Finite Group Databasebeta

← C31×#13400 #21470159

Subgroups — C31×#13400 #21470159

Order 7936.

402 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3060C211yesmaximal, characteristic
2C2×C31×#365C211yesmaximal, characteristic, complemented
3C31×#2148C211yesmaximal, characteristic, complemented
4C31×#2145C211yesmaximal, characteristic, complemented
5C31×#2117C211yesmaximal, characteristic, complemented
6C31×#1814C211yesmaximal, characteristic, complemented
7C31×#1386C211yesmaximal, characteristic, complemented
8C2×C31×#135C2211yescharacteristic
9C2×C31×#131C2211yescharacteristic
10C31×#537—21no—
11C2×C31×M32C2211yescharacteristic
12C2×C31×M32C2211yescharacteristic
13C31×#470—21no—
14C31×#469—21no—
15C31×#465—22no—
16C2×C31×#108C2211yescharacteristic
17C31×#427C2211yescharacteristic
18C2×C31×#106C2211yescharacteristic
19C31×#421—21no—
20C31×#417—21no—
21C31×#365—22no—
22C31×#362—21no—
23C31×#361—21no—
24C31×#360—22no—
25C31×#350—22no—
26C31×#344—21no—
27C2×#41×C31—21no—
28C2×#41×C31D411yescharacteristic
29C31×#135—21no—
30C31×#135—21no—
31C31×#135—21no—
32C31×#135—21no—
33C2×Q16×C31D411yescharacteristic
34C2×SD16×C31—21no—
35C2×D8×C31D411yescharacteristic
36C31×#131—21no—
37C31×#131—21no—
38C31×#131—21no—
39C31×#131—21no—
40C2×M16×C31—21no—
41C2×M16×C31—21no—
42C2×M16×C31D411yescharacteristic
43C22×C8×C31—21no—
44C22×C8×C31C2311yescharacteristic
45C31×C22⋊Q8—22no—
46C31×C22⋊Q8—41no—
47C31×#121—22no—
48C31×#121—42no—
49C31×#121—41no—
50C31×#117—21no—
51C2×C4⋊C4×C31—21no—
52C31×M32—21no—
53C31×M32—21no—
54C31×M32—21no—
55C31×M32D412yescomplemented
56C2×C16×C31—21no—
57C2×C16×C31—21no—
58C31×#108—21no—
59C31×#108—21no—
60C31×#107—21no—
61C31×#106—21no—
62C31×#106—21no—
63C31×#106D412yes—
64C31×#104—42no—
65C31×#103—22no—
66C31×#102—22no—
67#41×C31—21no—
68#41×C31—21no—
69#41×C31—21no—
70#41×C31—21no—
71#41×C31—41no—
72#41×C31—41no—
73#41×C31—41no—
74#41×C31—41no—
75C2×Q8×C31—21no—
76C2×Q8×C31SD1611yescharacteristic
77C2×D4×C31—21no—
78C2×D4×C31—21no—
79C2×D4×C31—41no—
80C2×D4×C31—42no—
81C2×D4×C31SD1611yescharacteristic
82C22×C4×C31—21no—
83C22×C4×C31—41no—
84C22×C4×C31—41no—
85C22×C4×C31C2×D411yescharacteristic
86Q16×C31—21no—
87Q16×C31—21no—
88SD16×C31—41no—
89SD16×C31—41no—
90D8×C31—21no—
91D8×C31—21no—
92M16×C31—21no—
93M16×C31—21no—
94M16×C31—41no—
95M16×C31—41no—
96M16×C31—41no—
97M16×C31—41no—
98C2×C8×C31—21no—
99C2×C8×C31—41no—
100C2×C8×C31—41no—
101C2×C8×C31—41no—
102C2×C8×C31C2×D411yescharacteristic
103C2×C8×C31C2×D411yescharacteristic
104C2×C8×C31C2×D411yescharacteristic
105C2×C8×C31#4111yescharacteristic
106C2×C8×C31#4111yescharacteristic
107C2×C8×C31#4111yescharacteristic
108C4⋊C4×C31—22no—
109C4⋊C4×C31—42no—
110C4⋊C4×C31—41no—
111C4⋊C4×C31—41no—
112C22⋊C4×C31—42no—
113C22⋊C4×C31—42no—
114C22⋊C4×C31—41no—
115C42×C31—41no—
116C16×C31—22no—
117C16×C31—41no—
118#13400C3111yesmaximal, characteristic, direct product factor, Sylow
119C23×C31—21no—
120C23×C31—41no—
