Finite Group Databasebeta

← C37×#25508 #22646761

Subgroups — C37×#25508 #22646761

Order 9472.

1198 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#540C211yesmaximal, characteristic, complemented
2C2×C37×#469C211yesmaximal, characteristic, complemented
3C2×C37×#466C211yesmaximal, characteristic, complemented
4C37×#2624C211yesmaximal, characteristic, complemented
5C37×#2059C211yesmaximal, characteristic, complemented
6C37×#2041C211yesmaximal, characteristic, complemented
7C37×#2025C211yesmaximal, characteristic, complemented
8C37×#2011C211yesmaximal, characteristic, complemented
9C37×#1895C211yesmaximal, characteristic, complemented
10C37×#1893C211yesmaximal, characteristic, complemented
11C37×#1879C211yesmaximal, characteristic, complemented
12C37×#1879C211yesmaximal, characteristic, complemented
13C37×#1864C211yesmaximal, characteristic, complemented
14C37×#1862C211yesmaximal, characteristic, complemented
15C37×#1729C211yesmaximal, characteristic, complemented
16C22×D8×C37C2211yescharacteristic
17C22×D8×C37C2211yescharacteristic
18C22×M16×C37C2211yescharacteristic
19C23×C8×C37C2211yescharacteristic
20C37×#540—24no—
21C37×#540—24no—
22C2×#127×C37C2211yescharacteristic
23C2×#125×C37C2211yescharacteristic
24C2×#123×C37—21no—
25C2×#123×C37—21no—
26C2×#121×C37—21no—
27C2×#121×C37—21no—
28C2×#121×C37C2211yescharacteristic
29C2×#121×C37C2211yescharacteristic
30C2×#121×C37C2211yescharacteristic
31C2×C4×D4×C37C2211yescharacteristic
32C2×C4×D4×C37C2211yescharacteristic
33C2×#117×C37C2211yescharacteristic
34C37×#469—24no—
35C37×#466—24no—
36C2×#107×C37C2211yescharacteristic
37C2×#106×C37C2211yescharacteristic
38C2×#102×C37C2211yescharacteristic
39C2×#102×C37C2211yescharacteristic
40C2×#102×C37C2211yescharacteristic
41C2×#102×C37C2211yescharacteristic
42C2×#102×C37C2211yescharacteristic
43C2×#102×C37C2211yescharacteristic
44C2×#102×C37C2211yescharacteristic
45C2×#102×C37C2211yescharacteristic
46C37×#399—21no—
47C37×#397—21no—
48C37×#394—21no—
49C37×#394—21no—
50C37×#390C2211yescharacteristic
51C37×#390C2211yescharacteristic
52C37×#389C2211yescharacteristic
53C37×#389C2211yescharacteristic
54C37×#380C2211yescharacteristic
55C37×#340C2211yescharacteristic
56C37×#340C2211yescharacteristic
57C37×#340C2211yescharacteristic
58C37×#340C2211yescharacteristic
59C37×#336C2211yescharacteristic
60C37×#336C2211yescharacteristic
61C37×#336C2211yescharacteristic
62C37×#336C2211yescharacteristic
63C22×D4×C37—21no—
64C22×D4×C37—21no—
65C22×D4×C37—21no—
66C22×D4×C37—21no—
67C22×D4×C37—21no—
68C22×D4×C37C2311yescharacteristic
69C22×D4×C37C2311yescharacteristic
70C22×D4×C37C2311yescharacteristic
71C23×C4×C37—21no—
72C23×C4×C37—21no—
73C23×C4×C37C2311yescharacteristic
74C2×D8×C37—22no—
75C2×D8×C37—22no—
76C2×D8×C37—22no—
77C2×D8×C37—22no—
78C2×D8×C37—41no—
79C2×D8×C37—41no—
80C2×M16×C37—22no—
81C2×M16×C37—22no—
82C2×M16×C37—41no—
83C22×C8×C37—22no—
