Finite Group Databasebeta

← C31×#10341 #21467100

Subgroups — C31×#10341 #21467100

Order 7936.

684 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2659C211yesmaximal, characteristic
2C31×#1787C212yesmaximal
3C31×#1446C211yesmaximal, characteristic
4C31×#1294C212yesmaximal
5C31×#1280C211yesmaximal, characteristic
6C23×Q8×C31C2211yescharacteristic
7C2×C31×C22⋊Q8—21no—
8C2×C31×#103—22no—
9C2×C31×#103—22no—
10C2×C31×C22⋊C8C2212yes—
11C31×#398—22no—
12C31×#395—22no—
13C31×#380—21no—
14C31×#380C2212yes—
15C2×C31×#95—21no—
16C2×C31×#95—21no—
17C2×C31×#95C2211yescharacteristic
18C2×C31×#95C2211yescharacteristic
19C22×Q8×C31—21no—
20C22×Q8×C31—21no—
21C22×Q8×C31—22no—
22C22×Q8×C31—22no—
23C22×Q8×C31—42no—
24C22×Q8×C31—42no—
25C22×Q8×C31Q812yescomplemented
26C23×C4×C31—21no—
27C23×C4×C31—21no—
28C23×C4×C31D411yescharacteristic
29C23×C4×C31D411yescharacteristic
30C23×C4×C31C2311yescharacteristic
31C22×C8×C31—22no—
32C31×C22⋊Q8—42no—
33C31×C22⋊Q8—42no—
34C2×C4⋊C4×C31—22no—
35C2×C4⋊C4×C31—21no—
36C2×C4⋊C4×C31—21no—
37C2×C4⋊C4×C31—21no—
38C2×C4⋊C4×C31D412yes—
39C2×C4⋊C4×C31D412yes—
40C2×C22⋊C4×C31—22no—
41C31×#103—44no—
42C31×#103—44no—
43C31×C22⋊C8—22no—
44C31×C22⋊C8—22no—
45C31×#95—22no—
46C31×#95—22no—
47C31×#95—22no—
48C31×#95—22no—
49C31×#95—42no—
50C31×#95—42no—
51C24×C31C2×D411yescharacteristic
52C2×Q8×C31—24no—
53C2×Q8×C31—24no—
54C2×Q8×C31—24no—
55C2×Q8×C31—44no—
56C2×Q8×C31—42no—
57C2×Q8×C31—42no—
58C2×Q8×C31—44no—
59C2×Q8×C31—42no—
60C2×Q8×C31—48no—
61C2×Q8×C31—42no—
62C2×Q8×C31—81no—
63C2×Q8×C31—81no—
64C22×C4×C31—22no—
65C22×C4×C31—22no—
66C22×C4×C31—21no—
67C22×C4×C31—21no—
68C22×C4×C31—22no—
69C22×C4×C31—21no—
70C22×C4×C31—21no—
71C22×C4×C31—22no—
72C22×C4×C31—22no—
73C22×C4×C31—22no—
74C22×C4×C31—41no—
75C22×C4×C31—41no—
76C22×C4×C31—41no—
77C22×C4×C31—41no—
78C22×C4×C31—41no—
79C22×C4×C31—41no—
80C22×C4×C31—41no—
81C22×C4×C31—41no—
82C22×C4×C31—41no—
83C22×C4×C31—41no—
84C22×C4×C31—41no—
85C22×C4×C31—41no—
86C22×C4×C31—41no—
87C22×C4×C31—41no—
88C22×C4×C31—41no—
89C22×C4×C31—41no—
90C22×C4×C31SD1612yes—
91C22×C4×C31Q1612yes—
92C22×C4×C31C2×D412yes—
93C22×C4×C31C2×Q811yescharacteristic
94C22×C4×C31#4112yes—
95C22×C4×C31#4111yescharacteristic
96C2×C8×C31—42no—
97C2×C8×C31—42no—
98C2×C8×C31—42no—
99C4⋊C4×C31—42no—
100C4⋊C4×C31—44no—
101C4⋊C4×C31—42no—
102C4⋊C4×C31—42no—
103C4⋊C4×C31—81no—
104C4⋊C4×C31—81no—
105C22⋊C4×C31—42no—
106C22⋊C4×C31—42no—
107#10341C3111yesmaximal, characteristic, direct product factor, Sylow
108C23×C31—21no—
109C23×C31—21no—
110C23×C31—21no—
111C23×C31—21no—
112C23×C31#12011yescharacteristic
113C23×C31C22⋊Q811yescharacteristic
114C23×C31#12411yescharacteristic
115C23×C31C2×SD1611yescharacteristic
116C23×C31C2×Q1611yescharacteristic
117C23×C31AGL(1,ℤ/8)11yescharacteristic
