Finite Group Databasebeta

← C31×#10416 #21467175

Subgroups — C31×#10416 #21467175

Order 7936.

520 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2547C211yesmaximal, characteristic
2C31×#1990C211yesmaximal, characteristic, complemented
3C31×#1947C211yesmaximal, characteristic, complemented
4C31×#1802C211yesmaximal, characteristic
5C2×C31×#332C211yesmaximal, characteristic, complemented
6C2×C31×D4⋊C8C211yesmaximal, characteristic
7C31×#1279C211yesmaximal, characteristic, complemented
8C2×C31×C4⋊Q8C2211yescharacteristic
9C2×C31×#124—21no—
10C2×C4×D4×C31C2211yescharacteristic
11C2×C31×#107—21no—
12C2×C31×C4⋊C8C2211yescharacteristic
13C2×C31×C4⋊C8C2211yescharacteristic
14C2×C31×#102—21no—
15C2×C4×C8×C31C2211yescharacteristic
16C31×#397—22no—
17C31×#391—21no—
18C31×#384C2211yescharacteristic
19C31×#380—21no—
20C31×#380—21no—
21C4×C4⋊C4×C31C2211yescharacteristic
22C31×#340—21no—
23C31×#340—21no—
24C31×#340—22no—
25C31×#332—22no—
26C31×D4⋊C8—22no—
27C22×Q8×C31—21no—
28C22×D4×C31D411yescharacteristic
29C23×C4×C31—21no—
30C22×C8×C31—21no—
31C22×C8×C31—21no—
32C22×C8×C31—21no—
33C31×C4⋊Q8—21no—
34C31×C4⋊Q8—21no—
35C31×C4⋊Q8—21no—
36C31×C4⋊Q8—21no—
37C31×#124—42no—
38C31×#124—42no—
39C4×D4×C31—21no—
40C4×D4×C31—21no—
41C4×D4×C31—21no—
42C4×D4×C31—21no—
43C2×C4⋊C4×C31—21no—
44C2×C4⋊C4×C31—21no—
45C2×C4⋊C4×C31—21no—
46C2×C4⋊C4×C31—21no—
47C2×C4⋊C4×C31D412yes—
48C2×C4⋊C4×C31D411yescharacteristic
49C2×C4⋊C4×C31D411yescharacteristic
50C2×C4⋊C4×C31D411yescharacteristic
51C2×C22⋊C4×C31—22no—
52C2×C22⋊C4×C31—22no—
53C2×C22⋊C4×C31—21no—
54C2×C42×C31—21no—
55C2×C42×C31C2311yescharacteristic
56C31×#107—42no—
57C31×C4⋊C8—21no—
58C31×C4⋊C8—21no—
59C31×C4⋊C8—21no—
60C31×C4⋊C8D412yes—
61C31×#102—42no—
62C4×C8×C31—21no—
63C4×C8×C31—21no—
64C31×#95—22no—
65C31×#95—22no—
66C31×#95—21no—
67C24×C31—21no—
68C2×Q8×C31—41no—
69C2×Q8×C31—41no—
70C2×Q8×C31—41no—
71C2×Q8×C31—41no—
72C2×Q8×C31—41no—
73C2×Q8×C31—41no—
74C2×D4×C31—21no—
75C2×D4×C31—21no—
76C2×D4×C31—21no—
77C2×D4×C31—21no—
78C2×D4×C31—21no—
79C2×D4×C31D812yes—
80C22×C4×C31—21no—
81C22×C4×C31—21no—
82C22×C4×C31—21no—
83C22×C4×C31—22no—
84C22×C4×C31—41no—
85C22×C4×C31—41no—
86C22×C4×C31—41no—
87C22×C4×C31—41no—
88C22×C4×C31—41no—
89C22×C4×C31—41no—
90C22×C4×C31—41no—
91C22×C4×C31C2×D411yescharacteristic
92C22×C4×C31C2×D411yescharacteristic
93C22×C4×C31C2×D411yescharacteristic
94C2×C8×C31—22no—
95C2×C8×C31—22no—
96C2×C8×C31—41no—
97C2×C8×C31—41no—
98C2×C8×C31—41no—
99C2×C8×C31—41no—
100C2×C8×C31—41no—
101C2×C8×C31—41no—
102C2×C8×C31—41no—
103C4⋊C4×C31—21no—
104C4⋊C4×C31—22no—
105C4⋊C4×C31—21no—
106C4⋊C4×C31—22no—
107C4⋊C4×C31—21no—
108C4⋊C4×C31—21no—
109C4⋊C4×C31—21no—
110C4⋊C4×C31—21no—
111C4⋊C4×C31—42no—
112C4⋊C4×C31—41no—
113C4⋊C4×C31—41no—
114C4⋊C4×C31—41no—
115C4⋊C4×C31—41no—
116C4⋊C4×C31—41no—
117C4⋊C4×C31—41no—
118C22⋊C4×C31—44no—
119C22⋊C4×C31—44no—
120C22⋊C4×C31—41no—
121C22⋊C4×C31—41no—
122C42×C31—41no—
123C42×C31—41no—
124C42×C31C2×D411yescharacteristic
125C42×C31#4111yescharacteristic
126C42×C31#4111yescharacteristic
127C42×C31#4111yescharacteristic
128#10416C3111yesmaximal, characteristic, direct product factor, Sylow
129C23×C31—22no—
130C23×C31—41no—
131C23×C31—41no—
132C23×C31—41no—
133C23×C31—41no—
134C23×C31—41no—
135C23×C31—41no—
136C23×C31#12011yescharacteristic
137Q8×C31—81no—
138Q8×C31—81no—
139Q8×C31—81no—
140Q8×C31—81no—
141D4×C31—22no—
142D4×C31—22no—
143D4×C31—41no—
144D4×C31—41no—
145C2×C4×C31—21no—
146C2×C4×C31—21no—
147C2×C4×C31—41no—
148C2×C4×C31—42no—
