Finite Group Databasebeta

← C31×#25139 #21481898

Subgroups — C31×#25139 #21481898

Order 7936.

1194 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#468C211yesmaximal, characteristic, complemented
2C2×C31×#449C211yesmaximal, characteristic, complemented
3C2×C31×#436C211yesmaximal, characteristic, complemented
4C2×C31×#417C211yesmaximal, characteristic, complemented
5C31×#2416C211yesmaximal, characteristic, complemented
6C31×#2407C211yesmaximal, characteristic, complemented
7C31×#2067C211yesmaximal, characteristic, complemented
8C31×#2055C211yesmaximal, characteristic, complemented
9C31×#2036C211yesmaximal, characteristic, complemented
10C31×#1999C211yesmaximal, characteristic, complemented
11C31×#1970C211yesmaximal, characteristic, complemented
12C31×#1933C211yesmaximal, characteristic, complemented
13C31×#1895C211yesmaximal, characteristic, complemented
14C31×#1895C211yesmaximal, characteristic, complemented
15C31×#1852C211yesmaximal, characteristic, complemented
16C22×#41×C31C2211yescharacteristic
17C22×SD16×C31C2211yescharacteristic
18C22×D8×C31C2211yescharacteristic
19C22×M16×C31C2211yescharacteristic
20C22×M16×C31C2211yescharacteristic
21C2×C31×C22⋊Q8C2211yescharacteristic
22C2×C31×#121—21no—
23C2×C31×#121C2211yescharacteristic
24C2×C31×#121C2211yescharacteristic
25C2×C31×#121C2211yescharacteristic
26C2×C4×D4×C31C2211yescharacteristic
27C22×C4⋊C4×C31C2211yescharacteristic
28C31×#468—24no—
29C31×#449—24no—
30C31×#436—24no—
31C2×C31×#107C2211yescharacteristic
32C2×C31×#107C2211yescharacteristic
33C2×C31×C4⋊C8C2211yescharacteristic
34C31×#417—24no—
35C2×C31×#103C2211yescharacteristic
36C2×C31×#103C2211yescharacteristic
37C2×C31×#103C2211yescharacteristic
38C2×C31×#102C2211yescharacteristic
39C2×C31×#102C2211yescharacteristic
40C2×C31×#102C2211yescharacteristic
41C2×C31×#102C2211yescharacteristic
42C2×C31×#102C2211yescharacteristic
43C2×C31×C22⋊C8C2211yescharacteristic
44C2×C31×C22⋊C8C2211yescharacteristic
45C2×C4×C8×C31C2211yescharacteristic
46C31×#396—21no—
47C31×#394—21no—
48C31×#394—21no—
49C31×#392—21no—
50C31×#391C2211yescharacteristic
51C31×#390C2211yescharacteristic
52C31×#390C2211yescharacteristic
53C31×#389C2211yescharacteristic
54C31×#386—21no—
55C31×#386—21no—
56C31×#385—21no—
57C31×#380C2211yescharacteristic
58C31×#380C2211yescharacteristic
59C31×#340C2211yescharacteristic
60C31×#340C2211yescharacteristic
61C31×#340C2211yescharacteristic
62C31×#340C2211yescharacteristic
63C2×#41×C31—22no—
64C2×#41×C31—22no—
65C2×#41×C31—22no—
66C2×#41×C31—22no—
67C2×#41×C31—41no—
68C2×#41×C31—41no—
69C22×Q8×C31C2311yescharacteristic
70C22×D4×C31—21no—
71C22×D4×C31—21no—
72C22×D4×C31—21no—
73C22×D4×C31—21no—
74C22×D4×C31D411yescharacteristic
75C22×D4×C31C2311yescharacteristic
76C22×D4×C31C2311yescharacteristic
77C23×C4×C31—21no—
78C23×C4×C31—21no—
79C23×C4×C31C2311yescharacteristic
80C23×C4×C31C2311yescharacteristic
81C2×SD16×C31—22no—
82C2×SD16×C31—22no—
83C2×SD16×C31—41no—
84C2×D8×C31—22no—
85C2×D8×C31—22no—
86C2×D8×C31—41no—
87C2×M16×C31—22no—
88C2×M16×C31—22no—
89C2×M16×C31—22no—
90C2×M16×C31—22no—
91C2×M16×C31—41no—
