Finite Group Databasebeta

← C31×#10563 #21467322

Subgroups — C31×#10563 #21467322

Order 7936.

438 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 94 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×#3195C211yesmaximal, characteristic
2C31×#1901C211yesmaximal, characteristic
3C31×#1894C211yesmaximal, characteristic
4C31×#1855C211yesmaximal, characteristic
5C31×#1520C211yesmaximal, characteristic
6C31×#1472C211yesmaximal, characteristic
7C31×#1305C211yesmaximal, characteristic
8C22×M16×C31C2211yescharacteristic
9C2×C31×C22⋊Q8C2211yescharacteristic
10C2×C31×C22⋊Q8C2211yescharacteristic
11C31×#483—21no—
12C31×#483—21no—
13C31×#470—21no—
14C31×#470—21no—
15C31×#451—21no—
16C31×#451—21no—
17C2×C31×#108—21no—
18C2×C31×#103—21no—
19C2×C31×#101—21no—
20C31×#407C2211yescharacteristic
21C31×#407C2211yescharacteristic
22C2×C31×C22⋊C8C2211yescharacteristic
23C31×#380C2211yescharacteristic
24C31×#343—21no—
25C31×#341—21no—
26C31×#340—21no—
27C31×#328—22no—
28C31×#324—22no—
29C22×Q8×C31D411yescharacteristic
30C22×Q8×C31D411yescharacteristic
31C23×C4×C31C2311yescharacteristic
32C2×Q16×C31—21no—
33C2×Q16×C31—21no—
34C2×M16×C31—21no—
35C2×M16×C31—21no—
36C2×M16×C31—21no—
37C2×M16×C31—42no—
38C2×M16×C31D411yescharacteristic
39C2×M16×C31D411yescharacteristic
40C22×C8×C31—21no—
41C22×C8×C31—21no—
42C31×C22⋊Q8—21no—
43C31×C22⋊Q8—21no—
44C31×C22⋊Q8—21no—
45C31×C22⋊Q8—21no—
46C31×C22⋊Q8—21no—
47C31×C22⋊Q8—21no—
48C31×C22⋊Q8—21no—
49C31×C22⋊Q8—21no—
50C2×C4⋊C4×C31—21no—
51C2×C4⋊C4×C31—21no—
52C2×C4⋊C4×C31—21no—
53C2×C4⋊C4×C31D411yescharacteristic
54C2×C4⋊C4×C31D411yescharacteristic
55C2×C22⋊C4×C31—21no—
56C2×C22⋊C4×C31—21no—
57C2×C22⋊C4×C31—21no—
58C31×#108—42no—
59C31×#106—21no—
60C31×#106—21no—
61C31×#103—21no—
62C31×#103—21no—
63C31×#103—21no—
64C31×#103—21no—
65C31×#103—42no—
66C31×#101—42no—
67C31×C22⋊C8—21no—
68C31×C22⋊C8—21no—
69C31×C22⋊C8—21no—
70C31×C22⋊C8—21no—
71C31×C22⋊C8—21no—
72C31×C22⋊C8D412yes—
73C31×#95—21no—
74C24×C31#4111yescharacteristic
75C2×Q8×C31—21no—
76C2×Q8×C31—21no—
77C2×Q8×C31—21no—
78C2×Q8×C31—21no—
79C2×Q8×C31—41no—
80C2×Q8×C31—41no—
81C2×Q8×C31—41no—
82C2×Q8×C31—41no—
83C22×C4×C31—21no—
84C22×C4×C31—21no—
85C22×C4×C31—21no—
86C22×C4×C31—21no—
87C22×C4×C31—41no—
88C22×C4×C31—41no—
89C22×C4×C31—41no—
90C22×C4×C31C2×D411yescharacteristic
91C22×C4×C31C2×D411yescharacteristic
92C22×C4×C31C2×D411yescharacteristic
93C22×C4×C31C2×D411yescharacteristic
94C22×C4×C31#4111yescharacteristic
95C22×C4×C31#4111yescharacteristic
96Q16×C31—81no—
97Q16×C31—81no—
98M16×C31—22no—
99M16×C31—22no—
100M16×C31—41no—
101M16×C31—41no—
102M16×C31—41no—
103M16×C31—41no—
104M16×C31—41no—
105M16×C31—41no—
106C2×C8×C31—22no—
107C2×C8×C31—21no—
108C2×C8×C31—21no—
109C2×C8×C31—22no—
110C2×C8×C31—41no—
111C2×C8×C31—41no—
112C2×C8×C31—41no—
113C2×C8×C31—41no—
114C2×C8×C31—41no—
115C4⋊C4×C31—21no—
116C4⋊C4×C31—21no—
117C4⋊C4×C31—21no—
