Finite Group Databasebeta

← C31×#9962 #21466721

Subgroups — C31×#9962 #21466721

Order 7936.

1160 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 1160 conjugacy classes of subgroups — too many to draw. Only its 138 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
1C2×C31×#447C212yesmaximal, complemented
2C31×#2656C211yesmaximal, characteristic, complemented
3C2×C31×#327C212yesmaximal, complemented
4C31×#1438C211yesmaximal, characteristic, complemented
5C31×#1280C211yesmaximal, characteristic, complemented
6C23×D4×C31C2211yescharacteristic
7C22×D8×C31—22no—
8C2×C31×#121—22no—
9C2×C31×#121C2212yes—
10C22×C22⋊C4×C31—22no—
11C31×#447—24no—
12C31×#447—24no—
13C2×C31×#102—22no—
14C2×C31×C22⋊C8C2212yes—
15C31×#399—22no—
16C31×#392—22no—
17C2×C31×#95C2211yescharacteristic
18C2×C31×#95C2211yescharacteristic
19C31×#327—24no—
20C25×C31—21no—
21C22×D4×C31—22no—
22C22×D4×C31—22no—
23C22×D4×C31—22no—
24C22×D4×C31—22no—
25C22×D4×C31—21no—
26C22×D4×C31—44no—
27C22×D4×C31D412yes—
28C22×D4×C31D412yescomplemented
29C23×C4×C31—21no—
30C23×C4×C31D412yes—
31C23×C4×C31C2311yescharacteristic
32C2×D8×C31—28no—
33C2×D8×C31—48no—
34C22×C8×C31—22no—
35C31×#121—22no—
36C31×#121—22no—
37C31×#121—22no—
38C31×#121—22no—
39C31×#121—44no—
40C31×#121—44no—
41C2×C4⋊C4×C31—22no—
42C2×C4⋊C4×C31D412yes—
43C2×C22⋊C4×C31—24no—
44C2×C22⋊C4×C31—22no—
45C2×C22⋊C4×C31—44no—
46C2×C22⋊C4×C31—44no—
47C2×C22⋊C4×C31—44no—
48C31×#102—28no—
49C31×C22⋊C8—22no—
50C31×C22⋊C8D414yescomplemented
51C31×#95—22no—
52C31×#95—22no—
53C24×C31—24no—
54C24×C31—22no—
55C24×C31—22no—
56C24×C31—42no—
57C24×C31—42no—
58C24×C31—42no—
59C24×C31—41no—
60C24×C31—41no—
61C24×C31—42no—
62C24×C31—42no—
63C24×C31C2×D411yescharacteristic
64C2×D4×C31—28no—
65C2×D4×C31—24no—
66C2×D4×C31—22no—
67C2×D4×C31—22no—
68C2×D4×C31—44no—
69C2×D4×C31—44no—
70C2×D4×C31—44no—
71C2×D4×C31—44no—
72C2×D4×C31—48no—
73C2×D4×C31—44no—
74C2×D4×C31—42no—
75C2×D4×C31—42no—
76C2×D4×C31—44no—
77C2×D4×C31—44no—
78C2×D4×C31—42no—
79C2×D4×C31—82no—
80C2×D4×C31—82no—
81C22×C4×C31—22no—
82C22×C4×C31—22no—
83C22×C4×C31—22no—
84C22×C4×C31—22no—
85C22×C4×C31—42no—
86C22×C4×C31—42no—
87C22×C4×C31—42no—
88C22×C4×C31—42no—
89C22×C4×C31—41no—
90C22×C4×C31—41no—
91C22×C4×C31—42no—
92C22×C4×C31D814yescomplemented
93C22×C4×C31C2×D412yes—
94C22×C4×C31C2×D411yescharacteristic
95C22×C4×C31C2×D412yes—
96C22×C4×C31#4111yescharacteristic
97D8×C31—416no—
98C2×C8×C31—24no—
99C2×C8×C31—44no—
100C4⋊C4×C31—22no—
101C4⋊C4×C31—22no—
102C4⋊C4×C31—44no—
103C22⋊C4×C31—48no—
104C22⋊C4×C31—416no—
105C22⋊C4×C31—42no—
106C22⋊C4×C31—42no—
107#9962C3111yesmaximal, characteristic, direct product factor, Sylow
108C23×C31—21no—
109C23×C31—21no—
110C23×C31—22no—
111C23×C31—24no—
112C23×C31—44no—
113C23×C31—44no—
114C23×C31—42no—
115C23×C31—44no—
116C23×C31—44no—
117C23×C31—44no—
118C23×C31—44no—
119C23×C31—42no—
120C23×C31—44no—
121C23×C31—44no—
122C23×C31—42no—
123C23×C31—44no—
124C23×C31—42no—
125C23×C31—42no—
126C23×C31—44no—
127C23×C31—82no—
128C23×C31—82no—
129C23×C31—82no—
130C23×C31—82no—
131C23×C31—82no—
132C23×C31—82no—
133C23×C31—81no—