92C2×M16×C31—41no—
93C22×C8×C31C2311yescharacteristic
94C22×C8×C31C2311yescharacteristic
95C22×C8×C31C2311yescharacteristic
96C22×C8×C31C2311yescharacteristic
97C31×C22⋊Q8—22no—
98C31×C22⋊Q8—41no—
99C31×#121—22no—
100C31×#121—22no—
101C31×#121—22no—
102C31×#121—22no—
103C31×#121—41no—
104C31×#121—41no—
105C31×#121—44no—
106C4×D4×C31—22no—
107C4×D4×C31—22no—
108C2×C4⋊C4×C31—22no—
109C2×C4⋊C4×C31—21no—
110C2×C4⋊C4×C31—21no—
111C2×C4⋊C4×C31—21no—
112C2×C4⋊C4×C31—41no—
113C2×C4⋊C4×C31D411yescharacteristic
114C2×C4⋊C4×C31C2311yescharacteristic
115C2×C4⋊C4×C31C2311yescharacteristic
116C2×C4⋊C4×C31C2311yescharacteristic
117C2×C4⋊C4×C31C2311yescharacteristic
118C2×C4⋊C4×C31C2311yescharacteristic
119C2×C22⋊C4×C31—21no—
120C2×C22⋊C4×C31—21no—
121C2×C22⋊C4×C31—21no—
122C2×C22⋊C4×C31—21no—
123C2×C22⋊C4×C31—21no—
124C2×C22⋊C4×C31—21no—
125C2×C22⋊C4×C31—21no—
126C2×C22⋊C4×C31—21no—
127C2×C22⋊C4×C31—21no—
128C2×C22⋊C4×C31—21no—
129C2×C22⋊C4×C31D411yescharacteristic
130C2×C22⋊C4×C31D411yescharacteristic
131C2×C42×C31C2311yescharacteristic
132C31×#107—22no—
133C31×#107—41no—
134C31×C4⋊C8—22no—
135C31×#103—22no—
136C31×#103—22no—
137C31×#103D414yescomplemented
138C31×#102—22no—
139C31×#102—22no—
140C31×#102—22no—
141C31×#102—22no—
142C31×#102—41no—
143C31×C22⋊C8—22no—
144C31×C22⋊C8D414yescomplemented
145C4×C8×C31—22no—
146C31×#95—21no—
147C31×#95—21no—
148C31×#95—21no—
149C31×#95—21no—
150C31×#95—21no—
151C24×C31—21no—
152C24×C31—21no—
153C24×C31C2×D411yescharacteristic
154C24×C31C2×D411yescharacteristic
155#41×C31—28no—
156#41×C31—44no—
157#41×C31—44no—
158#41×C31—44no—
159C2×Q8×C31—21no—
160C2×Q8×C31—21no—
161C2×Q8×C31—21no—
162C2×Q8×C31—21no—
163C2×Q8×C31—21no—
164C2×Q8×C31C2×D412yes—
165C2×D4×C31—22no—
166C2×D4×C31—22no—
167C2×D4×C31—21no—
168C2×D4×C31—21no—
169C2×D4×C31—21no—
170C2×D4×C31—21no—
171C2×D4×C31—21no—
172C2×D4×C31—21no—
173C2×D4×C31—21no—
174C2×D4×C31—21no—
175C2×D4×C31—21no—
176C2×D4×C31—21no—
177C2×D4×C31—21no—
178C2×D4×C31—41no—
179C2×D4×C31—42no—
180C2×D4×C31—42no—
181C2×D4×C31—42no—
182C2×D4×C31—42no—
183C2×D4×C31—42no—
184C2×D4×C31—42no—
185C2×D4×C31—42no—
186C2×D4×C31—42no—
187C2×D4×C31—42no—
188C2×D4×C31—42no—
189C2×D4×C31—81no—
190C2×D4×C31—81no—
191C2×D4×C31#4112yes—
192C22×C4×C31—21no—
193C22×C4×C31—21no—
194C22×C4×C31—21no—
195C22×C4×C31—21no—
196C22×C4×C31—21no—
197C22×C4×C31—21no—
198C22×C4×C31—21no—
199C22×C4×C31—21no—
200C22×C4×C31—21no—
201C22×C4×C31—21no—
202C22×C4×C31—21no—
203C22×C4×C31—21no—
204C22×C4×C31—21no—
205C22×C4×C31—21no—
206C22×C4×C31—21no—
207C22×C4×C31—21no—
208C22×C4×C31—42no—
209C22×C4×C31—42no—
210C22×C4×C31—42no—
211C22×C4×C31—42no—
212C22×C4×C31—42no—
213C22×C4×C31—81no—
214C22×C4×C31C2×D411yescharacteristic
215C22×C4×C31C2×D411yescharacteristic
216C22×C4×C31C2×D411yescharacteristic
217C22×C4×C31C2×D412yes—
218C22×C4×C31C2×D411yescharacteristic
219C22×C4×C31#4112yes—
220C22×C4×C31C2411yescharacteristic
221SD16×C31—44no—
222D8×C31—44no—
223M16×C31—44no—
224M16×C31—44no—
225C2×C8×C31—21no—
226C2×C8×C31—21no—
227C2×C8×C31—21no—
228C2×C8×C31—21no—
229C2×C8×C31—21no—
230C2×C8×C31—21no—
