Finite Group Databasebeta

← C31×#19513 #21476272

Subgroups — C31×#19513 #21476272

Order 7936.

610 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
1C31×#3227C211yesmaximal, characteristic, complemented
2C31×#3227C211yesmaximal, characteristic, complemented
3C31×#3214C211yesmaximal, characteristic
4C31×#2981C211yesmaximal, characteristic, complemented
5C31×#1697C212yesmaximal, complemented
6C31×#1691C212yesmaximal, complemented
7C31×#1677C212yesmaximal, complemented
8C31×#1671C212yesmaximal, complemented
9C31×#1572C211yesmaximal, characteristic, complemented
10C31×#1558C211yesmaximal, characteristic, complemented
11C31×#1553C211yesmaximal, characteristic, complemented
12C31×#532C2211yescharacteristic
13C31×#532C2211yescharacteristic
14C2×C31×C4⋊Q8C2211yescharacteristic
15C31×#498—21no—
16C31×#498C2211yescharacteristic
17C31×#498C2211yescharacteristic
18C31×#496—21no—
19C31×#489—21no—
20C31×#486—21no—
21C31×#486C2211yescharacteristic
22C31×#486C2211yescharacteristic
23C31×#481—22no—
24C31×#481—22no—
25C31×#476—22no—
26C31×#476C2212yes—
27C31×#476C2212yes—
28C31×#461C2212yes—
29C31×#459C2212yes—
30C31×#449—22no—
31C31×#436C2212yes—
32C31×#435—22no—
33C8×D4×C31C2212yes—
34C31×#432C2211yescharacteristic
35C31×#432C2211yescharacteristic
36C31×#431C2211yescharacteristic
37C31×#431C2211yescharacteristic
38C31×#408—22no—
39C31×#335C2212yes—
40C31×#334C2212yes—
41C31×#333C2212yes—
42C31×#333C2212yes—
43C31×#332C2212yes—
44C31×#331C2212yes—
45C2×#41×C31—21no—
46C2×#41×C31—21no—
47C22×Q8×C31—21no—
48C2×SD16×C31—22no—
49C2×D8×C31—22no—
50C2×M16×C31—22no—
51C22×C8×C31—22no—
52C31×C4⋊Q8—21no—
53C31×C4⋊Q8—21no—
54C31×C4⋊Q8—21no—
55C31×C4⋊Q8D411yescharacteristic
56C31×C4⋊Q8C2311yescharacteristic
57C31×C4⋊Q8C2311yescharacteristic
58C31×C4⋊Q8C2311yescharacteristic
59C31×#127D411yescharacteristic
60C31×#127C2311yescharacteristic
61C31×#124—21no—
62C31×#124—21no—
63C31×#121—21no—
64C31×#121—21no—
65C31×#121—21no—
66C31×#121D412yes—
67C4×D4×C31—21no—
68C4×D4×C31—21no—
69C4×D4×C31—21no—
70C4×D4×C31C2312yes—
71C2×C4⋊C4×C31—21no—
72C2×C4⋊C4×C31—21no—
73C2×C42×C31C2311yescharacteristic
74C31×#106—22no—
75C31×#106—22no—
76C31×#106—22no—
77C31×#106—22no—
78C31×C4⋊C8D412yes—
79C31×C4⋊C8C2312yes—
80C31×C4⋊C8C2312yes—
81C31×C4⋊C8C2312yes—
82C31×#103—22no—
83C31×#102—22no—
84C31×#102—22no—
85C31×#102—22no—
86C31×#102—22no—
87C31×#102—22no—
88C31×C22⋊C8—21no—
89C31×C22⋊C8—21no—
90C31×C22⋊C8—21no—
91C31×C22⋊C8—22no—
92C31×C22⋊C8—22no—
93C31×C22⋊C8D412yes—
94C31×#97—21no—
95C31×#97—21no—
96C4×C8×C31—21no—
97C4×C8×C31C2311yescharacteristic
