Finite Group Databasebeta

← C31×#17115 #21473874

Subgroups — C31×#17115 #21473874

Order 7936.

1874 conjugacy classes of subgroups.

The subgroup lattice has 1292 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#397C211yesmaximal, characteristic, complemented
2C2×C31×#394C211yesmaximal, characteristic, complemented
3C2×C31×#394C211yesmaximal, characteristic, complemented
4C2×C31×#392C211yesmaximal, characteristic
5C31×#1443C211yesmaximal, characteristic, complemented
6C31×#1441C211yesmaximal, characteristic, complemented
7C31×#1440C211yesmaximal, characteristic, complemented
8C31×#1439C211yesmaximal, characteristic, complemented
9C31×#1439C211yesmaximal, characteristic, complemented
10C31×#1439C211yesmaximal, characteristic, complemented
11C31×#1439C211yesmaximal, 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×C4⋊C4×C31C2211yescharacteristic
21C22×C4⋊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
35C22×C22⋊C4×C31C2211yescharacteristic
36C22×C22⋊C4×C31C2211yescharacteristic
37C31×#397—24no—
38C31×#394—24no—
39C31×#394—24no—
40C31×#392—24no—
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
53C2×C31×#95C2211yescharacteristic
54C2×C31×#95C2211yescharacteristic
55C25×C31C2311yescharacteristic
56C25×C31C2311yescharacteristic
57C25×C31C2311yescharacteristic
58C22×D4×C31—22no—
59C22×D4×C31—22no—
60C22×D4×C31—22no—
61C22×D4×C31—22no—
62C22×D4×C31—22no—
63C22×D4×C31—22no—
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×C31—41no—
77C22×D4×C31—41no—
78C22×D4×C31D414yes—
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
89C23×C4×C31C2311yescharacteristic
90C23×C4×C31C2311yescharacteristic
91C2×C4⋊C4×C31—22no—
92C2×C4⋊C4×C31—41no—
93C2×C4⋊C4×C31—41no—
94C2×C4⋊C4×C31—41no—
95C2×C4⋊C4×C31—41no—
96C2×C4⋊C4×C31—41no—
97C2×C4⋊C4×C31—41no—
98C2×C4⋊C4×C31—41no—
99C2×C4⋊C4×C31D414yescomplemented
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—22no—
106C2×C22⋊C4×C31—22no—
107C2×C22⋊C4×C31—22no—
108C2×C22⋊C4×C31—22no—
109C2×C22⋊C4×C31—22no—
110C2×C22⋊C4×C31—22no—
111C2×C22⋊C4×C31—22no—
112C2×C22⋊C4×C31—22no—
113C2×C22⋊C4×C31—22no—
114C2×C22⋊C4×C31—22no—
115C2×C22⋊C4×C31—22no—
116C2×C22⋊C4×C31—22no—
117C2×C22⋊C4×C31—22no—
118C2×C22⋊C4×C31—22no—
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—
137C2×C22⋊C4×C31—41no—
138C2×C22⋊C4×C31—41no—
139C2×C22⋊C4×C31—41no—
140C2×C22⋊C4×C31—41no—
141C2×C22⋊C4×C31—41no—
142C2×C22⋊C4×C31—41no—
143C2×C22⋊C4×C31—41no—
144C2×C22⋊C4×C31—41no—
145C31×#95—22no—
146C31×#95—22no—
147C31×#95—22no—
148C31×#95—22no—
149C31×#95—22no—
150C31×#95—22no—
151C31×#95—22no—
152C31×#95—41no—
153C31×#95—41no—
154C31×#95—41no—
155C31×#95—41no—
156C31×#95—41no—
157C31×#95—41no—
158C31×#95—41no—
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×C31—21no—
196C24×C31—21no—
197C24×C31—21no—
198C24×C31—21no—
199C24×C31—21no—
200C24×C31—21no—
201C24×C31C2×D412yes—
202C24×C31C2×D412yes—
203C24×C31#4112yes—
