Finite Group Databasebeta

← C2×C31×#2444 #21491427

Subgroups — C2×C31×#2444 #21491427

Order 7936.

3546 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#121C211yesmaximal, characteristic
2C22×C4×D4×C31C211yesmaximal, characteristic, complemented
3C31×#2444C2116yesmaximal, direct product factor
4C2×C31×#400C211yesmaximal, characteristic, complemented
5C2×C31×#397C211yesmaximal, characteristic, complemented
6C2×C31×#397C211yesmaximal, characteristic, complemented
7C2×C31×#394C211yesmaximal, characteristic, complemented
8C2×C31×#388C211yesmaximal, characteristic, complemented
9C2×C31×#387C211yesmaximal, characteristic, complemented
10C2×C31×#386C211yesmaximal, characteristic, complemented
11C2×C31×#386C211yesmaximal, characteristic, complemented
12C2×C31×#386C211yesmaximal, characteristic, complemented
13C2×C31×#386C211yesmaximal, characteristic, complemented
14C2×C31×#385C211yesmaximal, characteristic, complemented
15C2×C31×#381C211yesmaximal, characteristic, complemented
16C22×C31×#95C211yesmaximal, characteristic, complemented
17C23×D4×C31C2211yescharacteristic
18C23×D4×C31C2211yescharacteristic
19C23×D4×C31C2211yescharacteristic
20C24×C4×C31C2211yescharacteristic
21C24×C4×C31C2211yescharacteristic
22C24×C4×C31C2211yescharacteristic
23C24×C4×C31C2211yescharacteristic
24C2×C31×#121—28no—
25C2×C31×#121C2218yes—
26C2×C4×D4×C31—28no—
27C2×C4×D4×C31C2218yescomplemented
28C22×C4⋊C4×C31C2211yescharacteristic
29C22×C4⋊C4×C31C2211yescharacteristic
30C22×C4⋊C4×C31C2211yescharacteristic
31C22×C4⋊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
40C22×C22⋊C4×C31C2211yescharacteristic
41C22×C22⋊C4×C31C2211yescharacteristic
42C22×C22⋊C4×C31C2211yescharacteristic
43C22×C42×C31C2211yescharacteristic
44C31×#400C2218yescomplemented
45C31×#397C2218yescomplemented
46C31×#397C2218yescomplemented
47C31×#394C2218yescomplemented
48C31×#388C2218yescomplemented
49C31×#387C2218yescomplemented
50C31×#386C2218yescomplemented
51C31×#386C2218yescomplemented
52C31×#386C2218yescomplemented
53C31×#386C2218yescomplemented
54C31×#385C2218yescomplemented
55C31×#381C2218yescomplemented
56C2×C31×#95C2211yescharacteristic
57C2×C31×#95C2211yescharacteristic
58C2×C31×#95C2211yescharacteristic
59C2×C31×#95C2211yescharacteristic
60C2×C31×#95C2211yescharacteristic
61C2×C31×#95C2211yescharacteristic
62C2×C31×#95C2211yescharacteristic
63C2×C31×#95C2211yescharacteristic
64C2×C31×#95C2211yescharacteristic
65C2×C31×#95C2211yescharacteristic
66C2×C31×#95C2211yescharacteristic
67C2×C31×#95C2211yescharacteristic
68C2×C31×#95C2218yescomplemented
69C25×C31C2311yescharacteristic
70C25×C31C2311yescharacteristic