84C22×C8×C37—22no—
85C22×C8×C37—41no—
86C22×C8×C37C2311yescharacteristic
87C22×C8×C37C2311yescharacteristic
88C22×C8×C37C2311yescharacteristic
89C22×C8×C37C2311yescharacteristic
90#127×C37—22no—
91#127×C37—22no—
92#125×C37—22no—
93#125×C37—22no—
94#123×C37—28no—
95#123×C37—28no—
96#121×C37—28no—
97#121×C37—28no—
98#121×C37—22no—
99#121×C37—22no—
100#121×C37—22no—
101#121×C37—22no—
102#121×C37D414yes—
103#121×C37D414yes—
104C4×D4×C37—22no—
105C4×D4×C37—22no—
106C4×D4×C37—22no—
107C4×D4×C37—22no—
108#117×C37—22no—
109#117×C37—22no—
110C2×C4⋊C4×C37—21no—
111C2×C4⋊C4×C37—21no—
112C2×C4⋊C4×C37—21no—
113C2×C4⋊C4×C37—21no—
114C2×C4⋊C4×C37D411yescharacteristic
115C2×C4⋊C4×C37D411yescharacteristic
116C2×C4⋊C4×C37C2311yescharacteristic
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×C37—21no—
131C2×C22⋊C4×C37D411yescharacteristic
132C2×C22⋊C4×C37D411yescharacteristic
133C2×C42×C37C2311yescharacteristic
134C2×C42×C37C2311yescharacteristic
135#107×C37—22no—
136#106×C37—22no—
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—41no—
144#102×C37—41no—
145#95×C37—21no—
146#95×C37—21no—
147#95×C37—21no—
148C24×C37—21no—
149C24×C37—21no—
150C24×C37—21no—
151C24×C37C2×D411yescharacteristic
152C2×D4×C37—24no—
153C2×D4×C37—24no—
154C2×D4×C37—24no—
155C2×D4×C37—24no—
156C2×D4×C37—21no—
157C2×D4×C37—21no—
158C2×D4×C37—21no—
159C2×D4×C37—21no—
160C2×D4×C37—21no—
161C2×D4×C37—21no—
162C2×D4×C37—21no—
163C2×D4×C37—21no—
164C2×D4×C37—21no—
165C2×D4×C37—21no—
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—42no—
173C2×D4×C37—81no—
174C2×D4×C37—81no—
175C2×D4×C37—81no—
176C2×D4×C37—81no—
177C2×D4×C37—81no—
178C2×D4×C37—81no—
179C2×D4×C37—81no—
180C2×D4×C37—81no—
181C2×D4×C37—81no—
182C2×D4×C37—81no—
183C2×D4×C37C2×D412yes—
184C2×D4×C37C2×D412yes—
185C22×C4×C37—21no—
186C22×C4×C37—21no—
187C22×C4×C37—21no—
188C22×C4×C37—21no—
189C22×C4×C37—21no—
190C22×C4×C37—21no—
191C22×C4×C37—24no—
192C22×C4×C37—24no—
193C22×C4×C37—21no—
194C22×C4×C37—21no—
195C22×C4×C37—21no—
196C22×C4×C37—81no—
197C22×C4×C37—81no—
198C22×C4×C37—81no—
199C22×C4×C37—81no—
200C22×C4×C37C2×D411yescharacteristic
201C22×C4×C37C2×D411yescharacteristic
202C22×C4×C37C2×D411yescharacteristic
203C22×C4×C37C2×D411yescharacteristic
204C22×C4×C37C2×D411yescharacteristic
205C22×C4×C37C2×D412yes—
206C22×C4×C37C2×D412yes—
207C22×C4×C37C2411yescharacteristic
208D8×C37—44no—
209D8×C37—44no—
210M16×C37—44no—
211C2×C8×C37—21no—
212C2×C8×C37—21no—
213C2×C8×C37—21no—
214C2×C8×C37—21no—
215C2×C8×C37—21no—
216C2×C8×C37—21no—
217C2×C8×C37—21no—
218C2×C8×C37—21no—
219C2×C8×C37—21no—
220C2×C8×C37—21no—
221C2×C8×C37—44no—
222C2×C8×C37#4112yes—
223C2×C8×C37#4112yes—
224C4⋊C4×C37—24no—
225C4⋊C4×C37—24no—
226C4⋊C4×C37—22no—
227C4⋊C4×C37—22no—
228C4⋊C4×C37—21no—
229C4⋊C4×C37—21no—
230C4⋊C4×C37—21no—
231C4⋊C4×C37—21no—
232C4⋊C4×C37—21no—
233C4⋊C4×C37—21no—
234C4⋊C4×C37—21no—
235C4⋊C4×C37—21no—
