Finite Group Databasebeta

← C31×#9123 #21465882

Subgroups — C31×#9123 #21465882

Order 7936.

600 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#432C211yesmaximal, characteristic, complemented
2C31×#2850C211yesmaximal, characteristic
3C31×#1749C211yesmaximal, characteristic, complemented
4C2×C31×#329C212yesmaximal, complemented
5C31×#1295C212yesmaximal, complemented
6C2×C31×#124C2211yescharacteristic
7C2×C31×C22⋊Q8C411yescharacteristic
8C2×C31×#121C411yescharacteristic
9C22×C42×C31C2211yescharacteristic
10C31×#432—24no—
11C2×C31×C4⋊C8—21no—
12C2×C31×C22⋊C8—21no—
13C2×C31×C22⋊C8—21no—
14C2×C31×#97C2212yes—
15C2×C31×#97C2212yes—
16C31×#391C411yescharacteristic
17C31×#390C411yescharacteristic
18C31×#388—21no—
19C31×#388—21no—
20C31×#386—21no—
21C31×#386—21no—
22C31×#382C2211yescharacteristic
23C31×#336—21no—
24C31×#329—24no—
25C22×Q8×C31C2×C411yescharacteristic
26C22×D4×C31—21no—
27C22×D4×C31C2×C411yescharacteristic
28C23×C4×C31C2×C411yescharacteristic
29C23×C4×C31D411yescharacteristic
30C23×C4×C31D411yescharacteristic
31C22×C8×C31—22no—
32C22×C8×C31—22no—
33C31×#124—22no—
34C31×#124—22no—
35C31×C22⋊Q8—42no—
36C31×#121—42no—
37C2×C4⋊C4×C31—21no—
38C2×C4⋊C4×C31C2×C411yescharacteristic
39C2×C4⋊C4×C31C2×C411yescharacteristic
40C2×C22⋊C4×C31—21no—
41C2×C22⋊C4×C31—21no—
42C2×C22⋊C4×C31—21no—
43C2×C22⋊C4×C31—21no—
44C2×C22⋊C4×C31—21no—
45C2×C22⋊C4×C31—21no—
46C2×C42×C31—22no—
47C2×C42×C31—22no—
48C2×C42×C31C2×C411yescharacteristic
49C2×C42×C31D411yescharacteristic
50C2×C42×C31D411yescharacteristic
51C2×C42×C31C2311yescharacteristic
52C31×C4⋊C8—24no—
53C31×C22⋊C8—24no—
54C31×C22⋊C8—24no—
55C31×#97—22no—
56C31×#97—22no—
57C31×#97—22no—
58C31×#97D414yescomplemented
59C31×#95—21no—
60C31×#95—21no—
61C31×#95—21no—
62C31×#95—21no—
63C24×C31—21no—
64C24×C31C22⋊C411yescharacteristic
65C2×Q8×C31—22no—
66C2×Q8×C31—41no—
67C2×Q8×C31—41no—
68C2×D4×C31—22no—
69C2×D4×C31—41no—
70C2×D4×C31—41no—
71C2×D4×C31—42no—
72C2×D4×C31—42no—
73C2×D4×C31—42no—
74C22×C4×C31—22no—
75C22×C4×C31—22no—
76C22×C4×C31—22no—
77C22×C4×C31—21no—
78C22×C4×C31—22no—
79C22×C4×C31—21no—
80C22×C4×C31—21no—
81C22×C4×C31—21no—
82C22×C4×C31—21no—
83C22×C4×C31—41no—
84C22×C4×C31—41no—
85C22×C4×C31—41no—
86C22×C4×C31—41no—
87C22×C4×C31C22⋊C411yescharacteristic
88C22×C4×C31C22⋊C411yescharacteristic
89C22×C4×C31C22⋊C411yescharacteristic
90C22×C4×C31C22×C411yescharacteristic
91C22×C4×C31C2×D411yescharacteristic
92C22×C4×C31C2×D411yescharacteristic
93C2×C8×C31—24no—
94C2×C8×C31—24no—
95C2×C8×C31—42no—
96C2×C8×C31—42no—
97C2×C8×C31—42no—
98C2×C8×C31—42no—
99C4⋊C4×C31—41no—
100C4⋊C4×C31—41no—
101C4⋊C4×C31—42no—
102C22⋊C4×C31—42no—
103C22⋊C4×C31—42no—
104C22⋊C4×C31—42no—
105C22⋊C4×C31—42no—
106C22⋊C4×C31—41no—
107C22⋊C4×C31—42no—
108C22⋊C4×C31—41no—
109C42×C31—22no—
110C42×C31—21no—
111C42×C31—22no—
112C42×C31—21no—
113C42×C31C2×D412yes—
114C42×C31#4112yes—
115#9123C3111yesmaximal, characteristic, direct product factor, Sylow
116C23×C31—21no—
117C23×C31—21no—
118C23×C31—21no—
119C23×C31—21no—
120C23×C31—21no—
121C23×C31—21no—
122C23×C31—41no—
123C23×C31—41no—
124C23×C31—41no—
125C23×C31—41no—
126C23×C31—41no—
