Finite Group Databasebeta

← C31×#19023 #21475782

Subgroups — C31×#19023 #21475782

Order 7936.

880 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3559C211yesmaximal, characteristic
2C31×#3239C211yesmaximal, characteristic, complemented
3C31×#3141C211yesmaximal, characteristic, complemented
4C2×C31×#491C211yesmaximal, characteristic, complemented
5C31×#1664C214yesmaximal, complemented
6C31×#1662C214yesmaximal, complemented
7C31×#1530C211yesmaximal, characteristic, complemented
8C31×#1528C211yesmaximal, characteristic, complemented
9C31×#1524C211yesmaximal, characteristic, complemented
10C31×#563C2212yes—
11C31×#562C2212yes—
12C31×#554—21no—
13C31×#553—21no—
14C31×#553—21no—
15C31×#547—22no—
16C31×#547—21no—
17C31×#544—21no—
18C31×#540—21no—
19C31×#539—22no—
20C31×#539—21no—
21C31×#537—21no—
22C31×#532C2211yescharacteristic
23C2×C31×C4⋊Q8C2211yescharacteristic
24C31×#529C2211yescharacteristic
25C2×C31×#125C2211yescharacteristic
26C31×#501C2212yes—
27C31×#491—22no—
28C31×#491C2214yes—
29C31×#489C2214yes—
30C31×#489C2212yes—
31C31×#487—21no—
32C31×#486—21no—
33C31×#484—21no—
34C31×#481—21no—
35C31×#475—21no—
36C31×#474—21no—
37C31×#432C2211yescharacteristic
38C31×#417—22no—
39C2×C31×#103—21no—
40C2×C31×#103—21no—
41C4×M16×C31C2211yescharacteristic
42C2×C31×#97C2211yescharacteristic
43C31×#330C2214yes—
44C31×#330C2212yes—
45C31×#329C2212yes—
46C31×#329C2214yes—
47C2×#41×C31—22no—
48C2×#41×C31D412yes—
49C22×Q8×C31—21no—
50C2×M16×C31—21no—
51C22×C8×C31—21no—
52C31×C4⋊Q8—21no—
53C31×C4⋊Q8—22no—
54C31×C4⋊Q8—21no—
55C31×C4⋊Q8—21no—
56C31×C4⋊Q8—21no—
57C31×C4⋊Q8D411yescharacteristic
58C31×C4⋊Q8C2312yes—
59C31×#127D411yescharacteristic
60C31×#126—22no—
61C31×#126—22no—
62C31×#126—21no—
63C31×#125—22no—
64C31×#125—21no—
65C31×#125—21no—
66C31×#125—21no—
67C31×#125D412yes—
68C31×#125C2312yes—
69C31×#125C2311yescharacteristic
70C31×#124C2311yescharacteristic
71C31×#124C2312yes—
72C31×#123—22no—
73C31×#123—22no—
74C31×#123—22no—
75C31×#123—22no—
76C31×#123—21no—
77C31×#123—22no—
78C31×#123—22no—
79C31×C22⋊Q8—22no—
80C31×C22⋊Q8—22no—
81C31×C22⋊Q8—22no—
82C31×C22⋊Q8—22no—
83C31×C22⋊Q8—22no—
84C31×C22⋊Q8—22no—
85C31×C22⋊Q8D411yescharacteristic
86C31×#121—22no—
87C31×#121—22no—
88C31×#121—21no—
89C31×#121—21no—
90C31×#121—22no—
91C31×#121—22no—
92C31×#121—21no—
93C31×#121—21no—
94C31×#121D411yescharacteristic
95C4×Q8×C31D411yescharacteristic
96C4×D4×C31—22no—
97C4×D4×C31—22no—
98C4×D4×C31—21no—
99C4×D4×C31—21no—
100C4×D4×C31—21no—
101C4×D4×C31—21no—
102C4×D4×C31—21no—
103C4×D4×C31D411yescharacteristic
104C31×#117—21no—
105C31×#117—21no—
106C2×C4⋊C4×C31—22no—
107C2×C4⋊C4×C31—21no—
108C2×C4⋊C4×C31—21no—
109C2×C4⋊C4×C31—21no—
110C2×C4⋊C4×C31—21no—
111C2×C4⋊C4×C31—21no—
112C2×C4⋊C4×C31D411yescharacteristic
113C2×C4⋊C4×C31D411yescharacteristic
114C2×C42×C31C2311yescharacteristic
115C31×#107—22no—
116C31×#106—22no—
117C31×C4⋊C8—21no—
118C31×#103—24no—
119C31×#103—22no—
120C31×#103—24no—
121C31×#103—24no—
122C31×#102—24no—
123C31×#102—22no—
124C31×C22⋊C8—21no—
125C31×#97—21no—
126C31×#97C2312yes—
