Finite Group Databasebeta

← C37×#25097 #22646350

Subgroups — C37×#25097 #22646350

Order 9472.

1378 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#469C211yesmaximal, characteristic, complemented
2C2×C37×#459C211yesmaximal, characteristic, complemented
3C2×C37×#447C211yesmaximal, characteristic, complemented
4C2×C37×#418C211yesmaximal, characteristic, complemented
5C37×#2433C211yesmaximal, characteristic, complemented
6C37×#2363C211yesmaximal, characteristic, complemented
7C37×#2065C211yesmaximal, characteristic, complemented
8C37×#2054C211yesmaximal, characteristic, complemented
9C37×#2041C211yesmaximal, characteristic, complemented
10C37×#2011C211yesmaximal, characteristic, complemented
11C37×#1982C211yesmaximal, characteristic, complemented
12C37×#1926C211yesmaximal, characteristic, complemented
13C37×#1879C211yesmaximal, characteristic, complemented
14C37×#1875C211yesmaximal, characteristic, complemented
15C37×#1851C211yesmaximal, characteristic, complemented
16C23×D4×C37C2211yescharacteristic
17C22×D8×C37C2211yescharacteristic
18C22×D8×C37C2211yescharacteristic
19C22×D8×C37C2211yescharacteristic, complemented
20C22×M16×C37C2211yescharacteristic
21C2×#127×C37C2211yescharacteristic
22C2×#127×C37C2211yescharacteristic
23C2×#121×C37C2211yescharacteristic
24C2×#121×C37C2211yescharacteristic
25C2×#120×C37—21no—
26C2×#120×C37—21no—
27C2×C4×D4×C37C2211yescharacteristic, complemented
28C2×#117×C37C2211yescharacteristic
29C37×#469—24no—
30C37×#459—24no—
31C37×#447—24no—
32C2×#106×C37C2211yescharacteristic, complemented
33C2×C4⋊C8×C37C2211yescharacteristic, complemented
34C2×C4⋊C8×C37C2211yescharacteristic, complemented
35C37×#418—24no—
36C2×#102×C37C2211yescharacteristic
37C2×#102×C37C2211yescharacteristic
38C2×#102×C37C2211yescharacteristic
39C2×#102×C37C2211yescharacteristic
40C2×#102×C37C2211yescharacteristic
41C2×#102×C37C2211yescharacteristic
42C2×#102×C37C2211yescharacteristic, complemented
43C2×#102×C37C2211yescharacteristic, complemented
44C2×#102×C37C2211yescharacteristic, complemented
45C2×#102×C37C2211yescharacteristic, complemented
46C2×C22⋊C8×C37C2211yescharacteristic
47C37×#392—21no—
48C37×#392—21no—
49C37×#390—21no—
50C37×#390C2211yescharacteristic
51C37×#390C2211yescharacteristic
52C37×#390C2211yescharacteristic, complemented
53C37×#389C2211yescharacteristic, complemented
54C37×#388—21no—
55C37×#386—21no—
56C4×C4⋊C4×C37C2211yescharacteristic, complemented
57C4×C22⋊C4×C37—21no—
58C4×C22⋊C4×C37C2211yescharacteristic
59C37×#340C2211yescharacteristic, complemented
60C37×#340C2211yescharacteristic, complemented
61C37×#336C2211yescharacteristic, complemented
62C37×#336C2211yescharacteristic, complemented
63C25×C37—21no—
64C22×D4×C37—22no—
65C22×D4×C37—22no—
66C22×D4×C37—21no—
67C22×D4×C37—21no—
68C22×D4×C37—22no—
69C22×D4×C37—21no—
70C22×D4×C37—21no—
71C22×D4×C37—21no—
72C22×D4×C37—21no—
73C22×D4×C37—21no—
74C22×D4×C37—22no—
75C22×D4×C37—41no—
76C22×D4×C37—41no—
