Finite Group Databasebeta

← C31×#16654 #21473413

Subgroups — C31×#16654 #21473413

Order 7936.

2226 conjugacy classes of subgroups.

The subgroup lattice has 1320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#123C211yesmaximal, characteristic, complemented
2C2×C31×#394C211yesmaximal, characteristic, complemented
3C2×C31×#392C211yesmaximal, characteristic
4C2×C31×#386C211yesmaximal, characteristic, complemented
5C31×#1442C211yesmaximal, characteristic, complemented
6C31×#1441C211yesmaximal, characteristic, complemented
7C31×#1440C211yesmaximal, characteristic, complemented
8C31×#1440C211yesmaximal, 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×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C31C2211yescharacteristic
17C23×D4×C31C2211yescharacteristic
18C23×D4×C31C2211yescharacteristic
19C24×C4×C31C2211yescharacteristic
20C2×C31×#123—24no—
21C2×C31×#123—24no—
22C2×C31×#123—24no—
23C22×C4⋊C4×C31C2211yescharacteristic
24C22×C4⋊C4×C31C2211yescharacteristic
25C22×C4⋊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
37C22×C22⋊C4×C31C2211yescharacteristic
38C22×C22⋊C4×C31C2211yescharacteristic
39C22×C22⋊C4×C31C2211yescharacteristic
40C31×#394—24no—
41C31×#392—24no—
42C31×#386—24no—
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
55C2×C31×#95C2211yescharacteristic
56C2×C31×#95C2211yescharacteristic
57C25×C31C2311yescharacteristic
58C25×C31C2311yescharacteristic
59C25×C31C2311yescharacteristic
60C22×D4×C31—22no—
61C22×D4×C31—22no—
62C22×D4×C31—22no—
63C22×D4×C31—22no—
64C22×D4×C31—22no—
65C22×D4×C31—22no—
66C22×D4×C31—22no—
67C22×D4×C31—22no—
68C22×D4×C31—22no—
69C22×D4×C31—22no—
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×C31—41no—
79C22×D4×C31—41no—
80C22×D4×C31D414yes—
81C23×C4×C31—22no—
82C23×C4×C31—22no—
83C23×C4×C31—41no—
84C23×C4×C31—41no—
85C23×C4×C31—41no—
86C23×C4×C31—41no—
87C23×C4×C31D414yescomplemented
88C23×C4×C31C2311yescharacteristic
89C23×C4×C31C2311yescharacteristic
90C23×C4×C31C2311yescharacteristic
91C23×C4×C31C2311yescharacteristic
92C23×C4×C31C2311yescharacteristic
93C23×C4×C31C2311yescharacteristic
94C23×C4×C31C2311yescharacteristic
95C23×C4×C31C2311yescharacteristic
96C23×C4×C31C2311yescharacteristic
97C23×C4×C31C2311yescharacteristic
98C23×C4×C31C2311yescharacteristic
99C23×C4×C31C2311yescharacteristic
100C31×#123—232no—
101C2×C4⋊C4×C31—22no—
102C2×C4⋊C4×C31—22no—
103C2×C4⋊C4×C31—22no—
104C2×C4⋊C4×C31—22no—
105C2×C4⋊C4×C31—22no—
106C2×C4⋊C4×C31—22no—
107C2×C4⋊C4×C31—22no—
108C2×C4⋊C4×C31—22no—
109C2×C4⋊C4×C31—41no—
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—22no—
120C2×C22⋊C4×C31—22no—
121C2×C22⋊C4×C31—22no—
122C2×C22⋊C4×C31—22no—
123C2×C22⋊C4×C31—22no—
124C2×C22⋊C4×C31—22no—
125C2×C22⋊C4×C31—22no—
126C2×C22⋊C4×C31—22no—
127C2×C22⋊C4×C31—22no—
128C2×C22⋊C4×C31—22no—
129C2×C22⋊C4×C31—22no—
