Finite Group Databasebeta

← C31×#22036 #21478795

Subgroups — C31×#22036 #21478795

Order 7936.

1162 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#435C211yesmaximal, characteristic, complemented
2C2×C31×#407C211yesmaximal, characteristic, complemented
3C4×C31×#120C211yesmaximal, characteristic
4C31×#1955C211yesmaximal, characteristic, complemented
5C31×#1954C211yesmaximal, characteristic, complemented
6C31×#1924C211yesmaximal, characteristic, complemented
7C31×#1924C211yesmaximal, characteristic, complemented
8C31×#1924C211yesmaximal, characteristic, complemented
9C31×#1923C211yesmaximal, characteristic, complemented
10C31×#1870C211yesmaximal, characteristic, complemented
11C31×#1869C211yesmaximal, characteristic, complemented
12C31×#1869C211yesmaximal, characteristic, complemented
13C31×#1851C211yesmaximal, characteristic, complemented
14C31×#1779C211yesmaximal, characteristic, complemented
15C31×#1753C211yesmaximal, characteristic, complemented
16C24×C4×C31C2211yescharacteristic
17C22×M16×C31C2211yescharacteristic
18C22×M16×C31C2211yescharacteristic
19C23×C8×C31C2211yescharacteristic, complemented
20C2×C31×#120C411yescharacteristic
21C2×C4×D4×C31C2211yescharacteristic
22C2×C4×D4×C31C2211yescharacteristic
23C2×C4×D4×C31C2211yescharacteristic
24C31×#435—24no—
25C2×C31×C4⋊C8C2211yescharacteristic, complemented
26C2×C31×C4⋊C8C2211yescharacteristic, complemented
27C2×C31×C4⋊C8C2211yescharacteristic, complemented
28C31×#407—24no—
29C2×C31×C22⋊C8C2211yescharacteristic
30C2×C31×C22⋊C8C2211yescharacteristic
31C2×C31×C22⋊C8C2211yescharacteristic
32C2×C31×C22⋊C8C2211yescharacteristic
33C2×C31×C22⋊C8C2211yescharacteristic
34C2×C31×C22⋊C8C2211yescharacteristic
35C2×C31×C22⋊C8C2211yescharacteristic
36C2×C31×C22⋊C8C2211yescharacteristic
37C2×C31×C22⋊C8C2211yescharacteristic
38C2×C31×C22⋊C8C2211yescharacteristic
39C2×C31×C22⋊C8C2211yescharacteristic, complemented
40C2×C31×C22⋊C8C2211yescharacteristic, complemented
41C2×C31×C22⋊C8C2211yescharacteristic, complemented
42C2×C31×#97C2211yescharacteristic, complemented
43C2×C31×#97C2211yescharacteristic, complemented
44C2×C4×C8×C31C2211yescharacteristic, complemented
45C31×#386C411yescharacteristic
46C31×#386C411yescharacteristic
47C31×#386C411yescharacteristic
48C31×#385C411yescharacteristic
49C31×#385C411yescharacteristic
50C31×#385C411yescharacteristic
51C31×#379C411yescharacteristic
52C4×C22⋊C4×C31C2211yescharacteristic
53C4×C22⋊C4×C31C2211yescharacteristic
54C4×C22⋊C4×C31C2211yescharacteristic
55C31×#336C2211yescharacteristic, complemented
56C31×#336C2211yescharacteristic, complemented
57C31×#336C2211yescharacteristic, complemented
