Finite Group Databasebeta

← C31×#19530 #21476289

Subgroups — C31×#19530 #21476289

Order 7936.

582 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3226C211yesmaximal, characteristic
2C31×#3216C211yesmaximal, characteristic
3C31×#3209C211yesmaximal, characteristic, complemented
4C31×#2985C211yesmaximal, characteristic, complemented
5C31×#1702C212yesmaximal, complemented
6C31×#1694C212yesmaximal, complemented
7C31×#1682C212yesmaximal, complemented
8C31×#1674C212yesmaximal, complemented
9C31×#1572C211yesmaximal, characteristic, complemented
10C31×#1556C211yesmaximal, characteristic, complemented
11C31×#1553C211yesmaximal, characteristic
12C31×#533C2211yescharacteristic
13C31×#532C2211yescharacteristic
14C2×C31×C4⋊Q8C2211yescharacteristic
15C31×#500C2211yescharacteristic
16C31×#500C2211yescharacteristic
17C31×#497—21no—
18C31×#494—21no—
19C31×#489—21no—
20C31×#487—21no—
21C31×#486C2211yescharacteristic
22C31×#486C2211yescharacteristic
23C31×#480—22no—
24C31×#474—22no—
25C31×#462C2212yes—
26C31×#462C2212yes—
27C31×#462C2212yes—
28C31×#460C2212yes—
29C31×#452—22no—
30C31×#451—22no—
31C31×#446—22no—
32C31×#446C2212yes—
33C8×Q8×C31C2212yes—
34C31×#433—22no—
35C31×#432C2211yescharacteristic
36C31×#432C2211yescharacteristic
37C31×#431C2211yescharacteristic
38C31×#431C2211yescharacteristic
39C31×#335C2212yes—
40C31×#334C2212yes—
41C31×#332C2212yes—
42C31×#332C2212yes—
43C31×#332C2212yes—
44C31×#331C2212yes—
45C2×#41×C31—21no—
46C22×Q8×C31—21no—
47C2×Q16×C31—22no—
48C2×Q16×C31—22no—
49C2×Q16×C31—22no—
50C2×SD16×C31—22no—
51C31×C4⋊Q8—21no—
52C31×C4⋊Q8—21no—
53C31×C4⋊Q8—21no—
54C31×C4⋊Q8D411yescharacteristic
55C31×C4⋊Q8D411yescharacteristic
56C31×C4⋊Q8C2311yescharacteristic
57C31×C4⋊Q8C2311yescharacteristic
58C31×C4⋊Q8C2311yescharacteristic
59C31×#127C2311yescharacteristic
60C31×#125—21no—
61C31×#124—21no—
62C31×C22⋊Q8—21no—
63C31×C22⋊Q8D412yes—
64C31×#121—21no—
65C31×#121—21no—
66C4×Q8×C31—21no—
67C4×Q8×C31C2312yes—
68C4×D4×C31—21no—
69C4×D4×C31—21no—
70C31×#117—21no—
71C2×C4⋊C4×C31—21no—
72C2×C4⋊C4×C31—21no—
73C2×C42×C31C2311yescharacteristic
74C31×#107—22no—
75C31×#107—22no—
76C31×C4⋊C8—22no—
77C31×C4⋊C8—22no—
78C31×C4⋊C8D412yes—
79C31×C4⋊C8C2312yes—
80C31×C4⋊C8C2312yes—
81C31×C4⋊C8C2312yes—
82C31×#103—22no—
83C31×#103—22no—
84C31×#103—22no—
85C31×#102—22no—
86C31×#102—22no—
87C31×#102—22no—
88C31×C22⋊C8—21no—
89C31×C22⋊C8—21no—
90C31×C22⋊C8—21no—
91C31×C22⋊C8D412yes—
92C31×#97—22no—
93C31×#97—21no—
94C31×#97—21no—
95C4×C8×C31—22no—
96C4×C8×C31—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—41no—
105C2×Q8×C31—82no—
106C2×Q8×C31C2×D412yes—
107C2×D4×C31—21no—
108C2×D4×C31—21no—
109C2×D4×C31—21no—
110C2×D4×C31—41no—
111C22×C4×C31—41no—
112C22×C4×C31—41no—
113C22×C4×C31C2×D411yescharacteristic
114C22×C4×C31C2×D411yescharacteristic
115C22×C4×C31#4111yescharacteristic
116Q16×C31—82no—
117Q16×C31—82no—
118Q16×C31—82no—
119SD16×C31—82no—
120C2×C8×C31—22no—
121C2×C8×C31—22no—
122C2×C8×C31—22no—
123C2×C8×C31C2×D412yes—
124C2×C8×C31C2×D412yes—
125C4⋊C4×C31—21no—
126C4⋊C4×C31—21no—
127C4⋊C4×C31—21no—
128C4⋊C4×C31—22no—
129C4⋊C4×C31—22no—
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—41no—
137C4⋊C4×C31—41no—
