Finite Group Databasebeta

← C31×#12128 #21468887

Subgroups — C31×#12128 #21468887

Order 7936.

408 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 74 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×#2799C211yesmaximal, characteristic, complemented
2C31×#2007C211yesmaximal, characteristic
3C31×#1616C211yesmaximal, characteristic
4C31×#1604C211yesmaximal, characteristic
5C31×#1354C211yesmaximal, characteristic, complemented
6C31×#1353C211yesmaximal, characteristic, complemented
7C31×#1319C211yesmaximal, characteristic, complemented
8C2×C31×#137—21no—
9C31×#537C2211yescharacteristic
10C31×#481—21no—
11C31×#448—21no—
12C2×C31×#104—21no—
13C31×#400—21no—
14C31×#400C2211yescharacteristic
15C31×#398—21no—
16C31×#395C2211yescharacteristic
17C31×#391—21no—
18C31×#391—21no—
19C31×#391C2211yescharacteristic
20C31×#387—21no—
21C31×#387—21no—
22C31×#343C2211yescharacteristic
23C31×#327—21no—
24C31×#327—21no—
25C31×#324C2211yescharacteristic
26C31×#324C2211yescharacteristic
27C2×#41×C31—21no—
28C22×Q8×C31D411yescharacteristic
29C22×Q8×C31D411yescharacteristic
30C31×#137—42no—
31C31×#137—42no—
32C2×Q16×C31—41no—
33C2×SD16×C31—41no—
34C2×SD16×C31—41no—
35C2×M16×C31—21no—
36C31×C22⋊Q8—41no—
37C31×#121—21no—
38C31×#121—21no—
39C31×#121—41no—
40C2×C4⋊C4×C31—21no—
41C2×C4⋊C4×C31—21no—
42C2×C4⋊C4×C31—21no—
43C2×C4⋊C4×C31—21no—
44C2×C4⋊C4×C31D411yescharacteristic
45C2×C4⋊C4×C31C2311yescharacteristic
46C2×C42×C31—21no—
47C2×C42×C31D411yescharacteristic
48C31×#106—41no—
49C31×#104—42no—
50C31×#103—41no—
51C31×#102—41no—
52C31×C22⋊C8—21no—
53C31×C22⋊C8—21no—
54C31×#95—21no—
55C31×#95—21no—
56C31×#95—21no—
57C31×#95—21no—
58C31×#95—21no—
59C31×#95—21no—
60C31×#95—21no—
61C31×#95—21no—
62C31×#95—21no—
63C31×#95D411yescharacteristic
64C31×#95D411yescharacteristic
65#41×C31—41no—
66#41×C31—41no—
67#41×C31—41no—
68#41×C31—41no—
69C2×Q8×C31—21no—
70C2×Q8×C31—21no—
71C2×Q8×C31—42no—
72C2×Q8×C31—41no—
73C2×Q8×C31—41no—
74C2×Q8×C31—41no—
75C2×Q8×C31SD1612yescomplemented
76C2×D4×C31—21no—
77C2×D4×C31—21no—
78C2×D4×C31—21no—
79C2×D4×C31—41no—
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—41no—
87C22×C4×C31C2×D411yescharacteristic
88C22×C4×C31C2×D411yescharacteristic
89C22×C4×C31C2×D411yescharacteristic
90Q16×C31—44no—
91SD16×C31—44no—
92SD16×C31—82no—
93M16×C31—22no—
94M16×C31—41no—
95C2×C8×C31—41no—
96C2×C8×C31—41no—
97C2×C8×C31—41no—
98C4⋊C4×C31—21no—
99C4⋊C4×C31—21no—
100C4⋊C4×C31—41no—
101C4⋊C4×C31—42no—
102C4⋊C4×C31—42no—
103C4⋊C4×C31—41no—
104C4⋊C4×C31—81no—
105C4⋊C4×C31—81no—
106C22⋊C4×C31—41no—
107C22⋊C4×C31—41no—
108C42×C31—41no—
109C42×C31—81no—
110#12128C3111yesmaximal, characteristic, direct product factor, Sylow
111C23×C31—41no—
112C23×C31#12011yescharacteristic
113Q8×C31—42no—
114Q8×C31—41no—
115Q8×C31—41no—
116Q8×C31—42no—
117Q8×C31—81no—
118Q8×C31—81no—
119D4×C31—41no—
120D4×C31—41no—
121D4×C31—81no—
122D4×C31—81no—
123D4×C31—81no—
124D4×C31—81no—
125C2×C4×C31—21no—
126C2×C4×C31—21no—
127C2×C4×C31—22no—
128C2×C4×C31—22no—
129C2×C4×C31—21no—
130C2×C4×C31—21no—
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—41no—
138C2×C4×C31—41no—
139C2×C4×C31—41no—
140C2×C4×C31—41no—
141C2×C4×C31—41no—
142C2×C4×C31—41no—
143C2×C4×C31—42no—
144C2×C4×C31—41no—
145C2×C4×C31—41no—
146C2×C4×C31—41no—
147C2×C4×C31—41no—
148C2×C4×C31—41no—
149C2×C4×C31—81no—
150C2×C4×C31—81no—
151C2×C4×C31C2×SD1611yescharacteristic
152C2×C4×C31#13711yescharacteristic
153C8×C31—42no—
154C8×C31—81no—
155C8×C31—81no—
156#2799C2×C3111yescharacteristic, complemented
157#2007C2×C3111yescharacteristic
158#1616C2×C3111yescharacteristic
159#1604C2×C3111yescharacteristic
160#1354C2×C3111yescharacteristic, complemented
161#1353C2×C3111yescharacteristic, complemented
162#1319C2×C3111yescharacteristic, complemented
163C22×C31—21no—
164C22×C31—21no—
165C22×C31—81no—
166C22×C31—81no—
167C22×C31—81no—
168C22×C31#44811yescharacteristic
