Finite Group Databasebeta

← C2×C37×#2424 #22655903

Subgroups — C2×C37×#2424 #22655903

Order 9472.

5898 conjugacy classes of subgroups.

The subgroup lattice has 1112 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#121×C37C211yesmaximal, characteristic, complemented
2C22×#121×C37C211yesmaximal, characteristic, complemented
3C22×#120×C37C211yesmaximal, characteristic, complemented
4C22×#120×C37C211yesmaximal, characteristic, complemented
5C22×C4×D4×C37C211yesmaximal, characteristic, complemented
6C23×C22⋊C4×C37C211yesmaximal, characteristic, complemented
7C37×#2424C2116yesmaximal, direct product factor
8C2×C37×#396C211yesmaximal, characteristic, complemented
9C2×C37×#394C211yesmaximal, characteristic, complemented
10C2×C37×#394C211yesmaximal, characteristic, complemented
11C2×C37×#392C211yesmaximal, characteristic, complemented
12C2×C37×#390C211yesmaximal, characteristic, complemented
13C2×C37×#388C211yesmaximal, characteristic, complemented
14C2×C37×#386C211yesmaximal, characteristic, complemented
15C2×C37×#386C211yesmaximal, characteristic, complemented
16C2×C37×#385C211yesmaximal, characteristic, complemented
17C26×C37C2211yescharacteristic
18C23×D4×C37C2211yescharacteristic
19C23×D4×C37C2211yescharacteristic
20C23×D4×C37C2211yescharacteristic
21C23×D4×C37C2211yescharacteristic
22C23×D4×C37C2211yescharacteristic
23C23×D4×C37C2211yescharacteristic
24C23×D4×C37C2211yescharacteristic, complemented
25C24×C4×C37C2211yescharacteristic
26C24×C4×C37C2211yescharacteristic
27C24×C4×C37C2211yescharacteristic, complemented
28C2×#121×C37—28no—
29C2×#121×C37—28no—
30C2×#121×C37C2218yescomplemented
31C2×#121×C37C2218yescomplemented
32C2×#120×C37—28no—
33C2×#120×C37—28no—
34C2×#120×C37C2218yescomplemented
35C2×#120×C37C2218yescomplemented
36C2×C4×D4×C37—28no—
37C2×C4×D4×C37C2218yescomplemented
38C22×C4⋊C4×C37C2211yescharacteristic, complemented
39C22×C4⋊C4×C37C2211yescharacteristic, complemented
40C22×C4⋊C4×C37C2211yescharacteristic, complemented
41C22×C4⋊C4×C37C2211yescharacteristic, complemented
42C22×C22⋊C4×C37—28no—
43C22×C22⋊C4×C37C2211yescharacteristic
44C22×C22⋊C4×C37C2211yescharacteristic
45C22×C22⋊C4×C37C2211yescharacteristic
46C22×C22⋊C4×C37C2211yescharacteristic
47C22×C22⋊C4×C37C2211yescharacteristic
48C22×C22⋊C4×C37C2211yescharacteristic
49C22×C22⋊C4×C37C2211yescharacteristic
50C22×C22⋊C4×C37C2211yescharacteristic
51C22×C22⋊C4×C37C2211yescharacteristic
52C22×C22⋊C4×C37C2211yescharacteristic
53C22×C22⋊C4×C37C2218yescomplemented
54C22×C22⋊C4×C37C2211yescharacteristic, complemented
55C22×C22⋊C4×C37C2211yescharacteristic, complemented
56C22×C22⋊C4×C37C2211yescharacteristic, complemented
57C22×C22⋊C4×C37C2211yescharacteristic, complemented
58C22×C22⋊C4×C37C2211yescharacteristic, complemented
59C22×C42×C37C2211yescharacteristic, complemented
60C37×#396C2218yescomplemented
61C37×#394C2218yescomplemented
62C37×#394C2218yescomplemented
63C37×#392C2218yescomplemented
64C37×#390C2218yescomplemented
65C37×#388C2218yescomplemented
66C37×#386C2218yescomplemented
67C37×#386C2218yescomplemented
68C37×#385C2218yescomplemented
69C2×#95×C37C2211yescharacteristic, complemented
70C2×#95×C37C2211yescharacteristic, complemented
71C2×#95×C37C2211yescharacteristic, complemented
72C2×#95×C37C2211yescharacteristic, complemented
73C25×C37—24no—
74C25×C37—24no—
75C25×C37—24no—
76C25×C37—24no—
77C25×C37—24no—
78C25×C37—42no—
79C25×C37—42no—
80C25×C37C2311yescharacteristic
81C25×C37C2311yescharacteristic
82C25×C37C2311yescharacteristic
83C25×C37C2311yescharacteristic
84C25×C37C2314yes—
85C25×C37C2311yescharacteristic
86C22×D4×C37—24no—
87C22×D4×C37—24no—
88C22×D4×C37—24no—
89C22×D4×C37—24no—