231C2×C8×C31—21no—
232C2×C8×C31—21no—
233C2×C8×C31—21no—
234C2×C8×C31C2×D412yes—
235C2×C8×C31C2×D412yes—
236C2×C8×C31C2×D412yes—
237C4⋊C4×C31—22no—
238C4⋊C4×C31—21no—
239C4⋊C4×C31—21no—
240C4⋊C4×C31—21no—
241C4⋊C4×C31—21no—
242C4⋊C4×C31—21no—
243C4⋊C4×C31—21no—
244C4⋊C4×C31—21no—
245C4⋊C4×C31—21no—
246C4⋊C4×C31—21no—
247C4⋊C4×C31—42no—
248C4⋊C4×C31—42no—
249C4⋊C4×C31—42no—
250C4⋊C4×C31C2×D412yes—
251C22⋊C4×C31—22no—
252C22⋊C4×C31—22no—
253C22⋊C4×C31—42no—
254C22⋊C4×C31—42no—
255C22⋊C4×C31—42no—
256C22⋊C4×C31—42no—
257C22⋊C4×C31—42no—
258C22⋊C4×C31—42no—
259C22⋊C4×C31—42no—
260C22⋊C4×C31—81no—
261C22⋊C4×C31—81no—
262C22⋊C4×C31—81no—
263C42×C31—21no—
264C42×C31—21no—
265#25139C3111yesmaximal, characteristic, direct product factor, Sylow
266C23×C31—21no—
267C23×C31—21no—
268C23×C31—21no—
269C23×C31—21no—
270C23×C31—21no—
271C23×C31—21no—
272C23×C31—21no—
273C23×C31—21no—
274C23×C31—22no—
275C23×C31—21no—
276C23×C31—21no—
277C23×C31—21no—
278C23×C31—21no—
279C23×C31—21no—
280C23×C31—41no—
281C23×C31—41no—
282C23×C31—41no—
283C23×C31—41no—
284C23×C31—41no—
285C23×C31—41no—
286C23×C31—41no—
287C23×C31—41no—
288C23×C31—41no—
289C23×C31—41no—
290C23×C31—41no—
291C23×C31—41no—
292C23×C31—41no—
293C23×C31#12112yes—
294C23×C31C22×D411yescharacteristic
295Q8×C31—22no—
296Q8×C31—22no—
297Q8×C31—41no—
298Q8×C31—41no—
299D4×C31—22no—
300D4×C31—22no—
301D4×C31—44no—
302D4×C31—48no—
303D4×C31—41no—
304D4×C31—41no—
305D4×C31—41no—
306D4×C31—41no—
307D4×C31—41no—
308D4×C31—41no—
309D4×C31—84no—
310D4×C31—84no—
311D4×C31—84no—
312C2×C4×C31—21no—
313C2×C4×C31—21no—
314C2×C4×C31—21no—
315C2×C4×C31—21no—
316C2×C4×C31—22no—
317C2×C4×C31—22no—
318C2×C4×C31—22no—
319C2×C4×C31—22no—
320C2×C4×C31—21no—
321C2×C4×C31—21no—
322C2×C4×C31—21no—
323C2×C4×C31—22no—
324C2×C4×C31—22no—
325C2×C4×C31—21no—
326C2×C4×C31—21no—
327C2×C4×C31—21no—
328C2×C4×C31—48no—
329C2×C4×C31—41no—
330C2×C4×C31—41no—
331C2×C4×C31—41no—
332C2×C4×C31—41no—
333C2×C4×C31—41no—
334C2×C4×C31—41no—
335C2×C4×C31—41no—
336C2×C4×C31—41no—
337C2×C4×C31—41no—
338C2×C4×C31—41no—
339C2×C4×C31—41no—
340C2×C4×C31—41no—
341C2×C4×C31—41no—
342C2×C4×C31—41no—
343C2×C4×C31—41no—
344C2×C4×C31—41no—
345C2×C4×C31—41no—
346C2×C4×C31—41no—
347C2×C4×C31—41no—
348C2×C4×C31—41no—
349C2×C4×C31—84no—
350C2×C4×C31#12112yes—
351C2×C4×C31AGL(1,ℤ/8)12yes—
352C2×C4×C31C22×D411yescharacteristic
353C2×C4×C31C22×D411yescharacteristic
354C2×C4×C31C2×#4111yescharacteristic
355C2×C4×C31C2×#4111yescharacteristic
356C2×C4×C31H(5,𝔽2)11yescharacteristic
357C2×C4×C31H(5,𝔽2)11yescharacteristic
358C8×C31—22no—
359C8×C31—22no—
360C8×C31—22no—
361C8×C31—41no—
362C2×#468C2×C3111yescharacteristic, complemented
363C2×#449C2×C3111yescharacteristic, complemented
364C2×#436C2×C3111yescharacteristic, complemented
365C2×#417C2×C3111yescharacteristic, complemented
366#2416C2×C3111yescharacteristic, complemented
367#2407C2×C3111yescharacteristic, complemented
368#2067C2×C3111yescharacteristic, complemented
369#2055C2×C3111yescharacteristic, complemented
370#2036C2×C3111yescharacteristic, complemented
371#1999C2×C3111yescharacteristic, complemented
