Finite Group Databasebeta

← C31×#11839 #21468598

Subgroups — C31×#11839 #21468598

Order 7936.

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

normal subgroups only

This group has 698 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×#2404C211yesmaximal, characteristic
2C31×#1819C211yesmaximal, characteristic, complemented
3C2×C31×#323C211yesmaximal, characteristic, complemented
4C31×#1351C212yesmaximal, complemented
5C31×#1343C212yesmaximal, complemented
6C22×#41×C31C411yescharacteristic, complemented
7C2×C31×#120—21no—
8C22×C22⋊C4×C31C2211yescharacteristic
9C2×C31×C22⋊C8—21no—
10C31×#393C411yescharacteristic, complemented
11C31×#393C2211yescharacteristic
12C31×#392C411yescharacteristic, complemented
13C31×#392C2211yescharacteristic
14C31×#386—21no—
15C31×#386—21no—
16C31×#386—21no—
17C31×#381C411yescharacteristic, complemented
18C31×#379—21no—
19C31×#342—21no—
20C31×#342C2212yes—
21C31×#323—21no—
22C31×#323C2212yes—
23C25×C31D411yescharacteristic
24C2×#41×C31—41no—
25C2×#41×C31—41no—
26C2×#41×C31—44no—
27C22×Q8×C31C2×C411yescharacteristic
28C22×D4×C31—21no—
29C22×D4×C31—21no—
30C22×D4×C31—21no—
31C22×D4×C31C2×C411yescharacteristic
32C23×C4×C31—21no—
33C23×C4×C31C2×C411yescharacteristic
34C23×C4×C31D411yescharacteristic
35C22×C8×C31—41no—
36C31×#120—44no—
37C2×C22⋊C4×C31—21no—
38C2×C22⋊C4×C31—21no—
39C2×C22⋊C4×C31—21no—
40C2×C22⋊C4×C31—22no—
41C2×C22⋊C4×C31—21no—
42C2×C22⋊C4×C31—21no—
43C2×C22⋊C4×C31—41no—
44C2×C22⋊C4×C31—41no—
45C2×C22⋊C4×C31—41no—
46C2×C22⋊C4×C31—41no—
47C2×C22⋊C4×C31C2×C411yescharacteristic
48C2×C22⋊C4×C31D411yescharacteristic
49C2×C22⋊C4×C31D411yescharacteristic
50C2×C22⋊C4×C31C2311yescharacteristic
51C31×C22⋊C8—22no—
52C31×C22⋊C8—41no—
53C31×#95—21no—
54C31×#95—21no—
55C31×#95—21no—
56C31×#95C2×C411yescharacteristic
57C31×#95C2×C411yescharacteristic
58C24×C31—21no—
59C24×C31—21no—
60C24×C31—21no—
61C24×C31—22no—
62C24×C31—41no—
63C24×C31—42no—
64C24×C31—81no—
65C24×C31C22⋊C411yescharacteristic
66C24×C31C22⋊C411yescharacteristic
67C24×C31C2×D411yescharacteristic
68#41×C31—44no—
69#41×C31—44no—
70#41×C31—44no—
71#41×C31—44no—
72C2×Q8×C31—42no—
73C2×Q8×C31—41no—
74C2×D4×C31—24no—
75C2×D4×C31—41no—
76C2×D4×C31—42no—
77C2×D4×C31—41no—
78C2×D4×C31—41no—
79C2×D4×C31—42no—
80C2×D4×C31—42no—
81C2×D4×C31—42no—
82C2×D4×C31—42no—
83C2×D4×C31—42no—
84C2×D4×C31—81no—
85C2×D4×C31—81no—
86C22×C4×C31—21no—
87C22×C4×C31—21no—
88C22×C4×C31—21no—
89C22×C4×C31—21no—
90C22×C4×C31—21no—
91C22×C4×C31—21no—
92C22×C4×C31—21no—
93C22×C4×C31—42no—
94C22×C4×C31—42no—
95C22×C4×C31—42no—
96C22×C4×C31—42no—
97C22×C4×C31—42no—
