Finite Group Databasebeta

← C37×#25128 #22646381

Subgroups — C37×#25128 #22646381

Order 9472.

1292 conjugacy classes of subgroups.

The subgroup lattice has 860 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×#435C211yesmaximal, characteristic, complemented
4C22×#102×C37C211yesmaximal, characteristic, complemented
5C37×#2417C211yesmaximal, characteristic, complemented
6C37×#2408C211yesmaximal, characteristic
7C37×#2067C211yesmaximal, characteristic, complemented
8C37×#2055C211yesmaximal, characteristic, complemented
9C37×#2033C211yesmaximal, characteristic, complemented
10C37×#2000C211yesmaximal, characteristic, complemented
11C37×#1973C211yesmaximal, characteristic, complemented
12C37×#1936C211yesmaximal, characteristic, complemented
13C37×#1895C211yesmaximal, characteristic, complemented
14C37×#1892C211yesmaximal, characteristic, complemented
15C37×#1852C211yesmaximal, characteristic, complemented
16C23×D4×C37C2211yescharacteristic
17C22×SD16×C37C2211yescharacteristic
18C22×SD16×C37C2211yescharacteristic
19C22×M16×C37C2211yescharacteristic, complemented
20C23×C8×C37C2211yescharacteristic
21C2×C22⋊Q8×C37C2211yescharacteristic
22C2×C22⋊Q8×C37C2211yescharacteristic, complemented
23C2×#121×C37C2211yescharacteristic
24C2×#121×C37C2211yescharacteristic
25C2×#120×C37—21no—
26C2×C4×D4×C37C2211yescharacteristic
27C22×C4⋊C4×C37C2211yescharacteristic
28C37×#468—24no—
29C37×#450—24no—
30C37×#435—24no—
31C2×#107×C37C2211yescharacteristic, complemented
32C2×#107×C37C2211yescharacteristic, complemented
33C2×C4⋊C8×C37C2211yescharacteristic, complemented
34C2×#103×C37C2211yescharacteristic, complemented
35C2×#103×C37C2211yescharacteristic, complemented
36C2×#102×C37—24no—
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×#97×C37C2211yescharacteristic, complemented
46C37×#398—21no—
47C37×#396—21no—
48C37×#394—21no—
49C37×#392—21no—
50C37×#391C2211yescharacteristic, complemented
51C37×#390C2211yescharacteristic
52C37×#390C2211yescharacteristic
53C37×#389C2211yescharacteristic, complemented
54C37×#386—21no—
55C37×#380—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×C37—21no—
78C23×C4×C37C2311yescharacteristic
79C23×C4×C37C2311yescharacteristic
80C2×SD16×C37—22no—
81C2×SD16×C37—22no—
82C2×SD16×C37—22no—
83C2×SD16×C37—22no—
84C2×SD16×C37—41no—
85C2×SD16×C37—41no—
86C2×M16×C37—22no—
87C2×M16×C37—22no—
88C2×M16×C37—41no—
89C22×C8×C37—22no—
90C22×C8×C37—22no—
91C22×C8×C37—41no—
92C22×C8×C37C2311yescharacteristic
93C22×C8×C37C2311yescharacteristic
94C22×C8×C37C2311yescharacteristic
95C22×C8×C37C2311yescharacteristic
96C22⋊Q8×C37—22no—
97C22⋊Q8×C37—22no—
98C22⋊Q8×C37—22no—
99C22⋊Q8×C37—41no—
100#121×C37—22no—
101#121×C37—22no—
102#121×C37—41no—
103#121×C37—41no—
104#120×C37—44no—
105C4×D4×C37—22no—
106C4×D4×C37—22no—
107C2×C4⋊C4×C37—22no—
108C2×C4⋊C4×C37—21no—
109C2×C4⋊C4×C37—21no—
110C2×C4⋊C4×C37—21no—
111C2×C4⋊C4×C37—21no—
112C2×C4⋊C4×C37—41no—
113C2×C4⋊C4×C37D411yescharacteristic
114C2×C4⋊C4×C37C2311yescharacteristic
115C2×C4⋊C4×C37C2311yescharacteristic
116C2×C4⋊C4×C37C2311yescharacteristic
117C2×C4⋊C4×C37C2311yescharacteristic
118C2×C4⋊C4×C37C2311yescharacteristic
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×C37—21no—
129C2×C22⋊C4×C37D411yescharacteristic
130C2×C22⋊C4×C37D411yescharacteristic
131C2×C42×C37C2311yescharacteristic
132#107×C37—22no—
133#107×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
