Finite Group Databasebeta

← C31×#8978 #21465737

Subgroups — C31×#8978 #21465737

Order 7936.

616 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#460C211yesmaximal, characteristic
2C31×#2355C211yesmaximal, characteristic, complemented
3C31×#1982C211yesmaximal, characteristic
4C31×#1957C211yesmaximal, characteristic
5C2×C31×Q8⋊C8C211yesmaximal, characteristic, complemented
6C31×#1296C211yesmaximal, characteristic, complemented
7C31×#1279C211yesmaximal, characteristic, complemented
8C22×SD16×C31—21no—
9C2×C31×#127C2211yescharacteristic
10C2×C4×Q8×C31C2211yescharacteristic
11C31×#460—22no—
12C31×#460C414yescomplemented
13C2×C31×C4⋊C8C2211yescharacteristic
14C2×C31×C4⋊C8C2211yescharacteristic
15C2×C31×#102—21no—
16C2×C31×#102—22no—
17C2×C31×#102—21no—
18C2×C31×#102—21no—
19C2×C4×C8×C31C2211yescharacteristic
20C31×#391—21no—
21C31×#387—22no—
22C31×#384C2211yescharacteristic
23C31×#382—21no—
24C4×C4⋊C4×C31—21no—
25C4×C4⋊C4×C31—21no—
26C4×C4⋊C4×C31C2211yescharacteristic
27C31×Q8⋊C8—22no—
28C22×Q8×C31D411yescharacteristic
29C22×D4×C31—21no—
30C22×D4×C31—21no—
31C22×D4×C31—21no—
32C2×SD16×C31—24no—
33C2×SD16×C31—42no—
34C2×SD16×C31—42no—
35C22×C8×C31—21no—
36C22×C8×C31—21no—
37C22×C8×C31—21no—
38C31×#127—21no—
39C31×#127—21no—
40C31×#127—21no—
41C31×#127C2×C412yes—
42C4×Q8×C31—21no—
43C4×Q8×C31—21no—
44C4×Q8×C31C2×C412yes—
45C4×Q8×C31D412yes—
46C2×C4⋊C4×C31—21no—
47C2×C4⋊C4×C31—21no—
48C2×C4⋊C4×C31—21no—
49C2×C4⋊C4×C31D411yescharacteristic
50C2×C4⋊C4×C31D411yescharacteristic
51C2×C4⋊C4×C31D411yescharacteristic
52C2×C4⋊C4×C31D412yes—
53C2×C42×C31—21no—
54C2×C42×C31—21no—
55C2×C42×C31—22no—
56C2×C42×C31C2311yescharacteristic
57C31×C4⋊C8—21no—
58C31×C4⋊C8—21no—
59C31×C4⋊C8—21no—
60C31×C4⋊C8C2×C412yes—
61C31×#102—24no—
62C31×#102—42no—
63C31×#102—44no—
64C31×#102—42no—
65C4×C8×C31—21no—
66C4×C8×C31—21no—
67C31×#95—22no—
68C31×#95—22no—
69C31×#95—22no—
70C31×#95—21no—
71C24×C31—41no—
72C2×Q8×C31—21no—
73C2×Q8×C31—21no—
74C2×Q8×C31—21no—
75C2×Q8×C31—21no—
76C2×Q8×C31—21no—
77C2×Q8×C31C22⋊C412yes—
78C2×D4×C31—22no—
79C2×D4×C31—22no—
80C2×D4×C31—22no—
81C2×D4×C31—42no—
82C2×D4×C31—42no—
83C2×D4×C31—41no—
84C2×D4×C31—41no—
85C2×D4×C31—41no—
86C2×D4×C31—41no—
87C2×D4×C31—41no—
88C2×D4×C31—41no—
89C2×D4×C31—41no—
90C2×D4×C31—41no—
91C2×D4×C31—41no—
92C2×D4×C31—41no—
93C2×D4×C31—41no—
94C22×C4×C31—21no—
95C22×C4×C31—21no—
96C22×C4×C31—21no—
97C22×C4×C31—21no—
98C22×C4×C31—22no—
99C22×C4×C31C2×D411yescharacteristic
100C22×C4×C31C2×D411yescharacteristic
101C22×C4×C31C2×D411yescharacteristic
102SD16×C31—48no—
103C2×C8×C31—22no—
104C2×C8×C31—22no—
105C2×C8×C31—41no—
106C2×C8×C31—41no—
107C2×C8×C31—41no—
108C2×C8×C31—41no—
109C2×C8×C31—41no—
110C2×C8×C31—41no—
111C2×C8×C31—41no—
