Finite Group Databasebeta

← C37×#25553 #22646806

Subgroups — C37×#25553 #22646806

Order 9472.

1200 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#553C211yesmaximal, characteristic, complemented
2C2×C37×#480C211yesmaximal, characteristic, complemented
3C2×C37×#469C211yesmaximal, characteristic, complemented
4C37×#2414C211yesmaximal, characteristic, complemented
5C37×#2059C211yesmaximal, characteristic, complemented
6C37×#2033C211yesmaximal, characteristic, complemented
7C37×#2025C211yesmaximal, characteristic, complemented
8C37×#1999C211yesmaximal, characteristic, complemented
9C37×#1879C211yesmaximal, characteristic, complemented
10C37×#1875C211yesmaximal, characteristic, complemented
11C37×#1875C211yesmaximal, characteristic, complemented
12C37×#1870C211yesmaximal, characteristic, complemented
13C37×#1862C211yesmaximal, characteristic, complemented
14C37×#1854C211yesmaximal, characteristic, complemented
15C37×#1736C211yesmaximal, characteristic, complemented
16C22×D8×C37C2211yescharacteristic
17C22×M16×C37C2211yescharacteristic
18C37×#553—24no—
19C37×#553—24no—
20C2×#126×C37—21no—
21C2×#125×C37C2211yescharacteristic
22C2×#123×C37—21no—
23C2×#121×C37—21no—
24C2×#121×C37C2211yescharacteristic
25C2×#121×C37C2211yescharacteristic
26C2×#121×C37C2211yescharacteristic
27C2×#121×C37C2211yescharacteristic
28C2×C4×D4×C37—21no—
29C2×C4×D4×C37C2211yescharacteristic
30C2×C4×D4×C37C2211yescharacteristic
31C2×#117×C37C2211yescharacteristic
32C2×#117×C37C2211yescharacteristic
33C22×C4⋊C4×C37C2211yescharacteristic
34C37×#480—24no—
35C37×#469—24no—
36C2×#107×C37C2211yescharacteristic
37C2×#107×C37C2211yescharacteristic
38C2×#106×C37C2211yescharacteristic
39C2×#102×C37C2211yescharacteristic
40C2×#102×C37C2211yescharacteristic
41C2×#102×C37C2211yescharacteristic
42C2×#102×C37C2211yescharacteristic
43C2×#102×C37C2211yescharacteristic
44C2×#102×C37C2211yescharacteristic
45C2×C22⋊C8×C37C2211yescharacteristic
46C2×C22⋊C8×C37C2211yescharacteristic
47C2×C22⋊C8×C37C2211yescharacteristic
48C37×#394—21no—
49C37×#392—21no—
50C37×#390—21no—
51C37×#390C2211yescharacteristic
52C37×#389C2211yescharacteristic
53C37×#388—21no—
54C37×#380C2211yescharacteristic
55C37×#340C2211yescharacteristic
56C37×#340C2211yescharacteristic
57C37×#340C2211yescharacteristic
58C37×#340C2211yescharacteristic
59C37×#340C2211yescharacteristic
60C37×#340C2211yescharacteristic
61C37×#336C2211yescharacteristic
62C37×#336C2211yescharacteristic
63C22×D4×C37—21no—
64C22×D4×C37—21no—
65C22×D4×C37—21no—
66C22×D4×C37—21no—
67C22×D4×C37D411yescharacteristic
68C22×D4×C37C2311yescharacteristic
69C22×D4×C37C2311yescharacteristic
70C23×C4×C37—21no—
71C23×C4×C37—21no—
72C23×C4×C37C2311yescharacteristic
73C23×C4×C37C2311yescharacteristic
74C2×D8×C37—22no—
75C2×D8×C37—22no—
76C2×D8×C37—41no—
77C2×M16×C37—22no—
78C2×M16×C37—22no—
79C2×M16×C37—41no—
80C22×C8×C37C2311yescharacteristic
81C22×C8×C37C2311yescharacteristic
82C22×C8×C37C2311yescharacteristic
83C22×C8×C37C2311yescharacteristic
84#126×C37—28no—
85#125×C37—22no—
86#125×C37—22no—
87#123×C37—28no—
88#121×C37—28no—
89#121×C37—22no—
90#121×C37—22no—
91#121×C37—22no—
92#121×C37—22no—
93#121×C37—22no—
94#121×C37—22no—
95#121×C37—41no—
96#121×C37D414yescomplemented