77C22×D4×C37C2311yescharacteristic
78C22×D4×C37C2311yescharacteristic
79C22×D4×C37C2311yescharacteristic
80C22×D4×C37C2311yescharacteristic
81C23×C4×C37—21no—
82C23×C4×C37C2311yescharacteristic
83C2×D8×C37—22no—
84C2×D8×C37—22no—
85C2×D8×C37—22no—
86C2×D8×C37—22no—
87C2×D8×C37—22no—
88C2×D8×C37—22no—
89C2×D8×C37—41no—
90C2×D8×C37—41no—
91C2×D8×C37—41no—
92C2×M16×C37—22no—
93C2×M16×C37—22no—
94C2×M16×C37—41no—
95C22×C8×C37C2311yescharacteristic
96C22×C8×C37C2311yescharacteristic
97C22×C8×C37C2311yescharacteristic
98C22×C8×C37C2311yescharacteristic
99#127×C37—22no—
100#127×C37—22no—
101#127×C37—41no—
102#127×C37—41no—
103#121×C37—22no—
104#121×C37—22no—
105#121×C37—22no—
106#121×C37D414yescomplemented
107#120×C37—44no—
108#120×C37—44no—
109C4×D4×C37—22no—
110C4×D4×C37—41no—
111#117×C37—22no—
112#117×C37—41no—
113C2×C4⋊C4×C37—21no—
114C2×C4⋊C4×C37C2311yescharacteristic
115C2×C4⋊C4×C37C2311yescharacteristic
116C2×C4⋊C4×C37C2311yescharacteristic
117C2×C4⋊C4×C37C2311yescharacteristic
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×C37—21no—
132C2×C42×C37C2311yescharacteristic
133C2×C42×C37C2311yescharacteristic
134#106×C37—22no—
135C4⋊C8×C37—22no—
136C4⋊C8×C37—41no—
137#102×C37—22no—
138#102×C37—22no—
139#102×C37—22no—
140#102×C37—22no—
141#102×C37—22no—
142#102×C37—22no—
143#102×C37—22no—
144#102×C37—22no—
145#102×C37—41no—
146#102×C37D414yescomplemented
147C22⋊C8×C37—22no—
148#95×C37—21no—
149#95×C37—21no—
150#95×C37D411yescharacteristic
151#95×C37D411yescharacteristic
152C24×C37—21no—
153C24×C37—21no—
154C24×C37—21no—
155C24×C37—21no—
156C24×C37—42no—
157C24×C37—42no—
158C24×C37—42no—
159C24×C37—42no—
160C24×C37—42no—
161C24×C37—81no—
162C24×C37—81no—
163C24×C37C2×D411yescharacteristic
164C2×D4×C37—28no—
165C2×D4×C37—24no—
166C2×D4×C37—21no—
167C2×D4×C37—21no—
168C2×D4×C37—21no—
169C2×D4×C37—21no—
170C2×D4×C37—21no—
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—21no—
182C2×D4×C37—21no—
183C2×D4×C37—21no—
184C2×D4×C37—21no—
185C2×D4×C37—21no—
186C2×D4×C37—21no—
187C2×D4×C37—44no—
188C2×D4×C37—44no—
189C2×D4×C37—42no—
190C2×D4×C37—42no—
191C2×D4×C37—44no—
192C2×D4×C37—42no—
193C2×D4×C37—42no—
194C2×D4×C37—42no—
195C2×D4×C37—42no—
196C2×D4×C37—42no—
197C2×D4×C37—42no—
198C2×D4×C37—42no—
199C2×D4×C37—42no—
200C2×D4×C37—42no—
201C2×D4×C37—42no—
202C2×D4×C37—42no—
203C2×D4×C37—42no—
204C2×D4×C37—81no—
205C2×D4×C37—81no—
206C2×D4×C37—81no—
207C2×D4×C37—81no—
208C2×D4×C37—81no—
209C2×D4×C37—81no—
210C2×D4×C37C2×D412yes—
211C2×D4×C37C2×D412yes—
212C2×D4×C37#4112yes—
213C22×C4×C37—21no—
214C22×C4×C37—21no—
215C22×C4×C37—21no—
216C22×C4×C37—21no—
217C22×C4×C37—21no—
218C22×C4×C37—21no—
219C22×C4×C37—21no—
220C22×C4×C37—21no—
221C22×C4×C37—42no—
222C22×C4×C37—42no—
223C22×C4×C37—81no—
224C22×C4×C37C2×D411yescharacteristic
225C22×C4×C37C2×D411yescharacteristic
226C22×C4×C37C2×D411yescharacteristic
227C22×C4×C37C2×D412yes—
228C22×C4×C37C2×D411yescharacteristic
