Finite Group Databasebeta

← C31×#10066 #21466825

Subgroups — C31×#10066 #21466825

Order 7936.

634 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#500C211yesmaximal, characteristic, complemented
2C2×C31×#461C211yesmaximal, characteristic
3C31×#2547C211yesmaximal, characteristic
4C31×#1988C211yesmaximal, characteristic, complemented
5C2×C31×#332C211yesmaximal, characteristic, complemented
6C2×C31×D4⋊C8C211yesmaximal, characteristic
7C31×#1279C211yesmaximal, characteristic, complemented
8C22×SD16×C31—21no—
9C2×C31×C4⋊Q8C2211yescharacteristic
10C2×C31×C4⋊Q8C2211yescharacteristic
11C2×C31×#124—21no—
12C2×C4×D4×C31C2211yescharacteristic
13C31×#500—22no—
14C31×#500—22no—
15C31×#461—22no—
16C31×#461—22no—
17C2×C31×#107—22no—
18C2×C31×C4⋊C8C2211yescharacteristic
19C2×C31×C4⋊C8C2211yescharacteristic
20C2×C31×#103—21no—
21C2×C4×C8×C31C2211yescharacteristic
22C31×#397—22no—
23C31×#391—21no—
24C31×#380—22no—
25C4×C4⋊C4×C31C2211yescharacteristic
26C31×#340—22no—
27C31×#332—22no—
28C31×D4⋊C8—22no—
29C22×Q8×C31—21no—
30C22×Q8×C31—21no—
31C22×D4×C31D411yescharacteristic
32C23×C4×C31—21no—
33C2×SD16×C31—24no—
34C2×SD16×C31—42no—
35C2×SD16×C31—42no—
36C22×C8×C31—21no—
37C22×C8×C31—21no—
38C22×C8×C31—21no—
39C31×C4⋊Q8—21no—
40C31×C4⋊Q8—21no—
41C31×C4⋊Q8—21no—
42C31×C4⋊Q8—21no—
43C31×C4⋊Q8—21no—
44C31×C4⋊Q8—21no—
45C31×C4⋊Q8—21no—
46C31×C4⋊Q8D412yes—
47C31×#124—42no—
48C31×#124—42no—
49C4×D4×C31—21no—
50C4×D4×C31—21no—
51C4×D4×C31—21no—
52C4×D4×C31—21no—
53C2×C4⋊C4×C31—21no—
54C2×C4⋊C4×C31—21no—
55C2×C4⋊C4×C31—21no—
56C2×C4⋊C4×C31D412yes—
57C2×C4⋊C4×C31D411yescharacteristic
58C2×C4⋊C4×C31D412yes—
59C2×C22⋊C4×C31—24no—
60C2×C22⋊C4×C31—21no—
61C2×C42×C31—21no—
62C2×C42×C31C2311yescharacteristic
63C31×#107—28no—
64C31×C4⋊C8—21no—
65C31×C4⋊C8—21no—
66C31×C4⋊C8—21no—
67C31×C4⋊C8D412yes—
68C31×#103—24no—
69C4×C8×C31—21no—
70C4×C8×C31D412yes—
71C31×#95—24no—
72C31×#95—21no—
73C24×C31—21no—
74C2×Q8×C31—22no—
75C2×Q8×C31—41no—
76C2×Q8×C31—41no—
77C2×Q8×C31—41no—
78C2×Q8×C31—41no—
79C2×Q8×C31—41no—
80C2×Q8×C31—41no—
81C2×Q8×C31—41no—
82C2×Q8×C31—41no—
83C2×Q8×C31—41no—
84C2×Q8×C31—41no—
85C2×Q8×C31—41no—
86C2×D4×C31—21no—
87C2×D4×C31—21no—
88C2×D4×C31—21no—
89C2×D4×C31—21no—
90C2×D4×C31—21no—
91C2×D4×C31D812yes—
92C22×C4×C31—21no—
93C22×C4×C31—22no—
94C22×C4×C31—22no—
95C22×C4×C31—41no—
96C22×C4×C31—41no—
97C22×C4×C31—41no—
98C22×C4×C31—42no—
99C22×C4×C31—42no—
100C22×C4×C31C2×D411yescharacteristic
101C22×C4×C31C2×D411yescharacteristic
102C22×C4×C31C2×D411yescharacteristic
103SD16×C31—48no—
104C2×C8×C31—24no—
105C2×C8×C31—22no—
106C2×C8×C31—22no—
107C2×C8×C31—41no—
108C2×C8×C31—41no—
109C2×C8×C31—41no—
110C2×C8×C31—42no—
111C4⋊C4×C31—21no—
112C4⋊C4×C31—22no—
113C4⋊C4×C31—22no—
114C4⋊C4×C31—22no—
115C4⋊C4×C31—21no—
116C4⋊C4×C31—22no—
117C4⋊C4×C31—22no—
118C4⋊C4×C31—22no—
119C4⋊C4×C31—41no—
120C4⋊C4×C31—41no—
121C4⋊C4×C31—41no—
122C4⋊C4×C31—41no—
123C22⋊C4×C31—48no—
124C22⋊C4×C31—41no—
125C22⋊C4×C31—41no—
126C42×C31—41no—
127C42×C31—41no—
128C42×C31C2×D411yescharacteristic
129C42×C31C2×D411yescharacteristic
130C42×C31C2×D411yescharacteristic
131C42×C31#4111yescharacteristic
132#10066C3111yesmaximal, characteristic, direct product factor, Sylow
