Finite Group Databasebeta

← C31×#13386 #21470145

Subgroups — C31×#13386 #21470145

Order 7936.

432 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3054C211yesmaximal, characteristic
2C31×#2159C211yesmaximal, characteristic, complemented
3C2×C31×#360C211yesmaximal, characteristic, complemented
4C31×#2139C211yesmaximal, characteristic, complemented
5C2×C31×#349C211yesmaximal, characteristic, complemented
6C31×#1809C211yesmaximal, characteristic, complemented
7C31×#1386C211yesmaximal, characteristic, complemented
8C2×C31×#135C2211yescharacteristic
9C22×M16×C31C2211yescharacteristic
10C31×#525—21no—
11C2×C31×M32C2211yescharacteristic
12C2×C31×M32C2211yescharacteristic
13C31×#470—21no—
14C31×#469—21no—
15C31×#468—21no—
16C31×#468—21no—
17C31×#427C2211yescharacteristic
18C2×C31×#107C2211yescharacteristic
19C2×C31×#106C2211yescharacteristic
20C31×#416—21no—
21C31×#380—21no—
22C31×#367—21no—
23C31×#366—21no—
24C31×#360—22no—
25C31×#358—21no—
26C31×#357—21no—
27C31×#349—22no—
28C31×#340—21no—
29C2×#41×C31—21no—
30C23×C4×C31D411yescharacteristic
31C31×#135—21no—
32C31×#135—21no—
33C31×#135—21no—
34C31×#135—21no—
35C2×Q16×C31D411yescharacteristic
36C2×SD16×C31—21no—
37C2×D8×C31D411yescharacteristic
38C2×M16×C31—21no—
39C2×M16×C31—21no—
40C2×M16×C31—21no—
41C2×M16×C31—21no—
42C2×M16×C31—21no—
43C2×M16×C31—21no—
44C22×C8×C31D411yescharacteristic
45C22×C8×C31C2311yescharacteristic
46C31×#123—41no—
47C31×C22⋊Q8—21no—
48C31×C22⋊Q8—21no—
49C31×#121—21no—
50C31×#121—21no—
51C31×#120—41no—
52C4×D4×C31—41no—
53C4×D4×C31—41no—
54C31×#117—21no—
55C2×C4⋊C4×C31—21no—
56C2×C4⋊C4×C31—21no—
57C2×C22⋊C4×C31—41no—
58C31×M32—21no—
59C31×M32—21no—
60C31×M32—21no—
61C31×M32D412yescomplemented
62C2×C16×C31—21no—
63C2×C16×C31—21no—
64C31×#107—21no—
65C31×#107—21no—
66C31×#107D411yescharacteristic
67C31×#107D411yescharacteristic
68C31×#106—21no—
69C31×#106—21no—
70C31×#106—21no—
71C31×#103—21no—
72C31×#103—21no—
73C31×#102—21no—
74C31×#102—21no—
75C31×#95—41no—
76C24×C31D811yescharacteristic
77#41×C31—41no—
78#41×C31—41no—
79#41×C31—41no—
80#41×C31—41no—
81C2×Q8×C31—21no—
82C2×D4×C31—21no—
83C2×D4×C31—41no—
84C2×D4×C31—41no—
85C2×D4×C31—41no—
86C22×C4×C31—21no—
87C22×C4×C31—21no—
88C22×C4×C31—21no—
89C22×C4×C31—21no—
90C22×C4×C31—21no—
91C22×C4×C31—21no—
92C22×C4×C31—41no—
93C22×C4×C31—41no—
94C22×C4×C31—41no—
95C22×C4×C31D811yescharacteristic
96C22×C4×C31C2×D411yescharacteristic
97Q16×C31—21no—
98Q16×C31—21no—
99SD16×C31—41no—
100SD16×C31—41no—
101D8×C31—21no—
102D8×C31—21no—
103M16×C31—41no—
104M16×C31—41no—
105M16×C31—41no—
106M16×C31—41no—
107C2×C8×C31—21no—
108C2×C8×C31—21no—
109C2×C8×C31—21no—
110C2×C8×C31C2×D411yescharacteristic
111C2×C8×C31C2×D411yescharacteristic
112C2×C8×C31C2×D411yescharacteristic
113C2×C8×C31#4111yescharacteristic
114C2×C8×C31#4111yescharacteristic
115C2×C8×C31#4111yescharacteristic
116C4⋊C4×C31—21no—
117C4⋊C4×C31—21no—
118C4⋊C4×C31—41no—
119C4⋊C4×C31—41no—
120C4⋊C4×C31—41no—
121C4⋊C4×C31—41no—
122C4⋊C4×C31—41no—
123C4⋊C4×C31—41no—
124C22⋊C4×C31—41no—
125C22⋊C4×C31—41no—
126C22⋊C4×C31—41no—
127C22⋊C4×C31—41no—
128C22⋊C4×C31—41no—
129C22⋊C4×C31—82no—
130C42×C31—41no—
131C16×C31—22no—
132C16×C31—41no—
