Finite Group Databasebeta

← C37×#13967 #22635220

Subgroups — C37×#13967 #22635220

Order 9472.

4478 conjugacy classes of subgroups.

The subgroup lattice has 1062 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#120×C37C211yesmaximal, characteristic
2C22×C4×D4×C37C211yesmaximal, characteristic, complemented
3C23×C22⋊C4×C37C211yesmaximal, characteristic, complemented
4C2×C37×#386C211yesmaximal, characteristic, complemented
5C2×C37×#386C212yesmaximal, complemented
6C2×C37×#379C211yesmaximal, characteristic, complemented
7C37×#1439C212yesmaximal, complemented
8C37×#1438C212yesmaximal, complemented
9C37×#1437C212yesmaximal, complemented
10C37×C22⋊#95C211yesmaximal, characteristic, complemented
11C37×C22⋊#95C211yesmaximal, characteristic, complemented
12C26×C37C2211yescharacteristic
13C23×D4×C37C2212yes—
14C23×D4×C37C2211yescharacteristic
15C24×C4×C37C2211yescharacteristic
16C24×C4×C37C2211yescharacteristic
17C24×C4×C37C2211yescharacteristic, complemented
18C2×#120×C37—24no—
19C2×#120×C37—24no—
20C2×#120×C37C418yescomplemented
21C2×C4×D4×C37—24no—
22C2×C4×D4×C37—24no—
23C2×C4×D4×C37—24no—
24C22×C4⋊C4×C37C2211yescharacteristic, complemented
25C22×C22⋊C4×C37—24no—
26C22×C22⋊C4×C37—28no—
27C22×C22⋊C4×C37C2212yes—
28C22×C22⋊C4×C37C2211yescharacteristic
29C22×C22⋊C4×C37C2212yes—
30C22×C22⋊C4×C37C2212yes—
31C22×C22⋊C4×C37C2211yescharacteristic
32C22×C22⋊C4×C37C2212yes—
33C22×C22⋊C4×C37C2212yes—
34C22×C22⋊C4×C37C2211yescharacteristic
35C22×C22⋊C4×C37C2211yescharacteristic, complemented
36C22×C22⋊C4×C37C2212yescomplemented
37C22×C42×C37C2211yescharacteristic, complemented
38C37×#386—24no—
39C37×#386—28no—
40C37×#379—24no—
41C2×#95×C37C2212yescomplemented
42C2×#95×C37C2212yescomplemented
43C2×#95×C37C2212yescomplemented
44C2×#95×C37C2212yescomplemented
45C2×#95×C37C2212yescomplemented
46C25×C37—24no—
47C25×C37—22no—
48C25×C37—24no—
49C25×C37—22no—
50C25×C37—22no—
51C25×C37—22no—
52C25×C37—22no—
53C25×C37—22no—
54C25×C37—42no—
55C25×C37—42no—
56C25×C37C2×C414yescomplemented
57C25×C37C2311yescharacteristic
58C25×C37C2312yes—
59C25×C37C2311yescharacteristic
60C22×D4×C37—22no—
61C22×D4×C37—22no—
62C22×D4×C37—22no—
63C22×D4×C37—22no—
64C22×D4×C37—24no—
65C22×D4×C37—24no—
66C22×D4×C37—24no—
67C22×D4×C37—24no—
68C22×D4×C37—42no—
69C22×D4×C37—42no—
70C22×D4×C37C2×C414yes—
71C22×D4×C37C2×C418yescomplemented
72C22×D4×C37D414yes—
73C22×D4×C37D414yes—
74C23×C4×C37—22no—
75C23×C4×C37—22no—
76C23×C4×C37—22no—
77C23×C4×C37—22no—
78C23×C4×C37—24no—
79C23×C4×C37—24no—
80C23×C4×C37—22no—
81C23×C4×C37—22no—
82C23×C4×C37—22no—
83C23×C4×C37—22no—
84C23×C4×C37—24no—
85C23×C4×C37—42no—
86C23×C4×C37—42no—
87C23×C4×C37—42no—
88C23×C4×C37D414yescomplemented
89C23×C4×C37C2312yes—
90C23×C4×C37C2312yes—
91C23×C4×C37C2312yes—
92C23×C4×C37C2311yescharacteristic
93C23×C4×C37C2311yescharacteristic
94C23×C4×C37C2311yescharacteristic
95C23×C4×C37C2311yescharacteristic
96C23×C4×C37C2311yescharacteristic
97#120×C37—232no—
98C4×D4×C37—232no—
99C2×C4⋊C4×C37—22no—
