Finite Group Databasebeta

← C31×#19085 #21475844

Subgroups — C31×#19085 #21475844

Order 7936.

842 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3553C211yesmaximal, characteristic
2C31×#3181C212yesmaximal, complemented
3C31×#3166C211yesmaximal, characteristic, complemented
4C31×#1664C212yesmaximal, complemented
5C31×#1663C212yesmaximal, complemented
6C31×#1661C212yesmaximal, complemented
7C31×#1660C212yesmaximal, complemented
8C31×#1524C212yesmaximal, complemented
9C2×C31×#330C211yesmaximal, characteristic, complemented
10C31×#564C2211yescharacteristic
11C31×#563C2212yes—
12C31×#562C2211yescharacteristic
13C31×#554—22no—
14C31×#553—22no—
15C31×#552—22no—
16C31×#541—22no—
17C31×#539—22no—
18C31×#539—22no—
19C31×#533C2211yescharacteristic
20C31×#529C2212yes—
21C2×C31×#125C2211yescharacteristic
22C31×#501C2212yes—
23C31×#501C2212yes—
24C31×#501C2212yes—
25C31×#499—22no—
26C31×#497C2212yes—
27C31×#491C2212yes—
28C31×#489C2212yes—
29C31×#467—22no—
30C31×#465—22no—
31C31×#441—22no—
32C31×#440—22no—
33C31×#428—22no—
34C4×M16×C31C2211yescharacteristic
35C2×C31×#97C2212yes—
36C31×#330C2211yescharacteristic
37C31×#330C2212yes—
38C31×#330C2212yes—
39C31×#330C2212yes—
40C31×#330C2211yescharacteristic
41C31×#329C2212yes—
42C31×#329C2212yes—
43C2×Q16×C31—22no—
44C2×SD16×C31—22no—
45C2×M16×C31—21no—
46C22×C8×C31—22no—
47C31×C4⋊Q8—22no—
48C31×C4⋊Q8C2312yes—
49C31×#126—22no—
50C31×#126—22no—
51C31×#126—22no—
52C31×#126—22no—
53C31×#126—22no—
54C31×#125—22no—
55C31×#125—22no—
56C31×#125—22no—
57C31×#125—22no—
58C31×#125—22no—
59C31×#125—22no—
60C31×#125—21no—
61C31×#125D412yes—
62C31×#125C2312yes—
63C31×#125C2311yescharacteristic
64C31×#125C2311yescharacteristic
65C31×#124C2312yes—
66C31×#123—22no—
67C31×#123—22no—
68C31×#123—22no—
69C31×#123—22no—
70C31×#123—22no—
71C31×C22⋊Q8—22no—
72C31×C22⋊Q8—22no—
73C31×C22⋊Q8—22no—
74C31×C22⋊Q8—22no—
75C31×C22⋊Q8—22no—
76C31×C22⋊Q8—22no—
77C31×C22⋊Q8—22no—
78C31×C22⋊Q8D412yes—
79C31×#121—22no—
80C31×#121—22no—
81C31×#121D412yes—
82C4×Q8×C31—22no—
83C4×Q8×C31—22no—
84C4×Q8×C31D412yes—
85C4×D4×C31—22no—
86C4×D4×C31—22no—
87C4×D4×C31—22no—
88C4×D4×C31—22no—
89C4×D4×C31D412yes—
90C31×#117—22no—
91C31×#117—22no—
92C31×#117—21no—
93C2×C4⋊C4×C31—22no—
94C2×C4⋊C4×C31—22no—
95C2×C4⋊C4×C31D412yes—
96C2×C42×C31C2311yescharacteristic
97C31×#107—22no—
98C31×#107—22no—
99C31×#107—22no—
100C31×#106—22no—
101C31×#106—22no—
102C31×#106—22no—
103C31×#103—22no—
104C31×#103—22no—
105C31×#103—22no—
106C31×#102—22no—
107C31×#97—22no—
108C31×#97C2312yes—
109C31×#97C2312yes—
110C31×#97C2312yes—
111C4×C8×C31—21no—
112C2×Q8×C31—22no—
113C2×Q8×C31—22no—
114C2×Q8×C31C2×D412yes—
115C2×D4×C31—22no—
116C2×D4×C31—22no—
117C2×D4×C31C2×D412yes—
118C22×C4×C31—22no—
119C22×C4×C31—22no—
120C22×C4×C31—22no—
121C22×C4×C31—22no—
122C22×C4×C31C2×D411yescharacteristic
123C22×C4×C31C2×D412yes—
124Q16×C31—44no—
125SD16×C31—44no—
126M16×C31—24no—
127C2×C8×C31—22no—
128C2×C8×C31—22no—
129C2×C8×C31—22no—
130C2×C8×C31—44no—
131C4⋊C4×C31—22no—
132C4⋊C4×C31—22no—
133C4⋊C4×C31—22no—
134C4⋊C4×C31—22no—
135C4⋊C4×C31—22no—
136C4⋊C4×C31—22no—
137C4⋊C4×C31—22no—
138C4⋊C4×C31—22no—
139C4⋊C4×C31—22no—
140C4⋊C4×C31—22no—