145#97×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—22no—
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—21no—
182C2×D4×C37—44no—
183C2×D4×C37—44no—
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×C37—42no—
213C22×C4×C37—42no—
214C22×C4×C37—81no—
215C22×C4×C37C2×D411yescharacteristic
216C22×C4×C37C2×D411yescharacteristic
217C22×C4×C37C2×D411yescharacteristic
218C22×C4×C37C2×D411yescharacteristic
219C22×C4×C37C2×D412yes—
220C22×C4×C37#4112yes—
221C22×C4×C37C2411yescharacteristic
222SD16×C37—44no—
223SD16×C37—44no—
224M16×C37—44no—
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×C37—21no—
233C2×C8×C37—21no—
234C2×C8×C37—44no—
235C2×C8×C37C2×D412yes—
236C2×C8×C37C2×D412yes—
237C2×C8×C37C2×D412yes—
238C4⋊C4×C37—22no—
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—21no—
246C4⋊C4×C37—21no—
247C4⋊C4×C37—21no—
248C4⋊C4×C37—42no—
249C4⋊C4×C37—42no—
250C4⋊C4×C37—42no—
251C4⋊C4×C37—81no—
252C4⋊C4×C37C2×D412yes—
253C22⋊C4×C37—22no—
254C22⋊C4×C37—22no—
255C22⋊C4×C37—42no—
256C22⋊C4×C37—42no—
257C22⋊C4×C37—42no—
258C22⋊C4×C37—42no—
259C22⋊C4×C37—42no—
260C22⋊C4×C37—42no—
261C22⋊C4×C37—42no—
262C22⋊C4×C37—81no—
263C22⋊C4×C37—81no—
264C22⋊C4×C37—81no—
265C42×C37—21no—
266C42×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×C37AGL(1,ℤ/8)12yes—
301C23×C37#13712yes—
302C23×C37C22×D411yescharacteristic
303Q8×C37—41no—
304Q8×C37—41no—
305Q8×C37—41no—
306Q8×C37—41no—
307D4×C37—22no—
308D4×C37—22no—
309D4×C37—22no—
310D4×C37—22no—
311D4×C37—48no—
312D4×C37—44no—
313D4×C37—41no—
314D4×C37—41no—
315D4×C37—41no—
316D4×C37—41no—
317D4×C37—84no—
318D4×C37—84no—
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—21no—
328C2×C4×C37—21no—
329C2×C4×C37—22no—
330C2×C4×C37—21no—
331C2×C4×C37—21no—
332C2×C4×C37—21no—
333C2×C4×C37—21no—
334C2×C4×C37—21no—
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—41no—
354C2×C4×C37—41no—
355C2×C4×C37—41no—
356C2×C4×C37—84no—
357C2×C4×C37#12112yes—
358C2×C4×C37C22×D411yescharacteristic
359C2×C4×C37C22×D411yescharacteristic
360C2×C4×C37C2×#4111yescharacteristic
361C2×C4×C37C2×#4111yescharacteristic
362C2×C4×C37H(5,𝔽2)11yescharacteristic
363C2×C4×C37H(5,𝔽2)11yescharacteristic
364C8×C37—22no—
365C8×C37—22no—
366C8×C37—22no—
367C8×C37—41no—
368#25128C3711yesmaximal, characteristic, direct product factor, Sylow
369C22×C37—22no—
370C22×C37—22no—
371C22×C37—22no—
372C22×C37—22no—
373C22×C37—22no—
374C22×C37—22no—
375C22×C37—41no—
376C22×C37—42no—
377C22×C37—42no—
378C22×C37—41no—
379C22×C37—42no—
380C22×C37—41no—
381C22×C37—42no—
382C22×C37—41no—
383C22×C37—41no—
384C22×C37—42no—
385C22×C37—41no—
386C22×C37—42no—
387C22×C37—41no—
388C22×C37—816no—
389C22×C37—81no—
390C22×C37—81no—
391C22×C37—81no—
392C22×C37—81no—
393C22×C37—81no—
394C22×C37—81no—
395C22×C37—81no—
396C22×C37—81no—
397C22×C37#46814yescomplemented
398C22×C37C2×#12111yescharacteristic
399C22×C37D4211yescharacteristic
400C22×C37#54611yescharacteristic
401C22×C37C2×AGL(1,ℤ/8)11yescharacteristic
402C22×C37C2×#13711yescharacteristic
403C22×C37#57611yescharacteristic
404C22×C37#57711yescharacteristic
405C4×C37—22no—
406C4×C37—41no—
407C4×C37—42no—
408C4×C37—41no—
409C4×C37—41no—
410C4×C37—81no—
411C4×C37—81no—
412C4×C37—81no—
413C4×C37—81no—
414C4×C37—81no—
415C4×C37#52511yescharacteristic
416C4×C37#53811yescharacteristic
417C4×C37D4211yescharacteristic
418C4×C37#54611yescharacteristic
419C2×#468C2×C3711yescharacteristic, complemented