118C4⋊C4×C31—21no—
119C4⋊C4×C31—41no—
120C4⋊C4×C31—41no—
121C4⋊C4×C31—41no—
122C4⋊C4×C31—41no—
123C4⋊C4×C31—41no—
124C4⋊C4×C31—41no—
125C22⋊C4×C31—41no—
126C22⋊C4×C31—41no—
127C22⋊C4×C31—41no—
128C22⋊C4×C31—41no—
129C22⋊C4×C31—81no—
130#10563C3111yesmaximal, characteristic, direct product factor, Sylow
131C23×C31—21no—
132C23×C31—21no—
133C23×C31—41no—
134C23×C31—41no—
135C23×C31#12111yescharacteristic
136C23×C31#12311yescharacteristic
137C23×C31#12411yescharacteristic
138Q8×C31—42no—
139Q8×C31—41no—
140Q8×C31—41no—
141Q8×C31—41no—
142Q8×C31—41no—
143Q8×C31—81no—
144C2×C4×C31—21no—
145C2×C4×C31—21no—
146C2×C4×C31—21no—
147C2×C4×C31—21no—
148C2×C4×C31—21no—
149C2×C4×C31—21no—
150C2×C4×C31—41no—
151C2×C4×C31—41no—
152C2×C4×C31—41no—
153C2×C4×C31—42no—
154C2×C4×C31—41no—
155C2×C4×C31—41no—
156C2×C4×C31—41no—
157C2×C4×C31—41no—
158C2×C4×C31—41no—
159C2×C4×C31—41no—
160C2×C4×C31—81no—
161C2×C4×C31—81no—
162C2×C4×C31—81no—
163C2×C4×C31—81no—
164C2×C4×C31—81no—
165C2×C4×C31#12011yescharacteristic
166C2×C4×C31#12111yescharacteristic
167C2×C4×C31#12111yescharacteristic
168C2×C4×C31#12311yescharacteristic
169C8×C31—42no—
170C8×C31—42no—
171C8×C31—41no—
172C8×C31—41no—
173C8×C31—81no—
174#3195C2×C3111yescharacteristic
175#1901C2×C3111yescharacteristic
176#1894C2×C3111yescharacteristic
177#1855C2×C3111yescharacteristic
178#1520C2×C3111yescharacteristic
179#1472C2×C3111yescharacteristic
180#1305C2×C3111yescharacteristic
181C22×C31—21no—
182C22×C31—21no—
183C22×C31—21no—
184C22×C31—21no—
185C22×C31—21no—
186C22×C31—21no—
187C22×C31—21no—
188C22×C31—21no—
189C22×C31—81no—
190C22×C31—81no—
191C22×C31#39411yescharacteristic
192C22×C31#47111yescharacteristic
193C22×C31#47311yescharacteristic
194C4×C31—21no—
195C4×C31—21no—
196C4×C31—21no—
197C4×C31—81no—
198C4×C31—81no—
199C4×C31—81no—
200C4×C31—81no—
201C4×C31—161no—
202C4×C31B(4,𝔽2)11yescharacteristic
203C4×C31#45811yescharacteristic
204C22×M16C22×C3111yescharacteristic
205C2×C22⋊Q8C22×C3111yescharacteristic
206C2×C22⋊Q8C22×C3111yescharacteristic
207#483—21no—
208#483—21no—
209#470—21no—
210#470—21no—
211#451—21no—
212#451—21no—
213C2×#108—21no—
214C2×#103—21no—
215C2×#101—21no—
216#407C22×C3111yescharacteristic
217#407C22×C3111yescharacteristic
218C2×C22⋊C8C22×C3111yescharacteristic
219#380C22×C3111yescharacteristic
220#343—21no—
221#341—21no—
222#340—21no—
223#328—22no—
224#324—22no—
225C2×C31—21no—
226C2×C31—21no—
227C2×C31—41no—
228C2×C31—41no—
229C2×C31#204411yescharacteristic
230C2×C31#204911yescharacteristic
231C2×C31#205211yescharacteristic
232C22×Q8D4×C3111yescharacteristic
233C22×Q8D4×C3111yescharacteristic
234C23×C4C23×C3111yescharacteristic
235C2×Q16—21no—
236C2×Q16—21no—
237C2×M16—21no—
238C2×M16—21no—
239C2×M16—21no—
240C2×M16—42no—
241C2×M16D4×C3111yescharacteristic
242C2×M16D4×C3111yescharacteristic
243C22×C8—21no—
244C22×C8—21no—
245C22⋊Q8—21no—
246C22⋊Q8—21no—
247C22⋊Q8—21no—