204C24×C31C2411yescharacteristic
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—
220C2×D4×C31—44no—
221C2×D4×C31—44no—
222C2×D4×C31—44no—
223C2×D4×C31—44no—
224C2×D4×C31—44no—
225C2×D4×C31—44no—
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×C31—21no—
301C22×C4×C31—21no—
302C22×C4×C31—21no—
303C22×C4×C31—21no—
304C22×C4×C31C2×D412yes—
305C22×C4×C31C2×D412yes—
306C22×C4×C31C2×D412yes—
307C22×C4×C31C2×D412yes—
308C22×C4×C31#4112yes—
309C22×C4×C31#4112yes—
310C4⋊C4×C31—44no—
311C4⋊C4×C31—44no—
312C4⋊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—
320C22⋊C4×C31—44no—
321C22⋊C4×C31—44no—
322C22⋊C4×C31—44no—
323C22⋊C4×C31—44no—
324C22⋊C4×C31—44no—
325C22⋊C4×C31—44no—
326C22⋊C4×C31—44no—
327C22⋊C4×C31—44no—
328#17115C3111yesmaximal, characteristic, direct product factor, Sylow
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—22no—
343C23×C31—22no—
344C23×C31—22no—
345C23×C31—22no—
346C23×C31—22no—
347C23×C31—22no—
348C23×C31—22no—
349C23×C31—22no—
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×C31—41no—
427C23×C31—41no—
428C23×C31—41no—
429C23×C31—41no—
430C23×C31—41no—
431C23×C31—41no—
432C23×C31—41no—
433C23×C31—41no—
434C23×C31C22×D411yescharacteristic
435C23×C31C22×D411yescharacteristic
436C23×C31C2×#4111yescharacteristic
437C23×C31C2×#4111yescharacteristic
438C23×C31C2×#4111yescharacteristic
439C23×C31H(5,𝔽2)11yescharacteristic
440C23×C31H(5,𝔽2)11yescharacteristic
441C23×C31H(5,𝔽2)11yescharacteristic
442C23×C31H(5,𝔽2)11yescharacteristic
443C23×C31H(5,𝔽2)11yescharacteristic
444C23×C31H(5,𝔽2)11yescharacteristic
445C23×C31H(5,𝔽2)11yescharacteristic
446C23×C31H(5,𝔽2)11yescharacteristic
447C23×C31H(5,𝔽2)11yescharacteristic
448C23×C312−1+411yescharacteristic
449D4×C31—416no—
450D4×C31—416no—
451D4×C31—416no—
452C2×C4×C31—22no—
453C2×C4×C31—22no—
454C2×C4×C31—22no—
455C2×C4×C31—22no—
456C2×C4×C31—22no—
457C2×C4×C31—22no—
458C2×C4×C31—22no—
459C2×C4×C31—22no—
460C2×C4×C31—22no—
461C2×C4×C31—22no—
462C2×C4×C31—22no—
463C2×C4×C31—22no—
464C2×C4×C31—22no—
465C2×C4×C31—22no—
466C2×C4×C31—22no—
467C2×C4×C31—22no—
468C2×C4×C31—22no—
469C2×C4×C31—22no—
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×C4×C31—41no—
529C2×C4×C31—41no—
530C2×C4×C31—41no—
531C2×C4×C31—41no—
532C2×C4×C31—41no—
533C2×C4×C31—41no—
534C2×C4×C31—41no—
535C2×C4×C31—41no—
536C2×#397C2×C3111yescharacteristic, complemented
537C2×#394C2×C3111yescharacteristic, complemented
538C2×#394C2×C3111yescharacteristic, complemented
539C2×#392C2×C3111yescharacteristic
540#1443C2×C3111yescharacteristic, complemented
541#1441C2×C3111yescharacteristic, complemented
542#1440C2×C3111yescharacteristic, complemented
543#1439C2×C3111yescharacteristic, complemented
544#1439C2×C3111yescharacteristic, complemented
545#1439C2×C3111yescharacteristic, complemented
546#1439C2×C3111yescharacteristic, complemented
547#1438C2×C3111yescharacteristic, complemented