130C2×C22⋊C4×C31—22no—
131C2×C22⋊C4×C31—22no—
132C2×C22⋊C4×C31—22no—
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—
145C2×C22⋊C4×C31—41no—
146C2×C22⋊C4×C31—41no—
147C2×C22⋊C4×C31—41no—
148C2×C22⋊C4×C31—41no—
149C2×C22⋊C4×C31—41no—
150C2×C22⋊C4×C31—41no—
151C2×C22⋊C4×C31D414yescomplemented
152C31×#95—22no—
153C31×#95—22no—
154C31×#95—22no—
155C31×#95—22no—
156C31×#95—22no—
157C31×#95—41no—
158C31×#95—41no—
159C31×#95—41no—
160C31×#95—41no—
161C31×#95—41no—
162C31×#95—41no—
163C31×#95—41no—
164C31×#95—41no—
165C31×#95—41no—
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×C31—21no—
202C24×C31—21no—
203C24×C31—21no—
204C24×C31—21no—
205C24×C31—21no—
206C24×C31C2×D412yes—
207C24×C31C2×D412yes—
208C24×C31C2×D412yes—
209C24×C31C2×D412yes—
210C24×C31#4112yes—
211C24×C31C2411yescharacteristic
212C2×D4×C31—28no—
213C2×D4×C31—28no—
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—
226C2×D4×C31—44no—
227C2×D4×C31—44no—
228C2×D4×C31—44no—
229C2×D4×C31—44no—
230C2×D4×C31—44no—
231C2×D4×C31—44no—
232C2×D4×C31—44no—
233C22×C4×C31—28no—
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×C31—21no—
305C22×C4×C31—21no—
306C22×C4×C31—21no—
307C22×C4×C31—21no—
308C22×C4×C31—21no—
309C22×C4×C31—21no—
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×C31C2×D412yes—
317C22×C4×C31C2×D412yes—
318C22×C4×C31C2×D412yes—
319C22×C4×C31C2×D412yes—
320C22×C4×C31C2×D412yes—
321C22×C4×C31#4112yes—
322C22×C4×C31#4112yes—
323C22×C4×C31#4112yes—
324C4⋊C4×C31—28no—
325C4⋊C4×C31—28no—
326C4⋊C4×C31—44no—
327C22⋊C4×C31—28no—
328C22⋊C4×C31—28no—
329C22⋊C4×C31—28no—
330C22⋊C4×C31—44no—
331C22⋊C4×C31—44no—
332C22⋊C4×C31—44no—
333C22⋊C4×C31—44no—
334C22⋊C4×C31—44no—
335C22⋊C4×C31—44no—
336C22⋊C4×C31—44no—
337C22⋊C4×C31—44no—
338C22⋊C4×C31—44no—
339C22⋊C4×C31—44no—
340C22⋊C4×C31—44no—
341#16654C3111yesmaximal, characteristic, direct product factor, Sylow
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—22no—
351C23×C31—22no—
352C23×C31—22no—
353C23×C31—22no—
354C23×C31—22no—
355C23×C31—22no—
356C23×C31—22no—
357C23×C31—22no—
358C23×C31—22no—
359C23×C31—22no—
360C23×C31—22no—
361C23×C31—22no—
362C23×C31—22no—
363C23×C31—22no—
364C23×C31—22no—
365C23×C31—22no—
366C23×C31—22no—
367C23×C31—22no—
368C23×C31—22no—
369C23×C31—22no—
370C23×C31—22no—
371C23×C31—22no—
372C23×C31—22no—
373C23×C31—22no—
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×C31—41no—
435C23×C31—41no—
436C23×C31—41no—
437C23×C31—41no—
438C23×C31—41no—
439C23×C31—41no—
440C23×C31—41no—
441C23×C31—41no—
442C23×C31—41no—
443C23×C31—41no—
444C23×C31—41no—
445C23×C31—41no—
446C23×C31#12014yes—
447C23×C31C22×D411yescharacteristic
448C23×C31C22×D411yescharacteristic
449C23×C31C22×D411yescharacteristic
450C23×C31C2×#4111yescharacteristic
451C23×C31C2×#4111yescharacteristic
452C23×C31C2×#4111yescharacteristic
