Finite Group Databasebeta

← C31×#17138 #21473897

Subgroups — C31×#17138 #21473897

Order 7936.

1790 conjugacy classes of subgroups.

The subgroup lattice has 1276 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#394C211yesmaximal, characteristic, complemented
2C2×C31×#392C211yesmaximal, characteristic
3C31×#1443C211yesmaximal, characteristic, complemented
4C31×#1442C211yesmaximal, characteristic, complemented
5C31×#1440C211yesmaximal, characteristic, complemented
6C31×#1440C211yesmaximal, characteristic, complemented
7C31×#1440C211yesmaximal, characteristic, complemented
8C31×#1440C211yesmaximal, characteristic, complemented
9C31×#1440C211yesmaximal, characteristic, complemented
10C31×#1439C211yesmaximal, characteristic, complemented
11C31×#1438C211yesmaximal, characteristic, complemented
12C31×#1438C211yesmaximal, characteristic, complemented
13C31×#1438C211yesmaximal, characteristic, complemented
14C31×#1438C211yesmaximal, characteristic, complemented
15C31×#1438C211yesmaximal, characteristic, complemented
16C23×D4×C31C2211yescharacteristic
17C23×D4×C31C2211yescharacteristic
18C23×D4×C31C2211yescharacteristic
19C22×C4⋊C4×C31C2211yescharacteristic
20C22×C22⋊C4×C31C2211yescharacteristic
21C22×C22⋊C4×C31C2211yescharacteristic
22C22×C22⋊C4×C31C2211yescharacteristic
23C22×C22⋊C4×C31C2211yescharacteristic
24C22×C22⋊C4×C31C2211yescharacteristic
25C22×C22⋊C4×C31C2211yescharacteristic
26C22×C22⋊C4×C31C2211yescharacteristic
27C22×C22⋊C4×C31C2211yescharacteristic
28C22×C22⋊C4×C31C2211yescharacteristic
29C22×C22⋊C4×C31C2211yescharacteristic
30C22×C22⋊C4×C31C2211yescharacteristic
31C22×C22⋊C4×C31C2211yescharacteristic
32C22×C22⋊C4×C31C2211yescharacteristic
33C22×C22⋊C4×C31C2211yescharacteristic
34C22×C22⋊C4×C31C2211yescharacteristic
35C31×#394—24no—
36C31×#392—24no—
37C2×C31×#95C2211yescharacteristic
38C2×C31×#95C2211yescharacteristic
39C2×C31×#95C2211yescharacteristic
40C2×C31×#95C2211yescharacteristic
41C2×C31×#95C2211yescharacteristic
42C2×C31×#95C2211yescharacteristic
43C2×C31×#95C2211yescharacteristic
44C2×C31×#95C2211yescharacteristic
45C2×C31×#95C2211yescharacteristic
46C2×C31×#95C2211yescharacteristic
47C2×C31×#95C2211yescharacteristic
48C2×C31×#95C2211yescharacteristic
49C2×C31×#95C2211yescharacteristic
50C2×C31×#95C2211yescharacteristic
51C2×C31×#95C2211yescharacteristic
52C2×C31×#95C2211yescharacteristic
53C25×C31C2311yescharacteristic
54C25×C31C2311yescharacteristic
55C25×C31C2311yescharacteristic
56C22×D4×C31—22no—
57C22×D4×C31—22no—
58C22×D4×C31—22no—
59C22×D4×C31—22no—
60C22×D4×C31—22no—
61C22×D4×C31—22no—
62C22×D4×C31—41no—
63C22×D4×C31—41no—
64C22×D4×C31—41no—
65C22×D4×C31—41no—
66C22×D4×C31—41no—
67C22×D4×C31—41no—
68C22×D4×C31—41no—
69C22×D4×C31—41no—
70C22×D4×C31—41no—
71C22×D4×C31—41no—
72C22×D4×C31—41no—
73C22×D4×C31—41no—
74C22×D4×C31—41no—
75C22×D4×C31—41no—
76C22×D4×C31D414yes—
77C23×C4×C31C2311yescharacteristic
78C23×C4×C31C2311yescharacteristic
79C23×C4×C31C2311yescharacteristic
80C23×C4×C31C2311yescharacteristic
81C23×C4×C31C2311yescharacteristic
82C23×C4×C31C2311yescharacteristic
83C23×C4×C31C2311yescharacteristic