98C4×C8×C31C2311yescharacteristic
99#41×C31—82no—
100#41×C31—82no—
101C2×Q8×C31—21no—
102C2×Q8×C31—21no—
103C2×Q8×C31—21no—
104C2×Q8×C31—21no—
105C2×Q8×C31—41no—
106C2×Q8×C31—82no—
107C2×D4×C31—22no—
108C2×D4×C31—21no—
109C2×D4×C31—21no—
110C2×D4×C31—21no—
111C2×D4×C31—21no—
112C2×D4×C31—21no—
113C2×D4×C31—41no—
114C2×D4×C31C2×D412yes—
115C22×C4×C31—22no—
116C22×C4×C31—41no—
117C22×C4×C31—41no—
118C22×C4×C31C2×D411yescharacteristic
119C22×C4×C31C2×D411yescharacteristic
120C22×C4×C31#4111yescharacteristic
121SD16×C31—82no—
122D8×C31—82no—
123M16×C31—82no—
124C2×C8×C31—22no—
125C2×C8×C31—22no—
126C2×C8×C31—22no—
127C2×C8×C31—82no—
128C2×C8×C31C2×D412yes—
129C2×C8×C31C2×D412yes—
130C4⋊C4×C31—21no—
131C4⋊C4×C31—21no—
132C4⋊C4×C31—21no—
133C4⋊C4×C31—21no—
134C4⋊C4×C31—21no—
135C4⋊C4×C31—21no—
136C4⋊C4×C31—21no—
137C4⋊C4×C31—41no—
138C4⋊C4×C31—41no—
139C4⋊C4×C31C2×D412yes—
140C22⋊C4×C31—22no—
141C22⋊C4×C31—22no—
142C22⋊C4×C31—41no—
143C22⋊C4×C31—41no—
144C42×C31C2×D411yescharacteristic
145C42×C31C2×D411yescharacteristic
146C42×C31#4111yescharacteristic
147C42×C31C2411yescharacteristic
148#19513C3111yesmaximal, characteristic, direct product factor, Sylow
149C23×C31—22no—
150C23×C31—41no—
151C23×C31#12111yescharacteristic
152Q8×C31—42no—
153Q8×C31—81no—
154Q8×C31—81no—
155Q8×C31—81no—
156Q8×C31—82no—
157D4×C31—22no—
158D4×C31—22no—
159D4×C31—42no—
160D4×C31—42no—
161D4×C31—81no—
162D4×C31—81no—
163D4×C31—81no—
164D4×C31—82no—
165D4×C31—82no—
166C2×C4×C31—22no—
167C2×C4×C31—22no—
168C2×C4×C31—22no—
169C2×C4×C31—41no—
170C2×C4×C31—42no—
171C2×C4×C31—42no—
172C2×C4×C31—41no—
173C2×C4×C31—41no—
174C2×C4×C31—41no—
175C2×C4×C31—82no—
176C2×C4×C31—82no—
177C2×C4×C31#12111yescharacteristic
178C2×C4×C31#12111yescharacteristic
179C2×C4×C31#12111yescharacteristic
180C2×C4×C31C22×D411yescharacteristic
181C2×C4×C31C22×D411yescharacteristic
182C2×C4×C31C2×#4111yescharacteristic
183C8×C31—22no—
184C8×C31—22no—
185C8×C31—42no—
186C8×C31—42no—
187C8×C31—42no—
188#3227C2×C3111yescharacteristic, complemented
189#3227C2×C3111yescharacteristic, complemented
190#3214C2×C3111yescharacteristic
191#2981C2×C3111yescharacteristic, complemented
192#1697C2×C3112yescomplemented
193#1691C2×C3112yescomplemented
194#1677C2×C3112yescomplemented
195#1671C2×C3112yescomplemented
196#1572C2×C3111yescharacteristic, complemented
197#1558C2×C3111yescharacteristic, complemented
198#1553C2×C3111yescharacteristic, complemented
199C22×C31—21no—
200C22×C31—21no—
201C22×C31—21no—
202C22×C31—42no—
203C22×C31—42no—
204C22×C31—42no—
205C22×C31—81no—
206C22×C31—81no—
207C22×C31—81no—
