Finite Group Databasebeta

← C31×#8886 #21465645

Subgroups — C31×#8886 #21465645

Order 7936.

618 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×C4⋊C4×C31C211yesmaximal, characteristic
2C31×#1948C211yesmaximal, characteristic, complemented
3C31×#1844C211yesmaximal, characteristic, complemented
4C31×#1802C211yesmaximal, characteristic
5C2×C31×D4⋊C8C211yesmaximal, characteristic
6C31×#1296C211yesmaximal, characteristic, complemented
7C31×#1279C211yesmaximal, characteristic, complemented
8C2×C4×D4×C31—21no—
9C2×C4×D4×C31C2211yescharacteristic
10C22×C4⋊C4×C31—21no—
11C2×C31×#106—22no—
12C2×C31×#106—21no—
13C2×C31×C4⋊C8C2211yescharacteristic
14C2×C31×C4⋊C8C2211yescharacteristic
15C2×C31×#102—21no—
16C2×C4×C8×C31C2211yescharacteristic
17C31×#389—21no—
18C31×#385—22no—
19C31×#384C2211yescharacteristic
20C31×#384C2211yescharacteristic
21C31×#380—21no—
22C4×C4⋊C4×C31C2211yescharacteristic
23C31×#340—21no—
24C31×#340—21no—
25C31×D4⋊C8C414yescomplemented
26C22×D4×C31D411yescharacteristic
27C23×C4×C31—21no—
28C23×C4×C31—22no—
29C22×C8×C31—21no—
30C22×C8×C31—21no—
31C22×C8×C31—21no—
32C4×D4×C31—21no—
33C4×D4×C31—21no—
34C4×D4×C31—42no—
35C4×D4×C31—42no—
36C4×D4×C31C2×C412yes—
37C4×D4×C31Q812yes—
38C2×C4⋊C4×C31—22no—
39C2×C4⋊C4×C31—21no—
40C2×C4⋊C4×C31—21no—
41C2×C4⋊C4×C31—21no—
42C2×C4⋊C4×C31—21no—
43C2×C4⋊C4×C31—21no—
44C2×C4⋊C4×C31—42no—
45C2×C4⋊C4×C31—42no—
46C2×C4⋊C4×C31D411yescharacteristic
47C2×C4⋊C4×C31D411yescharacteristic
48C2×C4⋊C4×C31D411yescharacteristic
49C2×C4⋊C4×C31D412yes—
50C2×C22⋊C4×C31—21no—
51C2×C22⋊C4×C31—22no—
52C2×C42×C31—21no—
53C2×C42×C31C2311yescharacteristic
54C31×#106—42no—
55C31×#106—44no—
56C31×C4⋊C8—21no—
57C31×C4⋊C8—21no—
58C31×C4⋊C8—21no—
59C31×C4⋊C8C2×C412yescomplemented
60C31×#102—42no—
61C4×C8×C31—21no—
62C4×C8×C31C2×C412yescomplemented
63C31×#95—22no—
64C31×#95—21no—
65C24×C31—21no—
66C2×D4×C31—21no—
67C2×D4×C31—21no—
68C2×D4×C31—21no—
69C2×D4×C31C4⋊C412yes—
70C2×D4×C31SD1612yes—
71C2×D4×C31SD1612yes—
72C22×C4×C31—21no—
73C22×C4×C31—21no—
74C22×C4×C31—22no—
75C22×C4×C31—22no—
76C22×C4×C31—21no—
77C22×C4×C31—22no—
78C22×C4×C31—44no—
79C22×C4×C31—41no—
80C22×C4×C31—41no—
81C22×C4×C31—41no—
82C22×C4×C31—41no—
83C22×C4×C31—44no—
84C22×C4×C31—41no—
85C22×C4×C31—82no—
86C22×C4×C31C2×D411yescharacteristic
87C22×C4×C31C2×D411yescharacteristic
88C22×C4×C31C2×D411yescharacteristic
89C2×C8×C31—22no—
90C2×C8×C31—22no—
91C2×C8×C31—22no—
92C2×C8×C31—22no—
93C2×C8×C31—41no—
94C2×C8×C31—41no—
95C2×C8×C31—41no—
96C2×C8×C31—41no—
97C2×C8×C31—41no—
98C4⋊C4×C31—21no—
99C4⋊C4×C31—21no—
100C4⋊C4×C31—21no—
101C4⋊C4×C31—21no—
102C4⋊C4×C31—44no—
103C4⋊C4×C31—42no—
104C4⋊C4×C31—42no—
105C4⋊C4×C31—41no—
