Finite Group Databasebeta

← C31×#8432 #21465191

Subgroups — C31×#8432 #21465191

Order 7936.

740 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3501C211yesmaximal, characteristic
2C31×#1804C211yesmaximal, characteristic
3C31×#1542C211yesmaximal, characteristic, complemented
4C31×#1518C211yesmaximal, characteristic, complemented
5C31×#1518C211yesmaximal, characteristic, complemented
6C31×#1481C211yesmaximal, characteristic, complemented
7C31×#1478C211yesmaximal, characteristic
8C31×#554—21no—
9C31×#554—22no—
10C31×#554—22no—
11C31×#554C412yescomplemented
12D4×Q8×C31—21no—
13D4×Q8×C31C412yescomplemented
14C31×#544—21no—
15C31×#543—22no—
16C31×#533C2211yescharacteristic
17C31×#533C2211yescharacteristic
18C2×C31×C22⋊Q8—22no—
19C31×#518—21no—
20C2×C4×D4×C31C2211yescharacteristic
21C31×#431C2211yescharacteristic
22C31×#431C2211yescharacteristic
23C2×C31×C4⋊C8C2211yescharacteristic
24C2×C31×#102—21no—
25C31×#382C2211yescharacteristic
26C31×#340—21no—
27C31×#333—21no—
28C31×#332—21no—
29C31×#328—22no—
30C31×#328—22no—
31C31×Q8⋊C8—22no—
32C31×D4⋊C8—22no—
33C22×Q8×C31—22no—
34C22×D4×C31D411yescharacteristic
35C23×C4×C31—21no—
36C22×C8×C31—21no—
37C31×C4⋊Q8—22no—
38C31×C4⋊Q8—22no—
39C31×C4⋊Q8C2×C411yescharacteristic
40C31×C4⋊Q8C2×C411yescharacteristic
41C31×C4⋊Q8D411yescharacteristic
42C31×C4⋊Q8D411yescharacteristic
43C31×#125—22no—
44C31×#125—22no—
45C31×#125—21no—
46C31×#125—21no—
47C31×C22⋊Q8—24no—
48C31×C22⋊Q8—24no—
49C31×C22⋊Q8—24no—
50C31×C22⋊Q8—24no—
51C31×C22⋊Q8—22no—
52C31×C22⋊Q8—24no—
53C31×C22⋊Q8—21no—
54C31×C22⋊Q8—21no—
55C31×C22⋊Q8—22no—
56C31×C22⋊Q8—24no—
57C31×C22⋊Q8D412yes—
58C31×C22⋊Q8D412yes—
59C4×Q8×C31—21no—
60C4×Q8×C31—21no—
61C4×Q8×C31C2×C412yes—
62C4×Q8×C31D412yes—
63C4×D4×C31—22no—
64C4×D4×C31—22no—
65C4×D4×C31—22no—
66C4×D4×C31—22no—
67C4×D4×C31—21no—
68C4×D4×C31—21no—
69C4×D4×C31C2×C412yes—
70C4×D4×C31D412yes—
71C31×#117—21no—
72C31×#117—21no—
73C2×C4⋊C4×C31—24no—
74C2×C4⋊C4×C31—22no—
75C2×C4⋊C4×C31—21no—
76C2×C4⋊C4×C31D411yescharacteristic
77C2×C22⋊C4×C31—24no—
78C2×C22⋊C4×C31—21no—
79C2×C42×C31C2311yescharacteristic
80C31×C4⋊C8—21no—
81C31×C4⋊C8—21no—
82C31×C4⋊C8—21no—
83C31×C4⋊C8—21no—
84C31×#102—42no—
85C31×C22⋊C8—21no—
86C31×C22⋊C8—21no—
87C4×C8×C31—21no—
88C4×C8×C31—21no—
89C31×#95—21no—
90C31×#95—21no—
91C24×C31—21no—
92C2×Q8×C31—24no—
93C2×Q8×C31—21no—
94C2×Q8×C31—21no—
95C2×Q8×C31—84no—
96C2×Q8×C31C22⋊C412yes—
97C2×Q8×C31C22⋊C412yes—
98C2×D4×C31—21no—
99C2×D4×C31—21no—
100C2×D4×C31—21no—
101C2×D4×C31C22⋊C412yes—
102C2×D4×C31SD1612yes—
103C2×D4×C31Q1612yes—
104C22×C4×C31—24no—
105C22×C4×C31—24no—
106C22×C4×C31—21no—