84C23×C4×C31C2311yescharacteristic
85C23×C4×C31C2311yescharacteristic
86C23×C4×C31C2311yescharacteristic
87C23×C4×C31C2311yescharacteristic
88C23×C4×C31C2311yescharacteristic
89C2×C4⋊C4×C31—22no—
90C2×C4⋊C4×C31—41no—
91C2×C4⋊C4×C31—41no—
92C2×C22⋊C4×C31—22no—
93C2×C22⋊C4×C31—22no—
94C2×C22⋊C4×C31—22no—
95C2×C22⋊C4×C31—22no—
96C2×C22⋊C4×C31—22no—
97C2×C22⋊C4×C31—22no—
98C2×C22⋊C4×C31—22no—
99C2×C22⋊C4×C31—22no—
100C2×C22⋊C4×C31—22no—
101C2×C22⋊C4×C31—22no—
102C2×C22⋊C4×C31—22no—
103C2×C22⋊C4×C31—22no—
104C2×C22⋊C4×C31—22no—
105C2×C22⋊C4×C31—41no—
106C2×C22⋊C4×C31—41no—
107C2×C22⋊C4×C31—41no—
108C2×C22⋊C4×C31—41no—
109C2×C22⋊C4×C31—41no—
110C2×C22⋊C4×C31—41no—
111C2×C22⋊C4×C31—41no—
112C2×C22⋊C4×C31—41no—
113C2×C22⋊C4×C31—41no—
114C2×C22⋊C4×C31—41no—
115C2×C22⋊C4×C31—41no—
116C2×C22⋊C4×C31—41no—
117C2×C22⋊C4×C31—41no—
118C2×C22⋊C4×C31—41no—
119C2×C22⋊C4×C31—41no—
120C2×C22⋊C4×C31—41no—
121C2×C22⋊C4×C31—41no—
122C2×C22⋊C4×C31—41no—
123C2×C22⋊C4×C31—41no—
124C2×C22⋊C4×C31—41no—
125C2×C22⋊C4×C31—41no—
126C2×C22⋊C4×C31—41no—
127C2×C22⋊C4×C31—41no—
128C2×C22⋊C4×C31—41no—
129C2×C22⋊C4×C31—41no—
130C2×C22⋊C4×C31—41no—
131C2×C22⋊C4×C31—41no—
132C2×C22⋊C4×C31—41no—
133C2×C22⋊C4×C31—41no—
134C2×C22⋊C4×C31—41no—
135C2×C22⋊C4×C31—41no—
136C2×C22⋊C4×C31—41no—
137C31×#95—22no—
138C31×#95—22no—
139C31×#95—22no—
140C31×#95—22no—
141C31×#95—41no—
142C31×#95—41no—
143C31×#95—41no—
144C31×#95—41no—
145C31×#95—41no—
146C31×#95—41no—
147C31×#95—41no—
148C31×#95—41no—
149C31×#95—41no—
150C31×#95—41no—
151C31×#95—41no—
152C31×#95—41no—
153C24×C31—21no—
154C24×C31—21no—
155C24×C31—21no—
156C24×C31—21no—
157C24×C31—21no—
158C24×C31—21no—
159C24×C31—21no—
160C24×C31—21no—
161C24×C31—21no—
162C24×C31—21no—
163C24×C31—21no—
164C24×C31—21no—
165C24×C31—21no—
166C24×C31—21no—
167C24×C31—21no—
168C24×C31—21no—
169C24×C31—21no—
170C24×C31—21no—
171C24×C31—21no—
172C24×C31—21no—
173C24×C31—21no—
174C24×C31—21no—
175C24×C31—21no—
176C24×C31—21no—
177C24×C31—21no—
178C24×C31—21no—
179C24×C31—21no—
180C24×C31—21no—
181C24×C31—21no—
182C24×C31—21no—
183C24×C31—21no—
184C24×C31—21no—
185C24×C31—21no—
186C24×C31—21no—
187C24×C31—21no—
188C24×C31—21no—
189C24×C31—21no—
190C24×C31—21no—
191C24×C31—21no—
192C24×C31—21no—
193C24×C31—21no—
194C24×C31—21no—
195C24×C31C2×D412yes—
196C24×C31C2×D412yes—
197C24×C31#4112yes—
198C24×C31C2411yescharacteristic
199C2×D4×C31—44no—
200C2×D4×C31—44no—
201C2×D4×C31—44no—
202C2×D4×C31—44no—
203C2×D4×C31—44no—
204C2×D4×C31—44no—
205C2×D4×C31—44no—
206C2×D4×C31—44no—
207C2×D4×C31—44no—
208C2×D4×C31—44no—
209C2×D4×C31—44no—
210C2×D4×C31—44no—
211C2×D4×C31—44no—
212C2×D4×C31—44no—
213C2×D4×C31—44no—
214C2×D4×C31—44no—
215C2×D4×C31—44no—
216C2×D4×C31—44no—
217C2×D4×C31—44no—
218C2×D4×C31—44no—
219C2×D4×C31—44no—
220C22×C4×C31—21no—
221C22×C4×C31—21no—
222C22×C4×C31—21no—
223C22×C4×C31—21no—
224C22×C4×C31—21no—
225C22×C4×C31—21no—
226C22×C4×C31—21no—
227C22×C4×C31—21no—
228C22×C4×C31—21no—
229C22×C4×C31—21no—
230C22×C4×C31—21no—
231C22×C4×C31—21no—
232C22×C4×C31—21no—
233C22×C4×C31—21no—
234C22×C4×C31—21no—
235C22×C4×C31—21no—
236C22×C4×C31—21no—