97C4×D4×C37—28no—
98C4×D4×C37—22no—
99C4×D4×C37—22no—
100C4×D4×C37—22no—
101C4×D4×C37—22no—
102#117×C37—22no—
103#117×C37—22no—
104#117×C37—22no—
105#117×C37—41no—
106C2×C4⋊C4×C37—21no—
107C2×C4⋊C4×C37—21no—
108C2×C4⋊C4×C37—21no—
109C2×C4⋊C4×C37—22no—
110C2×C4⋊C4×C37—21no—
111C2×C4⋊C4×C37D411yescharacteristic
112C2×C4⋊C4×C37D414yescomplemented
113C2×C4⋊C4×C37C2311yescharacteristic
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×C37—21no—
132C2×C42×C37—21no—
133C2×C42×C37C2311yescharacteristic
134#107×C37—22no—
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—41no—
143C22⋊C8×C37—22no—
144C22⋊C8×C37—22no—
145C22⋊C8×C37—41no—
146#95×C37—21no—
147#95×C37—21no—
148C24×C37—21no—
149C24×C37—21no—
150C24×C37C2×D411yescharacteristic
151C24×C37C2×D411yescharacteristic
152C2×D4×C37—22no—
153C2×D4×C37—24no—
154C2×D4×C37—24no—
155C2×D4×C37—21no—
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—41no—
167C2×D4×C37—41no—
168C2×D4×C37—42no—
169C2×D4×C37—42no—
170C2×D4×C37—42no—
171C2×D4×C37—42no—
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×C37C2×D412yes—
179C22×C4×C37—21no—
180C22×C4×C37—21no—
181C22×C4×C37—21no—
182C22×C4×C37—21no—
183C22×C4×C37—21no—
184C22×C4×C37—21no—
185C22×C4×C37—21no—
186C22×C4×C37—21no—
187C22×C4×C37—24no—
188C22×C4×C37—24no—
189C22×C4×C37—21no—
190C22×C4×C37—21no—
191C22×C4×C37—21no—
192C22×C4×C37—21no—
193C22×C4×C37—21no—
194C22×C4×C37—21no—
195C22×C4×C37—21no—
196C22×C4×C37—21no—
197C22×C4×C37—81no—
198C22×C4×C37—81no—
199C22×C4×C37—81no—
200C22×C4×C37—81no—
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—
209M16×C37—44no—
210C2×C8×C37—21no—
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#4112yes—
222C4⋊C4×C37—24no—
223C4⋊C4×C37—24no—
224C4⋊C4×C37—24no—
225C4⋊C4×C37—22no—
226C4⋊C4×C37—21no—
227C4⋊C4×C37—21no—
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—81no—
235C4⋊C4×C37C2×D412yes—
236C4⋊C4×C37C2×D412yes—
237C4⋊C4×C37C2×D412yes—
238C4⋊C4×C37#4112yes—
239C22⋊C4×C37—24no—
240C22⋊C4×C37—24no—
241C22⋊C4×C37—24no—
242C22⋊C4×C37—22no—
243C22⋊C4×C37—24no—
244C22⋊C4×C37—22no—
245C22⋊C4×C37—42no—
246C22⋊C4×C37—42no—
247C22⋊C4×C37—42no—
248C22⋊C4×C37—42no—
249C22⋊C4×C37—81no—
250C22⋊C4×C37—81no—
251C42×C37—24no—
252C42×C37—21no—
253C42×C37—21no—
254C42×C37—42no—
255C23×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—21no—
264C23×C37—21no—
265C23×C37—21no—
266C23×C37—21no—
267C23×C37—21no—
268C23×C37—21no—
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#12012yes—
283C23×C37C22×D411yescharacteristic
284D4×C37—22no—
285D4×C37—22no—
286D4×C37—44no—
287D4×C37—48no—
288D4×C37—41no—
289D4×C37—41no—
290D4×C37—41no—
291D4×C37—41no—
292D4×C37—41no—
293D4×C37—41no—
294D4×C37—84no—
295D4×C37—84no—
296D4×C37—84no—
297C2×C4×C37—21no—
298C2×C4×C37—21no—
299C2×C4×C37—22no—
300C2×C4×C37—22no—
301C2×C4×C37—22no—
302C2×C4×C37—22no—
303C2×C4×C37—21no—
304C2×C4×C37—21no—
305C2×C4×C37—22no—
306C2×C4×C37—21no—
307C2×C4×C37—22no—
308C2×C4×C37—22no—
309C2×C4×C37—22no—
310C2×C4×C37—21no—
311C2×C4×C37—21no—
312C2×C4×C37—21no—
313C2×C4×C37—21no—
314C2×C4×C37—21no—
315C2×C4×C37—21no—
316C2×C4×C37—41no—
317C2×C4×C37—41no—
318C2×C4×C37—41no—
319C2×C4×C37—41no—
320C2×C4×C37—41no—
321C2×C4×C37—41no—
