Finite Group Databasebeta

← C31×#9927 #21466686

Subgroups — C31×#9927 #21466686

Order 7936.

654 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×#483C211yesmaximal, characteristic
2C31×#2627C211yesmaximal, characteristic
3C2×C31×#398C211yesmaximal, characteristic
4C31×#1823C211yesmaximal, characteristic
5C2×C31×#328C211yesmaximal, characteristic
6C2×C31×#324C211yesmaximal, characteristic
7C31×#1294C211yesmaximal, characteristic
8C2×C31×C22⋊Q8C2211yescharacteristic
9C22×C4⋊C4×C31—21no—
10C22×C4⋊C4×C31C2211yescharacteristic
11C22×C4⋊C4×C31C2211yescharacteristic
12C31×#483—22no—
13C31×#483—22no—
14C2×C31×#106—21no—
15C2×C31×#103—21no—
16C2×C31×C22⋊C8C2211yescharacteristic
17C2×C31×C22⋊C8C2211yescharacteristic
18C31×#400—21no—
19C31×#398—22no—
20C31×#398—22no—
21C31×#398—22no—
22C31×#395—21no—
23C31×#385—21no—
24C31×#381—21no—
25C31×#380C2211yescharacteristic
26C2×C31×#95—21no—
27C2×C31×#95C2211yescharacteristic
28C31×#340—22no—
29C31×#328—22no—
30C31×#324—22no—
31C22×Q8×C31D411yescharacteristic
32C23×C4×C31—21no—
33C23×C4×C31—21no—
34C23×C4×C31D411yescharacteristic
35C23×C4×C31D411yescharacteristic
36C23×C4×C31C2311yescharacteristic
37C22×C8×C31—21no—
38C22×C8×C31—21no—
39C31×C22⋊Q8—21no—
40C31×C22⋊Q8—21no—
41C31×C22⋊Q8—21no—
42C31×C22⋊Q8—21no—
43C2×C4⋊C4×C31—21no—
44C2×C4⋊C4×C31—21no—
45C2×C4⋊C4×C31—21no—
46C2×C4⋊C4×C31—21no—
47C2×C4⋊C4×C31—24no—
48C2×C4⋊C4×C31—21no—
49C2×C4⋊C4×C31—21no—
50C2×C4⋊C4×C31—21no—
51C2×C4⋊C4×C31—21no—
52C2×C4⋊C4×C31—21no—
53C2×C4⋊C4×C31—21no—
54C2×C4⋊C4×C31—21no—
55C2×C4⋊C4×C31—21no—
56C2×C4⋊C4×C31—22no—
57C2×C4⋊C4×C31—42no—
58C2×C4⋊C4×C31—42no—
59C2×C4⋊C4×C31D412yes—
60C2×C4⋊C4×C31D411yescharacteristic
61C2×C4⋊C4×C31D412yes—
62C2×C22⋊C4×C31—21no—
63C2×C22⋊C4×C31—21no—
64C31×#106—24no—
65C31×#103—24no—
66C31×C22⋊C8—21no—
67C31×C22⋊C8—21no—
68C31×C22⋊C8—21no—
69C31×C22⋊C8D412yes—
70C31×#95—22no—
71C31×#95—24no—
72C31×#95—22no—
73C31×#95—22no—
74C31×#95—21no—
75C31×#95—21no—
76C31×#95D412yes—
77C24×C31C2×D411yescharacteristic
78C2×Q8×C31—21no—
79C2×Q8×C31—21no—
80C2×Q8×C31—42no—
81C22×C4×C31—24no—
82C22×C4×C31—22no—
83C22×C4×C31—21no—
84C22×C4×C31—21no—
85C22×C4×C31—21no—
86C22×C4×C31—21no—
87C22×C4×C31—21no—
88C22×C4×C31—21no—
89C22×C4×C31—21no—
90C22×C4×C31—22no—
91C22×C4×C31—21no—
92C22×C4×C31—22no—
93C22×C4×C31—21no—
94C22×C4×C31—21no—
95C22×C4×C31—21no—
96C22×C4×C31—42no—
97C22×C4×C31—42no—
98C22×C4×C31—41no—
99C22×C4×C31—41no—
100C22×C4×C31—42no—
101C22×C4×C31—41no—
102C22×C4×C31—41no—
103C22×C4×C31—41no—
104C22×C4×C31—41no—
105C22×C4×C31—41no—
106C22×C4×C31—41no—
107C22×C4×C31SD1612yes—
108C22×C4×C31C2×D411yescharacteristic
109C22×C4×C31C2×D411yescharacteristic
110C22×C4×C31C2×D411yescharacteristic
111C22×C4×C31C2×D411yescharacteristic
112C22×C4×C31C2×D411yescharacteristic
113C22×C4×C31#4111yescharacteristic
114C2×C8×C31—22no—
115C2×C8×C31—42no—
116C2×C8×C31—42no—
117C2×C8×C31—41no—
118C4⋊C4×C31—22no—
119C4⋊C4×C31—21no—
120C4⋊C4×C31—22no—
121C4⋊C4×C31—21no—
122C4⋊C4×C31—48no—
123C4⋊C4×C31—42no—
124C4⋊C4×C31—41no—
125C4⋊C4×C31—41no—
126C4⋊C4×C31—41no—
127C4⋊C4×C31—41no—
128C4⋊C4×C31—41no—
129C4⋊C4×C31—41no—
130C4⋊C4×C31—41no—
131C4⋊C4×C31—41no—
132C4⋊C4×C31—82no—
133C22⋊C4×C31—41no—
134C22⋊C4×C31—41no—
