Finite Group Databasebeta

← C31×#7761 #21464520

Subgroups — C31×#7761 #21464520

Order 7936.

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

normal subgroups only

This group has 436 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×#2806C211yesmaximal, characteristic
2C31×#2058C211yesmaximal, characteristic
3C31×#2024C211yesmaximal, characteristic
4C31×#2016C211yesmaximal, characteristic
5C31×#1272C211yesmaximal, characteristic
6C31×#1272C211yesmaximal, characteristic
7C31×#1271C211yesmaximal, characteristic
8C22×Q16×C31—21no—
9C2×C31×C4⋊Q8C2211yescharacteristic
10C2×C31×#106—21no—
11C2×C31×#103—21no—
12C2×C31×#103—21no—
13C31×#398—21no—
14C31×#398—21no—
15C31×#395—21no—
16C31×#391—21no—
17C31×#391C2211yescharacteristic
18C31×#391C2211yescharacteristic
19C31×#389—21no—
20C31×#389C2211yescharacteristic
21C31×#387—21no—
22C31×#340—21no—
23C31×#340—21no—
24C31×#336C2211yescharacteristic
25C31×#336C2211yescharacteristic
26C31×#336C2211yescharacteristic
27C22×Q8×C31—21no—
28C22×Q8×C31D411yescharacteristic
29C22×Q8×C31D411yescharacteristic
30C2×Q16×C31—42no—
31C2×Q16×C31—42no—
32C2×Q16×C31—42no—
33C22×C8×C31—21no—
34C22×C8×C31—21no—
35C22×C8×C31—21no—
36C31×C4⋊Q8—42no—
37C2×C4⋊C4×C31—21no—
38C2×C4⋊C4×C31—21no—
39C2×C4⋊C4×C31—21no—
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×C31D411yescharacteristic
46C2×C4⋊C4×C31D411yescharacteristic
47C2×C4⋊C4×C31D411yescharacteristic
48C2×C42×C31—21no—
49C2×C42×C31C2311yescharacteristic
50C31×#106—42no—
51C31×#103—42no—
52C31×#103—42no—
53C31×#95—21no—
54C31×#95—21no—
55C31×#95—21no—
56C31×#95—21no—
57C31×#95—21no—
58C31×#95—21no—
59C31×#95—21no—
60C31×#95—21no—
61C2×Q8×C31—21no—
62C2×Q8×C31—22no—
63C2×Q8×C31—21no—
64C2×Q8×C31—21no—
65C2×Q8×C31—41no—
66C2×Q8×C31—41no—
67C2×Q8×C31—41no—
68C2×Q8×C31—41no—
69C2×Q8×C31—41no—
70C2×Q8×C31—41no—
71C2×Q8×C31—41no—
72C2×Q8×C31—41no—
73C2×Q8×C31—41no—
74C2×Q8×C31SD1612yes—
75C22×C4×C31—21no—
76C22×C4×C31—21no—
77C22×C4×C31—21no—
78C22×C4×C31—21no—
79C22×C4×C31—21no—
80C22×C4×C31—21no—
81C22×C4×C31—41no—
82C22×C4×C31C2×D411yescharacteristic
83C22×C4×C31C2×D411yescharacteristic
84C22×C4×C31C2×D411yescharacteristic
85Q16×C31—48no—
86C2×C8×C31—22no—
87C2×C8×C31—22no—
88C2×C8×C31—41no—
89C2×C8×C31—41no—
90C2×C8×C31—41no—
91C2×C8×C31—41no—
92C2×C8×C31—41no—
93C2×C8×C31—41no—
94C2×C8×C31—41no—
95C4⋊C4×C31—21no—
96C4⋊C4×C31—22no—
97C4⋊C4×C31—22no—
98C4⋊C4×C31—41no—
99C4⋊C4×C31—41no—
100C4⋊C4×C31—41no—
101C4⋊C4×C31—41no—
102C4⋊C4×C31—41no—
103C4⋊C4×C31—41no—
104C4⋊C4×C31—41no—
105C4⋊C4×C31—81no—
106C4⋊C4×C31—81no—
107C4⋊C4×C31—81no—
108C4⋊C4×C31—81no—
109C4⋊C4×C31Q1612yescomplemented
110C42×C31—41no—
111C42×C31—81no—
112#7761C3111yesmaximal, characteristic, direct product factor, Sylow
113C23×C31#12011yescharacteristic
114Q8×C31—42no—
115Q8×C31—42no—
116Q8×C31—42no—
117Q8×C31—42no—
118Q8×C31—81no—
119Q8×C31—81no—
120Q8×C31—81no—
121Q8×C31—81no—
122C2×C4×C31—21no—
123C2×C4×C31—21no—
124C2×C4×C31—21no—
125C2×C4×C31—21no—
126C2×C4×C31—21no—
127C2×C4×C31—21no—
128C2×C4×C31—22no—
129C2×C4×C31—22no—
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—41no—
138C2×C4×C31—41no—
139C2×C4×C31—41no—
140C2×C4×C31—41no—
141C2×C4×C31—41no—
142C2×C4×C31—41no—
143C2×C4×C31—41no—
144C2×C4×C31—42no—
145C2×C4×C31—41no—
146C2×C4×C31—41no—
147C2×C4×C31—81no—
148C2×C4×C31—81no—
149C2×C4×C31C2×SD1611yescharacteristic
150C2×C4×C31C2×Q1611yescharacteristic
151C2×C4×C31#13511yescharacteristic
152C2×C4×C31#13711yescharacteristic
153C2×C4×C31#13711yescharacteristic
154C2×C4×C31#13711yescharacteristic
155C8×C31—42no—
156C8×C31—42no—
157C8×C31—81no—
158#2806C2×C3111yescharacteristic
159#2058C2×C3111yescharacteristic
160#2024C2×C3111yescharacteristic
161#2016C2×C3111yescharacteristic
162#1272C2×C3111yescharacteristic
163#1272C2×C3111yescharacteristic
164#1271C2×C3111yescharacteristic
165C22×C31#44811yescharacteristic
166C22×C31#45111yescharacteristic
167C22×C31#45211yescharacteristic
168C22×C31#45311yescharacteristic
169C22×C31#45511yescharacteristic