127C31×#97C2312yes—
128C31×#97C2312yes—
129C4×C8×C31—21no—
130#41×C31—44no—
131#41×C31—84no—
132C2×Q8×C31—22no—
133C2×Q8×C31—22no—
134C2×Q8×C31—44no—
135C2×Q8×C31—41no—
136C2×Q8×C31C2×D411yescharacteristic
137C2×Q8×C31C2×D412yes—
138C2×D4×C31—22no—
139C2×D4×C31—21no—
140C2×D4×C31—22no—
141C2×D4×C31—22no—
142C2×D4×C31—21no—
143C2×D4×C31—21no—
144C2×D4×C31C2×D411yescharacteristic
145C2×D4×C31C2×D412yes—
146C22×C4×C31—21no—
147C22×C4×C31—22no—
148C22×C4×C31—22no—
149C22×C4×C31—22no—
150C22×C4×C31—21no—
151C22×C4×C31—21no—
152C22×C4×C31—22no—
153C22×C4×C31—41no—
154C22×C4×C31C2×D411yescharacteristic
155C22×C4×C31C2×D411yescharacteristic
156C22×C4×C31C2×D411yescharacteristic
157M16×C31—42no—
158C2×C8×C31—22no—
159C2×C8×C31—22no—
160C2×C8×C31—22no—
161C2×C8×C31—42no—
162C4⋊C4×C31—22no—
163C4⋊C4×C31—22no—
164C4⋊C4×C31—22no—
165C4⋊C4×C31—22no—
166C4⋊C4×C31—22no—
167C4⋊C4×C31—21no—
168C4⋊C4×C31—21no—
169C4⋊C4×C31—21no—
170C4⋊C4×C31—22no—
171C4⋊C4×C31—21no—
172C4⋊C4×C31—21no—
173C4⋊C4×C31—21no—
174C4⋊C4×C31—22no—
175C4⋊C4×C31—22no—
176C4⋊C4×C31—21no—
177C4⋊C4×C31—21no—
178C4⋊C4×C31—22no—
179C4⋊C4×C31—22no—
180C4⋊C4×C31—41no—
181C4⋊C4×C31—41no—
182C4⋊C4×C31C2×D412yes—
183C4⋊C4×C31C2×D412yes—
184C4⋊C4×C31C2×D411yescharacteristic
185C4⋊C4×C31C2×D411yescharacteristic
186C22⋊C4×C31—22no—
187C22⋊C4×C31—22no—
188C22⋊C4×C31—22no—
189C22⋊C4×C31—22no—
190C22⋊C4×C31—22no—
191C22⋊C4×C31—21no—
192C22⋊C4×C31—21no—
193C22⋊C4×C31—21no—
194C22⋊C4×C31—21no—
195C22⋊C4×C31—22no—
196C22⋊C4×C31—22no—
197C22⋊C4×C31—21no—
198C42×C31—22no—
199C42×C31—21no—
200C42×C31C2×D411yescharacteristic
201C42×C31C2×D411yescharacteristic
202C42×C31C2×D411yescharacteristic
203C42×C31C2411yescharacteristic
204#19023C3111yesmaximal, characteristic, direct product factor, Sylow
205C23×C31—22no—
206C23×C31—21no—
207C23×C31#12011yescharacteristic
208Q8×C31—41no—
209Q8×C31—42no—
210Q8×C31—44no—
211Q8×C31—82no—
212Q8×C31—82no—
213D4×C31—41no—
214D4×C31—42no—
215D4×C31—44no—
216D4×C31—42no—
217D4×C31—42no—
218D4×C31—81no—
219D4×C31—82no—
220D4×C31—82no—
221C2×C4×C31—22no—
222C2×C4×C31—22no—
223C2×C4×C31—21no—
224C2×C4×C31—21no—
225C2×C4×C31—22no—
226C2×C4×C31—22no—
227C2×C4×C31—21no—
228C2×C4×C31—22no—
229C2×C4×C31—41no—
230C2×C4×C31—42no—
231C2×C4×C31—42no—
232C2×C4×C31—42no—
233C2×C4×C31—82no—
234C2×C4×C31—81no—
235C2×C4×C31—82no—
236C2×C4×C31—82no—
237C2×C4×C31—82no—
238C2×C4×C31—82no—
239C2×C4×C31#12011yescharacteristic
240C2×C4×C31#12011yescharacteristic
241C2×C4×C31#12011yescharacteristic
242C2×C4×C31C22×D411yescharacteristic
243C2×C4×C31C22×D411yescharacteristic
244C2×C4×C31C22×D411yescharacteristic
245C8×C31—42no—
246C8×C31—42no—
247C8×C31—42no—
248#3559C2×C3111yescharacteristic
249#3239C2×C3111yescharacteristic, complemented
250#3141C2×C3111yescharacteristic, complemented
251C2×#491C2×C3111yescharacteristic, complemented
252#1664C2×C3114yescomplemented
253#1662C2×C3114yescomplemented
254#1530C2×C3111yescharacteristic, complemented
255#1528C2×C3111yescharacteristic, complemented
256#1524C2×C3111yescharacteristic, complemented
