Finite Group Databasebeta

← C31×#8485 #21465244

Subgroups — C31×#8485 #21465244

Order 7936.

630 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3563C211yesmaximal, characteristic
2C31×#1998C211yesmaximal, characteristic, complemented
3C31×#1559C211yesmaximal, characteristic, complemented
4C31×#1529C211yesmaximal, characteristic
5C31×#1495C211yesmaximal, characteristic
6C31×#1485C211yesmaximal, characteristic, complemented
7C31×#1470C211yesmaximal, characteristic, complemented
8C31×#564—21no—
9C31×#563—21no—
10C31×#557—21no—
11C31×#554—21no—
12C31×#552—21no—
13C31×#552—22no—
14C31×#552—21no—
15C31×#544—21no—
16C31×#544C412yes—
17C31×#541—21no—
18C31×#541—22no—
19C31×#539C412yes—
20C31×#533C2211yescharacteristic
21C31×#529C2211yescharacteristic
22C2×C31×#125C2211yescharacteristic
23C31×#432C2211yescharacteristic
24C31×#431C2211yescharacteristic
25C31×#423C2211yescharacteristic
26C4×M16×C31C2211yescharacteristic
27C31×#343—21no—
28C31×#343—21no—
29C31×#333—21no—
30C31×#332—21no—
31C31×#330—21no—
32C31×#329—21no—
33C31×Q8⋊C8—22no—
34C31×Q8⋊C8—21no—
35C31×D4⋊C8—21no—
36C31×#324—22no—
37C2×M16×C31—21no—
38C2×M16×C31—21no—
39C31×C4⋊Q8—21no—
40C31×C4⋊Q8—22no—
41C31×C4⋊Q8—22no—
42C31×C4⋊Q8D411yescharacteristic
43C31×C4⋊Q8D411yescharacteristic
44C31×#126—22no—
45C31×#126—22no—
46C31×#126—22no—
47C31×#126—22no—
48C31×#126—21no—
49C31×#125—22no—
50C31×#125—22no—
51C31×#125—22no—
52C31×#125—22no—
53C31×#125—21no—
54C31×#125—22no—
55C31×#125—22no—
56C31×#125—22no—
57C31×#125—22no—
58C31×#125—21no—
59C31×#125—21no—
60C31×#125—21no—
61C31×#125—21no—
62C31×#125—21no—
63C31×#125D411yescharacteristic
64C31×#124D411yescharacteristic
65C31×#123—22no—
66C31×#123—22no—
67C31×#123—21no—
68C31×C22⋊Q8—21no—
69C31×C22⋊Q8—21no—
70C31×C22⋊Q8—22no—
71C31×C22⋊Q8—22no—
72C31×C22⋊Q8—22no—
73C31×C22⋊Q8—22no—
74C31×C22⋊Q8—21no—
75C31×C22⋊Q8C2×C411yescharacteristic
76C31×C22⋊Q8C2×C412yes—
77C31×#121C2×C411yescharacteristic
78C4×Q8×C31—21no—
79C4×Q8×C31—22no—
80C4×Q8×C31—21no—
81C4×Q8×C31—21no—
82C4×Q8×C31D411yescharacteristic
83C4×Q8×C31D412yes—
84C4×D4×C31—22no—
85C4×D4×C31—21no—
86C4×D4×C31D411yescharacteristic
87C31×#117—22no—
88C31×#117—21no—
89C31×#117—22no—
90C31×#117—21no—
91C31×#117—21no—
92C2×C4⋊C4×C31—21no—
93C2×C4⋊C4×C31C2×C412yes—
94C2×C4⋊C4×C31D412yes—
95C2×C4⋊C4×C31D411yescharacteristic
96C2×C4⋊C4×C31D411yescharacteristic
97C2×C42×C31C2311yescharacteristic
98C31×C4⋊C8—21no—
99C31×C4⋊C8—21no—
100C31×C4⋊C8—21no—
101C31×C4⋊C8—21no—
102C31×C22⋊C8—21no—
103C31×C22⋊C8—21no—
104C31×#97—21no—
105C31×#97—21no—
106C4×C8×C31—21no—
107C4×C8×C31—21no—
108C2×Q8×C31—22no—
109C2×Q8×C31—21no—
110C2×Q8×C31C22⋊C412yes—