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—84no—
335C2×C4×C37—84no—
336C2×C4×C37#12012yes—
337C2×C4×C37C22×D411yescharacteristic
338C2×C4×C37C22×D411yescharacteristic
339C2×C4×C37C2×#4111yescharacteristic
340C2×C4×C37C2×#4111yescharacteristic
341C2×C4×C37H(5,𝔽2)11yescharacteristic
342C2×C4×C372−1+411yescharacteristic
343C8×C37—22no—
344C8×C37—41no—
345C8×C37—41no—
346C8×C37—41no—
347#25553C3711yesmaximal, characteristic, direct product factor, Sylow
348C22×C37—22no—
349C22×C37—22no—
350C22×C37—22no—
351C22×C37—41no—
352C22×C37—41no—
353C22×C37—41no—
354C22×C37—41no—
355C22×C37—41no—
356C22×C37—41no—
357C22×C37—41no—
358C22×C37—42no—
359C22×C37—41no—
360C22×C37—42no—
361C22×C37—42no—
362C22×C37—41no—
363C22×C37—41no—
364C22×C37—41no—
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×C37C2×#12011yescharacteristic
377C22×C37#54611yescharacteristic
378C22×C37#54711yescharacteristic
379C22×C37#57511yescharacteristic
380C22×C37#57511yescharacteristic
381C22×C37#57611yescharacteristic
382C22×C37#57611yescharacteristic
383C4×C37—22no—
384C4×C37—41no—
385C4×C37—41no—
386C4×C37—42no—
387C4×C37—41no—
388C4×C37—42no—
389C4×C37—42no—
390C4×C37—42no—
391C4×C37—81no—
392C4×C37—81no—
393C4×C37#53211yescharacteristic
394C4×C37#53711yescharacteristic
395C4×C37#54611yescharacteristic
396C4×C37#54711yescharacteristic
397C2×#553C2×C3711yescharacteristic, complemented
398C2×#480C2×C3711yescharacteristic, complemented
399C2×#469C2×C3711yescharacteristic, complemented
400#2414C2×C3711yescharacteristic, complemented
401#2059C2×C3711yescharacteristic, complemented
402#2033C2×C3711yescharacteristic, complemented
403#2025C2×C3711yescharacteristic, complemented
404#1999C2×C3711yescharacteristic, complemented
405#1879C2×C3711yescharacteristic, complemented
406#1875C2×C3711yescharacteristic, complemented
407#1875C2×C3711yescharacteristic, complemented
408#1870C2×C3711yescharacteristic, complemented
409#1862C2×C3711yescharacteristic, complemented
410#1854C2×C3711yescharacteristic, complemented
411#1736C2×C3711yescharacteristic, complemented
412C2×C37—42no—
413C2×C37—81no—
414C2×C37—82no—
415C2×C37—161no—
416C2×C37#243011yescharacteristic
417C2×C37#300511yescharacteristic
418C2×C37#300811yescharacteristic
419C2×C37#330911yescharacteristic
420C2×C37#332211yescharacteristic
421C2×C37#334711yescharacteristic
422C2×C37#335511yescharacteristic
423C22×D8C22×C3711yescharacteristic
424C22×M16C22×C3711yescharacteristic
425#553—24no—
426#553—24no—
427C2×#126—21no—
428C2×#125C22×C3711yescharacteristic
429C2×#123—21no—
430C2×#121—21no—
431C2×#121C22×C3711yescharacteristic
432C2×#121C22×C3711yescharacteristic
433C2×#121C22×C3711yescharacteristic
434C2×#121C22×C3711yescharacteristic
435C2×C4×D4—21no—
436C2×C4×D4C22×C3711yescharacteristic
437C2×C4×D4C22×C3711yescharacteristic
438C2×#117C22×C3711yescharacteristic
439C2×#117C22×C3711yescharacteristic
440C22×C4⋊C4C22×C3711yescharacteristic
441#480—24no—
442#469—24no—
443C2×#107C22×C3711yescharacteristic
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×C22⋊C8C22×C3711yescharacteristic
453C2×C22⋊C8C22×C3711yescharacteristic
454C2×C22⋊C8C22×C3711yescharacteristic
455#394—21no—
456#392—21no—
457#390—21no—
458#390C22×C3711yescharacteristic
459#389C22×C3711yescharacteristic
