Finite Group Databasebeta

← C31×#9522 #21466281

Subgroups — C31×#9522 #21466281

Order 7936.

472 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3092C211yesmaximal, characteristic
2C31×#2976C211yesmaximal, characteristic
3C31×#1823C211yesmaximal, characteristic, complemented
4C31×#1821C211yesmaximal, characteristic, complemented
5C31×#1513C211yesmaximal, characteristic
6C31×#1305C211yesmaximal, characteristic, complemented
7C31×#1293C211yesmaximal, characteristic, complemented
8C31×#525C2211yescharacteristic
9C22×C4⋊C4×C31C2211yescharacteristic
10C31×#484C412yescomplemented
11C31×#483—21no—
12C31×#481C412yescomplemented
13C31×#480—21no—
14C31×#436—21no—
15C31×#435—21no—
16C31×#435—21no—
17C8×D4×C31—21no—
18C31×#433—21no—
19C31×#428—21no—
20C31×#417—21no—
21C31×#408—21no—
22C31×#407C2211yescharacteristic
23C31×#407C2211yescharacteristic
24C31×#407C2211yescharacteristic
25C2×C31×C22⋊C8C2211yescharacteristic
26C31×#380C2211yescharacteristic
27C31×#343—21no—
28C31×#343—21no—
29C31×#340—21no—
30C31×#340—21no—
31C31×#328—21no—
32C31×#327—21no—
33C2×#41×C31D411yescharacteristic
34C23×C4×C31—21no—
35C23×C4×C31C2311yescharacteristic
36C2×M16×C31—21no—
37C2×M16×C31—21no—
38C2×M16×C31—21no—
39C2×M16×C31D411yescharacteristic
40C2×M16×C31D411yescharacteristic
41C22×C8×C31—21no—
42C22×C8×C31D411yescharacteristic
43C22×C8×C31D411yescharacteristic
44C31×#123—21no—
45C31×C22⋊Q8C2×C411yescharacteristic
46C31×C22⋊Q8D411yescharacteristic
47C31×#121C2×C411yescharacteristic
48C31×#121D411yescharacteristic
49C31×#120—21no—
50C4×D4×C31—21no—
51C4×D4×C31—21no—
52C31×#117D411yescharacteristic
53C2×C4⋊C4×C31—21no—
54C2×C4⋊C4×C31—21no—
55C2×C4⋊C4×C31—21no—
56C2×C4⋊C4×C31—21no—
57C2×C4⋊C4×C31—21no—
58C2×C4⋊C4×C31—21no—
59C2×C4⋊C4×C31C2×C412yes—
60C2×C22⋊C4×C31—21no—
61C31×#107—22no—
62C31×#106—22no—
63C31×C4⋊C8—21no—
64C31×C4⋊C8—21no—
65C31×#103—22no—
66C31×#102—22no—
67C31×C22⋊C8—21no—
68C31×C22⋊C8—21no—
69C31×C22⋊C8—21no—
70C31×C22⋊C8—21no—
71C31×C22⋊C8—21no—
72C31×C22⋊C8—21no—
73C31×C22⋊C8—21no—
74C31×C22⋊C8—21no—
75C31×C22⋊C8—21no—
76C31×C22⋊C8C2×C412yes—
77C31×#97—21no—
78C4×C8×C31—21no—
79C31×#95—21no—
80C24×C31#4111yescharacteristic
81#41×C31—41no—
82#41×C31—41no—
83C2×Q8×C31C22⋊C411yescharacteristic
84C2×D4×C31—21no—
85C2×D4×C31—21no—
86C2×D4×C31—21no—
87C2×D4×C31C22⋊C411yescharacteristic
88C22×C4×C31—21no—
89C22×C4×C31—22no—
90C22×C4×C31—41no—
91C22×C4×C31—41no—
92C22×C4×C31—41no—
93C22×C4×C31—41no—
94C22×C4×C31—41no—
95C22×C4×C31—81no—
96C22×C4×C31—81no—
97C22×C4×C31C22×C411yescharacteristic
98C22×C4×C31C2×D411yescharacteristic
99C22×C4×C31C2×D411yescharacteristic
100C22×C4×C31C2×D411yescharacteristic
101C22×C4×C31C2×D411yescharacteristic
102C22×C4×C31#4111yescharacteristic
103M16×C31—41no—
104M16×C31—41no—
105M16×C31—41no—
106M16×C31—41no—
107M16×C31—41no—
108M16×C31—41no—
109M16×C31—81no—
110C2×C8×C31—22no—
111C2×C8×C31—21no—
112C2×C8×C31—21no—
113C2×C8×C31—21no—
114C2×C8×C31—21no—
115C2×C8×C31—41no—
116C2×C8×C31—41no—
117C2×C8×C31—41no—
118C2×C8×C31—81no—
119C4⋊C4×C31—21no—
120C4⋊C4×C31—21no—
121C4⋊C4×C31—22no—
122C4⋊C4×C31—22no—
123C4⋊C4×C31—41no—
124C4⋊C4×C31—41no—
125C4⋊C4×C31—41no—
126C4⋊C4×C31—41no—
127C4⋊C4×C31C22⋊C411yescharacteristic
128C4⋊C4×C31C22⋊C411yescharacteristic
129C22⋊C4×C31—21no—