248C22⋊Q8—21no—
249C22⋊Q8—21no—
250C22⋊Q8—21no—
251C22⋊Q8—21no—
252C22⋊Q8—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4D4×C3111yescharacteristic
257C2×C4⋊C4D4×C3111yescharacteristic
258C2×C22⋊C4—21no—
259C2×C22⋊C4—21no—
260C2×C22⋊C4—21no—
261#108—42no—
262#106—21no—
263#106—21no—
264#103—21no—
265#103—21no—
266#103—21no—
267#103—21no—
268#103—42no—
269#101—42no—
270C22⋊C8—21no—
271C22⋊C8—21no—
272C22⋊C8—21no—
273C22⋊C8—21no—
274C22⋊C8—21no—
275C22⋊C8D4×C3112yes—
276#95—21no—
277C31#1056311yescharacteristic, direct product factor, Sylow
278C24#41×C3111yescharacteristic
279C2×Q8—21no—
280C2×Q8—21no—
281C2×Q8—21no—
282C2×Q8—21no—
283C2×Q8—41no—
284C2×Q8—41no—
285C2×Q8—41no—
286C2×Q8—41no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—41no—
292C22×C4—41no—
293C22×C4—41no—
294C22×C4C2×D4×C3111yescharacteristic
295C22×C4C2×D4×C3111yescharacteristic
296C22×C4C2×D4×C3111yescharacteristic
297C22×C4C2×D4×C3111yescharacteristic
298C22×C4#41×C3111yescharacteristic
299C22×C4#41×C3111yescharacteristic
300Q16—81no—
301Q16—81no—
302M16—22no—
303M16—22no—
304M16—41no—
305M16—41no—
306M16—41no—
307M16—41no—
308M16—41no—
309M16—41no—
310C2×C8—22no—
311C2×C8—21no—
312C2×C8—21no—
313C2×C8—22no—
314C2×C8—41no—
315C2×C8—41no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—41no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C22⋊C4—41no—
330C22⋊C4—41no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—81no—
334C23—21no—
335C23—21no—
336C23—41no—
337C23—41no—
338C23C31×#12111yescharacteristic
339C23C31×#12311yescharacteristic
340C23C31×#12411yescharacteristic
341Q8—42no—
342Q8—41no—
343Q8—41no—
344Q8—41no—
345Q8—41no—
346Q8—81no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—42no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—81no—
364C2×C4—81no—
365C2×C4—81no—
366C2×C4—81no—
367C2×C4—81no—
368C2×C4C31×#12011yescharacteristic
369C2×C4C31×#12111yescharacteristic
370C2×C4C31×#12111yescharacteristic
371C2×C4C31×#12311yescharacteristic
372C8—42no—
373C8—42no—
374C8—41no—
375C8—41no—
376C8—81no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—81no—
386C22—81no—
387C22C31×#39411yescharacteristic
388C22C31×#47111yescharacteristic
389C22C31×#47311yescharacteristic
390C4—21no—
391C4—21no—
392C4—21no—
393C4—81no—
394C4—81no—
395C4—81no—
396C4—81no—
397C4—161no—
398C4C31×B(4,𝔽2)11yescharacteristic
399C4C31×#45811yescharacteristic
400C2—21no—
401C2—21no—
402C2—41no—
403C2—41no—
404C2C31×#204411yescharacteristic
405C2C31×#204911yescharacteristic
406C2C31×#205211yescharacteristic
subgroupG/H
center, socleC22×C31#394
commutator, Frattini, cosocleC23×C4C23×C31
prime radicalC24×C31#41
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
130. #10563C31direct (N × H)
277. C31#10563direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#31952
C31×#19012
C31×#18942
C31×#18552
C31×#15202
C31×#14722
C31×#13052
#1056331