236C4⋊C4×C37—81no—
237C4⋊C4×C37—81no—
238C4⋊C4×C37C2×D412yes—
239C4⋊C4×C37C2×D412yes—
240C22⋊C4×C37—24no—
241C22⋊C4×C37—24no—
242C22⋊C4×C37—22no—
243C22⋊C4×C37—22no—
244C22⋊C4×C37—24no—
245C22⋊C4×C37—24no—
246C22⋊C4×C37—42no—
247C22⋊C4×C37—81no—
248C22⋊C4×C37—81no—
249C22⋊C4×C37—81no—
250C22⋊C4×C37—81no—
251C22⋊C4×C37—81no—
252C42×C37—21no—
253C42×C37—21no—
254C42×C37—21no—
255C42×C37—21no—
256C23×C37—21no—
257C23×C37—21no—
258C23×C37—21no—
259C23×C37—21no—
260C23×C37—21no—
261C23×C37—21no—
262C23×C37—22no—
263C23×C37—22no—
264C23×C37—41no—
265C23×C37—41no—
266C23×C37—41no—
267C23×C37—41no—
268C23×C37—41no—
269C23×C37—41no—
270C23×C37—41no—
271C23×C37—41no—
272C23×C37—41no—
273C23×C37—41no—
274C23×C37—41no—
275C23×C37—41no—
276C23×C37—41no—
277C23×C37—41no—
278C23×C37—41no—
279C23×C37—41no—
280C23×C37—41no—
281C23×C37—41no—
282C23×C37—41no—
283C23×C37#12012yes—
284C23×C37C22×D411yescharacteristic
285D4×C37—22no—
286D4×C37—22no—
287D4×C37—22no—
288D4×C37—22no—
289D4×C37—41no—
290D4×C37—41no—
291D4×C37—41no—
292D4×C37—41no—
293D4×C37—41no—
294D4×C37—41no—
295D4×C37—41no—
296D4×C37—41no—
297D4×C37—84no—
298D4×C37—84no—
299D4×C37—84no—
300D4×C37—84no—
301D4×C37—84no—
302C2×C4×C37—21no—
303C2×C4×C37—21no—
304C2×C4×C37—22no—
305C2×C4×C37—22no—
306C2×C4×C37—22no—
307C2×C4×C37—22no—
308C2×C4×C37—21no—
309C2×C4×C37—21no—
310C2×C4×C37—21no—
311C2×C4×C37—21no—
312C2×C4×C37—22no—
313C2×C4×C37—22no—
314C2×C4×C37—21no—
315C2×C4×C37—21no—
316C2×C4×C37—21no—
317C2×C4×C37—21no—
318C2×C4×C37—21no—
319C2×C4×C37—21no—
320C2×C4×C37—21no—
321C2×C4×C37—21no—
322C2×C4×C37—41no—
323C2×C4×C37—41no—
324C2×C4×C37—41no—
325C2×C4×C37—41no—
326C2×C4×C37—41no—
327C2×C4×C37—41no—
328C2×C4×C37—41no—
329C2×C4×C37—41no—
330C2×C4×C37—41no—
331C2×C4×C37—41no—
332C2×C4×C37—41no—
333C2×C4×C37—41no—
334C2×C4×C37—41no—
335C2×C4×C37—84no—
336C2×C4×C37—84no—
337C2×C4×C37#12012yes—
338C2×C4×C37C22×D411yescharacteristic
339C2×C4×C37C22×D411yescharacteristic
340C2×C4×C37C2×#4111yescharacteristic
341C2×C4×C37C2×#4111yescharacteristic
342C2×C4×C37H(5,𝔽2)11yescharacteristic
343C2×C4×C372−1+411yescharacteristic
344C8×C37—22no—
345C8×C37—22no—
346C8×C37—41no—
347C8×C37—41no—
348#25508C3711yesmaximal, characteristic, direct product factor, Sylow
349C22×C37—22no—
350C22×C37—22no—
351C22×C37—22no—
352C22×C37—41no—
353C22×C37—41no—
354C22×C37—41no—
355C22×C37—41no—
356C22×C37—42no—
357C22×C37—42no—
358C22×C37—42no—
359C22×C37—42no—
360C22×C37—42no—
361C22×C37—42no—
362C22×C37—81no—
363C22×C37—81no—
364C22×C37—81no—
365C22×C37—81no—
366C22×C37—81no—
367C22×C37—81no—
368C22×C37—81no—
369C22×C37—81no—
370C22×C37—81no—
371C22×C37—81no—
372C22×C37—81no—
373C22×C37—81no—
374C22×C37—81no—
375C22×C37—81no—
376C22×C37—81no—
377C22×C37C2×#12011yescharacteristic
378C22×C37#53211yescharacteristic
379C22×C37#53711yescharacteristic
380C22×C37#57611yescharacteristic