372#1970C2×C3111yescharacteristic, complemented
373#1933C2×C3111yescharacteristic, complemented
374#1895C2×C3111yescharacteristic, complemented
375#1895C2×C3111yescharacteristic, complemented
376#1852C2×C3111yescharacteristic, complemented
377C22×C31—22no—
378C22×C31—22no—
379C22×C31—22no—
380C22×C31—41no—
381C22×C31—41no—
382C22×C31—41no—
383C22×C31—41no—
384C22×C31—41no—
385C22×C31—42no—
386C22×C31—42no—
387C22×C31—41no—
388C22×C31—41no—
389C22×C31—41no—
390C22×C31—41no—
391C22×C31—41no—
392C22×C31—41no—
393C22×C31—42no—
394C22×C31—81no—
395C22×C31—81no—
396C22×C31—81no—
397C22×C31—81no—
398C22×C31—81no—
399C22×C31—81no—
400C22×C31—81no—
401C22×C31—81no—
402C22×C31—81no—
403C22×C31—81no—
404C22×C31—81no—
405C22×C31C2×#12111yescharacteristic
406C22×C31D4211yescharacteristic
407C22×C31#54611yescharacteristic
408C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
409C22×C31#57511yescharacteristic
410C22×C31#57611yescharacteristic
411C22×C31#57811yescharacteristic
412C4×C31—22no—
413C4×C31—22no—
414C4×C31—41no—
415C4×C31—42no—
416C4×C31—42no—
417C4×C31—41no—
418C4×C31—81no—
419C4×C31—81no—
420C4×C31—81no—
421C4×C31—81no—
422C4×C31#52511yescharacteristic
423C4×C31#53811yescharacteristic
424C4×C31D4211yescharacteristic
425C4×C31#54611yescharacteristic
426C22×#41C22×C3111yescharacteristic
427C22×SD16C22×C3111yescharacteristic
428C22×D8C22×C3111yescharacteristic
429C22×M16C22×C3111yescharacteristic
430C22×M16C22×C3111yescharacteristic
431C2×C22⋊Q8C22×C3111yescharacteristic
432C2×#121—21no—
433C2×#121C22×C3111yescharacteristic
434C2×#121C22×C3111yescharacteristic
435C2×#121C22×C3111yescharacteristic
436C2×C4×D4C22×C3111yescharacteristic
437C22×C4⋊C4C22×C3111yescharacteristic
438#468—24no—
439#449—24no—
440#436—24no—
441C2×#107C22×C3111yescharacteristic
442C2×#107C22×C3111yescharacteristic
443C2×C4⋊C8C22×C3111yescharacteristic
444#417—24no—
445C2×#103C22×C3111yescharacteristic
446C2×#103C22×C3111yescharacteristic
447C2×#103C22×C3111yescharacteristic
448C2×#102C22×C3111yescharacteristic
449C2×#102C22×C3111yescharacteristic
450C2×#102C22×C3111yescharacteristic
451C2×#102C22×C3111yescharacteristic
452C2×#102C22×C3111yescharacteristic
453C2×C22⋊C8C22×C3111yescharacteristic
454C2×C22⋊C8C22×C3111yescharacteristic
455C2×C4×C8C22×C3111yescharacteristic
456#396—21no—
457#394—21no—
458#394—21no—
459#392—21no—
460#391C22×C3111yescharacteristic
461#390C22×C3111yescharacteristic
462#390C22×C3111yescharacteristic
463#389C22×C3111yescharacteristic
464#386—21no—
465#386—21no—
466#385—21no—
467#380C22×C3111yescharacteristic
468#380C22×C3111yescharacteristic
469#340C22×C3111yescharacteristic
470#340C22×C3111yescharacteristic
471#340C22×C3111yescharacteristic
472#340C22×C3111yescharacteristic
473C2×C31—42no—
474C2×C31—81no—
475C2×C31—82no—
476C2×C31—161no—
477C2×C31#242411yescharacteristic
478C2×C31#305511yescharacteristic
479C2×C31#306111yescharacteristic
480C2×C31#327411yescharacteristic
481C2×C31#327711yescharacteristic
482C2×C31#332211yescharacteristic
483C2×C31#333011yescharacteristic
484C2×#41—22no—
485C2×#41—22no—