100C2×C4⋊C4×C37—22no—
101C2×C4⋊C4×C37—22no—
102C2×C22⋊C4×C37—232no—
103C2×C22⋊C4×C37—22no—
104C2×C22⋊C4×C37—22no—
105C2×C22⋊C4×C37—24no—
106C2×C22⋊C4×C37—22no—
107C2×C22⋊C4×C37—22no—
108C2×C22⋊C4×C37—22no—
109C2×C22⋊C4×C37—24no—
110C2×C22⋊C4×C37—24no—
111C2×C22⋊C4×C37—24no—
112C2×C22⋊C4×C37—24no—
113C2×C22⋊C4×C37—24no—
114C2×C22⋊C4×C37—24no—
115C2×C22⋊C4×C37—22no—
116C2×C22⋊C4×C37—22no—
117C2×C22⋊C4×C37—22no—
118C2×C22⋊C4×C37—24no—
119C2×C22⋊C4×C37—22no—
120C2×C22⋊C4×C37—24no—
121C2×C22⋊C4×C37—24no—
122C2×C22⋊C4×C37—22no—
123C2×C22⋊C4×C37—24no—
124C2×C22⋊C4×C37—24no—
125C2×C22⋊C4×C37—24no—
126C2×C22⋊C4×C37—42no—
127C2×C22⋊C4×C37—42no—
128C2×C22⋊C4×C37—42no—
129C2×C22⋊C4×C37C2×C414yescomplemented
130C2×C22⋊C4×C37C2×C418yescomplemented
131C2×C22⋊C4×C37D414yescomplemented
132C2×C22⋊C4×C37D418yescomplemented
133C2×C42×C37—22no—
134C2×C42×C37—22no—
135C2×C42×C37—22no—
136#95×C37—24no—
137#95×C37—24no—
138#95×C37—24no—
139#95×C37—42no—
140#95×C37—42no—
141C24×C37—22no—
142C24×C37—22no—
143C24×C37—22no—
144C24×C37—22no—
145C24×C37—28no—
146C24×C37—28no—
147C24×C37—216no—
148C24×C37—28no—
149C24×C37—216no—
150C24×C37—22no—
151C24×C37—22no—
152C24×C37—22no—
153C24×C37—21no—
154C24×C37—21no—
155C24×C37—22no—
156C24×C37—22no—
157C24×C37—22no—
158C24×C37—21no—
159C24×C37—21no—
160C24×C37—22no—
161C24×C37—22no—
162C24×C37—22no—
163C24×C37—22no—
164C24×C37—22no—
165C24×C37—22no—
166C24×C37—22no—
167C24×C37—22no—
168C24×C37—22no—
169C24×C37—22no—
170C24×C37—28no—
171C24×C37—28no—
172C24×C37—48no—
173C24×C37—48no—
174C24×C37—48no—
175C24×C37—48no—
176C24×C37—48no—
177C24×C37—48no—
178C24×C37—48no—
179C24×C37—48no—
180C24×C37—48no—
181C24×C37—44no—
182C24×C37—44no—
183C24×C37—48no—
184C24×C37—44no—
185C24×C37—44no—
186C24×C37—44no—
187C24×C37—44no—
188C24×C37C22×C412yes—
189C24×C37C22×C414yes—
190C24×C37C22×C412yes—
191C24×C37C2×D412yes—
192C24×C37C2×D412yes—
193C24×C37C2×D414yes—
194C24×C37C2×D412yes—
195C24×C37C2×D412yes—
196C24×C37C2×D412yes—
197C24×C37C2×D412yes—
198C24×C37#4114yes—
199C24×C37#4112yes—
200C24×C37#4112yes—
201C24×C37C2411yescharacteristic
202C2×D4×C37—28no—
203C2×D4×C37—28no—
204C2×D4×C37—28no—
205C2×D4×C37—28no—
206C2×D4×C37—28no—
207C2×D4×C37—28no—
208C2×D4×C37—216no—
209C2×D4×C37—216no—
210C2×D4×C37—48no—
211C2×D4×C37—48no—
212C2×D4×C37—48no—
213C2×D4×C37—48no—
214C2×D4×C37—48no—
215C2×D4×C37C22⋊C4116yescomplemented
216C22×C4×C37—21no—
217C22×C4×C37—21no—
218C22×C4×C37—21no—
219C22×C4×C37—21no—
220C22×C4×C37—21no—
221C22×C4×C37—21no—
222C22×C4×C37—22no—
223C22×C4×C37—28no—
224C22×C4×C37—28no—
225C22×C4×C37—28no—
226C22×C4×C37—22no—
227C22×C4×C37—22no—
228C22×C4×C37—22no—
229C22×C4×C37—21no—
230C22×C4×C37—21no—
231C22×C4×C37—22no—
232C22×C4×C37—22no—
233C22×C4×C37—22no—
234C22×C4×C37—22no—
235C22×C4×C37—22no—
236C22×C4×C37—21no—
237C22×C4×C37—21no—
238C22×C4×C37—21no—
239C22×C4×C37—21no—
240C22×C4×C37—22no—
241C22×C4×C37—22no—
242C22×C4×C37—22no—
243C22×C4×C37—22no—
244C22×C4×C37—22no—
245C22×C4×C37—22no—
246C22×C4×C37—22no—