381C22×C37#57611yescharacteristic
382C22×C37#57611yescharacteristic
383C22×C37#57711yescharacteristic
384C4×C37—22no—
385C4×C37—41no—
386C4×C37—41no—
387C4×C37—42no—
388C4×C37—41no—
389C4×C37—41no—
390C4×C37—42no—
391C4×C37—81no—
392C4×C37—81no—
393C4×C37—81no—
394C4×C37#54611yescharacteristic
395C4×C37#54611yescharacteristic
396C4×C37#54711yescharacteristic
397C4×C37#54711yescharacteristic
398C2×#540C2×C3711yescharacteristic, complemented
399C2×#469C2×C3711yescharacteristic, complemented
400C2×#466C2×C3711yescharacteristic, complemented
401#2624C2×C3711yescharacteristic, complemented
402#2059C2×C3711yescharacteristic, complemented
403#2041C2×C3711yescharacteristic, complemented
404#2025C2×C3711yescharacteristic, complemented
405#2011C2×C3711yescharacteristic, complemented
406#1895C2×C3711yescharacteristic, complemented
407#1893C2×C3711yescharacteristic, complemented
408#1879C2×C3711yescharacteristic, complemented
409#1879C2×C3711yescharacteristic, complemented
410#1864C2×C3711yescharacteristic, complemented
411#1862C2×C3711yescharacteristic, complemented
412#1729C2×C3711yescharacteristic, complemented
413C2×C37—42no—
414C2×C37—82no—
415C2×C37—82no—
416C2×C37—161no—
417C2×C37#243011yescharacteristic
418C2×C37#300811yescharacteristic
419C2×C37#301211yescharacteristic
420C2×C37#317611yescharacteristic
421C2×C37#317911yescharacteristic
422C2×C37#325711yescharacteristic
423C2×C37#325911yescharacteristic
424C22×D8C22×C3711yescharacteristic
425C22×D8C22×C3711yescharacteristic
426C22×M16C22×C3711yescharacteristic
427C23×C8C22×C3711yescharacteristic
428#540—24no—
429#540—24no—
430C2×#127C22×C3711yescharacteristic
431C2×#125C22×C3711yescharacteristic
432C2×#123—21no—
433C2×#123—21no—
434C2×#121—21no—
435C2×#121—21no—
436C2×#121C22×C3711yescharacteristic
437C2×#121C22×C3711yescharacteristic
438C2×#121C22×C3711yescharacteristic
439C2×C4×D4C22×C3711yescharacteristic
440C2×C4×D4C22×C3711yescharacteristic
441C2×#117C22×C3711yescharacteristic
442#469—24no—
443#466—24no—
444C2×#107C22×C3711yescharacteristic
445C2×#106C22×C3711yescharacteristic
446C2×#102C22×C3711yescharacteristic
447C2×#102C22×C3711yescharacteristic
448C2×#102C22×C3711yescharacteristic
449C2×#102C22×C3711yescharacteristic
450C2×#102C22×C3711yescharacteristic
451C2×#102C22×C3711yescharacteristic
452C2×#102C22×C3711yescharacteristic
453C2×#102C22×C3711yescharacteristic
454#399—21no—
455#397—21no—
456#394—21no—
457#394—21no—
458#390C22×C3711yescharacteristic
459#390C22×C3711yescharacteristic
460#389C22×C3711yescharacteristic
461#389C22×C3711yescharacteristic
462#380C22×C3711yescharacteristic
463#340C22×C3711yescharacteristic
464#340C22×C3711yescharacteristic
465#340C22×C3711yescharacteristic
466#340C22×C3711yescharacteristic
467#336C22×C3711yescharacteristic
468#336C22×C3711yescharacteristic
469#336C22×C3711yescharacteristic
470#336C22×C3711yescharacteristic
