteristic
144C22×C31#45811yescharacteristic
145C4×C31—21no—
146C4×C31—21no—
147C4×C31—42no—
148C4×C31—82no—
149C4×C31—81no—
150C4×C31—81no—
151C4×C31—81no—
152C4×C31—82no—
153C4×C31—162no—
154C2×#123C22×C3112yes—
155#518C22×C3111yescharacteristic
156#428—21no—
157C2×#100C22×C3111yescharacteristic
158C2×#99C22×C3112yes—
159#398—21no—
160#397—22no—
161#390C22×C3111yescharacteristic
162#389—21no—
163#385—22no—
164#381—22no—
165#352—24no—
166#342—22no—
167#339—21no—
168C2×C31—21no—
169C2×C31—21no—
170C2×C31—42no—
171C2×C31—42no—
172C2×C31#204411yescharacteristic
173C2×C31#219811yescharacteristic
174C2×C31#220111yescharacteristic
175C22×D4C23×C3111yescharacteristic
176C23×C4D4×C3112yes—
177C2×M16—21no—
178#123—22no—
179#123—22no—
180#123—22no—
181#123—22no—
182C4×D4—41no—
183C4×D4—41no—
184#117—21no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—22no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4D4×C3111yescharacteristic
190C2×C22⋊C4—22no—
191C2×C22⋊C4—22no—
192C2×C22⋊C4—22no—
193C2×C22⋊C4—22no—
194C2×C22⋊C4D4×C3112yes—
195C2×C42D4×C3111yescharacteristic
196#107—41no—
197#106—41no—
198#100—21no—
199#100D4×C3112yes—
200#99—22no—
201#99—22no—
202#95—22no—
203#95—22no—
204#95—21no—
205#95—42no—
206#95—42no—
207C31#1342111yescharacteristic, direct product factor, Sylow
208C24C2×D4×C3112yes—
209C2×D4—41no—
210C2×D4—41no—
211C2×D4C2×D4×C3111yescharacteristic
212C2×D4#41×C3111yescharacteristic
213C2×D4#41×C3112yes—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—22no—
221C22×C4—22no—
222C22×C4—42no—
223C22×C4—42no—
224C22×C4—42no—
225C22×C4C2×D4×C3111yescharacteristic
226M16—22no—
227M16—41no—
228C2×C8—41no—
229C4⋊C4—21no—
230C4⋊C4—21no—
231C4⋊C4—41no—
232C4⋊C4—42no—
233C4⋊C4—42no—
234C4⋊C4—42no—
235C4⋊C4—81no—
236C4⋊C4—81no—
237C22⋊C4—22no—
238C22⋊C4—22no—
239C22⋊C4—44no—
240C22⋊C4—42no—
241C22⋊C4—41no—
242C22⋊C4—42no—
243C22⋊C4—42no—
244C22⋊C4—42no—
245C22⋊C4—42no—
246C42—41no—
247C42—41no—
248C23—22no—
249C23—22no—
250C23—42no—
251C23—42no—
252C23C31×#12011yescharacteristic
253C23C31×#12112yes—
254C23C31×#12312yes—
255D4—41no—
256D4—41no—
257D4—42no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—22no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—44no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—82no—
275C2×C4—82no—
276C2×C4—82no—
277C2×C4—82no—
278C2×C4—82no—
279C2×C4—82no—
280C2×C4C31×#12111yescharacteristic
281C2×C4C31×#12411yescharacteristic
282C8—42no—
283C22—21no—
284C22—21no—
285C22—22no—
286C22—22no—
287C22—42no—
288C22—42no—
289C22—42no—
290C22—42no—
291C22—82no—
292C22C31×#39411yescharacteristic
293C22C31×B(4,𝔽2)11yescharacteristic
294C22C31×#45811yescharacteristic
295C4—21no—
296C4—21no—
297C4—42no—
298C4—82no—
299C4—81no—
300C4—81no—
301C4—81no—
302C4—82no—
303C4—162no—
304C2—21no—
305C2—21no—
306C2—42no—
307C2—42no—
308C2C31×#204411yescharacteristic
309C2C31×#219811yescharacteristic
310C2C31×#220111yescharacteristic
subgroupG/H
center, socleC22×C31B(4,𝔽2)
commutator, Frattini, cosocleC22×D4C23×C31
prime radicalC22×D4×C31C23
LCSG ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C31 ◁ C22×D4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
92. #13421C31direct (N × H)
207. C31#13421direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#27242
C2×C31×#3522
C31×#18902
C31×#18562
C31×#13932
#1342131