127C23×C31—41no—
128C23×C31—41no—
129C23×C31#10412yes—
130C23×C31C2×C22⋊C411yescharacteristic
131Q8×C31—82no—
132D4×C31—82no—
133D4×C31—84no—
134C2×C4×C31—21no—
135C2×C4×C31—21no—
136C2×C4×C31—21no—
137C2×C4×C31—21no—
138C2×C4×C31—21no—
139C2×C4×C31—21no—
140C2×C4×C31—21no—
141C2×C4×C31—21no—
142C2×C4×C31—21no—
143C2×C4×C31—21no—
144C2×C4×C31—21no—
145C2×C4×C31—21no—
146C2×C4×C31—21no—
147C2×C4×C31—21no—
148C2×C4×C31—44no—
149C2×C4×C31—44no—
150C2×C4×C31—42no—
151C2×C4×C31—42no—
152C2×C4×C31—41no—
153C2×C4×C31—41no—
154C2×C4×C31—41no—
155C2×C4×C31—41no—
156C2×C4×C31—41no—
157C2×C4×C31—41no—
158C2×C4×C31—41no—
159C2×C4×C31—41no—
160C2×C4×C31—41no—
161C2×C4×C31#10012yes—
162C2×C4×C31C4×D412yes—
163C2×C4×C31#12011yescharacteristic
164C2×C4×C31#12112yes—
165C2×C4×C31#12311yescharacteristic
166C8×C31—44no—
167C8×C31—44no—
168C2×#432C2×C3111yescharacteristic, complemented
169#2850C2×C3111yescharacteristic
170#1749C2×C3111yescharacteristic, complemented
171C2×#329C2×C3112yescomplemented
172#1295C2×C3112yescomplemented
173C22×C31—22no—
174C22×C31—22no—
175C22×C31—22no—
176C22×C31—41no—
177C22×C31—41no—
178C22×C31—41no—
179C22×C31—41no—
180C22×C31—81no—
181C22×C31—81no—
182C22×C31—81no—
183C22×C31—81no—
184C22×C31—81no—
185C22×C31—81no—
186C22×C31—81no—
187C22×C31#38611yescharacteristic
188C22×C31C2×#10011yescharacteristic
189C22×C31#41311yescharacteristic
190C22×C31C2×#10411yescharacteristic
191C22×C31#42111yescharacteristic
192C22×C31#42111yescharacteristic
193C22×C31#42111yescharacteristic
194C4×C31—22no—
195C4×C31—21no—
196C4×C31—21no—
197C4×C31—22no—
198C4×C31—22no—
199C4×C31—41no—
200C4×C31—41no—
201C4×C31—81no—
202C4×C31—81no—
203C4×C31—81no—
204C2×#124C22×C3111yescharacteristic
205C2×C22⋊Q8C4×C3111yescharacteristic
206C2×#121C4×C3111yescharacteristic
207C22×C42C22×C3111yescharacteristic
208#432—24no—
209C2×C4⋊C8—21no—
210C2×C22⋊C8—21no—
211C2×C22⋊C8—21no—
212C2×#97C22×C3112yes—
213C2×#97C22×C3112yes—
214#391C4×C3111yescharacteristic
215#390C4×C3111yescharacteristic
216#388—21no—
217#388—21no—
218#386—21no—
219#386—21no—
220#382C22×C3111yescharacteristic
221#336—21no—
222#329—24no—
223C2×C31—42no—
224C2×C31—161no—
225C2×C31#152711yescharacteristic
226C2×C31#153211yescharacteristic
227C2×C31#153511yescharacteristic
228C2×C31#153611yescharacteristic
229C2×C31#187111yescharacteristic
230C2×C31#189711yescharacteristic
231C2×C31#190011yescharacteristic
232C22×Q8C2×C4×C3111yescharacteristic
233C22×D4—21no—
234C22×D4C2×C4×C3111yescharacteristic
235C23×C4C2×C4×C3111yescharacteristic
236C23×C4D4×C3111yescharacteristic
237C23×C4D4×C3111yescharacteristic
238C22×C8—22no—
239C22×C8—22no—
240#124—22no—
241#124—22no—
242C22⋊Q8—42no—
243#121—42no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4C2×C4×C3111yescharacteristic
246C2×C4⋊C4C2×C4×C3111yescharacteristic
247C2×C22⋊C4—21no—
248C2×C22⋊C4—21no—
249C2×C22⋊C4—21no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4—21no—
253C2×C42—22no—
254C2×C42—22no—
255C2×C42C2×C4×C3111yescharacteristic
256C2×C42D4×C3111yescharacteristic
257C2×C42D4×C3111yescharacteristic
258C2×C42C23×C3111yescharacteristic
259C4⋊C8—24no—
260C22⋊C8—24no—