133#13386C3111yesmaximal, characteristic, direct product factor, Sylow
134C23×C31—21no—
135C23×C31—21no—
136C23×C31—21no—
137C23×C31—41no—
138C23×C31—41no—
139C23×C31—41no—
140C23×C31C2×D811yescharacteristic
141Q8×C31—41no—
142Q8×C31—41no—
143D4×C31—41no—
144D4×C31—41no—
145D4×C31—82no—
146D4×C31—82no—
147D4×C31—81no—
148D4×C31—81no—
149C2×C4×C31—21no—
150C2×C4×C31—21no—
151C2×C4×C31—21no—
152C2×C4×C31—41no—
153C2×C4×C31—41no—
154C2×C4×C31—41no—
155C2×C4×C31—41no—
156C2×C4×C31—41no—
157C2×C4×C31—41no—
158C2×C4×C31—41no—
159C2×C4×C31—81no—
160C2×C4×C31—81no—
161C2×C4×C31—81no—
162C2×C4×C31—81no—
163C2×C4×C31—81no—
164C2×C4×C31—81no—
165C2×C4×C31—81no—
166C2×C4×C31—81no—
167C2×C4×C31#12011yescharacteristic
168C2×C4×C31#12111yescharacteristic
169C2×C4×C31#12311yescharacteristic
170C2×C4×C31#13511yescharacteristic
171C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
172C2×C4×C31#13711yescharacteristic
173C8×C31—41no—
174C8×C31#12111yescharacteristic
175C8×C31#12111yescharacteristic
176C8×C31#12311yescharacteristic
177C8×C31#12411yescharacteristic
178#3054C2×C3111yescharacteristic
179#2159C2×C3111yescharacteristic, complemented
180C2×#360C2×C3111yescharacteristic, complemented
181#2139C2×C3111yescharacteristic, complemented
182C2×#349C2×C3111yescharacteristic, complemented
183#1809C2×C3111yescharacteristic, complemented
184#1386C2×C3111yescharacteristic, complemented
185C22×C31—21no—
186C22×C31—21no—
187C22×C31—42no—
188C22×C31—41no—
189C22×C31—41no—
190C22×C31—41no—
191C22×C31—81no—
192C22×C31—81no—
193C22×C31—81no—
194C22×C31—81no—
195C22×C31#44711yescharacteristic
196C22×C31#46611yescharacteristic
197C22×C31#48011yescharacteristic
198C4×C31—41no—
199C4×C31—81no—
200C4×C31—81no—
201C4×C31—81no—
202C4×C31—161no—
203C4×C31—161no—
204C4×C31#39411yescharacteristic
205C4×C31#45211yescharacteristic
206C4×C31#46811yescharacteristic
207C4×C31#48211yescharacteristic
208C2×#135C22×C3111yescharacteristic
209C22×M16C22×C3111yescharacteristic
210#525—21no—
211C2×M32C22×C3111yescharacteristic
212C2×M32C22×C3111yescharacteristic
213#470—21no—
214#469—21no—
215#468—21no—
216#468—21no—
217#427C22×C3111yescharacteristic
218C2×#107C22×C3111yescharacteristic
219C2×#106C22×C3111yescharacteristic
220#416—21no—
221#380—21no—
222#367—21no—
223#366—21no—
224#360—22no—
225#358—21no—
226#357—21no—
227#349—22no—
228#340—21no—
229C2×C31—21no—
230C2×C31—21no—
231C2×C31—81no—
232C2×C31—161no—
233C2×C31#203311yescharacteristic
234C2×C31#219011yescharacteristic
235C2×C31#219111yescharacteristic
236C2×#41—21no—
237C23×C4D4×C3111yescharacteristic
238#135—21no—
239#135—21no—
240#135—21no—
241#135—21no—
242C2×Q16D4×C3111yescharacteristic
243C2×SD16—21no—
244C2×D8D4×C3111yescharacteristic
245C2×M16—21no—
246C2×M16—21no—
247C2×M16—21no—
248C2×M16—21no—
249C2×M16—21no—
250C2×M16—21no—
251C22×C8D4×C3111yescharacteristic
252C22×C8C23×C3111yescharacteristic
253#123—41no—
254C22⋊Q8—21no—
255C22⋊Q8—21no—
256#121—21no—
257#121—21no—
258#120—41no—
259C4×D4—41no—
260C4×D4—41no—
261#117—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C22⋊C4—41no—
265M32—21no—
266M32—21no—
267M32—21no—
268M32D4×C3112yescomplemented
269C2×C16—21no—
270C2×C16—21no—
271#107—21no—
272#107—21no—