229C22×C4×C37C2×D411yescharacteristic
230C22×C4×C37#4112yes—
231C22×C4×C37C2411yescharacteristic
232D8×C37—44no—
233D8×C37—44no—
234D8×C37—44no—
235M16×C37—44no—
236C2×C8×C37—21no—
237C2×C8×C37—21no—
238C2×C8×C37—21no—
239C2×C8×C37—21no—
240C2×C8×C37—21no—
241C2×C8×C37—21no—
242C2×C8×C37—21no—
243C2×C8×C37—21no—
244C2×C8×C37—21no—
245C2×C8×C37—21no—
246C2×C8×C37—21no—
247C2×C8×C37C2×D412yes—
248C4⋊C4×C37—21no—
249C4⋊C4×C37—21no—
250C4⋊C4×C37—21no—
251C4⋊C4×C37—21no—
252C4⋊C4×C37—21no—
253C4⋊C4×C37—21no—
254C4⋊C4×C37—81no—
255C4⋊C4×C37C2×D412yes—
256C4⋊C4×C37C2×D412yes—
257C22⋊C4×C37—24no—
258C22⋊C4×C37—22no—
259C22⋊C4×C37—22no—
260C22⋊C4×C37—42no—
261C22⋊C4×C37—42no—
262C22⋊C4×C37—42no—
263C22⋊C4×C37—42no—
264C22⋊C4×C37—42no—
265C22⋊C4×C37—42no—
266C22⋊C4×C37—42no—
267C22⋊C4×C37—42no—
268C22⋊C4×C37—81no—
269C42×C37—21no—
270C42×C37—21no—
271C42×C37—21no—
272C42×C37—21no—
273C42×C37—42no—
274C42×C37—81no—
275C23×C37—21no—
276C23×C37—21no—
277C23×C37—21no—
278C23×C37—21no—
279C23×C37—21no—
280C23×C37—21no—
281C23×C37—22no—
282C23×C37—22no—
283C23×C37—22no—
284C23×C37—48no—
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—41no—
294C23×C37—41no—
295C23×C37—41no—
296C23×C37—41no—
297C23×C37—41no—
298C23×C37—41no—
299C23×C37—41no—
300C23×C37—41no—
301C23×C37—41no—
302C23×C37—41no—
303C23×C37—41no—
304C23×C37—41no—
305C23×C37—41no—
306C23×C37—41no—
307C23×C37—41no—
308C23×C37—41no—
309C23×C37—41no—
310C23×C37—84no—
311C23×C37—84no—
312C23×C37—84no—
313C23×C37—84no—
314C23×C37—84no—
315C23×C37—84no—
316C23×C37#12112yes—
317C23×C37C22×D411yescharacteristic
318D4×C37—22no—
319D4×C37—22no—
320D4×C37—22no—
321D4×C37—22no—
322D4×C37—22no—
323D4×C37—22no—
324D4×C37—48no—
325D4×C37—41no—
326D4×C37—41no—
327D4×C37—41no—
328D4×C37—41no—
329D4×C37—41no—
330D4×C37—41no—
331D4×C37—41no—
332D4×C37—41no—
333D4×C37—41no—
334D4×C37—41no—
335D4×C37—84no—
336D4×C37—84no—
337D4×C37—84no—
338D4×C37—84no—
339D4×C37—84no—
340D4×C37—84no—
341C2×C4×C37—21no—
342C2×C4×C37—21no—
343C2×C4×C37—21no—
344C2×C4×C37—21no—
345C2×C4×C37—21no—
346C2×C4×C37—21no—
347C2×C4×C37—22no—
348C2×C4×C37—22no—
349C2×C4×C37—22no—
350C2×C4×C37—22no—
351C2×C4×C37—22no—
352C2×C4×C37—21no—
353C2×C4×C37—22no—
354C2×C4×C37—21no—
355C2×C4×C37—21no—
356C2×C4×C37—21no—
357C2×C4×C37—21no—
358C2×C4×C37—21no—
359C2×C4×C37—41no—
360C2×C4×C37—41no—
361C2×C4×C37—41no—
362C2×C4×C37—41no—
363C2×C4×C37—41no—
364C2×C4×C37—41no—
365C2×C4×C37—41no—
366C2×C4×C37—41no—
367C2×C4×C37—41no—
368C2×C4×C37—41no—
369C2×C4×C37—84no—
370C2×C4×C37#12112yes—
371C2×C4×C37AGL(1,ℤ/8)12yes—
372C2×C4×C37AGL(1,ℤ/8)12yes—
373C2×C4×C37C22×D411yescharacteristic
374C2×C4×C37C22×D411yescharacteristic
375C2×C4×C37C2×#4111yescharacteristic
376C2×C4×C37C2×#4111yescharacteristic
377C2×C4×C37H(5,𝔽2)11yescharacteristic
378C2×C4×C37H(5,𝔽2)11yescharacteristic
379C8×C37—22no—
380C8×C37—41no—
381C8×C37—41no—
382C8×C37—41no—
383#25097C3711yesmaximal, characteristic, direct product factor, Sylow
