Finite Group Databasebeta

← C31×#10177 #21466936

Subgroups — C31×#10177 #21466936

Order 7936.

614 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3205C211yesmaximal, characteristic
2C31×#3037C211yesmaximal, characteristic, complemented
3C2×C31×#460C211yesmaximal, characteristic, complemented
4C31×#1545C211yesmaximal, characteristic, complemented
5C31×#1480C211yesmaximal, characteristic, complemented
6C31×#1461C211yesmaximal, characteristic, complemented
7C31×#1301C211yesmaximal, characteristic, complemented
8C2×C31×#137—21no—
9C22×SD16×C31—21no—
10C31×#532C2211yescharacteristic
11C2×C31×#127C2211yescharacteristic
12C2×C4×Q8×C31C2211yescharacteristic
13C31×#493—21no—
14C31×#486—21no—
15C31×#464—22no—
16C31×#462—21no—
17C31×#460—22no—
18C31×#460—21no—
19C31×#460—22no—
20C31×#459—22no—
21C31×#447—22no—
22C31×#431C2211yescharacteristic
23C31×#431C2211yescharacteristic
24C31×#423C2211yescharacteristic
25C2×C31×C4⋊C8C2211yescharacteristic
26C31×#417—21no—
27C2×C31×#102—21no—
28C31×#331—22no—
29C31×D4⋊C8—22no—
30C31×#324—22no—
31C2×#41×C31—21no—
32C22×Q8×C31D411yescharacteristic
33C22×D4×C31—21no—
34C22×D4×C31—21no—
35C22×D4×C31—21no—
36C31×#137—42no—
37C31×#137—42no—
38C2×Q16×C31—22no—
39C2×SD16×C31—24no—
40C2×SD16×C31—22no—
41C2×SD16×C31—42no—
42C2×SD16×C31—42no—
43C2×D8×C31—24no—
44C2×M16×C31—21no—
45C22×C8×C31—21no—
46C31×C4⋊Q8D411yescharacteristic
47C31×#127—21no—
48C31×#127—21no—
49C31×#127—21no—
50C31×#127D412yes—
51C31×#127D411yescharacteristic
52C31×#124—21no—
53C31×#121—21no—
54C31×#121—21no—
55C4×Q8×C31—21no—
56C4×Q8×C31—21no—
57C4×Q8×C31—21no—
58C4×Q8×C31—21no—
59C4×D4×C31—21no—
60C4×D4×C31—21no—
61C2×C4⋊C4×C31—21no—
62C2×C4⋊C4×C31D411yescharacteristic
63C2×C42×C31—21no—
64C2×C42×C31C2311yescharacteristic
65C31×C4⋊C8—21no—
66C31×C4⋊C8—21no—
67C31×C4⋊C8—21no—
68C31×C4⋊C8—21no—
69C31×C4⋊C8D412yes—
70C31×C4⋊C8D412yes—
71C31×#103—22no—
72C31×#102—24no—
73C31×#102—22no—
74C31×#102—24no—
75C31×C22⋊C8—21no—
76C31×C22⋊C8D412yes—
77C4×C8×C31—21no—
78C4×C8×C31—21no—
79C24×C31—41no—
80#41×C31—41no—
81#41×C31—41no—
82#41×C31—41no—
83#41×C31—41no—
84C2×Q8×C31—21no—
85C2×Q8×C31—21no—
86C2×Q8×C31—21no—
87C2×Q8×C31—21no—
88C2×Q8×C31—21no—
89C2×Q8×C31—21no—
90C2×Q8×C31D812yescomplemented
91C2×D4×C31—21no—
92C2×D4×C31—22no—
93C2×D4×C31—22no—
94C2×D4×C31—21no—
95C2×D4×C31—21no—
96C2×D4×C31—22no—
97C2×D4×C31—41no—
98C2×D4×C31—41no—
99C2×D4×C31—41no—
100C2×D4×C31—41no—
101C2×D4×C31—41no—
102C2×D4×C31—41no—
103C2×D4×C31—41no—
104C2×D4×C31—41no—
105C2×D4×C31—82no—
106C2×D4×C31—82no—
107C22×C4×C31—21no—
108C22×C4×C31—21no—
109C22×C4×C31—41no—
110C22×C4×C31C2×D411yescharacteristic
111C22×C4×C31C2×D411yescharacteristic
112C22×C4×C31#4111yescharacteristic
113Q16×C31—44no—
114SD16×C31—48no—
115SD16×C31—44no—
116D8×C31—84no—
117M16×C31—41no—
118M16×C31—41no—
119C2×C8×C31—22no—
120C2×C8×C31—22no—
121C2×C8×C31—22no—
122C2×C8×C31—41no—
123C2×C8×C31—41no—
124C2×C8×C31—41no—
125C4⋊C4×C31—21no—
126C4⋊C4×C31—21no—
127C4⋊C4×C31—21no—
128C4⋊C4×C31—21no—
129C4⋊C4×C31—41no—
130C4⋊C4×C31—41no—
131C22⋊C4×C31—41no—
132C22⋊C4×C31—41no—
133C42×C31—41no—
134C42×C31—41no—
135C42×C31C2×D411yescharacteristic
136C42×C31C2×D411yescharacteristic
137C42×C31C2×D411yescharacteristic
138C42×C31C2×D411yescharacteristic
139#10177C3111yesmaximal, characteristic, direct product factor, Sylow
140C23×C31—41no—
141C23×C31—42no—
142C23×C31—82no—
143C23×C31—82no—
144C23×C31—81no—