58C31×#336C2211yescharacteristic, complemented
59C31×#336C2211yescharacteristic, complemented
60C31×#336C2211yescharacteristic, complemented
61C25×C31C2×C411yescharacteristic
62C22×D4×C31C2×C411yescharacteristic
63C22×D4×C31C2×C411yescharacteristic
64C22×D4×C31C2×C411yescharacteristic
65C23×C4×C31—22no—
66C23×C4×C31—22no—
67C23×C4×C31—41no—
68C23×C4×C31—41no—
69C23×C4×C31—41no—
70C23×C4×C31—41no—
71C23×C4×C31C2×C411yescharacteristic
72C23×C4×C31C2×C411yescharacteristic
73C23×C4×C31C2×C411yescharacteristic
74C23×C4×C31C2311yescharacteristic
75C23×C4×C31C2311yescharacteristic
76C23×C4×C31C2311yescharacteristic
77C23×C4×C31C2311yescharacteristic
78C2×M16×C31—22no—
79C2×M16×C31—41no—
80C2×M16×C31—41no—
81C2×M16×C31—41no—
82C2×M16×C31—41no—
83C2×M16×C31D414yescomplemented
84C22×C8×C31—22no—
85C22×C8×C31—41no—
86C22×C8×C31—41no—
87C22×C8×C31C2311yescharacteristic
88C22×C8×C31C2311yescharacteristic
89C22×C8×C31C2311yescharacteristic
90C22×C8×C31C2311yescharacteristic
91C22×C8×C31C2311yescharacteristic
92C22×C8×C31C2311yescharacteristic
93C22×C8×C31C2311yescharacteristic
94C22×C8×C31C2311yescharacteristic
95C31×#120—24no—
96C4×D4×C31—22no—
97C4×D4×C31—22no—
98C4×D4×C31—41no—
99C4×D4×C31—41no—
100C4×D4×C31—41no—
101C4×D4×C31—41no—
102C2×C4⋊C4×C31C2×C411yescharacteristic
103C2×C4⋊C4×C31C2×C411yescharacteristic
104C2×C4⋊C4×C31C2×C411yescharacteristic
105C2×C22⋊C4×C31C2×C411yescharacteristic
106C2×C22⋊C4×C31C2×C411yescharacteristic
107C2×C22⋊C4×C31C2×C411yescharacteristic
108C2×C22⋊C4×C31C2×C411yescharacteristic
109C2×C22⋊C4×C31C2×C411yescharacteristic
110C2×C22⋊C4×C31C2×C411yescharacteristic
111C2×C22⋊C4×C31C2×C411yescharacteristic
112C2×C22⋊C4×C31C2×C411yescharacteristic
113C2×C22⋊C4×C31C2×C411yescharacteristic
114C2×C22⋊C4×C31C2×C411yescharacteristic
115C2×C22⋊C4×C31C2×C411yescharacteristic
116C2×C22⋊C4×C31C2×C411yescharacteristic
117C2×C42×C31C2311yescharacteristic
118C2×C42×C31C2311yescharacteristic
119C2×C42×C31C2311yescharacteristic
120C31×C4⋊C8—22no—
121C31×C4⋊C8—41no—
122C31×C4⋊C8—41no—
123C31×C22⋊C8—22no—
124C31×C22⋊C8—22no—
125C31×C22⋊C8—22no—
126C31×C22⋊C8—22no—
127C31×C22⋊C8—22no—
128C31×C22⋊C8—22no—
129C31×C22⋊C8—22no—
130C31×C22⋊C8—41no—
131C31×C22⋊C8—41no—
132C31×C22⋊C8—41no—
133C31×C22⋊C8—41no—
134C31×C22⋊C8—41no—
135C31×C22⋊C8—41no—
136C31×#97—22no—
137C31×#97—41no—
138C4×C8×C31—41no—
139C31×#95C2×C411yescharacteristic
140C31×#95C2×C411yescharacteristic
141C31×#95C2×C411yescharacteristic
142C31×#95C2×C411yescharacteristic
143C31×#95C2×C411yescharacteristic
144C31×#95C2×C411yescharacteristic
145C24×C31—22no—
146C24×C31—22no—
147C24×C31—22no—
148C24×C31—41no—
149C24×C31—41no—
150C24×C31—41no—