135C22⋊C4×C31—41no—
136C22⋊C4×C31—41no—
137#9927C3111yesmaximal, characteristic, direct product factor, Sylow
138C23×C31—22no—
139C23×C31—22no—
140C23×C31#12011yescharacteristic
141C23×C31#12011yescharacteristic
142C23×C31#12111yescharacteristic
143C23×C31C2×SD1611yescharacteristic
144C23×C31#13511yescharacteristic
145C23×C31AGL(1,ℤ/8)11yescharacteristic
146C23×C31#13711yescharacteristic
147Q8×C31—42no—
148Q8×C31—81no—
149C2×C4×C31—22no—
150C2×C4×C31—22no—
151C2×C4×C31—24no—
152C2×C4×C31—22no—
153C2×C4×C31—22no—
154C2×C4×C31—22no—
155C2×C4×C31—41no—
156C2×C4×C31—41no—
157C2×C4×C31—41no—
158C2×C4×C31—41no—
159C2×C4×C31—44no—
160C2×C4×C31—44no—
161C2×C4×C31—42no—
162C2×C4×C31—41no—
163C2×C4×C31—41no—
164C2×C4×C31—42no—
165C2×C4×C31—41no—
166C2×C4×C31—41no—
167C2×C4×C31—42no—
168C2×C4×C31—41no—
169C2×C4×C31—41no—
170C2×C4×C31—42no—
171C2×C4×C31—41no—
172C2×C4×C31—42no—
173C2×C4×C31—42no—
174C2×C4×C31—42no—
175C2×C4×C31—42no—
176C2×C4×C31—42no—
177C2×C4×C31—42no—
178C2×C4×C31—42no—
179C2×C4×C31—42no—
180C2×C4×C31—81no—
181C2×C4×C31—81no—
182C2×C4×C31—81no—
183C2×C4×C31—81no—
184C2×C4×C31—81no—
185C2×C4×C31#12011yescharacteristic
186C2×C4×C31#12111yescharacteristic
187C2×C4×C31#12111yescharacteristic
188C2×C4×C31#12711yescharacteristic
189C8×C31—42no—
190C8×C31—81no—
191C2×#483C2×C3111yescharacteristic
192#2627C2×C3111yescharacteristic
193C2×#398C2×C3111yescharacteristic
194#1823C2×C3111yescharacteristic
195C2×#328C2×C3111yescharacteristic
196C2×#324C2×C3111yescharacteristic
197#1294C2×C3111yescharacteristic
198C22×C31—22no—
199C22×C31—22no—
200C22×C31—22no—
201C22×C31—22no—
202C22×C31—21no—
203C22×C31—21no—
204C22×C31—21no—
205C22×C31—21no—
206C22×C31#39211yescharacteristic
207C22×C31#44811yescharacteristic
208C22×C31#44911yescharacteristic
209C22×C31#45011yescharacteristic
210C22×C31#45211yescharacteristic
211C22×C31#45612yes—
212C22×C31#45812yes—
213C22×C31#46511yescharacteristic
214C22×C31#46811yescharacteristic
215C4×C31—21no—
216C4×C31—21no—
217C4×C31—21no—
218C4×C31—21no—
219C4×C31—44no—
220C4×C31—42no—
221C4×C31—82no—
222C4×C31—82no—
223C4×C31—81no—
224C4×C31—81no—
225C4×C31—81no—
226C2×C22⋊Q8C22×C3111yescharacteristic
227C22×C4⋊C4—21no—
228C22×C4⋊C4C22×C3111yescharacteristic
229C22×C4⋊C4C22×C3111yescharacteristic
230#483—22no—
231#483—22no—
232C2×#106—21no—
233C2×#103—21no—
234C2×C22⋊C8C22×C3111yescharacteristic
235C2×C22⋊C8C22×C3111yescharacteristic
236#400—21no—
237#398—22no—
238#398—22no—
239#398—22no—
240#395—21no—
241#385—21no—
242#381—21no—
243#380C22×C3111yescharacteristic
244C2×#95—21no—
245C2×#95C22×C3111yescharacteristic
246#340—22no—
247#328—22no—
248#324—22no—
249C2×C31—21no—
250C2×C31—21no—
251C2×C31—21no—
252C2×C31—21no—
253C2×C31#160912yes—
254C2×C31#161112yes—
255C2×C31#200011yescharacteristic
256C2×C31#200511yescharacteristic
257C2×C31#202211yescharacteristic
258C22×Q8D4×C3111yescharacteristic
259C23×C4—21no—
260C23×C4—21no—
261C23×C4D4×C3111yescharacteristic
262C23×C4D4×C3111yescharacteristic
263C23×C4C23×C3111yescharacteristic
264C22×C8—21no—
265C22×C8—21no—
266C22⋊Q8—21no—
267C22⋊Q8—21no—
268C22⋊Q8—21no—
269C22⋊Q8—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—42no—
285C2×C4⋊C4—42no—
286C2×C4⋊C4D4×C3112yes—
