Finite Group Databasebeta

← C31×#18197 #21474956

Subgroups — C31×#18197 #21474956

Order 7936.

1174 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3501C211yesmaximal, characteristic
2C2×C31×#451C212yesmaximal, complemented
3C31×#2409C211yesmaximal, characteristic
4C31×#1605C214yesmaximal, complemented
5C31×#1602C214yesmaximal, complemented
6C31×#1520C212yesmaximal, complemented
7C31×#1459C211yesmaximal, characteristic
8C23×Q8×C31C2211yescharacteristic
9C22×Q16×C31—22no—
10C31×#554—24no—
11C31×#554—22no—
12D4×Q8×C31—22no—
13C31×#544C2212yes—
14C31×#543—21no—
15C31×#543C2212yes—
16C31×#533—21no—
17C2×C31×C22⋊Q8—21no—
18C2×C31×C22⋊Q8—21no—
19C2×C31×C22⋊Q8C2212yes—
20C31×#518—21no—
21C2×C4×D4×C31C2211yescharacteristic
22C31×#451—24no—
23C31×#451C2218yes—
24C2×C31×#103—22no—
25C2×C31×C22⋊C8C2212yes—
26C31×#395C2212yes—
27C31×#393C2212yes—
28C31×#391—21no—
29C31×#386—21no—
30C31×#385—21no—
31C31×#380C2211yescharacteristic
32C31×#328C2218yes—
33C31×#324C2212yes—
34C31×#323C2212yes—
35C22×Q8×C31—21no—
36C22×Q8×C31—21no—
37C22×Q8×C31—22no—
38C22×Q8×C31—22no—
39C22×Q8×C31—44no—
40C22×Q8×C31D412yes—
41C22×Q8×C31C2312yes—
42C22×D4×C31D411yescharacteristic
43C23×C4×C31—21no—
44C23×C4×C31D411yescharacteristic
45C23×C4×C31C2311yescharacteristic
46C2×Q16×C31—28no—
47C2×Q16×C31—48no—
48C22×C8×C31—22no—
49C31×C4⋊Q8—21no—
50C31×C4⋊Q8—21no—
51C31×C4⋊Q8—24no—
52C31×#125—22no—
53C31×#125—24no—
54C31×C22⋊Q8—22no—
55C31×C22⋊Q8—22no—
56C31×C22⋊Q8—24no—
57C31×C22⋊Q8—24no—
58C31×C22⋊Q8—24no—
59C31×C22⋊Q8—22no—
60C31×C22⋊Q8—22no—
61C31×C22⋊Q8—22no—
62C31×C22⋊Q8—22no—
63C31×C22⋊Q8—24no—
64C31×C22⋊Q8—44no—
65C31×C22⋊Q8D414yes—
66C31×C22⋊Q8C2314yes—
67C4×Q8×C31—22no—
68C4×Q8×C31—22no—
69C4×D4×C31—24no—
70C4×D4×C31—24no—
71C4×D4×C31—22no—
72C4×D4×C31—22no—
73C31×#117—22no—
74C2×C4⋊C4×C31—21no—
75C2×C4⋊C4×C31—22no—
76C2×C4⋊C4×C31—22no—
77C2×C4⋊C4×C31—22no—
78C2×C4⋊C4×C31—21no—
79C2×C4⋊C4×C31D412yes—
80C2×C4⋊C4×C31C2311yescharacteristic
81C2×C22⋊C4×C31—22no—
82C2×C22⋊C4×C31—22no—
83C2×C22⋊C4×C31—22no—
84C2×C22⋊C4×C31—21no—
85C2×C22⋊C4×C31D411yescharacteristic
86C2×C22⋊C4×C31C2311yescharacteristic
87C2×C42×C31D411yescharacteristic
88C31×#103—28no—
89C31×C22⋊C8—22no—
90C31×C22⋊C8C2314yes—
91C31×#95—22no—
92C31×#95—22no—
93C31×#95C2312yes—
94C24×C31C2×D411yescharacteristic
95C24×C31C2×D411yescharacteristic
96C2×Q8×C31—24no—
97C2×Q8×C31—22no—
98C2×Q8×C31—22no—
99C2×Q8×C31—22no—
100C2×Q8×C31—28no—
101C2×Q8×C31—24no—
102C2×Q8×C31—44no—
103C2×Q8×C31—42no—
104C2×Q8×C31—44no—
105C2×Q8×C31—44no—
106C2×Q8×C31—48no—
107C2×Q8×C31—41no—
108C2×Q8×C31—41no—
109C2×Q8×C31—82no—
110C2×Q8×C31C2×D414yes—
111C2×D4×C31—22no—