237C22×C4×C31—21no—
238C22×C4×C31—21no—
239C22×C4×C31—21no—
240C22×C4×C31—21no—
241C22×C4×C31—21no—
242C22×C4×C31—21no—
243C22×C4×C31—21no—
244C22×C4×C31—21no—
245C22×C4×C31—21no—
246C22×C4×C31—21no—
247C22×C4×C31—21no—
248C22×C4×C31—21no—
249C22×C4×C31—21no—
250C22×C4×C31—21no—
251C22×C4×C31—21no—
252C22×C4×C31—21no—
253C22×C4×C31—21no—
254C22×C4×C31—21no—
255C22×C4×C31—21no—
256C22×C4×C31—21no—
257C22×C4×C31—21no—
258C22×C4×C31—21no—
259C22×C4×C31—21no—
260C22×C4×C31—21no—
261C22×C4×C31—21no—
262C22×C4×C31—21no—
263C22×C4×C31—21no—
264C22×C4×C31—21no—
265C22×C4×C31—21no—
266C22×C4×C31—21no—
267C22×C4×C31—21no—
268C22×C4×C31—21no—
269C22×C4×C31—21no—
270C22×C4×C31—21no—
271C22×C4×C31—21no—
272C22×C4×C31—21no—
273C22×C4×C31—21no—
274C22×C4×C31—21no—
275C22×C4×C31—21no—
276C22×C4×C31—21no—
277C22×C4×C31—21no—
278C22×C4×C31—21no—
279C22×C4×C31—21no—
280C22×C4×C31—21no—
281C22×C4×C31—21no—
282C22×C4×C31—21no—
283C22×C4×C31—21no—
284C22×C4×C31—21no—
285C22×C4×C31—21no—
286C22×C4×C31—21no—
287C22×C4×C31—21no—
288C22×C4×C31—21no—
289C22×C4×C31—21no—
290C22×C4×C31—21no—
291C22×C4×C31—21no—
292C22×C4×C31—21no—
293C22×C4×C31—21no—
294C22×C4×C31—21no—
295C22×C4×C31—21no—
296C22×C4×C31—21no—
297C22×C4×C31—21no—
298C22×C4×C31—21no—
299C22×C4×C31—21no—
300C22×C4×C31C2×D412yes—
301C22×C4×C31#4112yes—
302C22×C4×C31#4112yes—
303C22×C4×C31#4112yes—
304C4⋊C4×C31—44no—
305C22⋊C4×C31—44no—
306C22⋊C4×C31—44no—
307C22⋊C4×C31—44no—
308C22⋊C4×C31—44no—
309C22⋊C4×C31—44no—
310C22⋊C4×C31—44no—
311C22⋊C4×C31—44no—
312C22⋊C4×C31—44no—
313C22⋊C4×C31—44no—
314C22⋊C4×C31—44no—
315C22⋊C4×C31—44no—
316C22⋊C4×C31—44no—
317C22⋊C4×C31—44no—
318C22⋊C4×C31—44no—
319C22⋊C4×C31—44no—
320#17138C3111yesmaximal, characteristic, direct product factor, Sylow
321C23×C31—22no—
322C23×C31—22no—
323C23×C31—22no—
324C23×C31—22no—
325C23×C31—22no—
326C23×C31—22no—
327C23×C31—22no—
328C23×C31—22no—
329C23×C31—22no—
330C23×C31—22no—
331C23×C31—22no—
332C23×C31—22no—
333C23×C31—22no—
334C23×C31—22no—
335C23×C31—22no—
336C23×C31—22no—
337C23×C31—22no—
338C23×C31—22no—
339C23×C31—22no—
340C23×C31—22no—
341C23×C31—22no—
342C23×C31—41no—
343C23×C31—41no—
344C23×C31—41no—
345C23×C31—41no—
346C23×C31—41no—
347C23×C31—41no—
348C23×C31—41no—
349C23×C31—41no—
350C23×C31—41no—
351C23×C31—41no—
352C23×C31—41no—
353C23×C31—41no—
354C23×C31—41no—
355C23×C31—41no—
356C23×C31—41no—
357C23×C31—41no—
358C23×C31—41no—
359C23×C31—41no—
360C23×C31—41no—
361C23×C31—41no—
362C23×C31—41no—
363C23×C31—41no—
364C23×C31—41no—
365C23×C31—41no—
366C23×C31—41no—
367C23×C31—41no—
368C23×C31—41no—
369C23×C31—41no—
370C23×C31—41no—
371C23×C31—41no—
372C23×C31—41no—
373C23×C31—41no—
374C23×C31—41no—
375C23×C31—41no—
376C23×C31—41no—
377C23×C31—41no—
378C23×C31—41no—
379C23×C31—41no—
380C23×C31—41no—
381C23×C31—41no—
382C23×C31—41no—
383C23×C31—41no—
384C23×C31—41no—
385C23×C31—41no—
386C23×C31—41no—
387C23×C31—41no—
388C23×C31—41no—
389C23×C31—41no—
390C23×C31—41no—
391C23×C31—41no—
392C23×C31—41no—
393C23×C31—41no—
394C23×C31—41no—
395C23×C31—41no—
396C23×C31—41no—
397C23×C31—41no—
398C23×C31—41no—
399C23×C31—41no—
400C23×C31—41no—
