Finite Group Databasebeta

← C2×C31×#2472 #21491417

Subgroups — C2×C31×#2472 #21491417

Order 7936.

4946 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#124C211yesmaximal, characteristic, complemented
2C22×C31×C22⋊Q8C211yesmaximal, characteristic, complemented
3C22×C31×#120C211yesmaximal, characteristic
4C23×C22⋊C4×C31C211yesmaximal, characteristic, complemented
5C31×#2472C2116yesmaximal, direct product factor
6C2×C31×#397C211yesmaximal, characteristic, complemented
7C2×C31×#394C211yesmaximal, characteristic, complemented
8C2×C31×#394C211yesmaximal, characteristic, complemented
9C2×C31×#393C211yesmaximal, characteristic, complemented
10C2×C31×#390C211yesmaximal, characteristic, complemented
11C2×C31×#388C211yesmaximal, characteristic, complemented
12C2×C31×#388C211yesmaximal, characteristic, complemented
13C2×C31×#386C211yesmaximal, characteristic, complemented
14C2×C31×#386C211yesmaximal, characteristic, complemented
15C2×C31×#379C211yesmaximal, characteristic, complemented
16C2×C4×C22⋊C4×C31C211yesmaximal, characteristic, complemented
17C26×C31C2211yescharacteristic
18C23×Q8×C31C2211yescharacteristic, complemented
19C23×D4×C31C2211yescharacteristic
20C23×D4×C31C2211yescharacteristic
21C23×D4×C31C2211yescharacteristic
22C24×C4×C31C2211yescharacteristic
23C24×C4×C31C2211yescharacteristic
24C2×C31×#124—28no—
25C2×C31×#124C2218yescomplemented
26C2×C31×C22⋊Q8—28no—
27C2×C31×C22⋊Q8C2218yescomplemented
28C2×C31×#120—28no—
29C2×C31×#120C2218yes—
30C22×C4⋊C4×C31C2211yescharacteristic, complemented
31C22×C4⋊C4×C31C2211yescharacteristic, complemented
32C22×C4⋊C4×C31C2211yescharacteristic, complemented
33C22×C22⋊C4×C31—28no—
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×C22⋊C4×C31C2211yescharacteristic
44C22×C22⋊C4×C31C2211yescharacteristic
45C22×C22⋊C4×C31C2211yescharacteristic
46C22×C22⋊C4×C31C2211yescharacteristic
47C22×C22⋊C4×C31C2218yescomplemented
48C22×C22⋊C4×C31C2211yescharacteristic, complemented
49C22×C22⋊C4×C31C2211yescharacteristic, complemented
50C22×C22⋊C4×C31C2211yescharacteristic, complemented
51C22×C22⋊C4×C31C2211yescharacteristic, complemented
52C22×C42×C31C2211yescharacteristic, complemented
53C22×C42×C31C2211yescharacteristic, complemented
54C31×#397C2218yescomplemented
55C31×#394C2218yescomplemented
56C31×#394C2218yescomplemented
57C31×#393C2218yescomplemented
58C31×#390C2218yescomplemented
59C31×#388C2218yescomplemented
60C31×#388C2218yescomplemented
61C31×#386C2218yescomplemented
62C31×#386C2218yescomplemented
63C31×#379C2218yescomplemented
64C4×C22⋊C4×C31C2218yescomplemented
65C2×C31×#95C2211yescharacteristic, complemented
66C2×C31×#95C2211yescharacteristic, complemented
67C2×C31×#95C2211yescharacteristic, complemented
68C2×C31×#95C2211yescharacteristic, complemented
69C2×C31×#95C2211yescharacteristic, complemented
70C2×C31×#95C2211yescharacteristic, complemented
71C25×C31—24no—
72C25×C31—24no—
73C25×C31—24no—
74C25×C31—24no—
75C25×C31—24no—
76C25×C31—42no—
77C25×C31—42no—
78C25×C31C2311yescharacteristic
79C25×C31C2311yescharacteristic
80C25×C31C2311yescharacteristic
81C25×C31C2314yes—
82C25×C31C2311yescharacteristic
83C22×Q8×C31—24no—
84C22×Q8×C31—24no—
85C22×Q8×C31—42no—
86C22×Q8×C31C2314yescomplemented
87C22×D4×C31—24no—
88C22×D4×C31—24no—
89C22×D4×C31—24no—
90C22×D4×C31—24no—
91C22×D4×C31—24no—
92C22×D4×C31—24no—