71C25×C31C2311yescharacteristic
72C22×D4×C31—24no—
73C22×D4×C31—24no—
74C22×D4×C31—24no—
75C22×D4×C31—24no—
76C22×D4×C31—24no—
77C22×D4×C31—24no—
78C22×D4×C31—24no—
79C22×D4×C31—42no—
80C22×D4×C31D418yes—
81C22×D4×C31C2314yes—
82C22×D4×C31C2314yes—
83C22×D4×C31C2314yes—
84C23×C4×C31—24no—
85C23×C4×C31—24no—
86C23×C4×C31—24no—
87C23×C4×C31—24no—
88C23×C4×C31—24no—
89C23×C4×C31—24no—
90C23×C4×C31—24no—
91C23×C4×C31—42no—
92C23×C4×C31—42no—
93C23×C4×C31—42no—
94C23×C4×C31—42no—
95C23×C4×C31—42no—
96C23×C4×C31C2311yescharacteristic
97C23×C4×C31C2311yescharacteristic
98C23×C4×C31C2311yescharacteristic
99C23×C4×C31C2311yescharacteristic
100C23×C4×C31C2311yescharacteristic
101C23×C4×C31C2311yescharacteristic
102C23×C4×C31C2311yescharacteristic
103C23×C4×C31C2311yescharacteristic
104C23×C4×C31C2311yescharacteristic
105C23×C4×C31C2314yes—
106C23×C4×C31C2314yes—
107C23×C4×C31C2314yes—
108C23×C4×C31C2311yescharacteristic
109C23×C4×C31C2311yescharacteristic
110C23×C4×C31C2311yescharacteristic
111C23×C4×C31C2314yes—
112C31×#121—232no—
113C4×D4×C31—232no—
114C2×C4⋊C4×C31—24no—
115C2×C4⋊C4×C31—24no—
116C2×C4⋊C4×C31—24no—
117C2×C4⋊C4×C31—42no—
118C2×C4⋊C4×C31C2314yes—
119C2×C4⋊C4×C31C2314yes—
120C2×C4⋊C4×C31C2314yes—
121C2×C4⋊C4×C31C2314yes—
122C2×C22⋊C4×C31—24no—
123C2×C22⋊C4×C31—24no—
124C2×C22⋊C4×C31—24no—
125C2×C22⋊C4×C31—24no—
126C2×C22⋊C4×C31—24no—
127C2×C22⋊C4×C31—24no—
128C2×C22⋊C4×C31—42no—
129C2×C22⋊C4×C31—42no—
130C2×C22⋊C4×C31—42no—
131C2×C22⋊C4×C31—42no—
132C2×C22⋊C4×C31—42no—
133C2×C22⋊C4×C31C2314yes—
134C2×C22⋊C4×C31C2314yes—
135C2×C22⋊C4×C31C2314yes—
136C2×C22⋊C4×C31C2314yes—
137C2×C22⋊C4×C31C2314yes—
138C2×C22⋊C4×C31C2314yes—
139C2×C22⋊C4×C31C2314yes—
140C2×C22⋊C4×C31C2314yes—
141C2×C22⋊C4×C31C2314yes—
142C2×C22⋊C4×C31C2314yes—
143C2×C22⋊C4×C31C2314yes—
144C2×C42×C31—24no—
145C2×C42×C31C2314yes—
146C31×#95C2314yes—
147C31×#95C2314yes—
148C31×#95C2314yes—
149C31×#95C2314yes—
150C31×#95C2314yes—
151C31×#95C2314yes—
152C31×#95C2314yes—
153C31×#95C2314yes—
154C31×#95C2314yes—
155C31×#95C2314yes—
156C31×#95C2314yes—
157C31×#95C2314yes—
158C24×C31—22no—
159C24×C31—22no—
160C24×C31—22no—
161C24×C31—22no—
162C24×C31—22no—
163C24×C31—22no—
164C24×C31—22no—
165C24×C31—22no—
166C24×C31—22no—
167C24×C31—22no—
168C24×C31—22no—
169C24×C31—22no—
170C24×C31—22no—
171C24×C31—22no—
172C24×C31—22no—
173C24×C31—22no—
174C24×C31—22no—
175C24×C31C2×D414yes—
176C24×C31C2×D414yes—
177C24×C31#4114yes—
178C24×C31#4114yes—
179C24×C31C2412yes—
180C24×C31C2412yes—
181C24×C31C2412yes—
182C24×C31C2411yescharacteristic
183C2×D4×C31—232no—
184C2×D4×C31—28no—
185C2×D4×C31—28no—
186C2×D4×C31—28no—
187C2×D4×C31—28no—