401C23×C31—41no—
402C23×C31—41no—
403C23×C31—41no—
404C23×C31—41no—
405C23×C31—41no—
406C23×C31—41no—
407C23×C31—41no—
408C23×C31—41no—
409C23×C31—41no—
410C23×C31—41no—
411C23×C31—41no—
412C23×C31—41no—
413C23×C31—41no—
414C23×C31—41no—
415C23×C31—41no—
416C23×C31—41no—
417C23×C31—41no—
418C23×C31—41no—
419C23×C31—41no—
420C23×C31—41no—
421C23×C31—41no—
422C23×C31—41no—
423C23×C31—41no—
424C23×C31—41no—
425C23×C31—41no—
426C23×C31C22×D411yescharacteristic
427C23×C31C2×#4111yescharacteristic
428C23×C31C2×#4111yescharacteristic
429C23×C31C2×#4111yescharacteristic
430C23×C31C2×#4111yescharacteristic
431C23×C31H(5,𝔽2)11yescharacteristic
432C23×C31H(5,𝔽2)11yescharacteristic
433C23×C31H(5,𝔽2)11yescharacteristic
434C23×C31H(5,𝔽2)11yescharacteristic
435C23×C31H(5,𝔽2)11yescharacteristic
436C23×C31H(5,𝔽2)11yescharacteristic
437C23×C31H(5,𝔽2)11yescharacteristic
438C23×C31H(5,𝔽2)11yescharacteristic
439C23×C31H(5,𝔽2)11yescharacteristic
440C23×C31H(5,𝔽2)11yescharacteristic
441D4×C31—416no—
442D4×C31—416no—
443D4×C31—416no—
444C2×C4×C31—22no—
445C2×C4×C31—22no—
446C2×C4×C31—22no—
447C2×C4×C31—22no—
448C2×C4×C31—22no—
449C2×C4×C31—22no—
450C2×C4×C31—22no—
451C2×C4×C31—22no—
452C2×C4×C31—22no—
453C2×C4×C31—22no—
454C2×C4×C31—22no—
455C2×C4×C31—22no—
456C2×C4×C31—41no—
457C2×C4×C31—41no—
458C2×C4×C31—41no—
459C2×C4×C31—41no—
460C2×C4×C31—41no—
461C2×C4×C31—41no—
462C2×C4×C31—41no—
463C2×C4×C31—41no—
464C2×C4×C31—41no—
465C2×C4×C31—41no—
466C2×C4×C31—41no—
467C2×C4×C31—41no—
468C2×C4×C31—41no—
469C2×C4×C31—41no—
470C2×C4×C31—41no—
471C2×C4×C31—41no—
472C2×C4×C31—41no—
473C2×C4×C31—41no—
474C2×C4×C31—41no—
475C2×C4×C31—41no—
476C2×C4×C31—41no—
477C2×C4×C31—41no—
478C2×C4×C31—41no—
479C2×C4×C31—41no—
480C2×C4×C31—41no—
481C2×C4×C31—41no—
482C2×C4×C31—41no—
483C2×C4×C31—41no—
484C2×C4×C31—41no—
485C2×C4×C31—41no—
486C2×C4×C31—41no—
487C2×C4×C31—41no—
488C2×C4×C31—41no—
489C2×C4×C31—41no—
490C2×C4×C31—41no—
491C2×C4×C31—41no—
492C2×C4×C31—41no—
493C2×C4×C31—41no—
494C2×C4×C31—41no—
495C2×C4×C31—41no—
496C2×C4×C31—41no—
497C2×C4×C31—41no—
498C2×C4×C31—41no—
499C2×C4×C31—41no—
500C2×C4×C31—41no—
501C2×C4×C31—41no—
502C2×C4×C31—41no—
503C2×C4×C31—41no—
504C2×C4×C31—41no—
505C2×C4×C31—41no—
506C2×C4×C31—41no—
507C2×C4×C31—41no—
508C2×C4×C31—41no—
509C2×C4×C31—41no—
510C2×C4×C31—41no—
511C2×C4×C31—41no—
512C2×C4×C31—41no—
513C2×C4×C31—41no—
514C2×C4×C31—41no—
515C2×C4×C31—41no—
516C2×C4×C31—41no—
517C2×C4×C31—41no—
518C2×C4×C31—41no—
519C2×C4×C31—41no—
520C2×C4×C31—41no—
521C2×C4×C31—41no—
522C2×C4×C31—41no—
523C2×C4×C31—41no—
524C2×C4×C31—41no—
525C2×C4×C31—41no—
526C2×C4×C31—41no—
527C2×C4×C31—41no—
528C2×#394C2×C3111yescharacteristic, complemented
529C2×#392C2×C3111yescharacteristic
530#1443C2×C3111yescharacteristic, complemented
531#1442C2×C3111yescharacteristic, complemented
532#1440C2×C3111yescharacteristic, complemented
533#1440C2×C3111yescharacteristic, complemented
534#1440C2×C3111yescharacteristic, complemented
535#1440C2×C3111yescharacteristic, complemented
536#1440C2×C3111yescharacteristic, complemented
537#1439C2×C3111yescharacteristic, complemented