151C24×C31—41no—
152C24×C31C22×C411yescharacteristic
153C24×C31C22×C411yescharacteristic
154C24×C31C22×C411yescharacteristic
155C24×C31C22×C411yescharacteristic
156C2×D4×C31—22no—
157C2×D4×C31—22no—
158C2×D4×C31—22no—
159C2×D4×C31—22no—
160C2×D4×C31—41no—
161C2×D4×C31—41no—
162C2×D4×C31—41no—
163C2×D4×C31—41no—
164C2×D4×C31M1614yescomplemented
165C22×C4×C31—21no—
166C22×C4×C31—21no—
167C22×C4×C31—21no—
168C22×C4×C31—21no—
169C22×C4×C31—22no—
170C22×C4×C31—22no—
171C22×C4×C31—22no—
172C22×C4×C31—21no—
173C22×C4×C31—21no—
174C22×C4×C31—21no—
175C22×C4×C31—21no—
176C22×C4×C31—21no—
177C22×C4×C31—21no—
178C22×C4×C31—21no—
179C22×C4×C31—21no—
180C22×C4×C31—21no—
181C22×C4×C31—21no—
182C22×C4×C31—21no—
183C22×C4×C31—21no—
184C22×C4×C31—21no—
185C22×C4×C31—21no—
186C22×C4×C31—21no—
187C22×C4×C31—21no—
188C22×C4×C31—21no—
189C22×C4×C31—21no—
190C22×C4×C31—41no—
191C22×C4×C31—41no—
192C22×C4×C31—41no—
193C22×C4×C31—41no—
194C22×C4×C31—41no—
195C22×C4×C31—41no—
196C22×C4×C31—44no—
197C22×C4×C31—44no—
198C22×C4×C31—44no—
199C22×C4×C31—44no—
200C22×C4×C31C22×C411yescharacteristic
201C22×C4×C31C22×C411yescharacteristic
202C22×C4×C31C22×C411yescharacteristic
203C22×C4×C31C22×C411yescharacteristic
204C22×C4×C31C22×C411yescharacteristic
205C22×C4×C31C22×C411yescharacteristic
206C22×C4×C31C22×C411yescharacteristic
207C22×C4×C31C22×C411yescharacteristic
208C22×C4×C31C22×C411yescharacteristic
209C22×C4×C31C22×C411yescharacteristic
210C22×C4×C31C2×D412yes—
211C22×C4×C31#4112yes—
212C22×C4×C31C2411yescharacteristic
213M16×C31—44no—
214M16×C31—44no—
215C2×C8×C31—21no—
216C2×C8×C31—21no—
217C2×C8×C31—21no—
218C2×C8×C31—21no—
219C2×C8×C31—21no—
220C2×C8×C31—21no—
221C2×C8×C31—21no—
222C2×C8×C31—21no—
223C2×C8×C31—21no—
224C2×C8×C31—21no—
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×C31—21no—
235C2×C8×C31—21no—
236C2×C8×C31—21no—
237C2×C8×C31—44no—
238C2×C8×C31C2×D412yes—
239C2×C8×C31C2×D412yes—
240C4⋊C4×C31—22no—
241C4⋊C4×C31—41no—
242C4⋊C4×C31—41no—
243C22⋊C4×C31—22no—
244C22⋊C4×C31—22no—
245C22⋊C4×C31—22no—
246C22⋊C4×C31—22no—
247C22⋊C4×C31—22no—
248C22⋊C4×C31—22no—
249C22⋊C4×C31—41no—
250C22⋊C4×C31—41no—
251C22⋊C4×C31—41no—
252C22⋊C4×C31—41no—
253C22⋊C4×C31—41no—
254C22⋊C4×C31—41no—
255C42×C31—21no—
256C42×C31—21no—
257C42×C31—21no—
258C42×C31—21no—
259C42×C31—21no—
260C42×C31—21no—
261#22036C3111yesmaximal, characteristic, direct product factor, Sylow
262C23×C31—21no—
263C23×C31—21no—
264C23×C31—21no—
265C23×C31—21no—
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—21no—
275C23×C31—21no—
276C23×C31—21no—
277C23×C31—21no—
278C23×C31—21no—
279C23×C31—21no—
280C23×C31—21no—
281C23×C31—21no—
282C23×C31—21no—