247C22×C4×C37—22no—
248C22×C4×C37—22no—
249C22×C4×C37—22no—
250C22×C4×C37—28no—
251C22×C4×C37—22no—
252C22×C4×C37—22no—
253C22×C4×C37—22no—
254C22×C4×C37—22no—
255C22×C4×C37—22no—
256C22×C4×C37—22no—
257C22×C4×C37—22no—
258C22×C4×C37—44no—
259C22×C4×C37—48no—
260C22×C4×C37—48no—
261C22×C4×C37—48no—
262C22×C4×C37—48no—
263C22×C4×C37—48no—
264C22×C4×C37—48no—
265C22×C4×C37—44no—
266C22×C4×C37—44no—
267C22×C4×C37—44no—
268C22×C4×C37—44no—
269C22×C4×C37C22×C414yes—
270C22×C4×C37C22×C412yes—
271C22×C4×C37C2×D414yes—
272C22×C4×C37C2×D412yes—
273C22×C4×C37C2×D412yes—
274C22×C4×C37C2×D412yes—
275C22×C4×C37C2×D412yes—
276C22×C4×C37C2×D412yes—
277C22×C4×C37C2×D414yes—
278C22×C4×C37C2×D412yes—
279C4⋊C4×C37—28no—
280C22⋊C4×C37—216no—
281C22⋊C4×C37—28no—
282C22⋊C4×C37—28no—
283C22⋊C4×C37—28no—
284C22⋊C4×C37—216no—
285C22⋊C4×C37—216no—
286C22⋊C4×C37—48no—
287C22⋊C4×C37—48no—
288C22⋊C4×C37—48no—
289C22⋊C4×C37—44no—
290C42×C37—28no—
291C23×C37—24no—
292C23×C37—24no—
293C23×C37—22no—
294C23×C37—22no—
295C23×C37—24no—
296C23×C37—22no—
297C23×C37—22no—
298C23×C37—24no—
299C23×C37—24no—
300C23×C37—24no—
301C23×C37—24no—
302C23×C37—24no—
303C23×C37—24no—
304C23×C37—24no—
305C23×C37—24no—
306C23×C37—24no—
307C23×C37—232no—
308C23×C37—24no—
309C23×C37—24no—
310C23×C37—22no—
311C23×C37—22no—
312C23×C37—24no—
313C23×C37—24no—
314C23×C37—24no—
315C23×C37—24no—
316C23×C37—24no—
317C23×C37—24no—
318C23×C37—24no—
319C23×C37—22no—
320C23×C37—22no—
321C23×C37—22no—
322C23×C37—22no—
323C23×C37—24no—
324C23×C37—24no—
325C23×C37—24no—
326C23×C37—24no—
327C23×C37—24no—
328C23×C37—24no—
329C23×C37—24no—
330C23×C37—24no—
331C23×C37—24no—
332C23×C37—24no—
333C23×C37—24no—
334C23×C37—24no—
335C23×C37—24no—
336C23×C37—24no—
337C23×C37—24no—
338C23×C37—432no—
339C23×C37—432no—
340C23×C37—416no—
341C23×C37—416no—
342C23×C37—416no—
343C23×C37—416no—
344C23×C37—432no—
345C23×C37—432no—
346C23×C37—416no—
347C23×C37—41no—
348C23×C37—42no—
349C23×C37—42no—
350C23×C37—42no—
351C23×C37—42no—
352C23×C37—41no—
353C23×C37—42no—
354C23×C37—41no—
355C23×C37—42no—
356C23×C37—41no—
357C23×C37—42no—
358C23×C37—42no—
359C23×C37—42no—
360C23×C37—42no—
361C23×C37—42no—
362C23×C37—42no—
363C23×C37—42no—
364C23×C37—42no—
365C23×C37—42no—
366C23×C37—42no—
367C23×C37—42no—
368C23×C37—42no—
369C23×C37—42no—
370C23×C37—42no—
371C23×C37—42no—
372C23×C37—42no—
373C23×C37—416no—
374C23×C37C2×C22⋊C414yes—
375C23×C37C2×C22⋊C414yescomplemented
376C23×C37C4×D414yes—
377C23×C37C4×D414yes—
378C23×C37C4×D418yescomplemented
379C23×C37#12014yes—
380C23×C37#12114yes—
381C23×C37#12114yes—
382C23×C37#12314yes—
383C23×C37C23×C411yescharacteristic
384C23×C37C22×D411yescharacteristic
385C23×C37C22×D411yescharacteristic
386C23×C37C22×D411yescharacteristic
387C23×C37C22×D411yescharacteristic
388C23×C37C22×D412yes—
389C23×C37C2×#4111yescharacteristic
390C23×C37C2×#4111yescharacteristic
391C23×C37C2×#4112yes—
392C23×C37H(5,𝔽2)12yes—
393C23×C37H(5,𝔽2)12yes—
394D4×C37—232no—
395D4×C37—432no—
396C2×C4×C37—22no—