106C4⋊C4×C31—41no—
107C4⋊C4×C31—41no—
108C4⋊C4×C31—41no—
109C4⋊C4×C31—41no—
110C4⋊C4×C31—41no—
111C4⋊C4×C31—41no—
112C4⋊C4×C31—41no—
113C4⋊C4×C31C4⋊C412yes—
114C4⋊C4×C31SD1612yes—
115C22⋊C4×C31—22no—
116C22⋊C4×C31—22no—
117C22⋊C4×C31—44no—
118C42×C31—41no—
119C42×C31—41no—
120C42×C31C22×C411yescharacteristic
121C42×C31C2×Q811yescharacteristic
122C42×C31#4111yescharacteristic
123C42×C31#4111yescharacteristic
124#8886C3111yesmaximal, characteristic, direct product factor, Sylow
125C23×C31—22no—
126C23×C31—22no—
127C23×C31—22no—
128C23×C31—41no—
129C23×C31—41no—
130C23×C31—41no—
131C23×C31—41no—
132C23×C31#12011yescharacteristic
133D4×C31—22no—
134D4×C31—22no—
135D4×C31—22no—
136D4×C31#10614yescomplemented
137C2×C4×C31—21no—
138C2×C4×C31—21no—
139C2×C4×C31—22no—
140C2×C4×C31—22no—
141C2×C4×C31—41no—
142C2×C4×C31—41no—
143C2×C4×C31—41no—
144C2×C4×C31—41no—
145C2×C4×C31—42no—
146C2×C4×C31—42no—
147C2×C4×C31—42no—
148C2×C4×C31—42no—
149C2×C4×C31—41no—
150C2×C4×C31—41no—
151C2×C4×C31—42no—
152C2×C4×C31—42no—
153C2×C4×C31—42no—
154C2×C4×C31—41no—
155C2×C4×C31—88no—
156C2×C4×C31—81no—
157C2×C4×C31—81no—
158C2×C4×C31—81no—
159C2×C4×C31C2×C4⋊C411yescharacteristic
160C2×C4×C31C4×D411yescharacteristic
161C2×C4×C31C4×D411yescharacteristic
162C2×C4×C31C22⋊Q811yescharacteristic
163C2×C4×C31C22⋊Q811yescharacteristic
164C2×C4×C31#12311yescharacteristic
165C2×C4×C31C2×SD1611yescharacteristic
166C2×C4×C31C2×SD1611yescharacteristic
167C2×C4×C31C2×SD1611yescharacteristic
168C2×C4×C31#13511yescharacteristic
169C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
170C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
171C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
172C2×C4×C31#13711yescharacteristic
173C8×C31—24no—
174C8×C31—42no—
175C8×C31—81no—
176D4×C4⋊C4C2×C3111yescharacteristic
177#1948C2×C3111yescharacteristic, complemented
178#1844C2×C3111yescharacteristic, complemented
179#1802C2×C3111yescharacteristic
180C2×D4⋊C8C2×C3111yescharacteristic
181#1296C2×C3111yescharacteristic, complemented
182#1279C2×C3111yescharacteristic, complemented
183C22×C31—24no—
184C22×C31—42no—
185C22×C31—42no—
186C22×C31—42no—
187C22×C31—42no—
188C22×C31—42no—
189C22×C31—42no—
190C22×C31#38511yescharacteristic
191C22×C31#44811yescharacteristic
192C22×C31#44911yescharacteristic
193C22×C31#45011yescharacteristic
194C22×C31#45011yescharacteristic
195C22×C31#45311yescharacteristic
196C22×C31#45611yescharacteristic
197C4×C31—21no—
198C4×C31—21no—
199C4×C31—42no—
200C4×C31—42no—
201C4×C31—82no—
202C4×C31—81no—
203C4×C31—161no—
204C4×C31C2×#10611yescharacteristic
205C4×C31#42811yescharacteristic
206C4×C31C4×SD1611yescharacteristic