188C2×D4×C31—28no—
189C2×D4×C31—28no—
190C2×D4×C31—28no—
191C2×D4×C31—44no—
192C2×D4×C31—416no—
193C2×D4×C31—416no—
194C2×D4×C31C2×D4116yes—
195C22×C4×C31—22no—
196C22×C4×C31—22no—
197C22×C4×C31—22no—
198C22×C4×C31—22no—
199C22×C4×C31—22no—
200C22×C4×C31—22no—
201C22×C4×C31—22no—
202C22×C4×C31—22no—
203C22×C4×C31—22no—
204C22×C4×C31—22no—
205C22×C4×C31—22no—
206C22×C4×C31—28no—
207C22×C4×C31—28no—
208C22×C4×C31—28no—
209C22×C4×C31—22no—
210C22×C4×C31—22no—
211C22×C4×C31—22no—
212C22×C4×C31—22no—
213C22×C4×C31—22no—
214C22×C4×C31—28no—
215C22×C4×C31—22no—
216C22×C4×C31—22no—
217C22×C4×C31—22no—
218C22×C4×C31—22no—
219C22×C4×C31—22no—
220C22×C4×C31—22no—
221C22×C4×C31—22no—
222C22×C4×C31—22no—
223C22×C4×C31—22no—
224C22×C4×C31—22no—
225C22×C4×C31—22no—
226C22×C4×C31—22no—
227C22×C4×C31—22no—
228C22×C4×C31—22no—
229C22×C4×C31—22no—
230C22×C4×C31—22no—
231C22×C4×C31—22no—
232C22×C4×C31—28no—
233C22×C4×C31—28no—
234C22×C4×C31—28no—
235C22×C4×C31—44no—
236C22×C4×C31—44no—
237C22×C4×C31—44no—
238C22×C4×C31—44no—
239C22×C4×C31—44no—
240C22×C4×C31—416no—
241C22×C4×C31—416no—
242C22×C4×C31—416no—
243C22×C4×C31—416no—
244C22×C4×C31C2×D414yes—
245C22×C4×C31#4114yes—
246C22×C4×C31#4114yes—
247C22×C4×C31C2412yes—
248C22×C4×C31C2412yes—
249C22×C4×C31C2412yes—
250C22×C4×C31C2412yes—
251C22×C4×C31C2412yes—
252C22×C4×C31C2412yes—
253C22×C4×C31C2412yes—
254C22×C4×C31C2412yes—
255C22×C4×C31C2412yes—
256C22×C4×C31C2412yes—
257C22×C4×C31C2412yes—
258C22×C4×C31C2412yes—
259C4⋊C4×C31—28no—
260C4⋊C4×C31—28no—
261C4⋊C4×C31—28no—
262C4⋊C4×C31—44no—
263C22⋊C4×C31—28no—
264C22⋊C4×C31—28no—
265C22⋊C4×C31—28no—
266C22⋊C4×C31—28no—
267C22⋊C4×C31—28no—
268C22⋊C4×C31—28no—
269C22⋊C4×C31—44no—
270C22⋊C4×C31—44no—
271C22⋊C4×C31—44no—
272C22⋊C4×C31—44no—
273C22⋊C4×C31—44no—
274C42×C31—28no—
275C2×#2444C3111yesmaximal, characteristic, direct product factor, Sylow
276C23×C31—28no—
277C23×C31—28no—
278C23×C31—28no—
279C23×C31—28no—
280C23×C31—28no—
281C23×C31—28no—
282C23×C31—22no—
283C23×C31—22no—
284C23×C31—22no—
285C23×C31—22no—
286C23×C31—28no—
287C23×C31—28no—
288C23×C31—28no—
289C23×C31—22no—
290C23×C31—22no—
291C23×C31—22no—
292C23×C31—22no—
293C23×C31—22no—
294C23×C31—22no—
295C23×C31—22no—
296C23×C31—22no—
297C23×C31—22no—
298C23×C31—22no—
299C23×C31—22no—
300C23×C31—22no—
301C23×C31—22no—
302C23×C31—44no—
303C23×C31—44no—
304C23×C31—44no—
305C23×C31—44no—
306C23×C31—44no—
307C23×C31—44no—
308C23×C31—44no—
309C23×C31—44no—
310C23×C31—44no—
311C23×C31—44no—
312C23×C31—44no—
313C23×C31#123116yes—
314C23×C31C22×D414yes—
315C23×C31C22×D414yes—
316C23×C31C22×D412yes—
317C23×C31C2×#4114yes—
318C23×C31C2×#4114yes—