118C23×C31#13711yescharacteristic
119Q8×C31—28no—
120Q8×C31—44no—
121Q8×C31—44no—
122Q8×C31—44no—
123Q8×C31—84no—
124C2×C4×C31—22no—
125C2×C4×C31—22no—
126C2×C4×C31—24no—
127C2×C4×C31—22no—
128C2×C4×C31—22no—
129C2×C4×C31—41no—
130C2×C4×C31—41no—
131C2×C4×C31—42no—
132C2×C4×C31—42no—
133C2×C4×C31—42no—
134C2×C4×C31—42no—
135C2×C4×C31—42no—
136C2×C4×C31—41no—
137C2×C4×C31—41no—
138C2×C4×C31—41no—
139C2×C4×C31—42no—
140C2×C4×C31—42no—
141C2×C4×C31—41no—
142C2×C4×C31—42no—
143C2×C4×C31—42no—
144C2×C4×C31—42no—
145C2×C4×C31—42no—
146C2×C4×C31—42no—
147C2×C4×C31—42no—
148C2×C4×C31—42no—
149C2×C4×C31—42no—
150C2×C4×C31—42no—
151C2×C4×C31—42no—
152C2×C4×C31—42no—
153C2×C4×C31—81no—
154C2×C4×C31—81no—
155C2×C4×C31—81no—
156C2×C4×C31—81no—
157C2×C4×C31—81no—
158C2×C4×C31—81no—
159C2×C4×C31C22⋊Q812yes—
160C2×C4×C31#12412yes—
161C8×C31—82no—
162#2659C2×C3111yescharacteristic
163#1787C2×C3112yes—
164#1446C2×C3111yescharacteristic
165#1294C2×C3112yes—
166#1280C2×C3111yescharacteristic
167C22×C31—21no—
168C22×C31—21no—
169C22×C31—21no—
170C22×C31—21no—
171C22×C31—21no—
172C22×C31—21no—
173C22×C31—21no—
174C22×C31—21no—
175C22×C31—21no—
176C22×C31—21no—
177C22×C31—21no—
178C22×C31—21no—
179C22×C31#39311yescharacteristic
180C22×C31#45011yescharacteristic
181C22×C31#45111yescharacteristic
182C22×C31#45511yescharacteristic
183C22×C31#45611yescharacteristic
184C22×C31B(4,𝔽2)11yescharacteristic
185C22×C31B(4,𝔽2)11yescharacteristic
186C22×C31#47511yescharacteristic
187C22×C31#47711yescharacteristic
188C22×C31#48711yescharacteristic
189C22×C31#48911yescharacteristic
190C4×C31—22no—
191C4×C31—22no—
192C4×C31—42no—
193C4×C31—42no—
194C4×C31—44no—
195C4×C31—82no—
196C4×C31—82no—
197C4×C31—82no—
198C23×Q8C22×C3111yescharacteristic
199C2×C22⋊Q8—21no—
200C2×#103—22no—
201C2×#103—22no—
202C2×C22⋊C8C22×C3112yes—
203#398—22no—
204#395—22no—
205#380—21no—
206#380C22×C3112yes—
207C2×#95—21no—
208C2×#95—21no—
209C2×#95C22×C3111yescharacteristic
210C2×#95C22×C3111yescharacteristic
211C2×C31—21no—
212C2×C31—21no—
213C2×C31—21no—
214C2×C31—21no—
215C2×C31#160111yescharacteristic
216C2×C31#160211yescharacteristic
217C2×C31#160411yescharacteristic
218C2×C31#160511yescharacteristic
219C2×C31#202411yescharacteristic
220C2×C31#202811yescharacteristic
221C2×C31#202911yescharacteristic
222C22×Q8—21no—
223C22×Q8—21no—
224C22×Q8—22no—
225C22×Q8—22no—
226C22×Q8—42no—
227C22×Q8—42no—
228C22×Q8Q8×C3112yescomplemented
229C23×C4—21no—
230C23×C4—21no—
231C23×C4D4×C3111yescharacteristic
232C23×C4D4×C3111yescharacteristic
233C23×C4C23×C3111yescharacteristic
234C22×C8—22no—
235C22⋊Q8—42no—
236C22⋊Q8—42no—
237C2×C4⋊C4—22no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4D4×C3112yes—
242C2×C4⋊C4D4×C3112yes—
243C2×C22⋊C4—22no—
244#103—44no—
245#103—44no—
246C22⋊C8—22no—