486C2×#41—22no—
487C2×#41—22no—
488C2×#41—41no—
489C2×#41—41no—
490C22×Q8C23×C3111yescharacteristic
491C22×D4—21no—
492C22×D4—21no—
493C22×D4—21no—
494C22×D4—21no—
495C22×D4D4×C3111yescharacteristic
496C22×D4C23×C3111yescharacteristic
497C22×D4C23×C3111yescharacteristic
498C23×C4—21no—
499C23×C4—21no—
500C23×C4C23×C3111yescharacteristic
501C23×C4C23×C3111yescharacteristic
502C2×SD16—22no—
503C2×SD16—22no—
504C2×SD16—41no—
505C2×D8—22no—
506C2×D8—22no—
507C2×D8—41no—
508C2×M16—22no—
509C2×M16—22no—
510C2×M16—22no—
511C2×M16—22no—
512C2×M16—41no—
513C2×M16—41no—
514C22×C8C23×C3111yescharacteristic
515C22×C8C23×C3111yescharacteristic
516C22×C8C23×C3111yescharacteristic
517C22×C8C23×C3111yescharacteristic
518C22⋊Q8—22no—
519C22⋊Q8—41no—
520#121—22no—
521#121—22no—
522#121—22no—
523#121—22no—
524#121—41no—
525#121—41no—
526#121—44no—
527C4×D4—22no—
528C4×D4—22no—
529C2×C4⋊C4—22no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—41no—
534C2×C4⋊C4D4×C3111yescharacteristic
535C2×C4⋊C4C23×C3111yescharacteristic
536C2×C4⋊C4C23×C3111yescharacteristic
537C2×C4⋊C4C23×C3111yescharacteristic
538C2×C4⋊C4C23×C3111yescharacteristic
539C2×C4⋊C4C23×C3111yescharacteristic
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4D4×C3111yescharacteristic
551C2×C22⋊C4D4×C3111yescharacteristic
552C2×C42C23×C3111yescharacteristic
553#107—22no—
554#107—41no—
555C4⋊C8—22no—
556#103—22no—
557#103—22no—
558#103D4×C3114yescomplemented
559#102—22no—
560#102—22no—
561#102—22no—
562#102—22no—
563#102—41no—
564C22⋊C8—22no—
565C22⋊C8D4×C3114yescomplemented
566C4×C8—22no—
567#95—21no—
568#95—21no—
569#95—21no—
570#95—21no—
571#95—21no—
572C31#2513911yescharacteristic, direct product factor, Sylow
573C24—21no—
574C24—21no—
575C24C2×D4×C3111yescharacteristic
576C24C2×D4×C3111yescharacteristic
577#41—28no—
578#41—44no—
579#41—44no—
580#41—44no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8C2×D4×C3112yes—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—41no—
601C2×D4—42no—
602C2×D4—42no—
603C2×D4—42no—
604C2×D4—42no—
605C2×D4—42no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—42no—
609C2×D4—42no—
610C2×D4—42no—
611C2×D4—81no—
612C2×D4—81no—
613C2×D4#41×C3112yes—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—42no—
631C22×C4—42no—
632C22×C4—42no—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4—81no—
636C22×C4C2×D4×C3111yescharacteristic
637C22×C4C2×D4×C3111yescharacteristic
638C22×C4C2×D4×C3111yescharacteristic
639C22×C4C2×D4×C3112yes—
640C22×C4C2×D4×C3111yescharacteristic
641C22×C4#41×C3112yes—
642C22×C4C24×C3111yescharacteristic
643SD16—44no—
644D8—44no—
645M16—44no—
646M16—44no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8C2×D4×C3112yes—
657C2×C8C2×D4×C3112yes—
658C2×C8C2×D4×C3112yes—
659C4⋊C4—22no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—42no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4C2×D4×C3112yes—
673C22⋊C4—22no—
674C22⋊C4—22no—
675C22⋊C4—42no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—81no—
683C22⋊C4—81no—
684C22⋊C4—81no—
685C42—21no—