112C2×D4×C31—22no—
113C2×D4×C31Q1614yescomplemented
114C22×C4×C31—22no—
115C22×C4×C31—22no—
116C22×C4×C31—22no—
117C22×C4×C31—22no—
118C22×C4×C31—22no—
119C22×C4×C31—21no—
120C22×C4×C31—21no—
121C22×C4×C31—22no—
122C22×C4×C31—42no—
123C22×C4×C31—44no—
124C22×C4×C31—42no—
125C22×C4×C31—42no—
126C22×C4×C31C2×D411yescharacteristic
127C22×C4×C31C2×D412yes—
128C22×C4×C31C2×D411yescharacteristic
129C22×C4×C31C2×D411yescharacteristic
130C22×C4×C31C2×D411yescharacteristic
131C22×C4×C31C2×D412yes—
132C22×C4×C31C2411yescharacteristic
133Q16×C31—416no—
134C2×C8×C31—24no—
135C2×C8×C31—44no—
136C4⋊C4×C31—22no—
137C4⋊C4×C31—24no—
138C4⋊C4×C31—22no—
139C4⋊C4×C31—22no—
140C4⋊C4×C31—24no—
141C4⋊C4×C31—22no—
142C4⋊C4×C31—24no—
143C4⋊C4×C31—22no—
144C4⋊C4×C31—24no—
145C4⋊C4×C31—22no—
146C4⋊C4×C31—42no—
147C4⋊C4×C31—44no—
148C4⋊C4×C31C2×D414yes—
149C22⋊C4×C31—24no—
150C22⋊C4×C31—24no—
151C22⋊C4×C31—22no—
152C22⋊C4×C31—24no—
153C22⋊C4×C31—22no—
154C22⋊C4×C31—44no—
155C22⋊C4×C31—42no—
156C42×C31—24no—
157C42×C31—21no—
158C42×C31—21no—
159#18197C3111yesmaximal, characteristic, direct product factor, Sylow
160C23×C31—21no—
161C23×C31—21no—
162C23×C31—41no—
163C23×C31—41no—
164C23×C31—41no—
165C23×C31—41no—
166C23×C31#12012yes—
167C23×C31C2×Q1612yes—
168C23×C31C2×Q1612yescomplemented
169C23×C31#13712yes—
170C23×C31C22×D411yescharacteristic
171Q8×C31—28no—
172Q8×C31—44no—
173Q8×C31—44no—
174Q8×C31—44no—
175Q8×C31—44no—
176Q8×C31—44no—
177Q8×C31—82no—
178Q8×C31—82no—
179D4×C31—28no—
180C2×C4×C31—21no—
181C2×C4×C31—21no—
182C2×C4×C31—22no—
183C2×C4×C31—24no—
184C2×C4×C31—24no—
185C2×C4×C31—21no—
186C2×C4×C31—24no—
187C2×C4×C31—24no—
188C2×C4×C31—21no—
189C2×C4×C31—42no—
190C2×C4×C31—41no—
191C2×C4×C31—42no—
192C2×C4×C31—48no—
193C2×C4×C31—42no—
194C2×C4×C31—42no—
195C2×C4×C31—41no—
196C2×C4×C31—41no—
197C2×C4×C31—42no—
198C2×C4×C31—42no—
199C2×C4×C31—42no—
200C2×C4×C31—81no—
201C2×C4×C31—82no—
202C2×C4×C31—82no—
203C2×C4×C31—82no—
204C2×C4×C31—82no—
205C2×C4×C31#12011yescharacteristic
206C2×C4×C31#12011yescharacteristic
207C2×C4×C31C2×Q1612yescomplemented
208C2×C4×C31C22×D412yes—
209C8×C31—44no—
210#3501C2×C3111yescharacteristic
211C2×#451C2×C3112yescomplemented
212#2409C2×C3111yescharacteristic
213#1605C2×C3114yescomplemented
214#1602C2×C3114yescomplemented
215#1520C2×C3112yescomplemented
216#1459C2×C3111yescharacteristic
217C22×C31—21no—
218C22×C31—22no—
219C22×C31—21no—
220C22×C31—22no—
221C22×C31—22no—
222C22×C31—42no—
223C22×C31—42no—
224C22×C31—42no—
225C22×C31—41no—
226C22×C31—41no—
227C22×C31—81no—
228C22×C31#45114yes—
229C22×C31C2×#12011yescharacteristic
230C22×C31C22×Q1611yescharacteristic
