Finite Group Databasebeta

← C2×C31×#1617 #21474877

Subgroups — C2×C31×#1617 #21474877

Order 7936.

984 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#544C211yesmaximal, characteristic
2C2×C31×#484C212yesmaximal
3C2×C31×#400C211yesmaximal, characteristic
4C31×#1617C218yesmaximal, direct product factor
5C2×C31×#328C212yesmaximal
6C2×C31×#324C211yesmaximal, characteristic
7C31×#544—24no—
8C31×#544—22no—
9C31×#544C2214yes—
10C2×C31×C4⋊Q8—22no—
11C2×C31×#125—22no—
12C2×C31×C22⋊Q8—21no—
13C2×C31×C22⋊Q8C2212yes—
14C2×C31×#117—21no—
15C22×C4⋊C4×C31C2211yescharacteristic
16C22×C4⋊C4×C31C2211yescharacteristic
17C31×#484—24no—
18C31×#484C2218yes—
19C2×C31×#107—22no—
20C2×C31×#103—22no—
21C2×C31×C22⋊C8C2212yes—
22C31×#400—22no—
23C31×#400C2214yes—
24C2×C31×#95—21no—
25C2×C31×#95—21no—
26C2×C31×#95C2211yescharacteristic
27C31×#328C2218yes—
28C31×#324C2214yes—
29C22×Q8×C31—21no—
30C22×Q8×C31D412yes—
31C23×C4×C31—21no—
32C23×C4×C31—21no—
33C23×C4×C31D411yescharacteristic
34C23×C4×C31D411yescharacteristic
35C23×C4×C31C2311yescharacteristic
36C22×C8×C31—22no—
37C31×C4⋊Q8—28no—
38C31×C4⋊Q8—28no—
39C31×#125—28no—
40C31×#125—28no—
41C31×C22⋊Q8—24no—
42C31×C22⋊Q8—24no—
43C31×C22⋊Q8—22no—
44C31×C22⋊Q8—22no—
45C31×C22⋊Q8D414yes—
46C31×C22⋊Q8C2314yes—
47C31×#117—24no—
48C31×#117—24no—
49C2×C4⋊C4×C31—21no—
50C2×C4⋊C4×C31—21no—
51C2×C4⋊C4×C31—21no—
52C2×C4⋊C4×C31—22no—
53C2×C4⋊C4×C31—22no—
54C2×C4⋊C4×C31—22no—
55C2×C4⋊C4×C31—22no—
56C2×C4⋊C4×C31—22no—
57C2×C4⋊C4×C31—22no—
58C2×C4⋊C4×C31—21no—
59C2×C4⋊C4×C31D412yes—
60C2×C4⋊C4×C31D412yes—
61C2×C4⋊C4×C31C2312yes—
62C2×C4⋊C4×C31C2312yes—
63C2×C22⋊C4×C31—22no—
64C2×C42×C31—22no—
65C31×#107—28no—
66C31×#103—28no—
67C31×C22⋊C8—22no—
68C31×C22⋊C8C2314yes—
69C31×#95—21no—
70C31×#95—24no—
71C31×#95—24no—
72C31×#95C2312yes—
73C24×C31C2×D411yescharacteristic
74C2×Q8×C31—24no—
75C2×Q8×C31—22no—
76C2×Q8×C31—44no—
77C2×Q8×C31—82no—
78C2×Q8×C31C2×D414yes—
79C22×C4×C31—21no—
80C22×C4×C31—21no—
81C22×C4×C31—22no—
82C22×C4×C31—22no—
83C22×C4×C31—22no—
84C22×C4×C31—21no—
85C22×C4×C31—21no—
86C22×C4×C31—22no—
87C22×C4×C31—22no—
88C22×C4×C31—42no—
89C22×C4×C31—42no—
90C22×C4×C31—42no—
91C22×C4×C31—42no—
92C22×C4×C31—44no—
93C22×C4×C31—41no—
94C22×C4×C31—41no—
95C22×C4×C31—42no—
96C22×C4×C31Q1614yes—
97C22×C4×C31C2×D412yes—
98C22×C4×C31C2×D412yes—
99C22×C4×C31C2×D412yes—
100C22×C4×C31C2×D411yescharacteristic
101C22×C4×C31C2×D412yes—
102C22×C4×C31C2411yescharacteristic
103C2×C8×C31—24no—
104C2×C8×C31—44no—
105C4⋊C4×C31—24no—
106C4⋊C4×C31—24no—
107C4⋊C4×C31—24no—
108C4⋊C4×C31—28no—
109C4⋊C4×C31—24no—
110C4⋊C4×C31—24no—
111C4⋊C4×C31—22no—
112C4⋊C4×C31—24no—
113C4⋊C4×C31—24no—
114C4⋊C4×C31—24no—
115C4⋊C4×C31—42no—
116C4⋊C4×C31C2×D414yes—
117C22⋊C4×C31—24no—
118C22⋊C4×C31—24no—
119C42×C31—28no—