397C2×C4×C37—22no—
398C2×C4×C37—22no—
399C2×C4×C37—22no—
400C2×C4×C37—22no—
401C2×C4×C37—22no—
402C2×C4×C37—22no—
403C2×C4×C37—22no—
404C2×C4×C37—24no—
405C2×C4×C37—24no—
406C2×C4×C37—24no—
407C2×C4×C37—24no—
408C2×C4×C37—24no—
409C2×C4×C37—22no—
410C2×C4×C37—22no—
411C2×C4×C37—24no—
412C2×C4×C37—22no—
413C2×C4×C37—22no—
414C2×C4×C37—22no—
415C2×C4×C37—24no—
416C2×C4×C37—24no—
417C2×C4×C37—24no—
418C2×C4×C37—24no—
419C2×C4×C37—416no—
420C2×C4×C37—416no—
421C2×C4×C37—416no—
422C2×C4×C37—41no—
423C2×C4×C37—42no—
424C2×C4×C37—41no—
425C2×C4×C37—41no—
426C2×C4×C37—41no—
427C2×C4×C37—42no—
428C2×C4×C37—42no—
429C2×C4×C37—42no—
430C2×C4×C37—42no—
431C2×C4×C37—42no—
432C2×C4×C37—42no—
433C2×C4×C37—42no—
434C2×C4×C37—42no—
435C2×C4×C37—42no—
436C2×C4×C37—42no—
437C2×C4×C37—42no—
438C2×C4×C37—42no—
439C2×C4×C37—42no—
440C2×C4×C37—42no—
441C2×C4×C37—42no—
442C2×C4×C37—42no—
443C2×C4×C37—42no—
444C2×C4×C37—42no—
445C2×C4×C37C2×C22⋊C414yescomplemented
446C2×C4×C37#12014yescomplemented
447#13967C3711yesmaximal, characteristic, direct product factor, Sylow
448C22×C37—24no—
449C22×C37—28no—
450C22×C37—28no—
451C22×C37—24no—
452C22×C37—24no—
453C22×C37—24no—
454C22×C37—28no—
455C22×C37—28no—
456C22×C37—24no—
457C22×C37—24no—
458C22×C37—28no—
459C22×C37—28no—
460C22×C37—28no—
461C22×C37—24no—
462C22×C37—28no—
463C22×C37—464no—
464C22×C37—42no—
465C22×C37—44no—
466C22×C37—44no—
467C22×C37—44no—
468C22×C37—44no—
469C22×C37—42no—
470C22×C37—44no—
471C22×C37—42no—
472C22×C37—44no—
473C22×C37—42no—
474C22×C37—44no—
475C22×C37—44no—
476C22×C37—44no—
477C22×C37—44no—
478C22×C37—44no—
479C22×C37—44no—
480C22×C37—44no—
481C22×C37—42no—
482C22×C37—44no—
483C22×C37—44no—
484C22×C37—42no—
485C22×C37#38618yescomplemented
486C22×C37C22×C22⋊C411yescharacteristic
487C22×C37C2×C4×D411yescharacteristic
488C22×C37C2×C4×D412yes—
489C22×C37C2×C4×D411yescharacteristic
490C22×C37#51812yes—
491C22×C37C2×#12011yescharacteristic
492C22×C37C2×#12011yescharacteristic
493C22×C37C2×#12111yescharacteristic
494C22×C37C2×#12111yescharacteristic
495C22×C37C2×#12311yescharacteristic
496C22×C37#52511yescharacteristic
497C22×C37#52512yes—
498C22×C37#53411yescharacteristic
499C22×C37#53511yescharacteristic
500C22×C37#53812yes—
501C22×C37D4212yes—
502C22×C37D4212yes—
503C22×C37D4212yes—
504C22×C37#54612yes—
505C22×C37#54612yes—
506C22×C37#54612yes—
507C22×C37#54612yes—
508C22×C37#55112yes—
509C4×C37—24no—
510C4×C37—24no—
511C4×C37—44no—
512C4×C37—42no—
513C4×C37—42no—
514C4×C37—42no—
515C4×C37—44no—
516C4×C37—82no—
517C22×#120C2×C3711yescharacteristic
518C22×C4×D4C2×C3711yescharacteristic, complemented
519C23×C22⋊C4C2×C3711yescharacteristic, complemented
520C2×#386C2×C3712yescomplemented
521C2×#386C2×C3711yescharacteristic, complemented
522C2×#379C2×C3711yescharacteristic, complemented
523#1439C2×C3712yescomplemented
524#1438C2×C3712yescomplemented
525#1437C2×C3712yescomplemented
526C22⋊#95C2×C3711yescharacteristic, complemented
527C22⋊#95C2×C3711yescharacteristic, complemented
528C2×C37—28no—
