Finite Group Databasebeta

← C31×#23484 #21480243

Subgroups — C31×#23484 #21480243

Order 7936.

1418 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#536C211yesmaximal, characteristic
2C2×C31×#428C211yesmaximal, characteristic, complemented
3C2×C31×#419C211yesmaximal, characteristic, complemented
4C22×C31×#103C211yesmaximal, characteristic, complemented
5C2×C31×#408C211yesmaximal, characteristic
6C31×#2311C211yesmaximal, characteristic
7C31×#2036C214yesmaximal, complemented
8C31×#2035C214yesmaximal, complemented
9C31×#1735C211yesmaximal, characteristic, complemented
10C22×#41×C31C2211yescharacteristic
11C23×Q8×C31C2211yescharacteristic
12C22×M16×C31C2211yescharacteristic
13C23×C8×C31C2211yescharacteristic
14C31×#536—24no—
15C31×#536—24no—
16C2×C31×C4⋊Q8—21no—
17C2×C31×#124—21no—
18C2×C31×#123—22no—
19C2×C31×C22⋊Q8C2212yes—
20C2×C31×C22⋊Q8C2212yes—
21C2×C31×#117C2211yescharacteristic
22C2×C31×#117C2211yescharacteristic
23C22×C4⋊C4×C31C2211yescharacteristic
24C31×#428—24no—
25C2×C31×#107C2212yes—
26C2×C31×#106C2212yes—
27C31×#419—24no—
28C2×C31×#103—24no—
29C2×C31×#103C2214yes—
30C2×C31×#103C2214yes—
31C31×#408—24no—
32C2×C31×C22⋊C8C2214yes—
33C31×#391—21no—
34C31×#390—21no—
35C31×#386—22no—
36C31×#380C2214yes—
37C31×#340C2212yes—
38C31×#340C2212yes—
39C2×#41×C31—22no—
40C2×#41×C31—22no—
41C2×#41×C31—22no—
42C2×#41×C31—22no—
43C2×#41×C31—22no—
44C2×#41×C31—22no—
45C22×Q8×C31—21no—
46C22×Q8×C31—22no—
47C22×Q8×C31—22no—
48C22×Q8×C31—22no—
49C22×Q8×C31—22no—
50C22×Q8×C31—22no—
51C22×Q8×C31D414yes—
52C22×Q8×C31D411yescharacteristic
53C22×Q8×C31C2312yes—
54C22×D4×C31D412yes—
55C22×D4×C31D411yescharacteristic
56C23×C4×C31—21no—
57C23×C4×C31—21no—
58C23×C4×C31C2312yes—
59C23×C4×C31C2311yescharacteristic
60C2×M16×C31—22no—
61C2×M16×C31—22no—
62C2×M16×C31D414yes—
63C22×C8×C31—22no—
64C22×C8×C31—22no—
65C22×C8×C31—22no—
66C22×C8×C31C2312yes—
67C22×C8×C31C2312yes—
68C31×C4⋊Q8—28no—
69C31×#124—28no—
70C31×#123—216no—
71C31×C22⋊Q8—24no—
72C31×C22⋊Q8—24no—
73C31×C22⋊Q8—24no—
74C31×C22⋊Q8—24no—
75C31×#117—22no—
76C31×#117—22no—
77C31×#117—22no—
78C31×#117D414yes—
79C2×C4⋊C4×C31—22no—
80C2×C4⋊C4×C31—22no—
81C2×C4⋊C4×C31—22no—
82C2×C4⋊C4×C31—22no—
83C2×C4⋊C4×C31—21no—
84C2×C4⋊C4×C31C2312yes—
85C2×C4⋊C4×C31C2312yes—
86C2×C4⋊C4×C31C2311yescharacteristic
87C2×C4⋊C4×C31C2311yescharacteristic
88C2×C22⋊C4×C31—21no—
89C2×C22⋊C4×C31—22no—
90C2×C22⋊C4×C31—22no—
91C2×C22⋊C4×C31—21no—
92C2×C22⋊C4×C31—24no—
93C2×C42×C31—21no—
94C2×C42×C31—21no—
95C31×#107—24no—
96C31×#106—24no—
97C31×#103—28no—
98C31×#103—28no—
99C31×C22⋊C8—28no—
100C31×#95—24no—
101C24×C31C2×D412yes—
102C24×C31C2×D411yescharacteristic
103#41×C31—44no—
104#41×C31—44no—
105#41×C31—44no—
106#41×C31—44no—
107C2×Q8×C31—24no—
108C2×Q8×C31—22no—
109C2×Q8×C31—22no—
110C2×Q8×C31—22no—
111C2×Q8×C31—22no—
112C2×Q8×C31—28no—
113C2×Q8×C31—28no—
114C2×Q8×C31—22no—
115C2×Q8×C31—22no—
116C2×Q8×C31—22no—
117C2×Q8×C31—22no—
118C2×Q8×C31—42no—
119C2×Q8×C31—44no—
120C2×Q8×C31—42no—
121C2×Q8×C31—44no—
