Finite Group Databasebeta

← C37×#25076 #22646329

Subgroups — C37×#25076 #22646329

Order 9472.

1440 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#466C211yesmaximal, characteristic, complemented
2C2×C37×#459C211yesmaximal, characteristic, complemented
3C2×C37×#447C211yesmaximal, characteristic, complemented
4C22×#102×C37C211yesmaximal, characteristic, complemented
5C37×#2433C211yesmaximal, characteristic, complemented
6C37×#2361C211yesmaximal, characteristic, complemented
7C37×#2067C211yesmaximal, characteristic, complemented
8C37×#2054C211yesmaximal, characteristic, complemented
9C37×#2041C211yesmaximal, characteristic, complemented
10C37×#2011C211yesmaximal, characteristic, complemented
11C37×#1982C211yesmaximal, characteristic, complemented
12C37×#1925C211yesmaximal, characteristic, complemented
13C37×#1879C211yesmaximal, characteristic, complemented
14C37×#1874C211yesmaximal, characteristic, complemented
15C37×#1850C211yesmaximal, characteristic, complemented
16C23×D4×C37C2211yescharacteristic
17C22×D8×C37C2211yescharacteristic
18C22×D8×C37C2211yescharacteristic
19C22×D8×C37C2211yescharacteristic, complemented
20C23×C8×C37C2211yescharacteristic
21C2×#127×C37C2211yescharacteristic
22C2×#127×C37C2211yescharacteristic
23C2×#121×C37C2211yescharacteristic
24C2×#121×C37C2211yescharacteristic
25C2×#120×C37—21no—
26C2×#120×C37—21no—
27C2×C4×D4×C37—21no—
28C2×C4×D4×C37C2211yescharacteristic, complemented
29C22×C4⋊C4×C37C2211yescharacteristic
30C37×#466—24no—
31C37×#459—24no—
32C37×#447—24no—
33C2×#107×C37C2211yescharacteristic, complemented
34C2×C4⋊C8×C37C2211yescharacteristic, complemented
35C2×C4⋊C8×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×#102×C37C2211yescharacteristic, complemented
44C2×#102×C37C2211yescharacteristic, complemented
45C2×#102×C37C2211yescharacteristic, complemented
46C2×#102×C37C2211yescharacteristic, complemented
47C2×C22⋊C8×C37C2211yescharacteristic
48C37×#392—21no—
49C37×#392—21no—
50C37×#390C2211yescharacteristic
51C37×#390C2211yescharacteristic
52C37×#390C2211yescharacteristic, complemented
53C37×#389C2211yescharacteristic, complemented
54C37×#388—21no—
55C37×#386—21no—
56C37×#385—21no—
57C4×C4⋊C4×C37C2211yescharacteristic, complemented
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×C37—21no—
83C23×C4×C37C2311yescharacteristic
84C2×D8×C37—22no—
85C2×D8×C37—22no—
86C2×D8×C37—22no—
87C2×D8×C37—22no—
88C2×D8×C37—22no—
89C2×D8×C37—22no—
90C2×D8×C37—41no—
91C2×D8×C37—41no—
92C2×D8×C37—41no—
93C22×C8×C37—22no—
94C22×C8×C37—22no—
95C22×C8×C37—41no—
96C22×C8×C37C2311yescharacteristic
97C22×C8×C37C2311yescharacteristic
98C22×C8×C37C2311yescharacteristic
99C22×C8×C37C2311yescharacteristic
100#127×C37—22no—
101#127×C37—22no—
102#127×C37—41no—
103#127×C37—41no—
104#121×C37—22no—
105#121×C37—22no—
106#121×C37—22no—
107#121×C37D414yescomplemented
108#120×C37—44no—
109#120×C37—44no—
110C4×D4×C37—22no—
111C4×D4×C37—41no—
112C4×D4×C37—44no—
113C2×C4⋊C4×C37—22no—
114C2×C4⋊C4×C37—21no—
115C2×C4⋊C4×C37—21no—
116C2×C4⋊C4×C37—41no—
117C2×C4⋊C4×C37C2311yescharacteristic
118C2×C4⋊C4×C37C2311yescharacteristic
119C2×C4⋊C4×C37C2311yescharacteristic
120C2×C4⋊C4×C37C2311yescharacteristic