98C22×C4×C31—81no—
99C22×C4×C31C22⋊C411yescharacteristic
100C22×C4×C31C22⋊C411yescharacteristic
101C22×C4×C31C22×C411yescharacteristic
102C22×C4×C31C2×D411yescharacteristic
103C2×C8×C31—42no—
104C2×C8×C31—82no—
105C22⋊C4×C31—41no—
106C22⋊C4×C31—41no—
107C22⋊C4×C31—41no—
108C22⋊C4×C31—41no—
109C22⋊C4×C31—42no—
110C22⋊C4×C31—42no—
111C22⋊C4×C31—42no—
112C22⋊C4×C31—42no—
113C22⋊C4×C31—42no—
114C22⋊C4×C31—81no—
115C22⋊C4×C31—81no—
116C22⋊C4×C31—82no—
117C22⋊C4×C31—82no—
118#11839C3111yesmaximal, characteristic, direct product factor, Sylow
119C23×C31—22no—
120C23×C31—21no—
121C23×C31—21no—
122C23×C31—21no—
123C23×C31—21no—
124C23×C31—22no—
125C23×C31—21no—
126C23×C31—21no—
127C23×C31—21no—
128C23×C31—41no—
129C23×C31—42no—
130C23×C31—42no—
131C23×C31—41no—
132C23×C31—41no—
133C23×C31—41no—
134C23×C31—41no—
135C23×C31—41no—
136C23×C31—41no—
137C23×C31—42no—
138C23×C31—41no—
139C23×C31—42no—
140C23×C31—41no—
141C23×C31—41no—
142C23×C31—41no—
143C23×C31—81no—
144C23×C31—81no—
145C23×C31—84no—
146C23×C31—84no—
147C23×C31#9911yescharacteristic
148C23×C31#9911yescharacteristic
149C23×C31C2×C22⋊C411yescharacteristic
150C23×C31#13512yes—
151Q8×C31—42no—
152Q8×C31—42no—
153D4×C31—44no—
154D4×C31—42no—
155D4×C31—42no—
156D4×C31—44no—
157D4×C31—84no—
158D4×C31—84no—
159C2×C4×C31—22no—
160C2×C4×C31—21no—
161C2×C4×C31—21no—
162C2×C4×C31—21no—
163C2×C4×C31—21no—
164C2×C4×C31—42no—
165C2×C4×C31—41no—
166C2×C4×C31—42no—
167C2×C4×C31—48no—
168C2×C4×C31—42no—
169C2×C4×C31—41no—
170C2×C4×C31—41no—
171C2×C4×C31—41no—
172C2×C4×C31—41no—
173C2×C4×C31—41no—
174C2×C4×C31—41no—
175C2×C4×C31—41no—
176C2×C4×C31—41no—
177C2×C4×C31—41no—
178C2×C4×C31—41no—
179C2×C4×C31—41no—
180C2×C4×C31—81no—
181C2×C4×C31—82no—
182C2×C4×C31—82no—
183C2×C4×C31—82no—
184C8×C31—82no—
185#2404C2×C3111yescharacteristic
186#1819C2×C3111yescharacteristic, complemented
187C2×#323C2×C3111yescharacteristic, complemented
188#1351C2×C3112yescomplemented
189#1343C2×C3112yescomplemented
190C22×C31—21no—
191C22×C31—21no—
192C22×C31—21no—
193C22×C31—21no—
194C22×C31—21no—
195C22×C31—21no—
196C22×C31—22no—
197C22×C31—21no—
198C22×C31—42no—
199C22×C31—42no—
200C22×C31—42no—
201C22×C31—42no—
202C22×C31—42no—
203C22×C31—42no—
204C22×C31—41no—
205C22×C31—41no—
206C22×C31—42no—
207C22×C31—41no—
208C22×C31—41no—
209C22×C31—41no—
210C22×C31—81no—
211C22×C31—84no—
212C22×C31—81no—
213C22×C31—81no—
214C22×C31—81no—
215C22×C31—84no—
216C22×C31—81no—
217C22×C31—81no—
218C22×C31AΣL(1,𝔽16)12yes—
219C22×C31C2×#9911yescharacteristic
220C22×C31#41611yescharacteristic
221C22×C31#42111yescharacteristic
