Finite Group Databasebeta

← C31×#13352 #21470111

Subgroups — C31×#13352 #21470111

Order 7936.

682 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 682 conjugacy classes of subgroups — too many to draw. Only its 94 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×#3202C211yesmaximal, characteristic, complemented
2C31×#3028C212yesmaximal
3C31×#2129C212yesmaximal, complemented
4C31×#1794C211yesmaximal, characteristic
5C31×#1391C211yesmaximal, characteristic, complemented
6C31×#585C2211yescharacteristic
7C31×#536—22no—
8C31×#536C2212yes—
9C31×#485—22no—
10C31×#470—21no—
11C31×#467—21no—
12C31×#458—24no—
13C31×#458—24no—
14C31×#451—22no—
15C31×#421—21no—
16C31×#416—21no—
17C31×#410—22no—
18C31×#410C2211yescharacteristic
19C31×#410C2212yes—
20C31×#408C2211yescharacteristic
21C31×#354—24no—
22C31×2−1+4—21no—
23C31×2−1+4—41no—
24C31×H(5,𝔽2)—22no—
25C31×H(5,𝔽2)—41no—
26C31×H(5,𝔽2)D412yes—
27C2×#41×C31—22no—
28C2×#41×C31—21no—
29C2×#41×C31—42no—
30C2×#41×C31C2311yescharacteristic
31C22×Q8×C31D412yes—
32C2×Q16×C31—21no—
33C2×Q16×C31—21no—
34C2×M16×C31D411yescharacteristic
35C22×C8×C31D411yescharacteristic
36C31×C4⋊Q8—22no—
37C31×C4⋊Q8—42no—
38C31×#124—22no—
39C31×#124—42no—
40C31×#123—28no—
41C31×#123—22no—
42C31×#123—22no—
43C31×C22⋊Q8—22no—
44C31×C22⋊Q8—22no—
45C31×C22⋊Q8—44no—
46C31×#117—22no—
47C31×#117—21no—
48C31×#117D412yes—
49C31×#107—21no—
50C31×#106—21no—
51C31×#104—42no—
52C31×#103—22no—
53C31×#103—22no—
54C31×#103—41no—
55C31×#102—41no—
56C31×#99—28no—
57C31×#99—22no—
58C31×#99—22no—
59C31×#99D414yes—
60C31×C22⋊C8—22no—
61#41×C31—22no—
62#41×C31—22no—
63#41×C31—41no—
64#41×C31—41no—
65#41×C31—42no—
66#41×C31—42no—
67#41×C31—42no—
68#41×C31—41no—
69#41×C31—44no—
70#41×C31—42no—
71#41×C31—41no—
72#41×C31—42no—
73C2×Q8×C31—22no—
74C2×Q8×C31—21no—
75C2×Q8×C31—22no—
76C2×Q8×C31—22no—
77C2×Q8×C31—42no—
78C2×Q8×C31—42no—
79C2×Q8×C31—42no—
80C2×Q8×C31#4111yescharacteristic
81C2×D4×C31—21no—
82C2×D4×C31—22no—
83C2×D4×C31—24no—
84C2×D4×C31—42no—
85C2×D4×C31—44no—
86C2×D4×C31—41no—
87C2×D4×C31C2×D411yescharacteristic
88C2×D4×C31C2×D412yes—
89C22×C4×C31—24no—
90C22×C4×C31—22no—
91C22×C4×C31—41no—
92C22×C4×C31C2×D412yes—
93C22×C4×C31C2×D411yescharacteristic
94Q16×C31—81no—
95Q16×C31—81no—
96M16×C31—41no—
97C2×C8×C31—21no—
98C2×C8×C31—21no—
99C2×C8×C31—41no—
100C4⋊C4×C31—22no—
101C4⋊C4×C31—42no—
102C4⋊C4×C31—48no—
103C4⋊C4×C31—41no—
104C4⋊C4×C31—42no—
105C4⋊C4×C31—42no—
106C22⋊C4×C31—22no—
107C22⋊C4×C31—24no—
108C22⋊C4×C31—48no—
