Finite Group Databasebeta

← C31×#19212 #21475971

Subgroups — C31×#19212 #21475971

Order 7936.

646 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3230C211yesmaximal, characteristic, complemented
2C31×#3208C211yesmaximal, characteristic
3C2×C31×#486C211yesmaximal, characteristic
4C31×#2960C211yesmaximal, characteristic, complemented
5C31×#1698C214yesmaximal, complemented
6C31×#1678C214yesmaximal, complemented
7C31×#1564C211yesmaximal, characteristic, complemented
8C31×#1548C211yesmaximal, characteristic, complemented
9C31×#1545C211yesmaximal, characteristic
10C31×#533C2211yescharacteristic
11C2×C31×C4⋊Q8C2211yescharacteristic
12C2×C31×#127C2211yescharacteristic
13C31×#500—21no—
14C31×#492—21no—
15C31×#487—21no—
16C31×#486—21no—
17C31×#486—21no—
18C31×#486—21no—
19C31×#486C2212yes—
20C31×#486C2212yes—
21C31×#484—22no—
22C31×#477C2214yescomplemented
23C31×#460C2214yes—
24C31×#450—22no—
25C31×#446—21no—
26C31×#446C2212yescomplemented
27C8×Q8×C31—21no—
28C8×Q8×C31C2212yescomplemented
29C31×#431C2211yescharacteristic
30C31×#431C2211yescharacteristic
31C31×#424—21no—
32C31×#423C2211yescharacteristic
33C2×C31×#102—21no—
34C2×C31×#102—21no—
35C31×#405—21no—
36C2×C4×C8×C31C2211yescharacteristic
37C31×#335C2212yescomplemented
38C31×#334C2212yescomplemented
39C31×#333C2214yescomplemented
40C31×#331C2214yes—
41C22×Q8×C31—21no—
42C22×D4×C31—21no—
43C22×D4×C31—21no—
44C22×D4×C31—21no—
45C2×SD16×C31—24no—
46C2×M16×C31—21no—
47C22×C8×C31D411yescharacteristic
48C22×C8×C31D411yescharacteristic
49C31×C4⋊Q8—21no—
50C31×C4⋊Q8—21no—
51C31×C4⋊Q8—21no—
52C31×C4⋊Q8D411yescharacteristic
53C31×C4⋊Q8D411yescharacteristic
54C31×C4⋊Q8C2312yes—
55C31×#127—21no—
56C31×#127—21no—
57C31×#127—21no—
58C31×#127C2312yes—
59C31×#125—21no—
60C31×C22⋊Q8—21no—
61C31×C22⋊Q8D412yes—
62C4×Q8×C31—21no—
63C4×Q8×C31C2312yes—
64C31×#117—21no—
65C2×C4⋊C4×C31—21no—
66C2×C4⋊C4×C31—21no—
67C2×C42×C31C2311yescharacteristic
68C31×#107—24no—
69C31×C4⋊C8—22no—
70C31×C4⋊C8—22no—
71C31×C4⋊C8—21no—
72C31×C4⋊C8C2312yes—
73C31×C4⋊C8C2312yes—
74C31×C4⋊C8C2312yes—
75C31×#103—24no—
76C31×#102—22no—
77C31×#102—22no—
78C31×#102—22no—
79C31×#102—22no—
80C31×#102—24no—
81C31×C22⋊C8—21no—
82C31×C22⋊C8—21no—
83C31×#97—22no—
84C4×C8×C31—22no—
85C4×C8×C31—21no—
86C4×C8×C31—21no—
87C4×C8×C31D411yescharacteristic
88C4×C8×C31D411yescharacteristic
89C4×C8×C31C2311yescharacteristic
90C4×C8×C31C2311yescharacteristic
91C24×C31—41no—
92C2×Q8×C31—21no—
93C2×Q8×C31—22no—
94C2×Q8×C31—41no—
95C2×Q8×C31—82no—
96C2×Q8×C31C2×D412yes—
97C2×D4×C31—22no—
98C2×D4×C31—22no—
99C2×D4×C31—22no—
100C2×D4×C31—41no—
101C2×D4×C31—41no—
102C2×D4×C31—41no—
103C2×D4×C31—42no—
104C2×D4×C31—42no—
105C2×D4×C31—82no—
106C2×D4×C31—82no—
107C22×C4×C31—41no—
108C22×C4×C31C2×D411yescharacteristic
109C22×C4×C31C2×D411yescharacteristic
110C22×C4×C31#4111yescharacteristic
111SD16×C31—84no—
112M16×C31—42no—
113C2×C8×C31—22no—
114C2×C8×C31—22no—
115C2×C8×C31—22no—
116C2×C8×C31—22no—
117C2×C8×C31—22no—
118C2×C8×C31C2×D411yescharacteristic
119C2×C8×C31C2×D411yescharacteristic
120C2×C8×C31C2×D411yescharacteristic
121C2×C8×C31C2×D411yescharacteristic
122C4⋊C4×C31—21no—
123C4⋊C4×C31—21no—
124C4⋊C4×C31—21no—
125C4⋊C4×C31—22no—
126C4⋊C4×C31—22no—
127C4⋊C4×C31—22no—
128C4⋊C4×C31—22no—
129C4⋊C4×C31—41no—
130C4⋊C4×C31—41no—
131C4⋊C4×C31C2×D412yes—
132C22⋊C4×C31—22no—
133C42×C31—22no—
