Finite Group Databasebeta

← C31×#11843 #21468602

Subgroups — C31×#11843 #21468602

Order 7936.

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

normal subgroups only

This group has 620 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×#2539C211yesmaximal, characteristic
2C31×#1819C211yesmaximal, characteristic, complemented
3C2×C31×#323C211yesmaximal, characteristic, complemented
4C31×#1352C212yesmaximal, complemented
5C31×#1343C212yesmaximal, complemented
6C2×C31×#123—21no—
7C2×C31×#121C411yescharacteristic, complemented
8C2×C31×#120—21no—
9C22×C22⋊C4×C31C2211yescharacteristic
10C2×C31×C22⋊C8—21no—
11C31×#399C411yescharacteristic, complemented
12C31×#399C2211yescharacteristic
13C31×#392C411yescharacteristic, complemented
14C31×#392C2211yescharacteristic
15C31×#390—21no—
16C31×#390—21no—
17C31×#379—21no—
18C4×C22⋊C4×C31C411yescharacteristic, complemented
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
30C22×C8×C31—41no—
31C31×#123—44no—
32C31×#121—41no—
33C31×#121—41no—
34C31×#120—44no—
35C2×C4⋊C4×C31—21no—
36C2×C4⋊C4×C31—21no—
37C2×C4⋊C4×C31C2×C411yescharacteristic
38C2×C22⋊C4×C31—21no—
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×C31—22no—
45C2×C22⋊C4×C31—41no—
46C2×C22⋊C4×C31—41no—
47C2×C22⋊C4×C31—41no—
48C2×C22⋊C4×C31—41no—
49C2×C22⋊C4×C31C2×C411yescharacteristic
50C2×C22⋊C4×C31D411yescharacteristic
51C2×C22⋊C4×C31D411yescharacteristic
52C2×C22⋊C4×C31C2311yescharacteristic
53C2×C42×C31—21no—
54C31×C22⋊C8—22no—
55C31×C22⋊C8—41no—
56C31×#95C2×C411yescharacteristic
57C31×#95C2×C411yescharacteristic
58C24×C31—21no—
59C24×C31—21no—
60C24×C31—22no—
61C24×C31—21no—
62C24×C31—41no—
63C24×C31—42no—
64C24×C31—81no—
65C24×C31C22⋊C411yescharacteristic
66C24×C31C22⋊C411yescharacteristic
67C24×C31C2×D411yescharacteristic
68C2×D4×C31—42no—
69C2×D4×C31—42no—
70C2×D4×C31—41no—
71C2×D4×C31—42no—
72C2×D4×C31—42no—
73C2×D4×C31—42no—
74C2×D4×C31—41no—
75C2×D4×C31—41no—
76C2×D4×C31—42no—
77C2×D4×C31—81no—
78C2×D4×C31—81no—
79C2×D4×C31—81no—
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—21no—
87C22×C4×C31—42no—
88C22×C4×C31—42no—
89C22×C4×C31—81no—
90C22×C4×C31C22⋊C411yescharacteristic
91C22×C4×C31C22⋊C411yescharacteristic
92C22×C4×C31C22×C411yescharacteristic
93C22×C4×C31C2×D411yescharacteristic
94C2×C8×C31—42no—
95C2×C8×C31—82no—
96C4⋊C4×C31—42no—
97C4⋊C4×C31—42no—
98C4⋊C4×C31—41no—
99C22⋊C4×C31—24no—
100C22⋊C4×C31—41no—
101C22⋊C4×C31—41no—
102C22⋊C4×C31—41no—
103C22⋊C4×C31—41no—
104C22⋊C4×C31—42no—
105C22⋊C4×C31—42no—
106C22⋊C4×C31—42no—
107C22⋊C4×C31—42no—
108C22⋊C4×C31—42no—
109C22⋊C4×C31—42no—
110C22⋊C4×C31—42no—
111C22⋊C4×C31—82no—
112C22⋊C4×C31—82no—
113C42×C31—81no—
114#11843C3111yesmaximal, characteristic, direct product factor, Sylow
115C23×C31—22no—
116C23×C31—21no—
117C23×C31—21no—
118C23×C31—21no—
119C23×C31—21no—
120C23×C31—21no—
121C23×C31—21no—
122C23×C31—21no—
123C23×C31—41no—
124C23×C31—42no—
125C23×C31—42no—
126C23×C31—41no—
127C23×C31—41no—
128C23×C31—41no—
129C23×C31—41no—
130C23×C31—42no—
131C23×C31—41no—
132C23×C31—41no—
133C23×C31—41no—
134C23×C31—41no—
135C23×C31—42no—
136C23×C31—41no—
137C23×C31—41no—
138C23×C31—41no—