122C2×Q8×C31C2×D414yes—
123C2×D4×C31—24no—
124C2×D4×C31—24no—
125C2×D4×C31—24no—
126C2×D4×C31—22no—
127C2×D4×C31—22no—
128C2×D4×C31—22no—
129C22×C4×C31—24no—
130C22×C4×C31—21no—
131C22×C4×C31—21no—
132C22×C4×C31—22no—
133C22×C4×C31—22no—
134C22×C4×C31—22no—
135C22×C4×C31—22no—
136C22×C4×C31—22no—
137C22×C4×C31—22no—
138C22×C4×C31—22no—
139C22×C4×C31—22no—
140C22×C4×C31—22no—
141C22×C4×C31—42no—
142C22×C4×C31—42no—
143C22×C4×C31—42no—
144C22×C4×C31—82no—
145C22×C4×C31C2×D412yes—
146C22×C4×C31C2×D411yescharacteristic
147C22×C4×C31C2×D412yes—
148C22×C4×C31C2×D412yes—
149C22×C4×C31C2×D412yes—
150C22×C4×C31#4112yes—
151C22×C4×C31#4112yes—
152C22×C4×C31#4112yes—
153C22×C4×C31C2411yescharacteristic
154M16×C31—28no—
155C2×C8×C31—22no—
156C2×C8×C31—22no—
157C2×C8×C31—22no—
158C2×C8×C31—22no—
159C2×C8×C31—22no—
160C2×C8×C31—44no—
161C2×C8×C31C2×D414yes—
162C4⋊C4×C31—28no—
163C4⋊C4×C31—28no—
164C4⋊C4×C31—21no—
165C4⋊C4×C31—21no—
166C4⋊C4×C31—22no—
167C4⋊C4×C31—22no—
168C4⋊C4×C31—22no—
169C4⋊C4×C31—22no—
170C4⋊C4×C31—42no—
171C4⋊C4×C31C2×D412yes—
172C4⋊C4×C31C2×D412yes—
173C22⋊C4×C31—28no—
174C22⋊C4×C31—28no—
175C22⋊C4×C31—24no—
176C22⋊C4×C31—42no—
177C22⋊C4×C31—84no—
178C42×C31—24no—
179C42×C31—42no—
180#23484C3111yesmaximal, characteristic, direct product factor, Sylow
181C23×C31—22no—
182C23×C31—22no—
183C23×C31—22no—
184C23×C31—22no—
185C23×C31—22no—
186C23×C31—24no—
187C23×C31—24no—
188C23×C31#12012yes—
189C23×C31#12112yes—
190C23×C31#12312yes—
191C23×C31C22×D411yescharacteristic
192Q8×C31—24no—
193Q8×C31—24no—
194Q8×C31—42no—
195Q8×C31—42no—
196Q8×C31—48no—
197Q8×C31—44no—
198D4×C31—48no—
199D4×C31—44no—
200C2×C4×C31—22no—
201C2×C4×C31—22no—
202C2×C4×C31—24no—
203C2×C4×C31—22no—
204C2×C4×C31—22no—
205C2×C4×C31—22no—
206C2×C4×C31—42no—
207C2×C4×C31—42no—
208C2×C4×C31—42no—
209C2×C4×C31—42no—
210C2×C4×C31—48no—
211C2×C4×C31—42no—
212C2×C4×C31—42no—
213C2×C4×C31—42no—
214C2×C4×C31—42no—
215C2×C4×C31—42no—
216C2×C4×C31—42no—
217C2×C4×C31—42no—
218C2×C4×C31—44no—
219C2×C4×C31—42no—
220C2×C4×C31—84no—
221C2×C4×C31#12012yes—
222C2×C4×C31#12114yes—
223C2×C4×C31#12114yes—
224C2×C4×C31#12112yes—
225C2×C4×C31#12314yes—
226C2×C4×C31#12312yes—
227C2×C4×C31#12414yes—
228C2×C4×C31C22×D411yescharacteristic
229C2×C4×C31C22×D411yescharacteristic
230C2×C4×C31C22×D411yescharacteristic
231C2×C4×C31C2×#4111yescharacteristic
232C2×C4×C31C2×#4111yescharacteristic
233C2×C4×C31C2×#4111yescharacteristic
234C8×C31—24no—
235C8×C31—42no—
236C2×#536C2×C3111yescharacteristic
237C2×#428C2×C3111yescharacteristic, complemented
238C2×#419C2×C3111yescharacteristic, complemented
239C22×#103C2×C3111yescharacteristic, complemented
240C2×#408C2×C3111yescharacteristic
241#2311C2×C3111yescharacteristic
242#2036C2×C3114yescomplemented
243#2035C2×C3114yescomplemented
244#1735C2×C3111yescharacteristic, complemented
245C22×C31—24no—
246C22×C31—22no—
247C22×C31—22no—
248C22×C31—24no—
249C22×C31—44no—
250C22×C31—42no—
251C22×C31—42no—
252C22×C31—42no—
253C22×C31—44no—
254C22×C31#39414yes—
