Finite Group Databasebeta

← C31×#8574 #21465333

Subgroups — C31×#8574 #21465333

Order 7936.

614 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
1C4×C31×C22⋊Q8C211yesmaximal, characteristic
2C31×#1797C211yesmaximal, characteristic
3C2×C31×#328C212yesmaximal
4C31×#1434C211yesmaximal, characteristic
5C31×#1294C212yesmaximal
6C2×C31×C22⋊Q8C2211yescharacteristic
7C2×C4×Q8×C31C411yescharacteristic, complemented
8C22×C42×C31C2211yescharacteristic
9C2×C31×C4⋊C8—21no—
10C2×C31×C22⋊C8C2212yes—
11C31×#391C411yescharacteristic, complemented
12C31×#389C411yescharacteristic, complemented
13C31×#387—21no—
14C31×#385—21no—
15C31×#380C2211yescharacteristic
16C4×C4⋊C4×C31—21no—
17C4×C4⋊C4×C31C411yescharacteristic, complemented
18C4×C22⋊C4×C31—21no—
19C2×C31×#95—21no—
20C2×C31×#95—21no—
21C2×C31×#95C2212yes—
22C31×#336—21no—
23C31×#328—24no—
24C22×Q8×C31C2×C411yescharacteristic
25C23×C4×C31—22no—
26C23×C4×C31D411yescharacteristic
27C23×C4×C31D411yescharacteristic
28C23×C4×C31C2311yescharacteristic
29C22×C8×C31—22no—
30C31×C22⋊Q8—21no—
31C31×C22⋊Q8—21no—
32C31×C22⋊Q8D412yes—
33C31×C22⋊Q8Q812yes—
34C4×Q8×C31—42no—
35C2×C4⋊C4×C31—21no—
36C2×C4⋊C4×C31—21no—
37C2×C4⋊C4×C31—21no—
38C2×C4⋊C4×C31C2×C411yescharacteristic
39C2×C4⋊C4×C31C2×C411yescharacteristic
40C2×C4⋊C4×C31C2×C411yescharacteristic
41C2×C22⋊C4×C31—21no—
42C2×C22⋊C4×C31—21no—
43C2×C42×C31—21no—
44C2×C42×C31—21no—
45C2×C42×C31—42no—
46C2×C42×C31C2×C411yescharacteristic
47C2×C42×C31C2×C411yescharacteristic
48C2×C42×C31D411yescharacteristic
49C2×C42×C31D411yescharacteristic
50C31×C4⋊C8—42no—
51C31×C22⋊C8—22no—
52C31×C22⋊C8—22no—
53C31×#95—24no—
54C31×#95—21no—
55C31×#95—21no—
56C31×#95—21no—
57C31×#95—21no—
58C31×#95—21no—
59C31×#95—22no—
60C31×#95—22no—
61C31×#95—42no—
62C24×C31C2×D411yescharacteristic
63C2×Q8×C31—21no—
64C2×Q8×C31—41no—
65C2×Q8×C31—41no—
66C2×Q8×C31C4⋊C412yes—
67C22×C4×C31—21no—
68C22×C4×C31—21no—
69C22×C4×C31—22no—
70C22×C4×C31—22no—
71C22×C4×C31—22no—
72C22×C4×C31—22no—
73C22×C4×C31—24no—
74C22×C4×C31—21no—
75C22×C4×C31—21no—
76C22×C4×C31—41no—
77C22×C4×C31—41no—
78C22×C4×C31—41no—
79C22×C4×C31—41no—
80C22×C4×C31—42no—
81C22×C4×C31—42no—
82C22×C4×C31—42no—
83C22×C4×C31—42no—
84C22×C4×C31—42no—
85C22×C4×C31—42no—
86C22×C4×C31C22⋊C411yescharacteristic
87C22×C4×C31C22⋊C411yescharacteristic
88C22×C4×C31C22⋊C411yescharacteristic
89C22×C4×C31C22⋊C411yescharacteristic
90C22×C4×C31C22×C411yescharacteristic
91C22×C4×C31C2×D411yescharacteristic
92C22×C4×C31C2×D411yescharacteristic
93C22×C4×C31C2×Q811yescharacteristic
94C22×C4×C31#4111yescharacteristic
95C22×C4×C31#4111yescharacteristic
96C2×C8×C31—42no—
97C2×C8×C31—42no—
98C2×C8×C31—42no—
99C4⋊C4×C31—21no—
100C4⋊C4×C31—22no—
101C4⋊C4×C31—22no—
102C4⋊C4×C31—42no—
103C4⋊C4×C31—41no—
104C4⋊C4×C31—41no—
105C4⋊C4×C31—42no—
106C4⋊C4×C31C4⋊C412yes—
107C22⋊C4×C31—22no—
108C22⋊C4×C31—22no—
109C22⋊C4×C31—42no—
110C42×C31—22no—
111C42×C31—22no—
112C42×C31—41no—
113C42×C31—41no—
114C42×C31—42no—
115C42×C31—42no—
116#8574C3111yesmaximal, characteristic, direct product factor, Sylow
117C23×C31—21no—
118C23×C31—21no—
119C23×C31—21no—
120C23×C31—21no—
121C23×C31C2×C22⋊C411yescharacteristic
122C23×C31#12111yescharacteristic
123C23×C31C22⋊Q811yescharacteristic
124C23×C31#13512yes—
125C23×C31#13712yes—
126Q8×C31—42no—
127Q8×C31—42no—