139C23×C31—81no—
140C23×C31—81no—
141C23×C31—84no—
142C23×C31—84no—
143C23×C31#9911yescharacteristic
144C23×C31#9911yescharacteristic
145C23×C31C2×C22⋊C411yescharacteristic
146C23×C31#13512yes—
147D4×C31—84no—
148D4×C31—84no—
149D4×C31—82no—
150D4×C31—82no—
151D4×C31—82no—
152C2×C4×C31—22no—
153C2×C4×C31—22no—
154C2×C4×C31—21no—
155C2×C4×C31—21no—
156C2×C4×C31—21no—
157C2×C4×C31—21no—
158C2×C4×C31—41no—
159C2×C4×C31—41no—
160C2×C4×C31—42no—
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—41no—
168C2×C4×C31—41no—
169C2×C4×C31—41no—
170C2×C4×C31—81no—
171C2×C4×C31—81no—
172C2×C4×C31—81no—
173C2×C4×C31—82no—
174C2×C4×C31—82no—
175C2×C4×C31—82no—
176C8×C31—82no—
177#2539C2×C3111yescharacteristic
178#1819C2×C3111yescharacteristic, complemented
179C2×#323C2×C3111yescharacteristic, complemented
180#1352C2×C3112yescomplemented
181#1343C2×C3112yescomplemented
182C22×C31—21no—
183C22×C31—21no—
184C22×C31—21no—
185C22×C31—21no—
186C22×C31—21no—
187C22×C31—21no—
188C22×C31—22no—
189C22×C31—21no—
190C22×C31—42no—
191C22×C31—42no—
192C22×C31—42no—
193C22×C31—42no—
194C22×C31—41no—
195C22×C31—41no—
196C22×C31—41no—
197C22×C31—41no—
198C22×C31—41no—
199C22×C31—81no—
200C22×C31—84no—
201C22×C31—81no—
202C22×C31—81no—
203C22×C31—81no—
204C22×C31—81no—
205C22×C31—81no—
206C22×C31—84no—
207C22×C31—81no—
208C22×C31—81no—
209C22×C31—81no—
210C22×C31#35312yes—
211C22×C31C2×#9911yescharacteristic
212C22×C31#41611yescharacteristic
213C22×C31#42111yescharacteristic
214C4×C31—42no—
215C4×C31—42no—
216C4×C31—41no—
217C4×C31—41no—
218C4×C31—41no—
219C4×C31—41no—
220C4×C31—81no—
221C4×C31—162no—
222C2×#123—21no—
223C2×#121C4×C3111yescharacteristic, complemented
224C2×#120—21no—
225C22×C22⋊C4C22×C3111yescharacteristic
226C2×C22⋊C8—21no—
227#399C4×C3111yescharacteristic, complemented
228#399C22×C3111yescharacteristic
229#392C4×C3111yescharacteristic, complemented
230#392C22×C3111yescharacteristic
231#390—21no—
232#390—21no—
233#379—21no—
234C4×C22⋊C4C4×C3111yescharacteristic, complemented
235#342—21no—
236#342C22×C3112yes—
237#323—21no—
238#323C22×C3112yes—
239C2×C31—21no—
240C2×C31—21no—
241C2×C31—22no—
242C2×C31—42no—
243C2×C31—41no—
244C2×C31—81no—
245C2×C31—161no—
246C2×C31#151611yescharacteristic
247C2×C31#212111yescharacteristic
248C2×C31C2×#35311yescharacteristic
249C25D4×C3111yescharacteristic
250C22×D4—21no—
251C22×D4—21no—
252C22×D4—21no—
253C22×D4C2×C4×C3111yescharacteristic
254C23×C4C2×C4×C3111yescharacteristic
255C23×C4D4×C3111yescharacteristic
256C22×C8—41no—
257#123—44no—
258#121—41no—
259#121—41no—
260#120—44no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4C2×C4×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—22no—
271C2×C22⋊C4—41no—
272C2×C22⋊C4—41no—
273C2×C22⋊C4—41no—
274C2×C22⋊C4—41no—
275C2×C22⋊C4C2×C4×C3111yescharacteristic
276C2×C22⋊C4D4×C3111yescharacteristic
277C2×C22⋊C4D4×C3111yescharacteristic
278C2×C22⋊C4C23×C3111yescharacteristic
279C2×C42—21no—
280C22⋊C8—22no—
281C22⋊C8—41no—
282#95C2×C4×C3111yescharacteristic
283#95C2×C4×C3111yescharacteristic
284C31#1184311yescharacteristic, direct product factor, Sylow
285C24—21no—
286C24—21no—
287C24—22no—
288C24—21no—