134C23×C31—81no—
135C23×C31—81no—
136C23×C31—81no—
137C23×C31#12011yescharacteristic
138C23×C31#12111yescharacteristic
139C23×C31#12711yescharacteristic
140C23×C31C2×D812yes—
141C23×C31AGL(1,ℤ/8)12yes—
142D4×C31—28no—
143D4×C31—44no—
144D4×C31—48no—
145D4×C31—44no—
146D4×C31—82no—
147D4×C31—88no—
148D4×C31—84no—
149D4×C31—82no—
150D4×C31—82no—
151C2×C4×C31—24no—
152C2×C4×C31—24no—
153C2×C4×C31—41no—
154C2×C4×C31—42no—
155C2×C4×C31—41no—
156C2×C4×C31—42no—
157C2×C4×C31—42no—
158C2×C4×C31—44no—
159C2×C4×C31—44no—
160C2×C4×C31—42no—
161C2×C4×C31—42no—
162C2×C4×C31—44no—
163C2×C4×C31—82no—
164C2×C4×C31—82no—
165C2×C4×C31—81no—
166C2×C4×C31—81no—
167C2×C4×C31#12012yes—
168C2×C4×C31#12112yes—
169C8×C31—44no—
170C2×#447C2×C3112yescomplemented
171#2656C2×C3111yescharacteristic, complemented
172C2×#327C2×C3112yescomplemented
173#1438C2×C3111yescharacteristic, complemented
174#1280C2×C3111yescharacteristic, complemented
175C22×C31—22no—
176C22×C31—22no—
177C22×C31—22no—
178C22×C31—22no—
179C22×C31—21no—
180C22×C31—21no—
181C22×C31—21no—
182C22×C31—21no—
183C22×C31—48no—
184C22×C31—44no—
185C22×C31—84no—
186C22×C31—84no—
187C22×C31—84no—
188C22×C31—84no—
189C22×C31—84no—
190C22×C31—82no—
191C22×C31—82no—
192C22×C31—84no—
193C22×C31—84no—
194C22×C31—82no—
195C22×C31—82no—
196C22×C31—82no—
197C22×C31#39211yescharacteristic
198C22×C31#44712yes—
199C22×C31#45311yescharacteristic
200C22×C31#45411yescharacteristic
201C22×C31B(4,𝔽2)12yes—
202C22×C31#45912yes—
203C22×C31#49311yescharacteristic
204C22×C31#49611yescharacteristic
205C4×C31—22no—
206C4×C31—22no—
207C4×C31—44no—
208C4×C31—82no—
209C4×C31—82no—
210C23×D4C22×C3111yescharacteristic
211C22×D8—22no—
212C2×#121—22no—
213C2×#121C22×C3112yes—
214C22×C22⋊C4—22no—
215#447—24no—
216#447—24no—
217C2×#102—22no—
218C2×C22⋊C8C22×C3112yes—
219#399—22no—
220#392—22no—
221C2×#95C22×C3111yescharacteristic
222C2×#95C22×C3111yescharacteristic
223#327—24no—
224C2×C31—21no—
225C2×C31—22no—
226C2×C31—21no—
227C2×C31—84no—
228C2×C31—162no—
229C2×C31#159512yes—
230C2×C31#159812yes—
231C2×C31#200611yescharacteristic
232C2×C31#201111yescharacteristic
233C2×C31#202111yescharacteristic
234C25—21no—
235C22×D4—22no—
236C22×D4—22no—
237C22×D4—22no—
238C22×D4—22no—
239C22×D4—21no—
240C22×D4—44no—
241C22×D4D4×C3112yes—
242C22×D4D4×C3112yescomplemented
243C23×C4—21no—
244C23×C4D4×C3112yes—
245C23×C4C23×C3111yescharacteristic
246C2×D8—28no—
247C2×D8—48no—
248C22×C8—22no—
249#121—22no—
250#121—22no—
251#121—22no—
252#121—22no—
253#121—44no—
254#121—44no—
255C2×C4⋊C4—22no—
256C2×C4⋊C4D4×C3112yes—
257C2×C22⋊C4—24no—
258C2×C22⋊C4—22no—
259C2×C22⋊C4—44no—
260C2×C22⋊C4—44no—
261C2×C22⋊C4—44no—
262#102—28no—
263C22⋊C8—22no—
264C22⋊C8D4×C3114yescomplemented
265#95—22no—
266#95—22no—
267C31#996211yescharacteristic, direct product factor, Sylow
268C24—24no—
269C24—22no—
270C24—22no—
271C24—42no—
272C24—42no—
273C24—42no—
274C24—41no—
275C24—41no—
276C24—42no—
277C24—42no—
278C24C2×D4×C3111yescharacteristic
279C2×D4—28no—
280C2×D4—24no—
281C2×D4—22no—
282C2×D4—22no—
283C2×D4—44no—
284C2×D4—44no—
285C2×D4—44no—
286C2×D4—44no—