529C2×C37—44no—
530C2×C37—48no—
531C2×C37C2×#38611yescharacteristic
532C2×C37C4×#12011yescharacteristic
533C2×C37#232111yescharacteristic
534C2×C37D4×C22⋊C412yes—
535C2×C37#235812yes—
536C2×C37#240311yescharacteristic
537C2×C37#240411yescharacteristic
538C2×C37#240811yescharacteristic
539C2×C37#241812yes—
540C2×C37#242412yes—
541C2×C37#253411yescharacteristic
542C26C22×C3711yescharacteristic
543C23×D4C22×C3712yes—
544C23×D4C22×C3711yescharacteristic
545C24×C4C22×C3711yescharacteristic
546C24×C4C22×C3711yescharacteristic
547C24×C4C22×C3711yescharacteristic, complemented
548C2×#120—24no—
549C2×#120—24no—
550C2×#120C4×C3718yescomplemented
551C2×C4×D4—24no—
552C2×C4×D4—24no—
553C2×C4×D4—24no—
554C22×C4⋊C4C22×C3711yescharacteristic, complemented
555C22×C22⋊C4—24no—
556C22×C22⋊C4—28no—
557C22×C22⋊C4C22×C3712yes—
558C22×C22⋊C4C22×C3711yescharacteristic
559C22×C22⋊C4C22×C3712yes—
560C22×C22⋊C4C22×C3712yes—
561C22×C22⋊C4C22×C3711yescharacteristic
562C22×C22⋊C4C22×C3712yes—
563C22×C22⋊C4C22×C3712yes—
564C22×C22⋊C4C22×C3711yescharacteristic
565C22×C22⋊C4C22×C3711yescharacteristic, complemented
566C22×C22⋊C4C22×C3712yescomplemented
567C22×C42C22×C3711yescharacteristic, complemented
568#386—24no—
569#386—28no—
570#379—24no—
571C2×#95C22×C3712yescomplemented
572C2×#95C22×C3712yescomplemented
573C2×#95C22×C3712yescomplemented
574C2×#95C22×C3712yescomplemented
575C2×#95C22×C3712yescomplemented
576C37#1396711yescharacteristic, direct product factor, Sylow
577C25—24no—
578C25—22no—
579C25—24no—
580C25—22no—
581C25—22no—
582C25—22no—
583C25—22no—
584C25—22no—
585C25—42no—
586C25—42no—
587C25C2×C4×C3714yescomplemented
588C25C23×C3711yescharacteristic
589C25C23×C3712yes—
590C25C23×C3711yescharacteristic
591C22×D4—22no—
592C22×D4—22no—
593C22×D4—22no—
594C22×D4—22no—
595C22×D4—24no—
596C22×D4—24no—
597C22×D4—24no—
598C22×D4—24no—
599C22×D4—42no—
600C22×D4—42no—
601C22×D4C2×C4×C3714yes—
602C22×D4C2×C4×C3718yescomplemented
603C22×D4D4×C3714yes—
604C22×D4D4×C3714yes—
605C23×C4—22no—
606C23×C4—22no—
607C23×C4—22no—
608C23×C4—22no—
609C23×C4—24no—
610C23×C4—24no—
611C23×C4—22no—
612C23×C4—22no—
613C23×C4—22no—
614C23×C4—22no—
615C23×C4—24no—
616C23×C4—42no—
617C23×C4—42no—
618C23×C4—42no—
619C23×C4D4×C3714yescomplemented
620C23×C4C23×C3712yes—
621C23×C4C23×C3712yes—
622C23×C4C23×C3711yescharacteristic
623C23×C4C23×C3711yescharacteristic
624C23×C4C23×C3711yescharacteristic
625C23×C4C23×C3712yes—
626C23×C4C23×C3711yescharacteristic
627C23×C4C23×C3711yescharacteristic
628#120—232no—
629C4×D4—232no—
630C2×C4⋊C4—22no—
631C2×C4⋊C4—22no—
632C2×C4⋊C4—22no—
633C2×C22⋊C4—232no—
634C2×C22⋊C4—24no—
635C2×C22⋊C4—22no—
636C2×C22⋊C4—22no—
637C2×C22⋊C4—22no—
638C2×C22⋊C4—22no—
639C2×C22⋊C4—22no—
640C2×C22⋊C4—24no—
641C2×C22⋊C4—24no—
642C2×C22⋊C4—24no—
643C2×C22⋊C4—24no—
644C2×C22⋊C4—24no—
645C2×C22⋊C4—24no—
646C2×C22⋊C4—22no—
647C2×C22⋊C4—22no—
648C2×C22⋊C4—22no—
649C2×C22⋊C4—24no—
650C2×C22⋊C4—22no—
651C2×C22⋊C4—24no—
652C2×C22⋊C4—24no—
653C2×C22⋊C4—22no—