170C22×C31#45611yescharacteristic
171C22×C31B(4,𝔽2)11yescharacteristic
172C4×C31—21no—
173C4×C31—21no—
174C4×C31—21no—
175C4×C31—21no—
176C4×C31—21no—
177C4×C31—21no—
178C4×C31—42no—
179C4×C31—42no—
180C4×C31—82no—
181C4×C31—81no—
182C4×C31—81no—
183C4×C31—81no—
184C4×C31—81no—
185C22×Q16—21no—
186C2×C4⋊Q8C22×C3111yescharacteristic
187C2×#106—21no—
188C2×#103—21no—
189C2×#103—21no—
190#398—21no—
191#398—21no—
192#395—21no—
193#391—21no—
194#391C22×C3111yescharacteristic
195#391C22×C3111yescharacteristic
196#389—21no—
197#389C22×C3111yescharacteristic
198#387—21no—
199#340—21no—
200#340—21no—
201#336C22×C3111yescharacteristic
202#336C22×C3111yescharacteristic
203#336C22×C3111yescharacteristic
204C2×C31#159611yescharacteristic
205C2×C31#160511yescharacteristic
206C2×C31#160611yescharacteristic
207C2×C31#163211yescharacteristic
208C2×C31#164511yescharacteristic
209C2×C31#165311yescharacteristic
210C2×C31#166111yescharacteristic
211C22×Q8—21no—
212C22×Q8D4×C3111yescharacteristic
213C22×Q8D4×C3111yescharacteristic
214C2×Q16—42no—
215C2×Q16—42no—
216C2×Q16—42no—
217C22×C8—21no—
218C22×C8—21no—
219C22×C8—21no—
220C4⋊Q8—42no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4D4×C3111yescharacteristic
229C2×C4⋊C4D4×C3111yescharacteristic
230C2×C4⋊C4D4×C3111yescharacteristic
231C2×C4⋊C4D4×C3111yescharacteristic
232C2×C42—21no—
233C2×C42C23×C3111yescharacteristic
234#106—42no—
235#103—42no—
236#103—42no—
237#95—21no—
238#95—21no—
239#95—21no—
240#95—21no—
241#95—21no—
242#95—21no—
243#95—21no—
244#95—21no—
245C31#776111yescharacteristic, direct product factor, Sylow
246C2×Q8—21no—
247C2×Q8—22no—
248C2×Q8—21no—
249C2×Q8—21no—
250C2×Q8—41no—
251C2×Q8—41no—
252C2×Q8—41no—
253C2×Q8—41no—
254C2×Q8—41no—
255C2×Q8—41no—
256C2×Q8—41no—
257C2×Q8—41no—
258C2×Q8—41no—
259C2×Q8SD16×C3112yes—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—41no—
267C22×C4C2×D4×C3111yescharacteristic
268C22×C4C2×D4×C3111yescharacteristic
269C22×C4C2×D4×C3111yescharacteristic
270Q16—48no—
271C2×C8—22no—
272C2×C8—22no—
273C2×C8—41no—
274C2×C8—41no—
275C2×C8—41no—
276C2×C8—41no—
277C2×C8—41no—
278C2×C8—41no—
279C2×C8—41no—
280C4⋊C4—21no—
281C4⋊C4—22no—
282C4⋊C4—22no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—81no—
291C4⋊C4—81no—
292C4⋊C4—81no—
293C4⋊C4—81no—
294C4⋊C4Q16×C3112yescomplemented
295C42—41no—
296C42—81no—
297C23C31×#12011yescharacteristic
298Q8—42no—
299Q8—42no—
300Q8—42no—
301Q8—42no—
302Q8—81no—
303Q8—81no—
304Q8—81no—
305Q8—81no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—22no—
313C2×C4—22no—
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—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—42no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4C2×SD16×C3111yescharacteristic
334C2×C4C2×Q16×C3111yescharacteristic
335C2×C4C31×#13511yescharacteristic
336C2×C4C31×#13711yescharacteristic
337C2×C4C31×#13711yescharacteristic
338C2×C4C31×#13711yescharacteristic
339C8—42no—
340C8—42no—
341C8—81no—
342C22C31×#44811yescharacteristic
343C22C31×#45111yescharacteristic
344C22C31×#45211yescharacteristic
345C22C31×#45311yescharacteristic
346C22C31×#45511yescharacteristic
347C22C31×#45611yescharacteristic
348C22C31×B(4,𝔽2)11yescharacteristic
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—21no—
355C4—42no—
356C4—42no—
357C4—82no—
358C4—81no—
359C4—81no—
360C4—81no—
361C4—81no—
362C2C31×#159611yescharacteristic
363C2C31×#160511yescharacteristic
364C2C31×#160611yescharacteristic
365C2C31×#163211yescharacteristic
366C2C31×#164511yescharacteristic
367C2C31×#165311yescharacteristic
368C2C31×#166111yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C31#120
commutator, Frattini, cosocleC2×C42C23×C31
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
109. C4⋊C4×C31Q16semidirect
112. #7761C31direct (N × H)
245. C31#7761direct (N × H)
294. C4⋊C4Q16×C31semidirect

Maximal subgroups

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

subgroupindex
C31×#28062
C31×#20582
C31×#20242
C31×#20162
C31×#12722
C31×#12712
#776131