Finite Group Databasebeta

← C31×#9249 #21466008

Subgroups — C31×#9249 #21466008

Order 7936.

512 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#476C211yesmaximal, characteristic
2D4×M16×C31C211yesmaximal, characteristic
3C31×#1997C211yesmaximal, characteristic, complemented
4C31×#1549C211yesmaximal, characteristic, complemented
5C31×#1486C211yesmaximal, characteristic
6C31×#1292C211yesmaximal, characteristic, complemented
7C31×#1283C211yesmaximal, characteristic, complemented
8C22×M16×C31—21no—
9C2×C31×C4⋊Q8C2211yescharacteristic
10C2×C4×D4×C31C2211yescharacteristic
11C31×#476—21no—
12C31×#476—21no—
13C31×#476—21no—
14C31×#476—21no—
15C31×#436—21no—
16C31×#435—22no—
17C8×D4×C31—21no—
18C31×#431C2211yescharacteristic
19C2×C31×#106C412yes—
20C31×#423C2211yescharacteristic
21C31×#423C2211yescharacteristic
22C2×C31×C4⋊C8C2211yescharacteristic
23C2×C31×#102C412yes—
24C31×#407—21no—
25C4×M16×C31C2211yescharacteristic
26C31×#343—21no—
27C31×#343—21no—
28C31×#332—22no—
29C31×D4⋊C8—21no—
30C31×D4⋊C8—21no—
31C22×Q8×C31—21no—
32C22×D4×C31C2×C411yescharacteristic
33C23×C4×C31—21no—
34C2×M16×C31—22no—
35C2×M16×C31—21no—
36C2×M16×C31—21no—
37C2×M16×C31—42no—
38C2×M16×C31—42no—
39C2×M16×C31D411yescharacteristic
40C2×M16×C31D411yescharacteristic
41C22×C8×C31—22no—
42C22×C8×C31C2×C412yes—
43C31×C4⋊Q8—21no—
44C31×C4⋊Q8—21no—
45C31×C4⋊Q8—21no—
46C31×C4⋊Q8—21no—
47C4×D4×C31—21no—
48C4×D4×C31—21no—
49C4×D4×C31D411yescharacteristic
50C4×D4×C31D411yescharacteristic
51C4×D4×C31D411yescharacteristic
52C4×D4×C31D411yescharacteristic
53C2×C4⋊C4×C31—21no—
54C2×C4⋊C4×C31C2×C412yes—
55C2×C4⋊C4×C31C2×C411yescharacteristic
56C2×C22⋊C4×C31—21no—
57C2×C42×C31C2311yescharacteristic
58C31×#106—22no—
59C31×#106—22no—
60C31×C4⋊C8—21no—
61C31×C4⋊C8—21no—
62C31×C4⋊C8—21no—
63C31×C4⋊C8—21no—
64C31×C4⋊C8—21no—
65C31×C4⋊C8—21no—
66C31×C4⋊C8D412yes—
67C31×#102—22no—
68C31×#102—22no—
69C31×C22⋊C8—22no—
70C31×C22⋊C8—22no—
71C31×C22⋊C8—21no—
72C31×#97—21no—
73C4×C8×C31—21no—
74C4×C8×C31—21no—
75C24×C31—21no—
76C2×Q8×C31—41no—
77C2×Q8×C31—41no—
78C2×Q8×C31—82no—
79C2×D4×C31—22no—
80C2×D4×C31—21no—
81C2×D4×C31—41no—
82C2×D4×C31C22⋊C411yescharacteristic
83C2×D4×C31C22⋊C411yescharacteristic
84C22×C4×C31—21no—
85C22×C4×C31—21no—
86C22×C4×C31—21no—
87C22×C4×C31—21no—
88C22×C4×C31—21no—
89C22×C4×C31—22no—
90C22×C4×C31—41no—
91C22×C4×C31—41no—
92C22×C4×C31—41no—
93C22×C4×C31—41no—
94C22×C4×C31C22×C411yescharacteristic
95C22×C4×C31C2×D411yescharacteristic
96C22×C4×C31#4111yescharacteristic
97M16×C31—21no—
98M16×C31—21no—
99M16×C31—21no—
100M16×C31—44no—
101M16×C31—41no—
102M16×C31—41no—
103M16×C31—41no—
104M16×C31—41no—
105M16×C31SD1612yes—
106C2×C8×C31—21no—
107C2×C8×C31—22no—
108C2×C8×C31—21no—
109C2×C8×C31—22no—
110C2×C8×C31—44no—
111C2×C8×C31—42no—
112C2×C8×C31—41no—
113C2×C8×C31—41no—
114C4⋊C4×C31—21no—
115C4⋊C4×C31—22no—
116C4⋊C4×C31—22no—
117C4⋊C4×C31—41no—
118C4⋊C4×C31—41no—
119C4⋊C4×C31C22⋊C411yescharacteristic
120C4⋊C4×C31C22⋊C411yescharacteristic
121C22⋊C4×C31—21no—
122C22⋊C4×C31—21no—
123C22⋊C4×C31—21no—
124C22⋊C4×C31—21no—
125C42×C31C2×D411yescharacteristic
126C42×C31C2×D411yescharacteristic
127C42×C31C2×D411yescharacteristic
128C42×C31#4111yescharacteristic
129#9249C3111yesmaximal, characteristic, direct product factor, Sylow