222C4×C31—41no—
223C4×C31—42no—
224C4×C31—41no—
225C4×C31—41no—
226C4×C31—41no—
227C4×C31—81no—
228C4×C31—81no—
229C4×C31—162no—
230C22×#41C4×C3111yescharacteristic, complemented
231C2×#120—21no—
232C22×C22⋊C4C22×C3111yescharacteristic
233C2×C22⋊C8—21no—
234#393C4×C3111yescharacteristic, complemented
235#393C22×C3111yescharacteristic
236#392C4×C3111yescharacteristic, complemented
237#392C22×C3111yescharacteristic
238#386—21no—
239#386—21no—
240#386—21no—
241#381C4×C3111yescharacteristic, complemented
242#379—21no—
243#342—21no—
244#342C22×C3112yes—
245#323—21no—
246#323C22×C3112yes—
247C2×C31—21no—
248C2×C31—21no—
249C2×C31—22no—
250C2×C31—42no—
251C2×C31—41no—
252C2×C31—81no—
253C2×C31—82no—
254C2×C31#151611yescharacteristic
255C2×C31C2×AΣL(1,𝔽16)11yescharacteristic
256C2×C31#212711yescharacteristic
257C25D4×C3111yescharacteristic
258C2×#41—41no—
259C2×#41—41no—
260C2×#41—44no—
261C22×Q8C2×C4×C3111yescharacteristic
262C22×D4—21no—
263C22×D4—21no—
264C22×D4—21no—
265C22×D4C2×C4×C3111yescharacteristic
266C23×C4—21no—
267C23×C4C2×C4×C3111yescharacteristic
268C23×C4D4×C3111yescharacteristic
269C22×C8—41no—
270#120—44no—
271C2×C22⋊C4—21no—
272C2×C22⋊C4—21no—
273C2×C22⋊C4—21no—
274C2×C22⋊C4—22no—
275C2×C22⋊C4—21no—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—41no—
278C2×C22⋊C4—41no—
279C2×C22⋊C4—41no—
280C2×C22⋊C4—41no—
281C2×C22⋊C4C2×C4×C3111yescharacteristic
282C2×C22⋊C4D4×C3111yescharacteristic
283C2×C22⋊C4D4×C3111yescharacteristic
284C2×C22⋊C4C23×C3111yescharacteristic
285C22⋊C8—22no—
286C22⋊C8—41no—
287#95—21no—
288#95—21no—
289#95—21no—
290#95C2×C4×C3111yescharacteristic
291#95C2×C4×C3111yescharacteristic
292C31#1183911yescharacteristic, direct product factor, Sylow
293C24—21no—
294C24—21no—
295C24—21no—
296C24—22no—
297C24—41no—
298C24—42no—
299C24—81no—
300C24C22⋊C4×C3111yescharacteristic
301C24C22⋊C4×C3111yescharacteristic
302C24C2×D4×C3111yescharacteristic
303#41—44no—
304#41—44no—
305#41—44no—
306#41—44no—
307C2×Q8—42no—
308C2×Q8—41no—
309C2×D4—24no—
310C2×D4—41no—
311C2×D4—42no—
312C2×D4—41no—
313C2×D4—41no—
314C2×D4—42no—
315C2×D4—42no—
316C2×D4—42no—
317C2×D4—42no—
318C2×D4—42no—
319C2×D4—81no—
320C2×D4—81no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—42no—
329C22×C4—42no—
330C22×C4—42no—
331C22×C4—42no—
332C22×C4—42no—
333C22×C4—81no—
334C22×C4C22⋊C4×C3111yescharacteristic
335C22×C4C22⋊C4×C3111yescharacteristic
336C22×C4C22×C4×C3111yescharacteristic
337C22×C4C2×D4×C3111yescharacteristic
338C2×C8—42no—
339C2×C8—82no—
340C22⋊C4—41no—
341C22⋊C4—41no—
342C22⋊C4—41no—
343C22⋊C4—41no—
344C22⋊C4—42no—