654C2×C22⋊C4—24no—
655C2×C22⋊C4—24no—
656C2×C22⋊C4—24no—
657C2×C22⋊C4—42no—
658C2×C22⋊C4—42no—
659C2×C22⋊C4—42no—
660C2×C22⋊C4C2×C4×C3714yescomplemented
661C2×C22⋊C4C2×C4×C3718yescomplemented
662C2×C22⋊C4D4×C3718yescomplemented
663C2×C22⋊C4D4×C3714yescomplemented
664C2×C42—22no—
665C2×C42—22no—
666C2×C42—22no—
667#95—24no—
668#95—24no—
669#95—24no—
670#95—42no—
671#95—42no—
672C24—22no—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—28no—
677C24—28no—
678C24—216no—
679C24—28no—
680C24—216no—
681C24—22no—
682C24—22no—
683C24—22no—
684C24—21no—
685C24—21no—
686C24—22no—
687C24—22no—
688C24—22no—
689C24—21no—
690C24—21no—
691C24—22no—
692C24—22no—
693C24—22no—
694C24—22no—
695C24—22no—
696C24—22no—
697C24—22no—
698C24—22no—
699C24—22no—
700C24—22no—
701C24—28no—
702C24—28no—
703C24—48no—
704C24—48no—
705C24—48no—
706C24—48no—
707C24—48no—
708C24—48no—
709C24—48no—
710C24—48no—
711C24—48no—
712C24—44no—
713C24—44no—
714C24—48no—
715C24—44no—
716C24—44no—
717C24—44no—
718C24—44no—
719C24C22×C4×C3712yes—
720C24C22×C4×C3714yes—
721C24C22×C4×C3712yes—
722C24C2×D4×C3712yes—
723C24C2×D4×C3712yes—
724C24C2×D4×C3714yes—
725C24C2×D4×C3712yes—
726C24C2×D4×C3712yes—
727C24C2×D4×C3712yes—
728C24C2×D4×C3712yes—
729C24#41×C3714yes—
730C24#41×C3712yes—
731C24#41×C3712yes—
732C24C24×C3711yescharacteristic
733C2×D4—28no—
734C2×D4—28no—
735C2×D4—28no—
736C2×D4—28no—
737C2×D4—28no—
738C2×D4—28no—
739C2×D4—216no—
740C2×D4—216no—
741C2×D4—48no—
742C2×D4—48no—
743C2×D4—48no—
744C2×D4—48no—
745C2×D4—48no—
746C2×D4C22⋊C4×C37116yescomplemented
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—22no—
754C22×C4—28no—
755C22×C4—28no—
756C22×C4—28no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—28no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—44no—
790C22×C4—48no—
791C22×C4—48no—
792C22×C4—48no—
793C22×C4—48no—
794C22×C4—48no—
795C22×C4—48no—
796C22×C4—44no—
797C22×C4—44no—
798C22×C4—44no—
799C22×C4—44no—
800C22×C4C22×C4×C3714yes—
801C22×C4C22×C4×C3712yes—
802C22×C4C2×D4×C3714yes—
803C22×C4C2×D4×C3712yes—
804C22×C4C2×D4×C3712yes—
805C22×C4C2×D4×C3712yes—
806C22×C4C2×D4×C3712yes—
807C22×C4C2×D4×C3712yes—
808C22×C4C2×D4×C3714yes—
809C22×C4C2×D4×C3712yes—
810C4⋊C4—28no—
811C22⋊C4—216no—
812C22⋊C4—28no—
813C22⋊C4—28no—
814C22⋊C4—28no—
815C22⋊C4—216no—
816C22⋊C4—216no—
817C22⋊C4—48no—
818C22⋊C4—48no—
819C22⋊C4—48no—
820C22⋊C4—44no—
821C42—28no—
822C23—22no—
823C23—22no—
824C23—24no—
825C23—22no—
826C23—22no—
827C23—24no—
828C23—24no—
829C23—24no—
830C23—24no—
831C23—24no—
832C23—24no—
833C23—24no—
834C23—24no—
835C23—24no—
836C23—24no—
837C23—24no—
838C23—232no—
839C23—24no—
840C23—22no—
841C23—22no—
842C23—22no—
843C23—22no—
844C23—24no—
845C23—24no—
846C23—24no—
847C23—24no—
848C23—24no—
849C23—24no—
850C23—24no—
851C23—24no—
852C23—24no—
853C23—24no—
854C23—24no—
855C23—24no—
856C23—24no—
857C23—24no—
858C23—24no—
859C23—24no—
860C23—22no—
861C23—22no—
862C23—24no—
863C23—24no—
864C23—24no—
865C23—24no—
866C23—24no—
867C23—24no—
868C23—24no—