128C2×C4×C31—21no—
129C2×C4×C31—21no—
130C2×C4×C31—21no—
131C2×C4×C31—21no—
132C2×C4×C31—21no—
133C2×C4×C31—21no—
134C2×C4×C31—21no—
135C2×C4×C31—21no—
136C2×C4×C31—22no—
137C2×C4×C31—22no—
138C2×C4×C31—21no—
139C2×C4×C31—21no—
140C2×C4×C31—21no—
141C2×C4×C31—21no—
142C2×C4×C31—21no—
143C2×C4×C31—21no—
144C2×C4×C31—41no—
145C2×C4×C31—41no—
146C2×C4×C31—41no—
147C2×C4×C31—41no—
148C2×C4×C31—44no—
149C2×C4×C31—44no—
150C2×C4×C31—41no—
151C2×C4×C31—41no—
152C2×C4×C31—41no—
153C2×C4×C31—41no—
154C2×C4×C31—44no—
155C2×C4×C31—44no—
156C2×C4×C31—44no—
157C2×C4×C31—41no—
158C2×C4×C31—41no—
159C2×C4×C31—41no—
160C2×C4×C31—41no—
161C2×C4×C31—41no—
162C2×C4×C31—41no—
163C2×C4×C31—82no—
164C2×C4×C31—82no—
165C2×C4×C31—82no—
166C2×C4×C31—82no—
167C2×C4×C31#9912yes—
168C2×C4×C31#10412yes—
169C2×C4×C31C2×C4⋊C411yescharacteristic
170C2×C4×C31#11711yescharacteristic
171C2×C4×C31#12111yescharacteristic
172C2×C4×C31C22⋊Q811yescharacteristic
173C8×C31—82no—
174C4×C22⋊Q8C2×C3111yescharacteristic
175#1797C2×C3111yescharacteristic
176C2×#328C2×C3112yes—
177#1434C2×C3111yescharacteristic
178#1294C2×C3112yes—
179C22×C31—21no—
180C22×C31—21no—
181C22×C31—21no—
182C22×C31—21no—
183C22×C31—22no—
184C22×C31—22no—
185C22×C31—22no—
186C22×C31—22no—
187C22×C31#38011yescharacteristic
188C22×C31C2×#9911yescharacteristic
189C22×C31#41011yescharacteristic
190C22×C31#41611yescharacteristic
191C22×C31#41911yescharacteristic
192C22×C31C2×#10411yescharacteristic
193C22×C31#42111yescharacteristic
194C22×C31#46412yes—
195C22×C31#47912yes—
196C4×C31—21no—
197C4×C31—21no—
198C4×C31—21no—
199C4×C31—21no—
200C4×C31—22no—
201C4×C31—22no—
202C4×C31—42no—
203C4×C31—42no—
204C4×C31—41no—
205C4×C31—41no—
206C4×C31—84no—
207C4×C31—81no—
208C4×C31—81no—
209C2×C22⋊Q8C22×C3111yescharacteristic
210C2×C4×Q8C4×C3111yescharacteristic, complemented
211C22×C42C22×C3111yescharacteristic
212C2×C4⋊C8—21no—
213C2×C22⋊C8C22×C3112yes—
214#391C4×C3111yescharacteristic, complemented
215#389C4×C3111yescharacteristic, complemented
216#387—21no—
217#385—21no—
218#380C22×C3111yescharacteristic
219C4×C4⋊C4—21no—
220C4×C4⋊C4C4×C3111yescharacteristic, complemented
221C4×C22⋊C4—21no—
222C2×#95—21no—
223C2×#95—21no—
224C2×#95C22×C3112yes—
225#336—21no—
226#328—24no—
227C2×C31—22no—
228C2×C31—22no—
229C2×C31#150011yescharacteristic
230C2×C31#150811yescharacteristic
231C2×C31#151511yescharacteristic
232C2×C31#151611yescharacteristic
233C2×C31#179911yescharacteristic
234C2×C31#180511yescharacteristic
235C2×C31#180611yescharacteristic
236C22×Q8C2×C4×C3111yescharacteristic
237C23×C4—22no—
238C23×C4D4×C3111yescharacteristic
239C23×C4D4×C3111yescharacteristic
240C23×C4C23×C3111yescharacteristic
241C22×C8—22no—
242C22⋊Q8—21no—
243C22⋊Q8—21no—
244C22⋊Q8D4×C3112yes—
245C22⋊Q8Q8×C3112yes—
246C4×Q8—42no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4C2×C4×C3111yescharacteristic
251C2×C4⋊C4C2×C4×C3111yescharacteristic
252C2×C4⋊C4C2×C4×C3111yescharacteristic
253C2×C22⋊C4—21no—
254C2×C22⋊C4—21no—
255C2×C42—21no—
256C2×C42—21no—
257C2×C42—42no—
258C2×C42C2×C4×C3111yescharacteristic
259C2×C42C2×C4×C3111yescharacteristic
260C2×C42D4×C3111yescharacteristic
261C2×C42D4×C3111yescharacteristic
262C4⋊C8—42no—
263C22⋊C8—22no—
264C22⋊C8—22no—
265#95—24no—
266#95—21no—
267#95—21no—
268#95—21no—
269#95—21no—
270#95—21no—