90C22×D4×C37—24no—
91C22×D4×C37—24no—
92C22×D4×C37—24no—
93C22×D4×C37—24no—
94C22×D4×C37—24no—
95C22×D4×C37—24no—
96C22×D4×C37—24no—
97C22×D4×C37—24no—
98C22×D4×C37—24no—
99C22×D4×C37—24no—
100C22×D4×C37—24no—
101C22×D4×C37—42no—
102C22×D4×C37—42no—
103C22×D4×C37—42no—
104C22×D4×C37—42no—
105C22×D4×C37—42no—
106C22×D4×C37D418yescomplemented
107C22×D4×C37C2314yes—
108C22×D4×C37C2314yes—
109C22×D4×C37C2314yes—
110C22×D4×C37C2314yes—
111C22×D4×C37C2314yes—
112C22×D4×C37C2314yes—
113C22×D4×C37C2314yescomplemented
114C23×C4×C37—24no—
115C23×C4×C37—24no—
116C23×C4×C37—24no—
117C23×C4×C37—24no—
118C23×C4×C37—24no—
119C23×C4×C37—24no—
120C23×C4×C37—42no—
121C23×C4×C37—42no—
122C23×C4×C37—42no—
123C23×C4×C37C2311yescharacteristic
124C23×C4×C37C2311yescharacteristic
125C23×C4×C37C2311yescharacteristic
126C23×C4×C37C2311yescharacteristic
127C23×C4×C37C2311yescharacteristic
128C23×C4×C37C2314yes—
129C23×C4×C37C2314yes—
130C23×C4×C37C2311yescharacteristic
131C23×C4×C37C2311yescharacteristic
132C23×C4×C37C2311yescharacteristic
133C23×C4×C37C2311yescharacteristic
134C23×C4×C37C2311yescharacteristic
135C23×C4×C37C2314yescomplemented
136#121×C37—232no—
137#121×C37—232no—
138#120×C37—232no—
139#120×C37—232no—
140C4×D4×C37—232no—
141C2×C4⋊C4×C37—24no—
142C2×C4⋊C4×C37—24no—
143C2×C4⋊C4×C37—24no—
144C2×C4⋊C4×C37—42no—
145C2×C4⋊C4×C37C2314yescomplemented
146C2×C4⋊C4×C37C2314yescomplemented
147C2×C4⋊C4×C37C2314yescomplemented
148C2×C4⋊C4×C37C2314yescomplemented
149C2×C22⋊C4×C37—24no—
150C2×C22⋊C4×C37—24no—
151C2×C22⋊C4×C37—24no—
152C2×C22⋊C4×C37—24no—
153C2×C22⋊C4×C37—24no—
154C2×C22⋊C4×C37—24no—
155C2×C22⋊C4×C37—24no—
156C2×C22⋊C4×C37—24no—
157C2×C22⋊C4×C37—24no—
158C2×C22⋊C4×C37—24no—
159C2×C22⋊C4×C37—24no—
160C2×C22⋊C4×C37—24no—
161C2×C22⋊C4×C37—232no—
162C2×C22⋊C4×C37—42no—
163C2×C22⋊C4×C37D418yescomplemented
164C2×C22⋊C4×C37D418yescomplemented
165C2×C22⋊C4×C37C2314yes—
166C2×C22⋊C4×C37C2314yes—
167C2×C22⋊C4×C37C2314yes—
168C2×C22⋊C4×C37C2314yes—
169C2×C22⋊C4×C37C2314yes—
170C2×C22⋊C4×C37C2314yes—
171C2×C22⋊C4×C37C2314yes—
172C2×C22⋊C4×C37C2314yes—
173C2×C22⋊C4×C37C2314yes—
174C2×C22⋊C4×C37C2314yes—
175C2×C22⋊C4×C37C2314yescomplemented
176C2×C22⋊C4×C37C2314yescomplemented
177C2×C22⋊C4×C37C2314yescomplemented
178C2×C22⋊C4×C37C2314yescomplemented
179C2×C22⋊C4×C37C2314yescomplemented
180C2×C42×C37—24no—
181C2×C42×C37C2314yescomplemented
182#95×C37C2314yescomplemented
183#95×C37C2314yescomplemented
184#95×C37C2314yescomplemented
185#95×C37C2314yescomplemented
186C24×C37—22no—
187C24×C37—22no—
188C24×C37—22no—
189C24×C37—22no—
190C24×C37—232no—
191C24×C37—28no—
192C24×C37—22no—
193C24×C37—22no—
194C24×C37—22no—
195C24×C37—22no—
196C24×C37—22no—
197C24×C37—22no—
198C24×C37—22no—
199C24×C37—22no—
200C24×C37—22no—
201C24×C37—28no—
202C24×C37—28no—
203C24×C37—22no—
204C24×C37—22no—
205C24×C37—22no—
206C24×C37—22no—
207C24×C37—22no—
208C24×C37—22no—
209C24×C37—22no—
210C24×C37—22no—
211C24×C37—22no—
212C24×C37—22no—
213C24×C37—22no—
214C24×C37—28no—
215C24×C37—28no—
216C24×C37—22no—
217C24×C37—22no—
218C24×C37—22no—
219C24×C37—22no—
220C24×C37—22no—
221C24×C37—44no—
222C24×C37—44no—
223C24×C37—416no—
224C24×C37—416no—
225C24×C37—416no—
226C24×C37—416no—
227C24×C37—416no—
228C24×C37—416no—
229C24×C37C2×D414yes—
230C24×C37C2×D414yes—
231C24×C37C2×D414yes—
232C24×C37C2×D414yes—
233C24×C37#4114yes—
234C24×C37#4114yes—
235C24×C37C2412yes—
236C24×C37C2412yes—
237C24×C37C2412yes—
238C24×C37C2412yes—
239C24×C37C2412yes—
240C24×C37C2411yescharacteristic
241C2×D4×C37—232no—
242C2×D4×C37—28no—
243C2×D4×C37—28no—
244C2×D4×C37—28no—
245C2×D4×C37—28no—
246C2×D4×C37—28no—
247C2×D4×C37—28no—
248C2×D4×C37—28no—
249C2×D4×C37—28no—