420C2×#450C2×C3711yescharacteristic, complemented
421C2×#435C2×C3711yescharacteristic, complemented
422C22×#102C2×C3711yescharacteristic, complemented
423#2417C2×C3711yescharacteristic, complemented
424#2408C2×C3711yescharacteristic
425#2067C2×C3711yescharacteristic, complemented
426#2055C2×C3711yescharacteristic, complemented
427#2033C2×C3711yescharacteristic, complemented
428#2000C2×C3711yescharacteristic, complemented
429#1973C2×C3711yescharacteristic, complemented
430#1936C2×C3711yescharacteristic, complemented
431#1895C2×C3711yescharacteristic, complemented
432#1892C2×C3711yescharacteristic, complemented
433#1852C2×C3711yescharacteristic, complemented
434C2×C37—24no—
435C2×C37—81no—
436C2×C37—82no—
437C2×C37—82no—
438C2×C37#242411yescharacteristic
439C2×C37C2×#46811yescharacteristic
440C2×C37#306211yescharacteristic
441C2×C37#326411yescharacteristic
442C2×C37#326611yescharacteristic
443C2×C37#331011yescharacteristic
444C2×C37#331411yescharacteristic
445C23×D4C22×C3711yescharacteristic
446C22×SD16C22×C3711yescharacteristic
447C22×SD16C22×C3711yescharacteristic
448C22×M16C22×C3711yescharacteristic, complemented
449C23×C8C22×C3711yescharacteristic
450C2×C22⋊Q8C22×C3711yescharacteristic
451C2×C22⋊Q8C22×C3711yescharacteristic, complemented
452C2×#121C22×C3711yescharacteristic
453C2×#121C22×C3711yescharacteristic
454C2×#120—21no—
455C2×C4×D4C22×C3711yescharacteristic
456C22×C4⋊C4C22×C3711yescharacteristic
457#468—24no—
458#450—24no—
459#435—24no—
460C2×#107C22×C3711yescharacteristic, complemented
461C2×#107C22×C3711yescharacteristic, complemented
462C2×C4⋊C8C22×C3711yescharacteristic, complemented
463C2×#103C22×C3711yescharacteristic, complemented
464C2×#103C22×C3711yescharacteristic, complemented
465C2×#102—24no—
466C2×#102C22×C3711yescharacteristic
467C2×#102C22×C3711yescharacteristic
468C2×#102C22×C3711yescharacteristic
469C2×#102C22×C3711yescharacteristic
470C2×#102C22×C3711yescharacteristic
471C2×#102C22×C3711yescharacteristic
472C2×C22⋊C8C22×C3711yescharacteristic
473C2×C22⋊C8C22×C3711yescharacteristic, complemented
474C2×#97C22×C3711yescharacteristic, complemented
475#398—21no—
476#396—21no—
477#394—21no—
478#392—21no—
479#391C22×C3711yescharacteristic, complemented
480#390C22×C3711yescharacteristic
481#390C22×C3711yescharacteristic
482#389C22×C3711yescharacteristic, complemented
483#386—21no—
484#380—21no—
485#380C22×C3711yescharacteristic
486#380C22×C3711yescharacteristic, complemented
487#379—21no—
488#340C22×C3711yescharacteristic, complemented
489#340C22×C3711yescharacteristic, complemented
490#340C22×C3711yescharacteristic, complemented
491#340C22×C3711yescharacteristic, complemented
492C37#2512811yescharacteristic, direct product factor, Sylow
493C25—21no—
494C22×Q8C23×C3711yescharacteristic
495C22×D4—22no—
496C22×D4—22no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—22no—
500C22×D4—21no—
501C22×D4—22no—
502C22×D4—41no—
503C22×D4—41no—
504C22×D4D4×C3711yescharacteristic
505C22×D4C23×C3711yescharacteristic
506C22×D4C23×C3711yescharacteristic
507C23×C4—21no—
508C23×C4C23×C3711yescharacteristic
509C23×C4C23×C3711yescharacteristic
510C2×SD16—22no—
511C2×SD16—22no—
512C2×SD16—22no—
513C2×SD16—22no—
514C2×SD16—41no—
515C2×SD16—41no—
516C2×M16—22no—
517C2×M16—22no—
518C2×M16—41no—
519C22×C8—22no—
520C22×C8—22no—
521C22×C8—41no—
522C22×C8C23×C3711yescharacteristic
523C22×C8C23×C3711yescharacteristic