133C23×C31—22no—
134C23×C31—41no—
135C23×C31—41no—
136C23×C31—42no—
137C23×C31—42no—
138C23×C31#12011yescharacteristic
139Q8×C31—42no—
140Q8×C31—42no—
141Q8×C31—81no—
142Q8×C31—81no—
143Q8×C31—81no—
144Q8×C31—81no—
145Q8×C31—81no—
146Q8×C31—81no—
147D4×C31—22no—
148D4×C31—22no—
149D4×C31—41no—
150D4×C31—41no—
151C2×C4×C31—22no—
152C2×C4×C31—41no—
153C2×C4×C31—42no—
154C2×C4×C31—42no—
155C2×C4×C31—42no—
156C2×C4×C31—42no—
157C2×C4×C31—42no—
158C2×C4×C31—42no—
159C2×C4×C31—42no—
160C2×C4×C31—42no—
161C2×C4×C31—81no—
162C2×C4×C31—81no—
163C2×C4×C31—82no—
164C2×C4×C31—81no—
165C2×C4×C31—81no—
166C2×C4×C31#12011yescharacteristic
167C2×C4×C31#12011yescharacteristic
168C2×C4×C31#12111yescharacteristic
169C2×C4×C31#12111yescharacteristic
170C2×C4×C31#12111yescharacteristic
171C2×C4×C31#12711yescharacteristic
172C2×C4×C31C2×D811yescharacteristic
173C2×C4×C31#13511yescharacteristic
174C2×C4×C31#13512yes—
175C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
176C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
177C2×C4×C31#13712yes—
178C8×C31—24no—
179C8×C31—42no—
180C8×C31—81no—
181C2×#500C2×C3111yescharacteristic, complemented
182C2×#461C2×C3111yescharacteristic
183#2547C2×C3111yescharacteristic
184#1988C2×C3111yescharacteristic, complemented
185C2×#332C2×C3111yescharacteristic, complemented
186C2×D4⋊C8C2×C3111yescharacteristic
187#1279C2×C3111yescharacteristic, complemented
188C22×C31—44no—
189C22×C31—42no—
190C22×C31—82no—
191C22×C31—81no—
192C22×C31—81no—
193C22×C31#39211yescharacteristic
194C22×C31#44711yescharacteristic
195C22×C31#44911yescharacteristic
196C22×C31#45212yes—
197C22×C31#45612yes—
198C4×C31—21no—
199C4×C31—21no—
200C4×C31—82no—
201C4×C31—82no—
202C4×C31—82no—
203C4×C31—81no—
204C4×C31#44711yescharacteristic
205C4×C31#44911yescharacteristic
206C4×C31#46412yes—
207C4×C31#46611yescharacteristic
208C4×C31#46911yescharacteristic
209C4×C31#49511yescharacteristic
210C4×C31#49711yescharacteristic
211C22×SD16—21no—
212C2×C4⋊Q8C22×C3111yescharacteristic
213C2×C4⋊Q8C22×C3111yescharacteristic
214C2×#124—21no—
215C2×C4×D4C22×C3111yescharacteristic
216#500—22no—
217#500—22no—
218#461—22no—
219#461—22no—
220C2×#107—22no—
221C2×C4⋊C8C22×C3111yescharacteristic
222C2×C4⋊C8C22×C3111yescharacteristic
223C2×#103—21no—
224C2×C4×C8C22×C3111yescharacteristic
225#397—22no—
226#391—21no—
227#380—22no—
228C4×C4⋊C4C22×C3111yescharacteristic
229#340—22no—
230#332—22no—
231D4⋊C8—22no—
232C2×C31—82no—
233C2×C31#164712yes—
234C2×C31#165012yes—
235C2×C31#199911yescharacteristic
236C2×C31#200511yescharacteristic
237C2×C31#201511yescharacteristic
238C22×Q8—21no—
239C22×Q8—21no—
240C22×D4D4×C3111yescharacteristic
241C23×C4—21no—
242C2×SD16—24no—
243C2×SD16—42no—
244C2×SD16—42no—
245C22×C8—21no—
246C22×C8—21no—
247C22×C8—21no—
248C4⋊Q8—21no—
249C4⋊Q8—21no—
250C4⋊Q8—21no—
251C4⋊Q8—21no—
252C4⋊Q8—21no—
253C4⋊Q8—21no—
254C4⋊Q8—21no—
255C4⋊Q8D4×C3112yes—
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⋊C4D4×C3111yescharacteristic
266C2×C4⋊C4D4×C3112yes—
267C2×C4⋊C4D4×C3112yes—
268C2×C22⋊C4—24no—
269C2×C22⋊C4—21no—
270C2×C42—21no—
271C2×C42C23×C3111yescharacteristic
272#107—28no—
273C4⋊C8—21no—
274C4⋊C8—21no—
275C4⋊C8—21no—
