Finite Group Databasebeta

← C37×#25136 #22646389

Subgroups — C37×#25136 #22646389

Order 9472.

1264 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#468C211yesmaximal, characteristic, complemented
2C2×C37×#450C211yesmaximal, characteristic, complemented
3C2×C37×#436C211yesmaximal, characteristic, complemented
4C2×C37×#418C211yesmaximal, characteristic, complemented
5C37×#2415C211yesmaximal, characteristic, complemented
6C37×#2408C211yesmaximal, characteristic
7C37×#2067C211yesmaximal, characteristic, complemented
8C37×#2055C211yesmaximal, characteristic, complemented
9C37×#2034C211yesmaximal, characteristic, complemented
10C37×#2000C211yesmaximal, characteristic, complemented
11C37×#1968C211yesmaximal, characteristic, complemented
12C37×#1934C211yesmaximal, characteristic, complemented
13C37×#1895C211yesmaximal, characteristic, complemented
14C37×#1894C211yesmaximal, characteristic, complemented
15C37×#1854C211yesmaximal, characteristic, complemented
16C23×D4×C37C2211yescharacteristic
17C22×SD16×C37C2211yescharacteristic
18C22×SD16×C37C2211yescharacteristic
19C22×M16×C37C2211yescharacteristic
20C22×M16×C37C2211yescharacteristic, complemented
21C2×C22⋊Q8×C37C2211yescharacteristic
22C2×C22⋊Q8×C37C2211yescharacteristic, complemented
23C2×#121×C37C2211yescharacteristic
24C2×#121×C37C2211yescharacteristic
25C2×#120×C37—21no—
26C2×C4×D4×C37C2211yescharacteristic
27C2×#117×C37C2211yescharacteristic
28C37×#468—24no—
29C37×#450—24no—
30C37×#436—24no—
31C2×#107×C37C2211yescharacteristic, complemented
32C2×#106×C37C2211yescharacteristic, complemented
33C2×C4⋊C8×C37C2211yescharacteristic, complemented
34C37×#418—24no—
35C2×#103×C37C2211yescharacteristic, complemented
36C2×#103×C37C2211yescharacteristic, complemented
37C2×#102×C37C2211yescharacteristic
38C2×#102×C37C2211yescharacteristic
39C2×#102×C37C2211yescharacteristic
40C2×#102×C37C2211yescharacteristic
41C2×#102×C37C2211yescharacteristic
42C2×#102×C37C2211yescharacteristic
43C2×C22⋊C8×C37C2211yescharacteristic
44C2×C22⋊C8×C37C2211yescharacteristic, complemented
45C2×C4×C8×C37C2211yescharacteristic, complemented
46C37×#397—21no—
47C37×#394—21no—
48C37×#394—21no—
49C37×#392—21no—
50C37×#391C2211yescharacteristic, complemented
51C37×#390C2211yescharacteristic
52C37×#390C2211yescharacteristic
53C37×#389—21no—
54C37×#389C2211yescharacteristic, complemented
55C37×#388—21no—
56C37×#380C2211yescharacteristic
57C37×#380C2211yescharacteristic, complemented
58C37×#379—21no—
59C37×#340C2211yescharacteristic, complemented
60C37×#340C2211yescharacteristic, complemented
61C37×#340C2211yescharacteristic, complemented
62C37×#340C2211yescharacteristic, complemented
63C25×C37—21no—
64C22×Q8×C37C2311yescharacteristic
65C22×D4×C37—22no—
66C22×D4×C37—22no—
67C22×D4×C37—21no—
68C22×D4×C37—21no—
69C22×D4×C37—22no—
70C22×D4×C37—21no—
71C22×D4×C37—22no—
72C22×D4×C37—41no—