107C22×C4×C31—22no—
108C22×C4×C31—22no—
109C22×C4×C31—41no—
110C22×C4×C31—82no—
111C22×C4×C31C2×D411yescharacteristic
112C22×C4×C31C2×D411yescharacteristic
113C22×C4×C31C2×D411yescharacteristic
114C2×C8×C31—41no—
115C2×C8×C31—41no—
116C2×C8×C31—41no—
117C2×C8×C31—41no—
118C2×C8×C31—41no—
119C4⋊C4×C31—24no—
120C4⋊C4×C31—24no—
121C4⋊C4×C31—24no—
122C4⋊C4×C31—21no—
123C4⋊C4×C31—21no—
124C4⋊C4×C31—21no—
125C4⋊C4×C31—22no—
126C4⋊C4×C31—22no—
127C4⋊C4×C31—22no—
128C4⋊C4×C31—21no—
129C4⋊C4×C31—21no—
130C4⋊C4×C31—21no—
131C4⋊C4×C31—21no—
132C4⋊C4×C31—22no—
133C4⋊C4×C31—41no—
134C4⋊C4×C31—41no—
135C4⋊C4×C31C22⋊C412yes—
136C4⋊C4×C31C22⋊C412yes—
137C4⋊C4×C31C22⋊C412yes—
138C22⋊C4×C31—24no—
139C22⋊C4×C31—24no—
140C22⋊C4×C31—22no—
141C22⋊C4×C31—22no—
142C22⋊C4×C31—22no—
143C22⋊C4×C31—22no—
144C42×C31—22no—
145C42×C31—22no—
146C42×C31C22×C411yescharacteristic
147C42×C31C2×D411yescharacteristic
148C42×C31C2×D411yescharacteristic
149C42×C31C2×D411yescharacteristic
150#8432C3111yesmaximal, characteristic, direct product factor, Sylow
151C23×C31—22no—
152C23×C31—22no—
153C23×C31—22no—
154C23×C31—81no—
155C23×C31—81no—
156C23×C31#12011yescharacteristic
157Q8×C31—42no—
158Q8×C31—42no—
159Q8×C31—42no—
160Q8×C31—81no—
161Q8×C31—84no—
162D4×C31—22no—
163D4×C31—22no—
164D4×C31—22no—
165D4×C31#10314yes—
166C2×C4×C31—22no—
167C2×C4×C31—22no—
168C2×C4×C31—22no—
169C2×C4×C31—22no—
170C2×C4×C31—22no—
171C2×C4×C31—41no—
172C2×C4×C31—41no—
173C2×C4×C31—44no—
174C2×C4×C31—82no—
175C2×C4×C31—81no—
176C2×C4×C31—84no—
177C2×C4×C31—84no—
178C2×C4×C31—81no—
179C2×C4×C31—81no—
180C2×C4×C31—81no—
181C2×C4×C31C2×C22⋊C411yescharacteristic
182C2×C4×C31C2×C22⋊C411yescharacteristic
183C2×C4×C31C2×C22⋊C411yescharacteristic
184C2×C4×C31#12011yescharacteristic
185C2×C4×C31#12011yescharacteristic
186C2×C4×C31#12011yescharacteristic
187C2×C4×C31C2×SD1611yescharacteristic
188C2×C4×C31C2×Q1611yescharacteristic
189C2×C4×C31#13711yescharacteristic
190C2×C4×C31#13711yescharacteristic
191C8×C31—81no—
192C8×C31—81no—
193C8×C31—81no—
194#3501C2×C3111yescharacteristic
195#1804C2×C3111yescharacteristic
196#1542C2×C3111yescharacteristic, complemented
197#1518C2×C3111yescharacteristic, complemented
198#1518C2×C3111yescharacteristic, complemented
199#1481C2×C3111yescharacteristic, complemented
200#1478C2×C3111yescharacteristic
201C22×C31—21no—
202C22×C31—21no—
203C22×C31—24no—
204C22×C31—42no—
205C22×C31—42no—
206C22×C31—82no—
207C22×C31—82no—
208C22×C31#37911yescharacteristic
209C22×C31#44811yescharacteristic
210C22×C31#45111yescharacteristic
211C4×C31—21no—
212C4×C31—21no—
213C4×C31—21no—
214C4×C31—21no—
215C4×C31—42no—
