Finite Group Databasebeta

← C31×#13094 #21469853

Subgroups — C31×#13094 #21469853

Order 7936.

676 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#101C211yesmaximal, characteristic
2C31×#2434C211yesmaximal, characteristic
3C2×C31×#356C212yesmaximal, complemented
4C31×#1784C211yesmaximal, characteristic
5C31×#1394C212yesmaximal, complemented
6C23×Q8×C31C2211yescharacteristic
7C22×M16×C31—21no—
8C2×C31×C4⋊Q8C411yescharacteristic
9C2×C31×C4⋊Q8C2211yescharacteristic
10C2×C31×C22⋊Q8C411yescharacteristic
11C2×C31×#101—21no—
12C2×C31×#101—24no—
13C2×C31×#101—21no—
14C2×C31×#101C2212yes—
15C2×C31×#101C2212yes—
16C31×#407—21no—
17C31×#395—21no—
18C31×#395—21no—
19C31×#391C411yescharacteristic
20C31×#391C2211yescharacteristic
21C31×#385—21no—
22C31×#385—21no—
23C4×C22⋊C4×C31C411yescharacteristic
24C31×#356—24no—
25C22×Q8×C31—22no—
26C22×Q8×C31—22no—
27C22×Q8×C31—41no—
28C22×Q8×C31—41no—
29C22×Q8×C31—42no—
30C22×Q8×C31C2×C411yescharacteristic
31C22×Q8×C31C2×C411yescharacteristic
32C22×Q8×C31D411yescharacteristic
33C22×Q8×C31D411yescharacteristic
34C22×Q8×C31C2311yescharacteristic
35C23×C4×C31C2×C411yescharacteristic
36C23×C4×C31D411yescharacteristic
37C23×C4×C31D411yescharacteristic
38C2×M16×C31—24no—
39C2×M16×C31—22no—
40C2×M16×C31—22no—
41C2×M16×C31—41no—
42C2×M16×C31—42no—
43C22×C8×C31—41no—
44C31×C4⋊Q8—22no—
45C31×C4⋊Q8—22no—
46C31×C4⋊Q8—42no—
47C31×C22⋊Q8—41no—
48C31×C22⋊Q8—41no—
49C2×C4⋊C4×C31—21no—
50C2×C4⋊C4×C31—21no—
51C2×C4⋊C4×C31—21no—
52C2×C4⋊C4×C31—21no—
53C2×C4⋊C4×C31—21no—
54C2×C4⋊C4×C31C2×C411yescharacteristic
55C2×C22⋊C4×C31—21no—
56C2×C22⋊C4×C31—21no—
57C2×C42×C31C2×C411yescharacteristic
58C2×C42×C31C2×C411yescharacteristic
59C31×#101—24no—
60C31×#101—22no—
61C31×#101—22no—
62C31×#101—22no—
63C31×#101—42no—
64C31×#101D414yes—
65C31×C22⋊C8—41no—
66C31×C22⋊C8—41no—
67C31×#95—21no—
68C31×#95—21no—
69C31×#95—21no—
70C31×#95—21no—
71C31×#95—21no—
72C24×C31C22⋊C411yescharacteristic
73C2×Q8×C31—22no—
74C2×Q8×C31—22no—
75C2×Q8×C31—22no—
76C2×Q8×C31—21no—
77C2×Q8×C31—22no—
78C2×Q8×C31—21no—
79C2×Q8×C31—22no—
80C2×Q8×C31—41no—
81C2×Q8×C31—41no—
82C2×Q8×C31—41no—
83C2×Q8×C31—41no—
84C2×Q8×C31—41no—
85C2×Q8×C31—41no—
86C2×Q8×C31—44no—
87C2×Q8×C31—44no—
88C2×Q8×C31—44no—
89C2×Q8×C31—44no—
90C2×Q8×C31—41no—
91C2×Q8×C31—41no—
92C2×Q8×C31C2×D412yes—
93C2×Q8×C31#4112yes—
94C22×C4×C31—21no—
95C22×C4×C31—21no—
96C22×C4×C31—22no—
97C22×C4×C31—21no—
98C22×C4×C31—21no—
99C22×C4×C31—21no—
100C22×C4×C31—21no—
101C22×C4×C31—21no—
102C22×C4×C31—21no—
103C22×C4×C31—21no—
104C22×C4×C31—21no—
105C22×C4×C31—22no—
106C22×C4×C31—22no—
107C22×C4×C31—21no—
108C22×C4×C31—21no—
109C22×C4×C31—41no—
110C22×C4×C31—41no—
111C22×C4×C31C22⋊C411yescharacteristic
112C22×C4×C31C22⋊C411yescharacteristic
113C22×C4×C31C22⋊C411yescharacteristic
114C22×C4×C31C22×C411yescharacteristic
115C22×C4×C31C2×D411yescharacteristic
116C22×C4×C31C2×D411yescharacteristic
117M16×C31—24no—
118M16×C31—44no—
119M16×C31—42no—
120M16×C31—42no—
121M16×C31—42no—
122C2×C8×C31—44no—
123C2×C8×C31—42no—
124C2×C8×C31—42no—
125C4⋊C4×C31—42no—
126C4⋊C4×C31—42no—
127C4⋊C4×C31—41no—
128C4⋊C4×C31—42no—
