Finite Group Databasebeta

← C31×#11775 #21468534

Subgroups — C31×#11775 #21468534

Order 7936.

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

normal subgroups only

This group has 532 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×#2543C211yesmaximal, characteristic
2C4×C31×#99C211yesmaximal, characteristic, complemented
3C31×#1466C211yesmaximal, characteristic, complemented
4C31×#1344C212yesmaximal, complemented
5C31×#1343C212yesmaximal, complemented
6C2×C31×#121—21no—
7C2×C31×#121C411yescharacteristic, complemented
8C2×C4×D4×C31C2211yescharacteristic
9C31×#432—21no—
10C2×C31×#99—21no—
11C31×#398C411yescharacteristic, complemented
12C31×#397C2211yescharacteristic
13C31×#394C411yescharacteristic, complemented
14C31×#392C2211yescharacteristic
15C31×#388—21no—
16C31×#386—21no—
17C31×#386—21no—
18C4×C22⋊C4×C31—21no—
19C2×C31×#95C411yescharacteristic, complemented
20C31×#342C2212yes—
21C31×#323—21no—
22C31×#323C2212yes—
23C22×D4×C31—21no—
24C22×D4×C31—21no—
25C22×D4×C31C2×C411yescharacteristic
26C22×D4×C31D411yescharacteristic
27C23×C4×C31—21no—
28C23×C4×C31C2×C411yescharacteristic
29C23×C4×C31D411yescharacteristic
30C31×#121—44no—
31C31×#121—41no—
32C31×#121—41no—
33C4×D4×C31—41no—
34C4×D4×C31—41no—
35C2×C4⋊C4×C31—21no—
36C2×C4⋊C4×C31C2×C411yescharacteristic
37C2×C4⋊C4×C31C2×C411yescharacteristic
38C2×C22⋊C4×C31—22no—
39C2×C22⋊C4×C31—21no—
40C2×C22⋊C4×C31—21no—
41C2×C22⋊C4×C31—21no—
42C2×C22⋊C4×C31—21no—
43C2×C22⋊C4×C31—21no—
44C2×C22⋊C4×C31D411yescharacteristic
45C2×C22⋊C4×C31C2311yescharacteristic
46C2×C42×C31—41no—
47C2×C42×C31D411yescharacteristic
48C31×C4⋊C8—41no—
49C31×#99—24no—
50C31×C22⋊C8—22no—
51C31×#97—41no—
52C31×#95—21no—
53C31×#95—21no—
54C31×#95—21no—
55C31×#95—41no—
56C31×#95C2×C411yescharacteristic
57C31×#95C2×C411yescharacteristic
58C24×C31—21no—
59C24×C31C22⋊C411yescharacteristic
60C24×C31C2×D411yescharacteristic
61C2×D4×C31—22no—
62C2×D4×C31—22no—
63C2×D4×C31—41no—
64C2×D4×C31—42no—
65C2×D4×C31—41no—
66C2×D4×C31—42no—
67C2×D4×C31—42no—
68C2×D4×C31—42no—
69C2×D4×C31—42no—
70C2×D4×C31—81no—
71C2×D4×C31—81no—
72C22×C4×C31—21no—
73C22×C4×C31—21no—
74C22×C4×C31—21no—
75C22×C4×C31—21no—
76C22×C4×C31—21no—
77C22×C4×C31—21no—
78C22×C4×C31—21no—
79C22×C4×C31—42no—
80C22×C4×C31—42no—
81C22×C4×C31—42no—
82C22×C4×C31—81no—
83C22×C4×C31—81no—
84C22×C4×C31—81no—
85C22×C4×C31C22⋊C411yescharacteristic
86C22×C4×C31C22⋊C411yescharacteristic
87C22×C4×C31C22⋊C411yescharacteristic
88C22×C4×C31C22×C411yescharacteristic
89C22×C4×C31C2×D411yescharacteristic
90C2×C8×C31—42no—
91C4⋊C4×C31—41no—
92C4⋊C4×C31—42no—
93C4⋊C4×C31—41no—
94C22⋊C4×C31—24no—
95C22⋊C4×C31—41no—
96C22⋊C4×C31—41no—
97C22⋊C4×C31—42no—
98C22⋊C4×C31—42no—
99C22⋊C4×C31—42no—
100C22⋊C4×C31—42no—
101C22⋊C4×C31—41no—
102C22⋊C4×C31—41no—
103C22⋊C4×C31—81no—
104C42×C31—21no—
105C42×C31—21no—
106C42×C31—82no—
107#11775C3111yesmaximal, characteristic, direct product factor, Sylow
108C23×C31—21no—
109C23×C31—21no—
110C23×C31—21no—
111C23×C31—21no—
112C23×C31—41no—
113C23×C31—41no—
114C23×C31—41no—
115C23×C31—41no—
116C23×C31—41no—
