Finite Group Databasebeta

← C31×#8581 #21465340

Subgroups — C31×#8581 #21465340

Order 7936.

540 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C31×#124C211yesmaximal, characteristic
2C31×#1767C211yesmaximal, characteristic, complemented
3C31×#1767C211yesmaximal, characteristic, complemented
4C2×C31×#329C212yesmaximal
5C31×#1295C212yesmaximal, complemented
6C2×C31×#124C2211yescharacteristic
7C2×C4×Q8×C31C411yescharacteristic
8C2×C4×D4×C31C411yescharacteristic
9C2×C31×C4⋊C8—21no—
10C2×C31×C4⋊C8—21no—
11C2×C31×#97C2212yes—
12C2×C31×#97C2212yes—
13C31×#391C411yescharacteristic
14C31×#390C411yescharacteristic
15C31×#388—21no—
16C31×#388—21no—
17C31×#382C2211yescharacteristic
18C4×C22⋊C4×C31—21no—
19C4×C22⋊C4×C31—21no—
20C43×C31C2211yescharacteristic
21C31×#336—21no—
22C31×#336—21no—
23C31×#329—24no—
24C22×Q8×C31C2×C411yescharacteristic
25C22×D4×C31C2×C411yescharacteristic
26C23×C4×C31—21no—
27C22×C8×C31—22no—
28C22×C8×C31—22no—
29C31×#124—21no—
30C31×#124—21no—
31C31×#124D412yes—
32C31×#124Q812yes—
33C4×Q8×C31—42no—
34C4×D4×C31—42no—
35C2×C4⋊C4×C31—21no—
36C2×C4⋊C4×C31C2×C411yescharacteristic
37C2×C4⋊C4×C31C2×C411yescharacteristic
38C2×C22⋊C4×C31—21no—
39C2×C22⋊C4×C31—21no—
40C2×C22⋊C4×C31—21no—
41C2×C22⋊C4×C31—21no—
42C2×C22⋊C4×C31—21no—
43C2×C42×C31—21no—
44C2×C42×C31C2×C411yescharacteristic
45C2×C42×C31C2×C411yescharacteristic
46C2×C42×C31D411yescharacteristic
47C2×C42×C31D411yescharacteristic
48C2×C42×C31D411yescharacteristic
49C2×C42×C31D411yescharacteristic
50C2×C42×C31C2311yescharacteristic
51C31×C4⋊C8—24no—
52C31×C4⋊C8—24no—
53C31×#97—22no—
54C31×#97—22no—
55C31×#97—22no—
56C31×#97—22no—
57C31×#95—21no—
58C31×#95—21no—
59C31×#95—21no—
60C31×#95—21no—
61C24×C31—21no—
62C2×Q8×C31—21no—
63C2×Q8×C31—41no—
64C2×Q8×C31—41no—
65C2×Q8×C31C4⋊C412yes—
66C2×D4×C31—21no—
67C2×D4×C31—41no—
68C2×D4×C31—41no—
69C2×D4×C31C4⋊C412yes—
70C22×C4×C31—21no—
71C22×C4×C31—21no—
72C22×C4×C31—21no—
73C22×C4×C31—42no—
74C22×C4×C31—42no—
75C22×C4×C31—42no—
76C22×C4×C31C22⋊C411yescharacteristic
77C22×C4×C31C22⋊C411yescharacteristic
78C22×C4×C31C22⋊C411yescharacteristic
79C22×C4×C31C22⋊C411yescharacteristic
80C22×C4×C31C22×C411yescharacteristic
81C22×C4×C31C2×D411yescharacteristic
82C22×C4×C31C2×D411yescharacteristic
83C2×C8×C31—24no—
84C2×C8×C31—24no—
85C2×C8×C31—42no—
86C2×C8×C31—42no—
87C2×C8×C31—42no—
88C2×C8×C31—42no—
89C4⋊C4×C31—41no—
90C4⋊C4×C31—41no—
91C4⋊C4×C31—42no—
92C22⋊C4×C31—22no—
93C22⋊C4×C31—22no—
94C22⋊C4×C31—22no—
95C22⋊C4×C31—22no—
96C22⋊C4×C31—42no—
97C22⋊C4×C31—42no—
98C22⋊C4×C31—42no—
99C42×C31—22no—
100C42×C31—22no—
101C42×C31—22no—
102C42×C31—41no—
103C42×C31—41no—
104C42×C31—41no—
105C42×C31—42no—
106C42×C31C2×D411yescharacteristic
107C42×C31C2×Q811yescharacteristic
108C42×C31#4111yescharacteristic
109C42×C31#4111yescharacteristic
110#8581C3111yesmaximal, characteristic, direct product factor, Sylow
111C23×C31—22no—
112C23×C31—41no—
113C23×C31—41no—
114C23×C31—41no—
115C23×C31—41no—
116C23×C31—41no—
117C23×C31—41no—
118C23×C31C2×C22⋊C411yescharacteristic
