Finite Group Databasebeta

← C31×#8373 #21465132

Subgroups — C31×#8373 #21465132

Order 7936.

814 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#553C211yesmaximal, characteristic
2C4×C31×#100C211yesmaximal, characteristic, complemented
3C31×#1528C212yesmaximal, complemented
4C31×#1490C212yesmaximal, complemented
5C31×#1466C211yesmaximal, characteristic, complemented
6C31×#553—24no—
7C31×#553—24no—
8C2×C31×#126—21no—
9C2×C31×#125C2211yescharacteristic
10C2×C31×#123—21no—
11C2×C31×#121—21no—
12C2×C31×#121C411yescharacteristic
13C2×C31×#121C411yescharacteristic
14C2×C4×D4×C31—21no—
15C2×C4×D4×C31C2211yescharacteristic
16C2×C4×D4×C31C2211yescharacteristic
17C2×C31×#117C411yescharacteristic
18C22×C4⋊C4×C31C411yescharacteristic
19C31×#432C2212yes—
20C2×C31×#100—21no—
21C4×M16×C31C2212yes—
22C31×#343—21no—
23C31×#330—24no—
24C31×D4⋊C8—24no—
25C31×#323—21no—
26C31×#323—21no—
27C22×D4×C31—21no—
28C22×D4×C31—21no—
29C22×D4×C31C2×C411yescharacteristic
30C22×D4×C31D411yescharacteristic
31C23×C4×C31—21no—
32C23×C4×C31—21no—
33C23×C4×C31C2×C411yescharacteristic
34C23×C4×C31C2×C411yescharacteristic
35C2×M16×C31—22no—
36C31×#126—28no—
37C31×#125—22no—
38C31×#125D414yes—
39C31×#123—28no—
40C31×#121—28no—
41C31×#121—22no—
42C31×#121—22no—
43C31×#121—22no—
44C31×#121—22no—
45C4×D4×C31—28no—
46C4×D4×C31—22no—
47C4×D4×C31—22no—
48C4×D4×C31—22no—
49C4×D4×C31D414yes—
50C31×#117—22no—
51C31×#117—22no—
52C2×C4⋊C4×C31—21no—
53C2×C4⋊C4×C31—21no—
54C2×C4⋊C4×C31—21no—
55C2×C4⋊C4×C31—22no—
56C2×C4⋊C4×C31—22no—
57C2×C4⋊C4×C31C2×C411yescharacteristic
58C2×C4⋊C4×C31C2×C411yescharacteristic
59C2×C4⋊C4×C31C2×C411yescharacteristic
60C2×C4⋊C4×C31D411yescharacteristic
61C2×C22⋊C4×C31—21no—
62C2×C22⋊C4×C31—21no—
63C2×C22⋊C4×C31—21no—
64C2×C22⋊C4×C31—21no—
65C2×C22⋊C4×C31D411yescharacteristic
66C2×C22⋊C4×C31D411yescharacteristic
67C2×C42×C31—21no—
68C2×C42×C31C2311yescharacteristic
69C31×C4⋊C8—22no—
70C31×#100—24no—
71C31×C22⋊C8—22no—
72C31×#97—22no—
73C31×#97—22no—
74C4×C8×C31—22no—
75C24×C31—21no—
76C24×C31C22⋊C411yescharacteristic
77C24×C31C22⋊C411yescharacteristic
78C2×D4×C31—24no—
79C2×D4×C31—22no—
80C2×D4×C31—24no—
81C2×D4×C31—21no—
82C2×D4×C31—22no—
83C2×D4×C31—42no—
84C2×D4×C31—41no—
85C2×D4×C31—42no—
86C2×D4×C31—42no—
87C2×D4×C31—82no—
88C2×D4×C31C22⋊C412yes—
89C22×C4×C31—21no—
90C22×C4×C31—21no—
91C22×C4×C31—21no—
92C22×C4×C31—24no—
93C22×C4×C31—21no—
94C22×C4×C31—21no—
95C22×C4×C31—21no—
96C22×C4×C31—21no—
97C22×C4×C31—24no—
98C22×C4×C31—42no—
99C22×C4×C31—42no—
100C22×C4×C31—82no—
101C22×C4×C31—82no—
102C22×C4×C31C22⋊C411yescharacteristic
103C22×C4×C31C22⋊C411yescharacteristic
104C22×C4×C31C22×C411yescharacteristic
105C22×C4×C31C2×D411yescharacteristic
106C22×C4×C31C2×D411yescharacteristic
107M16×C31—24no—
108M16×C31—42no—
109C2×C8×C31—42no—
110C2×C8×C31—42no—
111C4⋊C4×C31—24no—
112C4⋊C4×C31—21no—
113C4⋊C4×C31—21no—
114C4⋊C4×C31—21no—
115C4⋊C4×C31—24no—
116C4⋊C4×C31—24no—
117C4⋊C4×C31—22no—
118C4⋊C4×C31C22⋊C412yes—
119C4⋊C4×C31C22⋊C412yes—
120C4⋊C4×C31C22⋊C412yes—
121C22⋊C4×C31—24no—
122C22⋊C4×C31—24no—
123C22⋊C4×C31—24no—
124C22⋊C4×C31—24no—
125C22⋊C4×C31—22no—
126C22⋊C4×C31—22no—
127C42×C31—24no—
128C42×C31C2×D412yes—