149C2×C4×C31—41no—
150C2×C4×C31—41no—
151C2×C4×C31—42no—
152C2×C4×C31—41no—
153C2×C4×C31—41no—
154C2×C4×C31—41no—
155C2×C4×C31—41no—
156C2×C4×C31—42no—
157C2×C4×C31—41no—
158C2×C4×C31—41no—
159C2×C4×C31—81no—
160C2×C4×C31—81no—
161C2×C4×C31—81no—
162C2×C4×C31—81no—
163C2×C4×C31—81no—
164C2×C4×C31—81no—
165C2×C4×C31—81no—
166C2×C4×C31#12111yescharacteristic
167C2×C4×C31#12111yescharacteristic
168C2×C4×C31#12111yescharacteristic
169C2×C4×C31#12311yescharacteristic
170C2×C4×C31#12311yescharacteristic
171C2×C4×C31#12411yescharacteristic
172C2×C4×C31C2×D811yescharacteristic
173C2×C4×C31#13511yescharacteristic
174C2×C4×C31#13511yescharacteristic
175C2×C4×C31#13511yescharacteristic
176C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
177C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
178C2×C4×C31#13711yescharacteristic
179C2×C4×C31#13711yescharacteristic
180C8×C31—42no—
181C8×C31—42no—
182C8×C31—81no—
183#2547C2×C3111yescharacteristic
184#1990C2×C3111yescharacteristic, complemented
185#1947C2×C3111yescharacteristic, complemented
186#1802C2×C3111yescharacteristic
187C2×#332C2×C3111yescharacteristic, complemented
188C2×D4⋊C8C2×C3111yescharacteristic
189#1279C2×C3111yescharacteristic, complemented
190C22×C31—42no—
191C22×C31—42no—
192C22×C31—42no—
193C22×C31—81no—
194C22×C31—81no—
195C22×C31—81no—
196C22×C31—81no—
197C22×C31#39411yescharacteristic
198C22×C31#44711yescharacteristic
199C22×C31#44911yescharacteristic
200C22×C31#45211yescharacteristic
201C22×C31#45211yescharacteristic
202C22×C31#45411yescharacteristic
203C22×C31#45611yescharacteristic
204C4×C31—21no—
205C4×C31—21no—
206C4×C31—81no—
207C4×C31—81no—
208C4×C31—82no—
209C4×C31—81no—
210C4×C31—161no—
211C4×C31#46311yescharacteristic
212C4×C31#46411yescharacteristic
213C4×C31#46611yescharacteristic
214C4×C31#46811yescharacteristic
215C4×C31#48011yescharacteristic
216C4×C31#48211yescharacteristic
217C4×C31#48811yescharacteristic
218C4×C31#48911yescharacteristic
219C2×C4⋊Q8C22×C3111yescharacteristic
220C2×#124—21no—
221C2×C4×D4C22×C3111yescharacteristic
222C2×#107—21no—
223C2×C4⋊C8C22×C3111yescharacteristic
224C2×C4⋊C8C22×C3111yescharacteristic
225C2×#102—21no—
226C2×C4×C8C22×C3111yescharacteristic
227#397—22no—
228#391—21no—
229#384C22×C3111yescharacteristic
230#380—21no—
231#380—21no—
232C4×C4⋊C4C22×C3111yescharacteristic
233#340—21no—
234#340—21no—
235#340—22no—
236#332—22no—
237D4⋊C8—22no—
238C2×C31—82no—
239C2×C31#162511yescharacteristic
240C2×C31#163811yescharacteristic
241C2×C31#164711yescharacteristic
242C2×C31#165211yescharacteristic
243C2×C31#203311yescharacteristic
244C2×C31#203811yescharacteristic
245C2×C31#204211yescharacteristic
246C22×Q8—21no—
247C22×D4D4×C3111yescharacteristic
248C23×C4—21no—
249C22×C8—21no—
250C22×C8—21no—
251C22×C8—21no—
252C4⋊Q8—21no—
253C4⋊Q8—21no—
254C4⋊Q8—21no—
255C4⋊Q8—21no—
256#124—42no—
257#124—42no—
258C4×D4—21no—
259C4×D4—21no—
260C4×D4—21no—
261C4×D4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4D4×C3111yescharacteristic
267C2×C4⋊C4D4×C3112yes—
268C2×C4⋊C4D4×C3111yescharacteristic
269C2×C4⋊C4D4×C3111yescharacteristic
270C2×C22⋊C4—22no—
271C2×C22⋊C4—22no—
272C2×C22⋊C4—21no—
273C2×C42—21no—
274C2×C42C23×C3111yescharacteristic
275#107—42no—
276C4⋊C8—21no—
277C4⋊C8—21no—
278C4⋊C8—21no—
279C4⋊C8D4×C3112yes—
280#102—42no—
281C4×C8—21no—
282C4×C8—21no—
283#95—22no—
284#95—22no—
285#95—21no—
286C31#1041611yescharacteristic, direct product factor, Sylow
287C24—21no—
288C2×Q8—41no—
289C2×Q8—41no—
290C2×Q8—41no—
291C2×Q8—41no—