129C4⋊C4×C31—41no—
130C4⋊C4×C31—42no—
131C4⋊C4×C31—41no—
132C22⋊C4×C31—24no—
133C22⋊C4×C31—41no—
134C22⋊C4×C31—41no—
135C42×C31—22no—
136C42×C31—41no—
137#13094C3111yesmaximal, characteristic, direct product factor, Sylow
138C23×C31—22no—
139C23×C31—21no—
140C23×C31—21no—
141C23×C31—41no—
142C23×C31#9911yescharacteristic
143C23×C31#9911yescharacteristic
144C23×C31C2×C22⋊C411yescharacteristic
145Q8×C31—42no—
146Q8×C31—42no—
147Q8×C31—44no—
148Q8×C31—44no—
149Q8×C31—42no—
150Q8×C31—42no—
151Q8×C31—82no—
152C2×C4×C31—22no—
153C2×C4×C31—22no—
154C2×C4×C31—22no—
155C2×C4×C31—22no—
156C2×C4×C31—21no—
157C2×C4×C31—21no—
158C2×C4×C31—21no—
159C2×C4×C31—21no—
160C2×C4×C31—21no—
161C2×C4×C31—21no—
162C2×C4×C31—21no—
163C2×C4×C31—21no—
164C2×C4×C31—22no—
165C2×C4×C31—22no—
166C2×C4×C31—21no—
167C2×C4×C31—21no—
168C2×C4×C31—21no—
169C2×C4×C31—21no—
170C2×C4×C31—21no—
171C2×C4×C31—21no—
172C2×C4×C31—42no—
173C2×C4×C31—42no—
174C2×C4×C31—42no—
175C2×C4×C31—42no—
176C2×C4×C31—41no—
177C2×C4×C31—41no—
178C2×C4×C31—41no—
179C2×C4×C31—41no—
180C2×C4×C31—42no—
181C2×C4×C31—41no—
182C2×C4×C31—41no—
183C2×C4×C31—41no—
184C2×C4×C31—41no—
185C2×C4×C31#9912yes—
186C2×C4×C31C4×D412yes—
187C2×C4×C31#12011yescharacteristic
188C2×C4×C31#12112yes—
189C2×C4×C31#12311yescharacteristic
190C8×C31—44no—
191C8×C31—82no—
192C22×#101C2×C3111yescharacteristic
193#2434C2×C3111yescharacteristic
194C2×#356C2×C3112yescomplemented
195#1784C2×C3111yescharacteristic
196#1394C2×C3112yescomplemented
197C22×C31—21no—
198C22×C31—21no—
199C22×C31—21no—
200C22×C31—21no—
201C22×C31—21no—
202C22×C31—21no—
203C22×C31—21no—
204C22×C31—42no—
205C22×C31—42no—
206C22×C31#35612yescomplemented
207C22×C31#38611yescharacteristic
208C22×C31C2×#9911yescharacteristic
209C22×C31C2×#9911yescharacteristic
210C4×C31—21no—
211C4×C31—22no—
212C4×C31—22no—
213C4×C31—21no—
214C4×C31—22no—
215C4×C31—42no—
216C4×C31—42no—
217C4×C31—41no—
218C4×C31—41no—
219C4×C31—81no—
220C4×C31—81no—
221C23×Q8C22×C3111yescharacteristic
222C22×M16—21no—
223C2×C4⋊Q8C4×C3111yescharacteristic
224C2×C4⋊Q8C22×C3111yescharacteristic
225C2×C22⋊Q8C4×C3111yescharacteristic
226C2×#101—21no—
227C2×#101—24no—
228C2×#101—21no—
229C2×#101C22×C3112yes—
230C2×#101C22×C3112yes—
231#407—21no—
232#395—21no—
233#395—21no—
234#391C4×C3111yescharacteristic
235#391C22×C3111yescharacteristic
236#385—21no—
237#385—21no—
238C4×C22⋊C4C4×C3111yescharacteristic
239#356—24no—
240C2×C31—21no—
241C2×C31—21no—
242C2×C31—22no—
243C2×C31—41no—
244C2×C31#189811yescharacteristic
245C2×C31C2×#35611yescharacteristic
246C2×C31#213311yescharacteristic
247C22×Q8—22no—
248C22×Q8—22no—
249C22×Q8—41no—
250C22×Q8—41no—
251C22×Q8—42no—
252C22×Q8C2×C4×C3111yescharacteristic
253C22×Q8C2×C4×C3111yescharacteristic
254C22×Q8D4×C3111yescharacteristic
255C22×Q8D4×C3111yescharacteristic
256C22×Q8C23×C3111yescharacteristic
257C23×C4C2×C4×C3111yescharacteristic
258C23×C4D4×C3111yescharacteristic
259C23×C4D4×C3111yescharacteristic
260C2×M16—24no—
261C2×M16—22no—
262C2×M16—22no—
263C2×M16—41no—
264C2×M16—42no—
265C22×C8—41no—
266C4⋊Q8—22no—
267C4⋊Q8—22no—
268C4⋊Q8—42no—
269C22⋊Q8—41no—