130C23×C31—21no—
131C23×C31—21no—
132C23×C31—42no—
133C23×C31—41no—
134C23×C31—41no—
135C23×C31—81no—
136C23×C31C4×D411yescharacteristic
137Q8×C31—82no—
138Q8×C31—82no—
139D4×C31—21no—
140D4×C31—21no—
141D4×C31—21no—
142D4×C31—42no—
143D4×C31#10112yes—
144C2×C4×C31—21no—
145C2×C4×C31—21no—
146C2×C4×C31—21no—
147C2×C4×C31—21no—
148C2×C4×C31—41no—
149C2×C4×C31—41no—
150C2×C4×C31—41no—
151C2×C4×C31—41no—
152C2×C4×C31—41no—
153C2×C4×C31—41no—
154C2×C4×C31—41no—
155C2×C4×C31—41no—
156C2×C4×C31—41no—
157C2×C4×C31—41no—
158C2×C4×C31—41no—
159C2×C4×C31—42no—
160C2×C4×C31—82no—
161C2×C4×C31C2×C22⋊C411yescharacteristic
162C2×C4×C31C4×D411yescharacteristic
163C2×C4×C31#12011yescharacteristic
164C2×C4×C31#12111yescharacteristic
165C2×C4×C31#12111yescharacteristic
166C2×C4×C31#12311yescharacteristic
167C2×C4×C31C2×SD1611yescharacteristic
168C2×C4×C31#13511yescharacteristic
169C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
170C2×C4×C31#13711yescharacteristic
171C8×C31—22no—
172C8×C31—42no—
173C8×C31—42no—
174C8×C31—41no—
175C8×C31—81no—
176C8×C31—81no—
177C2×#476C2×C3111yescharacteristic
178D4×M16C2×C3111yescharacteristic
179#1997C2×C3111yescharacteristic, complemented
180#1549C2×C3111yescharacteristic, complemented
181#1486C2×C3111yescharacteristic
182#1292C2×C3111yescharacteristic, complemented
183#1283C2×C3111yescharacteristic, complemented
184C22×C31—21no—
185C22×C31—21no—
186C22×C31—22no—
187C22×C31—41no—
188C22×C31—41no—
189C22×C31—41no—
190C22×C31—41no—
191C22×C31—41no—
192C22×C31—82no—
193C22×C31—82no—
194C22×C31#38611yescharacteristic
195C22×C31C4×SD1611yescharacteristic
196C22×C31#44011yescharacteristic
197C4×C31—21no—
198C4×C31—21no—
199C4×C31—21no—
200C4×C31—41no—
201C4×C31—41no—
202C4×C31—82no—
203C4×C31C2×#10111yescharacteristic
204C4×C31#41311yescharacteristic
205C4×C31#45011yescharacteristic
206C4×C31#45211yescharacteristic
207C4×C31#46111yescharacteristic
208C4×C31#46311yescharacteristic
209C22×M16—21no—
210C2×C4⋊Q8C22×C3111yescharacteristic
211C2×C4×D4C22×C3111yescharacteristic
212#476—21no—
213#476—21no—
214#476—21no—
215#476—21no—
216#436—21no—
217#435—22no—
218C8×D4—21no—
219#431C22×C3111yescharacteristic
220C2×#106C4×C3112yes—
221#423C22×C3111yescharacteristic
222#423C22×C3111yescharacteristic
223C2×C4⋊C8C22×C3111yescharacteristic
224C2×#102C4×C3112yes—
225#407—21no—
226C4×M16C22×C3111yescharacteristic
227#343—21no—
228#343—21no—
229#332—22no—
230D4⋊C8—21no—
231D4⋊C8—21no—
232C2×C31—21no—
233C2×C31—21no—
234C2×C31—42no—
235C2×C31—81no—
236C2×C31#187711yescharacteristic
237C2×C31#190111yescharacteristic
238C2×C31#190311yescharacteristic
239C22×Q8—21no—
240C22×D4C2×C4×C3111yescharacteristic
241C23×C4—21no—
242C2×M16—22no—
243C2×M16—21no—
244C2×M16—21no—
245C2×M16—42no—
246C2×M16—42no—
247C2×M16D4×C3111yescharacteristic
248C2×M16D4×C3111yescharacteristic
249C22×C8—22no—
250C22×C8C2×C4×C3112yes—
251C4⋊Q8—21no—
252C4⋊Q8—21no—
253C4⋊Q8—21no—
254C4⋊Q8—21no—
255C4×D4—21no—
256C4×D4—21no—
257C4×D4D4×C3111yescharacteristic
258C4×D4D4×C3111yescharacteristic
259C4×D4D4×C3111yescharacteristic
260C4×D4D4×C3111yescharacteristic
261C2×C4⋊C4—21no—
262C2×C4⋊C4C2×C4×C3112yes—
263C2×C4⋊C4C2×C4×C3111yescharacteristic
264C2×C22⋊C4—21no—
265C2×C42C23×C3111yescharacteristic
266#106—22no—