287C2×C4⋊C4D4×C3111yescharacteristic
288C2×C4⋊C4D4×C3112yes—
289C2×C22⋊C4—21no—
290C2×C22⋊C4—21no—
291#106—24no—
292#103—24no—
293C22⋊C8—21no—
294C22⋊C8—21no—
295C22⋊C8—21no—
296C22⋊C8D4×C3112yes—
297#95—24no—
298#95—22no—
299#95—22no—
300#95—22no—
301#95—21no—
302#95—21no—
303#95D4×C3112yes—
304C31#992711yescharacteristic, direct product factor, Sylow
305C24C2×D4×C3111yescharacteristic
306C2×Q8—21no—
307C2×Q8—21no—
308C2×Q8—42no—
309C22×C4—24no—
310C22×C4—21no—
311C22×C4—22no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—22no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—22no—
323C22×C4—21no—
324C22×C4—42no—
325C22×C4—42no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—42no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—41no—
333C22×C4—41no—
334C22×C4—41no—
335C22×C4SD16×C3112yes—
336C22×C4C2×D4×C3111yescharacteristic
337C22×C4C2×D4×C3111yescharacteristic
338C22×C4C2×D4×C3111yescharacteristic
339C22×C4C2×D4×C3111yescharacteristic
340C22×C4C2×D4×C3111yescharacteristic
341C22×C4#41×C3111yescharacteristic
342C2×C8—22no—
343C2×C8—42no—
344C2×C8—42no—
345C2×C8—41no—
346C4⋊C4—22no—
347C4⋊C4—21no—
348C4⋊C4—22no—
349C4⋊C4—21no—
350C4⋊C4—42no—
351C4⋊C4—48no—
352C4⋊C4—41no—
353C4⋊C4—41no—
354C4⋊C4—41no—
355C4⋊C4—41no—
356C4⋊C4—41no—
357C4⋊C4—41no—
358C4⋊C4—41no—
359C4⋊C4—41no—
360C4⋊C4—82no—
361C22⋊C4—41no—
362C22⋊C4—41no—
363C22⋊C4—41no—
364C22⋊C4—41no—
365C23—22no—
366C23—22no—
367C23C31×#12011yescharacteristic
368C23C31×#12011yescharacteristic
369C23C31×#12111yescharacteristic
370C23C2×SD16×C3111yescharacteristic
371C23C31×#13511yescharacteristic
372C23C31×AGL(1,ℤ/8)11yescharacteristic
373C23C31×#13711yescharacteristic
374Q8—42no—
375Q8—81no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—24no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—44no—
387C2×C4—44no—
388C2×C4—42no—
389C2×C4—41no—
390C2×C4—42no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—42no—
406C2×C4—41no—
407C2×C4—81no—
408C2×C4—81no—
409C2×C4—81no—
410C2×C4—81no—
411C2×C4—81no—
412C2×C4C31×#12011yescharacteristic
413C2×C4C31×#12111yescharacteristic
414C2×C4C31×#12111yescharacteristic
415C2×C4C31×#12711yescharacteristic
416C8—42no—
417C8—81no—
418C22—22no—
419C22—22no—
420C22—22no—
421C22—22no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22C31×#39211yescharacteristic
427C22C31×#44811yescharacteristic
428C22C31×#44911yescharacteristic
429C22C31×#45011yescharacteristic
430C22C31×#45211yescharacteristic
431C22C31×#45612yes—
432C22C31×#45812yes—
433C22C31×#46511yescharacteristic
434C22C31×#46811yescharacteristic
435C4—21no—
436C4—21no—
437C4—21no—
438C4—21no—
439C4—44no—
440C4—42no—
441C4—82no—
442C4—82no—
443C4—81no—
444C4—81no—
445C4—81no—
446C2—21no—
447C2—21no—
448C2—21no—
449C2—21no—
450C2C31×#160912yes—
451C2C31×#161112yes—
452C2C31×#200011yescharacteristic
453C2C31×#200511yescharacteristic
454C2C31×#202211yescharacteristic
subgroupG/H
center, socleC23×C31#120
commutator, Frattini, cosocleC23×C4C23×C31
prime radicalC24×C31C2×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
137. #9927C31direct (N × H)
304. C31#9927direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4832
C31×#26272
C2×C31×#3982
C31×#18232
C2×C31×#3282
C2×C31×#3242
C31×#12942
#992731