548#1438C2×C3111yescharacteristic, complemented
549#1438C2×C3111yescharacteristic, complemented
550#1438C2×C3111yescharacteristic, complemented
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—42no—
565C22×C31—42no—
566C22×C31—42no—
567C22×C31—42no—
568C22×C31—42no—
569C22×C31—42no—
570C22×C31—42no—
571C22×C31—42no—
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—81no—
589C22×C31—81no—
590C22×C31—81no—
591C22×C31—81no—
592C22×C31—81no—
593C22×C31—81no—
594C22×C31—81no—
595C22×C31—81no—
596C22×C31#53411yescharacteristic
597C22×C31#53411yescharacteristic
598C22×C31#53411yescharacteristic
599C22×C31#53411yescharacteristic
600C22×C31#53511yescharacteristic
601C22×C31#53711yescharacteristic
602C22×C31#53811yescharacteristic
603C22×C31#53811yescharacteristic
604C22×C31#53811yescharacteristic
605C22×C31#53811yescharacteristic
606C22×C31#53811yescharacteristic
607C22×C31#53811yescharacteristic
608C22×C31#53911yescharacteristic
609C22×C31#54011yescharacteristic
610C22×C31#54211yescharacteristic
611C22×C31D4211yescharacteristic
612C22×C31#54611yescharacteristic
613C22×C31#54611yescharacteristic
614C22×C31#54611yescharacteristic
615C22×C31#54711yescharacteristic
616C22×C31#55011yescharacteristic
617C22×C31#55011yescharacteristic
618C22×C31#55111yescharacteristic
619C22×C31#55311yescharacteristic
620C22×C31#55511yescharacteristic
621C22×C31#56011yescharacteristic
622C22×C31#56011yescharacteristic
623C22×C31#56011yescharacteristic
624C22×C31#56011yescharacteristic
625C22×C31#56011yescharacteristic
626C22×C31#56011yescharacteristic
627C22×C31H(3,𝔽4)11yescharacteristic
628C22×C31#56211yescharacteristic
629C22×C31#56211yescharacteristic
630C22×C31#56211yescharacteristic
631C4×C31—42no—
632C4×C31—42no—
633C4×C31—42no—
634C4×C31—42no—
635C4×C31—42no—
636C4×C31—42no—
637C4×C31—81no—
638C4×C31—81no—
639C4×C31—81no—
640C4×C31—81no—
641C4×C31—81no—
642C4×C31—81no—
643C23×D4C22×C3111yescharacteristic
644C23×D4C22×C3111yescharacteristic
645C23×D4C22×C3111yescharacteristic
646C22×C4⋊C4C22×C3111yescharacteristic
647C22×C4⋊C4C22×C3111yescharacteristic
648C22×C4⋊C4C22×C3111yescharacteristic
649C22×C22⋊C4C22×C3111yescharacteristic
650C22×C22⋊C4C22×C3111yescharacteristic
651C22×C22⋊C4C22×C3111yescharacteristic
652C22×C22⋊C4C22×C3111yescharacteristic
653C22×C22⋊C4C22×C3111yescharacteristic
654C22×C22⋊C4C22×C3111yescharacteristic
655C22×C22⋊C4C22×C3111yescharacteristic
656C22×C22⋊C4C22×C3111yescharacteristic
657C22×C22⋊C4C22×C3111yescharacteristic
658C22×C22⋊C4C22×C3111yescharacteristic
659C22×C22⋊C4C22×C3111yescharacteristic
660C22×C22⋊C4C22×C3111yescharacteristic
661C22×C22⋊C4C22×C3111yescharacteristic
662C22×C22⋊C4C22×C3111yescharacteristic
663C22×C22⋊C4C22×C3111yescharacteristic
664#397—24no—
665#394—24no—
666#394—24no—
667#392—24no—
668C2×#95C22×C3111yescharacteristic
669C2×#95C22×C3111yescharacteristic
670C2×#95C22×C3111yescharacteristic