138C4⋊C4×C31C2×D412yes—
139C22⋊C4×C31—22no—
140C22⋊C4×C31—41no—
141C22⋊C4×C31—41no—
142C42×C31—22no—
143C42×C31C2×D411yescharacteristic
144C42×C31C2×D411yescharacteristic
145C42×C31#4111yescharacteristic
146C42×C31C2411yescharacteristic
147#19530C3111yesmaximal, characteristic, direct product factor, Sylow
148C23×C31—41no—
149C23×C31#12111yescharacteristic
150Q8×C31—22no—
151Q8×C31—22no—
152Q8×C31—42no—
153Q8×C31—42no—
154Q8×C31—42no—
155Q8×C31—81no—
156Q8×C31—82no—
157D4×C31—42no—
158D4×C31—42no—
159D4×C31—81no—
160D4×C31—82no—
161C2×C4×C31—22no—
162C2×C4×C31—22no—
163C2×C4×C31—22no—
164C2×C4×C31—22no—
165C2×C4×C31—41no—
166C2×C4×C31—41no—
167C2×C4×C31—41no—
168C2×C4×C31—41no—
169C2×C4×C31—82no—
170C2×C4×C31—82no—
171C2×C4×C31#12111yescharacteristic
172C2×C4×C31#12111yescharacteristic
173C2×C4×C31#12111yescharacteristic
174C2×C4×C31C22×D411yescharacteristic
175C2×C4×C31C22×D411yescharacteristic
176C2×C4×C31C2×#4111yescharacteristic
177C8×C31—22no—
178C8×C31—22no—
179C8×C31—42no—
180C8×C31—42no—
181C8×C31—42no—
182#3226C2×C3111yescharacteristic
183#3216C2×C3111yescharacteristic
184#3209C2×C3111yescharacteristic, complemented
185#2985C2×C3111yescharacteristic, complemented
186#1702C2×C3112yescomplemented
187#1694C2×C3112yescomplemented
188#1682C2×C3112yescomplemented
189#1674C2×C3112yescomplemented
190#1572C2×C3111yescharacteristic, complemented
191#1556C2×C3111yescharacteristic, complemented
192#1553C2×C3111yescharacteristic
193C22×C31—21no—
194C22×C31—21no—
195C22×C31—21no—
196C22×C31—81no—
197C22×C31—81no—
198C22×C31—81no—
199C22×C31C2×#12111yescharacteristic
200C4×C31—21no—
201C4×C31—21no—
202C4×C31—21no—
203C4×C31—21no—
204C4×C31—42no—
205C4×C31—42no—
206C4×C31—81no—
207C4×C31—81no—
208C4×C31—81no—
209C4×C31#57612yes—
210C4×C31#57812yes—
211#533C22×C3111yescharacteristic
212#532C22×C3111yescharacteristic
213C2×C4⋊Q8C22×C3111yescharacteristic
214#500C22×C3111yescharacteristic
215#500C22×C3111yescharacteristic
216#497—21no—
217#494—21no—
218#489—21no—
219#487—21no—
220#486C22×C3111yescharacteristic
221#486C22×C3111yescharacteristic
222#480—22no—
223#474—22no—
224#462C22×C3112yes—
225#462C22×C3112yes—
226#462C22×C3112yes—
227#460C22×C3112yes—
228#452—22no—
229#451—22no—
230#446—22no—
231#446C22×C3112yes—
232C8×Q8C22×C3112yes—
233#433—22no—
234#432C22×C3111yescharacteristic
235#432C22×C3111yescharacteristic
236#431C22×C3111yescharacteristic
237#431C22×C3111yescharacteristic
238#335C22×C3112yes—
239#334C22×C3112yes—
240#332C22×C3112yes—
241#332C22×C3112yes—
242#332C22×C3112yes—
243#331C22×C3112yes—
244C2×C31—41no—
245C2×C31—161no—
246C2×C31#304411yescharacteristic
247C2×C31#305811yescharacteristic
248C2×C31#306911yescharacteristic
249C2×#41—21no—
250C22×Q8—21no—
251C2×Q16—22no—
252C2×Q16—22no—
253C2×Q16—22no—
254C2×SD16—22no—
255C4⋊Q8—21no—
256C4⋊Q8—21no—
257C4⋊Q8—21no—
258C4⋊Q8D4×C3111yescharacteristic
259C4⋊Q8D4×C3111yescharacteristic
260C4⋊Q8C23×C3111yescharacteristic
261C4⋊Q8C23×C3111yescharacteristic
262C4⋊Q8C23×C3111yescharacteristic
263#127C23×C3111yescharacteristic
264#125—21no—
265#124—21no—
266C22⋊Q8—21no—
267C22⋊Q8D4×C3112yes—
268#121—21no—
269#121—21no—
270C4×Q8—21no—
271C4×Q8C23×C3112yes—