73C22×D4×C37—41no—
74C22×D4×C37D411yescharacteristic
75C22×D4×C37C2311yescharacteristic
76C22×D4×C37C2311yescharacteristic
77C23×C4×C37C2311yescharacteristic
78C23×C4×C37C2311yescharacteristic
79C2×SD16×C37—22no—
80C2×SD16×C37—22no—
81C2×SD16×C37—22no—
82C2×SD16×C37—22no—
83C2×SD16×C37—41no—
84C2×SD16×C37—41no—
85C2×M16×C37—22no—
86C2×M16×C37—22no—
87C2×M16×C37—22no—
88C2×M16×C37—22no—
89C2×M16×C37—41no—
90C2×M16×C37—41no—
91C22×C8×C37C2311yescharacteristic
92C22×C8×C37C2311yescharacteristic
93C22×C8×C37C2311yescharacteristic
94C22×C8×C37C2311yescharacteristic
95C22⋊Q8×C37—22no—
96C22⋊Q8×C37—22no—
97C22⋊Q8×C37—22no—
98C22⋊Q8×C37—41no—
99#121×C37—22no—
100#121×C37—22no—
101#121×C37—41no—
102#121×C37—41no—
103#120×C37—44no—
104C4×D4×C37—22no—
105C4×D4×C37—22no—
106#117×C37—22no—
107#117×C37—41no—
108C2×C4⋊C4×C37—21no—
109C2×C4⋊C4×C37—21no—
110C2×C4⋊C4×C37—21no—
111C2×C4⋊C4×C37D411yescharacteristic
112C2×C4⋊C4×C37C2311yescharacteristic
113C2×C4⋊C4×C37C2311yescharacteristic
114C2×C4⋊C4×C37C2311yescharacteristic
115C2×C4⋊C4×C37C2311yescharacteristic
116C2×C4⋊C4×C37C2311yescharacteristic
117C2×C22⋊C4×C37—21no—
118C2×C22⋊C4×C37—21no—
119C2×C22⋊C4×C37—21no—
120C2×C22⋊C4×C37—21no—
121C2×C22⋊C4×C37—21no—
122C2×C22⋊C4×C37—21no—
123C2×C22⋊C4×C37—21no—
124C2×C22⋊C4×C37—21no—
125C2×C22⋊C4×C37—21no—
126C2×C22⋊C4×C37—21no—
127C2×C22⋊C4×C37—21no—
128C2×C22⋊C4×C37D411yescharacteristic
129C2×C22⋊C4×C37D411yescharacteristic
130C2×C42×C37—21no—
131C2×C42×C37C2311yescharacteristic
132#107×C37—22no—
133#106×C37—41no—
134C4⋊C8×C37—22no—
135#103×C37—22no—
136#103×C37—41no—
137#102×C37—22no—
138#102×C37—22no—
139#102×C37—22no—
140#102×C37—22no—
141#102×C37—22no—
142#102×C37D414yescomplemented
143C22⋊C8×C37—22no—
144C22⋊C8×C37D414yescomplemented
145C4×C8×C37—22no—
146#95×C37—21no—
147#95×C37—21no—
148#95×C37—21no—
149#95×C37—21no—
150#95×C37—21no—
151C24×C37—21no—
152C24×C37—21no—
153C24×C37—42no—
154C24×C37—42no—
155C24×C37—42no—
156C24×C37—42no—
157C24×C37—42no—
158C24×C37—81no—
159C24×C37—81no—
160C24×C37C2×D411yescharacteristic
161C24×C37C2×D411yescharacteristic
162C2×Q8×C37—21no—
163C2×Q8×C37—21no—
164C2×Q8×C37—21no—
165C2×Q8×C37—21no—
166C2×Q8×C37—21no—
167C2×Q8×C37—21no—
168C2×D4×C37—28no—
169C2×D4×C37—22no—
170C2×D4×C37—22no—
171C2×D4×C37—21no—
172C2×D4×C37—21no—
173C2×D4×C37—21no—
174C2×D4×C37—21no—
175C2×D4×C37—21no—
176C2×D4×C37—21no—
177C2×D4×C37—21no—
178C2×D4×C37—21no—
179C2×D4×C37—21no—
180C2×D4×C37—21no—
181C2×D4×C37—44no—
182C2×D4×C37—44no—
183C2×D4×C37—41no—
184C2×D4×C37—42no—
185C2×D4×C37—42no—
186C2×D4×C37—44no—
187C2×D4×C37—42no—
188C2×D4×C37—42no—
189C2×D4×C37—42no—
190C2×D4×C37—42no—
191C2×D4×C37—42no—
192C2×D4×C37—81no—
193C2×D4×C37—81no—
194C2×D4×C37C2×D412yes—
195C2×D4×C37#4112yes—
196C22×C4×C37—21no—
197C22×C4×C37—21no—
198C22×C4×C37—21no—
199C22×C4×C37—21no—
200C22×C4×C37—21no—
201C22×C4×C37—21no—
202C22×C4×C37—21no—