117C23×C31—41no—
118C23×C31—41no—
119C23×C31—41no—
120C23×C31—41no—
121C23×C31—41no—
122C23×C31—41no—
123C23×C31#10412yes—
124C23×C31C2×C22⋊C411yescharacteristic
125C23×C31AGL(1,ℤ/8)12yes—
126D4×C31—44no—
127D4×C31—84no—
128D4×C31—82no—
129D4×C31—84no—
130C2×C4×C31—22no—
131C2×C4×C31—21no—
132C2×C4×C31—21no—
133C2×C4×C31—21no—
134C2×C4×C31—21no—
135C2×C4×C31—21no—
136C2×C4×C31—21no—
137C2×C4×C31—41no—
138C2×C4×C31—42no—
139C2×C4×C31—41no—
140C2×C4×C31—41no—
141C2×C4×C31—41no—
142C2×C4×C31—41no—
143C2×C4×C31—41no—
144C2×C4×C31—44no—
145C2×C4×C31—41no—
146C2×C4×C31—41no—
147C2×C4×C31—41no—
148C2×C4×C31—41no—
149C2×C4×C31—41no—
150C2×C4×C31—41no—
151C2×C4×C31—81no—
152C2×C4×C31—81no—
153C2×C4×C31—81no—
154C2×C4×C31—84no—
155C2×C4×C31—82no—
156C2×C4×C31—82no—
157C2×C4×C31#9911yescharacteristic
158C2×C4×C31#9911yescharacteristic
159C8×C31—82no—
160#2543C2×C3111yescharacteristic
161C4×#99C2×C3111yescharacteristic, complemented
162#1466C2×C3111yescharacteristic, complemented
163#1344C2×C3112yescomplemented
164#1343C2×C3112yescomplemented
165C22×C31—21no—
166C22×C31—21no—
167C22×C31—22no—
168C22×C31—22no—
169C22×C31—42no—
170C22×C31—42no—
171C22×C31—42no—
172C22×C31—41no—
173C22×C31—41no—
174C22×C31—41no—
175C22×C31—41no—
176C22×C31—81no—
177C22×C31—81no—
178C22×C31—81no—
179C22×C31—81no—
180C22×C31—81no—
181C22×C31—81no—
182C22×C31—81no—
183C22×C31—81no—
184C22×C31C2×#9911yescharacteristic
185C22×C31#41811yescharacteristic
186C22×C31C2×#10411yescharacteristic
187C4×C31—21no—
188C4×C31—21no—
189C4×C31—42no—
190C4×C31—41no—
191C4×C31—41no—
192C4×C31—41no—
193C4×C31—41no—
194C4×C31—81no—
195C4×C31—84no—
196C4×C31—81no—
197C2×#121—21no—
198C2×#121C4×C3111yescharacteristic, complemented
199C2×C4×D4C22×C3111yescharacteristic
200#432—21no—
201C2×#99—21no—
202#398C4×C3111yescharacteristic, complemented
203#397C22×C3111yescharacteristic
204#394C4×C3111yescharacteristic, complemented
205#392C22×C3111yescharacteristic
206#388—21no—
207#386—21no—
208#386—21no—
209C4×C22⋊C4—21no—
210C2×#95C4×C3111yescharacteristic, complemented
211#342C22×C3112yes—
212#323—21no—
213#323C22×C3112yes—
214C2×C31—21no—
215C2×C31—21no—
216C2×C31—42no—
217C2×C31—42no—
218C2×C31—161no—
219C2×C31#150711yescharacteristic
220C2×C31#212111yescharacteristic
221C2×C31#212611yescharacteristic
222C22×D4—21no—
223C22×D4—21no—
224C22×D4C2×C4×C3111yescharacteristic
225C22×D4D4×C3111yescharacteristic
226C23×C4—21no—
227C23×C4C2×C4×C3111yescharacteristic
228C23×C4D4×C3111yescharacteristic
229#121—44no—
230#121—41no—
231#121—41no—
232C4×D4—41no—
233C4×D4—41no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4C2×C4×C3111yescharacteristic
236C2×C4⋊C4C2×C4×C3111yescharacteristic
237C2×C22⋊C4—22no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—21no—
240C2×C22⋊C4—21no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4D4×C3111yescharacteristic
244C2×C22⋊C4C23×C3111yescharacteristic
245C2×C42—41no—
246C2×C42D4×C3111yescharacteristic
247C4⋊C8—41no—
248#99—24no—
249C22⋊C8—22no—
250#97—41no—
251#95—21no—
252#95—21no—
253#95—21no—
254#95—41no—