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×C37—21no—
130C2×C22⋊C4×C37D411yescharacteristic
131C2×C22⋊C4×C37D411yescharacteristic
132C2×C42×C37—21no—
133C2×C42×C37C2311yescharacteristic
134C2×C42×C37C2311yescharacteristic
135#107×C37—22no—
136C4⋊C8×C37—22no—
137C4⋊C8×C37—41no—
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—22no—
146#102×C37—41no—
147#102×C37D414yescomplemented
148C22⋊C8×C37—22no—
149#95×C37—21no—
150#95×C37—21no—
151#95×C37D411yescharacteristic
152#95×C37D411yescharacteristic
153C24×C37—21no—
154C24×C37—21no—
155C24×C37—21no—
156C24×C37—21no—
157C24×C37—42no—
158C24×C37—42no—
159C24×C37—42no—
160C24×C37—42no—
161C24×C37—42no—
162C24×C37—81no—
163C24×C37—81no—
164C24×C37C2×D411yescharacteristic
165C2×D4×C37—28no—
166C2×D4×C37—24no—
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—21no—
188C2×D4×C37—44no—
189C2×D4×C37—44no—
190C2×D4×C37—42no—
191C2×D4×C37—42no—
192C2×D4×C37—44no—
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—42no—
205C2×D4×C37—42no—
206C2×D4×C37—42no—
207C2×D4×C37—81no—
208C2×D4×C37—81no—
209C2×D4×C37—81no—
210C2×D4×C37—81no—
211C2×D4×C37C2×D412yes—
212C2×D4×C37C2×D412yes—
213C2×D4×C37#4112yes—
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—21no—
222C22×C4×C37—42no—
223C22×C4×C37—42no—
224C22×C4×C37—42no—
225C22×C4×C37—42no—
226C22×C4×C37—81no—
227C22×C4×C37—81no—
228C22×C4×C37C2×D411yescharacteristic
229C22×C4×C37C2×D411yescharacteristic
230C22×C4×C37C2×D411yescharacteristic
231C22×C4×C37C2×D412yes—
232C22×C4×C37C2×D411yescharacteristic
233C22×C4×C37C2×D411yescharacteristic
234C22×C4×C37#4112yes—
235C22×C4×C37C2411yescharacteristic
236D8×C37—44no—
237D8×C37—44no—
238D8×C37—44no—
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×C37—21no—
248C2×C8×C37—21no—
249C2×C8×C37—21no—
250C2×C8×C37—44no—
251C2×C8×C37C2×D412yes—
252C4⋊C4×C37—21no—
253C4⋊C4×C37—21no—
254C4⋊C4×C37—21no—
255C4⋊C4×C37—21no—
256C4⋊C4×C37—21no—
257C4⋊C4×C37—21no—
258C4⋊C4×C37—42no—
259C4⋊C4×C37—42no—
260C4⋊C4×C37C2×D412yes—
261C4⋊C4×C37C2×D412yes—
262C22⋊C4×C37—22no—
263C22⋊C4×C37—24no—
264C22⋊C4×C37—42no—
265C22⋊C4×C37—42no—
266C22⋊C4×C37—42no—
267C22⋊C4×C37—42no—
268C22⋊C4×C37—42no—
269C22⋊C4×C37—42no—
270C22⋊C4×C37—42no—
271C22⋊C4×C37—81no—
272C22⋊C4×C37D814yescomplemented
273C42×C37—21no—
274C42×C37—21no—
275C42×C37—21no—
276C42×C37—21no—
277C42×C37—42no—
278C23×C37—21no—
279C23×C37—21no—
280C23×C37—21no—
281C23×C37—21no—
282C23×C37—22no—
283C23×C37—22no—
284C23×C37—22no—
285C23×C37—48no—
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—41no—
311C23×C37—84no—
312C23×C37—84no—
313C23×C37—84no—
314C23×C37—84no—
315C23×C37—84no—
316C23×C37—84no—
317C23×C37#12112yes—
318C23×C37C2×D812yes—
319C23×C37AGL(1,ℤ/8)12yes—
320C23×C37C22×D411yescharacteristic
321D4×C37—22no—
322D4×C37—22no—
323D4×C37—22no—
324D4×C37—22no—
325D4×C37—22no—
326D4×C37—22no—
327D4×C37—48no—
328D4×C37—48no—
329D4×C37—41no—
330D4×C37—41no—
331D4×C37—41no—
332D4×C37—41no—
333D4×C37—41no—
334D4×C37—41no—
335D4×C37—41no—
336D4×C37—41no—
337D4×C37—41no—
338D4×C37—41no—
339D4×C37—84no—
340D4×C37—84no—
341D4×C37—84no—
342D4×C37—84no—
343D4×C37—84no—
344C2×C4×C37—21no—
345C2×C4×C37—21no—
346C2×C4×C37—21no—