686C42—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—22no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23C31×#12112yes—
715C23C22×D4×C3111yescharacteristic
716Q8—22no—
717Q8—22no—
718Q8—41no—
719Q8—41no—
720D4—22no—
721D4—22no—
722D4—44no—
723D4—48no—
724D4—41no—
725D4—41no—
726D4—41no—
727D4—41no—
728D4—41no—
729D4—41no—
730D4—84no—
731D4—84no—
732D4—84no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—48no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—84no—
771C2×C4C31×#12112yes—
772C2×C4C31×AGL(1,ℤ/8)12yes—
773C2×C4C22×D4×C3111yescharacteristic
774C2×C4C22×D4×C3111yescharacteristic
775C2×C4C2×#41×C3111yescharacteristic
776C2×C4C2×#41×C3111yescharacteristic
777C2×C4C31×H(5,𝔽2)11yescharacteristic
778C2×C4C31×H(5,𝔽2)11yescharacteristic
779C8—22no—
780C8—22no—
781C8—22no—
782C8—41no—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—42no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—42no—
798C22—41no—
799C22—42no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22—81no—
808C22—81no—
809C22—81no—
810C22—81no—
811C22C2×C31×#12111yescharacteristic
812C22D42×C3111yescharacteristic
813C22C31×#54611yescharacteristic
814C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
815C22C31×#57511yescharacteristic
816C22C31×#57611yescharacteristic
817C22C31×#57811yescharacteristic
818C4—22no—
819C4—22no—
820C4—41no—
821C4—42no—
822C4—42no—
823C4—41no—
824C4—81no—
825C4—81no—
826C4—81no—
827C4—81no—
828C4C31×#52511yescharacteristic
829C4C31×#53811yescharacteristic
830C4D42×C3111yescharacteristic
831C4C31×#54611yescharacteristic
832C2—42no—
833C2—81no—
834C2—82no—
835C2—161no—
836C2C31×#242411yescharacteristic
837C2C31×#305511yescharacteristic
838C2C31×#306111yescharacteristic
839C2C31×#327411yescharacteristic
840C2C31×#327711yescharacteristic
841C2C31×#332211yescharacteristic
842C2C31×#333011yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C4×D4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#468C2semidirect
2. C2×C31×#449C2semidirect
3. C2×C31×#436C2semidirect
4. C2×C31×#417C2semidirect
5. C31×#2416C2semidirect
6. C31×#2407C2semidirect
7. C31×#2067C2semidirect
8. C31×#2055C2semidirect
9. C31×#2036C2semidirect
10. C31×#1999C2semidirect
11. C31×#1970C2semidirect
12. C31×#1933C2semidirect
13. C31×#1895C2semidirect
14. C31×#1895C2semidirect
15. C31×#1852C2semidirect
137. C31×#103D4semidirect
144. C31×C22⋊C8D4semidirect
265. #25139C31direct (N × H)
362. C2×#468C2×C31semidirect
363. C2×#449C2×C31semidirect
364. C2×#436C2×C31semidirect
365. C2×#417C2×C31semidirect
366. #2416C2×C31semidirect
367. #2407C2×C31semidirect
368. #2067C2×C31semidirect
369. #2055C2×C31semidirect
370. #2036C2×C31semidirect
371. #1999C2×C31semidirect
372. #1970C2×C31semidirect
373. #1933C2×C31semidirect
374. #1895C2×C31semidirect
375. #1895C2×C31semidirect
376. #1852C2×C31semidirect
558. #103D4×C31semidirect
565. C22⋊C8D4×C31semidirect
572. C31#25139direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4682
C2×C31×#4492
C2×C31×#4362
C2×C31×#4172
C31×#24162
C31×#24072
C31×#20672
C31×#20552
C31×#20362
C31×#19992
C31×#19702
C31×#19332
C31×#18952
C31×#18522
#2513931