Finite Group Databasebeta

← C31×#11799 #21468558

Subgroups — C31×#11799 #21468558

Order 7936.

574 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 574 conjugacy classes of subgroups — too many to draw. Only its 98 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×#2617C211yesmaximal, characteristic
2C31×#1819C211yesmaximal, characteristic, complemented
3C31×#1462C211yesmaximal, characteristic, complemented
4C31×#1344C212yesmaximal, complemented
5C31×#1343C212yesmaximal, complemented
6C2×C31×#121C411yescharacteristic, complemented
7C2×C31×#120—21no—
8C22×C22⋊C4×C31C2211yescharacteristic
9C31×#407—21no—
10C31×#397C411yescharacteristic, complemented
11C31×#397C2211yescharacteristic
12C31×#394—21no—
13C31×#394—21no—
14C31×#392C411yescharacteristic, complemented
15C31×#392C2211yescharacteristic
16C31×#386—21no—
17C31×#380C411yescharacteristic, complemented
18C31×#379—21no—
19C31×#342—21no—
20C31×#342C2212yes—
21C31×#323—21no—
22C31×#323C2212yes—
23C25×C31D411yescharacteristic
24C22×D4×C31—21no—
25C22×D4×C31—21no—
26C22×D4×C31—21no—
27C22×D4×C31C2×C411yescharacteristic
28C23×C4×C31C2×C411yescharacteristic
29C23×C4×C31D411yescharacteristic
30C2×M16×C31—41no—
31C31×#121—41no—
32C31×#121—41no—
33C31×#120—44no—
34C2×C4⋊C4×C31—21no—
35C2×C4⋊C4×C31C2×C411yescharacteristic
36C2×C22⋊C4×C31—21no—
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×#95C2×C411yescharacteristic
56C31×#95C2×C411yescharacteristic
57C24×C31—21no—
58C24×C31—21no—
59C24×C31—22no—
60C24×C31—21no—
61C24×C31—41no—
62C24×C31—81no—
63C24×C31—81no—
64C24×C31C22⋊C411yescharacteristic
65C24×C31C22⋊C411yescharacteristic
66C24×C31C2×D411yescharacteristic
67C2×D4×C31—41no—
68C2×D4×C31—42no—
69C2×D4×C31—42no—
70C2×D4×C31—42no—
71C2×D4×C31—41no—
72C2×D4×C31—41no—
73C2×D4×C31—42no—
74C2×D4×C31—81no—
75C2×D4×C31—81no—
76C2×D4×C31—81no—
77C2×D4×C31—81no—
78C2×D4×C31—81no—
79C22×C4×C31—21no—
80C22×C4×C31—21no—
81C22×C4×C31—21no—
82C22×C4×C31—21no—
83C22×C4×C31—21no—
84C22×C4×C31—21no—
85C22×C4×C31—21no—
86C22×C4×C31—42no—
87C22×C4×C31—81no—
88C22×C4×C31—81no—
89C22×C4×C31C22⋊C411yescharacteristic
90C22×C4×C31C22⋊C411yescharacteristic
91C22×C4×C31C22×C411yescharacteristic
92C22×C4×C31C2×D411yescharacteristic
93M16×C31—82no—
94C2×C8×C31—42no—
95C4⋊C4×C31—41no—
96C4⋊C4×C31—81no—
97C22⋊C4×C31—41no—
98C22⋊C4×C31—41no—
99C22⋊C4×C31—41no—
100C22⋊C4×C31—41no—
101C22⋊C4×C31—42no—
102C22⋊C4×C31—42no—
103C22⋊C4×C31—42no—
104C22⋊C4×C31—42no—
105C22⋊C4×C31—42no—
106C22⋊C4×C31—42no—
107C22⋊C4×C31—81no—
108C22⋊C4×C31—81no—
109C22⋊C4×C31—82no—
110C22⋊C4×C31—82no—
111#11799C3111yesmaximal, characteristic, direct product factor, Sylow
112C23×C31—21no—
113C23×C31—21no—
114C23×C31—21no—
115C23×C31—21no—
116C23×C31—21no—
117C23×C31—21no—
118C23×C31—21no—
119C23×C31—41no—
120C23×C31—41no—
121C23×C31—42no—
122C23×C31—42no—
123C23×C31—41no—
124C23×C31—41no—
125C23×C31—41no—
126C23×C31—41no—
127C23×C31—42no—
128C23×C31—42no—
129C23×C31—41no—
130C23×C31—41no—
131C23×C31—41no—
132C23×C31—41no—
133C23×C31—41no—
134C23×C31—41no—
135C23×C31—41no—
136C23×C31—81no—
137C23×C31—81no—