208C22×C31C2×#12111yescharacteristic
209C4×C31—21no—
210C4×C31—21no—
211C4×C31—21no—
212C4×C31—21no—
213C4×C31—42no—
214C4×C31—81no—
215C4×C31—81no—
216C4×C31—81no—
217C4×C31#57712yes—
218C4×C31#57712yes—
219#532C22×C3111yescharacteristic
220#532C22×C3111yescharacteristic
221C2×C4⋊Q8C22×C3111yescharacteristic
222#498—21no—
223#498C22×C3111yescharacteristic
224#498C22×C3111yescharacteristic
225#496—21no—
226#489—21no—
227#486—21no—
228#486C22×C3111yescharacteristic
229#486C22×C3111yescharacteristic
230#481—22no—
231#481—22no—
232#476—22no—
233#476C22×C3112yes—
234#476C22×C3112yes—
235#461C22×C3112yes—
236#459C22×C3112yes—
237#449—22no—
238#436C22×C3112yes—
239#435—22no—
240C8×D4C22×C3112yes—
241#432C22×C3111yescharacteristic
242#432C22×C3111yescharacteristic
243#431C22×C3111yescharacteristic
244#431C22×C3111yescharacteristic
245#408—22no—
246#335C22×C3112yes—
247#334C22×C3112yes—
248#333C22×C3112yes—
249#333C22×C3112yes—
250#332C22×C3112yes—
251#331C22×C3112yes—
252C2×C31—41no—
253C2×C31—82no—
254C2×C31—161no—
255C2×C31#304211yescharacteristic
256C2×C31#305711yescharacteristic
257C2×C31#306811yescharacteristic
258C2×#41—21no—
259C2×#41—21no—
260C22×Q8—21no—
261C2×SD16—22no—
262C2×D8—22no—
263C2×M16—22no—
264C22×C8—22no—
265C4⋊Q8—21no—
266C4⋊Q8—21no—
267C4⋊Q8—21no—
268C4⋊Q8D4×C3111yescharacteristic
269C4⋊Q8C23×C3111yescharacteristic
270C4⋊Q8C23×C3111yescharacteristic
271C4⋊Q8C23×C3111yescharacteristic
272#127D4×C3111yescharacteristic
273#127C23×C3111yescharacteristic
274#124—21no—
275#124—21no—
276#121—21no—
277#121—21no—
278#121—21no—
279#121D4×C3112yes—
280C4×D4—21no—
281C4×D4—21no—
282C4×D4—21no—
283C4×D4C23×C3112yes—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C42C23×C3111yescharacteristic
287#106—22no—
288#106—22no—
289#106—22no—
290#106—22no—
291C4⋊C8D4×C3112yes—
292C4⋊C8C23×C3112yes—
293C4⋊C8C23×C3112yes—
294C4⋊C8C23×C3112yes—
295#103—22no—
296#102—22no—
297#102—22no—
298#102—22no—
299#102—22no—
300#102—22no—
301C22⋊C8—21no—
302C22⋊C8—21no—
303C22⋊C8—21no—
304C22⋊C8—22no—
305C22⋊C8—22no—
306C22⋊C8D4×C3112yes—
307#97—21no—
308#97—21no—
309C4×C8—21no—
310C4×C8C23×C3111yescharacteristic
311C4×C8C23×C3111yescharacteristic
312C31#1951311yescharacteristic, direct product factor, Sylow
313#41—82no—
314#41—82no—
315C2×Q8—21no—
316C2×Q8—21no—
317C2×Q8—21no—
318C2×Q8—21no—
319C2×Q8—41no—
320C2×Q8—82no—
321C2×D4—22no—
322C2×D4—21no—
323C2×D4—21no—
324C2×D4—21no—
325C2×D4—21no—
326C2×D4—21no—
327C2×D4—41no—
328C2×D4C2×D4×C3112yes—
329C22×C4—22no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4C2×D4×C3111yescharacteristic