347C2×C4×C37—21no—
348C2×C4×C37—21no—
349C2×C4×C37—21no—
350C2×C4×C37—22no—
351C2×C4×C37—22no—
352C2×C4×C37—22no—
353C2×C4×C37—22no—
354C2×C4×C37—22no—
355C2×C4×C37—21no—
356C2×C4×C37—22no—
357C2×C4×C37—21no—
358C2×C4×C37—21no—
359C2×C4×C37—21no—
360C2×C4×C37—21no—
361C2×C4×C37—21no—
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—41no—
370C2×C4×C37—41no—
371C2×C4×C37—41no—
372C2×C4×C37—84no—
373C2×C4×C37—84no—
374C2×C4×C37#12112yes—
375C2×C4×C37C2×D812yes—
376C2×C4×C37C2×D812yes—
377C2×C4×C37C22×D411yescharacteristic
378C2×C4×C37C22×D411yescharacteristic
379C2×C4×C37C2×#4111yescharacteristic
380C2×C4×C37C2×#4111yescharacteristic
381C2×C4×C37H(5,𝔽2)11yescharacteristic
382C2×C4×C37H(5,𝔽2)11yescharacteristic
383C8×C37—22no—
384C8×C37—41no—
385C8×C37—41no—
386C8×C37—41no—
387#25076C3711yesmaximal, characteristic, direct product factor, Sylow
388C22×C37—22no—
389C22×C37—22no—
390C22×C37—22no—
391C22×C37—22no—
392C22×C37—22no—
393C22×C37—22no—
394C22×C37—42no—
395C22×C37—42no—
396C22×C37—42no—
397C22×C37—42no—
398C22×C37—42no—
399C22×C37—42no—
400C22×C37—42no—
401C22×C37—42no—
402C22×C37—42no—
403C22×C37—816no—
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×C37—81no—
421C22×C37—81no—
422C22×C37—81no—
423C22×C37#45914yescomplemented
424C22×C37C2×#12111yescharacteristic
425C22×C37D4211yescharacteristic
426C22×C37#54611yescharacteristic
427C22×C37C22×D811yescharacteristic
428C22×C37C2×AGL(1,ℤ/8)11yescharacteristic
429C22×C37#57611yescharacteristic
430C22×C37#57711yescharacteristic
431C4×C37—22no—
432C4×C37—22no—
433C4×C37—22no—
434C4×C37—41no—
435C4×C37—42no—
436C4×C37—42no—
437C4×C37—41no—
438C4×C37—81no—
439C4×C37—81no—
440C4×C37#52511yescharacteristic
441C4×C37#53811yescharacteristic
442C4×C37D4211yescharacteristic
443C4×C37#54611yescharacteristic
444C2×#466C2×C3711yescharacteristic, complemented
445C2×#459C2×C3711yescharacteristic, complemented
446C2×#447C2×C3711yescharacteristic, complemented
447C22×#102C2×C3711yescharacteristic, complemented
448#2433C2×C3711yescharacteristic, complemented
449#2361C2×C3711yescharacteristic, complemented
450#2067C2×C3711yescharacteristic, complemented
451#2054C2×C3711yescharacteristic, complemented
452#2041C2×C3711yescharacteristic, complemented
453#2011C2×C3711yescharacteristic, complemented
454#1982C2×C3711yescharacteristic, complemented
455#1925C2×C3711yescharacteristic, complemented
456#1879C2×C3711yescharacteristic, complemented
457#1874C2×C3711yescharacteristic, complemented
458#1850C2×C3711yescharacteristic, complemented
459C2×C37—24no—
460C2×C37—82no—
461C2×C37—82no—
462C2×C37—82no—
463C2×C37—161no—
464C2×C37#242411yescharacteristic
465C2×C37C2×#45911yescharacteristic
466C2×C37#304511yescharacteristic
467C2×C37#326511yescharacteristic
468C2×C37D4×D811yescharacteristic
469C2×C37#329411yescharacteristic
470C2×C37#331811yescharacteristic
471C23×D4C22×C3711yescharacteristic
472C22×D8C22×C3711yescharacteristic
473C22×D8C22×C3711yescharacteristic
474C22×D8C22×C3711yescharacteristic, complemented
475C23×C8C22×C3711yescharacteristic
476C2×#127C22×C3711yescharacteristic
477C2×#127C22×C3711yescharacteristic
478C2×#121C22×C3711yescharacteristic
479C2×#121C22×C3711yescharacteristic