203C22×C4×C37—21no—
204C22×C4×C37—21no—
205C22×C4×C37—21no—
206C22×C4×C37—21no—
207C22×C4×C37—21no—
208C22×C4×C37—21no—
209C22×C4×C37—21no—
210C22×C4×C37—21no—
211C22×C4×C37—21no—
212C22×C4×C37C2×D411yescharacteristic
213C22×C4×C37C2×D411yescharacteristic
214C22×C4×C37C2×D411yescharacteristic
215C22×C4×C37C2×D412yes—
216C22×C4×C37C2×D411yescharacteristic
217C22×C4×C37#4112yes—
218C22×C4×C37C2411yescharacteristic
219SD16×C37—44no—
220SD16×C37—44no—
221M16×C37—44no—
222M16×C37—44no—
223C2×C8×C37—21no—
224C2×C8×C37—21no—
225C2×C8×C37—21no—
226C2×C8×C37—21no—
227C2×C8×C37—21no—
228C2×C8×C37—21no—
229C2×C8×C37—21no—
230C2×C8×C37—21no—
231C2×C8×C37—21no—
232C2×C8×C37C2×D412yes—
233C2×C8×C37C2×D412yes—
234C2×C8×C37C2×D412yes—
235C4⋊C4×C37—22no—
236C4⋊C4×C37—21no—
237C4⋊C4×C37—21no—
238C4⋊C4×C37—21no—
239C4⋊C4×C37—21no—
240C4⋊C4×C37—21no—
241C4⋊C4×C37—21no—
242C4⋊C4×C37—21no—
243C4⋊C4×C37—21no—
244C4⋊C4×C37—21no—
245C4⋊C4×C37—42no—
246C4⋊C4×C37—42no—
247C4⋊C4×C37—42no—
248C4⋊C4×C37C2×D412yes—
249C22⋊C4×C37—22no—
250C22⋊C4×C37—22no—
251C22⋊C4×C37—42no—
252C22⋊C4×C37—42no—
253C22⋊C4×C37—42no—
254C22⋊C4×C37—42no—
255C22⋊C4×C37—42no—
256C22⋊C4×C37—42no—
257C22⋊C4×C37—42no—
258C22⋊C4×C37—42no—
259C22⋊C4×C37—42no—
260C22⋊C4×C37—81no—
261C22⋊C4×C37—81no—
262C42×C37—21no—
263C42×C37—21no—
264C42×C37—42no—
265C23×C37—21no—
266C23×C37—21no—
267C23×C37—21no—
268C23×C37—21no—
269C23×C37—21no—
270C23×C37—21no—
271C23×C37—21no—
272C23×C37—21no—
273C23×C37—22no—
274C23×C37—22no—
275C23×C37—21no—
276C23×C37—21no—
277C23×C37—21no—
278C23×C37—21no—
279C23×C37—21no—
280C23×C37—48no—
281C23×C37—41no—
282C23×C37—41no—
283C23×C37—41no—
284C23×C37—41no—
285C23×C37—41no—
286C23×C37—41no—
287C23×C37—41no—
288C23×C37—41no—
289C23×C37—41no—
290C23×C37—41no—
291C23×C37—41no—
292C23×C37—41no—
293C23×C37—84no—
294C23×C37—84no—
295C23×C37—84no—
296C23×C37—84no—
297C23×C37—84no—
298C23×C37—84no—
299C23×C37#12112yes—
300C23×C37C22×D411yescharacteristic
301Q8×C37—41no—
302Q8×C37—41no—
303Q8×C37—41no—
304Q8×C37—41no—
305D4×C37—22no—
306D4×C37—22no—
307D4×C37—22no—
308D4×C37—22no—
309D4×C37—44no—
310D4×C37—48no—
311D4×C37—41no—
312D4×C37—41no—
313D4×C37—41no—
314D4×C37—41no—
315D4×C37—84no—
316D4×C37—84no—
317C2×C4×C37—21no—
318C2×C4×C37—21no—
319C2×C4×C37—21no—
320C2×C4×C37—21no—
321C2×C4×C37—22no—
322C2×C4×C37—22no—
323C2×C4×C37—22no—
324C2×C4×C37—22no—
325C2×C4×C37—21no—
326C2×C4×C37—21no—
327C2×C4×C37—22no—
328C2×C4×C37—21no—
329C2×C4×C37—21no—
330C2×C4×C37—21no—
331C2×C4×C37—21no—
332C2×C4×C37—41no—
333C2×C4×C37—41no—
334C2×C4×C37—41no—
335C2×C4×C37—41no—
336C2×C4×C37—41no—
337C2×C4×C37—41no—
338C2×C4×C37—41no—
339C2×C4×C37—41no—
340C2×C4×C37—41no—
341C2×C4×C37—41no—
342C2×C4×C37—41no—
343C2×C4×C37—41no—
344C2×C4×C37—41no—
345C2×C4×C37—41no—
346C2×C4×C37—41no—
347C2×C4×C37—41no—
348C2×C4×C37—41no—
349C2×C4×C37—41no—
350C2×C4×C37—41no—