319C23×C31C2×#4112yes—
320C23×C31C2×#4112yes—
321C23×C31C2×#4112yes—
322C23×C31C2×#4112yes—
323C23×C31H(5,𝔽2)12yes—
324C23×C31H(5,𝔽2)12yes—
325C23×C31C2511yescharacteristic
326D4×C31—232no—
327D4×C31—416no—
328D4×C31—416no—
329C2×C4×C31—28no—
330C2×C4×C31—28no—
331C2×C4×C31—28no—
332C2×C4×C31—22no—
333C2×C4×C31—22no—
334C2×C4×C31—22no—
335C2×C4×C31—22no—
336C2×C4×C31—22no—
337C2×C4×C31—22no—
338C2×C4×C31—22no—
339C2×C4×C31—22no—
340C2×C4×C31—22no—
341C2×C4×C31—22no—
342C2×C4×C31—22no—
343C2×C4×C31—22no—
344C2×C4×C31—22no—
345C2×C4×C31—22no—
346C2×C4×C31—22no—
347C2×C4×C31—22no—
348C2×C4×C31—22no—
349C2×C4×C31—22no—
350C2×C4×C31—22no—
351C2×C4×C31—22no—
352C2×C4×C31—22no—
353C2×C4×C31—22no—
354C2×C4×C31—22no—
355C2×C4×C31—22no—
356C2×C4×C31—22no—
357C2×C4×C31—22no—
358C2×C4×C31—22no—
359C2×C4×C31—22no—
360C2×C4×C31—22no—
361C2×C4×C31—22no—
362C2×C4×C31—22no—
363C2×C4×C31—22no—
364C2×C4×C31—22no—
365C2×C4×C31—416no—
366C2×C4×C31—416no—
367C2×C4×C31—416no—
368C2×C4×C31—416no—
369C2×C4×C31—44no—
370C2×C4×C31—44no—
371C2×C4×C31—44no—
372C2×C4×C31—44no—
373C2×C4×C31—44no—
374C2×C4×C31—44no—
375C2×C4×C31—44no—
376C2×C4×C31—44no—
377C2×C4×C31—44no—
378C2×C4×C31C22×D414yes—
379C2×C4×C31C2×#4114yes—
380C2×C4×C31C2×#4114yes—
381C22×#121C2×C3111yescharacteristic
382C22×C4×D4C2×C3111yescharacteristic, complemented
383#2444C2×C31116yesdirect product factor
384C2×#400C2×C3111yescharacteristic, complemented
385C2×#397C2×C3111yescharacteristic, complemented
386C2×#397C2×C3111yescharacteristic, complemented
387C2×#394C2×C3111yescharacteristic, complemented
388C2×#388C2×C3111yescharacteristic, complemented
389C2×#387C2×C3111yescharacteristic, complemented
390C2×#386C2×C3111yescharacteristic, complemented
391C2×#386C2×C3111yescharacteristic, complemented
392C2×#386C2×C3111yescharacteristic, complemented
393C2×#386C2×C3111yescharacteristic, complemented
394C2×#385C2×C3111yescharacteristic, complemented
395C2×#381C2×C3111yescharacteristic, complemented
396C22×#95C2×C3111yescharacteristic, complemented
397C22×C31—24no—
398C22×C31—24no—
399C22×C31—24no—
400C22×C31—24no—
401C22×C31—232no—
402C22×C31—24no—
403C22×C31—24no—
404C22×C31—24no—
405C22×C31—24no—
406C22×C31—24no—
407C22×C31—42no—
408C22×C31—42no—
409C22×C31—416no—
410C22×C31—42no—
411C22×C31—42no—
412C22×C31—42no—
413C22×C31—42no—
414C22×C31—42no—
415C22×C31—42no—
416C22×C31—42no—
417C22×C31—42no—
418C22×C31—42no—
419C22×C31—88no—
420C22×C31C2×#12318yes—
421C22×C31C2×#12314yes—
422C22×C31#52914yes—
423C22×C31#53814yes—
424C22×C31#54614yes—
425C22×C31#54614yes—
426C22×C31#55314yes—
427C22×C31#55314yes—
428C22×C31C23×D411yescharacteristic
