Finite Group Databasebeta

← C31×#19517 #21476276

Subgroups — C31×#19517 #21476276

Order 7936.

580 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3254C211yesmaximal, characteristic
2C31×#3246C211yesmaximal, characteristic
3C31×#3231C211yesmaximal, characteristic, complemented
4C31×#2981C211yesmaximal, characteristic
5C31×#1703C212yesmaximal, complemented
6C31×#1693C212yesmaximal, complemented
7C31×#1679C212yesmaximal, complemented
8C31×#1671C212yesmaximal, complemented
9C31×#1570C211yesmaximal, characteristic, complemented
10C31×#1559C211yesmaximal, characteristic, complemented
11C31×#1552C211yesmaximal, characteristic, complemented
12C31×#533C2211yescharacteristic
13C31×#533C2211yescharacteristic
14C31×#532C2211yescharacteristic
15C31×#500C2211yescharacteristic
16C31×#498C2211yescharacteristic
17C31×#487C2211yescharacteristic
18C31×#487C2211yescharacteristic
19C31×#485—22no—
20C31×#479—22no—
21C31×#477—21no—
22C31×#476C2212yes—
23C31×#475—21no—
24C31×#474C2212yes—
25C31×#468—22no—
26C31×#465—22no—
27C31×#461C2212yes—
28C31×#461C2212yes—
29C31×#460—21no—
30C31×#460—21no—
31C31×#436C2212yes—
32C31×#435—22no—
33C8×D4×C31C2212yes—
34C31×#432C2211yescharacteristic
35C31×#431C2211yescharacteristic
36C31×#423C2211yescharacteristic
37C2×C31×C4⋊C8C2211yescharacteristic
38C31×#408—22no—
39C31×#334C2212yes—
40C31×#334C2212yes—
41C31×#333C2212yes—
42C31×#332C2212yes—
43C31×#332C2212yes—
44C31×#332C2212yes—
45C2×#41×C31—21no—
46C2×SD16×C31—22no—
47C2×SD16×C31—22no—
48C2×M16×C31—21no—
49C2×M16×C31—22no—
50C22×C8×C31—21no—
51C22×C8×C31—22no—
52C31×C4⋊Q8D411yescharacteristic
53C31×C4⋊Q8C2311yescharacteristic
54C31×C4⋊Q8C2311yescharacteristic
55C31×C4⋊Q8C2311yescharacteristic
56C31×C4⋊Q8C2311yescharacteristic
57C31×#127D411yescharacteristic
58C31×#125—21no—
59C31×#125—21no—
60C31×#124—21no—
61C31×C22⋊Q8—21no—
62C31×C22⋊Q8—21no—
63C31×C22⋊Q8—21no—
64C31×C22⋊Q8—21no—
65C31×#121—21no—
66C31×#121D412yes—
67C4×Q8×C31—21no—
68C4×Q8×C31—21no—
69C4×Q8×C31—21no—
70C4×Q8×C31—21no—
71C4×D4×C31—21no—
72C4×D4×C31C2312yes—
73C31×#117—21no—
74C31×#117—21no—
75C2×C42×C31C2311yescharacteristic
76C31×#107—22no—
77C31×#107—22no—
78C31×#106—22no—
79C31×#106—22no—
80C31×C4⋊C8—21no—
81C31×C4⋊C8—21no—
82C31×C4⋊C8D412yes—
83C31×C4⋊C8C2312yes—
84C31×C4⋊C8C2312yes—
85C31×C4⋊C8C2312yes—
86C31×#103—22no—
87C31×#103—22no—
88C31×#103—22no—
89C31×#103—22no—
90C31×#102—22no—
91C31×#102—22no—
92C31×C22⋊C8—21no—
93C31×C22⋊C8—22no—
94C31×C22⋊C8—22no—
95C31×C22⋊C8D412yes—
96C31×#97—21no—
97C4×C8×C31C2311yescharacteristic
98C4×C8×C31C2311yescharacteristic
99#41×C31—82no—
100C2×Q8×C31—21no—
101C2×Q8×C31—21no—
102C2×Q8×C31—21no—
103C2×Q8×C31—21no—
104C2×Q8×C31—21no—
105C2×D4×C31—22no—
106C2×D4×C31—21no—
107C2×D4×C31—21no—
108C2×D4×C31C2×D412yes—
109C22×C4×C31—22no—
110C22×C4×C31C2×D411yescharacteristic
111C22×C4×C31C2×D411yescharacteristic
112C22×C4×C31#4111yescharacteristic
113SD16×C31—82no—
114SD16×C31—82no—
115M16×C31—82no—
116M16×C31—81no—
117C2×C8×C31—22no—
118C2×C8×C31—22no—
119C2×C8×C31—22no—
120C2×C8×C31—82no—
121C2×C8×C31—81no—
122C2×C8×C31C2×D412yes—
123C2×C8×C31C2×D412yes—
124C4⋊C4×C31—21no—
125C4⋊C4×C31—21no—
126C4⋊C4×C31—21no—
127C4⋊C4×C31—21no—
128C4⋊C4×C31—21no—
129C4⋊C4×C31—21no—
130C4⋊C4×C31—21no—
131C4⋊C4×C31—21no—
132C4⋊C4×C31—21no—
133C4⋊C4×C31—41no—
134C4⋊C4×C31—41no—
135C4⋊C4×C31—41no—