524C22×C8C23×C3711yescharacteristic
525C22×C8C23×C3711yescharacteristic
526C22⋊Q8—22no—
527C22⋊Q8—22no—
528C22⋊Q8—22no—
529C22⋊Q8—41no—
530#121—22no—
531#121—22no—
532#121—41no—
533#121—41no—
534#120—44no—
535C4×D4—22no—
536C4×D4—22no—
537C2×C4⋊C4—22no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—41no—
543C2×C4⋊C4D4×C3711yescharacteristic
544C2×C4⋊C4C23×C3711yescharacteristic
545C2×C4⋊C4C23×C3711yescharacteristic
546C2×C4⋊C4C23×C3711yescharacteristic
547C2×C4⋊C4C23×C3711yescharacteristic
548C2×C4⋊C4C23×C3711yescharacteristic
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⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4D4×C3711yescharacteristic
560C2×C22⋊C4D4×C3711yescharacteristic
561C2×C42C23×C3711yescharacteristic
562#107—22no—
563#107—41no—
564C4⋊C8—22no—
565#103—22no—
566#103—41no—
567#102—22no—
568#102—22no—
569#102—22no—
570#102—22no—
571#102—22no—
572#102D4×C3714yescomplemented
573C22⋊C8—22no—
574C22⋊C8D4×C3714yescomplemented
575#97—22no—
576#95—21no—
577#95—21no—
578#95—21no—
579#95—21no—
580#95—21no—
581C24—21no—
582C24—21no—
583C24—42no—
584C24—42no—
585C24—42no—
586C24—42no—
587C24—42no—
588C24—81no—
589C24—81no—
590C24C2×D4×C3711yescharacteristic
591C24C2×D4×C3711yescharacteristic
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×D4—28no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—44no—
613C2×D4—44no—
614C2×D4—42no—
615C2×D4—42no—
616C2×D4—44no—
617C2×D4—42no—
618C2×D4—42no—
619C2×D4—42no—
620C2×D4—42no—
621C2×D4—42no—
622C2×D4—81no—
623C2×D4—81no—
624C2×D4C2×D4×C3712yes—
625C2×D4#41×C3712yes—
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×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—42no—
643C22×C4—42no—
644C22×C4—81no—
645C22×C4C2×D4×C3711yescharacteristic
646C22×C4C2×D4×C3711yescharacteristic
647C22×C4C2×D4×C3711yescharacteristic
648C22×C4C2×D4×C3711yescharacteristic
649C22×C4C2×D4×C3712yes—
650C22×C4#41×C3712yes—
651C22×C4C24×C3711yescharacteristic
652SD16—44no—
653SD16—44no—
654M16—44no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—44no—
665C2×C8C2×D4×C3712yes—
666C2×C8C2×D4×C3712yes—
667C2×C8C2×D4×C3712yes—
668C4⋊C4—22no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—42no—
679C4⋊C4—42no—
680C4⋊C4—42no—
681C4⋊C4—81no—
682C4⋊C4C2×D4×C3712yes—
683C22⋊C4—22no—
684C22⋊C4—22no—
685C22⋊C4—42no—
686C22⋊C4—42no—
687C22⋊C4—42no—
688C22⋊C4—42no—
689C22⋊C4—42no—
690C22⋊C4—42no—
691C22⋊C4—42no—
692C22⋊C4—81no—
693C22⋊C4—81no—
694C22⋊C4—81no—
695C42—21no—
696C42—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—22no—
704C23—22no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—48no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—84no—
724C23—84no—
725C23—84no—
726C23—84no—
727C23—84no—
728C23—84no—
729C23#121×C3712yes—
730C23AGL(1,ℤ/8)×C3712yes—
731C23#137×C3712yes—
732C23C22×D4×C3711yescharacteristic
733Q8—41no—
734Q8—41no—
735Q8—41no—
736Q8—41no—
737D4—22no—
738D4—22no—
739D4—22no—
740D4—22no—
741D4—48no—
742D4—44no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—84no—
748D4—84no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—22no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
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—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—84no—
787C2×C4#121×C3712yes—
788C2×C4C22×D4×C3711yescharacteristic
789C2×C4C22×D4×C3711yescharacteristic
790C2×C4C2×#41×C3711yescharacteristic
791C2×C4C2×#41×C3711yescharacteristic