255#95C2×C4×C3111yescharacteristic
256#95C2×C4×C3111yescharacteristic
257C31#1177511yescharacteristic, direct product factor, Sylow
258C24—21no—
259C24C22⋊C4×C3111yescharacteristic
260C24C2×D4×C3111yescharacteristic
261C2×D4—22no—
262C2×D4—22no—
263C2×D4—41no—
264C2×D4—41no—
265C2×D4—42no—
266C2×D4—42no—
267C2×D4—42no—
268C2×D4—42no—
269C2×D4—42no—
270C2×D4—81no—
271C2×D4—81no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—42no—
280C22×C4—42no—
281C22×C4—42no—
282C22×C4—81no—
283C22×C4—81no—
284C22×C4—81no—
285C22×C4C22⋊C4×C3111yescharacteristic
286C22×C4C22⋊C4×C3111yescharacteristic
287C22×C4C22⋊C4×C3111yescharacteristic
288C22×C4C22×C4×C3111yescharacteristic
289C22×C4C2×D4×C3111yescharacteristic
290C2×C8—42no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—42no—
294C22⋊C4—24no—
295C22⋊C4—41no—
296C22⋊C4—41no—
297C22⋊C4—42no—
298C22⋊C4—42no—
299C22⋊C4—42no—
300C22⋊C4—42no—
301C22⋊C4—41no—
302C22⋊C4—41no—
303C22⋊C4—81no—
304C42—21no—
305C42—21no—
306C42—82no—
307C23—21no—
308C23—21no—
309C23—21no—
310C23—21no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23C31×#10412yes—
323C23C2×C22⋊C4×C3111yescharacteristic
324C23C31×AGL(1,ℤ/8)12yes—
325D4—44no—
326D4—84no—
327D4—82no—
328D4—84no—
329C2×C4—22no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—41no—
337C2×C4—42no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—44no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—81no—
351C2×C4—81no—
352C2×C4—81no—
353C2×C4—84no—
354C2×C4—82no—
355C2×C4—82no—
356C2×C4C31×#9911yescharacteristic
357C2×C4C31×#9911yescharacteristic
358C8—82no—
359C22—21no—
360C22—21no—
361C22—22no—
362C22—22no—
363C22—42no—
364C22—42no—
365C22—42no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—81no—
371C22—81no—
372C22—81no—
373C22—81no—
374C22—81no—
375C22—81no—
376C22—81no—
377C22—81no—
378C22C2×C31×#9911yescharacteristic
379C22C31×#41811yescharacteristic
380C22C2×C31×#10411yescharacteristic
381C4—21no—
382C4—21no—
383C4—42no—
384C4—41no—
385C4—41no—
386C4—41no—
387C4—41no—
388C4—81no—
389C4—84no—
390C4—81no—
391C2—21no—
392C2—21no—
393C2—42no—
394C2—42no—
395C2—161no—
396C2C31×#150711yescharacteristic
397C2C31×#212111yescharacteristic
398C2C31×#212611yescharacteristic
subgroupG/H
center, socleC22×C31C2×#99
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C22⋊C4C23×C31
prime radicalC31×#2543C2
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C22×C4×C31 ◁ C2×C4×D4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×C31×#99C2semidirect
3. C31×#1466C2semidirect
4. C31×#1344C2semidirect
5. C31×#1343C2semidirect
7. C2×C31×#121C4semidirect
11. C31×#398C4semidirect
13. C31×#394C4semidirect
19. C2×C31×#95C4semidirect
107. #11775C31direct (N × H)
161. C4×#99C2×C31semidirect
162. #1466C2×C31semidirect
163. #1344C2×C31semidirect
164. #1343C2×C31semidirect
198. C2×#121C4×C31semidirect
202. #398C4×C31semidirect
204. #394C4×C31semidirect
210. C2×#95C4×C31semidirect
257. C31#11775direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#25432
C4×C31×#992
C31×#14662
C31×#13442
C31×#13432
#1177531