121C23×C31AGL(1,ℤ/8)11yescharacteristic
122Q8×C31—21no—
123Q8×C31—21no—
124Q8×C31—41no—
125Q8×C31—41no—
126D4×C31—21no—
127D4×C31—21no—
128D4×C31—41no—
129D4×C31—41no—
130D4×C31—41no—
131D4×C31—41no—
132D4×C31—81no—
133D4×C31—81no—
134D4×C31—162no—
135C2×C4×C31—21no—
136C2×C4×C31—41no—
137C2×C4×C31—41no—
138C2×C4×C31—42no—
139C2×C4×C31—41no—
140C2×C4×C31—81no—
141C2×C4×C31—81no—
142C2×C4×C31—81no—
143C2×C4×C31—161no—
144C2×C4×C31#12011yescharacteristic
145C2×C4×C31#12111yescharacteristic
146C2×C4×C31#12311yescharacteristic
147C2×C4×C31C2×SD1611yescharacteristic
148C2×C4×C31#13511yescharacteristic
149C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
150C8×C31—41no—
151C8×C31—81no—
152C8×C31#12111yescharacteristic
153C8×C31#12111yescharacteristic
154C8×C31#12311yescharacteristic
155C8×C31#12411yescharacteristic
156#3060C2×C3111yescharacteristic
157C2×#365C2×C3111yescharacteristic, complemented
158#2148C2×C3111yescharacteristic, complemented
159#2145C2×C3111yescharacteristic, complemented
160#2117C2×C3111yescharacteristic, complemented
161#1814C2×C3111yescharacteristic, complemented
162#1386C2×C3111yescharacteristic, complemented
163C22×C31—41no—
164C22×C31—42no—
165C22×C31—41no—
166C22×C31—81no—
167C22×C31—81no—
168C22×C31—81no—
169C22×C31#45011yescharacteristic
170C22×C31#46911yescharacteristic
171C22×C31#48211yescharacteristic
172C4×C31—41no—
173C4×C31—82no—
174C4×C31—81no—
175C4×C31—161no—
176C4×C31#39411yescharacteristic
177C4×C31#44911yescharacteristic
178C4×C31#46511yescharacteristic
179C4×C31#48111yescharacteristic
180C2×#135C22×C3111yescharacteristic
181C2×#131C22×C3111yescharacteristic
182#537—21no—
183C2×M32C22×C3111yescharacteristic
184C2×M32C22×C3111yescharacteristic
185#470—21no—
186#469—21no—
187#465—22no—
188C2×#108C22×C3111yescharacteristic
189#427C22×C3111yescharacteristic
190C2×#106C22×C3111yescharacteristic
191#421—21no—
192#417—21no—
193#365—22no—
194#362—21no—
195#361—21no—
196#360—22no—
197#350—22no—
198#344—21no—
199C2×C31—21no—
200C2×C31—21no—
201C2×C31—21no—
202C2×C31—81no—
203C2×C31—161no—
204C2×C31#203411yescharacteristic
205C2×#41—21no—
206C2×#41D4×C3111yescharacteristic
207#135—21no—
208#135—21no—
209#135—21no—
210#135—21no—
211C2×Q16D4×C3111yescharacteristic
212C2×SD16—21no—
213C2×D8D4×C3111yescharacteristic
214#131—21no—
215#131—21no—
216#131—21no—
217#131—21no—
218C2×M16—21no—
219C2×M16—21no—
220C2×M16D4×C3111yescharacteristic
221C22×C8—21no—
222C22×C8C23×C3111yescharacteristic
223C22⋊Q8—22no—
224C22⋊Q8—41no—
225#121—22no—
226#121—42no—
227#121—41no—
228#117—21no—
229C2×C4⋊C4—21no—
230M32—21no—
231M32—21no—
232M32—21no—
233M32D4×C3112yescomplemented
234C2×C16—21no—
235C2×C16—21no—
236#108—21no—
237#108—21no—
238#107—21no—
239#106—21no—
240#106—21no—
241#106D4×C3112yes—
242#104—42no—
243#103—22no—
244#102—22no—
245C31#1340011yescharacteristic, direct product factor, Sylow
246#41—21no—
247#41—21no—
248#41—21no—
249#41—21no—
250#41—41no—