792C2×C4H(5,𝔽2)×C3711yescharacteristic
793C2×C4H(5,𝔽2)×C3711yescharacteristic
794C8—22no—
795C8—22no—
796C8—22no—
797C8—41no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—22no—
804C22—41no—
805C22—42no—
806C22—42no—
807C22—41no—
808C22—42no—
809C22—41no—
810C22—42no—
811C22—41no—
812C22—41no—
813C22—42no—
814C22—41no—
815C22—42no—
816C22—41no—
817C22—816no—
818C22—81no—
819C22—81no—
820C22—81no—
821C22—81no—
822C22—81no—
823C22—81no—
824C22—81no—
825C22—81no—
826C22C37×#46814yescomplemented
827C22C2×#121×C3711yescharacteristic
828C22D42×C3711yescharacteristic
829C22C37×#54611yescharacteristic
830C22C2×AGL(1,ℤ/8)×C3711yescharacteristic
831C22C2×#137×C3711yescharacteristic
832C22C37×#57611yescharacteristic
833C22C37×#57711yescharacteristic
834C4—22no—
835C4—41no—
836C4—42no—
837C4—41no—
838C4—41no—
839C4—81no—
840C4—81no—
841C4—81no—
842C4—81no—
843C4—81no—
844C4C37×#52511yescharacteristic
845C4C37×#53811yescharacteristic
846C4D42×C3711yescharacteristic
847C4C37×#54611yescharacteristic
848C2—24no—
849C2—81no—
850C2—82no—
851C2—82no—
852C2C37×#242411yescharacteristic
853C2C2×C37×#46811yescharacteristic
854C2C37×#306211yescharacteristic
855C2C37×#326411yescharacteristic
856C2C37×#326611yescharacteristic
857C2C37×#331011yescharacteristic
858C2C37×#331411yescharacteristic
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×#435C2semidirect
4. C22×#102×C37C2semidirect
5. C37×#2417C2semidirect
7. C37×#2067C2semidirect
8. C37×#2055C2semidirect
9. C37×#2033C2semidirect
10. C37×#2000C2semidirect
11. C37×#1973C2semidirect
12. C37×#1936C2semidirect
13. C37×#1895C2semidirect
14. C37×#1892C2semidirect
15. C37×#1852C2semidirect
19. C22×M16×C37C22semidirect
22. C2×C22⋊Q8×C37C22semidirect
31. C2×#107×C37C22semidirect
32. C2×#107×C37C22semidirect
33. C2×C4⋊C8×C37C22semidirect
34. C2×#103×C37C22semidirect
35. C2×#103×C37C22semidirect
44. C2×C22⋊C8×C37C22semidirect
45. C2×#97×C37C22semidirect
50. C37×#391C22semidirect
53. C37×#389C22semidirect
57. C37×#380C22semidirect
59. C37×#340C22semidirect
60. C37×#340C22semidirect
61. C37×#340C22semidirect
62. C37×#340C22semidirect
142. #102×C37D4semidirect
144. C22⋊C8×C37D4semidirect
368. #25128C37direct (N × H)
397. C22×C37#468semidirect
419. C2×#468C2×C37semidirect
420. C2×#450C2×C37semidirect
421. C2×#435C2×C37semidirect
422. C22×#102C2×C37semidirect
423. #2417C2×C37semidirect
425. #2067C2×C37semidirect
426. #2055C2×C37semidirect
427. #2033C2×C37semidirect
428. #2000C2×C37semidirect
429. #1973C2×C37semidirect
430. #1936C2×C37semidirect
431. #1895C2×C37semidirect
432. #1892C2×C37semidirect
433. #1852C2×C37semidirect
448. C22×M16C22×C37semidirect
451. C2×C22⋊Q8C22×C37semidirect
460. C2×#107C22×C37semidirect
461. C2×#107C22×C37semidirect
462. C2×C4⋊C8C22×C37semidirect
463. C2×#103C22×C37semidirect
464. C2×#103C22×C37semidirect
473. C2×C22⋊C8C22×C37semidirect
474. C2×#97C22×C37semidirect
479. #391C22×C37semidirect
482. #389C22×C37semidirect
486. #380C22×C37semidirect
488. #340C22×C37semidirect
489. #340C22×C37semidirect
490. #340C22×C37semidirect
491. #340C22×C37semidirect
492. C37#25128direct (N × H)
572. #102D4×C37semidirect
574. C22⋊C8D4×C37semidirect
826. C22C37×#468semidirect

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×#4352
C22×#102×C372
C37×#24172
C37×#24082
C37×#20672
C37×#20552
C37×#20332
C37×#20002
C37×#19732
C37×#19362
C37×#18952
C37×#18922
C37×#18522
#2512837