250C2×D4×C37—28no—
251C2×D4×C37—28no—
252C2×D4×C37—28no—
253C2×D4×C37—28no—
254C2×D4×C37—28no—
255C2×D4×C37—28no—
256C2×D4×C37—28no—
257C2×D4×C37—44no—
258C2×D4×C37—44no—
259C2×D4×C37—44no—
260C2×D4×C37—44no—
261C2×D4×C37—44no—
262C2×D4×C37—416no—
263C2×D4×C37—416no—
264C2×D4×C37—416no—
265C2×D4×C37—416no—
266C2×D4×C37—416no—
267C2×D4×C37—416no—
268C2×D4×C37C2×D4116yescomplemented
269C22×C4×C37—22no—
270C22×C4×C37—22no—
271C22×C4×C37—22no—
272C22×C4×C37—22no—
273C22×C4×C37—22no—
274C22×C4×C37—22no—
275C22×C4×C37—22no—
276C22×C4×C37—22no—
277C22×C4×C37—22no—
278C22×C4×C37—22no—
279C22×C4×C37—22no—
280C22×C4×C37—22no—
281C22×C4×C37—22no—
282C22×C4×C37—22no—
283C22×C4×C37—22no—
284C22×C4×C37—22no—
285C22×C4×C37—22no—
286C22×C4×C37—22no—
287C22×C4×C37—22no—
288C22×C4×C37—28no—
289C22×C4×C37—28no—
290C22×C4×C37—22no—
291C22×C4×C37—22no—
292C22×C4×C37—22no—
293C22×C4×C37—22no—
294C22×C4×C37—22no—
295C22×C4×C37—22no—
296C22×C4×C37—28no—
297C22×C4×C37—28no—
298C22×C4×C37—28no—
299C22×C4×C37—28no—
300C22×C4×C37—44no—
301C22×C4×C37—44no—
302C22×C4×C37—44no—
303C22×C4×C37—416no—
304C22×C4×C37—416no—
305C22×C4×C37—416no—
306C22×C4×C37C2×D414yes—
307C22×C4×C37C2×D414yes—
308C22×C4×C37C2×D414yes—
309C22×C4×C37C2×D414yes—
310C22×C4×C37C2×D414yes—
311C22×C4×C37C2412yes—
312C22×C4×C37C2412yes—
313C22×C4×C37C2412yes—
314C22×C4×C37C2412yes—
315C22×C4×C37C2412yes—
316C22×C4×C37C2412yes—
317C22×C4×C37C2412yes—
318C22×C4×C37C2412yes—
319C22×C4×C37C2412yes—
320C22×C4×C37C2412yes—
321C4⋊C4×C37—28no—
322C4⋊C4×C37—28no—
323C4⋊C4×C37—28no—
324C4⋊C4×C37—44no—
325C22⋊C4×C37—28no—
326C22⋊C4×C37—28no—
327C22⋊C4×C37—28no—
328C22⋊C4×C37—28no—
329C22⋊C4×C37—28no—
330C22⋊C4×C37—28no—
331C22⋊C4×C37—28no—
332C22⋊C4×C37—28no—
333C22⋊C4×C37—28no—
334C22⋊C4×C37—28no—
335C22⋊C4×C37—28no—
336C22⋊C4×C37—28no—
337C22⋊C4×C37—44no—
338C22⋊C4×C37C2×D4116yescomplemented
339C22⋊C4×C37C2×D4116yescomplemented
340C42×C37—28no—
341C23×C37—28no—
342C23×C37—28no—
343C23×C37—28no—
344C23×C37—28no—
345C23×C37—28no—
346C23×C37—28no—
347C23×C37—22no—
348C23×C37—22no—
349C23×C37—22no—
350C23×C37—22no—
351C23×C37—232no—
352C23×C37—28no—
353C23×C37—28no—
354C23×C37—28no—
355C23×C37—28no—
356C23×C37—28no—
357C23×C37—28no—
358C23×C37—28no—
359C23×C37—28no—
360C23×C37—28no—
361C23×C37—22no—
362C23×C37—22no—
363C23×C37—22no—
364C23×C37—22no—
365C23×C37—22no—
366C23×C37—22no—
367C23×C37—22no—
368C23×C37—22no—
369C23×C37—22no—
370C23×C37—22no—
371C23×C37—22no—
372C23×C37—22no—
373C23×C37—22no—
374C23×C37—22no—
375C23×C37—22no—
376C23×C37—22no—
377C23×C37—22no—
378C23×C37—22no—
379C23×C37—22no—
380C23×C37—22no—
381C23×C37—22no—
382C23×C37—22no—
383C23×C37—22no—
384C23×C37—22no—
385C23×C37—22no—
386C23×C37—416no—
387C23×C37—416no—
388C23×C37—416no—
389C23×C37—416no—
390C23×C37—4128no—
391C23×C37—416no—
392C23×C37—44no—
393C23×C37—44no—
394C23×C37—416no—
395C23×C37—44no—
396C23×C37—44no—
397C23×C37—44no—
398C23×C37—44no—
399C23×C37—44no—
400C23×C37—44no—
401C23×C37—44no—
402C23×C37—44no—
403C23×C37—44no—
404C23×C37—44no—
405C23×C37—44no—
406C23×C37—44no—
407C23×C37—44no—
408C23×C37—44no—
409C23×C37—44no—
410C23×C37—44no—
411C23×C37—44no—
412C23×C37#121116yescomplemented
413C23×C37C22×D414yes—
414C23×C37C22×D414yes—
415C23×C37C22×D414yes—
416C23×C37C22×D414yes—
417C23×C37C22×D412yes—
418C23×C37C22×D412yes—
419C23×C37C22×D412yes—
420C23×C37C2×#4114yes—
421C23×C37C2×#4114yes—
422C23×C37C2×#4112yes—
423C23×C37C2×#4112yes—
424C23×C37H(5,𝔽2)12yes—
425C23×C37H(5,𝔽2)12yes—
426C23×C37C2511yescharacteristic
427D4×C37—232no—
428D4×C37—416no—
429D4×C37—416no—
430D4×C37—416no—
431D4×C37—416no—
432D4×C37—416no—
433D4×C37—416no—
434C2×C4×C37—28no—
435C2×C4×C37—28no—