480C2×#120—21no—
481C2×#120—21no—
482C2×C4×D4—21no—
483C2×C4×D4C22×C3711yescharacteristic, complemented
484C22×C4⋊C4C22×C3711yescharacteristic
485#466—24no—
486#459—24no—
487#447—24no—
488C2×#107C22×C3711yescharacteristic, complemented
489C2×C4⋊C8C22×C3711yescharacteristic, complemented
490C2×C4⋊C8C22×C3711yescharacteristic, complemented
491C2×#102—24no—
492C2×#102C22×C3711yescharacteristic
493C2×#102C22×C3711yescharacteristic
494C2×#102C22×C3711yescharacteristic
495C2×#102C22×C3711yescharacteristic
496C2×#102C22×C3711yescharacteristic
497C2×#102C22×C3711yescharacteristic
498C2×#102C22×C3711yescharacteristic, complemented
499C2×#102C22×C3711yescharacteristic, complemented
500C2×#102C22×C3711yescharacteristic, complemented
501C2×#102C22×C3711yescharacteristic, complemented
502C2×C22⋊C8C22×C3711yescharacteristic
503#392—21no—
504#392—21no—
505#390C22×C3711yescharacteristic
506#390C22×C3711yescharacteristic
507#390C22×C3711yescharacteristic, complemented
508#389C22×C3711yescharacteristic, complemented
509#388—21no—
510#386—21no—
511#385—21no—
512C4×C4⋊C4C22×C3711yescharacteristic, complemented
513C4×C22⋊C4C22×C3711yescharacteristic
514#340C22×C3711yescharacteristic, complemented
515#340C22×C3711yescharacteristic, complemented
516#336C22×C3711yescharacteristic, complemented
517#336C22×C3711yescharacteristic, complemented
518C37#2507611yescharacteristic, direct product factor, Sylow
519C25—21no—
520C22×D4—22no—
521C22×D4—22no—
522C22×D4—21no—
523C22×D4—21no—
524C22×D4—22no—
525C22×D4—21no—
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—21no—
529C22×D4—21no—
530C22×D4—22no—
531C22×D4—41no—
532C22×D4—41no—
533C22×D4C23×C3711yescharacteristic
534C22×D4C23×C3711yescharacteristic
535C22×D4C23×C3711yescharacteristic
536C22×D4C23×C3711yescharacteristic
537C23×C4—21no—
538C23×C4—21no—
539C23×C4C23×C3711yescharacteristic
540C2×D8—22no—
541C2×D8—22no—
542C2×D8—22no—
543C2×D8—22no—
544C2×D8—22no—
545C2×D8—22no—
546C2×D8—41no—
547C2×D8—41no—
548C2×D8—41no—
549C22×C8—22no—
550C22×C8—22no—
551C22×C8—41no—
552C22×C8C23×C3711yescharacteristic
553C22×C8C23×C3711yescharacteristic
554C22×C8C23×C3711yescharacteristic
555C22×C8C23×C3711yescharacteristic
556#127—22no—
557#127—22no—
558#127—41no—
559#127—41no—
560#121—22no—
561#121—22no—
562#121—22no—
563#121D4×C3714yescomplemented
564#120—44no—
565#120—44no—
566C4×D4—22no—
567C4×D4—41no—
568C4×D4—44no—
569C2×C4⋊C4—22no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—41no—
573C2×C4⋊C4C23×C3711yescharacteristic
574C2×C4⋊C4C23×C3711yescharacteristic
575C2×C4⋊C4C23×C3711yescharacteristic
576C2×C4⋊C4C23×C3711yescharacteristic
577C2×C22⋊C4—21no—
578C2×C22⋊C4—21no—
579C2×C22⋊C4—21no—
580C2×C22⋊C4—21no—
581C2×C22⋊C4—21no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4D4×C3711yescharacteristic
587C2×C22⋊C4D4×C3711yescharacteristic
588C2×C42—21no—
589C2×C42C23×C3711yescharacteristic
590C2×C42C23×C3711yescharacteristic
591#107—22no—
592C4⋊C8—22no—
593C4⋊C8—41no—
594#102—22no—
595#102—22no—
596#102—22no—
597#102—22no—
598#102—22no—
599#102—22no—
600#102—22no—
601#102—22no—
602#102—41no—
603#102D4×C3714yescomplemented
604C22⋊C8—22no—
605#95—21no—
606#95—21no—
607#95D4×C3711yescharacteristic