251#41—41no—
252#41—41no—
253#41—41no—
254C2×Q8—21no—
255C2×Q8SD16×C3111yescharacteristic
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—41no—
259C2×D4—42no—
260C2×D4SD16×C3111yescharacteristic
261C22×C4—21no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4C2×D4×C3111yescharacteristic
265Q16—21no—
266Q16—21no—
267SD16—41no—
268SD16—41no—
269D8—21no—
270D8—21no—
271M16—21no—
272M16—21no—
273M16—41no—
274M16—41no—
275M16—41no—
276M16—41no—
277C2×C8—21no—
278C2×C8—41no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8C2×D4×C3111yescharacteristic
282C2×C8C2×D4×C3111yescharacteristic
283C2×C8C2×D4×C3111yescharacteristic
284C2×C8#41×C3111yescharacteristic
285C2×C8#41×C3111yescharacteristic
286C2×C8#41×C3111yescharacteristic
287C4⋊C4—22no—
288C4⋊C4—42no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C22⋊C4—42no—
292C22⋊C4—42no—
293C22⋊C4—41no—
294C42—41no—
295C16—22no—
296C16—41no—
297C23—21no—
298C23—41no—
299C23C31×AGL(1,ℤ/8)11yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—41no—
303Q8—41no—
304D4—21no—
305D4—21no—
306D4—41no—
307D4—41no—
308D4—41no—
309D4—41no—
310D4—81no—
311D4—81no—
312D4—162no—
313C2×C4—21no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—42no—
317C2×C4—41no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—161no—
322C2×C4C31×#12011yescharacteristic
323C2×C4C31×#12111yescharacteristic
324C2×C4C31×#12311yescharacteristic
325C2×C4C2×SD16×C3111yescharacteristic
326C2×C4C31×#13511yescharacteristic
327C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
328C8—41no—
329C8—81no—
330C8C31×#12111yescharacteristic
331C8C31×#12111yescharacteristic
332C8C31×#12311yescharacteristic
333C8C31×#12411yescharacteristic
334C22—41no—
335C22—42no—
336C22—41no—
337C22—81no—
338C22—81no—
339C22—81no—
340C22C31×#45011yescharacteristic
341C22C31×#46911yescharacteristic
342C22C31×#48211yescharacteristic
343C4—41no—
344C4—82no—
345C4—81no—
346C4—161no—
347C4C31×#39411yescharacteristic
348C4C31×#44911yescharacteristic
349C4C31×#46511yescharacteristic
350C4C31×#48111yescharacteristic
351C2—21no—
352C2—21no—
353C2—21no—
354C2—81no—
355C2—161no—
356C2C31×#203411yescharacteristic
subgroupG/H
center, socleC2×C31#2034
commutator, Frattini, cosocleC22×C8C23×C31
prime radicalC31×#3060C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C31 ◁ C22×C4×C31 ◁ C2×C31×#131 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#365C2semidirect
3. C31×#2148C2semidirect
4. C31×#2145C2semidirect
5. C31×#2117C2semidirect
6. C31×#1814C2semidirect
7. C31×#1386C2semidirect
55. C31×M32D4semidirect
118. #13400C31direct (N × H)
157. C2×#365C2×C31semidirect
158. #2148C2×C31semidirect
159. #2145C2×C31semidirect
160. #2117C2×C31semidirect
161. #1814C2×C31semidirect
162. #1386C2×C31semidirect
233. M32D4×C31semidirect
245. C31#13400direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#30602
C2×C31×#3652
C31×#21482
C31×#21452
C31×#21172
C31×#18142
C31×#13862
#1340031