129C42×C31C2×D412yes—
130#8373C3111yesmaximal, characteristic, direct product factor, Sylow
131C23×C31—21no—
132C23×C31—21no—
133C23×C31—21no—
134C23×C31—22no—
135C23×C31—21no—
136C23×C31—21no—
137C23×C31—41no—
138C23×C31—41no—
139C23×C31—42no—
140C23×C31—42no—
141C23×C31—41no—
142C23×C31—41no—
143C23×C31—41no—
144C23×C31—41no—
145C23×C31#10412yes—
146C23×C31C2×C22⋊C411yescharacteristic
147D4×C31—24no—
148D4×C31—44no—
149D4×C31—42no—
150D4×C31—48no—
151D4×C31—84no—
152C2×C4×C31—21no—
153C2×C4×C31—21no—
154C2×C4×C31—22no—
155C2×C4×C31—21no—
156C2×C4×C31—22no—
157C2×C4×C31—22no—
158C2×C4×C31—21no—
159C2×C4×C31—22no—
160C2×C4×C31—41no—
161C2×C4×C31—42no—
162C2×C4×C31—42no—
163C2×C4×C31—42no—
164C2×C4×C31—42no—
165C2×C4×C31—41no—
166C2×C4×C31—41no—
167C2×C4×C31—42no—
168C2×C4×C31—42no—
169C2×C4×C31—41no—
170C2×C4×C31—41no—
171C2×C4×C31—84no—
172C2×C4×C31—84no—
173C2×C4×C31C2×C22⋊C411yescharacteristic
174C2×C4×C31C2×C22⋊C411yescharacteristic
175C2×C4×C31#12012yes—
176C2×C4×C31#12012yes—
177C8×C31—44no—
178C8×C31—82no—
179C2×#553C2×C3111yescharacteristic
180C4×#100C2×C3111yescharacteristic, complemented
181#1528C2×C3112yescomplemented
182#1490C2×C3112yescomplemented
183#1466C2×C3111yescharacteristic, complemented
184C22×C31—21no—
185C22×C31—21no—
186C22×C31—22no—
187C22×C31—42no—
188C22×C31—42no—
189C22×C31—41no—
190C22×C31—41no—
191C22×C31—42no—
192C22×C31—41no—
193C22×C31—41no—
194C22×C31—42no—
195C22×C31—41no—
196C22×C31—42no—
197C22×C31—81no—
198C22×C31—81no—
199C22×C31—82no—
200C22×C31—82no—
201C22×C31#37911yescharacteristic
202C22×C31C2×#10411yescharacteristic
203C22×C31#42111yescharacteristic
204C4×C31—22no—
205C4×C31—21no—
206C4×C31—22no—
207C4×C31—42no—
208C4×C31—42no—
209C4×C31—41no—
210C4×C31—41no—
211C4×C31—42no—
212C4×C31#41312yes—
213#553—24no—
214#553—24no—
215C2×#126—21no—
216C2×#125C22×C3111yescharacteristic
217C2×#123—21no—
218C2×#121—21no—
219C2×#121C4×C3111yescharacteristic
220C2×#121C4×C3111yescharacteristic
221C2×C4×D4—21no—
222C2×C4×D4C22×C3111yescharacteristic
223C2×C4×D4C22×C3111yescharacteristic
224C2×#117C4×C3111yescharacteristic
225C22×C4⋊C4C4×C3111yescharacteristic
226#432C22×C3112yes—
227C2×#100—21no—
228C4×M16C22×C3112yes—
229#343—21no—
230#330—24no—
231D4⋊C8—24no—
232#323—21no—
233#323—21no—
234C2×C31—21no—
235C2×C31—21no—
236C2×C31—42no—
237C2×C31—81no—
238C2×C31—82no—
239C2×C31#178511yescharacteristic
240C2×C31#178911yescharacteristic
241C2×C31#179511yescharacteristic
242C22×D4—21no—
243C22×D4—21no—
244C22×D4C2×C4×C3111yescharacteristic
245C22×D4D4×C3111yescharacteristic
246C23×C4—21no—
247C23×C4—21no—
248C23×C4C2×C4×C3111yescharacteristic
249C23×C4C2×C4×C3111yescharacteristic
250C2×M16—22no—
251#126—28no—
252#125—22no—
253#125D4×C3114yes—
254#123—28no—
255#121—28no—
256#121—22no—
257#121—22no—
258#121—22no—
259#121—22no—
260C4×D4—28no—
261C4×D4—22no—
262C4×D4—22no—
263C4×D4—22no—
264C4×D4D4×C3114yes—
265#117—22no—
266#117—22no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4C2×C4×C3111yescharacteristic
273C2×C4⋊C4C2×C4×C3111yescharacteristic
274C2×C4⋊C4C2×C4×C3111yescharacteristic
275C2×C4⋊C4D4×C3111yescharacteristic
276C2×C22⋊C4—21no—
277C2×C22⋊C4—21no—