289C24—41no—
290C24—42no—
291C24—81no—
292C24C22⋊C4×C3111yescharacteristic
293C24C22⋊C4×C3111yescharacteristic
294C24C2×D4×C3111yescharacteristic
295C2×D4—41no—
296C2×D4—42no—
297C2×D4—42no—
298C2×D4—42no—
299C2×D4—42no—
300C2×D4—42no—
301C2×D4—41no—
302C2×D4—41no—
303C2×D4—42no—
304C2×D4—81no—
305C2×D4—81no—
306C2×D4—81no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—42no—
315C22×C4—42no—
316C22×C4—81no—
317C22×C4C22⋊C4×C3111yescharacteristic
318C22×C4C22⋊C4×C3111yescharacteristic
319C22×C4C22×C4×C3111yescharacteristic
320C22×C4C2×D4×C3111yescharacteristic
321C2×C8—42no—
322C2×C8—82no—
323C4⋊C4—41no—
324C4⋊C4—42no—
325C4⋊C4—42no—
326C22⋊C4—24no—
327C22⋊C4—41no—
328C22⋊C4—41no—
329C22⋊C4—41no—
330C22⋊C4—41no—
331C22⋊C4—42no—
332C22⋊C4—42no—
333C22⋊C4—42no—
334C22⋊C4—42no—
335C22⋊C4—42no—
336C22⋊C4—42no—
337C22⋊C4—42no—
338C22⋊C4—82no—
339C22⋊C4—82no—
340C42—81no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—22no—
345C23—21no—
346C23—21no—
347C23—21no—
348C23—21no—
349C23—41no—
350C23—42no—
351C23—42no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23—42no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—41no—
361C23—42no—
362C23—41no—
363C23—41no—
364C23—41no—
365C23—81no—
366C23—81no—
367C23—84no—
368C23—84no—
369C23C31×#9911yescharacteristic
370C23C31×#9911yescharacteristic
371C23C2×C22⋊C4×C3111yescharacteristic
372C23C31×#13512yes—
373D4—84no—
374D4—84no—
375D4—82no—
376D4—82no—
377D4—82no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—42no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—81no—
397C2×C4—81no—
398C2×C4—81no—
399C2×C4—82no—
400C2×C4—82no—
401C2×C4—82no—
402C8—82no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—21no—
408C22—21no—
409C22—22no—
410C22—21no—
411C22—42no—
412C22—42no—
413C22—42no—
414C22—42no—
415C22—41no—
416C22—41no—
417C22—41no—
418C22—41no—
419C22—41no—
420C22—81no—
421C22—84no—
422C22—81no—
423C22—81no—
424C22—81no—
425C22—81no—
426C22—81no—
427C22—84no—
428C22—81no—
429C22—81no—
430C22—81no—
431C22C31×#35312yes—
432C22C2×C31×#9911yescharacteristic
433C22C31×#41611yescharacteristic
434C22C31×#42111yescharacteristic
435C4—42no—
436C4—42no—
437C4—41no—
438C4—41no—
439C4—41no—
440C4—41no—
441C4—81no—
442C4—162no—
443C2—21no—
444C2—21no—
445C2—22no—
446C2—42no—
447C2—41no—
448C2—81no—
449C2—161no—
450C2C31×#151611yescharacteristic
451C2C31×#212111yescharacteristic
452C2C2×C31×#35311yescharacteristic
subgroupG/H
center, socleC22×C31C2×#99
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C22⋊C4C23×C31
prime radicalC31×#2539C2
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×#1352C2semidirect
5. C31×#1343C2semidirect
7. C2×C31×#121C4semidirect
11. C31×#399C4semidirect
13. C31×#392C4semidirect
18. C4×C22⋊C4×C31C4semidirect
114. #11843C31direct (N × H)
178. #1819C2×C31semidirect
179. C2×#323C2×C31semidirect
180. #1352C2×C31semidirect
181. #1343C2×C31semidirect
223. C2×#121C4×C31semidirect
227. #399C4×C31semidirect
229. #392C4×C31semidirect
234. C4×C22⋊C4C4×C31semidirect
284. C31#11843direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#25392
C31×#18192
C2×C31×#3232
C31×#13522
C31×#13432
#1184331