267#106—22no—
268C4⋊C8—21no—
269C4⋊C8—21no—
270C4⋊C8—21no—
271C4⋊C8—21no—
272C4⋊C8—21no—
273C4⋊C8—21no—
274C4⋊C8D4×C3112yes—
275#102—22no—
276#102—22no—
277C22⋊C8—22no—
278C22⋊C8—22no—
279C22⋊C8—21no—
280#97—21no—
281C4×C8—21no—
282C4×C8—21no—
283C31#924911yescharacteristic, direct product factor, Sylow
284C24—21no—
285C2×Q8—41no—
286C2×Q8—41no—
287C2×Q8—82no—
288C2×D4—22no—
289C2×D4—21no—
290C2×D4—41no—
291C2×D4C22⋊C4×C3111yescharacteristic
292C2×D4C22⋊C4×C3111yescharacteristic
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—22no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4—41no—
303C22×C4C22×C4×C3111yescharacteristic
304C22×C4C2×D4×C3111yescharacteristic
305C22×C4#41×C3111yescharacteristic
306M16—21no—
307M16—21no—
308M16—21no—
309M16—44no—
310M16—41no—
311M16—41no—
312M16—41no—
313M16—41no—
314M16SD16×C3112yes—
315C2×C8—21no—
316C2×C8—22no—
317C2×C8—21no—
318C2×C8—22no—
319C2×C8—44no—
320C2×C8—42no—
321C2×C8—41no—
322C2×C8—41no—
323C4⋊C4—21no—
324C4⋊C4—22no—
325C4⋊C4—22no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4C22⋊C4×C3111yescharacteristic
329C4⋊C4C22⋊C4×C3111yescharacteristic
330C22⋊C4—21no—
331C22⋊C4—21no—
332C22⋊C4—21no—
333C22⋊C4—21no—
334C42C2×D4×C3111yescharacteristic
335C42C2×D4×C3111yescharacteristic
336C42C2×D4×C3111yescharacteristic
337C42#41×C3111yescharacteristic
338C23—21no—
339C23—21no—
340C23—42no—
341C23—41no—
342C23—41no—
343C23—81no—
344C23C4×D4×C3111yescharacteristic
345Q8—82no—
346Q8—82no—
347D4—21no—
348D4—21no—
349D4—21no—
350D4—42no—
351D4C31×#10112yes—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—42no—
368C2×C4—82no—
369C2×C4C2×C22⋊C4×C3111yescharacteristic
370C2×C4C4×D4×C3111yescharacteristic
371C2×C4C31×#12011yescharacteristic
372C2×C4C31×#12111yescharacteristic
373C2×C4C31×#12111yescharacteristic
374C2×C4C31×#12311yescharacteristic
375C2×C4C2×SD16×C3111yescharacteristic
376C2×C4C31×#13511yescharacteristic
377C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
378C2×C4C31×#13711yescharacteristic
379C8—22no—
380C8—42no—
381C8—42no—
382C8—41no—
383C8—81no—
384C8—81no—
385C22—21no—
386C22—21no—
387C22—22no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—82no—
394C22—82no—
395C22C31×#38611yescharacteristic
396C22C4×SD16×C3111yescharacteristic
397C22C31×#44011yescharacteristic
398C4—21no—
399C4—21no—
400C4—21no—
401C4—41no—
402C4—41no—
403C4—82no—
404C4C2×C31×#10111yescharacteristic
405C4C31×#41311yescharacteristic
406C4C31×#45011yescharacteristic
407C4C31×#45211yescharacteristic
408C4C31×#46111yescharacteristic
409C4C31×#46311yescharacteristic
410C2—21no—
411C2—21no—
412C2—42no—
413C2—81no—
414C2C31×#187711yescharacteristic
415C2C31×#190111yescharacteristic
416C2C31×#190311yescharacteristic
subgroupG/H
center, socleC22×C31#386
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC22×D4×C31C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
3. C31×#1997C2semidirect
4. C31×#1549C2semidirect
6. C31×#1292C2semidirect
7. C31×#1283C2semidirect
129. #9249C31direct (N × H)
179. #1997C2×C31semidirect
180. #1549C2×C31semidirect
182. #1292C2×C31semidirect
183. #1283C2×C31semidirect
283. C31#9249direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4762
D4×M16×C312
C31×#19972
C31×#15492
C31×#14862
C31×#12922
C31×#12832
#924931