Finite Group Databasebeta

← C31×#10179 #21466938

Subgroups — C31×#10179 #21466938

Order 7936.

560 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3208C211yesmaximal, characteristic
2C31×#3078C211yesmaximal, characteristic, complemented
3C2×C31×#460C211yesmaximal, characteristic
4C31×#1545C211yesmaximal, characteristic
5C31×#1481C211yesmaximal, characteristic, complemented
6C31×#1461C211yesmaximal, characteristic, complemented
7C31×#1301C211yesmaximal, characteristic, complemented
8C22×SD16×C31—21no—
9C31×#533C2211yescharacteristic
10C2×C31×#127C2211yescharacteristic
11C2×C4×Q8×C31C2211yescharacteristic
12C31×#492—21no—
13C31×#486—21no—
14C31×#479—22no—
15C31×#477—21no—
16C31×#475—21no—
17C31×#460—22no—
18C31×#460—22no—
19C31×#460—22no—
20C31×#450—22no—
21C31×#431C2211yescharacteristic
22C31×#431C2211yescharacteristic
23C31×#428—21no—
24C31×#423C2211yescharacteristic
25C2×C31×C4⋊C8C2211yescharacteristic
26C31×#419—21no—
27C2×C31×#102—21no—
28C31×#331—22no—
29C31×Q8⋊C8—22no—
30C31×#324—22no—
31C22×Q8×C31D411yescharacteristic
32C22×D4×C31—21no—
33C22×D4×C31—21no—
34C22×D4×C31—21no—
35C2×SD16×C31—24no—
36C2×SD16×C31—24no—
37C2×SD16×C31—42no—
38C2×SD16×C31—42no—
39C2×M16×C31—21no—
40C22×C8×C31—21no—
41C31×C4⋊Q8D411yescharacteristic
42C31×C4⋊Q8D411yescharacteristic
43C31×#127—21no—
44C31×#127—21no—
45C31×#127—21no—
46C31×#127D412yes—
47C31×#125—21no—
48C31×C22⋊Q8—21no—
49C31×C22⋊Q8—21no—
50C4×Q8×C31—21no—
51C4×Q8×C31—21no—
52C4×Q8×C31—21no—
53C4×Q8×C31—21no—
54C4×Q8×C31—21no—
55C4×Q8×C31—21no—
56C31×#117—21no—
57C2×C4⋊C4×C31—21no—
58C2×C4⋊C4×C31D411yescharacteristic
59C2×C42×C31—21no—
60C2×C42×C31C2311yescharacteristic
61C31×#107—22no—
62C31×#106—22no—
63C31×C4⋊C8—21no—
64C31×C4⋊C8—21no—
65C31×C4⋊C8—21no—
66C31×C4⋊C8—21no—
67C31×C4⋊C8D412yes—
68C31×C4⋊C8D412yes—
69C31×#103—22no—
70C31×#103—22no—
71C31×#102—24no—
72C31×#102—24no—
73C31×C22⋊C8—21no—
74C31×C22⋊C8D412yes—
75C4×C8×C31—21no—
76C4×C8×C31—21no—
77C24×C31—41no—
78C2×Q8×C31—21no—
79C2×Q8×C31—21no—
80C2×Q8×C31—21no—
81C2×Q8×C31—21no—
82C2×Q8×C31—21no—
83C2×Q8×C31—21no—
84C2×Q8×C31—21no—
85C2×Q8×C31SD1612yescomplemented
86C2×D4×C31—22no—
87C2×D4×C31—22no—
88C2×D4×C31—22no—
89C2×D4×C31—41no—
90C2×D4×C31—41no—
91C2×D4×C31—41no—
92C2×D4×C31—41no—
93C2×D4×C31—41no—
94C2×D4×C31—41no—
95C2×D4×C31—41no—
96C2×D4×C31—82no—
97C2×D4×C31—82no—
98C22×C4×C31—21no—
99C22×C4×C31—21no—
100C22×C4×C31C2×D411yescharacteristic
101C22×C4×C31C2×D411yescharacteristic
102C22×C4×C31#4111yescharacteristic
103SD16×C31—48no—
104SD16×C31—84no—
105M16×C31—41no—
106M16×C31—41no—
107C2×C8×C31—22no—
108C2×C8×C31—22no—
109C2×C8×C31—22no—
110C2×C8×C31—41no—
111C2×C8×C31—41no—
112C2×C8×C31—41no—
113C4⋊C4×C31—21no—
114C4⋊C4×C31—21no—
115C4⋊C4×C31—21no—
116C4⋊C4×C31—21no—
117C4⋊C4×C31—21no—
118C4⋊C4×C31—21no—
119C4⋊C4×C31—41no—
120C4⋊C4×C31—41no—
121C4⋊C4×C31—41no—
122C4⋊C4×C31—41no—
123C22⋊C4×C31—41no—
124C42×C31—41no—
125C42×C31—41no—
126C42×C31—41no—
127C42×C31C2×D411yescharacteristic
128C42×C31C2×D411yescharacteristic
129C42×C31C2×D411yescharacteristic
130C42×C31C2×D411yescharacteristic