671C2×#95C22×C3111yescharacteristic
672C2×#95C22×C3111yescharacteristic
673C2×#95C22×C3111yescharacteristic
674C2×#95C22×C3111yescharacteristic
675C2×#95C22×C3111yescharacteristic
676C2×#95C22×C3111yescharacteristic
677C2×#95C22×C3111yescharacteristic
678C2×#95C22×C3111yescharacteristic
679C2×#95C22×C3111yescharacteristic
680C2×#95C22×C3111yescharacteristic
681C2×#95C22×C3111yescharacteristic
682C2×C31—82no—
683C2×C31—82no—
684C2×C31—82no—
685C2×C31#266811yescharacteristic
686C2×C31#267311yescharacteristic
687C2×C31#268211yescharacteristic
688C2×C31#268611yescharacteristic
689C2×C31#269711yescharacteristic
690C2×C31#270511yescharacteristic
691C2×C31#270811yescharacteristic
692C2×C31#271411yescharacteristic
693C2×C31#273311yescharacteristic
694C2×C31#275611yescharacteristic
695C2×C31#281211yescharacteristic
696C2×C31#281311yescharacteristic
697C2×C31#282411yescharacteristic
698C2×C31#282511yescharacteristic
699C2×C31#282911yescharacteristic
700C25C23×C3111yescharacteristic
701C25C23×C3111yescharacteristic
702C25C23×C3111yescharacteristic
703C22×D4—22no—
704C22×D4—22no—
705C22×D4—22no—
706C22×D4—22no—
707C22×D4—22no—
708C22×D4—22no—
709C22×D4—41no—
710C22×D4—41no—
711C22×D4—41no—
712C22×D4—41no—
713C22×D4—41no—
714C22×D4—41no—
715C22×D4—41no—
716C22×D4—41no—
717C22×D4—41no—
718C22×D4—41no—
719C22×D4—41no—
720C22×D4—41no—
721C22×D4—41no—
722C22×D4—41no—
723C22×D4D4×C3114yes—
724C23×C4C23×C3111yescharacteristic
725C23×C4C23×C3111yescharacteristic
726C23×C4C23×C3111yescharacteristic
727C23×C4C23×C3111yescharacteristic
728C23×C4C23×C3111yescharacteristic
729C23×C4C23×C3111yescharacteristic
730C23×C4C23×C3111yescharacteristic
731C23×C4C23×C3111yescharacteristic
732C23×C4C23×C3111yescharacteristic
733C23×C4C23×C3111yescharacteristic
734C23×C4C23×C3111yescharacteristic
735C23×C4C23×C3111yescharacteristic
736C2×C4⋊C4—22no—
737C2×C4⋊C4—41no—
738C2×C4⋊C4—41no—
739C2×C4⋊C4—41no—
740C2×C4⋊C4—41no—
741C2×C4⋊C4—41no—
742C2×C4⋊C4—41no—
743C2×C4⋊C4—41no—
744C2×C4⋊C4D4×C3114yescomplemented
745C2×C22⋊C4—22no—
746C2×C22⋊C4—22no—
747C2×C22⋊C4—22no—
748C2×C22⋊C4—22no—
749C2×C22⋊C4—22no—
750C2×C22⋊C4—22no—
751C2×C22⋊C4—22no—
752C2×C22⋊C4—22no—
753C2×C22⋊C4—22no—
754C2×C22⋊C4—22no—
755C2×C22⋊C4—22no—
756C2×C22⋊C4—22no—
757C2×C22⋊C4—22no—
758C2×C22⋊C4—22no—
759C2×C22⋊C4—22no—
760C2×C22⋊C4—22no—
761C2×C22⋊C4—22no—
762C2×C22⋊C4—22no—
763C2×C22⋊C4—22no—
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—
774C2×C22⋊C4—41no—
775C2×C22⋊C4—41no—
776C2×C22⋊C4—41no—
777C2×C22⋊C4—41no—
778C2×C22⋊C4—41no—
779C2×C22⋊C4—41no—
780C2×C22⋊C4—41no—
781C2×C22⋊C4—41no—
782C2×C22⋊C4—41no—
783C2×C22⋊C4—41no—
784C2×C22⋊C4—41no—
785C2×C22⋊C4—41no—
786C2×C22⋊C4—41no—
787C2×C22⋊C4—41no—
788C2×C22⋊C4—41no—
789C2×C22⋊C4—41no—
790#95—22no—
791#95—22no—
792#95—22no—
793#95—22no—
794#95—22no—
795#95—22no—
796#95—22no—
797#95—41no—
798#95—41no—
799#95—41no—
800#95—41no—
801#95—41no—
802#95—41no—