257C22×C31—21no—
258C22×C31—21no—
259C22×C31—42no—
260C22×C31—41no—
261C22×C31—41no—
262C22×C31—42no—
263C22×C31—42no—
264C22×C31—41no—
265C22×C31#45512yes—
266C22×C31C2×#12011yescharacteristic
267C4×C31—21no—
268C4×C31—21no—
269C4×C31—21no—
270C4×C31—21no—
271C4×C31—21no—
272C4×C31—42no—
273C4×C31—42no—
274C4×C31—41no—
275C4×C31—41no—
276C4×C31—42no—
277C4×C31—41no—
278C4×C31—82no—
279C4×C31#45412yes—
280#563C22×C3112yes—
281#562C22×C3112yes—
282#554—21no—
283#553—21no—
284#553—21no—
285#547—22no—
286#547—21no—
287#544—21no—
288#540—21no—
289#539—22no—
290#539—21no—
291#537—21no—
292#532C22×C3111yescharacteristic
293C2×C4⋊Q8C22×C3111yescharacteristic
294#529C22×C3111yescharacteristic
295C2×#125C22×C3111yescharacteristic
296#501C22×C3112yes—
297#491—22no—
298#491C22×C3114yes—
299#489C22×C3114yes—
300#489C22×C3112yes—
301#487—21no—
302#486—21no—
303#484—21no—
304#481—21no—
305#475—21no—
306#474—21no—
307#432C22×C3111yescharacteristic
308#417—22no—
309C2×#103—21no—
310C2×#103—21no—
311C4×M16C22×C3111yescharacteristic
312C2×#97C22×C3111yescharacteristic
313#330C22×C3114yes—
314#330C22×C3112yes—
315#329C22×C3112yes—
316#329C22×C3114yes—
317C2×C31—22no—
318C2×C31—82no—
319C2×C31—81no—
320C2×C31C2×#45511yescharacteristic
321C2×C31C2×#45411yescharacteristic
322C2×C31#302211yescharacteristic
323C2×#41—22no—
324C2×#41D4×C3112yes—
325C22×Q8—21no—
326C2×M16—21no—
327C22×C8—21no—
328C4⋊Q8—21no—
329C4⋊Q8—22no—
330C4⋊Q8—21no—
331C4⋊Q8—21no—
332C4⋊Q8—21no—
333C4⋊Q8D4×C3111yescharacteristic
334C4⋊Q8C23×C3112yes—
335#127D4×C3111yescharacteristic
336#126—22no—
337#126—22no—
338#126—21no—
339#125—22no—
340#125—21no—
341#125—21no—
342#125—21no—
343#125D4×C3112yes—
344#125C23×C3112yes—
345#125C23×C3111yescharacteristic
346#124C23×C3111yescharacteristic
347#124C23×C3112yes—
348#123—22no—
349#123—22no—
350#123—22no—
351#123—22no—
352#123—21no—
353#123—22no—
354#123—22no—
355C22⋊Q8—22no—
356C22⋊Q8—22no—
357C22⋊Q8—22no—
358C22⋊Q8—22no—
359C22⋊Q8—22no—
360C22⋊Q8—22no—
361C22⋊Q8D4×C3111yescharacteristic
362#121—22no—
363#121—22no—
364#121—21no—
365#121—21no—
366#121—22no—
367#121—22no—
368#121—21no—
369#121—21no—
370#121D4×C3111yescharacteristic
371C4×Q8D4×C3111yescharacteristic
372C4×D4—22no—
373C4×D4—22no—
374C4×D4—21no—
375C4×D4—21no—
376C4×D4—21no—
377C4×D4—21no—
378C4×D4—21no—
379C4×D4D4×C3111yescharacteristic
380#117—21no—
381#117—21no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4D4×C3111yescharacteristic
389C2×C4⋊C4D4×C3111yescharacteristic
390C2×C42C23×C3111yescharacteristic
391#107—22no—
392#106—22no—
393C4⋊C8—21no—
394#103—24no—
395#103—22no—
396#103—24no—
397#103—24no—
398#102—24no—
399#102—22no—
400C22⋊C8—21no—
401#97—21no—
402#97C23×C3112yes—
403#97C23×C3112yes—
404#97C23×C3112yes—
405C4×C8—21no—
406C31#1902311yescharacteristic, direct product factor, Sylow
407#41—44no—
408#41—84no—
409C2×Q8—22no—
410C2×Q8—22no—
411C2×Q8—44no—
412C2×Q8—41no—
413C2×Q8C2×D4×C3111yescharacteristic
414C2×Q8C2×D4×C3112yes—
415C2×D4—22no—
416C2×D4—21no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4C2×D4×C3111yescharacteristic