351C2×C4×C37—41no—
352C2×C4×C37—41no—
353C2×C4×C37#12112yes—
354C2×C4×C37AGL(1,ℤ/8)12yes—
355C2×C4×C37C22×D411yescharacteristic
356C2×C4×C37C22×D411yescharacteristic
357C2×C4×C37C2×#4111yescharacteristic
358C2×C4×C37C2×#4111yescharacteristic
359C2×C4×C37H(5,𝔽2)11yescharacteristic
360C2×C4×C37H(5,𝔽2)11yescharacteristic
361C8×C37—22no—
362C8×C37—22no—
363C8×C37—22no—
364C8×C37—41no—
365#25136C3711yesmaximal, characteristic, direct product factor, Sylow
366C22×C37—22no—
367C22×C37—22no—
368C22×C37—22no—
369C22×C37—41no—
370C22×C37—41no—
371C22×C37—41no—
372C22×C37—41no—
373C22×C37—41no—
374C22×C37—42no—
375C22×C37—42no—
376C22×C37—41no—
377C22×C37—42no—
378C22×C37—41no—
379C22×C37—42no—
380C22×C37—41no—
381C22×C37—41no—
382C22×C37—41no—
383C22×C37—42no—
384C22×C37—41no—
385C22×C37—42no—
386C22×C37—816no—
387C22×C37—81no—
388C22×C37—81no—
389C22×C37—81no—
390C22×C37—81no—
391C22×C37—81no—
392C22×C37—81no—
393C22×C37—81no—
394C22×C37—81no—
395C22×C37C2×#12111yescharacteristic
396C22×C37D4211yescharacteristic
397C22×C37#54611yescharacteristic
398C22×C37C2×AGL(1,ℤ/8)11yescharacteristic
399C22×C37#57511yescharacteristic
400C22×C37#57711yescharacteristic
401C22×C37#57711yescharacteristic
402C4×C37—22no—
403C4×C37—22no—
404C4×C37—41no—
405C4×C37—42no—
406C4×C37—41no—
407C4×C37—81no—
408C4×C37—81no—
409C4×C37—81no—
410C4×C37—81no—
411C4×C37—81no—
412C4×C37#52511yescharacteristic
413C4×C37#53811yescharacteristic
414C4×C37D4211yescharacteristic
415C4×C37#54611yescharacteristic
416C2×#468C2×C3711yescharacteristic, complemented
417C2×#450C2×C3711yescharacteristic, complemented
418C2×#436C2×C3711yescharacteristic, complemented
419C2×#418C2×C3711yescharacteristic, complemented
420#2415C2×C3711yescharacteristic, complemented
421#2408C2×C3711yescharacteristic
422#2067C2×C3711yescharacteristic, complemented
423#2055C2×C3711yescharacteristic, complemented
424#2034C2×C3711yescharacteristic, complemented
425#2000C2×C3711yescharacteristic, complemented
426#1968C2×C3711yescharacteristic, complemented
427#1934C2×C3711yescharacteristic, complemented
428#1895C2×C3711yescharacteristic, complemented
429#1894C2×C3711yescharacteristic, complemented
430#1854C2×C3711yescharacteristic, complemented
431C2×C37—42no—
432C2×C37—81no—
433C2×C37—82no—
434C2×C37—82no—
435C2×C37#242411yescharacteristic
436C2×C37#305511yescharacteristic
437C2×C37#305711yescharacteristic
438C2×C37#327211yescharacteristic
439C2×C37#327511yescharacteristic
440C2×C37#332311yescharacteristic
441C2×C37#332411yescharacteristic
442C23×D4C22×C3711yescharacteristic
443C22×SD16C22×C3711yescharacteristic
444C22×SD16C22×C3711yescharacteristic
445C22×M16C22×C3711yescharacteristic
446C22×M16C22×C3711yescharacteristic, complemented
447C2×C22⋊Q8C22×C3711yescharacteristic
448C2×C22⋊Q8C22×C3711yescharacteristic, complemented
449C2×#121C22×C3711yescharacteristic
450C2×#121C22×C3711yescharacteristic