345C22⋊C4—42no—
346C22⋊C4—42no—
347C22⋊C4—42no—
348C22⋊C4—42no—
349C22⋊C4—81no—
350C22⋊C4—81no—
351C22⋊C4—82no—
352C22⋊C4—82no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—22no—
357C23—21no—
358C23—22no—
359C23—21no—
360C23—21no—
361C23—21no—
362C23—41no—
363C23—42no—
364C23—42no—
365C23—41no—
366C23—41no—
367C23—41no—
368C23—41no—
369C23—41no—
370C23—41no—
371C23—42no—
372C23—41no—
373C23—41no—
374C23—41no—
375C23—41no—
376C23—42no—
377C23—81no—
378C23—81no—
379C23—84no—
380C23—84no—
381C23C31×#9911yescharacteristic
382C23C31×#9911yescharacteristic
383C23C2×C22⋊C4×C3111yescharacteristic
384C23C31×#13512yes—
385Q8—42no—
386Q8—42no—
387D4—44no—
388D4—42no—
389D4—42no—
390D4—44no—
391D4—84no—
392D4—84no—
393C2×C4—22no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—42no—
399C2×C4—41no—
400C2×C4—42no—
401C2×C4—48no—
402C2×C4—41no—
403C2×C4—42no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—81no—
415C2×C4—82no—
416C2×C4—82no—
417C2×C4—82no—
418C8—82no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—22no—
426C22—21no—
427C22—42no—
428C22—42no—
429C22—42no—
430C22—42no—
431C22—42no—
432C22—42no—
433C22—41no—
434C22—41no—
435C22—42no—
436C22—41no—
437C22—41no—
438C22—41no—
439C22—81no—
440C22—84no—
441C22—81no—
442C22—81no—
443C22—81no—
444C22—84no—
445C22—81no—
446C22—81no—
447C22C31×AΣL(1,𝔽16)12yes—
448C22C2×C31×#9911yescharacteristic
449C22C31×#41611yescharacteristic
450C22C31×#42111yescharacteristic
451C4—41no—
452C4—42no—
453C4—41no—
454C4—41no—
455C4—41no—
456C4—81no—
457C4—81no—
458C4—162no—
459C2—21no—
460C2—21no—
461C2—22no—
462C2—42no—
463C2—41no—
464C2—81no—
465C2—82no—
466C2C31×#151611yescharacteristic
467C2C2×C31×AΣL(1,𝔽16)11yescharacteristic
468C2C31×#212711yescharacteristic
subgroupG/H
center, socleC22×C31C2×#99
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C22⋊C4C23×C31
prime radicalC31×#2404C2
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C24×C31 ◁ C22×C22⋊C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#1819C2semidirect
3. C2×C31×#323C2semidirect
4. C31×#1351C2semidirect
5. C31×#1343C2semidirect
6. C22×#41×C31C4semidirect
10. C31×#393C4semidirect
12. C31×#392C4semidirect
17. C31×#381C4semidirect
118. #11839C31direct (N × H)
186. #1819C2×C31semidirect
187. C2×#323C2×C31semidirect
188. #1351C2×C31semidirect
189. #1343C2×C31semidirect
230. C22×#41C4×C31semidirect
234. #393C4×C31semidirect
236. #392C4×C31semidirect
241. #381C4×C31semidirect
292. C31#11839direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#24042
C31×#18192
C2×C31×#3232
C31×#13512
C31×#13432
#1183931