134C42×C31C2×D411yescharacteristic
135C42×C31C2×D411yescharacteristic
136C42×C31#4111yescharacteristic
137C42×C31C2411yescharacteristic
138#19212C3111yesmaximal, characteristic, direct product factor, Sylow
139C23×C31—42no—
140C23×C31—82no—
141C23×C31—82no—
142C23×C31—82no—
143C23×C31#12111yescharacteristic
144Q8×C31—24no—
145Q8×C31—42no—
146Q8×C31—82no—
147Q8×C31—82no—
148D4×C31—42no—
149D4×C31—42no—
150D4×C31—44no—
151D4×C31—82no—
152D4×C31—82no—
153D4×C31—82no—
154D4×C31—82no—
155C2×C4×C31—22no—
156C2×C4×C31—22no—
157C2×C4×C31—22no—
158C2×C4×C31—22no—
159C2×C4×C31—42no—
160C2×C4×C31—82no—
161C2×C4×C31#12111yescharacteristic
162C2×C4×C31#12111yescharacteristic
163C2×C4×C31#12111yescharacteristic
164C2×C4×C31#13512yes—
165C2×C4×C31#13712yes—
166C2×C4×C31C22×D411yescharacteristic
167C2×C4×C31C22×D411yescharacteristic
168C2×C4×C31C2×#4111yescharacteristic
169C8×C31—21no—
170C8×C31—21no—
171C8×C31—21no—
172C8×C31—21no—
173C8×C31—42no—
174C8×C31—42no—
175C8×C31—42no—
176#3230C2×C3111yescharacteristic, complemented
177#3208C2×C3111yescharacteristic
178C2×#486C2×C3111yescharacteristic
179#2960C2×C3111yescharacteristic, complemented
180#1698C2×C3114yescomplemented
181#1678C2×C3114yescomplemented
182#1564C2×C3111yescharacteristic, complemented
183#1548C2×C3111yescharacteristic, complemented
184#1545C2×C3111yescharacteristic
185C22×C31—21no—
186C22×C31—21no—
187C22×C31—82no—
188C22×C31—82no—
189C22×C31—82no—
190C22×C31—164no—
191C22×C31#46412yes—
192C22×C31C2×#12111yescharacteristic
193C4×C31—21no—
194C4×C31—21no—
195C4×C31—42no—
196C4×C31—42no—
197C4×C31—82no—
198C4×C31#46412yes—
199C4×C31#47212yes—
200C4×C31C2×#13511yescharacteristic
201C4×C31C2×#13711yescharacteristic
202C4×C31#57712yes—
203#533C22×C3111yescharacteristic
204C2×C4⋊Q8C22×C3111yescharacteristic
205C2×#127C22×C3111yescharacteristic
206#500—21no—
207#492—21no—
208#487—21no—
209#486—21no—
210#486—21no—
211#486—21no—
212#486C22×C3112yes—
213#486C22×C3112yes—
214#484—22no—
215#477C22×C3114yescomplemented
216#460C22×C3114yes—
217#450—22no—
218#446—21no—
219#446C22×C3112yescomplemented
220C8×Q8—21no—
221C8×Q8C22×C3112yescomplemented
222#431C22×C3111yescharacteristic
223#431C22×C3111yescharacteristic
224#424—21no—
225#423C22×C3111yescharacteristic
226C2×#102—21no—
227C2×#102—21no—
228#405—21no—
229C2×C4×C8C22×C3111yescharacteristic
230#335C22×C3112yescomplemented
231#334C22×C3112yescomplemented
232#333C22×C3114yescomplemented
233#331C22×C3114yes—
234C2×C31—22no—
235C2×C31—162no—
236C2×C31C2×#46411yescharacteristic
237C2×C31#305711yescharacteristic
238C2×C31C2×#47211yescharacteristic
239C22×Q8—21no—
240C22×D4—21no—
241C22×D4—21no—
242C22×D4—21no—
243C2×SD16—24no—
244C2×M16—21no—
245C22×C8D4×C3111yescharacteristic
246C22×C8D4×C3111yescharacteristic
247C4⋊Q8—21no—
248C4⋊Q8—21no—
249C4⋊Q8—21no—
250C4⋊Q8D4×C3111yescharacteristic
251C4⋊Q8D4×C3111yescharacteristic
252C4⋊Q8C23×C3112yes—
253#127—21no—
254#127—21no—
255#127—21no—
256#127C23×C3112yes—
257#125—21no—
258C22⋊Q8—21no—
259C22⋊Q8D4×C3112yes—
260C4×Q8—21no—
261C4×Q8C23×C3112yes—
262#117—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C42C23×C3111yescharacteristic
266#107—24no—
267C4⋊C8—22no—
268C4⋊C8—22no—
269C4⋊C8—21no—
270C4⋊C8C23×C3112yes—
271C4⋊C8C23×C3112yes—
272C4⋊C8C23×C3112yes—
273#103—24no—
274#102—22no—
275#102—22no—
276#102—22no—
277#102—22no—
278#102—24no—
279C22⋊C8—21no—
