Finite Group Databasebeta

← C2×C31×#1614 #21474863

Subgroups — C2×C31×#1614 #21474863

Order 7936.

1180 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#543C211yesmaximal, characteristic
2C2×C31×#484C212yesmaximal, complemented
3C2×C31×#399C211yesmaximal, characteristic
4C31×#1614C218yesmaximal, direct product factor
5C2×C31×#328C212yesmaximal, complemented
6C2×C31×#323C211yesmaximal, characteristic
7C31×#543—24no—
8C31×#543—22no—
9C31×#543C2214yes—
10C2×C31×C22⋊Q8—22no—
11C2×C31×C22⋊Q8—21no—
12C2×C31×C22⋊Q8—22no—
13C2×C31×C22⋊Q8C2212yes—
14C22×C4⋊C4×C31—21no—
15C22×C4⋊C4×C31C2211yescharacteristic
16C22×C22⋊C4×C31—21no—
17C22×C22⋊C4×C31—21no—
18C22×C22⋊C4×C31C2211yescharacteristic
19C31×#484—24no—
20C31×#484C2218yescomplemented
21C2×C31×#107—22no—
22C2×C31×#103—22no—
23C2×C31×C22⋊C8C2212yes—
24C31×#399—22no—
25C31×#399C2214yes—
26C2×C31×#95C2211yescharacteristic
27C31×#328C2218yescomplemented
28C31×#323C2214yes—
29C25×C31D411yescharacteristic
30C22×Q8×C31—21no—
31C22×Q8×C31D412yes—
32C23×C4×C31—21no—
33C23×C4×C31—21no—
34C23×C4×C31—21no—
35C23×C4×C31—21no—
36C23×C4×C31D411yescharacteristic
37C23×C4×C31C2311yescharacteristic
38C22×C8×C31—22no—
39C31×C22⋊Q8—28no—
40C31×C22⋊Q8—28no—
41C31×C22⋊Q8—24no—
42C31×C22⋊Q8—28no—
43C31×C22⋊Q8—24no—
44C31×C22⋊Q8—22no—
45C31×C22⋊Q8—22no—
46C31×C22⋊Q8—28no—
47C31×C22⋊Q8D414yes—
48C31×C22⋊Q8C2314yes—
49C2×C4⋊C4×C31—21no—
50C2×C4⋊C4×C31—22no—
51C2×C4⋊C4×C31—22no—
52C2×C4⋊C4×C31—22no—
53C2×C4⋊C4×C31—22no—
54C2×C4⋊C4×C31—21no—
55C2×C4⋊C4×C31—24no—
56C2×C4⋊C4×C31—44no—
57C2×C4⋊C4×C31D412yes—
58C2×C4⋊C4×C31C2312yes—
59C2×C22⋊C4×C31—22no—
60C2×C22⋊C4×C31—24no—
61C2×C22⋊C4×C31—22no—
62C2×C22⋊C4×C31—24no—
63C2×C22⋊C4×C31—22no—
64C2×C22⋊C4×C31—22no—
65C2×C22⋊C4×C31—24no—
66C2×C22⋊C4×C31—44no—
67C2×C22⋊C4×C31D412yes—
68C2×C22⋊C4×C31C2312yes—
69C31×#107—28no—
70C31×#103—28no—
71C31×C22⋊C8—22no—
72C31×C22⋊C8C2314yes—
73C31×#95—21no—
74C31×#95C2312yes—
75C24×C31—21no—
76C24×C31—21no—
77C24×C31—22no—
78C24×C31—42no—
79C24×C31—42no—
80C24×C31Q1614yes—
81C24×C31C2×D411yescharacteristic
82C24×C31C2×D412yes—
83C2×Q8×C31—24no—
84C2×Q8×C31—22no—
85C2×Q8×C31—44no—
86C2×Q8×C31—82no—
87C2×Q8×C31C2×D414yes—
88C22×C4×C31—24no—
89C22×C4×C31—22no—
90C22×C4×C31—21no—
91C22×C4×C31—22no—
92C22×C4×C31—22no—
93C22×C4×C31—24no—
94C22×C4×C31—24no—
95C22×C4×C31—21no—
96C22×C4×C31—22no—
97C22×C4×C31—42no—
98C22×C4×C31—42no—
99C22×C4×C31—42no—
100C22×C4×C31—42no—
101C22×C4×C31—42no—
102C22×C4×C31—42no—
103C22×C4×C31—41no—
104C22×C4×C31—41no—
105C22×C4×C31—82no—
106C22×C4×C31—82no—
107C22×C4×C31C2×D412yes—
108C22×C4×C31C2×D412yes—
109C22×C4×C31C2×D411yescharacteristic
110C22×C4×C31C2×D412yes—
111C22×C4×C31C2411yescharacteristic
112C2×C8×C31—24no—
113C2×C8×C31—44no—
114C4⋊C4×C31—24no—
115C4⋊C4×C31—28no—
116C4⋊C4×C31—24no—
117C4⋊C4×C31—22no—
118C4⋊C4×C31—24no—
119C4⋊C4×C31—24no—
120C4⋊C4×C31—48no—
121C4⋊C4×C31—42no—
122C4⋊C4×C31C2×D414yes—
123C22⋊C4×C31—28no—
124C22⋊C4×C31—24no—
125C22⋊C4×C31—24no—
126C22⋊C4×C31—24no—
127C22⋊C4×C31—24no—
128C22⋊C4×C31—48no—
129C2×#1614C3111yesmaximal, characteristic, direct product factor, Sylow
130C23×C31—22no—
131C23×C31—22no—
132C23×C31—22no—
133C23×C31—24no—
134C23×C31—22no—
135C23×C31—24no—