384C22×C37—22no—
385C22×C37—22no—
386C22×C37—22no—
387C22×C37—41no—
388C22×C37—41no—
389C22×C37—41no—
390C22×C37—41no—
391C22×C37—42no—
392C22×C37—42no—
393C22×C37—42no—
394C22×C37—42no—
395C22×C37—42no—
396C22×C37—42no—
397C22×C37—42no—
398C22×C37—42no—
399C22×C37—42no—
400C22×C37—816no—
401C22×C37—81no—
402C22×C37—81no—
403C22×C37—81no—
404C22×C37—81no—
405C22×C37—81no—
406C22×C37—81no—
407C22×C37—81no—
408C22×C37—81no—
409C22×C37—81no—
410C22×C37—81no—
411C22×C37—81no—
412C22×C37—81no—
413C22×C37—81no—
414C22×C37—81no—
415C22×C37—81no—
416C22×C37—81no—
417C22×C37—81no—
418C22×C37—81no—
419C22×C37—81no—
420C22×C37C2×#12111yescharacteristic
421C22×C37D4211yescharacteristic
422C22×C37#54611yescharacteristic
423C22×C37C2×AGL(1,ℤ/8)11yescharacteristic
424C22×C37C2×AGL(1,ℤ/8)11yescharacteristic
425C22×C37#57611yescharacteristic
426C22×C37#57611yescharacteristic
427C4×C37—22no—
428C4×C37—22no—
429C4×C37—22no—
430C4×C37—42no—
431C4×C37—41no—
432C4×C37—42no—
433C4×C37—41no—
434C4×C37—81no—
435C4×C37—81no—
436C4×C37#52511yescharacteristic
437C4×C37#53811yescharacteristic
438C4×C37D4211yescharacteristic
439C4×C37#54611yescharacteristic
440C2×#469C2×C3711yescharacteristic, complemented
441C2×#459C2×C3711yescharacteristic, complemented
442C2×#447C2×C3711yescharacteristic, complemented
443C2×#418C2×C3711yescharacteristic, complemented
444#2433C2×C3711yescharacteristic, complemented
445#2363C2×C3711yescharacteristic, complemented
446#2065C2×C3711yescharacteristic, complemented
447#2054C2×C3711yescharacteristic, complemented
448#2041C2×C3711yescharacteristic, complemented
449#2011C2×C3711yescharacteristic, complemented
450#1982C2×C3711yescharacteristic, complemented
451#1926C2×C3711yescharacteristic, complemented
452#1879C2×C3711yescharacteristic, complemented
453#1875C2×C3711yescharacteristic, complemented
454#1851C2×C3711yescharacteristic, complemented
455C2×C37—42no—
456C2×C37—82no—
457C2×C37—82no—
458C2×C37—82no—
459C2×C37—161no—
460C2×C37#242411yescharacteristic
461C2×C37#303811yescharacteristic
462C2×C37#304111yescharacteristic
463C2×C37#326411yescharacteristic
464C2×C37#327411yescharacteristic
465C2×C37#331811yescharacteristic
466C2×C37#332511yescharacteristic
467C23×D4C22×C3711yescharacteristic
468C22×D8C22×C3711yescharacteristic
469C22×D8C22×C3711yescharacteristic
470C22×D8C22×C3711yescharacteristic, complemented
471C22×M16C22×C3711yescharacteristic
472C2×#127C22×C3711yescharacteristic
473C2×#127C22×C3711yescharacteristic
474C2×#121C22×C3711yescharacteristic
475C2×#121C22×C3711yescharacteristic
476C2×#120—21no—
477C2×#120—21no—
478C2×C4×D4C22×C3711yescharacteristic, complemented
479C2×#117C22×C3711yescharacteristic
480#469—24no—
481#459—24no—
482#447—24no—
483C2×#106C22×C3711yescharacteristic, complemented
484C2×C4⋊C8C22×C3711yescharacteristic, complemented
485C2×C4⋊C8C22×C3711yescharacteristic, complemented
486#418—24no—
487C2×#102C22×C3711yescharacteristic