231C22×C31C2×#13711yescharacteristic
232C4×C31—22no—
233C4×C31—22no—
234C4×C31—21no—
235C4×C31—41no—
236C4×C31—44no—
237C4×C31—44no—
238C4×C31—41no—
239C4×C31—44no—
240C4×C31—82no—
241C4×C31B(4,𝔽2)12yes—
242C23×Q8C22×C3111yescharacteristic
243C22×Q16—22no—
244#554—24no—
245#554—22no—
246D4×Q8—22no—
247#544C22×C3112yes—
248#543—21no—
249#543C22×C3112yes—
250#533—21no—
251C2×C22⋊Q8—21no—
252C2×C22⋊Q8—21no—
253C2×C22⋊Q8C22×C3112yes—
254#518—21no—
255C2×C4×D4C22×C3111yescharacteristic
256#451—24no—
257#451C22×C3118yes—
258C2×#103—22no—
259C2×C22⋊C8C22×C3112yes—
260#395C22×C3112yes—
261#393C22×C3112yes—
262#391—21no—
263#386—21no—
264#385—21no—
265#380C22×C3111yescharacteristic
266#328C22×C3118yes—
267#324C22×C3112yes—
268#323C22×C3112yes—
269C2×C31—21no—
270C2×C31—21no—
271C2×C31—24no—
272C2×C31—42no—
273C2×C31C2×#45111yescharacteristic
274C2×C31#302211yescharacteristic
275C2×C31C2×B(4,𝔽2)11yescharacteristic
276C22×Q8—21no—
277C22×Q8—21no—
278C22×Q8—22no—
279C22×Q8—22no—
280C22×Q8—44no—
281C22×Q8D4×C3112yes—
282C22×Q8C23×C3112yes—
283C22×D4D4×C3111yescharacteristic
284C23×C4—21no—
285C23×C4D4×C3111yescharacteristic
286C23×C4C23×C3111yescharacteristic
287C2×Q16—28no—
288C2×Q16—48no—
289C22×C8—22no—
290C4⋊Q8—21no—
291C4⋊Q8—21no—
292C4⋊Q8—24no—
293#125—22no—
294#125—24no—
295C22⋊Q8—22no—
296C22⋊Q8—22no—
297C22⋊Q8—24no—
298C22⋊Q8—24no—
299C22⋊Q8—24no—
300C22⋊Q8—22no—
301C22⋊Q8—22no—
302C22⋊Q8—22no—
303C22⋊Q8—22no—
304C22⋊Q8—24no—
305C22⋊Q8—44no—
306C22⋊Q8D4×C3114yes—
307C22⋊Q8C23×C3114yes—
308C4×Q8—22no—
309C4×Q8—22no—
310C4×D4—24no—
311C4×D4—24no—
312C4×D4—22no—
313C4×D4—22no—
314#117—22no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4D4×C3112yes—
321C2×C4⋊C4C23×C3111yescharacteristic
322C2×C22⋊C4—22no—
323C2×C22⋊C4—22no—
324C2×C22⋊C4—22no—
325C2×C22⋊C4—21no—
326C2×C22⋊C4D4×C3111yescharacteristic
327C2×C22⋊C4C23×C3111yescharacteristic
328C2×C42D4×C3111yescharacteristic
329#103—28no—
330C22⋊C8—22no—
331C22⋊C8C23×C3114yes—
332#95—22no—
333#95—22no—
334#95C23×C3112yes—
335C31#1819711yescharacteristic, direct product factor, Sylow
336C24C2×D4×C3111yescharacteristic
337C24C2×D4×C3111yescharacteristic
338C2×Q8—24no—
339C2×Q8—22no—
340C2×Q8—22no—
341C2×Q8—22no—
342C2×Q8—28no—
343C2×Q8—24no—
344C2×Q8—44no—
345C2×Q8—42no—
346C2×Q8—44no—
347C2×Q8—44no—
348C2×Q8—48no—
349C2×Q8—41no—
350C2×Q8—41no—
351C2×Q8—82no—
352C2×Q8C2×D4×C3114yes—
353C2×D4—22no—
354C2×D4—22no—
355C2×D4Q16×C3114yescomplemented
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—22no—
364C22×C4—42no—
365C22×C4—44no—
366C22×C4—42no—
367C22×C4—42no—
368C22×C4C2×D4×C3111yescharacteristic
369C22×C4C2×D4×C3112yes—