283C23×C31—21no—
284C23×C31—21no—
285C23×C31—21no—
286C23×C31—44no—
287C23×C31—44no—
288C23×C31—44no—
289C23×C31—44no—
290C23×C31—44no—
291C23×C31—44no—
292C23×C31—44no—
293C23×C31C4×D412yes—
294C23×C31C2×M1612yes—
295C23×C31C2×M1612yes—
296C23×C31#13112yes—
297C23×C31C23×C411yescharacteristic
298D4×C31—44no—
299D4×C31—44no—
300D4×C31—44no—
301C2×C4×C31—21no—
302C2×C4×C31—21no—
303C2×C4×C31—21no—
304C2×C4×C31—21no—
305C2×C4×C31—22no—
306C2×C4×C31—22no—
307C2×C4×C31—22no—
308C2×C4×C31—22no—
309C2×C4×C31—21no—
310C2×C4×C31—21no—
311C2×C4×C31—21no—
312C2×C4×C31—21no—
313C2×C4×C31—21no—
314C2×C4×C31—21no—
315C2×C4×C31—21no—
316C2×C4×C31—21no—
317C2×C4×C31—21no—
318C2×C4×C31—21no—
319C2×C4×C31—21no—
320C2×C4×C31—21no—
321C2×C4×C31—21no—
322C2×C4×C31—21no—
323C2×C4×C31—21no—
324C2×C4×C31—21no—
325C2×C4×C31—21no—
326C2×C4×C31—21no—
327C2×C4×C31—21no—
328C2×C4×C31—21no—
329C2×C4×C31—21no—
330C2×C4×C31—21no—
331C2×C4×C31—21no—
332C2×C4×C31—21no—
333C2×C4×C31—44no—
334C2×C4×C31—44no—
335C2×C4×C31—44no—
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×C31C4×D412yes—
349C2×C4×C31C2×M1612yes—
350C2×C4×C31C22×D411yescharacteristic
351C2×C4×C31C2×#4111yescharacteristic
352C2×C4×C31H(5,𝔽2)11yescharacteristic
353C2×C4×C31H(5,𝔽2)11yescharacteristic
354C2×C4×C31H(5,𝔽2)11yescharacteristic
355C2×C4×C31H(5,𝔽2)11yescharacteristic
356C8×C31—22no—
357C8×C31—22no—
358C8×C31—41no—
359C8×C31—41no—
360C8×C31—41no—
361C8×C31—41no—
362C8×C31—41no—
363C8×C31—41no—
364C2×#435C2×C3111yescharacteristic, complemented
365C2×#407C2×C3111yescharacteristic, complemented
366C4×#120C2×C3111yescharacteristic
367#1955C2×C3111yescharacteristic, complemented
368#1954C2×C3111yescharacteristic, complemented
369#1924C2×C3111yescharacteristic, complemented
370#1924C2×C3111yescharacteristic, complemented
371#1924C2×C3111yescharacteristic, complemented
372#1923C2×C3111yescharacteristic, complemented
373#1870C2×C3111yescharacteristic, complemented
374#1869C2×C3111yescharacteristic, complemented
375#1869C2×C3111yescharacteristic, complemented
376#1851C2×C3111yescharacteristic, complemented
377#1779C2×C3111yescharacteristic, complemented
378#1753C2×C3111yescharacteristic, complemented
379C22×C31—22no—
380C22×C31—22no—
381C22×C31—22no—
382C22×C31—22no—
383C22×C31—22no—
384C22×C31—22no—
385C22×C31—22no—
386C22×C31—22no—
387C22×C31—22no—
388C22×C31—22no—
389C22×C31—22no—
390C22×C31—22no—
391C22×C31—416no—
392C22×C31—41no—
393C22×C31—41no—
394C22×C31—41no—
395C22×C31—41no—
396C22×C31—41no—
397C22×C31—41no—
398C22×C31—41no—
399C22×C31—41no—
400C22×C31—41no—
401C22×C31—41no—
402C22×C31—41no—
403C22×C31—41no—
404C22×C31—41no—
405C22×C31—41no—