869C23—432no—
870C23—432no—
871C23—416no—
872C23—416no—
873C23—416no—
874C23—432no—
875C23—432no—
876C23—416no—
877C23—416no—
878C23—41no—
879C23—42no—
880C23—42no—
881C23—42no—
882C23—42no—
883C23—41no—
884C23—42no—
885C23—41no—
886C23—42no—
887C23—42no—
888C23—41no—
889C23—42no—
890C23—42no—
891C23—42no—
892C23—42no—
893C23—42no—
894C23—42no—
895C23—42no—
896C23—42no—
897C23—42no—
898C23—42no—
899C23—42no—
900C23—42no—
901C23—42no—
902C23—42no—
903C23—42no—
904C23—416no—
905C23C2×C22⋊C4×C3714yes—
906C23C2×C22⋊C4×C3714yescomplemented
907C23C4×D4×C3714yes—
908C23C4×D4×C3714yes—
909C23C4×D4×C3718yescomplemented
910C23#120×C3714yes—
911C23#121×C3714yes—
912C23#121×C3714yes—
913C23#123×C3714yes—
914C23C23×C4×C3711yescharacteristic
915C23C22×D4×C3711yescharacteristic
916C23C22×D4×C3711yescharacteristic
917C23C22×D4×C3711yescharacteristic
918C23C22×D4×C3712yes—
919C23C22×D4×C3711yescharacteristic
920C23C2×#41×C3711yescharacteristic
921C23C2×#41×C3711yescharacteristic
922C23C2×#41×C3712yes—
923C23H(5,𝔽2)×C3712yes—
924C23H(5,𝔽2)×C3712yes—
925D4—232no—
926D4—432no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—24no—
934C2×C4—24no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—24no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—24no—
944C2×C4—24no—
945C2×C4—24no—
946C2×C4—24no—
947C2×C4—24no—
948C2×C4—24no—
949C2×C4—24no—
950C2×C4—416no—
951C2×C4—416no—
952C2×C4—416no—
953C2×C4—41no—
954C2×C4—42no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—42no—
958C2×C4—41no—
959C2×C4—42no—
960C2×C4—42no—
961C2×C4—42no—
962C2×C4—42no—
963C2×C4—42no—
964C2×C4—42no—
965C2×C4—42no—
966C2×C4—42no—
967C2×C4—42no—
968C2×C4—42no—
969C2×C4—42no—
970C2×C4—42no—
971C2×C4—42no—
972C2×C4—42no—
973C2×C4—42no—
974C2×C4—42no—
975C2×C4—42no—
976C2×C4C2×C22⋊C4×C3714yescomplemented
977C2×C4#120×C3714yescomplemented
978C22—28no—
979C22—24no—
980C22—24no—
981C22—24no—
982C22—28no—
983C22—28no—
984C22—24no—
985C22—24no—
986C22—24no—
987C22—28no—
988C22—28no—
989C22—24no—
990C22—28no—
991C22—28no—
992C22—28no—
993C22—464no—
994C22—44no—
995C22—44no—
996C22—42no—
997C22—44no—
998C22—44no—
999C22—42no—
1000C22—44no—
1001C22—42no—
1002C22—44no—
1003C22—44no—
1004C22—44no—
1005C22—44no—
1006C22—44no—
1007C22—44no—
1008C22—44no—
1009C22—42no—
1010C22—44no—
1011C22—42no—
1012C22—44no—
1013C22—42no—
1014C22—44no—
1015C22C37×#38618yescomplemented
1016C22C22×C22⋊C4×C3711yescharacteristic
1017C22C2×C4×D4×C3711yescharacteristic
1018C22C2×C4×D4×C3712yes—
1019C22C2×C4×D4×C3711yescharacteristic
1020C22C37×#51812yes—
1021C22C2×#120×C3711yescharacteristic
1022C22C2×#120×C3711yescharacteristic
1023C22C2×#121×C3711yescharacteristic
1024C22C2×#121×C3711yescharacteristic
1025C22C2×#123×C3711yescharacteristic
1026C22C37×#52511yescharacteristic
1027C22C37×#52512yes—
1028C22C37×#53411yescharacteristic
1029C22C37×#53511yescharacteristic
1030C22C37×#53812yes—
1031C22D42×C3712yes—
1032C22D42×C3712yes—
1033C22D42×C3712yes—
1034C22C37×#54612yes—
1035C22C37×#54612yes—