120C2×#1617C3111yesmaximal, characteristic, direct product factor, Sylow
121C23×C31—22no—
122C23×C31—22no—
123C23×C31#12011yescharacteristic
124C23×C31#12011yescharacteristic
125C23×C31C2×Q1612yes—
126C23×C31#13712yes—
127C23×C31C22×D411yescharacteristic
128Q8×C31—44no—
129Q8×C31—82no—
130Q8×C31—84no—
131C2×C4×C31—22no—
132C2×C4×C31—22no—
133C2×C4×C31—24no—
134C2×C4×C31—24no—
135C2×C4×C31—24no—
136C2×C4×C31—24no—
137C2×C4×C31—24no—
138C2×C4×C31—22no—
139C2×C4×C31—42no—
140C2×C4×C31—41no—
141C2×C4×C31—41no—
142C2×C4×C31—44no—
143C2×C4×C31—42no—
144C2×C4×C31—44no—
145C2×C4×C31—42no—
146C2×C4×C31—42no—
147C2×C4×C31—42no—
148C2×C4×C31—44no—
149C2×C4×C31—42no—
150C2×C4×C31—42no—
151C2×C4×C31—81no—
152C2×C4×C31—84no—
153C2×C4×C31—82no—
154C2×C4×C31—82no—
155C2×C4×C31#12012yes—
156C2×C4×C31C2×Q1614yes—
157C2×C4×C31C22×D412yes—
158C8×C31—44no—
159C2×#544C2×C3111yescharacteristic
160C2×#484C2×C3112yes—
161C2×#400C2×C3111yescharacteristic
162#1617C2×C3118yesdirect product factor
163C2×#328C2×C3112yes—
164C2×#324C2×C3111yescharacteristic
165C22×C31—24no—
166C22×C31—24no—
167C22×C31—21no—
168C22×C31—21no—
169C22×C31—21no—
170C22×C31—21no—
171C22×C31#45112yes—
172C22×C31#45112yes—
173C22×C31#45412yes—
174C22×C31#45812yes—
175C22×C31C2×#12011yescharacteristic
176C22×C31C22×Q1611yescharacteristic
177C22×C31C2×#13711yescharacteristic
178C4×C31—24no—
179C4×C31—22no—
180C4×C31—22no—
181C4×C31—44no—
182C4×C31—42no—
183C4×C31—44no—
184C4×C31—82no—
185C4×C31—82no—
186#544—24no—
187#544—22no—
188#544C22×C3114yes—
189C2×C4⋊Q8—22no—
190C2×#125—22no—
191C2×C22⋊Q8—21no—
192C2×C22⋊Q8C22×C3112yes—
193C2×#117—21no—
194C22×C4⋊C4C22×C3111yescharacteristic
195C22×C4⋊C4C22×C3111yescharacteristic
196#484—24no—
197#484C22×C3118yes—
198C2×#107—22no—
199C2×#103—22no—
200C2×C22⋊C8C22×C3112yes—
201#400—22no—
202#400C22×C3114yes—
203C2×#95—21no—
204C2×#95—21no—
205C2×#95C22×C3111yescharacteristic
206#328C22×C3118yes—
207#324C22×C3114yes—
208C2×C31—21no—
209C2×C31—21no—
210C2×C31—22no—
211C2×C31#161714yesdirect product factor
212C2×C31C2×#45111yescharacteristic
213C2×C31C2×#45411yescharacteristic
214C2×C31C2×#45811yescharacteristic
215C22×Q8—21no—
216C22×Q8D4×C3112yes—
217C23×C4—21no—
218C23×C4—21no—
219C23×C4D4×C3111yescharacteristic
220C23×C4D4×C3111yescharacteristic
221C23×C4C23×C3111yescharacteristic
222C22×C8—22no—
223C4⋊Q8—28no—
224C4⋊Q8—28no—
225#125—28no—
226#125—28no—
227C22⋊Q8—24no—
228C22⋊Q8—24no—
229C22⋊Q8—22no—
230C22⋊Q8—22no—
231C22⋊Q8D4×C3114yes—
232C22⋊Q8C23×C3114yes—
233#117—24no—
234#117—24no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—22no—
239C2×C4⋊C4—22no—
240C2×C4⋊C4—22no—
241C2×C4⋊C4—22no—
242C2×C4⋊C4—22no—
243C2×C4⋊C4—22no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4D4×C3112yes—
