Finite Group Databasebeta

← C31×#8988 #21465747

Subgroups — C31×#8988 #21465747

Order 7936.

608 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#461C211yesmaximal, characteristic
2C31×#2354C211yesmaximal, characteristic
3C31×#1990C211yesmaximal, characteristic, complemented
4C31×#1988C211yesmaximal, characteristic, complemented
5C2×C31×D4⋊C8C211yesmaximal, characteristic
6C31×#1296C211yesmaximal, characteristic, complemented
7C31×#1279C211yesmaximal, characteristic, complemented
8C22×SD16×C31—21no—
9C2×C31×C4⋊Q8C2211yescharacteristic
10C2×C4×D4×C31C2211yescharacteristic
11C2×C31×#117—21no—
12C31×#461—22no—
13C31×#461C414yescomplemented
14C2×C31×C4⋊C8C2211yescharacteristic
15C2×C31×C4⋊C8C2211yescharacteristic
16C2×C31×#103—21no—
17C2×C4×C8×C31C2211yescharacteristic
18C31×#390—21no—
19C31×#388—22no—
20C31×#384C2211yescharacteristic
21C31×#380—21no—
22C4×C4⋊C4×C31—21no—
23C4×C4⋊C4×C31C2211yescharacteristic
24C31×#340—21no—
25C31×#340—21no—
26C31×#340—22no—
27C31×D4⋊C8—22no—
28C22×Q8×C31—21no—
29C22×D4×C31D411yescharacteristic
30C23×C4×C31—21no—
31C2×SD16×C31—24no—
32C2×SD16×C31—42no—
33C2×SD16×C31—42no—
34C22×C8×C31—21no—
35C22×C8×C31—21no—
36C22×C8×C31—21no—
37C31×C4⋊Q8—21no—
38C31×C4⋊Q8—21no—
39C31×C4⋊Q8—21no—
40C31×C4⋊Q8C2×C412yes—
41C4×D4×C31—21no—
42C4×D4×C31—21no—
43C4×D4×C31C2×C412yes—
44C4×D4×C31D412yes—
45C31×#117—42no—
46C31×#117—42no—
47C2×C4⋊C4×C31—21no—
48C2×C4⋊C4×C31—21no—
49C2×C4⋊C4×C31—21no—
50C2×C4⋊C4×C31—21no—
51C2×C4⋊C4×C31D411yescharacteristic
52C2×C4⋊C4×C31D411yescharacteristic
53C2×C4⋊C4×C31D411yescharacteristic
54C2×C4⋊C4×C31D412yes—
55C2×C22⋊C4×C31—21no—
56C2×C22⋊C4×C31—22no—
57C2×C22⋊C4×C31—22no—
58C2×C42×C31—22no—
59C2×C42×C31—21no—
60C2×C42×C31C2311yescharacteristic
61C31×C4⋊C8—21no—
62C31×C4⋊C8—21no—
63C31×C4⋊C8—21no—
64C31×C4⋊C8C2×C412yes—
65C31×#103—24no—
66C4×C8×C31—21no—
67C4×C8×C31—21no—
68C31×#95—22no—
69C31×#95—21no—
70C24×C31—21no—
71C2×Q8×C31—22no—
72C2×Q8×C31—41no—
73C2×Q8×C31—41no—
74C2×Q8×C31—41no—
75C2×Q8×C31—41no—
76C2×Q8×C31—41no—
77C2×D4×C31—21no—
78C2×D4×C31—21no—
79C2×D4×C31—21no—
80C2×D4×C31—21no—
81C2×D4×C31—21no—
82C2×D4×C31C22⋊C412yes—
83C22×C4×C31—21no—
84C22×C4×C31—21no—
85C22×C4×C31—22no—
86C22×C4×C31—22no—
87C22×C4×C31—21no—
88C22×C4×C31—22no—
89C22×C4×C31—41no—
90C22×C4×C31—41no—
91C22×C4×C31—41no—
92C22×C4×C31—41no—
93C22×C4×C31—41no—
94C22×C4×C31C2×D411yescharacteristic
95C22×C4×C31C2×D411yescharacteristic
96C22×C4×C31C2×D411yescharacteristic
97SD16×C31—48no—
98C2×C8×C31—22no—
99C2×C8×C31—22no—
100C2×C8×C31—41no—
101C2×C8×C31—41no—
102C2×C8×C31—41no—
103C2×C8×C31—41no—
104C2×C8×C31—41no—
105C2×C8×C31—41no—
106C2×C8×C31—41no—
107C4⋊C4×C31—21no—
108C4⋊C4×C31—21no—
109C4⋊C4×C31—22no—
110C4⋊C4×C31—22no—