451C2×#120—21no—
452C2×C4×D4C22×C3711yescharacteristic
453C2×#117C22×C3711yescharacteristic
454#468—24no—
455#450—24no—
456#436—24no—
457C2×#107C22×C3711yescharacteristic, complemented
458C2×#106C22×C3711yescharacteristic, complemented
459C2×C4⋊C8C22×C3711yescharacteristic, complemented
460#418—24no—
461C2×#103C22×C3711yescharacteristic, complemented
462C2×#103C22×C3711yescharacteristic, complemented
463C2×#102C22×C3711yescharacteristic
464C2×#102C22×C3711yescharacteristic
465C2×#102C22×C3711yescharacteristic
466C2×#102C22×C3711yescharacteristic
467C2×#102C22×C3711yescharacteristic
468C2×#102C22×C3711yescharacteristic
469C2×C22⋊C8C22×C3711yescharacteristic
470C2×C22⋊C8C22×C3711yescharacteristic, complemented
471C2×C4×C8C22×C3711yescharacteristic, complemented
472#397—21no—
473#394—21no—
474#394—21no—
475#392—21no—
476#391C22×C3711yescharacteristic, complemented
477#390C22×C3711yescharacteristic
478#390C22×C3711yescharacteristic
479#389—21no—
480#389C22×C3711yescharacteristic, complemented
481#388—21no—
482#380C22×C3711yescharacteristic
483#380C22×C3711yescharacteristic, complemented
484#379—21no—
485#340C22×C3711yescharacteristic, complemented
486#340C22×C3711yescharacteristic, complemented
487#340C22×C3711yescharacteristic, complemented
488#340C22×C3711yescharacteristic, complemented
489C37#2513611yescharacteristic, direct product factor, Sylow
490C25—21no—
491C22×Q8C23×C3711yescharacteristic
492C22×D4—22no—
493C22×D4—22no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—22no—
497C22×D4—21no—
498C22×D4—22no—
499C22×D4—41no—
500C22×D4—41no—
501C22×D4D4×C3711yescharacteristic
502C22×D4C23×C3711yescharacteristic
503C22×D4C23×C3711yescharacteristic
504C23×C4C23×C3711yescharacteristic
505C23×C4C23×C3711yescharacteristic
506C2×SD16—22no—
507C2×SD16—22no—
508C2×SD16—22no—
509C2×SD16—22no—
510C2×SD16—41no—
511C2×SD16—41no—
512C2×M16—22no—
513C2×M16—22no—
514C2×M16—22no—
515C2×M16—22no—
516C2×M16—41no—
517C2×M16—41no—
518C22×C8C23×C3711yescharacteristic
519C22×C8C23×C3711yescharacteristic
520C22×C8C23×C3711yescharacteristic
521C22×C8C23×C3711yescharacteristic
522C22⋊Q8—22no—
523C22⋊Q8—22no—
524C22⋊Q8—22no—
525C22⋊Q8—41no—
526#121—22no—
527#121—22no—
528#121—41no—
529#121—41no—
530#120—44no—
531C4×D4—22no—
532C4×D4—22no—
533#117—22no—
534#117—41no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4D4×C3711yescharacteristic
539C2×C4⋊C4C23×C3711yescharacteristic
540C2×C4⋊C4C23×C3711yescharacteristic
541C2×C4⋊C4C23×C3711yescharacteristic
542C2×C4⋊C4C23×C3711yescharacteristic
543C2×C4⋊C4C23×C3711yescharacteristic
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4D4×C3711yescharacteristic
556C2×C22⋊C4D4×C3711yescharacteristic
557C2×C42—21no—
558C2×C42C23×C3711yescharacteristic
559#107—22no—
560#106—41no—
561C4⋊C8—22no—
562#103—22no—
563#103—41no—
564#102—22no—
565#102—22no—
566#102—22no—