608#95D4×C3711yescharacteristic
609C24—21no—
610C24—21no—
611C24—21no—
612C24—21no—
613C24—42no—
614C24—42no—
615C24—42no—
616C24—42no—
617C24—42no—
618C24—81no—
619C24—81no—
620C24C2×D4×C3711yescharacteristic
621C2×D4—28no—
622C2×D4—24no—
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—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—44no—
645C2×D4—44no—
646C2×D4—42no—
647C2×D4—42no—
648C2×D4—44no—
649C2×D4—42no—
650C2×D4—42no—
651C2×D4—42no—
652C2×D4—42no—
653C2×D4—42no—
654C2×D4—42no—
655C2×D4—42no—
656C2×D4—42no—
657C2×D4—42no—
658C2×D4—42no—
659C2×D4—42no—
660C2×D4—42no—
661C2×D4—42no—
662C2×D4—42no—
663C2×D4—81no—
664C2×D4—81no—
665C2×D4—81no—
666C2×D4—81no—
667C2×D4C2×D4×C3712yes—
668C2×D4C2×D4×C3712yes—
669C2×D4#41×C3712yes—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—42no—
679C22×C4—42no—
680C22×C4—42no—
681C22×C4—42no—
682C22×C4—81no—
683C22×C4—81no—
684C22×C4C2×D4×C3711yescharacteristic
685C22×C4C2×D4×C3711yescharacteristic
686C22×C4C2×D4×C3711yescharacteristic
687C22×C4C2×D4×C3712yes—
688C22×C4C2×D4×C3711yescharacteristic
689C22×C4C2×D4×C3711yescharacteristic
690C22×C4#41×C3712yes—
691C22×C4C24×C3711yescharacteristic
692D8—44no—
693D8—44no—
694D8—44no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—21no—
702C2×C8—21no—
703C2×C8—21no—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—44no—
707C2×C8C2×D4×C3712yes—
708C4⋊C4—21no—
709C4⋊C4—21no—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—42no—
715C4⋊C4—42no—
716C4⋊C4C2×D4×C3712yes—
717C4⋊C4C2×D4×C3712yes—
718C22⋊C4—22no—
719C22⋊C4—24no—
720C22⋊C4—42no—
721C22⋊C4—42no—
722C22⋊C4—42no—
723C22⋊C4—42no—
724C22⋊C4—42no—
725C22⋊C4—42no—
726C22⋊C4—42no—
727C22⋊C4—81no—
728C22⋊C4D8×C3714yescomplemented
729C42—21no—
730C42—21no—
731C42—21no—
732C42—21no—
733C42—42no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—48no—
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—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—84no—
768C23—84no—
769C23—84no—
770C23—84no—
771C23—84no—
772C23—84no—
773C23#121×C3712yes—
774C23C2×D8×C3712yes—
775C23AGL(1,ℤ/8)×C3712yes—
776C23C22×D4×C3711yescharacteristic
777D4—22no—
778D4—22no—
779D4—22no—
780D4—22no—
781D4—22no—
782D4—22no—
783D4—48no—
784D4—48no—
785D4—41no—
786D4—41no—
787D4—41no—
788D4—41no—
789D4—41no—
790D4—41no—
791D4—41no—
792D4—41no—
793D4—41no—
794D4—41no—
795D4—84no—
796D4—84no—
797D4—84no—
798D4—84no—
799D4—84no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—21no—
812C2×C4—22no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—84no—
829C2×C4—84no—
830C2×C4#121×C3712yes—
831C2×C4C2×D8×C3712yes—
832C2×C4C2×D8×C3712yes—
833C2×C4C22×D4×C3711yescharacteristic
834C2×C4C22×D4×C3711yescharacteristic
835C2×C4C2×#41×C3711yescharacteristic
836C2×C4C2×#41×C3711yescharacteristic
837C2×C4H(5,𝔽2)×C3711yescharacteristic
838C2×C4H(5,𝔽2)×C3711yescharacteristic
839C8—22no—
840C8—41no—
841C8—41no—
842C8—41no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—816no—
859C22—81no—
860C22—81no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22—81no—
865C22—81no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22—81no—
871C22—81no—
872C22—81no—
873C22—81no—
874C22—81no—