538#1438C2×C3111yescharacteristic, complemented
539#1438C2×C3111yescharacteristic, complemented
540#1438C2×C3111yescharacteristic, complemented
541#1438C2×C3111yescharacteristic, complemented
542#1438C2×C3111yescharacteristic, complemented
543C22×C31—42no—
544C22×C31—42no—
545C22×C31—42no—
546C22×C31—42no—
547C22×C31—42no—
548C22×C31—42no—
549C22×C31—42no—
550C22×C31—42no—
551C22×C31—42no—
552C22×C31—42no—
553C22×C31—42no—
554C22×C31—42no—
555C22×C31—42no—
556C22×C31—42no—
557C22×C31—42no—
558C22×C31—42no—
559C22×C31—42no—
560C22×C31—42no—
561C22×C31—42no—
562C22×C31—42no—
563C22×C31—42no—
564C22×C31—81no—
565C22×C31—81no—
566C22×C31—81no—
567C22×C31—81no—
568C22×C31—81no—
569C22×C31—81no—
570C22×C31—81no—
571C22×C31—81no—
572C22×C31—81no—
573C22×C31—81no—
574C22×C31—81no—
575C22×C31—81no—
576C22×C31—81no—
577C22×C31—81no—
578C22×C31—81no—
579C22×C31—81no—
580C22×C31—81no—
581C22×C31—81no—
582C22×C31—81no—
583C22×C31—81no—
584C22×C31—81no—
585C22×C31—81no—
586C22×C31—81no—
587C22×C31—81no—
588C22×C31#53411yescharacteristic
589C22×C31#53411yescharacteristic
590C22×C31#53411yescharacteristic
591C22×C31#53811yescharacteristic
592C22×C31#53811yescharacteristic
593C22×C31#53811yescharacteristic
594C22×C31#53811yescharacteristic
595C22×C31#53811yescharacteristic
596C22×C31#53811yescharacteristic
597C22×C31#54011yescharacteristic
598C22×C31#54011yescharacteristic
599C22×C31#54011yescharacteristic
600C22×C31#54011yescharacteristic
601C22×C31#54011yescharacteristic
602C22×C31#54011yescharacteristic
603C22×C31#54611yescharacteristic
604C22×C31#54611yescharacteristic
605C22×C31#54611yescharacteristic
606C22×C31#54611yescharacteristic
607C22×C31#55111yescharacteristic
608C22×C31#55111yescharacteristic
609C22×C31#55311yescharacteristic
610C22×C31#55311yescharacteristic
611C22×C31#55511yescharacteristic
612C22×C31#55911yescharacteristic
613C22×C31#56011yescharacteristic
614C22×C31#56011yescharacteristic
615C22×C31#56011yescharacteristic
616C22×C31#56011yescharacteristic
617C22×C31#56011yescharacteristic
618C22×C31#56011yescharacteristic
619C22×C31#56011yescharacteristic
620C22×C31#56011yescharacteristic
621C22×C31H(3,𝔽4)11yescharacteristic
622C22×C31H(3,𝔽4)11yescharacteristic
623C4×C31—42no—
624C4×C31—42no—
625C4×C31—42no—
626C4×C31—42no—
627C4×C31—81no—
628C4×C31—81no—
629C4×C31—81no—
630C4×C31—81no—
631C4×C31—81no—
632C4×C31—81no—
633C4×C31—81no—
634C4×C31—81no—
635C23×D4C22×C3111yescharacteristic
636C23×D4C22×C3111yescharacteristic
637C23×D4C22×C3111yescharacteristic
638C22×C4⋊C4C22×C3111yescharacteristic
639C22×C22⋊C4C22×C3111yescharacteristic
640C22×C22⋊C4C22×C3111yescharacteristic
641C22×C22⋊C4C22×C3111yescharacteristic
642C22×C22⋊C4C22×C3111yescharacteristic
643C22×C22⋊C4C22×C3111yescharacteristic
644C22×C22⋊C4C22×C3111yescharacteristic
645C22×C22⋊C4C22×C3111yescharacteristic
646C22×C22⋊C4C22×C3111yescharacteristic
647C22×C22⋊C4C22×C3111yescharacteristic
648C22×C22⋊C4C22×C3111yescharacteristic
649C22×C22⋊C4C22×C3111yescharacteristic
650C22×C22⋊C4C22×C3111yescharacteristic
651C22×C22⋊C4C22×C3111yescharacteristic
652C22×C22⋊C4C22×C3111yescharacteristic