406C22×C31—41no—
407C22×C31—41no—
408C22×C31C2×C4×D411yescharacteristic
409C22×C31#51811yescharacteristic
410C22×C31#51811yescharacteristic
411C22×C31C22×M1611yescharacteristic
412C22×C31C2×#13111yescharacteristic
413C22×C31#56811yescharacteristic
414C22×C31#56811yescharacteristic
415C4×C31—22no—
416C4×C31—22no—
417C4×C31—41no—
418C4×C31—41no—
419C4×C31—41no—
420C4×C31—41no—
421C4×C31—41no—
422C4×C31—41no—
423C4×C31—41no—
424C4×C31—41no—
425C4×C31#53411yescharacteristic
426C4×C31#53511yescharacteristic
427C4×C31#53811yescharacteristic
428C4×C31#53811yescharacteristic
429C24×C4C22×C3111yescharacteristic
430C22×M16C22×C3111yescharacteristic
431C22×M16C22×C3111yescharacteristic
432C23×C8C22×C3111yescharacteristic, complemented
433C2×#120C4×C3111yescharacteristic
434C2×C4×D4C22×C3111yescharacteristic
435C2×C4×D4C22×C3111yescharacteristic
436C2×C4×D4C22×C3111yescharacteristic
437#435—24no—
438C2×C4⋊C8C22×C3111yescharacteristic, complemented
439C2×C4⋊C8C22×C3111yescharacteristic, complemented
440C2×C4⋊C8C22×C3111yescharacteristic, complemented
441#407—24no—
442C2×C22⋊C8C22×C3111yescharacteristic
443C2×C22⋊C8C22×C3111yescharacteristic
444C2×C22⋊C8C22×C3111yescharacteristic
445C2×C22⋊C8C22×C3111yescharacteristic
446C2×C22⋊C8C22×C3111yescharacteristic
447C2×C22⋊C8C22×C3111yescharacteristic
448C2×C22⋊C8C22×C3111yescharacteristic
449C2×C22⋊C8C22×C3111yescharacteristic
450C2×C22⋊C8C22×C3111yescharacteristic
451C2×C22⋊C8C22×C3111yescharacteristic
452C2×C22⋊C8C22×C3111yescharacteristic, complemented
453C2×C22⋊C8C22×C3111yescharacteristic, complemented
454C2×C22⋊C8C22×C3111yescharacteristic, complemented
455C2×#97C22×C3111yescharacteristic, complemented
456C2×#97C22×C3111yescharacteristic, complemented
457C2×C4×C8C22×C3111yescharacteristic, complemented
458#386C4×C3111yescharacteristic
459#386C4×C3111yescharacteristic
460#386C4×C3111yescharacteristic
461#385C4×C3111yescharacteristic
462#385C4×C3111yescharacteristic
463#385C4×C3111yescharacteristic
464#379C4×C3111yescharacteristic
465C4×C22⋊C4C22×C3111yescharacteristic
466C4×C22⋊C4C22×C3111yescharacteristic
467C4×C22⋊C4C22×C3111yescharacteristic
468#336C22×C3111yescharacteristic, complemented
469#336C22×C3111yescharacteristic, complemented
470#336C22×C3111yescharacteristic, complemented
471#336C22×C3111yescharacteristic, complemented
472#336C22×C3111yescharacteristic, complemented
473#336C22×C3111yescharacteristic, complemented
474C2×C31—42no—
475C2×C31—42no—
476C2×C31—42no—
477C2×C31—42no—
478C2×C31#232111yescharacteristic
479C2×C31#293311yescharacteristic
480C2×C31D4×M1611yescharacteristic
481C2×C31#297311yescharacteristic
482C2×C31#297411yescharacteristic