119Q8×C31—42no—
120Q8×C31—42no—
121D4×C31—42no—
122D4×C31—42no—
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—21no—
130C2×C4×C31—21no—
131C2×C4×C31—21no—
132C2×C4×C31—21no—
133C2×C4×C31—21no—
134C2×C4×C31—21no—
135C2×C4×C31—22no—
136C2×C4×C31—21no—
137C2×C4×C31—21no—
138C2×C4×C31—21no—
139C2×C4×C31—41no—
140C2×C4×C31—41no—
141C2×C4×C31—41no—
142C2×C4×C31—41no—
143C2×C4×C31—41no—
144C2×C4×C31—41no—
145C2×C4×C31—41no—
146C2×C4×C31—41no—
147C2×C4×C31—84no—
148C2×C4×C31#10012yes—
149C2×C4×C31#10412yes—
150C2×C4×C31#10412yes—
151C2×C4×C31C2×C4⋊C411yescharacteristic
152C2×C4×C31#11711yescharacteristic
153C2×C4×C31#12111yescharacteristic
154C2×C4×C31#12111yescharacteristic
155C2×C4×C31C22⋊Q811yescharacteristic
156C2×C4×C31C22⋊Q811yescharacteristic
157C8×C31—44no—
158C8×C31—44no—
159C4×#124C2×C3111yescharacteristic
160#1767C2×C3111yescharacteristic, complemented
161#1767C2×C3111yescharacteristic, complemented
162C2×#329C2×C3112yes—
163#1295C2×C3112yescomplemented
164C22×C31—42no—
165C22×C31—42no—
166C22×C31—42no—
167C22×C31—81no—
168C22×C31—81no—
169C22×C31—81no—
170C22×C31—81no—
171C22×C31#38011yescharacteristic
172C22×C31C2×#10011yescharacteristic
173C22×C31#41311yescharacteristic
174C22×C31C2×#10411yescharacteristic
175C22×C31C2×#10411yescharacteristic
176C22×C31#42111yescharacteristic
177C22×C31#42111yescharacteristic
178C4×C31—21no—
179C4×C31—21no—
180C4×C31—21no—
181C4×C31—21no—
182C4×C31—21no—
183C4×C31—21no—
184C4×C31—22no—
185C4×C31—22no—
186C4×C31—22no—
187C4×C31—42no—
188C4×C31—41no—
189C4×C31—81no—
190C4×C31—81no—
191C2×#124C22×C3111yescharacteristic
192C2×C4×Q8C4×C3111yescharacteristic
193C2×C4×D4C4×C3111yescharacteristic
194C2×C4⋊C8—21no—
195C2×C4⋊C8—21no—
196C2×#97C22×C3112yes—
197C2×#97C22×C3112yes—
198#391C4×C3111yescharacteristic
199#390C4×C3111yescharacteristic
200#388—21no—
201#388—21no—
202#382C22×C3111yescharacteristic
203C4×C22⋊C4—21no—
204C4×C22⋊C4—21no—
205C43C22×C3111yescharacteristic
206#336—21no—
207#336—21no—
208#329—24no—
209C2×C31—82no—
210C2×C31#152411yescharacteristic
211C2×C31#152711yescharacteristic
212C2×C31#153011yescharacteristic
213C2×C31#153511yescharacteristic
214C2×C31#180011yescharacteristic
215C2×C31#180611yescharacteristic
216C2×C31#180611yescharacteristic
217C22×Q8C2×C4×C3111yescharacteristic
218C22×D4C2×C4×C3111yescharacteristic
219C23×C4—21no—
220C22×C8—22no—
221C22×C8—22no—
222#124—21no—
223#124—21no—
224#124D4×C3112yes—
225#124Q8×C3112yes—
226C4×Q8—42no—
227C4×D4—42no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4C2×C4×C3111yescharacteristic
230C2×C4⋊C4C2×C4×C3111yescharacteristic
231C2×C22⋊C4—21no—
232C2×C22⋊C4—21no—
233C2×C22⋊C4—21no—
234C2×C22⋊C4—21no—
235C2×C22⋊C4—21no—
236C2×C42—21no—
237C2×C42C2×C4×C3111yescharacteristic
238C2×C42C2×C4×C3111yescharacteristic
239C2×C42D4×C3111yescharacteristic
240C2×C42D4×C3111yescharacteristic
241C2×C42D4×C3111yescharacteristic
242C2×C42D4×C3111yescharacteristic
243C2×C42C23×C3111yescharacteristic
244C4⋊C8—24no—
245C4⋊C8—24no—
246#97—22no—
247#97—22no—
248#97—22no—
249#97—22no—