803#95—41no—
804C31#1711511yescharacteristic, direct product factor, Sylow
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—
833C24—21no—
834C24—21no—
835C24—21no—
836C24—21no—
837C24—21no—
838C24—21no—
839C24—21no—
840C24—21no—
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24C2×D4×C3112yes—
848C24C2×D4×C3112yes—
849C24#41×C3112yes—
850C24C24×C3111yescharacteristic
851C2×D4—44no—
852C2×D4—44no—
853C2×D4—44no—
854C2×D4—44no—
855C2×D4—44no—
856C2×D4—44no—
857C2×D4—44no—
858C2×D4—44no—
859C2×D4—44no—
860C2×D4—44no—
861C2×D4—44no—
862C2×D4—44no—
863C2×D4—44no—
864C2×D4—44no—
865C2×D4—44no—
866C2×D4—44no—
867C2×D4—44no—
868C2×D4—44no—
869C2×D4—44no—
870C2×D4—44no—
871C2×D4—44no—
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×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4C2×D4×C3112yes—
951C22×C4C2×D4×C3112yes—
952C22×C4C2×D4×C3112yes—
953C22×C4C2×D4×C3112yes—
954C22×C4#41×C3112yes—
955C22×C4#41×C3112yes—
956C4⋊C4—44no—
957C4⋊C4—44no—
958C4⋊C4—44no—
959C22⋊C4—44no—
960C22⋊C4—44no—
961C22⋊C4—44no—
962C22⋊C4—44no—
963C22⋊C4—44no—
964C22⋊C4—44no—
965C22⋊C4—44no—
966C22⋊C4—44no—
967C22⋊C4—44no—
968C22⋊C4—44no—
969C22⋊C4—44no—
970C22⋊C4—44no—
971C22⋊C4—44no—
972C22⋊C4—44no—
973C22⋊C4—44no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
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—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23C22×D4×C3111yescharacteristic
1080C23C22×D4×C3111yescharacteristic
1081C23C2×#41×C3111yescharacteristic
1082C23C2×#41×C3111yescharacteristic
1083C23C2×#41×C3111yescharacteristic
1084C23C31×H(5,𝔽2)11yescharacteristic
1085C23C31×H(5,𝔽2)11yescharacteristic
1086C23C31×H(5,𝔽2)11yescharacteristic
1087C23C31×H(5,𝔽2)11yescharacteristic
1088C23C31×H(5,𝔽2)11yescharacteristic
1089C23C31×H(5,𝔽2)11yescharacteristic
1090C23C31×H(5,𝔽2)11yescharacteristic
1091C23C31×H(5,𝔽2)11yescharacteristic
1092C23C31×H(5,𝔽2)11yescharacteristic
1093C23C31×2−1+411yescharacteristic
1094D4—416no—
1095D4—416no—
1096D4—416no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—22no—
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—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C22—42no—
1182C22—42no—
1183C22—42no—
1184C22—42no—
1185C22—42no—
1186C22—42no—
1187C22—42no—
1188C22—42no—
1189C22—42no—
1190C22—42no—
1191C22—42no—
1192C22—42no—
1193C22—42no—
1194C22—42no—
1195C22—42no—
1196C22—42no—
1197C22—42no—
1198C22—42no—
1199C22—42no—
1200C22—42no—
1201C22—42no—
1202C22—81no—
1203C22—81no—
1204C22—81no—
1205C22—81no—
1206C22—81no—
1207C22—81no—
1208C22—81no—
1209C22—81no—
1210C22—81no—
1211C22—81no—
1212C22—81no—
1213C22—81no—
1214C22—81no—
1215C22—81no—
1216C22—81no—
1217C22—81no—
1218C22—81no—
1219C22—81no—
1220C22—81no—
1221C22—81no—
1222C22—81no—
1223C22—81no—
1224C22—81no—
1225C22—81no—
1226C22C31×#53411yescharacteristic
1227C22C31×#53411yescharacteristic
1228C22C31×#53411yescharacteristic