131#10179C3111yesmaximal, characteristic, direct product factor, Sylow
132C23×C31—42no—
133C23×C31—82no—
134C23×C31—82no—
135C23×C31—81no—
136C23×C31—81no—
137C23×C31#12111yescharacteristic
138Q8×C31—22no—
139Q8×C31—22no—
140Q8×C31—42no—
141Q8×C31—41no—
142Q8×C31—41no—
143Q8×C31—42no—
144D4×C31—44no—
145D4×C31—42no—
146D4×C31—42no—
147D4×C31—82no—
148D4×C31—82no—
149D4×C31—81no—
150D4×C31—81no—
151D4×C31—82no—
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—41no—
159C2×C4×C31—41no—
160C2×C4×C31—81no—
161C2×C4×C31#12011yescharacteristic
162C2×C4×C31#12011yescharacteristic
163C2×C4×C31#12011yescharacteristic
164C2×C4×C31#12111yescharacteristic
165C2×C4×C31#12111yescharacteristic
166C2×C4×C31#12711yescharacteristic
167C2×C4×C31C2×SD1611yescharacteristic
168C2×C4×C31#13511yescharacteristic
169C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
170C2×C4×C31#13711yescharacteristic
171C8×C31—42no—
172C8×C31—42no—
173C8×C31—42no—
174C8×C31—81no—
175#3208C2×C3111yescharacteristic
176#3078C2×C3111yescharacteristic, complemented
177C2×#460C2×C3111yescharacteristic
178#1545C2×C3111yescharacteristic
179#1481C2×C3111yescharacteristic, complemented
180#1461C2×C3111yescharacteristic, complemented
181#1301C2×C3111yescharacteristic, complemented
182C22×C31—21no—
183C22×C31—21no—
184C22×C31—82no—
185C22×C31—82no—
186C22×C31—82no—
187C22×C31—162no—
188C22×C31—162no—
189C22×C31#39211yescharacteristic
190C22×C31#46511yescharacteristic
191C22×C31#46811yescharacteristic
192C4×C31—21no—
193C4×C31—21no—
194C4×C31—21no—
195C4×C31—42no—
196C4×C31—81no—
197C4×C31—81no—
198C4×C31—81no—
199C4×C31#44811yescharacteristic
200C4×C31#44911yescharacteristic
201C4×C31#45011yescharacteristic
202C4×C31#45211yescharacteristic
203C4×C31#47112yes—
204C22×SD16—21no—
205#533C22×C3111yescharacteristic
206C2×#127C22×C3111yescharacteristic
207C2×C4×Q8C22×C3111yescharacteristic
208#492—21no—
209#486—21no—
210#479—22no—
211#477—21no—
212#475—21no—
213#460—22no—
214#460—22no—
215#460—22no—
216#450—22no—
217#431C22×C3111yescharacteristic
218#431C22×C3111yescharacteristic
219#428—21no—
220#423C22×C3111yescharacteristic
221C2×C4⋊C8C22×C3111yescharacteristic
222#419—21no—
223C2×#102—21no—
224#331—22no—
225Q8⋊C8—22no—
226#324—22no—
227C2×C31—21no—
228C2×C31—21no—
229C2×C31—162no—
230C2×C31#200011yescharacteristic
231C2×C31#200811yescharacteristic
232C2×C31#201911yescharacteristic
233C22×Q8D4×C3111yescharacteristic
234C22×D4—21no—
235C22×D4—21no—
236C22×D4—21no—
237C2×SD16—24no—
238C2×SD16—24no—
239C2×SD16—42no—
240C2×SD16—42no—
241C2×M16—21no—
242C22×C8—21no—
243C4⋊Q8D4×C3111yescharacteristic
244C4⋊Q8D4×C3111yescharacteristic
245#127—21no—
246#127—21no—
247#127—21no—
248#127D4×C3112yes—
249#125—21no—
250C22⋊Q8—21no—
251C22⋊Q8—21no—
252C4×Q8—21no—
253C4×Q8—21no—
254C4×Q8—21no—
255C4×Q8—21no—
256C4×Q8—21no—
257C4×Q8—21no—
258#117—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4D4×C3111yescharacteristic
261C2×C42—21no—
262C2×C42C23×C3111yescharacteristic
263#107—22no—
264#106—22no—
265C4⋊C8—21no—
266C4⋊C8—21no—
267C4⋊C8—21no—
268C4⋊C8—21no—
269C4⋊C8D4×C3112yes—