93C22×D4×C31—24no—
94C22×D4×C31—42no—
95C22×D4×C31—42no—
96C22×D4×C31C2314yes—
97C22×D4×C31C2314yes—
98C22×D4×C31C2314yes—
99C23×C4×C31—24no—
100C23×C4×C31—24no—
101C23×C4×C31—24no—
102C23×C4×C31—24no—
103C23×C4×C31—42no—
104C23×C4×C31—42no—
105C23×C4×C31C2311yescharacteristic
106C23×C4×C31C2311yescharacteristic
107C23×C4×C31C2311yescharacteristic
108C23×C4×C31C2311yescharacteristic
109C23×C4×C31C2311yescharacteristic
110C23×C4×C31C2311yescharacteristic
111C23×C4×C31C2311yescharacteristic
112C23×C4×C31C2314yes—
113C23×C4×C31C2314yes—
114C23×C4×C31C2311yescharacteristic
115C23×C4×C31C2311yescharacteristic
116C23×C4×C31C2311yescharacteristic
117C23×C4×C31C2311yescharacteristic
118C31×#124—232no—
119C31×C22⋊Q8—232no—
120C31×#120—232no—
121C2×C4⋊C4×C31—24no—
122C2×C4⋊C4×C31—24no—
123C2×C4⋊C4×C31—24no—
124C2×C4⋊C4×C31C2314yescomplemented
125C2×C4⋊C4×C31C2314yescomplemented
126C2×C4⋊C4×C31C2314yescomplemented
127C2×C22⋊C4×C31—24no—
128C2×C22⋊C4×C31—24no—
129C2×C22⋊C4×C31—24no—
130C2×C22⋊C4×C31—24no—
131C2×C22⋊C4×C31—24no—
132C2×C22⋊C4×C31—24no—
133C2×C22⋊C4×C31—24no—
134C2×C22⋊C4×C31—24no—
135C2×C22⋊C4×C31—24no—
136C2×C22⋊C4×C31—24no—
137C2×C22⋊C4×C31—24no—
138C2×C22⋊C4×C31—232no—
139C2×C22⋊C4×C31—42no—
140C2×C22⋊C4×C31—42no—
141C2×C22⋊C4×C31—42no—
142C2×C22⋊C4×C31—42no—
143C2×C22⋊C4×C31D418yes—
144C2×C22⋊C4×C31D418yescomplemented
145C2×C22⋊C4×C31C2314yes—
146C2×C22⋊C4×C31C2314yes—
147C2×C22⋊C4×C31C2314yes—
148C2×C22⋊C4×C31C2314yes—
149C2×C22⋊C4×C31C2314yes—
150C2×C22⋊C4×C31C2314yes—
151C2×C22⋊C4×C31C2314yes—
152C2×C22⋊C4×C31C2314yes—
153C2×C22⋊C4×C31C2314yes—
154C2×C22⋊C4×C31C2314yes—
155C2×C22⋊C4×C31C2314yes—
156C2×C22⋊C4×C31C2314yes—
157C2×C22⋊C4×C31C2314yes—
158C2×C22⋊C4×C31C2314yescomplemented
159C2×C22⋊C4×C31C2314yescomplemented
160C2×C22⋊C4×C31C2314yescomplemented
161C2×C22⋊C4×C31C2314yescomplemented
162C2×C42×C31—24no—
163C2×C42×C31—42no—
164C2×C42×C31C2314yescomplemented
165C2×C42×C31C2314yescomplemented
166C31×#95C2314yescomplemented
167C31×#95C2314yescomplemented
168C31×#95C2314yescomplemented
169C31×#95C2314yescomplemented
170C31×#95C2314yescomplemented
171C31×#95C2314yescomplemented
172C24×C31—22no—
173C24×C31—22no—
174C24×C31—22no—
175C24×C31—22no—
176C24×C31—232no—
177C24×C31—28no—
178C24×C31—22no—
179C24×C31—22no—
180C24×C31—22no—
181C24×C31—28no—
182C24×C31—28no—
183C24×C31—22no—
184C24×C31—22no—
185C24×C31—22no—
186C24×C31—22no—
187C24×C31—22no—
188C24×C31—22no—
189C24×C31—22no—
190C24×C31—22no—
191C24×C31—22no—
192C24×C31—22no—
193C24×C31—28no—
194C24×C31—22no—
195C24×C31—22no—
196C24×C31—22no—
197C24×C31—22no—
198C24×C31—28no—
199C24×C31—22no—
200C24×C31—22no—
201C24×C31—44no—
202C24×C31—44no—
203C24×C31—416no—
204C24×C31—416no—
205C24×C31—416no—
206C24×C31—416no—
207C24×C31—416no—
208C24×C31—416no—
209C24×C31C2×D414yes—
210C24×C31C2×D414yes—
211C24×C31#4114yes—
212C24×C31#4114yes—
213C24×C31#4114yes—
214C24×C31C2412yes—
215C24×C31C2412yes—
216C24×C31C2412yes—
217C24×C31C2412yes—
218C24×C31C2411yescharacteristic
219C2×Q8×C31—28no—
220C2×Q8×C31—28no—
221C2×Q8×C31—44no—
222C2×Q8×C31—416no—
223C2×D4×C31—28no—
224C2×D4×C31—28no—
225C2×D4×C31—28no—
226C2×D4×C31—28no—
227C2×D4×C31—28no—
228C2×D4×C31—28no—
229C2×D4×C31—28no—
230C2×D4×C31—44no—
231C2×D4×C31—44no—
232C2×D4×C31—416no—
233C2×D4×C31—416no—
234C2×D4×C31—416no—
235C22×C4×C31—22no—
