Finite Group Databasebeta

← C31×#11834 #21468593

Subgroups — C31×#11834 #21468593

Order 7936.

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

normal subgroups only

This group has 400 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×#2638C211yesmaximal, characteristic
2C31×#1800C211yesmaximal, characteristic
3C31×#1465C211yesmaximal, characteristic
4C31×#1354C212yesmaximal, complemented
5C31×#1346C212yesmaximal, complemented
6C2×C31×C22⋊Q8C411yescharacteristic
7C2×C4×D4×C31C2211yescharacteristic
8C31×#423—21no—
9C2×C31×#100—21no—
10C31×#407—21no—
11C31×#398C2211yescharacteristic
12C31×#397—21no—
13C31×#397C411yescharacteristic
14C31×#395C2211yescharacteristic
15C31×#394—21no—
16C31×#393C411yescharacteristic
17C31×#387—21no—
18C31×#385—21no—
19C31×#381C411yescharacteristic
20C31×#343C2212yes—
21C31×#324C2212yes—
22C31×#323—21no—
23C22×Q8×C31C2×C411yescharacteristic
24C22×D4×C31D411yescharacteristic
25C23×C4×C31C2×C411yescharacteristic
26C23×C4×C31D411yescharacteristic
27C2×M16×C31—22no—
28C2×M16×C31—41no—
29C31×C22⋊Q8—41no—
30C31×C22⋊Q8—41no—
31C4×D4×C31—41no—
32C4×D4×C31—41no—
33C2×C4⋊C4×C31—21no—
34C2×C4⋊C4×C31—21no—
35C2×C4⋊C4×C31—21no—
36C2×C4⋊C4×C31C2×C411yescharacteristic
37C2×C4⋊C4×C31C2311yescharacteristic
38C2×C22⋊C4×C31—21no—
39C2×C22⋊C4×C31—21no—
40C2×C22⋊C4×C31—21no—
41C2×C22⋊C4×C31—21no—
42C2×C22⋊C4×C31C2×C411yescharacteristic
43C2×C22⋊C4×C31D411yescharacteristic
44C2×C42×C31D411yescharacteristic
45C31×C4⋊C8—41no—
46C31×C4⋊C8—41no—
47C31×#100—42no—
48C31×C22⋊C8—22no—
49C31×C22⋊C8—41no—
50C31×#95—21no—
51C31×#95—21no—
52C31×#95—21no—
53C31×#95—21no—
54C31×#95—21no—
55C31×#95C2×C411yescharacteristic
56C31×#95C2×C411yescharacteristic
57C24×C31C22⋊C411yescharacteristic
58C24×C31C22⋊C411yescharacteristic
59C2×Q8×C31—41no—
60C2×Q8×C31—81no—
61C2×D4×C31—21no—
62C2×D4×C31—21no—
63C2×D4×C31—41no—
64C2×D4×C31—41no—
65C22×C4×C31—21no—
66C22×C4×C31—21no—
67C22×C4×C31—21no—
68C22×C4×C31—21no—
69C22×C4×C31—21no—
70C22×C4×C31—21no—
71C22×C4×C31—21no—
72C22×C4×C31—21no—
73C22×C4×C31—81no—
74C22×C4×C31—81no—
75C22×C4×C31C22⋊C411yescharacteristic
76C22×C4×C31C22⋊C411yescharacteristic
77C22×C4×C31C22×C411yescharacteristic
78C22×C4×C31C2×D411yescharacteristic
79C22×C4×C31C2×D411yescharacteristic
80M16×C31—42no—
81M16×C31—42no—
82M16×C31—82no—
83C2×C8×C31—42no—
84C2×C8×C31—42no—
85C4⋊C4×C31—41no—
86C4⋊C4×C31—41no—
87C4⋊C4×C31—41no—
88C4⋊C4×C31—41no—
89C4⋊C4×C31—41no—
90C4⋊C4×C31—41no—
91C4⋊C4×C31—81no—
92C22⋊C4×C31—41no—
93C22⋊C4×C31—41no—
94C22⋊C4×C31—42no—
95C22⋊C4×C31—42no—
96C22⋊C4×C31—81no—
97C22⋊C4×C31—81no—
98C42×C31—21no—
99C42×C31—21no—
100#11834C3111yesmaximal, characteristic, direct product factor, Sylow
101C23×C31—21no—
102C23×C31—21no—
103C23×C31—21no—
104C23×C31—21no—
105C23×C31—21no—
106C23×C31—21no—
107C23×C31—41no—
108C23×C31—41no—
109C23×C31—41no—
110C23×C31—41no—
111C23×C31C2×C22⋊C411yescharacteristic
112Q8×C31—82no—
113D4×C31—42no—
114D4×C31—42no—
115C2×C4×C31—21no—
116C2×C4×C31—21no—
117C2×C4×C31—21no—
118C2×C4×C31—21no—
119C2×C4×C31—21no—
120C2×C4×C31—41no—
121C2×C4×C31—42no—
122C2×C4×C31—41no—
123C2×C4×C31—41no—
124C2×C4×C31—41no—
125C2×C4×C31—41no—
126C2×C4×C31—41no—
127C2×C4×C31—41no—
128C2×C4×C31—41no—
129C2×C4×C31—41no—
130C2×C4×C31—41no—
131C2×C4×C31—41no—
132C2×C4×C31—41no—
133C2×C4×C31—41no—
134C2×C4×C31—41no—
135C2×C4×C31—41no—
136C2×C4×C31—41no—
137C2×C4×C31—81no—
138C2×C4×C31—81no—
139C2×C4×C31—81no—
140C2×C4×C31#9911yescharacteristic
141C2×C4×C31#9911yescharacteristic
142C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C31#13711yescharacteristic
144C8×C31—82no—
145C8×C31—82no—
146#2638C2×C3111yescharacteristic
147#1800C2×C3111yescharacteristic
148#1465C2×C3111yescharacteristic
149#1354C2×C3112yescomplemented
150#1346C2×C3112yescomplemented
151C22×C31—21no—
152C22×C31—21no—
153C22×C31—42no—
154C22×C31—41no—
155C22×C31—41no—
156C22×C31—41no—
157C22×C31—41no—