1036C22C37×#54612yes—
1037C22C37×#54612yes—
1038C22C37×#55112yes—
1039C4—24no—
1040C4—24no—
1041C4—42no—
1042C4—42no—
1043C4—42no—
1044C4—44no—
1045C4—44no—
1046C4—82no—
1047C2—28no—
1048C2—48no—
1049C2—44no—
1050C2C2×C37×#38611yescharacteristic
1051C2C4×#120×C3711yescharacteristic
1052C2C37×#232111yescharacteristic
1053C2D4×C22⋊C4×C3712yes—
1054C2C37×#235812yes—
1055C2C37×#240311yescharacteristic
1056C2C37×#240411yescharacteristic
1057C2C37×#240811yescharacteristic
1058C2C37×#241812yes—
1059C2C37×#242412yes—
1060C2C37×#253411yescharacteristic
subgroupG/H
center, socleC24×C37C24
commutatorC23C23×C4×C37
Frattini, cosocleC24C24×C37
prime radicalC22×#120×C37C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C4×D4×C37C2semidirect
3. C23×C22⋊C4×C37C2semidirect
4. C2×C37×#386C2semidirect
5. C2×C37×#386C2semidirect
6. C2×C37×#379C2semidirect
7. C37×#1439C2semidirect
8. C37×#1438C2semidirect
9. C37×#1437C2semidirect
10. C37×C22⋊#95C2semidirect
11. C37×C22⋊#95C2semidirect
17. C24×C4×C37C22semidirect
20. C2×#120×C37C4semidirect
24. C22×C4⋊C4×C37C22semidirect
35. C22×C22⋊C4×C37C22semidirect
36. C22×C22⋊C4×C37C22semidirect
37. C22×C42×C37C22semidirect
41. C2×#95×C37C22semidirect
42. C2×#95×C37C22semidirect
43. C2×#95×C37C22semidirect
44. C2×#95×C37C22semidirect
45. C2×#95×C37C22semidirect
56. C25×C37C2×C4semidirect
71. C22×D4×C37C2×C4semidirect
88. C23×C4×C37D4semidirect
129. C2×C22⋊C4×C37C2×C4semidirect
130. C2×C22⋊C4×C37C2×C4semidirect
131. C2×C22⋊C4×C37D4semidirect
132. C2×C22⋊C4×C37D4semidirect
215. C2×D4×C37C22⋊C4semidirect
375. C23×C37C2×C22⋊C4semidirect
378. C23×C37C4×D4semidirect
445. C2×C4×C37C2×C22⋊C4semidirect
446. C2×C4×C37#120semidirect
447. #13967C37direct (N × H)
485. C22×C37#386semidirect
518. C22×C4×D4C2×C37semidirect
519. C23×C22⋊C4C2×C37semidirect
520. C2×#386C2×C37semidirect
521. C2×#386C2×C37semidirect
522. C2×#379C2×C37semidirect
523. #1439C2×C37semidirect
524. #1438C2×C37semidirect
525. #1437C2×C37semidirect
526. C22⋊#95C2×C37semidirect
527. C22⋊#95C2×C37semidirect
547. C24×C4C22×C37semidirect
550. C2×#120C4×C37semidirect
554. C22×C4⋊C4C22×C37semidirect
565. C22×C22⋊C4C22×C37semidirect
566. C22×C22⋊C4C22×C37semidirect
567. C22×C42C22×C37semidirect
571. C2×#95C22×C37semidirect
572. C2×#95C22×C37semidirect
573. C2×#95C22×C37semidirect
574. C2×#95C22×C37semidirect
575. C2×#95C22×C37semidirect
576. C37#13967direct (N × H)
587. C25C2×C4×C37semidirect
602. C22×D4C2×C4×C37semidirect
619. C23×C4D4×C37semidirect
660. C2×C22⋊C4C2×C4×C37semidirect
661. C2×C22⋊C4C2×C4×C37semidirect
662. C2×C22⋊C4D4×C37semidirect
663. C2×C22⋊C4D4×C37semidirect
746. C2×D4C22⋊C4×C37semidirect
906. C23C2×C22⋊C4×C37semidirect
909. C23C4×D4×C37semidirect
976. C2×C4C2×C22⋊C4×C37semidirect
977. C2×C4#120×C37semidirect
1015. C22C37×#386semidirect

Maximal subgroups

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

subgroupindex
C22×#120×C372
C22×C4×D4×C372
C23×C22⋊C4×C372
C2×C37×#3862
C2×C37×#3792
C37×#14392
C37×#14382
C37×#14372
C37×C22⋊#952
#1396737