422C2×D4C2×D4×C3112yes—
423C22×C4—21no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—22no—
430C22×C4—41no—
431C22×C4C2×D4×C3111yescharacteristic
432C22×C4C2×D4×C3111yescharacteristic
433C22×C4C2×D4×C3111yescharacteristic
434M16—42no—
435C2×C8—22no—
436C2×C8—22no—
437C2×C8—22no—
438C2×C8—42no—
439C4⋊C4—22no—
440C4⋊C4—22no—
441C4⋊C4—22no—
442C4⋊C4—22no—
443C4⋊C4—22no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—22no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—22no—
452C4⋊C4—22no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—22no—
456C4⋊C4—22no—
457C4⋊C4—41no—
458C4⋊C4—41no—
459C4⋊C4C2×D4×C3112yes—
460C4⋊C4C2×D4×C3112yes—
461C4⋊C4C2×D4×C3111yescharacteristic
462C4⋊C4C2×D4×C3111yescharacteristic
463C22⋊C4—22no—
464C22⋊C4—22no—
465C22⋊C4—22no—
466C22⋊C4—22no—
467C22⋊C4—22no—
468C22⋊C4—21no—
469C22⋊C4—21no—
470C22⋊C4—21no—
471C22⋊C4—21no—
472C22⋊C4—22no—
473C22⋊C4—22no—
474C22⋊C4—21no—
475C42—22no—
476C42—21no—
477C42C2×D4×C3111yescharacteristic
478C42C2×D4×C3111yescharacteristic
479C42C2×D4×C3111yescharacteristic
480C42C24×C3111yescharacteristic
481C23—22no—
482C23—21no—
483C23C31×#12011yescharacteristic
484Q8—41no—
485Q8—42no—
486Q8—44no—
487Q8—82no—
488Q8—82no—
489D4—41no—
490D4—42no—
491D4—44no—
492D4—42no—
493D4—42no—
494D4—81no—
495D4—82no—
496D4—82no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—21no—
504C2×C4—22no—
505C2×C4—41no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—82no—
510C2×C4—81no—
511C2×C4—82no—
512C2×C4—82no—
513C2×C4—82no—
514C2×C4—82no—
515C2×C4C31×#12011yescharacteristic
516C2×C4C31×#12011yescharacteristic
517C2×C4C31×#12011yescharacteristic
518C2×C4C22×D4×C3111yescharacteristic
519C2×C4C22×D4×C3111yescharacteristic
520C2×C4C22×D4×C3111yescharacteristic
521C8—42no—
522C8—42no—
523C8—42no—
524C22—21no—
525C22—21no—
526C22—42no—
527C22—41no—
528C22—41no—
529C22—42no—
530C22—42no—
531C22—41no—
532C22C31×#45512yes—
533C22C2×C31×#12011yescharacteristic
534C4—21no—
535C4—21no—
536C4—21no—
537C4—21no—
538C4—21no—
539C4—42no—
540C4—42no—
541C4—41no—
542C4—41no—
543C4—42no—
544C4—41no—
545C4—82no—
546C4C31×#45412yes—
547C2—22no—
548C2—82no—
549C2—81no—
550C2C2×C31×#45511yescharacteristic
551C2C2×C31×#45411yescharacteristic
552C2C31×#302211yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC42C24×C31
prime radicalC31×#3559C2
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
2. C31×#3239C2semidirect
3. C31×#3141C2semidirect
4. C2×C31×#491C2semidirect
5. C31×#1664C2semidirect
6. C31×#1662C2semidirect
7. C31×#1530C2semidirect
8. C31×#1528C2semidirect
9. C31×#1524C2semidirect
204. #19023C31direct (N × H)
249. #3239C2×C31semidirect
250. #3141C2×C31semidirect
251. C2×#491C2×C31semidirect
252. #1664C2×C31semidirect
253. #1662C2×C31semidirect
254. #1530C2×C31semidirect
255. #1528C2×C31semidirect
256. #1524C2×C31semidirect
406. C31#19023direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35592
C31×#32392
C31×#31412
C2×C31×#4912
C31×#16642
C31×#16622
C31×#15302
C31×#15282
C31×#15242
#1902331