488C2×#102C22×C3711yescharacteristic
489C2×#102C22×C3711yescharacteristic
490C2×#102C22×C3711yescharacteristic
491C2×#102C22×C3711yescharacteristic
492C2×#102C22×C3711yescharacteristic
493C2×#102C22×C3711yescharacteristic, complemented
494C2×#102C22×C3711yescharacteristic, complemented
495C2×#102C22×C3711yescharacteristic, complemented
496C2×#102C22×C3711yescharacteristic, complemented
497C2×C22⋊C8C22×C3711yescharacteristic
498#392—21no—
499#392—21no—
500#390—21no—
501#390C22×C3711yescharacteristic
502#390C22×C3711yescharacteristic
503#390C22×C3711yescharacteristic, complemented
504#389C22×C3711yescharacteristic, complemented
505#388—21no—
506#386—21no—
507C4×C4⋊C4C22×C3711yescharacteristic, complemented
508C4×C22⋊C4—21no—
509C4×C22⋊C4C22×C3711yescharacteristic
510#340C22×C3711yescharacteristic, complemented
511#340C22×C3711yescharacteristic, complemented
512#336C22×C3711yescharacteristic, complemented
513#336C22×C3711yescharacteristic, complemented
514C37#2509711yescharacteristic, direct product factor, Sylow
515C25—21no—
516C22×D4—22no—
517C22×D4—22no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—22no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—21no—
524C22×D4—21no—
525C22×D4—21no—
526C22×D4—22no—
527C22×D4—41no—
528C22×D4—41no—
529C22×D4C23×C3711yescharacteristic
530C22×D4C23×C3711yescharacteristic
531C22×D4C23×C3711yescharacteristic
532C22×D4C23×C3711yescharacteristic
533C23×C4—21no—
534C23×C4C23×C3711yescharacteristic
535C2×D8—22no—
536C2×D8—22no—
537C2×D8—22no—
538C2×D8—22no—
539C2×D8—22no—
540C2×D8—22no—
541C2×D8—41no—
542C2×D8—41no—
543C2×D8—41no—
544C2×M16—22no—
545C2×M16—22no—
546C2×M16—41no—
547C22×C8C23×C3711yescharacteristic
548C22×C8C23×C3711yescharacteristic
549C22×C8C23×C3711yescharacteristic
550C22×C8C23×C3711yescharacteristic
551#127—22no—
552#127—22no—
553#127—41no—
554#127—41no—
555#121—22no—
556#121—22no—
557#121—22no—
558#121D4×C3714yescomplemented
559#120—44no—
560#120—44no—
561C4×D4—22no—
562C4×D4—41no—
563#117—22no—
564#117—41no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4C23×C3711yescharacteristic
567C2×C4⋊C4C23×C3711yescharacteristic
568C2×C4⋊C4C23×C3711yescharacteristic
569C2×C4⋊C4C23×C3711yescharacteristic
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4—21no—
578C2×C22⋊C4—21no—
579C2×C22⋊C4—21no—
580C2×C22⋊C4D4×C3711yescharacteristic
581C2×C22⋊C4D4×C3711yescharacteristic
582C2×C42—21no—
583C2×C42—21no—
584C2×C42C23×C3711yescharacteristic
585C2×C42C23×C3711yescharacteristic
586#106—22no—
587C4⋊C8—22no—
588C4⋊C8—41no—
589#102—22no—
590#102—22no—
591#102—22no—
592#102—22no—
593#102—22no—
594#102—22no—
595#102—22no—
596#102—22no—
597#102—41no—
598#102D4×C3714yescomplemented
599C22⋊C8—22no—
600#95—21no—
601#95—21no—
602#95D4×C3711yescharacteristic
603#95D4×C3711yescharacteristic
604C24—21no—
605C24—21no—
606C24—21no—
607C24—21no—
608C24—42no—
609C24—42no—
610C24—42no—
611C24—42no—
612C24—42no—
613C24—81no—
614C24—81no—