436C2×C4×C37—28no—
437C2×C4×C37—28no—
438C2×C4×C37—28no—
439C2×C4×C37—22no—
440C2×C4×C37—22no—
441C2×C4×C37—22no—
442C2×C4×C37—22no—
443C2×C4×C37—22no—
444C2×C4×C37—22no—
445C2×C4×C37—22no—
446C2×C4×C37—22no—
447C2×C4×C37—22no—
448C2×C4×C37—22no—
449C2×C4×C37—22no—
450C2×C4×C37—22no—
451C2×C4×C37—22no—
452C2×C4×C37—22no—
453C2×C4×C37—22no—
454C2×C4×C37—22no—
455C2×C4×C37—22no—
456C2×C4×C37—22no—
457C2×C4×C37—22no—
458C2×C4×C37—22no—
459C2×C4×C37—22no—
460C2×C4×C37—22no—
461C2×C4×C37—22no—
462C2×C4×C37—22no—
463C2×C4×C37—22no—
464C2×C4×C37—416no—
465C2×C4×C37—416no—
466C2×C4×C37—416no—
467C2×C4×C37—44no—
468C2×C4×C37—44no—
469C2×C4×C37—44no—
470C2×C4×C37—44no—
471C2×C4×C37—44no—
472C2×C4×C37C22×D414yes—
473C2×C4×C37C22×D414yes—
474C2×C4×C37C22×D414yes—
475C2×C4×C37C22×D414yes—
476C2×C4×C37C22×D414yes—
477C2×#2424C3711yesmaximal, characteristic, direct product factor, Sylow
478C22×C37—24no—
479C22×C37—232no—
480C22×C37—24no—
481C22×C37—24no—
482C22×C37—24no—
483C22×C37—24no—
484C22×C37—24no—
485C22×C37—24no—
486C22×C37—24no—
487C22×C37—24no—
488C22×C37—24no—
489C22×C37—24no—
490C22×C37—24no—
491C22×C37—24no—
492C22×C37—24no—
493C22×C37—24no—
494C22×C37—464no—
495C22×C37—42no—
496C22×C37—42no—
497C22×C37—42no—
498C22×C37—416no—
499C22×C37—416no—
500C22×C37—416no—
501C22×C37—42no—
502C22×C37—42no—
503C22×C37—42no—
504C22×C37—42no—
505C22×C37—42no—
506C22×C37—42no—
507C22×C37—42no—
508C22×C37—42no—
509C22×C37—42no—
510C22×C37—42no—
511C22×C37—42no—
512C22×C37—42no—
513C22×C37—42no—
514C22×C37—42no—
515C22×C37—42no—
516C22×C37—42no—
517C22×C37—88no—
518C22×C37C2×#12114yes—
519C22×C37C2×#12118yescomplemented
520C22×C37#52514yes—
521C22×C37#53814yes—
522C22×C37D4214yes—
523C22×C37D4214yes—
524C22×C37#54614yes—
525C22×C37#54614yes—
526C22×C37C23×D411yescharacteristic
527C22×C37C23×D411yescharacteristic
528C22×C37C23×D411yescharacteristic
529C22×C37C22×#4111yescharacteristic
530C22×C37C22×#4111yescharacteristic
531C22×C37C2×H(5,𝔽2)11yescharacteristic
532C22×C37C2×H(5,𝔽2)11yescharacteristic
533C4×C37—24no—
534C4×C37—24no—
535C4×C37—24no—
536C4×C37—24no—
537C4×C37—24no—
538C4×C37—42no—
539C4×C37—42no—
540C4×C37—42no—
541C4×C37—42no—
542C4×C37—42no—
543C22×#121C2×C3711yescharacteristic, complemented
544C22×#121C2×C3711yescharacteristic, complemented
545C22×#120C2×C3711yescharacteristic, complemented
546C22×#120C2×C3711yescharacteristic, complemented
547C22×C4×D4C2×C3711yescharacteristic, complemented
548C23×C22⋊C4C2×C3711yescharacteristic, complemented
549#2424C2×C37116yesdirect product factor
550C2×#396C2×C3711yescharacteristic, complemented
551C2×#394C2×C3711yescharacteristic, complemented
552C2×#394C2×C3711yescharacteristic, complemented
553C2×#392C2×C3711yescharacteristic, complemented
554C2×#390C2×C3711yescharacteristic, complemented
555C2×#388C2×C3711yescharacteristic, complemented
556C2×#386C2×C3711yescharacteristic, complemented
557C2×#386C2×C3711yescharacteristic, complemented
558C2×#385C2×C3711yescharacteristic, complemented
559C2×C37—28no—
560C2×C37—44no—
561C2×C37—44no—
562C2×C37—44no—
563C2×C37—82no—
564C2×C37#242418yesdirect product factor
565C2×C37C22×#12111yescharacteristic
566C2×C37C2×#52511yescharacteristic
567C2×C37C2×#53811yescharacteristic
568C2×C37C2×D4211yescharacteristic
569C2×C37C2×D4211yescharacteristic
570C2×C37C2×#54611yescharacteristic
571C2×C37C2×#54611yescharacteristic
572C26C22×C3711yescharacteristic
573C23×D4C22×C3711yescharacteristic
574C23×D4C22×C3711yescharacteristic
575C23×D4C22×C3711yescharacteristic
576C23×D4C22×C3711yescharacteristic
577C23×D4C22×C3711yescharacteristic
578C23×D4C22×C3711yescharacteristic
579C23×D4C22×C3711yescharacteristic, complemented