111C2×Q8×C31C22⋊C411yescharacteristic
112C2×D4×C31—21no—
113C2×D4×C31C22⋊C411yescharacteristic
114C22×C4×C31—22no—
115C22×C4×C31—21no—
116C22×C4×C31C22⋊C412yes—
117C22×C4×C31C22⋊C412yes—
118C22×C4×C31C22×C411yescharacteristic
119C22×C4×C31C2×D411yescharacteristic
120C22×C4×C31C2×D411yescharacteristic
121M16×C31—22no—
122M16×C31—41no—
123M16×C31—42no—
124C2×C8×C31—41no—
125C2×C8×C31—41no—
126C2×C8×C31—41no—
127C2×C8×C31—41no—
128C4⋊C4×C31—22no—
129C4⋊C4×C31—22no—
130C4⋊C4×C31—22no—
131C4⋊C4×C31—22no—
132C4⋊C4×C31—22no—
133C4⋊C4×C31—22no—
134C4⋊C4×C31—22no—
135C4⋊C4×C31—22no—
136C4⋊C4×C31—22no—
137C4⋊C4×C31—22no—
138C4⋊C4×C31—21no—
139C4⋊C4×C31—22no—
140C4⋊C4×C31—21no—
141C4⋊C4×C31—21no—
142C4⋊C4×C31—21no—
143C4⋊C4×C31—22no—
144C4⋊C4×C31—21no—
145C4⋊C4×C31—22no—
146C4⋊C4×C31—21no—
147C4⋊C4×C31—21no—
148C4⋊C4×C31—21no—
149C4⋊C4×C31—21no—
150C4⋊C4×C31—21no—
151C4⋊C4×C31—21no—
152C4⋊C4×C31—22no—
153C4⋊C4×C31C22⋊C411yescharacteristic
154C4⋊C4×C31C22⋊C411yescharacteristic
155C4⋊C4×C31C22⋊C412yes—
156C22⋊C4×C31—22no—
157C22⋊C4×C31—22no—
158C22⋊C4×C31—22no—
159C22⋊C4×C31—22no—
160C22⋊C4×C31—21no—
161C22⋊C4×C31—21no—
162C22⋊C4×C31—21no—
163C22⋊C4×C31—21no—
164C22⋊C4×C31—21no—
165C42×C31—22no—
166C42×C31—22no—
167C42×C31—22no—
168C42×C31—22no—
169C42×C31—21no—
170C42×C31C2×D411yescharacteristic
171C42×C31C2×D411yescharacteristic
172C42×C31C2×D411yescharacteristic
173C42×C31C2×D411yescharacteristic
174#8485C3111yesmaximal, characteristic, direct product factor, Sylow
175C23×C31—21no—
176C23×C31C2×C22⋊C411yescharacteristic
177Q8×C31—41no—
178Q8×C31—42no—
179Q8×C31—41no—
180Q8×C31—41no—
181Q8×C31—82no—
182D4×C31—41no—
183D4×C31—42no—
184C2×C4×C31—21no—
185C2×C4×C31—21no—
186C2×C4×C31—22no—
187C2×C4×C31—21no—
188C2×C4×C31—21no—
189C2×C4×C31—22no—
190C2×C4×C31—21no—
191C2×C4×C31—22no—
192C2×C4×C31—22no—
193C2×C4×C31—41no—
194C2×C4×C31—41no—
195C2×C4×C31—41no—
196C2×C4×C31—41no—
197C2×C4×C31—42no—
198C2×C4×C31—42no—
199C2×C4×C31—82no—
200C2×C4×C31C2×C22⋊C411yescharacteristic
201C2×C4×C31C2×C22⋊C411yescharacteristic
202C2×C4×C31#12011yescharacteristic
203C2×C4×C31#12011yescharacteristic
204C2×C4×C31#12011yescharacteristic
205C2×C4×C31#12011yescharacteristic
206C8×C31—42no—
207C8×C31—81no—
208C8×C31—81no—
209C8×C31—81no—
210#3563C2×C3111yescharacteristic
211#1998C2×C3111yescharacteristic, complemented
212#1559C2×C3111yescharacteristic, complemented
213#1529C2×C3111yescharacteristic
214#1495C2×C3111yescharacteristic
215#1485C2×C3111yescharacteristic, complemented
216#1470C2×C3111yescharacteristic, complemented
217C22×C31—21no—
218C22×C31—21no—
219C22×C31—21no—
220C22×C31—41no—
221C22×C31—41no—