109C22⋊C4×C31—42no—
110C22⋊C4×C31—42no—
111C22⋊C4×C31—41no—
112C42×C31—22no—
113C42×C31—42no—
114C42×C31—41no—
115#13352C3111yesmaximal, characteristic, direct product factor, Sylow
116C23×C31—24no—
117C23×C31—41no—
118C23×C31#12012yes—
119C23×C31#12711yescharacteristic
120Q8×C31—22no—
121Q8×C31—41no—
122Q8×C31—42no—
123Q8×C31—41no—
124Q8×C31—42no—
125Q8×C31—42no—
126Q8×C31—82no—
127D4×C31—22no—
128D4×C31—41no—
129D4×C31—42no—
130D4×C31—42no—
131D4×C31—44no—
132D4×C31—42no—
133D4×C31—42no—
134D4×C31—41no—
135C2×C4×C31—21no—
136C2×C4×C31—22no—
137C2×C4×C31—21no—
138C2×C4×C31—22no—
139C2×C4×C31—24no—
140C2×C4×C31—44no—
141C2×C4×C31—42no—
142C2×C4×C31—41no—
143C2×C4×C31—42no—
144C2×C4×C31—44no—
145C2×C4×C31—44no—
146C2×C4×C31—42no—
147C2×C4×C31—42no—
148C2×C4×C31—81no—
149C2×C4×C31#12011yescharacteristic
150C2×C4×C31#12112yes—
151C2×C4×C31#12111yescharacteristic
152C8×C31—41no—
153C8×C31—41no—
154#3202C2×C3111yescharacteristic, complemented
155#3028C2×C3112yes—
156#2129C2×C3112yescomplemented
157#1794C2×C3111yescharacteristic
158#1391C2×C3111yescharacteristic, complemented
159C22×C31—22no—
160C22×C31—21no—
161C22×C31—42no—
162C22×C31—41no—
163C22×C31—42no—
164C22×C31—84no—
165C22×C31—161no—
166C22×C31#39211yescharacteristic
167C4×C31—21no—
168C4×C31—22no—
169C4×C31—42no—
170C4×C31—82no—
171C4×C31—84no—
172C4×C31—82no—
173C4×C31—161no—
174C4×C31B(4,𝔽2)11yescharacteristic
175C4×C31B(4,𝔽2)11yescharacteristic
176#585C22×C3111yescharacteristic
177#536—22no—
178#536C22×C3112yes—
179#485—22no—
180#470—21no—
181#467—21no—
182#458—24no—
183#458—24no—
184#451—22no—
185#421—21no—
186#416—21no—
187#410—22no—
188#410C22×C3111yescharacteristic
189#410C22×C3112yes—
190#408C22×C3111yescharacteristic
191#354—24no—
192C2×C31—21no—
193C2×C31—42no—
194C2×C31—41no—
195C2×C31—82no—
196C2×C31#202111yescharacteristic
1972−1+4—21no—
1982−1+4—41no—
199H(5,𝔽2)—22no—
200H(5,𝔽2)—41no—
201H(5,𝔽2)D4×C3112yes—
202C2×#41—22no—
203C2×#41—21no—
204C2×#41—42no—
205C2×#41C23×C3111yescharacteristic
206C22×Q8D4×C3112yes—
207C2×Q16—21no—
208C2×Q16—21no—
209C2×M16D4×C3111yescharacteristic
210C22×C8D4×C3111yescharacteristic
211C4⋊Q8—22no—
212C4⋊Q8—42no—
213#124—22no—
214#124—42no—
215#123—28no—
216#123—22no—
217#123—22no—
218C22⋊Q8—22no—
219C22⋊Q8—22no—
220C22⋊Q8—44no—
221#117—22no—
222#117—21no—
223#117D4×C3112yes—
224#107—21no—
225#106—21no—
226#104—42no—
227#103—22no—
228#103—22no—
229#103—41no—
230#102—41no—
231#99—28no—
232#99—22no—
233#99—22no—
234#99D4×C3114yes—