429C22×C31C22×#4111yescharacteristic
430C22×C31C22×#4111yescharacteristic
431C22×C31C22×#4111yescharacteristic
432C22×C31C22×#4111yescharacteristic
433C22×C31C2×H(5,𝔽2)11yescharacteristic
434C22×C31C2×H(5,𝔽2)11yescharacteristic
435C4×C31—24no—
436C4×C31—24no—
437C4×C31—24no—
438C4×C31—42no—
439C4×C31—42no—
440C4×C31—42no—
441C4×C31—42no—
442C4×C31—42no—
443C4×C31—42no—
444C4×C31—42no—
445C4×C31—42no—
446C4×C31—42no—
447C23×D4C22×C3111yescharacteristic
448C23×D4C22×C3111yescharacteristic
449C23×D4C22×C3111yescharacteristic
450C24×C4C22×C3111yescharacteristic
451C24×C4C22×C3111yescharacteristic
452C24×C4C22×C3111yescharacteristic
453C24×C4C22×C3111yescharacteristic
454C2×#121—28no—
455C2×#121C22×C3118yes—
456C2×C4×D4—28no—
457C2×C4×D4C22×C3118yescomplemented
458C22×C4⋊C4C22×C3111yescharacteristic
459C22×C4⋊C4C22×C3111yescharacteristic
460C22×C4⋊C4C22×C3111yescharacteristic
461C22×C4⋊C4C22×C3111yescharacteristic
462C22×C22⋊C4C22×C3111yescharacteristic
463C22×C22⋊C4C22×C3111yescharacteristic
464C22×C22⋊C4C22×C3111yescharacteristic
465C22×C22⋊C4C22×C3111yescharacteristic
466C22×C22⋊C4C22×C3111yescharacteristic
467C22×C22⋊C4C22×C3111yescharacteristic
468C22×C22⋊C4C22×C3111yescharacteristic
469C22×C22⋊C4C22×C3111yescharacteristic
470C22×C22⋊C4C22×C3111yescharacteristic
471C22×C22⋊C4C22×C3111yescharacteristic
472C22×C22⋊C4C22×C3111yescharacteristic
473C22×C42C22×C3111yescharacteristic
474#400C22×C3118yescomplemented
475#397C22×C3118yescomplemented
476#397C22×C3118yescomplemented
477#394C22×C3118yescomplemented
478#388C22×C3118yescomplemented
479#387C22×C3118yescomplemented
480#386C22×C3118yescomplemented
481#386C22×C3118yescomplemented
482#386C22×C3118yescomplemented
483#386C22×C3118yescomplemented
484#385C22×C3118yescomplemented
485#381C22×C3118yescomplemented
486C2×#95C22×C3111yescharacteristic
487C2×#95C22×C3111yescharacteristic
488C2×#95C22×C3111yescharacteristic
489C2×#95C22×C3111yescharacteristic
490C2×#95C22×C3111yescharacteristic
491C2×#95C22×C3111yescharacteristic
492C2×#95C22×C3111yescharacteristic
493C2×#95C22×C3111yescharacteristic
494C2×#95C22×C3111yescharacteristic
495C2×#95C22×C3111yescharacteristic
496C2×#95C22×C3111yescharacteristic
497C2×#95C22×C3111yescharacteristic
498C2×#95C22×C3118yescomplemented
499C2×C31—28no—
500C2×C31—44no—
501C2×C31—82no—
502C2×C31#244418yesdirect product factor
503C2×C31C22×#12311yescharacteristic
504C2×C31C2×#52911yescharacteristic
505C2×C31C2×#53811yescharacteristic
506C2×C31C2×#54611yescharacteristic
507C2×C31C2×#54611yescharacteristic
508C2×C31C2×#55311yescharacteristic
509C2×C31C2×#55311yescharacteristic
510C25C23×C3111yescharacteristic