255C22×C31C2×#12011yescharacteristic
256C22×C31C2×#12111yescharacteristic
257C22×C31C2×#12311yescharacteristic
258C22×C31#57712yes—
259C22×C31#57812yes—
260C4×C31—42no—
261C4×C31—44no—
262C4×C31—42no—
263C4×C31—42no—
264C4×C31—82no—
265C4×C31—82no—
266C4×C31#39414yes—
267C4×C31C2×#12111yescharacteristic
268C4×C31C2×#12111yescharacteristic
269C4×C31C2×#12311yescharacteristic
270C4×C31C2×#12411yescharacteristic
271C22×#41C22×C3111yescharacteristic
272C23×Q8C22×C3111yescharacteristic
273C22×M16C22×C3111yescharacteristic
274C23×C8C22×C3111yescharacteristic
275#536—24no—
276#536—24no—
277C2×C4⋊Q8—21no—
278C2×#124—21no—
279C2×#123—22no—
280C2×C22⋊Q8C22×C3112yes—
281C2×C22⋊Q8C22×C3112yes—
282C2×#117C22×C3111yescharacteristic
283C2×#117C22×C3111yescharacteristic
284C22×C4⋊C4C22×C3111yescharacteristic
285#428—24no—
286C2×#107C22×C3112yes—
287C2×#106C22×C3112yes—
288#419—24no—
289C2×#103—24no—
290C2×#103C22×C3114yes—
291C2×#103C22×C3114yes—
292#408—24no—
293C2×C22⋊C8C22×C3114yes—
294#391—21no—
295#390—21no—
296#386—22no—
297#380C22×C3114yes—
298#340C22×C3112yes—
299#340C22×C3112yes—
300C2×C31—24no—
301C2×C31—82no—
302C2×C31C2×#39411yescharacteristic
303C2×C31#301011yescharacteristic
304C2×C31#301111yescharacteristic
305C2×C31#306312yes—
306C2×C31#309712yes—
307C2×#41—22no—
308C2×#41—22no—
309C2×#41—22no—
310C2×#41—22no—
311C2×#41—22no—
312C2×#41—22no—
313C22×Q8—21no—
314C22×Q8—22no—
315C22×Q8—22no—
316C22×Q8—22no—
317C22×Q8—22no—
318C22×Q8—22no—
319C22×Q8D4×C3114yes—
320C22×Q8D4×C3111yescharacteristic
321C22×Q8C23×C3112yes—
322C22×D4D4×C3112yes—
323C22×D4D4×C3111yescharacteristic
324C23×C4—21no—
325C23×C4—21no—
326C23×C4C23×C3112yes—
327C23×C4C23×C3111yescharacteristic
328C2×M16—22no—
329C2×M16—22no—
330C2×M16D4×C3114yes—
331C22×C8—22no—
332C22×C8—22no—
333C22×C8—22no—
334C22×C8C23×C3112yes—
335C22×C8C23×C3112yes—
336C4⋊Q8—28no—
337#124—28no—
338#123—216no—
339C22⋊Q8—24no—
340C22⋊Q8—24no—
341C22⋊Q8—24no—
342C22⋊Q8—24no—
343#117—22no—
344#117—22no—
345#117—22no—
346#117D4×C3114yes—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4C23×C3112yes—
353C2×C4⋊C4C23×C3112yes—
354C2×C4⋊C4C23×C3111yescharacteristic
355C2×C4⋊C4C23×C3111yescharacteristic
356C2×C22⋊C4—21no—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—24no—
361C2×C42—21no—
362C2×C42—21no—
363#107—24no—
364#106—24no—
365#103—28no—
366#103—28no—
367C22⋊C8—28no—
368#95—24no—
369C31#2348411yescharacteristic, direct product factor, Sylow
370C24C2×D4×C3112yes—
371C24C2×D4×C3111yescharacteristic
372#41—44no—
373#41—44no—
374#41—44no—
375#41—44no—
376C2×Q8—24no—
377C2×Q8—22no—
378C2×Q8—22no—
379C2×Q8—22no—
380C2×Q8—22no—
381C2×Q8—28no—
382C2×Q8—28no—
383C2×Q8—22no—
384C2×Q8—22no—
385C2×Q8—22no—
386C2×Q8—22no—
387C2×Q8—42no—
388C2×Q8—44no—
389C2×Q8—42no—
390C2×Q8—44no—
391C2×Q8C2×D4×C3114yes—
392C2×D4—24no—
393C2×D4—24no—
394C2×D4—24no—
395C2×D4—22no—
396C2×D4—22no—
397C2×D4—22no—
398C22×C4—24no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—42no—
411C22×C4—42no—
412C22×C4—42no—