471C37#2550811yescharacteristic, direct product factor, Sylow
472C22×D4—21no—
473C22×D4—21no—
474C22×D4—21no—
475C22×D4—21no—
476C22×D4—21no—
477C22×D4C23×C3711yescharacteristic
478C22×D4C23×C3711yescharacteristic
479C22×D4C23×C3711yescharacteristic
480C23×C4—21no—
481C23×C4—21no—
482C23×C4C23×C3711yescharacteristic
483C2×D8—22no—
484C2×D8—22no—
485C2×D8—22no—
486C2×D8—22no—
487C2×D8—41no—
488C2×D8—41no—
489C2×M16—22no—
490C2×M16—22no—
491C2×M16—41no—
492C22×C8—22no—
493C22×C8—22no—
494C22×C8—41no—
495C22×C8C23×C3711yescharacteristic
496C22×C8C23×C3711yescharacteristic
497C22×C8C23×C3711yescharacteristic
498C22×C8C23×C3711yescharacteristic
499#127—22no—
500#127—22no—
501#125—22no—
502#125—22no—
503#123—28no—
504#123—28no—
505#121—28no—
506#121—28no—
507#121—22no—
508#121—22no—
509#121—22no—
510#121—22no—
511#121D4×C3714yes—
512#121D4×C3714yes—
513C4×D4—22no—
514C4×D4—22no—
515C4×D4—22no—
516C4×D4—22no—
517#117—22no—
518#117—22no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4D4×C3711yescharacteristic
524C2×C4⋊C4D4×C3711yescharacteristic
525C2×C4⋊C4C23×C3711yescharacteristic
526C2×C4⋊C4C23×C3711yescharacteristic
527C2×C4⋊C4C23×C3711yescharacteristic
528C2×C4⋊C4C23×C3711yescharacteristic
529C2×C4⋊C4C23×C3711yescharacteristic
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4D4×C3711yescharacteristic
541C2×C22⋊C4D4×C3711yescharacteristic
542C2×C42C23×C3711yescharacteristic
543C2×C42C23×C3711yescharacteristic
544#107—22no—
545#106—22no—
546#102—22no—
547#102—22no—
548#102—22no—
549#102—22no—
550#102—22no—
551#102—22no—
552#102—41no—
553#102—41no—
554#95—21no—
555#95—21no—
556#95—21no—
557C24—21no—
558C24—21no—
559C24—21no—
560C24C2×D4×C3711yescharacteristic
561C2×D4—24no—
562C2×D4—24no—
563C2×D4—24no—
564C2×D4—24no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—42no—
582C2×D4—81no—
583C2×D4—81no—
584C2×D4—81no—
585C2×D4—81no—
586C2×D4—81no—
587C2×D4—81no—
588C2×D4—81no—
589C2×D4—81no—
590C2×D4—81no—
591C2×D4—81no—
592C2×D4C2×D4×C3712yes—
593C2×D4C2×D4×C3712yes—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—24no—
601C22×C4—24no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—81no—
606C22×C4—81no—
607C22×C4—81no—
608C22×C4—81no—
609C22×C4C2×D4×C3711yescharacteristic
610C22×C4C2×D4×C3711yescharacteristic
611C22×C4C2×D4×C3711yescharacteristic
612C22×C4C2×D4×C3711yescharacteristic
613C22×C4C2×D4×C3711yescharacteristic
614C22×C4C2×D4×C3712yes—
615C22×C4C2×D4×C3712yes—
616C22×C4C24×C3711yescharacteristic
617D8—44no—
618D8—44no—
619M16—44no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—44no—
631C2×C8#41×C3712yes—
632C2×C8#41×C3712yes—
633C4⋊C4—24no—
634C4⋊C4—24no—
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—81no—
646C4⋊C4—81no—
647C4⋊C4C2×D4×C3712yes—
648C4⋊C4C2×D4×C3712yes—
649C22⋊C4—24no—
650C22⋊C4—24no—
651C22⋊C4—22no—
652C22⋊C4—22no—
653C22⋊C4—24no—
654C22⋊C4—24no—
655C22⋊C4—42no—
656C22⋊C4—81no—