511C25C23×C3111yescharacteristic
512C25C23×C3111yescharacteristic
513C22×D4—24no—
514C22×D4—24no—
515C22×D4—24no—
516C22×D4—24no—
517C22×D4—24no—
518C22×D4—24no—
519C22×D4—24no—
520C22×D4—42no—
521C22×D4D4×C3118yes—
522C22×D4C23×C3114yes—
523C22×D4C23×C3114yes—
524C22×D4C23×C3114yes—
525C23×C4—24no—
526C23×C4—24no—
527C23×C4—24no—
528C23×C4—24no—
529C23×C4—24no—
530C23×C4—24no—
531C23×C4—24no—
532C23×C4—42no—
533C23×C4—42no—
534C23×C4—42no—
535C23×C4—42no—
536C23×C4—42no—
537C23×C4C23×C3111yescharacteristic
538C23×C4C23×C3111yescharacteristic
539C23×C4C23×C3111yescharacteristic
540C23×C4C23×C3111yescharacteristic
541C23×C4C23×C3111yescharacteristic
542C23×C4C23×C3111yescharacteristic
543C23×C4C23×C3111yescharacteristic
544C23×C4C23×C3111yescharacteristic
545C23×C4C23×C3111yescharacteristic
546C23×C4C23×C3114yes—
547C23×C4C23×C3114yes—
548C23×C4C23×C3114yes—
549C23×C4C23×C3111yescharacteristic
550C23×C4C23×C3111yescharacteristic
551C23×C4C23×C3111yescharacteristic
552C23×C4C23×C3114yes—
553#121—232no—
554C4×D4—232no—
555C2×C4⋊C4—24no—
556C2×C4⋊C4—24no—
557C2×C4⋊C4—24no—
558C2×C4⋊C4—42no—
559C2×C4⋊C4C23×C3114yes—
560C2×C4⋊C4C23×C3114yes—
561C2×C4⋊C4C23×C3114yes—
562C2×C4⋊C4C23×C3114yes—
563C2×C22⋊C4—24no—
564C2×C22⋊C4—24no—
565C2×C22⋊C4—24no—
566C2×C22⋊C4—24no—
567C2×C22⋊C4—24no—
568C2×C22⋊C4—24no—
569C2×C22⋊C4—42no—
570C2×C22⋊C4—42no—
571C2×C22⋊C4—42no—
572C2×C22⋊C4—42no—
573C2×C22⋊C4—42no—
574C2×C22⋊C4C23×C3114yes—
575C2×C22⋊C4C23×C3114yes—
576C2×C22⋊C4C23×C3114yes—
577C2×C22⋊C4C23×C3114yes—
578C2×C22⋊C4C23×C3114yes—
579C2×C22⋊C4C23×C3114yes—
580C2×C22⋊C4C23×C3114yes—
581C2×C22⋊C4C23×C3114yes—
582C2×C22⋊C4C23×C3114yes—
583C2×C22⋊C4C23×C3114yes—
584C2×C22⋊C4C23×C3114yes—
585C2×C42—24no—
586C2×C42C23×C3114yes—
587#95C23×C3114yes—
588#95C23×C3114yes—
589#95C23×C3114yes—
590#95C23×C3114yes—
591#95C23×C3114yes—
592#95C23×C3114yes—
593#95C23×C3114yes—
594#95C23×C3114yes—
595#95C23×C3114yes—
596#95C23×C3114yes—
597#95C23×C3114yes—
598#95C23×C3114yes—
599C31C2×#244411yescharacteristic, direct product factor, Sylow
600C24—22no—
601C24—22no—
602C24—22no—
603C24—22no—
604C24—22no—
605C24—22no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—22no—
615C24—22no—
616C24—22no—
617C24C2×D4×C3114yes—
618C24C2×D4×C3114yes—
619C24#41×C3114yes—
620C24#41×C3114yes—
621C24C24×C3112yes—
622C24C24×C3112yes—
623C24C24×C3112yes—
624C24C24×C3111yescharacteristic
625C2×D4—232no—
626C2×D4—28no—
627C2×D4—28no—
628C2×D4—28no—
629C2×D4—28no—
630C2×D4—28no—
631C2×D4—28no—
632C2×D4—28no—
633C2×D4—44no—
634C2×D4—416no—
635C2×D4—416no—
636C2×D4C2×D4×C31116yes—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—28no—