111C4⋊C4×C31—21no—
112C4⋊C4×C31—21no—
113C4⋊C4×C31—42no—
114C4⋊C4×C31—41no—
115C4⋊C4×C31—41no—
116C4⋊C4×C31—41no—
117C4⋊C4×C31—41no—
118C4⋊C4×C31—41no—
119C4⋊C4×C31—41no—
120C4⋊C4×C31C22⋊C412yes—
121C4⋊C4×C31SD1612yescomplemented
122C22⋊C4×C31—22no—
123C22⋊C4×C31—22no—
124C22⋊C4×C31—44no—
125C22⋊C4×C31—82no—
126C42×C31—44no—
127C42×C31—41no—
128C42×C31—41no—
129C42×C31C22×C411yescharacteristic
130C42×C31C2×D411yescharacteristic
131C42×C31#4111yescharacteristic
132C42×C31#4111yescharacteristic
133#8988C3111yesmaximal, characteristic, direct product factor, Sylow
134C23×C31—22no—
135C23×C31—41no—
136C23×C31—41no—
137C23×C31—41no—
138C23×C31—41no—
139C23×C31—41no—
140C23×C31—41no—
141C23×C31#12011yescharacteristic
142Q8×C31—42no—
143Q8×C31—42no—
144Q8×C31—81no—
145Q8×C31—81no—
146D4×C31—22no—
147D4×C31—22no—
148D4×C31—41no—
149D4×C31—41no—
150C2×C4×C31—21no—
151C2×C4×C31—21no—
152C2×C4×C31—22no—
153C2×C4×C31—22no—
154C2×C4×C31—41no—
155C2×C4×C31—41no—
156C2×C4×C31—41no—
157C2×C4×C31—41no—
158C2×C4×C31—42no—
159C2×C4×C31—42no—
160C2×C4×C31—42no—
161C2×C4×C31—42no—
162C2×C4×C31—42no—
163C2×C4×C31—41no—
164C2×C4×C31—42no—
165C2×C4×C31—42no—
166C2×C4×C31—41no—
167C2×C4×C31—41no—
168C2×C4×C31—42no—
169C2×C4×C31—81no—
170C2×C4×C31—81no—
171C2×C4×C31C2×C22⋊C411yescharacteristic
172C2×C4×C31C4×D411yescharacteristic
173C2×C4×C31C4×D411yescharacteristic
174C2×C4×C31#12111yescharacteristic
175C2×C4×C31#12111yescharacteristic
176C2×C4×C31#12311yescharacteristic
177C2×C4×C31C2×SD1611yescharacteristic
178C2×C4×C31#13511yescharacteristic
179C2×C4×C31#13511yescharacteristic
180C2×C4×C31#13511yescharacteristic
181C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
182C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
183C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
184C2×C4×C31#13711yescharacteristic
185C8×C31—42no—
186C8×C31—42no—
187C8×C31—81no—
188C2×#461C2×C3111yescharacteristic
189#2354C2×C3111yescharacteristic
190#1990C2×C3111yescharacteristic, complemented
191#1988C2×C3111yescharacteristic, complemented
192C2×D4⋊C8C2×C3111yescharacteristic
193#1296C2×C3111yescharacteristic, complemented
194#1279C2×C3111yescharacteristic, complemented
195C22×C31—42no—
196C22×C31—42no—
197C22×C31—42no—
198C22×C31—81no—
199C22×C31—81no—
200C22×C31—81no—
201C22×C31—81no—
202C22×C31#38611yescharacteristic
203C22×C31#44911yescharacteristic
204C22×C31#44911yescharacteristic
205C22×C31#45011yescharacteristic
206C22×C31#45211yescharacteristic
207C22×C31#45511yescharacteristic
208C22×C31#45611yescharacteristic
209C4×C31—21no—
210C4×C31—21no—
211C4×C31—42no—
212C4×C31—42no—
213C4×C31—82no—
214C4×C31—82no—
215C4×C31—81no—
216C4×C31#41611yescharacteristic
217C4×C31#41811yescharacteristic
