Finite Group Databasebeta

← C31×#7825 #21464584

Subgroups — C31×#7825 #21464584

Order 7936.

516 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2682C211yesmaximal, characteristic
2C31×#2100C211yesmaximal, characteristic, complemented
3C31×#2094C211yesmaximal, characteristic, complemented
4C31×#2094C211yesmaximal, characteristic, complemented
5C31×#1271C211yesmaximal, characteristic, complemented
6C31×#1270C211yesmaximal, characteristic, complemented
7C31×#1270C211yesmaximal, characteristic, complemented
8C2×C31×#123—21no—
9C2×C31×#121—21no—
10C2×C31×#106—21no—
11C2×C31×#106—21no—
12C2×C31×#102—21no—
13C2×C31×#102—21no—
14C31×#396—21no—
15C31×#394—21no—
16C31×#392—21no—
17C31×#390C2211yescharacteristic
18C31×#390C2211yescharacteristic
19C31×#389C2211yescharacteristic
20C31×#385—21no—
21C31×#384C2211yescharacteristic
22C31×#340—21no—
23C31×#340—21no—
24C31×#336C2211yescharacteristic
25C31×#336C2211yescharacteristic
26C31×#336C2211yescharacteristic
27C22×D4×C31—21no—
28C22×D4×C31—21no—
29C22×D4×C31D411yescharacteristic
30C22×D4×C31D411yescharacteristic
31C23×C4×C31—21no—
32C22×C8×C31—21no—
33C22×C8×C31—21no—
34C22×C8×C31—21no—
35C31×#123—42no—
36C31×#123—42no—
37C31×#121—42no—
38C31×#121—42no—
39C2×C4⋊C4×C31—21no—
40C2×C4⋊C4×C31—21no—
41C2×C4⋊C4×C31—21no—
42C2×C4⋊C4×C31—21no—
43C2×C4⋊C4×C31—21no—
44C2×C4⋊C4×C31D411yescharacteristic
45C2×C4⋊C4×C31D411yescharacteristic
46C2×C4⋊C4×C31D411yescharacteristic
47C2×C4⋊C4×C31D411yescharacteristic
48C2×C22⋊C4×C31—21no—
49C2×C22⋊C4×C31—21no—
50C2×C22⋊C4×C31—21no—
51C2×C22⋊C4×C31—21no—
52C2×C22⋊C4×C31—21no—
53C2×C22⋊C4×C31—21no—
54C2×C22⋊C4×C31—21no—
55C2×C42×C31C2311yescharacteristic
56C31×#106—42no—
57C31×#106—42no—
58C31×#102—42no—
59C31×#102—42no—
60C31×#95—21no—
61C31×#95—21no—
62C24×C31—21no—
63C24×C31—21no—
64C2×D4×C31—21no—
65C2×D4×C31—21no—
66C2×D4×C31—21no—
67C2×D4×C31—41no—
68C2×D4×C31—41no—
69C2×D4×C31—41no—
70C2×D4×C31—41no—
71C2×D4×C31—42no—
72C2×D4×C31—42no—
73C2×D4×C31—42no—
74C2×D4×C31—81no—
75C2×D4×C31—81no—
76C2×D4×C31—81no—
77C2×D4×C31SD1612yes—
78C22×C4×C31—21no—
79C22×C4×C31—21no—
80C22×C4×C31—21no—
81C22×C4×C31—21no—
82C22×C4×C31—42no—
83C22×C4×C31—42no—
84C22×C4×C31—41no—
85C22×C4×C31—81no—
86C22×C4×C31C2×D411yescharacteristic
87C22×C4×C31C2×D411yescharacteristic
88C22×C4×C31C2×D411yescharacteristic
89C2×C8×C31—22no—
90C2×C8×C31—22no—
91C2×C8×C31—41no—
92C2×C8×C31—41no—
93C2×C8×C31—41no—
94C2×C8×C31—41no—
95C2×C8×C31—41no—
96C2×C8×C31—41no—
97C2×C8×C31—41no—
98C4⋊C4×C31—21no—
99C4⋊C4×C31—42no—
100C4⋊C4×C31—41no—
101C4⋊C4×C31—41no—
102C4⋊C4×C31—41no—
103C4⋊C4×C31—41no—
104C4⋊C4×C31—41no—
105C4⋊C4×C31—41no—
106C4⋊C4×C31—41no—
107C4⋊C4×C31—42no—
108C4⋊C4×C31—41no—
109C4⋊C4×C31—41no—
110C4⋊C4×C31SD1612yes—
111C22⋊C4×C31—42no—
112C22⋊C4×C31—42no—
113C22⋊C4×C31—41no—
114C22⋊C4×C31—41no—
115C22⋊C4×C31—41no—
116C22⋊C4×C31—41no—
117C22⋊C4×C31—41no—
118C22⋊C4×C31—41no—
119C22⋊C4×C31—41no—
120C22⋊C4×C31—41no—
121C22⋊C4×C31—81no—
122C42×C31—41no—
123#7825C3111yesmaximal, characteristic, direct product factor, Sylow
124C23×C31—22no—
125C23×C31—41no—
126C23×C31—41no—
127C23×C31—41no—
128C23×C31—41no—
129C23×C31—41no—
130C23×C31—41no—
131C23×C31—41no—
132C23×C31—41no—
133C23×C31—41no—
