Finite Group Databasebeta

← C31×#7793 #21464552

Subgroups — C31×#7793 #21464552

Order 7936.

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

normal subgroups only

This group has 420 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×#2727C211yesmaximal, characteristic
2C31×#2093C211yesmaximal, characteristic
3C31×#2084C211yesmaximal, characteristic, complemented
4C31×#2083C211yesmaximal, characteristic, complemented
5C31×#1271C211yesmaximal, characteristic, complemented
6C31×#1271C211yesmaximal, characteristic, complemented
7C31×#1270C211yesmaximal, characteristic
8C2×C31×#126—21no—
9C2×C31×#107—21no—
10C2×C31×#107—21no—
11C2×C31×#106—21no—
12C2×C31×#102—21no—
13C31×#399—21no—
14C31×#396—21no—
15C31×#394—21no—
16C31×#390C2211yescharacteristic
17C31×#389—21no—
18C31×#389C2211yescharacteristic
19C31×#389C2211yescharacteristic
20C31×#388—21no—
21C31×#384C2211yescharacteristic
22C31×#340—21no—
23C31×#340—21no—
24C31×#336C2211yescharacteristic
25C31×#336C2211yescharacteristic
26C31×#336C2211yescharacteristic
27C22×D4×C31D411yescharacteristic
28C22×C8×C31—21no—
29C22×C8×C31—21no—
30C22×C8×C31—21no—
31C31×#126—42no—
32C31×#126—42no—
33C2×C4⋊C4×C31—21no—
34C2×C4⋊C4×C31—21no—
35C2×C4⋊C4×C31—21no—
36C2×C4⋊C4×C31—21no—
37C2×C4⋊C4×C31—21no—
38C2×C4⋊C4×C31—21no—
39C2×C4⋊C4×C31—21no—
40C2×C4⋊C4×C31D411yescharacteristic
41C2×C4⋊C4×C31D411yescharacteristic
42C2×C4⋊C4×C31D411yescharacteristic
43C2×C4⋊C4×C31D411yescharacteristic
44C2×C4⋊C4×C31D411yescharacteristic
45C2×C22⋊C4×C31—21no—
46C2×C22⋊C4×C31—21no—
47C2×C22⋊C4×C31—21no—
48C2×C22⋊C4×C31—21no—
49C2×C22⋊C4×C31—21no—
50C2×C22⋊C4×C31—21no—
51C2×C42×C31—21no—
52C2×C42×C31C2311yescharacteristic
53C31×#107—42no—
54C31×#107—42no—
55C31×#106—42no—
56C31×#102—42no—
57C31×#95—21no—
58C31×#95—21no—
59C31×#95—21no—
60C24×C31—21no—
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—41no—
71C22×C4×C31C2×D411yescharacteristic
72C22×C4×C31C2×D411yescharacteristic
73C22×C4×C31C2×D411yescharacteristic
74C2×C8×C31—22no—
75C2×C8×C31—22no—
76C2×C8×C31—22no—
77C2×C8×C31—41no—
78C2×C8×C31—41no—
79C2×C8×C31—41no—
80C2×C8×C31—41no—
81C2×C8×C31—41no—
82C2×C8×C31—41no—
83C4⋊C4×C31—21no—
84C4⋊C4×C31—21no—
85C4⋊C4×C31—21no—
86C4⋊C4×C31—42no—
87C4⋊C4×C31—41no—
88C4⋊C4×C31—41no—
89C4⋊C4×C31—41no—
90C4⋊C4×C31—41no—
91C4⋊C4×C31—41no—
92C4⋊C4×C31—41no—
93C4⋊C4×C31—41no—
94C4⋊C4×C31—41no—
95C4⋊C4×C31—41no—
96C4⋊C4×C31—41no—
97C4⋊C4×C31—41no—
98C4⋊C4×C31—41no—
99C4⋊C4×C31—41no—
100C4⋊C4×C31—81no—
101C4⋊C4×C31D812yes—
102C22⋊C4×C31—42no—
103C22⋊C4×C31—42no—
104C22⋊C4×C31—41no—
105C22⋊C4×C31—41no—
106C22⋊C4×C31—41no—
107C22⋊C4×C31—41no—
108C22⋊C4×C31—81no—
109C22⋊C4×C31—81no—
110C42×C31—41no—
111C42×C31—42no—
112#7793C3111yesmaximal, characteristic, direct product factor, Sylow
113C23×C31—41no—
114C23×C31—41no—
115C23×C31—41no—
116C23×C31—41no—
117C23×C31—41no—
118C23×C31—41no—
119C23×C31—41no—
120C23×C31#12011yescharacteristic
121D4×C31—42no—
122D4×C31—81no—
123C2×C4×C31—21no—
124C2×C4×C31—21no—
125C2×C4×C31—21no—
126C2×C4×C31—21no—
127C2×C4×C31—21no—
128C2×C4×C31—21no—
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—81no—
145C2×C4×C31—81no—
146C2×C4×C31—81no—
147C2×C4×C31C2×D811yescharacteristic
148C2×C4×C31#13511yescharacteristic
149C2×C4×C31#13511yescharacteristic
150C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C31#13711yescharacteristic
153C8×C31—42no—
154C8×C31—42no—
155C8×C31—42no—
156#2727C2×C3111yescharacteristic
157#2093C2×C3111yescharacteristic
158#2084C2×C3111yescharacteristic, complemented
159#2083C2×C3111yescharacteristic, complemented
160#1271C2×C3111yescharacteristic, complemented
161#1271C2×C3111yescharacteristic, complemented
162#1270C2×C3111yescharacteristic
163C22×C31—81no—
164C22×C31—81no—
165C22×C31—81no—
166C22×C31—81no—
167C22×C31—81no—
168C22×C31—81no—
169C22×C31—81no—
170C22×C31#44711yescharacteristic
171C22×C31#44911yescharacteristic
172C22×C31#45211yescharacteristic
173C22×C31#45311yescharacteristic
174C22×C31#45611yescharacteristic
175C22×C31#45611yescharacteristic
176C22×C31#45811yescharacteristic
177C4×C31—21no—
178C4×C31—21no—
179C4×C31—21no—