483C2×C31#297611yescharacteristic
484C2×C31#297811yescharacteristic
485C25C2×C4×C3111yescharacteristic
486C22×D4C2×C4×C3111yescharacteristic
487C22×D4C2×C4×C3111yescharacteristic
488C22×D4C2×C4×C3111yescharacteristic
489C23×C4—22no—
490C23×C4—22no—
491C23×C4—41no—
492C23×C4—41no—
493C23×C4—41no—
494C23×C4—41no—
495C23×C4C2×C4×C3111yescharacteristic
496C23×C4C2×C4×C3111yescharacteristic
497C23×C4C2×C4×C3111yescharacteristic
498C23×C4C23×C3111yescharacteristic
499C23×C4C23×C3111yescharacteristic
500C23×C4C23×C3111yescharacteristic
501C23×C4C23×C3111yescharacteristic
502C2×M16—22no—
503C2×M16—41no—
504C2×M16—41no—
505C2×M16—41no—
506C2×M16—41no—
507C2×M16D4×C3114yescomplemented
508C22×C8—22no—
509C22×C8—41no—
510C22×C8—41no—
511C22×C8C23×C3111yescharacteristic
512C22×C8C23×C3111yescharacteristic
513C22×C8C23×C3111yescharacteristic
514C22×C8C23×C3111yescharacteristic
515C22×C8C23×C3111yescharacteristic
516C22×C8C23×C3111yescharacteristic
517C22×C8C23×C3111yescharacteristic
518C22×C8C23×C3111yescharacteristic
519#120—24no—
520C4×D4—22no—
521C4×D4—22no—
522C4×D4—41no—
523C4×D4—41no—
524C4×D4—41no—
525C4×D4—41no—
526C2×C4⋊C4C2×C4×C3111yescharacteristic
527C2×C4⋊C4C2×C4×C3111yescharacteristic
528C2×C4⋊C4C2×C4×C3111yescharacteristic
529C2×C22⋊C4C2×C4×C3111yescharacteristic
530C2×C22⋊C4C2×C4×C3111yescharacteristic
531C2×C22⋊C4C2×C4×C3111yescharacteristic
532C2×C22⋊C4C2×C4×C3111yescharacteristic
533C2×C22⋊C4C2×C4×C3111yescharacteristic
534C2×C22⋊C4C2×C4×C3111yescharacteristic
535C2×C22⋊C4C2×C4×C3111yescharacteristic
536C2×C22⋊C4C2×C4×C3111yescharacteristic
537C2×C22⋊C4C2×C4×C3111yescharacteristic
538C2×C22⋊C4C2×C4×C3111yescharacteristic
539C2×C22⋊C4C2×C4×C3111yescharacteristic
540C2×C22⋊C4C2×C4×C3111yescharacteristic
541C2×C42C23×C3111yescharacteristic
542C2×C42C23×C3111yescharacteristic
543C2×C42C23×C3111yescharacteristic
544C4⋊C8—22no—
545C4⋊C8—41no—
546C4⋊C8—41no—
547C22⋊C8—22no—
548C22⋊C8—22no—
549C22⋊C8—22no—
550C22⋊C8—22no—
551C22⋊C8—22no—
552C22⋊C8—22no—
553C22⋊C8—22no—
554C22⋊C8—41no—
555C22⋊C8—41no—
556C22⋊C8—41no—
557C22⋊C8—41no—
558C22⋊C8—41no—
559C22⋊C8—41no—
560#97—22no—
561#97—41no—
562C4×C8—41no—
563#95C2×C4×C3111yescharacteristic
564#95C2×C4×C3111yescharacteristic
565#95C2×C4×C3111yescharacteristic
566#95C2×C4×C3111yescharacteristic
567#95C2×C4×C3111yescharacteristic
568#95C2×C4×C3111yescharacteristic
569C31#2203611yescharacteristic, direct product factor, Sylow
570C24—22no—
571C24—22no—
572C24—22no—
573C24—41no—
574C24—41no—
575C24—41no—
576C24—41no—
577C24C22×C4×C3111yescharacteristic
578C24C22×C4×C3111yescharacteristic
579C24C22×C4×C3111yescharacteristic