333C22×C4C2×D4×C3111yescharacteristic
334C22×C4#41×C3111yescharacteristic
335SD16—82no—
336D8—82no—
337M16—82no—
338C2×C8—22no—
339C2×C8—22no—
340C2×C8—22no—
341C2×C8—82no—
342C2×C8C2×D4×C3112yes—
343C2×C8C2×D4×C3112yes—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4—21no—
348C4⋊C4—21no—
349C4⋊C4—21no—
350C4⋊C4—21no—
351C4⋊C4—41no—
352C4⋊C4—41no—
353C4⋊C4C2×D4×C3112yes—
354C22⋊C4—22no—
355C22⋊C4—22no—
356C22⋊C4—41no—
357C22⋊C4—41no—
358C42C2×D4×C3111yescharacteristic
359C42C2×D4×C3111yescharacteristic
360C42#41×C3111yescharacteristic
361C42C24×C3111yescharacteristic
362C23—22no—
363C23—41no—
364C23C31×#12111yescharacteristic
365Q8—42no—
366Q8—81no—
367Q8—81no—
368Q8—81no—
369Q8—82no—
370D4—22no—
371D4—22no—
372D4—42no—
373D4—42no—
374D4—81no—
375D4—81no—
376D4—81no—
377D4—82no—
378D4—82no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—41no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—82no—
389C2×C4—82no—
390C2×C4C31×#12111yescharacteristic
391C2×C4C31×#12111yescharacteristic
392C2×C4C31×#12111yescharacteristic
393C2×C4C22×D4×C3111yescharacteristic
394C2×C4C22×D4×C3111yescharacteristic
395C2×C4C2×#41×C3111yescharacteristic
396C8—22no—
397C8—22no—
398C8—42no—
399C8—42no—
400C8—42no—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—42no—
405C22—42no—
406C22—42no—
407C22—81no—
408C22—81no—
409C22—81no—
410C22C2×C31×#12111yescharacteristic
411C4—21no—
412C4—21no—
413C4—21no—
414C4—21no—
415C4—42no—
416C4—81no—
417C4—81no—
418C4—81no—
419C4C31×#57712yes—
420C4C31×#57712yes—
421C2—41no—
422C2—82no—
423C2—161no—
424C2C31×#304211yescharacteristic
425C2C31×#305711yescharacteristic
426C2C31×#306811yescharacteristic
subgroupG/H
center, socleC22×C31C2×#121
commutator, Frattini, cosocleC42C24×C31
prime radicalC31×#3214C2
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
1. C31×#3227C2semidirect
2. C31×#3227C2semidirect
4. C31×#2981C2semidirect
5. C31×#1697C2semidirect
6. C31×#1691C2semidirect
7. C31×#1677C2semidirect
8. C31×#1671C2semidirect
9. C31×#1572C2semidirect
10. C31×#1558C2semidirect
11. C31×#1553C2semidirect
148. #19513C31direct (N × H)
188. #3227C2×C31semidirect
189. #3227C2×C31semidirect
191. #2981C2×C31semidirect
192. #1697C2×C31semidirect
193. #1691C2×C31semidirect
194. #1677C2×C31semidirect
195. #1671C2×C31semidirect
196. #1572C2×C31semidirect
197. #1558C2×C31semidirect
198. #1553C2×C31semidirect
312. C31#19513direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#32272
C31×#32142
C31×#29812
C31×#16972
C31×#16912
C31×#16772
C31×#16712
C31×#15722
C31×#15582
C31×#15532
#1951331