580C24×C4C22×C3711yescharacteristic
581C24×C4C22×C3711yescharacteristic
582C24×C4C22×C3711yescharacteristic, complemented
583C2×#121—28no—
584C2×#121—28no—
585C2×#121C22×C3718yescomplemented
586C2×#121C22×C3718yescomplemented
587C2×#120—28no—
588C2×#120—28no—
589C2×#120C22×C3718yescomplemented
590C2×#120C22×C3718yescomplemented
591C2×C4×D4—28no—
592C2×C4×D4C22×C3718yescomplemented
593C22×C4⋊C4C22×C3711yescharacteristic, complemented
594C22×C4⋊C4C22×C3711yescharacteristic, complemented
595C22×C4⋊C4C22×C3711yescharacteristic, complemented
596C22×C4⋊C4C22×C3711yescharacteristic, complemented
597C22×C22⋊C4—28no—
598C22×C22⋊C4C22×C3711yescharacteristic
599C22×C22⋊C4C22×C3711yescharacteristic
600C22×C22⋊C4C22×C3711yescharacteristic
601C22×C22⋊C4C22×C3711yescharacteristic
602C22×C22⋊C4C22×C3711yescharacteristic
603C22×C22⋊C4C22×C3711yescharacteristic
604C22×C22⋊C4C22×C3711yescharacteristic
605C22×C22⋊C4C22×C3711yescharacteristic
606C22×C22⋊C4C22×C3711yescharacteristic
607C22×C22⋊C4C22×C3711yescharacteristic
608C22×C22⋊C4C22×C3718yescomplemented
609C22×C22⋊C4C22×C3711yescharacteristic, complemented
610C22×C22⋊C4C22×C3711yescharacteristic, complemented
611C22×C22⋊C4C22×C3711yescharacteristic, complemented
612C22×C22⋊C4C22×C3711yescharacteristic, complemented
613C22×C22⋊C4C22×C3711yescharacteristic, complemented
614C22×C42C22×C3711yescharacteristic, complemented
615#396C22×C3718yescomplemented
616#394C22×C3718yescomplemented
617#394C22×C3718yescomplemented
618#392C22×C3718yescomplemented
619#390C22×C3718yescomplemented
620#388C22×C3718yescomplemented
621#386C22×C3718yescomplemented
622#386C22×C3718yescomplemented
623#385C22×C3718yescomplemented
624C2×#95C22×C3711yescharacteristic, complemented
625C2×#95C22×C3711yescharacteristic, complemented
626C2×#95C22×C3711yescharacteristic, complemented
627C2×#95C22×C3711yescharacteristic, complemented
628C37C2×#242411yescharacteristic, direct product factor, Sylow
629C25—24no—
630C25—24no—
631C25—24no—
632C25—24no—
633C25—24no—
634C25—42no—
635C25—42no—
636C25C23×C3711yescharacteristic
637C25C23×C3711yescharacteristic
638C25C23×C3711yescharacteristic
639C25C23×C3711yescharacteristic
640C25C23×C3714yes—
641C25C23×C3711yescharacteristic
642C22×D4—24no—
643C22×D4—24no—
644C22×D4—24no—
645C22×D4—24no—
646C22×D4—24no—
647C22×D4—24no—
648C22×D4—24no—
649C22×D4—24no—
650C22×D4—24no—
651C22×D4—24no—
652C22×D4—24no—
653C22×D4—24no—
654C22×D4—24no—
655C22×D4—24no—
656C22×D4—24no—
657C22×D4—42no—
658C22×D4—42no—
659C22×D4—42no—
660C22×D4—42no—
661C22×D4—42no—
662C22×D4D4×C3718yescomplemented
663C22×D4C23×C3714yes—
664C22×D4C23×C3714yes—
665C22×D4C23×C3714yes—
666C22×D4C23×C3714yes—
667C22×D4C23×C3714yes—
668C22×D4C23×C3714yes—
669C22×D4C23×C3714yescomplemented
670C23×C4—24no—
671C23×C4—24no—
672C23×C4—24no—
673C23×C4—24no—
674C23×C4—24no—
675C23×C4—24no—
676C23×C4—42no—
677C23×C4—42no—
678C23×C4—42no—
679C23×C4C23×C3711yescharacteristic
680C23×C4C23×C3711yescharacteristic
681C23×C4C23×C3711yescharacteristic
682C23×C4C23×C3711yescharacteristic
683C23×C4C23×C3711yescharacteristic
684C23×C4C23×C3714yes—
685C23×C4C23×C3714yes—
686C23×C4C23×C3711yescharacteristic
687C23×C4C23×C3711yescharacteristic
688C23×C4C23×C3711yescharacteristic
689C23×C4C23×C3711yescharacteristic
690C23×C4C23×C3711yescharacteristic
691C23×C4C23×C3714yescomplemented
692#121—232no—
693#121—232no—
694#120—232no—
695#120—232no—
696C4×D4—232no—
697C2×C4⋊C4—24no—
698C2×C4⋊C4—24no—
699C2×C4⋊C4—24no—
700C2×C4⋊C4—42no—
701C2×C4⋊C4C23×C3714yescomplemented
702C2×C4⋊C4C23×C3714yescomplemented
703C2×C4⋊C4C23×C3714yescomplemented
704C2×C4⋊C4C23×C3714yescomplemented
705C2×C22⋊C4—24no—
706C2×C22⋊C4—24no—