207C4×C31#44211yescharacteristic
208C4×C31#47611yescharacteristic
209C4×C31#47811yescharacteristic
210C4×C31#48111yescharacteristic
211C4×C31#48311yescharacteristic
212C2×C4×D4—21no—
213C2×C4×D4C22×C3111yescharacteristic
214C22×C4⋊C4—21no—
215C2×#106—22no—
216C2×#106—21no—
217C2×C4⋊C8C22×C3111yescharacteristic
218C2×C4⋊C8C22×C3111yescharacteristic
219C2×#102—21no—
220C2×C4×C8C22×C3111yescharacteristic
221#389—21no—
222#385—22no—
223#384C22×C3111yescharacteristic
224#384C22×C3111yescharacteristic
225#380—21no—
226C4×C4⋊C4C22×C3111yescharacteristic
227#340—21no—
228#340—21no—
229D4⋊C8C4×C3114yescomplemented
230C2×C31—44no—
231C2×C31#162211yescharacteristic
232C2×C31#162911yescharacteristic
233C2×C31#165111yescharacteristic
234C2×C31#165411yescharacteristic
235C2×C31#185311yescharacteristic
236C2×C31#185911yescharacteristic
237C2×C31#186411yescharacteristic
238C22×D4D4×C3111yescharacteristic
239C23×C4—21no—
240C23×C4—22no—
241C22×C8—21no—
242C22×C8—21no—
243C22×C8—21no—
244C4×D4—21no—
245C4×D4—21no—
246C4×D4—42no—
247C4×D4—42no—
248C4×D4C2×C4×C3112yes—
249C4×D4Q8×C3112yes—
250C2×C4⋊C4—22no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—42no—
257C2×C4⋊C4—42no—
258C2×C4⋊C4D4×C3111yescharacteristic
259C2×C4⋊C4D4×C3111yescharacteristic
260C2×C4⋊C4D4×C3111yescharacteristic
261C2×C4⋊C4D4×C3112yes—
262C2×C22⋊C4—21no—
263C2×C22⋊C4—22no—
264C2×C42—21no—
265C2×C42C23×C3111yescharacteristic
266#106—42no—
267#106—44no—
268C4⋊C8—21no—
269C4⋊C8—21no—
270C4⋊C8—21no—
271C4⋊C8C2×C4×C3112yescomplemented
272#102—42no—
273C4×C8—21no—
274C4×C8C2×C4×C3112yescomplemented
275#95—22no—
276#95—21no—
277C31#888611yescharacteristic, direct product factor, Sylow
278C24—21no—
279C2×D4—21no—
280C2×D4—21no—
281C2×D4—21no—
282C2×D4C4⋊C4×C3112yes—
283C2×D4SD16×C3112yes—
284C2×D4SD16×C3112yes—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—21no—
290C22×C4—22no—
291C22×C4—44no—
292C22×C4—41no—
293C22×C4—41no—
294C22×C4—41no—
295C22×C4—41no—
296C22×C4—44no—
297C22×C4—41no—
298C22×C4—82no—
299C22×C4C2×D4×C3111yescharacteristic
300C22×C4C2×D4×C3111yescharacteristic
301C22×C4C2×D4×C3111yescharacteristic
302C2×C8—22no—
303C2×C8—22no—
304C2×C8—22no—
305C2×C8—22no—
306C2×C8—41no—
307C2×C8—41no—
308C2×C8—41no—
309C2×C8—41no—
310C2×C8—41no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—42no—
316C4⋊C4—44no—
317C4⋊C4—42no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4C4⋊C4×C3112yes—
327C4⋊C4SD16×C3112yes—
328C22⋊C4—22no—
329C22⋊C4—22no—
330C22⋊C4—44no—
331C42—41no—
332C42—41no—
333C42C22×C4×C3111yescharacteristic
334C42C2×Q8×C3111yescharacteristic
335C42#41×C3111yescharacteristic
336C42#41×C3111yescharacteristic
337C23—22no—
338C23—22no—
339C23—22no—