236C22×C4×C31—22no—
237C22×C4×C31—22no—
238C22×C4×C31—22no—
239C22×C4×C31—22no—
240C22×C4×C31—22no—
241C22×C4×C31—22no—
242C22×C4×C31—22no—
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—22no—
250C22×C4×C31—22no—
251C22×C4×C31—28no—
252C22×C4×C31—22no—
253C22×C4×C31—22no—
254C22×C4×C31—22no—
255C22×C4×C31—22no—
256C22×C4×C31—28no—
257C22×C4×C31—22no—
258C22×C4×C31—22no—
259C22×C4×C31—22no—
260C22×C4×C31—22no—
261C22×C4×C31—22no—
262C22×C4×C31—22no—
263C22×C4×C31—22no—
264C22×C4×C31—22no—
265C22×C4×C31—22no—
266C22×C4×C31—28no—
267C22×C4×C31—28no—
268C22×C4×C31—44no—
269C22×C4×C31—44no—
270C22×C4×C31—416no—
271C22×C4×C31—416no—
272C22×C4×C31C2×D414yes—
273C22×C4×C31C2×D414yes—
274C22×C4×C31C2×D414yes—
275C22×C4×C31C2×D414yes—
276C22×C4×C31C2412yes—
277C22×C4×C31C2412yes—
278C22×C4×C31C2412yes—
279C22×C4×C31C2412yes—
280C22×C4×C31C2412yes—
281C22×C4×C31C2412yes—
282C22×C4×C31C2412yes—
283C22×C4×C31C2412yes—
284C22×C4×C31C2412yes—
285C22×C4×C31C2412yes—
286C22×C4×C31C2412yes—
287C4⋊C4×C31—28no—
288C4⋊C4×C31—28no—
289C4⋊C4×C31—28no—
290C22⋊C4×C31—28no—
291C22⋊C4×C31—28no—
292C22⋊C4×C31—28no—
293C22⋊C4×C31—28no—
294C22⋊C4×C31—28no—
295C22⋊C4×C31—28no—
296C22⋊C4×C31—28no—
297C22⋊C4×C31—28no—
298C22⋊C4×C31—28no—
299C22⋊C4×C31—28no—
300C22⋊C4×C31—28no—
301C22⋊C4×C31—44no—
302C22⋊C4×C31—44no—
303C22⋊C4×C31—44no—
304C22⋊C4×C31—44no—
305C22⋊C4×C31C2×D4116yes—
306C22⋊C4×C31C2×D4116yescomplemented
307C42×C31—28no—
308C42×C31—44no—
309C2×#2472C3111yesmaximal, characteristic, direct product factor, Sylow
310C23×C31—28no—
311C23×C31—28no—
312C23×C31—28no—
313C23×C31—28no—
314C23×C31—28no—
315C23×C31—28no—
316C23×C31—22no—
317C23×C31—22no—
318C23×C31—22no—
319C23×C31—22no—
320C23×C31—232no—
321C23×C31—28no—
322C23×C31—28no—
323C23×C31—28no—
324C23×C31—28no—
325C23×C31—28no—
326C23×C31—28no—
327C23×C31—22no—
328C23×C31—22no—
329C23×C31—22no—
330C23×C31—22no—
331C23×C31—22no—
332C23×C31—22no—
333C23×C31—22no—
334C23×C31—22no—
335C23×C31—22no—
336C23×C31—22no—
337C23×C31—22no—
338C23×C31—22no—
339C23×C31—22no—
340C23×C31—22no—
341C23×C31—22no—
342C23×C31—22no—
343C23×C31—22no—
344C23×C31—22no—
345C23×C31—22no—
346C23×C31—416no—
347C23×C31—416no—
348C23×C31—416no—
349C23×C31—416no—
350C23×C31—416no—
351C23×C31—4128no—
352C23×C31—44no—
353C23×C31—44no—
354C23×C31—416no—
355C23×C31—44no—
356C23×C31—44no—
357C23×C31—44no—
358C23×C31—44no—
359C23×C31—44no—
360C23×C31—44no—
361C23×C31—44no—
362C23×C31—44no—
363C23×C31—44no—
364C23×C31—44no—
365C23×C31—44no—
366C23×C31—44no—
367C23×C31—44no—
368C23×C31#124116yescomplemented
369C23×C31C22×D414yes—
370C23×C31C22×D414yes—
371C23×C31C22×D412yes—
372C23×C31C22×D412yes—
373C23×C31C2×#4114yes—
374C23×C31C2×#4114yes—
375C23×C31C2×#4114yes—
376C23×C31C2×#4112yes—
377C23×C31C2×#4112yes—
378C23×C31C2×#4112yes—
379C23×C31H(5,𝔽2)12yes—
380C23×C31H(5,𝔽2)12yes—
381C23×C31C2511yescharacteristic
382Q8×C31—416no—
383D4×C31—416no—
384D4×C31—416no—
385D4×C31—416no—
386C2×C4×C31—28no—
387C2×C4×C31—28no—
388C2×C4×C31—28no—
389C2×C4×C31—28no—
390C2×C4×C31—22no—
391C2×C4×C31—22no—
392C2×C4×C31—22no—
393C2×C4×C31—22no—
394C2×C4×C31—22no—
395C2×C4×C31—22no—
396C2×C4×C31—22no—
397C2×C4×C31—22no—
398C2×C4×C31—22no—
399C2×C4×C31—22no—
400C2×C4×C31—22no—
401C2×C4×C31—22no—
402C2×C4×C31—22no—
403C2×C4×C31—22no—
404C2×C4×C31—22no—
405C2×C4×C31—22no—