112C4⋊C4×C31—22no—
113C4⋊C4×C31—22no—
114C4⋊C4×C31—21no—
115C4⋊C4×C31—21no—
116C4⋊C4×C31—21no—
117C4⋊C4×C31—21no—
118C4⋊C4×C31—42no—
119C4⋊C4×C31—41no—
120C4⋊C4×C31—41no—
121C4⋊C4×C31—41no—
122C4⋊C4×C31—41no—
123C4⋊C4×C31C22⋊C412yes—
124C4⋊C4×C31SD1612yescomplemented
125C42×C31—22no—
126C42×C31—22no—
127C42×C31—41no—
128C42×C31—41no—
129C42×C31—82no—
130C42×C31C22×C411yescharacteristic
131C42×C31C2×D411yescharacteristic
132C42×C31#4111yescharacteristic
133C42×C31#4111yescharacteristic
134#8978C3111yesmaximal, characteristic, direct product factor, Sylow
135C23×C31—42no—
136C23×C31—81no—
137C23×C31—81no—
138C23×C31—81no—
139C23×C31—81no—
140C23×C31—81no—
141C23×C31—81no—
142C23×C31#12011yescharacteristic
143Q8×C31—22no—
144Q8×C31—22no—
145Q8×C31—41no—
146Q8×C31—41no—
147D4×C31—44no—
148D4×C31—42no—
149D4×C31—42no—
150D4×C31—42no—
151D4×C31—42no—
152D4×C31—82no—
153D4×C31—81no—
154D4×C31—81no—
155D4×C31—81no—
156D4×C31—81no—
157C2×C4×C31—21no—
158C2×C4×C31—21no—
159C2×C4×C31—22no—
160C2×C4×C31—22no—
161C2×C4×C31—22no—
162C2×C4×C31—41no—
163C2×C4×C31—41no—
164C2×C4×C31—41no—
165C2×C4×C31—41no—
166C2×C4×C31—41no—
167C2×C4×C31—41no—
168C2×C4×C31—41no—
169C2×C4×C31—41no—
170C2×C4×C31—42no—
171C2×C4×C31—42no—
172C2×C4×C31—42no—
173C2×C4×C31—41no—
174C2×C4×C31C2×C22⋊C411yescharacteristic
175C2×C4×C31C4×D411yescharacteristic
176C2×C4×C31C4×D411yescharacteristic
177C2×C4×C31#12111yescharacteristic
178C2×C4×C31#12111yescharacteristic
179C2×C4×C31#12311yescharacteristic
180C2×C4×C31C2×SD1611yescharacteristic
181C2×C4×C31#13511yescharacteristic
182C2×C4×C31#13511yescharacteristic
183C2×C4×C31#13511yescharacteristic
184C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
185C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
186C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
187C2×C4×C31#13711yescharacteristic
188C8×C31—42no—
189C8×C31—42no—
190C8×C31—81no—
191C2×#460C2×C3111yescharacteristic
192#2355C2×C3111yescharacteristic, complemented
193#1982C2×C3111yescharacteristic
194#1957C2×C3111yescharacteristic
195C2×Q8⋊C8C2×C3111yescharacteristic, complemented
196#1296C2×C3111yescharacteristic, complemented
197#1279C2×C3111yescharacteristic, complemented
198C22×C31—82no—
199C22×C31—82no—
200C22×C31—82no—
201C22×C31—161no—
202C22×C31—161no—
203C22×C31—161no—
204C22×C31—161no—
205C22×C31#38611yescharacteristic
206C22×C31#44811yescharacteristic
207C22×C31#44911yescharacteristic
208C22×C31#44911yescharacteristic
209C22×C31#44911yescharacteristic
210C22×C31#45311yescharacteristic
211C22×C31#45411yescharacteristic
212C4×C31—21no—
213C4×C31—21no—
214C4×C31—42no—
215C4×C31—42no—
216C4×C31—42no—
217C4×C31—82no—
218C4×C31—81no—
219C4×C31#41611yescharacteristic