247C22⋊C8—22no—
248#95—22no—
249#95—22no—
250#95—22no—
251#95—22no—
252#95—42no—
253#95—42no—
254C31#1034111yescharacteristic, direct product factor, Sylow
255C24C2×D4×C3111yescharacteristic
256C2×Q8—24no—
257C2×Q8—24no—
258C2×Q8—24no—
259C2×Q8—44no—
260C2×Q8—42no—
261C2×Q8—42no—
262C2×Q8—44no—
263C2×Q8—42no—
264C2×Q8—48no—
265C2×Q8—42no—
266C2×Q8—81no—
267C2×Q8—81no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—22no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4—41no—
288C22×C4—41no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4—41no—
293C22×C4—41no—
294C22×C4SD16×C3112yes—
295C22×C4Q16×C3112yes—
296C22×C4C2×D4×C3112yes—
297C22×C4C2×Q8×C3111yescharacteristic
298C22×C4#41×C3112yes—
299C22×C4#41×C3111yescharacteristic
300C2×C8—42no—
301C2×C8—42no—
302C2×C8—42no—
303C4⋊C4—42no—
304C4⋊C4—42no—
305C4⋊C4—42no—
306C4⋊C4—44no—
307C4⋊C4—81no—
308C4⋊C4—81no—
309C22⋊C4—42no—
310C22⋊C4—42no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23C31×#12011yescharacteristic
316C23C31×C22⋊Q811yescharacteristic
317C23C31×#12411yescharacteristic
318C23C2×SD16×C3111yescharacteristic
319C23C2×Q16×C3111yescharacteristic
320C23C31×AGL(1,ℤ/8)11yescharacteristic
321C23C31×#13711yescharacteristic
322Q8—28no—
323Q8—44no—
324Q8—44no—
325Q8—44no—
326Q8—84no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—24no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—41no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—81no—
357C2×C4—81no—
358C2×C4—81no—
359C2×C4—81no—
360C2×C4—81no—
361C2×C4—81no—
362C2×C4C31×C22⋊Q812yes—
363C2×C4C31×#12412yes—
364C8—82no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22C31×#39311yescharacteristic
378C22C31×#45011yescharacteristic
379C22C31×#45111yescharacteristic
380C22C31×#45511yescharacteristic
381C22C31×#45611yescharacteristic
382C22C31×B(4,𝔽2)11yescharacteristic
383C22C31×B(4,𝔽2)11yescharacteristic
384C22C31×#47511yescharacteristic
385C22C31×#47711yescharacteristic
386C22C31×#48711yescharacteristic
387C22C31×#48911yescharacteristic
388C4—22no—
389C4—22no—
390C4—42no—
391C4—42no—
392C4—44no—
393C4—82no—
394C4—82no—
395C4—82no—
396C2—21no—
397C2—21no—
398C2—21no—
399C2—21no—
400C2C31×#160111yescharacteristic
401C2C31×#160211yescharacteristic
402C2C31×#160411yescharacteristic
403C2C31×#160511yescharacteristic
404C2C31×#202411yescharacteristic
405C2C31×#202811yescharacteristic
406C2C31×#202911yescharacteristic
subgroupG/H
center, socleC23×C31#120
commutator, Frattini, cosocleC23×C4C23×C31
prime radicalC24×C31C2×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
25. C22×Q8×C31Q8semidirect
107. #10341C31direct (N × H)
228. C22×Q8Q8×C31semidirect
254. C31#10341direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#26592
C31×#17872
C31×#14462
C31×#12942
C31×#12802
#1034131