707C2×C22⋊C4—24no—
708C2×C22⋊C4—24no—
709C2×C22⋊C4—24no—
710C2×C22⋊C4—24no—
711C2×C22⋊C4—24no—
712C2×C22⋊C4—24no—
713C2×C22⋊C4—24no—
714C2×C22⋊C4—24no—
715C2×C22⋊C4—24no—
716C2×C22⋊C4—24no—
717C2×C22⋊C4—232no—
718C2×C22⋊C4—42no—
719C2×C22⋊C4D4×C3718yescomplemented
720C2×C22⋊C4D4×C3718yescomplemented
721C2×C22⋊C4C23×C3714yes—
722C2×C22⋊C4C23×C3714yes—
723C2×C22⋊C4C23×C3714yes—
724C2×C22⋊C4C23×C3714yes—
725C2×C22⋊C4C23×C3714yes—
726C2×C22⋊C4C23×C3714yes—
727C2×C22⋊C4C23×C3714yes—
728C2×C22⋊C4C23×C3714yes—
729C2×C22⋊C4C23×C3714yes—
730C2×C22⋊C4C23×C3714yes—
731C2×C22⋊C4C23×C3714yescomplemented
732C2×C22⋊C4C23×C3714yescomplemented
733C2×C22⋊C4C23×C3714yescomplemented
734C2×C22⋊C4C23×C3714yescomplemented
735C2×C22⋊C4C23×C3714yescomplemented
736C2×C42—24no—
737C2×C42C23×C3714yescomplemented
738#95C23×C3714yescomplemented
739#95C23×C3714yescomplemented
740#95C23×C3714yescomplemented
741#95C23×C3714yescomplemented
742C24—22no—
743C24—22no—
744C24—22no—
745C24—22no—
746C24—232no—
747C24—28no—
748C24—22no—
749C24—22no—
750C24—22no—
751C24—22no—
752C24—22no—
753C24—22no—
754C24—22no—
755C24—22no—
756C24—22no—
757C24—28no—
758C24—28no—
759C24—22no—
760C24—22no—
761C24—22no—
762C24—22no—
763C24—22no—
764C24—22no—
765C24—22no—
766C24—22no—
767C24—22no—
768C24—22no—
769C24—22no—
770C24—28no—
771C24—28no—
772C24—22no—
773C24—22no—
774C24—22no—
775C24—22no—
776C24—22no—
777C24—44no—
778C24—44no—
779C24—416no—
780C24—416no—
781C24—416no—
782C24—416no—
783C24—416no—
784C24—416no—
785C24C2×D4×C3714yes—
786C24C2×D4×C3714yes—
787C24C2×D4×C3714yes—
788C24C2×D4×C3714yes—
789C24#41×C3714yes—
790C24#41×C3714yes—
791C24C24×C3712yes—
792C24C24×C3712yes—
793C24C24×C3712yes—
794C24C24×C3712yes—
795C24C24×C3712yes—
796C24C24×C3711yescharacteristic
797C2×D4—232no—
798C2×D4—28no—
799C2×D4—28no—
800C2×D4—28no—
801C2×D4—28no—
802C2×D4—28no—
803C2×D4—28no—
804C2×D4—28no—
805C2×D4—28no—
806C2×D4—28no—
807C2×D4—28no—
808C2×D4—28no—
809C2×D4—28no—
810C2×D4—28no—
811C2×D4—28no—
812C2×D4—28no—
813C2×D4—44no—
814C2×D4—44no—
815C2×D4—44no—
816C2×D4—44no—
817C2×D4—44no—
818C2×D4—416no—
819C2×D4—416no—
820C2×D4—416no—
821C2×D4—416no—
822C2×D4—416no—
823C2×D4—416no—
824C2×D4C2×D4×C37116yescomplemented
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—22no—
841C22×C4—22no—
842C22×C4—22no—
843C22×C4—22no—
844C22×C4—28no—
845C22×C4—28no—
846C22×C4—22no—
847C22×C4—22no—
848C22×C4—22no—
849C22×C4—22no—
850C22×C4—22no—
851C22×C4—22no—
852C22×C4—28no—
853C22×C4—28no—
854C22×C4—28no—
855C22×C4—28no—
856C22×C4—44no—
857C22×C4—44no—
858C22×C4—44no—
859C22×C4—416no—
860C22×C4—416no—
861C22×C4—416no—
862C22×C4C2×D4×C3714yes—
863C22×C4C2×D4×C3714yes—
864C22×C4C2×D4×C3714yes—
865C22×C4C2×D4×C3714yes—
866C22×C4C2×D4×C3714yes—
867C22×C4C24×C3712yes—
868C22×C4C24×C3712yes—
869C22×C4C24×C3712yes—
870C22×C4C24×C3712yes—
871C22×C4C24×C3712yes—
872C22×C4C24×C3712yes—
873C22×C4C24×C3712yes—
874C22×C4C24×C3712yes—
875C22×C4C24×C3712yes—
876C22×C4C24×C3712yes—
877C4⋊C4—28no—
878C4⋊C4—28no—
879C4⋊C4—28no—
880C4⋊C4—44no—
881C22⋊C4—28no—
882C22⋊C4—28no—
883C22⋊C4—28no—
884C22⋊C4—28no—
885C22⋊C4—28no—
886C22⋊C4—28no—
887C22⋊C4—28no—
888C22⋊C4—28no—
889C22⋊C4—28no—
890C22⋊C4—28no—
891C22⋊C4—28no—
892C22⋊C4—28no—
893C22⋊C4—44no—
894C22⋊C4C2×D4×C37116yescomplemented
895C22⋊C4C2×D4×C37116yescomplemented
896C42—28no—
897C23—28no—
898C23—28no—
899C23—28no—
900C23—28no—
901C23—28no—
902C23—28no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—232no—
908C23—28no—
909C23—28no—
910C23—28no—
911C23—28no—
912C23—28no—
913C23—28no—
914C23—28no—
915C23—28no—
916C23—28no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—416no—
943C23—416no—