453C23×C31C2×#4111yescharacteristic
454C23×C31H(5,𝔽2)11yescharacteristic
455C23×C31H(5,𝔽2)11yescharacteristic
456C23×C31H(5,𝔽2)11yescharacteristic
457C23×C31H(5,𝔽2)11yescharacteristic
458C23×C31H(5,𝔽2)11yescharacteristic
459C23×C31H(5,𝔽2)11yescharacteristic
460C23×C31H(5,𝔽2)11yescharacteristic
461C23×C312−1+411yescharacteristic
462D4×C31—416no—
463D4×C31—416no—
464D4×C31—416no—
465C2×C4×C31—22no—
466C2×C4×C31—22no—
467C2×C4×C31—22no—
468C2×C4×C31—22no—
469C2×C4×C31—22no—
470C2×C4×C31—22no—
471C2×C4×C31—22no—
472C2×C4×C31—22no—
473C2×C4×C31—22no—
474C2×C4×C31—22no—
475C2×C4×C31—22no—
476C2×C4×C31—22no—
477C2×C4×C31—22no—
478C2×C4×C31—22no—
479C2×C4×C31—22no—
480C2×C4×C31—22no—
481C2×C4×C31—22no—
482C2×C4×C31—22no—
483C2×C4×C31—22no—
484C2×C4×C31—22no—
485C2×C4×C31—22no—
486C2×C4×C31—22no—
487C2×C4×C31—22no—
488C2×C4×C31—22no—
489C2×C4×C31—416no—
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×C4×C31—41no—
537C2×C4×C31—41no—
538C2×C4×C31—41no—
539C2×C4×C31—41no—
540C2×C4×C31—41no—
541C2×C4×C31—41no—
542C2×C4×C31—41no—
543C2×C4×C31—41no—
544C2×C4×C31—41no—
545C2×C4×C31—41no—
546C2×C4×C31—41no—
547C2×C4×C31—41no—
548C2×C4×C31—41no—
549C2×C4×C31—41no—
550C22×#123C2×C3111yescharacteristic, complemented
551C2×#394C2×C3111yescharacteristic, complemented
552C2×#392C2×C3111yescharacteristic
553C2×#386C2×C3111yescharacteristic, complemented
554#1442C2×C3111yescharacteristic, complemented
555#1441C2×C3111yescharacteristic, complemented
556#1440C2×C3111yescharacteristic, complemented
557#1440C2×C3111yescharacteristic, complemented
558#1439C2×C3111yescharacteristic, complemented
559#1439C2×C3111yescharacteristic, complemented
560#1439C2×C3111yescharacteristic, complemented
561#1438C2×C3111yescharacteristic, complemented
562#1438C2×C3111yescharacteristic, complemented
563#1438C2×C3111yescharacteristic, complemented
564C22⋊#95C2×C3111yescharacteristic, complemented
565C22×C31—24no—
566C22×C31—24no—
567C22×C31—24no—
568C22×C31—42no—
569C22×C31—42no—
570C22×C31—42no—
571C22×C31—42no—
572C22×C31—42no—
573C22×C31—42no—
574C22×C31—42no—
575C22×C31—42no—
576C22×C31—42no—
577C22×C31—42no—
578C22×C31—42no—
579C22×C31—42no—
580C22×C31—42no—
581C22×C31—42no—
582C22×C31—42no—
583C22×C31—42no—
584C22×C31—42no—
585C22×C31—42no—
586C22×C31—42no—
587C22×C31—42no—
588C22×C31—42no—
589C22×C31—42no—
590C22×C31—42no—
591C22×C31—42no—
592C22×C31—42no—
593C22×C31—42no—
594C22×C31—81no—
595C22×C31—81no—
596C22×C31—81no—
597C22×C31—81no—
598C22×C31—81no—
599C22×C31—81no—
600C22×C31—81no—
601C22×C31—81no—
602C22×C31—81no—
603C22×C31—81no—
604C22×C31—81no—
605C22×C31—81no—
606C22×C31—81no—
607C22×C31—81no—
608C22×C31—81no—
609C22×C31—81no—
610C22×C31C2×#12011yescharacteristic
611C22×C31#52511yescharacteristic
612C22×C31#53211yescharacteristic
613C22×C31#53411yescharacteristic