653C22×C22⋊C4C22×C3111yescharacteristic
654#394—24no—
655#392—24no—
656C2×#95C22×C3111yescharacteristic
657C2×#95C22×C3111yescharacteristic
658C2×#95C22×C3111yescharacteristic
659C2×#95C22×C3111yescharacteristic
660C2×#95C22×C3111yescharacteristic
661C2×#95C22×C3111yescharacteristic
662C2×#95C22×C3111yescharacteristic
663C2×#95C22×C3111yescharacteristic
664C2×#95C22×C3111yescharacteristic
665C2×#95C22×C3111yescharacteristic
666C2×#95C22×C3111yescharacteristic
667C2×#95C22×C3111yescharacteristic
668C2×#95C22×C3111yescharacteristic
669C2×#95C22×C3111yescharacteristic
670C2×#95C22×C3111yescharacteristic
671C2×#95C22×C3111yescharacteristic
672C2×C31—82no—
673C2×C31—82no—
674C2×C31—82no—
675C2×C31#268411yescharacteristic
676C2×C31#268811yescharacteristic
677C2×C31#268811yescharacteristic
678C2×C31#269711yescharacteristic
679C2×C31#269911yescharacteristic
680C2×C31#270911yescharacteristic
681C2×C31#275211yescharacteristic
682C2×C31#275311yescharacteristic
683C2×C31#275611yescharacteristic
684C2×C31#280311yescharacteristic
685C2×C31#281211yescharacteristic
686C2×C31#282511yescharacteristic
687C2×C31#282811yescharacteristic
688C2×C31#282811yescharacteristic
689C2×C31#282811yescharacteristic
690C25C23×C3111yescharacteristic
691C25C23×C3111yescharacteristic
692C25C23×C3111yescharacteristic
693C22×D4—22no—
694C22×D4—22no—
695C22×D4—22no—
696C22×D4—22no—
697C22×D4—22no—
698C22×D4—22no—
699C22×D4—41no—
700C22×D4—41no—
701C22×D4—41no—
702C22×D4—41no—
703C22×D4—41no—
704C22×D4—41no—
705C22×D4—41no—
706C22×D4—41no—
707C22×D4—41no—
708C22×D4—41no—
709C22×D4—41no—
710C22×D4—41no—
711C22×D4—41no—
712C22×D4—41no—
713C22×D4D4×C3114yes—
714C23×C4C23×C3111yescharacteristic
715C23×C4C23×C3111yescharacteristic
716C23×C4C23×C3111yescharacteristic
717C23×C4C23×C3111yescharacteristic
718C23×C4C23×C3111yescharacteristic
719C23×C4C23×C3111yescharacteristic
720C23×C4C23×C3111yescharacteristic
721C23×C4C23×C3111yescharacteristic
722C23×C4C23×C3111yescharacteristic
723C23×C4C23×C3111yescharacteristic
724C23×C4C23×C3111yescharacteristic
725C23×C4C23×C3111yescharacteristic
726C2×C4⋊C4—22no—
727C2×C4⋊C4—41no—
728C2×C4⋊C4—41no—
729C2×C22⋊C4—22no—
730C2×C22⋊C4—22no—
731C2×C22⋊C4—22no—
732C2×C22⋊C4—22no—
733C2×C22⋊C4—22no—
734C2×C22⋊C4—22no—
735C2×C22⋊C4—22no—
736C2×C22⋊C4—22no—
737C2×C22⋊C4—22no—
738C2×C22⋊C4—22no—
739C2×C22⋊C4—22no—
740C2×C22⋊C4—22no—
741C2×C22⋊C4—22no—
742C2×C22⋊C4—41no—
743C2×C22⋊C4—41no—
744C2×C22⋊C4—41no—
745C2×C22⋊C4—41no—
746C2×C22⋊C4—41no—
747C2×C22⋊C4—41no—
748C2×C22⋊C4—41no—
749C2×C22⋊C4—41no—
750C2×C22⋊C4—41no—
751C2×C22⋊C4—41no—
752C2×C22⋊C4—41no—
753C2×C22⋊C4—41no—
754C2×C22⋊C4—41no—
755C2×C22⋊C4—41no—
756C2×C22⋊C4—41no—
757C2×C22⋊C4—41no—
758C2×C22⋊C4—41no—
759C2×C22⋊C4—41no—
760C2×C22⋊C4—41no—
761C2×C22⋊C4—41no—
762C2×C22⋊C4—41no—
763C2×C22⋊C4—41no—
764C2×C22⋊C4—41no—
765C2×C22⋊C4—41no—
766C2×C22⋊C4—41no—
767C2×C22⋊C4—41no—
768C2×C22⋊C4—41no—
769C2×C22⋊C4—41no—
770C2×C22⋊C4—41no—
771C2×C22⋊C4—41no—
772C2×C22⋊C4—41no—
773C2×C22⋊C4—41no—
774#95—22no—
775#95—22no—
776#95—22no—
777#95—22no—
778#95—41no—
779#95—41no—
780#95—41no—
781#95—41no—
782#95—41no—