273#107D4×C3111yescharacteristic
274#107D4×C3111yescharacteristic
275#106—21no—
276#106—21no—
277#106—21no—
278#103—21no—
279#103—21no—
280#102—21no—
281#102—21no—
282#95—41no—
283C31#1338611yescharacteristic, direct product factor, Sylow
284C24D8×C3111yescharacteristic
285#41—41no—
286#41—41no—
287#41—41no—
288#41—41no—
289C2×Q8—21no—
290C2×D4—21no—
291C2×D4—41no—
292C2×D4—41no—
293C2×D4—41no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4—41no—
303C22×C4D8×C3111yescharacteristic
304C22×C4C2×D4×C3111yescharacteristic
305Q16—21no—
306Q16—21no—
307SD16—41no—
308SD16—41no—
309D8—21no—
310D8—21no—
311M16—41no—
312M16—41no—
313M16—41no—
314M16—41no—
315C2×C8—21no—
316C2×C8—21no—
317C2×C8—21no—
318C2×C8C2×D4×C3111yescharacteristic
319C2×C8C2×D4×C3111yescharacteristic
320C2×C8C2×D4×C3111yescharacteristic
321C2×C8#41×C3111yescharacteristic
322C2×C8#41×C3111yescharacteristic
323C2×C8#41×C3111yescharacteristic
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—41no—
334C22⋊C4—41no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C22⋊C4—82no—
338C42—41no—
339C16—22no—
340C16—41no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23C2×D8×C3111yescharacteristic
348Q8—41no—
349Q8—41no—
350D4—41no—
351D4—41no—
352D4—82no—
353D4—82no—
354D4—81no—
355D4—81no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—81no—
367C2×C4—81no—
368C2×C4—81no—
369C2×C4—81no—
370C2×C4—81no—
371C2×C4—81no—
372C2×C4—81no—
373C2×C4—81no—
374C2×C4C31×#12011yescharacteristic
375C2×C4C31×#12111yescharacteristic
376C2×C4C31×#12311yescharacteristic
377C2×C4C31×#13511yescharacteristic
378C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
379C2×C4C31×#13711yescharacteristic
380C8—41no—
381C8C31×#12111yescharacteristic
382C8C31×#12111yescharacteristic
383C8C31×#12311yescharacteristic
384C8C31×#12411yescharacteristic
385C22—21no—
386C22—21no—
387C22—42no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—81no—
392C22—81no—
393C22—81no—
394C22—81no—
395C22C31×#44711yescharacteristic
396C22C31×#46611yescharacteristic
397C22C31×#48011yescharacteristic
398C4—41no—
399C4—81no—
400C4—81no—
401C4—81no—
402C4—161no—
403C4—161no—
404C4C31×#39411yescharacteristic
405C4C31×#45211yescharacteristic
406C4C31×#46811yescharacteristic
407C4C31×#48211yescharacteristic
408C2—21no—
409C2—21no—
410C2—81no—
411C2—161no—
412C2C31×#203311yescharacteristic
413C2C31×#219011yescharacteristic
414C2C31×#219111yescharacteristic
subgroupG/H
center, socleC22×C31#447
commutator, Frattini, cosocleC22×C8C23×C31
prime radicalC31×#3054C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C22×C4×C31 ◁ C22×M16×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#2159C2semidirect
3. C2×C31×#360C2semidirect
4. C31×#2139C2semidirect
5. C2×C31×#349C2semidirect
6. C31×#1809C2semidirect
7. C31×#1386C2semidirect
61. C31×M32D4semidirect
133. #13386C31direct (N × H)
179. #2159C2×C31semidirect
180. C2×#360C2×C31semidirect
181. #2139C2×C31semidirect
182. C2×#349C2×C31semidirect
183. #1809C2×C31semidirect
184. #1386C2×C31semidirect
268. M32D4×C31semidirect
283. C31#13386direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#30542
C31×#21592
C2×C31×#3602
C31×#21392
C2×C31×#3492
C31×#18092
C31×#13862
#1338631