130C22⋊C4×C31—21no—
131C22⋊C4×C31—21no—
132C22⋊C4×C31—21no—
133C22⋊C4×C31—21no—
134C22⋊C4×C31—81no—
135C42×C31—21no—
136#9522C3111yesmaximal, characteristic, direct product factor, Sylow
137C23×C31—21no—
138C23×C31—21no—
139C23×C31—21no—
140C23×C31—41no—
141C23×C31—41no—
142C23×C31C4×D411yescharacteristic
143C23×C31#12111yescharacteristic
144C23×C31#12311yescharacteristic
145Q8×C31—41no—
146D4×C31—41no—
147D4×C31—41no—
148D4×C31—41no—
149D4×C31—81no—
150D4×C31—81no—
151C2×C4×C31—21no—
152C2×C4×C31—21no—
153C2×C4×C31—21no—
154C2×C4×C31—21no—
155C2×C4×C31—21no—
156C2×C4×C31—21no—
157C2×C4×C31—21no—
158C2×C4×C31—21no—
159C2×C4×C31—21no—
160C2×C4×C31—41no—
161C2×C4×C31—41no—
162C2×C4×C31—41no—
163C2×C4×C31—41no—
164C2×C4×C31—41no—
165C2×C4×C31—42no—
166C2×C4×C31—82no—
167C2×C4×C31—81no—
168C2×C4×C31—81no—
169C2×C4×C31—82no—
170C2×C4×C31—81no—
171C2×C4×C31—81no—
172C2×C4×C31—81no—
173C2×C4×C31C2×C22⋊C411yescharacteristic
174C2×C4×C31C4×D411yescharacteristic
175C2×C4×C31#12011yescharacteristic
176C2×C4×C31#12111yescharacteristic
177C8×C31—42no—
178C8×C31—41no—
179C8×C31—41no—
180C8×C31—41no—
181C8×C31—41no—
182C8×C31—81no—
183#3092C2×C3111yescharacteristic
184#2976C2×C3111yescharacteristic
185#1823C2×C3111yescharacteristic, complemented
186#1821C2×C3111yescharacteristic, complemented
187#1513C2×C3111yescharacteristic
188#1305C2×C3111yescharacteristic, complemented
189#1293C2×C3111yescharacteristic, complemented
190C22×C31—21no—
191C22×C31—21no—
192C22×C31—21no—
193C22×C31—21no—
194C22×C31—21no—
195C22×C31—21no—
196C22×C31—21no—
197C22×C31—21no—
198C22×C31—42no—
199C22×C31—42no—
200C22×C31—41no—
201C22×C31—41no—
202C22×C31—41no—
203C22×C31#38611yescharacteristic
204C22×C31#47111yescharacteristic
205C22×C31#47211yescharacteristic
206C4×C31—21no—
207C4×C31—21no—
208C4×C31—21no—
209C4×C31—41no—
210C4×C31—41no—
211C4×C31—41no—
212C4×C31—82no—
213C4×C31—161no—
214C4×C31#45811yescharacteristic
215C4×C31#45811yescharacteristic
216#525C22×C3111yescharacteristic
217C22×C4⋊C4C22×C3111yescharacteristic
218#484C4×C3112yescomplemented
219#483—21no—
220#481C4×C3112yescomplemented
221#480—21no—
222#436—21no—
223#435—21no—
224#435—21no—
225C8×D4—21no—
226#433—21no—
227#428—21no—
228#417—21no—
229#408—21no—
230#407C22×C3111yescharacteristic
231#407C22×C3111yescharacteristic
232#407C22×C3111yescharacteristic
233C2×C22⋊C8C22×C3111yescharacteristic
234#380C22×C3111yescharacteristic
235#343—21no—
236#343—21no—
237#340—21no—
238#340—21no—
239#328—21no—
240#327—21no—
241C2×C31—21no—
242C2×C31—21no—
243C2×C31—41no—
244C2×C31—41no—
245C2×C31—81no—
246C2×C31#189011yescharacteristic
247C2×C31#190211yescharacteristic
248C2×C31#190711yescharacteristic
249C2×#41D4×C3111yescharacteristic
250C23×C4—21no—
251C23×C4C23×C3111yescharacteristic
252C2×M16—21no—
253C2×M16—21no—
254C2×M16—21no—
255C2×M16D4×C3111yescharacteristic
256C2×M16D4×C3111yescharacteristic
257C22×C8—21no—
258C22×C8D4×C3111yescharacteristic
259C22×C8D4×C3111yescharacteristic
260#123—21no—
261C22⋊Q8C2×C4×C3111yescharacteristic
262C22⋊Q8D4×C3111yescharacteristic
263#121C2×C4×C3111yescharacteristic
264#121D4×C3111yescharacteristic
265#120—21no—
266C4×D4—21no—
267C4×D4—21no—
268#117D4×C3111yescharacteristic
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4C2×C4×C3112yes—