406C2×C4×C31—22no—
407C2×C4×C31—22no—
408C2×C4×C31—22no—
409C2×C4×C31—22no—
410C2×C4×C31—22no—
411C2×C4×C31—22no—
412C2×C4×C31—22no—
413C2×C4×C31—22no—
414C2×C4×C31—22no—
415C2×C4×C31—22no—
416C2×C4×C31—22no—
417C2×C4×C31—22no—
418C2×C4×C31—22no—
419C2×C4×C31—416no—
420C2×C4×C31—416no—
421C2×C4×C31—44no—
422C2×C4×C31—44no—
423C2×C4×C31—44no—
424C2×C4×C31—44no—
425C2×C4×C31—44no—
426C2×C4×C31—44no—
427C2×C4×C31—44no—
428C2×C4×C31C22×D414yes—
429C2×C4×C31C22×D414yes—
430C2×C4×C31C22×D414yes—
431C2×C4×C31C22×D414yes—
432C22×#124C2×C3111yescharacteristic, complemented
433C22×C22⋊Q8C2×C3111yescharacteristic, complemented
434C22×#120C2×C3111yescharacteristic
435C23×C22⋊C4C2×C3111yescharacteristic, complemented
436#2472C2×C31116yesdirect product factor
437C2×#397C2×C3111yescharacteristic, complemented
438C2×#394C2×C3111yescharacteristic, complemented
439C2×#394C2×C3111yescharacteristic, complemented
440C2×#393C2×C3111yescharacteristic, complemented
441C2×#390C2×C3111yescharacteristic, complemented
442C2×#388C2×C3111yescharacteristic, complemented
443C2×#388C2×C3111yescharacteristic, complemented
444C2×#386C2×C3111yescharacteristic, complemented
445C2×#386C2×C3111yescharacteristic, complemented
446C2×#379C2×C3111yescharacteristic, complemented
447C2×C4×C22⋊C4C2×C3111yescharacteristic, complemented
448C22×C31—24no—
449C22×C31—24no—
450C22×C31—24no—
451C22×C31—24no—
452C22×C31—24no—
453C22×C31—24no—
454C22×C31—232no—
455C22×C31—24no—
456C22×C31—24no—
457C22×C31—24no—
458C22×C31—24no—
459C22×C31—24no—
460C22×C31—24no—
461C22×C31—464no—
462C22×C31—42no—
463C22×C31—42no—
464C22×C31—42no—
465C22×C31—42no—
466C22×C31—42no—
467C22×C31—42no—
468C22×C31—42no—
469C22×C31—42no—
470C22×C31—416no—
471C22×C31—416no—
472C22×C31—42no—
473C22×C31—42no—
474C22×C31—42no—
475C22×C31—42no—
476C22×C31—42no—
477C22×C31—42no—
478C22×C31—42no—
479C22×C31—88no—
480C22×C31#52514yes—
481C22×C31C2×#12414yes—
482C22×C31C2×#12418yescomplemented
483C22×C31#53814yes—
484C22×C31D4214yes—
485C22×C31#54614yes—
486C22×C31#54614yes—
487C22×C31#55114yes—
488C22×C31C23×D411yescharacteristic
489C22×C31C23×D411yescharacteristic
490C22×C31C22×#4111yescharacteristic
491C22×C31C22×#4111yescharacteristic
492C22×C31C22×#4111yescharacteristic
493C22×C31C2×H(5,𝔽2)11yescharacteristic
494C22×C31C2×H(5,𝔽2)11yescharacteristic
495C4×C31—24no—
496C4×C31—24no—
497C4×C31—24no—
498C4×C31—24no—
499C4×C31—42no—
500C4×C31—42no—
501C4×C31—42no—
502C4×C31—42no—
503C4×C31—42no—
504C4×C31—42no—
505C4×C31—42no—
506C26C22×C3111yescharacteristic
507C23×Q8C22×C3111yescharacteristic, complemented
508C23×D4C22×C3111yescharacteristic
509C23×D4C22×C3111yescharacteristic
510C23×D4C22×C3111yescharacteristic
511C24×C4C22×C3111yescharacteristic
512C24×C4C22×C3111yescharacteristic
513C2×#124—28no—
514C2×#124C22×C3118yescomplemented
515C2×C22⋊Q8—28no—
516C2×C22⋊Q8C22×C3118yescomplemented
517C2×#120—28no—
518C2×#120C22×C3118yes—
519C22×C4⋊C4C22×C3111yescharacteristic, complemented
520C22×C4⋊C4C22×C3111yescharacteristic, complemented
521C22×C4⋊C4C22×C3111yescharacteristic, complemented
522C22×C22⋊C4—28no—
523C22×C22⋊C4C22×C3111yescharacteristic
524C22×C22⋊C4C22×C3111yescharacteristic
525C22×C22⋊C4C22×C3111yescharacteristic
526C22×C22⋊C4C22×C3111yescharacteristic
527C22×C22⋊C4C22×C3111yescharacteristic
528C22×C22⋊C4C22×C3111yescharacteristic