261C22⋊C8—24no—
262#97—22no—
263#97—22no—
264#97—22no—
265#97D4×C3114yescomplemented
266#95—21no—
267#95—21no—
268#95—21no—
269#95—21no—
270C31#912311yescharacteristic, direct product factor, Sylow
271C24—21no—
272C24C22⋊C4×C3111yescharacteristic
273C2×Q8—22no—
274C2×Q8—41no—
275C2×Q8—41no—
276C2×D4—22no—
277C2×D4—41no—
278C2×D4—41no—
279C2×D4—42no—
280C2×D4—42no—
281C2×D4—42no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—22no—
285C22×C4—21no—
286C22×C4—22no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—41no—
292C22×C4—41no—
293C22×C4—41no—
294C22×C4—41no—
295C22×C4C22⋊C4×C3111yescharacteristic
296C22×C4C22⋊C4×C3111yescharacteristic
297C22×C4C22⋊C4×C3111yescharacteristic
298C22×C4C22×C4×C3111yescharacteristic
299C22×C4C2×D4×C3111yescharacteristic
300C22×C4C2×D4×C3111yescharacteristic
301C2×C8—24no—
302C2×C8—24no—
303C2×C8—42no—
304C2×C8—42no—
305C2×C8—42no—
306C2×C8—42no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4—42no—
310C22⋊C4—42no—
311C22⋊C4—42no—
312C22⋊C4—42no—
313C22⋊C4—42no—
314C22⋊C4—41no—
315C22⋊C4—42no—
316C22⋊C4—41no—
317C42—22no—
318C42—21no—
319C42—22no—
320C42—21no—
321C42C2×D4×C3112yes—
322C42#41×C3112yes—
323C23—21no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—41no—
330C23—41no—
331C23—41no—
332C23—41no—
333C23—41no—
334C23—41no—
335C23—41no—
336C23C31×#10412yes—
337C23C2×C22⋊C4×C3111yescharacteristic
338Q8—82no—
339D4—82no—
340D4—84no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—44no—
356C2×C4—44no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4C31×#10012yes—
369C2×C4C4×D4×C3112yes—
370C2×C4C31×#12011yescharacteristic
371C2×C4C31×#12112yes—
372C2×C4C31×#12311yescharacteristic
373C8—44no—
374C8—44no—
375C22—22no—
376C22—22no—
377C22—22no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—81no—
383C22—81no—
384C22—81no—
385C22—81no—
386C22—81no—
387C22—81no—
388C22—81no—
389C22C31×#38611yescharacteristic
390C22C2×C31×#10011yescharacteristic
391C22C31×#41311yescharacteristic
392C22C2×C31×#10411yescharacteristic
393C22C31×#42111yescharacteristic
394C22C31×#42111yescharacteristic
395C22C31×#42111yescharacteristic
396C4—22no—
397C4—21no—
398C4—21no—
399C4—22no—
400C4—22no—
401C4—41no—
402C4—41no—
403C4—81no—
404C4—81no—
405C4—81no—
406C2—42no—
407C2—161no—
408C2C31×#152711yescharacteristic
409C2C31×#153211yescharacteristic
410C2C31×#153511yescharacteristic
411C2C31×#153611yescharacteristic
412C2C31×#187111yescharacteristic
413C2C31×#189711yescharacteristic
414C2C31×#190011yescharacteristic
subgroupG/H
center, socleC23×C31C2×C22⋊C4
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC2×C31×#121C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C22×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#432C2semidirect
3. C31×#1749C2semidirect
4. C2×C31×#329C2semidirect
5. C31×#1295C2semidirect
58. C31×#97D4semidirect
115. #9123C31direct (N × H)
168. C2×#432C2×C31semidirect
170. #1749C2×C31semidirect
171. C2×#329C2×C31semidirect
172. #1295C2×C31semidirect
265. #97D4×C31semidirect
270. C31#9123direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4322
C31×#28502
C31×#17492
C2×C31×#3292
C31×#12952
#912331