136C4⋊C4×C31—41no—
137C4⋊C4×C31C2×D412yes—
138C22⋊C4×C31—22no—
139C22⋊C4×C31—22no—
140C22⋊C4×C31—41no—
141C22⋊C4×C31—41no—
142C42×C31—41no—
143C42×C31—41no—
144C42×C31C2×D411yescharacteristic
145C42×C31C2×D411yescharacteristic
146C42×C31#4111yescharacteristic
147C42×C31C2411yescharacteristic
148#19517C3111yesmaximal, characteristic, direct product factor, Sylow
149C23×C31—22no—
150C23×C31#12111yescharacteristic
151Q8×C31—41no—
152Q8×C31—41no—
153Q8×C31—42no—
154Q8×C31—41no—
155Q8×C31—41no—
156Q8×C31—81no—
157Q8×C31—81no—
158D4×C31—22no—
159D4×C31—22no—
160D4×C31—81no—
161D4×C31—81no—
162D4×C31—82no—
163C2×C4×C31—21no—
164C2×C4×C31—21no—
165C2×C4×C31—22no—
166C2×C4×C31—22no—
167C2×C4×C31—41no—
168C2×C4×C31—42no—
169C2×C4×C31—42no—
170C2×C4×C31—41no—
171C2×C4×C31—41no—
172C2×C4×C31—41no—
173C2×C4×C31—41no—
174C2×C4×C31#12111yescharacteristic
175C2×C4×C31#12111yescharacteristic
176C2×C4×C31#12111yescharacteristic
177C2×C4×C31C22×D411yescharacteristic
178C2×C4×C31C22×D411yescharacteristic
179C2×C4×C31C2×#4111yescharacteristic
180C8×C31—22no—
181C8×C31—22no—
182C8×C31—42no—
183C8×C31—42no—
184C8×C31—42no—
185#3254C2×C3111yescharacteristic
186#3246C2×C3111yescharacteristic
187#3231C2×C3111yescharacteristic, complemented
188#2981C2×C3111yescharacteristic
189#1703C2×C3112yescomplemented
190#1693C2×C3112yescomplemented
191#1679C2×C3112yescomplemented
192#1671C2×C3112yescomplemented
193#1570C2×C3111yescharacteristic, complemented
194#1559C2×C3111yescharacteristic, complemented
195#1552C2×C3111yescharacteristic, complemented
196C22×C31—21no—
197C22×C31—21no—
198C22×C31—21no—
199C22×C31—42no—
200C22×C31—42no—
201C22×C31—42no—
202C22×C31C2×#12111yescharacteristic
203C4×C31—21no—
204C4×C31—21no—
205C4×C31—21no—
206C4×C31—21no—
207C4×C31—42no—
208C4×C31—81no—
209C4×C31—81no—
210C4×C31—81no—
211C4×C31—81no—
212C4×C31#57712yes—
213C4×C31#57711yescharacteristic
214C4×C31#57711yescharacteristic
215#533C22×C3111yescharacteristic
216#533C22×C3111yescharacteristic
217#532C22×C3111yescharacteristic
218#500C22×C3111yescharacteristic
219#498C22×C3111yescharacteristic
220#487C22×C3111yescharacteristic
221#487C22×C3111yescharacteristic
222#485—22no—
223#479—22no—
224#477—21no—
225#476C22×C3112yes—
226#475—21no—
227#474C22×C3112yes—
228#468—22no—
229#465—22no—
230#461C22×C3112yes—
231#461C22×C3112yes—
232#460—21no—
233#460—21no—
234#436C22×C3112yes—
235#435—22no—
236C8×D4C22×C3112yes—
237#432C22×C3111yescharacteristic
238#431C22×C3111yescharacteristic
239#423C22×C3111yescharacteristic
240C2×C4⋊C8C22×C3111yescharacteristic
241#408—22no—
242#334C22×C3112yes—
243#334C22×C3112yes—
244#333C22×C3112yes—
245#332C22×C3112yes—
246#332C22×C3112yes—
247#332C22×C3112yes—
248C2×C31—41no—
249C2×C31—82no—
250C2×C31#304211yescharacteristic
251C2×C31#306011yescharacteristic
252C2×C31#306911yescharacteristic
253C2×#41—21no—
254C2×SD16—22no—
255C2×SD16—22no—
256C2×M16—21no—
257C2×M16—22no—
258C22×C8—21no—
259C22×C8—22no—
260C4⋊Q8D4×C3111yescharacteristic
261C4⋊Q8C23×C3111yescharacteristic
262C4⋊Q8C23×C3111yescharacteristic
263C4⋊Q8C23×C3111yescharacteristic
264C4⋊Q8C23×C3111yescharacteristic
265#127D4×C3111yescharacteristic
266#125—21no—
267#125—21no—
268#124—21no—
269C22⋊Q8—21no—
270C22⋊Q8—21no—
271C22⋊Q8—21no—
272C22⋊Q8—21no—
273#121—21no—
274#121D4×C3112yes—
275C4×Q8—21no—
276C4×Q8—21no—
277C4×Q8—21no—