141C4⋊C4×C31—22no—
142C4⋊C4×C31—22no—
143C4⋊C4×C31—22no—
144C4⋊C4×C31—22no—
145C4⋊C4×C31—22no—
146C4⋊C4×C31—22no—
147C4⋊C4×C31—22no—
148C4⋊C4×C31—42no—
149C4⋊C4×C31C2×D412yes—
150C4⋊C4×C31C2×D412yes—
151C4⋊C4×C31C2×D412yes—
152C4⋊C4×C31C2×D412yes—
153C22⋊C4×C31—22no—
154C22⋊C4×C31—22no—
155C22⋊C4×C31—22no—
156C22⋊C4×C31—22no—
157C22⋊C4×C31—22no—
158C22⋊C4×C31—22no—
159C22⋊C4×C31—22no—
160C22⋊C4×C31—22no—
161C22⋊C4×C31—22no—
162C22⋊C4×C31—41no—
163C42×C31—22no—
164C42×C31—22no—
165C42×C31—22no—
166C42×C31—41no—
167C42×C31C2×D411yescharacteristic
168C42×C31C2×D412yes—
169C42×C31C2411yescharacteristic
170#19085C3111yesmaximal, characteristic, direct product factor, Sylow
171C23×C31—22no—
172C23×C31#12011yescharacteristic
173Q8×C31—42no—
174Q8×C31—42no—
175Q8×C31—42no—
176Q8×C31—82no—
177D4×C31—42no—
178D4×C31—44no—
179D4×C31—82no—
180C2×C4×C31—22no—
181C2×C4×C31—22no—
182C2×C4×C31—22no—
183C2×C4×C31—22no—
184C2×C4×C31—22no—
185C2×C4×C31—22no—
186C2×C4×C31—42no—
187C2×C4×C31—42no—
188C2×C4×C31—82no—
189C2×C4×C31—82no—
190C2×C4×C31—82no—
191C2×C4×C31—82no—
192C2×C4×C31#12012yes—
193C2×C4×C31#12011yescharacteristic
194C2×C4×C31C22×D411yescharacteristic
195C2×C4×C31C22×D412yes—
196C8×C31—24no—
197C8×C31—24no—
198C8×C31—42no—
199#3553C2×C3111yescharacteristic
200#3181C2×C3112yescomplemented
201#3166C2×C3111yescharacteristic, complemented
202#1664C2×C3112yescomplemented
203#1663C2×C3112yescomplemented
204#1661C2×C3112yescomplemented
205#1660C2×C3112yescomplemented
206#1524C2×C3112yescomplemented
207C2×#330C2×C3111yescharacteristic, complemented
208C22×C31—22no—
209C22×C31—42no—
210C22×C31—42no—
211C22×C31—42no—
212C22×C31#45612yes—
213C22×C31C2×#12011yescharacteristic
214C4×C31—21no—
215C4×C31—21no—
216C4×C31—22no—
217C4×C31—22no—
218C4×C31—42no—
219C4×C31—42no—
220C4×C31—42no—
221C4×C31—42no—
222C4×C31—42no—
223C4×C31—82no—
224#564C22×C3111yescharacteristic
225#563C22×C3112yes—
226#562C22×C3111yescharacteristic
227#554—22no—
228#553—22no—
229#552—22no—
230#541—22no—
231#539—22no—
232#539—22no—
233#533C22×C3111yescharacteristic
234#529C22×C3112yes—
235C2×#125C22×C3111yescharacteristic
236#501C22×C3112yes—
237#501C22×C3112yes—
238#501C22×C3112yes—
239#499—22no—
240#497C22×C3112yes—
241#491C22×C3112yes—
242#489C22×C3112yes—
243#467—22no—
244#465—22no—
245#441—22no—
246#440—22no—
247#428—22no—
248C4×M16C22×C3111yescharacteristic
249C2×#97C22×C3112yes—
250#330C22×C3111yescharacteristic
251#330C22×C3112yes—
252#330C22×C3112yes—
253#330C22×C3112yes—
254#330C22×C3111yescharacteristic
255#329C22×C3112yes—
256#329C22×C3112yes—
257C2×C31—22no—
258C2×C31—82no—
259C2×C31C2×#45611yescharacteristic
260C2×C31#301812yes—
261C2×Q16—22no—
262C2×SD16—22no—
263C2×M16—21no—
264C22×C8—22no—
265C4⋊Q8—22no—
266C4⋊Q8C23×C3112yes—
267#126—22no—
268#126—22no—
269#126—22no—
270#126—22no—
271#126—22no—
272#125—22no—
273#125—22no—
274#125—22no—
275#125—22no—
276#125—22no—
277#125—22no—
278#125—21no—
279#125D4×C3112yes—
280#125C23×C3111yescharacteristic
281#125C23×C3111yescharacteristic
282#125C23×C3112yes—
283#124C23×C3112yes—
284#123—22no—
285#123—22no—
286#123—22no—
287#123—22no—
288#123—22no—
289C22⋊Q8—22no—
290C22⋊Q8—22no—
291C22⋊Q8—22no—