529C22×C22⋊C4C22×C3111yescharacteristic
530C22×C22⋊C4C22×C3111yescharacteristic
531C22×C22⋊C4C22×C3111yescharacteristic
532C22×C22⋊C4C22×C3111yescharacteristic
533C22×C22⋊C4C22×C3111yescharacteristic
534C22×C22⋊C4C22×C3111yescharacteristic
535C22×C22⋊C4C22×C3111yescharacteristic
536C22×C22⋊C4C22×C3118yescomplemented
537C22×C22⋊C4C22×C3111yescharacteristic, complemented
538C22×C22⋊C4C22×C3111yescharacteristic, complemented
539C22×C22⋊C4C22×C3111yescharacteristic, complemented
540C22×C22⋊C4C22×C3111yescharacteristic, complemented
541C22×C42C22×C3111yescharacteristic, complemented
542C22×C42C22×C3111yescharacteristic, complemented
543#397C22×C3118yescomplemented
544#394C22×C3118yescomplemented
545#394C22×C3118yescomplemented
546#393C22×C3118yescomplemented
547#390C22×C3118yescomplemented
548#388C22×C3118yescomplemented
549#388C22×C3118yescomplemented
550#386C22×C3118yescomplemented
551#386C22×C3118yescomplemented
552#379C22×C3118yescomplemented
553C4×C22⋊C4C22×C3118yescomplemented
554C2×#95C22×C3111yescharacteristic, complemented
555C2×#95C22×C3111yescharacteristic, complemented
556C2×#95C22×C3111yescharacteristic, complemented
557C2×#95C22×C3111yescharacteristic, complemented
558C2×#95C22×C3111yescharacteristic, complemented
559C2×#95C22×C3111yescharacteristic, complemented
560C2×C31—28no—
561C2×C31—44no—
562C2×C31—44no—
563C2×C31—82no—
564C2×C31#247218yesdirect product factor
565C2×C31C2×#52511yescharacteristic
566C2×C31C22×#12411yescharacteristic
567C2×C31C2×#53811yescharacteristic
568C2×C31C2×D4211yescharacteristic
569C2×C31C2×#54611yescharacteristic
570C2×C31C2×#54611yescharacteristic
571C2×C31C2×#55111yescharacteristic
572C25—24no—
573C25—24no—
574C25—24no—
575C25—24no—
576C25—24no—
577C25—42no—
578C25—42no—
579C25C23×C3111yescharacteristic
580C25C23×C3111yescharacteristic
581C25C23×C3111yescharacteristic
582C25C23×C3114yes—
583C25C23×C3111yescharacteristic
584C22×Q8—24no—
585C22×Q8—24no—
586C22×Q8—42no—
587C22×Q8C23×C3114yescomplemented
588C22×D4—24no—
589C22×D4—24no—
590C22×D4—24no—
591C22×D4—24no—
592C22×D4—24no—
593C22×D4—24no—
594C22×D4—24no—
595C22×D4—42no—
596C22×D4—42no—
597C22×D4C23×C3114yes—
598C22×D4C23×C3114yes—
599C22×D4C23×C3114yes—
600C23×C4—24no—
601C23×C4—24no—
602C23×C4—24no—
603C23×C4—24no—
604C23×C4—42no—
605C23×C4—42no—
606C23×C4C23×C3111yescharacteristic
607C23×C4C23×C3111yescharacteristic
608C23×C4C23×C3111yescharacteristic
609C23×C4C23×C3111yescharacteristic
610C23×C4C23×C3111yescharacteristic
611C23×C4C23×C3111yescharacteristic
612C23×C4C23×C3111yescharacteristic
613C23×C4C23×C3114yes—
614C23×C4C23×C3114yes—
615C23×C4C23×C3111yescharacteristic
616C23×C4C23×C3111yescharacteristic
617C23×C4C23×C3111yescharacteristic
618C23×C4C23×C3111yescharacteristic
619#124—232no—
620C22⋊Q8—232no—
621#120—232no—
622C2×C4⋊C4—24no—
623C2×C4⋊C4—24no—
624C2×C4⋊C4—24no—
625C2×C4⋊C4C23×C3114yescomplemented
626C2×C4⋊C4C23×C3114yescomplemented
627C2×C4⋊C4C23×C3114yescomplemented
628C2×C22⋊C4—24no—
629C2×C22⋊C4—24no—
630C2×C22⋊C4—24no—
631C2×C22⋊C4—24no—
632C2×C22⋊C4—24no—
633C2×C22⋊C4—24no—
634C2×C22⋊C4—24no—
635C2×C22⋊C4—24no—
636C2×C22⋊C4—24no—
637C2×C22⋊C4—24no—
638C2×C22⋊C4—24no—
639C2×C22⋊C4—232no—
640C2×C22⋊C4—42no—
641C2×C22⋊C4—42no—
642C2×C22⋊C4—42no—
643C2×C22⋊C4—42no—
644C2×C22⋊C4D4×C3118yes—
645C2×C22⋊C4D4×C3118yescomplemented