278C2×C22⋊C4—21no—
279C2×C22⋊C4—21no—
280C2×C22⋊C4D4×C3111yescharacteristic
281C2×C22⋊C4D4×C3111yescharacteristic
282C2×C42—21no—
283C2×C42C23×C3111yescharacteristic
284C4⋊C8—22no—
285#100—24no—
286C22⋊C8—22no—
287#97—22no—
288#97—22no—
289C4×C8—22no—
290C31#837311yescharacteristic, direct product factor, Sylow
291C24—21no—
292C24C22⋊C4×C3111yescharacteristic
293C24C22⋊C4×C3111yescharacteristic
294C2×D4—24no—
295C2×D4—22no—
296C2×D4—24no—
297C2×D4—21no—
298C2×D4—22no—
299C2×D4—42no—
300C2×D4—41no—
301C2×D4—42no—
302C2×D4—42no—
303C2×D4—82no—
304C2×D4C22⋊C4×C3112yes—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—24no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—24no—
314C22×C4—42no—
315C22×C4—42no—
316C22×C4—82no—
317C22×C4—82no—
318C22×C4C22⋊C4×C3111yescharacteristic
319C22×C4C22⋊C4×C3111yescharacteristic
320C22×C4C22×C4×C3111yescharacteristic
321C22×C4C2×D4×C3111yescharacteristic
322C22×C4C2×D4×C3111yescharacteristic
323M16—24no—
324M16—42no—
325C2×C8—42no—
326C2×C8—42no—
327C4⋊C4—24no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—24no—
332C4⋊C4—24no—
333C4⋊C4—22no—
334C4⋊C4C22⋊C4×C3112yes—
335C4⋊C4C22⋊C4×C3112yes—
336C4⋊C4C22⋊C4×C3112yes—
337C22⋊C4—24no—
338C22⋊C4—24no—
339C22⋊C4—24no—
340C22⋊C4—24no—
341C22⋊C4—22no—
342C22⋊C4—22no—
343C42—24no—
344C42C2×D4×C3112yes—
345C42C2×D4×C3112yes—
346C23—21no—
347C23—21no—
348C23—21no—
349C23—22no—
350C23—21no—
351C23—21no—
352C23—41no—
353C23—41no—
354C23—42no—
355C23—42no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23C31×#10412yes—
361C23C2×C22⋊C4×C3111yescharacteristic
362D4—24no—
363D4—44no—
364D4—42no—
365D4—48no—
366D4—84no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—22no—
370C2×C4—21no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—21no—
374C2×C4—22no—
375C2×C4—41no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—84no—
387C2×C4—84no—
388C2×C4C2×C22⋊C4×C3111yescharacteristic
389C2×C4C2×C22⋊C4×C3111yescharacteristic
390C2×C4C31×#12012yes—
391C2×C4C31×#12012yes—
392C8—44no—
393C8—82no—
394C22—21no—
395C22—21no—
396C22—22no—
397C22—42no—
398C22—42no—
399C22—41no—
400C22—41no—
401C22—42no—
402C22—41no—
403C22—41no—
404C22—42no—
405C22—41no—
406C22—42no—
407C22—81no—
408C22—81no—
409C22—82no—
410C22—82no—
411C22C31×#37911yescharacteristic
412C22C2×C31×#10411yescharacteristic
413C22C31×#42111yescharacteristic
414C4—22no—
415C4—21no—
416C4—22no—
417C4—42no—
418C4—42no—
419C4—41no—
420C4—41no—
421C4—42no—
422C4C31×#41312yes—
423C2—21no—
424C2—21no—
425C2—42no—
426C2—82no—
427C2—81no—
428C2C31×#178511yescharacteristic
429C2C31×#178911yescharacteristic
430C2C31×#179511yescharacteristic
subgroupG/H
center, socleC22×C31#379
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC2×C31×#553C2
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
2. C4×C31×#100C2semidirect
3. C31×#1528C2semidirect
4. C31×#1490C2semidirect
5. C31×#1466C2semidirect
130. #8373C31direct (N × H)
180. C4×#100C2×C31semidirect
181. #1528C2×C31semidirect
182. #1490C2×C31semidirect
183. #1466C2×C31semidirect
290. C31#8373direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5532
C4×C31×#1002
C31×#15282
C31×#14902
C31×#14662
#837331