649C22×C4—28no—
650C22×C4—28no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—28no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—28no—
675C22×C4—28no—
676C22×C4—28no—
677C22×C4—44no—
678C22×C4—44no—
679C22×C4—44no—
680C22×C4—44no—
681C22×C4—44no—
682C22×C4—416no—
683C22×C4—416no—
684C22×C4—416no—
685C22×C4—416no—
686C22×C4C2×D4×C3114yes—
687C22×C4#41×C3114yes—
688C22×C4#41×C3114yes—
689C22×C4C24×C3112yes—
690C22×C4C24×C3112yes—
691C22×C4C24×C3112yes—
692C22×C4C24×C3112yes—
693C22×C4C24×C3112yes—
694C22×C4C24×C3112yes—
695C22×C4C24×C3112yes—
696C22×C4C24×C3112yes—
697C22×C4C24×C3112yes—
698C22×C4C24×C3112yes—
699C22×C4C24×C3112yes—
700C22×C4C24×C3112yes—
701C4⋊C4—28no—
702C4⋊C4—28no—
703C4⋊C4—28no—
704C4⋊C4—44no—
705C22⋊C4—28no—
706C22⋊C4—28no—
707C22⋊C4—28no—
708C22⋊C4—28no—
709C22⋊C4—28no—
710C22⋊C4—28no—
711C22⋊C4—44no—
712C22⋊C4—44no—
713C22⋊C4—44no—
714C22⋊C4—44no—
715C22⋊C4—44no—
716C42—28no—
717C23—28no—
718C23—28no—
719C23—28no—
720C23—28no—
721C23—28no—
722C23—28no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—28no—
728C23—28no—
729C23—28no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—44no—
744C23—44no—
745C23—44no—
746C23—44no—
747C23—44no—
748C23—44no—
749C23—44no—
750C23—44no—
751C23—44no—
752C23—44no—
753C23—44no—
754C23C31×#123116yes—
755C23C22×D4×C3114yes—
756C23C22×D4×C3114yes—
757C23C22×D4×C3112yes—
758C23C2×#41×C3114yes—
759C23C2×#41×C3114yes—
760C23C2×#41×C3112yes—
761C23C2×#41×C3112yes—
762C23C2×#41×C3112yes—
763C23C2×#41×C3112yes—
764C23C31×H(5,𝔽2)12yes—
765C23C31×H(5,𝔽2)12yes—
766C23C25×C3111yescharacteristic
767D4—232no—
768D4—416no—
769D4—416no—
770C2×C4—28no—
771C2×C4—28no—
772C2×C4—28no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—416no—
807C2×C4—416no—
808C2×C4—416no—
809C2×C4—416no—
810C2×C4—44no—
811C2×C4—44no—
812C2×C4—44no—
813C2×C4—44no—
814C2×C4—44no—
815C2×C4—44no—
816C2×C4—44no—
817C2×C4—44no—
818C2×C4—44no—
819C2×C4C22×D4×C3114yes—
820C2×C4C2×#41×C3114yes—
821C2×C4C2×#41×C3114yes—
822C22—24no—
823C22—24no—
824C22—24no—
825C22—24no—
826C22—232no—
827C22—24no—
828C22—24no—
829C22—24no—
830C22—24no—
831C22—24no—
832C22—42no—
833C22—42no—
834C22—416no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—42no—
844C22—88no—
845C22C2×C31×#12318yes—
846C22C2×C31×#12314yes—
847C22C31×#52914yes—
848C22C31×#53814yes—
849C22C31×#54614yes—
850C22C31×#54614yes—
851C22C31×#55314yes—
852C22C31×#55314yes—
853C22C23×D4×C3111yescharacteristic
854C22C22×#41×C3111yescharacteristic
855C22C22×#41×C3111yescharacteristic
856C22C22×#41×C3111yescharacteristic
857C22C22×#41×C3111yescharacteristic