646C2×C22⋊C4C23×C3114yes—
647C2×C22⋊C4C23×C3114yes—
648C2×C22⋊C4C23×C3114yes—
649C2×C22⋊C4C23×C3114yes—
650C2×C22⋊C4C23×C3114yes—
651C2×C22⋊C4C23×C3114yes—
652C2×C22⋊C4C23×C3114yes—
653C2×C22⋊C4C23×C3114yes—
654C2×C22⋊C4C23×C3114yes—
655C2×C22⋊C4C23×C3114yes—
656C2×C22⋊C4C23×C3114yes—
657C2×C22⋊C4C23×C3114yes—
658C2×C22⋊C4C23×C3114yes—
659C2×C22⋊C4C23×C3114yescomplemented
660C2×C22⋊C4C23×C3114yescomplemented
661C2×C22⋊C4C23×C3114yescomplemented
662C2×C22⋊C4C23×C3114yescomplemented
663C2×C42—24no—
664C2×C42—42no—
665C2×C42C23×C3114yescomplemented
666C2×C42C23×C3114yescomplemented
667#95C23×C3114yescomplemented
668#95C23×C3114yescomplemented
669#95C23×C3114yescomplemented
670#95C23×C3114yescomplemented
671#95C23×C3114yescomplemented
672#95C23×C3114yescomplemented
673C31C2×#247211yescharacteristic, direct product factor, Sylow
674C24—22no—
675C24—22no—
676C24—22no—
677C24—22no—
678C24—232no—
679C24—28no—
680C24—22no—
681C24—22no—
682C24—22no—
683C24—28no—
684C24—28no—
685C24—22no—
686C24—22no—
687C24—22no—
688C24—22no—
689C24—22no—
690C24—22no—
691C24—22no—
692C24—22no—
693C24—22no—
694C24—22no—
695C24—28no—
696C24—22no—
697C24—22no—
698C24—22no—
699C24—22no—
700C24—28no—
701C24—22no—
702C24—22no—
703C24—44no—
704C24—44no—
705C24—416no—
706C24—416no—
707C24—416no—
708C24—416no—
709C24—416no—
710C24—416no—
711C24C2×D4×C3114yes—
712C24C2×D4×C3114yes—
713C24#41×C3114yes—
714C24#41×C3114yes—
715C24#41×C3114yes—
716C24C24×C3112yes—
717C24C24×C3112yes—
718C24C24×C3112yes—
719C24C24×C3112yes—
720C24C24×C3111yescharacteristic
721C2×Q8—28no—
722C2×Q8—28no—
723C2×Q8—44no—
724C2×Q8—416no—
725C2×D4—28no—
726C2×D4—28no—
727C2×D4—28no—
728C2×D4—28no—
729C2×D4—28no—
730C2×D4—28no—
731C2×D4—28no—
732C2×D4—44no—
733C2×D4—44no—
734C2×D4—416no—
735C2×D4—416no—
736C2×D4—416no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—22no—
744C22×C4—22no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—28no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—22no—
757C22×C4—22no—
758C22×C4—28no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—28no—
769C22×C4—28no—
770C22×C4—44no—
771C22×C4—44no—
772C22×C4—416no—
773C22×C4—416no—
774C22×C4C2×D4×C3114yes—
775C22×C4C2×D4×C3114yes—
776C22×C4C2×D4×C3114yes—
777C22×C4C2×D4×C3114yes—
778C22×C4C24×C3112yes—
779C22×C4C24×C3112yes—
780C22×C4C24×C3112yes—
781C22×C4C24×C3112yes—
782C22×C4C24×C3112yes—
783C22×C4C24×C3112yes—
784C22×C4C24×C3112yes—
785C22×C4C24×C3112yes—
786C22×C4C24×C3112yes—
787C22×C4C24×C3112yes—
788C22×C4C24×C3112yes—
789C4⋊C4—28no—
790C4⋊C4—28no—
791C4⋊C4—28no—
792C22⋊C4—28no—
793C22⋊C4—28no—
794C22⋊C4—28no—
795C22⋊C4—28no—
796C22⋊C4—28no—
797C22⋊C4—28no—
798C22⋊C4—28no—
799C22⋊C4—28no—
800C22⋊C4—28no—
801C22⋊C4—28no—
802C22⋊C4—28no—
803C22⋊C4—44no—
804C22⋊C4—44no—
805C22⋊C4—44no—
806C22⋊C4—44no—
807C22⋊C4C2×D4×C31116yes—
808C22⋊C4C2×D4×C31116yescomplemented
809C42—28no—
810C42—44no—
811C23—28no—
812C23—28no—
813C23—28no—
814C23—28no—
815C23—28no—
816C23—28no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—232no—
822C23—28no—
823C23—28no—
824C23—28no—
825C23—28no—
826C23—28no—
827C23—28no—
828C23—22no—
829C23—22no—
830C23—22no—
831C23—22no—
832C23—22no—
833C23—22no—
834C23—22no—
835C23—22no—
836C23—22no—
837C23—22no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—22no—