460#388—21no—
461#380C22×C3711yescharacteristic
462#340C22×C3711yescharacteristic
463#340C22×C3711yescharacteristic
464#340C22×C3711yescharacteristic
465#340C22×C3711yescharacteristic
466#340C22×C3711yescharacteristic
467#340C22×C3711yescharacteristic
468#336C22×C3711yescharacteristic
469#336C22×C3711yescharacteristic
470C37#2555311yescharacteristic, direct product factor, Sylow
471C22×D4—21no—
472C22×D4—21no—
473C22×D4—21no—
474C22×D4—21no—
475C22×D4D4×C3711yescharacteristic
476C22×D4C23×C3711yescharacteristic
477C22×D4C23×C3711yescharacteristic
478C23×C4—21no—
479C23×C4—21no—
480C23×C4C23×C3711yescharacteristic
481C23×C4C23×C3711yescharacteristic
482C2×D8—22no—
483C2×D8—22no—
484C2×D8—41no—
485C2×M16—22no—
486C2×M16—22no—
487C2×M16—41no—
488C22×C8C23×C3711yescharacteristic
489C22×C8C23×C3711yescharacteristic
490C22×C8C23×C3711yescharacteristic
491C22×C8C23×C3711yescharacteristic
492#126—28no—
493#125—22no—
494#125—22no—
495#123—28no—
496#121—28no—
497#121—22no—
498#121—22no—
499#121—22no—
500#121—22no—
501#121—22no—
502#121—22no—
503#121—41no—
504#121D4×C3714yescomplemented
505C4×D4—28no—
506C4×D4—22no—
507C4×D4—22no—
508C4×D4—22no—
509C4×D4—22no—
510#117—22no—
511#117—22no—
512#117—22no—
513#117—41no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—22no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4D4×C3711yescharacteristic
520C2×C4⋊C4D4×C3714yescomplemented
521C2×C4⋊C4C23×C3711yescharacteristic
522C2×C4⋊C4C23×C3711yescharacteristic
523C2×C4⋊C4C23×C3711yescharacteristic
524C2×C4⋊C4C23×C3711yescharacteristic
525C2×C4⋊C4C23×C3711yescharacteristic
526C2×C4⋊C4C23×C3711yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
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⋊C4D4×C3711yescharacteristic
538C2×C22⋊C4D4×C3711yescharacteristic
539C2×C42—21no—
540C2×C42—21no—
541C2×C42C23×C3711yescharacteristic
542#107—22no—
543#107—22no—
544#106—22no—
545#102—22no—
546#102—22no—
547#102—22no—
548#102—22no—
549#102—22no—
550#102—41no—
551C22⋊C8—22no—
552C22⋊C8—22no—
553C22⋊C8—41no—
554#95—21no—
555#95—21no—
556C24—21no—
557C24—21no—
558C24C2×D4×C3711yescharacteristic
559C24C2×D4×C3711yescharacteristic
560C2×D4—22no—
561C2×D4—24no—
562C2×D4—24no—
563C2×D4—21no—
564C2×D4—21no—
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—41no—
575C2×D4—41no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—42no—
579C2×D4—42no—
580C2×D4—42no—
581C2×D4—81no—
582C2×D4—81no—
583C2×D4—81no—
584C2×D4—81no—
585C2×D4—81no—
586C2×D4C2×D4×C3712yes—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—24no—
596C22×C4—24no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
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×C3712yes—
614C22×C4C2×D4×C3712yes—
615C22×C4C24×C3711yescharacteristic
616D8—44no—
617M16—44no—
618C2×C8—21no—
619C2×C8—21no—
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#41×C3712yes—
630C4⋊C4—24no—
631C4⋊C4—24no—
632C4⋊C4—24no—
633C4⋊C4—22no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—81no—
643C4⋊C4C2×D4×C3712yes—
644C4⋊C4C2×D4×C3712yes—
645C4⋊C4C2×D4×C3712yes—
646C4⋊C4#41×C3712yes—
647C22⋊C4—24no—
648C22⋊C4—24no—
649C22⋊C4—24no—
650C22⋊C4—22no—
651C22⋊C4—24no—
652C22⋊C4—22no—
653C22⋊C4—42no—
654C22⋊C4—42no—