158C22×C31—41no—
159C22×C31—41no—
160C22×C31—81no—
161C22×C31—81no—
162C22×C31—81no—
163C22×C31C2×#9911yescharacteristic
164C22×C31#41711yescharacteristic
165C22×C31#42111yescharacteristic
166C4×C31—21no—
167C4×C31—21no—
168C4×C31—21no—
169C4×C31—21no—
170C4×C31—41no—
171C4×C31—41no—
172C4×C31—41no—
173C4×C31—81no—
174C4×C31—81no—
175C4×C31—81no—
176C4×C31—81no—
177C2×C22⋊Q8C4×C3111yescharacteristic
178C2×C4×D4C22×C3111yescharacteristic
179#423—21no—
180C2×#100—21no—
181#407—21no—
182#398C22×C3111yescharacteristic
183#397—21no—
184#397C4×C3111yescharacteristic
185#395C22×C3111yescharacteristic
186#394—21no—
187#393C4×C3111yescharacteristic
188#387—21no—
189#385—21no—
190#381C4×C3111yescharacteristic
191#343C22×C3112yes—
192#324C22×C3112yes—
193#323—21no—
194C2×C31—21no—
195C2×C31—21no—
196C2×C31—81no—
197C2×C31—81no—
198C2×C31#151311yescharacteristic
199C2×C31#212111yescharacteristic
200C2×C31#213511yescharacteristic
201C22×Q8C2×C4×C3111yescharacteristic
202C22×D4D4×C3111yescharacteristic
203C23×C4C2×C4×C3111yescharacteristic
204C23×C4D4×C3111yescharacteristic
205C2×M16—22no—
206C2×M16—41no—
207C22⋊Q8—41no—
208C22⋊Q8—41no—
209C4×D4—41no—
210C4×D4—41no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4C2×C4×C3111yescharacteristic
215C2×C4⋊C4C23×C3111yescharacteristic
216C2×C22⋊C4—21no—
217C2×C22⋊C4—21no—
218C2×C22⋊C4—21no—
219C2×C22⋊C4—21no—
220C2×C22⋊C4C2×C4×C3111yescharacteristic
221C2×C22⋊C4D4×C3111yescharacteristic
222C2×C42D4×C3111yescharacteristic
223C4⋊C8—41no—
224C4⋊C8—41no—
225#100—42no—
226C22⋊C8—22no—
227C22⋊C8—41no—
228#95—21no—
229#95—21no—
230#95—21no—
231#95—21no—
232#95—21no—
233#95C2×C4×C3111yescharacteristic
234#95C2×C4×C3111yescharacteristic
235C31#1183411yescharacteristic, direct product factor, Sylow
236C24C22⋊C4×C3111yescharacteristic
237C24C22⋊C4×C3111yescharacteristic
238C2×Q8—41no—
239C2×Q8—81no—
240C2×D4—21no—
241C2×D4—21no—
242C2×D4—41no—
243C2×D4—41no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—81no—
253C22×C4—81no—
254C22×C4C22⋊C4×C3111yescharacteristic
255C22×C4C22⋊C4×C3111yescharacteristic
256C22×C4C22×C4×C3111yescharacteristic
257C22×C4C2×D4×C3111yescharacteristic
258C22×C4C2×D4×C3111yescharacteristic
259M16—42no—
260M16—42no—
261M16—82no—
262C2×C8—42no—
263C2×C8—42no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—81no—
271C22⋊C4—41no—
272C22⋊C4—41no—
273C22⋊C4—42no—
274C22⋊C4—42no—
275C22⋊C4—81no—
276C22⋊C4—81no—
277C42—21no—
278C42—21no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23—21no—
283C23—21no—
284C23—21no—
285C23—41no—
286C23—41no—
287C23—41no—
288C23—41no—
289C23C2×C22⋊C4×C3111yescharacteristic
290Q8—82no—
291D4—42no—
292D4—42no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—41no—
299C2×C4—42no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4C31×#9911yescharacteristic
319C2×C4C31×#9911yescharacteristic
320C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
321C2×C4C31×#13711yescharacteristic
322C8—82no—
323C8—82no—
324C22—21no—
325C22—21no—
326C22—42no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—81no—
334C22—81no—
335C22—81no—
336C22C2×C31×#9911yescharacteristic
337C22C31×#41711yescharacteristic
338C22C31×#42111yescharacteristic
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—81no—
347C4—81no—
348C4—81no—
349C4—81no—
350C2—21no—
351C2—21no—
352C2—81no—
353C2—81no—
354C2C31×#151311yescharacteristic
355C2C31×#212111yescharacteristic
356C2C31×#213511yescharacteristic
subgroupG/H
center, socleC22×C31C2×#99
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C4⋊C4C23×C31
prime radicalC22×D4×C31D4
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
4. C31×#1354C2semidirect
5. C31×#1346C2semidirect
100. #11834C31direct (N × H)
149. #1354C2×C31semidirect
150. #1346C2×C31semidirect
235. C31#11834direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#26382
C31×#18002
C31×#14652
C31×#13542
C31×#13462
#1183431