216C4×C31—42no—
217C4×C31—42no—
218C4×C31—42no—
219C4×C31—42no—
220C4×C31—161no—
221C4×C31C2×#10311yescharacteristic
222C4×C31#41911yescharacteristic
223C4×C31#44811yescharacteristic
224C4×C31#45111yescharacteristic
225#554—21no—
226#554—22no—
227#554—22no—
228#554C4×C3112yescomplemented
229D4×Q8—21no—
230D4×Q8C4×C3112yescomplemented
231#544—21no—
232#543—22no—
233#533C22×C3111yescharacteristic
234#533C22×C3111yescharacteristic
235C2×C22⋊Q8—22no—
236#518—21no—
237C2×C4×D4C22×C3111yescharacteristic
238#431C22×C3111yescharacteristic
239#431C22×C3111yescharacteristic
240C2×C4⋊C8C22×C3111yescharacteristic
241C2×#102—21no—
242#382C22×C3111yescharacteristic
243#340—21no—
244#333—21no—
245#332—21no—
246#328—22no—
247#328—22no—
248Q8⋊C8—22no—
249D4⋊C8—22no—
250C2×C31—21no—
251C2×C31—21no—
252C2×C31—44no—
253C2×C31#178711yescharacteristic
254C2×C31#179411yescharacteristic
255C2×C31#179511yescharacteristic
256C22×Q8—22no—
257C22×D4D4×C3111yescharacteristic
258C23×C4—21no—
259C22×C8—21no—
260C4⋊Q8—22no—
261C4⋊Q8—22no—
262C4⋊Q8C2×C4×C3111yescharacteristic
263C4⋊Q8C2×C4×C3111yescharacteristic
264C4⋊Q8D4×C3111yescharacteristic
265C4⋊Q8D4×C3111yescharacteristic
266#125—22no—
267#125—22no—
268#125—21no—
269#125—21no—
270C22⋊Q8—24no—
271C22⋊Q8—24no—
272C22⋊Q8—24no—
273C22⋊Q8—24no—
274C22⋊Q8—22no—
275C22⋊Q8—24no—
276C22⋊Q8—21no—
277C22⋊Q8—21no—
278C22⋊Q8—22no—
279C22⋊Q8—24no—
280C22⋊Q8D4×C3112yes—
281C22⋊Q8D4×C3112yes—
282C4×Q8—21no—
283C4×Q8—21no—
284C4×Q8C2×C4×C3112yes—
285C4×Q8D4×C3112yes—
286C4×D4—22no—
287C4×D4—22no—
288C4×D4—22no—
289C4×D4—22no—
290C4×D4—21no—
291C4×D4—21no—
292C4×D4C2×C4×C3112yes—
293C4×D4D4×C3112yes—
294#117—21no—
295#117—21no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4D4×C3111yescharacteristic
300C2×C22⋊C4—24no—
301C2×C22⋊C4—21no—
302C2×C42C23×C3111yescharacteristic
303C4⋊C8—21no—
304C4⋊C8—21no—
305C4⋊C8—21no—
306C4⋊C8—21no—
307#102—42no—
308C22⋊C8—21no—
309C22⋊C8—21no—
310C4×C8—21no—
311C4×C8—21no—
312#95—21no—
313#95—21no—
314C31#843211yescharacteristic, direct product factor, Sylow
315C24—21no—
316C2×Q8—24no—
317C2×Q8—21no—
318C2×Q8—21no—
319C2×Q8—84no—
320C2×Q8C22⋊C4×C3112yes—
321C2×Q8C22⋊C4×C3112yes—
322C2×D4—21no—
323C2×D4—21no—
324C2×D4—21no—
325C2×D4C22⋊C4×C3112yes—
326C2×D4SD16×C3112yes—
327C2×D4Q16×C3112yes—
328C22×C4—24no—
329C22×C4—24no—
330C22×C4—21no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—41no—
334C22×C4—82no—
335C22×C4C2×D4×C3111yescharacteristic
336C22×C4C2×D4×C3111yescharacteristic
337C22×C4C2×D4×C3111yescharacteristic
338C2×C8—41no—
339C2×C8—41no—
340C2×C8—41no—
341C2×C8—41no—
342C2×C8—41no—
343C4⋊C4—24no—