218C4×C31C4×SD1611yescharacteristic
219C4×C31#44011yescharacteristic
220C4×C31#46111yescharacteristic
221C4×C31#46311yescharacteristic
222C4×C31#48211yescharacteristic
223C4×C31#48211yescharacteristic
224C22×SD16—21no—
225C2×C4⋊Q8C22×C3111yescharacteristic
226C2×C4×D4C22×C3111yescharacteristic
227C2×#117—21no—
228#461—22no—
229#461C4×C3114yescomplemented
230C2×C4⋊C8C22×C3111yescharacteristic
231C2×C4⋊C8C22×C3111yescharacteristic
232C2×#103—21no—
233C2×C4×C8C22×C3111yescharacteristic
234#390—21no—
235#388—22no—
236#384C22×C3111yescharacteristic
237#380—21no—
238C4×C4⋊C4—21no—
239C4×C4⋊C4C22×C3111yescharacteristic
240#340—21no—
241#340—21no—
242#340—22no—
243D4⋊C8—22no—
244C2×C31—82no—
245C2×C31#164211yescharacteristic
246C2×C31#164611yescharacteristic
247C2×C31#165011yescharacteristic
248C2×C31#165411yescharacteristic
249C2×C31#187511yescharacteristic
250C2×C31#187711yescharacteristic
251C2×C31#188211yescharacteristic
252C22×Q8—21no—
253C22×D4D4×C3111yescharacteristic
254C23×C4—21no—
255C2×SD16—24no—
256C2×SD16—42no—
257C2×SD16—42no—
258C22×C8—21no—
259C22×C8—21no—
260C22×C8—21no—
261C4⋊Q8—21no—
262C4⋊Q8—21no—
263C4⋊Q8—21no—
264C4⋊Q8C2×C4×C3112yes—
265C4×D4—21no—
266C4×D4—21no—
267C4×D4C2×C4×C3112yes—
268C4×D4D4×C3112yes—
269#117—42no—
270#117—42no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4D4×C3111yescharacteristic
276C2×C4⋊C4D4×C3111yescharacteristic
277C2×C4⋊C4D4×C3111yescharacteristic
278C2×C4⋊C4D4×C3112yes—
279C2×C22⋊C4—21no—
280C2×C22⋊C4—22no—
281C2×C22⋊C4—22no—
282C2×C42—22no—
283C2×C42—21no—
284C2×C42C23×C3111yescharacteristic
285C4⋊C8—21no—
286C4⋊C8—21no—
287C4⋊C8—21no—
288C4⋊C8C2×C4×C3112yes—
289#103—24no—
290C4×C8—21no—
291C4×C8—21no—
292#95—22no—
293#95—21no—
294C31#898811yescharacteristic, direct product factor, Sylow
295C24—21no—
296C2×Q8—22no—
297C2×Q8—41no—
298C2×Q8—41no—
299C2×Q8—41no—
300C2×Q8—41no—
301C2×Q8—41no—
302C2×D4—21no—
303C2×D4—21no—
304C2×D4—21no—
305C2×D4—21no—
306C2×D4—21no—
307C2×D4C22⋊C4×C3112yes—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—21no—
313C22×C4—22no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4—41no—
319C22×C4C2×D4×C3111yescharacteristic
320C22×C4C2×D4×C3111yescharacteristic
321C22×C4C2×D4×C3111yescharacteristic
322SD16—48no—
323C2×C8—22no—
324C2×C8—22no—
325C2×C8—41no—
326C2×C8—41no—
327C2×C8—41no—
328C2×C8—41no—
329C2×C8—41no—
330C2×C8—41no—
331C2×C8—41no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—22no—
335C4⋊C4—22no—
336C4⋊C4—21no—
337C4⋊C4—21no—
338C4⋊C4—42no—
339C4⋊C4—41no—
340C4⋊C4—41no—
341C4⋊C4—41no—
342C4⋊C4—41no—
343C4⋊C4—41no—
344C4⋊C4—41no—
345C4⋊C4C22⋊C4×C3112yes—
346C4⋊C4SD16×C3112yescomplemented
347C22⋊C4—22no—
348C22⋊C4—22no—
349C22⋊C4—44no—
350C22⋊C4—82no—
351C42—44no—
352C42—41no—