340C23—41no—
341C23—41no—
342C23—41no—
343C23—41no—
344C23C31×#12011yescharacteristic
345D4—22no—
346D4—22no—
347D4—22no—
348D4C31×#10614yescomplemented
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—41no—
367C2×C4—88no—
368C2×C4—81no—
369C2×C4—81no—
370C2×C4—81no—
371C2×C4C2×C4⋊C4×C3111yescharacteristic
372C2×C4C4×D4×C3111yescharacteristic
373C2×C4C4×D4×C3111yescharacteristic
374C2×C4C31×C22⋊Q811yescharacteristic
375C2×C4C31×C22⋊Q811yescharacteristic
376C2×C4C31×#12311yescharacteristic
377C2×C4C2×SD16×C3111yescharacteristic
378C2×C4C2×SD16×C3111yescharacteristic
379C2×C4C2×SD16×C3111yescharacteristic
380C2×C4C31×#13511yescharacteristic
381C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
382C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
383C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
384C2×C4C31×#13711yescharacteristic
385C8—24no—
386C8—42no—
387C8—81no—
388C22—24no—
389C22—42no—
390C22—42no—
391C22—42no—
392C22—42no—
393C22—42no—
394C22—42no—
395C22C31×#38511yescharacteristic
396C22C31×#44811yescharacteristic
397C22C31×#44911yescharacteristic
398C22C31×#45011yescharacteristic
399C22C31×#45011yescharacteristic
400C22C31×#45311yescharacteristic
401C22C31×#45611yescharacteristic
402C4—21no—
403C4—21no—
404C4—42no—
405C4—42no—
406C4—82no—
407C4—81no—
408C4—161no—
409C4C2×C31×#10611yescharacteristic
410C4C31×#42811yescharacteristic
411C4C4×SD16×C3111yescharacteristic
412C4C31×#44211yescharacteristic
413C4C31×#47611yescharacteristic
414C4C31×#47811yescharacteristic
415C4C31×#48111yescharacteristic
416C4C31×#48311yescharacteristic
417C2—44no—
418C2C31×#162211yescharacteristic
419C2C31×#162911yescharacteristic
420C2C31×#165111yescharacteristic
421C2C31×#165411yescharacteristic
422C2C31×#185311yescharacteristic
423C2C31×#185911yescharacteristic
424C2C31×#186411yescharacteristic
subgroupG/H
center, socleC23×C31#120
commutatorC42C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC22×D4×C31D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#1948C2semidirect
3. C31×#1844C2semidirect
6. C31×#1296C2semidirect
7. C31×#1279C2semidirect
25. C31×D4⋊C8C4semidirect
59. C31×C4⋊C8C2×C4semidirect
62. C4×C8×C31C2×C4semidirect
124. #8886C31direct (N × H)
136. D4×C31#106semidirect
177. #1948C2×C31semidirect
178. #1844C2×C31semidirect
181. #1296C2×C31semidirect
182. #1279C2×C31semidirect
229. D4⋊C8C4×C31semidirect
271. C4⋊C8C2×C4×C31semidirect
274. C4×C8C2×C4×C31semidirect
277. C31#8886direct (N × H)
348. D4C31×#106semidirect

Maximal subgroups

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

subgroupindex
D4×C4⋊C4×C312
C31×#19482
C31×#18442
C31×#18022
C2×C31×D4⋊C82
C31×#12962
C31×#12792
#888631