292C2×Q8—41no—
293C2×Q8—41no—
294C2×D4—21no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—21no—
298C2×D4—21no—
299C2×D4D8×C3112yes—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—22no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4C2×D4×C3111yescharacteristic
312C22×C4C2×D4×C3111yescharacteristic
313C22×C4C2×D4×C3111yescharacteristic
314C2×C8—22no—
315C2×C8—22no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—41no—
319C2×C8—41no—
320C2×C8—41no—
321C2×C8—41no—
322C2×C8—41no—
323C4⋊C4—21no—
324C4⋊C4—22no—
325C4⋊C4—21no—
326C4⋊C4—22no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—42no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C22⋊C4—44no—
339C22⋊C4—44no—
340C22⋊C4—41no—
341C22⋊C4—41no—
342C42—41no—
343C42—41no—
344C42C2×D4×C3111yescharacteristic
345C42#41×C3111yescharacteristic
346C42#41×C3111yescharacteristic
347C42#41×C3111yescharacteristic
348C23—22no—
349C23—41no—
350C23—41no—
351C23—41no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23C31×#12011yescharacteristic
356Q8—81no—
357Q8—81no—
358Q8—81no—
359Q8—81no—
360D4—22no—
361D4—22no—
362D4—41no—
363D4—41no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—42no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—42no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—42no—
378C2×C4—81no—
379C2×C4—81no—
380C2×C4—81no—
381C2×C4—81no—
382C2×C4—81no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4C31×#12111yescharacteristic
386C2×C4C31×#12111yescharacteristic
387C2×C4C31×#12111yescharacteristic
388C2×C4C31×#12311yescharacteristic
389C2×C4C31×#12311yescharacteristic
390C2×C4C31×#12411yescharacteristic
391C2×C4C2×D8×C3111yescharacteristic
392C2×C4C31×#13511yescharacteristic
393C2×C4C31×#13511yescharacteristic
394C2×C4C31×#13511yescharacteristic
395C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
396C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
397C2×C4C31×#13711yescharacteristic
398C2×C4C31×#13711yescharacteristic
399C8—42no—
400C8—42no—
401C8—81no—
402C22—42no—
403C22—42no—
404C22—42no—
405C22—81no—
406C22—81no—
407C22—81no—
408C22—81no—
409C22C31×#39411yescharacteristic
410C22C31×#44711yescharacteristic
411C22C31×#44911yescharacteristic
412C22C31×#45211yescharacteristic
413C22C31×#45211yescharacteristic
414C22C31×#45411yescharacteristic
415C22C31×#45611yescharacteristic
416C4—21no—
417C4—21no—
418C4—81no—
419C4—81no—
420C4—82no—
421C4—81no—
422C4—161no—
423C4C31×#46311yescharacteristic
424C4C31×#46411yescharacteristic
425C4C31×#46611yescharacteristic
426C4C31×#46811yescharacteristic
427C4C31×#48011yescharacteristic
428C4C31×#48211yescharacteristic
429C4C31×#48811yescharacteristic
430C4C31×#48911yescharacteristic
431C2—82no—
432C2C31×#162511yescharacteristic
433C2C31×#163811yescharacteristic
434C2C31×#164711yescharacteristic
435C2C31×#165211yescharacteristic
436C2C31×#203311yescharacteristic
437C2C31×#203811yescharacteristic
438C2C31×#204211yescharacteristic
subgroupG/H
center, socleC23×C31#120
commutator, Frattini, cosocleC2×C42C23×C31
prime radicalC22×D4×C31D4
LCSG ▷ C2×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×#1990C2semidirect
3. C31×#1947C2semidirect
5. C2×C31×#332C2semidirect
7. C31×#1279C2semidirect
128. #10416C31direct (N × H)
184. #1990C2×C31semidirect
185. #1947C2×C31semidirect
187. C2×#332C2×C31semidirect
189. #1279C2×C31semidirect
286. C31#10416direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#25472
C31×#19902
C31×#19472
C31×#18022
C2×C31×#3322
C2×C31×D4⋊C82
C31×#12792
#1041631