614C22×C31#53411yescharacteristic
615C22×C31#53411yescharacteristic
616C22×C31#53411yescharacteristic
617C22×C31#53511yescharacteristic
618C22×C31#53511yescharacteristic
619C22×C31#53511yescharacteristic
620C22×C31#53711yescharacteristic
621C22×C31#53811yescharacteristic
622C22×C31#53811yescharacteristic
623C22×C31#53811yescharacteristic
624C22×C31#53911yescharacteristic
625C22×C31#54011yescharacteristic
626C22×C31#54011yescharacteristic
627C22×C31#54011yescharacteristic
628C22×C31#54211yescharacteristic
629C22×C31#54611yescharacteristic
630C22×C31#54611yescharacteristic
631C22×C31#54611yescharacteristic
632C22×C31#54611yescharacteristic
633C22×C31#54611yescharacteristic
634C22×C31#54611yescharacteristic
635C22×C31#54711yescharacteristic
636C22×C31#54711yescharacteristic
637C22×C31#55111yescharacteristic
638C22×C31#55311yescharacteristic
639C22×C31#55311yescharacteristic
640C22×C31#55911yescharacteristic
641C22×C31#56011yescharacteristic
642C22×C31#56011yescharacteristic
643C22×C31#56211yescharacteristic
644C22×C31#56211yescharacteristic
645C4×C31—42no—
646C4×C31—42no—
647C4×C31—42no—
648C4×C31—42no—
649C4×C31—42no—
650C4×C31—42no—
651C4×C31—42no—
652C4×C31—42no—
653C4×C31—81no—
654C4×C31—81no—
655C4×C31—81no—
656C4×C31—81no—
657C23×D4C22×C3111yescharacteristic
658C23×D4C22×C3111yescharacteristic
659C23×D4C22×C3111yescharacteristic
660C24×C4C22×C3111yescharacteristic
661C2×#123—24no—
662C2×#123—24no—
663C2×#123—24no—
664C22×C4⋊C4C22×C3111yescharacteristic
665C22×C4⋊C4C22×C3111yescharacteristic
666C22×C4⋊C4C22×C3111yescharacteristic
667C22×C22⋊C4C22×C3111yescharacteristic
668C22×C22⋊C4C22×C3111yescharacteristic
669C22×C22⋊C4C22×C3111yescharacteristic
670C22×C22⋊C4C22×C3111yescharacteristic
671C22×C22⋊C4C22×C3111yescharacteristic
672C22×C22⋊C4C22×C3111yescharacteristic
673C22×C22⋊C4C22×C3111yescharacteristic
674C22×C22⋊C4C22×C3111yescharacteristic
675C22×C22⋊C4C22×C3111yescharacteristic
676C22×C22⋊C4C22×C3111yescharacteristic
677C22×C22⋊C4C22×C3111yescharacteristic
678C22×C22⋊C4C22×C3111yescharacteristic
679C22×C22⋊C4C22×C3111yescharacteristic
680C22×C22⋊C4C22×C3111yescharacteristic
681#394—24no—
682#392—24no—
683#386—24no—
684C2×#95C22×C3111yescharacteristic
685C2×#95C22×C3111yescharacteristic
686C2×#95C22×C3111yescharacteristic
687C2×#95C22×C3111yescharacteristic
688C2×#95C22×C3111yescharacteristic
689C2×#95C22×C3111yescharacteristic
690C2×#95C22×C3111yescharacteristic
691C2×#95C22×C3111yescharacteristic
692C2×#95C22×C3111yescharacteristic
693C2×#95C22×C3111yescharacteristic
694C2×#95C22×C3111yescharacteristic
695C2×#95C22×C3111yescharacteristic
696C2×#95C22×C3111yescharacteristic
697C2×#95C22×C3111yescharacteristic
698C2×C31—44no—
699C2×C31—82no—
700C2×C31—82no—
701C2×C31#240411yescharacteristic
702C2×C31#243011yescharacteristic