292C22⋊Q8—22no—
293C22⋊Q8—22no—
294C22⋊Q8—22no—
295C22⋊Q8—22no—
296C22⋊Q8D4×C3112yes—
297#121—22no—
298#121—22no—
299#121D4×C3112yes—
300C4×Q8—22no—
301C4×Q8—22no—
302C4×Q8D4×C3112yes—
303C4×D4—22no—
304C4×D4—22no—
305C4×D4—22no—
306C4×D4—22no—
307C4×D4D4×C3112yes—
308#117—22no—
309#117—22no—
310#117—21no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4D4×C3112yes—
314C2×C42C23×C3111yescharacteristic
315#107—22no—
316#107—22no—
317#107—22no—
318#106—22no—
319#106—22no—
320#106—22no—
321#103—22no—
322#103—22no—
323#103—22no—
324#102—22no—
325#97—22no—
326#97C23×C3112yes—
327#97C23×C3112yes—
328#97C23×C3112yes—
329C4×C8—21no—
330C31#1908511yescharacteristic, direct product factor, Sylow
331C2×Q8—22no—
332C2×Q8—22no—
333C2×Q8C2×D4×C3112yes—
334C2×D4—22no—
335C2×D4—22no—
336C2×D4C2×D4×C3112yes—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4C2×D4×C3111yescharacteristic
342C22×C4C2×D4×C3112yes—
343Q16—44no—
344SD16—44no—
345M16—24no—
346C2×C8—22no—
347C2×C8—22no—
348C2×C8—22no—
349C2×C8—44no—
350C4⋊C4—22no—
351C4⋊C4—22no—
352C4⋊C4—22no—
353C4⋊C4—22no—
354C4⋊C4—22no—
355C4⋊C4—22no—
356C4⋊C4—22no—
357C4⋊C4—22no—
358C4⋊C4—22no—
359C4⋊C4—22no—
360C4⋊C4—22no—
361C4⋊C4—22no—
362C4⋊C4—22no—
363C4⋊C4—22no—
364C4⋊C4—22no—
365C4⋊C4—22no—
366C4⋊C4—22no—
367C4⋊C4—42no—
368C4⋊C4C2×D4×C3112yes—
369C4⋊C4C2×D4×C3112yes—
370C4⋊C4C2×D4×C3112yes—
371C4⋊C4C2×D4×C3112yes—
372C22⋊C4—22no—
373C22⋊C4—22no—
374C22⋊C4—22no—
375C22⋊C4—22no—
376C22⋊C4—22no—
377C22⋊C4—22no—
378C22⋊C4—22no—
379C22⋊C4—22no—
380C22⋊C4—22no—
381C22⋊C4—41no—
382C42—22no—
383C42—22no—
384C42—22no—
385C42—41no—
386C42C2×D4×C3111yescharacteristic
387C42C2×D4×C3112yes—
388C42C24×C3111yescharacteristic
389C23—22no—
390C23C31×#12011yescharacteristic
391Q8—42no—
392Q8—42no—
393Q8—42no—
394Q8—82no—
395D4—42no—
396D4—44no—
397D4—82no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—82no—
407C2×C4—82no—
408C2×C4—82no—
409C2×C4—82no—
410C2×C4C31×#12012yes—
411C2×C4C31×#12011yescharacteristic
412C2×C4C22×D4×C3111yescharacteristic
413C2×C4C22×D4×C3112yes—
414C8—24no—
415C8—24no—
416C8—42no—
417C22—22no—
418C22—42no—
419C22—42no—
420C22—42no—
421C22C31×#45612yes—
422C22C2×C31×#12011yescharacteristic
423C4—21no—
424C4—21no—
425C4—22no—
426C4—22no—
427C4—42no—
428C4—42no—
429C4—42no—
430C4—42no—
431C4—42no—
432C4—82no—
433C2—22no—
434C2—82no—
435C2C2×C31×#45611yescharacteristic
436C2C31×#301812yes—
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC42C24×C31
prime radicalC31×#3553C2
LCSG ▷ 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×#3181C2semidirect
3. C31×#3166C2semidirect
4. C31×#1664C2semidirect
5. C31×#1663C2semidirect
6. C31×#1661C2semidirect
7. C31×#1660C2semidirect
8. C31×#1524C2semidirect
9. C2×C31×#330C2semidirect
170. #19085C31direct (N × H)
200. #3181C2×C31semidirect
201. #3166C2×C31semidirect
202. #1664C2×C31semidirect
203. #1663C2×C31semidirect
204. #1661C2×C31semidirect
205. #1660C2×C31semidirect
206. #1524C2×C31semidirect
207. C2×#330C2×C31semidirect
330. C31#19085direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35532
C31×#31812
C31×#31662
C31×#16642
C31×#16632
C31×#16612
C31×#16602
C31×#15242
C2×C31×#3302
#1908531