134C23×C31—41no—
135C23×C31—41no—
136C23×C31—41no—
137C23×C31—41no—
138C23×C31#12011yescharacteristic
139D4×C31—42no—
140D4×C31—42no—
141D4×C31—81no—
142D4×C31—81no—
143D4×C31—84no—
144D4×C31—84no—
145C2×C4×C31—21no—
146C2×C4×C31—21no—
147C2×C4×C31—21no—
148C2×C4×C31—21no—
149C2×C4×C31—21no—
150C2×C4×C31—21no—
151C2×C4×C31—22no—
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—41no—
162C2×C4×C31—41no—
163C2×C4×C31—84no—
164C2×C4×C31—81no—
165C2×C4×C31—81no—
166C2×C4×C31—81no—
167C2×C4×C31C2×SD1611yescharacteristic
168C2×C4×C31C2×SD1611yescharacteristic
169C2×C4×C31#13511yescharacteristic
170C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
171C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
172C2×C4×C31#13711yescharacteristic
173C8×C31—42no—
174C8×C31—42no—
175C8×C31—81no—
176#2682C2×C3111yescharacteristic
177#2100C2×C3111yescharacteristic, complemented
178#2094C2×C3111yescharacteristic, complemented
179#2094C2×C3111yescharacteristic, complemented
180#1271C2×C3111yescharacteristic, complemented
181#1270C2×C3111yescharacteristic, complemented
182#1270C2×C3111yescharacteristic, complemented
183C22×C31—42no—
184C22×C31—42no—
185C22×C31—42no—
186C22×C31—81no—
187C22×C31—81no—
188C22×C31—81no—
189C22×C31—81no—
190C22×C31—81no—
191C22×C31—81no—
192C22×C31—81no—
193C22×C31—81no—
194C22×C31—81no—
195C22×C31—81no—
196C22×C31—81no—
197C22×C31#45011yescharacteristic
198C22×C31#45011yescharacteristic
199C22×C31#45211yescharacteristic
200C22×C31#45311yescharacteristic
201C22×C31#45311yescharacteristic
202C22×C31#45411yescharacteristic
203C22×C31#45811yescharacteristic
204C4×C31—21no—
205C4×C31—21no—
206C4×C31—21no—
207C4×C31—21no—
208C4×C31—21no—
209C4×C31—21no—
210C4×C31—42no—
211C4×C31—81no—
212C4×C31—81no—
213C4×C31—81no—
214C4×C31—161no—
215C2×#123—21no—
216C2×#121—21no—
217C2×#106—21no—
218C2×#106—21no—
219C2×#102—21no—
220C2×#102—21no—
221#396—21no—
222#394—21no—
223#392—21no—
224#390C22×C3111yescharacteristic
225#390C22×C3111yescharacteristic
226#389C22×C3111yescharacteristic
227#385—21no—
228#384C22×C3111yescharacteristic
229#340—21no—
230#340—21no—
231#336C22×C3111yescharacteristic
232#336C22×C3111yescharacteristic
233#336C22×C3111yescharacteristic
234C2×C31—82no—
235C2×C31—161no—
236C2×C31#161311yescharacteristic
237C2×C31#161611yescharacteristic
238C2×C31#161811yescharacteristic
239C2×C31#162911yescharacteristic
240C2×C31#163111yescharacteristic
241C2×C31#163511yescharacteristic
242C2×C31#165611yescharacteristic
243C22×D4—21no—
244C22×D4—21no—
245C22×D4D4×C3111yescharacteristic
246C22×D4D4×C3111yescharacteristic
247C23×C4—21no—
248C22×C8—21no—
249C22×C8—21no—
250C22×C8—21no—
251#123—42no—
252#123—42no—
253#121—42no—
254#121—42no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4D4×C3111yescharacteristic
261C2×C4⋊C4D4×C3111yescharacteristic
262C2×C4⋊C4D4×C3111yescharacteristic
263C2×C4⋊C4D4×C3111yescharacteristic
264C2×C22⋊C4—21no—
265C2×C22⋊C4—21no—
266C2×C22⋊C4—21no—
267C2×C22⋊C4—21no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—21no—
271C2×C42C23×C3111yescharacteristic
272#106—42no—
273#106—42no—
274#102—42no—
275#102—42no—
276#95—21no—
277#95—21no—
278C31#782511yescharacteristic, direct product factor, Sylow