180C4×C31—21no—
181C4×C31—21no—
182C4×C31—21no—
183C4×C31—42no—
184C4×C31—81no—
185C4×C31—81no—
186C4×C31—81no—
187C4×C31—81no—
188C4×C31—161no—
189C2×#126—21no—
190C2×#107—21no—
191C2×#107—21no—
192C2×#106—21no—
193C2×#102—21no—
194#399—21no—
195#396—21no—
196#394—21no—
197#390C22×C3111yescharacteristic
198#389—21no—
199#389C22×C3111yescharacteristic
200#389C22×C3111yescharacteristic
201#388—21no—
202#384C22×C3111yescharacteristic
203#340—21no—
204#340—21no—
205#336C22×C3111yescharacteristic
206#336C22×C3111yescharacteristic
207#336C22×C3111yescharacteristic
208C2×C31—161no—
209C2×C31#160911yescharacteristic
210C2×C31#161011yescharacteristic
211C2×C31#161811yescharacteristic
212C2×C31#162111yescharacteristic
213C2×C31#164711yescharacteristic
214C2×C31#165211yescharacteristic
215C2×C31#166011yescharacteristic
216C22×D4D4×C3111yescharacteristic
217C22×C8—21no—
218C22×C8—21no—
219C22×C8—21no—
220#126—42no—
221#126—42no—
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⋊C4—21no—
229C2×C4⋊C4D4×C3111yescharacteristic
230C2×C4⋊C4D4×C3111yescharacteristic
231C2×C4⋊C4D4×C3111yescharacteristic
232C2×C4⋊C4D4×C3111yescharacteristic
233C2×C4⋊C4D4×C3111yescharacteristic
234C2×C22⋊C4—21no—
235C2×C22⋊C4—21no—
236C2×C22⋊C4—21no—
237C2×C22⋊C4—21no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—21no—
240C2×C42—21no—
241C2×C42C23×C3111yescharacteristic
242#107—42no—
243#107—42no—
244#106—42no—
245#102—42no—
246#95—21no—
247#95—21no—
248#95—21no—
249C31#779311yescharacteristic, direct product factor, Sylow
250C24—21no—
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—41no—
254C2×D4—41no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—41no—
261C22×C4C2×D4×C3111yescharacteristic
262C22×C4C2×D4×C3111yescharacteristic
263C22×C4C2×D4×C3111yescharacteristic
264C2×C8—22no—
265C2×C8—22no—
266C2×C8—22no—
267C2×C8—41no—
268C2×C8—41no—
269C2×C8—41no—
270C2×C8—41no—
271C2×C8—41no—
272C2×C8—41no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—42no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
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⋊C4D8×C3112yes—
292C22⋊C4—42no—
293C22⋊C4—42no—
294C22⋊C4—41no—
295C22⋊C4—41no—
296C22⋊C4—41no—
297C22⋊C4—41no—
298C22⋊C4—81no—
299C22⋊C4—81no—
300C42—41no—
301C42—42no—
302C23—41no—
303C23—41no—
304C23—41no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23C31×#12011yescharacteristic
310D4—42no—
311D4—81no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—22no—
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—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4C2×D8×C3111yescharacteristic
337C2×C4C31×#13511yescharacteristic
338C2×C4C31×#13511yescharacteristic
339C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
340C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
341C2×C4C31×#13711yescharacteristic
342C8—42no—
343C8—42no—
344C8—42no—
345C22—81no—
346C22—81no—
347C22—81no—
348C22—81no—
349C22—81no—
350C22—81no—
351C22—81no—
352C22C31×#44711yescharacteristic
353C22C31×#44911yescharacteristic
354C22C31×#45211yescharacteristic
355C22C31×#45311yescharacteristic
356C22C31×#45611yescharacteristic
357C22C31×#45611yescharacteristic
358C22C31×#45811yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—21no—
365C4—42no—
366C4—81no—
367C4—81no—
368C4—81no—
369C4—81no—
370C4—161no—
371C2—161no—
372C2C31×#160911yescharacteristic
373C2C31×#161011yescharacteristic
374C2C31×#161811yescharacteristic
375C2C31×#162111yescharacteristic
376C2C31×#164711yescharacteristic
377C2C31×#165211yescharacteristic
378C2C31×#166011yescharacteristic
subgroupG/H
center, socleC23×C31#120
commutator, Frattini, cosocleC2×C42C23×C31
prime radicalC22×D4×C31D4
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
3. C31×#2084C2semidirect
4. C31×#2083C2semidirect
5. C31×#1271C2semidirect
6. C31×#1271C2semidirect
112. #7793C31direct (N × H)
158. #2084C2×C31semidirect
159. #2083C2×C31semidirect
160. #1271C2×C31semidirect
161. #1271C2×C31semidirect
249. C31#7793direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#27272
C31×#20932
C31×#20842
C31×#20832
C31×#12712
C31×#12702
#779331