280C22⋊C8—21no—
281#97—22no—
282C4×C8—22no—
283C4×C8—21no—
284C4×C8—21no—
285C4×C8D4×C3111yescharacteristic
286C4×C8D4×C3111yescharacteristic
287C4×C8C23×C3111yescharacteristic
288C4×C8C23×C3111yescharacteristic
289C31#1921211yescharacteristic, direct product factor, Sylow
290C24—41no—
291C2×Q8—21no—
292C2×Q8—22no—
293C2×Q8—41no—
294C2×Q8—82no—
295C2×Q8C2×D4×C3112yes—
296C2×D4—22no—
297C2×D4—22no—
298C2×D4—22no—
299C2×D4—41no—
300C2×D4—41no—
301C2×D4—41no—
302C2×D4—42no—
303C2×D4—42no—
304C2×D4—82no—
305C2×D4—82no—
306C22×C4—41no—
307C22×C4C2×D4×C3111yescharacteristic
308C22×C4C2×D4×C3111yescharacteristic
309C22×C4#41×C3111yescharacteristic
310SD16—84no—
311M16—42no—
312C2×C8—22no—
313C2×C8—22no—
314C2×C8—22no—
315C2×C8—22no—
316C2×C8—22no—
317C2×C8C2×D4×C3111yescharacteristic
318C2×C8C2×D4×C3111yescharacteristic
319C2×C8C2×D4×C3111yescharacteristic
320C2×C8C2×D4×C3111yescharacteristic
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—22no—
325C4⋊C4—22no—
326C4⋊C4—22no—
327C4⋊C4—22no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4C2×D4×C3112yes—
331C22⋊C4—22no—
332C42—22no—
333C42C2×D4×C3111yescharacteristic
334C42C2×D4×C3111yescharacteristic
335C42#41×C3111yescharacteristic
336C42C24×C3111yescharacteristic
337C23—42no—
338C23—82no—
339C23—82no—
340C23—82no—
341C23C31×#12111yescharacteristic
342Q8—24no—
343Q8—42no—
344Q8—82no—
345Q8—82no—
346D4—42no—
347D4—42no—
348D4—44no—
349D4—82no—
350D4—82no—
351D4—82no—
352D4—82no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—42no—
358C2×C4—82no—
359C2×C4C31×#12111yescharacteristic
360C2×C4C31×#12111yescharacteristic
361C2×C4C31×#12111yescharacteristic
362C2×C4C31×#13512yes—
363C2×C4C31×#13712yes—
364C2×C4C22×D4×C3111yescharacteristic
365C2×C4C22×D4×C3111yescharacteristic
366C2×C4C2×#41×C3111yescharacteristic
367C8—21no—
368C8—21no—
369C8—21no—
370C8—21no—
371C8—42no—
372C8—42no—
373C8—42no—
374C22—21no—
375C22—21no—
376C22—82no—
377C22—82no—
378C22—82no—
379C22—164no—
380C22C31×#46412yes—
381C22C2×C31×#12111yescharacteristic
382C4—21no—
383C4—21no—
384C4—42no—
385C4—42no—
386C4—82no—
387C4C31×#46412yes—
388C4C31×#47212yes—
389C4C2×C31×#13511yescharacteristic
390C4C2×C31×#13711yescharacteristic
391C4C31×#57712yes—
392C2—22no—
393C2—162no—
394C2C2×C31×#46411yescharacteristic
395C2C31×#305711yescharacteristic
396C2C2×C31×#47211yescharacteristic
subgroupG/H
center, socleC22×C31C2×#121
commutator, Frattini, cosocleC42C24×C31
prime radicalC2×C31×#127C22
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×#3230C2semidirect
4. C31×#2960C2semidirect
5. C31×#1698C2semidirect
6. C31×#1678C2semidirect
7. C31×#1564C2semidirect
8. C31×#1548C2semidirect
22. C31×#477C22semidirect
26. C31×#446C22semidirect
28. C8×Q8×C31C22semidirect
37. C31×#335C22semidirect
38. C31×#334C22semidirect
39. C31×#333C22semidirect
138. #19212C31direct (N × H)
176. #3230C2×C31semidirect
179. #2960C2×C31semidirect
180. #1698C2×C31semidirect
181. #1678C2×C31semidirect
182. #1564C2×C31semidirect
183. #1548C2×C31semidirect
215. #477C22×C31semidirect
219. #446C22×C31semidirect
221. C8×Q8C22×C31semidirect
230. #335C22×C31semidirect
231. #334C22×C31semidirect
232. #333C22×C31semidirect
289. C31#19212direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#32302
C31×#32082
C2×C31×#4862
C31×#29602
C31×#16982
C31×#16782
C31×#15642
C31×#15482
C31×#15452
#1921231