858C22C2×C31×H(5,𝔽2)11yescharacteristic
859C22C2×C31×H(5,𝔽2)11yescharacteristic
860C4—24no—
861C4—24no—
862C4—24no—
863C4—42no—
864C4—42no—
865C4—42no—
866C4—42no—
867C4—42no—
868C4—42no—
869C4—42no—
870C4—42no—
871C4—42no—
872C2—28no—
873C2—44no—
874C2—82no—
875C2C31×#244418yesdirect product factor
876C2C22×C31×#12311yescharacteristic
877C2C2×C31×#52911yescharacteristic
878C2C2×C31×#53811yescharacteristic
879C2C2×C31×#54611yescharacteristic
880C2C2×C31×#54611yescharacteristic
881C2C2×C31×#55311yescharacteristic
882C2C2×C31×#55311yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutator, Frattini, cosocleC23C25×C31
prime radicalC22×C31×#121C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C4×D4×C31C2semidirect
3. C31×#2444C2direct (N × H)
4. C2×C31×#400C2semidirect
5. C2×C31×#397C2semidirect
6. C2×C31×#397C2semidirect
7. C2×C31×#394C2semidirect
8. C2×C31×#388C2semidirect
9. C2×C31×#387C2semidirect
10. C2×C31×#386C2semidirect
11. C2×C31×#386C2semidirect
12. C2×C31×#386C2semidirect
13. C2×C31×#386C2semidirect
14. C2×C31×#385C2semidirect
15. C2×C31×#381C2semidirect
16. C22×C31×#95C2semidirect
27. C2×C4×D4×C31C22semidirect
44. C31×#400C22semidirect
45. C31×#397C22semidirect
46. C31×#397C22semidirect
47. C31×#394C22semidirect
48. C31×#388C22semidirect
49. C31×#387C22semidirect
50. C31×#386C22semidirect
51. C31×#386C22semidirect
52. C31×#386C22semidirect
53. C31×#386C22semidirect
54. C31×#385C22semidirect
55. C31×#381C22semidirect
68. C2×C31×#95C22semidirect
275. C2×#2444C31direct (N × H)
382. C22×C4×D4C2×C31semidirect
383. #2444C2×C31direct (N × H)
384. C2×#400C2×C31semidirect
385. C2×#397C2×C31semidirect
386. C2×#397C2×C31semidirect
387. C2×#394C2×C31semidirect
388. C2×#388C2×C31semidirect
389. C2×#387C2×C31semidirect
390. C2×#386C2×C31semidirect
391. C2×#386C2×C31semidirect
392. C2×#386C2×C31semidirect
393. C2×#386C2×C31semidirect
394. C2×#385C2×C31semidirect
395. C2×#381C2×C31semidirect
396. C22×#95C2×C31semidirect
457. C2×C4×D4C22×C31semidirect
474. #400C22×C31semidirect
475. #397C22×C31semidirect
476. #397C22×C31semidirect
477. #394C22×C31semidirect
478. #388C22×C31semidirect
479. #387C22×C31semidirect
480. #386C22×C31semidirect
481. #386C22×C31semidirect
482. #386C22×C31semidirect
483. #386C22×C31semidirect
484. #385C22×C31semidirect
485. #381C22×C31semidirect
498. C2×#95C22×C31semidirect
502. C2×C31#2444direct (N × H)
599. C31C2×#2444direct (N × H)
875. C2C31×#2444direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C31×#1212
C22×C4×D4×C312
C31×#24442
C2×C31×#4002
C2×C31×#3972
C2×C31×#3942
C2×C31×#3882
C2×C31×#3872
C2×C31×#3862
C2×C31×#3852
C2×C31×#3812
C22×C31×#952
C2×#244431