344C4⋊C4—24no—
345C4⋊C4—24no—
346C4⋊C4—21no—
347C4⋊C4—21no—
348C4⋊C4—21no—
349C4⋊C4—22no—
350C4⋊C4—22no—
351C4⋊C4—22no—
352C4⋊C4—21no—
353C4⋊C4—21no—
354C4⋊C4—21no—
355C4⋊C4—21no—
356C4⋊C4—22no—
357C4⋊C4—41no—
358C4⋊C4—41no—
359C4⋊C4C22⋊C4×C3112yes—
360C4⋊C4C22⋊C4×C3112yes—
361C4⋊C4C22⋊C4×C3112yes—
362C22⋊C4—24no—
363C22⋊C4—24no—
364C22⋊C4—22no—
365C22⋊C4—22no—
366C22⋊C4—22no—
367C22⋊C4—22no—
368C42—22no—
369C42—22no—
370C42C22×C4×C3111yescharacteristic
371C42C2×D4×C3111yescharacteristic
372C42C2×D4×C3111yescharacteristic
373C42C2×D4×C3111yescharacteristic
374C23—22no—
375C23—22no—
376C23—22no—
377C23—81no—
378C23—81no—
379C23C31×#12011yescharacteristic
380Q8—42no—
381Q8—42no—
382Q8—42no—
383Q8—81no—
384Q8—84no—
385D4—22no—
386D4—22no—
387D4—22no—
388D4C31×#10314yes—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—44no—
397C2×C4—82no—
398C2×C4—81no—
399C2×C4—84no—
400C2×C4—84no—
401C2×C4—81no—
402C2×C4—81no—
403C2×C4—81no—
404C2×C4C2×C22⋊C4×C3111yescharacteristic
405C2×C4C2×C22⋊C4×C3111yescharacteristic
406C2×C4C2×C22⋊C4×C3111yescharacteristic
407C2×C4C31×#12011yescharacteristic
408C2×C4C31×#12011yescharacteristic
409C2×C4C31×#12011yescharacteristic
410C2×C4C2×SD16×C3111yescharacteristic
411C2×C4C2×Q16×C3111yescharacteristic
412C2×C4C31×#13711yescharacteristic
413C2×C4C31×#13711yescharacteristic
414C8—81no—
415C8—81no—
416C8—81no—
417C22—21no—
418C22—21no—
419C22—24no—
420C22—42no—
421C22—42no—
422C22—82no—
423C22—82no—
424C22C31×#37911yescharacteristic
425C22C31×#44811yescharacteristic
426C22C31×#45111yescharacteristic
427C4—21no—
428C4—21no—
429C4—21no—
430C4—21no—
431C4—42no—
432C4—42no—
433C4—42no—
434C4—42no—
435C4—42no—
436C4—161no—
437C4C2×C31×#10311yescharacteristic
438C4C31×#41911yescharacteristic
439C4C31×#44811yescharacteristic
440C4C31×#45111yescharacteristic
441C2—21no—
442C2—21no—
443C2—44no—
444C2C31×#178711yescharacteristic
445C2C31×#179411yescharacteristic
446C2C31×#179511yescharacteristic
subgroupG/H
center, socleC22×C31#379
commutatorC42C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC22×D4×C31D4
LCSG ▷ C42 ▷ 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×#1542C2semidirect
4. C31×#1518C2semidirect
5. C31×#1518C2semidirect
6. C31×#1481C2semidirect
11. C31×#554C4semidirect
13. D4×Q8×C31C4semidirect
150. #8432C31direct (N × H)
196. #1542C2×C31semidirect
197. #1518C2×C31semidirect
198. #1518C2×C31semidirect
199. #1481C2×C31semidirect
228. #554C4×C31semidirect
230. D4×Q8C4×C31semidirect
314. C31#8432direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35012
C31×#18042
C31×#15422
C31×#15182
C31×#14812
C31×#14782
#843231