169C22×C31#45311yescharacteristic
170C22×C31B(4,𝔽2)11yescharacteristic
171C4×C31—21no—
172C4×C31—21no—
173C4×C31—42no—
174C4×C31—41no—
175C4×C31—41no—
176C4×C31—42no—
177C4×C31—81no—
178C4×C31—81no—
179C4×C31—81no—
180C4×C31—81no—
181C4×C31—81no—
182C2×#137—21no—
183#537C22×C3111yescharacteristic
184#481—21no—
185#448—21no—
186C2×#104—21no—
187#400—21no—
188#400C22×C3111yescharacteristic
189#398—21no—
190#395C22×C3111yescharacteristic
191#391—21no—
192#391—21no—
193#391C22×C3111yescharacteristic
194#387—21no—
195#387—21no—
196#343C22×C3111yescharacteristic
197#327—21no—
198#327—21no—
199#324C22×C3111yescharacteristic
200#324C22×C3111yescharacteristic
201C2×C31—21no—
202C2×C31—21no—
203C2×C31—161no—
204C2×C31#159611yescharacteristic
205C2×C31#219711yescharacteristic
206C2×C31#220311yescharacteristic
207C2×#41—21no—
208C22×Q8D4×C3111yescharacteristic
209C22×Q8D4×C3111yescharacteristic
210#137—42no—
211#137—42no—
212C2×Q16—41no—
213C2×SD16—41no—
214C2×SD16—41no—
215C2×M16—21no—
216C22⋊Q8—41no—
217#121—21no—
218#121—21no—
219#121—41no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4D4×C3111yescharacteristic
225C2×C4⋊C4C23×C3111yescharacteristic
226C2×C42—21no—
227C2×C42D4×C3111yescharacteristic
228#106—41no—
229#104—42no—
230#103—41no—
231#102—41no—
232C22⋊C8—21no—
233C22⋊C8—21no—
234#95—21no—
235#95—21no—
236#95—21no—
237#95—21no—
238#95—21no—
239#95—21no—
240#95—21no—
241#95—21no—
242#95—21no—
243#95D4×C3111yescharacteristic
244#95D4×C3111yescharacteristic
245C31#1212811yescharacteristic, direct product factor, Sylow
246#41—41no—
247#41—41no—
248#41—41no—
249#41—41no—
250C2×Q8—21no—
251C2×Q8—21no—
252C2×Q8—42no—
253C2×Q8—41no—
254C2×Q8—41no—
255C2×Q8—41no—
256C2×Q8SD16×C3112yescomplemented
257C2×D4—21no—
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—41no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—41no—
268C22×C4C2×D4×C3111yescharacteristic
269C22×C4C2×D4×C3111yescharacteristic
270C22×C4C2×D4×C3111yescharacteristic
271Q16—44no—
272SD16—44no—
273SD16—82no—
274M16—22no—
275M16—41no—
276C2×C8—41no—
277C2×C8—41no—
278C2×C8—41no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—42no—
284C4⋊C4—42no—
285C4⋊C4—81no—
286C4⋊C4—81no—
287C22⋊C4—41no—
288C22⋊C4—41no—
289C42—41no—
290C42—81no—
291C23—41no—
292C23C31×#12011yescharacteristic
293Q8—42no—
294Q8—41no—
295Q8—41no—
296Q8—42no—
297Q8—81no—
298Q8—81no—
299D4—41no—
300D4—41no—
301D4—81no—
302D4—81no—
303D4—81no—
304D4—81no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—42no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—81no—
330C2×C4—81no—
331C2×C4C2×SD16×C3111yescharacteristic
332C2×C4C31×#13711yescharacteristic
333C8—42no—
334C8—81no—
335C8—81no—
336C22—21no—
337C22—21no—
338C22—81no—
339C22—81no—
340C22—81no—
341C22C31×#44811yescharacteristic
342C22C31×#45311yescharacteristic
343C22C31×B(4,𝔽2)11yescharacteristic
344C4—21no—
345C4—21no—
346C4—42no—
347C4—41no—
348C4—41no—
349C4—42no—
350C4—81no—
351C4—81no—
352C4—81no—
353C4—81no—
354C4—81no—
355C2—21no—
356C2—21no—
357C2—161no—
358C2C31×#159611yescharacteristic
359C2C31×#219711yescharacteristic
360C2C31×#220311yescharacteristic
subgroupG/H
center, socleC22×C31B(4,𝔽2)
commutator, Frattini, cosocleC2×C4⋊C4C23×C31
prime radicalC31×#537C22
LCSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C31 ◁ C2×C4⋊C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#2799C2semidirect
5. C31×#1354C2semidirect
6. C31×#1353C2semidirect
7. C31×#1319C2semidirect
75. C2×Q8×C31SD16semidirect
110. #12128C31direct (N × H)
156. #2799C2×C31semidirect
160. #1354C2×C31semidirect
161. #1353C2×C31semidirect
162. #1319C2×C31semidirect
245. C31#12128direct (N × H)
256. C2×Q8SD16×C31semidirect

Maximal subgroups

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

subgroupindex
C31×#27992
C31×#20072
C31×#16162
C31×#16042
C31×#13542
C31×#13532
C31×#13192
#1212831