250#95—21no—
251#95—21no—
252#95—21no—
253#95—21no—
254C31#858111yescharacteristic, direct product factor, Sylow
255C24—21no—
256C2×Q8—21no—
257C2×Q8—41no—
258C2×Q8—41no—
259C2×Q8C4⋊C4×C3112yes—
260C2×D4—21no—
261C2×D4—41no—
262C2×D4—41no—
263C2×D4C4⋊C4×C3112yes—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—42no—
268C22×C4—42no—
269C22×C4—42no—
270C22×C4C22⋊C4×C3111yescharacteristic
271C22×C4C22⋊C4×C3111yescharacteristic
272C22×C4C22⋊C4×C3111yescharacteristic
273C22×C4C22⋊C4×C3111yescharacteristic
274C22×C4C22×C4×C3111yescharacteristic
275C22×C4C2×D4×C3111yescharacteristic
276C22×C4C2×D4×C3111yescharacteristic
277C2×C8—24no—
278C2×C8—24no—
279C2×C8—42no—
280C2×C8—42no—
281C2×C8—42no—
282C2×C8—42no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—42no—
286C22⋊C4—22no—
287C22⋊C4—22no—
288C22⋊C4—22no—
289C22⋊C4—22no—
290C22⋊C4—42no—
291C22⋊C4—42no—
292C22⋊C4—42no—
293C42—22no—
294C42—22no—
295C42—22no—
296C42—41no—
297C42—41no—
298C42—41no—
299C42—42no—
300C42C2×D4×C3111yescharacteristic
301C42C2×Q8×C3111yescharacteristic
302C42#41×C3111yescharacteristic
303C42#41×C3111yescharacteristic
304C23—22no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23C2×C22⋊C4×C3111yescharacteristic
312Q8—42no—
313Q8—42no—
314D4—42no—
315D4—42no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—22no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—84no—
341C2×C4C31×#10012yes—
342C2×C4C31×#10412yes—
343C2×C4C31×#10412yes—
344C2×C4C2×C4⋊C4×C3111yescharacteristic
345C2×C4C31×#11711yescharacteristic
346C2×C4C31×#12111yescharacteristic
347C2×C4C31×#12111yescharacteristic
348C2×C4C31×C22⋊Q811yescharacteristic
349C2×C4C31×C22⋊Q811yescharacteristic
350C8—44no—
351C8—44no—
352C22—42no—
353C22—42no—
354C22—42no—
355C22—81no—
356C22—81no—
357C22—81no—
358C22—81no—
359C22C31×#38011yescharacteristic
360C22C2×C31×#10011yescharacteristic
361C22C31×#41311yescharacteristic
362C22C2×C31×#10411yescharacteristic
363C22C2×C31×#10411yescharacteristic
364C22C31×#42111yescharacteristic
365C22C31×#42111yescharacteristic
366C4—21no—
367C4—21no—
368C4—21no—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—22no—
373C4—22no—
374C4—22no—
375C4—42no—
376C4—41no—
377C4—81no—
378C4—81no—
379C2—82no—
380C2C31×#152411yescharacteristic
381C2C31×#152711yescharacteristic
382C2C31×#153011yescharacteristic
383C2C31×#153511yescharacteristic
384C2C31×#180011yescharacteristic
385C2C31×#180611yescharacteristic
386C2C31×#180611yescharacteristic
subgroupG/H
center, socleC23×C31C2×C22⋊C4
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC22×D4×C31C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C43×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#1767C2semidirect
3. C31×#1767C2semidirect
5. C31×#1295C2semidirect
110. #8581C31direct (N × H)
160. #1767C2×C31semidirect
161. #1767C2×C31semidirect
163. #1295C2×C31semidirect
254. C31#8581direct (N × H)

Maximal subgroups

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

subgroupindex
C4×C31×#1242
C31×#17672
C2×C31×#3292
C31×#12952
#858131