235C22⋊C8—22no—
236C31#1335211yescharacteristic, direct product factor, Sylow
237#41—22no—
238#41—22no—
239#41—41no—
240#41—41no—
241#41—42no—
242#41—42no—
243#41—42no—
244#41—41no—
245#41—44no—
246#41—42no—
247#41—41no—
248#41—42no—
249C2×Q8—22no—
250C2×Q8—21no—
251C2×Q8—22no—
252C2×Q8—22no—
253C2×Q8—42no—
254C2×Q8—42no—
255C2×Q8—42no—
256C2×Q8#41×C3111yescharacteristic
257C2×D4—21no—
258C2×D4—22no—
259C2×D4—24no—
260C2×D4—42no—
261C2×D4—44no—
262C2×D4—41no—
263C2×D4C2×D4×C3111yescharacteristic
264C2×D4C2×D4×C3112yes—
265C22×C4—24no—
266C22×C4—22no—
267C22×C4—41no—
268C22×C4C2×D4×C3112yes—
269C22×C4C2×D4×C3111yescharacteristic
270Q16—81no—
271Q16—81no—
272M16—41no—
273C2×C8—21no—
274C2×C8—21no—
275C2×C8—41no—
276C4⋊C4—22no—
277C4⋊C4—42no—
278C4⋊C4—48no—
279C4⋊C4—41no—
280C4⋊C4—42no—
281C4⋊C4—42no—
282C22⋊C4—22no—
283C22⋊C4—24no—
284C22⋊C4—48no—
285C22⋊C4—42no—
286C22⋊C4—42no—
287C22⋊C4—41no—
288C42—22no—
289C42—42no—
290C42—41no—
291C23—24no—
292C23—41no—
293C23C31×#12012yes—
294C23C31×#12711yescharacteristic
295Q8—22no—
296Q8—41no—
297Q8—42no—
298Q8—41no—
299Q8—42no—
300Q8—42no—
301Q8—82no—
302D4—22no—
303D4—41no—
304D4—42no—
305D4—42no—
306D4—44no—
307D4—42no—
308D4—42no—
309D4—41no—
310C2×C4—21no—
311C2×C4—22no—
312C2×C4—21no—
313C2×C4—22no—
314C2×C4—24no—
315C2×C4—44no—
316C2×C4—42no—
317C2×C4—41no—
318C2×C4—42no—
319C2×C4—44no—
320C2×C4—44no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—81no—
324C2×C4C31×#12011yescharacteristic
325C2×C4C31×#12112yes—
326C2×C4C31×#12111yescharacteristic
327C8—41no—
328C8—41no—
329C22—22no—
330C22—21no—
331C22—42no—
332C22—41no—
333C22—42no—
334C22—84no—
335C22—161no—
336C22C31×#39211yescharacteristic
337C4—21no—
338C4—22no—
339C4—42no—
340C4—82no—
341C4—84no—
342C4—82no—
343C4—161no—
344C4C31×B(4,𝔽2)11yescharacteristic
345C4C31×B(4,𝔽2)11yescharacteristic
346C2—21no—
347C2—42no—
348C2—41no—
349C2—82no—
350C2C31×#202111yescharacteristic
subgroupG/H
center, socleC2×C31#2021
commutator, Frattini, cosocleC2×#41C23×C31
prime radicalC31×#585C22
LCSG ▷ C2×#41 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C31 ◁ C2×C4×C31 ◁ C2×#41×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#3202C2semidirect
3. C31×#2129C2semidirect
5. C31×#1391C2semidirect
115. #13352C31direct (N × H)
154. #3202C2×C31semidirect
156. #2129C2×C31semidirect
158. #1391C2×C31semidirect
236. C31#13352direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#32022
C31×#30282
C31×#21292
C31×#17942
C31×#13912
#1335231