138C23×C31—84no—
139C23×C31—84no—
140C23×C31#9911yescharacteristic
141C23×C31#9911yescharacteristic
142C23×C31C2×C22⋊C411yescharacteristic
143C23×C31AGL(1,ℤ/8)12yes—
144D4×C31—82no—
145D4×C31—82no—
146D4×C31—82no—
147D4×C31—84no—
148D4×C31—84no—
149C2×C4×C31—21no—
150C2×C4×C31—21no—
151C2×C4×C31—21no—
152C2×C4×C31—21no—
153C2×C4×C31—42no—
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—41no—
164C2×C4×C31—41no—
165C2×C4×C31—41no—
166C2×C4×C31—41no—
167C2×C4×C31—81no—
168C2×C4×C31—81no—
169C2×C4×C31—81no—
170C2×C4×C31—82no—
171C2×C4×C31—82no—
172C2×C4×C31—82no—
173C8×C31—82no—
174#2617C2×C3111yescharacteristic
175#1819C2×C3111yescharacteristic, complemented
176#1462C2×C3111yescharacteristic, complemented
177#1344C2×C3112yescomplemented
178#1343C2×C3112yescomplemented
179C22×C31—21no—
180C22×C31—21no—
181C22×C31—21no—
182C22×C31—21no—
183C22×C31—21no—
184C22×C31—21no—
185C22×C31—22no—
186C22×C31—21no—
187C22×C31—21no—
188C22×C31—42no—
189C22×C31—42no—
190C22×C31—42no—
191C22×C31—42no—
192C22×C31—41no—
193C22×C31—41no—
194C22×C31—41no—
195C22×C31—41no—
196C22×C31—41no—
197C22×C31—81no—
198C22×C31—81no—
199C22×C31—81no—
200C22×C31—81no—
201C22×C31—81no—
202C22×C31—81no—
203C22×C31—84no—
204C22×C31—84no—
205C22×C31—81no—
206C22×C31—81no—
207C22×C31—81no—
208C22×C31C2×#9911yescharacteristic
209C22×C31#41811yescharacteristic
210C22×C31#42111yescharacteristic
211C4×C31—41no—
212C4×C31—41no—
213C4×C31—41no—
214C4×C31—41no—
215C4×C31—81no—
216C4×C31—81no—
217C4×C31—81no—
218C4×C31—162no—
219C2×#121C4×C3111yescharacteristic, complemented
220C2×#120—21no—
221C22×C22⋊C4C22×C3111yescharacteristic
222#407—21no—
223#397C4×C3111yescharacteristic, complemented
224#397C22×C3111yescharacteristic
225#394—21no—
226#394—21no—
227#392C4×C3111yescharacteristic, complemented
228#392C22×C3111yescharacteristic
229#386—21no—
230#380C4×C3111yescharacteristic, complemented
231#379—21no—
232#342—21no—
233#342C22×C3112yes—
234#323—21no—
235#323C22×C3112yes—
236C2×C31—21no—
237C2×C31—21no—
238C2×C31—42no—
239C2×C31—41no—
240C2×C31—41no—
241C2×C31—81no—
242C2×C31—161no—
243C2×C31#151011yescharacteristic
244C2×C31#212111yescharacteristic
245C2×C31#212711yescharacteristic
246C25D4×C3111yescharacteristic
247C22×D4—21no—
248C22×D4—21no—
249C22×D4—21no—
250C22×D4C2×C4×C3111yescharacteristic
251C23×C4C2×C4×C3111yescharacteristic
252C23×C4D4×C3111yescharacteristic
253C2×M16—41no—
254#121—41no—
255#121—41no—
256#120—44no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4C2×C4×C3111yescharacteristic
259C2×C22⋊C4—21no—
260C2×C22⋊C4—21no—
261C2×C22⋊C4—21no—
262C2×C22⋊C4—21no—
263C2×C22⋊C4—22no—
264C2×C22⋊C4—21no—
265C2×C22⋊C4—21no—
266C2×C22⋊C4—41no—
267C2×C22⋊C4—41no—
268C2×C22⋊C4—41no—
269C2×C22⋊C4—41no—
270C2×C22⋊C4C2×C4×C3111yescharacteristic
271C2×C22⋊C4D4×C3111yescharacteristic
272C2×C22⋊C4D4×C3111yescharacteristic
273C2×C22⋊C4C23×C3111yescharacteristic
274C22⋊C8—22no—
275C22⋊C8—41no—
276#95—21no—
277#95—21no—
278#95C2×C4×C3111yescharacteristic
279#95C2×C4×C3111yescharacteristic
280C31#1179911yescharacteristic, direct product factor, Sylow