944C23—416no—
945C23—416no—
946C23—4128no—
947C23—416no—
948C23—44no—
949C23—44no—
950C23—416no—
951C23—44no—
952C23—44no—
953C23—44no—
954C23—44no—
955C23—44no—
956C23—44no—
957C23—44no—
958C23—44no—
959C23—44no—
960C23—44no—
961C23—44no—
962C23—44no—
963C23—44no—
964C23—44no—
965C23—44no—
966C23—44no—
967C23—44no—
968C23#121×C37116yescomplemented
969C23C22×D4×C3714yes—
970C23C22×D4×C3714yes—
971C23C22×D4×C3714yes—
972C23C22×D4×C3714yes—
973C23C22×D4×C3712yes—
974C23C22×D4×C3712yes—
975C23C22×D4×C3712yes—
976C23C2×#41×C3714yes—
977C23C2×#41×C3714yes—
978C23C2×#41×C3712yes—
979C23C2×#41×C3712yes—
980C23H(5,𝔽2)×C3712yes—
981C23H(5,𝔽2)×C3712yes—
982C23C25×C3711yescharacteristic
983D4—232no—
984D4—416no—
985D4—416no—
986D4—416no—
987D4—416no—
988D4—416no—
989D4—416no—
990C2×C4—28no—
991C2×C4—28no—
992C2×C4—28no—
993C2×C4—28no—
994C2×C4—28no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—416no—
1021C2×C4—416no—
1022C2×C4—416no—
1023C2×C4—44no—
1024C2×C4—44no—
1025C2×C4—44no—
1026C2×C4—44no—
1027C2×C4—44no—
1028C2×C4C22×D4×C3714yes—
1029C2×C4C22×D4×C3714yes—
1030C2×C4C22×D4×C3714yes—
1031C2×C4C22×D4×C3714yes—
1032C2×C4C22×D4×C3714yes—
1033C22—24no—
1034C22—232no—
1035C22—24no—
1036C22—24no—
1037C22—24no—
1038C22—24no—
1039C22—24no—
1040C22—24no—
1041C22—24no—
1042C22—24no—
1043C22—24no—
1044C22—24no—
1045C22—24no—
1046C22—24no—
1047C22—24no—
1048C22—24no—
1049C22—464no—
1050C22—42no—
1051C22—42no—
1052C22—42no—
1053C22—416no—
1054C22—416no—
1055C22—416no—
1056C22—42no—
1057C22—42no—
1058C22—42no—
1059C22—42no—
1060C22—42no—
1061C22—42no—
1062C22—42no—
1063C22—42no—
1064C22—42no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22—42no—
1070C22—42no—
1071C22—42no—
1072C22—88no—
1073C22C2×#121×C3714yes—
1074C22C2×#121×C3718yescomplemented
1075C22C37×#52514yes—
1076C22C37×#53814yes—
1077C22D42×C3714yes—
1078C22D42×C3714yes—
1079C22C37×#54614yes—
1080C22C37×#54614yes—
1081C22C23×D4×C3711yescharacteristic
1082C22C23×D4×C3711yescharacteristic
1083C22C23×D4×C3711yescharacteristic
1084C22C22×#41×C3711yescharacteristic
1085C22C22×#41×C3711yescharacteristic
1086C22C2×H(5,𝔽2)×C3711yescharacteristic
1087C22C2×H(5,𝔽2)×C3711yescharacteristic
1088C4—24no—
1089C4—24no—
1090C4—24no—
1091C4—24no—
1092C4—24no—
1093C4—42no—
1094C4—42no—
1095C4—42no—
1096C4—42no—
1097C4—42no—
1098C2—28no—
1099C2—44no—
1100C2—44no—
1101C2—44no—
1102C2—82no—
1103C2C37×#242418yesdirect product factor
1104C2C22×#121×C3711yescharacteristic
1105C2C2×C37×#52511yescharacteristic
1106C2C2×C37×#53811yescharacteristic
1107C2C2×D42×C3711yescharacteristic
1108C2C2×D42×C3711yescharacteristic
1109C2C2×C37×#54611yescharacteristic
1110C2C2×C37×#54611yescharacteristic
subgroupG/H
center, socleC24×C37C24
commutator, Frattini, cosocleC23C25×C37
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#121×C37C2semidirect
2. C22×#121×C37C2semidirect
3. C22×#120×C37C2semidirect
4. C22×#120×C37C2semidirect
5. C22×C4×D4×C37C2semidirect
6. C23×C22⋊C4×C37C2semidirect
7. C37×#2424C2direct (N × H)
8. C2×C37×#396C2semidirect
9. C2×C37×#394C2semidirect
10. C2×C37×#394C2semidirect
11. C2×C37×#392C2semidirect
12. C2×C37×#390C2semidirect
13. C2×C37×#388C2semidirect
14. C2×C37×#386C2semidirect
15. C2×C37×#386C2semidirect
16. C2×C37×#385C2semidirect
24. C23×D4×C37C22semidirect
27. C24×C4×C37C22semidirect
30. C2×#121×C37C22semidirect
31. C2×#121×C37C22semidirect
34. C2×#120×C37C22semidirect
35. C2×#120×C37C22semidirect
37. C2×C4×D4×C37C22semidirect
38. C22×C4⋊C4×C37C22semidirect
39. C22×C4⋊C4×C37C22semidirect
40. C22×C4⋊C4×C37C22semidirect
41. C22×C4⋊C4×C37C22semidirect
53. C22×C22⋊C4×C37C22semidirect
54. C22×C22⋊C4×C37C22semidirect
55. C22×C22⋊C4×C37C22semidirect