353C42—41no—
354C42C22×C4×C3111yescharacteristic
355C42C2×D4×C3111yescharacteristic
356C42#41×C3111yescharacteristic
357C42#41×C3111yescharacteristic
358C23—22no—
359C23—41no—
360C23—41no—
361C23—41no—
362C23—41no—
363C23—41no—
364C23—41no—
365C23C31×#12011yescharacteristic
366Q8—42no—
367Q8—42no—
368Q8—81no—
369Q8—81no—
370D4—22no—
371D4—22no—
372D4—41no—
373D4—41no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—41no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—81no—
394C2×C4—81no—
395C2×C4C2×C22⋊C4×C3111yescharacteristic
396C2×C4C4×D4×C3111yescharacteristic
397C2×C4C4×D4×C3111yescharacteristic
398C2×C4C31×#12111yescharacteristic
399C2×C4C31×#12111yescharacteristic
400C2×C4C31×#12311yescharacteristic
401C2×C4C2×SD16×C3111yescharacteristic
402C2×C4C31×#13511yescharacteristic
403C2×C4C31×#13511yescharacteristic
404C2×C4C31×#13511yescharacteristic
405C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
406C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
407C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
408C2×C4C31×#13711yescharacteristic
409C8—42no—
410C8—42no—
411C8—81no—
412C22—42no—
413C22—42no—
414C22—42no—
415C22—81no—
416C22—81no—
417C22—81no—
418C22—81no—
419C22C31×#38611yescharacteristic
420C22C31×#44911yescharacteristic
421C22C31×#44911yescharacteristic
422C22C31×#45011yescharacteristic
423C22C31×#45211yescharacteristic
424C22C31×#45511yescharacteristic
425C22C31×#45611yescharacteristic
426C4—21no—
427C4—21no—
428C4—42no—
429C4—42no—
430C4—82no—
431C4—82no—
432C4—81no—
433C4C31×#41611yescharacteristic
434C4C31×#41811yescharacteristic
435C4C4×SD16×C3111yescharacteristic
436C4C31×#44011yescharacteristic
437C4C31×#46111yescharacteristic
438C4C31×#46311yescharacteristic
439C4C31×#48211yescharacteristic
440C4C31×#48211yescharacteristic
441C2—82no—
442C2C31×#164211yescharacteristic
443C2C31×#164611yescharacteristic
444C2C31×#165011yescharacteristic
445C2C31×#165411yescharacteristic
446C2C31×#187511yescharacteristic
447C2C31×#187711yescharacteristic
448C2C31×#188211yescharacteristic
subgroupG/H
center, socleC23×C31#120
commutatorC42C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC22×D4×C31D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
3. C31×#1990C2semidirect
4. C31×#1988C2semidirect
6. C31×#1296C2semidirect
7. C31×#1279C2semidirect
13. C31×#461C4semidirect
121. C4⋊C4×C31SD16semidirect
133. #8988C31direct (N × H)
190. #1990C2×C31semidirect
191. #1988C2×C31semidirect
193. #1296C2×C31semidirect
194. #1279C2×C31semidirect
229. #461C4×C31semidirect
294. C31#8988direct (N × H)
346. C4⋊C4SD16×C31semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#4612
C31×#23542
C31×#19902
C31×#19882
C2×C31×D4⋊C82
C31×#12962
C31×#12792
#898831