270C22⋊Q8—41no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4C2×C4×C3111yescharacteristic
277C2×C22⋊C4—21no—
278C2×C22⋊C4—21no—
279C2×C42C2×C4×C3111yescharacteristic
280C2×C42C2×C4×C3111yescharacteristic
281#101—24no—
282#101—22no—
283#101—22no—
284#101—22no—
285#101—42no—
286#101D4×C3114yes—
287C22⋊C8—41no—
288C22⋊C8—41no—
289#95—21no—
290#95—21no—
291#95—21no—
292#95—21no—
293#95—21no—
294C31#1309411yescharacteristic, direct product factor, Sylow
295C24C22⋊C4×C3111yescharacteristic
296C2×Q8—22no—
297C2×Q8—22no—
298C2×Q8—22no—
299C2×Q8—21no—
300C2×Q8—22no—
301C2×Q8—21no—
302C2×Q8—22no—
303C2×Q8—41no—
304C2×Q8—41no—
305C2×Q8—41no—
306C2×Q8—41no—
307C2×Q8—41no—
308C2×Q8—41no—
309C2×Q8—44no—
310C2×Q8—44no—
311C2×Q8—44no—
312C2×Q8—44no—
313C2×Q8—41no—
314C2×Q8—41no—
315C2×Q8C2×D4×C3112yes—
316C2×Q8#41×C3112yes—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—22no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—41no—
333C22×C4—41no—
334C22×C4C22⋊C4×C3111yescharacteristic
335C22×C4C22⋊C4×C3111yescharacteristic
336C22×C4C22⋊C4×C3111yescharacteristic
337C22×C4C22×C4×C3111yescharacteristic
338C22×C4C2×D4×C3111yescharacteristic
339C22×C4C2×D4×C3111yescharacteristic
340M16—24no—
341M16—44no—
342M16—42no—
343M16—42no—
344M16—42no—
345C2×C8—44no—
346C2×C8—42no—
347C2×C8—42no—
348C4⋊C4—41no—
349C4⋊C4—42no—
350C4⋊C4—42no—
351C4⋊C4—42no—
352C4⋊C4—41no—
353C4⋊C4—42no—
354C4⋊C4—41no—
355C22⋊C4—24no—
356C22⋊C4—41no—
357C22⋊C4—41no—
358C42—22no—
359C42—41no—
360C23—21no—
361C23—22no—
362C23—21no—
363C23—41no—
364C23C31×#9911yescharacteristic
365C23C31×#9911yescharacteristic
366C23C2×C22⋊C4×C3111yescharacteristic
367Q8—42no—
368Q8—42no—
369Q8—44no—
370Q8—44no—
371Q8—42no—
372Q8—42no—
373Q8—82no—
374C2×C4—22no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—42no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4C31×#9912yes—
408C2×C4C4×D4×C3112yes—
409C2×C4C31×#12011yescharacteristic
410C2×C4C31×#12112yes—
411C2×C4C31×#12311yescharacteristic
412C8—44no—
413C8—82no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—42no—
422C22—42no—
423C22C31×#35612yescomplemented
424C22C31×#38611yescharacteristic
425C22C2×C31×#9911yescharacteristic
426C22C2×C31×#9911yescharacteristic
427C4—21no—
428C4—22no—
429C4—22no—
430C4—21no—
431C4—22no—
432C4—42no—
433C4—42no—
434C4—41no—
435C4—41no—
436C4—81no—
437C4—81no—
438C2—21no—
439C2—21no—
440C2—22no—
441C2—41no—
442C2C31×#189811yescharacteristic
443C2C2×C31×#35611yescharacteristic
444C2C31×#213311yescharacteristic
subgroupG/H
center, socleC22×C31C2×#99
commutatorC22×C4C22×C4×C31
Frattini, cosocleC22×Q8C23×C31
prime radicalC24×C31C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C24×C31 ◁ C23×Q8×C31 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C31×#356C2semidirect
5. C31×#1394C2semidirect
137. #13094C31direct (N × H)
194. C2×#356C2×C31semidirect
196. #1394C2×C31semidirect
206. C22×C31#356semidirect
294. C31#13094direct (N × H)
423. C22C31×#356semidirect

Maximal subgroups

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

subgroupindex
C22×C31×#1012
C31×#24342
C2×C31×#3562
C31×#17842
C31×#13942
#1309431