567#102—22no—
568#102—22no—
569#102D4×C3714yescomplemented
570C22⋊C8—22no—
571C22⋊C8D4×C3714yescomplemented
572C4×C8—22no—
573#95—21no—
574#95—21no—
575#95—21no—
576#95—21no—
577#95—21no—
578C24—21no—
579C24—21no—
580C24—42no—
581C24—42no—
582C24—42no—
583C24—42no—
584C24—42no—
585C24—81no—
586C24—81no—
587C24C2×D4×C3711yescharacteristic
588C24C2×D4×C3711yescharacteristic
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×D4—28no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—44no—
609C2×D4—44no—
610C2×D4—41no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—44no—
614C2×D4—42no—
615C2×D4—42no—
616C2×D4—42no—
617C2×D4—42no—
618C2×D4—42no—
619C2×D4—81no—
620C2×D4—81no—
621C2×D4C2×D4×C3712yes—
622C2×D4#41×C3712yes—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4C2×D4×C3711yescharacteristic
640C22×C4C2×D4×C3711yescharacteristic
641C22×C4C2×D4×C3711yescharacteristic
642C22×C4C2×D4×C3712yes—
643C22×C4C2×D4×C3711yescharacteristic
644C22×C4#41×C3712yes—
645C22×C4C24×C3711yescharacteristic
646SD16—44no—
647SD16—44no—
648M16—44no—
649M16—44no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8C2×D4×C3712yes—
660C2×C8C2×D4×C3712yes—
661C2×C8C2×D4×C3712yes—
662C4⋊C4—22no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—42no—
673C4⋊C4—42no—
674C4⋊C4—42no—
675C4⋊C4C2×D4×C3712yes—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C22⋊C4—42no—
686C22⋊C4—42no—
687C22⋊C4—81no—
688C22⋊C4—81no—
689C42—21no—
690C42—21no—
691C42—42no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—22no—
701C23—22no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—48no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—84no—
721C23—84no—
722C23—84no—
723C23—84no—
724C23—84no—
725C23—84no—
726C23#121×C3712yes—
727C23C22×D4×C3711yescharacteristic
728Q8—41no—
729Q8—41no—
730Q8—41no—
731Q8—41no—
732D4—22no—
733D4—22no—
734D4—22no—
735D4—22no—
736D4—44no—
737D4—48no—
738D4—41no—
739D4—41no—
740D4—41no—
741D4—41no—
742D4—84no—
743D4—84no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4#121×C3712yes—
781C2×C4AGL(1,ℤ/8)×C3712yes—
782C2×C4C22×D4×C3711yescharacteristic
783C2×C4C22×D4×C3711yescharacteristic
784C2×C4C2×#41×C3711yescharacteristic
785C2×C4C2×#41×C3711yescharacteristic
786C2×C4H(5,𝔽2)×C3711yescharacteristic
787C2×C4H(5,𝔽2)×C3711yescharacteristic
788C8—22no—
789C8—22no—
790C8—22no—
791C8—41no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—42no—
801C22—42no—
802C22—41no—
803C22—42no—
804C22—41no—
805C22—42no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—42no—
810C22—41no—
811C22—42no—
812C22—816no—
813C22—81no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22—81no—
818C22—81no—
819C22—81no—
820C22—81no—
821C22C2×#121×C3711yescharacteristic
822C22D42×C3711yescharacteristic
823C22C37×#54611yescharacteristic
824C22C2×AGL(1,ℤ/8)×C3711yescharacteristic
825C22C37×#57511yescharacteristic