370C22×C4C2×D4×C3111yescharacteristic
371C22×C4C2×D4×C3111yescharacteristic
372C22×C4C2×D4×C3111yescharacteristic
373C22×C4C2×D4×C3112yes—
374C22×C4C24×C3111yescharacteristic
375Q16—416no—
376C2×C8—24no—
377C2×C8—44no—
378C4⋊C4—22no—
379C4⋊C4—24no—
380C4⋊C4—22no—
381C4⋊C4—22no—
382C4⋊C4—24no—
383C4⋊C4—22no—
384C4⋊C4—24no—
385C4⋊C4—22no—
386C4⋊C4—24no—
387C4⋊C4—22no—
388C4⋊C4—42no—
389C4⋊C4—44no—
390C4⋊C4C2×D4×C3114yes—
391C22⋊C4—24no—
392C22⋊C4—24no—
393C22⋊C4—22no—
394C22⋊C4—24no—
395C22⋊C4—22no—
396C22⋊C4—44no—
397C22⋊C4—42no—
398C42—24no—
399C42—21no—
400C42—21no—
401C23—21no—
402C23—21no—
403C23—41no—
404C23—41no—
405C23—41no—
406C23—41no—
407C23C31×#12012yes—
408C23C2×Q16×C3112yes—
409C23C2×Q16×C3112yescomplemented
410C23C31×#13712yes—
411C23C22×D4×C3111yescharacteristic
412Q8—28no—
413Q8—44no—
414Q8—44no—
415Q8—44no—
416Q8—44no—
417Q8—44no—
418Q8—82no—
419Q8—82no—
420D4—28no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—22no—
424C2×C4—24no—
425C2×C4—24no—
426C2×C4—21no—
427C2×C4—24no—
428C2×C4—24no—
429C2×C4—21no—
430C2×C4—42no—
431C2×C4—41no—
432C2×C4—42no—
433C2×C4—48no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—81no—
442C2×C4—82no—
443C2×C4—82no—
444C2×C4—82no—
445C2×C4—82no—
446C2×C4C31×#12011yescharacteristic
447C2×C4C31×#12011yescharacteristic
448C2×C4C2×Q16×C3112yescomplemented
449C2×C4C22×D4×C3112yes—
450C8—44no—
451C22—21no—
452C22—22no—
453C22—21no—
454C22—22no—
455C22—22no—
456C22—42no—
457C22—42no—
458C22—42no—
459C22—41no—
460C22—41no—
461C22—81no—
462C22C31×#45114yes—
463C22C2×C31×#12011yescharacteristic
464C22C22×Q16×C3111yescharacteristic
465C22C2×C31×#13711yescharacteristic
466C4—22no—
467C4—22no—
468C4—21no—
469C4—41no—
470C4—44no—
471C4—44no—
472C4—41no—
473C4—44no—
474C4—82no—
475C4C31×B(4,𝔽2)12yes—
476C2—21no—
477C2—21no—
478C2—24no—
479C2—42no—
480C2C2×C31×#45111yescharacteristic
481C2C31×#302211yescharacteristic
482C2C2×C31×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC22×D4×C31D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#451C2semidirect
4. C31×#1605C2semidirect
5. C31×#1602C2semidirect
6. C31×#1520C2semidirect
113. C2×D4×C31Q16semidirect
159. #18197C31direct (N × H)
168. C23×C31C2×Q16semidirect
207. C2×C4×C31C2×Q16semidirect
211. C2×#451C2×C31semidirect
213. #1605C2×C31semidirect
214. #1602C2×C31semidirect
215. #1520C2×C31semidirect
335. C31#18197direct (N × H)
355. C2×D4Q16×C31semidirect
409. C23C2×Q16×C31semidirect
448. C2×C4C2×Q16×C31semidirect

Maximal subgroups

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

subgroupindex
C31×#35012
C2×C31×#4512
C31×#24092
C31×#16052
C31×#16022
C31×#15202
C31×#14592
#1819731