615C24C2×D4×C3711yescharacteristic
616C2×D4—28no—
617C2×D4—24no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—44no—
640C2×D4—44no—
641C2×D4—42no—
642C2×D4—42no—
643C2×D4—44no—
644C2×D4—42no—
645C2×D4—42no—
646C2×D4—42no—
647C2×D4—42no—
648C2×D4—42no—
649C2×D4—42no—
650C2×D4—42no—
651C2×D4—42no—
652C2×D4—42no—
653C2×D4—42no—
654C2×D4—42no—
655C2×D4—42no—
656C2×D4—81no—
657C2×D4—81no—
658C2×D4—81no—
659C2×D4—81no—
660C2×D4—81no—
661C2×D4—81no—
662C2×D4C2×D4×C3712yes—
663C2×D4C2×D4×C3712yes—
664C2×D4#41×C3712yes—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—42no—
674C22×C4—42no—
675C22×C4—81no—
676C22×C4C2×D4×C3711yescharacteristic
677C22×C4C2×D4×C3711yescharacteristic
678C22×C4C2×D4×C3711yescharacteristic
679C22×C4C2×D4×C3712yes—
680C22×C4C2×D4×C3711yescharacteristic
681C22×C4C2×D4×C3711yescharacteristic
682C22×C4#41×C3712yes—
683C22×C4C24×C3711yescharacteristic
684D8—44no—
685D8—44no—
686D8—44no—
687M16—44no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8C2×D4×C3712yes—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—81no—
707C4⋊C4C2×D4×C3712yes—
708C4⋊C4C2×D4×C3712yes—
709C22⋊C4—24no—
710C22⋊C4—22no—
711C22⋊C4—22no—
712C22⋊C4—42no—
713C22⋊C4—42no—
714C22⋊C4—42no—
715C22⋊C4—42no—
716C22⋊C4—42no—
717C22⋊C4—42no—
718C22⋊C4—42no—
719C22⋊C4—42no—
720C22⋊C4—81no—
721C42—21no—
722C42—21no—
723C42—21no—
724C42—21no—
725C42—42no—
726C42—81no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—48no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—84no—
763C23—84no—
764C23—84no—
765C23—84no—
766C23—84no—
767C23—84no—
768C23#121×C3712yes—
769C23C22×D4×C3711yescharacteristic
770D4—22no—
771D4—22no—
772D4—22no—
773D4—22no—
774D4—22no—
775D4—22no—
776D4—48no—
777D4—41no—
778D4—41no—
779D4—41no—
780D4—41no—
781D4—41no—
782D4—41no—
783D4—41no—
784D4—41no—
785D4—41no—
786D4—41no—
787D4—84no—
788D4—84no—
789D4—84no—
790D4—84no—
791D4—84no—
792D4—84no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—21no—
805C2×C4—22no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—84no—
822C2×C4#121×C3712yes—
823C2×C4AGL(1,ℤ/8)×C3712yes—
824C2×C4AGL(1,ℤ/8)×C3712yes—
825C2×C4C22×D4×C3711yescharacteristic
826C2×C4C22×D4×C3711yescharacteristic
827C2×C4C2×#41×C3711yescharacteristic
828C2×C4C2×#41×C3711yescharacteristic
829C2×C4H(5,𝔽2)×C3711yescharacteristic
830C2×C4H(5,𝔽2)×C3711yescharacteristic
831C8—22no—
832C8—41no—
833C8—41no—
834C8—41no—
835C22—22no—
836C22—22no—
837C22—22no—
838C22—41no—
839C22—41no—
840C22—41no—
841C22—41no—
842C22—42no—
843C22—42no—
844C22—42no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—816no—
852C22—81no—
853C22—81no—
854C22—81no—
855C22—81no—
856C22—81no—
857C22—81no—
858C22—81no—
859C22—81no—
860C22—81no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22—81no—
865C22—81no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22—81no—
871C22C2×#121×C3711yescharacteristic
872C22D42×C3711yescharacteristic
873C22C37×#54611yescharacteristic