657C22⋊C4—81no—
658C22⋊C4—81no—
659C22⋊C4—81no—
660C22⋊C4—81no—
661C42—21no—
662C42—21no—
663C42—21no—
664C42—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—22no—
672C23—22no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23#120×C3712yes—
693C23C22×D4×C3711yescharacteristic
694D4—22no—
695D4—22no—
696D4—22no—
697D4—22no—
698D4—41no—
699D4—41no—
700D4—41no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—84no—
707D4—84no—
708D4—84no—
709D4—84no—
710D4—84no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—84no—
745C2×C4—84no—
746C2×C4#120×C3712yes—
747C2×C4C22×D4×C3711yescharacteristic
748C2×C4C22×D4×C3711yescharacteristic
749C2×C4C2×#41×C3711yescharacteristic
750C2×C4C2×#41×C3711yescharacteristic
751C2×C4H(5,𝔽2)×C3711yescharacteristic
752C2×C42−1+4×C3711yescharacteristic
753C8—22no—
754C8—22no—
755C8—41no—
756C8—41no—
757C22—22no—
758C22—22no—
759C22—22no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22C2×#120×C3711yescharacteristic
786C22C37×#53211yescharacteristic
787C22C37×#53711yescharacteristic
788C22C37×#57611yescharacteristic
789C22C37×#57611yescharacteristic
790C22C37×#57611yescharacteristic
791C22C37×#57711yescharacteristic
792C4—22no—
793C4—41no—
794C4—41no—
795C4—42no—
796C4—41no—
797C4—41no—
798C4—42no—
799C4—81no—
800C4—81no—
801C4—81no—
802C4C37×#54611yescharacteristic
803C4C37×#54611yescharacteristic
804C4C37×#54711yescharacteristic
805C4C37×#54711yescharacteristic
806C2—42no—
807C2—82no—
808C2—82no—
809C2—161no—
810C2C37×#243011yescharacteristic
811C2C37×#300811yescharacteristic
812C2C37×#301211yescharacteristic
813C2C37×#317611yescharacteristic
814C2C37×#317911yescharacteristic
815C2C37×#325711yescharacteristic
816C2C37×#325911yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C37 ◁ C2×#117×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C37×#540C2semidirect
2. C2×C37×#469C2semidirect
3. C2×C37×#466C2semidirect
4. C37×#2624C2semidirect
5. C37×#2059C2semidirect
6. C37×#2041C2semidirect
7. C37×#2025C2semidirect
8. C37×#2011C2semidirect
9. C37×#1895C2semidirect
10. C37×#1893C2semidirect
11. C37×#1879C2semidirect
12. C37×#1879C2semidirect
13. C37×#1864C2semidirect
14. C37×#1862C2semidirect
15. C37×#1729C2semidirect
348. #25508C37direct (N × H)
398. C2×#540C2×C37semidirect
399. C2×#469C2×C37semidirect
400. C2×#466C2×C37semidirect
401. #2624C2×C37semidirect
402. #2059C2×C37semidirect
403. #2041C2×C37semidirect
404. #2025C2×C37semidirect
405. #2011C2×C37semidirect
406. #1895C2×C37semidirect
407. #1893C2×C37semidirect
408. #1879C2×C37semidirect
409. #1879C2×C37semidirect
410. #1864C2×C37semidirect
411. #1862C2×C37semidirect
412. #1729C2×C37semidirect
471. C37#25508direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C37×#5402
C2×C37×#4692
C2×C37×#4662
C37×#26242
C37×#20592
C37×#20412
C37×#20252
C37×#20112
C37×#18952
C37×#18932
C37×#18792
C37×#18642
C37×#18622
C37×#17292
#2550837