136C23×C31—42no—
137C23×C31—48no—
138C23×C31—42no—
139C23×C31—42no—
140C23×C31—42no—
141C23×C31—84no—
142C23×C31—81no—
143C23×C31—81no—
144C23×C31#12011yescharacteristic
145C23×C31#12011yescharacteristic
146C23×C31C2×Q1612yes—
147C23×C31C2×Q1614yes—
148C23×C31#13712yes—
149C23×C31C22×D411yescharacteristic
150Q8×C31—44no—
151Q8×C31—82no—
152Q8×C31—84no—
153C2×C4×C31—24no—
154C2×C4×C31—24no—
155C2×C4×C31—24no—
156C2×C4×C31—22no—
157C2×C4×C31—24no—
158C2×C4×C31—42no—
159C2×C4×C31—41no—
160C2×C4×C31—41no—
161C2×C4×C31—48no—
162C2×C4×C31—42no—
163C2×C4×C31—42no—
164C2×C4×C31—42no—
165C2×C4×C31—44no—
166C2×C4×C31—44no—
167C2×C4×C31—42no—
168C2×C4×C31—42no—
169C2×C4×C31—42no—
170C2×C4×C31—42no—
171C2×C4×C31—81no—
172C2×C4×C31—84no—
173C2×C4×C31—84no—
174C2×C4×C31—82no—
175C2×C4×C31—82no—
176C2×C4×C31#12012yes—
177C2×C4×C31C22×D412yes—
178C8×C31—44no—
179C2×#543C2×C3111yescharacteristic
180C2×#484C2×C3112yescomplemented
181C2×#399C2×C3111yescharacteristic
182#1614C2×C3118yesdirect product factor
183C2×#328C2×C3112yescomplemented
184C2×#323C2×C3111yescharacteristic
185C22×C31—24no—
186C22×C31—24no—
187C22×C31—21no—
188C22×C31—21no—
189C22×C31—21no—
190C22×C31—21no—
191C22×C31—24no—
192C22×C31—44no—
193C22×C31—48no—
194C22×C31—42no—
195C22×C31—42no—
196C22×C31—82no—
197C22×C31—84no—
198C22×C31#45112yes—
199C22×C31#45112yes—
200C22×C31#45312yes—
201C22×C31#45812yes—
202C22×C31C2×#12011yescharacteristic
203C22×C31C22×Q1611yescharacteristic
204C22×C31C2×#13711yescharacteristic
205C4×C31—22no—
206C4×C31—22no—
207C4×C31—44no—
208C4×C31—42no—
209C4×C31—44no—
210C4×C31—44no—
211C4×C31—82no—
212#543—24no—
213#543—22no—
214#543C22×C3114yes—
215C2×C22⋊Q8—22no—
216C2×C22⋊Q8—21no—
217C2×C22⋊Q8—22no—
218C2×C22⋊Q8C22×C3112yes—
219C22×C4⋊C4—21no—
220C22×C4⋊C4C22×C3111yescharacteristic
221C22×C22⋊C4—21no—
222C22×C22⋊C4—21no—
223C22×C22⋊C4C22×C3111yescharacteristic
224#484—24no—
225#484C22×C3118yescomplemented
226C2×#107—22no—
227C2×#103—22no—
228C2×C22⋊C8C22×C3112yes—
229#399—22no—
230#399C22×C3114yes—
231C2×#95C22×C3111yescharacteristic
232#328C22×C3118yescomplemented
233#323C22×C3114yes—
234C2×C31—21no—
235C2×C31—21no—
236C2×C31—22no—
237C2×C31—44no—
238C2×C31#161414yesdirect product factor
239C2×C31C2×#45111yescharacteristic
240C2×C31C2×#45311yescharacteristic
241C2×C31C2×#45811yescharacteristic
242C25D4×C3111yescharacteristic
243C22×Q8—21no—
244C22×Q8D4×C3112yes—
245C23×C4—21no—
246C23×C4—21no—
247C23×C4—21no—
248C23×C4—21no—
249C23×C4D4×C3111yescharacteristic
250C23×C4C23×C3111yescharacteristic
251C22×C8—22no—
252C22⋊Q8—28no—
253C22⋊Q8—28no—
254C22⋊Q8—24no—
255C22⋊Q8—28no—
256C22⋊Q8—24no—
257C22⋊Q8—22no—
258C22⋊Q8—22no—
259C22⋊Q8—28no—
260C22⋊Q8D4×C3114yes—
261C22⋊Q8C23×C3114yes—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—22no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—24no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—44no—
270C2×C4⋊C4D4×C3112yes—
271C2×C4⋊C4C23×C3112yes—
272C2×C22⋊C4—22no—
273C2×C22⋊C4—24no—
274C2×C22⋊C4—22no—
275C2×C22⋊C4—24no—
276C2×C22⋊C4—22no—
277C2×C22⋊C4—22no—
278C2×C22⋊C4—24no—
279C2×C22⋊C4—44no—
280C2×C22⋊C4D4×C3112yes—
281C2×C22⋊C4C23×C3112yes—
282#107—28no—
283#103—28no—
284C22⋊C8—22no—