874C22C2×AGL(1,ℤ/8)×C3711yescharacteristic
875C22C2×AGL(1,ℤ/8)×C3711yescharacteristic
876C22C37×#57611yescharacteristic
877C22C37×#57611yescharacteristic
878C4—22no—
879C4—22no—
880C4—22no—
881C4—42no—
882C4—41no—
883C4—42no—
884C4—41no—
885C4—81no—
886C4—81no—
887C4C37×#52511yescharacteristic
888C4C37×#53811yescharacteristic
889C4D42×C3711yescharacteristic
890C4C37×#54611yescharacteristic
891C2—42no—
892C2—82no—
893C2—82no—
894C2—82no—
895C2—161no—
896C2C37×#242411yescharacteristic
897C2C37×#303811yescharacteristic
898C2C37×#304111yescharacteristic
899C2C37×#326411yescharacteristic
900C2C37×#327411yescharacteristic
901C2C37×#331811yescharacteristic
902C2C37×#332511yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C37 ◁ C4×C22⋊C4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C37×#469C2semidirect
2. C2×C37×#459C2semidirect
3. C2×C37×#447C2semidirect
4. C2×C37×#418C2semidirect
5. C37×#2433C2semidirect
6. C37×#2363C2semidirect
7. C37×#2065C2semidirect
8. C37×#2054C2semidirect
9. C37×#2041C2semidirect
10. C37×#2011C2semidirect
11. C37×#1982C2semidirect
12. C37×#1926C2semidirect
13. C37×#1879C2semidirect
14. C37×#1875C2semidirect
15. C37×#1851C2semidirect
19. C22×D8×C37C22semidirect
27. C2×C4×D4×C37C22semidirect
32. C2×#106×C37C22semidirect
33. C2×C4⋊C8×C37C22semidirect
34. C2×C4⋊C8×C37C22semidirect
42. C2×#102×C37C22semidirect
43. C2×#102×C37C22semidirect
44. C2×#102×C37C22semidirect
45. C2×#102×C37C22semidirect
52. C37×#390C22semidirect
53. C37×#389C22semidirect
56. C4×C4⋊C4×C37C22semidirect
59. C37×#340C22semidirect
60. C37×#340C22semidirect
61. C37×#336C22semidirect
62. C37×#336C22semidirect
106. #121×C37D4semidirect
146. #102×C37D4semidirect
383. #25097C37direct (N × H)
440. C2×#469C2×C37semidirect
441. C2×#459C2×C37semidirect
442. C2×#447C2×C37semidirect
443. C2×#418C2×C37semidirect
444. #2433C2×C37semidirect
445. #2363C2×C37semidirect
446. #2065C2×C37semidirect
447. #2054C2×C37semidirect
448. #2041C2×C37semidirect
449. #2011C2×C37semidirect
450. #1982C2×C37semidirect
451. #1926C2×C37semidirect
452. #1879C2×C37semidirect
453. #1875C2×C37semidirect
454. #1851C2×C37semidirect
470. C22×D8C22×C37semidirect
478. C2×C4×D4C22×C37semidirect
483. C2×#106C22×C37semidirect
484. C2×C4⋊C8C22×C37semidirect
485. C2×C4⋊C8C22×C37semidirect
493. C2×#102C22×C37semidirect
494. C2×#102C22×C37semidirect
495. C2×#102C22×C37semidirect
496. C2×#102C22×C37semidirect
503. #390C22×C37semidirect
504. #389C22×C37semidirect
507. C4×C4⋊C4C22×C37semidirect
510. #340C22×C37semidirect
511. #340C22×C37semidirect
512. #336C22×C37semidirect
513. #336C22×C37semidirect
514. C37#25097direct (N × H)
558. #121D4×C37semidirect
598. #102D4×C37semidirect

Maximal subgroups

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

subgroupindex
C2×C37×#4692
C2×C37×#4592
C2×C37×#4472
C2×C37×#4182
C37×#24332
C37×#23632
C37×#20652
C37×#20542
C37×#20412
C37×#20112
C37×#19822
C37×#19262
C37×#18792
C37×#18752
C37×#18512
#2509737