222C22×C31—41no—
223C22×C31#37911yescharacteristic
224C4×C31—21no—
225C4×C31—21no—
226C4×C31—21no—
227C4×C31—21no—
228C4×C31—21no—
229C4×C31—41no—
230C4×C31—42no—
231C4×C31—42no—
232C4×C31—41no—
233C4×C31—42no—
234C4×C31—42no—
235C4×C31—41no—
236C4×C31#45411yescharacteristic
237C4×C31#45611yescharacteristic
238#564—21no—
239#563—21no—
240#557—21no—
241#554—21no—
242#552—21no—
243#552—22no—
244#552—21no—
245#544—21no—
246#544C4×C3112yes—
247#541—21no—
248#541—22no—
249#539C4×C3112yes—
250#533C22×C3111yescharacteristic
251#529C22×C3111yescharacteristic
252C2×#125C22×C3111yescharacteristic
253#432C22×C3111yescharacteristic
254#431C22×C3111yescharacteristic
255#423C22×C3111yescharacteristic
256C4×M16C22×C3111yescharacteristic
257#343—21no—
258#343—21no—
259#333—21no—
260#332—21no—
261#330—21no—
262#329—21no—
263Q8⋊C8—22no—
264Q8⋊C8—21no—
265D4⋊C8—21no—
266#324—22no—
267C2×C31—41no—
268C2×C31—81no—
269C2×C31#179111yescharacteristic
270C2×C31#179311yescharacteristic
271C2×C31#179611yescharacteristic
272C2×M16—21no—
273C2×M16—21no—
274C4⋊Q8—21no—
275C4⋊Q8—22no—
276C4⋊Q8—22no—
277C4⋊Q8D4×C3111yescharacteristic
278C4⋊Q8D4×C3111yescharacteristic
279#126—22no—
280#126—22no—
281#126—22no—
282#126—22no—
283#126—21no—
284#125—22no—
285#125—22no—
286#125—22no—
287#125—22no—
288#125—21no—
289#125—22no—
290#125—22no—
291#125—22no—
292#125—22no—
293#125—21no—
294#125—21no—
295#125—21no—
296#125—21no—
297#125—21no—
298#125D4×C3111yescharacteristic
299#124D4×C3111yescharacteristic
300#123—22no—
301#123—22no—
302#123—21no—
303C22⋊Q8—21no—
304C22⋊Q8—21no—
305C22⋊Q8—22no—
306C22⋊Q8—22no—
307C22⋊Q8—22no—
308C22⋊Q8—22no—
309C22⋊Q8—21no—
310C22⋊Q8C2×C4×C3111yescharacteristic
311C22⋊Q8C2×C4×C3112yes—
312#121C2×C4×C3111yescharacteristic
313C4×Q8—21no—
314C4×Q8—22no—
315C4×Q8—21no—
316C4×Q8—21no—
317C4×Q8D4×C3111yescharacteristic
318C4×Q8D4×C3112yes—
319C4×D4—22no—
320C4×D4—21no—
321C4×D4D4×C3111yescharacteristic
322#117—22no—
323#117—21no—
324#117—22no—
325#117—21no—
326#117—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4C2×C4×C3112yes—
329C2×C4⋊C4D4×C3112yes—
330C2×C4⋊C4D4×C3111yescharacteristic
331C2×C4⋊C4D4×C3111yescharacteristic
332C2×C42C23×C3111yescharacteristic
333C4⋊C8—21no—
334C4⋊C8—21no—
335C4⋊C8—21no—
336C4⋊C8—21no—
337C22⋊C8—21no—
338C22⋊C8—21no—
339#97—21no—
340#97—21no—
341C4×C8—21no—
342C4×C8—21no—
343C31#848511yescharacteristic, direct product factor, Sylow
344C2×Q8—22no—
345C2×Q8—21no—
346C2×Q8C22⋊C4×C3112yes—
347C2×Q8C22⋊C4×C3111yescharacteristic
348C2×D4—21no—
349C2×D4C22⋊C4×C3111yescharacteristic
350C22×C4—22no—
351C22×C4—21no—
352C22×C4C22⋊C4×C3112yes—
353C22×C4C22⋊C4×C3112yes—