281C24—21no—
282C24—21no—
283C24—22no—
284C24—21no—
285C24—41no—
286C24—81no—
287C24—81no—
288C24C22⋊C4×C3111yescharacteristic
289C24C22⋊C4×C3111yescharacteristic
290C24C2×D4×C3111yescharacteristic
291C2×D4—41no—
292C2×D4—42no—
293C2×D4—42no—
294C2×D4—42no—
295C2×D4—41no—
296C2×D4—41no—
297C2×D4—42no—
298C2×D4—81no—
299C2×D4—81no—
300C2×D4—81no—
301C2×D4—81no—
302C2×D4—81no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—42no—
311C22×C4—81no—
312C22×C4—81no—
313C22×C4C22⋊C4×C3111yescharacteristic
314C22×C4C22⋊C4×C3111yescharacteristic
315C22×C4C22×C4×C3111yescharacteristic
316C22×C4C2×D4×C3111yescharacteristic
317M16—82no—
318C2×C8—42no—
319C4⋊C4—41no—
320C4⋊C4—81no—
321C22⋊C4—41no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C22⋊C4—41no—
325C22⋊C4—42no—
326C22⋊C4—42no—
327C22⋊C4—42no—
328C22⋊C4—42no—
329C22⋊C4—42no—
330C22⋊C4—42no—
331C22⋊C4—81no—
332C22⋊C4—81no—
333C22⋊C4—82no—
334C22⋊C4—82no—
335C23—21no—
336C23—21no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—41no—
343C23—41no—
344C23—42no—
345C23—42no—
346C23—41no—
347C23—41no—
348C23—41no—
349C23—41no—
350C23—42no—
351C23—42no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23—81no—
360C23—81no—
361C23—84no—
362C23—84no—
363C23C31×#9911yescharacteristic
364C23C31×#9911yescharacteristic
365C23C2×C22⋊C4×C3111yescharacteristic
366C23C31×AGL(1,ℤ/8)12yes—
367D4—82no—
368D4—82no—
369D4—82no—
370D4—84no—
371D4—84no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—42no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—81no—
391C2×C4—81no—
392C2×C4—81no—
393C2×C4—82no—
394C2×C4—82no—
395C2×C4—82no—
396C8—82no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—22no—
404C22—21no—
405C22—21no—
406C22—42no—
407C22—42no—
408C22—42no—
409C22—42no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—81no—
416C22—81no—
417C22—81no—
418C22—81no—
419C22—81no—
420C22—81no—
421C22—84no—
422C22—84no—
423C22—81no—
424C22—81no—
425C22—81no—
426C22C2×C31×#9911yescharacteristic
427C22C31×#41811yescharacteristic
428C22C31×#42111yescharacteristic
429C4—41no—
430C4—41no—
431C4—41no—
432C4—41no—
433C4—81no—
434C4—81no—
435C4—81no—
436C4—162no—
437C2—21no—
438C2—21no—
439C2—42no—
440C2—41no—
441C2—41no—
442C2—81no—
443C2—161no—
444C2C31×#151011yescharacteristic
445C2C31×#212111yescharacteristic
446C2C31×#212711yescharacteristic
subgroupG/H
center, socleC22×C31C2×#99
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C22⋊C4C23×C31
prime radicalC31×#2617C2
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. C31×#1462C2semidirect
4. C31×#1344C2semidirect
5. C31×#1343C2semidirect
6. C2×C31×#121C4semidirect
10. C31×#397C4semidirect
14. C31×#392C4semidirect
17. C31×#380C4semidirect
111. #11799C31direct (N × H)
175. #1819C2×C31semidirect
176. #1462C2×C31semidirect
177. #1344C2×C31semidirect
178. #1343C2×C31semidirect
219. C2×#121C4×C31semidirect
223. #397C4×C31semidirect
227. #392C4×C31semidirect
230. #380C4×C31semidirect
280. C31#11799direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#26172
C31×#18192
C31×#14622
C31×#13442
C31×#13432
#1179931