1229C22C31×#53411yescharacteristic
1230C22C31×#53511yescharacteristic
1231C22C31×#53711yescharacteristic
1232C22C31×#53811yescharacteristic
1233C22C31×#53811yescharacteristic
1234C22C31×#53811yescharacteristic
1235C22C31×#53811yescharacteristic
1236C22C31×#53811yescharacteristic
1237C22C31×#53811yescharacteristic
1238C22C31×#53911yescharacteristic
1239C22C31×#54011yescharacteristic
1240C22C31×#54211yescharacteristic
1241C22D42×C3111yescharacteristic
1242C22C31×#54611yescharacteristic
1243C22C31×#54611yescharacteristic
1244C22C31×#54611yescharacteristic
1245C22C31×#54711yescharacteristic
1246C22C31×#55011yescharacteristic
1247C22C31×#55011yescharacteristic
1248C22C31×#55111yescharacteristic
1249C22C31×#55311yescharacteristic
1250C22C31×#55511yescharacteristic
1251C22C31×#56011yescharacteristic
1252C22C31×#56011yescharacteristic
1253C22C31×#56011yescharacteristic
1254C22C31×#56011yescharacteristic
1255C22C31×#56011yescharacteristic
1256C22C31×#56011yescharacteristic
1257C22C31×H(3,𝔽4)11yescharacteristic
1258C22C31×#56211yescharacteristic
1259C22C31×#56211yescharacteristic
1260C22C31×#56211yescharacteristic
1261C4—42no—
1262C4—42no—
1263C4—42no—
1264C4—42no—
1265C4—42no—
1266C4—42no—
1267C4—81no—
1268C4—81no—
1269C4—81no—
1270C4—81no—
1271C4—81no—
1272C4—81no—
1273C2—82no—
1274C2—82no—
1275C2—82no—
1276C2C31×#266811yescharacteristic
1277C2C31×#267311yescharacteristic
1278C2C31×#268211yescharacteristic
1279C2C31×#268611yescharacteristic
1280C2C31×#269711yescharacteristic
1281C2C31×#270511yescharacteristic
1282C2C31×#270811yescharacteristic
1283C2C31×#271411yescharacteristic
1284C2C31×#273311yescharacteristic
1285C2C31×#275611yescharacteristic
1286C2C31×#281211yescharacteristic
1287C2C31×#281311yescharacteristic
1288C2C31×#282411yescharacteristic
1289C2C31×#282511yescharacteristic
1290C2C31×#282911yescharacteristic
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×#397C2semidirect
2. C2×C31×#394C2semidirect
3. C2×C31×#394C2semidirect
5. C31×#1443C2semidirect
6. C31×#1441C2semidirect
7. C31×#1440C2semidirect
8. C31×#1439C2semidirect
9. C31×#1439C2semidirect
10. C31×#1439C2semidirect
11. C31×#1439C2semidirect
12. C31×#1438C2semidirect
13. C31×#1438C2semidirect
14. C31×#1438C2semidirect
15. C31×#1438C2semidirect
99. C2×C4⋊C4×C31D4semidirect
328. #17115C31direct (N × H)
536. C2×#397C2×C31semidirect
537. C2×#394C2×C31semidirect
538. C2×#394C2×C31semidirect
540. #1443C2×C31semidirect
541. #1441C2×C31semidirect
542. #1440C2×C31semidirect
543. #1439C2×C31semidirect
544. #1439C2×C31semidirect
545. #1439C2×C31semidirect
546. #1439C2×C31semidirect
547. #1438C2×C31semidirect
548. #1438C2×C31semidirect
549. #1438C2×C31semidirect
550. #1438C2×C31semidirect
744. C2×C4⋊C4D4×C31semidirect
804. C31#17115direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3972
C2×C31×#3942
C2×C31×#3922
C31×#14432
C31×#14412
C31×#14402
C31×#14392
C31×#14382
#1711531