278C4×Q8—21no—
279C4×D4—21no—
280C4×D4C23×C3112yes—
281#117—21no—
282#117—21no—
283C2×C42C23×C3111yescharacteristic
284#107—22no—
285#107—22no—
286#106—22no—
287#106—22no—
288C4⋊C8—21no—
289C4⋊C8—21no—
290C4⋊C8D4×C3112yes—
291C4⋊C8C23×C3112yes—
292C4⋊C8C23×C3112yes—
293C4⋊C8C23×C3112yes—
294#103—22no—
295#103—22no—
296#103—22no—
297#103—22no—
298#102—22no—
299#102—22no—
300C22⋊C8—21no—
301C22⋊C8—22no—
302C22⋊C8—22no—
303C22⋊C8D4×C3112yes—
304#97—21no—
305C4×C8C23×C3111yescharacteristic
306C4×C8C23×C3111yescharacteristic
307C31#1951711yescharacteristic, direct product factor, Sylow
308#41—82no—
309C2×Q8—21no—
310C2×Q8—21no—
311C2×Q8—21no—
312C2×Q8—21no—
313C2×Q8—21no—
314C2×D4—22no—
315C2×D4—21no—
316C2×D4—21no—
317C2×D4C2×D4×C3112yes—
318C22×C4—22no—
319C22×C4C2×D4×C3111yescharacteristic
320C22×C4C2×D4×C3111yescharacteristic
321C22×C4#41×C3111yescharacteristic
322SD16—82no—
323SD16—82no—
324M16—82no—
325M16—81no—
326C2×C8—22no—
327C2×C8—22no—
328C2×C8—22no—
329C2×C8—82no—
330C2×C8—81no—
331C2×C8C2×D4×C3112yes—
332C2×C8C2×D4×C3112yes—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4—21no—
338C4⋊C4—21no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—41no—
343C4⋊C4—41no—
344C4⋊C4—41no—
345C4⋊C4—41no—
346C4⋊C4C2×D4×C3112yes—
347C22⋊C4—22no—
348C22⋊C4—22no—
349C22⋊C4—41no—
350C22⋊C4—41no—
351C42—41no—
352C42—41no—
353C42C2×D4×C3111yescharacteristic
354C42C2×D4×C3111yescharacteristic
355C42#41×C3111yescharacteristic
356C42C24×C3111yescharacteristic
357C23—22no—
358C23C31×#12111yescharacteristic
359Q8—41no—
360Q8—41no—
361Q8—42no—
362Q8—41no—
363Q8—41no—
364Q8—81no—
365Q8—81no—
366D4—22no—
367D4—22no—
368D4—81no—
369D4—81no—
370D4—82no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—22no—
374C2×C4—22no—
375C2×C4—41no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4C31×#12111yescharacteristic
383C2×C4C31×#12111yescharacteristic
384C2×C4C31×#12111yescharacteristic
385C2×C4C22×D4×C3111yescharacteristic
386C2×C4C22×D4×C3111yescharacteristic
387C2×C4C2×#41×C3111yescharacteristic
388C8—22no—
389C8—22no—
390C8—42no—
391C8—42no—
392C8—42no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—42no—
397C22—42no—
398C22—42no—
399C22C2×C31×#12111yescharacteristic
400C4—21no—
401C4—21no—
402C4—21no—
403C4—21no—
404C4—42no—
405C4—81no—
406C4—81no—
407C4—81no—
408C4—81no—
409C4C31×#57712yes—
410C4C31×#57711yescharacteristic
411C4C31×#57711yescharacteristic
412C2—41no—
413C2—82no—
414C2C31×#304211yescharacteristic
415C2C31×#306011yescharacteristic
416C2C31×#306911yescharacteristic
subgroupG/H
center, socleC22×C31C2×#121
commutator, Frattini, cosocleC42C24×C31
prime radicalC31×#532C22
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
3. C31×#3231C2semidirect
5. C31×#1703C2semidirect
6. C31×#1693C2semidirect
7. C31×#1679C2semidirect
8. C31×#1671C2semidirect
9. C31×#1570C2semidirect
10. C31×#1559C2semidirect
11. C31×#1552C2semidirect
148. #19517C31direct (N × H)
187. #3231C2×C31semidirect
189. #1703C2×C31semidirect
190. #1693C2×C31semidirect
191. #1679C2×C31semidirect
192. #1671C2×C31semidirect
193. #1570C2×C31semidirect
194. #1559C2×C31semidirect
195. #1552C2×C31semidirect
307. C31#19517direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#32542
C31×#32462
C31×#32312
C31×#29812
C31×#17032
C31×#16932
C31×#16792
C31×#16712
C31×#15702
C31×#15592
C31×#15522
#1951731