842C23—22no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—416no—
848C23—416no—
849C23—416no—
850C23—416no—
851C23—416no—
852C23—4128no—
853C23—44no—
854C23—44no—
855C23—416no—
856C23—44no—
857C23—44no—
858C23—44no—
859C23—44no—
860C23—44no—
861C23—44no—
862C23—44no—
863C23—44no—
864C23—44no—
865C23—44no—
866C23—44no—
867C23—44no—
868C23—44no—
869C23C31×#124116yescomplemented
870C23C22×D4×C3114yes—
871C23C22×D4×C3114yes—
872C23C22×D4×C3112yes—
873C23C22×D4×C3112yes—
874C23C2×#41×C3114yes—
875C23C2×#41×C3114yes—
876C23C2×#41×C3114yes—
877C23C2×#41×C3112yes—
878C23C2×#41×C3112yes—
879C23C2×#41×C3112yes—
880C23C31×H(5,𝔽2)12yes—
881C23C31×H(5,𝔽2)12yes—
882C23C25×C3111yescharacteristic
883Q8—416no—
884D4—416no—
885D4—416no—
886D4—416no—
887C2×C4—28no—
888C2×C4—28no—
889C2×C4—28no—
890C2×C4—28no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—416no—
921C2×C4—416no—
922C2×C4—44no—
923C2×C4—44no—
924C2×C4—44no—
925C2×C4—44no—
926C2×C4—44no—
927C2×C4—44no—
928C2×C4—44no—
929C2×C4C22×D4×C3114yes—
930C2×C4C22×D4×C3114yes—
931C2×C4C22×D4×C3114yes—
932C2×C4C22×D4×C3114yes—
933C22—24no—
934C22—24no—
935C22—24no—
936C22—24no—
937C22—24no—
938C22—24no—
939C22—232no—
940C22—24no—
941C22—24no—
942C22—24no—
943C22—24no—
944C22—24no—
945C22—24no—
946C22—464no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—416no—
956C22—416no—
957C22—42no—
958C22—42no—
959C22—42no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—88no—
965C22C31×#52514yes—
966C22C2×C31×#12414yes—
967C22C2×C31×#12418yescomplemented
968C22C31×#53814yes—
969C22D42×C3114yes—
970C22C31×#54614yes—
971C22C31×#54614yes—
972C22C31×#55114yes—
973C22C23×D4×C3111yescharacteristic
974C22C23×D4×C3111yescharacteristic
975C22C22×#41×C3111yescharacteristic
976C22C22×#41×C3111yescharacteristic
977C22C22×#41×C3111yescharacteristic
978C22C2×C31×H(5,𝔽2)11yescharacteristic
979C22C2×C31×H(5,𝔽2)11yescharacteristic
980C4—24no—
981C4—24no—
982C4—24no—
983C4—24no—
984C4—42no—
985C4—42no—
986C4—42no—
987C4—42no—
988C4—42no—
989C4—42no—
990C4—42no—
991C2—28no—
992C2—44no—
993C2—44no—
994C2—82no—
995C2C31×#247218yesdirect product factor
996C2C2×C31×#52511yescharacteristic
997C2C22×C31×#12411yescharacteristic
998C2C2×C31×#53811yescharacteristic
999C2C2×D42×C3111yescharacteristic
1000C2C2×C31×#54611yescharacteristic
1001C2C2×C31×#54611yescharacteristic
1002C2C2×C31×#55111yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutator, Frattini, cosocleC23C25×C31
prime radicalC22×C31×#120C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C31×#124C2semidirect
2. C22×C31×C22⋊Q8C2semidirect
4. C23×C22⋊C4×C31C2semidirect
5. C31×#2472C2direct (N × H)
6. C2×C31×#397C2semidirect
7. C2×C31×#394C2semidirect
8. C2×C31×#394C2semidirect
9. C2×C31×#393C2semidirect
10. C2×C31×#390C2semidirect
11. C2×C31×#388C2semidirect
12. C2×C31×#388C2semidirect
13. C2×C31×#386C2semidirect
14. C2×C31×#386C2semidirect
15. C2×C31×#379C2semidirect
16. C2×C4×C22⋊C4×C31C2semidirect
18. C23×Q8×C31C22semidirect
25. C2×C31×#124C22semidirect
27. C2×C31×C22⋊Q8C22semidirect
30. C22×C4⋊C4×C31C22semidirect
31. C22×C4⋊C4×C31C22semidirect
32. C22×C4⋊C4×C31C22semidirect
47. C22×C22⋊C4×C31C22semidirect
48. C22×C22⋊C4×C31C22semidirect
49. C22×C22⋊C4×C31C22semidirect
50. C22×C22⋊C4×C31C22semidirect
51. C22×C22⋊C4×C31C22semidirect
52. C22×C42×C31C22semidirect
53. C22×C42×C31C22semidirect