703C2×C31#260211yescharacteristic
704C2×C31#261311yescharacteristic
705C2×C31#263011yescharacteristic
706C2×C31#266111yescharacteristic
707C2×C31#269711yescharacteristic
708C2×C31#270111yescharacteristic
709C2×C31#270311yescharacteristic
710C2×C31#270311yescharacteristic
711C2×C31#270611yescharacteristic
712C2×C31#270811yescharacteristic
713C2×C31#270911yescharacteristic
714C2×C31#271011yescharacteristic
715C2×C31#281311yescharacteristic
716C25C23×C3111yescharacteristic
717C25C23×C3111yescharacteristic
718C25C23×C3111yescharacteristic
719C22×D4—22no—
720C22×D4—22no—
721C22×D4—22no—
722C22×D4—22no—
723C22×D4—22no—
724C22×D4—22no—
725C22×D4—22no—
726C22×D4—22no—
727C22×D4—22no—
728C22×D4—22no—
729C22×D4—41no—
730C22×D4—41no—
731C22×D4—41no—
732C22×D4—41no—
733C22×D4—41no—
734C22×D4—41no—
735C22×D4—41no—
736C22×D4—41no—
737C22×D4—41no—
738C22×D4—41no—
739C22×D4D4×C3114yes—
740C23×C4—22no—
741C23×C4—22no—
742C23×C4—41no—
743C23×C4—41no—
744C23×C4—41no—
745C23×C4—41no—
746C23×C4D4×C3114yescomplemented
747C23×C4C23×C3111yescharacteristic
748C23×C4C23×C3111yescharacteristic
749C23×C4C23×C3111yescharacteristic
750C23×C4C23×C3111yescharacteristic
751C23×C4C23×C3111yescharacteristic
752C23×C4C23×C3111yescharacteristic
753C23×C4C23×C3111yescharacteristic
754C23×C4C23×C3111yescharacteristic
755C23×C4C23×C3111yescharacteristic
756C23×C4C23×C3111yescharacteristic
757C23×C4C23×C3111yescharacteristic
758C23×C4C23×C3111yescharacteristic
759#123—232no—
760C2×C4⋊C4—22no—
761C2×C4⋊C4—22no—
762C2×C4⋊C4—22no—
763C2×C4⋊C4—22no—
764C2×C4⋊C4—22no—
765C2×C4⋊C4—22no—
766C2×C4⋊C4—22no—
767C2×C4⋊C4—22no—
768C2×C4⋊C4—41no—
769C2×C22⋊C4—22no—
770C2×C22⋊C4—22no—
771C2×C22⋊C4—22no—
772C2×C22⋊C4—22no—
773C2×C22⋊C4—22no—
774C2×C22⋊C4—22no—
775C2×C22⋊C4—22no—
776C2×C22⋊C4—22no—
777C2×C22⋊C4—22no—
778C2×C22⋊C4—22no—
779C2×C22⋊C4—22no—
780C2×C22⋊C4—22no—
781C2×C22⋊C4—22no—
782C2×C22⋊C4—22no—
783C2×C22⋊C4—22no—
784C2×C22⋊C4—22no—
785C2×C22⋊C4—22no—
786C2×C22⋊C4—22no—
787C2×C22⋊C4—22no—
788C2×C22⋊C4—22no—
789C2×C22⋊C4—22no—
790C2×C22⋊C4—22no—
791C2×C22⋊C4—22no—
792C2×C22⋊C4—41no—
793C2×C22⋊C4—41no—
794C2×C22⋊C4—41no—
795C2×C22⋊C4—41no—
796C2×C22⋊C4—41no—
797C2×C22⋊C4—41no—
798C2×C22⋊C4—41no—
799C2×C22⋊C4—41no—
800C2×C22⋊C4—41no—
801C2×C22⋊C4—41no—
802C2×C22⋊C4—41no—
803C2×C22⋊C4—41no—
804C2×C22⋊C4—41no—
805C2×C22⋊C4—41no—
806C2×C22⋊C4—41no—
807C2×C22⋊C4—41no—
808C2×C22⋊C4—41no—
809C2×C22⋊C4—41no—
810C2×C22⋊C4D4×C3114yescomplemented
811#95—22no—
812#95—22no—
813#95—22no—
814#95—22no—
815#95—22no—
816#95—41no—
817#95—41no—
818#95—41no—
819#95—41no—
820#95—41no—
821#95—41no—
822#95—41no—
823#95—41no—
824#95—41no—
825C31#1665411yescharacteristic, direct product factor, Sylow
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—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24—21no—