287C2×D4—48no—
288C2×D4—44no—
289C2×D4—42no—
290C2×D4—42no—
291C2×D4—44no—
292C2×D4—44no—
293C2×D4—42no—
294C2×D4—82no—
295C2×D4—82no—
296C22×C4—22no—
297C22×C4—22no—
298C22×C4—22no—
299C22×C4—22no—
300C22×C4—42no—
301C22×C4—42no—
302C22×C4—42no—
303C22×C4—42no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—42no—
307C22×C4D8×C3114yescomplemented
308C22×C4C2×D4×C3112yes—
309C22×C4C2×D4×C3111yescharacteristic
310C22×C4C2×D4×C3112yes—
311C22×C4#41×C3111yescharacteristic
312D8—416no—
313C2×C8—24no—
314C2×C8—44no—
315C4⋊C4—22no—
316C4⋊C4—22no—
317C4⋊C4—44no—
318C22⋊C4—48no—
319C22⋊C4—416no—
320C22⋊C4—42no—
321C22⋊C4—42no—
322C23—21no—
323C23—21no—
324C23—22no—
325C23—24no—
326C23—44no—
327C23—44no—
328C23—42no—
329C23—44no—
330C23—44no—
331C23—44no—
332C23—44no—
333C23—44no—
334C23—44no—
335C23—42no—
336C23—44no—
337C23—42no—
338C23—42no—
339C23—44no—
340C23—42no—
341C23—82no—
342C23—82no—
343C23—82no—
344C23—82no—
345C23—82no—
346C23—82no—
347C23—81no—
348C23—81no—
349C23—81no—
350C23—81no—
351C23C31×#12011yescharacteristic
352C23C31×#12111yescharacteristic
353C23C31×#12711yescharacteristic
354C23C2×D8×C3112yes—
355C23C31×AGL(1,ℤ/8)12yes—
356D4—28no—
357D4—44no—
358D4—48no—
359D4—44no—
360D4—82no—
361D4—88no—
362D4—84no—
363D4—82no—
364D4—82no—
365C2×C4—24no—
366C2×C4—24no—
367C2×C4—41no—
368C2×C4—42no—
369C2×C4—41no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—44no—
373C2×C4—44no—
374C2×C4—42no—
375C2×C4—44no—
376C2×C4—42no—
377C2×C4—82no—
378C2×C4—82no—
379C2×C4—81no—
380C2×C4—81no—
381C2×C4C31×#12012yes—
382C2×C4C31×#12112yes—
383C8—44no—
384C22—22no—
385C22—22no—
386C22—22no—
387C22—22no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—48no—
393C22—44no—
394C22—84no—
395C22—84no—
396C22—84no—
397C22—84no—
398C22—84no—
399C22—82no—
400C22—82no—
401C22—84no—
402C22—84no—
403C22—82no—
404C22—82no—
405C22—82no—
406C22C31×#39211yescharacteristic
407C22C31×#44712yes—
408C22C31×#45311yescharacteristic
409C22C31×#45411yescharacteristic
410C22C31×B(4,𝔽2)12yes—
411C22C31×#45912yes—
412C22C31×#49311yescharacteristic
413C22C31×#49611yescharacteristic
414C4—22no—
415C4—22no—
416C4—44no—
417C4—82no—
418C4—82no—
419C2—21no—
420C2—22no—
421C2—21no—
422C2—84no—
423C2—162no—
424C2C31×#159512yes—
425C2C31×#159812yes—
426C2C31×#200611yescharacteristic
427C2C31×#201111yescharacteristic
428C2C31×#202111yescharacteristic
subgroupG/H
center, socleC23×C31#120
commutator, Frattini, cosocleC23×C4C23×C31
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#447C2semidirect
2. C31×#2656C2semidirect
3. C2×C31×#327C2semidirect
4. C31×#1438C2semidirect
5. C31×#1280C2semidirect
28. C22×D4×C31D4semidirect
50. C31×C22⋊C8D4semidirect
92. C22×C4×C31D8semidirect
107. #9962C31direct (N × H)
170. C2×#447C2×C31semidirect
171. #2656C2×C31semidirect
172. C2×#327C2×C31semidirect
173. #1438C2×C31semidirect
174. #1280C2×C31semidirect
242. C22×D4D4×C31semidirect
264. C22⋊C8D4×C31semidirect
267. C31#9962direct (N × H)
307. C22×C4D8×C31semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#4472
C31×#26562
C2×C31×#3272
C31×#14382
C31×#12802
#996231