271#95—22no—
272#95—22no—
273#95—42no—
274C31#857411yescharacteristic, direct product factor, Sylow
275C24C2×D4×C3111yescharacteristic
276C2×Q8—21no—
277C2×Q8—41no—
278C2×Q8—41no—
279C2×Q8C4⋊C4×C3112yes—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—22no—
285C22×C4—22no—
286C22×C4—24no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4—41no—
293C22×C4—42no—
294C22×C4—42no—
295C22×C4—42no—
296C22×C4—42no—
297C22×C4—42no—
298C22×C4—42no—
299C22×C4C22⋊C4×C3111yescharacteristic
300C22×C4C22⋊C4×C3111yescharacteristic
301C22×C4C22⋊C4×C3111yescharacteristic
302C22×C4C22⋊C4×C3111yescharacteristic
303C22×C4C22×C4×C3111yescharacteristic
304C22×C4C2×D4×C3111yescharacteristic
305C22×C4C2×D4×C3111yescharacteristic
306C22×C4C2×Q8×C3111yescharacteristic
307C22×C4#41×C3111yescharacteristic
308C22×C4#41×C3111yescharacteristic
309C2×C8—42no—
310C2×C8—42no—
311C2×C8—42no—
312C4⋊C4—21no—
313C4⋊C4—22no—
314C4⋊C4—22no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—42no—
318C4⋊C4—42no—
319C4⋊C4C4⋊C4×C3112yes—
320C22⋊C4—22no—
321C22⋊C4—22no—
322C22⋊C4—42no—
323C42—22no—
324C42—22no—
325C42—41no—
326C42—41no—
327C42—42no—
328C42—42no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23C2×C22⋊C4×C3111yescharacteristic
334C23C31×#12111yescharacteristic
335C23C31×C22⋊Q811yescharacteristic
336C23C31×#13512yes—
337C23C31×#13712yes—
338Q8—42no—
339Q8—42no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—44no—
361C2×C4—44no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—44no—
367C2×C4—44no—
368C2×C4—44no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—82no—
376C2×C4—82no—
377C2×C4—82no—
378C2×C4—82no—
379C2×C4C31×#9912yes—
380C2×C4C31×#10412yes—
381C2×C4C2×C4⋊C4×C3111yescharacteristic
382C2×C4C31×#11711yescharacteristic
383C2×C4C31×#12111yescharacteristic
384C2×C4C31×C22⋊Q811yescharacteristic
385C8—82no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—22no—
391C22—22no—
392C22—22no—
393C22—22no—
394C22C31×#38011yescharacteristic
395C22C2×C31×#9911yescharacteristic
396C22C31×#41011yescharacteristic
397C22C31×#41611yescharacteristic
398C22C31×#41911yescharacteristic
399C22C2×C31×#10411yescharacteristic
400C22C31×#42111yescharacteristic
401C22C31×#46412yes—
402C22C31×#47912yes—
403C4—21no—
404C4—21no—
405C4—21no—
406C4—21no—
407C4—22no—
408C4—22no—
409C4—42no—
410C4—42no—
411C4—41no—
412C4—41no—
413C4—84no—
414C4—81no—
415C4—81no—
416C2—22no—
417C2—22no—
418C2C31×#150011yescharacteristic
419C2C31×#150811yescharacteristic
420C2C31×#151511yescharacteristic
421C2C31×#151611yescharacteristic
422C2C31×#179911yescharacteristic
423C2C31×#180511yescharacteristic
424C2C31×#180611yescharacteristic
subgroupG/H
center, socleC23×C31C2×C22⋊C4
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC24×C31C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C22×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
7. C2×C4×Q8×C31C4semidirect
11. C31×#391C4semidirect
12. C31×#389C4semidirect
17. C4×C4⋊C4×C31C4semidirect
116. #8574C31direct (N × H)
210. C2×C4×Q8C4×C31semidirect
214. #391C4×C31semidirect
215. #389C4×C31semidirect
220. C4×C4⋊C4C4×C31semidirect
274. C31#8574direct (N × H)

Maximal subgroups

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

subgroupindex
C4×C31×C22⋊Q82
C31×#17972
C2×C31×#3282
C31×#14342
C31×#12942
#857431