856C24—21no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—21no—
862C24—21no—
863C24—21no—
864C24—21no—
865C24—21no—
866C24C2×D4×C3112yes—
867C24C2×D4×C3112yes—
868C24C2×D4×C3112yes—
869C24C2×D4×C3112yes—
870C24#41×C3112yes—
871C24C24×C3111yescharacteristic
872C2×D4—28no—
873C2×D4—28no—
874C2×D4—44no—
875C2×D4—44no—
876C2×D4—44no—
877C2×D4—44no—
878C2×D4—44no—
879C2×D4—44no—
880C2×D4—44no—
881C2×D4—44no—
882C2×D4—44no—
883C2×D4—44no—
884C2×D4—44no—
885C2×D4—44no—
886C2×D4—44no—
887C2×D4—44no—
888C2×D4—44no—
889C2×D4—44no—
890C2×D4—44no—
891C2×D4—44no—
892C2×D4—44no—
893C22×C4—28no—
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×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—44no—
971C22×C4—44no—
972C22×C4—44no—
973C22×C4—44no—
974C22×C4—44no—
975C22×C4—44no—
976C22×C4C2×D4×C3112yes—
977C22×C4C2×D4×C3112yes—
978C22×C4C2×D4×C3112yes—
979C22×C4C2×D4×C3112yes—
980C22×C4C2×D4×C3112yes—
981C22×C4#41×C3112yes—
982C22×C4#41×C3112yes—
983C22×C4#41×C3112yes—
984C4⋊C4—28no—
985C4⋊C4—28no—
986C4⋊C4—44no—
987C22⋊C4—28no—
988C22⋊C4—28no—
989C22⋊C4—28no—
990C22⋊C4—44no—
991C22⋊C4—44no—
992C22⋊C4—44no—
993C22⋊C4—44no—
994C22⋊C4—44no—
995C22⋊C4—44no—
996C22⋊C4—44no—
997C22⋊C4—44no—
998C22⋊C4—44no—
999C22⋊C4—44no—
1000C22⋊C4—44no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
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—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23C31×#12014yes—
1106C23C22×D4×C3111yescharacteristic
1107C23C22×D4×C3111yescharacteristic
1108C23C22×D4×C3111yescharacteristic
1109C23C2×#41×C3111yescharacteristic
1110C23C2×#41×C3111yescharacteristic
1111C23C2×#41×C3111yescharacteristic
1112C23C2×#41×C3111yescharacteristic
1113C23C31×H(5,𝔽2)11yescharacteristic
1114C23C31×H(5,𝔽2)11yescharacteristic
1115C23C31×H(5,𝔽2)11yescharacteristic
1116C23C31×H(5,𝔽2)11yescharacteristic
1117C23C31×H(5,𝔽2)11yescharacteristic
1118C23C31×H(5,𝔽2)11yescharacteristic
1119C23C31×H(5,𝔽2)11yescharacteristic
1120C23C31×2−1+411yescharacteristic
1121D4—416no—
1122D4—416no—
1123D4—416no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—416no—
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—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C22—24no—
1210C22—24no—
1211C22—24no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—42no—
1221C22—42no—
1222C22—42no—
1223C22—42no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—42no—
1235C22—42no—
1236C22—42no—
1237C22—42no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22—81no—
1252C22—81no—
1253C22—81no—
1254C22C2×C31×#12011yescharacteristic
1255C22C31×#52511yescharacteristic
1256C22C31×#53211yescharacteristic
1257C22C31×#53411yescharacteristic
1258C22C31×#53411yescharacteristic
1259C22C31×#53411yescharacteristic
1260C22C31×#53411yescharacteristic
1261C22C31×#53511yescharacteristic