276C2×C22⋊C4—21no—
277#107—22no—
278#106—22no—
279C4⋊C8—21no—
280C4⋊C8—21no—
281#103—22no—
282#102—22no—
283C22⋊C8—21no—
284C22⋊C8—21no—
285C22⋊C8—21no—
286C22⋊C8—21no—
287C22⋊C8—21no—
288C22⋊C8—21no—
289C22⋊C8—21no—
290C22⋊C8—21no—
291C22⋊C8—21no—
292C22⋊C8C2×C4×C3112yes—
293#97—21no—
294C4×C8—21no—
295#95—21no—
296C31#952211yescharacteristic, direct product factor, Sylow
297C24#41×C3111yescharacteristic
298#41—41no—
299#41—41no—
300C2×Q8C22⋊C4×C3111yescharacteristic
301C2×D4—21no—
302C2×D4—21no—
303C2×D4—21no—
304C2×D4C22⋊C4×C3111yescharacteristic
305C22×C4—21no—
306C22×C4—22no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—81no—
313C22×C4—81no—
314C22×C4C22×C4×C3111yescharacteristic
315C22×C4C2×D4×C3111yescharacteristic
316C22×C4C2×D4×C3111yescharacteristic
317C22×C4C2×D4×C3111yescharacteristic
318C22×C4C2×D4×C3111yescharacteristic
319C22×C4#41×C3111yescharacteristic
320M16—41no—
321M16—41no—
322M16—41no—
323M16—41no—
324M16—41no—
325M16—41no—
326M16—81no—
327C2×C8—22no—
328C2×C8—21no—
329C2×C8—21no—
330C2×C8—21no—
331C2×C8—21no—
332C2×C8—41no—
333C2×C8—41no—
334C2×C8—41no—
335C2×C8—81no—
336C4⋊C4—21no—
337C4⋊C4—21no—
338C4⋊C4—22no—
339C4⋊C4—22no—
340C4⋊C4—41no—
341C4⋊C4—41no—
342C4⋊C4—41no—
343C4⋊C4—41no—
344C4⋊C4C22⋊C4×C3111yescharacteristic
345C4⋊C4C22⋊C4×C3111yescharacteristic
346C22⋊C4—21no—
347C22⋊C4—21no—
348C22⋊C4—21no—
349C22⋊C4—21no—
350C22⋊C4—21no—
351C22⋊C4—81no—
352C42—21no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—41no—
357C23—41no—
358C23C4×D4×C3111yescharacteristic
359C23C31×#12111yescharacteristic
360C23C31×#12311yescharacteristic
361Q8—41no—
362D4—41no—
363D4—41no—
364D4—41no—
365D4—81no—
366D4—81no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—42no—
382C2×C4—82no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4—82no—
386C2×C4—81no—
387C2×C4—81no—
388C2×C4—81no—
389C2×C4C2×C22⋊C4×C3111yescharacteristic
390C2×C4C4×D4×C3111yescharacteristic
391C2×C4C31×#12011yescharacteristic
392C2×C4C31×#12111yescharacteristic
393C8—42no—
394C8—41no—
395C8—41no—
396C8—41no—
397C8—41no—
398C8—81no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—42no—
408C22—42no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22C31×#38611yescharacteristic
413C22C31×#47111yescharacteristic
414C22C31×#47211yescharacteristic
415C4—21no—
416C4—21no—
417C4—21no—
418C4—41no—
419C4—41no—
420C4—41no—
421C4—82no—
422C4—161no—
423C4C31×#45811yescharacteristic
424C4C31×#45811yescharacteristic
425C2—21no—
426C2—21no—
427C2—41no—
428C2—41no—
429C2—81no—
430C2C31×#189011yescharacteristic
431C2C31×#190211yescharacteristic
432C2C31×#190711yescharacteristic
subgroupG/H
center, socleC22×C31#386
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC31×#525C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. C31×#1823C2semidirect
4. C31×#1821C2semidirect
6. C31×#1305C2semidirect
7. C31×#1293C2semidirect
10. C31×#484C4semidirect
12. C31×#481C4semidirect
136. #9522C31direct (N × H)
185. #1823C2×C31semidirect
186. #1821C2×C31semidirect
188. #1305C2×C31semidirect
189. #1293C2×C31semidirect
218. #484C4×C31semidirect
220. #481C4×C31semidirect
296. C31#9522direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#30922
C31×#29762
C31×#18232
C31×#18212
C31×#15132
C31×#13052
C31×#12932
#952231