220C4×C31#41811yescharacteristic
221C4×C31C4×SD1611yescharacteristic
222C4×C31#44011yescharacteristic
223C4×C31#46011yescharacteristic
224C4×C31#46411yescharacteristic
225C4×C31#48211yescharacteristic
226C4×C31#48211yescharacteristic
227C22×SD16—21no—
228C2×#127C22×C3111yescharacteristic
229C2×C4×Q8C22×C3111yescharacteristic
230#460—22no—
231#460C4×C3114yescomplemented
232C2×C4⋊C8C22×C3111yescharacteristic
233C2×C4⋊C8C22×C3111yescharacteristic
234C2×#102—21no—
235C2×#102—22no—
236C2×#102—21no—
237C2×#102—21no—
238C2×C4×C8C22×C3111yescharacteristic
239#391—21no—
240#387—22no—
241#384C22×C3111yescharacteristic
242#382—21no—
243C4×C4⋊C4—21no—
244C4×C4⋊C4—21no—
245C4×C4⋊C4C22×C3111yescharacteristic
246Q8⋊C8—22no—
247C2×C31—162no—
248C2×C31#162011yescharacteristic
249C2×C31#162211yescharacteristic
250C2×C31#162611yescharacteristic
251C2×C31#162811yescharacteristic
252C2×C31#187511yescharacteristic
253C2×C31#188011yescharacteristic
254C2×C31#188311yescharacteristic
255C22×Q8D4×C3111yescharacteristic
256C22×D4—21no—
257C22×D4—21no—
258C22×D4—21no—
259C2×SD16—24no—
260C2×SD16—42no—
261C2×SD16—42no—
262C22×C8—21no—
263C22×C8—21no—
264C22×C8—21no—
265#127—21no—
266#127—21no—
267#127—21no—
268#127C2×C4×C3112yes—
269C4×Q8—21no—
270C4×Q8—21no—
271C4×Q8C2×C4×C3112yes—
272C4×Q8D4×C3112yes—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4D4×C3111yescharacteristic
277C2×C4⋊C4D4×C3111yescharacteristic
278C2×C4⋊C4D4×C3111yescharacteristic
279C2×C4⋊C4D4×C3112yes—
280C2×C42—21no—
281C2×C42—21no—
282C2×C42—22no—
283C2×C42C23×C3111yescharacteristic
284C4⋊C8—21no—
285C4⋊C8—21no—
286C4⋊C8—21no—
287C4⋊C8C2×C4×C3112yes—
288#102—24no—
289#102—42no—
290#102—44no—
291#102—42no—
292C4×C8—21no—
293C4×C8—21no—
294#95—22no—
295#95—22no—
296#95—22no—
297#95—21no—
298C31#897811yescharacteristic, direct product factor, Sylow
299C24—41no—
300C2×Q8—21no—
301C2×Q8—21no—
302C2×Q8—21no—
303C2×Q8—21no—
304C2×Q8—21no—
305C2×Q8C22⋊C4×C3112yes—
306C2×D4—22no—
307C2×D4—22no—
308C2×D4—22no—
309C2×D4—42no—
310C2×D4—42no—
311C2×D4—41no—
312C2×D4—41no—
313C2×D4—41no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—41no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—22no—
327C22×C4C2×D4×C3111yescharacteristic
328C22×C4C2×D4×C3111yescharacteristic
329C22×C4C2×D4×C3111yescharacteristic
330SD16—48no—
331C2×C8—22no—
332C2×C8—22no—
333C2×C8—41no—
334C2×C8—41no—
335C2×C8—41no—
336C2×C8—41no—
337C2×C8—41no—
338C2×C8—41no—
339C2×C8—41no—
340C4⋊C4—22no—
341C4⋊C4—22no—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—42no—
347C4⋊C4—41no—
348C4⋊C4—41no—
349C4⋊C4—41no—
350C4⋊C4—41no—
351C4⋊C4C22⋊C4×C3112yes—
352C4⋊C4SD16×C3112yescomplemented
353C42—22no—
354C42—22no—
355C42—41no—
356C42—41no—
357C42—82no—