145C23×C31—81no—
146C23×C31#12111yescharacteristic
147Q8×C31—22no—
148Q8×C31—22no—
149Q8×C31—41no—
150Q8×C31—41no—
151Q8×C31—41no—
152Q8×C31—41no—
153D4×C31—42no—
154D4×C31—44no—
155D4×C31—42no—
156D4×C31—41no—
157D4×C31—42no—
158D4×C31—41no—
159D4×C31—42no—
160D4×C31—82no—
161D4×C31—82no—
162D4×C31—81no—
163D4×C31—81no—
164D4×C31—81no—
165D4×C31—81no—
166D4×C31—82no—
167C2×C4×C31—22no—
168C2×C4×C31—22no—
169C2×C4×C31—41no—
170C2×C4×C31—41no—
171C2×C4×C31—41no—
172C2×C4×C31—41no—
173C2×C4×C31—41no—
174C2×C4×C31—81no—
175C2×C4×C31—81no—
176C2×C4×C31—81no—
177C2×C4×C31#12011yescharacteristic
178C2×C4×C31#12011yescharacteristic
179C2×C4×C31#12011yescharacteristic
180C2×C4×C31#12111yescharacteristic
181C2×C4×C31#12111yescharacteristic
182C2×C4×C31#12711yescharacteristic
183C2×C4×C31C2×D811yescharacteristic
184C2×C4×C31#13511yescharacteristic
185C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
186C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
187C8×C31—42no—
188C8×C31—42no—
189C8×C31—42no—
190C8×C31—81no—
191#3205C2×C3111yescharacteristic
192#3037C2×C3111yescharacteristic, complemented
193C2×#460C2×C3111yescharacteristic, complemented
194#1545C2×C3111yescharacteristic, complemented
195#1480C2×C3111yescharacteristic, complemented
196#1461C2×C3111yescharacteristic, complemented
197#1301C2×C3111yescharacteristic, complemented
198C22×C31—21no—
199C22×C31—21no—
200C22×C31—81no—
201C22×C31—82no—
202C22×C31—82no—
203C22×C31—81no—
204C22×C31—81no—
205C22×C31—82no—
206C22×C31—162no—
207C22×C31—162no—
208C22×C31#39211yescharacteristic
209C22×C31#46611yescharacteristic
210C22×C31#46911yescharacteristic
211C4×C31—21no—
212C4×C31—21no—
213C4×C31—21no—
214C4×C31—42no—
215C4×C31—81no—
216C4×C31—81no—
217C4×C31#44711yescharacteristic
218C4×C31#44711yescharacteristic
219C4×C31#44911yescharacteristic
220C4×C31#44911yescharacteristic
221C4×C31#47112yes—
222C2×#137—21no—
223C22×SD16—21no—
224#532C22×C3111yescharacteristic
225C2×#127C22×C3111yescharacteristic
226C2×C4×Q8C22×C3111yescharacteristic
227#493—21no—
228#486—21no—
229#464—22no—
230#462—21no—
231#460—22no—
232#460—21no—
233#460—22no—
234#459—22no—
235#447—22no—
236#431C22×C3111yescharacteristic
237#431C22×C3111yescharacteristic
238#423C22×C3111yescharacteristic
239C2×C4⋊C8C22×C3111yescharacteristic
240#417—21no—
241C2×#102—21no—
242#331—22no—
243D4⋊C8—22no—
244#324—22no—
245C2×C31—21no—
246C2×C31—21no—
247C2×C31—161no—
248C2×C31—162no—
249C2×C31#199911yescharacteristic
250C2×C31#200811yescharacteristic
251C2×C31#201911yescharacteristic
252C2×#41—21no—
253C22×Q8D4×C3111yescharacteristic
254C22×D4—21no—
255C22×D4—21no—
256C22×D4—21no—
257#137—42no—
258#137—42no—
259C2×Q16—22no—
260C2×SD16—24no—
261C2×SD16—22no—
262C2×SD16—42no—
263C2×SD16—42no—
264C2×D8—24no—
265C2×M16—21no—
266C22×C8—21no—
267C4⋊Q8D4×C3111yescharacteristic
268#127—21no—
269#127—21no—
270#127—21no—
271#127D4×C3112yes—
272#127D4×C3111yescharacteristic
273#124—21no—
274#121—21no—
275#121—21no—
276C4×Q8—21no—
277C4×Q8—21no—
278C4×Q8—21no—
279C4×Q8—21no—
280C4×D4—21no—
281C4×D4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4D4×C3111yescharacteristic
284C2×C42—21no—
285C2×C42C23×C3111yescharacteristic
286C4⋊C8—21no—
287C4⋊C8—21no—
288C4⋊C8—21no—
289C4⋊C8—21no—
290C4⋊C8D4×C3112yes—
291C4⋊C8D4×C3112yes—
292#103—22no—
293#102—24no—
294#102—22no—
295#102—24no—
296C22⋊C8—21no—
297C22⋊C8D4×C3112yes—
298C4×C8—21no—
299C4×C8—21no—