285C22⋊C8C23×C3114yes—
286#95—21no—
287#95C23×C3112yes—
288C31C2×#161411yescharacteristic, direct product factor, Sylow
289C24—21no—
290C24—21no—
291C24—22no—
292C24—42no—
293C24—42no—
294C24Q16×C3114yes—
295C24C2×D4×C3111yescharacteristic
296C24C2×D4×C3112yes—
297C2×Q8—24no—
298C2×Q8—22no—
299C2×Q8—44no—
300C2×Q8—82no—
301C2×Q8C2×D4×C3114yes—
302C22×C4—24no—
303C22×C4—22no—
304C22×C4—21no—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—24no—
308C22×C4—24no—
309C22×C4—21no—
310C22×C4—22no—
311C22×C4—42no—
312C22×C4—42no—
313C22×C4—42no—
314C22×C4—42no—
315C22×C4—42no—
316C22×C4—42no—
317C22×C4—41no—
318C22×C4—41no—
319C22×C4—82no—
320C22×C4—82no—
321C22×C4C2×D4×C3112yes—
322C22×C4C2×D4×C3112yes—
323C22×C4C2×D4×C3111yescharacteristic
324C22×C4C2×D4×C3112yes—
325C22×C4C24×C3111yescharacteristic
326C2×C8—24no—
327C2×C8—44no—
328C4⋊C4—24no—
329C4⋊C4—28no—
330C4⋊C4—24no—
331C4⋊C4—22no—
332C4⋊C4—24no—
333C4⋊C4—24no—
334C4⋊C4—48no—
335C4⋊C4—42no—
336C4⋊C4C2×D4×C3114yes—
337C22⋊C4—28no—
338C22⋊C4—24no—
339C22⋊C4—24no—
340C22⋊C4—24no—
341C22⋊C4—24no—
342C22⋊C4—48no—
343C23—22no—
344C23—22no—
345C23—24no—
346C23—22no—
347C23—24no—
348C23—22no—
349C23—42no—
350C23—48no—
351C23—42no—
352C23—42no—
353C23—42no—
354C23—84no—
355C23—81no—
356C23—81no—
357C23C31×#12011yescharacteristic
358C23C31×#12011yescharacteristic
359C23C2×Q16×C3112yes—
360C23C2×Q16×C3114yes—
361C23C31×#13712yes—
362C23C22×D4×C3111yescharacteristic
363Q8—44no—
364Q8—82no—
365Q8—84no—
366C2×C4—24no—
367C2×C4—24no—
368C2×C4—24no—
369C2×C4—22no—
370C2×C4—24no—
371C2×C4—42no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—48no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—44no—
378C2×C4—44no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—81no—
385C2×C4—84no—
386C2×C4—84no—
387C2×C4—82no—
388C2×C4—82no—
389C2×C4C31×#12012yes—
390C2×C4C22×D4×C3112yes—
391C8—44no—
392C22—24no—
393C22—24no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—24no—
399C22—44no—
400C22—48no—
401C22—42no—
402C22—42no—
403C22—82no—
404C22—84no—
405C22C31×#45112yes—
406C22C31×#45112yes—
407C22C31×#45312yes—
408C22C31×#45812yes—
409C22C2×C31×#12011yescharacteristic
410C22C22×Q16×C3111yescharacteristic
411C22C2×C31×#13711yescharacteristic
412C4—22no—
413C4—22no—
414C4—44no—
415C4—42no—
416C4—44no—
417C4—44no—
418C4—82no—
419C2—21no—
420C2—21no—
421C2—22no—
422C2—44no—
423C2C31×#161414yesdirect product factor
424C2C2×C31×#45111yescharacteristic
425C2C2×C31×#45311yescharacteristic
426C2C2×C31×#45811yescharacteristic
subgroupG/H
center, socleC23×C31#120
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC25×C31D4
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
2. C2×C31×#484C2semidirect
4. C31×#1614C2direct (N × H)
5. C2×C31×#328C2semidirect
20. C31×#484C22semidirect
27. C31×#328C22semidirect
129. C2×#1614C31direct (N × H)
180. C2×#484C2×C31semidirect
182. #1614C2×C31direct (N × H)
183. C2×#328C2×C31semidirect
225. #484C22×C31semidirect
232. #328C22×C31semidirect
238. C2×C31#1614direct (N × H)
288. C31C2×#1614direct (N × H)
423. C2C31×#1614direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5432
C2×C31×#4842
C2×C31×#3992
C31×#16142
C2×C31×#3282
C2×C31×#3232
C2×#161431