270C4⋊C8D4×C3112yes—
271#103—22no—
272#103—22no—
273#102—24no—
274#102—24no—
275C22⋊C8—21no—
276C22⋊C8D4×C3112yes—
277C4×C8—21no—
278C4×C8—21no—
279C31#1017911yescharacteristic, direct product factor, Sylow
280C24—41no—
281C2×Q8—21no—
282C2×Q8—21no—
283C2×Q8—21no—
284C2×Q8—21no—
285C2×Q8—21no—
286C2×Q8—21no—
287C2×Q8—21no—
288C2×Q8SD16×C3112yescomplemented
289C2×D4—22no—
290C2×D4—22no—
291C2×D4—22no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—82no—
300C2×D4—82no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4C2×D4×C3111yescharacteristic
304C22×C4C2×D4×C3111yescharacteristic
305C22×C4#41×C3111yescharacteristic
306SD16—48no—
307SD16—84no—
308M16—41no—
309M16—41no—
310C2×C8—22no—
311C2×C8—22no—
312C2×C8—22no—
313C2×C8—41no—
314C2×C8—41no—
315C2×C8—41no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—21no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C22⋊C4—41no—
327C42—41no—
328C42—41no—
329C42—41no—
330C42C2×D4×C3111yescharacteristic
331C42C2×D4×C3111yescharacteristic
332C42C2×D4×C3111yescharacteristic
333C42C2×D4×C3111yescharacteristic
334C23—42no—
335C23—82no—
336C23—82no—
337C23—81no—
338C23—81no—
339C23C31×#12111yescharacteristic
340Q8—22no—
341Q8—22no—
342Q8—42no—
343Q8—41no—
344Q8—41no—
345Q8—42no—
346D4—44no—
347D4—42no—
348D4—42no—
349D4—82no—
350D4—82no—
351D4—81no—
352D4—81no—
353D4—82no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—81no—
363C2×C4C31×#12011yescharacteristic
364C2×C4C31×#12011yescharacteristic
365C2×C4C31×#12011yescharacteristic
366C2×C4C31×#12111yescharacteristic
367C2×C4C31×#12111yescharacteristic
368C2×C4C31×#12711yescharacteristic
369C2×C4C2×SD16×C3111yescharacteristic
370C2×C4C31×#13511yescharacteristic
371C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
372C2×C4C31×#13711yescharacteristic
373C8—42no—
374C8—42no—
375C8—42no—
376C8—81no—
377C22—21no—
378C22—21no—
379C22—82no—
380C22—82no—
381C22—82no—
382C22—162no—
383C22—162no—
384C22C31×#39211yescharacteristic
385C22C31×#46511yescharacteristic
386C22C31×#46811yescharacteristic
387C4—21no—
388C4—21no—
389C4—21no—
390C4—42no—
391C4—81no—
392C4—81no—
393C4—81no—
394C4C31×#44811yescharacteristic
395C4C31×#44911yescharacteristic
396C4C31×#45011yescharacteristic
397C4C31×#45211yescharacteristic
398C4C31×#47112yes—
399C2—21no—
400C2—21no—
401C2—162no—
402C2C31×#200011yescharacteristic
403C2C31×#200811yescharacteristic
404C2C31×#201911yescharacteristic
subgroupG/H
center, socleC22×C31#392
commutator, Frattini, cosocleC2×C42C23×C31
prime radicalC2×C31×#127C22
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×#3078C2semidirect
5. C31×#1481C2semidirect
6. C31×#1461C2semidirect
7. C31×#1301C2semidirect
85. C2×Q8×C31SD16semidirect
131. #10179C31direct (N × H)
176. #3078C2×C31semidirect
179. #1481C2×C31semidirect
180. #1461C2×C31semidirect
181. #1301C2×C31semidirect
279. C31#10179direct (N × H)
288. C2×Q8SD16×C31semidirect

Maximal subgroups

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

subgroupindex
C31×#32082
C31×#30782
C2×C31×#4602
C31×#15452
C31×#14812
C31×#14612
C31×#13012
#1017931