272C4×D4—21no—
273C4×D4—21no—
274#117—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C42C23×C3111yescharacteristic
278#107—22no—
279#107—22no—
280C4⋊C8—22no—
281C4⋊C8—22no—
282C4⋊C8D4×C3112yes—
283C4⋊C8C23×C3112yes—
284C4⋊C8C23×C3112yes—
285C4⋊C8C23×C3112yes—
286#103—22no—
287#103—22no—
288#103—22no—
289#102—22no—
290#102—22no—
291#102—22no—
292C22⋊C8—21no—
293C22⋊C8—21no—
294C22⋊C8—21no—
295C22⋊C8D4×C3112yes—
296#97—22no—
297#97—21no—
298#97—21no—
299C4×C8—22no—
300C4×C8—21no—
301C4×C8C23×C3111yescharacteristic
302C4×C8C23×C3111yescharacteristic
303C31#1953011yescharacteristic, direct product factor, Sylow
304#41—82no—
305C2×Q8—21no—
306C2×Q8—21no—
307C2×Q8—21no—
308C2×Q8—21no—
309C2×Q8—41no—
310C2×Q8—82no—
311C2×Q8C2×D4×C3112yes—
312C2×D4—21no—
313C2×D4—21no—
314C2×D4—21no—
315C2×D4—41no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4C2×D4×C3111yescharacteristic
319C22×C4C2×D4×C3111yescharacteristic
320C22×C4#41×C3111yescharacteristic
321Q16—82no—
322Q16—82no—
323Q16—82no—
324SD16—82no—
325C2×C8—22no—
326C2×C8—22no—
327C2×C8—22no—
328C2×C8C2×D4×C3112yes—
329C2×C8C2×D4×C3112yes—
330C4⋊C4—21no—
331C4⋊C4—21no—
332C4⋊C4—21no—
333C4⋊C4—22no—
334C4⋊C4—22no—
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4—21no—
338C4⋊C4—21no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—41no—
342C4⋊C4—41no—
343C4⋊C4C2×D4×C3112yes—
344C22⋊C4—22no—
345C22⋊C4—41no—
346C22⋊C4—41no—
347C42—22no—
348C42C2×D4×C3111yescharacteristic
349C42C2×D4×C3111yescharacteristic
350C42#41×C3111yescharacteristic
351C42C24×C3111yescharacteristic
352C23—41no—
353C23C31×#12111yescharacteristic
354Q8—22no—
355Q8—22no—
356Q8—42no—
357Q8—42no—
358Q8—42no—
359Q8—81no—
360Q8—82no—
361D4—42no—
362D4—42no—
363D4—81no—
364D4—82no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—82no—
374C2×C4—82no—
375C2×C4C31×#12111yescharacteristic
376C2×C4C31×#12111yescharacteristic
377C2×C4C31×#12111yescharacteristic
378C2×C4C22×D4×C3111yescharacteristic
379C2×C4C22×D4×C3111yescharacteristic
380C2×C4C2×#41×C3111yescharacteristic
381C8—22no—
382C8—22no—
383C8—42no—
384C8—42no—
385C8—42no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—81no—
390C22—81no—
391C22—81no—
392C22C2×C31×#12111yescharacteristic
393C4—21no—
394C4—21no—
395C4—21no—
396C4—21no—
397C4—42no—
398C4—42no—
399C4—81no—
400C4—81no—
401C4—81no—
402C4C31×#57612yes—
403C4C31×#57812yes—
404C2—41no—
405C2—161no—
406C2C31×#304411yescharacteristic
407C2C31×#305811yescharacteristic
408C2C31×#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×#3209C2semidirect
4. C31×#2985C2semidirect
5. C31×#1702C2semidirect
6. C31×#1694C2semidirect
7. C31×#1682C2semidirect
8. C31×#1674C2semidirect
9. C31×#1572C2semidirect
10. C31×#1556C2semidirect
147. #19530C31direct (N × H)
184. #3209C2×C31semidirect
185. #2985C2×C31semidirect
186. #1702C2×C31semidirect
187. #1694C2×C31semidirect
188. #1682C2×C31semidirect
189. #1674C2×C31semidirect
190. #1572C2×C31semidirect
191. #1556C2×C31semidirect
303. C31#19530direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#32262
C31×#32162
C31×#32092
C31×#29852
C31×#17022
C31×#16942
C31×#16822
C31×#16742
C31×#15722
C31×#15562
C31×#15532
#1953031