655C22⋊C4—42no—
656C22⋊C4—42no—
657C22⋊C4—81no—
658C22⋊C4—81no—
659C42—24no—
660C42—21no—
661C42—21no—
662C42—42no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—22no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
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#120×C3712yes—
691C23C22×D4×C3711yescharacteristic
692D4—22no—
693D4—22no—
694D4—44no—
695D4—48no—
696D4—41no—
697D4—41no—
698D4—41no—
699D4—41no—
700D4—41no—
701D4—41no—
702D4—84no—
703D4—84no—
704D4—84no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—22no—
714C2×C4—21no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
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—84no—
743C2×C4—84no—
744C2×C4#120×C3712yes—
745C2×C4C22×D4×C3711yescharacteristic
746C2×C4C22×D4×C3711yescharacteristic
747C2×C4C2×#41×C3711yescharacteristic
748C2×C4C2×#41×C3711yescharacteristic
749C2×C4H(5,𝔽2)×C3711yescharacteristic
750C2×C42−1+4×C3711yescharacteristic
751C8—22no—
752C8—41no—
753C8—41no—
754C8—41no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—42no—
764C22—41no—
765C22—42no—
766C22—42no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22C2×#120×C3711yescharacteristic
784C22C37×#54611yescharacteristic
785C22C37×#54711yescharacteristic
786C22C37×#57511yescharacteristic
787C22C37×#57511yescharacteristic
788C22C37×#57611yescharacteristic
789C22C37×#57611yescharacteristic
790C4—22no—
791C4—41no—
792C4—41no—
793C4—42no—
794C4—41no—
795C4—42no—
796C4—42no—
797C4—42no—
798C4—81no—
799C4—81no—
800C4C37×#53211yescharacteristic
801C4C37×#53711yescharacteristic
802C4C37×#54611yescharacteristic
803C4C37×#54711yescharacteristic
804C2—42no—
805C2—81no—
806C2—82no—
807C2—161no—
808C2C37×#243011yescharacteristic
809C2C37×#300511yescharacteristic
810C2C37×#300811yescharacteristic
811C2C37×#330911yescharacteristic
812C2C37×#332211yescharacteristic
813C2C37×#334711yescharacteristic
814C2C37×#335511yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
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×#553C2semidirect
2. C2×C37×#480C2semidirect
3. C2×C37×#469C2semidirect
4. C37×#2414C2semidirect
5. C37×#2059C2semidirect
6. C37×#2033C2semidirect
7. C37×#2025C2semidirect
8. C37×#1999C2semidirect
9. C37×#1879C2semidirect
10. C37×#1875C2semidirect
11. C37×#1875C2semidirect
12. C37×#1870C2semidirect
13. C37×#1862C2semidirect
14. C37×#1854C2semidirect
15. C37×#1736C2semidirect
96. #121×C37D4semidirect
112. C2×C4⋊C4×C37D4semidirect
347. #25553C37direct (N × H)
397. C2×#553C2×C37semidirect
398. C2×#480C2×C37semidirect
399. C2×#469C2×C37semidirect
400. #2414C2×C37semidirect
401. #2059C2×C37semidirect
402. #2033C2×C37semidirect
403. #2025C2×C37semidirect
404. #1999C2×C37semidirect
405. #1879C2×C37semidirect
406. #1875C2×C37semidirect
407. #1875C2×C37semidirect
408. #1870C2×C37semidirect
409. #1862C2×C37semidirect
410. #1854C2×C37semidirect
411. #1736C2×C37semidirect
470. C37#25553direct (N × H)
504. #121D4×C37semidirect
520. C2×C4⋊C4D4×C37semidirect

Maximal subgroups

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

subgroupindex
C2×C37×#5532
C2×C37×#4802
C2×C37×#4692
C37×#24142
C37×#20592
C37×#20332
C37×#20252
C37×#19992
C37×#18792
C37×#18752
C37×#18702
C37×#18622
C37×#18542
C37×#17362
#2555337