826C22C37×#57711yescharacteristic
827C22C37×#57711yescharacteristic
828C4—22no—
829C4—22no—
830C4—41no—
831C4—42no—
832C4—41no—
833C4—81no—
834C4—81no—
835C4—81no—
836C4—81no—
837C4—81no—
838C4C37×#52511yescharacteristic
839C4C37×#53811yescharacteristic
840C4D42×C3711yescharacteristic
841C4C37×#54611yescharacteristic
842C2—42no—
843C2—81no—
844C2—82no—
845C2—82no—
846C2C37×#242411yescharacteristic
847C2C37×#305511yescharacteristic
848C2C37×#305711yescharacteristic
849C2C37×#327211yescharacteristic
850C2C37×#327511yescharacteristic
851C2C37×#332311yescharacteristic
852C2C37×#332411yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC37×#2408C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C37 ◁ C2×C4×D4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C37×#468C2semidirect
2. C2×C37×#450C2semidirect
3. C2×C37×#436C2semidirect
4. C2×C37×#418C2semidirect
5. C37×#2415C2semidirect
7. C37×#2067C2semidirect
8. C37×#2055C2semidirect
9. C37×#2034C2semidirect
10. C37×#2000C2semidirect
11. C37×#1968C2semidirect
12. C37×#1934C2semidirect
13. C37×#1895C2semidirect
14. C37×#1894C2semidirect
15. C37×#1854C2semidirect
20. C22×M16×C37C22semidirect
22. C2×C22⋊Q8×C37C22semidirect
31. C2×#107×C37C22semidirect
32. C2×#106×C37C22semidirect
33. C2×C4⋊C8×C37C22semidirect
35. C2×#103×C37C22semidirect
36. C2×#103×C37C22semidirect
44. C2×C22⋊C8×C37C22semidirect
45. C2×C4×C8×C37C22semidirect
50. C37×#391C22semidirect
54. C37×#389C22semidirect
57. C37×#380C22semidirect
59. C37×#340C22semidirect
60. C37×#340C22semidirect
61. C37×#340C22semidirect
62. C37×#340C22semidirect
142. #102×C37D4semidirect
144. C22⋊C8×C37D4semidirect
365. #25136C37direct (N × H)
416. C2×#468C2×C37semidirect
417. C2×#450C2×C37semidirect
418. C2×#436C2×C37semidirect
419. C2×#418C2×C37semidirect
420. #2415C2×C37semidirect
422. #2067C2×C37semidirect
423. #2055C2×C37semidirect
424. #2034C2×C37semidirect
425. #2000C2×C37semidirect
426. #1968C2×C37semidirect
427. #1934C2×C37semidirect
428. #1895C2×C37semidirect
429. #1894C2×C37semidirect
430. #1854C2×C37semidirect
446. C22×M16C22×C37semidirect
448. C2×C22⋊Q8C22×C37semidirect
457. C2×#107C22×C37semidirect
458. C2×#106C22×C37semidirect
459. C2×C4⋊C8C22×C37semidirect
461. C2×#103C22×C37semidirect
462. C2×#103C22×C37semidirect
470. C2×C22⋊C8C22×C37semidirect
471. C2×C4×C8C22×C37semidirect
476. #391C22×C37semidirect
480. #389C22×C37semidirect
483. #380C22×C37semidirect
485. #340C22×C37semidirect
486. #340C22×C37semidirect
487. #340C22×C37semidirect
488. #340C22×C37semidirect
489. C37#25136direct (N × H)
569. #102D4×C37semidirect
571. C22⋊C8D4×C37semidirect

Maximal subgroups

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

subgroupindex
C2×C37×#4682
C2×C37×#4502
C2×C37×#4362
C2×C37×#4182
C37×#24152
C37×#24082
C37×#20672
C37×#20552
C37×#20342
C37×#20002
C37×#19682
C37×#19342
C37×#18952
C37×#18942
C37×#18542
#2513637