413C22×C4—82no—
414C22×C4C2×D4×C3112yes—
415C22×C4C2×D4×C3111yescharacteristic
416C22×C4C2×D4×C3112yes—
417C22×C4C2×D4×C3112yes—
418C22×C4C2×D4×C3112yes—
419C22×C4#41×C3112yes—
420C22×C4#41×C3112yes—
421C22×C4#41×C3112yes—
422C22×C4C24×C3111yescharacteristic
423M16—28no—
424C2×C8—22no—
425C2×C8—22no—
426C2×C8—22no—
427C2×C8—22no—
428C2×C8—22no—
429C2×C8—44no—
430C2×C8C2×D4×C3114yes—
431C4⋊C4—28no—
432C4⋊C4—28no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—22no—
436C4⋊C4—22no—
437C4⋊C4—22no—
438C4⋊C4—22no—
439C4⋊C4—42no—
440C4⋊C4C2×D4×C3112yes—
441C4⋊C4C2×D4×C3112yes—
442C22⋊C4—28no—
443C22⋊C4—28no—
444C22⋊C4—24no—
445C22⋊C4—42no—
446C22⋊C4—84no—
447C42—24no—
448C42—42no—
449C23—22no—
450C23—22no—
451C23—22no—
452C23—22no—
453C23—22no—
454C23—24no—
455C23—24no—
456C23C31×#12012yes—
457C23C31×#12112yes—
458C23C31×#12312yes—
459C23C22×D4×C3111yescharacteristic
460Q8—24no—
461Q8—24no—
462Q8—42no—
463Q8—42no—
464Q8—48no—
465Q8—44no—
466D4—48no—
467D4—44no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—24no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—48no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—44no—
487C2×C4—42no—
488C2×C4—84no—
489C2×C4C31×#12012yes—
490C2×C4C31×#12114yes—
491C2×C4C31×#12114yes—
492C2×C4C31×#12112yes—
493C2×C4C31×#12314yes—
494C2×C4C31×#12312yes—
495C2×C4C31×#12414yes—
496C2×C4C22×D4×C3111yescharacteristic
497C2×C4C22×D4×C3111yescharacteristic
498C2×C4C22×D4×C3111yescharacteristic
499C2×C4C2×#41×C3111yescharacteristic
500C2×C4C2×#41×C3111yescharacteristic
501C2×C4C2×#41×C3111yescharacteristic
502C8—24no—
503C8—42no—
504C22—24no—
505C22—22no—
506C22—22no—
507C22—24no—
508C22—44no—
509C22—42no—
510C22—42no—
511C22—42no—
512C22—44no—
513C22C31×#39414yes—
514C22C2×C31×#12011yescharacteristic
515C22C2×C31×#12111yescharacteristic
516C22C2×C31×#12311yescharacteristic
517C22C31×#57712yes—
518C22C31×#57812yes—
519C4—42no—
520C4—44no—
521C4—42no—
522C4—42no—
523C4—82no—
524C4—82no—
525C4C31×#39414yes—
526C4C2×C31×#12111yescharacteristic
527C4C2×C31×#12111yescharacteristic
528C4C2×C31×#12311yescharacteristic
529C4C2×C31×#12411yescharacteristic
530C2—24no—
531C2—82no—
532C2C2×C31×#39411yescharacteristic
533C2C31×#301011yescharacteristic
534C2C31×#301111yescharacteristic
535C2C31×#306312yes—
536C2C31×#309712yes—
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC22×#41×C31C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C22×#41×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#428C2semidirect
3. C2×C31×#419C2semidirect
4. C22×C31×#103C2semidirect
7. C31×#2036C2semidirect
8. C31×#2035C2semidirect
9. C31×#1735C2semidirect
180. #23484C31direct (N × H)
237. C2×#428C2×C31semidirect
238. C2×#419C2×C31semidirect
239. C22×#103C2×C31semidirect
242. #2036C2×C31semidirect
243. #2035C2×C31semidirect
244. #1735C2×C31semidirect
369. C31#23484direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5362
C2×C31×#4282
C2×C31×#4192
C22×C31×#1032
C2×C31×#4082
C31×#23112
C31×#20362
C31×#20352
C31×#17352
#2348431