875C22—81no—
876C22—81no—
877C22—81no—
878C22C37×#45914yescomplemented
879C22C2×#121×C3711yescharacteristic
880C22D42×C3711yescharacteristic
881C22C37×#54611yescharacteristic
882C22C22×D8×C3711yescharacteristic
883C22C2×AGL(1,ℤ/8)×C3711yescharacteristic
884C22C37×#57611yescharacteristic
885C22C37×#57711yescharacteristic
886C4—22no—
887C4—22no—
888C4—22no—
889C4—41no—
890C4—42no—
891C4—42no—
892C4—41no—
893C4—81no—
894C4—81no—
895C4C37×#52511yescharacteristic
896C4C37×#53811yescharacteristic
897C4D42×C3711yescharacteristic
898C4C37×#54611yescharacteristic
899C2—24no—
900C2—82no—
901C2—82no—
902C2—82no—
903C2—161no—
904C2C37×#242411yescharacteristic
905C2C2×C37×#45911yescharacteristic
906C2C37×#304511yescharacteristic
907C2C37×#326511yescharacteristic
908C2D4×D8×C3711yescharacteristic
909C2C37×#329411yescharacteristic
910C2C37×#331811yescharacteristic
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×#466C2semidirect
2. C2×C37×#459C2semidirect
3. C2×C37×#447C2semidirect
4. C22×#102×C37C2semidirect
5. C37×#2433C2semidirect
6. C37×#2361C2semidirect
7. C37×#2067C2semidirect
8. C37×#2054C2semidirect
9. C37×#2041C2semidirect
10. C37×#2011C2semidirect
11. C37×#1982C2semidirect
12. C37×#1925C2semidirect
13. C37×#1879C2semidirect
14. C37×#1874C2semidirect
15. C37×#1850C2semidirect
19. C22×D8×C37C22semidirect
28. C2×C4×D4×C37C22semidirect
33. C2×#107×C37C22semidirect
34. C2×C4⋊C8×C37C22semidirect
35. C2×C4⋊C8×C37C22semidirect
43. C2×#102×C37C22semidirect
44. C2×#102×C37C22semidirect
45. C2×#102×C37C22semidirect
46. C2×#102×C37C22semidirect
52. C37×#390C22semidirect
53. C37×#389C22semidirect
57. C4×C4⋊C4×C37C22semidirect
59. C37×#340C22semidirect
60. C37×#340C22semidirect
61. C37×#336C22semidirect
62. C37×#336C22semidirect
107. #121×C37D4semidirect
147. #102×C37D4semidirect
272. C22⋊C4×C37D8semidirect
387. #25076C37direct (N × H)
423. C22×C37#459semidirect
444. C2×#466C2×C37semidirect
445. C2×#459C2×C37semidirect
446. C2×#447C2×C37semidirect
447. C22×#102C2×C37semidirect
448. #2433C2×C37semidirect
449. #2361C2×C37semidirect
450. #2067C2×C37semidirect
451. #2054C2×C37semidirect
452. #2041C2×C37semidirect
453. #2011C2×C37semidirect
454. #1982C2×C37semidirect
455. #1925C2×C37semidirect
456. #1879C2×C37semidirect
457. #1874C2×C37semidirect
458. #1850C2×C37semidirect
474. C22×D8C22×C37semidirect
483. C2×C4×D4C22×C37semidirect
488. C2×#107C22×C37semidirect
489. C2×C4⋊C8C22×C37semidirect
490. C2×C4⋊C8C22×C37semidirect
498. C2×#102C22×C37semidirect
499. C2×#102C22×C37semidirect
500. C2×#102C22×C37semidirect
501. C2×#102C22×C37semidirect
507. #390C22×C37semidirect
508. #389C22×C37semidirect
512. C4×C4⋊C4C22×C37semidirect
514. #340C22×C37semidirect
515. #340C22×C37semidirect
516. #336C22×C37semidirect
517. #336C22×C37semidirect
518. C37#25076direct (N × H)
563. #121D4×C37semidirect
603. #102D4×C37semidirect
728. C22⋊C4D8×C37semidirect
878. C22C37×#459semidirect

Maximal subgroups

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

subgroupindex
C2×C37×#4662
C2×C37×#4592
C2×C37×#4472
C22×#102×C372
C37×#24332
C37×#23612
C37×#20672
C37×#20542
C37×#20412
C37×#20112
C37×#19822
C37×#19252
C37×#18792
C37×#18742
C37×#18502
#2507637