783#95—41no—
784#95—41no—
785#95—41no—
786#95—41no—
787#95—41no—
788#95—41no—
789#95—41no—
790C31#1713811yescharacteristic, direct product factor, Sylow
791C24—21no—
792C24—21no—
793C24—21no—
794C24—21no—
795C24—21no—
796C24—21no—
797C24—21no—
798C24—21no—
799C24—21no—
800C24—21no—
801C24—21no—
802C24—21no—
803C24—21no—
804C24—21no—
805C24—21no—
806C24—21no—
807C24—21no—
808C24—21no—
809C24—21no—
810C24—21no—
811C24—21no—
812C24—21no—
813C24—21no—
814C24—21no—
815C24—21no—
816C24—21no—
817C24—21no—
818C24—21no—
819C24—21no—
820C24—21no—
821C24—21no—
822C24—21no—
823C24—21no—
824C24—21no—
825C24—21no—
826C24—21no—
827C24—21no—
828C24—21no—
829C24—21no—
830C24—21no—
831C24—21no—
832C24—21no—
833C24C2×D4×C3112yes—
834C24C2×D4×C3112yes—
835C24#41×C3112yes—
836C24C24×C3111yescharacteristic
837C2×D4—44no—
838C2×D4—44no—
839C2×D4—44no—
840C2×D4—44no—
841C2×D4—44no—
842C2×D4—44no—
843C2×D4—44no—
844C2×D4—44no—
845C2×D4—44no—
846C2×D4—44no—
847C2×D4—44no—
848C2×D4—44no—
849C2×D4—44no—
850C2×D4—44no—
851C2×D4—44no—
852C2×D4—44no—
853C2×D4—44no—
854C2×D4—44no—
855C2×D4—44no—
856C2×D4—44no—
857C2×D4—44no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4C2×D4×C3112yes—
939C22×C4#41×C3112yes—
940C22×C4#41×C3112yes—
941C22×C4#41×C3112yes—
942C4⋊C4—44no—
943C22⋊C4—44no—
944C22⋊C4—44no—
945C22⋊C4—44no—
946C22⋊C4—44no—
947C22⋊C4—44no—
948C22⋊C4—44no—
949C22⋊C4—44no—
950C22⋊C4—44no—
951C22⋊C4—44no—
952C22⋊C4—44no—
953C22⋊C4—44no—
954C22⋊C4—44no—
955C22⋊C4—44no—
956C22⋊C4—44no—
957C22⋊C4—44no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—41no—
980C23—41no—
981C23—41no—
982C23—41no—
983C23—41no—
984C23—41no—
985C23—41no—
986C23—41no—
987C23—41no—
988C23—41no—
989C23—41no—
990C23—41no—
991C23—41no—
992C23—41no—
993C23—41no—
994C23—41no—
995C23—41no—
996C23—41no—
997C23—41no—
998C23—41no—
999C23—41no—
1000C23—41no—
1001C23—41no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23C22×D4×C3111yescharacteristic
1064C23C2×#41×C3111yescharacteristic
1065C23C2×#41×C3111yescharacteristic
1066C23C2×#41×C3111yescharacteristic
1067C23C2×#41×C3111yescharacteristic
1068C23C31×H(5,𝔽2)11yescharacteristic
1069C23C31×H(5,𝔽2)11yescharacteristic
1070C23C31×H(5,𝔽2)11yescharacteristic
1071C23C31×H(5,𝔽2)11yescharacteristic
1072C23C31×H(5,𝔽2)11yescharacteristic
1073C23C31×H(5,𝔽2)11yescharacteristic
1074C23C31×H(5,𝔽2)11yescharacteristic
1075C23C31×H(5,𝔽2)11yescharacteristic
1076C23C31×H(5,𝔽2)11yescharacteristic
1077C23C31×H(5,𝔽2)11yescharacteristic
1078D4—416no—
1079D4—416no—
1080D4—416no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C22—42no—
1166C22—42no—
1167C22—42no—
1168C22—42no—
1169C22—42no—
1170C22—42no—
1171C22—42no—
1172C22—42no—
1173C22—42no—
1174C22—42no—
1175C22—42no—
1176C22—42no—
1177C22—42no—
1178C22—42no—
1179C22—42no—
1180C22—42no—
1181C22—42no—
1182C22—42no—
1183C22—42no—
1184C22—42no—
1185C22—42no—
1186C22—81no—
1187C22—81no—
1188C22—81no—
1189C22—81no—
1190C22—81no—
1191C22—81no—
1192C22—81no—
1193C22—81no—
1194C22—81no—
1195C22—81no—
1196C22—81no—
1197C22—81no—
1198C22—81no—
1199C22—81no—
1200C22—81no—
1201C22—81no—
1202C22—81no—
1203C22—81no—