54. C31×#397C22semidirect
55. C31×#394C22semidirect
56. C31×#394C22semidirect
57. C31×#393C22semidirect
58. C31×#390C22semidirect
59. C31×#388C22semidirect
60. C31×#388C22semidirect
61. C31×#386C22semidirect
62. C31×#386C22semidirect
63. C31×#379C22semidirect
64. C4×C22⋊C4×C31C22semidirect
65. C2×C31×#95C22semidirect
66. C2×C31×#95C22semidirect
67. C2×C31×#95C22semidirect
68. C2×C31×#95C22semidirect
69. C2×C31×#95C22semidirect
70. C2×C31×#95C22semidirect
86. C22×Q8×C31C23semidirect
124. C2×C4⋊C4×C31C23semidirect
125. C2×C4⋊C4×C31C23semidirect
126. C2×C4⋊C4×C31C23semidirect
144. C2×C22⋊C4×C31D4semidirect
158. C2×C22⋊C4×C31C23semidirect
159. C2×C22⋊C4×C31C23semidirect
160. C2×C22⋊C4×C31C23semidirect
161. C2×C22⋊C4×C31C23semidirect
164. C2×C42×C31C23semidirect
165. C2×C42×C31C23semidirect
166. C31×#95C23semidirect
167. C31×#95C23semidirect
168. C31×#95C23semidirect
169. C31×#95C23semidirect
170. C31×#95C23semidirect
171. C31×#95C23semidirect
306. C22⋊C4×C31C2×D4semidirect
309. C2×#2472C31direct (N × H)
368. C23×C31#124semidirect
432. C22×#124C2×C31semidirect
433. C22×C22⋊Q8C2×C31semidirect
435. C23×C22⋊C4C2×C31semidirect
436. #2472C2×C31direct (N × H)
437. C2×#397C2×C31semidirect
438. C2×#394C2×C31semidirect
439. C2×#394C2×C31semidirect
440. C2×#393C2×C31semidirect
441. C2×#390C2×C31semidirect
442. C2×#388C2×C31semidirect
443. C2×#388C2×C31semidirect
444. C2×#386C2×C31semidirect
445. C2×#386C2×C31semidirect
446. C2×#379C2×C31semidirect
447. C2×C4×C22⋊C4C2×C31semidirect
482. C22×C31C2×#124semidirect
507. C23×Q8C22×C31semidirect
514. C2×#124C22×C31semidirect
516. C2×C22⋊Q8C22×C31semidirect
519. C22×C4⋊C4C22×C31semidirect
520. C22×C4⋊C4C22×C31semidirect
521. C22×C4⋊C4C22×C31semidirect
536. C22×C22⋊C4C22×C31semidirect
537. C22×C22⋊C4C22×C31semidirect
538. C22×C22⋊C4C22×C31semidirect
539. C22×C22⋊C4C22×C31semidirect
540. C22×C22⋊C4C22×C31semidirect
541. C22×C42C22×C31semidirect
542. C22×C42C22×C31semidirect
543. #397C22×C31semidirect
544. #394C22×C31semidirect
545. #394C22×C31semidirect
546. #393C22×C31semidirect
547. #390C22×C31semidirect
548. #388C22×C31semidirect
549. #388C22×C31semidirect
550. #386C22×C31semidirect
551. #386C22×C31semidirect
552. #379C22×C31semidirect
553. C4×C22⋊C4C22×C31semidirect
554. C2×#95C22×C31semidirect
555. C2×#95C22×C31semidirect
556. C2×#95C22×C31semidirect
557. C2×#95C22×C31semidirect
558. C2×#95C22×C31semidirect
559. C2×#95C22×C31semidirect
564. C2×C31#2472direct (N × H)
587. C22×Q8C23×C31semidirect
625. C2×C4⋊C4C23×C31semidirect
626. C2×C4⋊C4C23×C31semidirect
627. C2×C4⋊C4C23×C31semidirect
645. C2×C22⋊C4D4×C31semidirect
659. C2×C22⋊C4C23×C31semidirect
660. C2×C22⋊C4C23×C31semidirect
661. C2×C22⋊C4C23×C31semidirect
662. C2×C22⋊C4C23×C31semidirect
665. C2×C42C23×C31semidirect
666. C2×C42C23×C31semidirect
667. #95C23×C31semidirect
668. #95C23×C31semidirect
669. #95C23×C31semidirect
670. #95C23×C31semidirect
671. #95C23×C31semidirect
672. #95C23×C31semidirect
673. C31C2×#2472direct (N × H)
808. C22⋊C4C2×D4×C31semidirect
869. C23C31×#124semidirect
967. C22C2×C31×#124semidirect
995. C2C31×#2472direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C31×#1242
C22×C31×C22⋊Q82
C22×C31×#1202
C23×C22⋊C4×C312
C31×#24722
C2×C31×#3972
C2×C31×#3942
C2×C31×#3932
C2×C31×#3902
C2×C31×#3882
C2×C31×#3862
C2×C31×#3792
C2×C4×C22⋊C4×C312
C2×#247231