300C31#1017711yescharacteristic, direct product factor, Sylow
301C24—41no—
302#41—41no—
303#41—41no—
304#41—41no—
305#41—41no—
306C2×Q8—21no—
307C2×Q8—21no—
308C2×Q8—21no—
309C2×Q8—21no—
310C2×Q8—21no—
311C2×Q8—21no—
312C2×Q8D8×C3112yescomplemented
313C2×D4—21no—
314C2×D4—22no—
315C2×D4—22no—
316C2×D4—21no—
317C2×D4—21no—
318C2×D4—22no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—41no—
322C2×D4—41no—
323C2×D4—41no—
324C2×D4—41no—
325C2×D4—41no—
326C2×D4—41no—
327C2×D4—82no—
328C2×D4—82no—
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—41no—
332C22×C4C2×D4×C3111yescharacteristic
333C22×C4C2×D4×C3111yescharacteristic
334C22×C4#41×C3111yescharacteristic
335Q16—44no—
336SD16—48no—
337SD16—44no—
338D8—84no—
339M16—41no—
340M16—41no—
341C2×C8—22no—
342C2×C8—22no—
343C2×C8—22no—
344C2×C8—41no—
345C2×C8—41no—
346C2×C8—41no—
347C4⋊C4—21no—
348C4⋊C4—21no—
349C4⋊C4—21no—
350C4⋊C4—21no—
351C4⋊C4—41no—
352C4⋊C4—41no—
353C22⋊C4—41no—
354C22⋊C4—41no—
355C42—41no—
356C42—41no—
357C42C2×D4×C3111yescharacteristic
358C42C2×D4×C3111yescharacteristic
359C42C2×D4×C3111yescharacteristic
360C42C2×D4×C3111yescharacteristic
361C23—41no—
362C23—42no—
363C23—82no—
364C23—82no—
365C23—81no—
366C23—81no—
367C23C31×#12111yescharacteristic
368Q8—22no—
369Q8—22no—
370Q8—41no—
371Q8—41no—
372Q8—41no—
373Q8—41no—
374D4—42no—
375D4—44no—
376D4—42no—
377D4—41no—
378D4—42no—
379D4—41no—
380D4—42no—
381D4—82no—
382D4—82no—
383D4—81no—
384D4—81no—
385D4—81no—
386D4—81no—
387D4—82no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—81no—
396C2×C4—81no—
397C2×C4—81no—
398C2×C4C31×#12011yescharacteristic
399C2×C4C31×#12011yescharacteristic
400C2×C4C31×#12011yescharacteristic
401C2×C4C31×#12111yescharacteristic
402C2×C4C31×#12111yescharacteristic
403C2×C4C31×#12711yescharacteristic
404C2×C4C2×D8×C3111yescharacteristic
405C2×C4C31×#13511yescharacteristic
406C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
407C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
408C8—42no—
409C8—42no—
410C8—42no—
411C8—81no—
412C22—21no—
413C22—21no—
414C22—81no—
415C22—82no—
416C22—82no—
417C22—81no—
418C22—81no—
419C22—82no—
420C22—162no—
421C22—162no—
422C22C31×#39211yescharacteristic
423C22C31×#46611yescharacteristic
424C22C31×#46911yescharacteristic
425C4—21no—
426C4—21no—
427C4—21no—
428C4—42no—
429C4—81no—
430C4—81no—
431C4C31×#44711yescharacteristic
432C4C31×#44711yescharacteristic
433C4C31×#44911yescharacteristic
434C4C31×#44911yescharacteristic
435C4C31×#47112yes—
436C2—21no—
437C2—21no—
438C2—162no—
439C2—161no—
440C2C31×#199911yescharacteristic
441C2C31×#200811yescharacteristic
442C2C31×#201911yescharacteristic
subgroupG/H
center, socleC22×C31#392
commutator, Frattini, cosocleC2×C42C23×C31
prime radicalC31×#3205C2
LCSG ▷ C2×C42 ▷ 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×#3037C2semidirect
3. C2×C31×#460C2semidirect
4. C31×#1545C2semidirect
5. C31×#1480C2semidirect
6. C31×#1461C2semidirect
7. C31×#1301C2semidirect
90. C2×Q8×C31D8semidirect
139. #10177C31direct (N × H)
192. #3037C2×C31semidirect
193. C2×#460C2×C31semidirect
194. #1545C2×C31semidirect
195. #1480C2×C31semidirect
196. #1461C2×C31semidirect
197. #1301C2×C31semidirect
300. C31#10177direct (N × H)
312. C2×Q8D8×C31semidirect

Maximal subgroups

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

subgroupindex
C31×#32052
C31×#30372
C2×C31×#4602
C31×#15452
C31×#14802
C31×#14612
C31×#13012
#1017731