1204C22—81no—
1205C22—81no—
1206C22—81no—
1207C22—81no—
1208C22—81no—
1209C22—81no—
1210C22C31×#53411yescharacteristic
1211C22C31×#53411yescharacteristic
1212C22C31×#53411yescharacteristic
1213C22C31×#53811yescharacteristic
1214C22C31×#53811yescharacteristic
1215C22C31×#53811yescharacteristic
1216C22C31×#53811yescharacteristic
1217C22C31×#53811yescharacteristic
1218C22C31×#53811yescharacteristic
1219C22C31×#54011yescharacteristic
1220C22C31×#54011yescharacteristic
1221C22C31×#54011yescharacteristic
1222C22C31×#54011yescharacteristic
1223C22C31×#54011yescharacteristic
1224C22C31×#54011yescharacteristic
1225C22C31×#54611yescharacteristic
1226C22C31×#54611yescharacteristic
1227C22C31×#54611yescharacteristic
1228C22C31×#54611yescharacteristic
1229C22C31×#55111yescharacteristic
1230C22C31×#55111yescharacteristic
1231C22C31×#55311yescharacteristic
1232C22C31×#55311yescharacteristic
1233C22C31×#55511yescharacteristic
1234C22C31×#55911yescharacteristic
1235C22C31×#56011yescharacteristic
1236C22C31×#56011yescharacteristic
1237C22C31×#56011yescharacteristic
1238C22C31×#56011yescharacteristic
1239C22C31×#56011yescharacteristic
1240C22C31×#56011yescharacteristic
1241C22C31×#56011yescharacteristic
1242C22C31×#56011yescharacteristic
1243C22C31×H(3,𝔽4)11yescharacteristic
1244C22C31×H(3,𝔽4)11yescharacteristic
1245C4—42no—
1246C4—42no—
1247C4—42no—
1248C4—42no—
1249C4—81no—
1250C4—81no—
1251C4—81no—
1252C4—81no—
1253C4—81no—
1254C4—81no—
1255C4—81no—
1256C4—81no—
1257C2—82no—
1258C2—82no—
1259C2—82no—
1260C2C31×#268411yescharacteristic
1261C2C31×#268811yescharacteristic
1262C2C31×#268811yescharacteristic
1263C2C31×#269711yescharacteristic
1264C2C31×#269911yescharacteristic
1265C2C31×#270911yescharacteristic
1266C2C31×#275211yescharacteristic
1267C2C31×#275311yescharacteristic
1268C2C31×#275611yescharacteristic
1269C2C31×#280311yescharacteristic
1270C2C31×#281211yescharacteristic
1271C2C31×#282511yescharacteristic
1272C2C31×#282811yescharacteristic
1273C2C31×#282811yescharacteristic
1274C2C31×#282811yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutator, Frattini, cosocleC24C24×C31
prime radicalC2×C31×#392C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#394C2semidirect
3. C31×#1443C2semidirect
4. C31×#1442C2semidirect
5. C31×#1440C2semidirect
6. C31×#1440C2semidirect
7. C31×#1440C2semidirect
8. C31×#1440C2semidirect
9. C31×#1440C2semidirect
10. C31×#1439C2semidirect
11. C31×#1438C2semidirect
12. C31×#1438C2semidirect
13. C31×#1438C2semidirect
14. C31×#1438C2semidirect
15. C31×#1438C2semidirect
320. #17138C31direct (N × H)
528. C2×#394C2×C31semidirect
530. #1443C2×C31semidirect
531. #1442C2×C31semidirect
532. #1440C2×C31semidirect
533. #1440C2×C31semidirect
534. #1440C2×C31semidirect
535. #1440C2×C31semidirect
536. #1440C2×C31semidirect
537. #1439C2×C31semidirect
538. #1438C2×C31semidirect
539. #1438C2×C31semidirect
540. #1438C2×C31semidirect
541. #1438C2×C31semidirect
542. #1438C2×C31semidirect
790. C31#17138direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3942
C2×C31×#3922
C31×#14432
C31×#14422
C31×#14402
C31×#14392
C31×#14382
#1713831