246C2×C4⋊C4D4×C3112yes—
247C2×C4⋊C4C23×C3112yes—
248C2×C4⋊C4C23×C3112yes—
249C2×C22⋊C4—22no—
250C2×C42—22no—
251#107—28no—
252#103—28no—
253C22⋊C8—22no—
254C22⋊C8C23×C3114yes—
255#95—24no—
256#95—24no—
257#95—21no—
258#95C23×C3112yes—
259C31C2×#161711yescharacteristic, direct product factor, Sylow
260C24C2×D4×C3111yescharacteristic
261C2×Q8—24no—
262C2×Q8—22no—
263C2×Q8—44no—
264C2×Q8—82no—
265C2×Q8C2×D4×C3114yes—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—42no—
276C22×C4—42no—
277C22×C4—42no—
278C22×C4—42no—
279C22×C4—44no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4—42no—
283C22×C4Q16×C3114yes—
284C22×C4C2×D4×C3112yes—
285C22×C4C2×D4×C3112yes—
286C22×C4C2×D4×C3112yes—
287C22×C4C2×D4×C3111yescharacteristic
288C22×C4C2×D4×C3112yes—
289C22×C4C24×C3111yescharacteristic
290C2×C8—24no—
291C2×C8—44no—
292C4⋊C4—24no—
293C4⋊C4—24no—
294C4⋊C4—24no—
295C4⋊C4—28no—
296C4⋊C4—24no—
297C4⋊C4—24no—
298C4⋊C4—22no—
299C4⋊C4—24no—
300C4⋊C4—24no—
301C4⋊C4—24no—
302C4⋊C4—42no—
303C4⋊C4C2×D4×C3114yes—
304C22⋊C4—24no—
305C22⋊C4—24no—
306C42—28no—
307C23—22no—
308C23—22no—
309C23C31×#12011yescharacteristic
310C23C31×#12011yescharacteristic
311C23C2×Q16×C3112yes—
312C23C31×#13712yes—
313C23C22×D4×C3111yescharacteristic
314Q8—44no—
315Q8—82no—
316Q8—84no—
317C2×C4—24no—
318C2×C4—24no—
319C2×C4—24no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—24no—
323C2×C4—24no—
324C2×C4—22no—
325C2×C4—42no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—44no—
329C2×C4—42no—
330C2×C4—44no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—44no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—81no—
338C2×C4—84no—
339C2×C4—82no—
340C2×C4—82no—
341C2×C4C31×#12012yes—
342C2×C4C2×Q16×C3114yes—
343C2×C4C22×D4×C3112yes—
344C8—44no—
345C22—24no—
346C22—24no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22C31×#45112yes—
352C22C31×#45112yes—
353C22C31×#45412yes—
354C22C31×#45812yes—
355C22C2×C31×#12011yescharacteristic
356C22C22×Q16×C3111yescharacteristic
357C22C2×C31×#13711yescharacteristic
358C4—24no—
359C4—22no—
360C4—22no—
361C4—44no—
362C4—42no—
363C4—44no—
364C4—82no—
365C4—82no—
366C2—21no—
367C2—22no—
368C2—21no—
369C2C31×#161714yesdirect product factor
370C2C2×C31×#45111yescharacteristic
371C2C2×C31×#45411yescharacteristic
372C2C2×C31×#45811yescharacteristic
subgroupG/H
center, socleC23×C31#120
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC24×C31C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
4. C31×#1617C2direct (N × H)
120. C2×#1617C31direct (N × H)
162. #1617C2×C31direct (N × H)
211. C2×C31#1617direct (N × H)
259. C31C2×#1617direct (N × H)
369. C2C31×#1617direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5442
C2×C31×#4842
C2×C31×#4002
C31×#16172
C2×C31×#3282
C2×C31×#3242
C2×#161731