276C4⋊C8D4×C3112yes—
277#103—24no—
278C4×C8—21no—
279C4×C8D4×C3112yes—
280#95—24no—
281#95—21no—
282C31#1006611yescharacteristic, direct product factor, Sylow
283C24—21no—
284C2×Q8—22no—
285C2×Q8—41no—
286C2×Q8—41no—
287C2×Q8—41no—
288C2×Q8—41no—
289C2×Q8—41no—
290C2×Q8—41no—
291C2×Q8—41no—
292C2×Q8—41no—
293C2×Q8—41no—
294C2×Q8—41no—
295C2×Q8—41no—
296C2×D4—21no—
297C2×D4—21no—
298C2×D4—21no—
299C2×D4—21no—
300C2×D4—21no—
301C2×D4D8×C3112yes—
302C22×C4—21no—
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—42no—
309C22×C4—42no—
310C22×C4C2×D4×C3111yescharacteristic
311C22×C4C2×D4×C3111yescharacteristic
312C22×C4C2×D4×C3111yescharacteristic
313SD16—48no—
314C2×C8—24no—
315C2×C8—22no—
316C2×C8—22no—
317C2×C8—41no—
318C2×C8—41no—
319C2×C8—41no—
320C2×C8—42no—
321C4⋊C4—21no—
322C4⋊C4—22no—
323C4⋊C4—22no—
324C4⋊C4—22no—
325C4⋊C4—21no—
326C4⋊C4—22no—
327C4⋊C4—22no—
328C4⋊C4—22no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C22⋊C4—48no—
334C22⋊C4—41no—
335C22⋊C4—41no—
336C42—41no—
337C42—41no—
338C42C2×D4×C3111yescharacteristic
339C42C2×D4×C3111yescharacteristic
340C42C2×D4×C3111yescharacteristic
341C42#41×C3111yescharacteristic
342C23—22no—
343C23—41no—
344C23—42no—
345C23—42no—
346C23—41no—
347C23C31×#12011yescharacteristic
348Q8—42no—
349Q8—42no—
350Q8—81no—
351Q8—81no—
352Q8—81no—
353Q8—81no—
354Q8—81no—
355Q8—81no—
356D4—22no—
357D4—22no—
358D4—41no—
359D4—41no—
360C2×C4—22no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—41no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—81no—
371C2×C4—81no—
372C2×C4—82no—
373C2×C4—81no—
374C2×C4—81no—
375C2×C4C31×#12011yescharacteristic
376C2×C4C31×#12011yescharacteristic
377C2×C4C31×#12111yescharacteristic
378C2×C4C31×#12111yescharacteristic
379C2×C4C31×#12111yescharacteristic
380C2×C4C31×#12711yescharacteristic
381C2×C4C2×D8×C3111yescharacteristic
382C2×C4C31×#13511yescharacteristic
383C2×C4C31×#13512yes—
384C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
385C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
386C2×C4C31×#13712yes—
387C8—24no—
388C8—42no—
389C8—81no—
390C22—44no—
391C22—42no—
392C22—82no—
393C22—81no—
394C22—81no—
395C22C31×#39211yescharacteristic
396C22C31×#44711yescharacteristic
397C22C31×#44911yescharacteristic
398C22C31×#45212yes—
399C22C31×#45612yes—
400C4—21no—
401C4—21no—
402C4—82no—
403C4—82no—
404C4—82no—
405C4—81no—
406C4C31×#44711yescharacteristic
407C4C31×#44911yescharacteristic
408C4C31×#46412yes—
409C4C31×#46611yescharacteristic
410C4C31×#46911yescharacteristic
411C4C31×#49511yescharacteristic
412C4C31×#49711yescharacteristic
413C2—82no—
414C2C31×#164712yes—
415C2C31×#165012yes—
416C2C31×#199911yescharacteristic
417C2C31×#200511yescharacteristic
418C2C31×#201511yescharacteristic
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
1. C2×C31×#500C2semidirect
4. C31×#1988C2semidirect
5. C2×C31×#332C2semidirect
7. C31×#1279C2semidirect
132. #10066C31direct (N × H)
181. C2×#500C2×C31semidirect
184. #1988C2×C31semidirect
185. C2×#332C2×C31semidirect
187. #1279C2×C31semidirect
282. C31#10066direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5002
C2×C31×#4612
C31×#25472
C31×#19882
C2×C31×#3322
C2×C31×D4⋊C82
C31×#12792
#1006631