580C24C22×C4×C3111yescharacteristic
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—41no—
586C2×D4—41no—
587C2×D4—41no—
588C2×D4—41no—
589C2×D4M16×C3114yescomplemented
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—41no—
616C22×C4—41no—
617C22×C4—41no—
618C22×C4—41no—
619C22×C4—41no—
620C22×C4—41no—
621C22×C4—44no—
622C22×C4—44no—
623C22×C4—44no—
624C22×C4—44no—
625C22×C4C22×C4×C3111yescharacteristic
626C22×C4C22×C4×C3111yescharacteristic
627C22×C4C22×C4×C3111yescharacteristic
628C22×C4C22×C4×C3111yescharacteristic
629C22×C4C22×C4×C3111yescharacteristic
630C22×C4C22×C4×C3111yescharacteristic
631C22×C4C22×C4×C3111yescharacteristic
632C22×C4C22×C4×C3111yescharacteristic
633C22×C4C22×C4×C3111yescharacteristic
634C22×C4C22×C4×C3111yescharacteristic
635C22×C4C2×D4×C3112yes—
636C22×C4#41×C3112yes—
637C22×C4C24×C3111yescharacteristic
638M16—44no—
639M16—44no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
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×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—44no—
663C2×C8C2×D4×C3112yes—
664C2×C8C2×D4×C3112yes—
665C4⋊C4—22no—
666C4⋊C4—41no—
667C4⋊C4—41no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—22no—
672C22⋊C4—22no—
673C22⋊C4—22no—
674C22⋊C4—41no—
675C22⋊C4—41no—
676C22⋊C4—41no—
677C22⋊C4—41no—
678C22⋊C4—41no—
679C22⋊C4—41no—
680C42—21no—
681C42—21no—
682C42—21no—
683C42—21no—
684C42—21no—
685C42—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—44no—
711C23—44no—
712C23—44no—
713C23—44no—
714C23—44no—
715C23—44no—
716C23—44no—
717C23C4×D4×C3112yes—
718C23C2×M16×C3112yes—
719C23C2×M16×C3112yes—
720C23C31×#13112yes—
721C23C23×C4×C3111yescharacteristic
722D4—44no—
723D4—44no—
724D4—44no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—44no—
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—41no—
771C2×C4—41no—
772C2×C4C4×D4×C3112yes—
773C2×C4C2×M16×C3112yes—
774C2×C4C22×D4×C3111yescharacteristic
775C2×C4C2×#41×C3111yescharacteristic
776C2×C4C31×H(5,𝔽2)11yescharacteristic
777C2×C4C31×H(5,𝔽2)11yescharacteristic
778C2×C4C31×H(5,𝔽2)11yescharacteristic
779C2×C4C31×H(5,𝔽2)11yescharacteristic
780C8—22no—
781C8—22no—
782C8—41no—
783C8—41no—
784C8—41no—
785C8—41no—
786C8—41no—
787C8—41no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—416no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22C2×C4×D4×C3111yescharacteristic
818C22C31×#51811yescharacteristic
819C22C31×#51811yescharacteristic
820C22C22×M16×C3111yescharacteristic
821C22C2×C31×#13111yescharacteristic
822C22C31×#56811yescharacteristic
823C22C31×#56811yescharacteristic
824C4—22no—
825C4—22no—
826C4—41no—
827C4—41no—
828C4—41no—
829C4—41no—
830C4—41no—
831C4—41no—