1262C22C31×#53511yescharacteristic
1263C22C31×#53511yescharacteristic
1264C22C31×#53711yescharacteristic
1265C22C31×#53811yescharacteristic
1266C22C31×#53811yescharacteristic
1267C22C31×#53811yescharacteristic
1268C22C31×#53911yescharacteristic
1269C22C31×#54011yescharacteristic
1270C22C31×#54011yescharacteristic
1271C22C31×#54011yescharacteristic
1272C22C31×#54211yescharacteristic
1273C22C31×#54611yescharacteristic
1274C22C31×#54611yescharacteristic
1275C22C31×#54611yescharacteristic
1276C22C31×#54611yescharacteristic
1277C22C31×#54611yescharacteristic
1278C22C31×#54611yescharacteristic
1279C22C31×#54711yescharacteristic
1280C22C31×#54711yescharacteristic
1281C22C31×#55111yescharacteristic
1282C22C31×#55311yescharacteristic
1283C22C31×#55311yescharacteristic
1284C22C31×#55911yescharacteristic
1285C22C31×#56011yescharacteristic
1286C22C31×#56011yescharacteristic
1287C22C31×#56211yescharacteristic
1288C22C31×#56211yescharacteristic
1289C4—42no—
1290C4—42no—
1291C4—42no—
1292C4—42no—
1293C4—42no—
1294C4—42no—
1295C4—42no—
1296C4—42no—
1297C4—81no—
1298C4—81no—
1299C4—81no—
1300C4—81no—
1301C2—44no—
1302C2—82no—
1303C2—82no—
1304C2C31×#240411yescharacteristic
1305C2C31×#243011yescharacteristic
1306C2C31×#260211yescharacteristic
1307C2C31×#261311yescharacteristic
1308C2C31×#263011yescharacteristic
1309C2C31×#266111yescharacteristic
1310C2C31×#269711yescharacteristic
1311C2C31×#270111yescharacteristic
1312C2C31×#270311yescharacteristic
1313C2C31×#270311yescharacteristic
1314C2C31×#270611yescharacteristic
1315C2C31×#270811yescharacteristic
1316C2C31×#270911yescharacteristic
1317C2C31×#271011yescharacteristic
1318C2C31×#281311yescharacteristic
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. C22×C31×#123C2semidirect
2. C2×C31×#394C2semidirect
4. C2×C31×#386C2semidirect
5. C31×#1442C2semidirect
6. C31×#1441C2semidirect
7. C31×#1440C2semidirect
8. C31×#1440C2semidirect
9. C31×#1439C2semidirect
10. C31×#1439C2semidirect
11. C31×#1439C2semidirect
12. C31×#1438C2semidirect
13. C31×#1438C2semidirect
14. C31×#1438C2semidirect
15. C31×C22⋊#95C2semidirect
87. C23×C4×C31D4semidirect
151. C2×C22⋊C4×C31D4semidirect
341. #16654C31direct (N × H)
550. C22×#123C2×C31semidirect
551. C2×#394C2×C31semidirect
553. C2×#386C2×C31semidirect
554. #1442C2×C31semidirect
555. #1441C2×C31semidirect
556. #1440C2×C31semidirect
557. #1440C2×C31semidirect
558. #1439C2×C31semidirect
559. #1439C2×C31semidirect
560. #1439C2×C31semidirect
561. #1438C2×C31semidirect
562. #1438C2×C31semidirect
563. #1438C2×C31semidirect
564. C22⋊#95C2×C31semidirect
746. C23×C4D4×C31semidirect
810. C2×C22⋊C4D4×C31semidirect
825. C31#16654direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C31×#1232
C2×C31×#3942
C2×C31×#3922
C2×C31×#3862
C31×#14422
C31×#14412
C31×#14402
C31×#14392
C31×#14382
C31×C22⋊#952
#1665431