358C42C22×C4×C3111yescharacteristic
359C42C2×D4×C3111yescharacteristic
360C42#41×C3111yescharacteristic
361C42#41×C3111yescharacteristic
362C23—42no—
363C23—81no—
364C23—81no—
365C23—81no—
366C23—81no—
367C23—81no—
368C23—81no—
369C23C31×#12011yescharacteristic
370Q8—22no—
371Q8—22no—
372Q8—41no—
373Q8—41no—
374D4—44no—
375D4—42no—
376D4—42no—
377D4—42no—
378D4—42no—
379D4—82no—
380D4—81no—
381D4—81no—
382D4—81no—
383D4—81no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—41no—
401C2×C4C2×C22⋊C4×C3111yescharacteristic
402C2×C4C4×D4×C3111yescharacteristic
403C2×C4C4×D4×C3111yescharacteristic
404C2×C4C31×#12111yescharacteristic
405C2×C4C31×#12111yescharacteristic
406C2×C4C31×#12311yescharacteristic
407C2×C4C2×SD16×C3111yescharacteristic
408C2×C4C31×#13511yescharacteristic
409C2×C4C31×#13511yescharacteristic
410C2×C4C31×#13511yescharacteristic
411C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
412C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
413C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
414C2×C4C31×#13711yescharacteristic
415C8—42no—
416C8—42no—
417C8—81no—
418C22—82no—
419C22—82no—
420C22—82no—
421C22—161no—
422C22—161no—
423C22—161no—
424C22—161no—
425C22C31×#38611yescharacteristic
426C22C31×#44811yescharacteristic
427C22C31×#44911yescharacteristic
428C22C31×#44911yescharacteristic
429C22C31×#44911yescharacteristic
430C22C31×#45311yescharacteristic
431C22C31×#45411yescharacteristic
432C4—21no—
433C4—21no—
434C4—42no—
435C4—42no—
436C4—42no—
437C4—82no—
438C4—81no—
439C4C31×#41611yescharacteristic
440C4C31×#41811yescharacteristic
441C4C4×SD16×C3111yescharacteristic
442C4C31×#44011yescharacteristic
443C4C31×#46011yescharacteristic
444C4C31×#46411yescharacteristic
445C4C31×#48211yescharacteristic
446C4C31×#48211yescharacteristic
447C2—162no—
448C2C31×#162011yescharacteristic
449C2C31×#162211yescharacteristic
450C2C31×#162611yescharacteristic
451C2C31×#162811yescharacteristic
452C2C31×#187511yescharacteristic
453C2C31×#188011yescharacteristic
454C2C31×#188311yescharacteristic
subgroupG/H
center, socleC23×C31#120
commutatorC42C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC2×C31×#127C22
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×#2355C2semidirect
5. C2×C31×Q8⋊C8C2semidirect
6. C31×#1296C2semidirect
7. C31×#1279C2semidirect
12. C31×#460C4semidirect
124. C4⋊C4×C31SD16semidirect
134. #8978C31direct (N × H)
192. #2355C2×C31semidirect
195. C2×Q8⋊C8C2×C31semidirect
196. #1296C2×C31semidirect
197. #1279C2×C31semidirect
231. #460C4×C31semidirect
298. C31#8978direct (N × H)
352. C4⋊C4SD16×C31semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#4602
C31×#23552
C31×#19822
C31×#19572
C2×C31×Q8⋊C82
C31×#12962
C31×#12792
#897831