832C4—41no—
833C4—41no—
834C4C31×#53411yescharacteristic
835C4C31×#53511yescharacteristic
836C4C31×#53811yescharacteristic
837C4C31×#53811yescharacteristic
838C2—42no—
839C2—42no—
840C2—42no—
841C2—42no—
842C2C31×#232111yescharacteristic
843C2C31×#293311yescharacteristic
844C2D4×M16×C3111yescharacteristic
845C2C31×#297311yescharacteristic
846C2C31×#297411yescharacteristic
847C2C31×#297611yescharacteristic
848C2C31×#297811yescharacteristic
subgroupG/H
centerC22×C4×C31C24
commutatorC23C23×C4×C31
Frattini, cosocleC22×C4C24×C31
socleC23×C31C23×C4
prime radicalC2×C31×#120C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#435C2semidirect
2. C2×C31×#407C2semidirect
4. C31×#1955C2semidirect
5. C31×#1954C2semidirect
6. C31×#1924C2semidirect
7. C31×#1924C2semidirect
8. C31×#1924C2semidirect
9. C31×#1923C2semidirect
10. C31×#1870C2semidirect
11. C31×#1869C2semidirect
12. C31×#1869C2semidirect
13. C31×#1851C2semidirect
14. C31×#1779C2semidirect
15. C31×#1753C2semidirect
19. C23×C8×C31C22semidirect
25. C2×C31×C4⋊C8C22semidirect
26. C2×C31×C4⋊C8C22semidirect
27. C2×C31×C4⋊C8C22semidirect
39. C2×C31×C22⋊C8C22semidirect
40. C2×C31×C22⋊C8C22semidirect
41. C2×C31×C22⋊C8C22semidirect
42. C2×C31×#97C22semidirect
43. C2×C31×#97C22semidirect
44. C2×C4×C8×C31C22semidirect
55. C31×#336C22semidirect
56. C31×#336C22semidirect
57. C31×#336C22semidirect
58. C31×#336C22semidirect
59. C31×#336C22semidirect
60. C31×#336C22semidirect
83. C2×M16×C31D4semidirect
164. C2×D4×C31M16semidirect
261. #22036C31direct (N × H)
364. C2×#435C2×C31semidirect
365. C2×#407C2×C31semidirect
367. #1955C2×C31semidirect
368. #1954C2×C31semidirect
369. #1924C2×C31semidirect
370. #1924C2×C31semidirect
371. #1924C2×C31semidirect
372. #1923C2×C31semidirect
373. #1870C2×C31semidirect
374. #1869C2×C31semidirect
375. #1869C2×C31semidirect
376. #1851C2×C31semidirect
377. #1779C2×C31semidirect
378. #1753C2×C31semidirect
432. C23×C8C22×C31semidirect
438. C2×C4⋊C8C22×C31semidirect
439. C2×C4⋊C8C22×C31semidirect
440. C2×C4⋊C8C22×C31semidirect
452. C2×C22⋊C8C22×C31semidirect
453. C2×C22⋊C8C22×C31semidirect
454. C2×C22⋊C8C22×C31semidirect
455. C2×#97C22×C31semidirect
456. C2×#97C22×C31semidirect
457. C2×C4×C8C22×C31semidirect
468. #336C22×C31semidirect
469. #336C22×C31semidirect
470. #336C22×C31semidirect
471. #336C22×C31semidirect
472. #336C22×C31semidirect
473. #336C22×C31semidirect
507. C2×M16D4×C31semidirect
569. C31#22036direct (N × H)
589. C2×D4M16×C31semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#4352
C2×C31×#4072
C4×C31×#1202
C31×#19552
C31×#19542
C31×#19242
C31×#19232
C31×#18702
C31×#18692
C31×#18512
C31×#17792
C31×#17532
#2203631