56. C22×C22⋊C4×C37C22semidirect
57. C22×C22⋊C4×C37C22semidirect
58. C22×C22⋊C4×C37C22semidirect
59. C22×C42×C37C22semidirect
60. C37×#396C22semidirect
61. C37×#394C22semidirect
62. C37×#394C22semidirect
63. C37×#392C22semidirect
64. C37×#390C22semidirect
65. C37×#388C22semidirect
66. C37×#386C22semidirect
67. C37×#386C22semidirect
68. C37×#385C22semidirect
69. C2×#95×C37C22semidirect
70. C2×#95×C37C22semidirect
71. C2×#95×C37C22semidirect
72. C2×#95×C37C22semidirect
106. C22×D4×C37D4semidirect
113. C22×D4×C37C23semidirect
135. C23×C4×C37C23semidirect
145. C2×C4⋊C4×C37C23semidirect
146. C2×C4⋊C4×C37C23semidirect
147. C2×C4⋊C4×C37C23semidirect
148. C2×C4⋊C4×C37C23semidirect
163. C2×C22⋊C4×C37D4semidirect
164. C2×C22⋊C4×C37D4semidirect
175. C2×C22⋊C4×C37C23semidirect
176. C2×C22⋊C4×C37C23semidirect
177. C2×C22⋊C4×C37C23semidirect
178. C2×C22⋊C4×C37C23semidirect
179. C2×C22⋊C4×C37C23semidirect
181. C2×C42×C37C23semidirect
182. #95×C37C23semidirect
183. #95×C37C23semidirect
184. #95×C37C23semidirect
185. #95×C37C23semidirect
268. C2×D4×C37C2×D4semidirect
338. C22⋊C4×C37C2×D4semidirect
339. C22⋊C4×C37C2×D4semidirect
412. C23×C37#121semidirect
477. C2×#2424C37direct (N × H)
519. C22×C37C2×#121semidirect
543. C22×#121C2×C37semidirect
544. C22×#121C2×C37semidirect
545. C22×#120C2×C37semidirect
546. C22×#120C2×C37semidirect
547. C22×C4×D4C2×C37semidirect
548. C23×C22⋊C4C2×C37semidirect
549. #2424C2×C37direct (N × H)
550. C2×#396C2×C37semidirect
551. C2×#394C2×C37semidirect
552. C2×#394C2×C37semidirect
553. C2×#392C2×C37semidirect
554. C2×#390C2×C37semidirect
555. C2×#388C2×C37semidirect
556. C2×#386C2×C37semidirect
557. C2×#386C2×C37semidirect
558. C2×#385C2×C37semidirect
564. C2×C37#2424direct (N × H)
579. C23×D4C22×C37semidirect
582. C24×C4C22×C37semidirect
585. C2×#121C22×C37semidirect
586. C2×#121C22×C37semidirect
589. C2×#120C22×C37semidirect
590. C2×#120C22×C37semidirect
592. C2×C4×D4C22×C37semidirect
593. C22×C4⋊C4C22×C37semidirect
594. C22×C4⋊C4C22×C37semidirect
595. C22×C4⋊C4C22×C37semidirect
596. C22×C4⋊C4C22×C37semidirect
608. C22×C22⋊C4C22×C37semidirect
609. C22×C22⋊C4C22×C37semidirect
610. C22×C22⋊C4C22×C37semidirect
611. C22×C22⋊C4C22×C37semidirect
612. C22×C22⋊C4C22×C37semidirect
613. C22×C22⋊C4C22×C37semidirect
614. C22×C42C22×C37semidirect
615. #396C22×C37semidirect
616. #394C22×C37semidirect
617. #394C22×C37semidirect
618. #392C22×C37semidirect
619. #390C22×C37semidirect
620. #388C22×C37semidirect
621. #386C22×C37semidirect
622. #386C22×C37semidirect
623. #385C22×C37semidirect
624. C2×#95C22×C37semidirect
625. C2×#95C22×C37semidirect
626. C2×#95C22×C37semidirect
627. C2×#95C22×C37semidirect
628. C37C2×#2424direct (N × H)
662. C22×D4D4×C37semidirect
669. C22×D4C23×C37semidirect
691. C23×C4C23×C37semidirect
701. C2×C4⋊C4C23×C37semidirect
702. C2×C4⋊C4C23×C37semidirect
703. C2×C4⋊C4C23×C37semidirect
704. C2×C4⋊C4C23×C37semidirect
719. C2×C22⋊C4D4×C37semidirect
720. C2×C22⋊C4D4×C37semidirect
731. C2×C22⋊C4C23×C37semidirect
732. C2×C22⋊C4C23×C37semidirect
733. C2×C22⋊C4C23×C37semidirect
734. C2×C22⋊C4C23×C37semidirect
735. C2×C22⋊C4C23×C37semidirect
737. C2×C42C23×C37semidirect
738. #95C23×C37semidirect
739. #95C23×C37semidirect
740. #95C23×C37semidirect
741. #95C23×C37semidirect
824. C2×D4C2×D4×C37semidirect
894. C22⋊C4C2×D4×C37semidirect
895. C22⋊C4C2×D4×C37semidirect
968. C23#121×C37semidirect
1074. C22C2×#121×C37semidirect
1103. C2C37×#2424direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#121×C372
C22×#120×C372
C22×C4×D4×C372
C23×C22⋊C4×C372
C37×#24242
C2×C37×#3962
C2×C37×#3942
C2×C37×#3922
C2×C37×#3902
C2×C37×#3882
C2×C37×#3862
C2×C37×#3852
C2×#242437