279C24—21no—
280C24—21no—
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—21no—
284C2×D4—41no—
285C2×D4—41no—
286C2×D4—41no—
287C2×D4—41no—
288C2×D4—42no—
289C2×D4—42no—
290C2×D4—42no—
291C2×D4—81no—
292C2×D4—81no—
293C2×D4—81no—
294C2×D4SD16×C3112yes—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—42no—
300C22×C4—42no—
301C22×C4—41no—
302C22×C4—81no—
303C22×C4C2×D4×C3111yescharacteristic
304C22×C4C2×D4×C3111yescharacteristic
305C22×C4C2×D4×C3111yescharacteristic
306C2×C8—22no—
307C2×C8—22no—
308C2×C8—41no—
309C2×C8—41no—
310C2×C8—41no—
311C2×C8—41no—
312C2×C8—41no—
313C2×C8—41no—
314C2×C8—41no—
315C4⋊C4—21no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—42no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4—42no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4SD16×C3112yes—
328C22⋊C4—42no—
329C22⋊C4—42no—
330C22⋊C4—41no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—41no—
334C22⋊C4—41no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—81no—
339C42—41no—
340C23—22no—
341C23—41no—
342C23—41no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23—41no—
348C23—41no—
349C23—41no—
350C23—41no—
351C23—41no—
352C23—41no—
353C23—41no—
354C23C31×#12011yescharacteristic
355D4—42no—
356D4—42no—
357D4—81no—
358D4—81no—
359D4—84no—
360D4—84no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—22no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—84no—
380C2×C4—81no—
381C2×C4—81no—
382C2×C4—81no—
383C2×C4C2×SD16×C3111yescharacteristic
384C2×C4C2×SD16×C3111yescharacteristic
385C2×C4C31×#13511yescharacteristic
386C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
387C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
388C2×C4C31×#13711yescharacteristic
389C8—42no—
390C8—42no—
391C8—81no—
392C22—42no—
393C22—42no—
394C22—42no—
395C22—81no—
396C22—81no—
397C22—81no—
398C22—81no—
399C22—81no—
400C22—81no—
401C22—81no—
402C22—81no—
403C22—81no—
404C22—81no—
405C22—81no—
406C22C31×#45011yescharacteristic
407C22C31×#45011yescharacteristic
408C22C31×#45211yescharacteristic
409C22C31×#45311yescharacteristic
410C22C31×#45311yescharacteristic
411C22C31×#45411yescharacteristic
412C22C31×#45811yescharacteristic
413C4—21no—
414C4—21no—
415C4—21no—
416C4—21no—
417C4—21no—
418C4—21no—
419C4—42no—
420C4—81no—
421C4—81no—
422C4—81no—
423C4—161no—
424C2—82no—
425C2—161no—
426C2C31×#161311yescharacteristic
427C2C31×#161611yescharacteristic
428C2C31×#161811yescharacteristic
429C2C31×#162911yescharacteristic
430C2C31×#163111yescharacteristic
431C2C31×#163511yescharacteristic
432C2C31×#165611yescharacteristic
subgroupG/H
center, socleC23×C31#120
commutator, Frattini, cosocleC2×C42C23×C31
prime radicalC31×#2682C2
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#2100C2semidirect
3. C31×#2094C2semidirect
4. C31×#2094C2semidirect
5. C31×#1271C2semidirect
6. C31×#1270C2semidirect
7. C31×#1270C2semidirect
123. #7825C31direct (N × H)
177. #2100C2×C31semidirect
178. #2094C2×C31semidirect
179. #2094C2×C31semidirect
180. #1271C2×C31semidirect
181. #1270C2×C31semidirect
182. #1270C2×C31semidirect
278. C31#7825direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#26822
C31×#21002
C31×#20942
C31×#12712
C31×#12702
#782531