354C22×C4C22×C4×C3111yescharacteristic
355C22×C4C2×D4×C3111yescharacteristic
356C22×C4C2×D4×C3111yescharacteristic
357M16—22no—
358M16—41no—
359M16—42no—
360C2×C8—41no—
361C2×C8—41no—
362C2×C8—41no—
363C2×C8—41no—
364C4⋊C4—22no—
365C4⋊C4—22no—
366C4⋊C4—22no—
367C4⋊C4—22no—
368C4⋊C4—22no—
369C4⋊C4—22no—
370C4⋊C4—22no—
371C4⋊C4—22no—
372C4⋊C4—22no—
373C4⋊C4—22no—
374C4⋊C4—21no—
375C4⋊C4—22no—
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—22no—
380C4⋊C4—21no—
381C4⋊C4—22no—
382C4⋊C4—21no—
383C4⋊C4—21no—
384C4⋊C4—21no—
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—22no—
389C4⋊C4C22⋊C4×C3111yescharacteristic
390C4⋊C4C22⋊C4×C3111yescharacteristic
391C4⋊C4C22⋊C4×C3112yes—
392C22⋊C4—22no—
393C22⋊C4—22no—
394C22⋊C4—22no—
395C22⋊C4—22no—
396C22⋊C4—21no—
397C22⋊C4—21no—
398C22⋊C4—21no—
399C22⋊C4—21no—
400C22⋊C4—21no—
401C42—22no—
402C42—22no—
403C42—22no—
404C42—22no—
405C42—21no—
406C42C2×D4×C3111yescharacteristic
407C42C2×D4×C3111yescharacteristic
408C42C2×D4×C3111yescharacteristic
409C42C2×D4×C3111yescharacteristic
410C23—21no—
411C23C2×C22⋊C4×C3111yescharacteristic
412Q8—41no—
413Q8—42no—
414Q8—41no—
415Q8—41no—
416Q8—82no—
417D4—41no—
418D4—42no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—22no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—22no—
425C2×C4—21no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—82no—
435C2×C4C2×C22⋊C4×C3111yescharacteristic
436C2×C4C2×C22⋊C4×C3111yescharacteristic
437C2×C4C31×#12011yescharacteristic
438C2×C4C31×#12011yescharacteristic
439C2×C4C31×#12011yescharacteristic
440C2×C4C31×#12011yescharacteristic
441C8—42no—
442C8—81no—
443C8—81no—
444C8—81no—
445C22—21no—
446C22—21no—
447C22—21no—
448C22—41no—
449C22—41no—
450C22—41no—
451C22C31×#37911yescharacteristic
452C4—21no—
453C4—21no—
454C4—21no—
455C4—21no—
456C4—21no—
457C4—42no—
458C4—41no—
459C4—42no—
460C4—42no—
461C4—41no—
462C4—41no—
463C4—42no—
464C4C31×#45411yescharacteristic
465C4C31×#45611yescharacteristic
466C2—41no—
467C2—81no—
468C2C31×#179111yescharacteristic
469C2C31×#179311yescharacteristic
470C2C31×#179611yescharacteristic
subgroupG/H
center, socleC22×C31#379
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC31×#121C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#1998C2semidirect
3. C31×#1559C2semidirect
6. C31×#1485C2semidirect
7. C31×#1470C2semidirect
174. #8485C31direct (N × H)
211. #1998C2×C31semidirect
212. #1559C2×C31semidirect
215. #1485C2×C31semidirect
216. #1470C2×C31semidirect
343. C31#8485direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35632
C31×#19982
C31×#15592
C31×#15292
C31×#14952
C31×#14852
C31×#14702
#848531